Subgroups — C₇×#61154 #13238370

Order 1792.

2132 conjugacy classes of subgroups.

The subgroup lattice has 1210 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3475	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×D₄×#41	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3333	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#3332	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#3331	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#3330	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#3329	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#3328	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#3327	C₂	1	2	yes	maximal, complemented
10	C₇×#3326	C₂	1	2	yes	maximal, complemented
11	C₇×#3325	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#3324	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#3323	C₂	1	2	yes	maximal, complemented
14	C₇×#3322	C₂	1	2	yes	maximal, complemented
15	C₇×#3131	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#3091	C₂	1	2	yes	maximal, complemented
17	C₇×#3076	C₂	1	1	yes	maximal, characteristic, complemented
18	C₇×#3054	C₂	1	2	yes	maximal, complemented
19	C₇×#3035	C₂	1	1	yes	maximal, characteristic, complemented
20	C₇×#3002	C₂	1	2	yes	maximal, complemented
21	C₄×C₇×#135	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₇×#436	C₂	1	1	yes	maximal, characteristic, complemented
23	C₇×#2896	C₂	1	2	yes	maximal, complemented
24	C₂²×C₇×#41	C₂²	1	2	yes	—
25	C₂×C₇×#135	C₂²	1	1	yes	characteristic
26	C₂×C₇×#135	C₂²	1	2	yes	complemented
27	C₂²×C₇×M₁₆	C₂²	1	2	yes	complemented
28	C₇×#556	C₂²	1	1	yes	characteristic
29	C₇×#555	C₂²	1	1	yes	characteristic
30	C₇×#554	C₂²	1	1	yes	characteristic, complemented
31	C₇×#553	C₂²	1	2	yes	complemented
32	C₇×#552	—	2	1	no	—
33	C₇×#552	C₂²	1	2	yes	complemented
34	C₇×#551	—	2	2	no	—
35	C₇×#550	C₂²	1	1	yes	characteristic
36	C₇×D₄×Q₈	C₂²	1	1	yes	characteristic
37	C₇×#548	C₂²	1	2	yes	—
38	C₇×#547	—	2	1	no	—
39	C₇×#547	C₂²	1	1	yes	characteristic
40	C₇×#547	C₂²	1	1	yes	characteristic, complemented
41	C₇×#546	—	2	1	no	—
42	C₇×#546	—	2	2	no	—
43	C₇×#546	C₂²	1	2	yes	—
44	C₇×D₄²	—	2	1	no	—
45	C₇×D₄²	C₂²	1	1	yes	characteristic
46	C₇×#533	C₂²	1	1	yes	characteristic, complemented
47	C₇×#532	—	2	1	no	—
48	C₇×#532	C₂²	1	1	yes	characteristic
49	C₇×#529	—	2	2	no	—
50	C₇×#529	—	2	1	no	—
51	C₇×#525	—	2	2	no	—
52	C₇×#525	C₂²	1	2	yes	—
53	C₇×#525	C₂²	1	2	yes	complemented
54	C₄×C₇×#41	—	2	1	no	—
55	C₄×C₇×#41	C₂²	1	1	yes	characteristic
56	C₄×C₇×#41	C₂²	1	1	yes	characteristic, complemented
57	C₂×C₄×C₇×D₄	—	2	1	no	—
58	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
59	C₂×C₇×#117	C₂²	1	2	yes	complemented
60	C₇×#488	C₂²	1	2	yes	complemented
61	C₇×#488	C₂²	1	2	yes	complemented
62	C₇×#487	C₂²	1	1	yes	characteristic, complemented
63	C₇×#487	C₂²	1	1	yes	characteristic, complemented
64	C₇×#486	C₂²	1	1	yes	characteristic, complemented
65	C₇×#486	C₂²	1	1	yes	characteristic, complemented
66	C₇×#485	C₂²	1	2	yes	complemented
67	C₇×#485	C₂²	1	2	yes	complemented
68	C₇×#484	C₂²	1	2	yes	complemented
69	C₇×#483	C₂²	1	2	yes	complemented
70	C₇×#482	C₂²	1	2	yes	complemented
71	C₇×#482	C₂²	1	2	yes	complemented
72	C₇×#481	C₂²	1	2	yes	complemented
73	C₇×#480	C₂²	1	2	yes	complemented
74	C₇×#479	C₂²	1	2	yes	complemented
75	C₇×#478	C₂²	1	2	yes	complemented
76	C₇×#477	C₂²	1	1	yes	characteristic, complemented
77	C₇×#476	C₂²	1	1	yes	characteristic, complemented
78	C₇×#475	C₂²	1	1	yes	characteristic, complemented
79	C₇×#474	C₂²	1	1	yes	characteristic, complemented
80	C₇×#470	C₂²	1	2	yes	complemented
81	C₇×#470	C₂²	1	2	yes	complemented
82	C₇×#469	C₂²	1	2	yes	complemented
83	C₇×#469	C₂²	1	2	yes	complemented
84	C₇×#468	C₂²	1	2	yes	complemented
85	C₇×#468	C₂²	1	2	yes	complemented
86	C₇×#468	C₂²	1	2	yes	complemented
87	C₇×#468	C₂²	1	2	yes	complemented
88	C₇×#464	C₂²	1	2	yes	complemented
89	C₇×#463	C₂²	1	2	yes	complemented
90	C₇×#462	C₂²	1	1	yes	characteristic, complemented
91	C₇×#461	C₂²	1	1	yes	characteristic, complemented
92	C₇×#460	C₂²	1	1	yes	characteristic, complemented
93	C₇×#459	C₂²	1	1	yes	characteristic, complemented
94	C₇×#452	C₂²	1	2	yes	complemented
95	C₇×#452	C₂²	1	2	yes	complemented
96	C₇×#451	C₂²	1	2	yes	complemented
97	C₇×#450	C₂²	1	2	yes	complemented
98	C₇×#449	C₂²	1	2	yes	complemented
99	C₇×#449	C₂²	1	2	yes	complemented
100	C₇×#448	C₂²	1	2	yes	complemented
101	C₇×#447	C₂²	1	2	yes	complemented
102	C₄×C₇×Q₁₆	C₂²	1	1	yes	characteristic, complemented
103	C₄×C₇×Q₁₆	C₂²	1	1	yes	characteristic, complemented
104	C₄×C₇×SD₁₆	C₂²	1	1	yes	characteristic, complemented
105	C₄×C₇×SD₁₆	C₂²	1	1	yes	characteristic, complemented
106	C₄×C₇×SD₁₆	C₂²	1	1	yes	characteristic, complemented
107	C₄×C₇×SD₁₆	C₂²	1	1	yes	characteristic, complemented
108	C₄×C₇×D₈	C₂²	1	1	yes	characteristic, complemented
109	C₄×C₇×D₈	C₂²	1	1	yes	characteristic, complemented
110	C₇×#436	C₂²	1	1	yes	characteristic
111	C₇×#436	C₂²	1	1	yes	characteristic
112	C₇×#436	C₂²	1	2	yes	complemented
113	C₇×#436	C₂²	1	2	yes	complemented
114	C₇×#436	C₂²	1	1	yes	characteristic, complemented
115	C₇×#436	C₂²	1	1	yes	characteristic, complemented
116	C₇×#427	C₂²	1	1	yes	characteristic, complemented
117	C₇×#427	C₂²	1	2	yes	complemented
118	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
119	C₇×#419	C₂²	1	2	yes	complemented
120	C₇×#419	C₂²	1	2	yes	complemented
121	C₇×#418	C₂²	1	2	yes	complemented
122	C₇×#418	C₂²	1	2	yes	complemented
123	C₇×#417	C₂²	1	2	yes	complemented
124	C₇×#417	C₂²	1	2	yes	complemented
125	C₇×#417	C₂²	1	2	yes	complemented
126	C₇×#417	C₂²	1	2	yes	complemented
127	C₇×#416	C₂²	1	1	yes	characteristic
128	C₇×#416	C₂²	1	2	yes	—
129	C₇×#416	C₂²	1	1	yes	characteristic, complemented
130	C₇×#416	C₂²	1	2	yes	complemented
131	C₇×#416	C₂²	1	2	yes	complemented
132	C₇×#416	C₂²	1	2	yes	complemented
133	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	complemented
134	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic, complemented
135	#61154	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
136	C₂×C₇×#41	—	2	1	no	—
137	C₂×C₇×#41	—	2	2	no	—
138	C₂×C₇×#41	—	2	2	no	—
139	C₂×C₇×#41	—	2	8	no	—
140	C₂×C₇×#41	—	4	4	no	—
141	C₂×C₇×#41	C₂³	1	2	yes	—
142	C₂×C₇×#41	C₂³	1	1	yes	characteristic
143	C₂×C₇×#41	C₂³	1	2	yes	—
144	C₂×C₇×#41	C₂³	1	2	yes	—
145	C₂×C₇×#41	C₂³	1	1	yes	characteristic
146	C₂²×C₇×Q₈	C₂³	1	2	yes	—
147	C₂²×C₇×D₄	—	2	2	no	—
148	C₂²×C₇×D₄	—	2	1	no	—
149	C₂²×C₇×D₄	D₄	1	1	yes	characteristic
150	C₂²×C₇×D₄	C₂³	1	2	yes	—
151	C₂³×C₄×C₇	—	2	2	no	—
152	C₂³×C₄×C₇	C₂³	1	2	yes	—
153	C₇×#135	—	2	4	no	—
154	C₇×#135	—	4	4	no	—
155	C₂×C₇×Q₁₆	C₂³	1	1	yes	characteristic
156	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
157	C₂×C₇×SD₁₆	C₂³	1	1	yes	characteristic
158	C₂×C₇×SD₁₆	C₂³	1	1	yes	characteristic
159	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
160	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
161	C₂×C₇×D₈	C₂³	1	1	yes	characteristic
162	C₂×C₇×D₈	C₂³	1	2	yes	—
163	C₂×C₇×M₁₆	—	4	4	no	—
164	C₂×C₇×M₁₆	C₂³	1	2	yes	—
165	C₂×C₇×M₁₆	C₂³	1	2	yes	—
166	C₂×C₇×M₁₆	C₂³	1	2	yes	—
167	C₂×C₇×M₁₆	C₂³	1	2	yes	—
168	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
169	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
170	C₂²×C₇×C₈	C₂³	1	2	yes	—
171	C₇×C₄⋊Q₈	—	2	1	no	—
172	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
173	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
174	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
175	C₇×#127	—	2	1	no	—
176	C₇×#127	C₂³	1	1	yes	characteristic
177	C₇×#126	—	2	2	no	—
178	C₇×#126	—	2	2	no	—
179	C₇×#126	—	2	2	no	—
180	C₇×#125	—	2	2	no	—
181	C₇×#125	—	2	1	no	—
182	C₇×#125	C₂³	1	2	yes	—
183	C₇×#124	—	2	1	no	—
184	C₇×#124	—	2	2	no	—
185	C₇×#124	—	2	2	no	—
186	C₇×#124	C₂³	1	2	yes	—
187	C₇×#123	—	2	2	no	—
188	C₇×#123	—	2	2	no	—
189	C₇×#123	—	2	2	no	—
190	C₇×#123	—	2	2	no	—
191	C₇×#123	—	2	2	no	—
192	C₇×#123	—	2	2	no	—
193	C₇×#123	—	2	2	no	—
194	C₇×C₂²⋊Q₈	—	2	1	no	—
195	C₇×C₂²⋊Q₈	—	2	1	no	—
196	C₇×C₂²⋊Q₈	—	2	2	no	—
197	C₇×C₂²⋊Q₈	—	2	1	no	—
198	C₇×C₂²⋊Q₈	—	2	2	no	—
199	C₇×C₂²⋊Q₈	—	2	2	no	—
200	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
201	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
202	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
203	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
204	C₇×#121	—	2	2	no	—
205	C₇×#121	—	2	2	no	—
206	C₇×#121	—	2	1	no	—
207	C₇×#121	—	2	1	no	—
208	C₇×#121	—	2	1	no	—
209	C₇×#121	—	2	1	no	—
210	C₇×#121	—	2	1	no	—
211	C₇×#121	—	2	2	no	—
212	C₇×#121	—	2	2	no	—
213	C₇×#121	C₂³	1	2	yes	—
214	C₇×#121	C₂³	1	2	yes	—
215	C₇×#121	C₂³	1	2	yes	—
216	C₇×#121	C₂³	1	2	yes	—
217	C₇×#120	—	2	2	no	—
218	C₇×#120	—	2	2	no	—
219	C₇×#120	—	2	2	no	—
220	C₇×#120	—	2	2	no	—
221	C₄×C₇×Q₈	—	2	1	no	—
222	C₄×C₇×Q₈	—	2	1	no	—
223	C₄×C₇×Q₈	—	2	1	no	—
224	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
225	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
226	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
227	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
228	C₄×C₇×D₄	—	2	1	no	—
229	C₄×C₇×D₄	—	2	1	no	—
230	C₄×C₇×D₄	—	2	2	no	—
231	C₄×C₇×D₄	—	2	2	no	—
232	C₄×C₇×D₄	—	2	1	no	—
233	C₄×C₇×D₄	—	2	1	no	—
234	C₄×C₇×D₄	—	2	1	no	—
235	C₄×C₇×D₄	—	2	1	no	—
236	C₄×C₇×D₄	—	2	2	no	—
237	C₄×C₇×D₄	—	2	2	no	—
238	C₄×C₇×D₄	—	2	1	no	—
239	C₄×C₇×D₄	—	2	2	no	—
240	C₄×C₇×D₄	—	2	2	no	—
241	C₄×C₇×D₄	—	2	1	no	—
242	C₄×C₇×D₄	—	2	1	no	—
243	C₄×C₇×D₄	D₄	1	1	yes	characteristic
244	C₄×C₇×D₄	D₄	1	1	yes	characteristic
245	C₄×C₇×D₄	D₄	1	2	yes	—
246	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
247	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
248	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
249	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
250	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
251	C₄×C₇×D₄	C₂³	1	2	yes	—
252	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
253	C₇×#117	—	2	2	no	—
254	C₇×#117	—	2	2	no	—
255	C₇×#117	—	2	1	no	—
256	C₇×#117	—	2	2	no	—
257	C₇×#117	—	2	1	no	—
258	C₇×#117	—	2	1	no	—
259	C₇×#117	C₂³	1	2	yes	—
260	C₇×#117	C₂³	1	2	yes	—
261	C₇×#117	C₂³	1	1	yes	characteristic
262	C₇×#117	C₂³	1	2	yes	—
263	C₇×#117	C₂³	1	1	yes	characteristic
264	C₂×C₇×C₄⋊C₄	—	2	1	no	—
265	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
266	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
267	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
268	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
269	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
270	C₂×C₇×C₂²⋊C₄	D₄	1	2	yes	—
271	C₂×C₄²×C₇	—	2	2	no	—
272	C₂×C₄²×C₇	—	2	1	no	—
273	C₂×C₄²×C₇	—	2	1	no	—
274	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
275	C₇×#107	C₂³	1	2	yes	—
276	C₇×#107	C₂³	1	2	yes	—
277	C₇×#107	C₂³	1	1	yes	characteristic
278	C₇×#107	C₂³	1	1	yes	characteristic
279	C₇×#106	C₂³	1	2	yes	—
280	C₇×#106	C₂³	1	2	yes	—
281	C₇×#106	C₂³	1	1	yes	characteristic
282	C₇×#106	C₂³	1	1	yes	characteristic
283	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
284	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
285	C₇×C₄⋊C₈	C₂³	1	2	yes	—
286	C₇×#103	C₂³	1	1	yes	characteristic
287	C₇×#103	C₂³	1	1	yes	characteristic
288	C₇×#103	C₂³	1	2	yes	—
289	C₇×#103	C₂³	1	2	yes	—
290	C₇×#103	C₂³	1	2	yes	—
291	C₇×#103	C₂³	1	2	yes	—
292	C₇×#103	C₂³	1	2	yes	—
293	C₇×#103	C₂³	1	2	yes	—
294	C₇×#103	C₂³	1	2	yes	—
295	C₇×#103	C₂³	1	2	yes	—
296	C₇×#103	C₂³	1	1	yes	characteristic
297	C₇×#103	C₂³	1	1	yes	characteristic
298	C₇×#102	C₂³	1	1	yes	characteristic
299	C₇×#102	C₂³	1	1	yes	characteristic
300	C₇×#102	C₂³	1	2	yes	—
301	C₇×#102	C₂³	1	2	yes	—
302	C₇×#102	C₂³	1	2	yes	—
303	C₇×#102	C₂³	1	2	yes	—
304	C₇×#102	C₂³	1	2	yes	—
305	C₇×#102	C₂³	1	2	yes	—
306	C₇×#102	C₂³	1	2	yes	—
307	C₇×#102	C₂³	1	2	yes	—
308	C₇×#102	C₂³	1	1	yes	characteristic
309	C₇×#102	C₂³	1	1	yes	characteristic
310	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
311	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
312	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
313	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
314	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
315	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
316	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
317	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
318	#3475	C₂×C₇	1	1	yes	characteristic, complemented
319	D₄×#41	C₂×C₇	1	1	yes	characteristic, complemented
320	#3333	C₂×C₇	1	1	yes	characteristic, complemented
321	#3332	C₂×C₇	1	1	yes	characteristic, complemented
322	#3331	C₂×C₇	1	1	yes	characteristic, complemented
323	#3330	C₂×C₇	1	1	yes	characteristic, complemented
324	#3329	C₂×C₇	1	1	yes	characteristic, complemented
325	#3328	C₂×C₇	1	1	yes	characteristic, complemented
326	#3327	C₂×C₇	1	2	yes	complemented
327	#3326	C₂×C₇	1	2	yes	complemented
328	#3325	C₂×C₇	1	1	yes	characteristic, complemented
329	#3324	C₂×C₇	1	1	yes	characteristic, complemented
330	#3323	C₂×C₇	1	2	yes	complemented
331	#3322	C₂×C₇	1	2	yes	complemented
332	#3131	C₂×C₇	1	1	yes	characteristic, complemented
333	#3091	C₂×C₇	1	2	yes	complemented
334	#3076	C₂×C₇	1	1	yes	characteristic, complemented
335	#3054	C₂×C₇	1	2	yes	complemented
336	#3035	C₂×C₇	1	1	yes	characteristic, complemented
337	#3002	C₂×C₇	1	2	yes	complemented
338	C₄×#135	C₂×C₇	1	1	yes	characteristic, complemented
339	C₂×#436	C₂×C₇	1	1	yes	characteristic, complemented
340	#2896	C₂×C₇	1	2	yes	complemented
341	C₂⁴×C₇	—	2	2	no	—
342	C₂⁴×C₇	C₂×D₄	1	2	yes	—
343	C₇×#41	—	2	2	no	—
344	C₇×#41	—	2	4	no	—
345	C₇×#41	—	2	4	no	—
346	C₇×#41	—	2	2	no	—
347	C₇×#41	—	2	4	no	—
348	C₇×#41	—	2	2	no	—
349	C₇×#41	—	2	4	no	—
350	C₇×#41	—	4	8	no	—
351	C₇×#41	—	4	2	no	—
352	C₇×#41	—	4	2	no	—
353	C₇×#41	—	4	8	no	—
354	C₇×#41	—	4	4	no	—
355	C₇×#41	#41	1	4	yes	complemented
356	C₂×C₇×Q₈	—	2	1	no	—
357	C₂×C₇×Q₈	—	2	2	no	—
358	C₂×C₇×Q₈	—	2	1	no	—
359	C₂×C₇×Q₈	—	2	4	no	—
360	C₂×C₇×Q₈	—	4	2	no	—
361	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
362	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
363	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
364	C₂×C₇×D₄	—	2	1	no	—
365	C₂×C₇×D₄	—	2	4	no	—
366	C₂×C₇×D₄	—	2	2	no	—
367	C₂×C₇×D₄	—	2	1	no	—
368	C₂×C₇×D₄	—	2	2	no	—
369	C₂×C₇×D₄	—	2	2	no	—
370	C₂×C₇×D₄	—	2	2	no	—
371	C₂×C₇×D₄	—	2	2	no	—
372	C₂×C₇×D₄	—	2	2	no	—
373	C₂×C₇×D₄	—	2	2	no	—
374	C₂×C₇×D₄	—	2	1	no	—
375	C₂×C₇×D₄	—	2	2	no	—
376	C₂×C₇×D₄	—	2	1	no	—
377	C₂×C₇×D₄	—	4	2	no	—
378	C₂×C₇×D₄	—	4	2	no	—
379	C₂×C₇×D₄	—	4	8	no	—
380	C₂×C₇×D₄	—	4	4	no	—
381	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
382	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
383	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
384	C₂×C₇×D₄	C₂⁴	1	2	yes	—
385	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
386	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
387	C₂²×C₄×C₇	—	2	1	no	—
388	C₂²×C₄×C₇	—	2	4	no	—
389	C₂²×C₄×C₇	—	2	4	no	—
390	C₂²×C₄×C₇	—	2	2	no	—
391	C₂²×C₄×C₇	—	2	2	no	—
392	C₂²×C₄×C₇	—	2	2	no	—
393	C₂²×C₄×C₇	—	2	1	no	—
394	C₂²×C₄×C₇	—	2	1	no	—
395	C₂²×C₄×C₇	—	2	2	no	—
396	C₂²×C₄×C₇	—	2	2	no	—
397	C₂²×C₄×C₇	—	2	1	no	—
398	C₂²×C₄×C₇	—	2	2	no	—
399	C₂²×C₄×C₇	—	2	1	no	—
400	C₂²×C₄×C₇	—	2	1	no	—
401	C₂²×C₄×C₇	—	4	8	no	—
402	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
403	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
404	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
405	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
406	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
407	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
408	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
409	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
410	C₇×Q₁₆	—	2	2	no	—
411	C₇×Q₁₆	—	4	2	no	—
412	C₇×SD₁₆	—	2	2	no	—
413	C₇×SD₁₆	—	2	2	no	—
414	C₇×SD₁₆	—	4	2	no	—
415	C₇×SD₁₆	—	4	2	no	—
416	C₇×D₈	—	2	2	no	—
417	C₇×D₈	—	4	2	no	—
418	C₇×M₁₆	—	4	2	no	—
419	C₇×M₁₆	—	4	2	no	—
420	C₇×M₁₆	—	4	2	no	—
421	C₇×M₁₆	—	4	2	no	—
422	C₂×C₇×C₈	—	2	2	no	—
423	C₂×C₇×C₈	—	2	2	no	—
424	C₂×C₇×C₈	—	2	4	no	—
425	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
426	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
427	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
428	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
429	C₂×C₇×C₈	C₂⁴	1	2	yes	—
430	C₂×C₇×C₈	C₂⁴	1	2	yes	—
431	C₇×C₄⋊C₄	—	2	1	no	—
432	C₇×C₄⋊C₄	—	2	2	no	—
433	C₇×C₄⋊C₄	—	2	2	no	—
434	C₇×C₄⋊C₄	—	2	2	no	—
435	C₇×C₄⋊C₄	—	2	1	no	—
436	C₇×C₄⋊C₄	—	2	2	no	—
437	C₇×C₄⋊C₄	—	2	2	no	—
438	C₇×C₄⋊C₄	—	2	1	no	—
439	C₇×C₄⋊C₄	—	2	1	no	—
440	C₇×C₄⋊C₄	—	2	1	no	—
441	C₇×C₄⋊C₄	—	2	1	no	—
442	C₇×C₄⋊C₄	—	2	1	no	—
443	C₇×C₄⋊C₄	—	2	2	no	—
444	C₇×C₄⋊C₄	—	2	2	no	—
445	C₇×C₄⋊C₄	—	2	2	no	—
446	C₇×C₄⋊C₄	—	2	1	no	—
447	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
448	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
449	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
450	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
451	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
452	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
453	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
454	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
455	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
456	C₇×C₂²⋊C₄	—	2	1	no	—
457	C₇×C₂²⋊C₄	—	2	2	no	—
458	C₇×C₂²⋊C₄	—	2	2	no	—
459	C₇×C₂²⋊C₄	—	2	2	no	—
460	C₇×C₂²⋊C₄	—	2	2	no	—
461	C₇×C₂²⋊C₄	—	2	2	no	—
462	C₇×C₂²⋊C₄	—	2	1	no	—
463	C₇×C₂²⋊C₄	—	2	2	no	—
464	C₇×C₂²⋊C₄	—	2	2	no	—
465	C₇×C₂²⋊C₄	—	2	2	no	—
466	C₇×C₂²⋊C₄	—	2	2	no	—
467	C₇×C₂²⋊C₄	—	2	2	no	—
468	C₇×C₂²⋊C₄	—	2	1	no	—
469	C₇×C₂²⋊C₄	—	2	1	no	—
470	C₇×C₂²⋊C₄	—	2	1	no	—
471	C₇×C₂²⋊C₄	—	2	1	no	—
472	C₇×C₂²⋊C₄	—	2	2	no	—
473	C₇×C₂²⋊C₄	—	2	2	no	—
474	C₇×C₂²⋊C₄	—	2	2	no	—
475	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
476	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
477	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
478	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
479	C₄²×C₇	—	2	2	no	—
480	C₄²×C₇	—	2	1	no	—
481	C₄²×C₇	—	2	2	no	—
482	C₄²×C₇	—	2	1	no	—
483	C₄²×C₇	—	2	1	no	—
484	C₄²×C₇	—	2	1	no	—
485	C₄²×C₇	—	2	1	no	—
486	C₄²×C₇	—	2	1	no	—
487	C₄²×C₇	—	2	2	no	—
488	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
489	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
490	C₄²×C₇	C₂⁴	1	1	yes	characteristic
491	C₄²×C₇	C₂⁴	1	1	yes	characteristic
492	C₂²×#41	C₂²×C₇	1	2	yes	—
493	C₂×#135	C₂²×C₇	1	1	yes	characteristic
494	C₂×#135	C₂²×C₇	1	2	yes	complemented
495	C₂²×M₁₆	C₂²×C₇	1	2	yes	complemented
496	#556	C₂²×C₇	1	1	yes	characteristic
497	#555	C₂²×C₇	1	1	yes	characteristic
498	#554	C₂²×C₇	1	1	yes	characteristic, complemented
499	#553	C₂²×C₇	1	2	yes	complemented
500	#552	—	2	1	no	—
501	#552	C₂²×C₇	1	2	yes	complemented
502	#551	—	2	2	no	—
503	#550	C₂²×C₇	1	1	yes	characteristic
504	D₄×Q₈	C₂²×C₇	1	1	yes	characteristic
505	#548	C₂²×C₇	1	2	yes	—
506	#547	—	2	1	no	—
507	#547	C₂²×C₇	1	1	yes	characteristic
508	#547	C₂²×C₇	1	1	yes	characteristic, complemented
509	#546	—	2	1	no	—
510	#546	—	2	2	no	—
511	#546	C₂²×C₇	1	2	yes	—
512	D₄²	—	2	1	no	—
513	D₄²	C₂²×C₇	1	1	yes	characteristic
514	#533	C₂²×C₇	1	1	yes	characteristic, complemented
515	#532	—	2	1	no	—
516	#532	C₂²×C₇	1	1	yes	characteristic
517	#529	—	2	2	no	—
518	#529	—	2	1	no	—
519	#525	—	2	2	no	—
520	#525	C₂²×C₇	1	2	yes	—
521	#525	C₂²×C₇	1	2	yes	complemented
522	C₄×#41	—	2	1	no	—
523	C₄×#41	C₂²×C₇	1	1	yes	characteristic
524	C₄×#41	C₂²×C₇	1	1	yes	characteristic, complemented
525	C₂×C₄×D₄	—	2	1	no	—
526	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
527	C₂×#117	C₂²×C₇	1	2	yes	complemented
528	#488	C₂²×C₇	1	2	yes	complemented
529	#488	C₂²×C₇	1	2	yes	complemented
530	#487	C₂²×C₇	1	1	yes	characteristic, complemented
531	#487	C₂²×C₇	1	1	yes	characteristic, complemented
532	#486	C₂²×C₇	1	1	yes	characteristic, complemented
533	#486	C₂²×C₇	1	1	yes	characteristic, complemented
534	#485	C₂²×C₇	1	2	yes	complemented
535	#485	C₂²×C₇	1	2	yes	complemented
536	#484	C₂²×C₇	1	2	yes	complemented
537	#483	C₂²×C₇	1	2	yes	complemented
538	#482	C₂²×C₇	1	2	yes	complemented
539	#482	C₂²×C₇	1	2	yes	complemented
540	#481	C₂²×C₇	1	2	yes	complemented
541	#480	C₂²×C₇	1	2	yes	complemented
542	#479	C₂²×C₇	1	2	yes	complemented
543	#478	C₂²×C₇	1	2	yes	complemented
544	#477	C₂²×C₇	1	1	yes	characteristic, complemented
545	#476	C₂²×C₇	1	1	yes	characteristic, complemented
546	#475	C₂²×C₇	1	1	yes	characteristic, complemented
547	#474	C₂²×C₇	1	1	yes	characteristic, complemented
548	#470	C₂²×C₇	1	2	yes	complemented
549	#470	C₂²×C₇	1	2	yes	complemented
550	#469	C₂²×C₇	1	2	yes	complemented
551	#469	C₂²×C₇	1	2	yes	complemented
552	#468	C₂²×C₇	1	2	yes	complemented
553	#468	C₂²×C₇	1	2	yes	complemented
554	#468	C₂²×C₇	1	2	yes	complemented
555	#468	C₂²×C₇	1	2	yes	complemented
556	#464	C₂²×C₇	1	2	yes	complemented
557	#463	C₂²×C₇	1	2	yes	complemented
558	#462	C₂²×C₇	1	1	yes	characteristic, complemented
559	#461	C₂²×C₇	1	1	yes	characteristic, complemented
560	#460	C₂²×C₇	1	1	yes	characteristic, complemented
561	#459	C₂²×C₇	1	1	yes	characteristic, complemented
562	#452	C₂²×C₇	1	2	yes	complemented
563	#452	C₂²×C₇	1	2	yes	complemented
564	#451	C₂²×C₇	1	2	yes	complemented
565	#450	C₂²×C₇	1	2	yes	complemented
566	#449	C₂²×C₇	1	2	yes	complemented
567	#449	C₂²×C₇	1	2	yes	complemented
568	#448	C₂²×C₇	1	2	yes	complemented
569	#447	C₂²×C₇	1	2	yes	complemented
570	C₄×Q₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
571	C₄×Q₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
572	C₄×SD₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
573	C₄×SD₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
574	C₄×SD₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
575	C₄×SD₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
576	C₄×D₈	C₂²×C₇	1	1	yes	characteristic, complemented
577	C₄×D₈	C₂²×C₇	1	1	yes	characteristic, complemented
578	#436	C₂²×C₇	1	1	yes	characteristic
579	#436	C₂²×C₇	1	1	yes	characteristic
580	#436	C₂²×C₇	1	1	yes	characteristic, complemented
581	#436	C₂²×C₇	1	1	yes	characteristic, complemented
582	#436	C₂²×C₇	1	2	yes	complemented
583	#436	C₂²×C₇	1	2	yes	complemented
584	#427	C₂²×C₇	1	2	yes	complemented
585	#427	C₂²×C₇	1	1	yes	characteristic, complemented
586	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic, complemented
587	#419	C₂²×C₇	1	2	yes	complemented
588	#419	C₂²×C₇	1	2	yes	complemented
589	#418	C₂²×C₇	1	2	yes	complemented
590	#418	C₂²×C₇	1	2	yes	complemented
591	#417	C₂²×C₇	1	2	yes	complemented
592	#417	C₂²×C₇	1	2	yes	complemented
593	#417	C₂²×C₇	1	2	yes	complemented
594	#417	C₂²×C₇	1	2	yes	complemented
595	#416	C₂²×C₇	1	2	yes	—
596	#416	C₂²×C₇	1	1	yes	characteristic
597	#416	C₂²×C₇	1	2	yes	complemented
598	#416	C₂²×C₇	1	2	yes	complemented
599	#416	C₂²×C₇	1	2	yes	complemented
600	#416	C₂²×C₇	1	1	yes	characteristic, complemented
601	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	complemented
602	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic, complemented
603	C₂³×C₇	—	2	1	no	—
604	C₂³×C₇	—	2	4	no	—
605	C₂³×C₇	—	2	1	no	—
606	C₂³×C₇	—	2	2	no	—
607	C₂³×C₇	—	4	2	no	—
608	C₂³×C₇	—	4	2	no	—
609	C₂³×C₇	—	4	4	no	—
610	C₂³×C₇	—	4	4	no	—
611	C₂³×C₇	—	8	2	no	—
612	C₂³×C₇	C₂²×D₄	1	2	yes	—
613	C₂³×C₇	C₂²×D₄	1	2	yes	—
614	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
615	C₇×Q₈	—	2	1	no	—
616	C₇×Q₈	—	2	1	no	—
617	C₇×Q₈	—	2	2	no	—
618	C₇×Q₈	—	2	1	no	—
619	C₇×Q₈	—	2	2	no	—
620	C₇×Q₈	—	4	4	no	—
621	C₇×Q₈	—	4	2	no	—
622	C₇×Q₈	—	8	1	no	—
623	C₇×Q₈	C₂×#41	1	2	yes	—
624	C₇×D₄	—	2	4	no	—
625	C₇×D₄	—	2	2	no	—
626	C₇×D₄	—	2	2	no	—
627	C₇×D₄	—	2	1	no	—
628	C₇×D₄	—	2	2	no	—
629	C₇×D₄	—	2	1	no	—
630	C₇×D₄	—	2	1	no	—
631	C₇×D₄	—	2	2	no	—
632	C₇×D₄	—	4	2	no	—
633	C₇×D₄	—	4	4	no	—
634	C₇×D₄	—	4	4	no	—
635	C₇×D₄	—	4	4	no	—
636	C₇×D₄	—	4	4	no	—
637	C₇×D₄	—	4	4	no	—
638	C₇×D₄	—	4	4	no	—
639	C₇×D₄	—	4	2	no	—
640	C₇×D₄	—	4	2	no	—
641	C₇×D₄	—	8	1	no	—
642	C₇×D₄	—	8	2	no	—
643	C₇×D₄	—	8	2	no	—
644	C₇×D₄	C₂×#41	1	2	yes	—
645	C₂×C₄×C₇	—	2	4	no	—
646	C₂×C₄×C₇	—	2	1	no	—
647	C₂×C₄×C₇	—	2	4	no	—
648	C₂×C₄×C₇	—	2	4	no	—
649	C₂×C₄×C₇	—	2	4	no	—
650	C₂×C₄×C₇	—	2	2	no	—
651	C₂×C₄×C₇	—	2	2	no	—
652	C₂×C₄×C₇	—	2	2	no	—
653	C₂×C₄×C₇	—	2	2	no	—
654	C₂×C₄×C₇	—	2	2	no	—
655	C₂×C₄×C₇	—	2	1	no	—
656	C₂×C₄×C₇	—	2	1	no	—
657	C₂×C₄×C₇	—	2	1	no	—
658	C₂×C₄×C₇	—	2	1	no	—
659	C₂×C₄×C₇	—	2	1	no	—
660	C₂×C₄×C₇	—	2	2	no	—
661	C₂×C₄×C₇	—	2	2	no	—
662	C₂×C₄×C₇	—	2	2	no	—
663	C₂×C₄×C₇	—	4	1	no	—
664	C₂×C₄×C₇	—	4	4	no	—
665	C₂×C₄×C₇	—	4	4	no	—
666	C₂×C₄×C₇	—	4	4	no	—
667	C₂×C₄×C₇	—	4	4	no	—
668	C₂×C₄×C₇	—	4	4	no	—
669	C₂×C₄×C₇	—	4	2	no	—
670	C₂×C₄×C₇	—	4	2	no	—
671	C₂×C₄×C₇	—	4	2	no	—
672	C₂×C₄×C₇	—	8	1	no	—
673	C₂×C₄×C₇	—	8	1	no	—
674	C₂×C₄×C₇	—	8	2	no	—
675	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
676	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
677	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
678	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
679	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
680	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
681	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
682	C₂×C₄×C₇	C₂×#41	1	2	yes	—
683	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
684	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
685	C₇×C₈	—	2	1	no	—
686	C₇×C₈	—	2	1	no	—
687	C₇×C₈	—	2	1	no	—
688	C₇×C₈	—	2	1	no	—
689	C₇×C₈	—	2	2	no	—
690	C₇×C₈	—	2	2	no	—
691	C₂×#41	—	2	1	no	—
692	C₂×#41	—	2	2	no	—
693	C₂×#41	—	2	2	no	—
694	C₂×#41	—	2	8	no	—
695	C₂×#41	—	4	4	no	—
696	C₂×#41	C₂³×C₇	1	1	yes	characteristic
697	C₂×#41	C₂³×C₇	1	2	yes	—
698	C₂×#41	C₂³×C₇	1	2	yes	—
699	C₂×#41	C₂³×C₇	1	2	yes	—
700	C₂×#41	C₂³×C₇	1	1	yes	characteristic
701	C₂²×Q₈	C₂³×C₇	1	2	yes	—
702	C₂²×D₄	—	2	2	no	—
703	C₂²×D₄	—	2	1	no	—
704	C₂²×D₄	C₇×D₄	1	1	yes	characteristic
705	C₂²×D₄	C₂³×C₇	1	2	yes	—
706	C₂³×C₄	—	2	2	no	—
707	C₂³×C₄	C₂³×C₇	1	2	yes	—
708	#135	—	2	4	no	—
709	#135	—	4	4	no	—
710	C₂×Q₁₆	C₂³×C₇	1	1	yes	characteristic
711	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
712	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
713	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
714	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
715	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
716	C₂×D₈	C₂³×C₇	1	1	yes	characteristic
717	C₂×D₈	C₂³×C₇	1	2	yes	—
718	C₂×M₁₆	—	4	4	no	—
719	C₂×M₁₆	C₂³×C₇	1	2	yes	—
720	C₂×M₁₆	C₂³×C₇	1	2	yes	—
721	C₂×M₁₆	C₂³×C₇	1	2	yes	—
722	C₂×M₁₆	C₂³×C₇	1	2	yes	—
723	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
724	C₂²×C₈	C₂³×C₇	1	2	yes	—
725	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
726	C₄⋊Q₈	—	2	1	no	—
727	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
728	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
729	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
730	#127	—	2	1	no	—
731	#127	C₂³×C₇	1	1	yes	characteristic
732	#126	—	2	2	no	—
733	#126	—	2	2	no	—
734	#126	—	2	2	no	—
735	#125	—	2	2	no	—
736	#125	—	2	1	no	—
737	#125	C₂³×C₇	1	2	yes	—
738	#124	—	2	1	no	—
739	#124	—	2	2	no	—
740	#124	—	2	2	no	—
741	#124	C₂³×C₇	1	2	yes	—
742	#123	—	2	2	no	—
743	#123	—	2	2	no	—
744	#123	—	2	2	no	—
745	#123	—	2	2	no	—
746	#123	—	2	2	no	—
747	#123	—	2	2	no	—
748	#123	—	2	2	no	—
749	C₂²⋊Q₈	—	2	1	no	—
750	C₂²⋊Q₈	—	2	1	no	—
751	C₂²⋊Q₈	—	2	2	no	—
752	C₂²⋊Q₈	—	2	1	no	—
753	C₂²⋊Q₈	—	2	2	no	—
754	C₂²⋊Q₈	—	2	2	no	—
755	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
756	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
757	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
758	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
759	#121	—	2	2	no	—
760	#121	—	2	2	no	—
761	#121	—	2	1	no	—
762	#121	—	2	1	no	—
763	#121	—	2	1	no	—
764	#121	—	2	1	no	—
765	#121	—	2	1	no	—
766	#121	—	2	2	no	—
767	#121	—	2	2	no	—
768	#121	C₂³×C₇	1	2	yes	—
769	#121	C₂³×C₇	1	2	yes	—
770	#121	C₂³×C₇	1	2	yes	—
771	#121	C₂³×C₇	1	2	yes	—
772	#120	—	2	2	no	—
773	#120	—	2	2	no	—
774	#120	—	2	2	no	—
775	#120	—	2	2	no	—
776	C₄×Q₈	—	2	1	no	—
777	C₄×Q₈	—	2	1	no	—
778	C₄×Q₈	—	2	1	no	—
779	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
780	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
781	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
782	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
783	C₄×D₄	—	2	1	no	—
784	C₄×D₄	—	2	1	no	—
785	C₄×D₄	—	2	2	no	—
786	C₄×D₄	—	2	2	no	—
787	C₄×D₄	—	2	1	no	—
788	C₄×D₄	—	2	1	no	—
789	C₄×D₄	—	2	1	no	—
790	C₄×D₄	—	2	1	no	—
791	C₄×D₄	—	2	2	no	—
792	C₄×D₄	—	2	2	no	—
793	C₄×D₄	—	2	1	no	—
794	C₄×D₄	—	2	2	no	—
795	C₄×D₄	—	2	2	no	—
796	C₄×D₄	—	2	1	no	—
797	C₄×D₄	—	2	1	no	—
798	C₄×D₄	C₇×D₄	1	1	yes	characteristic
799	C₄×D₄	C₇×D₄	1	1	yes	characteristic
800	C₄×D₄	C₇×D₄	1	2	yes	—
801	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
802	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
803	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
804	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
805	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
806	C₄×D₄	C₂³×C₇	1	2	yes	—
807	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
808	#117	—	2	2	no	—
809	#117	—	2	2	no	—
810	#117	—	2	1	no	—
811	#117	—	2	2	no	—
812	#117	—	2	1	no	—
813	#117	—	2	1	no	—
814	#117	C₂³×C₇	1	1	yes	characteristic
815	#117	C₂³×C₇	1	2	yes	—
816	#117	C₂³×C₇	1	2	yes	—
817	#117	C₂³×C₇	1	2	yes	—
818	#117	C₂³×C₇	1	1	yes	characteristic
819	C₂×C₄⋊C₄	—	2	1	no	—
820	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
821	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
822	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
823	C₂×C₂²⋊C₄	—	2	2	no	—
824	C₂×C₂²⋊C₄	—	2	2	no	—
825	C₂×C₂²⋊C₄	C₇×D₄	1	2	yes	—
826	C₂×C₄²	—	2	2	no	—
827	C₂×C₄²	—	2	1	no	—
828	C₂×C₄²	—	2	1	no	—
829	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
830	#107	C₂³×C₇	1	1	yes	characteristic
831	#107	C₂³×C₇	1	1	yes	characteristic
832	#107	C₂³×C₇	1	2	yes	—
833	#107	C₂³×C₇	1	2	yes	—
834	#106	C₂³×C₇	1	1	yes	characteristic
835	#106	C₂³×C₇	1	1	yes	characteristic
836	#106	C₂³×C₇	1	2	yes	—
837	#106	C₂³×C₇	1	2	yes	—
838	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
839	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
840	C₄⋊C₈	C₂³×C₇	1	2	yes	—
841	#103	C₂³×C₇	1	1	yes	characteristic
842	#103	C₂³×C₇	1	1	yes	characteristic
843	#103	C₂³×C₇	1	2	yes	—
844	#103	C₂³×C₇	1	2	yes	—
845	#103	C₂³×C₇	1	2	yes	—
846	#103	C₂³×C₇	1	2	yes	—
847	#103	C₂³×C₇	1	2	yes	—
848	#103	C₂³×C₇	1	2	yes	—
849	#103	C₂³×C₇	1	1	yes	characteristic
850	#103	C₂³×C₇	1	1	yes	characteristic
851	#103	C₂³×C₇	1	2	yes	—
852	#103	C₂³×C₇	1	2	yes	—
853	#102	C₂³×C₇	1	1	yes	characteristic
854	#102	C₂³×C₇	1	1	yes	characteristic
855	#102	C₂³×C₇	1	2	yes	—
856	#102	C₂³×C₇	1	2	yes	—
857	#102	C₂³×C₇	1	2	yes	—
858	#102	C₂³×C₇	1	2	yes	—
859	#102	C₂³×C₇	1	2	yes	—
860	#102	C₂³×C₇	1	2	yes	—
861	#102	C₂³×C₇	1	1	yes	characteristic
862	#102	C₂³×C₇	1	1	yes	characteristic
863	#102	C₂³×C₇	1	2	yes	—
864	#102	C₂³×C₇	1	2	yes	—
865	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
866	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
867	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
868	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
869	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
870	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
871	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
872	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
873	C₂²×C₇	—	2	1	no	—
874	C₂²×C₇	—	2	1	no	—
875	C₂²×C₇	—	2	2	no	—
876	C₂²×C₇	—	2	2	no	—
877	C₂²×C₇	—	2	2	no	—
878	C₂²×C₇	—	2	2	no	—
879	C₂²×C₇	—	2	2	no	—
880	C₂²×C₇	—	2	2	no	—
881	C₂²×C₇	—	2	2	no	—
882	C₂²×C₇	—	4	1	no	—
883	C₂²×C₇	—	4	1	no	—
884	C₂²×C₇	—	4	1	no	—
885	C₂²×C₇	—	4	2	no	—
886	C₂²×C₇	—	4	2	no	—
887	C₂²×C₇	—	4	1	no	—
888	C₂²×C₇	—	4	1	no	—
889	C₂²×C₇	—	4	2	no	—
890	C₂²×C₇	—	8	4	no	—
891	C₂²×C₇	—	8	8	no	—
892	C₂²×C₇	#546	1	2	yes	—
893	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
894	C₄×C₇	—	2	1	no	—
895	C₄×C₇	—	2	1	no	—
896	C₄×C₇	—	2	2	no	—
897	C₄×C₇	—	2	2	no	—
898	C₄×C₇	—	2	2	no	—
899	C₄×C₇	—	2	1	no	—
900	C₄×C₇	—	4	1	no	—
901	C₄×C₇	—	4	1	no	—
902	C₄×C₇	—	4	2	no	—
903	C₄×C₇	—	4	2	no	—
904	C₄×C₇	—	4	1	no	—
905	C₄×C₇	—	4	1	no	—
906	C₄×C₇	—	4	1	no	—
907	C₄×C₇	—	4	2	no	—
908	C₄×C₇	#546	1	2	yes	—
909	C₄×C₇	#575	1	2	yes	—
910	C₄×C₇	C₂²×#41	1	1	yes	characteristic
911	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
912	C₂⁴	—	2	2	no	—
913	C₂⁴	C₂×C₇×D₄	1	2	yes	—
914	#41	—	2	2	no	—
915	#41	—	2	4	no	—
916	#41	—	2	4	no	—
917	#41	—	2	2	no	—
918	#41	—	2	4	no	—
919	#41	—	2	2	no	—
920	#41	—	2	4	no	—
921	#41	—	4	8	no	—
922	#41	—	4	2	no	—
923	#41	—	4	2	no	—
924	#41	—	4	8	no	—
925	#41	—	4	4	no	—
926	#41	C₇×#41	1	4	yes	complemented
927	C₂×Q₈	—	2	1	no	—
928	C₂×Q₈	—	2	2	no	—
929	C₂×Q₈	—	2	1	no	—
930	C₂×Q₈	—	2	4	no	—
931	C₂×Q₈	—	4	2	no	—
932	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
933	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
934	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
935	C₂×D₄	—	2	1	no	—
936	C₂×D₄	—	2	4	no	—
937	C₂×D₄	—	2	2	no	—
938	C₂×D₄	—	2	1	no	—
939	C₂×D₄	—	2	2	no	—
940	C₂×D₄	—	2	2	no	—
941	C₂×D₄	—	2	2	no	—
942	C₂×D₄	—	2	2	no	—
943	C₂×D₄	—	2	2	no	—
944	C₂×D₄	—	2	2	no	—
945	C₂×D₄	—	2	1	no	—
946	C₂×D₄	—	2	2	no	—
947	C₂×D₄	—	2	1	no	—
948	C₂×D₄	—	4	2	no	—
949	C₂×D₄	—	4	2	no	—
950	C₂×D₄	—	4	8	no	—
951	C₂×D₄	—	4	4	no	—
952	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
953	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
954	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
955	C₂×D₄	C₂⁴×C₇	1	2	yes	—
956	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
957	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
958	C₂²×C₄	—	2	1	no	—
959	C₂²×C₄	—	2	4	no	—
960	C₂²×C₄	—	2	4	no	—
961	C₂²×C₄	—	2	2	no	—
962	C₂²×C₄	—	2	2	no	—
963	C₂²×C₄	—	2	2	no	—
964	C₂²×C₄	—	2	1	no	—
965	C₂²×C₄	—	2	1	no	—
966	C₂²×C₄	—	2	1	no	—
967	C₂²×C₄	—	2	2	no	—
968	C₂²×C₄	—	2	2	no	—
969	C₂²×C₄	—	2	2	no	—
970	C₂²×C₄	—	2	1	no	—
971	C₂²×C₄	—	2	1	no	—
972	C₂²×C₄	—	4	8	no	—
973	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
974	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
975	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
976	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
977	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
978	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
979	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
980	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
981	Q₁₆	—	2	2	no	—
982	Q₁₆	—	4	2	no	—
983	SD₁₆	—	2	2	no	—
984	SD₁₆	—	2	2	no	—
985	SD₁₆	—	4	2	no	—
986	SD₁₆	—	4	2	no	—
987	D₈	—	2	2	no	—
988	D₈	—	4	2	no	—
989	M₁₆	—	4	2	no	—
990	M₁₆	—	4	2	no	—
991	M₁₆	—	4	2	no	—
992	M₁₆	—	4	2	no	—
993	C₂×C₈	—	2	2	no	—
994	C₂×C₈	—	2	2	no	—
995	C₂×C₈	—	2	4	no	—
996	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
997	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
998	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
999	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
1000	C₂×C₈	C₂⁴×C₇	1	2	yes	—
1001	C₂×C₈	C₂⁴×C₇	1	2	yes	—
1002	C₄⋊C₄	—	2	1	no	—
1003	C₄⋊C₄	—	2	2	no	—
1004	C₄⋊C₄	—	2	2	no	—
1005	C₄⋊C₄	—	2	2	no	—
1006	C₄⋊C₄	—	2	1	no	—
1007	C₄⋊C₄	—	2	2	no	—
1008	C₄⋊C₄	—	2	2	no	—
1009	C₄⋊C₄	—	2	1	no	—
1010	C₄⋊C₄	—	2	1	no	—
1011	C₄⋊C₄	—	2	1	no	—
1012	C₄⋊C₄	—	2	1	no	—
1013	C₄⋊C₄	—	2	1	no	—
1014	C₄⋊C₄	—	2	2	no	—
1015	C₄⋊C₄	—	2	2	no	—
1016	C₄⋊C₄	—	2	2	no	—
1017	C₄⋊C₄	—	2	1	no	—
1018	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1019	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1020	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
1021	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1022	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1023	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
1024	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
1025	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1026	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1027	C₂²⋊C₄	—	2	1	no	—
1028	C₂²⋊C₄	—	2	2	no	—
1029	C₂²⋊C₄	—	2	2	no	—
1030	C₂²⋊C₄	—	2	2	no	—
1031	C₂²⋊C₄	—	2	2	no	—
1032	C₂²⋊C₄	—	2	2	no	—
1033	C₂²⋊C₄	—	2	1	no	—
1034	C₂²⋊C₄	—	2	2	no	—
1035	C₂²⋊C₄	—	2	2	no	—
1036	C₂²⋊C₄	—	2	2	no	—
1037	C₂²⋊C₄	—	2	2	no	—
1038	C₂²⋊C₄	—	2	2	no	—
1039	C₂²⋊C₄	—	2	1	no	—
1040	C₂²⋊C₄	—	2	1	no	—
1041	C₂²⋊C₄	—	2	1	no	—
1042	C₂²⋊C₄	—	2	1	no	—
1043	C₂²⋊C₄	—	2	2	no	—
1044	C₂²⋊C₄	—	2	2	no	—
1045	C₂²⋊C₄	—	2	2	no	—
1046	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1047	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1048	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1049	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1050	C₄²	—	2	1	no	—
1051	C₄²	—	2	2	no	—
1052	C₄²	—	2	1	no	—
1053	C₄²	—	2	1	no	—
1054	C₄²	—	2	2	no	—
1055	C₄²	—	2	2	no	—
1056	C₄²	—	2	1	no	—
1057	C₄²	—	2	1	no	—
1058	C₄²	—	2	1	no	—
1059	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
1060	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
1061	C₄²	C₂⁴×C₇	1	1	yes	characteristic
1062	C₄²	C₂⁴×C₇	1	1	yes	characteristic
1063	C₂×C₇	—	2	2	no	—
1064	C₂×C₇	—	4	2	no	—
1065	C₂×C₇	—	4	2	no	—
1066	C₂×C₇	—	4	2	no	—
1067	C₂×C₇	—	8	1	no	—
1068	C₂×C₇	—	8	2	no	—
1069	C₂×C₇	C₂×#546	1	1	yes	characteristic
1070	C₂×C₇	C₂×#575	1	1	yes	characteristic
1071	C₂×C₇	#3584	1	1	yes	characteristic
1072	C₂³	—	2	1	no	—
1073	C₂³	—	2	4	no	—
1074	C₂³	—	2	1	no	—
1075	C₂³	—	2	2	no	—
1076	C₂³	—	4	2	no	—
1077	C₂³	—	4	2	no	—
1078	C₂³	—	4	4	no	—
1079	C₂³	—	4	4	no	—
1080	C₂³	—	8	2	no	—
1081	C₂³	C₂²×C₇×D₄	1	2	yes	—
1082	C₂³	C₂²×C₇×D₄	1	2	yes	—
1083	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
1084	Q₈	—	2	1	no	—
1085	Q₈	—	2	1	no	—
1086	Q₈	—	2	2	no	—
1087	Q₈	—	2	1	no	—
1088	Q₈	—	2	2	no	—
1089	Q₈	—	4	4	no	—
1090	Q₈	—	4	2	no	—
1091	Q₈	—	8	1	no	—
1092	Q₈	C₂×C₇×#41	1	2	yes	—
1093	D₄	—	2	4	no	—
1094	D₄	—	2	1	no	—
1095	D₄	—	2	2	no	—
1096	D₄	—	2	1	no	—
1097	D₄	—	2	1	no	—
1098	D₄	—	2	2	no	—
1099	D₄	—	2	2	no	—
1100	D₄	—	2	2	no	—
1101	D₄	—	4	2	no	—
1102	D₄	—	4	4	no	—
1103	D₄	—	4	4	no	—
1104	D₄	—	4	4	no	—
1105	D₄	—	4	4	no	—
1106	D₄	—	4	4	no	—
1107	D₄	—	4	4	no	—
1108	D₄	—	4	2	no	—
1109	D₄	—	4	2	no	—
1110	D₄	—	8	1	no	—
1111	D₄	—	8	2	no	—
1112	D₄	—	8	2	no	—
1113	D₄	C₂×C₇×#41	1	2	yes	—
1114	C₂×C₄	—	2	1	no	—
1115	C₂×C₄	—	2	4	no	—
1116	C₂×C₄	—	2	2	no	—
1117	C₂×C₄	—	2	2	no	—
1118	C₂×C₄	—	2	2	no	—
1119	C₂×C₄	—	2	2	no	—
1120	C₂×C₄	—	2	4	no	—
1121	C₂×C₄	—	2	4	no	—
1122	C₂×C₄	—	2	4	no	—
1123	C₂×C₄	—	2	2	no	—
1124	C₂×C₄	—	2	1	no	—
1125	C₂×C₄	—	2	1	no	—
1126	C₂×C₄	—	2	1	no	—
1127	C₂×C₄	—	2	1	no	—
1128	C₂×C₄	—	2	1	no	—
1129	C₂×C₄	—	2	2	no	—
1130	C₂×C₄	—	2	2	no	—
1131	C₂×C₄	—	2	2	no	—
1132	C₂×C₄	—	4	1	no	—
1133	C₂×C₄	—	4	4	no	—
1134	C₂×C₄	—	4	4	no	—
1135	C₂×C₄	—	4	4	no	—
1136	C₂×C₄	—	4	4	no	—
1137	C₂×C₄	—	4	4	no	—
1138	C₂×C₄	—	4	2	no	—
1139	C₂×C₄	—	4	2	no	—
1140	C₂×C₄	—	4	2	no	—
1141	C₂×C₄	—	8	1	no	—
1142	C₂×C₄	—	8	1	no	—
1143	C₂×C₄	—	8	2	no	—
1144	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1145	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1146	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1147	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1148	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1149	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1150	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1151	C₂×C₄	C₂×C₇×#41	1	2	yes	—
1152	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
1153	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
1154	C₈	—	2	1	no	—
1155	C₈	—	2	1	no	—
1156	C₈	—	2	1	no	—
1157	C₈	—	2	1	no	—
1158	C₈	—	2	2	no	—
1159	C₈	—	2	2	no	—
1160	C₇	#61154	1	1	yes	characteristic, direct product factor, Sylow
1161	C₂²	—	2	1	no	—
1162	C₂²	—	2	1	no	—
1163	C₂²	—	2	2	no	—
1164	C₂²	—	2	2	no	—
1165	C₂²	—	2	2	no	—
1166	C₂²	—	2	2	no	—
1167	C₂²	—	2	2	no	—
1168	C₂²	—	2	2	no	—
1169	C₂²	—	2	2	no	—
1170	C₂²	—	4	1	no	—
1171	C₂²	—	4	1	no	—
1172	C₂²	—	4	1	no	—
1173	C₂²	—	4	2	no	—
1174	C₂²	—	4	1	no	—
1175	C₂²	—	4	2	no	—
1176	C₂²	—	4	2	no	—
1177	C₂²	—	4	1	no	—
1178	C₂²	—	8	4	no	—
1179	C₂²	—	8	8	no	—
1180	C₂²	C₇×#546	1	2	yes	—
1181	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
1182	C₄	—	2	1	no	—
1183	C₄	—	2	1	no	—
1184	C₄	—	2	1	no	—
1185	C₄	—	2	2	no	—
1186	C₄	—	2	2	no	—
1187	C₄	—	2	2	no	—
1188	C₄	—	4	1	no	—
1189	C₄	—	4	1	no	—
1190	C₄	—	4	2	no	—
1191	C₄	—	4	1	no	—
1192	C₄	—	4	1	no	—
1193	C₄	—	4	2	no	—
1194	C₄	—	4	2	no	—
1195	C₄	—	4	1	no	—
1196	C₄	C₇×#546	1	2	yes	—
1197	C₄	C₇×#575	1	2	yes	—
1198	C₄	C₂²×C₇×#41	1	1	yes	characteristic
1199	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
1200	C₂	—	2	2	no	—
1201	C₂	—	4	2	no	—
1202	C₂	—	4	2	no	—
1203	C₂	—	4	2	no	—
1204	C₂	—	8	2	no	—
1205	C₂	—	8	1	no	—
1206	C₂	C₂×C₇×#546	1	1	yes	characteristic
1207	C₂	C₂×C₇×#575	1	1	yes	characteristic
1208	C₂	C₇×#3584	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
socle	C₂²×C₇	C₂³×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₇ ◁ C₂×C₄×C₇×D₄ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₇×#3475	C₂	semidirect
2. C₇×D₄×#41	C₂	semidirect
3. C₇×#3333	C₂	semidirect
4. C₇×#3332	C₂	semidirect
5. C₇×#3331	C₂	semidirect
6. C₇×#3330	C₂	semidirect
7. C₇×#3329	C₂	semidirect
8. C₇×#3328	C₂	semidirect
9. C₇×#3327	C₂	semidirect
10. C₇×#3326	C₂	semidirect
11. C₇×#3325	C₂	semidirect
12. C₇×#3324	C₂	semidirect
13. C₇×#3323	C₂	semidirect
14. C₇×#3322	C₂	semidirect
15. C₇×#3131	C₂	semidirect
16. C₇×#3091	C₂	semidirect
17. C₇×#3076	C₂	semidirect
18. C₇×#3054	C₂	semidirect
19. C₇×#3035	C₂	semidirect
20. C₇×#3002	C₂	semidirect
21. C₄×C₇×#135	C₂	semidirect
22. C₂×C₇×#436	C₂	semidirect
23. C₇×#2896	C₂	semidirect
26. C₂×C₇×#135	C₂²	semidirect
27. C₂²×C₇×M₁₆	C₂²	semidirect
30. C₇×#554	C₂²	semidirect
31. C₇×#553	C₂²	semidirect
33. C₇×#552	C₂²	semidirect
40. C₇×#547	C₂²	semidirect
46. C₇×#533	C₂²	semidirect
53. C₇×#525	C₂²	semidirect
56. C₄×C₇×#41	C₂²	semidirect
59. C₂×C₇×#117	C₂²	semidirect
60. C₇×#488	C₂²	semidirect
61. C₇×#488	C₂²	semidirect
62. C₇×#487	C₂²	semidirect
63. C₇×#487	C₂²	semidirect
64. C₇×#486	C₂²	semidirect
65. C₇×#486	C₂²	semidirect
66. C₇×#485	C₂²	semidirect
67. C₇×#485	C₂²	semidirect
68. C₇×#484	C₂²	semidirect
69. C₇×#483	C₂²	semidirect
70. C₇×#482	C₂²	semidirect
71. C₇×#482	C₂²	semidirect
72. C₇×#481	C₂²	semidirect
73. C₇×#480	C₂²	semidirect
74. C₇×#479	C₂²	semidirect
75. C₇×#478	C₂²	semidirect
76. C₇×#477	C₂²	semidirect
77. C₇×#476	C₂²	semidirect
78. C₇×#475	C₂²	semidirect
79. C₇×#474	C₂²	semidirect
80. C₇×#470	C₂²	semidirect
81. C₇×#470	C₂²	semidirect
82. C₇×#469	C₂²	semidirect
83. C₇×#469	C₂²	semidirect
84. C₇×#468	C₂²	semidirect
85. C₇×#468	C₂²	semidirect
86. C₇×#468	C₂²	semidirect
87. C₇×#468	C₂²	semidirect
88. C₇×#464	C₂²	semidirect
89. C₇×#463	C₂²	semidirect
90. C₇×#462	C₂²	semidirect
91. C₇×#461	C₂²	semidirect
92. C₇×#460	C₂²	semidirect
93. C₇×#459	C₂²	semidirect
94. C₇×#452	C₂²	semidirect
95. C₇×#452	C₂²	semidirect
96. C₇×#451	C₂²	semidirect
97. C₇×#450	C₂²	semidirect
98. C₇×#449	C₂²	semidirect
99. C₇×#449	C₂²	semidirect
100. C₇×#448	C₂²	semidirect
101. C₇×#447	C₂²	semidirect
102. C₄×C₇×Q₁₆	C₂²	semidirect
103. C₄×C₇×Q₁₆	C₂²	semidirect
104. C₄×C₇×SD₁₆	C₂²	semidirect
105. C₄×C₇×SD₁₆	C₂²	semidirect
106. C₄×C₇×SD₁₆	C₂²	semidirect
107. C₄×C₇×SD₁₆	C₂²	semidirect
108. C₄×C₇×D₈	C₂²	semidirect
109. C₄×C₇×D₈	C₂²	semidirect
112. C₇×#436	C₂²	semidirect
113. C₇×#436	C₂²	semidirect
114. C₇×#436	C₂²	semidirect
115. C₇×#436	C₂²	semidirect
116. C₇×#427	C₂²	semidirect
117. C₇×#427	C₂²	semidirect
118. C₂×C₇×C₄⋊C₈	C₂²	semidirect
119. C₇×#419	C₂²	semidirect
120. C₇×#419	C₂²	semidirect
121. C₇×#418	C₂²	semidirect
122. C₇×#418	C₂²	semidirect
123. C₇×#417	C₂²	semidirect
124. C₇×#417	C₂²	semidirect
125. C₇×#417	C₂²	semidirect
126. C₇×#417	C₂²	semidirect
129. C₇×#416	C₂²	semidirect
130. C₇×#416	C₂²	semidirect
131. C₇×#416	C₂²	semidirect
132. C₇×#416	C₂²	semidirect
133. C₂×C₇×C₂²⋊C₈	C₂²	semidirect
134. C₂×C₄×C₇×C₈	C₂²	semidirect
135. #61154	C₇	direct (N × H)
318. #3475	C₂×C₇	semidirect
319. D₄×#41	C₂×C₇	semidirect
320. #3333	C₂×C₇	semidirect
321. #3332	C₂×C₇	semidirect
322. #3331	C₂×C₇	semidirect
323. #3330	C₂×C₇	semidirect
324. #3329	C₂×C₇	semidirect
325. #3328	C₂×C₇	semidirect
326. #3327	C₂×C₇	semidirect
327. #3326	C₂×C₇	semidirect
328. #3325	C₂×C₇	semidirect
329. #3324	C₂×C₇	semidirect
330. #3323	C₂×C₇	semidirect
331. #3322	C₂×C₇	semidirect
332. #3131	C₂×C₇	semidirect
333. #3091	C₂×C₇	semidirect
334. #3076	C₂×C₇	semidirect
335. #3054	C₂×C₇	semidirect
336. #3035	C₂×C₇	semidirect
337. #3002	C₂×C₇	semidirect
338. C₄×#135	C₂×C₇	semidirect
339. C₂×#436	C₂×C₇	semidirect
340. #2896	C₂×C₇	semidirect
355. C₇×#41	#41	semidirect
494. C₂×#135	C₂²×C₇	semidirect
495. C₂²×M₁₆	C₂²×C₇	semidirect
498. #554	C₂²×C₇	semidirect
499. #553	C₂²×C₇	semidirect
501. #552	C₂²×C₇	semidirect
508. #547	C₂²×C₇	semidirect
514. #533	C₂²×C₇	semidirect
521. #525	C₂²×C₇	semidirect
524. C₄×#41	C₂²×C₇	semidirect
527. C₂×#117	C₂²×C₇	semidirect
528. #488	C₂²×C₇	semidirect
529. #488	C₂²×C₇	semidirect
530. #487	C₂²×C₇	semidirect
531. #487	C₂²×C₇	semidirect
532. #486	C₂²×C₇	semidirect
533. #486	C₂²×C₇	semidirect
534. #485	C₂²×C₇	semidirect
535. #485	C₂²×C₇	semidirect
536. #484	C₂²×C₇	semidirect
537. #483	C₂²×C₇	semidirect
538. #482	C₂²×C₇	semidirect
539. #482	C₂²×C₇	semidirect
540. #481	C₂²×C₇	semidirect
541. #480	C₂²×C₇	semidirect
542. #479	C₂²×C₇	semidirect
543. #478	C₂²×C₇	semidirect
544. #477	C₂²×C₇	semidirect
545. #476	C₂²×C₇	semidirect
546. #475	C₂²×C₇	semidirect
547. #474	C₂²×C₇	semidirect
548. #470	C₂²×C₇	semidirect
549. #470	C₂²×C₇	semidirect
550. #469	C₂²×C₇	semidirect
551. #469	C₂²×C₇	semidirect
552. #468	C₂²×C₇	semidirect
553. #468	C₂²×C₇	semidirect
554. #468	C₂²×C₇	semidirect
555. #468	C₂²×C₇	semidirect
556. #464	C₂²×C₇	semidirect
557. #463	C₂²×C₇	semidirect
558. #462	C₂²×C₇	semidirect
559. #461	C₂²×C₇	semidirect
560. #460	C₂²×C₇	semidirect
561. #459	C₂²×C₇	semidirect
562. #452	C₂²×C₇	semidirect
563. #452	C₂²×C₇	semidirect
564. #451	C₂²×C₇	semidirect
565. #450	C₂²×C₇	semidirect
566. #449	C₂²×C₇	semidirect
567. #449	C₂²×C₇	semidirect
568. #448	C₂²×C₇	semidirect
569. #447	C₂²×C₇	semidirect
570. C₄×Q₁₆	C₂²×C₇	semidirect
571. C₄×Q₁₆	C₂²×C₇	semidirect
572. C₄×SD₁₆	C₂²×C₇	semidirect
573. C₄×SD₁₆	C₂²×C₇	semidirect
574. C₄×SD₁₆	C₂²×C₇	semidirect
575. C₄×SD₁₆	C₂²×C₇	semidirect
576. C₄×D₈	C₂²×C₇	semidirect
577. C₄×D₈	C₂²×C₇	semidirect
580. #436	C₂²×C₇	semidirect
581. #436	C₂²×C₇	semidirect
582. #436	C₂²×C₇	semidirect
583. #436	C₂²×C₇	semidirect
584. #427	C₂²×C₇	semidirect
585. #427	C₂²×C₇	semidirect
586. C₂×C₄⋊C₈	C₂²×C₇	semidirect
587. #419	C₂²×C₇	semidirect
588. #419	C₂²×C₇	semidirect
589. #418	C₂²×C₇	semidirect
590. #418	C₂²×C₇	semidirect
591. #417	C₂²×C₇	semidirect
592. #417	C₂²×C₇	semidirect
593. #417	C₂²×C₇	semidirect
594. #417	C₂²×C₇	semidirect
597. #416	C₂²×C₇	semidirect
598. #416	C₂²×C₇	semidirect
599. #416	C₂²×C₇	semidirect
600. #416	C₂²×C₇	semidirect
601. C₂×C₂²⋊C₈	C₂²×C₇	semidirect
602. C₂×C₄×C₈	C₂²×C₇	semidirect
926. #41	C₇×#41	semidirect
1160. C₇	#61154	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₇×#3475	2
C₇×D₄×#41	2
C₇×#3333	2
C₇×#3332	2
C₇×#3331	2
C₇×#3330	2
C₇×#3329	2
C₇×#3328	2
C₇×#3327	2
C₇×#3326	2
C₇×#3325	2
C₇×#3324	2
C₇×#3323	2
C₇×#3322	2
C₇×#3131	2
C₇×#3091	2
C₇×#3076	2
C₇×#3054	2
C₇×#3035	2
C₇×#3002	2
C₄×C₇×#135	2
C₂×C₇×#436	2
C₇×#2896	2
#61154	7

Subgroups — C7×#61154 #13238370

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#61154 #13238370