Subgroups — C₇×#61038 #13238254

Order 1792.

2790 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#575	C₂	1	2	yes	maximal, complemented
2	C₇×D₄×#41	C₂	1	2	yes	maximal, complemented
3	C₇×#3278	C₂	1	2	yes	maximal, complemented
4	C₇×#3277	C₂	1	2	yes	maximal, complemented
5	C₇×#3276	C₂	1	2	yes	maximal, complemented
6	C₇×#3275	C₂	1	4	yes	maximal, complemented
7	C₇×#3274	C₂	1	2	yes	maximal, complemented
8	C₇×#3273	C₂	1	2	yes	maximal, complemented
9	C₇×#3272	C₂	1	2	yes	maximal, complemented
10	C₇×#3147	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#3054	C₂	1	2	yes	maximal, complemented
12	C₇×#3035	C₂	1	2	yes	maximal, complemented
13	C₇×#3002	C₂	1	4	yes	maximal, complemented
14	C₄×C₇×#135	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₇×#436	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₇×#41	C₂²	1	4	yes	complemented
17	C₇×#575	—	2	16	no	—
18	C₂×C₇×#137	C₂²	1	4	yes	complemented
19	C₂×C₇×#137	C₂²	1	4	yes	complemented
20	C₂×C₇×AGL(1,ℤ/8)	C₂²	1	4	yes	complemented
21	C₂×C₇×AGL(1,ℤ/8)	C₂²	1	4	yes	complemented
22	C₂×C₇×#135	C₂²	1	1	yes	characteristic
23	C₂×C₇×#135	C₂²	1	4	yes	complemented
24	C₂×C₇×#135	C₂²	1	2	yes	complemented
25	C₂×C₇×#135	C₂²	1	2	yes	complemented
26	C₂²×C₇×M₁₆	C₂²	1	2	yes	complemented
27	C₇×#550	C₂²	1	2	yes	—
28	C₇×D₄×Q₈	C₂²	1	2	yes	complemented
29	C₇×#548	C₂²	1	4	yes	complemented
30	C₇×#547	—	2	2	no	—
31	C₇×#547	C₂²	1	2	yes	—
32	C₇×#546	—	2	4	no	—
33	C₇×#546	C₂²	1	4	yes	complemented
34	C₇×D₄²	—	2	2	no	—
35	C₇×D₄²	C₂²	1	2	yes	complemented
36	C₇×#532	—	2	2	no	—
37	C₇×#532	C₂²	1	2	yes	complemented
38	C₇×#525	—	2	4	no	—
39	C₇×#525	C₂²	1	4	yes	complemented
40	C₄×C₇×#41	C₂²	1	2	yes	complemented
41	C₂×C₄×C₇×D₄	—	2	2	no	—
42	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
43	C₇×#495	C₂²	1	2	yes	complemented
44	C₇×#495	C₂²	1	2	yes	complemented
45	C₇×#494	C₂²	1	1	yes	characteristic, complemented
46	C₇×#493	C₂²	1	1	yes	characteristic, complemented
47	C₇×#492	C₂²	1	2	yes	complemented
48	C₇×#470	C₂²	1	4	yes	complemented
49	C₇×#469	C₂²	1	4	yes	complemented
50	C₇×#468	C₂²	1	4	yes	complemented
51	C₇×#468	C₂²	1	4	yes	complemented
52	C₇×#464	C₂²	1	4	yes	complemented
53	C₇×#463	C₂²	1	4	yes	complemented
54	C₇×#462	C₂²	1	2	yes	complemented
55	C₇×#461	C₂²	1	2	yes	complemented
56	C₇×#460	C₂²	1	2	yes	complemented
57	C₇×#459	C₂²	1	2	yes	complemented
58	C₇×#452	C₂²	1	4	yes	complemented
59	C₇×#452	C₂²	1	4	yes	complemented
60	C₇×#451	C₂²	1	4	yes	complemented
61	C₇×#450	C₂²	1	4	yes	complemented
62	C₇×#449	C₂²	1	4	yes	complemented
63	C₇×#449	C₂²	1	4	yes	complemented
64	C₇×#448	C₂²	1	4	yes	complemented
65	C₇×#447	C₂²	1	4	yes	complemented
66	C₄×C₇×Q₁₆	C₂²	1	1	yes	characteristic, complemented
67	C₄×C₇×Q₁₆	C₂²	1	1	yes	characteristic, complemented
68	C₄×C₇×SD₁₆	C₂²	1	2	yes	complemented
69	C₄×C₇×SD₁₆	C₂²	1	2	yes	complemented
70	C₄×C₇×D₈	C₂²	1	1	yes	characteristic, complemented
71	C₄×C₇×D₈	C₂²	1	1	yes	characteristic, complemented
72	C₇×#436	C₂²	1	2	yes	complemented
73	C₇×#436	C₂²	1	2	yes	complemented
74	C₇×#436	C₂²	1	2	yes	complemented
75	C₇×#436	C₂²	1	2	yes	complemented
76	C₇×#427	C₂²	1	1	yes	characteristic, complemented
77	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
78	C₇×#416	C₂²	1	2	yes	complemented
79	C₇×#416	C₂²	1	4	yes	complemented
80	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	complemented
81	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic, complemented
82	#61038	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
83	C₂×C₇×#41	—	2	4	no	—
84	C₂×C₇×#41	—	2	4	no	—
85	C₂×C₇×#41	—	2	16	no	—
86	C₂×C₇×#41	—	4	8	no	—
87	C₂×C₇×#41	C₂³	1	4	yes	—
88	C₂×C₇×#41	C₂³	1	4	yes	—
89	C₂×C₇×#41	C₂³	1	4	yes	—
90	C₂×C₇×#41	C₂³	1	2	yes	—
91	C₂²×C₇×Q₈	C₂³	1	4	yes	—
92	C₂²×C₇×D₄	—	2	4	no	—
93	C₂²×C₇×D₄	—	2	2	no	—
94	C₂²×C₇×D₄	D₄	1	1	yes	characteristic
95	C₂²×C₇×D₄	C₂³	1	4	yes	—
96	C₂³×C₄×C₇	—	2	4	no	—
97	C₂³×C₄×C₇	C₂³	1	2	yes	—
98	C₇×#137	—	2	16	no	—
99	C₇×#137	—	2	16	no	—
100	C₇×AGL(1,ℤ/8)	—	2	16	no	—
101	C₇×AGL(1,ℤ/8)	—	2	16	no	—
102	C₇×#135	—	2	16	no	—
103	C₇×#135	—	2	8	no	—
104	C₇×#135	—	4	4	no	—
105	C₇×#135	D₄	1	8	yes	complemented
106	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
107	C₂×C₇×Q₁₆	C₂³	1	4	yes	—
108	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
109	C₂×C₇×Q₁₆	C₂³	1	1	yes	characteristic
110	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
111	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
112	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
113	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
114	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
115	C₂×C₇×D₈	C₂³	1	2	yes	—
116	C₂×C₇×D₈	C₂³	1	4	yes	—
117	C₂×C₇×D₈	C₂³	1	2	yes	—
118	C₂×C₇×D₈	C₂³	1	1	yes	characteristic
119	C₂×C₇×M₁₆	—	2	8	no	—
120	C₂×C₇×M₁₆	C₂³	1	4	yes	—
121	C₂×C₇×M₁₆	C₂³	1	4	yes	—
122	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
123	C₂²×C₇×C₈	C₂³	1	2	yes	—
124	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
125	C₇×C₄⋊Q₈	—	2	2	no	—
126	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
127	C₇×#127	—	2	2	no	—
128	C₇×#127	C₂³	1	2	yes	—
129	C₇×#124	—	2	4	no	—
130	C₇×#124	C₂³	1	4	yes	—
131	C₇×#123	—	2	4	no	—
132	C₇×#123	—	2	4	no	—
133	C₇×#123	—	2	4	no	—
134	C₇×C₂²⋊Q₈	—	2	4	no	—
135	C₇×C₂²⋊Q₈	—	2	4	no	—
136	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
137	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
138	C₇×#121	—	2	4	no	—
139	C₇×#121	—	2	2	no	—
140	C₇×#121	—	2	2	no	—
141	C₇×#121	—	2	2	no	—
142	C₇×#121	—	2	2	no	—
143	C₇×#121	—	2	4	no	—
144	C₇×#121	—	2	4	no	—
145	C₇×#121	C₂³	1	4	yes	—
146	C₇×#121	C₂³	1	4	yes	—
147	C₇×#120	—	2	4	no	—
148	C₇×#120	—	2	4	no	—
149	C₇×#120	—	2	4	no	—
150	C₄×C₇×Q₈	C₂³	1	2	yes	—
151	C₄×C₇×Q₈	C₂³	1	2	yes	—
152	C₄×C₇×D₄	—	2	2	no	—
153	C₄×C₇×D₄	—	2	4	no	—
154	C₄×C₇×D₄	—	2	2	no	—
155	C₄×C₇×D₄	—	2	2	no	—
156	C₄×C₇×D₄	—	2	4	no	—
157	C₄×C₇×D₄	—	2	2	no	—
158	C₄×C₇×D₄	—	2	4	no	—
159	C₄×C₇×D₄	—	2	2	no	—
160	C₄×C₇×D₄	—	2	2	no	—
161	C₄×C₇×D₄	D₄	1	2	yes	—
162	C₄×C₇×D₄	D₄	1	2	yes	—
163	C₄×C₇×D₄	C₂³	1	2	yes	—
164	C₄×C₇×D₄	C₂³	1	2	yes	—
165	C₄×C₇×D₄	C₂³	1	2	yes	—
166	C₄×C₇×D₄	C₂³	1	2	yes	—
167	C₇×#117	—	2	2	no	—
168	C₇×#117	C₂³	1	2	yes	—
169	C₂×C₇×C₄⋊C₄	—	2	2	no	—
170	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
171	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
172	C₂×C₇×C₂²⋊C₄	D₄	1	2	yes	—
173	C₂×C₄²×C₇	—	2	2	no	—
174	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
175	C₇×#107	C₂³	1	1	yes	characteristic
176	C₇×#107	C₂³	1	1	yes	characteristic
177	C₇×#106	C₂³	1	2	yes	—
178	C₇×C₄⋊C₈	C₂³	1	2	yes	—
179	C₇×C₄⋊C₈	C₂³	1	2	yes	—
180	C₇×#103	C₂³	1	4	yes	—
181	C₇×#103	C₂³	1	4	yes	—
182	C₇×#103	C₂³	1	2	yes	—
183	C₇×#103	C₂³	1	2	yes	—
184	C₇×#102	C₂³	1	4	yes	—
185	C₇×#102	C₂³	1	4	yes	—
186	C₇×#102	C₂³	1	2	yes	—
187	C₇×#102	C₂³	1	2	yes	—
188	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
189	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
190	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
191	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
192	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
193	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
194	C₂×#575	C₂×C₇	1	2	yes	complemented
195	D₄×#41	C₂×C₇	1	2	yes	complemented
196	#3278	C₂×C₇	1	2	yes	complemented
197	#3277	C₂×C₇	1	2	yes	complemented
198	#3276	C₂×C₇	1	2	yes	complemented
199	#3275	C₂×C₇	1	4	yes	complemented
200	#3274	C₂×C₇	1	2	yes	complemented
201	#3273	C₂×C₇	1	2	yes	complemented
202	#3272	C₂×C₇	1	2	yes	complemented
203	#3147	C₂×C₇	1	1	yes	characteristic, complemented
204	#3054	C₂×C₇	1	2	yes	complemented
205	#3035	C₂×C₇	1	2	yes	complemented
206	#3002	C₂×C₇	1	4	yes	complemented
207	C₄×#135	C₂×C₇	1	1	yes	characteristic, complemented
208	C₂×#436	C₂×C₇	1	1	yes	characteristic, complemented
209	C₂⁴×C₇	—	2	4	no	—
210	C₂⁴×C₇	C₂×D₄	1	2	yes	—
211	C₇×#41	—	2	4	no	—
212	C₇×#41	—	2	8	no	—
213	C₇×#41	—	2	8	no	—
214	C₇×#41	—	2	8	no	—
215	C₇×#41	—	2	8	no	—
216	C₇×#41	—	4	16	no	—
217	C₇×#41	—	4	4	no	—
218	C₇×#41	—	4	4	no	—
219	C₇×#41	—	4	16	no	—
220	C₇×#41	C₂×D₄	1	8	yes	complemented
221	C₂×C₇×Q₈	—	2	4	no	—
222	C₂×C₇×Q₈	—	2	8	no	—
223	C₂×C₇×Q₈	—	4	4	no	—
224	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
225	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
226	C₂×C₇×D₄	—	2	2	no	—
227	C₂×C₇×D₄	—	2	8	no	—
228	C₂×C₇×D₄	—	2	4	no	—
229	C₂×C₇×D₄	—	2	4	no	—
230	C₂×C₇×D₄	—	2	4	no	—
231	C₂×C₇×D₄	—	2	4	no	—
232	C₂×C₇×D₄	—	2	4	no	—
233	C₂×C₇×D₄	—	2	2	no	—
234	C₂×C₇×D₄	—	2	4	no	—
235	C₂×C₇×D₄	—	2	2	no	—
236	C₂×C₇×D₄	—	4	2	no	—
237	C₂×C₇×D₄	—	4	4	no	—
238	C₂×C₇×D₄	—	4	16	no	—
239	C₂×C₇×D₄	—	4	8	no	—
240	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
241	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
242	C₂×C₇×D₄	C₂⁴	1	4	yes	—
243	C₂×C₇×D₄	C₂⁴	1	2	yes	—
244	C₂²×C₄×C₇	—	2	4	no	—
245	C₂²×C₄×C₇	—	2	2	no	—
246	C₂²×C₄×C₇	—	2	4	no	—
247	C₂²×C₄×C₇	—	2	4	no	—
248	C₂²×C₄×C₇	—	2	2	no	—
249	C₂²×C₄×C₇	—	2	4	no	—
250	C₂²×C₄×C₇	—	2	4	no	—
251	C₂²×C₄×C₇	—	2	4	no	—
252	C₂²×C₄×C₇	—	2	2	no	—
253	C₂²×C₄×C₇	—	4	16	no	—
254	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
255	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
256	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
257	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
258	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
259	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
260	C₇×Q₁₆	—	2	8	no	—
261	C₇×Q₁₆	—	2	4	no	—
262	C₇×Q₁₆	—	4	2	no	—
263	C₇×Q₁₆	C₂×D₄	1	4	yes	complemented
264	C₇×SD₁₆	—	2	8	no	—
265	C₇×SD₁₆	—	2	8	no	—
266	C₇×SD₁₆	—	2	8	no	—
267	C₇×SD₁₆	—	4	4	no	—
268	C₇×SD₁₆	C₂×D₄	1	8	yes	complemented
269	C₇×D₈	—	2	8	no	—
270	C₇×D₈	—	2	4	no	—
271	C₇×D₈	—	4	2	no	—
272	C₇×D₈	C₂×D₄	1	4	yes	complemented
273	C₇×M₁₆	—	2	8	no	—
274	C₇×M₁₆	—	2	8	no	—
275	C₂×C₇×C₈	—	2	4	no	—
276	C₂×C₇×C₈	—	2	2	no	—
277	C₂×C₇×C₈	C₂×D₄	1	4	yes	complemented
278	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
279	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
280	C₂×C₇×C₈	C₂⁴	1	4	yes	—
281	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
282	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
283	C₇×C₄⋊C₄	—	2	2	no	—
284	C₇×C₄⋊C₄	—	2	4	no	—
285	C₇×C₄⋊C₄	—	2	2	no	—
286	C₇×C₄⋊C₄	—	2	2	no	—
287	C₇×C₄⋊C₄	—	2	2	no	—
288	C₇×C₄⋊C₄	—	2	4	no	—
289	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
290	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
291	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
292	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
293	C₇×C₂²⋊C₄	—	2	4	no	—
294	C₇×C₂²⋊C₄	—	2	2	no	—
295	C₇×C₂²⋊C₄	—	2	4	no	—
296	C₇×C₂²⋊C₄	—	2	4	no	—
297	C₇×C₂²⋊C₄	—	2	4	no	—
298	C₇×C₂²⋊C₄	—	2	2	no	—
299	C₇×C₂²⋊C₄	—	2	2	no	—
300	C₇×C₂²⋊C₄	—	2	4	no	—
301	C₇×C₂²⋊C₄	—	2	4	no	—
302	C₇×C₂²⋊C₄	C₂×D₄	1	4	yes	—
303	C₇×C₂²⋊C₄	C₂×D₄	1	4	yes	—
304	C₄²×C₇	—	2	2	no	—
305	C₄²×C₇	—	2	2	no	—
306	C₄²×C₇	—	2	2	no	—
307	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
308	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
309	C₄²×C₇	C₂⁴	1	1	yes	characteristic
310	C₄²×C₇	C₂⁴	1	1	yes	characteristic
311	C₂²×#41	C₂²×C₇	1	4	yes	complemented
312	#575	—	2	16	no	—
313	C₂×#137	C₂²×C₇	1	4	yes	complemented
314	C₂×#137	C₂²×C₇	1	4	yes	complemented
315	C₂×AGL(1,ℤ/8)	C₂²×C₇	1	4	yes	complemented
316	C₂×AGL(1,ℤ/8)	C₂²×C₇	1	4	yes	complemented
317	C₂×#135	C₂²×C₇	1	1	yes	characteristic
318	C₂×#135	C₂²×C₇	1	2	yes	complemented
319	C₂×#135	C₂²×C₇	1	4	yes	complemented
320	C₂×#135	C₂²×C₇	1	2	yes	complemented
321	C₂²×M₁₆	C₂²×C₇	1	2	yes	complemented
322	#550	C₂²×C₇	1	2	yes	—
323	D₄×Q₈	C₂²×C₇	1	2	yes	complemented
324	#548	C₂²×C₇	1	4	yes	complemented
325	#547	—	2	2	no	—
326	#547	C₂²×C₇	1	2	yes	—
327	#546	—	2	4	no	—
328	#546	C₂²×C₇	1	4	yes	complemented
329	D₄²	—	2	2	no	—
330	D₄²	C₂²×C₇	1	2	yes	complemented
331	#532	—	2	2	no	—
332	#532	C₂²×C₇	1	2	yes	complemented
333	#525	—	2	4	no	—
334	#525	C₂²×C₇	1	4	yes	complemented
335	C₄×#41	C₂²×C₇	1	2	yes	complemented
336	C₂×C₄×D₄	—	2	2	no	—
337	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
338	#495	C₂²×C₇	1	2	yes	complemented
339	#495	C₂²×C₇	1	2	yes	complemented
340	#494	C₂²×C₇	1	1	yes	characteristic, complemented
341	#493	C₂²×C₇	1	1	yes	characteristic, complemented
342	#492	C₂²×C₇	1	2	yes	complemented
343	#470	C₂²×C₇	1	4	yes	complemented
344	#469	C₂²×C₇	1	4	yes	complemented
345	#468	C₂²×C₇	1	4	yes	complemented
346	#468	C₂²×C₇	1	4	yes	complemented
347	#464	C₂²×C₇	1	4	yes	complemented
348	#463	C₂²×C₇	1	4	yes	complemented
349	#462	C₂²×C₇	1	2	yes	complemented
350	#461	C₂²×C₇	1	2	yes	complemented
351	#460	C₂²×C₇	1	2	yes	complemented
352	#459	C₂²×C₇	1	2	yes	complemented
353	#452	C₂²×C₇	1	4	yes	complemented
354	#452	C₂²×C₇	1	4	yes	complemented
355	#451	C₂²×C₇	1	4	yes	complemented
356	#450	C₂²×C₇	1	4	yes	complemented
357	#449	C₂²×C₇	1	4	yes	complemented
358	#449	C₂²×C₇	1	4	yes	complemented
359	#448	C₂²×C₇	1	4	yes	complemented
360	#447	C₂²×C₇	1	4	yes	complemented
361	C₄×Q₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
362	C₄×Q₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
363	C₄×SD₁₆	C₂²×C₇	1	2	yes	complemented
364	C₄×SD₁₆	C₂²×C₇	1	2	yes	complemented
365	C₄×D₈	C₂²×C₇	1	1	yes	characteristic, complemented
366	C₄×D₈	C₂²×C₇	1	1	yes	characteristic, complemented
367	#436	C₂²×C₇	1	2	yes	complemented
368	#436	C₂²×C₇	1	2	yes	complemented
369	#436	C₂²×C₇	1	2	yes	complemented
370	#436	C₂²×C₇	1	2	yes	complemented
371	#427	C₂²×C₇	1	1	yes	characteristic, complemented
372	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic, complemented
373	#416	C₂²×C₇	1	2	yes	complemented
374	#416	C₂²×C₇	1	4	yes	complemented
375	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	complemented
376	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic, complemented
377	C₂³×C₇	—	2	2	no	—
378	C₂³×C₇	—	2	4	no	—
379	C₂³×C₇	—	2	4	no	—
380	C₂³×C₇	—	4	2	no	—
381	C₂³×C₇	—	4	2	no	—
382	C₂³×C₇	—	4	8	no	—
383	C₂³×C₇	—	4	8	no	—
384	C₂³×C₇	—	8	4	no	—
385	C₂³×C₇	C₂²×D₄	1	4	yes	—
386	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
387	C₇×Q₈	—	2	2	no	—
388	C₇×Q₈	—	2	4	no	—
389	C₇×Q₈	—	2	4	no	—
390	C₇×Q₈	—	4	8	no	—
391	C₇×Q₈	C₂²×D₄	1	4	yes	—
392	C₇×D₄	—	2	8	no	—
393	C₇×D₄	—	2	4	no	—
394	C₇×D₄	—	2	4	no	—
395	C₇×D₄	—	2	2	no	—
396	C₇×D₄	—	2	4	no	—
397	C₇×D₄	—	4	2	no	—
398	C₇×D₄	—	4	8	no	—
399	C₇×D₄	—	4	8	no	—
400	C₇×D₄	—	4	8	no	—
401	C₇×D₄	—	4	8	no	—
402	C₇×D₄	—	4	8	no	—
403	C₇×D₄	—	4	4	no	—
404	C₇×D₄	—	8	2	no	—
405	C₇×D₄	—	8	4	no	—
406	C₇×D₄	C₂²×D₄	1	4	yes	—
407	C₂×C₄×C₇	—	2	4	no	—
408	C₂×C₄×C₇	—	2	2	no	—
409	C₂×C₄×C₇	—	2	8	no	—
410	C₂×C₄×C₇	—	2	8	no	—
411	C₂×C₄×C₇	—	2	2	no	—
412	C₂×C₄×C₇	—	2	4	no	—
413	C₂×C₄×C₇	—	2	4	no	—
414	C₂×C₄×C₇	—	2	2	no	—
415	C₂×C₄×C₇	—	2	2	no	—
416	C₂×C₄×C₇	—	2	4	no	—
417	C₂×C₄×C₇	—	4	1	no	—
418	C₂×C₄×C₇	—	4	8	no	—
419	C₂×C₄×C₇	—	4	8	no	—
420	C₂×C₄×C₇	—	4	8	no	—
421	C₂×C₄×C₇	—	4	8	no	—
422	C₂×C₄×C₇	—	4	4	no	—
423	C₂×C₄×C₇	—	8	2	no	—
424	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
425	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
426	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
427	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
428	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
429	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
430	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
431	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
432	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
433	C₇×C₈	—	2	4	no	—
434	C₇×C₈	—	2	1	no	—
435	C₇×C₈	—	2	1	no	—
436	C₇×C₈	C₂²×D₄	1	2	yes	—
437	C₇×C₈	C₂²×D₄	1	2	yes	—
438	C₂×#41	—	2	4	no	—
439	C₂×#41	—	2	4	no	—
440	C₂×#41	—	2	16	no	—
441	C₂×#41	—	4	8	no	—
442	C₂×#41	C₂³×C₇	1	4	yes	—
443	C₂×#41	C₂³×C₇	1	4	yes	—
444	C₂×#41	C₂³×C₇	1	4	yes	—
445	C₂×#41	C₂³×C₇	1	2	yes	—
446	C₂²×Q₈	C₂³×C₇	1	4	yes	—
447	C₂²×D₄	—	2	4	no	—
448	C₂²×D₄	—	2	2	no	—
449	C₂²×D₄	C₇×D₄	1	1	yes	characteristic
450	C₂²×D₄	C₂³×C₇	1	4	yes	—
451	C₂³×C₄	—	2	4	no	—
452	C₂³×C₄	C₂³×C₇	1	2	yes	—
453	#137	—	2	16	no	—
454	#137	—	2	16	no	—
455	AGL(1,ℤ/8)	—	2	16	no	—
456	AGL(1,ℤ/8)	—	2	16	no	—
457	#135	—	2	16	no	—
458	#135	—	2	8	no	—
459	#135	—	4	4	no	—
460	#135	C₇×D₄	1	8	yes	complemented
461	C₂×Q₁₆	C₂³×C₇	1	4	yes	—
462	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
463	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
464	C₂×Q₁₆	C₂³×C₇	1	1	yes	characteristic
465	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
466	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
467	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
468	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
469	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
470	C₂×D₈	C₂³×C₇	1	4	yes	—
471	C₂×D₈	C₂³×C₇	1	2	yes	—
472	C₂×D₈	C₂³×C₇	1	2	yes	—
473	C₂×D₈	C₂³×C₇	1	1	yes	characteristic
474	C₂×M₁₆	—	2	8	no	—
475	C₂×M₁₆	C₂³×C₇	1	4	yes	—
476	C₂×M₁₆	C₂³×C₇	1	4	yes	—
477	C₂²×C₈	C₂³×C₇	1	2	yes	—
478	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
479	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
480	C₄⋊Q₈	—	2	2	no	—
481	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
482	#127	—	2	2	no	—
483	#127	C₂³×C₇	1	2	yes	—
484	#124	—	2	4	no	—
485	#124	C₂³×C₇	1	4	yes	—
486	#123	—	2	4	no	—
487	#123	—	2	4	no	—
488	#123	—	2	4	no	—
489	C₂²⋊Q₈	—	2	4	no	—
490	C₂²⋊Q₈	—	2	4	no	—
491	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
492	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
493	#121	—	2	4	no	—
494	#121	—	2	2	no	—
495	#121	—	2	2	no	—
496	#121	—	2	2	no	—
497	#121	—	2	2	no	—
498	#121	—	2	4	no	—
499	#121	—	2	4	no	—
500	#121	C₂³×C₇	1	4	yes	—
501	#121	C₂³×C₇	1	4	yes	—
502	#120	—	2	4	no	—
503	#120	—	2	4	no	—
504	#120	—	2	4	no	—
505	C₄×Q₈	C₂³×C₇	1	2	yes	—
506	C₄×Q₈	C₂³×C₇	1	2	yes	—
507	C₄×D₄	—	2	2	no	—
508	C₄×D₄	—	2	4	no	—
509	C₄×D₄	—	2	2	no	—
510	C₄×D₄	—	2	2	no	—
511	C₄×D₄	—	2	4	no	—
512	C₄×D₄	—	2	2	no	—
513	C₄×D₄	—	2	4	no	—
514	C₄×D₄	—	2	2	no	—
515	C₄×D₄	—	2	2	no	—
516	C₄×D₄	C₇×D₄	1	2	yes	—
517	C₄×D₄	C₇×D₄	1	2	yes	—
518	C₄×D₄	C₂³×C₇	1	2	yes	—
519	C₄×D₄	C₂³×C₇	1	2	yes	—
520	C₄×D₄	C₂³×C₇	1	2	yes	—
521	C₄×D₄	C₂³×C₇	1	2	yes	—
522	#117	—	2	2	no	—
523	#117	C₂³×C₇	1	2	yes	—
524	C₂×C₄⋊C₄	—	2	2	no	—
525	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
526	C₂×C₂²⋊C₄	—	2	4	no	—
527	C₂×C₂²⋊C₄	C₇×D₄	1	2	yes	—
528	C₂×C₄²	—	2	2	no	—
529	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
530	#107	C₂³×C₇	1	1	yes	characteristic
531	#107	C₂³×C₇	1	1	yes	characteristic
532	#106	C₂³×C₇	1	2	yes	—
533	C₄⋊C₈	C₂³×C₇	1	2	yes	—
534	C₄⋊C₈	C₂³×C₇	1	2	yes	—
535	#103	C₂³×C₇	1	2	yes	—
536	#103	C₂³×C₇	1	2	yes	—
537	#103	C₂³×C₇	1	4	yes	—
538	#103	C₂³×C₇	1	4	yes	—
539	#102	C₂³×C₇	1	2	yes	—
540	#102	C₂³×C₇	1	2	yes	—
541	#102	C₂³×C₇	1	4	yes	—
542	#102	C₂³×C₇	1	4	yes	—
543	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
544	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
545	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
546	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
547	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
548	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
549	C₂²×C₇	—	2	1	no	—
550	C₂²×C₇	—	2	1	no	—
551	C₂²×C₇	—	2	4	no	—
552	C₂²×C₇	—	2	4	no	—
553	C₂²×C₇	—	2	4	no	—
554	C₂²×C₇	—	2	4	no	—
555	C₂²×C₇	—	4	2	no	—
556	C₂²×C₇	—	4	2	no	—
557	C₂²×C₇	—	4	4	no	—
558	C₂²×C₇	—	4	4	no	—
559	C₂²×C₇	—	4	4	no	—
560	C₂²×C₇	—	8	4	no	—
561	C₂²×C₇	—	8	16	no	—
562	C₂²×C₇	D₄²	1	2	yes	—
563	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
564	C₄×C₇	—	2	1	no	—
565	C₄×C₇	—	2	1	no	—
566	C₄×C₇	—	2	4	no	—
567	C₄×C₇	—	2	4	no	—
568	C₄×C₇	—	2	1	no	—
569	C₄×C₇	—	4	2	no	—
570	C₄×C₇	—	4	4	no	—
571	C₄×C₇	—	4	2	no	—
572	C₄×C₇	D₄²	1	2	yes	—
573	C₄×C₇	#575	1	2	yes	complemented
574	C₄×C₇	C₂³×D₄	1	1	yes	characteristic
575	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
576	C₂⁴	—	2	4	no	—
577	C₂⁴	C₂×C₇×D₄	1	2	yes	—
578	#41	—	2	4	no	—
579	#41	—	2	8	no	—
580	#41	—	2	8	no	—
581	#41	—	2	8	no	—
582	#41	—	2	8	no	—
583	#41	—	4	16	no	—
584	#41	—	4	4	no	—
585	#41	—	4	4	no	—
586	#41	—	4	16	no	—
587	#41	C₂×C₇×D₄	1	8	yes	complemented
588	C₂×Q₈	—	2	4	no	—
589	C₂×Q₈	—	2	8	no	—
590	C₂×Q₈	—	4	4	no	—
591	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
592	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
593	C₂×D₄	—	2	2	no	—
594	C₂×D₄	—	2	8	no	—
595	C₂×D₄	—	2	4	no	—
596	C₂×D₄	—	2	4	no	—
597	C₂×D₄	—	2	4	no	—
598	C₂×D₄	—	2	4	no	—
599	C₂×D₄	—	2	4	no	—
600	C₂×D₄	—	2	2	no	—
601	C₂×D₄	—	2	4	no	—
602	C₂×D₄	—	2	2	no	—
603	C₂×D₄	—	4	2	no	—
604	C₂×D₄	—	4	4	no	—
605	C₂×D₄	—	4	16	no	—
606	C₂×D₄	—	4	8	no	—
607	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
608	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
609	C₂×D₄	C₂⁴×C₇	1	4	yes	—
610	C₂×D₄	C₂⁴×C₇	1	2	yes	—
611	C₂²×C₄	—	2	2	no	—
612	C₂²×C₄	—	2	4	no	—
613	C₂²×C₄	—	2	4	no	—
614	C₂²×C₄	—	2	4	no	—
615	C₂²×C₄	—	2	2	no	—
616	C₂²×C₄	—	2	4	no	—
617	C₂²×C₄	—	2	4	no	—
618	C₂²×C₄	—	2	4	no	—
619	C₂²×C₄	—	2	2	no	—
620	C₂²×C₄	—	4	16	no	—
621	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
622	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
623	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
624	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
625	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
626	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
627	Q₁₆	—	2	8	no	—
628	Q₁₆	—	2	4	no	—
629	Q₁₆	—	4	2	no	—
630	Q₁₆	C₂×C₇×D₄	1	4	yes	complemented
631	SD₁₆	—	2	8	no	—
632	SD₁₆	—	2	8	no	—
633	SD₁₆	—	2	8	no	—
634	SD₁₆	—	4	4	no	—
635	SD₁₆	C₂×C₇×D₄	1	8	yes	complemented
636	D₈	—	2	8	no	—
637	D₈	—	2	4	no	—
638	D₈	—	4	2	no	—
639	D₈	C₂×C₇×D₄	1	4	yes	complemented
640	M₁₆	—	2	8	no	—
641	M₁₆	—	2	8	no	—
642	C₂×C₈	—	2	4	no	—
643	C₂×C₈	—	2	2	no	—
644	C₂×C₈	C₂×C₇×D₄	1	4	yes	complemented
645	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
646	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
647	C₂×C₈	C₂⁴×C₇	1	4	yes	—
648	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
649	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
650	C₄⋊C₄	—	2	2	no	—
651	C₄⋊C₄	—	2	4	no	—
652	C₄⋊C₄	—	2	2	no	—
653	C₄⋊C₄	—	2	2	no	—
654	C₄⋊C₄	—	2	2	no	—
655	C₄⋊C₄	—	2	4	no	—
656	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
657	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
658	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
659	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
660	C₂²⋊C₄	—	2	4	no	—
661	C₂²⋊C₄	—	2	2	no	—
662	C₂²⋊C₄	—	2	4	no	—
663	C₂²⋊C₄	—	2	4	no	—
664	C₂²⋊C₄	—	2	4	no	—
665	C₂²⋊C₄	—	2	2	no	—
666	C₂²⋊C₄	—	2	2	no	—
667	C₂²⋊C₄	—	2	4	no	—
668	C₂²⋊C₄	—	2	4	no	—
669	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
670	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
671	C₄²	—	2	2	no	—
672	C₄²	—	2	2	no	—
673	C₄²	—	2	2	no	—
674	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
675	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
676	C₄²	C₂⁴×C₇	1	1	yes	characteristic
677	C₄²	C₂⁴×C₇	1	1	yes	characteristic
678	C₂×C₇	—	2	2	no	—
679	C₂×C₇	—	4	4	no	—
680	C₂×C₇	—	4	4	no	—
681	C₂×C₇	—	8	4	no	—
682	C₂×C₇	C₂×D₄²	1	1	yes	characteristic
683	C₂×C₇	C₂×#575	1	1	yes	characteristic
684	C₂×C₇	#3584	1	1	yes	characteristic
685	C₂³	—	2	2	no	—
686	C₂³	—	2	4	no	—
687	C₂³	—	2	4	no	—
688	C₂³	—	4	2	no	—
689	C₂³	—	4	2	no	—
690	C₂³	—	4	8	no	—
691	C₂³	—	4	8	no	—
692	C₂³	—	8	4	no	—
693	C₂³	C₂²×C₇×D₄	1	4	yes	—
694	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
695	Q₈	—	2	2	no	—
696	Q₈	—	2	4	no	—
697	Q₈	—	2	4	no	—
698	Q₈	—	4	8	no	—
699	Q₈	C₂²×C₇×D₄	1	4	yes	—
700	D₄	—	2	8	no	—
701	D₄	—	2	4	no	—
702	D₄	—	2	2	no	—
703	D₄	—	2	4	no	—
704	D₄	—	2	4	no	—
705	D₄	—	4	2	no	—
706	D₄	—	4	8	no	—
707	D₄	—	4	8	no	—
708	D₄	—	4	8	no	—
709	D₄	—	4	8	no	—
710	D₄	—	4	8	no	—
711	D₄	—	4	4	no	—
712	D₄	—	8	2	no	—
713	D₄	—	8	4	no	—
714	D₄	C₂²×C₇×D₄	1	4	yes	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	2	4	no	—
717	C₂×C₄	—	2	4	no	—
718	C₂×C₄	—	2	4	no	—
719	C₂×C₄	—	2	8	no	—
720	C₂×C₄	—	2	8	no	—
721	C₂×C₄	—	2	2	no	—
722	C₂×C₄	—	2	2	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	4	no	—
725	C₂×C₄	—	4	1	no	—
726	C₂×C₄	—	4	8	no	—
727	C₂×C₄	—	4	8	no	—
728	C₂×C₄	—	4	8	no	—
729	C₂×C₄	—	4	8	no	—
730	C₂×C₄	—	4	4	no	—
731	C₂×C₄	—	8	2	no	—
732	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
733	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
734	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
735	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
736	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
737	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
738	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
739	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
740	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
741	C₈	—	2	4	no	—
742	C₈	—	2	1	no	—
743	C₈	—	2	1	no	—
744	C₈	C₂²×C₇×D₄	1	2	yes	—
745	C₈	C₂²×C₇×D₄	1	2	yes	—
746	C₇	#61038	1	1	yes	characteristic, direct product factor, Sylow
747	C₂²	—	2	1	no	—
748	C₂²	—	2	1	no	—
749	C₂²	—	2	4	no	—
750	C₂²	—	2	4	no	—
751	C₂²	—	2	4	no	—
752	C₂²	—	2	4	no	—
753	C₂²	—	4	2	no	—
754	C₂²	—	4	2	no	—
755	C₂²	—	4	4	no	—
756	C₂²	—	4	4	no	—
757	C₂²	—	4	4	no	—
758	C₂²	—	8	4	no	—
759	C₂²	—	8	16	no	—
760	C₂²	C₇×D₄²	1	2	yes	—
761	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
762	C₄	—	2	1	no	—
763	C₄	—	2	1	no	—
764	C₄	—	2	1	no	—
765	C₄	—	2	4	no	—
766	C₄	—	2	4	no	—
767	C₄	—	4	2	no	—
768	C₄	—	4	2	no	—
769	C₄	—	4	4	no	—
770	C₄	C₇×D₄²	1	2	yes	—
771	C₄	C₇×#575	1	2	yes	complemented
772	C₄	C₂³×C₇×D₄	1	1	yes	characteristic
773	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
774	C₂	—	2	2	no	—
775	C₂	—	4	4	no	—
776	C₂	—	4	4	no	—
777	C₂	—	8	4	no	—
778	C₂	C₂×C₇×D₄²	1	1	yes	characteristic
779	C₂	C₂×C₇×#575	1	1	yes	characteristic
780	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. C₂×C₇×#575	C₂	semidirect
2. C₇×D₄×#41	C₂	semidirect
3. C₇×#3278	C₂	semidirect
4. C₇×#3277	C₂	semidirect
5. C₇×#3276	C₂	semidirect
6. C₇×#3275	C₂	semidirect
7. C₇×#3274	C₂	semidirect
8. C₇×#3273	C₂	semidirect
9. C₇×#3272	C₂	semidirect
10. C₇×#3147	C₂	semidirect
11. C₇×#3054	C₂	semidirect
12. C₇×#3035	C₂	semidirect
13. C₇×#3002	C₂	semidirect
14. C₄×C₇×#135	C₂	semidirect
15. C₂×C₇×#436	C₂	semidirect
16. C₂²×C₇×#41	C₂²	semidirect
18. C₂×C₇×#137	C₂²	semidirect
19. C₂×C₇×#137	C₂²	semidirect
20. C₂×C₇×AGL(1,ℤ/8)	C₂²	semidirect
21. C₂×C₇×AGL(1,ℤ/8)	C₂²	semidirect
23. C₂×C₇×#135	C₂²	semidirect
24. C₂×C₇×#135	C₂²	semidirect
25. C₂×C₇×#135	C₂²	semidirect
26. C₂²×C₇×M₁₆	C₂²	semidirect
28. C₇×D₄×Q₈	C₂²	semidirect
29. C₇×#548	C₂²	semidirect
33. C₇×#546	C₂²	semidirect
35. C₇×D₄²	C₂²	semidirect
37. C₇×#532	C₂²	semidirect
39. C₇×#525	C₂²	semidirect
40. C₄×C₇×#41	C₂²	semidirect
43. C₇×#495	C₂²	semidirect
44. C₇×#495	C₂²	semidirect
45. C₇×#494	C₂²	semidirect
46. C₇×#493	C₂²	semidirect
47. C₇×#492	C₂²	semidirect
48. C₇×#470	C₂²	semidirect
49. C₇×#469	C₂²	semidirect
50. C₇×#468	C₂²	semidirect
51. C₇×#468	C₂²	semidirect
52. C₇×#464	C₂²	semidirect
53. C₇×#463	C₂²	semidirect
54. C₇×#462	C₂²	semidirect
55. C₇×#461	C₂²	semidirect
56. C₇×#460	C₂²	semidirect
57. C₇×#459	C₂²	semidirect
58. C₇×#452	C₂²	semidirect
59. C₇×#452	C₂²	semidirect
60. C₇×#451	C₂²	semidirect
61. C₇×#450	C₂²	semidirect
62. C₇×#449	C₂²	semidirect
63. C₇×#449	C₂²	semidirect
64. C₇×#448	C₂²	semidirect
65. C₇×#447	C₂²	semidirect
66. C₄×C₇×Q₁₆	C₂²	semidirect
67. C₄×C₇×Q₁₆	C₂²	semidirect
68. C₄×C₇×SD₁₆	C₂²	semidirect
69. C₄×C₇×SD₁₆	C₂²	semidirect
70. C₄×C₇×D₈	C₂²	semidirect
71. C₄×C₇×D₈	C₂²	semidirect
72. C₇×#436	C₂²	semidirect
73. C₇×#436	C₂²	semidirect
74. C₇×#436	C₂²	semidirect
75. C₇×#436	C₂²	semidirect
76. C₇×#427	C₂²	semidirect
77. C₂×C₇×C₄⋊C₈	C₂²	semidirect
78. C₇×#416	C₂²	semidirect
79. C₇×#416	C₂²	semidirect
80. C₂×C₇×C₂²⋊C₈	C₂²	semidirect
81. C₂×C₄×C₇×C₈	C₂²	semidirect
82. #61038	C₇	direct (N × H)
105. C₇×#135	D₄	semidirect
194. C₂×#575	C₂×C₇	semidirect
195. D₄×#41	C₂×C₇	semidirect
196. #3278	C₂×C₇	semidirect
197. #3277	C₂×C₇	semidirect
198. #3276	C₂×C₇	semidirect
199. #3275	C₂×C₇	semidirect
200. #3274	C₂×C₇	semidirect
201. #3273	C₂×C₇	semidirect
202. #3272	C₂×C₇	semidirect
203. #3147	C₂×C₇	semidirect
204. #3054	C₂×C₇	semidirect
205. #3035	C₂×C₇	semidirect
206. #3002	C₂×C₇	semidirect
207. C₄×#135	C₂×C₇	semidirect
208. C₂×#436	C₂×C₇	semidirect
220. C₇×#41	C₂×D₄	semidirect
263. C₇×Q₁₆	C₂×D₄	semidirect
268. C₇×SD₁₆	C₂×D₄	semidirect
272. C₇×D₈	C₂×D₄	semidirect
277. C₂×C₇×C₈	C₂×D₄	semidirect
311. C₂²×#41	C₂²×C₇	semidirect
313. C₂×#137	C₂²×C₇	semidirect
314. C₂×#137	C₂²×C₇	semidirect
315. C₂×AGL(1,ℤ/8)	C₂²×C₇	semidirect
316. C₂×AGL(1,ℤ/8)	C₂²×C₇	semidirect
318. C₂×#135	C₂²×C₇	semidirect
319. C₂×#135	C₂²×C₇	semidirect
320. C₂×#135	C₂²×C₇	semidirect
321. C₂²×M₁₆	C₂²×C₇	semidirect
323. D₄×Q₈	C₂²×C₇	semidirect
324. #548	C₂²×C₇	semidirect
328. #546	C₂²×C₇	semidirect
330. D₄²	C₂²×C₇	semidirect
332. #532	C₂²×C₇	semidirect
334. #525	C₂²×C₇	semidirect
335. C₄×#41	C₂²×C₇	semidirect
338. #495	C₂²×C₇	semidirect
339. #495	C₂²×C₇	semidirect
340. #494	C₂²×C₇	semidirect
341. #493	C₂²×C₇	semidirect
342. #492	C₂²×C₇	semidirect
343. #470	C₂²×C₇	semidirect
344. #469	C₂²×C₇	semidirect
345. #468	C₂²×C₇	semidirect
346. #468	C₂²×C₇	semidirect
347. #464	C₂²×C₇	semidirect
348. #463	C₂²×C₇	semidirect
349. #462	C₂²×C₇	semidirect
350. #461	C₂²×C₇	semidirect
351. #460	C₂²×C₇	semidirect
352. #459	C₂²×C₇	semidirect
353. #452	C₂²×C₇	semidirect
354. #452	C₂²×C₇	semidirect
355. #451	C₂²×C₇	semidirect
356. #450	C₂²×C₇	semidirect
357. #449	C₂²×C₇	semidirect
358. #449	C₂²×C₇	semidirect
359. #448	C₂²×C₇	semidirect
360. #447	C₂²×C₇	semidirect
361. C₄×Q₁₆	C₂²×C₇	semidirect
362. C₄×Q₁₆	C₂²×C₇	semidirect
363. C₄×SD₁₆	C₂²×C₇	semidirect
364. C₄×SD₁₆	C₂²×C₇	semidirect
365. C₄×D₈	C₂²×C₇	semidirect
366. C₄×D₈	C₂²×C₇	semidirect
367. #436	C₂²×C₇	semidirect
368. #436	C₂²×C₇	semidirect
369. #436	C₂²×C₇	semidirect
370. #436	C₂²×C₇	semidirect
371. #427	C₂²×C₇	semidirect
372. C₂×C₄⋊C₈	C₂²×C₇	semidirect
373. #416	C₂²×C₇	semidirect
374. #416	C₂²×C₇	semidirect
375. C₂×C₂²⋊C₈	C₂²×C₇	semidirect
376. C₂×C₄×C₈	C₂²×C₇	semidirect
460. #135	C₇×D₄	semidirect
573. C₄×C₇	#575	semidirect
587. #41	C₂×C₇×D₄	semidirect
630. Q₁₆	C₂×C₇×D₄	semidirect
635. SD₁₆	C₂×C₇×D₄	semidirect
639. D₈	C₂×C₇×D₄	semidirect
644. C₂×C₈	C₂×C₇×D₄	semidirect
746. C₇	#61038	direct (N × H)
771. C₄	C₇×#575	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₇×#575	2
C₇×D₄×#41	2
C₇×#3278	2
C₇×#3277	2
C₇×#3276	2
C₇×#3275	2
C₇×#3274	2
C₇×#3273	2
C₇×#3272	2
C₇×#3147	2
C₇×#3054	2
C₇×#3035	2
C₇×#3002	2
C₄×C₇×#135	2
C₂×C₇×#436	2
#61038	7

Subgroups — C7×#61038 #13238254

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#61038 #13238254