Subgroups — C₇×#61327 #13238543

Order 1792.

1802 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3506	C₂	1	1	yes	maximal, characteristic
2	C₇×#3502	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3371	C₂	1	4	yes	maximal, complemented
4	C₇×#3369	C₂	1	2	yes	maximal, complemented
5	C₇×#3368	C₂	1	2	yes	maximal, complemented
6	C₇×#3365	C₂	1	4	yes	maximal, complemented
7	C₇×#3364	C₂	1	2	yes	maximal, complemented
8	C₇×#3362	C₂	1	2	yes	maximal, complemented
9	C₇×#3136	C₂	1	2	yes	maximal, complemented
10	C₇×#3131	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#3084	C₂	1	2	yes	maximal, complemented
12	C₇×#3077	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#3043	C₂	1	2	yes	maximal, complemented
14	C₇×#3037	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#2960	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#2947	C₂	1	2	yes	maximal, complemented
17	C₂×C₄×C₇×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₇×#137	C₂²	1	2	yes	—
19	C₂²×C₇×SD₁₆	C₂²	1	1	yes	characteristic
20	C₇×#559	C₂²	1	4	yes	—
21	C₇×Q₈²	—	2	1	no	—
22	C₇×Q₈²	C₂²	1	2	yes	complemented
23	C₇×#557	—	2	1	no	—
24	C₇×#557	—	2	2	no	—
25	C₇×#557	C₂²	1	2	yes	complemented
26	C₇×#557	C₂²	1	4	yes	complemented
27	C₇×#556	C₂²	1	2	yes	—
28	C₇×#555	—	2	1	no	—
29	C₇×#553	—	2	2	no	—
30	C₇×#550	C₂²	1	2	yes	—
31	C₇×#547	—	2	1	no	—
32	C₇×#544	—	2	2	no	—
33	C₇×#544	C₂²	1	2	yes	—
34	C₇×#538	—	2	2	no	—
35	C₇×#535	C₂²	1	2	yes	—
36	C₇×#533	—	2	2	no	—
37	C₇×#533	C₂²	1	1	yes	characteristic
38	C₇×#533	C₂²	1	1	yes	characteristic
39	C₇×#532	C₂²	1	1	yes	characteristic
40	C₇×#525	—	2	2	no	—
41	C₇×#520	C₂²	1	2	yes	—
42	C₇×#519	C₂²	1	2	yes	—
43	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
44	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
45	C₇×#490	C₂²	1	4	yes	—
46	C₇×#489	C₂²	1	4	yes	—
47	C₇×#488	C₂²	1	4	yes	—
48	C₇×#488	C₂²	1	2	yes	complemented
49	C₇×#488	C₂²	1	2	yes	complemented
50	C₇×#487	C₂²	1	1	yes	characteristic, complemented
51	C₇×#487	C₂²	1	1	yes	characteristic, complemented
52	C₇×#486	C₂²	1	4	yes	—
53	C₇×#486	C₂²	1	1	yes	characteristic, complemented
54	C₇×#486	C₂²	1	1	yes	characteristic, complemented
55	C₇×#479	C₂²	1	4	yes	complemented
56	C₇×#478	C₂²	1	4	yes	—
57	C₇×#478	C₂²	1	4	yes	complemented
58	C₇×#476	C₂²	1	2	yes	—
59	C₇×#476	C₂²	1	4	yes	complemented
60	C₇×#475	C₂²	1	4	yes	complemented
61	C₇×#474	C₂²	1	2	yes	—
62	C₇×#464	C₂²	1	4	yes	—
63	C₇×#464	C₂²	1	4	yes	—
64	C₇×#464	C₂²	1	4	yes	complemented
65	C₇×#462	C₂²	1	2	yes	complemented
66	C₇×#460	C₂²	1	4	yes	—
67	C₇×#460	C₂²	1	4	yes	—
68	C₇×#460	C₂²	1	2	yes	complemented
69	C₇×#446	C₂²	1	2	yes	complemented
70	C₇×#446	C₂²	1	2	yes	complemented
71	C₇×C₈×Q₈	C₂²	1	2	yes	complemented
72	C₇×C₈×Q₈	C₂²	1	2	yes	complemented
73	C₇×#441	C₂²	1	4	yes	complemented
74	C₇×#440	C₂²	1	4	yes	complemented
75	C₄×C₇×Q₁₆	C₂²	1	4	yes	complemented
76	C₄×C₇×SD₁₆	C₂²	1	2	yes	—
77	C₄×C₇×SD₁₆	C₂²	1	2	yes	—
78	C₄×C₇×SD₁₆	C₂²	1	2	yes	—
79	C₄×C₇×SD₁₆	C₂²	1	2	yes	—
80	C₄×C₇×SD₁₆	C₂²	1	4	yes	complemented
81	C₇×#428	C₂²	1	2	yes	—
82	C₂×C₇×#106	C₂²	1	1	yes	characteristic
83	C₇×#424	C₂²	1	2	yes	—
84	C₇×#423	C₂²	1	1	yes	characteristic
85	C₇×#418	C₂²	1	2	yes	—
86	C₇×#417	C₂²	1	2	yes	—
87	C₇×#416	C₂²	1	2	yes	—
88	C₇×#416	C₂²	1	2	yes	—
89	C₂×C₇×#103	C₂²	1	1	yes	characteristic
90	C₂×C₇×#102	C₂²	1	1	yes	characteristic
91	C₇×#405	C₂²	1	2	yes	—
92	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
93	#61327	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
94	C₂×C₇×#41	—	2	2	no	—
95	C₂×C₇×#41	C₂³	1	2	yes	—
96	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
97	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
98	C₂³×C₄×C₇	—	2	1	no	—
99	C₇×#137	—	2	8	no	—
100	C₂×C₇×Q₁₆	C₂³	1	4	yes	—
101	C₂×C₇×SD₁₆	—	2	4	no	—
102	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
103	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
104	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
105	C₂×C₇×M₁₆	C₂³	1	2	yes	—
106	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
107	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
108	C₇×C₄⋊Q₈	—	2	2	no	—
109	C₇×C₄⋊Q₈	—	2	4	no	—
110	C₇×C₄⋊Q₈	—	2	2	no	—
111	C₇×C₄⋊Q₈	—	2	4	no	—
112	C₇×C₄⋊Q₈	—	2	2	no	—
113	C₇×C₄⋊Q₈	D₄	1	1	yes	characteristic
114	C₇×C₄⋊Q₈	D₄	1	1	yes	characteristic
115	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
116	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
117	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
118	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
119	C₇×#127	C₂³	1	4	yes	—
120	C₇×#127	C₂³	1	1	yes	characteristic
121	C₇×#126	—	2	4	no	—
122	C₇×#125	—	2	4	no	—
123	C₇×#125	—	2	4	no	—
124	C₇×#125	—	2	4	no	—
125	C₇×#125	—	2	2	no	—
126	C₇×#125	D₄	1	2	yes	—
127	C₇×#125	C₂³	1	2	yes	—
128	C₇×#125	C₂³	1	4	yes	—
129	C₇×#124	—	2	4	no	—
130	C₇×#124	C₂³	1	4	yes	—
131	C₇×#124	C₂³	1	2	yes	—
132	C₇×#123	—	2	4	no	—
133	C₇×#123	—	2	4	no	—
134	C₇×C₂²⋊Q₈	—	2	2	no	—
135	C₇×C₂²⋊Q₈	—	2	1	no	—
136	C₇×C₂²⋊Q₈	—	2	1	no	—
137	C₇×C₂²⋊Q₈	—	2	4	no	—
138	C₇×C₂²⋊Q₈	D₄	1	2	yes	—
139	C₇×C₂²⋊Q₈	D₄	1	2	yes	—
140	C₇×#121	—	2	1	no	—
141	C₇×#121	—	2	1	no	—
142	C₇×#121	—	2	2	no	—
143	C₇×#121	—	2	2	no	—
144	C₇×#121	—	2	2	no	—
145	C₇×#121	—	2	4	no	—
146	C₇×#120	—	2	4	no	—
147	C₄×C₇×Q₈	—	2	2	no	—
148	C₄×C₇×Q₈	—	2	2	no	—
149	C₄×C₇×Q₈	—	2	2	no	—
150	C₄×C₇×Q₈	—	2	4	no	—
151	C₄×C₇×Q₈	—	2	2	no	—
152	C₄×C₇×Q₈	—	2	1	no	—
153	C₄×C₇×Q₈	—	2	1	no	—
154	C₄×C₇×Q₈	—	2	1	no	—
155	C₄×C₇×Q₈	—	2	1	no	—
156	C₄×C₇×Q₈	C₂³	1	4	yes	—
157	C₄×C₇×Q₈	C₂³	1	2	yes	—
158	C₄×C₇×Q₈	C₂³	1	2	yes	—
159	C₄×C₇×Q₈	C₂³	1	4	yes	—
160	C₄×C₇×Q₈	C₂³	1	4	yes	—
161	C₄×C₇×Q₈	C₂³	1	2	yes	—
162	C₄×C₇×Q₈	C₂³	1	2	yes	—
163	C₄×C₇×D₄	—	2	4	no	—
164	C₄×C₇×D₄	—	2	4	no	—
165	C₄×C₇×D₄	—	2	1	no	—
166	C₄×C₇×D₄	—	2	1	no	—
167	C₄×C₇×D₄	—	2	1	no	—
168	C₄×C₇×D₄	—	2	1	no	—
169	C₄×C₇×D₄	C₂³	1	2	yes	—
170	C₄×C₇×D₄	C₂³	1	4	yes	—
171	C₄×C₇×D₄	C₂³	1	2	yes	—
172	C₇×#117	—	2	2	no	—
173	C₇×#117	—	2	2	no	—
174	C₇×#117	—	2	4	no	—
175	C₇×#117	C₂³	1	2	yes	—
176	C₇×#117	C₂³	1	2	yes	—
177	C₂×C₇×C₄⋊C₄	—	2	1	no	—
178	C₂×C₇×C₄⋊C₄	—	2	2	no	—
179	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
180	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
181	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
182	C₂×C₄²×C₇	—	2	1	no	—
183	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
184	C₇×#107	C₂³	1	4	yes	—
185	C₇×#106	C₂³	1	2	yes	—
186	C₇×#106	C₂³	1	4	yes	—
187	C₇×#106	C₂³	1	2	yes	—
188	C₇×C₄⋊C₈	C₂³	1	2	yes	—
189	C₇×C₄⋊C₈	C₂³	1	4	yes	—
190	C₇×C₄⋊C₈	C₂³	1	4	yes	—
191	C₇×C₄⋊C₈	C₂³	1	2	yes	—
192	C₇×#103	C₂³	1	2	yes	—
193	C₇×#103	C₂³	1	4	yes	—
194	C₇×#103	C₂³	1	2	yes	—
195	C₇×#103	C₂³	1	2	yes	—
196	C₇×#103	C₂³	1	2	yes	—
197	C₇×#103	C₂³	1	2	yes	—
198	C₇×#103	C₂³	1	2	yes	—
199	C₇×#102	C₂³	1	4	yes	—
200	C₇×#102	C₂³	1	4	yes	—
201	C₇×#102	C₂³	1	2	yes	—
202	C₇×#102	C₂³	1	4	yes	—
203	C₇×#102	C₂³	1	2	yes	—
204	C₇×#102	C₂³	1	2	yes	—
205	C₇×#102	C₂³	1	2	yes	—
206	C₇×#102	C₂³	1	2	yes	—
207	C₇×#102	C₂³	1	2	yes	—
208	C₇×#97	C₂³	1	4	yes	—
209	C₄×C₇×C₈	C₂³	1	4	yes	—
210	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
211	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
212	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
213	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
214	#3506	C₂×C₇	1	1	yes	characteristic
215	#3502	C₂×C₇	1	1	yes	characteristic, complemented
216	#3371	C₂×C₇	1	4	yes	complemented
217	#3369	C₂×C₇	1	2	yes	complemented
218	#3368	C₂×C₇	1	2	yes	complemented
219	#3365	C₂×C₇	1	4	yes	complemented
220	#3364	C₂×C₇	1	2	yes	complemented
221	#3362	C₂×C₇	1	2	yes	complemented
222	#3136	C₂×C₇	1	2	yes	complemented
223	#3131	C₂×C₇	1	1	yes	characteristic, complemented
224	#3084	C₂×C₇	1	2	yes	complemented
225	#3077	C₂×C₇	1	1	yes	characteristic, complemented
226	#3043	C₂×C₇	1	2	yes	complemented
227	#3037	C₂×C₇	1	1	yes	characteristic, complemented
228	#2960	C₂×C₇	1	1	yes	characteristic, complemented
229	#2947	C₂×C₇	1	2	yes	complemented
230	C₂×C₄×SD₁₆	C₂×C₇	1	1	yes	characteristic, complemented
231	C₂⁴×C₇	—	2	1	no	—
232	C₇×#41	—	2	4	no	—
233	C₇×#41	—	2	4	no	—
234	C₇×#41	—	8	4	no	—
235	C₂×C₇×Q₈	—	2	1	no	—
236	C₂×C₇×Q₈	—	2	1	no	—
237	C₂×C₇×Q₈	—	2	1	no	—
238	C₂×C₇×Q₈	—	2	4	no	—
239	C₂×C₇×Q₈	—	2	2	no	—
240	C₂×C₇×Q₈	C₂×D₄	1	2	yes	—
241	C₂×C₇×Q₈	C₂×D₄	1	2	yes	—
242	C₂×C₇×Q₈	#41	1	4	yes	complemented
243	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
244	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
245	C₂×C₇×D₄	—	2	2	no	—
246	C₂×C₇×D₄	—	2	1	no	—
247	C₂×C₇×D₄	—	2	1	no	—
248	C₂×C₇×D₄	—	2	4	no	—
249	C₂×C₇×D₄	—	2	1	no	—
250	C₂×C₇×D₄	—	2	4	no	—
251	C₂×C₇×D₄	—	2	2	no	—
252	C₂×C₇×D₄	—	2	2	no	—
253	C₂×C₇×D₄	C₂⁴	1	2	yes	—
254	C₂×C₇×D₄	C₂⁴	1	2	yes	—
255	C₂²×C₄×C₇	—	2	1	no	—
256	C₂²×C₄×C₇	—	2	1	no	—
257	C₂²×C₄×C₇	—	2	1	no	—
258	C₂²×C₄×C₇	—	2	2	no	—
259	C₂²×C₄×C₇	—	2	2	no	—
260	C₂²×C₄×C₇	—	2	4	no	—
261	C₂²×C₄×C₇	—	2	2	no	—
262	C₂²×C₄×C₇	—	8	2	no	—
263	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
264	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
265	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
266	C₇×Q₁₆	—	2	8	no	—
267	C₇×SD₁₆	—	2	4	no	—
268	C₇×SD₁₆	—	2	4	no	—
269	C₇×SD₁₆	—	2	8	no	—
270	C₇×M₁₆	—	2	4	no	—
271	C₂×C₇×C₈	—	2	2	no	—
272	C₂×C₇×C₈	—	2	2	no	—
273	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
274	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
275	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
276	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
277	C₂×C₇×C₈	C₂⁴	1	4	yes	—
278	C₇×C₄⋊C₄	—	2	1	no	—
279	C₇×C₄⋊C₄	—	2	4	no	—
280	C₇×C₄⋊C₄	—	2	2	no	—
281	C₇×C₄⋊C₄	—	2	2	no	—
282	C₇×C₄⋊C₄	—	2	1	no	—
283	C₇×C₄⋊C₄	—	2	1	no	—
284	C₇×C₄⋊C₄	—	2	4	no	—
285	C₇×C₄⋊C₄	—	2	4	no	—
286	C₇×C₄⋊C₄	—	2	1	no	—
287	C₇×C₄⋊C₄	—	2	2	no	—
288	C₇×C₄⋊C₄	—	2	1	no	—
289	C₇×C₄⋊C₄	—	2	1	no	—
290	C₇×C₄⋊C₄	—	2	4	no	—
291	C₇×C₄⋊C₄	—	2	4	no	—
292	C₇×C₄⋊C₄	—	2	2	no	—
293	C₇×C₄⋊C₄	—	2	4	no	—
294	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
295	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
296	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
297	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
298	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
299	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
300	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
301	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
302	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
303	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
304	C₇×C₂²⋊C₄	—	2	2	no	—
305	C₇×C₂²⋊C₄	—	2	2	no	—
306	C₇×C₂²⋊C₄	—	2	2	no	—
307	C₇×C₂²⋊C₄	—	2	4	no	—
308	C₇×C₂²⋊C₄	—	2	4	no	—
309	C₇×C₂²⋊C₄	—	2	2	no	—
310	C₇×C₂²⋊C₄	—	2	4	no	—
311	C₇×C₂²⋊C₄	—	2	2	no	—
312	C₇×C₂²⋊C₄	C₂×D₄	1	4	yes	—
313	C₄²×C₇	—	2	2	no	—
314	C₄²×C₇	—	2	2	no	—
315	C₄²×C₇	—	2	4	no	—
316	C₄²×C₇	—	2	4	no	—
317	C₄²×C₇	—	2	4	no	—
318	C₄²×C₇	—	2	2	no	—
319	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
320	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
321	C₄²×C₇	C₂⁴	1	1	yes	characteristic
322	C₄²×C₇	C₂⁴	1	1	yes	characteristic
323	C₄²×C₇	C₂⁴	1	4	yes	—
324	C₂×#137	C₂²×C₇	1	2	yes	—
325	C₂²×SD₁₆	C₂²×C₇	1	1	yes	characteristic
326	#559	C₂²×C₇	1	4	yes	—
327	Q₈²	—	2	1	no	—
328	Q₈²	C₂²×C₇	1	2	yes	complemented
329	#557	—	2	1	no	—
330	#557	—	2	2	no	—
331	#557	C₂²×C₇	1	2	yes	complemented
332	#557	C₂²×C₇	1	4	yes	complemented
333	#556	C₂²×C₇	1	2	yes	—
334	#555	—	2	1	no	—
335	#553	—	2	2	no	—
336	#550	C₂²×C₇	1	2	yes	—
337	#547	—	2	1	no	—
338	#544	—	2	2	no	—
339	#544	C₂²×C₇	1	2	yes	—
340	#538	—	2	2	no	—
341	#535	C₂²×C₇	1	2	yes	—
342	#533	—	2	2	no	—
343	#533	C₂²×C₇	1	1	yes	characteristic
344	#533	C₂²×C₇	1	1	yes	characteristic
345	#532	C₂²×C₇	1	1	yes	characteristic
346	#525	—	2	2	no	—
347	#520	C₂²×C₇	1	2	yes	—
348	#519	C₂²×C₇	1	2	yes	—
349	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
350	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
351	#490	C₂²×C₇	1	4	yes	—
352	#489	C₂²×C₇	1	4	yes	—
353	#488	C₂²×C₇	1	4	yes	—
354	#488	C₂²×C₇	1	2	yes	complemented
355	#488	C₂²×C₇	1	2	yes	complemented
356	#487	C₂²×C₇	1	1	yes	characteristic, complemented
357	#487	C₂²×C₇	1	1	yes	characteristic, complemented
358	#486	C₂²×C₇	1	4	yes	—
359	#486	C₂²×C₇	1	1	yes	characteristic, complemented
360	#486	C₂²×C₇	1	1	yes	characteristic, complemented
361	#479	C₂²×C₇	1	4	yes	complemented
362	#478	C₂²×C₇	1	4	yes	—
363	#478	C₂²×C₇	1	4	yes	complemented
364	#476	C₂²×C₇	1	2	yes	—
365	#476	C₂²×C₇	1	4	yes	complemented
366	#475	C₂²×C₇	1	4	yes	complemented
367	#474	C₂²×C₇	1	2	yes	—
368	#464	C₂²×C₇	1	4	yes	—
369	#464	C₂²×C₇	1	4	yes	—
370	#464	C₂²×C₇	1	4	yes	complemented
371	#462	C₂²×C₇	1	2	yes	complemented
372	#460	C₂²×C₇	1	4	yes	—
373	#460	C₂²×C₇	1	4	yes	—
374	#460	C₂²×C₇	1	2	yes	complemented
375	#446	C₂²×C₇	1	2	yes	complemented
376	#446	C₂²×C₇	1	2	yes	complemented
377	C₈×Q₈	C₂²×C₇	1	2	yes	complemented
378	C₈×Q₈	C₂²×C₇	1	2	yes	complemented
379	#441	C₂²×C₇	1	4	yes	complemented
380	#440	C₂²×C₇	1	4	yes	complemented
381	C₄×Q₁₆	C₂²×C₇	1	4	yes	complemented
382	C₄×SD₁₆	C₂²×C₇	1	2	yes	—
383	C₄×SD₁₆	C₂²×C₇	1	2	yes	—
384	C₄×SD₁₆	C₂²×C₇	1	2	yes	—
385	C₄×SD₁₆	C₂²×C₇	1	2	yes	—
386	C₄×SD₁₆	C₂²×C₇	1	4	yes	complemented
387	#428	C₂²×C₇	1	2	yes	—
388	C₂×#106	C₂²×C₇	1	1	yes	characteristic
389	#424	C₂²×C₇	1	2	yes	—
390	#423	C₂²×C₇	1	1	yes	characteristic
391	#418	C₂²×C₇	1	2	yes	—
392	#417	C₂²×C₇	1	2	yes	—
393	#416	C₂²×C₇	1	2	yes	—
394	#416	C₂²×C₇	1	2	yes	—
395	C₂×#103	C₂²×C₇	1	1	yes	characteristic
396	C₂×#102	C₂²×C₇	1	1	yes	characteristic
397	#405	C₂²×C₇	1	2	yes	—
398	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
399	C₂³×C₇	—	2	2	no	—
400	C₂³×C₇	—	2	2	no	—
401	C₂³×C₇	—	4	2	no	—
402	C₂³×C₇	—	8	1	no	—
403	C₂³×C₇	—	8	1	no	—
404	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
405	C₇×Q₈	—	2	4	no	—
406	C₇×Q₈	—	2	4	no	—
407	C₇×Q₈	—	2	2	no	—
408	C₇×Q₈	—	2	2	no	—
409	C₇×Q₈	—	2	2	no	—
410	C₇×Q₈	—	4	2	no	—
411	C₇×Q₈	—	4	2	no	—
412	C₇×Q₈	—	8	1	no	—
413	C₇×Q₈	—	8	4	no	—
414	C₇×Q₈	C₂×#41	1	4	yes	—
415	C₇×D₄	—	2	2	no	—
416	C₇×D₄	—	2	2	no	—
417	C₇×D₄	—	2	2	no	—
418	C₇×D₄	—	2	2	no	—
419	C₇×D₄	—	4	4	no	—
420	C₇×D₄	—	4	2	no	—
421	C₇×D₄	—	4	2	no	—
422	C₇×D₄	—	8	1	no	—
423	C₇×D₄	—	8	4	no	—
424	C₇×D₄	—	8	4	no	—
425	C₂×C₄×C₇	—	2	4	no	—
426	C₂×C₄×C₇	—	2	2	no	—
427	C₂×C₄×C₇	—	2	2	no	—
428	C₂×C₄×C₇	—	2	2	no	—
429	C₂×C₄×C₇	—	2	2	no	—
430	C₂×C₄×C₇	—	2	2	no	—
431	C₂×C₄×C₇	—	2	2	no	—
432	C₂×C₄×C₇	—	2	2	no	—
433	C₂×C₄×C₇	—	4	1	no	—
434	C₂×C₄×C₇	—	4	4	no	—
435	C₂×C₄×C₇	—	4	4	no	—
436	C₂×C₄×C₇	—	8	2	no	—
437	C₂×C₄×C₇	—	8	4	no	—
438	C₂×C₄×C₇	—	8	1	no	—
439	C₂×C₄×C₇	—	8	1	no	—
440	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
441	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
442	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
443	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
444	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
445	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
446	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
447	C₂×C₄×C₇	C₂×#41	1	2	yes	—
448	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
449	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
450	C₇×C₈	—	2	1	no	—
451	C₇×C₈	—	2	1	no	—
452	C₇×C₈	—	2	4	no	—
453	C₇×C₈	—	2	1	no	—
454	C₇×C₈	—	2	1	no	—
455	C₂×#41	—	2	2	no	—
456	C₂×#41	C₂³×C₇	1	2	yes	—
457	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
458	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
459	C₂³×C₄	—	2	1	no	—
460	#137	—	2	8	no	—
461	C₂×Q₁₆	C₂³×C₇	1	4	yes	—
462	C₂×SD₁₆	—	2	4	no	—
463	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
464	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
465	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
466	C₂×M₁₆	C₂³×C₇	1	2	yes	—
467	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
468	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
469	C₄⋊Q₈	—	2	2	no	—
470	C₄⋊Q₈	—	2	4	no	—
471	C₄⋊Q₈	—	2	2	no	—
472	C₄⋊Q₈	—	2	4	no	—
473	C₄⋊Q₈	—	2	2	no	—
474	C₄⋊Q₈	C₇×D₄	1	1	yes	characteristic
475	C₄⋊Q₈	C₇×D₄	1	1	yes	characteristic
476	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
477	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
478	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
479	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
480	#127	C₂³×C₇	1	1	yes	characteristic
481	#127	C₂³×C₇	1	4	yes	—
482	#126	—	2	4	no	—
483	#125	—	2	4	no	—
484	#125	—	2	4	no	—
485	#125	—	2	4	no	—
486	#125	—	2	2	no	—
487	#125	C₇×D₄	1	2	yes	—
488	#125	C₂³×C₇	1	2	yes	—
489	#125	C₂³×C₇	1	4	yes	—
490	#124	—	2	4	no	—
491	#124	C₂³×C₇	1	2	yes	—
492	#124	C₂³×C₇	1	4	yes	—
493	#123	—	2	4	no	—
494	#123	—	2	4	no	—
495	C₂²⋊Q₈	—	2	2	no	—
496	C₂²⋊Q₈	—	2	1	no	—
497	C₂²⋊Q₈	—	2	1	no	—
498	C₂²⋊Q₈	—	2	4	no	—
499	C₂²⋊Q₈	C₇×D₄	1	2	yes	—
500	C₂²⋊Q₈	C₇×D₄	1	2	yes	—
501	#121	—	2	1	no	—
502	#121	—	2	1	no	—
503	#121	—	2	2	no	—
504	#121	—	2	2	no	—
505	#121	—	2	2	no	—
506	#121	—	2	4	no	—
507	#120	—	2	4	no	—
508	C₄×Q₈	—	2	2	no	—
509	C₄×Q₈	—	2	2	no	—
510	C₄×Q₈	—	2	2	no	—
511	C₄×Q₈	—	2	4	no	—
512	C₄×Q₈	—	2	2	no	—
513	C₄×Q₈	—	2	1	no	—
514	C₄×Q₈	—	2	1	no	—
515	C₄×Q₈	—	2	1	no	—
516	C₄×Q₈	—	2	1	no	—
517	C₄×Q₈	C₂³×C₇	1	2	yes	—
518	C₄×Q₈	C₂³×C₇	1	2	yes	—
519	C₄×Q₈	C₂³×C₇	1	4	yes	—
520	C₄×Q₈	C₂³×C₇	1	4	yes	—
521	C₄×Q₈	C₂³×C₇	1	4	yes	—
522	C₄×Q₈	C₂³×C₇	1	2	yes	—
523	C₄×Q₈	C₂³×C₇	1	2	yes	—
524	C₄×D₄	—	2	4	no	—
525	C₄×D₄	—	2	4	no	—
526	C₄×D₄	—	2	1	no	—
527	C₄×D₄	—	2	1	no	—
528	C₄×D₄	—	2	1	no	—
529	C₄×D₄	—	2	1	no	—
530	C₄×D₄	C₂³×C₇	1	2	yes	—
531	C₄×D₄	C₂³×C₇	1	2	yes	—
532	C₄×D₄	C₂³×C₇	1	4	yes	—
533	#117	—	2	2	no	—
534	#117	—	2	2	no	—
535	#117	—	2	4	no	—
536	#117	C₂³×C₇	1	2	yes	—
537	#117	C₂³×C₇	1	2	yes	—
538	C₂×C₄⋊C₄	—	2	1	no	—
539	C₂×C₄⋊C₄	—	2	2	no	—
540	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
541	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
542	C₂×C₂²⋊C₄	—	2	1	no	—
543	C₂×C₄²	—	2	1	no	—
544	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
545	#107	C₂³×C₇	1	4	yes	—
546	#106	C₂³×C₇	1	2	yes	—
547	#106	C₂³×C₇	1	2	yes	—
548	#106	C₂³×C₇	1	4	yes	—
549	C₄⋊C₈	C₂³×C₇	1	2	yes	—
550	C₄⋊C₈	C₂³×C₇	1	2	yes	—
551	C₄⋊C₈	C₂³×C₇	1	4	yes	—
552	C₄⋊C₈	C₂³×C₇	1	4	yes	—
553	#103	C₂³×C₇	1	2	yes	—
554	#103	C₂³×C₇	1	2	yes	—
555	#103	C₂³×C₇	1	2	yes	—
556	#103	C₂³×C₇	1	2	yes	—
557	#103	C₂³×C₇	1	2	yes	—
558	#103	C₂³×C₇	1	2	yes	—
559	#103	C₂³×C₇	1	4	yes	—
560	#102	C₂³×C₇	1	2	yes	—
561	#102	C₂³×C₇	1	2	yes	—
562	#102	C₂³×C₇	1	2	yes	—
563	#102	C₂³×C₇	1	2	yes	—
564	#102	C₂³×C₇	1	2	yes	—
565	#102	C₂³×C₇	1	2	yes	—
566	#102	C₂³×C₇	1	4	yes	—
567	#102	C₂³×C₇	1	4	yes	—
568	#102	C₂³×C₇	1	4	yes	—
569	#97	C₂³×C₇	1	4	yes	—
570	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
571	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
572	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
573	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
574	C₄×C₈	C₂³×C₇	1	4	yes	—
575	C₂²×C₇	—	2	1	no	—
576	C₂²×C₇	—	2	1	no	—
577	C₂²×C₇	—	4	2	no	—
578	C₂²×C₇	—	4	2	no	—
579	C₂²×C₇	—	4	2	no	—
580	C₂²×C₇	—	4	2	no	—
581	C₂²×C₇	—	4	2	no	—
582	C₂²×C₇	—	4	2	no	—
583	C₂²×C₇	—	8	4	no	—
584	C₂²×C₇	#548	1	2	yes	—
585	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
586	C₄×C₇	—	2	1	no	—
587	C₄×C₇	—	2	1	no	—
588	C₄×C₇	—	2	4	no	—
589	C₄×C₇	—	2	4	no	—
590	C₄×C₇	—	2	1	no	—
591	C₄×C₇	—	2	4	no	—
592	C₄×C₇	—	4	2	no	—
593	C₄×C₇	—	4	2	no	—
594	C₄×C₇	—	4	2	no	—
595	C₄×C₇	—	4	2	no	—
596	C₄×C₇	—	4	2	no	—
597	C₄×C₇	#548	1	2	yes	—
598	C₄×C₇	#577	1	2	yes	—
599	C₄×C₇	C₂²×#41	1	1	yes	characteristic
600	C₄×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
601	C₂⁴	—	2	1	no	—
602	#41	—	2	4	no	—
603	#41	—	2	4	no	—
604	#41	—	8	4	no	—
605	C₂×Q₈	—	2	1	no	—
606	C₂×Q₈	—	2	1	no	—
607	C₂×Q₈	—	2	1	no	—
608	C₂×Q₈	—	2	4	no	—
609	C₂×Q₈	—	2	2	no	—
610	C₂×Q₈	C₂×C₇×D₄	1	2	yes	—
611	C₂×Q₈	C₂×C₇×D₄	1	2	yes	—
612	C₂×Q₈	C₇×#41	1	4	yes	complemented
613	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
614	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
615	C₂×D₄	—	2	2	no	—
616	C₂×D₄	—	2	1	no	—
617	C₂×D₄	—	2	1	no	—
618	C₂×D₄	—	2	4	no	—
619	C₂×D₄	—	2	1	no	—
620	C₂×D₄	—	2	4	no	—
621	C₂×D₄	—	2	2	no	—
622	C₂×D₄	—	2	2	no	—
623	C₂×D₄	C₂⁴×C₇	1	2	yes	—
624	C₂×D₄	C₂⁴×C₇	1	2	yes	—
625	C₂²×C₄	—	2	1	no	—
626	C₂²×C₄	—	2	1	no	—
627	C₂²×C₄	—	2	1	no	—
628	C₂²×C₄	—	2	2	no	—
629	C₂²×C₄	—	2	2	no	—
630	C₂²×C₄	—	2	4	no	—
631	C₂²×C₄	—	2	2	no	—
632	C₂²×C₄	—	8	2	no	—
633	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
634	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
635	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
636	Q₁₆	—	2	8	no	—
637	SD₁₆	—	2	4	no	—
638	SD₁₆	—	2	4	no	—
639	SD₁₆	—	2	8	no	—
640	M₁₆	—	2	4	no	—
641	C₂×C₈	—	2	2	no	—
642	C₂×C₈	—	2	2	no	—
643	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
644	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
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	C₄⋊C₄	—	2	1	no	—
649	C₄⋊C₄	—	2	4	no	—
650	C₄⋊C₄	—	2	2	no	—
651	C₄⋊C₄	—	2	2	no	—
652	C₄⋊C₄	—	2	1	no	—
653	C₄⋊C₄	—	2	1	no	—
654	C₄⋊C₄	—	2	4	no	—
655	C₄⋊C₄	—	2	4	no	—
656	C₄⋊C₄	—	2	1	no	—
657	C₄⋊C₄	—	2	2	no	—
658	C₄⋊C₄	—	2	1	no	—
659	C₄⋊C₄	—	2	1	no	—
660	C₄⋊C₄	—	2	4	no	—
661	C₄⋊C₄	—	2	4	no	—
662	C₄⋊C₄	—	2	2	no	—
663	C₄⋊C₄	—	2	4	no	—
664	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
665	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
666	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
667	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
668	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
669	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
670	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
671	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
672	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
673	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
674	C₂²⋊C₄	—	2	2	no	—
675	C₂²⋊C₄	—	2	2	no	—
676	C₂²⋊C₄	—	2	2	no	—
677	C₂²⋊C₄	—	2	4	no	—
678	C₂²⋊C₄	—	2	4	no	—
679	C₂²⋊C₄	—	2	2	no	—
680	C₂²⋊C₄	—	2	4	no	—
681	C₂²⋊C₄	—	2	2	no	—
682	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
683	C₄²	—	2	2	no	—
684	C₄²	—	2	2	no	—
685	C₄²	—	2	4	no	—
686	C₄²	—	2	4	no	—
687	C₄²	—	2	4	no	—
688	C₄²	—	2	2	no	—
689	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
690	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
691	C₄²	C₂⁴×C₇	1	1	yes	characteristic
692	C₄²	C₂⁴×C₇	1	1	yes	characteristic
693	C₄²	C₂⁴×C₇	1	4	yes	—
694	C₂×C₇	—	2	2	no	—
695	C₂×C₇	—	8	2	no	—
696	C₂×C₇	—	8	2	no	—
697	C₂×C₇	C₂×#548	1	1	yes	characteristic
698	C₂×C₇	C₂×#577	1	1	yes	characteristic
699	C₂×C₇	#3584	1	1	yes	characteristic
700	C₂³	—	2	2	no	—
701	C₂³	—	2	2	no	—
702	C₂³	—	4	2	no	—
703	C₂³	—	8	1	no	—
704	C₂³	—	8	1	no	—
705	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
706	Q₈	—	2	2	no	—
707	Q₈	—	2	4	no	—
708	Q₈	—	2	4	no	—
709	Q₈	—	2	2	no	—
710	Q₈	—	2	2	no	—
711	Q₈	—	4	2	no	—
712	Q₈	—	4	2	no	—
713	Q₈	—	8	1	no	—
714	Q₈	—	8	4	no	—
715	Q₈	C₂×C₇×#41	1	4	yes	—
716	D₄	—	2	2	no	—
717	D₄	—	2	2	no	—
718	D₄	—	2	2	no	—
719	D₄	—	2	2	no	—
720	D₄	—	4	4	no	—
721	D₄	—	4	2	no	—
722	D₄	—	4	2	no	—
723	D₄	—	8	1	no	—
724	D₄	—	8	4	no	—
725	D₄	—	8	4	no	—
726	C₂×C₄	—	2	2	no	—
727	C₂×C₄	—	2	4	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	2	2	no	—
734	C₂×C₄	—	4	1	no	—
735	C₂×C₄	—	4	4	no	—
736	C₂×C₄	—	4	4	no	—
737	C₂×C₄	—	8	2	no	—
738	C₂×C₄	—	8	4	no	—
739	C₂×C₄	—	8	1	no	—
740	C₂×C₄	—	8	1	no	—
741	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
742	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
743	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
744	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
745	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
746	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
747	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
748	C₂×C₄	C₂×C₇×#41	1	2	yes	—
749	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
750	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
751	C₈	—	2	1	no	—
752	C₈	—	2	1	no	—
753	C₈	—	2	4	no	—
754	C₈	—	2	1	no	—
755	C₈	—	2	1	no	—
756	C₇	#61327	1	1	yes	characteristic, direct product factor, Sylow
757	C₂²	—	2	1	no	—
758	C₂²	—	2	1	no	—
759	C₂²	—	4	2	no	—
760	C₂²	—	4	2	no	—
761	C₂²	—	4	2	no	—
762	C₂²	—	4	2	no	—
763	C₂²	—	4	2	no	—
764	C₂²	—	4	2	no	—
765	C₂²	—	8	4	no	—
766	C₂²	C₇×#548	1	2	yes	—
767	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
768	C₄	—	2	1	no	—
769	C₄	—	2	4	no	—
770	C₄	—	2	1	no	—
771	C₄	—	2	1	no	—
772	C₄	—	2	4	no	—
773	C₄	—	2	4	no	—
774	C₄	—	4	2	no	—
775	C₄	—	4	2	no	—
776	C₄	—	4	2	no	—
777	C₄	—	4	2	no	—
778	C₄	—	4	2	no	—
779	C₄	C₇×#548	1	2	yes	—
780	C₄	C₇×#577	1	2	yes	—
781	C₄	C₂²×C₇×#41	1	1	yes	characteristic
782	C₄	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
783	C₂	—	2	2	no	—
784	C₂	—	8	2	no	—
785	C₂	—	8	2	no	—
786	C₂	C₂×C₇×#548	1	1	yes	characteristic
787	C₂	C₂×C₇×#577	1	1	yes	characteristic
788	C₂	C₇×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
prime radical	C₇×#3506	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₇×#533 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇×#3502	C₂	semidirect
3. C₇×#3371	C₂	semidirect
4. C₇×#3369	C₂	semidirect
5. C₇×#3368	C₂	semidirect
6. C₇×#3365	C₂	semidirect
7. C₇×#3364	C₂	semidirect
8. C₇×#3362	C₂	semidirect
9. C₇×#3136	C₂	semidirect
10. C₇×#3131	C₂	semidirect
11. C₇×#3084	C₂	semidirect
12. C₇×#3077	C₂	semidirect
13. C₇×#3043	C₂	semidirect
14. C₇×#3037	C₂	semidirect
15. C₇×#2960	C₂	semidirect
16. C₇×#2947	C₂	semidirect
17. C₂×C₄×C₇×SD₁₆	C₂	semidirect
22. C₇×Q₈²	C₂²	semidirect
25. C₇×#557	C₂²	semidirect
26. C₇×#557	C₂²	semidirect
48. C₇×#488	C₂²	semidirect
49. C₇×#488	C₂²	semidirect
50. C₇×#487	C₂²	semidirect
51. C₇×#487	C₂²	semidirect
53. C₇×#486	C₂²	semidirect
54. C₇×#486	C₂²	semidirect
55. C₇×#479	C₂²	semidirect
57. C₇×#478	C₂²	semidirect
59. C₇×#476	C₂²	semidirect
60. C₇×#475	C₂²	semidirect
64. C₇×#464	C₂²	semidirect
65. C₇×#462	C₂²	semidirect
68. C₇×#460	C₂²	semidirect
69. C₇×#446	C₂²	semidirect
70. C₇×#446	C₂²	semidirect
71. C₇×C₈×Q₈	C₂²	semidirect
72. C₇×C₈×Q₈	C₂²	semidirect
73. C₇×#441	C₂²	semidirect
74. C₇×#440	C₂²	semidirect
75. C₄×C₇×Q₁₆	C₂²	semidirect
80. C₄×C₇×SD₁₆	C₂²	semidirect
93. #61327	C₇	direct (N × H)
215. #3502	C₂×C₇	semidirect
216. #3371	C₂×C₇	semidirect
217. #3369	C₂×C₇	semidirect
218. #3368	C₂×C₇	semidirect
219. #3365	C₂×C₇	semidirect
220. #3364	C₂×C₇	semidirect
221. #3362	C₂×C₇	semidirect
222. #3136	C₂×C₇	semidirect
223. #3131	C₂×C₇	semidirect
224. #3084	C₂×C₇	semidirect
225. #3077	C₂×C₇	semidirect
226. #3043	C₂×C₇	semidirect
227. #3037	C₂×C₇	semidirect
228. #2960	C₂×C₇	semidirect
229. #2947	C₂×C₇	semidirect
230. C₂×C₄×SD₁₆	C₂×C₇	semidirect
242. C₂×C₇×Q₈	#41	semidirect
328. Q₈²	C₂²×C₇	semidirect
331. #557	C₂²×C₇	semidirect
332. #557	C₂²×C₇	semidirect
354. #488	C₂²×C₇	semidirect
355. #488	C₂²×C₇	semidirect
356. #487	C₂²×C₇	semidirect
357. #487	C₂²×C₇	semidirect
359. #486	C₂²×C₇	semidirect
360. #486	C₂²×C₇	semidirect
361. #479	C₂²×C₇	semidirect
363. #478	C₂²×C₇	semidirect
365. #476	C₂²×C₇	semidirect
366. #475	C₂²×C₇	semidirect
370. #464	C₂²×C₇	semidirect
371. #462	C₂²×C₇	semidirect
374. #460	C₂²×C₇	semidirect
375. #446	C₂²×C₇	semidirect
376. #446	C₂²×C₇	semidirect
377. C₈×Q₈	C₂²×C₇	semidirect
378. C₈×Q₈	C₂²×C₇	semidirect
379. #441	C₂²×C₇	semidirect
380. #440	C₂²×C₇	semidirect
381. C₄×Q₁₆	C₂²×C₇	semidirect
386. C₄×SD₁₆	C₂²×C₇	semidirect
612. C₂×Q₈	C₇×#41	semidirect
756. C₇	#61327	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×#3506	2
C₇×#3502	2
C₇×#3371	2
C₇×#3369	2
C₇×#3368	2
C₇×#3365	2
C₇×#3364	2
C₇×#3362	2
C₇×#3136	2
C₇×#3131	2
C₇×#3084	2
C₇×#3077	2
C₇×#3043	2
C₇×#3037	2
C₇×#2960	2
C₇×#2947	2
C₂×C₄×C₇×SD₁₆	2
#61327	7

Subgroups — C7×#61327 #13238543

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#61327 #13238543