Subgroups — C₇×#61371 #13238587

Order 1792.

1750 conjugacy classes of subgroups.

The subgroup lattice has 762 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3502	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#3501	C₂	1	1	yes	maximal, characteristic
3	C₇×#3388	C₂	1	4	yes	maximal, complemented
4	C₇×#3386	C₂	1	2	yes	maximal, complemented
5	C₇×#3385	C₂	1	2	yes	maximal, complemented
6	C₇×#3381	C₂	1	2	yes	maximal, complemented
7	C₇×#3381	C₂	1	4	yes	maximal, complemented
8	C₇×Q₈×SD₁₆	C₂	1	2	yes	maximal, complemented
9	C₇×#3163	C₂	1	2	yes	maximal, complemented
10	C₇×#3160	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#3082	C₂	1	2	yes	maximal, complemented
12	C₇×#3081	C₂	1	2	yes	maximal
13	C₇×#3078	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#3077	C₂	1	1	yes	maximal, characteristic
15	C₇×#2960	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#2949	C₂	1	2	yes	maximal
17	C₂×C₄×C₇×SD₁₆	C₂	1	1	yes	maximal, characteristic
18	C₂²×C₇×SD₁₆	C₂²	1	1	yes	characteristic
19	C₇×Q₈²	—	2	1	no	—
20	C₇×Q₈²	C₂²	1	2	yes	complemented
21	C₇×#557	—	2	1	no	—
22	C₇×#557	—	2	2	no	—
23	C₇×#557	C₂²	1	2	yes	complemented
24	C₇×#557	C₂²	1	4	yes	complemented
25	C₇×#554	—	2	1	no	—
26	C₇×#554	—	2	2	no	—
27	C₇×#554	C₂²	1	2	yes	—
28	C₇×#554	C₂²	1	4	yes	—
29	C₇×D₄×Q₈	—	2	1	no	—
30	C₇×D₄×Q₈	C₂²	1	2	yes	—
31	C₇×#544	—	2	2	no	—
32	C₇×#544	C₂²	1	2	yes	—
33	C₇×#544	C₂²	1	2	yes	—
34	C₇×#543	—	2	2	no	—
35	C₇×#533	—	2	2	no	—
36	C₇×#533	C₂²	1	1	yes	characteristic
37	C₇×#533	C₂²	1	1	yes	characteristic
38	C₇×#533	C₂²	1	1	yes	characteristic
39	C₂×C₇×C₂²⋊Q₈	—	2	2	no	—
40	C₇×#519	C₂²	1	2	yes	—
41	C₇×#518	C₂²	1	2	yes	—
42	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
43	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
44	C₇×#501	C₂²	1	4	yes	complemented
45	C₇×#501	C₂²	1	4	yes	complemented
46	C₇×#500	C₂²	1	1	yes	characteristic, complemented
47	C₇×#500	C₂²	1	1	yes	characteristic, complemented
48	C₇×#499	C₂²	1	2	yes	complemented
49	C₇×#499	C₂²	1	2	yes	complemented
50	C₇×#499	C₂²	1	4	yes	complemented
51	C₇×#498	C₂²	1	1	yes	characteristic, complemented
52	C₇×#498	C₂²	1	1	yes	characteristic, complemented
53	C₇×#498	C₂²	1	4	yes	complemented
54	C₇×#479	C₂²	1	4	yes	complemented
55	C₇×#479	C₂²	1	4	yes	complemented
56	C₇×#479	C₂²	1	4	yes	complemented
57	C₇×#478	C₂²	1	4	yes	—
58	C₇×#478	C₂²	1	4	yes	—
59	C₇×#478	C₂²	1	4	yes	—
60	C₇×#477	C₂²	1	2	yes	complemented
61	C₇×#477	C₂²	1	4	yes	complemented
62	C₇×#476	C₂²	1	2	yes	—
63	C₇×#476	C₂²	1	4	yes	—
64	C₇×#475	C₂²	1	2	yes	complemented
65	C₇×#475	C₂²	1	4	yes	complemented
66	C₇×#474	C₂²	1	2	yes	—
67	C₇×#474	C₂²	1	4	yes	—
68	C₇×#446	C₂²	1	2	yes	complemented
69	C₇×#446	C₂²	1	2	yes	complemented
70	C₇×C₈×Q₈	C₂²	1	2	yes	complemented
71	C₇×C₈×Q₈	C₂²	1	2	yes	complemented
72	C₇×#440	C₂²	1	4	yes	—
73	C₇×#440	C₂²	1	4	yes	—
74	C₄×C₇×SD₁₆	C₂²	1	2	yes	—
75	C₄×C₇×SD₁₆	C₂²	1	2	yes	—
76	C₄×C₇×SD₁₆	C₂²	1	2	yes	—
77	C₄×C₇×SD₁₆	C₂²	1	2	yes	—
78	C₄×C₇×SD₁₆	C₂²	1	4	yes	—
79	C₄×C₇×SD₁₆	C₂²	1	4	yes	—
80	C₇×#428	C₂²	1	2	yes	—
81	C₇×#428	C₂²	1	2	yes	—
82	C₇×#427	C₂²	1	2	yes	—
83	C₇×#427	C₂²	1	2	yes	—
84	C₂×C₇×#106	C₂²	1	1	yes	characteristic
85	C₇×#424	C₂²	1	2	yes	—
86	C₇×#423	C₂²	1	1	yes	characteristic
87	C₇×#419	C₂²	1	2	yes	—
88	C₇×#418	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	#61371	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
94	C₂²×C₇×Q₈	—	2	2	no	—
95	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
96	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₇	—	2	1	no	—
98	C₂×C₇×SD₁₆	Q₈	1	8	yes	complemented
99	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
100	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
101	C₂×C₇×M₁₆	C₂³	1	2	yes	—
102	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
103	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
104	C₇×C₄⋊Q₈	—	2	2	no	—
105	C₇×C₄⋊Q₈	—	2	4	no	—
106	C₇×C₄⋊Q₈	—	2	2	no	—
107	C₇×C₄⋊Q₈	—	2	4	no	—
108	C₇×C₄⋊Q₈	—	2	2	no	—
109	C₇×C₄⋊Q₈	—	2	2	no	—
110	C₇×C₄⋊Q₈	D₄	1	1	yes	characteristic
111	C₇×C₄⋊Q₈	D₄	1	1	yes	characteristic
112	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
113	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
114	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
115	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
116	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
117	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
118	C₇×#125	—	2	4	no	—
119	C₇×#125	—	2	4	no	—
120	C₇×#125	—	2	4	no	—
121	C₇×#125	—	2	2	no	—
122	C₇×#125	—	2	2	no	—
123	C₇×#125	D₄	1	2	yes	—
124	C₇×#125	C₂³	1	2	yes	—
125	C₇×#125	C₂³	1	4	yes	—
126	C₇×#125	C₂³	1	2	yes	—
127	C₇×#125	C₂³	1	4	yes	—
128	C₇×C₂²⋊Q₈	—	2	2	no	—
129	C₇×C₂²⋊Q₈	—	2	4	no	—
130	C₇×C₂²⋊Q₈	—	2	1	no	—
131	C₇×C₂²⋊Q₈	—	2	1	no	—
132	C₇×C₂²⋊Q₈	—	2	1	no	—
133	C₇×C₂²⋊Q₈	—	2	1	no	—
134	C₇×C₂²⋊Q₈	—	2	2	no	—
135	C₇×C₂²⋊Q₈	—	2	4	no	—
136	C₇×C₂²⋊Q₈	—	2	4	no	—
137	C₇×C₂²⋊Q₈	—	2	4	no	—
138	C₇×C₂²⋊Q₈	—	2	4	no	—
139	C₇×C₂²⋊Q₈	—	2	4	no	—
140	C₇×C₂²⋊Q₈	—	2	4	no	—
141	C₇×C₂²⋊Q₈	D₄	1	2	yes	—
142	C₇×C₂²⋊Q₈	D₄	1	2	yes	—
143	C₄×C₇×Q₈	—	2	2	no	—
144	C₄×C₇×Q₈	—	2	2	no	—
145	C₄×C₇×Q₈	—	2	2	no	—
146	C₄×C₇×Q₈	—	2	4	no	—
147	C₄×C₇×Q₈	—	2	2	no	—
148	C₄×C₇×Q₈	—	2	1	no	—
149	C₄×C₇×Q₈	—	2	1	no	—
150	C₄×C₇×Q₈	—	2	1	no	—
151	C₄×C₇×Q₈	—	2	1	no	—
152	C₄×C₇×Q₈	—	2	1	no	—
153	C₄×C₇×Q₈	—	2	1	no	—
154	C₄×C₇×Q₈	C₂³	1	2	yes	—
155	C₄×C₇×Q₈	C₂³	1	4	yes	—
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	2	yes	—
160	C₄×C₇×D₄	—	2	2	no	—
161	C₄×C₇×D₄	—	2	2	no	—
162	C₄×C₇×D₄	—	2	1	no	—
163	C₄×C₇×D₄	—	2	1	no	—
164	C₄×C₇×D₄	C₂³	1	2	yes	—
165	C₄×C₇×D₄	C₂³	1	4	yes	—
166	C₄×C₇×D₄	C₂³	1	4	yes	—
167	C₄×C₇×D₄	C₂³	1	2	yes	—
168	C₇×#117	—	2	4	no	—
169	C₇×#117	C₂³	1	2	yes	—
170	C₇×#117	C₂³	1	2	yes	—
171	C₇×#117	C₂³	1	2	yes	—
172	C₂×C₇×C₄⋊C₄	—	2	1	no	—
173	C₂×C₇×C₄⋊C₄	—	2	4	no	—
174	C₂×C₇×C₄⋊C₄	—	2	2	no	—
175	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
176	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
177	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
178	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
179	C₂×C₄²×C₇	—	2	1	no	—
180	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
181	C₇×#107	C₂³	1	2	yes	—
182	C₇×#107	C₂³	1	4	yes	—
183	C₇×#107	C₂³	1	4	yes	—
184	C₇×#107	C₂³	1	2	yes	—
185	C₇×#107	C₂³	1	2	yes	—
186	C₇×#107	C₂³	1	2	yes	—
187	C₇×#106	C₂³	1	2	yes	—
188	C₇×#106	C₂³	1	4	yes	—
189	C₇×#106	C₂³	1	4	yes	—
190	C₇×#106	C₂³	1	2	yes	—
191	C₇×#106	C₂³	1	2	yes	—
192	C₇×#106	C₂³	1	2	yes	—
193	C₇×#106	C₂³	1	2	yes	—
194	C₇×#106	C₂³	1	2	yes	—
195	C₇×C₄⋊C₈	C₂³	1	2	yes	—
196	C₇×C₄⋊C₈	C₂³	1	4	yes	—
197	C₇×C₄⋊C₈	C₂³	1	4	yes	—
198	C₇×C₄⋊C₈	C₂³	1	2	yes	—
199	C₇×#103	C₂³	1	4	yes	—
200	C₇×#103	C₂³	1	2	yes	—
201	C₇×#103	C₂³	1	2	yes	—
202	C₇×#103	C₂³	1	4	yes	—
203	C₇×#102	C₂³	1	2	yes	—
204	C₇×#102	C₂³	1	4	yes	—
205	C₇×#102	C₂³	1	4	yes	—
206	C₇×#102	C₂³	1	2	yes	—
207	C₇×#97	C₂³	1	4	yes	—
208	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
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	#3502	C₂×C₇	1	1	yes	characteristic, complemented
214	#3501	C₂×C₇	1	1	yes	characteristic
215	#3388	C₂×C₇	1	4	yes	complemented
216	#3386	C₂×C₇	1	2	yes	complemented
217	#3385	C₂×C₇	1	2	yes	complemented
218	#3381	C₂×C₇	1	2	yes	complemented
219	#3381	C₂×C₇	1	4	yes	complemented
220	Q₈×SD₁₆	C₂×C₇	1	2	yes	complemented
221	#3163	C₂×C₇	1	2	yes	complemented
222	#3160	C₂×C₇	1	1	yes	characteristic, complemented
223	#3082	C₂×C₇	1	2	yes	complemented
224	#3081	C₂×C₇	1	2	yes	—
225	#3078	C₂×C₇	1	1	yes	characteristic, complemented
226	#3077	C₂×C₇	1	1	yes	characteristic
227	#2960	C₂×C₇	1	1	yes	characteristic, complemented
228	#2949	C₂×C₇	1	2	yes	—
229	C₂×C₄×SD₁₆	C₂×C₇	1	1	yes	characteristic
230	C₂⁴×C₇	—	2	1	no	—
231	C₂×C₇×Q₈	—	2	1	no	—
232	C₂×C₇×Q₈	—	2	1	no	—
233	C₂×C₇×Q₈	—	2	1	no	—
234	C₂×C₇×Q₈	—	2	1	no	—
235	C₂×C₇×Q₈	—	2	1	no	—
236	C₂×C₇×Q₈	—	2	4	no	—
237	C₂×C₇×Q₈	—	2	4	no	—
238	C₂×C₇×Q₈	—	2	2	no	—
239	C₂×C₇×Q₈	—	8	4	no	—
240	C₂×C₇×Q₈	C₂×D₄	1	2	yes	—
241	C₂×C₇×Q₈	C₂×D₄	1	2	yes	—
242	C₂×C₇×Q₈	C₂×Q₈	1	4	yes	complemented
243	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
244	C₂×C₇×D₄	—	2	1	no	—
245	C₂×C₇×D₄	—	2	2	no	—
246	C₂×C₇×D₄	C₂×Q₈	1	4	yes	—
247	C₂×C₇×D₄	C₂⁴	1	2	yes	—
248	C₂²×C₄×C₇	—	2	1	no	—
249	C₂²×C₄×C₇	—	2	1	no	—
250	C₂²×C₄×C₇	—	2	1	no	—
251	C₂²×C₄×C₇	—	2	2	no	—
252	C₂²×C₄×C₇	—	2	4	no	—
253	C₂²×C₄×C₇	—	2	4	no	—
254	C₂²×C₄×C₇	—	2	2	no	—
255	C₂²×C₄×C₇	—	8	2	no	—
256	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
257	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
258	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
259	C₇×SD₁₆	C₂×Q₈	1	8	yes	complemented
260	C₇×SD₁₆	C₂×Q₈	1	8	yes	complemented
261	C₇×M₁₆	—	2	4	no	—
262	C₂×C₇×C₈	—	2	2	no	—
263	C₂×C₇×C₈	C₂×Q₈	1	4	yes	complemented
264	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
265	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
266	C₂×C₇×C₈	C₂⁴	1	4	yes	—
267	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
268	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
269	C₇×C₄⋊C₄	—	2	2	no	—
270	C₇×C₄⋊C₄	—	2	1	no	—
271	C₇×C₄⋊C₄	—	2	2	no	—
272	C₇×C₄⋊C₄	—	2	2	no	—
273	C₇×C₄⋊C₄	—	2	4	no	—
274	C₇×C₄⋊C₄	—	2	4	no	—
275	C₇×C₄⋊C₄	—	2	4	no	—
276	C₇×C₄⋊C₄	—	2	1	no	—
277	C₇×C₄⋊C₄	—	2	1	no	—
278	C₇×C₄⋊C₄	—	2	4	no	—
279	C₇×C₄⋊C₄	—	2	4	no	—
280	C₇×C₄⋊C₄	—	2	2	no	—
281	C₇×C₄⋊C₄	—	2	1	no	—
282	C₇×C₄⋊C₄	—	2	2	no	—
283	C₇×C₄⋊C₄	—	2	1	no	—
284	C₇×C₄⋊C₄	—	2	1	no	—
285	C₇×C₄⋊C₄	—	2	4	no	—
286	C₇×C₄⋊C₄	—	2	4	no	—
287	C₇×C₄⋊C₄	—	2	2	no	—
288	C₇×C₄⋊C₄	—	2	4	no	—
289	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
290	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
291	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
292	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
293	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
294	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
295	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
296	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
297	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
298	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
299	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
300	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
301	C₇×C₂²⋊C₄	—	2	2	no	—
302	C₇×C₂²⋊C₄	—	2	2	no	—
303	C₇×C₂²⋊C₄	—	2	4	no	—
304	C₇×C₂²⋊C₄	—	2	4	no	—
305	C₇×C₂²⋊C₄	—	2	2	no	—
306	C₇×C₂²⋊C₄	—	2	2	no	—
307	C₇×C₂²⋊C₄	C₂×D₄	1	4	yes	—
308	C₄²×C₇	—	2	2	no	—
309	C₄²×C₇	—	2	2	no	—
310	C₄²×C₇	—	2	4	no	—
311	C₄²×C₇	—	2	4	no	—
312	C₄²×C₇	—	2	2	no	—
313	C₄²×C₇	—	2	2	no	—
314	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
315	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
316	C₄²×C₇	C₂⁴	1	1	yes	characteristic
317	C₄²×C₇	C₂⁴	1	1	yes	characteristic
318	C₄²×C₇	C₂⁴	1	4	yes	—
319	C₂²×SD₁₆	C₂²×C₇	1	1	yes	characteristic
320	Q₈²	—	2	1	no	—
321	Q₈²	C₂²×C₇	1	2	yes	complemented
322	#557	—	2	1	no	—
323	#557	—	2	2	no	—
324	#557	C₂²×C₇	1	2	yes	complemented
325	#557	C₂²×C₇	1	4	yes	complemented
326	#554	—	2	1	no	—
327	#554	—	2	2	no	—
328	#554	C₂²×C₇	1	2	yes	—
329	#554	C₂²×C₇	1	4	yes	—
330	D₄×Q₈	—	2	1	no	—
331	D₄×Q₈	C₂²×C₇	1	2	yes	—
332	#544	—	2	2	no	—
333	#544	C₂²×C₇	1	2	yes	—
334	#544	C₂²×C₇	1	2	yes	—
335	#543	—	2	2	no	—
336	#533	—	2	2	no	—
337	#533	C₂²×C₇	1	1	yes	characteristic
338	#533	C₂²×C₇	1	1	yes	characteristic
339	#533	C₂²×C₇	1	1	yes	characteristic
340	C₂×C₂²⋊Q₈	—	2	2	no	—
341	#519	C₂²×C₇	1	2	yes	—
342	#518	C₂²×C₇	1	2	yes	—
343	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
344	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
345	#501	C₂²×C₇	1	4	yes	complemented
346	#501	C₂²×C₇	1	4	yes	complemented
347	#500	C₂²×C₇	1	1	yes	characteristic, complemented
348	#500	C₂²×C₇	1	1	yes	characteristic, complemented
349	#499	C₂²×C₇	1	2	yes	complemented
350	#499	C₂²×C₇	1	4	yes	complemented
351	#499	C₂²×C₇	1	2	yes	complemented
352	#498	C₂²×C₇	1	1	yes	characteristic, complemented
353	#498	C₂²×C₇	1	4	yes	complemented
354	#498	C₂²×C₇	1	1	yes	characteristic, complemented
355	#479	C₂²×C₇	1	4	yes	complemented
356	#479	C₂²×C₇	1	4	yes	complemented
357	#479	C₂²×C₇	1	4	yes	complemented
358	#478	C₂²×C₇	1	4	yes	—
359	#478	C₂²×C₇	1	4	yes	—
360	#478	C₂²×C₇	1	4	yes	—
361	#477	C₂²×C₇	1	2	yes	complemented
362	#477	C₂²×C₇	1	4	yes	complemented
363	#476	C₂²×C₇	1	2	yes	—
364	#476	C₂²×C₇	1	4	yes	—
365	#475	C₂²×C₇	1	2	yes	complemented
366	#475	C₂²×C₇	1	4	yes	complemented
367	#474	C₂²×C₇	1	2	yes	—
368	#474	C₂²×C₇	1	4	yes	—
369	#446	C₂²×C₇	1	2	yes	complemented
370	#446	C₂²×C₇	1	2	yes	complemented
371	C₈×Q₈	C₂²×C₇	1	2	yes	complemented
372	C₈×Q₈	C₂²×C₇	1	2	yes	complemented
373	#440	C₂²×C₇	1	4	yes	—
374	#440	C₂²×C₇	1	4	yes	—
375	C₄×SD₁₆	C₂²×C₇	1	2	yes	—
376	C₄×SD₁₆	C₂²×C₇	1	4	yes	—
377	C₄×SD₁₆	C₂²×C₇	1	2	yes	—
378	C₄×SD₁₆	C₂²×C₇	1	4	yes	—
379	C₄×SD₁₆	C₂²×C₇	1	2	yes	—
380	C₄×SD₁₆	C₂²×C₇	1	2	yes	—
381	#428	C₂²×C₇	1	2	yes	—
382	#428	C₂²×C₇	1	2	yes	—
383	#427	C₂²×C₇	1	2	yes	—
384	#427	C₂²×C₇	1	2	yes	—
385	C₂×#106	C₂²×C₇	1	1	yes	characteristic
386	#424	C₂²×C₇	1	2	yes	—
387	#423	C₂²×C₇	1	1	yes	characteristic
388	#419	C₂²×C₇	1	2	yes	—
389	#418	C₂²×C₇	1	2	yes	—
390	C₂×#103	C₂²×C₇	1	1	yes	characteristic
391	C₂×#102	C₂²×C₇	1	1	yes	characteristic
392	#405	C₂²×C₇	1	2	yes	—
393	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
394	C₂³×C₇	—	2	2	no	—
395	C₂³×C₇	—	2	4	no	—
396	C₂³×C₇	—	8	1	no	—
397	C₂³×C₇	—	8	1	no	—
398	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
399	C₇×Q₈	—	2	4	no	—
400	C₇×Q₈	—	2	4	no	—
401	C₇×Q₈	—	2	2	no	—
402	C₇×Q₈	—	4	2	no	—
403	C₇×Q₈	—	4	2	no	—
404	C₇×Q₈	—	4	2	no	—
405	C₇×Q₈	—	8	1	no	—
406	C₇×Q₈	—	8	1	no	—
407	C₇×Q₈	—	8	4	no	—
408	C₇×Q₈	—	8	4	no	—
409	C₇×Q₈	C₂²×Q₈	1	4	yes	—
410	C₇×D₄	—	2	4	no	—
411	C₇×D₄	—	2	2	no	—
412	C₇×D₄	C₂²×Q₈	1	4	yes	—
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	2	no	—
417	C₂×C₄×C₇	—	2	2	no	—
418	C₂×C₄×C₇	—	2	2	no	—
419	C₂×C₄×C₇	—	2	2	no	—
420	C₂×C₄×C₇	—	2	2	no	—
421	C₂×C₄×C₇	—	2	2	no	—
422	C₂×C₄×C₇	—	4	1	no	—
423	C₂×C₄×C₇	—	4	4	no	—
424	C₂×C₄×C₇	—	8	4	no	—
425	C₂×C₄×C₇	—	8	2	no	—
426	C₂×C₄×C₇	—	8	4	no	—
427	C₂×C₄×C₇	—	8	1	no	—
428	C₂×C₄×C₇	—	8	1	no	—
429	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
430	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
431	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
432	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
433	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
434	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
435	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
436	C₂×C₄×C₇	C₂²×Q₈	1	2	yes	—
437	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
438	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
439	C₇×C₈	—	2	1	no	—
440	C₇×C₈	—	2	1	no	—
441	C₇×C₈	—	2	4	no	—
442	C₇×C₈	C₂²×Q₈	1	2	yes	—
443	C₇×C₈	C₂²×Q₈	1	2	yes	—
444	C₂²×Q₈	—	2	2	no	—
445	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
446	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
447	C₂³×C₄	—	2	1	no	—
448	C₂×SD₁₆	C₇×Q₈	1	8	yes	complemented
449	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
450	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
451	C₂×M₁₆	C₂³×C₇	1	2	yes	—
452	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
453	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
454	C₄⋊Q₈	—	2	2	no	—
455	C₄⋊Q₈	—	2	4	no	—
456	C₄⋊Q₈	—	2	2	no	—
457	C₄⋊Q₈	—	2	4	no	—
458	C₄⋊Q₈	—	2	2	no	—
459	C₄⋊Q₈	—	2	2	no	—
460	C₄⋊Q₈	C₇×D₄	1	1	yes	characteristic
461	C₄⋊Q₈	C₇×D₄	1	1	yes	characteristic
462	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
463	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
464	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
465	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
466	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
467	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
468	#125	—	2	4	no	—
469	#125	—	2	4	no	—
470	#125	—	2	4	no	—
471	#125	—	2	2	no	—
472	#125	—	2	2	no	—
473	#125	C₇×D₄	1	2	yes	—
474	#125	C₂³×C₇	1	2	yes	—
475	#125	C₂³×C₇	1	2	yes	—
476	#125	C₂³×C₇	1	4	yes	—
477	#125	C₂³×C₇	1	4	yes	—
478	C₂²⋊Q₈	—	2	2	no	—
479	C₂²⋊Q₈	—	2	4	no	—
480	C₂²⋊Q₈	—	2	1	no	—
481	C₂²⋊Q₈	—	2	1	no	—
482	C₂²⋊Q₈	—	2	1	no	—
483	C₂²⋊Q₈	—	2	1	no	—
484	C₂²⋊Q₈	—	2	2	no	—
485	C₂²⋊Q₈	—	2	4	no	—
486	C₂²⋊Q₈	—	2	4	no	—
487	C₂²⋊Q₈	—	2	4	no	—
488	C₂²⋊Q₈	—	2	4	no	—
489	C₂²⋊Q₈	—	2	4	no	—
490	C₂²⋊Q₈	—	2	4	no	—
491	C₂²⋊Q₈	C₇×D₄	1	2	yes	—
492	C₂²⋊Q₈	C₇×D₄	1	2	yes	—
493	C₄×Q₈	—	2	2	no	—
494	C₄×Q₈	—	2	2	no	—
495	C₄×Q₈	—	2	2	no	—
496	C₄×Q₈	—	2	4	no	—
497	C₄×Q₈	—	2	2	no	—
498	C₄×Q₈	—	2	1	no	—
499	C₄×Q₈	—	2	1	no	—
500	C₄×Q₈	—	2	1	no	—
501	C₄×Q₈	—	2	1	no	—
502	C₄×Q₈	—	2	1	no	—
503	C₄×Q₈	—	2	1	no	—
504	C₄×Q₈	C₂³×C₇	1	2	yes	—
505	C₄×Q₈	C₂³×C₇	1	2	yes	—
506	C₄×Q₈	C₂³×C₇	1	4	yes	—
507	C₄×Q₈	C₂³×C₇	1	4	yes	—
508	C₄×Q₈	C₂³×C₇	1	2	yes	—
509	C₄×Q₈	C₂³×C₇	1	2	yes	—
510	C₄×D₄	—	2	2	no	—
511	C₄×D₄	—	2	2	no	—
512	C₄×D₄	—	2	1	no	—
513	C₄×D₄	—	2	1	no	—
514	C₄×D₄	C₂³×C₇	1	2	yes	—
515	C₄×D₄	C₂³×C₇	1	2	yes	—
516	C₄×D₄	C₂³×C₇	1	4	yes	—
517	C₄×D₄	C₂³×C₇	1	4	yes	—
518	#117	—	2	4	no	—
519	#117	C₂³×C₇	1	2	yes	—
520	#117	C₂³×C₇	1	2	yes	—
521	#117	C₂³×C₇	1	2	yes	—
522	C₂×C₄⋊C₄	—	2	1	no	—
523	C₂×C₄⋊C₄	—	2	4	no	—
524	C₂×C₄⋊C₄	—	2	2	no	—
525	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
526	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
527	C₂×C₂²⋊C₄	—	2	1	no	—
528	C₂×C₂²⋊C₄	—	2	4	no	—
529	C₂×C₄²	—	2	1	no	—
530	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
531	#107	C₂³×C₇	1	2	yes	—
532	#107	C₂³×C₇	1	2	yes	—
533	#107	C₂³×C₇	1	2	yes	—
534	#107	C₂³×C₇	1	2	yes	—
535	#107	C₂³×C₇	1	4	yes	—
536	#107	C₂³×C₇	1	4	yes	—
537	#106	C₂³×C₇	1	2	yes	—
538	#106	C₂³×C₇	1	2	yes	—
539	#106	C₂³×C₇	1	2	yes	—
540	#106	C₂³×C₇	1	2	yes	—
541	#106	C₂³×C₇	1	2	yes	—
542	#106	C₂³×C₇	1	2	yes	—
543	#106	C₂³×C₇	1	4	yes	—
544	#106	C₂³×C₇	1	4	yes	—
545	C₄⋊C₈	C₂³×C₇	1	2	yes	—
546	C₄⋊C₈	C₂³×C₇	1	2	yes	—
547	C₄⋊C₈	C₂³×C₇	1	4	yes	—
548	C₄⋊C₈	C₂³×C₇	1	4	yes	—
549	#103	C₂³×C₇	1	2	yes	—
550	#103	C₂³×C₇	1	2	yes	—
551	#103	C₂³×C₇	1	4	yes	—
552	#103	C₂³×C₇	1	4	yes	—
553	#102	C₂³×C₇	1	2	yes	—
554	#102	C₂³×C₇	1	2	yes	—
555	#102	C₂³×C₇	1	4	yes	—
556	#102	C₂³×C₇	1	4	yes	—
557	#97	C₂³×C₇	1	4	yes	—
558	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
559	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
560	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
561	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
562	C₄×C₈	C₂³×C₇	1	4	yes	—
563	C₂²×C₇	—	2	1	no	—
564	C₂²×C₇	—	2	1	no	—
565	C₂²×C₇	—	2	4	no	—
566	C₂²×C₇	—	4	2	no	—
567	C₂²×C₇	—	4	2	no	—
568	C₂²×C₇	—	8	4	no	—
569	C₂²×C₇	D₄×Q₈	1	2	yes	—
570	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
571	C₄×C₇	—	2	1	no	—
572	C₄×C₇	—	2	1	no	—
573	C₄×C₇	—	2	4	no	—
574	C₄×C₇	—	2	4	no	—
575	C₄×C₇	—	2	1	no	—
576	C₄×C₇	—	2	4	no	—
577	C₄×C₇	—	4	2	no	—
578	C₄×C₇	—	4	2	no	—
579	C₄×C₇	—	4	2	no	—
580	C₄×C₇	—	4	2	no	—
581	C₄×C₇	—	4	2	no	—
582	C₄×C₇	—	4	2	no	—
583	C₄×C₇	D₄×Q₈	1	2	yes	—
584	C₄×C₇	#577	1	2	yes	—
585	C₄×C₇	C₂³×Q₈	1	1	yes	characteristic
586	C₄×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
587	C₂⁴	—	2	1	no	—
588	C₂×Q₈	—	2	1	no	—
589	C₂×Q₈	—	2	1	no	—
590	C₂×Q₈	—	2	1	no	—
591	C₂×Q₈	—	2	1	no	—
592	C₂×Q₈	—	2	1	no	—
593	C₂×Q₈	—	2	4	no	—
594	C₂×Q₈	—	2	4	no	—
595	C₂×Q₈	—	2	2	no	—
596	C₂×Q₈	—	8	4	no	—
597	C₂×Q₈	C₂×C₇×D₄	1	2	yes	—
598	C₂×Q₈	C₂×C₇×D₄	1	2	yes	—
599	C₂×Q₈	C₂×C₇×Q₈	1	4	yes	complemented
600	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
601	C₂×D₄	—	2	1	no	—
602	C₂×D₄	—	2	2	no	—
603	C₂×D₄	C₂×C₇×Q₈	1	4	yes	—
604	C₂×D₄	C₂⁴×C₇	1	2	yes	—
605	C₂²×C₄	—	2	1	no	—
606	C₂²×C₄	—	2	1	no	—
607	C₂²×C₄	—	2	1	no	—
608	C₂²×C₄	—	2	2	no	—
609	C₂²×C₄	—	2	4	no	—
610	C₂²×C₄	—	2	4	no	—
611	C₂²×C₄	—	2	2	no	—
612	C₂²×C₄	—	8	2	no	—
613	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
614	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
615	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
616	SD₁₆	C₂×C₇×Q₈	1	8	yes	complemented
617	SD₁₆	C₂×C₇×Q₈	1	8	yes	complemented
618	M₁₆	—	2	4	no	—
619	C₂×C₈	—	2	2	no	—
620	C₂×C₈	C₂×C₇×Q₈	1	4	yes	complemented
621	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
622	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
623	C₂×C₈	C₂⁴×C₇	1	4	yes	—
624	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
625	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
626	C₄⋊C₄	—	2	2	no	—
627	C₄⋊C₄	—	2	1	no	—
628	C₄⋊C₄	—	2	2	no	—
629	C₄⋊C₄	—	2	2	no	—
630	C₄⋊C₄	—	2	4	no	—
631	C₄⋊C₄	—	2	4	no	—
632	C₄⋊C₄	—	2	4	no	—
633	C₄⋊C₄	—	2	1	no	—
634	C₄⋊C₄	—	2	1	no	—
635	C₄⋊C₄	—	2	4	no	—
636	C₄⋊C₄	—	2	4	no	—
637	C₄⋊C₄	—	2	2	no	—
638	C₄⋊C₄	—	2	1	no	—
639	C₄⋊C₄	—	2	2	no	—
640	C₄⋊C₄	—	2	1	no	—
641	C₄⋊C₄	—	2	1	no	—
642	C₄⋊C₄	—	2	4	no	—
643	C₄⋊C₄	—	2	4	no	—
644	C₄⋊C₄	—	2	2	no	—
645	C₄⋊C₄	—	2	4	no	—
646	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
647	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
648	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
649	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
650	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
651	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
652	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
653	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
654	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
655	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
656	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
657	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
658	C₂²⋊C₄	—	2	2	no	—
659	C₂²⋊C₄	—	2	2	no	—
660	C₂²⋊C₄	—	2	4	no	—
661	C₂²⋊C₄	—	2	4	no	—
662	C₂²⋊C₄	—	2	2	no	—
663	C₂²⋊C₄	—	2	2	no	—
664	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
665	C₄²	—	2	2	no	—
666	C₄²	—	2	2	no	—
667	C₄²	—	2	4	no	—
668	C₄²	—	2	4	no	—
669	C₄²	—	2	2	no	—
670	C₄²	—	2	2	no	—
671	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
672	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
673	C₄²	C₂⁴×C₇	1	1	yes	characteristic
674	C₄²	C₂⁴×C₇	1	1	yes	characteristic
675	C₄²	C₂⁴×C₇	1	4	yes	—
676	C₂×C₇	—	2	2	no	—
677	C₂×C₇	—	4	4	no	—
678	C₂×C₇	C₂×D₄×Q₈	1	1	yes	characteristic
679	C₂×C₇	C₂×#577	1	1	yes	characteristic
680	C₂×C₇	#3584	1	1	yes	characteristic
681	C₂³	—	2	2	no	—
682	C₂³	—	2	4	no	—
683	C₂³	—	8	1	no	—
684	C₂³	—	8	1	no	—
685	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
686	Q₈	—	2	2	no	—
687	Q₈	—	2	4	no	—
688	Q₈	—	2	4	no	—
689	Q₈	—	4	2	no	—
690	Q₈	—	4	2	no	—
691	Q₈	—	4	2	no	—
692	Q₈	—	8	1	no	—
693	Q₈	—	8	1	no	—
694	Q₈	—	8	4	no	—
695	Q₈	—	8	4	no	—
696	Q₈	C₂²×C₇×Q₈	1	4	yes	—
697	D₄	—	2	2	no	—
698	D₄	—	2	4	no	—
699	D₄	C₂²×C₇×Q₈	1	4	yes	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	4	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	4	1	no	—
710	C₂×C₄	—	4	4	no	—
711	C₂×C₄	—	8	4	no	—
712	C₂×C₄	—	8	2	no	—
713	C₂×C₄	—	8	4	no	—
714	C₂×C₄	—	8	1	no	—
715	C₂×C₄	—	8	1	no	—
716	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
717	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
718	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
719	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
720	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
721	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
722	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
723	C₂×C₄	C₂²×C₇×Q₈	1	2	yes	—
724	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
725	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
726	C₈	—	2	1	no	—
727	C₈	—	2	1	no	—
728	C₈	—	2	4	no	—
729	C₈	C₂²×C₇×Q₈	1	2	yes	—
730	C₈	C₂²×C₇×Q₈	1	2	yes	—
731	C₇	#61371	1	1	yes	characteristic, direct product factor, Sylow
732	C₂²	—	2	1	no	—
733	C₂²	—	2	1	no	—
734	C₂²	—	2	4	no	—
735	C₂²	—	4	2	no	—
736	C₂²	—	4	2	no	—
737	C₂²	—	8	4	no	—
738	C₂²	C₇×D₄×Q₈	1	2	yes	—
739	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
740	C₄	—	2	1	no	—
741	C₄	—	2	4	no	—
742	C₄	—	2	1	no	—
743	C₄	—	2	1	no	—
744	C₄	—	2	4	no	—
745	C₄	—	2	4	no	—
746	C₄	—	4	2	no	—
747	C₄	—	4	2	no	—
748	C₄	—	4	2	no	—
749	C₄	—	4	2	no	—
750	C₄	—	4	2	no	—
751	C₄	—	4	2	no	—
752	C₄	C₇×D₄×Q₈	1	2	yes	—
753	C₄	C₇×#577	1	2	yes	—
754	C₄	C₂³×C₇×Q₈	1	1	yes	characteristic
755	C₄	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
756	C₂	—	2	2	no	—
757	C₂	—	4	4	no	—
758	C₂	C₂×C₇×D₄×Q₈	1	1	yes	characteristic
759	C₂	C₂×C₇×#577	1	1	yes	characteristic
760	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	C₂²×C₇×D₄	C₂³
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
1. C₇×#3502	C₂	semidirect
3. C₇×#3388	C₂	semidirect
4. C₇×#3386	C₂	semidirect
5. C₇×#3385	C₂	semidirect
6. C₇×#3381	C₂	semidirect
7. C₇×#3381	C₂	semidirect
8. C₇×Q₈×SD₁₆	C₂	semidirect
9. C₇×#3163	C₂	semidirect
10. C₇×#3160	C₂	semidirect
11. C₇×#3082	C₂	semidirect
13. C₇×#3078	C₂	semidirect
15. C₇×#2960	C₂	semidirect
20. C₇×Q₈²	C₂²	semidirect
23. C₇×#557	C₂²	semidirect
24. C₇×#557	C₂²	semidirect
44. C₇×#501	C₂²	semidirect
45. C₇×#501	C₂²	semidirect
46. C₇×#500	C₂²	semidirect
47. C₇×#500	C₂²	semidirect
48. C₇×#499	C₂²	semidirect
49. C₇×#499	C₂²	semidirect
50. C₇×#499	C₂²	semidirect
51. C₇×#498	C₂²	semidirect
52. C₇×#498	C₂²	semidirect
53. C₇×#498	C₂²	semidirect
54. C₇×#479	C₂²	semidirect
55. C₇×#479	C₂²	semidirect
56. C₇×#479	C₂²	semidirect
60. C₇×#477	C₂²	semidirect
61. C₇×#477	C₂²	semidirect
64. C₇×#475	C₂²	semidirect
65. C₇×#475	C₂²	semidirect
68. C₇×#446	C₂²	semidirect
69. C₇×#446	C₂²	semidirect
70. C₇×C₈×Q₈	C₂²	semidirect
71. C₇×C₈×Q₈	C₂²	semidirect
93. #61371	C₇	direct (N × H)
98. C₂×C₇×SD₁₆	Q₈	semidirect
213. #3502	C₂×C₇	semidirect
215. #3388	C₂×C₇	semidirect
216. #3386	C₂×C₇	semidirect
217. #3385	C₂×C₇	semidirect
218. #3381	C₂×C₇	semidirect
219. #3381	C₂×C₇	semidirect
220. Q₈×SD₁₆	C₂×C₇	semidirect
221. #3163	C₂×C₇	semidirect
222. #3160	C₂×C₇	semidirect
223. #3082	C₂×C₇	semidirect
225. #3078	C₂×C₇	semidirect
227. #2960	C₂×C₇	semidirect
242. C₂×C₇×Q₈	C₂×Q₈	semidirect
259. C₇×SD₁₆	C₂×Q₈	semidirect
260. C₇×SD₁₆	C₂×Q₈	semidirect
263. C₂×C₇×C₈	C₂×Q₈	semidirect
321. Q₈²	C₂²×C₇	semidirect
324. #557	C₂²×C₇	semidirect
325. #557	C₂²×C₇	semidirect
345. #501	C₂²×C₇	semidirect
346. #501	C₂²×C₇	semidirect
347. #500	C₂²×C₇	semidirect
348. #500	C₂²×C₇	semidirect
349. #499	C₂²×C₇	semidirect
350. #499	C₂²×C₇	semidirect
351. #499	C₂²×C₇	semidirect
352. #498	C₂²×C₇	semidirect
353. #498	C₂²×C₇	semidirect
354. #498	C₂²×C₇	semidirect
355. #479	C₂²×C₇	semidirect
356. #479	C₂²×C₇	semidirect
357. #479	C₂²×C₇	semidirect
361. #477	C₂²×C₇	semidirect
362. #477	C₂²×C₇	semidirect
365. #475	C₂²×C₇	semidirect
366. #475	C₂²×C₇	semidirect
369. #446	C₂²×C₇	semidirect
370. #446	C₂²×C₇	semidirect
371. C₈×Q₈	C₂²×C₇	semidirect
372. C₈×Q₈	C₂²×C₇	semidirect
448. C₂×SD₁₆	C₇×Q₈	semidirect
599. C₂×Q₈	C₂×C₇×Q₈	semidirect
616. SD₁₆	C₂×C₇×Q₈	semidirect
617. SD₁₆	C₂×C₇×Q₈	semidirect
620. C₂×C₈	C₂×C₇×Q₈	semidirect
731. C₇	#61371	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×#3502	2
C₇×#3501	2
C₇×#3388	2
C₇×#3386	2
C₇×#3385	2
C₇×#3381	2
C₇×Q₈×SD₁₆	2
C₇×#3163	2
C₇×#3160	2
C₇×#3082	2
C₇×#3081	2
C₇×#3078	2
C₇×#3077	2
C₇×#2960	2
C₇×#2949	2
C₂×C₄×C₇×SD₁₆	2
#61371	7

Subgroups — C7×#61371 #13238587

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#61371 #13238587