Subgroups — C₇×#61478 #13238694

Order 1792.

1768 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3518	C₂	1	2	yes	maximal, complemented
2	C₇×#3393	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×Q₈×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#3369	C₂	1	2	yes	maximal, complemented
5	C₇×#3342	C₂	1	2	yes	maximal, complemented
6	C₇×#3341	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#3329	C₂	1	2	yes	maximal, complemented
8	C₇×#3313	C₂	1	4	yes	maximal, complemented
9	C₇×D₄×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#3285	C₂	1	2	yes	maximal, complemented
11	C₇×#3175	C₂	1	2	yes	maximal, complemented
12	C₇×#3170	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#3121	C₂	1	4	yes	maximal, complemented
14	C₇×#3116	C₂	1	2	yes	maximal, complemented
15	C₇×#2966	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#2950	C₂	1	2	yes	maximal, complemented
17	C₄×C₇×#135	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₇×#135	C₂²	1	1	yes	characteristic
19	C₂²×C₇×Q₁₆	C₂²	1	2	yes	—
20	C₇×Q₈²	C₂²	1	2	yes	—
21	C₇×#556	—	2	4	no	—
22	C₇×#556	—	2	2	no	—
23	C₇×#556	C₂²	1	2	yes	—
24	C₇×#556	C₂²	1	4	yes	—
25	C₇×#555	—	2	2	no	—
26	C₇×#555	C₂²	1	2	yes	—
27	C₇×D₄×Q₈	C₂²	1	2	yes	—
28	C₇×#548	C₂²	1	4	yes	—
29	C₇×#542	—	2	4	no	—
30	C₇×#542	C₂²	1	4	yes	—
31	C₇×#533	—	2	2	no	—
32	C₇×#533	C₂²	1	2	yes	—
33	C₇×#529	—	2	2	no	—
34	C₇×#529	C₂²	1	1	yes	characteristic
35	C₇×#519	C₂²	1	4	yes	—
36	C₄×C₇×#41	C₂²	1	2	yes	—
37	C₇×#500	C₂²	1	1	yes	characteristic
38	C₇×#500	C₂²	1	2	yes	—
39	C₇×#495	C₂²	1	2	yes	—
40	C₇×#494	C₂²	1	1	yes	characteristic
41	C₇×#489	C₂²	1	4	yes	—
42	C₇×#487	C₂²	1	2	yes	—
43	C₇×#485	C₂²	1	4	yes	—
44	C₇×#485	C₂²	1	4	yes	—
45	C₇×#482	C₂²	1	4	yes	—
46	C₇×#477	C₂²	1	4	yes	—
47	C₇×#477	C₂²	1	2	yes	—
48	C₇×#476	C₂²	1	2	yes	—
49	C₇×#475	C₂²	1	4	yes	—
50	C₇×#468	C₂²	1	4	yes	—
51	C₇×#467	C₂²	1	2	yes	—
52	C₇×#467	C₂²	1	2	yes	—
53	C₇×#467	C₂²	1	2	yes	—
54	C₇×#466	C₂²	1	2	yes	—
55	C₇×#464	C₂²	1	4	yes	—
56	C₇×#464	C₂²	1	4	yes	—
57	C₇×#462	C₂²	1	2	yes	—
58	C₇×#461	C₂²	1	2	yes	—
59	C₇×#452	C₂²	1	4	yes	—
60	C₇×#451	C₂²	1	4	yes	—
61	C₇×#448	C₂²	1	4	yes	—
62	C₇×#446	C₂²	1	1	yes	characteristic
63	C₇×C₈×Q₈	C₂²	1	1	yes	characteristic
64	C₇×#441	C₂²	1	4	yes	—
65	C₇×#441	C₂²	1	4	yes	—
66	C₇×#440	C₂²	1	4	yes	—
67	C₄×C₇×Q₁₆	C₂²	1	2	yes	—
68	C₄×C₇×Q₁₆	C₂²	1	2	yes	—
69	C₄×C₇×Q₁₆	C₂²	1	1	yes	characteristic
70	C₄×C₇×Q₁₆	C₂²	1	1	yes	characteristic
71	C₄×C₇×Q₁₆	C₂²	1	2	yes	—
72	C₄×C₇×Q₁₆	C₂²	1	2	yes	—
73	C₄×C₇×SD₁₆	C₂²	1	2	yes	—
74	C₄×C₇×SD₁₆	C₂²	1	2	yes	—
75	C₄×C₇×D₈	C₂²	1	1	yes	characteristic
76	C₄×C₇×D₈	C₂²	1	1	yes	characteristic
77	C₇×#436	C₂²	1	1	yes	characteristic
78	C₇×#435	C₂²	1	2	yes	—
79	C₇×C₈×D₄	C₂²	1	2	yes	—
80	C₇×C₈×D₄	C₂²	1	1	yes	characteristic
81	C₇×#433	C₂²	1	2	yes	—
82	C₇×#432	C₂²	1	1	yes	characteristic
83	C₇×#427	C₂²	1	1	yes	characteristic
84	C₇×#427	C₂²	1	2	yes	—
85	C₇×#419	C₂²	1	4	yes	—
86	C₇×#416	C₂²	1	2	yes	—
87	C₇×#405	C₂²	1	2	yes	—
88	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
89	#61478	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
90	C₂×C₇×#41	C₂³	1	2	yes	—
91	C₂²×C₇×Q₈	C₂³	1	4	yes	—
92	C₇×#135	—	2	4	no	—
93	C₂×C₇×Q₁₆	—	2	8	no	—
94	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
95	C₂×C₇×Q₁₆	C₂³	1	4	yes	—
96	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
97	C₂×C₇×Q₁₆	C₂³	1	1	yes	characteristic
98	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
99	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
100	C₂×C₇×D₈	C₂³	1	1	yes	characteristic
101	C₂×C₇×M₁₆	C₂³	1	2	yes	—
102	C₂²×C₇×C₈	C₂³	1	2	yes	—
103	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
104	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
105	C₇×C₄⋊Q₈	—	2	2	no	—
106	C₇×C₄⋊Q₈	—	2	2	no	—
107	C₇×C₄⋊Q₈	—	2	4	no	—
108	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
109	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
110	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
111	C₇×#126	—	2	4	no	—
112	C₇×#126	—	2	4	no	—
113	C₇×#126	—	2	4	no	—
114	C₇×#126	—	2	4	no	—
115	C₇×#126	D₄	1	2	yes	—
116	C₇×#125	—	2	2	no	—
117	C₇×#125	D₄	1	1	yes	characteristic
118	C₇×#124	—	2	4	no	—
119	C₇×#124	—	2	4	no	—
120	C₇×#124	—	2	4	no	—
121	C₇×#124	—	2	4	no	—
122	C₇×#124	D₄	1	1	yes	characteristic
123	C₇×#124	C₂³	1	4	yes	—
124	C₇×#123	—	2	4	no	—
125	C₇×#123	D₄	1	2	yes	—
126	C₇×C₂²⋊Q₈	—	2	2	no	—
127	C₇×C₂²⋊Q₈	—	2	2	no	—
128	C₇×C₂²⋊Q₈	—	2	4	no	—
129	C₇×C₂²⋊Q₈	—	2	4	no	—
130	C₇×C₂²⋊Q₈	—	2	4	no	—
131	C₇×C₂²⋊Q₈	D₄	1	1	yes	characteristic
132	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
133	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
134	C₇×#121	—	2	2	no	—
135	C₇×#121	—	2	4	no	—
136	C₇×#121	D₄	1	1	yes	characteristic
137	C₇×#121	C₂³	1	4	yes	—
138	C₄×C₇×Q₈	—	2	2	no	—
139	C₄×C₇×Q₈	—	2	4	no	—
140	C₄×C₇×Q₈	—	2	4	no	—
141	C₄×C₇×Q₈	—	2	4	no	—
142	C₄×C₇×Q₈	—	2	2	no	—
143	C₄×C₇×Q₈	C₂³	1	4	yes	—
144	C₄×C₇×Q₈	C₂³	1	2	yes	—
145	C₄×C₇×Q₈	C₂³	1	4	yes	—
146	C₄×C₇×Q₈	C₂³	1	2	yes	—
147	C₄×C₇×Q₈	C₂³	1	4	yes	—
148	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
149	C₄×C₇×D₄	—	2	2	no	—
150	C₄×C₇×D₄	—	2	2	no	—
151	C₄×C₇×D₄	—	2	2	no	—
152	C₄×C₇×D₄	—	2	4	no	—
153	C₄×C₇×D₄	C₂³	1	2	yes	—
154	C₄×C₇×D₄	C₂³	1	2	yes	—
155	C₄×C₇×D₄	C₂³	1	2	yes	—
156	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
157	C₇×#117	—	2	2	no	—
158	C₇×#117	—	2	2	no	—
159	C₇×#117	—	2	2	no	—
160	C₇×#117	—	2	4	no	—
161	C₇×#117	—	2	4	no	—
162	C₇×#117	—	2	2	no	—
163	C₇×#117	C₂³	1	4	yes	—
164	C₇×#117	C₂³	1	2	yes	—
165	C₇×#117	C₂³	1	2	yes	—
166	C₂×C₄²×C₇	—	2	2	no	—
167	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
168	C₇×#107	C₂³	1	2	yes	—
169	C₇×#107	C₂³	1	1	yes	characteristic
170	C₇×#107	C₂³	1	2	yes	—
171	C₇×#107	C₂³	1	4	yes	—
172	C₇×#107	C₂³	1	1	yes	characteristic
173	C₇×#106	C₂³	1	2	yes	—
174	C₇×#106	C₂³	1	4	yes	—
175	C₇×C₄⋊C₈	C₂³	1	2	yes	—
176	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
177	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
178	C₇×C₄⋊C₈	C₂³	1	2	yes	—
179	C₇×#103	C₂³	1	4	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	4	yes	—
184	C₇×#103	C₂³	1	4	yes	—
185	C₇×#103	C₂³	1	2	yes	—
186	C₇×#102	C₂³	1	4	yes	—
187	C₇×#102	C₂³	1	2	yes	—
188	C₇×#102	C₂³	1	2	yes	—
189	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
190	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
191	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
192	C₇×#97	C₂³	1	2	yes	—
193	C₇×#97	C₂³	1	2	yes	—
194	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
195	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
196	C₄×C₇×C₈	C₂³	1	2	yes	—
197	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
198	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
199	#3518	C₂×C₇	1	2	yes	complemented
200	#3393	C₂×C₇	1	1	yes	characteristic, complemented
201	Q₈×Q₁₆	C₂×C₇	1	1	yes	characteristic, complemented
202	#3369	C₂×C₇	1	2	yes	complemented
203	#3342	C₂×C₇	1	2	yes	complemented
204	#3341	C₂×C₇	1	1	yes	characteristic, complemented
205	#3329	C₂×C₇	1	2	yes	complemented
206	#3313	C₂×C₇	1	4	yes	complemented
207	D₄×Q₁₆	C₂×C₇	1	1	yes	characteristic, complemented
208	#3285	C₂×C₇	1	2	yes	complemented
209	#3175	C₂×C₇	1	2	yes	complemented
210	#3170	C₂×C₇	1	1	yes	characteristic, complemented
211	#3121	C₂×C₇	1	4	yes	complemented
212	#3116	C₂×C₇	1	2	yes	complemented
213	#2966	C₂×C₇	1	1	yes	characteristic, complemented
214	#2950	C₂×C₇	1	2	yes	complemented
215	C₄×#135	C₂×C₇	1	1	yes	characteristic, complemented
216	C₇×#41	—	2	4	no	—
217	C₇×#41	—	4	2	no	—
218	C₂×C₇×Q₈	—	2	4	no	—
219	C₂×C₇×Q₈	—	2	2	no	—
220	C₂×C₇×Q₈	—	2	4	no	—
221	C₂×C₇×Q₈	—	2	8	no	—
222	C₂×C₇×Q₈	—	4	4	no	—
223	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
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	4	no	—
228	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
229	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
230	C₂×C₇×D₄	C₂⁴	1	2	yes	—
231	C₂²×C₄×C₇	—	2	4	no	—
232	C₂²×C₄×C₇	—	2	2	no	—
233	C₂²×C₄×C₇	—	2	2	no	—
234	C₂²×C₄×C₇	—	2	2	no	—
235	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
236	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
237	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
238	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
239	C₇×Q₁₆	—	2	8	no	—
240	C₇×Q₁₆	—	2	4	no	—
241	C₇×Q₁₆	—	4	2	no	—
242	C₇×Q₁₆	#41	1	4	yes	—
243	C₇×SD₁₆	—	2	4	no	—
244	C₇×SD₁₆	—	4	4	no	—
245	C₇×D₈	—	2	2	no	—
246	C₇×M₁₆	—	4	2	no	—
247	C₂×C₇×C₈	—	2	4	no	—
248	C₂×C₇×C₈	—	2	2	no	—
249	C₂×C₇×C₈	—	4	1	no	—
250	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
251	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
252	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
253	C₂×C₇×C₈	C₂⁴	1	2	yes	—
254	C₂×C₇×C₈	C₂⁴	1	2	yes	—
255	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
256	C₇×C₄⋊C₄	—	2	2	no	—
257	C₇×C₄⋊C₄	—	2	2	no	—
258	C₇×C₄⋊C₄	—	2	2	no	—
259	C₇×C₄⋊C₄	—	2	2	no	—
260	C₇×C₄⋊C₄	—	2	4	no	—
261	C₇×C₄⋊C₄	—	2	4	no	—
262	C₇×C₄⋊C₄	—	2	4	no	—
263	C₇×C₄⋊C₄	—	2	4	no	—
264	C₇×C₄⋊C₄	—	2	2	no	—
265	C₇×C₄⋊C₄	—	2	4	no	—
266	C₇×C₄⋊C₄	—	2	4	no	—
267	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
268	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
269	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
270	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
271	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
272	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
273	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
274	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
275	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
276	C₇×C₂²⋊C₄	—	2	4	no	—
277	C₇×C₂²⋊C₄	—	2	4	no	—
278	C₇×C₂²⋊C₄	—	2	2	no	—
279	C₇×C₂²⋊C₄	—	2	4	no	—
280	C₇×C₂²⋊C₄	—	2	2	no	—
281	C₇×C₂²⋊C₄	—	2	2	no	—
282	C₇×C₂²⋊C₄	—	2	4	no	—
283	C₇×C₂²⋊C₄	—	2	4	no	—
284	C₇×C₂²⋊C₄	—	2	4	no	—
285	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
286	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
287	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
288	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
289	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
290	C₄²×C₇	—	2	2	no	—
291	C₄²×C₇	—	2	2	no	—
292	C₄²×C₇	—	2	2	no	—
293	C₄²×C₇	—	2	4	no	—
294	C₄²×C₇	—	2	4	no	—
295	C₄²×C₇	—	2	4	no	—
296	C₄²×C₇	—	2	4	no	—
297	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
298	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
299	C₄²×C₇	C₂⁴	1	1	yes	characteristic
300	C₄²×C₇	C₂⁴	1	1	yes	characteristic
301	C₄²×C₇	C₂⁴	1	2	yes	—
302	C₂×#135	C₂²×C₇	1	1	yes	characteristic
303	C₂²×Q₁₆	C₂²×C₇	1	2	yes	—
304	Q₈²	C₂²×C₇	1	2	yes	—
305	#556	—	2	4	no	—
306	#556	—	2	2	no	—
307	#556	C₂²×C₇	1	2	yes	—
308	#556	C₂²×C₇	1	4	yes	—
309	#555	—	2	2	no	—
310	#555	C₂²×C₇	1	2	yes	—
311	D₄×Q₈	C₂²×C₇	1	2	yes	—
312	#548	C₂²×C₇	1	4	yes	—
313	#542	—	2	4	no	—
314	#542	C₂²×C₇	1	4	yes	—
315	#533	—	2	2	no	—
316	#533	C₂²×C₇	1	2	yes	—
317	#529	—	2	2	no	—
318	#529	C₂²×C₇	1	1	yes	characteristic
319	#519	C₂²×C₇	1	4	yes	—
320	C₄×#41	C₂²×C₇	1	2	yes	—
321	#500	C₂²×C₇	1	1	yes	characteristic
322	#500	C₂²×C₇	1	2	yes	—
323	#495	C₂²×C₇	1	2	yes	—
324	#494	C₂²×C₇	1	1	yes	characteristic
325	#489	C₂²×C₇	1	4	yes	—
326	#487	C₂²×C₇	1	2	yes	—
327	#485	C₂²×C₇	1	4	yes	—
328	#485	C₂²×C₇	1	4	yes	—
329	#482	C₂²×C₇	1	4	yes	—
330	#477	C₂²×C₇	1	2	yes	—
331	#477	C₂²×C₇	1	4	yes	—
332	#476	C₂²×C₇	1	2	yes	—
333	#475	C₂²×C₇	1	4	yes	—
334	#468	C₂²×C₇	1	4	yes	—
335	#467	C₂²×C₇	1	2	yes	—
336	#467	C₂²×C₇	1	2	yes	—
337	#467	C₂²×C₇	1	2	yes	—
338	#466	C₂²×C₇	1	2	yes	—
339	#464	C₂²×C₇	1	4	yes	—
340	#464	C₂²×C₇	1	4	yes	—
341	#462	C₂²×C₇	1	2	yes	—
342	#461	C₂²×C₇	1	2	yes	—
343	#452	C₂²×C₇	1	4	yes	—
344	#451	C₂²×C₇	1	4	yes	—
345	#448	C₂²×C₇	1	4	yes	—
346	#446	C₂²×C₇	1	1	yes	characteristic
347	C₈×Q₈	C₂²×C₇	1	1	yes	characteristic
348	#441	C₂²×C₇	1	4	yes	—
349	#441	C₂²×C₇	1	4	yes	—
350	#440	C₂²×C₇	1	4	yes	—
351	C₄×Q₁₆	C₂²×C₇	1	2	yes	—
352	C₄×Q₁₆	C₂²×C₇	1	2	yes	—
353	C₄×Q₁₆	C₂²×C₇	1	1	yes	characteristic
354	C₄×Q₁₆	C₂²×C₇	1	2	yes	—
355	C₄×Q₁₆	C₂²×C₇	1	2	yes	—
356	C₄×Q₁₆	C₂²×C₇	1	1	yes	characteristic
357	C₄×SD₁₆	C₂²×C₇	1	2	yes	—
358	C₄×SD₁₆	C₂²×C₇	1	2	yes	—
359	C₄×D₈	C₂²×C₇	1	1	yes	characteristic
360	C₄×D₈	C₂²×C₇	1	1	yes	characteristic
361	#436	C₂²×C₇	1	1	yes	characteristic
362	#435	C₂²×C₇	1	2	yes	—
363	C₈×D₄	C₂²×C₇	1	1	yes	characteristic
364	C₈×D₄	C₂²×C₇	1	2	yes	—
365	#433	C₂²×C₇	1	2	yes	—
366	#432	C₂²×C₇	1	1	yes	characteristic
367	#427	C₂²×C₇	1	2	yes	—
368	#427	C₂²×C₇	1	1	yes	characteristic
369	#419	C₂²×C₇	1	4	yes	—
370	#416	C₂²×C₇	1	2	yes	—
371	#405	C₂²×C₇	1	2	yes	—
372	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
373	C₂³×C₇	—	2	2	no	—
374	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
375	C₂³×C₇	C₂²×D₄	1	2	yes	—
376	C₇×Q₈	—	2	2	no	—
377	C₇×Q₈	—	2	2	no	—
378	C₇×Q₈	—	2	4	no	—
379	C₇×Q₈	—	2	4	no	—
380	C₇×Q₈	—	4	8	no	—
381	C₇×Q₈	—	8	2	no	—
382	C₇×Q₈	—	8	4	no	—
383	C₇×Q₈	C₂×#41	1	4	yes	—
384	C₇×D₄	—	2	2	no	—
385	C₇×D₄	—	2	2	no	—
386	C₇×D₄	—	2	2	no	—
387	C₇×D₄	—	4	2	no	—
388	C₇×D₄	—	4	4	no	—
389	C₇×D₄	—	8	4	no	—
390	C₂×C₄×C₇	—	2	2	no	—
391	C₂×C₄×C₇	—	2	2	no	—
392	C₂×C₄×C₇	—	2	2	no	—
393	C₂×C₄×C₇	—	2	1	no	—
394	C₂×C₄×C₇	—	2	1	no	—
395	C₂×C₄×C₇	—	2	2	no	—
396	C₂×C₄×C₇	—	2	2	no	—
397	C₂×C₄×C₇	—	2	4	no	—
398	C₂×C₄×C₇	—	2	4	no	—
399	C₂×C₄×C₇	—	2	2	no	—
400	C₂×C₄×C₇	—	4	1	no	—
401	C₂×C₄×C₇	—	4	4	no	—
402	C₂×C₄×C₇	—	4	8	no	—
403	C₂×C₄×C₇	—	4	4	no	—
404	C₂×C₄×C₇	—	8	2	no	—
405	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
406	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
407	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
408	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
409	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
410	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
411	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
412	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
413	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
414	C₇×C₈	—	2	1	no	—
415	C₇×C₈	—	2	2	no	—
416	C₇×C₈	—	2	1	no	—
417	C₇×C₈	—	2	1	no	—
418	C₇×C₈	—	2	2	no	—
419	C₇×C₈	C₂×#41	1	2	yes	—
420	C₂×#41	C₂³×C₇	1	2	yes	—
421	C₂²×Q₈	C₂³×C₇	1	4	yes	—
422	#135	—	2	4	no	—
423	C₂×Q₁₆	—	2	8	no	—
424	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
425	C₂×Q₁₆	C₂³×C₇	1	4	yes	—
426	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
427	C₂×Q₁₆	C₂³×C₇	1	1	yes	characteristic
428	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
429	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
430	C₂×D₈	C₂³×C₇	1	1	yes	characteristic
431	C₂×M₁₆	C₂³×C₇	1	2	yes	—
432	C₂²×C₈	C₂³×C₇	1	2	yes	—
433	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
434	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
435	C₄⋊Q₈	—	2	2	no	—
436	C₄⋊Q₈	—	2	2	no	—
437	C₄⋊Q₈	—	2	4	no	—
438	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
439	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
440	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
441	#126	—	2	4	no	—
442	#126	—	2	4	no	—
443	#126	—	2	4	no	—
444	#126	—	2	4	no	—
445	#126	C₇×D₄	1	2	yes	—
446	#125	—	2	2	no	—
447	#125	C₇×D₄	1	1	yes	characteristic
448	#124	—	2	4	no	—
449	#124	—	2	4	no	—
450	#124	—	2	4	no	—
451	#124	—	2	4	no	—
452	#124	C₇×D₄	1	1	yes	characteristic
453	#124	C₂³×C₇	1	4	yes	—
454	#123	—	2	4	no	—
455	#123	C₇×D₄	1	2	yes	—
456	C₂²⋊Q₈	—	2	2	no	—
457	C₂²⋊Q₈	—	2	2	no	—
458	C₂²⋊Q₈	—	2	4	no	—
459	C₂²⋊Q₈	—	2	4	no	—
460	C₂²⋊Q₈	—	2	4	no	—
461	C₂²⋊Q₈	C₇×D₄	1	1	yes	characteristic
462	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
463	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
464	#121	—	2	2	no	—
465	#121	—	2	4	no	—
466	#121	C₇×D₄	1	1	yes	characteristic
467	#121	C₂³×C₇	1	4	yes	—
468	C₄×Q₈	—	2	2	no	—
469	C₄×Q₈	—	2	4	no	—
470	C₄×Q₈	—	2	4	no	—
471	C₄×Q₈	—	2	4	no	—
472	C₄×Q₈	—	2	2	no	—
473	C₄×Q₈	C₂³×C₇	1	2	yes	—
474	C₄×Q₈	C₂³×C₇	1	2	yes	—
475	C₄×Q₈	C₂³×C₇	1	4	yes	—
476	C₄×Q₈	C₂³×C₇	1	4	yes	—
477	C₄×Q₈	C₂³×C₇	1	4	yes	—
478	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
479	C₄×D₄	—	2	2	no	—
480	C₄×D₄	—	2	2	no	—
481	C₄×D₄	—	2	2	no	—
482	C₄×D₄	—	2	4	no	—
483	C₄×D₄	C₂³×C₇	1	2	yes	—
484	C₄×D₄	C₂³×C₇	1	2	yes	—
485	C₄×D₄	C₂³×C₇	1	2	yes	—
486	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
487	#117	—	2	2	no	—
488	#117	—	2	2	no	—
489	#117	—	2	2	no	—
490	#117	—	2	4	no	—
491	#117	—	2	4	no	—
492	#117	—	2	2	no	—
493	#117	C₂³×C₇	1	2	yes	—
494	#117	C₂³×C₇	1	4	yes	—
495	#117	C₂³×C₇	1	2	yes	—
496	C₂×C₄²	—	2	2	no	—
497	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
498	#107	C₂³×C₇	1	1	yes	characteristic
499	#107	C₂³×C₇	1	1	yes	characteristic
500	#107	C₂³×C₇	1	2	yes	—
501	#107	C₂³×C₇	1	2	yes	—
502	#107	C₂³×C₇	1	4	yes	—
503	#106	C₂³×C₇	1	2	yes	—
504	#106	C₂³×C₇	1	4	yes	—
505	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
506	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
507	C₄⋊C₈	C₂³×C₇	1	2	yes	—
508	C₄⋊C₈	C₂³×C₇	1	2	yes	—
509	#103	C₂³×C₇	1	2	yes	—
510	#103	C₂³×C₇	1	2	yes	—
511	#103	C₂³×C₇	1	4	yes	—
512	#103	C₂³×C₇	1	4	yes	—
513	#103	C₂³×C₇	1	4	yes	—
514	#103	C₂³×C₇	1	4	yes	—
515	#103	C₂³×C₇	1	4	yes	—
516	#102	C₂³×C₇	1	2	yes	—
517	#102	C₂³×C₇	1	2	yes	—
518	#102	C₂³×C₇	1	4	yes	—
519	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
520	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
521	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
522	#97	C₂³×C₇	1	2	yes	—
523	#97	C₂³×C₇	1	2	yes	—
524	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
525	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
526	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
527	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
528	C₄×C₈	C₂³×C₇	1	2	yes	—
529	C₂²×C₇	—	2	1	no	—
530	C₂²×C₇	—	2	2	no	—
531	C₂²×C₇	—	2	2	no	—
532	C₂²×C₇	—	2	1	no	—
533	C₂²×C₇	—	2	1	no	—
534	C₂²×C₇	—	2	2	no	—
535	C₂²×C₇	—	4	2	no	—
536	C₂²×C₇	—	4	2	no	—
537	C₂²×C₇	—	4	2	no	—
538	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
539	C₄×C₇	—	2	1	no	—
540	C₄×C₇	—	2	1	no	—
541	C₄×C₇	—	2	2	no	—
542	C₄×C₇	—	2	1	no	—
543	C₄×C₇	—	2	2	no	—
544	C₄×C₇	—	2	4	no	—
545	C₄×C₇	—	2	1	no	—
546	C₄×C₇	—	2	2	no	—
547	C₄×C₇	—	4	2	no	—
548	C₄×C₇	—	4	4	no	—
549	C₄×C₇	—	4	4	no	—
550	C₄×C₇	—	4	2	no	—
551	C₄×C₇	#578	1	2	yes	—
552	C₄×C₇	C₂²×#41	1	1	yes	characteristic
553	C₄×C₇	#585	1	1	yes	characteristic
554	#41	—	2	4	no	—
555	#41	—	4	2	no	—
556	C₂×Q₈	—	2	4	no	—
557	C₂×Q₈	—	2	2	no	—
558	C₂×Q₈	—	2	4	no	—
559	C₂×Q₈	—	2	8	no	—
560	C₂×Q₈	—	4	4	no	—
561	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
562	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
563	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
564	C₂×D₄	—	2	2	no	—
565	C₂×D₄	—	2	4	no	—
566	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
567	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
568	C₂×D₄	C₂⁴×C₇	1	2	yes	—
569	C₂²×C₄	—	2	4	no	—
570	C₂²×C₄	—	2	2	no	—
571	C₂²×C₄	—	2	2	no	—
572	C₂²×C₄	—	2	2	no	—
573	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
574	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
575	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
576	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
577	Q₁₆	—	2	8	no	—
578	Q₁₆	—	2	4	no	—
579	Q₁₆	—	4	2	no	—
580	Q₁₆	C₇×#41	1	4	yes	—
581	SD₁₆	—	2	4	no	—
582	SD₁₆	—	4	4	no	—
583	D₈	—	2	2	no	—
584	M₁₆	—	4	2	no	—
585	C₂×C₈	—	2	4	no	—
586	C₂×C₈	—	2	2	no	—
587	C₂×C₈	—	4	1	no	—
588	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
589	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
590	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
591	C₂×C₈	C₂⁴×C₇	1	2	yes	—
592	C₂×C₈	C₂⁴×C₇	1	2	yes	—
593	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
594	C₄⋊C₄	—	2	2	no	—
595	C₄⋊C₄	—	2	2	no	—
596	C₄⋊C₄	—	2	2	no	—
597	C₄⋊C₄	—	2	2	no	—
598	C₄⋊C₄	—	2	4	no	—
599	C₄⋊C₄	—	2	4	no	—
600	C₄⋊C₄	—	2	4	no	—
601	C₄⋊C₄	—	2	4	no	—
602	C₄⋊C₄	—	2	2	no	—
603	C₄⋊C₄	—	2	4	no	—
604	C₄⋊C₄	—	2	4	no	—
605	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
606	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
607	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
608	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
609	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
610	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
611	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
612	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
613	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
614	C₂²⋊C₄	—	2	4	no	—
615	C₂²⋊C₄	—	2	4	no	—
616	C₂²⋊C₄	—	2	2	no	—
617	C₂²⋊C₄	—	2	4	no	—
618	C₂²⋊C₄	—	2	2	no	—
619	C₂²⋊C₄	—	2	2	no	—
620	C₂²⋊C₄	—	2	4	no	—
621	C₂²⋊C₄	—	2	4	no	—
622	C₂²⋊C₄	—	2	4	no	—
623	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
624	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
625	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
626	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
627	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
628	C₄²	—	2	2	no	—
629	C₄²	—	2	2	no	—
630	C₄²	—	2	2	no	—
631	C₄²	—	2	4	no	—
632	C₄²	—	2	4	no	—
633	C₄²	—	2	4	no	—
634	C₄²	—	2	4	no	—
635	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
636	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
637	C₄²	C₂⁴×C₇	1	1	yes	characteristic
638	C₄²	C₂⁴×C₇	1	1	yes	characteristic
639	C₄²	C₂⁴×C₇	1	2	yes	—
640	C₂×C₇	—	4	1	no	—
641	C₂×C₇	—	4	2	no	—
642	C₂×C₇	—	8	2	no	—
643	C₂×C₇	D₄×#41	1	1	yes	characteristic
644	C₂×C₇	C₂×#578	1	1	yes	characteristic
645	C₂×C₇	#3584	1	1	yes	characteristic
646	C₂³	—	2	2	no	—
647	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
648	C₂³	C₂²×C₇×D₄	1	2	yes	—
649	Q₈	—	2	2	no	—
650	Q₈	—	2	2	no	—
651	Q₈	—	2	4	no	—
652	Q₈	—	2	4	no	—
653	Q₈	—	4	8	no	—
654	Q₈	—	8	2	no	—
655	Q₈	—	8	4	no	—
656	Q₈	C₂×C₇×#41	1	4	yes	—
657	D₄	—	2	2	no	—
658	D₄	—	2	2	no	—
659	D₄	—	2	2	no	—
660	D₄	—	4	2	no	—
661	D₄	—	4	4	no	—
662	D₄	—	8	4	no	—
663	C₂×C₄	—	2	2	no	—
664	C₂×C₄	—	2	2	no	—
665	C₂×C₄	—	2	1	no	—
666	C₂×C₄	—	2	1	no	—
667	C₂×C₄	—	2	2	no	—
668	C₂×C₄	—	2	2	no	—
669	C₂×C₄	—	2	2	no	—
670	C₂×C₄	—	2	4	no	—
671	C₂×C₄	—	2	4	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	4	1	no	—
674	C₂×C₄	—	4	4	no	—
675	C₂×C₄	—	4	8	no	—
676	C₂×C₄	—	4	4	no	—
677	C₂×C₄	—	8	2	no	—
678	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
679	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
680	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
681	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
682	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
683	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
684	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
685	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
686	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
687	C₈	—	2	1	no	—
688	C₈	—	2	2	no	—
689	C₈	—	2	1	no	—
690	C₈	—	2	1	no	—
691	C₈	—	2	2	no	—
692	C₈	C₂×C₇×#41	1	2	yes	—
693	C₇	#61478	1	1	yes	characteristic, direct product factor, Sylow
694	C₂²	—	2	1	no	—
695	C₂²	—	2	2	no	—
696	C₂²	—	2	1	no	—
697	C₂²	—	2	2	no	—
698	C₂²	—	2	2	no	—
699	C₂²	—	2	1	no	—
700	C₂²	—	4	2	no	—
701	C₂²	—	4	2	no	—
702	C₂²	—	4	2	no	—
703	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
704	C₄	—	2	1	no	—
705	C₄	—	2	2	no	—
706	C₄	—	2	1	no	—
707	C₄	—	2	1	no	—
708	C₄	—	2	2	no	—
709	C₄	—	2	1	no	—
710	C₄	—	2	2	no	—
711	C₄	—	2	4	no	—
712	C₄	—	4	2	no	—
713	C₄	—	4	2	no	—
714	C₄	—	4	4	no	—
715	C₄	—	4	4	no	—
716	C₄	C₇×#578	1	2	yes	—
717	C₄	C₂²×C₇×#41	1	1	yes	characteristic
718	C₄	C₇×#585	1	1	yes	characteristic
719	C₂	—	4	1	no	—
720	C₂	—	4	2	no	—
721	C₂	—	8	2	no	—
722	C₂	C₇×D₄×#41	1	1	yes	characteristic
723	C₂	C₂×C₇×#578	1	1	yes	characteristic
724	C₂	C₇×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₇×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3518	C₂	semidirect
2. C₇×#3393	C₂	semidirect
3. C₇×Q₈×Q₁₆	C₂	semidirect
4. C₇×#3369	C₂	semidirect
5. C₇×#3342	C₂	semidirect
6. C₇×#3341	C₂	semidirect
7. C₇×#3329	C₂	semidirect
8. C₇×#3313	C₂	semidirect
9. C₇×D₄×Q₁₆	C₂	semidirect
10. C₇×#3285	C₂	semidirect
11. C₇×#3175	C₂	semidirect
12. C₇×#3170	C₂	semidirect
13. C₇×#3121	C₂	semidirect
14. C₇×#3116	C₂	semidirect
15. C₇×#2966	C₂	semidirect
16. C₇×#2950	C₂	semidirect
17. C₄×C₇×#135	C₂	semidirect
89. #61478	C₇	direct (N × H)
199. #3518	C₂×C₇	semidirect
200. #3393	C₂×C₇	semidirect
201. Q₈×Q₁₆	C₂×C₇	semidirect
202. #3369	C₂×C₇	semidirect
203. #3342	C₂×C₇	semidirect
204. #3341	C₂×C₇	semidirect
205. #3329	C₂×C₇	semidirect
206. #3313	C₂×C₇	semidirect
207. D₄×Q₁₆	C₂×C₇	semidirect
208. #3285	C₂×C₇	semidirect
209. #3175	C₂×C₇	semidirect
210. #3170	C₂×C₇	semidirect
211. #3121	C₂×C₇	semidirect
212. #3116	C₂×C₇	semidirect
213. #2966	C₂×C₇	semidirect
214. #2950	C₂×C₇	semidirect
215. C₄×#135	C₂×C₇	semidirect
693. C₇	#61478	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×#3518	2
C₇×#3393	2
C₇×Q₈×Q₁₆	2
C₇×#3369	2
C₇×#3342	2
C₇×#3341	2
C₇×#3329	2
C₇×#3313	2
C₇×D₄×Q₁₆	2
C₇×#3285	2
C₇×#3175	2
C₇×#3170	2
C₇×#3121	2
C₇×#3116	2
C₇×#2966	2
C₇×#2950	2
C₄×C₇×#135	2
#61478	7

Subgroups — C7×#61478 #13238694

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#61478 #13238694