Subgroups — C₇×#61293 #13238509

Order 1792.

1874 conjugacy classes of subgroups.

The subgroup lattice has 468 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	2	yes	maximal, complemented
2	C₇×#3347	C₂	1	8	yes	maximal, complemented
3	C₇×#3345	C₂	1	8	yes	maximal, complemented
4	C₇×#3162	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#3096	C₂	1	4	yes	maximal, complemented
6	C₇×#3077	C₂	1	2	yes	maximal, complemented
7	C₇×#3058	C₂	1	2	yes	maximal, complemented
8	C₂×C₇×#442	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#2932	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#2912	C₂	1	2	yes	maximal, complemented
11	C₂²×C₇×D₈	C₂²	1	1	yes	characteristic
12	C₂×C₇×#131	C₂²	1	2	yes	—
13	C₇×#559	—	2	4	no	—
14	C₇×#556	—	2	2	no	—
15	C₇×#555	C₂²	1	4	yes	complemented
16	C₇×#553	C₂²	1	8	yes	complemented
17	C₇×#550	—	2	2	no	—
18	C₇×#547	C₂²	1	4	yes	complemented
19	C₇×#538	—	2	4	no	—
20	C₇×#535	C₂²	1	4	yes	—
21	C₇×#533	C₂²	1	2	yes	—
22	C₇×#532	C₂²	1	1	yes	characteristic
23	C₇×#525	—	2	4	no	—
24	C₇×#520	C₂²	1	4	yes	—
25	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
26	C₇×#501	C₂²	1	4	yes	complemented
27	C₇×#501	C₂²	1	4	yes	complemented
28	C₇×#482	C₂²	1	8	yes	complemented
29	C₇×#482	C₂²	1	8	yes	complemented
30	C₇×#481	C₂²	1	8	yes	complemented
31	C₇×#480	C₂²	1	8	yes	complemented
32	C₇×#478	C₂²	1	8	yes	complemented
33	C₇×#476	C₂²	1	4	yes	complemented
34	C₇×#474	C₂²	1	4	yes	complemented
35	C₇×#469	C₂²	1	4	yes	—
36	C₇×#469	C₂²	1	4	yes	—
37	C₇×#466	C₂²	1	8	yes	—
38	C₇×#442	C₂²	1	8	yes	—
39	C₇×#435	C₂²	1	8	yes	complemented
40	C₇×#428	C₂²	1	4	yes	—
41	C₇×#428	C₂²	1	8	yes	complemented
42	C₇×#427	C₂²	1	2	yes	—
43	C₇×#427	C₂²	1	2	yes	—
44	C₇×#427	C₂²	1	4	yes	complemented
45	C₂×C₇×#106	C₂²	1	1	yes	characteristic
46	C₂×C₇×#106	C₂²	1	4	yes	complemented
47	C₇×#423	C₂²	1	1	yes	characteristic
48	C₇×#418	C₂²	1	4	yes	—
49	C₂×C₇×#102	C₂²	1	2	yes	—
50	C₇×#408	C₂²	1	2	yes	—
51	C₂×C₇×#97	C₂²	1	1	yes	characteristic
52	#61293	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
53	C₂×C₇×#41	—	2	4	no	—
54	C₂×C₇×#41	C₂³	1	2	yes	—
55	C₂²×C₇×D₄	C₂³	1	2	yes	—
56	C₂³×C₄×C₇	—	2	2	no	—
57	C₂×C₇×D₈	—	2	4	no	—
58	C₂×C₇×D₈	C₂³	1	4	yes	—
59	C₇×#131	—	2	8	no	—
60	C₂×C₇×M₁₆	C₂³	1	4	yes	—
61	C₂×C₇×M₁₆	C₂³	1	2	yes	—
62	C₂²×C₇×C₈	C₂³	1	4	yes	—
63	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
64	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
65	C₇×C₄⋊Q₈	D₄	1	1	yes	characteristic
66	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
67	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
68	C₇×#127	—	2	4	no	—
69	C₇×#127	D₄	1	1	yes	characteristic
70	C₇×#126	—	2	8	no	—
71	C₇×#125	C₂³	1	4	yes	—
72	C₇×#124	—	2	4	no	—
73	C₇×#124	—	2	8	no	—
74	C₇×#124	D₄	1	2	yes	—
75	C₇×#123	—	2	8	no	—
76	C₇×#123	—	2	8	no	—
77	C₇×C₂²⋊Q₈	—	2	2	no	—
78	C₇×C₂²⋊Q₈	—	2	2	no	—
79	C₇×C₂²⋊Q₈	—	2	4	no	—
80	C₇×#121	—	2	4	no	—
81	C₇×#121	—	2	8	no	—
82	C₇×#121	D₄	1	4	yes	—
83	C₇×#121	C₂³	1	8	yes	—
84	C₇×#121	C₂³	1	8	yes	—
85	C₇×#120	—	2	8	no	—
86	C₄×C₇×Q₈	—	2	4	no	—
87	C₄×C₇×Q₈	—	2	2	no	—
88	C₄×C₇×Q₈	—	2	2	no	—
89	C₄×C₇×D₄	—	2	8	no	—
90	C₄×C₇×D₄	—	2	4	no	—
91	C₄×C₇×D₄	—	2	8	no	—
92	C₄×C₇×D₄	—	2	2	no	—
93	C₄×C₇×D₄	—	2	2	no	—
94	C₄×C₇×D₄	C₂³	1	4	yes	—
95	C₄×C₇×D₄	C₂³	1	4	yes	—
96	C₄×C₇×D₄	C₂³	1	4	yes	—
97	C₇×#117	—	2	4	no	—
98	C₇×#117	C₂³	1	8	yes	—
99	C₇×#117	C₂³	1	4	yes	—
100	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	—
101	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
102	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
103	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
104	C₇×#107	C₂³	1	4	yes	—
105	C₇×#107	C₂³	1	8	yes	—
106	C₇×#107	C₂³	1	4	yes	—
107	C₇×#106	C₂³	1	2	yes	—
108	C₇×#106	C₂³	1	2	yes	—
109	C₇×#106	C₂³	1	8	yes	—
110	C₇×#106	C₂³	1	2	yes	—
111	C₇×#106	C₂³	1	2	yes	—
112	C₇×#106	C₂³	1	4	yes	—
113	C₇×C₄⋊C₈	C₂³	1	4	yes	—
114	C₇×#102	C₂³	1	8	yes	—
115	C₇×#102	C₂³	1	8	yes	—
116	C₇×#102	C₂³	1	8	yes	—
117	C₇×C₂²⋊C₈	C₂³	1	8	yes	—
118	C₇×#97	C₂³	1	4	yes	—
119	#3506	C₂×C₇	1	2	yes	complemented
120	#3347	C₂×C₇	1	8	yes	complemented
121	#3345	C₂×C₇	1	8	yes	complemented
122	#3162	C₂×C₇	1	1	yes	characteristic, complemented
123	#3096	C₂×C₇	1	4	yes	complemented
124	#3077	C₂×C₇	1	2	yes	complemented
125	#3058	C₂×C₇	1	2	yes	complemented
126	C₂×#442	C₂×C₇	1	1	yes	characteristic, complemented
127	#2932	C₂×C₇	1	1	yes	characteristic, complemented
128	#2912	C₂×C₇	1	2	yes	complemented
129	C₂⁴×C₇	—	2	2	no	—
130	C₇×#41	—	2	4	no	—
131	C₇×#41	—	2	4	no	—
132	C₇×#41	—	8	8	no	—
133	C₂×C₇×Q₈	—	2	2	no	—
134	C₂×C₇×Q₈	—	2	2	no	—
135	C₂×C₇×Q₈	C₂×D₄	1	2	yes	—
136	C₂×C₇×D₄	—	2	8	no	—
137	C₂×C₇×D₄	—	2	8	no	—
138	C₂×C₇×D₄	—	2	2	no	—
139	C₂×C₇×D₄	—	2	4	no	—
140	C₂×C₇×D₄	—	2	4	no	—
141	C₂×C₇×D₄	C₂×D₄	1	4	yes	—
142	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
143	C₂×C₇×D₄	C₂×D₄	1	4	yes	—
144	C₂×C₇×D₄	C₂⁴	1	4	yes	—
145	C₂²×C₄×C₇	—	2	2	no	—
146	C₂²×C₄×C₇	—	2	8	no	—
147	C₂²×C₄×C₇	—	2	4	no	—
148	C₂²×C₄×C₇	—	2	4	no	—
149	C₂²×C₄×C₇	—	8	4	no	—
150	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
151	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
152	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
153	C₇×D₈	—	2	8	no	—
154	C₇×M₁₆	—	2	4	no	—
155	C₇×M₁₆	—	2	8	no	—
156	C₂×C₇×C₈	—	2	2	no	—
157	C₂×C₇×C₈	—	2	8	no	—
158	C₂×C₇×C₈	#41	1	4	yes	complemented
159	C₂×C₇×C₈	C₂⁴	1	2	yes	—
160	C₂×C₇×C₈	C₂⁴	1	4	yes	—
161	C₂×C₇×C₈	C₂⁴	1	2	yes	—
162	C₇×C₄⋊C₄	—	2	2	no	—
163	C₇×C₄⋊C₄	—	2	8	no	—
164	C₇×C₄⋊C₄	—	2	2	no	—
165	C₇×C₄⋊C₄	—	2	4	no	—
166	C₇×C₄⋊C₄	—	2	4	no	—
167	C₇×C₄⋊C₄	—	2	2	no	—
168	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
169	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
170	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
171	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
172	C₇×C₂²⋊C₄	—	2	4	no	—
173	C₇×C₂²⋊C₄	—	2	8	no	—
174	C₇×C₂²⋊C₄	—	2	4	no	—
175	C₇×C₂²⋊C₄	—	2	4	no	—
176	C₇×C₂²⋊C₄	—	2	8	no	—
177	C₇×C₂²⋊C₄	—	2	8	no	—
178	C₇×C₂²⋊C₄	C₂×D₄	1	8	yes	—
179	C₄²×C₇	—	2	8	no	—
180	C₄²×C₇	—	2	4	no	—
181	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
182	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
183	C₄²×C₇	C₂⁴	1	2	yes	—
184	C₂²×D₈	C₂²×C₇	1	1	yes	characteristic
185	C₂×#131	C₂²×C₇	1	2	yes	—
186	#559	—	2	4	no	—
187	#556	—	2	2	no	—
188	#555	C₂²×C₇	1	4	yes	complemented
189	#553	C₂²×C₇	1	8	yes	complemented
190	#550	—	2	2	no	—
191	#547	C₂²×C₇	1	4	yes	complemented
192	#538	—	2	4	no	—
193	#535	C₂²×C₇	1	4	yes	—
194	#533	C₂²×C₇	1	2	yes	—
195	#532	C₂²×C₇	1	1	yes	characteristic
196	#525	—	2	4	no	—
197	#520	C₂²×C₇	1	4	yes	—
198	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
199	#501	C₂²×C₇	1	4	yes	complemented
200	#501	C₂²×C₇	1	4	yes	complemented
201	#482	C₂²×C₇	1	8	yes	complemented
202	#482	C₂²×C₇	1	8	yes	complemented
203	#481	C₂²×C₇	1	8	yes	complemented
204	#480	C₂²×C₇	1	8	yes	complemented
205	#478	C₂²×C₇	1	8	yes	complemented
206	#476	C₂²×C₇	1	4	yes	complemented
207	#474	C₂²×C₇	1	4	yes	complemented
208	#469	C₂²×C₇	1	4	yes	—
209	#469	C₂²×C₇	1	4	yes	—
210	#466	C₂²×C₇	1	8	yes	—
211	#442	C₂²×C₇	1	8	yes	—
212	#435	C₂²×C₇	1	8	yes	complemented
213	#428	C₂²×C₇	1	4	yes	—
214	#428	C₂²×C₇	1	8	yes	complemented
215	#427	C₂²×C₇	1	2	yes	—
216	#427	C₂²×C₇	1	2	yes	—
217	#427	C₂²×C₇	1	4	yes	complemented
218	C₂×#106	C₂²×C₇	1	1	yes	characteristic
219	C₂×#106	C₂²×C₇	1	4	yes	complemented
220	#423	C₂²×C₇	1	1	yes	characteristic
221	#418	C₂²×C₇	1	4	yes	—
222	C₂×#102	C₂²×C₇	1	2	yes	—
223	#408	C₂²×C₇	1	2	yes	—
224	C₂×#97	C₂²×C₇	1	1	yes	characteristic
225	C₂³×C₇	—	2	4	no	—
226	C₂³×C₇	—	4	4	no	—
227	C₂³×C₇	—	8	2	no	—
228	C₂³×C₇	—	8	2	no	—
229	C₂³×C₇	C₂²×D₄	1	4	yes	—
230	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
231	C₇×Q₈	—	2	4	no	—
232	C₇×Q₈	—	4	4	no	—
233	C₇×Q₈	—	8	2	no	—
234	C₇×D₄	—	2	8	no	—
235	C₇×D₄	—	2	4	no	—
236	C₇×D₄	—	2	4	no	—
237	C₇×D₄	—	2	4	no	—
238	C₇×D₄	—	4	4	no	—
239	C₇×D₄	—	4	4	no	—
240	C₇×D₄	—	8	8	no	—
241	C₇×D₄	—	8	8	no	—
242	C₂×C₄×C₇	—	2	4	no	—
243	C₂×C₄×C₇	—	2	4	no	—
244	C₂×C₄×C₇	—	2	4	no	—
245	C₂×C₄×C₇	—	2	4	no	—
246	C₂×C₄×C₇	—	2	4	no	—
247	C₂×C₄×C₇	—	4	2	no	—
248	C₂×C₄×C₇	—	4	8	no	—
249	C₂×C₄×C₇	—	8	4	no	—
250	C₂×C₄×C₇	—	8	2	no	—
251	C₂×C₄×C₇	—	8	8	no	—
252	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
253	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
254	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
255	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
256	C₂×C₄×C₇	C₂×#41	1	2	yes	—
257	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
258	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
259	C₇×C₈	—	2	4	no	—
260	C₇×C₈	—	2	2	no	—
261	C₇×C₈	C₂×#41	1	4	yes	—
262	C₂×#41	—	2	4	no	—
263	C₂×#41	C₂³×C₇	1	2	yes	—
264	C₂²×D₄	C₂³×C₇	1	2	yes	—
265	C₂³×C₄	—	2	2	no	—
266	C₂×D₈	—	2	4	no	—
267	C₂×D₈	C₂³×C₇	1	4	yes	—
268	#131	—	2	8	no	—
269	C₂×M₁₆	C₂³×C₇	1	2	yes	—
270	C₂×M₁₆	C₂³×C₇	1	4	yes	—
271	C₂²×C₈	C₂³×C₇	1	4	yes	—
272	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
273	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
274	C₄⋊Q₈	C₇×D₄	1	1	yes	characteristic
275	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
276	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
277	#127	—	2	4	no	—
278	#127	C₇×D₄	1	1	yes	characteristic
279	#126	—	2	8	no	—
280	#125	C₂³×C₇	1	4	yes	—
281	#124	—	2	4	no	—
282	#124	—	2	8	no	—
283	#124	C₇×D₄	1	2	yes	—
284	#123	—	2	8	no	—
285	#123	—	2	8	no	—
286	C₂²⋊Q₈	—	2	2	no	—
287	C₂²⋊Q₈	—	2	2	no	—
288	C₂²⋊Q₈	—	2	4	no	—
289	#121	—	2	4	no	—
290	#121	—	2	8	no	—
291	#121	C₇×D₄	1	4	yes	—
292	#121	C₂³×C₇	1	8	yes	—
293	#121	C₂³×C₇	1	8	yes	—
294	#120	—	2	8	no	—
295	C₄×Q₈	—	2	4	no	—
296	C₄×Q₈	—	2	2	no	—
297	C₄×Q₈	—	2	2	no	—
298	C₄×D₄	—	2	8	no	—
299	C₄×D₄	—	2	4	no	—
300	C₄×D₄	—	2	8	no	—
301	C₄×D₄	—	2	2	no	—
302	C₄×D₄	—	2	2	no	—
303	C₄×D₄	C₂³×C₇	1	4	yes	—
304	C₄×D₄	C₂³×C₇	1	4	yes	—
305	C₄×D₄	C₂³×C₇	1	4	yes	—
306	#117	—	2	4	no	—
307	#117	C₂³×C₇	1	4	yes	—
308	#117	C₂³×C₇	1	8	yes	—
309	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
310	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	—
311	C₂×C₂²⋊C₄	—	2	2	no	—
312	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
313	#107	C₂³×C₇	1	4	yes	—
314	#107	C₂³×C₇	1	4	yes	—
315	#107	C₂³×C₇	1	8	yes	—
316	#106	C₂³×C₇	1	4	yes	—
317	#106	C₂³×C₇	1	2	yes	—
318	#106	C₂³×C₇	1	8	yes	—
319	#106	C₂³×C₇	1	2	yes	—
320	#106	C₂³×C₇	1	2	yes	—
321	#106	C₂³×C₇	1	2	yes	—
322	C₄⋊C₈	C₂³×C₇	1	4	yes	—
323	#102	C₂³×C₇	1	8	yes	—
324	#102	C₂³×C₇	1	8	yes	—
325	#102	C₂³×C₇	1	8	yes	—
326	C₂²⋊C₈	C₂³×C₇	1	8	yes	—
327	#97	C₂³×C₇	1	4	yes	—
328	C₂²×C₇	—	2	2	no	—
329	C₂²×C₇	—	2	8	no	—
330	C₂²×C₇	—	2	4	no	—
331	C₂²×C₇	—	4	4	no	—
332	C₂²×C₇	—	4	4	no	—
333	C₂²×C₇	—	4	4	no	—
334	C₂²×C₇	—	8	8	no	—
335	C₂²×C₇	#547	1	2	yes	—
336	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
337	C₄×C₇	—	2	2	no	—
338	C₄×C₇	—	2	2	no	—
339	C₄×C₇	—	2	4	no	—
340	C₄×C₇	—	4	4	no	—
341	C₄×C₇	—	4	4	no	—
342	C₄×C₇	—	4	4	no	—
343	C₄×C₇	#547	1	2	yes	—
344	C₄×C₇	C₂²×#41	1	1	yes	characteristic
345	C₄×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
346	C₂⁴	—	2	2	no	—
347	#41	—	2	4	no	—
348	#41	—	2	4	no	—
349	#41	—	8	8	no	—
350	C₂×Q₈	—	2	2	no	—
351	C₂×Q₈	—	2	2	no	—
352	C₂×Q₈	C₂×C₇×D₄	1	2	yes	—
353	C₂×D₄	—	2	8	no	—
354	C₂×D₄	—	2	8	no	—
355	C₂×D₄	—	2	2	no	—
356	C₂×D₄	—	2	4	no	—
357	C₂×D₄	—	2	4	no	—
358	C₂×D₄	C₂×C₇×D₄	1	4	yes	—
359	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
360	C₂×D₄	C₂×C₇×D₄	1	4	yes	—
361	C₂×D₄	C₂⁴×C₇	1	4	yes	—
362	C₂²×C₄	—	2	2	no	—
363	C₂²×C₄	—	2	8	no	—
364	C₂²×C₄	—	2	4	no	—
365	C₂²×C₄	—	2	4	no	—
366	C₂²×C₄	—	8	4	no	—
367	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
368	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
369	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
370	D₈	—	2	8	no	—
371	M₁₆	—	2	4	no	—
372	M₁₆	—	2	8	no	—
373	C₂×C₈	—	2	2	no	—
374	C₂×C₈	—	2	8	no	—
375	C₂×C₈	C₇×#41	1	4	yes	complemented
376	C₂×C₈	C₂⁴×C₇	1	2	yes	—
377	C₂×C₈	C₂⁴×C₇	1	4	yes	—
378	C₂×C₈	C₂⁴×C₇	1	2	yes	—
379	C₄⋊C₄	—	2	2	no	—
380	C₄⋊C₄	—	2	8	no	—
381	C₄⋊C₄	—	2	2	no	—
382	C₄⋊C₄	—	2	4	no	—
383	C₄⋊C₄	—	2	4	no	—
384	C₄⋊C₄	—	2	2	no	—
385	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
386	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
387	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
388	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
389	C₂²⋊C₄	—	2	4	no	—
390	C₂²⋊C₄	—	2	8	no	—
391	C₂²⋊C₄	—	2	4	no	—
392	C₂²⋊C₄	—	2	4	no	—
393	C₂²⋊C₄	—	2	8	no	—
394	C₂²⋊C₄	—	2	8	no	—
395	C₂²⋊C₄	C₂×C₇×D₄	1	8	yes	—
396	C₄²	—	2	8	no	—
397	C₄²	—	2	4	no	—
398	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
399	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
400	C₄²	C₂⁴×C₇	1	2	yes	—
401	C₂×C₇	—	2	2	no	—
402	C₂×C₇	—	4	4	no	—
403	C₂×C₇	—	8	4	no	—
404	C₂×C₇	C₂×#547	1	1	yes	characteristic
405	C₂×C₇	#3585	1	2	yes	—
406	C₂³	—	2	4	no	—
407	C₂³	—	4	4	no	—
408	C₂³	—	8	2	no	—
409	C₂³	—	8	2	no	—
410	C₂³	C₂²×C₇×D₄	1	4	yes	—
411	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
412	Q₈	—	2	4	no	—
413	Q₈	—	4	4	no	—
414	Q₈	—	8	2	no	—
415	D₄	—	2	8	no	—
416	D₄	—	2	4	no	—
417	D₄	—	2	4	no	—
418	D₄	—	2	4	no	—
419	D₄	—	4	4	no	—
420	D₄	—	4	4	no	—
421	D₄	—	8	8	no	—
422	D₄	—	8	8	no	—
423	C₂×C₄	—	2	4	no	—
424	C₂×C₄	—	2	4	no	—
425	C₂×C₄	—	2	4	no	—
426	C₂×C₄	—	2	4	no	—
427	C₂×C₄	—	2	4	no	—
428	C₂×C₄	—	4	2	no	—
429	C₂×C₄	—	4	8	no	—
430	C₂×C₄	—	8	4	no	—
431	C₂×C₄	—	8	2	no	—
432	C₂×C₄	—	8	8	no	—
433	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
434	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
435	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
436	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
437	C₂×C₄	C₂×C₇×#41	1	2	yes	—
438	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
439	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
440	C₈	—	2	4	no	—
441	C₈	—	2	2	no	—
442	C₈	C₂×C₇×#41	1	4	yes	—
443	C₇	#61293	1	1	yes	characteristic, direct product factor, Sylow
444	C₂²	—	2	2	no	—
445	C₂²	—	2	8	no	—
446	C₂²	—	2	4	no	—
447	C₂²	—	4	4	no	—
448	C₂²	—	4	4	no	—
449	C₂²	—	4	4	no	—
450	C₂²	—	8	8	no	—
451	C₂²	C₇×#547	1	2	yes	—
452	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
453	C₄	—	2	2	no	—
454	C₄	—	2	2	no	—
455	C₄	—	2	4	no	—
456	C₄	—	4	4	no	—
457	C₄	—	4	4	no	—
458	C₄	—	4	4	no	—
459	C₄	C₇×#547	1	2	yes	—
460	C₄	C₂²×C₇×#41	1	1	yes	characteristic
461	C₄	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
462	C₂	—	2	2	no	—
463	C₂	—	4	4	no	—
464	C₂	—	8	4	no	—
465	C₂	C₂×C₇×#547	1	1	yes	characteristic
466	C₂	C₇×#3585	1	2	yes	—

	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×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3506	C₂	semidirect
2. C₇×#3347	C₂	semidirect
3. C₇×#3345	C₂	semidirect
4. C₇×#3162	C₂	semidirect
5. C₇×#3096	C₂	semidirect
6. C₇×#3077	C₂	semidirect
7. C₇×#3058	C₂	semidirect
8. C₂×C₇×#442	C₂	semidirect
9. C₇×#2932	C₂	semidirect
10. C₇×#2912	C₂	semidirect
15. C₇×#555	C₂²	semidirect
16. C₇×#553	C₂²	semidirect
18. C₇×#547	C₂²	semidirect
26. C₇×#501	C₂²	semidirect
27. C₇×#501	C₂²	semidirect
28. C₇×#482	C₂²	semidirect
29. C₇×#482	C₂²	semidirect
30. C₇×#481	C₂²	semidirect
31. C₇×#480	C₂²	semidirect
32. C₇×#478	C₂²	semidirect
33. C₇×#476	C₂²	semidirect
34. C₇×#474	C₂²	semidirect
39. C₇×#435	C₂²	semidirect
41. C₇×#428	C₂²	semidirect
44. C₇×#427	C₂²	semidirect
46. C₂×C₇×#106	C₂²	semidirect
52. #61293	C₇	direct (N × H)
119. #3506	C₂×C₇	semidirect
120. #3347	C₂×C₇	semidirect
121. #3345	C₂×C₇	semidirect
122. #3162	C₂×C₇	semidirect
123. #3096	C₂×C₇	semidirect
124. #3077	C₂×C₇	semidirect
125. #3058	C₂×C₇	semidirect
126. C₂×#442	C₂×C₇	semidirect
127. #2932	C₂×C₇	semidirect
128. #2912	C₂×C₇	semidirect
158. C₂×C₇×C₈	#41	semidirect
188. #555	C₂²×C₇	semidirect
189. #553	C₂²×C₇	semidirect
191. #547	C₂²×C₇	semidirect
199. #501	C₂²×C₇	semidirect
200. #501	C₂²×C₇	semidirect
201. #482	C₂²×C₇	semidirect
202. #482	C₂²×C₇	semidirect
203. #481	C₂²×C₇	semidirect
204. #480	C₂²×C₇	semidirect
205. #478	C₂²×C₇	semidirect
206. #476	C₂²×C₇	semidirect
207. #474	C₂²×C₇	semidirect
212. #435	C₂²×C₇	semidirect
214. #428	C₂²×C₇	semidirect
217. #427	C₂²×C₇	semidirect
219. C₂×#106	C₂²×C₇	semidirect
375. C₂×C₈	C₇×#41	semidirect
443. C₇	#61293	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×#3347	2
C₇×#3345	2
C₇×#3162	2
C₇×#3096	2
C₇×#3077	2
C₇×#3058	2
C₂×C₇×#442	2
C₇×#2932	2
C₇×#2912	2
#61293	7

Subgroups — C7×#61293 #13238509

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#61293 #13238509