Subgroups — #11743313

Order 896.

1232 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#532	C₂	1	1	yes	maximal, characteristic, complemented
2	#90525	C₂	1	2	yes	maximal, complemented
3	#90520	C₂	1	2	yes	maximal, complemented
4	#90419	C₂	1	1	yes	maximal, characteristic, complemented
5	#90416	C₂	1	1	yes	maximal, characteristic, complemented
6	#90407	C₂	1	1	yes	maximal, characteristic, complemented
7	D₇×#127	C₂	1	1	yes	maximal, characteristic, complemented
8	#90372	C₂	1	2	yes	maximal, complemented
9	#90367	C₂	1	2	yes	maximal, complemented
10	#90310	C₂	1	2	yes	maximal, complemented
11	#90303	C₂	1	2	yes	maximal, complemented
12	#90298	C₂	1	2	yes	maximal, complemented
13	#90290	C₂	1	2	yes	maximal, complemented
14	#90253	C₂	1	2	yes	maximal, complemented
15	#90250	C₂	1	2	yes	maximal, complemented
16	#90245	C₂	1	2	yes	maximal, complemented
17	#90236	C₂	1	2	yes	maximal, complemented
18	#90168	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×#1157	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₇×#41	C₂²	1	2	yes	complemented
21	C₂×#1161	C₂²	1	2	yes	complemented
22	C₂×#1159	C₂²	1	2	yes	complemented
23	C₂×D₄×D₇	C₂²	1	2	yes	—
24	C₂×D₄×D₇	C₂²	1	2	yes	—
25	C₂×D₄×D₇	C₂²	1	2	yes	—
26	C₂×#1157	C₂²	1	1	yes	characteristic
27	C₂×#1157	C₂²	1	2	yes	complemented
28	C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
29	C₇×#127	C₂²	1	1	yes	characteristic
30	C₇×#124	C₂²	1	2	yes	complemented
31	C₇×#121	C₂²	1	2	yes	complemented
32	C₇×#121	C₂²	1	2	yes	complemented
33	C₄×C₇×D₄	C₂²	1	2	yes	complemented
34	C₄×C₇×D₄	C₂²	1	2	yes	complemented
35	C₂×C₄²×C₇	C₂²	1	1	yes	characteristic, complemented
36	#6510	C₂²	1	2	yes	complemented
37	#6509	C₂²	1	2	yes	—
38	Q₈×Dic₇	C₂²	1	2	yes	complemented
39	#6503	C₂²	1	2	yes	—
40	#6503	C₂²	1	2	yes	—
41	#6503	C₂²	1	2	yes	—
42	#6503	C₂²	1	4	yes	complemented
43	#6502	C₂²	1	4	yes	complemented
44	#6501	C₂²	1	2	yes	complemented
45	#6501	C₂²	1	2	yes	complemented
46	#6501	C₂²	1	4	yes	complemented
47	#6500	C₂²	1	4	yes	—
48	#6499	C₂²	1	2	yes	complemented
49	D₄×Dic₇	C₂²	1	2	yes	complemented
50	D₄×Dic₇	C₂²	1	2	yes	complemented
51	#6493	C₂²	1	2	yes	complemented
52	#6493	C₂²	1	2	yes	complemented
53	#6493	C₂²	1	4	yes	complemented
54	#6492	C₂²	1	4	yes	complemented
55	C₄×C₂²⋊D₇	C₂²	1	1	yes	characteristic
56	C₄×C₂²⋊D₇	C₂²	1	1	yes	characteristic
57	C₄×C₂²⋊D₇	C₂²	1	1	yes	characteristic, complemented
58	C₄×C₂²⋊D₇	C₂²	1	1	yes	characteristic, complemented
59	C₄×C₂²⋊D₇	C₂²	1	4	yes	complemented
60	C₂×(C₂×D₇)⋊C₄	C₂²	1	4	yes	—
61	#6489	C₂²	1	1	yes	characteristic, complemented
62	#6460	C₂²	1	2	yes	—
63	#6458	C₂²	1	2	yes	complemented
64	#6458	C₂²	1	2	yes	complemented
65	#6456	C₂²	1	2	yes	complemented
66	#6456	C₂²	1	2	yes	complemented
67	#6455	C₂²	1	2	yes	—
68	#6453	C₂²	1	2	yes	complemented
69	#6450	C₂²	1	2	yes	complemented
70	#6449	C₂²	1	4	yes	complemented
71	#6448	C₂²	1	4	yes	complemented
72	#6447	C₂²	1	4	yes	complemented
73	#6446	C₂²	1	4	yes	complemented
74	#6446	C₂²	1	4	yes	complemented
75	#6445	C₂²	1	4	yes	—
76	(C₂²⋊D₇)⋊C₄	C₂²	1	4	yes	complemented
77	D₇×C₂²⋊C₄	C₂²	1	4	yes	—
78	#6438	C₂²	1	2	yes	complemented
79	#6437	C₂²	1	1	yes	characteristic
80	C₄×D₂₈	C₂²	1	1	yes	characteristic
81	C₄×D₂₈	C₂²	1	1	yes	characteristic
82	C₄×D₂₈	C₂²	1	2	yes	complemented
83	C₄×D₂₈	C₂²	1	2	yes	complemented
84	#6435	C₂²	1	1	yes	characteristic
85	#6435	C₂²	1	1	yes	characteristic, complemented
86	C₄²×D₇	C₂²	1	1	yes	characteristic
87	C₄²×D₇	C₂²	1	1	yes	characteristic, complemented
88	#6432	C₂²	1	1	yes	characteristic, complemented
89	C₄×Dic₁₄	C₂²	1	1	yes	characteristic, complemented
90	C₄×Dic₁₄	C₂²	1	1	yes	characteristic, complemented
91	#3508	—	7	1	no	maximal, Sylow
92	C₂³×D₇	C₂³	1	4	yes	—
93	C₇×#41	—	4	4	no	—
94	C₂×C₇×Q₈	C₂³	1	2	yes	—
95	C₂×C₇×D₄	C₂³	1	2	yes	—
96	C₂×C₇×D₄	C₂³	1	2	yes	—
97	C₂×C₇×D₄	C₂³	1	2	yes	—
98	C₂×C₇×D₄	C₂³	1	4	yes	—
99	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
100	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
101	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
102	C₂²×C₄×C₇	C₂³	1	4	yes	—
103	C₂×C₂²⋊D₇	C₂³	1	4	yes	—
104	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
105	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
106	C₂×C₂²⋊D₇	C₂³	1	4	yes	—
107	C₂×C₂²⋊D₇	C₂³	1	4	yes	—
108	C₂×C₂²⋊D₇	C₂³	1	4	yes	—
109	C₂×C₂²⋊D₇	C₂³	1	4	yes	—
110	C₂²×Dic₇	C₂³	1	4	yes	—
111	#1161	—	4	4	no	—
112	#1159	—	4	4	no	—
113	D₄×D₇	—	2	8	no	—
114	D₄×D₇	—	4	4	no	—
115	D₄×D₇	—	4	4	no	—
116	#1157	—	2	4	no	—
117	#1157	—	4	4	no	—
118	C₂×D₂₈	C₂³	1	1	yes	characteristic
119	C₂×D₂₈	C₂³	1	2	yes	—
120	C₂×D₂₈	C₂³	1	2	yes	—
121	C₂×D₂₈	C₂³	1	2	yes	—
122	C₂×D₂₈	C₂³	1	4	yes	—
123	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
124	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
125	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
126	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
127	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
128	C₂×C₄×D₇	C₂³	1	4	yes	—
129	C₂×C₄×D₇	C₂³	1	4	yes	—
130	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
131	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
132	C₂×Dic₁₄	C₂³	1	2	yes	—
133	C₇×C₄⋊C₄	C₂³	1	2	yes	—
134	C₇×C₄⋊C₄	C₂³	1	2	yes	—
135	C₇×C₂²⋊C₄	C₂³	1	4	yes	—
136	C₇×C₂²⋊C₄	C₂³	1	4	yes	—
137	C₄²×C₇	C₂³	1	1	yes	characteristic
138	C₄²×C₇	C₂³	1	1	yes	characteristic
139	C₄²×C₇	C₂³	1	1	yes	characteristic
140	C₄²×C₇	C₂³	1	1	yes	characteristic
141	C₂²⋊Dic₇	C₂³	1	4	yes	—
142	C₂²⋊Dic₇	C₂³	1	4	yes	—
143	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
144	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
145	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
146	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
147	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
148	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
149	(C₂×D₇)⋊C₄	C₂³	1	4	yes	—
150	(C₂×D₇)⋊C₄	C₂³	1	4	yes	—
151	(C₂×D₇)⋊C₄	C₂³	1	4	yes	—
152	(C₂×D₇)⋊C₄	C₂³	1	4	yes	—
153	(C₂×D₇)⋊C₄	C₂³	1	4	yes	—
154	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
155	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
156	C₄⋊Dic₇	C₂³	1	2	yes	—
157	C₄⋊Dic₇	C₂³	1	2	yes	—
158	C₄⋊Dic₇	C₂³	1	4	yes	—
159	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
160	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
161	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
162	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
163	Dic₇⋊C₄	C₂³	1	4	yes	—
164	C₄×Dic₇	C₂³	1	1	yes	characteristic
165	C₄×Dic₇	C₂³	1	1	yes	characteristic
166	C₄×Dic₇	C₂³	1	1	yes	characteristic
167	C₄×Dic₇	C₂³	1	1	yes	characteristic
168	C₄×Dic₇	C₂³	1	1	yes	characteristic
169	C₄×Dic₇	C₂³	1	1	yes	characteristic
170	C₄×Dic₇	C₂³	1	4	yes	—
171	#559	—	7	2	no	—
172	#559	—	7	2	no	—
173	#550	—	7	2	no	—
174	#550	—	7	2	no	—
175	#546	—	7	2	no	—
176	#546	—	7	2	no	—
177	#546	—	7	2	no	—
178	#546	—	7	2	no	—
179	#540	—	7	2	no	—
180	#540	—	7	2	no	—
181	#535	—	7	2	no	—
182	#533	—	7	1	no	—
183	#532	—	7	1	no	—
184	#532	—	7	1	no	—
185	#532	—	7	1	no	—
186	#532	D₇	1	1	yes	characteristic, complemented
187	C₂×#127	—	7	1	no	—
188	#518	—	7	2	no	—
189	C₄×#41	—	7	1	no	—
190	C₂³×C₇	C₂⁴	1	4	yes	—
191	C₂³×C₇	C₂⁴	1	1	yes	characteristic
192	C₂²×D₇	—	2	8	no	—
193	C₂²×D₇	—	4	4	no	—
194	C₂²×D₇	—	4	4	no	—
195	C₂²×D₇	C₂⁴	1	4	yes	—
196	C₂²×D₇	C₂⁴	1	1	yes	characteristic
197	C₂²×D₇	C₂⁴	1	1	yes	characteristic
198	C₇×Q₈	—	2	4	no	—
199	C₇×D₄	—	2	4	no	—
200	C₇×D₄	—	2	4	no	—
201	C₇×D₄	—	2	4	no	—
202	C₇×D₄	—	4	4	no	—
203	C₂×C₄×C₇	—	2	2	no	—
204	C₂×C₄×C₇	—	2	2	no	—
205	C₂×C₄×C₇	—	2	2	no	—
206	C₂×C₄×C₇	—	4	4	no	—
207	C₂×C₄×C₇	C₂⁴	1	4	yes	—
208	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
209	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
210	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
211	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
212	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
213	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
214	C₂²⋊D₇	—	2	2	no	—
215	C₂²⋊D₇	—	2	2	no	—
216	C₂²⋊D₇	—	2	8	no	—
217	C₂²⋊D₇	—	4	4	no	—
218	C₂²⋊D₇	—	4	4	no	—
219	C₂²⋊D₇	—	4	4	no	—
220	C₂²⋊D₇	—	4	4	no	—
221	C₂×Dic₇	—	4	4	no	—
222	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
223	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
224	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
225	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
226	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
227	C₂×Dic₇	C₂⁴	1	4	yes	—
228	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
229	D₂₈	—	2	2	no	—
230	D₂₈	—	2	4	no	—
231	D₂₈	—	2	4	no	—
232	D₂₈	—	2	4	no	—
233	D₂₈	—	4	4	no	—
234	C₄×D₇	—	2	2	no	—
235	C₄×D₇	—	2	2	no	—
236	C₄×D₇	—	2	2	no	—
237	C₄×D₇	—	2	2	no	—
238	C₄×D₇	—	2	2	no	—
239	C₄×D₇	—	4	4	no	—
240	C₄×D₇	—	4	4	no	—
241	C₄×D₇	#41	1	4	yes	complemented
242	Dic₁₄	—	2	4	no	—
243	Dic₁₄	—	2	2	no	—
244	C₂×#41	—	7	2	no	—
245	C₂×#41	—	7	2	no	—
246	C₂×#41	—	7	1	no	—
247	C₂×#41	—	7	2	no	—
248	C₂×#41	C₂×D₇	1	2	yes	complemented
249	C₂²×D₄	—	7	2	no	—
250	C₂²×D₄	—	7	2	no	—
251	C₂²×D₄	—	7	2	no	—
252	C₄⋊Q₈	—	7	1	no	—
253	C₄⋊Q₈	C₂×D₇	1	1	yes	characteristic, complemented
254	#127	—	7	2	no	—
255	#127	—	7	2	no	—
256	#127	—	7	2	no	—
257	#127	—	7	4	no	—
258	#127	—	7	1	no	—
259	#127	C₂×D₇	1	1	yes	characteristic
260	#125	—	7	2	no	—
261	#124	—	7	2	no	—
262	#124	—	7	2	no	—
263	#124	—	7	4	no	—
264	#124	—	7	2	no	—
265	#124	C₂×D₇	1	2	yes	complemented
266	#123	—	7	4	no	—
267	#123	—	7	4	no	—
268	#123	—	7	4	no	—
269	#123	—	7	4	no	—
270	C₂²⋊Q₈	—	7	2	no	—
271	C₂²⋊Q₈	—	7	2	no	—
272	#121	—	7	2	no	—
273	#121	—	7	2	no	—
274	#121	—	7	4	no	—
275	#121	—	7	4	no	—
276	#121	—	7	2	no	—
277	#121	—	7	2	no	—
278	#121	—	7	4	no	—
279	#121	—	7	2	no	—
280	#121	—	7	2	no	—
281	#121	—	7	4	no	—
282	#121	C₂×D₇	1	2	yes	complemented
283	#121	C₂×D₇	1	2	yes	complemented
284	#120	—	7	4	no	—
285	#120	—	7	4	no	—
286	C₄×Q₈	—	7	2	no	—
287	C₄×Q₈	—	7	2	no	—
288	C₄×Q₈	—	7	1	no	—
289	C₄×Q₈	—	7	1	no	—
290	C₄×D₄	—	7	2	no	—
291	C₄×D₄	—	7	2	no	—
292	C₄×D₄	—	7	1	no	—
293	C₄×D₄	—	7	1	no	—
294	C₄×D₄	—	7	1	no	—
295	C₄×D₄	—	7	1	no	—
296	C₄×D₄	—	7	4	no	—
297	C₄×D₄	—	7	2	no	—
298	C₄×D₄	—	7	2	no	—
299	C₄×D₄	—	7	4	no	—
300	C₄×D₄	—	7	1	no	—
301	C₄×D₄	—	7	1	no	—
302	C₄×D₄	—	7	2	no	—
303	C₄×D₄	—	7	2	no	—
304	C₄×D₄	C₂×D₇	1	2	yes	complemented
305	C₄×D₄	C₂×D₇	1	2	yes	complemented
306	#117	—	7	1	no	—
307	#117	—	7	2	no	—
308	#117	—	7	1	no	—
309	#117	—	7	1	no	—
310	C₂×C₂²⋊C₄	—	7	4	no	—
311	C₂×C₂²⋊C₄	—	7	4	no	—
312	C₂×C₄²	—	7	1	no	—
313	C₂×C₄²	—	7	1	no	—
314	C₂×C₄²	C₂×D₇	1	1	yes	characteristic, complemented
315	C₂²×C₇	—	2	1	no	—
316	C₂²×C₇	—	2	4	no	—
317	C₂²×C₇	—	2	4	no	—
318	C₂²×C₇	—	2	1	no	—
319	C₂²×C₇	—	2	4	no	—
320	C₂²×C₇	—	2	1	no	—
321	C₂²×C₇	C₂⁵	1	1	yes	characteristic
322	C₂×D₇	—	2	1	no	—
323	C₂×D₇	—	2	1	no	—
324	C₂×D₇	—	2	1	no	—
325	C₂×D₇	—	2	4	no	—
326	C₂×D₇	—	2	1	no	—
327	C₂×D₇	—	2	1	no	—
328	C₂×D₇	—	2	4	no	—
329	C₂×D₇	—	2	4	no	—
330	C₂×D₇	—	8	8	no	—
331	C₂×D₇	C₂×#41	1	2	yes	—
332	C₄×C₇	—	2	1	no	—
333	C₄×C₇	—	2	1	no	—
334	C₄×C₇	—	2	4	no	—
335	C₄×C₇	—	2	1	no	—
336	C₄×C₇	C₂×#41	1	2	yes	—
337	C₄×C₇	H(5,𝔽₂)	1	2	yes	—
338	C₄×C₇	H(5,𝔽₂)	1	2	yes	—
339	Dic₇	—	2	1	no	—
340	Dic₇	—	2	4	no	—
341	Dic₇	—	2	1	no	—
342	Dic₇	—	2	1	no	—
343	Dic₇	—	2	1	no	—
344	Dic₇	—	2	1	no	—
345	Dic₇	C₂×#41	1	2	yes	—
346	C₂⁴	—	7	4	no	—
347	#41	—	4	4	no	—
348	#41	—	14	4	no	—
349	#41	—	28	4	no	—
350	#41	—	28	4	no	—
351	#41	—	28	4	no	—
352	C₂×Q₈	—	7	1	no	—
353	C₂×Q₈	—	7	2	no	—
354	C₂×Q₈	C₂²×D₇	1	2	yes	—
355	C₂×D₄	—	7	1	no	—
356	C₂×D₄	—	7	4	no	—
357	C₂×D₄	—	7	1	no	—
358	C₂×D₄	—	7	4	no	—
359	C₂×D₄	—	7	4	no	—
360	C₂×D₄	—	7	4	no	—
361	C₂×D₄	—	7	4	no	—
362	C₂×D₄	—	7	1	no	—
363	C₂×D₄	—	7	2	no	—
364	C₂×D₄	—	7	2	no	—
365	C₂×D₄	—	7	2	no	—
366	C₂×D₄	—	7	4	no	—
367	C₂×D₄	—	14	8	no	—
368	C₂×D₄	—	28	4	no	—
369	C₂×D₄	—	28	4	no	—
370	C₂×D₄	C₂²×D₇	1	2	yes	—
371	C₂×D₄	C₂²×D₇	1	2	yes	—
372	C₂×D₄	C₂²×D₇	1	2	yes	—
373	C₂×D₄	C₂²×D₇	1	4	yes	—
374	C₂²×C₄	—	7	1	no	—
375	C₂²×C₄	—	7	4	no	—
376	C₂²×C₄	—	7	1	no	—
377	C₂²×C₄	—	7	1	no	—
378	C₂²×C₄	—	7	1	no	—
379	C₂²×C₄	—	7	1	no	—
380	C₂²×C₄	—	7	1	no	—
381	C₂²×C₄	—	7	4	no	—
382	C₂²×C₄	—	7	4	no	—
383	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
384	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
385	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
386	C₂²×C₄	C₂²×D₇	1	4	yes	—
387	C₄⋊C₄	—	7	1	no	—
388	C₄⋊C₄	—	7	1	no	—
389	C₄⋊C₄	—	7	1	no	—
390	C₄⋊C₄	—	7	1	no	—
391	C₄⋊C₄	—	7	4	no	—
392	C₄⋊C₄	—	7	2	no	—
393	C₄⋊C₄	—	7	1	no	—
394	C₄⋊C₄	—	7	1	no	—
395	C₄⋊C₄	—	7	2	no	—
396	C₄⋊C₄	—	7	4	no	—
397	C₄⋊C₄	C₂²×D₇	1	2	yes	—
398	C₄⋊C₄	C₂²×D₇	1	2	yes	—
399	C₂²⋊C₄	—	7	4	no	—
400	C₂²⋊C₄	—	7	1	no	—
401	C₂²⋊C₄	—	7	1	no	—
402	C₂²⋊C₄	—	7	4	no	—
403	C₂²⋊C₄	—	7	1	no	—
404	C₂²⋊C₄	—	7	1	no	—
405	C₂²⋊C₄	—	7	4	no	—
406	C₂²⋊C₄	—	7	4	no	—
407	C₂²⋊C₄	—	7	4	no	—
408	C₂²⋊C₄	—	7	1	no	—
409	C₂²⋊C₄	—	7	1	no	—
410	C₂²⋊C₄	—	7	4	no	—
411	C₂²⋊C₄	—	7	4	no	—
412	C₂²⋊C₄	C₂²×D₇	1	4	yes	—
413	C₂²⋊C₄	C₂²×D₇	1	4	yes	—
414	C₄²	—	7	1	no	—
415	C₄²	—	7	1	no	—
416	C₄²	—	7	1	no	—
417	C₄²	—	7	1	no	—
418	C₄²	—	7	1	no	—
419	C₄²	—	7	1	no	—
420	C₄²	—	7	4	no	—
421	C₄²	C₂²×D₇	1	1	yes	characteristic
422	C₄²	C₂²×D₇	1	1	yes	characteristic
423	C₄²	C₂²×D₇	1	1	yes	characteristic
424	C₄²	C₂²×D₇	1	1	yes	characteristic
425	C₂×C₇	—	4	4	no	—
426	C₂×C₇	—	4	1	no	—
427	C₂×C₇	C₂²×#41	1	1	yes	characteristic
428	C₂×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
429	C₂×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
430	D₇	—	2	2	no	—
431	D₇	—	4	1	no	—
432	D₇	—	4	4	no	—
433	C₂³	—	7	1	no	—
434	C₂³	—	7	4	no	—
435	C₂³	—	7	1	no	—
436	C₂³	—	14	8	no	—
437	C₂³	—	28	4	no	—
438	C₂³	—	28	4	no	—
439	C₂³	C₂³×D₇	1	4	yes	—
440	C₂³	C₂³×D₇	1	1	yes	characteristic
441	Q₈	—	2	4	no	—
442	Q₈	—	14	2	no	—
443	Q₈	—	14	4	no	—
444	D₄	—	2	4	no	—
445	D₄	—	2	4	no	—
446	D₄	—	2	4	no	—
447	D₄	—	4	4	no	—
448	D₄	—	14	2	no	—
449	D₄	—	14	8	no	—
450	D₄	—	14	2	no	—
451	D₄	—	14	2	no	—
452	D₄	—	14	4	no	—
453	D₄	—	14	4	no	—
454	D₄	—	14	4	no	—
455	D₄	—	28	4	no	—
456	D₄	—	28	4	no	—
457	D₄	—	28	4	no	—
458	D₄	—	28	4	no	—
459	D₄	—	28	4	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	4	4	no	—
464	C₂×C₄	—	7	1	no	—
465	C₂×C₄	—	7	4	no	—
466	C₂×C₄	—	7	1	no	—
467	C₂×C₄	—	7	1	no	—
468	C₂×C₄	—	7	1	no	—
469	C₂×C₄	—	7	1	no	—
470	C₂×C₄	—	7	1	no	—
471	C₂×C₄	—	7	4	no	—
472	C₂×C₄	—	14	2	no	—
473	C₂×C₄	—	14	2	no	—
474	C₂×C₄	—	14	2	no	—
475	C₂×C₄	—	14	2	no	—
476	C₂×C₄	—	14	2	no	—
477	C₂×C₄	—	28	4	no	—
478	C₂×C₄	—	28	4	no	—
479	C₂×C₄	—	28	4	no	—
480	C₂×C₄	C₂³×D₇	1	4	yes	—
481	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
482	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
483	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
484	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
485	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
486	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
487	C₇	#3508	1	1	yes	characteristic, complemented, Sylow
488	C₂²	—	2	1	no	—
489	C₂²	—	2	4	no	—
490	C₂²	—	2	1	no	—
491	C₂²	—	2	4	no	—
492	C₂²	—	2	1	no	—
493	C₂²	—	2	4	no	—
494	C₂²	—	7	2	no	—
495	C₂²	—	14	1	no	—
496	C₂²	—	14	1	no	—
497	C₂²	—	14	1	no	—
498	C₂²	—	14	4	no	—
499	C₂²	—	14	1	no	—
500	C₂²	—	14	4	no	—
501	C₂²	—	14	1	no	—
502	C₂²	—	14	4	no	—
503	C₂²	—	56	8	no	—
504	C₂²	C₂⁴×D₇	1	1	yes	characteristic
505	C₄	—	2	1	no	—
506	C₄	—	2	4	no	—
507	C₄	—	2	1	no	—
508	C₄	—	2	1	no	—
509	C₄	—	7	2	no	—
510	C₄	—	14	1	no	—
511	C₄	—	14	1	no	—
512	C₄	—	14	1	no	—
513	C₄	—	14	1	no	—
514	C₄	—	14	1	no	—
515	C₄	—	14	4	no	—
516	C₄	#6548	1	2	yes	—
517	C₄	D₇×#41	1	2	yes	—
518	C₄	#6553	1	2	yes	—
519	C₂	—	4	4	no	—
520	C₂	—	4	1	no	—
521	C₂	—	14	2	no	—
522	C₂	—	28	4	no	—
523	C₂	—	28	1	no	—
524	C₂	C₂×#6548	1	1	yes	characteristic
525	C₂	C₂×D₇×#41	1	1	yes	characteristic
526	C₂	C₂×#6553	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₇
commutator, socle, cosocle	C₂²×C₇	C₂⁵
Fitting	C₇×#532	C₂
hypercenter	#532	D₇
hypocenter	C₇	#3508
LCS	G ▷ C₂²×C₇ ▷ C₇
UCS	C₁ ◁ C₂² ◁ #532

Complements

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

N	H ≅ G/N	type
1. C₇×#532	C₂	semidirect
2. #90525	C₂	semidirect
3. #90520	C₂	semidirect
4. #90419	C₂	semidirect
5. #90416	C₂	semidirect
6. #90407	C₂	semidirect
7. D₇×#127	C₂	semidirect
8. #90372	C₂	semidirect
9. #90367	C₂	semidirect
10. #90310	C₂	semidirect
11. #90303	C₂	semidirect
12. #90298	C₂	semidirect
13. #90290	C₂	semidirect
14. #90253	C₂	semidirect
15. #90250	C₂	semidirect
16. #90245	C₂	semidirect
17. #90236	C₂	semidirect
18. #90168	C₂	semidirect
19. C₄×#1157	C₂	semidirect
20. C₂×C₇×#41	C₂²	semidirect
21. C₂×#1161	C₂²	semidirect
22. C₂×#1159	C₂²	semidirect
27. C₂×#1157	C₂²	semidirect
28. C₇×C₄⋊Q₈	C₂²	semidirect
30. C₇×#124	C₂²	semidirect
31. C₇×#121	C₂²	semidirect
32. C₇×#121	C₂²	semidirect
33. C₄×C₇×D₄	C₂²	semidirect
34. C₄×C₇×D₄	C₂²	semidirect
35. C₂×C₄²×C₇	C₂²	semidirect
36. #6510	C₂²	semidirect
38. Q₈×Dic₇	C₂²	semidirect
42. #6503	C₂²	semidirect
43. #6502	C₂²	semidirect
44. #6501	C₂²	semidirect
45. #6501	C₂²	semidirect
46. #6501	C₂²	semidirect
48. #6499	C₂²	semidirect
49. D₄×Dic₇	C₂²	semidirect
50. D₄×Dic₇	C₂²	semidirect
51. #6493	C₂²	semidirect
52. #6493	C₂²	semidirect
53. #6493	C₂²	semidirect
54. #6492	C₂²	semidirect
57. C₄×C₂²⋊D₇	C₂²	semidirect
58. C₄×C₂²⋊D₇	C₂²	semidirect
59. C₄×C₂²⋊D₇	C₂²	semidirect
61. #6489	C₂²	semidirect
63. #6458	C₂²	semidirect
64. #6458	C₂²	semidirect
65. #6456	C₂²	semidirect
66. #6456	C₂²	semidirect
68. #6453	C₂²	semidirect
69. #6450	C₂²	semidirect
70. #6449	C₂²	semidirect
71. #6448	C₂²	semidirect
72. #6447	C₂²	semidirect
73. #6446	C₂²	semidirect
74. #6446	C₂²	semidirect
76. (C₂²⋊D₇)⋊C₄	C₂²	semidirect
78. #6438	C₂²	semidirect
82. C₄×D₂₈	C₂²	semidirect
83. C₄×D₂₈	C₂²	semidirect
85. #6435	C₂²	semidirect
87. C₄²×D₇	C₂²	semidirect
88. #6432	C₂²	semidirect
89. C₄×Dic₁₄	C₂²	semidirect
90. C₄×Dic₁₄	C₂²	semidirect
186. #532	D₇	semidirect
241. C₄×D₇	#41	semidirect
248. C₂×#41	C₂×D₇	semidirect
253. C₄⋊Q₈	C₂×D₇	semidirect
265. #124	C₂×D₇	semidirect
282. #121	C₂×D₇	semidirect
283. #121	C₂×D₇	semidirect
304. C₄×D₄	C₂×D₇	semidirect
305. C₄×D₄	C₂×D₇	semidirect
314. C₂×C₄²	C₂×D₇	semidirect
487. C₇	#3508	semidirect

Maximal subgroups

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

subgroup	index
C₇×#532	2
#90525	2
#90520	2
#90419	2
#90416	2
#90407	2
D₇×#127	2
#90372	2
#90367	2
#90310	2
#90303	2
#90298	2
#90290	2
#90253	2
#90250	2
#90245	2
#90236	2
#90168	2
C₄×#1157	2
#3508	7