Subgroups — #11743798

Order 896.

1160 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#548	C₂	1	1	yes	maximal, characteristic, complemented
2	#90521	C₂	1	1	yes	maximal, characteristic, complemented
3	#90520	C₂	1	1	yes	maximal, characteristic, complemented
4	#90508	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#6510	C₂	1	1	yes	maximal, characteristic, complemented
6	#90374	C₂	1	2	yes	maximal, complemented
7	#90372	C₂	1	1	yes	maximal, characteristic, complemented
8	#90369	C₂	1	2	yes	maximal, complemented
9	#90365	C₂	1	1	yes	maximal, characteristic, complemented
10	#90338	C₂	1	2	yes	maximal, complemented
11	#90335	C₂	1	2	yes	maximal, complemented
12	#90334	C₂	1	1	yes	maximal, characteristic, complemented
13	#90321	C₂	1	1	yes	maximal, characteristic, complemented
14	#90301	C₂	1	2	yes	maximal, complemented
15	#90300	C₂	1	1	yes	maximal, characteristic, complemented
16	#90296	C₂	1	2	yes	maximal, complemented
17	#90287	C₂	1	1	yes	maximal, characteristic, complemented
18	#90276	C₂	1	1	yes	maximal, characteristic, complemented
19	#90273	C₂	1	1	yes	maximal, characteristic, complemented
20	#90251	C₂	1	2	yes	maximal, complemented
21	#90245	C₂	1	2	yes	maximal, complemented
22	D₄×D₂₈	C₂	1	1	yes	maximal, characteristic, complemented
23	#90229	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₇×#41	C₂²	1	1	yes	characteristic, complemented
25	C₂²×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
26	C₂×#1161	C₂²	1	1	yes	characteristic, complemented
27	C₂×#1159	C₂²	1	2	yes	complemented
28	C₂×D₄×D₇	C₂²	1	2	yes	complemented
29	C₂×D₄×D₇	C₂²	1	2	yes	complemented
30	C₂×D₄×D₇	C₂²	1	1	yes	characteristic, complemented
31	C₂²×D₂₈	C₂²	1	1	yes	characteristic
32	C₂²×D₂₈	C₂²	1	1	yes	characteristic, complemented
33	C₇×#124	C₂²	1	2	yes	complemented
34	C₇×#124	C₂²	1	1	yes	characteristic, complemented
35	C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
36	C₇×C₂²⋊Q₈	C₂²	1	2	yes	complemented
37	C₇×#121	C₂²	1	1	yes	characteristic, complemented
38	C₇×#121	C₂²	1	2	yes	complemented
39	C₄×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
40	C₄×C₇×D₄	C₂²	1	1	yes	characteristic, complemented
41	C₄×C₇×D₄	C₂²	1	2	yes	complemented
42	#6510	C₂²	1	2	yes	complemented
43	#6510	C₂²	1	1	yes	characteristic, complemented
44	#6510	C₂²	1	2	yes	complemented
45	#6510	C₂²	1	2	yes	complemented
46	#6510	C₂²	1	1	yes	characteristic, complemented
47	#6510	C₂²	1	1	yes	characteristic, complemented
48	#6510	C₂²	1	1	yes	characteristic, complemented
49	#6510	C₂²	1	1	yes	characteristic, complemented
50	#6509	C₂²	1	2	yes	complemented
51	#6509	C₂²	1	1	yes	characteristic, complemented
52	Q₈×Dic₇	C₂²	1	1	yes	characteristic, complemented
53	#6503	C₂²	1	1	yes	characteristic
54	#6503	C₂²	1	1	yes	characteristic, complemented
55	#6502	C₂²	1	1	yes	characteristic
56	#6502	C₂²	1	2	yes	complemented
57	#6502	C₂²	1	2	yes	complemented
58	#6500	C₂²	1	2	yes	complemented
59	#6500	C₂²	1	2	yes	complemented
60	#6500	C₂²	1	2	yes	complemented
61	#6500	C₂²	1	2	yes	complemented
62	#6498	C₂²	1	1	yes	characteristic, complemented
63	D₄×Dic₇	C₂²	1	1	yes	characteristic, complemented
64	#6493	C₂²	1	1	yes	characteristic
65	#6493	C₂²	1	1	yes	characteristic, complemented
66	#6493	C₂²	1	2	yes	complemented
67	#6493	C₂²	1	2	yes	complemented
68	#6493	C₂²	1	2	yes	complemented
69	#6492	C₂²	1	2	yes	complemented
70	C₄×C₂²⋊D₇	C₂²	1	1	yes	characteristic, complemented
71	C₄×C₂²⋊D₇	C₂²	1	1	yes	characteristic, complemented
72	C₄×C₂²⋊D₇	C₂²	1	2	yes	complemented
73	C₂×(C₂×D₇)⋊C₄	C₂²	1	2	yes	complemented
74	C₂×(C₂×D₇)⋊C₄	C₂²	1	2	yes	complemented
75	C₂×(C₂×D₇)⋊C₄	C₂²	1	2	yes	complemented
76	#6489	C₂²	1	1	yes	characteristic, complemented
77	C₂×C₄×Dic₇	C₂²	1	1	yes	characteristic, complemented
78	#6461	C₂²	1	1	yes	characteristic, complemented
79	#6461	C₂²	1	2	yes	complemented
80	#6460	C₂²	1	2	yes	complemented
81	#6459	C₂²	1	2	yes	complemented
82	#6458	C₂²	1	1	yes	characteristic
83	#6458	C₂²	1	2	yes	complemented
84	#6458	C₂²	1	2	yes	complemented
85	#6457	C₂²	1	2	yes	complemented
86	#6457	C₂²	1	2	yes	complemented
87	#6457	C₂²	1	2	yes	complemented
88	#6457	C₂²	1	2	yes	complemented
89	#6456	C₂²	1	1	yes	characteristic, complemented
90	#6456	C₂²	1	1	yes	characteristic, complemented
91	#6452	C₂²	1	1	yes	characteristic, complemented
92	#6451	C₂²	1	1	yes	characteristic, complemented
93	#6449	C₂²	1	2	yes	complemented
94	#6449	C₂²	1	1	yes	characteristic, complemented
95	#6448	C₂²	1	2	yes	complemented
96	#6448	C₂²	1	1	yes	characteristic, complemented
97	#6448	C₂²	1	2	yes	complemented
98	#6448	C₂²	1	2	yes	complemented
99	#6447	C₂²	1	2	yes	complemented
100	#6447	C₂²	1	2	yes	complemented
101	#6447	C₂²	1	2	yes	complemented
102	#6446	C₂²	1	2	yes	complemented
103	#6446	C₂²	1	2	yes	complemented
104	#6445	C₂²	1	2	yes	complemented
105	#6445	C₂²	1	2	yes	complemented
106	#6445	C₂²	1	2	yes	complemented
107	#6445	C₂²	1	2	yes	complemented
108	#6445	C₂²	1	2	yes	complemented
109	#6445	C₂²	1	2	yes	complemented
110	(C₂²⋊D₇)⋊C₄	C₂²	1	2	yes	complemented
111	(C₂²⋊D₇)⋊C₄	C₂²	1	2	yes	complemented
112	D₇×C₂²⋊C₄	C₂²	1	2	yes	complemented
113	#6442	C₂²	1	1	yes	characteristic, complemented
114	#6441	C₂²	1	1	yes	characteristic, complemented
115	#6439	C₂²	1	2	yes	complemented
116	#6438	C₂²	1	2	yes	complemented
117	#6438	C₂²	1	2	yes	complemented
118	#6437	C₂²	1	1	yes	characteristic
119	C₄×D₂₈	C₂²	1	2	yes	complemented
120	C₄×D₂₈	C₂²	1	1	yes	characteristic, complemented
121	#6435	C₂²	1	1	yes	characteristic, complemented
122	C₄×Dic₁₄	C₂²	1	1	yes	characteristic, complemented
123	#3558	—	7	1	no	maximal, Sylow
124	C₂³×D₇	C₂³	1	2	yes	—
125	C₂³×D₇	C₂³	1	2	yes	—
126	C₂³×D₇	C₂³	1	2	yes	—
127	C₇×#41	—	4	2	no	—
128	C₂×C₇×Q₈	—	4	2	no	—
129	C₂×C₇×Q₈	C₂³	1	1	yes	characteristic
130	C₂×C₇×Q₈	C₂³	1	1	yes	characteristic
131	C₂×C₇×Q₈	C₂³	1	2	yes	—
132	C₂×C₇×D₄	C₂³	1	1	yes	characteristic
133	C₂×C₇×D₄	C₂³	1	1	yes	characteristic
134	C₂×C₇×D₄	C₂³	1	2	yes	—
135	C₂×C₇×D₄	C₂³	1	2	yes	—
136	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
137	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
138	C₂²×C₄×C₇	C₂³	1	2	yes	—
139	C₂²×C₄×C₇	C₂³	1	2	yes	—
140	C₂×C₂²⋊D₇	C₂³	1	2	yes	—
141	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
142	C₂×C₂²⋊D₇	C₂³	1	2	yes	—
143	C₂×C₂²⋊D₇	C₂³	1	2	yes	—
144	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
145	C₂×C₂²⋊D₇	C₂³	1	2	yes	—
146	C₂×C₂²⋊D₇	C₂³	1	2	yes	—
147	C₂×C₂²⋊D₇	C₂³	1	2	yes	—
148	C₂×C₂²⋊D₇	C₂³	1	2	yes	—
149	C₂²×Dic₇	C₂³	1	1	yes	characteristic
150	C₂²×Dic₇	C₂³	1	1	yes	characteristic
151	C₂²×Dic₇	C₂³	1	2	yes	—
152	#1161	—	4	2	no	—
153	#1159	—	4	4	no	—
154	D₄×D₇	—	4	2	no	—
155	D₄×D₇	—	4	4	no	—
156	D₄×D₇	—	4	4	no	—
157	C₂×D₂₈	—	4	2	no	—
158	C₂×D₂₈	—	4	2	no	—
159	C₂×D₂₈	C₂³	1	1	yes	characteristic
160	C₂×D₂₈	C₂³	1	1	yes	characteristic
161	C₂×D₂₈	C₂³	1	1	yes	characteristic
162	C₂×D₂₈	C₂³	1	2	yes	—
163	C₂×D₂₈	C₂³	1	2	yes	—
164	C₂×D₂₈	C₂³	1	2	yes	—
165	C₂×D₂₈	C₂³	1	2	yes	—
166	C₂×D₂₈	C₂³	1	2	yes	—
167	C₂×D₂₈	C₂³	1	2	yes	—
168	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
169	C₂×C₄×D₇	C₂³	1	2	yes	—
170	C₂×C₄×D₇	C₂³	1	2	yes	—
171	C₂×C₄×D₇	C₂³	1	2	yes	—
172	C₂×C₄×D₇	C₂³	1	2	yes	—
173	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
174	C₂×Dic₁₄	C₂³	1	2	yes	—
175	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
176	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
177	C₇×C₄⋊C₄	C₂³	1	2	yes	—
178	C₇×C₄⋊C₄	C₂³	1	2	yes	—
179	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
180	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
181	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
182	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
183	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
184	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
185	C₄²×C₇	C₂³	1	1	yes	characteristic
186	C₄²×C₇	C₂³	1	2	yes	—
187	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
188	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
189	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
190	C₂²⋊Dic₇	C₂³	1	2	yes	—
191	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
192	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
193	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
194	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
195	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
196	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
197	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
198	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
199	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
200	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
201	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
202	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
203	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
204	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
205	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
206	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
207	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
208	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
209	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
210	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
211	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
212	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
213	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
214	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
215	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
216	C₄⋊Dic₇	C₂³	1	2	yes	—
217	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
218	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
219	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
220	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
221	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
222	Dic₇⋊C₄	C₂³	1	2	yes	—
223	Dic₇⋊C₄	C₂³	1	2	yes	—
224	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
225	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
226	C₄×Dic₇	C₂³	1	1	yes	characteristic
227	C₄×Dic₇	C₂³	1	1	yes	characteristic
228	C₄×Dic₇	C₂³	1	1	yes	characteristic
229	C₄×Dic₇	C₂³	1	1	yes	characteristic
230	C₄×Dic₇	C₂³	1	2	yes	—
231	C₄×Dic₇	C₂³	1	1	yes	characteristic
232	#562	—	7	2	no	—
233	H(3,𝔽₄)	—	7	2	no	—
234	#559	—	7	1	no	—
235	#559	—	7	1	no	—
236	#548	—	7	1	no	—
237	#548	D₇	1	1	yes	characteristic, complemented
238	#546	—	7	1	no	—
239	#546	—	7	1	no	—
240	#546	—	7	2	no	—
241	#546	—	7	2	no	—
242	D₄²	—	7	1	no	—
243	D₄²	—	7	1	no	—
244	#542	—	7	1	no	—
245	#542	—	7	1	no	—
246	#538	—	7	2	no	—
247	#538	—	7	2	no	—
248	#538	—	7	2	no	—
249	#535	—	7	1	no	—
250	#535	—	7	1	no	—
251	#534	—	7	2	no	—
252	#532	—	7	1	no	—
253	#529	—	7	1	no	—
254	C₂×#124	—	7	1	no	—
255	C₂³×C₇	C₂⁴	1	1	yes	characteristic
256	C₂³×C₇	C₂⁴	1	2	yes	—
257	C₂³×C₇	C₂⁴	1	1	yes	characteristic
258	C₂²×D₇	—	2	4	no	—
259	C₂²×D₇	—	4	2	no	—
260	C₂²×D₇	—	4	2	no	—
261	C₂²×D₇	—	4	2	no	—
262	C₂²×D₇	—	4	2	no	—
263	C₂²×D₇	—	4	2	no	—
264	C₂²×D₇	—	4	2	no	—
265	C₂²×D₇	—	4	2	no	—
266	C₂²×D₇	—	4	2	no	—
267	C₂²×D₇	C₂⁴	1	1	yes	characteristic
268	C₂²×D₇	C₂⁴	1	2	yes	—
269	C₂²×D₇	C₂⁴	1	2	yes	—
270	C₂²×D₇	C₂⁴	1	2	yes	—
271	C₇×Q₈	—	2	2	no	—
272	C₇×Q₈	—	2	2	no	—
273	C₇×Q₈	—	4	2	no	—
274	C₇×D₄	—	2	2	no	—
275	C₇×D₄	—	2	4	no	—
276	C₇×D₄	—	2	2	no	—
277	C₇×D₄	—	4	2	no	—
278	C₂×C₄×C₇	—	2	2	no	—
279	C₂×C₄×C₇	—	2	2	no	—
280	C₂×C₄×C₇	—	4	2	no	—
281	C₂×C₄×C₇	—	4	2	no	—
282	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
283	C₂×C₄×C₇	C₂⁴	1	2	yes	—
284	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
285	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
286	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
287	C₂×C₄×C₇	C₂⁴	1	2	yes	—
288	C₂×C₄×C₇	C₂⁴	1	2	yes	—
289	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
290	C₂²⋊D₇	—	2	2	no	—
291	C₂²⋊D₇	—	2	4	no	—
292	C₂²⋊D₇	—	4	2	no	—
293	C₂²⋊D₇	—	4	2	no	—
294	C₂²⋊D₇	—	4	2	no	—
295	C₂²⋊D₇	—	4	2	no	—
296	C₂²⋊D₇	—	4	1	no	—
297	C₂²⋊D₇	—	4	2	no	—
298	C₂²⋊D₇	—	4	2	no	—
299	C₂×Dic₇	—	2	2	no	—
300	C₂×Dic₇	—	4	2	no	—
301	C₂×Dic₇	—	4	1	no	—
302	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
303	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
304	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
305	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
306	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
307	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
308	C₂×Dic₇	C₂⁴	1	2	yes	—
309	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
310	D₂₈	—	2	2	no	—
311	D₂₈	—	2	2	no	—
312	D₂₈	—	2	2	no	—
313	D₂₈	—	4	2	no	—
314	D₂₈	—	4	2	no	—
315	D₂₈	—	4	2	no	—
316	D₂₈	—	4	2	no	—
317	D₂₈	—	4	2	no	—
318	D₂₈	—	4	2	no	—
319	C₄×D₇	—	2	2	no	—
320	C₄×D₇	—	4	2	no	—
321	C₄×D₇	—	4	2	no	—
322	C₄×D₇	—	4	2	no	—
323	C₄×D₇	—	4	2	no	—
324	Dic₁₄	—	4	1	no	—
325	Dic₁₄	—	4	2	no	—
326	C₂×#41	—	7	1	no	—
327	C₂×#41	—	7	2	no	—
328	C₂×#41	C₂×D₇	1	1	yes	characteristic, complemented
329	C₂²×Q₈	C₂×D₇	1	1	yes	characteristic, complemented
330	C₂²×D₄	—	7	2	no	—
331	C₂²×D₄	—	7	2	no	—
332	C₂²×D₄	—	7	1	no	—
333	C₂²×D₄	—	7	1	no	—
334	C₂²×D₄	—	7	1	no	—
335	C₄⋊Q₈	—	7	1	no	—
336	#127	—	7	1	no	—
337	#127	—	7	1	no	—
338	#127	—	7	1	no	—
339	#126	—	7	1	no	—
340	#126	—	7	2	no	—
341	#126	—	7	1	no	—
342	#126	—	7	2	no	—
343	#125	—	7	1	no	—
344	#124	—	7	1	no	—
345	#124	—	7	1	no	—
346	#124	—	7	2	no	—
347	#124	—	7	1	no	—
348	#124	—	7	1	no	—
349	#124	—	7	2	no	—
350	#124	—	7	1	no	—
351	#124	—	7	2	no	—
352	#124	—	7	1	no	—
353	#124	—	7	2	no	—
354	#124	—	7	2	no	—
355	#124	—	7	2	no	—
356	#124	—	7	2	no	—
357	#124	—	7	2	no	—
358	#124	C₂×D₇	1	1	yes	characteristic, complemented
359	#124	C₂×D₇	1	2	yes	complemented
360	#123	—	7	1	no	—
361	#123	—	7	2	no	—
362	#123	—	7	2	no	—
363	#123	—	7	2	no	—
364	#123	—	7	2	no	—
365	#123	—	7	2	no	—
366	#123	—	7	1	no	—
367	#123	—	7	2	no	—
368	#123	—	7	2	no	—
369	#123	—	7	2	no	—
370	C₂²⋊Q₈	—	7	2	no	—
371	C₂²⋊Q₈	—	7	1	no	—
372	C₂²⋊Q₈	—	7	2	no	—
373	C₂²⋊Q₈	—	7	2	no	—
374	C₂²⋊Q₈	—	7	1	no	—
375	C₂²⋊Q₈	C₂×D₇	1	2	yes	complemented
376	C₂²⋊Q₈	C₂×D₇	1	1	yes	characteristic, complemented
377	#121	—	7	1	no	—
378	#121	—	7	2	no	—
379	#121	—	7	2	no	—
380	#121	—	7	1	no	—
381	#121	—	7	2	no	—
382	#121	—	7	2	no	—
383	#121	—	7	2	no	—
384	#121	—	7	1	no	—
385	#121	—	7	2	no	—
386	#121	—	7	2	no	—
387	#121	—	7	1	no	—
388	#121	—	7	2	no	—
389	#121	—	7	2	no	—
390	#121	—	7	2	no	—
391	#121	C₂×D₇	1	1	yes	characteristic, complemented
392	#121	C₂×D₇	1	2	yes	complemented
393	#120	—	7	2	no	—
394	#120	—	7	2	no	—
395	#120	—	7	2	no	—
396	#120	—	7	2	no	—
397	#120	—	7	2	no	—
398	#120	—	7	2	no	—
399	#120	—	7	2	no	—
400	#120	—	7	2	no	—
401	#120	—	7	2	no	—
402	#120	—	7	2	no	—
403	C₄×Q₈	—	7	1	no	—
404	C₄×Q₈	—	7	1	no	—
405	C₄×Q₈	C₂×D₇	1	1	yes	characteristic, complemented
406	C₄×D₄	—	7	1	no	—
407	C₄×D₄	—	7	1	no	—
408	C₄×D₄	—	7	1	no	—
409	C₄×D₄	—	7	2	no	—
410	C₄×D₄	—	7	1	no	—
411	C₄×D₄	—	7	1	no	—
412	C₄×D₄	—	7	2	no	—
413	C₄×D₄	—	7	2	no	—
414	C₄×D₄	—	7	2	no	—
415	C₄×D₄	—	7	1	no	—
416	C₄×D₄	C₂×D₇	1	1	yes	characteristic, complemented
417	C₄×D₄	C₂×D₇	1	2	yes	complemented
418	#117	—	7	1	no	—
419	#117	—	7	1	no	—
420	C₂×C₂²⋊C₄	—	7	2	no	—
421	C₂×C₂²⋊C₄	—	7	2	no	—
422	C₂×C₂²⋊C₄	—	7	2	no	—
423	C₂×C₂²⋊C₄	—	7	2	no	—
424	C₂×C₄²	—	7	1	no	—
425	C₂²×C₇	—	2	1	no	—
426	C₂²×C₇	—	2	1	no	—
427	C₂²×C₇	—	2	2	no	—
428	C₂²×C₇	—	2	1	no	—
429	C₂²×C₇	—	2	2	no	—
430	C₂²×C₇	—	2	1	no	—
431	C₂²×C₇	—	2	2	no	—
432	C₂²×C₇	—	2	1	no	—
433	C₂²×C₇	H(5,𝔽₂)	1	2	yes	—
434	C₂²×C₇	C₂⁵	1	1	yes	characteristic
435	C₂×D₇	—	2	1	no	—
436	C₂×D₇	—	2	2	no	—
437	C₂×D₇	—	2	2	no	—
438	C₂×D₇	—	2	2	no	—
439	C₂×D₇	—	2	2	no	—
440	C₂×D₇	—	2	2	no	—
441	C₂×D₇	—	2	2	no	—
442	C₂×D₇	—	2	1	no	—
443	C₂×D₇	—	2	2	no	—
444	C₂×D₇	—	2	2	no	—
445	C₂×D₇	—	2	1	no	—
446	C₂×D₇	—	2	2	no	—
447	C₂×D₇	—	8	4	no	—
448	C₂×D₇	—	8	4	no	—
449	C₂×D₇	—	8	4	no	—
450	C₄×C₇	—	2	2	no	—
451	C₄×C₇	—	2	1	no	—
452	C₄×C₇	—	2	2	no	—
453	C₄×C₇	—	2	1	no	—
454	C₄×C₇	—	2	1	no	—
455	C₄×C₇	—	2	2	no	—
456	C₄×C₇	—	2	1	no	—
457	C₄×C₇	H(5,𝔽₂)	1	2	yes	—
458	Dic₇	—	2	1	no	—
459	Dic₇	—	2	2	no	—
460	Dic₇	—	2	1	no	—
461	Dic₇	—	2	1	no	—
462	Dic₇	—	2	1	no	—
463	Dic₇	—	2	1	no	—
464	Dic₇	—	2	1	no	—
465	Dic₇	—	2	1	no	—
466	C₂⁴	—	7	2	no	—
467	C₂⁴	—	7	2	no	—
468	C₂⁴	—	7	2	no	—
469	#41	—	4	2	no	—
470	#41	—	28	4	no	—
471	#41	—	28	2	no	—
472	C₂×Q₈	—	4	2	no	—
473	C₂×Q₈	—	7	1	no	—
474	C₂×Q₈	—	7	2	no	—
475	C₂×Q₈	C₂²×D₇	1	1	yes	characteristic
476	C₂×Q₈	C₂²×D₇	1	1	yes	characteristic
477	C₂×Q₈	C₂²×D₇	1	2	yes	—
478	C₂×D₄	—	7	2	no	—
479	C₂×D₄	—	7	1	no	—
480	C₂×D₄	—	7	1	no	—
481	C₂×D₄	—	7	2	no	—
482	C₂×D₄	—	7	2	no	—
483	C₂×D₄	—	7	2	no	—
484	C₂×D₄	—	7	2	no	—
485	C₂×D₄	—	7	2	no	—
486	C₂×D₄	—	7	2	no	—
487	C₂×D₄	—	7	1	no	—
488	C₂×D₄	—	7	1	no	—
489	C₂×D₄	—	7	1	no	—
490	C₂×D₄	—	7	2	no	—
491	C₂×D₄	—	7	2	no	—
492	C₂×D₄	—	7	2	no	—
493	C₂×D₄	—	7	2	no	—
494	C₂×D₄	—	7	2	no	—
495	C₂×D₄	—	7	2	no	—
496	C₂×D₄	—	28	2	no	—
497	C₂×D₄	—	28	2	no	—
498	C₂×D₄	—	28	2	no	—
499	C₂×D₄	—	28	4	no	—
500	C₂×D₄	—	28	4	no	—
501	C₂×D₄	C₂²×D₇	1	1	yes	characteristic
502	C₂×D₄	C₂²×D₇	1	2	yes	—
503	C₂×D₄	C₂²×D₇	1	1	yes	characteristic
504	C₂×D₄	C₂²×D₇	1	2	yes	—
505	C₂²×C₄	—	7	1	no	—
506	C₂²×C₄	—	7	1	no	—
507	C₂²×C₄	—	7	2	no	—
508	C₂²×C₄	—	7	1	no	—
509	C₂²×C₄	—	7	2	no	—
510	C₂²×C₄	—	7	2	no	—
511	C₂²×C₄	—	7	2	no	—
512	C₂²×C₄	—	7	2	no	—
513	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
514	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
515	C₂²×C₄	C₂²×D₇	1	2	yes	—
516	C₂²×C₄	C₂²×D₇	1	2	yes	—
517	C₄⋊C₄	—	7	1	no	—
518	C₄⋊C₄	—	7	1	no	—
519	C₄⋊C₄	—	7	1	no	—
520	C₄⋊C₄	—	7	1	no	—
521	C₄⋊C₄	—	7	2	no	—
522	C₄⋊C₄	—	7	2	no	—
523	C₄⋊C₄	—	7	1	no	—
524	C₄⋊C₄	—	7	1	no	—
525	C₄⋊C₄	—	7	1	no	—
526	C₄⋊C₄	—	7	1	no	—
527	C₄⋊C₄	—	7	1	no	—
528	C₄⋊C₄	—	7	1	no	—
529	C₄⋊C₄	—	7	2	no	—
530	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
531	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
532	C₄⋊C₄	C₂²×D₇	1	2	yes	—
533	C₄⋊C₄	C₂²×D₇	1	2	yes	—
534	C₂²⋊C₄	—	7	1	no	—
535	C₂²⋊C₄	—	7	1	no	—
536	C₂²⋊C₄	—	7	1	no	—
537	C₂²⋊C₄	—	7	1	no	—
538	C₂²⋊C₄	—	7	2	no	—
539	C₂²⋊C₄	—	7	1	no	—
540	C₂²⋊C₄	—	7	2	no	—
541	C₂²⋊C₄	—	7	2	no	—
542	C₂²⋊C₄	—	7	2	no	—
543	C₂²⋊C₄	—	7	2	no	—
544	C₂²⋊C₄	—	7	2	no	—
545	C₂²⋊C₄	—	7	2	no	—
546	C₂²⋊C₄	—	7	2	no	—
547	C₂²⋊C₄	—	7	2	no	—
548	C₂²⋊C₄	—	7	2	no	—
549	C₂²⋊C₄	—	7	2	no	—
550	C₂²⋊C₄	—	7	2	no	—
551	C₂²⋊C₄	—	7	1	no	—
552	C₂²⋊C₄	—	7	1	no	—
553	C₂²⋊C₄	—	7	2	no	—
554	C₂²⋊C₄	—	7	2	no	—
555	C₂²⋊C₄	—	7	1	no	—
556	C₂²⋊C₄	—	7	2	no	—
557	C₂²⋊C₄	—	7	2	no	—
558	C₂²⋊C₄	—	7	2	no	—
559	C₂²⋊C₄	—	7	2	no	—
560	C₂²⋊C₄	C₂²×D₇	1	2	yes	—
561	C₂²⋊C₄	C₂²×D₇	1	2	yes	—
562	C₂²⋊C₄	C₂²×D₇	1	2	yes	—
563	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
564	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
565	C₂²⋊C₄	C₂²×D₇	1	2	yes	—
566	C₄²	—	7	1	no	—
567	C₄²	—	7	1	no	—
568	C₄²	—	7	1	no	—
569	C₄²	—	7	1	no	—
570	C₄²	—	7	1	no	—
571	C₄²	—	7	2	no	—
572	C₄²	C₂²×D₇	1	1	yes	characteristic
573	C₄²	C₂²×D₇	1	2	yes	—
574	C₂×C₇	—	2	2	no	—
575	C₂×C₇	—	4	1	no	—
576	C₂×C₇	—	4	2	no	—
577	C₂×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
578	C₂×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
579	C₂×C₇	#585	1	1	yes	characteristic
580	D₇	—	4	2	no	—
581	D₇	—	4	1	no	—
582	D₇	—	4	2	no	—
583	D₇	—	4	2	no	—
584	C₂³	—	7	1	no	—
585	C₂³	—	7	2	no	—
586	C₂³	—	7	2	no	—
587	C₂³	—	7	2	no	—
588	C₂³	—	14	4	no	—
589	C₂³	—	28	2	no	—
590	C₂³	—	28	2	no	—
591	C₂³	—	28	2	no	—
592	C₂³	—	28	2	no	—
593	C₂³	—	28	2	no	—
594	C₂³	—	28	2	no	—
595	C₂³	—	28	2	no	—
596	C₂³	—	28	2	no	—
597	C₂³	C₂³×D₇	1	1	yes	characteristic
598	C₂³	C₂³×D₇	1	2	yes	—
599	C₂³	C₂³×D₇	1	1	yes	characteristic
600	Q₈	—	2	2	no	—
601	Q₈	—	2	2	no	—
602	Q₈	—	4	2	no	—
603	Q₈	—	28	1	no	—
604	Q₈	—	28	2	no	—
605	D₄	—	2	2	no	—
606	D₄	—	2	4	no	—
607	D₄	—	2	2	no	—
608	D₄	—	4	2	no	—
609	D₄	—	14	2	no	—
610	D₄	—	14	4	no	—
611	D₄	—	14	2	no	—
612	D₄	—	14	2	no	—
613	D₄	—	14	2	no	—
614	D₄	—	28	2	no	—
615	D₄	—	28	2	no	—
616	D₄	—	28	2	no	—
617	D₄	—	28	2	no	—
618	D₄	—	28	2	no	—
619	D₄	—	28	2	no	—
620	D₄	—	28	2	no	—
621	D₄	—	28	1	no	—
622	D₄	—	28	2	no	—
623	D₄	—	28	2	no	—
624	D₄	—	28	2	no	—
625	D₄	—	28	2	no	—
626	D₄	—	28	2	no	—
627	C₂×C₄	—	2	2	no	—
628	C₂×C₄	—	2	2	no	—
629	C₂×C₄	—	4	2	no	—
630	C₂×C₄	—	4	2	no	—
631	C₂×C₄	—	7	1	no	—
632	C₂×C₄	—	7	1	no	—
633	C₂×C₄	—	7	1	no	—
634	C₂×C₄	—	7	1	no	—
635	C₂×C₄	—	7	1	no	—
636	C₂×C₄	—	7	2	no	—
637	C₂×C₄	—	7	1	no	—
638	C₂×C₄	—	7	1	no	—
639	C₂×C₄	—	14	2	no	—
640	C₂×C₄	—	14	2	no	—
641	C₂×C₄	—	28	2	no	—
642	C₂×C₄	—	28	2	no	—
643	C₂×C₄	—	28	2	no	—
644	C₂×C₄	—	28	2	no	—
645	C₂×C₄	—	28	1	no	—
646	C₂×C₄	—	28	2	no	—
647	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
648	C₂×C₄	C₂³×D₇	1	2	yes	—
649	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
650	C₂×C₄	C₂³×D₇	1	2	yes	—
651	C₂×C₄	C₂³×D₇	1	2	yes	—
652	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
653	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
654	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
655	C₇	#3558	1	1	yes	characteristic, complemented, Sylow
656	C₂²	—	2	1	no	—
657	C₂²	—	2	1	no	—
658	C₂²	—	2	1	no	—
659	C₂²	—	2	2	no	—
660	C₂²	—	2	2	no	—
661	C₂²	—	2	1	no	—
662	C₂²	—	2	2	no	—
663	C₂²	—	2	1	no	—
664	C₂²	—	14	1	no	—
665	C₂²	—	14	2	no	—
666	C₂²	—	14	2	no	—
667	C₂²	—	14	2	no	—
668	C₂²	—	14	2	no	—
669	C₂²	—	14	2	no	—
670	C₂²	—	14	2	no	—
671	C₂²	—	14	1	no	—
672	C₂²	—	14	2	no	—
673	C₂²	—	14	2	no	—
674	C₂²	—	14	1	no	—
675	C₂²	—	14	2	no	—
676	C₂²	—	56	4	no	—
677	C₂²	—	56	4	no	—
678	C₂²	—	56	4	no	—
679	C₂²	#6553	1	2	yes	—
680	C₂²	C₂⁴×D₇	1	1	yes	characteristic
681	C₄	—	2	1	no	—
682	C₄	—	2	1	no	—
683	C₄	—	2	2	no	—
684	C₄	—	2	2	no	—
685	C₄	—	2	1	no	—
686	C₄	—	2	2	no	—
687	C₄	—	2	1	no	—
688	C₄	—	14	1	no	—
689	C₄	—	14	1	no	—
690	C₄	—	14	1	no	—
691	C₄	—	14	1	no	—
692	C₄	—	14	2	no	—
693	C₄	—	14	1	no	—
694	C₄	—	14	1	no	—
695	C₄	—	14	1	no	—
696	C₄	#6548	1	2	yes	—
697	C₂	—	2	2	no	—
698	C₂	—	4	1	no	—
699	C₂	—	4	2	no	—
700	C₂	—	28	1	no	—
701	C₂	—	28	2	no	—
702	C₂	—	28	2	no	—
703	C₂	—	28	2	no	—
704	C₂	C₂×#6548	1	1	yes	characteristic
705	C₂	C₂×#6553	1	1	yes	characteristic
706	C₂	#90620	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₇
commutator, socle, cosocle	C₂²×C₇	C₂⁵
Fitting	C₇×#548	C₂
hypercenter	#548	D₇
hypocenter	C₇	#3558
LCS	G ▷ C₂²×C₇ ▷ C₇
UCS	C₁ ◁ C₂² ◁ #548

Complements

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

N	H ≅ G/N	type
1. C₇×#548	C₂	semidirect
2. #90521	C₂	semidirect
3. #90520	C₂	semidirect
4. #90508	C₂	semidirect
5. C₂×#6510	C₂	semidirect
6. #90374	C₂	semidirect
7. #90372	C₂	semidirect
8. #90369	C₂	semidirect
9. #90365	C₂	semidirect
10. #90338	C₂	semidirect
11. #90335	C₂	semidirect
12. #90334	C₂	semidirect
13. #90321	C₂	semidirect
14. #90301	C₂	semidirect
15. #90300	C₂	semidirect
16. #90296	C₂	semidirect
17. #90287	C₂	semidirect
18. #90276	C₂	semidirect
19. #90273	C₂	semidirect
20. #90251	C₂	semidirect
21. #90245	C₂	semidirect
22. D₄×D₂₈	C₂	semidirect
23. #90229	C₂	semidirect
24. C₂×C₇×#41	C₂²	semidirect
25. C₂²×C₇×Q₈	C₂²	semidirect
26. C₂×#1161	C₂²	semidirect
27. C₂×#1159	C₂²	semidirect
28. C₂×D₄×D₇	C₂²	semidirect
29. C₂×D₄×D₇	C₂²	semidirect
30. C₂×D₄×D₇	C₂²	semidirect
32. C₂²×D₂₈	C₂²	semidirect
33. C₇×#124	C₂²	semidirect
34. C₇×#124	C₂²	semidirect
35. C₇×C₂²⋊Q₈	C₂²	semidirect
36. C₇×C₂²⋊Q₈	C₂²	semidirect
37. C₇×#121	C₂²	semidirect
38. C₇×#121	C₂²	semidirect
39. C₄×C₇×Q₈	C₂²	semidirect
40. C₄×C₇×D₄	C₂²	semidirect
41. C₄×C₇×D₄	C₂²	semidirect
42. #6510	C₂²	semidirect
43. #6510	C₂²	semidirect
44. #6510	C₂²	semidirect
45. #6510	C₂²	semidirect
46. #6510	C₂²	semidirect
47. #6510	C₂²	semidirect
48. #6510	C₂²	semidirect
49. #6510	C₂²	semidirect
50. #6509	C₂²	semidirect
51. #6509	C₂²	semidirect
52. Q₈×Dic₇	C₂²	semidirect
54. #6503	C₂²	semidirect
56. #6502	C₂²	semidirect
57. #6502	C₂²	semidirect
58. #6500	C₂²	semidirect
59. #6500	C₂²	semidirect
60. #6500	C₂²	semidirect
61. #6500	C₂²	semidirect
62. #6498	C₂²	semidirect
63. D₄×Dic₇	C₂²	semidirect
65. #6493	C₂²	semidirect
66. #6493	C₂²	semidirect
67. #6493	C₂²	semidirect
68. #6493	C₂²	semidirect
69. #6492	C₂²	semidirect
70. C₄×C₂²⋊D₇	C₂²	semidirect
71. C₄×C₂²⋊D₇	C₂²	semidirect
72. C₄×C₂²⋊D₇	C₂²	semidirect
73. C₂×(C₂×D₇)⋊C₄	C₂²	semidirect
74. C₂×(C₂×D₇)⋊C₄	C₂²	semidirect
75. C₂×(C₂×D₇)⋊C₄	C₂²	semidirect
76. #6489	C₂²	semidirect
77. C₂×C₄×Dic₇	C₂²	semidirect
78. #6461	C₂²	semidirect
79. #6461	C₂²	semidirect
80. #6460	C₂²	semidirect
81. #6459	C₂²	semidirect
83. #6458	C₂²	semidirect
84. #6458	C₂²	semidirect
85. #6457	C₂²	semidirect
86. #6457	C₂²	semidirect
87. #6457	C₂²	semidirect
88. #6457	C₂²	semidirect
89. #6456	C₂²	semidirect
90. #6456	C₂²	semidirect
91. #6452	C₂²	semidirect
92. #6451	C₂²	semidirect
93. #6449	C₂²	semidirect
94. #6449	C₂²	semidirect
95. #6448	C₂²	semidirect
96. #6448	C₂²	semidirect
97. #6448	C₂²	semidirect
98. #6448	C₂²	semidirect
99. #6447	C₂²	semidirect
100. #6447	C₂²	semidirect
101. #6447	C₂²	semidirect
102. #6446	C₂²	semidirect
103. #6446	C₂²	semidirect
104. #6445	C₂²	semidirect
105. #6445	C₂²	semidirect
106. #6445	C₂²	semidirect
107. #6445	C₂²	semidirect
108. #6445	C₂²	semidirect
109. #6445	C₂²	semidirect
110. (C₂²⋊D₇)⋊C₄	C₂²	semidirect
111. (C₂²⋊D₇)⋊C₄	C₂²	semidirect
112. D₇×C₂²⋊C₄	C₂²	semidirect
113. #6442	C₂²	semidirect
114. #6441	C₂²	semidirect
115. #6439	C₂²	semidirect
116. #6438	C₂²	semidirect
117. #6438	C₂²	semidirect
119. C₄×D₂₈	C₂²	semidirect
120. C₄×D₂₈	C₂²	semidirect
121. #6435	C₂²	semidirect
122. C₄×Dic₁₄	C₂²	semidirect
237. #548	D₇	semidirect
328. C₂×#41	C₂×D₇	semidirect
329. C₂²×Q₈	C₂×D₇	semidirect
358. #124	C₂×D₇	semidirect
359. #124	C₂×D₇	semidirect
375. C₂²⋊Q₈	C₂×D₇	semidirect
376. C₂²⋊Q₈	C₂×D₇	semidirect
391. #121	C₂×D₇	semidirect
392. #121	C₂×D₇	semidirect
405. C₄×Q₈	C₂×D₇	semidirect
416. C₄×D₄	C₂×D₇	semidirect
417. C₄×D₄	C₂×D₇	semidirect
655. C₇	#3558	semidirect

Maximal subgroups

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

subgroup	index
C₇×#548	2
#90521	2
#90520	2
#90508	2
C₂×#6510	2
#90374	2
#90372	2
#90369	2
#90365	2
#90338	2
#90335	2
#90334	2
#90321	2
#90301	2
#90300	2
#90296	2
#90287	2
#90276	2
#90273	2
#90251	2
#90245	2
D₄×D₂₈	2
#90229	2
#3558	7