Subgroups — #11743944

Order 896.

1242 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#553	C₂	1	1	yes	maximal, characteristic, complemented
2	#90397	C₂	1	2	yes	maximal, complemented
3	#90396	C₂	1	2	yes	maximal, complemented
4	#90382	C₂	1	1	yes	maximal, characteristic, complemented
5	#90381	C₂	1	1	yes	maximal, characteristic, complemented
6	#90352	C₂	1	2	yes	maximal, complemented
7	#90347	C₂	1	2	yes	maximal, complemented
8	#90303	C₂	1	1	yes	maximal, characteristic, complemented
9	#90301	C₂	1	2	yes	maximal, complemented
10	#90300	C₂	1	1	yes	maximal, characteristic, complemented
11	#90297	C₂	1	2	yes	maximal, complemented
12	#90291	C₂	1	1	yes	maximal, characteristic, complemented
13	#90287	C₂	1	1	yes	maximal, characteristic, complemented
14	#90250	C₂	1	1	yes	maximal, characteristic, complemented
15	#90247	C₂	1	2	yes	maximal, complemented
16	#90241	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×D₄×D₇	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×D₄×D₇	C₂	1	2	yes	maximal, complemented
19	C₄×#1159	C₂	1	1	yes	maximal, characteristic, complemented
20	#90221	C₂	1	1	yes	maximal, characteristic, complemented
21	#90213	C₂	1	1	yes	maximal, characteristic, complemented
22	#90202	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×#6456	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#1159	C₂²	1	1	yes	characteristic
25	C₂×#1159	C₂²	1	2	yes	complemented
26	C₂×D₄×D₇	C₂²	1	2	yes	—
27	C₂×D₄×D₇	C₂²	1	1	yes	characteristic
28	C₂×#1157	C₂²	1	1	yes	characteristic
29	C₂²×D₂₈	C₂²	1	1	yes	characteristic
30	C₂²×C₄×D₇	C₂²	1	2	yes	complemented
31	C₂²×C₄×D₇	C₂²	1	2	yes	complemented
32	C₇×#126	C₂²	1	2	yes	complemented
33	C₇×#125	C₂²	1	1	yes	characteristic, complemented
34	C₇×#123	C₂²	1	2	yes	complemented
35	C₇×#121	C₂²	1	1	yes	characteristic
36	C₇×#121	C₂²	1	1	yes	characteristic, complemented
37	C₇×#121	C₂²	1	2	yes	complemented
38	C₄×C₇×D₄	C₂²	1	1	yes	characteristic, complemented
39	C₄×C₇×D₄	C₂²	1	2	yes	complemented
40	C₄×C₇×D₄	C₂²	1	1	yes	characteristic, complemented
41	C₇×#117	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
43	#6503	C₂²	1	1	yes	characteristic
44	#6502	C₂²	1	2	yes	complemented
45	#6501	C₂²	1	2	yes	complemented
46	#6500	C₂²	1	2	yes	—
47	#6500	C₂²	1	2	yes	complemented
48	#6500	C₂²	1	2	yes	complemented
49	#6499	C₂²	1	1	yes	characteristic, complemented
50	#6498	C₂²	1	2	yes	complemented
51	D₄×Dic₇	C₂²	1	1	yes	characteristic, complemented
52	D₄×Dic₇	C₂²	1	1	yes	characteristic, complemented
53	D₄×Dic₇	C₂²	1	2	yes	complemented
54	#6493	C₂²	1	1	yes	characteristic, complemented
55	#6492	C₂²	1	2	yes	complemented
56	C₄×C₂²⋊D₇	C₂²	1	1	yes	characteristic
57	C₄×C₂²⋊D₇	C₂²	1	2	yes	—
58	C₄×C₂²⋊D₇	C₂²	1	1	yes	characteristic, complemented
59	C₄×C₂²⋊D₇	C₂²	1	2	yes	complemented
60	C₄×C₂²⋊D₇	C₂²	1	2	yes	complemented
61	C₂×(C₂×D₇)⋊C₄	C₂²	1	2	yes	complemented
62	#6487	C₂²	1	1	yes	characteristic, complemented
63	#6487	C₂²	1	2	yes	complemented
64	C₂×C₄×Dic₇	C₂²	1	1	yes	characteristic, complemented
65	C₂×C₄×Dic₇	C₂²	1	1	yes	characteristic, complemented
66	#6461	C₂²	1	2	yes	complemented
67	#6460	C₂²	1	2	yes	complemented
68	#6460	C₂²	1	1	yes	characteristic, complemented
69	#6459	C₂²	1	2	yes	complemented
70	#6459	C₂²	1	2	yes	complemented
71	#6459	C₂²	1	2	yes	complemented
72	#6458	C₂²	1	1	yes	characteristic
73	#6457	C₂²	1	2	yes	complemented
74	#6457	C₂²	1	2	yes	complemented
75	#6456	C₂²	1	1	yes	characteristic
76	#6456	C₂²	1	1	yes	characteristic
77	#6456	C₂²	1	1	yes	characteristic
78	#6456	C₂²	1	1	yes	characteristic, complemented
79	#6456	C₂²	1	2	yes	complemented
80	#6456	C₂²	1	2	yes	complemented
81	#6456	C₂²	1	2	yes	complemented
82	#6456	C₂²	1	1	yes	characteristic, complemented
83	#6455	C₂²	1	2	yes	complemented
84	#6455	C₂²	1	1	yes	characteristic, complemented
85	D₇×C₄⋊C₄	C₂²	1	2	yes	complemented
86	D₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
87	#6453	C₂²	1	1	yes	characteristic, complemented
88	#6452	C₂²	1	2	yes	complemented
89	#6451	C₂²	1	1	yes	characteristic, complemented
90	#6450	C₂²	1	1	yes	characteristic, complemented
91	#6450	C₂²	1	1	yes	characteristic, complemented
92	#6450	C₂²	1	1	yes	characteristic, complemented
93	#6448	C₂²	1	2	yes	complemented
94	#6448	C₂²	1	2	yes	complemented
95	#6447	C₂²	1	2	yes	—
96	#6447	C₂²	1	2	yes	complemented
97	#6447	C₂²	1	2	yes	complemented
98	#6446	C₂²	1	2	yes	complemented
99	#6446	C₂²	1	2	yes	complemented
100	#6446	C₂²	1	2	yes	complemented
101	#6445	C₂²	1	2	yes	—
102	(C₂²⋊D₇)⋊C₄	C₂²	1	1	yes	characteristic
103	(C₂²⋊D₇)⋊C₄	C₂²	1	2	yes	complemented
104	(C₂²⋊D₇)⋊C₄	C₂²	1	2	yes	complemented
105	(C₂²⋊D₇)⋊C₄	C₂²	1	2	yes	complemented
106	(C₂²⋊D₇)⋊C₄	C₂²	1	2	yes	complemented
107	(C₂²⋊D₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
108	D₇×C₂²⋊C₄	C₂²	1	2	yes	complemented
109	D₇×C₂²⋊C₄	C₂²	1	2	yes	complemented
110	D₇×C₂²⋊C₄	C₂²	1	2	yes	complemented
111	#6442	C₂²	1	2	yes	complemented
112	#6440	C₂²	1	2	yes	complemented
113	#6440	C₂²	1	1	yes	characteristic, complemented
114	#6440	C₂²	1	1	yes	characteristic, complemented
115	#6439	C₂²	1	2	yes	complemented
116	#6438	C₂²	1	1	yes	characteristic, complemented
117	C₄×D₂₈	C₂²	1	1	yes	characteristic
118	C₄×D₂₈	C₂²	1	2	yes	complemented
119	#6435	C₂²	1	2	yes	complemented
120	C₄²×D₇	C₂²	1	1	yes	characteristic, complemented
121	C₄²×D₇	C₂²	1	2	yes	complemented
122	C₄×Dic₁₄	C₂²	1	1	yes	characteristic, complemented
123	#3481	—	7	1	no	maximal, Sylow
124	C₂³×D₇	C₂³	1	2	yes	—
125	C₂³×D₇	C₂³	1	2	yes	—
126	C₂×C₇×D₄	C₂³	1	2	yes	—
127	C₂×C₇×D₄	C₂³	1	1	yes	characteristic
128	C₂×C₇×D₄	C₂³	1	1	yes	characteristic
129	C₂×C₇×D₄	C₂³	1	2	yes	—
130	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
131	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
132	C₂²×C₄×C₇	C₂³	1	2	yes	—
133	C₂²×C₄×C₇	C₂³	1	2	yes	—
134	C₂×C₂²⋊D₇	C₂³	1	2	yes	—
135	C₂×C₂²⋊D₇	C₂³	1	2	yes	—
136	C₂×C₂²⋊D₇	C₂³	1	2	yes	—
137	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
138	C₂×C₂²⋊D₇	C₂³	1	2	yes	—
139	C₂×C₂²⋊D₇	C₂³	1	2	yes	—
140	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
141	C₂²×Dic₇	C₂³	1	1	yes	characteristic
142	C₂²×Dic₇	C₂³	1	2	yes	—
143	C₂²×Dic₇	C₂³	1	1	yes	characteristic
144	C₂²×Dic₇	C₂³	1	1	yes	characteristic
145	C₂²×Dic₇	C₂³	1	1	yes	characteristic
146	#1159	—	2	4	no	—
147	#1159	—	4	4	no	—
148	D₄×D₇	—	2	8	no	—
149	D₄×D₇	—	2	4	no	—
150	#1157	—	2	4	no	—
151	C₂×D₂₈	—	2	4	no	—
152	C₂×D₂₈	C₂³	1	2	yes	—
153	C₂×D₂₈	C₂³	1	1	yes	characteristic
154	C₂×D₂₈	C₂³	1	2	yes	—
155	C₂×D₂₈	C₂³	1	1	yes	characteristic
156	C₂×C₄×D₇	—	4	4	no	—
157	C₂×C₄×D₇	—	4	4	no	—
158	C₂×C₄×D₇	C₂³	1	2	yes	—
159	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
160	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
161	C₂×C₄×D₇	C₂³	1	2	yes	—
162	C₂×C₄×D₇	C₂³	1	2	yes	—
163	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
164	C₂×C₄×D₇	C₂³	1	2	yes	—
165	C₂×C₄×D₇	C₂³	1	2	yes	—
166	C₂×C₄×D₇	C₂³	1	2	yes	—
167	C₂×C₄×D₇	C₂³	1	2	yes	—
168	C₂×C₄×D₇	C₂³	1	2	yes	—
169	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
170	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
171	C₂×Dic₁₄	C₂³	1	2	yes	—
172	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
173	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
174	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
175	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
176	C₇×C₄⋊C₄	C₂³	1	2	yes	—
177	C₇×C₄⋊C₄	C₂³	1	2	yes	—
178	C₇×C₄⋊C₄	C₂³	1	2	yes	—
179	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
180	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
181	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
189	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
190	C₂²⋊Dic₇	C₂³	1	2	yes	—
191	C₂²⋊Dic₇	C₂³	1	2	yes	—
192	C₂²⋊Dic₇	C₂³	1	2	yes	—
193	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
194	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
195	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
196	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
204	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
205	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
206	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
207	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
208	C₄⋊Dic₇	C₂³	1	2	yes	—
209	C₄⋊Dic₇	C₂³	1	2	yes	—
210	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
211	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
212	Dic₇⋊C₄	C₂³	1	2	yes	—
213	Dic₇⋊C₄	C₂³	1	2	yes	—
214	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
215	Dic₇⋊C₄	C₂³	1	2	yes	—
216	Dic₇⋊C₄	C₂³	1	2	yes	—
217	Dic₇⋊C₄	C₂³	1	2	yes	—
218	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
219	Dic₇⋊C₄	C₂³	1	2	yes	—
220	C₄×Dic₇	C₂³	1	1	yes	characteristic
221	C₄×Dic₇	C₂³	1	1	yes	characteristic
222	C₄×Dic₇	C₂³	1	1	yes	characteristic
223	C₄×Dic₇	C₂³	1	1	yes	characteristic
224	C₄×Dic₇	C₂³	1	2	yes	—
225	C₄×Dic₇	C₂³	1	1	yes	characteristic
226	C₄×Dic₇	C₂³	1	2	yes	—
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	1	yes	characteristic
231	#559	—	7	1	no	—
232	#554	—	7	1	no	—
233	#554	—	7	1	no	—
234	#553	—	7	2	no	—
235	#553	—	7	1	no	—
236	#553	D₇	1	1	yes	characteristic, complemented
237	#551	—	7	2	no	—
238	#551	—	7	2	no	—
239	#546	—	7	2	no	—
240	#546	—	7	1	no	—
241	#546	—	7	1	no	—
242	D₄²	—	7	1	no	—
243	#532	—	7	1	no	—
244	#529	—	7	2	no	—
245	#529	—	7	1	no	—
246	#529	—	7	1	no	—
247	#525	—	7	2	no	—
248	#525	—	7	2	no	—
249	C₄×#41	—	7	1	no	—
250	C₄×#41	—	7	1	no	—
251	C₂×C₄×D₄	—	7	2	no	—
252	C₂×C₄×D₄	—	7	1	no	—
253	C₂×C₄×D₄	—	7	1	no	—
254	C₂³×C₇	C₂⁴	1	2	yes	—
255	C₂³×C₇	C₂⁴	1	1	yes	characteristic
256	C₂³×C₇	C₂⁴	1	1	yes	characteristic
257	C₂²×D₇	—	2	4	no	—
258	C₂²×D₇	—	2	4	no	—
259	C₂²×D₇	—	2	4	no	—
260	C₂²×D₇	—	2	4	no	—
261	C₂²×D₇	—	4	2	no	—
262	C₂²×D₇	—	4	2	no	—
263	C₂²×D₇	C₂⁴	1	2	yes	—
264	C₂²×D₇	C₂⁴	1	1	yes	characteristic
265	C₂²×D₇	C₂⁴	1	2	yes	—
266	C₇×D₄	—	2	4	no	—
267	C₇×D₄	—	2	2	no	—
268	C₇×D₄	—	2	2	no	—
269	C₇×D₄	—	4	2	no	—
270	C₂×C₄×C₇	—	2	2	no	—
271	C₂×C₄×C₇	—	2	2	no	—
272	C₂×C₄×C₇	—	4	2	no	—
273	C₂×C₄×C₇	—	4	2	no	—
274	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
275	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
276	C₂×C₄×C₇	C₂⁴	1	2	yes	—
277	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
278	C₂×C₄×C₇	C₂⁴	1	2	yes	—
279	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
280	C₂×C₄×C₇	C₂⁴	1	2	yes	—
281	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
282	C₂²⋊D₇	—	2	4	no	—
283	C₂²⋊D₇	—	2	4	no	—
284	C₂²⋊D₇	—	2	2	no	—
285	C₂²⋊D₇	—	2	4	no	—
286	C₂²⋊D₇	—	4	2	no	—
287	C₂²⋊D₇	—	4	2	no	—
288	C₂²⋊D₇	#41	1	4	yes	complemented
289	C₂×Dic₇	—	2	2	no	—
290	C₂×Dic₇	—	2	2	no	—
291	C₂×Dic₇	—	2	2	no	—
292	C₂×Dic₇	—	2	4	no	—
293	C₂×Dic₇	—	2	2	no	—
294	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
295	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
296	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
297	C₂×Dic₇	C₂⁴	1	2	yes	—
298	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
299	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
300	C₂×Dic₇	C₂⁴	1	2	yes	—
301	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
302	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
303	D₂₈	—	2	4	no	—
304	D₂₈	—	2	4	no	—
305	D₂₈	—	2	2	no	—
306	D₂₈	#41	1	4	yes	complemented
307	C₄×D₇	—	2	4	no	—
308	C₄×D₇	—	2	2	no	—
309	C₄×D₇	—	2	2	no	—
310	C₄×D₇	—	2	4	no	—
311	C₄×D₇	—	2	2	no	—
312	C₄×D₇	—	2	4	no	—
313	C₄×D₇	—	2	4	no	—
314	C₄×D₇	—	4	2	no	—
315	C₄×D₇	—	4	2	no	—
316	C₄×D₇	—	4	2	no	—
317	C₄×D₇	—	4	2	no	—
318	Dic₁₄	—	2	2	no	—
319	Dic₁₄	—	2	2	no	—
320	Dic₁₄	—	4	2	no	—
321	C₂×#41	—	7	1	no	—
322	C₂×#41	—	7	2	no	—
323	C₂×#41	—	7	1	no	—
324	C₂²×D₄	—	7	2	no	—
325	C₂²×D₄	—	7	1	no	—
326	C₂²×D₄	—	7	1	no	—
327	C₂³×C₄	—	7	2	no	—
328	C₂³×C₄	—	7	2	no	—
329	C₄⋊Q₈	—	7	1	no	—
330	#127	—	7	1	no	—
331	#126	—	7	2	no	—
332	#126	—	7	2	no	—
333	#126	—	7	2	no	—
334	#126	C₂×D₇	1	2	yes	complemented
335	#125	—	7	2	no	—
336	#125	—	7	1	no	—
337	#125	C₂×D₇	1	1	yes	characteristic, complemented
338	#124	—	7	1	no	—
339	#124	—	7	2	no	—
340	#124	—	7	2	no	—
341	#124	—	7	1	no	—
342	#123	—	7	2	no	—
343	#123	—	7	2	no	—
344	#123	—	7	2	no	—
345	#123	—	7	2	no	—
346	#123	—	7	2	no	—
347	#123	—	7	2	no	—
348	#123	—	7	2	no	—
349	#123	C₂×D₇	1	2	yes	complemented
350	C₂²⋊Q₈	—	7	2	no	—
351	C₂²⋊Q₈	—	7	1	no	—
352	C₂²⋊Q₈	—	7	2	no	—
353	C₂²⋊Q₈	—	7	2	no	—
354	C₂²⋊Q₈	—	7	2	no	—
355	C₂²⋊Q₈	—	7	2	no	—
356	C₂²⋊Q₈	—	7	1	no	—
357	#121	—	7	2	no	—
358	#121	—	7	2	no	—
359	#121	—	7	1	no	—
360	#121	—	7	1	no	—
361	#121	—	7	2	no	—
362	#121	—	7	2	no	—
363	#121	—	7	2	no	—
364	#121	C₂×D₇	1	1	yes	characteristic
365	#121	C₂×D₇	1	2	yes	complemented
366	#121	C₂×D₇	1	1	yes	characteristic, complemented
367	#120	—	7	2	no	—
368	#120	—	7	2	no	—
369	#120	—	7	2	no	—
370	#120	—	7	2	no	—
371	C₄×Q₈	—	7	1	no	—
372	C₄×Q₈	—	7	1	no	—
373	C₄×Q₈	—	7	1	no	—
374	C₄×Q₈	—	7	1	no	—
375	C₄×D₄	—	7	2	no	—
376	C₄×D₄	—	7	1	no	—
377	C₄×D₄	—	7	1	no	—
378	C₄×D₄	—	7	2	no	—
379	C₄×D₄	—	7	2	no	—
380	C₄×D₄	—	7	2	no	—
381	C₄×D₄	—	7	1	no	—
382	C₄×D₄	—	7	1	no	—
383	C₄×D₄	—	7	1	no	—
384	C₄×D₄	—	7	2	no	—
385	C₄×D₄	—	7	2	no	—
386	C₄×D₄	—	7	1	no	—
387	C₄×D₄	—	7	1	no	—
388	C₄×D₄	—	7	2	no	—
389	C₄×D₄	—	7	1	no	—
390	C₄×D₄	—	7	1	no	—
391	C₄×D₄	—	7	1	no	—
392	C₄×D₄	—	7	2	no	—
393	C₄×D₄	—	7	2	no	—
394	C₄×D₄	—	7	1	no	—
395	C₄×D₄	—	7	2	no	—
396	C₄×D₄	—	7	2	no	—
397	C₄×D₄	—	7	1	no	—
398	C₄×D₄	—	7	2	no	—
399	C₄×D₄	C₂×D₇	1	2	yes	complemented
400	C₄×D₄	C₂×D₇	1	1	yes	characteristic, complemented
401	C₄×D₄	C₂×D₇	1	1	yes	characteristic, complemented
402	#117	—	7	1	no	—
403	#117	—	7	2	no	—
404	#117	—	7	1	no	—
405	#117	—	7	1	no	—
406	#117	—	7	2	no	—
407	#117	—	7	2	no	—
408	#117	C₂×D₇	1	1	yes	characteristic, complemented
409	C₂×C₄⋊C₄	—	7	2	no	—
410	C₂×C₄⋊C₄	—	7	1	no	—
411	C₂×C₄⋊C₄	C₂×D₇	1	1	yes	characteristic, complemented
412	C₂×C₂²⋊C₄	—	7	2	no	—
413	C₂×C₂²⋊C₄	—	7	2	no	—
414	C₂×C₂²⋊C₄	—	7	2	no	—
415	C₂×C₂²⋊C₄	—	7	2	no	—
416	C₂×C₄²	—	7	1	no	—
417	C₂×C₄²	—	7	1	no	—
418	C₂×C₄²	—	7	1	no	—
419	C₂×C₄²	—	7	2	no	—
420	C₂²×C₇	—	2	1	no	—
421	C₂²×C₇	—	2	1	no	—
422	C₂²×C₇	—	2	1	no	—
423	C₂²×C₇	—	2	1	no	—
424	C₂²×C₇	—	2	2	no	—
425	C₂²×C₇	—	2	2	no	—
426	C₂²×C₇	—	2	1	no	—
427	C₂²×C₇	—	2	2	no	—
428	C₂²×C₇	C₂×#41	1	2	yes	—
429	C₂²×C₇	C₂⁵	1	1	yes	characteristic
430	C₂×D₇	—	2	1	no	—
431	C₂×D₇	—	2	2	no	—
432	C₂×D₇	—	2	1	no	—
433	C₂×D₇	—	2	2	no	—
434	C₂×D₇	—	2	2	no	—
435	C₂×D₇	—	2	2	no	—
436	C₂×D₇	—	2	2	no	—
437	C₂×D₇	—	4	8	no	—
438	C₂×D₇	—	4	8	no	—
439	C₂×D₇	C₂×#41	1	2	yes	—
440	C₂×D₇	C₂×#41	1	4	yes	—
441	C₄×C₇	—	2	1	no	—
442	C₄×C₇	—	2	1	no	—
443	C₄×C₇	—	2	2	no	—
444	C₄×C₇	—	2	1	no	—
445	C₄×C₇	—	2	2	no	—
446	C₄×C₇	—	2	1	no	—
447	C₄×C₇	—	2	2	no	—
448	C₄×C₇	C₂×#41	1	2	yes	—
449	Dic₇	—	2	2	no	—
450	Dic₇	—	2	1	no	—
451	Dic₇	—	2	1	no	—
452	Dic₇	—	2	1	no	—
453	Dic₇	—	2	1	no	—
454	Dic₇	—	2	2	no	—
455	Dic₇	—	2	1	no	—
456	Dic₇	C₂×#41	1	2	yes	—
457	Dic₇	H(5,𝔽₂)	1	2	yes	—
458	C₂⁴	—	7	2	no	—
459	C₂⁴	—	7	2	no	—
460	#41	—	14	4	no	—
461	#41	—	14	4	no	—
462	#41	—	28	4	no	—
463	C₂×Q₈	—	7	1	no	—
464	C₂×Q₈	—	7	1	no	—
465	C₂×Q₈	—	7	2	no	—
466	C₂×D₄	—	7	1	no	—
467	C₂×D₄	—	7	1	no	—
468	C₂×D₄	—	7	2	no	—
469	C₂×D₄	—	7	2	no	—
470	C₂×D₄	—	7	2	no	—
471	C₂×D₄	—	7	2	no	—
472	C₂×D₄	—	7	2	no	—
473	C₂×D₄	—	7	1	no	—
474	C₂×D₄	—	7	2	no	—
475	C₂×D₄	—	7	2	no	—
476	C₂×D₄	—	7	1	no	—
477	C₂×D₄	—	14	4	no	—
478	C₂×D₄	—	14	8	no	—
479	C₂×D₄	—	14	4	no	—
480	C₂×D₄	C₂²×D₇	1	1	yes	characteristic
481	C₂×D₄	C₂²×D₇	1	2	yes	—
482	C₂×D₄	C₂²×D₇	1	1	yes	characteristic
483	C₂×D₄	C₂²×D₇	1	2	yes	—
484	C₂²×C₄	—	7	1	no	—
485	C₂²×C₄	—	7	1	no	—
486	C₂²×C₄	—	7	1	no	—
487	C₂²×C₄	—	7	1	no	—
488	C₂²×C₄	—	7	2	no	—
489	C₂²×C₄	—	7	1	no	—
490	C₂²×C₄	—	7	2	no	—
491	C₂²×C₄	—	7	2	no	—
492	C₂²×C₄	—	7	1	no	—
493	C₂²×C₄	—	7	2	no	—
494	C₂²×C₄	—	7	1	no	—
495	C₂²×C₄	—	7	2	no	—
496	C₂²×C₄	—	7	2	no	—
497	C₂²×C₄	—	7	2	no	—
498	C₂²×C₄	—	7	2	no	—
499	C₂²×C₄	—	7	2	no	—
500	C₂²×C₄	—	28	4	no	—
501	C₂²×C₄	—	28	4	no	—
502	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
503	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
504	C₂²×C₄	C₂²×D₇	1	2	yes	—
505	C₂²×C₄	C₂²×D₇	1	2	yes	—
506	C₄⋊C₄	—	7	1	no	—
507	C₄⋊C₄	—	7	2	no	—
508	C₄⋊C₄	—	7	2	no	—
509	C₄⋊C₄	—	7	1	no	—
510	C₄⋊C₄	—	7	1	no	—
511	C₄⋊C₄	—	7	2	no	—
512	C₄⋊C₄	—	7	2	no	—
513	C₄⋊C₄	—	7	1	no	—
514	C₄⋊C₄	—	7	2	no	—
515	C₄⋊C₄	—	7	2	no	—
516	C₄⋊C₄	—	7	1	no	—
517	C₄⋊C₄	—	7	2	no	—
518	C₄⋊C₄	—	7	1	no	—
519	C₄⋊C₄	—	7	2	no	—
520	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
521	C₄⋊C₄	C₂²×D₇	1	2	yes	—
522	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
523	C₄⋊C₄	C₂²×D₇	1	2	yes	—
524	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
525	C₄⋊C₄	C₂²×D₇	1	2	yes	—
526	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
527	C₂²⋊C₄	—	7	2	no	—
528	C₂²⋊C₄	—	7	2	no	—
529	C₂²⋊C₄	—	7	2	no	—
530	C₂²⋊C₄	—	7	1	no	—
531	C₂²⋊C₄	—	7	1	no	—
532	C₂²⋊C₄	—	7	2	no	—
533	C₂²⋊C₄	—	7	2	no	—
534	C₂²⋊C₄	—	7	1	no	—
535	C₂²⋊C₄	—	7	2	no	—
536	C₂²⋊C₄	—	7	2	no	—
537	C₂²⋊C₄	—	7	2	no	—
538	C₂²⋊C₄	—	7	2	no	—
539	C₂²⋊C₄	—	7	2	no	—
540	C₂²⋊C₄	—	7	2	no	—
541	C₂²⋊C₄	—	7	2	no	—
542	C₂²⋊C₄	—	7	1	no	—
543	C₂²⋊C₄	—	7	2	no	—
544	C₂²⋊C₄	—	7	2	no	—
545	C₂²⋊C₄	—	7	2	no	—
546	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
547	C₂²⋊C₄	C₂²×D₇	1	2	yes	—
548	C₂²⋊C₄	C₂²×D₇	1	2	yes	—
549	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
550	C₂²⋊C₄	C₂²×D₇	1	2	yes	—
551	C₂²⋊C₄	C₂²×D₇	1	2	yes	—
552	C₄²	—	7	1	no	—
553	C₄²	—	7	1	no	—
554	C₄²	—	7	1	no	—
555	C₄²	—	7	1	no	—
556	C₄²	—	7	2	no	—
557	C₄²	—	7	1	no	—
558	C₄²	—	7	1	no	—
559	C₄²	—	7	1	no	—
560	C₄²	—	7	2	no	—
561	C₄²	—	7	1	no	—
562	C₄²	—	7	1	no	—
563	C₄²	C₂²×D₇	1	2	yes	—
564	C₄²	C₂²×D₇	1	1	yes	characteristic
565	C₂×C₇	—	2	2	no	—
566	C₂×C₇	—	4	2	no	—
567	C₂×C₇	—	4	1	no	—
568	C₂×C₇	C₂²×#41	1	1	yes	characteristic
569	C₂×C₇	C₂²×#41	1	1	yes	characteristic
570	C₂×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
571	D₇	—	2	2	no	—
572	D₇	—	2	4	no	—
573	D₇	—	4	2	no	—
574	C₂³	—	7	1	no	—
575	C₂³	—	7	2	no	—
576	C₂³	—	7	2	no	—
577	C₂³	—	14	4	no	—
578	C₂³	—	14	4	no	—
579	C₂³	—	14	4	no	—
580	C₂³	—	14	4	no	—
581	C₂³	—	28	2	no	—
582	C₂³	—	28	2	no	—
583	C₂³	C₂³×D₇	1	2	yes	—
584	C₂³	C₂³×D₇	1	1	yes	characteristic
585	C₂³	C₂³×D₇	1	1	yes	characteristic
586	Q₈	—	14	2	no	—
587	Q₈	—	14	2	no	—
588	Q₈	—	28	2	no	—
589	D₄	—	2	4	no	—
590	D₄	—	2	2	no	—
591	D₄	—	2	2	no	—
592	D₄	—	4	2	no	—
593	D₄	—	7	4	no	—
594	D₄	—	7	4	no	—
595	D₄	—	14	4	no	—
596	D₄	—	14	4	no	—
597	D₄	—	14	4	no	—
598	D₄	—	14	4	no	—
599	D₄	—	14	4	no	—
600	D₄	—	14	2	no	—
601	D₄	—	14	2	no	—
602	D₄	—	28	2	no	—
603	D₄	—	28	2	no	—
604	C₂×C₄	—	2	2	no	—
605	C₂×C₄	—	2	2	no	—
606	C₂×C₄	—	4	2	no	—
607	C₂×C₄	—	4	2	no	—
608	C₂×C₄	—	7	1	no	—
609	C₂×C₄	—	7	1	no	—
610	C₂×C₄	—	7	1	no	—
611	C₂×C₄	—	7	2	no	—
612	C₂×C₄	—	7	1	no	—
613	C₂×C₄	—	7	1	no	—
614	C₂×C₄	—	7	1	no	—
615	C₂×C₄	—	7	1	no	—
616	C₂×C₄	—	7	2	no	—
617	C₂×C₄	—	14	2	no	—
618	C₂×C₄	—	14	4	no	—
619	C₂×C₄	—	14	4	no	—
620	C₂×C₄	—	14	4	no	—
621	C₂×C₄	—	14	4	no	—
622	C₂×C₄	—	14	2	no	—
623	C₂×C₄	—	14	2	no	—
624	C₂×C₄	—	14	4	no	—
625	C₂×C₄	—	14	2	no	—
626	C₂×C₄	—	14	2	no	—
627	C₂×C₄	—	14	2	no	—
628	C₂×C₄	—	14	2	no	—
629	C₂×C₄	—	28	2	no	—
630	C₂×C₄	—	28	2	no	—
631	C₂×C₄	—	28	2	no	—
632	C₂×C₄	—	28	2	no	—
633	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
634	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
635	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
636	C₂×C₄	C₂³×D₇	1	2	yes	—
637	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
638	C₂×C₄	C₂³×D₇	1	2	yes	—
639	C₂×C₄	C₂³×D₇	1	2	yes	—
640	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
641	C₇	#3481	1	1	yes	characteristic, complemented, Sylow
642	C₂²	—	2	1	no	—
643	C₂²	—	2	1	no	—
644	C₂²	—	2	1	no	—
645	C₂²	—	2	1	no	—
646	C₂²	—	2	2	no	—
647	C₂²	—	2	2	no	—
648	C₂²	—	2	2	no	—
649	C₂²	—	2	1	no	—
650	C₂²	—	7	2	no	—
651	C₂²	—	7	4	no	—
652	C₂²	—	14	2	no	—
653	C₂²	—	14	1	no	—
654	C₂²	—	14	2	no	—
655	C₂²	—	14	1	no	—
656	C₂²	—	14	2	no	—
657	C₂²	—	14	2	no	—
658	C₂²	—	14	2	no	—
659	C₂²	—	28	8	no	—
660	C₂²	—	28	8	no	—
661	C₂²	D₇×#41	1	2	yes	—
662	C₂²	C₂⁴×D₇	1	1	yes	characteristic
663	C₄	—	2	1	no	—
664	C₄	—	2	1	no	—
665	C₄	—	2	2	no	—
666	C₄	—	2	1	no	—
667	C₄	—	2	1	no	—
668	C₄	—	2	2	no	—
669	C₄	—	2	2	no	—
670	C₄	—	7	2	no	—
671	C₄	—	7	2	no	—
672	C₄	—	14	1	no	—
673	C₄	—	14	1	no	—
674	C₄	—	14	1	no	—
675	C₄	—	14	2	no	—
676	C₄	—	14	1	no	—
677	C₄	—	14	2	no	—
678	C₄	—	14	1	no	—
679	C₄	D₇×#41	1	2	yes	—
680	C₂	—	2	2	no	—
681	C₂	—	4	2	no	—
682	C₂	—	4	1	no	—
683	C₂	—	14	4	no	—
684	C₂	—	14	2	no	—
685	C₂	—	28	2	no	—
686	C₂	C₂×D₇×#41	1	1	yes	characteristic
687	C₂	C₂×D₇×#41	1	1	yes	characteristic
688	C₂	D₇×H(5,𝔽₂)	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₇
commutator, socle, cosocle	C₂²×C₇	C₂⁵
Fitting	C₇×#553	C₂
hypercenter	#553	D₇
hypocenter	C₇	#3481
LCS	G ▷ C₂²×C₇ ▷ C₇
UCS	C₁ ◁ C₂² ◁ #553

Complements

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

N	H ≅ G/N	type
1. C₇×#553	C₂	semidirect
2. #90397	C₂	semidirect
3. #90396	C₂	semidirect
4. #90382	C₂	semidirect
5. #90381	C₂	semidirect
6. #90352	C₂	semidirect
7. #90347	C₂	semidirect
8. #90303	C₂	semidirect
9. #90301	C₂	semidirect
10. #90300	C₂	semidirect
11. #90297	C₂	semidirect
12. #90291	C₂	semidirect
13. #90287	C₂	semidirect
14. #90250	C₂	semidirect
15. #90247	C₂	semidirect
16. #90241	C₂	semidirect
17. C₄×D₄×D₇	C₂	semidirect
18. C₄×D₄×D₇	C₂	semidirect
19. C₄×#1159	C₂	semidirect
20. #90221	C₂	semidirect
21. #90213	C₂	semidirect
22. #90202	C₂	semidirect
23. C₂×#6456	C₂	semidirect
25. C₂×#1159	C₂²	semidirect
30. C₂²×C₄×D₇	C₂²	semidirect
31. C₂²×C₄×D₇	C₂²	semidirect
32. C₇×#126	C₂²	semidirect
33. C₇×#125	C₂²	semidirect
34. C₇×#123	C₂²	semidirect
36. C₇×#121	C₂²	semidirect
37. C₇×#121	C₂²	semidirect
38. C₄×C₇×D₄	C₂²	semidirect
39. C₄×C₇×D₄	C₂²	semidirect
40. C₄×C₇×D₄	C₂²	semidirect
41. C₇×#117	C₂²	semidirect
42. C₂×C₇×C₄⋊C₄	C₂²	semidirect
44. #6502	C₂²	semidirect
45. #6501	C₂²	semidirect
47. #6500	C₂²	semidirect
48. #6500	C₂²	semidirect
49. #6499	C₂²	semidirect
50. #6498	C₂²	semidirect
51. D₄×Dic₇	C₂²	semidirect
52. D₄×Dic₇	C₂²	semidirect
53. D₄×Dic₇	C₂²	semidirect
54. #6493	C₂²	semidirect
55. #6492	C₂²	semidirect
58. C₄×C₂²⋊D₇	C₂²	semidirect
59. C₄×C₂²⋊D₇	C₂²	semidirect
60. C₄×C₂²⋊D₇	C₂²	semidirect
61. C₂×(C₂×D₇)⋊C₄	C₂²	semidirect
62. #6487	C₂²	semidirect
63. #6487	C₂²	semidirect
64. C₂×C₄×Dic₇	C₂²	semidirect
65. C₂×C₄×Dic₇	C₂²	semidirect
66. #6461	C₂²	semidirect
67. #6460	C₂²	semidirect
68. #6460	C₂²	semidirect
69. #6459	C₂²	semidirect
70. #6459	C₂²	semidirect
71. #6459	C₂²	semidirect
73. #6457	C₂²	semidirect
74. #6457	C₂²	semidirect
78. #6456	C₂²	semidirect
79. #6456	C₂²	semidirect
80. #6456	C₂²	semidirect
81. #6456	C₂²	semidirect
82. #6456	C₂²	semidirect
83. #6455	C₂²	semidirect
84. #6455	C₂²	semidirect
85. D₇×C₄⋊C₄	C₂²	semidirect
86. D₇×C₄⋊C₄	C₂²	semidirect
87. #6453	C₂²	semidirect
88. #6452	C₂²	semidirect
89. #6451	C₂²	semidirect
90. #6450	C₂²	semidirect
91. #6450	C₂²	semidirect
92. #6450	C₂²	semidirect
93. #6448	C₂²	semidirect
94. #6448	C₂²	semidirect
96. #6447	C₂²	semidirect
97. #6447	C₂²	semidirect
98. #6446	C₂²	semidirect
99. #6446	C₂²	semidirect
100. #6446	C₂²	semidirect
103. (C₂²⋊D₇)⋊C₄	C₂²	semidirect
104. (C₂²⋊D₇)⋊C₄	C₂²	semidirect
105. (C₂²⋊D₇)⋊C₄	C₂²	semidirect
106. (C₂²⋊D₇)⋊C₄	C₂²	semidirect
107. (C₂²⋊D₇)⋊C₄	C₂²	semidirect
108. D₇×C₂²⋊C₄	C₂²	semidirect
109. D₇×C₂²⋊C₄	C₂²	semidirect
110. D₇×C₂²⋊C₄	C₂²	semidirect
111. #6442	C₂²	semidirect
112. #6440	C₂²	semidirect
113. #6440	C₂²	semidirect
114. #6440	C₂²	semidirect
115. #6439	C₂²	semidirect
116. #6438	C₂²	semidirect
118. C₄×D₂₈	C₂²	semidirect
119. #6435	C₂²	semidirect
120. C₄²×D₇	C₂²	semidirect
121. C₄²×D₇	C₂²	semidirect
122. C₄×Dic₁₄	C₂²	semidirect
236. #553	D₇	semidirect
288. C₂²⋊D₇	#41	semidirect
306. D₂₈	#41	semidirect
334. #126	C₂×D₇	semidirect
337. #125	C₂×D₇	semidirect
349. #123	C₂×D₇	semidirect
365. #121	C₂×D₇	semidirect
366. #121	C₂×D₇	semidirect
399. C₄×D₄	C₂×D₇	semidirect
400. C₄×D₄	C₂×D₇	semidirect
401. C₄×D₄	C₂×D₇	semidirect
408. #117	C₂×D₇	semidirect
411. C₂×C₄⋊C₄	C₂×D₇	semidirect
641. C₇	#3481	semidirect

Maximal subgroups

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

subgroup	index
C₇×#553	2
#90397	2
#90396	2
#90382	2
#90381	2
#90352	2
#90347	2
#90303	2
#90301	2
#90300	2
#90297	2
#90291	2
#90287	2
#90250	2
#90247	2
#90241	2
C₄×D₄×D₇	2
C₄×#1159	2
#90221	2
#90213	2
#90202	2
C₂×#6456	2
#3481	7