Subgroups — #11743785

Order 896.

1142 conjugacy classes of subgroups.

The subgroup lattice has 688 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	#90523	C₂	1	1	yes	maximal, characteristic, complemented
3	#90520	C₂	1	1	yes	maximal, characteristic, complemented
4	Q₈×C₂²⋊D₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#6510	C₂	1	1	yes	maximal, characteristic, complemented
6	#90372	C₂	1	1	yes	maximal, characteristic, complemented
7	#90369	C₂	1	2	yes	maximal, complemented
8	D₇×#124	C₂	1	1	yes	maximal, characteristic, complemented
9	#90361	C₂	1	2	yes	maximal, complemented
10	#90331	C₂	1	2	yes	maximal, complemented
11	#90328	C₂	1	2	yes	maximal, complemented
12	#90324	C₂	1	1	yes	maximal, characteristic, complemented
13	#90315	C₂	1	1	yes	maximal, characteristic, complemented
14	#90308	C₂	1	2	yes	maximal, complemented
15	#90301	C₂	1	2	yes	maximal, complemented
16	#90300	C₂	1	1	yes	maximal, characteristic, complemented
17	#90291	C₂	1	1	yes	maximal, characteristic, complemented
18	#90271	C₂	1	1	yes	maximal, characteristic, complemented
19	#90259	C₂	1	1	yes	maximal, characteristic, complemented
20	#90247	C₂	1	2	yes	maximal, complemented
21	#90241	C₂	1	1	yes	maximal, characteristic, complemented
22	#90236	C₂	1	2	yes	maximal, complemented
23	C₄×#1159	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×Q₈×D₇	C₂²	1	1	yes	characteristic, complemented
27	C₂×#1159	C₂²	1	1	yes	characteristic
28	C₂×D₄×D₇	C₂²	1	2	yes	—
29	C₂×D₄×D₇	C₂²	1	1	yes	characteristic
30	C₂×#1157	C₂²	1	1	yes	characteristic, complemented
31	C₂²×D₂₈	C₂²	1	1	yes	characteristic
32	C₇×#124	C₂²	1	2	yes	complemented
33	C₇×#124	C₂²	1	1	yes	characteristic, complemented
34	C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
35	C₇×C₂²⋊Q₈	C₂²	1	2	yes	complemented
36	C₇×#121	C₂²	1	1	yes	characteristic
37	C₇×#121	C₂²	1	2	yes	complemented
38	C₄×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
39	C₄×C₇×D₄	C₂²	1	1	yes	characteristic, complemented
40	C₄×C₇×D₄	C₂²	1	2	yes	complemented
41	#6510	C₂²	1	1	yes	characteristic
42	#6510	C₂²	1	1	yes	characteristic
43	#6510	C₂²	1	2	yes	complemented
44	#6510	C₂²	1	1	yes	characteristic, complemented
45	#6510	C₂²	1	1	yes	characteristic, complemented
46	#6510	C₂²	1	2	yes	complemented
47	#6509	C₂²	1	2	yes	complemented
48	#6509	C₂²	1	1	yes	characteristic, complemented
49	Q₈×Dic₇	C₂²	1	1	yes	characteristic, complemented
50	#6507	C₂²	1	1	yes	characteristic, complemented
51	#6507	C₂²	1	2	yes	complemented
52	#6503	C₂²	1	1	yes	characteristic
53	#6502	C₂²	1	2	yes	complemented
54	#6502	C₂²	1	2	yes	complemented
55	#6502	C₂²	1	2	yes	complemented
56	#6500	C₂²	1	2	yes	—
57	#6500	C₂²	1	2	yes	complemented
58	#6500	C₂²	1	2	yes	complemented
59	#6499	C₂²	1	1	yes	characteristic, complemented
60	#6498	C₂²	1	2	yes	complemented
61	D₄×Dic₇	C₂²	1	1	yes	characteristic, complemented
62	D₄×Dic₇	C₂²	1	1	yes	characteristic, complemented
63	D₄×Dic₇	C₂²	1	2	yes	complemented
64	#6493	C₂²	1	1	yes	characteristic
65	#6492	C₂²	1	2	yes	complemented
66	C₄×C₂²⋊D₇	C₂²	1	1	yes	characteristic
67	C₄×C₂²⋊D₇	C₂²	1	2	yes	—
68	C₄×C₂²⋊D₇	C₂²	1	1	yes	characteristic, complemented
69	C₄×C₂²⋊D₇	C₂²	1	2	yes	complemented
70	C₄×C₂²⋊D₇	C₂²	1	2	yes	complemented
71	C₂×(C₂×D₇)⋊C₄	C₂²	1	2	yes	complemented
72	C₂×(C₂×D₇)⋊C₄	C₂²	1	2	yes	complemented
73	C₂×(C₂×D₇)⋊C₄	C₂²	1	2	yes	complemented
74	#6487	C₂²	1	1	yes	characteristic, complemented
75	#6487	C₂²	1	2	yes	complemented
76	C₂×C₄×Dic₇	C₂²	1	1	yes	characteristic, complemented
77	C₂×C₄×Dic₇	C₂²	1	1	yes	characteristic, complemented
78	#6461	C₂²	1	2	yes	complemented
79	#6461	C₂²	1	2	yes	complemented
80	#6461	C₂²	1	2	yes	complemented
81	#6459	C₂²	1	2	yes	complemented
82	#6459	C₂²	1	2	yes	complemented
83	#6458	C₂²	1	1	yes	characteristic
84	#6457	C₂²	1	2	yes	complemented
85	#6457	C₂²	1	2	yes	complemented
86	#6456	C₂²	1	1	yes	characteristic
87	#6456	C₂²	1	2	yes	complemented
88	#6455	C₂²	1	1	yes	characteristic, complemented
89	#6455	C₂²	1	2	yes	complemented
90	#6453	C₂²	1	1	yes	characteristic, complemented
91	#6450	C₂²	1	1	yes	characteristic, complemented
92	#6450	C₂²	1	1	yes	characteristic, complemented
93	#6449	C₂²	1	2	yes	complemented
94	#6449	C₂²	1	2	yes	complemented
95	#6448	C₂²	1	2	yes	complemented
96	#6448	C₂²	1	2	yes	complemented
97	#6448	C₂²	1	2	yes	complemented
98	#6448	C₂²	1	2	yes	complemented
99	#6447	C₂²	1	2	yes	—
100	#6447	C₂²	1	2	yes	complemented
101	#6447	C₂²	1	2	yes	complemented
102	#6446	C₂²	1	2	yes	complemented
103	#6445	C₂²	1	2	yes	—
104	(C₂²⋊D₇)⋊C₄	C₂²	1	1	yes	characteristic
105	(C₂²⋊D₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
106	(C₂²⋊D₇)⋊C₄	C₂²	1	2	yes	complemented
107	(C₂²⋊D₇)⋊C₄	C₂²	1	2	yes	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	1	yes	characteristic, complemented
113	#6440	C₂²	1	1	yes	characteristic, complemented
114	#6440	C₂²	1	2	yes	complemented
115	#6439	C₂²	1	2	yes	complemented
116	#6438	C₂²	1	1	yes	characteristic
117	C₄×D₂₈	C₂²	1	2	yes	complemented
118	C₄×D₂₈	C₂²	1	1	yes	characteristic, complemented
119	#6435	C₂²	1	2	yes	complemented
120	#6435	C₂²	1	2	yes	complemented
121	C₄²×D₇	C₂²	1	1	yes	characteristic, complemented
122	C₄×Dic₁₄	C₂²	1	1	yes	characteristic, complemented
123	#3514	—	7	1	no	maximal, Sylow
124	C₂³×D₇	C₂³	1	2	yes	—
125	C₂³×D₇	C₂³	1	2	yes	—
126	C₇×#41	—	4	2	no	—
127	C₂×C₇×Q₈	—	4	2	no	—
128	C₂×C₇×Q₈	C₂³	1	1	yes	characteristic
129	C₂×C₇×Q₈	C₂³	1	1	yes	characteristic
130	C₂×C₇×Q₈	C₂³	1	2	yes	—
131	C₂×C₇×D₄	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	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
136	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
137	C₂²×C₄×C₇	C₂³	1	2	yes	—
138	C₂²×C₄×C₇	C₂³	1	2	yes	—
139	C₂×C₂²⋊D₇	C₂³	1	2	yes	—
140	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
141	C₂×C₂²⋊D₇	C₂³	1	2	yes	—
142	C₂×C₂²⋊D₇	C₂³	1	2	yes	—
143	C₂×C₂²⋊D₇	C₂³	1	2	yes	—
144	C₂×C₂²⋊D₇	C₂³	1	2	yes	—
145	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
146	C₂²×Dic₇	C₂³	1	1	yes	characteristic
147	C₂²×Dic₇	C₂³	1	1	yes	characteristic
148	C₂²×Dic₇	C₂³	1	2	yes	—
149	C₂²×Dic₇	C₂³	1	1	yes	characteristic
150	C₂²×Dic₇	C₂³	1	1	yes	characteristic
151	Q₈×D₇	—	4	2	no	—
152	#1159	—	2	4	no	—
153	D₄×D₇	—	2	8	no	—
154	D₄×D₇	—	4	2	no	—
155	#1157	—	4	2	no	—
156	C₂×D₂₈	—	4	2	no	—
157	C₂×D₂₈	C₂³	1	2	yes	—
158	C₂×D₂₈	C₂³	1	1	yes	characteristic
159	C₂×D₂₈	C₂³	1	1	yes	characteristic
160	C₂×D₂₈	C₂³	1	2	yes	—
161	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
162	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
163	C₂×C₄×D₇	C₂³	1	2	yes	—
164	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
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×Dic₁₄	C₂³	1	1	yes	characteristic
169	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
170	C₂×Dic₁₄	C₂³	1	2	yes	—
171	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
172	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
173	C₇×C₄⋊C₄	C₂³	1	2	yes	—
174	C₇×C₄⋊C₄	C₂³	1	2	yes	—
175	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
176	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
177	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
178	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
179	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
180	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
181	C₄²×C₇	C₂³	1	1	yes	characteristic
182	C₄²×C₇	C₂³	1	2	yes	—
183	C₂²⋊Dic₇	C₂³	1	2	yes	—
184	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
185	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
186	C₂²⋊Dic₇	C₂³	1	2	yes	—
187	C₂²⋊Dic₇	C₂³	1	2	yes	—
188	C₂²⋊Dic₇	C₂³	1	2	yes	—
189	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
190	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
191	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
192	(C₂×D₇)⋊C₄	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	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	1	yes	characteristic
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	2	yes	—
208	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
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	2	yes	—
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	1	yes	characteristic
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	1	yes	characteristic
225	C₄×Dic₇	C₂³	1	2	yes	—
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	#559	—	7	1	no	—
232	#556	—	7	1	no	—
233	#555	—	7	2	no	—
234	#551	—	7	2	no	—
235	#551	—	7	2	no	—
236	D₄×Q₈	—	7	1	no	—
237	#548	—	7	1	no	—
238	#548	D₇	1	1	yes	characteristic, complemented
239	#546	—	7	1	no	—
240	#546	—	7	2	no	—
241	#546	—	7	1	no	—
242	D₄²	—	7	1	no	—
243	#542	—	7	2	no	—
244	#538	—	7	2	no	—
245	#538	—	7	2	no	—
246	#532	—	7	1	no	—
247	#529	—	7	1	no	—
248	#529	—	7	1	no	—
249	#529	—	7	1	no	—
250	C₂×#124	—	7	1	no	—
251	C₂×#124	—	7	1	no	—
252	#518	—	7	2	no	—
253	C₄×#41	—	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	—	4	2	no	—
260	C₂²×D₇	—	4	2	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	2	yes	—
265	C₂²×D₇	C₂⁴	1	1	yes	characteristic
266	C₇×Q₈	—	2	2	no	—
267	C₇×Q₈	—	2	2	no	—
268	C₇×Q₈	—	4	2	no	—
269	C₇×D₄	—	2	4	no	—
270	C₇×D₄	—	2	2	no	—
271	C₇×D₄	—	2	2	no	—
272	C₇×D₄	—	4	2	no	—
273	C₂×C₄×C₇	—	2	2	no	—
274	C₂×C₄×C₇	—	2	2	no	—
275	C₂×C₄×C₇	—	4	2	no	—
276	C₂×C₄×C₇	—	4	2	no	—
277	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
278	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
279	C₂×C₄×C₇	C₂⁴	1	2	yes	—
280	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
281	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
282	C₂×C₄×C₇	C₂⁴	1	2	yes	—
283	C₂×C₄×C₇	C₂⁴	1	2	yes	—
284	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
285	C₂²⋊D₇	—	2	2	no	—
286	C₂²⋊D₇	—	2	4	no	—
287	C₂²⋊D₇	—	4	2	no	—
288	C₂²⋊D₇	—	4	2	no	—
289	C₂²⋊D₇	—	4	2	no	—
290	C₂²⋊D₇	—	4	2	no	—
291	C₂²⋊D₇	#41	1	4	yes	complemented
292	C₂×Dic₇	—	2	2	no	—
293	C₂×Dic₇	—	2	2	no	—
294	C₂×Dic₇	—	4	1	no	—
295	C₂×Dic₇	—	4	1	no	—
296	C₂×Dic₇	—	4	2	no	—
297	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
298	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
299	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
300	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
301	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
302	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
303	C₂×Dic₇	C₂⁴	1	2	yes	—
304	C₂×Dic₇	C₂⁴	1	2	yes	—
305	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
306	D₂₈	—	2	4	no	—
307	D₂₈	—	2	2	no	—
308	D₂₈	—	2	2	no	—
309	D₂₈	—	4	2	no	—
310	C₄×D₇	—	2	2	no	—
311	C₄×D₇	—	2	2	no	—
312	C₄×D₇	—	2	4	no	—
313	C₄×D₇	—	4	1	no	—
314	C₄×D₇	—	4	2	no	—
315	C₄×D₇	—	4	2	no	—
316	C₄×D₇	—	4	2	no	—
317	Dic₁₄	—	2	2	no	—
318	Dic₁₄	—	2	2	no	—
319	Dic₁₄	—	4	2	no	—
320	C₂×#41	—	7	1	no	—
321	C₂×#41	—	7	1	no	—
322	C₂×#41	C₂×D₇	1	1	yes	characteristic, complemented
323	C₂²×Q₈	—	7	1	no	—
324	C₂²×Q₈	C₂×D₇	1	1	yes	characteristic, complemented
325	C₂²×D₄	—	7	2	no	—
326	C₂²×D₄	—	7	1	no	—
327	C₂²×D₄	—	7	1	no	—
328	C₄⋊Q₈	—	7	1	no	—
329	C₄⋊Q₈	—	7	2	no	—
330	#127	—	7	1	no	—
331	#126	—	7	2	no	—
332	#126	—	7	2	no	—
333	#126	—	7	2	no	—
334	#126	—	7	2	no	—
335	#126	—	7	2	no	—
336	#125	—	7	1	no	—
337	#124	—	7	1	no	—
338	#124	—	7	1	no	—
339	#124	—	7	2	no	—
340	#124	—	7	1	no	—
341	#124	—	7	1	no	—
342	#124	—	7	2	no	—
343	#124	—	7	1	no	—
344	#124	—	7	2	no	—
345	#124	—	7	2	no	—
346	#124	—	7	2	no	—
347	#124	—	7	2	no	—
348	#124	—	7	1	no	—
349	#124	C₂×D₇	1	1	yes	characteristic, complemented
350	#124	C₂×D₇	1	2	yes	complemented
351	#123	—	7	2	no	—
352	#123	—	7	2	no	—
353	#123	—	7	2	no	—
354	#123	—	7	2	no	—
355	#123	—	7	2	no	—
356	#123	—	7	2	no	—
357	#123	—	7	2	no	—
358	C₂²⋊Q₈	—	7	1	no	—
359	C₂²⋊Q₈	—	7	2	no	—
360	C₂²⋊Q₈	—	7	1	no	—
361	C₂²⋊Q₈	—	7	2	no	—
362	C₂²⋊Q₈	—	7	2	no	—
363	C₂²⋊Q₈	—	7	2	no	—
364	C₂²⋊Q₈	C₂×D₇	1	1	yes	characteristic, complemented
365	C₂²⋊Q₈	C₂×D₇	1	2	yes	complemented
366	#121	—	7	2	no	—
367	#121	—	7	2	no	—
368	#121	—	7	2	no	—
369	#121	—	7	1	no	—
370	#121	—	7	1	no	—
371	#121	—	7	2	no	—
372	#121	—	7	2	no	—
373	#121	—	7	2	no	—
374	#121	C₂×D₇	1	1	yes	characteristic
375	#121	C₂×D₇	1	2	yes	complemented
376	#120	—	7	2	no	—
377	#120	—	7	2	no	—
378	#120	—	7	2	no	—
379	#120	—	7	2	no	—
380	C₄×Q₈	—	7	1	no	—
381	C₄×Q₈	—	7	1	no	—
382	C₄×Q₈	—	7	1	no	—
383	C₄×Q₈	—	7	1	no	—
384	C₄×Q₈	C₂×D₇	1	1	yes	characteristic, complemented
385	C₄×D₄	—	7	1	no	—
386	C₄×D₄	—	7	2	no	—
387	C₄×D₄	—	7	1	no	—
388	C₄×D₄	—	7	1	no	—
389	C₄×D₄	—	7	1	no	—
390	C₄×D₄	—	7	2	no	—
391	C₄×D₄	—	7	2	no	—
392	C₄×D₄	—	7	2	no	—
393	C₄×D₄	—	7	2	no	—
394	C₄×D₄	—	7	1	no	—
395	C₄×D₄	—	7	1	no	—
396	C₄×D₄	—	7	1	no	—
397	C₄×D₄	—	7	2	no	—
398	C₄×D₄	—	7	2	no	—
399	C₄×D₄	—	7	2	no	—
400	C₄×D₄	—	7	1	no	—
401	C₄×D₄	C₂×D₇	1	1	yes	characteristic, complemented
402	C₄×D₄	C₂×D₇	1	2	yes	complemented
403	#117	—	7	1	no	—
404	#117	—	7	2	no	—
405	#117	—	7	1	no	—
406	#117	—	7	1	no	—
407	#117	—	7	2	no	—
408	#117	—	7	2	no	—
409	#117	—	7	2	no	—
410	C₂×C₂²⋊C₄	—	7	2	no	—
411	C₂×C₂²⋊C₄	—	7	2	no	—
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	C₂²×C₇	—	2	1	no	—
420	C₂²×C₇	—	2	1	no	—
421	C₂²×C₇	—	2	1	no	—
422	C₂²×C₇	—	2	2	no	—
423	C₂²×C₇	—	2	1	no	—
424	C₂²×C₇	—	2	2	no	—
425	C₂²×C₇	—	2	1	no	—
426	C₂²×C₇	—	2	2	no	—
427	C₂²×C₇	C₂×#41	1	2	yes	—
428	C₂²×C₇	C₂⁵	1	1	yes	characteristic
429	C₂×D₇	—	2	1	no	—
430	C₂×D₇	—	2	1	no	—
431	C₂×D₇	—	2	2	no	—
432	C₂×D₇	—	2	2	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	—	8	4	no	—
438	C₂×D₇	—	8	4	no	—
439	C₂×D₇	C₂×#41	1	2	yes	—
440	C₄×C₇	—	2	1	no	—
441	C₄×C₇	—	2	2	no	—
442	C₄×C₇	—	2	2	no	—
443	C₄×C₇	—	2	1	no	—
444	C₄×C₇	—	2	1	no	—
445	C₄×C₇	—	2	2	no	—
446	C₄×C₇	—	2	1	no	—
447	C₄×C₇	H(5,𝔽₂)	1	2	yes	—
448	Dic₇	—	2	1	no	—
449	Dic₇	—	2	1	no	—
450	Dic₇	—	2	2	no	—
451	Dic₇	—	2	1	no	—
452	Dic₇	—	2	1	no	—
453	Dic₇	—	2	2	no	—
454	Dic₇	—	2	1	no	—
455	Dic₇	—	2	1	no	—
456	Dic₇	C₂×#41	1	2	yes	—
457	C₂⁴	—	7	2	no	—
458	C₂⁴	—	7	2	no	—
459	#41	—	4	2	no	—
460	#41	—	14	4	no	—
461	#41	—	28	2	no	—
462	C₂×Q₈	—	4	2	no	—
463	C₂×Q₈	—	7	1	no	—
464	C₂×Q₈	—	7	1	no	—
465	C₂×Q₈	—	7	2	no	—
466	C₂×Q₈	—	28	2	no	—
467	C₂×Q₈	C₂²×D₇	1	1	yes	characteristic
468	C₂×Q₈	C₂²×D₇	1	1	yes	characteristic
469	C₂×Q₈	C₂²×D₇	1	2	yes	—
470	C₂×D₄	—	7	1	no	—
471	C₂×D₄	—	7	1	no	—
472	C₂×D₄	—	7	2	no	—
473	C₂×D₄	—	7	2	no	—
474	C₂×D₄	—	7	2	no	—
475	C₂×D₄	—	7	2	no	—
476	C₂×D₄	—	7	2	no	—
477	C₂×D₄	—	7	2	no	—
478	C₂×D₄	—	7	1	no	—
479	C₂×D₄	—	7	1	no	—
480	C₂×D₄	—	7	2	no	—
481	C₂×D₄	—	14	8	no	—
482	C₂×D₄	—	28	2	no	—
483	C₂×D₄	—	28	2	no	—
484	C₂×D₄	C₂²×D₇	1	1	yes	characteristic
485	C₂×D₄	C₂²×D₇	1	2	yes	—
486	C₂×D₄	C₂²×D₇	1	1	yes	characteristic
487	C₂×D₄	C₂²×D₇	1	2	yes	—
488	C₂²×C₄	—	7	1	no	—
489	C₂²×C₄	—	7	1	no	—
490	C₂²×C₄	—	7	1	no	—
491	C₂²×C₄	—	7	1	no	—
492	C₂²×C₄	—	7	2	no	—
493	C₂²×C₄	—	7	1	no	—
494	C₂²×C₄	—	7	1	no	—
495	C₂²×C₄	—	7	2	no	—
496	C₂²×C₄	—	7	1	no	—
497	C₂²×C₄	—	7	2	no	—
498	C₂²×C₄	—	7	2	no	—
499	C₂²×C₄	—	7	2	no	—
500	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
501	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
502	C₂²×C₄	C₂²×D₇	1	2	yes	—
503	C₂²×C₄	C₂²×D₇	1	2	yes	—
504	C₄⋊C₄	—	7	1	no	—
505	C₄⋊C₄	—	7	2	no	—
506	C₄⋊C₄	—	7	2	no	—
507	C₄⋊C₄	—	7	1	no	—
508	C₄⋊C₄	—	7	1	no	—
509	C₄⋊C₄	—	7	1	no	—
510	C₄⋊C₄	—	7	2	no	—
511	C₄⋊C₄	—	7	2	no	—
512	C₄⋊C₄	—	7	2	no	—
513	C₄⋊C₄	—	7	2	no	—
514	C₄⋊C₄	—	7	2	no	—
515	C₄⋊C₄	—	7	1	no	—
516	C₄⋊C₄	—	7	1	no	—
517	C₄⋊C₄	—	7	2	no	—
518	C₄⋊C₄	C₂²×D₇	1	2	yes	—
519	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
520	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
521	C₄⋊C₄	C₂²×D₇	1	2	yes	—
522	C₂²⋊C₄	—	7	2	no	—
523	C₂²⋊C₄	—	7	2	no	—
524	C₂²⋊C₄	—	7	2	no	—
525	C₂²⋊C₄	—	7	1	no	—
526	C₂²⋊C₄	—	7	1	no	—
527	C₂²⋊C₄	—	7	2	no	—
528	C₂²⋊C₄	—	7	1	no	—
529	C₂²⋊C₄	—	7	2	no	—
530	C₂²⋊C₄	—	7	2	no	—
531	C₂²⋊C₄	—	7	2	no	—
532	C₂²⋊C₄	—	7	2	no	—
533	C₂²⋊C₄	—	7	2	no	—
534	C₂²⋊C₄	—	7	2	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	1	no	—
542	C₂²⋊C₄	—	7	2	no	—
543	C₂²⋊C₄	—	7	2	no	—
544	C₂²⋊C₄	—	7	2	no	—
545	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
546	C₂²⋊C₄	C₂²×D₇	1	2	yes	—
547	C₂²⋊C₄	C₂²×D₇	1	2	yes	—
548	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
549	C₂²⋊C₄	C₂²×D₇	1	2	yes	—
550	C₂²⋊C₄	C₂²×D₇	1	2	yes	—
551	C₄²	—	7	1	no	—
552	C₄²	—	7	1	no	—
553	C₄²	—	7	1	no	—
554	C₄²	—	7	1	no	—
555	C₄²	—	7	1	no	—
556	C₄²	—	7	1	no	—
557	C₄²	—	7	1	no	—
558	C₄²	—	7	1	no	—
559	C₄²	—	7	1	no	—
560	C₄²	—	7	2	no	—
561	C₄²	—	7	2	no	—
562	C₄²	C₂²×D₇	1	1	yes	characteristic
563	C₄²	C₂²×D₇	1	2	yes	—
564	C₂×C₇	—	2	2	no	—
565	C₂×C₇	—	4	2	no	—
566	C₂×C₇	—	4	1	no	—
567	C₂×C₇	C₂²×#41	1	1	yes	characteristic
568	C₂×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
569	C₂×C₇	#585	1	1	yes	characteristic
570	D₇	—	2	2	no	—
571	D₇	—	4	2	no	—
572	D₇	—	4	2	no	—
573	C₂³	—	7	1	no	—
574	C₂³	—	7	2	no	—
575	C₂³	—	7	2	no	—
576	C₂³	—	14	4	no	—
577	C₂³	—	14	4	no	—
578	C₂³	—	28	2	no	—
579	C₂³	—	28	2	no	—
580	C₂³	—	28	2	no	—
581	C₂³	—	28	2	no	—
582	C₂³	C₂³×D₇	1	2	yes	—
583	C₂³	C₂³×D₇	1	1	yes	characteristic
584	C₂³	C₂³×D₇	1	1	yes	characteristic
585	Q₈	—	2	2	no	—
586	Q₈	—	2	2	no	—
587	Q₈	—	4	2	no	—
588	Q₈	—	14	2	no	—
589	Q₈	—	14	2	no	—
590	Q₈	—	28	2	no	—
591	D₄	—	2	4	no	—
592	D₄	—	2	2	no	—
593	D₄	—	2	2	no	—
594	D₄	—	4	2	no	—
595	D₄	—	7	4	no	—
596	D₄	—	14	4	no	—
597	D₄	—	14	4	no	—
598	D₄	—	14	2	no	—
599	D₄	—	14	2	no	—
600	D₄	—	14	2	no	—
601	D₄	—	28	2	no	—
602	D₄	—	28	2	no	—
603	D₄	—	28	2	no	—
604	D₄	—	28	2	no	—
605	D₄	—	28	2	no	—
606	C₂×C₄	—	2	2	no	—
607	C₂×C₄	—	2	2	no	—
608	C₂×C₄	—	4	2	no	—
609	C₂×C₄	—	4	2	no	—
610	C₂×C₄	—	7	1	no	—
611	C₂×C₄	—	7	1	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	1	no	—
617	C₂×C₄	—	7	2	no	—
618	C₂×C₄	—	7	2	no	—
619	C₂×C₄	—	14	4	no	—
620	C₂×C₄	—	14	2	no	—
621	C₂×C₄	—	14	2	no	—
622	C₂×C₄	—	14	2	no	—
623	C₂×C₄	—	14	2	no	—
624	C₂×C₄	—	28	1	no	—
625	C₂×C₄	—	28	2	no	—
626	C₂×C₄	—	28	2	no	—
627	C₂×C₄	—	28	2	no	—
628	C₂×C₄	—	28	1	no	—
629	C₂×C₄	—	28	2	no	—
630	C₂×C₄	—	28	1	no	—
631	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
632	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
633	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
634	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
635	C₂×C₄	C₂³×D₇	1	2	yes	—
636	C₂×C₄	C₂³×D₇	1	2	yes	—
637	C₂×C₄	C₂³×D₇	1	2	yes	—
638	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
639	C₇	#3514	1	1	yes	characteristic, complemented, Sylow
640	C₂²	—	2	1	no	—
641	C₂²	—	2	1	no	—
642	C₂²	—	2	1	no	—
643	C₂²	—	2	2	no	—
644	C₂²	—	2	1	no	—
645	C₂²	—	2	2	no	—
646	C₂²	—	2	1	no	—
647	C₂²	—	2	2	no	—
648	C₂²	—	7	2	no	—
649	C₂²	—	14	1	no	—
650	C₂²	—	14	1	no	—
651	C₂²	—	14	2	no	—
652	C₂²	—	14	2	no	—
653	C₂²	—	14	2	no	—
654	C₂²	—	14	2	no	—
655	C₂²	—	14	2	no	—
656	C₂²	—	14	2	no	—
657	C₂²	—	56	4	no	—
658	C₂²	—	56	4	no	—
659	C₂²	D₇×#41	1	2	yes	—
660	C₂²	C₂⁴×D₇	1	1	yes	characteristic
661	C₄	—	2	1	no	—
662	C₄	—	2	1	no	—
663	C₄	—	2	2	no	—
664	C₄	—	2	2	no	—
665	C₄	—	2	2	no	—
666	C₄	—	2	1	no	—
667	C₄	—	2	1	no	—
668	C₄	—	7	2	no	—
669	C₄	—	14	1	no	—
670	C₄	—	14	2	no	—
671	C₄	—	14	1	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	#6548	1	2	yes	—
678	C₂	—	2	2	no	—
679	C₂	—	4	2	no	—
680	C₂	—	4	1	no	—
681	C₂	—	14	2	no	—
682	C₂	—	28	2	no	—
683	C₂	—	28	2	no	—
684	C₂	C₂×#6548	1	1	yes	characteristic
685	C₂	C₂×D₇×#41	1	1	yes	characteristic
686	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	#3514
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. #90523	C₂	semidirect
3. #90520	C₂	semidirect
4. Q₈×C₂²⋊D₇	C₂	semidirect
5. C₂×#6510	C₂	semidirect
6. #90372	C₂	semidirect
7. #90369	C₂	semidirect
8. D₇×#124	C₂	semidirect
9. #90361	C₂	semidirect
10. #90331	C₂	semidirect
11. #90328	C₂	semidirect
12. #90324	C₂	semidirect
13. #90315	C₂	semidirect
14. #90308	C₂	semidirect
15. #90301	C₂	semidirect
16. #90300	C₂	semidirect
17. #90291	C₂	semidirect
18. #90271	C₂	semidirect
19. #90259	C₂	semidirect
20. #90247	C₂	semidirect
21. #90241	C₂	semidirect
22. #90236	C₂	semidirect
23. C₄×#1159	C₂	semidirect
24. C₂×C₇×#41	C₂²	semidirect
25. C₂²×C₇×Q₈	C₂²	semidirect
26. C₂×Q₈×D₇	C₂²	semidirect
30. C₂×#1157	C₂²	semidirect
32. C₇×#124	C₂²	semidirect
33. C₇×#124	C₂²	semidirect
34. C₇×C₂²⋊Q₈	C₂²	semidirect
35. C₇×C₂²⋊Q₈	C₂²	semidirect
37. C₇×#121	C₂²	semidirect
38. C₄×C₇×Q₈	C₂²	semidirect
39. C₄×C₇×D₄	C₂²	semidirect
40. C₄×C₇×D₄	C₂²	semidirect
43. #6510	C₂²	semidirect
44. #6510	C₂²	semidirect
45. #6510	C₂²	semidirect
46. #6510	C₂²	semidirect
47. #6509	C₂²	semidirect
48. #6509	C₂²	semidirect
49. Q₈×Dic₇	C₂²	semidirect
50. #6507	C₂²	semidirect
51. #6507	C₂²	semidirect
53. #6502	C₂²	semidirect
54. #6502	C₂²	semidirect
55. #6502	C₂²	semidirect
57. #6500	C₂²	semidirect
58. #6500	C₂²	semidirect
59. #6499	C₂²	semidirect
60. #6498	C₂²	semidirect
61. D₄×Dic₇	C₂²	semidirect
62. D₄×Dic₇	C₂²	semidirect
63. D₄×Dic₇	C₂²	semidirect
65. #6492	C₂²	semidirect
68. C₄×C₂²⋊D₇	C₂²	semidirect
69. C₄×C₂²⋊D₇	C₂²	semidirect
70. C₄×C₂²⋊D₇	C₂²	semidirect
71. C₂×(C₂×D₇)⋊C₄	C₂²	semidirect
72. C₂×(C₂×D₇)⋊C₄	C₂²	semidirect
73. C₂×(C₂×D₇)⋊C₄	C₂²	semidirect
74. #6487	C₂²	semidirect
75. #6487	C₂²	semidirect
76. C₂×C₄×Dic₇	C₂²	semidirect
77. C₂×C₄×Dic₇	C₂²	semidirect
78. #6461	C₂²	semidirect
79. #6461	C₂²	semidirect
80. #6461	C₂²	semidirect
81. #6459	C₂²	semidirect
82. #6459	C₂²	semidirect
84. #6457	C₂²	semidirect
85. #6457	C₂²	semidirect
87. #6456	C₂²	semidirect
88. #6455	C₂²	semidirect
89. #6455	C₂²	semidirect
90. #6453	C₂²	semidirect
91. #6450	C₂²	semidirect
92. #6450	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
100. #6447	C₂²	semidirect
101. #6447	C₂²	semidirect
102. #6446	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
117. C₄×D₂₈	C₂²	semidirect
118. C₄×D₂₈	C₂²	semidirect
119. #6435	C₂²	semidirect
120. #6435	C₂²	semidirect
121. C₄²×D₇	C₂²	semidirect
122. C₄×Dic₁₄	C₂²	semidirect
238. #548	D₇	semidirect
291. C₂²⋊D₇	#41	semidirect
322. C₂×#41	C₂×D₇	semidirect
324. C₂²×Q₈	C₂×D₇	semidirect
349. #124	C₂×D₇	semidirect
350. #124	C₂×D₇	semidirect
364. C₂²⋊Q₈	C₂×D₇	semidirect
365. C₂²⋊Q₈	C₂×D₇	semidirect
375. #121	C₂×D₇	semidirect
384. C₄×Q₈	C₂×D₇	semidirect
401. C₄×D₄	C₂×D₇	semidirect
402. C₄×D₄	C₂×D₇	semidirect
639. C₇	#3514	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
#90523	2
#90520	2
Q₈×C₂²⋊D₇	2
C₂×#6510	2
#90372	2
#90369	2
D₇×#124	2
#90361	2
#90331	2
#90328	2
#90324	2
#90315	2
#90308	2
#90301	2
#90300	2
#90291	2
#90271	2
#90259	2
#90247	2
#90241	2
#90236	2
C₄×#1159	2
#3514	7