Subgroups — #11744003

Order 896.

1042 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#554	C₂	1	1	yes	maximal, characteristic, complemented
2	#90424	C₂	1	1	yes	maximal, characteristic, complemented
3	#90423	C₂	1	1	yes	maximal, characteristic, complemented
4	#90388	C₂	1	1	yes	maximal, characteristic, complemented
5	#90386	C₂	1	1	yes	maximal, characteristic, complemented
6	#90385	C₂	1	1	yes	maximal, characteristic, complemented
7	#90382	C₂	1	1	yes	maximal, characteristic, complemented
8	#90336	C₂	1	2	yes	maximal, complemented
9	#90335	C₂	1	2	yes	maximal, complemented
10	#90333	C₂	1	2	yes	maximal, complemented
11	#90328	C₂	1	2	yes	maximal, complemented
12	#90328	C₂	1	2	yes	maximal, complemented
13	#90315	C₂	1	2	yes	maximal, complemented
14	#90275	C₂	1	1	yes	maximal, characteristic, complemented
15	#90271	C₂	1	1	yes	maximal, characteristic, complemented
16	#90246	C₂	1	1	yes	maximal, characteristic, complemented
17	#90245	C₂	1	1	yes	maximal, characteristic, complemented
18	#90245	C₂	1	1	yes	maximal, characteristic, complemented
19	#90237	C₂	1	1	yes	maximal, characteristic, complemented
20	#90236	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×#1159	C₂	1	1	yes	maximal, characteristic, complemented
22	#90205	C₂	1	2	yes	maximal, complemented
23	C₂×#6461	C₂	1	2	yes	maximal, complemented
24	C₂×#1159	C₂²	1	1	yes	characteristic
25	C₂×#1159	C₂²	1	1	yes	characteristic
26	C₂×D₄×D₇	C₂²	1	1	yes	characteristic
27	C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
28	C₇×#125	C₂²	1	1	yes	characteristic, complemented
29	C₇×#125	C₂²	1	1	yes	characteristic, complemented
30	C₇×C₂²⋊Q₈	C₂²	1	2	yes	complemented
31	C₇×C₂²⋊Q₈	C₂²	1	2	yes	complemented
32	C₇×C₂²⋊Q₈	C₂²	1	2	yes	complemented
33	C₄×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
34	C₄×C₇×D₄	C₂²	1	1	yes	characteristic
35	C₄×C₇×D₄	C₂²	1	1	yes	characteristic
36	C₄×C₇×D₄	C₂²	1	1	yes	characteristic
37	C₂×C₇×C₄⋊C₄	C₂²	1	2	yes	complemented
38	#6510	C₂²	1	2	yes	—
39	#6510	C₂²	1	1	yes	characteristic
40	#6510	C₂²	1	2	yes	complemented
41	#6509	C₂²	1	2	yes	complemented
42	#6509	C₂²	1	1	yes	characteristic, complemented
43	#6509	C₂²	1	2	yes	complemented
44	Q₈×Dic₇	C₂²	1	2	yes	complemented
45	D₄×Dic₇	C₂²	1	1	yes	characteristic
46	#6493	C₂²	1	2	yes	—
47	#6493	C₂²	1	2	yes	—
48	#6493	C₂²	1	2	yes	complemented
49	C₄×C₂²⋊D₇	C₂²	1	2	yes	—
50	C₄×C₂²⋊D₇	C₂²	1	2	yes	complemented
51	C₄×C₂²⋊D₇	C₂²	1	2	yes	complemented
52	C₂×(C₂×D₇)⋊C₄	C₂²	1	2	yes	—
53	C₂×(C₂×D₇)⋊C₄	C₂²	1	2	yes	—
54	C₂×(C₂×D₇)⋊C₄	C₂²	1	2	yes	—
55	C₂×C₄⋊Dic₇	C₂²	1	2	yes	complemented
56	C₂×Dic₇⋊C₄	C₂²	1	2	yes	complemented
57	C₂×C₄×Dic₇	C₂²	1	2	yes	complemented
58	#6461	C₂²	1	2	yes	—
59	#6461	C₂²	1	2	yes	—
60	#6461	C₂²	1	2	yes	—
61	#6461	C₂²	1	2	yes	—
62	#6461	C₂²	1	1	yes	characteristic
63	#6461	C₂²	1	2	yes	complemented
64	#6461	C₂²	1	2	yes	complemented
65	#6461	C₂²	1	2	yes	complemented
66	#6461	C₂²	1	2	yes	complemented
67	#6461	C₂²	1	2	yes	complemented
68	#6461	C₂²	1	1	yes	characteristic, complemented
69	#6461	C₂²	1	2	yes	complemented
70	#6460	C₂²	1	1	yes	characteristic
71	#6460	C₂²	1	1	yes	characteristic
72	#6460	C₂²	1	1	yes	characteristic, complemented
73	#6460	C₂²	1	1	yes	characteristic, complemented
74	#6458	C₂²	1	1	yes	characteristic
75	#6458	C₂²	1	1	yes	characteristic
76	#6458	C₂²	1	1	yes	characteristic
77	#6458	C₂²	1	2	yes	complemented
78	#6457	C₂²	1	2	yes	—
79	#6457	C₂²	1	1	yes	characteristic
80	#6457	C₂²	1	2	yes	complemented
81	#6457	C₂²	1	2	yes	complemented
82	#6457	C₂²	1	2	yes	complemented
83	#6457	C₂²	1	1	yes	characteristic, complemented
84	#6456	C₂²	1	1	yes	characteristic
85	#6456	C₂²	1	2	yes	complemented
86	#6456	C₂²	1	2	yes	complemented
87	#6455	C₂²	1	1	yes	characteristic
88	#6455	C₂²	1	2	yes	complemented
89	#6455	C₂²	1	2	yes	complemented
90	#6455	C₂²	1	1	yes	characteristic, complemented
91	#6455	C₂²	1	2	yes	complemented
92	D₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
93	#6453	C₂²	1	2	yes	complemented
94	#6453	C₂²	1	2	yes	complemented
95	#6453	C₂²	1	2	yes	complemented
96	#6453	C₂²	1	1	yes	characteristic, complemented
97	#6450	C₂²	1	1	yes	characteristic, complemented
98	#6450	C₂²	1	1	yes	characteristic, complemented
99	#6449	C₂²	1	2	yes	—
100	#6449	C₂²	1	2	yes	—
101	#6449	C₂²	1	2	yes	complemented
102	#6449	C₂²	1	2	yes	complemented
103	#6445	C₂²	1	2	yes	—
104	#6445	C₂²	1	2	yes	—
105	(C₂²⋊D₇)⋊C₄	C₂²	1	2	yes	—
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	—
109	#6440	C₂²	1	2	yes	complemented
110	#6440	C₂²	1	2	yes	complemented
111	#6438	C₂²	1	1	yes	characteristic
112	#6438	C₂²	1	1	yes	characteristic
113	C₄×D₂₈	C₂²	1	1	yes	characteristic
114	C₄×D₂₈	C₂²	1	1	yes	characteristic
115	C₄×D₂₈	C₂²	1	1	yes	characteristic
116	C₄×D₂₈	C₂²	1	1	yes	characteristic, complemented
117	#6435	C₂²	1	1	yes	characteristic
118	#6435	C₂²	1	1	yes	characteristic, complemented
119	C₄²×D₇	C₂²	1	1	yes	characteristic, complemented
120	#6432	C₂²	1	1	yes	characteristic, complemented
121	C₄×Dic₁₄	C₂²	1	1	yes	characteristic, complemented
122	C₄×Dic₁₄	C₂²	1	1	yes	characteristic, complemented
123	#3521	—	7	1	no	maximal, Sylow
124	C₂³×D₇	C₂³	1	2	yes	—
125	C₂×C₇×Q₈	C₂³	1	2	yes	—
126	C₂×C₇×Q₈	C₂³	1	1	yes	characteristic
127	C₂×C₇×D₄	C₂³	1	1	yes	characteristic
128	C₂²×C₄×C₇	C₂³	1	2	yes	—
129	C₂²×C₄×C₇	C₂³	1	2	yes	—
130	C₂²×C₄×C₇	C₂³	1	2	yes	—
131	C₂×C₂²⋊D₇	C₂³	1	2	yes	—
132	C₂×C₂²⋊D₇	C₂³	1	2	yes	—
133	C₂×C₂²⋊D₇	C₂³	1	2	yes	—
134	C₂²×Dic₇	C₂³	1	2	yes	—
135	C₂²×Dic₇	C₂³	1	2	yes	—
136	C₂²×Dic₇	C₂³	1	2	yes	—
137	#1159	—	2	4	no	—
138	#1159	—	2	4	no	—
139	D₄×D₇	—	2	4	no	—
140	C₂×D₂₈	C₂³	1	1	yes	characteristic
141	C₂×D₂₈	C₂³	1	1	yes	characteristic
142	C₂×D₂₈	C₂³	1	1	yes	characteristic
143	C₂×D₂₈	C₂³	1	1	yes	characteristic
144	C₂×D₂₈	C₂³	1	2	yes	—
145	C₂×D₂₈	C₂³	1	2	yes	—
146	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
147	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
148	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
149	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
150	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
151	C₂×C₄×D₇	C₂³	1	2	yes	—
152	C₂×C₄×D₇	C₂³	1	2	yes	—
153	C₂×C₄×D₇	C₂³	1	2	yes	—
154	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
155	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
156	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
157	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
158	C₇×C₄⋊C₄	C₂³	1	2	yes	—
159	C₇×C₄⋊C₄	C₂³	1	2	yes	—
160	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
161	C₇×C₄⋊C₄	C₂³	1	2	yes	—
162	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
163	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
164	C₇×C₄⋊C₄	C₂³	1	2	yes	—
165	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
166	C₇×C₄⋊C₄	C₂³	1	2	yes	—
167	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
168	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
169	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
170	C₄²×C₇	C₂³	1	1	yes	characteristic
171	C₄²×C₇	C₂³	1	1	yes	characteristic
172	C₄²×C₇	C₂³	1	1	yes	characteristic
173	C₂²⋊Dic₇	C₂³	1	2	yes	—
174	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
175	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
176	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
177	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
178	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
179	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
180	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
181	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
182	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
183	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
184	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
185	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
186	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
187	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
188	(C₂×D₇)⋊C₄	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	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
199	C₄⋊Dic₇	C₂³	1	2	yes	—
200	C₄⋊Dic₇	C₂³	1	2	yes	—
201	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
202	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
203	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
204	C₄⋊Dic₇	C₂³	1	2	yes	—
205	C₄⋊Dic₇	C₂³	1	2	yes	—
206	C₄⋊Dic₇	C₂³	1	2	yes	—
207	C₄⋊Dic₇	C₂³	1	2	yes	—
208	Dic₇⋊C₄	C₂³	1	2	yes	—
209	Dic₇⋊C₄	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	1	yes	characteristic
213	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
214	Dic₇⋊C₄	C₂³	1	2	yes	—
215	Dic₇⋊C₄	C₂³	1	2	yes	—
216	Dic₇⋊C₄	C₂³	1	2	yes	—
217	C₄×Dic₇	C₂³	1	2	yes	—
218	C₄×Dic₇	C₂³	1	2	yes	—
219	C₄×Dic₇	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	2	yes	—
223	C₄×Dic₇	C₂³	1	2	yes	—
224	C₄×Dic₇	C₂³	1	2	yes	—
225	C₄×Dic₇	C₂³	1	2	yes	—
226	#556	—	7	1	no	—
227	#556	—	7	1	no	—
228	#554	D₇	1	1	yes	characteristic, complemented
229	#553	—	7	1	no	—
230	#553	—	7	2	no	—
231	#552	—	7	1	no	—
232	#552	—	7	2	no	—
233	#551	—	7	2	no	—
234	#551	—	7	2	no	—
235	#547	—	7	1	no	—
236	#546	—	7	1	no	—
237	#546	—	7	1	no	—
238	#542	—	7	1	no	—
239	#541	—	7	1	no	—
240	#539	—	7	2	no	—
241	#538	—	7	2	no	—
242	#529	—	7	1	no	—
243	#529	—	7	2	no	—
244	#529	—	7	1	no	—
245	C₂×#126	—	7	2	no	—
246	#520	—	7	1	no	—
247	#518	—	7	1	no	—
248	C₄×#41	—	7	1	no	—
249	C₂³×C₇	C₂⁴	1	2	yes	—
250	C₂²×D₇	—	2	4	no	—
251	C₂²×D₇	—	4	2	no	—
252	C₂²×D₇	—	4	2	no	—
253	C₂²×D₇	C₂⁴	1	1	yes	characteristic
254	C₂²×D₇	C₂⁴	1	2	yes	—
255	C₂²×D₇	C₂⁴	1	1	yes	characteristic
256	C₂²×D₇	C₂⁴	1	1	yes	characteristic
257	C₇×Q₈	—	4	1	no	—
258	C₇×Q₈	—	4	2	no	—
259	C₇×D₄	#41	1	4	yes	—
260	C₂×C₄×C₇	—	4	2	no	—
261	C₂×C₄×C₇	—	4	2	no	—
262	C₂×C₄×C₇	—	4	2	no	—
263	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
264	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
265	C₂×C₄×C₇	C₂⁴	1	2	yes	—
266	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
267	C₂×C₄×C₇	C₂⁴	1	2	yes	—
268	C₂×C₄×C₇	C₂⁴	1	2	yes	—
269	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
270	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
271	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
272	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
273	C₂²⋊D₇	—	2	4	no	—
274	C₂²⋊D₇	—	2	4	no	—
275	C₂²⋊D₇	—	2	4	no	—
276	C₂×Dic₇	—	2	4	no	—
277	C₂×Dic₇	—	2	4	no	—
278	C₂×Dic₇	—	4	2	no	—
279	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
280	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
281	C₂×Dic₇	C₂⁴	1	2	yes	—
282	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
283	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
284	C₂×Dic₇	C₂⁴	1	2	yes	—
285	C₂×Dic₇	C₂⁴	1	2	yes	—
286	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
287	D₂₈	—	2	2	no	—
288	D₂₈	—	4	2	no	—
289	D₂₈	—	4	1	no	—
290	D₂₈	—	4	1	no	—
291	D₂₈	—	4	2	no	—
292	D₂₈	—	4	1	no	—
293	C₄×D₇	—	2	2	no	—
294	C₄×D₇	—	2	2	no	—
295	C₄×D₇	—	2	2	no	—
296	C₄×D₇	—	4	1	no	—
297	C₄×D₇	—	4	2	no	—
298	C₄×D₇	—	4	2	no	—
299	C₄×D₇	—	4	2	no	—
300	C₄×D₇	—	4	1	no	—
301	Dic₁₄	—	2	2	no	—
302	Dic₁₄	—	2	2	no	—
303	C₂×#41	—	7	1	no	—
304	C₂×#41	—	7	1	no	—
305	C₂²×D₄	—	7	1	no	—
306	C₄⋊Q₈	—	7	1	no	—
307	C₄⋊Q₈	C₂×D₇	1	1	yes	characteristic, complemented
308	#126	—	7	1	no	—
309	#126	—	7	2	no	—
310	#126	—	7	2	no	—
311	#126	—	7	2	no	—
312	#126	—	7	2	no	—
313	#126	—	7	2	no	—
314	#126	—	7	2	no	—
315	#126	—	7	2	no	—
316	#126	—	7	1	no	—
317	#126	—	7	2	no	—
318	#126	—	7	2	no	—
319	#126	—	7	2	no	—
320	#125	—	7	2	no	—
321	#125	—	7	1	no	—
322	#125	—	7	2	no	—
323	#125	—	7	2	no	—
324	#125	C₂×D₇	1	1	yes	characteristic, complemented
325	#125	C₂×D₇	1	1	yes	characteristic, complemented
326	#124	—	7	2	no	—
327	#124	—	7	1	no	—
328	#124	—	7	2	no	—
329	#124	—	7	1	no	—
330	#124	—	7	1	no	—
331	#123	—	7	2	no	—
332	#123	—	7	1	no	—
333	#123	—	7	1	no	—
334	#123	—	7	2	no	—
335	#123	—	7	2	no	—
336	#123	—	7	2	no	—
337	#123	—	7	2	no	—
338	#123	—	7	2	no	—
339	#123	—	7	2	no	—
340	#123	—	7	2	no	—
341	C₂²⋊Q₈	—	7	1	no	—
342	C₂²⋊Q₈	—	7	2	no	—
343	C₂²⋊Q₈	—	7	2	no	—
344	C₂²⋊Q₈	—	7	1	no	—
345	C₂²⋊Q₈	—	7	1	no	—
346	C₂²⋊Q₈	—	7	1	no	—
347	C₂²⋊Q₈	—	7	1	no	—
348	C₂²⋊Q₈	C₂×D₇	1	2	yes	complemented
349	C₂²⋊Q₈	C₂×D₇	1	2	yes	complemented
350	C₂²⋊Q₈	C₂×D₇	1	2	yes	complemented
351	#121	—	7	2	no	—
352	#121	—	7	2	no	—
353	#121	—	7	2	no	—
354	#121	—	7	1	no	—
355	#121	—	7	1	no	—
356	#121	—	7	2	no	—
357	#121	—	7	1	no	—
358	#120	—	7	2	no	—
359	#120	—	7	2	no	—
360	C₄×Q₈	—	7	2	no	—
361	C₄×Q₈	—	7	1	no	—
362	C₄×Q₈	—	7	1	no	—
363	C₄×Q₈	—	7	1	no	—
364	C₄×Q₈	—	7	1	no	—
365	C₄×Q₈	C₂×D₇	1	1	yes	characteristic, complemented
366	C₄×D₄	—	7	1	no	—
367	C₄×D₄	—	7	2	no	—
368	C₄×D₄	—	7	2	no	—
369	C₄×D₄	—	7	2	no	—
370	C₄×D₄	—	7	1	no	—
371	C₄×D₄	—	7	2	no	—
372	C₄×D₄	—	7	2	no	—
373	C₄×D₄	—	7	2	no	—
374	C₄×D₄	—	7	2	no	—
375	C₄×D₄	—	7	2	no	—
376	C₄×D₄	—	7	1	no	—
377	C₄×D₄	—	7	1	no	—
378	C₄×D₄	—	7	1	no	—
379	C₄×D₄	—	7	1	no	—
380	C₄×D₄	C₂×D₇	1	1	yes	characteristic
381	C₄×D₄	C₂×D₇	1	1	yes	characteristic
382	C₄×D₄	C₂×D₇	1	1	yes	characteristic
383	#117	—	7	1	no	—
384	#117	—	7	1	no	—
385	#117	—	7	2	no	—
386	#117	—	7	2	no	—
387	#117	—	7	2	no	—
388	#117	—	7	2	no	—
389	#117	—	7	2	no	—
390	#117	—	7	1	no	—
391	#117	—	7	1	no	—
392	C₂×C₄⋊C₄	—	7	2	no	—
393	C₂×C₄⋊C₄	—	7	2	no	—
394	C₂×C₄⋊C₄	—	7	1	no	—
395	C₂×C₄⋊C₄	C₂×D₇	1	2	yes	complemented
396	C₂×C₂²⋊C₄	—	7	2	no	—
397	C₂×C₂²⋊C₄	—	7	2	no	—
398	C₂×C₂²⋊C₄	—	7	2	no	—
399	C₂×C₂²⋊C₄	—	7	2	no	—
400	C₂×C₄²	—	7	2	no	—
401	C₂×C₄²	—	7	1	no	—
402	C₂²×C₇	—	2	2	no	—
403	C₂²×C₇	—	2	2	no	—
404	C₂²×C₇	C₂×#41	1	4	yes	—
405	C₂²×C₇	C₂⁵	1	1	yes	characteristic
406	C₂×D₇	—	2	1	no	—
407	C₂×D₇	—	2	1	no	—
408	C₂×D₇	—	2	1	no	—
409	C₂×D₇	—	2	2	no	—
410	C₂×D₇	—	2	1	no	—
411	C₂×D₇	—	2	1	no	—
412	C₂×D₇	—	2	1	no	—
413	C₂×D₇	—	2	2	no	—
414	C₂×D₇	—	2	2	no	—
415	C₂×D₇	—	2	1	no	—
416	C₂×D₇	—	2	1	no	—
417	C₂×D₇	—	2	1	no	—
418	C₂×D₇	—	8	4	no	—
419	C₄×C₇	—	2	1	no	—
420	C₄×C₇	—	2	2	no	—
421	C₄×C₇	—	2	1	no	—
422	C₄×C₇	—	2	1	no	—
423	C₄×C₇	—	2	2	no	—
424	C₄×C₇	—	2	1	no	—
425	C₄×C₇	—	2	2	no	—
426	C₄×C₇	—	2	1	no	—
427	C₄×C₇	—	2	1	no	—
428	C₄×C₇	C₂×#41	1	2	yes	—
429	Dic₇	—	2	2	no	—
430	Dic₇	—	2	2	no	—
431	Dic₇	—	2	1	no	—
432	Dic₇	—	2	1	no	—
433	Dic₇	—	2	1	no	—
434	Dic₇	—	2	1	no	—
435	Dic₇	—	2	2	no	—
436	Dic₇	—	2	1	no	—
437	C₂⁴	—	7	2	no	—
438	#41	—	14	4	no	—
439	#41	—	14	4	no	—
440	C₂×Q₈	—	7	1	no	—
441	C₂×Q₈	—	7	1	no	—
442	C₂×Q₈	C₂²×D₇	1	2	yes	—
443	C₂×Q₈	C₂²×D₇	1	1	yes	characteristic
444	C₂×D₄	—	7	2	no	—
445	C₂×D₄	—	7	2	no	—
446	C₂×D₄	—	7	2	no	—
447	C₂×D₄	—	7	1	no	—
448	C₂×D₄	—	7	1	no	—
449	C₂×D₄	—	7	1	no	—
450	C₂×D₄	—	7	2	no	—
451	C₂×D₄	—	7	2	no	—
452	C₂×D₄	—	7	1	no	—
453	C₂×D₄	—	14	4	no	—
454	C₂×D₄	C₂²×D₇	1	1	yes	characteristic
455	C₂²×C₄	—	7	2	no	—
456	C₂²×C₄	—	7	2	no	—
457	C₂²×C₄	—	7	2	no	—
458	C₂²×C₄	—	7	1	no	—
459	C₂²×C₄	—	7	1	no	—
460	C₂²×C₄	—	7	1	no	—
461	C₂²×C₄	—	7	1	no	—
462	C₂²×C₄	—	7	1	no	—
463	C₂²×C₄	—	7	2	no	—
464	C₂²×C₄	—	7	2	no	—
465	C₂²×C₄	—	7	2	no	—
466	C₂²×C₄	C₂²×D₇	1	2	yes	—
467	C₂²×C₄	C₂²×D₇	1	2	yes	—
468	C₂²×C₄	C₂²×D₇	1	2	yes	—
469	C₄⋊C₄	—	7	1	no	—
470	C₄⋊C₄	—	7	2	no	—
471	C₄⋊C₄	—	7	2	no	—
472	C₄⋊C₄	—	7	2	no	—
473	C₄⋊C₄	—	7	1	no	—
474	C₄⋊C₄	—	7	1	no	—
475	C₄⋊C₄	—	7	1	no	—
476	C₄⋊C₄	—	7	2	no	—
477	C₄⋊C₄	—	7	2	no	—
478	C₄⋊C₄	—	7	1	no	—
479	C₄⋊C₄	—	7	1	no	—
480	C₄⋊C₄	—	7	2	no	—
481	C₄⋊C₄	—	7	2	no	—
482	C₄⋊C₄	—	7	2	no	—
483	C₄⋊C₄	—	7	2	no	—
484	C₄⋊C₄	—	7	2	no	—
485	C₄⋊C₄	—	7	1	no	—
486	C₄⋊C₄	—	7	1	no	—
487	C₄⋊C₄	—	7	2	no	—
488	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
489	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
490	C₄⋊C₄	C₂²×D₇	1	2	yes	—
491	C₄⋊C₄	C₂²×D₇	1	2	yes	—
492	C₄⋊C₄	C₂²×D₇	1	2	yes	—
493	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
494	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
495	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
496	C₄⋊C₄	C₂²×D₇	1	2	yes	—
497	C₄⋊C₄	C₂²×D₇	1	2	yes	—
498	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
499	C₂²⋊C₄	—	7	2	no	—
500	C₂²⋊C₄	—	7	1	no	—
501	C₂²⋊C₄	—	7	2	no	—
502	C₂²⋊C₄	—	7	1	no	—
503	C₂²⋊C₄	—	7	1	no	—
504	C₂²⋊C₄	—	7	1	no	—
505	C₂²⋊C₄	—	7	2	no	—
506	C₂²⋊C₄	—	7	2	no	—
507	C₂²⋊C₄	—	7	2	no	—
508	C₂²⋊C₄	—	7	2	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	—	7	1	no	—
514	C₂²⋊C₄	—	7	2	no	—
515	C₂²⋊C₄	—	7	1	no	—
516	C₂²⋊C₄	—	7	1	no	—
517	C₂²⋊C₄	—	7	2	no	—
518	C₂²⋊C₄	—	7	2	no	—
519	C₂²⋊C₄	—	7	2	no	—
520	C₂²⋊C₄	—	7	1	no	—
521	C₂²⋊C₄	—	7	1	no	—
522	C₂²⋊C₄	—	7	2	no	—
523	C₂²⋊C₄	—	7	1	no	—
524	C₂²⋊C₄	C₂²×D₇	1	2	yes	—
525	C₂²⋊C₄	C₂²×D₇	1	2	yes	—
526	C₂²⋊C₄	C₂²×D₇	1	2	yes	—
527	C₄²	—	7	1	no	—
528	C₄²	—	7	1	no	—
529	C₄²	—	7	1	no	—
530	C₄²	—	7	2	no	—
531	C₄²	—	7	2	no	—
532	C₄²	—	7	2	no	—
533	C₄²	—	7	2	no	—
534	C₄²	—	7	2	no	—
535	C₄²	—	7	2	no	—
536	C₄²	C₂²×D₇	1	1	yes	characteristic
537	C₄²	C₂²×D₇	1	1	yes	characteristic
538	C₄²	C₂²×D₇	1	1	yes	characteristic
539	C₂×C₇	—	2	4	no	—
540	C₂×C₇	C₂²×#41	1	1	yes	characteristic
541	C₂×C₇	#585	1	1	yes	characteristic
542	C₂×C₇	#585	1	1	yes	characteristic
543	D₇	—	4	1	no	—
544	D₇	—	4	1	no	—
545	D₇	—	4	2	no	—
546	D₇	—	4	1	no	—
547	C₂³	—	7	1	no	—
548	C₂³	—	7	2	no	—
549	C₂³	—	7	1	no	—
550	C₂³	—	7	1	no	—
551	C₂³	—	14	4	no	—
552	C₂³	—	28	2	no	—
553	C₂³	—	28	2	no	—
554	C₂³	C₂³×D₇	1	2	yes	—
555	Q₈	—	4	1	no	—
556	Q₈	—	4	2	no	—
557	Q₈	—	14	2	no	—
558	Q₈	—	14	2	no	—
559	D₄	—	14	4	no	—
560	D₄	—	14	4	no	—
561	D₄	—	14	4	no	—
562	D₄	—	14	2	no	—
563	D₄	—	28	2	no	—
564	D₄	—	28	1	no	—
565	D₄	—	28	1	no	—
566	D₄	—	28	2	no	—
567	D₄	—	28	1	no	—
568	D₄	#1161	1	4	yes	—
569	C₂×C₄	—	4	2	no	—
570	C₂×C₄	—	4	2	no	—
571	C₂×C₄	—	4	2	no	—
572	C₂×C₄	—	7	1	no	—
573	C₂×C₄	—	7	1	no	—
574	C₂×C₄	—	7	2	no	—
575	C₂×C₄	—	7	1	no	—
576	C₂×C₄	—	7	2	no	—
577	C₂×C₄	—	7	2	no	—
578	C₂×C₄	—	7	1	no	—
579	C₂×C₄	—	7	1	no	—
580	C₂×C₄	—	14	4	no	—
581	C₂×C₄	—	14	4	no	—
582	C₂×C₄	—	14	2	no	—
583	C₂×C₄	—	14	2	no	—
584	C₂×C₄	—	14	2	no	—
585	C₂×C₄	—	28	2	no	—
586	C₂×C₄	—	28	2	no	—
587	C₂×C₄	—	28	1	no	—
588	C₂×C₄	—	28	1	no	—
589	C₂×C₄	—	28	2	no	—
590	C₂×C₄	—	28	2	no	—
591	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
592	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
593	C₂×C₄	C₂³×D₇	1	2	yes	—
594	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
595	C₂×C₄	C₂³×D₇	1	2	yes	—
596	C₂×C₄	C₂³×D₇	1	2	yes	—
597	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
598	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
599	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
600	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
601	C₇	#3521	1	1	yes	characteristic, complemented, Sylow
602	C₂²	—	2	2	no	—
603	C₂²	—	2	2	no	—
604	C₂²	—	14	1	no	—
605	C₂²	—	14	1	no	—
606	C₂²	—	14	1	no	—
607	C₂²	—	14	2	no	—
608	C₂²	—	14	1	no	—
609	C₂²	—	14	1	no	—
610	C₂²	—	14	2	no	—
611	C₂²	—	14	1	no	—
612	C₂²	—	14	1	no	—
613	C₂²	—	14	2	no	—
614	C₂²	—	14	1	no	—
615	C₂²	—	14	1	no	—
616	C₂²	—	56	4	no	—
617	C₂²	C₂×#1161	1	4	yes	—
618	C₂²	C₂⁴×D₇	1	1	yes	characteristic
619	C₄	—	2	1	no	—
620	C₄	—	2	2	no	—
621	C₄	—	2	1	no	—
622	C₄	—	2	1	no	—
623	C₄	—	2	1	no	—
624	C₄	—	2	1	no	—
625	C₄	—	2	2	no	—
626	C₄	—	2	2	no	—
627	C₄	—	2	1	no	—
628	C₄	—	14	1	no	—
629	C₄	—	14	1	no	—
630	C₄	—	14	1	no	—
631	C₄	—	14	2	no	—
632	C₄	—	14	2	no	—
633	C₄	—	14	2	no	—
634	C₄	—	14	1	no	—
635	C₄	—	14	1	no	—
636	C₄	C₂×#1161	1	2	yes	—
637	C₂	—	2	4	no	—
638	C₂	—	28	1	no	—
639	C₂	—	28	2	no	—
640	C₂	—	28	1	no	—
641	C₂	—	28	1	no	—
642	C₂	C₂²×#1161	1	1	yes	characteristic
643	C₂	#90616	1	1	yes	characteristic
644	C₂	#90618	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₇
commutator, socle, cosocle	C₂²×C₇	C₂⁵
Fitting	C₇×#554	C₂
hypercenter	#554	D₇
hypocenter	C₇	#3521
LCS	G ▷ C₂²×C₇ ▷ C₇
UCS	C₁ ◁ C₂² ◁ #554

Complements

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

N	H ≅ G/N	type
1. C₇×#554	C₂	semidirect
2. #90424	C₂	semidirect
3. #90423	C₂	semidirect
4. #90388	C₂	semidirect
5. #90386	C₂	semidirect
6. #90385	C₂	semidirect
7. #90382	C₂	semidirect
8. #90336	C₂	semidirect
9. #90335	C₂	semidirect
10. #90333	C₂	semidirect
11. #90328	C₂	semidirect
12. #90328	C₂	semidirect
13. #90315	C₂	semidirect
14. #90275	C₂	semidirect
15. #90271	C₂	semidirect
16. #90246	C₂	semidirect
17. #90245	C₂	semidirect
18. #90245	C₂	semidirect
19. #90237	C₂	semidirect
20. #90236	C₂	semidirect
21. C₄×#1159	C₂	semidirect
22. #90205	C₂	semidirect
23. C₂×#6461	C₂	semidirect
27. C₇×C₄⋊Q₈	C₂²	semidirect
28. C₇×#125	C₂²	semidirect
29. C₇×#125	C₂²	semidirect
30. C₇×C₂²⋊Q₈	C₂²	semidirect
31. C₇×C₂²⋊Q₈	C₂²	semidirect
32. C₇×C₂²⋊Q₈	C₂²	semidirect
33. C₄×C₇×Q₈	C₂²	semidirect
37. C₂×C₇×C₄⋊C₄	C₂²	semidirect
40. #6510	C₂²	semidirect
41. #6509	C₂²	semidirect
42. #6509	C₂²	semidirect
43. #6509	C₂²	semidirect
44. Q₈×Dic₇	C₂²	semidirect
48. #6493	C₂²	semidirect
50. C₄×C₂²⋊D₇	C₂²	semidirect
51. C₄×C₂²⋊D₇	C₂²	semidirect
55. C₂×C₄⋊Dic₇	C₂²	semidirect
56. C₂×Dic₇⋊C₄	C₂²	semidirect
57. C₂×C₄×Dic₇	C₂²	semidirect
63. #6461	C₂²	semidirect
64. #6461	C₂²	semidirect
65. #6461	C₂²	semidirect
66. #6461	C₂²	semidirect
67. #6461	C₂²	semidirect
68. #6461	C₂²	semidirect
69. #6461	C₂²	semidirect
72. #6460	C₂²	semidirect
73. #6460	C₂²	semidirect
77. #6458	C₂²	semidirect
80. #6457	C₂²	semidirect
81. #6457	C₂²	semidirect
82. #6457	C₂²	semidirect
83. #6457	C₂²	semidirect
85. #6456	C₂²	semidirect
86. #6456	C₂²	semidirect
88. #6455	C₂²	semidirect
89. #6455	C₂²	semidirect
90. #6455	C₂²	semidirect
91. #6455	C₂²	semidirect
92. D₇×C₄⋊C₄	C₂²	semidirect
93. #6453	C₂²	semidirect
94. #6453	C₂²	semidirect
95. #6453	C₂²	semidirect
96. #6453	C₂²	semidirect
97. #6450	C₂²	semidirect
98. #6450	C₂²	semidirect
101. #6449	C₂²	semidirect
102. #6449	C₂²	semidirect
106. (C₂²⋊D₇)⋊C₄	C₂²	semidirect
107. (C₂²⋊D₇)⋊C₄	C₂²	semidirect
109. #6440	C₂²	semidirect
110. #6440	C₂²	semidirect
116. C₄×D₂₈	C₂²	semidirect
118. #6435	C₂²	semidirect
119. C₄²×D₇	C₂²	semidirect
120. #6432	C₂²	semidirect
121. C₄×Dic₁₄	C₂²	semidirect
122. C₄×Dic₁₄	C₂²	semidirect
228. #554	D₇	semidirect
307. C₄⋊Q₈	C₂×D₇	semidirect
324. #125	C₂×D₇	semidirect
325. #125	C₂×D₇	semidirect
348. C₂²⋊Q₈	C₂×D₇	semidirect
349. C₂²⋊Q₈	C₂×D₇	semidirect
350. C₂²⋊Q₈	C₂×D₇	semidirect
365. C₄×Q₈	C₂×D₇	semidirect
395. C₂×C₄⋊C₄	C₂×D₇	semidirect
601. C₇	#3521	semidirect

Maximal subgroups

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

subgroup	index
C₇×#554	2
#90424	2
#90423	2
#90388	2
#90386	2
#90385	2
#90382	2
#90336	2
#90335	2
#90333	2
#90328	2
#90315	2
#90275	2
#90271	2
#90246	2
#90245	2
#90237	2
#90236	2
C₄×#1159	2
#90205	2
C₂×#6461	2
#3521	7