Subgroups — #11744002

Order 896.

1124 conjugacy classes of subgroups.

The subgroup lattice has 660 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	#90418	C₂	1	1	yes	maximal, characteristic, complemented
4	#90384	C₂	1	2	yes	maximal, complemented
5	#90383	C₂	1	2	yes	maximal, complemented
6	#90334	C₂	1	1	yes	maximal, characteristic, complemented
7	#90329	C₂	1	2	yes	maximal, complemented
8	#90328	C₂	1	2	yes	maximal, complemented
9	#90324	C₂	1	2	yes	maximal, complemented
10	#90322	C₂	1	1	yes	maximal, characteristic, complemented
11	#90321	C₂	1	1	yes	maximal, characteristic, complemented
12	D₇×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
13	#90313	C₂	1	1	yes	maximal, characteristic, complemented
14	#90265	C₂	1	1	yes	maximal, characteristic, complemented
15	#90259	C₂	1	1	yes	maximal, characteristic, complemented
16	#90247	C₂	1	2	yes	maximal, complemented
17	#90241	C₂	1	1	yes	maximal, characteristic, complemented
18	#90238	C₂	1	2	yes	maximal, complemented
19	#90229	C₂	1	1	yes	maximal, characteristic, complemented
20	#90202	C₂	1	1	yes	maximal, characteristic, complemented
21	#90198	C₂	1	1	yes	maximal, characteristic, complemented
22	#90195	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×#6456	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#1161	C₂²	1	1	yes	characteristic
25	C₂×Q₈×D₇	C₂²	1	2	yes	complemented
26	C₂×#1157	C₂²	1	1	yes	characteristic
27	C₂×#1157	C₂²	1	2	yes	complemented
28	C₂²×D₂₈	C₂²	1	1	yes	characteristic
29	C₂²×C₄×D₇	C₂²	1	2	yes	—
30	C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
31	C₇×#125	C₂²	1	2	yes	complemented
32	C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
33	C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
34	C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
35	C₇×C₂²⋊Q₈	C₂²	1	2	yes	complemented
36	C₄×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
37	C₄×C₇×D₄	C₂²	1	1	yes	characteristic
38	C₄×C₇×D₄	C₂²	1	2	yes	—
39	C₂×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
40	C₂×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
41	#6510	C₂²	1	1	yes	characteristic
42	#6510	C₂²	1	2	yes	complemented
43	#6509	C₂²	1	2	yes	complemented
44	#6509	C₂²	1	2	yes	complemented
45	Q₈×Dic₇	C₂²	1	1	yes	characteristic, complemented
46	#6507	C₂²	1	1	yes	characteristic, complemented
47	#6502	C₂²	1	1	yes	characteristic
48	#6500	C₂²	1	2	yes	—
49	#6498	C₂²	1	1	yes	characteristic
50	#6493	C₂²	1	1	yes	characteristic
51	#6492	C₂²	1	2	yes	complemented
52	C₄×C₂²⋊D₇	C₂²	1	1	yes	characteristic
53	C₄×C₂²⋊D₇	C₂²	1	2	yes	—
54	C₄×C₂²⋊D₇	C₂²	1	2	yes	complemented
55	C₄×C₂²⋊D₇	C₂²	1	2	yes	complemented
56	C₄×C₂²⋊D₇	C₂²	1	1	yes	characteristic, complemented
57	C₂×(C₂×D₇)⋊C₄	C₂²	1	2	yes	—
58	#6489	C₂²	1	1	yes	characteristic, complemented
59	#6487	C₂²	1	1	yes	characteristic
60	#6487	C₂²	1	2	yes	—
61	C₂×C₄×Dic₇	C₂²	1	1	yes	characteristic
62	#6461	C₂²	1	1	yes	characteristic, complemented
63	#6461	C₂²	1	2	yes	complemented
64	#6461	C₂²	1	2	yes	complemented
65	#6461	C₂²	1	2	yes	complemented
66	#6460	C₂²	1	2	yes	complemented
67	#6460	C₂²	1	1	yes	characteristic, complemented
68	#6459	C₂²	1	2	yes	complemented
69	#6459	C₂²	1	2	yes	complemented
70	#6459	C₂²	1	2	yes	complemented
71	#6459	C₂²	1	2	yes	complemented
72	#6459	C₂²	1	2	yes	complemented
73	#6458	C₂²	1	2	yes	—
74	#6458	C₂²	1	1	yes	characteristic
75	#6457	C₂²	1	2	yes	—
76	#6457	C₂²	1	2	yes	—
77	#6457	C₂²	1	2	yes	complemented
78	#6457	C₂²	1	2	yes	complemented
79	#6457	C₂²	1	2	yes	complemented
80	#6456	C₂²	1	2	yes	—
81	#6456	C₂²	1	2	yes	—
82	#6456	C₂²	1	1	yes	characteristic
83	#6456	C₂²	1	1	yes	characteristic
84	#6456	C₂²	1	1	yes	characteristic
85	#6456	C₂²	1	1	yes	characteristic
86	#6456	C₂²	1	1	yes	characteristic
87	#6456	C₂²	1	2	yes	complemented
88	#6455	C₂²	1	2	yes	complemented
89	D₇×C₄⋊C₄	C₂²	1	2	yes	complemented
90	D₇×C₄⋊C₄	C₂²	1	2	yes	complemented
91	D₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
92	D₇×C₄⋊C₄	C₂²	1	2	yes	complemented
93	#6452	C₂²	1	2	yes	complemented
94	#6452	C₂²	1	1	yes	characteristic, complemented
95	#6452	C₂²	1	2	yes	complemented
96	#6451	C₂²	1	1	yes	characteristic, complemented
97	#6451	C₂²	1	1	yes	characteristic, complemented
98	#6450	C₂²	1	2	yes	complemented
99	#6450	C₂²	1	1	yes	characteristic, complemented
100	#6450	C₂²	1	1	yes	characteristic, complemented
101	#6449	C₂²	1	1	yes	characteristic
102	#6448	C₂²	1	1	yes	characteristic, complemented
103	#6448	C₂²	1	2	yes	complemented
104	#6447	C₂²	1	2	yes	—
105	#6447	C₂²	1	2	yes	complemented
106	#6446	C₂²	1	2	yes	complemented
107	#6446	C₂²	1	2	yes	complemented
108	#6445	C₂²	1	2	yes	—
109	D₇×C₂²⋊C₄	C₂²	1	2	yes	—
110	D₇×C₂²⋊C₄	C₂²	1	2	yes	—
111	#6442	C₂²	1	1	yes	characteristic, complemented
112	#6441	C₂²	1	1	yes	characteristic
113	#6441	C₂²	1	2	yes	—
114	#6440	C₂²	1	2	yes	—
115	#6439	C₂²	1	2	yes	complemented
116	#6438	C₂²	1	1	yes	characteristic
117	C₄×D₂₈	C₂²	1	1	yes	characteristic
118	C₄×D₂₈	C₂²	1	2	yes	complemented
119	#6435	C₂²	1	2	yes	complemented
120	#6435	C₂²	1	2	yes	complemented
121	#6435	C₂²	1	1	yes	characteristic, complemented
122	C₄×Dic₁₄	C₂²	1	1	yes	characteristic, complemented
123	#3520	—	7	1	no	maximal, Sylow
124	C₂³×D₇	C₂³	1	2	yes	—
125	C₂×C₇×Q₈	C₂³	1	1	yes	characteristic
126	C₂×C₇×Q₈	C₂³	1	2	yes	—
127	C₂×C₇×D₄	C₂³	1	1	yes	characteristic
128	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
129	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
130	C₂²×C₄×C₇	C₂³	1	2	yes	—
131	C₂²×C₄×C₇	C₂³	1	2	yes	—
132	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
133	C₂×C₂²⋊D₇	C₂³	1	2	yes	—
134	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
135	C₂×C₂²⋊D₇	C₂³	1	2	yes	—
136	C₂²×Dic₇	C₂³	1	1	yes	characteristic
137	C₂²×Dic₇	C₂³	1	1	yes	characteristic
138	#1161	—	2	4	no	—
139	Q₈×D₇	—	4	4	no	—
140	#1157	—	2	4	no	—
141	#1157	—	4	4	no	—
142	C₂×D₂₈	—	2	4	no	—
143	C₂×D₂₈	C₂³	1	2	yes	—
144	C₂×D₂₈	C₂³	1	1	yes	characteristic
145	C₂×D₂₈	C₂³	1	2	yes	—
146	C₂×D₂₈	C₂³	1	2	yes	—
147	C₂×D₂₈	C₂³	1	1	yes	characteristic
148	C₂×C₄×D₇	—	4	4	no	—
149	C₂×C₄×D₇	C₂³	1	2	yes	—
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×C₄×D₇	C₂³	1	2	yes	—
155	C₂×C₄×D₇	C₂³	1	2	yes	—
156	C₂×C₄×D₇	C₂³	1	2	yes	—
157	C₂×C₄×D₇	C₂³	1	2	yes	—
158	C₂×C₄×D₇	C₂³	1	2	yes	—
159	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
160	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
161	C₂×Dic₁₄	C₂³	1	2	yes	—
162	C₂×Dic₁₄	C₂³	1	2	yes	—
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	1	yes	characteristic
167	C₇×C₄⋊C₄	C₂³	1	2	yes	—
168	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
169	C₇×C₄⋊C₄	C₂³	1	2	yes	—
170	C₇×C₄⋊C₄	C₂³	1	2	yes	—
171	C₇×C₄⋊C₄	C₂³	1	2	yes	—
172	C₇×C₄⋊C₄	C₂³	1	2	yes	—
173	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
174	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
175	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
176	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
177	C₄²×C₇	C₂³	1	1	yes	characteristic
178	C₄²×C₇	C₂³	1	2	yes	—
179	C₂²⋊Dic₇	C₂³	1	2	yes	—
180	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
181	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
182	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
183	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
184	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
185	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
186	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
187	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
188	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
200	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
201	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
202	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
203	C₄⋊Dic₇	C₂³	1	2	yes	—
204	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
205	C₄⋊Dic₇	C₂³	1	2	yes	—
206	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
207	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
208	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
209	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
210	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
211	Dic₇⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
218	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
219	Dic₇⋊C₄	C₂³	1	2	yes	—
220	Dic₇⋊C₄	C₂³	1	2	yes	—
221	C₄×Dic₇	C₂³	1	1	yes	characteristic
222	C₄×Dic₇	C₂³	1	1	yes	characteristic
223	C₄×Dic₇	C₂³	1	2	yes	—
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	#556	—	7	1	no	—
230	#554	—	7	1	no	—
231	#554	D₇	1	1	yes	characteristic, complemented
232	#552	—	7	2	no	—
233	#551	—	7	2	no	—
234	#551	—	7	2	no	—
235	D₄×Q₈	—	7	1	no	—
236	#548	—	7	2	no	—
237	#547	—	7	1	no	—
238	#547	—	7	1	no	—
239	#546	—	7	1	no	—
240	#546	—	7	1	no	—
241	#542	—	7	1	no	—
242	#542	—	7	1	no	—
243	#539	—	7	2	no	—
244	#539	—	7	2	no	—
245	#533	—	7	1	no	—
246	#529	—	7	1	no	—
247	#525	—	7	2	no	—
248	C₂×C₂²⋊Q₈	—	7	2	no	—
249	#520	—	7	1	no	—
250	#520	—	7	1	no	—
251	C₂×C₄×D₄	—	7	1	no	—
252	C₂³×C₇	C₂⁴	1	1	yes	characteristic
253	C₂³×C₇	C₂⁴	1	1	yes	characteristic
254	C₂²×D₇	—	2	4	no	—
255	C₂²×D₇	—	2	4	no	—
256	C₂²×D₇	—	4	2	no	—
257	C₂²×D₇	C₂⁴	1	2	yes	—
258	C₂²×D₇	C₂⁴	1	1	yes	characteristic
259	C₂²×D₇	C₂⁴	1	2	yes	—
260	C₇×Q₈	—	2	2	no	—
261	C₇×Q₈	—	4	2	no	—
262	C₇×D₄	—	2	2	no	—
263	C₂×C₄×C₇	—	2	2	no	—
264	C₂×C₄×C₇	—	2	2	no	—
265	C₂×C₄×C₇	—	4	2	no	—
266	C₂×C₄×C₇	—	4	2	no	—
267	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
268	C₂×C₄×C₇	C₂⁴	1	2	yes	—
269	C₂×C₄×C₇	C₂⁴	1	2	yes	—
270	C₂×C₄×C₇	C₂⁴	1	2	yes	—
271	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
272	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
273	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
274	C₂×C₄×C₇	C₂⁴	1	2	yes	—
275	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
276	C₂²⋊D₇	—	2	2	no	—
277	C₂²⋊D₇	—	2	4	no	—
278	C₂²⋊D₇	—	2	2	no	—
279	C₂²⋊D₇	—	4	2	no	—
280	C₂×Dic₇	—	2	2	no	—
281	C₂×Dic₇	—	2	2	no	—
282	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
283	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
284	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
285	C₂×Dic₇	C₂⁴	1	2	yes	—
286	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
287	C₂×Dic₇	C₂⁴	1	2	yes	—
288	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
289	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
290	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
291	D₂₈	—	2	4	no	—
292	D₂₈	—	2	4	no	—
293	D₂₈	—	2	2	no	—
294	D₂₈	—	4	2	no	—
295	D₂₈	#41	1	4	yes	complemented
296	C₄×D₇	—	2	4	no	—
297	C₄×D₇	—	2	4	no	—
298	C₄×D₇	—	2	2	no	—
299	C₄×D₇	—	2	4	no	—
300	C₄×D₇	—	2	4	no	—
301	C₄×D₇	—	4	2	no	—
302	C₄×D₇	—	4	2	no	—
303	C₄×D₇	—	4	2	no	—
304	C₄×D₇	—	4	2	no	—
305	C₄×D₇	—	4	2	no	—
306	Dic₁₄	—	2	2	no	—
307	Dic₁₄	—	2	4	no	—
308	Dic₁₄	—	2	2	no	—
309	Dic₁₄	—	4	2	no	—
310	C₂×#41	—	7	1	no	—
311	C₂×#41	—	7	1	no	—
312	C₂×#41	—	7	2	no	—
313	C₂²×Q₈	—	7	2	no	—
314	C₂²×D₄	—	7	1	no	—
315	C₂³×C₄	—	7	2	no	—
316	C₄⋊Q₈	—	7	1	no	—
317	C₄⋊Q₈	—	7	1	no	—
318	C₄⋊Q₈	—	7	1	no	—
319	C₄⋊Q₈	C₂×D₇	1	1	yes	characteristic, complemented
320	#126	—	7	1	no	—
321	#126	—	7	2	no	—
322	#126	—	7	2	no	—
323	#126	—	7	2	no	—
324	#126	—	7	1	no	—
325	#126	—	7	2	no	—
326	#125	—	7	1	no	—
327	#125	—	7	2	no	—
328	#125	—	7	2	no	—
329	#125	C₂×D₇	1	2	yes	complemented
330	#124	—	7	1	no	—
331	#124	—	7	2	no	—
332	#124	—	7	1	no	—
333	#124	—	7	2	no	—
334	#124	—	7	1	no	—
335	#123	—	7	1	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	#123	—	7	2	no	—
342	#123	—	7	2	no	—
343	#123	—	7	1	no	—
344	#123	—	7	2	no	—
345	C₂²⋊Q₈	—	7	2	no	—
346	C₂²⋊Q₈	—	7	2	no	—
347	C₂²⋊Q₈	—	7	2	no	—
348	C₂²⋊Q₈	—	7	1	no	—
349	C₂²⋊Q₈	—	7	2	no	—
350	C₂²⋊Q₈	—	7	2	no	—
351	C₂²⋊Q₈	—	7	2	no	—
352	C₂²⋊Q₈	—	7	2	no	—
353	C₂²⋊Q₈	—	7	2	no	—
354	C₂²⋊Q₈	—	7	2	no	—
355	C₂²⋊Q₈	—	7	1	no	—
356	C₂²⋊Q₈	—	7	1	no	—
357	C₂²⋊Q₈	—	7	2	no	—
358	C₂²⋊Q₈	C₂×D₇	1	2	yes	—
359	C₂²⋊Q₈	C₂×D₇	1	1	yes	characteristic
360	C₂²⋊Q₈	C₂×D₇	1	2	yes	complemented
361	C₂²⋊Q₈	C₂×D₇	1	1	yes	characteristic, complemented
362	#121	—	7	1	no	—
363	#121	—	7	1	no	—
364	#121	—	7	2	no	—
365	#121	—	7	1	no	—
366	#121	—	7	2	no	—
367	#121	—	7	2	no	—
368	#120	—	7	2	no	—
369	#120	—	7	2	no	—
370	C₄×Q₈	—	7	1	no	—
371	C₄×Q₈	—	7	1	no	—
372	C₄×Q₈	—	7	1	no	—
373	C₄×Q₈	—	7	2	no	—
374	C₄×Q₈	—	7	1	no	—
375	C₄×Q₈	C₂×D₇	1	1	yes	characteristic, complemented
376	C₄×D₄	—	7	2	no	—
377	C₄×D₄	—	7	2	no	—
378	C₄×D₄	—	7	2	no	—
379	C₄×D₄	—	7	1	no	—
380	C₄×D₄	—	7	1	no	—
381	C₄×D₄	—	7	1	no	—
382	C₄×D₄	—	7	2	no	—
383	C₄×D₄	—	7	1	no	—
384	C₄×D₄	—	7	1	no	—
385	C₄×D₄	—	7	1	no	—
386	C₄×D₄	—	7	2	no	—
387	C₄×D₄	—	7	1	no	—
388	C₄×D₄	—	7	2	no	—
389	C₄×D₄	—	7	2	no	—
390	C₄×D₄	—	7	1	no	—
391	C₄×D₄	C₂×D₇	1	2	yes	—
392	C₄×D₄	C₂×D₇	1	1	yes	characteristic
393	#117	—	7	1	no	—
394	#117	—	7	2	no	—
395	#117	—	7	2	no	—
396	#117	—	7	1	no	—
397	#117	—	7	2	no	—
398	#117	—	7	2	no	—
399	C₂×C₄⋊C₄	—	7	2	no	—
400	C₂×C₄⋊C₄	—	7	2	no	—
401	C₂×C₄⋊C₄	—	7	1	no	—
402	C₂×C₄⋊C₄	—	7	2	no	—
403	C₂×C₄⋊C₄	C₂×D₇	1	1	yes	characteristic
404	C₂×C₄⋊C₄	C₂×D₇	1	1	yes	characteristic, complemented
405	C₂×C₂²⋊C₄	—	7	2	no	—
406	C₂×C₂²⋊C₄	—	7	2	no	—
407	C₂×C₂²⋊C₄	—	7	2	no	—
408	C₂×C₄²	—	7	1	no	—
409	C₂²×C₇	—	2	1	no	—
410	C₂²×C₇	—	2	1	no	—
411	C₂²×C₇	—	2	1	no	—
412	C₂²×C₇	—	2	1	no	—
413	C₂²×C₇	—	2	1	no	—
414	C₂²×C₇	2₋¹⁺⁴	1	2	yes	—
415	C₂²×C₇	C₂⁵	1	1	yes	characteristic
416	C₂×D₇	—	2	2	no	—
417	C₂×D₇	—	2	2	no	—
418	C₂×D₇	—	2	1	no	—
419	C₂×D₇	—	2	2	no	—
420	C₂×D₇	—	2	2	no	—
421	C₂×D₇	—	2	1	no	—
422	C₂×D₇	—	2	1	no	—
423	C₂×D₇	—	2	2	no	—
424	C₂×D₇	—	4	8	no	—
425	C₂×D₇	C₂×#41	1	4	yes	—
426	C₄×C₇	—	2	1	no	—
427	C₄×C₇	—	2	2	no	—
428	C₄×C₇	—	2	1	no	—
429	C₄×C₇	—	2	1	no	—
430	C₄×C₇	—	2	2	no	—
431	C₄×C₇	—	2	2	no	—
432	C₄×C₇	—	2	2	no	—
433	C₄×C₇	—	2	1	no	—
434	C₄×C₇	C₂×#41	1	2	yes	—
435	Dic₇	—	2	2	no	—
436	Dic₇	—	2	1	no	—
437	Dic₇	—	2	1	no	—
438	Dic₇	—	2	2	no	—
439	Dic₇	—	2	1	no	—
440	Dic₇	—	2	1	no	—
441	Dic₇	—	2	1	no	—
442	Dic₇	—	2	1	no	—
443	Dic₇	H(5,𝔽₂)	1	2	yes	—
444	C₂⁴	—	7	2	no	—
445	#41	—	14	4	no	—
446	#41	—	14	4	no	—
447	#41	—	28	4	no	—
448	C₂×Q₈	—	7	1	no	—
449	C₂×Q₈	—	7	1	no	—
450	C₂×Q₈	—	7	2	no	—
451	C₂×Q₈	—	7	2	no	—
452	C₂×Q₈	—	28	4	no	—
453	C₂×Q₈	C₂²×D₇	1	1	yes	characteristic
454	C₂×Q₈	C₂²×D₇	1	2	yes	—
455	C₂×D₄	—	7	1	no	—
456	C₂×D₄	—	7	2	no	—
457	C₂×D₄	—	7	1	no	—
458	C₂×D₄	—	7	2	no	—
459	C₂×D₄	—	7	1	no	—
460	C₂×D₄	—	7	2	no	—
461	C₂×D₄	—	7	2	no	—
462	C₂×D₄	—	7	1	no	—
463	C₂×D₄	—	7	2	no	—
464	C₂×D₄	—	14	4	no	—
465	C₂×D₄	C₂²×D₇	1	1	yes	characteristic
466	C₂²×C₄	—	7	1	no	—
467	C₂²×C₄	—	7	1	no	—
468	C₂²×C₄	—	7	2	no	—
469	C₂²×C₄	—	7	2	no	—
470	C₂²×C₄	—	7	1	no	—
471	C₂²×C₄	—	7	2	no	—
472	C₂²×C₄	—	7	2	no	—
473	C₂²×C₄	—	7	2	no	—
474	C₂²×C₄	—	7	2	no	—
475	C₂²×C₄	—	7	2	no	—
476	C₂²×C₄	—	7	2	no	—
477	C₂²×C₄	—	7	2	no	—
478	C₂²×C₄	—	28	4	no	—
479	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
480	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
481	C₂²×C₄	C₂²×D₇	1	2	yes	—
482	C₂²×C₄	C₂²×D₇	1	2	yes	—
483	C₄⋊C₄	—	7	1	no	—
484	C₄⋊C₄	—	7	2	no	—
485	C₄⋊C₄	—	7	1	no	—
486	C₄⋊C₄	—	7	2	no	—
487	C₄⋊C₄	—	7	2	no	—
488	C₄⋊C₄	—	7	2	no	—
489	C₄⋊C₄	—	7	1	no	—
490	C₄⋊C₄	—	7	1	no	—
491	C₄⋊C₄	—	7	2	no	—
492	C₄⋊C₄	—	7	2	no	—
493	C₄⋊C₄	—	7	2	no	—
494	C₄⋊C₄	—	7	1	no	—
495	C₄⋊C₄	—	7	2	no	—
496	C₄⋊C₄	—	7	1	no	—
497	C₄⋊C₄	—	7	1	no	—
498	C₄⋊C₄	—	7	1	no	—
499	C₄⋊C₄	—	7	2	no	—
500	C₄⋊C₄	—	7	2	no	—
501	C₄⋊C₄	—	7	1	no	—
502	C₄⋊C₄	—	7	1	no	—
503	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
504	C₄⋊C₄	C₂²×D₇	1	2	yes	—
505	C₄⋊C₄	C₂²×D₇	1	2	yes	—
506	C₄⋊C₄	C₂²×D₇	1	2	yes	—
507	C₄⋊C₄	C₂²×D₇	1	2	yes	—
508	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
509	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
510	C₄⋊C₄	C₂²×D₇	1	2	yes	—
511	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
512	C₄⋊C₄	C₂²×D₇	1	2	yes	—
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	1	no	—
518	C₂²⋊C₄	—	7	2	no	—
519	C₂²⋊C₄	—	7	2	no	—
520	C₂²⋊C₄	—	7	2	no	—
521	C₂²⋊C₄	—	7	2	no	—
522	C₂²⋊C₄	—	7	2	no	—
523	C₂²⋊C₄	—	7	2	no	—
524	C₂²⋊C₄	—	7	2	no	—
525	C₂²⋊C₄	—	7	2	no	—
526	C₂²⋊C₄	—	7	2	no	—
527	C₂²⋊C₄	—	7	2	no	—
528	C₂²⋊C₄	—	7	1	no	—
529	C₂²⋊C₄	—	7	1	no	—
530	C₂²⋊C₄	—	7	2	no	—
531	C₂²⋊C₄	—	7	2	no	—
532	C₂²⋊C₄	—	7	1	no	—
533	C₂²⋊C₄	—	7	2	no	—
534	C₂²⋊C₄	—	7	1	no	—
535	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
536	C₂²⋊C₄	C₂²×D₇	1	2	yes	—
537	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
538	C₂²⋊C₄	C₂²×D₇	1	2	yes	—
539	C₄²	—	7	1	no	—
540	C₄²	—	7	1	no	—
541	C₄²	—	7	1	no	—
542	C₄²	—	7	1	no	—
543	C₄²	—	7	2	no	—
544	C₄²	—	7	2	no	—
545	C₄²	—	7	2	no	—
546	C₄²	—	7	1	no	—
547	C₄²	C₂²×D₇	1	2	yes	—
548	C₄²	C₂²×D₇	1	1	yes	characteristic
549	C₂×C₇	—	2	2	no	—
550	C₂×C₇	—	4	1	no	—
551	C₂×C₇	C₂²×#41	1	1	yes	characteristic
552	C₂×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
553	C₂×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
554	D₇	—	2	4	no	—
555	D₇	—	4	1	no	—
556	D₇	—	4	2	no	—
557	C₂³	—	7	2	no	—
558	C₂³	—	7	2	no	—
559	C₂³	—	7	1	no	—
560	C₂³	—	14	4	no	—
561	C₂³	—	14	4	no	—
562	C₂³	—	28	2	no	—
563	C₂³	C₂³×D₇	1	1	yes	characteristic
564	C₂³	C₂³×D₇	1	1	yes	characteristic
565	Q₈	—	2	2	no	—
566	Q₈	—	4	2	no	—
567	Q₈	—	14	2	no	—
568	Q₈	—	14	4	no	—
569	Q₈	—	14	2	no	—
570	Q₈	—	28	2	no	—
571	D₄	—	2	2	no	—
572	D₄	—	7	4	no	—
573	D₄	—	14	4	no	—
574	D₄	—	14	4	no	—
575	D₄	—	14	2	no	—
576	D₄	—	14	4	no	—
577	D₄	—	14	2	no	—
578	D₄	—	14	2	no	—
579	D₄	—	28	2	no	—
580	D₄	—	28	2	no	—
581	C₂×C₄	—	2	2	no	—
582	C₂×C₄	—	2	2	no	—
583	C₂×C₄	—	4	2	no	—
584	C₂×C₄	—	4	2	no	—
585	C₂×C₄	—	7	1	no	—
586	C₂×C₄	—	7	1	no	—
587	C₂×C₄	—	7	1	no	—
588	C₂×C₄	—	7	1	no	—
589	C₂×C₄	—	7	2	no	—
590	C₂×C₄	—	7	1	no	—
591	C₂×C₄	—	7	1	no	—
592	C₂×C₄	—	7	2	no	—
593	C₂×C₄	—	7	1	no	—
594	C₂×C₄	—	14	4	no	—
595	C₂×C₄	—	14	4	no	—
596	C₂×C₄	—	14	4	no	—
597	C₂×C₄	—	14	4	no	—
598	C₂×C₄	—	14	2	no	—
599	C₂×C₄	—	14	2	no	—
600	C₂×C₄	—	14	2	no	—
601	C₂×C₄	—	28	2	no	—
602	C₂×C₄	—	28	2	no	—
603	C₂×C₄	—	28	2	no	—
604	C₂×C₄	—	28	2	no	—
605	C₂×C₄	—	28	2	no	—
606	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
607	C₂×C₄	C₂³×D₇	1	2	yes	—
608	C₂×C₄	C₂³×D₇	1	2	yes	—
609	C₂×C₄	C₂³×D₇	1	2	yes	—
610	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
611	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
612	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
613	C₂×C₄	C₂³×D₇	1	2	yes	—
614	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
615	C₇	#3520	1	1	yes	characteristic, complemented, Sylow
616	C₂²	—	2	1	no	—
617	C₂²	—	2	1	no	—
618	C₂²	—	2	1	no	—
619	C₂²	—	2	1	no	—
620	C₂²	—	2	1	no	—
621	C₂²	—	7	4	no	—
622	C₂²	—	14	2	no	—
623	C₂²	—	14	2	no	—
624	C₂²	—	14	1	no	—
625	C₂²	—	14	2	no	—
626	C₂²	—	14	1	no	—
627	C₂²	—	14	2	no	—
628	C₂²	—	14	2	no	—
629	C₂²	—	14	1	no	—
630	C₂²	—	28	8	no	—
631	C₂²	#6551	1	2	yes	—
632	C₂²	C₂⁴×D₇	1	1	yes	characteristic
633	C₄	—	2	1	no	—
634	C₄	—	2	1	no	—
635	C₄	—	2	1	no	—
636	C₄	—	2	2	no	—
637	C₄	—	2	2	no	—
638	C₄	—	2	2	no	—
639	C₄	—	2	2	no	—
640	C₄	—	2	1	no	—
641	C₄	—	7	2	no	—
642	C₄	—	14	1	no	—
643	C₄	—	14	1	no	—
644	C₄	—	14	1	no	—
645	C₄	—	14	1	no	—
646	C₄	—	14	2	no	—
647	C₄	—	14	1	no	—
648	C₄	—	14	2	no	—
649	C₄	—	14	1	no	—
650	C₄	D₇×#41	1	2	yes	—
651	C₂	—	2	2	no	—
652	C₂	—	4	1	no	—
653	C₂	—	14	4	no	—
654	C₂	—	28	2	no	—
655	C₂	—	28	1	no	—
656	C₂	C₂×#6551	1	1	yes	characteristic
657	C₂	C₂×D₇×#41	1	1	yes	characteristic
658	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×#554	C₂
hypercenter	#554	D₇
hypocenter	C₇	#3520
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. #90418	C₂	semidirect
4. #90384	C₂	semidirect
5. #90383	C₂	semidirect
6. #90334	C₂	semidirect
7. #90329	C₂	semidirect
8. #90328	C₂	semidirect
9. #90324	C₂	semidirect
10. #90322	C₂	semidirect
11. #90321	C₂	semidirect
12. D₇×C₂²⋊Q₈	C₂	semidirect
13. #90313	C₂	semidirect
14. #90265	C₂	semidirect
15. #90259	C₂	semidirect
16. #90247	C₂	semidirect
17. #90241	C₂	semidirect
18. #90238	C₂	semidirect
19. #90229	C₂	semidirect
20. #90202	C₂	semidirect
21. #90198	C₂	semidirect
22. #90195	C₂	semidirect
23. C₂×#6456	C₂	semidirect
25. C₂×Q₈×D₇	C₂²	semidirect
27. C₂×#1157	C₂²	semidirect
30. C₇×C₄⋊Q₈	C₂²	semidirect
31. C₇×#125	C₂²	semidirect
34. C₇×C₂²⋊Q₈	C₂²	semidirect
35. C₇×C₂²⋊Q₈	C₂²	semidirect
36. C₄×C₇×Q₈	C₂²	semidirect
40. C₂×C₇×C₄⋊C₄	C₂²	semidirect
42. #6510	C₂²	semidirect
43. #6509	C₂²	semidirect
44. #6509	C₂²	semidirect
45. Q₈×Dic₇	C₂²	semidirect
46. #6507	C₂²	semidirect
51. #6492	C₂²	semidirect
54. C₄×C₂²⋊D₇	C₂²	semidirect
55. C₄×C₂²⋊D₇	C₂²	semidirect
56. C₄×C₂²⋊D₇	C₂²	semidirect
58. #6489	C₂²	semidirect
62. #6461	C₂²	semidirect
63. #6461	C₂²	semidirect
64. #6461	C₂²	semidirect
65. #6461	C₂²	semidirect
66. #6460	C₂²	semidirect
67. #6460	C₂²	semidirect
68. #6459	C₂²	semidirect
69. #6459	C₂²	semidirect
70. #6459	C₂²	semidirect
71. #6459	C₂²	semidirect
72. #6459	C₂²	semidirect
77. #6457	C₂²	semidirect
78. #6457	C₂²	semidirect
79. #6457	C₂²	semidirect
87. #6456	C₂²	semidirect
88. #6455	C₂²	semidirect
89. D₇×C₄⋊C₄	C₂²	semidirect
90. D₇×C₄⋊C₄	C₂²	semidirect
91. D₇×C₄⋊C₄	C₂²	semidirect
92. D₇×C₄⋊C₄	C₂²	semidirect
93. #6452	C₂²	semidirect
94. #6452	C₂²	semidirect
95. #6452	C₂²	semidirect
96. #6451	C₂²	semidirect
97. #6451	C₂²	semidirect
98. #6450	C₂²	semidirect
99. #6450	C₂²	semidirect
100. #6450	C₂²	semidirect
102. #6448	C₂²	semidirect
103. #6448	C₂²	semidirect
105. #6447	C₂²	semidirect
106. #6446	C₂²	semidirect
107. #6446	C₂²	semidirect
111. #6442	C₂²	semidirect
115. #6439	C₂²	semidirect
118. C₄×D₂₈	C₂²	semidirect
119. #6435	C₂²	semidirect
120. #6435	C₂²	semidirect
121. #6435	C₂²	semidirect
122. C₄×Dic₁₄	C₂²	semidirect
231. #554	D₇	semidirect
295. D₂₈	#41	semidirect
319. C₄⋊Q₈	C₂×D₇	semidirect
329. #125	C₂×D₇	semidirect
360. C₂²⋊Q₈	C₂×D₇	semidirect
361. C₂²⋊Q₈	C₂×D₇	semidirect
375. C₄×Q₈	C₂×D₇	semidirect
404. C₂×C₄⋊C₄	C₂×D₇	semidirect
615. C₇	#3520	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
#90418	2
#90384	2
#90383	2
#90334	2
#90329	2
#90328	2
#90324	2
#90322	2
#90321	2
D₇×C₂²⋊Q₈	2
#90313	2
#90265	2
#90259	2
#90247	2
#90241	2
#90238	2
#90229	2
#90202	2
#90198	2
#90195	2
C₂×#6456	2
#3520	7