Subgroups — #11743624

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×#542	C₂	1	1	yes	maximal, characteristic, complemented
2	#90421	C₂	1	1	yes	maximal, characteristic, complemented
3	#90418	C₂	1	1	yes	maximal, characteristic, complemented
4	#90399	C₂	1	2	yes	maximal, complemented
5	#90396	C₂	1	2	yes	maximal, complemented
6	#90370	C₂	1	2	yes	maximal, complemented
7	#90368	C₂	1	2	yes	maximal, complemented
8	#90367	C₂	1	1	yes	maximal, characteristic, complemented
9	#90362	C₂	1	1	yes	maximal, characteristic, complemented
10	#90351	C₂	1	2	yes	maximal, complemented
11	#90347	C₂	1	2	yes	maximal, complemented
12	#90329	C₂	1	2	yes	maximal, complemented
13	#90326	C₂	1	1	yes	maximal, characteristic, complemented
14	#90322	C₂	1	1	yes	maximal, characteristic, complemented
15	D₇×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
16	#90303	C₂	1	1	yes	maximal, characteristic, complemented
17	#90302	C₂	1	1	yes	maximal, characteristic, complemented
18	#90269	C₂	1	1	yes	maximal, characteristic, complemented
19	#90265	C₂	1	1	yes	maximal, characteristic, complemented
20	#90252	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×D₄×D₇	C₂	1	1	yes	maximal, characteristic, complemented
22	#90219	C₂	1	1	yes	maximal, characteristic, complemented
23	#90214	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×#1159	C₂²	1	2	yes	complemented
27	C₂×D₄×D₇	C₂²	1	1	yes	characteristic
28	C₂×#1157	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×#126	C₂²	1	2	yes	complemented
32	C₇×#124	C₂²	1	1	yes	characteristic
33	C₇×#124	C₂²	1	2	yes	complemented
34	C₇×#123	C₂²	1	2	yes	complemented
35	C₇×C₂²⋊Q₈	C₂²	1	2	yes	complemented
36	C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
37	C₇×#121	C₂²	1	1	yes	characteristic
38	C₄×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
39	C₄×C₇×D₄	C₂²	1	1	yes	characteristic
40	C₇×#117	C₂²	1	1	yes	characteristic, complemented
41	#6509	C₂²	1	2	yes	—
42	#6509	C₂²	1	1	yes	characteristic
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	#6501	C₂²	1	2	yes	—
48	#6501	C₂²	1	1	yes	characteristic
49	#6500	C₂²	1	2	yes	—
50	#6499	C₂²	1	1	yes	characteristic
51	#6498	C₂²	1	2	yes	complemented
52	D₄×Dic₇	C₂²	1	1	yes	characteristic
53	#6492	C₂²	1	2	yes	complemented
54	C₄×C₂²⋊D₇	C₂²	1	1	yes	characteristic
55	C₄×C₂²⋊D₇	C₂²	1	2	yes	—
56	C₄×C₂²⋊D₇	C₂²	1	1	yes	characteristic, complemented
57	C₂×C₄⋊Dic₇	C₂²	1	1	yes	characteristic, complemented
58	#6487	C₂²	1	2	yes	complemented
59	#6461	C₂²	1	1	yes	characteristic, complemented
60	#6460	C₂²	1	2	yes	—
61	#6460	C₂²	1	1	yes	characteristic
62	#6460	C₂²	1	1	yes	characteristic, complemented
63	#6459	C₂²	1	1	yes	characteristic
64	#6459	C₂²	1	2	yes	—
65	#6459	C₂²	1	2	yes	complemented
66	#6459	C₂²	1	2	yes	complemented
67	#6457	C₂²	1	1	yes	characteristic
68	#6457	C₂²	1	2	yes	complemented
69	#6456	C₂²	1	2	yes	—
70	#6456	C₂²	1	1	yes	characteristic
71	#6456	C₂²	1	1	yes	characteristic
72	#6456	C₂²	1	2	yes	complemented
73	#6455	C₂²	1	2	yes	complemented
74	D₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
75	D₇×C₄⋊C₄	C₂²	1	2	yes	complemented
76	D₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
77	D₇×C₄⋊C₄	C₂²	1	2	yes	complemented
78	D₇×C₄⋊C₄	C₂²	1	2	yes	complemented
79	#6453	C₂²	1	2	yes	complemented
80	#6452	C₂²	1	1	yes	characteristic, complemented
81	#6452	C₂²	1	2	yes	complemented
82	#6452	C₂²	1	2	yes	complemented
83	#6451	C₂²	1	1	yes	characteristic, complemented
84	#6451	C₂²	1	1	yes	characteristic, complemented
85	#6448	C₂²	1	1	yes	characteristic, complemented
86	#6448	C₂²	1	2	yes	complemented
87	#6447	C₂²	1	2	yes	—
88	#6447	C₂²	1	1	yes	characteristic
89	#6447	C₂²	1	2	yes	complemented
90	#6446	C₂²	1	1	yes	characteristic
91	#6446	C₂²	1	2	yes	—
92	#6446	C₂²	1	2	yes	—
93	#6446	C₂²	1	2	yes	complemented
94	#6446	C₂²	1	2	yes	complemented
95	#6445	C₂²	1	2	yes	—
96	(C₂²⋊D₇)⋊C₄	C₂²	1	2	yes	—
97	(C₂²⋊D₇)⋊C₄	C₂²	1	2	yes	—
98	(C₂²⋊D₇)⋊C₄	C₂²	1	2	yes	complemented
99	(C₂²⋊D₇)⋊C₄	C₂²	1	2	yes	complemented
100	D₇×C₂²⋊C₄	C₂²	1	2	yes	—
101	D₇×C₂²⋊C₄	C₂²	1	2	yes	—
102	D₇×C₂²⋊C₄	C₂²	1	2	yes	—
103	#6442	C₂²	1	2	yes	complemented
104	#6442	C₂²	1	2	yes	complemented
105	#6442	C₂²	1	2	yes	complemented
106	#6442	C₂²	1	1	yes	characteristic, complemented
107	#6441	C₂²	1	2	yes	complemented
108	#6441	C₂²	1	2	yes	complemented
109	#6441	C₂²	1	2	yes	complemented
110	#6440	C₂²	1	2	yes	complemented
111	C₄×D₂₈	C₂²	1	1	yes	characteristic
112	C₄×D₂₈	C₂²	1	1	yes	characteristic
113	C₄×D₂₈	C₂²	1	1	yes	characteristic
114	C₄×D₂₈	C₂²	1	2	yes	complemented
115	#6435	C₂²	1	2	yes	—
116	#6435	C₂²	1	2	yes	complemented
117	#6435	C₂²	1	1	yes	characteristic, complemented
118	C₄²×D₇	C₂²	1	1	yes	characteristic
119	C₄×Dic₁₄	C₂²	1	2	yes	complemented
120	C₄×Dic₁₄	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	#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	C₂×C₇×D₄	C₂³	1	2	yes	—
129	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
130	C₂²×C₄×C₇	C₂³	1	2	yes	—
131	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
132	C₂×C₂²⋊D₇	C₂³	1	2	yes	—
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	2	yes	—
137	C₂²×Dic₇	C₂³	1	2	yes	—
138	#1161	—	2	4	no	—
139	Q₈×D₇	—	4	4	no	—
140	#1159	—	4	4	no	—
141	D₄×D₇	—	2	4	no	—
142	#1157	—	2	4	no	—
143	C₂×D₂₈	C₂³	1	1	yes	characteristic
144	C₂×D₂₈	C₂³	1	2	yes	—
145	C₂×D₂₈	C₂³	1	1	yes	characteristic
146	C₂×C₄×D₇	—	4	4	no	—
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×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	1	yes	characteristic
165	C₇×C₄⋊C₄	C₂³	1	2	yes	—
166	C₇×C₄⋊C₄	C₂³	1	2	yes	—
167	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
168	C₇×C₄⋊C₄	C₂³	1	2	yes	—
169	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
170	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
171	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
172	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
173	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
174	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
175	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
176	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
177	C₄²×C₇	C₂³	1	1	yes	characteristic
178	C₄²×C₇	C₂³	1	1	yes	characteristic
179	C₄²×C₇	C₂³	1	2	yes	—
180	C₂²⋊Dic₇	C₂³	1	2	yes	—
181	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
182	C₂²⋊Dic₇	C₂³	1	2	yes	—
183	C₂²⋊Dic₇	C₂³	1	2	yes	—
184	C₂²⋊Dic₇	C₂³	1	2	yes	—
185	C₂²⋊Dic₇	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	2	yes	—
189	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
190	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
191	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
192	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
193	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
194	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
195	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
196	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
197	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
198	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
199	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
200	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
201	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
202	C₄⋊Dic₇	C₂³	1	2	yes	—
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	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
208	Dic₇⋊C₄	C₂³	1	2	yes	—
209	Dic₇⋊C₄	C₂³	1	2	yes	—
210	Dic₇⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
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	Dic₇⋊C₄	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	1	yes	characteristic
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	2	yes	—
229	#556	—	7	1	no	—
230	#554	—	7	1	no	—
231	#554	—	7	1	no	—
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	D₇	1	1	yes	characteristic, complemented
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	2	yes	—
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	1	yes	characteristic
258	C₂²×D₇	C₂⁴	1	2	yes	—
259	C₂²×D₇	C₂⁴	1	1	yes	characteristic
260	C₇×Q₈	—	2	2	no	—
261	C₇×Q₈	—	4	2	no	—
262	C₇×D₄	—	2	2	no	—
263	C₇×D₄	—	4	2	no	—
264	C₂×C₄×C₇	—	2	2	no	—
265	C₂×C₄×C₇	—	4	2	no	—
266	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
267	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
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	2	yes	—
273	C₂×C₄×C₇	C₂⁴	1	2	yes	—
274	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
275	C₂²⋊D₇	—	2	4	no	—
276	C₂²⋊D₇	—	2	4	no	—
277	C₂²⋊D₇	—	2	2	no	—
278	C₂²⋊D₇	—	2	2	no	—
279	C₂²⋊D₇	—	4	2	no	—
280	C₂×Dic₇	—	2	4	no	—
281	C₂×Dic₇	—	4	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	2	yes	—
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	2	no	—
293	D₂₈	#41	1	4	yes	complemented
294	C₄×D₇	—	2	4	no	—
295	C₄×D₇	—	2	4	no	—
296	C₄×D₇	—	2	2	no	—
297	C₄×D₇	—	2	2	no	—
298	C₄×D₇	—	2	2	no	—
299	C₄×D₇	—	2	2	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	2	no	—
312	C₂×#41	—	7	1	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	1	no	—
322	#126	—	7	2	no	—
323	#126	—	7	2	no	—
324	#126	—	7	2	no	—
325	#126	C₂×D₇	1	2	yes	complemented
326	#125	—	7	1	no	—
327	#125	—	7	2	no	—
328	#125	—	7	2	no	—
329	#125	—	7	2	no	—
330	#124	—	7	1	no	—
331	#124	—	7	1	no	—
332	#124	—	7	2	no	—
333	#124	C₂×D₇	1	1	yes	characteristic
334	#124	C₂×D₇	1	2	yes	complemented
335	#123	—	7	2	no	—
336	#123	—	7	2	no	—
337	#123	—	7	1	no	—
338	#123	—	7	2	no	—
339	#123	—	7	1	no	—
340	#123	—	7	2	no	—
341	#123	—	7	2	no	—
342	#123	—	7	2	no	—
343	#123	—	7	2	no	—
344	#123	C₂×D₇	1	2	yes	complemented
345	C₂²⋊Q₈	—	7	2	no	—
346	C₂²⋊Q₈	—	7	1	no	—
347	C₂²⋊Q₈	—	7	2	no	—
348	C₂²⋊Q₈	—	7	2	no	—
349	C₂²⋊Q₈	—	7	2	no	—
350	C₂²⋊Q₈	—	7	1	no	—
351	C₂²⋊Q₈	—	7	2	no	—
352	C₂²⋊Q₈	—	7	2	no	—
353	C₂²⋊Q₈	—	7	2	no	—
354	C₂²⋊Q₈	—	7	1	no	—
355	C₂²⋊Q₈	—	7	2	no	—
356	C₂²⋊Q₈	—	7	1	no	—
357	C₂²⋊Q₈	—	7	2	no	—
358	C₂²⋊Q₈	—	7	2	no	—
359	C₂²⋊Q₈	—	7	2	no	—
360	C₂²⋊Q₈	C₂×D₇	1	2	yes	complemented
361	C₂²⋊Q₈	C₂×D₇	1	1	yes	characteristic, complemented
362	#121	—	7	2	no	—
363	#121	—	7	1	no	—
364	#121	—	7	1	no	—
365	#121	—	7	2	no	—
366	#121	—	7	2	no	—
367	#121	C₂×D₇	1	1	yes	characteristic
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	1	no	—
374	C₄×Q₈	—	7	2	no	—
375	C₄×Q₈	C₂×D₇	1	1	yes	characteristic, complemented
376	C₄×D₄	—	7	1	no	—
377	C₄×D₄	—	7	2	no	—
378	C₄×D₄	—	7	1	no	—
379	C₄×D₄	—	7	1	no	—
380	C₄×D₄	—	7	1	no	—
381	C₄×D₄	—	7	2	no	—
382	C₄×D₄	—	7	1	no	—
383	C₄×D₄	—	7	2	no	—
384	C₄×D₄	—	7	2	no	—
385	C₄×D₄	—	7	2	no	—
386	C₄×D₄	—	7	2	no	—
387	C₄×D₄	—	7	2	no	—
388	C₄×D₄	—	7	1	no	—
389	C₄×D₄	—	7	1	no	—
390	C₄×D₄	—	7	2	no	—
391	C₄×D₄	—	7	1	no	—
392	C₄×D₄	C₂×D₇	1	1	yes	characteristic
393	#117	—	7	2	no	—
394	#117	—	7	2	no	—
395	#117	—	7	1	no	—
396	#117	—	7	2	no	—
397	#117	—	7	2	no	—
398	#117	C₂×D₇	1	1	yes	characteristic, complemented
399	C₂×C₄⋊C₄	—	7	1	no	—
400	C₂×C₄⋊C₄	—	7	1	no	—
401	C₂×C₄⋊C₄	—	7	2	no	—
402	C₂×C₄⋊C₄	—	7	2	no	—
403	C₂×C₄⋊C₄	—	7	1	no	—
404	C₂×C₄⋊C₄	—	7	2	no	—
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	2	no	—
411	C₂²×C₇	—	2	2	no	—
412	C₂²×C₇	—	2	1	no	—
413	C₂²×C₇	—	2	1	no	—
414	C₂²×C₇	—	2	2	no	—
415	C₂²×C₇	C₂⁵	1	1	yes	characteristic
416	C₂×D₇	—	2	1	no	—
417	C₂×D₇	—	2	2	no	—
418	C₂×D₇	—	2	1	no	—
419	C₂×D₇	—	2	2	no	—
420	C₂×D₇	—	2	1	no	—
421	C₂×D₇	—	2	1	no	—
422	C₂×D₇	—	2	1	no	—
423	C₂×D₇	—	4	8	no	—
424	C₂×D₇	C₂×#41	1	4	yes	—
425	C₂×D₇	2₋¹⁺⁴	1	2	yes	—
426	C₄×C₇	—	2	1	no	—
427	C₄×C₇	—	2	2	no	—
428	C₄×C₇	—	2	2	no	—
429	C₄×C₇	—	2	1	no	—
430	C₄×C₇	—	2	2	no	—
431	C₄×C₇	—	2	1	no	—
432	C₄×C₇	—	2	1	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	1	no	—
439	Dic₇	—	2	2	no	—
440	Dic₇	—	2	2	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	2	no	—
458	C₂×D₄	—	7	1	no	—
459	C₂×D₄	—	7	2	no	—
460	C₂×D₄	—	7	1	no	—
461	C₂×D₄	—	7	1	no	—
462	C₂×D₄	—	7	2	no	—
463	C₂×D₄	—	14	4	no	—
464	C₂×D₄	C₂²×D₇	1	1	yes	characteristic
465	C₂×D₄	C₂²×D₇	1	2	yes	—
466	C₂²×C₄	—	7	2	no	—
467	C₂²×C₄	—	7	2	no	—
468	C₂²×C₄	—	7	1	no	—
469	C₂²×C₄	—	7	1	no	—
470	C₂²×C₄	—	7	1	no	—
471	C₂²×C₄	—	7	2	no	—
472	C₂²×C₄	—	7	2	no	—
473	C₂²×C₄	—	7	1	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	—	7	2	no	—
479	C₂²×C₄	—	7	2	no	—
480	C₂²×C₄	—	28	4	no	—
481	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
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	2	no	—
490	C₄⋊C₄	—	7	1	no	—
491	C₄⋊C₄	—	7	1	no	—
492	C₄⋊C₄	—	7	2	no	—
493	C₄⋊C₄	—	7	2	no	—
494	C₄⋊C₄	—	7	2	no	—
495	C₄⋊C₄	—	7	1	no	—
496	C₄⋊C₄	—	7	2	no	—
497	C₄⋊C₄	—	7	1	no	—
498	C₄⋊C₄	—	7	1	no	—
499	C₄⋊C₄	—	7	2	no	—
500	C₄⋊C₄	—	7	1	no	—
501	C₄⋊C₄	—	7	2	no	—
502	C₄⋊C₄	—	7	2	no	—
503	C₄⋊C₄	—	7	1	no	—
504	C₄⋊C₄	—	7	2	no	—
505	C₄⋊C₄	—	7	1	no	—
506	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
507	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
508	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
509	C₄⋊C₄	C₂²×D₇	1	2	yes	—
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	2	no	—
514	C₂²⋊C₄	—	7	2	no	—
515	C₂²⋊C₄	—	7	2	no	—
516	C₂²⋊C₄	—	7	2	no	—
517	C₂²⋊C₄	—	7	1	no	—
518	C₂²⋊C₄	—	7	1	no	—
519	C₂²⋊C₄	—	7	1	no	—
520	C₂²⋊C₄	—	7	1	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	1	no	—
528	C₂²⋊C₄	—	7	1	no	—
529	C₂²⋊C₄	—	7	1	no	—
530	C₂²⋊C₄	—	7	2	no	—
531	C₂²⋊C₄	—	7	1	no	—
532	C₂²⋊C₄	C₂²×D₇	1	2	yes	—
533	C₂²⋊C₄	C₂²×D₇	1	2	yes	—
534	C₂²⋊C₄	C₂²×D₇	1	2	yes	—
535	C₂²⋊C₄	C₂²×D₇	1	2	yes	—
536	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
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	2	no	—
543	C₄²	—	7	2	no	—
544	C₄²	—	7	2	no	—
545	C₄²	—	7	1	no	—
546	C₄²	C₂²×D₇	1	1	yes	characteristic
547	C₄²	C₂²×D₇	1	2	yes	—
548	C₄²	C₂²×D₇	1	1	yes	characteristic
549	C₂×C₇	—	4	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	2	no	—
555	D₇	—	2	4	no	—
556	D₇	—	4	1	no	—
557	C₂³	—	7	1	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	2	yes	—
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	—	4	2	no	—
573	D₄	—	7	4	no	—
574	D₄	—	14	2	no	—
575	D₄	—	14	4	no	—
576	D₄	—	14	2	no	—
577	D₄	—	14	2	no	—
578	D₄	—	14	4	no	—
579	D₄	—	14	4	no	—
580	D₄	—	28	2	no	—
581	C₂×C₄	—	2	2	no	—
582	C₂×C₄	—	4	2	no	—
583	C₂×C₄	—	7	1	no	—
584	C₂×C₄	—	7	1	no	—
585	C₂×C₄	—	7	1	no	—
586	C₂×C₄	—	7	2	no	—
587	C₂×C₄	—	7	1	no	—
588	C₂×C₄	—	7	2	no	—
589	C₂×C₄	—	7	1	no	—
590	C₂×C₄	—	7	2	no	—
591	C₂×C₄	—	7	1	no	—
592	C₂×C₄	—	14	2	no	—
593	C₂×C₄	—	14	4	no	—
594	C₂×C₄	—	14	2	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	—	28	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	1	yes	characteristic
608	C₂×C₄	C₂³×D₇	1	2	yes	—
609	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
610	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
611	C₂×C₄	C₂³×D₇	1	2	yes	—
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	2	no	—
618	C₂²	—	2	2	no	—
619	C₂²	—	2	1	no	—
620	C₂²	—	2	1	no	—
621	C₂²	—	2	2	no	—
622	C₂²	—	7	4	no	—
623	C₂²	—	7	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	1	no	—
629	C₂²	—	14	1	no	—
630	C₂²	—	14	1	no	—
631	C₂²	—	28	8	no	—
632	C₂²	C₂⁴×D₇	1	1	yes	characteristic
633	C₄	—	2	1	no	—
634	C₄	—	2	2	no	—
635	C₄	—	2	1	no	—
636	C₄	—	2	2	no	—
637	C₄	—	2	2	no	—
638	C₄	—	2	1	no	—
639	C₄	—	2	1	no	—
640	C₄	—	2	1	no	—
641	C₄	—	7	2	no	—
642	C₄	—	14	1	no	—
643	C₄	—	14	1	no	—
644	C₄	—	14	2	no	—
645	C₄	—	14	2	no	—
646	C₄	—	14	2	no	—
647	C₄	—	14	1	no	—
648	C₄	—	14	1	no	—
649	C₄	—	14	1	no	—
650	C₄	D₇×#41	1	2	yes	—
651	C₂	—	4	2	no	—
652	C₂	—	4	1	no	—
653	C₂	—	14	2	no	—
654	C₂	—	14	4	no	—
655	C₂	—	28	1	no	—
656	C₂	C₂×D₇×#41	1	1	yes	characteristic
657	C₂	D₇×H(5,𝔽₂)	1	1	yes	characteristic
658	C₂	D₇×2₋¹⁺⁴	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₇
commutator, socle, cosocle	C₂²×C₇	C₂⁵
Fitting	C₇×#542	C₂
hypercenter	#542	D₇
hypocenter	C₇	#3520
LCS	G ▷ C₂²×C₇ ▷ C₇
UCS	C₁ ◁ C₂² ◁ #542

Complements

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

N	H ≅ G/N	type
1. C₇×#542	C₂	semidirect
2. #90421	C₂	semidirect
3. #90418	C₂	semidirect
4. #90399	C₂	semidirect
5. #90396	C₂	semidirect
6. #90370	C₂	semidirect
7. #90368	C₂	semidirect
8. #90367	C₂	semidirect
9. #90362	C₂	semidirect
10. #90351	C₂	semidirect
11. #90347	C₂	semidirect
12. #90329	C₂	semidirect
13. #90326	C₂	semidirect
14. #90322	C₂	semidirect
15. D₇×C₂²⋊Q₈	C₂	semidirect
16. #90303	C₂	semidirect
17. #90302	C₂	semidirect
18. #90269	C₂	semidirect
19. #90265	C₂	semidirect
20. #90252	C₂	semidirect
21. C₄×D₄×D₇	C₂	semidirect
22. #90219	C₂	semidirect
23. #90214	C₂	semidirect
25. C₂×Q₈×D₇	C₂²	semidirect
26. C₂×#1159	C₂²	semidirect
30. C₇×C₄⋊Q₈	C₂²	semidirect
31. C₇×#126	C₂²	semidirect
33. C₇×#124	C₂²	semidirect
34. C₇×#123	C₂²	semidirect
35. C₇×C₂²⋊Q₈	C₂²	semidirect
36. C₇×C₂²⋊Q₈	C₂²	semidirect
38. C₄×C₇×Q₈	C₂²	semidirect
40. C₇×#117	C₂²	semidirect
43. #6509	C₂²	semidirect
44. #6509	C₂²	semidirect
45. Q₈×Dic₇	C₂²	semidirect
46. #6507	C₂²	semidirect
51. #6498	C₂²	semidirect
53. #6492	C₂²	semidirect
56. C₄×C₂²⋊D₇	C₂²	semidirect
57. C₂×C₄⋊Dic₇	C₂²	semidirect
58. #6487	C₂²	semidirect
59. #6461	C₂²	semidirect
62. #6460	C₂²	semidirect
65. #6459	C₂²	semidirect
66. #6459	C₂²	semidirect
68. #6457	C₂²	semidirect
72. #6456	C₂²	semidirect
73. #6455	C₂²	semidirect
75. D₇×C₄⋊C₄	C₂²	semidirect
76. D₇×C₄⋊C₄	C₂²	semidirect
77. D₇×C₄⋊C₄	C₂²	semidirect
78. D₇×C₄⋊C₄	C₂²	semidirect
79. #6453	C₂²	semidirect
80. #6452	C₂²	semidirect
81. #6452	C₂²	semidirect
82. #6452	C₂²	semidirect
83. #6451	C₂²	semidirect
84. #6451	C₂²	semidirect
85. #6448	C₂²	semidirect
86. #6448	C₂²	semidirect
89. #6447	C₂²	semidirect
93. #6446	C₂²	semidirect
94. #6446	C₂²	semidirect
98. (C₂²⋊D₇)⋊C₄	C₂²	semidirect
99. (C₂²⋊D₇)⋊C₄	C₂²	semidirect
103. #6442	C₂²	semidirect
104. #6442	C₂²	semidirect
105. #6442	C₂²	semidirect
106. #6442	C₂²	semidirect
107. #6441	C₂²	semidirect
108. #6441	C₂²	semidirect
109. #6441	C₂²	semidirect
110. #6440	C₂²	semidirect
114. C₄×D₂₈	C₂²	semidirect
116. #6435	C₂²	semidirect
117. #6435	C₂²	semidirect
119. C₄×Dic₁₄	C₂²	semidirect
120. C₄×Dic₁₄	C₂²	semidirect
121. C₄×Dic₁₄	C₂²	semidirect
122. C₄×Dic₁₄	C₂²	semidirect
242. #542	D₇	semidirect
293. D₂₈	#41	semidirect
319. C₄⋊Q₈	C₂×D₇	semidirect
325. #126	C₂×D₇	semidirect
334. #124	C₂×D₇	semidirect
344. #123	C₂×D₇	semidirect
360. C₂²⋊Q₈	C₂×D₇	semidirect
361. C₂²⋊Q₈	C₂×D₇	semidirect
375. C₄×Q₈	C₂×D₇	semidirect
398. #117	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×#542	2
#90421	2
#90418	2
#90399	2
#90396	2
#90370	2
#90368	2
#90367	2
#90362	2
#90351	2
#90347	2
#90329	2
#90326	2
#90322	2
D₇×C₂²⋊Q₈	2
#90303	2
#90302	2
#90269	2
#90265	2
#90252	2
C₄×D₄×D₇	2
#90219	2
#90214	2
#3520	7