Subgroups — #11744030

Order 896.

1142 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#555	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	#90370	C₂	1	2	yes	maximal, complemented
5	#90369	C₂	1	2	yes	maximal, complemented
6	#90368	C₂	1	2	yes	maximal, complemented
7	D₇×#124	C₂	1	2	yes	maximal, complemented
8	#90304	C₂	1	2	yes	maximal, complemented
9	#90303	C₂	1	1	yes	maximal, characteristic, complemented
10	#90301	C₂	1	2	yes	maximal, complemented
11	#90300	C₂	1	1	yes	maximal, characteristic, complemented
12	#90294	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	#90241	C₂	1	1	yes	maximal, characteristic, complemented
16	#90236	C₂	1	1	yes	maximal, characteristic, complemented
17	#90229	C₂	1	1	yes	maximal, characteristic, complemented
18	#90224	C₂	1	1	yes	maximal, characteristic, complemented
19	#90223	C₂	1	1	yes	maximal, characteristic, complemented
20	#90219	C₂	1	2	yes	maximal, complemented
21	#90218	C₂	1	2	yes	maximal, complemented
22	#90213	C₂	1	1	yes	maximal, characteristic, complemented
23	#90212	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×Q₈×D₇	C₂²	1	2	yes	complemented
25	C₂×#1159	C₂²	1	2	yes	complemented
26	C₂×D₄×D₇	C₂²	1	1	yes	characteristic
27	C₂×D₄×D₇	C₂²	1	2	yes	—
28	C₂×#1157	C₂²	1	1	yes	characteristic
29	C₂²×D₂₈	C₂²	1	1	yes	characteristic
30	C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
31	C₇×#124	C₂²	1	2	yes	complemented
32	C₇×#124	C₂²	1	2	yes	complemented
33	C₇×#121	C₂²	1	1	yes	characteristic
34	C₇×#121	C₂²	1	1	yes	characteristic, complemented
35	C₇×#121	C₂²	1	2	yes	complemented
36	C₄×C₇×D₄	C₂²	1	1	yes	characteristic, complemented
37	C₄×C₇×D₄	C₂²	1	1	yes	characteristic, complemented
38	C₇×#117	C₂²	1	1	yes	characteristic, complemented
39	C₇×#117	C₂²	1	1	yes	characteristic, complemented
40	C₇×#117	C₂²	1	2	yes	complemented
41	#6510	C₂²	1	2	yes	complemented
42	#6509	C₂²	1	2	yes	complemented
43	#6509	C₂²	1	2	yes	complemented
44	#6503	C₂²	1	1	yes	characteristic
45	#6502	C₂²	1	1	yes	characteristic
46	#6502	C₂²	1	2	yes	complemented
47	#6501	C₂²	1	2	yes	complemented
48	#6500	C₂²	1	2	yes	—
49	#6500	C₂²	1	2	yes	complemented
50	#6500	C₂²	1	2	yes	complemented
51	#6499	C₂²	1	1	yes	characteristic, complemented
52	#6499	C₂²	1	2	yes	complemented
53	#6498	C₂²	1	2	yes	complemented
54	#6498	C₂²	1	1	yes	characteristic, complemented
55	D₄×Dic₇	C₂²	1	1	yes	characteristic, complemented
56	#6493	C₂²	1	1	yes	characteristic, complemented
57	#6492	C₂²	1	2	yes	complemented
58	C₄×C₂²⋊D₇	C₂²	1	1	yes	characteristic
59	C₄×C₂²⋊D₇	C₂²	1	2	yes	complemented
60	C₄×C₂²⋊D₇	C₂²	1	2	yes	complemented
61	C₄×C₂²⋊D₇	C₂²	1	1	yes	characteristic, complemented
62	C₂×(C₂×D₇)⋊C₄	C₂²	1	2	yes	complemented
63	#6489	C₂²	1	1	yes	characteristic, complemented
64	#6487	C₂²	1	1	yes	characteristic, complemented
65	C₂×C₄×Dic₇	C₂²	1	1	yes	characteristic, complemented
66	#6461	C₂²	1	2	yes	complemented
67	#6461	C₂²	1	1	yes	characteristic, complemented
68	#6460	C₂²	1	1	yes	characteristic, complemented
69	#6459	C₂²	1	2	yes	complemented
70	#6459	C₂²	1	2	yes	complemented
71	#6458	C₂²	1	1	yes	characteristic
72	#6457	C₂²	1	2	yes	complemented
73	#6457	C₂²	1	2	yes	complemented
74	#6456	C₂²	1	1	yes	characteristic
75	#6456	C₂²	1	1	yes	characteristic
76	#6456	C₂²	1	1	yes	characteristic
77	#6456	C₂²	1	1	yes	characteristic, complemented
78	#6456	C₂²	1	1	yes	characteristic, complemented
79	#6455	C₂²	1	1	yes	characteristic, complemented
80	#6452	C₂²	1	1	yes	characteristic, complemented
81	#6451	C₂²	1	1	yes	characteristic, complemented
82	#6451	C₂²	1	1	yes	characteristic, complemented
83	#6450	C₂²	1	1	yes	characteristic, complemented
84	#6450	C₂²	1	1	yes	characteristic, complemented
85	#6449	C₂²	1	1	yes	characteristic, complemented
86	#6448	C₂²	1	2	yes	—
87	#6448	C₂²	1	1	yes	characteristic
88	#6448	C₂²	1	2	yes	complemented
89	#6448	C₂²	1	2	yes	complemented
90	#6448	C₂²	1	2	yes	complemented
91	#6447	C₂²	1	2	yes	—
92	#6447	C₂²	1	2	yes	complemented
93	#6447	C₂²	1	2	yes	complemented
94	#6446	C₂²	1	2	yes	complemented
95	#6446	C₂²	1	2	yes	complemented
96	#6445	C₂²	1	2	yes	—
97	(C₂²⋊D₇)⋊C₄	C₂²	1	2	yes	complemented
98	(C₂²⋊D₇)⋊C₄	C₂²	1	2	yes	complemented
99	(C₂²⋊D₇)⋊C₄	C₂²	1	2	yes	complemented
100	(C₂²⋊D₇)⋊C₄	C₂²	1	2	yes	complemented
101	D₇×C₂²⋊C₄	C₂²	1	2	yes	complemented
102	D₇×C₂²⋊C₄	C₂²	1	2	yes	complemented
103	D₇×C₂²⋊C₄	C₂²	1	2	yes	complemented
104	D₇×C₂²⋊C₄	C₂²	1	2	yes	complemented
105	D₇×C₂²⋊C₄	C₂²	1	2	yes	complemented
106	#6442	C₂²	1	2	yes	complemented
107	#6442	C₂²	1	1	yes	characteristic, complemented
108	#6442	C₂²	1	2	yes	complemented
109	#6441	C₂²	1	1	yes	characteristic, complemented
110	#6441	C₂²	1	2	yes	complemented
111	#6439	C₂²	1	2	yes	complemented
112	#6438	C₂²	1	1	yes	characteristic, complemented
113	#6438	C₂²	1	2	yes	complemented
114	C₄×D₂₈	C₂²	1	1	yes	characteristic
115	C₄×D₂₈	C₂²	1	2	yes	complemented
116	C₄×D₂₈	C₂²	1	2	yes	complemented
117	#6435	C₂²	1	2	yes	complemented
118	#6435	C₂²	1	2	yes	complemented
119	#6435	C₂²	1	1	yes	characteristic, complemented
120	C₄²×D₇	C₂²	1	2	yes	complemented
121	C₄×Dic₁₄	C₂²	1	2	yes	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	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	C₂×C₇×D₄	C₂³	1	1	yes	characteristic
130	C₂×C₇×D₄	C₂³	1	2	yes	—
131	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
132	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
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	Q₈×D₇	—	4	4	no	—
145	#1159	—	4	4	no	—
146	D₄×D₇	—	2	4	no	—
147	D₄×D₇	—	4	4	no	—
148	#1157	—	2	4	no	—
149	C₂×D₂₈	—	2	4	no	—
150	C₂×D₂₈	C₂³	1	2	yes	—
151	C₂×D₂₈	C₂³	1	1	yes	characteristic
152	C₂×D₂₈	C₂³	1	2	yes	—
153	C₂×D₂₈	C₂³	1	1	yes	characteristic
154	C₂×C₄×D₇	C₂³	1	2	yes	—
155	C₂×C₄×D₇	C₂³	1	2	yes	—
156	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
157	C₂×C₄×D₇	C₂³	1	2	yes	—
158	C₂×C₄×D₇	C₂³	1	2	yes	—
159	C₂×C₄×D₇	C₂³	1	2	yes	—
160	C₂×C₄×D₇	C₂³	1	2	yes	—
161	C₂×C₄×D₇	C₂³	1	2	yes	—
162	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
163	C₂×Dic₁₄	C₂³	1	2	yes	—
164	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
165	C₂×Dic₁₄	C₂³	1	2	yes	—
166	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
167	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
168	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
169	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
170	C₇×C₄⋊C₄	C₂³	1	2	yes	—
171	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
172	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
173	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
174	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
175	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
176	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
177	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
178	C₄²×C₇	C₂³	1	1	yes	characteristic
179	C₄²×C₇	C₂³	1	2	yes	—
180	C₄²×C₇	C₂³	1	2	yes	—
181	C₂²⋊Dic₇	C₂³	1	2	yes	—
182	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
183	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
184	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
185	C₂²⋊Dic₇	C₂³	1	2	yes	—
186	C₂²⋊Dic₇	C₂³	1	2	yes	—
187	C₂²⋊Dic₇	C₂³	1	2	yes	—
188	C₂²⋊Dic₇	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	1	yes	characteristic
192	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
193	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
194	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
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	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	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
206	C₄⋊Dic₇	C₂³	1	2	yes	—
207	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
208	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
209	C₄⋊Dic₇	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	1	yes	characteristic
213	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
214	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
215	Dic₇⋊C₄	C₂³	1	2	yes	—
216	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
217	Dic₇⋊C₄	C₂³	1	2	yes	—
218	Dic₇⋊C₄	C₂³	1	2	yes	—
219	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
220	Dic₇⋊C₄	C₂³	1	2	yes	—
221	C₄×Dic₇	C₂³	1	2	yes	—
222	C₄×Dic₇	C₂³	1	2	yes	—
223	C₄×Dic₇	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
229	#559	—	7	1	no	—
230	#556	—	7	1	no	—
231	#555	—	7	1	no	—
232	#555	D₇	1	1	yes	characteristic, complemented
233	#551	—	7	2	no	—
234	#551	—	7	2	no	—
235	D₄×Q₈	—	7	1	no	—
236	#548	—	7	2	no	—
237	#546	—	7	2	no	—
238	#546	—	7	1	no	—
239	#546	—	7	1	no	—
240	D₄²	—	7	1	no	—
241	#542	—	7	1	no	—
242	#542	—	7	1	no	—
243	#538	—	7	2	no	—
244	#538	—	7	2	no	—
245	#532	—	7	1	no	—
246	#529	—	7	1	no	—
247	#529	—	7	2	no	—
248	C₂×#124	—	7	2	no	—
249	#518	—	7	1	no	—
250	#518	—	7	1	no	—
251	C₄×#41	—	7	1	no	—
252	C₂³×C₇	C₂⁴	1	1	yes	characteristic
253	C₂³×C₇	C₂⁴	1	2	yes	—
254	C₂³×C₇	C₂⁴	1	1	yes	characteristic
255	C₂²×D₇	—	2	4	no	—
256	C₂²×D₇	—	2	4	no	—
257	C₂²×D₇	—	4	2	no	—
258	C₂²×D₇	—	4	2	no	—
259	C₂²×D₇	—	4	2	no	—
260	C₂²×D₇	—	4	2	no	—
261	C₂²×D₇	C₂⁴	1	1	yes	characteristic
262	C₂²×D₇	C₂⁴	1	2	yes	—
263	C₂²×D₇	C₂⁴	1	2	yes	—
264	C₇×Q₈	—	4	2	no	—
265	C₇×D₄	—	2	2	no	—
266	C₇×D₄	—	4	2	no	—
267	C₇×D₄	—	4	2	no	—
268	C₇×D₄	—	4	1	no	—
269	C₂×C₄×C₇	—	2	2	no	—
270	C₂×C₄×C₇	—	2	2	no	—
271	C₂×C₄×C₇	—	4	2	no	—
272	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
273	C₂×C₄×C₇	C₂⁴	1	2	yes	—
274	C₂×C₄×C₇	C₂⁴	1	2	yes	—
275	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
276	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
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	C₂²⋊D₇	—	2	4	no	—
281	C₂²⋊D₇	—	2	4	no	—
282	C₂²⋊D₇	—	2	2	no	—
283	C₂²⋊D₇	—	2	4	no	—
284	C₂²⋊D₇	—	4	2	no	—
285	C₂²⋊D₇	—	4	1	no	—
286	C₂²⋊D₇	—	4	2	no	—
287	C₂×Dic₇	—	2	2	no	—
288	C₂×Dic₇	—	4	2	no	—
289	C₂×Dic₇	—	4	1	no	—
290	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
291	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
292	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
293	C₂×Dic₇	C₂⁴	1	2	yes	—
294	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
295	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
296	C₂×Dic₇	C₂⁴	1	2	yes	—
297	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
298	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
299	D₂₈	—	2	4	no	—
300	D₂₈	—	2	2	no	—
301	D₂₈	—	4	2	no	—
302	D₂₈	#41	1	4	yes	complemented
303	C₄×D₇	—	2	4	no	—
304	C₄×D₇	—	2	2	no	—
305	C₄×D₇	—	2	4	no	—
306	C₄×D₇	—	4	2	no	—
307	C₄×D₇	—	4	2	no	—
308	C₄×D₇	—	4	2	no	—
309	C₄×D₇	—	4	2	no	—
310	C₄×D₇	—	4	2	no	—
311	Dic₁₄	—	2	2	no	—
312	Dic₁₄	—	2	4	no	—
313	Dic₁₄	—	2	2	no	—
314	Dic₁₄	—	4	2	no	—
315	C₂×#41	—	7	2	no	—
316	C₂×#41	—	7	1	no	—
317	C₂²×Q₈	—	7	2	no	—
318	C₂²×D₄	—	7	1	no	—
319	C₂²×D₄	—	7	2	no	—
320	C₂²×D₄	—	7	1	no	—
321	C₄⋊Q₈	—	7	1	no	—
322	C₄⋊Q₈	—	7	1	no	—
323	C₄⋊Q₈	C₂×D₇	1	1	yes	characteristic, complemented
324	#127	—	7	1	no	—
325	#126	—	7	2	no	—
326	#126	—	7	1	no	—
327	#126	—	7	2	no	—
328	#126	—	7	1	no	—
329	#126	—	7	2	no	—
330	#126	—	7	2	no	—
331	#125	—	7	1	no	—
332	#124	—	7	2	no	—
333	#124	—	7	2	no	—
334	#124	—	7	1	no	—
335	#124	—	7	1	no	—
336	#124	—	7	2	no	—
337	#124	—	7	2	no	—
338	#124	—	7	2	no	—
339	#124	—	7	2	no	—
340	#124	—	7	2	no	—
341	#124	—	7	1	no	—
342	#124	C₂×D₇	1	2	yes	complemented
343	#124	C₂×D₇	1	2	yes	complemented
344	#123	—	7	1	no	—
345	#123	—	7	2	no	—
346	#123	—	7	2	no	—
347	#123	—	7	2	no	—
348	#123	—	7	2	no	—
349	#123	—	7	1	no	—
350	#123	—	7	2	no	—
351	#123	—	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	2	no	—
357	C₂²⋊Q₈	—	7	1	no	—
358	C₂²⋊Q₈	—	7	1	no	—
359	C₂²⋊Q₈	—	7	2	no	—
360	#121	—	7	1	no	—
361	#121	—	7	2	no	—
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	—	7	2	no	—
368	#121	C₂×D₇	1	1	yes	characteristic
369	#121	C₂×D₇	1	1	yes	characteristic, complemented
370	#121	C₂×D₇	1	2	yes	complemented
371	#120	—	7	2	no	—
372	#120	—	7	2	no	—
373	#120	—	7	2	no	—
374	#120	—	7	2	no	—
375	C₄×Q₈	—	7	1	no	—
376	C₄×Q₈	—	7	1	no	—
377	C₄×Q₈	—	7	2	no	—
378	C₄×Q₈	—	7	1	no	—
379	C₄×D₄	—	7	1	no	—
380	C₄×D₄	—	7	2	no	—
381	C₄×D₄	—	7	1	no	—
382	C₄×D₄	—	7	1	no	—
383	C₄×D₄	—	7	2	no	—
384	C₄×D₄	—	7	1	no	—
385	C₄×D₄	—	7	1	no	—
386	C₄×D₄	—	7	1	no	—
387	C₄×D₄	—	7	1	no	—
388	C₄×D₄	—	7	1	no	—
389	C₄×D₄	—	7	2	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	2	no	—
396	C₄×D₄	C₂×D₇	1	1	yes	characteristic, complemented
397	C₄×D₄	C₂×D₇	1	1	yes	characteristic, complemented
398	#117	—	7	1	no	—
399	#117	—	7	1	no	—
400	#117	—	7	2	no	—
401	#117	—	7	1	no	—
402	#117	—	7	2	no	—
403	#117	C₂×D₇	1	1	yes	characteristic, complemented
404	#117	C₂×D₇	1	1	yes	characteristic, complemented
405	#117	C₂×D₇	1	2	yes	complemented
406	C₂×C₂²⋊C₄	—	7	2	no	—
407	C₂×C₂²⋊C₄	—	7	2	no	—
408	C₂×C₂²⋊C₄	—	7	2	no	—
409	C₂×C₂²⋊C₄	—	7	2	no	—
410	C₂×C₂²⋊C₄	—	7	2	no	—
411	C₂×C₂²⋊C₄	—	7	2	no	—
412	C₂×C₄²	—	7	1	no	—
413	C₂×C₄²	—	7	2	no	—
414	C₂²×C₇	—	2	1	no	—
415	C₂²×C₇	—	2	2	no	—
416	C₂²×C₇	—	2	1	no	—
417	C₂²×C₇	—	2	1	no	—
418	C₂²×C₇	—	2	2	no	—
419	C₂²×C₇	—	2	1	no	—
420	C₂²×C₇	—	2	1	no	—
421	C₂²×C₇	—	2	2	no	—
422	C₂²×C₇	—	2	1	no	—
423	C₂²×C₇	C₂⁵	1	1	yes	characteristic
424	C₂×D₇	—	2	2	no	—
425	C₂×D₇	—	2	2	no	—
426	C₂×D₇	—	2	1	no	—
427	C₂×D₇	—	2	2	no	—
428	C₂×D₇	—	2	2	no	—
429	C₂×D₇	—	2	1	no	—
430	C₂×D₇	—	2	2	no	—
431	C₂×D₇	—	2	1	no	—
432	C₂×D₇	—	8	4	no	—
433	C₂×D₇	—	8	4	no	—
434	C₂×D₇	C₂×#41	1	4	yes	—
435	C₄×C₇	—	2	1	no	—
436	C₄×C₇	—	2	1	no	—
437	C₄×C₇	—	2	2	no	—
438	C₄×C₇	—	2	1	no	—
439	C₄×C₇	—	2	2	no	—
440	C₄×C₇	—	2	2	no	—
441	C₄×C₇	—	2	1	no	—
442	C₄×C₇	C₂×#41	1	2	yes	—
443	Dic₇	—	2	2	no	—
444	Dic₇	—	2	1	no	—
445	Dic₇	—	2	1	no	—
446	Dic₇	—	2	2	no	—
447	Dic₇	—	2	1	no	—
448	Dic₇	—	2	1	no	—
449	Dic₇	—	2	1	no	—
450	Dic₇	—	2	1	no	—
451	Dic₇	H(5,𝔽₂)	1	2	yes	—
452	C₂⁴	—	7	2	no	—
453	C₂⁴	—	7	2	no	—
454	#41	—	14	4	no	—
455	#41	—	28	4	no	—
456	C₂×Q₈	—	7	1	no	—
457	C₂×Q₈	—	7	1	no	—
458	C₂×Q₈	—	7	2	no	—
459	C₂×Q₈	—	7	2	no	—
460	C₂×Q₈	—	28	4	no	—
461	C₂×Q₈	C₂²×D₇	1	2	yes	—
462	C₂×D₄	—	7	2	no	—
463	C₂×D₄	—	7	2	no	—
464	C₂×D₄	—	7	1	no	—
465	C₂×D₄	—	7	2	no	—
466	C₂×D₄	—	7	1	no	—
467	C₂×D₄	—	7	2	no	—
468	C₂×D₄	—	7	2	no	—
469	C₂×D₄	—	7	1	no	—
470	C₂×D₄	—	7	2	no	—
471	C₂×D₄	—	7	1	no	—
472	C₂×D₄	—	7	2	no	—
473	C₂×D₄	—	14	4	no	—
474	C₂×D₄	—	14	4	no	—
475	C₂×D₄	—	28	4	no	—
476	C₂×D₄	C₂²×D₇	1	1	yes	characteristic
477	C₂×D₄	C₂²×D₇	1	1	yes	characteristic
478	C₂×D₄	C₂²×D₇	1	2	yes	—
479	C₂×D₄	C₂²×D₇	1	2	yes	—
480	C₂²×C₄	—	7	1	no	—
481	C₂²×C₄	—	7	1	no	—
482	C₂²×C₄	—	7	2	no	—
483	C₂²×C₄	—	7	2	no	—
484	C₂²×C₄	—	7	2	no	—
485	C₂²×C₄	—	7	1	no	—
486	C₂²×C₄	—	7	2	no	—
487	C₂²×C₄	—	7	2	no	—
488	C₂²×C₄	—	7	2	no	—
489	C₂²×C₄	—	7	2	no	—
490	C₂²×C₄	—	7	2	no	—
491	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
492	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
493	C₂²×C₄	C₂²×D₇	1	2	yes	—
494	C₄⋊C₄	—	7	1	no	—
495	C₄⋊C₄	—	7	1	no	—
496	C₄⋊C₄	—	7	1	no	—
497	C₄⋊C₄	—	7	2	no	—
498	C₄⋊C₄	—	7	2	no	—
499	C₄⋊C₄	—	7	2	no	—
500	C₄⋊C₄	—	7	1	no	—
501	C₄⋊C₄	—	7	1	no	—
502	C₄⋊C₄	—	7	2	no	—
503	C₄⋊C₄	—	7	2	no	—
504	C₄⋊C₄	—	7	1	no	—
505	C₄⋊C₄	—	7	1	no	—
506	C₄⋊C₄	—	7	1	no	—
507	C₄⋊C₄	—	7	1	no	—
508	C₄⋊C₄	—	7	2	no	—
509	C₄⋊C₄	—	7	1	no	—
510	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
511	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
512	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
513	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
514	C₄⋊C₄	C₂²×D₇	1	2	yes	—
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	2	no	—
522	C₂²⋊C₄	—	7	1	no	—
523	C₂²⋊C₄	—	7	2	no	—
524	C₂²⋊C₄	—	7	1	no	—
525	C₂²⋊C₄	—	7	2	no	—
526	C₂²⋊C₄	—	7	1	no	—
527	C₂²⋊C₄	—	7	1	no	—
528	C₂²⋊C₄	—	7	2	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	1	no	—
538	C₂²⋊C₄	—	7	2	no	—
539	C₂²⋊C₄	C₂²×D₇	1	2	yes	—
540	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
541	C₂²⋊C₄	C₂²×D₇	1	2	yes	—
542	C₂²⋊C₄	C₂²×D₇	1	2	yes	—
543	C₂²⋊C₄	C₂²×D₇	1	2	yes	—
544	C₂²⋊C₄	C₂²×D₇	1	2	yes	—
545	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
546	C₄²	—	7	1	no	—
547	C₄²	—	7	1	no	—
548	C₄²	—	7	1	no	—
549	C₄²	—	7	2	no	—
550	C₄²	—	7	1	no	—
551	C₄²	—	7	2	no	—
552	C₄²	—	7	2	no	—
553	C₄²	—	7	1	no	—
554	C₄²	C₂²×D₇	1	2	yes	—
555	C₄²	C₂²×D₇	1	1	yes	characteristic
556	C₄²	C₂²×D₇	1	2	yes	—
557	C₂×C₇	—	4	1	no	—
558	C₂×C₇	—	4	2	no	—
559	C₂×C₇	—	4	1	no	—
560	C₂×C₇	C₂²×#41	1	1	yes	characteristic
561	C₂×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
562	C₂×C₇	#585	1	1	yes	characteristic
563	D₇	—	2	4	no	—
564	D₇	—	4	2	no	—
565	D₇	—	4	1	no	—
566	C₂³	—	7	2	no	—
567	C₂³	—	7	1	no	—
568	C₂³	—	7	2	no	—
569	C₂³	—	14	4	no	—
570	C₂³	—	14	4	no	—
571	C₂³	—	28	2	no	—
572	C₂³	—	28	2	no	—
573	C₂³	—	28	2	no	—
574	C₂³	—	28	2	no	—
575	C₂³	C₂³×D₇	1	1	yes	characteristic
576	C₂³	C₂³×D₇	1	2	yes	—
577	C₂³	C₂³×D₇	1	1	yes	characteristic
578	Q₈	—	4	2	no	—
579	Q₈	—	14	2	no	—
580	Q₈	—	14	4	no	—
581	Q₈	—	14	2	no	—
582	Q₈	—	28	2	no	—
583	D₄	—	2	2	no	—
584	D₄	—	4	2	no	—
585	D₄	—	4	1	no	—
586	D₄	—	4	2	no	—
587	D₄	—	7	4	no	—
588	D₄	—	14	4	no	—
589	D₄	—	14	2	no	—
590	D₄	—	14	4	no	—
591	D₄	—	14	4	no	—
592	D₄	—	14	4	no	—
593	D₄	—	14	2	no	—
594	D₄	—	28	2	no	—
595	D₄	—	28	1	no	—
596	D₄	—	28	2	no	—
597	D₄	—	28	2	no	—
598	C₂×C₄	—	2	2	no	—
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	4	2	no	—
601	C₂×C₄	—	7	1	no	—
602	C₂×C₄	—	7	1	no	—
603	C₂×C₄	—	7	2	no	—
604	C₂×C₄	—	7	1	no	—
605	C₂×C₄	—	7	1	no	—
606	C₂×C₄	—	7	1	no	—
607	C₂×C₄	—	7	1	no	—
608	C₂×C₄	—	7	1	no	—
609	C₂×C₄	—	7	2	no	—
610	C₂×C₄	—	14	4	no	—
611	C₂×C₄	—	14	4	no	—
612	C₂×C₄	—	14	2	no	—
613	C₂×C₄	—	14	2	no	—
614	C₂×C₄	—	28	2	no	—
615	C₂×C₄	—	28	2	no	—
616	C₂×C₄	—	28	2	no	—
617	C₂×C₄	—	28	2	no	—
618	C₂×C₄	—	28	2	no	—
619	C₂×C₄	—	28	1	no	—
620	C₂×C₄	—	28	2	no	—
621	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
622	C₂×C₄	C₂³×D₇	1	2	yes	—
623	C₂×C₄	C₂³×D₇	1	2	yes	—
624	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
625	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
626	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
627	C₂×C₄	C₂³×D₇	1	2	yes	—
628	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
629	C₇	#3514	1	1	yes	characteristic, complemented, Sylow
630	C₂²	—	2	1	no	—
631	C₂²	—	2	1	no	—
632	C₂²	—	2	2	no	—
633	C₂²	—	2	2	no	—
634	C₂²	—	2	1	no	—
635	C₂²	—	2	1	no	—
636	C₂²	—	2	1	no	—
637	C₂²	—	2	2	no	—
638	C₂²	—	2	1	no	—
639	C₂²	—	7	4	no	—
640	C₂²	—	14	2	no	—
641	C₂²	—	14	2	no	—
642	C₂²	—	14	1	no	—
643	C₂²	—	14	2	no	—
644	C₂²	—	14	2	no	—
645	C₂²	—	14	1	no	—
646	C₂²	—	14	2	no	—
647	C₂²	—	14	1	no	—
648	C₂²	—	56	4	no	—
649	C₂²	—	56	4	no	—
650	C₂²	C₂⁴×D₇	1	1	yes	characteristic
651	C₄	—	2	1	no	—
652	C₄	—	2	1	no	—
653	C₄	—	2	1	no	—
654	C₄	—	2	2	no	—
655	C₄	—	2	2	no	—
656	C₄	—	2	2	no	—
657	C₄	—	2	1	no	—
658	C₄	—	7	2	no	—
659	C₄	—	14	1	no	—
660	C₄	—	14	2	no	—
661	C₄	—	14	1	no	—
662	C₄	—	14	1	no	—
663	C₄	—	14	1	no	—
664	C₄	—	14	1	no	—
665	C₄	—	14	2	no	—
666	C₄	—	14	1	no	—
667	C₄	D₇×#41	1	2	yes	—
668	C₂	—	4	1	no	—
669	C₂	—	4	2	no	—
670	C₂	—	4	1	no	—
671	C₂	—	14	4	no	—
672	C₂	—	28	1	no	—
673	C₂	—	28	2	no	—
674	C₂	C₂×D₇×#41	1	1	yes	characteristic
675	C₂	#90616	1	1	yes	characteristic
676	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×#555	C₂
hypercenter	#555	D₇
hypocenter	C₇	#3514
LCS	G ▷ C₂²×C₇ ▷ C₇
UCS	C₁ ◁ C₂² ◁ #555

Complements

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

N	H ≅ G/N	type
1. C₇×#555	C₂	semidirect
2. #90424	C₂	semidirect
3. #90418	C₂	semidirect
4. #90370	C₂	semidirect
5. #90369	C₂	semidirect
6. #90368	C₂	semidirect
7. D₇×#124	C₂	semidirect
8. #90304	C₂	semidirect
9. #90303	C₂	semidirect
10. #90301	C₂	semidirect
11. #90300	C₂	semidirect
12. #90294	C₂	semidirect
13. #90287	C₂	semidirect
14. #90250	C₂	semidirect
15. #90241	C₂	semidirect
16. #90236	C₂	semidirect
17. #90229	C₂	semidirect
18. #90224	C₂	semidirect
19. #90223	C₂	semidirect
20. #90219	C₂	semidirect
21. #90218	C₂	semidirect
22. #90213	C₂	semidirect
23. #90212	C₂	semidirect
24. C₂×Q₈×D₇	C₂²	semidirect
25. C₂×#1159	C₂²	semidirect
30. C₇×C₄⋊Q₈	C₂²	semidirect
31. C₇×#124	C₂²	semidirect
32. C₇×#124	C₂²	semidirect
34. C₇×#121	C₂²	semidirect
35. C₇×#121	C₂²	semidirect
36. C₄×C₇×D₄	C₂²	semidirect
37. C₄×C₇×D₄	C₂²	semidirect
38. C₇×#117	C₂²	semidirect
39. C₇×#117	C₂²	semidirect
40. C₇×#117	C₂²	semidirect
41. #6510	C₂²	semidirect
42. #6509	C₂²	semidirect
43. #6509	C₂²	semidirect
46. #6502	C₂²	semidirect
47. #6501	C₂²	semidirect
49. #6500	C₂²	semidirect
50. #6500	C₂²	semidirect
51. #6499	C₂²	semidirect
52. #6499	C₂²	semidirect
53. #6498	C₂²	semidirect
54. #6498	C₂²	semidirect
55. D₄×Dic₇	C₂²	semidirect
56. #6493	C₂²	semidirect
57. #6492	C₂²	semidirect
59. C₄×C₂²⋊D₇	C₂²	semidirect
60. C₄×C₂²⋊D₇	C₂²	semidirect
61. C₄×C₂²⋊D₇	C₂²	semidirect
62. C₂×(C₂×D₇)⋊C₄	C₂²	semidirect
63. #6489	C₂²	semidirect
64. #6487	C₂²	semidirect
65. C₂×C₄×Dic₇	C₂²	semidirect
66. #6461	C₂²	semidirect
67. #6461	C₂²	semidirect
68. #6460	C₂²	semidirect
69. #6459	C₂²	semidirect
70. #6459	C₂²	semidirect
72. #6457	C₂²	semidirect
73. #6457	C₂²	semidirect
77. #6456	C₂²	semidirect
78. #6456	C₂²	semidirect
79. #6455	C₂²	semidirect
80. #6452	C₂²	semidirect
81. #6451	C₂²	semidirect
82. #6451	C₂²	semidirect
83. #6450	C₂²	semidirect
84. #6450	C₂²	semidirect
85. #6449	C₂²	semidirect
88. #6448	C₂²	semidirect
89. #6448	C₂²	semidirect
90. #6448	C₂²	semidirect
92. #6447	C₂²	semidirect
93. #6447	C₂²	semidirect
94. #6446	C₂²	semidirect
95. #6446	C₂²	semidirect
97. (C₂²⋊D₇)⋊C₄	C₂²	semidirect
98. (C₂²⋊D₇)⋊C₄	C₂²	semidirect
99. (C₂²⋊D₇)⋊C₄	C₂²	semidirect
100. (C₂²⋊D₇)⋊C₄	C₂²	semidirect
101. D₇×C₂²⋊C₄	C₂²	semidirect
102. D₇×C₂²⋊C₄	C₂²	semidirect
103. D₇×C₂²⋊C₄	C₂²	semidirect
104. D₇×C₂²⋊C₄	C₂²	semidirect
105. D₇×C₂²⋊C₄	C₂²	semidirect
106. #6442	C₂²	semidirect
107. #6442	C₂²	semidirect
108. #6442	C₂²	semidirect
109. #6441	C₂²	semidirect
110. #6441	C₂²	semidirect
111. #6439	C₂²	semidirect
112. #6438	C₂²	semidirect
113. #6438	C₂²	semidirect
115. C₄×D₂₈	C₂²	semidirect
116. C₄×D₂₈	C₂²	semidirect
117. #6435	C₂²	semidirect
118. #6435	C₂²	semidirect
119. #6435	C₂²	semidirect
120. C₄²×D₇	C₂²	semidirect
121. C₄×Dic₁₄	C₂²	semidirect
122. C₄×Dic₁₄	C₂²	semidirect
232. #555	D₇	semidirect
302. D₂₈	#41	semidirect
323. C₄⋊Q₈	C₂×D₇	semidirect
342. #124	C₂×D₇	semidirect
343. #124	C₂×D₇	semidirect
369. #121	C₂×D₇	semidirect
370. #121	C₂×D₇	semidirect
396. C₄×D₄	C₂×D₇	semidirect
397. C₄×D₄	C₂×D₇	semidirect
403. #117	C₂×D₇	semidirect
404. #117	C₂×D₇	semidirect
405. #117	C₂×D₇	semidirect
629. 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×#555	2
#90424	2
#90418	2
#90370	2
#90369	2
#90368	2
D₇×#124	2
#90304	2
#90303	2
#90301	2
#90300	2
#90294	2
#90287	2
#90250	2
#90241	2
#90236	2
#90229	2
#90224	2
#90223	2
#90219	2
#90218	2
#90213	2
#90212	2
#3514	7