Subgroups — #11743024

Order 896.

1160 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#121	C₂	1	1	yes	maximal, characteristic, complemented
2	#90497	C₂	1	1	yes	maximal, characteristic, complemented
3	#90496	C₂	1	2	yes	maximal, complemented
4	#90495	C₂	1	2	yes	maximal, complemented
5	D₄×C₂²⋊D₇	C₂	1	1	yes	maximal, characteristic, complemented
6	#90482	C₂	1	1	yes	maximal, characteristic, complemented
7	#90482	C₂	1	1	yes	maximal, characteristic, complemented
8	#90312	C₂	1	2	yes	maximal, complemented
9	#90311	C₂	1	2	yes	maximal, complemented
10	#90310	C₂	1	1	yes	maximal, characteristic, complemented
11	#90307	C₂	1	1	yes	maximal, characteristic, complemented
12	#90306	C₂	1	2	yes	maximal, complemented
13	#90305	C₂	1	1	yes	maximal, characteristic, complemented
14	#90304	C₂	1	2	yes	maximal, complemented
15	#90303	C₂	1	1	yes	maximal, characteristic, complemented
16	#90299	C₂	1	1	yes	maximal, characteristic, complemented
17	#90298	C₂	1	1	yes	maximal, characteristic, complemented
18	#90294	C₂	1	1	yes	maximal, characteristic, complemented
19	#90290	C₂	1	1	yes	maximal, characteristic, complemented
20	#90204	C₂	1	1	yes	maximal, characteristic, complemented
21	#90198	C₂	1	1	yes	maximal, characteristic, complemented
22	#90186	C₂	1	2	yes	maximal, complemented
23	#90181	C₂	1	2	yes	maximal, complemented
24	C₂²×C₇×D₄	C₂²	1	1	yes	characteristic
25	C₂²×C₇×D₄	C₂²	1	2	yes	complemented
26	C₂³×C₄×C₇	C₂²	1	1	yes	characteristic, complemented
27	C₂²×C₂²⋊D₇	C₂²	1	2	yes	—
28	C₂×#1159	C₂²	1	1	yes	characteristic, complemented
29	C₂×D₄×D₇	C₂²	1	1	yes	characteristic, complemented
30	C₂×#1157	C₂²	1	2	yes	complemented
31	C₂×#1157	C₂²	1	1	yes	characteristic, complemented
32	C₂×#1157	C₂²	1	1	yes	characteristic, complemented
33	C₇×#121	C₂²	1	1	yes	characteristic
34	C₇×#121	C₂²	1	1	yes	characteristic
35	C₇×#121	C₂²	1	1	yes	characteristic, complemented
36	C₇×#121	C₂²	1	1	yes	characteristic, complemented
37	C₇×#121	C₂²	1	2	yes	complemented
38	C₇×#121	C₂²	1	2	yes	complemented
39	C₂×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
40	C₂×C₇×C₂²⋊C₄	C₂²	1	2	yes	complemented
41	#6516	C₂²	1	2	yes	—
42	#6516	C₂²	1	1	yes	characteristic
43	#6516	C₂²	1	2	yes	complemented
44	#6516	C₂²	1	2	yes	complemented
45	#6516	C₂²	1	1	yes	characteristic, complemented
46	C₂×C₂²⋊Dic₇	C₂²	1	2	yes	complemented
47	#6503	C₂²	1	1	yes	characteristic, complemented
48	#6503	C₂²	1	2	yes	complemented
49	#6503	C₂²	1	2	yes	complemented
50	#6502	C₂²	1	2	yes	complemented
51	#6502	C₂²	1	2	yes	complemented
52	#6502	C₂²	1	2	yes	complemented
53	#6502	C₂²	1	2	yes	complemented
54	#6502	C₂²	1	2	yes	complemented
55	#6502	C₂²	1	2	yes	complemented
56	#6501	C₂²	1	1	yes	characteristic, complemented
57	#6501	C₂²	1	2	yes	complemented
58	#6501	C₂²	1	2	yes	complemented
59	#6501	C₂²	1	2	yes	complemented
60	#6501	C₂²	1	2	yes	complemented
61	#6501	C₂²	1	1	yes	characteristic, complemented
62	#6500	C₂²	1	2	yes	complemented
63	#6500	C₂²	1	2	yes	complemented
64	#6500	C₂²	1	2	yes	complemented
65	#6499	C₂²	1	2	yes	complemented
66	#6499	C₂²	1	2	yes	complemented
67	#6499	C₂²	1	1	yes	characteristic, complemented
68	#6498	C₂²	1	2	yes	complemented
69	#6498	C₂²	1	2	yes	complemented
70	#6498	C₂²	1	2	yes	complemented
71	D₄×Dic₇	C₂²	1	1	yes	characteristic, complemented
72	D₄×Dic₇	C₂²	1	1	yes	characteristic, complemented
73	#6493	C₂²	1	1	yes	characteristic
74	#6493	C₂²	1	1	yes	characteristic
75	#6493	C₂²	1	1	yes	characteristic, complemented
76	#6493	C₂²	1	1	yes	characteristic, complemented
77	#6492	C₂²	1	2	yes	—
78	#6492	C₂²	1	2	yes	complemented
79	#6492	C₂²	1	1	yes	characteristic, complemented
80	#6492	C₂²	1	1	yes	characteristic, complemented
81	#6492	C₂²	1	2	yes	complemented
82	C₄×C₂²⋊D₇	C₂²	1	1	yes	characteristic
83	C₄×C₂²⋊D₇	C₂²	1	2	yes	complemented
84	C₄×C₂²⋊D₇	C₂²	1	1	yes	characteristic, complemented
85	C₄×C₂²⋊D₇	C₂²	1	1	yes	characteristic, complemented
86	C₄×C₂²⋊D₇	C₂²	1	1	yes	characteristic, complemented
87	C₄×C₂²⋊D₇	C₂²	1	2	yes	complemented
88	#6489	C₂²	1	2	yes	complemented
89	#6489	C₂²	1	1	yes	characteristic, complemented
90	#6489	C₂²	1	1	yes	characteristic, complemented
91	#6487	C₂²	1	1	yes	characteristic, complemented
92	#6487	C₂²	1	1	yes	characteristic, complemented
93	#6487	C₂²	1	1	yes	characteristic, complemented
94	#6487	C₂²	1	1	yes	characteristic, complemented
95	#6461	C₂²	1	2	yes	complemented
96	#6460	C₂²	1	1	yes	characteristic, complemented
97	#6459	C₂²	1	2	yes	complemented
98	#6458	C₂²	1	1	yes	characteristic, complemented
99	#6457	C₂²	1	2	yes	complemented
100	#6456	C₂²	1	1	yes	characteristic, complemented
101	#6455	C₂²	1	1	yes	characteristic, complemented
102	D₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
103	#6453	C₂²	1	1	yes	characteristic, complemented
104	#6452	C₂²	1	2	yes	complemented
105	#6451	C₂²	1	1	yes	characteristic, complemented
106	#6450	C₂²	1	1	yes	characteristic, complemented
107	#6449	C₂²	1	2	yes	complemented
108	#6448	C₂²	1	2	yes	complemented
109	#6448	C₂²	1	2	yes	complemented
110	#6447	C₂²	1	2	yes	complemented
111	#6447	C₂²	1	2	yes	complemented
112	#6446	C₂²	1	2	yes	complemented
113	#6446	C₂²	1	2	yes	complemented
114	#6445	C₂²	1	2	yes	complemented
115	(C₂²⋊D₇)⋊C₄	C₂²	1	2	yes	complemented
116	(C₂²⋊D₇)⋊C₄	C₂²	1	2	yes	complemented
117	D₇×C₂²⋊C₄	C₂²	1	2	yes	complemented
118	#6442	C₂²	1	2	yes	complemented
119	#6442	C₂²	1	2	yes	complemented
120	#6441	C₂²	1	2	yes	complemented
121	#6441	C₂²	1	2	yes	complemented
122	#6440	C₂²	1	2	yes	complemented
123	#3542	—	7	1	no	maximal, Sylow
124	C₂⁴×C₇	C₂³	1	2	yes	—
125	C₂⁴×C₇	C₂³	1	1	yes	characteristic
126	C₂³×D₇	C₂³	1	2	yes	—
127	C₂×C₇×D₄	—	4	2	no	—
128	C₂×C₇×D₄	—	4	4	no	—
129	C₂×C₇×D₄	C₂³	1	1	yes	characteristic
130	C₂×C₇×D₄	C₂³	1	1	yes	characteristic
131	C₂×C₇×D₄	C₂³	1	2	yes	—
132	C₂×C₇×D₄	C₂³	1	2	yes	—
133	C₂×C₇×D₄	C₂³	1	2	yes	—
134	C₂×C₇×D₄	C₂³	1	2	yes	—
135	C₂×C₇×D₄	C₂³	1	2	yes	—
136	C₂²×C₄×C₇	—	4	2	no	—
137	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
138	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
139	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
140	C₂²×C₄×C₇	C₂³	1	2	yes	—
141	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
142	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
143	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
144	C₂×C₂²⋊D₇	—	4	4	no	—
145	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
146	C₂×C₂²⋊D₇	C₂³	1	2	yes	—
147	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
148	C₂×C₂²⋊D₇	C₂³	1	2	yes	—
149	C₂×C₂²⋊D₇	C₂³	1	2	yes	—
150	C₂×C₂²⋊D₇	C₂³	1	2	yes	—
151	C₂×C₂²⋊D₇	C₂³	1	2	yes	—
152	C₂×C₂²⋊D₇	C₂³	1	2	yes	—
153	C₂×C₂²⋊D₇	C₂³	1	2	yes	—
154	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
155	C₂×C₂²⋊D₇	C₂³	1	2	yes	—
156	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
157	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
158	C₂×C₂²⋊D₇	C₂³	1	2	yes	—
159	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
160	C₂²×Dic₇	C₂³	1	2	yes	—
161	C₂²×Dic₇	C₂³	1	2	yes	—
162	C₂²×Dic₇	C₂³	1	2	yes	—
163	#1159	—	4	2	no	—
164	D₄×D₇	—	4	2	no	—
165	#1157	—	4	2	no	—
166	#1157	—	4	2	no	—
167	#1157	—	4	4	no	—
168	C₂×D₂₈	C₂³	1	1	yes	characteristic
169	C₂×D₂₈	C₂³	1	1	yes	characteristic
170	C₂×D₂₈	C₂³	1	2	yes	—
171	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
172	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
173	C₂×C₄×D₇	C₂³	1	2	yes	—
174	C₂×C₄×D₇	C₂³	1	2	yes	—
175	C₂×C₄×D₇	C₂³	1	2	yes	—
176	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
177	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
178	C₂×Dic₁₄	C₂³	1	2	yes	—
179	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
180	C₇×C₄⋊C₄	C₂³	1	2	yes	—
181	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
182	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
183	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
184	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
185	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
186	C₂²⋊Dic₇	C₂³	1	2	yes	—
187	C₂²⋊Dic₇	C₂³	1	2	yes	—
188	C₂²⋊Dic₇	C₂³	1	2	yes	—
189	C₂²⋊Dic₇	C₂³	1	2	yes	—
190	C₂²⋊Dic₇	C₂³	1	2	yes	—
191	C₂²⋊Dic₇	C₂³	1	2	yes	—
192	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
193	C₂²⋊Dic₇	C₂³	1	2	yes	—
194	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
195	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
196	C₂²⋊Dic₇	C₂³	1	2	yes	—
197	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
198	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
199	C₂²⋊Dic₇	C₂³	1	2	yes	—
200	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
201	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
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	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
206	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
207	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
208	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
209	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
210	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
211	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
212	C₄⋊Dic₇	C₂³	1	2	yes	—
213	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
214	C₄⋊Dic₇	C₂³	1	2	yes	—
215	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
216	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
217	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
218	Dic₇⋊C₄	C₂³	1	2	yes	—
219	Dic₇⋊C₄	C₂³	1	2	yes	—
220	Dic₇⋊C₄	C₂³	1	2	yes	—
221	Dic₇⋊C₄	C₂³	1	2	yes	—
222	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
223	Dic₇⋊C₄	C₂³	1	2	yes	—
224	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
225	Dic₇⋊C₄	C₂³	1	2	yes	—
226	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
227	C₄×Dic₇	C₂³	1	2	yes	—
228	C₄×Dic₇	C₂³	1	2	yes	—
229	C₄×Dic₇	C₂³	1	2	yes	—
230	C₄×Dic₇	C₂³	1	1	yes	characteristic
231	C₄×Dic₇	C₂³	1	1	yes	characteristic
232	#562	—	7	2	no	—
233	#560	—	7	2	no	—
234	#555	—	7	1	no	—
235	#553	—	7	1	no	—
236	#552	—	7	1	no	—
237	#551	—	7	2	no	—
238	#550	—	7	1	no	—
239	#547	—	7	1	no	—
240	#546	—	7	1	no	—
241	#546	—	7	1	no	—
242	#546	—	7	2	no	—
243	D₄²	—	7	1	no	—
244	#542	—	7	1	no	—
245	#540	—	7	2	no	—
246	#540	—	7	1	no	—
247	#538	—	7	2	no	—
248	#537	—	7	1	no	—
249	#535	—	7	2	no	—
250	#535	—	7	1	no	—
251	#534	—	7	2	no	—
252	#525	—	7	1	no	—
253	#525	—	7	1	no	—
254	C₂×#121	D₇	1	1	yes	characteristic, complemented
255	C₂³×C₇	—	2	2	no	—
256	C₂³×C₇	—	2	4	no	—
257	C₂³×C₇	—	4	1	no	—
258	C₂³×C₇	—	4	1	no	—
259	C₂³×C₇	—	4	2	no	—
260	C₂³×C₇	—	4	2	no	—
261	C₂³×C₇	C₂⁴	1	2	yes	—
262	C₂³×C₇	C₂⁴	1	1	yes	characteristic
263	C₂³×C₇	C₂⁴	1	1	yes	characteristic
264	C₂³×C₇	C₂⁴	1	2	yes	—
265	C₂³×C₇	C₂⁴	1	1	yes	characteristic
266	C₂²×D₇	—	4	2	no	—
267	C₂²×D₇	—	4	2	no	—
268	C₂²×D₇	—	4	2	no	—
269	C₂²×D₇	C₂⁴	1	1	yes	characteristic
270	C₂²×D₇	C₂⁴	1	2	yes	—
271	C₂²×D₇	C₂⁴	1	1	yes	characteristic
272	C₇×D₄	—	2	2	no	—
273	C₇×D₄	—	2	2	no	—
274	C₇×D₄	—	4	2	no	—
275	C₇×D₄	—	4	2	no	—
276	C₇×D₄	—	4	2	no	—
277	C₇×D₄	—	4	2	no	—
278	C₇×D₄	—	4	2	no	—
279	C₂×C₄×C₇	—	2	4	no	—
280	C₂×C₄×C₇	—	2	2	no	—
281	C₂×C₄×C₇	—	2	2	no	—
282	C₂×C₄×C₇	—	2	2	no	—
283	C₂×C₄×C₇	—	4	1	no	—
284	C₂×C₄×C₇	—	4	1	no	—
285	C₂×C₄×C₇	—	4	1	no	—
286	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
287	C₂×C₄×C₇	C₂⁴	1	2	yes	—
288	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
289	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
290	C₂×C₄×C₇	C₂⁴	1	2	yes	—
291	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
292	C₂²⋊D₇	—	2	2	no	—
293	C₂²⋊D₇	—	2	4	no	—
294	C₂²⋊D₇	—	2	2	no	—
295	C₂²⋊D₇	—	4	2	no	—
296	C₂²⋊D₇	—	4	1	no	—
297	C₂²⋊D₇	—	4	1	no	—
298	C₂²⋊D₇	—	4	2	no	—
299	C₂²⋊D₇	—	4	2	no	—
300	C₂²⋊D₇	—	4	2	no	—
301	C₂²⋊D₇	—	4	2	no	—
302	C₂²⋊D₇	—	4	1	no	—
303	C₂²⋊D₇	—	4	2	no	—
304	C₂²⋊D₇	—	4	2	no	—
305	C₂²⋊D₇	—	4	1	no	—
306	C₂²⋊D₇	—	4	2	no	—
307	C₂×Dic₇	—	4	2	no	—
308	C₂×Dic₇	—	4	2	no	—
309	C₂×Dic₇	—	4	2	no	—
310	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
311	C₂×Dic₇	C₂⁴	1	2	yes	—
312	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
313	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
314	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
315	C₂×Dic₇	C₂⁴	1	2	yes	—
316	C₂×Dic₇	C₂⁴	1	2	yes	—
317	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
318	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
319	D₂₈	—	2	2	no	—
320	D₂₈	—	4	1	no	—
321	D₂₈	—	4	2	no	—
322	C₄×D₇	—	2	2	no	—
323	C₄×D₇	—	2	2	no	—
324	C₄×D₇	—	4	2	no	—
325	C₄×D₇	—	4	2	no	—
326	C₄×D₇	—	4	2	no	—
327	Dic₁₄	—	2	2	no	—
328	Dic₁₄	—	4	2	no	—
329	Dic₁₄	—	4	1	no	—
330	C₂×#41	—	7	1	no	—
331	C₂×#41	—	7	1	no	—
332	C₂×#41	—	7	1	no	—
333	C₂×#41	—	7	2	no	—
334	C₂²×D₄	—	7	2	no	—
335	C₂²×D₄	—	7	1	no	—
336	C₂²×D₄	C₂×D₇	1	1	yes	characteristic
337	C₂²×D₄	C₂×D₇	1	2	yes	complemented
338	C₂³×C₄	C₂×D₇	1	1	yes	characteristic, complemented
339	C₄⋊Q₈	—	7	1	no	—
340	#127	—	7	2	no	—
341	#127	—	7	2	no	—
342	#127	—	7	1	no	—
343	#126	—	7	2	no	—
344	#126	—	7	2	no	—
345	#126	—	7	2	no	—
346	#125	—	7	1	no	—
347	#125	—	7	2	no	—
348	#124	—	7	2	no	—
349	#124	—	7	2	no	—
350	#124	—	7	1	no	—
351	#124	—	7	2	no	—
352	#124	—	7	2	no	—
353	#123	—	7	2	no	—
354	#123	—	7	2	no	—
355	#123	—	7	2	no	—
356	#123	—	7	1	no	—
357	#123	—	7	1	no	—
358	#123	—	7	2	no	—
359	#123	—	7	2	no	—
360	#123	—	7	2	no	—
361	#123	—	7	2	no	—
362	#123	—	7	2	no	—
363	#123	—	7	2	no	—
364	#123	—	7	2	no	—
365	C₂²⋊Q₈	—	7	1	no	—
366	C₂²⋊Q₈	—	7	1	no	—
367	C₂²⋊Q₈	—	7	1	no	—
368	C₂²⋊Q₈	—	7	1	no	—
369	C₂²⋊Q₈	—	7	1	no	—
370	C₂²⋊Q₈	—	7	2	no	—
371	C₂²⋊Q₈	—	7	2	no	—
372	C₂²⋊Q₈	—	7	2	no	—
373	#121	—	7	2	no	—
374	#121	—	7	2	no	—
375	#121	—	7	2	no	—
376	#121	—	7	2	no	—
377	#121	—	7	2	no	—
378	#121	—	7	2	no	—
379	#121	—	7	1	no	—
380	#121	—	7	2	no	—
381	#121	—	7	2	no	—
382	#121	—	7	1	no	—
383	#121	—	7	2	no	—
384	#121	—	7	2	no	—
385	#121	—	7	1	no	—
386	#121	—	7	1	no	—
387	#121	—	7	1	no	—
388	#121	—	7	1	no	—
389	#121	—	7	1	no	—
390	#121	—	7	2	no	—
391	#121	—	7	2	no	—
392	#121	C₂×D₇	1	1	yes	characteristic
393	#121	C₂×D₇	1	1	yes	characteristic
394	#121	C₂×D₇	1	1	yes	characteristic, complemented
395	#121	C₂×D₇	1	2	yes	complemented
396	#121	C₂×D₇	1	1	yes	characteristic, complemented
397	#121	C₂×D₇	1	2	yes	complemented
398	#120	—	7	1	no	—
399	#120	—	7	2	no	—
400	#120	—	7	1	no	—
401	#120	—	7	2	no	—
402	#120	—	7	2	no	—
403	#120	—	7	2	no	—
404	#120	—	7	2	no	—
405	#120	—	7	2	no	—
406	#120	—	7	2	no	—
407	C₄×Q₈	—	7	1	no	—
408	C₄×D₄	—	7	1	no	—
409	C₄×D₄	—	7	1	no	—
410	C₄×D₄	—	7	2	no	—
411	C₄×D₄	—	7	1	no	—
412	C₄×D₄	—	7	1	no	—
413	C₄×D₄	—	7	2	no	—
414	C₄×D₄	—	7	1	no	—
415	C₄×D₄	—	7	1	no	—
416	C₄×D₄	—	7	1	no	—
417	C₄×D₄	—	7	2	no	—
418	C₄×D₄	—	7	2	no	—
419	#117	—	7	1	no	—
420	#117	—	7	1	no	—
421	#117	—	7	2	no	—
422	#117	—	7	1	no	—
423	#117	—	7	2	no	—
424	C₂×C₄⋊C₄	—	7	1	no	—
425	C₂×C₄⋊C₄	C₂×D₇	1	1	yes	characteristic, complemented
426	C₂×C₂²⋊C₄	—	7	2	no	—
427	C₂×C₂²⋊C₄	—	7	2	no	—
428	C₂×C₂²⋊C₄	C₂×D₇	1	2	yes	complemented
429	C₂²×C₇	—	2	1	no	—
430	C₂²×C₇	—	2	1	no	—
431	C₂²×C₇	—	2	2	no	—
432	C₂²×C₇	—	2	2	no	—
433	C₂²×C₇	—	2	1	no	—
434	C₂²×C₇	—	2	1	no	—
435	C₂²×C₇	—	2	2	no	—
436	C₂²×C₇	—	2	2	no	—
437	C₂²×C₇	—	2	1	no	—
438	C₂²×C₇	—	2	1	no	—
439	C₂²×C₇	—	2	2	no	—
440	C₂²×C₇	—	2	1	no	—
441	C₂²×C₇	—	2	1	no	—
442	C₂²×C₇	—	2	2	no	—
443	C₂²×C₇	—	4	4	no	—
444	C₂²×C₇	—	8	4	no	—
445	C₂²×C₇	H(5,𝔽₂)	1	2	yes	—
446	C₂²×C₇	C₂⁵	1	1	yes	characteristic
447	C₂×D₇	—	2	1	no	—
448	C₂×D₇	—	2	1	no	—
449	C₂×D₇	—	2	1	no	—
450	C₂×D₇	—	2	2	no	—
451	C₂×D₇	—	2	2	no	—
452	C₂×D₇	—	2	1	no	—
453	C₂×D₇	—	2	1	no	—
454	C₂×D₇	—	2	2	no	—
455	C₂×D₇	—	2	1	no	—
456	C₂×D₇	—	8	4	no	—
457	C₄×C₇	—	2	1	no	—
458	C₄×C₇	—	2	2	no	—
459	C₄×C₇	—	2	1	no	—
460	C₄×C₇	—	2	2	no	—
461	C₄×C₇	—	2	1	no	—
462	C₄×C₇	H(5,𝔽₂)	1	2	yes	—
463	Dic₇	—	2	2	no	—
464	Dic₇	—	2	1	no	—
465	Dic₇	—	2	1	no	—
466	Dic₇	—	2	1	no	—
467	Dic₇	—	2	2	no	—
468	Dic₇	—	2	1	no	—
469	Dic₇	—	2	1	no	—
470	Dic₇	—	2	2	no	—
471	Dic₇	—	2	1	no	—
472	C₂⁴	—	7	2	no	—
473	C₂⁴	C₂²×D₇	1	2	yes	—
474	C₂⁴	C₂²×D₇	1	1	yes	characteristic
475	#41	—	28	2	no	—
476	#41	—	28	4	no	—
477	#41	—	28	2	no	—
478	#41	—	28	2	no	—
479	C₂×Q₈	—	7	1	no	—
480	C₂×Q₈	—	7	1	no	—
481	C₂×Q₈	—	7	2	no	—
482	C₂×D₄	—	4	2	no	—
483	C₂×D₄	—	4	4	no	—
484	C₂×D₄	—	7	1	no	—
485	C₂×D₄	—	7	2	no	—
486	C₂×D₄	—	7	1	no	—
487	C₂×D₄	—	7	1	no	—
488	C₂×D₄	—	7	2	no	—
489	C₂×D₄	—	7	2	no	—
490	C₂×D₄	—	7	2	no	—
491	C₂×D₄	—	7	1	no	—
492	C₂×D₄	—	7	1	no	—
493	C₂×D₄	—	7	2	no	—
494	C₂×D₄	—	7	2	no	—
495	C₂×D₄	—	7	2	no	—
496	C₂×D₄	—	7	2	no	—
497	C₂×D₄	—	7	1	no	—
498	C₂×D₄	—	7	2	no	—
499	C₂×D₄	—	7	1	no	—
500	C₂×D₄	—	7	1	no	—
501	C₂×D₄	—	7	2	no	—
502	C₂×D₄	—	28	2	no	—
503	C₂×D₄	—	28	4	no	—
504	C₂×D₄	C₂²×D₇	1	1	yes	characteristic
505	C₂×D₄	C₂²×D₇	1	1	yes	characteristic
506	C₂×D₄	C₂²×D₇	1	2	yes	—
507	C₂×D₄	C₂²×D₇	1	2	yes	—
508	C₂×D₄	C₂²×D₇	1	2	yes	—
509	C₂×D₄	C₂²×D₇	1	2	yes	—
510	C₂×D₄	C₂²×D₇	1	2	yes	—
511	C₂²×C₄	—	4	2	no	—
512	C₂²×C₄	—	7	2	no	—
513	C₂²×C₄	—	7	2	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	C₂²×D₇	1	2	yes	—
521	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
522	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
523	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
524	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
525	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
526	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
527	C₄⋊C₄	—	7	2	no	—
528	C₄⋊C₄	—	7	1	no	—
529	C₄⋊C₄	—	7	2	no	—
530	C₄⋊C₄	—	7	1	no	—
531	C₄⋊C₄	—	7	1	no	—
532	C₄⋊C₄	—	7	2	no	—
533	C₄⋊C₄	—	7	2	no	—
534	C₄⋊C₄	—	7	2	no	—
535	C₄⋊C₄	—	7	1	no	—
536	C₄⋊C₄	—	7	2	no	—
537	C₄⋊C₄	—	7	1	no	—
538	C₄⋊C₄	—	7	1	no	—
539	C₄⋊C₄	—	7	2	no	—
540	C₄⋊C₄	—	7	2	no	—
541	C₄⋊C₄	—	7	1	no	—
542	C₄⋊C₄	—	7	1	no	—
543	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
544	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
545	C₄⋊C₄	C₂²×D₇	1	2	yes	—
546	C₂²⋊C₄	—	7	1	no	—
547	C₂²⋊C₄	—	7	2	no	—
548	C₂²⋊C₄	—	7	2	no	—
549	C₂²⋊C₄	—	7	2	no	—
550	C₂²⋊C₄	—	7	2	no	—
551	C₂²⋊C₄	—	7	1	no	—
552	C₂²⋊C₄	—	7	2	no	—
553	C₂²⋊C₄	—	7	1	no	—
554	C₂²⋊C₄	—	7	2	no	—
555	C₂²⋊C₄	—	7	1	no	—
556	C₂²⋊C₄	—	7	2	no	—
557	C₂²⋊C₄	—	7	1	no	—
558	C₂²⋊C₄	—	7	2	no	—
559	C₂²⋊C₄	—	7	1	no	—
560	C₂²⋊C₄	—	7	2	no	—
561	C₂²⋊C₄	—	7	1	no	—
562	C₂²⋊C₄	—	7	2	no	—
563	C₂²⋊C₄	—	7	2	no	—
564	C₂²⋊C₄	—	7	1	no	—
565	C₂²⋊C₄	—	7	1	no	—
566	C₂²⋊C₄	—	7	2	no	—
567	C₂²⋊C₄	—	7	2	no	—
568	C₂²⋊C₄	—	7	2	no	—
569	C₂²⋊C₄	—	7	2	no	—
570	C₂²⋊C₄	—	7	1	no	—
571	C₂²⋊C₄	C₂²×D₇	1	2	yes	—
572	C₂²⋊C₄	C₂²×D₇	1	2	yes	—
573	C₂²⋊C₄	C₂²×D₇	1	2	yes	—
574	C₂²⋊C₄	C₂²×D₇	1	2	yes	—
575	C₄²	—	7	2	no	—
576	C₄²	—	7	2	no	—
577	C₄²	—	7	1	no	—
578	C₄²	—	7	1	no	—
579	C₄²	—	7	2	no	—
580	C₂×C₇	—	2	2	no	—
581	C₂×C₇	—	4	2	no	—
582	C₂×C₇	—	4	1	no	—
583	C₂×C₇	—	4	1	no	—
584	C₂×C₇	—	4	2	no	—
585	C₂×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
586	C₂×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
587	C₂×C₇	#585	1	1	yes	characteristic
588	D₇	—	4	1	no	—
589	D₇	—	4	2	no	—
590	D₇	—	4	1	no	—
591	C₂³	—	2	2	no	—
592	C₂³	—	2	4	no	—
593	C₂³	—	4	1	no	—
594	C₂³	—	4	1	no	—
595	C₂³	—	4	2	no	—
596	C₂³	—	4	2	no	—
597	C₂³	—	7	1	no	—
598	C₂³	—	7	2	no	—
599	C₂³	—	7	1	no	—
600	C₂³	—	28	2	no	—
601	C₂³	—	28	2	no	—
602	C₂³	—	28	2	no	—
603	C₂³	C₂³×D₇	1	2	yes	—
604	C₂³	C₂³×D₇	1	1	yes	characteristic
605	C₂³	C₂³×D₇	1	1	yes	characteristic
606	C₂³	C₂³×D₇	1	2	yes	—
607	C₂³	C₂³×D₇	1	1	yes	characteristic
608	Q₈	—	14	2	no	—
609	Q₈	—	28	1	no	—
610	Q₈	—	28	2	no	—
611	D₄	—	2	2	no	—
612	D₄	—	2	2	no	—
613	D₄	—	4	2	no	—
614	D₄	—	4	2	no	—
615	D₄	—	4	2	no	—
616	D₄	—	4	2	no	—
617	D₄	—	4	2	no	—
618	D₄	—	14	2	no	—
619	D₄	—	14	4	no	—
620	D₄	—	14	2	no	—
621	D₄	—	14	2	no	—
622	D₄	—	28	1	no	—
623	D₄	—	28	2	no	—
624	D₄	—	28	1	no	—
625	D₄	—	28	2	no	—
626	D₄	—	28	2	no	—
627	D₄	—	28	2	no	—
628	D₄	—	28	1	no	—
629	D₄	—	28	2	no	—
630	D₄	—	28	2	no	—
631	D₄	—	28	2	no	—
632	D₄	—	28	1	no	—
633	D₄	—	28	1	no	—
634	D₄	—	28	2	no	—
635	D₄	—	28	2	no	—
636	C₂×C₄	—	2	4	no	—
637	C₂×C₄	—	2	2	no	—
638	C₂×C₄	—	2	2	no	—
639	C₂×C₄	—	2	2	no	—
640	C₂×C₄	—	4	1	no	—
641	C₂×C₄	—	4	1	no	—
642	C₂×C₄	—	4	1	no	—
643	C₂×C₄	—	7	1	no	—
644	C₂×C₄	—	7	2	no	—
645	C₂×C₄	—	7	1	no	—
646	C₂×C₄	—	7	1	no	—
647	C₂×C₄	—	7	1	no	—
648	C₂×C₄	—	7	2	no	—
649	C₂×C₄	—	7	2	no	—
650	C₂×C₄	—	7	1	no	—
651	C₂×C₄	—	7	1	no	—
652	C₂×C₄	—	14	2	no	—
653	C₂×C₄	—	14	2	no	—
654	C₂×C₄	—	28	2	no	—
655	C₂×C₄	—	28	2	no	—
656	C₂×C₄	—	28	2	no	—
657	C₂×C₄	—	28	2	no	—
658	C₂×C₄	—	28	2	no	—
659	C₂×C₄	—	28	2	no	—
660	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
661	C₂×C₄	C₂³×D₇	1	2	yes	—
662	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
663	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
664	C₂×C₄	C₂³×D₇	1	2	yes	—
665	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
666	C₇	#3542	1	1	yes	characteristic, complemented, Sylow
667	C₂²	—	2	1	no	—
668	C₂²	—	2	1	no	—
669	C₂²	—	2	1	no	—
670	C₂²	—	2	1	no	—
671	C₂²	—	2	2	no	—
672	C₂²	—	2	2	no	—
673	C₂²	—	2	2	no	—
674	C₂²	—	2	1	no	—
675	C₂²	—	2	1	no	—
676	C₂²	—	2	2	no	—
677	C₂²	—	2	2	no	—
678	C₂²	—	2	1	no	—
679	C₂²	—	2	1	no	—
680	C₂²	—	2	2	no	—
681	C₂²	—	4	4	no	—
682	C₂²	—	8	4	no	—
683	C₂²	—	14	1	no	—
684	C₂²	—	14	1	no	—
685	C₂²	—	14	1	no	—
686	C₂²	—	14	2	no	—
687	C₂²	—	14	2	no	—
688	C₂²	—	14	1	no	—
689	C₂²	—	14	1	no	—
690	C₂²	—	14	2	no	—
691	C₂²	—	14	1	no	—
692	C₂²	—	56	4	no	—
693	C₂²	#6548	1	2	yes	—
694	C₂²	C₂⁴×D₇	1	1	yes	characteristic
695	C₄	—	2	1	no	—
696	C₄	—	2	1	no	—
697	C₄	—	2	1	no	—
698	C₄	—	2	2	no	—
699	C₄	—	2	2	no	—
700	C₄	—	14	1	no	—
701	C₄	—	14	1	no	—
702	C₄	—	14	1	no	—
703	C₄	—	14	2	no	—
704	C₄	—	14	1	no	—
705	C₄	—	14	2	no	—
706	C₄	—	14	1	no	—
707	C₄	—	14	2	no	—
708	C₄	—	14	1	no	—
709	C₄	#6548	1	2	yes	—
710	C₂	—	2	2	no	—
711	C₂	—	4	1	no	—
712	C₂	—	4	1	no	—
713	C₂	—	4	2	no	—
714	C₂	—	4	2	no	—
715	C₂	—	28	1	no	—
716	C₂	—	28	2	no	—
717	C₂	—	28	1	no	—
718	C₂	C₂×#6548	1	1	yes	characteristic
719	C₂	C₂×#6548	1	1	yes	characteristic
720	C₂	#90616	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₇
commutator, socle, cosocle	C₂²×C₇	C₂⁵
Fitting	C₂×C₇×#121	C₂
hypercenter	C₂×#121	D₇
hypocenter	C₇	#3542
LCS	G ▷ C₂²×C₇ ▷ C₇
UCS	C₁ ◁ C₂² ◁ C₂×#121

Complements

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

N	H ≅ G/N	type
1. C₂×C₇×#121	C₂	semidirect
2. #90497	C₂	semidirect
3. #90496	C₂	semidirect
4. #90495	C₂	semidirect
5. D₄×C₂²⋊D₇	C₂	semidirect
6. #90482	C₂	semidirect
7. #90482	C₂	semidirect
8. #90312	C₂	semidirect
9. #90311	C₂	semidirect
10. #90310	C₂	semidirect
11. #90307	C₂	semidirect
12. #90306	C₂	semidirect
13. #90305	C₂	semidirect
14. #90304	C₂	semidirect
15. #90303	C₂	semidirect
16. #90299	C₂	semidirect
17. #90298	C₂	semidirect
18. #90294	C₂	semidirect
19. #90290	C₂	semidirect
20. #90204	C₂	semidirect
21. #90198	C₂	semidirect
22. #90186	C₂	semidirect
23. #90181	C₂	semidirect
25. C₂²×C₇×D₄	C₂²	semidirect
26. C₂³×C₄×C₇	C₂²	semidirect
28. C₂×#1159	C₂²	semidirect
29. C₂×D₄×D₇	C₂²	semidirect
30. C₂×#1157	C₂²	semidirect
31. C₂×#1157	C₂²	semidirect
32. C₂×#1157	C₂²	semidirect
35. C₇×#121	C₂²	semidirect
36. C₇×#121	C₂²	semidirect
37. C₇×#121	C₂²	semidirect
38. C₇×#121	C₂²	semidirect
39. C₂×C₇×C₄⋊C₄	C₂²	semidirect
40. C₂×C₇×C₂²⋊C₄	C₂²	semidirect
43. #6516	C₂²	semidirect
44. #6516	C₂²	semidirect
45. #6516	C₂²	semidirect
46. C₂×C₂²⋊Dic₇	C₂²	semidirect
47. #6503	C₂²	semidirect
48. #6503	C₂²	semidirect
49. #6503	C₂²	semidirect
50. #6502	C₂²	semidirect
51. #6502	C₂²	semidirect
52. #6502	C₂²	semidirect
53. #6502	C₂²	semidirect
54. #6502	C₂²	semidirect
55. #6502	C₂²	semidirect
56. #6501	C₂²	semidirect
57. #6501	C₂²	semidirect
58. #6501	C₂²	semidirect
59. #6501	C₂²	semidirect
60. #6501	C₂²	semidirect
61. #6501	C₂²	semidirect
62. #6500	C₂²	semidirect
63. #6500	C₂²	semidirect
64. #6500	C₂²	semidirect
65. #6499	C₂²	semidirect
66. #6499	C₂²	semidirect
67. #6499	C₂²	semidirect
68. #6498	C₂²	semidirect
69. #6498	C₂²	semidirect
70. #6498	C₂²	semidirect
71. D₄×Dic₇	C₂²	semidirect
72. D₄×Dic₇	C₂²	semidirect
75. #6493	C₂²	semidirect
76. #6493	C₂²	semidirect
78. #6492	C₂²	semidirect
79. #6492	C₂²	semidirect
80. #6492	C₂²	semidirect
81. #6492	C₂²	semidirect
83. C₄×C₂²⋊D₇	C₂²	semidirect
84. C₄×C₂²⋊D₇	C₂²	semidirect
85. C₄×C₂²⋊D₇	C₂²	semidirect
86. C₄×C₂²⋊D₇	C₂²	semidirect
87. C₄×C₂²⋊D₇	C₂²	semidirect
88. #6489	C₂²	semidirect
89. #6489	C₂²	semidirect
90. #6489	C₂²	semidirect
91. #6487	C₂²	semidirect
92. #6487	C₂²	semidirect
93. #6487	C₂²	semidirect
94. #6487	C₂²	semidirect
95. #6461	C₂²	semidirect
96. #6460	C₂²	semidirect
97. #6459	C₂²	semidirect
98. #6458	C₂²	semidirect
99. #6457	C₂²	semidirect
100. #6456	C₂²	semidirect
101. #6455	C₂²	semidirect
102. D₇×C₄⋊C₄	C₂²	semidirect
103. #6453	C₂²	semidirect
104. #6452	C₂²	semidirect
105. #6451	C₂²	semidirect
106. #6450	C₂²	semidirect
107. #6449	C₂²	semidirect
108. #6448	C₂²	semidirect
109. #6448	C₂²	semidirect
110. #6447	C₂²	semidirect
111. #6447	C₂²	semidirect
112. #6446	C₂²	semidirect
113. #6446	C₂²	semidirect
114. #6445	C₂²	semidirect
115. (C₂²⋊D₇)⋊C₄	C₂²	semidirect
116. (C₂²⋊D₇)⋊C₄	C₂²	semidirect
117. D₇×C₂²⋊C₄	C₂²	semidirect
118. #6442	C₂²	semidirect
119. #6442	C₂²	semidirect
120. #6441	C₂²	semidirect
121. #6441	C₂²	semidirect
122. #6440	C₂²	semidirect
254. C₂×#121	D₇	semidirect
337. C₂²×D₄	C₂×D₇	semidirect
338. C₂³×C₄	C₂×D₇	semidirect
394. #121	C₂×D₇	semidirect
395. #121	C₂×D₇	semidirect
396. #121	C₂×D₇	semidirect
397. #121	C₂×D₇	semidirect
425. C₂×C₄⋊C₄	C₂×D₇	semidirect
428. C₂×C₂²⋊C₄	C₂×D₇	semidirect
666. C₇	#3542	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₇×#121	2
#90497	2
#90496	2
#90495	2
D₄×C₂²⋊D₇	2
#90482	2
#90312	2
#90311	2
#90310	2
#90307	2
#90306	2
#90305	2
#90304	2
#90303	2
#90299	2
#90298	2
#90294	2
#90290	2
#90204	2
#90198	2
#90186	2
#90181	2
#3542	7