Subgroups — #13325065

Order 1792.

592 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3108	C₂	1	1	yes	maximal, characteristic
2	#11740577	C₂	1	1	yes	maximal, characteristic
3	#11739882	C₂	1	1	yes	maximal, characteristic, complemented
4	#11729506	C₂	1	1	yes	maximal, characteristic
5	C₂×Q₈⋊(C₇⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
6	#11728660	C₂	1	1	yes	maximal, characteristic, complemented
7	#11728657	C₂	1	1	yes	maximal, characteristic, complemented
8	#11728657	C₂	1	1	yes	maximal, characteristic, complemented
9	#11728656	C₂	1	1	yes	maximal, characteristic, complemented
10	#11728654	C₂	1	1	yes	maximal, characteristic, complemented
11	#11728650	C₂	1	1	yes	maximal, characteristic, complemented
12	#11728649	C₂	1	1	yes	maximal, characteristic, complemented
13	SD₁₆⋊(C₇⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
14	#11728506	C₂	1	1	yes	maximal, characteristic, complemented
15	#11728496	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#529	C₂²	1	1	yes	characteristic
17	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
18	C₇×#483	C₄	1	1	yes	characteristic
19	C₇×#480	C₄	1	1	yes	characteristic
20	C₇×#479	C₄	1	1	yes	characteristic
21	C₇×#479	C₄	1	1	yes	characteristic
22	C₇×#464	C₄	1	1	yes	characteristic
23	C₇×#464	C₄	1	1	yes	characteristic
24	C₇×#451	C₄	1	1	yes	characteristic
25	C₇×#448	C₄	1	1	yes	characteristic
26	C₄×C₇×Q₁₆	C₂²	1	1	yes	characteristic
27	C₄×C₇×Q₁₆	C₂²	1	1	yes	characteristic
28	C₄×C₇×SD₁₆	C₂²	1	1	yes	characteristic
29	C₄×C₇×SD₁₆	C₂²	1	1	yes	characteristic
30	C₇×#431	C₂²	1	1	yes	characteristic
31	#89796	—	2	1	no	—
32	#89796	—	2	1	no	—
33	#89796	C₂²	1	1	yes	characteristic
34	#89796	C₂²	1	1	yes	characteristic
35	#89796	C₂²	1	1	yes	characteristic
36	Q₈×C₇⋊C₈	C₂²	1	1	yes	characteristic
37	Q₈×C₇⋊C₈	C₂²	1	1	yes	characteristic
38	Q₈×C₇⋊C₈	C₂²	1	1	yes	characteristic
39	#89784	C₂²	1	1	yes	characteristic
40	#89783	—	2	1	no	—
41	D₄×C₇⋊C₈	—	2	1	no	—
42	D₄×C₇⋊C₈	C₂²	1	1	yes	characteristic
43	#89772	—	2	1	no	—
44	#89771	—	2	1	no	—
45	#89698	—	2	1	no	—
46	#89698	C₂²	1	1	yes	characteristic
47	#89697	—	2	1	no	—
48	#89697	C₂²	1	1	yes	characteristic
49	C₂×C₄⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic
50	C₂×C₄×C₇⋊C₈	C₂²	1	1	yes	characteristic
51	Q₈⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic
52	Q₈⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic
53	Q₈⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic
54	Q₈⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic
55	Q₈⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic
56	Q₈⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic
57	D₄⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic
58	D₄⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic
59	#89253	C₂²	1	1	yes	characteristic
60	#89253	C₂²	1	1	yes	characteristic
61	#89252	C₂²	1	1	yes	characteristic
62	#89252	C₂²	1	1	yes	characteristic
63	#89250	C₂²	1	1	yes	characteristic
64	#89250	C₂²	1	1	yes	characteristic
65	#89249	C₂²	1	1	yes	characteristic
66	#89249	C₂²	1	1	yes	characteristic
67	#18023	—	7	1	no	maximal, Sylow
68	C₂²×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
69	C₂×C₇×Q₁₆	C₂×C₄	1	1	yes	characteristic
70	C₂×C₇×Q₁₆	C₂×C₄	1	1	yes	characteristic
71	C₂×C₇×SD₁₆	C₂×C₄	1	1	yes	characteristic
72	C₂×C₇×SD₁₆	C₂×C₄	1	1	yes	characteristic
73	C₇×#126	—	2	1	no	—
74	C₇×#125	C₂×C₄	1	1	yes	characteristic
75	C₇×#124	C₂×C₄	1	1	yes	characteristic
76	C₇×#123	—	2	1	no	—
77	C₇×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
78	C₇×#121	C₂×C₄	1	1	yes	characteristic
79	C₄×C₇×Q₈	—	2	1	no	—
80	C₄×C₇×Q₈	—	2	1	no	—
81	C₄×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
82	C₄×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
83	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
84	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
85	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
86	C₄×C₇×D₄	—	2	1	no	—
87	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
88	C₇×#117	—	2	1	no	—
89	C₂×C₇×C₄⋊C₄	—	2	1	no	—
90	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
91	C₂×C₄²×C₇	—	2	1	no	—
92	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
93	C₂×#1136	—	2	1	no	—
94	C₂²×C₇⋊C₈	—	2	1	no	—
95	C₂²×C₇⋊C₈	—	2	1	no	—
96	C₂²×C₇⋊C₈	—	2	1	no	—
97	C₇×#107	C₂×C₄	1	1	yes	characteristic
98	C₇×#107	C₂×C₄	1	1	yes	characteristic
99	C₇×#106	C₂×C₄	1	1	yes	characteristic
100	C₇×#106	C₂×C₄	1	1	yes	characteristic
101	C₇×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
102	C₇×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
103	C₇×#103	C₂×C₄	1	1	yes	characteristic
104	C₇×#103	C₂×C₄	1	1	yes	characteristic
105	C₇×#103	C₂×C₄	1	1	yes	characteristic
106	C₇×#103	C₂×C₄	1	1	yes	characteristic
107	C₇×#103	C₂×C₄	1	1	yes	characteristic
108	C₇×#103	C₂×C₄	1	1	yes	characteristic
109	C₇×#102	C₂×C₄	1	1	yes	characteristic
110	C₇×#102	C₂×C₄	1	1	yes	characteristic
111	C₇×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
112	C₇×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
113	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
114	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
115	C₂²⋊(C₇⋊C₈)	—	2	1	no	—
116	C₂²⋊(C₇⋊C₈)	—	2	1	no	—
117	C₂²⋊(C₇⋊C₈)	—	2	1	no	—
118	C₂²⋊(C₇⋊C₈)	D₄	1	1	yes	characteristic
119	C₂²⋊(C₇⋊C₈)	D₄	1	1	yes	characteristic
120	C₄⋊(C₇⋊C₈)	—	2	1	no	—
121	C₄⋊(C₇⋊C₈)	—	2	1	no	—
122	C₄⋊(C₇⋊C₈)	—	2	1	no	—
123	C₄⋊(C₇⋊C₈)	—	2	1	no	—
124	C₄⋊(C₇⋊C₈)	—	2	1	no	—
125	C₄⋊(C₇⋊C₈)	—	2	1	no	—
126	C₄⋊(C₇⋊C₈)	—	2	1	no	—
127	C₄⋊(C₇⋊C₈)	D₄	1	1	yes	characteristic
128	C₄⋊(C₇⋊C₈)	D₄	1	1	yes	characteristic
129	C₄⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
130	C₄⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
131	C₄⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
132	C₄⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
133	#6377	—	2	1	no	—
134	#6377	—	2	1	no	—
135	#6377	—	2	1	no	—
136	#6377	—	2	1	no	—
137	C₄×C₇⋊C₈	—	2	1	no	—
138	C₄×C₇⋊C₈	—	2	1	no	—
139	C₄×C₇⋊C₈	—	2	1	no	—
140	C₄×C₇⋊C₈	—	2	1	no	—
141	C₄×C₇⋊C₈	C₂³	1	1	yes	characteristic
142	C₄×C₇⋊C₈	C₂³	1	1	yes	characteristic
143	C₄×C₇⋊C₈	C₂³	1	1	yes	characteristic
144	C₄×C₇⋊C₈	C₂³	1	1	yes	characteristic
145	#3108	D₇	1	1	yes	characteristic
146	#2994	—	7	1	no	—
147	#2984	—	7	1	no	—
148	#1593	—	7	1	no	—
149	#1592	—	7	1	no	—
150	#1584	—	7	1	no	—
151	#1584	—	7	1	no	—
152	#1583	—	7	1	no	—
153	#1582	—	7	1	no	—
154	#1579	—	7	1	no	—
155	SD₁₆⋊C₈	—	7	1	no	—
156	#1573	—	7	1	no	—
157	#1494	—	7	1	no	—
158	C₂×Q₈⋊C₈	—	7	1	no	—
159	#1452	—	7	1	no	—
160	C₂×C₇×Q₈	—	2	1	no	—
161	C₂×C₇×Q₈	—	2	2	no	—
162	C₂×C₇×Q₈	—	4	1	no	—
163	C₂×C₇×Q₈	C₂²×C₄	1	1	yes	characteristic
164	C₂×C₇×Q₈	C₂²×C₄	1	1	yes	characteristic
165	C₂×C₇×Q₈	C₂²×C₄	1	1	yes	characteristic
166	C₂×C₇×D₄	—	2	1	no	—
167	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
168	C₂²×C₄×C₇	—	2	1	no	—
169	C₂²×C₄×C₇	—	2	1	no	—
170	C₂²×C₄×C₇	—	2	1	no	—
171	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
172	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₇	#41	1	1	yes	characteristic
174	C₇×Q₁₆	—	2	2	no	—
175	C₇×Q₁₆	—	4	1	no	—
176	C₇×SD₁₆	—	2	2	no	—
177	C₇×SD₁₆	—	4	1	no	—
178	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
179	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
180	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
181	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
182	C₇×C₄⋊C₄	—	2	1	no	—
183	C₇×C₄⋊C₄	—	2	1	no	—
184	C₇×C₄⋊C₄	—	2	1	no	—
185	C₇×C₄⋊C₄	—	2	1	no	—
186	C₇×C₄⋊C₄	—	2	1	no	—
187	C₇×C₄⋊C₄	—	2	1	no	—
188	C₇×C₄⋊C₄	—	2	1	no	—
189	C₇×C₄⋊C₄	—	2	1	no	—
190	C₇×C₄⋊C₄	—	2	1	no	—
191	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
192	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
193	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
194	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
195	C₇×C₂²⋊C₄	—	2	1	no	—
196	C₇×C₂²⋊C₄	—	2	1	no	—
197	C₇×C₂²⋊C₄	—	2	1	no	—
198	C₇×C₂²⋊C₄	—	2	1	no	—
199	C₇×C₂²⋊C₄	—	2	1	no	—
200	C₄²×C₇	—	2	1	no	—
201	C₄²×C₇	—	2	1	no	—
202	C₄²×C₇	—	2	1	no	—
203	C₄²×C₇	—	2	1	no	—
204	C₄²×C₇	—	2	1	no	—
205	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
206	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
207	C₄²×C₇	#41	1	1	yes	characteristic
208	C₄²×C₇	C₂⁴	1	1	yes	characteristic
209	#1136	—	8	1	no	—
210	C₂×C₇⋊C₈	—	2	1	no	—
211	C₂×C₇⋊C₈	—	2	1	no	—
212	C₂×C₇⋊C₈	—	2	1	no	—
213	C₂×C₇⋊C₈	—	2	1	no	—
214	C₂×C₇⋊C₈	—	2	1	no	—
215	C₂×C₇⋊C₈	—	2	1	no	—
216	C₂×C₇⋊C₈	—	4	2	no	—
217	C₂×C₇⋊C₈	—	8	1	no	—
218	C₂×C₇⋊C₈	—	8	1	no	—
219	C₂×C₇⋊C₈	C₂×D₄	1	1	yes	characteristic
220	C₂×C₇⋊C₈	C₂×D₄	1	1	yes	characteristic
221	C₂×C₇⋊C₈	C₂×D₄	1	1	yes	characteristic
222	C₂×C₇⋊C₈	C₂×D₄	1	1	yes	characteristic
223	#529	C₂×D₇	1	1	yes	characteristic
224	C₂×C₄×Q₈	C₂×D₇	1	1	yes	characteristic
225	#483	Dic₇	1	1	yes	characteristic
226	#480	Dic₇	1	1	yes	characteristic
227	#479	Dic₇	1	1	yes	characteristic
228	#479	Dic₇	1	1	yes	characteristic
229	#464	Dic₇	1	1	yes	characteristic
230	#464	Dic₇	1	1	yes	characteristic
231	#451	Dic₇	1	1	yes	characteristic
232	#448	Dic₇	1	1	yes	characteristic
233	#446	—	7	1	no	—
234	#446	—	7	1	no	—
235	#446	—	7	1	no	—
236	#446	—	14	1	no	—
237	#446	—	14	1	no	—
238	C₈×Q₈	—	7	1	no	—
239	C₈×Q₈	—	7	1	no	—
240	C₈×Q₈	—	7	1	no	—
241	C₄×Q₁₆	C₂×D₇	1	1	yes	characteristic
242	C₄×Q₁₆	C₂×D₇	1	1	yes	characteristic
243	C₄×SD₁₆	C₂×D₇	1	1	yes	characteristic
244	C₄×SD₁₆	C₂×D₇	1	1	yes	characteristic
245	#436	—	7	1	no	—
246	#435	—	14	1	no	—
247	C₈×D₄	—	7	1	no	—
248	C₈×D₄	—	14	1	no	—
249	#433	—	14	1	no	—
250	#432	—	7	1	no	—
251	#432	—	14	1	no	—
252	#431	—	7	1	no	—
253	#431	—	14	1	no	—
254	#431	C₂×D₇	1	1	yes	characteristic
255	#424	—	14	1	no	—
256	C₂×C₄⋊C₈	—	7	1	no	—
257	C₂×C₄×C₈	—	7	1	no	—
258	#335	—	7	1	no	—
259	#335	—	7	1	no	—
260	#334	—	7	1	no	—
261	#334	—	7	1	no	—
262	Q₈⋊C₈	—	7	1	no	—
263	Q₈⋊C₈	—	7	1	no	—
264	Q₈⋊C₈	—	7	1	no	—
265	Q₈⋊C₈	—	7	1	no	—
266	Q₈⋊C₈	—	7	1	no	—
267	Q₈⋊C₈	—	7	1	no	—
268	D₄⋊C₈	—	7	1	no	—
269	D₄⋊C₈	—	7	1	no	—
270	#322	—	7	1	no	—
271	#322	—	7	1	no	—
272	#322	—	7	1	no	—
273	#322	—	7	1	no	—
274	C₂³×C₇	—	2	1	no	—
275	C₂³×C₇	C₄×D₄	1	1	yes	characteristic
276	C₇×Q₈	—	2	1	no	—
277	C₇×Q₈	—	2	1	no	—
278	C₇×Q₈	—	2	1	no	—
279	C₇×Q₈	—	2	1	no	—
280	C₇×Q₈	—	2	1	no	—
281	C₇×Q₈	—	4	2	no	—
282	C₇×Q₈	#131	1	2	yes	—
283	C₇×D₄	—	2	1	no	—
284	C₇×D₄	—	2	1	no	—
285	C₇×D₄	—	4	2	no	—
286	C₂×C₄×C₇	—	2	1	no	—
287	C₂×C₄×C₇	—	2	2	no	—
288	C₂×C₄×C₇	—	2	1	no	—
289	C₂×C₄×C₇	—	2	1	no	—
290	C₂×C₄×C₇	—	2	1	no	—
291	C₂×C₄×C₇	—	2	1	no	—
292	C₂×C₄×C₇	—	2	1	no	—
293	C₂×C₄×C₇	—	2	1	no	—
294	C₂×C₄×C₇	—	2	1	no	—
295	C₂×C₄×C₇	—	2	1	no	—
296	C₂×C₄×C₇	—	2	1	no	—
297	C₂×C₄×C₇	—	2	1	no	—
298	C₂×C₄×C₇	—	4	2	no	—
299	C₂×C₄×C₇	—	4	2	no	—
300	C₂×C₄×C₇	—	4	1	no	—
301	C₂×C₄×C₇	—	4	1	no	—
302	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
303	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
304	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
305	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
306	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
307	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
308	C₇×C₈	—	2	1	no	—
309	C₇×C₈	—	2	1	no	—
310	C₇×C₈	—	2	1	no	—
311	C₇×C₈	—	2	1	no	—
312	C₇⋊C₈	—	2	1	no	—
313	C₇⋊C₈	—	2	1	no	—
314	C₇⋊C₈	—	2	1	no	—
315	C₇⋊C₈	—	2	1	no	—
316	C₇⋊C₈	—	4	1	no	—
317	C₇⋊C₈	—	4	1	no	—
318	C₇⋊C₈	—	4	1	no	—
319	C₇⋊C₈	—	4	1	no	—
320	C₇⋊C₈	—	4	1	no	—
321	C₇⋊C₈	—	4	1	no	—
322	C₂²×Q₈	C₂×Dic₇	1	1	yes	characteristic
323	C₂×Q₁₆	C₂×Dic₇	1	1	yes	characteristic
324	C₂×Q₁₆	C₂×Dic₇	1	1	yes	characteristic
325	C₂×SD₁₆	C₂×Dic₇	1	1	yes	characteristic
326	C₂×SD₁₆	C₂×Dic₇	1	1	yes	characteristic
327	C₂×M₁₆	—	14	1	no	—
328	C₂²×C₈	—	14	1	no	—
329	C₂²×C₈	—	14	1	no	—
330	C₂²×C₈	—	14	1	no	—
331	#126	—	2	1	no	—
332	#125	C₂×Dic₇	1	1	yes	characteristic
333	#124	C₂×Dic₇	1	1	yes	characteristic
334	#123	—	2	1	no	—
335	C₂²⋊Q₈	C₂×Dic₇	1	1	yes	characteristic
336	#121	C₂×Dic₇	1	1	yes	characteristic
337	C₄×Q₈	—	2	1	no	—
338	C₄×Q₈	—	2	1	no	—
339	C₄×Q₈	C₂×Dic₇	1	1	yes	characteristic
340	C₄×Q₈	C₂×Dic₇	1	1	yes	characteristic
341	C₄×Q₈	C₂²×D₇	1	1	yes	characteristic
342	C₄×Q₈	C₂²×D₇	1	1	yes	characteristic
343	C₄×Q₈	C₂²×D₇	1	1	yes	characteristic
344	C₄×D₄	—	2	1	no	—
345	C₄×D₄	C₂²×D₇	1	1	yes	characteristic
346	#117	—	2	1	no	—
347	C₂×C₄⋊C₄	—	2	1	no	—
348	C₂×C₄⋊C₄	C₂×Dic₇	1	1	yes	characteristic
349	C₂×C₄²	—	2	1	no	—
350	C₂×C₄²	C₂²×D₇	1	1	yes	characteristic
351	#107	C₂×Dic₇	1	1	yes	characteristic
352	#107	C₂×Dic₇	1	1	yes	characteristic
353	#106	C₂×Dic₇	1	1	yes	characteristic
354	#106	C₂×Dic₇	1	1	yes	characteristic
355	C₄⋊C₈	—	7	1	no	—
356	C₄⋊C₈	—	7	1	no	—
357	C₄⋊C₈	—	7	1	no	—
358	C₄⋊C₈	—	7	1	no	—
359	C₄⋊C₈	—	7	1	no	—
360	C₄⋊C₈	—	7	1	no	—
361	C₄⋊C₈	—	14	1	no	—
362	C₄⋊C₈	—	14	1	no	—
363	C₄⋊C₈	—	14	1	no	—
364	C₄⋊C₈	—	14	1	no	—
365	C₄⋊C₈	—	14	1	no	—
366	C₄⋊C₈	—	14	1	no	—
367	C₄⋊C₈	—	14	1	no	—
368	C₄⋊C₈	C₂×Dic₇	1	1	yes	characteristic
369	C₄⋊C₈	C₂×Dic₇	1	1	yes	characteristic
370	#103	C₂×Dic₇	1	1	yes	characteristic
371	#103	C₂×Dic₇	1	1	yes	characteristic
372	#103	C₂×Dic₇	1	1	yes	characteristic
373	#103	C₂×Dic₇	1	1	yes	characteristic
374	#103	C₂×Dic₇	1	1	yes	characteristic
375	#103	C₂×Dic₇	1	1	yes	characteristic
376	#102	C₂×Dic₇	1	1	yes	characteristic
377	#102	C₂×Dic₇	1	1	yes	characteristic
378	C₂²⋊C₈	—	7	1	no	—
379	C₂²⋊C₈	—	7	1	no	—
380	C₂²⋊C₈	—	14	1	no	—
381	C₂²⋊C₈	—	14	1	no	—
382	C₂²⋊C₈	—	14	1	no	—
383	C₂²⋊C₈	C₂×Dic₇	1	1	yes	characteristic
384	C₂²⋊C₈	C₂×Dic₇	1	1	yes	characteristic
385	#97	—	14	1	no	—
386	#97	—	14	1	no	—
387	#97	—	14	1	no	—
388	#97	—	14	1	no	—
389	C₄×C₈	—	7	1	no	—
390	C₄×C₈	—	7	1	no	—
391	C₄×C₈	—	7	1	no	—
392	C₄×C₈	—	7	1	no	—
393	C₄×C₈	—	14	1	no	—
394	C₄×C₈	—	14	1	no	—
395	C₄×C₈	—	14	1	no	—
396	C₄×C₈	—	14	1	no	—
397	C₄×C₈	C₂²×D₇	1	1	yes	characteristic
398	C₄×C₈	C₂²×D₇	1	1	yes	characteristic
399	C₂²×C₇	—	2	1	no	—
400	C₂²×C₇	—	2	1	no	—
401	C₂²×C₇	—	4	1	no	—
402	C₂²×C₇	—	4	1	no	—
403	C₂²×C₇	—	4	1	no	—
404	C₂²×C₇	#444	1	2	yes	—
405	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
406	C₄×C₇	—	2	1	no	—
407	C₄×C₇	—	2	2	no	—
408	C₄×C₇	—	2	1	no	—
409	C₄×C₇	—	2	1	no	—
410	C₄×C₇	—	2	1	no	—
411	C₄×C₇	—	4	1	no	—
412	C₄×C₇	—	4	1	no	—
413	C₄×C₇	—	4	1	no	—
414	C₄×C₇	—	4	1	no	—
415	C₄×C₇	—	4	1	no	—
416	C₄×C₇	—	4	1	no	—
417	C₄×C₇	C₂×#131	1	1	yes	characteristic
418	C₄×C₇	#568	1	1	yes	characteristic
419	C₄×C₇	#577	1	1	yes	characteristic
420	C₄×C₇	#578	1	1	yes	characteristic
421	C₂×Q₈	—	2	1	no	—
422	C₂×Q₈	—	2	2	no	—
423	C₂×Q₈	—	4	1	no	—
424	C₂×Q₈	C₂²×Dic₇	1	1	yes	characteristic
425	C₂×Q₈	C₂²×Dic₇	1	1	yes	characteristic
426	C₂×Q₈	C₂²×Dic₇	1	1	yes	characteristic
427	C₂×D₄	—	2	1	no	—
428	C₂×D₄	C₂²×Dic₇	1	1	yes	characteristic
429	C₂²×C₄	—	2	1	no	—
430	C₂²×C₄	—	2	1	no	—
431	C₂²×C₄	—	2	1	no	—
432	C₂²×C₄	D₄×D₇	1	1	yes	characteristic
433	C₂²×C₄	#1159	1	1	yes	characteristic
434	C₂²×C₄	C₂²×Dic₇	1	1	yes	characteristic
435	Q₁₆	—	2	2	no	—
436	Q₁₆	—	4	1	no	—
437	SD₁₆	—	2	2	no	—
438	SD₁₆	—	4	1	no	—
439	M₁₆	—	56	1	no	—
440	C₂×C₈	—	7	1	no	—
441	C₂×C₈	—	7	1	no	—
442	C₂×C₈	—	7	1	no	—
443	C₂×C₈	—	7	1	no	—
444	C₂×C₈	—	14	1	no	—
445	C₂×C₈	—	14	1	no	—
446	C₂×C₈	—	14	1	no	—
447	C₂×C₈	—	14	1	no	—
448	C₂×C₈	—	14	1	no	—
449	C₂×C₈	—	14	1	no	—
450	C₂×C₈	—	28	2	no	—
451	C₂×C₈	—	56	1	no	—
452	C₂×C₈	—	56	1	no	—
453	C₂×C₈	C₂²×Dic₇	1	1	yes	characteristic
454	C₂×C₈	C₂²×Dic₇	1	1	yes	characteristic
455	C₂×C₈	C₂²×Dic₇	1	1	yes	characteristic
456	C₂×C₈	C₂²×Dic₇	1	1	yes	characteristic
457	C₄⋊C₄	—	2	1	no	—
458	C₄⋊C₄	—	2	1	no	—
459	C₄⋊C₄	—	2	1	no	—
460	C₄⋊C₄	—	2	1	no	—
461	C₄⋊C₄	—	2	1	no	—
462	C₄⋊C₄	—	2	1	no	—
463	C₄⋊C₄	—	2	1	no	—
464	C₄⋊C₄	—	2	1	no	—
465	C₄⋊C₄	—	2	1	no	—
466	C₄⋊C₄	C₂²×Dic₇	1	1	yes	characteristic
467	C₄⋊C₄	C₂²×Dic₇	1	1	yes	characteristic
468	C₄⋊C₄	C₂²×Dic₇	1	1	yes	characteristic
469	C₄⋊C₄	C₂²×Dic₇	1	1	yes	characteristic
470	C₂²⋊C₄	—	2	1	no	—
471	C₂²⋊C₄	—	2	1	no	—
472	C₂²⋊C₄	—	2	1	no	—
473	C₂²⋊C₄	—	2	1	no	—
474	C₂²⋊C₄	—	2	1	no	—
475	C₄²	—	2	1	no	—
476	C₄²	—	2	1	no	—
477	C₄²	—	2	1	no	—
478	C₄²	—	2	1	no	—
479	C₄²	—	2	1	no	—
480	C₄²	D₄×D₇	1	1	yes	characteristic
481	C₄²	#1159	1	1	yes	characteristic
482	C₄²	C₂²×Dic₇	1	1	yes	characteristic
483	C₄²	C₂³×D₇	1	1	yes	characteristic
484	C₂×C₇	—	2	2	no	—
485	C₂×C₇	—	8	1	no	—
486	C₂×C₇	#2933	1	1	yes	characteristic
487	C₂×C₇	#2947	1	1	yes	characteristic
488	C₂×C₇	C₂×#444	1	1	yes	characteristic
489	C₂³	—	2	1	no	—
490	C₂³	D₄×Dic₇	1	1	yes	characteristic
491	Q₈	—	2	1	no	—
492	Q₈	—	2	1	no	—
493	Q₈	—	2	1	no	—
494	Q₈	—	2	1	no	—
495	Q₈	—	2	1	no	—
496	Q₈	—	4	2	no	—
497	Q₈	#6511	1	2	yes	—
498	D₄	—	2	1	no	—
499	D₄	—	2	1	no	—
500	D₄	—	4	2	no	—
501	C₂×C₄	—	2	2	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	4	2	no	—
514	C₂×C₄	—	4	2	no	—
515	C₂×C₄	—	4	1	no	—
516	C₂×C₄	—	4	1	no	—
517	C₂×C₄	D₄×Dic₇	1	1	yes	characteristic
518	C₂×C₄	D₄×Dic₇	1	1	yes	characteristic
519	C₂×C₄	D₄×Dic₇	1	1	yes	characteristic
520	C₂×C₄	C₂×D₄×D₇	1	1	yes	characteristic
521	C₂×C₄	C₂×#1159	1	1	yes	characteristic
522	C₂×C₄	C₂³×Dic₇	1	1	yes	characteristic
523	C₈	—	2	1	no	—
524	C₈	—	2	1	no	—
525	C₈	—	2	1	no	—
526	C₈	—	2	1	no	—
527	C₈	—	14	1	no	—
528	C₈	—	14	1	no	—
529	C₈	—	14	1	no	—
530	C₈	—	14	1	no	—
531	C₈	—	28	1	no	—
532	C₈	—	28	1	no	—
533	C₈	—	28	1	no	—
534	C₈	—	28	1	no	—
535	C₈	—	28	1	no	—
536	C₈	—	28	1	no	—
537	C₇	#18023	1	1	yes	characteristic, complemented, Sylow
538	C₂²	—	2	1	no	—
539	C₂²	—	2	1	no	—
540	C₂²	—	4	1	no	—
541	C₂²	—	4	1	no	—
542	C₂²	—	4	1	no	—
543	C₂²	#89969	1	2	yes	—
544	C₂²	C₂×D₄×Dic₇	1	1	yes	characteristic
545	C₄	—	2	1	no	—
546	C₄	—	2	1	no	—
547	C₄	—	2	1	no	—
548	C₄	—	2	2	no	—
549	C₄	—	2	1	no	—
550	C₄	—	4	1	no	—
551	C₄	—	4	1	no	—
552	C₄	—	4	1	no	—
553	C₄	—	4	1	no	—
554	C₄	—	4	1	no	—
555	C₄	—	4	1	no	—
556	C₄	#90469	1	1	yes	characteristic
557	C₄	#90470	1	1	yes	characteristic
558	C₄	C₂×#6511	1	1	yes	characteristic
559	C₄	#90510	1	1	yes	characteristic
560	C₂	—	2	2	no	—
561	C₂	—	8	1	no	—
562	C₂	#11740363	1	1	yes	characteristic
563	C₂	C₂×#89969	1	1	yes	characteristic
564	C₂	#11741410	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₇
commutator	C₂×C₄×C₇	C₂³×C₄
Frattini	C₄²	C₂³×D₇
Fitting	C₇×#3108	C₂
socle	C₂²×C₇	C₂×C₄×D₄
prime radical	C₇×#121	C₂×C₄
cosocle	C₄²×C₇	C₂⁴
hypercenter	#3108	D₇
hypocenter	C₇	#18023
LCS	G ▷ C₂×C₄×C₇ ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3108

Complements

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

N	H ≅ G/N	type
3. #11739882	C₂	semidirect
5. C₂×Q₈⋊(C₇⋊C₈)	C₂	semidirect
6. #11728660	C₂	semidirect
7. #11728657	C₂	semidirect
8. #11728657	C₂	semidirect
9. #11728656	C₂	semidirect
10. #11728654	C₂	semidirect
11. #11728650	C₂	semidirect
12. #11728649	C₂	semidirect
13. SD₁₆⋊(C₇⋊C₈)	C₂	semidirect
14. #11728506	C₂	semidirect
15. #11728496	C₂	semidirect
537. C₇	#18023	semidirect

Maximal subgroups

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

subgroup	index
C₇×#3108	2
#11740577	2
#11739882	2
#11729506	2
C₂×Q₈⋊(C₇⋊C₈)	2
#11728660	2
#11728657	2
#11728656	2
#11728654	2
#11728650	2
#11728649	2
SD₁₆⋊(C₇⋊C₈)	2
#11728506	2
#11728496	2
#18023	7