Subgroups — #13324613

Order 1792.

606 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3171	C₂	1	1	yes	maximal, characteristic
2	#11740725	C₂	1	1	yes	maximal, characteristic, complemented
3	#11740576	C₂	1	1	yes	maximal, characteristic, complemented
4	#11729556	C₂	1	1	yes	maximal, characteristic, complemented
5	#11729506	C₂	1	1	yes	maximal, characteristic, complemented
6	#11728652	C₂	1	1	yes	maximal, characteristic, complemented
7	#11728651	C₂	1	1	yes	maximal, characteristic, complemented
8	#11728650	C₂	1	1	yes	maximal, characteristic, complemented
9	#11728649	C₂	1	1	yes	maximal, characteristic, complemented
10	#11728634	C₂	1	1	yes	maximal, characteristic, complemented
11	#11728634	C₂	1	1	yes	maximal, characteristic, complemented
12	#11728633	C₂	1	1	yes	maximal, characteristic, complemented
13	#11728633	C₂	1	1	yes	maximal, characteristic, complemented
14	#11727605	C₂	1	1	yes	maximal, characteristic, complemented
15	#11727601	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#532	C₂²	1	1	yes	characteristic
17	C₇×#529	C₂²	1	1	yes	characteristic
18	C₇×#501	C₄	1	1	yes	characteristic
19	C₇×#496	C₄	1	1	yes	characteristic
20	C₇×#490	C₄	1	1	yes	characteristic
21	C₇×#489	C₄	1	1	yes	characteristic
22	C₇×#469	C₄	1	1	yes	characteristic
23	C₇×#469	C₄	1	1	yes	characteristic
24	C₇×#468	C₄	1	1	yes	characteristic
25	C₇×#468	C₄	1	1	yes	characteristic
26	C₄×C₇×SD₁₆	C₂²	1	1	yes	characteristic
27	C₄×C₇×SD₁₆	C₂²	1	1	yes	characteristic
28	C₄×C₇×D₈	C₂²	1	1	yes	characteristic
29	C₄×C₇×D₈	C₂²	1	1	yes	characteristic
30	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic
31	#90006	—	2	1	no	—
32	#90006	—	2	1	no	—
33	#89796	C₂²	1	1	yes	characteristic
34	Q₈×C₇⋊C₈	C₂²	1	1	yes	characteristic
35	#89784	—	2	1	no	—
36	#89784	C₂²	1	1	yes	characteristic
37	#89784	C₂²	1	1	yes	characteristic
38	#89784	C₂²	1	1	yes	characteristic
39	#89783	—	2	1	no	—
40	#89783	—	2	1	no	—
41	#89783	—	2	1	no	—
42	D₄×C₇⋊C₈	C₂²	1	1	yes	characteristic
43	D₄×C₇⋊C₈	C₂²	1	1	yes	characteristic
44	D₄×C₇⋊C₈	C₂²	1	1	yes	characteristic
45	#89772	—	2	1	no	—
46	#89771	—	2	1	no	—
47	#89698	C₂²	1	1	yes	characteristic
48	#89697	C₂²	1	1	yes	characteristic
49	#89696	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	D₄⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic
54	D₄⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic
55	D₄⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic
56	D₄⋊(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	#89249	C₂²	1	1	yes	characteristic
64	#89249	C₂²	1	1	yes	characteristic
65	#89249	C₂²	1	1	yes	characteristic
66	#89249	C₂²	1	1	yes	characteristic
67	#17987	—	7	1	no	maximal, Sylow
68	C₂×C₇×#41	—	2	1	no	—
69	C₂×C₇×SD₁₆	C₂×C₄	1	1	yes	characteristic
70	C₂×C₇×SD₁₆	C₂×C₄	1	1	yes	characteristic
71	C₂×C₇×D₈	C₂×C₄	1	1	yes	characteristic
72	C₂×C₇×D₈	C₂×C₄	1	1	yes	characteristic
73	C₂×C₇×M₁₆	C₂×C₄	1	1	yes	characteristic
74	C₂×C₇×M₁₆	C₂×C₄	1	1	yes	characteristic
75	C₇×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
76	C₇×#127	C₂×C₄	1	1	yes	characteristic
77	C₇×#126	—	2	1	no	—
78	C₇×#125	C₂×C₄	1	1	yes	characteristic
79	C₇×#124	—	2	1	no	—
80	C₇×#124	C₂×C₄	1	1	yes	characteristic
81	C₇×#123	—	2	1	no	—
82	C₇×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
83	C₇×#121	—	2	1	no	—
84	C₇×#121	C₂×C₄	1	1	yes	characteristic
85	C₇×#121	C₂×C₄	1	1	yes	characteristic
86	C₇×#121	C₂×C₄	1	1	yes	characteristic
87	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
88	C₄×C₇×D₄	—	2	1	no	—
89	C₄×C₇×D₄	—	2	1	no	—
90	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
91	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
92	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
93	C₇×#117	—	2	1	no	—
94	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
95	C₂×#1136	—	2	1	no	—
96	C₂×#1136	—	2	1	no	—
97	C₂×#1136	—	2	1	no	—
98	C₂×#1136	—	2	1	no	—
99	C₂²×C₇⋊C₈	—	2	1	no	—
100	C₂²×C₇⋊C₈	—	2	1	no	—
101	C₂²×C₇⋊C₈	—	2	1	no	—
102	C₂²×C₇⋊C₈	—	2	1	no	—
103	C₇×#107	C₂×C₄	1	1	yes	characteristic
104	C₇×#107	C₂×C₄	1	1	yes	characteristic
105	C₇×#106	C₂×C₄	1	1	yes	characteristic
106	C₇×#106	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×#102	C₂×C₄	1	1	yes	characteristic
112	C₇×#102	C₂×C₄	1	1	yes	characteristic
113	C₇×#102	C₂×C₄	1	1	yes	characteristic
114	C₇×#102	C₂×C₄	1	1	yes	characteristic
115	C₇×#97	C₂×C₄	1	1	yes	characteristic
116	C₇×#97	C₂×C₄	1	1	yes	characteristic
117	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
118	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
119	C₂²⋊(C₇⋊C₈)	—	2	1	no	—
120	C₂²⋊(C₇⋊C₈)	—	2	1	no	—
121	C₂²⋊(C₇⋊C₈)	—	2	1	no	—
122	C₂²⋊(C₇⋊C₈)	—	2	1	no	—
123	C₂²⋊(C₇⋊C₈)	—	2	1	no	—
124	C₂²⋊(C₇⋊C₈)	—	2	1	no	—
125	C₂²⋊(C₇⋊C₈)	—	2	1	no	—
126	C₂²⋊(C₇⋊C₈)	D₄	1	1	yes	characteristic
127	C₂²⋊(C₇⋊C₈)	D₄	1	1	yes	characteristic
128	C₄⋊(C₇⋊C₈)	—	2	1	no	—
129	C₄⋊(C₇⋊C₈)	—	2	1	no	—
130	C₄⋊(C₇⋊C₈)	—	2	1	no	—
131	C₄⋊(C₇⋊C₈)	D₄	1	1	yes	characteristic
132	C₄⋊(C₇⋊C₈)	D₄	1	1	yes	characteristic
133	C₄⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
134	C₄⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
135	C₄⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
136	C₄⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
137	#6377	—	2	1	no	—
138	#6377	—	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	#3171	D₇	1	1	yes	characteristic
146	#2993	—	7	1	no	—
147	#2981	—	7	1	no	—
148	#1588	—	7	1	no	—
149	#1586	—	7	1	no	—
150	#1586	—	7	1	no	—
151	#1585	—	7	1	no	—
152	#1583	—	7	1	no	—
153	#1582	—	7	1	no	—
154	#1581	—	7	1	no	—
155	#1581	—	7	1	no	—
156	#1569	—	7	1	no	—
157	#1494	—	7	1	no	—
158	#1492	—	7	1	no	—
159	#1451	—	7	1	no	—
160	C₇×#41	—	8	1	no	—
161	C₇×#41	—	8	1	no	—
162	C₂×C₇×Q₈	—	2	1	no	—
163	C₂×C₇×Q₈	C₂²×C₄	1	1	yes	characteristic
164	C₂×C₇×D₄	—	2	1	no	—
165	C₂×C₇×D₄	—	2	1	no	—
166	C₂×C₇×D₄	—	2	1	no	—
167	C₂×C₇×D₄	—	2	1	no	—
168	C₂×C₇×D₄	—	2	1	no	—
169	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
170	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
171	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
172	C₂²×C₄×C₇	—	2	1	no	—
173	C₂²×C₄×C₇	—	2	1	no	—
174	C₂²×C₄×C₇	—	2	1	no	—
175	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
176	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
177	C₂²×C₄×C₇	#41	1	1	yes	characteristic
178	C₇×SD₁₆	—	4	1	no	—
179	C₇×SD₁₆	—	4	1	no	—
180	C₇×D₈	—	4	1	no	—
181	C₇×D₈	—	4	1	no	—
182	C₇×M₁₆	—	4	1	no	—
183	C₇×M₁₆	—	4	1	no	—
184	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
185	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
186	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
187	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
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	—	2	1	no	—
192	C₇×C₄⋊C₄	—	2	1	no	—
193	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
194	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
195	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
196	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
197	C₇×C₂²⋊C₄	—	2	1	no	—
198	C₇×C₂²⋊C₄	—	2	1	no	—
199	C₇×C₂²⋊C₄	—	2	1	no	—
200	C₇×C₂²⋊C₄	—	2	1	no	—
201	C₇×C₂²⋊C₄	—	2	1	no	—
202	C₇×C₂²⋊C₄	—	2	1	no	—
203	C₇×C₂²⋊C₄	—	2	1	no	—
204	C₇×C₂²⋊C₄	—	2	1	no	—
205	C₇×C₂²⋊C₄	—	2	1	no	—
206	C₄²×C₇	—	2	1	no	—
207	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
208	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
209	C₄²×C₇	#41	1	1	yes	characteristic
210	C₄²×C₇	C₂⁴	1	1	yes	characteristic
211	#1136	—	8	1	no	—
212	#1136	—	8	1	no	—
213	#1136	—	8	1	no	—
214	#1136	—	8	1	no	—
215	C₂×C₇⋊C₈	—	2	1	no	—
216	C₂×C₇⋊C₈	—	2	1	no	—
217	C₂×C₇⋊C₈	—	2	1	no	—
218	C₂×C₇⋊C₈	—	2	1	no	—
219	C₂×C₇⋊C₈	—	2	1	no	—
220	C₂×C₇⋊C₈	—	2	1	no	—
221	C₂×C₇⋊C₈	—	4	2	no	—
222	C₂×C₇⋊C₈	—	8	1	no	—
223	C₂×C₇⋊C₈	—	8	1	no	—
224	C₂×C₇⋊C₈	—	8	1	no	—
225	C₂×C₇⋊C₈	C₂×D₄	1	1	yes	characteristic
226	C₂×C₇⋊C₈	C₂×D₄	1	1	yes	characteristic
227	C₂×C₇⋊C₈	C₂×D₄	1	1	yes	characteristic
228	C₂×C₇⋊C₈	C₂×D₄	1	1	yes	characteristic
229	#532	C₂×D₇	1	1	yes	characteristic
230	#529	C₂×D₇	1	1	yes	characteristic
231	#501	Dic₇	1	1	yes	characteristic
232	#496	Dic₇	1	1	yes	characteristic
233	#490	Dic₇	1	1	yes	characteristic
234	#489	Dic₇	1	1	yes	characteristic
235	#469	Dic₇	1	1	yes	characteristic
236	#469	Dic₇	1	1	yes	characteristic
237	#468	Dic₇	1	1	yes	characteristic
238	#468	Dic₇	1	1	yes	characteristic
239	#446	—	7	1	no	—
240	C₈×Q₈	—	7	1	no	—
241	C₄×SD₁₆	C₂×D₇	1	1	yes	characteristic
242	C₄×SD₁₆	C₂×D₇	1	1	yes	characteristic
243	C₄×D₈	C₂×D₇	1	1	yes	characteristic
244	C₄×D₈	C₂×D₇	1	1	yes	characteristic
245	#436	—	7	1	no	—
246	#436	—	7	1	no	—
247	#436	—	7	1	no	—
248	#436	—	14	1	no	—
249	#435	—	14	1	no	—
250	#435	—	14	1	no	—
251	#435	—	14	1	no	—
252	C₈×D₄	—	7	1	no	—
253	C₈×D₄	—	7	1	no	—
254	C₈×D₄	—	7	1	no	—
255	#433	—	14	1	no	—
256	#432	—	7	1	no	—
257	#431	—	7	1	no	—
258	#424	—	14	1	no	—
259	#423	—	7	1	no	—
260	#408	—	14	1	no	—
261	#408	—	14	1	no	—
262	C₄×M₁₆	C₂×D₇	1	1	yes	characteristic
263	C₂×C₄×C₈	—	7	1	no	—
264	#335	—	7	1	no	—
265	#335	—	7	1	no	—
266	#334	—	7	1	no	—
267	#334	—	7	1	no	—
268	Q₈⋊C₈	—	7	1	no	—
269	Q₈⋊C₈	—	7	1	no	—
270	D₄⋊C₈	—	7	1	no	—
271	D₄⋊C₈	—	7	1	no	—
272	D₄⋊C₈	—	7	1	no	—
273	D₄⋊C₈	—	7	1	no	—
274	D₄⋊C₈	—	7	1	no	—
275	D₄⋊C₈	—	7	1	no	—
276	#322	—	7	1	no	—
277	#322	—	7	1	no	—
278	#322	—	7	1	no	—
279	#322	—	7	1	no	—
280	C₂³×C₇	—	2	1	no	—
281	C₂³×C₇	—	2	1	no	—
282	C₂³×C₇	—	2	1	no	—
283	C₂³×C₇	C₄×D₄	1	1	yes	characteristic
284	C₇×Q₈	—	2	1	no	—
285	C₇×Q₈	—	2	1	no	—
286	C₇×Q₈	—	8	1	no	—
287	C₇×D₄	—	2	1	no	—
288	C₇×D₄	—	2	1	no	—
289	C₇×D₄	—	2	1	no	—
290	C₇×D₄	—	2	1	no	—
291	C₇×D₄	—	2	1	no	—
292	C₇×D₄	—	2	1	no	—
293	C₇×D₄	—	8	1	no	—
294	C₇×D₄	—	8	1	no	—
295	C₇×D₄	—	8	1	no	—
296	C₇×D₄	—	8	1	no	—
297	C₇×D₄	—	8	1	no	—
298	C₂×C₄×C₇	—	2	1	no	—
299	C₂×C₄×C₇	—	2	1	no	—
300	C₂×C₄×C₇	—	2	1	no	—
301	C₂×C₄×C₇	—	2	1	no	—
302	C₂×C₄×C₇	—	2	1	no	—
303	C₂×C₄×C₇	—	2	1	no	—
304	C₂×C₄×C₇	—	2	1	no	—
305	C₂×C₄×C₇	—	2	1	no	—
306	C₂×C₄×C₇	—	2	1	no	—
307	C₂×C₄×C₇	—	4	1	no	—
308	C₂×C₄×C₇	—	4	1	no	—
309	C₂×C₄×C₇	—	4	1	no	—
310	C₂×C₄×C₇	—	4	1	no	—
311	C₂×C₄×C₇	—	4	1	no	—
312	C₂×C₄×C₇	—	4	1	no	—
313	C₂×C₄×C₇	—	4	1	no	—
314	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
315	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
316	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
317	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
318	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
319	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
320	C₇×C₈	—	2	1	no	—
321	C₇×C₈	—	2	1	no	—
322	C₇×C₈	—	2	1	no	—
323	C₇×C₈	—	2	1	no	—
324	C₇⋊C₈	—	2	2	no	—
325	C₇⋊C₈	—	2	1	no	—
326	C₇⋊C₈	—	2	1	no	—
327	C₇⋊C₈	—	2	1	no	—
328	C₇⋊C₈	—	2	1	no	—
329	C₇⋊C₈	—	4	1	no	—
330	C₇⋊C₈	—	4	1	no	—
331	C₇⋊C₈	—	4	1	no	—
332	C₇⋊C₈	—	4	1	no	—
333	C₇⋊C₈	—	4	1	no	—
334	C₂×#41	—	2	1	no	—
335	C₂×SD₁₆	C₂×Dic₇	1	1	yes	characteristic
336	C₂×SD₁₆	C₂×Dic₇	1	1	yes	characteristic
337	C₂×D₈	C₂×Dic₇	1	1	yes	characteristic
338	C₂×D₈	C₂×Dic₇	1	1	yes	characteristic
339	C₂×M₁₆	—	14	1	no	—
340	C₂×M₁₆	—	14	1	no	—
341	C₂×M₁₆	—	14	1	no	—
342	C₂×M₁₆	—	14	1	no	—
343	C₂×M₁₆	C₂×Dic₇	1	1	yes	characteristic
344	C₂×M₁₆	C₂×Dic₇	1	1	yes	characteristic
345	C₂²×C₈	—	14	1	no	—
346	C₂²×C₈	—	14	1	no	—
347	C₂²×C₈	—	14	1	no	—
348	C₂²×C₈	—	14	1	no	—
349	C₄⋊Q₈	C₂×Dic₇	1	1	yes	characteristic
350	#127	C₂×Dic₇	1	1	yes	characteristic
351	#126	—	2	1	no	—
352	#125	C₂×Dic₇	1	1	yes	characteristic
353	#124	—	2	1	no	—
354	#124	C₂×Dic₇	1	1	yes	characteristic
355	#123	—	2	1	no	—
356	C₂²⋊Q₈	C₂×Dic₇	1	1	yes	characteristic
357	#121	—	2	1	no	—
358	#121	C₂×Dic₇	1	1	yes	characteristic
359	#121	C₂×Dic₇	1	1	yes	characteristic
360	#121	C₂×Dic₇	1	1	yes	characteristic
361	C₄×Q₈	C₂²×D₇	1	1	yes	characteristic
362	C₄×D₄	—	2	1	no	—
363	C₄×D₄	—	2	1	no	—
364	C₄×D₄	C₂²×D₇	1	1	yes	characteristic
365	C₄×D₄	C₂²×D₇	1	1	yes	characteristic
366	C₄×D₄	C₂²×D₇	1	1	yes	characteristic
367	#117	—	2	1	no	—
368	C₂×C₄²	C₂²×D₇	1	1	yes	characteristic
369	#107	C₂×Dic₇	1	1	yes	characteristic
370	#107	C₂×Dic₇	1	1	yes	characteristic
371	#106	C₂×Dic₇	1	1	yes	characteristic
372	#106	C₂×Dic₇	1	1	yes	characteristic
373	C₄⋊C₈	—	7	1	no	—
374	C₄⋊C₈	—	7	1	no	—
375	C₄⋊C₈	—	7	1	no	—
376	C₄⋊C₈	—	7	1	no	—
377	C₄⋊C₈	—	7	1	no	—
378	C₄⋊C₈	—	7	1	no	—
379	C₄⋊C₈	—	14	1	no	—
380	C₄⋊C₈	—	14	1	no	—
381	C₄⋊C₈	—	14	1	no	—
382	#103	C₂×Dic₇	1	1	yes	characteristic
383	#103	C₂×Dic₇	1	1	yes	characteristic
384	#102	C₂×Dic₇	1	1	yes	characteristic
385	#102	C₂×Dic₇	1	1	yes	characteristic
386	#102	C₂×Dic₇	1	1	yes	characteristic
387	#102	C₂×Dic₇	1	1	yes	characteristic
388	#102	C₂×Dic₇	1	1	yes	characteristic
389	#102	C₂×Dic₇	1	1	yes	characteristic
390	C₂²⋊C₈	—	7	1	no	—
391	C₂²⋊C₈	—	7	1	no	—
392	C₂²⋊C₈	—	14	1	no	—
393	C₂²⋊C₈	—	14	1	no	—
394	C₂²⋊C₈	—	14	1	no	—
395	C₂²⋊C₈	—	14	1	no	—
396	C₂²⋊C₈	—	14	1	no	—
397	C₂²⋊C₈	—	14	1	no	—
398	C₂²⋊C₈	—	14	1	no	—
399	#97	—	14	1	no	—
400	#97	—	14	1	no	—
401	#97	C₂×Dic₇	1	1	yes	characteristic
402	#97	C₂×Dic₇	1	1	yes	characteristic
403	C₄×C₈	—	7	1	no	—
404	C₄×C₈	—	7	1	no	—
405	C₄×C₈	—	7	1	no	—
406	C₄×C₈	—	7	1	no	—
407	C₄×C₈	—	14	1	no	—
408	C₄×C₈	—	14	1	no	—
409	C₄×C₈	C₂²×D₇	1	1	yes	characteristic
410	C₄×C₈	C₂²×D₇	1	1	yes	characteristic
411	C₂²×C₇	—	2	1	no	—
412	C₂²×C₇	—	2	1	no	—
413	C₂²×C₇	—	2	1	no	—
414	C₂²×C₇	—	4	1	no	—
415	C₂²×C₇	—	4	1	no	—
416	C₂²×C₇	—	4	1	no	—
417	C₂²×C₇	—	4	1	no	—
418	C₂²×C₇	—	4	1	no	—
419	C₂²×C₇	—	4	1	no	—
420	C₂²×C₇	—	4	1	no	—
421	C₂²×C₇	—	4	1	no	—
422	C₂²×C₇	—	4	1	no	—
423	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
424	C₄×C₇	—	2	1	no	—
425	C₄×C₇	—	2	1	no	—
426	C₄×C₇	—	2	1	no	—
427	C₄×C₇	—	2	1	no	—
428	C₄×C₇	—	4	1	no	—
429	C₄×C₇	—	4	1	no	—
430	C₄×C₇	—	4	1	no	—
431	C₄×C₇	—	4	1	no	—
432	C₄×C₇	—	4	1	no	—
433	C₄×C₇	#568	1	1	yes	characteristic
434	C₄×C₇	#568	1	1	yes	characteristic
435	C₄×C₇	#576	1	1	yes	characteristic
436	C₄×C₇	#577	1	1	yes	characteristic
437	#41	—	8	1	no	—
438	#41	—	8	1	no	—
439	C₂×Q₈	—	2	1	no	—
440	C₂×Q₈	C₂²×Dic₇	1	1	yes	characteristic
441	C₂×D₄	—	2	1	no	—
442	C₂×D₄	—	2	1	no	—
443	C₂×D₄	—	2	1	no	—
444	C₂×D₄	—	2	1	no	—
445	C₂×D₄	—	2	1	no	—
446	C₂×D₄	C₂²×Dic₇	1	1	yes	characteristic
447	C₂×D₄	C₂²×Dic₇	1	1	yes	characteristic
448	C₂×D₄	C₂²×Dic₇	1	1	yes	characteristic
449	C₂²×C₄	—	2	1	no	—
450	C₂²×C₄	—	2	1	no	—
451	C₂²×C₄	—	2	1	no	—
452	C₂²×C₄	D₄×D₇	1	1	yes	characteristic
453	C₂²×C₄	#1159	1	1	yes	characteristic
454	C₂²×C₄	C₂²×Dic₇	1	1	yes	characteristic
455	SD₁₆	—	4	1	no	—
456	SD₁₆	—	4	1	no	—
457	D₈	—	4	1	no	—
458	D₈	—	4	1	no	—
459	M₁₆	—	4	1	no	—
460	M₁₆	—	4	1	no	—
461	M₁₆	—	56	1	no	—
462	M₁₆	—	56	1	no	—
463	M₁₆	—	56	1	no	—
464	M₁₆	—	56	1	no	—
465	C₂×C₈	—	7	1	no	—
466	C₂×C₈	—	7	1	no	—
467	C₂×C₈	—	7	1	no	—
468	C₂×C₈	—	7	1	no	—
469	C₂×C₈	—	14	1	no	—
470	C₂×C₈	—	14	1	no	—
471	C₂×C₈	—	14	1	no	—
472	C₂×C₈	—	14	1	no	—
473	C₂×C₈	—	14	1	no	—
474	C₂×C₈	—	14	1	no	—
475	C₂×C₈	—	28	2	no	—
476	C₂×C₈	—	56	1	no	—
477	C₂×C₈	—	56	1	no	—
478	C₂×C₈	—	56	1	no	—
479	C₂×C₈	C₂²×Dic₇	1	1	yes	characteristic
480	C₂×C₈	C₂²×Dic₇	1	1	yes	characteristic
481	C₂×C₈	C₂²×Dic₇	1	1	yes	characteristic
482	C₂×C₈	C₂²×Dic₇	1	1	yes	characteristic
483	C₄⋊C₄	—	2	1	no	—
484	C₄⋊C₄	—	2	1	no	—
485	C₄⋊C₄	—	2	1	no	—
486	C₄⋊C₄	—	2	1	no	—
487	C₄⋊C₄	—	2	1	no	—
488	C₄⋊C₄	C₂²×Dic₇	1	1	yes	characteristic
489	C₄⋊C₄	C₂²×Dic₇	1	1	yes	characteristic
490	C₄⋊C₄	C₂²×Dic₇	1	1	yes	characteristic
491	C₄⋊C₄	C₂²×Dic₇	1	1	yes	characteristic
492	C₂²⋊C₄	—	2	1	no	—
493	C₂²⋊C₄	—	2	1	no	—
494	C₂²⋊C₄	—	2	1	no	—
495	C₂²⋊C₄	—	2	1	no	—
496	C₂²⋊C₄	—	2	1	no	—
497	C₂²⋊C₄	—	2	1	no	—
498	C₂²⋊C₄	—	2	1	no	—
499	C₂²⋊C₄	—	2	1	no	—
500	C₂²⋊C₄	—	2	1	no	—
501	C₄²	—	2	1	no	—
502	C₄²	D₄×D₇	1	1	yes	characteristic
503	C₄²	#1159	1	1	yes	characteristic
504	C₄²	C₂²×Dic₇	1	1	yes	characteristic
505	C₄²	C₂³×D₇	1	1	yes	characteristic
506	C₂×C₇	—	4	1	no	—
507	C₂×C₇	—	8	1	no	—
508	C₂×C₇	—	8	1	no	—
509	C₂×C₇	—	8	1	no	—
510	C₂×C₇	#2932	1	1	yes	characteristic
511	C₂×C₇	#2946	1	1	yes	characteristic
512	C₂×C₇	#2956	1	1	yes	characteristic
513	C₂³	—	2	1	no	—
514	C₂³	—	2	1	no	—
515	C₂³	—	2	1	no	—
516	C₂³	D₄×Dic₇	1	1	yes	characteristic
517	Q₈	—	2	1	no	—
518	Q₈	—	2	1	no	—
519	Q₈	—	8	1	no	—
520	D₄	—	2	1	no	—
521	D₄	—	2	1	no	—
522	D₄	—	2	1	no	—
523	D₄	—	2	1	no	—
524	D₄	—	2	1	no	—
525	D₄	—	2	1	no	—
526	D₄	—	8	1	no	—
527	D₄	—	8	1	no	—
528	D₄	—	8	1	no	—
529	D₄	—	8	1	no	—
530	D₄	—	8	1	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	2	1	no	—
540	C₂×C₄	—	4	1	no	—
541	C₂×C₄	—	4	1	no	—
542	C₂×C₄	—	4	1	no	—
543	C₂×C₄	—	4	1	no	—
544	C₂×C₄	—	4	1	no	—
545	C₂×C₄	—	4	1	no	—
546	C₂×C₄	—	4	1	no	—
547	C₂×C₄	D₄×Dic₇	1	1	yes	characteristic
548	C₂×C₄	D₄×Dic₇	1	1	yes	characteristic
549	C₂×C₄	D₄×Dic₇	1	1	yes	characteristic
550	C₂×C₄	C₂×D₄×D₇	1	1	yes	characteristic
551	C₂×C₄	C₂×#1159	1	1	yes	characteristic
552	C₂×C₄	C₂³×Dic₇	1	1	yes	characteristic
553	C₈	—	2	1	no	—
554	C₈	—	2	1	no	—
555	C₈	—	2	1	no	—
556	C₈	—	2	1	no	—
557	C₈	—	14	2	no	—
558	C₈	—	14	1	no	—
559	C₈	—	14	1	no	—
560	C₈	—	14	1	no	—
561	C₈	—	14	1	no	—
562	C₈	—	28	1	no	—
563	C₈	—	28	1	no	—
564	C₈	—	28	1	no	—
565	C₈	—	28	1	no	—
566	C₈	—	28	1	no	—
567	C₇	#17987	1	1	yes	characteristic, complemented, Sylow
568	C₂²	—	2	1	no	—
569	C₂²	—	2	1	no	—
570	C₂²	—	2	1	no	—
571	C₂²	—	4	1	no	—
572	C₂²	—	4	1	no	—
573	C₂²	—	4	1	no	—
574	C₂²	—	4	1	no	—
575	C₂²	—	4	1	no	—
576	C₂²	—	4	1	no	—
577	C₂²	—	4	1	no	—
578	C₂²	—	4	1	no	—
579	C₂²	—	4	1	no	—
580	C₂²	C₂×D₄×Dic₇	1	1	yes	characteristic
581	C₄	—	2	1	no	—
582	C₄	—	2	1	no	—
583	C₄	—	2	1	no	—
584	C₄	—	2	1	no	—
585	C₄	—	4	1	no	—
586	C₄	—	4	1	no	—
587	C₄	—	4	1	no	—
588	C₄	—	4	1	no	—
589	C₄	—	4	1	no	—
590	C₄	#90465	1	1	yes	characteristic
591	C₄	#90466	1	1	yes	characteristic
592	C₄	#90510	1	1	yes	characteristic
593	C₄	#90510	1	1	yes	characteristic
594	C₂	—	4	1	no	—
595	C₂	—	8	1	no	—
596	C₂	—	8	1	no	—
597	C₂	—	8	1	no	—
598	C₂	#11740721	1	1	yes	characteristic
599	C₂	#11741375	1	1	yes	characteristic
600	C₂	#11741445	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₇
commutator	C₂×C₄×C₇	C₂³×C₄
Frattini	C₄²	C₂³×D₇
Fitting, prime radical	C₇×#3171	C₂
socle	C₂²×C₇	C₂×C₄×D₄
cosocle	C₄²×C₇	C₂⁴
hypercenter	#3171	D₇
hypocenter	C₇	#17987
LCS	G ▷ C₂×C₄×C₇ ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3171

Complements

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

N	H ≅ G/N	type
2. #11740725	C₂	semidirect
3. #11740576	C₂	semidirect
4. #11729556	C₂	semidirect
5. #11729506	C₂	semidirect
6. #11728652	C₂	semidirect
7. #11728651	C₂	semidirect
8. #11728650	C₂	semidirect
9. #11728649	C₂	semidirect
10. #11728634	C₂	semidirect
11. #11728634	C₂	semidirect
12. #11728633	C₂	semidirect
13. #11728633	C₂	semidirect
14. #11727605	C₂	semidirect
15. #11727601	C₂	semidirect
567. C₇	#17987	semidirect

Maximal subgroups

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

subgroup	index
C₇×#3171	2
#11740725	2
#11740576	2
#11729556	2
#11729506	2
#11728652	2
#11728651	2
#11728650	2
#11728649	2
#11728634	2
#11728633	2
#11727605	2
#11727601	2
#17987	7