Subgroups — #13323697

Order 1792.

634 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11737384	C₂	1	1	yes	maximal, characteristic, complemented
2	#11737097	C₂	1	1	yes	maximal, characteristic
3	C₈×#1159	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#1582	C₂	1	1	yes	maximal, characteristic, complemented
5	#11728710	C₂	1	1	yes	maximal, characteristic, complemented
6	SD₁₆×C₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	#11728595	C₂	1	1	yes	maximal, characteristic, complemented
8	#11726287	C₂	1	1	yes	maximal, characteristic, complemented
9	#11726270	C₂	1	1	yes	maximal, characteristic, complemented
10	#11725987	C₂	1	1	yes	maximal, characteristic, complemented
11	#11725967	C₂	1	1	yes	maximal, characteristic, complemented
12	#11725927	C₂	1	1	yes	maximal, characteristic, complemented
13	#11725902	C₂	1	1	yes	maximal, characteristic, complemented
14	#11725839	C₂	1	1	yes	maximal, characteristic, complemented
15	#11725822	C₂	1	1	yes	maximal, characteristic, complemented
16	#90271	C₂²	1	1	yes	characteristic
17	C₄×#1159	C₂²	1	1	yes	characteristic
18	C₇×#446	C₂²	1	1	yes	characteristic
19	C₄×C₇×SD₁₆	C₂²	1	1	yes	characteristic
20	C₇×C₈×D₄	C₂²	1	1	yes	characteristic
21	#89945	C₄	1	1	yes	characteristic
22	#89937	C₄	1	1	yes	characteristic
23	C₈×C₂²⋊D₇	—	2	1	no	—
24	C₂×C₈×Dic₇	—	2	1	no	—
25	C₄×#1144	C₂²	1	1	yes	characteristic
26	Q₈×C₇⋊C₈	C₂²	1	1	yes	characteristic
27	C₄×#1141	C₂²	1	1	yes	characteristic
28	D₄×C₇⋊C₈	C₂²	1	1	yes	characteristic
29	#89638	C₄	1	1	yes	characteristic
30	#89629	C₄	1	1	yes	characteristic
31	#89612	—	2	1	no	—
32	#89607	C₂²	1	1	yes	characteristic
33	#89606	—	2	1	no	—
34	#89606	C₂²	1	1	yes	characteristic
35	#89605	C₂²	1	1	yes	characteristic
36	#89602	C₂²	1	1	yes	characteristic
37	#89587	C₄	1	1	yes	characteristic
38	#89570	C₄	1	1	yes	characteristic
39	#89553	C₄	1	1	yes	characteristic
40	#89535	C₄	1	1	yes	characteristic
41	(C₂²⋊D₇)⋊C₈	—	2	1	no	—
42	#89490	—	2	1	no	—
43	#89480	—	2	1	no	—
44	#89478	—	2	1	no	—
45	C₄×#1132	C₂²	1	1	yes	characteristic
46	#89460	C₂²	1	1	yes	characteristic
47	#89457	C₂²	1	1	yes	characteristic
48	#89457	C₂²	1	1	yes	characteristic
49	C₄×C₈×D₇	C₂²	1	1	yes	characteristic
50	C₈×Dic₁₄	C₂²	1	1	yes	characteristic
51	C₇×#334	C₂²	1	1	yes	characteristic
52	C₇×Q₈⋊C₈	C₂²	1	1	yes	characteristic
53	C₇×D₄⋊C₈	C₂²	1	1	yes	characteristic
54	C₇×#322	C₂²	1	1	yes	characteristic
55	Q₈⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic
56	D₄⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic
57	#89279	C₂²	1	1	yes	characteristic
58	#89278	C₂²	1	1	yes	characteristic
59	#89274	C₂²	1	1	yes	characteristic
60	#89274	C₂²	1	1	yes	characteristic
61	#89254	C₂²	1	1	yes	characteristic
62	#89252	C₂²	1	1	yes	characteristic
63	#89251	C₂²	1	1	yes	characteristic
64	#89250	C₂²	1	1	yes	characteristic
65	C₈×C₇⋊C₈	C₂²	1	1	yes	characteristic
66	C₈×C₇⋊C₈	C₂²	1	1	yes	characteristic
67	#17904	—	7	1	no	maximal, Sylow
68	C₂×#1159	C₂×C₄	1	1	yes	characteristic
69	C₂×C₇×SD₁₆	C₂×C₄	1	1	yes	characteristic
70	C₂²×C₇×C₈	—	2	1	no	—
71	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
72	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
73	#6510	C₂×C₄	1	1	yes	characteristic
74	#6509	C₂×C₄	1	1	yes	characteristic
75	C₂×#1144	C₂×C₄	1	1	yes	characteristic
76	D₄×Dic₇	C₂×C₄	1	1	yes	characteristic
77	C₂×#1141	C₂×C₄	1	1	yes	characteristic
78	C₄×C₂²⋊D₇	—	2	1	no	—
79	C₂×C₄×Dic₇	—	2	1	no	—
80	C₂²×C₇⋊C₈	—	2	1	no	—
81	C₂×#1132	C₂×C₄	1	1	yes	characteristic
82	C₂×#1131	—	2	1	no	—
83	C₂×C₈×D₇	—	2	1	no	—
84	C₂×C₈×D₇	D₄	1	1	yes	characteristic
85	C₂×C₈×D₇	D₄	1	1	yes	characteristic
86	#6461	—	2	1	no	—
87	#6458	C₂×C₄	1	1	yes	characteristic
88	#6457	—	2	1	no	—
89	#6455	C₂×C₄	1	1	yes	characteristic
90	#6453	C₂×C₄	1	1	yes	characteristic
91	#6450	C₂×C₄	1	1	yes	characteristic
92	(C₂²⋊D₇)⋊C₄	—	2	1	no	—
93	#6440	—	2	1	no	—
94	C₄×D₂₈	—	2	1	no	—
95	C₄×D₂₈	C₂³	1	1	yes	characteristic
96	#6435	—	2	1	no	—
97	C₄²×D₇	C₂³	1	1	yes	characteristic
98	C₄×Dic₁₄	C₂³	1	1	yes	characteristic
99	C₇×#106	C₂×C₄	1	1	yes	characteristic
100	C₇×C₄⋊C₈	—	2	1	no	—
101	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
102	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
103	C₇×#103	C₂×C₄	1	1	yes	characteristic
104	C₇×#102	C₂×C₄	1	1	yes	characteristic
105	C₇×C₂²⋊C₈	—	2	1	no	—
106	C₇×#97	—	2	1	no	—
107	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
108	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
109	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
110	#6409	C₂×C₄	1	1	yes	characteristic
111	#6406	C₂×C₄	1	1	yes	characteristic
112	C₂²⋊(C₇⋊C₈)	—	2	1	no	—
113	#6395	C₂×C₄	1	1	yes	characteristic
114	(C₂×D₇)⋊C₈	—	2	1	no	—
115	(C₂×D₇)⋊C₈	—	2	1	no	—
116	(C₂×D₇)⋊C₈	—	2	1	no	—
117	(C₂×D₇)⋊C₈	—	2	1	no	—
118	(C₂×D₇)⋊C₈	—	2	1	no	—
119	(C₂×D₇)⋊C₈	C₂×C₄	1	1	yes	characteristic
120	(C₂×D₇)⋊C₈	C₂×C₄	1	1	yes	characteristic
121	#6391	C₂×C₄	1	1	yes	characteristic
122	#6390	C₂×C₄	1	1	yes	characteristic
123	#6389	—	2	1	no	—
124	Dic₇⋊C₈	—	2	1	no	—
125	Dic₇⋊C₈	—	2	1	no	—
126	Dic₇⋊C₈	—	2	1	no	—
127	Dic₇⋊C₈	C₂×C₄	1	1	yes	characteristic
128	Dic₇⋊C₈	C₂×C₄	1	1	yes	characteristic
129	C₈×Dic₇	—	2	1	no	—
130	C₈×Dic₇	—	2	1	no	—
131	C₈×Dic₇	—	2	1	no	—
132	C₈×Dic₇	D₄	1	1	yes	characteristic
133	C₈×Dic₇	D₄	1	1	yes	characteristic
134	#6384	C₂×C₄	1	1	yes	characteristic
135	#6383	C₂×C₄	1	1	yes	characteristic
136	#6381	C₂×C₄	1	1	yes	characteristic
137	#6381	C₂×C₄	1	1	yes	characteristic
138	C₄⋊(C₇⋊C₈)	—	2	1	no	—
139	C₄⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
140	C₄⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
141	C₄×C₇⋊C₈	—	2	1	no	—
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	#3102	—	7	1	no	—
146	#2966	—	7	1	no	—
147	C₈×#41	—	7	1	no	—
148	#1584	—	7	1	no	—
149	#1583	—	7	1	no	—
150	#1582	D₇	1	1	yes	characteristic, complemented
151	#1581	—	7	1	no	—
152	C₈×Q₁₆	—	7	1	no	—
153	C₈×SD₁₆	—	7	1	no	—
154	C₈×SD₁₆	—	7	1	no	—
155	C₈×D₈	—	7	1	no	—
156	#1572	—	7	1	no	—
157	#1488	—	7	1	no	—
158	#1482	—	7	1	no	—
159	#1450	—	7	1	no	—
160	C₂×C₇×Q₈	C₂²×C₄	1	1	yes	characteristic
161	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
162	C₂²×C₄×C₇	—	2	1	no	—
163	C₂×C₂²⋊D₇	—	2	1	no	—
164	C₂²×Dic₇	—	2	1	no	—
165	C₂²×Dic₇	—	2	1	no	—
166	#1159	—	2	2	no	—
167	#1159	—	2	2	no	—
168	C₂×D₂₈	—	2	1	no	—
169	C₂×D₂₈	C₂²×C₄	1	1	yes	characteristic
170	C₂×C₄×D₇	—	2	1	no	—
171	C₂×C₄×D₇	C₂²×C₄	1	1	yes	characteristic
172	C₂×C₄×D₇	C₂×D₄	1	1	yes	characteristic
173	C₂×C₄×D₇	#41	1	1	yes	characteristic
174	C₂×Dic₁₄	C₂²×C₄	1	1	yes	characteristic
175	C₇×SD₁₆	—	2	2	no	—
176	C₂×C₇×C₈	—	2	1	no	—
177	C₂×C₇×C₈	—	2	1	no	—
178	C₂×C₇×C₈	—	2	1	no	—
179	C₂×C₇×C₈	—	4	2	no	—
180	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
181	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
182	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
183	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
184	C₇×C₄⋊C₄	—	2	1	no	—
185	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
186	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
187	C₇×C₂²⋊C₄	—	2	1	no	—
188	C₄²×C₇	—	2	1	no	—
189	C₄²×C₇	C₂⁴	1	1	yes	characteristic
190	C₂²⋊Dic₇	—	2	1	no	—
191	#1144	—	2	2	no	—
192	#1141	—	2	2	no	—
193	(C₂×D₇)⋊C₄	—	2	1	no	—
194	(C₂×D₇)⋊C₄	—	2	1	no	—
195	(C₂×D₇)⋊C₄	—	2	1	no	—
196	(C₂×D₇)⋊C₄	—	2	1	no	—
197	(C₂×D₇)⋊C₄	—	2	1	no	—
198	(C₂×D₇)⋊C₄	—	2	1	no	—
199	C₄⋊Dic₇	—	2	1	no	—
200	C₄⋊Dic₇	C₂²×C₄	1	1	yes	characteristic
201	C₄⋊Dic₇	C₂²×C₄	1	1	yes	characteristic
202	Dic₇⋊C₄	—	2	1	no	—
203	Dic₇⋊C₄	—	2	1	no	—
204	Dic₇⋊C₄	—	2	1	no	—
205	Dic₇⋊C₄	—	2	1	no	—
206	C₄×Dic₇	—	2	1	no	—
207	C₄×Dic₇	—	2	1	no	—
208	C₄×Dic₇	—	2	1	no	—
209	C₄×Dic₇	C₂²×C₄	1	1	yes	characteristic
210	C₄×Dic₇	C₂×D₄	1	1	yes	characteristic
211	C₄×Dic₇	#41	1	1	yes	characteristic
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	—	4	2	no	—
216	C₂×C₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
217	C₂×C₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
218	C₂×C₇⋊C₈	C₂×D₄	1	1	yes	characteristic
219	C₂×C₇⋊C₈	C₂×D₄	1	1	yes	characteristic
220	#1132	—	2	2	no	—
221	#1131	—	4	2	no	—
222	C₈×D₇	—	2	2	no	—
223	C₈×D₇	—	2	2	no	—
224	C₈×D₇	—	4	2	no	—
225	#529	—	7	1	no	—
226	C₄×#41	—	7	1	no	—
227	#485	—	7	1	no	—
228	#482	—	7	1	no	—
229	#479	—	7	1	no	—
230	#478	—	7	1	no	—
231	#464	—	7	1	no	—
232	#463	—	7	1	no	—
233	#452	—	7	1	no	—
234	#449	—	7	1	no	—
235	#446	C₂×D₇	1	1	yes	characteristic
236	C₈×Q₈	—	7	1	no	—
237	C₈×Q₈	—	7	1	no	—
238	C₈×Q₈	—	7	1	no	—
239	C₄×Q₁₆	—	7	1	no	—
240	C₄×SD₁₆	—	7	1	no	—
241	C₄×SD₁₆	C₂×D₇	1	1	yes	characteristic
242	C₄×D₈	—	7	1	no	—
243	#436	—	7	1	no	—
244	#435	—	14	1	no	—
245	C₈×D₄	—	7	1	no	—
246	C₈×D₄	—	7	1	no	—
247	C₈×D₄	—	14	1	no	—
248	C₈×D₄	—	14	1	no	—
249	C₈×D₄	—	14	1	no	—
250	C₈×D₄	C₂×D₇	1	1	yes	characteristic
251	#433	—	14	1	no	—
252	#432	—	7	1	no	—
253	#431	—	7	1	no	—
254	#431	—	7	1	no	—
255	#431	—	7	1	no	—
256	#431	—	14	1	no	—
257	#405	—	14	1	no	—
258	C₂×C₄×C₈	—	7	1	no	—
259	C₂×C₄×C₈	—	14	1	no	—
260	#335	—	7	1	no	—
261	#335	—	7	1	no	—
262	#334	—	7	1	no	—
263	#334	C₂×D₇	1	1	yes	characteristic
264	Q₈⋊C₈	—	7	1	no	—
265	Q₈⋊C₈	—	7	1	no	—
266	Q₈⋊C₈	—	7	1	no	—
267	Q₈⋊C₈	C₂×D₇	1	1	yes	characteristic
268	D₄⋊C₈	—	7	1	no	—
269	D₄⋊C₈	—	7	1	no	—
270	D₄⋊C₈	—	7	1	no	—
271	D₄⋊C₈	C₂×D₇	1	1	yes	characteristic
272	#322	—	7	1	no	—
273	#322	C₂×D₇	1	1	yes	characteristic
274	C₈²	—	7	1	no	—
275	C₈²	—	7	1	no	—
276	C₂³×C₇	—	2	1	no	—
277	C₂²×D₇	—	2	1	no	—
278	C₂²×D₇	C₄×D₄	1	1	yes	characteristic
279	C₇×Q₈	—	2	1	no	—
280	C₇×Q₈	—	2	1	no	—
281	C₇×D₄	—	2	1	no	—
282	C₇×D₄	#131	1	2	yes	—
283	C₂×C₄×C₇	—	2	1	no	—
284	C₂×C₄×C₇	—	2	1	no	—
285	C₂×C₄×C₇	—	2	1	no	—
286	C₂×C₄×C₇	—	4	1	no	—
287	C₂×C₄×C₇	—	4	1	no	—
288	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
289	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
290	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
291	C₂²⋊D₇	—	2	4	no	—
292	C₂×Dic₇	—	2	4	no	—
293	C₂×Dic₇	—	2	1	no	—
294	C₂×Dic₇	—	2	1	no	—
295	C₂×Dic₇	—	2	1	no	—
296	C₂×Dic₇	—	4	2	no	—
297	C₂×Dic₇	C₄×D₄	1	1	yes	characteristic
298	C₂×Dic₇	C₄×D₄	1	1	yes	characteristic
299	C₂×Dic₇	C₄×D₄	1	1	yes	characteristic
300	D₂₈	—	2	1	no	—
301	D₂₈	—	2	1	no	—
302	D₂₈	—	4	2	no	—
303	C₄×D₇	—	2	1	no	—
304	C₄×D₇	—	2	1	no	—
305	C₄×D₇	—	2	1	no	—
306	C₄×D₇	—	2	1	no	—
307	C₄×D₇	—	4	1	no	—
308	C₄×D₇	—	4	1	no	—
309	C₄×D₇	—	4	1	no	—
310	Dic₁₄	—	2	1	no	—
311	Dic₁₄	#131	1	2	yes	—
312	C₇×C₈	—	2	1	no	—
313	C₇×C₈	—	2	1	no	—
314	C₇×C₈	—	2	1	no	—
315	C₇×C₈	—	4	1	no	—
316	C₇×C₈	—	4	1	no	—
317	C₇×C₈	—	4	1	no	—
318	C₇×C₈	#135	1	2	yes	—
319	C₇⋊C₈	—	2	1	no	—
320	C₇⋊C₈	—	2	1	no	—
321	C₇⋊C₈	—	2	1	no	—
322	C₇⋊C₈	—	4	1	no	—
323	C₇⋊C₈	—	4	1	no	—
324	C₇⋊C₈	—	4	1	no	—
325	C₇⋊C₈	#135	1	2	yes	—
326	C₂×#41	—	7	1	no	—
327	C₂×Q₁₆	—	7	1	no	—
328	C₂×SD₁₆	—	7	1	no	—
329	C₂×SD₁₆	C₄×D₇	1	1	yes	characteristic
330	C₂×D₈	—	7	1	no	—
331	C₂×M₁₆	—	14	1	no	—
332	C₂²×C₈	—	2	1	no	—
333	C₂²×C₈	—	7	1	no	—
334	C₂²×C₈	—	7	1	no	—
335	C₂²×C₈	—	14	1	no	—
336	C₂²×C₈	—	14	1	no	—
337	#126	—	14	1	no	—
338	#125	—	7	1	no	—
339	#124	—	7	1	no	—
340	#123	—	14	1	no	—
341	C₂²⋊Q₈	—	7	1	no	—
342	#121	—	7	1	no	—
343	C₄×Q₈	—	7	1	no	—
344	C₄×Q₈	—	7	1	no	—
345	C₄×Q₈	C₂²×D₇	1	1	yes	characteristic
346	C₄×D₄	—	7	1	no	—
347	C₄×D₄	—	7	1	no	—
348	C₄×D₄	—	14	1	no	—
349	C₄×D₄	—	14	1	no	—
350	C₄×D₄	—	14	1	no	—
351	C₄×D₄	C₂²×D₇	1	1	yes	characteristic
352	#117	—	7	1	no	—
353	#117	—	14	1	no	—
354	#117	—	14	1	no	—
355	C₂×C₄²	—	7	1	no	—
356	C₂×C₄²	—	14	1	no	—
357	#107	—	7	1	no	—
358	#107	—	7	1	no	—
359	#106	—	7	1	no	—
360	#106	C₄×D₇	1	1	yes	characteristic
361	C₄⋊C₈	—	2	1	no	—
362	C₄⋊C₈	—	7	1	no	—
363	C₄⋊C₈	—	7	1	no	—
364	C₄⋊C₈	—	7	1	no	—
365	C₄⋊C₈	—	7	1	no	—
366	C₄⋊C₈	—	14	1	no	—
367	C₄⋊C₈	—	14	1	no	—
368	C₄⋊C₈	—	14	1	no	—
369	C₄⋊C₈	—	14	1	no	—
370	C₄⋊C₈	C₂²×D₇	1	1	yes	characteristic
371	C₄⋊C₈	C₂²×D₇	1	1	yes	characteristic
372	#103	—	7	1	no	—
373	#103	—	7	1	no	—
374	#103	—	7	1	no	—
375	#103	C₄×D₇	1	1	yes	characteristic
376	#102	—	7	1	no	—
377	#102	—	7	1	no	—
378	#102	—	7	1	no	—
379	#102	C₄×D₇	1	1	yes	characteristic
380	C₂²⋊C₈	—	2	1	no	—
381	C₂²⋊C₈	—	7	1	no	—
382	C₂²⋊C₈	—	7	1	no	—
383	C₂²⋊C₈	—	14	1	no	—
384	C₂²⋊C₈	—	14	1	no	—
385	C₂²⋊C₈	—	14	1	no	—
386	C₂²⋊C₈	—	14	1	no	—
387	C₂²⋊C₈	—	14	1	no	—
388	C₂²⋊C₈	—	14	1	no	—
389	#97	—	2	1	no	—
390	#97	—	14	1	no	—
391	C₄×C₈	—	7	1	no	—
392	C₄×C₈	—	7	1	no	—
393	C₄×C₈	—	7	1	no	—
394	C₄×C₈	—	7	1	no	—
395	C₄×C₈	—	7	1	no	—
396	C₄×C₈	—	14	1	no	—
397	C₄×C₈	—	14	1	no	—
398	C₄×C₈	—	14	1	no	—
399	C₄×C₈	—	14	1	no	—
400	C₄×C₈	C₂²×D₇	1	1	yes	characteristic
401	C₄×C₈	C₂²×D₇	1	1	yes	characteristic
402	C₄×C₈	C₂²×D₇	1	1	yes	characteristic
403	C₂²×C₇	—	2	2	no	—
404	C₂²×C₇	—	4	1	no	—
405	C₂²×C₇	—	4	1	no	—
406	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
407	C₂×D₇	—	2	1	no	—
408	C₂×D₇	—	2	1	no	—
409	C₂×D₇	—	2	1	no	—
410	C₂×D₇	—	4	1	no	—
411	C₂×D₇	—	4	1	no	—
412	C₂×D₇	—	4	1	no	—
413	C₄×C₇	—	2	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	C₂×#131	1	1	yes	characteristic
419	C₄×C₇	C₂×#135	1	1	yes	characteristic
420	C₄×C₇	C₂×#135	1	1	yes	characteristic
421	Dic₇	—	2	2	no	—
422	Dic₇	—	2	1	no	—
423	Dic₇	—	2	1	no	—
424	Dic₇	—	2	1	no	—
425	Dic₇	—	4	1	no	—
426	Dic₇	—	4	1	no	—
427	#41	—	14	2	no	—
428	#41	—	14	2	no	—
429	C₂×Q₈	—	7	1	no	—
430	C₂×Q₈	C₂×C₄×D₇	1	1	yes	characteristic
431	C₂×D₄	—	7	1	no	—
432	C₂×D₄	—	14	1	no	—
433	C₂×D₄	—	14	1	no	—
434	C₂×D₄	C₂×C₄×D₇	1	1	yes	characteristic
435	C₂²×C₄	—	2	1	no	—
436	C₂²×C₄	—	7	1	no	—
437	C₂²×C₄	—	7	1	no	—
438	C₂²×C₄	—	7	1	no	—
439	C₂²×C₄	—	14	1	no	—
440	C₂²×C₄	—	14	1	no	—
441	C₂²×C₄	—	14	1	no	—
442	Q₁₆	—	14	2	no	—
443	SD₁₆	—	2	2	no	—
444	SD₁₆	—	14	2	no	—
445	D₈	—	14	2	no	—
446	M₁₆	—	28	2	no	—
447	C₂×C₈	—	2	1	no	—
448	C₂×C₈	—	2	1	no	—
449	C₂×C₈	—	2	1	no	—
450	C₂×C₈	—	4	2	no	—
451	C₂×C₈	—	7	1	no	—
452	C₂×C₈	—	7	1	no	—
453	C₂×C₈	—	7	1	no	—
454	C₂×C₈	—	7	1	no	—
455	C₂×C₈	—	14	2	no	—
456	C₂×C₈	—	14	2	no	—
457	C₂×C₈	—	14	1	no	—
458	C₂×C₈	—	14	1	no	—
459	C₂×C₈	—	14	1	no	—
460	C₂×C₈	—	28	2	no	—
461	C₂×C₈	—	28	2	no	—
462	C₂×C₈	C₂×C₄×D₇	1	1	yes	characteristic
463	C₂×C₈	C₂×C₄×D₇	1	1	yes	characteristic
464	C₂×C₈	D₄×D₇	1	1	yes	characteristic
465	C₂×C₈	D₄×D₇	1	1	yes	characteristic
466	C₄⋊C₄	—	2	1	no	—
467	C₄⋊C₄	—	7	1	no	—
468	C₄⋊C₄	—	7	1	no	—
469	C₄⋊C₄	—	14	1	no	—
470	C₄⋊C₄	—	14	1	no	—
471	C₄⋊C₄	—	14	1	no	—
472	C₄⋊C₄	—	14	1	no	—
473	C₄⋊C₄	—	14	1	no	—
474	C₄⋊C₄	C₂×C₄×D₇	1	1	yes	characteristic
475	C₄⋊C₄	C₂×C₄×D₇	1	1	yes	characteristic
476	C₂²⋊C₄	—	2	1	no	—
477	C₂²⋊C₄	—	14	1	no	—
478	C₂²⋊C₄	—	14	1	no	—
479	C₂²⋊C₄	—	14	1	no	—
480	C₂²⋊C₄	—	14	1	no	—
481	C₂²⋊C₄	—	14	1	no	—
482	C₂²⋊C₄	—	14	1	no	—
483	C₂²⋊C₄	—	14	1	no	—
484	C₄²	—	2	1	no	—
485	C₄²	—	7	1	no	—
486	C₄²	—	7	1	no	—
487	C₄²	—	7	1	no	—
488	C₄²	—	14	1	no	—
489	C₄²	—	14	1	no	—
490	C₄²	—	14	1	no	—
491	C₄²	C₂³×D₇	1	1	yes	characteristic
492	C₂×C₇	—	4	2	no	—
493	C₂×C₇	#2929	1	1	yes	characteristic
494	C₂×C₇	C₄×#135	1	1	yes	characteristic
495	C₂×C₇	#2955	1	1	yes	characteristic
496	D₇	—	4	1	no	—
497	D₇	—	8	1	no	—
498	C₂³	—	2	1	no	—
499	C₂³	—	7	1	no	—
500	C₂³	—	14	1	no	—
501	Q₈	—	2	1	no	—
502	Q₈	—	2	1	no	—
503	Q₈	—	7	2	no	—
504	Q₈	—	14	1	no	—
505	D₄	—	2	1	no	—
506	D₄	—	14	4	no	—
507	D₄	—	14	1	no	—
508	D₄	—	14	1	no	—
509	D₄	—	28	2	no	—
510	D₄	#6470	1	2	yes	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	4	1	no	—
515	C₂×C₄	—	4	1	no	—
516	C₂×C₄	—	7	1	no	—
517	C₂×C₄	—	7	1	no	—
518	C₂×C₄	—	7	1	no	—
519	C₂×C₄	—	14	4	no	—
520	C₂×C₄	—	14	1	no	—
521	C₂×C₄	—	14	1	no	—
522	C₂×C₄	—	14	1	no	—
523	C₂×C₄	—	14	1	no	—
524	C₂×C₄	—	14	1	no	—
525	C₂×C₄	—	14	1	no	—
526	C₂×C₄	—	14	1	no	—
527	C₂×C₄	—	28	1	no	—
528	C₂×C₄	—	28	2	no	—
529	C₂×C₄	—	28	1	no	—
530	C₂×C₄	—	28	1	no	—
531	C₂×C₄	C₂²×C₄×D₇	1	1	yes	characteristic
532	C₂×C₄	C₂×D₄×D₇	1	1	yes	characteristic
533	C₂×C₄	D₇×#41	1	1	yes	characteristic
534	C₈	—	2	1	no	—
535	C₈	—	2	1	no	—
536	C₈	—	2	1	no	—
537	C₈	—	4	1	no	—
538	C₈	—	4	1	no	—
539	C₈	—	4	1	no	—
540	C₈	—	7	2	no	—
541	C₈	—	14	1	no	—
542	C₈	—	14	1	no	—
543	C₈	—	14	1	no	—
544	C₈	—	28	1	no	—
545	C₈	—	28	1	no	—
546	C₈	—	28	1	no	—
547	C₈	#6479	1	2	yes	—
548	C₇	#17904	1	1	yes	characteristic, complemented, Sylow
549	C₂²	—	2	2	no	—
550	C₂²	—	4	1	no	—
551	C₂²	—	4	1	no	—
552	C₂²	—	14	1	no	—
553	C₂²	—	14	1	no	—
554	C₂²	—	14	1	no	—
555	C₂²	—	28	1	no	—
556	C₂²	—	28	1	no	—
557	C₂²	—	28	1	no	—
558	C₂²	C₄×D₄×D₇	1	1	yes	characteristic
559	C₄	—	2	1	no	—
560	C₄	—	4	1	no	—
561	C₄	—	4	1	no	—
562	C₄	—	4	1	no	—
563	C₄	—	14	1	no	—
564	C₄	—	14	1	no	—
565	C₄	—	14	2	no	—
566	C₄	—	14	1	no	—
567	C₄	—	28	1	no	—
568	C₄	—	28	1	no	—
569	C₄	C₂×#6470	1	1	yes	characteristic
570	C₄	D₇×#131	1	1	yes	characteristic
571	C₄	C₂×#6479	1	1	yes	characteristic
572	C₄	D₇×#135	1	1	yes	characteristic
573	C₂	—	4	2	no	—
574	C₂	—	28	1	no	—
575	C₂	—	56	1	no	—
576	C₂	#11736923	1	1	yes	characteristic
577	C₂	C₄×#6479	1	1	yes	characteristic
578	C₂	#11737342	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×#1582	C₂
socle	C₂²×C₇	C₂×C₄×D₄
prime radical	#89553	C₄
cosocle	C₄²×C₇	C₂⁴
hypercenter	#1582	D₇
hypocenter	C₇	#17904
LCS	G ▷ C₂×C₄×C₇ ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #1582

Complements

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

N	H ≅ G/N	type
1. #11737384	C₂	semidirect
3. C₈×#1159	C₂	semidirect
4. C₇×#1582	C₂	semidirect
5. #11728710	C₂	semidirect
6. SD₁₆×C₇⋊C₈	C₂	semidirect
7. #11728595	C₂	semidirect
8. #11726287	C₂	semidirect
9. #11726270	C₂	semidirect
10. #11725987	C₂	semidirect
11. #11725967	C₂	semidirect
12. #11725927	C₂	semidirect
13. #11725902	C₂	semidirect
14. #11725839	C₂	semidirect
15. #11725822	C₂	semidirect
150. #1582	D₇	semidirect
548. C₇	#17904	semidirect

Maximal subgroups

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

subgroup	index
#11737384	2
#11737097	2
C₈×#1159	2
C₇×#1582	2
#11728710	2
SD₁₆×C₇⋊C₈	2
#11728595	2
#11726287	2
#11726270	2
#11725987	2
#11725967	2
#11725927	2
#11725902	2
#11725839	2
#11725822	2
#17904	7