Subgroups — #13507318

Order 1792.

558 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×#1157	C₂	1	1	yes	maximal, characteristic
2	C₄×C₇×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	#11729187	C₂	1	2	yes	maximal, complemented
4	#11729184	C₂	1	2	yes	maximal, complemented
5	#11727498	C₂	1	1	yes	maximal, characteristic, complemented
6	#11726829	C₂	1	2	yes	maximal, complemented
7	#11726822	C₂	1	2	yes	maximal, complemented
8	#11726806	C₂	1	1	yes	maximal, characteristic, complemented
9	#11726806	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×#6372	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×D₇×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×#1157	C₄	1	1	yes	characteristic
13	C₂×C₇×M₃₂	C₂²	1	2	yes	—
14	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
15	C₈×C₂²⋊D₇	C₄	1	1	yes	characteristic
16	C₈×C₂²⋊D₇	C₄	1	1	yes	characteristic
17	C₈×C₂²⋊D₇	C₂²	1	1	yes	characteristic
18	C₈×C₂²⋊D₇	C₂²	1	1	yes	characteristic
19	#89697	C₄	1	1	yes	characteristic
20	C₂×#6372	C₂²	1	2	yes	—
21	C₂×D₇×C₁₆	C₂²	1	2	yes	—
22	C₈×D₂₈	C₄	1	1	yes	characteristic
23	C₈×D₂₈	C₂²	1	1	yes	characteristic
24	#89457	C₄	1	1	yes	characteristic
25	#89457	C₄	1	1	yes	characteristic
26	C₄×C₈×D₇	C₂²	1	1	yes	characteristic
27	C₄×C₈×D₇	C₂²	1	1	yes	characteristic
28	C₈×Dic₁₄	C₄	1	1	yes	characteristic
29	C₈×Dic₁₄	C₂²	1	1	yes	characteristic
30	C₇×#346	C₂²	1	2	yes	—
31	C₄×C₇×C₁₆	C₂²	1	1	yes	characteristic
32	C₄×C₇×C₁₆	C₂²	1	1	yes	characteristic
33	C₂²⋊(C₇⋊C₁₆)	C₂²	1	2	yes	—
34	(C₂×D₇)⋊C₁₆	C₂²	1	2	yes	—
35	(C₂×D₇)⋊C₁₆	C₂²	1	2	yes	—
36	#89297	C₂²	1	2	yes	—
37	Dic₇⋊C₁₆	C₂²	1	2	yes	—
38	Dic₇⋊C₁₆	C₂²	1	2	yes	—
39	C₁₆×Dic₇	C₂²	1	2	yes	—
40	C₄⋊(C₇⋊C₁₆)	C₂²	1	2	yes	—
41	C₄×C₇⋊C₁₆	C₂²	1	1	yes	characteristic
42	C₄×C₇⋊C₁₆	C₂²	1	1	yes	characteristic
43	#33479	—	7	1	no	maximal, Sylow
44	C₂×#1157	C₈	1	1	yes	characteristic
45	C₂²×C₇×C₈	C₂×C₄	1	1	yes	characteristic
46	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
47	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
48	C₄×C₂²⋊D₇	C₈	1	1	yes	characteristic
49	C₄×C₂²⋊D₇	C₈	1	1	yes	characteristic
50	C₄×C₂²⋊D₇	C₂×C₄	1	1	yes	characteristic
51	C₄×C₂²⋊D₇	C₂×C₄	1	1	yes	characteristic
52	#6489	C₈	1	1	yes	characteristic
53	C₂×C₈×D₇	C₂×C₄	1	1	yes	characteristic
54	C₂×C₈×D₇	C₂×C₄	1	1	yes	characteristic
55	C₂×C₈×D₇	C₂³	1	1	yes	characteristic
56	C₂×C₈×D₇	C₂³	1	1	yes	characteristic
57	C₄×D₂₈	C₈	1	1	yes	characteristic
58	C₄×D₂₈	C₂×C₄	1	1	yes	characteristic
59	#6435	C₈	1	1	yes	characteristic
60	#6435	C₈	1	1	yes	characteristic
61	C₄²×D₇	C₂×C₄	1	1	yes	characteristic
62	C₄²×D₇	C₂×C₄	1	1	yes	characteristic
63	C₄×Dic₁₄	C₈	1	1	yes	characteristic
64	C₄×Dic₁₄	C₂×C₄	1	1	yes	characteristic
65	C₇×M₃₂	—	2	4	no	—
66	C₂×C₇×C₁₆	C₂³	1	2	yes	—
67	C₂×C₇×C₁₆	C₂³	1	2	yes	—
68	C₄×C₇×C₈	C₂×C₄	1	1	yes	characteristic
69	C₄×C₇×C₈	C₂×C₄	1	1	yes	characteristic
70	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
71	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
72	C₂²⋊(C₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
73	C₂²⋊(C₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
74	(C₂×D₇)⋊C₈	C₂×C₄	1	1	yes	characteristic
75	(C₂×D₇)⋊C₈	C₂×C₄	1	1	yes	characteristic
76	(C₂×D₇)⋊C₈	C₂×C₄	1	1	yes	characteristic
77	(C₂×D₇)⋊C₈	C₂×C₄	1	1	yes	characteristic
78	Dic₇⋊C₈	C₂×C₄	1	1	yes	characteristic
79	Dic₇⋊C₈	C₂×C₄	1	1	yes	characteristic
80	Dic₇⋊C₈	C₂×C₄	1	1	yes	characteristic
81	Dic₇⋊C₈	C₂×C₄	1	1	yes	characteristic
82	C₈×Dic₇	C₂×C₄	1	1	yes	characteristic
83	C₈×Dic₇	C₂×C₄	1	1	yes	characteristic
84	C₈×Dic₇	C₂³	1	1	yes	characteristic
85	C₈×Dic₇	C₂³	1	1	yes	characteristic
86	C₂×C₇⋊C₁₆	C₂³	1	2	yes	—
87	C₂×C₇⋊C₁₆	C₂³	1	2	yes	—
88	C₄⋊(C₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
89	C₄⋊(C₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
90	C₄×C₇⋊C₈	C₂×C₄	1	1	yes	characteristic
91	C₄×C₇⋊C₈	C₂×C₄	1	1	yes	characteristic
92	#6372	—	2	4	no	—
93	D₇×C₁₆	—	2	4	no	—
94	C₈×#41	—	7	1	no	—
95	#2183	—	7	2	no	—
96	#2169	—	7	2	no	—
97	#2168	—	7	2	no	—
98	#2168	—	7	2	no	—
99	#2162	—	7	1	no	—
100	#2162	—	7	1	no	—
101	#2162	—	7	1	no	—
102	C₄×M₃₂	—	7	1	no	—
103	C₄×M₃₂	D₇	1	1	yes	characteristic, complemented
104	C₂×C₄×C₁₆	—	7	1	no	—
105	C₂²×C₄×C₇	C₂×C₈	1	1	yes	characteristic
106	C₂²×C₄×C₇	C₂×C₈	1	1	yes	characteristic
107	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
108	C₂×C₂²⋊D₇	C₂×C₈	1	1	yes	characteristic
109	C₂×C₂²⋊D₇	C₂×C₈	1	1	yes	characteristic
110	#1157	—	2	4	no	—
111	C₂×D₂₈	C₂×C₈	1	1	yes	characteristic
112	C₂×C₄×D₇	C₂×C₈	1	1	yes	characteristic
113	C₂×C₄×D₇	C₂×C₈	1	1	yes	characteristic
114	C₂×C₄×D₇	C₂×C₈	1	1	yes	characteristic
115	C₂×C₄×D₇	C₂×C₈	1	1	yes	characteristic
116	C₂×C₄×D₇	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₄×D₇	C₂²×C₄	1	1	yes	characteristic
118	C₂×Dic₁₄	C₂×C₈	1	1	yes	characteristic
119	C₂×C₇×C₈	—	2	2	no	—
120	C₂×C₇×C₈	—	2	2	no	—
121	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
122	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
123	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
124	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
125	C₄²×C₇	C₂×C₈	1	1	yes	characteristic
126	C₄²×C₇	C₂×C₈	1	1	yes	characteristic
127	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
128	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
129	C₂²⋊Dic₇	C₂×C₈	1	1	yes	characteristic
130	C₂²⋊Dic₇	C₂×C₈	1	1	yes	characteristic
131	(C₂×D₇)⋊C₄	C₂×C₈	1	1	yes	characteristic
132	(C₂×D₇)⋊C₄	C₂×C₈	1	1	yes	characteristic
133	(C₂×D₇)⋊C₄	C₂×C₈	1	1	yes	characteristic
134	(C₂×D₇)⋊C₄	C₂×C₈	1	1	yes	characteristic
135	C₄⋊Dic₇	C₂×C₈	1	1	yes	characteristic
136	C₄⋊Dic₇	C₂×C₈	1	1	yes	characteristic
137	Dic₇⋊C₄	C₂×C₈	1	1	yes	characteristic
138	Dic₇⋊C₄	C₂×C₈	1	1	yes	characteristic
139	Dic₇⋊C₄	C₂×C₈	1	1	yes	characteristic
140	Dic₇⋊C₄	C₂×C₈	1	1	yes	characteristic
141	C₄×Dic₇	C₂×C₈	1	1	yes	characteristic
142	C₄×Dic₇	C₂×C₈	1	1	yes	characteristic
143	C₄×Dic₇	C₂×C₈	1	1	yes	characteristic
144	C₄×Dic₇	C₂×C₈	1	1	yes	characteristic
145	C₄×Dic₇	C₂²×C₄	1	1	yes	characteristic
146	C₄×Dic₇	C₂²×C₄	1	1	yes	characteristic
147	C₂×C₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
148	C₂×C₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
149	C₂×C₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
150	C₂×C₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
151	C₈×D₇	—	2	2	no	—
152	C₈×D₇	—	2	2	no	—
153	C₈×D₇	—	2	2	no	—
154	C₈×D₇	—	2	2	no	—
155	C₇×C₁₆	—	2	2	no	—
156	C₇×C₁₆	#41	1	4	yes	complemented
157	C₇⋊C₁₆	—	2	2	no	—
158	C₇⋊C₁₆	—	2	2	no	—
159	C₄×#41	—	7	1	no	—
160	C₂×M₃₂	—	7	2	no	—
161	C₂×M₃₂	C₂×D₇	1	2	yes	—
162	C₂²×C₁₆	—	7	2	no	—
163	C₈×Q₈	—	7	1	no	—
164	C₈×Q₈	—	7	1	no	—
165	C₈×D₄	—	7	1	no	—
166	C₈×D₄	—	7	1	no	—
167	C₈×D₄	—	7	1	no	—
168	C₈×D₄	—	7	1	no	—
169	C₈×D₄	—	7	1	no	—
170	C₈×D₄	—	7	1	no	—
171	#431	—	7	1	no	—
172	#431	—	7	1	no	—
173	#431	—	7	1	no	—
174	C₂×C₄×C₈	—	7	1	no	—
175	C₂×C₄×C₈	—	7	1	no	—
176	C₂×C₄×C₈	C₂×D₇	1	1	yes	characteristic
177	C₄⋊C₁₆	—	7	2	no	—
178	C₄⋊C₁₆	—	7	2	no	—
179	C₄⋊C₁₆	—	7	2	no	—
180	C₂²⋊C₁₆	—	7	2	no	—
181	C₂²⋊C₁₆	—	7	2	no	—
182	C₂²⋊C₁₆	—	7	2	no	—
183	#346	—	7	2	no	—
184	#346	C₂×D₇	1	2	yes	—
185	C₄×C₁₆	—	7	2	no	—
186	C₄×C₁₆	—	7	1	no	—
187	C₄×C₁₆	—	7	1	no	—
188	C₄×C₁₆	C₂×D₇	1	1	yes	characteristic
189	C₄×C₁₆	C₂×D₇	1	1	yes	characteristic
190	C₂³×C₇	C₂²×C₈	1	1	yes	characteristic
191	C₂²×D₇	C₂²×C₈	1	1	yes	characteristic
192	C₂²×D₇	C₂²×C₈	1	1	yes	characteristic
193	C₂×C₄×C₇	—	2	1	no	—
194	C₂×C₄×C₇	—	2	1	no	—
195	C₂×C₄×C₇	—	2	2	no	—
196	C₂×C₄×C₇	—	2	2	no	—
197	C₂×C₄×C₇	C₂²×C₈	1	1	yes	characteristic
198	C₂×C₄×C₇	C₂²×C₈	1	1	yes	characteristic
199	C₂×C₄×C₇	C₂²×C₈	1	1	yes	characteristic
200	C₂×C₄×C₇	C₂²×C₈	1	1	yes	characteristic
201	C₂×C₄×C₇	C₂²×C₈	1	1	yes	characteristic
202	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
203	C₂²⋊D₇	—	2	2	no	—
204	C₂²⋊D₇	—	2	2	no	—
205	C₂×Dic₇	C₂²×C₈	1	1	yes	characteristic
206	C₂×Dic₇	C₂²×C₈	1	1	yes	characteristic
207	C₂×Dic₇	C₂²×C₈	1	1	yes	characteristic
208	C₂×Dic₇	C₂²×C₈	1	1	yes	characteristic
209	C₂×Dic₇	C₂²×C₈	1	1	yes	characteristic
210	C₂×Dic₇	C₂²×C₈	1	1	yes	characteristic
211	D₂₈	—	2	2	no	—
212	C₄×D₇	—	2	1	no	—
213	C₄×D₇	—	2	1	no	—
214	C₄×D₇	—	2	1	no	—
215	C₄×D₇	—	2	1	no	—
216	C₄×D₇	—	2	2	no	—
217	C₄×D₇	—	2	2	no	—
218	C₄×D₇	—	2	2	no	—
219	C₄×D₇	M₃₂	1	4	yes	complemented
220	Dic₁₄	—	2	2	no	—
221	C₇×C₈	—	2	1	no	—
222	C₇×C₈	—	2	1	no	—
223	C₇×C₈	#131	1	2	yes	—
224	C₇×C₈	C₂×#41	1	2	yes	—
225	C₇⋊C₈	—	2	1	no	—
226	C₇⋊C₈	—	2	1	no	—
227	C₇⋊C₈	—	2	1	no	—
228	C₇⋊C₈	—	2	1	no	—
229	C₂×#41	—	7	1	no	—
230	C₂²×C₈	—	7	1	no	—
231	C₂²×C₈	—	7	1	no	—
232	C₂²×C₈	—	7	1	no	—
233	C₂²×C₈	—	7	1	no	—
234	C₂²×C₈	C₄×D₇	1	1	yes	characteristic
235	C₂²×C₈	C₂²×D₇	1	1	yes	characteristic
236	C₄×Q₈	—	7	1	no	—
237	C₄×Q₈	—	7	1	no	—
238	C₄×D₄	—	7	1	no	—
239	C₄×D₄	—	7	1	no	—
240	C₄×D₄	—	7	1	no	—
241	C₄×D₄	—	7	1	no	—
242	C₄×D₄	—	7	1	no	—
243	C₄×D₄	—	7	1	no	—
244	#117	—	7	1	no	—
245	#117	—	7	1	no	—
246	#117	—	7	1	no	—
247	C₂×C₄²	—	7	1	no	—
248	C₂×C₄²	—	7	1	no	—
249	C₂×C₄²	C₄×D₇	1	1	yes	characteristic
250	M₃₂	—	2	4	no	—
251	M₃₂	—	14	4	no	—
252	C₂×C₁₆	—	7	2	no	—
253	C₂×C₁₆	—	7	2	no	—
254	C₂×C₁₆	—	14	4	no	—
255	C₂×C₁₆	C₂²×D₇	1	2	yes	—
256	C₂×C₁₆	C₂²×D₇	1	2	yes	—
257	C₄⋊C₈	—	7	1	no	—
258	C₄⋊C₈	—	7	1	no	—
259	C₄⋊C₈	—	7	1	no	—
260	C₄⋊C₈	—	7	1	no	—
261	C₄⋊C₈	—	7	1	no	—
262	C₄⋊C₈	—	7	1	no	—
263	C₂²⋊C₈	—	7	1	no	—
264	C₂²⋊C₈	—	7	1	no	—
265	C₂²⋊C₈	—	7	1	no	—
266	C₂²⋊C₈	—	7	1	no	—
267	C₂²⋊C₈	—	7	1	no	—
268	C₂²⋊C₈	—	7	1	no	—
269	C₄×C₈	—	7	1	no	—
270	C₄×C₈	—	7	1	no	—
271	C₄×C₈	—	7	1	no	—
272	C₄×C₈	—	7	1	no	—
273	C₄×C₈	—	7	1	no	—
274	C₄×C₈	—	7	1	no	—
275	C₄×C₈	C₄×D₇	1	1	yes	characteristic
276	C₄×C₈	C₄×D₇	1	1	yes	characteristic
277	C₄×C₈	C₂²×D₇	1	1	yes	characteristic
278	C₄×C₈	C₂²×D₇	1	1	yes	characteristic
279	C₂²×C₇	—	2	1	no	—
280	C₂²×C₇	—	2	1	no	—
281	C₂²×C₇	—	2	1	no	—
282	C₂²×C₇	C₂³×C₈	1	1	yes	characteristic
283	C₂×D₇	—	2	1	no	—
284	C₂×D₇	—	2	1	no	—
285	C₂×D₇	—	2	1	no	—
286	C₂×D₇	—	2	1	no	—
287	C₂×D₇	—	2	1	no	—
288	C₂×D₇	C₂×M₃₂	1	2	yes	—
289	C₄×C₇	—	2	1	no	—
290	C₄×C₇	—	2	1	no	—
291	C₄×C₇	—	2	1	no	—
292	C₄×C₇	C₂×M₃₂	1	2	yes	—
293	C₄×C₇	#504	1	2	yes	—
294	C₄×C₇	C₄×#41	1	1	yes	characteristic
295	C₄×C₇	C₂×#131	1	1	yes	characteristic
296	Dic₇	—	2	1	no	—
297	Dic₇	—	2	1	no	—
298	Dic₇	—	2	1	no	—
299	Dic₇	—	2	1	no	—
300	Dic₇	—	2	1	no	—
301	Dic₇	C₂×M₃₂	1	2	yes	—
302	#41	—	14	4	no	—
303	C₂×Q₈	—	7	1	no	—
304	C₂×D₄	—	7	1	no	—
305	C₂×D₄	—	7	1	no	—
306	C₂×D₄	—	7	1	no	—
307	C₂²×C₄	—	7	1	no	—
308	C₂²×C₄	—	7	1	no	—
309	C₂²×C₄	—	7	1	no	—
310	C₂²×C₄	—	7	1	no	—
311	C₂²×C₄	—	7	1	no	—
312	C₂²×C₄	—	7	1	no	—
313	C₂²×C₄	C₈×D₇	1	1	yes	characteristic
314	C₂²×C₄	C₈×D₇	1	1	yes	characteristic
315	C₂²×C₄	C₂×C₄×D₇	1	1	yes	characteristic
316	C₂×C₈	—	2	2	no	—
317	C₂×C₈	—	2	2	no	—
318	C₂×C₈	—	7	1	no	—
319	C₂×C₈	—	7	1	no	—
320	C₂×C₈	—	7	1	no	—
321	C₂×C₈	—	7	1	no	—
322	C₂×C₈	—	14	2	no	—
323	C₂×C₈	—	14	2	no	—
324	C₂×C₈	—	14	2	no	—
325	C₂×C₈	—	14	2	no	—
326	C₂×C₈	C₂×C₄×D₇	1	1	yes	characteristic
327	C₂×C₈	C₂×C₄×D₇	1	1	yes	characteristic
328	C₂×C₈	C₂×C₄×D₇	1	1	yes	characteristic
329	C₂×C₈	C₂³×D₇	1	1	yes	characteristic
330	C₄⋊C₄	—	7	1	no	—
331	C₄⋊C₄	—	7	1	no	—
332	C₄⋊C₄	—	7	1	no	—
333	C₄⋊C₄	—	7	1	no	—
334	C₄⋊C₄	—	7	1	no	—
335	C₄⋊C₄	—	7	1	no	—
336	C₂²⋊C₄	—	7	1	no	—
337	C₂²⋊C₄	—	7	1	no	—
338	C₂²⋊C₄	—	7	1	no	—
339	C₂²⋊C₄	—	7	1	no	—
340	C₂²⋊C₄	—	7	1	no	—
341	C₂²⋊C₄	—	7	1	no	—
342	C₄²	—	7	1	no	—
343	C₄²	—	7	1	no	—
344	C₄²	—	7	1	no	—
345	C₄²	—	7	1	no	—
346	C₄²	—	7	1	no	—
347	C₄²	—	7	1	no	—
348	C₄²	C₈×D₇	1	1	yes	characteristic
349	C₄²	C₈×D₇	1	1	yes	characteristic
350	C₄²	C₂×C₄×D₇	1	1	yes	characteristic
351	C₄²	C₂×C₄×D₇	1	1	yes	characteristic
352	C₁₆	—	2	2	no	—
353	C₁₆	—	14	2	no	—
354	C₁₆	—	14	2	no	—
355	C₁₆	#1157	1	4	yes	complemented
356	C₂×C₇	—	4	1	no	—
357	C₂×C₇	C₈×#41	1	1	yes	characteristic
358	C₂×C₇	C₂²×M₃₂	1	1	yes	characteristic
359	C₂×C₇	C₂×#504	1	1	yes	characteristic
360	D₇	—	2	2	no	—
361	D₇	—	4	1	no	—
362	C₂³	—	7	1	no	—
363	C₂³	—	7	1	no	—
364	C₂³	C₂×C₈×D₇	1	1	yes	characteristic
365	Q₈	—	14	2	no	—
366	D₄	—	14	2	no	—
367	D₄	—	14	2	no	—
368	D₄	—	14	2	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	7	1	no	—
374	C₂×C₄	—	7	4	no	—
375	C₂×C₄	—	7	1	no	—
376	C₂×C₄	—	7	1	no	—
377	C₂×C₄	—	7	1	no	—
378	C₂×C₄	—	7	1	no	—
379	C₂×C₄	—	7	1	no	—
380	C₂×C₄	—	14	1	no	—
381	C₂×C₄	—	14	1	no	—
382	C₂×C₄	—	14	1	no	—
383	C₂×C₄	—	14	1	no	—
384	C₂×C₄	—	14	2	no	—
385	C₂×C₄	—	14	2	no	—
386	C₂×C₄	—	14	2	no	—
387	C₂×C₄	C₂×C₈×D₇	1	1	yes	characteristic
388	C₂×C₄	C₂×C₈×D₇	1	1	yes	characteristic
389	C₂×C₄	C₂×C₈×D₇	1	1	yes	characteristic
390	C₂×C₄	C₂×C₈×D₇	1	1	yes	characteristic
391	C₂×C₄	C₂×C₈×D₇	1	1	yes	characteristic
392	C₂×C₄	C₂²×C₄×D₇	1	1	yes	characteristic
393	C₈	—	2	1	no	—
394	C₈	—	2	1	no	—
395	C₈	—	14	1	no	—
396	C₈	—	14	1	no	—
397	C₈	—	14	1	no	—
398	C₈	—	14	1	no	—
399	C₈	#6464	1	2	yes	—
400	C₈	C₂×#1157	1	2	yes	—
401	C₇	#33479	1	1	yes	characteristic, complemented, Sylow
402	C₂²	—	2	1	no	—
403	C₂²	—	2	1	no	—
404	C₂²	—	2	1	no	—
405	C₂²	—	7	2	no	—
406	C₂²	—	14	1	no	—
407	C₂²	—	14	1	no	—
408	C₂²	—	14	1	no	—
409	C₂²	—	14	1	no	—
410	C₂²	—	14	1	no	—
411	C₂²	C₂²×C₈×D₇	1	1	yes	characteristic
412	C₄	—	2	1	no	—
413	C₄	—	2	1	no	—
414	C₄	—	2	1	no	—
415	C₄	—	7	2	no	—
416	C₄	—	14	1	no	—
417	C₄	—	14	1	no	—
418	C₄	—	14	1	no	—
419	C₄	—	14	1	no	—
420	C₄	—	14	1	no	—
421	C₄	D₇×M₃₂	1	2	yes	—
422	C₄	#89679	1	2	yes	—
423	C₄	C₄×#1157	1	1	yes	characteristic
424	C₄	C₂×#6464	1	1	yes	characteristic
425	C₂	—	4	1	no	—
426	C₂	—	14	2	no	—
427	C₂	—	28	1	no	—
428	C₂	C₈×#1157	1	1	yes	characteristic
429	C₂	C₂×D₇×M₃₂	1	1	yes	characteristic
430	C₂	C₂×#89679	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₈	C₂²×D₇
commutator, socle	C₂²×C₇	C₂³×C₈
Frattini	C₂×C₈	C₂³×D₇
Fitting	C₄×C₇×M₃₂	C₂
prime radical	C₂×#1157	C₈
cosocle	C₂×C₇×C₈	C₂⁴
hypercenter	C₄×M₃₂	D₇
hypocenter	C₇	#33479
LCS	G ▷ C₂²×C₇ ▷ C₇
UCS	C₁ ◁ C₄×C₈ ◁ C₄×M₃₂

Complements

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

N	H ≅ G/N	type
2. C₄×C₇×M₃₂	C₂	semidirect
3. #11729187	C₂	semidirect
4. #11729184	C₂	semidirect
5. #11727498	C₂	semidirect
6. #11726829	C₂	semidirect
7. #11726822	C₂	semidirect
8. #11726806	C₂	semidirect
9. #11726806	C₂	semidirect
10. C₄×#6372	C₂	semidirect
11. C₄×D₇×C₁₆	C₂	semidirect
103. C₄×M₃₂	D₇	semidirect
156. C₇×C₁₆	#41	semidirect
219. C₄×D₇	M₃₂	semidirect
355. C₁₆	#1157	semidirect
401. C₇	#33479	semidirect

Maximal subgroups

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

subgroup	index
C₈×#1157	2
C₄×C₇×M₃₂	2
#11729187	2
#11729184	2
#11727498	2
#11726829	2
#11726822	2
#11726806	2
C₄×#6372	2
C₄×D₇×C₁₆	2
#33479	7