Subgroups — #72234308

Order 8192.

1808 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72234305	C₂	1	2	yes	maximal
2	#72234301	C₄	1	8	yes	—
3	#72234298	C₂	1	2	yes	maximal
4	#72234295	C₄	1	4	yes	—
5	#72234292	C₄	1	4	yes	—
6	#72234291	C₂	1	2	yes	maximal
7	#72234284	C₄	1	4	yes	—
8	#72234283	C₄	1	4	yes	—
9	#72234281	C₂²	1	4	yes	—
10	#72234279	C₂×C₄	1	8	yes	—
11	#72234278	C₂×C₄	1	8	yes	—
12	#72234277	C₂×C₄	1	8	yes	—
13	#72234256	C₂	1	1	yes	maximal, characteristic
14	#72234250	C₄	1	1	yes	characteristic
15	#72234250	C₂²	1	1	yes	characteristic
16	C₂×#93666	C₈	1	4	yes	—
17	C₂×#93666	C₂×C₄	1	4	yes	—
18	#72234246	C₄	1	1	yes	characteristic
19	#72234246	C₂²	1	1	yes	characteristic
20	C₂×#93664	C₈	1	2	yes	—
21	C₂×#93664	C₂×C₄	1	2	yes	—
22	#72234241	C₄	1	1	yes	characteristic
23	#72234237	C₈	1	4	yes	—
24	C₈×#1397	C₂×C₄	1	1	yes	characteristic
25	C₈×#1397	C₂×C₄	1	1	yes	characteristic
26	#72234235	C₄	1	1	yes	characteristic
27	C₄×#7329	C₈	1	2	yes	—
28	C₄×#7329	C₂×C₄	1	1	yes	characteristic
29	#72234231	C₂²	1	1	yes	characteristic
30	#72234227	C₂×C₄	1	2	yes	—
31	#72234226	C₂×C₄	1	1	yes	characteristic
32	#72234226	C₂³	1	1	yes	characteristic
33	#72234224	C₂×C₄	1	1	yes	characteristic
34	#72225071	C₈	1	16	yes	complemented
35	#72225038	C₈	1	8	yes	complemented
36	#72210645	C₂×C₄	1	2	yes	—
37	C₄×C₈×C₃₂	C₈	1	2	yes	—
38	C₄×C₈×C₃₂	C₂×C₄	1	1	yes	characteristic
39	C₂×C₁₆×C₃₂	C₈	1	2	yes	—
40	C₂×C₁₆×C₃₂	C₂×C₄	1	2	yes	—
41	C₃₂²	C₈	1	8	yes	complemented
42	C₄×#1397	C₂×C₈	1	2	yes	—
43	C₄×#1397	C₂×C₈	1	2	yes	—
44	C₄²×C₃₂	C₂×C₈	1	1	yes	characteristic
45	C₄²×C₃₂	C₂×C₈	1	2	yes	—
46	C₄²×C₃₂	C₂×C₈	1	1	yes	characteristic
47	#149510	C₄²	1	16	yes	—
48	C₂×#7329	C₁₆	1	8	yes	—
49	C₂×#7329	C₄²	1	2	yes	—
50	C₂×#7329	C₄²	1	2	yes	—
51	C₂×#7329	C₂×C₈	1	2	yes	—
52	C₂×#7329	C₂×C₈	1	2	yes	—
53	C₂×C₈×C₃₂	C₁₆	1	8	yes	—
54	C₂×C₈×C₃₂	C₄²	1	1	yes	characteristic
55	C₂×C₈×C₃₂	C₄²	1	2	yes	—
56	C₂×C₈×C₃₂	C₄²	1	1	yes	characteristic
57	C₂×C₈×C₃₂	C₂×C₈	1	1	yes	characteristic
58	C₂×C₈×C₃₂	C₂×C₈	1	2	yes	—
59	C₂×C₈×C₃₂	C₂×C₈	1	1	yes	characteristic
60	#126530	C₄²	1	2	yes	—
61	#126530	C₂²×C₄	1	2	yes	—
62	C₄×#1311	C₄²	1	1	yes	characteristic
63	C₄×#1311	C₂×C₈	1	2	yes	—
64	C₄×C₈×C₁₆	C₂×C₈	1	2	yes	—
65	C₄×C₈×C₁₆	C₂²×C₄	1	1	yes	characteristic
66	C₂×#7052	C₂×C₈	1	2	yes	—
67	C₂×#7052	C₂²×C₄	1	2	yes	—
68	C₂×C₁₆²	C₂×C₈	1	2	yes	—
69	C₂×C₁₆²	C₂²×C₄	1	2	yes	—
70	#94852	C₄²	1	1	yes	characteristic
71	#94005	—	2	8	no	—
72	#93998	—	2	8	no	—
73	#93990	—	2	8	no	—
74	#93667	—	2	16	no	—
75	#93666	—	2	8	no	—
76	#93666	—	2	8	no	—
77	#93665	C₂×C₈	1	16	yes	—
78	#93664	C₁₆	1	8	yes	—
79	#93664	C₂×C₈	1	8	yes	—
80	C₁₆×C₃₂	C₁₆	1	8	yes	—
81	C₁₆×C₃₂	C₂×C₈	1	4	yes	—
82	C₁₆×C₃₂	C₂×C₈	1	16	yes	—
83	C₁₆×C₃₂	C₂×C₈	1	4	yes	—
84	#93249	—	2	4	no	—
85	#92896	—	2	4	no	—
86	#13639	—	2	16	no	—
87	C₂×#1397	—	2	4	no	—
88	C₂×#1397	M₃₂	1	8	yes	—
89	C₂×C₄×C₃₂	C₄×C₈	1	4	yes	—
90	C₂×C₄×C₃₂	C₄×C₈	1	4	yes	—
91	C₂×C₄×C₃₂	C₄×C₈	1	1	yes	characteristic
92	C₂×C₄×C₃₂	C₄×C₈	1	1	yes	characteristic
93	C₂×C₄×C₃₂	C₄×C₈	1	1	yes	characteristic
94	C₂×C₄×C₃₂	C₄×C₈	1	4	yes	—
95	C₂×C₄×C₃₂	C₄×C₈	1	1	yes	characteristic
96	C₂×C₄×C₃₂	C₂×C₁₆	1	4	yes	—
97	C₂×C₄×C₃₂	C₂×C₁₆	1	4	yes	—
98	C₂×C₄×C₃₂	C₂×C₁₆	1	4	yes	—
99	C₂×C₄×C₃₂	C₂×C₁₆	1	4	yes	—
100	#12590	—	2	2	no	—
101	#12590	#131	1	4	yes	—
102	C₄²×C₁₆	C₄×C₈	1	2	yes	—
103	C₄²×C₁₆	C₂²×C₈	1	1	yes	characteristic
104	C₄²×C₁₆	C₂²×C₈	1	1	yes	characteristic
105	C₂×#1312	—	2	2	no	—
106	C₂×#1312	#131	1	4	yes	—
107	C₂×#1311	—	2	2	no	—
108	C₂×#1311	—	2	4	no	—
109	C₂×C₈×C₁₆	C₄×C₈	1	4	yes	—
110	C₂×C₈×C₁₆	C₂×C₁₆	1	4	yes	—
111	C₂×C₈×C₁₆	C₂×C₁₆	1	4	yes	—
112	C₂×C₈×C₁₆	C₂×C₄²	1	1	yes	characteristic
113	C₂×C₈×C₁₆	C₂×C₄²	1	4	yes	—
114	C₂×C₈×C₁₆	C₂×C₄²	1	1	yes	characteristic
115	C₂×C₈×C₁₆	C₂²×C₈	1	1	yes	characteristic
116	C₂×C₈×C₁₆	C₂²×C₈	1	1	yes	characteristic
117	#8131	—	2	2	no	—
118	C₄×C₈²	C₄×C₈	1	2	yes	—
119	C₄×C₈²	C₂×C₄²	1	1	yes	characteristic
120	#7331	—	2	16	no	—
121	#7329	—	2	16	no	—
122	#7329	—	2	4	no	—
123	#7329	—	2	4	no	—
124	#7329	—	2	4	no	—
125	#7329	M₃₂	1	8	yes	—
126	C₈×C₃₂	C₃₂	1	32	yes	complemented
127	C₈×C₃₂	C₄×C₈	1	32	yes	—
128	C₈×C₃₂	C₄×C₈	1	2	yes	—
129	C₈×C₃₂	C₄×C₈	1	4	yes	—
130	C₈×C₃₂	C₄×C₈	1	4	yes	—
131	C₈×C₃₂	C₄×C₈	1	4	yes	—
132	C₈×C₃₂	C₄×C₈	1	2	yes	—
133	C₈×C₃₂	C₂×C₁₆	1	4	yes	—
134	C₈×C₃₂	C₂×C₁₆	1	4	yes	—
135	C₈×C₃₂	C₂×C₁₆	1	4	yes	—
136	C₈×C₃₂	C₂×C₁₆	1	4	yes	—
137	#7052	—	2	4	no	—
138	#7052	#131	1	8	yes	—
139	C₁₆²	C₂×C₁₆	1	4	yes	—
140	C₁₆²	C₂×C₁₆	1	4	yes	—
141	C₁₆²	C₂²×C₈	1	4	yes	—
142	C₁₆²	C₂²×C₈	1	4	yes	—
143	C₂²×C₃₂	—	2	4	no	—
144	C₂²×C₃₂	C₄×C₁₆	1	8	yes	—
145	C₂²×C₃₂	C₄×C₁₆	1	2	yes	—
146	C₂²×C₃₂	C₄×C₁₆	1	2	yes	—
147	C₂²×C₃₂	C₄×C₁₆	1	2	yes	—
148	C₂²×C₃₂	C₄×C₁₆	1	2	yes	—
149	C₂²×C₃₂	#346	1	8	yes	—
150	C₂×C₄×C₁₆	—	2	4	no	—
151	C₂×C₄×C₁₆	—	2	2	no	—
152	C₂×C₄×C₁₆	—	2	2	no	—
153	C₂×C₄×C₁₆	C₄×C₁₆	1	4	yes	—
154	C₂×C₄×C₁₆	C₂×C₄×C₈	1	1	yes	characteristic
155	C₂×C₄×C₁₆	C₂×C₄×C₈	1	1	yes	characteristic
156	C₂×C₄×C₁₆	C₂×C₄×C₈	1	1	yes	characteristic
157	C₂×C₄×C₁₆	C₂×C₄×C₈	1	1	yes	characteristic
158	C₂×C₄×C₁₆	#405	1	8	yes	—
159	C₂×C₄×C₁₆	C₂²×C₁₆	1	2	yes	—
160	C₂×C₄×C₁₆	C₂²×C₁₆	1	2	yes	—
161	C₂×C₄×C₁₆	C₂×M₃₂	1	4	yes	—
162	C₄²×C₈	—	2	2	no	—
163	C₄²×C₈	C₂×C₄×C₈	1	1	yes	characteristic
164	C₄²×C₈	#405	1	2	yes	—
165	C₂×C₈²	—	2	2	no	—
166	C₂×C₈²	C₄×C₁₆	1	4	yes	—
167	C₂×C₈²	C₄³	1	1	yes	characteristic
168	C₂×C₈²	C₂×C₄×C₈	1	1	yes	characteristic
169	C₂×C₈²	#405	1	2	yes	—
170	C₄⋊C₃₂	—	4	16	no	—
171	C₂²⋊C₃₂	—	4	16	no	—
172	#1397	—	4	8	no	—
173	#1397	—	4	8	no	—
174	C₄×C₃₂	—	2	4	no	—
175	C₄×C₃₂	—	2	4	no	—
176	C₄×C₃₂	—	2	4	no	—
177	C₄×C₃₂	—	2	32	no	—
178	C₄×C₃₂	—	2	8	no	—
179	C₄×C₃₂	C₈²	1	2	yes	—
180	C₄×C₃₂	C₈²	1	2	yes	—
181	C₄×C₃₂	C₈²	1	1	yes	characteristic
182	C₄×C₃₂	C₈²	1	2	yes	—
183	C₄×C₃₂	C₈²	1	8	yes	—
184	C₄×C₃₂	C₈²	1	1	yes	characteristic
185	C₄×C₃₂	C₄×C₁₆	1	8	yes	—
186	C₄×C₃₂	C₄×C₁₆	1	2	yes	—
187	C₄×C₃₂	C₄×C₁₆	1	2	yes	—
188	C₄×C₃₂	C₄×C₁₆	1	2	yes	—
189	C₄×C₃₂	C₄×C₁₆	1	2	yes	—
190	C₄×C₃₂	#346	1	8	yes	—
191	C₄×C₃₂	C₂×C₃₂	1	16	yes	—
192	C₄×C₃₂	C₂×C₃₂	1	16	yes	—
193	C₄×C₃₂	M₆₄	1	16	yes	—
194	#1374	—	4	4	no	—
195	#1374	—	4	4	no	—
196	#1312	—	4	4	no	—
197	#1312	—	4	4	no	—
198	#1311	—	4	4	no	—
199	#1311	—	4	8	no	—
200	C₈×C₁₆	—	2	8	no	—
201	C₈×C₁₆	—	2	4	no	—
202	C₈×C₁₆	C₄×C₁₆	1	8	yes	—
203	C₈×C₁₆	C₂×C₃₂	1	16	yes	—
204	C₈×C₁₆	C₂×C₄×C₈	1	2	yes	—
205	C₈×C₁₆	C₂×C₄×C₈	1	2	yes	—
206	C₈×C₁₆	C₂×C₄×C₈	1	8	yes	—
207	C₈×C₁₆	#405	1	4	yes	—
208	C₈×C₁₆	#405	1	8	yes	—
209	C₈×C₁₆	C₂²×C₁₆	1	2	yes	—
210	C₈×C₁₆	C₂²×C₁₆	1	2	yes	—
211	C₈×C₁₆	C₂×M₃₂	1	4	yes	—
212	#1273	—	4	4	no	—
213	C₂²×C₁₆	—	2	4	no	—
214	C₂²×C₁₆	—	2	8	no	—
215	C₂²×C₁₆	—	4	4	no	—
216	C₂²×C₁₆	C₂×C₄×C₁₆	1	1	yes	characteristic
217	C₂²×C₁₆	C₂×C₄×C₁₆	1	1	yes	characteristic
218	C₂²×C₁₆	C₂×C₄×C₁₆	1	2	yes	—
219	C₂²×C₁₆	C₂×#346	1	2	yes	—
220	C₂²×C₁₆	C₄×M₃₂	1	2	yes	—
221	C₂×C₄×C₈	—	2	4	no	—
222	C₂×C₄×C₈	—	2	4	no	—
223	C₂×C₄×C₈	—	4	4	no	—
224	C₂×C₄×C₈	#1450	1	1	yes	characteristic
225	C₂×C₄×C₈	#1450	1	2	yes	—
226	C₂×C₄×C₈	C₄²×C₈	1	1	yes	characteristic
227	C₂×C₄×C₈	#1726	1	2	yes	—
228	C₂×C₄×C₈	C₂×C₄×C₁₆	1	2	yes	—
229	C₂×C₄×C₈	C₄×M₃₂	1	2	yes	—
230	C₄³	#1450	1	1	yes	characteristic
231	C₂×C₃₂	—	2	8	no	—
232	C₂×C₃₂	—	2	8	no	—
233	C₂×C₃₂	—	2	16	no	—
234	C₂×C₃₂	—	2	8	no	—
235	C₂×C₃₂	—	4	8	no	—
236	C₂×C₃₂	—	4	32	no	—
237	C₂×C₃₂	C₈×C₁₆	1	4	yes	—
238	C₂×C₃₂	C₈×C₁₆	1	2	yes	—
239	C₂×C₃₂	C₈×C₁₆	1	2	yes	—
240	C₂×C₃₂	C₈×C₁₆	1	4	yes	—
241	C₂×C₃₂	C₈×C₁₆	1	4	yes	—
242	C₂×C₃₂	#1311	1	16	yes	—
243	C₂×C₃₂	C₄×C₃₂	1	16	yes	—
244	C₂×C₃₂	C₄×C₃₂	1	8	yes	—
245	C₂×C₃₂	C₄×C₃₂	1	8	yes	—
246	C₂×C₃₂	#1397	1	8	yes	—
247	C₂×C₃₂	#1397	1	8	yes	—
248	C₄×C₁₆	—	2	8	no	—
249	C₄×C₁₆	—	2	8	no	—
250	C₄×C₁₆	—	2	4	no	—
251	C₄×C₁₆	—	2	8	no	—
252	C₄×C₁₆	—	4	4	no	—
253	C₄×C₁₆	—	4	4	no	—
254	C₄×C₁₆	—	4	4	no	—
255	C₄×C₁₆	C₄×C₃₂	1	8	yes	—
256	C₄×C₁₆	C₂×C₈²	1	1	yes	characteristic
257	C₄×C₁₆	C₂×C₈²	1	1	yes	characteristic
258	C₄×C₁₆	C₂×C₈²	1	2	yes	—
259	C₄×C₁₆	#1450	1	16	yes	—
260	C₄×C₁₆	#1450	1	2	yes	—
261	C₄×C₁₆	#1450	1	2	yes	—
262	C₄×C₁₆	C₂×C₄×C₁₆	1	1	yes	characteristic
263	C₄×C₁₆	C₂×C₄×C₁₆	1	1	yes	characteristic
264	C₄×C₁₆	C₂×C₄×C₁₆	1	2	yes	—
265	C₄×C₁₆	C₂×#346	1	2	yes	—
266	C₄×C₁₆	C₄×M₃₂	1	2	yes	—
267	C₄×C₁₆	C₂²×C₃₂	1	8	yes	—
268	C₄×C₁₆	C₂×M₆₄	1	8	yes	—
269	C₈²	—	2	4	no	—
270	C₈²	—	2	4	no	—
271	C₈²	—	4	4	no	—
272	C₈²	C₄×C₃₂	1	8	yes	—
273	C₈²	C₄²×C₈	1	2	yes	—
274	C₈²	#1726	1	2	yes	—
275	C₈²	C₂×C₄×C₁₆	1	2	yes	—
276	C₈²	C₄×M₃₂	1	2	yes	—
277	C₂²×C₈	—	2	2	no	—
278	C₂²×C₈	—	4	4	no	—
279	C₂²×C₈	#11410	1	2	yes	—
280	C₂²×C₈	C₄²×C₁₆	1	1	yes	characteristic
281	C₂²×C₈	C₄×#346	1	1	yes	characteristic
282	C₂²×C₈	#12542	1	4	yes	—
283	C₂×C₄²	—	2	2	no	—
284	C₂×C₄²	#7841	1	1	yes	characteristic
285	C₂×C₄²	#11410	1	2	yes	—
286	C₂×C₁₆	—	2	4	no	—
287	C₂×C₁₆	—	2	8	no	—
288	C₂×C₁₆	—	2	16	no	—
289	C₂×C₁₆	—	4	4	no	—
290	C₂×C₁₆	—	4	4	no	—
291	C₂×C₁₆	—	4	8	no	—
292	C₂×C₁₆	—	8	8	no	—
293	C₂×C₁₆	—	8	8	no	—
294	C₂×C₁₆	C₂×C₈×C₁₆	1	1	yes	characteristic
295	C₂×C₁₆	C₂×C₈×C₁₆	1	1	yes	characteristic
296	C₂×C₁₆	C₂×C₈×C₁₆	1	1	yes	characteristic
297	C₂×C₁₆	C₂×C₈×C₁₆	1	1	yes	characteristic
298	C₂×C₁₆	C₂×#1311	1	4	yes	—
299	C₂×C₁₆	#11410	1	4	yes	—
300	C₂×C₁₆	#11410	1	4	yes	—
301	C₂×C₁₆	C₂×C₄×C₃₂	1	4	yes	—
302	C₂×C₁₆	C₂×C₄×C₃₂	1	4	yes	—
303	C₂×C₁₆	C₂×#1397	1	4	yes	—
304	C₂×C₁₆	C₄×M₆₄	1	4	yes	—
305	C₂×C₁₆	#13551	1	8	yes	—
306	C₄×C₈	—	2	4	no	—
307	C₄×C₈	—	2	8	no	—
308	C₄×C₈	—	2	2	no	—
309	C₄×C₈	—	2	2	no	—
310	C₄×C₈	—	4	4	no	—
311	C₄×C₈	—	8	4	no	—
312	C₄×C₈	—	8	8	no	—
313	C₄×C₈	C₄×C₈²	1	1	yes	characteristic
314	C₄×C₈	#7841	1	1	yes	characteristic
315	C₄×C₈	#7841	1	4	yes	—
316	C₄×C₈	#11410	1	4	yes	—
317	C₄×C₈	C₄²×C₁₆	1	1	yes	characteristic
318	C₄×C₈	C₄×#346	1	1	yes	characteristic
319	C₄×C₈	#12542	1	4	yes	—
320	C₄×C₈	C₂×C₄×C₃₂	1	4	yes	—
321	C₄×C₈	C₄×M₆₄	1	4	yes	—
322	C₃₂	—	2	16	no	—
323	C₃₂	—	2	16	no	—
324	C₃₂	—	4	8	no	—
325	C₃₂	—	8	32	no	—
326	C₃₂	C₈×C₃₂	1	8	yes	—
327	C₃₂	C₈×C₃₂	1	4	yes	—
328	C₃₂	C₈×C₃₂	1	4	yes	—
329	C₃₂	#7329	1	8	yes	—
330	C₃₂	#7329	1	8	yes	—
331	C₂²×C₄	—	2	2	no	—
332	C₂²×C₄	#126530	1	1	yes	characteristic
333	C₂²×C₄	#126533	1	2	yes	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	2	2	no	—
336	C₂×C₈	—	2	4	no	—
337	C₂×C₈	—	4	4	no	—
338	C₂×C₈	—	4	4	no	—
339	C₂×C₈	—	4	8	no	—
340	C₂×C₈	—	8	8	no	—
341	C₂×C₈	C₄×C₈×C₁₆	1	1	yes	characteristic
342	C₂×C₈	C₄×#1311	1	1	yes	characteristic
343	C₂×C₈	#126530	1	1	yes	characteristic
344	C₂×C₈	#126530	1	1	yes	characteristic
345	C₂×C₈	#126533	1	8	yes	—
346	C₂×C₈	#149510	1	4	yes	—
347	C₂×C₈	C₄²×C₃₂	1	2	yes	—
348	C₂×C₈	C₄×#1397	1	2	yes	—
349	C₂×C₈	#151750	1	4	yes	—
350	C₄²	—	2	2	no	—
351	C₄²	—	4	4	no	—
352	C₄²	#94852	1	1	yes	characteristic
353	C₄²	#126530	1	1	yes	characteristic
354	C₄²	#126533	1	2	yes	—
355	C₄²	#149510	1	4	yes	—
356	C₁₆	—	2	4	no	—
357	C₁₆	—	4	16	no	—
358	C₁₆	—	4	8	no	—
359	C₁₆	—	8	8	no	—
360	C₁₆	C₂×C₈×C₃₂	1	2	yes	—
361	C₁₆	C₂×C₈×C₃₂	1	2	yes	—
362	C₁₆	C₂×#7329	1	2	yes	—
363	C₁₆	C₂×#7329	1	2	yes	—
364	C₁₆	#149496	1	8	yes	—
365	C₁₆	#149510	1	8	yes	—
366	C₂³	#72210619	1	1	yes	characteristic
367	C₂×C₄	—	2	4	no	—
368	C₂×C₄	—	2	4	no	—
369	C₂×C₄	—	4	4	no	—
370	C₂×C₄	#72210602	1	2	yes	—
371	C₂×C₄	#72210619	1	2	yes	—
372	C₂×C₄	#72210619	1	1	yes	characteristic
373	C₂×C₄	#72210680	1	2	yes	—
374	C₂×C₄	#72234228	1	1	yes	characteristic
375	C₂×C₄	#72234280	1	2	yes	—
376	C₈	—	2	8	no	—
377	C₈	—	2	4	no	—
378	C₈	—	4	4	no	—
379	C₈	—	8	8	no	—
380	C₈	C₄×C₈×C₃₂	1	1	yes	characteristic
381	C₈	#72210680	1	2	yes	—
382	C₈	C₄×#7329	1	1	yes	characteristic
383	C₈	#72234239	1	2	yes	—
384	C₈	#72234280	1	2	yes	—
385	C₂²	—	2	2	no	—
386	C₂²	#72234231	1	1	yes	characteristic
387	C₂²	#72234281	1	2	yes	—
388	C₄	—	2	2	no	—
389	C₄	—	4	4	no	—
390	C₄	#72234241	1	1	yes	characteristic
391	C₄	#72234273	1	4	yes	—
392	C₄	#72234281	1	2	yes	—
393	C₄	#72234306	1	1	yes	characteristic
394	C₂	—	2	2	no	—
395	C₂	#72234274	1	2	yes	—
396	C₂	#72234307	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₃₂	C₈²
commutator	C₈	C₄×C₈×C₃₂
Frattini, cosocle	#72234226	C₂³
socle	C₂²	#72234231
prime radical	C₂³	#72210619
LCS	G ▷ C₈ ▷ C₁
UCS	C₁ ◁ C₄×C₃₂ ◁ G
LECS	G ▷ #72234226 ▷ C₂×C₈² ▷ C₄² ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
34. #72225071	C₈	semidirect
35. #72225038	C₈	semidirect
41. C₃₂²	C₈	semidirect
126. C₈×C₃₂	C₃₂	semidirect

Maximal subgroups

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

subgroup	index
#72234305	2
#72234298	2
#72234291	2
#72234256	2