Subgroups — #26235285

Order 12032.

622 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×#10625329	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689254	C₂	1	1	yes	maximal, characteristic
3	#20244163	C₂	1	2	yes	maximal
4	#20244163	C₂	1	1	yes	maximal, characteristic
5	#20244161	C₂	1	1	yes	maximal, characteristic
6	#20244161	C₂	1	2	yes	maximal
7	#20243528	C₂	1	2	yes	maximal
8	#20243525	C₂	1	1	yes	maximal, characteristic
9	#20243295	C₂	1	2	yes	maximal
10	C₄×#13093959	C₂	1	1	yes	maximal, characteristic
11	Q₈×M₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic
12	#15689254	—	2	1	no	—
13	#15689254	—	2	2	no	—
14	#15689254	C₄	1	2	yes	—
15	#15689254	C₄	1	2	yes	—
16	#15689254	C₄	1	4	yes	—
17	Q₈×C₄₇⋊C₈	—	2	1	no	—
18	C₂×#13093959	C₂²	1	1	yes	characteristic
19	C₂×#13093959	C₂²	1	1	yes	characteristic
20	C₂×#13093959	C₂²	1	2	yes	—
21	C₂×#13093959	C₂²	1	2	yes	—
22	#15689147	C₂²	1	1	yes	characteristic
23	#15689147	C₂²	1	2	yes	—
24	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
26	C₄×#10625329	C₂²	1	1	yes	characteristic
27	C₄×#10625329	C₂²	1	2	yes	—
28	C₂×#13093935	C₂²	1	2	yes	—
29	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
30	#15688887	C₂²	1	2	yes	—
31	#15688887	C₂²	1	2	yes	—
32	#15688887	C₂²	1	1	yes	characteristic
33	#15688887	C₂²	1	2	yes	—
34	#15688887	C₂²	1	2	yes	—
35	#15688887	C₂²	1	1	yes	characteristic
36	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
37	C₄₇×#446	—	2	1	no	—
38	C₄₇×#446	—	2	2	no	—
39	C₈×Q₈×C₄₇	—	2	1	no	—
40	C₄₇×#423	C₂²	1	1	yes	characteristic
41	C₄₇×#423	C₂²	1	2	yes	—
42	C₄×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
43	C₄×M₁₆×C₄₇	C₂²	1	2	yes	—
44	C₂×#10625329	C₂³	1	1	yes	characteristic
45	C₂×#10625329	C₂³	1	2	yes	—
46	C₂×#10625329	C₂³	1	1	yes	characteristic
47	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
48	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
49	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
50	#13093959	—	2	2	no	—
51	#13093959	—	2	4	no	—
52	#13093959	—	2	2	no	—
53	#13093959	—	2	4	no	—
54	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
55	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
56	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
57	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
58	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	4	yes	—
59	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	4	yes	—
60	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	2	yes	—
61	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	2	yes	—
62	#13093935	—	2	2	no	—
63	#13093935	—	2	1	no	—
64	#13093935	C₂×C₄	1	4	yes	—
65	#13093935	C₂×C₄	1	4	yes	—
66	C₄×C₄₇⋊C₈	—	2	1	no	—
67	C₄×C₄₇⋊C₈	—	2	2	no	—
68	C₄×C₄₇⋊C₈	C₂×C₄	1	2	yes	—
69	C₄×C₄₇⋊C₈	C₂×C₄	1	2	yes	—
70	C₂²×Q₈×C₄₇	Q₈	1	1	yes	characteristic
71	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
72	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
73	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
74	C₄×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
75	C₄×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
76	C₄×Q₈×C₄₇	C₂×C₄	1	2	yes	—
77	C₄×Q₈×C₄₇	D₄	1	1	yes	characteristic
78	C₄×Q₈×C₄₇	D₄	1	1	yes	characteristic
79	C₄×Q₈×C₄₇	D₄	1	2	yes	—
80	C₂×C₄⋊C₄×C₄₇	Q₈	1	1	yes	characteristic
81	C₂×C₄⋊C₄×C₄₇	Q₈	1	2	yes	—
82	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
83	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
84	C₄⋊C₈×C₄₇	—	2	1	no	—
85	C₄⋊C₈×C₄₇	—	2	2	no	—
86	C₄⋊C₈×C₄₇	—	2	2	no	—
87	C₄⋊C₈×C₄₇	—	2	1	no	—
88	#97×C₄₇	—	2	2	no	—
89	#97×C₄₇	—	2	1	no	—
90	C₄×C₈×C₄₇	—	2	1	no	—
91	C₄×C₈×C₄₇	—	2	2	no	—
92	C₂×Q₈×C₄₇	—	4	2	no	—
93	C₂×Q₈×C₄₇	C₄⋊C₄	1	1	yes	characteristic
94	C₂×Q₈×C₄₇	C₄⋊C₄	1	1	yes	characteristic
95	C₂×Q₈×C₄₇	C₄⋊C₄	1	2	yes	—
96	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
97	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
98	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
99	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
100	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
101	M₁₆×C₄₇	—	2	1	no	—
102	M₁₆×C₄₇	—	2	2	no	—
103	M₁₆×C₄₇	—	2	1	no	—
104	M₁₆×C₄₇	—	2	2	no	—
105	M₁₆×C₄₇	—	2	1	no	—
106	M₁₆×C₄₇	#41	1	2	yes	—
107	C₂×C₈×C₄₇	—	2	1	no	—
108	C₂×C₈×C₄₇	—	2	2	no	—
109	C₂×C₈×C₄₇	—	2	1	no	—
110	C₄⋊C₄×C₄₇	C₄⋊C₄	1	2	yes	—
111	C₄⋊C₄×C₄₇	C₄⋊C₄	1	2	yes	—
112	C₄⋊C₄×C₄₇	C₄⋊C₄	1	2	yes	—
113	C₄⋊C₄×C₄₇	C₄⋊C₄	1	2	yes	—
114	C₄⋊C₄×C₄₇	C₄⋊C₄	1	2	yes	—
115	C₄⋊C₄×C₄₇	C₄⋊C₄	1	1	yes	characteristic
116	C₄⋊C₄×C₄₇	C₄⋊C₄	1	1	yes	characteristic
117	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
118	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
119	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
120	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
121	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
122	C₄²×C₄₇	C₂×D₄	1	2	yes	—
123	C₄²×C₄₇	C₂×D₄	1	2	yes	—
124	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
125	#10625329	—	2	1	no	—
126	#10625329	—	2	1	no	—
127	#10625329	—	2	2	no	—
128	#10625329	—	2	1	no	—
129	#10625329	—	2	2	no	—
130	#10625329	#41	1	2	yes	—
131	C₂×C₄₇⋊C₈	—	2	1	no	—
132	C₂×C₄₇⋊C₈	—	2	1	no	—
133	C₂×C₄₇⋊C₈	—	2	2	no	—
134	C₂×C₄₇⋊C₈	—	2	1	no	—
135	C₂×C₄₇⋊C₈	—	2	2	no	—
136	C₂×C₄₇⋊C₈	—	2	1	no	—
137	C₂×C₄₇⋊C₈	—	2	1	no	—
138	C₂×C₄₇⋊C₈	—	2	1	no	—
139	C₂×C₄₇⋊C₈	—	2	2	no	—
140	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
141	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
142	C₂×C₄₇⋊C₈	C₂²×C₄	1	4	yes	—
143	C₂³×C₄₇	C₂²×Q₈	1	1	yes	characteristic
144	Q₈×C₄₇	—	2	2	no	—
145	Q₈×C₄₇	—	2	2	no	—
146	Q₈×C₄₇	—	4	2	no	—
147	C₂×C₄×C₄₇	—	2	2	no	—
148	C₂×C₄×C₄₇	—	4	1	no	—
149	C₂×C₄×C₄₇	—	4	2	no	—
150	C₂×C₄×C₄₇	—	4	2	no	—
151	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
152	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
153	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
154	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
155	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
156	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
157	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
158	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
159	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
160	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
161	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
162	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
163	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
164	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
165	C₈×C₄₇	—	2	2	no	—
166	C₈×C₄₇	—	4	2	no	—
167	C₈×C₄₇	—	4	1	no	—
168	C₄₇⋊C₈	—	2	2	no	—
169	C₄₇⋊C₈	—	2	4	no	—
170	C₄₇⋊C₈	—	2	2	no	—
171	C₄₇⋊C₈	—	2	2	no	—
172	C₄₇⋊C₈	—	4	1	no	—
173	C₄₇⋊C₈	—	4	2	no	—
174	#22747	—	47	1	no	maximal, Sylow
175	C₂²×C₄₇	—	2	1	no	—
176	C₂²×C₄₇	—	2	1	no	—
177	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
178	C₂²×C₄₇	#557	1	1	yes	characteristic
179	C₂²×C₄₇	#557	1	1	yes	characteristic
180	C₄×C₄₇	—	2	1	no	—
181	C₄×C₄₇	—	2	2	no	—
182	C₄×C₄₇	—	2	2	no	—
183	C₄×C₄₇	—	2	1	no	—
184	C₄×C₄₇	—	2	1	no	—
185	C₄×C₄₇	—	2	2	no	—
186	C₄×C₄₇	—	2	2	no	—
187	C₄×C₄₇	#430	1	2	yes	—
188	C₄×C₄₇	C₄×#41	1	1	yes	characteristic
189	C₄×C₄₇	#519	1	1	yes	characteristic
190	C₄×C₄₇	#548	1	1	yes	characteristic
191	C₄×C₄₇	#548	1	1	yes	characteristic
192	Q₈×M₁₆	—	47	1	no	—
193	Q₈×M₁₆	D₄₇	1	1	yes	characteristic
194	C₂×#446	—	47	1	no	—
195	#1950	—	47	2	no	—
196	#1950	—	47	1	no	—
197	#1950	—	47	2	no	—
198	#1950	—	47	1	no	—
199	#1838	—	47	2	no	—
200	#1837	—	47	1	no	—
201	#1778	—	47	2	no	—
202	C₄×#108	—	47	1	no	—
203	C₂×C₄₇	—	2	1	no	—
204	C₂×C₄₇	—	2	1	no	—
205	C₂×C₄₇	#2351	1	1	yes	characteristic
206	C₂×C₄₇	C₂×#430	1	1	yes	characteristic
207	C₂×C₄₇	#2916	1	1	yes	characteristic
208	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
209	#446	—	2	1	no	—
210	#446	—	2	2	no	—
211	#446	—	47	2	no	—
212	#446	—	47	2	no	—
213	#446	—	47	4	no	—
214	#446	—	94	1	no	—
215	#446	—	94	2	no	—
216	C₈×Q₈	—	2	1	no	—
217	C₈×Q₈	—	94	1	no	—
218	C₂×#108	—	47	1	no	—
219	C₂×#108	—	47	1	no	—
220	C₂×#108	—	47	2	no	—
221	C₂×#108	—	47	2	no	—
222	#423	—	47	1	no	—
223	#423	—	47	2	no	—
224	#423	C₂×D₄₇	1	1	yes	characteristic
225	#423	C₂×D₄₇	1	2	yes	—
226	C₂×C₄⋊C₈	—	47	1	no	—
227	C₂×C₄⋊C₈	—	47	2	no	—
228	C₄×M₁₆	—	47	1	no	—
229	C₄×M₁₆	—	47	2	no	—
230	C₄×M₁₆	C₂×D₄₇	1	1	yes	characteristic
231	C₄×M₁₆	C₂×D₄₇	1	2	yes	—
232	C₂×#97	—	47	2	no	—
233	C₂×C₄×C₈	—	47	1	no	—
234	#341	—	47	2	no	—
235	#341	—	47	2	no	—
236	#341	—	47	1	no	—
237	#341	—	47	2	no	—
238	#341	—	47	2	no	—
239	#341	—	47	1	no	—
240	C₄₇	#22747	1	1	yes	characteristic, complemented, Sylow
241	C₂²×Q₈	Dic₉₄	1	1	yes	characteristic
242	C₂×M₁₆	—	47	1	no	—
243	C₂×M₁₆	—	47	2	no	—
244	C₂×M₁₆	—	47	1	no	—
245	C₂×M₁₆	C₂²×D₄₇	1	2	yes	—
246	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
247	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
248	C₂²×C₈	—	47	1	no	—
249	C₂²×C₈	—	47	1	no	—
250	C₂²×C₈	—	47	2	no	—
251	C₄×Q₈	C₄×D₄₇	1	1	yes	characteristic
252	C₄×Q₈	C₄×D₄₇	1	1	yes	characteristic
253	C₄×Q₈	C₄×D₄₇	1	2	yes	—
254	C₄×Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
255	C₄×Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
256	C₄×Q₈	C₂²⋊D₄₇	1	2	yes	—
257	C₂×C₄⋊C₄	Dic₉₄	1	1	yes	characteristic
258	C₂×C₄⋊C₄	Dic₉₄	1	2	yes	—
259	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
260	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
261	#108	—	94	2	no	—
262	#108	—	94	4	no	—
263	#108	—	94	2	no	—
264	#108	—	94	4	no	—
265	C₄⋊C₈	—	2	1	no	—
266	C₄⋊C₈	—	2	2	no	—
267	C₄⋊C₈	—	2	2	no	—
268	C₄⋊C₈	—	2	1	no	—
269	C₄⋊C₈	—	47	2	no	—
270	C₄⋊C₈	—	47	2	no	—
271	C₄⋊C₈	—	47	4	no	—
272	C₄⋊C₈	—	47	4	no	—
273	C₄⋊C₈	—	94	1	no	—
274	C₄⋊C₈	—	94	2	no	—
275	C₄⋊C₈	—	94	2	no	—
276	C₄⋊C₈	—	94	1	no	—
277	#97	—	2	2	no	—
278	#97	—	2	1	no	—
279	#97	—	47	4	no	—
280	#97	—	47	4	no	—
281	#97	—	94	2	no	—
282	#97	—	94	1	no	—
283	C₄×C₈	—	2	1	no	—
284	C₄×C₈	—	2	2	no	—
285	C₄×C₈	—	47	2	no	—
286	C₄×C₈	—	47	2	no	—
287	C₄×C₈	—	94	1	no	—
288	C₄×C₈	—	94	2	no	—
289	C₂×Q₈	—	4	2	no	—
290	C₂×Q₈	Dic₄₇⋊C₄	1	1	yes	characteristic
291	C₂×Q₈	Dic₄₇⋊C₄	1	1	yes	characteristic
292	C₂×Q₈	Dic₄₇⋊C₄	1	2	yes	—
293	C₂²×C₄	C₂×Dic₉₄	1	1	yes	characteristic
294	C₂²×C₄	C₂×Dic₉₄	1	1	yes	characteristic
295	C₂²×C₄	C₂×Dic₉₄	1	2	yes	—
296	C₂²×C₄	C₂×Dic₉₄	1	2	yes	—
297	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
298	M₁₆	—	2	1	no	—
299	M₁₆	—	2	1	no	—
300	M₁₆	—	2	2	no	—
301	M₁₆	—	2	2	no	—
302	M₁₆	—	2	1	no	—
303	M₁₆	—	47	2	no	—
304	M₁₆	—	94	1	no	—
305	M₁₆	—	94	1	no	—
306	M₁₆	—	94	2	no	—
307	M₁₆	—	94	2	no	—
308	M₁₆	—	94	1	no	—
309	M₁₆	#10625354	1	2	yes	—
310	C₂×C₈	—	2	1	no	—
311	C₂×C₈	—	2	1	no	—
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	—	47	2	no	—
314	C₂×C₈	—	47	2	no	—
315	C₂×C₈	—	47	4	no	—
316	C₂×C₈	—	94	1	no	—
317	C₂×C₈	—	94	1	no	—
318	C₂×C₈	—	94	2	no	—
319	C₂×C₈	—	94	1	no	—
320	C₂×C₈	—	94	2	no	—
321	C₂×C₈	—	94	1	no	—
322	C₂×C₈	—	94	1	no	—
323	C₂×C₈	—	94	1	no	—
324	C₂×C₈	—	94	2	no	—
325	C₄⋊C₄	Dic₄₇⋊C₄	1	2	yes	—
326	C₄⋊C₄	Dic₄₇⋊C₄	1	2	yes	—
327	C₄⋊C₄	Dic₄₇⋊C₄	1	2	yes	—
328	C₄⋊C₄	Dic₄₇⋊C₄	1	2	yes	—
329	C₄⋊C₄	Dic₄₇⋊C₄	1	2	yes	—
330	C₄⋊C₄	Dic₄₇⋊C₄	1	1	yes	characteristic
331	C₄⋊C₄	Dic₄₇⋊C₄	1	1	yes	characteristic
332	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
333	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
334	C₄²	C₂×C₄×D₄₇	1	2	yes	—
335	C₄²	C₂×C₄×D₄₇	1	2	yes	—
336	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
337	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
338	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
339	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
340	C₂³	C₂²×Dic₉₄	1	1	yes	characteristic
341	Q₈	—	2	2	no	—
342	Q₈	—	2	2	no	—
343	Q₈	—	4	2	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	4	1	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	—	4	2	no	—
348	C₂×C₄	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
349	C₂×C₄	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
350	C₂×C₄	C₂×Dic₄₇⋊C₄	1	2	yes	—
351	C₂×C₄	C₂×Dic₄₇⋊C₄	1	2	yes	—
352	C₂×C₄	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
353	C₂×C₄	C₂×Dic₄₇⋊C₄	1	2	yes	—
354	C₂×C₄	C₂×Dic₄₇⋊C₄	1	2	yes	—
355	C₂×C₄	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
356	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
357	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
358	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
359	C₂×C₄	C₂×#10625354	1	1	yes	characteristic
360	C₂×C₄	#13094071	1	1	yes	characteristic
361	C₂×C₄	#13094072	1	1	yes	characteristic
362	C₈	—	2	2	no	—
363	C₈	—	4	1	no	—
364	C₈	—	4	2	no	—
365	C₈	—	94	2	no	—
366	C₈	—	94	2	no	—
367	C₈	—	94	4	no	—
368	C₈	—	94	2	no	—
369	C₈	—	188	1	no	—
370	C₈	—	188	2	no	—
371	C₂²	—	2	1	no	—
372	C₂²	—	2	1	no	—
373	C₂²	C₂²×Dic₄₇⋊C₄	1	1	yes	characteristic
374	C₂²	#15689849	1	1	yes	characteristic
375	C₂²	#15689852	1	1	yes	characteristic
376	C₄	—	2	1	no	—
377	C₄	—	2	2	no	—
378	C₄	—	2	2	no	—
379	C₄	—	2	1	no	—
380	C₄	—	2	1	no	—
381	C₄	—	2	2	no	—
382	C₄	—	2	2	no	—
383	C₄	#15689171	1	2	yes	—
384	C₄	C₄×#10625354	1	1	yes	characteristic
385	C₄	#15689599	1	1	yes	characteristic
386	C₄	#15689780	1	1	yes	characteristic
387	C₄	#15689784	1	1	yes	characteristic
388	C₂	—	2	1	no	—
389	C₂	—	2	1	no	—
390	C₂	#20246306	1	1	yes	characteristic
391	C₂	C₂×#15689171	1	1	yes	characteristic
392	C₂	#20251997	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	Q₈×M₁₆×C₄₇	C₂
socle	C₂²×C₄₇	C₂²×C₄⋊C₄
prime radical	C₂³×C₄₇	C₂²×Q₈
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	Q₈×M₁₆	D₄₇
hypocenter	C₄₇	#22747
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×Q₈ ◁ Q₈×M₁₆

Complements

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

N	H ≅ G/N	type
240. C₄₇	#22747	semidirect

Maximal subgroups

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

subgroup	index
Q₈×#10625329	2
C₂×#15689254	2
#20244163	2
#20244161	2
#20243528	2
#20243525	2
#20243295	2
C₄×#13093959	2
Q₈×M₁₆×C₄₇	2
#22747	47