Subgroups — #29572701

Order 15616.

588 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	#21445971	C₂	1	1	yes	maximal, characteristic
2	C₄×C₄⋊#92418	C₂	1	1	yes	maximal, characteristic
3	C₂×Q₈⋊#92418	C₂	1	2	yes	maximal
4	#21443660	C₂	1	2	yes	maximal
5	C₄²×Q₈×C₆₁	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊#92418	—	2	1	no	—
7	C₂×C₄⋊#92418	—	2	1	no	—
8	C₂×C₄⋊#92418	—	2	1	no	—
9	C₂×C₄⋊#92418	C₂²	1	2	yes	—
10	C₂×C₄×#92418	C₂²	1	2	yes	—
11	#16839517	—	2	1	no	—
12	Q₈⋊#92418	—	2	4	no	—
13	C₂×C₄×Q₈×C₆₁	C₄	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₆₁	C₄	1	1	yes	characteristic
15	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
16	C₄×C₄⋊C₄×C₆₁	—	2	1	no	—
17	C₄×C₄⋊C₄×C₆₁	—	2	1	no	—
18	C₄×C₄⋊C₄×C₆₁	—	2	1	no	—
19	C₄×C₄⋊C₄×C₆₁	C₄	1	1	yes	characteristic
20	C₄×C₄⋊C₄×C₆₁	C₄	1	1	yes	characteristic
21	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
22	C₄³×C₆₁	—	2	1	no	—
23	C₄³×C₆₁	C₂²	1	1	yes	characteristic
24	C₂²×#92418	—	2	2	no	—
25	C₂²×#92418	—	2	2	no	—
26	C₄⋊#92418	—	2	4	no	—
27	C₄⋊#92418	—	2	2	no	—
28	C₄⋊#92418	—	2	2	no	—
29	C₄⋊#92418	—	4	2	no	—
30	C₄⋊#92418	—	4	2	no	—
31	C₄×#92418	—	2	2	no	—
32	C₄×#92418	—	2	2	no	—
33	C₂²×Q₈×C₆₁	C₂×C₄	1	1	yes	characteristic
34	C₄×Q₈×C₆₁	—	2	2	no	—
35	C₄×Q₈×C₆₁	—	2	2	no	—
36	C₄×Q₈×C₆₁	—	2	2	no	—
37	C₄×Q₈×C₆₁	—	2	1	no	—
38	C₄×Q₈×C₆₁	—	2	1	no	—
39	C₄×Q₈×C₆₁	C₈	1	4	yes	complemented
40	C₄×Q₈×C₆₁	D₄	1	2	yes	—
41	C₄×Q₈×C₆₁	Q₈	1	2	yes	—
42	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
43	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
44	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
45	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄²×C₆₁	—	2	1	no	—
49	C₂×C₄²×C₆₁	—	2	1	no	—
50	C₂×C₄²×C₆₁	—	2	1	no	—
51	C₂×C₄²×C₆₁	—	2	1	no	—
52	C₂×C₄²×C₆₁	—	2	1	no	—
53	C₂×C₄²×C₆₁	—	2	1	no	—
54	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
57	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
58	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
59	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
60	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
61	#95×C₆₁	—	2	1	no	—
62	#95×C₆₁	—	2	1	no	—
63	#95×C₆₁	—	2	1	no	—
64	C₂×Q₈×C₆₁	—	2	1	no	—
65	C₂×Q₈×C₆₁	—	2	1	no	—
66	C₂×Q₈×C₆₁	—	2	1	no	—
67	C₂×Q₈×C₆₁	C₄⋊C₄	1	2	yes	—
68	C₂×Q₈×C₆₁	C₂×C₈	1	2	yes	—
69	C₂×Q₈×C₆₁	M₁₆	1	2	yes	—
70	C₂²×C₄×C₆₁	—	2	1	no	—
71	C₂²×C₄×C₆₁	—	2	1	no	—
72	C₂²×C₄×C₆₁	—	2	1	no	—
73	C₂²×C₄×C₆₁	—	2	1	no	—
74	C₂²×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
75	C₂²×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
76	C₂²×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
77	C₂²×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
78	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
79	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
80	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
81	C₄⋊C₄×C₆₁	—	2	4	no	—
82	C₄⋊C₄×C₆₁	—	2	4	no	—
83	C₄⋊C₄×C₆₁	—	2	1	no	—
84	C₄⋊C₄×C₆₁	—	2	2	no	—
85	C₄⋊C₄×C₆₁	—	2	2	no	—
86	C₄⋊C₄×C₆₁	—	2	1	no	—
87	C₄⋊C₄×C₆₁	—	2	1	no	—
88	C₄⋊C₄×C₆₁	C₄⋊C₄	1	2	yes	—
89	C₄⋊C₄×C₆₁	C₂×C₈	1	2	yes	—
90	C₄⋊C₄×C₆₁	M₁₆	1	2	yes	—
91	C₄²×C₆₁	—	2	4	no	—
92	C₄²×C₆₁	—	2	4	no	—
93	C₄²×C₆₁	—	2	2	no	—
94	C₄²×C₆₁	—	2	2	no	—
95	C₄²×C₆₁	—	2	2	no	—
96	C₄²×C₆₁	—	2	1	no	—
97	C₄²×C₆₁	—	2	1	no	—
98	C₄²×C₆₁	—	2	1	no	—
99	C₄²×C₆₁	—	2	1	no	—
100	C₄²×C₆₁	—	4	1	no	—
101	C₄²×C₆₁	—	4	2	no	—
102	C₄²×C₆₁	—	4	2	no	—
103	C₄²×C₆₁	—	4	1	no	—
104	C₄²×C₆₁	—	4	1	no	—
105	C₄²×C₆₁	C₂×C₈	1	2	yes	—
106	C₄²×C₆₁	M₁₆	1	2	yes	—
107	C₄²×C₆₁	SD₁₆	1	2	yes	—
108	C₄²×C₆₁	Q₁₆	1	2	yes	—
109	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
110	C₄²×C₆₁	C₂×Q₈	1	1	yes	characteristic
111	C₄²×C₆₁	#41	1	1	yes	characteristic
112	C₄²×C₆₁	#41	1	1	yes	characteristic
113	C₂×#92418	—	2	4	no	—
114	C₂×#92418	—	4	2	no	—
115	C₂×#92418	—	4	2	no	—
116	C₂×#92418	—	4	2	no	—
117	C₂×#92418	—	4	2	no	—
118	C₂×#92418	—	4	2	no	—
119	C₂³×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
120	Q₈×C₆₁	—	2	2	no	—
121	Q₈×C₆₁	—	2	2	no	—
122	Q₈×C₆₁	—	2	2	no	—
123	Q₈×C₆₁	C₄⋊C₈	1	4	yes	complemented
124	C₂×C₄×C₆₁	—	2	2	no	—
125	C₂×C₄×C₆₁	—	2	2	no	—
126	C₂×C₄×C₆₁	—	2	1	no	—
127	C₂×C₄×C₆₁	—	2	2	no	—
128	C₂×C₄×C₆₁	—	2	1	no	—
129	C₂×C₄×C₆₁	—	2	1	no	—
130	C₂×C₄×C₆₁	—	2	1	no	—
131	C₂×C₄×C₆₁	—	2	1	no	—
132	C₂×C₄×C₆₁	—	2	1	no	—
133	C₂×C₄×C₆₁	—	2	2	no	—
134	C₂×C₄×C₆₁	—	2	2	no	—
135	C₂×C₄×C₆₁	—	2	1	no	—
136	C₂×C₄×C₆₁	—	2	2	no	—
137	C₂×C₄×C₆₁	—	2	1	no	—
138	C₂×C₄×C₆₁	—	2	1	no	—
139	C₂×C₄×C₆₁	—	4	1	no	—
140	C₂×C₄×C₆₁	—	4	1	no	—
141	C₂×C₄×C₆₁	—	4	1	no	—
142	C₂×C₄×C₆₁	—	4	1	no	—
143	C₂×C₄×C₆₁	—	4	1	no	—
144	C₂×C₄×C₆₁	—	4	1	no	—
145	C₂×C₄×C₆₁	C₂²⋊C₈	1	2	yes	—
146	C₂×C₄×C₆₁	C₂²⋊C₈	1	2	yes	—
147	C₂×C₄×C₆₁	#103	1	2	yes	—
148	C₂×C₄×C₆₁	#103	1	2	yes	—
149	C₂×C₄×C₆₁	#104	1	2	yes	—
150	C₂×C₄×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
151	C₂×C₄×C₆₁	#117	1	1	yes	characteristic
152	C₂×C₄×C₆₁	#121	1	1	yes	characteristic
153	C₂×C₄×C₆₁	#121	1	1	yes	characteristic
154	C₂×C₄×C₆₁	C₂²⋊Q₈	1	1	yes	characteristic
155	C₂×C₄×C₆₁	C₂²⋊Q₈	1	1	yes	characteristic
156	C₂×C₄×C₆₁	C₂²×C₈	1	1	yes	characteristic
157	C₂×C₄×C₆₁	C₂×M₁₆	1	1	yes	characteristic
158	C₂×C₄×C₆₁	C₂×M₁₆	1	1	yes	characteristic
159	C₂×C₄×C₆₁	C₂×M₁₆	1	1	yes	characteristic
160	C₂×C₄×C₆₁	C₂×SD₁₆	1	1	yes	characteristic
161	C₂×C₄×C₆₁	C₂×Q₁₆	1	1	yes	characteristic
162	C₂×C₄×C₆₁	AGL(1,ℤ/8)	1	1	yes	characteristic
163	C₂×C₄×C₆₁	#137	1	1	yes	characteristic
164	#92418	—	4	4	no	—
165	#92418	—	8	2	no	—
166	#8564	—	61	1	no	maximal, Sylow
167	C₂²×C₆₁	#380	1	1	yes	characteristic
168	C₂²×C₆₁	C₂×C₂²⋊C₈	1	1	yes	characteristic
169	C₂²×C₆₁	#407	1	1	yes	characteristic
170	C₂²×C₆₁	C₂×#103	1	1	yes	characteristic
171	C₂²×C₆₁	#417	1	1	yes	characteristic
172	C₂²×C₆₁	C₂×#104	1	1	yes	characteristic
173	C₂²×C₆₁	#421	1	1	yes	characteristic
174	C₄×C₆₁	—	2	4	no	—
175	C₄×C₆₁	—	2	1	no	—
176	C₄×C₆₁	—	2	1	no	—
177	C₄×C₆₁	—	2	2	no	—
178	C₄×C₆₁	—	2	2	no	—
179	C₄×C₆₁	—	4	2	no	—
180	C₄×C₆₁	—	4	2	no	—
181	C₄×C₆₁	—	4	1	no	—
182	C₄×C₆₁	—	4	2	no	—
183	C₄×C₆₁	Q₈⋊C₈	1	4	yes	complemented
184	C₄×C₆₁	C₂×C₄⋊C₈	1	1	yes	characteristic
185	C₄×C₆₁	#423	1	1	yes	characteristic
186	C₄×C₆₁	#431	1	1	yes	characteristic
187	C₄×C₆₁	#432	1	1	yes	characteristic
188	C₄×C₆₁	#460	1	1	yes	characteristic
189	C₄×C₆₁	#462	1	1	yes	characteristic
190	C₄×C₆₁	#475	1	1	yes	characteristic
191	C₄×C₆₁	#477	1	1	yes	characteristic
192	C₄²×Q₈	D₆₁	1	1	yes	characteristic
193	#1842	—	61	1	no	—
194	C₄×C₄⋊C₈	—	61	1	no	—
195	C₂×Q₈⋊C₈	—	61	2	no	—
196	#1279	—	61	2	no	—
197	C₂×C₆₁	C₂×Q₈⋊C₈	1	1	yes	characteristic
198	C₂×C₆₁	#1477	1	1	yes	characteristic
199	C₂×C₆₁	#1487	1	1	yes	characteristic
200	C₂×C₆₁	#1489	1	1	yes	characteristic
201	C₂×C₆₁	#1797	1	1	yes	characteristic
202	C₂×C₆₁	#1803	1	1	yes	characteristic
203	C₂×C₆₁	#1806	1	1	yes	characteristic
204	C₂×C₄×Q₈	Dic₆₁	1	1	yes	characteristic
205	C₂×C₄×Q₈	Dic₆₁	1	1	yes	characteristic
206	C₂×C₄×Q₈	C₂×D₆₁	1	1	yes	characteristic
207	C₂×C₄⋊C₈	—	61	2	no	—
208	C₂×C₄⋊C₈	—	122	1	no	—
209	C₂×C₄⋊C₈	—	122	1	no	—
210	C₂×C₄⋊C₈	—	122	1	no	—
211	C₂×C₄×C₈	—	61	2	no	—
212	C₄×C₄⋊C₄	—	2	1	no	—
213	C₄×C₄⋊C₄	—	2	1	no	—
214	C₄×C₄⋊C₄	—	2	1	no	—
215	C₄×C₄⋊C₄	Dic₆₁	1	1	yes	characteristic
216	C₄×C₄⋊C₄	Dic₆₁	1	1	yes	characteristic
217	C₄×C₄⋊C₄	C₂×D₆₁	1	1	yes	characteristic
218	C₄³	—	2	1	no	—
219	C₄³	C₂×D₆₁	1	1	yes	characteristic
220	#336	—	122	1	no	—
221	Q₈⋊C₈	—	122	4	no	—
222	C₆₁	#8564	1	1	yes	characteristic, complemented, Sylow
223	C₂²×Q₈	C₂×Dic₆₁	1	1	yes	characteristic
224	C₂²×C₈	—	122	2	no	—
225	C₂²×C₈	—	122	2	no	—
226	C₄×Q₈	—	2	2	no	—
227	C₄×Q₈	—	2	2	no	—
228	C₄×Q₈	—	2	2	no	—
229	C₄×Q₈	—	2	1	no	—
230	C₄×Q₈	—	2	1	no	—
231	C₄×Q₈	#92418	1	4	yes	complemented
232	C₄×Q₈	Dic₁₂₂	1	2	yes	—
233	C₄×Q₈	D₂₄₄	1	2	yes	—
234	C₂×C₄⋊C₄	—	2	1	no	—
235	C₂×C₄⋊C₄	—	2	1	no	—
236	C₂×C₄⋊C₄	—	2	1	no	—
237	C₂×C₄⋊C₄	C₂×Dic₆₁	1	1	yes	characteristic
238	C₂×C₄⋊C₄	C₂×Dic₆₁	1	1	yes	characteristic
239	C₂×C₄⋊C₄	C₂×Dic₆₁	1	1	yes	characteristic
240	C₂×C₄²	—	2	1	no	—
241	C₂×C₄²	—	2	1	no	—
242	C₂×C₄²	—	2	1	no	—
243	C₂×C₄²	—	2	1	no	—
244	C₂×C₄²	—	2	1	no	—
245	C₂×C₄²	—	2	1	no	—
246	C₂×C₄²	C₂×Dic₆₁	1	1	yes	characteristic
247	C₂×C₄²	C₂×Dic₆₁	1	1	yes	characteristic
248	C₂×C₄²	C₂²⋊D₆₁	1	1	yes	characteristic
249	C₂×C₄²	C₂²⋊D₆₁	1	1	yes	characteristic
250	C₂×C₄²	C₂²⋊D₆₁	1	1	yes	characteristic
251	C₂×C₄²	C₂²⋊D₆₁	1	1	yes	characteristic
252	C₂×C₄²	C₂²×D₆₁	1	1	yes	characteristic
253	C₄⋊C₈	—	122	4	no	—
254	C₄⋊C₈	—	122	2	no	—
255	C₄⋊C₈	—	122	2	no	—
256	C₄⋊C₈	—	244	2	no	—
257	C₄⋊C₈	—	244	2	no	—
258	C₄×C₈	—	122	2	no	—
259	C₄×C₈	—	122	2	no	—
260	#95	—	2	1	no	—
261	#95	—	2	1	no	—
262	#95	—	2	1	no	—
263	C₂×Q₈	—	2	1	no	—
264	C₂×Q₈	—	2	1	no	—
265	C₂×Q₈	—	2	1	no	—
266	C₂×Q₈	C₂×#92418	1	2	yes	—
267	C₂×Q₈	#11758194	1	2	yes	—
268	C₂×Q₈	C₄⋊Dic₆₁	1	2	yes	—
269	C₂²×C₄	—	2	1	no	—
270	C₂²×C₄	—	2	1	no	—
271	C₂²×C₄	—	2	1	no	—
272	C₂²×C₄	—	2	1	no	—
273	C₂²×C₄	C₂²⋊Dic₆₁	1	1	yes	characteristic
274	C₂²×C₄	C₂²⋊Dic₆₁	1	1	yes	characteristic
275	C₂²×C₄	C₂²⋊Dic₆₁	1	1	yes	characteristic
276	C₂²×C₄	C₂²⋊Dic₆₁	1	1	yes	characteristic
277	C₂²×C₄	C₂²×Dic₆₁	1	1	yes	characteristic
278	C₂²×C₄	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
279	C₂²×C₄	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
280	C₂×C₈	—	122	4	no	—
281	C₂×C₈	—	244	2	no	—
282	C₂×C₈	—	244	2	no	—
283	C₂×C₈	—	244	2	no	—
284	C₂×C₈	—	244	2	no	—
285	C₂×C₈	—	244	2	no	—
286	C₄⋊C₄	—	2	4	no	—
287	C₄⋊C₄	—	2	4	no	—
288	C₄⋊C₄	—	2	1	no	—
289	C₄⋊C₄	—	2	2	no	—
290	C₄⋊C₄	—	2	2	no	—
291	C₄⋊C₄	—	2	1	no	—
292	C₄⋊C₄	—	2	1	no	—
293	C₄⋊C₄	C₂×#92418	1	2	yes	—
294	C₄⋊C₄	#11758194	1	2	yes	—
295	C₄⋊C₄	C₄⋊Dic₆₁	1	2	yes	—
296	C₄²	—	2	4	no	—
297	C₄²	—	2	4	no	—
298	C₄²	—	2	2	no	—
299	C₄²	—	2	2	no	—
300	C₄²	—	2	2	no	—
301	C₄²	—	2	1	no	—
302	C₄²	—	2	1	no	—
303	C₄²	—	2	1	no	—
304	C₄²	—	2	1	no	—
305	C₄²	—	4	1	no	—
306	C₄²	—	4	2	no	—
307	C₄²	—	4	2	no	—
308	C₄²	—	4	1	no	—
309	C₄²	—	4	1	no	—
310	C₄²	C₂×#92418	1	2	yes	—
311	C₄²	#11758194	1	2	yes	—
312	C₄²	#11758201	1	2	yes	—
313	C₄²	#11758202	1	2	yes	—
314	C₄²	C₂×Dic₁₂₂	1	1	yes	characteristic
315	C₄²	C₂×D₂₄₄	1	1	yes	characteristic
316	C₄²	#11758222	1	1	yes	characteristic
317	C₄²	#11758222	1	1	yes	characteristic
318	C₂³	C₂×C₂²⋊Dic₆₁	1	1	yes	characteristic
319	Q₈	—	2	2	no	—
320	Q₈	—	2	2	no	—
321	Q₈	—	2	2	no	—
322	Q₈	C₄⋊#92418	1	4	yes	complemented
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	2	1	no	—
327	C₂×C₄	—	2	1	no	—
328	C₂×C₄	—	2	1	no	—
329	C₂×C₄	—	2	1	no	—
330	C₂×C₄	—	2	1	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	4	1	no	—
339	C₂×C₄	—	4	1	no	—
340	C₂×C₄	—	4	1	no	—
341	C₂×C₄	—	4	1	no	—
342	C₂×C₄	—	4	1	no	—
343	C₂×C₄	—	4	1	no	—
344	C₂×C₄	C₂²⋊#92418	1	2	yes	—
345	C₂×C₄	C₂²⋊#92418	1	2	yes	—
346	C₂×C₄	#14519701	1	2	yes	—
347	C₂×C₄	#14519701	1	2	yes	—
348	C₂×C₄	#14519704	1	2	yes	—
349	C₂×C₄	C₂×C₄⋊Dic₆₁	1	1	yes	characteristic
350	C₂×C₄	#14519736	1	1	yes	characteristic
351	C₂×C₄	#14519751	1	1	yes	characteristic
352	C₂×C₄	#14519751	1	1	yes	characteristic
353	C₂×C₄	#14519756	1	1	yes	characteristic
354	C₂×C₄	#14519756	1	1	yes	characteristic
355	C₂×C₄	C₂²×#92418	1	1	yes	characteristic
356	C₂×C₄	C₂×#11758194	1	1	yes	characteristic
357	C₂×C₄	C₂×#11758194	1	1	yes	characteristic
358	C₂×C₄	C₂×#11758194	1	1	yes	characteristic
359	C₂×C₄	C₂×#11758201	1	1	yes	characteristic
360	C₂×C₄	C₂×#11758202	1	1	yes	characteristic
361	C₂×C₄	#14519802	1	1	yes	characteristic
362	C₂×C₄	#14519807	1	1	yes	characteristic
363	C₈	—	488	2	no	—
364	C₈	—	244	4	no	—
365	C₂²	#16839622	1	1	yes	characteristic
366	C₂²	C₂×C₂²⋊#92418	1	1	yes	characteristic
367	C₂²	#16839726	1	1	yes	characteristic
368	C₂²	C₂×#14519701	1	1	yes	characteristic
369	C₂²	#16839763	1	1	yes	characteristic
370	C₂²	C₂×#14519704	1	1	yes	characteristic
371	C₂²	#16839779	1	1	yes	characteristic
372	C₄	—	2	2	no	—
373	C₄	—	2	2	no	—
374	C₄	—	2	4	no	—
375	C₄	—	2	1	no	—
376	C₄	—	2	1	no	—
377	C₄	—	4	2	no	—
378	C₄	—	4	1	no	—
379	C₄	—	4	2	no	—
380	C₄	—	4	2	no	—
381	C₄	Q₈⋊#92418	1	4	yes	complemented
382	C₄	C₂×C₄⋊#92418	1	1	yes	characteristic
383	C₄	#16839786	1	1	yes	characteristic
384	C₄	#16839815	1	1	yes	characteristic
385	C₄	#16839819	1	1	yes	characteristic
386	C₄	#16839962	1	1	yes	characteristic
387	C₄	#16839972	1	1	yes	characteristic
388	C₄	#16840047	1	1	yes	characteristic
389	C₄	#16840057	1	1	yes	characteristic
390	C₂	C₂×Q₈⋊#92418	1	1	yes	characteristic
391	C₂	#21444206	1	1	yes	characteristic
392	C₂	#21444248	1	1	yes	characteristic
393	C₂	#21444258	1	1	yes	characteristic
394	C₂	#21445799	1	1	yes	characteristic
395	C₂	#21445824	1	1	yes	characteristic
396	C₂	#21445839	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×C₂²⋊D₆₁
commutator	C₂×C₄×C₆₁	C₂²×C₈
Frattini	C₂×C₄²	C₂²×D₆₁
Fitting	C₄²×Q₈×C₆₁	C₂
socle, prime radical	C₂³×C₆₁	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₆₁	C₂³
hypercenter	C₄²×Q₈	D₆₁
hypocenter	C₆₁	#8564
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ C₄²×Q₈

Complements

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

N	H ≅ G/N	type
39. C₄×Q₈×C₆₁	C₈	semidirect
123. Q₈×C₆₁	C₄⋊C₈	semidirect
183. C₄×C₆₁	Q₈⋊C₈	semidirect
222. C₆₁	#8564	semidirect
231. C₄×Q₈	#92418	semidirect
322. Q₈	C₄⋊#92418	semidirect
381. C₄	Q₈⋊#92418	semidirect

Maximal subgroups

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

subgroup	index
#21445971	2
C₄×C₄⋊#92418	2
C₂×Q₈⋊#92418	2
#21443660	2
C₄²×Q₈×C₆₁	2
#8564	61