Subgroups — C₂²×Q₈×C₂²⋊D₆₁ #30586927

Order 15616.

11798 conjugacy classes of subgroups.

The subgroup lattice has 318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×Q₈×D₆₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×Q₈×C₂²⋊D₆₁	C₂	1	48	yes	maximal, direct product factor
3	C₂²×#14519775	C₂	1	3	yes	maximal, complemented
4	C₂²×#14519756	C₂	1	3	yes	maximal, complemented
5	C₂²×#14519753	C₂	1	3	yes	maximal, complemented
6	C₂²×Q₈×Dic₆₁	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×C₄×C₂²⋊D₆₁	C₂	1	3	yes	maximal
8	C₂⁴×Q₈×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×Dic₁₂₂	C₂²	1	3	yes	—
10	C₂²×Q₈×D₆₁	—	2	16	no	—
11	C₂²×Q₈×D₆₁	C₂²	1	24	yes	complemented
12	C₂³×C₂²⋊D₆₁	C₂²	1	1	yes	characteristic
13	C₂³×C₄×D₆₁	C₂²	1	3	yes	—
14	Q₈×C₂²⋊D₆₁	C₂²	1	256	yes	direct product factor
15	C₂×#14519775	C₂²	1	72	yes	complemented
16	C₂×#14519756	C₂²	1	72	yes	complemented
17	C₂×#14519753	C₂²	1	72	yes	complemented
18	C₂×Q₈×Dic₆₁	C₂²	1	24	yes	complemented
19	C₂×C₄×C₂²⋊D₆₁	C₂²	1	72	yes	—
20	C₂²×C₄⋊Dic₆₁	C₂²	1	3	yes	—
21	C₂²×#11758196	C₂²	1	3	yes	—
22	C₂²×#11758196	C₂²	1	6	yes	—
23	C₂²×C₂²⋊Dic₆₁	C₂²	1	3	yes	—
24	C₂²×#11758198	C₂²	1	3	yes	—
25	C₂²×C₄×Dic₆₁	C₂²	1	3	yes	—
26	C₂³×Q₈×C₆₁	—	2	16	no	—
27	C₂³×Q₈×C₆₁	C₂²	1	3	yes	—
28	C₂³×Q₈×C₆₁	C₂²	1	1	yes	characteristic
29	C₂³×Q₈×C₆₁	C₂²	1	24	yes	complemented
30	C₂⁴×C₄×C₆₁	C₂²	1	3	yes	—
31	C₂⁴×D₆₁	C₂³	1	1	yes	characteristic
32	C₂²×Dic₁₂₂	—	2	24	no	—
33	C₂²×Dic₁₂₂	C₂³	1	36	yes	—
34	C₂×Q₈×D₆₁	—	2	192	no	—
35	C₂×Q₈×D₆₁	C₂³	1	64	yes	complemented
36	C₂²×C₂²⋊D₆₁	Q₈	1	16	yes	direct product factor
37	C₂²×C₂²⋊D₆₁	C₂³	1	12	yes	—
38	C₂³×Dic₆₁	C₂³	1	3	yes	—
39	C₂³×Dic₆₁	C₂³	1	3	yes	—
40	C₂³×Dic₆₁	C₂³	1	1	yes	characteristic
41	C₂²×C₄×D₆₁	—	2	24	no	—
42	C₂²×C₄×D₆₁	C₂³	1	36	yes	—
43	#14519775	C₂³	1	192	yes	complemented
44	#14519756	C₂³	1	192	yes	complemented
45	#14519753	C₂³	1	192	yes	complemented
46	Q₈×Dic₆₁	C₂³	1	64	yes	complemented
47	C₄×C₂²⋊D₆₁	C₂³	1	192	yes	—
48	C₂×C₄⋊Dic₆₁	C₂³	1	36	yes	—
49	C₂×#11758196	C₂³	1	36	yes	—
50	C₂×#11758196	C₂³	1	72	yes	—
51	C₂×C₂²⋊Dic₆₁	C₂³	1	36	yes	—
52	C₂×#11758198	C₂³	1	36	yes	—
53	C₂×C₄×Dic₆₁	C₂³	1	36	yes	—
54	C₂⁵×C₆₁	C₂³	1	1	yes	characteristic
55	C₂²×Q₈×C₆₁	—	2	192	no	—
56	C₂²×Q₈×C₆₁	—	2	24	no	—
57	C₂²×Q₈×C₆₁	D₄	1	16	yes	complemented
58	C₂²×Q₈×C₆₁	C₂³	1	36	yes	—
59	C₂²×Q₈×C₆₁	C₂³	1	12	yes	—
60	C₂²×Q₈×C₆₁	C₂³	1	64	yes	complemented
61	C₂³×C₄×C₆₁	—	2	24	no	—
62	C₂³×C₄×C₆₁	C₂³	1	3	yes	—
63	C₂³×C₄×C₆₁	C₂³	1	36	yes	—
64	C₂³×C₄×C₆₁	C₂³	1	3	yes	—
65	C₂⁴×C₆₁	—	2	4	no	—
66	C₂⁴×C₆₁	—	2	4	no	—
67	C₂⁴×C₆₁	C₂×Q₈	1	8	yes	complemented
68	C₂⁴×C₆₁	C₂⁴	1	6	yes	—
69	C₂⁴×C₆₁	C₂⁴	1	1	yes	characteristic
70	C₂³×D₆₁	—	2	4	no	—
71	C₂³×D₆₁	—	2	4	no	—
72	C₂³×D₆₁	C₂×Q₈	1	8	yes	complemented
73	C₂³×D₆₁	C₂⁴	1	6	yes	—
74	C₂×Q₈×C₆₁	—	2	256	no	—
75	C₂×Q₈×C₆₁	—	2	144	no	—
76	C₂×Q₈×C₆₁	C₂×D₄	1	96	yes	complemented
77	C₂×Q₈×C₆₁	C₂⁴	1	48	yes	—
78	C₂×Q₈×C₆₁	C₂⁴	1	16	yes	—
79	C₂²×C₄×C₆₁	—	2	12	no	—
80	C₂²×C₄×C₆₁	—	2	144	no	—
81	C₂²×C₄×C₆₁	C₂×D₄	1	24	yes	—
82	C₂²×C₄×C₆₁	C₂⁴	1	18	yes	—
83	C₂²×C₄×C₆₁	C₂⁴	1	48	yes	—
84	C₂²×C₄×C₆₁	C₂⁴	1	18	yes	—
85	C₂×C₂²⋊D₆₁	C₂×Q₈	1	96	yes	direct product factor
86	C₂×C₂²⋊D₆₁	C₂⁴	1	16	yes	—
87	C₂²×Dic₆₁	—	2	12	no	—
88	C₂²×Dic₆₁	—	2	12	no	—
89	C₂²×Dic₆₁	C₂×Q₈	1	8	yes	complemented
90	C₂²×Dic₆₁	C₂⁴	1	18	yes	—
91	C₂²×Dic₆₁	C₂⁴	1	18	yes	—
92	C₂²×Dic₆₁	C₂⁴	1	6	yes	—
93	Q₈×D₆₁	—	2	256	no	—
94	C₂×C₄×D₆₁	—	2	144	no	—
95	C₂×C₄×D₆₁	C₂⁴	1	48	yes	—
96	C₂×Dic₁₂₂	—	2	144	no	—
97	C₂×Dic₁₂₂	C₂⁴	1	48	yes	—
98	C₂²⋊Dic₆₁	C₂⁴	1	48	yes	—
99	#11758198	C₂⁴	1	48	yes	—
100	C₄⋊Dic₆₁	C₂⁴	1	48	yes	—
101	#11758196	C₂⁴	1	48	yes	—
102	#11758196	C₂⁴	1	96	yes	—
103	C₄×Dic₆₁	C₂⁴	1	48	yes	—
104	C₂³×C₆₁	—	2	32	no	—
105	C₂³×C₆₁	—	2	12	no	—
106	C₂³×C₆₁	—	2	12	no	—
107	C₂³×C₆₁	C₂²×D₄	1	4	yes	—
108	C₂³×C₆₁	C₂²×Q₈	1	4	yes	—
109	C₂³×C₆₁	C₂²×Q₈	1	24	yes	complemented
110	C₂³×C₆₁	2₋¹⁺⁴	1	4	yes	—
111	C₂³×C₆₁	C₂⁵	1	4	yes	—
112	C₂³×C₆₁	C₂⁵	1	3	yes	—
113	C₂²×D₆₁	—	2	32	no	—
114	C₂²×D₆₁	—	2	12	no	—
115	C₂²×D₆₁	—	2	12	no	—
116	C₂²×D₆₁	C₂²×Q₈	1	24	yes	complemented
117	C₂²×D₆₁	C₂⁵	1	4	yes	—
118	Q₈×C₆₁	—	2	96	no	—
119	Q₈×C₆₁	C₂²×D₄	1	64	yes	complemented
120	C₂×C₄×C₆₁	—	2	36	no	—
121	C₂×C₄×C₆₁	—	2	96	no	—
122	C₂×C₄×C₆₁	C₂²×D₄	1	72	yes	—
123	C₂×C₄×C₆₁	C₂⁵	1	12	yes	—
124	C₂×C₄×C₆₁	C₂⁵	1	12	yes	—
125	C₂²⋊D₆₁	C₂²×Q₈	1	64	yes	direct product factor
126	C₂×Dic₆₁	—	2	36	no	—
127	C₂×Dic₆₁	—	2	36	no	—
128	C₂×Dic₆₁	C₂²×Q₈	1	24	yes	complemented
129	C₂×Dic₆₁	C₂⁵	1	12	yes	—
130	C₂×Dic₆₁	C₂⁵	1	12	yes	—
131	C₂×Dic₆₁	C₂⁵	1	4	yes	—
132	C₄×D₆₁	—	2	96	no	—
133	Dic₁₂₂	—	2	96	no	—
134	C₂²×D₄×Q₈	—	61	1	no	maximal, Sylow
135	C₂²×C₆₁	—	2	4	no	—
136	C₂²×C₆₁	—	2	4	no	—
137	C₂²×C₆₁	—	2	48	no	—
138	C₂²×C₆₁	D₄×Q₈	1	16	yes	complemented
139	C₂²×C₆₁	C₂³×D₄	1	6	yes	—
140	C₂²×C₆₁	C₂³×Q₈	1	6	yes	—
141	C₂²×C₆₁	C₂³×Q₈	1	8	yes	complemented
142	C₂²×C₆₁	C₂×2₋¹⁺⁴	1	6	yes	—
143	C₂²×C₆₁	C₂⁶	1	1	yes	characteristic
144	C₂×D₆₁	—	2	4	no	—
145	C₂×D₆₁	—	2	4	no	—
146	C₂×D₆₁	—	2	48	no	—
147	C₂×D₆₁	C₂³×Q₈	1	8	yes	complemented
148	C₄×C₆₁	—	2	12	no	—
149	C₄×C₆₁	C₂³×D₄	1	24	yes	—
150	Dic₆₁	—	2	12	no	—
151	Dic₆₁	—	2	12	no	—
152	Dic₆₁	C₂³×Q₈	1	8	yes	complemented
153	C₂⁴×Q₈	—	61	1	no	—
154	C₂⁴×Q₈	D₆₁	1	1	yes	characteristic, complemented
155	C₂×D₄×Q₈	—	61	48	no	—
156	C₂²×C₄⋊Q₈	—	61	3	no	—
157	C₂²×C₂²⋊Q₈	—	61	3	no	—
158	C₂²×C₂²⋊Q₈	—	61	3	no	—
159	C₂²×C₄×Q₈	—	61	1	no	—
160	C₂²×C₄×D₄	—	61	3	no	—
161	C₂×C₆₁	—	2	8	no	—
162	C₂×C₆₁	C₂×D₄×Q₈	1	12	yes	complemented
163	C₂×C₆₁	C₂⁴×D₄	1	1	yes	characteristic
164	C₂×C₆₁	C₂⁴×Q₈	1	1	yes	characteristic
165	C₂×C₆₁	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
166	D₆₁	—	2	8	no	—
167	C₂³×Q₈	—	2	16	no	—
168	C₂³×Q₈	—	61	24	no	—
169	C₂³×Q₈	—	61	3	no	—
170	C₂³×Q₈	—	122	16	no	—
171	C₂³×Q₈	C₂×D₆₁	1	3	yes	—
172	C₂³×Q₈	C₂×D₆₁	1	1	yes	characteristic
173	C₂³×Q₈	C₂×D₆₁	1	24	yes	complemented
174	C₂³×D₄	—	61	1	no	—
175	C₂⁴×C₄	—	61	3	no	—
176	C₂⁴×C₄	C₂×D₆₁	1	3	yes	—
177	D₄×Q₈	—	61	256	no	—
178	C₂×C₄⋊Q₈	—	61	72	no	—
179	C₂×C₂²⋊Q₈	—	61	72	no	—
180	C₂×C₂²⋊Q₈	—	61	72	no	—
181	C₂×C₄×Q₈	—	61	24	no	—
182	C₂×C₄×D₄	—	61	72	no	—
183	C₂²×C₄⋊C₄	—	61	3	no	—
184	C₂²×C₄⋊C₄	—	61	6	no	—
185	C₂²×C₄⋊C₄	—	61	3	no	—
186	C₂²×C₂²⋊C₄	—	61	3	no	—
187	C₂²×C₂²⋊C₄	—	61	3	no	—
188	C₂²×C₄²	—	61	3	no	—
189	C₆₁	C₂²×D₄×Q₈	1	1	yes	characteristic, complemented, Sylow
190	C₂⁵	—	61	1	no	—
191	C₂⁵	C₂²×D₆₁	1	1	yes	characteristic
192	C₂²×Q₈	—	2	192	no	—
193	C₂²×Q₈	—	2	24	no	—
194	C₂²×Q₈	—	61	64	no	—
195	C₂²×Q₈	—	61	36	no	—
196	C₂²×Q₈	—	122	192	no	—
197	C₂²×Q₈	—	122	24	no	—
198	C₂²×Q₈	C₂²⋊D₆₁	1	16	yes	direct product factor
199	C₂²×Q₈	C₂²×D₆₁	1	36	yes	—
200	C₂²×Q₈	C₂²×D₆₁	1	12	yes	—
201	C₂²×Q₈	C₂²×D₆₁	1	64	yes	complemented
202	C₂²×D₄	—	61	16	no	—
203	C₂²×D₄	—	61	12	no	—
204	C₂³×C₄	—	2	24	no	—
205	C₂³×C₄	—	61	1	no	—
206	C₂³×C₄	—	61	3	no	—
207	C₂³×C₄	—	61	3	no	—
208	C₂³×C₄	—	61	36	no	—
209	C₂³×C₄	—	122	24	no	—
210	C₂³×C₄	C₂²×D₆₁	1	36	yes	—
211	C₂³×C₄	C₂²×D₆₁	1	3	yes	—
212	C₂³×C₄	C₂²×D₆₁	1	3	yes	—
213	C₄⋊Q₈	—	61	192	no	—
214	C₂²⋊Q₈	—	61	192	no	—
215	C₂²⋊Q₈	—	61	192	no	—
216	C₄×Q₈	—	61	64	no	—
217	C₄×D₄	—	61	192	no	—
218	C₂×C₄⋊C₄	—	61	36	no	—
219	C₂×C₄⋊C₄	—	61	36	no	—
220	C₂×C₄⋊C₄	—	61	72	no	—
221	C₂×C₂²⋊C₄	—	61	36	no	—
222	C₂×C₂²⋊C₄	—	61	36	no	—
223	C₂×C₄²	—	61	36	no	—
224	C₂⁴	—	2	4	no	—
225	C₂⁴	—	2	4	no	—
226	C₂⁴	—	61	8	no	—
227	C₂⁴	—	61	6	no	—
228	C₂⁴	—	122	4	no	—
229	C₂⁴	—	122	4	no	—
230	C₂⁴	Q₈×D₆₁	1	8	yes	complemented
231	C₂⁴	C₂³×D₆₁	1	6	yes	—
232	C₂⁴	C₂³×D₆₁	1	1	yes	characteristic
233	C₂×Q₈	—	2	256	no	—
234	C₂×Q₈	—	2	144	no	—
235	C₂×Q₈	—	61	48	no	—
236	C₂×Q₈	—	122	256	no	—
237	C₂×Q₈	—	122	144	no	—
238	C₂×Q₈	C₂×C₂²⋊D₆₁	1	96	yes	direct product factor
239	C₂×Q₈	C₂³×D₆₁	1	48	yes	—
240	C₂×Q₈	C₂³×D₆₁	1	16	yes	—
241	C₂×D₄	—	61	96	no	—
242	C₂×D₄	—	61	16	no	—
243	C₂²×C₄	—	2	12	no	—
244	C₂²×C₄	—	2	144	no	—
245	C₂²×C₄	—	61	8	no	—
246	C₂²×C₄	—	61	6	no	—
247	C₂²×C₄	—	61	18	no	—
248	C₂²×C₄	—	61	18	no	—
249	C₂²×C₄	—	61	48	no	—
250	C₂²×C₄	—	122	12	no	—
251	C₂²×C₄	—	122	12	no	—
252	C₂²×C₄	—	122	144	no	—
253	C₂²×C₄	C₂×C₂²⋊D₆₁	1	24	yes	—
254	C₂²×C₄	C₂³×D₆₁	1	18	yes	—
255	C₂²×C₄	C₂³×D₆₁	1	48	yes	—
256	C₂²×C₄	C₂³×D₆₁	1	18	yes	—
257	C₄⋊C₄	—	61	48	no	—
258	C₄⋊C₄	—	61	96	no	—
259	C₄⋊C₄	—	61	48	no	—
260	C₂²⋊C₄	—	61	48	no	—
261	C₂²⋊C₄	—	61	48	no	—
262	C₄²	—	61	48	no	—
263	C₂³	—	2	12	no	—
264	C₂³	—	2	12	no	—
265	C₂³	—	2	32	no	—
266	C₂³	—	61	24	no	—
267	C₂³	—	61	4	no	—
268	C₂³	—	122	12	no	—
269	C₂³	—	122	12	no	—
270	C₂³	—	122	32	no	—
271	C₂³	C₂²×C₂²⋊D₆₁	1	4	yes	—
272	C₂³	C₂×Q₈×D₆₁	1	4	yes	—
273	C₂³	C₂×Q₈×D₆₁	1	24	yes	complemented
274	C₂³	#14519825	1	4	yes	—
275	C₂³	C₂⁴×D₆₁	1	4	yes	—
276	C₂³	C₂⁴×D₆₁	1	3	yes	—
277	Q₈	—	2	96	no	—
278	Q₈	—	122	96	no	—
279	Q₈	C₂²×C₂²⋊D₆₁	1	64	yes	direct product factor
280	D₄	—	61	64	no	—
281	C₂×C₄	—	2	36	no	—
282	C₂×C₄	—	2	96	no	—
283	C₂×C₄	—	61	24	no	—
284	C₂×C₄	—	61	4	no	—
285	C₂×C₄	—	61	12	no	—
286	C₂×C₄	—	61	12	no	—
287	C₂×C₄	—	122	36	no	—
288	C₂×C₄	—	122	36	no	—
289	C₂×C₄	—	122	96	no	—
290	C₂×C₄	C₂²×C₂²⋊D₆₁	1	72	yes	—
291	C₂×C₄	C₂⁴×D₆₁	1	12	yes	—
292	C₂×C₄	C₂⁴×D₆₁	1	12	yes	—
293	C₂²	—	2	48	no	—
294	C₂²	—	2	4	no	—
295	C₂²	—	2	4	no	—
296	C₂²	—	61	8	no	—
297	C₂²	—	122	48	no	—
298	C₂²	—	122	4	no	—
299	C₂²	—	122	4	no	—
300	C₂²	Q₈×C₂²⋊D₆₁	1	16	yes	direct product factor
301	C₂²	C₂³×C₂²⋊D₆₁	1	6	yes	—
302	C₂²	C₂²×Q₈×D₆₁	1	6	yes	—
303	C₂²	C₂²×Q₈×D₆₁	1	8	yes	complemented
304	C₂²	C₂×#14519825	1	6	yes	—
305	C₂²	C₂⁵×D₆₁	1	1	yes	characteristic
306	C₄	—	2	12	no	—
307	C₄	—	61	8	no	—
308	C₄	—	122	12	no	—
309	C₄	—	122	12	no	—
310	C₄	C₂³×C₂²⋊D₆₁	1	24	yes	—
311	C₂	—	2	8	no	—
312	C₂	—	122	8	no	—
313	C₂	C₂×Q₈×C₂²⋊D₆₁	1	12	yes	direct product factor
314	C₂	C₂⁴×C₂²⋊D₆₁	1	1	yes	characteristic
315	C₂	C₂³×Q₈×D₆₁	1	1	yes	characteristic
316	C₂	C₂²×#14519825	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂³×D₆₁
commutator, cosocle	C₂²×C₆₁	C₂⁶
Frattini	C₂²	C₂⁵×D₆₁
Fitting	C₂⁴×Q₈×C₆₁	C₂
socle	C₂⁴×C₆₁	C₂⁴
prime radical	C₂³×C₂²⋊D₆₁	C₂²
hypercenter	C₂⁴×Q₈	D₆₁
hypocenter	C₆₁	C₂²×D₄×Q₈
LCS	G ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂⁴ ◁ C₂⁴×Q₈

Complements

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

N	H ≅ G/N	type
1. C₂³×Q₈×D₆₁	C₂	semidirect
2. C₂×Q₈×C₂²⋊D₆₁	C₂	direct (N × H)
3. C₂²×#14519775	C₂	semidirect
4. C₂²×#14519756	C₂	semidirect
5. C₂²×#14519753	C₂	semidirect
6. C₂²×Q₈×Dic₆₁	C₂	semidirect
8. C₂⁴×Q₈×C₆₁	C₂	semidirect
11. C₂²×Q₈×D₆₁	C₂²	semidirect
14. Q₈×C₂²⋊D₆₁	C₂²	direct (N × H)
15. C₂×#14519775	C₂²	semidirect
16. C₂×#14519756	C₂²	semidirect
17. C₂×#14519753	C₂²	semidirect
18. C₂×Q₈×Dic₆₁	C₂²	semidirect
29. C₂³×Q₈×C₆₁	C₂²	semidirect
35. C₂×Q₈×D₆₁	C₂³	semidirect
36. C₂²×C₂²⋊D₆₁	Q₈	direct (N × H)
43. #14519775	C₂³	semidirect
44. #14519756	C₂³	semidirect
45. #14519753	C₂³	semidirect
46. Q₈×Dic₆₁	C₂³	semidirect
57. C₂²×Q₈×C₆₁	D₄	semidirect
60. C₂²×Q₈×C₆₁	C₂³	semidirect
67. C₂⁴×C₆₁	C₂×Q₈	semidirect
72. C₂³×D₆₁	C₂×Q₈	semidirect
76. C₂×Q₈×C₆₁	C₂×D₄	semidirect
85. C₂×C₂²⋊D₆₁	C₂×Q₈	direct (N × H)
89. C₂²×Dic₆₁	C₂×Q₈	semidirect
109. C₂³×C₆₁	C₂²×Q₈	semidirect
116. C₂²×D₆₁	C₂²×Q₈	semidirect
119. Q₈×C₆₁	C₂²×D₄	semidirect
125. C₂²⋊D₆₁	C₂²×Q₈	direct (N × H)
128. C₂×Dic₆₁	C₂²×Q₈	semidirect
138. C₂²×C₆₁	D₄×Q₈	semidirect
141. C₂²×C₆₁	C₂³×Q₈	semidirect
147. C₂×D₆₁	C₂³×Q₈	semidirect
152. Dic₆₁	C₂³×Q₈	semidirect
154. C₂⁴×Q₈	D₆₁	semidirect
162. C₂×C₆₁	C₂×D₄×Q₈	semidirect
173. C₂³×Q₈	C₂×D₆₁	semidirect
189. C₆₁	C₂²×D₄×Q₈	semidirect
198. C₂²×Q₈	C₂²⋊D₆₁	direct (N × H)
201. C₂²×Q₈	C₂²×D₆₁	semidirect
230. C₂⁴	Q₈×D₆₁	semidirect
238. C₂×Q₈	C₂×C₂²⋊D₆₁	direct (N × H)
273. C₂³	C₂×Q₈×D₆₁	semidirect
279. Q₈	C₂²×C₂²⋊D₆₁	direct (N × H)
300. C₂²	Q₈×C₂²⋊D₆₁	direct (N × H)
303. C₂²	C₂²×Q₈×D₆₁	semidirect
313. C₂	C₂×Q₈×C₂²⋊D₆₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×Q₈×D₆₁	2
C₂×Q₈×C₂²⋊D₆₁	2
C₂²×#14519775	2
C₂²×#14519756	2
C₂²×#14519753	2
C₂²×Q₈×Dic₆₁	2
C₂²×C₄×C₂²⋊D₆₁	2
C₂⁴×Q₈×C₆₁	2
C₂²×D₄×Q₈	61

Subgroups — C22×Q8×C22⋊D61 #30586927

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×Q₈×C₂²⋊D₆₁ #30586927