Subgroups — C₂²×#16839834 #30543852

Order 15616.

3350 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×#11758194	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂⁴×#92418	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#16839834	C₂	1	24	yes	maximal, direct product factor
4	C₂²×C₄⋊#92418	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×C₂²⋊#92418	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₂²⋊#92418	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×#14519688	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₄×D₄×C₆₁	C₂	1	1	yes	maximal, characteristic
9	C₂²×#11758194	—	2	8	no	—
10	C₂²×#11758194	C₂²	1	12	yes	complemented
11	C₂³×#92418	—	2	8	no	—
12	C₂³×#92418	C₂²	1	1	yes	characteristic
13	C₂³×#92418	C₂²	1	1	yes	characteristic
14	C₂³×#92418	C₂²	1	1	yes	characteristic
15	C₂³×#92418	C₂²	1	1	yes	characteristic
16	C₂³×#92418	C₂²	1	12	yes	complemented
17	#16839834	C₂²	1	64	yes	direct product factor
18	C₂×C₄⋊#92418	C₂²	1	12	yes	complemented
19	C₂×C₂²⋊#92418	C₂²	1	12	yes	complemented
20	C₂×C₂²⋊#92418	C₂²	1	12	yes	complemented
21	C₂×#14519688	C₂²	1	12	yes	complemented
22	C₂³×D₄×C₆₁	C₄	1	1	yes	characteristic
23	C₂⁴×C₄×C₆₁	C₂²	1	1	yes	characteristic
24	C₂⁴×C₄×C₆₁	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₄×C₆₁	C₄	1	12	yes	—
26	C₂×C₄×D₄×C₆₁	C₂²	1	12	yes	—
27	C₂²×C₄⋊C₄×C₆₁	C₄	1	1	yes	characteristic
28	C₂²×C₂²⋊C₄×C₆₁	C₄	1	1	yes	characteristic
29	C₂²×C₂²⋊C₄×C₆₁	C₄	1	1	yes	characteristic
30	C₂²×C₄²×C₆₁	C₂²	1	1	yes	characteristic
31	C₂×#11758194	—	2	48	no	—
32	C₂×#11758194	C₂³	1	16	yes	complemented
33	C₂²×#92418	—	2	4	no	—
34	C₂²×#92418	—	2	4	no	—
35	C₂²×#92418	—	2	4	no	—
36	C₂²×#92418	—	2	48	no	—
37	C₂²×#92418	D₄	1	8	yes	complemented
38	C₂²×#92418	C₂³	1	6	yes	—
39	C₂²×#92418	C₂³	1	6	yes	—
40	C₂²×#92418	C₂³	1	6	yes	—
41	C₂²×#92418	C₂³	1	6	yes	—
42	C₂²×#92418	C₂³	1	16	yes	complemented
43	C₄⋊#92418	C₂³	1	16	yes	complemented
44	C₂²⋊#92418	C₂³	1	16	yes	complemented
45	C₂²⋊#92418	C₂³	1	16	yes	complemented
46	#14519688	C₂³	1	16	yes	complemented
47	C₂⁵×C₆₁	C₂×C₄	1	1	yes	characteristic
48	C₂⁵×C₆₁	C₂×C₄	1	1	yes	characteristic
49	C₂²×D₄×C₆₁	—	2	8	no	—
50	C₂²×D₄×C₆₁	C₂×C₄	1	12	yes	—
51	C₂³×C₄×C₆₁	—	2	4	no	—
52	C₂³×C₄×C₆₁	—	2	4	no	—
53	C₂³×C₄×C₆₁	—	2	4	no	—
54	C₂³×C₄×C₆₁	—	2	4	no	—
55	C₂³×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
56	C₂³×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
57	C₂³×C₄×C₆₁	C₂×C₄	1	6	yes	—
58	C₂³×C₄×C₆₁	C₂×C₄	1	6	yes	—
59	C₂³×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
60	C₂³×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
61	C₂³×C₄×C₆₁	C₂³	1	6	yes	—
62	C₂³×C₄×C₆₁	C₂³	1	6	yes	—
63	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
64	C₄×D₄×C₆₁	C₂×C₄	1	48	yes	—
65	C₄×D₄×C₆₁	C₂³	1	16	yes	—
66	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	12	yes	—
67	C₂×C₂²⋊C₄×C₆₁	C₂×C₄	1	12	yes	—
68	C₂×C₂²⋊C₄×C₆₁	C₂×C₄	1	12	yes	—
69	C₂×C₄²×C₆₁	C₂×C₄	1	6	yes	—
70	C₂×C₄²×C₆₁	C₂³	1	6	yes	—
71	C₂⁴×C₆₁	—	2	4	no	—
72	C₂⁴×C₆₁	—	2	4	no	—
73	C₂⁴×C₆₁	—	2	4	no	—
74	C₂⁴×C₆₁	—	2	4	no	—
75	C₂⁴×C₆₁	—	2	4	no	—
76	C₂⁴×C₆₁	M₁₆	1	8	yes	complemented
77	C₂⁴×C₆₁	C₂²×C₄	1	6	yes	—
78	C₂⁴×C₆₁	C₂²×C₄	1	6	yes	—
79	C₂⁴×C₆₁	C₂²×C₄	1	1	yes	characteristic
80	C₂×D₄×C₆₁	—	2	48	no	—
81	C₂×D₄×C₆₁	C₂²×C₄	1	16	yes	—
82	C₂²×C₄×C₆₁	—	2	4	no	—
83	C₂²×C₄×C₆₁	—	2	4	no	—
84	C₂²×C₄×C₆₁	—	2	4	no	—
85	C₂²×C₄×C₆₁	—	2	4	no	—
86	C₂²×C₄×C₆₁	—	2	24	no	—
87	C₂²×C₄×C₆₁	—	2	24	no	—
88	C₂²×C₄×C₆₁	—	2	12	no	—
89	C₂²×C₄×C₆₁	—	2	12	no	—
90	C₂²×C₄×C₆₁	—	2	12	no	—
91	C₂²×C₄×C₆₁	—	2	12	no	—
92	C₂²×C₄×C₆₁	C₂²×C₄	1	6	yes	—
93	C₂²×C₄×C₆₁	C₂²×C₄	1	6	yes	—
94	C₂²×C₄×C₆₁	C₂²×C₄	1	6	yes	—
95	C₂²×C₄×C₆₁	C₂²×C₄	1	6	yes	—
96	C₂²×C₄×C₆₁	C₂²×C₄	1	12	yes	—
97	C₂²×C₄×C₆₁	C₂²×C₄	1	12	yes	—
98	C₂²×C₄×C₆₁	C₂²×C₄	1	3	yes	—
99	C₂²×C₄×C₆₁	C₂×D₄	1	4	yes	—
100	C₂²×C₄×C₆₁	#41	1	4	yes	—
101	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
102	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
103	C₂²×C₄×C₆₁	C₂⁴	1	3	yes	—
104	C₄⋊C₄×C₆₁	C₂²×C₄	1	16	yes	—
105	C₂²⋊C₄×C₆₁	C₂²×C₄	1	16	yes	—
106	C₂²⋊C₄×C₆₁	C₂²×C₄	1	16	yes	—
107	C₄²×C₆₁	C₂²×C₄	1	12	yes	—
108	C₄²×C₆₁	C₂⁴	1	4	yes	—
109	#11758194	—	2	32	no	—
110	C₂×#92418	—	2	12	no	—
111	C₂×#92418	—	2	12	no	—
112	C₂×#92418	—	2	12	no	—
113	C₂×#92418	—	2	32	no	—
114	C₂×#92418	C₂×D₄	1	24	yes	complemented
115	C₂×#92418	C₂⁴	1	4	yes	—
116	C₂×#92418	C₂⁴	1	4	yes	—
117	C₂×#92418	C₂⁴	1	4	yes	—
118	C₂×#92418	C₂⁴	1	4	yes	—
119	C₂³×C₆₁	—	2	12	no	—
120	C₂³×C₆₁	—	2	12	no	—
121	C₂³×C₆₁	—	2	32	no	—
122	C₂³×C₆₁	—	2	12	no	—
123	C₂³×C₆₁	—	2	12	no	—
124	C₂³×C₆₁	—	2	12	no	—
125	C₂³×C₆₁	—	4	16	no	—
126	C₂³×C₆₁	C₄×D₄	1	4	yes	—
127	C₂³×C₆₁	C₂×M₁₆	1	4	yes	—
128	C₂³×C₆₁	C₂×M₁₆	1	24	yes	complemented
129	C₂³×C₆₁	#131	1	4	yes	—
130	C₂³×C₆₁	C₂³×C₄	1	4	yes	—
131	C₂³×C₆₁	C₂³×C₄	1	4	yes	—
132	C₂³×C₆₁	C₂³×C₄	1	3	yes	—
133	D₄×C₆₁	—	2	32	no	—
134	C₂×C₄×C₆₁	—	2	12	no	—
135	C₂×C₄×C₆₁	—	2	12	no	—
136	C₂×C₄×C₆₁	—	2	12	no	—
137	C₂×C₄×C₆₁	—	2	12	no	—
138	C₂×C₄×C₆₁	—	2	24	no	—
139	C₂×C₄×C₆₁	—	2	24	no	—
140	C₂×C₄×C₆₁	—	2	4	no	—
141	C₂×C₄×C₆₁	—	2	4	no	—
142	C₂×C₄×C₆₁	—	2	4	no	—
143	C₂×C₄×C₆₁	—	2	4	no	—
144	C₂×C₄×C₆₁	C₄×D₄	1	12	yes	—
145	C₂×C₄×C₆₁	C₂³×C₄	1	4	yes	—
146	C₂×C₄×C₆₁	C₂³×C₄	1	4	yes	—
147	C₂×C₄×C₆₁	C₂³×C₄	1	4	yes	—
148	C₂×C₄×C₆₁	C₂³×C₄	1	4	yes	—
149	C₂×C₄×C₆₁	C₂³×C₄	1	3	yes	—
150	C₂×C₄×C₆₁	C₂²×D₄	1	6	yes	—
151	C₂×C₄×C₆₁	C₂×#41	1	6	yes	—
152	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
153	#92418	—	2	4	no	—
154	#92418	—	2	4	no	—
155	#92418	—	2	4	no	—
156	#92418	C₂²×D₄	1	8	yes	complemented
157	C₂²×#435	—	61	1	no	maximal, Sylow
158	C₂²×C₆₁	—	2	4	no	—
159	C₂²×C₆₁	—	2	48	no	—
160	C₂²×C₆₁	—	2	4	no	—
161	C₂²×C₆₁	—	2	4	no	—
162	C₂²×C₆₁	—	2	4	no	—
163	C₂²×C₆₁	—	2	4	no	—
164	C₂²×C₆₁	—	4	24	no	—
165	C₂²×C₆₁	#435	1	16	yes	complemented
166	C₂²×C₆₁	C₂×C₄×D₄	1	6	yes	—
167	C₂²×C₆₁	C₂²×M₁₆	1	6	yes	—
168	C₂²×C₆₁	C₂²×M₁₆	1	8	yes	complemented
169	C₂²×C₆₁	C₂×#131	1	6	yes	—
170	C₂²×C₆₁	C₂⁴×C₄	1	1	yes	characteristic
171	C₄×C₆₁	—	2	4	no	—
172	C₄×C₆₁	—	2	4	no	—
173	C₄×C₆₁	—	2	4	no	—
174	C₄×C₆₁	—	2	4	no	—
175	C₄×C₆₁	C₂×C₄×D₄	1	6	yes	—
176	C₄×C₆₁	C₂³×D₄	1	1	yes	characteristic
177	C₄×C₆₁	C₂²×#41	1	1	yes	characteristic
178	C₂³×M₁₆	—	61	1	no	—
179	C₂⁴×C₈	—	61	1	no	—
180	C₂²×C₄×D₄	D₆₁	1	1	yes	characteristic
181	C₂×#435	—	61	24	no	—
182	C₂²×C₄⋊C₈	—	61	1	no	—
183	C₂²×C₂²⋊C₈	—	61	1	no	—
184	C₂²×C₂²⋊C₈	—	61	1	no	—
185	C₂²×#97	—	61	1	no	—
186	C₂×C₆₁	—	2	8	no	—
187	C₂×C₆₁	—	4	4	no	—
188	C₂×C₆₁	C₂×#435	1	12	yes	complemented
189	C₂×C₆₁	C₂²×C₄×D₄	1	1	yes	characteristic
190	C₂×C₆₁	C₂³×M₁₆	1	1	yes	characteristic
191	C₂×C₆₁	C₂²×#131	1	1	yes	characteristic
192	C₂³×D₄	Dic₆₁	1	1	yes	characteristic
193	C₂⁴×C₄	C₂×D₆₁	1	1	yes	characteristic
194	C₂⁴×C₄	C₂×D₆₁	1	1	yes	characteristic
195	C₂²×M₁₆	—	61	12	no	—
196	C₂²×M₁₆	—	122	8	no	—
197	C₂³×C₈	—	61	1	no	—
198	C₂³×C₈	—	61	12	no	—
199	C₂³×C₈	—	61	1	no	—
200	C₂³×C₈	—	61	1	no	—
201	C₂³×C₈	—	61	1	no	—
202	C₂³×C₈	—	122	8	no	—
203	C₂×C₄×D₄	Dic₆₁	1	12	yes	—
204	C₂×C₄×D₄	C₂×D₆₁	1	12	yes	—
205	C₂²×C₄⋊C₄	Dic₆₁	1	1	yes	characteristic
206	C₂²×C₂²⋊C₄	Dic₆₁	1	1	yes	characteristic
207	C₂²×C₂²⋊C₄	Dic₆₁	1	1	yes	characteristic
208	C₂²×C₄²	C₂×D₆₁	1	1	yes	characteristic
209	#435	—	61	64	no	—
210	C₂×C₄⋊C₈	—	61	12	no	—
211	C₂×C₂²⋊C₈	—	61	12	no	—
212	C₂×C₂²⋊C₈	—	61	12	no	—
213	C₂×#97	—	61	12	no	—
214	C₆₁	C₂²×#435	1	1	yes	characteristic, complemented, Sylow
215	C₂⁵	C₂×Dic₆₁	1	1	yes	characteristic
216	C₂⁵	C₂×Dic₆₁	1	1	yes	characteristic
217	C₂²×D₄	—	2	8	no	—
218	C₂²×D₄	C₂×Dic₆₁	1	12	yes	—
219	C₂³×C₄	—	2	4	no	—
220	C₂³×C₄	—	2	4	no	—
221	C₂³×C₄	—	2	4	no	—
222	C₂³×C₄	—	2	4	no	—
223	C₂³×C₄	C₂×Dic₆₁	1	1	yes	characteristic
224	C₂³×C₄	C₂×Dic₆₁	1	1	yes	characteristic
225	C₂³×C₄	C₂×Dic₆₁	1	1	yes	characteristic
226	C₂³×C₄	C₂×Dic₆₁	1	1	yes	characteristic
227	C₂³×C₄	C₂×Dic₆₁	1	6	yes	—
228	C₂³×C₄	C₂×Dic₆₁	1	6	yes	—
229	C₂³×C₄	C₂²×D₆₁	1	6	yes	—
230	C₂³×C₄	C₂²×D₆₁	1	6	yes	—
231	C₂³×C₄	C₂²×D₆₁	1	1	yes	characteristic
232	C₂×M₁₆	—	61	16	no	—
233	C₂×M₁₆	—	122	48	no	—
234	C₂²×C₈	—	61	8	no	—
235	C₂²×C₈	—	61	6	no	—
236	C₂²×C₈	—	61	6	no	—
237	C₂²×C₈	—	61	16	no	—
238	C₂²×C₈	—	61	6	no	—
239	C₂²×C₈	—	61	6	no	—
240	C₂²×C₈	—	122	48	no	—
241	C₂²×C₈	—	122	4	no	—
242	C₂²×C₈	—	122	4	no	—
243	C₂²×C₈	—	122	4	no	—
244	C₄×D₄	C₂×Dic₆₁	1	48	yes	—
245	C₄×D₄	C₂²×D₆₁	1	16	yes	—
246	C₂×C₄⋊C₄	C₂×Dic₆₁	1	12	yes	—
247	C₂×C₂²⋊C₄	C₂×Dic₆₁	1	12	yes	—
248	C₂×C₂²⋊C₄	C₂×Dic₆₁	1	12	yes	—
249	C₂×C₄²	C₂×Dic₆₁	1	6	yes	—
250	C₂×C₄²	C₂²×D₆₁	1	6	yes	—
251	C₄⋊C₈	—	61	16	no	—
252	C₂²⋊C₈	—	61	16	no	—
253	C₂²⋊C₈	—	61	16	no	—
254	#97	—	61	16	no	—
255	C₂⁴	—	2	4	no	—
256	C₂⁴	—	2	4	no	—
257	C₂⁴	—	2	4	no	—
258	C₂⁴	—	2	4	no	—
259	C₂⁴	—	2	4	no	—
260	C₂⁴	#11758194	1	8	yes	complemented
261	C₂⁴	C₂²×Dic₆₁	1	6	yes	—
262	C₂⁴	C₂²×Dic₆₁	1	6	yes	—
263	C₂⁴	C₂²×Dic₆₁	1	1	yes	characteristic
264	C₂×D₄	—	2	48	no	—
265	C₂×D₄	C₂²×Dic₆₁	1	16	yes	—
266	C₂²×C₄	—	2	4	no	—
267	C₂²×C₄	—	2	4	no	—
268	C₂²×C₄	—	2	4	no	—
269	C₂²×C₄	—	2	4	no	—
270	C₂²×C₄	—	2	12	no	—
271	C₂²×C₄	—	2	12	no	—
272	C₂²×C₄	—	2	12	no	—
273	C₂²×C₄	—	2	12	no	—
274	C₂²×C₄	—	2	24	no	—
275	C₂²×C₄	—	2	24	no	—
276	C₂²×C₄	D₄×D₆₁	1	4	yes	—
277	C₂²×C₄	#11758224	1	4	yes	—
278	C₂²×C₄	C₂²×Dic₆₁	1	6	yes	—
279	C₂²×C₄	C₂²×Dic₆₁	1	6	yes	—
280	C₂²×C₄	C₂²×Dic₆₁	1	6	yes	—
281	C₂²×C₄	C₂²×Dic₆₁	1	6	yes	—
282	C₂²×C₄	C₂²×Dic₆₁	1	12	yes	—
283	C₂²×C₄	C₂²×Dic₆₁	1	12	yes	—
284	C₂²×C₄	C₂²×Dic₆₁	1	3	yes	—
285	C₂²×C₄	C₂³×D₆₁	1	4	yes	—
286	C₂²×C₄	C₂³×D₆₁	1	4	yes	—
287	C₂²×C₄	C₂³×D₆₁	1	3	yes	—
288	M₁₆	—	122	32	no	—
289	C₂×C₈	—	61	24	no	—
290	C₂×C₈	—	61	4	no	—
291	C₂×C₈	—	61	4	no	—
292	C₂×C₈	—	61	4	no	—
293	C₂×C₈	—	61	4	no	—
294	C₂×C₈	—	122	32	no	—
295	C₂×C₈	—	122	12	no	—
296	C₂×C₈	—	122	12	no	—
297	C₂×C₈	—	122	12	no	—
298	C₄⋊C₄	C₂²×Dic₆₁	1	16	yes	—
299	C₂²⋊C₄	C₂²×Dic₆₁	1	16	yes	—
300	C₂²⋊C₄	C₂²×Dic₆₁	1	16	yes	—
301	C₄²	C₂²×Dic₆₁	1	12	yes	—
302	C₄²	C₂³×D₆₁	1	4	yes	—
303	C₂³	—	2	12	no	—
304	C₂³	—	2	12	no	—
305	C₂³	—	2	32	no	—
306	C₂³	—	2	12	no	—
307	C₂³	—	2	12	no	—
308	C₂³	—	2	12	no	—
309	C₂³	—	4	16	no	—
310	C₂³	D₄×Dic₆₁	1	4	yes	—
311	C₂³	C₂×#11758194	1	4	yes	—
312	C₂³	C₂×#11758194	1	24	yes	complemented
313	C₂³	#14519784	1	4	yes	—
314	C₂³	C₂³×Dic₆₁	1	4	yes	—
315	C₂³	C₂³×Dic₆₁	1	4	yes	—
316	C₂³	C₂³×Dic₆₁	1	3	yes	—
317	D₄	—	2	32	no	—
318	C₂×C₄	—	2	12	no	—
319	C₂×C₄	—	2	12	no	—
320	C₂×C₄	—	2	12	no	—
321	C₂×C₄	—	2	12	no	—
322	C₂×C₄	—	2	24	no	—
323	C₂×C₄	—	2	24	no	—
324	C₂×C₄	—	2	4	no	—
325	C₂×C₄	—	2	4	no	—
326	C₂×C₄	—	2	4	no	—
327	C₂×C₄	—	2	4	no	—
328	C₂×C₄	D₄×Dic₆₁	1	12	yes	—
329	C₂×C₄	C₂³×Dic₆₁	1	4	yes	—
330	C₂×C₄	C₂³×Dic₆₁	1	4	yes	—
331	C₂×C₄	C₂³×Dic₆₁	1	4	yes	—
332	C₂×C₄	C₂³×Dic₆₁	1	4	yes	—
333	C₂×C₄	C₂³×Dic₆₁	1	3	yes	—
334	C₂×C₄	C₂×D₄×D₆₁	1	6	yes	—
335	C₂×C₄	C₂×#11758224	1	6	yes	—
336	C₂×C₄	C₂⁴×D₆₁	1	1	yes	characteristic
337	C₈	—	61	8	no	—
338	C₈	—	122	4	no	—
339	C₈	—	122	4	no	—
340	C₈	—	122	4	no	—
341	C₂²	—	2	4	no	—
342	C₂²	—	2	4	no	—
343	C₂²	—	2	48	no	—
344	C₂²	—	2	4	no	—
345	C₂²	—	2	4	no	—
346	C₂²	—	2	4	no	—
347	C₂²	—	4	24	no	—
348	C₂²	#16839834	1	16	yes	direct product factor
349	C₂²	C₂×D₄×Dic₆₁	1	6	yes	—
350	C₂²	C₂²×#11758194	1	6	yes	—
351	C₂²	C₂²×#11758194	1	8	yes	complemented
352	C₂²	C₂×#14519784	1	6	yes	—
353	C₂²	C₂⁴×Dic₆₁	1	1	yes	characteristic
354	C₄	—	2	4	no	—
355	C₄	—	2	4	no	—
356	C₄	—	2	4	no	—
357	C₄	—	2	4	no	—
358	C₄	C₂×D₄×Dic₆₁	1	6	yes	—
359	C₄	C₂²×D₄×D₆₁	1	1	yes	characteristic
360	C₄	C₂²×#11758224	1	1	yes	characteristic
361	C₂	—	2	8	no	—
362	C₂	—	4	4	no	—
363	C₂	C₂×#16839834	1	12	yes	direct product factor
364	C₂	C₂²×D₄×Dic₆₁	1	1	yes	characteristic
365	C₂	C₂³×#11758194	1	1	yes	characteristic
366	C₂	C₂²×#14519784	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₄	C₂²×D₆₁
commutator	C₂²×C₆₁	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₆₁
Fitting	C₂²×C₄×D₄×C₆₁	C₂
socle	C₂⁴×C₆₁	C₂²×C₄
prime radical	C₂³×D₄×C₆₁	C₄
cosocle	C₂×C₄×C₆₁	C₂⁵
hypercenter	C₂²×C₄×D₄	D₆₁
hypocenter	C₆₁	C₂²×#435
LCS	G ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂³×C₄ ◁ C₂²×C₄×D₄

Complements

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

N	H ≅ G/N	type
1. C₂³×#11758194	C₂	semidirect
2. C₂⁴×#92418	C₂	semidirect
3. C₂×#16839834	C₂	direct (N × H)
4. C₂²×C₄⋊#92418	C₂	semidirect
5. C₂²×C₂²⋊#92418	C₂	semidirect
6. C₂²×C₂²⋊#92418	C₂	semidirect
7. C₂²×#14519688	C₂	semidirect
10. C₂²×#11758194	C₂²	semidirect
16. C₂³×#92418	C₂²	semidirect
17. #16839834	C₂²	direct (N × H)
18. C₂×C₄⋊#92418	C₂²	semidirect
19. C₂×C₂²⋊#92418	C₂²	semidirect
20. C₂×C₂²⋊#92418	C₂²	semidirect
21. C₂×#14519688	C₂²	semidirect
32. C₂×#11758194	C₂³	semidirect
37. C₂²×#92418	D₄	semidirect
42. C₂²×#92418	C₂³	semidirect
43. C₄⋊#92418	C₂³	semidirect
44. C₂²⋊#92418	C₂³	semidirect
45. C₂²⋊#92418	C₂³	semidirect
46. #14519688	C₂³	semidirect
76. C₂⁴×C₆₁	M₁₆	semidirect
114. C₂×#92418	C₂×D₄	semidirect
128. C₂³×C₆₁	C₂×M₁₆	semidirect
156. #92418	C₂²×D₄	semidirect
165. C₂²×C₆₁	#435	semidirect
168. C₂²×C₆₁	C₂²×M₁₆	semidirect
188. C₂×C₆₁	C₂×#435	semidirect
214. C₆₁	C₂²×#435	semidirect
260. C₂⁴	#11758194	semidirect
312. C₂³	C₂×#11758194	semidirect
348. C₂²	#16839834	direct (N × H)
351. C₂²	C₂²×#11758194	semidirect
363. C₂	C₂×#16839834	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×#11758194	2
C₂⁴×#92418	2
C₂×#16839834	2
C₂²×C₄⋊#92418	2
C₂²×C₂²⋊#92418	2
C₂²×#14519688	2
C₂²×C₄×D₄×C₆₁	2
C₂²×#435	61

Subgroups — C22×#16839834 #30543852

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#16839834 #30543852