Subgroups — D₄×C₄⋊#92418 #29698035

Order 15616.

1200 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×#92418	C₂	1	2	yes	maximal
2	C₂²×C₄⋊#92418	C₂	1	2	yes	maximal, complemented
3	#21446538	C₂	1	2	yes	maximal, complemented
4	#21445999	C₂	1	4	yes	maximal, complemented
5	#21445971	C₂	1	1	yes	maximal, characteristic, complemented
6	#21445799	C₂	1	2	yes	maximal, complemented
7	C₄×C₄⋊#92418	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄²×D₄×C₆₁	C₂	1	1	yes	maximal, characteristic
9	C₂³×#92418	C₂²	1	4	yes	—
10	D₄×#92418	—	2	8	no	—
11	C₂×C₄⋊#92418	—	2	8	no	—
12	C₂×C₄⋊#92418	C₂²	1	2	yes	—
13	C₂×C₄⋊#92418	C₂²	1	4	yes	—
14	C₂×C₄⋊#92418	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊#92418	C₂²	1	2	yes	—
16	C₂×C₄⋊#92418	C₂²	1	2	yes	—
17	C₂×C₄⋊#92418	C₂²	1	1	yes	characteristic
18	C₂×C₂²⋊#92418	C₂²	1	4	yes	—
19	C₂×C₄×#92418	C₂²	1	2	yes	—
20	#16839517	C₂²	1	2	yes	—
21	#16839517	C₂²	1	4	yes	—
22	C₂×C₄×D₄×C₆₁	C₄	1	1	yes	characteristic
23	C₂×C₄×D₄×C₆₁	C₄	1	1	yes	characteristic
24	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
25	C₂²×C₄²×C₆₁	C₂²	1	2	yes	—
26	C₄×C₄⋊C₄×C₆₁	C₄	1	1	yes	characteristic
27	C₄×C₄⋊C₄×C₆₁	C₄	1	1	yes	characteristic
28	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
29	C₄×C₂²⋊C₄×C₆₁	C₄	1	2	yes	—
30	C₄×C₂²⋊C₄×C₆₁	C₄	1	2	yes	—
31	C₄×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	—
32	C₄³×C₆₁	C₂²	1	1	yes	characteristic
33	C₂²×#92418	—	2	8	no	—
34	C₂²×#92418	—	2	8	no	—
35	C₂²×#92418	—	4	4	no	—
36	C₂²×#92418	C₂³	1	2	yes	—
37	C₂²×#92418	C₂³	1	4	yes	—
38	C₂²×#92418	C₂³	1	2	yes	—
39	C₄⋊#92418	—	2	4	no	—
40	C₄⋊#92418	—	2	4	no	—
41	C₄⋊#92418	—	2	2	no	—
42	C₄⋊#92418	—	2	8	no	—
43	C₄⋊#92418	—	4	2	no	—
44	C₄⋊#92418	D₄	1	4	yes	direct product factor
45	C₂²⋊#92418	—	2	8	no	—
46	C₄×#92418	—	2	4	no	—
47	C₂²×D₄×C₆₁	C₂×C₄	1	1	yes	characteristic
48	C₂³×C₄×C₆₁	C₂×C₄	1	2	yes	—
49	C₂³×C₄×C₆₁	C₂×C₄	1	2	yes	—
50	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
51	C₄×D₄×C₆₁	—	2	4	no	—
52	C₄×D₄×C₆₁	C₈	1	8	yes	complemented
53	C₄×D₄×C₆₁	D₄	1	4	yes	—
54	C₄×D₄×C₆₁	Q₈	1	4	yes	—
55	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
58	C₂×C₂²⋊C₄×C₆₁	C₂×C₄	1	2	yes	—
59	C₂×C₂²⋊C₄×C₆₁	C₂×C₄	1	2	yes	—
60	C₂×C₂²⋊C₄×C₆₁	C₂×C₄	1	2	yes	—
61	C₂×C₄²×C₆₁	—	2	4	no	—
62	C₂×C₄²×C₆₁	—	2	4	no	—
63	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
64	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄²×C₆₁	C₂×C₄	1	2	yes	—
66	C₂×C₄²×C₆₁	C₂×C₄	1	2	yes	—
67	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
68	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
69	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
70	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
71	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
72	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
73	#95×C₆₁	C₂×C₄	1	2	yes	—
74	#95×C₆₁	C₂×C₄	1	2	yes	—
75	#95×C₆₁	C₂×C₄	1	2	yes	—
76	C₂⁴×C₆₁	C₂²×C₄	1	2	yes	—
77	C₂×D₄×C₆₁	C₄⋊C₄	1	4	yes	—
78	C₂×D₄×C₆₁	C₂×C₈	1	4	yes	—
79	C₂×D₄×C₆₁	M₁₆	1	4	yes	—
80	C₂²×C₄×C₆₁	—	2	4	no	—
81	C₂²×C₄×C₆₁	—	2	4	no	—
82	C₂²×C₄×C₆₁	—	2	2	no	—
83	C₂²×C₄×C₆₁	—	2	2	no	—
84	C₂²×C₄×C₆₁	—	2	2	no	—
85	C₂²×C₄×C₆₁	—	2	2	no	—
86	C₂²×C₄×C₆₁	—	2	4	no	—
87	C₂²×C₄×C₆₁	—	2	4	no	—
88	C₂²×C₄×C₆₁	—	4	2	no	—
89	C₂²×C₄×C₆₁	C₂×C₈	1	8	yes	complemented
90	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₆₁	C₂²×C₄	1	2	yes	—
92	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
93	C₂²×C₄×C₆₁	C₂²×C₄	1	2	yes	—
94	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
96	C₂²×C₄×C₆₁	C₂²×C₄	1	2	yes	—
97	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₆₁	C₂×D₄	1	4	yes	—
100	C₂²×C₄×C₆₁	C₂×Q₈	1	4	yes	—
101	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
102	C₄⋊C₄×C₆₁	—	2	2	no	—
103	C₄⋊C₄×C₆₁	C₄⋊C₄	1	4	yes	—
104	C₄⋊C₄×C₆₁	C₂×C₈	1	4	yes	complemented
105	C₂²⋊C₄×C₆₁	—	2	4	no	—
106	C₂²⋊C₄×C₆₁	C₄⋊C₄	1	8	yes	—
107	C₂²⋊C₄×C₆₁	C₂×C₈	1	8	yes	complemented
108	C₄²×C₆₁	—	2	4	no	—
109	C₄²×C₆₁	—	2	4	no	—
110	C₄²×C₆₁	—	2	2	no	—
111	C₄²×C₆₁	—	2	2	no	—
112	C₄²×C₆₁	—	2	2	no	—
113	C₄²×C₆₁	—	2	2	no	—
114	C₄²×C₆₁	—	2	1	no	—
115	C₄²×C₆₁	—	2	1	no	—
116	C₄²×C₆₁	—	4	1	no	—
117	C₄²×C₆₁	C₂×C₈	1	4	yes	complemented
118	C₄²×C₆₁	C₂×D₄	1	2	yes	—
119	C₄²×C₆₁	C₂×D₄	1	2	yes	—
120	C₄²×C₆₁	C₂×Q₈	1	2	yes	—
121	C₄²×C₆₁	#41	1	2	yes	—
122	C₂×#92418	—	2	2	no	—
123	C₂×#92418	—	2	2	no	—
124	C₂×#92418	—	2	2	no	—
125	C₂×#92418	—	2	4	no	—
126	C₂×#92418	—	2	4	no	—
127	C₂×#92418	—	2	2	no	—
128	C₂×#92418	—	2	4	no	—
129	C₂×#92418	—	2	2	no	—
130	C₂×#92418	—	4	16	no	—
131	C₂×#92418	C₂×D₄	1	4	yes	—
132	C₂³×C₆₁	—	2	2	no	—
133	C₂³×C₆₁	—	2	2	no	—
134	C₂³×C₆₁	—	2	2	no	—
135	C₂³×C₆₁	—	2	2	no	—
136	C₂³×C₆₁	C₂×C₄⋊C₄	1	4	yes	—
137	C₂³×C₆₁	C₂²×C₈	1	4	yes	—
138	C₂³×C₆₁	C₂×M₁₆	1	4	yes	—
139	C₂³×C₆₁	C₂³×C₄	1	1	yes	characteristic
140	D₄×C₆₁	C₄⋊C₈	1	16	yes	complemented
141	C₂×C₄×C₆₁	—	2	2	no	—
142	C₂×C₄×C₆₁	—	2	2	no	—
143	C₂×C₄×C₆₁	—	2	1	no	—
144	C₂×C₄×C₆₁	—	2	2	no	—
145	C₂×C₄×C₆₁	—	2	1	no	—
146	C₂×C₄×C₆₁	—	2	1	no	—
147	C₂×C₄×C₆₁	—	2	2	no	—
148	C₂×C₄×C₆₁	—	2	1	no	—
149	C₂×C₄×C₆₁	—	2	1	no	—
150	C₂×C₄×C₆₁	—	2	1	no	—
151	C₂×C₄×C₆₁	—	2	4	no	—
152	C₂×C₄×C₆₁	—	2	4	no	—
153	C₂×C₄×C₆₁	—	2	4	no	—
154	C₂×C₄×C₆₁	—	2	4	no	—
155	C₂×C₄×C₆₁	—	2	16	no	—
156	C₂×C₄×C₆₁	—	2	2	no	—
157	C₂×C₄×C₆₁	—	2	1	no	—
158	C₂×C₄×C₆₁	—	2	1	no	—
159	C₂×C₄×C₆₁	—	2	2	no	—
160	C₂×C₄×C₆₁	—	2	1	no	—
161	C₂×C₄×C₆₁	—	2	2	no	—
162	C₂×C₄×C₆₁	—	4	8	no	—
163	C₂×C₄×C₆₁	C₂×C₄⋊C₄	1	2	yes	—
164	C₂×C₄×C₆₁	C₂×C₄⋊C₄	1	4	yes	—
165	C₂×C₄×C₆₁	C₂×C₄⋊C₄	1	2	yes	—
166	C₂×C₄×C₆₁	C₄×D₄	1	2	yes	—
167	C₂×C₄×C₆₁	C₄×D₄	1	2	yes	—
168	C₂×C₄×C₆₁	C₂²×C₈	1	2	yes	—
169	C₂×C₄×C₆₁	C₂²×C₈	1	4	yes	—
170	C₂×C₄×C₆₁	C₂²×C₈	1	2	yes	—
171	C₂×C₄×C₆₁	C₂²×C₈	1	2	yes	—
172	C₂×C₄×C₆₁	C₂×M₁₆	1	2	yes	—
173	C₂×C₄×C₆₁	#131	1	2	yes	—
174	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
175	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
176	C₂×C₄×C₆₁	C₂²×Q₈	1	1	yes	characteristic
177	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
178	C₂×C₄×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
179	C₂×C₄×C₆₁	2₋¹⁺⁴	1	1	yes	characteristic
180	#92418	—	2	4	no	—
181	#92418	—	4	4	no	—
182	#92418	—	4	2	no	—
183	D₄×C₄⋊C₈	—	61	1	no	maximal, Sylow
184	C₂²×C₆₁	—	2	4	no	—
185	C₂²×C₆₁	—	2	4	no	—
186	C₂²×C₆₁	—	2	4	no	—
187	C₂²×C₆₁	—	2	4	no	—
188	C₂²×C₆₁	—	2	4	no	—
189	C₂²×C₆₁	—	2	4	no	—
190	C₂²×C₆₁	C₂×C₄⋊C₈	1	8	yes	complemented
191	C₂²×C₆₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
192	C₂²×C₆₁	C₂×C₄×D₄	1	1	yes	characteristic
193	C₂²×C₆₁	#520	1	1	yes	characteristic
194	C₂²×C₆₁	C₂³×C₈	1	1	yes	characteristic
195	C₂²×C₆₁	C₂²×M₁₆	1	1	yes	characteristic
196	C₂²×C₆₁	C₂×#131	1	1	yes	characteristic
197	C₂²×C₆₁	#568	1	1	yes	characteristic
198	C₄×C₆₁	—	2	4	no	—
199	C₄×C₆₁	—	2	2	no	—
200	C₄×C₆₁	—	2	4	no	—
201	C₄×C₆₁	—	2	2	no	—
202	C₄×C₆₁	—	2	2	no	—
203	C₄×C₆₁	—	4	2	no	—
204	C₄×C₆₁	—	4	1	no	—
205	C₄×C₆₁	C₂×C₄⋊C₈	1	4	yes	complemented
206	C₄×C₆₁	C₈×D₄	1	4	yes	complemented
207	C₄×C₆₁	D₄²	1	1	yes	characteristic
208	C₄×C₆₁	#547	1	1	yes	characteristic
209	C₄×C₆₁	D₄×Q₈	1	1	yes	characteristic
210	C₄×C₆₁	#554	1	1	yes	characteristic
211	C₂×C₈×D₄	—	61	2	no	—
212	C₂²×C₄⋊C₈	—	61	2	no	—
213	C₄²×D₄	D₆₁	1	1	yes	characteristic
214	#1939	—	61	2	no	—
215	#1850	—	61	4	no	—
216	#1842	—	61	1	no	—
217	#1797	—	61	2	no	—
218	C₄×C₄⋊C₈	—	61	1	no	—
219	C₂×C₆₁	—	2	8	no	—
220	C₂×C₆₁	D₄×C₄⋊C₄	1	1	yes	characteristic
221	C₂×C₆₁	C₂²×C₄⋊C₈	1	1	yes	characteristic
222	C₂×C₆₁	#2906	1	1	yes	characteristic
223	C₂×C₆₁	C₂×C₈×D₄	1	1	yes	characteristic
224	C₂×C₆₁	D₄×M₁₆	1	1	yes	characteristic
225	C₂×C₆₁	#2988	1	1	yes	characteristic
226	C₂×C₆₁	#2990	1	1	yes	characteristic
227	C₂³×C₈	—	61	4	no	—
228	C₂×C₄×D₄	Dic₆₁	1	1	yes	characteristic
229	C₂×C₄×D₄	Dic₆₁	1	1	yes	characteristic
230	C₂×C₄×D₄	C₂×D₆₁	1	1	yes	characteristic
231	C₂²×C₄²	C₂×D₆₁	1	2	yes	—
232	C₈×D₄	—	122	8	no	—
233	C₂×C₄⋊C₈	—	61	1	no	—
234	C₂×C₄⋊C₈	—	61	1	no	—
235	C₂×C₄⋊C₈	—	61	2	no	—
236	C₂×C₄⋊C₈	—	61	2	no	—
237	C₂×C₄⋊C₈	—	61	4	no	—
238	C₂×C₄⋊C₈	—	61	2	no	—
239	C₂×C₄⋊C₈	—	122	8	no	—
240	C₂×C₂²⋊C₈	—	61	4	no	—
241	C₂×C₄×C₈	—	61	2	no	—
242	C₄×C₄⋊C₄	Dic₆₁	1	1	yes	characteristic
243	C₄×C₄⋊C₄	Dic₆₁	1	1	yes	characteristic
244	C₄×C₄⋊C₄	C₂×D₆₁	1	1	yes	characteristic
245	C₄×C₂²⋊C₄	Dic₆₁	1	2	yes	—
246	C₄×C₂²⋊C₄	Dic₆₁	1	2	yes	—
247	C₄×C₂²⋊C₄	C₂×D₆₁	1	2	yes	—
248	C₄³	C₂×D₆₁	1	1	yes	characteristic
249	#336	—	61	4	no	—
250	#336	—	61	2	no	—
251	C₆₁	D₄×C₄⋊C₈	1	1	yes	characteristic, complemented, Sylow
252	C₂²×D₄	C₂×Dic₆₁	1	1	yes	characteristic
253	C₂³×C₄	C₂×Dic₆₁	1	2	yes	—
254	C₂³×C₄	C₂×Dic₆₁	1	2	yes	—
255	C₂³×C₄	C₂²×D₆₁	1	2	yes	—
256	C₂²×C₈	—	61	2	no	—
257	C₂²×C₈	—	61	4	no	—
258	C₂²×C₈	—	61	2	no	—
259	C₂²×C₈	—	122	8	no	—
260	C₂²×C₈	—	122	8	no	—
261	C₂²×C₈	—	244	4	no	—
262	C₄×D₄	—	2	4	no	—
263	C₄×D₄	#92418	1	8	yes	complemented
264	C₄×D₄	Dic₁₂₂	1	4	yes	—
265	C₄×D₄	D₂₄₄	1	4	yes	—
266	C₂×C₄⋊C₄	C₂×Dic₆₁	1	1	yes	characteristic
267	C₂×C₄⋊C₄	C₂×Dic₆₁	1	1	yes	characteristic
268	C₂×C₄⋊C₄	C₂×Dic₆₁	1	1	yes	characteristic
269	C₂×C₂²⋊C₄	C₂×Dic₆₁	1	2	yes	—
270	C₂×C₂²⋊C₄	C₂×Dic₆₁	1	2	yes	—
271	C₂×C₂²⋊C₄	C₂×Dic₆₁	1	2	yes	—
272	C₂×C₄²	—	2	4	no	—
273	C₂×C₄²	—	2	4	no	—
274	C₂×C₄²	C₂×Dic₆₁	1	1	yes	characteristic
275	C₂×C₄²	C₂×Dic₆₁	1	1	yes	characteristic
276	C₂×C₄²	C₂×Dic₆₁	1	2	yes	—
277	C₂×C₄²	C₂×Dic₆₁	1	2	yes	—
278	C₂×C₄²	C₂×Dic₆₁	1	1	yes	characteristic
279	C₂×C₄²	C₂×Dic₆₁	1	1	yes	characteristic
280	C₂×C₄²	C₂²×D₆₁	1	1	yes	characteristic
281	C₂×C₄²	C₂²×D₆₁	1	2	yes	—
282	C₂×C₄²	C₂²×D₆₁	1	1	yes	characteristic
283	C₂×C₄²	C₂²×D₆₁	1	1	yes	characteristic
284	C₄⋊C₈	—	61	4	no	—
285	C₄⋊C₈	—	122	8	no	—
286	C₄⋊C₈	—	122	4	no	—
287	C₄⋊C₈	—	122	4	no	—
288	C₄⋊C₈	—	122	2	no	—
289	C₄⋊C₈	—	244	2	no	—
290	C₂²⋊C₈	—	122	8	no	—
291	C₄×C₈	—	122	4	no	—
292	#95	C₂×Dic₆₁	1	2	yes	—
293	#95	C₂×Dic₆₁	1	2	yes	—
294	#95	C₂×Dic₆₁	1	2	yes	—
295	C₂⁴	C₂²×Dic₆₁	1	2	yes	—
296	C₂×D₄	C₂×#92418	1	4	yes	—
297	C₂×D₄	#11758194	1	4	yes	—
298	C₂×D₄	C₄⋊Dic₆₁	1	4	yes	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	2	4	no	—
304	C₂²×C₄	—	2	4	no	—
305	C₂²×C₄	—	2	4	no	—
306	C₂²×C₄	—	2	4	no	—
307	C₂²×C₄	—	4	2	no	—
308	C₂²×C₄	C₂×#92418	1	8	yes	complemented
309	C₂²×C₄	C₂×Dic₁₂₂	1	4	yes	—
310	C₂²×C₄	C₂×D₂₄₄	1	4	yes	—
311	C₂²×C₄	C₂²×Dic₆₁	1	1	yes	characteristic
312	C₂²×C₄	C₂²×Dic₆₁	1	2	yes	—
313	C₂²×C₄	C₂²×Dic₆₁	1	1	yes	characteristic
314	C₂²×C₄	C₂²×Dic₆₁	1	2	yes	—
315	C₂²×C₄	C₂²×Dic₆₁	1	1	yes	characteristic
316	C₂²×C₄	C₂²×Dic₆₁	1	1	yes	characteristic
317	C₂²×C₄	C₂²×Dic₆₁	1	2	yes	—
318	C₂²×C₄	C₂²×Dic₆₁	1	1	yes	characteristic
319	C₂²×C₄	C₂²×Dic₆₁	1	1	yes	characteristic
320	C₂²×C₄	C₂³×D₆₁	1	1	yes	characteristic
321	C₂×C₈	—	61	4	no	—
322	C₂×C₈	—	122	2	no	—
323	C₂×C₈	—	122	2	no	—
324	C₂×C₈	—	122	4	no	—
325	C₂×C₈	—	122	2	no	—
326	C₂×C₈	—	122	4	no	—
327	C₂×C₈	—	122	2	no	—
328	C₂×C₈	—	122	4	no	—
329	C₂×C₈	—	122	2	no	—
330	C₂×C₈	—	244	16	no	—
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	C₂×#92418	1	4	yes	complemented
333	C₄⋊C₄	C₄⋊Dic₆₁	1	4	yes	—
334	C₂²⋊C₄	—	2	4	no	—
335	C₂²⋊C₄	C₂×#92418	1	8	yes	complemented
336	C₂²⋊C₄	C₄⋊Dic₆₁	1	8	yes	—
337	C₄²	—	2	2	no	—
338	C₄²	—	2	2	no	—
339	C₄²	—	2	1	no	—
340	C₄²	—	2	1	no	—
341	C₄²	—	2	4	no	—
342	C₄²	—	2	4	no	—
343	C₄²	—	2	2	no	—
344	C₄²	—	2	2	no	—
345	C₄²	—	4	1	no	—
346	C₄²	C₂×#92418	1	4	yes	complemented
347	C₄²	C₂×Dic₁₂₂	1	2	yes	—
348	C₄²	C₂×D₂₄₄	1	2	yes	—
349	C₄²	D₄×D₆₁	1	2	yes	—
350	C₄²	#11758224	1	2	yes	—
351	C₂³	—	2	2	no	—
352	C₂³	—	2	2	no	—
353	C₂³	—	2	2	no	—
354	C₂³	—	2	2	no	—
355	C₂³	C₂×C₄⋊Dic₆₁	1	4	yes	—
356	C₂³	C₂²×#92418	1	4	yes	—
357	C₂³	C₂×#11758194	1	4	yes	—
358	C₂³	C₂³×Dic₆₁	1	1	yes	characteristic
359	D₄	C₄⋊#92418	1	16	yes	direct product factor
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	4	no	—
371	C₂×C₄	—	2	16	no	—
372	C₂×C₄	—	2	4	no	—
373	C₂×C₄	—	2	4	no	—
374	C₂×C₄	—	2	4	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	4	8	no	—
382	C₂×C₄	C₂×C₄⋊Dic₆₁	1	2	yes	—
383	C₂×C₄	C₂×C₄⋊Dic₆₁	1	4	yes	—
384	C₂×C₄	C₂×C₄⋊Dic₆₁	1	2	yes	—
385	C₂×C₄	D₄×Dic₆₁	1	2	yes	—
386	C₂×C₄	D₄×Dic₆₁	1	2	yes	—
387	C₂×C₄	C₂²×#92418	1	2	yes	—
388	C₂×C₄	C₂²×#92418	1	4	yes	—
389	C₂×C₄	C₂²×#92418	1	2	yes	—
390	C₂×C₄	C₂²×#92418	1	2	yes	—
391	C₂×C₄	C₂×#11758194	1	2	yes	—
392	C₂×C₄	#14519784	1	2	yes	—
393	C₂×C₄	C₂×D₄×D₆₁	1	1	yes	characteristic
394	C₂×C₄	C₂²×D₂₄₄	1	1	yes	characteristic
395	C₂×C₄	C₂²×Dic₁₂₂	1	1	yes	characteristic
396	C₂×C₄	C₂×#11758224	1	1	yes	characteristic
397	C₂×C₄	#14519823	1	1	yes	characteristic
398	C₂×C₄	#14519824	1	1	yes	characteristic
399	C₈	—	122	4	no	—
400	C₈	—	244	4	no	—
401	C₈	—	244	2	no	—
402	C₂²	—	2	4	no	—
403	C₂²	—	2	4	no	—
404	C₂²	—	2	4	no	—
405	C₂²	—	2	4	no	—
406	C₂²	—	2	4	no	—
407	C₂²	—	2	4	no	—
408	C₂²	C₂×C₄⋊#92418	1	8	yes	complemented
409	C₂²	C₂²×C₄⋊Dic₆₁	1	1	yes	characteristic
410	C₂²	C₂×D₄×Dic₆₁	1	1	yes	characteristic
411	C₂²	#16840245	1	1	yes	characteristic
412	C₂²	C₂³×#92418	1	1	yes	characteristic
413	C₂²	C₂²×#11758194	1	1	yes	characteristic
414	C₂²	C₂×#14519784	1	1	yes	characteristic
415	C₂²	#16840529	1	1	yes	characteristic
416	C₄	—	2	4	no	—
417	C₄	—	2	2	no	—
418	C₄	—	2	2	no	—
419	C₄	—	2	4	no	—
420	C₄	—	2	2	no	—
421	C₄	—	4	1	no	—
422	C₄	—	4	2	no	—
423	C₄	C₂×C₄⋊#92418	1	4	yes	complemented
424	C₄	D₄×#92418	1	4	yes	complemented
425	C₄	D₄×D₂₄₄	1	1	yes	characteristic
426	C₄	#16840416	1	1	yes	characteristic
427	C₄	D₄×Dic₁₂₂	1	1	yes	characteristic
428	C₄	#16840469	1	1	yes	characteristic
429	C₂	—	2	8	no	—
430	C₂	D₄×C₄⋊Dic₆₁	1	1	yes	characteristic
431	C₂	C₂²×C₄⋊#92418	1	1	yes	characteristic
432	C₂	#21454387	1	1	yes	characteristic
433	C₂	C₂×D₄×#92418	1	1	yes	characteristic
434	C₂	D₄×#11758194	1	1	yes	characteristic
435	C₂	#21454930	1	1	yes	characteristic
436	C₂	#21454944	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₆₁
commutator	C₂²×C₆₁	C₂³×C₈
Fitting	C₄²×D₄×C₆₁	C₂
socle	C₂³×C₆₁	C₂³×C₄
prime radical	C₂²×D₄×C₆₁	C₂×C₄
cosocle	C₂²×C₄×C₆₁	C₂⁴
hypercenter	C₄²×D₄	D₆₁
hypocenter	C₆₁	D₄×C₄⋊C₈
LCS	G ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂²×C₄ ◁ C₄²×D₄

Complements

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

N	H ≅ G/N	type
2. C₂²×C₄⋊#92418	C₂	semidirect
3. #21446538	C₂	semidirect
4. #21445999	C₂	semidirect
5. #21445971	C₂	semidirect
6. #21445799	C₂	semidirect
7. C₄×C₄⋊#92418	C₂	semidirect
44. C₄⋊#92418	D₄	direct (N × H)
52. C₄×D₄×C₆₁	C₈	semidirect
89. C₂²×C₄×C₆₁	C₂×C₈	semidirect
104. C₄⋊C₄×C₆₁	C₂×C₈	semidirect
107. C₂²⋊C₄×C₆₁	C₂×C₈	semidirect
117. C₄²×C₆₁	C₂×C₈	semidirect
140. D₄×C₆₁	C₄⋊C₈	semidirect
190. C₂²×C₆₁	C₂×C₄⋊C₈	semidirect
205. C₄×C₆₁	C₂×C₄⋊C₈	semidirect
206. C₄×C₆₁	C₈×D₄	semidirect
251. C₆₁	D₄×C₄⋊C₈	semidirect
263. C₄×D₄	#92418	semidirect
308. C₂²×C₄	C₂×#92418	semidirect
332. C₄⋊C₄	C₂×#92418	semidirect
335. C₂²⋊C₄	C₂×#92418	semidirect
346. C₄²	C₂×#92418	semidirect
359. D₄	C₄⋊#92418	direct (N × H)
408. C₂²	C₂×C₄⋊#92418	semidirect
423. C₄	C₂×C₄⋊#92418	semidirect
424. C₄	D₄×#92418	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₄×#92418	2
C₂²×C₄⋊#92418	2
#21446538	2
#21445999	2
#21445971	2
#21445799	2
C₄×C₄⋊#92418	2
C₄²×D₄×C₆₁	2
D₄×C₄⋊C₈	61

Subgroups — D4×C4⋊#92418 #29698035

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄×C₄⋊#92418 #29698035