Subgroups — C₄×#11758561 #16858916

Order 3968.

1660 conjugacy classes of subgroups.

The subgroup lattice has 316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11758561	C₂	1	1	yes	maximal, characteristic
2	#14521530	C₂	1	2	yes	maximal, complemented
3	#14521528	C₂	1	4	yes	maximal, complemented
4	#14521524	C₂	1	1	yes	maximal, characteristic, complemented
5	#14521522	C₂	1	4	yes	maximal, complemented
6	#14521521	C₂	1	4	yes	maximal, complemented
7	C₄×#92495	C₂	1	2	yes	maximal, complemented
8	C₄×#92497	C₂	1	4	yes	maximal, complemented
9	C₂×C₄×C₂²⋊D₃₁	C₂	1	4	yes	maximal, complemented
10	C₄×D₄×D₃₁	C₂	1	4	yes	maximal, complemented
11	C₂×C₄×D₄×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×D₄×C₃₁	C₂²	1	1	yes	characteristic
13	C₂³×C₄×C₃₁	C₂²	1	2	yes	complemented
14	C₂²×C₂²⋊D₃₁	C₂²	1	4	yes	—
15	#11758561	C₄	1	16	yes	direct product factor
16	C₂×#92497	C₂²	1	4	yes	—
17	C₂×D₄×D₃₁	C₂²	1	4	yes	—
18	C₂×#92495	C₂²	1	2	yes	—
19	C₂²×C₄×D₃₁	C₂²	1	4	yes	complemented
20	C₄×D₄×C₃₁	C₂²	1	4	yes	complemented
21	C₄×D₄×C₃₁	C₂²	1	4	yes	complemented
22	C₂×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	complemented
24	C₂×C₄²×C₃₁	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₂²⋊Dic₃₁	C₂²	1	4	yes	complemented
26	D₄×Dic₃₁	C₂²	1	4	yes	complemented
27	D₄×Dic₃₁	C₂²	1	4	yes	complemented
28	C₄×C₂²⋊D₃₁	C₂²	1	8	yes	complemented
29	C₄×C₂²⋊D₃₁	C₂²	1	4	yes	complemented
30	C₄×C₂²⋊D₃₁	C₂²	1	8	yes	complemented
31	C₄×C₂²⋊D₃₁	C₂²	1	8	yes	complemented
32	C₄×C₂²⋊D₃₁	C₂²	1	4	yes	complemented
33	C₂×(C₂×D₃₁)⋊C₄	C₂²	1	4	yes	complemented
34	#11758503	C₂²	1	2	yes	complemented
35	C₂×Dic₃₁⋊C₄	C₂²	1	4	yes	complemented
36	C₂×C₄×Dic₃₁	C₂²	1	4	yes	complemented
37	#11758470	C₂²	1	4	yes	complemented
38	#11758469	C₂²	1	4	yes	complemented
39	C₄⋊C₄×D₃₁	C₂²	1	4	yes	complemented
40	#11758464	C₂²	1	4	yes	complemented
41	(C₂²⋊D₃₁)⋊C₄	C₂²	1	8	yes	complemented
42	(C₂²⋊D₃₁)⋊C₄	C₂²	1	8	yes	complemented
43	C₂²⋊C₄×D₃₁	C₂²	1	8	yes	complemented
44	#11758454	C₂²	1	8	yes	complemented
45	C₄×D₁₂₄	C₂²	1	2	yes	complemented
46	C₄×D₁₂₄	C₂²	1	2	yes	complemented
47	#11758449	C₂²	1	4	yes	complemented
48	C₄²×D₃₁	C₂²	1	4	yes	complemented
49	C₄×Dic₆₂	C₂²	1	2	yes	complemented
50	C₄×Dic₆₂	C₂²	1	2	yes	complemented
51	C₂⁴×C₃₁	C₂³	1	2	yes	—
52	C₂³×D₃₁	C₂³	1	4	yes	—
53	C₂×D₄×C₃₁	C₂×C₄	1	8	yes	complemented
54	C₂×D₄×C₃₁	C₂³	1	4	yes	—
55	C₂²×C₄×C₃₁	—	4	4	no	—
56	C₂²×C₄×C₃₁	C₂³	1	4	yes	—
57	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
58	C₂²×C₄×C₃₁	C₂³	1	4	yes	—
59	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
60	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
61	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
62	C₂×C₂²⋊D₃₁	C₂×C₄	1	32	yes	complemented
63	C₂×C₂²⋊D₃₁	C₂³	1	8	yes	—
64	C₂×C₂²⋊D₃₁	C₂³	1	4	yes	—
65	C₂²×Dic₃₁	C₂³	1	4	yes	—
66	C₂²×Dic₃₁	C₂³	1	4	yes	—
67	C₂²×Dic₃₁	C₂³	1	4	yes	—
68	#92497	C₂×C₄	1	32	yes	complemented
69	D₄×D₃₁	C₂×C₄	1	32	yes	complemented
70	#92495	C₂×C₄	1	16	yes	complemented
71	C₂×D₁₂₄	C₂³	1	2	yes	—
72	C₂×C₄×D₃₁	—	4	8	no	—
73	C₂×C₄×D₃₁	C₂³	1	4	yes	—
74	C₂×C₄×D₃₁	C₂³	1	4	yes	—
75	C₂×C₄×D₃₁	C₂³	1	8	yes	—
76	C₂×C₄×D₃₁	C₂³	1	4	yes	—
77	C₂×Dic₆₂	C₂³	1	2	yes	—
78	C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
79	C₂²⋊C₄×C₃₁	C₂³	1	8	yes	—
80	C₄²×C₃₁	C₂³	1	2	yes	—
81	C₄²×C₃₁	C₂³	1	2	yes	—
82	C₂²⋊Dic₃₁	C₂³	1	8	yes	—
83	C₂²⋊Dic₃₁	C₂³	1	4	yes	—
84	(C₂×D₃₁)⋊C₄	C₂³	1	4	yes	—
85	(C₂×D₃₁)⋊C₄	C₂³	1	4	yes	—
86	(C₂×D₃₁)⋊C₄	C₂³	1	8	yes	—
87	C₄⋊Dic₃₁	C₂³	1	2	yes	—
88	C₄⋊Dic₃₁	C₂³	1	2	yes	—
89	Dic₃₁⋊C₄	C₂³	1	4	yes	—
90	Dic₃₁⋊C₄	C₂³	1	4	yes	—
91	Dic₃₁⋊C₄	C₂³	1	8	yes	—
92	C₄×Dic₃₁	C₂³	1	4	yes	—
93	C₄×Dic₃₁	C₂³	1	4	yes	—
94	C₄×Dic₃₁	C₂³	1	4	yes	—
95	C₄×Dic₃₁	C₂³	1	8	yes	—
96	C₂³×C₃₁	—	4	2	no	—
97	C₂³×C₃₁	—	4	2	no	—
98	C₂³×C₃₁	C₂²×C₄	1	8	yes	complemented
99	C₂³×C₃₁	C₂⁴	1	1	yes	characteristic
100	C₂³×C₃₁	C₂⁴	1	4	yes	—
101	C₂²×D₃₁	—	4	4	no	—
102	C₂²×D₃₁	—	4	4	no	—
103	C₂²×D₃₁	C₂²×C₄	1	16	yes	complemented
104	C₂²×D₃₁	C₂⁴	1	4	yes	—
105	D₄×C₃₁	C₂²×C₄	1	16	yes	complemented
106	C₂×C₄×C₃₁	—	2	8	no	—
107	C₂×C₄×C₃₁	—	2	2	no	—
108	C₂×C₄×C₃₁	—	4	2	no	—
109	C₂×C₄×C₃₁	—	4	4	no	—
110	C₂×C₄×C₃₁	—	4	1	no	—
111	C₂×C₄×C₃₁	C₂²×C₄	1	4	yes	complemented
112	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
113	C₂×C₄×C₃₁	C₂⁴	1	4	yes	—
114	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
115	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
116	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
117	C₂²⋊D₃₁	C₂²×C₄	1	16	yes	complemented
118	C₂²⋊D₃₁	C₂²×C₄	1	32	yes	complemented
119	C₂×Dic₃₁	—	4	4	no	—
120	C₂×Dic₃₁	—	4	4	no	—
121	C₂×Dic₃₁	C₂²×C₄	1	16	yes	complemented
122	C₂×Dic₃₁	C₂⁴	1	4	yes	—
123	C₂×Dic₃₁	C₂⁴	1	4	yes	—
124	C₂×Dic₃₁	C₂⁴	1	4	yes	—
125	D₁₂₄	C₂²×C₄	1	8	yes	complemented
126	C₄×D₃₁	—	2	8	no	—
127	C₄×D₃₁	—	4	8	no	—
128	C₄×D₃₁	—	4	4	no	—
129	C₄×D₃₁	C₂²×C₄	1	16	yes	complemented
130	Dic₆₂	C₂²×C₄	1	8	yes	complemented
131	C₄×H(5,𝔽₂)	—	31	1	no	maximal, Sylow
132	C₂²×C₃₁	—	2	4	no	—
133	C₂²×C₃₁	—	2	1	no	—
134	C₂²×C₃₁	—	2	4	no	—
135	C₂²×C₃₁	—	2	1	no	—
136	C₂²×C₃₁	—	4	8	no	—
137	C₂²×C₃₁	C₂³×C₄	1	8	yes	—
138	C₂²×C₃₁	C₂³×C₄	1	2	yes	—
139	C₂²×C₃₁	C₂⁵	1	1	yes	characteristic
140	C₂×D₃₁	—	2	4	no	—
141	C₂×D₃₁	—	2	4	no	—
142	C₂×D₃₁	—	4	16	no	—
143	C₂×D₃₁	C₂³×C₄	1	8	yes	—
144	C₄×C₃₁	—	2	4	no	—
145	C₄×C₃₁	—	2	1	no	—
146	C₄×C₃₁	—	2	2	no	—
147	C₄×C₃₁	C₂³×C₄	1	4	yes	—
148	C₄×C₃₁	H(5,𝔽₂)	1	2	yes	complemented
149	Dic₃₁	—	2	4	no	—
150	Dic₃₁	—	2	4	no	—
151	Dic₃₁	C₂³×C₄	1	8	yes	—
152	C₂×H(5,𝔽₂)	—	31	1	no	—
153	#520	—	31	4	no	—
154	#520	—	31	2	no	—
155	#518	—	31	1	no	—
156	#518	—	31	4	no	—
157	#518	—	31	4	no	—
158	C₄×#41	—	31	4	no	—
159	C₄×#41	—	31	2	no	—
160	C₂×C₄×D₄	—	31	4	no	—
161	C₂×C₄×D₄	—	31	4	no	—
162	C₂×C₄×D₄	D₃₁	1	1	yes	characteristic, complemented
163	C₂×C₃₁	—	2	8	no	—
164	C₂×C₃₁	—	2	2	no	—
165	C₂×C₃₁	C₂⁴×C₄	1	1	yes	characteristic
166	C₂×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
167	C₂×C₃₁	#585	1	1	yes	characteristic
168	D₃₁	—	2	8	no	—
169	H(5,𝔽₂)	—	31	16	no	—
170	C₂×#41	—	31	4	no	—
171	C₂×#41	—	31	2	no	—
172	C₂²×D₄	—	31	4	no	—
173	C₂²×D₄	—	31	4	no	—
174	C₂²×D₄	C₂×D₃₁	1	1	yes	characteristic
175	C₂³×C₄	—	31	4	no	—
176	C₂³×C₄	C₂×D₃₁	1	2	yes	complemented
177	C₄×Q₈	—	31	4	no	—
178	C₄×Q₈	—	31	2	no	—
179	C₄×Q₈	—	31	2	no	—
180	C₄×D₄	—	31	4	no	—
181	C₄×D₄	—	31	4	no	—
182	C₄×D₄	—	31	8	no	—
183	C₄×D₄	—	31	4	no	—
184	C₄×D₄	—	31	8	no	—
185	C₄×D₄	—	31	8	no	—
186	C₄×D₄	—	31	4	no	—
187	C₄×D₄	—	31	4	no	—
188	C₄×D₄	—	31	8	no	—
189	C₄×D₄	—	31	8	no	—
190	C₄×D₄	—	31	2	no	—
191	C₄×D₄	—	31	2	no	—
192	C₄×D₄	C₂×D₃₁	1	4	yes	complemented
193	C₄×D₄	C₂×D₃₁	1	4	yes	complemented
194	#117	—	31	2	no	—
195	#117	—	31	4	no	—
196	#117	—	31	8	no	—
197	#117	—	31	4	no	—
198	C₂×C₄⋊C₄	—	31	4	no	—
199	C₂×C₄⋊C₄	—	31	4	no	—
200	C₂×C₄⋊C₄	C₂×D₃₁	1	1	yes	characteristic, complemented
201	C₂×C₂²⋊C₄	—	31	4	no	—
202	C₂×C₂²⋊C₄	—	31	4	no	—
203	C₂×C₂²⋊C₄	—	31	8	no	—
204	C₂×C₂²⋊C₄	C₂×D₃₁	1	2	yes	complemented
205	C₂×C₄²	—	31	4	no	—
206	C₂×C₄²	—	31	4	no	—
207	C₂×C₄²	C₂×D₃₁	1	1	yes	characteristic, complemented
208	C₃₁	C₄×H(5,𝔽₂)	1	1	yes	characteristic, complemented, Sylow
209	C₂⁴	—	31	4	no	—
210	C₂⁴	C₂²×D₃₁	1	2	yes	—
211	#41	—	31	32	no	—
212	#41	—	31	16	no	—
213	C₂×Q₈	—	31	2	no	—
214	C₂×D₄	—	31	32	no	—
215	C₂×D₄	—	31	4	no	—
216	C₂×D₄	—	31	8	no	—
217	C₂×D₄	—	31	32	no	—
218	C₂×D₄	—	31	2	no	—
219	C₂×D₄	C₄×D₃₁	1	8	yes	complemented
220	C₂×D₄	C₂²×D₃₁	1	4	yes	—
221	C₂²×C₄	—	4	4	no	—
222	C₂²×C₄	—	31	4	no	—
223	C₂²×C₄	—	31	4	no	—
224	C₂²×C₄	—	31	4	no	—
225	C₂²×C₄	—	31	4	no	—
226	C₂²×C₄	—	31	4	no	—
227	C₂²×C₄	—	31	4	no	—
228	C₂²×C₄	—	31	8	no	—
229	C₂²×C₄	—	124	8	no	—
230	C₂²×C₄	C₂²×D₃₁	1	4	yes	—
231	C₂²×C₄	C₂²×D₃₁	1	1	yes	characteristic
232	C₂²×C₄	C₂²×D₃₁	1	1	yes	characteristic
233	C₂²×C₄	C₂²×D₃₁	1	4	yes	—
234	C₂²×C₄	C₂²×D₃₁	1	2	yes	—
235	C₂²×C₄	C₂²×D₃₁	1	1	yes	characteristic
236	C₄⋊C₄	—	31	8	no	—
237	C₄⋊C₄	—	31	4	no	—
238	C₄⋊C₄	—	31	4	no	—
239	C₄⋊C₄	—	31	2	no	—
240	C₄⋊C₄	—	31	2	no	—
241	C₄⋊C₄	C₂²×D₃₁	1	4	yes	—
242	C₂²⋊C₄	—	31	4	no	—
243	C₂²⋊C₄	—	31	8	no	—
244	C₂²⋊C₄	—	31	8	no	—
245	C₂²⋊C₄	—	31	4	no	—
246	C₂²⋊C₄	—	31	4	no	—
247	C₂²⋊C₄	C₂²×D₃₁	1	8	yes	—
248	C₄²	—	31	8	no	—
249	C₄²	—	31	4	no	—
250	C₄²	—	31	4	no	—
251	C₄²	—	31	4	no	—
252	C₄²	C₂²×D₃₁	1	2	yes	—
253	C₄²	C₂²×D₃₁	1	2	yes	—
254	C₂³	—	4	2	no	—
255	C₂³	—	4	2	no	—
256	C₂³	—	31	4	no	—
257	C₂³	—	31	16	no	—
258	C₂³	—	124	4	no	—
259	C₂³	—	124	4	no	—
260	C₂³	C₂×C₄×D₃₁	1	8	yes	complemented
261	C₂³	C₂³×D₃₁	1	1	yes	characteristic
262	C₂³	C₂³×D₃₁	1	4	yes	—
263	Q₈	—	31	8	no	—
264	D₄	—	31	32	no	—
265	D₄	—	31	16	no	—
266	D₄	—	31	8	no	—
267	D₄	C₂×C₄×D₃₁	1	16	yes	complemented
268	C₂×C₄	—	2	2	no	—
269	C₂×C₄	—	2	8	no	—
270	C₂×C₄	—	4	4	no	—
271	C₂×C₄	—	4	2	no	—
272	C₂×C₄	—	4	1	no	—
273	C₂×C₄	—	31	16	no	—
274	C₂×C₄	—	31	4	no	—
275	C₂×C₄	—	31	16	no	—
276	C₂×C₄	—	31	4	no	—
277	C₂×C₄	—	31	4	no	—
278	C₂×C₄	—	62	8	no	—
279	C₂×C₄	—	124	4	no	—
280	C₂×C₄	—	124	8	no	—
281	C₂×C₄	—	124	4	no	—
282	C₂×C₄	—	124	4	no	—
283	C₂×C₄	C₂×C₄×D₃₁	1	4	yes	complemented
284	C₂×C₄	C₂³×D₃₁	1	2	yes	—
285	C₂×C₄	C₂³×D₃₁	1	4	yes	—
286	C₂×C₄	C₂³×D₃₁	1	1	yes	characteristic
287	C₂×C₄	C₂³×D₃₁	1	2	yes	—
288	C₂×C₄	C₂³×D₃₁	1	1	yes	characteristic
289	C₂²	—	2	1	no	—
290	C₂²	—	2	4	no	—
291	C₂²	—	2	1	no	—
292	C₂²	—	2	4	no	—
293	C₂²	—	4	8	no	—
294	C₂²	—	31	8	no	—
295	C₂²	—	62	4	no	—
296	C₂²	—	62	4	no	—
297	C₂²	—	124	16	no	—
298	C₂²	C₂²×C₄×D₃₁	1	8	yes	—
299	C₂²	C₂²×C₄×D₃₁	1	2	yes	—
300	C₂²	C₂⁴×D₃₁	1	1	yes	characteristic
301	C₄	—	2	1	no	—
302	C₄	—	2	4	no	—
303	C₄	—	2	2	no	—
304	C₄	—	31	8	no	—
305	C₄	—	62	4	no	—
306	C₄	—	62	4	no	—
307	C₄	C₂²×C₄×D₃₁	1	4	yes	—
308	C₄	#11758561	1	2	yes	direct product factor
309	C₂	—	2	2	no	—
310	C₂	—	2	8	no	—
311	C₂	—	62	8	no	—
312	C₂	C₂³×C₄×D₃₁	1	1	yes	characteristic
313	C₂	C₂×#11758561	1	1	yes	characteristic
314	C₂	#14521885	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂³×D₃₁
commutator	C₂×C₃₁	C₂⁴×C₄
Frattini	C₂²	C₂⁴×D₃₁
Fitting	C₂×C₄×D₄×C₃₁	C₂
socle, cosocle	C₂²×C₃₁	C₂⁵
prime radical	C₂×#11758561	C₂
hypercenter	C₂×C₄×D₄	D₃₁
hypocenter	C₃₁	C₄×H(5,𝔽₂)
LCS	G ▷ C₂×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×D₄

Complements

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

N	H ≅ G/N	type
2. #14521530	C₂	semidirect
3. #14521528	C₂	semidirect
4. #14521524	C₂	semidirect
5. #14521522	C₂	semidirect
6. #14521521	C₂	semidirect
7. C₄×#92495	C₂	semidirect
8. C₄×#92497	C₂	semidirect
9. C₂×C₄×C₂²⋊D₃₁	C₂	semidirect
10. C₄×D₄×D₃₁	C₂	semidirect
11. C₂×C₄×D₄×C₃₁	C₂	semidirect
13. C₂³×C₄×C₃₁	C₂²	semidirect
15. #11758561	C₄	direct (N × H)
19. C₂²×C₄×D₃₁	C₂²	semidirect
20. C₄×D₄×C₃₁	C₂²	semidirect
21. C₄×D₄×C₃₁	C₂²	semidirect
22. C₂×C₄⋊C₄×C₃₁	C₂²	semidirect
23. C₂×C₂²⋊C₄×C₃₁	C₂²	semidirect
24. C₂×C₄²×C₃₁	C₂²	semidirect
25. C₂×C₂²⋊Dic₃₁	C₂²	semidirect
26. D₄×Dic₃₁	C₂²	semidirect
27. D₄×Dic₃₁	C₂²	semidirect
28. C₄×C₂²⋊D₃₁	C₂²	semidirect
29. C₄×C₂²⋊D₃₁	C₂²	semidirect
30. C₄×C₂²⋊D₃₁	C₂²	semidirect
31. C₄×C₂²⋊D₃₁	C₂²	semidirect
32. C₄×C₂²⋊D₃₁	C₂²	semidirect
33. C₂×(C₂×D₃₁)⋊C₄	C₂²	semidirect
34. #11758503	C₂²	semidirect
35. C₂×Dic₃₁⋊C₄	C₂²	semidirect
36. C₂×C₄×Dic₃₁	C₂²	semidirect
37. #11758470	C₂²	semidirect
38. #11758469	C₂²	semidirect
39. C₄⋊C₄×D₃₁	C₂²	semidirect
40. #11758464	C₂²	semidirect
41. (C₂²⋊D₃₁)⋊C₄	C₂²	semidirect
42. (C₂²⋊D₃₁)⋊C₄	C₂²	semidirect
43. C₂²⋊C₄×D₃₁	C₂²	semidirect
44. #11758454	C₂²	semidirect
45. C₄×D₁₂₄	C₂²	semidirect
46. C₄×D₁₂₄	C₂²	semidirect
47. #11758449	C₂²	semidirect
48. C₄²×D₃₁	C₂²	semidirect
49. C₄×Dic₆₂	C₂²	semidirect
50. C₄×Dic₆₂	C₂²	semidirect
53. C₂×D₄×C₃₁	C₂×C₄	semidirect
62. C₂×C₂²⋊D₃₁	C₂×C₄	semidirect
68. #92497	C₂×C₄	semidirect
69. D₄×D₃₁	C₂×C₄	semidirect
70. #92495	C₂×C₄	semidirect
98. C₂³×C₃₁	C₂²×C₄	semidirect
103. C₂²×D₃₁	C₂²×C₄	semidirect
105. D₄×C₃₁	C₂²×C₄	semidirect
111. C₂×C₄×C₃₁	C₂²×C₄	semidirect
117. C₂²⋊D₃₁	C₂²×C₄	semidirect
118. C₂²⋊D₃₁	C₂²×C₄	semidirect
121. C₂×Dic₃₁	C₂²×C₄	semidirect
125. D₁₂₄	C₂²×C₄	semidirect
129. C₄×D₃₁	C₂²×C₄	semidirect
130. Dic₆₂	C₂²×C₄	semidirect
148. C₄×C₃₁	H(5,𝔽₂)	semidirect
162. C₂×C₄×D₄	D₃₁	semidirect
176. C₂³×C₄	C₂×D₃₁	semidirect
192. C₄×D₄	C₂×D₃₁	semidirect
193. C₄×D₄	C₂×D₃₁	semidirect
200. C₂×C₄⋊C₄	C₂×D₃₁	semidirect
204. C₂×C₂²⋊C₄	C₂×D₃₁	semidirect
207. C₂×C₄²	C₂×D₃₁	semidirect
208. C₃₁	C₄×H(5,𝔽₂)	semidirect
219. C₂×D₄	C₄×D₃₁	semidirect
260. C₂³	C₂×C₄×D₃₁	semidirect
267. D₄	C₂×C₄×D₃₁	semidirect
283. C₂×C₄	C₂×C₄×D₃₁	semidirect
308. C₄	#11758561	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#11758561	2
#14521530	2
#14521528	2
#14521524	2
#14521522	2
#14521521	2
C₄×#92495	2
C₄×#92497	2
C₂×C₄×C₂²⋊D₃₁	2
C₄×D₄×D₃₁	2
C₂×C₄×D₄×C₃₁	2
C₄×H(5,𝔽₂)	31

Subgroups — C4×#11758561 #16858916

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#11758561 #16858916