Subgroups — C₂×#14521726 #16859209

Order 3968.

1328 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14521726	C₂	1	16	yes	maximal, direct product factor
2	C₂×#11758475	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#11758475	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#11758524	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#11758471	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#11758471	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#11758463	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#11758523	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#11758459	C₂	1	1	yes	maximal, characteristic
10	C₂×#11758470	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄×C₂²⋊D₃₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#11758469	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#11758454	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²×(C₂×D₃₁)⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₂²⋊C₄×D₃₁	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₃₁×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂⁴×D₃₁	C₂²	1	1	yes	characteristic
18	C₂²×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
19	C₂³×C₄×C₃₁	C₂²	1	1	yes	characteristic
20	C₂²×C₂²⋊D₃₁	C₂²	1	1	yes	characteristic
21	C₂³×Dic₃₁	C₂²	1	1	yes	characteristic
22	C₂²×D₁₂₄	C₂²	1	1	yes	characteristic
23	C₂²×D₁₂₄	C₂²	1	1	yes	characteristic
24	C₂²×C₄×D₃₁	C₂²	1	1	yes	characteristic
25	C₂²×C₄×D₃₁	C₂²	1	1	yes	characteristic
26	C₂²×C₄×D₃₁	C₂²	1	1	yes	characteristic, complemented
27	C₃₁×C₂²⋊Q₈	C₂²	1	8	yes	complemented
28	C₂×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
32	C₂×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
33	C₂×C₂²⋊Dic₃₁	C₂²	1	1	yes	characteristic
34	#11758524	C₂²	1	8	yes	complemented
35	#11758523	C₂²	1	8	yes	complemented
36	C₄×C₂²⋊D₃₁	C₂²	1	8	yes	complemented
37	C₂×(C₂×D₃₁)⋊C₄	C₂²	1	1	yes	characteristic
38	C₂×(C₂×D₃₁)⋊C₄	C₂²	1	1	yes	characteristic
39	C₂×(C₂×D₃₁)⋊C₄	C₂²	1	1	yes	characteristic
40	C₂×(C₂×D₃₁)⋊C₄	C₂²	1	1	yes	characteristic
41	C₂×(C₂×D₃₁)⋊C₄	C₂²	1	1	yes	characteristic
42	C₂×(C₂×D₃₁)⋊C₄	C₂²	1	1	yes	characteristic
43	C₂×(C₂×D₃₁)⋊C₄	C₂²	1	1	yes	characteristic
44	C₂×(C₂×D₃₁)⋊C₄	C₂²	1	1	yes	characteristic
45	C₂×(C₂×D₃₁)⋊C₄	C₂²	1	8	yes	complemented
46	C₂×(C₂×D₃₁)⋊C₄	C₂²	1	1	yes	characteristic, complemented
47	C₂×(C₂×D₃₁)⋊C₄	C₂²	1	1	yes	characteristic, complemented
48	C₂×(C₂×D₃₁)⋊C₄	C₂²	1	1	yes	characteristic, complemented
49	C₂×C₄⋊Dic₃₁	C₂²	1	1	yes	characteristic, complemented
50	C₂×C₄⋊Dic₃₁	C₂²	1	1	yes	characteristic, complemented
51	C₂×Dic₃₁⋊C₄	C₂²	1	1	yes	characteristic, complemented
52	C₂×Dic₃₁⋊C₄	C₂²	1	1	yes	characteristic, complemented
53	C₂×Dic₃₁⋊C₄	C₂²	1	1	yes	characteristic, complemented
54	C₂×C₄×Dic₃₁	C₂²	1	1	yes	characteristic, complemented
55	C₂×C₄×Dic₃₁	C₂²	1	1	yes	characteristic, complemented
56	C₂×C₄×Dic₃₁	C₂²	1	1	yes	characteristic, complemented
57	#11758475	C₂²	1	8	yes	complemented
58	#11758475	C₂²	1	8	yes	complemented
59	#11758471	C₂²	1	8	yes	complemented
60	#11758471	C₂²	1	8	yes	complemented
61	#11758470	C₂²	1	8	yes	complemented
62	#11758469	C₂²	1	8	yes	complemented
63	#11758463	C₂²	1	8	yes	complemented
64	#11758459	C₂²	1	8	yes	—
65	C₂²⋊C₄×D₃₁	C₂²	1	8	yes	complemented
66	#11758454	C₂²	1	8	yes	complemented
67	C₂⁴×C₃₁	C₂³	1	1	yes	characteristic
68	C₂³×D₃₁	—	2	4	no	—
69	C₂³×D₃₁	—	2	4	no	—
70	C₂³×D₃₁	—	4	2	no	—
71	C₂³×D₃₁	C₂³	1	1	yes	characteristic
72	C₂³×D₃₁	C₂³	1	1	yes	characteristic
73	C₂³×D₃₁	C₂³	1	4	yes	—
74	C₂³×D₃₁	C₂³	1	1	yes	characteristic
75	C₂×Q₈×C₃₁	—	4	2	no	—
76	C₂×Q₈×C₃₁	C₂³	1	4	yes	complemented
77	C₂²×C₄×C₃₁	—	4	2	no	—
78	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
79	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
80	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
81	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
82	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
83	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
84	C₂²×C₄×C₃₁	C₂³	1	4	yes	—
85	C₂×C₂²⋊D₃₁	—	2	4	no	—
86	C₂×C₂²⋊D₃₁	C₂³	1	4	yes	—
87	C₂²×Dic₃₁	—	2	4	no	—
88	C₂²×Dic₃₁	C₂³	1	4	yes	—
89	C₂²×Dic₃₁	C₂³	1	1	yes	characteristic
90	C₂²×Dic₃₁	C₂³	1	1	yes	characteristic
91	C₂²×Dic₃₁	C₂³	1	1	yes	characteristic
92	C₂²×Dic₃₁	C₂³	1	1	yes	characteristic
93	C₂²×Dic₃₁	C₂³	1	1	yes	characteristic
94	C₂×D₁₂₄	—	2	4	no	—
95	C₂×D₁₂₄	—	4	2	no	—
96	C₂×D₁₂₄	C₂³	1	4	yes	—
97	C₂×D₁₂₄	C₂³	1	4	yes	—
98	C₂×C₄×D₃₁	—	2	4	no	—
99	C₂×C₄×D₃₁	—	4	2	no	—
100	C₂×C₄×D₃₁	—	4	2	no	—
101	C₂×C₄×D₃₁	C₂³	1	4	yes	—
102	C₂×C₄×D₃₁	C₂³	1	4	yes	—
103	C₂×C₄×D₃₁	C₂³	1	4	yes	complemented
104	C₄⋊C₄×C₃₁	C₂³	1	4	yes	complemented
105	C₄⋊C₄×C₃₁	C₂³	1	4	yes	complemented
106	C₄⋊C₄×C₃₁	C₂³	1	4	yes	complemented
107	C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
108	C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
109	C₂²⋊Dic₃₁	C₂³	1	4	yes	—
110	(C₂×D₃₁)⋊C₄	C₂³	1	4	yes	—
111	(C₂×D₃₁)⋊C₄	C₂³	1	4	yes	—
112	(C₂×D₃₁)⋊C₄	C₂³	1	4	yes	—
113	(C₂×D₃₁)⋊C₄	C₂³	1	4	yes	—
114	(C₂×D₃₁)⋊C₄	C₂³	1	4	yes	—
115	(C₂×D₃₁)⋊C₄	C₂³	1	4	yes	—
116	(C₂×D₃₁)⋊C₄	C₂³	1	4	yes	—
117	(C₂×D₃₁)⋊C₄	C₂³	1	4	yes	—
118	(C₂×D₃₁)⋊C₄	C₂³	1	4	yes	complemented
119	(C₂×D₃₁)⋊C₄	C₂³	1	4	yes	complemented
120	(C₂×D₃₁)⋊C₄	C₂³	1	4	yes	complemented
121	C₄⋊Dic₃₁	C₂³	1	4	yes	complemented
122	C₄⋊Dic₃₁	C₂³	1	4	yes	complemented
123	Dic₃₁⋊C₄	C₂³	1	4	yes	complemented
124	Dic₃₁⋊C₄	C₂³	1	4	yes	complemented
125	Dic₃₁⋊C₄	C₂³	1	4	yes	complemented
126	C₄×Dic₃₁	C₂³	1	4	yes	complemented
127	C₄×Dic₃₁	C₂³	1	4	yes	complemented
128	C₄×Dic₃₁	C₂³	1	4	yes	complemented
129	C₂³×C₃₁	—	2	2	no	—
130	C₂³×C₃₁	—	2	2	no	—
131	C₂³×C₃₁	#41	1	4	yes	—
132	C₂³×C₃₁	C₂⁴	1	2	yes	—
133	C₂³×C₃₁	C₂⁴	1	1	yes	characteristic
134	C₂²×D₃₁	—	2	2	no	—
135	C₂²×D₃₁	—	2	2	no	—
136	C₂²×D₃₁	—	2	2	no	—
137	C₂²×D₃₁	—	2	2	no	—
138	C₂²×D₃₁	—	2	8	no	—
139	C₂²×D₃₁	—	2	2	no	—
140	C₂²×D₃₁	—	2	2	no	—
141	C₂²×D₃₁	—	2	2	no	—
142	C₂²×D₃₁	—	2	2	no	—
143	C₂²×D₃₁	—	2	8	no	—
144	C₂²×D₃₁	—	4	4	no	—
145	C₂²×D₃₁	—	4	16	no	—
146	C₂²×D₃₁	#41	1	4	yes	—
147	C₂²×D₃₁	C₂⁴	1	2	yes	—
148	C₂²×D₃₁	C₂⁴	1	2	yes	—
149	C₂²×D₃₁	C₂⁴	1	2	yes	—
150	Q₈×C₃₁	—	4	4	no	—
151	C₂×C₄×C₃₁	—	2	2	no	—
152	C₂×C₄×C₃₁	—	2	2	no	—
153	C₂×C₄×C₃₁	—	2	2	no	—
154	C₂×C₄×C₃₁	—	2	2	no	—
155	C₂×C₄×C₃₁	—	2	2	no	—
156	C₂×C₄×C₃₁	—	2	2	no	—
157	C₂×C₄×C₃₁	—	4	4	no	—
158	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
159	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
160	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
161	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
162	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
163	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
164	C₂²⋊D₃₁	—	2	8	no	—
165	C₂×Dic₃₁	—	2	2	no	—
166	C₂×Dic₃₁	—	2	8	no	—
167	C₂×Dic₃₁	—	2	2	no	—
168	C₂×Dic₃₁	—	2	2	no	—
169	C₂×Dic₃₁	—	2	2	no	—
170	C₂×Dic₃₁	—	2	2	no	—
171	C₂×Dic₃₁	C₂⁴	1	2	yes	—
172	C₂×Dic₃₁	C₂⁴	1	2	yes	—
173	C₂×Dic₃₁	C₂⁴	1	2	yes	—
174	C₂×Dic₃₁	C₂⁴	1	2	yes	—
175	C₂×Dic₃₁	C₂⁴	1	2	yes	—
176	D₁₂₄	—	2	8	no	—
177	D₁₂₄	—	4	4	no	—
178	C₄×D₃₁	—	2	8	no	—
179	C₄×D₃₁	—	4	4	no	—
180	C₄×D₃₁	—	4	4	no	—
181	C₂×#551	—	31	1	no	maximal, Sylow
182	C₂²×C₃₁	—	2	8	no	—
183	C₂²×C₃₁	—	2	2	no	—
184	C₂²×C₃₁	—	2	2	no	—
185	C₂²×C₃₁	C₂×#41	1	4	yes	—
186	C₂²×C₃₁	C₂×#41	1	2	yes	—
187	C₂²×C₃₁	C₂×#41	1	2	yes	—
188	C₂²×C₃₁	H(5,𝔽₂)	1	2	yes	—
189	C₂²×C₃₁	C₂⁵	1	1	yes	characteristic
190	C₂×D₃₁	—	2	8	no	—
191	C₂×D₃₁	—	2	2	no	—
192	C₂×D₃₁	—	2	2	no	—
193	C₂×D₃₁	—	2	2	no	—
194	C₂×D₃₁	—	2	2	no	—
195	C₂×D₃₁	—	2	2	no	—
196	C₂×D₃₁	—	2	2	no	—
197	C₂×D₃₁	—	2	2	no	—
198	C₂×D₃₁	—	2	2	no	—
199	C₂×D₃₁	—	4	16	no	—
200	C₂×D₃₁	—	4	4	no	—
201	C₂×D₃₁	—	4	4	no	—
202	C₂×D₃₁	C₂×#41	1	4	yes	—
203	C₄×C₃₁	—	2	2	no	—
204	C₄×C₃₁	—	2	2	no	—
205	C₄×C₃₁	—	2	2	no	—
206	C₄×C₃₁	—	2	2	no	—
207	C₄×C₃₁	—	2	2	no	—
208	C₄×C₃₁	—	2	2	no	—
209	Dic₃₁	—	2	2	no	—
210	Dic₃₁	—	2	2	no	—
211	Dic₃₁	—	2	2	no	—
212	Dic₃₁	—	2	2	no	—
213	Dic₃₁	—	2	2	no	—
214	#551	—	31	16	no	—
215	C₂×#126	—	31	1	no	—
216	C₂×#126	—	31	1	no	—
217	C₂×#124	—	31	1	no	—
218	C₂×#123	—	31	1	no	—
219	C₂×#123	—	31	1	no	—
220	C₂×#123	—	31	1	no	—
221	C₂×C₂²⋊Q₈	—	31	1	no	—
222	C₂×C₂²⋊Q₈	D₃₁	1	1	yes	characteristic, complemented
223	C₂×#120	—	31	1	no	—
224	C₂×C₄×D₄	—	31	1	no	—
225	C₂×C₄×D₄	—	31	1	no	—
226	C₂×#117	—	31	1	no	—
227	C₂×#117	—	31	1	no	—
228	C₂²×C₂²⋊C₄	—	31	1	no	—
229	C₂²×C₂²⋊C₄	—	31	1	no	—
230	C₂×C₃₁	—	2	4	no	—
231	C₂×C₃₁	#551	1	4	yes	complemented
232	C₂×C₃₁	C₂²×#41	1	1	yes	characteristic
233	C₂×C₃₁	C₂²×#41	1	1	yes	characteristic
234	C₂×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
235	D₃₁	—	2	4	no	—
236	D₃₁	—	4	2	no	—
237	D₃₁	—	4	2	no	—
238	C₂⁵	—	31	1	no	—
239	C₂²×Q₈	C₂×D₃₁	1	1	yes	characteristic, complemented
240	C₂²×D₄	—	31	1	no	—
241	C₂²×D₄	—	31	1	no	—
242	C₂²×D₄	—	31	1	no	—
243	C₂³×C₄	—	31	1	no	—
244	C₂³×C₄	—	31	1	no	—
245	C₂³×C₄	—	31	1	no	—
246	C₂³×C₄	—	31	1	no	—
247	C₂³×C₄	C₂×D₃₁	1	1	yes	characteristic
248	#126	—	31	8	no	—
249	#126	—	31	8	no	—
250	#124	—	31	8	no	—
251	#123	—	31	8	no	—
252	#123	—	31	8	no	—
253	#123	—	31	8	no	—
254	C₂²⋊Q₈	—	31	8	no	—
255	C₂²⋊Q₈	C₂×D₃₁	1	8	yes	complemented
256	#120	—	31	8	no	—
257	C₄×D₄	—	31	8	no	—
258	C₄×D₄	—	31	8	no	—
259	#117	—	31	8	no	—
260	#117	—	31	8	no	—
261	C₂×C₄⋊C₄	—	31	1	no	—
262	C₂×C₄⋊C₄	—	31	1	no	—
263	C₂×C₄⋊C₄	—	31	1	no	—
264	C₂×C₄⋊C₄	—	31	1	no	—
265	C₂×C₄⋊C₄	—	31	1	no	—
266	C₂×C₄⋊C₄	C₂×D₃₁	1	1	yes	characteristic, complemented
267	C₂×C₄⋊C₄	C₂×D₃₁	1	1	yes	characteristic, complemented
268	C₂×C₄⋊C₄	C₂×D₃₁	1	1	yes	characteristic, complemented
269	C₂×C₂²⋊C₄	—	31	1	no	—
270	C₂×C₂²⋊C₄	—	31	1	no	—
271	C₂×C₂²⋊C₄	—	31	1	no	—
272	C₂×C₂²⋊C₄	—	31	1	no	—
273	C₂×C₂²⋊C₄	—	31	1	no	—
274	C₂×C₂²⋊C₄	—	31	1	no	—
275	C₂×C₂²⋊C₄	—	31	1	no	—
276	C₂×C₂²⋊C₄	—	31	8	no	—
277	C₂×C₂²⋊C₄	—	31	1	no	—
278	C₂×C₂²⋊C₄	—	31	1	no	—
279	C₂×C₂²⋊C₄	—	31	1	no	—
280	C₂×C₂²⋊C₄	—	31	1	no	—
281	C₂×C₂²⋊C₄	—	31	1	no	—
282	C₂×C₂²⋊C₄	—	31	8	no	—
283	C₂×C₂²⋊C₄	C₂×D₃₁	1	1	yes	characteristic
284	C₂×C₂²⋊C₄	C₂×D₃₁	1	1	yes	characteristic
285	C₂×C₄²	—	31	1	no	—
286	C₂×C₄²	—	31	1	no	—
287	C₂×C₄²	—	31	1	no	—
288	C₃₁	C₂×#551	1	1	yes	characteristic, complemented, Sylow
289	C₂⁴	—	31	1	no	—
290	C₂⁴	—	31	1	no	—
291	C₂⁴	—	31	1	no	—
292	C₂⁴	—	31	4	no	—
293	C₂⁴	—	62	4	no	—
294	C₂⁴	—	62	4	no	—
295	C₂⁴	—	124	2	no	—
296	C₂⁴	C₂²×D₃₁	1	1	yes	characteristic
297	C₂×Q₈	—	4	2	no	—
298	C₂×Q₈	C₂²×D₃₁	1	4	yes	complemented
299	C₂×D₄	—	31	4	no	—
300	C₂×D₄	—	31	4	no	—
301	C₂×D₄	—	31	4	no	—
302	C₂×D₄	—	62	4	no	—
303	C₂×D₄	—	62	4	no	—
304	C₂×D₄	—	124	2	no	—
305	C₂²×C₄	—	4	2	no	—
306	C₂²×C₄	—	31	4	no	—
307	C₂²×C₄	—	31	1	no	—
308	C₂²×C₄	—	31	1	no	—
309	C₂²×C₄	—	31	1	no	—
310	C₂²×C₄	—	31	1	no	—
311	C₂²×C₄	—	31	1	no	—
312	C₂²×C₄	—	31	4	no	—
313	C₂²×C₄	—	31	4	no	—
314	C₂²×C₄	—	31	4	no	—
315	C₂²×C₄	—	62	4	no	—
316	C₂²×C₄	—	62	4	no	—
317	C₂²×C₄	—	124	2	no	—
318	C₂²×C₄	—	124	2	no	—
319	C₂²×C₄	C₂²×D₃₁	1	1	yes	characteristic
320	C₂²×C₄	C₂²×D₃₁	1	1	yes	characteristic
321	C₂²×C₄	C₂²×D₃₁	1	1	yes	characteristic
322	C₂²×C₄	C₂²×D₃₁	1	1	yes	characteristic
323	C₂²×C₄	C₂²×D₃₁	1	1	yes	characteristic
324	C₂²×C₄	C₂²×D₃₁	1	1	yes	characteristic
325	C₂²×C₄	C₂²×D₃₁	1	4	yes	—
326	C₄⋊C₄	—	31	4	no	—
327	C₄⋊C₄	—	31	4	no	—
328	C₄⋊C₄	—	31	4	no	—
329	C₄⋊C₄	—	31	4	no	—
330	C₄⋊C₄	—	31	4	no	—
331	C₄⋊C₄	C₂²×D₃₁	1	4	yes	complemented
332	C₄⋊C₄	C₂²×D₃₁	1	4	yes	complemented
333	C₄⋊C₄	C₂²×D₃₁	1	4	yes	complemented
334	C₂²⋊C₄	—	31	4	no	—
335	C₂²⋊C₄	—	31	4	no	—
336	C₂²⋊C₄	—	31	4	no	—
337	C₂²⋊C₄	—	31	4	no	—
338	C₂²⋊C₄	—	31	4	no	—
339	C₂²⋊C₄	—	31	4	no	—
340	C₂²⋊C₄	—	31	4	no	—
341	C₂²⋊C₄	—	31	4	no	—
342	C₂²⋊C₄	—	31	4	no	—
343	C₂²⋊C₄	—	31	4	no	—
344	C₂²⋊C₄	—	31	4	no	—
345	C₂²⋊C₄	—	31	4	no	—
346	C₂²⋊C₄	C₂²×D₃₁	1	4	yes	—
347	C₂²⋊C₄	C₂²×D₃₁	1	4	yes	—
348	C₄²	—	31	4	no	—
349	C₄²	—	31	4	no	—
350	C₄²	—	31	4	no	—
351	C₂³	—	2	2	no	—
352	C₂³	—	2	2	no	—
353	C₂³	—	31	4	no	—
354	C₂³	—	31	2	no	—
355	C₂³	—	31	2	no	—
356	C₂³	—	31	2	no	—
357	C₂³	—	62	8	no	—
358	C₂³	—	62	2	no	—
359	C₂³	—	62	2	no	—
360	C₂³	—	62	2	no	—
361	C₂³	—	62	2	no	—
362	C₂³	—	62	2	no	—
363	C₂³	—	62	8	no	—
364	C₂³	—	62	2	no	—
365	C₂³	—	62	2	no	—
366	C₂³	—	62	2	no	—
367	C₂³	—	124	4	no	—
368	C₂³	—	124	16	no	—
369	C₂³	#92499	1	4	yes	—
370	C₂³	C₂³×D₃₁	1	2	yes	—
371	C₂³	C₂³×D₃₁	1	1	yes	characteristic
372	Q₈	—	4	4	no	—
373	D₄	—	62	8	no	—
374	D₄	—	62	8	no	—
375	D₄	—	124	4	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	4	4	no	—
383	C₂×C₄	—	31	2	no	—
384	C₂×C₄	—	31	2	no	—
385	C₂×C₄	—	31	2	no	—
386	C₂×C₄	—	31	2	no	—
387	C₂×C₄	—	31	2	no	—
388	C₂×C₄	—	62	8	no	—
389	C₂×C₄	—	62	2	no	—
390	C₂×C₄	—	62	8	no	—
391	C₂×C₄	—	62	2	no	—
392	C₂×C₄	—	62	2	no	—
393	C₂×C₄	—	62	2	no	—
394	C₂×C₄	—	62	2	no	—
395	C₂×C₄	—	124	4	no	—
396	C₂×C₄	—	124	4	no	—
397	C₂×C₄	C₂³×D₃₁	1	2	yes	—
398	C₂×C₄	C₂³×D₃₁	1	2	yes	—
399	C₂×C₄	C₂³×D₃₁	1	2	yes	—
400	C₂×C₄	C₂³×D₃₁	1	2	yes	—
401	C₂×C₄	C₂³×D₃₁	1	2	yes	—
402	C₂×C₄	C₂³×D₃₁	1	2	yes	—
403	C₂²	—	2	2	no	—
404	C₂²	—	2	2	no	—
405	C₂²	—	2	8	no	—
406	C₂²	—	31	4	no	—
407	C₂²	—	62	2	no	—
408	C₂²	—	62	2	no	—
409	C₂²	—	62	8	no	—
410	C₂²	—	62	2	no	—
411	C₂²	—	62	2	no	—
412	C₂²	—	62	2	no	—
413	C₂²	—	62	2	no	—
414	C₂²	—	62	2	no	—
415	C₂²	—	62	2	no	—
416	C₂²	—	124	16	no	—
417	C₂²	—	124	4	no	—
418	C₂²	—	124	4	no	—
419	C₂²	#11758561	1	2	yes	—
420	C₂²	C₂×#92499	1	4	yes	—
421	C₂²	C₂×#92499	1	2	yes	—
422	C₂²	#41×D₃₁	1	2	yes	—
423	C₂²	C₂⁴×D₃₁	1	1	yes	characteristic
424	C₄	—	2	2	no	—
425	C₄	—	2	2	no	—
426	C₄	—	2	2	no	—
427	C₄	—	2	2	no	—
428	C₄	—	2	2	no	—
429	C₄	—	2	2	no	—
430	C₄	—	62	2	no	—
431	C₄	—	62	2	no	—
432	C₄	—	62	2	no	—
433	C₄	—	62	2	no	—
434	C₄	—	62	2	no	—
435	C₂	—	2	4	no	—
436	C₂	—	62	4	no	—
437	C₂	—	124	2	no	—
438	C₂	—	124	2	no	—
439	C₂	#14521726	1	4	yes	direct product factor
440	C₂	C₂×#41×D₃₁	1	1	yes	characteristic
441	C₂	C₂²×#92499	1	1	yes	characteristic
442	C₂	C₂×#11758561	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂³×D₃₁
commutator, cosocle	C₂²×C₃₁	C₂⁵
Frattini	C₂²	C₂⁴×D₃₁
Fitting	C₂×C₃₁×C₂²⋊Q₈	C₂
socle	C₂³×C₃₁	C₂⁴
prime radical	C₂×#11758459	C₂
hypercenter	C₂×C₂²⋊Q₈	D₃₁
hypocenter	C₃₁	C₂×#551
LCS	G ▷ C₂²×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂³ ◁ C₂×C₂²⋊Q₈

Complements

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

N	H ≅ G/N	type
1. #14521726	C₂	direct (N × H)
2. C₂×#11758475	C₂	semidirect
3. C₂×#11758475	C₂	semidirect
4. C₂×#11758524	C₂	semidirect
5. C₂×#11758471	C₂	semidirect
6. C₂×#11758471	C₂	semidirect
7. C₂×#11758463	C₂	semidirect
8. C₂×#11758523	C₂	semidirect
10. C₂×#11758470	C₂	semidirect
11. C₂×C₄×C₂²⋊D₃₁	C₂	semidirect
12. C₂×#11758469	C₂	semidirect
13. C₂×#11758454	C₂	semidirect
14. C₂²×(C₂×D₃₁)⋊C₄	C₂	semidirect
15. C₂×C₂²⋊C₄×D₃₁	C₂	semidirect
16. C₂×C₃₁×C₂²⋊Q₈	C₂	semidirect
18. C₂²×Q₈×C₃₁	C₂²	semidirect
26. C₂²×C₄×D₃₁	C₂²	semidirect
27. C₃₁×C₂²⋊Q₈	C₂²	semidirect
28. C₂×C₄⋊C₄×C₃₁	C₂²	semidirect
29. C₂×C₄⋊C₄×C₃₁	C₂²	semidirect
30. C₂×C₄⋊C₄×C₃₁	C₂²	semidirect
34. #11758524	C₂²	semidirect
35. #11758523	C₂²	semidirect
36. C₄×C₂²⋊D₃₁	C₂²	semidirect
45. C₂×(C₂×D₃₁)⋊C₄	C₂²	semidirect
46. C₂×(C₂×D₃₁)⋊C₄	C₂²	semidirect
47. C₂×(C₂×D₃₁)⋊C₄	C₂²	semidirect
48. C₂×(C₂×D₃₁)⋊C₄	C₂²	semidirect
49. C₂×C₄⋊Dic₃₁	C₂²	semidirect
50. C₂×C₄⋊Dic₃₁	C₂²	semidirect
51. C₂×Dic₃₁⋊C₄	C₂²	semidirect
52. C₂×Dic₃₁⋊C₄	C₂²	semidirect
53. C₂×Dic₃₁⋊C₄	C₂²	semidirect
54. C₂×C₄×Dic₃₁	C₂²	semidirect
55. C₂×C₄×Dic₃₁	C₂²	semidirect
56. C₂×C₄×Dic₃₁	C₂²	semidirect
57. #11758475	C₂²	semidirect
58. #11758475	C₂²	semidirect
59. #11758471	C₂²	semidirect
60. #11758471	C₂²	semidirect
61. #11758470	C₂²	semidirect
62. #11758469	C₂²	semidirect
63. #11758463	C₂²	semidirect
65. C₂²⋊C₄×D₃₁	C₂²	semidirect
66. #11758454	C₂²	semidirect
76. C₂×Q₈×C₃₁	C₂³	semidirect
103. C₂×C₄×D₃₁	C₂³	semidirect
104. C₄⋊C₄×C₃₁	C₂³	semidirect
105. C₄⋊C₄×C₃₁	C₂³	semidirect
106. C₄⋊C₄×C₃₁	C₂³	semidirect
118. (C₂×D₃₁)⋊C₄	C₂³	semidirect
119. (C₂×D₃₁)⋊C₄	C₂³	semidirect
120. (C₂×D₃₁)⋊C₄	C₂³	semidirect
121. C₄⋊Dic₃₁	C₂³	semidirect
122. C₄⋊Dic₃₁	C₂³	semidirect
123. Dic₃₁⋊C₄	C₂³	semidirect
124. Dic₃₁⋊C₄	C₂³	semidirect
125. Dic₃₁⋊C₄	C₂³	semidirect
126. C₄×Dic₃₁	C₂³	semidirect
127. C₄×Dic₃₁	C₂³	semidirect
128. C₄×Dic₃₁	C₂³	semidirect
222. C₂×C₂²⋊Q₈	D₃₁	semidirect
231. C₂×C₃₁	#551	semidirect
239. C₂²×Q₈	C₂×D₃₁	semidirect
255. C₂²⋊Q₈	C₂×D₃₁	semidirect
266. C₂×C₄⋊C₄	C₂×D₃₁	semidirect
267. C₂×C₄⋊C₄	C₂×D₃₁	semidirect
268. C₂×C₄⋊C₄	C₂×D₃₁	semidirect
288. C₃₁	C₂×#551	semidirect
298. C₂×Q₈	C₂²×D₃₁	semidirect
331. C₄⋊C₄	C₂²×D₃₁	semidirect
332. C₄⋊C₄	C₂²×D₃₁	semidirect
333. C₄⋊C₄	C₂²×D₃₁	semidirect
439. C₂	#14521726	direct (N × H)

Maximal subgroups

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

subgroup	index
#14521726	2
C₂×#11758475	2
C₂×#11758524	2
C₂×#11758471	2
C₂×#11758463	2
C₂×#11758523	2
C₂×#11758459	2
C₂×#11758470	2
C₂×C₄×C₂²⋊D₃₁	2
C₂×#11758469	2
C₂×#11758454	2
C₂²×(C₂×D₃₁)⋊C₄	2
C₂×C₂²⋊C₄×D₃₁	2
C₂×C₃₁×C₂²⋊Q₈	2
C₂×#551	31

Subgroups — C2×#14521726 #16859209

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#14521726 #16859209