Subgroups — C₂×#13093121 #15686925

Order 2944.

1200 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13093121	C₂	1	16	yes	maximal, direct product factor
2	C₂×#10625115	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#10625060	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#10625060	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#10625067	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#10625067	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#10625049	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#10625049	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#10625117	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#10625058	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄×C₂²⋊D₂₃	C₂	1	1	yes	maximal, characteristic
12	C₂×(C₂²⋊D₂₃)⋊C₄	C₂	1	1	yes	maximal, characteristic
13	C₂×(C₂²⋊D₂₃)⋊C₄	C₂	1	1	yes	maximal, characteristic
14	C₂²×Dic₂₃⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₄⋊C₄×D₂₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₂₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×Q₈×C₂₃	C₂²	1	1	yes	characteristic
18	C₂³×C₄×C₂₃	C₂²	1	1	yes	characteristic
19	C₂²×C₂²⋊D₂₃	C₂²	1	1	yes	characteristic
20	C₂³×Dic₂₃	C₂²	1	1	yes	characteristic
21	C₂³×Dic₂₃	C₂²	1	1	yes	characteristic
22	C₂²×C₄×D₂₃	C₂²	1	1	yes	characteristic
23	C₂²×C₄×D₂₃	C₂²	1	1	yes	characteristic
24	C₂²×C₄×D₂₃	C₂²	1	1	yes	characteristic
25	C₂²×Dic₄₆	C₂²	1	1	yes	characteristic
26	C₂²×Dic₄₆	C₂²	1	1	yes	characteristic
27	C₂₃×C₂²⋊Q₈	C₂²	1	8	yes	complemented
28	C₂×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
29	C₂×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
30	C₂×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
31	C₂×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
32	C₂×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
33	C₂×C₂²⋊Dic₂₃	C₂²	1	1	yes	characteristic
34	#10625117	C₂²	1	8	yes	complemented
35	#10625115	C₂²	1	8	yes	complemented
36	C₄×C₂²⋊D₂₃	C₂²	1	8	yes	—
37	C₂×(C₂×D₂₃)⋊C₄	C₂²	1	1	yes	characteristic
38	C₂×(C₂×D₂₃)⋊C₄	C₂²	1	1	yes	characteristic
39	C₂×(C₂×D₂₃)⋊C₄	C₂²	1	1	yes	characteristic
40	C₂×C₄⋊Dic₂₃	C₂²	1	1	yes	characteristic
41	C₂×C₄⋊Dic₂₃	C₂²	1	1	yes	characteristic
42	C₂×Dic₂₃⋊C₄	C₂²	1	1	yes	characteristic
43	C₂×Dic₂₃⋊C₄	C₂²	1	1	yes	characteristic
44	C₂×Dic₂₃⋊C₄	C₂²	1	1	yes	characteristic
45	C₂×Dic₂₃⋊C₄	C₂²	1	1	yes	characteristic
46	C₂×Dic₂₃⋊C₄	C₂²	1	1	yes	characteristic
47	C₂×Dic₂₃⋊C₄	C₂²	1	1	yes	characteristic
48	C₂×Dic₂₃⋊C₄	C₂²	1	1	yes	characteristic
49	C₂×Dic₂₃⋊C₄	C₂²	1	1	yes	characteristic
50	C₂×Dic₂₃⋊C₄	C₂²	1	1	yes	characteristic
51	C₂×Dic₂₃⋊C₄	C₂²	1	1	yes	characteristic
52	C₂×Dic₂₃⋊C₄	C₂²	1	1	yes	characteristic
53	C₂×Dic₂₃⋊C₄	C₂²	1	8	yes	complemented
54	C₂×C₄×Dic₂₃	C₂²	1	1	yes	characteristic
55	C₂×C₄×Dic₂₃	C₂²	1	1	yes	characteristic
56	C₂×C₄×Dic₂₃	C₂²	1	1	yes	characteristic
57	#10625067	C₂²	1	8	yes	complemented
58	#10625067	C₂²	1	8	yes	complemented
59	C₄⋊C₄×D₂₃	C₂²	1	8	yes	complemented
60	#10625060	C₂²	1	8	yes	complemented
61	#10625060	C₂²	1	8	yes	complemented
62	#10625058	C₂²	1	8	yes	complemented
63	(C₂²⋊D₂₃)⋊C₄	C₂²	1	8	yes	—
64	(C₂²⋊D₂₃)⋊C₄	C₂²	1	8	yes	—
65	#10625049	C₂²	1	8	yes	complemented
66	#10625049	C₂²	1	8	yes	complemented
67	C₂⁴×C₂₃	C₂³	1	1	yes	characteristic
68	C₂³×D₂₃	C₂³	1	1	yes	characteristic
69	C₂×Q₈×C₂₃	—	4	2	no	—
70	C₂×Q₈×C₂₃	C₂³	1	4	yes	—
71	C₂²×C₄×C₂₃	—	4	2	no	—
72	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
73	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
74	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
75	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
76	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
77	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
78	C₂²×C₄×C₂₃	C₂³	1	4	yes	—
79	C₂×C₂²⋊D₂₃	Q₈	1	8	yes	complemented
80	C₂×C₂²⋊D₂₃	C₂³	1	4	yes	—
81	C₂²×Dic₂₃	—	2	4	no	—
82	C₂²×Dic₂₃	—	4	2	no	—
83	C₂²×Dic₂₃	C₂³	1	4	yes	—
84	C₂²×Dic₂₃	C₂³	1	1	yes	characteristic
85	C₂²×Dic₂₃	C₂³	1	1	yes	characteristic
86	C₂²×Dic₂₃	C₂³	1	1	yes	characteristic
87	C₂²×Dic₂₃	C₂³	1	1	yes	characteristic
88	C₂²×Dic₂₃	C₂³	1	1	yes	characteristic
89	C₂²×Dic₂₃	C₂³	1	4	yes	—
90	C₂²×Dic₂₃	C₂³	1	1	yes	characteristic
91	C₂²×Dic₂₃	C₂³	1	1	yes	characteristic
92	C₂×C₄×D₂₃	—	2	4	no	—
93	C₂×C₄×D₂₃	—	4	2	no	—
94	C₂×C₄×D₂₃	—	4	2	no	—
95	C₂×C₄×D₂₃	C₂³	1	4	yes	—
96	C₂×C₄×D₂₃	C₂³	1	4	yes	—
97	C₂×C₄×D₂₃	C₂³	1	4	yes	—
98	C₂×Dic₄₆	—	2	4	no	—
99	C₂×Dic₄₆	—	4	2	no	—
100	C₂×Dic₄₆	C₂³	1	4	yes	—
101	C₂×Dic₄₆	C₂³	1	4	yes	—
102	C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
103	C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
104	C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
105	C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
106	C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
107	C₂²⋊Dic₂₃	C₂³	1	4	yes	—
108	(C₂×D₂₃)⋊C₄	C₂³	1	4	yes	—
109	(C₂×D₂₃)⋊C₄	C₂³	1	4	yes	—
110	(C₂×D₂₃)⋊C₄	C₂³	1	4	yes	—
111	C₄⋊Dic₂₃	C₂³	1	4	yes	—
112	C₄⋊Dic₂₃	C₂³	1	4	yes	—
113	Dic₂₃⋊C₄	C₂³	1	4	yes	—
114	Dic₂₃⋊C₄	C₂³	1	4	yes	—
115	Dic₂₃⋊C₄	C₂³	1	4	yes	—
116	Dic₂₃⋊C₄	C₂³	1	4	yes	—
117	Dic₂₃⋊C₄	C₂³	1	4	yes	—
118	Dic₂₃⋊C₄	C₂³	1	4	yes	—
119	Dic₂₃⋊C₄	C₂³	1	4	yes	—
120	Dic₂₃⋊C₄	C₂³	1	4	yes	—
121	Dic₂₃⋊C₄	C₂³	1	4	yes	—
122	Dic₂₃⋊C₄	C₂³	1	4	yes	—
123	Dic₂₃⋊C₄	C₂³	1	4	yes	—
124	C₄×Dic₂₃	C₂³	1	4	yes	—
125	C₄×Dic₂₃	C₂³	1	4	yes	—
126	C₄×Dic₂₃	C₂³	1	4	yes	—
127	C₂³×C₂₃	—	2	2	no	—
128	C₂³×C₂₃	—	2	2	no	—
129	C₂³×C₂₃	C₂×Q₈	1	4	yes	—
130	C₂³×C₂₃	C₂⁴	1	2	yes	—
131	C₂³×C₂₃	C₂⁴	1	1	yes	characteristic
132	C₂²×D₂₃	—	2	2	no	—
133	C₂²×D₂₃	—	2	2	no	—
134	C₂²×D₂₃	C₂×Q₈	1	4	yes	—
135	C₂²×D₂₃	C₂⁴	1	2	yes	—
136	Q₈×C₂₃	—	4	4	no	—
137	C₂×C₄×C₂₃	—	2	2	no	—
138	C₂×C₄×C₂₃	—	2	2	no	—
139	C₂×C₄×C₂₃	—	2	2	no	—
140	C₂×C₄×C₂₃	—	2	2	no	—
141	C₂×C₄×C₂₃	—	2	2	no	—
142	C₂×C₄×C₂₃	—	2	2	no	—
143	C₂×C₄×C₂₃	—	4	4	no	—
144	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
145	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
146	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
147	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
148	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
149	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
150	C₂²⋊D₂₃	C₂×Q₈	1	16	yes	complemented
151	C₂×Dic₂₃	—	2	2	no	—
152	C₂×Dic₂₃	—	2	2	no	—
153	C₂×Dic₂₃	—	2	2	no	—
154	C₂×Dic₂₃	—	2	2	no	—
155	C₂×Dic₂₃	—	2	2	no	—
156	C₂×Dic₂₃	—	2	8	no	—
157	C₂×Dic₂₃	—	4	4	no	—
158	C₂×Dic₂₃	C₂×Q₈	1	4	yes	—
159	C₂×Dic₂₃	#41	1	4	yes	—
160	C₂×Dic₂₃	C₂⁴	1	2	yes	—
161	C₂×Dic₂₃	C₂⁴	1	2	yes	—
162	C₂×Dic₂₃	C₂⁴	1	2	yes	—
163	C₂×Dic₂₃	C₂⁴	1	2	yes	—
164	C₂×Dic₂₃	C₂⁴	1	2	yes	—
165	C₂×Dic₂₃	C₂⁴	1	2	yes	—
166	C₂×Dic₂₃	C₂⁴	1	2	yes	—
167	C₄×D₂₃	—	2	8	no	—
168	C₄×D₂₃	—	4	4	no	—
169	C₄×D₂₃	—	4	4	no	—
170	Dic₄₆	—	2	8	no	—
171	Dic₄₆	—	4	4	no	—
172	C₂×#554	—	23	1	no	maximal, Sylow
173	C₂²×C₂₃	—	2	8	no	—
174	C₂²×C₂₃	—	2	2	no	—
175	C₂²×C₂₃	—	2	2	no	—
176	C₂²×C₂₃	C₂²×Q₈	1	4	yes	—
177	C₂²×C₂₃	C₂²×Q₈	1	2	yes	—
178	C₂²×C₂₃	C₂×#41	1	2	yes	—
179	C₂²×C₂₃	H(5,𝔽₂)	1	2	yes	—
180	C₂²×C₂₃	C₂⁵	1	1	yes	characteristic
181	C₂×D₂₃	—	2	8	no	—
182	C₂×D₂₃	—	2	2	no	—
183	C₂×D₂₃	—	2	2	no	—
184	C₂×D₂₃	C₂²×Q₈	1	4	yes	—
185	C₄×C₂₃	—	2	2	no	—
186	C₄×C₂₃	—	2	2	no	—
187	C₄×C₂₃	—	2	2	no	—
188	C₄×C₂₃	—	2	2	no	—
189	C₄×C₂₃	—	2	2	no	—
190	C₄×C₂₃	—	2	2	no	—
191	Dic₂₃	—	2	2	no	—
192	Dic₂₃	—	2	2	no	—
193	Dic₂₃	—	2	2	no	—
194	Dic₂₃	—	2	2	no	—
195	Dic₂₃	—	2	2	no	—
196	Dic₂₃	C₂²×Q₈	1	4	yes	—
197	Dic₂₃	C₂×#41	1	4	yes	—
198	#554	—	23	16	no	—
199	C₂×C₄⋊Q₈	—	23	1	no	—
200	C₂×#125	—	23	1	no	—
201	C₂×#125	—	23	1	no	—
202	C₂×C₂²⋊Q₈	—	23	1	no	—
203	C₂×C₂²⋊Q₈	—	23	1	no	—
204	C₂×C₂²⋊Q₈	—	23	1	no	—
205	C₂×C₂²⋊Q₈	—	23	1	no	—
206	C₂×C₂²⋊Q₈	—	23	1	no	—
207	C₂×C₂²⋊Q₈	D₂₃	1	1	yes	characteristic, complemented
208	C₂×C₄×Q₈	—	23	1	no	—
209	C₂×C₄×D₄	—	23	1	no	—
210	C₂×C₄×D₄	—	23	1	no	—
211	C₂×C₄×D₄	—	23	1	no	—
212	C₂²×C₄⋊C₄	—	23	1	no	—
213	C₂²×C₄⋊C₄	—	23	1	no	—
214	C₂×C₂₃	—	2	4	no	—
215	C₂×C₂₃	#554	1	4	yes	complemented
216	C₂×C₂₃	C₂³×Q₈	1	1	yes	characteristic
217	C₂×C₂₃	C₂²×#41	1	1	yes	characteristic
218	C₂×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
219	D₂₃	—	2	4	no	—
220	C₂²×Q₈	—	23	1	no	—
221	C₂²×Q₈	—	23	1	no	—
222	C₂²×Q₈	C₂×D₂₃	1	1	yes	characteristic
223	C₂²×D₄	—	23	1	no	—
224	C₂³×C₄	—	23	1	no	—
225	C₂³×C₄	—	23	1	no	—
226	C₂³×C₄	—	23	1	no	—
227	C₂³×C₄	—	23	1	no	—
228	C₂³×C₄	—	23	1	no	—
229	C₂³×C₄	C₂×D₂₃	1	1	yes	characteristic
230	C₄⋊Q₈	—	23	8	no	—
231	#125	—	23	8	no	—
232	#125	—	23	8	no	—
233	C₂²⋊Q₈	—	23	8	no	—
234	C₂²⋊Q₈	—	23	8	no	—
235	C₂²⋊Q₈	—	23	8	no	—
236	C₂²⋊Q₈	—	23	8	no	—
237	C₂²⋊Q₈	—	23	8	no	—
238	C₂²⋊Q₈	C₂×D₂₃	1	8	yes	complemented
239	C₄×Q₈	—	23	8	no	—
240	C₄×D₄	—	23	8	no	—
241	C₄×D₄	—	23	8	no	—
242	C₄×D₄	—	23	8	no	—
243	C₂×C₄⋊C₄	—	23	1	no	—
244	C₂×C₄⋊C₄	—	23	1	no	—
245	C₂×C₄⋊C₄	—	23	1	no	—
246	C₂×C₄⋊C₄	—	23	1	no	—
247	C₂×C₄⋊C₄	—	23	1	no	—
248	C₂×C₄⋊C₄	—	23	1	no	—
249	C₂×C₄⋊C₄	—	23	8	no	—
250	C₂×C₄⋊C₄	—	23	1	no	—
251	C₂×C₄⋊C₄	—	23	1	no	—
252	C₂×C₄⋊C₄	—	23	1	no	—
253	C₂×C₄⋊C₄	—	23	1	no	—
254	C₂×C₄⋊C₄	—	23	1	no	—
255	C₂×C₄⋊C₄	—	23	1	no	—
256	C₂×C₄⋊C₄	—	23	1	no	—
257	C₂×C₄⋊C₄	—	23	8	no	—
258	C₂×C₄⋊C₄	C₂×D₂₃	1	1	yes	characteristic
259	C₂×C₄⋊C₄	C₂×D₂₃	1	1	yes	characteristic
260	C₂×C₄⋊C₄	C₂×D₂₃	1	1	yes	characteristic
261	C₂×C₂²⋊C₄	—	23	1	no	—
262	C₂×C₂²⋊C₄	—	23	1	no	—
263	C₂×C₂²⋊C₄	—	23	1	no	—
264	C₂×C₂²⋊C₄	—	23	1	no	—
265	C₂×C₂²⋊C₄	C₂×D₂₃	1	1	yes	characteristic
266	C₂×C₂²⋊C₄	C₂×D₂₃	1	1	yes	characteristic
267	C₂×C₄²	—	23	1	no	—
268	C₂×C₄²	—	23	1	no	—
269	C₂×C₄²	—	23	1	no	—
270	C₂₃	C₂×#554	1	1	yes	characteristic, complemented, Sylow
271	C₂⁴	—	23	1	no	—
272	C₂⁴	C₂²×D₂₃	1	1	yes	characteristic
273	C₂×Q₈	—	4	2	no	—
274	C₂×Q₈	—	23	4	no	—
275	C₂×Q₈	—	23	4	no	—
276	C₂×Q₈	—	46	4	no	—
277	C₂×Q₈	—	92	2	no	—
278	C₂×Q₈	C₂²×D₂₃	1	4	yes	—
279	C₂×D₄	—	23	8	no	—
280	C₂×D₄	—	23	4	no	—
281	C₂²×C₄	—	4	2	no	—
282	C₂²×C₄	—	23	1	no	—
283	C₂²×C₄	—	23	1	no	—
284	C₂²×C₄	—	23	4	no	—
285	C₂²×C₄	—	23	1	no	—
286	C₂²×C₄	—	23	1	no	—
287	C₂²×C₄	—	23	1	no	—
288	C₂²×C₄	—	23	1	no	—
289	C₂²×C₄	—	23	1	no	—
290	C₂²×C₄	—	23	4	no	—
291	C₂²×C₄	—	23	4	no	—
292	C₂²×C₄	—	23	4	no	—
293	C₂²×C₄	—	23	4	no	—
294	C₂²×C₄	—	46	4	no	—
295	C₂²×C₄	—	46	4	no	—
296	C₂²×C₄	—	92	2	no	—
297	C₂²×C₄	—	92	2	no	—
298	C₂²×C₄	—	92	2	no	—
299	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
300	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
301	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
302	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
303	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
304	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
305	C₂²×C₄	C₂²×D₂₃	1	4	yes	—
306	C₄⋊C₄	—	23	4	no	—
307	C₄⋊C₄	—	23	4	no	—
308	C₄⋊C₄	—	23	4	no	—
309	C₄⋊C₄	—	23	4	no	—
310	C₄⋊C₄	—	23	4	no	—
311	C₄⋊C₄	—	23	4	no	—
312	C₄⋊C₄	—	23	4	no	—
313	C₄⋊C₄	—	23	4	no	—
314	C₄⋊C₄	—	23	4	no	—
315	C₄⋊C₄	—	23	4	no	—
316	C₄⋊C₄	—	23	4	no	—
317	C₄⋊C₄	—	23	4	no	—
318	C₄⋊C₄	—	23	4	no	—
319	C₄⋊C₄	C₂²×D₂₃	1	4	yes	—
320	C₄⋊C₄	C₂²×D₂₃	1	4	yes	—
321	C₄⋊C₄	C₂²×D₂₃	1	4	yes	—
322	C₂²⋊C₄	—	23	4	no	—
323	C₂²⋊C₄	—	23	4	no	—
324	C₂²⋊C₄	—	23	4	no	—
325	C₂²⋊C₄	—	23	4	no	—
326	C₂²⋊C₄	C₂²×D₂₃	1	4	yes	—
327	C₂²⋊C₄	C₂²×D₂₃	1	4	yes	—
328	C₄²	—	23	4	no	—
329	C₄²	—	23	4	no	—
330	C₄²	—	23	4	no	—
331	C₂³	—	2	2	no	—
332	C₂³	—	2	2	no	—
333	C₂³	—	23	4	no	—
334	C₂³	—	23	2	no	—
335	C₂³	—	46	2	no	—
336	C₂³	—	46	2	no	—
337	C₂³	Q₈×D₂₃	1	4	yes	—
338	C₂³	C₂³×D₂₃	1	2	yes	—
339	C₂³	C₂³×D₂₃	1	1	yes	characteristic
340	Q₈	—	4	4	no	—
341	Q₈	—	46	8	no	—
342	Q₈	—	92	4	no	—
343	D₄	—	23	16	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	4	4	no	—
351	C₂×C₄	—	23	4	no	—
352	C₂×C₄	—	23	4	no	—
353	C₂×C₄	—	23	2	no	—
354	C₂×C₄	—	23	2	no	—
355	C₂×C₄	—	23	2	no	—
356	C₂×C₄	—	23	2	no	—
357	C₂×C₄	—	23	2	no	—
358	C₂×C₄	—	23	2	no	—
359	C₂×C₄	—	23	2	no	—
360	C₂×C₄	—	46	8	no	—
361	C₂×C₄	—	46	8	no	—
362	C₂×C₄	—	46	2	no	—
363	C₂×C₄	—	46	2	no	—
364	C₂×C₄	—	46	2	no	—
365	C₂×C₄	—	46	2	no	—
366	C₂×C₄	—	46	2	no	—
367	C₂×C₄	—	92	4	no	—
368	C₂×C₄	—	92	4	no	—
369	C₂×C₄	—	92	4	no	—
370	C₂×C₄	C₂³×D₂₃	1	2	yes	—
371	C₂×C₄	C₂³×D₂₃	1	2	yes	—
372	C₂×C₄	C₂³×D₂₃	1	2	yes	—
373	C₂×C₄	C₂³×D₂₃	1	2	yes	—
374	C₂×C₄	C₂³×D₂₃	1	2	yes	—
375	C₂×C₄	C₂³×D₂₃	1	2	yes	—
376	C₂²	—	2	8	no	—
377	C₂²	—	2	2	no	—
378	C₂²	—	2	2	no	—
379	C₂²	—	23	4	no	—
380	C₂²	—	46	8	no	—
381	C₂²	—	46	2	no	—
382	C₂²	—	46	2	no	—
383	C₂²	#10625155	1	2	yes	—
384	C₂²	C₂×Q₈×D₂₃	1	4	yes	—
385	C₂²	C₂×Q₈×D₂₃	1	2	yes	—
386	C₂²	#41×D₂₃	1	2	yes	—
387	C₂²	C₂⁴×D₂₃	1	1	yes	characteristic
388	C₄	—	2	2	no	—
389	C₄	—	2	2	no	—
390	C₄	—	2	2	no	—
391	C₄	—	2	2	no	—
392	C₄	—	2	2	no	—
393	C₄	—	2	2	no	—
394	C₄	—	23	4	no	—
395	C₄	—	23	4	no	—
396	C₄	—	46	2	no	—
397	C₄	—	46	2	no	—
398	C₄	—	46	2	no	—
399	C₄	—	46	2	no	—
400	C₄	—	46	2	no	—
401	C₂	—	2	4	no	—
402	C₂	—	46	4	no	—
403	C₂	#13093121	1	4	yes	direct product factor
404	C₂	C₂²×Q₈×D₂₃	1	1	yes	characteristic
405	C₂	C₂×#41×D₂₃	1	1	yes	characteristic
406	C₂	C₂×#10625155	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂³×D₂₃
commutator, cosocle	C₂²×C₂₃	C₂⁵
Frattini	C₂²	C₂⁴×D₂₃
Fitting	C₂×C₂₃×C₂²⋊Q₈	C₂
socle	C₂³×C₂₃	C₂⁴
prime radical	C₂²×C₂²⋊D₂₃	C₂²
hypercenter	C₂×C₂²⋊Q₈	D₂₃
hypocenter	C₂₃	C₂×#554
LCS	G ▷ C₂²×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₂²⋊Q₈

Complements

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

N	H ≅ G/N	type
1. #13093121	C₂	direct (N × H)
2. C₂×#10625115	C₂	semidirect
3. C₂×#10625060	C₂	semidirect
4. C₂×#10625060	C₂	semidirect
5. C₂×#10625067	C₂	semidirect
6. C₂×#10625067	C₂	semidirect
7. C₂×#10625049	C₂	semidirect
8. C₂×#10625049	C₂	semidirect
9. C₂×#10625117	C₂	semidirect
10. C₂×#10625058	C₂	semidirect
14. C₂²×Dic₂₃⋊C₄	C₂	semidirect
15. C₂×C₄⋊C₄×D₂₃	C₂	semidirect
16. C₂×C₂₃×C₂²⋊Q₈	C₂	semidirect
27. C₂₃×C₂²⋊Q₈	C₂²	semidirect
34. #10625117	C₂²	semidirect
35. #10625115	C₂²	semidirect
53. C₂×Dic₂₃⋊C₄	C₂²	semidirect
57. #10625067	C₂²	semidirect
58. #10625067	C₂²	semidirect
59. C₄⋊C₄×D₂₃	C₂²	semidirect
60. #10625060	C₂²	semidirect
61. #10625060	C₂²	semidirect
62. #10625058	C₂²	semidirect
65. #10625049	C₂²	semidirect
66. #10625049	C₂²	semidirect
79. C₂×C₂²⋊D₂₃	Q₈	semidirect
150. C₂²⋊D₂₃	C₂×Q₈	semidirect
207. C₂×C₂²⋊Q₈	D₂₃	semidirect
215. C₂×C₂₃	#554	semidirect
238. C₂²⋊Q₈	C₂×D₂₃	semidirect
270. C₂₃	C₂×#554	semidirect
403. C₂	#13093121	direct (N × H)

Maximal subgroups

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

subgroup	index
#13093121	2
C₂×#10625115	2
C₂×#10625060	2
C₂×#10625067	2
C₂×#10625049	2
C₂×#10625117	2
C₂×#10625058	2
C₂×C₄×C₂²⋊D₂₃	2
C₂×(C₂²⋊D₂₃)⋊C₄	2
C₂²×Dic₂₃⋊C₄	2
C₂×C₄⋊C₄×D₂₃	2
C₂×C₂₃×C₂²⋊Q₈	2
C₂×#554	23

Subgroups — C2×#13093121 #15686925

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13093121 #15686925