Subgroups — C₂×#13093031 #15686768

Order 2944.

1132 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13093031	C₂	1	16	yes	maximal, direct product factor
2	C₂×#10625115	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#10625047	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#10625050	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#10625056	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#10625056	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#10625054	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#10625106	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#10625049	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#10625049	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#10625117	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#10625110	C₂	1	1	yes	maximal, characteristic
13	C₂×C₄×Dic₄₆	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×(C₂²⋊D₂₃)⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#10625048	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₂₃×#124	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×Q₈×C₂₃	C₂²	1	1	yes	characteristic
18	C₂²×D₄×C₂₃	C₂²	1	1	yes	characteristic
19	C₂²×C₂²⋊D₂₃	C₂²	1	1	yes	characteristic
20	C₂²×C₂²⋊D₂₃	C₂²	1	1	yes	characteristic
21	C₂³×Dic₂₃	C₂²	1	1	yes	characteristic
22	C₂³×Dic₂₃	C₂²	1	1	yes	characteristic
23	C₂²×C₄×D₂₃	C₂²	1	1	yes	characteristic
24	C₂²×Dic₄₆	C₂²	1	1	yes	characteristic
25	C₂²×Dic₄₆	C₂²	1	1	yes	characteristic
26	C₂₃×#124	C₂²	1	8	yes	complemented
27	C₂×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
28	C₂×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
29	C₂×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
30	C₂×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
31	C₂×C₄²×C₂₃	C₂²	1	1	yes	characteristic
32	C₂×C₂²⋊Dic₂₃	C₂²	1	1	yes	characteristic
33	C₂×C₂²⋊Dic₂₃	C₂²	1	1	yes	characteristic
34	C₂×C₂²⋊Dic₂₃	C₂²	1	1	yes	characteristic
35	C₂×C₂²⋊Dic₂₃	C₂²	1	1	yes	characteristic
36	#10625117	C₂²	1	8	yes	complemented
37	#10625115	C₂²	1	8	yes	complemented
38	#10625110	C₂²	1	8	yes	—
39	#10625106	C₂²	1	8	yes	complemented
40	C₂×(C₂×D₂₃)⋊C₄	C₂²	1	1	yes	characteristic
41	C₂×(C₂×D₂₃)⋊C₄	C₂²	1	1	yes	characteristic
42	C₂×(C₂×D₂₃)⋊C₄	C₂²	1	1	yes	characteristic
43	C₂×(C₂×D₂₃)⋊C₄	C₂²	1	1	yes	characteristic
44	C₂×C₄⋊Dic₂₃	C₂²	1	1	yes	characteristic
45	C₂×C₄⋊Dic₂₃	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	1	yes	characteristic
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	#10625056	C₂²	1	8	yes	complemented
58	#10625056	C₂²	1	8	yes	complemented
59	#10625054	C₂²	1	8	yes	complemented
60	(C₂²⋊D₂₃)⋊C₄	C₂²	1	8	yes	complemented
61	#10625050	C₂²	1	8	yes	complemented
62	#10625049	C₂²	1	8	yes	complemented
63	#10625049	C₂²	1	8	yes	complemented
64	#10625048	C₂²	1	8	yes	complemented
65	#10625047	C₂²	1	8	yes	complemented
66	C₄×Dic₄₆	C₂²	1	8	yes	complemented
67	C₂⁴×C₂₃	C₂³	1	1	yes	characteristic
68	C₂⁴×C₂₃	C₂³	1	1	yes	characteristic
69	C₂³×D₂₃	C₂³	1	1	yes	characteristic
70	C₂×Q₈×C₂₃	—	4	2	no	—
71	C₂×Q₈×C₂₃	C₂³	1	4	yes	—
72	C₂×D₄×C₂₃	—	4	2	no	—
73	C₂×D₄×C₂₃	C₂³	1	4	yes	—
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	1	yes	characteristic
79	C₂×C₂²⋊D₂₃	—	2	4	no	—
80	C₂×C₂²⋊D₂₃	—	4	2	no	—
81	C₂×C₂²⋊D₂₃	C₂³	1	4	yes	—
82	C₂×C₂²⋊D₂₃	C₂³	1	4	yes	—
83	C₂²×Dic₂₃	—	2	4	no	—
84	C₂²×Dic₂₃	—	4	2	no	—
85	C₂²×Dic₂₃	C₂³	1	4	yes	—
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	1	yes	characteristic
90	C₂²×Dic₂₃	C₂³	1	1	yes	characteristic
91	C₂²×Dic₂₃	C₂³	1	1	yes	characteristic
92	C₂²×Dic₂₃	C₂³	1	4	yes	—
93	C₂²×Dic₂₃	C₂³	1	1	yes	characteristic
94	C₂×C₄×D₂₃	—	4	2	no	—
95	C₂×C₄×D₂₃	C₂³	1	4	yes	—
96	C₂×Dic₄₆	—	2	4	no	—
97	C₂×Dic₄₆	—	4	2	no	—
98	C₂×Dic₄₆	C₂³	1	4	yes	—
99	C₂×Dic₄₆	C₂³	1	4	yes	—
100	C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
101	C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
102	C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
103	C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
104	C₄²×C₂₃	C₂³	1	4	yes	—
105	C₂²⋊Dic₂₃	C₂³	1	4	yes	—
106	C₂²⋊Dic₂₃	C₂³	1	4	yes	—
107	C₂²⋊Dic₂₃	C₂³	1	4	yes	—
108	C₂²⋊Dic₂₃	C₂³	1	4	yes	—
109	(C₂×D₂₃)⋊C₄	C₂³	1	4	yes	—
110	(C₂×D₂₃)⋊C₄	C₂³	1	4	yes	—
111	(C₂×D₂₃)⋊C₄	C₂³	1	4	yes	—
112	(C₂×D₂₃)⋊C₄	C₂³	1	4	yes	—
113	C₄⋊Dic₂₃	C₂³	1	4	yes	—
114	C₄⋊Dic₂₃	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	C₄×Dic₂₃	C₂³	1	4	yes	—
124	C₄×Dic₂₃	C₂³	1	4	yes	—
125	C₄×Dic₂₃	C₂³	1	4	yes	—
126	C₂³×C₂₃	—	2	2	no	—
127	C₂³×C₂₃	—	2	2	no	—
128	C₂³×C₂₃	—	2	2	no	—
129	C₂³×C₂₃	—	2	2	no	—
130	C₂³×C₂₃	—	2	2	no	—
131	C₂³×C₂₃	—	2	2	no	—
132	C₂³×C₂₃	C₂⁴	1	2	yes	—
133	C₂³×C₂₃	C₂⁴	1	2	yes	—
134	C₂³×C₂₃	C₂⁴	1	1	yes	characteristic
135	C₂²×D₂₃	—	2	2	no	—
136	C₂²×D₂₃	—	2	2	no	—
137	C₂²×D₂₃	—	2	2	no	—
138	C₂²×D₂₃	C₂⁴	1	2	yes	—
139	Q₈×C₂₃	—	4	4	no	—
140	D₄×C₂₃	—	4	4	no	—
141	C₂×C₄×C₂₃	—	2	2	no	—
142	C₂×C₄×C₂₃	—	2	2	no	—
143	C₂×C₄×C₂₃	—	2	2	no	—
144	C₂×C₄×C₂₃	—	2	2	no	—
145	C₂×C₄×C₂₃	—	2	2	no	—
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	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
151	C₂²⋊D₂₃	—	2	8	no	—
152	C₂²⋊D₂₃	—	4	4	no	—
153	C₂×Dic₂₃	—	2	2	no	—
154	C₂×Dic₂₃	—	2	2	no	—
155	C₂×Dic₂₃	—	2	2	no	—
156	C₂×Dic₂₃	—	2	2	no	—
157	C₂×Dic₂₃	—	2	2	no	—
158	C₂×Dic₂₃	—	2	2	no	—
159	C₂×Dic₂₃	—	2	8	no	—
160	C₂×Dic₂₃	—	4	4	no	—
161	C₂×Dic₂₃	#41	1	4	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	C₂×Dic₂₃	C₂⁴	1	2	yes	—
168	C₂×Dic₂₃	C₂⁴	1	2	yes	—
169	C₄×D₂₃	—	4	4	no	—
170	Dic₄₆	—	2	8	no	—
171	Dic₄₆	—	4	4	no	—
172	C₂×#542	—	23	1	no	maximal, Sylow
173	C₂²×C₂₃	—	2	2	no	—
174	C₂²×C₂₃	—	2	2	no	—
175	C₂²×C₂₃	—	2	2	no	—
176	C₂²×C₂₃	—	2	2	no	—
177	C₂²×C₂₃	—	2	2	no	—
178	C₂²×C₂₃	—	2	2	no	—
179	C₂²×C₂₃	—	4	4	no	—
180	C₂²×C₂₃	—	4	4	no	—
181	C₂²×C₂₃	C₂×#41	1	2	yes	—
182	C₂²×C₂₃	H(5,𝔽₂)	1	2	yes	—
183	C₂²×C₂₃	2₋¹⁺⁴	1	2	yes	—
184	C₂²×C₂₃	C₂⁵	1	1	yes	characteristic
185	C₂×D₂₃	—	2	2	no	—
186	C₂×D₂₃	—	2	2	no	—
187	C₂×D₂₃	—	2	2	no	—
188	C₂×D₂₃	—	4	4	no	—
189	C₄×C₂₃	—	2	2	no	—
190	C₄×C₂₃	—	2	2	no	—
191	C₄×C₂₃	—	2	2	no	—
192	C₄×C₂₃	—	2	2	no	—
193	C₄×C₂₃	—	2	2	no	—
194	Dic₂₃	—	2	2	no	—
195	Dic₂₃	—	2	2	no	—
196	Dic₂₃	—	2	2	no	—
197	Dic₂₃	—	2	2	no	—
198	Dic₂₃	—	2	2	no	—
199	Dic₂₃	—	2	2	no	—
200	Dic₂₃	C₂×#41	1	4	yes	—
201	#542	—	23	16	no	—
202	C₂×C₄⋊Q₈	—	23	1	no	—
203	C₂×#126	—	23	1	no	—
204	C₂×#126	—	23	1	no	—
205	C₂×#124	—	23	1	no	—
206	C₂×#124	—	23	1	no	—
207	C₂×#124	D₂₃	1	1	yes	characteristic, complemented
208	C₂×#123	—	23	1	no	—
209	C₂×#123	—	23	1	no	—
210	C₂×C₂²⋊Q₈	—	23	1	no	—
211	C₂×C₂²⋊Q₈	—	23	1	no	—
212	C₂×C₂²⋊Q₈	—	23	1	no	—
213	C₂×#121	—	23	1	no	—
214	C₂×C₄×Q₈	—	23	1	no	—
215	C₂×C₄×D₄	—	23	1	no	—
216	C₂×#117	—	23	1	no	—
217	C₂×C₂₃	—	4	2	no	—
218	C₂×C₂₃	—	4	2	no	—
219	C₂×C₂₃	#542	1	4	yes	complemented
220	C₂×C₂₃	C₂²×#41	1	1	yes	characteristic
221	C₂×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
222	C₂×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
223	D₂₃	—	4	2	no	—
224	C₂²×Q₈	—	23	1	no	—
225	C₂²×Q₈	—	23	1	no	—
226	C₂²×Q₈	C₂×D₂₃	1	1	yes	characteristic
227	C₂²×D₄	—	23	1	no	—
228	C₂²×D₄	—	23	1	no	—
229	C₂²×D₄	C₂×D₂₃	1	1	yes	characteristic
230	C₂³×C₄	—	23	1	no	—
231	C₂³×C₄	—	23	1	no	—
232	C₂³×C₄	—	23	1	no	—
233	C₄⋊Q₈	—	23	8	no	—
234	#126	—	23	8	no	—
235	#126	—	23	8	no	—
236	#124	—	23	8	no	—
237	#124	—	23	8	no	—
238	#124	C₂×D₂₃	1	8	yes	complemented
239	#123	—	23	8	no	—
240	#123	—	23	8	no	—
241	C₂²⋊Q₈	—	23	8	no	—
242	C₂²⋊Q₈	—	23	8	no	—
243	C₂²⋊Q₈	—	23	8	no	—
244	#121	—	23	8	no	—
245	C₄×Q₈	—	23	8	no	—
246	C₄×D₄	—	23	8	no	—
247	#117	—	23	8	no	—
248	C₂×C₄⋊C₄	—	23	1	no	—
249	C₂×C₄⋊C₄	—	23	1	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	1	no	—
258	C₂×C₂²⋊C₄	—	23	1	no	—
259	C₂×C₂²⋊C₄	—	23	1	no	—
260	C₂×C₂²⋊C₄	—	23	1	no	—
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	—	23	1	no	—
266	C₂×C₂²⋊C₄	C₂×D₂₃	1	1	yes	characteristic
267	C₂×C₂²⋊C₄	C₂×D₂₃	1	1	yes	characteristic
268	C₂×C₂²⋊C₄	C₂×D₂₃	1	1	yes	characteristic
269	C₂×C₂²⋊C₄	C₂×D₂₃	1	1	yes	characteristic
270	C₂×C₄²	—	23	1	no	—
271	C₂×C₄²	—	23	1	no	—
272	C₂×C₄²	—	23	1	no	—
273	C₂×C₄²	C₂×D₂₃	1	1	yes	characteristic
274	C₂₃	C₂×#542	1	1	yes	characteristic, complemented, Sylow
275	C₂⁴	—	23	1	no	—
276	C₂⁴	C₂²×D₂₃	1	1	yes	characteristic
277	C₂⁴	C₂²×D₂₃	1	1	yes	characteristic
278	C₂×Q₈	—	4	2	no	—
279	C₂×Q₈	—	23	4	no	—
280	C₂×Q₈	—	23	4	no	—
281	C₂×Q₈	—	46	4	no	—
282	C₂×Q₈	—	92	2	no	—
283	C₂×Q₈	C₂²×D₂₃	1	4	yes	—
284	C₂×D₄	—	4	2	no	—
285	C₂×D₄	—	23	4	no	—
286	C₂×D₄	—	23	4	no	—
287	C₂×D₄	—	46	4	no	—
288	C₂×D₄	—	92	2	no	—
289	C₂×D₄	C₂²×D₂₃	1	4	yes	—
290	C₂²×C₄	—	23	1	no	—
291	C₂²×C₄	—	23	4	no	—
292	C₂²×C₄	—	23	1	no	—
293	C₂²×C₄	—	23	1	no	—
294	C₂²×C₄	—	23	1	no	—
295	C₂²×C₄	—	23	1	no	—
296	C₂²×C₄	—	23	1	no	—
297	C₂²×C₄	—	23	1	no	—
298	C₂²×C₄	—	23	4	no	—
299	C₂²×C₄	—	23	4	no	—
300	C₂²×C₄	—	46	4	no	—
301	C₂²×C₄	—	92	2	no	—
302	C₂²×C₄	—	92	2	no	—
303	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
304	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
305	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
306	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
307	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
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	C₂²⋊C₄	—	23	4	no	—
319	C₂²⋊C₄	—	23	4	no	—
320	C₂²⋊C₄	—	23	4	no	—
321	C₂²⋊C₄	—	23	4	no	—
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	C₂²⋊C₄	C₂²×D₂₃	1	4	yes	—
329	C₂²⋊C₄	C₂²×D₂₃	1	4	yes	—
330	C₄²	—	23	4	no	—
331	C₄²	—	23	4	no	—
332	C₄²	—	23	4	no	—
333	C₄²	C₂²×D₂₃	1	4	yes	—
334	C₂³	—	2	2	no	—
335	C₂³	—	2	2	no	—
336	C₂³	—	2	2	no	—
337	C₂³	—	2	2	no	—
338	C₂³	—	2	2	no	—
339	C₂³	—	2	2	no	—
340	C₂³	—	23	2	no	—
341	C₂³	—	46	2	no	—
342	C₂³	—	46	2	no	—
343	C₂³	—	46	2	no	—
344	C₂³	C₂³×D₂₃	1	2	yes	—
345	C₂³	C₂³×D₂₃	1	2	yes	—
346	C₂³	C₂³×D₂₃	1	1	yes	characteristic
347	Q₈	—	4	4	no	—
348	Q₈	—	46	8	no	—
349	Q₈	—	92	4	no	—
350	D₄	—	4	4	no	—
351	D₄	—	46	8	no	—
352	D₄	—	92	4	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	23	4	no	—
359	C₂×C₄	—	23	2	no	—
360	C₂×C₄	—	23	2	no	—
361	C₂×C₄	—	23	2	no	—
362	C₂×C₄	—	23	2	no	—
363	C₂×C₄	—	23	2	no	—
364	C₂×C₄	—	23	2	no	—
365	C₂×C₄	—	23	2	no	—
366	C₂×C₄	—	46	8	no	—
367	C₂×C₄	—	46	2	no	—
368	C₂×C₄	—	46	2	no	—
369	C₂×C₄	—	46	2	no	—
370	C₂×C₄	—	46	2	no	—
371	C₂×C₄	—	46	2	no	—
372	C₂×C₄	—	46	2	no	—
373	C₂×C₄	—	92	4	no	—
374	C₂×C₄	—	92	4	no	—
375	C₂×C₄	C₂³×D₂₃	1	2	yes	—
376	C₂×C₄	C₂³×D₂₃	1	2	yes	—
377	C₂×C₄	C₂³×D₂₃	1	2	yes	—
378	C₂×C₄	C₂³×D₂₃	1	2	yes	—
379	C₂×C₄	C₂³×D₂₃	1	2	yes	—
380	C₂²	—	2	2	no	—
381	C₂²	—	2	2	no	—
382	C₂²	—	2	2	no	—
383	C₂²	—	2	2	no	—
384	C₂²	—	2	2	no	—
385	C₂²	—	2	2	no	—
386	C₂²	—	4	4	no	—
387	C₂²	—	4	4	no	—
388	C₂²	—	46	2	no	—
389	C₂²	—	46	2	no	—
390	C₂²	—	46	2	no	—
391	C₂²	—	92	4	no	—
392	C₂²	#10625155	1	2	yes	—
393	C₂²	#41×D₂₃	1	2	yes	—
394	C₂²	#10625161	1	2	yes	—
395	C₂²	C₂⁴×D₂₃	1	1	yes	characteristic
396	C₄	—	2	2	no	—
397	C₄	—	2	2	no	—
398	C₄	—	2	2	no	—
399	C₄	—	2	2	no	—
400	C₄	—	2	2	no	—
401	C₄	—	23	4	no	—
402	C₄	—	46	2	no	—
403	C₄	—	46	2	no	—
404	C₄	—	46	2	no	—
405	C₄	—	46	2	no	—
406	C₄	—	46	2	no	—
407	C₄	—	46	2	no	—
408	C₂	—	4	2	no	—
409	C₂	—	4	2	no	—
410	C₂	—	92	2	no	—
411	C₂	#13093031	1	4	yes	direct product factor
412	C₂	C₂×#41×D₂₃	1	1	yes	characteristic
413	C₂	C₂×#10625155	1	1	yes	characteristic
414	C₂	C₂×#10625161	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂³×D₂₃
commutator, cosocle	C₂²×C₂₃	C₂⁵
Frattini	C₂²	C₂⁴×D₂₃
Fitting	C₂×C₂₃×#124	C₂
socle	C₂³×C₂₃	C₂⁴
prime radical	C₂×#10625110	C₂
hypercenter	C₂×#124	D₂₃
hypocenter	C₂₃	C₂×#542
LCS	G ▷ C₂²×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂³ ◁ C₂×#124

Complements

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

N	H ≅ G/N	type
1. #13093031	C₂	direct (N × H)
2. C₂×#10625115	C₂	semidirect
3. C₂×#10625047	C₂	semidirect
4. C₂×#10625050	C₂	semidirect
5. C₂×#10625056	C₂	semidirect
6. C₂×#10625056	C₂	semidirect
7. C₂×#10625054	C₂	semidirect
8. C₂×#10625106	C₂	semidirect
9. C₂×#10625049	C₂	semidirect
10. C₂×#10625049	C₂	semidirect
11. C₂×#10625117	C₂	semidirect
13. C₂×C₄×Dic₄₆	C₂	semidirect
14. C₂×(C₂²⋊D₂₃)⋊C₄	C₂	semidirect
15. C₂×#10625048	C₂	semidirect
16. C₂×C₂₃×#124	C₂	semidirect
26. C₂₃×#124	C₂²	semidirect
36. #10625117	C₂²	semidirect
37. #10625115	C₂²	semidirect
39. #10625106	C₂²	semidirect
57. #10625056	C₂²	semidirect
58. #10625056	C₂²	semidirect
59. #10625054	C₂²	semidirect
60. (C₂²⋊D₂₃)⋊C₄	C₂²	semidirect
61. #10625050	C₂²	semidirect
62. #10625049	C₂²	semidirect
63. #10625049	C₂²	semidirect
64. #10625048	C₂²	semidirect
65. #10625047	C₂²	semidirect
66. C₄×Dic₄₆	C₂²	semidirect
207. C₂×#124	D₂₃	semidirect
219. C₂×C₂₃	#542	semidirect
238. #124	C₂×D₂₃	semidirect
274. C₂₃	C₂×#542	semidirect
411. C₂	#13093031	direct (N × H)

Maximal subgroups

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

subgroup	index
#13093031	2
C₂×#10625115	2
C₂×#10625047	2
C₂×#10625050	2
C₂×#10625056	2
C₂×#10625054	2
C₂×#10625106	2
C₂×#10625049	2
C₂×#10625117	2
C₂×#10625110	2
C₂×C₄×Dic₄₆	2
C₂×(C₂²⋊D₂₃)⋊C₄	2
C₂×#10625048	2
C₂×C₂₃×#124	2
C₂×#542	23

Subgroups — C2×#13093031 #15686768

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13093031 #15686768