Subgroups — #15686955

Order 2944.

1132 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13093137	C₂	1	1	yes	maximal, characteristic, complemented
2	#13093132	C₂	1	1	yes	maximal, characteristic, complemented
3	#13093124	C₂	1	1	yes	maximal, characteristic, complemented
4	#13093113	C₂	1	2	yes	maximal, complemented
5	#13093107	C₂	1	2	yes	maximal, complemented
6	#13093102	C₂	1	2	yes	maximal, complemented
7	#13093093	C₂	1	4	yes	maximal, complemented
8	#13093071	C₂	1	1	yes	maximal, characteristic, complemented
9	#13093061	C₂	1	2	yes	maximal, complemented
10	#13092974	C₂	1	1	yes	maximal, characteristic, complemented
11	#13092949	C₂	1	2	yes	maximal, complemented
12	#13092947	C₂	1	4	yes	maximal, complemented
13	#13092928	C₂	1	2	yes	maximal, complemented
14	C₄×#67288	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×#67290	C₂	1	2	yes	maximal, complemented
16	C₂×#10625097	C₂	1	2	yes	maximal, complemented
17	C₂×C₄×D₄×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×D₄×C₂₃	C₂²	1	1	yes	characteristic
19	C₂³×C₄×C₂₃	C₂²	1	2	yes	—
20	C₂×#67290	C₂²	1	2	yes	—
21	C₂×#67288	C₂²	1	1	yes	characteristic
22	C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
23	C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
24	C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
25	C₄×D₄×C₂₃	C₂²	1	2	yes	—
26	C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
27	C₄×D₄×C₂₃	C₂²	1	2	yes	—
28	C₂×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
29	C₂×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
30	C₂×C₄²×C₂₃	C₂²	1	1	yes	characteristic
31	#10625124	C₂²	1	4	yes	—
32	C₂×C₂²⋊Dic₂₃	C₂²	1	4	yes	—
33	#10625110	C₂²	1	4	yes	—
34	#10625109	C₂²	1	2	yes	—
35	#10625107	C₂²	1	2	yes	—
36	#10625106	C₂²	1	4	yes	—
37	D₄×Dic₂₃	C₂²	1	2	yes	—
38	#10625101	C₂²	1	2	yes	complemented
39	#10625101	C₂²	1	2	yes	complemented
40	#10625100	C₂²	1	4	yes	—
41	C₄×C₂²⋊D₂₃	C₂²	1	2	yes	—
42	C₄×C₂²⋊D₂₃	C₂²	1	2	yes	—
43	C₄×C₂²⋊D₂₃	C₂²	1	4	yes	complemented
44	C₄×C₂²⋊D₂₃	C₂²	1	4	yes	complemented
45	#10625097	C₂²	1	1	yes	characteristic
46	#10625097	C₂²	1	2	yes	—
47	#10625097	C₂²	1	4	yes	—
48	#10625097	C₂²	1	2	yes	complemented
49	#10625097	C₂²	1	2	yes	complemented
50	#10625097	C₂²	1	4	yes	complemented
51	C₂×C₄⋊Dic₂₃	C₂²	1	2	yes	complemented
52	C₂×C₄⋊Dic₂₃	C₂²	1	2	yes	complemented
53	#10625095	C₂²	1	2	yes	—
54	#10625095	C₂²	1	2	yes	—
55	#10625095	C₂²	1	2	yes	complemented
56	#10625095	C₂²	1	2	yes	complemented
57	C₂×C₄×Dic₂₃	C₂²	1	4	yes	complemented
58	#10625069	C₂²	1	4	yes	complemented
59	#10625068	C₂²	1	2	yes	complemented
60	#10625063	C₂²	1	2	yes	complemented
61	#10625061	C₂²	1	2	yes	complemented
62	#10625060	C₂²	1	4	yes	complemented
63	#10625058	C₂²	1	2	yes	complemented
64	#10625057	C₂²	1	4	yes	complemented
65	#10625056	C₂²	1	4	yes	complemented
66	#10625054	C₂²	1	4	yes	complemented
67	(C₂²⋊D₂₃)⋊C₄	C₂²	1	4	yes	complemented
68	#10625050	C₂²	1	4	yes	complemented
69	#10625050	C₂²	1	4	yes	complemented
70	#10625049	C₂²	1	4	yes	complemented
71	#10625048	C₂²	1	4	yes	complemented
72	C₄×D₉₂	C₂²	1	1	yes	characteristic, complemented
73	C₄×D₉₂	C₂²	1	1	yes	characteristic, complemented
74	#10625043	C₂²	1	2	yes	complemented
75	C₄²×D₂₃	C₂²	1	2	yes	complemented
76	#10625041	C₂²	1	2	yes	complemented
77	#10625040	C₂²	1	1	yes	characteristic, complemented
78	#10625040	C₂²	1	1	yes	characteristic, complemented
79	C₄×Dic₄₆	C₂²	1	1	yes	characteristic, complemented
80	C₄×Dic₄₆	C₂²	1	2	yes	complemented
81	C₄×Dic₄₆	C₂²	1	1	yes	characteristic, complemented
82	C₄×Dic₄₆	C₂²	1	2	yes	complemented
83	C₂⁴×C₂₃	C₂³	1	2	yes	—
84	C₂×D₄×C₂₃	—	2	4	no	—
85	C₂×D₄×C₂₃	C₂³	1	2	yes	—
86	C₂×D₄×C₂₃	C₂³	1	1	yes	characteristic
87	C₂×D₄×C₂₃	C₂³	1	1	yes	characteristic
88	C₂²×C₄×C₂₃	—	2	8	no	—
89	C₂²×C₄×C₂₃	C₂³	1	2	yes	—
90	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
91	C₂²×C₄×C₂₃	C₂³	1	2	yes	—
92	C₂²×C₄×C₂₃	C₂³	1	2	yes	—
93	C₂²×C₄×C₂₃	C₂³	1	2	yes	—
94	C₂²×C₄×C₂₃	C₂³	1	2	yes	—
95	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
96	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
97	C₂×C₂²⋊D₂₃	C₂³	1	4	yes	—
98	C₂×C₂²⋊D₂₃	C₂³	1	2	yes	—
99	C₂×C₂²⋊D₂₃	C₂³	1	4	yes	—
100	C₂²×Dic₂₃	C₂³	1	4	yes	—
101	C₂²×Dic₂₃	C₂³	1	4	yes	—
102	#67290	—	2	8	no	—
103	#67288	—	2	4	no	—
104	C₂×D₉₂	C₂³	1	1	yes	characteristic
105	C₂×C₄×D₂₃	C₂³	1	2	yes	—
106	C₂×C₄×D₂₃	C₂³	1	2	yes	—
107	C₂×C₄×D₂₃	C₂³	1	2	yes	—
108	C₂×Dic₄₆	C₂³	1	1	yes	characteristic
109	C₂×Dic₄₆	C₂³	1	2	yes	—
110	C₂×Dic₄₆	C₂³	1	2	yes	—
111	C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
112	C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
113	C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
114	C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
115	C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
116	C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
117	C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
118	C₄²×C₂₃	C₂³	1	1	yes	characteristic
119	C₄²×C₂₃	C₂³	1	1	yes	characteristic
120	C₄²×C₂₃	C₂³	1	1	yes	characteristic
121	C₄²×C₂₃	C₂³	1	1	yes	characteristic
122	C₂²⋊Dic₂₃	C₂³	1	4	yes	—
123	C₂²⋊Dic₂₃	C₂³	1	4	yes	—
124	C₂²⋊Dic₂₃	C₂³	1	4	yes	—
125	C₂²⋊Dic₂₃	C₂³	1	4	yes	—
126	C₂²⋊Dic₂₃	C₂³	1	4	yes	—
127	C₂²⋊Dic₂₃	C₂³	1	2	yes	—
128	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
129	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
130	(C₂×D₂₃)⋊C₄	C₂³	1	4	yes	—
131	(C₂×D₂₃)⋊C₄	C₂³	1	4	yes	—
132	C₄⋊Dic₂₃	C₂³	1	2	yes	—
133	C₄⋊Dic₂₃	C₂³	1	2	yes	—
134	C₄⋊Dic₂₃	C₂³	1	1	yes	characteristic
135	C₄⋊Dic₂₃	C₂³	1	1	yes	characteristic
136	C₄⋊Dic₂₃	C₂³	1	2	yes	—
137	C₄⋊Dic₂₃	C₂³	1	2	yes	—
138	C₄⋊Dic₂₃	C₂³	1	4	yes	—
139	C₄⋊Dic₂₃	C₂³	1	4	yes	—
140	Dic₂₃⋊C₄	C₂³	1	4	yes	—
141	Dic₂₃⋊C₄	C₂³	1	4	yes	—
142	Dic₂₃⋊C₄	C₂³	1	2	yes	—
143	Dic₂₃⋊C₄	C₂³	1	2	yes	—
144	Dic₂₃⋊C₄	C₂³	1	4	yes	—
145	Dic₂₃⋊C₄	C₂³	1	4	yes	—
146	C₄×Dic₂₃	C₂³	1	4	yes	—
147	C₄×Dic₂₃	C₂³	1	2	yes	—
148	C₄×Dic₂₃	C₂³	1	2	yes	—
149	C₄×Dic₂₃	C₂³	1	2	yes	—
150	C₄×Dic₂₃	C₂³	1	4	yes	—
151	C₄×Dic₂₃	C₂³	1	4	yes	—
152	C₂³×C₂₃	—	2	4	no	—
153	C₂³×C₂₃	—	2	4	no	—
154	C₂³×C₂₃	—	4	2	no	—
155	C₂³×C₂₃	C₂⁴	1	2	yes	—
156	C₂³×C₂₃	C₂⁴	1	1	yes	characteristic
157	C₂³×C₂₃	C₂⁴	1	2	yes	—
158	C₂²×D₂₃	C₂⁴	1	2	yes	—
159	D₄×C₂₃	—	2	4	no	—
160	D₄×C₂₃	—	2	2	no	—
161	D₄×C₂₃	#41	1	4	yes	complemented
162	C₂×C₄×C₂₃	—	2	4	no	—
163	C₂×C₄×C₂₃	—	2	4	no	—
164	C₂×C₄×C₂₃	—	2	4	no	—
165	C₂×C₄×C₂₃	—	2	4	no	—
166	C₂×C₄×C₂₃	—	2	4	no	—
167	C₂×C₄×C₂₃	—	2	2	no	—
168	C₂×C₄×C₂₃	—	4	1	no	—
169	C₂×C₄×C₂₃	#41	1	4	yes	complemented
170	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
171	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
172	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
173	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
174	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
175	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
176	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
177	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
178	C₂²⋊D₂₃	—	2	4	no	—
179	C₂²⋊D₂₃	—	2	8	no	—
180	C₂²⋊D₂₃	—	4	4	no	—
181	C₂×Dic₂₃	—	2	8	no	—
182	C₂×Dic₂₃	—	4	4	no	—
183	C₂×Dic₂₃	C₂⁴	1	2	yes	—
184	C₂×Dic₂₃	C₂⁴	1	2	yes	—
185	C₂×Dic₂₃	C₂⁴	1	2	yes	—
186	C₂×Dic₂₃	C₂⁴	1	4	yes	—
187	C₂×Dic₂₃	C₂⁴	1	4	yes	—
188	D₉₂	—	2	2	no	—
189	C₄×D₂₃	—	2	4	no	—
190	C₄×D₂₃	—	2	4	no	—
191	C₄×D₂₃	—	4	2	no	—
192	Dic₄₆	—	2	2	no	—
193	Dic₄₆	—	2	4	no	—
194	Dic₄₆	—	4	2	no	—
195	#3475	—	23	1	no	maximal, Sylow
196	C₂²×C₂₃	—	2	2	no	—
197	C₂²×C₂₃	—	2	1	no	—
198	C₂²×C₂₃	—	2	2	no	—
199	C₂²×C₂₃	—	2	1	no	—
200	C₂²×C₂₃	—	2	2	no	—
201	C₂²×C₂₃	—	2	2	no	—
202	C₂²×C₂₃	—	2	2	no	—
203	C₂²×C₂₃	—	4	8	no	—
204	C₂²×C₂₃	C₂×#41	1	4	yes	—
205	C₂²×C₂₃	C₂×#41	1	2	yes	—
206	C₂²×C₂₃	C₂⁵	1	1	yes	characteristic
207	C₂×D₂₃	—	2	2	no	—
208	C₂×D₂₃	—	2	2	no	—
209	C₂×D₂₃	—	2	2	no	—
210	C₄×C₂₃	—	2	2	no	—
211	C₄×C₂₃	—	2	2	no	—
212	C₄×C₂₃	—	2	1	no	—
213	C₄×C₂₃	—	2	1	no	—
214	C₄×C₂₃	—	2	1	no	—
215	C₄×C₂₃	C₂×#41	1	2	yes	—
216	C₄×C₂₃	C₂×#41	1	2	yes	—
217	C₄×C₂₃	C₂×#41	1	2	yes	—
218	Dic₂₃	—	2	2	no	—
219	Dic₂₃	—	2	4	no	—
220	Dic₂₃	—	2	2	no	—
221	Dic₂₃	—	2	4	no	—
222	Dic₂₃	—	2	2	no	—
223	#556	—	23	1	no	—
224	#555	—	23	1	no	—
225	#554	—	23	1	no	—
226	#553	—	23	2	no	—
227	#552	—	23	2	no	—
228	#552	—	23	2	no	—
229	#551	—	23	4	no	—
230	#547	—	23	1	no	—
231	#546	—	23	2	no	—
232	#533	—	23	1	no	—
233	#529	—	23	4	no	—
234	#529	—	23	2	no	—
235	#525	—	23	2	no	—
236	C₄×#41	—	23	2	no	—
237	C₄×#41	—	23	1	no	—
238	C₂×C₄×D₄	D₂₃	1	1	yes	characteristic, complemented
239	C₂×#117	—	23	2	no	—
240	C₂×C₂₃	—	2	2	no	—
241	C₂×C₂₃	—	2	4	no	—
242	C₂×C₂₃	—	4	2	no	—
243	C₂×C₂₃	C₂²×#41	1	1	yes	characteristic
244	C₂×C₂₃	C₂²×#41	1	1	yes	characteristic
245	C₂×C₂₃	#585	1	1	yes	characteristic
246	D₂₃	—	4	2	no	—
247	C₂×#41	—	23	2	no	—
248	C₂×#41	—	23	1	no	—
249	C₂²×D₄	C₂×D₂₃	1	1	yes	characteristic
250	C₂³×C₄	C₂×D₂₃	1	2	yes	—
251	C₄⋊Q₈	—	23	1	no	—
252	C₄⋊Q₈	—	23	1	no	—
253	#126	—	23	4	no	—
254	#126	—	23	4	no	—
255	#126	—	23	4	no	—
256	#125	—	23	4	no	—
257	#125	—	23	2	no	—
258	#125	—	23	2	no	—
259	#124	—	23	2	no	—
260	#124	—	23	4	no	—
261	#123	—	23	4	no	—
262	#123	—	23	4	no	—
263	#123	—	23	4	no	—
264	#123	—	23	4	no	—
265	C₂²⋊Q₈	—	23	2	no	—
266	C₂²⋊Q₈	—	23	2	no	—
267	C₂²⋊Q₈	—	23	2	no	—
268	C₂²⋊Q₈	—	23	2	no	—
269	C₂²⋊Q₈	—	23	2	no	—
270	C₂²⋊Q₈	—	23	4	no	—
271	#121	—	23	4	no	—
272	#121	—	23	2	no	—
273	#121	—	23	2	no	—
274	#121	—	23	2	no	—
275	#120	—	23	4	no	—
276	C₄×Q₈	—	23	2	no	—
277	C₄×Q₈	—	23	2	no	—
278	C₄×Q₈	—	23	1	no	—
279	C₄×Q₈	—	23	1	no	—
280	C₄×Q₈	—	23	2	no	—
281	C₄×D₄	—	23	2	no	—
282	C₄×D₄	—	23	4	no	—
283	C₄×D₄	—	23	2	no	—
284	C₄×D₄	—	23	2	no	—
285	C₄×D₄	—	23	4	no	—
286	C₄×D₄	—	23	4	no	—
287	C₄×D₄	—	23	1	no	—
288	C₄×D₄	—	23	1	no	—
289	C₄×D₄	C₂×D₂₃	1	1	yes	characteristic
290	C₄×D₄	C₂×D₂₃	1	1	yes	characteristic
291	C₄×D₄	C₂×D₂₃	1	2	yes	—
292	C₄×D₄	C₂×D₂₃	1	1	yes	characteristic
293	C₄×D₄	C₂×D₂₃	1	2	yes	—
294	C₄×D₄	C₂×D₂₃	1	1	yes	characteristic
295	#117	—	23	1	no	—
296	#117	—	23	2	no	—
297	#117	—	23	4	no	—
298	#117	—	23	4	no	—
299	#117	—	23	2	no	—
300	#117	—	23	2	no	—
301	#117	—	23	2	no	—
302	#117	—	23	4	no	—
303	#117	—	23	2	no	—
304	C₂×C₄⋊C₄	—	23	2	no	—
305	C₂×C₄⋊C₄	—	23	2	no	—
306	C₂×C₄⋊C₄	C₂×D₂₃	1	1	yes	characteristic
307	C₂×C₂²⋊C₄	—	23	4	no	—
308	C₂×C₂²⋊C₄	C₂×D₂₃	1	2	yes	—
309	C₂×C₄²	—	23	4	no	—
310	C₂×C₄²	—	23	2	no	—
311	C₂×C₄²	C₂×D₂₃	1	1	yes	characteristic
312	C₂₃	#3475	1	1	yes	characteristic, complemented, Sylow
313	C₂⁴	C₂²×D₂₃	1	2	yes	—
314	#41	—	46	8	no	—
315	#41	—	46	4	no	—
316	C₂×Q₈	—	23	1	no	—
317	C₂×Q₈	—	23	2	no	—
318	C₂×Q₈	—	23	2	no	—
319	C₂×D₄	—	2	4	no	—
320	C₂×D₄	—	23	2	no	—
321	C₂×D₄	—	23	4	no	—
322	C₂×D₄	—	23	4	no	—
323	C₂×D₄	—	23	1	no	—
324	C₂×D₄	C₂²×D₂₃	1	2	yes	—
325	C₂×D₄	C₂²×D₂₃	1	1	yes	characteristic
326	C₂×D₄	C₂²×D₂₃	1	1	yes	characteristic
327	C₂²×C₄	—	2	8	no	—
328	C₂²×C₄	—	23	4	no	—
329	C₂²×C₄	—	23	4	no	—
330	C₂²×C₄	—	23	2	no	—
331	C₂²×C₄	—	23	2	no	—
332	C₂²×C₄	—	23	2	no	—
333	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
334	C₂²×C₄	C₂²×D₂₃	1	2	yes	—
335	C₂²×C₄	C₂²×D₂₃	1	2	yes	—
336	C₂²×C₄	C₂²×D₂₃	1	2	yes	—
337	C₂²×C₄	C₂²×D₂₃	1	2	yes	—
338	C₂²×C₄	C₂²×D₂₃	1	2	yes	—
339	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
340	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
341	C₄⋊C₄	—	23	1	no	—
342	C₄⋊C₄	—	23	1	no	—
343	C₄⋊C₄	—	23	2	no	—
344	C₄⋊C₄	—	23	2	no	—
345	C₄⋊C₄	—	23	4	no	—
346	C₄⋊C₄	—	23	4	no	—
347	C₄⋊C₄	—	23	2	no	—
348	C₄⋊C₄	—	23	2	no	—
349	C₄⋊C₄	—	23	4	no	—
350	C₄⋊C₄	—	23	4	no	—
351	C₄⋊C₄	—	23	2	no	—
352	C₄⋊C₄	—	23	4	no	—
353	C₄⋊C₄	—	23	4	no	—
354	C₄⋊C₄	—	23	2	no	—
355	C₄⋊C₄	C₂²×D₂₃	1	1	yes	characteristic
356	C₄⋊C₄	C₂²×D₂₃	1	1	yes	characteristic
357	C₄⋊C₄	C₂²×D₂₃	1	2	yes	—
358	C₂²⋊C₄	—	23	2	no	—
359	C₂²⋊C₄	—	23	4	no	—
360	C₂²⋊C₄	—	23	4	no	—
361	C₂²⋊C₄	—	23	4	no	—
362	C₂²⋊C₄	—	23	4	no	—
363	C₂²⋊C₄	—	23	4	no	—
364	C₂²⋊C₄	—	23	2	no	—
365	C₂²⋊C₄	—	23	4	no	—
366	C₂²⋊C₄	—	23	2	no	—
367	C₂²⋊C₄	—	23	4	no	—
368	C₂²⋊C₄	C₂²×D₂₃	1	2	yes	—
369	C₂²⋊C₄	C₂²×D₂₃	1	2	yes	—
370	C₂²⋊C₄	C₂²×D₂₃	1	2	yes	—
371	C₂²⋊C₄	C₂²×D₂₃	1	2	yes	—
372	C₄²	—	23	4	no	—
373	C₄²	—	23	4	no	—
374	C₄²	—	23	2	no	—
375	C₄²	—	23	2	no	—
376	C₄²	—	23	2	no	—
377	C₄²	—	23	4	no	—
378	C₄²	C₂²×D₂₃	1	1	yes	characteristic
379	C₄²	C₂²×D₂₃	1	1	yes	characteristic
380	C₄²	C₂²×D₂₃	1	1	yes	characteristic
381	C₄²	C₂²×D₂₃	1	1	yes	characteristic
382	C₂³	—	2	4	no	—
383	C₂³	—	2	4	no	—
384	C₂³	—	4	2	no	—
385	C₂³	—	23	2	no	—
386	C₂³	C₂³×D₂₃	1	2	yes	—
387	C₂³	C₂³×D₂₃	1	2	yes	—
388	C₂³	C₂³×D₂₃	1	1	yes	characteristic
389	Q₈	—	46	4	no	—
390	Q₈	—	46	2	no	—
391	Q₈	—	92	2	no	—
392	D₄	—	2	4	no	—
393	D₄	—	2	2	no	—
394	D₄	—	46	8	no	—
395	D₄	—	46	4	no	—
396	D₄	—	46	2	no	—
397	D₄	—	92	4	no	—
398	D₄	#67288	1	4	yes	complemented
399	C₂×C₄	—	2	4	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	4	no	—
402	C₂×C₄	—	2	4	no	—
403	C₂×C₄	—	2	4	no	—
404	C₂×C₄	—	2	4	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	23	2	no	—
407	C₂×C₄	—	23	2	no	—
408	C₂×C₄	—	23	2	no	—
409	C₂×C₄	—	23	4	no	—
410	C₂×C₄	—	23	4	no	—
411	C₂×C₄	—	46	8	no	—
412	C₂×C₄	—	46	4	no	—
413	C₂×C₄	—	46	4	no	—
414	C₂×C₄	—	92	2	no	—
415	C₂×C₄	—	92	4	no	—
416	C₂×C₄	#67290	1	4	yes	complemented
417	C₂×C₄	C₂³×D₂₃	1	2	yes	—
418	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
419	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
420	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
421	C₂×C₄	C₂³×D₂₃	1	2	yes	—
422	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
423	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
424	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
425	C₂²	—	2	2	no	—
426	C₂²	—	2	1	no	—
427	C₂²	—	2	1	no	—
428	C₂²	—	2	2	no	—
429	C₂²	—	2	2	no	—
430	C₂²	—	2	2	no	—
431	C₂²	—	2	2	no	—
432	C₂²	—	4	8	no	—
433	C₂²	—	46	2	no	—
434	C₂²	—	46	2	no	—
435	C₂²	—	46	2	no	—
436	C₂²	C₂×#67288	1	4	yes	—
437	C₂²	C₂×#67290	1	2	yes	—
438	C₂²	C₂⁴×D₂₃	1	1	yes	characteristic
439	C₄	—	2	2	no	—
440	C₄	—	2	2	no	—
441	C₄	—	2	1	no	—
442	C₄	—	2	1	no	—
443	C₄	—	2	1	no	—
444	C₄	—	46	2	no	—
445	C₄	—	46	2	no	—
446	C₄	—	46	4	no	—
447	C₄	—	46	2	no	—
448	C₄	—	46	4	no	—
449	C₄	C₂×#67288	1	2	yes	—
450	C₄	C₂×#67290	1	2	yes	—
451	C₄	C₂×#67290	1	2	yes	—
452	C₂	—	2	2	no	—
453	C₂	—	2	4	no	—
454	C₂	—	4	2	no	—
455	C₂	—	92	2	no	—
456	C₂	C₂²×#67290	1	1	yes	characteristic
457	C₂	C₂²×#67288	1	1	yes	characteristic
458	C₂	#13093253	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂³×D₂₃
commutator, socle, cosocle	C₂²×C₂₃	C₂⁵
Frattini	C₂²	C₂⁴×D₂₃
Fitting	C₂×C₄×D₄×C₂₃	C₂
hypercenter	C₂×C₄×D₄	D₂₃
hypocenter	C₂₃	#3475
LCS	G ▷ C₂²×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×D₄

Complements

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

N	H ≅ G/N	type
1. #13093137	C₂	semidirect
2. #13093132	C₂	semidirect
3. #13093124	C₂	semidirect
4. #13093113	C₂	semidirect
5. #13093107	C₂	semidirect
6. #13093102	C₂	semidirect
7. #13093093	C₂	semidirect
8. #13093071	C₂	semidirect
9. #13093061	C₂	semidirect
10. #13092974	C₂	semidirect
11. #13092949	C₂	semidirect
12. #13092947	C₂	semidirect
13. #13092928	C₂	semidirect
14. C₄×#67288	C₂	semidirect
15. C₄×#67290	C₂	semidirect
16. C₂×#10625097	C₂	semidirect
17. C₂×C₄×D₄×C₂₃	C₂	semidirect
38. #10625101	C₂²	semidirect
39. #10625101	C₂²	semidirect
43. C₄×C₂²⋊D₂₃	C₂²	semidirect
44. C₄×C₂²⋊D₂₃	C₂²	semidirect
48. #10625097	C₂²	semidirect
49. #10625097	C₂²	semidirect
50. #10625097	C₂²	semidirect
51. C₂×C₄⋊Dic₂₃	C₂²	semidirect
52. C₂×C₄⋊Dic₂₃	C₂²	semidirect
55. #10625095	C₂²	semidirect
56. #10625095	C₂²	semidirect
57. C₂×C₄×Dic₂₃	C₂²	semidirect
58. #10625069	C₂²	semidirect
59. #10625068	C₂²	semidirect
60. #10625063	C₂²	semidirect
61. #10625061	C₂²	semidirect
62. #10625060	C₂²	semidirect
63. #10625058	C₂²	semidirect
64. #10625057	C₂²	semidirect
65. #10625056	C₂²	semidirect
66. #10625054	C₂²	semidirect
67. (C₂²⋊D₂₃)⋊C₄	C₂²	semidirect
68. #10625050	C₂²	semidirect
69. #10625050	C₂²	semidirect
70. #10625049	C₂²	semidirect
71. #10625048	C₂²	semidirect
72. C₄×D₉₂	C₂²	semidirect
73. C₄×D₉₂	C₂²	semidirect
74. #10625043	C₂²	semidirect
75. C₄²×D₂₃	C₂²	semidirect
76. #10625041	C₂²	semidirect
77. #10625040	C₂²	semidirect
78. #10625040	C₂²	semidirect
79. C₄×Dic₄₆	C₂²	semidirect
80. C₄×Dic₄₆	C₂²	semidirect
81. C₄×Dic₄₆	C₂²	semidirect
82. C₄×Dic₄₆	C₂²	semidirect
161. D₄×C₂₃	#41	semidirect
169. C₂×C₄×C₂₃	#41	semidirect
238. C₂×C₄×D₄	D₂₃	semidirect
312. C₂₃	#3475	semidirect
398. D₄	#67288	semidirect
416. C₂×C₄	#67290	semidirect

Maximal subgroups

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

subgroup	index
#13093137	2
#13093132	2
#13093124	2
#13093113	2
#13093107	2
#13093102	2
#13093093	2
#13093071	2
#13093061	2
#13092974	2
#13092949	2
#13092947	2
#13092928	2
C₄×#67288	2
C₄×#67290	2
C₂×#10625097	2
C₂×C₄×D₄×C₂₃	2
#3475	23