Subgroups — D₄×#67290 #15686879

Order 2944.

1648 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#67290	C₂	1	2	yes	maximal, complemented
2	#13093087	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×Dic₄₆	C₂	1	1	yes	maximal, characteristic, complemented
4	#13093073	C₂	1	2	yes	maximal, complemented
5	#13093071	C₂	1	1	yes	maximal, characteristic, complemented
6	#13093067	C₂	1	2	yes	maximal, complemented
7	#13093061	C₂	1	2	yes	maximal, complemented
8	#13093054	C₂	1	4	yes	maximal, complemented
9	D₄×C₂²⋊D₂₃	C₂	1	2	yes	maximal, complemented
10	#13092965	C₂	1	1	yes	maximal, characteristic, complemented
11	#13092962	C₂	1	2	yes	maximal, complemented
12	#13092927	C₂	1	2	yes	maximal, complemented
13	#13092923	C₂	1	4	yes	maximal, complemented
14	C₄×#67290	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×D₄×Dic₂₃	C₂	1	2	yes	maximal, complemented
16	C₄×D₄×D₂₃	C₂	1	1	yes	maximal, characteristic, complemented
17	D₄²×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×D₄×C₂₃	C₂²	1	2	yes	—
19	C₂²×D₄×C₂₃	C₂²	1	2	yes	complemented
20	C₂²×C₂²⋊D₂₃	C₂²	1	4	yes	complemented
21	C₂³×Dic₂₃	C₂²	1	4	yes	complemented
22	C₂×#67290	—	2	16	no	—
23	C₂×#67290	C₂²	1	1	yes	characteristic
24	C₂×#67290	C₂²	1	4	yes	complemented
25	C₂×#67290	C₂²	1	2	yes	complemented
26	C₂×#67290	C₂²	1	4	yes	complemented
27	C₂×#67290	C₂²	1	2	yes	complemented
28	C₂×#67290	C₂²	1	2	yes	complemented
29	C₂×D₄×D₂₃	C₂²	1	1	yes	characteristic
30	C₂²×C₄×D₂₃	C₂²	1	2	yes	complemented
31	C₂²×Dic₄₆	C₂²	1	2	yes	complemented
32	C₂₃×#127	C₂²	1	1	yes	characteristic, complemented
33	C₂₃×#121	C₂²	1	2	yes	complemented
34	C₂₃×#121	C₂²	1	2	yes	complemented
35	C₂₃×#120	C₂²	1	4	yes	complemented
36	C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
37	C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
38	#10625124	C₂²	1	4	yes	complemented
39	C₂×C₂²⋊Dic₂₃	C₂²	1	4	yes	complemented
40	#10625111	C₂²	1	2	yes	complemented
41	#10625110	C₂²	1	4	yes	complemented
42	#10625110	C₂²	1	4	yes	complemented
43	#10625110	C₂²	1	4	yes	complemented
44	#10625109	C₂²	1	2	yes	complemented
45	#10625109	C₂²	1	2	yes	complemented
46	#10625109	C₂²	1	2	yes	complemented
47	#10625108	C₂²	1	4	yes	complemented
48	#10625107	C₂²	1	2	yes	complemented
49	#10625106	C₂²	1	4	yes	complemented
50	D₄×Dic₂₃	C₂²	1	1	yes	characteristic
51	D₄×Dic₂₃	C₂²	1	2	yes	—
52	D₄×Dic₂₃	C₂²	1	4	yes	complemented
53	D₄×Dic₂₃	C₂²	1	2	yes	complemented
54	D₄×Dic₂₃	C₂²	1	4	yes	complemented
55	D₄×Dic₂₃	C₂²	1	2	yes	complemented
56	D₄×Dic₂₃	C₂²	1	1	yes	characteristic, complemented
57	D₄×Dic₂₃	C₂²	1	2	yes	complemented
58	#10625101	C₂²	1	2	yes	complemented
59	C₄×C₂²⋊D₂₃	C₂²	1	2	yes	complemented
60	C₄×C₂²⋊D₂₃	C₂²	1	2	yes	complemented
61	C₂×C₄⋊Dic₂₃	C₂²	1	2	yes	complemented
62	#10625095	C₂²	1	2	yes	complemented
63	C₂×C₄×Dic₂₃	C₂²	1	2	yes	complemented
64	#10625068	C₂²	1	2	yes	complemented
65	#10625064	C₂²	1	1	yes	characteristic, complemented
66	#10625063	C₂²	1	1	yes	characteristic, complemented
67	C₄⋊C₄×D₂₃	C₂²	1	1	yes	characteristic, complemented
68	#10625059	C₂²	1	2	yes	complemented
69	#10625058	C₂²	1	1	yes	characteristic, complemented
70	#10625057	C₂²	1	4	yes	complemented
71	#10625056	C₂²	1	4	yes	complemented
72	#10625054	C₂²	1	4	yes	complemented
73	(C₂²⋊D₂₃)⋊C₄	C₂²	1	2	yes	complemented
74	(C₂²⋊D₂₃)⋊C₄	C₂²	1	2	yes	complemented
75	(C₂²⋊D₂₃)⋊C₄	C₂²	1	4	yes	complemented
76	C₂²⋊C₄×D₂₃	C₂²	1	2	yes	complemented
77	#10625049	C₂²	1	4	yes	complemented
78	#10625049	C₂²	1	4	yes	complemented
79	#10625048	C₂²	1	2	yes	complemented
80	C₄×D₉₂	C₂²	1	1	yes	characteristic, complemented
81	C₄²×D₂₃	C₂²	1	1	yes	characteristic, complemented
82	#10625040	C₂²	1	1	yes	characteristic, complemented
83	C₄×Dic₄₆	C₂²	1	1	yes	characteristic, complemented
84	C₂⁴×C₂₃	C₂³	1	4	yes	—
85	C₂³×D₂₃	C₂³	1	2	yes	—
86	C₂×D₄×C₂₃	—	2	8	no	—
87	C₂×D₄×C₂₃	—	2	8	no	—
88	C₂×D₄×C₂₃	C₂³	1	4	yes	—
89	C₂×D₄×C₂₃	C₂³	1	2	yes	—
90	C₂×D₄×C₂₃	C₂³	1	4	yes	—
91	C₂×D₄×C₂₃	C₂³	1	2	yes	—
92	C₂×D₄×C₂₃	C₂³	1	2	yes	—
93	C₂×D₄×C₂₃	C₂³	1	1	yes	characteristic
94	C₂×D₄×C₂₃	C₂³	1	1	yes	characteristic
95	C₂²×C₄×C₂₃	C₂³	1	2	yes	—
96	C₂²×C₄×C₂₃	C₂³	1	2	yes	—
97	C₂×C₂²⋊D₂₃	—	2	16	no	—
98	C₂×C₂²⋊D₂₃	C₂³	1	2	yes	—
99	C₂×C₂²⋊D₂₃	C₂³	1	4	yes	—
100	C₂×C₂²⋊D₂₃	C₂³	1	4	yes	—
101	C₂×C₂²⋊D₂₃	C₂³	1	4	yes	—
102	C₂×C₂²⋊D₂₃	C₂³	1	4	yes	—
103	C₂×C₂²⋊D₂₃	C₂³	1	2	yes	—
104	C₂²×Dic₂₃	—	2	16	no	—
105	C₂²×Dic₂₃	C₂³	1	4	yes	—
106	C₂²×Dic₂₃	C₂³	1	4	yes	—
107	C₂²×Dic₂₃	C₂³	1	2	yes	—
108	C₂²×Dic₂₃	C₂³	1	4	yes	—
109	C₂²×Dic₂₃	C₂³	1	4	yes	—
110	C₂²×Dic₂₃	C₂³	1	2	yes	—
111	C₂²×Dic₂₃	C₂³	1	2	yes	—
112	#67290	—	2	8	no	—
113	#67290	—	2	16	no	—
114	#67290	—	2	16	no	—
115	#67290	—	2	8	no	—
116	#67290	—	2	8	no	—
117	#67290	D₄	1	8	yes	direct product factor
118	D₄×D₂₃	—	2	4	no	—
119	C₂×D₉₂	C₂³	1	1	yes	characteristic
120	C₂×C₄×D₂₃	—	2	8	no	—
121	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
122	C₂×C₄×D₂₃	C₂³	1	2	yes	—
123	C₂×C₄×D₂₃	C₂³	1	2	yes	—
124	C₂×C₄×D₂₃	C₂³	1	2	yes	—
125	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
126	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
127	C₂×Dic₄₆	—	2	8	no	—
128	C₂×Dic₄₆	C₂³	1	2	yes	—
129	C₂×Dic₄₆	C₂³	1	4	yes	—
130	C₂×Dic₄₆	C₂³	1	1	yes	characteristic
131	C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
132	C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
133	C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
134	C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
135	C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
136	C₄²×C₂₃	C₂³	1	1	yes	characteristic
137	C₂²⋊Dic₂₃	C₂³	1	2	yes	—
138	C₂²⋊Dic₂₃	C₂³	1	4	yes	—
139	C₂²⋊Dic₂₃	C₂³	1	4	yes	—
140	C₂²⋊Dic₂₃	C₂³	1	2	yes	—
141	C₂²⋊Dic₂₃	C₂³	1	4	yes	—
142	C₂²⋊Dic₂₃	C₂³	1	4	yes	—
143	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
144	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
145	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
146	(C₂×D₂₃)⋊C₄	C₂³	1	4	yes	—
147	C₄⋊Dic₂₃	C₂³	1	1	yes	characteristic
148	C₄⋊Dic₂₃	C₂³	1	2	yes	—
149	C₄⋊Dic₂₃	C₂³	1	2	yes	—
150	C₄⋊Dic₂₃	C₂³	1	1	yes	characteristic
151	C₄⋊Dic₂₃	C₂³	1	4	yes	—
152	Dic₂₃⋊C₄	C₂³	1	2	yes	—
153	Dic₂₃⋊C₄	C₂³	1	2	yes	—
154	Dic₂₃⋊C₄	C₂³	1	2	yes	—
155	Dic₂₃⋊C₄	C₂³	1	4	yes	—
156	C₄×Dic₂₃	C₂³	1	2	yes	—
157	C₄×Dic₂₃	C₂³	1	1	yes	characteristic
158	C₄×Dic₂₃	C₂³	1	1	yes	characteristic
159	C₄×Dic₂₃	C₂³	1	1	yes	characteristic
160	C₄×Dic₂₃	C₂³	1	2	yes	—
161	C₄×Dic₂₃	C₂³	1	2	yes	—
162	C₂³×C₂₃	—	2	8	no	—
163	C₂³×C₂₃	—	2	8	no	—
164	C₂³×C₂₃	—	4	4	no	—
165	C₂³×C₂₃	C₂⁴	1	4	yes	—
166	C₂³×C₂₃	C₂⁴	1	2	yes	—
167	C₂³×C₂₃	C₂⁴	1	2	yes	—
168	C₂²×D₂₃	—	2	4	no	—
169	C₂²×D₂₃	—	2	4	no	—
170	C₂²×D₂₃	—	4	2	no	—
171	C₂²×D₂₃	C₂⁴	1	2	yes	—
172	C₂²×D₂₃	C₂⁴	1	1	yes	characteristic
173	D₄×C₂₃	—	2	8	no	—
174	D₄×C₂₃	—	2	8	no	—
175	D₄×C₂₃	—	2	4	no	—
176	D₄×C₂₃	—	2	4	no	—
177	D₄×C₂₃	—	4	2	no	—
178	D₄×C₂₃	C₂×D₄	1	4	yes	complemented
179	D₄×C₂₃	#41	1	4	yes	complemented
180	C₂×C₄×C₂₃	—	2	4	no	—
181	C₂×C₄×C₂₃	—	2	4	no	—
182	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
183	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
184	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
185	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
186	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
187	C₂²⋊D₂₃	—	2	8	no	—
188	C₂²⋊D₂₃	—	2	4	no	—
189	C₂²⋊D₂₃	—	2	8	no	—
190	C₂²⋊D₂₃	—	2	8	no	—
191	C₂²⋊D₂₃	—	4	4	no	—
192	C₂²⋊D₂₃	C₂×D₄	1	8	yes	complemented
193	C₂×Dic₂₃	—	2	8	no	—
194	C₂×Dic₂₃	—	2	8	no	—
195	C₂×Dic₂₃	—	2	4	no	—
196	C₂×Dic₂₃	—	2	8	no	—
197	C₂×Dic₂₃	—	2	8	no	—
198	C₂×Dic₂₃	—	4	2	no	—
199	C₂×Dic₂₃	C₂×D₄	1	8	yes	complemented
200	C₂×Dic₂₃	C₂⁴	1	1	yes	characteristic
201	C₂×Dic₂₃	C₂⁴	1	1	yes	characteristic
202	C₂×Dic₂₃	C₂⁴	1	2	yes	—
203	C₂×Dic₂₃	C₂⁴	1	4	yes	—
204	C₂×Dic₂₃	C₂⁴	1	2	yes	—
205	C₂×Dic₂₃	C₂⁴	1	1	yes	characteristic
206	C₂×Dic₂₃	C₂⁴	1	2	yes	—
207	D₉₂	—	2	2	no	—
208	C₄×D₂₃	—	2	4	no	—
209	C₄×D₂₃	—	2	4	no	—
210	C₄×D₂₃	—	2	2	no	—
211	C₄×D₂₃	—	2	4	no	—
212	C₄×D₂₃	—	4	1	no	—
213	C₄×D₂₃	C₂×D₄	1	4	yes	complemented
214	Dic₄₆	—	2	4	no	—
215	Dic₄₆	—	2	8	no	—
216	Dic₄₆	C₂×D₄	1	4	yes	complemented
217	D₄×#41	—	23	1	no	maximal, Sylow
218	C₂²×C₂₃	—	2	2	no	—
219	C₂²×C₂₃	—	2	2	no	—
220	C₂²×C₂₃	—	2	2	no	—
221	C₂²×C₂₃	—	2	2	no	—
222	C₂²×C₂₃	—	2	4	no	—
223	C₂²×C₂₃	—	2	4	no	—
224	C₂²×C₂₃	—	2	4	no	—
225	C₂²×C₂₃	—	4	16	no	—
226	C₂²×C₂₃	C₂²×D₄	1	4	yes	—
227	C₂²×C₂₃	C₂×#41	1	4	yes	complemented
228	C₂²×C₂₃	C₂⁵	1	1	yes	characteristic
229	C₂×D₂₃	—	2	1	no	—
230	C₂×D₂₃	—	2	1	no	—
231	C₂×D₂₃	—	2	2	no	—
232	C₂×D₂₃	—	2	2	no	—
233	C₂×D₂₃	—	2	2	no	—
234	C₂×D₂₃	—	4	8	no	—
235	C₂×D₂₃	C₂²×D₄	1	2	yes	—
236	C₄×C₂₃	—	2	2	no	—
237	C₄×C₂₃	—	2	2	no	—
238	C₄×C₂₃	—	2	1	no	—
239	C₄×C₂₃	C₂²×D₄	1	2	yes	—
240	C₄×C₂₃	C₂×#41	1	2	yes	complemented
241	Dic₂₃	—	2	4	no	—
242	Dic₂₃	—	2	2	no	—
243	Dic₂₃	—	2	1	no	—
244	Dic₂₃	—	2	1	no	—
245	Dic₂₃	—	2	2	no	—
246	Dic₂₃	C₂²×D₄	1	4	yes	—
247	Dic₂₃	C₂²×D₄	1	2	yes	—
248	C₂²×#41	—	23	2	no	—
249	#550	—	23	1	no	—
250	D₄×Q₈	—	23	1	no	—
251	#548	—	23	2	no	—
252	#547	—	23	2	no	—
253	#547	—	23	1	no	—
254	#546	—	23	2	no	—
255	#546	—	23	4	no	—
256	D₄²	—	23	2	no	—
257	D₄²	D₂₃	1	1	yes	characteristic, complemented
258	#532	—	23	1	no	—
259	#532	—	23	2	no	—
260	#525	—	23	2	no	—
261	#525	—	23	4	no	—
262	C₄×#41	—	23	1	no	—
263	C₂×C₄×D₄	—	23	2	no	—
264	C₂×C₄×D₄	—	23	1	no	—
265	C₂×C₂₃	—	2	4	no	—
266	C₂×C₂₃	—	2	4	no	—
267	C₂×C₂₃	—	4	4	no	—
268	C₂×C₂₃	C₂³×D₄	1	1	yes	characteristic
269	C₂×C₂₃	C₂²×#41	1	1	yes	characteristic
270	C₂×C₂₃	#585	1	1	yes	characteristic
271	D₂₃	—	2	2	no	—
272	D₂₃	—	4	2	no	—
273	C₂×#41	—	23	1	no	—
274	C₂×#41	—	23	4	no	—
275	C₂×#41	—	23	2	no	—
276	C₂×#41	—	23	2	no	—
277	C₂×#41	—	23	4	no	—
278	C₂×#41	—	23	2	no	—
279	C₂×#41	—	46	16	no	—
280	C₂²×Q₈	—	23	2	no	—
281	C₂²×D₄	—	23	4	no	—
282	C₂²×D₄	—	23	1	no	—
283	C₂²×D₄	C₂×D₂₃	1	2	yes	—
284	C₂²×D₄	C₂×D₂₃	1	2	yes	complemented
285	C₂³×C₄	—	23	4	no	—
286	C₂³×C₄	—	23	2	no	—
287	C₄⋊Q₈	—	23	2	no	—
288	C₄⋊Q₈	—	23	1	no	—
289	#127	—	23	2	no	—
290	#127	C₂×D₂₃	1	1	yes	characteristic, complemented
291	#124	—	23	2	no	—
292	#124	—	23	4	no	—
293	#123	—	23	4	no	—
294	#123	—	23	4	no	—
295	#123	—	23	4	no	—
296	C₂²⋊Q₈	—	23	2	no	—
297	C₂²⋊Q₈	—	23	2	no	—
298	C₂²⋊Q₈	—	23	4	no	—
299	C₂²⋊Q₈	—	23	4	no	—
300	#121	—	23	4	no	—
301	#121	—	23	2	no	—
302	#121	—	23	4	no	—
303	#121	—	23	2	no	—
304	#121	—	23	2	no	—
305	#121	—	23	4	no	—
306	#121	—	23	2	no	—
307	#121	C₂×D₂₃	1	2	yes	complemented
308	#121	C₂×D₂₃	1	2	yes	complemented
309	#120	—	23	4	no	—
310	#120	—	23	4	no	—
311	#120	C₂×D₂₃	1	4	yes	complemented
312	C₄×Q₈	—	23	1	no	—
313	C₄×Q₈	—	23	1	no	—
314	C₄×D₄	—	23	1	no	—
315	C₄×D₄	—	23	4	no	—
316	C₄×D₄	—	23	2	no	—
317	C₄×D₄	—	23	2	no	—
318	C₄×D₄	—	23	4	no	—
319	C₄×D₄	—	23	2	no	—
320	C₄×D₄	—	23	1	no	—
321	C₄×D₄	—	23	2	no	—
322	C₄×D₄	—	23	2	no	—
323	C₄×D₄	—	23	2	no	—
324	C₄×D₄	—	23	1	no	—
325	C₄×D₄	—	23	2	no	—
326	C₄×D₄	—	23	2	no	—
327	C₄×D₄	—	23	4	no	—
328	C₄×D₄	—	23	1	no	—
329	C₄×D₄	C₂×D₂₃	1	1	yes	characteristic
330	C₄×D₄	C₂×D₂₃	1	1	yes	characteristic, complemented
331	#117	—	23	1	no	—
332	#117	—	23	2	no	—
333	C₂×C₄⋊C₄	—	23	2	no	—
334	C₂×C₄⋊C₄	—	23	1	no	—
335	C₂×C₂²⋊C₄	—	23	4	no	—
336	C₂×C₂²⋊C₄	—	23	2	no	—
337	C₂×C₄²	—	23	2	no	—
338	C₂×C₄²	—	23	1	no	—
339	C₂₃	D₄×#41	1	1	yes	characteristic, complemented, Sylow
340	C₂⁴	—	23	2	no	—
341	C₂⁴	C₂²×D₂₃	1	4	yes	—
342	#41	—	23	8	no	—
343	#41	—	46	16	no	—
344	#41	—	46	8	no	—
345	#41	—	46	16	no	—
346	#41	—	46	8	no	—
347	#41	—	46	8	no	—
348	C₂×Q₈	—	23	1	no	—
349	C₂×Q₈	—	23	4	no	—
350	C₂×Q₈	—	23	2	no	—
351	C₂×Q₈	—	46	8	no	—
352	C₂×D₄	—	2	8	no	—
353	C₂×D₄	—	2	8	no	—
354	C₂×D₄	—	23	2	no	—
355	C₂×D₄	—	23	2	no	—
356	C₂×D₄	—	23	4	no	—
357	C₂×D₄	—	23	4	no	—
358	C₂×D₄	—	23	4	no	—
359	C₂×D₄	—	23	4	no	—
360	C₂×D₄	—	23	1	no	—
361	C₂×D₄	—	46	16	no	—
362	C₂×D₄	—	46	4	no	—
363	C₂×D₄	C₂²×D₂₃	1	4	yes	—
364	C₂×D₄	C₂²×D₂₃	1	2	yes	—
365	C₂×D₄	C₂²×D₂₃	1	4	yes	—
366	C₂×D₄	C₂²×D₂₃	1	2	yes	—
367	C₂×D₄	C₂²×D₂₃	1	2	yes	—
368	C₂×D₄	C₂²×D₂₃	1	1	yes	characteristic
369	C₂×D₄	C₂²×D₂₃	1	1	yes	characteristic
370	C₂²×C₄	—	23	2	no	—
371	C₂²×C₄	—	23	1	no	—
372	C₂²×C₄	—	23	4	no	—
373	C₂²×C₄	—	23	2	no	—
374	C₂²×C₄	—	23	4	no	—
375	C₂²×C₄	—	23	4	no	—
376	C₂²×C₄	—	23	4	no	—
377	C₂²×C₄	—	23	2	no	—
378	C₂²×C₄	—	23	1	no	—
379	C₂²×C₄	—	23	2	no	—
380	C₂²×C₄	—	23	2	no	—
381	C₂²×C₄	—	23	2	no	—
382	C₂²×C₄	—	23	1	no	—
383	C₂²×C₄	—	46	8	no	—
384	C₂²×C₄	—	46	16	no	—
385	C₂²×C₄	C₂²×D₂₃	1	2	yes	—
386	C₂²×C₄	C₂²×D₂₃	1	2	yes	—
387	C₄⋊C₄	—	23	1	no	—
388	C₄⋊C₄	—	23	2	no	—
389	C₄⋊C₄	—	23	2	no	—
390	C₄⋊C₄	—	23	4	no	—
391	C₄⋊C₄	—	23	2	no	—
392	C₄⋊C₄	—	23	2	no	—
393	C₄⋊C₄	—	23	1	no	—
394	C₄⋊C₄	—	23	4	no	—
395	C₄⋊C₄	—	23	2	no	—
396	C₄⋊C₄	C₂²×D₂₃	1	1	yes	characteristic
397	C₄⋊C₄	C₂²×D₂₃	1	1	yes	characteristic
398	C₂²⋊C₄	—	23	2	no	—
399	C₂²⋊C₄	—	23	4	no	—
400	C₂²⋊C₄	—	23	4	no	—
401	C₂²⋊C₄	—	23	4	no	—
402	C₂²⋊C₄	—	23	2	no	—
403	C₂²⋊C₄	—	23	4	no	—
404	C₂²⋊C₄	—	23	2	no	—
405	C₂²⋊C₄	—	23	2	no	—
406	C₂²⋊C₄	—	23	2	no	—
407	C₂²⋊C₄	—	23	4	no	—
408	C₂²⋊C₄	C₂²×D₂₃	1	2	yes	—
409	C₂²⋊C₄	C₂²×D₂₃	1	2	yes	—
410	C₂²⋊C₄	C₂²×D₂₃	1	4	yes	—
411	C₄²	—	23	1	no	—
412	C₄²	—	23	2	no	—
413	C₄²	—	23	1	no	—
414	C₄²	—	23	2	no	—
415	C₄²	—	23	1	no	—
416	C₄²	—	23	2	no	—
417	C₄²	C₂²×D₂₃	1	1	yes	characteristic
418	C₂³	—	2	8	no	—
419	C₂³	—	2	8	no	—
420	C₂³	—	4	4	no	—
421	C₂³	—	23	1	no	—
422	C₂³	—	23	2	no	—
423	C₂³	—	46	4	no	—
424	C₂³	—	46	4	no	—
425	C₂³	—	92	2	no	—
426	C₂³	C₂³×D₂₃	1	4	yes	—
427	C₂³	C₂³×D₂₃	1	2	yes	—
428	C₂³	C₂³×D₂₃	1	2	yes	—
429	Q₈	—	23	4	no	—
430	Q₈	—	46	8	no	—
431	Q₈	—	46	4	no	—
432	D₄	—	2	8	no	—
433	D₄	—	2	8	no	—
434	D₄	—	2	4	no	—
435	D₄	—	2	4	no	—
436	D₄	—	4	2	no	—
437	D₄	—	23	8	no	—
438	D₄	—	46	8	no	—
439	D₄	—	46	8	no	—
440	D₄	—	46	8	no	—
441	D₄	—	46	4	no	—
442	D₄	—	46	2	no	—
443	D₄	—	92	4	no	—
444	D₄	D₄×D₂₃	1	4	yes	complemented
445	D₄	#67290	1	4	yes	direct product factor
446	C₂×C₄	—	2	4	no	—
447	C₂×C₄	—	2	4	no	—
448	C₂×C₄	—	23	8	no	—
449	C₂×C₄	—	23	1	no	—
450	C₂×C₄	—	23	2	no	—
451	C₂×C₄	—	23	4	no	—
452	C₂×C₄	—	23	1	no	—
453	C₂×C₄	—	23	1	no	—
454	C₂×C₄	—	23	2	no	—
455	C₂×C₄	—	23	2	no	—
456	C₂×C₄	—	23	4	no	—
457	C₂×C₄	—	46	4	no	—
458	C₂×C₄	—	46	4	no	—
459	C₂×C₄	—	46	4	no	—
460	C₂×C₄	—	46	8	no	—
461	C₂×C₄	—	46	8	no	—
462	C₂×C₄	—	46	8	no	—
463	C₂×C₄	—	46	8	no	—
464	C₂×C₄	—	46	4	no	—
465	C₂×C₄	—	46	2	no	—
466	C₂×C₄	—	92	1	no	—
467	C₂×C₄	—	92	2	no	—
468	C₂×C₄	C₂³×D₂₃	1	2	yes	—
469	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
470	C₂×C₄	C₂³×D₂₃	1	2	yes	—
471	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
472	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
473	C₂²	—	2	2	no	—
474	C₂²	—	2	2	no	—
475	C₂²	—	2	2	no	—
476	C₂²	—	2	2	no	—
477	C₂²	—	2	4	no	—
478	C₂²	—	2	4	no	—
479	C₂²	—	2	4	no	—
480	C₂²	—	4	16	no	—
481	C₂²	—	23	2	no	—
482	C₂²	—	46	1	no	—
483	C₂²	—	46	1	no	—
484	C₂²	—	46	2	no	—
485	C₂²	—	46	2	no	—
486	C₂²	—	46	2	no	—
487	C₂²	—	92	8	no	—
488	C₂²	C₂×D₄×D₂₃	1	4	yes	—
489	C₂²	C₂×#67290	1	4	yes	complemented
490	C₂²	C₂⁴×D₂₃	1	1	yes	characteristic
491	C₄	—	2	2	no	—
492	C₄	—	2	2	no	—
493	C₄	—	2	1	no	—
494	C₄	—	23	2	no	—
495	C₄	—	23	4	no	—
496	C₄	—	46	2	no	—
497	C₄	—	46	4	no	—
498	C₄	—	46	1	no	—
499	C₄	—	46	1	no	—
500	C₄	—	46	2	no	—
501	C₄	C₂×D₄×D₂₃	1	2	yes	—
502	C₄	C₂×#67290	1	2	yes	complemented
503	C₂	—	2	4	no	—
504	C₂	—	2	4	no	—
505	C₂	—	4	4	no	—
506	C₂	—	46	2	no	—
507	C₂	—	92	2	no	—
508	C₂	C₂²×D₄×D₂₃	1	1	yes	characteristic
509	C₂	C₂²×#67290	1	1	yes	characteristic
510	C₂	#13093252	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₂₃
commutator, socle, cosocle	C₂²×C₂₃	C₂⁵
Fitting	D₄²×C₂₃	C₂
hypercenter	D₄²	D₂₃
hypocenter	C₂₃	D₄×#41
LCS	G ▷ C₂²×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂² ◁ D₄²

Complements

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

N	H ≅ G/N	type
1. C₂²×#67290	C₂	semidirect
2. #13093087	C₂	semidirect
3. D₄×Dic₄₆	C₂	semidirect
4. #13093073	C₂	semidirect
5. #13093071	C₂	semidirect
6. #13093067	C₂	semidirect
7. #13093061	C₂	semidirect
8. #13093054	C₂	semidirect
9. D₄×C₂²⋊D₂₃	C₂	semidirect
10. #13092965	C₂	semidirect
11. #13092962	C₂	semidirect
12. #13092927	C₂	semidirect
13. #13092923	C₂	semidirect
14. C₄×#67290	C₂	semidirect
15. C₂×D₄×Dic₂₃	C₂	semidirect
16. C₄×D₄×D₂₃	C₂	semidirect
17. D₄²×C₂₃	C₂	semidirect
19. C₂²×D₄×C₂₃	C₂²	semidirect
20. C₂²×C₂²⋊D₂₃	C₂²	semidirect
21. C₂³×Dic₂₃	C₂²	semidirect
24. C₂×#67290	C₂²	semidirect
25. C₂×#67290	C₂²	semidirect
26. C₂×#67290	C₂²	semidirect
27. C₂×#67290	C₂²	semidirect
28. C₂×#67290	C₂²	semidirect
30. C₂²×C₄×D₂₃	C₂²	semidirect
31. C₂²×Dic₄₆	C₂²	semidirect
32. C₂₃×#127	C₂²	semidirect
33. C₂₃×#121	C₂²	semidirect
34. C₂₃×#121	C₂²	semidirect
35. C₂₃×#120	C₂²	semidirect
37. C₄×D₄×C₂₃	C₂²	semidirect
38. #10625124	C₂²	semidirect
39. C₂×C₂²⋊Dic₂₃	C₂²	semidirect
40. #10625111	C₂²	semidirect
41. #10625110	C₂²	semidirect
42. #10625110	C₂²	semidirect
43. #10625110	C₂²	semidirect
44. #10625109	C₂²	semidirect
45. #10625109	C₂²	semidirect
46. #10625109	C₂²	semidirect
47. #10625108	C₂²	semidirect
48. #10625107	C₂²	semidirect
49. #10625106	C₂²	semidirect
52. D₄×Dic₂₃	C₂²	semidirect
53. D₄×Dic₂₃	C₂²	semidirect
54. D₄×Dic₂₃	C₂²	semidirect
55. D₄×Dic₂₃	C₂²	semidirect
56. D₄×Dic₂₃	C₂²	semidirect
57. D₄×Dic₂₃	C₂²	semidirect
58. #10625101	C₂²	semidirect
59. C₄×C₂²⋊D₂₃	C₂²	semidirect
60. C₄×C₂²⋊D₂₃	C₂²	semidirect
61. C₂×C₄⋊Dic₂₃	C₂²	semidirect
62. #10625095	C₂²	semidirect
63. C₂×C₄×Dic₂₃	C₂²	semidirect
64. #10625068	C₂²	semidirect
65. #10625064	C₂²	semidirect
66. #10625063	C₂²	semidirect
67. C₄⋊C₄×D₂₃	C₂²	semidirect
68. #10625059	C₂²	semidirect
69. #10625058	C₂²	semidirect
70. #10625057	C₂²	semidirect
71. #10625056	C₂²	semidirect
72. #10625054	C₂²	semidirect
73. (C₂²⋊D₂₃)⋊C₄	C₂²	semidirect
74. (C₂²⋊D₂₃)⋊C₄	C₂²	semidirect
75. (C₂²⋊D₂₃)⋊C₄	C₂²	semidirect
76. C₂²⋊C₄×D₂₃	C₂²	semidirect
77. #10625049	C₂²	semidirect
78. #10625049	C₂²	semidirect
79. #10625048	C₂²	semidirect
80. C₄×D₉₂	C₂²	semidirect
81. C₄²×D₂₃	C₂²	semidirect
82. #10625040	C₂²	semidirect
83. C₄×Dic₄₆	C₂²	semidirect
117. #67290	D₄	direct (N × H)
178. D₄×C₂₃	C₂×D₄	semidirect
179. D₄×C₂₃	#41	semidirect
192. C₂²⋊D₂₃	C₂×D₄	semidirect
199. C₂×Dic₂₃	C₂×D₄	semidirect
213. C₄×D₂₃	C₂×D₄	semidirect
216. Dic₄₆	C₂×D₄	semidirect
227. C₂²×C₂₃	C₂×#41	semidirect
240. C₄×C₂₃	C₂×#41	semidirect
257. D₄²	D₂₃	semidirect
284. C₂²×D₄	C₂×D₂₃	semidirect
290. #127	C₂×D₂₃	semidirect
307. #121	C₂×D₂₃	semidirect
308. #121	C₂×D₂₃	semidirect
311. #120	C₂×D₂₃	semidirect
330. C₄×D₄	C₂×D₂₃	semidirect
339. C₂₃	D₄×#41	semidirect
444. D₄	D₄×D₂₃	semidirect
445. D₄	#67290	direct (N × H)
489. C₂²	C₂×#67290	semidirect
502. C₄	C₂×#67290	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#67290	2
#13093087	2
D₄×Dic₄₆	2
#13093073	2
#13093071	2
#13093067	2
#13093061	2
#13093054	2
D₄×C₂²⋊D₂₃	2
#13092965	2
#13092962	2
#13092927	2
#13092923	2
C₄×#67290	2
C₂×D₄×Dic₂₃	2
C₄×D₄×D₂₃	2
D₄²×C₂₃	2
D₄×#41	23

Subgroups — D4×#67290 #15686879

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄×#67290 #15686879