Subgroups — D₄×#67288 #15686885

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×#67288	C₂	1	2	yes	maximal, complemented
2	#13093088	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×Dic₄₆	C₂	1	1	yes	maximal, characteristic, complemented
4	#13093076	C₂	1	2	yes	maximal, complemented
5	#13093072	C₂	1	1	yes	maximal, characteristic, complemented
6	#13093068	C₂	1	2	yes	maximal, complemented
7	#13093063	C₂	1	2	yes	maximal, complemented
8	#13093057	C₂	1	4	yes	maximal, complemented
9	D₄×D₉₂	C₂	1	1	yes	maximal, characteristic, complemented
10	D₄×C₂²⋊D₂₃	C₂	1	2	yes	maximal, complemented
11	#13092967	C₂	1	1	yes	maximal, characteristic, complemented
12	#13092964	C₂	1	2	yes	maximal, complemented
13	#13092928	C₂	1	2	yes	maximal, complemented
14	#13092926	C₂	1	4	yes	maximal, complemented
15	C₄×#67288	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×D₄×D₂₃	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	complemented
20	C₂²×C₂²⋊D₂₃	C₂²	1	4	yes	complemented
21	C₂×D₄×D₂₃	C₂²	1	2	yes	—
22	C₂×#67288	—	2	16	no	—
23	C₂×#67288	C₂²	1	1	yes	characteristic
24	C₂×#67288	C₂²	1	4	yes	complemented
25	C₂×#67288	C₂²	1	2	yes	complemented
26	C₂×#67288	C₂²	1	4	yes	complemented
27	C₂×#67288	C₂²	1	2	yes	complemented
28	C₂×#67288	C₂²	1	2	yes	complemented
29	C₂²×D₉₂	C₂²	1	2	yes	complemented
30	C₂²×C₄×D₂₃	C₂²	1	4	yes	complemented
31	C₂²×Dic₄₆	C₂²	1	2	yes	complemented
32	C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
33	C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
34	C₄×D₄×C₂₃	C₂²	1	2	yes	complemented
35	C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
36	C₄×D₄×C₂₃	C₂²	1	2	yes	complemented
37	C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	complemented
40	C₂×C₄²×C₂₃	C₂²	1	1	yes	characteristic, complemented
41	#10625124	C₂²	1	4	yes	complemented
42	#10625111	C₂²	1	2	yes	complemented
43	#10625110	C₂²	1	4	yes	complemented
44	#10625109	C₂²	1	2	yes	complemented
45	#10625108	C₂²	1	4	yes	complemented
46	D₄×Dic₂₃	C₂²	1	2	yes	—
47	#10625101	C₂²	1	2	yes	complemented
48	#10625101	C₂²	1	2	yes	complemented
49	#10625101	C₂²	1	2	yes	complemented
50	#10625101	C₂²	1	2	yes	complemented
51	#10625100	C₂²	1	4	yes	complemented
52	C₄×C₂²⋊D₂₃	C₂²	1	4	yes	complemented
53	C₄×C₂²⋊D₂₃	C₂²	1	2	yes	complemented
54	C₄×C₂²⋊D₂₃	C₂²	1	2	yes	complemented
55	C₄×C₂²⋊D₂₃	C₂²	1	4	yes	complemented
56	#10625097	C₂²	1	1	yes	characteristic, complemented
57	#10625095	C₂²	1	2	yes	complemented
58	#10625095	C₂²	1	2	yes	complemented
59	#10625067	C₂²	1	4	yes	complemented
60	#10625066	C₂²	1	2	yes	complemented
61	#10625065	C₂²	1	4	yes	complemented
62	#10625064	C₂²	1	2	yes	complemented
63	C₄⋊C₄×D₂₃	C₂²	1	2	yes	complemented
64	#10625059	C₂²	1	2	yes	complemented
65	#10625056	C₂²	1	4	yes	complemented
66	#10625055	C₂²	1	4	yes	complemented
67	#10625055	C₂²	1	4	yes	complemented
68	#10625054	C₂²	1	4	yes	complemented
69	#10625053	C₂²	1	4	yes	complemented
70	(C₂²⋊D₂₃)⋊C₄	C₂²	1	4	yes	complemented
71	C₂²⋊C₄×D₂₃	C₂²	1	4	yes	complemented
72	#10625049	C₂²	1	4	yes	complemented
73	#10625046	C₂²	1	2	yes	complemented
74	#10625045	C₂²	1	1	yes	characteristic, complemented
75	C₄×D₉₂	C₂²	1	2	yes	complemented
76	C₄×D₉₂	C₂²	1	1	yes	characteristic, complemented
77	C₄×D₉₂	C₂²	1	1	yes	characteristic, complemented
78	C₄×D₉₂	C₂²	1	2	yes	complemented
79	#10625043	C₂²	1	2	yes	complemented
80	C₄²×D₂₃	C₂²	1	2	yes	complemented
81	#10625040	C₂²	1	1	yes	characteristic, complemented
82	C₄×Dic₄₆	C₂²	1	1	yes	characteristic, complemented
83	C₄×Dic₄₆	C₂²	1	1	yes	characteristic, complemented
84	C₂⁴×C₂₃	C₂³	1	2	yes	—
85	C₂³×D₂₃	C₂³	1	4	yes	—
86	C₂×D₄×C₂₃	—	2	4	no	—
87	C₂×D₄×C₂₃	C₂³	1	2	yes	—
88	C₂×D₄×C₂₃	C₂³	1	1	yes	characteristic
89	C₂×D₄×C₂₃	C₂³	1	1	yes	characteristic
90	C₂²×C₄×C₂₃	—	2	8	no	—
91	C₂²×C₄×C₂₃	C₂³	1	2	yes	—
92	C₂²×C₄×C₂₃	C₂³	1	2	yes	—
93	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
94	C₂²×C₄×C₂₃	C₂³	1	2	yes	—
95	C₂²×C₄×C₂₃	C₂³	1	2	yes	—
96	C₂²×C₄×C₂₃	C₂³	1	2	yes	—
97	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
98	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
99	C₂×C₂²⋊D₂₃	—	2	16	no	—
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	4	yes	—
104	C₂×C₂²⋊D₂₃	C₂³	1	4	yes	—
105	C₂×C₂²⋊D₂₃	C₂³	1	2	yes	—
106	C₂²×Dic₂₃	C₂³	1	4	yes	—
107	D₄×D₂₃	—	2	8	no	—
108	#67288	—	2	8	no	—
109	#67288	—	2	16	no	—
110	#67288	—	2	8	no	—
111	#67288	—	2	16	no	—
112	#67288	—	2	8	no	—
113	#67288	D₄	1	8	yes	direct product factor
114	C₂×D₉₂	—	2	8	no	—
115	C₂×D₉₂	C₂³	1	2	yes	—
116	C₂×D₉₂	C₂³	1	2	yes	—
117	C₂×D₉₂	C₂³	1	4	yes	—
118	C₂×D₉₂	C₂³	1	2	yes	—
119	C₂×D₉₂	C₂³	1	1	yes	characteristic
120	C₂×C₄×D₂₃	—	2	16	no	—
121	C₂×C₄×D₂₃	C₂³	1	2	yes	—
122	C₂×C₄×D₂₃	C₂³	1	4	yes	—
123	C₂×C₄×D₂₃	C₂³	1	4	yes	—
124	C₂×C₄×D₂₃	C₂³	1	4	yes	—
125	C₂×C₄×D₂₃	C₂³	1	2	yes	—
126	C₂×C₄×D₂₃	C₂³	1	2	yes	—
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	C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
134	C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
135	C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
136	C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
137	C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
138	C₄²×C₂₃	C₂³	1	1	yes	characteristic
139	C₄²×C₂₃	C₂³	1	1	yes	characteristic
140	C₄²×C₂₃	C₂³	1	1	yes	characteristic
141	C₄²×C₂₃	C₂³	1	1	yes	characteristic
142	C₂²⋊Dic₂₃	C₂³	1	4	yes	—
143	C₂²⋊Dic₂₃	C₂³	1	4	yes	—
144	C₂²⋊Dic₂₃	C₂³	1	2	yes	—
145	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
146	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
147	(C₂×D₂₃)⋊C₄	C₂³	1	4	yes	—
148	(C₂×D₂₃)⋊C₄	C₂³	1	4	yes	—
149	(C₂×D₂₃)⋊C₄	C₂³	1	4	yes	—
150	(C₂×D₂₃)⋊C₄	C₂³	1	4	yes	—
151	C₄⋊Dic₂₃	C₂³	1	1	yes	characteristic
152	C₄⋊Dic₂₃	C₂³	1	1	yes	characteristic
153	C₄⋊Dic₂₃	C₂³	1	2	yes	—
154	C₄⋊Dic₂₃	C₂³	1	2	yes	—
155	Dic₂₃⋊C₄	C₂³	1	2	yes	—
156	Dic₂₃⋊C₄	C₂³	1	2	yes	—
157	Dic₂₃⋊C₄	C₂³	1	4	yes	—
158	Dic₂₃⋊C₄	C₂³	1	4	yes	—
159	C₄×Dic₂₃	C₂³	1	2	yes	—
160	C₄×Dic₂₃	C₂³	1	2	yes	—
161	C₄×Dic₂₃	C₂³	1	2	yes	—
162	C₂³×C₂₃	—	2	4	no	—
163	C₂³×C₂₃	—	2	4	no	—
164	C₂³×C₂₃	—	4	2	no	—
165	C₂³×C₂₃	C₂⁴	1	2	yes	—
166	C₂³×C₂₃	C₂⁴	1	1	yes	characteristic
167	C₂³×C₂₃	C₂⁴	1	2	yes	—
168	C₂²×D₂₃	—	2	8	no	—
169	C₂²×D₂₃	—	2	8	no	—
170	C₂²×D₂₃	—	4	4	no	—
171	C₂²×D₂₃	C₂⁴	1	4	yes	—
172	C₂²×D₂₃	C₂⁴	1	2	yes	—
173	D₄×C₂₃	—	2	4	no	—
174	D₄×C₂₃	—	2	2	no	—
175	D₄×C₂₃	#41	1	4	yes	complemented
176	C₂×C₄×C₂₃	—	2	4	no	—
177	C₂×C₄×C₂₃	—	2	4	no	—
178	C₂×C₄×C₂₃	—	2	4	no	—
179	C₂×C₄×C₂₃	—	2	4	no	—
180	C₂×C₄×C₂₃	—	2	4	no	—
181	C₂×C₄×C₂₃	—	2	2	no	—
182	C₂×C₄×C₂₃	—	4	1	no	—
183	C₂×C₄×C₂₃	C₂×D₄	1	4	yes	complemented
184	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
185	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
186	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
187	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
188	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
189	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
190	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
191	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
192	C₂²⋊D₂₃	—	2	8	no	—
193	C₂²⋊D₂₃	—	2	8	no	—
194	C₂²⋊D₂₃	—	2	8	no	—
195	C₂²⋊D₂₃	—	2	8	no	—
196	C₂²⋊D₂₃	—	4	4	no	—
197	C₂²⋊D₂₃	C₂×D₄	1	8	yes	complemented
198	C₂×Dic₂₃	—	2	8	no	—
199	C₂×Dic₂₃	C₂⁴	1	2	yes	—
200	C₂×Dic₂₃	C₂⁴	1	2	yes	—
201	C₂×Dic₂₃	C₂⁴	1	4	yes	—
202	C₂×Dic₂₃	C₂⁴	1	2	yes	—
203	D₉₂	—	2	8	no	—
204	D₉₂	—	2	4	no	—
205	D₉₂	—	2	4	no	—
206	D₉₂	—	4	2	no	—
207	D₉₂	C₂×D₄	1	4	yes	complemented
208	C₄×D₂₃	—	2	8	no	—
209	C₄×D₂₃	—	2	8	no	—
210	C₄×D₂₃	—	2	4	no	—
211	C₄×D₂₃	—	2	8	no	—
212	C₄×D₂₃	—	4	2	no	—
213	C₄×D₂₃	C₂×D₄	1	8	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	1	no	—
220	C₂²×C₂₃	—	2	1	no	—
221	C₂²×C₂₃	—	2	2	no	—
222	C₂²×C₂₃	—	2	2	no	—
223	C₂²×C₂₃	—	2	2	no	—
224	C₂²×C₂₃	—	2	2	no	—
225	C₂²×C₂₃	—	4	8	no	—
226	C₂²×C₂₃	C₂²×D₄	1	2	yes	—
227	C₂²×C₂₃	C₂×#41	1	4	yes	complemented
228	C₂²×C₂₃	C₂⁵	1	1	yes	characteristic
229	C₂×D₂₃	—	2	2	no	—
230	C₂×D₂₃	—	2	2	no	—
231	C₂×D₂₃	—	2	4	no	—
232	C₂×D₂₃	—	2	4	no	—
233	C₂×D₂₃	—	2	4	no	—
234	C₂×D₂₃	—	4	16	no	—
235	C₂×D₂₃	C₂²×D₄	1	4	yes	—
236	C₄×C₂₃	—	2	2	no	—
237	C₄×C₂₃	—	2	2	no	—
238	C₄×C₂₃	—	2	1	no	—
239	C₄×C₂₃	—	2	1	no	—
240	C₄×C₂₃	—	2	1	no	—
241	C₄×C₂₃	C₂²×D₄	1	2	yes	—
242	C₄×C₂₃	C₂²×D₄	1	2	yes	—
243	C₄×C₂₃	C₂×#41	1	2	yes	complemented
244	Dic₂₃	—	2	4	no	—
245	Dic₂₃	—	2	2	no	—
246	Dic₂₃	—	2	2	no	—
247	Dic₂₃	C₂²×D₄	1	4	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	1	no	—
253	#547	—	23	2	no	—
254	#546	—	23	2	no	—
255	#546	—	23	4	no	—
256	D₄²	—	23	2	no	—
257	D₄²	—	23	1	no	—
258	#532	—	23	2	no	—
259	#532	—	23	1	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	D₂₃	1	1	yes	characteristic, complemented
265	C₂×C₂₃	—	2	4	no	—
266	C₂×C₂₃	—	2	2	no	—
267	C₂×C₂₃	—	4	2	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	4	no	—
272	D₂₃	—	4	4	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	2	no	—
283	C₂²×D₄	—	23	2	no	—
284	C₂²×D₄	C₂×D₂₃	1	1	yes	characteristic
285	C₂³×C₄	—	23	4	no	—
286	C₂³×C₄	C₂×D₂₃	1	2	yes	complemented
287	C₄⋊Q₈	—	23	2	no	—
288	C₄⋊Q₈	—	23	1	no	—
289	#127	—	23	2	no	—
290	#127	—	23	1	no	—
291	#124	—	23	4	no	—
292	#124	—	23	2	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	2	no	—
303	#121	—	23	2	no	—
304	#121	—	23	2	no	—
305	#121	—	23	2	no	—
306	#121	—	23	2	no	—
307	#121	—	23	4	no	—
308	#121	—	23	4	no	—
309	#120	—	23	4	no	—
310	#120	—	23	4	no	—
311	#120	—	23	4	no	—
312	C₄×Q₈	—	23	1	no	—
313	C₄×Q₈	—	23	1	no	—
314	C₄×D₄	—	23	2	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	4	no	—
321	C₄×D₄	—	23	2	no	—
322	C₄×D₄	—	23	1	no	—
323	C₄×D₄	—	23	1	no	—
324	C₄×D₄	—	23	2	no	—
325	C₄×D₄	C₂×D₂₃	1	1	yes	characteristic
326	C₄×D₄	C₂×D₂₃	1	1	yes	characteristic
327	C₄×D₄	C₂×D₂₃	1	2	yes	complemented
328	C₄×D₄	C₂×D₂₃	1	1	yes	characteristic, complemented
329	C₄×D₄	C₂×D₂₃	1	2	yes	complemented
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	C₂×D₂₃	1	1	yes	characteristic, complemented
335	C₂×C₂²⋊C₄	—	23	4	no	—
336	C₂×C₂²⋊C₄	C₂×D₂₃	1	2	yes	complemented
337	C₂×C₄²	—	23	2	no	—
338	C₂×C₄²	C₂×D₂₃	1	1	yes	characteristic, complemented
339	C₂₃	D₄×#41	1	1	yes	characteristic, complemented, Sylow
340	C₂⁴	—	23	4	no	—
341	C₂⁴	C₂²×D₂₃	1	2	yes	—
342	#41	—	23	8	no	—
343	#41	—	46	16	no	—
344	#41	—	46	16	no	—
345	#41	—	46	8	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	4	no	—
353	C₂×D₄	—	23	2	no	—
354	C₂×D₄	—	23	4	no	—
355	C₂×D₄	—	23	4	no	—
356	C₂×D₄	—	23	4	no	—
357	C₂×D₄	—	23	4	no	—
358	C₂×D₄	—	23	4	no	—
359	C₂×D₄	—	23	1	no	—
360	C₂×D₄	—	23	2	no	—
361	C₂×D₄	—	23	4	no	—
362	C₂×D₄	—	23	2	no	—
363	C₂×D₄	—	23	2	no	—
364	C₂×D₄	—	46	8	no	—
365	C₂×D₄	—	46	16	no	—
366	C₂×D₄	—	46	8	no	—
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	—	2	8	no	—
371	C₂²×C₄	—	23	2	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	—	46	16	no	—
379	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
380	C₂²×C₄	C₂²×D₂₃	1	2	yes	—
381	C₂²×C₄	C₂²×D₂₃	1	2	yes	—
382	C₂²×C₄	C₂²×D₂₃	1	2	yes	—
383	C₂²×C₄	C₂²×D₂₃	1	2	yes	—
384	C₂²×C₄	C₂²×D₂₃	1	2	yes	—
385	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
386	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
387	C₄⋊C₄	—	23	2	no	—
388	C₄⋊C₄	—	23	4	no	—
389	C₄⋊C₄	—	23	2	no	—
390	C₄⋊C₄	—	23	2	no	—
391	C₄⋊C₄	—	23	1	no	—
392	C₄⋊C₄	—	23	1	no	—
393	C₄⋊C₄	—	23	4	no	—
394	C₄⋊C₄	—	23	2	no	—
395	C₄⋊C₄	C₂²×D₂₃	1	1	yes	characteristic
396	C₄⋊C₄	C₂²×D₂₃	1	1	yes	characteristic
397	C₄⋊C₄	C₂²×D₂₃	1	2	yes	—
398	C₂²⋊C₄	—	23	4	no	—
399	C₂²⋊C₄	—	23	2	no	—
400	C₂²⋊C₄	—	23	4	no	—
401	C₂²⋊C₄	—	23	4	no	—
402	C₂²⋊C₄	—	23	4	no	—
403	C₂²⋊C₄	—	23	2	no	—
404	C₂²⋊C₄	—	23	2	no	—
405	C₂²⋊C₄	—	23	4	no	—
406	C₂²⋊C₄	—	23	4	no	—
407	C₂²⋊C₄	C₂²×D₂₃	1	2	yes	—
408	C₂²⋊C₄	C₂²×D₂₃	1	2	yes	—
409	C₂²⋊C₄	C₂²×D₂₃	1	2	yes	—
410	C₂²⋊C₄	C₂²×D₂₃	1	2	yes	—
411	C₄²	—	23	2	no	—
412	C₄²	—	23	2	no	—
413	C₄²	—	23	2	no	—
414	C₄²	C₂²×D₂₃	1	1	yes	characteristic
415	C₄²	C₂²×D₂₃	1	1	yes	characteristic
416	C₄²	C₂²×D₂₃	1	1	yes	characteristic
417	C₄²	C₂²×D₂₃	1	1	yes	characteristic
418	C₂³	—	2	4	no	—
419	C₂³	—	2	4	no	—
420	C₂³	—	4	2	no	—
421	C₂³	—	23	2	no	—
422	C₂³	—	23	4	no	—
423	C₂³	—	46	8	no	—
424	C₂³	—	46	8	no	—
425	C₂³	—	92	4	no	—
426	C₂³	C₂³×D₂₃	1	2	yes	—
427	C₂³	C₂³×D₂₃	1	2	yes	—
428	C₂³	C₂³×D₂₃	1	1	yes	characteristic
429	Q₈	—	23	4	no	—
430	Q₈	—	46	8	no	—
431	Q₈	—	46	4	no	—
432	D₄	—	2	4	no	—
433	D₄	—	2	2	no	—
434	D₄	—	23	8	no	—
435	D₄	—	23	4	no	—
436	D₄	—	46	8	no	—
437	D₄	—	46	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	4	no	—
443	D₄	—	92	2	no	—
444	D₄	—	92	4	no	—
445	D₄	#67288	1	4	yes	direct product factor
446	C₂×C₄	—	2	4	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	4	no	—
449	C₂×C₄	—	2	4	no	—
450	C₂×C₄	—	2	4	no	—
451	C₂×C₄	—	2	4	no	—
452	C₂×C₄	—	4	1	no	—
453	C₂×C₄	—	23	2	no	—
454	C₂×C₄	—	23	8	no	—
455	C₂×C₄	—	23	2	no	—
456	C₂×C₄	—	23	2	no	—
457	C₂×C₄	—	23	4	no	—
458	C₂×C₄	—	46	8	no	—
459	C₂×C₄	—	46	8	no	—
460	C₂×C₄	—	46	8	no	—
461	C₂×C₄	—	46	4	no	—
462	C₂×C₄	—	46	8	no	—
463	C₂×C₄	—	92	2	no	—
464	C₂×C₄	D₄×D₂₃	1	4	yes	complemented
465	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
466	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
467	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
468	C₂×C₄	C₂³×D₂₃	1	2	yes	—
469	C₂×C₄	C₂³×D₂₃	1	2	yes	—
470	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
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	1	no	—
475	C₂²	—	2	1	no	—
476	C₂²	—	2	2	no	—
477	C₂²	—	2	2	no	—
478	C₂²	—	2	2	no	—
479	C₂²	—	2	2	no	—
480	C₂²	—	4	8	no	—
481	C₂²	—	23	4	no	—
482	C₂²	—	46	2	no	—
483	C₂²	—	46	2	no	—
484	C₂²	—	46	4	no	—
485	C₂²	—	46	4	no	—
486	C₂²	—	46	4	no	—
487	C₂²	—	92	16	no	—
488	C₂²	C₂×#67288	1	4	yes	complemented
489	C₂²	C₂×D₄×D₂₃	1	2	yes	—
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	—	2	1	no	—
495	C₄	—	2	1	no	—
496	C₄	—	23	4	no	—
497	C₄	—	46	4	no	—
498	C₄	—	46	2	no	—
499	C₄	—	46	2	no	—
500	C₄	C₂×#67288	1	2	yes	complemented
501	C₄	C₂×D₄×D₂₃	1	2	yes	—
502	C₄	C₂×D₄×D₂₃	1	2	yes	—
503	C₂	—	2	2	no	—
504	C₂	—	2	4	no	—
505	C₂	—	4	2	no	—
506	C₂	—	46	4	no	—
507	C₂	—	92	4	no	—
508	C₂	C₂²×D₄×D₂₃	1	1	yes	characteristic
509	C₂	C₂²×#67288	1	1	yes	characteristic
510	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	D₄×#41
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. C₂²×#67288	C₂	semidirect
2. #13093088	C₂	semidirect
3. D₄×Dic₄₆	C₂	semidirect
4. #13093076	C₂	semidirect
5. #13093072	C₂	semidirect
6. #13093068	C₂	semidirect
7. #13093063	C₂	semidirect
8. #13093057	C₂	semidirect
9. D₄×D₉₂	C₂	semidirect
10. D₄×C₂²⋊D₂₃	C₂	semidirect
11. #13092967	C₂	semidirect
12. #13092964	C₂	semidirect
13. #13092928	C₂	semidirect
14. #13092926	C₂	semidirect
15. C₄×#67288	C₂	semidirect
16. C₄×D₄×D₂₃	C₂	semidirect
17. C₂×C₄×D₄×C₂₃	C₂	semidirect
19. C₂³×C₄×C₂₃	C₂²	semidirect
20. C₂²×C₂²⋊D₂₃	C₂²	semidirect
24. C₂×#67288	C₂²	semidirect
25. C₂×#67288	C₂²	semidirect
26. C₂×#67288	C₂²	semidirect
27. C₂×#67288	C₂²	semidirect
28. C₂×#67288	C₂²	semidirect
29. C₂²×D₉₂	C₂²	semidirect
30. C₂²×C₄×D₂₃	C₂²	semidirect
31. C₂²×Dic₄₆	C₂²	semidirect
34. C₄×D₄×C₂₃	C₂²	semidirect
35. C₄×D₄×C₂₃	C₂²	semidirect
36. C₄×D₄×C₂₃	C₂²	semidirect
37. C₄×D₄×C₂₃	C₂²	semidirect
38. C₂×C₄⋊C₄×C₂₃	C₂²	semidirect
39. C₂×C₂²⋊C₄×C₂₃	C₂²	semidirect
40. C₂×C₄²×C₂₃	C₂²	semidirect
41. #10625124	C₂²	semidirect
42. #10625111	C₂²	semidirect
43. #10625110	C₂²	semidirect
44. #10625109	C₂²	semidirect
45. #10625108	C₂²	semidirect
47. #10625101	C₂²	semidirect
48. #10625101	C₂²	semidirect
49. #10625101	C₂²	semidirect
50. #10625101	C₂²	semidirect
51. #10625100	C₂²	semidirect
52. C₄×C₂²⋊D₂₃	C₂²	semidirect
53. C₄×C₂²⋊D₂₃	C₂²	semidirect
54. C₄×C₂²⋊D₂₃	C₂²	semidirect
55. C₄×C₂²⋊D₂₃	C₂²	semidirect
56. #10625097	C₂²	semidirect
57. #10625095	C₂²	semidirect
58. #10625095	C₂²	semidirect
59. #10625067	C₂²	semidirect
60. #10625066	C₂²	semidirect
61. #10625065	C₂²	semidirect
62. #10625064	C₂²	semidirect
63. C₄⋊C₄×D₂₃	C₂²	semidirect
64. #10625059	C₂²	semidirect
65. #10625056	C₂²	semidirect
66. #10625055	C₂²	semidirect
67. #10625055	C₂²	semidirect
68. #10625054	C₂²	semidirect
69. #10625053	C₂²	semidirect
70. (C₂²⋊D₂₃)⋊C₄	C₂²	semidirect
71. C₂²⋊C₄×D₂₃	C₂²	semidirect
72. #10625049	C₂²	semidirect
73. #10625046	C₂²	semidirect
74. #10625045	C₂²	semidirect
75. C₄×D₉₂	C₂²	semidirect
76. C₄×D₉₂	C₂²	semidirect
77. C₄×D₉₂	C₂²	semidirect
78. C₄×D₉₂	C₂²	semidirect
79. #10625043	C₂²	semidirect
80. C₄²×D₂₃	C₂²	semidirect
81. #10625040	C₂²	semidirect
82. C₄×Dic₄₆	C₂²	semidirect
83. C₄×Dic₄₆	C₂²	semidirect
113. #67288	D₄	direct (N × H)
175. D₄×C₂₃	#41	semidirect
183. C₂×C₄×C₂₃	C₂×D₄	semidirect
197. C₂²⋊D₂₃	C₂×D₄	semidirect
207. D₉₂	C₂×D₄	semidirect
213. C₄×D₂₃	C₂×D₄	semidirect
216. Dic₄₆	C₂×D₄	semidirect
227. C₂²×C₂₃	C₂×#41	semidirect
243. C₄×C₂₃	C₂×#41	semidirect
264. C₂×C₄×D₄	D₂₃	semidirect
286. C₂³×C₄	C₂×D₂₃	semidirect
327. C₄×D₄	C₂×D₂₃	semidirect
328. C₄×D₄	C₂×D₂₃	semidirect
329. C₄×D₄	C₂×D₂₃	semidirect
330. C₄×D₄	C₂×D₂₃	semidirect
334. C₂×C₄⋊C₄	C₂×D₂₃	semidirect
336. C₂×C₂²⋊C₄	C₂×D₂₃	semidirect
338. C₂×C₄²	C₂×D₂₃	semidirect
339. C₂₃	D₄×#41	semidirect
445. D₄	#67288	direct (N × H)
464. C₂×C₄	D₄×D₂₃	semidirect
488. C₂²	C₂×#67288	semidirect
500. C₄	C₂×#67288	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#67288	2
#13093088	2
D₄×Dic₄₆	2
#13093076	2
#13093072	2
#13093068	2
#13093063	2
#13093057	2
D₄×D₉₂	2
D₄×C₂²⋊D₂₃	2
#13092967	2
#13092964	2
#13092928	2
#13092926	2
C₄×#67288	2
C₄×D₄×D₂₃	2
C₂×C₄×D₄×C₂₃	2
D₄×#41	23

Subgroups — D4×#67288 #15686885

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄×#67288 #15686885