Subgroups — C₂²×C₃×#878 #11900316

Order 1152.

4017 conjugacy classes of subgroups.

The subgroup lattice has 429 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₃×Dic₃	C₂	1	1	yes	maximal, characteristic
2	C₂³×C₃×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₃²×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₃×#217	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₃×C₄⋊Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₃×Dic₃⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×C₃×Dic₃⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₃×#878	C₂	1	24	yes	maximal, direct product factor
9	C₂²×C₃×C₂²⋊Q₈	—	3	1	no	maximal
10	C₂²×#878	C₃	1	1	yes	maximal, characteristic, direct product factor
11	C₂⁵×C₃²	C₂²	1	1	yes	characteristic
12	C₂³×C₃²×C₄	C₂²	1	1	yes	characteristic
13	C₂³×C₃²×C₄	C₂²	1	1	yes	characteristic
14	C₂³×C₃×Dic₃	—	2	8	no	—
15	C₂³×C₃×Dic₃	C₂²	1	1	yes	characteristic
16	C₂³×C₃×Dic₃	C₂²	1	1	yes	characteristic
17	C₂³×C₃×Dic₃	C₂²	1	1	yes	characteristic
18	C₂³×C₃×Dic₃	C₂²	1	12	yes	—
19	C₂³×C₃×Dic₃	C₂²	1	1	yes	characteristic
20	C₂²×C₃×Dic₆	—	2	8	no	—
21	C₂²×C₃×Dic₆	C₂²	1	12	yes	complemented
22	C₂×C₃²×C₂²⋊C₄	C₂²	1	12	yes	—
23	C₂×C₃×#217	C₂²	1	12	yes	—
24	C₂×C₃×C₄⋊Dic₃	C₂²	1	12	yes	complemented
25	C₂×C₃×Dic₃⋊C₄	C₂²	1	12	yes	complemented
26	C₂×C₃×Dic₃⋊C₄	C₂²	1	12	yes	complemented
27	C₃×#878	C₂²	1	64	yes	direct product factor
28	C₂³×C₃×Q₈	—	3	1	no	—
29	C₂⁴×C₃×C₄	—	3	1	no	—
30	C₂⁴×Dic₃	C₂×C₃	1	1	yes	characteristic
31	C₂³×Dic₆	C₂×C₃	1	1	yes	characteristic, complemented
32	C₂×C₃×C₂²⋊Q₈	—	3	24	no	—
33	C₂²×C₃×C₄⋊C₄	—	3	1	no	—
34	C₂²×C₃×C₄⋊C₄	—	3	1	no	—
35	C₂²×C₃×C₄⋊C₄	—	3	1	no	—
36	C₂²×C₃×C₂²⋊C₄	—	2	1	no	—
37	C₂²×C₃×C₂²⋊C₄	—	3	1	no	—
38	C₂²×C₃×C₂²⋊C₄	D₃	1	1	yes	characteristic
39	C₂²×C₃×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic
40	C₂²×#217	C₂×C₃	1	1	yes	characteristic
41	C₂²×C₄⋊Dic₃	C₂×C₃	1	1	yes	characteristic, complemented
42	C₂²×Dic₃⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
43	C₂²×Dic₃⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
44	C₂×#878	C₂×C₃	1	24	yes	direct product factor
45	C₂⁴×C₃²	—	2	4	no	—
46	C₂⁴×C₃²	—	2	4	no	—
47	C₂⁴×C₃²	Q₈	1	8	yes	complemented
48	C₂⁴×C₃²	C₂³	1	6	yes	—
49	C₂⁴×C₃²	C₂³	1	1	yes	characteristic
50	C₂²×C₃²×C₄	—	2	4	no	—
51	C₂²×C₃²×C₄	—	2	4	no	—
52	C₂²×C₃²×C₄	C₂³	1	6	yes	—
53	C₂²×C₃²×C₄	C₂³	1	6	yes	—
54	C₂²×C₃×Dic₃	—	2	4	no	—
55	C₂²×C₃×Dic₃	—	2	4	no	—
56	C₂²×C₃×Dic₃	—	2	4	no	—
57	C₂²×C₃×Dic₃	—	2	48	no	—
58	C₂²×C₃×Dic₃	D₄	1	8	yes	—
59	C₂²×C₃×Dic₃	C₂³	1	16	yes	—
60	C₂²×C₃×Dic₃	C₂³	1	6	yes	—
61	C₂²×C₃×Dic₃	C₂³	1	6	yes	—
62	C₂²×C₃×Dic₃	C₂³	1	6	yes	—
63	C₂²×C₃×Dic₃	C₂³	1	6	yes	—
64	C₂×C₃×Dic₆	—	2	48	no	—
65	C₂×C₃×Dic₆	C₂³	1	16	yes	complemented
66	C₃²×C₂²⋊C₄	C₂³	1	16	yes	—
67	C₃×#217	C₂³	1	16	yes	—
68	C₃×C₄⋊Dic₃	C₂³	1	16	yes	complemented
69	C₃×Dic₃⋊C₄	C₂³	1	16	yes	complemented
70	C₃×Dic₃⋊C₄	C₂³	1	16	yes	complemented
71	C₂²×C₂²⋊Q₈	—	3	1	no	Sylow
72	C₂⁵×C₃	—	2	1	no	—
73	C₂⁵×C₃	C₂×D₃	1	1	yes	characteristic
74	C₂⁵×C₃	C₂²×C₃	1	1	yes	characteristic
75	C₂²×C₃×Q₈	—	3	12	no	—
76	C₂²×C₃×Q₈	—	6	8	no	—
77	C₂³×C₃×C₄	—	2	1	no	—
78	C₂³×C₃×C₄	—	2	1	no	—
79	C₂³×C₃×C₄	—	3	1	no	—
80	C₂³×C₃×C₄	—	3	12	no	—
81	C₂³×C₃×C₄	—	3	1	no	—
82	C₂³×C₃×C₄	—	3	1	no	—
83	C₂³×C₃×C₄	—	3	1	no	—
84	C₂³×C₃×C₄	—	6	8	no	—
85	C₂³×C₃×C₄	C₂×D₃	1	1	yes	characteristic
86	C₂³×C₃×C₄	C₂×D₃	1	1	yes	characteristic
87	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
88	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
89	C₂³×Dic₃	—	2	8	no	—
90	C₂³×Dic₃	C₂²×C₃	1	1	yes	characteristic
91	C₂³×Dic₃	C₂²×C₃	1	12	yes	—
92	C₂³×Dic₃	C₂²×C₃	1	1	yes	characteristic
93	C₂³×Dic₃	C₂²×C₃	1	1	yes	characteristic
94	C₂³×Dic₃	C₂²×C₃	1	1	yes	characteristic
95	C₂²×Dic₆	—	2	8	no	—
96	C₂²×Dic₆	C₂²×C₃	1	12	yes	complemented
97	C₃×C₂²⋊Q₈	—	3	64	no	—
98	C₂×C₃×C₄⋊C₄	—	3	12	no	—
99	C₂×C₃×C₄⋊C₄	—	3	12	no	—
100	C₂×C₃×C₄⋊C₄	—	3	12	no	—
101	C₂×C₃×C₂²⋊C₄	—	2	12	no	—
102	C₂×C₃×C₂²⋊C₄	—	3	12	no	—
103	C₂×C₃×C₂²⋊C₄	C₂×D₃	1	12	yes	—
104	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	12	yes	—
105	C₂×#217	C₂²×C₃	1	12	yes	—
106	C₂×C₄⋊Dic₃	C₂²×C₃	1	12	yes	complemented
107	C₂×Dic₃⋊C₄	C₂²×C₃	1	12	yes	complemented
108	C₂×Dic₃⋊C₄	C₂²×C₃	1	12	yes	complemented
109	#878	C₂²×C₃	1	64	yes	direct product factor
110	C₂³×C₃²	—	2	32	no	—
111	C₂³×C₃²	—	2	12	no	—
112	C₂³×C₃²	—	2	12	no	—
113	C₂³×C₃²	C₂×D₄	1	4	yes	—
114	C₂³×C₃²	C₂×Q₈	1	4	yes	—
115	C₂³×C₃²	C₂×Q₈	1	24	yes	complemented
116	C₂³×C₃²	#41	1	4	yes	—
117	C₂³×C₃²	C₂⁴	1	4	yes	—
118	C₂³×C₃²	C₂⁴	1	3	yes	—
119	C₂×C₃²×C₄	—	2	12	no	—
120	C₂×C₃²×C₄	—	2	12	no	—
121	C₂×C₃²×C₄	C₂⁴	1	4	yes	—
122	C₂×C₃²×C₄	C₂⁴	1	4	yes	—
123	C₂×C₃×Dic₃	—	2	12	no	—
124	C₂×C₃×Dic₃	—	2	12	no	—
125	C₂×C₃×Dic₃	—	2	12	no	—
126	C₂×C₃×Dic₃	—	2	32	no	—
127	C₂×C₃×Dic₃	C₂×D₄	1	24	yes	—
128	C₂×C₃×Dic₃	C₂⁴	1	4	yes	—
129	C₂×C₃×Dic₃	C₂⁴	1	4	yes	—
130	C₂×C₃×Dic₃	C₂⁴	1	4	yes	—
131	C₂×C₃×Dic₃	C₂⁴	1	4	yes	—
132	C₃×Dic₆	—	2	32	no	—
133	C₂³×Q₈	—	3	1	no	—
134	C₂⁴×C₄	—	3	1	no	—
135	C₂×C₂²⋊Q₈	—	3	24	no	—
136	C₂²×C₄⋊C₄	—	3	1	no	—
137	C₂²×C₄⋊C₄	—	3	1	no	—
138	C₂²×C₄⋊C₄	—	3	1	no	—
139	C₂²×C₂²⋊C₄	—	3	1	no	—
140	C₂²×C₂²⋊C₄	C₃×D₃	1	1	yes	characteristic
141	C₂⁴×C₃	—	2	4	no	—
142	C₂⁴×C₃	—	2	4	no	—
143	C₂⁴×C₃	—	2	4	no	—
144	C₂⁴×C₃	—	2	4	no	—
145	C₂⁴×C₃	—	2	8	no	—
146	C₂⁴×C₃	—	2	1	no	—
147	C₂⁴×C₃	—	2	6	no	—
148	C₂⁴×C₃	—	4	4	no	—
149	C₂⁴×C₃	—	4	4	no	—
150	C₂⁴×C₃	Dic₆	1	8	yes	complemented
151	C₂⁴×C₃	C₃×Q₈	1	8	yes	complemented
152	C₂⁴×C₃	C₂²×D₃	1	6	yes	—
153	C₂⁴×C₃	C₂²×D₃	1	1	yes	characteristic
154	C₂⁴×C₃	C₂³×C₃	1	6	yes	—
155	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
156	C₂×C₃×Q₈	—	3	16	no	—
157	C₂×C₃×Q₈	—	6	48	no	—
158	C₂²×C₃×C₄	—	2	4	no	—
159	C₂²×C₃×C₄	—	2	4	no	—
160	C₂²×C₃×C₄	—	2	4	no	—
161	C₂²×C₃×C₄	—	2	4	no	—
162	C₂²×C₃×C₄	—	2	6	no	—
163	C₂²×C₃×C₄	—	2	6	no	—
164	C₂²×C₃×C₄	—	3	8	no	—
165	C₂²×C₃×C₄	—	3	6	no	—
166	C₂²×C₃×C₄	—	3	6	no	—
167	C₂²×C₃×C₄	—	3	6	no	—
168	C₂²×C₃×C₄	—	3	6	no	—
169	C₂²×C₃×C₄	—	3	16	no	—
170	C₂²×C₃×C₄	—	4	4	no	—
171	C₂²×C₃×C₄	—	4	4	no	—
172	C₂²×C₃×C₄	—	6	48	no	—
173	C₂²×C₃×C₄	—	6	4	no	—
174	C₂²×C₃×C₄	—	6	4	no	—
175	C₂²×C₃×C₄	—	6	4	no	—
176	C₂²×C₃×C₄	C₂²×D₃	1	6	yes	—
177	C₂²×C₃×C₄	C₂²×D₃	1	6	yes	—
178	C₂²×C₃×C₄	C₂³×C₃	1	6	yes	—
179	C₂²×C₃×C₄	C₂³×C₃	1	6	yes	—
180	C₂²×Dic₃	—	2	4	no	—
181	C₂²×Dic₃	—	2	4	no	—
182	C₂²×Dic₃	—	2	4	no	—
183	C₂²×Dic₃	—	2	48	no	—
184	C₂²×Dic₃	C₃×D₄	1	8	yes	—
185	C₂²×Dic₃	C₂³×C₃	1	16	yes	—
186	C₂²×Dic₃	C₂³×C₃	1	6	yes	—
187	C₂²×Dic₃	C₂³×C₃	1	6	yes	—
188	C₂²×Dic₃	C₂³×C₃	1	6	yes	—
189	C₂²×Dic₃	C₂³×C₃	1	6	yes	—
190	C₂×Dic₆	—	2	48	no	—
191	C₂×Dic₆	C₂³×C₃	1	16	yes	complemented
192	C₃×C₄⋊C₄	—	3	16	no	—
193	C₃×C₄⋊C₄	—	3	16	no	—
194	C₃×C₄⋊C₄	—	3	16	no	—
195	C₃×C₂²⋊C₄	—	2	16	no	—
196	C₃×C₂²⋊C₄	—	3	16	no	—
197	C₃×C₂²⋊C₄	C₂²×D₃	1	16	yes	—
198	C₃×C₂²⋊C₄	C₂³×C₃	1	16	yes	—
199	#217	C₂³×C₃	1	16	yes	—
200	C₄⋊Dic₃	C₂³×C₃	1	16	yes	complemented
201	Dic₃⋊C₄	C₂³×C₃	1	16	yes	complemented
202	Dic₃⋊C₄	C₂³×C₃	1	16	yes	complemented
203	C₂²×C₃²	—	2	48	no	—
204	C₂²×C₃²	—	2	4	no	—
205	C₂²×C₃²	—	2	4	no	—
206	C₂²×C₃²	C₂²⋊Q₈	1	16	yes	complemented
207	C₂²×C₃²	C₂²×D₄	1	6	yes	—
208	C₂²×C₃²	C₂²×Q₈	1	6	yes	—
209	C₂²×C₃²	C₂²×Q₈	1	8	yes	complemented
210	C₂²×C₃²	C₂×#41	1	6	yes	—
211	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
212	C₃²×C₄	—	2	4	no	—
213	C₃²×C₄	—	2	4	no	—
214	C₃×Dic₃	—	2	4	no	—
215	C₃×Dic₃	—	2	4	no	—
216	C₃×Dic₃	—	2	4	no	—
217	C₃×Dic₃	C₂²×D₄	1	8	yes	—
218	C₂⁵	C₂×C₃×D₃	1	1	yes	characteristic
219	C₂²×Q₈	—	3	12	no	—
220	C₂²×Q₈	—	6	8	no	—
221	C₂³×C₄	—	3	1	no	—
222	C₂³×C₄	—	3	1	no	—
223	C₂³×C₄	—	3	1	no	—
224	C₂³×C₄	—	3	1	no	—
225	C₂³×C₄	—	3	12	no	—
226	C₂³×C₄	—	6	8	no	—
227	C₂³×C₄	C₂×C₃×D₃	1	1	yes	characteristic
228	C₂³×C₄	C₂×C₃×D₃	1	1	yes	characteristic
229	C₂²⋊Q₈	—	3	64	no	—
230	C₂×C₄⋊C₄	—	3	12	no	—
231	C₂×C₄⋊C₄	—	3	12	no	—
232	C₂×C₄⋊C₄	—	3	12	no	—
233	C₂×C₂²⋊C₄	—	3	12	no	—
234	C₂×C₂²⋊C₄	C₂×C₃×D₃	1	12	yes	—
235	C₂³×C₃	—	2	32	no	—
236	C₂³×C₃	—	2	32	no	—
237	C₂³×C₃	—	2	12	no	—
238	C₂³×C₃	—	2	12	no	—
239	C₂³×C₃	—	2	12	no	—
240	C₂³×C₃	—	2	12	no	—
241	C₂³×C₃	—	2	3	no	—
242	C₂³×C₃	—	2	4	no	—
243	C₂³×C₃	—	2	4	no	—
244	C₂³×C₃	—	2	24	no	—
245	C₂³×C₃	—	2	4	no	—
246	C₂³×C₃	—	2	4	no	—
247	C₂³×C₃	—	4	32	no	—
248	C₂³×C₃	—	4	12	no	—
249	C₂³×C₃	—	4	12	no	—
250	C₂³×C₃	C₂×Dic₆	1	4	yes	—
251	C₂³×C₃	C₂×Dic₆	1	24	yes	complemented
252	C₂³×C₃	D₃×D₄	1	4	yes	—
253	C₂³×C₃	#237	1	4	yes	—
254	C₂³×C₃	C₂×C₃×D₄	1	4	yes	—
255	C₂³×C₃	C₂×C₃×Q₈	1	4	yes	—
256	C₂³×C₃	C₂×C₃×Q₈	1	24	yes	complemented
257	C₂³×C₃	C₃×#41	1	4	yes	—
258	C₂³×C₃	C₂³×D₃	1	4	yes	—
259	C₂³×C₃	C₂³×D₃	1	3	yes	—
260	C₂³×C₃	C₂⁴×C₃	1	4	yes	—
261	C₂³×C₃	C₂⁴×C₃	1	3	yes	—
262	C₃×Q₈	—	6	32	no	—
263	C₂×C₃×C₄	—	2	12	no	—
264	C₂×C₃×C₄	—	2	12	no	—
265	C₂×C₃×C₄	—	2	12	no	—
266	C₂×C₃×C₄	—	2	12	no	—
267	C₂×C₃×C₄	—	2	4	no	—
268	C₂×C₃×C₄	—	2	4	no	—
269	C₂×C₃×C₄	—	3	24	no	—
270	C₂×C₃×C₄	—	3	4	no	—
271	C₂×C₃×C₄	—	3	4	no	—
272	C₂×C₃×C₄	—	3	4	no	—
273	C₂×C₃×C₄	—	3	4	no	—
274	C₂×C₃×C₄	—	4	12	no	—
275	C₂×C₃×C₄	—	4	12	no	—
276	C₂×C₃×C₄	—	6	32	no	—
277	C₂×C₃×C₄	—	6	12	no	—
278	C₂×C₃×C₄	—	6	12	no	—
279	C₂×C₃×C₄	—	6	12	no	—
280	C₂×C₃×C₄	C₂³×D₃	1	4	yes	—
281	C₂×C₃×C₄	C₂³×D₃	1	4	yes	—
282	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
283	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
284	C₂×Dic₃	—	2	12	no	—
285	C₂×Dic₃	—	2	12	no	—
286	C₂×Dic₃	—	2	12	no	—
287	C₂×Dic₃	—	2	32	no	—
288	C₂×Dic₃	C₂×C₃×D₄	1	24	yes	—
289	C₂×Dic₃	C₂⁴×C₃	1	4	yes	—
290	C₂×Dic₃	C₂⁴×C₃	1	4	yes	—
291	C₂×Dic₃	C₂⁴×C₃	1	4	yes	—
292	C₂×Dic₃	C₂⁴×C₃	1	4	yes	—
293	Dic₆	—	2	32	no	—
294	C₂×C₃²	—	2	8	no	—
295	C₂×C₃²	C₂×C₂²⋊Q₈	1	12	yes	complemented
296	C₂×C₃²	C₂³×D₄	1	1	yes	characteristic
297	C₂×C₃²	C₂³×Q₈	1	1	yes	characteristic
298	C₂×C₃²	C₂²×#41	1	1	yes	characteristic
299	C₂⁴	—	2	4	no	—
300	C₂⁴	—	2	4	no	—
301	C₂⁴	C₃×Dic₆	1	8	yes	complemented
302	C₂⁴	C₂²×C₃×D₃	1	6	yes	—
303	C₂⁴	C₂²×C₃×D₃	1	1	yes	characteristic
304	C₂×Q₈	—	3	16	no	—
305	C₂×Q₈	—	6	48	no	—
306	C₂²×C₄	—	2	4	no	—
307	C₂²×C₄	—	2	4	no	—
308	C₂²×C₄	—	3	6	no	—
309	C₂²×C₄	—	3	8	no	—
310	C₂²×C₄	—	3	6	no	—
311	C₂²×C₄	—	3	6	no	—
312	C₂²×C₄	—	3	6	no	—
313	C₂²×C₄	—	3	16	no	—
314	C₂²×C₄	—	6	48	no	—
315	C₂²×C₄	—	6	4	no	—
316	C₂²×C₄	—	6	4	no	—
317	C₂²×C₄	—	6	4	no	—
318	C₂²×C₄	C₂²×C₃×D₃	1	6	yes	—
319	C₂²×C₄	C₂²×C₃×D₃	1	6	yes	—
320	C₄⋊C₄	—	3	16	no	—
321	C₄⋊C₄	—	3	16	no	—
322	C₄⋊C₄	—	3	16	no	—
323	C₂²⋊C₄	—	3	16	no	—
324	C₂²⋊C₄	C₂²×C₃×D₃	1	16	yes	—
325	C₂²×C₃	—	2	4	no	—
326	C₂²×C₃	—	2	4	no	—
327	C₂²×C₃	—	2	4	no	—
328	C₂²×C₃	—	2	4	no	—
329	C₂²×C₃	—	2	48	no	—
330	C₂²×C₃	—	2	48	no	—
331	C₂²×C₃	—	2	16	no	—
332	C₂²×C₃	—	2	6	no	—
333	C₂²×C₃	—	2	8	no	—
334	C₂²×C₃	—	2	6	no	—
335	C₂²×C₃	—	2	6	no	—
336	C₂²×C₃	—	2	1	no	—
337	C₂²×C₃	—	4	4	no	—
338	C₂²×C₃	—	4	4	no	—
339	C₂²×C₃	—	4	48	no	—
340	C₂²×C₃	#878	1	16	yes	direct product factor
341	C₂²×C₃	C₃×C₂²⋊Q₈	1	16	yes	complemented
342	C₂²×C₃	C₂²×Dic₆	1	6	yes	—
343	C₂²×C₃	C₂²×Dic₆	1	8	yes	complemented
344	C₂²×C₃	C₂×D₃×D₄	1	6	yes	—
345	C₂²×C₃	C₂×#237	1	6	yes	—
346	C₂²×C₃	C₂²×C₃×D₄	1	6	yes	—
347	C₂²×C₃	C₂²×C₃×Q₈	1	6	yes	—
348	C₂²×C₃	C₂²×C₃×Q₈	1	8	yes	complemented
349	C₂²×C₃	C₂×C₃×#41	1	6	yes	—
350	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
351	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
352	C₃×C₄	—	2	4	no	—
353	C₃×C₄	—	2	4	no	—
354	C₃×C₄	—	2	4	no	—
355	C₃×C₄	—	2	4	no	—
356	C₃×C₄	—	3	8	no	—
357	C₃×C₄	—	4	4	no	—
358	C₃×C₄	—	4	4	no	—
359	C₃×C₄	—	6	4	no	—
360	C₃×C₄	—	6	4	no	—
361	C₃×C₄	—	6	4	no	—
362	Dic₃	—	2	4	no	—
363	Dic₃	—	2	4	no	—
364	Dic₃	—	2	4	no	—
365	Dic₃	C₂²×C₃×D₄	1	8	yes	—
366	C₃²	C₂²×C₂²⋊Q₈	1	1	yes	characteristic, complemented, Sylow
367	C₂³	—	2	32	no	—
368	C₂³	—	2	12	no	—
369	C₂³	—	2	12	no	—
370	C₂³	C₂×C₃×Dic₆	1	4	yes	—
371	C₂³	C₂×C₃×Dic₆	1	24	yes	complemented
372	C₂³	C₃×D₃×D₄	1	4	yes	—
373	C₂³	C₃×#237	1	4	yes	—
374	C₂³	C₂³×C₃×D₃	1	4	yes	—
375	C₂³	C₂³×C₃×D₃	1	3	yes	—
376	Q₈	—	6	32	no	—
377	C₂×C₄	—	2	12	no	—
378	C₂×C₄	—	2	12	no	—
379	C₂×C₄	—	3	24	no	—
380	C₂×C₄	—	3	4	no	—
381	C₂×C₄	—	3	4	no	—
382	C₂×C₄	—	3	4	no	—
383	C₂×C₄	—	3	4	no	—
384	C₂×C₄	—	6	32	no	—
385	C₂×C₄	—	6	12	no	—
386	C₂×C₄	—	6	12	no	—
387	C₂×C₄	—	6	12	no	—
388	C₂×C₄	C₂³×C₃×D₃	1	4	yes	—
389	C₂×C₄	C₂³×C₃×D₃	1	4	yes	—
390	C₂×C₃	—	2	8	no	—
391	C₂×C₃	—	2	8	no	—
392	C₂×C₃	—	2	1	no	—
393	C₂×C₃	—	2	1	no	—
394	C₂×C₃	—	2	1	no	—
395	C₂×C₃	—	2	12	no	—
396	C₂×C₃	—	4	8	no	—
397	C₂×C₃	C₂×#878	1	12	yes	direct product factor
398	C₂×C₃	C₂×C₃×C₂²⋊Q₈	1	12	yes	complemented
399	C₂×C₃	C₂³×Dic₆	1	1	yes	characteristic
400	C₂×C₃	C₂²×D₃×D₄	1	1	yes	characteristic
401	C₂×C₃	C₂²×#237	1	1	yes	characteristic
402	C₂×C₃	C₂³×C₃×D₄	1	1	yes	characteristic
403	C₂×C₃	C₂³×C₃×Q₈	1	1	yes	characteristic
404	C₂×C₃	C₂²×C₃×#41	1	1	yes	characteristic
405	C₂²	—	2	4	no	—
406	C₂²	—	2	4	no	—
407	C₂²	—	2	48	no	—
408	C₂²	C₃×#878	1	16	yes	direct product factor
409	C₂²	C₂²×C₃×Dic₆	1	6	yes	—
410	C₂²	C₂²×C₃×Dic₆	1	8	yes	complemented
411	C₂²	C₂×C₃×D₃×D₄	1	6	yes	—
412	C₂²	C₂×C₃×#237	1	6	yes	—
413	C₂²	C₂⁴×C₃×D₃	1	1	yes	characteristic
414	C₄	—	2	4	no	—
415	C₄	—	2	4	no	—
416	C₄	—	3	8	no	—
417	C₄	—	6	4	no	—
418	C₄	—	6	4	no	—
419	C₄	—	6	4	no	—
420	C₃	—	2	1	no	—
421	C₃	C₂²×#878	1	1	yes	characteristic, direct product factor
422	C₃	C₂²×C₃×C₂²⋊Q₈	1	1	yes	characteristic, complemented
423	C₂	—	2	8	no	—
424	C₂	C₂×C₃×#878	1	12	yes	direct product factor
425	C₂	C₂³×C₃×Dic₆	1	1	yes	characteristic
426	C₂	C₂²×C₃×D₃×D₄	1	1	yes	characteristic
427	C₂	C₂²×C₃×#237	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴×C₃	C₂²×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₃
Fitting	C₂²×C₃²×C₂²⋊C₄	C₂
socle	C₂⁴×C₃²	C₂³
prime radical	C₂⁵×C₃²	C₂²
hypercenter	C₂²×C₃×C₂²⋊C₄	D₃
hypocenter	C₃	C₂²×C₃×C₂²⋊Q₈
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂⁴×C₃ ◁ C₂²×C₃×C₂²⋊C₄

Complements

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

N	H ≅ G/N	type
2. C₂³×C₃×Dic₆	C₂	semidirect
5. C₂²×C₃×C₄⋊Dic₃	C₂	semidirect
6. C₂²×C₃×Dic₃⋊C₄	C₂	semidirect
7. C₂²×C₃×Dic₃⋊C₄	C₂	semidirect
8. C₂×C₃×#878	C₂	direct (N × H)
10. C₂²×#878	C₃	direct (N × H)
21. C₂²×C₃×Dic₆	C₂²	semidirect
24. C₂×C₃×C₄⋊Dic₃	C₂²	semidirect
25. C₂×C₃×Dic₃⋊C₄	C₂²	semidirect
26. C₂×C₃×Dic₃⋊C₄	C₂²	semidirect
27. C₃×#878	C₂²	direct (N × H)
31. C₂³×Dic₆	C₂×C₃	semidirect
41. C₂²×C₄⋊Dic₃	C₂×C₃	semidirect
42. C₂²×Dic₃⋊C₄	C₂×C₃	semidirect
43. C₂²×Dic₃⋊C₄	C₂×C₃	semidirect
44. C₂×#878	C₂×C₃	direct (N × H)
47. C₂⁴×C₃²	Q₈	semidirect
65. C₂×C₃×Dic₆	C₂³	semidirect
68. C₃×C₄⋊Dic₃	C₂³	semidirect
69. C₃×Dic₃⋊C₄	C₂³	semidirect
70. C₃×Dic₃⋊C₄	C₂³	semidirect
96. C₂²×Dic₆	C₂²×C₃	semidirect
106. C₂×C₄⋊Dic₃	C₂²×C₃	semidirect
107. C₂×Dic₃⋊C₄	C₂²×C₃	semidirect
108. C₂×Dic₃⋊C₄	C₂²×C₃	semidirect
109. #878	C₂²×C₃	direct (N × H)
115. C₂³×C₃²	C₂×Q₈	semidirect
150. C₂⁴×C₃	Dic₆	semidirect
151. C₂⁴×C₃	C₃×Q₈	semidirect
191. C₂×Dic₆	C₂³×C₃	semidirect
200. C₄⋊Dic₃	C₂³×C₃	semidirect
201. Dic₃⋊C₄	C₂³×C₃	semidirect
202. Dic₃⋊C₄	C₂³×C₃	semidirect
206. C₂²×C₃²	C₂²⋊Q₈	semidirect
209. C₂²×C₃²	C₂²×Q₈	semidirect
251. C₂³×C₃	C₂×Dic₆	semidirect
256. C₂³×C₃	C₂×C₃×Q₈	semidirect
295. C₂×C₃²	C₂×C₂²⋊Q₈	semidirect
301. C₂⁴	C₃×Dic₆	semidirect
340. C₂²×C₃	#878	direct (N × H)
341. C₂²×C₃	C₃×C₂²⋊Q₈	semidirect
343. C₂²×C₃	C₂²×Dic₆	semidirect
348. C₂²×C₃	C₂²×C₃×Q₈	semidirect
366. C₃²	C₂²×C₂²⋊Q₈	semidirect
371. C₂³	C₂×C₃×Dic₆	semidirect
397. C₂×C₃	C₂×#878	direct (N × H)
398. C₂×C₃	C₂×C₃×C₂²⋊Q₈	semidirect
408. C₂²	C₃×#878	direct (N × H)
410. C₂²	C₂²×C₃×Dic₆	semidirect
421. C₃	C₂²×#878	direct (N × H)
422. C₃	C₂²×C₃×C₂²⋊Q₈	semidirect
424. C₂	C₂×C₃×#878	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×C₃×Dic₃	2
C₂³×C₃×Dic₆	2
C₂²×C₃²×C₂²⋊C₄	2
C₂²×C₃×#217	2
C₂²×C₃×C₄⋊Dic₃	2
C₂²×C₃×Dic₃⋊C₄	2
C₂×C₃×#878	2
C₂²×C₃×C₂²⋊Q₈	3
C₂²×#878	3

Subgroups — C22×C3×#878 #11900316

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃×#878 #11900316