Subgroups — #11790038

Order 1152.

589 conjugacy classes of subgroups.

The subgroup lattice has 375 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊(C₃⋊(C₃⋊C₈))	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄×C₄⋊Dic₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×C₄×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₃⋊(C₃⋊C₈)	C₂	1	2	yes	maximal
5	#10589155	C₂	1	2	yes	maximal
6	#69786	—	3	1	no	maximal
7	#69484	—	3	1	no	maximal
8	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
9	C₂²×C₃⋊(C₃⋊C₈)	C₂²	1	2	yes	—
10	C₂×C₃×C₄⋊Dic₃	C₄	1	1	yes	characteristic
11	C₂×C₃×C₄⋊Dic₃	C₄	1	1	yes	characteristic
12	C₂×C₃×C₄×Dic₃	C₂²	1	2	yes	—
13	C₂²×C₃×C₃⋊C₈	C₂²	1	1	yes	characteristic
14	C₂²×C₃×C₃⋊C₈	C₂²	1	1	yes	characteristic
15	C₄⋊(C₃⋊(C₃⋊C₈))	—	2	2	no	—
16	C₃×C₃⋊#95	C₄	1	2	yes	—
17	C₃×C₄×C₃⋊C₈	—	2	2	no	—
18	Dic₃⋊(C₃⋊C₈)	—	2	4	no	—
19	C₂×C₃×C₄×C₈	—	3	1	no	—
20	C₃×C₄×C₄⋊C₄	—	3	1	no	—
21	C₂×Dic₃⋊C₈	—	3	2	no	—
22	C₄×C₄⋊Dic₃	D₃	1	1	yes	characteristic
23	C₂×C₄⋊(C₃⋊C₈)	—	3	1	no	—
24	C₂×C₄⋊(C₃⋊C₈)	—	3	1	no	—
25	C₂×C₄⋊(C₃⋊C₈)	—	3	2	no	—
26	C₂×C₄⋊(C₃⋊C₈)	—	6	1	no	—
27	C₂×C₄×C₃⋊C₈	D₃	1	1	yes	characteristic
28	#4550	—	3	2	no	—
29	#4524	—	3	2	no	—
30	C₂²×C₃²×C₄	C₂×C₄	1	1	yes	characteristic
31	C₂²×C₃²×C₄	C₂×C₄	1	1	yes	characteristic
32	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
33	C₂²×C₃×Dic₃	C₂×C₄	1	2	yes	—
34	C₂²×C₃×Dic₃	C₂×C₄	1	2	yes	—
35	C₃²×C₄²	D₄	1	2	yes	—
36	C₃²×C₄²	Q₈	1	2	yes	—
37	C₂×C₃⋊(C₃⋊C₈)	—	2	2	no	—
38	C₂×C₃⋊(C₃⋊C₈)	—	2	2	no	—
39	C₂×C₃⋊(C₃⋊C₈)	—	2	2	no	—
40	C₃×C₄⋊Dic₃	—	2	2	no	—
41	C₃×C₄⋊Dic₃	C₈	1	4	yes	complemented
42	C₃×C₄×Dic₃	—	2	2	no	—
43	C₃×C₄×Dic₃	—	2	2	no	—
44	C₂×C₃×C₃⋊C₈	—	2	1	no	—
45	C₂×C₃×C₃⋊C₈	—	2	1	no	—
46	C₂×C₃×C₃⋊C₈	—	2	1	no	—
47	C₂×C₃×C₃⋊C₈	—	2	1	no	—
48	C₂×C₃×C₃⋊C₈	D₄	1	2	yes	—
49	C₂×C₃×C₃⋊C₈	Q₈	1	2	yes	—
50	#1939	—	9	1	no	Sylow
51	C₂²×C₃×C₈	—	3	1	no	—
52	C₂²×C₃×C₈	—	3	1	no	—
53	C₂×C₃×C₄⋊C₄	—	3	1	no	—
54	C₂×C₃×C₄⋊C₄	—	3	1	no	—
55	C₂×C₃×C₄²	—	2	1	no	—
56	C₂×C₃×C₄²	—	3	2	no	—
57	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
58	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
59	C₂×C₄⋊Dic₃	Dic₃	1	1	yes	characteristic
60	C₂×C₄⋊Dic₃	Dic₃	1	1	yes	characteristic
61	C₂×C₄×Dic₃	C₂×D₃	1	2	yes	—
62	C₂²×C₃⋊C₈	—	3	2	no	—
63	C₂²×C₃⋊C₈	—	3	2	no	—
64	C₂²×C₃⋊C₈	—	6	2	no	—
65	C₂²×C₃⋊C₈	C₂×D₃	1	1	yes	characteristic
66	C₂²×C₃⋊C₈	C₂×D₃	1	1	yes	characteristic
67	C₃×C₄×C₈	—	6	2	no	—
68	C₃×#95	—	3	2	no	—
69	C₃⋊#95	Dic₃	1	2	yes	—
70	Dic₃⋊C₈	—	6	4	no	—
71	C₄⋊(C₃⋊C₈)	—	6	4	no	—
72	C₄⋊(C₃⋊C₈)	—	6	2	no	—
73	C₄⋊(C₃⋊C₈)	—	6	2	no	—
74	C₄⋊(C₃⋊C₈)	—	6	4	no	—
75	C₄×C₃⋊C₈	—	2	2	no	—
76	C₂³×C₃²	C₂²×C₄	1	1	yes	characteristic
77	C₂×C₃²×C₄	—	2	1	no	—
78	C₂×C₃²×C₄	—	2	1	no	—
79	C₂×C₃²×C₄	C₄⋊C₄	1	2	yes	—
80	C₂×C₃²×C₄	C₄⋊C₄	1	2	yes	—
81	C₂×C₃²×C₄	C₂×C₈	1	2	yes	—
82	C₂×C₃²×C₄	M₁₆	1	2	yes	—
83	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
84	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
85	C₂×C₃²×C₄	C₂×Q₈	1	1	yes	characteristic
86	C₂×C₃²×C₄	C₂×Q₈	1	1	yes	characteristic
87	C₂×C₃²×C₄	#41	1	1	yes	characteristic
88	C₂×C₃²×C₄	#41	1	1	yes	characteristic
89	C₂×C₃×Dic₃	—	2	2	no	—
90	C₂×C₃×Dic₃	—	2	2	no	—
91	C₂×C₃×Dic₃	—	2	2	no	—
92	C₂×C₃×Dic₃	—	2	2	no	—
93	C₂×C₃×Dic₃	—	2	2	no	—
94	C₂×C₃×Dic₃	C₂×C₈	1	4	yes	—
95	C₃⋊(C₃⋊C₈)	—	4	2	no	—
96	C₃×C₃⋊C₈	—	2	2	no	—
97	C₃×C₃⋊C₈	—	2	2	no	—
98	C₂×C₄⋊C₈	—	9	2	no	—
99	C₂×C₄⋊C₈	—	9	1	no	—
100	C₂×C₄×C₈	—	3	1	no	—
101	C₄×C₄⋊C₄	—	3	1	no	—
102	#336	—	9	2	no	—
103	C₂²×C₃×C₄	—	2	1	no	—
104	C₂²×C₃×C₄	—	2	1	no	—
105	C₂²×C₃×C₄	—	2	1	no	—
106	C₂²×C₃×C₄	—	3	2	no	—
107	C₂²×C₃×C₄	—	3	2	no	—
108	C₂²×C₃×C₄	C₄×D₃	1	1	yes	characteristic
109	C₂²×C₃×C₄	C₄×D₃	1	1	yes	characteristic
110	C₂²×C₃×C₄	C₂×Dic₃	1	1	yes	characteristic
111	C₂²×C₃×C₄	C₂×Dic₃	1	1	yes	characteristic
112	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
113	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
114	C₂²×Dic₃	C₂×Dic₃	1	2	yes	—
115	C₂²×Dic₃	C₂×Dic₃	1	2	yes	—
116	C₂×C₃×C₈	—	3	2	no	—
117	C₂×C₃×C₈	—	3	2	no	—
118	C₂×C₃×C₈	—	6	1	no	—
119	C₂×C₃×C₈	—	6	1	no	—
120	C₂×C₃×C₈	—	6	1	no	—
121	C₂×C₃×C₈	—	6	1	no	—
122	C₃×C₄⋊C₄	—	3	4	no	—
123	C₃×C₄⋊C₄	—	6	2	no	—
124	C₃×C₄²	—	2	2	no	—
125	C₃×C₄²	—	2	2	no	—
126	C₃×C₄²	—	6	2	no	—
127	C₃×C₄²	—	6	2	no	—
128	C₃×C₄²	Dic₆	1	2	yes	—
129	C₃×C₄²	Dic₆	1	2	yes	—
130	C₃×C₄²	D₁₂	1	2	yes	—
131	C₃×C₄²	#67	1	2	yes	—
132	C₄⋊Dic₃	—	2	2	no	—
133	C₄⋊Dic₃	C₃⋊C₈	1	4	yes	complemented
134	C₄×Dic₃	—	2	2	no	—
135	C₄×Dic₃	—	2	2	no	—
136	C₂×C₃⋊C₈	—	2	1	no	—
137	C₂×C₃⋊C₈	—	2	1	no	—
138	C₂×C₃⋊C₈	—	2	1	no	—
139	C₂×C₃⋊C₈	—	2	1	no	—
140	C₂×C₃⋊C₈	—	6	4	no	—
141	C₂×C₃⋊C₈	—	6	2	no	—
142	C₂×C₃⋊C₈	—	6	2	no	—
143	C₂×C₃⋊C₈	—	6	2	no	—
144	C₂×C₃⋊C₈	—	6	2	no	—
145	C₂×C₃⋊C₈	—	6	2	no	—
146	C₂×C₃⋊C₈	—	6	2	no	—
147	C₂×C₃⋊C₈	—	12	2	no	—
148	C₂×C₃⋊C₈	—	12	2	no	—
149	C₂×C₃⋊C₈	Dic₆	1	2	yes	—
150	C₂×C₃⋊C₈	D₁₂	1	2	yes	—
151	C₂²×C₃²	C₂×C₄⋊C₄	1	1	yes	characteristic
152	C₂²×C₃²	C₄×D₄	1	1	yes	characteristic
153	C₂²×C₃²	C₄×Q₈	1	1	yes	characteristic
154	C₂²×C₃²	C₂²×C₈	1	1	yes	characteristic
155	C₂²×C₃²	C₂×M₁₆	1	1	yes	characteristic
156	C₂²×C₃²	#131	1	1	yes	characteristic
157	C₂²×C₃²	#131	1	1	yes	characteristic
158	C₃²×C₄	—	2	2	no	—
159	C₃²×C₄	C₄⋊C₈	1	4	yes	complemented
160	C₃²×C₄	#121	1	1	yes	characteristic
161	C₃²×C₄	C₂²⋊Q₈	1	1	yes	characteristic
162	C₃²×C₄	#125	1	1	yes	characteristic
163	C₃²×C₄	C₄⋊Q₈	1	1	yes	characteristic
164	C₃×Dic₃	—	2	4	no	—
165	C₃×Dic₃	—	4	2	no	—
166	C₂²×C₈	—	3	1	no	—
167	C₂²×C₈	—	3	1	no	—
168	C₂²×C₈	—	9	2	no	—
169	C₂×C₄⋊C₄	—	3	1	no	—
170	C₂×C₄⋊C₄	—	3	1	no	—
171	C₂×C₄²	—	3	2	no	—
172	C₂×C₄²	D₃²	1	1	yes	characteristic
173	C₄⋊C₈	—	18	4	no	—
174	C₄⋊C₈	—	18	2	no	—
175	C₄×C₈	—	6	2	no	—
176	#95	—	3	2	no	—
177	C₂³×C₃	—	2	1	no	—
178	C₂³×C₃	C₂×C₄×D₃	1	1	yes	characteristic
179	C₂³×C₃	C₂²×Dic₃	1	1	yes	characteristic
180	C₂×C₃×C₄	—	2	1	no	—
181	C₂×C₃×C₄	—	2	1	no	—
182	C₂×C₃×C₄	—	2	1	no	—
183	C₂×C₃×C₄	—	2	1	no	—
184	C₂×C₃×C₄	—	2	2	no	—
185	C₂×C₃×C₄	—	2	2	no	—
186	C₂×C₃×C₄	—	2	2	no	—
187	C₂×C₃×C₄	—	2	2	no	—
188	C₂×C₃×C₄	—	2	1	no	—
189	C₂×C₃×C₄	—	2	1	no	—
190	C₂×C₃×C₄	—	2	1	no	—
191	C₂×C₃×C₄	—	2	1	no	—
192	C₂×C₃×C₄	—	2	1	no	—
193	C₂×C₃×C₄	—	2	1	no	—
194	C₂×C₃×C₄	—	3	4	no	—
195	C₂×C₃×C₄	—	4	1	no	—
196	C₂×C₃×C₄	—	4	1	no	—
197	C₂×C₃×C₄	—	6	2	no	—
198	C₂×C₃×C₄	—	6	2	no	—
199	C₂×C₃×C₄	—	6	2	no	—
200	C₂×C₃×C₄	—	6	2	no	—
201	C₂×C₃×C₄	—	6	2	no	—
202	C₂×C₃×C₄	D₃×C₈	1	2	yes	—
203	C₂×C₃×C₄	ΓL(1,𝔽₂₅)	1	2	yes	—
204	C₂×C₃×C₄	C₂×C₃⋊C₈	1	2	yes	—
205	C₂×C₃×C₄	#208	1	2	yes	—
206	C₂×C₃×C₄	Dic₃⋊C₄	1	2	yes	—
207	C₂×C₃×C₄	Dic₃⋊C₄	1	2	yes	—
208	C₂×C₃×C₄	C₄⋊Dic₃	1	2	yes	—
209	C₂×C₃×C₄	C₄⋊Dic₃	1	2	yes	—
210	C₂×C₃×C₄	C₂×Dic₆	1	1	yes	characteristic
211	C₂×C₃×C₄	C₂×Dic₆	1	1	yes	characteristic
212	C₂×C₃×C₄	C₂×Dic₆	1	1	yes	characteristic
213	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
214	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
215	C₂×C₃×C₄	#235	1	1	yes	characteristic
216	C₂×C₃×C₄	#235	1	1	yes	characteristic
217	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
218	C₂×C₃×C₄	#237	1	1	yes	characteristic
219	C₂×C₃×C₄	D₃×Q₈	1	1	yes	characteristic
220	C₂×C₃×C₄	#239	1	1	yes	characteristic
221	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
222	C₂×Dic₃	—	2	2	no	—
223	C₂×Dic₃	—	2	2	no	—
224	C₂×Dic₃	—	2	2	no	—
225	C₂×Dic₃	—	2	2	no	—
226	C₂×Dic₃	—	2	2	no	—
227	C₂×Dic₃	C₂×C₃⋊C₈	1	4	yes	—
228	C₃×C₈	—	6	2	no	—
229	C₃×C₈	—	6	2	no	—
230	C₃⋊C₈	—	2	2	no	—
231	C₃⋊C₈	—	2	2	no	—
232	C₃⋊C₈	—	12	4	no	—
233	C₃⋊C₈	—	12	2	no	—
234	C₃⋊C₈	—	12	2	no	—
235	C₂×C₃²	#389	1	1	yes	characteristic
236	C₂×C₃²	C₂×C₄⋊C₈	1	1	yes	characteristic
237	C₂×C₃²	#424	1	1	yes	characteristic
238	C₂×C₃²	C₈×D₄	1	1	yes	characteristic
239	C₂×C₃²	#436	1	1	yes	characteristic
240	C₂×C₃²	C₈×Q₈	1	1	yes	characteristic
241	C₂×C₃²	#446	1	1	yes	characteristic
242	C₂²×C₄	—	3	2	no	—
243	C₂²×C₄	—	3	2	no	—
244	C₂²×C₄	D₃×Dic₃	1	1	yes	characteristic
245	C₂²×C₄	D₃×Dic₃	1	1	yes	characteristic
246	C₂²×C₄	C₂×D₃²	1	1	yes	characteristic
247	C₂×C₈	—	3	2	no	—
248	C₂×C₈	—	3	2	no	—
249	C₂×C₈	—	6	1	no	—
250	C₂×C₈	—	6	1	no	—
251	C₂×C₈	—	6	1	no	—
252	C₂×C₈	—	6	1	no	—
253	C₂×C₈	—	18	2	no	—
254	C₂×C₈	—	18	2	no	—
255	C₂×C₈	—	18	2	no	—
256	C₄⋊C₄	—	3	4	no	—
257	C₄⋊C₄	—	6	2	no	—
258	C₄²	—	6	2	no	—
259	C₄²	—	6	2	no	—
260	C₄²	#626	1	2	yes	—
261	C₄²	#627	1	2	yes	—
262	C₂²×C₃	—	2	1	no	—
263	C₂²×C₃	—	2	1	no	—
264	C₂²×C₃	—	2	1	no	—
265	C₂²×C₃	—	2	1	no	—
266	C₂²×C₃	—	2	1	no	—
267	C₂²×C₃	—	2	1	no	—
268	C₂²×C₃	—	2	1	no	—
269	C₂²×C₃	C₄×Dic₆	1	1	yes	characteristic
270	C₂²×C₃	C₄×D₁₂	1	1	yes	characteristic
271	C₂²×C₃	C₂×D₃×C₈	1	1	yes	characteristic
272	C₂²×C₃	C₂×ΓL(1,𝔽₂₅)	1	1	yes	characteristic
273	C₂²×C₃	#901	1	1	yes	characteristic
274	C₂²×C₃	#901	1	1	yes	characteristic
275	C₂²×C₃	C₂²×C₃⋊C₈	1	1	yes	characteristic
276	C₂²×C₃	C₂×#208	1	1	yes	characteristic
277	C₂²×C₃	C₂×Dic₃⋊C₄	1	1	yes	characteristic
278	C₂²×C₃	C₂×C₄⋊Dic₃	1	1	yes	characteristic
279	C₂²×C₃	D₄×Dic₃	1	1	yes	characteristic
280	C₂²×C₃	Q₈×Dic₃	1	1	yes	characteristic
281	C₂²×C₃	#948	1	1	yes	characteristic
282	C₂²×C₃	#948	1	1	yes	characteristic
283	C₃×C₄	—	2	2	no	—
284	C₃×C₄	—	2	2	no	—
285	C₃×C₄	—	2	4	no	—
286	C₃×C₄	—	2	1	no	—
287	C₃×C₄	—	2	1	no	—
288	C₃×C₄	—	2	1	no	—
289	C₃×C₄	—	2	1	no	—
290	C₃×C₄	—	4	2	no	—
291	C₃×C₄	—	6	4	no	—
292	C₃×C₄	—	12	2	no	—
293	C₃×C₄	C₄⋊(C₃⋊C₈)	1	4	yes	complemented
294	C₃×C₄	Dic₃⋊C₈	1	4	yes	complemented
295	C₃×C₄	#869	1	1	yes	characteristic
296	C₃×C₄	#870	1	1	yes	characteristic
297	C₃×C₄	#888	1	1	yes	characteristic
298	C₃×C₄	#890	1	1	yes	characteristic
299	C₃×C₄	#895	1	1	yes	characteristic
300	C₃×C₄	#897	1	1	yes	characteristic
301	C₃×C₄	#924	1	1	yes	characteristic
302	C₃×C₄	#930	1	1	yes	characteristic
303	Dic₃	—	2	4	no	—
304	Dic₃	—	4	2	no	—
305	C₃²	#1939	1	1	yes	characteristic, complemented, Sylow
306	C₂³	C₂×D₃×Dic₃	1	1	yes	characteristic
307	C₂×C₄	—	2	1	no	—
308	C₂×C₄	—	2	1	no	—
309	C₂×C₄	—	3	4	no	—
310	C₂×C₄	—	6	2	no	—
311	C₂×C₄	—	6	2	no	—
312	C₂×C₄	—	6	2	no	—
313	C₂×C₄	—	6	2	no	—
314	C₂×C₄	—	6	2	no	—
315	C₂×C₄	D₃×C₃⋊C₈	1	2	yes	—
316	C₂×C₄	#3711	1	2	yes	—
317	C₂×C₄	Dic₃⋊Dic₃	1	2	yes	—
318	C₂×C₄	Dic₃⋊Dic₃	1	2	yes	—
319	C₂×C₄	D₃×Dic₆	1	1	yes	characteristic
320	C₂×C₄	#3795	1	1	yes	characteristic
321	C₂×C₄	#3799	1	1	yes	characteristic
322	C₂×C₄	D₃×D₁₂	1	1	yes	characteristic
323	C₂×C₄	C₂×#626	1	1	yes	characteristic
324	C₂×C₄	C₂×#627	1	1	yes	characteristic
325	C₈	—	6	2	no	—
326	C₈	—	6	2	no	—
327	C₈	—	36	2	no	—
328	C₂×C₃	—	2	1	no	—
329	C₂×C₃	—	2	1	no	—
330	C₂×C₃	—	2	1	no	—
331	C₂×C₃	—	2	1	no	—
332	C₂×C₃	—	2	1	no	—
333	C₂×C₃	—	2	1	no	—
334	C₂×C₃	—	2	1	no	—
335	C₂×C₃	C₈×Dic₆	1	1	yes	characteristic
336	C₂×C₃	#4679	1	1	yes	characteristic
337	C₂×C₃	C₈×D₁₂	1	1	yes	characteristic
338	C₂×C₃	#4688	1	1	yes	characteristic
339	C₂×C₃	C₂×C₄⋊(C₃⋊C₈)	1	1	yes	characteristic
340	C₂×C₃	#4928	1	1	yes	characteristic
341	C₂×C₃	#4984	1	1	yes	characteristic
342	C₂×C₃	#4999	1	1	yes	characteristic
343	C₂×C₃	D₄×C₃⋊C₈	1	1	yes	characteristic
344	C₂×C₃	#5012	1	1	yes	characteristic
345	C₂×C₃	Q₈×C₃⋊C₈	1	1	yes	characteristic
346	C₂×C₃	#5024	1	1	yes	characteristic
347	C₂×C₃	C₂×Dic₃⋊C₈	1	1	yes	characteristic
348	C₂×C₃	#5102	1	1	yes	characteristic
349	C₂²	C₂×D₃×C₃⋊C₈	1	1	yes	characteristic
350	C₂²	#63814	1	1	yes	characteristic
351	C₂²	#63814	1	1	yes	characteristic
352	C₂²	C₂×#3711	1	1	yes	characteristic
353	C₂²	Dic₃×Dic₆	1	1	yes	characteristic
354	C₂²	Dic₃×D₁₂	1	1	yes	characteristic
355	C₂²	C₂×Dic₃⋊Dic₃	1	1	yes	characteristic
356	C₄	—	2	2	no	—
357	C₄	—	6	4	no	—
358	C₄	—	12	2	no	—
359	C₄	Dic₃⋊(C₃⋊C₈)	1	4	yes	complemented
360	C₄	#63857	1	1	yes	characteristic
361	C₄	#63869	1	1	yes	characteristic
362	C₄	#63909	1	1	yes	characteristic
363	C₄	#63918	1	1	yes	characteristic
364	C₃	—	2	1	no	—
365	C₃	#69484	1	1	yes	characteristic, complemented
366	C₃	#69786	1	1	yes	characteristic, complemented
367	C₂	C₃⋊C₈×Dic₆	1	1	yes	characteristic
368	C₂	#10590258	1	1	yes	characteristic
369	C₂	C₃⋊C₈×D₁₂	1	1	yes	characteristic
370	C₂	#10590337	1	1	yes	characteristic
371	C₂	C₂×Dic₃⋊(C₃⋊C₈)	1	1	yes	characteristic
372	C₂	#10591116	1	1	yes	characteristic
373	C₂	#10591352	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂×D₃²
commutator	C₂²×C₃²	C₂²×C₈
Fitting	C₂×C₃²×C₄²	C₂²
socle, prime radical	C₂³×C₃²	C₂²×C₄
cosocle	C₂²×C₃²×C₄	C₂³
hypercenter	C₂×C₄²	D₃²
hypocenter	C₃²	#1939
LCS	G ▷ C₂²×C₃² ▷ C₃²
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
41. C₃×C₄⋊Dic₃	C₈	semidirect
133. C₄⋊Dic₃	C₃⋊C₈	semidirect
159. C₃²×C₄	C₄⋊C₈	semidirect
293. C₃×C₄	C₄⋊(C₃⋊C₈)	semidirect
294. C₃×C₄	Dic₃⋊C₈	semidirect
305. C₃²	#1939	semidirect
359. C₄	Dic₃⋊(C₃⋊C₈)	semidirect
365. C₃	#69484	semidirect
366. C₃	#69786	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄⋊(C₃⋊(C₃⋊C₈))	2
C₃×C₄×C₄⋊Dic₃	2
C₂×C₃×C₄×C₃⋊C₈	2
C₂×Dic₃⋊(C₃⋊C₈)	2
#10589155	2
#69786	3
#69484	3