Subgroups — C₂×C₃×#4893 #11858633

Order 1152.

973 conjugacy classes of subgroups.

The subgroup lattice has 381 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₃×M₁₆	C₂	1	2	yes	maximal
2	C₂²×C₃×ΓL(1,𝔽₂₅)	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃²×#108	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×#822	C₂	1	2	yes	maximal, complemented
5	C₂×C₃×#819	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#4893	C₂	1	8	yes	maximal, direct product factor
7	C₂×C₃×#430	—	3	1	no	maximal
8	C₂×#4893	C₃	1	1	yes	maximal, characteristic, direct product factor
9	C₂²×C₃×C₄×D₃	C₂²	1	1	yes	characteristic
10	C₂×C₃²×M₁₆	C₂²	1	2	yes	—
11	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
12	C₂×C₃×#208	C₂²	1	2	yes	—
13	C₂²×C₃×C₃⋊C₈	C₂²	1	1	yes	characteristic
14	C₃×D₃×M₁₆	—	2	4	no	—
15	C₃×D₃×M₁₆	C₂²	1	8	yes	—
16	C₂×C₃×ΓL(1,𝔽₂₅)	—	2	2	no	—
17	C₂×C₃×ΓL(1,𝔽₂₅)	C₄	1	4	yes	—
18	C₂×C₃×ΓL(1,𝔽₂₅)	C₄	1	4	yes	—
19	C₂×C₃×ΓL(1,𝔽₂₅)	C₂²	1	4	yes	—
20	C₂×C₃×D₃×C₈	—	2	2	no	—
21	C₃²×#108	C₂²	1	4	yes	complemented
22	C₃×#822	C₂²	1	8	yes	complemented
23	C₃×#819	C₂²	1	4	yes	complemented
24	C₂²×C₃×M₁₆	—	3	1	no	—
25	C₂²×C₃×M₁₆	—	3	2	no	—
26	C₂×D₃×M₁₆	C₂×C₃	1	2	yes	—
27	C₂²×ΓL(1,𝔽₂₅)	C₂×C₃	1	1	yes	characteristic
28	C₃×#430	—	3	8	no	—
29	C₂×C₃×#108	—	2	1	no	—
30	C₂×C₃×#108	—	3	2	no	—
31	C₂×C₃×#108	—	3	1	no	—
32	C₂×C₃×#108	D₃	1	1	yes	characteristic, complemented
33	C₂×C₃×#108	C₂×C₃	1	1	yes	characteristic, complemented
34	C₂×#822	C₂×C₃	1	2	yes	complemented
35	C₂×#819	C₂×C₃	1	1	yes	characteristic, complemented
36	#4893	C₂×C₃	1	8	yes	direct product factor
37	C₂³×C₃×D₃	Q₈	1	1	yes	characteristic
38	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
39	C₂²×C₃×Dic₃	Q₈	1	1	yes	characteristic
40	C₂×C₃×C₄×D₃	C₂×C₄	1	2	yes	—
41	C₂×C₃×C₄×D₃	C₂×C₄	1	2	yes	—
42	C₂×C₃×C₄×D₃	D₄	1	2	yes	—
43	C₂×C₃×C₄×D₃	D₄	1	2	yes	—
44	C₂×C₃×C₄×D₃	Q₈	1	2	yes	—
45	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
46	C₃²×M₁₆	—	2	2	no	—
47	C₃²×M₁₆	C₂³	1	4	yes	—
48	C₂×C₃²×C₈	—	2	2	no	—
49	C₂×C₃²×C₈	C₂×C₄	1	2	yes	—
50	C₂×C₃²×C₈	C₂×C₄	1	2	yes	—
51	C₂×C₃²×C₈	C₂³	1	2	yes	—
52	C₃×#208	—	2	2	no	—
53	C₃×#208	C₂³	1	4	yes	—
54	C₂×C₃×C₃⋊C₈	—	2	2	no	—
55	C₂×C₃×C₃⋊C₈	C₂×C₄	1	2	yes	—
56	C₂×C₃×C₃⋊C₈	C₂×C₄	1	2	yes	—
57	C₂×C₃×C₃⋊C₈	C₂³	1	2	yes	—
58	C₃×ΓL(1,𝔽₂₅)	—	2	8	no	—
59	C₃×ΓL(1,𝔽₂₅)	C₂×C₄	1	16	yes	—
60	C₃×D₃×C₈	—	2	8	no	—
61	C₂×#430	—	3	1	no	Sylow
62	C₂³×C₃×C₄	—	3	1	no	—
63	C₂²×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
64	C₂×C₃×M₁₆	—	2	2	no	—
65	C₂×C₃×M₁₆	—	3	4	no	—
66	C₂×C₃×M₁₆	—	3	4	no	—
67	C₂×C₃×M₁₆	—	3	4	no	—
68	C₂×C₃×M₁₆	—	3	2	no	—
69	C₂×C₃×M₁₆	—	3	8	no	—
70	C₂×C₃×M₁₆	—	6	2	no	—
71	C₂×C₃×M₁₆	—	6	4	no	—
72	C₂×C₃×M₁₆	C₂×D₃	1	2	yes	—
73	C₂×C₃×M₁₆	C₂²×C₃	1	2	yes	—
74	C₂²×C₃×C₈	—	2	1	no	—
75	C₂²×C₃×C₈	—	3	1	no	—
76	C₂²×C₃×C₈	—	6	2	no	—
77	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
78	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
79	C₂×#208	C₂²×C₃	1	2	yes	—
80	C₂²×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
81	D₃×M₁₆	—	2	4	no	—
82	D₃×M₁₆	C₂²×C₃	1	8	yes	—
83	C₂×ΓL(1,𝔽₂₅)	—	2	2	no	—
84	C₂×ΓL(1,𝔽₂₅)	C₃×C₄	1	4	yes	—
85	C₂×ΓL(1,𝔽₂₅)	C₃×C₄	1	4	yes	—
86	C₂×ΓL(1,𝔽₂₅)	C₂²×C₃	1	4	yes	—
87	C₂×D₃×C₈	—	2	2	no	—
88	C₃×#108	—	2	4	no	—
89	C₃×#108	—	3	8	no	—
90	C₃×#108	—	3	4	no	—
91	C₃×#108	C₂×D₃	1	4	yes	complemented
92	C₃×#108	C₂²×C₃	1	4	yes	complemented
93	#822	C₂²×C₃	1	8	yes	complemented
94	#819	C₂²×C₃	1	4	yes	complemented
95	C₂³×C₃²	C₂×Q₈	1	1	yes	characteristic
96	C₂²×C₃×D₃	—	4	2	no	—
97	C₂²×C₃×D₃	C₄⋊C₄	1	2	yes	—
98	C₂²×C₃×D₃	C₄⋊C₄	1	2	yes	—
99	C₂²×C₃×D₃	C₂×Q₈	1	2	yes	—
100	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
101	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
102	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
103	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
104	C₂×C₃²×C₄	C₂×Q₈	1	1	yes	characteristic
105	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
106	C₂×C₃×Dic₃	C₄⋊C₄	1	2	yes	—
107	C₂×C₃×Dic₃	C₄⋊C₄	1	2	yes	—
108	C₂×C₃×Dic₃	C₂×Q₈	1	2	yes	—
109	C₃×C₄×D₃	C₄⋊C₄	1	4	yes	—
110	C₃×C₄×D₃	C₄⋊C₄	1	4	yes	—
111	C₃×C₄×D₃	C₂²×C₄	1	4	yes	—
112	C₃×C₄×D₃	C₂×D₄	1	4	yes	—
113	C₃²×C₈	—	2	4	no	—
114	C₃²×C₈	C₂²×C₄	1	4	yes	—
115	C₃×C₃⋊C₈	—	2	4	no	—
116	C₃×C₃⋊C₈	C₂²×C₄	1	4	yes	—
117	C₂²×M₁₆	—	3	1	no	—
118	C₂²×M₁₆	—	3	2	no	—
119	#430	—	3	8	no	—
120	C₂×#108	—	3	2	no	—
121	C₂×#108	—	3	1	no	—
122	C₂×#108	C₃×D₃	1	1	yes	characteristic, complemented
123	C₂⁴×C₃	—	3	1	no	—
124	C₂³×D₃	C₃×Q₈	1	1	yes	characteristic
125	C₂²×C₃×C₄	—	2	1	no	—
126	C₂²×C₃×C₄	—	3	1	no	—
127	C₂²×C₃×C₄	—	3	2	no	—
128	C₂²×C₃×C₄	—	3	2	no	—
129	C₂²×C₃×C₄	—	3	2	no	—
130	C₂²×C₃×C₄	—	3	2	no	—
131	C₂²×C₃×C₄	—	3	2	no	—
132	C₂²×C₃×C₄	—	3	2	no	—
133	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
134	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
135	C₂²×Dic₃	C₃×Q₈	1	1	yes	characteristic
136	C₂×C₄×D₃	C₂×C₃×C₄	1	2	yes	—
137	C₂×C₄×D₃	C₂×C₃×C₄	1	2	yes	—
138	C₂×C₄×D₃	C₃×D₄	1	2	yes	—
139	C₂×C₄×D₃	C₃×D₄	1	2	yes	—
140	C₂×C₄×D₃	C₃×Q₈	1	2	yes	—
141	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
142	C₃×M₁₆	—	2	2	no	—
143	C₃×M₁₆	—	2	2	no	—
144	C₃×M₁₆	—	2	4	no	—
145	C₃×M₁₆	—	3	16	no	—
146	C₃×M₁₆	—	3	4	no	—
147	C₃×M₁₆	—	4	2	no	—
148	C₃×M₁₆	—	6	8	no	—
149	C₃×M₁₆	—	6	2	no	—
150	C₃×M₁₆	C₂²×D₃	1	4	yes	—
151	C₃×M₁₆	C₂³×C₃	1	4	yes	—
152	C₂×C₃×C₈	—	2	2	no	—
153	C₂×C₃×C₈	—	2	2	no	—
154	C₂×C₃×C₈	—	2	2	no	—
155	C₂×C₃×C₈	—	2	2	no	—
156	C₂×C₃×C₈	—	2	2	no	—
157	C₂×C₃×C₈	—	3	2	no	—
158	C₂×C₃×C₈	—	3	2	no	—
159	C₂×C₃×C₈	—	3	2	no	—
160	C₂×C₃×C₈	—	4	2	no	—
161	C₂×C₃×C₈	—	6	8	no	—
162	C₂×C₃×C₈	—	6	2	no	—
163	C₂×C₃×C₈	C₄×D₃	1	2	yes	—
164	C₂×C₃×C₈	C₄×D₃	1	2	yes	—
165	C₂×C₃×C₈	C₂×C₃×C₄	1	2	yes	—
166	C₂×C₃×C₈	C₂×C₃×C₄	1	2	yes	—
167	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
168	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
169	#208	—	2	2	no	—
170	#208	C₂³×C₃	1	4	yes	—
171	C₂×C₃⋊C₈	—	2	2	no	—
172	C₂×C₃⋊C₈	C₂×C₃×C₄	1	2	yes	—
173	C₂×C₃⋊C₈	C₂×C₃×C₄	1	2	yes	—
174	C₂×C₃⋊C₈	C₂³×C₃	1	2	yes	—
175	ΓL(1,𝔽₂₅)	—	2	8	no	—
176	ΓL(1,𝔽₂₅)	C₂×C₃×C₄	1	16	yes	—
177	D₃×C₈	—	2	8	no	—
178	C₂²×C₃²	—	2	2	no	—
179	C₂²×C₃²	C₂×C₄⋊C₄	1	1	yes	characteristic
180	C₂²×C₃²	C₂×C₄⋊C₄	1	1	yes	characteristic
181	C₂²×C₃²	C₂²×Q₈	1	1	yes	characteristic
182	C₂×C₃×D₃	—	2	4	no	—
183	C₂×C₃×D₃	—	4	2	no	—
184	C₂×C₃×D₃	—	4	2	no	—
185	C₂×C₃×D₃	C₂×C₄⋊C₄	1	4	yes	—
186	C₃²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
187	C₃²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
188	C₃²×C₄	C₂³×C₄	1	1	yes	characteristic
189	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
190	C₃×Dic₃	C₂×C₄⋊C₄	1	4	yes	—
191	C₂³×C₄	—	3	1	no	—
192	C₂×M₁₆	—	3	4	no	—
193	C₂×M₁₆	—	3	4	no	—
194	C₂×M₁₆	—	3	4	no	—
195	C₂×M₁₆	—	3	2	no	—
196	C₂×M₁₆	—	3	8	no	—
197	C₂×M₁₆	—	6	2	no	—
198	C₂×M₁₆	—	6	4	no	—
199	C₂×M₁₆	C₂×C₃×D₃	1	2	yes	—
200	C₂²×C₈	—	3	1	no	—
201	C₂²×C₈	—	6	2	no	—
202	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
203	#108	—	3	8	no	—
204	#108	—	3	4	no	—
205	#108	C₂×C₃×D₃	1	4	yes	complemented
206	C₂³×C₃	—	2	1	no	—
207	C₂³×C₃	—	3	2	no	—
208	C₂³×C₃	—	3	2	no	—
209	C₂³×C₃	—	3	2	no	—
210	C₂³×C₃	—	12	2	no	—
211	C₂³×C₃	D₃×Q₈	1	1	yes	characteristic
212	C₂³×C₃	C₂×C₃×Q₈	1	1	yes	characteristic
213	C₂²×D₃	—	4	2	no	—
214	C₂²×D₃	C₃×C₄⋊C₄	1	2	yes	—
215	C₂²×D₃	C₃×C₄⋊C₄	1	2	yes	—
216	C₂²×D₃	C₂×C₃×Q₈	1	2	yes	—
217	C₂×C₃×C₄	—	2	1	no	—
218	C₂×C₃×C₄	—	2	1	no	—
219	C₂×C₃×C₄	—	2	1	no	—
220	C₂×C₃×C₄	—	2	1	no	—
221	C₂×C₃×C₄	—	2	1	no	—
222	C₂×C₃×C₄	—	2	1	no	—
223	C₂×C₃×C₄	—	3	2	no	—
224	C₂×C₃×C₄	—	3	2	no	—
225	C₂×C₃×C₄	—	3	2	no	—
226	C₂×C₃×C₄	—	3	4	no	—
227	C₂×C₃×C₄	—	3	4	no	—
228	C₂×C₃×C₄	—	3	4	no	—
229	C₂×C₃×C₄	—	3	4	no	—
230	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
231	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
232	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
233	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
234	C₂×C₃×C₄	D₃×Q₈	1	1	yes	characteristic
235	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
236	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
237	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
238	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
239	C₂×C₃×C₄	C₂×C₃×Q₈	1	1	yes	characteristic
240	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
241	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
242	C₂×Dic₃	C₃×C₄⋊C₄	1	2	yes	—
243	C₂×Dic₃	C₃×C₄⋊C₄	1	2	yes	—
244	C₂×Dic₃	C₂×C₃×Q₈	1	2	yes	—
245	C₄×D₃	C₃×C₄⋊C₄	1	4	yes	—
246	C₄×D₃	C₃×C₄⋊C₄	1	4	yes	—
247	C₄×D₃	C₂²×C₃×C₄	1	4	yes	—
248	C₄×D₃	C₂×C₃×D₄	1	4	yes	—
249	C₃×C₈	—	2	4	no	—
250	C₃×C₈	—	2	4	no	—
251	C₃×C₈	—	2	4	no	—
252	C₃×C₈	—	3	4	no	—
253	C₃×C₈	—	4	4	no	—
254	C₃×C₈	—	6	4	no	—
255	C₃×C₈	C₂×C₄×D₃	1	4	yes	—
256	C₃×C₈	C₂²×C₃×C₄	1	4	yes	—
257	C₃⋊C₈	—	2	4	no	—
258	C₃⋊C₈	C₂²×C₃×C₄	1	4	yes	—
259	C₂×C₃²	—	2	1	no	—
260	C₂×C₃²	—	2	1	no	—
261	C₂×C₃²	#430	1	2	yes	complemented
262	C₂×C₃²	C₂²×C₄⋊C₄	1	1	yes	characteristic
263	C₃×D₃	—	2	4	no	—
264	C₂⁴	—	3	1	no	—
265	C₂²×C₄	—	3	1	no	—
266	C₂²×C₄	—	3	2	no	—
267	C₂²×C₄	—	3	2	no	—
268	C₂²×C₄	—	3	2	no	—
269	C₂²×C₄	—	3	2	no	—
270	C₂²×C₄	—	3	2	no	—
271	C₂²×C₄	—	3	2	no	—
272	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
273	M₁₆	—	2	2	no	—
274	M₁₆	—	3	16	no	—
275	M₁₆	—	3	4	no	—
276	M₁₆	—	6	8	no	—
277	M₁₆	—	6	2	no	—
278	M₁₆	C₂²×C₃×D₃	1	4	yes	—
279	C₂×C₈	—	2	2	no	—
280	C₂×C₈	—	3	2	no	—
281	C₂×C₈	—	3	2	no	—
282	C₂×C₈	—	3	2	no	—
283	C₂×C₈	—	6	8	no	—
284	C₂×C₈	—	6	2	no	—
285	C₂×C₈	C₃×C₄×D₃	1	2	yes	—
286	C₂×C₈	C₃×C₄×D₃	1	2	yes	—
287	C₂×C₈	C₂²×C₃×D₃	1	2	yes	—
288	C₂²×C₃	—	2	2	no	—
289	C₂²×C₃	—	2	2	no	—
290	C₂²×C₃	—	2	1	no	—
291	C₂²×C₃	—	2	1	no	—
292	C₂²×C₃	—	2	1	no	—
293	C₂²×C₃	—	3	4	no	—
294	C₂²×C₃	—	4	2	no	—
295	C₂²×C₃	—	6	4	no	—
296	C₂²×C₃	—	12	2	no	—
297	C₂²×C₃	—	12	2	no	—
298	C₂²×C₃	D₃×C₄⋊C₄	1	1	yes	characteristic
299	C₂²×C₃	D₃×C₄⋊C₄	1	1	yes	characteristic
300	C₂²×C₃	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
301	C₂²×C₃	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
302	C₂²×C₃	C₂×D₃×Q₈	1	1	yes	characteristic
303	C₂²×C₃	C₂²×C₃×Q₈	1	1	yes	characteristic
304	C₂×D₃	—	2	4	no	—
305	C₂×D₃	—	4	2	no	—
306	C₂×D₃	—	4	2	no	—
307	C₂×D₃	C₂×C₃×C₄⋊C₄	1	4	yes	—
308	C₃×C₄	—	2	1	no	—
309	C₃×C₄	—	2	1	no	—
310	C₃×C₄	—	2	1	no	—
311	C₃×C₄	—	2	1	no	—
312	C₃×C₄	—	3	4	no	—
313	C₃×C₄	D₃×C₄⋊C₄	1	1	yes	characteristic
314	C₃×C₄	D₃×C₄⋊C₄	1	1	yes	characteristic
315	C₃×C₄	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
316	C₃×C₄	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
317	C₃×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
318	C₃×C₄	C₂×D₃×D₄	1	1	yes	characteristic
319	C₃×C₄	C₂³×C₃×C₄	1	1	yes	characteristic
320	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
321	Dic₃	C₂×C₃×C₄⋊C₄	1	4	yes	—
322	C₃²	C₂×#430	1	1	yes	characteristic, complemented, Sylow
323	C₂³	—	3	2	no	—
324	C₂³	—	3	2	no	—
325	C₂³	—	3	2	no	—
326	C₂³	—	12	2	no	—
327	C₂³	C₃×D₃×Q₈	1	1	yes	characteristic
328	C₂×C₄	—	3	2	no	—
329	C₂×C₄	—	3	2	no	—
330	C₂×C₄	—	3	2	no	—
331	C₂×C₄	—	3	4	no	—
332	C₂×C₄	—	3	4	no	—
333	C₂×C₄	—	3	4	no	—
334	C₂×C₄	—	3	4	no	—
335	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
336	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
337	C₂×C₄	C₃×D₃×D₄	1	1	yes	characteristic
338	C₂×C₄	C₃×D₃×D₄	1	1	yes	characteristic
339	C₂×C₄	C₃×D₃×Q₈	1	1	yes	characteristic
340	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
341	C₈	—	2	4	no	—
342	C₈	—	3	4	no	—
343	C₈	—	6	4	no	—
344	C₈	C₂×C₃×C₄×D₃	1	4	yes	—
345	C₂×C₃	—	2	1	no	—
346	C₂×C₃	—	2	1	no	—
347	C₂×C₃	—	2	1	no	—
348	C₂×C₃	—	2	1	no	—
349	C₂×C₃	—	2	1	no	—
350	C₂×C₃	—	2	2	no	—
351	C₂×C₃	—	4	1	no	—
352	C₂×C₃	—	4	1	no	—
353	C₂×C₃	—	6	4	no	—
354	C₂×C₃	#4893	1	2	yes	direct product factor
355	C₂×C₃	C₃×#430	1	2	yes	complemented
356	C₂×C₃	C₂×D₃×C₄⋊C₄	1	1	yes	characteristic
357	C₂×C₃	C₂²×C₃×C₄⋊C₄	1	1	yes	characteristic
358	D₃	—	2	4	no	—
359	C₂²	—	2	2	no	—
360	C₂²	—	3	4	no	—
361	C₂²	—	6	4	no	—
362	C₂²	—	12	2	no	—
363	C₂²	—	12	2	no	—
364	C₂²	C₃×D₃×C₄⋊C₄	1	1	yes	characteristic
365	C₂²	C₃×D₃×C₄⋊C₄	1	1	yes	characteristic
366	C₂²	C₂×C₃×D₃×Q₈	1	1	yes	characteristic
367	C₄	—	3	4	no	—
368	C₄	C₃×D₃×C₄⋊C₄	1	1	yes	characteristic
369	C₄	C₃×D₃×C₄⋊C₄	1	1	yes	characteristic
370	C₄	C₂²×C₃×C₄×D₃	1	1	yes	characteristic
371	C₄	C₂×C₃×D₃×D₄	1	1	yes	characteristic
372	C₃	—	2	1	no	—
373	C₃	C₂×#4893	1	1	yes	characteristic, direct product factor
374	C₃	C₂×C₃×#430	1	1	yes	characteristic, complemented
375	C₂	—	2	1	no	—
376	C₂	—	2	1	no	—
377	C₂	—	6	4	no	—
378	C₂	C₃×#4893	1	2	yes	direct product factor
379	C₂	C₂×C₃×D₃×C₄⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	D₃×D₄
commutator	C₃×C₄	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₂×C₃²×#108	C₂
socle	C₂²×C₃²	C₂×C₄⋊C₄
prime radical	C₂³×C₃×D₃	Q₈
cosocle	C₂×C₃×C₄	C₂⁴×C₃
hypercenter	C₂×C₃×#108	D₃
hypocenter	C₃	C₂×C₃×#430
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂²×C₃×C₄ ◁ C₂×C₃×#108

Complements

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

N	H ≅ G/N	type
3. C₂×C₃²×#108	C₂	semidirect
4. C₂×C₃×#822	C₂	semidirect
5. C₂×C₃×#819	C₂	semidirect
6. C₃×#4893	C₂	direct (N × H)
8. C₂×#4893	C₃	direct (N × H)
21. C₃²×#108	C₂²	semidirect
22. C₃×#822	C₂²	semidirect
23. C₃×#819	C₂²	semidirect
32. C₂×C₃×#108	D₃	semidirect
33. C₂×C₃×#108	C₂×C₃	semidirect
34. C₂×#822	C₂×C₃	semidirect
35. C₂×#819	C₂×C₃	semidirect
36. #4893	C₂×C₃	direct (N × H)
91. C₃×#108	C₂×D₃	semidirect
92. C₃×#108	C₂²×C₃	semidirect
93. #822	C₂²×C₃	semidirect
94. #819	C₂²×C₃	semidirect
122. C₂×#108	C₃×D₃	semidirect
205. #108	C₂×C₃×D₃	semidirect
261. C₂×C₃²	#430	semidirect
322. C₃²	C₂×#430	semidirect
354. C₂×C₃	#4893	direct (N × H)
355. C₂×C₃	C₃×#430	semidirect
373. C₃	C₂×#4893	direct (N × H)
374. C₃	C₂×C₃×#430	semidirect
378. C₂	C₃×#4893	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×D₃×M₁₆	2
C₂²×C₃×ΓL(1,𝔽₂₅)	2
C₂×C₃²×#108	2
C₂×C₃×#822	2
C₂×C₃×#819	2
C₃×#4893	2
C₂×C₃×#430	3
C₂×#4893	3

Subgroups — C2×C3×#4893 #11858633

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#4893 #11858633