Subgroups — C₃×#79252 #11858661

Order 1152.

933 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#5745	C₂	1	2	yes	maximal
2	C₂×C₃×#901	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃²×#108	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#5124	C₂	1	2	yes	maximal, complemented
5	C₂×C₃×#819	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#4893	C₂	1	4	yes	maximal, complemented
7	C₃×D₃×#108	C₂	1	4	yes	maximal, complemented
8	C₃×#2916	—	3	1	no	maximal
9	#79252	C₃	1	1	yes	maximal, characteristic, direct product factor
10	C₂×C₃×#235	C₂²	1	1	yes	characteristic
11	C₂×C₃²×M₁₆	C₂²	1	2	yes	—
12	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
13	C₂×C₃×#208	C₂²	1	2	yes	—
14	C₂×C₃×#208	C₂²	1	1	yes	characteristic
15	C₃×#907	—	2	4	no	—
16	C₃×D₃×M₁₆	C₂²	1	8	yes	—
17	C₃×#901	—	2	4	no	—
18	C₃×#901	C₄	1	4	yes	—
19	C₃×#901	C₄	1	4	yes	—
20	C₂×C₃×ΓL(1,𝔽₂₅)	C₂²	1	2	yes	—
21	C₂×C₃×D₃×C₈	C₂²	1	2	yes	—
22	C₃²×#108	C₂²	1	2	yes	—
23	C₃²×#108	C₂²	1	2	yes	—
24	C₃×#822	C₂²	1	8	yes	—
25	C₃×#819	C₂²	1	2	yes	—
26	C₃×#819	C₂²	1	2	yes	—
27	C₃×#568	—	3	2	no	—
28	C₂×C₃×#131	—	3	1	no	—
29	#5745	C₂×C₃	1	2	yes	—
30	C₂×#901	C₂×C₃	1	1	yes	characteristic
31	C₃×#430	—	3	2	no	—
32	C₃×#430	—	3	4	no	—
33	C₂×C₃×#108	—	2	1	no	—
34	C₂×C₃×#108	—	3	1	no	—
35	C₂×C₃×#108	—	3	4	no	—
36	C₂×C₃×#108	D₃	1	1	yes	characteristic, complemented
37	C₂×C₃×#108	C₂×C₃	1	1	yes	characteristic, complemented
38	#5124	C₂×C₃	1	2	yes	complemented
39	C₂×#819	C₂×C₃	1	1	yes	characteristic, complemented
40	#4893	C₂×C₃	1	4	yes	complemented
41	D₃×#108	C₂×C₃	1	4	yes	complemented
42	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
43	C₂×C₃×#67	Q₈	1	2	yes	—
44	C₃×#235	C₂×C₄	1	2	yes	—
45	C₃×#235	C₂×C₄	1	2	yes	—
46	C₃×#235	D₄	1	2	yes	—
47	C₃×#235	D₄	1	2	yes	—
48	C₂×C₃×D₁₂	Q₈	1	1	yes	characteristic
49	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
50	C₂×C₃×Dic₆	Q₈	1	1	yes	characteristic
51	C₃²×M₁₆	—	2	2	no	—
52	C₃²×M₁₆	C₂³	1	4	yes	—
53	C₂×C₃²×C₈	—	2	2	no	—
54	C₂×C₃²×C₈	C₂×C₄	1	2	yes	—
55	C₂×C₃²×C₈	C₂×C₄	1	2	yes	—
56	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
57	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
58	C₃×#208	—	2	2	no	—
59	C₃×#208	C₂×C₄	1	2	yes	—
60	C₃×#208	C₂×C₄	1	2	yes	—
61	C₃×#208	C₂³	1	4	yes	—
62	C₂×C₃×C₃⋊C₈	—	2	2	no	—
63	C₂×C₃×C₃⋊C₈	C₂³	1	2	yes	—
64	C₃×ΓL(1,𝔽₂₅)	—	2	8	no	—
65	C₃×ΓL(1,𝔽₂₅)	C₂×C₄	1	8	yes	—
66	C₃×D₃×C₈	—	2	8	no	—
67	C₃×D₃×C₈	C₂×C₄	1	8	yes	—
68	#2916	—	3	1	no	Sylow
69	C₂×C₃×#41	—	3	1	no	—
70	C₂×#235	C₂²×C₃	1	1	yes	characteristic
71	C₃×#131	—	3	4	no	—
72	C₃×#131	—	3	4	no	—
73	C₃×#131	—	6	4	no	—
74	C₃×#131	—	6	4	no	—
75	C₂×C₃×M₁₆	—	2	2	no	—
76	C₂×C₃×M₁₆	—	3	1	no	—
77	C₂×C₃×M₁₆	—	3	2	no	—
78	C₂×C₃×M₁₆	—	3	2	no	—
79	C₂×C₃×M₁₆	—	3	8	no	—
80	C₂×C₃×M₁₆	C₂×D₃	1	2	yes	—
81	C₂×C₃×M₁₆	C₂²×C₃	1	2	yes	—
82	C₂²×C₃×C₈	—	2	1	no	—
83	C₂²×C₃×C₈	—	3	2	no	—
84	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
85	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
86	C₂×#208	C₂²×C₃	1	2	yes	—
87	C₂×#208	C₂²×C₃	1	1	yes	characteristic
88	#907	—	2	4	no	—
89	D₃×M₁₆	C₂²×C₃	1	8	yes	—
90	#901	—	2	4	no	—
91	#901	C₃×C₄	1	4	yes	—
92	#901	C₃×C₄	1	4	yes	—
93	C₂×ΓL(1,𝔽₂₅)	C₂²×C₃	1	2	yes	—
94	C₂×D₃×C₈	C₂²×C₃	1	2	yes	—
95	C₃×#108	—	2	2	no	—
96	C₃×#108	—	2	2	no	—
97	C₃×#108	—	3	8	no	—
98	C₃×#108	—	3	2	no	—
99	C₃×#108	—	3	2	no	—
100	C₃×#108	C₂×D₃	1	2	yes	—
101	C₃×#108	C₂×D₃	1	2	yes	—
102	C₃×#108	C₂²×C₃	1	2	yes	—
103	C₃×#108	C₂²×C₃	1	2	yes	—
104	#822	C₂²×C₃	1	8	yes	—
105	#819	C₂²×C₃	1	2	yes	—
106	#819	C₂²×C₃	1	2	yes	—
107	C₂³×C₃²	C₂×Q₈	1	1	yes	characteristic
108	C₂²×C₃×D₃	C₂×Q₈	1	2	yes	—
109	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
110	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
111	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
112	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
113	C₂×C₃²×C₄	C₂×Q₈	1	1	yes	characteristic
114	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
115	C₃×#67	C₄⋊C₄	1	4	yes	—
116	C₃×#67	C₄⋊C₄	1	4	yes	—
117	C₂×C₃×Dic₃	C₂×Q₈	1	2	yes	—
118	C₃×D₁₂	C₄⋊C₄	1	2	yes	—
119	C₃×D₁₂	C₄⋊C₄	1	2	yes	—
120	C₃×C₄×D₃	C₂²×C₄	1	4	yes	—
121	C₃×C₄×D₃	C₂×D₄	1	4	yes	—
122	C₃×Dic₆	C₄⋊C₄	1	2	yes	—
123	C₃×Dic₆	C₄⋊C₄	1	2	yes	—
124	C₃²×C₈	—	2	4	no	—
125	C₃²×C₈	C₂²×C₄	1	2	yes	—
126	C₃²×C₈	C₂²×C₄	1	2	yes	—
127	C₃×C₃⋊C₈	—	2	4	no	—
128	C₃×C₃⋊C₈	C₂²×C₄	1	4	yes	—
129	#568	—	3	2	no	—
130	C₂×#131	—	3	1	no	—
131	#430	—	3	2	no	—
132	#430	—	3	4	no	—
133	C₂×#108	—	3	1	no	—
134	C₂×#108	—	3	4	no	—
135	C₂×#108	C₃×D₃	1	1	yes	characteristic, complemented
136	C₃×#41	—	3	2	no	—
137	C₃×#41	—	3	2	no	—
138	C₃×#41	—	3	2	no	—
139	C₃×#41	—	3	2	no	—
140	C₂×C₃×Q₈	—	3	1	no	—
141	C₂×C₃×D₄	—	3	2	no	—
142	C₂×C₃×D₄	—	3	1	no	—
143	C₂²×C₃×C₄	—	2	1	no	—
144	C₂²×C₃×C₄	—	3	2	no	—
145	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
146	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
147	C₂×#67	C₃×Q₈	1	2	yes	—
148	#235	C₂×C₃×C₄	1	2	yes	—
149	#235	C₂×C₃×C₄	1	2	yes	—
150	#235	C₃×D₄	1	2	yes	—
151	#235	C₃×D₄	1	2	yes	—
152	C₂×D₁₂	C₃×Q₈	1	1	yes	characteristic
153	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
154	C₂×Dic₆	C₃×Q₈	1	1	yes	characteristic
155	C₃×M₁₆	—	2	2	no	—
156	C₃×M₁₆	—	2	2	no	—
157	C₃×M₁₆	—	2	4	no	—
158	C₃×M₁₆	—	3	2	no	—
159	C₃×M₁₆	—	3	2	no	—
160	C₃×M₁₆	—	3	8	no	—
161	C₃×M₁₆	—	3	4	no	—
162	C₃×M₁₆	—	4	2	no	—
163	C₃×M₁₆	—	6	8	no	—
164	C₃×M₁₆	—	6	2	no	—
165	C₃×M₁₆	C₂²×D₃	1	4	yes	—
166	C₃×M₁₆	C₂³×C₃	1	4	yes	—
167	C₂×C₃×C₈	—	2	2	no	—
168	C₂×C₃×C₈	—	2	2	no	—
169	C₂×C₃×C₈	—	2	2	no	—
170	C₂×C₃×C₈	—	2	2	no	—
171	C₂×C₃×C₈	—	2	1	no	—
172	C₂×C₃×C₈	—	2	1	no	—
173	C₂×C₃×C₈	—	3	2	no	—
174	C₂×C₃×C₈	—	3	8	no	—
175	C₂×C₃×C₈	—	4	2	no	—
176	C₂×C₃×C₈	—	6	8	no	—
177	C₂×C₃×C₈	—	6	2	no	—
178	C₂×C₃×C₈	C₄×D₃	1	2	yes	—
179	C₂×C₃×C₈	C₄×D₃	1	2	yes	—
180	C₂×C₃×C₈	C₂×C₃×C₄	1	2	yes	—
181	C₂×C₃×C₈	C₂×C₃×C₄	1	2	yes	—
182	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
183	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
184	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
185	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
186	#208	—	2	2	no	—
187	#208	C₂×C₃×C₄	1	2	yes	—
188	#208	C₂×C₃×C₄	1	2	yes	—
189	#208	C₂³×C₃	1	4	yes	—
190	C₂×C₃⋊C₈	—	2	2	no	—
191	C₂×C₃⋊C₈	C₂³×C₃	1	2	yes	—
192	ΓL(1,𝔽₂₅)	—	2	8	no	—
193	ΓL(1,𝔽₂₅)	C₂×C₃×C₄	1	8	yes	—
194	D₃×C₈	—	2	8	no	—
195	D₃×C₈	C₂×C₃×C₄	1	8	yes	—
196	C₂²×C₃²	—	4	1	no	—
197	C₂²×C₃²	C₂×C₄⋊C₄	1	1	yes	characteristic
198	C₂²×C₃²	C₂×C₄⋊C₄	1	1	yes	characteristic
199	C₂²×C₃²	C₂²×Q₈	1	1	yes	characteristic
200	C₂×C₃×D₃	—	4	2	no	—
201	C₂×C₃×D₃	C₂×C₄⋊C₄	1	4	yes	—
202	C₃²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
203	C₃²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
204	C₃²×C₄	C₂³×C₄	1	1	yes	characteristic
205	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
206	C₃×Dic₃	C₂×C₄⋊C₄	1	4	yes	—
207	C₂×#41	—	3	1	no	—
208	#131	—	3	4	no	—
209	#131	—	3	4	no	—
210	#131	—	6	4	no	—
211	#131	—	6	4	no	—
212	C₂×M₁₆	—	3	1	no	—
213	C₂×M₁₆	—	3	2	no	—
214	C₂×M₁₆	—	3	2	no	—
215	C₂×M₁₆	—	3	8	no	—
216	C₂×M₁₆	C₂×C₃×D₃	1	2	yes	—
217	C₂²×C₈	—	3	2	no	—
218	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
219	#108	—	3	8	no	—
220	#108	—	3	2	no	—
221	#108	—	3	2	no	—
222	#108	C₂×C₃×D₃	1	2	yes	—
223	#108	C₂×C₃×D₃	1	2	yes	—
224	C₂³×C₃	—	2	1	no	—
225	C₂³×C₃	—	3	2	no	—
226	C₂³×C₃	D₃×Q₈	1	1	yes	characteristic
227	C₂³×C₃	C₂×C₃×Q₈	1	1	yes	characteristic
228	C₂²×D₃	C₂×C₃×Q₈	1	2	yes	—
229	C₃×Q₈	—	3	2	no	—
230	C₃×Q₈	—	3	2	no	—
231	C₃×D₄	—	3	4	no	—
232	C₃×D₄	—	3	4	no	—
233	C₃×D₄	—	3	2	no	—
234	C₃×D₄	—	3	2	no	—
235	C₂×C₃×C₄	—	2	1	no	—
236	C₂×C₃×C₄	—	2	1	no	—
237	C₂×C₃×C₄	—	2	1	no	—
238	C₂×C₃×C₄	—	2	1	no	—
239	C₂×C₃×C₄	—	2	1	no	—
240	C₂×C₃×C₄	—	2	1	no	—
241	C₂×C₃×C₄	—	3	2	no	—
242	C₂×C₃×C₄	—	3	4	no	—
243	C₂×C₃×C₄	—	3	4	no	—
244	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
245	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
246	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
247	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
248	C₂×C₃×C₄	D₃×Q₈	1	1	yes	characteristic
249	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
250	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
251	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
252	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
253	C₂×C₃×C₄	C₂×C₃×Q₈	1	1	yes	characteristic
254	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
255	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
256	#67	C₃×C₄⋊C₄	1	4	yes	—
257	#67	C₃×C₄⋊C₄	1	4	yes	—
258	C₂×Dic₃	C₂×C₃×Q₈	1	2	yes	—
259	D₁₂	C₃×C₄⋊C₄	1	2	yes	—
260	D₁₂	C₃×C₄⋊C₄	1	2	yes	—
261	C₄×D₃	C₂²×C₃×C₄	1	4	yes	—
262	C₄×D₃	C₂×C₃×D₄	1	4	yes	—
263	Dic₆	C₃×C₄⋊C₄	1	2	yes	—
264	Dic₆	C₃×C₄⋊C₄	1	2	yes	—
265	C₃×C₈	—	2	4	no	—
266	C₃×C₈	—	2	4	no	—
267	C₃×C₈	—	2	2	no	—
268	C₃×C₈	—	2	2	no	—
269	C₃×C₈	—	3	4	no	—
270	C₃×C₈	—	4	4	no	—
271	C₃×C₈	—	6	4	no	—
272	C₃×C₈	C₂×C₄×D₃	1	2	yes	—
273	C₃×C₈	C₂×C₄×D₃	1	2	yes	—
274	C₃×C₈	C₂²×C₃×C₄	1	2	yes	—
275	C₃×C₈	C₂²×C₃×C₄	1	2	yes	—
276	C₃⋊C₈	—	2	4	no	—
277	C₃⋊C₈	C₂²×C₃×C₄	1	4	yes	—
278	C₂×C₃²	—	2	1	no	—
279	C₂×C₃²	—	2	1	no	—
280	C₂×C₃²	—	2	1	no	—
281	C₂×C₃²	C₂²×C₄⋊C₄	1	1	yes	characteristic
282	C₃×D₃	—	2	4	no	—
283	#41	—	3	2	no	—
284	#41	—	3	2	no	—
285	#41	—	3	2	no	—
286	#41	—	3	2	no	—
287	C₂×Q₈	—	3	1	no	—
288	C₂×D₄	—	3	2	no	—
289	C₂×D₄	—	3	1	no	—
290	C₂²×C₄	—	3	2	no	—
291	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
292	M₁₆	—	2	2	no	—
293	M₁₆	—	3	2	no	—
294	M₁₆	—	3	2	no	—
295	M₁₆	—	3	8	no	—
296	M₁₆	—	3	4	no	—
297	M₁₆	—	6	8	no	—
298	M₁₆	—	6	2	no	—
299	M₁₆	C₂²×C₃×D₃	1	4	yes	—
300	C₂×C₈	—	2	2	no	—
301	C₂×C₈	—	3	2	no	—
302	C₂×C₈	—	3	8	no	—
303	C₂×C₈	—	6	8	no	—
304	C₂×C₈	—	6	2	no	—
305	C₂×C₈	C₃×C₄×D₃	1	2	yes	—
306	C₂×C₈	C₃×C₄×D₃	1	2	yes	—
307	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
308	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
309	C₂²×C₃	—	2	1	no	—
310	C₂²×C₃	—	2	1	no	—
311	C₂²×C₃	—	2	1	no	—
312	C₂²×C₃	—	3	4	no	—
313	C₂²×C₃	—	4	1	no	—
314	C₂²×C₃	—	4	1	no	—
315	C₂²×C₃	—	4	2	no	—
316	C₂²×C₃	—	12	2	no	—
317	C₂²×C₃	D₃×C₄⋊C₄	1	1	yes	characteristic
318	C₂²×C₃	D₃×C₄⋊C₄	1	1	yes	characteristic
319	C₂²×C₃	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
320	C₂²×C₃	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
321	C₂²×C₃	C₂×D₃×Q₈	1	1	yes	characteristic
322	C₂²×C₃	C₂²×C₃×Q₈	1	1	yes	characteristic
323	C₂×D₃	—	4	2	no	—
324	C₂×D₃	C₂×C₃×C₄⋊C₄	1	4	yes	—
325	C₃×C₄	—	2	1	no	—
326	C₃×C₄	—	2	1	no	—
327	C₃×C₄	—	2	1	no	—
328	C₃×C₄	—	2	1	no	—
329	C₃×C₄	—	3	4	no	—
330	C₃×C₄	D₃×C₄⋊C₄	1	1	yes	characteristic
331	C₃×C₄	D₃×C₄⋊C₄	1	1	yes	characteristic
332	C₃×C₄	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
333	C₃×C₄	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
334	C₃×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
335	C₃×C₄	C₂×D₃×D₄	1	1	yes	characteristic
336	C₃×C₄	C₂³×C₃×C₄	1	1	yes	characteristic
337	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
338	Dic₃	C₂×C₃×C₄⋊C₄	1	4	yes	—
339	C₃²	#2916	1	1	yes	characteristic, complemented, Sylow
340	C₂³	—	3	2	no	—
341	C₂³	C₃×D₃×Q₈	1	1	yes	characteristic
342	Q₈	—	3	2	no	—
343	Q₈	—	3	2	no	—
344	D₄	—	3	4	no	—
345	D₄	—	3	4	no	—
346	D₄	—	3	2	no	—
347	D₄	—	3	2	no	—
348	C₂×C₄	—	3	2	no	—
349	C₂×C₄	—	3	4	no	—
350	C₂×C₄	—	3	4	no	—
351	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
352	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
353	C₂×C₄	C₃×D₃×D₄	1	1	yes	characteristic
354	C₂×C₄	C₃×D₃×D₄	1	1	yes	characteristic
355	C₂×C₄	C₃×D₃×Q₈	1	1	yes	characteristic
356	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
357	C₈	—	2	4	no	—
358	C₈	—	3	4	no	—
359	C₈	—	6	4	no	—
360	C₈	C₂×C₃×C₄×D₃	1	2	yes	—
361	C₈	C₂×C₃×C₄×D₃	1	2	yes	—
362	C₂×C₃	—	2	2	no	—
363	C₂×C₃	—	2	1	no	—
364	C₂×C₃	—	2	1	no	—
365	C₂×C₃	—	2	1	no	—
366	C₂×C₃	—	2	1	no	—
367	C₂×C₃	—	2	1	no	—
368	C₂×C₃	—	2	1	no	—
369	C₂×C₃	—	2	1	no	—
370	C₂×C₃	—	4	1	no	—
371	C₂×C₃	—	4	1	no	—
372	C₂×C₃	—	6	4	no	—
373	C₂×C₃	C₂×D₃×C₄⋊C₄	1	1	yes	characteristic
374	C₂×C₃	C₂²×C₃×C₄⋊C₄	1	1	yes	characteristic
375	D₃	—	2	4	no	—
376	C₂²	—	3	4	no	—
377	C₂²	—	4	1	no	—
378	C₂²	—	12	2	no	—
379	C₂²	C₃×D₃×C₄⋊C₄	1	1	yes	characteristic
380	C₂²	C₃×D₃×C₄⋊C₄	1	1	yes	characteristic
381	C₂²	C₂×C₃×D₃×Q₈	1	1	yes	characteristic
382	C₄	—	3	4	no	—
383	C₄	C₃×D₃×C₄⋊C₄	1	1	yes	characteristic
384	C₄	C₃×D₃×C₄⋊C₄	1	1	yes	characteristic
385	C₄	C₂²×C₃×C₄×D₃	1	1	yes	characteristic
386	C₄	C₂×C₃×D₃×D₄	1	1	yes	characteristic
387	C₃	—	2	1	no	—
388	C₃	#79252	1	1	yes	characteristic, direct product factor
389	C₃	C₃×#2916	1	1	yes	characteristic, complemented
390	C₂	—	2	1	no	—
391	C₂	—	2	1	no	—
392	C₂	—	2	1	no	—
393	C₂	—	6	4	no	—
394	C₂	C₂×C₃×D₃×C₄⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₄	C₂×D₃×D₄
commutator	C₃×C₄	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₂×C₃²×#108	C₂
socle	C₂×C₃²	C₂²×C₄⋊C₄
prime radical	C₂×C₃×#235	C₂²
cosocle	C₂×C₃×C₄	C₂⁴×C₃
hypercenter	C₂×C₃×#108	D₃
hypocenter	C₃	C₃×#2916
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ 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. C₃×#5124	C₂	semidirect
5. C₂×C₃×#819	C₂	semidirect
6. C₃×#4893	C₂	semidirect
7. C₃×D₃×#108	C₂	semidirect
9. #79252	C₃	direct (N × H)
36. C₂×C₃×#108	D₃	semidirect
37. C₂×C₃×#108	C₂×C₃	semidirect
38. #5124	C₂×C₃	semidirect
39. C₂×#819	C₂×C₃	semidirect
40. #4893	C₂×C₃	semidirect
41. D₃×#108	C₂×C₃	semidirect
135. C₂×#108	C₃×D₃	semidirect
339. C₃²	#2916	semidirect
388. C₃	#79252	direct (N × H)
389. C₃	C₃×#2916	semidirect

Maximal subgroups

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

subgroup	index
C₃×#5745	2
C₂×C₃×#901	2
C₂×C₃²×#108	2
C₃×#5124	2
C₂×C₃×#819	2
C₃×#4893	2
C₃×D₃×#108	2
C₃×#2916	3
#79252	3

Subgroups — C3×#79252 #11858661

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#79252 #11858661