Subgroups — C₃²×#3076 #11770125

Order 1152.

1164 conjugacy classes of subgroups.

The subgroup lattice has 405 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#533	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃²×C₄×#41	C₂	1	1	yes	maximal, characteristic
3	C₃²×#479	C₂	1	2	yes	maximal, complemented
4	C₃²×#478	C₂	1	2	yes	maximal, complemented
5	C₃²×#477	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃²×#476	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃²×#475	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃²×#474	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃²×#427	C₂	1	2	yes	maximal, complemented
10	C₂×C₃²×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃²×#416	C₂	1	2	yes	maximal
12	C₃×#3076	C₃	1	4	yes	maximal, direct product factor
13	C₂×C₃²×#41	C₂²	1	1	yes	characteristic
14	C₂²×C₃²×C₈	C₂²	1	2	yes	—
15	C₃²×C₄⋊Q₈	C₂²	1	1	yes	characteristic
16	C₃²×C₄⋊Q₈	C₂²	1	1	yes	characteristic
17	C₃²×#125	C₂²	1	2	yes	—
18	C₃²×C₂²⋊Q₈	—	2	1	no	—
19	C₃²×C₂²⋊Q₈	—	2	1	no	—
20	C₃²×C₄×Q₈	—	2	1	no	—
21	C₃²×C₄×Q₈	—	2	1	no	—
22	C₃²×C₄×Q₈	C₂²	1	1	yes	characteristic
23	C₃²×C₄×Q₈	C₂²	1	1	yes	characteristic
24	C₃²×C₄×D₄	—	2	1	no	—
25	C₃²×C₄×D₄	—	2	1	no	—
26	C₃²×C₄×D₄	C₂²	1	1	yes	characteristic
27	C₃²×C₄×D₄	C₂²	1	1	yes	characteristic
28	C₃²×#117	—	2	1	no	—
29	C₃²×#117	C₂²	1	2	yes	—
30	C₃²×#117	C₂²	1	1	yes	characteristic
31	C₂×C₃²×C₄²	—	2	1	no	—
32	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
33	C₃²×#107	C₂²	1	2	yes	—
34	C₃²×#107	C₂²	1	2	yes	—
35	C₃²×#106	C₂²	1	2	yes	—
36	C₃²×#106	C₂²	1	2	yes	—
37	C₃²×C₄⋊C₈	C₂²	1	1	yes	characteristic
38	C₃²×C₄⋊C₈	C₂²	1	1	yes	characteristic
39	C₃²×C₄⋊C₈	C₂²	1	2	yes	—
40	C₃²×#103	C₂²	1	2	yes	—
41	C₃²×#103	C₂²	1	2	yes	—
42	C₃²×#102	C₂²	1	2	yes	—
43	C₃²×#102	C₂²	1	2	yes	—
44	C₃×#533	C₂×C₃	1	4	yes	complemented
45	C₃×C₄×#41	C₂×C₃	1	4	yes	—
46	C₃×#479	C₂×C₃	1	8	yes	complemented
47	C₃×#478	C₂×C₃	1	8	yes	complemented
48	C₃×#477	C₂×C₃	1	4	yes	complemented
49	C₃×#476	C₂×C₃	1	4	yes	complemented
50	C₃×#475	C₂×C₃	1	4	yes	complemented
51	C₃×#474	C₂×C₃	1	4	yes	complemented
52	C₃×#427	C₂×C₃	1	8	yes	complemented
53	C₂×C₃×C₄⋊C₈	C₂×C₃	1	4	yes	complemented
54	C₃×#416	C₂×C₃	1	8	yes	—
55	C₃²×#41	—	2	2	no	—
56	C₃²×#41	Q₈	1	4	yes	complemented
57	C₂×C₃²×Q₈	—	2	1	no	—
58	C₂×C₃²×Q₈	—	2	1	no	—
59	C₂×C₃²×Q₈	C₂³	1	1	yes	characteristic
60	C₂×C₃²×D₄	—	2	1	no	—
61	C₂×C₃²×D₄	C₂³	1	1	yes	characteristic
62	C₂²×C₃²×C₄	—	2	1	no	—
63	C₂²×C₃²×C₄	—	2	1	no	—
64	C₂²×C₃²×C₄	—	2	1	no	—
65	C₂²×C₃²×C₄	D₄	1	1	yes	characteristic
66	C₂²×C₃²×C₄	D₄	1	1	yes	characteristic
67	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
68	C₂×C₃²×C₈	—	2	4	no	—
69	C₂×C₃²×C₈	C₂³	1	2	yes	—
70	C₂×C₃²×C₈	C₂³	1	2	yes	—
71	C₃²×C₄⋊C₄	—	2	1	no	—
72	C₃²×C₄⋊C₄	—	2	1	no	—
73	C₃²×C₄⋊C₄	—	2	2	no	—
74	C₃²×C₄⋊C₄	—	2	2	no	—
75	C₃²×C₄⋊C₄	—	2	1	no	—
76	C₃²×C₄⋊C₄	—	2	1	no	—
77	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
78	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
79	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
80	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
81	C₃²×C₂²⋊C₄	—	2	1	no	—
82	C₃²×C₂²⋊C₄	—	2	2	no	—
83	C₃²×C₂²⋊C₄	—	2	1	no	—
84	C₃²×C₂²⋊C₄	—	2	1	no	—
85	C₃²×C₄²	—	2	1	no	—
86	C₃²×C₄²	—	2	1	no	—
87	C₃²×C₄²	—	2	1	no	—
88	C₃²×C₄²	—	2	2	no	—
89	C₃²×C₄²	D₄	1	1	yes	characteristic
90	C₃²×C₄²	D₄	1	1	yes	characteristic
91	C₃²×C₄²	C₂³	1	1	yes	characteristic
92	C₃²×C₄²	C₂³	1	1	yes	characteristic
93	#3076	C₃²	1	1	yes	characteristic, direct product factor, Sylow
94	C₂×C₃×#41	C₂²×C₃	1	4	yes	—
95	C₂²×C₃×C₈	C₂²×C₃	1	8	yes	—
96	C₃×C₄⋊Q₈	C₂²×C₃	1	4	yes	—
97	C₃×C₄⋊Q₈	C₂²×C₃	1	4	yes	—
98	C₃×#125	C₂²×C₃	1	8	yes	—
99	C₃×C₂²⋊Q₈	—	2	4	no	—
100	C₃×C₂²⋊Q₈	—	2	4	no	—
101	C₃×C₄×Q₈	—	2	4	no	—
102	C₃×C₄×Q₈	—	2	4	no	—
103	C₃×C₄×Q₈	C₂²×C₃	1	4	yes	—
104	C₃×C₄×Q₈	C₂²×C₃	1	4	yes	—
105	C₃×C₄×D₄	—	2	4	no	—
106	C₃×C₄×D₄	—	2	4	no	—
107	C₃×C₄×D₄	C₂²×C₃	1	4	yes	—
108	C₃×C₄×D₄	C₂²×C₃	1	4	yes	—
109	C₃×#117	—	2	4	no	—
110	C₃×#117	C₂²×C₃	1	8	yes	—
111	C₃×#117	C₂²×C₃	1	4	yes	—
112	C₂×C₃×C₄²	—	2	4	no	—
113	C₂×C₃×C₄²	C₂²×C₃	1	4	yes	—
114	C₃×#107	C₂²×C₃	1	8	yes	—
115	C₃×#107	C₂²×C₃	1	8	yes	—
116	C₃×#106	C₂²×C₃	1	8	yes	—
117	C₃×#106	C₂²×C₃	1	8	yes	—
118	C₃×C₄⋊C₈	C₂²×C₃	1	4	yes	—
119	C₃×C₄⋊C₈	C₂²×C₃	1	4	yes	—
120	C₃×C₄⋊C₈	C₂²×C₃	1	8	yes	—
121	C₃×#103	C₂²×C₃	1	8	yes	—
122	C₃×#103	C₂²×C₃	1	8	yes	—
123	C₃×#102	C₂²×C₃	1	8	yes	—
124	C₃×#102	C₂²×C₃	1	8	yes	—
125	C₂³×C₃²	—	2	1	no	—
126	C₂³×C₃²	C₂×D₄	1	1	yes	characteristic
127	C₃²×Q₈	—	2	1	no	—
128	C₃²×Q₈	—	4	2	no	—
129	C₃²×Q₈	—	4	2	no	—
130	C₃²×Q₈	C₂×Q₈	1	2	yes	—
131	C₃²×D₄	—	2	4	no	—
132	C₃²×D₄	—	2	1	no	—
133	C₃²×D₄	C₂×Q₈	1	2	yes	—
134	C₂×C₃²×C₄	—	2	1	no	—
135	C₂×C₃²×C₄	—	2	4	no	—
136	C₂×C₃²×C₄	—	2	2	no	—
137	C₂×C₃²×C₄	—	2	1	no	—
138	C₂×C₃²×C₄	—	2	1	no	—
139	C₂×C₃²×C₄	—	2	2	no	—
140	C₂×C₃²×C₄	—	2	2	no	—
141	C₂×C₃²×C₄	—	4	1	no	—
142	C₂×C₃²×C₄	—	4	2	no	—
143	C₂×C₃²×C₄	—	4	2	no	—
144	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
145	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
146	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
147	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
148	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
149	C₂×C₃²×C₄	C₂×Q₈	1	2	yes	—
150	C₂×C₃²×C₄	#41	1	2	yes	—
151	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
152	C₃²×C₈	—	2	2	no	—
153	C₃²×C₈	—	2	2	no	—
154	#533	C₂×C₃²	1	1	yes	characteristic, complemented
155	C₄×#41	C₂×C₃²	1	1	yes	characteristic
156	#479	C₂×C₃²	1	2	yes	complemented
157	#478	C₂×C₃²	1	2	yes	complemented
158	#477	C₂×C₃²	1	1	yes	characteristic, complemented
159	#476	C₂×C₃²	1	1	yes	characteristic, complemented
160	#475	C₂×C₃²	1	1	yes	characteristic, complemented
161	#474	C₂×C₃²	1	1	yes	characteristic, complemented
162	#427	C₂×C₃²	1	2	yes	complemented
163	C₂×C₄⋊C₈	C₂×C₃²	1	1	yes	characteristic, complemented
164	#416	C₂×C₃²	1	2	yes	—
165	C₃×#41	—	2	8	no	—
166	C₃×#41	C₃×Q₈	1	16	yes	complemented
167	C₂×C₃×Q₈	—	2	4	no	—
168	C₂×C₃×Q₈	—	2	4	no	—
169	C₂×C₃×Q₈	C₂³×C₃	1	4	yes	—
170	C₂×C₃×D₄	—	2	4	no	—
171	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
172	C₂²×C₃×C₄	—	2	4	no	—
173	C₂²×C₃×C₄	—	2	4	no	—
174	C₂²×C₃×C₄	—	2	4	no	—
175	C₂²×C₃×C₄	C₃×D₄	1	4	yes	—
176	C₂²×C₃×C₄	C₃×D₄	1	4	yes	—
177	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
178	C₂×C₃×C₈	—	2	16	no	—
179	C₂×C₃×C₈	C₂³×C₃	1	8	yes	—
180	C₂×C₃×C₈	C₂³×C₃	1	8	yes	—
181	C₃×C₄⋊C₄	—	2	4	no	—
182	C₃×C₄⋊C₄	—	2	4	no	—
183	C₃×C₄⋊C₄	—	2	8	no	—
184	C₃×C₄⋊C₄	—	2	8	no	—
185	C₃×C₄⋊C₄	—	2	4	no	—
186	C₃×C₄⋊C₄	—	2	4	no	—
187	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
188	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
189	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
190	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
191	C₃×C₂²⋊C₄	—	2	4	no	—
192	C₃×C₂²⋊C₄	—	2	8	no	—
193	C₃×C₂²⋊C₄	—	2	4	no	—
194	C₃×C₂²⋊C₄	—	2	4	no	—
195	C₃×C₄²	—	2	4	no	—
196	C₃×C₄²	—	2	4	no	—
197	C₃×C₄²	—	2	4	no	—
198	C₃×C₄²	—	2	8	no	—
199	C₃×C₄²	C₃×D₄	1	4	yes	—
200	C₃×C₄²	C₃×D₄	1	4	yes	—
201	C₃×C₄²	C₂³×C₃	1	4	yes	—
202	C₃×C₄²	C₂³×C₃	1	4	yes	—
203	C₂²×C₃²	—	2	1	no	—
204	C₂²×C₃²	—	2	1	no	—
205	C₂²×C₃²	—	2	2	no	—
206	C₂²×C₃²	—	4	1	no	—
207	C₂²×C₃²	—	4	1	no	—
208	C₂²×C₃²	C₂²⋊Q₈	1	2	yes	—
209	C₂²×C₃²	C₂²×D₄	1	1	yes	characteristic
210	C₃²×C₄	—	2	2	no	—
211	C₃²×C₄	—	2	1	no	—
212	C₃²×C₄	—	2	1	no	—
213	C₃²×C₄	—	2	1	no	—
214	C₃²×C₄	—	4	1	no	—
215	C₃²×C₄	—	4	2	no	—
216	C₃²×C₄	—	4	1	no	—
217	C₃²×C₄	—	4	2	no	—
218	C₃²×C₄	C₂²⋊Q₈	1	2	yes	—
219	C₃²×C₄	#135	1	2	yes	—
220	C₃²×C₄	C₂²×Q₈	1	1	yes	characteristic
221	C₃²×C₄	C₂×#41	1	1	yes	characteristic
222	C₂×#41	C₂²×C₃²	1	1	yes	characteristic
223	C₂²×C₈	C₂²×C₃²	1	2	yes	—
224	C₄⋊Q₈	C₂²×C₃²	1	1	yes	characteristic
225	C₄⋊Q₈	C₂²×C₃²	1	1	yes	characteristic
226	#125	C₂²×C₃²	1	2	yes	—
227	C₂²⋊Q₈	—	2	1	no	—
228	C₂²⋊Q₈	—	2	1	no	—
229	C₄×Q₈	—	2	1	no	—
230	C₄×Q₈	—	2	1	no	—
231	C₄×Q₈	C₂²×C₃²	1	1	yes	characteristic
232	C₄×Q₈	C₂²×C₃²	1	1	yes	characteristic
233	C₄×D₄	—	2	1	no	—
234	C₄×D₄	—	2	1	no	—
235	C₄×D₄	C₂²×C₃²	1	1	yes	characteristic
236	C₄×D₄	C₂²×C₃²	1	1	yes	characteristic
237	#117	—	2	1	no	—
238	#117	C₂²×C₃²	1	1	yes	characteristic
239	#117	C₂²×C₃²	1	2	yes	—
240	C₂×C₄²	—	2	1	no	—
241	C₂×C₄²	C₂²×C₃²	1	1	yes	characteristic
242	#107	C₂²×C₃²	1	2	yes	—
243	#107	C₂²×C₃²	1	2	yes	—
244	#106	C₂²×C₃²	1	2	yes	—
245	#106	C₂²×C₃²	1	2	yes	—
246	C₄⋊C₈	C₂²×C₃²	1	1	yes	characteristic
247	C₄⋊C₈	C₂²×C₃²	1	1	yes	characteristic
248	C₄⋊C₈	C₂²×C₃²	1	2	yes	—
249	#103	C₂²×C₃²	1	2	yes	—
250	#103	C₂²×C₃²	1	2	yes	—
251	#102	C₂²×C₃²	1	2	yes	—
252	#102	C₂²×C₃²	1	2	yes	—
253	C₂³×C₃	—	2	4	no	—
254	C₂³×C₃	C₂×C₃×D₄	1	4	yes	—
255	C₃×Q₈	—	2	4	no	—
256	C₃×Q₈	—	4	8	no	—
257	C₃×Q₈	—	4	8	no	—
258	C₃×Q₈	C₂×C₃×Q₈	1	8	yes	—
259	C₃×D₄	—	2	16	no	—
260	C₃×D₄	—	2	4	no	—
261	C₃×D₄	C₂×C₃×Q₈	1	8	yes	—
262	C₂×C₃×C₄	—	2	4	no	—
263	C₂×C₃×C₄	—	2	16	no	—
264	C₂×C₃×C₄	—	2	8	no	—
265	C₂×C₃×C₄	—	2	4	no	—
266	C₂×C₃×C₄	—	2	4	no	—
267	C₂×C₃×C₄	—	2	8	no	—
268	C₂×C₃×C₄	—	2	8	no	—
269	C₂×C₃×C₄	—	4	4	no	—
270	C₂×C₃×C₄	—	4	8	no	—
271	C₂×C₃×C₄	—	4	8	no	—
272	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
273	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
274	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
275	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
276	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
277	C₂×C₃×C₄	C₂×C₃×Q₈	1	8	yes	—
278	C₂×C₃×C₄	C₃×#41	1	8	yes	—
279	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
280	C₃×C₈	—	2	8	no	—
281	C₃×C₈	—	2	8	no	—
282	C₂×C₃²	—	2	2	no	—
283	C₂×C₃²	—	4	2	no	—
284	C₂×C₃²	C₂×C₂²⋊Q₈	1	1	yes	characteristic
285	C₂×C₃²	C₂×#135	1	1	yes	characteristic
286	C₂×C₃²	#575	1	1	yes	characteristic
287	#41	—	2	2	no	—
288	#41	C₃²×Q₈	1	4	yes	complemented
289	C₂×Q₈	—	2	1	no	—
290	C₂×Q₈	—	2	1	no	—
291	C₂×Q₈	C₂³×C₃²	1	1	yes	characteristic
292	C₂×D₄	—	2	1	no	—
293	C₂×D₄	C₂³×C₃²	1	1	yes	characteristic
294	C₂²×C₄	—	2	1	no	—
295	C₂²×C₄	—	2	1	no	—
296	C₂²×C₄	—	2	1	no	—
297	C₂²×C₄	C₃²×D₄	1	1	yes	characteristic
298	C₂²×C₄	C₃²×D₄	1	1	yes	characteristic
299	C₂²×C₄	C₂³×C₃²	1	1	yes	characteristic
300	C₂×C₈	—	2	4	no	—
301	C₂×C₈	C₂³×C₃²	1	2	yes	—
302	C₂×C₈	C₂³×C₃²	1	2	yes	—
303	C₄⋊C₄	—	2	1	no	—
304	C₄⋊C₄	—	2	1	no	—
305	C₄⋊C₄	—	2	2	no	—
306	C₄⋊C₄	—	2	2	no	—
307	C₄⋊C₄	—	2	1	no	—
308	C₄⋊C₄	—	2	1	no	—
309	C₄⋊C₄	C₂³×C₃²	1	2	yes	—
310	C₄⋊C₄	C₂³×C₃²	1	2	yes	—
311	C₄⋊C₄	C₂³×C₃²	1	1	yes	characteristic
312	C₄⋊C₄	C₂³×C₃²	1	1	yes	characteristic
313	C₂²⋊C₄	—	2	1	no	—
314	C₂²⋊C₄	—	2	2	no	—
315	C₂²⋊C₄	—	2	1	no	—
316	C₂²⋊C₄	—	2	1	no	—
317	C₄²	—	2	1	no	—
318	C₄²	—	2	1	no	—
319	C₄²	—	2	1	no	—
320	C₄²	—	2	2	no	—
321	C₄²	C₃²×D₄	1	1	yes	characteristic
322	C₄²	C₃²×D₄	1	1	yes	characteristic
323	C₄²	C₂³×C₃²	1	1	yes	characteristic
324	C₄²	C₂³×C₃²	1	1	yes	characteristic
325	C₂²×C₃	—	2	4	no	—
326	C₂²×C₃	—	2	4	no	—
327	C₂²×C₃	—	2	8	no	—
328	C₂²×C₃	—	4	4	no	—
329	C₂²×C₃	—	4	4	no	—
330	C₂²×C₃	C₃×C₂²⋊Q₈	1	8	yes	—
331	C₂²×C₃	C₂²×C₃×D₄	1	4	yes	—
332	C₃×C₄	—	2	4	no	—
333	C₃×C₄	—	2	4	no	—
334	C₃×C₄	—	2	4	no	—
335	C₃×C₄	—	2	8	no	—
336	C₃×C₄	—	4	4	no	—
337	C₃×C₄	—	4	8	no	—
338	C₃×C₄	—	4	4	no	—
339	C₃×C₄	—	4	8	no	—
340	C₃×C₄	C₃×C₂²⋊Q₈	1	8	yes	—
341	C₃×C₄	C₃×#135	1	8	yes	—
342	C₃×C₄	C₂²×C₃×Q₈	1	4	yes	—
343	C₃×C₄	C₂×C₃×#41	1	4	yes	—
344	C₃²	#3076	1	1	yes	characteristic, direct product factor, Sylow
345	C₂³	—	2	1	no	—
346	C₂³	C₂×C₃²×D₄	1	1	yes	characteristic
347	Q₈	—	2	1	no	—
348	Q₈	—	4	2	no	—
349	Q₈	—	4	2	no	—
350	Q₈	C₂×C₃²×Q₈	1	2	yes	—
351	D₄	—	2	4	no	—
352	D₄	—	2	1	no	—
353	D₄	C₂×C₃²×Q₈	1	2	yes	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	4	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	4	1	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	C₂×C₃²×D₄	1	1	yes	characteristic
365	C₂×C₄	C₂×C₃²×D₄	1	1	yes	characteristic
366	C₂×C₄	C₂×C₃²×D₄	1	1	yes	characteristic
367	C₂×C₄	C₂×C₃²×D₄	1	1	yes	characteristic
368	C₂×C₄	C₂×C₃²×D₄	1	1	yes	characteristic
369	C₂×C₄	C₂×C₃²×Q₈	1	2	yes	—
370	C₂×C₄	C₃²×#41	1	2	yes	—
371	C₂×C₄	C₂⁴×C₃²	1	1	yes	characteristic
372	C₈	—	2	2	no	—
373	C₈	—	2	2	no	—
374	C₂×C₃	—	2	8	no	—
375	C₂×C₃	—	4	8	no	—
376	C₂×C₃	C₂×C₃×C₂²⋊Q₈	1	4	yes	—
377	C₂×C₃	C₂×C₃×#135	1	4	yes	—
378	C₂×C₃	C₃×#575	1	4	yes	—
379	C₂²	—	2	1	no	—
380	C₂²	—	2	1	no	—
381	C₂²	—	2	2	no	—
382	C₂²	—	4	1	no	—
383	C₂²	—	4	1	no	—
384	C₂²	C₃²×C₂²⋊Q₈	1	2	yes	—
385	C₂²	C₂²×C₃²×D₄	1	1	yes	characteristic
386	C₄	—	2	1	no	—
387	C₄	—	2	1	no	—
388	C₄	—	2	1	no	—
389	C₄	—	2	2	no	—
390	C₄	—	4	1	no	—
391	C₄	—	4	2	no	—
392	C₄	—	4	1	no	—
393	C₄	—	4	2	no	—
394	C₄	C₃²×C₂²⋊Q₈	1	2	yes	—
395	C₄	C₃²×#135	1	2	yes	—
396	C₄	C₂²×C₃²×Q₈	1	1	yes	characteristic
397	C₄	C₂×C₃²×#41	1	1	yes	characteristic
398	C₃	C₃×#3076	1	4	yes	direct product factor
399	C₂	—	2	2	no	—
400	C₂	—	4	2	no	—
401	C₂	C₂×C₃²×C₂²⋊Q₈	1	1	yes	characteristic
402	C₂	C₂×C₃²×#135	1	1	yes	characteristic
403	C₂	C₃²×#575	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃²×C₄	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃²
socle	C₂²×C₃²	C₂²×D₄
prime radical	C₂×C₃²×#41	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃²×C₄ ◁ C₂×C₃²×C₄² ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃²×#533	C₂	semidirect
3. C₃²×#479	C₂	semidirect
4. C₃²×#478	C₂	semidirect
5. C₃²×#477	C₂	semidirect
6. C₃²×#476	C₂	semidirect
7. C₃²×#475	C₂	semidirect
8. C₃²×#474	C₂	semidirect
9. C₃²×#427	C₂	semidirect
10. C₂×C₃²×C₄⋊C₈	C₂	semidirect
12. C₃×#3076	C₃	direct (N × H)
44. C₃×#533	C₂×C₃	semidirect
46. C₃×#479	C₂×C₃	semidirect
47. C₃×#478	C₂×C₃	semidirect
48. C₃×#477	C₂×C₃	semidirect
49. C₃×#476	C₂×C₃	semidirect
50. C₃×#475	C₂×C₃	semidirect
51. C₃×#474	C₂×C₃	semidirect
52. C₃×#427	C₂×C₃	semidirect
53. C₂×C₃×C₄⋊C₈	C₂×C₃	semidirect
56. C₃²×#41	Q₈	semidirect
93. #3076	C₃²	direct (N × H)
154. #533	C₂×C₃²	semidirect
156. #479	C₂×C₃²	semidirect
157. #478	C₂×C₃²	semidirect
158. #477	C₂×C₃²	semidirect
159. #476	C₂×C₃²	semidirect
160. #475	C₂×C₃²	semidirect
161. #474	C₂×C₃²	semidirect
162. #427	C₂×C₃²	semidirect
163. C₂×C₄⋊C₈	C₂×C₃²	semidirect
166. C₃×#41	C₃×Q₈	semidirect
288. #41	C₃²×Q₈	semidirect
344. C₃²	#3076	direct (N × H)
398. C₃	C₃×#3076	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×#533	2
C₃²×C₄×#41	2
C₃²×#479	2
C₃²×#478	2
C₃²×#477	2
C₃²×#476	2
C₃²×#475	2
C₃²×#474	2
C₃²×#427	2
C₂×C₃²×C₄⋊C₈	2
C₃²×#416	2
C₃×#3076	3

Subgroups — C32×#3076 #11770125

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#3076 #11770125