Subgroups — C₃²×#3091 #11770140

Order 1152.

1260 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#525	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃²×#117	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×#485	C₂	1	2	yes	maximal, complemented
4	C₃²×#484	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃²×#483	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃²×#482	C₂	1	2	yes	maximal, complemented
7	C₃²×#481	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃²×#480	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃²×#427	C₂	1	2	yes	maximal, complemented
10	C₃²×#416	C₂	1	2	yes	maximal, complemented
11	C₂×C₃²×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#3091	C₃	1	4	yes	maximal, direct product factor
13	C₂×C₃²×#41	C₂²	1	1	yes	characteristic
14	C₂³×C₃²×C₄	C₂²	1	1	yes	characteristic
15	C₂²×C₃²×C₈	C₂²	1	2	yes	—
16	C₃²×#123	—	2	1	no	—
17	C₃²×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
18	C₃²×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
19	C₃²×#121	C₂²	1	1	yes	characteristic
20	C₃²×#121	C₂²	1	1	yes	characteristic
21	C₃²×#120	—	2	1	no	—
22	C₃²×C₄×D₄	—	2	1	no	—
23	C₃²×C₄×D₄	—	2	1	no	—
24	C₃²×#117	—	2	1	no	—
25	C₃²×#117	—	2	1	no	—
26	C₃²×#117	C₂²	1	2	yes	—
27	C₃²×#117	C₂²	1	2	yes	—
28	C₃²×#117	C₂²	1	1	yes	characteristic
29	C₂×C₃²×C₄⋊C₄	C₂²	1	1	yes	characteristic
30	C₂×C₃²×C₄⋊C₄	C₂²	1	1	yes	characteristic
31	C₂×C₃²×C₂²⋊C₄	—	2	1	no	—
32	C₂×C₃²×C₄²	—	2	1	no	—
33	C₃²×#107	C₂²	1	2	yes	complemented
34	C₃²×#107	C₂²	1	2	yes	complemented
35	C₃²×#106	C₂²	1	2	yes	complemented
36	C₃²×#106	C₂²	1	2	yes	complemented
37	C₃²×#103	C₂²	1	2	yes	complemented
38	C₃²×#103	C₂²	1	2	yes	complemented
39	C₃²×#102	C₂²	1	2	yes	complemented
40	C₃²×#102	C₂²	1	2	yes	complemented
41	C₃²×C₂²⋊C₈	C₂²	1	1	yes	characteristic
42	C₃²×C₂²⋊C₈	C₂²	1	1	yes	characteristic
43	C₃²×C₂²⋊C₈	C₂²	1	2	yes	—
44	C₃×#525	C₂×C₃	1	4	yes	—
45	C₂×C₃×#117	C₂×C₃	1	4	yes	complemented
46	C₃×#485	C₂×C₃	1	8	yes	complemented
47	C₃×#484	C₂×C₃	1	4	yes	complemented
48	C₃×#483	C₂×C₃	1	4	yes	complemented
49	C₃×#482	C₂×C₃	1	8	yes	complemented
50	C₃×#481	C₂×C₃	1	4	yes	complemented
51	C₃×#480	C₂×C₃	1	4	yes	complemented
52	C₃×#427	C₂×C₃	1	8	yes	complemented
53	C₃×#416	C₂×C₃	1	8	yes	complemented
54	C₂×C₃×C₂²⋊C₈	C₂×C₃	1	4	yes	complemented
55	C₂⁴×C₃²	D₄	1	1	yes	characteristic
56	C₃²×#41	—	2	4	no	—
57	C₂×C₃²×Q₈	C₂³	1	1	yes	characteristic
58	C₂×C₃²×D₄	—	2	1	no	—
59	C₂×C₃²×D₄	—	2	1	no	—
60	C₂×C₃²×D₄	—	2	1	no	—
61	C₂×C₃²×D₄	C₂³	1	1	yes	characteristic
62	C₂²×C₃²×C₄	—	2	4	no	—
63	C₂²×C₃²×C₄	—	2	1	no	—
64	C₂²×C₃²×C₄	—	2	1	no	—
65	C₂²×C₃²×C₄	—	2	1	no	—
66	C₂²×C₃²×C₄	D₄	1	1	yes	characteristic
67	C₂²×C₃²×C₄	D₄	1	1	yes	characteristic
68	C₂²×C₃²×C₄	D₄	1	1	yes	characteristic
69	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
70	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
71	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
72	C₂×C₃²×C₈	—	2	4	no	—
73	C₂×C₃²×C₈	C₂³	1	2	yes	—
74	C₂×C₃²×C₈	C₂³	1	2	yes	—
75	C₃²×C₄⋊C₄	—	2	1	no	—
76	C₃²×C₄⋊C₄	—	2	1	no	—
77	C₃²×C₄⋊C₄	—	2	1	no	—
78	C₃²×C₄⋊C₄	—	2	1	no	—
79	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
80	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
81	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
82	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
83	C₃²×C₂²⋊C₄	—	2	2	no	—
84	C₃²×C₂²⋊C₄	—	2	2	no	—
85	C₃²×C₂²⋊C₄	—	2	1	no	—
86	C₃²×C₂²⋊C₄	—	2	1	no	—
87	C₃²×C₂²⋊C₄	—	2	1	no	—
88	C₃²×C₂²⋊C₄	—	2	1	no	—
89	C₃²×C₂²⋊C₄	—	2	1	no	—
90	C₃²×C₄²	—	2	2	no	—
91	C₃²×C₄²	—	2	2	no	—
92	C₃²×C₄²	—	2	1	no	—
93	#3091	C₃²	1	1	yes	characteristic, direct product factor, Sylow
94	C₂×C₃×#41	C₂²×C₃	1	4	yes	—
95	C₂³×C₃×C₄	C₂²×C₃	1	4	yes	—
96	C₂²×C₃×C₈	C₂²×C₃	1	8	yes	—
97	C₃×#123	—	2	4	no	—
98	C₃×C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
99	C₃×C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
100	C₃×#121	C₂²×C₃	1	4	yes	—
101	C₃×#121	C₂²×C₃	1	4	yes	—
102	C₃×#120	—	2	4	no	—
103	C₃×C₄×D₄	—	2	4	no	—
104	C₃×C₄×D₄	—	2	4	no	—
105	C₃×#117	—	2	4	no	—
106	C₃×#117	—	2	4	no	—
107	C₃×#117	C₂²×C₃	1	8	yes	—
108	C₃×#117	C₂²×C₃	1	4	yes	—
109	C₃×#117	C₂²×C₃	1	8	yes	—
110	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	4	yes	—
111	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	4	yes	—
112	C₂×C₃×C₂²⋊C₄	—	2	4	no	—
113	C₂×C₃×C₄²	—	2	4	no	—
114	C₃×#107	C₂²×C₃	1	8	yes	complemented
115	C₃×#107	C₂²×C₃	1	8	yes	complemented
116	C₃×#106	C₂²×C₃	1	8	yes	complemented
117	C₃×#106	C₂²×C₃	1	8	yes	complemented
118	C₃×#103	C₂²×C₃	1	8	yes	complemented
119	C₃×#103	C₂²×C₃	1	8	yes	complemented
120	C₃×#102	C₂²×C₃	1	8	yes	complemented
121	C₃×#102	C₂²×C₃	1	8	yes	complemented
122	C₃×C₂²⋊C₈	C₂²×C₃	1	4	yes	—
123	C₃×C₂²⋊C₈	C₂²×C₃	1	4	yes	—
124	C₃×C₂²⋊C₈	C₂²×C₃	1	8	yes	—
125	C₂³×C₃²	—	2	2	no	—
126	C₂³×C₃²	—	2	2	no	—
127	C₂³×C₃²	—	2	1	no	—
128	C₂³×C₃²	—	4	1	no	—
129	C₂³×C₃²	C₂×D₄	1	1	yes	characteristic
130	C₂³×C₃²	C₂×D₄	1	1	yes	characteristic
131	C₂³×C₃²	C₂×D₄	1	1	yes	characteristic
132	C₃²×Q₈	—	2	2	no	—
133	C₃²×D₄	—	2	2	no	—
134	C₃²×D₄	—	4	2	no	—
135	C₃²×D₄	—	4	2	no	—
136	C₃²×D₄	—	4	2	no	—
137	C₂×C₃²×C₄	—	2	2	no	—
138	C₂×C₃²×C₄	—	2	2	no	—
139	C₂×C₃²×C₄	—	2	2	no	—
140	C₂×C₃²×C₄	—	2	2	no	—
141	C₂×C₃²×C₄	—	2	2	no	—
142	C₂×C₃²×C₄	—	2	2	no	—
143	C₂×C₃²×C₄	—	2	2	no	—
144	C₂×C₃²×C₄	—	2	1	no	—
145	C₂×C₃²×C₄	—	2	1	no	—
146	C₂×C₃²×C₄	—	2	1	no	—
147	C₂×C₃²×C₄	—	4	2	no	—
148	C₂×C₃²×C₄	—	4	2	no	—
149	C₂×C₃²×C₄	—	4	2	no	—
150	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
151	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
152	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
153	C₂×C₃²×C₄	#41	1	4	yes	—
154	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
155	C₃²×C₈	—	2	2	no	—
156	C₃²×C₈	—	2	2	no	—
157	#525	C₂×C₃²	1	1	yes	characteristic
158	C₂×#117	C₂×C₃²	1	1	yes	characteristic, complemented
159	#485	C₂×C₃²	1	2	yes	complemented
160	#484	C₂×C₃²	1	1	yes	characteristic, complemented
161	#483	C₂×C₃²	1	1	yes	characteristic, complemented
162	#482	C₂×C₃²	1	2	yes	complemented
163	#481	C₂×C₃²	1	1	yes	characteristic, complemented
164	#480	C₂×C₃²	1	1	yes	characteristic, complemented
165	#427	C₂×C₃²	1	2	yes	complemented
166	#416	C₂×C₃²	1	2	yes	complemented
167	C₂×C₂²⋊C₈	C₂×C₃²	1	1	yes	characteristic, complemented
168	C₂⁴×C₃	C₃×D₄	1	4	yes	—
169	C₃×#41	—	2	16	no	—
170	C₂×C₃×Q₈	C₂³×C₃	1	4	yes	—
171	C₂×C₃×D₄	—	2	4	no	—
172	C₂×C₃×D₄	—	2	4	no	—
173	C₂×C₃×D₄	—	2	4	no	—
174	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
175	C₂²×C₃×C₄	—	2	16	no	—
176	C₂²×C₃×C₄	—	2	4	no	—
177	C₂²×C₃×C₄	—	2	4	no	—
178	C₂²×C₃×C₄	—	2	4	no	—
179	C₂²×C₃×C₄	C₃×D₄	1	4	yes	—
180	C₂²×C₃×C₄	C₃×D₄	1	4	yes	—
181	C₂²×C₃×C₄	C₃×D₄	1	4	yes	—
182	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
183	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
184	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
185	C₂×C₃×C₈	—	2	16	no	—
186	C₂×C₃×C₈	C₂³×C₃	1	8	yes	—
187	C₂×C₃×C₈	C₂³×C₃	1	8	yes	—
188	C₃×C₄⋊C₄	—	2	4	no	—
189	C₃×C₄⋊C₄	—	2	4	no	—
190	C₃×C₄⋊C₄	—	2	4	no	—
191	C₃×C₄⋊C₄	—	2	4	no	—
192	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
193	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
194	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
195	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
196	C₃×C₂²⋊C₄	—	2	8	no	—
197	C₃×C₂²⋊C₄	—	2	8	no	—
198	C₃×C₂²⋊C₄	—	2	4	no	—
199	C₃×C₂²⋊C₄	—	2	4	no	—
200	C₃×C₂²⋊C₄	—	2	4	no	—
201	C₃×C₂²⋊C₄	—	2	4	no	—
202	C₃×C₂²⋊C₄	—	2	4	no	—
203	C₃×C₄²	—	2	8	no	—
204	C₃×C₄²	—	2	8	no	—
205	C₃×C₄²	—	2	4	no	—
206	C₂²×C₃²	—	2	1	no	—
207	C₂²×C₃²	—	2	1	no	—
208	C₂²×C₃²	—	2	1	no	—
209	C₂²×C₃²	—	2	1	no	—
210	C₂²×C₃²	—	2	1	no	—
211	C₂²×C₃²	—	2	1	no	—
212	C₂²×C₃²	—	2	1	no	—
213	C₂²×C₃²	—	4	4	no	—
214	C₂²×C₃²	—	4	1	no	—
215	C₂²×C₃²	—	4	1	no	—
216	C₂²×C₃²	—	4	1	no	—
217	C₂²×C₃²	#123	1	2	yes	—
218	C₂²×C₃²	#135	1	2	yes	—
219	C₂²×C₃²	C₂²×D₄	1	1	yes	characteristic
220	C₃²×C₄	—	2	1	no	—
221	C₃²×C₄	—	2	1	no	—
222	C₃²×C₄	—	4	1	no	—
223	C₃²×C₄	—	4	2	no	—
224	C₃²×C₄	—	4	1	no	—
225	C₃²×C₄	—	4	2	no	—
226	C₃²×C₄	—	4	1	no	—
227	C₃²×C₄	#123	1	2	yes	—
228	C₃²×C₄	C₂×#41	1	2	yes	—
229	C₂×#41	C₂²×C₃²	1	1	yes	characteristic
230	C₂³×C₄	C₂²×C₃²	1	1	yes	characteristic
231	C₂²×C₈	C₂²×C₃²	1	2	yes	—
232	#123	—	2	1	no	—
233	C₂²⋊Q₈	C₂²×C₃²	1	1	yes	characteristic
234	C₂²⋊Q₈	C₂²×C₃²	1	1	yes	characteristic
235	#121	C₂²×C₃²	1	1	yes	characteristic
236	#121	C₂²×C₃²	1	1	yes	characteristic
237	#120	—	2	1	no	—
238	C₄×D₄	—	2	1	no	—
239	C₄×D₄	—	2	1	no	—
240	#117	—	2	1	no	—
241	#117	—	2	1	no	—
242	#117	C₂²×C₃²	1	2	yes	—
243	#117	C₂²×C₃²	1	2	yes	—
244	#117	C₂²×C₃²	1	1	yes	characteristic
245	C₂×C₄⋊C₄	C₂²×C₃²	1	1	yes	characteristic
246	C₂×C₄⋊C₄	C₂²×C₃²	1	1	yes	characteristic
247	C₂×C₂²⋊C₄	—	2	1	no	—
248	C₂×C₄²	—	2	1	no	—
249	#107	C₂²×C₃²	1	2	yes	complemented
250	#107	C₂²×C₃²	1	2	yes	complemented
251	#106	C₂²×C₃²	1	2	yes	complemented
252	#106	C₂²×C₃²	1	2	yes	complemented
253	#103	C₂²×C₃²	1	2	yes	complemented
254	#103	C₂²×C₃²	1	2	yes	complemented
255	#102	C₂²×C₃²	1	2	yes	complemented
256	#102	C₂²×C₃²	1	2	yes	complemented
257	C₂²⋊C₈	C₂²×C₃²	1	1	yes	characteristic
258	C₂²⋊C₈	C₂²×C₃²	1	1	yes	characteristic
259	C₂²⋊C₈	C₂²×C₃²	1	2	yes	—
260	C₂³×C₃	—	2	8	no	—
261	C₂³×C₃	—	2	8	no	—
262	C₂³×C₃	—	2	4	no	—
263	C₂³×C₃	—	4	4	no	—
264	C₂³×C₃	C₂×C₃×D₄	1	4	yes	—
265	C₂³×C₃	C₂×C₃×D₄	1	4	yes	—
266	C₂³×C₃	C₂×C₃×D₄	1	4	yes	—
267	C₃×Q₈	—	2	8	no	—
268	C₃×D₄	—	2	8	no	—
269	C₃×D₄	—	4	8	no	—
270	C₃×D₄	—	4	8	no	—
271	C₃×D₄	—	4	8	no	—
272	C₂×C₃×C₄	—	2	8	no	—
273	C₂×C₃×C₄	—	2	8	no	—
274	C₂×C₃×C₄	—	2	8	no	—
275	C₂×C₃×C₄	—	2	8	no	—
276	C₂×C₃×C₄	—	2	8	no	—
277	C₂×C₃×C₄	—	2	8	no	—
278	C₂×C₃×C₄	—	2	8	no	—
279	C₂×C₃×C₄	—	2	4	no	—
280	C₂×C₃×C₄	—	2	4	no	—
281	C₂×C₃×C₄	—	2	4	no	—
282	C₂×C₃×C₄	—	4	8	no	—
283	C₂×C₃×C₄	—	4	8	no	—
284	C₂×C₃×C₄	—	4	8	no	—
285	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
286	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
287	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
288	C₂×C₃×C₄	C₃×#41	1	16	yes	—
289	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
290	C₃×C₈	—	2	8	no	—
291	C₃×C₈	—	2	8	no	—
292	C₂×C₃²	—	2	2	no	—
293	C₂×C₃²	—	2	2	no	—
294	C₂×C₃²	—	4	1	no	—
295	C₂×C₃²	—	8	1	no	—
296	C₂×C₃²	C₂×#123	1	1	yes	characteristic
297	C₂×C₃²	C₂×#135	1	1	yes	characteristic
298	C₂×C₃²	#575	1	1	yes	characteristic
299	C₂⁴	C₃²×D₄	1	1	yes	characteristic
300	#41	—	2	4	no	—
301	C₂×Q₈	C₂³×C₃²	1	1	yes	characteristic
302	C₂×D₄	—	2	1	no	—
303	C₂×D₄	—	2	1	no	—
304	C₂×D₄	—	2	1	no	—
305	C₂×D₄	C₂³×C₃²	1	1	yes	characteristic
306	C₂²×C₄	—	2	4	no	—
307	C₂²×C₄	—	2	1	no	—
308	C₂²×C₄	—	2	1	no	—
309	C₂²×C₄	—	2	1	no	—
310	C₂²×C₄	C₃²×D₄	1	1	yes	characteristic
311	C₂²×C₄	C₃²×D₄	1	1	yes	characteristic
312	C₂²×C₄	C₃²×D₄	1	1	yes	characteristic
313	C₂²×C₄	C₂³×C₃²	1	1	yes	characteristic
314	C₂²×C₄	C₂³×C₃²	1	1	yes	characteristic
315	C₂²×C₄	C₂³×C₃²	1	1	yes	characteristic
316	C₂×C₈	—	2	4	no	—
317	C₂×C₈	C₂³×C₃²	1	2	yes	—
318	C₂×C₈	C₂³×C₃²	1	2	yes	—
319	C₄⋊C₄	—	2	1	no	—
320	C₄⋊C₄	—	2	1	no	—
321	C₄⋊C₄	—	2	1	no	—
322	C₄⋊C₄	—	2	1	no	—
323	C₄⋊C₄	C₂³×C₃²	1	2	yes	—
324	C₄⋊C₄	C₂³×C₃²	1	2	yes	—
325	C₄⋊C₄	C₂³×C₃²	1	1	yes	characteristic
326	C₄⋊C₄	C₂³×C₃²	1	1	yes	characteristic
327	C₂²⋊C₄	—	2	2	no	—
328	C₂²⋊C₄	—	2	2	no	—
329	C₂²⋊C₄	—	2	1	no	—
330	C₂²⋊C₄	—	2	1	no	—
331	C₂²⋊C₄	—	2	1	no	—
332	C₂²⋊C₄	—	2	1	no	—
333	C₂²⋊C₄	—	2	1	no	—
334	C₄²	—	2	2	no	—
335	C₄²	—	2	2	no	—
336	C₄²	—	2	1	no	—
337	C₂²×C₃	—	2	4	no	—
338	C₂²×C₃	—	2	4	no	—
339	C₂²×C₃	—	2	4	no	—
340	C₂²×C₃	—	2	4	no	—
341	C₂²×C₃	—	2	4	no	—
342	C₂²×C₃	—	2	4	no	—
343	C₂²×C₃	—	2	4	no	—
344	C₂²×C₃	—	4	16	no	—
345	C₂²×C₃	—	4	4	no	—
346	C₂²×C₃	—	4	4	no	—
347	C₂²×C₃	—	4	4	no	—
348	C₂²×C₃	C₃×#123	1	8	yes	—
349	C₂²×C₃	C₃×#135	1	8	yes	—
350	C₂²×C₃	C₂²×C₃×D₄	1	4	yes	—
351	C₃×C₄	—	2	4	no	—
352	C₃×C₄	—	2	4	no	—
353	C₃×C₄	—	4	8	no	—
354	C₃×C₄	—	4	4	no	—
355	C₃×C₄	—	4	8	no	—
356	C₃×C₄	—	4	4	no	—
357	C₃×C₄	—	4	4	no	—
358	C₃×C₄	C₃×#123	1	8	yes	—
359	C₃×C₄	C₂×C₃×#41	1	8	yes	—
360	C₃²	#3091	1	1	yes	characteristic, direct product factor, Sylow
361	C₂³	—	2	2	no	—
362	C₂³	—	2	2	no	—
363	C₂³	—	2	1	no	—
364	C₂³	—	4	1	no	—
365	C₂³	C₂×C₃²×D₄	1	1	yes	characteristic
366	C₂³	C₂×C₃²×D₄	1	1	yes	characteristic
367	C₂³	C₂×C₃²×D₄	1	1	yes	characteristic
368	Q₈	—	2	2	no	—
369	D₄	—	2	2	no	—
370	D₄	—	4	2	no	—
371	D₄	—	4	2	no	—
372	D₄	—	4	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	C₂×C₃²×D₄	1	1	yes	characteristic
387	C₂×C₄	C₂×C₃²×D₄	1	1	yes	characteristic
388	C₂×C₄	C₂×C₃²×D₄	1	1	yes	characteristic
389	C₂×C₄	C₃²×#41	1	4	yes	—
390	C₂×C₄	C₂⁴×C₃²	1	1	yes	characteristic
391	C₈	—	2	2	no	—
392	C₈	—	2	2	no	—
393	C₂×C₃	—	2	8	no	—
394	C₂×C₃	—	2	8	no	—
395	C₂×C₃	—	4	4	no	—
396	C₂×C₃	—	8	4	no	—
397	C₂×C₃	C₂×C₃×#123	1	4	yes	—
398	C₂×C₃	C₂×C₃×#135	1	4	yes	—
399	C₂×C₃	C₃×#575	1	4	yes	—
400	C₂²	—	2	1	no	—
401	C₂²	—	2	1	no	—
402	C₂²	—	2	1	no	—
403	C₂²	—	2	1	no	—
404	C₂²	—	2	1	no	—
405	C₂²	—	2	1	no	—
406	C₂²	—	2	1	no	—
407	C₂²	—	4	4	no	—
408	C₂²	—	4	1	no	—
409	C₂²	—	4	1	no	—
410	C₂²	—	4	1	no	—
411	C₂²	C₃²×#123	1	2	yes	—
412	C₂²	C₃²×#135	1	2	yes	—
413	C₂²	C₂²×C₃²×D₄	1	1	yes	characteristic
414	C₄	—	2	1	no	—
415	C₄	—	2	1	no	—
416	C₄	—	4	2	no	—
417	C₄	—	4	1	no	—
418	C₄	—	4	2	no	—
419	C₄	—	4	1	no	—
420	C₄	—	4	1	no	—
421	C₄	C₃²×#123	1	2	yes	—
422	C₄	C₂×C₃²×#41	1	2	yes	—
423	C₃	C₃×#3091	1	4	yes	direct product factor
424	C₂	—	2	2	no	—
425	C₂	—	2	2	no	—
426	C₂	—	4	1	no	—
427	C₂	—	8	1	no	—
428	C₂	C₂×C₃²×#123	1	1	yes	characteristic
429	C₂	C₂×C₃²×#135	1	1	yes	characteristic
430	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	C₃²×#525	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃²×C₄ ◁ C₂³×C₃²×C₄ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₃²×#117	C₂	semidirect
3. C₃²×#485	C₂	semidirect
4. C₃²×#484	C₂	semidirect
5. C₃²×#483	C₂	semidirect
6. C₃²×#482	C₂	semidirect
7. C₃²×#481	C₂	semidirect
8. C₃²×#480	C₂	semidirect
9. C₃²×#427	C₂	semidirect
10. C₃²×#416	C₂	semidirect
11. C₂×C₃²×C₂²⋊C₈	C₂	semidirect
12. C₃×#3091	C₃	direct (N × H)
33. C₃²×#107	C₂²	semidirect
34. C₃²×#107	C₂²	semidirect
35. C₃²×#106	C₂²	semidirect
36. C₃²×#106	C₂²	semidirect
37. C₃²×#103	C₂²	semidirect
38. C₃²×#103	C₂²	semidirect
39. C₃²×#102	C₂²	semidirect
40. C₃²×#102	C₂²	semidirect
45. C₂×C₃×#117	C₂×C₃	semidirect
46. C₃×#485	C₂×C₃	semidirect
47. C₃×#484	C₂×C₃	semidirect
48. C₃×#483	C₂×C₃	semidirect
49. C₃×#482	C₂×C₃	semidirect
50. C₃×#481	C₂×C₃	semidirect
51. C₃×#480	C₂×C₃	semidirect
52. C₃×#427	C₂×C₃	semidirect
53. C₃×#416	C₂×C₃	semidirect
54. C₂×C₃×C₂²⋊C₈	C₂×C₃	semidirect
93. #3091	C₃²	direct (N × H)
114. C₃×#107	C₂²×C₃	semidirect
115. C₃×#107	C₂²×C₃	semidirect
116. C₃×#106	C₂²×C₃	semidirect
117. C₃×#106	C₂²×C₃	semidirect
118. C₃×#103	C₂²×C₃	semidirect
119. C₃×#103	C₂²×C₃	semidirect
120. C₃×#102	C₂²×C₃	semidirect
121. C₃×#102	C₂²×C₃	semidirect
158. C₂×#117	C₂×C₃²	semidirect
159. #485	C₂×C₃²	semidirect
160. #484	C₂×C₃²	semidirect
161. #483	C₂×C₃²	semidirect
162. #482	C₂×C₃²	semidirect
163. #481	C₂×C₃²	semidirect
164. #480	C₂×C₃²	semidirect
165. #427	C₂×C₃²	semidirect
166. #416	C₂×C₃²	semidirect
167. C₂×C₂²⋊C₈	C₂×C₃²	semidirect
249. #107	C₂²×C₃²	semidirect
250. #107	C₂²×C₃²	semidirect
251. #106	C₂²×C₃²	semidirect
252. #106	C₂²×C₃²	semidirect
253. #103	C₂²×C₃²	semidirect
254. #103	C₂²×C₃²	semidirect
255. #102	C₂²×C₃²	semidirect
256. #102	C₂²×C₃²	semidirect
360. C₃²	#3091	direct (N × H)
423. C₃	C₃×#3091	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×#525	2
C₂×C₃²×#117	2
C₃²×#485	2
C₃²×#484	2
C₃²×#483	2
C₃²×#482	2
C₃²×#481	2
C₃²×#480	2
C₃²×#427	2
C₃²×#416	2
C₂×C₃²×C₂²⋊C₈	2
C₃×#3091	3

Subgroups — C32×#3091 #11770140

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#3091 #11770140