Subgroups — C₃²×#3276 #11770325

Order 1152.

1416 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	C₂×C₃²×#137	C₂	1	2	yes	maximal, complemented
2	C₃²×D₄×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×#547	C₂	1	1	yes	maximal, characteristic
4	C₃²×#494	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃²×#470	C₂	1	2	yes	maximal, complemented
6	C₃²×#462	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃²×#461	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃²×#452	C₂	1	2	yes	maximal, complemented
9	C₃²×#451	C₂	1	2	yes	maximal, complemented
10	C₃²×C₄×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃²×#436	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#3276	C₃	1	4	yes	maximal, direct product factor
13	C₂×C₃²×#41	C₂²	1	2	yes	—
14	C₂²×C₃²×Q₈	C₂²	1	2	yes	—
15	C₃²×#137	—	2	8	no	—
16	C₂×C₃²×Q₁₆	C₂²	1	2	yes	—
17	C₂×C₃²×Q₁₆	C₂²	1	2	yes	—
18	C₂×C₃²×Q₁₆	C₂²	1	2	yes	—
19	C₂×C₃²×SD₁₆	C₂²	1	2	yes	—
20	C₂×C₃²×SD₁₆	C₂²	1	1	yes	characteristic
21	C₂×C₃²×M₁₆	C₂²	1	2	yes	—
22	C₃²×C₄⋊Q₈	—	2	1	no	—
23	C₃²×C₄⋊Q₈	C₂²	1	1	yes	characteristic
24	C₃²×C₄⋊Q₈	C₂²	1	1	yes	characteristic
25	C₃²×#123	—	2	2	no	—
26	C₃²×C₂²⋊Q₈	—	2	2	no	—
27	C₃²×C₂²⋊Q₈	C₂²	1	2	yes	—
28	C₃²×C₂²⋊Q₈	C₂²	1	2	yes	—
29	C₃²×#121	—	2	1	no	—
30	C₃²×C₄×Q₈	C₂²	1	1	yes	characteristic
31	C₃²×C₄×D₄	—	2	1	no	—
32	C₃²×C₄×D₄	C₂²	1	1	yes	characteristic
33	C₃²×C₄×D₄	C₂²	1	1	yes	characteristic
34	C₂×C₃²×C₄⋊C₄	—	2	1	no	—
35	C₃²×#106	C₂²	1	1	yes	characteristic
36	C₃²×C₄⋊C₈	C₂²	1	1	yes	characteristic
37	C₃²×#103	C₂²	1	1	yes	characteristic
38	C₃²×#103	C₂²	1	2	yes	—
39	C₃²×#103	C₂²	1	2	yes	—
40	C₃²×#102	C₂²	1	1	yes	characteristic
41	C₃²×C₂²⋊C₈	C₂²	1	2	yes	—
42	C₃²×C₄×C₈	C₂²	1	1	yes	characteristic
43	C₂×C₃×#137	C₂×C₃	1	8	yes	complemented
44	C₃×D₄×Q₈	C₂×C₃	1	4	yes	complemented
45	C₃×#547	C₂×C₃	1	4	yes	—
46	C₃×#494	C₂×C₃	1	4	yes	complemented
47	C₃×#470	C₂×C₃	1	8	yes	complemented
48	C₃×#462	C₂×C₃	1	4	yes	complemented
49	C₃×#461	C₂×C₃	1	4	yes	complemented
50	C₃×#452	C₂×C₃	1	8	yes	complemented
51	C₃×#451	C₂×C₃	1	8	yes	complemented
52	C₃×C₄×SD₁₆	C₂×C₃	1	4	yes	complemented
53	C₃×#436	C₂×C₃	1	4	yes	complemented
54	C₃²×#41	—	2	4	no	—
55	C₃²×#41	—	4	2	no	—
56	C₂×C₃²×Q₈	—	2	2	no	—
57	C₂×C₃²×Q₈	—	2	4	no	—
58	C₂×C₃²×Q₈	—	4	2	no	—
59	C₂×C₃²×Q₈	C₂³	1	2	yes	—
60	C₂×C₃²×Q₈	C₂³	1	2	yes	—
61	C₂×C₃²×Q₈	C₂³	1	1	yes	characteristic
62	C₂×C₃²×D₄	—	2	2	no	—
63	C₂×C₃²×D₄	D₄	1	1	yes	characteristic
64	C₂×C₃²×D₄	C₂³	1	1	yes	characteristic
65	C₂²×C₃²×C₄	—	2	2	no	—
66	C₂²×C₃²×C₄	—	2	2	no	—
67	C₂²×C₃²×C₄	—	2	1	no	—
68	C₂²×C₃²×C₄	C₂³	1	2	yes	—
69	C₃²×Q₁₆	—	2	4	no	—
70	C₃²×Q₁₆	—	2	4	no	—
71	C₃²×Q₁₆	—	4	2	no	—
72	C₃²×SD₁₆	—	2	4	no	—
73	C₃²×SD₁₆	D₄	1	4	yes	complemented
74	C₃²×M₁₆	—	2	4	no	—
75	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
76	C₂×C₃²×C₈	C₂³	1	2	yes	—
77	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
78	C₃²×C₄⋊C₄	—	2	1	no	—
79	C₃²×C₄⋊C₄	—	2	2	no	—
80	C₃²×C₄⋊C₄	—	2	1	no	—
81	C₃²×C₄⋊C₄	—	2	1	no	—
82	C₃²×C₄⋊C₄	—	2	1	no	—
83	C₃²×C₄⋊C₄	—	2	2	no	—
84	C₃²×C₄⋊C₄	—	2	1	no	—
85	C₃²×C₄⋊C₄	D₄	1	1	yes	characteristic
86	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
87	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
88	C₃²×C₂²⋊C₄	—	2	2	no	—
89	C₃²×C₂²⋊C₄	—	2	2	no	—
90	C₃²×C₂²⋊C₄	—	2	1	no	—
91	C₃²×C₂²⋊C₄	D₄	1	2	yes	—
92	C₃²×C₄²	—	2	1	no	—
93	C₃²×C₄²	C₂³	1	1	yes	characteristic
94	#3276	C₃²	1	1	yes	characteristic, direct product factor, Sylow
95	C₂×C₃×#41	C₂²×C₃	1	8	yes	—
96	C₂²×C₃×Q₈	C₂²×C₃	1	8	yes	—
97	C₃×#137	—	2	32	no	—
98	C₂×C₃×Q₁₆	C₂²×C₃	1	8	yes	—
99	C₂×C₃×Q₁₆	C₂²×C₃	1	8	yes	—
100	C₂×C₃×Q₁₆	C₂²×C₃	1	8	yes	—
101	C₂×C₃×SD₁₆	C₂²×C₃	1	8	yes	—
102	C₂×C₃×SD₁₆	C₂²×C₃	1	4	yes	—
103	C₂×C₃×M₁₆	C₂²×C₃	1	8	yes	—
104	C₃×C₄⋊Q₈	—	2	4	no	—
105	C₃×C₄⋊Q₈	C₂²×C₃	1	4	yes	—
106	C₃×C₄⋊Q₈	C₂²×C₃	1	4	yes	—
107	C₃×#123	—	2	8	no	—
108	C₃×C₂²⋊Q₈	—	2	8	no	—
109	C₃×C₂²⋊Q₈	C₂²×C₃	1	8	yes	—
110	C₃×C₂²⋊Q₈	C₂²×C₃	1	8	yes	—
111	C₃×#121	—	2	4	no	—
112	C₃×C₄×Q₈	C₂²×C₃	1	4	yes	—
113	C₃×C₄×D₄	—	2	4	no	—
114	C₃×C₄×D₄	C₂²×C₃	1	4	yes	—
115	C₃×C₄×D₄	C₂²×C₃	1	4	yes	—
116	C₂×C₃×C₄⋊C₄	—	2	4	no	—
117	C₃×#106	C₂²×C₃	1	4	yes	—
118	C₃×C₄⋊C₈	C₂²×C₃	1	4	yes	—
119	C₃×#103	C₂²×C₃	1	4	yes	—
120	C₃×#103	C₂²×C₃	1	8	yes	—
121	C₃×#103	C₂²×C₃	1	8	yes	—
122	C₃×#102	C₂²×C₃	1	4	yes	—
123	C₃×C₂²⋊C₈	C₂²×C₃	1	8	yes	—
124	C₃×C₄×C₈	C₂²×C₃	1	4	yes	—
125	C₂³×C₃²	—	2	1	no	—
126	C₂³×C₃²	C₂×D₄	1	2	yes	—
127	C₃²×Q₈	—	2	1	no	—
128	C₃²×Q₈	—	2	2	no	—
129	C₃²×Q₈	—	2	2	no	—
130	C₃²×Q₈	—	2	2	no	—
131	C₃²×Q₈	—	2	2	no	—
132	C₃²×Q₈	—	4	4	no	—
133	C₃²×Q₈	C₂×D₄	1	2	yes	—
134	C₃²×D₄	—	2	2	no	—
135	C₃²×D₄	—	2	1	no	—
136	C₃²×D₄	—	4	4	no	—
137	C₃²×D₄	C₂×D₄	1	2	yes	—
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	—	2	1	no	—
142	C₂×C₃²×C₄	—	2	1	no	—
143	C₂×C₃²×C₄	—	2	2	no	—
144	C₂×C₃²×C₄	—	2	2	no	—
145	C₂×C₃²×C₄	—	4	4	no	—
146	C₂×C₃²×C₄	—	4	4	no	—
147	C₂×C₃²×C₄	—	4	2	no	—
148	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
149	C₂×C₃²×C₄	C₂×D₄	1	2	yes	—
150	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
151	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
152	C₃²×C₈	—	2	2	no	—
153	C₃²×C₈	—	2	1	no	—
154	C₃²×C₈	C₂×D₄	1	2	yes	—
155	C₂×#137	C₂×C₃²	1	2	yes	complemented
156	D₄×Q₈	C₂×C₃²	1	1	yes	characteristic, complemented
157	#547	C₂×C₃²	1	1	yes	characteristic
158	#494	C₂×C₃²	1	1	yes	characteristic, complemented
159	#470	C₂×C₃²	1	2	yes	complemented
160	#462	C₂×C₃²	1	1	yes	characteristic, complemented
161	#461	C₂×C₃²	1	1	yes	characteristic, complemented
162	#452	C₂×C₃²	1	2	yes	complemented
163	#451	C₂×C₃²	1	2	yes	complemented
164	C₄×SD₁₆	C₂×C₃²	1	1	yes	characteristic, complemented
165	#436	C₂×C₃²	1	1	yes	characteristic, complemented
166	C₃×#41	—	2	16	no	—
167	C₃×#41	—	4	8	no	—
168	C₂×C₃×Q₈	—	2	8	no	—
169	C₂×C₃×Q₈	—	2	16	no	—
170	C₂×C₃×Q₈	—	4	8	no	—
171	C₂×C₃×Q₈	C₂³×C₃	1	8	yes	—
172	C₂×C₃×Q₈	C₂³×C₃	1	8	yes	—
173	C₂×C₃×Q₈	C₂³×C₃	1	4	yes	—
174	C₂×C₃×D₄	—	2	8	no	—
175	C₂×C₃×D₄	C₃×D₄	1	4	yes	—
176	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
177	C₂²×C₃×C₄	—	2	8	no	—
178	C₂²×C₃×C₄	—	2	4	no	—
179	C₂²×C₃×C₄	—	2	8	no	—
180	C₂²×C₃×C₄	C₂³×C₃	1	8	yes	—
181	C₃×Q₁₆	—	2	16	no	—
182	C₃×Q₁₆	—	2	16	no	—
183	C₃×Q₁₆	—	4	8	no	—
184	C₃×SD₁₆	—	2	16	no	—
185	C₃×SD₁₆	C₃×D₄	1	16	yes	complemented
186	C₃×M₁₆	—	2	16	no	—
187	C₂×C₃×C₈	C₂³×C₃	1	4	yes	—
188	C₂×C₃×C₈	C₂³×C₃	1	8	yes	—
189	C₂×C₃×C₈	C₂³×C₃	1	4	yes	—
190	C₃×C₄⋊C₄	—	2	4	no	—
191	C₃×C₄⋊C₄	—	2	8	no	—
192	C₃×C₄⋊C₄	—	2	4	no	—
193	C₃×C₄⋊C₄	—	2	4	no	—
194	C₃×C₄⋊C₄	—	2	4	no	—
195	C₃×C₄⋊C₄	—	2	8	no	—
196	C₃×C₄⋊C₄	—	2	4	no	—
197	C₃×C₄⋊C₄	C₃×D₄	1	4	yes	—
198	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
199	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
200	C₃×C₂²⋊C₄	—	2	8	no	—
201	C₃×C₂²⋊C₄	—	2	8	no	—
202	C₃×C₂²⋊C₄	—	2	4	no	—
203	C₃×C₂²⋊C₄	C₃×D₄	1	8	yes	—
204	C₃×C₄²	—	2	4	no	—
205	C₃×C₄²	C₂³×C₃	1	4	yes	—
206	C₂²×C₃²	—	2	2	no	—
207	C₂²×C₃²	—	2	2	no	—
208	C₂²×C₃²	—	2	2	no	—
209	C₂²×C₃²	—	2	2	no	—
210	C₂²×C₃²	—	4	1	no	—
211	C₂²×C₃²	—	4	1	no	—
212	C₂²×C₃²	C₂²×D₄	1	1	yes	characteristic
213	C₃²×C₄	—	2	2	no	—
214	C₃²×C₄	—	2	2	no	—
215	C₃²×C₄	—	2	1	no	—
216	C₃²×C₄	—	4	2	no	—
217	C₃²×C₄	—	4	2	no	—
218	C₃²×C₄	—	4	1	no	—
219	C₃²×C₄	—	4	1	no	—
220	C₃²×C₄	#137	1	2	yes	complemented
221	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
222	C₃²×C₄	H(5,𝔽₂)	1	1	yes	characteristic
223	C₂×#41	C₂²×C₃²	1	2	yes	—
224	C₂²×Q₈	C₂²×C₃²	1	2	yes	—
225	#137	—	2	8	no	—
226	C₂×Q₁₆	C₂²×C₃²	1	2	yes	—
227	C₂×Q₁₆	C₂²×C₃²	1	2	yes	—
228	C₂×Q₁₆	C₂²×C₃²	1	2	yes	—
229	C₂×SD₁₆	C₂²×C₃²	1	2	yes	—
230	C₂×SD₁₆	C₂²×C₃²	1	1	yes	characteristic
231	C₂×M₁₆	C₂²×C₃²	1	2	yes	—
232	C₄⋊Q₈	—	2	1	no	—
233	C₄⋊Q₈	C₂²×C₃²	1	1	yes	characteristic
234	C₄⋊Q₈	C₂²×C₃²	1	1	yes	characteristic
235	#123	—	2	2	no	—
236	C₂²⋊Q₈	—	2	2	no	—
237	C₂²⋊Q₈	C₂²×C₃²	1	2	yes	—
238	C₂²⋊Q₈	C₂²×C₃²	1	2	yes	—
239	#121	—	2	1	no	—
240	C₄×Q₈	C₂²×C₃²	1	1	yes	characteristic
241	C₄×D₄	—	2	1	no	—
242	C₄×D₄	C₂²×C₃²	1	1	yes	characteristic
243	C₄×D₄	C₂²×C₃²	1	1	yes	characteristic
244	C₂×C₄⋊C₄	—	2	1	no	—
245	#106	C₂²×C₃²	1	1	yes	characteristic
246	C₄⋊C₈	C₂²×C₃²	1	1	yes	characteristic
247	#103	C₂²×C₃²	1	1	yes	characteristic
248	#103	C₂²×C₃²	1	2	yes	—
249	#103	C₂²×C₃²	1	2	yes	—
250	#102	C₂²×C₃²	1	1	yes	characteristic
251	C₂²⋊C₈	C₂²×C₃²	1	2	yes	—
252	C₄×C₈	C₂²×C₃²	1	1	yes	characteristic
253	C₂³×C₃	—	2	4	no	—
254	C₂³×C₃	C₂×C₃×D₄	1	8	yes	—
255	C₃×Q₈	—	2	4	no	—
256	C₃×Q₈	—	2	8	no	—
257	C₃×Q₈	—	2	8	no	—
258	C₃×Q₈	—	2	8	no	—
259	C₃×Q₈	—	2	8	no	—
260	C₃×Q₈	—	4	16	no	—
261	C₃×Q₈	C₂×C₃×D₄	1	8	yes	—
262	C₃×D₄	—	2	8	no	—
263	C₃×D₄	—	2	4	no	—
264	C₃×D₄	—	4	16	no	—
265	C₃×D₄	C₂×C₃×D₄	1	8	yes	—
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	—	2	4	no	—
270	C₂×C₃×C₄	—	2	4	no	—
271	C₂×C₃×C₄	—	2	8	no	—
272	C₂×C₃×C₄	—	2	8	no	—
273	C₂×C₃×C₄	—	4	16	no	—
274	C₂×C₃×C₄	—	4	16	no	—
275	C₂×C₃×C₄	—	4	8	no	—
276	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
277	C₂×C₃×C₄	C₂×C₃×D₄	1	8	yes	—
278	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
279	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
280	C₃×C₈	—	2	8	no	—
281	C₃×C₈	—	2	4	no	—
282	C₃×C₈	C₂×C₃×D₄	1	8	yes	—
283	C₂×C₃²	—	4	2	no	—
284	C₂×C₃²	—	4	2	no	—
285	C₂×C₃²	D₄²	1	1	yes	characteristic
286	C₂×C₃²	C₂×#137	1	1	yes	characteristic
287	C₂×C₃²	#578	1	1	yes	characteristic
288	#41	—	2	4	no	—
289	#41	—	4	2	no	—
290	C₂×Q₈	—	2	2	no	—
291	C₂×Q₈	—	2	4	no	—
292	C₂×Q₈	—	4	2	no	—
293	C₂×Q₈	C₂³×C₃²	1	2	yes	—
294	C₂×Q₈	C₂³×C₃²	1	2	yes	—
295	C₂×Q₈	C₂³×C₃²	1	1	yes	characteristic
296	C₂×D₄	—	2	2	no	—
297	C₂×D₄	C₃²×D₄	1	1	yes	characteristic
298	C₂×D₄	C₂³×C₃²	1	1	yes	characteristic
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	2	1	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	C₂³×C₃²	1	2	yes	—
303	Q₁₆	—	2	4	no	—
304	Q₁₆	—	2	4	no	—
305	Q₁₆	—	4	2	no	—
306	SD₁₆	—	2	4	no	—
307	SD₁₆	C₃²×D₄	1	4	yes	complemented
308	M₁₆	—	2	4	no	—
309	C₂×C₈	C₂³×C₃²	1	1	yes	characteristic
310	C₂×C₈	C₂³×C₃²	1	2	yes	—
311	C₂×C₈	C₂³×C₃²	1	1	yes	characteristic
312	C₄⋊C₄	—	2	1	no	—
313	C₄⋊C₄	—	2	2	no	—
314	C₄⋊C₄	—	2	1	no	—
315	C₄⋊C₄	—	2	1	no	—
316	C₄⋊C₄	—	2	1	no	—
317	C₄⋊C₄	—	2	2	no	—
318	C₄⋊C₄	—	2	1	no	—
319	C₄⋊C₄	C₃²×D₄	1	1	yes	characteristic
320	C₄⋊C₄	C₂³×C₃²	1	1	yes	characteristic
321	C₄⋊C₄	C₂³×C₃²	1	1	yes	characteristic
322	C₂²⋊C₄	—	2	2	no	—
323	C₂²⋊C₄	—	2	2	no	—
324	C₂²⋊C₄	—	2	1	no	—
325	C₂²⋊C₄	C₃²×D₄	1	2	yes	—
326	C₄²	—	2	1	no	—
327	C₄²	C₂³×C₃²	1	1	yes	characteristic
328	C₂²×C₃	—	2	8	no	—
329	C₂²×C₃	—	2	8	no	—
330	C₂²×C₃	—	2	8	no	—
331	C₂²×C₃	—	2	8	no	—
332	C₂²×C₃	—	4	4	no	—
333	C₂²×C₃	—	4	4	no	—
334	C₂²×C₃	C₂²×C₃×D₄	1	4	yes	—
335	C₃×C₄	—	2	4	no	—
336	C₃×C₄	—	2	8	no	—
337	C₃×C₄	—	2	8	no	—
338	C₃×C₄	—	4	4	no	—
339	C₃×C₄	—	4	4	no	—
340	C₃×C₄	—	4	8	no	—
341	C₃×C₄	—	4	8	no	—
342	C₃×C₄	C₃×#137	1	8	yes	complemented
343	C₃×C₄	C₂²×C₃×D₄	1	4	yes	—
344	C₃×C₄	C₃×H(5,𝔽₂)	1	4	yes	—
345	C₃²	#3276	1	1	yes	characteristic, direct product factor, Sylow
346	C₂³	—	2	1	no	—
347	C₂³	C₂×C₃²×D₄	1	2	yes	—
348	Q₈	—	2	1	no	—
349	Q₈	—	2	2	no	—
350	Q₈	—	2	2	no	—
351	Q₈	—	2	2	no	—
352	Q₈	—	2	2	no	—
353	Q₈	—	4	4	no	—
354	Q₈	C₂×C₃²×D₄	1	2	yes	—
355	D₄	—	2	1	no	—
356	D₄	—	2	2	no	—
357	D₄	—	4	4	no	—
358	D₄	C₂×C₃²×D₄	1	2	yes	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	4	4	no	—
367	C₂×C₄	—	4	4	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	C₂×C₃²×D₄	1	1	yes	characteristic
370	C₂×C₄	C₂×C₃²×D₄	1	2	yes	—
371	C₂×C₄	C₂×C₃²×D₄	1	1	yes	characteristic
372	C₂×C₄	C₂⁴×C₃²	1	1	yes	characteristic
373	C₈	—	2	2	no	—
374	C₈	—	2	1	no	—
375	C₈	C₂×C₃²×D₄	1	2	yes	—
376	C₂×C₃	—	4	8	no	—
377	C₂×C₃	—	4	8	no	—
378	C₂×C₃	C₃×D₄²	1	4	yes	—
379	C₂×C₃	C₂×C₃×#137	1	4	yes	—
380	C₂×C₃	C₃×#578	1	4	yes	—
381	C₂²	—	2	2	no	—
382	C₂²	—	2	2	no	—
383	C₂²	—	2	2	no	—
384	C₂²	—	2	2	no	—
385	C₂²	—	4	1	no	—
386	C₂²	—	4	1	no	—
387	C₂²	C₂²×C₃²×D₄	1	1	yes	characteristic
388	C₄	—	2	1	no	—
389	C₄	—	2	2	no	—
390	C₄	—	2	2	no	—
391	C₄	—	4	1	no	—
392	C₄	—	4	1	no	—
393	C₄	—	4	2	no	—
394	C₄	—	4	2	no	—
395	C₄	C₃²×#137	1	2	yes	complemented
396	C₄	C₂²×C₃²×D₄	1	1	yes	characteristic
397	C₄	C₃²×H(5,𝔽₂)	1	1	yes	characteristic
398	C₃	C₃×#3276	1	4	yes	direct product factor
399	C₂	—	4	2	no	—
400	C₂	—	4	2	no	—
401	C₂	C₃²×D₄²	1	1	yes	characteristic
402	C₂	C₂×C₃²×#137	1	1	yes	characteristic
403	C₂	C₃²×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃²	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃²
prime radical	C₃²×#547	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃² ◁ C₃²×C₄×D₄ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃²×#137	C₂	semidirect
2. C₃²×D₄×Q₈	C₂	semidirect
4. C₃²×#494	C₂	semidirect
5. C₃²×#470	C₂	semidirect
6. C₃²×#462	C₂	semidirect
7. C₃²×#461	C₂	semidirect
8. C₃²×#452	C₂	semidirect
9. C₃²×#451	C₂	semidirect
10. C₃²×C₄×SD₁₆	C₂	semidirect
11. C₃²×#436	C₂	semidirect
12. C₃×#3276	C₃	direct (N × H)
43. C₂×C₃×#137	C₂×C₃	semidirect
44. C₃×D₄×Q₈	C₂×C₃	semidirect
46. C₃×#494	C₂×C₃	semidirect
47. C₃×#470	C₂×C₃	semidirect
48. C₃×#462	C₂×C₃	semidirect
49. C₃×#461	C₂×C₃	semidirect
50. C₃×#452	C₂×C₃	semidirect
51. C₃×#451	C₂×C₃	semidirect
52. C₃×C₄×SD₁₆	C₂×C₃	semidirect
53. C₃×#436	C₂×C₃	semidirect
73. C₃²×SD₁₆	D₄	semidirect
94. #3276	C₃²	direct (N × H)
155. C₂×#137	C₂×C₃²	semidirect
156. D₄×Q₈	C₂×C₃²	semidirect
158. #494	C₂×C₃²	semidirect
159. #470	C₂×C₃²	semidirect
160. #462	C₂×C₃²	semidirect
161. #461	C₂×C₃²	semidirect
162. #452	C₂×C₃²	semidirect
163. #451	C₂×C₃²	semidirect
164. C₄×SD₁₆	C₂×C₃²	semidirect
165. #436	C₂×C₃²	semidirect
185. C₃×SD₁₆	C₃×D₄	semidirect
220. C₃²×C₄	#137	semidirect
307. SD₁₆	C₃²×D₄	semidirect
342. C₃×C₄	C₃×#137	semidirect
345. C₃²	#3276	direct (N × H)
395. C₄	C₃²×#137	semidirect
398. C₃	C₃×#3276	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×C₃²×#137	2
C₃²×D₄×Q₈	2
C₃²×#547	2
C₃²×#494	2
C₃²×#470	2
C₃²×#462	2
C₃²×#461	2
C₃²×#452	2
C₃²×#451	2
C₃²×C₄×SD₁₆	2
C₃²×#436	2
C₃×#3276	3

Subgroups — C32×#3276 #11770325

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#3276 #11770325