Subgroups — C₃²×#3278 #11770327

Order 1152.

1446 conjugacy classes of subgroups.

The subgroup lattice has 411 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×#550	C₂	1	1	yes	maximal, characteristic
3	C₃²×D₄×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃²×#492	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃²×#468	C₂	1	2	yes	maximal, complemented
6	C₃²×#462	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃²×#460	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃²×#452	C₂	1	2	yes	maximal, complemented
9	C₃²×#448	C₂	1	2	yes	maximal, complemented
10	C₃²×C₄×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃²×#436	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#3278	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	1	yes	characteristic
18	C₂×C₃²×SD₁₆	C₂²	1	2	yes	—
19	C₂×C₃²×SD₁₆	C₂²	1	2	yes	—
20	C₂×C₃²×SD₁₆	C₂²	1	2	yes	—
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×#127	—	2	1	no	—
25	C₃²×#127	C₂²	1	1	yes	characteristic
26	C₃²×C₂²⋊Q₈	—	2	2	no	—
27	C₃²×C₂²⋊Q₈	C₂²	1	2	yes	—
28	C₃²×#121	—	2	2	no	—
29	C₃²×#121	C₂²	1	2	yes	—
30	C₃²×C₄×Q₈	C₂²	1	1	yes	characteristic
31	C₃²×C₄×Q₈	C₂²	1	1	yes	characteristic
32	C₃²×C₄×D₄	—	2	1	no	—
33	C₃²×C₄×D₄	—	2	1	no	—
34	C₃²×C₄×D₄	C₂²	1	1	yes	characteristic
35	C₃²×#107	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	1	yes	characteristic
40	C₃²×#102	C₂²	1	2	yes	—
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×#550	C₂×C₃	1	4	yes	—
45	C₃×D₄×Q₈	C₂×C₃	1	4	yes	complemented
46	C₃×#492	C₂×C₃	1	4	yes	complemented
47	C₃×#468	C₂×C₃	1	8	yes	complemented
48	C₃×#462	C₂×C₃	1	4	yes	complemented
49	C₃×#460	C₂×C₃	1	4	yes	complemented
50	C₃×#452	C₂×C₃	1	8	yes	complemented
51	C₃×#448	C₂×C₃	1	8	yes	complemented
52	C₃×C₄×Q₁₆	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	1	yes	characteristic
61	C₂×C₃²×Q₈	C₂³	1	1	yes	characteristic
62	C₂×C₃²×D₄	—	2	2	no	—
63	C₂×C₃²×D₄	—	2	2	no	—
64	C₂×C₃²×D₄	—	2	1	no	—
65	C₂×C₃²×D₄	—	2	1	no	—
66	C₂×C₃²×D₄	D₄	1	1	yes	characteristic
67	C₂×C₃²×D₄	C₂³	1	2	yes	—
68	C₂²×C₃²×C₄	—	2	2	no	—
69	C₂²×C₃²×C₄	—	2	2	no	—
70	C₂²×C₃²×C₄	C₂³	1	2	yes	—
71	C₃²×Q₁₆	—	2	4	no	—
72	C₃²×Q₁₆	D₄	1	4	yes	complemented
73	C₃²×SD₁₆	—	2	4	no	—
74	C₃²×SD₁₆	—	2	4	no	—
75	C₃²×SD₁₆	—	4	2	no	—
76	C₃²×M₁₆	—	2	4	no	—
77	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
78	C₂×C₃²×C₈	C₂³	1	2	yes	—
79	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
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	1	no	—
84	C₃²×C₄⋊C₄	—	2	2	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	D₄	1	2	yes	—
91	C₃²×C₄²	—	2	1	no	—
92	C₃²×C₄²	—	2	1	no	—
93	C₃²×C₄²	C₂³	1	1	yes	characteristic
94	#3278	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	4	yes	—
100	C₂×C₃×SD₁₆	C₂²×C₃	1	8	yes	—
101	C₂×C₃×SD₁₆	C₂²×C₃	1	8	yes	—
102	C₂×C₃×SD₁₆	C₂²×C₃	1	8	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×#127	—	2	4	no	—
107	C₃×#127	C₂²×C₃	1	4	yes	—
108	C₃×C₂²⋊Q₈	—	2	8	no	—
109	C₃×C₂²⋊Q₈	C₂²×C₃	1	8	yes	—
110	C₃×#121	—	2	8	no	—
111	C₃×#121	C₂²×C₃	1	8	yes	—
112	C₃×C₄×Q₈	C₂²×C₃	1	4	yes	—
113	C₃×C₄×Q₈	C₂²×C₃	1	4	yes	—
114	C₃×C₄×D₄	—	2	4	no	—
115	C₃×C₄×D₄	—	2	4	no	—
116	C₃×C₄×D₄	C₂²×C₃	1	4	yes	—
117	C₃×#107	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	4	yes	—
121	C₃×#103	C₂²×C₃	1	8	yes	—
122	C₃×#102	C₂²×C₃	1	8	yes	—
123	C₃×C₂²⋊C₈	C₂²×C₃	1	8	yes	—
124	C₃×C₄×C₈	C₂²×C₃	1	4	yes	—
125	C₂³×C₃²	—	2	2	no	—
126	C₂³×C₃²	C₂×D₄	1	2	yes	—
127	C₃²×Q₈	—	2	1	no	—
128	C₃²×Q₈	—	2	1	no	—
129	C₃²×Q₈	—	2	2	no	—
130	C₃²×Q₈	—	2	2	no	—
131	C₃²×Q₈	—	4	4	no	—
132	C₃²×Q₈	C₂×D₄	1	2	yes	—
133	C₃²×Q₈	C₂×D₄	1	2	yes	—
134	C₃²×D₄	—	2	2	no	—
135	C₃²×D₄	—	2	2	no	—
136	C₃²×D₄	—	2	2	no	—
137	C₃²×D₄	—	4	4	no	—
138	C₃²×D₄	—	4	2	no	—
139	C₃²×D₄	—	8	1	no	—
140	C₃²×D₄	—	8	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	—	2	1	no	—
146	C₂×C₃²×C₄	—	2	1	no	—
147	C₂×C₃²×C₄	—	2	2	no	—
148	C₂×C₃²×C₄	—	4	4	no	—
149	C₂×C₃²×C₄	—	4	4	no	—
150	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
151	C₂×C₃²×C₄	C₂×D₄	1	2	yes	—
152	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
153	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
154	C₃²×C₈	—	2	2	no	—
155	C₃²×C₈	—	2	1	no	—
156	C₃²×C₈	C₂×D₄	1	2	yes	—
157	C₂×#137	C₂×C₃²	1	2	yes	complemented
158	#550	C₂×C₃²	1	1	yes	characteristic
159	D₄×Q₈	C₂×C₃²	1	1	yes	characteristic, complemented
160	#492	C₂×C₃²	1	1	yes	characteristic, complemented
161	#468	C₂×C₃²	1	2	yes	complemented
162	#462	C₂×C₃²	1	1	yes	characteristic, complemented
163	#460	C₂×C₃²	1	1	yes	characteristic, complemented
164	#452	C₂×C₃²	1	2	yes	complemented
165	#448	C₂×C₃²	1	2	yes	complemented
166	C₄×Q₁₆	C₂×C₃²	1	1	yes	characteristic, complemented
167	#436	C₂×C₃²	1	1	yes	characteristic, complemented
168	C₃×#41	—	2	16	no	—
169	C₃×#41	—	4	8	no	—
170	C₂×C₃×Q₈	—	2	8	no	—
171	C₂×C₃×Q₈	—	2	16	no	—
172	C₂×C₃×Q₈	—	4	8	no	—
173	C₂×C₃×Q₈	C₂³×C₃	1	8	yes	—
174	C₂×C₃×Q₈	C₂³×C₃	1	4	yes	—
175	C₂×C₃×Q₈	C₂³×C₃	1	4	yes	—
176	C₂×C₃×D₄	—	2	8	no	—
177	C₂×C₃×D₄	—	2	8	no	—
178	C₂×C₃×D₄	—	2	4	no	—
179	C₂×C₃×D₄	—	2	4	no	—
180	C₂×C₃×D₄	C₃×D₄	1	4	yes	—
181	C₂×C₃×D₄	C₂³×C₃	1	8	yes	—
182	C₂²×C₃×C₄	—	2	8	no	—
183	C₂²×C₃×C₄	—	2	8	no	—
184	C₂²×C₃×C₄	C₂³×C₃	1	8	yes	—
185	C₃×Q₁₆	—	2	16	no	—
186	C₃×Q₁₆	C₃×D₄	1	16	yes	complemented
187	C₃×SD₁₆	—	2	16	no	—
188	C₃×SD₁₆	—	2	16	no	—
189	C₃×SD₁₆	—	4	8	no	—
190	C₃×M₁₆	—	2	16	no	—
191	C₂×C₃×C₈	C₂³×C₃	1	4	yes	—
192	C₂×C₃×C₈	C₂³×C₃	1	8	yes	—
193	C₂×C₃×C₈	C₂³×C₃	1	4	yes	—
194	C₃×C₄⋊C₄	—	2	4	no	—
195	C₃×C₄⋊C₄	—	2	4	no	—
196	C₃×C₄⋊C₄	—	2	4	no	—
197	C₃×C₄⋊C₄	—	2	4	no	—
198	C₃×C₄⋊C₄	—	2	8	no	—
199	C₃×C₄⋊C₄	C₃×D₄	1	4	yes	—
200	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
201	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
202	C₃×C₂²⋊C₄	—	2	8	no	—
203	C₃×C₂²⋊C₄	—	2	8	no	—
204	C₃×C₂²⋊C₄	C₃×D₄	1	8	yes	—
205	C₃×C₄²	—	2	4	no	—
206	C₃×C₄²	—	2	4	no	—
207	C₃×C₄²	C₂³×C₃	1	4	yes	—
208	C₂²×C₃²	—	2	2	no	—
209	C₂²×C₃²	—	2	2	no	—
210	C₂²×C₃²	—	2	2	no	—
211	C₂²×C₃²	—	4	2	no	—
212	C₂²×C₃²	—	4	2	no	—
213	C₂²×C₃²	—	4	2	no	—
214	C₂²×C₃²	C₂²×D₄	1	1	yes	characteristic
215	C₃²×C₄	—	2	2	no	—
216	C₃²×C₄	—	2	2	no	—
217	C₃²×C₄	—	2	2	no	—
218	C₃²×C₄	—	2	1	no	—
219	C₃²×C₄	—	4	2	no	—
220	C₃²×C₄	—	4	1	no	—
221	C₃²×C₄	—	4	1	no	—
222	C₃²×C₄	#137	1	2	yes	complemented
223	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
224	C₃²×C₄	H(5,𝔽₂)	1	1	yes	characteristic
225	C₂×#41	C₂²×C₃²	1	2	yes	—
226	C₂²×Q₈	C₂²×C₃²	1	2	yes	—
227	#137	—	2	8	no	—
228	C₂×Q₁₆	C₂²×C₃²	1	2	yes	—
229	C₂×Q₁₆	C₂²×C₃²	1	1	yes	characteristic
230	C₂×SD₁₆	C₂²×C₃²	1	2	yes	—
231	C₂×SD₁₆	C₂²×C₃²	1	2	yes	—
232	C₂×SD₁₆	C₂²×C₃²	1	2	yes	—
233	C₂×M₁₆	C₂²×C₃²	1	2	yes	—
234	C₄⋊Q₈	—	2	1	no	—
235	C₄⋊Q₈	C₂²×C₃²	1	1	yes	characteristic
236	#127	—	2	1	no	—
237	#127	C₂²×C₃²	1	1	yes	characteristic
238	C₂²⋊Q₈	—	2	2	no	—
239	C₂²⋊Q₈	C₂²×C₃²	1	2	yes	—
240	#121	—	2	2	no	—
241	#121	C₂²×C₃²	1	2	yes	—
242	C₄×Q₈	C₂²×C₃²	1	1	yes	characteristic
243	C₄×Q₈	C₂²×C₃²	1	1	yes	characteristic
244	C₄×D₄	—	2	1	no	—
245	C₄×D₄	—	2	1	no	—
246	C₄×D₄	C₂²×C₃²	1	1	yes	characteristic
247	#107	C₂²×C₃²	1	1	yes	characteristic
248	C₄⋊C₈	C₂²×C₃²	1	1	yes	characteristic
249	#103	C₂²×C₃²	1	1	yes	characteristic
250	#103	C₂²×C₃²	1	1	yes	characteristic
251	#103	C₂²×C₃²	1	2	yes	—
252	#102	C₂²×C₃²	1	2	yes	—
253	C₂²⋊C₈	C₂²×C₃²	1	2	yes	—
254	C₄×C₈	C₂²×C₃²	1	1	yes	characteristic
255	C₂³×C₃	—	2	8	no	—
256	C₂³×C₃	C₂×C₃×D₄	1	8	yes	—
257	C₃×Q₈	—	2	4	no	—
258	C₃×Q₈	—	2	4	no	—
259	C₃×Q₈	—	2	8	no	—
260	C₃×Q₈	—	2	8	no	—
261	C₃×Q₈	—	4	16	no	—
262	C₃×Q₈	C₂×C₃×D₄	1	8	yes	—
263	C₃×Q₈	C₂×C₃×D₄	1	8	yes	—
264	C₃×D₄	—	2	8	no	—
265	C₃×D₄	—	2	8	no	—
266	C₃×D₄	—	2	8	no	—
267	C₃×D₄	—	4	16	no	—
268	C₃×D₄	—	4	8	no	—
269	C₃×D₄	—	8	4	no	—
270	C₃×D₄	—	8	8	no	—
271	C₂×C₃×C₄	—	2	4	no	—
272	C₂×C₃×C₄	—	2	4	no	—
273	C₂×C₃×C₄	—	2	8	no	—
274	C₂×C₃×C₄	—	2	8	no	—
275	C₂×C₃×C₄	—	2	4	no	—
276	C₂×C₃×C₄	—	2	4	no	—
277	C₂×C₃×C₄	—	2	8	no	—
278	C₂×C₃×C₄	—	4	16	no	—
279	C₂×C₃×C₄	—	4	16	no	—
280	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
281	C₂×C₃×C₄	C₂×C₃×D₄	1	8	yes	—
282	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
283	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
284	C₃×C₈	—	2	8	no	—
285	C₃×C₈	—	2	4	no	—
286	C₃×C₈	C₂×C₃×D₄	1	8	yes	—
287	C₂×C₃²	—	4	2	no	—
288	C₂×C₃²	—	8	2	no	—
289	C₂×C₃²	D₄²	1	1	yes	characteristic
290	C₂×C₃²	C₂×#137	1	1	yes	characteristic
291	C₂×C₃²	#577	1	1	yes	characteristic
292	#41	—	2	4	no	—
293	#41	—	4	2	no	—
294	C₂×Q₈	—	2	2	no	—
295	C₂×Q₈	—	2	4	no	—
296	C₂×Q₈	—	4	2	no	—
297	C₂×Q₈	C₂³×C₃²	1	2	yes	—
298	C₂×Q₈	C₂³×C₃²	1	1	yes	characteristic
299	C₂×Q₈	C₂³×C₃²	1	1	yes	characteristic
300	C₂×D₄	—	2	2	no	—
301	C₂×D₄	—	2	2	no	—
302	C₂×D₄	—	2	1	no	—
303	C₂×D₄	—	2	1	no	—
304	C₂×D₄	C₃²×D₄	1	1	yes	characteristic
305	C₂×D₄	C₂³×C₃²	1	2	yes	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	C₂³×C₃²	1	2	yes	—
309	Q₁₆	—	2	4	no	—
310	Q₁₆	C₃²×D₄	1	4	yes	complemented
311	SD₁₆	—	2	4	no	—
312	SD₁₆	—	2	4	no	—
313	SD₁₆	—	4	2	no	—
314	M₁₆	—	2	4	no	—
315	C₂×C₈	C₂³×C₃²	1	1	yes	characteristic
316	C₂×C₈	C₂³×C₃²	1	2	yes	—
317	C₂×C₈	C₂³×C₃²	1	1	yes	characteristic
318	C₄⋊C₄	—	2	1	no	—
319	C₄⋊C₄	—	2	1	no	—
320	C₄⋊C₄	—	2	1	no	—
321	C₄⋊C₄	—	2	1	no	—
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	C₃²×D₄	1	1	yes	characteristic
324	C₄⋊C₄	C₂³×C₃²	1	1	yes	characteristic
325	C₄⋊C₄	C₂³×C₃²	1	1	yes	characteristic
326	C₂²⋊C₄	—	2	2	no	—
327	C₂²⋊C₄	—	2	2	no	—
328	C₂²⋊C₄	C₃²×D₄	1	2	yes	—
329	C₄²	—	2	1	no	—
330	C₄²	—	2	1	no	—
331	C₄²	C₂³×C₃²	1	1	yes	characteristic
332	C₂²×C₃	—	2	8	no	—
333	C₂²×C₃	—	2	8	no	—
334	C₂²×C₃	—	2	8	no	—
335	C₂²×C₃	—	4	8	no	—
336	C₂²×C₃	—	4	8	no	—
337	C₂²×C₃	—	4	8	no	—
338	C₂²×C₃	C₂²×C₃×D₄	1	4	yes	—
339	C₃×C₄	—	2	4	no	—
340	C₃×C₄	—	2	8	no	—
341	C₃×C₄	—	2	8	no	—
342	C₃×C₄	—	2	8	no	—
343	C₃×C₄	—	4	4	no	—
344	C₃×C₄	—	4	4	no	—
345	C₃×C₄	—	4	8	no	—
346	C₃×C₄	C₃×#137	1	8	yes	complemented
347	C₃×C₄	C₂²×C₃×D₄	1	4	yes	—
348	C₃×C₄	C₃×H(5,𝔽₂)	1	4	yes	—
349	C₃²	#3278	1	1	yes	characteristic, direct product factor, Sylow
350	C₂³	—	2	2	no	—
351	C₂³	C₂×C₃²×D₄	1	2	yes	—
352	Q₈	—	2	1	no	—
353	Q₈	—	2	1	no	—
354	Q₈	—	2	2	no	—
355	Q₈	—	2	2	no	—
356	Q₈	—	4	4	no	—
357	Q₈	C₂×C₃²×D₄	1	2	yes	—
358	Q₈	C₂×C₃²×D₄	1	2	yes	—
359	D₄	—	2	2	no	—
360	D₄	—	2	2	no	—
361	D₄	—	2	2	no	—
362	D₄	—	4	4	no	—
363	D₄	—	4	2	no	—
364	D₄	—	8	1	no	—
365	D₄	—	8	2	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	4	4	no	—
374	C₂×C₄	—	4	4	no	—
375	C₂×C₄	C₂×C₃²×D₄	1	1	yes	characteristic
376	C₂×C₄	C₂×C₃²×D₄	1	2	yes	—
377	C₂×C₄	C₂×C₃²×D₄	1	1	yes	characteristic
378	C₂×C₄	C₂⁴×C₃²	1	1	yes	characteristic
379	C₈	—	2	2	no	—
380	C₈	—	2	1	no	—
381	C₈	C₂×C₃²×D₄	1	2	yes	—
382	C₂×C₃	—	4	8	no	—
383	C₂×C₃	—	8	8	no	—
384	C₂×C₃	C₃×D₄²	1	4	yes	—
385	C₂×C₃	C₂×C₃×#137	1	4	yes	—
386	C₂×C₃	C₃×#577	1	4	yes	—
387	C₂²	—	2	2	no	—
388	C₂²	—	2	2	no	—
389	C₂²	—	2	2	no	—
390	C₂²	—	4	2	no	—
391	C₂²	—	4	2	no	—
392	C₂²	—	4	2	no	—
393	C₂²	C₂²×C₃²×D₄	1	1	yes	characteristic
394	C₄	—	2	1	no	—
395	C₄	—	2	2	no	—
396	C₄	—	2	2	no	—
397	C₄	—	2	2	no	—
398	C₄	—	4	1	no	—
399	C₄	—	4	1	no	—
400	C₄	—	4	2	no	—
401	C₄	C₃²×#137	1	2	yes	complemented
402	C₄	C₂²×C₃²×D₄	1	1	yes	characteristic
403	C₄	C₃²×H(5,𝔽₂)	1	1	yes	characteristic
404	C₃	C₃×#3278	1	4	yes	direct product factor
405	C₂	—	4	2	no	—
406	C₂	—	8	2	no	—
407	C₂	C₃²×D₄²	1	1	yes	characteristic
408	C₂	C₂×C₃²×#137	1	1	yes	characteristic
409	C₂	C₃²×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃²	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃²
prime radical	C₃²×#550	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
3. C₃²×D₄×Q₈	C₂	semidirect
4. C₃²×#492	C₂	semidirect
5. C₃²×#468	C₂	semidirect
6. C₃²×#462	C₂	semidirect
7. C₃²×#460	C₂	semidirect
8. C₃²×#452	C₂	semidirect
9. C₃²×#448	C₂	semidirect
10. C₃²×C₄×Q₁₆	C₂	semidirect
11. C₃²×#436	C₂	semidirect
12. C₃×#3278	C₃	direct (N × H)
43. C₂×C₃×#137	C₂×C₃	semidirect
45. C₃×D₄×Q₈	C₂×C₃	semidirect
46. C₃×#492	C₂×C₃	semidirect
47. C₃×#468	C₂×C₃	semidirect
48. C₃×#462	C₂×C₃	semidirect
49. C₃×#460	C₂×C₃	semidirect
50. C₃×#452	C₂×C₃	semidirect
51. C₃×#448	C₂×C₃	semidirect
52. C₃×C₄×Q₁₆	C₂×C₃	semidirect
53. C₃×#436	C₂×C₃	semidirect
72. C₃²×Q₁₆	D₄	semidirect
94. #3278	C₃²	direct (N × H)
157. C₂×#137	C₂×C₃²	semidirect
159. D₄×Q₈	C₂×C₃²	semidirect
160. #492	C₂×C₃²	semidirect
161. #468	C₂×C₃²	semidirect
162. #462	C₂×C₃²	semidirect
163. #460	C₂×C₃²	semidirect
164. #452	C₂×C₃²	semidirect
165. #448	C₂×C₃²	semidirect
166. C₄×Q₁₆	C₂×C₃²	semidirect
167. #436	C₂×C₃²	semidirect
186. C₃×Q₁₆	C₃×D₄	semidirect
222. C₃²×C₄	#137	semidirect
310. Q₁₆	C₃²×D₄	semidirect
346. C₃×C₄	C₃×#137	semidirect
349. C₃²	#3278	direct (N × H)
401. C₄	C₃²×#137	semidirect
404. C₃	C₃×#3278	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×#550	2
C₃²×D₄×Q₈	2
C₃²×#492	2
C₃²×#468	2
C₃²×#462	2
C₃²×#460	2
C₃²×#452	2
C₃²×#448	2
C₃²×C₄×Q₁₆	2
C₃²×#436	2
C₃×#3278	3

Subgroups — C32×#3278 #11770327

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#3278 #11770327