Subgroups — C₃²×#3295 #11770344

Order 1152.

1386 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	C₃²×#554	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃²×D₄²	C₂	1	1	yes	maximal, characteristic
3	C₃²×#486	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃²×#481	C₂	1	2	yes	maximal, complemented
5	C₃²×#476	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃²×#465	C₂	1	2	yes	maximal, complemented
7	C₃²×#460	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃²×#450	C₂	1	2	yes	maximal, complemented
9	C₃²×C₄×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃²×C₈×D₄	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₃²×#102	C₂	1	2	yes	maximal, complemented
12	C₃×#3295	C₃	1	4	yes	maximal, direct product factor
13	C₂²×C₃²×D₄	—	2	1	no	—
14	C₂²×C₃²×D₄	C₂²	1	2	yes	—
15	C₂×C₃²×SD₁₆	C₂²	1	1	yes	characteristic
16	C₂×C₃²×SD₁₆	C₂²	1	2	yes	complemented
17	C₂²×C₃²×C₈	C₂²	1	2	yes	complemented
18	C₃²×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
19	C₃²×#127	C₂²	1	1	yes	characteristic
20	C₃²×#125	—	2	1	no	—
21	C₃²×C₂²⋊Q₈	—	2	2	no	—
22	C₃²×C₂²⋊Q₈	C₂²	1	2	yes	complemented
23	C₃²×#121	—	2	1	no	—
24	C₃²×#121	C₂²	1	2	yes	—
25	C₃²×#120	—	2	2	no	—
26	C₃²×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
27	C₃²×C₄×D₄	—	2	1	no	—
28	C₃²×C₄×D₄	C₂²	1	1	yes	characteristic
29	C₃²×C₄×D₄	C₂²	1	1	yes	characteristic
30	C₂×C₃²×C₄⋊C₄	C₂²	1	2	yes	complemented
31	C₃²×#106	C₂²	1	2	yes	complemented
32	C₃²×#106	C₂²	1	1	yes	characteristic, complemented
33	C₃²×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
34	C₃²×#103	C₂²	1	1	yes	characteristic, complemented
35	C₃²×#102	C₂²	1	2	yes	—
36	C₃²×#102	C₂²	1	1	yes	characteristic
37	C₃²×#102	C₂²	1	2	yes	complemented
38	C₃²×#102	C₂²	1	2	yes	complemented
39	C₃²×#102	C₂²	1	2	yes	complemented
40	C₃²×C₂²⋊C₈	C₂²	1	2	yes	complemented
41	C₃²×C₄×C₈	C₂²	1	1	yes	characteristic, complemented
42	C₃×#554	C₂×C₃	1	4	yes	complemented
43	C₃×D₄²	C₂×C₃	1	4	yes	—
44	C₃×#486	C₂×C₃	1	4	yes	complemented
45	C₃×#481	C₂×C₃	1	8	yes	complemented
46	C₃×#476	C₂×C₃	1	4	yes	complemented
47	C₃×#465	C₂×C₃	1	8	yes	complemented
48	C₃×#460	C₂×C₃	1	4	yes	complemented
49	C₃×#450	C₂×C₃	1	8	yes	complemented
50	C₃×C₄×SD₁₆	C₂×C₃	1	4	yes	complemented
51	C₃×C₈×D₄	C₂×C₃	1	4	yes	complemented
52	C₂×C₃×#102	C₂×C₃	1	8	yes	complemented
53	C₂⁴×C₃²	—	2	2	no	—
54	C₂×C₃²×Q₈	—	2	1	no	—
55	C₂×C₃²×Q₈	C₂³	1	1	yes	characteristic
56	C₂×C₃²×D₄	—	2	4	no	—
57	C₂×C₃²×D₄	—	2	2	no	—
58	C₂×C₃²×D₄	—	2	1	no	—
59	C₂×C₃²×D₄	—	2	2	no	—
60	C₂×C₃²×D₄	—	2	1	no	—
61	C₂×C₃²×D₄	—	4	2	no	—
62	C₂×C₃²×D₄	—	4	4	no	—
63	C₂×C₃²×D₄	D₄	1	1	yes	characteristic
64	C₂×C₃²×D₄	C₂³	1	2	yes	—
65	C₂×C₃²×D₄	C₂³	1	1	yes	characteristic
66	C₂²×C₃²×C₄	—	2	2	no	—
67	C₂²×C₃²×C₄	—	2	1	no	—
68	C₂²×C₃²×C₄	C₂³	1	2	yes	—
69	C₃²×SD₁₆	—	2	2	no	—
70	C₃²×SD₁₆	—	4	2	no	—
71	C₂×C₃²×C₈	—	4	2	no	—
72	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
73	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
74	C₂×C₃²×C₈	C₂³	1	2	yes	—
75	C₃²×C₄⋊C₄	—	2	2	no	—
76	C₃²×C₄⋊C₄	—	2	1	no	—
77	C₃²×C₄⋊C₄	—	2	1	no	—
78	C₃²×C₄⋊C₄	—	2	2	no	—
79	C₃²×C₄⋊C₄	D₄	1	1	yes	characteristic
80	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
81	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
82	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
83	C₃²×C₂²⋊C₄	—	2	2	no	—
84	C₃²×C₂²⋊C₄	—	2	1	no	—
85	C₃²×C₂²⋊C₄	—	2	2	no	—
86	C₃²×C₂²⋊C₄	D₄	1	2	yes	—
87	C₃²×C₄²	—	2	1	no	—
88	C₃²×C₄²	C₂³	1	1	yes	characteristic
89	#3295	C₃²	1	1	yes	characteristic, direct product factor, Sylow
90	C₂²×C₃×D₄	—	2	4	no	—
91	C₂²×C₃×D₄	C₂²×C₃	1	8	yes	—
92	C₂×C₃×SD₁₆	C₂²×C₃	1	4	yes	—
93	C₂×C₃×SD₁₆	C₂²×C₃	1	8	yes	complemented
94	C₂²×C₃×C₈	C₂²×C₃	1	8	yes	complemented
95	C₃×C₄⋊Q₈	C₂²×C₃	1	4	yes	complemented
96	C₃×#127	C₂²×C₃	1	4	yes	—
97	C₃×#125	—	2	4	no	—
98	C₃×C₂²⋊Q₈	—	2	8	no	—
99	C₃×C₂²⋊Q₈	C₂²×C₃	1	8	yes	complemented
100	C₃×#121	—	2	4	no	—
101	C₃×#121	C₂²×C₃	1	8	yes	—
102	C₃×#120	—	2	8	no	—
103	C₃×C₄×Q₈	C₂²×C₃	1	4	yes	complemented
104	C₃×C₄×D₄	—	2	4	no	—
105	C₃×C₄×D₄	C₂²×C₃	1	4	yes	—
106	C₃×C₄×D₄	C₂²×C₃	1	4	yes	—
107	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	8	yes	complemented
108	C₃×#106	C₂²×C₃	1	4	yes	complemented
109	C₃×#106	C₂²×C₃	1	8	yes	complemented
110	C₃×C₄⋊C₈	C₂²×C₃	1	4	yes	complemented
111	C₃×#103	C₂²×C₃	1	4	yes	complemented
112	C₃×#102	C₂²×C₃	1	4	yes	—
113	C₃×#102	C₂²×C₃	1	8	yes	—
114	C₃×#102	C₂²×C₃	1	8	yes	complemented
115	C₃×#102	C₂²×C₃	1	8	yes	complemented
116	C₃×#102	C₂²×C₃	1	8	yes	complemented
117	C₃×C₂²⋊C₈	C₂²×C₃	1	8	yes	complemented
118	C₃×C₄×C₈	C₂²×C₃	1	4	yes	complemented
119	C₂³×C₃²	—	2	1	no	—
120	C₂³×C₃²	—	2	2	no	—
121	C₂³×C₃²	—	4	4	no	—
122	C₂³×C₃²	—	4	4	no	—
123	C₂³×C₃²	—	8	2	no	—
124	C₂³×C₃²	C₂×D₄	1	2	yes	—
125	C₃²×Q₈	—	2	1	no	—
126	C₃²×Q₈	—	2	1	no	—
127	C₃²×Q₈	—	8	1	no	—
128	C₃²×D₄	—	2	2	no	—
129	C₃²×D₄	—	2	1	no	—
130	C₃²×D₄	—	2	2	no	—
131	C₃²×D₄	—	4	4	no	—
132	C₃²×D₄	—	4	4	no	—
133	C₃²×D₄	—	4	2	no	—
134	C₃²×D₄	—	8	1	no	—
135	C₃²×D₄	SD₁₆	1	4	yes	complemented
136	C₃²×D₄	#41	1	2	yes	—
137	C₂×C₃²×C₄	—	2	2	no	—
138	C₂×C₃²×C₄	—	2	2	no	—
139	C₂×C₃²×C₄	—	2	1	no	—
140	C₂×C₃²×C₄	—	2	1	no	—
141	C₂×C₃²×C₄	—	2	1	no	—
142	C₂×C₃²×C₄	—	2	2	no	—
143	C₂×C₃²×C₄	—	4	2	no	—
144	C₂×C₃²×C₄	—	8	2	no	—
145	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
146	C₂×C₃²×C₄	C₂×D₄	1	2	yes	—
147	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
148	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
149	C₃²×C₈	—	2	1	no	—
150	C₃²×C₈	—	2	1	no	—
151	C₃²×C₈	—	2	2	no	—
152	#554	C₂×C₃²	1	1	yes	characteristic, complemented
153	D₄²	C₂×C₃²	1	1	yes	characteristic
154	#486	C₂×C₃²	1	1	yes	characteristic, complemented
155	#481	C₂×C₃²	1	2	yes	complemented
156	#476	C₂×C₃²	1	1	yes	characteristic, complemented
157	#465	C₂×C₃²	1	2	yes	complemented
158	#460	C₂×C₃²	1	1	yes	characteristic, complemented
159	#450	C₂×C₃²	1	2	yes	complemented
160	C₄×SD₁₆	C₂×C₃²	1	1	yes	characteristic, complemented
161	C₈×D₄	C₂×C₃²	1	1	yes	characteristic, complemented
162	C₂×#102	C₂×C₃²	1	2	yes	complemented
163	C₂⁴×C₃	—	2	8	no	—
164	C₂×C₃×Q₈	—	2	4	no	—
165	C₂×C₃×Q₈	C₂³×C₃	1	4	yes	—
166	C₂×C₃×D₄	—	2	16	no	—
167	C₂×C₃×D₄	—	2	8	no	—
168	C₂×C₃×D₄	—	2	8	no	—
169	C₂×C₃×D₄	—	2	4	no	—
170	C₂×C₃×D₄	—	2	4	no	—
171	C₂×C₃×D₄	—	4	8	no	—
172	C₂×C₃×D₄	—	4	16	no	—
173	C₂×C₃×D₄	C₃×D₄	1	4	yes	—
174	C₂×C₃×D₄	C₂³×C₃	1	8	yes	—
175	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
176	C₂²×C₃×C₄	—	2	8	no	—
177	C₂²×C₃×C₄	—	2	4	no	—
178	C₂²×C₃×C₄	C₂³×C₃	1	8	yes	—
179	C₃×SD₁₆	—	2	8	no	—
180	C₃×SD₁₆	—	4	8	no	—
181	C₂×C₃×C₈	—	4	8	no	—
182	C₂×C₃×C₈	C₂³×C₃	1	4	yes	—
183	C₂×C₃×C₈	C₂³×C₃	1	4	yes	—
184	C₂×C₃×C₈	C₂³×C₃	1	8	yes	—
185	C₃×C₄⋊C₄	—	2	8	no	—
186	C₃×C₄⋊C₄	—	2	4	no	—
187	C₃×C₄⋊C₄	—	2	4	no	—
188	C₃×C₄⋊C₄	—	2	8	no	—
189	C₃×C₄⋊C₄	C₃×D₄	1	4	yes	—
190	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
191	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
192	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
193	C₃×C₂²⋊C₄	—	2	8	no	—
194	C₃×C₂²⋊C₄	—	2	4	no	—
195	C₃×C₂²⋊C₄	—	2	8	no	—
196	C₃×C₂²⋊C₄	C₃×D₄	1	8	yes	—
197	C₃×C₄²	—	2	4	no	—
198	C₃×C₄²	C₂³×C₃	1	4	yes	—
199	C₂²×C₃²	—	2	2	no	—
200	C₂²×C₃²	—	2	2	no	—
201	C₂²×C₃²	—	2	2	no	—
202	C₂²×C₃²	—	4	1	no	—
203	C₂²×C₃²	—	4	1	no	—
204	C₂²×C₃²	—	4	2	no	—
205	C₂²×C₃²	—	4	2	no	—
206	C₂²×C₃²	—	4	2	no	—
207	C₂²×C₃²	—	8	8	no	—
208	C₂²×C₃²	C₂×SD₁₆	1	4	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	—	4	1	no	—
213	C₃²×C₄	—	4	1	no	—
214	C₃²×C₄	—	4	1	no	—
215	C₃²×C₄	—	4	2	no	—
216	C₃²×C₄	C₂×SD₁₆	1	2	yes	—
217	C₃²×C₄	C₂×#41	1	1	yes	characteristic
218	C₃²×C₄	H(5,𝔽₂)	1	1	yes	characteristic
219	C₂²×D₄	—	2	1	no	—
220	C₂²×D₄	C₂²×C₃²	1	2	yes	—
221	C₂×SD₁₆	C₂²×C₃²	1	1	yes	characteristic
222	C₂×SD₁₆	C₂²×C₃²	1	2	yes	complemented
223	C₂²×C₈	C₂²×C₃²	1	2	yes	complemented
224	C₄⋊Q₈	C₂²×C₃²	1	1	yes	characteristic, complemented
225	#127	C₂²×C₃²	1	1	yes	characteristic
226	#125	—	2	1	no	—
227	C₂²⋊Q₈	—	2	2	no	—
228	C₂²⋊Q₈	C₂²×C₃²	1	2	yes	complemented
229	#121	—	2	1	no	—
230	#121	C₂²×C₃²	1	2	yes	—
231	#120	—	2	2	no	—
232	C₄×Q₈	C₂²×C₃²	1	1	yes	characteristic, complemented
233	C₄×D₄	—	2	1	no	—
234	C₄×D₄	C₂²×C₃²	1	1	yes	characteristic
235	C₄×D₄	C₂²×C₃²	1	1	yes	characteristic
236	C₂×C₄⋊C₄	C₂²×C₃²	1	2	yes	complemented
237	#106	C₂²×C₃²	1	1	yes	characteristic, complemented
238	#106	C₂²×C₃²	1	2	yes	complemented
239	C₄⋊C₈	C₂²×C₃²	1	1	yes	characteristic, complemented
240	#103	C₂²×C₃²	1	1	yes	characteristic, complemented
241	#102	C₂²×C₃²	1	1	yes	characteristic
242	#102	C₂²×C₃²	1	2	yes	—
243	#102	C₂²×C₃²	1	2	yes	complemented
244	#102	C₂²×C₃²	1	2	yes	complemented
245	#102	C₂²×C₃²	1	2	yes	complemented
246	C₂²⋊C₈	C₂²×C₃²	1	2	yes	complemented
247	C₄×C₈	C₂²×C₃²	1	1	yes	characteristic, complemented
248	C₂³×C₃	—	2	4	no	—
249	C₂³×C₃	—	2	8	no	—
250	C₂³×C₃	—	4	16	no	—
251	C₂³×C₃	—	4	16	no	—
252	C₂³×C₃	—	8	8	no	—
253	C₂³×C₃	C₂×C₃×D₄	1	8	yes	—
254	C₃×Q₈	—	2	4	no	—
255	C₃×Q₈	—	2	4	no	—
256	C₃×Q₈	—	8	4	no	—
257	C₃×D₄	—	2	8	no	—
258	C₃×D₄	—	2	4	no	—
259	C₃×D₄	—	2	8	no	—
260	C₃×D₄	—	4	16	no	—
261	C₃×D₄	—	4	16	no	—
262	C₃×D₄	—	4	8	no	—
263	C₃×D₄	—	8	4	no	—
264	C₃×D₄	C₃×SD₁₆	1	16	yes	complemented
265	C₃×D₄	C₃×#41	1	8	yes	—
266	C₂×C₃×C₄	—	2	8	no	—
267	C₂×C₃×C₄	—	2	8	no	—
268	C₂×C₃×C₄	—	2	4	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	—	4	8	no	—
273	C₂×C₃×C₄	—	8	8	no	—
274	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
275	C₂×C₃×C₄	C₂×C₃×D₄	1	8	yes	—
276	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
277	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
278	C₃×C₈	—	2	4	no	—
279	C₃×C₈	—	2	4	no	—
280	C₃×C₈	—	2	8	no	—
281	C₂×C₃²	—	2	4	no	—
282	C₂×C₃²	—	4	2	no	—
283	C₂×C₃²	—	8	2	no	—
284	C₂×C₃²	#546	1	1	yes	characteristic
285	C₂×C₃²	C₂²×SD₁₆	1	1	yes	characteristic
286	C₂×C₃²	#576	1	1	yes	characteristic
287	C₂⁴	—	2	2	no	—
288	C₂×Q₈	—	2	1	no	—
289	C₂×Q₈	C₂³×C₃²	1	1	yes	characteristic
290	C₂×D₄	—	2	4	no	—
291	C₂×D₄	—	2	2	no	—
292	C₂×D₄	—	2	2	no	—
293	C₂×D₄	—	2	1	no	—
294	C₂×D₄	—	2	1	no	—
295	C₂×D₄	—	4	2	no	—
296	C₂×D₄	—	4	4	no	—
297	C₂×D₄	C₃²×D₄	1	1	yes	characteristic
298	C₂×D₄	C₂³×C₃²	1	2	yes	—
299	C₂×D₄	C₂³×C₃²	1	1	yes	characteristic
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	2	1	no	—
302	C₂²×C₄	C₂³×C₃²	1	2	yes	—
303	SD₁₆	—	2	2	no	—
304	SD₁₆	—	4	2	no	—
305	C₂×C₈	—	4	2	no	—
306	C₂×C₈	C₂³×C₃²	1	1	yes	characteristic
307	C₂×C₈	C₂³×C₃²	1	1	yes	characteristic
308	C₂×C₈	C₂³×C₃²	1	2	yes	—
309	C₄⋊C₄	—	2	2	no	—
310	C₄⋊C₄	—	2	1	no	—
311	C₄⋊C₄	—	2	1	no	—
312	C₄⋊C₄	—	2	2	no	—
313	C₄⋊C₄	C₃²×D₄	1	1	yes	characteristic
314	C₄⋊C₄	C₂³×C₃²	1	1	yes	characteristic
315	C₄⋊C₄	C₂³×C₃²	1	2	yes	—
316	C₄⋊C₄	C₂³×C₃²	1	1	yes	characteristic
317	C₂²⋊C₄	—	2	2	no	—
318	C₂²⋊C₄	—	2	1	no	—
319	C₂²⋊C₄	—	2	2	no	—
320	C₂²⋊C₄	C₃²×D₄	1	2	yes	—
321	C₄²	—	2	1	no	—
322	C₄²	C₂³×C₃²	1	1	yes	characteristic
323	C₂²×C₃	—	2	8	no	—
324	C₂²×C₃	—	2	8	no	—
325	C₂²×C₃	—	2	8	no	—
326	C₂²×C₃	—	4	4	no	—
327	C₂²×C₃	—	4	4	no	—
328	C₂²×C₃	—	4	8	no	—
329	C₂²×C₃	—	4	8	no	—
330	C₂²×C₃	—	4	8	no	—
331	C₂²×C₃	—	8	32	no	—
332	C₂²×C₃	C₂×C₃×SD₁₆	1	16	yes	—
333	C₂²×C₃	C₂²×C₃×D₄	1	4	yes	—
334	C₃×C₄	—	2	4	no	—
335	C₃×C₄	—	2	8	no	—
336	C₃×C₄	—	4	4	no	—
337	C₃×C₄	—	4	4	no	—
338	C₃×C₄	—	4	8	no	—
339	C₃×C₄	—	4	4	no	—
340	C₃×C₄	C₂×C₃×SD₁₆	1	8	yes	—
341	C₃×C₄	C₂×C₃×#41	1	4	yes	—
342	C₃×C₄	C₃×H(5,𝔽₂)	1	4	yes	—
343	C₃²	#3295	1	1	yes	characteristic, direct product factor, Sylow
344	C₂³	—	2	1	no	—
345	C₂³	—	2	2	no	—
346	C₂³	—	4	4	no	—
347	C₂³	—	4	4	no	—
348	C₂³	—	8	2	no	—
349	C₂³	C₂×C₃²×D₄	1	2	yes	—
350	Q₈	—	2	1	no	—
351	Q₈	—	2	1	no	—
352	Q₈	—	8	1	no	—
353	D₄	—	2	2	no	—
354	D₄	—	2	1	no	—
355	D₄	—	2	2	no	—
356	D₄	—	4	4	no	—
357	D₄	—	4	4	no	—
358	D₄	—	4	2	no	—
359	D₄	—	8	1	no	—
360	D₄	C₃²×SD₁₆	1	4	yes	complemented
361	D₄	C₃²×#41	1	2	yes	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	8	2	no	—
370	C₂×C₄	C₂×C₃²×D₄	1	1	yes	characteristic
371	C₂×C₄	C₂×C₃²×D₄	1	2	yes	—
372	C₂×C₄	C₂×C₃²×D₄	1	1	yes	characteristic
373	C₂×C₄	C₂⁴×C₃²	1	1	yes	characteristic
374	C₈	—	2	1	no	—
375	C₈	—	2	1	no	—
376	C₈	—	2	2	no	—
377	C₂×C₃	—	2	16	no	—
378	C₂×C₃	—	4	8	no	—
379	C₂×C₃	—	8	8	no	—
380	C₂×C₃	C₃×#546	1	4	yes	—
381	C₂×C₃	C₂²×C₃×SD₁₆	1	4	yes	—
382	C₂×C₃	C₃×#576	1	4	yes	—
383	C₂²	—	2	2	no	—
384	C₂²	—	2	2	no	—
385	C₂²	—	2	2	no	—
386	C₂²	—	4	1	no	—
387	C₂²	—	4	1	no	—
388	C₂²	—	4	2	no	—
389	C₂²	—	4	2	no	—
390	C₂²	—	4	2	no	—
391	C₂²	—	8	8	no	—
392	C₂²	C₂×C₃²×SD₁₆	1	4	yes	—
393	C₂²	C₂²×C₃²×D₄	1	1	yes	characteristic
394	C₄	—	2	1	no	—
395	C₄	—	2	2	no	—
396	C₄	—	4	1	no	—
397	C₄	—	4	1	no	—
398	C₄	—	4	2	no	—
399	C₄	—	4	1	no	—
400	C₄	C₂×C₃²×SD₁₆	1	2	yes	—
401	C₄	C₂×C₃²×#41	1	1	yes	characteristic
402	C₄	C₃²×H(5,𝔽₂)	1	1	yes	characteristic
403	C₃	C₃×#3295	1	4	yes	direct product factor
404	C₂	—	2	4	no	—
405	C₂	—	4	2	no	—
406	C₂	—	8	2	no	—
407	C₂	C₃²×#546	1	1	yes	characteristic
408	C₂	C₂²×C₃²×SD₁₆	1	1	yes	characteristic
409	C₂	C₃²×#576	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃²	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃²
prime radical	C₃²×D₄²	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. C₃²×#554	C₂	semidirect
3. C₃²×#486	C₂	semidirect
4. C₃²×#481	C₂	semidirect
5. C₃²×#476	C₂	semidirect
6. C₃²×#465	C₂	semidirect
7. C₃²×#460	C₂	semidirect
8. C₃²×#450	C₂	semidirect
9. C₃²×C₄×SD₁₆	C₂	semidirect
10. C₃²×C₈×D₄	C₂	semidirect
11. C₂×C₃²×#102	C₂	semidirect
12. C₃×#3295	C₃	direct (N × H)
16. C₂×C₃²×SD₁₆	C₂²	semidirect
17. C₂²×C₃²×C₈	C₂²	semidirect
18. C₃²×C₄⋊Q₈	C₂²	semidirect
22. C₃²×C₂²⋊Q₈	C₂²	semidirect
26. C₃²×C₄×Q₈	C₂²	semidirect
30. C₂×C₃²×C₄⋊C₄	C₂²	semidirect
31. C₃²×#106	C₂²	semidirect
32. C₃²×#106	C₂²	semidirect
33. C₃²×C₄⋊C₈	C₂²	semidirect
34. C₃²×#103	C₂²	semidirect
37. C₃²×#102	C₂²	semidirect
38. C₃²×#102	C₂²	semidirect
39. C₃²×#102	C₂²	semidirect
40. C₃²×C₂²⋊C₈	C₂²	semidirect
41. C₃²×C₄×C₈	C₂²	semidirect
42. C₃×#554	C₂×C₃	semidirect
44. C₃×#486	C₂×C₃	semidirect
45. C₃×#481	C₂×C₃	semidirect
46. C₃×#476	C₂×C₃	semidirect
47. C₃×#465	C₂×C₃	semidirect
48. C₃×#460	C₂×C₃	semidirect
49. C₃×#450	C₂×C₃	semidirect
50. C₃×C₄×SD₁₆	C₂×C₃	semidirect
51. C₃×C₈×D₄	C₂×C₃	semidirect
52. C₂×C₃×#102	C₂×C₃	semidirect
89. #3295	C₃²	direct (N × H)
93. C₂×C₃×SD₁₆	C₂²×C₃	semidirect
94. C₂²×C₃×C₈	C₂²×C₃	semidirect
95. C₃×C₄⋊Q₈	C₂²×C₃	semidirect
99. C₃×C₂²⋊Q₈	C₂²×C₃	semidirect
103. C₃×C₄×Q₈	C₂²×C₃	semidirect
107. C₂×C₃×C₄⋊C₄	C₂²×C₃	semidirect
108. C₃×#106	C₂²×C₃	semidirect
109. C₃×#106	C₂²×C₃	semidirect
110. C₃×C₄⋊C₈	C₂²×C₃	semidirect
111. C₃×#103	C₂²×C₃	semidirect
114. C₃×#102	C₂²×C₃	semidirect
115. C₃×#102	C₂²×C₃	semidirect
116. C₃×#102	C₂²×C₃	semidirect
117. C₃×C₂²⋊C₈	C₂²×C₃	semidirect
118. C₃×C₄×C₈	C₂²×C₃	semidirect
135. C₃²×D₄	SD₁₆	semidirect
152. #554	C₂×C₃²	semidirect
154. #486	C₂×C₃²	semidirect
155. #481	C₂×C₃²	semidirect
156. #476	C₂×C₃²	semidirect
157. #465	C₂×C₃²	semidirect
158. #460	C₂×C₃²	semidirect
159. #450	C₂×C₃²	semidirect
160. C₄×SD₁₆	C₂×C₃²	semidirect
161. C₈×D₄	C₂×C₃²	semidirect
162. C₂×#102	C₂×C₃²	semidirect
222. C₂×SD₁₆	C₂²×C₃²	semidirect
223. C₂²×C₈	C₂²×C₃²	semidirect
224. C₄⋊Q₈	C₂²×C₃²	semidirect
228. C₂²⋊Q₈	C₂²×C₃²	semidirect
232. C₄×Q₈	C₂²×C₃²	semidirect
236. C₂×C₄⋊C₄	C₂²×C₃²	semidirect
237. #106	C₂²×C₃²	semidirect
238. #106	C₂²×C₃²	semidirect
239. C₄⋊C₈	C₂²×C₃²	semidirect
240. #103	C₂²×C₃²	semidirect
243. #102	C₂²×C₃²	semidirect
244. #102	C₂²×C₃²	semidirect
245. #102	C₂²×C₃²	semidirect
246. C₂²⋊C₈	C₂²×C₃²	semidirect
247. C₄×C₈	C₂²×C₃²	semidirect
264. C₃×D₄	C₃×SD₁₆	semidirect
343. C₃²	#3295	direct (N × H)
360. D₄	C₃²×SD₁₆	semidirect
403. C₃	C₃×#3295	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×#554	2
C₃²×D₄²	2
C₃²×#486	2
C₃²×#481	2
C₃²×#476	2
C₃²×#465	2
C₃²×#460	2
C₃²×#450	2
C₃²×C₄×SD₁₆	2
C₃²×C₈×D₄	2
C₂×C₃²×#102	2
C₃×#3295	3

Subgroups — C32×#3295 #11770344

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#3295 #11770344