Subgroups — C₃²×#3096 #11770145

Order 1152.

1254 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×#535	C₂	1	1	yes	maximal, characteristic
2	C₃²×#520	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×#482	C₂	1	2	yes	maximal, complemented
4	C₃²×#482	C₂	1	2	yes	maximal, complemented
5	C₃²×#481	C₂	1	2	yes	maximal, complemented
6	C₃²×#480	C₂	1	2	yes	maximal, complemented
7	C₃²×#428	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃²×#427	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃²×#418	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₃²×#102	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃²×#408	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#3096	C₃	1	4	yes	maximal, direct product factor
13	C₂×C₃²×#41	C₂²	1	1	yes	characteristic
14	C₂²×C₃²×D₄	C₂²	1	1	yes	characteristic
15	C₂×C₃²×M₁₆	C₂²	1	1	yes	characteristic
16	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
17	C₃²×#127	—	2	1	no	—
18	C₃²×#124	—	2	1	no	—
19	C₃²×#121	C₂²	1	2	yes	—
20	C₃²×#121	C₂²	1	2	yes	—
21	C₃²×#120	—	2	2	no	—
22	C₃²×C₄×Q₈	—	2	1	no	—
23	C₃²×C₄×D₄	—	2	1	no	—
24	C₃²×C₄×D₄	—	2	2	no	—
25	C₃²×#117	C₂²	1	1	yes	characteristic
26	C₃²×#117	C₂²	1	1	yes	characteristic
27	C₃²×#117	C₂²	1	2	yes	complemented
28	C₂×C₃²×C₄⋊C₄	C₂²	1	1	yes	characteristic
29	C₂×C₃²×C₄⋊C₄	C₂²	1	2	yes	complemented
30	C₃²×#107	C₂²	1	1	yes	characteristic, complemented
31	C₃²×#107	C₂²	1	2	yes	complemented
32	C₃²×#107	C₂²	1	1	yes	characteristic, complemented
33	C₃²×#106	C₂²	1	1	yes	characteristic, complemented
34	C₃²×#106	C₂²	1	2	yes	complemented
35	C₃²×#106	C₂²	1	1	yes	characteristic, complemented
36	C₃²×#102	C₂²	1	2	yes	—
37	C₃²×#102	C₂²	1	2	yes	—
38	C₃²×#102	C₂²	1	2	yes	—
39	C₃²×#102	C₂²	1	2	yes	—
40	C₃²×C₂²⋊C₈	C₂²	1	2	yes	complemented
41	C₃²×C₂²⋊C₈	C₂²	1	2	yes	complemented
42	C₃×#535	C₂×C₃	1	4	yes	—
43	C₃×#520	C₂×C₃	1	4	yes	complemented
44	C₃×#482	C₂×C₃	1	8	yes	complemented
45	C₃×#482	C₂×C₃	1	8	yes	complemented
46	C₃×#481	C₂×C₃	1	8	yes	complemented
47	C₃×#480	C₂×C₃	1	8	yes	complemented
48	C₃×#428	C₂×C₃	1	4	yes	complemented
49	C₃×#427	C₂×C₃	1	4	yes	complemented
50	C₃×#418	C₂×C₃	1	4	yes	complemented
51	C₂×C₃×#102	C₂×C₃	1	4	yes	complemented
52	C₃×#408	C₂×C₃	1	4	yes	complemented
53	C₂⁴×C₃²	—	2	1	no	—
54	C₃²×#41	—	2	2	no	—
55	C₃²×#41	—	2	2	no	—
56	C₂×C₃²×Q₈	D₄	1	1	yes	characteristic
57	C₂×C₃²×D₄	—	2	2	no	—
58	C₂×C₃²×D₄	—	2	2	no	—
59	C₂×C₃²×D₄	—	2	1	no	—
60	C₂×C₃²×D₄	—	2	2	no	—
61	C₂×C₃²×D₄	—	2	2	no	—
62	C₂×C₃²×D₄	D₄	1	2	yes	—
63	C₂×C₃²×D₄	D₄	1	1	yes	characteristic
64	C₂×C₃²×D₄	C₂³	1	2	yes	—
65	C₂²×C₃²×C₄	—	2	1	no	—
66	C₂²×C₃²×C₄	—	2	2	no	—
67	C₂²×C₃²×C₄	C₂³	1	2	yes	—
68	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
69	C₃²×M₁₆	—	2	2	no	—
70	C₂×C₃²×C₈	—	2	2	no	—
71	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
72	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
73	C₂×C₃²×C₈	C₂³	1	2	yes	—
74	C₃²×C₄⋊C₄	—	2	1	no	—
75	C₃²×C₄⋊C₄	—	2	2	no	—
76	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
77	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
78	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
79	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
80	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
81	C₃²×C₂²⋊C₄	—	2	1	no	—
82	C₃²×C₂²⋊C₄	—	2	1	no	—
83	C₃²×C₂²⋊C₄	—	2	2	no	—
84	C₃²×C₂²⋊C₄	—	2	2	no	—
85	C₃²×C₂²⋊C₄	—	2	2	no	—
86	C₃²×C₄²	—	2	1	no	—
87	C₃²×C₄²	—	2	1	no	—
88	C₃²×C₄²	—	2	2	no	—
89	#3096	C₃²	1	1	yes	characteristic, direct product factor, Sylow
90	C₂×C₃×#41	C₂²×C₃	1	4	yes	—
91	C₂²×C₃×D₄	C₂²×C₃	1	4	yes	—
92	C₂×C₃×M₁₆	C₂²×C₃	1	4	yes	—
93	C₂²×C₃×C₈	C₂²×C₃	1	4	yes	—
94	C₃×#127	—	2	4	no	—
95	C₃×#124	—	2	4	no	—
96	C₃×#121	C₂²×C₃	1	8	yes	—
97	C₃×#121	C₂²×C₃	1	8	yes	—
98	C₃×#120	—	2	8	no	—
99	C₃×C₄×Q₈	—	2	4	no	—
100	C₃×C₄×D₄	—	2	4	no	—
101	C₃×C₄×D₄	—	2	8	no	—
102	C₃×#117	C₂²×C₃	1	4	yes	—
103	C₃×#117	C₂²×C₃	1	4	yes	—
104	C₃×#117	C₂²×C₃	1	8	yes	complemented
105	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	4	yes	—
106	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	8	yes	complemented
107	C₃×#107	C₂²×C₃	1	4	yes	complemented
108	C₃×#107	C₂²×C₃	1	4	yes	complemented
109	C₃×#107	C₂²×C₃	1	8	yes	complemented
110	C₃×#106	C₂²×C₃	1	4	yes	complemented
111	C₃×#106	C₂²×C₃	1	4	yes	complemented
112	C₃×#106	C₂²×C₃	1	8	yes	complemented
113	C₃×#102	C₂²×C₃	1	8	yes	—
114	C₃×#102	C₂²×C₃	1	8	yes	—
115	C₃×#102	C₂²×C₃	1	8	yes	—
116	C₃×#102	C₂²×C₃	1	8	yes	—
117	C₃×C₂²⋊C₈	C₂²×C₃	1	8	yes	complemented
118	C₃×C₂²⋊C₈	C₂²×C₃	1	8	yes	complemented
119	C₂³×C₃²	—	2	2	no	—
120	C₂³×C₃²	—	4	2	no	—
121	C₂³×C₃²	—	8	1	no	—
122	C₂³×C₃²	—	8	1	no	—
123	C₂³×C₃²	C₂×D₄	1	2	yes	—
124	C₂³×C₃²	C₂×D₄	1	1	yes	characteristic
125	C₃²×Q₈	—	2	2	no	—
126	C₃²×D₄	—	2	4	no	—
127	C₃²×D₄	—	2	2	no	—
128	C₃²×D₄	—	2	2	no	—
129	C₃²×D₄	—	2	2	no	—
130	C₃²×D₄	—	4	2	no	—
131	C₃²×D₄	—	8	2	no	—
132	C₃²×D₄	—	8	2	no	—
133	C₂×C₃²×C₄	—	2	2	no	—
134	C₂×C₃²×C₄	—	2	2	no	—
135	C₂×C₃²×C₄	—	2	1	no	—
136	C₂×C₃²×C₄	—	2	1	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	—	8	1	no	—
141	C₂×C₃²×C₄	—	8	2	no	—
142	C₂×C₃²×C₄	C₂×D₄	1	2	yes	—
143	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
144	C₂×C₃²×C₄	#41	1	2	yes	—
145	C₂×C₃²×C₄	#41	1	2	yes	—
146	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
147	C₃²×C₈	—	2	1	no	—
148	C₃²×C₈	—	2	1	no	—
149	C₃²×C₈	—	2	2	no	—
150	#535	C₂×C₃²	1	1	yes	characteristic
151	#520	C₂×C₃²	1	1	yes	characteristic, complemented
152	#482	C₂×C₃²	1	2	yes	complemented
153	#482	C₂×C₃²	1	2	yes	complemented
154	#481	C₂×C₃²	1	2	yes	complemented
155	#480	C₂×C₃²	1	2	yes	complemented
156	#428	C₂×C₃²	1	1	yes	characteristic, complemented
157	#427	C₂×C₃²	1	1	yes	characteristic, complemented
158	#418	C₂×C₃²	1	1	yes	characteristic, complemented
159	C₂×#102	C₂×C₃²	1	1	yes	characteristic, complemented
160	#408	C₂×C₃²	1	1	yes	characteristic, complemented
161	C₂⁴×C₃	—	2	4	no	—
162	C₃×#41	—	2	8	no	—
163	C₃×#41	—	2	8	no	—
164	C₂×C₃×Q₈	C₃×D₄	1	4	yes	—
165	C₂×C₃×D₄	—	2	8	no	—
166	C₂×C₃×D₄	—	2	8	no	—
167	C₂×C₃×D₄	—	2	4	no	—
168	C₂×C₃×D₄	—	2	8	no	—
169	C₂×C₃×D₄	—	2	8	no	—
170	C₂×C₃×D₄	C₃×D₄	1	8	yes	—
171	C₂×C₃×D₄	C₃×D₄	1	4	yes	—
172	C₂×C₃×D₄	C₂³×C₃	1	8	yes	—
173	C₂²×C₃×C₄	—	2	4	no	—
174	C₂²×C₃×C₄	—	2	8	no	—
175	C₂²×C₃×C₄	C₂³×C₃	1	8	yes	—
176	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
177	C₃×M₁₆	—	2	8	no	—
178	C₂×C₃×C₈	—	2	8	no	—
179	C₂×C₃×C₈	C₂³×C₃	1	4	yes	—
180	C₂×C₃×C₈	C₂³×C₃	1	8	yes	—
181	C₂×C₃×C₈	C₂³×C₃	1	4	yes	—
182	C₃×C₄⋊C₄	—	2	4	no	—
183	C₃×C₄⋊C₄	—	2	8	no	—
184	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
185	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
186	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
187	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
188	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
189	C₃×C₂²⋊C₄	—	2	4	no	—
190	C₃×C₂²⋊C₄	—	2	4	no	—
191	C₃×C₂²⋊C₄	—	2	8	no	—
192	C₃×C₂²⋊C₄	—	2	8	no	—
193	C₃×C₂²⋊C₄	—	2	8	no	—
194	C₃×C₄²	—	2	4	no	—
195	C₃×C₄²	—	2	4	no	—
196	C₃×C₄²	—	2	8	no	—
197	C₂²×C₃²	—	2	1	no	—
198	C₂²×C₃²	—	2	1	no	—
199	C₂²×C₃²	—	2	2	no	—
200	C₂²×C₃²	—	2	2	no	—
201	C₂²×C₃²	—	2	2	no	—
202	C₂²×C₃²	—	4	2	no	—
203	C₂²×C₃²	—	4	2	no	—
204	C₂²×C₃²	—	4	2	no	—
205	C₂²×C₃²	—	8	4	no	—
206	C₂²×C₃²	#123	1	2	yes	—
207	C₂²×C₃²	C₂²×D₄	1	1	yes	characteristic
208	C₃²×C₄	—	2	2	no	—
209	C₃²×C₄	—	4	1	no	—
210	C₃²×C₄	—	4	2	no	—
211	C₃²×C₄	—	4	1	no	—
212	C₃²×C₄	—	4	1	no	—
213	C₃²×C₄	—	4	1	no	—
214	C₃²×C₄	#123	1	2	yes	—
215	C₃²×C₄	C₂×#41	1	1	yes	characteristic
216	C₃²×C₄	C₂×#41	1	1	yes	characteristic
217	C₂×#41	C₂²×C₃²	1	1	yes	characteristic
218	C₂²×D₄	C₂²×C₃²	1	1	yes	characteristic
219	C₂×M₁₆	C₂²×C₃²	1	1	yes	characteristic
220	C₂²×C₈	C₂²×C₃²	1	1	yes	characteristic
221	#127	—	2	1	no	—
222	#124	—	2	1	no	—
223	#121	C₂²×C₃²	1	2	yes	—
224	#121	C₂²×C₃²	1	2	yes	—
225	#120	—	2	2	no	—
226	C₄×Q₈	—	2	1	no	—
227	C₄×D₄	—	2	1	no	—
228	C₄×D₄	—	2	2	no	—
229	#117	C₂²×C₃²	1	1	yes	characteristic
230	#117	C₂²×C₃²	1	1	yes	characteristic
231	#117	C₂²×C₃²	1	2	yes	complemented
232	C₂×C₄⋊C₄	C₂²×C₃²	1	1	yes	characteristic
233	C₂×C₄⋊C₄	C₂²×C₃²	1	2	yes	complemented
234	#107	C₂²×C₃²	1	1	yes	characteristic, complemented
235	#107	C₂²×C₃²	1	1	yes	characteristic, complemented
236	#107	C₂²×C₃²	1	2	yes	complemented
237	#106	C₂²×C₃²	1	1	yes	characteristic, complemented
238	#106	C₂²×C₃²	1	1	yes	characteristic, complemented
239	#106	C₂²×C₃²	1	2	yes	complemented
240	#102	C₂²×C₃²	1	2	yes	—
241	#102	C₂²×C₃²	1	2	yes	—
242	#102	C₂²×C₃²	1	2	yes	—
243	#102	C₂²×C₃²	1	2	yes	—
244	C₂²⋊C₈	C₂²×C₃²	1	2	yes	complemented
245	C₂²⋊C₈	C₂²×C₃²	1	2	yes	complemented
246	C₂³×C₃	—	2	8	no	—
247	C₂³×C₃	—	4	8	no	—
248	C₂³×C₃	—	8	4	no	—
249	C₂³×C₃	—	8	4	no	—
250	C₂³×C₃	C₂×C₃×D₄	1	8	yes	—
251	C₂³×C₃	C₂×C₃×D₄	1	4	yes	—
252	C₃×Q₈	—	2	8	no	—
253	C₃×D₄	—	2	16	no	—
254	C₃×D₄	—	2	8	no	—
255	C₃×D₄	—	2	8	no	—
256	C₃×D₄	—	2	8	no	—
257	C₃×D₄	—	4	8	no	—
258	C₃×D₄	—	8	8	no	—
259	C₃×D₄	—	8	8	no	—
260	C₂×C₃×C₄	—	2	8	no	—
261	C₂×C₃×C₄	—	2	8	no	—
262	C₂×C₃×C₄	—	2	4	no	—
263	C₂×C₃×C₄	—	2	4	no	—
264	C₂×C₃×C₄	—	2	4	no	—
265	C₂×C₃×C₄	—	2	4	no	—
266	C₂×C₃×C₄	—	2	8	no	—
267	C₂×C₃×C₄	—	8	4	no	—
268	C₂×C₃×C₄	—	8	8	no	—
269	C₂×C₃×C₄	C₂×C₃×D₄	1	8	yes	—
270	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
271	C₂×C₃×C₄	C₃×#41	1	8	yes	—
272	C₂×C₃×C₄	C₃×#41	1	8	yes	—
273	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
274	C₃×C₈	—	2	4	no	—
275	C₃×C₈	—	2	4	no	—
276	C₃×C₈	—	2	8	no	—
277	C₂×C₃²	—	2	2	no	—
278	C₂×C₃²	—	4	2	no	—
279	C₂×C₃²	—	8	2	no	—
280	C₂×C₃²	C₂×#123	1	1	yes	characteristic
281	C₂×C₃²	#576	1	1	yes	characteristic
282	C₂×C₃²	#577	1	1	yes	characteristic
283	C₂⁴	—	2	1	no	—
284	#41	—	2	2	no	—
285	#41	—	2	2	no	—
286	C₂×Q₈	C₃²×D₄	1	1	yes	characteristic
287	C₂×D₄	—	2	2	no	—
288	C₂×D₄	—	2	2	no	—
289	C₂×D₄	—	2	1	no	—
290	C₂×D₄	—	2	2	no	—
291	C₂×D₄	—	2	2	no	—
292	C₂×D₄	C₃²×D₄	1	2	yes	—
293	C₂×D₄	C₃²×D₄	1	1	yes	characteristic
294	C₂×D₄	C₂³×C₃²	1	2	yes	—
295	C₂²×C₄	—	2	1	no	—
296	C₂²×C₄	—	2	2	no	—
297	C₂²×C₄	C₂³×C₃²	1	2	yes	—
298	C₂²×C₄	C₂³×C₃²	1	1	yes	characteristic
299	M₁₆	—	2	2	no	—
300	C₂×C₈	—	2	2	no	—
301	C₂×C₈	C₂³×C₃²	1	1	yes	characteristic
302	C₂×C₈	C₂³×C₃²	1	2	yes	—
303	C₂×C₈	C₂³×C₃²	1	1	yes	characteristic
304	C₄⋊C₄	—	2	1	no	—
305	C₄⋊C₄	—	2	2	no	—
306	C₄⋊C₄	C₂³×C₃²	1	2	yes	—
307	C₄⋊C₄	C₂³×C₃²	1	1	yes	characteristic
308	C₄⋊C₄	C₂³×C₃²	1	1	yes	characteristic
309	C₄⋊C₄	C₂³×C₃²	1	1	yes	characteristic
310	C₄⋊C₄	C₂³×C₃²	1	1	yes	characteristic
311	C₂²⋊C₄	—	2	1	no	—
312	C₂²⋊C₄	—	2	1	no	—
313	C₂²⋊C₄	—	2	2	no	—
314	C₂²⋊C₄	—	2	2	no	—
315	C₂²⋊C₄	—	2	2	no	—
316	C₄²	—	2	1	no	—
317	C₄²	—	2	1	no	—
318	C₄²	—	2	2	no	—
319	C₂²×C₃	—	2	4	no	—
320	C₂²×C₃	—	2	4	no	—
321	C₂²×C₃	—	2	8	no	—
322	C₂²×C₃	—	2	8	no	—
323	C₂²×C₃	—	2	8	no	—
324	C₂²×C₃	—	4	8	no	—
325	C₂²×C₃	—	4	8	no	—
326	C₂²×C₃	—	4	8	no	—
327	C₂²×C₃	—	8	16	no	—
328	C₂²×C₃	C₃×#123	1	8	yes	—
329	C₂²×C₃	C₂²×C₃×D₄	1	4	yes	—
330	C₃×C₄	—	2	8	no	—
331	C₃×C₄	—	4	4	no	—
332	C₃×C₄	—	4	8	no	—
333	C₃×C₄	—	4	4	no	—
334	C₃×C₄	—	4	4	no	—
335	C₃×C₄	—	4	4	no	—
336	C₃×C₄	C₃×#123	1	8	yes	—
337	C₃×C₄	C₂×C₃×#41	1	4	yes	—
338	C₃×C₄	C₂×C₃×#41	1	4	yes	—
339	C₃²	#3096	1	1	yes	characteristic, direct product factor, Sylow
340	C₂³	—	2	2	no	—
341	C₂³	—	4	2	no	—
342	C₂³	—	8	1	no	—
343	C₂³	—	8	1	no	—
344	C₂³	C₂×C₃²×D₄	1	2	yes	—
345	C₂³	C₂×C₃²×D₄	1	1	yes	characteristic
346	Q₈	—	2	2	no	—
347	D₄	—	2	4	no	—
348	D₄	—	2	2	no	—
349	D₄	—	2	2	no	—
350	D₄	—	2	2	no	—
351	D₄	—	4	2	no	—
352	D₄	—	8	2	no	—
353	D₄	—	8	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	8	1	no	—
362	C₂×C₄	—	8	2	no	—
363	C₂×C₄	C₂×C₃²×D₄	1	2	yes	—
364	C₂×C₄	C₂×C₃²×D₄	1	1	yes	characteristic
365	C₂×C₄	C₃²×#41	1	2	yes	—
366	C₂×C₄	C₃²×#41	1	2	yes	—
367	C₂×C₄	C₂⁴×C₃²	1	1	yes	characteristic
368	C₈	—	2	1	no	—
369	C₈	—	2	1	no	—
370	C₈	—	2	2	no	—
371	C₂×C₃	—	2	8	no	—
372	C₂×C₃	—	4	8	no	—
373	C₂×C₃	—	8	8	no	—
374	C₂×C₃	C₂×C₃×#123	1	4	yes	—
375	C₂×C₃	C₃×#576	1	4	yes	—
376	C₂×C₃	C₃×#577	1	4	yes	—
377	C₂²	—	2	1	no	—
378	C₂²	—	2	1	no	—
379	C₂²	—	2	2	no	—
380	C₂²	—	2	2	no	—
381	C₂²	—	2	2	no	—
382	C₂²	—	4	2	no	—
383	C₂²	—	4	2	no	—
384	C₂²	—	4	2	no	—
385	C₂²	—	8	4	no	—
386	C₂²	C₃²×#123	1	2	yes	—
387	C₂²	C₂²×C₃²×D₄	1	1	yes	characteristic
388	C₄	—	2	2	no	—
389	C₄	—	4	1	no	—
390	C₄	—	4	2	no	—
391	C₄	—	4	1	no	—
392	C₄	—	4	1	no	—
393	C₄	—	4	1	no	—
394	C₄	C₃²×#123	1	2	yes	—
395	C₄	C₂×C₃²×#41	1	1	yes	characteristic
396	C₄	C₂×C₃²×#41	1	1	yes	characteristic
397	C₃	C₃×#3096	1	4	yes	direct product factor
398	C₂	—	2	2	no	—
399	C₂	—	4	2	no	—
400	C₂	—	8	2	no	—
401	C₂	C₂×C₃²×#123	1	1	yes	characteristic
402	C₂	C₃²×#576	1	1	yes	characteristic
403	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×#535	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃² ◁ C₂×C₃²×#41 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃²×#520	C₂	semidirect
3. C₃²×#482	C₂	semidirect
4. C₃²×#482	C₂	semidirect
5. C₃²×#481	C₂	semidirect
6. C₃²×#480	C₂	semidirect
7. C₃²×#428	C₂	semidirect
8. C₃²×#427	C₂	semidirect
9. C₃²×#418	C₂	semidirect
10. C₂×C₃²×#102	C₂	semidirect
11. C₃²×#408	C₂	semidirect
12. C₃×#3096	C₃	direct (N × H)
27. C₃²×#117	C₂²	semidirect
29. C₂×C₃²×C₄⋊C₄	C₂²	semidirect
30. C₃²×#107	C₂²	semidirect
31. C₃²×#107	C₂²	semidirect
32. C₃²×#107	C₂²	semidirect
33. C₃²×#106	C₂²	semidirect
34. C₃²×#106	C₂²	semidirect
35. C₃²×#106	C₂²	semidirect
40. C₃²×C₂²⋊C₈	C₂²	semidirect
41. C₃²×C₂²⋊C₈	C₂²	semidirect
43. C₃×#520	C₂×C₃	semidirect
44. C₃×#482	C₂×C₃	semidirect
45. C₃×#482	C₂×C₃	semidirect
46. C₃×#481	C₂×C₃	semidirect
47. C₃×#480	C₂×C₃	semidirect
48. C₃×#428	C₂×C₃	semidirect
49. C₃×#427	C₂×C₃	semidirect
50. C₃×#418	C₂×C₃	semidirect
51. C₂×C₃×#102	C₂×C₃	semidirect
52. C₃×#408	C₂×C₃	semidirect
89. #3096	C₃²	direct (N × H)
104. C₃×#117	C₂²×C₃	semidirect
106. C₂×C₃×C₄⋊C₄	C₂²×C₃	semidirect
107. C₃×#107	C₂²×C₃	semidirect
108. C₃×#107	C₂²×C₃	semidirect
109. C₃×#107	C₂²×C₃	semidirect
110. C₃×#106	C₂²×C₃	semidirect
111. C₃×#106	C₂²×C₃	semidirect
112. C₃×#106	C₂²×C₃	semidirect
117. C₃×C₂²⋊C₈	C₂²×C₃	semidirect
118. C₃×C₂²⋊C₈	C₂²×C₃	semidirect
151. #520	C₂×C₃²	semidirect
152. #482	C₂×C₃²	semidirect
153. #482	C₂×C₃²	semidirect
154. #481	C₂×C₃²	semidirect
155. #480	C₂×C₃²	semidirect
156. #428	C₂×C₃²	semidirect
157. #427	C₂×C₃²	semidirect
158. #418	C₂×C₃²	semidirect
159. C₂×#102	C₂×C₃²	semidirect
160. #408	C₂×C₃²	semidirect
231. #117	C₂²×C₃²	semidirect
233. C₂×C₄⋊C₄	C₂²×C₃²	semidirect
234. #107	C₂²×C₃²	semidirect
235. #107	C₂²×C₃²	semidirect
236. #107	C₂²×C₃²	semidirect
237. #106	C₂²×C₃²	semidirect
238. #106	C₂²×C₃²	semidirect
239. #106	C₂²×C₃²	semidirect
244. C₂²⋊C₈	C₂²×C₃²	semidirect
245. C₂²⋊C₈	C₂²×C₃²	semidirect
339. C₃²	#3096	direct (N × H)
397. C₃	C₃×#3096	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×#535	2
C₃²×#520	2
C₃²×#482	2
C₃²×#481	2
C₃²×#480	2
C₃²×#428	2
C₃²×#427	2
C₃²×#418	2
C₂×C₃²×#102	2
C₃²×#408	2
C₃×#3096	3

Subgroups — C32×#3096 #11770145

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#3096 #11770145