Subgroups — C₃²×#3508 #11770557

Order 1152.

3696 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#559	C₂	1	4	yes	maximal, complemented
2	C₃²×#550	C₂	1	4	yes	maximal, complemented
3	C₃²×#546	C₂	1	8	yes	maximal, complemented
4	C₃²×#540	C₂	1	4	yes	maximal, complemented
5	C₃²×#535	C₂	1	2	yes	maximal, complemented
6	C₃²×#533	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃²×#532	C₂	1	4	yes	maximal, complemented
8	C₂×C₃²×#127	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃²×#518	C₂	1	2	yes	maximal, complemented
10	C₃²×C₄×#41	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#3508	C₃	1	4	yes	maximal, direct product factor
12	C₂×C₃²×#41	C₂²	1	1	yes	characteristic
13	C₂×C₃²×#41	C₂²	1	8	yes	complemented
14	C₂²×C₃²×D₄	C₂²	1	2	yes	—
15	C₂²×C₃²×D₄	C₂²	1	4	yes	—
16	C₃²×C₄⋊Q₈	C₂²	1	2	yes	complemented
17	C₃²×#127	C₂²	1	4	yes	—
18	C₃²×#127	C₂²	1	2	yes	—
19	C₃²×#127	C₂²	1	2	yes	—
20	C₃²×#127	C₂²	1	4	yes	complemented
21	C₃²×#125	C₂²	1	2	yes	complemented
22	C₃²×#124	C₂²	1	4	yes	complemented
23	C₃²×#124	C₂²	1	8	yes	complemented
24	C₃²×#123	C₂²	1	16	yes	complemented
25	C₃²×C₂²⋊Q₈	C₂²	1	4	yes	—
26	C₃²×#121	C₂²	1	8	yes	complemented
27	C₃²×#121	C₂²	1	8	yes	complemented
28	C₃²×#121	C₂²	1	16	yes	complemented
29	C₃²×#120	C₂²	1	8	yes	—
30	C₃²×C₄×Q₈	C₂²	1	2	yes	complemented
31	C₃²×C₄×Q₈	C₂²	1	4	yes	complemented
32	C₃²×C₄×D₄	C₂²	1	4	yes	—
33	C₃²×C₄×D₄	C₂²	1	8	yes	complemented
34	C₃²×C₄×D₄	C₂²	1	8	yes	complemented
35	C₃²×C₄×D₄	C₂²	1	2	yes	complemented
36	C₃²×C₄×D₄	C₂²	1	8	yes	complemented
37	C₃²×#117	C₂²	1	1	yes	characteristic
38	C₃²×#117	C₂²	1	2	yes	—
39	C₃²×#117	C₂²	1	2	yes	complemented
40	C₂×C₃²×C₂²⋊C₄	C₂²	1	8	yes	—
41	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
42	C₂×C₃²×C₄²	C₂²	1	2	yes	complemented
43	C₃×#559	C₂×C₃	1	16	yes	complemented
44	C₃×#550	C₂×C₃	1	16	yes	complemented
45	C₃×#546	C₂×C₃	1	32	yes	complemented
46	C₃×#540	C₂×C₃	1	16	yes	complemented
47	C₃×#535	C₂×C₃	1	8	yes	complemented
48	C₃×#533	C₂×C₃	1	4	yes	complemented
49	C₃×#532	C₂×C₃	1	16	yes	complemented
50	C₂×C₃×#127	C₂×C₃	1	4	yes	complemented
51	C₃×#518	C₂×C₃	1	8	yes	complemented
52	C₃×C₄×#41	C₂×C₃	1	4	yes	complemented
53	C₂⁴×C₃²	C₂³	1	4	yes	—
54	C₃²×#41	—	2	4	no	—
55	C₃²×#41	—	4	16	no	—
56	C₂×C₃²×Q₈	C₂³	1	1	yes	characteristic
57	C₂×C₃²×Q₈	C₂³	1	4	yes	—
58	C₂×C₃²×D₄	—	2	8	no	—
59	C₂×C₃²×D₄	—	4	8	no	—
60	C₂×C₃²×D₄	C₂³	1	8	yes	—
61	C₂×C₃²×D₄	C₂³	1	4	yes	—
62	C₂×C₃²×D₄	C₂³	1	4	yes	—
63	C₂×C₃²×D₄	C₂³	1	2	yes	—
64	C₂×C₃²×D₄	C₂³	1	1	yes	characteristic
65	C₂×C₃²×D₄	C₂³	1	8	yes	—
66	C₂×C₃²×D₄	C₂³	1	16	yes	—
67	C₂²×C₃²×C₄	C₂³	1	2	yes	—
68	C₂²×C₃²×C₄	C₂³	1	2	yes	—
69	C₂²×C₃²×C₄	C₂³	1	4	yes	—
70	C₂²×C₃²×C₄	C₂³	1	16	yes	—
71	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
72	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
73	C₃²×C₄⋊C₄	C₂³	1	4	yes	—
74	C₃²×C₄⋊C₄	C₂³	1	4	yes	—
75	C₃²×C₄⋊C₄	C₂³	1	4	yes	—
76	C₃²×C₄⋊C₄	C₂³	1	8	yes	—
77	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
78	C₃²×C₂²⋊C₄	C₂³	1	4	yes	—
79	C₃²×C₂²⋊C₄	C₂³	1	16	yes	—
80	C₃²×C₂²⋊C₄	C₂³	1	4	yes	—
81	C₃²×C₂²⋊C₄	C₂³	1	16	yes	—
82	C₃²×C₄²	C₂³	1	1	yes	characteristic
83	C₃²×C₄²	C₂³	1	1	yes	characteristic
84	C₃²×C₄²	C₂³	1	2	yes	—
85	C₃²×C₄²	C₂³	1	2	yes	—
86	C₃²×C₄²	C₂³	1	4	yes	—
87	C₃²×C₄²	C₂³	1	4	yes	—
88	#3508	C₃²	1	1	yes	characteristic, direct product factor, Sylow
89	C₂×C₃×#41	C₂²×C₃	1	4	yes	—
90	C₂×C₃×#41	C₂²×C₃	1	32	yes	complemented
91	C₂²×C₃×D₄	C₂²×C₃	1	8	yes	—
92	C₂²×C₃×D₄	C₂²×C₃	1	16	yes	—
93	C₃×C₄⋊Q₈	C₂²×C₃	1	8	yes	complemented
94	C₃×#127	C₂²×C₃	1	16	yes	—
95	C₃×#127	C₂²×C₃	1	8	yes	—
96	C₃×#127	C₂²×C₃	1	8	yes	—
97	C₃×#127	C₂²×C₃	1	16	yes	complemented
98	C₃×#125	C₂²×C₃	1	8	yes	complemented
99	C₃×#124	C₂²×C₃	1	16	yes	complemented
100	C₃×#124	C₂²×C₃	1	32	yes	complemented
101	C₃×#123	C₂²×C₃	1	64	yes	complemented
102	C₃×C₂²⋊Q₈	C₂²×C₃	1	16	yes	—
103	C₃×#121	C₂²×C₃	1	32	yes	complemented
104	C₃×#121	C₂²×C₃	1	32	yes	complemented
105	C₃×#121	C₂²×C₃	1	64	yes	complemented
106	C₃×#120	C₂²×C₃	1	32	yes	—
107	C₃×C₄×Q₈	C₂²×C₃	1	8	yes	complemented
108	C₃×C₄×Q₈	C₂²×C₃	1	16	yes	complemented
109	C₃×C₄×D₄	C₂²×C₃	1	16	yes	—
110	C₃×C₄×D₄	C₂²×C₃	1	32	yes	complemented
111	C₃×C₄×D₄	C₂²×C₃	1	32	yes	complemented
112	C₃×C₄×D₄	C₂²×C₃	1	8	yes	complemented
113	C₃×C₄×D₄	C₂²×C₃	1	32	yes	complemented
114	C₃×#117	C₂²×C₃	1	4	yes	—
115	C₃×#117	C₂²×C₃	1	8	yes	—
116	C₃×#117	C₂²×C₃	1	8	yes	complemented
117	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	32	yes	—
118	C₂×C₃×C₄²	C₂²×C₃	1	4	yes	—
119	C₂×C₃×C₄²	C₂²×C₃	1	8	yes	complemented
120	C₂³×C₃²	—	2	8	no	—
121	C₂³×C₃²	—	4	8	no	—
122	C₂³×C₃²	C₂⁴	1	8	yes	—
123	C₂³×C₃²	C₂⁴	1	2	yes	—
124	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
125	C₃²×Q₈	—	2	2	no	—
126	C₃²×Q₈	—	2	8	no	—
127	C₃²×D₄	—	2	4	no	—
128	C₃²×D₄	—	2	8	no	—
129	C₃²×D₄	—	2	8	no	—
130	C₃²×D₄	—	2	2	no	—
131	C₃²×D₄	—	2	16	no	—
132	C₃²×D₄	—	4	8	no	—
133	C₃²×D₄	—	4	16	no	—
134	C₂×C₃²×C₄	—	2	4	no	—
135	C₂×C₃²×C₄	—	2	4	no	—
136	C₂×C₃²×C₄	—	2	8	no	—
137	C₂×C₃²×C₄	—	4	16	no	—
138	C₂×C₃²×C₄	#41	1	4	yes	complemented
139	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
140	C₂×C₃²×C₄	C₂⁴	1	4	yes	—
141	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
142	C₂×C₃²×C₄	C₂⁴	1	8	yes	—
143	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
144	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
145	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
146	#559	C₂×C₃²	1	4	yes	complemented
147	#550	C₂×C₃²	1	4	yes	complemented
148	#546	C₂×C₃²	1	8	yes	complemented
149	#540	C₂×C₃²	1	4	yes	complemented
150	#535	C₂×C₃²	1	2	yes	complemented
151	#533	C₂×C₃²	1	1	yes	characteristic, complemented
152	#532	C₂×C₃²	1	4	yes	complemented
153	C₂×#127	C₂×C₃²	1	1	yes	characteristic, complemented
154	#518	C₂×C₃²	1	2	yes	complemented
155	C₄×#41	C₂×C₃²	1	1	yes	characteristic, complemented
156	C₂⁴×C₃	C₂³×C₃	1	16	yes	—
157	C₃×#41	—	2	16	no	—
158	C₃×#41	—	4	64	no	—
159	C₂×C₃×Q₈	C₂³×C₃	1	4	yes	—
160	C₂×C₃×Q₈	C₂³×C₃	1	16	yes	—
161	C₂×C₃×D₄	—	2	32	no	—
162	C₂×C₃×D₄	—	4	32	no	—
163	C₂×C₃×D₄	C₂³×C₃	1	8	yes	—
164	C₂×C₃×D₄	C₂³×C₃	1	16	yes	—
165	C₂×C₃×D₄	C₂³×C₃	1	16	yes	—
166	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
167	C₂×C₃×D₄	C₂³×C₃	1	32	yes	—
168	C₂×C₃×D₄	C₂³×C₃	1	64	yes	—
169	C₂×C₃×D₄	C₂³×C₃	1	32	yes	—
170	C₂²×C₃×C₄	C₂³×C₃	1	8	yes	—
171	C₂²×C₃×C₄	C₂³×C₃	1	8	yes	—
172	C₂²×C₃×C₄	C₂³×C₃	1	16	yes	—
173	C₂²×C₃×C₄	C₂³×C₃	1	64	yes	—
174	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
175	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
176	C₃×C₄⋊C₄	C₂³×C₃	1	16	yes	—
177	C₃×C₄⋊C₄	C₂³×C₃	1	16	yes	—
178	C₃×C₄⋊C₄	C₂³×C₃	1	16	yes	—
179	C₃×C₄⋊C₄	C₂³×C₃	1	32	yes	—
180	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
181	C₃×C₂²⋊C₄	C₂³×C₃	1	16	yes	—
182	C₃×C₂²⋊C₄	C₂³×C₃	1	64	yes	—
183	C₃×C₂²⋊C₄	C₂³×C₃	1	16	yes	—
184	C₃×C₂²⋊C₄	C₂³×C₃	1	64	yes	—
185	C₃×C₄²	C₂³×C₃	1	4	yes	—
186	C₃×C₄²	C₂³×C₃	1	4	yes	—
187	C₃×C₄²	C₂³×C₃	1	8	yes	—
188	C₃×C₄²	C₂³×C₃	1	8	yes	—
189	C₃×C₄²	C₂³×C₃	1	16	yes	—
190	C₃×C₄²	C₂³×C₃	1	16	yes	—
191	C₂²×C₃²	—	2	2	no	—
192	C₂²×C₃²	—	2	2	no	—
193	C₂²×C₃²	—	2	8	no	—
194	C₂²×C₃²	—	2	4	no	—
195	C₂²×C₃²	—	2	16	no	—
196	C₂²×C₃²	—	8	8	no	—
197	C₂²×C₃²	C₂×#41	1	2	yes	—
198	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
199	C₃²×C₄	—	2	2	no	—
200	C₃²×C₄	—	2	4	no	—
201	C₃²×C₄	—	2	2	no	—
202	C₃²×C₄	—	2	8	no	—
203	C₃²×C₄	C₂×#41	1	2	yes	—
204	C₃²×C₄	C₂×#41	1	2	yes	—
205	C₃²×C₄	H(5,𝔽₂)	1	4	yes	—
206	C₂×#41	C₂²×C₃²	1	1	yes	characteristic
207	C₂×#41	C₂²×C₃²	1	8	yes	complemented
208	C₂²×D₄	C₂²×C₃²	1	2	yes	—
209	C₂²×D₄	C₂²×C₃²	1	4	yes	—
210	C₄⋊Q₈	C₂²×C₃²	1	2	yes	complemented
211	#127	C₂²×C₃²	1	2	yes	—
212	#127	C₂²×C₃²	1	2	yes	—
213	#127	C₂²×C₃²	1	4	yes	—
214	#127	C₂²×C₃²	1	4	yes	complemented
215	#125	C₂²×C₃²	1	2	yes	complemented
216	#124	C₂²×C₃²	1	8	yes	complemented
217	#124	C₂²×C₃²	1	4	yes	complemented
218	#123	C₂²×C₃²	1	16	yes	complemented
219	C₂²⋊Q₈	C₂²×C₃²	1	4	yes	—
220	#121	C₂²×C₃²	1	8	yes	complemented
221	#121	C₂²×C₃²	1	8	yes	complemented
222	#121	C₂²×C₃²	1	16	yes	complemented
223	#120	C₂²×C₃²	1	8	yes	—
224	C₄×Q₈	C₂²×C₃²	1	2	yes	complemented
225	C₄×Q₈	C₂²×C₃²	1	4	yes	complemented
226	C₄×D₄	C₂²×C₃²	1	4	yes	—
227	C₄×D₄	C₂²×C₃²	1	2	yes	complemented
228	C₄×D₄	C₂²×C₃²	1	8	yes	complemented
229	C₄×D₄	C₂²×C₃²	1	8	yes	complemented
230	C₄×D₄	C₂²×C₃²	1	8	yes	complemented
231	#117	C₂²×C₃²	1	1	yes	characteristic
232	#117	C₂²×C₃²	1	2	yes	—
233	#117	C₂²×C₃²	1	2	yes	complemented
234	C₂×C₂²⋊C₄	C₂²×C₃²	1	8	yes	—
235	C₂×C₄²	C₂²×C₃²	1	1	yes	characteristic
236	C₂×C₄²	C₂²×C₃²	1	2	yes	complemented
237	C₂³×C₃	—	2	32	no	—
238	C₂³×C₃	—	4	32	no	—
239	C₂³×C₃	C₂⁴×C₃	1	32	yes	—
240	C₂³×C₃	C₂⁴×C₃	1	8	yes	—
241	C₂³×C₃	C₂⁴×C₃	1	4	yes	—
242	C₃×Q₈	—	2	8	no	—
243	C₃×Q₈	—	2	32	no	—
244	C₃×D₄	—	2	16	no	—
245	C₃×D₄	—	2	32	no	—
246	C₃×D₄	—	2	32	no	—
247	C₃×D₄	—	2	8	no	—
248	C₃×D₄	—	2	64	no	—
249	C₃×D₄	—	4	32	no	—
250	C₃×D₄	—	4	64	no	—
251	C₂×C₃×C₄	—	2	16	no	—
252	C₂×C₃×C₄	—	2	16	no	—
253	C₂×C₃×C₄	—	2	32	no	—
254	C₂×C₃×C₄	—	4	64	no	—
255	C₂×C₃×C₄	C₃×#41	1	16	yes	complemented
256	C₂×C₃×C₄	C₂⁴×C₃	1	8	yes	—
257	C₂×C₃×C₄	C₂⁴×C₃	1	16	yes	—
258	C₂×C₃×C₄	C₂⁴×C₃	1	8	yes	—
259	C₂×C₃×C₄	C₂⁴×C₃	1	32	yes	—
260	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
261	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
262	C₂×C₃×C₄	C₂⁴×C₃	1	8	yes	—
263	C₂×C₃²	—	2	2	no	—
264	C₂×C₃²	—	4	2	no	—
265	C₂×C₃²	—	4	8	no	—
266	C₂×C₃²	C₂²×#41	1	1	yes	characteristic
267	C₂×C₃²	C₂×H(5,𝔽₂)	1	2	yes	—
268	C₂⁴	C₂³×C₃²	1	4	yes	—
269	#41	—	2	4	no	—
270	#41	—	4	16	no	—
271	C₂×Q₈	C₂³×C₃²	1	1	yes	characteristic
272	C₂×Q₈	C₂³×C₃²	1	4	yes	—
273	C₂×D₄	—	2	8	no	—
274	C₂×D₄	—	4	8	no	—
275	C₂×D₄	C₂³×C₃²	1	2	yes	—
276	C₂×D₄	C₂³×C₃²	1	4	yes	—
277	C₂×D₄	C₂³×C₃²	1	4	yes	—
278	C₂×D₄	C₂³×C₃²	1	1	yes	characteristic
279	C₂×D₄	C₂³×C₃²	1	8	yes	—
280	C₂×D₄	C₂³×C₃²	1	16	yes	—
281	C₂×D₄	C₂³×C₃²	1	8	yes	—
282	C₂²×C₄	C₂³×C₃²	1	2	yes	—
283	C₂²×C₄	C₂³×C₃²	1	2	yes	—
284	C₂²×C₄	C₂³×C₃²	1	4	yes	—
285	C₂²×C₄	C₂³×C₃²	1	16	yes	—
286	C₂²×C₄	C₂³×C₃²	1	1	yes	characteristic
287	C₄⋊C₄	C₂³×C₃²	1	2	yes	—
288	C₄⋊C₄	C₂³×C₃²	1	4	yes	—
289	C₄⋊C₄	C₂³×C₃²	1	4	yes	—
290	C₄⋊C₄	C₂³×C₃²	1	4	yes	—
291	C₄⋊C₄	C₂³×C₃²	1	8	yes	—
292	C₂²⋊C₄	C₂³×C₃²	1	2	yes	—
293	C₂²⋊C₄	C₂³×C₃²	1	4	yes	—
294	C₂²⋊C₄	C₂³×C₃²	1	16	yes	—
295	C₂²⋊C₄	C₂³×C₃²	1	4	yes	—
296	C₂²⋊C₄	C₂³×C₃²	1	16	yes	—
297	C₄²	C₂³×C₃²	1	1	yes	characteristic
298	C₄²	C₂³×C₃²	1	1	yes	characteristic
299	C₄²	C₂³×C₃²	1	2	yes	—
300	C₄²	C₂³×C₃²	1	2	yes	—
301	C₄²	C₂³×C₃²	1	4	yes	—
302	C₄²	C₂³×C₃²	1	4	yes	—
303	C₂²×C₃	—	2	8	no	—
304	C₂²×C₃	—	2	8	no	—
305	C₂²×C₃	—	2	32	no	—
306	C₂²×C₃	—	2	16	no	—
307	C₂²×C₃	—	2	64	no	—
308	C₂²×C₃	—	8	32	no	—
309	C₂²×C₃	C₂×C₃×#41	1	8	yes	—
310	C₂²×C₃	C₂⁵×C₃	1	4	yes	—
311	C₃×C₄	—	2	8	no	—
312	C₃×C₄	—	2	16	no	—
313	C₃×C₄	—	2	8	no	—
314	C₃×C₄	—	2	32	no	—
315	C₃×C₄	C₂×C₃×#41	1	8	yes	—
316	C₃×C₄	C₂×C₃×#41	1	8	yes	—
317	C₃×C₄	C₃×H(5,𝔽₂)	1	16	yes	—
318	C₃²	#3508	1	1	yes	characteristic, direct product factor, Sylow
319	C₂³	—	2	8	no	—
320	C₂³	—	4	8	no	—
321	C₂³	C₂⁴×C₃²	1	8	yes	—
322	C₂³	C₂⁴×C₃²	1	2	yes	—
323	C₂³	C₂⁴×C₃²	1	1	yes	characteristic
324	Q₈	—	2	2	no	—
325	Q₈	—	2	8	no	—
326	D₄	—	2	4	no	—
327	D₄	—	2	8	no	—
328	D₄	—	2	8	no	—
329	D₄	—	2	2	no	—
330	D₄	—	2	16	no	—
331	D₄	—	4	8	no	—
332	D₄	—	4	16	no	—
333	C₂×C₄	—	2	4	no	—
334	C₂×C₄	—	2	4	no	—
335	C₂×C₄	—	2	8	no	—
336	C₂×C₄	—	4	16	no	—
337	C₂×C₄	C₃²×#41	1	4	yes	complemented
338	C₂×C₄	C₂⁴×C₃²	1	2	yes	—
339	C₂×C₄	C₂⁴×C₃²	1	4	yes	—
340	C₂×C₄	C₂⁴×C₃²	1	2	yes	—
341	C₂×C₄	C₂⁴×C₃²	1	8	yes	—
342	C₂×C₄	C₂⁴×C₃²	1	1	yes	characteristic
343	C₂×C₄	C₂⁴×C₃²	1	1	yes	characteristic
344	C₂×C₄	C₂⁴×C₃²	1	2	yes	—
345	C₂×C₃	—	2	8	no	—
346	C₂×C₃	—	4	32	no	—
347	C₂×C₃	—	4	8	no	—
348	C₂×C₃	C₂²×C₃×#41	1	4	yes	—
349	C₂×C₃	C₂×C₃×H(5,𝔽₂)	1	8	yes	—
350	C₂²	—	2	2	no	—
351	C₂²	—	2	2	no	—
352	C₂²	—	2	8	no	—
353	C₂²	—	2	4	no	—
354	C₂²	—	2	16	no	—
355	C₂²	—	8	8	no	—
356	C₂²	C₂×C₃²×#41	1	2	yes	—
357	C₂²	C₂⁵×C₃²	1	1	yes	characteristic
358	C₄	—	2	2	no	—
359	C₄	—	2	4	no	—
360	C₄	—	2	2	no	—
361	C₄	—	2	8	no	—
362	C₄	C₂×C₃²×#41	1	2	yes	—
363	C₄	C₂×C₃²×#41	1	2	yes	—
364	C₄	C₃²×H(5,𝔽₂)	1	4	yes	—
365	C₃	C₃×#3508	1	4	yes	direct product factor
366	C₂	—	2	2	no	—
367	C₂	—	4	8	no	—
368	C₂	—	4	2	no	—
369	C₂	C₂²×C₃²×#41	1	1	yes	characteristic
370	C₂	C₂×C₃²×H(5,𝔽₂)	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃²	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁵×C₃²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃² ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃²×#559	C₂	semidirect
2. C₃²×#550	C₂	semidirect
3. C₃²×#546	C₂	semidirect
4. C₃²×#540	C₂	semidirect
5. C₃²×#535	C₂	semidirect
6. C₃²×#533	C₂	semidirect
7. C₃²×#532	C₂	semidirect
8. C₂×C₃²×#127	C₂	semidirect
9. C₃²×#518	C₂	semidirect
10. C₃²×C₄×#41	C₂	semidirect
11. C₃×#3508	C₃	direct (N × H)
13. C₂×C₃²×#41	C₂²	semidirect
16. C₃²×C₄⋊Q₈	C₂²	semidirect
20. C₃²×#127	C₂²	semidirect
21. C₃²×#125	C₂²	semidirect
22. C₃²×#124	C₂²	semidirect
23. C₃²×#124	C₂²	semidirect
24. C₃²×#123	C₂²	semidirect
26. C₃²×#121	C₂²	semidirect
27. C₃²×#121	C₂²	semidirect
28. C₃²×#121	C₂²	semidirect
30. C₃²×C₄×Q₈	C₂²	semidirect
31. C₃²×C₄×Q₈	C₂²	semidirect
33. C₃²×C₄×D₄	C₂²	semidirect
34. C₃²×C₄×D₄	C₂²	semidirect
35. C₃²×C₄×D₄	C₂²	semidirect
36. C₃²×C₄×D₄	C₂²	semidirect
39. C₃²×#117	C₂²	semidirect
42. C₂×C₃²×C₄²	C₂²	semidirect
43. C₃×#559	C₂×C₃	semidirect
44. C₃×#550	C₂×C₃	semidirect
45. C₃×#546	C₂×C₃	semidirect
46. C₃×#540	C₂×C₃	semidirect
47. C₃×#535	C₂×C₃	semidirect
48. C₃×#533	C₂×C₃	semidirect
49. C₃×#532	C₂×C₃	semidirect
50. C₂×C₃×#127	C₂×C₃	semidirect
51. C₃×#518	C₂×C₃	semidirect
52. C₃×C₄×#41	C₂×C₃	semidirect
88. #3508	C₃²	direct (N × H)
90. C₂×C₃×#41	C₂²×C₃	semidirect
93. C₃×C₄⋊Q₈	C₂²×C₃	semidirect
97. C₃×#127	C₂²×C₃	semidirect
98. C₃×#125	C₂²×C₃	semidirect
99. C₃×#124	C₂²×C₃	semidirect
100. C₃×#124	C₂²×C₃	semidirect
101. C₃×#123	C₂²×C₃	semidirect
103. C₃×#121	C₂²×C₃	semidirect
104. C₃×#121	C₂²×C₃	semidirect
105. C₃×#121	C₂²×C₃	semidirect
107. C₃×C₄×Q₈	C₂²×C₃	semidirect
108. C₃×C₄×Q₈	C₂²×C₃	semidirect
110. C₃×C₄×D₄	C₂²×C₃	semidirect
111. C₃×C₄×D₄	C₂²×C₃	semidirect
112. C₃×C₄×D₄	C₂²×C₃	semidirect
113. C₃×C₄×D₄	C₂²×C₃	semidirect
116. C₃×#117	C₂²×C₃	semidirect
119. C₂×C₃×C₄²	C₂²×C₃	semidirect
138. C₂×C₃²×C₄	#41	semidirect
146. #559	C₂×C₃²	semidirect
147. #550	C₂×C₃²	semidirect
148. #546	C₂×C₃²	semidirect
149. #540	C₂×C₃²	semidirect
150. #535	C₂×C₃²	semidirect
151. #533	C₂×C₃²	semidirect
152. #532	C₂×C₃²	semidirect
153. C₂×#127	C₂×C₃²	semidirect
154. #518	C₂×C₃²	semidirect
155. C₄×#41	C₂×C₃²	semidirect
207. C₂×#41	C₂²×C₃²	semidirect
210. C₄⋊Q₈	C₂²×C₃²	semidirect
214. #127	C₂²×C₃²	semidirect
215. #125	C₂²×C₃²	semidirect
216. #124	C₂²×C₃²	semidirect
217. #124	C₂²×C₃²	semidirect
218. #123	C₂²×C₃²	semidirect
220. #121	C₂²×C₃²	semidirect
221. #121	C₂²×C₃²	semidirect
222. #121	C₂²×C₃²	semidirect
224. C₄×Q₈	C₂²×C₃²	semidirect
225. C₄×Q₈	C₂²×C₃²	semidirect
227. C₄×D₄	C₂²×C₃²	semidirect
228. C₄×D₄	C₂²×C₃²	semidirect
229. C₄×D₄	C₂²×C₃²	semidirect
230. C₄×D₄	C₂²×C₃²	semidirect
233. #117	C₂²×C₃²	semidirect
236. C₂×C₄²	C₂²×C₃²	semidirect
255. C₂×C₃×C₄	C₃×#41	semidirect
318. C₃²	#3508	direct (N × H)
337. C₂×C₄	C₃²×#41	semidirect
365. C₃	C₃×#3508	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×#559	2
C₃²×#550	2
C₃²×#546	2
C₃²×#540	2
C₃²×#535	2
C₃²×#533	2
C₃²×#532	2
C₂×C₃²×#127	2
C₃²×#518	2
C₃²×C₄×#41	2
C₃×#3508	3

Subgroups — C32×#3508 #11770557

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#3508 #11770557