Subgroups — C₃²×#3511 #11770560

Order 1152.

3312 conjugacy classes of subgroups.

The subgroup lattice has 531 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#556	C₂	1	2	yes	maximal, complemented
2	C₃²×#555	C₂	1	2	yes	maximal, complemented
3	C₃²×#554	C₂	1	2	yes	maximal, complemented
4	C₃²×#553	C₂	1	4	yes	maximal, complemented
5	C₃²×#548	C₂	1	4	yes	maximal, complemented
6	C₃²×#547	C₂	1	2	yes	maximal, complemented
7	C₃²×#542	C₂	1	4	yes	maximal, complemented
8	C₃²×#537	C₂	1	2	yes	maximal, complemented
9	C₃²×#533	C₂	1	2	yes	maximal, complemented
10	C₃²×#532	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃²×#532	C₂	1	2	yes	maximal, complemented
12	C₂×C₃²×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃²×#520	C₂	1	2	yes	maximal, complemented
14	C₃²×C₄×#41	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#3511	C₃	1	4	yes	maximal, direct product factor
16	C₂×C₃²×#41	C₂²	1	1	yes	characteristic
17	C₂×C₃²×#41	C₂²	1	2	yes	—
18	C₂×C₃²×#41	C₂²	1	4	yes	—
19	C₂²×C₃²×Q₈	C₂²	1	2	yes	—
20	C₃²×C₄⋊Q₈	C₂²	1	2	yes	—
21	C₃²×C₄⋊Q₈	C₂²	1	2	yes	—
22	C₃²×C₄⋊Q₈	C₂²	1	2	yes	—
23	C₃²×C₄⋊Q₈	C₂²	1	2	yes	—
24	C₃²×C₄⋊Q₈	C₂²	1	1	yes	characteristic
25	C₃²×#127	C₂²	1	1	yes	characteristic
26	C₃²×#126	C₂²	1	8	yes	—
27	C₃²×#125	C₂²	1	4	yes	—
28	C₃²×#124	C₂²	1	8	yes	—
29	C₃²×#124	C₂²	1	4	yes	—
30	C₃²×#124	C₂²	1	2	yes	—
31	C₃²×#123	C₂²	1	8	yes	—
32	C₃²×C₂²⋊Q₈	C₂²	1	4	yes	—
33	C₃²×C₂²⋊Q₈	C₂²	1	8	yes	—
34	C₃²×C₂²⋊Q₈	C₂²	1	4	yes	—
35	C₃²×C₂²⋊Q₈	C₂²	1	4	yes	—
36	C₃²×#121	C₂²	1	2	yes	—
37	C₃²×#121	C₂²	1	4	yes	—
38	C₃²×#121	C₂²	1	8	yes	—
39	C₃²×#121	C₂²	1	4	yes	—
40	C₃²×#121	C₂²	1	4	yes	—
41	C₃²×#121	C₂²	1	2	yes	—
42	C₃²×C₄×Q₈	C₂²	1	1	yes	characteristic
43	C₃²×C₄×Q₈	C₂²	1	1	yes	characteristic
44	C₃²×C₄×Q₈	C₂²	1	4	yes	—
45	C₃²×C₄×Q₈	C₂²	1	4	yes	—
46	C₃²×C₄×D₄	C₂²	1	2	yes	—
47	C₃²×C₄×D₄	C₂²	1	4	yes	—
48	C₃²×C₄×D₄	C₂²	1	8	yes	—
49	C₃²×C₄×D₄	C₂²	1	2	yes	—
50	C₃²×C₄×D₄	C₂²	1	1	yes	characteristic
51	C₃²×C₄×D₄	C₂²	1	2	yes	—
52	C₃²×C₄×D₄	C₂²	1	1	yes	characteristic
53	C₃²×C₄×D₄	C₂²	1	2	yes	—
54	C₃²×C₄×D₄	C₂²	1	4	yes	—
55	C₃²×#117	C₂²	1	4	yes	—
56	C₃²×#117	C₂²	1	4	yes	—
57	C₃²×#117	C₂²	1	1	yes	characteristic
58	C₃²×#117	C₂²	1	2	yes	—
59	C₂×C₃²×C₄⋊C₄	C₂²	1	2	yes	—
60	C₂×C₃²×C₄⋊C₄	C₂²	1	4	yes	—
61	C₂×C₃²×C₄⋊C₄	C₂²	1	2	yes	—
62	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
63	C₂×C₃²×C₄²	C₂²	1	2	yes	—
64	C₃×#556	C₂×C₃	1	8	yes	complemented
65	C₃×#555	C₂×C₃	1	8	yes	complemented
66	C₃×#554	C₂×C₃	1	8	yes	complemented
67	C₃×#553	C₂×C₃	1	16	yes	complemented
68	C₃×#548	C₂×C₃	1	16	yes	complemented
69	C₃×#547	C₂×C₃	1	8	yes	complemented
70	C₃×#542	C₂×C₃	1	16	yes	complemented
71	C₃×#537	C₂×C₃	1	8	yes	complemented
72	C₃×#533	C₂×C₃	1	8	yes	complemented
73	C₃×#532	C₂×C₃	1	4	yes	complemented
74	C₃×#532	C₂×C₃	1	8	yes	complemented
75	C₂×C₃×C₄⋊Q₈	C₂×C₃	1	4	yes	complemented
76	C₃×#520	C₂×C₃	1	8	yes	complemented
77	C₃×C₄×#41	C₂×C₃	1	4	yes	complemented
78	C₃²×#41	—	2	4	no	—
79	C₃²×#41	—	2	8	no	—
80	C₃²×#41	—	4	8	no	—
81	C₂×C₃²×Q₈	—	4	4	no	—
82	C₂×C₃²×Q₈	C₂³	1	4	yes	—
83	C₂×C₃²×Q₈	C₂³	1	1	yes	characteristic
84	C₂×C₃²×Q₈	C₂³	1	2	yes	—
85	C₂×C₃²×Q₈	C₂³	1	4	yes	—
86	C₂×C₃²×D₄	C₂³	1	2	yes	—
87	C₂×C₃²×D₄	C₂³	1	2	yes	—
88	C₂×C₃²×D₄	C₂³	1	4	yes	—
89	C₂×C₃²×D₄	C₂³	1	1	yes	characteristic
90	C₂×C₃²×D₄	C₂³	1	2	yes	—
91	C₂×C₃²×D₄	C₂³	1	2	yes	—
92	C₂×C₃²×D₄	C₂³	1	8	yes	—
93	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
94	C₂²×C₃²×C₄	C₂³	1	2	yes	—
95	C₂²×C₃²×C₄	C₂³	1	2	yes	—
96	C₂²×C₃²×C₄	C₂³	1	4	yes	—
97	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
98	C₂²×C₃²×C₄	C₂³	1	2	yes	—
99	C₂²×C₃²×C₄	C₂³	1	4	yes	—
100	C₂²×C₃²×C₄	C₂³	1	8	yes	—
101	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
102	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
103	C₃²×C₄⋊C₄	C₂³	1	4	yes	—
104	C₃²×C₄⋊C₄	C₂³	1	4	yes	—
105	C₃²×C₄⋊C₄	C₂³	1	4	yes	—
106	C₃²×C₄⋊C₄	C₂³	1	8	yes	—
107	C₃²×C₄⋊C₄	C₂³	1	4	yes	—
108	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
109	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
110	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
111	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
112	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
113	C₃²×C₄⋊C₄	C₂³	1	8	yes	—
114	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
115	C₃²×C₂²⋊C₄	C₂³	1	8	yes	—
116	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
117	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
118	C₃²×C₂²⋊C₄	C₂³	1	8	yes	—
119	C₃²×C₂²⋊C₄	C₂³	1	8	yes	—
120	C₃²×C₂²⋊C₄	C₂³	1	4	yes	—
121	C₃²×C₂²⋊C₄	C₂³	1	4	yes	—
122	C₃²×C₄²	C₂³	1	1	yes	characteristic
123	C₃²×C₄²	C₂³	1	2	yes	—
124	C₃²×C₄²	C₂³	1	1	yes	characteristic
125	C₃²×C₄²	C₂³	1	2	yes	—
126	C₃²×C₄²	C₂³	1	1	yes	characteristic
127	C₃²×C₄²	C₂³	1	1	yes	characteristic
128	C₃²×C₄²	C₂³	1	2	yes	—
129	C₃²×C₄²	C₂³	1	8	yes	—
130	#3511	C₃²	1	1	yes	characteristic, direct product factor, Sylow
131	C₂×C₃×#41	C₂²×C₃	1	4	yes	—
132	C₂×C₃×#41	C₂²×C₃	1	8	yes	—
133	C₂×C₃×#41	C₂²×C₃	1	16	yes	—
134	C₂²×C₃×Q₈	C₂²×C₃	1	8	yes	—
135	C₃×C₄⋊Q₈	C₂²×C₃	1	8	yes	—
136	C₃×C₄⋊Q₈	C₂²×C₃	1	8	yes	—
137	C₃×C₄⋊Q₈	C₂²×C₃	1	8	yes	—
138	C₃×C₄⋊Q₈	C₂²×C₃	1	8	yes	—
139	C₃×C₄⋊Q₈	C₂²×C₃	1	4	yes	—
140	C₃×#127	C₂²×C₃	1	4	yes	—
141	C₃×#126	C₂²×C₃	1	32	yes	—
142	C₃×#125	C₂²×C₃	1	16	yes	—
143	C₃×#124	C₂²×C₃	1	8	yes	—
144	C₃×#124	C₂²×C₃	1	16	yes	—
145	C₃×#124	C₂²×C₃	1	32	yes	—
146	C₃×#123	C₂²×C₃	1	32	yes	—
147	C₃×C₂²⋊Q₈	C₂²×C₃	1	16	yes	—
148	C₃×C₂²⋊Q₈	C₂²×C₃	1	16	yes	—
149	C₃×C₂²⋊Q₈	C₂²×C₃	1	16	yes	—
150	C₃×C₂²⋊Q₈	C₂²×C₃	1	32	yes	—
151	C₃×#121	C₂²×C₃	1	16	yes	—
152	C₃×#121	C₂²×C₃	1	8	yes	—
153	C₃×#121	C₂²×C₃	1	8	yes	—
154	C₃×#121	C₂²×C₃	1	16	yes	—
155	C₃×#121	C₂²×C₃	1	16	yes	—
156	C₃×#121	C₂²×C₃	1	32	yes	—
157	C₃×C₄×Q₈	C₂²×C₃	1	4	yes	—
158	C₃×C₄×Q₈	C₂²×C₃	1	4	yes	—
159	C₃×C₄×Q₈	C₂²×C₃	1	16	yes	—
160	C₃×C₄×Q₈	C₂²×C₃	1	16	yes	—
161	C₃×C₄×D₄	C₂²×C₃	1	4	yes	—
162	C₃×C₄×D₄	C₂²×C₃	1	8	yes	—
163	C₃×C₄×D₄	C₂²×C₃	1	8	yes	—
164	C₃×C₄×D₄	C₂²×C₃	1	4	yes	—
165	C₃×C₄×D₄	C₂²×C₃	1	16	yes	—
166	C₃×C₄×D₄	C₂²×C₃	1	32	yes	—
167	C₃×C₄×D₄	C₂²×C₃	1	8	yes	—
168	C₃×C₄×D₄	C₂²×C₃	1	16	yes	—
169	C₃×C₄×D₄	C₂²×C₃	1	8	yes	—
170	C₃×#117	C₂²×C₃	1	4	yes	—
171	C₃×#117	C₂²×C₃	1	8	yes	—
172	C₃×#117	C₂²×C₃	1	16	yes	—
173	C₃×#117	C₂²×C₃	1	16	yes	—
174	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	8	yes	—
175	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	16	yes	—
176	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	8	yes	—
177	C₂×C₃×C₄²	C₂²×C₃	1	4	yes	—
178	C₂×C₃×C₄²	C₂²×C₃	1	8	yes	—
179	C₂³×C₃²	C₂⁴	1	2	yes	—
180	C₂³×C₃²	C₂⁴	1	4	yes	—
181	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
182	C₃²×Q₈	—	2	2	no	—
183	C₃²×Q₈	—	2	4	no	—
184	C₃²×Q₈	—	2	8	no	—
185	C₃²×Q₈	—	4	4	no	—
186	C₃²×D₄	—	2	4	no	—
187	C₃²×D₄	—	2	8	no	—
188	C₃²×D₄	—	2	2	no	—
189	C₃²×D₄	—	2	4	no	—
190	C₃²×D₄	—	2	4	no	—
191	C₃²×D₄	—	2	4	no	—
192	C₃²×D₄	—	4	8	no	—
193	C₂×C₃²×C₄	—	2	8	no	—
194	C₂×C₃²×C₄	—	2	4	no	—
195	C₂×C₃²×C₄	—	2	2	no	—
196	C₂×C₃²×C₄	—	2	4	no	—
197	C₂×C₃²×C₄	—	2	2	no	—
198	C₂×C₃²×C₄	—	2	4	no	—
199	C₂×C₃²×C₄	—	4	4	no	—
200	C₂×C₃²×C₄	—	4	8	no	—
201	C₂×C₃²×C₄	#41	1	4	yes	complemented
202	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
203	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
204	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
205	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
206	C₂×C₃²×C₄	C₂⁴	1	4	yes	—
207	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
208	C₂×C₃²×C₄	C₂⁴	1	8	yes	—
209	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
210	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
211	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
212	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
213	#556	C₂×C₃²	1	2	yes	complemented
214	#555	C₂×C₃²	1	2	yes	complemented
215	#554	C₂×C₃²	1	2	yes	complemented
216	#553	C₂×C₃²	1	4	yes	complemented
217	#548	C₂×C₃²	1	4	yes	complemented
218	#547	C₂×C₃²	1	2	yes	complemented
219	#542	C₂×C₃²	1	4	yes	complemented
220	#537	C₂×C₃²	1	2	yes	complemented
221	#533	C₂×C₃²	1	2	yes	complemented
222	#532	C₂×C₃²	1	1	yes	characteristic, complemented
223	#532	C₂×C₃²	1	2	yes	complemented
224	C₂×C₄⋊Q₈	C₂×C₃²	1	1	yes	characteristic, complemented
225	#520	C₂×C₃²	1	2	yes	complemented
226	C₄×#41	C₂×C₃²	1	1	yes	characteristic, complemented
227	C₃×#41	—	2	16	no	—
228	C₃×#41	—	2	32	no	—
229	C₃×#41	—	4	32	no	—
230	C₂×C₃×Q₈	—	4	16	no	—
231	C₂×C₃×Q₈	C₂³×C₃	1	4	yes	—
232	C₂×C₃×Q₈	C₂³×C₃	1	8	yes	—
233	C₂×C₃×Q₈	C₂³×C₃	1	16	yes	—
234	C₂×C₃×Q₈	C₂³×C₃	1	16	yes	—
235	C₂×C₃×D₄	C₂³×C₃	1	8	yes	—
236	C₂×C₃×D₄	C₂³×C₃	1	8	yes	—
237	C₂×C₃×D₄	C₂³×C₃	1	16	yes	—
238	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
239	C₂×C₃×D₄	C₂³×C₃	1	8	yes	—
240	C₂×C₃×D₄	C₂³×C₃	1	8	yes	—
241	C₂×C₃×D₄	C₂³×C₃	1	32	yes	—
242	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
243	C₂²×C₃×C₄	C₂³×C₃	1	8	yes	—
244	C₂²×C₃×C₄	C₂³×C₃	1	8	yes	—
245	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
246	C₂²×C₃×C₄	C₂³×C₃	1	8	yes	—
247	C₂²×C₃×C₄	C₂³×C₃	1	16	yes	—
248	C₂²×C₃×C₄	C₂³×C₃	1	16	yes	—
249	C₂²×C₃×C₄	C₂³×C₃	1	32	yes	—
250	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
251	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
252	C₃×C₄⋊C₄	C₂³×C₃	1	16	yes	—
253	C₃×C₄⋊C₄	C₂³×C₃	1	16	yes	—
254	C₃×C₄⋊C₄	C₂³×C₃	1	16	yes	—
255	C₃×C₄⋊C₄	C₂³×C₃	1	32	yes	—
256	C₃×C₄⋊C₄	C₂³×C₃	1	16	yes	—
257	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
258	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
259	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
260	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
261	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
262	C₃×C₄⋊C₄	C₂³×C₃	1	32	yes	—
263	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
264	C₃×C₂²⋊C₄	C₂³×C₃	1	32	yes	—
265	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
266	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
267	C₃×C₂²⋊C₄	C₂³×C₃	1	32	yes	—
268	C₃×C₂²⋊C₄	C₂³×C₃	1	32	yes	—
269	C₃×C₂²⋊C₄	C₂³×C₃	1	16	yes	—
270	C₃×C₂²⋊C₄	C₂³×C₃	1	16	yes	—
271	C₃×C₄²	C₂³×C₃	1	4	yes	—
272	C₃×C₄²	C₂³×C₃	1	8	yes	—
273	C₃×C₄²	C₂³×C₃	1	4	yes	—
274	C₃×C₄²	C₂³×C₃	1	8	yes	—
275	C₃×C₄²	C₂³×C₃	1	4	yes	—
276	C₃×C₄²	C₂³×C₃	1	4	yes	—
277	C₃×C₄²	C₂³×C₃	1	8	yes	—
278	C₃×C₄²	C₂³×C₃	1	32	yes	—
279	C₂²×C₃²	—	2	1	no	—
280	C₂²×C₃²	—	2	1	no	—
281	C₂²×C₃²	—	2	2	no	—
282	C₂²×C₃²	—	2	4	no	—
283	C₂²×C₃²	—	2	2	no	—
284	C₂²×C₃²	—	2	4	no	—
285	C₂²×C₃²	—	2	2	no	—
286	C₂²×C₃²	—	2	4	no	—
287	C₂²×C₃²	C₂×#41	1	2	yes	—
288	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
289	C₃²×C₄	—	2	4	no	—
290	C₃²×C₄	—	2	2	no	—
291	C₃²×C₄	—	2	2	no	—
292	C₃²×C₄	—	2	1	no	—
293	C₃²×C₄	—	2	8	no	—
294	C₃²×C₄	—	2	2	no	—
295	C₃²×C₄	—	2	1	no	—
296	C₃²×C₄	C₂×#41	1	2	yes	—
297	C₃²×C₄	C₂×#41	1	2	yes	—
298	C₃²×C₄	H(5,𝔽₂)	1	2	yes	—
299	C₃²×C₄	2₋¹⁺⁴	1	2	yes	—
300	C₂×#41	C₂²×C₃²	1	1	yes	characteristic
301	C₂×#41	C₂²×C₃²	1	2	yes	—
302	C₂×#41	C₂²×C₃²	1	4	yes	—
303	C₂²×Q₈	C₂²×C₃²	1	2	yes	—
304	C₄⋊Q₈	C₂²×C₃²	1	2	yes	—
305	C₄⋊Q₈	C₂²×C₃²	1	2	yes	—
306	C₄⋊Q₈	C₂²×C₃²	1	2	yes	—
307	C₄⋊Q₈	C₂²×C₃²	1	2	yes	—
308	C₄⋊Q₈	C₂²×C₃²	1	1	yes	characteristic
309	#127	C₂²×C₃²	1	1	yes	characteristic
310	#126	C₂²×C₃²	1	8	yes	—
311	#125	C₂²×C₃²	1	4	yes	—
312	#124	C₂²×C₃²	1	2	yes	—
313	#124	C₂²×C₃²	1	4	yes	—
314	#124	C₂²×C₃²	1	8	yes	—
315	#123	C₂²×C₃²	1	8	yes	—
316	C₂²⋊Q₈	C₂²×C₃²	1	4	yes	—
317	C₂²⋊Q₈	C₂²×C₃²	1	4	yes	—
318	C₂²⋊Q₈	C₂²×C₃²	1	4	yes	—
319	C₂²⋊Q₈	C₂²×C₃²	1	8	yes	—
320	#121	C₂²×C₃²	1	4	yes	—
321	#121	C₂²×C₃²	1	2	yes	—
322	#121	C₂²×C₃²	1	2	yes	—
323	#121	C₂²×C₃²	1	4	yes	—
324	#121	C₂²×C₃²	1	4	yes	—
325	#121	C₂²×C₃²	1	8	yes	—
326	C₄×Q₈	C₂²×C₃²	1	1	yes	characteristic
327	C₄×Q₈	C₂²×C₃²	1	1	yes	characteristic
328	C₄×Q₈	C₂²×C₃²	1	4	yes	—
329	C₄×Q₈	C₂²×C₃²	1	4	yes	—
330	C₄×D₄	C₂²×C₃²	1	1	yes	characteristic
331	C₄×D₄	C₂²×C₃²	1	2	yes	—
332	C₄×D₄	C₂²×C₃²	1	2	yes	—
333	C₄×D₄	C₂²×C₃²	1	1	yes	characteristic
334	C₄×D₄	C₂²×C₃²	1	4	yes	—
335	C₄×D₄	C₂²×C₃²	1	8	yes	—
336	C₄×D₄	C₂²×C₃²	1	2	yes	—
337	C₄×D₄	C₂²×C₃²	1	4	yes	—
338	C₄×D₄	C₂²×C₃²	1	2	yes	—
339	#117	C₂²×C₃²	1	1	yes	characteristic
340	#117	C₂²×C₃²	1	2	yes	—
341	#117	C₂²×C₃²	1	4	yes	—
342	#117	C₂²×C₃²	1	4	yes	—
343	C₂×C₄⋊C₄	C₂²×C₃²	1	2	yes	—
344	C₂×C₄⋊C₄	C₂²×C₃²	1	4	yes	—
345	C₂×C₄⋊C₄	C₂²×C₃²	1	2	yes	—
346	C₂×C₄²	C₂²×C₃²	1	1	yes	characteristic
347	C₂×C₄²	C₂²×C₃²	1	2	yes	—
348	C₂³×C₃	C₂⁴×C₃	1	8	yes	—
349	C₂³×C₃	C₂⁴×C₃	1	16	yes	—
350	C₂³×C₃	C₂⁴×C₃	1	4	yes	—
351	C₃×Q₈	—	2	8	no	—
352	C₃×Q₈	—	2	16	no	—
353	C₃×Q₈	—	2	32	no	—
354	C₃×Q₈	—	4	16	no	—
355	C₃×D₄	—	2	16	no	—
356	C₃×D₄	—	2	32	no	—
357	C₃×D₄	—	2	8	no	—
358	C₃×D₄	—	2	16	no	—
359	C₃×D₄	—	2	16	no	—
360	C₃×D₄	—	2	16	no	—
361	C₃×D₄	—	4	32	no	—
362	C₂×C₃×C₄	—	2	32	no	—
363	C₂×C₃×C₄	—	2	16	no	—
364	C₂×C₃×C₄	—	2	8	no	—
365	C₂×C₃×C₄	—	2	16	no	—
366	C₂×C₃×C₄	—	2	8	no	—
367	C₂×C₃×C₄	—	2	16	no	—
368	C₂×C₃×C₄	—	4	16	no	—
369	C₂×C₃×C₄	—	4	32	no	—
370	C₂×C₃×C₄	C₃×#41	1	16	yes	complemented
371	C₂×C₃×C₄	C₂⁴×C₃	1	8	yes	—
372	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
373	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
374	C₂×C₃×C₄	C₂⁴×C₃	1	8	yes	—
375	C₂×C₃×C₄	C₂⁴×C₃	1	16	yes	—
376	C₂×C₃×C₄	C₂⁴×C₃	1	8	yes	—
377	C₂×C₃×C₄	C₂⁴×C₃	1	32	yes	—
378	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
379	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
380	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
381	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
382	C₂×C₃²	—	2	2	no	—
383	C₂×C₃²	—	4	2	no	—
384	C₂×C₃²	—	4	4	no	—
385	C₂×C₃²	C₂²×#41	1	1	yes	characteristic
386	C₂×C₃²	C₂×H(5,𝔽₂)	1	1	yes	characteristic
387	C₂×C₃²	C₂×2₋¹⁺⁴	1	1	yes	characteristic
388	#41	—	2	4	no	—
389	#41	—	2	8	no	—
390	#41	—	4	8	no	—
391	C₂×Q₈	—	4	4	no	—
392	C₂×Q₈	C₂³×C₃²	1	1	yes	characteristic
393	C₂×Q₈	C₂³×C₃²	1	2	yes	—
394	C₂×Q₈	C₂³×C₃²	1	4	yes	—
395	C₂×Q₈	C₂³×C₃²	1	4	yes	—
396	C₂×D₄	C₂³×C₃²	1	2	yes	—
397	C₂×D₄	C₂³×C₃²	1	2	yes	—
398	C₂×D₄	C₂³×C₃²	1	4	yes	—
399	C₂×D₄	C₂³×C₃²	1	1	yes	characteristic
400	C₂×D₄	C₂³×C₃²	1	2	yes	—
401	C₂×D₄	C₂³×C₃²	1	2	yes	—
402	C₂×D₄	C₂³×C₃²	1	8	yes	—
403	C₂²×C₄	C₂³×C₃²	1	1	yes	characteristic
404	C₂²×C₄	C₂³×C₃²	1	2	yes	—
405	C₂²×C₄	C₂³×C₃²	1	2	yes	—
406	C₂²×C₄	C₂³×C₃²	1	1	yes	characteristic
407	C₂²×C₄	C₂³×C₃²	1	2	yes	—
408	C₂²×C₄	C₂³×C₃²	1	4	yes	—
409	C₂²×C₄	C₂³×C₃²	1	4	yes	—
410	C₂²×C₄	C₂³×C₃²	1	8	yes	—
411	C₂²×C₄	C₂³×C₃²	1	1	yes	characteristic
412	C₄⋊C₄	C₂³×C₃²	1	1	yes	characteristic
413	C₄⋊C₄	C₂³×C₃²	1	4	yes	—
414	C₄⋊C₄	C₂³×C₃²	1	4	yes	—
415	C₄⋊C₄	C₂³×C₃²	1	4	yes	—
416	C₄⋊C₄	C₂³×C₃²	1	8	yes	—
417	C₄⋊C₄	C₂³×C₃²	1	4	yes	—
418	C₄⋊C₄	C₂³×C₃²	1	1	yes	characteristic
419	C₄⋊C₄	C₂³×C₃²	1	2	yes	—
420	C₄⋊C₄	C₂³×C₃²	1	2	yes	—
421	C₄⋊C₄	C₂³×C₃²	1	2	yes	—
422	C₄⋊C₄	C₂³×C₃²	1	2	yes	—
423	C₄⋊C₄	C₂³×C₃²	1	8	yes	—
424	C₂²⋊C₄	C₂³×C₃²	1	2	yes	—
425	C₂²⋊C₄	C₂³×C₃²	1	8	yes	—
426	C₂²⋊C₄	C₂³×C₃²	1	2	yes	—
427	C₂²⋊C₄	C₂³×C₃²	1	2	yes	—
428	C₂²⋊C₄	C₂³×C₃²	1	8	yes	—
429	C₂²⋊C₄	C₂³×C₃²	1	8	yes	—
430	C₂²⋊C₄	C₂³×C₃²	1	4	yes	—
431	C₂²⋊C₄	C₂³×C₃²	1	4	yes	—
432	C₄²	C₂³×C₃²	1	1	yes	characteristic
433	C₄²	C₂³×C₃²	1	2	yes	—
434	C₄²	C₂³×C₃²	1	1	yes	characteristic
435	C₄²	C₂³×C₃²	1	2	yes	—
436	C₄²	C₂³×C₃²	1	1	yes	characteristic
437	C₄²	C₂³×C₃²	1	1	yes	characteristic
438	C₄²	C₂³×C₃²	1	2	yes	—
439	C₄²	C₂³×C₃²	1	8	yes	—
440	C₂²×C₃	—	2	4	no	—
441	C₂²×C₃	—	2	4	no	—
442	C₂²×C₃	—	2	8	no	—
443	C₂²×C₃	—	2	16	no	—
444	C₂²×C₃	—	2	8	no	—
445	C₂²×C₃	—	2	16	no	—
446	C₂²×C₃	—	2	8	no	—
447	C₂²×C₃	—	2	16	no	—
448	C₂²×C₃	C₂×C₃×#41	1	8	yes	—
449	C₂²×C₃	C₂⁵×C₃	1	4	yes	—
450	C₃×C₄	—	2	16	no	—
451	C₃×C₄	—	2	8	no	—
452	C₃×C₄	—	2	8	no	—
453	C₃×C₄	—	2	4	no	—
454	C₃×C₄	—	2	32	no	—
455	C₃×C₄	—	2	8	no	—
456	C₃×C₄	—	2	4	no	—
457	C₃×C₄	C₂×C₃×#41	1	8	yes	—
458	C₃×C₄	C₂×C₃×#41	1	8	yes	—
459	C₃×C₄	C₃×H(5,𝔽₂)	1	8	yes	—
460	C₃×C₄	C₃×2₋¹⁺⁴	1	8	yes	—
461	C₃²	#3511	1	1	yes	characteristic, direct product factor, Sylow
462	C₂³	C₂⁴×C₃²	1	2	yes	—
463	C₂³	C₂⁴×C₃²	1	4	yes	—
464	C₂³	C₂⁴×C₃²	1	1	yes	characteristic
465	Q₈	—	2	2	no	—
466	Q₈	—	2	4	no	—
467	Q₈	—	2	8	no	—
468	Q₈	—	4	4	no	—
469	D₄	—	2	4	no	—
470	D₄	—	2	8	no	—
471	D₄	—	2	2	no	—
472	D₄	—	2	4	no	—
473	D₄	—	2	4	no	—
474	D₄	—	2	4	no	—
475	D₄	—	4	8	no	—
476	C₂×C₄	—	2	8	no	—
477	C₂×C₄	—	2	4	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	4	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	4	no	—
482	C₂×C₄	—	4	4	no	—
483	C₂×C₄	—	4	8	no	—
484	C₂×C₄	C₃²×#41	1	4	yes	complemented
485	C₂×C₄	C₂⁴×C₃²	1	2	yes	—
486	C₂×C₄	C₂⁴×C₃²	1	1	yes	characteristic
487	C₂×C₄	C₂⁴×C₃²	1	1	yes	characteristic
488	C₂×C₄	C₂⁴×C₃²	1	2	yes	—
489	C₂×C₄	C₂⁴×C₃²	1	4	yes	—
490	C₂×C₄	C₂⁴×C₃²	1	2	yes	—
491	C₂×C₄	C₂⁴×C₃²	1	8	yes	—
492	C₂×C₄	C₂⁴×C₃²	1	1	yes	characteristic
493	C₂×C₄	C₂⁴×C₃²	1	1	yes	characteristic
494	C₂×C₄	C₂⁴×C₃²	1	1	yes	characteristic
495	C₂×C₄	C₂⁴×C₃²	1	1	yes	characteristic
496	C₂×C₃	—	2	8	no	—
497	C₂×C₃	—	4	8	no	—
498	C₂×C₃	—	4	16	no	—
499	C₂×C₃	C₂²×C₃×#41	1	4	yes	—
500	C₂×C₃	C₂×C₃×H(5,𝔽₂)	1	4	yes	—
501	C₂×C₃	C₂×C₃×2₋¹⁺⁴	1	4	yes	—
502	C₂²	—	2	1	no	—
503	C₂²	—	2	1	no	—
504	C₂²	—	2	2	no	—
505	C₂²	—	2	4	no	—
506	C₂²	—	2	2	no	—
507	C₂²	—	2	4	no	—
508	C₂²	—	2	2	no	—
509	C₂²	—	2	4	no	—
510	C₂²	C₂×C₃²×#41	1	2	yes	—
511	C₂²	C₂⁵×C₃²	1	1	yes	characteristic
512	C₄	—	2	4	no	—
513	C₄	—	2	2	no	—
514	C₄	—	2	2	no	—
515	C₄	—	2	1	no	—
516	C₄	—	2	8	no	—
517	C₄	—	2	2	no	—
518	C₄	—	2	1	no	—
519	C₄	C₂×C₃²×#41	1	2	yes	—
520	C₄	C₂×C₃²×#41	1	2	yes	—
521	C₄	C₃²×H(5,𝔽₂)	1	2	yes	—
522	C₄	C₃²×2₋¹⁺⁴	1	2	yes	—
523	C₃	C₃×#3511	1	4	yes	direct product factor
524	C₂	—	2	2	no	—
525	C₂	—	4	2	no	—
526	C₂	—	4	4	no	—
527	C₂	C₂²×C₃²×#41	1	1	yes	characteristic
528	C₂	C₂×C₃²×H(5,𝔽₂)	1	1	yes	characteristic
529	C₂	C₂×C₃²×2₋¹⁺⁴	1	1	yes	characteristic

	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×#556	C₂	semidirect
2. C₃²×#555	C₂	semidirect
3. C₃²×#554	C₂	semidirect
4. C₃²×#553	C₂	semidirect
5. C₃²×#548	C₂	semidirect
6. C₃²×#547	C₂	semidirect
7. C₃²×#542	C₂	semidirect
8. C₃²×#537	C₂	semidirect
9. C₃²×#533	C₂	semidirect
10. C₃²×#532	C₂	semidirect
11. C₃²×#532	C₂	semidirect
12. C₂×C₃²×C₄⋊Q₈	C₂	semidirect
13. C₃²×#520	C₂	semidirect
14. C₃²×C₄×#41	C₂	semidirect
15. C₃×#3511	C₃	direct (N × H)
64. C₃×#556	C₂×C₃	semidirect
65. C₃×#555	C₂×C₃	semidirect
66. C₃×#554	C₂×C₃	semidirect
67. C₃×#553	C₂×C₃	semidirect
68. C₃×#548	C₂×C₃	semidirect
69. C₃×#547	C₂×C₃	semidirect
70. C₃×#542	C₂×C₃	semidirect
71. C₃×#537	C₂×C₃	semidirect
72. C₃×#533	C₂×C₃	semidirect
73. C₃×#532	C₂×C₃	semidirect
74. C₃×#532	C₂×C₃	semidirect
75. C₂×C₃×C₄⋊Q₈	C₂×C₃	semidirect
76. C₃×#520	C₂×C₃	semidirect
77. C₃×C₄×#41	C₂×C₃	semidirect
130. #3511	C₃²	direct (N × H)
201. C₂×C₃²×C₄	#41	semidirect
213. #556	C₂×C₃²	semidirect
214. #555	C₂×C₃²	semidirect
215. #554	C₂×C₃²	semidirect
216. #553	C₂×C₃²	semidirect
217. #548	C₂×C₃²	semidirect
218. #547	C₂×C₃²	semidirect
219. #542	C₂×C₃²	semidirect
220. #537	C₂×C₃²	semidirect
221. #533	C₂×C₃²	semidirect
222. #532	C₂×C₃²	semidirect
223. #532	C₂×C₃²	semidirect
224. C₂×C₄⋊Q₈	C₂×C₃²	semidirect
225. #520	C₂×C₃²	semidirect
226. C₄×#41	C₂×C₃²	semidirect
370. C₂×C₃×C₄	C₃×#41	semidirect
461. C₃²	#3511	direct (N × H)
484. C₂×C₄	C₃²×#41	semidirect
523. C₃	C₃×#3511	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×#556	2
C₃²×#555	2
C₃²×#554	2
C₃²×#553	2
C₃²×#548	2
C₃²×#547	2
C₃²×#542	2
C₃²×#537	2
C₃²×#533	2
C₃²×#532	2
C₂×C₃²×C₄⋊Q₈	2
C₃²×#520	2
C₃²×C₄×#41	2
C₃×#3511	3

Subgroups — C32×#3511 #11770560

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#3511 #11770560