Subgroups — C₃²×#3515 #11770564

Order 1152.

3042 conjugacy classes of subgroups.

The subgroup lattice has 651 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#557	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃²×#554	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×#554	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃²×#553	C₂	1	2	yes	maximal, complemented
5	C₃²×#552	C₂	1	2	yes	maximal, complemented
6	C₃²×#552	C₂	1	4	yes	maximal, complemented
7	C₃²×#552	C₂	1	2	yes	maximal, complemented
8	C₃²×#547	C₂	1	2	yes	maximal, complemented
9	C₃²×#547	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃²×#541	C₂	1	2	yes	maximal, complemented
11	C₃²×#539	C₂	1	4	yes	maximal, complemented
12	C₃²×#533	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃²×#529	C₂	1	2	yes	maximal, complemented
14	C₃²×#529	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₃²×#125	C₂	1	2	yes	maximal, complemented
16	C₃²×#520	C₂	1	2	yes	maximal, complemented
17	C₃²×C₄×#41	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃×#3515	C₃	1	4	yes	maximal, direct product factor
19	C₂×C₃²×#41	C₂²	1	1	yes	characteristic
20	C₂×C₃²×#41	C₂²	1	2	yes	—
21	C₃²×C₄⋊Q₈	C₂²	1	1	yes	characteristic
22	C₃²×C₄⋊Q₈	C₂²	1	1	yes	characteristic
23	C₃²×C₄⋊Q₈	C₂²	1	2	yes	—
24	C₃²×#126	C₂²	1	2	yes	—
25	C₃²×#126	C₂²	1	4	yes	—
26	C₃²×#126	C₂²	1	4	yes	—
27	C₃²×#126	C₂²	1	4	yes	—
28	C₃²×#125	C₂²	1	4	yes	—
29	C₃²×#125	C₂²	1	4	yes	—
30	C₃²×#125	C₂²	1	2	yes	—
31	C₃²×#125	C₂²	1	2	yes	—
32	C₃²×#125	C₂²	1	4	yes	—
33	C₃²×#125	C₂²	1	2	yes	—
34	C₃²×#125	C₂²	1	1	yes	characteristic
35	C₃²×#125	C₂²	1	2	yes	—
36	C₃²×#125	C₂²	1	4	yes	—
37	C₃²×#124	C₂²	1	1	yes	characteristic
38	C₃²×#123	C₂²	1	4	yes	—
39	C₃²×#123	C₂²	1	4	yes	—
40	C₃²×#123	C₂²	1	4	yes	—
41	C₃²×#123	C₂²	1	4	yes	—
42	C₃²×#123	C₂²	1	2	yes	—
43	C₃²×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
44	C₃²×C₂²⋊Q₈	C₂²	1	2	yes	—
45	C₃²×C₂²⋊Q₈	C₂²	1	4	yes	—
46	C₃²×C₂²⋊Q₈	C₂²	1	4	yes	—
47	C₃²×C₂²⋊Q₈	C₂²	1	2	yes	—
48	C₃²×C₂²⋊Q₈	C₂²	1	2	yes	—
49	C₃²×C₂²⋊Q₈	C₂²	1	2	yes	—
50	C₃²×C₂²⋊Q₈	C₂²	1	2	yes	—
51	C₃²×#121	C₂²	1	1	yes	characteristic
52	C₃²×#121	C₂²	1	2	yes	—
53	C₃²×#121	C₂²	1	4	yes	—
54	C₃²×C₄×Q₈	C₂²	1	2	yes	—
55	C₃²×C₄×Q₈	C₂²	1	2	yes	—
56	C₃²×C₄×Q₈	C₂²	1	2	yes	—
57	C₃²×C₄×Q₈	C₂²	1	1	yes	characteristic
58	C₃²×C₄×Q₈	C₂²	1	1	yes	characteristic
59	C₃²×C₄×Q₈	C₂²	1	1	yes	characteristic
60	C₃²×C₄×Q₈	C₂²	1	2	yes	—
61	C₃²×C₄×D₄	C₂²	1	2	yes	—
62	C₃²×C₄×D₄	C₂²	1	4	yes	—
63	C₃²×C₄×D₄	C₂²	1	2	yes	—
64	C₃²×C₄×D₄	C₂²	1	2	yes	—
65	C₃²×C₄×D₄	C₂²	1	1	yes	characteristic
66	C₃²×C₄×D₄	C₂²	1	2	yes	—
67	C₃²×C₄×D₄	C₂²	1	1	yes	characteristic
68	C₃²×C₄×D₄	C₂²	1	1	yes	characteristic
69	C₃²×C₄×D₄	C₂²	1	2	yes	—
70	C₃²×C₄×D₄	C₂²	1	4	yes	—
71	C₃²×#117	C₂²	1	1	yes	characteristic
72	C₃²×#117	C₂²	1	2	yes	—
73	C₃²×#117	C₂²	1	4	yes	—
74	C₃²×#117	C₂²	1	4	yes	—
75	C₃²×#117	C₂²	1	2	yes	—
76	C₃²×#117	C₂²	1	2	yes	—
77	C₂×C₃²×C₄⋊C₄	C₂²	1	2	yes	—
78	C₂×C₃²×C₄⋊C₄	C₂²	1	2	yes	—
79	C₂×C₃²×C₄⋊C₄	C₂²	1	4	yes	—
80	C₂×C₃²×C₄⋊C₄	C₂²	1	2	yes	—
81	C₂×C₃²×C₄⋊C₄	C₂²	1	4	yes	—
82	C₂×C₃²×C₄²	C₂²	1	2	yes	—
83	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
84	C₃×#557	C₂×C₃	1	4	yes	complemented
85	C₃×#554	C₂×C₃	1	4	yes	complemented
86	C₃×#554	C₂×C₃	1	4	yes	complemented
87	C₃×#553	C₂×C₃	1	8	yes	complemented
88	C₃×#552	C₂×C₃	1	8	yes	complemented
89	C₃×#552	C₂×C₃	1	16	yes	complemented
90	C₃×#552	C₂×C₃	1	8	yes	complemented
91	C₃×#547	C₂×C₃	1	4	yes	complemented
92	C₃×#547	C₂×C₃	1	8	yes	complemented
93	C₃×#541	C₂×C₃	1	8	yes	complemented
94	C₃×#539	C₂×C₃	1	16	yes	complemented
95	C₃×#533	C₂×C₃	1	4	yes	complemented
96	C₃×#529	C₂×C₃	1	8	yes	complemented
97	C₃×#529	C₂×C₃	1	4	yes	complemented
98	C₂×C₃×#125	C₂×C₃	1	8	yes	complemented
99	C₃×#520	C₂×C₃	1	8	yes	complemented
100	C₃×C₄×#41	C₂×C₃	1	4	yes	complemented
101	C₃²×#41	—	2	4	no	—
102	C₃²×#41	—	2	8	no	—
103	C₂×C₃²×Q₈	C₂³	1	1	yes	characteristic
104	C₂×C₃²×Q₈	C₂³	1	2	yes	—
105	C₂×C₃²×Q₈	C₂³	1	1	yes	characteristic
106	C₂×C₃²×Q₈	C₂³	1	2	yes	—
107	C₂×C₃²×D₄	C₂³	1	2	yes	—
108	C₂×C₃²×D₄	C₂³	1	4	yes	—
109	C₂×C₃²×D₄	C₂³	1	1	yes	characteristic
110	C₂×C₃²×D₄	C₂³	1	2	yes	—
111	C₂×C₃²×D₄	C₂³	1	1	yes	characteristic
112	C₂²×C₃²×C₄	C₂³	1	2	yes	—
113	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
114	C₂²×C₃²×C₄	C₂³	1	4	yes	—
115	C₂²×C₃²×C₄	C₂³	1	2	yes	—
116	C₂²×C₃²×C₄	C₂³	1	2	yes	—
117	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
118	C₂²×C₃²×C₄	C₂³	1	2	yes	—
119	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
120	C₂²×C₃²×C₄	C₂³	1	4	yes	—
121	C₂²×C₃²×C₄	C₂³	1	4	yes	—
122	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
123	C₃²×C₄⋊C₄	C₂³	1	4	yes	—
124	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
125	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
126	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
127	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
128	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
129	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
130	C₃²×C₄⋊C₄	C₂³	1	4	yes	—
131	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
132	C₃²×C₄⋊C₄	C₂³	1	4	yes	—
133	C₃²×C₄⋊C₄	C₂³	1	4	yes	—
134	C₃²×C₄⋊C₄	C₂³	1	4	yes	—
135	C₃²×C₄⋊C₄	C₂³	1	4	yes	—
136	C₃²×C₄⋊C₄	C₂³	1	4	yes	—
137	C₃²×C₄⋊C₄	C₂³	1	4	yes	—
138	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
139	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
140	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
141	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
142	C₃²×C₄⋊C₄	C₂³	1	4	yes	—
143	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
144	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
145	C₃²×C₄⋊C₄	C₂³	1	4	yes	—
146	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
147	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
148	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
149	C₃²×C₂²⋊C₄	C₂³	1	4	yes	—
150	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
151	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
152	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
153	C₃²×C₂²⋊C₄	C₂³	1	4	yes	—
154	C₃²×C₂²⋊C₄	C₂³	1	4	yes	—
155	C₃²×C₂²⋊C₄	C₂³	1	4	yes	—
156	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
157	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
158	C₃²×C₄²	C₂³	1	1	yes	characteristic
159	C₃²×C₄²	C₂³	1	2	yes	—
160	C₃²×C₄²	C₂³	1	1	yes	characteristic
161	C₃²×C₄²	C₂³	1	1	yes	characteristic
162	C₃²×C₄²	C₂³	1	2	yes	—
163	C₃²×C₄²	C₂³	1	1	yes	characteristic
164	C₃²×C₄²	C₂³	1	2	yes	—
165	C₃²×C₄²	C₂³	1	4	yes	—
166	C₃²×C₄²	C₂³	1	4	yes	—
167	C₃²×C₄²	C₂³	1	2	yes	—
168	#3515	C₃²	1	1	yes	characteristic, direct product factor, Sylow
169	C₂×C₃×#41	C₂²×C₃	1	4	yes	—
170	C₂×C₃×#41	C₂²×C₃	1	8	yes	—
171	C₃×C₄⋊Q₈	C₂²×C₃	1	4	yes	—
172	C₃×C₄⋊Q₈	C₂²×C₃	1	4	yes	—
173	C₃×C₄⋊Q₈	C₂²×C₃	1	8	yes	—
174	C₃×#126	C₂²×C₃	1	16	yes	—
175	C₃×#126	C₂²×C₃	1	8	yes	—
176	C₃×#126	C₂²×C₃	1	16	yes	—
177	C₃×#126	C₂²×C₃	1	16	yes	—
178	C₃×#125	C₂²×C₃	1	4	yes	—
179	C₃×#125	C₂²×C₃	1	8	yes	—
180	C₃×#125	C₂²×C₃	1	16	yes	—
181	C₃×#125	C₂²×C₃	1	16	yes	—
182	C₃×#125	C₂²×C₃	1	8	yes	—
183	C₃×#125	C₂²×C₃	1	8	yes	—
184	C₃×#125	C₂²×C₃	1	16	yes	—
185	C₃×#125	C₂²×C₃	1	16	yes	—
186	C₃×#125	C₂²×C₃	1	8	yes	—
187	C₃×#124	C₂²×C₃	1	4	yes	—
188	C₃×#123	C₂²×C₃	1	8	yes	—
189	C₃×#123	C₂²×C₃	1	16	yes	—
190	C₃×#123	C₂²×C₃	1	16	yes	—
191	C₃×#123	C₂²×C₃	1	16	yes	—
192	C₃×#123	C₂²×C₃	1	16	yes	—
193	C₃×C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
194	C₃×C₂²⋊Q₈	C₂²×C₃	1	8	yes	—
195	C₃×C₂²⋊Q₈	C₂²×C₃	1	8	yes	—
196	C₃×C₂²⋊Q₈	C₂²×C₃	1	8	yes	—
197	C₃×C₂²⋊Q₈	C₂²×C₃	1	16	yes	—
198	C₃×C₂²⋊Q₈	C₂²×C₃	1	16	yes	—
199	C₃×C₂²⋊Q₈	C₂²×C₃	1	8	yes	—
200	C₃×C₂²⋊Q₈	C₂²×C₃	1	8	yes	—
201	C₃×#121	C₂²×C₃	1	8	yes	—
202	C₃×#121	C₂²×C₃	1	4	yes	—
203	C₃×#121	C₂²×C₃	1	16	yes	—
204	C₃×C₄×Q₈	C₂²×C₃	1	4	yes	—
205	C₃×C₄×Q₈	C₂²×C₃	1	4	yes	—
206	C₃×C₄×Q₈	C₂²×C₃	1	8	yes	—
207	C₃×C₄×Q₈	C₂²×C₃	1	8	yes	—
208	C₃×C₄×Q₈	C₂²×C₃	1	8	yes	—
209	C₃×C₄×Q₈	C₂²×C₃	1	4	yes	—
210	C₃×C₄×Q₈	C₂²×C₃	1	8	yes	—
211	C₃×C₄×D₄	C₂²×C₃	1	4	yes	—
212	C₃×C₄×D₄	C₂²×C₃	1	8	yes	—
213	C₃×C₄×D₄	C₂²×C₃	1	4	yes	—
214	C₃×C₄×D₄	C₂²×C₃	1	8	yes	—
215	C₃×C₄×D₄	C₂²×C₃	1	16	yes	—
216	C₃×C₄×D₄	C₂²×C₃	1	8	yes	—
217	C₃×C₄×D₄	C₂²×C₃	1	16	yes	—
218	C₃×C₄×D₄	C₂²×C₃	1	8	yes	—
219	C₃×C₄×D₄	C₂²×C₃	1	4	yes	—
220	C₃×C₄×D₄	C₂²×C₃	1	8	yes	—
221	C₃×#117	C₂²×C₃	1	4	yes	—
222	C₃×#117	C₂²×C₃	1	8	yes	—
223	C₃×#117	C₂²×C₃	1	8	yes	—
224	C₃×#117	C₂²×C₃	1	16	yes	—
225	C₃×#117	C₂²×C₃	1	16	yes	—
226	C₃×#117	C₂²×C₃	1	8	yes	—
227	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	16	yes	—
228	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	8	yes	—
229	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	8	yes	—
230	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	16	yes	—
231	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	8	yes	—
232	C₂×C₃×C₄²	C₂²×C₃	1	8	yes	—
233	C₂×C₃×C₄²	C₂²×C₃	1	4	yes	—
234	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
235	C₂³×C₃²	C₂⁴	1	2	yes	—
236	C₂³×C₃²	C₂⁴	1	2	yes	—
237	C₃²×Q₈	—	2	2	no	—
238	C₃²×Q₈	—	2	4	no	—
239	C₃²×Q₈	—	2	2	no	—
240	C₃²×Q₈	—	4	2	no	—
241	C₃²×D₄	—	2	4	no	—
242	C₃²×D₄	—	2	8	no	—
243	C₃²×D₄	—	2	2	no	—
244	C₃²×D₄	—	4	2	no	—
245	C₃²×D₄	#41	1	4	yes	—
246	C₂×C₃²×C₄	—	2	4	no	—
247	C₂×C₃²×C₄	—	2	8	no	—
248	C₂×C₃²×C₄	—	2	2	no	—
249	C₂×C₃²×C₄	—	2	4	no	—
250	C₂×C₃²×C₄	—	2	4	no	—
251	C₂×C₃²×C₄	—	2	2	no	—
252	C₂×C₃²×C₄	—	4	2	no	—
253	C₂×C₃²×C₄	—	4	4	no	—
254	C₂×C₃²×C₄	—	4	1	no	—
255	C₂×C₃²×C₄	—	4	4	no	—
256	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
257	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
258	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
259	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
260	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
261	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
262	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
263	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
264	C₂×C₃²×C₄	C₂⁴	1	4	yes	—
265	C₂×C₃²×C₄	C₂⁴	1	4	yes	—
266	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
267	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
268	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
269	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
270	#557	C₂×C₃²	1	1	yes	characteristic, complemented
271	#554	C₂×C₃²	1	1	yes	characteristic, complemented
272	#554	C₂×C₃²	1	1	yes	characteristic, complemented
273	#553	C₂×C₃²	1	2	yes	complemented
274	#552	C₂×C₃²	1	2	yes	complemented
275	#552	C₂×C₃²	1	4	yes	complemented
276	#552	C₂×C₃²	1	2	yes	complemented
277	#547	C₂×C₃²	1	1	yes	characteristic, complemented
278	#547	C₂×C₃²	1	2	yes	complemented
279	#541	C₂×C₃²	1	2	yes	complemented
280	#539	C₂×C₃²	1	4	yes	complemented
281	#533	C₂×C₃²	1	1	yes	characteristic, complemented
282	#529	C₂×C₃²	1	2	yes	complemented
283	#529	C₂×C₃²	1	1	yes	characteristic, complemented
284	C₂×#125	C₂×C₃²	1	2	yes	complemented
285	#520	C₂×C₃²	1	2	yes	complemented
286	C₄×#41	C₂×C₃²	1	1	yes	characteristic, complemented
287	C₃×#41	—	2	16	no	—
288	C₃×#41	—	2	32	no	—
289	C₂×C₃×Q₈	C₂³×C₃	1	4	yes	—
290	C₂×C₃×Q₈	C₂³×C₃	1	4	yes	—
291	C₂×C₃×Q₈	C₂³×C₃	1	8	yes	—
292	C₂×C₃×Q₈	C₂³×C₃	1	8	yes	—
293	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
294	C₂×C₃×D₄	C₂³×C₃	1	8	yes	—
295	C₂×C₃×D₄	C₂³×C₃	1	16	yes	—
296	C₂×C₃×D₄	C₂³×C₃	1	8	yes	—
297	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
298	C₂²×C₃×C₄	C₂³×C₃	1	8	yes	—
299	C₂²×C₃×C₄	C₂³×C₃	1	8	yes	—
300	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
301	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
302	C₂²×C₃×C₄	C₂³×C₃	1	16	yes	—
303	C₂²×C₃×C₄	C₂³×C₃	1	8	yes	—
304	C₂²×C₃×C₄	C₂³×C₃	1	8	yes	—
305	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
306	C₂²×C₃×C₄	C₂³×C₃	1	16	yes	—
307	C₂²×C₃×C₄	C₂³×C₃	1	16	yes	—
308	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
309	C₃×C₄⋊C₄	C₂³×C₃	1	16	yes	—
310	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
311	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
312	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
313	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
314	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
315	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
316	C₃×C₄⋊C₄	C₂³×C₃	1	16	yes	—
317	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
318	C₃×C₄⋊C₄	C₂³×C₃	1	16	yes	—
319	C₃×C₄⋊C₄	C₂³×C₃	1	16	yes	—
320	C₃×C₄⋊C₄	C₂³×C₃	1	16	yes	—
321	C₃×C₄⋊C₄	C₂³×C₃	1	16	yes	—
322	C₃×C₄⋊C₄	C₂³×C₃	1	16	yes	—
323	C₃×C₄⋊C₄	C₂³×C₃	1	16	yes	—
324	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
325	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
326	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
327	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
328	C₃×C₄⋊C₄	C₂³×C₃	1	16	yes	—
329	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
330	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
331	C₃×C₄⋊C₄	C₂³×C₃	1	16	yes	—
332	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
333	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
334	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
335	C₃×C₂²⋊C₄	C₂³×C₃	1	16	yes	—
336	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
337	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
338	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
339	C₃×C₂²⋊C₄	C₂³×C₃	1	16	yes	—
340	C₃×C₂²⋊C₄	C₂³×C₃	1	16	yes	—
341	C₃×C₂²⋊C₄	C₂³×C₃	1	16	yes	—
342	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
343	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
344	C₃×C₄²	C₂³×C₃	1	4	yes	—
345	C₃×C₄²	C₂³×C₃	1	8	yes	—
346	C₃×C₄²	C₂³×C₃	1	4	yes	—
347	C₃×C₄²	C₂³×C₃	1	4	yes	—
348	C₃×C₄²	C₂³×C₃	1	8	yes	—
349	C₃×C₄²	C₂³×C₃	1	4	yes	—
350	C₃×C₄²	C₂³×C₃	1	8	yes	—
351	C₃×C₄²	C₂³×C₃	1	16	yes	—
352	C₃×C₄²	C₂³×C₃	1	16	yes	—
353	C₃×C₄²	C₂³×C₃	1	8	yes	—
354	C₂²×C₃²	—	2	2	no	—
355	C₂²×C₃²	—	2	2	no	—
356	C₂²×C₃²	—	2	1	no	—
357	C₂²×C₃²	—	2	2	no	—
358	C₂²×C₃²	—	2	1	no	—
359	C₂²×C₃²	—	2	2	no	—
360	C₂²×C₃²	—	2	2	no	—
361	C₂²×C₃²	—	2	1	no	—
362	C₂²×C₃²	C₂×#41	1	4	yes	—
363	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
364	C₃²×C₄	—	2	1	no	—
365	C₃²×C₄	—	2	2	no	—
366	C₃²×C₄	—	2	2	no	—
367	C₃²×C₄	—	2	4	no	—
368	C₃²×C₄	—	2	1	no	—
369	C₃²×C₄	—	2	2	no	—
370	C₃²×C₄	—	2	2	no	—
371	C₃²×C₄	—	2	1	no	—
372	C₃²×C₄	—	2	2	no	—
373	C₃²×C₄	—	2	2	no	—
374	C₃²×C₄	—	2	4	no	—
375	C₃²×C₄	—	2	1	no	—
376	C₃²×C₄	C₂×#41	1	2	yes	—
377	C₃²×C₄	2₋¹⁺⁴	1	2	yes	—
378	C₂×#41	C₂²×C₃²	1	1	yes	characteristic
379	C₂×#41	C₂²×C₃²	1	2	yes	—
380	C₄⋊Q₈	C₂²×C₃²	1	1	yes	characteristic
381	C₄⋊Q₈	C₂²×C₃²	1	1	yes	characteristic
382	C₄⋊Q₈	C₂²×C₃²	1	2	yes	—
383	#126	C₂²×C₃²	1	4	yes	—
384	#126	C₂²×C₃²	1	2	yes	—
385	#126	C₂²×C₃²	1	4	yes	—
386	#126	C₂²×C₃²	1	4	yes	—
387	#125	C₂²×C₃²	1	1	yes	characteristic
388	#125	C₂²×C₃²	1	2	yes	—
389	#125	C₂²×C₃²	1	4	yes	—
390	#125	C₂²×C₃²	1	4	yes	—
391	#125	C₂²×C₃²	1	2	yes	—
392	#125	C₂²×C₃²	1	2	yes	—
393	#125	C₂²×C₃²	1	4	yes	—
394	#125	C₂²×C₃²	1	4	yes	—
395	#125	C₂²×C₃²	1	2	yes	—
396	#124	C₂²×C₃²	1	1	yes	characteristic
397	#123	C₂²×C₃²	1	2	yes	—
398	#123	C₂²×C₃²	1	4	yes	—
399	#123	C₂²×C₃²	1	4	yes	—
400	#123	C₂²×C₃²	1	4	yes	—
401	#123	C₂²×C₃²	1	4	yes	—
402	C₂²⋊Q₈	C₂²×C₃²	1	1	yes	characteristic
403	C₂²⋊Q₈	C₂²×C₃²	1	2	yes	—
404	C₂²⋊Q₈	C₂²×C₃²	1	2	yes	—
405	C₂²⋊Q₈	C₂²×C₃²	1	2	yes	—
406	C₂²⋊Q₈	C₂²×C₃²	1	4	yes	—
407	C₂²⋊Q₈	C₂²×C₃²	1	4	yes	—
408	C₂²⋊Q₈	C₂²×C₃²	1	2	yes	—
409	C₂²⋊Q₈	C₂²×C₃²	1	2	yes	—
410	#121	C₂²×C₃²	1	2	yes	—
411	#121	C₂²×C₃²	1	1	yes	characteristic
412	#121	C₂²×C₃²	1	4	yes	—
413	C₄×Q₈	C₂²×C₃²	1	1	yes	characteristic
414	C₄×Q₈	C₂²×C₃²	1	1	yes	characteristic
415	C₄×Q₈	C₂²×C₃²	1	2	yes	—
416	C₄×Q₈	C₂²×C₃²	1	2	yes	—
417	C₄×Q₈	C₂²×C₃²	1	2	yes	—
418	C₄×Q₈	C₂²×C₃²	1	1	yes	characteristic
419	C₄×Q₈	C₂²×C₃²	1	2	yes	—
420	C₄×D₄	C₂²×C₃²	1	1	yes	characteristic
421	C₄×D₄	C₂²×C₃²	1	2	yes	—
422	C₄×D₄	C₂²×C₃²	1	1	yes	characteristic
423	C₄×D₄	C₂²×C₃²	1	2	yes	—
424	C₄×D₄	C₂²×C₃²	1	4	yes	—
425	C₄×D₄	C₂²×C₃²	1	2	yes	—
426	C₄×D₄	C₂²×C₃²	1	4	yes	—
427	C₄×D₄	C₂²×C₃²	1	2	yes	—
428	C₄×D₄	C₂²×C₃²	1	1	yes	characteristic
429	C₄×D₄	C₂²×C₃²	1	2	yes	—
430	#117	C₂²×C₃²	1	1	yes	characteristic
431	#117	C₂²×C₃²	1	2	yes	—
432	#117	C₂²×C₃²	1	2	yes	—
433	#117	C₂²×C₃²	1	4	yes	—
434	#117	C₂²×C₃²	1	4	yes	—
435	#117	C₂²×C₃²	1	2	yes	—
436	C₂×C₄⋊C₄	C₂²×C₃²	1	4	yes	—
437	C₂×C₄⋊C₄	C₂²×C₃²	1	2	yes	—
438	C₂×C₄⋊C₄	C₂²×C₃²	1	2	yes	—
439	C₂×C₄⋊C₄	C₂²×C₃²	1	4	yes	—
440	C₂×C₄⋊C₄	C₂²×C₃²	1	2	yes	—
441	C₂×C₄²	C₂²×C₃²	1	2	yes	—
442	C₂×C₄²	C₂²×C₃²	1	1	yes	characteristic
443	C₂³×C₃	C₂⁴×C₃	1	4	yes	—
444	C₂³×C₃	C₂⁴×C₃	1	8	yes	—
445	C₂³×C₃	C₂⁴×C₃	1	8	yes	—
446	C₃×Q₈	—	2	8	no	—
447	C₃×Q₈	—	2	16	no	—
448	C₃×Q₈	—	2	8	no	—
449	C₃×Q₈	—	4	8	no	—
450	C₃×D₄	—	2	16	no	—
451	C₃×D₄	—	2	32	no	—
452	C₃×D₄	—	2	8	no	—
453	C₃×D₄	—	4	8	no	—
454	C₃×D₄	C₃×#41	1	16	yes	—
455	C₂×C₃×C₄	—	2	16	no	—
456	C₂×C₃×C₄	—	2	32	no	—
457	C₂×C₃×C₄	—	2	8	no	—
458	C₂×C₃×C₄	—	2	16	no	—
459	C₂×C₃×C₄	—	2	16	no	—
460	C₂×C₃×C₄	—	2	8	no	—
461	C₂×C₃×C₄	—	4	8	no	—
462	C₂×C₃×C₄	—	4	16	no	—
463	C₂×C₃×C₄	—	4	4	no	—
464	C₂×C₃×C₄	—	4	16	no	—
465	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
466	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
467	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
468	C₂×C₃×C₄	C₂⁴×C₃	1	8	yes	—
469	C₂×C₃×C₄	C₂⁴×C₃	1	8	yes	—
470	C₂×C₃×C₄	C₂⁴×C₃	1	8	yes	—
471	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
472	C₂×C₃×C₄	C₂⁴×C₃	1	8	yes	—
473	C₂×C₃×C₄	C₂⁴×C₃	1	16	yes	—
474	C₂×C₃×C₄	C₂⁴×C₃	1	16	yes	—
475	C₂×C₃×C₄	C₂⁴×C₃	1	8	yes	—
476	C₂×C₃×C₄	C₂⁴×C₃	1	8	yes	—
477	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
478	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
479	C₂×C₃²	—	2	4	no	—
480	C₂×C₃²	—	4	1	no	—
481	C₂×C₃²	—	4	2	no	—
482	C₂×C₃²	C₂²×#41	1	1	yes	characteristic
483	C₂×C₃²	C₂×2₋¹⁺⁴	1	1	yes	characteristic
484	C₂×C₃²	#585	1	1	yes	characteristic
485	#41	—	2	4	no	—
486	#41	—	2	8	no	—
487	C₂×Q₈	C₂³×C₃²	1	1	yes	characteristic
488	C₂×Q₈	C₂³×C₃²	1	1	yes	characteristic
489	C₂×Q₈	C₂³×C₃²	1	2	yes	—
490	C₂×Q₈	C₂³×C₃²	1	2	yes	—
491	C₂×D₄	C₂³×C₃²	1	1	yes	characteristic
492	C₂×D₄	C₂³×C₃²	1	2	yes	—
493	C₂×D₄	C₂³×C₃²	1	4	yes	—
494	C₂×D₄	C₂³×C₃²	1	2	yes	—
495	C₂×D₄	C₂³×C₃²	1	1	yes	characteristic
496	C₂²×C₄	C₂³×C₃²	1	2	yes	—
497	C₂²×C₄	C₂³×C₃²	1	2	yes	—
498	C₂²×C₄	C₂³×C₃²	1	1	yes	characteristic
499	C₂²×C₄	C₂³×C₃²	1	1	yes	characteristic
500	C₂²×C₄	C₂³×C₃²	1	4	yes	—
501	C₂²×C₄	C₂³×C₃²	1	2	yes	—
502	C₂²×C₄	C₂³×C₃²	1	2	yes	—
503	C₂²×C₄	C₂³×C₃²	1	1	yes	characteristic
504	C₂²×C₄	C₂³×C₃²	1	4	yes	—
505	C₂²×C₄	C₂³×C₃²	1	4	yes	—
506	C₄⋊C₄	C₂³×C₃²	1	1	yes	characteristic
507	C₄⋊C₄	C₂³×C₃²	1	4	yes	—
508	C₄⋊C₄	C₂³×C₃²	1	2	yes	—
509	C₄⋊C₄	C₂³×C₃²	1	1	yes	characteristic
510	C₄⋊C₄	C₂³×C₃²	1	2	yes	—
511	C₄⋊C₄	C₂³×C₃²	1	1	yes	characteristic
512	C₄⋊C₄	C₂³×C₃²	1	2	yes	—
513	C₄⋊C₄	C₂³×C₃²	1	2	yes	—
514	C₄⋊C₄	C₂³×C₃²	1	4	yes	—
515	C₄⋊C₄	C₂³×C₃²	1	2	yes	—
516	C₄⋊C₄	C₂³×C₃²	1	4	yes	—
517	C₄⋊C₄	C₂³×C₃²	1	4	yes	—
518	C₄⋊C₄	C₂³×C₃²	1	4	yes	—
519	C₄⋊C₄	C₂³×C₃²	1	4	yes	—
520	C₄⋊C₄	C₂³×C₃²	1	4	yes	—
521	C₄⋊C₄	C₂³×C₃²	1	4	yes	—
522	C₄⋊C₄	C₂³×C₃²	1	2	yes	—
523	C₄⋊C₄	C₂³×C₃²	1	2	yes	—
524	C₄⋊C₄	C₂³×C₃²	1	1	yes	characteristic
525	C₄⋊C₄	C₂³×C₃²	1	2	yes	—
526	C₄⋊C₄	C₂³×C₃²	1	4	yes	—
527	C₄⋊C₄	C₂³×C₃²	1	2	yes	—
528	C₄⋊C₄	C₂³×C₃²	1	2	yes	—
529	C₄⋊C₄	C₂³×C₃²	1	4	yes	—
530	C₂²⋊C₄	C₂³×C₃²	1	2	yes	—
531	C₂²⋊C₄	C₂³×C₃²	1	2	yes	—
532	C₂²⋊C₄	C₂³×C₃²	1	2	yes	—
533	C₂²⋊C₄	C₂³×C₃²	1	4	yes	—
534	C₂²⋊C₄	C₂³×C₃²	1	2	yes	—
535	C₂²⋊C₄	C₂³×C₃²	1	2	yes	—
536	C₂²⋊C₄	C₂³×C₃²	1	2	yes	—
537	C₂²⋊C₄	C₂³×C₃²	1	4	yes	—
538	C₂²⋊C₄	C₂³×C₃²	1	4	yes	—
539	C₂²⋊C₄	C₂³×C₃²	1	4	yes	—
540	C₂²⋊C₄	C₂³×C₃²	1	2	yes	—
541	C₂²⋊C₄	C₂³×C₃²	1	2	yes	—
542	C₄²	C₂³×C₃²	1	1	yes	characteristic
543	C₄²	C₂³×C₃²	1	2	yes	—
544	C₄²	C₂³×C₃²	1	1	yes	characteristic
545	C₄²	C₂³×C₃²	1	1	yes	characteristic
546	C₄²	C₂³×C₃²	1	2	yes	—
547	C₄²	C₂³×C₃²	1	1	yes	characteristic
548	C₄²	C₂³×C₃²	1	2	yes	—
549	C₄²	C₂³×C₃²	1	4	yes	—
550	C₄²	C₂³×C₃²	1	4	yes	—
551	C₄²	C₂³×C₃²	1	2	yes	—
552	C₂²×C₃	—	2	8	no	—
553	C₂²×C₃	—	2	8	no	—
554	C₂²×C₃	—	2	4	no	—
555	C₂²×C₃	—	2	8	no	—
556	C₂²×C₃	—	2	4	no	—
557	C₂²×C₃	—	2	8	no	—
558	C₂²×C₃	—	2	8	no	—
559	C₂²×C₃	—	2	4	no	—
560	C₂²×C₃	C₂×C₃×#41	1	16	yes	—
561	C₂²×C₃	C₂⁵×C₃	1	4	yes	—
562	C₃×C₄	—	2	4	no	—
563	C₃×C₄	—	2	8	no	—
564	C₃×C₄	—	2	8	no	—
565	C₃×C₄	—	2	16	no	—
566	C₃×C₄	—	2	4	no	—
567	C₃×C₄	—	2	8	no	—
568	C₃×C₄	—	2	8	no	—
569	C₃×C₄	—	2	4	no	—
570	C₃×C₄	—	2	8	no	—
571	C₃×C₄	—	2	8	no	—
572	C₃×C₄	—	2	16	no	—
573	C₃×C₄	—	2	4	no	—
574	C₃×C₄	C₂×C₃×#41	1	8	yes	—
575	C₃×C₄	C₃×2₋¹⁺⁴	1	8	yes	—
576	C₃²	#3515	1	1	yes	characteristic, direct product factor, Sylow
577	C₂³	C₂⁴×C₃²	1	1	yes	characteristic
578	C₂³	C₂⁴×C₃²	1	2	yes	—
579	C₂³	C₂⁴×C₃²	1	2	yes	—
580	Q₈	—	2	2	no	—
581	Q₈	—	2	4	no	—
582	Q₈	—	2	2	no	—
583	Q₈	—	4	2	no	—
584	D₄	—	2	4	no	—
585	D₄	—	2	8	no	—
586	D₄	—	2	2	no	—
587	D₄	—	4	2	no	—
588	D₄	C₃²×#41	1	4	yes	—
589	C₂×C₄	—	2	4	no	—
590	C₂×C₄	—	2	8	no	—
591	C₂×C₄	—	2	2	no	—
592	C₂×C₄	—	2	4	no	—
593	C₂×C₄	—	2	4	no	—
594	C₂×C₄	—	2	2	no	—
595	C₂×C₄	—	4	2	no	—
596	C₂×C₄	—	4	4	no	—
597	C₂×C₄	—	4	1	no	—
598	C₂×C₄	—	4	4	no	—
599	C₂×C₄	C₂⁴×C₃²	1	1	yes	characteristic
600	C₂×C₄	C₂⁴×C₃²	1	1	yes	characteristic
601	C₂×C₄	C₂⁴×C₃²	1	1	yes	characteristic
602	C₂×C₄	C₂⁴×C₃²	1	2	yes	—
603	C₂×C₄	C₂⁴×C₃²	1	2	yes	—
604	C₂×C₄	C₂⁴×C₃²	1	2	yes	—
605	C₂×C₄	C₂⁴×C₃²	1	1	yes	characteristic
606	C₂×C₄	C₂⁴×C₃²	1	2	yes	—
607	C₂×C₄	C₂⁴×C₃²	1	4	yes	—
608	C₂×C₄	C₂⁴×C₃²	1	4	yes	—
609	C₂×C₄	C₂⁴×C₃²	1	2	yes	—
610	C₂×C₄	C₂⁴×C₃²	1	2	yes	—
611	C₂×C₄	C₂⁴×C₃²	1	1	yes	characteristic
612	C₂×C₄	C₂⁴×C₃²	1	1	yes	characteristic
613	C₂×C₃	—	2	16	no	—
614	C₂×C₃	—	4	4	no	—
615	C₂×C₃	—	4	8	no	—
616	C₂×C₃	C₂²×C₃×#41	1	4	yes	—
617	C₂×C₃	C₂×C₃×2₋¹⁺⁴	1	4	yes	—
618	C₂×C₃	C₃×#585	1	4	yes	—
619	C₂²	—	2	2	no	—
620	C₂²	—	2	2	no	—
621	C₂²	—	2	1	no	—
622	C₂²	—	2	2	no	—
623	C₂²	—	2	1	no	—
624	C₂²	—	2	2	no	—
625	C₂²	—	2	2	no	—
626	C₂²	—	2	1	no	—
627	C₂²	C₂×C₃²×#41	1	4	yes	—
628	C₂²	C₂⁵×C₃²	1	1	yes	characteristic
629	C₄	—	2	1	no	—
630	C₄	—	2	2	no	—
631	C₄	—	2	2	no	—
632	C₄	—	2	4	no	—
633	C₄	—	2	1	no	—
634	C₄	—	2	2	no	—
635	C₄	—	2	2	no	—
636	C₄	—	2	1	no	—
637	C₄	—	2	2	no	—
638	C₄	—	2	2	no	—
639	C₄	—	2	4	no	—
640	C₄	—	2	1	no	—
641	C₄	C₂×C₃²×#41	1	2	yes	—
642	C₄	C₃²×2₋¹⁺⁴	1	2	yes	—
643	C₃	C₃×#3515	1	4	yes	direct product factor
644	C₂	—	2	4	no	—
645	C₂	—	4	1	no	—
646	C₂	—	4	2	no	—
647	C₂	C₂²×C₃²×#41	1	1	yes	characteristic
648	C₂	C₂×C₃²×2₋¹⁺⁴	1	1	yes	characteristic
649	C₂	C₃²×#585	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×#557	C₂	semidirect
2. C₃²×#554	C₂	semidirect
3. C₃²×#554	C₂	semidirect
4. C₃²×#553	C₂	semidirect
5. C₃²×#552	C₂	semidirect
6. C₃²×#552	C₂	semidirect
7. C₃²×#552	C₂	semidirect
8. C₃²×#547	C₂	semidirect
9. C₃²×#547	C₂	semidirect
10. C₃²×#541	C₂	semidirect
11. C₃²×#539	C₂	semidirect
12. C₃²×#533	C₂	semidirect
13. C₃²×#529	C₂	semidirect
14. C₃²×#529	C₂	semidirect
15. C₂×C₃²×#125	C₂	semidirect
16. C₃²×#520	C₂	semidirect
17. C₃²×C₄×#41	C₂	semidirect
18. C₃×#3515	C₃	direct (N × H)
84. C₃×#557	C₂×C₃	semidirect
85. C₃×#554	C₂×C₃	semidirect
86. C₃×#554	C₂×C₃	semidirect
87. C₃×#553	C₂×C₃	semidirect
88. C₃×#552	C₂×C₃	semidirect
89. C₃×#552	C₂×C₃	semidirect
90. C₃×#552	C₂×C₃	semidirect
91. C₃×#547	C₂×C₃	semidirect
92. C₃×#547	C₂×C₃	semidirect
93. C₃×#541	C₂×C₃	semidirect
94. C₃×#539	C₂×C₃	semidirect
95. C₃×#533	C₂×C₃	semidirect
96. C₃×#529	C₂×C₃	semidirect
97. C₃×#529	C₂×C₃	semidirect
98. C₂×C₃×#125	C₂×C₃	semidirect
99. C₃×#520	C₂×C₃	semidirect
100. C₃×C₄×#41	C₂×C₃	semidirect
168. #3515	C₃²	direct (N × H)
270. #557	C₂×C₃²	semidirect
271. #554	C₂×C₃²	semidirect
272. #554	C₂×C₃²	semidirect
273. #553	C₂×C₃²	semidirect
274. #552	C₂×C₃²	semidirect
275. #552	C₂×C₃²	semidirect
276. #552	C₂×C₃²	semidirect
277. #547	C₂×C₃²	semidirect
278. #547	C₂×C₃²	semidirect
279. #541	C₂×C₃²	semidirect
280. #539	C₂×C₃²	semidirect
281. #533	C₂×C₃²	semidirect
282. #529	C₂×C₃²	semidirect
283. #529	C₂×C₃²	semidirect
284. C₂×#125	C₂×C₃²	semidirect
285. #520	C₂×C₃²	semidirect
286. C₄×#41	C₂×C₃²	semidirect
576. C₃²	#3515	direct (N × H)
643. C₃	C₃×#3515	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×#557	2
C₃²×#554	2
C₃²×#553	2
C₃²×#552	2
C₃²×#547	2
C₃²×#541	2
C₃²×#539	2
C₃²×#533	2
C₃²×#529	2
C₂×C₃²×#125	2
C₃²×#520	2
C₃²×C₄×#41	2
C₃×#3515	3

Subgroups — C32×#3515 #11770564

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#3515 #11770564