Subgroups — C₃²×#2716 #11769765

Order 1152.

1350 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃²×#126	C₂	1	1	yes	maximal, characteristic
3	C₃²×#400	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃²×#398	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃²×#397	C₂	1	1	yes	maximal, characteristic
6	C₃²×#396	C₂	1	1	yes	maximal, characteristic
7	C₃²×#393	C₂	1	1	yes	maximal, characteristic
8	C₃²×#393	C₂	1	1	yes	maximal, characteristic
9	C₃²×#391	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃²×#391	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃²×#388	C₂	1	1	yes	maximal, characteristic
12	C₃²×#388	C₂	1	1	yes	maximal, characteristic
13	C₃²×#387	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃²×#387	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃²×#387	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#2716	C₃	1	4	yes	maximal, direct product factor
17	C₂²×C₃²×Q₈	C₂²	1	1	yes	characteristic
18	C₂²×C₃²×Q₈	C₂²	1	1	yes	characteristic
19	C₃²×C₄⋊Q₈	—	2	4	no	—
20	C₃²×#126	—	2	4	no	—
21	C₂×C₃²×C₄⋊C₄	C₂²	1	1	yes	characteristic
22	C₂×C₃²×C₄⋊C₄	C₂²	1	1	yes	characteristic
23	C₂×C₃²×C₄⋊C₄	C₂²	1	1	yes	characteristic
24	C₂×C₃²×C₄⋊C₄	C₂²	1	1	yes	characteristic
25	C₂×C₃²×C₄⋊C₄	C₂²	1	1	yes	characteristic
26	C₂×C₃²×C₄⋊C₄	C₂²	1	1	yes	characteristic
27	C₂×C₃²×C₄⋊C₄	C₂²	1	1	yes	characteristic
28	C₂×C₃²×C₄⋊C₄	C₂²	1	1	yes	characteristic
29	C₂×C₃²×C₄⋊C₄	C₂²	1	1	yes	characteristic
30	C₂×C₃²×C₂²⋊C₄	C₂²	1	1	yes	characteristic
31	C₂×C₃²×C₂²⋊C₄	C₂²	1	1	yes	characteristic
32	C₂×C₃²×C₂²⋊C₄	C₂²	1	1	yes	characteristic
33	C₂×C₃²×C₂²⋊C₄	C₂²	1	1	yes	characteristic
34	C₂×C₃²×C₂²⋊C₄	C₂²	1	1	yes	characteristic
35	C₂×C₃²×C₂²⋊C₄	C₂²	1	1	yes	characteristic
36	C₂×C₃²×C₂²⋊C₄	C₂²	1	1	yes	characteristic
37	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
38	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
39	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
40	C₃²×#95	C₂²	1	1	yes	characteristic
41	C₃²×#95	C₂²	1	1	yes	characteristic
42	C₃²×#95	C₂²	1	1	yes	characteristic
43	C₃²×#95	C₂²	1	1	yes	characteristic
44	C₃²×#95	C₂²	1	1	yes	characteristic
45	C₃²×#95	C₂²	1	1	yes	characteristic
46	C₃²×#95	C₂²	1	1	yes	characteristic
47	C₃²×#95	C₂²	1	1	yes	characteristic
48	C₃²×#95	C₂²	1	1	yes	characteristic
49	C₃²×#95	C₂²	1	1	yes	characteristic
50	C₃²×#95	C₂²	1	1	yes	characteristic
51	C₃²×#95	C₂²	1	1	yes	characteristic
52	C₃²×#95	C₂²	1	1	yes	characteristic
53	C₃²×#95	C₂²	1	1	yes	characteristic
54	C₂×C₃×C₄⋊Q₈	C₂×C₃	1	4	yes	complemented
55	C₂×C₃×#126	C₂×C₃	1	4	yes	—
56	C₃×#400	C₂×C₃	1	4	yes	complemented
57	C₃×#398	C₂×C₃	1	4	yes	complemented
58	C₃×#397	C₂×C₃	1	4	yes	—
59	C₃×#396	C₂×C₃	1	4	yes	—
60	C₃×#393	C₂×C₃	1	4	yes	—
61	C₃×#393	C₂×C₃	1	4	yes	—
62	C₃×#391	C₂×C₃	1	4	yes	complemented
63	C₃×#391	C₂×C₃	1	4	yes	complemented
64	C₃×#388	C₂×C₃	1	4	yes	—
65	C₃×#388	C₂×C₃	1	4	yes	—
66	C₃×#387	C₂×C₃	1	4	yes	complemented
67	C₃×#387	C₂×C₃	1	4	yes	complemented
68	C₃×#387	C₂×C₃	1	4	yes	complemented
69	C₂⁴×C₃²	C₂³	1	1	yes	characteristic
70	C₂×C₃²×Q₈	—	2	2	no	—
71	C₂×C₃²×Q₈	—	2	2	no	—
72	C₂×C₃²×Q₈	—	2	2	no	—
73	C₂×C₃²×Q₈	—	2	2	no	—
74	C₂×C₃²×Q₈	—	4	1	no	—
75	C₂×C₃²×Q₈	—	4	1	no	—
76	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
77	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
78	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
79	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
80	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
81	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
82	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
83	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
84	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
85	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
86	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
87	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
88	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
89	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
90	C₃²×C₄⋊C₄	—	2	2	no	—
91	C₃²×C₄⋊C₄	—	2	2	no	—
92	C₃²×C₄⋊C₄	—	2	2	no	—
93	C₃²×C₄⋊C₄	—	2	2	no	—
94	C₃²×C₄⋊C₄	—	2	2	no	—
95	C₃²×C₄⋊C₄	—	2	2	no	—
96	C₃²×C₄⋊C₄	—	2	2	no	—
97	C₃²×C₄⋊C₄	—	4	1	no	—
98	C₃²×C₄⋊C₄	D₄	1	4	yes	—
99	C₃²×C₂²⋊C₄	—	2	2	no	—
100	C₃²×C₂²⋊C₄	—	2	2	no	—
101	C₃²×C₂²⋊C₄	—	2	2	no	—
102	C₃²×C₂²⋊C₄	—	2	2	no	—
103	C₃²×C₂²⋊C₄	—	2	2	no	—
104	C₃²×C₂²⋊C₄	—	4	1	no	—
105	C₃²×C₂²⋊C₄	—	4	1	no	—
106	C₃²×C₄²	—	2	2	no	—
107	C₃²×C₄²	—	2	2	no	—
108	C₃²×C₄²	—	4	1	no	—
109	#2716	C₃²	1	1	yes	characteristic, direct product factor, Sylow
110	C₂²×C₃×Q₈	C₂²×C₃	1	4	yes	—
111	C₂²×C₃×Q₈	C₂²×C₃	1	4	yes	—
112	C₃×C₄⋊Q₈	—	2	16	no	—
113	C₃×#126	—	2	16	no	—
114	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	4	yes	—
115	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	4	yes	—
116	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	4	yes	—
117	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	4	yes	—
118	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	4	yes	—
119	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	4	yes	—
120	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	4	yes	—
121	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	4	yes	—
122	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	4	yes	—
123	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
124	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
125	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
126	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
127	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
128	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
129	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
130	C₂×C₃×C₄²	C₂²×C₃	1	4	yes	—
131	C₂×C₃×C₄²	C₂²×C₃	1	4	yes	—
132	C₂×C₃×C₄²	C₂²×C₃	1	4	yes	—
133	C₃×#95	C₂²×C₃	1	4	yes	—
134	C₃×#95	C₂²×C₃	1	4	yes	—
135	C₃×#95	C₂²×C₃	1	4	yes	—
136	C₃×#95	C₂²×C₃	1	4	yes	—
137	C₃×#95	C₂²×C₃	1	4	yes	—
138	C₃×#95	C₂²×C₃	1	4	yes	—
139	C₃×#95	C₂²×C₃	1	4	yes	—
140	C₃×#95	C₂²×C₃	1	4	yes	—
141	C₃×#95	C₂²×C₃	1	4	yes	—
142	C₃×#95	C₂²×C₃	1	4	yes	—
143	C₃×#95	C₂²×C₃	1	4	yes	—
144	C₃×#95	C₂²×C₃	1	4	yes	—
145	C₃×#95	C₂²×C₃	1	4	yes	—
146	C₃×#95	C₂²×C₃	1	4	yes	—
147	C₂³×C₃²	—	2	1	no	—
148	C₂³×C₃²	—	2	1	no	—
149	C₂³×C₃²	—	2	1	no	—
150	C₂³×C₃²	—	2	1	no	—
151	C₂³×C₃²	—	2	1	no	—
152	C₂³×C₃²	—	2	1	no	—
153	C₂³×C₃²	—	2	1	no	—
154	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
155	C₃²×Q₈	—	4	4	no	—
156	C₃²×Q₈	—	4	4	no	—
157	C₂×C₃²×C₄	—	2	1	no	—
158	C₂×C₃²×C₄	—	2	1	no	—
159	C₂×C₃²×C₄	—	2	1	no	—
160	C₂×C₃²×C₄	—	2	1	no	—
161	C₂×C₃²×C₄	—	2	1	no	—
162	C₂×C₃²×C₄	—	2	1	no	—
163	C₂×C₃²×C₄	—	2	1	no	—
164	C₂×C₃²×C₄	—	2	1	no	—
165	C₂×C₃²×C₄	—	2	1	no	—
166	C₂×C₃²×C₄	—	2	1	no	—
167	C₂×C₃²×C₄	—	2	1	no	—
168	C₂×C₃²×C₄	—	2	1	no	—
169	C₂×C₃²×C₄	—	2	1	no	—
170	C₂×C₃²×C₄	—	2	1	no	—
171	C₂×C₃²×C₄	—	2	1	no	—
172	C₂×C₃²×C₄	—	2	1	no	—
173	C₂×C₃²×C₄	—	2	1	no	—
174	C₂×C₃²×C₄	—	2	1	no	—
175	C₂×C₃²×C₄	—	2	1	no	—
176	C₂×C₃²×C₄	—	2	1	no	—
177	C₂×C₃²×C₄	—	2	1	no	—
178	C₂×C₃²×C₄	—	2	1	no	—
179	C₂×C₃²×C₄	—	2	1	no	—
180	C₂×C₃²×C₄	—	2	1	no	—
181	C₂×C₃²×C₄	—	2	1	no	—
182	C₂×C₃²×C₄	—	2	1	no	—
183	C₂×C₃²×C₄	—	2	1	no	—
184	C₂×C₃²×C₄	—	2	1	no	—
185	C₂×C₃²×C₄	—	2	1	no	—
186	C₂×C₃²×C₄	—	2	1	no	—
187	C₂×C₃²×C₄	—	2	1	no	—
188	C₂×C₃²×C₄	—	2	1	no	—
189	C₂×C₃²×C₄	—	2	1	no	—
190	C₂×C₃²×C₄	—	2	1	no	—
191	C₂×C₃²×C₄	—	2	1	no	—
192	C₂×C₃²×C₄	—	2	1	no	—
193	C₂×C₃²×C₄	—	2	1	no	—
194	C₂×C₃²×C₄	C₂×D₄	1	2	yes	—
195	C₂×C₃²×C₄	C₂×D₄	1	2	yes	—
196	C₂×C₃²×C₄	C₂×D₄	1	2	yes	—
197	C₂×C₃²×C₄	#41	1	2	yes	—
198	C₂×C₃²×C₄	#41	1	2	yes	—
199	C₂×C₄⋊Q₈	C₂×C₃²	1	1	yes	characteristic, complemented
200	C₂×#126	C₂×C₃²	1	1	yes	characteristic
201	#400	C₂×C₃²	1	1	yes	characteristic, complemented
202	#398	C₂×C₃²	1	1	yes	characteristic, complemented
203	#397	C₂×C₃²	1	1	yes	characteristic
204	#396	C₂×C₃²	1	1	yes	characteristic
205	#393	C₂×C₃²	1	1	yes	characteristic
206	#393	C₂×C₃²	1	1	yes	characteristic
207	#391	C₂×C₃²	1	1	yes	characteristic, complemented
208	#391	C₂×C₃²	1	1	yes	characteristic, complemented
209	#388	C₂×C₃²	1	1	yes	characteristic
210	#388	C₂×C₃²	1	1	yes	characteristic
211	#387	C₂×C₃²	1	1	yes	characteristic, complemented
212	#387	C₂×C₃²	1	1	yes	characteristic, complemented
213	#387	C₂×C₃²	1	1	yes	characteristic, complemented
214	C₂⁴×C₃	C₂³×C₃	1	4	yes	—
215	C₂×C₃×Q₈	—	2	8	no	—
216	C₂×C₃×Q₈	—	2	8	no	—
217	C₂×C₃×Q₈	—	2	8	no	—
218	C₂×C₃×Q₈	—	2	8	no	—
219	C₂×C₃×Q₈	—	4	4	no	—
220	C₂×C₃×Q₈	—	4	4	no	—
221	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
222	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
223	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
224	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
225	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
226	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
227	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
228	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
229	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
230	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
231	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
232	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
233	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
234	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
235	C₃×C₄⋊C₄	—	2	8	no	—
236	C₃×C₄⋊C₄	—	2	8	no	—
237	C₃×C₄⋊C₄	—	2	8	no	—
238	C₃×C₄⋊C₄	—	2	8	no	—
239	C₃×C₄⋊C₄	—	2	8	no	—
240	C₃×C₄⋊C₄	—	2	8	no	—
241	C₃×C₄⋊C₄	—	2	8	no	—
242	C₃×C₄⋊C₄	—	4	4	no	—
243	C₃×C₄⋊C₄	C₃×D₄	1	16	yes	—
244	C₃×C₂²⋊C₄	—	2	8	no	—
245	C₃×C₂²⋊C₄	—	2	8	no	—
246	C₃×C₂²⋊C₄	—	2	8	no	—
247	C₃×C₂²⋊C₄	—	2	8	no	—
248	C₃×C₂²⋊C₄	—	2	8	no	—
249	C₃×C₂²⋊C₄	—	4	4	no	—
250	C₃×C₂²⋊C₄	—	4	4	no	—
251	C₃×C₄²	—	2	8	no	—
252	C₃×C₄²	—	2	8	no	—
253	C₃×C₄²	—	4	4	no	—
254	C₂²×C₃²	—	4	1	no	—
255	C₂²×C₃²	—	4	1	no	—
256	C₂²×C₃²	—	4	1	no	—
257	C₂²×C₃²	—	4	1	no	—
258	C₂²×C₃²	—	4	1	no	—
259	C₂²×C₃²	—	4	1	no	—
260	C₂²×C₃²	—	4	1	no	—
261	C₂²×C₃²	C₂²×D₄	1	1	yes	characteristic
262	C₂²×C₃²	C₂×#41	1	1	yes	characteristic
263	C₂²×C₃²	C₂×#41	1	1	yes	characteristic
264	C₂²×C₃²	H(5,𝔽₂)	1	1	yes	characteristic
265	C₂²×C₃²	2₋¹⁺⁴	1	1	yes	characteristic
266	C₂²×C₃²	2₋¹⁺⁴	1	1	yes	characteristic
267	C₂²×C₃²	2₋¹⁺⁴	1	1	yes	characteristic
268	C₃²×C₄	—	2	2	no	—
269	C₃²×C₄	—	2	2	no	—
270	C₃²×C₄	—	2	2	no	—
271	C₃²×C₄	—	2	2	no	—
272	C₃²×C₄	—	2	2	no	—
273	C₃²×C₄	—	4	1	no	—
274	C₃²×C₄	—	4	1	no	—
275	C₃²×C₄	—	4	1	no	—
276	C₃²×C₄	—	4	1	no	—
277	C₃²×C₄	—	4	1	no	—
278	C₃²×C₄	—	4	1	no	—
279	C₃²×C₄	—	4	1	no	—
280	C₃²×C₄	—	4	1	no	—
281	C₃²×C₄	—	4	1	no	—
282	C₂²×Q₈	C₂²×C₃²	1	1	yes	characteristic
283	C₂²×Q₈	C₂²×C₃²	1	1	yes	characteristic
284	C₄⋊Q₈	—	2	4	no	—
285	#126	—	2	4	no	—
286	C₂×C₄⋊C₄	C₂²×C₃²	1	1	yes	characteristic
287	C₂×C₄⋊C₄	C₂²×C₃²	1	1	yes	characteristic
288	C₂×C₄⋊C₄	C₂²×C₃²	1	1	yes	characteristic
289	C₂×C₄⋊C₄	C₂²×C₃²	1	1	yes	characteristic
290	C₂×C₄⋊C₄	C₂²×C₃²	1	1	yes	characteristic
291	C₂×C₄⋊C₄	C₂²×C₃²	1	1	yes	characteristic
292	C₂×C₄⋊C₄	C₂²×C₃²	1	1	yes	characteristic
293	C₂×C₄⋊C₄	C₂²×C₃²	1	1	yes	characteristic
294	C₂×C₄⋊C₄	C₂²×C₃²	1	1	yes	characteristic
295	C₂×C₂²⋊C₄	C₂²×C₃²	1	1	yes	characteristic
296	C₂×C₂²⋊C₄	C₂²×C₃²	1	1	yes	characteristic
297	C₂×C₂²⋊C₄	C₂²×C₃²	1	1	yes	characteristic
298	C₂×C₂²⋊C₄	C₂²×C₃²	1	1	yes	characteristic
299	C₂×C₂²⋊C₄	C₂²×C₃²	1	1	yes	characteristic
300	C₂×C₂²⋊C₄	C₂²×C₃²	1	1	yes	characteristic
301	C₂×C₂²⋊C₄	C₂²×C₃²	1	1	yes	characteristic
302	C₂×C₄²	C₂²×C₃²	1	1	yes	characteristic
303	C₂×C₄²	C₂²×C₃²	1	1	yes	characteristic
304	C₂×C₄²	C₂²×C₃²	1	1	yes	characteristic
305	#95	C₂²×C₃²	1	1	yes	characteristic
306	#95	C₂²×C₃²	1	1	yes	characteristic
307	#95	C₂²×C₃²	1	1	yes	characteristic
308	#95	C₂²×C₃²	1	1	yes	characteristic
309	#95	C₂²×C₃²	1	1	yes	characteristic
310	#95	C₂²×C₃²	1	1	yes	characteristic
311	#95	C₂²×C₃²	1	1	yes	characteristic
312	#95	C₂²×C₃²	1	1	yes	characteristic
313	#95	C₂²×C₃²	1	1	yes	characteristic
314	#95	C₂²×C₃²	1	1	yes	characteristic
315	#95	C₂²×C₃²	1	1	yes	characteristic
316	#95	C₂²×C₃²	1	1	yes	characteristic
317	#95	C₂²×C₃²	1	1	yes	characteristic
318	#95	C₂²×C₃²	1	1	yes	characteristic
319	C₂³×C₃	—	2	4	no	—
320	C₂³×C₃	—	2	4	no	—
321	C₂³×C₃	—	2	4	no	—
322	C₂³×C₃	—	2	4	no	—
323	C₂³×C₃	—	2	4	no	—
324	C₂³×C₃	—	2	4	no	—
325	C₂³×C₃	—	2	4	no	—
326	C₂³×C₃	C₂⁴×C₃	1	4	yes	—
327	C₃×Q₈	—	4	16	no	—
328	C₃×Q₈	—	4	16	no	—
329	C₂×C₃×C₄	—	2	4	no	—
330	C₂×C₃×C₄	—	2	4	no	—
331	C₂×C₃×C₄	—	2	4	no	—
332	C₂×C₃×C₄	—	2	4	no	—
333	C₂×C₃×C₄	—	2	4	no	—
334	C₂×C₃×C₄	—	2	4	no	—
335	C₂×C₃×C₄	—	2	4	no	—
336	C₂×C₃×C₄	—	2	4	no	—
337	C₂×C₃×C₄	—	2	4	no	—
338	C₂×C₃×C₄	—	2	4	no	—
339	C₂×C₃×C₄	—	2	4	no	—
340	C₂×C₃×C₄	—	2	4	no	—
341	C₂×C₃×C₄	—	2	4	no	—
342	C₂×C₃×C₄	—	2	4	no	—
343	C₂×C₃×C₄	—	2	4	no	—
344	C₂×C₃×C₄	—	2	4	no	—
345	C₂×C₃×C₄	—	2	4	no	—
346	C₂×C₃×C₄	—	2	4	no	—
347	C₂×C₃×C₄	—	2	4	no	—
348	C₂×C₃×C₄	—	2	4	no	—
349	C₂×C₃×C₄	—	2	4	no	—
350	C₂×C₃×C₄	—	2	4	no	—
351	C₂×C₃×C₄	—	2	4	no	—
352	C₂×C₃×C₄	—	2	4	no	—
353	C₂×C₃×C₄	—	2	4	no	—
354	C₂×C₃×C₄	—	2	4	no	—
355	C₂×C₃×C₄	—	2	4	no	—
356	C₂×C₃×C₄	—	2	4	no	—
357	C₂×C₃×C₄	—	2	4	no	—
358	C₂×C₃×C₄	—	2	4	no	—
359	C₂×C₃×C₄	—	2	4	no	—
360	C₂×C₃×C₄	—	2	4	no	—
361	C₂×C₃×C₄	—	2	4	no	—
362	C₂×C₃×C₄	—	2	4	no	—
363	C₂×C₃×C₄	—	2	4	no	—
364	C₂×C₃×C₄	—	2	4	no	—
365	C₂×C₃×C₄	—	2	4	no	—
366	C₂×C₃×C₄	C₂×C₃×D₄	1	8	yes	—
367	C₂×C₃×C₄	C₂×C₃×D₄	1	8	yes	—
368	C₂×C₃×C₄	C₂×C₃×D₄	1	8	yes	—
369	C₂×C₃×C₄	C₃×#41	1	8	yes	—
370	C₂×C₃×C₄	C₃×#41	1	8	yes	—
371	C₂×C₃²	—	8	1	no	—
372	C₂×C₃²	#536	1	1	yes	characteristic
373	C₂×C₃²	#541	1	1	yes	characteristic
374	C₂×C₃²	#542	1	1	yes	characteristic
375	C₂×C₃²	#546	1	1	yes	characteristic
376	C₂×C₃²	#548	1	1	yes	characteristic
377	C₂×C₃²	#556	1	1	yes	characteristic
378	C₂×C₃²	#563	1	1	yes	characteristic
379	C₂⁴	C₂³×C₃²	1	1	yes	characteristic
380	C₂×Q₈	—	2	2	no	—
381	C₂×Q₈	—	2	2	no	—
382	C₂×Q₈	—	2	2	no	—
383	C₂×Q₈	—	2	2	no	—
384	C₂×Q₈	—	4	1	no	—
385	C₂×Q₈	—	4	1	no	—
386	C₂²×C₄	C₂³×C₃²	1	1	yes	characteristic
387	C₂²×C₄	C₂³×C₃²	1	1	yes	characteristic
388	C₂²×C₄	C₂³×C₃²	1	1	yes	characteristic
389	C₂²×C₄	C₂³×C₃²	1	1	yes	characteristic
390	C₂²×C₄	C₂³×C₃²	1	1	yes	characteristic
391	C₂²×C₄	C₂³×C₃²	1	1	yes	characteristic
392	C₂²×C₄	C₂³×C₃²	1	1	yes	characteristic
393	C₂²×C₄	C₂³×C₃²	1	1	yes	characteristic
394	C₂²×C₄	C₂³×C₃²	1	1	yes	characteristic
395	C₂²×C₄	C₂³×C₃²	1	1	yes	characteristic
396	C₂²×C₄	C₂³×C₃²	1	1	yes	characteristic
397	C₂²×C₄	C₂³×C₃²	1	1	yes	characteristic
398	C₂²×C₄	C₂³×C₃²	1	1	yes	characteristic
399	C₂²×C₄	C₂³×C₃²	1	1	yes	characteristic
400	C₄⋊C₄	—	2	2	no	—
401	C₄⋊C₄	—	2	2	no	—
402	C₄⋊C₄	—	2	2	no	—
403	C₄⋊C₄	—	2	2	no	—
404	C₄⋊C₄	—	2	2	no	—
405	C₄⋊C₄	—	2	2	no	—
406	C₄⋊C₄	—	2	2	no	—
407	C₄⋊C₄	—	4	1	no	—
408	C₄⋊C₄	C₃²×D₄	1	4	yes	—
409	C₂²⋊C₄	—	2	2	no	—
410	C₂²⋊C₄	—	2	2	no	—
411	C₂²⋊C₄	—	2	2	no	—
412	C₂²⋊C₄	—	2	2	no	—
413	C₂²⋊C₄	—	2	2	no	—
414	C₂²⋊C₄	—	4	1	no	—
415	C₂²⋊C₄	—	4	1	no	—
416	C₄²	—	2	2	no	—
417	C₄²	—	2	2	no	—
418	C₄²	—	4	1	no	—
419	C₂²×C₃	—	4	4	no	—
420	C₂²×C₃	—	4	4	no	—
421	C₂²×C₃	—	4	4	no	—
422	C₂²×C₃	—	4	4	no	—
423	C₂²×C₃	—	4	4	no	—
424	C₂²×C₃	—	4	4	no	—
425	C₂²×C₃	—	4	4	no	—
426	C₂²×C₃	C₂²×C₃×D₄	1	4	yes	—
427	C₂²×C₃	C₂×C₃×#41	1	4	yes	—
428	C₂²×C₃	C₂×C₃×#41	1	4	yes	—
429	C₂²×C₃	C₃×H(5,𝔽₂)	1	4	yes	—
430	C₂²×C₃	C₃×2₋¹⁺⁴	1	4	yes	—
431	C₂²×C₃	C₃×2₋¹⁺⁴	1	4	yes	—
432	C₂²×C₃	C₃×2₋¹⁺⁴	1	4	yes	—
433	C₃×C₄	—	2	8	no	—
434	C₃×C₄	—	2	8	no	—
435	C₃×C₄	—	2	8	no	—
436	C₃×C₄	—	2	8	no	—
437	C₃×C₄	—	2	8	no	—
438	C₃×C₄	—	4	4	no	—
439	C₃×C₄	—	4	4	no	—
440	C₃×C₄	—	4	4	no	—
441	C₃×C₄	—	4	4	no	—
442	C₃×C₄	—	4	4	no	—
443	C₃×C₄	—	4	4	no	—
444	C₃×C₄	—	4	4	no	—
445	C₃×C₄	—	4	4	no	—
446	C₃×C₄	—	4	4	no	—
447	C₃²	#2716	1	1	yes	characteristic, direct product factor, Sylow
448	C₂³	—	2	1	no	—
449	C₂³	—	2	1	no	—
450	C₂³	—	2	1	no	—
451	C₂³	—	2	1	no	—
452	C₂³	—	2	1	no	—
453	C₂³	—	2	1	no	—
454	C₂³	—	2	1	no	—
455	C₂³	C₂⁴×C₃²	1	1	yes	characteristic
456	Q₈	—	4	4	no	—
457	Q₈	—	4	4	no	—
458	C₂×C₄	—	2	1	no	—
459	C₂×C₄	—	2	1	no	—
460	C₂×C₄	—	2	1	no	—
461	C₂×C₄	—	2	1	no	—
462	C₂×C₄	—	2	1	no	—
463	C₂×C₄	—	2	1	no	—
464	C₂×C₄	—	2	1	no	—
465	C₂×C₄	—	2	1	no	—
466	C₂×C₄	—	2	1	no	—
467	C₂×C₄	—	2	1	no	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	2	1	no	—
470	C₂×C₄	—	2	1	no	—
471	C₂×C₄	—	2	1	no	—
472	C₂×C₄	—	2	1	no	—
473	C₂×C₄	—	2	1	no	—
474	C₂×C₄	—	2	1	no	—
475	C₂×C₄	—	2	1	no	—
476	C₂×C₄	—	2	1	no	—
477	C₂×C₄	—	2	1	no	—
478	C₂×C₄	—	2	1	no	—
479	C₂×C₄	—	2	1	no	—
480	C₂×C₄	—	2	1	no	—
481	C₂×C₄	—	2	1	no	—
482	C₂×C₄	—	2	1	no	—
483	C₂×C₄	—	2	1	no	—
484	C₂×C₄	—	2	1	no	—
485	C₂×C₄	—	2	1	no	—
486	C₂×C₄	—	2	1	no	—
487	C₂×C₄	—	2	1	no	—
488	C₂×C₄	—	2	1	no	—
489	C₂×C₄	—	2	1	no	—
490	C₂×C₄	—	2	1	no	—
491	C₂×C₄	—	2	1	no	—
492	C₂×C₄	—	2	1	no	—
493	C₂×C₄	—	2	1	no	—
494	C₂×C₄	—	2	1	no	—
495	C₂×C₄	C₂×C₃²×D₄	1	2	yes	—
496	C₂×C₄	C₂×C₃²×D₄	1	2	yes	—
497	C₂×C₄	C₂×C₃²×D₄	1	2	yes	—
498	C₂×C₄	C₃²×#41	1	2	yes	—
499	C₂×C₄	C₃²×#41	1	2	yes	—
500	C₂×C₃	—	8	4	no	—
501	C₂×C₃	C₃×#536	1	4	yes	—
502	C₂×C₃	C₃×#541	1	4	yes	—
503	C₂×C₃	C₃×#542	1	4	yes	—
504	C₂×C₃	C₃×#546	1	4	yes	—
505	C₂×C₃	C₃×#548	1	4	yes	—
506	C₂×C₃	C₃×#556	1	4	yes	—
507	C₂×C₃	C₃×#563	1	4	yes	—
508	C₂²	—	4	1	no	—
509	C₂²	—	4	1	no	—
510	C₂²	—	4	1	no	—
511	C₂²	—	4	1	no	—
512	C₂²	—	4	1	no	—
513	C₂²	—	4	1	no	—
514	C₂²	—	4	1	no	—
515	C₂²	C₂²×C₃²×D₄	1	1	yes	characteristic
516	C₂²	C₂×C₃²×#41	1	1	yes	characteristic
517	C₂²	C₂×C₃²×#41	1	1	yes	characteristic
518	C₂²	C₃²×H(5,𝔽₂)	1	1	yes	characteristic
519	C₂²	C₃²×2₋¹⁺⁴	1	1	yes	characteristic
520	C₂²	C₃²×2₋¹⁺⁴	1	1	yes	characteristic
521	C₂²	C₃²×2₋¹⁺⁴	1	1	yes	characteristic
522	C₄	—	2	2	no	—
523	C₄	—	2	2	no	—
524	C₄	—	2	2	no	—
525	C₄	—	2	2	no	—
526	C₄	—	2	2	no	—
527	C₄	—	4	1	no	—
528	C₄	—	4	1	no	—
529	C₄	—	4	1	no	—
530	C₄	—	4	1	no	—
531	C₄	—	4	1	no	—
532	C₄	—	4	1	no	—
533	C₄	—	4	1	no	—
534	C₄	—	4	1	no	—
535	C₄	—	4	1	no	—
536	C₃	C₃×#2716	1	4	yes	direct product factor
537	C₂	—	8	1	no	—
538	C₂	C₃²×#536	1	1	yes	characteristic
539	C₂	C₃²×#541	1	1	yes	characteristic
540	C₂	C₃²×#542	1	1	yes	characteristic
541	C₂	C₃²×#546	1	1	yes	characteristic
542	C₂	C₃²×#548	1	1	yes	characteristic
543	C₂	C₃²×#556	1	1	yes	characteristic
544	C₂	C₃²×#563	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃²	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃²
prime radical	C₂⁴×C₃²	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₃² ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃²×C₄⋊Q₈	C₂	semidirect
3. C₃²×#400	C₂	semidirect
4. C₃²×#398	C₂	semidirect
9. C₃²×#391	C₂	semidirect
10. C₃²×#391	C₂	semidirect
13. C₃²×#387	C₂	semidirect
14. C₃²×#387	C₂	semidirect
15. C₃²×#387	C₂	semidirect
16. C₃×#2716	C₃	direct (N × H)
54. C₂×C₃×C₄⋊Q₈	C₂×C₃	semidirect
56. C₃×#400	C₂×C₃	semidirect
57. C₃×#398	C₂×C₃	semidirect
62. C₃×#391	C₂×C₃	semidirect
63. C₃×#391	C₂×C₃	semidirect
66. C₃×#387	C₂×C₃	semidirect
67. C₃×#387	C₂×C₃	semidirect
68. C₃×#387	C₂×C₃	semidirect
109. #2716	C₃²	direct (N × H)
199. C₂×C₄⋊Q₈	C₂×C₃²	semidirect
201. #400	C₂×C₃²	semidirect
202. #398	C₂×C₃²	semidirect
207. #391	C₂×C₃²	semidirect
208. #391	C₂×C₃²	semidirect
211. #387	C₂×C₃²	semidirect
212. #387	C₂×C₃²	semidirect
213. #387	C₂×C₃²	semidirect
447. C₃²	#2716	direct (N × H)
536. C₃	C₃×#2716	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₃²×C₄⋊Q₈	2
C₂×C₃²×#126	2
C₃²×#400	2
C₃²×#398	2
C₃²×#397	2
C₃²×#396	2
C₃²×#393	2
C₃²×#391	2
C₃²×#388	2
C₃²×#387	2
C₃×#2716	3

Subgroups — C32×#2716 #11769765

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#2716 #11769765