Subgroups — C₃²×D₄×SD₁₆ #11770330

Order 1152.

1638 conjugacy classes of subgroups.

The subgroup lattice has 435 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃²×SD₁₆	C₂	1	2	yes	maximal, complemented
2	C₃²×D₄×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×D₄²	C₂	1	1	yes	maximal, characteristic
4	C₃²×#492	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃²×#465	C₂	1	2	yes	maximal, complemented
6	C₃²×#461	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃²×#460	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃²×#450	C₂	1	2	yes	maximal, complemented
9	C₃²×#448	C₂	1	2	yes	maximal, complemented
10	C₃²×C₄×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃²×C₈×D₄	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×D₄×SD₁₆	C₃	1	4	yes	maximal, direct product factor
13	C₂²×C₃²×Q₈	C₂²	1	2	yes	complemented
14	C₂²×C₃²×D₄	—	2	1	no	—
15	C₂²×C₃²×D₄	C₂²	1	2	yes	—
16	C₂×C₃²×SD₁₆	—	2	8	no	—
17	C₂×C₃²×SD₁₆	C₂²	1	2	yes	—
18	C₂×C₃²×SD₁₆	C₂²	1	1	yes	characteristic
19	C₂×C₃²×SD₁₆	C₂²	1	2	yes	complemented
20	C₂×C₃²×SD₁₆	C₂²	1	2	yes	complemented
21	C₂×C₃²×SD₁₆	C₂²	1	2	yes	complemented
22	C₂²×C₃²×C₈	C₂²	1	2	yes	complemented
23	C₃²×C₄⋊Q₈	—	2	1	no	—
24	C₃²×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
25	C₃²×#127	C₂²	1	1	yes	characteristic
26	C₃²×C₂²⋊Q₈	—	2	2	no	—
27	C₃²×C₂²⋊Q₈	C₂²	1	2	yes	complemented
28	C₃²×#121	—	2	1	no	—
29	C₃²×#121	C₂²	1	2	yes	—
30	C₃²×#120	—	2	2	no	—
31	C₃²×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
32	C₃²×C₄×D₄	—	2	1	no	—
33	C₃²×C₄×D₄	C₂²	1	1	yes	characteristic
34	C₃²×C₄×D₄	C₂²	1	1	yes	characteristic
35	C₃²×#106	C₂²	1	1	yes	characteristic, complemented
36	C₃²×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
37	C₃²×#103	C₂²	1	2	yes	complemented
38	C₃²×#103	C₂²	1	1	yes	characteristic, complemented
39	C₃²×#102	C₂²	1	1	yes	characteristic
40	C₃²×#102	C₂²	1	2	yes	complemented
41	C₃²×C₂²⋊C₈	C₂²	1	2	yes	complemented
42	C₃²×C₄×C₈	C₂²	1	1	yes	characteristic, complemented
43	C₂²×C₃×SD₁₆	C₂×C₃	1	8	yes	complemented
44	C₃×D₄×Q₈	C₂×C₃	1	4	yes	complemented
45	C₃×D₄²	C₂×C₃	1	4	yes	—
46	C₃×#492	C₂×C₃	1	4	yes	complemented
47	C₃×#465	C₂×C₃	1	8	yes	complemented
48	C₃×#461	C₂×C₃	1	4	yes	complemented
49	C₃×#460	C₂×C₃	1	4	yes	complemented
50	C₃×#450	C₂×C₃	1	8	yes	complemented
51	C₃×#448	C₂×C₃	1	8	yes	complemented
52	C₃×C₄×SD₁₆	C₂×C₃	1	4	yes	complemented
53	C₃×C₈×D₄	C₂×C₃	1	4	yes	complemented
54	C₂⁴×C₃²	—	2	2	no	—
55	C₂×C₃²×Q₈	—	2	2	no	—
56	C₂×C₃²×Q₈	—	2	4	no	—
57	C₂×C₃²×Q₈	—	4	2	no	—
58	C₂×C₃²×Q₈	C₂³	1	2	yes	—
59	C₂×C₃²×Q₈	C₂³	1	1	yes	characteristic
60	C₂×C₃²×D₄	—	2	4	no	—
61	C₂×C₃²×D₄	—	2	2	no	—
62	C₂×C₃²×D₄	—	2	1	no	—
63	C₂×C₃²×D₄	—	2	2	no	—
64	C₂×C₃²×D₄	—	2	1	no	—
65	C₂×C₃²×D₄	—	4	2	no	—
66	C₂×C₃²×D₄	—	4	4	no	—
67	C₂×C₃²×D₄	D₄	1	1	yes	characteristic
68	C₂×C₃²×D₄	C₂³	1	2	yes	—
69	C₂×C₃²×D₄	C₂³	1	1	yes	characteristic
70	C₂²×C₃²×C₄	—	2	2	no	—
71	C₂²×C₃²×C₄	—	2	1	no	—
72	C₂²×C₃²×C₄	C₂³	1	2	yes	—
73	C₃²×SD₁₆	—	2	4	no	—
74	C₃²×SD₁₆	—	2	4	no	—
75	C₃²×SD₁₆	—	2	4	no	—
76	C₃²×SD₁₆	—	4	2	no	—
77	C₃²×SD₁₆	D₄	1	4	yes	direct product factor
78	C₂×C₃²×C₈	—	2	4	no	—
79	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
80	C₂×C₃²×C₈	C₂³	1	2	yes	—
81	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
82	C₃²×C₄⋊C₄	—	2	1	no	—
83	C₃²×C₄⋊C₄	—	2	1	no	—
84	C₃²×C₄⋊C₄	—	2	1	no	—
85	C₃²×C₄⋊C₄	—	2	2	no	—
86	C₃²×C₄⋊C₄	D₄	1	1	yes	characteristic
87	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
88	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
89	C₃²×C₂²⋊C₄	—	2	2	no	—
90	C₃²×C₂²⋊C₄	—	2	1	no	—
91	C₃²×C₂²⋊C₄	—	2	2	no	—
92	C₃²×C₂²⋊C₄	D₄	1	2	yes	—
93	C₃²×C₄²	—	2	1	no	—
94	C₃²×C₄²	C₂³	1	1	yes	characteristic
95	D₄×SD₁₆	C₃²	1	1	yes	characteristic, direct product factor, Sylow
96	C₂²×C₃×Q₈	C₂²×C₃	1	8	yes	complemented
97	C₂²×C₃×D₄	—	2	4	no	—
98	C₂²×C₃×D₄	C₂²×C₃	1	8	yes	—
99	C₂×C₃×SD₁₆	—	2	32	no	—
100	C₂×C₃×SD₁₆	C₂²×C₃	1	8	yes	—
101	C₂×C₃×SD₁₆	C₂²×C₃	1	4	yes	—
102	C₂×C₃×SD₁₆	C₂²×C₃	1	8	yes	complemented
103	C₂×C₃×SD₁₆	C₂²×C₃	1	8	yes	complemented
104	C₂×C₃×SD₁₆	C₂²×C₃	1	8	yes	complemented
105	C₂²×C₃×C₈	C₂²×C₃	1	8	yes	complemented
106	C₃×C₄⋊Q₈	—	2	4	no	—
107	C₃×C₄⋊Q₈	C₂²×C₃	1	4	yes	complemented
108	C₃×#127	C₂²×C₃	1	4	yes	—
109	C₃×C₂²⋊Q₈	—	2	8	no	—
110	C₃×C₂²⋊Q₈	C₂²×C₃	1	8	yes	complemented
111	C₃×#121	—	2	4	no	—
112	C₃×#121	C₂²×C₃	1	8	yes	—
113	C₃×#120	—	2	8	no	—
114	C₃×C₄×Q₈	C₂²×C₃	1	4	yes	complemented
115	C₃×C₄×D₄	—	2	4	no	—
116	C₃×C₄×D₄	C₂²×C₃	1	4	yes	—
117	C₃×C₄×D₄	C₂²×C₃	1	4	yes	—
118	C₃×#106	C₂²×C₃	1	4	yes	complemented
119	C₃×C₄⋊C₈	C₂²×C₃	1	4	yes	complemented
120	C₃×#103	C₂²×C₃	1	4	yes	complemented
121	C₃×#103	C₂²×C₃	1	8	yes	complemented
122	C₃×#102	C₂²×C₃	1	4	yes	—
123	C₃×#102	C₂²×C₃	1	8	yes	complemented
124	C₃×C₂²⋊C₈	C₂²×C₃	1	8	yes	complemented
125	C₃×C₄×C₈	C₂²×C₃	1	4	yes	complemented
126	C₂³×C₃²	—	2	1	no	—
127	C₂³×C₃²	—	2	2	no	—
128	C₂³×C₃²	—	4	4	no	—
129	C₂³×C₃²	—	4	4	no	—
130	C₂³×C₃²	—	8	2	no	—
131	C₂³×C₃²	C₂×D₄	1	2	yes	—
132	C₃²×Q₈	—	2	1	no	—
133	C₃²×Q₈	—	2	2	no	—
134	C₃²×Q₈	—	2	2	no	—
135	C₃²×Q₈	—	4	4	no	—
136	C₃²×Q₈	C₂×D₄	1	2	yes	complemented
137	C₃²×D₄	—	2	2	no	—
138	C₃²×D₄	—	2	1	no	—
139	C₃²×D₄	—	2	2	no	—
140	C₃²×D₄	—	4	4	no	—
141	C₃²×D₄	—	4	4	no	—
142	C₃²×D₄	—	4	2	no	—
143	C₃²×D₄	—	8	1	no	—
144	C₃²×D₄	SD₁₆	1	4	yes	direct product factor
145	C₃²×D₄	C₂×D₄	1	2	yes	—
146	C₂×C₃²×C₄	—	2	1	no	—
147	C₂×C₃²×C₄	—	2	2	no	—
148	C₂×C₃²×C₄	—	2	2	no	—
149	C₂×C₃²×C₄	—	2	1	no	—
150	C₂×C₃²×C₄	—	2	1	no	—
151	C₂×C₃²×C₄	—	2	2	no	—
152	C₂×C₃²×C₄	—	4	4	no	—
153	C₂×C₃²×C₄	—	4	2	no	—
154	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
155	C₂×C₃²×C₄	C₂×D₄	1	2	yes	—
156	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
157	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
158	C₃²×C₈	—	2	2	no	—
159	C₃²×C₈	—	2	1	no	—
160	C₃²×C₈	C₂×D₄	1	2	yes	complemented
161	C₂²×SD₁₆	C₂×C₃²	1	2	yes	complemented
162	D₄×Q₈	C₂×C₃²	1	1	yes	characteristic, complemented
163	D₄²	C₂×C₃²	1	1	yes	characteristic
164	#492	C₂×C₃²	1	1	yes	characteristic, complemented
165	#465	C₂×C₃²	1	2	yes	complemented
166	#461	C₂×C₃²	1	1	yes	characteristic, complemented
167	#460	C₂×C₃²	1	1	yes	characteristic, complemented
168	#450	C₂×C₃²	1	2	yes	complemented
169	#448	C₂×C₃²	1	2	yes	complemented
170	C₄×SD₁₆	C₂×C₃²	1	1	yes	characteristic, complemented
171	C₈×D₄	C₂×C₃²	1	1	yes	characteristic, complemented
172	C₂⁴×C₃	—	2	8	no	—
173	C₂×C₃×Q₈	—	2	8	no	—
174	C₂×C₃×Q₈	—	2	16	no	—
175	C₂×C₃×Q₈	—	4	8	no	—
176	C₂×C₃×Q₈	C₂³×C₃	1	8	yes	—
177	C₂×C₃×Q₈	C₂³×C₃	1	4	yes	—
178	C₂×C₃×D₄	—	2	16	no	—
179	C₂×C₃×D₄	—	2	8	no	—
180	C₂×C₃×D₄	—	2	8	no	—
181	C₂×C₃×D₄	—	2	4	no	—
182	C₂×C₃×D₄	—	2	4	no	—
183	C₂×C₃×D₄	—	4	8	no	—
184	C₂×C₃×D₄	—	4	16	no	—
185	C₂×C₃×D₄	C₃×D₄	1	4	yes	—
186	C₂×C₃×D₄	C₂³×C₃	1	8	yes	—
187	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
188	C₂²×C₃×C₄	—	2	8	no	—
189	C₂²×C₃×C₄	—	2	4	no	—
190	C₂²×C₃×C₄	C₂³×C₃	1	8	yes	—
191	C₃×SD₁₆	—	2	16	no	—
192	C₃×SD₁₆	—	2	16	no	—
193	C₃×SD₁₆	—	2	16	no	—
194	C₃×SD₁₆	—	4	8	no	—
195	C₃×SD₁₆	C₃×D₄	1	16	yes	direct product factor
196	C₂×C₃×C₈	—	2	16	no	—
197	C₂×C₃×C₈	C₂³×C₃	1	4	yes	—
198	C₂×C₃×C₈	C₂³×C₃	1	8	yes	—
199	C₂×C₃×C₈	C₂³×C₃	1	4	yes	—
200	C₃×C₄⋊C₄	—	2	4	no	—
201	C₃×C₄⋊C₄	—	2	4	no	—
202	C₃×C₄⋊C₄	—	2	4	no	—
203	C₃×C₄⋊C₄	—	2	8	no	—
204	C₃×C₄⋊C₄	C₃×D₄	1	4	yes	—
205	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
206	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
207	C₃×C₂²⋊C₄	—	2	8	no	—
208	C₃×C₂²⋊C₄	—	2	4	no	—
209	C₃×C₂²⋊C₄	—	2	8	no	—
210	C₃×C₂²⋊C₄	C₃×D₄	1	8	yes	—
211	C₃×C₄²	—	2	4	no	—
212	C₃×C₄²	C₂³×C₃	1	4	yes	—
213	C₂²×C₃²	—	2	2	no	—
214	C₂²×C₃²	—	2	2	no	—
215	C₂²×C₃²	—	2	2	no	—
216	C₂²×C₃²	—	4	1	no	—
217	C₂²×C₃²	—	4	1	no	—
218	C₂²×C₃²	—	4	2	no	—
219	C₂²×C₃²	—	4	2	no	—
220	C₂²×C₃²	—	4	2	no	—
221	C₂²×C₃²	—	8	8	no	—
222	C₂²×C₃²	C₂×SD₁₆	1	4	yes	complemented
223	C₂²×C₃²	C₂²×D₄	1	1	yes	characteristic
224	C₃²×C₄	—	2	2	no	—
225	C₃²×C₄	—	2	2	no	—
226	C₃²×C₄	—	2	1	no	—
227	C₃²×C₄	—	4	2	no	—
228	C₃²×C₄	—	4	1	no	—
229	C₃²×C₄	—	4	1	no	—
230	C₃²×C₄	C₂×SD₁₆	1	2	yes	complemented
231	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
232	C₃²×C₄	H(5,𝔽₂)	1	1	yes	characteristic
233	C₂²×Q₈	C₂²×C₃²	1	2	yes	complemented
234	C₂²×D₄	—	2	1	no	—
235	C₂²×D₄	C₂²×C₃²	1	2	yes	—
236	C₂×SD₁₆	—	2	8	no	—
237	C₂×SD₁₆	C₂²×C₃²	1	2	yes	—
238	C₂×SD₁₆	C₂²×C₃²	1	1	yes	characteristic
239	C₂×SD₁₆	C₂²×C₃²	1	2	yes	complemented
240	C₂×SD₁₆	C₂²×C₃²	1	2	yes	complemented
241	C₂×SD₁₆	C₂²×C₃²	1	2	yes	complemented
242	C₂²×C₈	C₂²×C₃²	1	2	yes	complemented
243	C₄⋊Q₈	—	2	1	no	—
244	C₄⋊Q₈	C₂²×C₃²	1	1	yes	characteristic, complemented
245	#127	C₂²×C₃²	1	1	yes	characteristic
246	C₂²⋊Q₈	—	2	2	no	—
247	C₂²⋊Q₈	C₂²×C₃²	1	2	yes	complemented
248	#121	—	2	1	no	—
249	#121	C₂²×C₃²	1	2	yes	—
250	#120	—	2	2	no	—
251	C₄×Q₈	C₂²×C₃²	1	1	yes	characteristic, complemented
252	C₄×D₄	—	2	1	no	—
253	C₄×D₄	C₂²×C₃²	1	1	yes	characteristic
254	C₄×D₄	C₂²×C₃²	1	1	yes	characteristic
255	#106	C₂²×C₃²	1	1	yes	characteristic, complemented
256	C₄⋊C₈	C₂²×C₃²	1	1	yes	characteristic, complemented
257	#103	C₂²×C₃²	1	1	yes	characteristic, complemented
258	#103	C₂²×C₃²	1	2	yes	complemented
259	#102	C₂²×C₃²	1	1	yes	characteristic
260	#102	C₂²×C₃²	1	2	yes	complemented
261	C₂²⋊C₈	C₂²×C₃²	1	2	yes	complemented
262	C₄×C₈	C₂²×C₃²	1	1	yes	characteristic, complemented
263	C₂³×C₃	—	2	4	no	—
264	C₂³×C₃	—	2	8	no	—
265	C₂³×C₃	—	4	16	no	—
266	C₂³×C₃	—	4	16	no	—
267	C₂³×C₃	—	8	8	no	—
268	C₂³×C₃	C₂×C₃×D₄	1	8	yes	—
269	C₃×Q₈	—	2	4	no	—
270	C₃×Q₈	—	2	8	no	—
271	C₃×Q₈	—	2	8	no	—
272	C₃×Q₈	—	4	16	no	—
273	C₃×Q₈	C₂×C₃×D₄	1	8	yes	complemented
274	C₃×D₄	—	2	8	no	—
275	C₃×D₄	—	2	4	no	—
276	C₃×D₄	—	2	8	no	—
277	C₃×D₄	—	4	16	no	—
278	C₃×D₄	—	4	16	no	—
279	C₃×D₄	—	4	8	no	—
280	C₃×D₄	—	8	4	no	—
281	C₃×D₄	C₃×SD₁₆	1	16	yes	direct product factor
282	C₃×D₄	C₂×C₃×D₄	1	8	yes	—
283	C₂×C₃×C₄	—	2	4	no	—
284	C₂×C₃×C₄	—	2	8	no	—
285	C₂×C₃×C₄	—	2	8	no	—
286	C₂×C₃×C₄	—	2	4	no	—
287	C₂×C₃×C₄	—	2	4	no	—
288	C₂×C₃×C₄	—	2	8	no	—
289	C₂×C₃×C₄	—	4	16	no	—
290	C₂×C₃×C₄	—	4	8	no	—
291	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
292	C₂×C₃×C₄	C₂×C₃×D₄	1	8	yes	—
293	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
294	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
295	C₃×C₈	—	2	8	no	—
296	C₃×C₈	—	2	4	no	—
297	C₃×C₈	C₂×C₃×D₄	1	8	yes	complemented
298	C₂×C₃²	—	2	4	no	—
299	C₂×C₃²	—	4	2	no	—
300	C₂×C₃²	—	8	2	no	—
301	C₂×C₃²	D₄²	1	1	yes	characteristic
302	C₂×C₃²	C₂²×SD₁₆	1	1	yes	characteristic
303	C₂×C₃²	#577	1	1	yes	characteristic
304	C₂⁴	—	2	2	no	—
305	C₂×Q₈	—	2	2	no	—
306	C₂×Q₈	—	2	4	no	—
307	C₂×Q₈	—	4	2	no	—
308	C₂×Q₈	C₂³×C₃²	1	2	yes	—
309	C₂×Q₈	C₂³×C₃²	1	1	yes	characteristic
310	C₂×D₄	—	2	4	no	—
311	C₂×D₄	—	2	2	no	—
312	C₂×D₄	—	2	2	no	—
313	C₂×D₄	—	2	1	no	—
314	C₂×D₄	—	2	1	no	—
315	C₂×D₄	—	4	2	no	—
316	C₂×D₄	—	4	4	no	—
317	C₂×D₄	C₃²×D₄	1	1	yes	characteristic
318	C₂×D₄	C₂³×C₃²	1	2	yes	—
319	C₂×D₄	C₂³×C₃²	1	1	yes	characteristic
320	C₂²×C₄	—	2	2	no	—
321	C₂²×C₄	—	2	1	no	—
322	C₂²×C₄	C₂³×C₃²	1	2	yes	—
323	SD₁₆	—	2	4	no	—
324	SD₁₆	—	2	4	no	—
325	SD₁₆	—	2	4	no	—
326	SD₁₆	—	4	2	no	—
327	SD₁₆	C₃²×D₄	1	4	yes	direct product factor
328	C₂×C₈	—	2	4	no	—
329	C₂×C₈	C₂³×C₃²	1	1	yes	characteristic
330	C₂×C₈	C₂³×C₃²	1	2	yes	—
331	C₂×C₈	C₂³×C₃²	1	1	yes	characteristic
332	C₄⋊C₄	—	2	1	no	—
333	C₄⋊C₄	—	2	1	no	—
334	C₄⋊C₄	—	2	1	no	—
335	C₄⋊C₄	—	2	2	no	—
336	C₄⋊C₄	C₃²×D₄	1	1	yes	characteristic
337	C₄⋊C₄	C₂³×C₃²	1	1	yes	characteristic
338	C₄⋊C₄	C₂³×C₃²	1	1	yes	characteristic
339	C₂²⋊C₄	—	2	2	no	—
340	C₂²⋊C₄	—	2	1	no	—
341	C₂²⋊C₄	—	2	2	no	—
342	C₂²⋊C₄	C₃²×D₄	1	2	yes	—
343	C₄²	—	2	1	no	—
344	C₄²	C₂³×C₃²	1	1	yes	characteristic
345	C₂²×C₃	—	2	8	no	—
346	C₂²×C₃	—	2	8	no	—
347	C₂²×C₃	—	2	8	no	—
348	C₂²×C₃	—	4	4	no	—
349	C₂²×C₃	—	4	4	no	—
350	C₂²×C₃	—	4	8	no	—
351	C₂²×C₃	—	4	8	no	—
352	C₂²×C₃	—	4	8	no	—
353	C₂²×C₃	—	8	32	no	—
354	C₂²×C₃	C₂×C₃×SD₁₆	1	16	yes	complemented
355	C₂²×C₃	C₂²×C₃×D₄	1	4	yes	—
356	C₃×C₄	—	2	4	no	—
357	C₃×C₄	—	2	8	no	—
358	C₃×C₄	—	2	8	no	—
359	C₃×C₄	—	4	4	no	—
360	C₃×C₄	—	4	4	no	—
361	C₃×C₄	—	4	8	no	—
362	C₃×C₄	C₂×C₃×SD₁₆	1	8	yes	complemented
363	C₃×C₄	C₂²×C₃×D₄	1	4	yes	—
364	C₃×C₄	C₃×H(5,𝔽₂)	1	4	yes	—
365	C₃²	D₄×SD₁₆	1	1	yes	characteristic, direct product factor, Sylow
366	C₂³	—	2	1	no	—
367	C₂³	—	2	2	no	—
368	C₂³	—	4	4	no	—
369	C₂³	—	4	4	no	—
370	C₂³	—	8	2	no	—
371	C₂³	C₂×C₃²×D₄	1	2	yes	—
372	Q₈	—	2	1	no	—
373	Q₈	—	2	2	no	—
374	Q₈	—	2	2	no	—
375	Q₈	—	4	4	no	—
376	Q₈	C₂×C₃²×D₄	1	2	yes	complemented
377	D₄	—	2	2	no	—
378	D₄	—	2	1	no	—
379	D₄	—	2	2	no	—
380	D₄	—	4	4	no	—
381	D₄	—	4	4	no	—
382	D₄	—	4	2	no	—
383	D₄	—	8	1	no	—
384	D₄	C₃²×SD₁₆	1	4	yes	direct product factor
385	D₄	C₂×C₃²×D₄	1	2	yes	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	4	4	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	C₂×C₃²×D₄	1	1	yes	characteristic
395	C₂×C₄	C₂×C₃²×D₄	1	2	yes	—
396	C₂×C₄	C₂×C₃²×D₄	1	1	yes	characteristic
397	C₂×C₄	C₂⁴×C₃²	1	1	yes	characteristic
398	C₈	—	2	2	no	—
399	C₈	—	2	1	no	—
400	C₈	C₂×C₃²×D₄	1	2	yes	complemented
401	C₂×C₃	—	2	16	no	—
402	C₂×C₃	—	4	8	no	—
403	C₂×C₃	—	8	8	no	—
404	C₂×C₃	C₃×D₄²	1	4	yes	—
405	C₂×C₃	C₂²×C₃×SD₁₆	1	4	yes	—
406	C₂×C₃	C₃×#577	1	4	yes	—
407	C₂²	—	2	2	no	—
408	C₂²	—	2	2	no	—
409	C₂²	—	2	2	no	—
410	C₂²	—	4	1	no	—
411	C₂²	—	4	1	no	—
412	C₂²	—	4	2	no	—
413	C₂²	—	4	2	no	—
414	C₂²	—	4	2	no	—
415	C₂²	—	8	8	no	—
416	C₂²	C₂×C₃²×SD₁₆	1	4	yes	complemented
417	C₂²	C₂²×C₃²×D₄	1	1	yes	characteristic
418	C₄	—	2	1	no	—
419	C₄	—	2	2	no	—
420	C₄	—	2	2	no	—
421	C₄	—	4	1	no	—
422	C₄	—	4	1	no	—
423	C₄	—	4	2	no	—
424	C₄	C₂×C₃²×SD₁₆	1	2	yes	complemented
425	C₄	C₂²×C₃²×D₄	1	1	yes	characteristic
426	C₄	C₃²×H(5,𝔽₂)	1	1	yes	characteristic
427	C₃	C₃×D₄×SD₁₆	1	4	yes	direct product factor
428	C₂	—	2	4	no	—
429	C₂	—	4	2	no	—
430	C₂	—	8	2	no	—
431	C₂	C₃²×D₄²	1	1	yes	characteristic
432	C₂	C₂²×C₃²×SD₁₆	1	1	yes	characteristic
433	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×D₄²	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃² ◁ C₃²×C₄×D₄ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃²×SD₁₆	C₂	semidirect
2. C₃²×D₄×Q₈	C₂	semidirect
4. C₃²×#492	C₂	semidirect
5. C₃²×#465	C₂	semidirect
6. C₃²×#461	C₂	semidirect
7. C₃²×#460	C₂	semidirect
8. C₃²×#450	C₂	semidirect
9. C₃²×#448	C₂	semidirect
10. C₃²×C₄×SD₁₆	C₂	semidirect
11. C₃²×C₈×D₄	C₂	semidirect
12. C₃×D₄×SD₁₆	C₃	direct (N × H)
13. C₂²×C₃²×Q₈	C₂²	semidirect
19. C₂×C₃²×SD₁₆	C₂²	semidirect
20. C₂×C₃²×SD₁₆	C₂²	semidirect
21. C₂×C₃²×SD₁₆	C₂²	semidirect
22. C₂²×C₃²×C₈	C₂²	semidirect
24. C₃²×C₄⋊Q₈	C₂²	semidirect
27. C₃²×C₂²⋊Q₈	C₂²	semidirect
31. C₃²×C₄×Q₈	C₂²	semidirect
35. C₃²×#106	C₂²	semidirect
36. C₃²×C₄⋊C₈	C₂²	semidirect
37. C₃²×#103	C₂²	semidirect
38. C₃²×#103	C₂²	semidirect
40. C₃²×#102	C₂²	semidirect
41. C₃²×C₂²⋊C₈	C₂²	semidirect
42. C₃²×C₄×C₈	C₂²	semidirect
43. C₂²×C₃×SD₁₆	C₂×C₃	semidirect
44. C₃×D₄×Q₈	C₂×C₃	semidirect
46. C₃×#492	C₂×C₃	semidirect
47. C₃×#465	C₂×C₃	semidirect
48. C₃×#461	C₂×C₃	semidirect
49. C₃×#460	C₂×C₃	semidirect
50. C₃×#450	C₂×C₃	semidirect
51. C₃×#448	C₂×C₃	semidirect
52. C₃×C₄×SD₁₆	C₂×C₃	semidirect
53. C₃×C₈×D₄	C₂×C₃	semidirect
77. C₃²×SD₁₆	D₄	direct (N × H)
95. D₄×SD₁₆	C₃²	direct (N × H)
96. C₂²×C₃×Q₈	C₂²×C₃	semidirect
102. C₂×C₃×SD₁₆	C₂²×C₃	semidirect
103. C₂×C₃×SD₁₆	C₂²×C₃	semidirect
104. C₂×C₃×SD₁₆	C₂²×C₃	semidirect
105. C₂²×C₃×C₈	C₂²×C₃	semidirect
107. C₃×C₄⋊Q₈	C₂²×C₃	semidirect
110. C₃×C₂²⋊Q₈	C₂²×C₃	semidirect
114. C₃×C₄×Q₈	C₂²×C₃	semidirect
118. C₃×#106	C₂²×C₃	semidirect
119. C₃×C₄⋊C₈	C₂²×C₃	semidirect
120. C₃×#103	C₂²×C₃	semidirect
121. C₃×#103	C₂²×C₃	semidirect
123. C₃×#102	C₂²×C₃	semidirect
124. C₃×C₂²⋊C₈	C₂²×C₃	semidirect
125. C₃×C₄×C₈	C₂²×C₃	semidirect
136. C₃²×Q₈	C₂×D₄	semidirect
144. C₃²×D₄	SD₁₆	direct (N × H)
160. C₃²×C₈	C₂×D₄	semidirect
161. C₂²×SD₁₆	C₂×C₃²	semidirect
162. D₄×Q₈	C₂×C₃²	semidirect
164. #492	C₂×C₃²	semidirect
165. #465	C₂×C₃²	semidirect
166. #461	C₂×C₃²	semidirect
167. #460	C₂×C₃²	semidirect
168. #450	C₂×C₃²	semidirect
169. #448	C₂×C₃²	semidirect
170. C₄×SD₁₆	C₂×C₃²	semidirect
171. C₈×D₄	C₂×C₃²	semidirect
195. C₃×SD₁₆	C₃×D₄	direct (N × H)
222. C₂²×C₃²	C₂×SD₁₆	semidirect
230. C₃²×C₄	C₂×SD₁₆	semidirect
233. C₂²×Q₈	C₂²×C₃²	semidirect
239. C₂×SD₁₆	C₂²×C₃²	semidirect
240. C₂×SD₁₆	C₂²×C₃²	semidirect
241. C₂×SD₁₆	C₂²×C₃²	semidirect
242. C₂²×C₈	C₂²×C₃²	semidirect
244. C₄⋊Q₈	C₂²×C₃²	semidirect
247. C₂²⋊Q₈	C₂²×C₃²	semidirect
251. C₄×Q₈	C₂²×C₃²	semidirect
255. #106	C₂²×C₃²	semidirect
256. C₄⋊C₈	C₂²×C₃²	semidirect
257. #103	C₂²×C₃²	semidirect
258. #103	C₂²×C₃²	semidirect
260. #102	C₂²×C₃²	semidirect
261. C₂²⋊C₈	C₂²×C₃²	semidirect
262. C₄×C₈	C₂²×C₃²	semidirect
273. C₃×Q₈	C₂×C₃×D₄	semidirect
281. C₃×D₄	C₃×SD₁₆	direct (N × H)
297. C₃×C₈	C₂×C₃×D₄	semidirect
327. SD₁₆	C₃²×D₄	direct (N × H)
354. C₂²×C₃	C₂×C₃×SD₁₆	semidirect
362. C₃×C₄	C₂×C₃×SD₁₆	semidirect
365. C₃²	D₄×SD₁₆	direct (N × H)
376. Q₈	C₂×C₃²×D₄	semidirect
384. D₄	C₃²×SD₁₆	direct (N × H)
400. C₈	C₂×C₃²×D₄	semidirect
416. C₂²	C₂×C₃²×SD₁₆	semidirect
424. C₄	C₂×C₃²×SD₁₆	semidirect
427. C₃	C₃×D₄×SD₁₆	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃²×SD₁₆	2
C₃²×D₄×Q₈	2
C₃²×D₄²	2
C₃²×#492	2
C₃²×#465	2
C₃²×#461	2
C₃²×#460	2
C₃²×#450	2
C₃²×#448	2
C₃²×C₄×SD₁₆	2
C₃²×C₈×D₄	2
C₃×D₄×SD₁₆	3

Subgroups — C32×D4×SD16 #11770330

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×D₄×SD₁₆ #11770330