Subgroups — C₃²×#3272 #11770321

Order 1152.

1638 conjugacy classes of subgroups.

The subgroup lattice has 447 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×AGL(1,ℤ/8)	C₂	1	2	yes	maximal, complemented
2	C₃²×#547	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×D₄²	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃²×#492	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃²×#468	C₂	1	2	yes	maximal, complemented
6	C₃²×#461	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃²×#459	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃²×#450	C₂	1	2	yes	maximal, complemented
9	C₃²×#449	C₂	1	2	yes	maximal, complemented
10	C₃²×C₄×D₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃²×#436	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#3272	C₃	1	4	yes	maximal, direct product factor
13	C₂×C₃²×#41	C₂²	1	2	yes	complemented
14	C₂²×C₃²×D₄	—	2	1	no	—
15	C₂²×C₃²×D₄	C₂²	1	2	yes	—
16	C₃²×AGL(1,ℤ/8)	—	2	8	no	—
17	C₂×C₃²×SD₁₆	C₂²	1	2	yes	—
18	C₂×C₃²×SD₁₆	C₂²	1	2	yes	complemented
19	C₂×C₃²×SD₁₆	C₂²	1	2	yes	complemented
20	C₂×C₃²×D₈	C₂²	1	1	yes	characteristic
21	C₂×C₃²×D₈	C₂²	1	2	yes	complemented
22	C₂×C₃²×M₁₆	C₂²	1	2	yes	complemented
23	C₃²×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
24	C₃²×#127	C₂²	1	1	yes	characteristic
25	C₃²×#123	—	2	2	no	—
26	C₃²×C₂²⋊Q₈	C₂²	1	2	yes	complemented
27	C₃²×#121	—	2	1	no	—
28	C₃²×#121	—	2	1	no	—
29	C₃²×#121	C₂²	1	2	yes	—
30	C₃²×#120	—	2	2	no	—
31	C₃²×C₄×D₄	C₂²	1	1	yes	characteristic
32	C₃²×C₄×D₄	C₂²	1	1	yes	characteristic
33	C₃²×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₃²×C₄⋊C₄	—	2	1	no	—
35	C₃²×#107	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×#102	C₂²	1	1	yes	characteristic
39	C₃²×#102	C₂²	1	2	yes	complemented
40	C₃²×#102	C₂²	1	1	yes	characteristic, complemented
41	C₃²×C₂²⋊C₈	C₂²	1	2	yes	complemented
42	C₃²×C₄×C₈	C₂²	1	1	yes	characteristic, complemented
43	C₂×C₃×AGL(1,ℤ/8)	C₂×C₃	1	8	yes	complemented
44	C₃×#547	C₂×C₃	1	4	yes	complemented
45	C₃×D₄²	C₂×C₃	1	4	yes	complemented
46	C₃×#492	C₂×C₃	1	4	yes	complemented
47	C₃×#468	C₂×C₃	1	8	yes	complemented
48	C₃×#461	C₂×C₃	1	4	yes	complemented
49	C₃×#459	C₂×C₃	1	4	yes	complemented
50	C₃×#450	C₂×C₃	1	8	yes	complemented
51	C₃×#449	C₂×C₃	1	8	yes	complemented
52	C₃×C₄×D₈	C₂×C₃	1	4	yes	complemented
53	C₃×#436	C₂×C₃	1	4	yes	complemented
54	C₂⁴×C₃²	—	2	2	no	—
55	C₃²×#41	—	2	4	no	—
56	C₃²×#41	—	4	2	no	—
57	C₂×C₃²×Q₈	C₂³	1	2	yes	—
58	C₂×C₃²×D₄	—	2	4	no	—
59	C₂×C₃²×D₄	—	2	2	no	—
60	C₂×C₃²×D₄	—	2	2	no	—
61	C₂×C₃²×D₄	—	2	1	no	—
62	C₂×C₃²×D₄	—	2	2	no	—
63	C₂×C₃²×D₄	—	2	1	no	—
64	C₂×C₃²×D₄	—	4	2	no	—
65	C₂×C₃²×D₄	—	4	4	no	—
66	C₂×C₃²×D₄	D₄	1	1	yes	characteristic
67	C₂×C₃²×D₄	C₂³	1	2	yes	—
68	C₂×C₃²×D₄	C₂³	1	1	yes	characteristic
69	C₂×C₃²×D₄	C₂³	1	1	yes	characteristic
70	C₂²×C₃²×C₄	—	2	1	no	—
71	C₂²×C₃²×C₄	—	2	2	no	—
72	C₂²×C₃²×C₄	—	2	1	no	—
73	C₂²×C₃²×C₄	C₂³	1	2	yes	—
74	C₃²×SD₁₆	—	2	4	no	—
75	C₃²×SD₁₆	—	2	4	no	—
76	C₃²×SD₁₆	—	4	2	no	—
77	C₃²×D₈	—	2	4	no	—
78	C₃²×D₈	D₄	1	4	yes	complemented
79	C₃²×M₁₆	—	2	4	no	—
80	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
81	C₂×C₃²×C₈	C₂³	1	2	yes	—
82	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
83	C₃²×C₄⋊C₄	—	2	1	no	—
84	C₃²×C₄⋊C₄	—	2	2	no	—
85	C₃²×C₄⋊C₄	—	2	1	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	1	no	—
92	C₃²×C₂²⋊C₄	—	2	2	no	—
93	C₃²×C₂²⋊C₄	D₄	1	2	yes	—
94	C₃²×C₄²	C₂³	1	1	yes	characteristic
95	#3272	C₃²	1	1	yes	characteristic, direct product factor, Sylow
96	C₂×C₃×#41	C₂²×C₃	1	8	yes	complemented
97	C₂²×C₃×D₄	—	2	4	no	—
98	C₂²×C₃×D₄	C₂²×C₃	1	8	yes	—
99	C₃×AGL(1,ℤ/8)	—	2	32	no	—
100	C₂×C₃×SD₁₆	C₂²×C₃	1	8	yes	—
101	C₂×C₃×SD₁₆	C₂²×C₃	1	8	yes	complemented
102	C₂×C₃×SD₁₆	C₂²×C₃	1	8	yes	complemented
103	C₂×C₃×D₈	C₂²×C₃	1	4	yes	—
104	C₂×C₃×D₈	C₂²×C₃	1	8	yes	complemented
105	C₂×C₃×M₁₆	C₂²×C₃	1	8	yes	complemented
106	C₃×C₄⋊Q₈	C₂²×C₃	1	4	yes	complemented
107	C₃×#127	C₂²×C₃	1	4	yes	—
108	C₃×#123	—	2	8	no	—
109	C₃×C₂²⋊Q₈	C₂²×C₃	1	8	yes	complemented
110	C₃×#121	—	2	4	no	—
111	C₃×#121	—	2	4	no	—
112	C₃×#121	C₂²×C₃	1	8	yes	—
113	C₃×#120	—	2	8	no	—
114	C₃×C₄×D₄	C₂²×C₃	1	4	yes	—
115	C₃×C₄×D₄	C₂²×C₃	1	4	yes	—
116	C₃×C₄×D₄	C₂²×C₃	1	4	yes	complemented
117	C₂×C₃×C₄⋊C₄	—	2	4	no	—
118	C₃×#107	C₂²×C₃	1	4	yes	complemented
119	C₃×C₄⋊C₈	C₂²×C₃	1	4	yes	complemented
120	C₃×#103	C₂²×C₃	1	8	yes	complemented
121	C₃×#102	C₂²×C₃	1	4	yes	—
122	C₃×#102	C₂²×C₃	1	4	yes	complemented
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	1	no	—
128	C₂³×C₃²	—	2	2	no	—
129	C₂³×C₃²	—	4	4	no	—
130	C₂³×C₃²	—	4	4	no	—
131	C₂³×C₃²	—	8	2	no	—
132	C₂³×C₃²	C₂×D₄	1	2	yes	—
133	C₃²×Q₈	—	2	2	no	—
134	C₃²×Q₈	—	2	2	no	—
135	C₃²×D₄	—	2	2	no	—
136	C₃²×D₄	—	2	2	no	—
137	C₃²×D₄	—	2	1	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	4	no	—
143	C₃²×D₄	—	4	2	no	—
144	C₃²×D₄	—	8	1	no	—
145	C₃²×D₄	C₂×D₄	1	2	yes	—
146	C₃²×D₄	C₂×D₄	1	2	yes	complemented
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	—	4	2	no	—
155	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
156	C₂×C₃²×C₄	C₂×D₄	1	2	yes	—
157	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
158	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
159	C₃²×C₈	—	2	2	no	—
160	C₃²×C₈	—	2	1	no	—
161	C₃²×C₈	C₂×D₄	1	2	yes	complemented
162	C₂×AGL(1,ℤ/8)	C₂×C₃²	1	2	yes	complemented
163	#547	C₂×C₃²	1	1	yes	characteristic, complemented
164	D₄²	C₂×C₃²	1	1	yes	characteristic, complemented
165	#492	C₂×C₃²	1	1	yes	characteristic, complemented
166	#468	C₂×C₃²	1	2	yes	complemented
167	#461	C₂×C₃²	1	1	yes	characteristic, complemented
168	#459	C₂×C₃²	1	1	yes	characteristic, complemented
169	#450	C₂×C₃²	1	2	yes	complemented
170	#449	C₂×C₃²	1	2	yes	complemented
171	C₄×D₈	C₂×C₃²	1	1	yes	characteristic, complemented
172	#436	C₂×C₃²	1	1	yes	characteristic, complemented
173	C₂⁴×C₃	—	2	8	no	—
174	C₃×#41	—	2	16	no	—
175	C₃×#41	—	4	8	no	—
176	C₂×C₃×Q₈	C₂³×C₃	1	8	yes	—
177	C₂×C₃×D₄	—	2	16	no	—
178	C₂×C₃×D₄	—	2	8	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	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
189	C₂²×C₃×C₄	—	2	4	no	—
190	C₂²×C₃×C₄	—	2	8	no	—
191	C₂²×C₃×C₄	—	2	4	no	—
192	C₂²×C₃×C₄	C₂³×C₃	1	8	yes	—
193	C₃×SD₁₆	—	2	16	no	—
194	C₃×SD₁₆	—	2	16	no	—
195	C₃×SD₁₆	—	4	8	no	—
196	C₃×D₈	—	2	16	no	—
197	C₃×D₈	C₃×D₄	1	16	yes	complemented
198	C₃×M₁₆	—	2	16	no	—
199	C₂×C₃×C₈	C₂³×C₃	1	4	yes	—
200	C₂×C₃×C₈	C₂³×C₃	1	8	yes	—
201	C₂×C₃×C₈	C₂³×C₃	1	4	yes	—
202	C₃×C₄⋊C₄	—	2	4	no	—
203	C₃×C₄⋊C₄	—	2	8	no	—
204	C₃×C₄⋊C₄	—	2	4	no	—
205	C₃×C₄⋊C₄	C₃×D₄	1	4	yes	—
206	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
207	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
208	C₃×C₂²⋊C₄	—	2	8	no	—
209	C₃×C₂²⋊C₄	—	2	4	no	—
210	C₃×C₂²⋊C₄	—	2	4	no	—
211	C₃×C₂²⋊C₄	—	2	8	no	—
212	C₃×C₂²⋊C₄	C₃×D₄	1	8	yes	—
213	C₃×C₄²	C₂³×C₃	1	4	yes	—
214	C₂²×C₃²	—	2	2	no	—
215	C₂²×C₃²	—	2	2	no	—
216	C₂²×C₃²	—	2	2	no	—
217	C₂²×C₃²	—	2	2	no	—
218	C₂²×C₃²	—	2	2	no	—
219	C₂²×C₃²	—	4	1	no	—
220	C₂²×C₃²	—	4	1	no	—
221	C₂²×C₃²	—	4	1	no	—
222	C₂²×C₃²	—	4	1	no	—
223	C₂²×C₃²	—	4	2	no	—
224	C₂²×C₃²	—	4	2	no	—
225	C₂²×C₃²	—	4	2	no	—
226	C₂²×C₃²	—	8	8	no	—
227	C₂²×C₃²	C₂²×D₄	1	1	yes	characteristic
228	C₃²×C₄	—	2	2	no	—
229	C₃²×C₄	—	2	1	no	—
230	C₃²×C₄	—	4	2	no	—
231	C₃²×C₄	—	4	1	no	—
232	C₃²×C₄	—	4	1	no	—
233	C₃²×C₄	AGL(1,ℤ/8)	1	2	yes	complemented
234	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
235	C₃²×C₄	H(5,𝔽₂)	1	1	yes	characteristic
236	C₂×#41	C₂²×C₃²	1	2	yes	complemented
237	C₂²×D₄	—	2	1	no	—
238	C₂²×D₄	C₂²×C₃²	1	2	yes	—
239	AGL(1,ℤ/8)	—	2	8	no	—
240	C₂×SD₁₆	C₂²×C₃²	1	2	yes	—
241	C₂×SD₁₆	C₂²×C₃²	1	2	yes	complemented
242	C₂×SD₁₆	C₂²×C₃²	1	2	yes	complemented
243	C₂×D₈	C₂²×C₃²	1	1	yes	characteristic
244	C₂×D₈	C₂²×C₃²	1	2	yes	complemented
245	C₂×M₁₆	C₂²×C₃²	1	2	yes	complemented
246	C₄⋊Q₈	C₂²×C₃²	1	1	yes	characteristic, complemented
247	#127	C₂²×C₃²	1	1	yes	characteristic
248	#123	—	2	2	no	—
249	C₂²⋊Q₈	C₂²×C₃²	1	2	yes	complemented
250	#121	—	2	1	no	—
251	#121	—	2	1	no	—
252	#121	C₂²×C₃²	1	2	yes	—
253	#120	—	2	2	no	—
254	C₄×D₄	C₂²×C₃²	1	1	yes	characteristic
255	C₄×D₄	C₂²×C₃²	1	1	yes	characteristic
256	C₄×D₄	C₂²×C₃²	1	1	yes	characteristic, complemented
257	C₂×C₄⋊C₄	—	2	1	no	—
258	#107	C₂²×C₃²	1	1	yes	characteristic, complemented
259	C₄⋊C₈	C₂²×C₃²	1	1	yes	characteristic, complemented
260	#103	C₂²×C₃²	1	2	yes	complemented
261	#102	C₂²×C₃²	1	1	yes	characteristic
262	#102	C₂²×C₃²	1	1	yes	characteristic, complemented
263	#102	C₂²×C₃²	1	2	yes	complemented
264	C₂²⋊C₈	C₂²×C₃²	1	2	yes	complemented
265	C₄×C₈	C₂²×C₃²	1	1	yes	characteristic, complemented
266	C₂³×C₃	—	2	4	no	—
267	C₂³×C₃	—	2	4	no	—
268	C₂³×C₃	—	2	8	no	—
269	C₂³×C₃	—	4	16	no	—
270	C₂³×C₃	—	4	16	no	—
271	C₂³×C₃	—	8	8	no	—
272	C₂³×C₃	C₂×C₃×D₄	1	8	yes	—
273	C₃×Q₈	—	2	8	no	—
274	C₃×Q₈	—	2	8	no	—
275	C₃×D₄	—	2	8	no	—
276	C₃×D₄	—	2	8	no	—
277	C₃×D₄	—	2	4	no	—
278	C₃×D₄	—	2	4	no	—
279	C₃×D₄	—	2	8	no	—
280	C₃×D₄	—	4	16	no	—
281	C₃×D₄	—	4	16	no	—
282	C₃×D₄	—	4	16	no	—
283	C₃×D₄	—	4	8	no	—
284	C₃×D₄	—	8	4	no	—
285	C₃×D₄	C₂×C₃×D₄	1	8	yes	—
286	C₃×D₄	C₂×C₃×D₄	1	8	yes	complemented
287	C₂×C₃×C₄	—	2	8	no	—
288	C₂×C₃×C₄	—	2	8	no	—
289	C₂×C₃×C₄	—	2	4	no	—
290	C₂×C₃×C₄	—	2	4	no	—
291	C₂×C₃×C₄	—	2	8	no	—
292	C₂×C₃×C₄	—	4	16	no	—
293	C₂×C₃×C₄	—	4	8	no	—
294	C₂×C₃×C₄	—	4	8	no	—
295	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
296	C₂×C₃×C₄	C₂×C₃×D₄	1	8	yes	—
297	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
298	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
299	C₃×C₈	—	2	8	no	—
300	C₃×C₈	—	2	4	no	—
301	C₃×C₈	C₂×C₃×D₄	1	8	yes	complemented
302	C₂×C₃²	—	4	2	no	—
303	C₂×C₃²	—	4	2	no	—
304	C₂×C₃²	—	4	2	no	—
305	C₂×C₃²	—	8	2	no	—
306	C₂×C₃²	D₄²	1	1	yes	characteristic
307	C₂×C₃²	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
308	C₂×C₃²	#577	1	1	yes	characteristic
309	C₂⁴	—	2	2	no	—
310	#41	—	2	4	no	—
311	#41	—	4	2	no	—
312	C₂×Q₈	C₂³×C₃²	1	2	yes	—
313	C₂×D₄	—	2	4	no	—
314	C₂×D₄	—	2	2	no	—
315	C₂×D₄	—	2	2	no	—
316	C₂×D₄	—	2	2	no	—
317	C₂×D₄	—	2	1	no	—
318	C₂×D₄	—	2	1	no	—
319	C₂×D₄	—	4	2	no	—
320	C₂×D₄	—	4	4	no	—
321	C₂×D₄	C₃²×D₄	1	1	yes	characteristic
322	C₂×D₄	C₂³×C₃²	1	2	yes	—
323	C₂×D₄	C₂³×C₃²	1	1	yes	characteristic
324	C₂×D₄	C₂³×C₃²	1	1	yes	characteristic
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	C₂³×C₃²	1	2	yes	—
329	SD₁₆	—	2	4	no	—
330	SD₁₆	—	2	4	no	—
331	SD₁₆	—	4	2	no	—
332	D₈	—	2	4	no	—
333	D₈	C₃²×D₄	1	4	yes	complemented
334	M₁₆	—	2	4	no	—
335	C₂×C₈	C₂³×C₃²	1	1	yes	characteristic
336	C₂×C₈	C₂³×C₃²	1	2	yes	—
337	C₂×C₈	C₂³×C₃²	1	1	yes	characteristic
338	C₄⋊C₄	—	2	1	no	—
339	C₄⋊C₄	—	2	2	no	—
340	C₄⋊C₄	—	2	1	no	—
341	C₄⋊C₄	C₃²×D₄	1	1	yes	characteristic
342	C₄⋊C₄	C₂³×C₃²	1	1	yes	characteristic
343	C₄⋊C₄	C₂³×C₃²	1	1	yes	characteristic
344	C₂²⋊C₄	—	2	2	no	—
345	C₂²⋊C₄	—	2	1	no	—
346	C₂²⋊C₄	—	2	1	no	—
347	C₂²⋊C₄	—	2	2	no	—
348	C₂²⋊C₄	C₃²×D₄	1	2	yes	—
349	C₄²	C₂³×C₃²	1	1	yes	characteristic
350	C₂²×C₃	—	2	8	no	—
351	C₂²×C₃	—	2	8	no	—
352	C₂²×C₃	—	2	8	no	—
353	C₂²×C₃	—	2	8	no	—
354	C₂²×C₃	—	2	8	no	—
355	C₂²×C₃	—	4	4	no	—
356	C₂²×C₃	—	4	4	no	—
357	C₂²×C₃	—	4	4	no	—
358	C₂²×C₃	—	4	4	no	—
359	C₂²×C₃	—	4	8	no	—
360	C₂²×C₃	—	4	8	no	—
361	C₂²×C₃	—	4	8	no	—
362	C₂²×C₃	—	8	32	no	—
363	C₂²×C₃	C₂²×C₃×D₄	1	4	yes	—
364	C₃×C₄	—	2	4	no	—
365	C₃×C₄	—	2	8	no	—
366	C₃×C₄	—	4	4	no	—
367	C₃×C₄	—	4	4	no	—
368	C₃×C₄	—	4	8	no	—
369	C₃×C₄	C₃×AGL(1,ℤ/8)	1	8	yes	complemented
370	C₃×C₄	C₂²×C₃×D₄	1	4	yes	—
371	C₃×C₄	C₃×H(5,𝔽₂)	1	4	yes	—
372	C₃²	#3272	1	1	yes	characteristic, direct product factor, Sylow
373	C₂³	—	2	1	no	—
374	C₂³	—	2	1	no	—
375	C₂³	—	2	2	no	—
376	C₂³	—	4	4	no	—
377	C₂³	—	4	4	no	—
378	C₂³	—	8	2	no	—
379	C₂³	C₂×C₃²×D₄	1	2	yes	—
380	Q₈	—	2	2	no	—
381	Q₈	—	2	2	no	—
382	D₄	—	2	2	no	—
383	D₄	—	2	1	no	—
384	D₄	—	2	1	no	—
385	D₄	—	2	2	no	—
386	D₄	—	2	2	no	—
387	D₄	—	4	4	no	—
388	D₄	—	4	4	no	—
389	D₄	—	4	4	no	—
390	D₄	—	4	2	no	—
391	D₄	—	8	1	no	—
392	D₄	C₂×C₃²×D₄	1	2	yes	—
393	D₄	C₂×C₃²×D₄	1	2	yes	complemented
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	4	4	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	C₂×C₃²×D₄	1	1	yes	characteristic
403	C₂×C₄	C₂×C₃²×D₄	1	2	yes	—
404	C₂×C₄	C₂×C₃²×D₄	1	1	yes	characteristic
405	C₂×C₄	C₂⁴×C₃²	1	1	yes	characteristic
406	C₈	—	2	2	no	—
407	C₈	—	2	1	no	—
408	C₈	C₂×C₃²×D₄	1	2	yes	complemented
409	C₂×C₃	—	4	8	no	—
410	C₂×C₃	—	4	8	no	—
411	C₂×C₃	—	4	8	no	—
412	C₂×C₃	—	8	8	no	—
413	C₂×C₃	C₃×D₄²	1	4	yes	—
414	C₂×C₃	C₂×C₃×AGL(1,ℤ/8)	1	4	yes	—
415	C₂×C₃	C₃×#577	1	4	yes	—
416	C₂²	—	2	2	no	—
417	C₂²	—	2	2	no	—
418	C₂²	—	2	2	no	—
419	C₂²	—	2	2	no	—
420	C₂²	—	2	2	no	—
421	C₂²	—	4	1	no	—
422	C₂²	—	4	1	no	—
423	C₂²	—	4	1	no	—
424	C₂²	—	4	1	no	—
425	C₂²	—	4	2	no	—
426	C₂²	—	4	2	no	—
427	C₂²	—	4	2	no	—
428	C₂²	—	8	8	no	—
429	C₂²	C₂²×C₃²×D₄	1	1	yes	characteristic
430	C₄	—	2	1	no	—
431	C₄	—	2	2	no	—
432	C₄	—	4	1	no	—
433	C₄	—	4	1	no	—
434	C₄	—	4	2	no	—
435	C₄	C₃²×AGL(1,ℤ/8)	1	2	yes	complemented
436	C₄	C₂²×C₃²×D₄	1	1	yes	characteristic
437	C₄	C₃²×H(5,𝔽₂)	1	1	yes	characteristic
438	C₃	C₃×#3272	1	4	yes	direct product factor
439	C₂	—	4	2	no	—
440	C₂	—	4	2	no	—
441	C₂	—	4	2	no	—
442	C₂	—	8	2	no	—
443	C₂	C₃²×D₄²	1	1	yes	characteristic
444	C₂	C₂×C₃²×AGL(1,ℤ/8)	1	1	yes	characteristic
445	C₂	C₃²×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃²	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃²
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. C₂×C₃²×AGL(1,ℤ/8)	C₂	semidirect
2. C₃²×#547	C₂	semidirect
3. C₃²×D₄²	C₂	semidirect
4. C₃²×#492	C₂	semidirect
5. C₃²×#468	C₂	semidirect
6. C₃²×#461	C₂	semidirect
7. C₃²×#459	C₂	semidirect
8. C₃²×#450	C₂	semidirect
9. C₃²×#449	C₂	semidirect
10. C₃²×C₄×D₈	C₂	semidirect
11. C₃²×#436	C₂	semidirect
12. C₃×#3272	C₃	direct (N × H)
13. C₂×C₃²×#41	C₂²	semidirect
18. C₂×C₃²×SD₁₆	C₂²	semidirect
19. C₂×C₃²×SD₁₆	C₂²	semidirect
21. C₂×C₃²×D₈	C₂²	semidirect
22. C₂×C₃²×M₁₆	C₂²	semidirect
23. C₃²×C₄⋊Q₈	C₂²	semidirect
26. C₃²×C₂²⋊Q₈	C₂²	semidirect
33. C₃²×C₄×D₄	C₂²	semidirect
35. C₃²×#107	C₂²	semidirect
36. C₃²×C₄⋊C₈	C₂²	semidirect
37. C₃²×#103	C₂²	semidirect
39. C₃²×#102	C₂²	semidirect
40. C₃²×#102	C₂²	semidirect
41. C₃²×C₂²⋊C₈	C₂²	semidirect
42. C₃²×C₄×C₈	C₂²	semidirect
43. C₂×C₃×AGL(1,ℤ/8)	C₂×C₃	semidirect
44. C₃×#547	C₂×C₃	semidirect
45. C₃×D₄²	C₂×C₃	semidirect
46. C₃×#492	C₂×C₃	semidirect
47. C₃×#468	C₂×C₃	semidirect
48. C₃×#461	C₂×C₃	semidirect
49. C₃×#459	C₂×C₃	semidirect
50. C₃×#450	C₂×C₃	semidirect
51. C₃×#449	C₂×C₃	semidirect
52. C₃×C₄×D₈	C₂×C₃	semidirect
53. C₃×#436	C₂×C₃	semidirect
78. C₃²×D₈	D₄	semidirect
95. #3272	C₃²	direct (N × H)
96. C₂×C₃×#41	C₂²×C₃	semidirect
101. C₂×C₃×SD₁₆	C₂²×C₃	semidirect
102. C₂×C₃×SD₁₆	C₂²×C₃	semidirect
104. C₂×C₃×D₈	C₂²×C₃	semidirect
105. C₂×C₃×M₁₆	C₂²×C₃	semidirect
106. C₃×C₄⋊Q₈	C₂²×C₃	semidirect
109. C₃×C₂²⋊Q₈	C₂²×C₃	semidirect
116. C₃×C₄×D₄	C₂²×C₃	semidirect
118. C₃×#107	C₂²×C₃	semidirect
119. C₃×C₄⋊C₈	C₂²×C₃	semidirect
120. C₃×#103	C₂²×C₃	semidirect
122. C₃×#102	C₂²×C₃	semidirect
123. C₃×#102	C₂²×C₃	semidirect
124. C₃×C₂²⋊C₈	C₂²×C₃	semidirect
125. C₃×C₄×C₈	C₂²×C₃	semidirect
146. C₃²×D₄	C₂×D₄	semidirect
161. C₃²×C₈	C₂×D₄	semidirect
162. C₂×AGL(1,ℤ/8)	C₂×C₃²	semidirect
163. #547	C₂×C₃²	semidirect
164. D₄²	C₂×C₃²	semidirect
165. #492	C₂×C₃²	semidirect
166. #468	C₂×C₃²	semidirect
167. #461	C₂×C₃²	semidirect
168. #459	C₂×C₃²	semidirect
169. #450	C₂×C₃²	semidirect
170. #449	C₂×C₃²	semidirect
171. C₄×D₈	C₂×C₃²	semidirect
172. #436	C₂×C₃²	semidirect
197. C₃×D₈	C₃×D₄	semidirect
233. C₃²×C₄	AGL(1,ℤ/8)	semidirect
236. C₂×#41	C₂²×C₃²	semidirect
241. C₂×SD₁₆	C₂²×C₃²	semidirect
242. C₂×SD₁₆	C₂²×C₃²	semidirect
244. C₂×D₈	C₂²×C₃²	semidirect
245. C₂×M₁₆	C₂²×C₃²	semidirect
246. C₄⋊Q₈	C₂²×C₃²	semidirect
249. C₂²⋊Q₈	C₂²×C₃²	semidirect
256. C₄×D₄	C₂²×C₃²	semidirect
258. #107	C₂²×C₃²	semidirect
259. C₄⋊C₈	C₂²×C₃²	semidirect
260. #103	C₂²×C₃²	semidirect
262. #102	C₂²×C₃²	semidirect
263. #102	C₂²×C₃²	semidirect
264. C₂²⋊C₈	C₂²×C₃²	semidirect
265. C₄×C₈	C₂²×C₃²	semidirect
286. C₃×D₄	C₂×C₃×D₄	semidirect
301. C₃×C₈	C₂×C₃×D₄	semidirect
333. D₈	C₃²×D₄	semidirect
369. C₃×C₄	C₃×AGL(1,ℤ/8)	semidirect
372. C₃²	#3272	direct (N × H)
393. D₄	C₂×C₃²×D₄	semidirect
408. C₈	C₂×C₃²×D₄	semidirect
435. C₄	C₃²×AGL(1,ℤ/8)	semidirect
438. C₃	C₃×#3272	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×AGL(1,ℤ/8)	2
C₃²×#547	2
C₃²×D₄²	2
C₃²×#492	2
C₃²×#468	2
C₃²×#461	2
C₃²×#459	2
C₃²×#450	2
C₃²×#449	2
C₃²×C₄×D₈	2
C₃²×#436	2
C₃×#3272	3

Subgroups — C32×#3272 #11770321

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#3272 #11770321