Subgroups — C₃²×#3280 #11770329

Order 1152.

1578 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×#135	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃²×D₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×#546	C₂	1	2	yes	maximal, complemented
4	C₃²×#495	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃²×#467	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃²×#466	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃²×#463	C₂	1	2	yes	maximal, 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×C₈×D₄	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#3280	C₃	1	4	yes	maximal, direct product factor
13	C₂×C₃²×#41	C₂²	1	2	yes	complemented
14	C₂²×C₃²×D₄	C₂²	1	2	yes	—
15	C₃²×#135	—	2	4	no	—
16	C₂×C₃²×Q₁₆	C₂²	1	1	yes	characteristic, complemented
17	C₂×C₃²×SD₁₆	C₂²	1	2	yes	complemented
18	C₂×C₃²×SD₁₆	C₂²	1	2	yes	complemented
19	C₂×C₃²×D₈	—	2	4	no	—
20	C₂×C₃²×D₈	C₂²	1	2	yes	—
21	C₂×C₃²×D₈	C₂²	1	1	yes	characteristic
22	C₂×C₃²×D₈	C₂²	1	1	yes	characteristic
23	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
24	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic, complemented
25	C₃²×#124	C₂²	1	2	yes	complemented
26	C₃²×#123	—	2	2	no	—
27	C₃²×C₂²⋊Q₈	C₂²	1	2	yes	—
28	C₃²×#121	—	2	2	no	—
29	C₃²×#121	C₂²	1	2	yes	complemented
30	C₃²×#120	—	2	2	no	—
31	C₃²×C₄×D₄	C₂²	1	1	yes	characteristic
32	C₃²×C₄×D₄	C₂²	1	2	yes	complemented
33	C₂×C₃²×C₂²⋊C₄	—	2	2	no	—
34	C₃²×#107	C₂²	1	1	yes	characteristic, complemented
35	C₃²×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
36	C₃²×#103	C₂²	1	2	yes	complemented
37	C₃²×#102	C₂²	1	2	yes	complemented
38	C₃²×#102	C₂²	1	2	yes	complemented
39	C₃²×C₂²⋊C₈	C₂²	1	1	yes	characteristic
40	C₃²×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
41	C₃²×C₄×C₈	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₃×#135	C₂×C₃	1	4	yes	complemented
43	C₂²×C₃×D₈	C₂×C₃	1	4	yes	complemented
44	C₃×#546	C₂×C₃	1	8	yes	complemented
45	C₃×#495	C₂×C₃	1	4	yes	complemented
46	C₃×#467	C₂×C₃	1	4	yes	complemented
47	C₃×#466	C₂×C₃	1	4	yes	complemented
48	C₃×#463	C₂×C₃	1	8	yes	complemented
49	C₃×#450	C₂×C₃	1	8	yes	complemented
50	C₃×#449	C₂×C₃	1	8	yes	complemented
51	C₃×C₄×D₈	C₂×C₃	1	4	yes	complemented
52	C₃×C₈×D₄	C₂×C₃	1	4	yes	complemented
53	C₂⁴×C₃²	—	2	2	no	—
54	C₃²×#41	—	2	4	no	—
55	C₃²×#41	—	4	2	no	—
56	C₂×C₃²×Q₈	C₂³	1	2	yes	—
57	C₂×C₃²×D₄	—	2	4	no	—
58	C₂×C₃²×D₄	—	2	2	no	—
59	C₂×C₃²×D₄	—	2	2	no	—
60	C₂×C₃²×D₄	—	2	2	no	—
61	C₂×C₃²×D₄	—	4	2	no	—
62	C₂×C₃²×D₄	D₄	1	1	yes	characteristic
63	C₂×C₃²×D₄	C₂³	1	2	yes	—
64	C₂×C₃²×D₄	C₂³	1	2	yes	—
65	C₂²×C₃²×C₄	—	2	2	no	—
66	C₂²×C₃²×C₄	—	2	2	no	—
67	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
68	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
69	C₃²×Q₁₆	—	2	2	no	—
70	C₃²×SD₁₆	—	2	4	no	—
71	C₃²×SD₁₆	—	4	2	no	—
72	C₃²×D₈	—	2	4	no	—
73	C₃²×D₈	—	2	2	no	—
74	C₃²×D₈	D₄	1	4	yes	complemented
75	C₂×C₃²×C₈	—	2	2	no	—
76	C₂×C₃²×C₈	—	2	2	no	—
77	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
78	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
79	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
80	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
81	C₃²×C₄⋊C₄	—	2	2	no	—
82	C₃²×C₄⋊C₄	D₄	1	1	yes	characteristic
83	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
84	C₃²×C₂²⋊C₄	—	2	2	no	—
85	C₃²×C₂²⋊C₄	—	2	2	no	—
86	C₃²×C₂²⋊C₄	—	2	2	no	—
87	C₃²×C₂²⋊C₄	—	2	2	no	—
88	C₃²×C₂²⋊C₄	—	2	2	no	—
89	C₃²×C₂²⋊C₄	D₄	1	1	yes	characteristic
90	C₃²×C₂²⋊C₄	D₄	1	1	yes	characteristic
91	C₃²×C₄²	C₂³	1	1	yes	characteristic
92	#3280	C₃²	1	1	yes	characteristic, direct product factor, Sylow
93	C₂×C₃×#41	C₂²×C₃	1	8	yes	complemented
94	C₂²×C₃×D₄	C₂²×C₃	1	8	yes	—
95	C₃×#135	—	2	16	no	—
96	C₂×C₃×Q₁₆	C₂²×C₃	1	4	yes	complemented
97	C₂×C₃×SD₁₆	C₂²×C₃	1	8	yes	complemented
98	C₂×C₃×SD₁₆	C₂²×C₃	1	8	yes	complemented
99	C₂×C₃×D₈	—	2	16	no	—
100	C₂×C₃×D₈	C₂²×C₃	1	8	yes	—
101	C₂×C₃×D₈	C₂²×C₃	1	4	yes	—
102	C₂×C₃×D₈	C₂²×C₃	1	4	yes	—
103	C₂²×C₃×C₈	C₂²×C₃	1	4	yes	—
104	C₂²×C₃×C₈	C₂²×C₃	1	4	yes	complemented
105	C₃×#124	C₂²×C₃	1	8	yes	complemented
106	C₃×#123	—	2	8	no	—
107	C₃×C₂²⋊Q₈	C₂²×C₃	1	8	yes	—
108	C₃×#121	—	2	8	no	—
109	C₃×#121	C₂²×C₃	1	8	yes	complemented
110	C₃×#120	—	2	8	no	—
111	C₃×C₄×D₄	C₂²×C₃	1	4	yes	—
112	C₃×C₄×D₄	C₂²×C₃	1	8	yes	complemented
113	C₂×C₃×C₂²⋊C₄	—	2	8	no	—
114	C₃×#107	C₂²×C₃	1	4	yes	complemented
115	C₃×C₄⋊C₈	C₂²×C₃	1	4	yes	complemented
116	C₃×#103	C₂²×C₃	1	8	yes	complemented
117	C₃×#102	C₂²×C₃	1	8	yes	complemented
118	C₃×#102	C₂²×C₃	1	8	yes	complemented
119	C₃×C₂²⋊C₈	C₂²×C₃	1	4	yes	—
120	C₃×C₂²⋊C₈	C₂²×C₃	1	4	yes	complemented
121	C₃×C₄×C₈	C₂²×C₃	1	4	yes	complemented
122	C₂³×C₃²	—	2	2	no	—
123	C₂³×C₃²	—	2	2	no	—
124	C₂³×C₃²	—	4	4	no	—
125	C₂³×C₃²	—	4	4	no	—
126	C₂³×C₃²	—	8	2	no	—
127	C₂³×C₃²	C₂×D₄	1	1	yes	characteristic
128	C₂³×C₃²	C₂×D₄	1	1	yes	characteristic
129	C₃²×Q₈	—	2	2	no	—
130	C₃²×Q₈	—	2	2	no	—
131	C₃²×D₄	—	2	2	no	—
132	C₃²×D₄	—	2	2	no	—
133	C₃²×D₄	—	2	2	no	—
134	C₃²×D₄	—	2	2	no	—
135	C₃²×D₄	—	4	4	no	—
136	C₃²×D₄	—	4	4	no	—
137	C₃²×D₄	—	8	2	no	—
138	C₃²×D₄	C₂×D₄	1	4	yes	—
139	C₂×C₃²×C₄	—	2	1	no	—
140	C₂×C₃²×C₄	—	2	1	no	—
141	C₂×C₃²×C₄	—	2	1	no	—
142	C₂×C₃²×C₄	—	2	1	no	—
143	C₂×C₃²×C₄	—	2	2	no	—
144	C₂×C₃²×C₄	—	2	2	no	—
145	C₂×C₃²×C₄	—	4	4	no	—
146	C₂×C₃²×C₄	—	8	2	no	—
147	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
148	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
149	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
150	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
151	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
152	C₃²×C₈	—	2	1	no	—
153	C₃²×C₈	—	2	1	no	—
154	C₃²×C₈	—	2	1	no	—
155	C₃²×C₈	C₂×D₄	1	2	yes	—
156	C₂×#135	C₂×C₃²	1	1	yes	characteristic, complemented
157	C₂²×D₈	C₂×C₃²	1	1	yes	characteristic, complemented
158	#546	C₂×C₃²	1	2	yes	complemented
159	#495	C₂×C₃²	1	1	yes	characteristic, complemented
160	#467	C₂×C₃²	1	1	yes	characteristic, complemented
161	#466	C₂×C₃²	1	1	yes	characteristic, complemented
162	#463	C₂×C₃²	1	2	yes	complemented
163	#450	C₂×C₃²	1	2	yes	complemented
164	#449	C₂×C₃²	1	2	yes	complemented
165	C₄×D₈	C₂×C₃²	1	1	yes	characteristic, complemented
166	C₈×D₄	C₂×C₃²	1	1	yes	characteristic, complemented
167	C₂⁴×C₃	—	2	8	no	—
168	C₃×#41	—	2	16	no	—
169	C₃×#41	—	4	8	no	—
170	C₂×C₃×Q₈	C₂³×C₃	1	8	yes	—
171	C₂×C₃×D₄	—	2	16	no	—
172	C₂×C₃×D₄	—	2	8	no	—
173	C₂×C₃×D₄	—	2	8	no	—
174	C₂×C₃×D₄	—	2	8	no	—
175	C₂×C₃×D₄	—	4	8	no	—
176	C₂×C₃×D₄	C₃×D₄	1	4	yes	—
177	C₂×C₃×D₄	C₂³×C₃	1	8	yes	—
178	C₂×C₃×D₄	C₂³×C₃	1	8	yes	—
179	C₂²×C₃×C₄	—	2	8	no	—
180	C₂²×C₃×C₄	—	2	8	no	—
181	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
182	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
183	C₃×Q₁₆	—	2	8	no	—
184	C₃×SD₁₆	—	2	16	no	—
185	C₃×SD₁₆	—	4	8	no	—
186	C₃×D₈	—	2	16	no	—
187	C₃×D₈	—	2	8	no	—
188	C₃×D₈	C₃×D₄	1	16	yes	complemented
189	C₂×C₃×C₈	—	2	8	no	—
190	C₂×C₃×C₈	—	2	8	no	—
191	C₂×C₃×C₈	C₂³×C₃	1	4	yes	—
192	C₂×C₃×C₈	C₂³×C₃	1	4	yes	—
193	C₂×C₃×C₈	C₂³×C₃	1	4	yes	—
194	C₂×C₃×C₈	C₂³×C₃	1	4	yes	—
195	C₃×C₄⋊C₄	—	2	8	no	—
196	C₃×C₄⋊C₄	C₃×D₄	1	4	yes	—
197	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
198	C₃×C₂²⋊C₄	—	2	8	no	—
199	C₃×C₂²⋊C₄	—	2	8	no	—
200	C₃×C₂²⋊C₄	—	2	8	no	—
201	C₃×C₂²⋊C₄	—	2	8	no	—
202	C₃×C₂²⋊C₄	—	2	8	no	—
203	C₃×C₂²⋊C₄	C₃×D₄	1	4	yes	—
204	C₃×C₂²⋊C₄	C₃×D₄	1	4	yes	—
205	C₃×C₄²	C₂³×C₃	1	4	yes	—
206	C₂²×C₃²	—	2	1	no	—
207	C₂²×C₃²	—	2	1	no	—
208	C₂²×C₃²	—	2	1	no	—
209	C₂²×C₃²	—	2	4	no	—
210	C₂²×C₃²	—	2	1	no	—
211	C₂²×C₃²	—	2	1	no	—
212	C₂²×C₃²	—	4	2	no	—
213	C₂²×C₃²	—	4	2	no	—
214	C₂²×C₃²	—	4	2	no	—
215	C₂²×C₃²	—	4	2	no	—
216	C₂²×C₃²	—	4	2	no	—
217	C₂²×C₃²	—	8	8	no	—
218	C₂²×C₃²	#135	1	2	yes	complemented
219	C₂²×C₃²	C₂²×D₄	1	1	yes	characteristic
220	C₃²×C₄	—	2	1	no	—
221	C₃²×C₄	—	2	1	no	—
222	C₃²×C₄	—	2	1	no	—
223	C₃²×C₄	—	2	1	no	—
224	C₃²×C₄	—	4	2	no	—
225	C₃²×C₄	—	4	2	no	—
226	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
227	C₃²×C₄	H(5,𝔽₂)	1	1	yes	characteristic
228	C₂×#41	C₂²×C₃²	1	2	yes	complemented
229	C₂²×D₄	C₂²×C₃²	1	2	yes	—
230	#135	—	2	4	no	—
231	C₂×Q₁₆	C₂²×C₃²	1	1	yes	characteristic, complemented
232	C₂×SD₁₆	C₂²×C₃²	1	2	yes	complemented
233	C₂×SD₁₆	C₂²×C₃²	1	2	yes	complemented
234	C₂×D₈	—	2	4	no	—
235	C₂×D₈	C₂²×C₃²	1	2	yes	—
236	C₂×D₈	C₂²×C₃²	1	1	yes	characteristic
237	C₂×D₈	C₂²×C₃²	1	1	yes	characteristic
238	C₂²×C₈	C₂²×C₃²	1	1	yes	characteristic
239	C₂²×C₈	C₂²×C₃²	1	1	yes	characteristic, complemented
240	#124	C₂²×C₃²	1	2	yes	complemented
241	#123	—	2	2	no	—
242	C₂²⋊Q₈	C₂²×C₃²	1	2	yes	—
243	#121	—	2	2	no	—
244	#121	C₂²×C₃²	1	2	yes	complemented
245	#120	—	2	2	no	—
246	C₄×D₄	C₂²×C₃²	1	1	yes	characteristic
247	C₄×D₄	C₂²×C₃²	1	2	yes	complemented
248	C₂×C₂²⋊C₄	—	2	2	no	—
249	#107	C₂²×C₃²	1	1	yes	characteristic, complemented
250	C₄⋊C₈	C₂²×C₃²	1	1	yes	characteristic, complemented
251	#103	C₂²×C₃²	1	2	yes	complemented
252	#102	C₂²×C₃²	1	2	yes	complemented
253	#102	C₂²×C₃²	1	2	yes	complemented
254	C₂²⋊C₈	C₂²×C₃²	1	1	yes	characteristic
255	C₂²⋊C₈	C₂²×C₃²	1	1	yes	characteristic, complemented
256	C₄×C₈	C₂²×C₃²	1	1	yes	characteristic, complemented
257	C₂³×C₃	—	2	8	no	—
258	C₂³×C₃	—	2	8	no	—
259	C₂³×C₃	—	4	16	no	—
260	C₂³×C₃	—	4	16	no	—
261	C₂³×C₃	—	8	8	no	—
262	C₂³×C₃	C₂×C₃×D₄	1	4	yes	—
263	C₂³×C₃	C₂×C₃×D₄	1	4	yes	—
264	C₃×Q₈	—	2	8	no	—
265	C₃×Q₈	—	2	8	no	—
266	C₃×D₄	—	2	8	no	—
267	C₃×D₄	—	2	8	no	—
268	C₃×D₄	—	2	8	no	—
269	C₃×D₄	—	2	8	no	—
270	C₃×D₄	—	4	16	no	—
271	C₃×D₄	—	4	16	no	—
272	C₃×D₄	—	8	8	no	—
273	C₃×D₄	C₂×C₃×D₄	1	16	yes	—
274	C₂×C₃×C₄	—	2	4	no	—
275	C₂×C₃×C₄	—	2	4	no	—
276	C₂×C₃×C₄	—	2	4	no	—
277	C₂×C₃×C₄	—	2	4	no	—
278	C₂×C₃×C₄	—	2	8	no	—
279	C₂×C₃×C₄	—	2	8	no	—
280	C₂×C₃×C₄	—	4	16	no	—
281	C₂×C₃×C₄	—	8	8	no	—
282	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
283	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
284	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
285	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
286	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
287	C₃×C₈	—	2	4	no	—
288	C₃×C₈	—	2	4	no	—
289	C₃×C₈	—	2	4	no	—
290	C₃×C₈	C₂×C₃×D₄	1	8	yes	—
291	C₂×C₃²	—	2	2	no	—
292	C₂×C₃²	—	4	1	no	—
293	C₂×C₃²	—	4	4	no	—
294	C₂×C₃²	—	8	2	no	—
295	C₂×C₃²	D₄²	1	1	yes	characteristic
296	C₂×C₃²	C₂×#135	1	1	yes	characteristic
297	C₂×C₃²	#576	1	1	yes	characteristic
298	C₂⁴	—	2	2	no	—
299	#41	—	2	4	no	—
300	#41	—	4	2	no	—
301	C₂×Q₈	C₂³×C₃²	1	2	yes	—
302	C₂×D₄	—	2	4	no	—
303	C₂×D₄	—	2	2	no	—
304	C₂×D₄	—	2	2	no	—
305	C₂×D₄	—	2	2	no	—
306	C₂×D₄	—	4	2	no	—
307	C₂×D₄	C₃²×D₄	1	1	yes	characteristic
308	C₂×D₄	C₂³×C₃²	1	2	yes	—
309	C₂×D₄	C₂³×C₃²	1	2	yes	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	C₂³×C₃²	1	1	yes	characteristic
313	C₂²×C₄	C₂³×C₃²	1	1	yes	characteristic
314	Q₁₆	—	2	2	no	—
315	SD₁₆	—	2	4	no	—
316	SD₁₆	—	4	2	no	—
317	D₈	—	2	4	no	—
318	D₈	—	2	2	no	—
319	D₈	C₃²×D₄	1	4	yes	complemented
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	C₂³×C₃²	1	1	yes	characteristic
323	C₂×C₈	C₂³×C₃²	1	1	yes	characteristic
324	C₂×C₈	C₂³×C₃²	1	1	yes	characteristic
325	C₂×C₈	C₂³×C₃²	1	1	yes	characteristic
326	C₄⋊C₄	—	2	2	no	—
327	C₄⋊C₄	C₃²×D₄	1	1	yes	characteristic
328	C₄⋊C₄	C₂³×C₃²	1	2	yes	—
329	C₂²⋊C₄	—	2	2	no	—
330	C₂²⋊C₄	—	2	2	no	—
331	C₂²⋊C₄	—	2	2	no	—
332	C₂²⋊C₄	—	2	2	no	—
333	C₂²⋊C₄	—	2	2	no	—
334	C₂²⋊C₄	C₃²×D₄	1	1	yes	characteristic
335	C₂²⋊C₄	C₃²×D₄	1	1	yes	characteristic
336	C₄²	C₂³×C₃²	1	1	yes	characteristic
337	C₂²×C₃	—	2	4	no	—
338	C₂²×C₃	—	2	4	no	—
339	C₂²×C₃	—	2	4	no	—
340	C₂²×C₃	—	2	4	no	—
341	C₂²×C₃	—	2	4	no	—
342	C₂²×C₃	—	2	16	no	—
343	C₂²×C₃	—	4	8	no	—
344	C₂²×C₃	—	4	8	no	—
345	C₂²×C₃	—	4	8	no	—
346	C₂²×C₃	—	4	8	no	—
347	C₂²×C₃	—	4	8	no	—
348	C₂²×C₃	—	8	32	no	—
349	C₂²×C₃	C₃×#135	1	8	yes	complemented
350	C₂²×C₃	C₂²×C₃×D₄	1	4	yes	—
351	C₃×C₄	—	2	4	no	—
352	C₃×C₄	—	2	4	no	—
353	C₃×C₄	—	2	4	no	—
354	C₃×C₄	—	2	4	no	—
355	C₃×C₄	—	4	8	no	—
356	C₃×C₄	—	4	8	no	—
357	C₃×C₄	C₂²×C₃×D₄	1	4	yes	—
358	C₃×C₄	C₃×H(5,𝔽₂)	1	4	yes	—
359	C₃²	#3280	1	1	yes	characteristic, direct product factor, Sylow
360	C₂³	—	2	2	no	—
361	C₂³	—	2	2	no	—
362	C₂³	—	4	4	no	—
363	C₂³	—	4	4	no	—
364	C₂³	—	8	2	no	—
365	C₂³	C₂×C₃²×D₄	1	1	yes	characteristic
366	C₂³	C₂×C₃²×D₄	1	1	yes	characteristic
367	Q₈	—	2	2	no	—
368	Q₈	—	2	2	no	—
369	D₄	—	2	2	no	—
370	D₄	—	2	2	no	—
371	D₄	—	2	2	no	—
372	D₄	—	2	2	no	—
373	D₄	—	4	4	no	—
374	D₄	—	4	4	no	—
375	D₄	—	8	2	no	—
376	D₄	C₂×C₃²×D₄	1	4	yes	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	4	4	no	—
384	C₂×C₄	—	8	2	no	—
385	C₂×C₄	C₂×C₃²×D₄	1	1	yes	characteristic
386	C₂×C₄	C₂×C₃²×D₄	1	1	yes	characteristic
387	C₂×C₄	C₂×C₃²×D₄	1	1	yes	characteristic
388	C₂×C₄	C₂×C₃²×D₄	1	1	yes	characteristic
389	C₂×C₄	C₂⁴×C₃²	1	1	yes	characteristic
390	C₈	—	2	1	no	—
391	C₈	—	2	1	no	—
392	C₈	—	2	1	no	—
393	C₈	C₂×C₃²×D₄	1	2	yes	—
394	C₂×C₃	—	2	8	no	—
395	C₂×C₃	—	4	4	no	—
396	C₂×C₃	—	4	16	no	—
397	C₂×C₃	—	8	8	no	—
398	C₂×C₃	C₃×D₄²	1	4	yes	—
399	C₂×C₃	C₂×C₃×#135	1	4	yes	—
400	C₂×C₃	C₃×#576	1	4	yes	—
401	C₂²	—	2	1	no	—
402	C₂²	—	2	1	no	—
403	C₂²	—	2	1	no	—
404	C₂²	—	2	1	no	—
405	C₂²	—	2	1	no	—
406	C₂²	—	2	4	no	—
407	C₂²	—	4	2	no	—
408	C₂²	—	4	2	no	—
409	C₂²	—	4	2	no	—
410	C₂²	—	4	2	no	—
411	C₂²	—	4	2	no	—
412	C₂²	—	8	8	no	—
413	C₂²	C₃²×#135	1	2	yes	complemented
414	C₂²	C₂²×C₃²×D₄	1	1	yes	characteristic
415	C₄	—	2	1	no	—
416	C₄	—	2	1	no	—
417	C₄	—	2	1	no	—
418	C₄	—	2	1	no	—
419	C₄	—	4	2	no	—
420	C₄	—	4	2	no	—
421	C₄	C₂²×C₃²×D₄	1	1	yes	characteristic
422	C₄	C₃²×H(5,𝔽₂)	1	1	yes	characteristic
423	C₃	C₃×#3280	1	4	yes	direct product factor
424	C₂	—	2	2	no	—
425	C₂	—	4	1	no	—
426	C₂	—	4	4	no	—
427	C₂	—	8	2	no	—
428	C₂	C₃²×D₄²	1	1	yes	characteristic
429	C₂	C₂×C₃²×#135	1	1	yes	characteristic
430	C₂	C₃²×#576	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×#135	C₂	semidirect
2. C₂²×C₃²×D₈	C₂	semidirect
3. C₃²×#546	C₂	semidirect
4. C₃²×#495	C₂	semidirect
5. C₃²×#467	C₂	semidirect
6. C₃²×#466	C₂	semidirect
7. C₃²×#463	C₂	semidirect
8. C₃²×#450	C₂	semidirect
9. C₃²×#449	C₂	semidirect
10. C₃²×C₄×D₈	C₂	semidirect
11. C₃²×C₈×D₄	C₂	semidirect
12. C₃×#3280	C₃	direct (N × H)
13. C₂×C₃²×#41	C₂²	semidirect
16. C₂×C₃²×Q₁₆	C₂²	semidirect
17. C₂×C₃²×SD₁₆	C₂²	semidirect
18. C₂×C₃²×SD₁₆	C₂²	semidirect
24. C₂²×C₃²×C₈	C₂²	semidirect
25. C₃²×#124	C₂²	semidirect
29. C₃²×#121	C₂²	semidirect
32. C₃²×C₄×D₄	C₂²	semidirect
34. C₃²×#107	C₂²	semidirect
35. C₃²×C₄⋊C₈	C₂²	semidirect
36. C₃²×#103	C₂²	semidirect
37. C₃²×#102	C₂²	semidirect
38. C₃²×#102	C₂²	semidirect
40. C₃²×C₂²⋊C₈	C₂²	semidirect
41. C₃²×C₄×C₈	C₂²	semidirect
42. C₂×C₃×#135	C₂×C₃	semidirect
43. C₂²×C₃×D₈	C₂×C₃	semidirect
44. C₃×#546	C₂×C₃	semidirect
45. C₃×#495	C₂×C₃	semidirect
46. C₃×#467	C₂×C₃	semidirect
47. C₃×#466	C₂×C₃	semidirect
48. C₃×#463	C₂×C₃	semidirect
49. C₃×#450	C₂×C₃	semidirect
50. C₃×#449	C₂×C₃	semidirect
51. C₃×C₄×D₈	C₂×C₃	semidirect
52. C₃×C₈×D₄	C₂×C₃	semidirect
74. C₃²×D₈	D₄	semidirect
92. #3280	C₃²	direct (N × H)
93. C₂×C₃×#41	C₂²×C₃	semidirect
96. C₂×C₃×Q₁₆	C₂²×C₃	semidirect
97. C₂×C₃×SD₁₆	C₂²×C₃	semidirect
98. C₂×C₃×SD₁₆	C₂²×C₃	semidirect
104. C₂²×C₃×C₈	C₂²×C₃	semidirect
105. C₃×#124	C₂²×C₃	semidirect
109. C₃×#121	C₂²×C₃	semidirect
112. C₃×C₄×D₄	C₂²×C₃	semidirect
114. C₃×#107	C₂²×C₃	semidirect
115. C₃×C₄⋊C₈	C₂²×C₃	semidirect
116. C₃×#103	C₂²×C₃	semidirect
117. C₃×#102	C₂²×C₃	semidirect
118. C₃×#102	C₂²×C₃	semidirect
120. C₃×C₂²⋊C₈	C₂²×C₃	semidirect
121. C₃×C₄×C₈	C₂²×C₃	semidirect
156. C₂×#135	C₂×C₃²	semidirect
157. C₂²×D₈	C₂×C₃²	semidirect
158. #546	C₂×C₃²	semidirect
159. #495	C₂×C₃²	semidirect
160. #467	C₂×C₃²	semidirect
161. #466	C₂×C₃²	semidirect
162. #463	C₂×C₃²	semidirect
163. #450	C₂×C₃²	semidirect
164. #449	C₂×C₃²	semidirect
165. C₄×D₈	C₂×C₃²	semidirect
166. C₈×D₄	C₂×C₃²	semidirect
188. C₃×D₈	C₃×D₄	semidirect
218. C₂²×C₃²	#135	semidirect
228. C₂×#41	C₂²×C₃²	semidirect
231. C₂×Q₁₆	C₂²×C₃²	semidirect
232. C₂×SD₁₆	C₂²×C₃²	semidirect
233. C₂×SD₁₆	C₂²×C₃²	semidirect
239. C₂²×C₈	C₂²×C₃²	semidirect
240. #124	C₂²×C₃²	semidirect
244. #121	C₂²×C₃²	semidirect
247. C₄×D₄	C₂²×C₃²	semidirect
249. #107	C₂²×C₃²	semidirect
250. C₄⋊C₈	C₂²×C₃²	semidirect
251. #103	C₂²×C₃²	semidirect
252. #102	C₂²×C₃²	semidirect
253. #102	C₂²×C₃²	semidirect
255. C₂²⋊C₈	C₂²×C₃²	semidirect
256. C₄×C₈	C₂²×C₃²	semidirect
319. D₈	C₃²×D₄	semidirect
349. C₂²×C₃	C₃×#135	semidirect
359. C₃²	#3280	direct (N × H)
413. C₂²	C₃²×#135	semidirect
423. C₃	C₃×#3280	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×#135	2
C₂²×C₃²×D₈	2
C₃²×#546	2
C₃²×#495	2
C₃²×#467	2
C₃²×#466	2
C₃²×#463	2
C₃²×#450	2
C₃²×#449	2
C₃²×C₄×D₈	2
C₃²×C₈×D₄	2
C₃×#3280	3

Subgroups — C32×#3280 #11770329

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#3280 #11770329