Subgroups — C₂²×C₃×#930 #11900278

Order 1152.

5737 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₃²×C₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₃×#67	C₂	1	2	yes	maximal, complemented
3	C₂³×C₃×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×#930	C₂	1	24	yes	maximal, direct product factor
5	C₂²×C₃×(C₂×D₃)⋊C₄	C₂	1	2	yes	maximal, complemented
6	C₂²×C₃×C₄⋊Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×C₃×#121	—	3	1	no	maximal
8	C₂²×#930	C₃	1	1	yes	maximal, characteristic, direct product factor
9	C₂⁵×C₃²	C₂²	1	1	yes	characteristic
10	C₂⁴×C₃×D₃	C₂²	1	2	yes	—
11	C₂³×C₃²×C₄	—	2	8	no	—
12	C₂³×C₃²×C₄	C₂²	1	1	yes	characteristic
13	C₂³×C₃²×C₄	C₂²	1	1	yes	characteristic
14	C₂³×C₃²×C₄	C₂²	1	12	yes	complemented
15	C₂²×C₃×#67	—	2	16	no	—
16	C₂²×C₃×#67	C₂²	1	24	yes	complemented
17	C₂³×C₃×Dic₃	C₂²	1	2	yes	—
18	C₂²×C₃×D₁₂	—	2	8	no	—
19	C₂²×C₃×D₁₂	C₂²	1	12	yes	complemented
20	C₃×#930	C₂²	1	64	yes	direct product factor
21	C₂×C₃×(C₂×D₃)⋊C₄	C₂²	1	24	yes	complemented
22	C₂×C₃×C₄⋊Dic₃	C₂²	1	12	yes	complemented
23	C₂³×C₃×D₄	—	3	1	no	—
24	C₂³×C₃×D₄	—	3	2	no	—
25	C₂⁴×C₃×C₄	—	2	1	no	—
26	C₂⁴×C₃×C₄	D₃	1	1	yes	characteristic, complemented
27	C₂⁴×C₃×C₄	C₂×C₃	1	1	yes	characteristic, complemented
28	C₂³×#67	C₂×C₃	1	2	yes	complemented
29	C₂³×D₁₂	C₂×C₃	1	1	yes	characteristic, complemented
30	C₂×C₃×#121	—	3	24	no	—
31	C₂²×C₃×C₄⋊C₄	—	3	1	no	—
32	C₂²×C₃×C₂²⋊C₄	—	3	2	no	—
33	C₂×#930	C₂×C₃	1	24	yes	direct product factor
34	C₂²×(C₂×D₃)⋊C₄	C₂×C₃	1	2	yes	complemented
35	C₂²×C₄⋊Dic₃	C₂×C₃	1	1	yes	characteristic, complemented
36	C₂⁴×C₃²	—	2	4	no	—
37	C₂⁴×C₃²	—	2	4	no	—
38	C₂⁴×C₃²	D₄	1	8	yes	complemented
39	C₂⁴×C₃²	C₂³	1	6	yes	—
40	C₂⁴×C₃²	C₂³	1	1	yes	characteristic
41	C₂³×C₃×D₃	—	2	8	no	—
42	C₂³×C₃×D₃	—	2	8	no	—
43	C₂³×C₃×D₃	—	2	8	no	—
44	C₂³×C₃×D₃	C₂³	1	12	yes	—
45	C₂²×C₃²×C₄	—	2	4	no	—
46	C₂²×C₃²×C₄	—	2	48	no	—
47	C₂²×C₃²×C₄	D₄	1	8	yes	complemented
48	C₂²×C₃²×C₄	C₂³	1	6	yes	—
49	C₂²×C₃²×C₄	C₂³	1	6	yes	—
50	C₂²×C₃²×C₄	C₂³	1	16	yes	complemented
51	C₂×C₃×#67	—	2	96	no	—
52	C₂×C₃×#67	C₂³	1	32	yes	complemented
53	C₂²×C₃×Dic₃	—	2	8	no	—
54	C₂²×C₃×Dic₃	C₂³	1	12	yes	—
55	C₂×C₃×D₁₂	—	2	48	no	—
56	C₂×C₃×D₁₂	C₂³	1	16	yes	complemented
57	C₃×(C₂×D₃)⋊C₄	C₂³	1	32	yes	complemented
58	C₃×C₄⋊Dic₃	C₂³	1	16	yes	complemented
59	C₂²×#121	—	3	1	no	Sylow
60	C₂⁵×C₃	—	2	1	no	—
61	C₂⁵×C₃	—	3	2	no	—
62	C₂⁵×C₃	C₂×D₃	1	1	yes	characteristic
63	C₂⁵×C₃	C₂²×C₃	1	1	yes	characteristic
64	C₂⁴×D₃	C₂²×C₃	1	2	yes	—
65	C₂²×C₃×D₄	—	3	24	no	—
66	C₂²×C₃×D₄	—	3	12	no	—
67	C₂²×C₃×D₄	—	6	16	no	—
68	C₂²×C₃×D₄	—	6	8	no	—
69	C₂³×C₃×C₄	—	2	16	no	—
70	C₂³×C₃×C₄	—	2	8	no	—
71	C₂³×C₃×C₄	—	2	8	no	—
72	C₂³×C₃×C₄	—	2	1	no	—
73	C₂³×C₃×C₄	—	2	1	no	—
74	C₂³×C₃×C₄	—	2	12	no	—
75	C₂³×C₃×C₄	—	3	2	no	—
76	C₂³×C₃×C₄	C₂×D₃	1	1	yes	characteristic
77	C₂³×C₃×C₄	C₂×D₃	1	1	yes	characteristic
78	C₂³×C₃×C₄	C₂×D₃	1	12	yes	complemented
79	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
80	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
81	C₂³×C₃×C₄	C₂²×C₃	1	12	yes	complemented
82	C₂²×#67	—	2	16	no	—
83	C₂²×#67	C₂²×C₃	1	24	yes	complemented
84	C₂³×Dic₃	C₂²×C₃	1	2	yes	—
85	C₂²×D₁₂	—	2	8	no	—
86	C₂²×D₁₂	C₂²×C₃	1	12	yes	complemented
87	C₃×#121	—	3	64	no	—
88	C₂×C₃×C₄⋊C₄	—	3	12	no	—
89	C₂×C₃×C₂²⋊C₄	—	3	24	no	—
90	#930	C₂²×C₃	1	64	yes	direct product factor
91	C₂×(C₂×D₃)⋊C₄	C₂²×C₃	1	24	yes	complemented
92	C₂×C₄⋊Dic₃	C₂²×C₃	1	12	yes	complemented
93	C₂³×C₃²	—	2	32	no	—
94	C₂³×C₃²	—	2	12	no	—
95	C₂³×C₃²	—	2	12	no	—
96	C₂³×C₃²	C₂×D₄	1	4	yes	—
97	C₂³×C₃²	C₂×D₄	1	4	yes	—
98	C₂³×C₃²	C₂×D₄	1	24	yes	complemented
99	C₂³×C₃²	#41	1	4	yes	—
100	C₂³×C₃²	C₂⁴	1	4	yes	—
101	C₂³×C₃²	C₂⁴	1	3	yes	—
102	C₂²×C₃×D₃	—	2	24	no	—
103	C₂²×C₃×D₃	—	2	24	no	—
104	C₂²×C₃×D₃	—	2	24	no	—
105	C₂²×C₃×D₃	—	4	32	no	—
106	C₂²×C₃×D₃	C₂⁴	1	8	yes	—
107	C₂×C₃²×C₄	—	2	12	no	—
108	C₂×C₃²×C₄	—	2	32	no	—
109	C₂×C₃²×C₄	C₂×D₄	1	24	yes	complemented
110	C₂×C₃²×C₄	C₂⁴	1	4	yes	—
111	C₂×C₃²×C₄	C₂⁴	1	4	yes	—
112	C₃×#67	—	2	64	no	—
113	C₂×C₃×Dic₃	—	2	24	no	—
114	C₂×C₃×Dic₃	C₂⁴	1	8	yes	—
115	C₃×D₁₂	—	2	32	no	—
116	C₂³×D₄	—	3	2	no	—
117	C₂³×D₄	—	3	1	no	—
118	C₂⁴×C₄	C₃×D₃	1	1	yes	characteristic, complemented
119	C₂×#121	—	3	24	no	—
120	C₂²×C₄⋊C₄	—	3	1	no	—
121	C₂²×C₂²⋊C₄	—	3	2	no	—
122	C₂⁴×C₃	—	2	8	no	—
123	C₂⁴×C₃	—	2	8	no	—
124	C₂⁴×C₃	—	2	4	no	—
125	C₂⁴×C₃	—	2	4	no	—
126	C₂⁴×C₃	—	2	4	no	—
127	C₂⁴×C₃	—	2	4	no	—
128	C₂⁴×C₃	—	2	8	no	—
129	C₂⁴×C₃	—	2	6	no	—
130	C₂⁴×C₃	—	2	1	no	—
131	C₂⁴×C₃	—	3	12	no	—
132	C₂⁴×C₃	—	6	8	no	—
133	C₂⁴×C₃	—	6	8	no	—
134	C₂⁴×C₃	—	6	8	no	—
135	C₂⁴×C₃	D₁₂	1	8	yes	complemented
136	C₂⁴×C₃	C₃×D₄	1	8	yes	complemented
137	C₂⁴×C₃	C₂²×D₃	1	6	yes	—
138	C₂⁴×C₃	C₂²×D₃	1	1	yes	characteristic
139	C₂⁴×C₃	C₂³×C₃	1	6	yes	—
140	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
141	C₂³×D₃	—	2	8	no	—
142	C₂³×D₃	—	2	8	no	—
143	C₂³×D₃	—	2	8	no	—
144	C₂³×D₃	C₂³×C₃	1	12	yes	—
145	C₂×C₃×D₄	—	3	32	no	—
146	C₂×C₃×D₄	—	3	16	no	—
147	C₂×C₃×D₄	—	6	96	no	—
148	C₂×C₃×D₄	—	6	48	no	—
149	C₂²×C₃×C₄	—	2	8	no	—
150	C₂²×C₃×C₄	—	2	96	no	—
151	C₂²×C₃×C₄	—	2	4	no	—
152	C₂²×C₃×C₄	—	2	4	no	—
153	C₂²×C₃×C₄	—	2	48	no	—
154	C₂²×C₃×C₄	—	2	48	no	—
155	C₂²×C₃×C₄	—	2	8	no	—
156	C₂²×C₃×C₄	—	2	6	no	—
157	C₂²×C₃×C₄	—	2	6	no	—
158	C₂²×C₃×C₄	—	2	16	no	—
159	C₂²×C₃×C₄	—	3	12	no	—
160	C₂²×C₃×C₄	—	6	8	no	—
161	C₂²×C₃×C₄	#67	1	8	yes	complemented
162	C₂²×C₃×C₄	C₃×D₄	1	8	yes	complemented
163	C₂²×C₃×C₄	C₂²×D₃	1	6	yes	—
164	C₂²×C₃×C₄	C₂²×D₃	1	6	yes	—
165	C₂²×C₃×C₄	C₂²×D₃	1	16	yes	complemented
166	C₂²×C₃×C₄	C₂³×C₃	1	6	yes	—
167	C₂²×C₃×C₄	C₂³×C₃	1	6	yes	—
168	C₂²×C₃×C₄	C₂³×C₃	1	16	yes	complemented
169	C₂×#67	—	2	96	no	—
170	C₂×#67	C₂³×C₃	1	32	yes	complemented
171	C₂²×Dic₃	—	2	8	no	—
172	C₂²×Dic₃	C₂³×C₃	1	12	yes	—
173	C₂×D₁₂	—	2	48	no	—
174	C₂×D₁₂	C₂³×C₃	1	16	yes	complemented
175	C₃×C₄⋊C₄	—	3	16	no	—
176	C₃×C₂²⋊C₄	—	3	32	no	—
177	(C₂×D₃)⋊C₄	C₂³×C₃	1	32	yes	complemented
178	C₄⋊Dic₃	C₂³×C₃	1	16	yes	complemented
179	C₂²×C₃²	—	2	48	no	—
180	C₂²×C₃²	—	2	4	no	—
181	C₂²×C₃²	—	2	4	no	—
182	C₂²×C₃²	#121	1	16	yes	complemented
183	C₂²×C₃²	C₂²×D₄	1	6	yes	—
184	C₂²×C₃²	C₂²×D₄	1	6	yes	—
185	C₂²×C₃²	C₂²×D₄	1	8	yes	complemented
186	C₂²×C₃²	C₂×#41	1	6	yes	—
187	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
188	C₂×C₃×D₃	—	2	8	no	—
189	C₂×C₃×D₃	—	2	8	no	—
190	C₂×C₃×D₃	—	2	8	no	—
191	C₂×C₃×D₃	—	4	48	no	—
192	C₃²×C₄	—	2	4	no	—
193	C₃²×C₄	C₂²×D₄	1	8	yes	complemented
194	C₃×Dic₃	—	2	8	no	—
195	C₂⁵	—	3	2	no	—
196	C₂⁵	C₂×C₃×D₃	1	1	yes	characteristic
197	C₂²×D₄	—	3	24	no	—
198	C₂²×D₄	—	3	12	no	—
199	C₂²×D₄	—	6	16	no	—
200	C₂²×D₄	—	6	8	no	—
201	C₂³×C₄	—	2	8	no	—
202	C₂³×C₄	—	3	2	no	—
203	C₂³×C₄	C₂×C₃×D₃	1	1	yes	characteristic
204	C₂³×C₄	C₂×C₃×D₃	1	1	yes	characteristic
205	C₂³×C₄	C₂×C₃×D₃	1	12	yes	complemented
206	#121	—	3	64	no	—
207	C₂×C₄⋊C₄	—	3	12	no	—
208	C₂×C₂²⋊C₄	—	3	24	no	—
209	C₂³×C₃	—	2	24	no	—
210	C₂³×C₃	—	2	64	no	—
211	C₂³×C₃	—	2	24	no	—
212	C₂³×C₃	—	2	32	no	—
213	C₂³×C₃	—	2	32	no	—
214	C₂³×C₃	—	2	12	no	—
215	C₂³×C₃	—	2	12	no	—
216	C₂³×C₃	—	2	12	no	—
217	C₂³×C₃	—	2	12	no	—
218	C₂³×C₃	—	2	4	no	—
219	C₂³×C₃	—	2	3	no	—
220	C₂³×C₃	—	2	4	no	—
221	C₂³×C₃	—	2	24	no	—
222	C₂³×C₃	—	2	4	no	—
223	C₂³×C₃	—	2	4	no	—
224	C₂³×C₃	—	3	8	no	—
225	C₂³×C₃	—	6	24	no	—
226	C₂³×C₃	—	6	24	no	—
227	C₂³×C₃	—	6	24	no	—
228	C₂³×C₃	—	12	32	no	—
229	C₂³×C₃	C₂×D₁₂	1	4	yes	—
230	C₂³×C₃	C₂×D₁₂	1	24	yes	complemented
231	C₂³×C₃	#235	1	4	yes	—
232	C₂³×C₃	C₂×#67	1	4	yes	—
233	C₂³×C₃	C₂×C₃×D₄	1	4	yes	—
234	C₂³×C₃	C₂×C₃×D₄	1	4	yes	—
235	C₂³×C₃	C₂×C₃×D₄	1	24	yes	complemented
236	C₂³×C₃	C₃×#41	1	4	yes	—
237	C₂³×C₃	C₂³×D₃	1	4	yes	—
238	C₂³×C₃	C₂³×D₃	1	3	yes	—
239	C₂³×C₃	C₂⁴×C₃	1	4	yes	—
240	C₂³×C₃	C₂⁴×C₃	1	3	yes	—
241	C₂²×D₃	—	2	24	no	—
242	C₂²×D₃	—	2	24	no	—
243	C₂²×D₃	—	2	24	no	—
244	C₂²×D₃	—	4	32	no	—
245	C₂²×D₃	C₂⁴×C₃	1	8	yes	—
246	C₃×D₄	—	6	64	no	—
247	C₃×D₄	—	6	32	no	—
248	C₂×C₃×C₄	—	2	24	no	—
249	C₂×C₃×C₄	—	2	64	no	—
250	C₂×C₃×C₄	—	2	12	no	—
251	C₂×C₃×C₄	—	2	12	no	—
252	C₂×C₃×C₄	—	2	32	no	—
253	C₂×C₃×C₄	—	2	32	no	—
254	C₂×C₃×C₄	—	2	4	no	—
255	C₂×C₃×C₄	—	2	4	no	—
256	C₂×C₃×C₄	—	2	24	no	—
257	C₂×C₃×C₄	—	3	8	no	—
258	C₂×C₃×C₄	—	6	24	no	—
259	C₂×C₃×C₄	C₂×#67	1	24	yes	complemented
260	C₂×C₃×C₄	C₂×C₃×D₄	1	24	yes	complemented
261	C₂×C₃×C₄	C₂³×D₃	1	4	yes	—
262	C₂×C₃×C₄	C₂³×D₃	1	4	yes	—
263	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
264	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
265	#67	—	2	64	no	—
266	C₂×Dic₃	—	2	24	no	—
267	C₂×Dic₃	C₂⁴×C₃	1	8	yes	—
268	D₁₂	—	2	32	no	—
269	C₂×C₃²	—	2	8	no	—
270	C₂×C₃²	C₂×#121	1	12	yes	complemented
271	C₂×C₃²	C₂³×D₄	1	1	yes	characteristic
272	C₂×C₃²	C₂³×D₄	1	1	yes	characteristic
273	C₂×C₃²	C₂²×#41	1	1	yes	characteristic
274	C₃×D₃	—	4	8	no	—
275	C₂⁴	—	2	4	no	—
276	C₂⁴	—	2	4	no	—
277	C₂⁴	—	3	12	no	—
278	C₂⁴	—	6	8	no	—
279	C₂⁴	—	6	8	no	—
280	C₂⁴	—	6	8	no	—
281	C₂⁴	C₃×D₁₂	1	8	yes	complemented
282	C₂⁴	C₂²×C₃×D₃	1	6	yes	—
283	C₂⁴	C₂²×C₃×D₃	1	1	yes	characteristic
284	C₂×D₄	—	3	32	no	—
285	C₂×D₄	—	3	16	no	—
286	C₂×D₄	—	6	96	no	—
287	C₂×D₄	—	6	48	no	—
288	C₂²×C₄	—	2	4	no	—
289	C₂²×C₄	—	2	48	no	—
290	C₂²×C₄	—	3	12	no	—
291	C₂²×C₄	—	6	8	no	—
292	C₂²×C₄	C₃×#67	1	8	yes	complemented
293	C₂²×C₄	C₂²×C₃×D₃	1	6	yes	—
294	C₂²×C₄	C₂²×C₃×D₃	1	6	yes	—
295	C₂²×C₄	C₂²×C₃×D₃	1	16	yes	complemented
296	C₄⋊C₄	—	3	16	no	—
297	C₂²⋊C₄	—	3	32	no	—
298	C₂²×C₃	—	2	8	no	—
299	C₂²×C₃	—	2	96	no	—
300	C₂²×C₃	—	2	8	no	—
301	C₂²×C₃	—	2	4	no	—
302	C₂²×C₃	—	2	4	no	—
303	C₂²×C₃	—	2	4	no	—
304	C₂²×C₃	—	2	4	no	—
305	C₂²×C₃	—	2	48	no	—
306	C₂²×C₃	—	2	48	no	—
307	C₂²×C₃	—	2	16	no	—
308	C₂²×C₃	—	2	6	no	—
309	C₂²×C₃	—	2	8	no	—
310	C₂²×C₃	—	2	6	no	—
311	C₂²×C₃	—	2	6	no	—
312	C₂²×C₃	—	2	1	no	—
313	C₂²×C₃	—	6	8	no	—
314	C₂²×C₃	—	6	8	no	—
315	C₂²×C₃	—	6	8	no	—
316	C₂²×C₃	—	12	48	no	—
317	C₂²×C₃	#930	1	16	yes	direct product factor
318	C₂²×C₃	C₃×#121	1	16	yes	complemented
319	C₂²×C₃	C₂²×D₁₂	1	6	yes	—
320	C₂²×C₃	C₂²×D₁₂	1	8	yes	complemented
321	C₂²×C₃	C₂×#235	1	6	yes	—
322	C₂²×C₃	C₂²×#67	1	6	yes	—
323	C₂²×C₃	C₂²×C₃×D₄	1	6	yes	—
324	C₂²×C₃	C₂²×C₃×D₄	1	6	yes	—
325	C₂²×C₃	C₂²×C₃×D₄	1	8	yes	complemented
326	C₂²×C₃	C₂×C₃×#41	1	6	yes	—
327	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
328	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
329	C₂×D₃	—	2	8	no	—
330	C₂×D₃	—	2	8	no	—
331	C₂×D₃	—	2	8	no	—
332	C₂×D₃	—	4	48	no	—
333	C₃×C₄	—	2	8	no	—
334	C₃×C₄	—	2	4	no	—
335	C₃×C₄	—	2	4	no	—
336	C₃×C₄	—	2	8	no	—
337	C₃×C₄	—	6	8	no	—
338	C₃×C₄	C₂²×#67	1	8	yes	complemented
339	C₃×C₄	C₂²×C₃×D₄	1	8	yes	complemented
340	Dic₃	—	2	8	no	—
341	C₃²	C₂²×#121	1	1	yes	characteristic, complemented, Sylow
342	C₂³	—	2	32	no	—
343	C₂³	—	2	12	no	—
344	C₂³	—	2	12	no	—
345	C₂³	—	3	8	no	—
346	C₂³	—	6	24	no	—
347	C₂³	—	6	24	no	—
348	C₂³	—	6	24	no	—
349	C₂³	—	12	32	no	—
350	C₂³	C₂×C₃×D₁₂	1	4	yes	—
351	C₂³	C₂×C₃×D₁₂	1	24	yes	complemented
352	C₂³	C₃×#235	1	4	yes	—
353	C₂³	C₂×C₃×#67	1	4	yes	—
354	C₂³	C₂³×C₃×D₃	1	4	yes	—
355	C₂³	C₂³×C₃×D₃	1	3	yes	—
356	D₄	—	6	64	no	—
357	D₄	—	6	32	no	—
358	C₂×C₄	—	2	12	no	—
359	C₂×C₄	—	2	32	no	—
360	C₂×C₄	—	3	8	no	—
361	C₂×C₄	—	6	24	no	—
362	C₂×C₄	C₂×C₃×#67	1	24	yes	complemented
363	C₂×C₄	C₂³×C₃×D₃	1	4	yes	—
364	C₂×C₄	C₂³×C₃×D₃	1	4	yes	—
365	C₂×C₃	—	2	16	no	—
366	C₂×C₃	—	2	8	no	—
367	C₂×C₃	—	2	8	no	—
368	C₂×C₃	—	2	12	no	—
369	C₂×C₃	—	2	1	no	—
370	C₂×C₃	—	2	1	no	—
371	C₂×C₃	—	2	1	no	—
372	C₂×C₃	—	12	8	no	—
373	C₂×C₃	C₂×#930	1	12	yes	direct product factor
374	C₂×C₃	C₂×C₃×#121	1	12	yes	complemented
375	C₂×C₃	C₂³×D₁₂	1	1	yes	characteristic
376	C₂×C₃	C₂²×#235	1	1	yes	characteristic
377	C₂×C₃	C₂³×#67	1	1	yes	characteristic
378	C₂×C₃	C₂³×C₃×D₄	1	1	yes	characteristic
379	C₂×C₃	C₂³×C₃×D₄	1	1	yes	characteristic
380	C₂×C₃	C₂²×C₃×#41	1	1	yes	characteristic
381	D₃	—	4	8	no	—
382	C₂²	—	2	48	no	—
383	C₂²	—	2	4	no	—
384	C₂²	—	2	4	no	—
385	C₂²	—	6	8	no	—
386	C₂²	—	6	8	no	—
387	C₂²	—	6	8	no	—
388	C₂²	—	12	48	no	—
389	C₂²	C₃×#930	1	16	yes	direct product factor
390	C₂²	C₂²×C₃×D₁₂	1	6	yes	—
391	C₂²	C₂²×C₃×D₁₂	1	8	yes	complemented
392	C₂²	C₂×C₃×#235	1	6	yes	—
393	C₂²	C₂²×C₃×#67	1	6	yes	—
394	C₂²	C₂⁴×C₃×D₃	1	1	yes	characteristic
395	C₄	—	2	4	no	—
396	C₄	—	6	8	no	—
397	C₄	C₂²×C₃×#67	1	8	yes	complemented
398	C₃	—	2	1	no	—
399	C₃	C₂²×#930	1	1	yes	characteristic, direct product factor
400	C₃	C₂²×C₃×#121	1	1	yes	characteristic, complemented
401	C₂	—	2	8	no	—
402	C₂	—	12	8	no	—
403	C₂	C₂×C₃×#930	1	12	yes	direct product factor
404	C₂	C₂³×C₃×D₁₂	1	1	yes	characteristic
405	C₂	C₂²×C₃×#235	1	1	yes	characteristic
406	C₂	C₂³×C₃×#67	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴×C₃	C₂²×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₃
Fitting	C₂⁴×C₃²×C₄	C₂
socle	C₂⁴×C₃²	C₂³
hypercenter	C₂⁴×C₃×C₄	D₃
hypocenter	C₃	C₂²×C₃×#121
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂⁴×C₃ ◁ C₂⁴×C₃×C₄

Complements

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

N	H ≅ G/N	type
1. C₂⁴×C₃²×C₄	C₂	semidirect
2. C₂³×C₃×#67	C₂	semidirect
3. C₂³×C₃×D₁₂	C₂	semidirect
4. C₂×C₃×#930	C₂	direct (N × H)
5. C₂²×C₃×(C₂×D₃)⋊C₄	C₂	semidirect
6. C₂²×C₃×C₄⋊Dic₃	C₂	semidirect
8. C₂²×#930	C₃	direct (N × H)
14. C₂³×C₃²×C₄	C₂²	semidirect
16. C₂²×C₃×#67	C₂²	semidirect
19. C₂²×C₃×D₁₂	C₂²	semidirect
20. C₃×#930	C₂²	direct (N × H)
21. C₂×C₃×(C₂×D₃)⋊C₄	C₂²	semidirect
22. C₂×C₃×C₄⋊Dic₃	C₂²	semidirect
26. C₂⁴×C₃×C₄	D₃	semidirect
27. C₂⁴×C₃×C₄	C₂×C₃	semidirect
28. C₂³×#67	C₂×C₃	semidirect
29. C₂³×D₁₂	C₂×C₃	semidirect
33. C₂×#930	C₂×C₃	direct (N × H)
34. C₂²×(C₂×D₃)⋊C₄	C₂×C₃	semidirect
35. C₂²×C₄⋊Dic₃	C₂×C₃	semidirect
38. C₂⁴×C₃²	D₄	semidirect
47. C₂²×C₃²×C₄	D₄	semidirect
50. C₂²×C₃²×C₄	C₂³	semidirect
52. C₂×C₃×#67	C₂³	semidirect
56. C₂×C₃×D₁₂	C₂³	semidirect
57. C₃×(C₂×D₃)⋊C₄	C₂³	semidirect
58. C₃×C₄⋊Dic₃	C₂³	semidirect
78. C₂³×C₃×C₄	C₂×D₃	semidirect
81. C₂³×C₃×C₄	C₂²×C₃	semidirect
83. C₂²×#67	C₂²×C₃	semidirect
86. C₂²×D₁₂	C₂²×C₃	semidirect
90. #930	C₂²×C₃	direct (N × H)
91. C₂×(C₂×D₃)⋊C₄	C₂²×C₃	semidirect
92. C₂×C₄⋊Dic₃	C₂²×C₃	semidirect
98. C₂³×C₃²	C₂×D₄	semidirect
109. C₂×C₃²×C₄	C₂×D₄	semidirect
118. C₂⁴×C₄	C₃×D₃	semidirect
135. C₂⁴×C₃	D₁₂	semidirect
136. C₂⁴×C₃	C₃×D₄	semidirect
161. C₂²×C₃×C₄	#67	semidirect
162. C₂²×C₃×C₄	C₃×D₄	semidirect
165. C₂²×C₃×C₄	C₂²×D₃	semidirect
168. C₂²×C₃×C₄	C₂³×C₃	semidirect
170. C₂×#67	C₂³×C₃	semidirect
174. C₂×D₁₂	C₂³×C₃	semidirect
177. (C₂×D₃)⋊C₄	C₂³×C₃	semidirect
178. C₄⋊Dic₃	C₂³×C₃	semidirect
182. C₂²×C₃²	#121	semidirect
185. C₂²×C₃²	C₂²×D₄	semidirect
193. C₃²×C₄	C₂²×D₄	semidirect
205. C₂³×C₄	C₂×C₃×D₃	semidirect
230. C₂³×C₃	C₂×D₁₂	semidirect
235. C₂³×C₃	C₂×C₃×D₄	semidirect
259. C₂×C₃×C₄	C₂×#67	semidirect
260. C₂×C₃×C₄	C₂×C₃×D₄	semidirect
270. C₂×C₃²	C₂×#121	semidirect
281. C₂⁴	C₃×D₁₂	semidirect
292. C₂²×C₄	C₃×#67	semidirect
295. C₂²×C₄	C₂²×C₃×D₃	semidirect
317. C₂²×C₃	#930	direct (N × H)
318. C₂²×C₃	C₃×#121	semidirect
320. C₂²×C₃	C₂²×D₁₂	semidirect
325. C₂²×C₃	C₂²×C₃×D₄	semidirect
338. C₃×C₄	C₂²×#67	semidirect
339. C₃×C₄	C₂²×C₃×D₄	semidirect
341. C₃²	C₂²×#121	semidirect
351. C₂³	C₂×C₃×D₁₂	semidirect
362. C₂×C₄	C₂×C₃×#67	semidirect
373. C₂×C₃	C₂×#930	direct (N × H)
374. C₂×C₃	C₂×C₃×#121	semidirect
389. C₂²	C₃×#930	direct (N × H)
391. C₂²	C₂²×C₃×D₁₂	semidirect
397. C₄	C₂²×C₃×#67	semidirect
399. C₃	C₂²×#930	direct (N × H)
400. C₃	C₂²×C₃×#121	semidirect
403. C₂	C₂×C₃×#930	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×C₃²×C₄	2
C₂³×C₃×#67	2
C₂³×C₃×D₁₂	2
C₂×C₃×#930	2
C₂²×C₃×(C₂×D₃)⋊C₄	2
C₂²×C₃×C₄⋊Dic₃	2
C₂²×C₃×#121	3
C₂²×#930	3

Subgroups — C22×C3×#930 #11900278

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃×#930 #11900278