Subgroups — C₂×C₃×#5083 #11865467

Order 1152.

1233 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×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×#215	C₂	1	2	yes	maximal
3	C₂×C₃×C₄×D₁₂	C₂	1	1	yes	maximal, characteristic
4	C₂×C₃×#835	C₂	1	2	yes	maximal, complemented
5	C₃×#5083	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₃×C₄⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃×#461	—	3	1	no	maximal
8	C₂×#5083	C₃	1	1	yes	maximal, characteristic, direct product factor
9	C₂²×C₃²×Q₈	C₂²	1	2	yes	—
10	C₂²×C₃×D₁₂	C₂²	1	1	yes	characteristic
11	C₂²×C₃×C₄×D₃	—	2	1	no	—
12	C₃²×C₄⋊Q₈	—	2	2	no	—
13	C₃²×C₄⋊Q₈	C₂²	1	4	yes	complemented
14	C₂×C₃²×C₄⋊C₄	—	2	1	no	—
15	C₂×C₃²×C₄⋊C₄	—	2	1	no	—
16	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
17	C₂×C₃×#215	—	2	8	no	—
18	C₂×C₃×#215	C₂²	1	8	yes	—
19	C₂×C₃×(C₂×D₃)⋊C₄	—	2	1	no	—
20	C₂×C₃×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
21	C₂²×C₃×C₃⋊C₈	C₂²	1	2	yes	—
22	C₃×C₄×D₁₂	—	2	2	no	—
23	C₃×C₄×D₁₂	C₂²	1	4	yes	—
24	C₃×#835	C₂²	1	8	yes	complemented
25	C₃×C₄⋊(C₃⋊C₈)	C₂²	1	4	yes	complemented
26	C₂²×C₃×SD₁₆	—	3	2	no	—
27	C₂×C₃×C₄⋊Q₈	—	2	1	no	—
28	C₂×C₃×C₄⋊Q₈	D₃	1	1	yes	characteristic, complemented
29	C₂×C₃×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
30	C₂×C₃×C₄×D₄	—	3	1	no	—
31	C₂²×#215	C₂×C₃	1	2	yes	—
32	C₂×C₄×D₁₂	C₂×C₃	1	1	yes	characteristic
33	C₃×#461	—	3	8	no	—
34	C₂×C₃×C₄⋊C₈	—	3	1	no	—
35	C₂×C₃×#103	—	3	2	no	—
36	C₂×#835	C₂×C₃	1	2	yes	complemented
37	#5083	C₂×C₃	1	8	yes	direct product factor
38	C₂×C₄⋊(C₃⋊C₈)	C₂×C₃	1	1	yes	characteristic, complemented
39	C₂³×C₃×D₃	—	2	1	no	—
40	C₂×C₃²×Q₈	—	2	2	no	—
41	C₂×C₃²×Q₈	—	2	4	no	—
42	C₂×C₃²×Q₈	—	2	4	no	—
43	C₂×C₃²×Q₈	C₂³	1	4	yes	—
44	C₂²×C₃²×C₄	—	2	2	no	—
45	C₂²×C₃²×C₄	D₄	1	1	yes	characteristic
46	C₂²×C₃²×C₄	D₄	1	1	yes	characteristic
47	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
48	C₂²×C₃×Dic₃	—	2	1	no	—
49	C₂×C₃×D₁₂	—	2	1	no	—
50	C₂×C₃×D₁₂	—	2	2	no	—
51	C₂×C₃×D₁₂	D₄	1	4	yes	—
52	C₂×C₃×D₁₂	C₂³	1	2	yes	—
53	C₂×C₃×C₄×D₃	—	2	4	no	—
54	C₂×C₃×C₄×D₃	—	4	4	no	—
55	C₃²×C₄⋊C₄	—	2	4	no	—
56	C₃²×C₄⋊C₄	—	2	4	no	—
57	C₃²×C₄²	D₄	1	2	yes	—
58	C₃²×C₄²	C₂³	1	2	yes	—
59	C₃×#215	—	2	16	no	—
60	C₃×(C₂×D₃)⋊C₄	—	2	4	no	—
61	C₃×C₄⋊Dic₃	—	2	1	no	—
62	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
63	C₂×C₃×C₃⋊C₈	—	2	4	no	—
64	C₂×C₃×C₃⋊C₈	C₂³	1	4	yes	—
65	C₂×#461	—	3	1	no	Sylow
66	C₂²×C₃×Q₈	—	2	2	no	—
67	C₂²×C₃×Q₈	C₂×D₃	1	2	yes	—
68	C₂²×C₃×Q₈	C₂²×C₃	1	2	yes	—
69	C₂²×C₃×D₄	—	3	1	no	—
70	C₂³×C₃×C₄	—	6	1	no	—
71	C₂²×D₁₂	C₂²×C₃	1	1	yes	characteristic
72	C₂²×C₄×D₃	—	2	1	no	—
73	C₂×C₃×SD₁₆	—	3	8	no	—
74	C₂×C₃×SD₁₆	—	6	8	no	—
75	C₂²×C₃×C₈	—	3	2	no	—
76	C₃×C₄⋊Q₈	—	2	4	no	—
77	C₃×C₄⋊Q₈	—	2	2	no	—
78	C₃×C₄⋊Q₈	—	2	2	no	—
79	C₃×C₄⋊Q₈	—	2	4	no	—
80	C₃×C₄⋊Q₈	C₂×D₃	1	4	yes	complemented
81	C₃×C₄⋊Q₈	C₂²×C₃	1	4	yes	complemented
82	C₃×C₄×D₄	—	3	4	no	—
83	C₃×C₄×D₄	—	6	2	no	—
84	C₂×C₃×C₄⋊C₄	—	2	2	no	—
85	C₂×C₃×C₄⋊C₄	—	2	2	no	—
86	C₂×C₃×C₄⋊C₄	—	2	1	no	—
87	C₂×C₃×C₄⋊C₄	—	2	1	no	—
88	C₂×C₃×C₄⋊C₄	—	2	1	no	—
89	C₂×C₃×C₄⋊C₄	—	2	1	no	—
90	C₂×C₃×C₄⋊C₄	—	3	1	no	—
91	C₂×C₃×C₂²⋊C₄	—	6	1	no	—
92	C₂×C₃×C₄²	—	2	1	no	—
93	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
94	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
95	C₂×#215	—	2	8	no	—
96	C₂×#215	C₂²×C₃	1	8	yes	—
97	C₂×(C₂×D₃)⋊C₄	—	2	1	no	—
98	C₂×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
99	C₂²×C₃⋊C₈	C₂²×C₃	1	2	yes	—
100	C₄×D₁₂	—	2	2	no	—
101	C₄×D₁₂	C₂²×C₃	1	4	yes	—
102	C₃×C₄⋊C₈	—	3	4	no	—
103	C₃×#103	—	3	8	no	—
104	#835	C₂²×C₃	1	8	yes	complemented
105	C₄⋊(C₃⋊C₈)	C₂²×C₃	1	4	yes	complemented
106	C₂³×C₃²	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₃×D₃	—	2	4	no	—
108	C₂²×C₃×D₃	—	2	2	no	—
109	C₂²×C₃×D₃	—	4	2	no	—
110	C₂²×C₃×D₃	—	4	2	no	—
111	C₃²×Q₈	—	2	4	no	—
112	C₃²×Q₈	—	2	4	no	—
113	C₃²×Q₈	—	4	4	no	—
114	C₂×C₃²×C₄	—	2	2	no	—
115	C₂×C₃²×C₄	—	2	4	no	—
116	C₂×C₃²×C₄	—	4	4	no	—
117	C₂×C₃²×C₄	SD₁₆	1	4	yes	complemented
118	C₂×C₃²×C₄	C₂×D₄	1	2	yes	—
119	C₂×C₃²×C₄	C₂×D₄	1	2	yes	—
120	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
121	C₂×C₃²×C₄	C₂×D₄	1	2	yes	—
122	C₂×C₃²×C₄	#41	1	2	yes	—
123	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
124	C₂×C₃×Dic₃	—	2	2	no	—
125	C₂×C₃×Dic₃	—	4	2	no	—
126	C₃×D₁₂	—	2	4	no	—
127	C₃×D₁₂	—	2	2	no	—
128	C₃×D₁₂	C₂×D₄	1	4	yes	—
129	C₃×C₄×D₃	—	4	8	no	—
130	C₃×C₃⋊C₈	—	2	4	no	—
131	C₂²×SD₁₆	—	3	2	no	—
132	C₂×C₄⋊Q₈	C₃×D₃	1	1	yes	characteristic, complemented
133	C₂×C₄×D₄	—	3	1	no	—
134	#461	—	3	8	no	—
135	C₂×C₄⋊C₈	—	3	1	no	—
136	C₂×#103	—	3	2	no	—
137	C₂⁴×C₃	—	6	1	no	—
138	C₂³×D₃	—	2	1	no	—
139	C₂×C₃×Q₈	—	2	4	no	—
140	C₂×C₃×Q₈	—	2	2	no	—
141	C₂×C₃×Q₈	—	2	2	no	—
142	C₂×C₃×Q₈	—	2	4	no	—
143	C₂×C₃×Q₈	—	2	4	no	—
144	C₂×C₃×Q₈	—	2	4	no	—
145	C₂×C₃×Q₈	—	2	4	no	—
146	C₂×C₃×Q₈	—	2	4	no	—
147	C₂×C₃×Q₈	—	4	4	no	—
148	C₂×C₃×Q₈	—	4	4	no	—
149	C₂×C₃×Q₈	C₂²×D₃	1	4	yes	—
150	C₂×C₃×Q₈	C₂³×C₃	1	4	yes	—
151	C₂×C₃×D₄	—	3	4	no	—
152	C₂×C₃×D₄	—	3	2	no	—
153	C₂×C₃×D₄	—	6	2	no	—
154	C₂×C₃×D₄	—	6	1	no	—
155	C₂²×C₃×C₄	—	2	4	no	—
156	C₂²×C₃×C₄	—	2	2	no	—
157	C₂²×C₃×C₄	—	2	2	no	—
158	C₂²×C₃×C₄	—	2	1	no	—
159	C₂²×C₃×C₄	—	2	1	no	—
160	C₂²×C₃×C₄	—	2	1	no	—
161	C₂²×C₃×C₄	—	6	1	no	—
162	C₂²×C₃×C₄	—	6	4	no	—
163	C₂²×C₃×C₄	—	12	4	no	—
164	C₂²×C₃×C₄	#67	1	1	yes	characteristic
165	C₂²×C₃×C₄	#67	1	1	yes	characteristic
166	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
167	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
168	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
169	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
170	C₂²×Dic₃	—	2	1	no	—
171	C₂×D₁₂	—	2	1	no	—
172	C₂×D₁₂	—	2	2	no	—
173	C₂×D₁₂	C₃×D₄	1	4	yes	—
174	C₂×D₁₂	C₂³×C₃	1	2	yes	—
175	C₂×C₄×D₃	—	2	4	no	—
176	C₂×C₄×D₃	—	4	4	no	—
177	C₃×SD₁₆	—	6	16	no	—
178	C₂×C₃×C₈	—	3	4	no	—
179	C₂×C₃×C₈	—	6	4	no	—
180	C₃×C₄⋊C₄	—	2	8	no	—
181	C₃×C₄⋊C₄	—	2	8	no	—
182	C₃×C₄⋊C₄	—	2	4	no	—
183	C₃×C₄⋊C₄	—	2	4	no	—
184	C₃×C₄⋊C₄	—	2	4	no	—
185	C₃×C₄⋊C₄	—	2	4	no	—
186	C₃×C₄⋊C₄	—	3	2	no	—
187	C₃×C₄⋊C₄	—	6	1	no	—
188	C₃×C₂²⋊C₄	—	6	4	no	—
189	C₃×C₄²	—	2	2	no	—
190	C₃×C₄²	—	2	2	no	—
191	C₃×C₄²	#67	1	2	yes	—
192	C₃×C₄²	C₃×D₄	1	2	yes	—
193	C₃×C₄²	C₂²×D₃	1	2	yes	—
194	C₃×C₄²	C₂³×C₃	1	2	yes	—
195	#215	—	2	16	no	—
196	(C₂×D₃)⋊C₄	—	2	4	no	—
197	C₄⋊Dic₃	—	2	1	no	—
198	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
199	C₂×C₃⋊C₈	—	2	4	no	—
200	C₂×C₃⋊C₈	C₂³×C₃	1	4	yes	—
201	C₂²×C₃²	#121	1	2	yes	—
202	C₂²×C₃²	C₂×SD₁₆	1	2	yes	—
203	C₂²×C₃²	#137	1	2	yes	—
204	C₂²×C₃²	C₂²×D₄	1	1	yes	characteristic
205	C₂×C₃×D₃	—	2	4	no	—
206	C₂×C₃×D₃	—	4	2	no	—
207	C₂×C₃×D₃	—	4	2	no	—
208	C₂×C₃×D₃	—	4	8	no	—
209	C₃²×C₄	—	2	2	no	—
210	C₃²×C₄	—	4	4	no	—
211	C₃²×C₄	#121	1	2	yes	—
212	C₃²×C₄	C₂×SD₁₆	1	4	yes	complemented
213	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
214	C₃²×C₄	C₂×#41	1	1	yes	characteristic
215	C₃×Dic₃	—	4	2	no	—
216	C₂²×Q₈	C₂×C₃×D₃	1	2	yes	—
217	C₂²×D₄	—	3	1	no	—
218	C₂³×C₄	—	6	1	no	—
219	C₂×SD₁₆	—	3	8	no	—
220	C₂×SD₁₆	—	6	8	no	—
221	C₂²×C₈	—	3	2	no	—
222	C₄⋊Q₈	—	2	2	no	—
223	C₄⋊Q₈	C₂×C₃×D₃	1	4	yes	complemented
224	C₄×D₄	—	3	4	no	—
225	C₄×D₄	—	6	2	no	—
226	C₂×C₄⋊C₄	—	2	1	no	—
227	C₂×C₄⋊C₄	—	2	1	no	—
228	C₂×C₄⋊C₄	—	3	1	no	—
229	C₂×C₂²⋊C₄	—	6	1	no	—
230	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
231	C₄⋊C₈	—	3	4	no	—
232	#103	—	3	8	no	—
233	C₂³×C₃	—	2	1	no	—
234	C₂³×C₃	—	6	4	no	—
235	C₂³×C₃	—	6	2	no	—
236	C₂³×C₃	—	12	2	no	—
237	C₂³×C₃	—	12	2	no	—
238	C₂³×C₃	C₂×#67	1	1	yes	characteristic
239	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
240	C₂²×D₃	—	2	4	no	—
241	C₂²×D₃	—	2	2	no	—
242	C₂²×D₃	—	4	2	no	—
243	C₂²×D₃	—	4	2	no	—
244	C₃×Q₈	—	2	4	no	—
245	C₃×Q₈	—	2	4	no	—
246	C₃×Q₈	—	2	4	no	—
247	C₃×Q₈	—	2	4	no	—
248	C₃×Q₈	—	4	4	no	—
249	C₃×Q₈	—	4	4	no	—
250	C₃×Q₈	—	4	8	no	—
251	C₃×Q₈	—	4	4	no	—
252	C₃×Q₈	—	4	4	no	—
253	C₃×D₄	—	3	4	no	—
254	C₃×D₄	—	6	4	no	—
255	C₃×D₄	—	6	2	no	—
256	C₂×C₃×C₄	—	2	4	no	—
257	C₂×C₃×C₄	—	2	2	no	—
258	C₂×C₃×C₄	—	2	2	no	—
259	C₂×C₃×C₄	—	2	8	no	—
260	C₂×C₃×C₄	—	2	4	no	—
261	C₂×C₃×C₄	—	2	4	no	—
262	C₂×C₃×C₄	—	2	1	no	—
263	C₂×C₃×C₄	—	2	4	no	—
264	C₂×C₃×C₄	—	2	2	no	—
265	C₂×C₃×C₄	—	2	2	no	—
266	C₂×C₃×C₄	—	2	2	no	—
267	C₂×C₃×C₄	—	2	2	no	—
268	C₂×C₃×C₄	—	2	1	no	—
269	C₂×C₃×C₄	—	4	8	no	—
270	C₂×C₃×C₄	—	4	4	no	—
271	C₂×C₃×C₄	—	4	4	no	—
272	C₂×C₃×C₄	—	6	2	no	—
273	C₂×C₃×C₄	—	12	2	no	—
274	C₂×C₃×C₄	—	12	8	no	—
275	C₂×C₃×C₄	#215	1	4	yes	complemented
276	C₂×C₃×C₄	C₃×SD₁₆	1	4	yes	complemented
277	C₂×C₃×C₄	D₃×D₄	1	2	yes	—
278	C₂×C₃×C₄	#237	1	2	yes	—
279	C₂×C₃×C₄	C₂×#67	1	2	yes	—
280	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
281	C₂×C₃×C₄	C₂×#67	1	2	yes	—
282	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
283	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
284	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
285	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
286	C₂×C₃×C₄	C₃×#41	1	2	yes	—
287	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
288	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
289	C₂×Dic₃	—	2	2	no	—
290	C₂×Dic₃	—	4	2	no	—
291	D₁₂	—	2	4	no	—
292	D₁₂	—	2	2	no	—
293	D₁₂	C₂×C₃×D₄	1	4	yes	—
294	C₄×D₃	—	4	8	no	—
295	C₃×C₈	—	6	4	no	—
296	C₃⋊C₈	—	2	4	no	—
297	C₂×C₃²	#461	1	4	yes	complemented
298	C₂×C₃²	C₂×#121	1	1	yes	characteristic
299	C₂×C₃²	C₂²×SD₁₆	1	1	yes	characteristic
300	C₂×C₃²	C₂×#137	1	1	yes	characteristic
301	C₃×D₃	—	4	4	no	—
302	C₂⁴	—	6	1	no	—
303	C₂×Q₈	—	2	2	no	—
304	C₂×Q₈	—	2	4	no	—
305	C₂×Q₈	—	2	4	no	—
306	C₂×Q₈	C₂²×C₃×D₃	1	4	yes	—
307	C₂×D₄	—	3	2	no	—
308	C₂×D₄	—	3	4	no	—
309	C₂×D₄	—	6	2	no	—
310	C₂×D₄	—	6	1	no	—
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	6	1	no	—
313	C₂²×C₄	—	6	4	no	—
314	C₂²×C₄	—	12	4	no	—
315	C₂²×C₄	C₃×#67	1	1	yes	characteristic
316	C₂²×C₄	C₃×#67	1	1	yes	characteristic
317	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
318	SD₁₆	—	6	16	no	—
319	C₂×C₈	—	3	4	no	—
320	C₂×C₈	—	6	4	no	—
321	C₄⋊C₄	—	2	4	no	—
322	C₄⋊C₄	—	2	4	no	—
323	C₄⋊C₄	—	3	2	no	—
324	C₄⋊C₄	—	6	1	no	—
325	C₂²⋊C₄	—	6	4	no	—
326	C₄²	C₃×#67	1	2	yes	—
327	C₄²	C₂²×C₃×D₃	1	2	yes	—
328	C₂²×C₃	—	2	2	no	—
329	C₂²×C₃	—	2	2	no	—
330	C₂²×C₃	—	2	2	no	—
331	C₂²×C₃	—	2	1	no	—
332	C₂²×C₃	—	6	4	no	—
333	C₂²×C₃	—	12	2	no	—
334	C₂²×C₃	—	12	2	no	—
335	C₂²×C₃	—	12	8	no	—
336	C₂²×C₃	#938	1	2	yes	—
337	C₂²×C₃	C₂×#215	1	2	yes	—
338	C₂²×C₃	#942	1	2	yes	—
339	C₂²×C₃	C₃×#121	1	2	yes	—
340	C₂²×C₃	C₂×C₃×SD₁₆	1	2	yes	—
341	C₂²×C₃	C₃×#137	1	2	yes	—
342	C₂²×C₃	C₂²×#67	1	1	yes	characteristic
343	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
344	C₂×D₃	—	2	4	no	—
345	C₂×D₃	—	4	2	no	—
346	C₂×D₃	—	4	2	no	—
347	C₂×D₃	—	4	8	no	—
348	C₃×C₄	—	2	4	no	—
349	C₃×C₄	—	2	2	no	—
350	C₃×C₄	—	2	2	no	—
351	C₃×C₄	—	2	2	no	—
352	C₃×C₄	—	2	4	no	—
353	C₃×C₄	—	2	1	no	—
354	C₃×C₄	—	2	1	no	—
355	C₃×C₄	—	4	8	no	—
356	C₃×C₄	—	4	4	no	—
357	C₃×C₄	—	4	4	no	—
358	C₃×C₄	—	12	2	no	—
359	C₃×C₄	#938	1	2	yes	—
360	C₃×C₄	C₂×#215	1	4	yes	complemented
361	C₃×C₄	C₃×#121	1	2	yes	—
362	C₃×C₄	C₂×C₃×SD₁₆	1	4	yes	complemented
363	C₃×C₄	C₂×D₃×D₄	1	1	yes	characteristic
364	C₃×C₄	C₂×#237	1	1	yes	characteristic
365	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
366	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
367	Dic₃	—	4	2	no	—
368	C₃²	C₂×#461	1	1	yes	characteristic, complemented, Sylow
369	C₂³	—	6	4	no	—
370	C₂³	—	6	2	no	—
371	C₂³	—	12	2	no	—
372	C₂³	—	12	2	no	—
373	C₂³	C₂×C₃×#67	1	1	yes	characteristic
374	Q₈	—	2	4	no	—
375	Q₈	—	2	4	no	—
376	Q₈	—	4	4	no	—
377	D₄	—	3	4	no	—
378	D₄	—	6	4	no	—
379	D₄	—	6	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	4	no	—
382	C₂×C₄	—	4	4	no	—
383	C₂×C₄	—	6	2	no	—
384	C₂×C₄	—	12	2	no	—
385	C₂×C₄	—	12	8	no	—
386	C₂×C₄	C₃×#215	1	4	yes	complemented
387	C₂×C₄	C₃×D₃×D₄	1	2	yes	—
388	C₂×C₄	C₃×#237	1	2	yes	—
389	C₂×C₄	C₂×C₃×#67	1	2	yes	—
390	C₂×C₄	C₂×C₃×#67	1	1	yes	characteristic
391	C₂×C₄	C₂×C₃×#67	1	2	yes	—
392	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
393	C₈	—	6	4	no	—
394	C₂×C₃	—	2	1	no	—
395	C₂×C₃	—	2	1	no	—
396	C₂×C₃	—	2	1	no	—
397	C₂×C₃	—	2	4	no	—
398	C₂×C₃	—	12	4	no	—
399	C₂×C₃	#5083	1	4	yes	direct product factor
400	C₂×C₃	C₃×#461	1	4	yes	complemented
401	C₂×C₃	C₂×#938	1	1	yes	characteristic
402	C₂×C₃	C₂²×#215	1	1	yes	characteristic
403	C₂×C₃	C₂×#942	1	1	yes	characteristic
404	C₂×C₃	C₂×C₃×#121	1	1	yes	characteristic
405	C₂×C₃	C₂²×C₃×SD₁₆	1	1	yes	characteristic
406	C₂×C₃	C₂×C₃×#137	1	1	yes	characteristic
407	D₃	—	4	4	no	—
408	C₂²	—	6	4	no	—
409	C₂²	—	12	2	no	—
410	C₂²	—	12	2	no	—
411	C₂²	—	12	8	no	—
412	C₂²	C₃×#938	1	2	yes	—
413	C₂²	C₂×C₃×#215	1	2	yes	—
414	C₂²	C₃×#942	1	2	yes	—
415	C₂²	C₂²×C₃×#67	1	1	yes	characteristic
416	C₄	—	2	2	no	—
417	C₄	—	4	4	no	—
418	C₄	—	12	2	no	—
419	C₄	C₃×#938	1	2	yes	—
420	C₄	C₂×C₃×#215	1	4	yes	complemented
421	C₄	C₂×C₃×D₃×D₄	1	1	yes	characteristic
422	C₄	C₂×C₃×#237	1	1	yes	characteristic
423	C₃	—	2	1	no	—
424	C₃	C₂×#5083	1	1	yes	characteristic, direct product factor
425	C₃	C₂×C₃×#461	1	1	yes	characteristic, complemented
426	C₂	—	12	4	no	—
427	C₂	C₃×#5083	1	4	yes	direct product factor
428	C₂	C₂×C₃×#938	1	1	yes	characteristic
429	C₂	C₂²×C₃×#215	1	1	yes	characteristic
430	C₂	C₂×C₃×#942	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃	C₂×#67
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₂×C₃²×C₄⋊Q₈	C₂
socle	C₂³×C₃²	C₂×D₄
prime radical	C₂²×C₃×D₁₂	C₂²
hypercenter	C₂×C₃×C₄⋊Q₈	D₃
hypocenter	C₃	C₂×C₃×#461
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₃ ◁ C₂×C₃×C₄² ◁ C₂×C₃×C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
1. C₂×C₃²×C₄⋊Q₈	C₂	semidirect
4. C₂×C₃×#835	C₂	semidirect
5. C₃×#5083	C₂	direct (N × H)
6. C₂×C₃×C₄⋊(C₃⋊C₈)	C₂	semidirect
8. C₂×#5083	C₃	direct (N × H)
13. C₃²×C₄⋊Q₈	C₂²	semidirect
24. C₃×#835	C₂²	semidirect
25. C₃×C₄⋊(C₃⋊C₈)	C₂²	semidirect
28. C₂×C₃×C₄⋊Q₈	D₃	semidirect
29. C₂×C₃×C₄⋊Q₈	C₂×C₃	semidirect
36. C₂×#835	C₂×C₃	semidirect
37. #5083	C₂×C₃	direct (N × H)
38. C₂×C₄⋊(C₃⋊C₈)	C₂×C₃	semidirect
80. C₃×C₄⋊Q₈	C₂×D₃	semidirect
81. C₃×C₄⋊Q₈	C₂²×C₃	semidirect
104. #835	C₂²×C₃	semidirect
105. C₄⋊(C₃⋊C₈)	C₂²×C₃	semidirect
117. C₂×C₃²×C₄	SD₁₆	semidirect
132. C₂×C₄⋊Q₈	C₃×D₃	semidirect
212. C₃²×C₄	C₂×SD₁₆	semidirect
223. C₄⋊Q₈	C₂×C₃×D₃	semidirect
275. C₂×C₃×C₄	#215	semidirect
276. C₂×C₃×C₄	C₃×SD₁₆	semidirect
297. C₂×C₃²	#461	semidirect
360. C₃×C₄	C₂×#215	semidirect
362. C₃×C₄	C₂×C₃×SD₁₆	semidirect
368. C₃²	C₂×#461	semidirect
386. C₂×C₄	C₃×#215	semidirect
399. C₂×C₃	#5083	direct (N × H)
400. C₂×C₃	C₃×#461	semidirect
420. C₄	C₂×C₃×#215	semidirect
424. C₃	C₂×#5083	direct (N × H)
425. C₃	C₂×C₃×#461	semidirect
427. C₂	C₃×#5083	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
C₂²×C₃×#215	2
C₂×C₃×C₄×D₁₂	2
C₂×C₃×#835	2
C₃×#5083	2
C₂×C₃×C₄⋊(C₃⋊C₈)	2
C₂×C₃×#461	3
C₂×#5083	3

Subgroups — C2×C3×#5083 #11865467

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#5083 #11865467