Subgroups — C₂×C₃×#5087 #11868229

Order 1152.

1105 conjugacy classes of subgroups.

The subgroup lattice has 409 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	C₂×C₃×C₄×D₁₂	C₂	1	1	yes	maximal, characteristic
3	C₃×#5087	C₂	1	8	yes	maximal, direct product factor
4	C₂×C₃×#809	C₂	1	2	yes	maximal
5	C₂×C₃×#807	C₂	1	2	yes	maximal, complemented
6	C₂×C₃×C₄⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃×#474	—	3	1	no	maximal
8	C₂×#5087	C₃	1	1	yes	maximal, characteristic, direct product factor
9	C₂²×C₃²×Q₈	—	2	1	no	—
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	C₂²	1	2	yes	—
16	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
17	C₂×C₃×(C₂×D₃)⋊C₄	—	2	1	no	—
18	C₂×C₃×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
19	C₂²×C₃×C₃⋊C₈	C₂²	1	2	yes	—
20	C₃×C₄×D₁₂	—	2	2	no	—
21	C₃×C₄×D₁₂	C₂²	1	4	yes	—
22	C₃×#809	C₂²	1	8	yes	—
23	C₃×#807	C₂²	1	8	yes	complemented
24	C₃×C₄⋊(C₃⋊C₈)	C₂²	1	4	yes	complemented
25	C₂×C₃×C₄⋊Q₈	—	2	1	no	—
26	C₂×C₃×C₄⋊Q₈	D₃	1	1	yes	characteristic, complemented
27	C₂×C₃×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
28	C₂×C₃×C₄×D₄	—	3	1	no	—
29	C₂×C₄×D₁₂	C₂×C₃	1	1	yes	characteristic
30	C₃×#474	—	3	8	no	—
31	C₂×C₃×#107	—	3	2	no	—
32	C₂×C₃×C₄⋊C₈	—	3	1	no	—
33	C₂×C₃×#102	—	3	2	no	—
34	#5087	C₂×C₃	1	8	yes	direct product factor
35	C₂×#809	C₂×C₃	1	2	yes	—
36	C₂×#807	C₂×C₃	1	2	yes	complemented
37	C₂×C₄⋊(C₃⋊C₈)	C₂×C₃	1	1	yes	characteristic, complemented
38	C₂³×C₃×D₃	—	2	1	no	—
39	C₂×C₃²×Q₈	—	2	4	no	—
40	C₂×C₃²×Q₈	—	4	4	no	—
41	C₂²×C₃²×C₄	—	2	2	no	—
42	C₂²×C₃²×C₄	D₄	1	1	yes	characteristic
43	C₂²×C₃²×C₄	D₄	1	1	yes	characteristic
44	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
45	C₂²×C₃×Dic₃	—	2	1	no	—
46	C₂×C₃×D₁₂	—	2	1	no	—
47	C₂×C₃×D₁₂	—	2	2	no	—
48	C₂×C₃×D₁₂	Q₈	1	4	yes	complemented
49	C₂×C₃×D₁₂	C₂³	1	2	yes	—
50	C₂×C₃×C₄×D₃	—	2	4	no	—
51	C₂×C₃×C₄×D₃	—	4	4	no	—
52	C₃²×C₄⋊C₄	—	2	4	no	—
53	C₃²×C₄⋊C₄	—	2	2	no	—
54	C₃²×C₄⋊C₄	C₂³	1	4	yes	—
55	C₃²×C₄²	D₄	1	2	yes	—
56	C₃²×C₄²	C₂³	1	2	yes	—
57	C₃×(C₂×D₃)⋊C₄	—	2	4	no	—
58	C₃×C₄⋊Dic₃	—	2	1	no	—
59	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
60	C₂×C₃×C₃⋊C₈	—	2	4	no	—
61	C₂×C₃×C₃⋊C₈	C₂³	1	4	yes	—
62	C₂×#474	—	3	1	no	Sylow
63	C₂²×C₃×Q₈	—	2	2	no	—
64	C₂²×C₃×Q₈	—	2	1	no	—
65	C₂²×C₃×Q₈	—	2	1	no	—
66	C₂²×C₃×D₄	—	3	1	no	—
67	C₂³×C₃×C₄	—	6	1	no	—
68	C₂²×D₁₂	C₂²×C₃	1	1	yes	characteristic
69	C₂²×C₄×D₃	—	2	1	no	—
70	C₂²×C₃×C₈	—	3	2	no	—
71	C₃×C₄⋊Q₈	—	2	4	no	—
72	C₃×C₄⋊Q₈	—	2	2	no	—
73	C₃×C₄⋊Q₈	—	2	2	no	—
74	C₃×C₄⋊Q₈	—	2	4	no	—
75	C₃×C₄⋊Q₈	C₂×D₃	1	4	yes	complemented
76	C₃×C₄⋊Q₈	C₂²×C₃	1	4	yes	complemented
77	C₃×C₄×D₄	—	3	4	no	—
78	C₃×C₄×D₄	—	6	2	no	—
79	C₂×C₃×C₄⋊C₄	—	2	2	no	—
80	C₂×C₃×C₄⋊C₄	—	2	1	no	—
81	C₂×C₃×C₄⋊C₄	—	2	1	no	—
82	C₂×C₃×C₄⋊C₄	—	2	2	no	—
83	C₂×C₃×C₄⋊C₄	—	3	1	no	—
84	C₂×C₃×C₄⋊C₄	C₂×D₃	1	2	yes	—
85	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
86	C₂×C₃×C₂²⋊C₄	—	6	1	no	—
87	C₂×C₃×C₄²	—	2	1	no	—
88	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
89	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
90	C₂×(C₂×D₃)⋊C₄	—	2	1	no	—
91	C₂×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
92	C₂²×C₃⋊C₈	C₂²×C₃	1	2	yes	—
93	C₄×D₁₂	—	2	2	no	—
94	C₄×D₁₂	C₂²×C₃	1	4	yes	—
95	C₃×#107	—	3	8	no	—
96	C₃×C₄⋊C₈	—	3	4	no	—
97	C₃×#102	—	3	8	no	—
98	#809	C₂²×C₃	1	8	yes	—
99	#807	C₂²×C₃	1	8	yes	complemented
100	C₄⋊(C₃⋊C₈)	C₂²×C₃	1	4	yes	complemented
101	C₂³×C₃²	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₃×D₃	—	2	4	no	—
103	C₂²×C₃×D₃	—	2	2	no	—
104	C₂²×C₃×D₃	—	4	2	no	—
105	C₂²×C₃×D₃	—	4	2	no	—
106	C₃²×Q₈	—	4	8	no	—
107	C₂×C₃²×C₄	—	2	2	no	—
108	C₂×C₃²×C₄	—	2	4	no	—
109	C₂×C₃²×C₄	—	4	4	no	—
110	C₂×C₃²×C₄	D₈	1	4	yes	—
111	C₂×C₃²×C₄	C₂×D₄	1	2	yes	—
112	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
113	C₂×C₃²×C₄	C₂×D₄	1	2	yes	—
114	C₂×C₃²×C₄	C₂×Q₈	1	2	yes	—
115	C₂×C₃²×C₄	#41	1	2	yes	—
116	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
117	C₂×C₃×Dic₃	—	2	2	no	—
118	C₂×C₃×Dic₃	—	4	2	no	—
119	C₃×D₁₂	—	2	4	no	—
120	C₃×D₁₂	—	2	2	no	—
121	C₃×D₁₂	C₂×Q₈	1	4	yes	complemented
122	C₃×C₄×D₃	—	4	8	no	—
123	C₃×C₃⋊C₈	—	2	4	no	—
124	C₂×C₄⋊Q₈	C₃×D₃	1	1	yes	characteristic, complemented
125	C₂×C₄×D₄	—	3	1	no	—
126	#474	—	3	8	no	—
127	C₂×#107	—	3	2	no	—
128	C₂×C₄⋊C₈	—	3	1	no	—
129	C₂×#102	—	3	2	no	—
130	C₂⁴×C₃	—	6	1	no	—
131	C₂³×D₃	—	2	1	no	—
132	C₂×C₃×Q₈	—	2	8	no	—
133	C₂×C₃×Q₈	—	2	4	no	—
134	C₂×C₃×Q₈	—	2	4	no	—
135	C₂×C₃×Q₈	—	4	8	no	—
136	C₂×C₃×Q₈	—	4	4	no	—
137	C₂×C₃×Q₈	—	4	4	no	—
138	C₂×C₃×D₄	—	3	4	no	—
139	C₂×C₃×D₄	—	3	2	no	—
140	C₂×C₃×D₄	—	6	2	no	—
141	C₂×C₃×D₄	—	6	1	no	—
142	C₂²×C₃×C₄	—	2	4	no	—
143	C₂²×C₃×C₄	—	2	2	no	—
144	C₂²×C₃×C₄	—	2	2	no	—
145	C₂²×C₃×C₄	—	2	1	no	—
146	C₂²×C₃×C₄	—	2	1	no	—
147	C₂²×C₃×C₄	—	2	1	no	—
148	C₂²×C₃×C₄	—	6	1	no	—
149	C₂²×C₃×C₄	—	6	4	no	—
150	C₂²×C₃×C₄	—	12	4	no	—
151	C₂²×C₃×C₄	#67	1	1	yes	characteristic
152	C₂²×C₃×C₄	#67	1	1	yes	characteristic
153	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
154	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
155	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
156	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
157	C₂²×Dic₃	—	2	1	no	—
158	C₂×D₁₂	—	2	1	no	—
159	C₂×D₁₂	—	2	2	no	—
160	C₂×D₁₂	C₃×Q₈	1	4	yes	complemented
161	C₂×D₁₂	C₂³×C₃	1	2	yes	—
162	C₂×C₄×D₃	—	2	4	no	—
163	C₂×C₄×D₃	—	4	4	no	—
164	C₂×C₃×C₈	—	3	4	no	—
165	C₂×C₃×C₈	—	6	4	no	—
166	C₃×C₄⋊C₄	—	2	8	no	—
167	C₃×C₄⋊C₄	—	2	4	no	—
168	C₃×C₄⋊C₄	—	2	4	no	—
169	C₃×C₄⋊C₄	—	2	2	no	—
170	C₃×C₄⋊C₄	—	2	4	no	—
171	C₃×C₄⋊C₄	—	2	2	no	—
172	C₃×C₄⋊C₄	—	2	4	no	—
173	C₃×C₄⋊C₄	—	3	2	no	—
174	C₃×C₄⋊C₄	—	6	1	no	—
175	C₃×C₄⋊C₄	C₂²×D₃	1	4	yes	—
176	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
177	C₃×C₂²⋊C₄	—	6	4	no	—
178	C₃×C₄²	—	2	2	no	—
179	C₃×C₄²	—	2	2	no	—
180	C₃×C₄²	#67	1	2	yes	—
181	C₃×C₄²	C₃×D₄	1	2	yes	—
182	C₃×C₄²	C₂²×D₃	1	2	yes	—
183	C₃×C₄²	C₂³×C₃	1	2	yes	—
184	(C₂×D₃)⋊C₄	—	2	4	no	—
185	C₄⋊Dic₃	—	2	1	no	—
186	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
187	C₂×C₃⋊C₈	—	2	4	no	—
188	C₂×C₃⋊C₈	C₂³×C₃	1	4	yes	—
189	C₂²×C₃²	C₂²⋊Q₈	1	2	yes	—
190	C₂²×C₃²	C₂×D₈	1	2	yes	—
191	C₂²×C₃²	#137	1	2	yes	—
192	C₂²×C₃²	C₂²×D₄	1	1	yes	characteristic
193	C₂×C₃×D₃	—	2	4	no	—
194	C₂×C₃×D₃	—	4	2	no	—
195	C₂×C₃×D₃	—	4	2	no	—
196	C₂×C₃×D₃	—	4	8	no	—
197	C₃²×C₄	—	2	2	no	—
198	C₃²×C₄	—	4	4	no	—
199	C₃²×C₄	C₂²⋊Q₈	1	2	yes	—
200	C₃²×C₄	C₂×D₈	1	4	yes	—
201	C₃²×C₄	C₂²×Q₈	1	1	yes	characteristic
202	C₃²×C₄	C₂×#41	1	1	yes	characteristic
203	C₃×Dic₃	—	4	2	no	—
204	C₂²×Q₈	—	2	1	no	—
205	C₂²×D₄	—	3	1	no	—
206	C₂³×C₄	—	6	1	no	—
207	C₂²×C₈	—	3	2	no	—
208	C₄⋊Q₈	—	2	2	no	—
209	C₄⋊Q₈	C₂×C₃×D₃	1	4	yes	complemented
210	C₄×D₄	—	3	4	no	—
211	C₄×D₄	—	6	2	no	—
212	C₂×C₄⋊C₄	—	2	1	no	—
213	C₂×C₄⋊C₄	—	3	1	no	—
214	C₂×C₄⋊C₄	C₂×C₃×D₃	1	2	yes	—
215	C₂×C₂²⋊C₄	—	6	1	no	—
216	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
217	#107	—	3	8	no	—
218	C₄⋊C₈	—	3	4	no	—
219	#102	—	3	8	no	—
220	C₂³×C₃	—	2	1	no	—
221	C₂³×C₃	—	6	4	no	—
222	C₂³×C₃	—	6	2	no	—
223	C₂³×C₃	—	12	2	no	—
224	C₂³×C₃	—	12	2	no	—
225	C₂³×C₃	C₂×#67	1	1	yes	characteristic
226	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
227	C₂²×D₃	—	2	4	no	—
228	C₂²×D₃	—	2	2	no	—
229	C₂²×D₃	—	4	2	no	—
230	C₂²×D₃	—	4	2	no	—
231	C₃×Q₈	—	4	16	no	—
232	C₃×Q₈	—	4	8	no	—
233	C₃×Q₈	—	4	8	no	—
234	C₃×D₄	—	3	4	no	—
235	C₃×D₄	—	6	4	no	—
236	C₃×D₄	—	6	2	no	—
237	C₂×C₃×C₄	—	2	4	no	—
238	C₂×C₃×C₄	—	2	2	no	—
239	C₂×C₃×C₄	—	2	2	no	—
240	C₂×C₃×C₄	—	2	8	no	—
241	C₂×C₃×C₄	—	2	4	no	—
242	C₂×C₃×C₄	—	2	4	no	—
243	C₂×C₃×C₄	—	2	1	no	—
244	C₂×C₃×C₄	—	2	4	no	—
245	C₂×C₃×C₄	—	2	2	no	—
246	C₂×C₃×C₄	—	2	2	no	—
247	C₂×C₃×C₄	—	2	2	no	—
248	C₂×C₃×C₄	—	2	1	no	—
249	C₂×C₃×C₄	—	2	2	no	—
250	C₂×C₃×C₄	—	4	8	no	—
251	C₂×C₃×C₄	—	4	4	no	—
252	C₂×C₃×C₄	—	4	4	no	—
253	C₂×C₃×C₄	—	6	2	no	—
254	C₂×C₃×C₄	—	12	2	no	—
255	C₂×C₃×C₄	—	12	8	no	—
256	C₂×C₃×C₄	#213	1	4	yes	—
257	C₂×C₃×C₄	C₃×D₈	1	4	yes	—
258	C₂×C₃×C₄	D₃×Q₈	1	2	yes	—
259	C₂×C₃×C₄	#239	1	2	yes	—
260	C₂×C₃×C₄	C₂×#67	1	2	yes	—
261	C₂×C₃×C₄	C₂×#67	1	2	yes	—
262	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
263	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
264	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
265	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
266	C₂×C₃×C₄	C₂×C₃×Q₈	1	2	yes	—
267	C₂×C₃×C₄	C₃×#41	1	2	yes	—
268	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
269	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
270	C₂×Dic₃	—	2	2	no	—
271	C₂×Dic₃	—	4	2	no	—
272	D₁₂	—	2	4	no	—
273	D₁₂	—	2	2	no	—
274	D₁₂	C₂×C₃×Q₈	1	4	yes	complemented
275	C₄×D₃	—	4	8	no	—
276	C₃×C₈	—	6	4	no	—
277	C₃⋊C₈	—	2	4	no	—
278	C₂×C₃²	#474	1	4	yes	complemented
279	C₂×C₃²	C₂×C₂²⋊Q₈	1	1	yes	characteristic
280	C₂×C₃²	C₂²×D₈	1	1	yes	characteristic
281	C₂×C₃²	C₂×#137	1	1	yes	characteristic
282	C₃×D₃	—	4	4	no	—
283	C₂⁴	—	6	1	no	—
284	C₂×Q₈	—	2	4	no	—
285	C₂×Q₈	—	4	4	no	—
286	C₂×D₄	—	3	2	no	—
287	C₂×D₄	—	3	4	no	—
288	C₂×D₄	—	6	2	no	—
289	C₂×D₄	—	6	1	no	—
290	C₂²×C₄	—	2	2	no	—
291	C₂²×C₄	—	6	1	no	—
292	C₂²×C₄	—	6	4	no	—
293	C₂²×C₄	—	12	4	no	—
294	C₂²×C₄	C₃×#67	1	1	yes	characteristic
295	C₂²×C₄	C₃×#67	1	1	yes	characteristic
296	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
297	C₂×C₈	—	3	4	no	—
298	C₂×C₈	—	6	4	no	—
299	C₄⋊C₄	—	2	4	no	—
300	C₄⋊C₄	—	2	2	no	—
301	C₄⋊C₄	—	3	2	no	—
302	C₄⋊C₄	—	6	1	no	—
303	C₄⋊C₄	C₂²×C₃×D₃	1	4	yes	—
304	C₂²⋊C₄	—	6	4	no	—
305	C₄²	C₃×#67	1	2	yes	—
306	C₄²	C₂²×C₃×D₃	1	2	yes	—
307	C₂²×C₃	—	2	2	no	—
308	C₂²×C₃	—	2	2	no	—
309	C₂²×C₃	—	2	2	no	—
310	C₂²×C₃	—	2	1	no	—
311	C₂²×C₃	—	6	4	no	—
312	C₂²×C₃	—	12	2	no	—
313	C₂²×C₃	—	12	2	no	—
314	C₂²×C₃	—	12	8	no	—
315	C₂²×C₃	C₂×#213	1	2	yes	—
316	C₂²×C₃	#942	1	2	yes	—
317	C₂²×C₃	#946	1	2	yes	—
318	C₂²×C₃	C₃×C₂²⋊Q₈	1	2	yes	—
319	C₂²×C₃	C₂×C₃×D₈	1	2	yes	—
320	C₂²×C₃	C₃×#137	1	2	yes	—
321	C₂²×C₃	C₂²×#67	1	1	yes	characteristic
322	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
323	C₂×D₃	—	2	4	no	—
324	C₂×D₃	—	4	2	no	—
325	C₂×D₃	—	4	2	no	—
326	C₂×D₃	—	4	8	no	—
327	C₃×C₄	—	2	4	no	—
328	C₃×C₄	—	2	2	no	—
329	C₃×C₄	—	2	2	no	—
330	C₃×C₄	—	2	4	no	—
331	C₃×C₄	—	2	2	no	—
332	C₃×C₄	—	2	1	no	—
333	C₃×C₄	—	2	1	no	—
334	C₃×C₄	—	4	8	no	—
335	C₃×C₄	—	4	4	no	—
336	C₃×C₄	—	4	4	no	—
337	C₃×C₄	—	12	2	no	—
338	C₃×C₄	C₂×#213	1	4	yes	—
339	C₃×C₄	#946	1	2	yes	—
340	C₃×C₄	C₃×C₂²⋊Q₈	1	2	yes	—
341	C₃×C₄	C₂×C₃×D₈	1	4	yes	—
342	C₃×C₄	C₂×D₃×Q₈	1	1	yes	characteristic
343	C₃×C₄	C₂×#239	1	1	yes	characteristic
344	C₃×C₄	C₂²×C₃×Q₈	1	1	yes	characteristic
345	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
346	Dic₃	—	4	2	no	—
347	C₃²	C₂×#474	1	1	yes	characteristic, complemented, Sylow
348	C₂³	—	6	4	no	—
349	C₂³	—	6	2	no	—
350	C₂³	—	12	2	no	—
351	C₂³	—	12	2	no	—
352	C₂³	C₂×C₃×#67	1	1	yes	characteristic
353	Q₈	—	4	8	no	—
354	D₄	—	3	4	no	—
355	D₄	—	6	4	no	—
356	D₄	—	6	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	4	no	—
359	C₂×C₄	—	4	4	no	—
360	C₂×C₄	—	6	2	no	—
361	C₂×C₄	—	12	2	no	—
362	C₂×C₄	—	12	8	no	—
363	C₂×C₄	C₃×#213	1	4	yes	—
364	C₂×C₄	C₃×D₃×Q₈	1	2	yes	—
365	C₂×C₄	C₃×#239	1	2	yes	—
366	C₂×C₄	C₂×C₃×#67	1	2	yes	—
367	C₂×C₄	C₂×C₃×#67	1	2	yes	—
368	C₂×C₄	C₂×C₃×#67	1	1	yes	characteristic
369	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
370	C₈	—	6	4	no	—
371	C₂×C₃	—	2	1	no	—
372	C₂×C₃	—	2	1	no	—
373	C₂×C₃	—	2	1	no	—
374	C₂×C₃	—	2	4	no	—
375	C₂×C₃	—	12	4	no	—
376	C₂×C₃	#5087	1	4	yes	direct product factor
377	C₂×C₃	C₃×#474	1	4	yes	complemented
378	C₂×C₃	C₂²×#213	1	1	yes	characteristic
379	C₂×C₃	C₂×#942	1	1	yes	characteristic
380	C₂×C₃	C₂×#946	1	1	yes	characteristic
381	C₂×C₃	C₂×C₃×C₂²⋊Q₈	1	1	yes	characteristic
382	C₂×C₃	C₂²×C₃×D₈	1	1	yes	characteristic
383	C₂×C₃	C₂×C₃×#137	1	1	yes	characteristic
384	D₃	—	4	4	no	—
385	C₂²	—	6	4	no	—
386	C₂²	—	12	2	no	—
387	C₂²	—	12	2	no	—
388	C₂²	—	12	8	no	—
389	C₂²	C₂×C₃×#213	1	2	yes	—
390	C₂²	C₃×#942	1	2	yes	—
391	C₂²	C₃×#946	1	2	yes	—
392	C₂²	C₂²×C₃×#67	1	1	yes	characteristic
393	C₄	—	2	2	no	—
394	C₄	—	4	4	no	—
395	C₄	—	12	2	no	—
396	C₄	C₂×C₃×#213	1	4	yes	—
397	C₄	C₃×#946	1	2	yes	—
398	C₄	C₂×C₃×D₃×Q₈	1	1	yes	characteristic
399	C₄	C₂×C₃×#239	1	1	yes	characteristic
400	C₃	—	2	1	no	—
401	C₃	C₂×#5087	1	1	yes	characteristic, direct product factor
402	C₃	C₂×C₃×#474	1	1	yes	characteristic, complemented
403	C₂	—	12	4	no	—
404	C₂	C₃×#5087	1	4	yes	direct product factor
405	C₂	C₂²×C₃×#213	1	1	yes	characteristic
406	C₂	C₂×C₃×#942	1	1	yes	characteristic
407	C₂	C₂×C₃×#946	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×#474
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
3. C₃×#5087	C₂	direct (N × H)
5. C₂×C₃×#807	C₂	semidirect
6. C₂×C₃×C₄⋊(C₃⋊C₈)	C₂	semidirect
8. C₂×#5087	C₃	direct (N × H)
13. C₃²×C₄⋊Q₈	C₂²	semidirect
23. C₃×#807	C₂²	semidirect
24. C₃×C₄⋊(C₃⋊C₈)	C₂²	semidirect
26. C₂×C₃×C₄⋊Q₈	D₃	semidirect
27. C₂×C₃×C₄⋊Q₈	C₂×C₃	semidirect
34. #5087	C₂×C₃	direct (N × H)
36. C₂×#807	C₂×C₃	semidirect
37. C₂×C₄⋊(C₃⋊C₈)	C₂×C₃	semidirect
48. C₂×C₃×D₁₂	Q₈	semidirect
75. C₃×C₄⋊Q₈	C₂×D₃	semidirect
76. C₃×C₄⋊Q₈	C₂²×C₃	semidirect
99. #807	C₂²×C₃	semidirect
100. C₄⋊(C₃⋊C₈)	C₂²×C₃	semidirect
121. C₃×D₁₂	C₂×Q₈	semidirect
124. C₂×C₄⋊Q₈	C₃×D₃	semidirect
160. C₂×D₁₂	C₃×Q₈	semidirect
209. C₄⋊Q₈	C₂×C₃×D₃	semidirect
274. D₁₂	C₂×C₃×Q₈	semidirect
278. C₂×C₃²	#474	semidirect
347. C₃²	C₂×#474	semidirect
376. C₂×C₃	#5087	direct (N × H)
377. C₂×C₃	C₃×#474	semidirect
401. C₃	C₂×#5087	direct (N × H)
402. C₃	C₂×C₃×#474	semidirect
404. C₂	C₃×#5087	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
C₂×C₃×C₄×D₁₂	2
C₃×#5087	2
C₂×C₃×#809	2
C₂×C₃×#807	2
C₂×C₃×C₄⋊(C₃⋊C₈)	2
C₂×C₃×#474	3
C₂×#5087	3

Subgroups — C2×C3×#5087 #11868229

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#5087 #11868229