Subgroups — C₂²×C₃×#942 #11918690

Order 1152.

3353 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃²×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×#235	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₃×#216	C₂	1	2	yes	maximal, complemented
4	C₂×C₃×#942	C₂	1	24	yes	maximal, direct product factor
5	C₂²×C₃×#215	C₂	1	2	yes	maximal, complemented
6	C₂²×C₃×#208	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×C₃×#137	—	3	1	no	maximal
8	C₂²×#942	C₃	1	1	yes	maximal, characteristic, direct product factor
9	C₂²×C₃²×Q₈	—	2	1	no	—
10	C₂²×C₃²×Q₈	—	2	6	no	—
11	C₂²×C₃²×Q₈	C₂²	1	2	yes	—
12	C₂²×C₃²×Q₈	C₂²	1	12	yes	complemented
13	C₂³×C₃²×C₄	—	2	1	no	—
14	C₂³×C₃²×C₄	C₂²	1	1	yes	characteristic
15	C₂²×C₃×#67	—	2	1	no	—
16	C₂×C₃×#235	—	2	6	no	—
17	C₂×C₃×#235	C₂²	1	12	yes	—
18	C₂²×C₃×D₁₂	C₂²	1	1	yes	characteristic
19	C₂²×C₃×C₄×D₃	—	2	1	no	—
20	C₂²×C₃×Dic₆	C₂²	1	1	yes	characteristic
21	C₂×C₃×#216	C₂²	1	24	yes	complemented
22	C₃×#942	C₂²	1	64	yes	direct product factor
23	C₂×C₃×#215	C₂²	1	24	yes	complemented
24	C₂×C₃×#208	C₂²	1	12	yes	complemented
25	C₂²×C₃×C₃⋊C₈	C₂²	1	2	yes	—
26	C₂²×C₃×#41	—	3	1	no	—
27	C₂³×C₃×Q₈	—	2	1	no	—
28	C₂³×C₃×Q₈	D₃	1	1	yes	characteristic, complemented
29	C₂³×C₃×Q₈	C₂×C₃	1	1	yes	characteristic, complemented
30	C₂²×#235	C₂×C₃	1	1	yes	characteristic
31	C₂×C₃×#137	—	3	24	no	—
32	C₂²×C₃×Q₁₆	—	3	2	no	—
33	C₂²×C₃×SD₁₆	—	3	2	no	—
34	C₂²×C₃×M₁₆	—	3	1	no	—
35	C₂²×#216	C₂×C₃	1	2	yes	complemented
36	C₂×#942	C₂×C₃	1	24	yes	direct product factor
37	C₂²×#215	C₂×C₃	1	2	yes	complemented
38	C₂²×#208	C₂×C₃	1	1	yes	characteristic, complemented
39	C₂⁴×C₃²	D₄	1	1	yes	characteristic
40	C₂³×C₃×D₃	—	2	1	no	—
41	C₂×C₃²×Q₈	—	2	6	no	—
42	C₂×C₃²×Q₈	—	2	12	no	—
43	C₂×C₃²×Q₈	—	2	24	no	—
44	C₂×C₃²×Q₈	C₂³	1	12	yes	—
45	C₂×C₃²×Q₈	C₂³	1	16	yes	complemented
46	C₂²×C₃²×C₄	—	2	2	no	—
47	C₂²×C₃²×C₄	—	2	12	no	—
48	C₂²×C₃²×C₄	D₄	1	1	yes	characteristic
49	C₂²×C₃²×C₄	D₄	1	6	yes	—
50	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
51	C₂²×C₃²×C₄	C₂³	1	6	yes	—
52	C₂×C₃×#67	—	2	12	no	—
53	C₂²×C₃×Dic₃	—	2	1	no	—
54	C₃×#235	—	2	24	no	—
55	C₃×#235	C₂³	1	16	yes	—
56	C₂×C₃×D₁₂	—	2	3	no	—
57	C₂×C₃×D₁₂	C₂³	1	6	yes	—
58	C₂×C₃×C₄×D₃	—	2	12	no	—
59	C₂×C₃×Dic₆	—	2	3	no	—
60	C₂×C₃×Dic₆	C₂³	1	6	yes	—
61	C₃×#216	C₂³	1	32	yes	complemented
62	C₃×#215	C₂³	1	32	yes	complemented
63	C₃×#208	C₂³	1	16	yes	complemented
64	C₂×C₃×C₃⋊C₈	C₂³	1	12	yes	—
65	C₂²×#137	—	3	1	no	Sylow
66	C₂×C₃×#41	—	3	12	no	—
67	C₂×C₃×#41	—	6	6	no	—
68	C₂²×C₃×Q₈	—	2	2	no	—
69	C₂²×C₃×Q₈	—	2	12	no	—
70	C₂²×C₃×Q₈	—	2	6	no	—
71	C₂²×C₃×Q₈	—	2	1	no	—
72	C₂²×C₃×Q₈	—	2	1	no	—
73	C₂²×C₃×Q₈	—	2	6	no	—
74	C₂²×C₃×Q₈	—	2	2	no	—
75	C₂²×C₃×Q₈	—	2	12	no	—
76	C₂²×C₃×Q₈	—	3	1	no	—
77	C₂²×C₃×Q₈	C₂×D₃	1	2	yes	—
78	C₂²×C₃×Q₈	C₂×D₃	1	12	yes	complemented
79	C₂²×C₃×Q₈	C₂²×C₃	1	2	yes	—
80	C₂²×C₃×Q₈	C₂²×C₃	1	12	yes	complemented
81	C₂²×C₃×D₄	—	3	1	no	—
82	C₂²×C₃×D₄	—	6	1	no	—
83	C₂³×C₃×C₄	—	2	2	no	—
84	C₂³×C₃×C₄	—	2	1	no	—
85	C₂³×C₃×C₄	—	2	1	no	—
86	C₂³×C₃×C₄	—	2	1	no	—
87	C₂³×C₃×C₄	—	6	1	no	—
88	C₂³×C₃×C₄	C₂×D₃	1	1	yes	characteristic
89	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
90	C₂²×#67	—	2	1	no	—
91	C₂×#235	—	2	6	no	—
92	C₂×#235	C₂²×C₃	1	12	yes	—
93	C₂²×D₁₂	C₂²×C₃	1	1	yes	characteristic
94	C₂²×C₄×D₃	—	2	1	no	—
95	C₂²×Dic₆	C₂²×C₃	1	1	yes	characteristic
96	C₃×#137	—	3	64	no	—
97	C₂×C₃×Q₁₆	—	3	24	no	—
98	C₂×C₃×SD₁₆	—	3	24	no	—
99	C₂×C₃×M₁₆	—	3	12	no	—
100	C₂²×C₃×C₈	—	3	2	no	—
101	C₂×#216	C₂²×C₃	1	24	yes	complemented
102	#942	C₂²×C₃	1	64	yes	direct product factor
103	C₂×#215	C₂²×C₃	1	24	yes	complemented
104	C₂×#208	C₂²×C₃	1	12	yes	complemented
105	C₂²×C₃⋊C₈	C₂²×C₃	1	2	yes	—
106	C₂³×C₃²	—	2	4	no	—
107	C₂³×C₃²	C₂×D₄	1	6	yes	—
108	C₂³×C₃²	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₃×D₃	—	2	6	no	—
110	C₂²×C₃×D₃	—	4	4	no	—
111	C₃²×Q₈	—	2	12	no	—
112	C₃²×Q₈	—	2	16	no	—
113	C₃²×Q₈	C₂⁴	1	8	yes	—
114	C₂×C₃²×C₄	—	2	12	no	—
115	C₂×C₃²×C₄	—	2	16	no	—
116	C₂×C₃²×C₄	C₂×D₄	1	3	yes	—
117	C₂×C₃²×C₄	C₂×D₄	1	6	yes	—
118	C₂×C₃²×C₄	C₂×D₄	1	12	yes	—
119	C₂×C₃²×C₄	C₂⁴	1	3	yes	—
120	C₂×C₃²×C₄	C₂⁴	1	4	yes	—
121	C₃×#67	—	2	16	no	—
122	C₂×C₃×Dic₃	—	2	6	no	—
123	C₃×D₁₂	—	2	6	no	—
124	C₃×D₁₂	C₂⁴	1	4	yes	—
125	C₃×C₄×D₃	—	2	16	no	—
126	C₃×Dic₆	—	2	6	no	—
127	C₃×Dic₆	C₂⁴	1	4	yes	—
128	C₃×C₃⋊C₈	C₂⁴	1	8	yes	—
129	C₂²×#41	—	3	1	no	—
130	C₂³×Q₈	C₃×D₃	1	1	yes	characteristic, complemented
131	C₂×#137	—	3	24	no	—
132	C₂²×Q₁₆	—	3	2	no	—
133	C₂²×SD₁₆	—	3	2	no	—
134	C₂²×M₁₆	—	3	1	no	—
135	C₂⁴×C₃	—	2	1	no	—
136	C₂⁴×C₃	—	6	1	no	—
137	C₂⁴×C₃	#67	1	1	yes	characteristic
138	C₂⁴×C₃	C₃×D₄	1	1	yes	characteristic
139	C₂³×D₃	—	2	1	no	—
140	C₃×#41	—	3	16	no	—
141	C₃×#41	—	6	24	no	—
142	C₂×C₃×Q₈	—	2	12	no	—
143	C₂×C₃×Q₈	—	2	24	no	—
144	C₂×C₃×Q₈	—	2	48	no	—
145	C₂×C₃×Q₈	—	2	6	no	—
146	C₂×C₃×Q₈	—	2	12	no	—
147	C₂×C₃×Q₈	—	2	24	no	—
148	C₂×C₃×Q₈	—	2	6	no	—
149	C₂×C₃×Q₈	—	2	12	no	—
150	C₂×C₃×Q₈	—	2	24	no	—
151	C₂×C₃×Q₈	—	2	12	no	—
152	C₂×C₃×Q₈	—	2	16	no	—
153	C₂×C₃×Q₈	—	3	6	no	—
154	C₂×C₃×Q₈	—	6	3	no	—
155	C₂×C₃×Q₈	C₂²×D₃	1	12	yes	—
156	C₂×C₃×Q₈	C₂²×D₃	1	16	yes	complemented
157	C₂×C₃×Q₈	C₂³×C₃	1	12	yes	—
158	C₂×C₃×Q₈	C₂³×C₃	1	16	yes	complemented
159	C₂×C₃×D₄	—	3	6	no	—
160	C₂×C₃×D₄	—	6	12	no	—
161	C₂×C₃×D₄	—	6	3	no	—
162	C₂²×C₃×C₄	—	2	4	no	—
163	C₂²×C₃×C₄	—	2	24	no	—
164	C₂²×C₃×C₄	—	2	12	no	—
165	C₂²×C₃×C₄	—	2	2	no	—
166	C₂²×C₃×C₄	—	2	2	no	—
167	C₂²×C₃×C₄	—	2	12	no	—
168	C₂²×C₃×C₄	—	2	1	no	—
169	C₂²×C₃×C₄	—	2	6	no	—
170	C₂²×C₃×C₄	—	2	1	no	—
171	C₂²×C₃×C₄	—	2	6	no	—
172	C₂²×C₃×C₄	—	6	1	no	—
173	C₂²×C₃×C₄	—	6	12	no	—
174	C₂²×C₃×C₄	#67	1	6	yes	—
175	C₂²×C₃×C₄	#67	1	1	yes	characteristic
176	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
177	C₂²×C₃×C₄	C₃×D₄	1	6	yes	—
178	C₂²×C₃×C₄	C₂²×D₃	1	6	yes	—
179	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
180	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
181	C₂²×C₃×C₄	C₂³×C₃	1	6	yes	—
182	C₂×#67	—	2	12	no	—
183	C₂²×Dic₃	—	2	1	no	—
184	#235	—	2	24	no	—
185	#235	C₂³×C₃	1	16	yes	—
186	C₂×D₁₂	—	2	3	no	—
187	C₂×D₁₂	C₂³×C₃	1	6	yes	—
188	C₂×C₄×D₃	—	2	12	no	—
189	C₂×Dic₆	—	2	3	no	—
190	C₂×Dic₆	C₂³×C₃	1	6	yes	—
191	C₃×Q₁₆	—	3	32	no	—
192	C₃×SD₁₆	—	3	32	no	—
193	C₃×M₁₆	—	3	16	no	—
194	C₂×C₃×C₈	—	3	12	no	—
195	#216	C₂³×C₃	1	32	yes	complemented
196	#215	C₂³×C₃	1	32	yes	complemented
197	#208	C₂³×C₃	1	16	yes	complemented
198	C₂×C₃⋊C₈	C₂³×C₃	1	12	yes	—
199	C₂²×C₃²	—	2	12	no	—
200	C₂²×C₃²	#137	1	4	yes	complemented
201	C₂²×C₃²	C₂²×D₄	1	4	yes	—
202	C₂²×C₃²	C₂²×D₄	1	3	yes	—
203	C₂×C₃×D₃	—	2	4	no	—
204	C₂×C₃×D₃	—	4	12	no	—
205	C₃²×C₄	—	2	8	no	—
206	C₃²×C₄	C₂²×D₄	1	3	yes	—
207	C₃²×C₄	C₂²×D₄	1	4	yes	—
208	C₃²×C₄	C₂⁵	1	1	yes	characteristic
209	C₃×Dic₃	—	2	4	no	—
210	C₂×#41	—	3	12	no	—
211	C₂×#41	—	6	6	no	—
212	C₂²×Q₈	—	2	1	no	—
213	C₂²×Q₈	—	2	6	no	—
214	C₂²×Q₈	—	3	1	no	—
215	C₂²×Q₈	C₂×C₃×D₃	1	2	yes	—
216	C₂²×Q₈	C₂×C₃×D₃	1	12	yes	complemented
217	C₂²×D₄	—	3	1	no	—
218	C₂²×D₄	—	6	1	no	—
219	C₂³×C₄	—	2	1	no	—
220	C₂³×C₄	—	6	1	no	—
221	C₂³×C₄	C₂×C₃×D₃	1	1	yes	characteristic
222	#137	—	3	64	no	—
223	C₂×Q₁₆	—	3	24	no	—
224	C₂×SD₁₆	—	3	24	no	—
225	C₂×M₁₆	—	3	12	no	—
226	C₂²×C₈	—	3	2	no	—
227	C₂³×C₃	—	2	8	no	—
228	C₂³×C₃	—	2	4	no	—
229	C₂³×C₃	—	2	4	no	—
230	C₂³×C₃	—	2	6	no	—
231	C₂³×C₃	—	2	1	no	—
232	C₂³×C₃	—	6	6	no	—
233	C₂³×C₃	—	12	4	no	—
234	C₂³×C₃	C₂×#67	1	6	yes	—
235	C₂³×C₃	C₂×#67	1	1	yes	characteristic
236	C₂³×C₃	C₂×C₃×D₄	1	6	yes	—
237	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
238	C₂²×D₃	—	2	6	no	—
239	C₂²×D₃	—	4	4	no	—
240	C₃×Q₈	—	2	24	no	—
241	C₃×Q₈	—	2	32	no	—
242	C₃×Q₈	—	2	12	no	—
243	C₃×Q₈	—	2	16	no	—
244	C₃×Q₈	—	2	12	no	—
245	C₃×Q₈	—	2	16	no	—
246	C₃×Q₈	—	2	8	no	—
247	C₃×Q₈	—	3	4	no	—
248	C₃×Q₈	—	6	6	no	—
249	C₃×Q₈	C₂³×D₃	1	8	yes	—
250	C₃×Q₈	C₂⁴×C₃	1	8	yes	—
251	C₃×D₄	—	3	4	no	—
252	C₃×D₄	—	6	16	no	—
253	C₃×D₄	—	6	6	no	—
254	C₂×C₃×C₄	—	2	24	no	—
255	C₂×C₃×C₄	—	2	32	no	—
256	C₂×C₃×C₄	—	2	12	no	—
257	C₂×C₃×C₄	—	2	16	no	—
258	C₂×C₃×C₄	—	2	12	no	—
259	C₂×C₃×C₄	—	2	16	no	—
260	C₂×C₃×C₄	—	2	3	no	—
261	C₂×C₃×C₄	—	2	4	no	—
262	C₂×C₃×C₄	—	2	6	no	—
263	C₂×C₃×C₄	—	2	3	no	—
264	C₂×C₃×C₄	—	2	12	no	—
265	C₂×C₃×C₄	—	6	6	no	—
266	C₂×C₃×C₄	—	6	16	no	—
267	C₂×C₃×C₄	C₂×#67	1	6	yes	—
268	C₂×C₃×C₄	C₂×#67	1	3	yes	—
269	C₂×C₃×C₄	C₂×#67	1	12	yes	—
270	C₂×C₃×C₄	C₂×C₃×D₄	1	3	yes	—
271	C₂×C₃×C₄	C₂×C₃×D₄	1	6	yes	—
272	C₂×C₃×C₄	C₂×C₃×D₄	1	12	yes	—
273	C₂×C₃×C₄	C₂³×D₃	1	3	yes	—
274	C₂×C₃×C₄	C₂³×D₃	1	4	yes	—
275	C₂×C₃×C₄	C₂⁴×C₃	1	3	yes	—
276	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
277	#67	—	2	16	no	—
278	C₂×Dic₃	—	2	6	no	—
279	D₁₂	—	2	6	no	—
280	D₁₂	C₂⁴×C₃	1	4	yes	—
281	C₄×D₃	—	2	16	no	—
282	Dic₆	—	2	6	no	—
283	Dic₆	C₂⁴×C₃	1	4	yes	—
284	C₃×C₈	—	3	8	no	—
285	C₃⋊C₈	C₂⁴×C₃	1	8	yes	—
286	C₂×C₃²	—	2	4	no	—
287	C₂×C₃²	C₂×#137	1	6	yes	complemented
288	C₂×C₃²	C₂³×D₄	1	1	yes	characteristic
289	C₃×D₃	—	4	4	no	—
290	C₂⁴	—	6	1	no	—
291	C₂⁴	C₃×#67	1	1	yes	characteristic
292	#41	—	3	16	no	—
293	#41	—	6	24	no	—
294	C₂×Q₈	—	2	6	no	—
295	C₂×Q₈	—	2	12	no	—
296	C₂×Q₈	—	2	24	no	—
297	C₂×Q₈	—	3	6	no	—
298	C₂×Q₈	—	6	3	no	—
299	C₂×Q₈	C₂²×C₃×D₃	1	12	yes	—
300	C₂×Q₈	C₂²×C₃×D₃	1	16	yes	complemented
301	C₂×D₄	—	3	6	no	—
302	C₂×D₄	—	6	12	no	—
303	C₂×D₄	—	6	3	no	—
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	—	2	12	no	—
306	C₂²×C₄	—	6	1	no	—
307	C₂²×C₄	—	6	12	no	—
308	C₂²×C₄	C₃×#67	1	1	yes	characteristic
309	C₂²×C₄	C₃×#67	1	6	yes	—
310	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
311	C₂²×C₄	C₂²×C₃×D₃	1	6	yes	—
312	Q₁₆	—	3	32	no	—
313	SD₁₆	—	3	32	no	—
314	M₁₆	—	3	16	no	—
315	C₂×C₈	—	3	12	no	—
316	C₂²×C₃	—	2	24	no	—
317	C₂²×C₃	—	2	12	no	—
318	C₂²×C₃	—	2	12	no	—
319	C₂²×C₃	—	2	4	no	—
320	C₂²×C₃	—	2	4	no	—
321	C₂²×C₃	—	2	3	no	—
322	C₂²×C₃	—	6	4	no	—
323	C₂²×C₃	—	12	12	no	—
324	C₂²×C₃	#942	1	4	yes	direct product factor
325	C₂²×C₃	C₃×#137	1	4	yes	complemented
326	C₂²×C₃	C₂²×#67	1	4	yes	—
327	C₂²×C₃	C₂²×#67	1	3	yes	—
328	C₂²×C₃	C₂²×C₃×D₄	1	4	yes	—
329	C₂²×C₃	C₂²×C₃×D₄	1	3	yes	—
330	C₂×D₃	—	2	4	no	—
331	C₂×D₃	—	4	12	no	—
332	C₃×C₄	—	2	16	no	—
333	C₃×C₄	—	2	8	no	—
334	C₃×C₄	—	2	8	no	—
335	C₃×C₄	—	2	4	no	—
336	C₃×C₄	—	2	3	no	—
337	C₃×C₄	—	2	1	no	—
338	C₃×C₄	—	6	4	no	—
339	C₃×C₄	C₂²×#67	1	4	yes	—
340	C₃×C₄	C₂²×#67	1	3	yes	—
341	C₃×C₄	C₂²×C₃×D₄	1	3	yes	—
342	C₃×C₄	C₂²×C₃×D₄	1	4	yes	—
343	C₃×C₄	C₂⁴×D₃	1	1	yes	characteristic
344	C₃×C₄	C₂⁵×C₃	1	1	yes	characteristic
345	Dic₃	—	2	4	no	—
346	C₃²	C₂²×#137	1	1	yes	characteristic, complemented, Sylow
347	C₂³	—	2	4	no	—
348	C₂³	—	6	6	no	—
349	C₂³	—	12	4	no	—
350	C₂³	C₂×C₃×#67	1	6	yes	—
351	C₂³	C₂×C₃×#67	1	1	yes	characteristic
352	Q₈	—	2	12	no	—
353	Q₈	—	2	16	no	—
354	Q₈	—	3	4	no	—
355	Q₈	—	6	6	no	—
356	Q₈	C₂³×C₃×D₃	1	8	yes	—
357	D₄	—	3	4	no	—
358	D₄	—	6	16	no	—
359	D₄	—	6	6	no	—
360	C₂×C₄	—	2	12	no	—
361	C₂×C₄	—	2	16	no	—
362	C₂×C₄	—	6	6	no	—
363	C₂×C₄	—	6	16	no	—
364	C₂×C₄	C₂×C₃×#67	1	6	yes	—
365	C₂×C₄	C₂×C₃×#67	1	3	yes	—
366	C₂×C₄	C₂×C₃×#67	1	12	yes	—
367	C₂×C₄	C₂³×C₃×D₃	1	3	yes	—
368	C₂×C₄	C₂³×C₃×D₃	1	4	yes	—
369	C₈	—	3	8	no	—
370	C₂×C₃	—	2	8	no	—
371	C₂×C₃	—	2	4	no	—
372	C₂×C₃	—	2	4	no	—
373	C₂×C₃	—	2	6	no	—
374	C₂×C₃	—	2	1	no	—
375	C₂×C₃	—	12	4	no	—
376	C₂×C₃	C₂×#942	1	6	yes	direct product factor
377	C₂×C₃	C₂×C₃×#137	1	6	yes	complemented
378	C₂×C₃	C₂³×#67	1	1	yes	characteristic
379	C₂×C₃	C₂³×C₃×D₄	1	1	yes	characteristic
380	D₃	—	4	4	no	—
381	C₂²	—	2	12	no	—
382	C₂²	—	6	4	no	—
383	C₂²	—	12	12	no	—
384	C₂²	C₃×#942	1	4	yes	direct product factor
385	C₂²	C₂²×C₃×#67	1	4	yes	—
386	C₂²	C₂²×C₃×#67	1	3	yes	—
387	C₄	—	2	8	no	—
388	C₄	—	6	4	no	—
389	C₄	C₂²×C₃×#67	1	4	yes	—
390	C₄	C₂²×C₃×#67	1	3	yes	—
391	C₄	C₂⁴×C₃×D₃	1	1	yes	characteristic
392	C₃	—	2	1	no	—
393	C₃	C₂²×#942	1	1	yes	characteristic, direct product factor
394	C₃	C₂²×C₃×#137	1	1	yes	characteristic, complemented
395	C₂	—	2	4	no	—
396	C₂	—	12	4	no	—
397	C₂	C₂×C₃×#942	1	6	yes	direct product factor
398	C₂	C₂³×C₃×#67	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃	C₂×#67
commutator, cosocle	C₃×C₄	C₂⁵×C₃
Frattini	C₄	C₂⁴×C₃×D₃
Fitting	C₂³×C₃²×Q₈	C₂
socle	C₂³×C₃²	C₂×D₄
prime radical	C₂²×C₃×#235	C₂
hypercenter	C₂³×C₃×Q₈	D₃
hypocenter	C₃	C₂²×C₃×#137
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₃ ◁ C₂³×C₃×C₄ ◁ C₂³×C₃×Q₈

Complements

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

N	H ≅ G/N	type
1. C₂³×C₃²×Q₈	C₂	semidirect
3. C₂²×C₃×#216	C₂	semidirect
4. C₂×C₃×#942	C₂	direct (N × H)
5. C₂²×C₃×#215	C₂	semidirect
6. C₂²×C₃×#208	C₂	semidirect
8. C₂²×#942	C₃	direct (N × H)
12. C₂²×C₃²×Q₈	C₂²	semidirect
21. C₂×C₃×#216	C₂²	semidirect
22. C₃×#942	C₂²	direct (N × H)
23. C₂×C₃×#215	C₂²	semidirect
24. C₂×C₃×#208	C₂²	semidirect
28. C₂³×C₃×Q₈	D₃	semidirect
29. C₂³×C₃×Q₈	C₂×C₃	semidirect
35. C₂²×#216	C₂×C₃	semidirect
36. C₂×#942	C₂×C₃	direct (N × H)
37. C₂²×#215	C₂×C₃	semidirect
38. C₂²×#208	C₂×C₃	semidirect
45. C₂×C₃²×Q₈	C₂³	semidirect
61. C₃×#216	C₂³	semidirect
62. C₃×#215	C₂³	semidirect
63. C₃×#208	C₂³	semidirect
78. C₂²×C₃×Q₈	C₂×D₃	semidirect
80. C₂²×C₃×Q₈	C₂²×C₃	semidirect
101. C₂×#216	C₂²×C₃	semidirect
102. #942	C₂²×C₃	direct (N × H)
103. C₂×#215	C₂²×C₃	semidirect
104. C₂×#208	C₂²×C₃	semidirect
130. C₂³×Q₈	C₃×D₃	semidirect
156. C₂×C₃×Q₈	C₂²×D₃	semidirect
158. C₂×C₃×Q₈	C₂³×C₃	semidirect
195. #216	C₂³×C₃	semidirect
196. #215	C₂³×C₃	semidirect
197. #208	C₂³×C₃	semidirect
200. C₂²×C₃²	#137	semidirect
216. C₂²×Q₈	C₂×C₃×D₃	semidirect
287. C₂×C₃²	C₂×#137	semidirect
300. C₂×Q₈	C₂²×C₃×D₃	semidirect
324. C₂²×C₃	#942	direct (N × H)
325. C₂²×C₃	C₃×#137	semidirect
346. C₃²	C₂²×#137	semidirect
376. C₂×C₃	C₂×#942	direct (N × H)
377. C₂×C₃	C₂×C₃×#137	semidirect
384. C₂²	C₃×#942	direct (N × H)
393. C₃	C₂²×#942	direct (N × H)
394. C₃	C₂²×C₃×#137	semidirect
397. C₂	C₂×C₃×#942	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₃²×Q₈	2
C₂²×C₃×#235	2
C₂²×C₃×#216	2
C₂×C₃×#942	2
C₂²×C₃×#215	2
C₂²×C₃×#208	2
C₂²×C₃×#137	3
C₂²×#942	3

Subgroups — C22×C3×#942 #11918690

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃×#942 #11918690