Subgroups — C₂²×C₃×#938 #11900269

Order 1152.

5737 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃²×D₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₃×#67	C₂	1	2	yes	maximal, complemented
3	C₂³×C₃×C₄×D₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₃×#217	C₂	1	2	yes	maximal, complemented
5	C₂×C₃×#938	C₂	1	24	yes	maximal, direct product factor
6	C₂²×C₃×C₄⋊Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×C₃×#121	—	3	1	no	maximal
8	C₂²×#938	C₃	1	1	yes	maximal, characteristic, direct product factor
9	C₂⁵×C₃²	C₂²	1	2	yes	—
10	C₂⁴×C₃×D₃	C₂²	1	1	yes	characteristic
11	C₂²×C₃²×D₄	—	2	8	no	—
12	C₂²×C₃²×D₄	C₂²	1	12	yes	complemented
13	C₂³×C₃²×C₄	C₂²	1	1	yes	characteristic
14	C₂²×C₃×#67	—	2	16	no	—
15	C₂²×C₃×#67	C₂²	1	24	yes	complemented
16	C₂³×C₃×Dic₃	C₂²	1	2	yes	—
17	C₂³×C₃×Dic₃	C₂²	1	1	yes	characteristic
18	C₂²×C₃×C₄×D₃	—	2	8	no	—
19	C₂²×C₃×C₄×D₃	C₂²	1	12	yes	complemented
20	C₂×C₃×#217	C₂²	1	24	yes	complemented
21	C₃×#938	C₂²	1	64	yes	direct product factor
22	C₂×C₃×C₄⋊Dic₃	C₂²	1	12	yes	complemented
23	C₂³×C₃×D₄	—	2	1	no	—
24	C₂³×C₃×D₄	—	3	2	no	—
25	C₂³×C₃×D₄	D₃	1	1	yes	characteristic, complemented
26	C₂³×C₃×D₄	C₂×C₃	1	1	yes	characteristic, complemented
27	C₂⁴×C₃×C₄	—	3	1	no	—
28	C₂³×#67	C₂×C₃	1	2	yes	complemented
29	C₂³×C₄×D₃	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	C₂²×#217	C₂×C₃	1	2	yes	complemented
34	C₂×#938	C₂×C₃	1	24	yes	direct product factor
35	C₂²×C₄⋊Dic₃	C₂×C₃	1	1	yes	characteristic, complemented
36	C₂⁴×C₃²	—	2	8	no	—
37	C₂⁴×C₃²	—	2	8	no	—
38	C₂⁴×C₃²	—	2	8	no	—
39	C₂⁴×C₃²	C₂³	1	12	yes	—
40	C₂⁴×C₃²	C₂³	1	1	yes	characteristic
41	C₂³×C₃×D₃	—	2	4	no	—
42	C₂³×C₃×D₃	—	2	4	no	—
43	C₂³×C₃×D₃	D₄	1	8	yes	complemented
44	C₂³×C₃×D₃	C₂³	1	6	yes	—
45	C₂×C₃²×D₄	—	2	48	no	—
46	C₂×C₃²×D₄	C₂³	1	16	yes	complemented
47	C₂²×C₃²×C₄	D₄	1	8	yes	complemented
48	C₂²×C₃²×C₄	C₂³	1	6	yes	—
49	C₂×C₃×#67	—	2	96	no	—
50	C₂×C₃×#67	C₂³	1	32	yes	complemented
51	C₂²×C₃×Dic₃	—	2	4	no	—
52	C₂²×C₃×Dic₃	—	2	8	no	—
53	C₂²×C₃×Dic₃	C₂³	1	12	yes	—
54	C₂²×C₃×Dic₃	C₂³	1	6	yes	—
55	C₂×C₃×C₄×D₃	—	2	48	no	—
56	C₂×C₃×C₄×D₃	C₂³	1	16	yes	complemented
57	C₃×#217	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	2	no	—
61	C₂⁵×C₃	—	3	1	no	—
62	C₂⁵×C₃	C₂×D₃	1	2	yes	—
63	C₂⁵×C₃	C₂²×C₃	1	2	yes	—
64	C₂⁴×D₃	C₂²×C₃	1	1	yes	characteristic
65	C₂²×C₃×D₄	—	2	16	no	—
66	C₂²×C₃×D₄	—	2	8	no	—
67	C₂²×C₃×D₄	—	2	8	no	—
68	C₂²×C₃×D₄	—	2	12	no	—
69	C₂²×C₃×D₄	—	3	24	no	—
70	C₂²×C₃×D₄	—	6	16	no	—
71	C₂²×C₃×D₄	C₂×D₃	1	12	yes	complemented
72	C₂²×C₃×D₄	C₂²×C₃	1	12	yes	complemented
73	C₂³×C₃×C₄	—	2	1	no	—
74	C₂³×C₃×C₄	—	3	1	no	—
75	C₂³×C₃×C₄	—	3	2	no	—
76	C₂³×C₃×C₄	—	3	12	no	—
77	C₂³×C₃×C₄	—	6	8	no	—
78	C₂³×C₃×C₄	C₂×D₃	1	1	yes	characteristic
79	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
80	C₂²×#67	—	2	16	no	—
81	C₂²×#67	C₂²×C₃	1	24	yes	complemented
82	C₂³×Dic₃	C₂²×C₃	1	1	yes	characteristic
83	C₂³×Dic₃	C₂²×C₃	1	2	yes	—
84	C₂²×C₄×D₃	—	2	8	no	—
85	C₂²×C₄×D₃	C₂²×C₃	1	12	yes	complemented
86	C₃×#121	—	3	64	no	—
87	C₂×C₃×C₄⋊C₄	—	3	12	no	—
88	C₂×C₃×C₂²⋊C₄	—	3	24	no	—
89	C₂×#217	C₂²×C₃	1	24	yes	complemented
90	#938	C₂²×C₃	1	64	yes	direct product factor
91	C₂×C₄⋊Dic₃	C₂²×C₃	1	12	yes	complemented
92	C₂³×C₃²	—	2	24	no	—
93	C₂³×C₃²	—	2	24	no	—
94	C₂³×C₃²	—	2	24	no	—
95	C₂³×C₃²	—	4	32	no	—
96	C₂³×C₃²	C₂×D₄	1	4	yes	—
97	C₂³×C₃²	C₂×D₄	1	4	yes	—
98	C₂³×C₃²	#41	1	4	yes	—
99	C₂³×C₃²	C₂⁴	1	8	yes	—
100	C₂³×C₃²	C₂⁴	1	3	yes	—
101	C₂²×C₃×D₃	—	2	32	no	—
102	C₂²×C₃×D₃	—	2	12	no	—
103	C₂²×C₃×D₃	—	2	12	no	—
104	C₂²×C₃×D₃	C₂×D₄	1	24	yes	complemented
105	C₂²×C₃×D₃	C₂⁴	1	4	yes	—
106	C₃²×D₄	—	2	32	no	—
107	C₂×C₃²×C₄	C₂×D₄	1	24	yes	complemented
108	C₂×C₃²×C₄	C₂⁴	1	4	yes	—
109	C₃×#67	—	2	64	no	—
110	C₂×C₃×Dic₃	—	2	12	no	—
111	C₂×C₃×Dic₃	—	2	24	no	—
112	C₂×C₃×Dic₃	C₂⁴	1	8	yes	—
113	C₂×C₃×Dic₃	C₂⁴	1	4	yes	—
114	C₃×C₄×D₃	—	2	32	no	—
115	C₂³×D₄	—	3	2	no	—
116	C₂³×D₄	C₃×D₃	1	1	yes	characteristic, complemented
117	C₂⁴×C₄	—	3	1	no	—
118	C₂×#121	—	3	24	no	—
119	C₂²×C₄⋊C₄	—	3	1	no	—
120	C₂²×C₂²⋊C₄	—	3	2	no	—
121	C₂⁴×C₃	—	2	16	no	—
122	C₂⁴×C₃	—	2	8	no	—
123	C₂⁴×C₃	—	2	8	no	—
124	C₂⁴×C₃	—	2	8	no	—
125	C₂⁴×C₃	—	2	8	no	—
126	C₂⁴×C₃	—	2	8	no	—
127	C₂⁴×C₃	—	2	8	no	—
128	C₂⁴×C₃	—	2	1	no	—
129	C₂⁴×C₃	—	2	12	no	—
130	C₂⁴×C₃	—	3	8	no	—
131	C₂⁴×C₃	—	3	6	no	—
132	C₂⁴×C₃	—	4	8	no	—
133	C₂⁴×C₃	—	4	8	no	—
134	C₂⁴×C₃	—	6	4	no	—
135	C₂⁴×C₃	—	6	4	no	—
136	C₂⁴×C₃	C₂²×D₃	1	12	yes	—
137	C₂⁴×C₃	C₂²×D₃	1	1	yes	characteristic
138	C₂⁴×C₃	C₂³×C₃	1	12	yes	—
139	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
140	C₂³×D₃	—	2	4	no	—
141	C₂³×D₃	—	2	4	no	—
142	C₂³×D₃	C₃×D₄	1	8	yes	complemented
143	C₂³×D₃	C₂³×C₃	1	6	yes	—
144	C₂×C₃×D₄	—	2	96	no	—
145	C₂×C₃×D₄	—	2	48	no	—
146	C₂×C₃×D₄	—	2	48	no	—
147	C₂×C₃×D₄	—	2	16	no	—
148	C₂×C₃×D₄	—	3	32	no	—
149	C₂×C₃×D₄	—	6	96	no	—
150	C₂×C₃×D₄	C₂²×D₃	1	16	yes	complemented
151	C₂×C₃×D₄	C₂³×C₃	1	16	yes	complemented
152	C₂²×C₃×C₄	—	2	8	no	—
153	C₂²×C₃×C₄	—	2	6	no	—
154	C₂²×C₃×C₄	—	3	6	no	—
155	C₂²×C₃×C₄	—	3	12	no	—
156	C₂²×C₃×C₄	—	3	16	no	—
157	C₂²×C₃×C₄	—	6	8	no	—
158	C₂²×C₃×C₄	—	6	4	no	—
159	C₂²×C₃×C₄	—	6	48	no	—
160	C₂²×C₃×C₄	#67	1	8	yes	complemented
161	C₂²×C₃×C₄	C₃×D₄	1	8	yes	complemented
162	C₂²×C₃×C₄	C₂²×D₃	1	6	yes	—
163	C₂²×C₃×C₄	C₂³×C₃	1	6	yes	—
164	C₂×#67	—	2	96	no	—
165	C₂×#67	C₂³×C₃	1	32	yes	complemented
166	C₂²×Dic₃	—	2	4	no	—
167	C₂²×Dic₃	—	2	8	no	—
168	C₂²×Dic₃	C₂³×C₃	1	12	yes	—
169	C₂²×Dic₃	C₂³×C₃	1	6	yes	—
170	C₂×C₄×D₃	—	2	48	no	—
171	C₂×C₄×D₃	C₂³×C₃	1	16	yes	complemented
172	C₃×C₄⋊C₄	—	3	16	no	—
173	C₃×C₂²⋊C₄	—	3	32	no	—
174	#217	C₂³×C₃	1	32	yes	complemented
175	C₄⋊Dic₃	C₂³×C₃	1	16	yes	complemented
176	C₂²×C₃²	—	2	8	no	—
177	C₂²×C₃²	—	2	8	no	—
178	C₂²×C₃²	—	2	8	no	—
179	C₂²×C₃²	—	4	48	no	—
180	C₂²×C₃²	#121	1	16	yes	complemented
181	C₂²×C₃²	C₂²×D₄	1	6	yes	—
182	C₂²×C₃²	C₂²×D₄	1	6	yes	—
183	C₂²×C₃²	C₂×#41	1	6	yes	—
184	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
185	C₂×C₃×D₃	—	2	48	no	—
186	C₂×C₃×D₃	—	2	4	no	—
187	C₂×C₃×D₃	—	2	4	no	—
188	C₂×C₃×D₃	C₂²×D₄	1	8	yes	complemented
189	C₃²×C₄	C₂²×D₄	1	8	yes	complemented
190	C₃×Dic₃	—	2	4	no	—
191	C₃×Dic₃	—	2	8	no	—
192	C₂⁵	—	3	1	no	—
193	C₂⁵	C₂×C₃×D₃	1	2	yes	—
194	C₂²×D₄	—	2	8	no	—
195	C₂²×D₄	—	3	24	no	—
196	C₂²×D₄	—	6	16	no	—
197	C₂²×D₄	C₂×C₃×D₃	1	12	yes	complemented
198	C₂³×C₄	—	3	1	no	—
199	C₂³×C₄	—	3	2	no	—
200	C₂³×C₄	—	3	12	no	—
201	C₂³×C₄	—	6	8	no	—
202	C₂³×C₄	C₂×C₃×D₃	1	1	yes	characteristic
203	#121	—	3	64	no	—
204	C₂×C₄⋊C₄	—	3	12	no	—
205	C₂×C₂²⋊C₄	—	3	24	no	—
206	C₂³×C₃	—	2	48	no	—
207	C₂³×C₃	—	2	24	no	—
208	C₂³×C₃	—	2	24	no	—
209	C₂³×C₃	—	2	24	no	—
210	C₂³×C₃	—	2	24	no	—
211	C₂³×C₃	—	2	24	no	—
212	C₂³×C₃	—	2	24	no	—
213	C₂³×C₃	—	2	3	no	—
214	C₂³×C₃	—	2	8	no	—
215	C₂³×C₃	—	2	4	no	—
216	C₂³×C₃	—	2	4	no	—
217	C₂³×C₃	—	2	4	no	—
218	C₂³×C₃	—	3	24	no	—
219	C₂³×C₃	—	3	4	no	—
220	C₂³×C₃	—	4	24	no	—
221	C₂³×C₃	—	4	24	no	—
222	C₂³×C₃	—	4	64	no	—
223	C₂³×C₃	—	4	32	no	—
224	C₂³×C₃	—	4	32	no	—
225	C₂³×C₃	—	6	32	no	—
226	C₂³×C₃	—	6	12	no	—
227	C₂³×C₃	—	6	12	no	—
228	C₂³×C₃	D₃×D₄	1	4	yes	—
229	C₂³×C₃	#237	1	4	yes	—
230	C₂³×C₃	C₂×#67	1	4	yes	—
231	C₂³×C₃	C₂×C₃×D₄	1	4	yes	—
232	C₂³×C₃	C₂×C₃×D₄	1	4	yes	—
233	C₂³×C₃	C₃×#41	1	4	yes	—
234	C₂³×C₃	C₂³×D₃	1	8	yes	—
235	C₂³×C₃	C₂³×D₃	1	3	yes	—
236	C₂³×C₃	C₂⁴×C₃	1	8	yes	—
237	C₂³×C₃	C₂⁴×C₃	1	3	yes	—
238	C₂²×D₃	—	2	32	no	—
239	C₂²×D₃	—	2	12	no	—
240	C₂²×D₃	—	2	12	no	—
241	C₂²×D₃	C₂×C₃×D₄	1	24	yes	complemented
242	C₂²×D₃	C₂⁴×C₃	1	4	yes	—
243	C₃×D₄	—	2	64	no	—
244	C₃×D₄	—	2	32	no	—
245	C₃×D₄	—	2	32	no	—
246	C₃×D₄	—	6	64	no	—
247	C₂×C₃×C₄	—	2	4	no	—
248	C₂×C₃×C₄	—	2	24	no	—
249	C₂×C₃×C₄	—	3	4	no	—
250	C₂×C₃×C₄	—	3	8	no	—
251	C₂×C₃×C₄	—	6	24	no	—
252	C₂×C₃×C₄	—	6	12	no	—
253	C₂×C₃×C₄	—	6	32	no	—
254	C₂×C₃×C₄	C₂×#67	1	24	yes	complemented
255	C₂×C₃×C₄	C₂×C₃×D₄	1	24	yes	complemented
256	C₂×C₃×C₄	C₂³×D₃	1	4	yes	—
257	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
258	#67	—	2	64	no	—
259	C₂×Dic₃	—	2	12	no	—
260	C₂×Dic₃	—	2	24	no	—
261	C₂×Dic₃	C₂⁴×C₃	1	8	yes	—
262	C₂×Dic₃	C₂⁴×C₃	1	4	yes	—
263	C₄×D₃	—	2	32	no	—
264	C₂×C₃²	—	4	8	no	—
265	C₂×C₃²	C₂×#121	1	12	yes	complemented
266	C₂×C₃²	C₂³×D₄	1	1	yes	characteristic
267	C₂×C₃²	C₂³×D₄	1	1	yes	characteristic
268	C₂×C₃²	C₂²×#41	1	1	yes	characteristic
269	C₃×D₃	—	2	8	no	—
270	C₂⁴	—	2	8	no	—
271	C₂⁴	—	2	8	no	—
272	C₂⁴	—	2	8	no	—
273	C₂⁴	—	3	6	no	—
274	C₂⁴	—	3	8	no	—
275	C₂⁴	—	6	4	no	—
276	C₂⁴	—	6	4	no	—
277	C₂⁴	C₂²×C₃×D₃	1	12	yes	—
278	C₂⁴	C₂²×C₃×D₃	1	1	yes	characteristic
279	C₂×D₄	—	2	48	no	—
280	C₂×D₄	—	3	32	no	—
281	C₂×D₄	—	6	96	no	—
282	C₂×D₄	C₂²×C₃×D₃	1	16	yes	complemented
283	C₂²×C₄	—	3	6	no	—
284	C₂²×C₄	—	3	12	no	—
285	C₂²×C₄	—	3	16	no	—
286	C₂²×C₄	—	6	8	no	—
287	C₂²×C₄	—	6	4	no	—
288	C₂²×C₄	—	6	48	no	—
289	C₂²×C₄	C₃×#67	1	8	yes	complemented
290	C₂²×C₄	C₂²×C₃×D₃	1	6	yes	—
291	C₄⋊C₄	—	3	16	no	—
292	C₂²⋊C₄	—	3	32	no	—
293	C₂²×C₃	—	2	16	no	—
294	C₂²×C₃	—	2	8	no	—
295	C₂²×C₃	—	2	8	no	—
296	C₂²×C₃	—	2	8	no	—
297	C₂²×C₃	—	2	8	no	—
298	C₂²×C₃	—	2	8	no	—
299	C₂²×C₃	—	2	8	no	—
300	C₂²×C₃	—	2	16	no	—
301	C₂²×C₃	—	2	6	no	—
302	C₂²×C₃	—	2	6	no	—
303	C₂²×C₃	—	2	6	no	—
304	C₂²×C₃	—	2	1	no	—
305	C₂²×C₃	—	3	8	no	—
306	C₂²×C₃	—	4	8	no	—
307	C₂²×C₃	—	4	8	no	—
308	C₂²×C₃	—	4	96	no	—
309	C₂²×C₃	—	4	48	no	—
310	C₂²×C₃	—	4	48	no	—
311	C₂²×C₃	—	6	4	no	—
312	C₂²×C₃	—	6	4	no	—
313	C₂²×C₃	—	6	48	no	—
314	C₂²×C₃	#938	1	16	yes	direct product factor
315	C₂²×C₃	C₃×#121	1	16	yes	complemented
316	C₂²×C₃	C₂×D₃×D₄	1	6	yes	—
317	C₂²×C₃	C₂×#237	1	6	yes	—
318	C₂²×C₃	C₂²×#67	1	6	yes	—
319	C₂²×C₃	C₂²×C₃×D₄	1	6	yes	—
320	C₂²×C₃	C₂²×C₃×D₄	1	6	yes	—
321	C₂²×C₃	C₂×C₃×#41	1	6	yes	—
322	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
323	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
324	C₂×D₃	—	2	4	no	—
325	C₂×D₃	—	2	4	no	—
326	C₂×D₃	—	2	48	no	—
327	C₂×D₃	C₂²×C₃×D₄	1	8	yes	complemented
328	C₃×C₄	—	2	8	no	—
329	C₃×C₄	—	6	8	no	—
330	C₃×C₄	—	6	4	no	—
331	C₃×C₄	C₂²×#67	1	8	yes	complemented
332	C₃×C₄	C₂²×C₃×D₄	1	8	yes	complemented
333	Dic₃	—	2	4	no	—
334	Dic₃	—	2	8	no	—
335	C₃²	C₂²×#121	1	1	yes	characteristic, complemented, Sylow
336	C₂³	—	2	24	no	—
337	C₂³	—	2	24	no	—
338	C₂³	—	2	24	no	—
339	C₂³	—	3	24	no	—
340	C₂³	—	3	4	no	—
341	C₂³	—	4	32	no	—
342	C₂³	—	6	32	no	—
343	C₂³	—	6	12	no	—
344	C₂³	—	6	12	no	—
345	C₂³	C₃×D₃×D₄	1	4	yes	—
346	C₂³	C₃×#237	1	4	yes	—
347	C₂³	C₂×C₃×#67	1	4	yes	—
348	C₂³	C₂³×C₃×D₃	1	8	yes	—
349	C₂³	C₂³×C₃×D₃	1	3	yes	—
350	D₄	—	2	32	no	—
351	D₄	—	6	64	no	—
352	C₂×C₄	—	3	4	no	—
353	C₂×C₄	—	3	8	no	—
354	C₂×C₄	—	6	24	no	—
355	C₂×C₄	—	6	12	no	—
356	C₂×C₄	—	6	32	no	—
357	C₂×C₄	C₂×C₃×#67	1	24	yes	complemented
358	C₂×C₄	C₂³×C₃×D₃	1	4	yes	—
359	C₂×C₃	—	2	12	no	—
360	C₂×C₃	—	2	1	no	—
361	C₂×C₃	—	2	1	no	—
362	C₂×C₃	—	2	1	no	—
363	C₂×C₃	—	4	16	no	—
364	C₂×C₃	—	4	8	no	—
365	C₂×C₃	—	4	8	no	—
366	C₂×C₃	—	6	8	no	—
367	C₂×C₃	C₂×#938	1	12	yes	direct product factor
368	C₂×C₃	C₂×C₃×#121	1	12	yes	complemented
369	C₂×C₃	C₂²×D₃×D₄	1	1	yes	characteristic
370	C₂×C₃	C₂²×#237	1	1	yes	characteristic
371	C₂×C₃	C₂³×#67	1	1	yes	characteristic
372	C₂×C₃	C₂³×C₃×D₄	1	1	yes	characteristic
373	C₂×C₃	C₂³×C₃×D₄	1	1	yes	characteristic
374	C₂×C₃	C₂²×C₃×#41	1	1	yes	characteristic
375	D₃	—	2	8	no	—
376	C₂²	—	2	8	no	—
377	C₂²	—	2	8	no	—
378	C₂²	—	2	8	no	—
379	C₂²	—	3	8	no	—
380	C₂²	—	4	48	no	—
381	C₂²	—	6	48	no	—
382	C₂²	—	6	4	no	—
383	C₂²	—	6	4	no	—
384	C₂²	C₃×#938	1	16	yes	direct product factor
385	C₂²	C₂×C₃×D₃×D₄	1	6	yes	—
386	C₂²	C₂×C₃×#237	1	6	yes	—
387	C₂²	C₂²×C₃×#67	1	6	yes	—
388	C₂²	C₂⁴×C₃×D₃	1	1	yes	characteristic
389	C₄	—	6	8	no	—
390	C₄	—	6	4	no	—
391	C₄	C₂²×C₃×#67	1	8	yes	complemented
392	C₃	—	2	1	no	—
393	C₃	C₂²×#938	1	1	yes	characteristic, direct product factor
394	C₃	C₂²×C₃×#121	1	1	yes	characteristic, complemented
395	C₂	—	4	8	no	—
396	C₂	—	6	8	no	—
397	C₂	C₂×C₃×#938	1	12	yes	direct product factor
398	C₂	C₂²×C₃×D₃×D₄	1	1	yes	characteristic
399	C₂	C₂²×C₃×#237	1	1	yes	characteristic
400	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	C₂³×C₃²×D₄	C₂
socle	C₂⁴×C₃²	C₂³
hypercenter	C₂³×C₃×D₄	D₃
hypocenter	C₃	C₂²×C₃×#121
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂⁴×C₃ ◁ C₂³×C₃×D₄

Complements

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

N	H ≅ G/N	type
1. C₂³×C₃²×D₄	C₂	semidirect
2. C₂³×C₃×#67	C₂	semidirect
3. C₂³×C₃×C₄×D₃	C₂	semidirect
4. C₂²×C₃×#217	C₂	semidirect
5. C₂×C₃×#938	C₂	direct (N × H)
6. C₂²×C₃×C₄⋊Dic₃	C₂	semidirect
8. C₂²×#938	C₃	direct (N × H)
12. C₂²×C₃²×D₄	C₂²	semidirect
15. C₂²×C₃×#67	C₂²	semidirect
19. C₂²×C₃×C₄×D₃	C₂²	semidirect
20. C₂×C₃×#217	C₂²	semidirect
21. C₃×#938	C₂²	direct (N × H)
22. C₂×C₃×C₄⋊Dic₃	C₂²	semidirect
25. C₂³×C₃×D₄	D₃	semidirect
26. C₂³×C₃×D₄	C₂×C₃	semidirect
28. C₂³×#67	C₂×C₃	semidirect
29. C₂³×C₄×D₃	C₂×C₃	semidirect
33. C₂²×#217	C₂×C₃	semidirect
34. C₂×#938	C₂×C₃	direct (N × H)
35. C₂²×C₄⋊Dic₃	C₂×C₃	semidirect
43. C₂³×C₃×D₃	D₄	semidirect
46. C₂×C₃²×D₄	C₂³	semidirect
47. C₂²×C₃²×C₄	D₄	semidirect
50. C₂×C₃×#67	C₂³	semidirect
56. C₂×C₃×C₄×D₃	C₂³	semidirect
57. C₃×#217	C₂³	semidirect
58. C₃×C₄⋊Dic₃	C₂³	semidirect
71. C₂²×C₃×D₄	C₂×D₃	semidirect
72. C₂²×C₃×D₄	C₂²×C₃	semidirect
81. C₂²×#67	C₂²×C₃	semidirect
85. C₂²×C₄×D₃	C₂²×C₃	semidirect
89. C₂×#217	C₂²×C₃	semidirect
90. #938	C₂²×C₃	direct (N × H)
91. C₂×C₄⋊Dic₃	C₂²×C₃	semidirect
104. C₂²×C₃×D₃	C₂×D₄	semidirect
107. C₂×C₃²×C₄	C₂×D₄	semidirect
116. C₂³×D₄	C₃×D₃	semidirect
142. C₂³×D₃	C₃×D₄	semidirect
150. C₂×C₃×D₄	C₂²×D₃	semidirect
151. C₂×C₃×D₄	C₂³×C₃	semidirect
160. C₂²×C₃×C₄	#67	semidirect
161. C₂²×C₃×C₄	C₃×D₄	semidirect
165. C₂×#67	C₂³×C₃	semidirect
171. C₂×C₄×D₃	C₂³×C₃	semidirect
174. #217	C₂³×C₃	semidirect
175. C₄⋊Dic₃	C₂³×C₃	semidirect
180. C₂²×C₃²	#121	semidirect
188. C₂×C₃×D₃	C₂²×D₄	semidirect
189. C₃²×C₄	C₂²×D₄	semidirect
197. C₂²×D₄	C₂×C₃×D₃	semidirect
241. C₂²×D₃	C₂×C₃×D₄	semidirect
254. C₂×C₃×C₄	C₂×#67	semidirect
255. C₂×C₃×C₄	C₂×C₃×D₄	semidirect
265. C₂×C₃²	C₂×#121	semidirect
282. C₂×D₄	C₂²×C₃×D₃	semidirect
289. C₂²×C₄	C₃×#67	semidirect
314. C₂²×C₃	#938	direct (N × H)
315. C₂²×C₃	C₃×#121	semidirect
327. C₂×D₃	C₂²×C₃×D₄	semidirect
331. C₃×C₄	C₂²×#67	semidirect
332. C₃×C₄	C₂²×C₃×D₄	semidirect
335. C₃²	C₂²×#121	semidirect
357. C₂×C₄	C₂×C₃×#67	semidirect
367. C₂×C₃	C₂×#938	direct (N × H)
368. C₂×C₃	C₂×C₃×#121	semidirect
384. C₂²	C₃×#938	direct (N × H)
391. C₄	C₂²×C₃×#67	semidirect
393. C₃	C₂²×#938	direct (N × H)
394. C₃	C₂²×C₃×#121	semidirect
397. C₂	C₂×C₃×#938	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×D₄	2
C₂³×C₃×#67	2
C₂³×C₃×C₄×D₃	2
C₂²×C₃×#217	2
C₂×C₃×#938	2
C₂²×C₃×C₄⋊Dic₃	2
C₂²×C₃×#121	3
C₂²×#938	3

Subgroups — C22×C3×#938 #11900269

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃×#938 #11900269