Subgroups — C₂²×C₃×#937 #11900243

Order 1152.

9769 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	C₂⁵×C₃×D₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₃²×D₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂³×C₃×#67	C₂	1	2	yes	maximal, complemented
4	C₂²×C₃×#217	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×#937	C₂	1	24	yes	maximal, direct product factor
6	C₂²×C₃×(C₂×D₃)⋊C₄	C₂	1	2	yes	maximal, complemented
7	C₂²×C₃×#120	—	3	1	no	maximal
8	C₂²×#937	C₃	1	1	yes	maximal, characteristic, direct product factor
9	C₂⁵×C₃²	C₂²	1	1	yes	characteristic
10	C₂⁵×C₃²	C₂²	1	1	yes	characteristic, complemented
11	C₂⁴×C₃×D₃	—	2	8	no	—
12	C₂⁴×C₃×D₃	—	2	16	no	—
13	C₂⁴×C₃×D₃	C₂²	1	2	yes	—
14	C₂⁴×C₃×D₃	C₂²	1	12	yes	complemented
15	C₂²×C₃²×D₄	—	2	8	no	—
16	C₂²×C₃²×D₄	C₂²	1	12	yes	complemented
17	C₂³×C₃²×C₄	C₂²	1	1	yes	characteristic, complemented
18	C₂²×C₃×#67	—	2	16	no	—
19	C₂²×C₃×#67	C₂²	1	24	yes	complemented
20	C₂³×C₃×Dic₃	C₂²	1	2	yes	complemented
21	C₂×C₃×#217	C₂²	1	12	yes	complemented
22	C₃×#937	C₂²	1	64	yes	direct product factor
23	C₂×C₃×(C₂×D₃)⋊C₄	C₂²	1	24	yes	complemented
24	C₂⁶×C₃	—	3	1	no	—
25	C₂⁵×D₃	C₂×C₃	1	1	yes	characteristic, complemented
26	C₂³×C₃×D₄	—	2	1	no	—
27	C₂³×C₃×D₄	—	3	2	no	—
28	C₂³×C₃×D₄	D₃	1	1	yes	characteristic, complemented
29	C₂³×C₃×D₄	C₂×C₃	1	1	yes	characteristic, complemented
30	C₂³×#67	C₂×C₃	1	2	yes	complemented
31	C₂×C₃×#120	—	3	24	no	—
32	C₂²×C₃×C₂²⋊C₄	—	3	2	no	—
33	C₂²×C₃×C₂²⋊C₄	—	3	1	no	—
34	C₂²×#217	C₂×C₃	1	1	yes	characteristic, complemented
35	C₂×#937	C₂×C₃	1	24	yes	direct product factor
36	C₂²×(C₂×D₃)⋊C₄	C₂×C₃	1	2	yes	complemented
37	C₂⁴×C₃²	—	2	8	no	—
38	C₂⁴×C₃²	—	2	4	no	—
39	C₂⁴×C₃²	—	2	8	no	—
40	C₂⁴×C₃²	D₄	1	8	yes	complemented
41	C₂⁴×C₃²	C₂³	1	6	yes	—
42	C₂⁴×C₃²	C₂³	1	1	yes	characteristic
43	C₂⁴×C₃²	C₂³	1	6	yes	complemented
44	C₂³×C₃×D₃	—	2	128	no	—
45	C₂³×C₃×D₃	—	2	8	no	—
46	C₂³×C₃×D₃	—	2	8	no	—
47	C₂³×C₃×D₃	—	2	48	no	—
48	C₂³×C₃×D₃	—	2	96	no	—
49	C₂³×C₃×D₃	D₄	1	16	yes	complemented
50	C₂³×C₃×D₃	C₂³	1	12	yes	—
51	C₂³×C₃×D₃	C₂³	1	16	yes	complemented
52	C₂×C₃²×D₄	—	2	48	no	—
53	C₂×C₃²×D₄	C₂³	1	16	yes	complemented
54	C₂²×C₃²×C₄	—	2	4	no	—
55	C₂²×C₃²×C₄	C₂³	1	6	yes	complemented
56	C₂×C₃×#67	—	2	96	no	—
57	C₂×C₃×#67	C₂³	1	32	yes	complemented
58	C₂²×C₃×Dic₃	—	2	8	no	—
59	C₂²×C₃×Dic₃	C₂³	1	12	yes	complemented
60	C₃×#217	C₂³	1	16	yes	complemented
61	C₃×(C₂×D₃)⋊C₄	C₂³	1	32	yes	complemented
62	C₂²×#120	—	3	1	no	Sylow
63	C₂⁵×C₃	—	2	1	no	—
64	C₂⁵×C₃	—	2	1	no	—
65	C₂⁵×C₃	—	3	2	no	—
66	C₂⁵×C₃	—	3	12	no	—
67	C₂⁵×C₃	—	6	16	no	—
68	C₂⁵×C₃	—	6	8	no	—
69	C₂⁵×C₃	C₂×D₃	1	1	yes	characteristic
70	C₂⁵×C₃	C₂×D₃	1	1	yes	characteristic, complemented
71	C₂⁵×C₃	C₂²×C₃	1	1	yes	characteristic
72	C₂⁵×C₃	C₂²×C₃	1	1	yes	characteristic, complemented
73	C₂⁴×D₃	—	2	8	no	—
74	C₂⁴×D₃	—	2	16	no	—
75	C₂⁴×D₃	C₂²×C₃	1	2	yes	—
76	C₂⁴×D₃	C₂²×C₃	1	12	yes	complemented
77	C₂²×C₃×D₄	—	2	16	no	—
78	C₂²×C₃×D₄	—	2	8	no	—
79	C₂²×C₃×D₄	—	2	8	no	—
80	C₂²×C₃×D₄	—	2	12	no	—
81	C₂²×C₃×D₄	—	3	24	no	—
82	C₂²×C₃×D₄	—	6	16	no	—
83	C₂²×C₃×D₄	C₂×D₃	1	12	yes	complemented
84	C₂²×C₃×D₄	C₂²×C₃	1	12	yes	complemented
85	C₂³×C₃×C₄	—	2	1	no	—
86	C₂³×C₃×C₄	—	3	2	no	—
87	C₂³×C₃×C₄	C₂×D₃	1	1	yes	characteristic, complemented
88	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic, complemented
89	C₂²×#67	—	2	16	no	—
90	C₂²×#67	C₂²×C₃	1	24	yes	complemented
91	C₂³×Dic₃	C₂²×C₃	1	2	yes	complemented
92	C₃×#120	—	3	64	no	—
93	C₂×C₃×C₂²⋊C₄	—	3	12	no	—
94	C₂×C₃×C₂²⋊C₄	—	3	24	no	—
95	C₂×#217	C₂²×C₃	1	12	yes	complemented
96	#937	C₂²×C₃	1	64	yes	direct product factor
97	C₂×(C₂×D₃)⋊C₄	C₂²×C₃	1	24	yes	complemented
98	C₂³×C₃²	—	2	12	no	—
99	C₂³×C₃²	—	2	32	no	—
100	C₂³×C₃²	—	2	24	no	—
101	C₂³×C₃²	—	2	24	no	—
102	C₂³×C₃²	—	4	16	no	—
103	C₂³×C₃²	C₂×D₄	1	8	yes	—
104	C₂³×C₃²	C₂×D₄	1	4	yes	—
105	C₂³×C₃²	C₂×D₄	1	24	yes	complemented
106	C₂³×C₃²	C₂⁴	1	4	yes	—
107	C₂³×C₃²	C₂⁴	1	3	yes	—
108	C₂³×C₃²	C₂⁴	1	4	yes	complemented
109	C₂²×C₃×D₃	—	2	384	no	—
110	C₂²×C₃×D₃	—	2	64	no	—
111	C₂²×C₃×D₃	—	2	24	no	—
112	C₂²×C₃×D₃	—	2	24	no	—
113	C₂²×C₃×D₃	—	2	32	no	—
114	C₂²×C₃×D₃	—	2	64	no	—
115	C₂²×C₃×D₃	C₂×D₄	1	48	yes	complemented
116	C₂²×C₃×D₃	C₂⁴	1	8	yes	—
117	C₃²×D₄	—	2	32	no	—
118	C₂×C₃²×C₄	—	2	12	no	—
119	C₂×C₃²×C₄	C₂⁴	1	4	yes	complemented
120	C₃×#67	—	2	64	no	—
121	C₂×C₃×Dic₃	—	2	24	no	—
122	C₂×C₃×Dic₃	C₂⁴	1	8	yes	complemented
123	C₂⁶	—	3	1	no	—
124	C₂³×D₄	—	3	2	no	—
125	C₂³×D₄	C₃×D₃	1	1	yes	characteristic, complemented
126	C₂×#120	—	3	24	no	—
127	C₂²×C₂²⋊C₄	—	3	1	no	—
128	C₂²×C₂²⋊C₄	—	3	2	no	—
129	C₂⁴×C₃	—	2	8	no	—
130	C₂⁴×C₃	—	2	8	no	—
131	C₂⁴×C₃	—	2	8	no	—
132	C₂⁴×C₃	—	2	8	no	—
133	C₂⁴×C₃	—	2	4	no	—
134	C₂⁴×C₃	—	2	8	no	—
135	C₂⁴×C₃	—	2	4	no	—
136	C₂⁴×C₃	—	2	8	no	—
137	C₂⁴×C₃	—	2	1	no	—
138	C₂⁴×C₃	—	2	6	no	—
139	C₂⁴×C₃	—	2	6	no	—
140	C₂⁴×C₃	—	3	16	no	—
141	C₂⁴×C₃	—	3	12	no	—
142	C₂⁴×C₃	—	3	16	no	—
143	C₂⁴×C₃	—	4	8	no	—
144	C₂⁴×C₃	—	4	8	no	—
145	C₂⁴×C₃	—	6	96	no	—
146	C₂⁴×C₃	—	6	128	no	—
147	C₂⁴×C₃	—	6	8	no	—
148	C₂⁴×C₃	—	6	8	no	—
149	C₂⁴×C₃	—	6	48	no	—
150	C₂⁴×C₃	#67	1	8	yes	complemented
151	C₂⁴×C₃	C₃×D₄	1	8	yes	complemented
152	C₂⁴×C₃	C₂²×D₃	1	6	yes	—
153	C₂⁴×C₃	C₂²×D₃	1	1	yes	characteristic
154	C₂⁴×C₃	C₂²×D₃	1	6	yes	complemented
155	C₂⁴×C₃	C₂³×C₃	1	6	yes	—
156	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
157	C₂⁴×C₃	C₂³×C₃	1	6	yes	complemented
158	C₂³×D₃	—	2	128	no	—
159	C₂³×D₃	—	2	8	no	—
160	C₂³×D₃	—	2	8	no	—
161	C₂³×D₃	—	2	48	no	—
162	C₂³×D₃	—	2	96	no	—
163	C₂³×D₃	C₃×D₄	1	16	yes	complemented
164	C₂³×D₃	C₂³×C₃	1	12	yes	—
165	C₂³×D₃	C₂³×C₃	1	16	yes	complemented
166	C₂×C₃×D₄	—	2	96	no	—
167	C₂×C₃×D₄	—	2	48	no	—
168	C₂×C₃×D₄	—	2	48	no	—
169	C₂×C₃×D₄	—	2	16	no	—
170	C₂×C₃×D₄	—	3	32	no	—
171	C₂×C₃×D₄	—	6	96	no	—
172	C₂×C₃×D₄	C₂²×D₃	1	16	yes	complemented
173	C₂×C₃×D₄	C₂³×C₃	1	16	yes	complemented
174	C₂²×C₃×C₄	—	2	8	no	—
175	C₂²×C₃×C₄	—	2	4	no	—
176	C₂²×C₃×C₄	—	2	4	no	—
177	C₂²×C₃×C₄	—	2	6	no	—
178	C₂²×C₃×C₄	—	3	12	no	—
179	C₂²×C₃×C₄	—	6	8	no	—
180	C₂²×C₃×C₄	C₂²×D₃	1	6	yes	complemented
181	C₂²×C₃×C₄	C₂³×C₃	1	6	yes	complemented
182	C₂×#67	—	2	96	no	—
183	C₂×#67	C₂³×C₃	1	32	yes	complemented
184	C₂²×Dic₃	—	2	8	no	—
185	C₂²×Dic₃	C₂³×C₃	1	12	yes	complemented
186	C₃×C₂²⋊C₄	—	3	16	no	—
187	C₃×C₂²⋊C₄	—	3	32	no	—
188	#217	C₂³×C₃	1	16	yes	complemented
189	(C₂×D₃)⋊C₄	C₂³×C₃	1	32	yes	complemented
190	C₂²×C₃²	—	2	4	no	—
191	C₂²×C₃²	—	2	48	no	—
192	C₂²×C₃²	—	2	8	no	—
193	C₂²×C₃²	—	2	8	no	—
194	C₂²×C₃²	—	4	24	no	—
195	C₂²×C₃²	#120	1	16	yes	complemented
196	C₂²×C₃²	C₂²×D₄	1	12	yes	—
197	C₂²×C₃²	C₂²×D₄	1	6	yes	—
198	C₂²×C₃²	C₂²×D₄	1	8	yes	complemented
199	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
200	C₂×C₃×D₃	—	2	128	no	—
201	C₂×C₃×D₃	—	2	96	no	—
202	C₂×C₃×D₃	—	2	8	no	—
203	C₂×C₃×D₃	—	2	8	no	—
204	C₂×C₃×D₃	C₂²×D₄	1	16	yes	complemented
205	C₃²×C₄	—	2	4	no	—
206	C₃×Dic₃	—	2	8	no	—
207	C₂⁵	—	3	2	no	—
208	C₂⁵	—	3	12	no	—
209	C₂⁵	—	6	16	no	—
210	C₂⁵	—	6	8	no	—
211	C₂⁵	C₂×C₃×D₃	1	1	yes	characteristic
212	C₂⁵	C₂×C₃×D₃	1	1	yes	characteristic, complemented
213	C₂²×D₄	—	2	8	no	—
214	C₂²×D₄	—	3	24	no	—
215	C₂²×D₄	—	6	16	no	—
216	C₂²×D₄	C₂×C₃×D₃	1	12	yes	complemented
217	C₂³×C₄	—	3	2	no	—
218	C₂³×C₄	C₂×C₃×D₃	1	1	yes	characteristic, complemented
219	#120	—	3	64	no	—
220	C₂×C₂²⋊C₄	—	3	12	no	—
221	C₂×C₂²⋊C₄	—	3	24	no	—
222	C₂³×C₃	—	2	32	no	—
223	C₂³×C₃	—	2	32	no	—
224	C₂³×C₃	—	2	24	no	—
225	C₂³×C₃	—	2	24	no	—
226	C₂³×C₃	—	2	24	no	—
227	C₂³×C₃	—	2	24	no	—
228	C₂³×C₃	—	2	12	no	—
229	C₂³×C₃	—	2	24	no	—
230	C₂³×C₃	—	2	12	no	—
231	C₂³×C₃	—	2	3	no	—
232	C₂³×C₃	—	2	4	no	—
233	C₂³×C₃	—	2	4	no	—
234	C₂³×C₃	—	2	8	no	—
235	C₂³×C₃	—	2	4	no	—
236	C₂³×C₃	—	2	24	no	—
237	C₂³×C₃	—	3	48	no	—
238	C₂³×C₃	—	3	8	no	—
239	C₂³×C₃	—	4	32	no	—
240	C₂³×C₃	—	4	24	no	—
241	C₂³×C₃	—	4	24	no	—
242	C₂³×C₃	—	4	32	no	—
243	C₂³×C₃	—	4	16	no	—
244	C₂³×C₃	—	4	16	no	—
245	C₂³×C₃	—	6	64	no	—
246	C₂³×C₃	—	6	384	no	—
247	C₂³×C₃	—	6	64	no	—
248	C₂³×C₃	—	6	24	no	—
249	C₂³×C₃	—	6	24	no	—
250	C₂³×C₃	—	6	32	no	—
251	C₂³×C₃	D₃×D₄	1	8	yes	—
252	C₂³×C₃	C₂×#67	1	4	yes	—
253	C₂³×C₃	C₂×#67	1	24	yes	complemented
254	C₂³×C₃	C₂×C₃×D₄	1	8	yes	—
255	C₂³×C₃	C₂×C₃×D₄	1	4	yes	—
256	C₂³×C₃	C₂×C₃×D₄	1	24	yes	complemented
257	C₂³×C₃	C₂³×D₃	1	4	yes	—
258	C₂³×C₃	C₂³×D₃	1	3	yes	—
259	C₂³×C₃	C₂³×D₃	1	4	yes	complemented
260	C₂³×C₃	C₂⁴×C₃	1	4	yes	—
261	C₂³×C₃	C₂⁴×C₃	1	3	yes	—
262	C₂³×C₃	C₂⁴×C₃	1	4	yes	complemented
263	C₂²×D₃	—	2	384	no	—
264	C₂²×D₃	—	2	64	no	—
265	C₂²×D₃	—	2	24	no	—
266	C₂²×D₃	—	2	24	no	—
267	C₂²×D₃	—	2	32	no	—
268	C₂²×D₃	—	2	64	no	—
269	C₂²×D₃	C₂×C₃×D₄	1	48	yes	complemented
270	C₂²×D₃	C₂⁴×C₃	1	8	yes	—
271	C₃×D₄	—	2	64	no	—
272	C₃×D₄	—	2	32	no	—
273	C₃×D₄	—	2	32	no	—
274	C₃×D₄	—	6	64	no	—
275	C₂×C₃×C₄	—	2	24	no	—
276	C₂×C₃×C₄	—	2	12	no	—
277	C₂×C₃×C₄	—	2	12	no	—
278	C₂×C₃×C₄	—	2	4	no	—
279	C₂×C₃×C₄	—	3	8	no	—
280	C₂×C₃×C₄	—	6	24	no	—
281	C₂×C₃×C₄	C₂³×D₃	1	4	yes	complemented
282	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	complemented
283	#67	—	2	64	no	—
284	C₂×Dic₃	—	2	24	no	—
285	C₂×Dic₃	C₂⁴×C₃	1	8	yes	complemented
286	C₂×C₃²	—	2	8	no	—
287	C₂×C₃²	—	4	4	no	—
288	C₂×C₃²	C₂×#120	1	12	yes	complemented
289	C₂×C₃²	C₂³×D₄	1	2	yes	—
290	C₂×C₃²	C₂³×D₄	1	1	yes	characteristic
291	C₃×D₃	—	2	16	no	—
292	C₂⁴	—	2	8	no	—
293	C₂⁴	—	2	8	no	—
294	C₂⁴	—	2	4	no	—
295	C₂⁴	—	3	12	no	—
296	C₂⁴	—	3	16	no	—
297	C₂⁴	—	3	16	no	—
298	C₂⁴	—	6	96	no	—
299	C₂⁴	—	6	128	no	—
300	C₂⁴	—	6	8	no	—
301	C₂⁴	—	6	8	no	—
302	C₂⁴	—	6	48	no	—
303	C₂⁴	C₃×#67	1	8	yes	complemented
304	C₂⁴	C₂²×C₃×D₃	1	6	yes	—
305	C₂⁴	C₂²×C₃×D₃	1	1	yes	characteristic
306	C₂⁴	C₂²×C₃×D₃	1	6	yes	complemented
307	C₂×D₄	—	2	48	no	—
308	C₂×D₄	—	3	32	no	—
309	C₂×D₄	—	6	96	no	—
310	C₂×D₄	C₂²×C₃×D₃	1	16	yes	complemented
311	C₂²×C₄	—	2	4	no	—
312	C₂²×C₄	—	3	12	no	—
313	C₂²×C₄	—	6	8	no	—
314	C₂²×C₄	C₂²×C₃×D₃	1	6	yes	complemented
315	C₂²⋊C₄	—	3	16	no	—
316	C₂²⋊C₄	—	3	32	no	—
317	C₂²×C₃	—	2	8	no	—
318	C₂²×C₃	—	2	8	no	—
319	C₂²×C₃	—	2	48	no	—
320	C₂²×C₃	—	2	48	no	—
321	C₂²×C₃	—	2	8	no	—
322	C₂²×C₃	—	2	8	no	—
323	C₂²×C₃	—	2	4	no	—
324	C₂²×C₃	—	2	8	no	—
325	C₂²×C₃	—	2	4	no	—
326	C₂²×C₃	—	2	16	no	—
327	C₂²×C₃	—	2	12	no	—
328	C₂²×C₃	—	2	6	no	—
329	C₂²×C₃	—	2	8	no	—
330	C₂²×C₃	—	2	1	no	—
331	C₂²×C₃	—	3	16	no	—
332	C₂²×C₃	—	4	48	no	—
333	C₂²×C₃	—	4	8	no	—
334	C₂²×C₃	—	4	8	no	—
335	C₂²×C₃	—	4	48	no	—
336	C₂²×C₃	—	4	24	no	—
337	C₂²×C₃	—	4	24	no	—
338	C₂²×C₃	—	6	128	no	—
339	C₂²×C₃	—	6	8	no	—
340	C₂²×C₃	—	6	8	no	—
341	C₂²×C₃	—	6	96	no	—
342	C₂²×C₃	#937	1	16	yes	direct product factor
343	C₂²×C₃	C₃×#120	1	16	yes	complemented
344	C₂²×C₃	C₂×D₃×D₄	1	12	yes	—
345	C₂²×C₃	C₂²×#67	1	6	yes	—
346	C₂²×C₃	C₂²×#67	1	8	yes	complemented
347	C₂²×C₃	C₂²×C₃×D₄	1	12	yes	—
348	C₂²×C₃	C₂²×C₃×D₄	1	6	yes	—
349	C₂²×C₃	C₂²×C₃×D₄	1	8	yes	complemented
350	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
351	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
352	C₂×D₃	—	2	128	no	—
353	C₂×D₃	—	2	8	no	—
354	C₂×D₃	—	2	8	no	—
355	C₂×D₃	—	2	96	no	—
356	C₂×D₃	C₂²×C₃×D₄	1	16	yes	complemented
357	C₃×C₄	—	2	8	no	—
358	C₃×C₄	—	2	4	no	—
359	C₃×C₄	—	2	4	no	—
360	C₃×C₄	—	6	8	no	—
361	Dic₃	—	2	8	no	—
362	C₃²	C₂²×#120	1	1	yes	characteristic, complemented, Sylow
363	C₂³	—	2	32	no	—
364	C₂³	—	2	24	no	—
365	C₂³	—	2	24	no	—
366	C₂³	—	2	12	no	—
367	C₂³	—	3	48	no	—
368	C₂³	—	3	8	no	—
369	C₂³	—	4	16	no	—
370	C₂³	—	6	64	no	—
371	C₂³	—	6	384	no	—
372	C₂³	—	6	64	no	—
373	C₂³	—	6	24	no	—
374	C₂³	—	6	24	no	—
375	C₂³	—	6	32	no	—
376	C₂³	C₃×D₃×D₄	1	8	yes	—
377	C₂³	C₂×C₃×#67	1	4	yes	—
378	C₂³	C₂×C₃×#67	1	24	yes	complemented
379	C₂³	C₂³×C₃×D₃	1	4	yes	—
380	C₂³	C₂³×C₃×D₃	1	3	yes	—
381	C₂³	C₂³×C₃×D₃	1	4	yes	complemented
382	D₄	—	2	32	no	—
383	D₄	—	6	64	no	—
384	C₂×C₄	—	2	12	no	—
385	C₂×C₄	—	3	8	no	—
386	C₂×C₄	—	6	24	no	—
387	C₂×C₄	C₂³×C₃×D₃	1	4	yes	complemented
388	C₂×C₃	—	2	8	no	—
389	C₂×C₃	—	2	8	no	—
390	C₂×C₃	—	2	12	no	—
391	C₂×C₃	—	2	2	no	—
392	C₂×C₃	—	2	1	no	—
393	C₂×C₃	—	4	8	no	—
394	C₂×C₃	—	4	8	no	—
395	C₂×C₃	—	4	4	no	—
396	C₂×C₃	—	4	4	no	—
397	C₂×C₃	—	6	16	no	—
398	C₂×C₃	C₂×#937	1	12	yes	direct product factor
399	C₂×C₃	C₂×C₃×#120	1	12	yes	complemented
400	C₂×C₃	C₂²×D₃×D₄	1	2	yes	—
401	C₂×C₃	C₂³×#67	1	1	yes	characteristic
402	C₂×C₃	C₂³×C₃×D₄	1	2	yes	—
403	C₂×C₃	C₂³×C₃×D₄	1	1	yes	characteristic
404	D₃	—	2	16	no	—
405	C₂²	—	2	48	no	—
406	C₂²	—	2	8	no	—
407	C₂²	—	2	8	no	—
408	C₂²	—	2	4	no	—
409	C₂²	—	3	16	no	—
410	C₂²	—	4	24	no	—
411	C₂²	—	6	128	no	—
412	C₂²	—	6	96	no	—
413	C₂²	—	6	8	no	—
414	C₂²	—	6	8	no	—
415	C₂²	C₃×#937	1	16	yes	direct product factor
416	C₂²	C₂×C₃×D₃×D₄	1	12	yes	—
417	C₂²	C₂²×C₃×#67	1	6	yes	—
418	C₂²	C₂²×C₃×#67	1	8	yes	complemented
419	C₂²	C₂⁴×C₃×D₃	1	1	yes	characteristic
420	C₄	—	2	4	no	—
421	C₄	—	6	8	no	—
422	C₃	—	2	1	no	—
423	C₃	C₂²×#937	1	1	yes	characteristic, direct product factor
424	C₃	C₂²×C₃×#120	1	1	yes	characteristic, complemented
425	C₂	—	2	8	no	—
426	C₂	—	4	4	no	—
427	C₂	—	6	16	no	—
428	C₂	C₂×C₃×#937	1	12	yes	direct product factor
429	C₂	C₂²×C₃×D₃×D₄	1	2	yes	—
430	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×#120
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. C₂⁵×C₃×D₃	C₂	semidirect
2. C₂³×C₃²×D₄	C₂	semidirect
3. C₂³×C₃×#67	C₂	semidirect
4. C₂²×C₃×#217	C₂	semidirect
5. C₂×C₃×#937	C₂	direct (N × H)
6. C₂²×C₃×(C₂×D₃)⋊C₄	C₂	semidirect
8. C₂²×#937	C₃	direct (N × H)
10. C₂⁵×C₃²	C₂²	semidirect
14. C₂⁴×C₃×D₃	C₂²	semidirect
16. C₂²×C₃²×D₄	C₂²	semidirect
17. C₂³×C₃²×C₄	C₂²	semidirect
19. C₂²×C₃×#67	C₂²	semidirect
20. C₂³×C₃×Dic₃	C₂²	semidirect
21. C₂×C₃×#217	C₂²	semidirect
22. C₃×#937	C₂²	direct (N × H)
23. C₂×C₃×(C₂×D₃)⋊C₄	C₂²	semidirect
25. C₂⁵×D₃	C₂×C₃	semidirect
28. C₂³×C₃×D₄	D₃	semidirect
29. C₂³×C₃×D₄	C₂×C₃	semidirect
30. C₂³×#67	C₂×C₃	semidirect
34. C₂²×#217	C₂×C₃	semidirect
35. C₂×#937	C₂×C₃	direct (N × H)
36. C₂²×(C₂×D₃)⋊C₄	C₂×C₃	semidirect
40. C₂⁴×C₃²	D₄	semidirect
43. C₂⁴×C₃²	C₂³	semidirect
49. C₂³×C₃×D₃	D₄	semidirect
51. C₂³×C₃×D₃	C₂³	semidirect
53. C₂×C₃²×D₄	C₂³	semidirect
55. C₂²×C₃²×C₄	C₂³	semidirect
57. C₂×C₃×#67	C₂³	semidirect
59. C₂²×C₃×Dic₃	C₂³	semidirect
60. C₃×#217	C₂³	semidirect
61. C₃×(C₂×D₃)⋊C₄	C₂³	semidirect
70. C₂⁵×C₃	C₂×D₃	semidirect
72. C₂⁵×C₃	C₂²×C₃	semidirect
76. C₂⁴×D₃	C₂²×C₃	semidirect
83. C₂²×C₃×D₄	C₂×D₃	semidirect
84. C₂²×C₃×D₄	C₂²×C₃	semidirect
87. C₂³×C₃×C₄	C₂×D₃	semidirect
88. C₂³×C₃×C₄	C₂²×C₃	semidirect
90. C₂²×#67	C₂²×C₃	semidirect
91. C₂³×Dic₃	C₂²×C₃	semidirect
95. C₂×#217	C₂²×C₃	semidirect
96. #937	C₂²×C₃	direct (N × H)
97. C₂×(C₂×D₃)⋊C₄	C₂²×C₃	semidirect
105. C₂³×C₃²	C₂×D₄	semidirect
108. C₂³×C₃²	C₂⁴	semidirect
115. C₂²×C₃×D₃	C₂×D₄	semidirect
119. C₂×C₃²×C₄	C₂⁴	semidirect
122. C₂×C₃×Dic₃	C₂⁴	semidirect
125. C₂³×D₄	C₃×D₃	semidirect
150. C₂⁴×C₃	#67	semidirect
151. C₂⁴×C₃	C₃×D₄	semidirect
154. C₂⁴×C₃	C₂²×D₃	semidirect
157. C₂⁴×C₃	C₂³×C₃	semidirect
163. C₂³×D₃	C₃×D₄	semidirect
165. C₂³×D₃	C₂³×C₃	semidirect
172. C₂×C₃×D₄	C₂²×D₃	semidirect
173. C₂×C₃×D₄	C₂³×C₃	semidirect
180. C₂²×C₃×C₄	C₂²×D₃	semidirect
181. C₂²×C₃×C₄	C₂³×C₃	semidirect
183. C₂×#67	C₂³×C₃	semidirect
185. C₂²×Dic₃	C₂³×C₃	semidirect
188. #217	C₂³×C₃	semidirect
189. (C₂×D₃)⋊C₄	C₂³×C₃	semidirect
195. C₂²×C₃²	#120	semidirect
198. C₂²×C₃²	C₂²×D₄	semidirect
204. C₂×C₃×D₃	C₂²×D₄	semidirect
212. C₂⁵	C₂×C₃×D₃	semidirect
216. C₂²×D₄	C₂×C₃×D₃	semidirect
218. C₂³×C₄	C₂×C₃×D₃	semidirect
253. C₂³×C₃	C₂×#67	semidirect
256. C₂³×C₃	C₂×C₃×D₄	semidirect
259. C₂³×C₃	C₂³×D₃	semidirect
262. C₂³×C₃	C₂⁴×C₃	semidirect
269. C₂²×D₃	C₂×C₃×D₄	semidirect
281. C₂×C₃×C₄	C₂³×D₃	semidirect
282. C₂×C₃×C₄	C₂⁴×C₃	semidirect
285. C₂×Dic₃	C₂⁴×C₃	semidirect
288. C₂×C₃²	C₂×#120	semidirect
303. C₂⁴	C₃×#67	semidirect
306. C₂⁴	C₂²×C₃×D₃	semidirect
310. C₂×D₄	C₂²×C₃×D₃	semidirect
314. C₂²×C₄	C₂²×C₃×D₃	semidirect
342. C₂²×C₃	#937	direct (N × H)
343. C₂²×C₃	C₃×#120	semidirect
346. C₂²×C₃	C₂²×#67	semidirect
349. C₂²×C₃	C₂²×C₃×D₄	semidirect
356. C₂×D₃	C₂²×C₃×D₄	semidirect
362. C₃²	C₂²×#120	semidirect
378. C₂³	C₂×C₃×#67	semidirect
381. C₂³	C₂³×C₃×D₃	semidirect
387. C₂×C₄	C₂³×C₃×D₃	semidirect
398. C₂×C₃	C₂×#937	direct (N × H)
399. C₂×C₃	C₂×C₃×#120	semidirect
415. C₂²	C₃×#937	direct (N × H)
418. C₂²	C₂²×C₃×#67	semidirect
423. C₃	C₂²×#937	direct (N × H)
424. C₃	C₂²×C₃×#120	semidirect
428. C₂	C₂×C₃×#937	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁵×C₃×D₃	2
C₂³×C₃²×D₄	2
C₂³×C₃×#67	2
C₂²×C₃×#217	2
C₂×C₃×#937	2
C₂²×C₃×(C₂×D₃)⋊C₄	2
C₂²×C₃×#120	3
C₂²×#937	3

Subgroups — C22×C3×#937 #11900243

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃×#937 #11900243