Subgroups — C₂²×C₃×#950 #11918597

Order 1152.

3453 conjugacy classes of subgroups.

The subgroup lattice has 491 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃²×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×#235	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#950	C₂	1	24	yes	maximal, direct product factor
4	C₂²×C₃×#216	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×C₃×#215	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₃×#214	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×C₃×#213	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂³×C₃×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₃×#135	—	3	1	no	maximal
10	C₂²×#950	C₃	1	1	yes	maximal, characteristic, direct product factor
11	C₂×C₃²×#41	—	2	6	no	—
12	C₂×C₃²×#41	C₂²	1	12	yes	complemented
13	C₂²×C₃²×Q₈	C₂²	1	1	yes	characteristic
14	C₂²×C₃²×D₄	—	2	1	no	—
15	C₂²×C₃²×D₄	C₂²	1	1	yes	characteristic
16	C₂³×C₃²×C₄	—	2	1	no	—
17	C₂³×C₃²×C₄	C₂²	1	1	yes	characteristic
18	C₂²×C₃×#67	—	2	1	no	—
19	C₂×C₃×#235	—	2	6	no	—
20	C₂×C₃×#235	C₂²	1	12	yes	complemented
21	C₂²×C₃×D₁₂	C₂²	1	1	yes	characteristic
22	C₂²×C₃×C₄×D₃	—	2	1	no	—
23	C₂²×C₃×Dic₆	C₂²	1	1	yes	characteristic
24	C₃×#950	C₂²	1	64	yes	direct product factor
25	C₂×C₃×#216	C₂²	1	12	yes	complemented
26	C₂×C₃×#215	C₂²	1	12	yes	complemented
27	C₂×C₃×#214	C₂²	1	12	yes	complemented
28	C₂×C₃×#213	C₂²	1	12	yes	complemented
29	C₂²×C₃×C₃⋊C₈	C₂²	1	1	yes	characteristic
30	C₂²×C₃×C₃⋊C₈	C₂²	1	1	yes	characteristic
31	C₂²×C₃×C₃⋊C₈	C₂²	1	12	yes	complemented
32	C₂²×C₃×#41	—	2	1	no	—
33	C₂²×C₃×#41	—	3	1	no	—
34	C₂²×C₃×#41	D₃	1	1	yes	characteristic, complemented
35	C₂²×C₃×#41	C₂×C₃	1	1	yes	characteristic, complemented
36	C₂²×#235	C₂×C₃	1	1	yes	characteristic, complemented
37	C₂×C₃×#135	—	3	24	no	—
38	C₂²×C₃×Q₁₆	—	3	1	no	—
39	C₂²×C₃×SD₁₆	—	3	1	no	—
40	C₂²×C₃×SD₁₆	—	3	1	no	—
41	C₂²×C₃×D₈	—	3	1	no	—
42	C₂³×C₃×C₈	—	3	1	no	—
43	C₂×#950	C₂×C₃	1	24	yes	direct product factor
44	C₂²×#216	C₂×C₃	1	1	yes	characteristic, complemented
45	C₂²×#215	C₂×C₃	1	1	yes	characteristic, complemented
46	C₂²×#214	C₂×C₃	1	1	yes	characteristic, complemented
47	C₂²×#213	C₂×C₃	1	1	yes	characteristic, complemented
48	C₂³×C₃⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
49	C₂⁴×C₃²	—	2	1	no	—
50	C₂⁴×C₃²	D₄	1	1	yes	characteristic
51	C₂³×C₃×D₃	—	2	1	no	—
52	C₃²×#41	—	2	24	no	—
53	C₃²×#41	C₂³	1	16	yes	complemented
54	C₂×C₃²×Q₈	—	2	3	no	—
55	C₂×C₃²×Q₈	C₂³	1	6	yes	—
56	C₂×C₃²×D₄	—	2	12	no	—
57	C₂×C₃²×D₄	—	2	3	no	—
58	C₂×C₃²×D₄	C₂³	1	6	yes	—
59	C₂²×C₃²×C₄	—	2	1	no	—
60	C₂²×C₃²×C₄	—	2	12	no	—
61	C₂²×C₃²×C₄	D₄	1	6	yes	—
62	C₂²×C₃²×C₄	D₄	1	1	yes	characteristic
63	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
64	C₂²×C₃²×C₄	C₂³	1	6	yes	—
65	C₂×C₃×#67	—	2	12	no	—
66	C₂²×C₃×Dic₃	—	2	1	no	—
67	C₃×#235	—	2	24	no	—
68	C₃×#235	C₂³	1	16	yes	complemented
69	C₂×C₃×D₁₂	—	2	3	no	—
70	C₂×C₃×D₁₂	C₂³	1	6	yes	—
71	C₂×C₃×C₄×D₃	—	2	12	no	—
72	C₂×C₃×Dic₆	—	2	3	no	—
73	C₂×C₃×Dic₆	C₂³	1	6	yes	—
74	C₃×#216	C₂³	1	16	yes	complemented
75	C₃×#215	C₂³	1	16	yes	complemented
76	C₃×#214	C₂³	1	16	yes	complemented
77	C₃×#213	C₂³	1	16	yes	complemented
78	C₂×C₃×C₃⋊C₈	C₂³	1	6	yes	—
79	C₂×C₃×C₃⋊C₈	C₂³	1	6	yes	—
80	C₂×C₃×C₃⋊C₈	C₂³	1	16	yes	complemented
81	C₂²×#135	—	3	1	no	Sylow
82	C₂×C₃×#41	—	2	12	no	—
83	C₂×C₃×#41	—	2	6	no	—
84	C₂×C₃×#41	—	2	6	no	—
85	C₂×C₃×#41	—	2	12	no	—
86	C₂×C₃×#41	—	3	12	no	—
87	C₂×C₃×#41	—	6	6	no	—
88	C₂×C₃×#41	C₂×D₃	1	12	yes	complemented
89	C₂×C₃×#41	C₂²×C₃	1	12	yes	complemented
90	C₂²×C₃×Q₈	—	2	1	no	—
91	C₂²×C₃×Q₈	—	3	1	no	—
92	C₂²×C₃×Q₈	C₂×D₃	1	1	yes	characteristic
93	C₂²×C₃×Q₈	C₂²×C₃	1	1	yes	characteristic
94	C₂²×C₃×D₄	—	2	2	no	—
95	C₂²×C₃×D₄	—	2	1	no	—
96	C₂²×C₃×D₄	—	2	1	no	—
97	C₂²×C₃×D₄	—	2	1	no	—
98	C₂²×C₃×D₄	—	3	1	no	—
99	C₂²×C₃×D₄	—	6	1	no	—
100	C₂²×C₃×D₄	C₂×D₃	1	1	yes	characteristic
101	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
102	C₂³×C₃×C₄	—	2	2	no	—
103	C₂³×C₃×C₄	—	2	1	no	—
104	C₂³×C₃×C₄	—	2	1	no	—
105	C₂³×C₃×C₄	—	2	1	no	—
106	C₂³×C₃×C₄	—	6	1	no	—
107	C₂³×C₃×C₄	C₂×D₃	1	1	yes	characteristic
108	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
109	C₂²×#67	—	2	1	no	—
110	C₂×#235	—	2	6	no	—
111	C₂×#235	C₂²×C₃	1	12	yes	complemented
112	C₂²×D₁₂	C₂²×C₃	1	1	yes	characteristic
113	C₂²×C₄×D₃	—	2	1	no	—
114	C₂²×Dic₆	C₂²×C₃	1	1	yes	characteristic
115	C₃×#135	—	3	64	no	—
116	C₂×C₃×Q₁₆	—	3	12	no	—
117	C₂×C₃×SD₁₆	—	3	12	no	—
118	C₂×C₃×SD₁₆	—	3	12	no	—
119	C₂×C₃×D₈	—	3	12	no	—
120	C₂²×C₃×C₈	—	3	1	no	—
121	C₂²×C₃×C₈	—	3	1	no	—
122	C₂²×C₃×C₈	—	3	12	no	—
123	#950	C₂²×C₃	1	64	yes	direct product factor
124	C₂×#216	C₂²×C₃	1	12	yes	complemented
125	C₂×#215	C₂²×C₃	1	12	yes	complemented
126	C₂×#214	C₂²×C₃	1	12	yes	complemented
127	C₂×#213	C₂²×C₃	1	12	yes	complemented
128	C₂²×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
129	C₂²×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
130	C₂²×C₃⋊C₈	C₂²×C₃	1	12	yes	complemented
131	C₂³×C₃²	—	2	6	no	—
132	C₂³×C₃²	—	2	4	no	—
133	C₂³×C₃²	—	4	4	no	—
134	C₂³×C₃²	C₂×D₄	1	6	yes	—
135	C₂³×C₃²	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₃×D₃	—	2	6	no	—
137	C₂²×C₃×D₃	—	4	4	no	—
138	C₃²×Q₈	—	2	6	no	—
139	C₃²×Q₈	C₂⁴	1	4	yes	—
140	C₃²×D₄	—	2	16	no	—
141	C₃²×D₄	—	2	6	no	—
142	C₃²×D₄	C₂⁴	1	4	yes	—
143	C₂×C₃²×C₄	—	2	6	no	—
144	C₂×C₃²×C₄	—	2	16	no	—
145	C₂×C₃²×C₄	C₂×D₄	1	3	yes	—
146	C₂×C₃²×C₄	C₂×D₄	1	6	yes	—
147	C₂×C₃²×C₄	C₂×D₄	1	12	yes	—
148	C₂×C₃²×C₄	C₂⁴	1	3	yes	—
149	C₂×C₃²×C₄	C₂⁴	1	4	yes	—
150	C₃×#67	—	2	16	no	—
151	C₂×C₃×Dic₃	—	2	6	no	—
152	C₃×D₁₂	—	2	6	no	—
153	C₃×D₁₂	C₂⁴	1	4	yes	—
154	C₃×C₄×D₃	—	2	16	no	—
155	C₃×Dic₆	—	2	6	no	—
156	C₃×Dic₆	C₂⁴	1	4	yes	—
157	C₃×C₃⋊C₈	C₂⁴	1	4	yes	—
158	C₃×C₃⋊C₈	C₂⁴	1	4	yes	—
159	C₂²×#41	—	3	1	no	—
160	C₂²×#41	C₃×D₃	1	1	yes	characteristic, complemented
161	C₂×#135	—	3	24	no	—
162	C₂²×Q₁₆	—	3	1	no	—
163	C₂²×SD₁₆	—	3	1	no	—
164	C₂²×SD₁₆	—	3	1	no	—
165	C₂²×D₈	—	3	1	no	—
166	C₂³×C₈	—	3	1	no	—
167	C₂⁴×C₃	—	2	2	no	—
168	C₂⁴×C₃	—	2	1	no	—
169	C₂⁴×C₃	—	2	1	no	—
170	C₂⁴×C₃	—	2	1	no	—
171	C₂⁴×C₃	—	6	1	no	—
172	C₂⁴×C₃	#67	1	1	yes	characteristic
173	C₂⁴×C₃	C₃×D₄	1	1	yes	characteristic
174	C₂³×D₃	—	2	1	no	—
175	C₃×#41	—	2	48	no	—
176	C₃×#41	—	2	24	no	—
177	C₃×#41	—	2	24	no	—
178	C₃×#41	—	2	16	no	—
179	C₃×#41	—	3	16	no	—
180	C₃×#41	—	6	24	no	—
181	C₃×#41	C₂²×D₃	1	16	yes	complemented
182	C₃×#41	C₂³×C₃	1	16	yes	complemented
183	C₂×C₃×Q₈	—	2	6	no	—
184	C₂×C₃×Q₈	—	2	3	no	—
185	C₂×C₃×Q₈	—	2	3	no	—
186	C₂×C₃×Q₈	—	2	6	no	—
187	C₂×C₃×Q₈	—	3	6	no	—
188	C₂×C₃×Q₈	—	6	3	no	—
189	C₂×C₃×Q₈	C₂²×D₃	1	6	yes	—
190	C₂×C₃×Q₈	C₂³×C₃	1	6	yes	—
191	C₂×C₃×D₄	—	2	24	no	—
192	C₂×C₃×D₄	—	2	6	no	—
193	C₂×C₃×D₄	—	2	12	no	—
194	C₂×C₃×D₄	—	2	12	no	—
195	C₂×C₃×D₄	—	2	3	no	—
196	C₂×C₃×D₄	—	2	3	no	—
197	C₂×C₃×D₄	—	2	6	no	—
198	C₂×C₃×D₄	—	3	6	no	—
199	C₂×C₃×D₄	—	6	12	no	—
200	C₂×C₃×D₄	—	6	3	no	—
201	C₂×C₃×D₄	C₂²×D₃	1	6	yes	—
202	C₂×C₃×D₄	C₂³×C₃	1	6	yes	—
203	C₂²×C₃×C₄	—	2	2	no	—
204	C₂²×C₃×C₄	—	2	24	no	—
205	C₂²×C₃×C₄	—	2	1	no	—
206	C₂²×C₃×C₄	—	2	1	no	—
207	C₂²×C₃×C₄	—	2	12	no	—
208	C₂²×C₃×C₄	—	2	12	no	—
209	C₂²×C₃×C₄	—	2	1	no	—
210	C₂²×C₃×C₄	—	2	6	no	—
211	C₂²×C₃×C₄	—	2	1	no	—
212	C₂²×C₃×C₄	—	2	6	no	—
213	C₂²×C₃×C₄	—	6	1	no	—
214	C₂²×C₃×C₄	—	6	12	no	—
215	C₂²×C₃×C₄	#67	1	6	yes	—
216	C₂²×C₃×C₄	#67	1	1	yes	characteristic
217	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
218	C₂²×C₃×C₄	C₃×D₄	1	6	yes	—
219	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
220	C₂²×C₃×C₄	C₂²×D₃	1	6	yes	—
221	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
222	C₂²×C₃×C₄	C₂³×C₃	1	6	yes	—
223	C₂×#67	—	2	12	no	—
224	C₂²×Dic₃	—	2	1	no	—
225	#235	—	2	24	no	—
226	#235	C₂³×C₃	1	16	yes	complemented
227	C₂×D₁₂	—	2	3	no	—
228	C₂×D₁₂	C₂³×C₃	1	6	yes	—
229	C₂×C₄×D₃	—	2	12	no	—
230	C₂×Dic₆	—	2	3	no	—
231	C₂×Dic₆	C₂³×C₃	1	6	yes	—
232	C₃×Q₁₆	—	3	16	no	—
233	C₃×SD₁₆	—	3	16	no	—
234	C₃×SD₁₆	—	3	16	no	—
235	C₃×D₈	—	3	16	no	—
236	C₂×C₃×C₈	—	3	6	no	—
237	C₂×C₃×C₈	—	3	6	no	—
238	C₂×C₃×C₈	—	3	16	no	—
239	#216	C₂³×C₃	1	16	yes	complemented
240	#215	C₂³×C₃	1	16	yes	complemented
241	#214	C₂³×C₃	1	16	yes	complemented
242	#213	C₂³×C₃	1	16	yes	complemented
243	C₂×C₃⋊C₈	C₂³×C₃	1	6	yes	—
244	C₂×C₃⋊C₈	C₂³×C₃	1	6	yes	—
245	C₂×C₃⋊C₈	C₂³×C₃	1	16	yes	complemented
246	C₂²×C₃²	—	2	4	no	—
247	C₂²×C₃²	—	2	12	no	—
248	C₂²×C₃²	—	4	12	no	—
249	C₂²×C₃²	#135	1	4	yes	complemented
250	C₂²×C₃²	C₂²×D₄	1	4	yes	—
251	C₂²×C₃²	C₂²×D₄	1	3	yes	—
252	C₂×C₃×D₃	—	2	4	no	—
253	C₂×C₃×D₃	—	4	12	no	—
254	C₃²×C₄	—	2	4	no	—
255	C₃²×C₄	C₂²×D₄	1	3	yes	—
256	C₃²×C₄	C₂²×D₄	1	4	yes	—
257	C₃²×C₄	C₂⁵	1	1	yes	characteristic
258	C₃×Dic₃	—	2	4	no	—
259	C₂×#41	—	2	6	no	—
260	C₂×#41	—	3	12	no	—
261	C₂×#41	—	6	6	no	—
262	C₂×#41	C₂×C₃×D₃	1	12	yes	complemented
263	C₂²×Q₈	—	3	1	no	—
264	C₂²×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
265	C₂²×D₄	—	2	1	no	—
266	C₂²×D₄	—	3	1	no	—
267	C₂²×D₄	—	6	1	no	—
268	C₂²×D₄	C₂×C₃×D₃	1	1	yes	characteristic
269	C₂³×C₄	—	2	1	no	—
270	C₂³×C₄	—	6	1	no	—
271	C₂³×C₄	C₂×C₃×D₃	1	1	yes	characteristic
272	#135	—	3	64	no	—
273	C₂×Q₁₆	—	3	12	no	—
274	C₂×SD₁₆	—	3	12	no	—
275	C₂×SD₁₆	—	3	12	no	—
276	C₂×D₈	—	3	12	no	—
277	C₂²×C₈	—	3	1	no	—
278	C₂²×C₈	—	3	1	no	—
279	C₂²×C₈	—	3	12	no	—
280	C₂³×C₃	—	2	4	no	—
281	C₂³×C₃	—	2	4	no	—
282	C₂³×C₃	—	2	12	no	—
283	C₂³×C₃	—	2	6	no	—
284	C₂³×C₃	—	2	6	no	—
285	C₂³×C₃	—	2	1	no	—
286	C₂³×C₃	—	2	6	no	—
287	C₂³×C₃	—	4	4	no	—
288	C₂³×C₃	—	4	8	no	—
289	C₂³×C₃	—	4	4	no	—
290	C₂³×C₃	—	4	4	no	—
291	C₂³×C₃	—	6	6	no	—
292	C₂³×C₃	—	12	4	no	—
293	C₂³×C₃	C₂×#67	1	6	yes	—
294	C₂³×C₃	C₂×#67	1	1	yes	characteristic
295	C₂³×C₃	C₂×C₃×D₄	1	6	yes	—
296	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
297	C₂²×D₃	—	2	6	no	—
298	C₂²×D₃	—	4	4	no	—
299	C₃×Q₈	—	2	12	no	—
300	C₃×Q₈	—	2	6	no	—
301	C₃×Q₈	—	2	6	no	—
302	C₃×Q₈	—	2	4	no	—
303	C₃×Q₈	—	3	4	no	—
304	C₃×Q₈	—	6	6	no	—
305	C₃×Q₈	C₂³×D₃	1	4	yes	—
306	C₃×Q₈	C₂⁴×C₃	1	4	yes	—
307	C₃×D₄	—	2	32	no	—
308	C₃×D₄	—	2	12	no	—
309	C₃×D₄	—	2	16	no	—
310	C₃×D₄	—	2	16	no	—
311	C₃×D₄	—	2	6	no	—
312	C₃×D₄	—	2	6	no	—
313	C₃×D₄	—	2	4	no	—
314	C₃×D₄	—	3	4	no	—
315	C₃×D₄	—	6	16	no	—
316	C₃×D₄	—	6	6	no	—
317	C₃×D₄	C₂³×D₃	1	4	yes	—
318	C₃×D₄	C₂⁴×C₃	1	4	yes	—
319	C₂×C₃×C₄	—	2	12	no	—
320	C₂×C₃×C₄	—	2	32	no	—
321	C₂×C₃×C₄	—	2	6	no	—
322	C₂×C₃×C₄	—	2	6	no	—
323	C₂×C₃×C₄	—	2	16	no	—
324	C₂×C₃×C₄	—	2	16	no	—
325	C₂×C₃×C₄	—	2	3	no	—
326	C₂×C₃×C₄	—	2	4	no	—
327	C₂×C₃×C₄	—	2	6	no	—
328	C₂×C₃×C₄	—	2	3	no	—
329	C₂×C₃×C₄	—	2	12	no	—
330	C₂×C₃×C₄	—	6	6	no	—
331	C₂×C₃×C₄	—	6	16	no	—
332	C₂×C₃×C₄	C₂×#67	1	6	yes	—
333	C₂×C₃×C₄	C₂×#67	1	3	yes	—
334	C₂×C₃×C₄	C₂×#67	1	12	yes	—
335	C₂×C₃×C₄	C₂×C₃×D₄	1	3	yes	—
336	C₂×C₃×C₄	C₂×C₃×D₄	1	6	yes	—
337	C₂×C₃×C₄	C₂×C₃×D₄	1	12	yes	—
338	C₂×C₃×C₄	C₂³×D₃	1	3	yes	—
339	C₂×C₃×C₄	C₂³×D₃	1	4	yes	—
340	C₂×C₃×C₄	C₂⁴×C₃	1	3	yes	—
341	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
342	#67	—	2	16	no	—
343	C₂×Dic₃	—	2	6	no	—
344	D₁₂	—	2	6	no	—
345	D₁₂	C₂⁴×C₃	1	4	yes	—
346	C₄×D₃	—	2	16	no	—
347	Dic₆	—	2	6	no	—
348	Dic₆	C₂⁴×C₃	1	4	yes	—
349	C₃×C₈	—	3	4	no	—
350	C₃×C₈	—	3	4	no	—
351	C₃⋊C₈	C₂⁴×C₃	1	4	yes	—
352	C₃⋊C₈	C₂⁴×C₃	1	4	yes	—
353	C₂×C₃²	—	2	4	no	—
354	C₂×C₃²	—	4	4	no	—
355	C₂×C₃²	C₂×#135	1	6	yes	complemented
356	C₂×C₃²	C₂³×D₄	1	1	yes	characteristic
357	C₃×D₃	—	4	4	no	—
358	C₂⁴	—	2	1	no	—
359	C₂⁴	—	6	1	no	—
360	C₂⁴	C₃×#67	1	1	yes	characteristic
361	#41	—	2	24	no	—
362	#41	—	3	16	no	—
363	#41	—	6	24	no	—
364	#41	C₂²×C₃×D₃	1	16	yes	complemented
365	C₂×Q₈	—	2	3	no	—
366	C₂×Q₈	—	3	6	no	—
367	C₂×Q₈	—	6	3	no	—
368	C₂×Q₈	C₂²×C₃×D₃	1	6	yes	—
369	C₂×D₄	—	2	12	no	—
370	C₂×D₄	—	2	3	no	—
371	C₂×D₄	—	3	6	no	—
372	C₂×D₄	—	6	12	no	—
373	C₂×D₄	—	6	3	no	—
374	C₂×D₄	C₂²×C₃×D₃	1	6	yes	—
375	C₂²×C₄	—	2	1	no	—
376	C₂²×C₄	—	2	12	no	—
377	C₂²×C₄	—	6	1	no	—
378	C₂²×C₄	—	6	12	no	—
379	C₂²×C₄	C₃×#67	1	1	yes	characteristic
380	C₂²×C₄	C₃×#67	1	6	yes	—
381	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
382	C₂²×C₄	C₂²×C₃×D₃	1	6	yes	—
383	Q₁₆	—	3	16	no	—
384	SD₁₆	—	3	16	no	—
385	SD₁₆	—	3	16	no	—
386	D₈	—	3	16	no	—
387	C₂×C₈	—	3	6	no	—
388	C₂×C₈	—	3	6	no	—
389	C₂×C₈	—	3	16	no	—
390	C₂²×C₃	—	2	12	no	—
391	C₂²×C₃	—	2	12	no	—
392	C₂²×C₃	—	2	8	no	—
393	C₂²×C₃	—	2	4	no	—
394	C₂²×C₃	—	2	4	no	—
395	C₂²×C₃	—	2	4	no	—
396	C₂²×C₃	—	2	3	no	—
397	C₂²×C₃	—	2	4	no	—
398	C₂²×C₃	—	4	12	no	—
399	C₂²×C₃	—	4	24	no	—
400	C₂²×C₃	—	4	12	no	—
401	C₂²×C₃	—	4	12	no	—
402	C₂²×C₃	—	6	4	no	—
403	C₂²×C₃	—	12	12	no	—
404	C₂²×C₃	#950	1	4	yes	direct product factor
405	C₂²×C₃	C₃×#135	1	4	yes	complemented
406	C₂²×C₃	C₂²×#67	1	4	yes	—
407	C₂²×C₃	C₂²×#67	1	3	yes	—
408	C₂²×C₃	C₂²×C₃×D₄	1	4	yes	—
409	C₂²×C₃	C₂²×C₃×D₄	1	3	yes	—
410	C₂×D₃	—	2	4	no	—
411	C₂×D₃	—	4	12	no	—
412	C₃×C₄	—	2	8	no	—
413	C₃×C₄	—	2	4	no	—
414	C₃×C₄	—	2	4	no	—
415	C₃×C₄	—	2	4	no	—
416	C₃×C₄	—	2	3	no	—
417	C₃×C₄	—	2	1	no	—
418	C₃×C₄	—	6	4	no	—
419	C₃×C₄	C₂²×#67	1	4	yes	—
420	C₃×C₄	C₂²×#67	1	3	yes	—
421	C₃×C₄	C₂²×C₃×D₄	1	3	yes	—
422	C₃×C₄	C₂²×C₃×D₄	1	4	yes	—
423	C₃×C₄	C₂⁴×D₃	1	1	yes	characteristic
424	C₃×C₄	C₂⁵×C₃	1	1	yes	characteristic
425	Dic₃	—	2	4	no	—
426	C₃²	C₂²×#135	1	1	yes	characteristic, complemented, Sylow
427	C₂³	—	2	4	no	—
428	C₂³	—	2	6	no	—
429	C₂³	—	4	4	no	—
430	C₂³	—	6	6	no	—
431	C₂³	—	12	4	no	—
432	C₂³	C₂×C₃×#67	1	6	yes	—
433	C₂³	C₂×C₃×#67	1	1	yes	characteristic
434	Q₈	—	2	6	no	—
435	Q₈	—	3	4	no	—
436	Q₈	—	6	6	no	—
437	Q₈	C₂³×C₃×D₃	1	4	yes	—
438	D₄	—	2	16	no	—
439	D₄	—	2	6	no	—
440	D₄	—	3	4	no	—
441	D₄	—	6	16	no	—
442	D₄	—	6	6	no	—
443	D₄	C₂³×C₃×D₃	1	4	yes	—
444	C₂×C₄	—	2	6	no	—
445	C₂×C₄	—	2	16	no	—
446	C₂×C₄	—	6	6	no	—
447	C₂×C₄	—	6	16	no	—
448	C₂×C₄	C₂×C₃×#67	1	6	yes	—
449	C₂×C₄	C₂×C₃×#67	1	3	yes	—
450	C₂×C₄	C₂×C₃×#67	1	12	yes	—
451	C₂×C₄	C₂³×C₃×D₃	1	3	yes	—
452	C₂×C₄	C₂³×C₃×D₃	1	4	yes	—
453	C₈	—	3	4	no	—
454	C₈	—	3	4	no	—
455	C₂×C₃	—	2	4	no	—
456	C₂×C₃	—	2	4	no	—
457	C₂×C₃	—	2	6	no	—
458	C₂×C₃	—	2	1	no	—
459	C₂×C₃	—	4	4	no	—
460	C₂×C₃	—	4	8	no	—
461	C₂×C₃	—	4	4	no	—
462	C₂×C₃	—	4	4	no	—
463	C₂×C₃	—	12	4	no	—
464	C₂×C₃	C₂×#950	1	6	yes	direct product factor
465	C₂×C₃	C₂×C₃×#135	1	6	yes	complemented
466	C₂×C₃	C₂³×#67	1	1	yes	characteristic
467	C₂×C₃	C₂³×C₃×D₄	1	1	yes	characteristic
468	D₃	—	4	4	no	—
469	C₂²	—	2	12	no	—
470	C₂²	—	2	4	no	—
471	C₂²	—	4	12	no	—
472	C₂²	—	6	4	no	—
473	C₂²	—	12	12	no	—
474	C₂²	C₃×#950	1	4	yes	direct product factor
475	C₂²	C₂²×C₃×#67	1	4	yes	—
476	C₂²	C₂²×C₃×#67	1	3	yes	—
477	C₄	—	2	4	no	—
478	C₄	—	6	4	no	—
479	C₄	C₂²×C₃×#67	1	4	yes	—
480	C₄	C₂²×C₃×#67	1	3	yes	—
481	C₄	C₂⁴×C₃×D₃	1	1	yes	characteristic
482	C₃	—	2	1	no	—
483	C₃	C₂²×#950	1	1	yes	characteristic, direct product factor
484	C₃	C₂²×C₃×#135	1	1	yes	characteristic, complemented
485	C₂	—	2	4	no	—
486	C₂	—	4	4	no	—
487	C₂	—	12	4	no	—
488	C₂	C₂×C₃×#950	1	6	yes	direct product factor
489	C₂	C₂³×C₃×#67	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃×C₄	#67
commutator, cosocle	C₃×C₄	C₂⁵×C₃
Frattini	C₄	C₂⁴×C₃×D₃
Fitting	C₂²×C₃²×#41	C₂
socle	C₂³×C₃²	C₂×D₄
hypercenter	C₂²×C₃×#41	D₃
hypocenter	C₃	C₂²×C₃×#135
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃×C₄ ◁ C₂³×C₃×C₄ ◁ C₂²×C₃×#41

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃²×#41	C₂	semidirect
2. C₂²×C₃×#235	C₂	semidirect
3. C₂×C₃×#950	C₂	direct (N × H)
4. C₂²×C₃×#216	C₂	semidirect
5. C₂²×C₃×#215	C₂	semidirect
6. C₂²×C₃×#214	C₂	semidirect
7. C₂²×C₃×#213	C₂	semidirect
8. C₂³×C₃×C₃⋊C₈	C₂	semidirect
10. C₂²×#950	C₃	direct (N × H)
12. C₂×C₃²×#41	C₂²	semidirect
20. C₂×C₃×#235	C₂²	semidirect
24. C₃×#950	C₂²	direct (N × H)
25. C₂×C₃×#216	C₂²	semidirect
26. C₂×C₃×#215	C₂²	semidirect
27. C₂×C₃×#214	C₂²	semidirect
28. C₂×C₃×#213	C₂²	semidirect
31. C₂²×C₃×C₃⋊C₈	C₂²	semidirect
34. C₂²×C₃×#41	D₃	semidirect
35. C₂²×C₃×#41	C₂×C₃	semidirect
36. C₂²×#235	C₂×C₃	semidirect
43. C₂×#950	C₂×C₃	direct (N × H)
44. C₂²×#216	C₂×C₃	semidirect
45. C₂²×#215	C₂×C₃	semidirect
46. C₂²×#214	C₂×C₃	semidirect
47. C₂²×#213	C₂×C₃	semidirect
48. C₂³×C₃⋊C₈	C₂×C₃	semidirect
53. C₃²×#41	C₂³	semidirect
68. C₃×#235	C₂³	semidirect
74. C₃×#216	C₂³	semidirect
75. C₃×#215	C₂³	semidirect
76. C₃×#214	C₂³	semidirect
77. C₃×#213	C₂³	semidirect
80. C₂×C₃×C₃⋊C₈	C₂³	semidirect
88. C₂×C₃×#41	C₂×D₃	semidirect
89. C₂×C₃×#41	C₂²×C₃	semidirect
111. C₂×#235	C₂²×C₃	semidirect
123. #950	C₂²×C₃	direct (N × H)
124. C₂×#216	C₂²×C₃	semidirect
125. C₂×#215	C₂²×C₃	semidirect
126. C₂×#214	C₂²×C₃	semidirect
127. C₂×#213	C₂²×C₃	semidirect
130. C₂²×C₃⋊C₈	C₂²×C₃	semidirect
160. C₂²×#41	C₃×D₃	semidirect
181. C₃×#41	C₂²×D₃	semidirect
182. C₃×#41	C₂³×C₃	semidirect
226. #235	C₂³×C₃	semidirect
239. #216	C₂³×C₃	semidirect
240. #215	C₂³×C₃	semidirect
241. #214	C₂³×C₃	semidirect
242. #213	C₂³×C₃	semidirect
245. C₂×C₃⋊C₈	C₂³×C₃	semidirect
249. C₂²×C₃²	#135	semidirect
262. C₂×#41	C₂×C₃×D₃	semidirect
355. C₂×C₃²	C₂×#135	semidirect
364. #41	C₂²×C₃×D₃	semidirect
404. C₂²×C₃	#950	direct (N × H)
405. C₂²×C₃	C₃×#135	semidirect
426. C₃²	C₂²×#135	semidirect
464. C₂×C₃	C₂×#950	direct (N × H)
465. C₂×C₃	C₂×C₃×#135	semidirect
474. C₂²	C₃×#950	direct (N × H)
483. C₃	C₂²×#950	direct (N × H)
484. C₃	C₂²×C₃×#135	semidirect
488. C₂	C₂×C₃×#950	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃²×#41	2
C₂²×C₃×#235	2
C₂×C₃×#950	2
C₂²×C₃×#216	2
C₂²×C₃×#215	2
C₂²×C₃×#214	2
C₂²×C₃×#213	2
C₂³×C₃×C₃⋊C₈	2
C₂²×C₃×#135	3
C₂²×#950	3

Subgroups — C22×C3×#950 #11918597

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃×#950 #11918597