Subgroups — C₂×C₃×#5115 #11866736

Order 1152.

1401 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃²×C₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#930	C₂	1	2	yes	maximal, complemented
3	C₂²×C₃×D₂₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#5115	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₃×#821	C₂	1	2	yes	maximal, complemented
6	C₂×C₃×#818	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃×#466	—	3	1	no	maximal
8	C₂×#5115	C₃	1	1	yes	maximal, characteristic, direct product factor
9	C₂³×C₃²×C₄	C₂²	1	1	yes	characteristic
10	C₂²×C₃×#67	—	2	2	no	—
11	C₂²×C₃×D₁₂	C₂²	1	2	yes	—
12	C₂²×C₃²×C₈	—	2	4	no	—
13	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
14	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
15	C₂²×C₃²×C₈	C₂²	1	4	yes	complemented
16	C₃×#930	—	2	4	no	—
17	C₃×#930	C₂²	1	8	yes	complemented
18	C₂×C₃×(C₂×D₃)⋊C₄	—	2	2	no	—
19	C₂×C₃×C₄⋊Dic₃	C₂²	1	2	yes	—
20	C₂×C₃×D₂₄	—	2	4	no	—
21	C₂×C₃×D₂₄	C₂²	1	4	yes	complemented
22	C₃×#821	C₂²	1	8	yes	complemented
23	C₃×#818	C₂²	1	4	yes	complemented
24	C₂²×C₃×D₈	—	3	1	no	—
25	C₂³×C₃×C₈	—	2	1	no	—
26	C₂³×C₃×C₈	D₃	1	1	yes	characteristic, complemented
27	C₂³×C₃×C₈	C₂×C₃	1	1	yes	characteristic, complemented
28	C₂×C₃×#121	—	3	2	no	—
29	C₂×#930	C₂×C₃	1	2	yes	complemented
30	C₂²×D₂₄	C₂×C₃	1	1	yes	characteristic, complemented
31	C₃×#466	—	3	8	no	—
32	C₂×C₃×#107	—	3	1	no	—
33	C₂×C₃×#102	—	3	2	no	—
34	#5115	C₂×C₃	1	8	yes	direct product factor
35	C₂×#821	C₂×C₃	1	2	yes	complemented
36	C₂×#818	C₂×C₃	1	1	yes	characteristic, complemented
37	C₂⁴×C₃²	D₄	1	1	yes	characteristic
38	C₂³×C₃×D₃	—	2	2	no	—
39	C₂²×C₃²×C₄	—	2	2	no	—
40	C₂²×C₃²×C₄	—	2	2	no	—
41	C₂²×C₃²×C₄	D₄	1	1	yes	characteristic
42	C₂²×C₃²×C₄	D₄	1	2	yes	—
43	C₂²×C₃²×C₄	C₂³	1	2	yes	—
44	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
45	C₂×C₃×#67	—	2	8	no	—
46	C₂×C₃×#67	—	4	8	no	—
47	C₂²×C₃×Dic₃	—	2	2	no	—
48	C₂×C₃×D₁₂	—	2	4	no	—
49	C₂×C₃×D₁₂	—	2	4	no	—
50	C₂×C₃×D₁₂	—	2	2	no	—
51	C₂×C₃×D₁₂	C₂³	1	4	yes	—
52	C₂×C₃²×C₈	—	2	2	no	—
53	C₂×C₃²×C₈	—	2	8	no	—
54	C₂×C₃²×C₈	D₄	1	4	yes	complemented
55	C₂×C₃²×C₈	C₂³	1	2	yes	—
56	C₂×C₃²×C₈	C₂³	1	2	yes	—
57	C₃×(C₂×D₃)⋊C₄	—	2	8	no	—
58	C₃×C₄⋊Dic₃	—	2	2	no	—
59	C₃×C₄⋊Dic₃	C₂³	1	4	yes	—
60	C₃×D₂₄	—	2	8	no	—
61	C₂×#466	—	3	1	no	Sylow
62	C₂²×C₃×D₄	—	3	2	no	—
63	C₂²×C₃×D₄	—	6	2	no	—
64	C₂³×C₃×C₄	—	2	1	no	—
65	C₂³×C₃×C₄	C₂×D₃	1	1	yes	characteristic
66	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
67	C₂²×#67	—	2	2	no	—
68	C₂²×D₁₂	C₂²×C₃	1	2	yes	—
69	C₂×C₃×D₈	—	3	4	no	—
70	C₂×C₃×D₈	—	6	4	no	—
71	C₂²×C₃×C₈	—	2	8	no	—
72	C₂²×C₃×C₈	—	2	4	no	—
73	C₂²×C₃×C₈	—	2	4	no	—
74	C₂²×C₃×C₈	—	2	1	no	—
75	C₂²×C₃×C₈	—	2	1	no	—
76	C₂²×C₃×C₈	—	2	4	no	—
77	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
78	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
79	C₂²×C₃×C₈	C₂×D₃	1	4	yes	complemented
80	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
81	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
82	C₂²×C₃×C₈	C₂²×C₃	1	4	yes	complemented
83	C₃×#121	—	3	8	no	—
84	C₃×#121	—	6	4	no	—
85	C₂×C₃×C₄⋊C₄	—	3	2	no	—
86	C₂×C₃×C₂²⋊C₄	—	6	2	no	—
87	#930	—	2	4	no	—
88	#930	C₂²×C₃	1	8	yes	complemented
89	C₂×(C₂×D₃)⋊C₄	—	2	2	no	—
90	C₂×C₄⋊Dic₃	C₂²×C₃	1	2	yes	—
91	C₂×D₂₄	—	2	4	no	—
92	C₂×D₂₄	C₂²×C₃	1	4	yes	complemented
93	C₃×#107	—	3	4	no	—
94	C₃×#102	—	3	8	no	—
95	#821	C₂²×C₃	1	8	yes	complemented
96	#818	C₂²×C₃	1	4	yes	complemented
97	C₂³×C₃²	—	2	2	no	—
98	C₂³×C₃²	—	2	2	no	—
99	C₂³×C₃²	D₈	1	4	yes	complemented
100	C₂³×C₃²	C₂×D₄	1	2	yes	—
101	C₂³×C₃²	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₃×D₃	—	2	4	no	—
103	C₂²×C₃×D₃	—	4	4	no	—
104	C₂²×C₃×D₃	—	4	4	no	—
105	C₂²×C₃×D₃	—	4	4	no	—
106	C₂×C₃²×C₄	—	2	2	no	—
107	C₂×C₃²×C₄	—	2	4	no	—
108	C₂×C₃²×C₄	—	2	2	no	—
109	C₂×C₃²×C₄	—	2	2	no	—
110	C₂×C₃²×C₄	C₂×D₄	1	2	yes	—
111	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
112	C₂×C₃²×C₄	C₂×D₄	1	2	yes	—
113	C₂×C₃²×C₄	#41	1	2	yes	—
114	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
115	C₃×#67	—	4	16	no	—
116	C₂×C₃×Dic₃	—	2	4	no	—
117	C₂×C₃×Dic₃	—	4	4	no	—
118	C₃×D₁₂	—	2	4	no	—
119	C₃×D₁₂	—	2	4	no	—
120	C₃×D₁₂	—	4	4	no	—
121	C₃²×C₈	—	2	2	no	—
122	C₃²×C₈	C₂×D₄	1	4	yes	complemented
123	C₂²×D₈	—	3	1	no	—
124	C₂³×C₈	C₃×D₃	1	1	yes	characteristic, complemented
125	C₂×#121	—	3	2	no	—
126	#466	—	3	8	no	—
127	C₂×#107	—	3	1	no	—
128	C₂×#102	—	3	2	no	—
129	C₂⁴×C₃	—	2	1	no	—
130	C₂⁴×C₃	—	6	2	no	—
131	C₂⁴×C₃	D₁₂	1	1	yes	characteristic
132	C₂⁴×C₃	C₃×D₄	1	1	yes	characteristic
133	C₂³×D₃	—	2	2	no	—
134	C₂×C₃×D₄	—	3	4	no	—
135	C₂×C₃×D₄	—	6	8	no	—
136	C₂×C₃×D₄	—	6	2	no	—
137	C₂×C₃×D₄	—	6	4	no	—
138	C₂×C₃×D₄	—	6	4	no	—
139	C₂×C₃×D₄	—	12	8	no	—
140	C₂²×C₃×C₄	—	2	4	no	—
141	C₂²×C₃×C₄	—	2	4	no	—
142	C₂²×C₃×C₄	—	2	2	no	—
143	C₂²×C₃×C₄	—	2	2	no	—
144	C₂²×C₃×C₄	—	2	2	no	—
145	C₂²×C₃×C₄	—	2	2	no	—
146	C₂²×C₃×C₄	—	2	1	no	—
147	C₂²×C₃×C₄	—	2	2	no	—
148	C₂²×C₃×C₄	—	2	2	no	—
149	C₂²×C₃×C₄	—	2	1	no	—
150	C₂²×C₃×C₄	—	6	2	no	—
151	C₂²×C₃×C₄	D₁₂	1	2	yes	—
152	C₂²×C₃×C₄	D₁₂	1	1	yes	characteristic
153	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
154	C₂²×C₃×C₄	C₃×D₄	1	2	yes	—
155	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
156	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
157	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
158	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
159	C₂×#67	—	2	8	no	—
160	C₂×#67	—	4	8	no	—
161	C₂²×Dic₃	—	2	2	no	—
162	C₂×D₁₂	—	2	4	no	—
163	C₂×D₁₂	—	2	4	no	—
164	C₂×D₁₂	—	2	2	no	—
165	C₂×D₁₂	C₂³×C₃	1	4	yes	—
166	C₃×D₈	—	6	8	no	—
167	C₂×C₃×C₈	—	2	4	no	—
168	C₂×C₃×C₈	—	2	16	no	—
169	C₂×C₃×C₈	—	2	2	no	—
170	C₂×C₃×C₈	—	2	2	no	—
171	C₂×C₃×C₈	—	2	8	no	—
172	C₂×C₃×C₈	—	2	8	no	—
173	C₂×C₃×C₈	—	2	4	no	—
174	C₂×C₃×C₈	—	2	2	no	—
175	C₂×C₃×C₈	—	2	2	no	—
176	C₂×C₃×C₈	#67	1	4	yes	complemented
177	C₂×C₃×C₈	C₃×D₄	1	4	yes	complemented
178	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
179	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
180	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
181	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
182	C₃×C₄⋊C₄	—	3	4	no	—
183	C₃×C₄⋊C₄	—	6	2	no	—
184	C₃×C₂²⋊C₄	—	6	8	no	—
185	(C₂×D₃)⋊C₄	—	2	8	no	—
186	C₄⋊Dic₃	—	2	2	no	—
187	C₄⋊Dic₃	C₂³×C₃	1	4	yes	—
188	D₂₄	—	2	8	no	—
189	C₂²×C₃²	—	2	2	no	—
190	C₂²×C₃²	—	2	2	no	—
191	C₂²×C₃²	—	2	8	no	—
192	C₂²×C₃²	#121	1	2	yes	—
193	C₂²×C₃²	C₂×D₈	1	2	yes	—
194	C₂²×C₃²	C₂×D₈	1	4	yes	complemented
195	C₂²×C₃²	#135	1	2	yes	—
196	C₂²×C₃²	C₂²×D₄	1	1	yes	characteristic
197	C₂×C₃×D₃	—	4	4	no	—
198	C₂×C₃×D₃	—	4	4	no	—
199	C₂×C₃×D₃	—	4	4	no	—
200	C₂×C₃×D₃	—	8	8	no	—
201	C₃²×C₄	—	2	2	no	—
202	C₃²×C₄	#121	1	2	yes	—
203	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
204	C₃²×C₄	C₂×#41	1	1	yes	characteristic
205	C₃×Dic₃	—	4	4	no	—
206	C₂²×D₄	—	3	2	no	—
207	C₂²×D₄	—	6	2	no	—
208	C₂³×C₄	C₂×C₃×D₃	1	1	yes	characteristic
209	C₂×D₈	—	3	4	no	—
210	C₂×D₈	—	6	4	no	—
211	C₂²×C₈	—	2	4	no	—
212	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
213	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
214	C₂²×C₈	C₂×C₃×D₃	1	4	yes	complemented
215	#121	—	3	8	no	—
216	#121	—	6	4	no	—
217	C₂×C₄⋊C₄	—	3	2	no	—
218	C₂×C₂²⋊C₄	—	6	2	no	—
219	#107	—	3	4	no	—
220	#102	—	3	8	no	—
221	C₂³×C₃	—	2	4	no	—
222	C₂³×C₃	—	2	4	no	—
223	C₂³×C₃	—	2	2	no	—
224	C₂³×C₃	—	2	2	no	—
225	C₂³×C₃	—	2	2	no	—
226	C₂³×C₃	—	2	2	no	—
227	C₂³×C₃	—	2	4	no	—
228	C₂³×C₃	—	2	2	no	—
229	C₂³×C₃	—	2	1	no	—
230	C₂³×C₃	—	6	4	no	—
231	C₂³×C₃	—	12	4	no	—
232	C₂³×C₃	—	12	4	no	—
233	C₂³×C₃	—	12	4	no	—
234	C₂³×C₃	D₂₄	1	4	yes	complemented
235	C₂³×C₃	C₃×D₈	1	4	yes	complemented
236	C₂³×C₃	C₂×D₁₂	1	2	yes	—
237	C₂³×C₃	C₂×D₁₂	1	1	yes	characteristic
238	C₂³×C₃	C₂×C₃×D₄	1	2	yes	—
239	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
240	C₂²×D₃	—	2	4	no	—
241	C₂²×D₃	—	4	4	no	—
242	C₂²×D₃	—	4	4	no	—
243	C₂²×D₃	—	4	4	no	—
244	C₃×D₄	—	6	4	no	—
245	C₃×D₄	—	6	4	no	—
246	C₃×D₄	—	12	16	no	—
247	C₃×D₄	—	12	4	no	—
248	C₂×C₃×C₄	—	2	4	no	—
249	C₂×C₃×C₄	—	2	4	no	—
250	C₂×C₃×C₄	—	2	8	no	—
251	C₂×C₃×C₄	—	2	4	no	—
252	C₂×C₃×C₄	—	2	2	no	—
253	C₂×C₃×C₄	—	2	2	no	—
254	C₂×C₃×C₄	—	2	4	no	—
255	C₂×C₃×C₄	—	2	4	no	—
256	C₂×C₃×C₄	—	2	2	no	—
257	C₂×C₃×C₄	—	2	2	no	—
258	C₂×C₃×C₄	—	2	2	no	—
259	C₂×C₃×C₄	—	2	2	no	—
260	C₂×C₃×C₄	—	2	1	no	—
261	C₂×C₃×C₄	—	2	2	no	—
262	C₂×C₃×C₄	—	2	1	no	—
263	C₂×C₃×C₄	—	2	2	no	—
264	C₂×C₃×C₄	—	2	2	no	—
265	C₂×C₃×C₄	—	6	4	no	—
266	C₂×C₃×C₄	—	12	4	no	—
267	C₂×C₃×C₄	C₂×D₁₂	1	2	yes	—
268	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
269	C₂×C₃×C₄	#235	1	2	yes	—
270	C₂×C₃×C₄	C₂×#67	1	2	yes	—
271	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
272	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
273	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
274	C₂×C₃×C₄	C₃×#41	1	2	yes	—
275	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
276	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
277	#67	—	4	16	no	—
278	C₂×Dic₃	—	2	4	no	—
279	C₂×Dic₃	—	4	4	no	—
280	D₁₂	—	2	4	no	—
281	D₁₂	—	2	4	no	—
282	D₁₂	—	4	4	no	—
283	C₃×C₈	—	2	4	no	—
284	C₃×C₈	—	2	2	no	—
285	C₃×C₈	—	2	2	no	—
286	C₃×C₈	—	2	4	no	—
287	C₃×C₈	C₂×#67	1	4	yes	complemented
288	C₃×C₈	C₂×C₃×D₄	1	4	yes	complemented
289	C₂×C₃²	—	2	4	no	—
290	C₂×C₃²	#466	1	4	yes	complemented
291	C₂×C₃²	C₂×#121	1	1	yes	characteristic
292	C₂×C₃²	C₂²×D₈	1	1	yes	characteristic
293	C₂×C₃²	C₂×#135	1	1	yes	characteristic
294	C₃×D₃	—	8	4	no	—
295	C₂⁴	—	6	2	no	—
296	C₂⁴	C₃×D₁₂	1	1	yes	characteristic
297	C₂×D₄	—	3	4	no	—
298	C₂×D₄	—	6	8	no	—
299	C₂×D₄	—	6	2	no	—
300	C₂×D₄	—	6	4	no	—
301	C₂×D₄	—	6	4	no	—
302	C₂×D₄	—	12	8	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	—	6	2	no	—
306	C₂²×C₄	C₃×D₁₂	1	1	yes	characteristic
307	C₂²×C₄	C₃×D₁₂	1	2	yes	—
308	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
309	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
310	D₈	—	6	8	no	—
311	C₂×C₈	—	2	2	no	—
312	C₂×C₈	—	2	8	no	—
313	C₂×C₈	C₃×#67	1	4	yes	complemented
314	C₂×C₈	C₂²×C₃×D₃	1	2	yes	—
315	C₂×C₈	C₂²×C₃×D₃	1	2	yes	—
316	C₄⋊C₄	—	3	4	no	—
317	C₄⋊C₄	—	6	2	no	—
318	C₂²⋊C₄	—	6	8	no	—
319	C₂²×C₃	—	2	4	no	—
320	C₂²×C₃	—	2	16	no	—
321	C₂²×C₃	—	2	4	no	—
322	C₂²×C₃	—	2	2	no	—
323	C₂²×C₃	—	2	2	no	—
324	C₂²×C₃	—	2	2	no	—
325	C₂²×C₃	—	2	8	no	—
326	C₂²×C₃	—	2	2	no	—
327	C₂²×C₃	—	2	8	no	—
328	C₂²×C₃	—	2	2	no	—
329	C₂²×C₃	—	2	4	no	—
330	C₂²×C₃	—	2	2	no	—
331	C₂²×C₃	—	2	2	no	—
332	C₂²×C₃	—	2	1	no	—
333	C₂²×C₃	—	12	4	no	—
334	C₂²×C₃	—	12	4	no	—
335	C₂²×C₃	—	12	4	no	—
336	C₂²×C₃	—	24	8	no	—
337	C₂²×C₃	C₂×D₂₄	1	2	yes	—
338	C₂²×C₃	C₂×D₂₄	1	4	yes	complemented
339	C₂²×C₃	#904	1	2	yes	—
340	C₂²×C₃	#930	1	2	yes	—
341	C₂²×C₃	C₃×#121	1	2	yes	—
342	C₂²×C₃	C₂×C₃×D₈	1	2	yes	—
343	C₂²×C₃	C₂×C₃×D₈	1	4	yes	complemented
344	C₂²×C₃	C₃×#135	1	2	yes	—
345	C₂²×C₃	C₂²×D₁₂	1	1	yes	characteristic
346	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
347	C₂×D₃	—	4	4	no	—
348	C₂×D₃	—	4	4	no	—
349	C₂×D₃	—	4	4	no	—
350	C₂×D₃	—	8	8	no	—
351	C₃×C₄	—	2	4	no	—
352	C₃×C₄	—	2	2	no	—
353	C₃×C₄	—	2	2	no	—
354	C₃×C₄	—	2	2	no	—
355	C₃×C₄	—	2	1	no	—
356	C₃×C₄	—	2	1	no	—
357	C₃×C₄	—	12	4	no	—
358	C₃×C₄	#930	1	2	yes	—
359	C₃×C₄	C₃×#121	1	2	yes	—
360	C₃×C₄	C₂×#235	1	1	yes	characteristic
361	C₃×C₄	C₂²×#67	1	1	yes	characteristic
362	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
363	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
364	Dic₃	—	4	4	no	—
365	C₃²	C₂×#466	1	1	yes	characteristic, complemented, Sylow
366	C₂³	—	2	2	no	—
367	C₂³	—	2	2	no	—
368	C₂³	—	6	4	no	—
369	C₂³	—	12	4	no	—
370	C₂³	—	12	4	no	—
371	C₂³	—	12	4	no	—
372	C₂³	C₃×D₂₄	1	4	yes	complemented
373	C₂³	C₂×C₃×D₁₂	1	2	yes	—
374	C₂³	C₂×C₃×D₁₂	1	1	yes	characteristic
375	D₄	—	6	4	no	—
376	D₄	—	6	4	no	—
377	D₄	—	12	16	no	—
378	D₄	—	12	4	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	4	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	6	4	no	—
384	C₂×C₄	—	12	4	no	—
385	C₂×C₄	C₂×C₃×D₁₂	1	2	yes	—
386	C₂×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
387	C₂×C₄	C₃×#235	1	2	yes	—
388	C₂×C₄	C₂×C₃×#67	1	2	yes	—
389	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
390	C₈	—	2	2	no	—
391	C₈	C₂×C₃×#67	1	4	yes	complemented
392	C₂×C₃	—	2	8	no	—
393	C₂×C₃	—	2	4	no	—
394	C₂×C₃	—	2	4	no	—
395	C₂×C₃	—	2	1	no	—
396	C₂×C₃	—	2	4	no	—
397	C₂×C₃	—	2	1	no	—
398	C₂×C₃	—	2	1	no	—
399	C₂×C₃	—	24	4	no	—
400	C₂×C₃	#5115	1	4	yes	direct product factor
401	C₂×C₃	C₃×#466	1	4	yes	complemented
402	C₂×C₃	C₂²×D₂₄	1	1	yes	characteristic
403	C₂×C₃	C₂×#904	1	1	yes	characteristic
404	C₂×C₃	C₂×#930	1	1	yes	characteristic
405	C₂×C₃	C₂×C₃×#121	1	1	yes	characteristic
406	C₂×C₃	C₂²×C₃×D₈	1	1	yes	characteristic
407	C₂×C₃	C₂×C₃×#135	1	1	yes	characteristic
408	D₃	—	8	4	no	—
409	C₂²	—	2	2	no	—
410	C₂²	—	2	8	no	—
411	C₂²	—	2	2	no	—
412	C₂²	—	12	4	no	—
413	C₂²	—	12	4	no	—
414	C₂²	—	12	4	no	—
415	C₂²	—	24	8	no	—
416	C₂²	C₂×C₃×D₂₄	1	2	yes	—
417	C₂²	C₂×C₃×D₂₄	1	4	yes	complemented
418	C₂²	C₃×#904	1	2	yes	—
419	C₂²	C₃×#930	1	2	yes	—
420	C₂²	C₂²×C₃×D₁₂	1	1	yes	characteristic
421	C₄	—	2	2	no	—
422	C₄	—	12	4	no	—
423	C₄	C₃×#930	1	2	yes	—
424	C₄	C₂×C₃×#235	1	1	yes	characteristic
425	C₄	C₂²×C₃×#67	1	1	yes	characteristic
426	C₃	—	2	1	no	—
427	C₃	C₂×#5115	1	1	yes	characteristic, direct product factor
428	C₃	C₂×C₃×#466	1	1	yes	characteristic, complemented
429	C₂	—	2	4	no	—
430	C₂	—	24	4	no	—
431	C₂	C₃×#5115	1	4	yes	direct product factor
432	C₂	C₂²×C₃×D₂₄	1	1	yes	characteristic
433	C₂	C₂×C₃×#904	1	1	yes	characteristic
434	C₂	C₂×C₃×#930	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃	C₂×D₁₂
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₂³×C₃²×C₈	C₂
socle	C₂³×C₃²	C₂×D₄
hypercenter	C₂³×C₃×C₈	D₃
hypocenter	C₃	C₂×C₃×#466
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₃ ◁ C₂³×C₃×C₄ ◁ C₂³×C₃×C₈

Complements

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

N	H ≅ G/N	type
1. C₂³×C₃²×C₈	C₂	semidirect
2. C₂×C₃×#930	C₂	semidirect
3. C₂²×C₃×D₂₄	C₂	semidirect
4. C₃×#5115	C₂	direct (N × H)
5. C₂×C₃×#821	C₂	semidirect
6. C₂×C₃×#818	C₂	semidirect
8. C₂×#5115	C₃	direct (N × H)
15. C₂²×C₃²×C₈	C₂²	semidirect
17. C₃×#930	C₂²	semidirect
21. C₂×C₃×D₂₄	C₂²	semidirect
22. C₃×#821	C₂²	semidirect
23. C₃×#818	C₂²	semidirect
26. C₂³×C₃×C₈	D₃	semidirect
27. C₂³×C₃×C₈	C₂×C₃	semidirect
29. C₂×#930	C₂×C₃	semidirect
30. C₂²×D₂₄	C₂×C₃	semidirect
34. #5115	C₂×C₃	direct (N × H)
35. C₂×#821	C₂×C₃	semidirect
36. C₂×#818	C₂×C₃	semidirect
54. C₂×C₃²×C₈	D₄	semidirect
79. C₂²×C₃×C₈	C₂×D₃	semidirect
82. C₂²×C₃×C₈	C₂²×C₃	semidirect
88. #930	C₂²×C₃	semidirect
92. C₂×D₂₄	C₂²×C₃	semidirect
95. #821	C₂²×C₃	semidirect
96. #818	C₂²×C₃	semidirect
99. C₂³×C₃²	D₈	semidirect
122. C₃²×C₈	C₂×D₄	semidirect
124. C₂³×C₈	C₃×D₃	semidirect
176. C₂×C₃×C₈	#67	semidirect
177. C₂×C₃×C₈	C₃×D₄	semidirect
194. C₂²×C₃²	C₂×D₈	semidirect
214. C₂²×C₈	C₂×C₃×D₃	semidirect
234. C₂³×C₃	D₂₄	semidirect
235. C₂³×C₃	C₃×D₈	semidirect
287. C₃×C₈	C₂×#67	semidirect
288. C₃×C₈	C₂×C₃×D₄	semidirect
290. C₂×C₃²	#466	semidirect
313. C₂×C₈	C₃×#67	semidirect
338. C₂²×C₃	C₂×D₂₄	semidirect
343. C₂²×C₃	C₂×C₃×D₈	semidirect
365. C₃²	C₂×#466	semidirect
372. C₂³	C₃×D₂₄	semidirect
391. C₈	C₂×C₃×#67	semidirect
400. C₂×C₃	#5115	direct (N × H)
401. C₂×C₃	C₃×#466	semidirect
417. C₂²	C₂×C₃×D₂₄	semidirect
427. C₃	C₂×#5115	direct (N × H)
428. C₃	C₂×C₃×#466	semidirect
431. C₂	C₃×#5115	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×C₈	2
C₂×C₃×#930	2
C₂²×C₃×D₂₄	2
C₃×#5115	2
C₂×C₃×#821	2
C₂×C₃×#818	2
C₂×C₃×#466	3
C₂×#5115	3

Subgroups — C2×C3×#5115 #11866736

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#5115 #11866736