Subgroups — C₂×C₃×#5157 #11866727

Order 1152.

1401 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃²×D₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#938	C₂	1	2	yes	maximal, complemented
3	C₂²×C₃×D₃×C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×#832	C₂	1	2	yes	maximal, complemented
5	C₃×#5157	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₃×#818	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃×#466	—	3	1	no	maximal
8	C₂×#5157	C₃	1	1	yes	maximal, characteristic, direct product factor
9	C₂²×C₃²×D₄	C₂²	1	2	yes	—
10	C₂²×C₃×#67	—	2	2	no	—
11	C₂²×C₃×C₄×D₃	C₂²	1	1	yes	characteristic
12	C₂×C₃²×D₈	—	2	4	no	—
13	C₂×C₃²×D₈	C₂²	1	4	yes	complemented
14	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
15	C₂×C₃×#217	—	2	2	no	—
16	C₃×#938	—	2	4	no	—
17	C₃×#938	C₂²	1	8	yes	complemented
18	C₂×C₃×C₄⋊Dic₃	C₂²	1	2	yes	—
19	C₂²×C₃×C₃⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₃×D₃×C₈	—	2	4	no	—
21	C₂×C₃×D₃×C₈	C₂²	1	4	yes	complemented
22	C₃×#832	C₂²	1	8	yes	complemented
23	C₃×#818	C₂²	1	4	yes	complemented
24	C₂²×C₃×D₈	—	2	1	no	—
25	C₂²×C₃×D₈	D₃	1	1	yes	characteristic, complemented
26	C₂²×C₃×D₈	C₂×C₃	1	1	yes	characteristic, complemented
27	C₂³×C₃×C₈	—	3	1	no	—
28	C₂×C₃×#121	—	3	2	no	—
29	C₂×#938	C₂×C₃	1	2	yes	complemented
30	C₂²×D₃×C₈	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	C₂×#832	C₂×C₃	1	2	yes	complemented
35	#5157	C₂×C₃	1	8	yes	direct product factor
36	C₂×#818	C₂×C₃	1	1	yes	characteristic, complemented
37	C₂⁴×C₃²	—	2	2	no	—
38	C₂³×C₃×D₃	D₄	1	1	yes	characteristic
39	C₂×C₃²×D₄	—	2	4	no	—
40	C₂×C₃²×D₄	—	2	2	no	—
41	C₂×C₃²×D₄	—	2	4	no	—
42	C₂×C₃²×D₄	C₂³	1	4	yes	—
43	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
44	C₂×C₃×#67	—	2	8	no	—
45	C₂×C₃×#67	—	4	8	no	—
46	C₂²×C₃×Dic₃	—	2	2	no	—
47	C₂²×C₃×Dic₃	D₄	1	1	yes	characteristic
48	C₂×C₃×C₄×D₃	—	2	2	no	—
49	C₂×C₃×C₄×D₃	—	2	2	no	—
50	C₂×C₃×C₄×D₃	D₄	1	2	yes	—
51	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
52	C₃²×D₈	—	2	8	no	—
53	C₂×C₃²×C₈	D₄	1	4	yes	complemented
54	C₂×C₃²×C₈	C₂³	1	2	yes	—
55	C₃×#217	—	2	8	no	—
56	C₃×C₄⋊Dic₃	—	2	2	no	—
57	C₃×C₄⋊Dic₃	C₂³	1	4	yes	—
58	C₂×C₃×C₃⋊C₈	—	2	2	no	—
59	C₂×C₃×C₃⋊C₈	C₂³	1	2	yes	—
60	C₃×D₃×C₈	—	2	8	no	—
61	C₂×#466	—	3	1	no	Sylow
62	C₂²×C₃×D₄	—	2	2	no	—
63	C₂²×C₃×D₄	—	6	2	no	—
64	C₂²×C₃×D₄	C₂×D₃	1	2	yes	—
65	C₂²×C₃×D₄	C₂²×C₃	1	2	yes	—
66	C₂³×C₃×C₄	—	3	1	no	—
67	C₂²×#67	—	2	2	no	—
68	C₂²×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
69	C₂×C₃×D₈	—	2	8	no	—
70	C₂×C₃×D₈	—	2	4	no	—
71	C₂×C₃×D₈	—	2	4	no	—
72	C₂×C₃×D₈	—	2	4	no	—
73	C₂×C₃×D₈	C₂×D₃	1	4	yes	complemented
74	C₂×C₃×D₈	C₂²×C₃	1	4	yes	complemented
75	C₂²×C₃×C₈	—	2	1	no	—
76	C₂²×C₃×C₈	—	3	1	no	—
77	C₂²×C₃×C₈	—	3	4	no	—
78	C₂²×C₃×C₈	—	6	4	no	—
79	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
80	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
81	C₃×#121	—	3	8	no	—
82	C₃×#121	—	6	4	no	—
83	C₂×C₃×C₄⋊C₄	—	3	2	no	—
84	C₂×C₃×C₂²⋊C₄	—	6	2	no	—
85	C₂×#217	—	2	2	no	—
86	#938	—	2	4	no	—
87	#938	C₂²×C₃	1	8	yes	complemented
88	C₂×C₄⋊Dic₃	C₂²×C₃	1	2	yes	—
89	C₂²×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
90	C₂×D₃×C₈	—	2	4	no	—
91	C₂×D₃×C₈	C₂²×C₃	1	4	yes	complemented
92	C₃×#107	—	3	4	no	—
93	C₃×#102	—	3	8	no	—
94	#832	C₂²×C₃	1	8	yes	complemented
95	#818	C₂²×C₃	1	4	yes	complemented
96	C₂³×C₃²	—	2	4	no	—
97	C₂³×C₃²	—	4	4	no	—
98	C₂³×C₃²	—	4	4	no	—
99	C₂³×C₃²	—	4	4	no	—
100	C₂³×C₃²	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₃×D₃	—	2	2	no	—
102	C₂²×C₃×D₃	—	2	2	no	—
103	C₂²×C₃×D₃	D₈	1	4	yes	complemented
104	C₂²×C₃×D₃	C₂×D₄	1	2	yes	—
105	C₃²×D₄	—	2	4	no	—
106	C₃²×D₄	—	2	4	no	—
107	C₃²×D₄	—	4	4	no	—
108	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
109	C₂×C₃²×C₄	C₂×D₄	1	2	yes	—
110	C₂×C₃²×C₄	#41	1	2	yes	—
111	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
112	C₃×#67	—	4	16	no	—
113	C₂×C₃×Dic₃	—	2	2	no	—
114	C₂×C₃×Dic₃	—	2	4	no	—
115	C₂×C₃×Dic₃	—	4	4	no	—
116	C₂×C₃×Dic₃	C₂×D₄	1	2	yes	—
117	C₃×C₄×D₃	—	2	4	no	—
118	C₃×C₄×D₃	—	2	2	no	—
119	C₃×C₄×D₃	—	2	2	no	—
120	C₃²×C₈	C₂×D₄	1	4	yes	complemented
121	C₃×C₃⋊C₈	—	2	2	no	—
122	C₂²×D₈	C₃×D₃	1	1	yes	characteristic, complemented
123	C₂³×C₈	—	3	1	no	—
124	C₂×#121	—	3	2	no	—
125	#466	—	3	8	no	—
126	C₂×#107	—	3	1	no	—
127	C₂×#102	—	3	2	no	—
128	C₂⁴×C₃	—	2	2	no	—
129	C₂⁴×C₃	—	2	2	no	—
130	C₂⁴×C₃	—	3	1	no	—
131	C₂⁴×C₃	—	4	2	no	—
132	C₂³×D₃	C₃×D₄	1	1	yes	characteristic
133	C₂×C₃×D₄	—	2	8	no	—
134	C₂×C₃×D₄	—	2	2	no	—
135	C₂×C₃×D₄	—	2	4	no	—
136	C₂×C₃×D₄	—	2	4	no	—
137	C₂×C₃×D₄	—	2	4	no	—
138	C₂×C₃×D₄	—	2	2	no	—
139	C₂×C₃×D₄	—	2	4	no	—
140	C₂×C₃×D₄	—	2	4	no	—
141	C₂×C₃×D₄	—	4	2	no	—
142	C₂×C₃×D₄	—	4	4	no	—
143	C₂×C₃×D₄	—	6	8	no	—
144	C₂×C₃×D₄	—	12	8	no	—
145	C₂×C₃×D₄	C₂²×D₃	1	4	yes	—
146	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
147	C₂²×C₃×C₄	—	2	1	no	—
148	C₂²×C₃×C₄	—	3	1	no	—
149	C₂²×C₃×C₄	—	3	2	no	—
150	C₂²×C₃×C₄	—	3	2	no	—
151	C₂²×C₃×C₄	—	6	2	no	—
152	C₂²×C₃×C₄	—	6	2	no	—
153	C₂²×C₃×C₄	—	6	2	no	—
154	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
155	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
156	C₂×#67	—	2	8	no	—
157	C₂×#67	—	4	8	no	—
158	C₂²×Dic₃	—	2	2	no	—
159	C₂²×Dic₃	C₃×D₄	1	1	yes	characteristic
160	C₂×C₄×D₃	—	2	2	no	—
161	C₂×C₄×D₃	—	2	2	no	—
162	C₂×C₄×D₃	C₃×D₄	1	2	yes	—
163	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
164	C₃×D₈	—	2	16	no	—
165	C₃×D₈	—	2	8	no	—
166	C₃×D₈	—	2	8	no	—
167	C₂×C₃×C₈	—	2	4	no	—
168	C₂×C₃×C₈	—	2	2	no	—
169	C₂×C₃×C₈	—	3	2	no	—
170	C₂×C₃×C₈	—	6	2	no	—
171	C₂×C₃×C₈	—	6	8	no	—
172	C₂×C₃×C₈	#67	1	4	yes	complemented
173	C₂×C₃×C₈	C₃×D₄	1	4	yes	complemented
174	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
175	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
176	C₃×C₄⋊C₄	—	3	4	no	—
177	C₃×C₄⋊C₄	—	6	2	no	—
178	C₃×C₂²⋊C₄	—	6	8	no	—
179	#217	—	2	8	no	—
180	C₄⋊Dic₃	—	2	2	no	—
181	C₄⋊Dic₃	C₂³×C₃	1	4	yes	—
182	C₂×C₃⋊C₈	—	2	2	no	—
183	C₂×C₃⋊C₈	C₂³×C₃	1	2	yes	—
184	D₃×C₈	—	2	8	no	—
185	C₂²×C₃²	—	4	4	no	—
186	C₂²×C₃²	—	4	4	no	—
187	C₂²×C₃²	—	4	4	no	—
188	C₂²×C₃²	—	8	8	no	—
189	C₂²×C₃²	#121	1	2	yes	—
190	C₂²×C₃²	C₂×D₈	1	2	yes	—
191	C₂²×C₃²	#135	1	2	yes	—
192	C₂²×C₃²	C₂²×D₄	1	1	yes	characteristic
193	C₂×C₃×D₃	—	2	2	no	—
194	C₂×C₃×D₃	—	2	2	no	—
195	C₂×C₃×D₃	—	2	8	no	—
196	C₂×C₃×D₃	C₂×D₈	1	4	yes	complemented
197	C₃²×C₄	#121	1	2	yes	—
198	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
199	C₃²×C₄	C₂×#41	1	1	yes	characteristic
200	C₃×Dic₃	—	2	2	no	—
201	C₃×Dic₃	—	4	4	no	—
202	C₂²×D₄	—	6	2	no	—
203	C₂²×D₄	C₂×C₃×D₃	1	2	yes	—
204	C₂³×C₄	—	3	1	no	—
205	C₂×D₈	—	2	4	no	—
206	C₂×D₈	C₂×C₃×D₃	1	4	yes	complemented
207	C₂²×C₈	—	3	1	no	—
208	C₂²×C₈	—	3	4	no	—
209	C₂²×C₈	—	6	4	no	—
210	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
211	#121	—	3	8	no	—
212	#121	—	6	4	no	—
213	C₂×C₄⋊C₄	—	3	2	no	—
214	C₂×C₂²⋊C₄	—	6	2	no	—
215	#107	—	3	4	no	—
216	#102	—	3	8	no	—
217	C₂³×C₃	—	2	4	no	—
218	C₂³×C₃	—	2	4	no	—
219	C₂³×C₃	—	2	1	no	—
220	C₂³×C₃	—	3	4	no	—
221	C₂³×C₃	—	3	2	no	—
222	C₂³×C₃	—	4	4	no	—
223	C₂³×C₃	—	4	8	no	—
224	C₂³×C₃	—	4	4	no	—
225	C₂³×C₃	—	4	4	no	—
226	C₂³×C₃	—	4	4	no	—
227	C₂³×C₃	—	4	4	no	—
228	C₂³×C₃	—	4	4	no	—
229	C₂³×C₃	—	4	4	no	—
230	C₂³×C₃	—	6	2	no	—
231	C₂³×C₃	—	6	2	no	—
232	C₂³×C₃	—	8	4	no	—
233	C₂³×C₃	—	8	4	no	—
234	C₂³×C₃	D₃×D₄	1	1	yes	characteristic
235	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
236	C₂²×D₃	—	2	2	no	—
237	C₂²×D₃	—	2	2	no	—
238	C₂²×D₃	C₃×D₈	1	4	yes	complemented
239	C₂²×D₃	C₂×C₃×D₄	1	2	yes	—
240	C₃×D₄	—	2	8	no	—
241	C₃×D₄	—	2	4	no	—
242	C₃×D₄	—	2	4	no	—
243	C₃×D₄	—	2	4	no	—
244	C₃×D₄	—	2	4	no	—
245	C₃×D₄	—	4	4	no	—
246	C₃×D₄	—	4	8	no	—
247	C₃×D₄	—	4	4	no	—
248	C₃×D₄	—	4	4	no	—
249	C₃×D₄	—	12	16	no	—
250	C₂×C₃×C₄	—	2	1	no	—
251	C₂×C₃×C₄	—	2	1	no	—
252	C₂×C₃×C₄	—	2	2	no	—
253	C₂×C₃×C₄	—	2	2	no	—
254	C₂×C₃×C₄	—	3	2	no	—
255	C₂×C₃×C₄	—	6	2	no	—
256	C₂×C₃×C₄	—	6	4	no	—
257	C₂×C₃×C₄	—	6	2	no	—
258	C₂×C₃×C₄	—	6	2	no	—
259	C₂×C₃×C₄	—	6	4	no	—
260	C₂×C₃×C₄	—	12	4	no	—
261	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
262	C₂×C₃×C₄	#237	1	2	yes	—
263	C₂×C₃×C₄	C₂×#67	1	2	yes	—
264	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
265	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
266	C₂×C₃×C₄	C₃×#41	1	2	yes	—
267	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
268	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
269	#67	—	4	16	no	—
270	C₂×Dic₃	—	2	2	no	—
271	C₂×Dic₃	—	2	4	no	—
272	C₂×Dic₃	—	4	4	no	—
273	C₂×Dic₃	C₂×C₃×D₄	1	2	yes	—
274	C₄×D₃	—	2	4	no	—
275	C₄×D₃	—	2	2	no	—
276	C₄×D₃	—	2	2	no	—
277	C₃×C₈	—	2	4	no	—
278	C₃×C₈	—	6	2	no	—
279	C₃×C₈	C₂×#67	1	4	yes	complemented
280	C₃×C₈	C₂×C₃×D₄	1	4	yes	complemented
281	C₃⋊C₈	—	2	2	no	—
282	C₂×C₃²	—	8	4	no	—
283	C₂×C₃²	#466	1	4	yes	complemented
284	C₂×C₃²	C₂×#121	1	1	yes	characteristic
285	C₂×C₃²	C₂²×D₈	1	1	yes	characteristic
286	C₂×C₃²	C₂×#135	1	1	yes	characteristic
287	C₃×D₃	—	2	4	no	—
288	C₂⁴	—	2	2	no	—
289	C₂⁴	—	3	1	no	—
290	C₂×D₄	—	2	2	no	—
291	C₂×D₄	—	2	4	no	—
292	C₂×D₄	—	2	4	no	—
293	C₂×D₄	—	6	8	no	—
294	C₂×D₄	—	12	8	no	—
295	C₂×D₄	C₂²×C₃×D₃	1	4	yes	—
296	C₂²×C₄	—	3	1	no	—
297	C₂²×C₄	—	3	2	no	—
298	C₂²×C₄	—	3	2	no	—
299	C₂²×C₄	—	6	2	no	—
300	C₂²×C₄	—	6	2	no	—
301	C₂²×C₄	—	6	2	no	—
302	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
303	D₈	—	2	8	no	—
304	C₂×C₈	—	3	2	no	—
305	C₂×C₈	—	6	2	no	—
306	C₂×C₈	—	6	8	no	—
307	C₂×C₈	C₃×#67	1	4	yes	complemented
308	C₂×C₈	C₂²×C₃×D₃	1	2	yes	—
309	C₄⋊C₄	—	3	4	no	—
310	C₄⋊C₄	—	6	2	no	—
311	C₂²⋊C₄	—	6	8	no	—
312	C₂²×C₃	—	2	2	no	—
313	C₂²×C₃	—	2	2	no	—
314	C₂²×C₃	—	2	2	no	—
315	C₂²×C₃	—	2	1	no	—
316	C₂²×C₃	—	3	4	no	—
317	C₂²×C₃	—	4	8	no	—
318	C₂²×C₃	—	4	4	no	—
319	C₂²×C₃	—	4	4	no	—
320	C₂²×C₃	—	4	4	no	—
321	C₂²×C₃	—	4	4	no	—
322	C₂²×C₃	—	4	4	no	—
323	C₂²×C₃	—	4	4	no	—
324	C₂²×C₃	—	6	8	no	—
325	C₂²×C₃	—	6	2	no	—
326	C₂²×C₃	—	6	2	no	—
327	C₂²×C₃	—	8	4	no	—
328	C₂²×C₃	—	8	4	no	—
329	C₂²×C₃	—	8	16	no	—
330	C₂²×C₃	—	8	8	no	—
331	C₂²×C₃	—	8	8	no	—
332	C₂²×C₃	D₃×D₈	1	2	yes	—
333	C₂²×C₃	#912	1	2	yes	—
334	C₂²×C₃	#938	1	2	yes	—
335	C₂²×C₃	C₃×#121	1	2	yes	—
336	C₂²×C₃	C₂×C₃×D₈	1	2	yes	—
337	C₂²×C₃	C₃×#135	1	2	yes	—
338	C₂²×C₃	C₂×D₃×D₄	1	1	yes	characteristic
339	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
340	C₂×D₃	—	2	2	no	—
341	C₂×D₃	—	2	8	no	—
342	C₂×D₃	—	2	2	no	—
343	C₂×D₃	C₂×C₃×D₈	1	4	yes	complemented
344	C₃×C₄	—	2	2	no	—
345	C₃×C₄	—	2	1	no	—
346	C₃×C₄	—	2	1	no	—
347	C₃×C₄	—	6	2	no	—
348	C₃×C₄	—	12	4	no	—
349	C₃×C₄	#938	1	2	yes	—
350	C₃×C₄	C₃×#121	1	2	yes	—
351	C₃×C₄	C₂×#237	1	1	yes	characteristic
352	C₃×C₄	C₂²×#67	1	1	yes	characteristic
353	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
354	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
355	Dic₃	—	2	2	no	—
356	Dic₃	—	4	4	no	—
357	C₃²	C₂×#466	1	1	yes	characteristic, complemented, Sylow
358	C₂³	—	2	4	no	—
359	C₂³	—	3	4	no	—
360	C₂³	—	3	2	no	—
361	C₂³	—	4	4	no	—
362	C₂³	—	4	4	no	—
363	C₂³	—	4	4	no	—
364	C₂³	—	6	2	no	—
365	C₂³	—	6	2	no	—
366	C₂³	C₃×D₃×D₄	1	1	yes	characteristic
367	D₄	—	2	4	no	—
368	D₄	—	2	4	no	—
369	D₄	—	4	4	no	—
370	D₄	—	12	16	no	—
371	C₂×C₄	—	3	2	no	—
372	C₂×C₄	—	6	2	no	—
373	C₂×C₄	—	6	4	no	—
374	C₂×C₄	—	6	2	no	—
375	C₂×C₄	—	6	2	no	—
376	C₂×C₄	—	6	4	no	—
377	C₂×C₄	—	12	4	no	—
378	C₂×C₄	C₃×D₃×D₄	1	1	yes	characteristic
379	C₂×C₄	C₃×#237	1	2	yes	—
380	C₂×C₄	C₂×C₃×#67	1	2	yes	—
381	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
382	C₈	—	6	2	no	—
383	C₈	C₂×C₃×#67	1	4	yes	complemented
384	C₂×C₃	—	2	1	no	—
385	C₂×C₃	—	2	1	no	—
386	C₂×C₃	—	2	1	no	—
387	C₂×C₃	—	2	4	no	—
388	C₂×C₃	—	6	4	no	—
389	C₂×C₃	—	8	8	no	—
390	C₂×C₃	—	8	4	no	—
391	C₂×C₃	—	8	4	no	—
392	C₂×C₃	#5157	1	4	yes	direct product factor
393	C₂×C₃	C₃×#466	1	4	yes	complemented
394	C₂×C₃	C₂×D₃×D₈	1	1	yes	characteristic
395	C₂×C₃	C₂×#912	1	1	yes	characteristic
396	C₂×C₃	C₂×#938	1	1	yes	characteristic
397	C₂×C₃	C₂×C₃×#121	1	1	yes	characteristic
398	C₂×C₃	C₂²×C₃×D₈	1	1	yes	characteristic
399	C₂×C₃	C₂×C₃×#135	1	1	yes	characteristic
400	D₃	—	2	4	no	—
401	C₂²	—	3	4	no	—
402	C₂²	—	4	4	no	—
403	C₂²	—	4	4	no	—
404	C₂²	—	4	4	no	—
405	C₂²	—	6	2	no	—
406	C₂²	—	6	2	no	—
407	C₂²	—	6	8	no	—
408	C₂²	—	8	8	no	—
409	C₂²	C₃×D₃×D₈	1	2	yes	—
410	C₂²	C₃×#912	1	2	yes	—
411	C₂²	C₃×#938	1	2	yes	—
412	C₂²	C₂×C₃×D₃×D₄	1	1	yes	characteristic
413	C₄	—	6	2	no	—
414	C₄	—	12	4	no	—
415	C₄	C₃×#938	1	2	yes	—
416	C₄	C₂×C₃×#237	1	1	yes	characteristic
417	C₄	C₂²×C₃×#67	1	1	yes	characteristic
418	C₃	—	2	1	no	—
419	C₃	C₂×#5157	1	1	yes	characteristic, direct product factor
420	C₃	C₂×C₃×#466	1	1	yes	characteristic, complemented
421	C₂	—	6	4	no	—
422	C₂	—	8	4	no	—
423	C₂	C₃×#5157	1	4	yes	direct product factor
424	C₂	C₂×C₃×D₃×D₈	1	1	yes	characteristic
425	C₂	C₂×C₃×#912	1	1	yes	characteristic
426	C₂	C₂×C₃×#938	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃	D₃×D₄
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₂²×C₃²×D₈	C₂
socle	C₂³×C₃²	C₂×D₄
hypercenter	C₂²×C₃×D₈	D₃
hypocenter	C₃	C₂×C₃×#466
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₃ ◁ C₂²×C₃×C₄ ◁ C₂²×C₃×D₈

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃²×D₈	C₂	semidirect
2. C₂×C₃×#938	C₂	semidirect
3. C₂²×C₃×D₃×C₈	C₂	semidirect
4. C₂×C₃×#832	C₂	semidirect
5. C₃×#5157	C₂	direct (N × H)
6. C₂×C₃×#818	C₂	semidirect
8. C₂×#5157	C₃	direct (N × H)
13. C₂×C₃²×D₈	C₂²	semidirect
17. C₃×#938	C₂²	semidirect
21. C₂×C₃×D₃×C₈	C₂²	semidirect
22. C₃×#832	C₂²	semidirect
23. C₃×#818	C₂²	semidirect
25. C₂²×C₃×D₈	D₃	semidirect
26. C₂²×C₃×D₈	C₂×C₃	semidirect
29. C₂×#938	C₂×C₃	semidirect
30. C₂²×D₃×C₈	C₂×C₃	semidirect
34. C₂×#832	C₂×C₃	semidirect
35. #5157	C₂×C₃	direct (N × H)
36. C₂×#818	C₂×C₃	semidirect
53. C₂×C₃²×C₈	D₄	semidirect
73. C₂×C₃×D₈	C₂×D₃	semidirect
74. C₂×C₃×D₈	C₂²×C₃	semidirect
87. #938	C₂²×C₃	semidirect
91. C₂×D₃×C₈	C₂²×C₃	semidirect
94. #832	C₂²×C₃	semidirect
95. #818	C₂²×C₃	semidirect
103. C₂²×C₃×D₃	D₈	semidirect
120. C₃²×C₈	C₂×D₄	semidirect
122. C₂²×D₈	C₃×D₃	semidirect
172. C₂×C₃×C₈	#67	semidirect
173. C₂×C₃×C₈	C₃×D₄	semidirect
196. C₂×C₃×D₃	C₂×D₈	semidirect
206. C₂×D₈	C₂×C₃×D₃	semidirect
238. C₂²×D₃	C₃×D₈	semidirect
279. C₃×C₈	C₂×#67	semidirect
280. C₃×C₈	C₂×C₃×D₄	semidirect
283. C₂×C₃²	#466	semidirect
307. C₂×C₈	C₃×#67	semidirect
343. C₂×D₃	C₂×C₃×D₈	semidirect
357. C₃²	C₂×#466	semidirect
383. C₈	C₂×C₃×#67	semidirect
392. C₂×C₃	#5157	direct (N × H)
393. C₂×C₃	C₃×#466	semidirect
419. C₃	C₂×#5157	direct (N × H)
420. C₃	C₂×C₃×#466	semidirect
423. C₂	C₃×#5157	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×D₈	2
C₂×C₃×#938	2
C₂²×C₃×D₃×C₈	2
C₂×C₃×#832	2
C₃×#5157	2
C₂×C₃×#818	2
C₂×C₃×#466	3
C₂×#5157	3

Subgroups — C2×C3×#5157 #11866727

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#5157 #11866727