Subgroups — C₃×#69776 #11791030

Order 1152.

849 conjugacy classes of subgroups.

The subgroup lattice has 387 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×D₂₄	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃²×C₄×C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#821	C₂	1	2	yes	maximal, complemented
4	C₂×C₃×#818	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#4939	C₂	1	2	yes	maximal, complemented
6	C₃×#1970	—	3	1	no	maximal
7	#69776	C₃	1	1	yes	maximal, characteristic, direct product factor
8	C₂²×C₃×D₁₂	C₂²	1	2	yes	—
9	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
10	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
11	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
12	C₂×C₃×(C₂×D₃)⋊C₄	—	2	4	no	—
13	C₂×C₃×C₄⋊Dic₃	C₂²	1	2	yes	—
14	C₂×C₃×D₂₄	—	2	2	no	—
15	C₂×C₃×D₂₄	—	2	2	no	—
16	C₂×C₃×D₂₄	C₄	1	4	yes	complemented
17	C₃²×C₄×C₈	—	2	2	no	—
18	C₃×#821	—	2	4	no	—
19	C₃×#818	—	2	2	no	—
20	C₂²×C₃×D₈	—	3	1	no	—
21	C₂²×D₂₄	C₂×C₃	1	1	yes	characteristic
22	C₂×C₃×#107	—	3	1	no	—
23	C₂×C₃×#102	—	3	2	no	—
24	C₂×C₃×C₄×C₈	—	2	1	no	—
25	C₂×C₃×C₄×C₈	D₃	1	1	yes	characteristic, complemented
26	C₂×C₃×C₄×C₈	C₂×C₃	1	1	yes	characteristic, complemented
27	C₃×#390	—	3	2	no	—
28	C₂×#821	C₂×C₃	1	2	yes	complemented
29	C₂×#818	C₂×C₃	1	1	yes	characteristic, complemented
30	#4939	C₂×C₃	1	2	yes	complemented
31	C₂³×C₃×D₃	—	2	2	no	—
32	C₂²×C₃²×C₄	D₄	1	2	yes	—
33	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
34	C₂²×C₃×Dic₃	—	2	2	no	—
35	C₂×C₃×D₁₂	—	2	2	no	—
36	C₂×C₃×D₁₂	—	2	2	no	—
37	C₂×C₃×D₁₂	—	2	2	no	—
38	C₂×C₃×D₁₂	—	2	2	no	—
39	C₂×C₃×D₁₂	—	2	2	no	—
40	C₂×C₃×D₁₂	C₂×C₄	1	4	yes	—
41	C₂×C₃²×C₈	—	2	1	no	—
42	C₂×C₃²×C₈	—	2	1	no	—
43	C₂×C₃²×C₈	C₂×C₄	1	2	yes	—
44	C₂×C₃²×C₈	D₄	1	2	yes	—
45	C₂×C₃²×C₈	D₄	1	2	yes	—
46	C₂×C₃²×C₈	D₄	1	2	yes	—
47	C₃²×C₄²	—	2	1	no	—
48	C₃²×C₄²	—	2	1	no	—
49	C₃×(C₂×D₃)⋊C₄	—	4	8	no	—
50	C₃×C₄⋊Dic₃	—	2	2	no	—
51	C₃×C₄⋊Dic₃	—	2	2	no	—
52	C₃×D₂₄	—	2	8	no	—
53	#1970	—	3	1	no	Sylow
54	C₂²×C₃×D₄	—	3	2	no	—
55	C₂²×D₁₂	C₂²×C₃	1	2	yes	—
56	C₂×C₃×D₈	—	3	4	no	—
57	C₂×C₃×D₈	—	6	2	no	—
58	C₂×C₃×D₈	—	6	2	no	—
59	C₂²×C₃×C₈	—	2	1	no	—
60	C₂²×C₃×C₈	—	2	1	no	—
61	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
62	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
63	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
64	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
65	C₂×C₃×C₄⋊C₄	—	3	2	no	—
66	C₂×C₃×C₂²⋊C₄	—	6	4	no	—
67	C₂×C₃×C₄²	—	2	1	no	—
68	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
69	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
70	C₂×(C₂×D₃)⋊C₄	—	2	4	no	—
71	C₂×C₄⋊Dic₃	C₂²×C₃	1	2	yes	—
72	C₂×D₂₄	—	2	2	no	—
73	C₂×D₂₄	—	2	2	no	—
74	C₂×D₂₄	C₃×C₄	1	4	yes	complemented
75	C₃×#107	—	6	2	no	—
76	C₃×#102	—	6	4	no	—
77	C₃×C₄×C₈	—	2	4	no	—
78	C₃×C₄×C₈	—	2	2	no	—
79	C₃×C₄×C₈	—	2	2	no	—
80	#821	—	2	4	no	—
81	#818	—	2	2	no	—
82	C₂³×C₃²	C₂×D₄	1	1	yes	characteristic
83	C₂²×C₃×D₃	—	2	4	no	—
84	C₂²×C₃×D₃	—	4	2	no	—
85	C₂²×C₃×D₃	—	4	2	no	—
86	C₂²×C₃×D₃	—	4	4	no	—
87	C₂²×C₃×D₃	—	4	4	no	—
88	C₂×C₃²×C₄	—	2	2	no	—
89	C₂×C₃²×C₄	—	2	2	no	—
90	C₂×C₃²×C₄	D₈	1	4	yes	complemented
91	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
92	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
93	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
94	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
95	C₂×C₃²×C₄	#41	1	1	yes	characteristic
96	C₂×C₃²×C₄	#41	1	1	yes	characteristic
97	C₂×C₃×Dic₃	—	4	2	no	—
98	C₂×C₃×Dic₃	—	4	4	no	—
99	C₃×D₁₂	—	2	4	no	—
100	C₃×D₁₂	—	2	4	no	—
101	C₃×D₁₂	—	4	2	no	—
102	C₃×D₁₂	—	4	2	no	—
103	C₃²×C₈	—	2	2	no	—
104	C₃²×C₈	C₂²⋊C₄	1	4	yes	complemented
105	C₂²×D₈	—	3	1	no	—
106	C₂×#107	—	3	1	no	—
107	C₂×#102	—	3	2	no	—
108	C₂×C₄×C₈	C₃×D₃	1	1	yes	characteristic, complemented
109	#390	—	3	2	no	—
110	C₂⁴×C₃	—	6	2	no	—
111	C₂³×D₃	—	2	2	no	—
112	C₂×C₃×D₄	—	3	4	no	—
113	C₂×C₃×D₄	—	6	2	no	—
114	C₂×C₃×D₄	—	6	2	no	—
115	C₂×C₃×D₄	—	6	2	no	—
116	C₂×C₃×D₄	—	6	2	no	—
117	C₂×C₃×D₄	—	6	2	no	—
118	C₂²×C₃×C₄	—	2	2	no	—
119	C₂²×C₃×C₄	—	2	1	no	—
120	C₂²×C₃×C₄	—	6	2	no	—
121	C₂²×C₃×C₄	D₁₂	1	2	yes	—
122	C₂²×C₃×C₄	C₃×D₄	1	2	yes	—
123	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
124	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
125	C₂²×Dic₃	—	2	2	no	—
126	C₂×D₁₂	—	2	2	no	—
127	C₂×D₁₂	—	2	2	no	—
128	C₂×D₁₂	—	2	2	no	—
129	C₂×D₁₂	—	2	2	no	—
130	C₂×D₁₂	—	2	2	no	—
131	C₂×D₁₂	C₂×C₃×C₄	1	4	yes	—
132	C₃×D₈	—	6	8	no	—
133	C₂×C₃×C₈	—	2	2	no	—
134	C₂×C₃×C₈	—	2	2	no	—
135	C₂×C₃×C₈	—	2	1	no	—
136	C₂×C₃×C₈	—	2	1	no	—
137	C₂×C₃×C₈	—	2	1	no	—
138	C₂×C₃×C₈	—	2	1	no	—
139	C₂×C₃×C₈	—	2	2	no	—
140	C₂×C₃×C₈	—	2	2	no	—
141	C₂×C₃×C₈	—	2	2	no	—
142	C₂×C₃×C₈	—	2	2	no	—
143	C₂×C₃×C₈	C₄×D₃	1	2	yes	—
144	C₂×C₃×C₈	D₁₂	1	2	yes	—
145	C₂×C₃×C₈	D₁₂	1	2	yes	—
146	C₂×C₃×C₈	#67	1	2	yes	—
147	C₂×C₃×C₈	C₂×C₃×C₄	1	2	yes	—
148	C₂×C₃×C₈	C₃×D₄	1	2	yes	—
149	C₂×C₃×C₈	C₃×D₄	1	2	yes	—
150	C₂×C₃×C₈	C₃×D₄	1	2	yes	—
151	C₃×C₄⋊C₄	—	6	2	no	—
152	C₃×C₄⋊C₄	—	6	2	no	—
153	C₃×C₂²⋊C₄	—	12	8	no	—
154	C₃×C₄²	—	2	2	no	—
155	C₃×C₄²	—	2	2	no	—
156	C₃×C₄²	—	2	1	no	—
157	C₃×C₄²	—	2	1	no	—
158	C₃×C₄²	—	2	1	no	—
159	C₃×C₄²	—	2	1	no	—
160	(C₂×D₃)⋊C₄	—	4	8	no	—
161	C₄⋊Dic₃	—	2	2	no	—
162	C₄⋊Dic₃	—	2	2	no	—
163	D₂₄	—	2	8	no	—
164	C₂²×C₃²	C₄×D₄	1	1	yes	characteristic
165	C₂²×C₃²	#121	1	1	yes	characteristic
166	C₂²×C₃²	#127	1	1	yes	characteristic
167	C₂²×C₃²	C₂×D₈	1	2	yes	—
168	C₂²×C₃²	#135	1	2	yes	—
169	C₂×C₃×D₃	—	4	4	no	—
170	C₂×C₃×D₃	—	4	8	no	—
171	C₂×C₃×D₃	—	8	4	no	—
172	C₂×C₃×D₃	—	8	2	no	—
173	C₂×C₃×D₃	—	8	2	no	—
174	C₃²×C₄	—	2	4	no	—
175	C₃²×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
176	C₃²×C₄	C₄×D₄	1	1	yes	characteristic
177	C₃²×C₄	#121	1	1	yes	characteristic
178	C₃²×C₄	#124	1	1	yes	characteristic
179	C₃×Dic₃	—	8	2	no	—
180	C₂²×D₄	—	3	2	no	—
181	C₂×D₈	—	3	4	no	—
182	C₂×D₈	—	6	2	no	—
183	C₂×D₈	—	6	2	no	—
184	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
185	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
186	C₂×C₄⋊C₄	—	3	2	no	—
187	C₂×C₂²⋊C₄	—	6	4	no	—
188	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
189	#107	—	6	2	no	—
190	#102	—	6	4	no	—
191	C₄×C₈	—	2	2	no	—
192	C₂³×C₃	—	2	1	no	—
193	C₂³×C₃	—	6	4	no	—
194	C₂³×C₃	—	12	2	no	—
195	C₂³×C₃	—	12	4	no	—
196	C₂³×C₃	—	12	4	no	—
197	C₂³×C₃	—	12	2	no	—
198	C₂³×C₃	C₂×D₁₂	1	1	yes	characteristic
199	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
200	C₂²×D₃	—	2	4	no	—
201	C₂²×D₃	—	4	2	no	—
202	C₂²×D₃	—	4	2	no	—
203	C₂²×D₃	—	4	4	no	—
204	C₂²×D₃	—	4	4	no	—
205	C₃×D₄	—	6	4	no	—
206	C₃×D₄	—	6	4	no	—
207	C₃×D₄	—	12	2	no	—
208	C₃×D₄	—	12	2	no	—
209	C₂×C₃×C₄	—	2	4	no	—
210	C₂×C₃×C₄	—	2	4	no	—
211	C₂×C₃×C₄	—	2	2	no	—
212	C₂×C₃×C₄	—	2	2	no	—
213	C₂×C₃×C₄	—	2	2	no	—
214	C₂×C₃×C₄	—	2	2	no	—
215	C₂×C₃×C₄	—	2	4	no	—
216	C₂×C₃×C₄	—	2	1	no	—
217	C₂×C₃×C₄	—	2	1	no	—
218	C₂×C₃×C₄	—	2	1	no	—
219	C₂×C₃×C₄	—	2	1	no	—
220	C₂×C₃×C₄	—	2	1	no	—
221	C₂×C₃×C₄	—	2	1	no	—
222	C₂×C₃×C₄	—	12	2	no	—
223	C₂×C₃×C₄	—	12	4	no	—
224	C₂×C₃×C₄	D₂₄	1	4	yes	complemented
225	C₂×C₃×C₄	C₃×D₈	1	4	yes	complemented
226	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
227	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
228	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
229	C₂×C₃×C₄	#235	1	1	yes	characteristic
230	C₂×C₃×C₄	#235	1	1	yes	characteristic
231	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
232	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
233	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
234	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
235	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
236	C₂×C₃×C₄	C₃×#41	1	1	yes	characteristic
237	C₂×C₃×C₄	C₃×#41	1	1	yes	characteristic
238	C₂×Dic₃	—	4	2	no	—
239	C₂×Dic₃	—	4	4	no	—
240	D₁₂	—	2	4	no	—
241	D₁₂	—	2	4	no	—
242	D₁₂	—	4	2	no	—
243	D₁₂	—	4	2	no	—
244	C₃×C₈	—	2	4	no	—
245	C₃×C₈	—	2	2	no	—
246	C₃×C₈	—	2	2	no	—
247	C₃×C₈	—	2	4	no	—
248	C₃×C₈	(C₂×D₃)⋊C₄	1	4	yes	complemented
249	C₃×C₈	C₃×C₂²⋊C₄	1	4	yes	complemented
250	C₂×C₃²	#390	1	1	yes	characteristic
251	C₂×C₃²	C₄×D₈	1	2	yes	—
252	C₂×C₃²	#466	1	2	yes	—
253	C₂×C₃²	#493	1	1	yes	characteristic
254	C₂×C₃²	#495	1	1	yes	characteristic
255	C₃×D₃	—	8	4	no	—
256	C₂⁴	—	6	2	no	—
257	C₂×D₄	—	3	4	no	—
258	C₂×D₄	—	6	2	no	—
259	C₂×D₄	—	6	2	no	—
260	C₂×D₄	—	6	2	no	—
261	C₂×D₄	—	6	2	no	—
262	C₂×D₄	—	6	2	no	—
263	C₂²×C₄	—	6	2	no	—
264	C₂²×C₄	C₃×D₁₂	1	2	yes	—
265	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
266	D₈	—	6	8	no	—
267	C₂×C₈	—	2	1	no	—
268	C₂×C₈	—	2	1	no	—
269	C₂×C₈	C₃×C₄×D₃	1	2	yes	—
270	C₂×C₈	C₃×D₁₂	1	2	yes	—
271	C₂×C₈	C₃×D₁₂	1	2	yes	—
272	C₂×C₈	C₃×#67	1	2	yes	—
273	C₄⋊C₄	—	6	2	no	—
274	C₄⋊C₄	—	6	2	no	—
275	C₂²⋊C₄	—	12	8	no	—
276	C₄²	—	2	1	no	—
277	C₄²	—	2	1	no	—
278	C₂²×C₃	—	2	2	no	—
279	C₂²×C₃	—	2	2	no	—
280	C₂²×C₃	—	2	1	no	—
281	C₂²×C₃	—	2	1	no	—
282	C₂²×C₃	—	2	1	no	—
283	C₂²×C₃	—	12	4	no	—
284	C₂²×C₃	—	12	8	no	—
285	C₂²×C₃	—	24	2	no	—
286	C₂²×C₃	—	24	2	no	—
287	C₂²×C₃	—	24	4	no	—
288	C₂²×C₃	C₄×D₁₂	1	1	yes	characteristic
289	C₂²×C₃	#874	1	1	yes	characteristic
290	C₂²×C₃	C₂×D₂₄	1	2	yes	—
291	C₂²×C₃	#904	1	2	yes	—
292	C₂²×C₃	#930	1	1	yes	characteristic
293	C₂²×C₃	C₃×C₄×D₄	1	1	yes	characteristic
294	C₂²×C₃	C₃×#121	1	1	yes	characteristic
295	C₂²×C₃	C₃×#127	1	1	yes	characteristic
296	C₂²×C₃	C₂×C₃×D₈	1	2	yes	—
297	C₂²×C₃	C₃×#135	1	2	yes	—
298	C₂×D₃	—	4	4	no	—
299	C₂×D₃	—	4	8	no	—
300	C₂×D₃	—	8	4	no	—
301	C₂×D₃	—	8	2	no	—
302	C₂×D₃	—	8	2	no	—
303	C₃×C₄	—	2	8	no	—
304	C₃×C₄	—	2	4	no	—
305	C₃×C₄	—	2	4	no	—
306	C₃×C₄	—	2	1	no	—
307	C₃×C₄	—	2	1	no	—
308	C₃×C₄	—	2	1	no	—
309	C₃×C₄	—	2	1	no	—
310	C₃×C₄	—	24	2	no	—
311	C₃×C₄	C₄×D₁₂	1	1	yes	characteristic
312	C₃×C₄	#875	1	1	yes	characteristic
313	C₃×C₄	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
314	C₃×C₄	#930	1	1	yes	characteristic
315	C₃×C₄	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
316	C₃×C₄	C₃×C₄×D₄	1	1	yes	characteristic
317	C₃×C₄	C₃×#121	1	1	yes	characteristic
318	C₃×C₄	C₃×#124	1	1	yes	characteristic
319	Dic₃	—	8	2	no	—
320	C₃²	#1970	1	1	yes	characteristic, complemented, Sylow
321	C₂³	—	6	4	no	—
322	C₂³	—	12	4	no	—
323	C₂³	—	12	4	no	—
324	C₂³	—	12	2	no	—
325	C₂³	—	12	2	no	—
326	C₂³	C₂×C₃×D₁₂	1	1	yes	characteristic
327	D₄	—	6	4	no	—
328	D₄	—	6	4	no	—
329	D₄	—	12	2	no	—
330	D₄	—	12	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	12	4	no	—
334	C₂×C₄	—	12	2	no	—
335	C₂×C₄	C₃×D₂₄	1	4	yes	complemented
336	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
337	C₂×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
338	C₂×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
339	C₂×C₄	C₃×#235	1	1	yes	characteristic
340	C₂×C₄	C₃×#235	1	1	yes	characteristic
341	C₂×C₄	C₂×C₃×#67	1	1	yes	characteristic
342	C₈	—	2	2	no	—
343	C₈	C₃×(C₂×D₃)⋊C₄	1	4	yes	complemented
344	C₂×C₃	—	2	1	no	—
345	C₂×C₃	—	2	2	no	—
346	C₂×C₃	—	2	1	no	—
347	C₂×C₃	—	2	1	no	—
348	C₂×C₃	—	2	2	no	—
349	C₂×C₃	—	24	4	no	—
350	C₂×C₃	C₄×D₂₄	1	2	yes	—
351	C₂×C₃	#4695	1	1	yes	characteristic
352	C₂×C₃	#4696	1	1	yes	characteristic
353	C₂×C₃	#4939	1	1	yes	characteristic
354	C₂×C₃	#5115	1	2	yes	—
355	C₂×C₃	C₃×#390	1	1	yes	characteristic
356	C₂×C₃	C₃×C₄×D₈	1	2	yes	—
357	C₂×C₃	C₃×#466	1	2	yes	—
358	C₂×C₃	C₃×#493	1	1	yes	characteristic
359	C₂×C₃	C₃×#495	1	1	yes	characteristic
360	D₃	—	8	4	no	—
361	C₂²	—	12	4	no	—
362	C₂²	—	12	8	no	—
363	C₂²	—	24	2	no	—
364	C₂²	—	24	2	no	—
365	C₂²	—	24	4	no	—
366	C₂²	C₃×C₄×D₁₂	1	1	yes	characteristic
367	C₂²	C₃×#874	1	1	yes	characteristic
368	C₂²	C₂×C₃×D₂₄	1	2	yes	—
369	C₂²	C₃×#904	1	2	yes	—
370	C₂²	C₃×#930	1	1	yes	characteristic
371	C₄	—	2	4	no	—
372	C₄	—	24	2	no	—
373	C₄	C₃×C₄×D₁₂	1	1	yes	characteristic
374	C₄	C₃×#875	1	1	yes	characteristic
375	C₄	C₂×C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
376	C₄	C₃×#930	1	1	yes	characteristic
377	C₃	—	2	1	no	—
378	C₃	#69776	1	1	yes	characteristic, direct product factor
379	C₃	C₃×#1970	1	1	yes	characteristic, complemented
380	C₂	—	24	4	no	—
381	C₂	C₃×C₄×D₂₄	1	2	yes	—
382	C₂	C₃×#4695	1	1	yes	characteristic
383	C₂	C₃×#4696	1	1	yes	characteristic
384	C₂	C₃×#4939	1	1	yes	characteristic
385	C₂	C₃×#5115	1	2	yes	—

	subgroup	G/H
center	C₂³×C₃	C₂×D₁₂
commutator	C₂×C₃×C₄	C₂²×C₃×C₄
Frattini	C₂²×C₄	C₂²×C₃×D₃
Fitting	C₂×C₃²×C₄×C₈	C₂
socle	C₂³×C₃²	C₂×D₄
prime radical	C₂²×C₃×D₂₄	C₂
cosocle	C₂²×C₃×C₄	C₂³×C₃
hypercenter	C₂×C₃×C₄×C₈	D₃
hypocenter	C₃	C₃×#1970
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₃ ◁ C₂×C₃×C₄² ◁ C₂×C₃×C₄×C₈

Complements

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

N	H ≅ G/N	type
2. C₂×C₃²×C₄×C₈	C₂	semidirect
3. C₂×C₃×#821	C₂	semidirect
4. C₂×C₃×#818	C₂	semidirect
5. C₃×#4939	C₂	semidirect
7. #69776	C₃	direct (N × H)
16. C₂×C₃×D₂₄	C₄	semidirect
25. C₂×C₃×C₄×C₈	D₃	semidirect
26. C₂×C₃×C₄×C₈	C₂×C₃	semidirect
28. C₂×#821	C₂×C₃	semidirect
29. C₂×#818	C₂×C₃	semidirect
30. #4939	C₂×C₃	semidirect
74. C₂×D₂₄	C₃×C₄	semidirect
90. C₂×C₃²×C₄	D₈	semidirect
104. C₃²×C₈	C₂²⋊C₄	semidirect
108. C₂×C₄×C₈	C₃×D₃	semidirect
224. C₂×C₃×C₄	D₂₄	semidirect
225. C₂×C₃×C₄	C₃×D₈	semidirect
248. C₃×C₈	(C₂×D₃)⋊C₄	semidirect
249. C₃×C₈	C₃×C₂²⋊C₄	semidirect
320. C₃²	#1970	semidirect
335. C₂×C₄	C₃×D₂₄	semidirect
343. C₈	C₃×(C₂×D₃)⋊C₄	semidirect
378. C₃	#69776	direct (N × H)
379. C₃	C₃×#1970	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₃×D₂₄	2
C₂×C₃²×C₄×C₈	2
C₂×C₃×#821	2
C₂×C₃×#818	2
C₃×#4939	2
C₃×#1970	3
#69776	3

Subgroups — C3×#69776 #11791030

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#69776 #11791030