Subgroups — #11776299

Order 1152.

625 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#64078	C₂	1	1	yes	maximal, characteristic
2	C₃×#4925	C₂	1	1	yes	maximal, characteristic
3	C₃×#4924	C₂	1	1	yes	maximal, characteristic
4	#10589094	C₂	1	4	yes	maximal, complemented
5	#70778	—	3	1	no	maximal
6	#70506	—	3	1	no	maximal
7	C₂²×#634	—	2	1	no	—
8	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
9	C₂×C₄⋊(C₃⋊Dic₃)	—	2	1	no	—
10	C₂×C₄⋊(C₃⋊Dic₃)	C₄	1	2	yes	—
11	#64078	—	2	1	no	—
12	#64078	—	2	1	no	—
13	#64078	C₄	1	2	yes	—
14	#64078	C₂²	1	2	yes	—
15	C₂×C₃×#208	—	2	1	no	—
16	C₃×#830	—	2	1	no	—
17	C₃×C₄⋊(C₃⋊C₈)	—	2	1	no	—
18	C₃×C₄⋊(C₃⋊C₈)	C₂²	1	2	yes	—
19	C₃×C₄⋊(C₃⋊C₈)	C₂²	1	2	yes	—
20	C₃×C₄×C₃⋊C₈	—	2	1	no	—
21	C₂×#869	—	3	1	no	—
22	C₂×#869	—	3	1	no	—
23	C₂×#869	—	6	1	no	—
24	C₃×#431	—	3	1	no	—
25	C₃×#423	—	3	1	no	—
26	#4925	D₃	1	1	yes	characteristic
27	#4924	D₃	1	1	yes	characteristic
28	#4486	—	3	4	no	—
29	#4482	—	3	4	no	—
30	C₂²×C₃²×C₄	C₂×C₄	1	1	yes	characteristic
31	C₂²×C₃²×C₄	D₄	1	1	yes	characteristic
32	C₂²×C₃²×C₄	D₄	1	1	yes	characteristic
33	C₂²×C₃⋊Dic₃	—	2	2	no	—
34	C₂×#634	—	2	2	no	—
35	C₂×#634	—	2	2	no	—
36	C₂×#634	—	4	2	no	—
37	C₂×#634	—	4	2	no	—
38	C₃²×C₄²	C₂×C₄	1	1	yes	characteristic
39	C₃²×C₄²	D₄	1	1	yes	characteristic
40	C₃²×C₄²	D₄	1	1	yes	characteristic
41	C₃²×C₄²	C₂³	1	1	yes	characteristic
42	C₄⋊(C₃⋊Dic₃)	—	2	2	no	—
43	C₄⋊(C₃⋊Dic₃)	—	2	2	no	—
44	C₄⋊(C₃⋊Dic₃)	—	2	2	no	—
45	C₄⋊(C₃⋊Dic₃)	C₂×C₄	1	4	yes	—
46	C₃×#208	—	4	2	no	—
47	C₂×C₃×C₃⋊C₈	—	2	2	no	—
48	C₂×C₃×C₃⋊C₈	—	2	2	no	—
49	#1546	—	9	1	no	Sylow
50	C₂²×Dic₆	—	6	2	no	—
51	C₂²×Dic₆	—	6	1	no	—
52	C₂²×Dic₆	—	6	1	no	—
53	C₂×C₃×M₁₆	—	6	1	no	—
54	C₂×C₃×C₄²	—	2	1	no	—
55	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
56	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
57	C₂×C₄⋊Dic₃	—	3	2	no	—
58	C₂×C₄⋊Dic₃	—	3	2	no	—
59	C₂×C₄⋊Dic₃	—	6	2	no	—
60	C₂×C₄⋊Dic₃	—	6	2	no	—
61	C₂×C₄⋊Dic₃	—	6	1	no	—
62	C₂×C₄⋊Dic₃	—	6	1	no	—
63	C₂×#208	—	2	1	no	—
64	#869	—	3	2	no	—
65	#869	—	3	2	no	—
66	#869	—	3	2	no	—
67	#869	—	3	2	no	—
68	#869	—	6	2	no	—
69	#869	—	6	2	no	—
70	#869	—	6	2	no	—
71	#869	—	6	2	no	—
72	#869	—	6	1	no	—
73	#869	—	6	1	no	—
74	#869	—	6	1	no	—
75	#869	—	6	1	no	—
76	C₃×C₄⋊C₈	—	3	2	no	—
77	C₃×C₄⋊C₈	—	3	2	no	—
78	C₃×C₄⋊C₈	—	6	1	no	—
79	C₃×C₂²⋊C₈	—	6	1	no	—
80	C₃×C₄×C₈	—	6	1	no	—
81	#830	—	2	1	no	—
82	C₄⋊(C₃⋊C₈)	—	2	1	no	—
83	C₄⋊(C₃⋊C₈)	C₂×D₃	1	2	yes	—
84	C₄⋊(C₃⋊C₈)	C₂×D₃	1	2	yes	—
85	C₄×C₃⋊C₈	—	2	1	no	—
86	C₂³×C₃²	C₂²⋊C₄	1	1	yes	characteristic
87	C₂×C₃²×C₄	—	2	2	no	—
88	C₂×C₃²×C₄	—	2	2	no	—
89	C₂×C₃²×C₄	C₂²⋊C₄	1	1	yes	characteristic
90	C₂×C₃²×C₄	C₂²⋊C₄	1	1	yes	characteristic
91	C₂×C₃²×C₄	C₂²⋊C₄	1	1	yes	characteristic
92	C₂×C₃²×C₄	D₈	1	2	yes	—
93	C₂×C₃²×C₄	SD₁₆	1	2	yes	—
94	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
95	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
96	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
97	C₂×C₃⋊Dic₃	—	2	4	no	—
98	C₂×C₃⋊Dic₃	—	4	4	no	—
99	#634	—	4	4	no	—
100	#634	—	4	2	no	—
101	#634	—	4	2	no	—
102	C₃×C₃⋊C₈	—	4	2	no	—
103	C₃×C₃⋊C₈	—	4	2	no	—
104	C₂×C₄⋊Q₈	—	9	1	no	—
105	#431	—	3	1	no	—
106	#423	—	3	1	no	—
107	#332	—	9	4	no	—
108	C₂²×C₃×C₄	—	2	1	no	—
109	C₂²×C₃×C₄	—	2	1	no	—
110	C₂²×C₃×C₄	—	2	1	no	—
111	C₂²×C₃×C₄	C₄×D₃	1	1	yes	characteristic
112	C₂²×C₃×C₄	C₄×D₃	1	1	yes	characteristic
113	C₂²×C₃×C₄	D₁₂	1	1	yes	characteristic
114	C₂²×C₃×C₄	D₁₂	1	1	yes	characteristic
115	C₂²×C₃×C₄	#67	1	1	yes	characteristic
116	C₂²×C₃×C₄	#67	1	1	yes	characteristic
117	C₂²×Dic₃	—	6	4	no	—
118	C₂²×Dic₃	—	6	2	no	—
119	C₂²×Dic₃	—	6	2	no	—
120	C₂×Dic₆	—	6	4	no	—
121	C₂×Dic₆	—	6	4	no	—
122	C₂×Dic₆	—	6	2	no	—
123	C₂×Dic₆	—	6	2	no	—
124	C₂×Dic₆	—	6	2	no	—
125	C₂×Dic₆	—	6	2	no	—
126	C₂×Dic₆	—	12	4	no	—
127	C₂×Dic₆	—	12	4	no	—
128	C₂×Dic₆	—	12	2	no	—
129	C₂×Dic₆	—	12	2	no	—
130	C₂×Dic₆	—	12	2	no	—
131	C₂×Dic₆	—	12	2	no	—
132	C₃×M₁₆	—	12	2	no	—
133	C₂×C₃×C₈	—	6	2	no	—
134	C₂×C₃×C₈	—	6	2	no	—
135	C₃×C₄²	—	2	1	no	—
136	C₃×C₄²	—	2	1	no	—
137	C₃×C₄²	—	2	1	no	—
138	C₃×C₄²	—	2	1	no	—
139	C₃×C₄²	C₄×D₃	1	1	yes	characteristic
140	C₃×C₄²	C₄×D₃	1	1	yes	characteristic
141	C₃×C₄²	D₁₂	1	1	yes	characteristic
142	C₃×C₄²	D₁₂	1	1	yes	characteristic
143	C₃×C₄²	#67	1	1	yes	characteristic
144	C₃×C₄²	#67	1	1	yes	characteristic
145	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
146	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
147	C₄⋊Dic₃	—	3	4	no	—
148	C₄⋊Dic₃	—	3	4	no	—
149	C₄⋊Dic₃	—	6	4	no	—
150	C₄⋊Dic₃	—	6	4	no	—
151	C₄⋊Dic₃	—	6	4	no	—
152	C₄⋊Dic₃	—	6	4	no	—
153	C₄⋊Dic₃	—	6	2	no	—
154	C₄⋊Dic₃	—	6	2	no	—
155	C₄⋊Dic₃	—	6	2	no	—
156	C₄⋊Dic₃	—	6	2	no	—
157	C₄⋊Dic₃	—	6	2	no	—
158	C₄⋊Dic₃	—	6	2	no	—
159	#208	—	4	2	no	—
160	C₂×C₃⋊C₈	—	2	2	no	—
161	C₂×C₃⋊C₈	—	2	2	no	—
162	C₂²×C₃²	—	2	1	no	—
163	C₂²×C₃²	—	2	1	no	—
164	C₂²×C₃²	#102	1	2	yes	—
165	C₂²×C₃²	C₂×C₂²⋊C₄	1	1	yes	characteristic
166	C₃²×C₄	—	2	1	no	—
167	C₃²×C₄	—	2	1	no	—
168	C₃²×C₄	#101	1	2	yes	—
169	C₃²×C₄	#102	1	2	yes	—
170	C₃²×C₄	C₂×D₈	1	1	yes	characteristic
171	C₃²×C₄	C₂×SD₁₆	1	1	yes	characteristic
172	C₃²×C₄	#137	1	2	yes	—
173	C₃⋊Dic₃	—	4	4	no	—
174	C₂²×Q₈	—	18	1	no	—
175	C₂×M₁₆	—	6	1	no	—
176	C₄⋊Q₈	—	9	2	no	—
177	C₄⋊Q₈	—	9	2	no	—
178	C₄⋊Q₈	—	18	1	no	—
179	C₄⋊Q₈	—	18	1	no	—
180	C₂×C₄⋊C₄	—	9	2	no	—
181	C₂×C₄⋊C₄	—	18	1	no	—
182	C₂×C₄²	D₃²	1	1	yes	characteristic
183	C₄⋊C₈	—	3	2	no	—
184	C₄⋊C₈	—	3	2	no	—
185	C₄⋊C₈	—	6	1	no	—
186	C₂²⋊C₈	—	6	1	no	—
187	C₄×C₈	—	6	1	no	—
188	C₂³×C₃	—	2	1	no	—
189	C₂³×C₃	(C₂×D₃)⋊C₄	1	1	yes	characteristic
190	C₂³×C₃	(C₂×D₃)⋊C₄	1	1	yes	characteristic
191	C₂×C₃×C₄	—	2	4	no	—
192	C₂×C₃×C₄	—	2	4	no	—
193	C₂×C₃×C₄	—	2	2	no	—
194	C₂×C₃×C₄	—	2	2	no	—
195	C₂×C₃×C₄	—	2	2	no	—
196	C₂×C₃×C₄	—	2	2	no	—
197	C₂×C₃×C₄	—	2	2	no	—
198	C₂×C₃×C₄	—	2	2	no	—
199	C₂×C₃×C₄	—	2	1	no	—
200	C₂×C₃×C₄	—	2	1	no	—
201	C₂×C₃×C₄	—	2	1	no	—
202	C₂×C₃×C₄	—	2	1	no	—
203	C₂×C₃×C₄	—	2	1	no	—
204	C₂×C₃×C₄	—	2	1	no	—
205	C₂×C₃×C₄	#204	1	2	yes	—
206	C₂×C₃×C₄	D₂₄	1	2	yes	—
207	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
208	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
209	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
210	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
211	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
212	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
213	C₂×C₃×C₄	#213	1	2	yes	—
214	C₂×C₃×C₄	#215	1	2	yes	—
215	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
216	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
217	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
218	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
219	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
220	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
221	C₂×Dic₃	—	6	8	no	—
222	C₂×Dic₃	—	6	4	no	—
223	C₂×Dic₃	—	6	4	no	—
224	C₂×Dic₃	—	12	8	no	—
225	C₂×Dic₃	—	12	4	no	—
226	C₂×Dic₃	—	12	4	no	—
227	Dic₆	—	12	8	no	—
228	Dic₆	—	12	4	no	—
229	Dic₆	—	12	4	no	—
230	Dic₆	—	12	4	no	—
231	Dic₆	—	12	4	no	—
232	Dic₆	—	12	2	no	—
233	Dic₆	—	12	2	no	—
234	Dic₆	—	12	2	no	—
235	Dic₆	—	12	2	no	—
236	C₃×C₈	—	12	2	no	—
237	C₃×C₈	—	12	2	no	—
238	C₃⋊C₈	—	4	2	no	—
239	C₃⋊C₈	—	4	2	no	—
240	C₂×C₃²	—	2	2	no	—
241	C₂×C₃²	C₂×#101	1	1	yes	characteristic
242	C₂×C₃²	C₂×#102	1	1	yes	characteristic
243	C₂×C₃²	#419	1	1	yes	characteristic
244	C₂×Q₈	—	18	2	no	—
245	C₂×Q₈	—	18	2	no	—
246	C₂×Q₈	—	36	2	no	—
247	C₂×Q₈	—	36	2	no	—
248	C₂²×C₄	—	18	2	no	—
249	C₂²×C₄	#624	1	1	yes	characteristic
250	C₂²×C₄	#626	1	1	yes	characteristic
251	C₂²×C₄	#626	1	1	yes	characteristic
252	M₁₆	—	12	2	no	—
253	C₂×C₈	—	6	2	no	—
254	C₂×C₈	—	6	2	no	—
255	C₄⋊C₄	—	9	4	no	—
256	C₄⋊C₄	—	18	2	no	—
257	C₄⋊C₄	—	18	2	no	—
258	C₄⋊C₄	—	18	2	no	—
259	C₄²	#624	1	1	yes	characteristic
260	C₄²	#626	1	1	yes	characteristic
261	C₄²	#626	1	1	yes	characteristic
262	C₄²	C₂×D₃²	1	1	yes	characteristic
263	C₂²×C₃	—	2	2	no	—
264	C₂²×C₃	—	2	2	no	—
265	C₂²×C₃	—	2	1	no	—
266	C₂²×C₃	—	2	1	no	—
267	C₂²×C₃	—	2	1	no	—
268	C₂²×C₃	—	2	1	no	—
269	C₂²×C₃	—	2	2	no	—
270	C₂²×C₃	—	2	1	no	—
271	C₂²×C₃	#809	1	2	yes	—
272	C₂²×C₃	#821	1	2	yes	—
273	C₂²×C₃	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
274	C₂²×C₃	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
275	C₃×C₄	—	2	2	no	—
276	C₃×C₄	—	2	2	no	—
277	C₃×C₄	—	2	1	no	—
278	C₃×C₄	—	2	1	no	—
279	C₃×C₄	—	2	1	no	—
280	C₃×C₄	—	2	1	no	—
281	C₃×C₄	—	2	2	no	—
282	C₃×C₄	—	2	2	no	—
283	C₃×C₄	—	2	1	no	—
284	C₃×C₄	—	2	2	no	—
285	C₃×C₄	—	2	1	no	—
286	C₃×C₄	#809	1	2	yes	—
287	C₃×C₄	#821	1	2	yes	—
288	C₃×C₄	#824	1	2	yes	—
289	C₃×C₄	#824	1	2	yes	—
290	C₃×C₄	C₂×#204	1	1	yes	characteristic
291	C₃×C₄	C₂×D₂₄	1	1	yes	characteristic
292	C₃×C₄	#909	1	2	yes	—
293	C₃×C₄	C₂×#213	1	1	yes	characteristic
294	C₃×C₄	C₂×#215	1	1	yes	characteristic
295	C₃×C₄	#951	1	2	yes	—
296	Dic₃	—	12	8	no	—
297	Dic₃	—	12	4	no	—
298	Dic₃	—	12	4	no	—
299	C₃²	#1546	1	1	yes	characteristic, complemented, Sylow
300	C₂³	#3722	1	1	yes	characteristic
301	Q₈	—	36	4	no	—
302	Q₈	—	36	2	no	—
303	Q₈	—	36	2	no	—
304	C₂×C₄	—	2	2	no	—
305	C₂×C₄	—	2	2	no	—
306	C₂×C₄	—	18	4	no	—
307	C₂×C₄	—	36	4	no	—
308	C₂×C₄	#3714	1	2	yes	—
309	C₂×C₄	#3717	1	2	yes	—
310	C₂×C₄	#3722	1	1	yes	characteristic
311	C₂×C₄	#3722	1	1	yes	characteristic
312	C₂×C₄	#3722	1	1	yes	characteristic
313	C₂×C₄	C₂×#624	1	1	yes	characteristic
314	C₂×C₄	C₂×#626	1	1	yes	characteristic
315	C₂×C₄	C₂×#626	1	1	yes	characteristic
316	C₈	—	12	2	no	—
317	C₈	—	12	2	no	—
318	C₂×C₃	—	2	4	no	—
319	C₂×C₃	—	2	2	no	—
320	C₂×C₃	—	2	2	no	—
321	C₂×C₃	—	2	1	no	—
322	C₂×C₃	—	2	1	no	—
323	C₂×C₃	—	2	1	no	—
324	C₂×C₃	C₂×#809	1	1	yes	characteristic
325	C₂×C₃	#5004	1	1	yes	characteristic
326	C₂×C₃	C₂×#821	1	1	yes	characteristic
327	C₂×C₃	#5120	1	1	yes	characteristic
328	C₂×C₃	C₂×#824	1	1	yes	characteristic
329	C₂×C₃	C₂×#824	1	1	yes	characteristic
330	C₂²	—	2	1	no	—
331	C₂²	—	2	1	no	—
332	C₂²	#63564	1	2	yes	—
333	C₂²	C₂×#3722	1	1	yes	characteristic
334	C₄	—	2	1	no	—
335	C₄	—	2	1	no	—
336	C₄	—	36	4	no	—
337	C₄	#63561	1	2	yes	—
338	C₄	#63564	1	2	yes	—
339	C₄	C₂×#3714	1	1	yes	characteristic
340	C₄	#63831	1	2	yes	—
341	C₄	C₂×#3717	1	1	yes	characteristic
342	C₃	—	2	1	no	—
343	C₃	#70506	1	1	yes	characteristic, complemented
344	C₃	#70778	1	1	yes	characteristic, complemented
345	C₂	—	2	2	no	—
346	C₂	C₂×#63561	1	1	yes	characteristic
347	C₂	C₂×#63564	1	1	yes	characteristic
348	C₂	#10591107	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#3722
commutator	C₂×C₃²×C₄	C₂²×C₄
Frattini	C₄²	C₂×D₃²
Fitting	C₂×C₃²×C₄²	C₂²
socle	C₂²×C₃²	C₂×C₂²⋊C₄
prime radical	C₂³×C₃²	C₂²⋊C₄
cosocle	C₃²×C₄²	C₂³
hypercenter	C₂×C₄²	D₃²
hypocenter	C₃²	#1546
LCS	G ▷ C₂×C₃²×C₄ ▷ C₂²×C₃² ▷ C₃²
UCS	C₁ ◁ C₂² ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
4. #10589094	C₂	semidirect
299. C₃²	#1546	semidirect
343. C₃	#70506	semidirect
344. C₃	#70778	semidirect

Maximal subgroups

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

subgroup	index
C₂×#64078	2
C₃×#4925	2
C₃×#4924	2
#10589094	2
#70778	3
#70506	3