Subgroups — #11878933

Order 1152.

591 conjugacy classes of subgroups.

The subgroup lattice has 339 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×#533	C₂	1	1	yes	maximal, characteristic, complemented
2	#10589579	C₂	1	1	yes	maximal, characteristic
3	#10588773	C₂	1	1	yes	maximal, characteristic, complemented
4	#10588770	C₂	1	1	yes	maximal, characteristic, complemented
5	#10588766	C₂	1	1	yes	maximal, characteristic, complemented
6	#10588765	C₂	1	1	yes	maximal, characteristic, complemented
7	#10588730	C₂	1	4	yes	maximal, complemented
8	#10588711	C₂	1	4	yes	maximal, complemented
9	#10588605	C₂	1	1	yes	maximal, characteristic, complemented
10	#83356	—	3	1	no	maximal
11	C₂×#3697	C₂²	1	2	yes	—
12	C₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₉×#125	—	2	1	no	—
15	C₉×C₂²⋊Q₈	—	2	1	no	—
16	C₉×C₂²⋊Q₈	C₂²	1	2	yes	—
17	C₄×Q₈×C₉	—	2	1	no	—
18	C₄×Q₈×C₉	C₂²	1	2	yes	—
19	C₉×#117	—	2	1	no	—
20	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
21	C₂×#3675	C₂²	1	4	yes	—
22	C₂×#3674	C₂²	1	4	yes	—
23	#63492	—	2	1	no	—
24	#63492	—	2	1	no	—
25	#63437	C₂²	1	2	yes	—
26	#63436	C₂²	1	1	yes	characteristic
27	C₄×D₃₆	—	2	1	no	—
28	C₄×D₃₆	—	2	1	no	—
29	#63431	C₂²	1	1	yes	characteristic
30	#63389	C₂²	1	2	yes	—
31	#63369	C₂²	1	4	yes	—
32	#63368	C₂²	1	4	yes	—
33	C₄⋊(C₉⋊C₈)	C₂²	1	2	yes	—
34	C₄×C₉⋊C₈	C₂²	1	1	yes	characteristic
35	C₄×C₉⋊C₈	C₂²	1	1	yes	characteristic
36	C₃×#533	D₃	1	1	yes	characteristic
37	#5477	—	3	1	no	—
38	#5093	—	3	1	no	—
39	#5092	—	3	1	no	—
40	#5088	—	3	1	no	—
41	#5085	—	3	1	no	—
42	#5047	—	3	4	no	—
43	#5028	—	3	4	no	—
44	#4925	—	3	1	no	—
45	C₂×Q₈×C₉	—	2	1	no	—
46	C₂×Q₈×C₉	C₂³	1	2	yes	—
47	C₂²×C₄×C₉	D₄	1	1	yes	characteristic
48	C₂²×C₄×C₉	D₄	1	1	yes	characteristic
49	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
50	C₂×#611	—	2	2	no	—
51	#3697	—	4	4	no	—
52	C₂×D₃₆	—	2	1	no	—
53	C₂×D₃₆	—	2	1	no	—
54	C₂×D₃₆	C₂³	1	2	yes	—
55	C₂×C₄×D₉	—	2	2	no	—
56	C₂×Dic₁₈	C₂³	1	2	yes	—
57	C₉×C₄⋊C₄	—	2	1	no	—
58	C₉×C₄⋊C₄	—	2	1	no	—
59	C₉×C₄⋊C₄	—	2	1	no	—
60	C₉×C₄⋊C₄	—	2	2	no	—
61	C₉×C₄⋊C₄	—	2	2	no	—
62	C₉×C₄⋊C₄	C₂³	1	2	yes	—
63	C₉×C₂²⋊C₄	—	2	2	no	—
64	C₄²×C₉	—	2	2	no	—
65	C₄²×C₉	D₄	1	1	yes	characteristic
66	C₄²×C₉	D₄	1	1	yes	characteristic
67	C₄²×C₉	C₂³	1	1	yes	characteristic
68	C₄²×C₉	C₂³	1	1	yes	characteristic
69	#3675	—	4	4	no	—
70	#3674	—	4	4	no	—
71	(C₂×D₉)⋊C₄	—	2	2	no	—
72	(C₂×D₉)⋊C₄	—	2	2	no	—
73	C₄⋊Dic₉	—	2	1	no	—
74	C₄⋊Dic₉	—	2	1	no	—
75	C₂×C₉⋊C₈	C₂³	1	2	yes	—
76	C₂×C₉⋊C₈	C₂³	1	2	yes	—
77	#3210	—	9	1	no	Sylow
78	C₂×#235	—	3	2	no	—
79	C₃×C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic
80	C₃×C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic
81	C₃×#125	—	2	1	no	—
82	C₃×C₂²⋊Q₈	—	2	1	no	—
83	C₃×C₂²⋊Q₈	C₂×D₃	1	2	yes	—
84	C₃×C₄×Q₈	—	2	1	no	—
85	C₃×C₄×Q₈	C₂×D₃	1	2	yes	—
86	C₃×#117	—	2	1	no	—
87	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
88	C₂×#216	—	3	4	no	—
89	C₂×#215	—	3	4	no	—
90	#930	—	6	1	no	—
91	#930	—	6	1	no	—
92	#875	—	3	2	no	—
93	#874	—	3	1	no	—
94	C₄×D₁₂	—	6	1	no	—
95	C₄×D₁₂	—	6	1	no	—
96	#869	—	3	1	no	—
97	#830	—	3	2	no	—
98	#810	—	3	4	no	—
99	#809	—	3	4	no	—
100	C₄⋊(C₃⋊C₈)	—	3	2	no	—
101	C₄×C₃⋊C₈	—	3	1	no	—
102	C₄×C₃⋊C₈	—	3	1	no	—
103	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
104	C₂²×D₉	—	2	2	no	—
105	Q₈×C₉	—	2	4	no	—
106	Q₈×C₉	—	4	2	no	—
107	C₂×C₄×C₉	—	2	2	no	—
108	C₂×C₄×C₉	—	2	2	no	—
109	C₂×C₄×C₉	—	2	2	no	—
110	C₂×C₄×C₉	—	2	2	no	—
111	C₂×C₄×C₉	—	2	2	no	—
112	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
113	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
114	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
115	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
116	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
117	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
118	#611	—	4	4	no	—
119	C₂×Dic₉	—	2	2	no	—
120	D₃₆	—	2	4	no	—
121	D₃₆	—	4	2	no	—
122	D₃₆	—	4	2	no	—
123	C₄×D₉	—	4	4	no	—
124	Dic₁₈	—	2	4	no	—
125	C₉⋊C₈	—	2	2	no	—
126	C₉⋊C₈	—	2	2	no	—
127	#533	D₉	1	1	yes	characteristic, complemented
128	#532	—	9	1	no	—
129	#494	—	9	1	no	—
130	#492	—	9	1	no	—
131	#487	—	9	1	no	—
132	#486	—	9	1	no	—
133	#464	—	9	4	no	—
134	#452	—	9	4	no	—
135	#431	—	9	1	no	—
136	C₂×C₃×Q₈	—	2	1	no	—
137	C₂×C₃×Q₈	C₂²×D₃	1	2	yes	—
138	C₂²×C₃×C₄	#67	1	1	yes	characteristic
139	C₂²×C₃×C₄	#67	1	1	yes	characteristic
140	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
141	C₂×#67	—	6	2	no	—
142	#235	—	12	4	no	—
143	C₂×D₁₂	—	3	2	no	—
144	C₂×D₁₂	—	6	1	no	—
145	C₂×D₁₂	—	6	1	no	—
146	C₂×C₄×D₃	—	6	2	no	—
147	C₂×Dic₆	—	3	2	no	—
148	C₃×C₄⋊C₄	—	2	1	no	—
149	C₃×C₄⋊C₄	—	2	1	no	—
150	C₃×C₄⋊C₄	—	2	1	no	—
151	C₃×C₄⋊C₄	—	2	2	no	—
152	C₃×C₄⋊C₄	—	2	2	no	—
153	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
154	C₃×C₂²⋊C₄	—	2	2	no	—
155	C₃×C₄²	—	2	2	no	—
156	C₃×C₄²	#67	1	1	yes	characteristic
157	C₃×C₄²	#67	1	1	yes	characteristic
158	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
159	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
160	#216	—	12	4	no	—
161	#215	—	12	4	no	—
162	(C₂×D₃)⋊C₄	—	6	2	no	—
163	(C₂×D₃)⋊C₄	—	6	2	no	—
164	C₄⋊Dic₃	—	6	1	no	—
165	C₄⋊Dic₃	—	6	1	no	—
166	C₂×C₃⋊C₈	—	3	2	no	—
167	C₂×C₃⋊C₈	—	3	2	no	—
168	C₂²×C₉	—	2	1	no	—
169	C₂²×C₉	—	2	1	no	—
170	C₂²×C₉	—	2	1	no	—
171	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
172	C₂×D₉	—	4	2	no	—
173	C₂×D₉	—	4	2	no	—
174	C₂×D₉	—	4	2	no	—
175	C₄×C₉	—	2	1	no	—
176	C₄×C₉	—	2	1	no	—
177	C₄×C₉	—	2	1	no	—
178	C₄×C₉	—	4	2	no	—
179	C₄×C₉	—	4	2	no	—
180	C₄×C₉	#135	1	2	yes	—
181	C₄×C₉	#137	1	2	yes	—
182	C₄×C₉	H(5,𝔽₂)	1	2	yes	—
183	Dic₉	—	4	2	no	—
184	C₂×#41	—	9	2	no	—
185	C₂×Q₁₆	—	9	4	no	—
186	C₂×SD₁₆	—	9	4	no	—
187	C₄⋊Q₈	—	9	1	no	—
188	C₄⋊Q₈	C₂×D₉	1	1	yes	characteristic
189	C₄⋊Q₈	C₂×D₉	1	1	yes	characteristic
190	#127	—	9	1	no	—
191	#125	—	2	1	no	—
192	#124	—	9	2	no	—
193	C₂²⋊Q₈	—	2	1	no	—
194	C₂²⋊Q₈	C₂×D₉	1	2	yes	—
195	#121	—	18	1	no	—
196	#121	—	18	1	no	—
197	C₄×Q₈	—	2	1	no	—
198	C₄×Q₈	C₂×D₉	1	2	yes	—
199	C₄×D₄	—	18	1	no	—
200	C₄×D₄	—	18	1	no	—
201	#117	—	2	1	no	—
202	C₂×C₄²	C₂×D₉	1	1	yes	characteristic
203	C₄⋊C₈	—	9	2	no	—
204	#103	—	9	4	no	—
205	#102	—	9	4	no	—
206	C₂²⋊C₈	—	9	2	no	—
207	C₄×C₈	—	9	1	no	—
208	C₄×C₈	—	9	1	no	—
209	C₂³×C₃	C₂×#67	1	1	yes	characteristic
210	C₂²×D₃	—	6	2	no	—
211	C₃×Q₈	—	2	4	no	—
212	C₃×Q₈	—	4	2	no	—
213	C₂×C₃×C₄	—	2	2	no	—
214	C₂×C₃×C₄	—	2	2	no	—
215	C₂×C₃×C₄	—	2	2	no	—
216	C₂×C₃×C₄	—	2	2	no	—
217	C₂×C₃×C₄	—	2	2	no	—
218	C₂×C₃×C₄	C₂×#67	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×C₃×C₄	C₂×#67	1	1	yes	characteristic
222	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
223	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
224	#67	—	12	4	no	—
225	C₂×Dic₃	—	6	2	no	—
226	D₁₂	—	6	4	no	—
227	D₁₂	—	12	2	no	—
228	D₁₂	—	12	2	no	—
229	C₄×D₃	—	12	4	no	—
230	Dic₆	—	6	4	no	—
231	C₃⋊C₈	—	6	2	no	—
232	C₃⋊C₈	—	6	2	no	—
233	C₂×C₉	—	4	1	no	—
234	C₂×C₉	#535	1	1	yes	characteristic
235	C₂×C₉	C₂×#135	1	1	yes	characteristic
236	C₂×C₉	C₂×#137	1	1	yes	characteristic
237	D₉	—	8	2	no	—
238	#41	—	36	4	no	—
239	C₂×Q₈	—	2	1	no	—
240	C₂×Q₈	—	9	2	no	—
241	C₂×Q₈	C₂²×D₉	1	2	yes	—
242	C₂×D₄	—	9	2	no	—
243	C₂×D₄	—	18	2	no	—
244	C₂×D₄	—	18	1	no	—
245	C₂×D₄	—	18	1	no	—
246	C₂²×C₄	—	18	2	no	—
247	C₂²×C₄	#611	1	1	yes	characteristic
248	C₂²×C₄	#611	1	1	yes	characteristic
249	C₂²×C₄	C₂²×D₉	1	1	yes	characteristic
250	Q₁₆	—	36	4	no	—
251	SD₁₆	—	36	4	no	—
252	C₂×C₈	—	9	2	no	—
253	C₂×C₈	—	9	2	no	—
254	C₄⋊C₄	—	2	1	no	—
255	C₄⋊C₄	—	2	1	no	—
256	C₄⋊C₄	—	2	1	no	—
257	C₄⋊C₄	—	2	2	no	—
258	C₄⋊C₄	—	2	2	no	—
259	C₄⋊C₄	—	18	1	no	—
260	C₄⋊C₄	—	18	1	no	—
261	C₄⋊C₄	C₂²×D₉	1	2	yes	—
262	C₂²⋊C₄	—	2	2	no	—
263	C₂²⋊C₄	—	18	2	no	—
264	C₂²⋊C₄	—	18	2	no	—
265	C₄²	—	2	2	no	—
266	C₄²	#611	1	1	yes	characteristic
267	C₄²	#611	1	1	yes	characteristic
268	C₄²	C₂²×D₉	1	1	yes	characteristic
269	C₄²	C₂²×D₉	1	1	yes	characteristic
270	C₂²×C₃	—	2	1	no	—
271	C₂²×C₃	—	2	1	no	—
272	C₂²×C₃	—	2	1	no	—
273	C₂²×C₃	C₂²×#67	1	1	yes	characteristic
274	C₂×D₃	—	12	2	no	—
275	C₂×D₃	—	12	2	no	—
276	C₂×D₃	—	12	2	no	—
277	C₃×C₄	—	2	1	no	—
278	C₃×C₄	—	2	1	no	—
279	C₃×C₄	—	2	1	no	—
280	C₃×C₄	—	4	2	no	—
281	C₃×C₄	—	4	2	no	—
282	C₃×C₄	#942	1	2	yes	—
283	C₃×C₄	#950	1	2	yes	—
284	C₃×C₄	#1009	1	2	yes	—
285	Dic₃	—	12	2	no	—
286	C₉	#3210	1	1	yes	characteristic, complemented, Sylow
287	C₂³	—	18	2	no	—
288	C₂³	C₂×#611	1	1	yes	characteristic
289	Q₈	—	2	4	no	—
290	Q₈	—	4	2	no	—
291	Q₈	—	18	4	no	—
292	D₄	—	18	4	no	—
293	D₄	—	36	4	no	—
294	D₄	—	36	2	no	—
295	D₄	—	36	2	no	—
296	C₂×C₄	—	2	2	no	—
297	C₂×C₄	—	2	2	no	—
298	C₂×C₄	—	2	2	no	—
299	C₂×C₄	—	2	2	no	—
300	C₂×C₄	—	2	2	no	—
301	C₂×C₄	—	18	2	no	—
302	C₂×C₄	—	36	4	no	—
303	C₂×C₄	C₂×#611	1	1	yes	characteristic
304	C₂×C₄	C₂×#611	1	1	yes	characteristic
305	C₂×C₄	C₂×#611	1	1	yes	characteristic
306	C₂×C₄	C₂×#611	1	1	yes	characteristic
307	C₂×C₄	C₂×#611	1	1	yes	characteristic
308	C₂×C₄	C₂³×D₉	1	1	yes	characteristic
309	C₈	—	18	2	no	—
310	C₈	—	18	2	no	—
311	C₂×C₃	—	4	1	no	—
312	C₂×C₃	C₂×#942	1	1	yes	characteristic
313	C₂×C₃	C₂×#950	1	1	yes	characteristic
314	C₂×C₃	#5830	1	1	yes	characteristic
315	D₃	—	24	2	no	—
316	C₂²	—	2	1	no	—
317	C₂²	—	2	1	no	—
318	C₂²	—	2	1	no	—
319	C₂²	—	36	2	no	—
320	C₂²	—	36	2	no	—
321	C₂²	—	36	2	no	—
322	C₂²	C₂²×#611	1	1	yes	characteristic
323	C₄	—	2	1	no	—
324	C₄	—	2	1	no	—
325	C₄	—	2	1	no	—
326	C₄	—	4	2	no	—
327	C₄	—	4	2	no	—
328	C₄	—	36	2	no	—
329	C₄	#63505	1	2	yes	—
330	C₄	#63513	1	2	yes	—
331	C₄	#63715	1	2	yes	—
332	C₃	#83356	1	1	yes	characteristic
333	C₂	—	4	1	no	—
334	C₂	—	72	2	no	—
335	C₂	C₂×#63505	1	1	yes	characteristic
336	C₂	C₂×#63513	1	1	yes	characteristic
337	C₂	#10589932	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×#611
commutator, cosocle	C₂×C₄×C₉	C₂⁴
Frattini	C₂×C₃×C₄	C₂³×D₃
Fitting	C₉×#533	C₂
socle	C₂²×C₃	C₂²×#67
prime radical	#10589579	C₂
hypercenter	#533	D₉
hypocenter	C₉	#3210
LCS	G ▷ C₂×C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #533

Complements

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

N	H ≅ G/N	type
1. C₉×#533	C₂	semidirect
3. #10588773	C₂	semidirect
4. #10588770	C₂	semidirect
5. #10588766	C₂	semidirect
6. #10588765	C₂	semidirect
7. #10588730	C₂	semidirect
8. #10588711	C₂	semidirect
9. #10588605	C₂	semidirect
127. #533	D₉	semidirect
286. C₉	#3210	semidirect

Maximal subgroups

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

subgroup	index
C₉×#533	2
#10589579	2
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