Subgroups — #26033069

Order 11392.

350 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19152331	C₂	1	1	yes	maximal, characteristic
2	#19152328	C₂	1	1	yes	maximal, characteristic, complemented
3	#19151960	C₂	1	1	yes	maximal, characteristic, complemented
4	#19151956	C₂	1	1	yes	maximal, characteristic, complemented
5	#19151943	C₂	1	1	yes	maximal, characteristic
6	#19151892	C₂	1	1	yes	maximal, characteristic, complemented
7	#19151877	C₂	1	1	yes	maximal, characteristic, complemented
8	#19151821	C₂	1	1	yes	maximal, characteristic, complemented
9	#19151819	C₂	1	1	yes	maximal, characteristic, complemented
10	#19151797	C₂	1	1	yes	maximal, characteristic
11	#19151727	C₂	1	1	yes	maximal, characteristic, complemented
12	#19151698	C₂	1	1	yes	maximal, characteristic, complemented
13	#19151697	C₂	1	1	yes	maximal, characteristic, complemented
14	#19151692	C₂	1	1	yes	maximal, characteristic, complemented
15	#474×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×Dic₃₅₆	C₂²	1	1	yes	characteristic
17	C₂×#13083563	C₂²	1	1	yes	characteristic
18	C₂×#13083562	C₂²	1	1	yes	characteristic
19	#15668011	—	2	1	no	—
20	#15668011	C₂²	1	1	yes	characteristic
21	#15668011	C₂²	1	1	yes	characteristic
22	#15668010	—	2	1	no	—
23	#15668010	—	2	1	no	—
24	#15668008	C₂²	1	1	yes	characteristic
25	#15668000	C₂²	1	1	yes	characteristic
26	#15667999	C₂²	1	1	yes	characteristic
27	#15667998	—	2	1	no	—
28	#15667995	—	2	1	no	—
29	#15667994	—	2	1	no	—
30	C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic
31	C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic
32	#15667977	—	2	1	no	—
33	#15667977	C₂²	1	1	yes	characteristic
34	#15667977	C₂²	1	1	yes	characteristic
35	#15667977	C₂²	1	1	yes	characteristic
36	#15667974	C₂²	1	1	yes	characteristic
37	C₄×C₂²⋊D₈₉	—	2	1	no	—
38	#15667945	C₂²	1	1	yes	characteristic
39	#15667941	C₂²	1	1	yes	characteristic
40	#15667941	C₂²	1	1	yes	characteristic
41	#15667937	C₂²	1	1	yes	characteristic
42	#15667935	C₂²	1	1	yes	characteristic
43	#15667935	C₂²	1	1	yes	characteristic
44	#15667935	C₂²	1	1	yes	characteristic
45	#15667934	C₂²	1	1	yes	characteristic
46	#15667933	C₂²	1	1	yes	characteristic
47	#15667932	C₂²	1	1	yes	characteristic
48	#15667932	C₂²	1	1	yes	characteristic
49	#15667923	C₂²	1	1	yes	characteristic
50	#15667922	C₂²	1	1	yes	characteristic
51	C₈×Dic₈₉	C₂²	1	1	yes	characteristic
52	C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
53	C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
54	#107×C₈₉	C₂²	1	1	yes	characteristic
55	#107×C₈₉	C₂²	1	1	yes	characteristic
56	C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
57	#102×C₈₉	C₂²	1	1	yes	characteristic
58	#102×C₈₉	C₂²	1	1	yes	characteristic
59	C₂×Dic₁₇₈	—	2	1	no	—
60	C₂×Dic₁₇₈	—	2	1	no	—
61	C₂×Dic₁₇₈	D₄	1	1	yes	characteristic
62	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
63	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
64	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
65	C₂×C₂²⋊D₈₉	—	2	1	no	—
66	C₂×C₂²⋊D₈₉	—	2	1	no	—
67	C₂×C₄×D₈₉	—	2	1	no	—
68	Dic₃₅₆	—	2	2	no	—
69	#13083563	—	2	2	no	—
70	#13083562	—	2	2	no	—
71	C₂×#10623494	C₂³	1	1	yes	characteristic
72	C₂×#10623494	C₂³	1	1	yes	characteristic
73	C₄⋊Dic₈₉	D₄	1	1	yes	characteristic
74	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
75	#13083553	—	2	1	no	—
76	#13083553	—	2	1	no	—
77	#13083553	—	2	1	no	—
78	#13083553	—	2	1	no	—
79	#13083553	—	2	1	no	—
80	#13083553	—	2	1	no	—
81	#13083553	D₄	1	1	yes	characteristic
82	#13083553	D₄	1	1	yes	characteristic
83	C₂²⋊Dic₈₉	—	2	1	no	—
84	C₂²⋊Dic₈₉	—	2	1	no	—
85	#13083551	—	2	1	no	—
86	#13083551	—	2	1	no	—
87	#13083551	—	2	1	no	—
88	C₄×Dic₈₉	—	2	1	no	—
89	C₄×Dic₈₉	—	2	1	no	—
90	C₄×Dic₈₉	—	2	1	no	—
91	C₄×Dic₈₉	—	2	1	no	—
92	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
93	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
94	C₂×Q₈×C₈₉	—	2	1	no	—
95	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
96	C₂²×C₄×C₈₉	—	2	1	no	—
97	C₂×C₈×C₈₉	C₂³	1	1	yes	characteristic
98	C₂×C₈×C₈₉	C₂³	1	1	yes	characteristic
99	C₄⋊C₄×C₈₉	—	2	1	no	—
100	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
101	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
102	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
103	C₂²⋊C₄×C₈₉	—	2	1	no	—
104	C₄²×C₈₉	C₂³	1	1	yes	characteristic
105	C₂³×C₈₉	—	2	1	no	—
106	C₂²×D₈₉	—	2	1	no	—
107	Q₈×C₈₉	—	8	1	no	—
108	D₄×C₈₉	—	2	1	no	—
109	D₄×C₈₉	—	2	1	no	—
110	C₂×C₄×C₈₉	—	2	1	no	—
111	C₂×C₄×C₈₉	—	2	1	no	—
112	C₂×C₄×C₈₉	—	2	1	no	—
113	C₂×C₄×C₈₉	—	8	1	no	—
114	C₂×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
115	C₂×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
116	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
117	C₂²⋊D₈₉	—	4	2	no	—
118	C₂²⋊D₈₉	—	8	1	no	—
119	C₂×Dic₈₉	—	2	1	no	—
120	C₂×Dic₈₉	—	2	1	no	—
121	C₂×Dic₈₉	—	2	1	no	—
122	C₂×Dic₈₉	C₂×D₄	1	1	yes	characteristic
123	C₂×Dic₈₉	C₂×D₄	1	1	yes	characteristic
124	C₂×Dic₈₉	C₂×D₄	1	1	yes	characteristic
125	C₂×Dic₈₉	C₂×D₄	1	1	yes	characteristic
126	D₃₅₆	—	2	1	no	—
127	D₃₅₆	—	2	1	no	—
128	C₄×D₈₉	—	8	1	no	—
129	Dic₁₇₈	—	2	1	no	—
130	Dic₁₇₈	—	2	2	no	—
131	Dic₁₇₈	—	2	1	no	—
132	Dic₁₇₈	—	2	1	no	—
133	Dic₁₇₈	—	8	1	no	—
134	Dic₁₇₈	—	8	1	no	—
135	Dic₁₇₈	#41	1	2	yes	—
136	C₈×C₈₉	—	2	1	no	—
137	C₈×C₈₉	—	2	1	no	—
138	#10623494	—	2	1	no	—
139	#10623494	—	2	1	no	—
140	C₂²×C₈₉	—	4	1	no	—
141	C₂²×C₈₉	—	4	1	no	—
142	C₂²×C₈₉	—	4	1	no	—
143	C₂²×C₈₉	C₂²×D₄	1	1	yes	characteristic
144	C₂×D₈₉	—	4	1	no	—
145	C₂×D₈₉	—	4	1	no	—
146	C₂×D₈₉	—	4	1	no	—
147	C₄×C₈₉	—	2	1	no	—
148	C₄×C₈₉	—	2	1	no	—
149	C₄×C₈₉	—	4	1	no	—
150	C₄×C₈₉	—	4	1	no	—
151	C₄×C₈₉	—	4	1	no	—
152	C₄×C₈₉	C₂×#41	1	1	yes	characteristic
153	C₄×C₈₉	2₋¹⁺⁴	1	1	yes	characteristic
154	Dic₈₉	—	2	2	no	—
155	Dic₈₉	—	2	1	no	—
156	Dic₈₉	—	2	1	no	—
157	Dic₈₉	—	2	1	no	—
158	Dic₈₉	—	4	1	no	—
159	Dic₈₉	—	4	1	no	—
160	Dic₈₉	#137	1	2	yes	—
161	C₂×C₈₉	—	8	1	no	—
162	C₂×C₈₉	#548	1	1	yes	characteristic
163	C₂×C₈₉	C₂×#137	1	1	yes	characteristic
164	C₂×C₈₉	#576	1	1	yes	characteristic
165	D₈₉	—	8	1	no	—
166	#3375	—	89	1	no	maximal, Sylow
167	C₈₉	#3375	1	1	yes	characteristic, complemented, Sylow
168	#559	—	89	1	no	—
169	Q₈²	—	89	1	no	—
170	#489	—	89	1	no	—
171	#489	—	89	1	no	—
172	#486	—	89	1	no	—
173	#477	—	89	1	no	—
174	#474	—	89	1	no	—
175	#474	D₈₉	1	1	yes	characteristic, complemented
176	#464	—	89	1	no	—
177	#464	—	89	1	no	—
178	#460	—	89	1	no	—
179	#446	—	89	1	no	—
180	#440	—	89	1	no	—
181	#440	—	89	1	no	—
182	C₄×Q₁₆	—	89	1	no	—
183	C₂×Q₁₆	—	89	1	no	—
184	C₂×SD₁₆	—	89	1	no	—
185	C₂×SD₁₆	—	89	1	no	—
186	C₄⋊Q₈	—	89	1	no	—
187	C₄⋊Q₈	—	89	1	no	—
188	C₄⋊Q₈	—	178	1	no	—
189	C₄⋊Q₈	—	178	1	no	—
190	C₄⋊Q₈	—	178	1	no	—
191	C₄⋊Q₈	C₂×D₈₉	1	1	yes	characteristic
192	#127	—	89	1	no	—
193	#124	—	89	1	no	—
194	#124	—	89	1	no	—
195	#124	—	178	1	no	—
196	#123	—	178	1	no	—
197	#123	—	178	1	no	—
198	C₄×Q₈	—	89	1	no	—
199	C₄×Q₈	—	89	1	no	—
200	C₄×Q₈	—	89	1	no	—
201	C₄×Q₈	—	89	1	no	—
202	C₄×Q₈	—	89	1	no	—
203	C₄×Q₈	—	178	1	no	—
204	C₄×D₄	—	89	1	no	—
205	C₄×D₄	—	178	1	no	—
206	C₄×D₄	C₂×D₈₉	1	1	yes	characteristic
207	#107	—	89	1	no	—
208	#107	C₂×D₈₉	1	1	yes	characteristic
209	#107	C₂×D₈₉	1	1	yes	characteristic
210	C₄⋊C₈	—	89	1	no	—
211	C₄⋊C₈	—	89	1	no	—
212	C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
213	#103	—	89	1	no	—
214	#103	—	89	1	no	—
215	#103	—	89	1	no	—
216	#103	—	89	1	no	—
217	#102	—	89	1	no	—
218	#102	—	89	1	no	—
219	#102	—	89	1	no	—
220	#102	—	89	1	no	—
221	#102	C₂×D₈₉	1	1	yes	characteristic
222	#102	C₂×D₈₉	1	1	yes	characteristic
223	#97	—	89	1	no	—
224	#97	—	89	1	no	—
225	C₄×C₈	—	89	1	no	—
226	C₂×Q₈	—	2	1	no	—
227	C₂×Q₈	—	89	1	no	—
228	C₂×Q₈	—	89	1	no	—
229	C₂×Q₈	—	89	1	no	—
230	C₂×Q₈	—	178	1	no	—
231	C₂×Q₈	—	178	1	no	—
232	C₂×D₄	—	89	1	no	—
233	C₂×D₄	—	178	1	no	—
234	C₂×D₄	—	178	1	no	—
235	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
236	C₂²×C₄	—	2	1	no	—
237	C₂²×C₄	—	178	1	no	—
238	Q₁₆	—	178	2	no	—
239	SD₁₆	—	178	2	no	—
240	SD₁₆	—	178	2	no	—
241	C₂×C₈	—	89	1	no	—
242	C₂×C₈	—	89	1	no	—
243	C₂×C₈	C₂²×D₈₉	1	1	yes	characteristic
244	C₂×C₈	C₂²×D₈₉	1	1	yes	characteristic
245	C₄⋊C₄	—	2	1	no	—
246	C₄⋊C₄	—	89	1	no	—
247	C₄⋊C₄	—	89	1	no	—
248	C₄⋊C₄	—	89	1	no	—
249	C₄⋊C₄	—	89	1	no	—
250	C₄⋊C₄	—	178	1	no	—
251	C₄⋊C₄	—	178	1	no	—
252	C₄⋊C₄	—	178	1	no	—
253	C₄⋊C₄	—	178	1	no	—
254	C₄⋊C₄	—	178	1	no	—
255	C₄⋊C₄	—	178	1	no	—
256	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
257	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
258	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
259	C₂²⋊C₄	—	2	1	no	—
260	C₂²⋊C₄	—	178	1	no	—
261	C₂²⋊C₄	—	178	1	no	—
262	C₂²⋊C₄	—	178	1	no	—
263	C₂²⋊C₄	—	178	1	no	—
264	C₂²⋊C₄	—	178	1	no	—
265	C₄²	—	89	1	no	—
266	C₄²	—	89	1	no	—
267	C₄²	—	178	1	no	—
268	C₄²	—	178	1	no	—
269	C₄²	—	178	1	no	—
270	C₄²	—	178	1	no	—
271	C₄²	C₂²×D₈₉	1	1	yes	characteristic
272	C₂³	—	2	1	no	—
273	C₂³	—	178	1	no	—
274	Q₈	—	8	1	no	—
275	Q₈	—	89	2	no	—
276	Q₈	—	178	2	no	—
277	Q₈	—	178	1	no	—
278	Q₈	—	178	1	no	—
279	Q₈	—	178	1	no	—
280	Q₈	—	712	1	no	—
281	Q₈	—	712	1	no	—
282	D₄	—	2	1	no	—
283	D₄	—	2	1	no	—
284	D₄	—	356	2	no	—
285	D₄	—	178	1	no	—
286	D₄	—	178	1	no	—
287	D₄	—	712	1	no	—
288	C₂×C₄	—	2	1	no	—
289	C₂×C₄	—	2	1	no	—
290	C₂×C₄	—	2	1	no	—
291	C₂×C₄	—	8	1	no	—
292	C₂×C₄	—	89	1	no	—
293	C₂×C₄	—	89	1	no	—
294	C₂×C₄	—	89	1	no	—
295	C₂×C₄	—	89	1	no	—
296	C₂×C₄	—	178	1	no	—
297	C₂×C₄	—	178	1	no	—
298	C₂×C₄	—	178	1	no	—
299	C₂×C₄	—	712	1	no	—
300	C₂×C₄	D₄×D₈₉	1	1	yes	characteristic
301	C₂×C₄	D₄×D₈₉	1	1	yes	characteristic
302	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
303	C₈	—	2	1	no	—
304	C₈	—	2	1	no	—
305	C₈	—	178	1	no	—
306	C₈	—	178	1	no	—
307	C₂²	—	4	1	no	—
308	C₂²	—	4	1	no	—
309	C₂²	—	4	1	no	—
310	C₂²	—	356	1	no	—
311	C₂²	—	356	1	no	—
312	C₂²	—	356	1	no	—
313	C₂²	C₂×D₄×D₈₉	1	1	yes	characteristic
314	C₄	—	2	1	no	—
315	C₄	—	2	1	no	—
316	C₄	—	4	1	no	—
317	C₄	—	4	1	no	—
318	C₄	—	4	1	no	—
319	C₄	—	89	2	no	—
320	C₄	—	356	1	no	—
321	C₄	—	356	1	no	—
322	C₄	—	178	1	no	—
323	C₄	—	178	1	no	—
324	C₄	—	178	1	no	—
325	C₄	—	178	2	no	—
326	C₄	#41×D₈₉	1	1	yes	characteristic
327	C₄	#15668060	1	1	yes	characteristic
328	C₂	—	8	1	no	—
329	C₂	—	712	1	no	—
330	C₂	#19152258	1	1	yes	characteristic
331	C₂	#137×D₈₉	1	1	yes	characteristic
332	C₂	#19152399	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₈₉
commutator, cosocle	C₂×C₄×C₈₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₈₉
Fitting	#474×C₈₉	C₂
socle	C₂²×C₈₉	C₂²×D₄
prime radical	#15668008	C₂²
hypercenter	#474	D₈₉
hypocenter	C₈₉	#3375
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #474

Complements

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

N	H ≅ G/N	type
2. #19152328	C₂	semidirect
3. #19151960	C₂	semidirect
4. #19151956	C₂	semidirect
6. #19151892	C₂	semidirect
7. #19151877	C₂	semidirect
8. #19151821	C₂	semidirect
9. #19151819	C₂	semidirect
11. #19151727	C₂	semidirect
12. #19151698	C₂	semidirect
13. #19151697	C₂	semidirect
14. #19151692	C₂	semidirect
15. #474×C₈₉	C₂	semidirect
167. C₈₉	#3375	semidirect
175. #474	D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#19152331	2
#19152328	2
#19151960	2
#19151956	2
#19151943	2
#19151892	2
#19151877	2
#19151821	2
#19151819	2
#19151797	2
#19151727	2
#19151698	2
#19151697	2
#19151692	2
#474×C₈₉	2
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