Subgroups — #26030401

Order 11392.

430 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19152145	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×#13083575	C₂	1	1	yes	maximal, characteristic, complemented
3	#19151925	C₂	1	1	yes	maximal, characteristic, complemented
4	#19151921	C₂	1	1	yes	maximal, characteristic, complemented
5	#19151881	C₂	1	1	yes	maximal, characteristic, complemented
6	#19151877	C₂	1	1	yes	maximal, characteristic, complemented
7	#19151796	C₂	1	1	yes	maximal, characteristic, complemented
8	#19151792	C₂	1	1	yes	maximal, characteristic, complemented
9	#19151746	C₂	1	1	yes	maximal, characteristic, complemented
10	#19151742	C₂	1	1	yes	maximal, characteristic, complemented
11	#19151711	C₂	1	1	yes	maximal, characteristic, complemented
12	#19151708	C₂	1	1	yes	maximal, characteristic, complemented
13	#19151696	C₂	1	1	yes	maximal, characteristic, complemented
14	#19151653	C₂	1	1	yes	maximal, characteristic, complemented
15	#440×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#13083575	C₂²	1	1	yes	characteristic
17	C₂×#13083574	—	2	1	no	—
18	C₂×#13083561	C₂²	1	1	yes	characteristic
19	C₂×D₇₁₂	C₂²	1	1	yes	characteristic
20	C₂×#13083559	C₂²	1	1	yes	characteristic
21	#15668011	C₂²	1	1	yes	characteristic
22	#15668008	C₂²	1	1	yes	characteristic
23	#15667998	—	2	1	no	—
24	#15667987	C₂²	1	1	yes	characteristic
25	#15667985	—	2	1	no	—
26	#15667983	C₂²	1	1	yes	characteristic
27	Q₈×Dic₈₉	C₂²	1	1	yes	characteristic
28	C₄×D₃₅₆	—	2	1	no	—
29	C₄×D₃₅₆	C₂²	1	1	yes	characteristic
30	C₄×D₃₅₆	C₂²	1	1	yes	characteristic
31	#15667974	—	2	1	no	—
32	#15667974	C₂²	1	1	yes	characteristic
33	C₄×C₂²⋊D₈₉	—	2	1	no	—
34	#15667970	—	2	1	no	—
35	#15667970	C₂²	1	1	yes	characteristic
36	C₄²×D₈₉	—	2	1	no	—
37	C₄²×D₈₉	C₂²	1	1	yes	characteristic
38	#15667945	C₂²	1	1	yes	characteristic
39	#15667944	C₂²	1	1	yes	characteristic
40	#15667943	C₂²	1	1	yes	characteristic
41	#15667941	C₂²	1	1	yes	characteristic
42	#15667941	C₂²	1	1	yes	characteristic
43	#15667936	C₂²	1	1	yes	characteristic
44	#15667934	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	#15667924	C₂²	1	1	yes	characteristic
50	#15667924	C₂²	1	1	yes	characteristic
51	#15667923	C₂²	1	1	yes	characteristic
52	C₂×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
53	C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
54	C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
55	#107×C₈₉	C₂²	1	1	yes	characteristic
56	#103×C₈₉	C₂²	1	1	yes	characteristic
57	#102×C₈₉	C₂²	1	1	yes	characteristic
58	#97×C₈₉	C₂²	1	1	yes	characteristic
59	#13083575	—	2	2	no	—
60	#13083575	—	2	2	no	—
61	#13083574	—	4	4	no	—
62	C₂×Dic₁₇₈	—	2	1	no	—
63	C₂×D₃₅₆	—	2	1	no	—
64	C₂×D₃₅₆	—	2	1	no	—
65	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
66	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
67	C₂×C₂²⋊D₈₉	—	2	1	no	—
68	C₂×C₂²⋊D₈₉	—	2	1	no	—
69	C₂×C₂²⋊D₈₉	—	2	1	no	—
70	C₂×C₄×D₈₉	—	2	1	no	—
71	C₂×C₄×D₈₉	—	2	1	no	—
72	C₂×C₄×D₈₉	—	2	1	no	—
73	C₂×C₄×D₈₉	—	2	1	no	—
74	C₂×C₄×D₈₉	D₄	1	1	yes	characteristic
75	C₂×C₄×D₈₉	D₄	1	1	yes	characteristic
76	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
77	#13083561	—	2	2	no	—
78	D₇₁₂	—	2	2	no	—
79	#13083559	—	2	2	no	—
80	C₂×#10623494	C₂³	1	1	yes	characteristic
81	C₂×#10623494	C₂³	1	1	yes	characteristic
82	C₄⋊Dic₈₉	—	2	1	no	—
83	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
84	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
85	#13083553	—	2	1	no	—
86	C₂²⋊Dic₈₉	—	2	1	no	—
87	#13083551	—	2	1	no	—
88	#13083551	—	2	1	no	—
89	#13083551	—	2	1	no	—
90	#13083551	—	2	1	no	—
91	#13083551	—	2	1	no	—
92	C₄×Dic₈₉	—	2	1	no	—
93	C₄×Dic₈₉	—	2	1	no	—
94	C₄×Dic₈₉	D₄	1	1	yes	characteristic
95	C₄×Dic₈₉	D₄	1	1	yes	characteristic
96	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
97	C₂×Q₈×C₈₉	C₂³	1	1	yes	characteristic
98	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
99	C₂²×C₄×C₈₉	—	2	1	no	—
100	SD₁₆×C₈₉	—	2	2	no	—
101	C₂×C₈×C₈₉	C₂³	1	1	yes	characteristic
102	C₂×C₈×C₈₉	C₂³	1	1	yes	characteristic
103	C₄⋊C₄×C₈₉	—	2	1	no	—
104	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
105	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
106	C₂²⋊C₄×C₈₉	—	2	1	no	—
107	C₄²×C₈₉	—	2	1	no	—
108	C₄²×C₈₉	C₂³	1	1	yes	characteristic
109	C₂³×C₈₉	—	2	1	no	—
110	C₂²×D₈₉	—	2	1	no	—
111	C₂²×D₈₉	—	2	1	no	—
112	C₂²×D₈₉	C₂×D₄	1	1	yes	characteristic
113	Q₈×C₈₉	—	2	1	no	—
114	Q₈×C₈₉	#41	1	2	yes	complemented
115	D₄×C₈₉	—	2	1	no	—
116	D₄×C₈₉	—	2	1	no	—
117	C₂×C₄×C₈₉	—	2	1	no	—
118	C₂×C₄×C₈₉	—	2	1	no	—
119	C₂×C₄×C₈₉	—	2	1	no	—
120	C₂×C₄×C₈₉	—	4	2	no	—
121	C₂×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
122	C₂×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
123	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
124	C₂²⋊D₈₉	—	4	2	no	—
125	C₂²⋊D₈₉	—	4	2	no	—
126	C₂²⋊D₈₉	—	4	2	no	—
127	C₂×Dic₈₉	—	2	1	no	—
128	C₂×Dic₈₉	—	2	1	no	—
129	C₂×Dic₈₉	C₂×D₄	1	1	yes	characteristic
130	C₂×Dic₈₉	C₂×D₄	1	1	yes	characteristic
131	C₂×Dic₈₉	C₂×D₄	1	1	yes	characteristic
132	D₃₅₆	—	2	4	no	—
133	D₃₅₆	—	2	1	no	—
134	D₃₅₆	—	2	1	no	—
135	D₃₅₆	—	2	1	no	—
136	D₃₅₆	—	4	2	no	—
137	D₃₅₆	#41	1	2	yes	complemented
138	C₄×D₈₉	—	2	4	no	—
139	C₄×D₈₉	—	2	1	no	—
140	C₄×D₈₉	—	2	1	no	—
141	C₄×D₈₉	—	2	2	no	—
142	C₄×D₈₉	—	4	1	no	—
143	C₄×D₈₉	—	4	2	no	—
144	C₄×D₈₉	—	4	2	no	—
145	C₄×D₈₉	—	4	2	no	—
146	Dic₁₇₈	—	4	2	no	—
147	C₈×C₈₉	—	2	1	no	—
148	C₈×C₈₉	—	2	1	no	—
149	#10623494	—	2	1	no	—
150	#10623494	—	2	1	no	—
151	C₂²×C₈₉	—	4	1	no	—
152	C₂²×C₈₉	—	4	1	no	—
153	C₂²×C₈₉	—	4	1	no	—
154	C₂²×C₈₉	C₂²×D₄	1	1	yes	characteristic
155	C₂×D₈₉	—	2	1	no	—
156	C₂×D₈₉	—	2	2	no	—
157	C₂×D₈₉	—	2	1	no	—
158	C₂×D₈₉	—	2	1	no	—
159	C₂×D₈₉	—	4	1	no	—
160	C₂×D₈₉	—	4	1	no	—
161	C₂×D₈₉	—	4	1	no	—
162	C₂×D₈₉	—	4	1	no	—
163	C₂×D₈₉	—	4	1	no	—
164	C₄×C₈₉	—	2	2	no	—
165	C₄×C₈₉	—	2	1	no	—
166	C₄×C₈₉	—	2	1	no	—
167	C₄×C₈₉	—	4	1	no	—
168	C₄×C₈₉	—	4	1	no	—
169	C₄×C₈₉	C₂×#41	1	1	yes	characteristic
170	C₄×C₈₉	C₂×#41	1	1	yes	characteristic
171	Dic₈₉	—	2	1	no	—
172	Dic₈₉	—	2	1	no	—
173	Dic₈₉	—	4	1	no	—
174	Dic₈₉	—	4	1	no	—
175	Dic₈₉	AGL(1,ℤ/8)	1	2	yes	—
176	C₂×C₈₉	—	8	1	no	—
177	C₂×C₈₉	#525	1	1	yes	characteristic
178	C₂×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
179	C₂×C₈₉	#575	1	1	yes	characteristic
180	D₈₉	—	4	1	no	—
181	D₈₉	—	4	2	no	—
182	D₈₉	—	8	1	no	—
183	#3115	—	89	1	no	maximal, Sylow
184	C₈₉	#3115	1	1	yes	characteristic, complemented, Sylow
185	#532	—	89	1	no	—
186	C₄×#41	—	89	1	no	—
187	#482	—	89	1	no	—
188	#482	—	89	1	no	—
189	#475	—	89	1	no	—
190	#474	—	89	1	no	—
191	#460	—	89	1	no	—
192	#459	—	89	1	no	—
193	#449	—	89	1	no	—
194	#449	—	89	1	no	—
195	#442	—	89	1	no	—
196	#442	—	89	1	no	—
197	#440	—	89	1	no	—
198	#440	D₈₉	1	1	yes	characteristic, complemented
199	#432	—	89	1	no	—
200	C₂×#41	—	89	1	no	—
201	C₂×#41	—	178	1	no	—
202	C₂×SD₁₆	—	89	1	no	—
203	C₂×SD₁₆	C₂×D₈₉	1	1	yes	characteristic
204	C₂×D₈	—	89	1	no	—
205	C₂×D₈	—	89	1	no	—
206	C₄⋊Q₈	—	89	1	no	—
207	#127	—	89	1	no	—
208	#124	—	178	1	no	—
209	#121	—	89	1	no	—
210	#121	—	89	1	no	—
211	#121	—	178	1	no	—
212	C₄×Q₈	—	89	1	no	—
213	C₄×Q₈	C₂×D₈₉	1	1	yes	characteristic
214	C₄×D₄	—	89	1	no	—
215	C₄×D₄	—	89	1	no	—
216	C₄×D₄	—	89	1	no	—
217	C₄×D₄	—	178	1	no	—
218	C₄×D₄	—	178	1	no	—
219	C₄×D₄	—	178	1	no	—
220	C₄×D₄	C₂×D₈₉	1	1	yes	characteristic
221	#117	—	89	1	no	—
222	#117	—	178	1	no	—
223	C₂×C₄²	—	89	1	no	—
224	C₂×C₄²	—	178	1	no	—
225	#107	—	89	1	no	—
226	#107	C₂×D₈₉	1	1	yes	characteristic
227	#106	—	89	1	no	—
228	#106	—	89	1	no	—
229	C₄⋊C₈	—	89	1	no	—
230	C₄⋊C₈	—	89	1	no	—
231	#103	—	89	1	no	—
232	#103	C₂×D₈₉	1	1	yes	characteristic
233	#102	—	89	1	no	—
234	#102	—	89	1	no	—
235	#102	—	89	1	no	—
236	#102	—	89	1	no	—
237	#102	—	89	1	no	—
238	#102	C₂×D₈₉	1	1	yes	characteristic
239	C₂²⋊C₈	—	89	1	no	—
240	C₂²⋊C₈	—	89	1	no	—
241	#97	—	89	1	no	—
242	#97	C₂×D₈₉	1	1	yes	characteristic
243	#41	—	356	4	no	—
244	#41	—	178	2	no	—
245	#41	—	178	2	no	—
246	C₂×Q₈	—	178	1	no	—
247	C₂×Q₈	C₂²×D₈₉	1	1	yes	characteristic
248	C₂×D₄	—	89	1	no	—
249	C₂×D₄	—	89	1	no	—
250	C₂×D₄	—	178	1	no	—
251	C₂×D₄	—	178	1	no	—
252	C₂×D₄	—	178	1	no	—
253	C₂×D₄	—	178	1	no	—
254	C₂×D₄	—	178	1	no	—
255	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
256	C₂²×C₄	—	2	1	no	—
257	C₂²×C₄	—	89	1	no	—
258	C₂²×C₄	—	89	1	no	—
259	C₂²×C₄	—	89	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	SD₁₆	—	2	2	no	—
265	SD₁₆	—	178	2	no	—
266	D₈	—	178	2	no	—
267	D₈	—	178	2	no	—
268	C₂×C₈	—	89	1	no	—
269	C₂×C₈	—	89	1	no	—
270	C₂×C₈	C₂²×D₈₉	1	1	yes	characteristic
271	C₂×C₈	C₂²×D₈₉	1	1	yes	characteristic
272	C₄⋊C₄	—	2	1	no	—
273	C₄⋊C₄	—	89	1	no	—
274	C₄⋊C₄	—	89	1	no	—
275	C₄⋊C₄	—	178	1	no	—
276	C₄⋊C₄	—	178	1	no	—
277	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
278	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
279	C₂²⋊C₄	—	2	1	no	—
280	C₂²⋊C₄	—	178	1	no	—
281	C₂²⋊C₄	—	178	1	no	—
282	C₂²⋊C₄	—	178	1	no	—
283	C₂²⋊C₄	—	178	1	no	—
284	C₂²⋊C₄	—	178	1	no	—
285	C₂²⋊C₄	—	178	1	no	—
286	C₄²	—	2	1	no	—
287	C₄²	—	89	1	no	—
288	C₄²	—	89	1	no	—
289	C₄²	—	89	1	no	—
290	C₄²	—	178	1	no	—
291	C₄²	—	178	1	no	—
292	C₄²	C₂²×D₈₉	1	1	yes	characteristic
293	C₂³	—	2	1	no	—
294	C₂³	—	89	1	no	—
295	C₂³	—	178	1	no	—
296	C₂³	—	178	1	no	—
297	Q₈	—	2	1	no	—
298	Q₈	—	356	2	no	—
299	Q₈	#13083574	1	2	yes	complemented
300	D₄	—	2	1	no	—
301	D₄	—	2	1	no	—
302	D₄	—	89	2	no	—
303	D₄	—	356	2	no	—
304	D₄	—	356	2	no	—
305	D₄	—	356	2	no	—
306	D₄	—	356	2	no	—
307	D₄	—	178	4	no	—
308	D₄	—	178	1	no	—
309	D₄	—	178	1	no	—
310	D₄	—	178	1	no	—
311	C₂×C₄	—	2	1	no	—
312	C₂×C₄	—	2	1	no	—
313	C₂×C₄	—	2	1	no	—
314	C₂×C₄	—	4	2	no	—
315	C₂×C₄	—	89	1	no	—
316	C₂×C₄	—	89	1	no	—
317	C₂×C₄	—	89	1	no	—
318	C₂×C₄	—	356	2	no	—
319	C₂×C₄	—	356	2	no	—
320	C₂×C₄	—	356	1	no	—
321	C₂×C₄	—	356	2	no	—
322	C₂×C₄	—	178	2	no	—
323	C₂×C₄	—	178	4	no	—
324	C₂×C₄	—	178	1	no	—
325	C₂×C₄	—	178	1	no	—
326	C₂×C₄	—	178	1	no	—
327	C₂×C₄	—	178	1	no	—
328	C₂×C₄	D₄×D₈₉	1	1	yes	characteristic
329	C₂×C₄	D₄×D₈₉	1	1	yes	characteristic
330	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
331	C₈	—	2	1	no	—
332	C₈	—	2	1	no	—
333	C₈	—	178	1	no	—
334	C₈	—	178	1	no	—
335	C₂²	—	4	1	no	—
336	C₂²	—	4	1	no	—
337	C₂²	—	4	1	no	—
338	C₂²	—	356	1	no	—
339	C₂²	—	356	1	no	—
340	C₂²	—	356	1	no	—
341	C₂²	—	356	1	no	—
342	C₂²	—	356	1	no	—
343	C₂²	—	178	1	no	—
344	C₂²	—	178	2	no	—
345	C₂²	—	178	1	no	—
346	C₂²	—	178	1	no	—
347	C₂²	C₂×D₄×D₈₉	1	1	yes	characteristic
348	C₄	—	2	1	no	—
349	C₄	—	2	2	no	—
350	C₄	—	2	1	no	—
351	C₄	—	4	1	no	—
352	C₄	—	4	1	no	—
353	C₄	—	89	2	no	—
354	C₄	—	356	1	no	—
355	C₄	—	356	1	no	—
356	C₄	—	178	1	no	—
357	C₄	—	178	1	no	—
358	C₄	#41×D₈₉	1	1	yes	characteristic
359	C₄	C₂×#13083574	1	1	yes	characteristic
360	C₂	—	8	1	no	—
361	C₂	—	356	2	no	—
362	C₂	—	356	1	no	—
363	C₂	—	712	1	no	—
364	C₂	#19152107	1	1	yes	characteristic
365	C₂	AGL(1,ℤ/8)×D₈₉	1	1	yes	characteristic
366	C₂	#19152397	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₈₉
commutator, cosocle	C₂×C₄×C₈₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₈₉
Fitting	#440×C₈₉	C₂
socle	C₂²×C₈₉	C₂²×D₄
hypercenter	#440	D₈₉
hypocenter	C₈₉	#3115
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #440

Complements

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

N	H ≅ G/N	type
1. #19152145	C₂	semidirect
2. C₄×#13083575	C₂	semidirect
3. #19151925	C₂	semidirect
4. #19151921	C₂	semidirect
5. #19151881	C₂	semidirect
6. #19151877	C₂	semidirect
7. #19151796	C₂	semidirect
8. #19151792	C₂	semidirect
9. #19151746	C₂	semidirect
10. #19151742	C₂	semidirect
11. #19151711	C₂	semidirect
12. #19151708	C₂	semidirect
13. #19151696	C₂	semidirect
14. #19151653	C₂	semidirect
15. #440×C₈₉	C₂	semidirect
114. Q₈×C₈₉	#41	semidirect
137. D₃₅₆	#41	semidirect
184. C₈₉	#3115	semidirect
198. #440	D₈₉	semidirect
299. Q₈	#13083574	semidirect

Maximal subgroups

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

subgroup	index
#19152145	2
C₄×#13083575	2
#19151925	2
#19151921	2
#19151881	2
#19151877	2
#19151796	2
#19151792	2
#19151746	2
#19151742	2
#19151711	2
#19151708	2
#19151696	2
#19151653	2
#440×C₈₉	2
#3115	89