Finite Group Databasebeta

← #26032746

Subgroups — #26032746

Order 11392.

360 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19152313C211yesmaximal, characteristic, complemented
2#19152008C211yesmaximal, characteristic, complemented
3#19151922C211yesmaximal, characteristic, complemented
4#19151919C211yesmaximal, characteristic, complemented
5#19151919C211yesmaximal, characteristic, complemented
6#19151911C211yesmaximal, characteristic, complemented
7#19151895C211yesmaximal, characteristic, complemented
8#19151878C211yesmaximal, characteristic, complemented
9#19151849C211yesmaximal, characteristic, complemented
10#19151832C211yesmaximal, characteristic, complemented
11#19151708C211yesmaximal, characteristic, complemented
12#19151670C211yesmaximal, characteristic, complemented
13#19151638C211yesmaximal, characteristic, complemented
14#19151634C211yesmaximal, characteristic, complemented
15#553×C89C211yesmaximal, characteristic, complemented
16C2×#13083559C2211yescharacteristic
17C2×#13083558C2211yescharacteristic
18C22×#10623494C2211yescharacteristic
19#15668012C2211yescharacteristic
20#15667998—21no—
21#15667998—21no—
22#15667986C2211yescharacteristic
23#15667986C2211yescharacteristic
24#15667983—21no—
25C4×D356C2211yescharacteristic
26#15667971C2211yescharacteristic
27#15667971C2211yescharacteristic
28#15667970—21no—
29#15667945C2211yescharacteristic
30#15667945C2211yescharacteristic
31#15667945C2211yescharacteristic
32#15667945C2211yescharacteristic
33#15667945C2211yescharacteristic
34#15667943C2211yescharacteristic
35#15667943C2211yescharacteristic
36#15667943C2211yescharacteristic
37#15667943C2211yescharacteristic
38C4⋊#10623494C2211yescharacteristic
39#15667933C2211yescharacteristic
40#15667933C2211yescharacteristic
41#15667933C2211yescharacteristic
42#15667932C2211yescharacteristic
43#15667932C2211yescharacteristic
44#15667932C2211yescharacteristic
45C22⋊#10623494C2211yescharacteristic
46C22⋊#10623494C2211yescharacteristic
47#15667923C2211yescharacteristic
48#126×C89—21no—
49#125×C89C2211yescharacteristic
50#123×C89—21no—
51#121×C89—21no—
52#121×C89C2211yescharacteristic
53#121×C89C2211yescharacteristic
54C4×D4×C89—21no—
55C4×D4×C89C2211yescharacteristic
56C4×D4×C89C2211yescharacteristic
57#117×C89C2211yescharacteristic
58C2×C4⋊C4×C89C2211yescharacteristic
59C2×Dic178—21no—
60C2×D356C2311yescharacteristic
61C2×C22⋊D89—21no—
62C2×C22⋊D89—21no—
63C2×C4×D89—21no—
64#13083559—22no—
65#13083558—22no—
66C2×#10623494—22no—
67C2×#10623494C2311yescharacteristic
68C2×#10623494C2311yescharacteristic
69C2×#10623494C2311yescharacteristic
70C2×#10623494C2311yescharacteristic
71C4⋊Dic89—21no—
72C4⋊Dic89C2311yescharacteristic
73C4⋊Dic89C2311yescharacteristic
74C4⋊Dic89C2311yescharacteristic
75C22⋊Dic89—21no—
76C22⋊Dic89—21no—
77#13083551—21no—
78#13083551—21no—
79#13083551—21no—
80C4×Dic89—21no—
81C4×Dic89—21no—
82C2×D4×C89—21no—
83C2×D4×C89—21no—
84C2×D4×C89D411yescharacteristic
85C2×D4×C89C2311yescharacteristic
86C22×C4×C89—21no—
87C22×C4×C89—21no—
88C22×C4×C89C2311yescharacteristic
89C22×C4×C89C2311yescharacteristic
90C4⋊C4×C89—21no—
91C4⋊C4×C89—21no—
92C4⋊C4×C89—21no—
93C4⋊C4×C89D411yescharacteristic
94C4⋊C4×C89C2311yescharacteristic
95C4⋊C4×C89C2311yescharacteristic
96C4⋊C4×C89C2311yescharacteristic
97C22⋊C4×C89—21no—
98C22⋊C4×C89—21no—
99C22⋊C4×C89—21no—
100C22⋊C4×C89—21no—
101C22⋊C4×C89D411yescharacteristic
102C22⋊C4×C89D411yescharacteristic
103C42×C89—21no—
104C42×C89C2311yescharacteristic
105C23×C89—21no—
106C23×C89C2×D411yescharacteristic
107C23×C89C2×D411yescharacteristic
108C22×D89—21no—
109D4×C89—21no—
110D4×C89—21no—
111D4×C89—41no—
112D4×C89—42no—
113D4×C89—81no—
114C2×C4×C89—21no—
115C2×C4×C89—21no—
116C2×C4×C89—21no—
117C2×C4×C89—21no—
118C2×C4×C89—21no—
119C2×C4×C89—21no—
120C2×C4×C89—21no—
121C2×C4×C89—81no—
122C2×C4×C89—81no—
123C2×C4×C89C2×D411yescharacteristic
124C2×C4×C89C2×D411yescharacteristic
125C2×C4×C89C2×D411yescharacteristic
126C2×C4×C89C2×D411yescharacteristic
127C2×C4×C89C2411yescharacteristic
128C22⋊D89—81no—
129C22⋊D89—81no—
130C2×Dic89—21no—
131C2×Dic89—21no—
132C2×Dic89—21no—
133D356—21no—
134D356—21no—
135C4×D89—42no—
136Dic178—81no—
137#10623494—21no—
138#10623494—21no—
139#10623494—21no—
140#10623494#4112yes—
141C22×C89—21no—
142C22×C89—21no—
143C22×C89—21no—
144C22×C89—21no—
145C22×C89—21no—
146C22×C89—21no—
147C22×C89—41no—
148C22×C89—41no—
149C22×C89—41no—
150C22×C89C22×D411yescharacteristic
151C2×D89—41no—
152C2×D89—41no—
153C2×D89—41no—
154C4×C89—21no—
155C4×C89—21no—
156C4×C89—21no—
157C4×C89—21no—
158C4×C89—41no—
159C4×C89—41no—
160C4×C89—41no—
161C4×C89C2×#4111yescharacteristic
162C4×C892−1+411yescharacteristic
163Dic89—41no—
164Dic89—41no—
165Dic89—41no—
166C2×C89—41no—
167C2×C89—41no—
168C2×C89—81no—
169C2×C89#54711yescharacteristic
170C2×C89#57511yescharacteristic
171C2×C89#57611yescharacteristic
172D89—81no—
173#3347—891nomaximal, Sylow
174C89#334711yescharacteristic, complemented, Sylow
175#555—891no—
176#553D8911yescharacteristic, complemented
177#501—891no—
178#482—891no—
179#482—891no—
180#482—891no—
181#480—891no—
182#478—891no—
183#474—891no—
184#469—891no—
185#466—891no—
186#442—891no—
187#435—891no—
188#428—891no—
189#427—891no—
190C2×D8—891no—
191C2×M16—891no—
192C22×C8—891no—
193C4⋊Q8—891no—
194#126—21no—
195#125C2×D8911yescharacteristic
196#124—1781no—
197#124—1781no—
198#123—21no—
199#121—21no—
200#121—891no—
201#121—891no—
202#121—1781no—
203#121C2×D8911yescharacteristic
204#121C2×D8911yescharacteristic
205C4×D4—21no—
206C4×D4—891no—
207C4×D4C2×D8911yescharacteristic
208C4×D4C2×D8911yescharacteristic
209#117—891no—
210#117—891no—
211#117—1781no—
212#117C2×D8911yescharacteristic
213C2×C4⋊C4C2×D8911yescharacteristic
214#107—891no—
215#107—891no—
216#107—891no—
217#107—891no—
218#107—891no—
219#106—891no—
220#106—891no—
221#106—891no—
222#106—891no—
223C4⋊C8—891no—
224#102—891no—
225#102—891no—
226#102—891no—
227#102—891no—
228#102—891no—
229#102—891no—
230C22⋊C8—891no—
231C22⋊C8—891no—
232#97—891no—
233C2×Q8—1781no—
234C2×D4—21no—
235C2×D4—21no—
236C2×D4—891no—
237C2×D4—1781no—
238C2×D4—1781no—
239C2×D4C22⋊D8911yescharacteristic
240C2×D4C22×D8911yescharacteristic
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—1781no—
244C22×C4C22×D8911yescharacteristic
245C22×C4C22×D8911yescharacteristic
246D8—1782no—
247M16—1782no—
248C2×C8—891no—
249C2×C8—891no—
250C2×C8—891no—
251C2×C8—891no—
252C2×C8—1782no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—891no—
257C4⋊C4—891no—
258C4⋊C4—891no—
259C4⋊C4—1781no—
260C4⋊C4C22⋊D8911yescharacteristic
261C4⋊C4C22×D8911yescharacteristic
262C4⋊C4C22×D8911yescharacteristic
263C4⋊C4C22×D8911yescharacteristic
264C22⋊C4—21no—
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4—1781no—
269C22⋊C4—1781no—
270C22⋊C4—1781no—
271C22⋊C4—1781no—
272C22⋊C4—1781no—
273C22⋊C4C22⋊D8911yescharacteristic
274C22⋊C4C22⋊D8911yescharacteristic
275C42—21no—
276C42—1781no—
277C42—1781no—
278C42C22×D8911yescharacteristic
279C23—21no—
280C23—1781no—
281C23C2×C22⋊D8911yescharacteristic
282C23C2×C22⋊D8911yescharacteristic
283Q8—7121no—
284D4—21no—
285D4—21no—
286D4—41no—
287D4—42no—
288D4—81no—
289D4—1781no—
290D4—1781no—
291D4—7121no—
292D4—7121no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—81no—
301C2×C4—81no—
302C2×C4—3562no—
303C2×C4—1781no—
304C2×C4—1781no—
305C2×C4—1781no—
306C2×C4C2×C22⋊D8911yescharacteristic
307C2×C4C2×C22⋊D8911yescharacteristic
308C2×C4C2×C22⋊D8911yescharacteristic
309C2×C4C2×C22⋊D8911yescharacteristic
310C2×C4C23×D8911yescharacteristic
311C8—892no—
312C8—1781no—
313C8—1781no—
314C8—1781no—
315C22—21no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—21no—
320C22—21no—
321C22—41no—
322C22—41no—
323C22—41no—
324C22—3561no—
325C22—3561no—
326C22—3561no—
327C22C22×C22⋊D8911yescharacteristic
328C4—21no—
329C4—21no—
330C4—21no—
331C4—21no—
332C4—41no—
333C4—41no—
334C4—41no—
335C4—3561no—
336C4—3561no—
337C4—3561no—
338C4#41×D8911yescharacteristic
339C4#1566805911yescharacteristic
340C2—41no—
341C2—41no—
342C2—81no—
343C2—7121no—
344C2#1915224711yescharacteristic
345C2#1915239611yescharacteristic
346C2#1915240111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D89
commutator, cosocleC2×C4×C89C24
FrattiniC2×C4C23×D89
Fitting#553×C89C2
socleC22×C89C22×D4
hypercenter#553D89
hypocenterC89#3347
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C22 ◁ C4×D4 ◁ #553

Complements

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

NH ≅ G/Ntype
1. #19152313C2semidirect
2. #19152008C2semidirect
3. #19151922C2semidirect
4. #19151919C2semidirect
5. #19151919C2semidirect
6. #19151911C2semidirect
7. #19151895C2semidirect
8. #19151878C2semidirect
9. #19151849C2semidirect
10. #19151832C2semidirect
11. #19151708C2semidirect
12. #19151670C2semidirect
13. #19151638C2semidirect
14. #19151634C2semidirect
15. #553×C89C2semidirect
174. C89#3347semidirect
176. #553D89semidirect

Maximal subgroups

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

subgroupindex
#191523132
#191520082
#191519222
#191519192
#191519112
#191518952
#191518782
#191518492
#191518322
#191517082
#191516702
#191516382
#191516342
#553×C892
#334789