Finite Group Databasebeta

← #26032357

Subgroups — #26032357

Order 11392.

388 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19152257C211yesmaximal, characteristic
2#19151960C211yesmaximal, characteristic, complemented
3#19151928C211yesmaximal, characteristic, complemented
4#19151916C211yesmaximal, characteristic, complemented
5#19151880C211yesmaximal, characteristic, complemented
6#19151854C211yesmaximal, characteristic, complemented
7#19151829C211yesmaximal, characteristic, complemented
8#19151820C211yesmaximal, characteristic, complemented
9#19151758C211yesmaximal, characteristic, complemented
10#19151753C211yesmaximal, characteristic, complemented
11#19151703C211yesmaximal, characteristic, complemented
12#19151670C211yesmaximal, characteristic, complemented
13#19151597C211yesmaximal, characteristic, complemented
14C2×#15667935C211yesmaximal, characteristic, complemented
15#554×C89C211yesmaximal, characteristic, complemented
16C2×#13083574C2211yescharacteristic
17C22×Dic178C2211yescharacteristic
18C2×#13083564C2211yescharacteristic
19C2×#13083564C2211yescharacteristic
20C2×#13083561C2211yescharacteristic
21C2×#13083558C2211yescharacteristic
22C22×#10623494C2211yescharacteristic
23#15668000C2211yescharacteristic
24#15667998—21no—
25#15667991C2211yescharacteristic
26#15667990—21no—
27#15667986C2211yescharacteristic
28#15667984—21no—
29C4×Dic178C2211yescharacteristic
30#15667972—21no—
31#15667943C2211yescharacteristic
32#15667943C2211yescharacteristic
33#15667943C2211yescharacteristic
34C4⋊#10623494C2211yescharacteristic
35#15667936C2211yescharacteristic
36#15667935C2211yescharacteristic
37#15667935C2211yescharacteristic
38#15667935C2211yescharacteristic
39#15667935C2211yescharacteristic
40#15667935C2211yescharacteristic
41#15667935C2211yescharacteristic
42#15667932C2211yescharacteristic
43#15667932C2211yescharacteristic
44#15667932C2211yescharacteristic
45C22⋊#10623494C2211yescharacteristic
46C22⋊#10623494C2211yescharacteristic
47#15667923C2211yescharacteristic
48C4⋊Q8×C89C2211yescharacteristic
49#125×C89—21no—
50C22⋊Q8×C89—21no—
51C22⋊Q8×C89—21no—
52C22⋊Q8×C89C2211yescharacteristic
53C22⋊Q8×C89C2211yescharacteristic
54C4×Q8×C89C2211yescharacteristic
55C4×D4×C89—21no—
56C4×D4×C89C2211yescharacteristic
57C2×C4⋊C4×C89C2211yescharacteristic
58C2×C4⋊C4×C89C2211yescharacteristic
59#13083574—22no—
60#13083574—41no—
61C2×Dic178—22no—
62C2×Dic178—21no—
63C2×Dic178—41no—
64C2×Dic178C2311yescharacteristic
65C2×Dic178C2311yescharacteristic
66C2×D356C2311yescharacteristic
67C2×C22⋊D89—21no—
68C2×C22⋊D89—21no—
69C22×Dic89—21no—
70C2×C4×D89—21no—
71#13083564—22no—
72#13083564—41no—
73#13083561—41no—
74#13083558—41no—
75C2×#10623494—41no—
76C2×#10623494C2311yescharacteristic
77C2×#10623494C2311yescharacteristic
78C2×#10623494C2311yescharacteristic
79C2×#10623494C2311yescharacteristic
80C4⋊Dic89C2311yescharacteristic
81#13083553—21no—
82#13083553—21no—
83C22⋊Dic89—21no—
84#13083551—21no—
85#13083551—21no—
86#13083551—21no—
87C4×Dic89—21no—
88C2×Q8×C89—21no—
89C2×Q8×C89C2311yescharacteristic
90C2×D4×C89D411yescharacteristic
91C22×C4×C89—21no—
92C22×C4×C89—21no—
93C22×C4×C89C2311yescharacteristic
94C22×C4×C89C2311yescharacteristic
95C4⋊C4×C89—21no—
96C4⋊C4×C89—21no—
97C4⋊C4×C89—21no—
98C4⋊C4×C89—21no—
99C4⋊C4×C89—21no—
100C4⋊C4×C89—21no—
101C4⋊C4×C89D411yescharacteristic
102C4⋊C4×C89C2311yescharacteristic
103C4⋊C4×C89C2311yescharacteristic
104C4⋊C4×C89C2311yescharacteristic
105C22⋊C4×C89—21no—
106C22⋊C4×C89—21no—
107C22⋊C4×C89D411yescharacteristic
108C22⋊C4×C89D411yescharacteristic
109C42×C89—21no—
110C42×C89C2311yescharacteristic
111C23×C89C2×D411yescharacteristic
112C23×C89C2×D411yescharacteristic
113C22×D89—21no—
114Q8×C89—21no—
115Q8×C89—21no—
116Q8×C89—81no—
117D4×C89—22no—
118C2×C4×C89—21no—
119C2×C4×C89—21no—
120C2×C4×C89—21no—
121C2×C4×C89—21no—
122C2×C4×C89—21no—
123C2×C4×C89—21no—
124C2×C4×C89—21no—
125C2×C4×C89—21no—
126C2×C4×C89—81no—
127C2×C4×C89—81no—
128C2×C4×C89C2×D411yescharacteristic
129C2×C4×C89C2×D411yescharacteristic
130C2×C4×C89C2×D411yescharacteristic
131C2×C4×C89C2×D411yescharacteristic
132C2×C4×C89C2411yescharacteristic
133C22⋊D89—42no—
134C22⋊D89—42no—
135C2×Dic89—21no—
136C2×Dic89—21no—
137C2×Dic89—21no—
138C2×Dic89—42no—
139D356—21no—
140D356—21no—
141C4×D89—42no—
142Dic178—21no—
143Dic178—21no—
144Dic178—21no—
145Dic178—42no—
146Dic178#4112yes—
147#10623494—21no—
148#10623494—21no—
149#10623494—21no—
150#10623494—21no—
151C22×C89—21no—
152C22×C89—21no—
153C22×C89—21no—
154C22×C89—21no—
155C22×C89—21no—
156C22×C89#13712yes—
157C22×C89C22×D411yescharacteristic
158C2×D89—41no—
159C2×D89—41no—
160C2×D89—41no—
161C4×C89—21no—
162C4×C89—21no—
163C4×C89—21no—
164C4×C89—21no—
165C4×C89—41no—
166C4×C89—41no—
167C4×C89—41no—
168C4×C89—41no—
169C4×C89C2×#4111yescharacteristic
170C4×C89H(5,𝔽2)11yescharacteristic
171Dic89—22no—
172Dic89—41no—
173Dic89—41no—
174C2×C89—22no—
175C2×C89—41no—
176C2×C89#54611yescharacteristic
177C2×C89C2×#13711yescharacteristic
178C2×C89#57711yescharacteristic
179D89—81no—
180#3316—891nomaximal, Sylow
181C89#331611yescharacteristic, complemented, Sylow
182#554D8911yescharacteristic, complemented
183#548—891no—
184#489—891no—
185#483—891no—
186#481—891no—
187#475—891no—
188#470—891no—
189#465—891no—
190#464—891no—
191#452—891no—
192#451—891no—
193#441—891no—
194#435—891no—
195#417—891no—
196C2×#103—891no—
197C2×#41—891no—
198C22×Q8—891no—
199C2×Q16—891no—
200C2×Q16—891no—
201C2×SD16—891no—
202C2×M16—891no—
203C22×C8—891no—
204C4⋊Q8C2×D8911yescharacteristic
205#125—21no—
206#124—891no—
207#124—1781no—
208C22⋊Q8—21no—
209C22⋊Q8—21no—
210C22⋊Q8—891no—
211C22⋊Q8—1781no—
212C22⋊Q8C2×D8911yescharacteristic
213C22⋊Q8C2×D8911yescharacteristic
214#121—891no—
215#121—1781no—
216C4×Q8—891no—
217C4×Q8C2×D8911yescharacteristic
218C4×D4—21no—
219C4×D4—1781no—
220C4×D4C2×D8911yescharacteristic
221C2×C4⋊C4C2×D8911yescharacteristic
222C2×C4⋊C4C2×D8911yescharacteristic
223#106—891no—
224#106—891no—
225#106—891no—
226C4⋊C8—891no—
227#103—891no—
228#103—891no—
229#103—891no—
230#103—891no—
231#103—891no—
232#103—891no—
233#103—891no—
234#102—891no—
235#102—891no—
236#102—891no—
237C22⋊C8—891no—
238C22⋊C8—891no—
239#97—891no—
240#41—3561no—
241#41—1782no—
242C2×Q8—21no—
243C2×Q8—891no—
244C2×Q8—891no—
245C2×Q8—3561no—
246C2×Q8—1782no—
247C2×Q8—1781no—
248C2×Q8C22×D8911yescharacteristic
249C2×D4—891no—
250C2×D4—1781no—
251C2×D4—1781no—
252C2×D4C22⋊D8911yescharacteristic
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—1781no—
256C22×C4—1781no—
257C22×C4C22×D8911yescharacteristic
258C22×C4C22×D8911yescharacteristic
259Q16—3561no—
260Q16—1782no—
261SD16—3561no—
262M16—3561no—
263C2×C8—891no—
264C2×C8—891no—
265C2×C8—891no—
266C2×C8—891no—
267C2×C8—3561no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—891no—
275C4⋊C4—1781no—
276C4⋊C4—1781no—
277C4⋊C4C22⋊D8911yescharacteristic
278C4⋊C4C22×D8911yescharacteristic
279C4⋊C4C22×D8911yescharacteristic
280C4⋊C4C22×D8911yescharacteristic
281C22⋊C4—21no—
282C22⋊C4—21no—
283C22⋊C4—1781no—
284C22⋊C4—1781no—
285C22⋊C4—1781no—
286C22⋊C4—1781no—
287C22⋊C4C22⋊D8911yescharacteristic
288C22⋊C4C22⋊D8911yescharacteristic
289C42—21no—
290C42—1781no—
291C42C22×D8911yescharacteristic
292C23—1781no—
293C23C2×C22⋊D8911yescharacteristic
294C23C2×C22⋊D8911yescharacteristic
295Q8—21no—
296Q8—21no—
297Q8—81no—
298Q8—892no—
299Q8—3562no—
300Q8—1781no—
301Q8—1781no—
302Q8—1781no—
303D4—22no—
304D4—3562no—
305D4—3562no—
306D4—1781no—
307D4—1781no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—81no—
317C2×C4—81no—
318C2×C4—3562no—
319C2×C4—3562no—
320C2×C4—1781no—
321C2×C4—1781no—
322C2×C4—1781no—
323C2×C4C2×C22⋊D8911yescharacteristic
324C2×C4C2×C22⋊D8911yescharacteristic
325C2×C4C2×C22⋊D8911yescharacteristic
326C2×C4C2×C22⋊D8911yescharacteristic
327C2×C4C23×D8911yescharacteristic
328C8—1781no—
329C8—1781no—
330C8—1781no—
331C8—1781no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—21no—
336C22—21no—
337C22—3561no—
338C22—3561no—
339C22—3561no—
340C22#1566804312yes—
341C22C22×C22⋊D8911yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—41no—
347C4—41no—
348C4—41no—
349C4—41no—
350C4—3561no—
351C4—3561no—
352C4—1782no—
353C4#41×D8911yescharacteristic
354C4#1566805811yescharacteristic
355C2—22no—
356C2—41no—
357C2—7121no—
358C2#1915223611yescharacteristic
359C2C2×#1566804311yescharacteristic
360C2#1915240911yescharacteristic
subgroupG/H
centerC22C22×C22⋊D89
commutator, cosocleC2×C4×C89C24
FrattiniC2×C4C23×D89
Fitting#554×C89C2
socleC22×C89C22×D4
prime radical#19152257C2
hypercenter#554D89
hypocenterC89#3316
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C22 ◁ C4×D4 ◁ #554

Complements

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

NH ≅ G/Ntype
2. #19151960C2semidirect
3. #19151928C2semidirect
4. #19151916C2semidirect
5. #19151880C2semidirect
6. #19151854C2semidirect
7. #19151829C2semidirect
8. #19151820C2semidirect
9. #19151758C2semidirect
10. #19151753C2semidirect
11. #19151703C2semidirect
12. #19151670C2semidirect
13. #19151597C2semidirect
14. C2×#15667935C2semidirect
15. #554×C89C2semidirect
181. C89#3316semidirect
182. #554D89semidirect

Maximal subgroups

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

subgroupindex
#191522572
#191519602
#191519282
#191519162
#191518802
#191518542
#191518292
#191518202
#191517582
#191517532
#191517032
#191516702
#191515972
C2×#156679352
#554×C892
#331689