Finite Group Databasebeta

← #26032363

Subgroups — #26032363

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#19152305C211yesmaximal, characteristic, complemented
2#19151957C211yesmaximal, characteristic, complemented
3#19151926C211yesmaximal, characteristic, complemented
4#19151914C211yesmaximal, characteristic, complemented
5#19151883C211yesmaximal, characteristic, complemented
6#19151854C211yesmaximal, characteristic, complemented
7#19151825C211yesmaximal, characteristic, complemented
8#19151817C211yesmaximal, characteristic, complemented
9#19151760C211yesmaximal, characteristic, complemented
10#19151754C211yesmaximal, characteristic, complemented
11#19151703C211yesmaximal, characteristic, complemented
12#19151670C211yesmaximal, characteristic, complemented
13#19151599C211yesmaximal, characteristic, complemented
14C2×#15667936C211yesmaximal, characteristic, complemented
15#548×C89C211yesmaximal, characteristic
16C2×#13083564C2211yescharacteristic
17C2×#13083564C2211yescharacteristic
18C2×#13083562C2211yescharacteristic
19C2×#13083558C2211yescharacteristic
20C22×#10623494C2211yescharacteristic
21#15668012C2211yescharacteristic
22#15668003—21no—
23#15667991C2211yescharacteristic
24#15667991C2211yescharacteristic
25#15667989—21no—
26#15667989—21no—
27C4×Dic178C2211yescharacteristic
28D4×Dic89—21no—
29C2×C4⋊Dic89C2211yescharacteristic
30C2×C4⋊Dic89C2211yescharacteristic
31#15667943C2211yescharacteristic
32#15667943C2211yescharacteristic
33#15667943C2211yescharacteristic
34C4⋊#10623494C2211yescharacteristic
35#15667936C2211yescharacteristic
36#15667936C2211yescharacteristic
37#15667936C2211yescharacteristic
38#15667936C2211yescharacteristic
39#15667936C2211yescharacteristic
40#15667936C2211yescharacteristic
41#15667935C2211yescharacteristic
42#15667933C2211yescharacteristic
43#15667933C2211yescharacteristic
44#15667933C2211yescharacteristic
45C22⋊#10623494C2211yescharacteristic
46C22⋊#10623494C2211yescharacteristic
47#15667923C2211yescharacteristic
48C2×#41×C89C2211yescharacteristic
49C22×Q8×C89C2211yescharacteristic
50#124×C89—21no—
51#124×C89C2211yescharacteristic
52C22⋊Q8×C89—21no—
53C22⋊Q8×C89C2211yescharacteristic
54#121×C89—21no—
55#121×C89C2211yescharacteristic
56C4×Q8×C89C2211yescharacteristic
57C4×D4×C89—21no—
58C4×D4×C89C2211yescharacteristic
59C2×Dic178—21no—
60C2×Dic178C2311yescharacteristic
61C22×Dic89—21no—
62C22×Dic89—21no—
63#13083564—22no—
64#13083564—41no—
65#13083562—41no—
66#13083558—41no—
67C2×#10623494—41no—
68C2×#10623494C2311yescharacteristic
69C2×#10623494C2311yescharacteristic
70C2×#10623494C2311yescharacteristic
71C2×#10623494C2311yescharacteristic
72C4⋊Dic89—21no—
73C4⋊Dic89—21no—
74C4⋊Dic89—21no—
75C4⋊Dic89C2311yescharacteristic
76C4⋊Dic89C2311yescharacteristic
77C4⋊Dic89C2311yescharacteristic
78#13083553—21no—
79#13083553—21no—
80#13083553—21no—
81C22⋊Dic89—21no—
82C22⋊Dic89—21no—
83C4×Dic89—21no—
84#41×C89—22no—
85#41×C89—41no—
86C2×Q8×C89—21no—
87C2×Q8×C89—22no—
88C2×Q8×C89—41no—
89C2×Q8×C89C2311yescharacteristic
90C2×Q8×C89C2311yescharacteristic
91C2×D4×C89—21no—
92C2×D4×C89—21no—
93C2×D4×C89D411yescharacteristic
94C2×D4×C89C2311yescharacteristic
95C22×C4×C89—21no—
96C22×C4×C89—21no—
97C22×C4×C89C2311yescharacteristic
98C22×C4×C89C2311yescharacteristic
99C4⋊C4×C89—21no—
100C4⋊C4×C89—21no—
101C4⋊C4×C89D411yescharacteristic
102C4⋊C4×C89C2311yescharacteristic
103C22⋊C4×C89—21no—
104C22⋊C4×C89—21no—
105C22⋊C4×C89—21no—
106C22⋊C4×C89—21no—
107C22⋊C4×C89D411yescharacteristic
108C22⋊C4×C89D411yescharacteristic
109C42×C89—21no—
110C42×C89C2311yescharacteristic
111C23×C89—21no—
112C23×C89C2×D411yescharacteristic
113C23×C89C2×D411yescharacteristic
114Q8×C89—21no—
115Q8×C89—21no—
116Q8×C89—21no—
117Q8×C89—42no—
118Q8×C89#4112yes—
119D4×C89—22no—
120D4×C89—21no—
121D4×C89—21no—
122D4×C89—42no—
123D4×C89—42no—
124C2×C4×C89—21no—
125C2×C4×C89—21no—
126C2×C4×C89—21no—
127C2×C4×C89—21no—
128C2×C4×C89—21no—
129C2×C4×C89—21no—
130C2×C4×C89—21no—
131C2×C4×C89—42no—
132C2×C4×C89—42no—
133C2×C4×C89C2×D411yescharacteristic
134C2×C4×C89C2×D411yescharacteristic
135C2×C4×C89C2×D411yescharacteristic
136C2×C4×C89C2×D411yescharacteristic
137C2×C4×C89C2411yescharacteristic
138C2×Dic89—21no—
139C2×Dic89—21no—
140C2×Dic89—21no—
141C2×Dic89—21no—
142C2×Dic89—81no—
143C2×Dic89—81no—
144Dic178—21no—
145Dic178—21no—
146Dic178—81no—
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—41no—
157C22×C89—41no—
158C22×C89—41no—
159C22×C89#13712yes—
160C22×C89C22×D411yescharacteristic
161C4×C89—21no—
162C4×C89—21no—
163C4×C89—22no—
164C4×C89—21no—
165C4×C89—21no—
166C4×C89—41no—
167C4×C89—41no—
168C4×C89C2×#4111yescharacteristic
169C4×C89H(5,𝔽2)11yescharacteristic
170Dic89—41no—
171Dic89—41no—
172Dic89—41no—
173Dic89—41no—
174C2×C89—22no—
175C2×C89—41no—
176C2×C89—81no—
177C2×C89#54611yescharacteristic
178C2×C89C2×#13711yescharacteristic
179C2×C89#57711yescharacteristic
180#3316—891nomaximal, Sylow
181C89#331611yescharacteristic, complemented, Sylow
182#554—891no—
183#548D8911yescharacteristic
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×#41C2×D8911yescharacteristic
198C22×Q8C2×D8911yescharacteristic
199C2×Q16—891no—
200C2×Q16—891no—
201C2×SD16—891no—
202C2×M16—891no—
203C22×C8—891no—
204C4⋊Q8—891no—
205#125—1781no—
206#124—21no—
207#124C2×D8911yescharacteristic
208C22⋊Q8—21no—
209C22⋊Q8—891no—
210C22⋊Q8—891no—
211C22⋊Q8—1781no—
212C22⋊Q8—1781no—
213C22⋊Q8C2×D8911yescharacteristic
214#121—21no—
215#121C2×D8911yescharacteristic
216C4×Q8—891no—
217C4×Q8C2×D8911yescharacteristic
218C4×D4—21no—
219C4×D4—1781no—
220C4×D4C2×D8911yescharacteristic
221C2×C4⋊C4—891no—
222C2×C4⋊C4—891no—
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—22no—
241#41—41no—
242C2×Q8—21no—
243C2×Q8—22no—
244C2×Q8—41no—
245C2×Q8—891no—
246C2×Q8—1781no—
247C2×Q8C22×D8911yescharacteristic
248C2×Q8C22×D8911yescharacteristic
249C2×D4—21no—
250C2×D4—21no—
251C2×D4C22⋊D8911yescharacteristic
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—891no—
271C4⋊C4—891no—
272C4⋊C4—891no—
273C4⋊C4—1781no—
274C4⋊C4—1781no—
275C4⋊C4—1781no—
276C4⋊C4—1781no—
277C4⋊C4—1781no—
278C4⋊C4—1781no—
279C4⋊C4C22⋊D8911yescharacteristic
280C4⋊C4C22×D8911yescharacteristic
281C22⋊C4—21no—
282C22⋊C4—21no—
283C22⋊C4—21no—
284C22⋊C4—21no—
285C22⋊C4—1781no—
286C22⋊C4—1781no—
287C22⋊C4C22⋊D8911yescharacteristic
288C22⋊C4C22⋊D8911yescharacteristic
289C42—21no—
290C42—1781no—
291C42C22×D8911yescharacteristic
292C23—21no—
293C23C2×C22⋊D8911yescharacteristic
294C23C2×C22⋊D8911yescharacteristic
295Q8—21no—
296Q8—21no—
297Q8—21no—
298Q8—42no—
299Q8—1781no—
300Q8—1781no—
301Q8—7121no—
302Q8#1308357312yes—
303D4—22no—
304D4—21no—
305D4—21no—
306D4—42no—
307D4—42no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—1781no—
318C2×C4—1781no—
319C2×C4—1781no—
320C2×C4—1781no—
321C2×C4—7121no—
322C2×C4—7121no—
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—41no—
338C22—41no—
339C22—41no—
340C22#1566804212yes—
341C22C22×C22⋊D8911yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—22no—
347C4—41no—
348C4—41no—
349C4—3561no—
350C4—3561no—
351C4—3561no—
352C4—3561no—
353C4C2×#1308357311yescharacteristic
354C4#1566805711yescharacteristic
355C2—22no—
356C2—41no—
357C2—81no—
358C2#1915224211yescharacteristic
359C2C2×#1566804211yescharacteristic
360C2#1915240611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D89
commutator, cosocleC2×C4×C89C24
FrattiniC2×C4C23×D89
Fitting, prime radical#548×C89C2
socleC22×C89C22×D4
hypercenter#548D89
hypocenterC89#3316
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C22 ◁ C4×D4 ◁ #548

Complements

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

NH ≅ G/Ntype
1. #19152305C2semidirect
2. #19151957C2semidirect
3. #19151926C2semidirect
4. #19151914C2semidirect
5. #19151883C2semidirect
6. #19151854C2semidirect
7. #19151825C2semidirect
8. #19151817C2semidirect
9. #19151760C2semidirect
10. #19151754C2semidirect
11. #19151703C2semidirect
12. #19151670C2semidirect
13. #19151599C2semidirect
14. C2×#15667936C2semidirect
181. C89#3316semidirect

Maximal subgroups

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

subgroupindex
#191523052
#191519572
#191519262
#191519142
#191518832
#191518542
#191518252
#191518172
#191517602
#191517542
#191517032
#191516702
#191515992
C2×#156679362
#548×C892
#331689