Finite Group Databasebeta

← #26032423

Subgroups — #26032423

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#19152294C211yesmaximal, characteristic
2#19151966C211yesmaximal, characteristic, complemented
3#19151936C211yesmaximal, characteristic, complemented
4#19151931C211yesmaximal, characteristic, complemented
5#19151905C211yesmaximal, characteristic, complemented
6#19151846C211yesmaximal, characteristic, complemented
7#19151829C211yesmaximal, characteristic, complemented
8#19151800C211yesmaximal, characteristic, complemented
9#19151737C211yesmaximal, characteristic, complemented
10#19151737C211yesmaximal, characteristic, complemented
11#19151696C211yesmaximal, characteristic, complemented
12#19151670C211yesmaximal, characteristic, complemented
13#19151607C211yesmaximal, characteristic, complemented
14C2×#15667936C211yesmaximal, characteristic, complemented
15D4×Q8×C89C211yesmaximal, characteristic, complemented
16C2×#13083561C2211yescharacteristic
17C2×#13083561C2211yescharacteristic
18C2×#13083561C2211yescharacteristic
19C2×#13083558C2211yescharacteristic
20C22×#10623494C2211yescharacteristic
21#15668007—21no—
22#15668004C2211yescharacteristic
23#15667994—21no—
24#15667986C2211yescharacteristic
25#15667986C2211yescharacteristic
26#15667984—21no—
27C4×D356C2211yescharacteristic
28#15667972—21no—
29#15667971C2211yescharacteristic
30C2×C4⋊Dic89C2211yescharacteristic
31#15667945C2211yescharacteristic
32#15667945C2211yescharacteristic
33#15667943C2211yescharacteristic
34C4⋊#10623494C2211yescharacteristic
35#15667936C2211yescharacteristic
36#15667936C2211yescharacteristic
37#15667936C2211yescharacteristic
38#15667936C2211yescharacteristic
39#15667936C2211yescharacteristic
40#15667936C2211yescharacteristic
41#15667936C2211yescharacteristic
42#15667936C2211yescharacteristic
43#15667936C2211yescharacteristic
44#15667932C2211yescharacteristic
45C22⋊#10623494C2211yescharacteristic
46C22⋊#10623494C2211yescharacteristic
47#15667923C2211yescharacteristic
48C22×Q8×C89C2211yescharacteristic
49C22×Q8×C89C2211yescharacteristic
50C4⋊Q8×C89—21no—
51C4⋊Q8×C89C2211yescharacteristic
52C22⋊Q8×C89—21no—
53C22⋊Q8×C89—21no—
54C22⋊Q8×C89C2211yescharacteristic
55C22⋊Q8×C89C2211yescharacteristic
56C4×Q8×C89C2211yescharacteristic
57C4×D4×C89—21no—
58C4×D4×C89C2211yescharacteristic
59C2×D356C2311yescharacteristic
60C2×C22⋊D89—21no—
61C2×C22⋊D89—21no—
62C22×Dic89—21no—
63C2×C4×D89—21no—
64#13083561—22no—
65#13083561—41no—
66#13083561—41no—
67#13083558—41no—
68C2×#10623494—41no—
69C2×#10623494C2311yescharacteristic
70C2×#10623494C2311yescharacteristic
71C2×#10623494C2311yescharacteristic
72C2×#10623494C2311yescharacteristic
73C4⋊Dic89—21no—
74C4⋊Dic89C2311yescharacteristic
75C4⋊Dic89C2311yescharacteristic
76C4⋊Dic89C2311yescharacteristic
77#13083553—21no—
78#13083553—21no—
79C22⋊Dic89—21no—
80#13083551—21no—
81#13083551—21no—
82#13083551—21no—
83C4×Dic89—21no—
84C2×Q8×C89—21no—
85C2×Q8×C89—21no—
86C2×Q8×C89—22no—
87C2×Q8×C89—22no—
88C2×Q8×C89—41no—
89C2×Q8×C89—41no—
90C2×Q8×C89C2311yescharacteristic
91C2×Q8×C89C2311yescharacteristic
92C2×Q8×C89C2311yescharacteristic
93C2×D4×C89D411yescharacteristic
94C22×C4×C89—21no—
95C22×C4×C89—21no—
96C22×C4×C89C2311yescharacteristic
97C22×C4×C89C2311yescharacteristic
98C4⋊C4×C89—21no—
99C4⋊C4×C89—21no—
100C4⋊C4×C89—21no—
101C4⋊C4×C89—21no—
102C4⋊C4×C89—21no—
103C4⋊C4×C89D411yescharacteristic
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—21no—
117Q8×C89—21no—
118Q8×C89—21no—
119Q8×C89—42no—
120Q8×C89—42no—
121Q8×C89#4112yes—
122D4×C89—22no—
123C2×C4×C89—21no—
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
138C22⋊D89—42no—
139C22⋊D89—81no—
140C2×Dic89—21no—
141C2×Dic89—21no—
142C2×Dic89—21no—
143C2×Dic89—81no—
144D356—21no—
145D356—21no—
146C4×D89—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#13712yes—
157C22×C89C22×D411yescharacteristic
158C2×D89—41no—
159C2×D89—41no—
160C2×D89—41no—
161C4×C89—21no—
162C4×C89—21no—
163C4×C89—22no—
164C4×C89—21no—
165C4×C89—21no—
166C4×C89—41no—
167C4×C89—41no—
168C4×C89—41no—
169C4×C89C2×#4111yescharacteristic
170C4×C89H(5,𝔽2)11yescharacteristic
171Dic89—41no—
172Dic89—41no—
173Dic89—41no—
174C2×C89—22no—
175C2×C89—41no—
176C2×C89#54611yescharacteristic
177C2×C89C2×#13711yescharacteristic
178C2×C89#57711yescharacteristic
179D89—81no—
180#3320—891nomaximal, Sylow
181C89#332011yescharacteristic, complemented, Sylow
182#553—891no—
183D4×Q8D8911yescharacteristic, complemented
184#491—891no—
185#485—891no—
186#484—891no—
187#479—891no—
188#468—891no—
189#465—891no—
190#461—891no—
191#448—891no—
192#448—891no—
193#440—891no—
194#435—891no—
195#419—891no—
196C2×#103—891no—
197C22×Q8C2×D8911yescharacteristic
198C22×Q8C2×D8911yescharacteristic
199C2×SD16—891no—
200C2×SD16—891no—
201C2×SD16—891no—
202C2×M16—891no—
203C22×C8—891no—
204C4⋊Q8—21no—
205C4⋊Q8C2×D8911yescharacteristic
206#126—1781no—
207#125—891no—
208#123—1781no—
209C22⋊Q8—21no—
210C22⋊Q8—21no—
211C22⋊Q8C2×D8911yescharacteristic
212C22⋊Q8C2×D8911yescharacteristic
213#121—891no—
214#121—891no—
215#121—1781no—
216C4×Q8C2×D8911yescharacteristic
217C4×D4—21no—
218C4×D4—891no—
219C4×D4—1781no—
220C4×D4C2×D8911yescharacteristic
221#117—891no—
222C2×C4⋊C4—891no—
223#107—891no—
224#107—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#103—891no—
235#103—891no—
236#102—891no—
237C22⋊C8—891no—
238C22⋊C8—891no—
239#97—891no—
240C2×Q8—21no—
241C2×Q8—21no—
242C2×Q8—22no—
243C2×Q8—22no—
244C2×Q8—41no—
245C2×Q8—41no—
246C2×Q8C22×D8911yescharacteristic
247C2×Q8C22×D8911yescharacteristic
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
259SD16—3561no—
260SD16—3561no—
261SD16—1782no—
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—891no—
274C4⋊C4—891no—
275C4⋊C4—891no—
276C4⋊C4—1781no—
277C4⋊C4—1781no—
278C4⋊C4—1781no—
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—21no—
298Q8—21no—
299Q8—21no—
300Q8—42no—
301Q8—42no—
302Q8#1308357312yes—
303D4—22no—
304D4—3562no—
305D4—1781no—
306D4—1781no—
307D4—7121no—
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—42no—
317C2×C4—42no—
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—3561no—
338C22—3561no—
339C22—3561no—
340C22#1566804312yes—
341C22C22×C22⋊D8911yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—22no—
347C4—41no—
348C4—41no—
349C4—41no—
350C4—3561no—
351C4—3561no—
352C4—3561no—
353C4C2×#1308357311yescharacteristic
354C4#1566805711yescharacteristic
355C2—22no—
356C2—41no—
357C2—7121no—
358C2#1915224211yescharacteristic
359C2C2×#1566804311yescharacteristic
360C2#1915240611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D89
commutator, cosocleC2×C4×C89C24
FrattiniC2×C4C23×D89
FittingD4×Q8×C89C2
socleC22×C89C22×D4
prime radical#19152294C2
hypercenterD4×Q8D89
hypocenterC89#3320
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C22 ◁ C4×D4 ◁ D4×Q8

Complements

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

NH ≅ G/Ntype
2. #19151966C2semidirect
3. #19151936C2semidirect
4. #19151931C2semidirect
5. #19151905C2semidirect
6. #19151846C2semidirect
7. #19151829C2semidirect
8. #19151800C2semidirect
9. #19151737C2semidirect
10. #19151737C2semidirect
11. #19151696C2semidirect
12. #19151670C2semidirect
13. #19151607C2semidirect
14. C2×#15667936C2semidirect
15. D4×Q8×C89C2semidirect
181. C89#3320semidirect
183. D4×Q8D89semidirect

Maximal subgroups

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

subgroupindex
#191522942
#191519662
#191519362
#191519312
#191519052
#191518462
#191518292
#191518002
#191517372
#191516962
#191516702
#191516072
C2×#156679362
D4×Q8×C892
#332089