Finite Group Databasebeta

← #26030430

Subgroups — #26030430

Order 11392.

406 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19152072C211yesmaximal, characteristic, complemented
2#19151936C211yesmaximal, characteristic, complemented
3#19151919C211yesmaximal, characteristic, complemented
4#19151885C211yesmaximal, characteristic, complemented
5#19151875C211yesmaximal, characteristic, complemented
6#19151810C211yesmaximal, characteristic, complemented
7#19151810C211yesmaximal, characteristic, complemented
8#19151748C211yesmaximal, characteristic, complemented
9#19151731C211yesmaximal, characteristic
10#19151708C211yesmaximal, characteristic, complemented
11#19151696C211yesmaximal, characteristic, complemented
12C4×#13083561C211yesmaximal, characteristic, complemented
13C4×#13083559C211yesmaximal, characteristic, complemented
14#19151659C211yesmaximal, characteristic, complemented
15#542×C89C211yesmaximal, characteristic, complemented
16C22×D356C2211yescharacteristic
17C2×#13083561C2211yescharacteristic
18C2×#13083561C2211yescharacteristic
19C2×#13083559C2211yescharacteristic
20C2×#13083559C2211yescharacteristic
21C4×D356C2211yescharacteristic
22C4×D356C2211yescharacteristic
23C4×D356C2211yescharacteristic
24C4×D356C2211yescharacteristic
25#15667974—21no—
26#15667974—21no—
27#15667971C2211yescharacteristic
28C22⋊C4×D89—21no—
29C22⋊C4×D89—21no—
30#15667945C2211yescharacteristic, complemented
31#15667945C2211yescharacteristic, complemented
32#15667943C2211yescharacteristic, complemented
33#15667943C2211yescharacteristic, complemented
34C4⋊#10623494C2211yescharacteristic, complemented
35C4⋊#10623494C2211yescharacteristic, complemented
36#15667936C2211yescharacteristic, complemented
37#15667936C2211yescharacteristic, complemented
38#15667933C2211yescharacteristic, complemented
39#15667933C2211yescharacteristic, complemented
40#15667932C2211yescharacteristic
41#15667932C2211yescharacteristic
42#15667932C2211yescharacteristic
43#15667932C2211yescharacteristic
44C22⋊#10623494C2211yescharacteristic
45C22⋊#10623494C2211yescharacteristic
46#15667923C2211yescharacteristic, complemented
47C4×#10623494C2211yescharacteristic, complemented
48C4⋊Q8×C89C2211yescharacteristic, complemented
49#126×C89—21no—
50#124×C89—21no—
51#124×C89C2211yescharacteristic, complemented
52#123×C89—21no—
53C22⋊Q8×C89—21no—
54C22⋊Q8×C89C2211yescharacteristic
55#121×C89C2211yescharacteristic
56C4×Q8×C89C2211yescharacteristic, complemented
57C4×D4×C89C2211yescharacteristic, complemented
58#117×C89C2211yescharacteristic
59C23×D89—21no—
60C2×D356—21no—
61C2×D356—22no—
62C2×D356—22no—
63C2×D356C2311yescharacteristic
64C2×D356C2311yescharacteristic
65C2×C4×D89—21no—
66C2×C4×D89—21no—
67C2×C4×D89—21no—
68C2×C4×D89—21no—
69#13083561—22no—
70#13083561—22no—
71#13083559—22no—
72#13083559—22no—
73C2×#10623494C2311yescharacteristic
74C2×#10623494C2311yescharacteristic
75C2×#10623494C2311yescharacteristic
76C2×#10623494C2311yescharacteristic
77C4⋊Dic89C2311yescharacteristic
78C4⋊Dic89C2311yescharacteristic
79C22⋊Dic89—21no—
80#13083551—21no—
81#13083551—21no—
82#13083551—21no—
83#13083551—21no—
84C4×Dic89—21no—
85C2×Q8×C89—21no—
86C2×Q8×C89C2311yescharacteristic
87C2×D4×C89—21no—
88C2×D4×C89C2311yescharacteristic
89C22×C4×C89—21no—
90C22×C4×C89C2311yescharacteristic
91C4⋊C4×C89—21no—
92C4⋊C4×C89—21no—
93C4⋊C4×C89—21no—
94C4⋊C4×C89D411yescharacteristic
95C4⋊C4×C89D411yescharacteristic
96C4⋊C4×C89C2311yescharacteristic
97C4⋊C4×C89C2311yescharacteristic
98C22⋊C4×C89—21no—
99C22⋊C4×C89—21no—
100C22⋊C4×C89—21no—
101C22⋊C4×C89—21no—
102C22⋊C4×C89—21no—
103C22⋊C4×C89D411yescharacteristic
104C22⋊C4×C89D411yescharacteristic
105C42×C89—21no—
106C42×C89C2311yescharacteristic
107C42×C89C2311yescharacteristic
108C23×C89—21no—
109C23×C89C2×D411yescharacteristic
110C22×D89—21no—
111C22×D89—21no—
112C22×D89—24no—
113C22×D89—81no—
114C22×D89—81no—
115Q8×C89—21no—
116Q8×C89—21no—
117Q8×C89—81no—
118D4×C89—21no—
119D4×C89—21no—
120D4×C89—81no—
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×C89C2×D411yescharacteristic
128C2×C4×C89C2×D411yescharacteristic
129C2×C4×C89C2×D411yescharacteristic
130C2×C4×C89C2×D411yescharacteristic
131C2×C4×C89C2×D411yescharacteristic
132C2×C4×C89C2411yescharacteristic
133C2×Dic89—21no—
134C2×Dic89—21no—
135D356—24no—
136D356—21no—
137D356—21no—
138D356#4112yes—
139D356#4112yes—
140C4×D89—81no—
141C4×D89—81no—
142C4×D89—81no—
143C4×D89—81no—
144#10623494—21no—
145#10623494—21no—
146#10623494—21no—
147#10623494—21no—
148C22×C89—21no—
149C22×C89—21no—
150C22×C89—21no—
151C22×C89—41no—
152C22×C89—41no—
153C22×C89—41no—
154C22×C89C22×D411yescharacteristic
155C2×D89—22no—
156C2×D89—22no—
157C2×D89—41no—
158C2×D89—41no—
159C2×D89—41no—
160C2×D89—41no—
161C2×D89—84no—
162C4×C89—21no—
163C4×C89—21no—
164C4×C89—21no—
165C4×C89—21no—
166C4×C89—21no—
167C4×C89—41no—
168C4×C89—41no—
169C4×C89—41no—
170C4×C89C2×#4111yescharacteristic
171C4×C89C2×#4111yescharacteristic
172Dic89—41no—
173Dic89—41no—
174C2×C89—41no—
175C2×C89—81no—
176C2×C89#52511yescharacteristic
177C2×C89#57611yescharacteristic
178C2×C89#57711yescharacteristic
179D89—42no—
180D89—42no—
181#3118—891nomaximal, Sylow
182C89#311811yescharacteristic, complemented, Sylow
183#542D8911yescharacteristic, complemented
184#518—891no—
185#485—891no—
186#482—891no—
187#476—891no—
188#474—891no—
189#463—891no—
190#463—891no—
191#450—891no—
192#447—891no—
193#442—891no—
194#440—891no—
195C4×SD16—891no—
196C4×D8—891no—
197#433—891no—
198C22×D4—891no—
199C2×SD16—891no—
200C2×SD16—891no—
201C2×D8—891no—
202C2×D8—891no—
203C4⋊Q8C2×D8911yescharacteristic, complemented
204#126—21no—
205#124—21no—
206#124C2×D8911yescharacteristic, complemented
207#123—21no—
208C22⋊Q8—21no—
209C22⋊Q8C2×D8911yescharacteristic
210#121C2×D8911yescharacteristic
211C4×Q8C2×D8911yescharacteristic, complemented
212C4×D4—891no—
213C4×D4—891no—
214C4×D4—891no—
215C4×D4—891no—
216C4×D4—1781no—
217C4×D4—1781no—
218C4×D4C2×D8911yescharacteristic, complemented
219#117—891no—
220#117C2×D8911yescharacteristic
221C2×C22⋊C4—1781no—
222C2×C22⋊C4—1781no—
223#107—891no—
224#107—891no—
225#106—891no—
226#106—891no—
227C4⋊C8—891no—
228C4⋊C8—891no—
229#103—891no—
230#103—891no—
231#102—891no—
232#102—891no—
233#102—891no—
234#102—891no—
235#102—891no—
236#102—891no—
237C22⋊C8—891no—
238C22⋊C8—891no—
239#97—891no—
240C4×C8—891no—
241C24—1781no—
242C2×Q8—21no—
243C2×Q8C22×D8911yescharacteristic
244C2×D4—21no—
245C2×D4—891no—
246C2×D4—891no—
247C2×D4—1782no—
248C2×D4—1782no—
249C2×D4—1781no—
250C2×D4C22×D8911yescharacteristic
251C22×C4—21no—
252C22×C4—1781no—
253C22×C4—1781no—
254C22×C4—1781no—
255C22×C4—1781no—
256C22×C4C22×D8911yescharacteristic
257SD16—1782no—
258SD16—1782no—
259D8—1782no—
260D8—1782no—
261C2×C8—891no—
262C2×C8—891no—
263C2×C8—891no—
264C2×C8—891no—
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—891no—
269C4⋊C4—891no—
270C4⋊C4C22⋊D8911yescharacteristic
271C4⋊C4C22⋊D8911yescharacteristic
272C4⋊C4C22×D8911yescharacteristic
273C4⋊C4C22×D8911yescharacteristic
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—1781no—
280C22⋊C4—1781no—
281C22⋊C4—1781no—
282C22⋊C4—1781no—
283C22⋊C4—1781no—
284C22⋊C4C22⋊D8911yescharacteristic
285C22⋊C4C22⋊D8911yescharacteristic
286C42—21no—
287C42—1781no—
288C42C22×D8911yescharacteristic
289C42C22×D8911yescharacteristic
290C23—21no—
291C23—1784no—
292C23—1781no—
293C23—1781no—
294C23—7121no—
295C23—7121no—
296C23C2×C22⋊D8911yescharacteristic
297Q8—21no—
298Q8—21no—
299Q8—81no—
300D4—21no—
301D4—21no—
302D4—81no—
303D4—892no—
304D4—892no—
305D4—1784no—
306D4—1781no—
307D4—1781no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—81no—
314C2×C4—1781no—
315C2×C4—1781no—
316C2×C4—7121no—
317C2×C4—7121no—
318C2×C4—7121no—
319C2×C4—7121no—
320C2×C4C2×C22⋊D8911yescharacteristic
321C2×C4C2×C22⋊D8911yescharacteristic
322C2×C4C2×C22⋊D8911yescharacteristic
323C2×C4C2×C22⋊D8911yescharacteristic
324C2×C4C2×C22⋊D8911yescharacteristic
325C2×C4C23×D8911yescharacteristic
326C8—1781no—
327C8—1781no—
328C8—1781no—
329C8—1781no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—3561no—
337C22—3561no—
338C22—3561no—
339C22—3561no—
340C22—1782no—
341C22—1782no—
342C22—7124no—
343C22C22×C22⋊D8911yescharacteristic
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—41no—
350C4—41no—
351C4—41no—
352C4—3561no—
353C4—3561no—
354C4#41×D8911yescharacteristic
355C4#41×D8911yescharacteristic
356C2—41no—
357C2—81no—
358C2—3562no—
359C2—3562no—
360C2#1915210511yescharacteristic
361C2#1915240111yescharacteristic
362C2#1915240611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D89
commutator, cosocleC2×C4×C89C24
FrattiniC2×C4C23×D89
Fitting#542×C89C2
socleC22×C89C22×D4
prime radical#19151731C2
hypercenter#542D89
hypocenterC89#3118
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C22 ◁ #117 ◁ #542

Complements

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

NH ≅ G/Ntype
1. #19152072C2semidirect
2. #19151936C2semidirect
3. #19151919C2semidirect
4. #19151885C2semidirect
5. #19151875C2semidirect
6. #19151810C2semidirect
7. #19151810C2semidirect
8. #19151748C2semidirect
10. #19151708C2semidirect
11. #19151696C2semidirect
12. C4×#13083561C2semidirect
13. C4×#13083559C2semidirect
14. #19151659C2semidirect
15. #542×C89C2semidirect
30. #15667945C22semidirect
31. #15667945C22semidirect
32. #15667943C22semidirect
33. #15667943C22semidirect
34. C4⋊#10623494C22semidirect
35. C4⋊#10623494C22semidirect
36. #15667936C22semidirect
37. #15667936C22semidirect
38. #15667933C22semidirect
39. #15667933C22semidirect
46. #15667923C22semidirect
47. C4×#10623494C22semidirect
48. C4⋊Q8×C89C22semidirect
51. #124×C89C22semidirect
56. C4×Q8×C89C22semidirect
57. C4×D4×C89C22semidirect
182. C89#3118semidirect
183. #542D89semidirect
203. C4⋊Q8C2×D89semidirect
206. #124C2×D89semidirect
211. C4×Q8C2×D89semidirect
218. C4×D4C2×D89semidirect

Maximal subgroups

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

subgroupindex
#191520722
#191519362
#191519192
#191518852
#191518752
#191518102
#191517482
#191517312
#191517082
#191516962
C4×#130835612
C4×#130835592
#191516592
#542×C892
#311889