Finite Group Databasebeta

← #26032404

Subgroups — #26032404

Order 11392.

414 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19152311C211yesmaximal, characteristic, complemented
2#19152236C211yesmaximal, characteristic, complemented
3#19151959C211yesmaximal, characteristic, complemented
4#19151938C211yesmaximal, characteristic, complemented
5#19151922C211yesmaximal, characteristic, complemented
6#19151876C211yesmaximal, characteristic, complemented
7#19151847C211yesmaximal, characteristic, complemented
8#19151834C211yesmaximal, characteristic, complemented
9#19151816C211yesmaximal, characteristic, complemented
10#19151743C211yesmaximal, characteristic, complemented
11#19151733C211yesmaximal, characteristic, complemented
12#19151707C211yesmaximal, characteristic, complemented
13#19151669C211yesmaximal, characteristic, complemented
14#19151601C211yesmaximal, characteristic, complemented
15#416×C89C211yesmaximal, characteristic, complemented
16C2×D4×D89C2211yescharacteristic
17C2×#13083561C2211yescharacteristic, complemented
18C2×D712C2211yescharacteristic
19C2×#13083559C2211yescharacteristic
20C2×#13083557C2211yescharacteristic
21#15668011C2211yescharacteristic, complemented
22#15668001C2211yescharacteristic
23#15668000—21no—
24#15667998—21no—
25#15667995—21no—
26#15667988C2211yescharacteristic
27#15667987C2211yescharacteristic
28#15667986C2211yescharacteristic
29#15667986C2211yescharacteristic, complemented
30#15667985—21no—
31#15667984—21no—
32#15667980—21no—
33D4×Dic89C2211yescharacteristic
34#15667974C2211yescharacteristic, complemented
35C4×C22⋊D89C2211yescharacteristic
36#15667970C2211yescharacteristic
37#15667969—21no—
38C2×#13083551—21no—
39#15667946C2211yescharacteristic, complemented
40#15667945C2211yescharacteristic, complemented
41#15667943C2211yescharacteristic, complemented
42#15667941C2211yescharacteristic, complemented
43#15667936C2211yescharacteristic, complemented
44#15667934C2211yescharacteristic
45#15667934C2211yescharacteristic, complemented
46#15667933C2211yescharacteristic
47#15667932C2211yescharacteristic
48#15667932C2211yescharacteristic
49C22⋊#10623494C2211yescharacteristic, complemented
50#15667924C2211yescharacteristic
51#15667922C2211yescharacteristic, complemented
52C2×#41×C89C2211yescharacteristic
53C22×C8×C89C2211yescharacteristic, complemented
54#117×C89C2211yescharacteristic, complemented
55#103×C89C2211yescharacteristic, complemented
56#103×C89C2211yescharacteristic, complemented
57#102×C89C2211yescharacteristic
58#102×C89C2211yescharacteristic
59C23×D89—21no—
60C2×Dic178—21no—
61C2×D356—21no—
62C2×D356C2311yescharacteristic
63C2×D356C2311yescharacteristic
64C2×C22⋊D89—21no—
65C2×C22⋊D89—21no—
66C2×C22⋊D89—21no—
67C2×C22⋊D89D411yescharacteristic
68D4×D89—22no—
69D4×D89—41no—
70C22×Dic89—21no—
71C2×C4×D89—21no—
72C2×C4×D89C2311yescharacteristic
73#13083561—41no—
74D712—41no—
75#13083559—22no—
76#13083557—41no—
77C2×#10623494C2311yescharacteristic
78C2×#10623494C2311yescharacteristic
79C4⋊Dic89C2311yescharacteristic
80C4⋊Dic89C2311yescharacteristic
81#13083553—21no—
82#13083553—21no—
83#13083553D411yescharacteristic
84C22⋊Dic89—21no—
85C22⋊Dic89D411yescharacteristic
86#13083551—21no—
87#13083551—21no—
88#13083551—21no—
89#13083551—21no—
90#13083551—21no—
91#13083551—21no—
92#13083551—21no—
93#13083551—21no—
94#13083551D411yescharacteristic
95C4×Dic89—21no—
96C4×Dic89C2311yescharacteristic
97#41×C89—22no—
98#41×C89—41no—
99C2×Q8×C89C2311yescharacteristic
100C2×D4×C89—21no—
101C2×D4×C89C2311yescharacteristic
102C22×C4×C89—21no—
103C22×C4×C89C2311yescharacteristic
104C2×C8×C89—41no—
105C2×C8×C89C2311yescharacteristic
106C2×C8×C89C2311yescharacteristic
107C4⋊C4×C89C2311yescharacteristic
108C4⋊C4×C89C2311yescharacteristic
109C22⋊C4×C89—21no—
110C42×C89—21no—
111C23×C89—21no—
112C23×C89C2×D411yescharacteristic
113C22×D89—21no—
114C22×D89—21no—
115C22×D89—42no—
116C22×D89—42no—
117C22×D89—81no—
118C22×D89C2×D411yescharacteristic
119Q8×C89—21no—
120Q8×C89—21no—
121D4×C89—21no—
122D4×C89—42no—
123D4×C89#4112yes—
124C2×C4×C89—21no—
125C2×C4×C89—21no—
126C2×C4×C89—21no—
127C2×C4×C89—21no—
128C2×C4×C89—21no—
129C2×C4×C89—42no—
130C2×C4×C89C2×D411yescharacteristic
131C2×C4×C89C2411yescharacteristic
132C22⋊D89—41no—
133C22⋊D89—42no—
134C22⋊D89—81no—
135C22⋊D89—81no—
136C2×Dic89—21no—
137C2×Dic89—21no—
138C2×Dic89—81no—
139C2×Dic89C2×D411yescharacteristic
140C2×Dic89C2×D411yescharacteristic
141C2×Dic89C2×D411yescharacteristic
142D356—21no—
143D356—21no—
144D356—21no—
145D356—21no—
146D356—81no—
147C4×D89—21no—
148C4×D89—21no—
149C4×D89—42no—
150Dic178—81no—
151C8×C89—21no—
152C8×C89—21no—
153#10623494—21no—
154#10623494—21no—
155C22×C89—22no—
156C22×C89—21no—
157C22×C89—21no—
158C22×C89—21no—
159C22×C89—41no—
160C22×C89—41no—
161C22×C89C22×D411yescharacteristic
162C2×D89—21no—
163C2×D89—21no—
164C2×D89—21no—
165C2×D89—41no—
166C2×D89—41no—
167C2×D89—41no—
168C2×D89—41no—
169C2×D89—41no—
170C2×D89—41no—
171C2×D89—84no—
172C4×C89—21no—
173C4×C89—41no—
174C4×C89—41no—
175C4×C89—41no—
176C4×C89C2×#4111yescharacteristic
177C4×C89H(5,𝔽2)11yescharacteristic
178Dic89—21no—
179Dic89—21no—
180Dic89—21no—
181Dic89—41no—
182Dic89—41no—
183C2×C89—42no—
184C2×C89—41no—
185C2×C89#54611yescharacteristic
186C2×C89#57511yescharacteristic
187C2×C89#57611yescharacteristic
188D89—41no—
189D89—81no—
190D89—81no—
191#3319—891nomaximal, Sylow
192C89#331911yescharacteristic, complemented, Sylow
193#555—891no—
194#546—891no—
195#489—891no—
196#485—891no—
197#482—891no—
198#474—891no—
199#468—891no—
200#466—891no—
201#463—891no—
202#449—891no—
203#447—891no—
204#442—891no—
205#435—891no—
206#418—891no—
207#416D8911yescharacteristic, complemented
208C2×#41C2×D8911yescharacteristic
209C22×D4—891no—
210C2×SD16—891no—
211C2×D8—891no—
212C2×D8—891no—
213C2×M16—891no—
214C22×C8C2×D8911yescharacteristic, complemented
215C4⋊Q8—891no—
216#124—891no—
217#124—1781no—
218#124—1781no—
219#123—1781no—
220C22⋊Q8—891no—
221#121—891no—
222#121—891no—
223#121—891no—
224#121—1781no—
225#121—1781no—
226#120—1781no—
227C4×D4—891no—
228C4×D4—891no—
229C4×D4—891no—
230#117—891no—
231#117—1781no—
232#117C2×D8911yescharacteristic, complemented
233C2×C22⋊C4—1781no—
234#107—891no—
235#107—891no—
236#106—891no—
237C4⋊C8—891no—
238#103—891no—
239#103C2×D8911yescharacteristic, complemented
240#103C2×D8911yescharacteristic, complemented
241#102—891no—
242#102—891no—
243#102—891no—
244#102—891no—
245#102—891no—
246#102C2×D8911yescharacteristic
247#102C2×D8911yescharacteristic
248C22⋊C8—891no—
249C22⋊C8—891no—
250#97—891no—
251C24—1781no—
252#41—22no—
253#41—41no—
254C2×Q8—1781no—
255C2×Q8C22×D8911yescharacteristic
256C2×D4—21no—
257C2×D4—891no—
258C2×D4—891no—
259C2×D4—891no—
260C2×D4—3561no—
261C2×D4—1781no—
262C2×D4—1781no—
263C2×D4—1782no—
264C2×D4—1781no—
265C2×D4—1781no—
266C2×D4C22×D8911yescharacteristic
267C22×C4—21no—
268C22×C4—891no—
269C22×C4—1781no—
270C22×C4—1781no—
271C22×C4C22×D8911yescharacteristic
272SD16—3561no—
273D8—3561no—
274D8—1782no—
275M16—3561no—
276C2×C8—41no—
277C2×C8—891no—
278C2×C8—891no—
279C2×C8C22×D8911yescharacteristic
280C2×C8C22×D8911yescharacteristic
281C4⋊C4—891no—
282C4⋊C4—891no—
283C4⋊C4—891no—
284C4⋊C4—1781no—
285C4⋊C4—1781no—
286C4⋊C4C22×D8911yescharacteristic
287C4⋊C4C22×D8911yescharacteristic
288C22⋊C4—21no—
289C22⋊C4—891no—
290C22⋊C4—891no—
291C22⋊C4—1781no—
292C22⋊C4—1781no—
293C22⋊C4—1781no—
294C22⋊C4—1781no—
295C22⋊C4—1781no—
296C22⋊C4—1781no—
297C22⋊C4—1781no—
298C22⋊C4—1781no—
299C22⋊C4—1781no—
300C42—21no—
301C42—891no—
302C42—1781no—
303C23—21no—
304C23—891no—
305C23—3562no—
306C23—3562no—
307C23—1781no—
308C23—1781no—
309C23—7121no—
310C23D4×D8911yescharacteristic
311Q8—21no—
312Q8—21no—
313Q8—7121no—
314D4—21no—
315D4—42no—
316D4—3562no—
317D4—3561no—
318D4—1781no—
319D4—1781no—
320D4—1781no—
321D4—1781no—
322D4—7121no—
323D4—7121no—
324D4—7121no—
325D4#1308357412yes—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—42no—
332C2×C4—891no—
333C2×C4—891no—
334C2×C4—891no—
335C2×C4—3562no—
336C2×C4—1781no—
337C2×C4—1781no—
338C2×C4—1781no—
339C2×C4—1781no—
340C2×C4—7121no—
341C2×C4D4×D8911yescharacteristic
342C2×C4C23×D8911yescharacteristic
343C8—21no—
344C8—21no—
345C8—1781no—
346C8—1781no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—22no—
351C22—41no—
352C22—41no—
353C22—3561no—
354C22—3561no—
355C22—3561no—
356C22—3561no—
357C22—3561no—
358C22—3561no—
359C22—1781no—
360C22—1781no—
361C22—1781no—
362C22—7124no—
363C22C2×D4×D8911yescharacteristic
364C4—21no—
365C4—41no—
366C4—41no—
367C4—41no—
368C4—3561no—
369C4—3561no—
370C4—1781no—
371C4—1781no—
372C4—1781no—
373C4C2×#1308357411yescharacteristic
374C4#1566805711yescharacteristic
375C2—41no—
376C2—42no—
377C2—3561no—
378C2—7121no—
379C2—7121no—
380C2#1915223811yescharacteristic
381C2#1915239511yescharacteristic
382C2#1915240011yescharacteristic
subgroupG/H
centerC22C2×D4×D89
commutator, cosocleC2×C4×C89C24
FrattiniC2×C4C23×D89
Fitting#416×C89C2
socleC22×C89C22×D4
hypercenter#416D89
hypocenterC89#3319
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C22 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
1. #19152311C2semidirect
2. #19152236C2semidirect
3. #19151959C2semidirect
4. #19151938C2semidirect
5. #19151922C2semidirect
6. #19151876C2semidirect
7. #19151847C2semidirect
8. #19151834C2semidirect
9. #19151816C2semidirect
10. #19151743C2semidirect
11. #19151733C2semidirect
12. #19151707C2semidirect
13. #19151669C2semidirect
14. #19151601C2semidirect
15. #416×C89C2semidirect
17. C2×#13083561C22semidirect
21. #15668011C22semidirect
29. #15667986C22semidirect
34. #15667974C22semidirect
39. #15667946C22semidirect
40. #15667945C22semidirect
41. #15667943C22semidirect
42. #15667941C22semidirect
43. #15667936C22semidirect
45. #15667934C22semidirect
49. C22⋊#10623494C22semidirect
51. #15667922C22semidirect
53. C22×C8×C89C22semidirect
54. #117×C89C22semidirect
55. #103×C89C22semidirect
56. #103×C89C22semidirect
192. C89#3319semidirect
207. #416D89semidirect
214. C22×C8C2×D89semidirect
232. #117C2×D89semidirect
239. #103C2×D89semidirect
240. #103C2×D89semidirect

Maximal subgroups

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

subgroupindex
#191523112
#191522362
#191519592
#191519382
#191519222
#191518762
#191518472
#191518342
#191518162
#191517432
#191517332
#191517072
#191516692
#191516012
#416×C892
#331989