Finite Group Databasebeta

← #26031098

Subgroups — #26031098

Order 11392.

422 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19152162C211yesmaximal, characteristic, complemented
2#19151936C211yesmaximal, characteristic, complemented
3#19151919C211yesmaximal, characteristic, complemented
4#19151916C211yesmaximal, characteristic, complemented
5#19151911C211yesmaximal, characteristic, complemented
6#19151849C211yesmaximal, characteristic, complemented
7#19151846C211yesmaximal, characteristic, complemented
8#19151832C211yesmaximal, characteristic, complemented
9#19151829C211yesmaximal, characteristic, complemented
10#19151748C211yesmaximal, characteristic, complemented
11#19151743C211yesmaximal, characteristic, complemented
12#19151743C211yesmaximal, characteristic, complemented
13#19151731C211yesmaximal, characteristic, complemented
14#19151565C211yesmaximal, characteristic, complemented
15#537×C89C211yesmaximal, characteristic, complemented
16C22×D356C2211yescharacteristic
17C2×#13083561C2211yescharacteristic
18C2×#13083561C2211yescharacteristic
19C2×#13083559C2211yescharacteristic
20C2×#13083559C2211yescharacteristic
21C2×#13083558C2211yescharacteristic, complemented
22C22×#10623494C2211yescharacteristic, complemented
23#15668008—21no—
24#15668001—21no—
25#15667986C2211yescharacteristic
26#15667986C2211yescharacteristic
27#15667986C2211yescharacteristic
28#15667986C2211yescharacteristic
29#15667980—21no—
30#15667980—21no—
31#15667971C2211yescharacteristic
32#15667945C2211yescharacteristic, complemented
33#15667945C2211yescharacteristic, complemented
34#15667943C2211yescharacteristic, complemented
35#15667943C2211yescharacteristic, 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
46C22⋊#10623494C2211yescharacteristic, complemented
47C22⋊#10623494C2211yescharacteristic, complemented
48C2×#41×C89C2211yescharacteristic
49C2×#41×C89C2211yescharacteristic, complemented
50C22⋊Q8×C89—21no—
51C22⋊Q8×C89C2211yescharacteristic
52C22⋊Q8×C89C2211yescharacteristic, complemented
53#121×C89—21no—
54#121×C89—21no—
55#121×C89—21no—
56#121×C89C2211yescharacteristic
57#121×C89C2211yescharacteristic, complemented
58C2×C4⋊C4×C89C2211yescharacteristic, complemented
59C23×D89—21no—
60C2×D356—21no—
61C2×D356—41no—
62C2×D356—41no—
63C2×D356C2311yescharacteristic
64C2×D356C2311yescharacteristic
65C2×C22⋊D89—21no—
66C2×C22⋊D89—21no—
67C2×C22⋊D89—21no—
68C2×C22⋊D89—21no—
69#13083561—41no—
70#13083561—41no—
71#13083559—41no—
72#13083559—41no—
73#13083558—41no—
74C2×#10623494—41no—
75C2×#10623494C2311yescharacteristic
76C2×#10623494C2311yescharacteristic
77C2×#10623494C2311yescharacteristic
78C2×#10623494C2311yescharacteristic
79C4⋊Dic89C2311yescharacteristic
80C4⋊Dic89C2311yescharacteristic
81C22⋊Dic89—21no—
82#13083551—21no—
83#13083551—21no—
84#13083551—21no—
85#13083551—21no—
86C4×Dic89—21no—
87#41×C89—41no—
88#41×C89—41no—
89#41×C89—41no—
90#41×C89—41no—
91C2×Q8×C89D411yescharacteristic
92C2×Q8×C89C2311yescharacteristic
93C2×D4×C89—21no—
94C2×D4×C89—21no—
95C2×D4×C89—21no—
96C2×D4×C89D411yescharacteristic
97C2×D4×C89D411yescharacteristic
98C2×D4×C89D411yescharacteristic
99C2×D4×C89C2311yescharacteristic
100C22×C4×C89—21no—
101C22×C4×C89—21no—
102C22×C4×C89C2311yescharacteristic
103C22×C4×C89C2311yescharacteristic
104C22×C4×C89C2311yescharacteristic
105C4⋊C4×C89—21no—
106C4⋊C4×C89—21no—
107C4⋊C4×C89—21no—
108C4⋊C4×C89C2311yescharacteristic
109C4⋊C4×C89C2311yescharacteristic
110C22⋊C4×C89—21no—
111C22⋊C4×C89—21no—
112C22⋊C4×C89—21no—
113C22⋊C4×C89—21no—
114C23×C89—21no—
115C23×C89C2×D411yescharacteristic
116C23×C89C2×D411yescharacteristic
117C23×C89C2×D411yescharacteristic
118C22×D89—21no—
119C22×D89—21no—
120C22×D89—42no—
121C22×D89—81no—
122C22×D89—81no—
123Q8×C89—21no—
124Q8×C89—21no—
125Q8×C89—41no—
126D4×C89—21no—
127D4×C89—21no—
128D4×C89—41no—
129D4×C89—41no—
130D4×C89—41no—
131D4×C89—42no—
132D4×C89—81no—
133D4×C89—81no—
134C2×C4×C89—21no—
135C2×C4×C89—21no—
136C2×C4×C89—21no—
137C2×C4×C89—21no—
138C2×C4×C89—21no—
139C2×C4×C89—21no—
140C2×C4×C89—21no—
141C2×C4×C89—21no—
142C2×C4×C89—21no—
143C2×C4×C89—42no—
144C2×C4×C89—81no—
145C2×C4×C89C2×D411yescharacteristic
146C2×C4×C89C2×D411yescharacteristic
147C2×C4×C89C2×D411yescharacteristic
148C2×C4×C89C2411yescharacteristic
149C22⋊D89—81no—
150C22⋊D89—81no—
151C22⋊D89—81no—
152C22⋊D89—81no—
153C2×Dic89—21no—
154C2×Dic89—21no—
155D356—21no—
156D356—21no—
157D356—21no—
158D356—21no—
159D356—42no—
160#10623494—21no—
161#10623494—21no—
162#10623494—21no—
163#10623494—21no—
164C22×C89—21no—
165C22×C89—21no—
166C22×C89—21no—
167C22×C89—21no—
168C22×C89—21no—
169C22×C89—21no—
170C22×C89—21no—
171C22×C89—21no—
172C22×C89—21no—
173C22×C89—41no—
174C22×C89—41no—
175C22×C89—41no—
176C22×C89C22×D411yescharacteristic
177C2×D89—41no—
178C2×D89—41no—
179C2×D89—41no—
180C2×D89—41no—
181C2×D89—41no—
182C2×D89—41no—
183C2×D89—84no—
184C4×C89—21no—
185C4×C89—21no—
186C4×C89—21no—
187C4×C89—41no—
188C4×C89—41no—
189C4×C89—41no—
190C4×C89H(5,𝔽2)11yescharacteristic
191C4×C89H(5,𝔽2)11yescharacteristic
192Dic89—41no—
193Dic89—41no—
194C2×C89—41no—
195C2×C89—41no—
196C2×C89—41no—
197C2×C89—81no—
198C2×C89#53411yescharacteristic
199C2×C89#57611yescharacteristic
200C2×C89#57711yescharacteristic
201D89—81no—
202D89—81no—
203#3198—891nomaximal, Sylow
204C89#319811yescharacteristic, complemented, Sylow
205#537D8911yescharacteristic, complemented
206#535—891no—
207#485—891no—
208#482—891no—
209#481—891no—
210#480—891no—
211#469—891no—
212#468—891no—
213#466—891no—
214#465—891no—
215#450—891no—
216#449—891no—
217#449—891no—
218#447—891no—
219#408—891no—
220C2×#41C2×D8911yescharacteristic
221C2×#41C2×D8911yescharacteristic, complemented
222C22×D4—891no—
223C2×SD16—891no—
224C2×SD16—891no—
225C2×D8—891no—
226C2×D8—891no—
227C2×M16—891no—
228C22×C8—891no—
229#127—1781no—
230#124—1781no—
231C22⋊Q8—21no—
232C22⋊Q8C2×D8911yescharacteristic
233C22⋊Q8C2×D8911yescharacteristic, complemented
234#121—21no—
235#121—21no—
236#121—21no—
237#121—891no—
238#121—891no—
239#121—891no—
240#121—891no—
241#121C2×D8911yescharacteristic
242#121C2×D8911yescharacteristic, complemented
243#120—1781no—
244#120—1781no—
245#117—891no—
246C2×C4⋊C4C2×D8911yescharacteristic, complemented
247#107—891no—
248#107—891no—
249#106—891no—
250#106—891no—
251#103—891no—
252#103—891no—
253#102—891no—
254#102—891no—
255#102—891no—
256#102—891no—
257#102—891no—
258#102—891no—
259C22⋊C8—891no—
260C22⋊C8—891no—
261C22⋊C8—891no—
262C22⋊C8—891no—
263C24—1781no—
264#41—41no—
265#41—41no—
266#41—41no—
267#41—41no—
268C2×Q8C22⋊D8911yescharacteristic
269C2×Q8C22×D8911yescharacteristic
270C2×D4—21no—
271C2×D4—21no—
272C2×D4—21no—
273C2×D4—891no—
274C2×D4—891no—
275C2×D4—3561no—
276C2×D4—3561no—
277C2×D4—1781no—
278C2×D4—1781no—
279C2×D4—1781no—
280C2×D4—1781no—
281C2×D4—1781no—
282C2×D4C22⋊D8911yescharacteristic
283C2×D4C22⋊D8911yescharacteristic
284C2×D4C22⋊D8911yescharacteristic
285C2×D4C22×D8911yescharacteristic
286C22×C4—21no—
287C22×C4—21no—
288C22×C4C22×D8911yescharacteristic
289C22×C4C22×D8911yescharacteristic
290C22×C4C22×D8911yescharacteristic
291SD16—3561no—
292SD16—3561no—
293D8—3561no—
294D8—3561no—
295M16—3561no—
296C2×C8—891no—
297C2×C8—891no—
298C2×C8—891no—
299C2×C8—891no—
300C2×C8—3561no—
301C4⋊C4—21no—
302C4⋊C4—21no—
303C4⋊C4—21no—
304C4⋊C4—891no—
305C4⋊C4—891no—
306C4⋊C4C22×D8911yescharacteristic
307C4⋊C4C22×D8911yescharacteristic
308C22⋊C4—21no—
309C22⋊C4—21no—
310C22⋊C4—21no—
311C22⋊C4—21no—
312C22⋊C4—1781no—
313C22⋊C4—1781no—
314C22⋊C4—1781no—
315C22⋊C4—1781no—
316C22⋊C4—1781no—
317C42—1781no—
318C23—21no—
319C23—3562no—
320C23—1781no—
321C23—1781no—
322C23—7121no—
323C23—7121no—
324C23C2×C22⋊D8911yescharacteristic
325C23C2×C22⋊D8911yescharacteristic
326C23C2×C22⋊D8911yescharacteristic
327Q8—21no—
328Q8—21no—
329Q8—41no—
330D4—21no—
331D4—21no—
332D4—41no—
333D4—41no—
334D4—41no—
335D4—42no—
336D4—81no—
337D4—81no—
338D4—3562no—
339D4—1781no—
340D4—1781no—
341D4—1781no—
342D4—1781no—
343D4—7121no—
344D4—7121no—
345D4—7121no—
346D4—7121no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—42no—
357C2×C4—81no—
358C2×C4—1781no—
359C2×C4—1781no—
360C2×C4C2×C22⋊D8911yescharacteristic
361C2×C4C2×C22⋊D8911yescharacteristic
362C2×C4C2×C22⋊D8911yescharacteristic
363C2×C4C23×D8911yescharacteristic
364C8—1781no—
365C8—1781no—
366C8—1781no—
367C8—1781no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—3561no—
381C22—3561no—
382C22—3561no—
383C22—3561no—
384C22—3561no—
385C22—3561no—
386C22—7124no—
387C22C22×C22⋊D8911yescharacteristic
388C4—21no—
389C4—21no—
390C4—21no—
391C4—41no—
392C4—41no—
393C4—41no—
394C4—3561no—
395C4—3561no—
396C4#1566805711yescharacteristic
397C4#1566805711yescharacteristic
398C2—41no—
399C2—41no—
400C2—41no—
401C2—81no—
402C2—7121no—
403C2—7121no—
404C2#1915215711yescharacteristic
405C2#1915240111yescharacteristic
406C2#1915240611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D89
commutator, cosocleC2×C4×C89C24
FrattiniC2×C4C23×D89
Fitting#537×C89C2
socleC22×C89C22×D4
hypercenter#537D89
hypocenterC89#3198
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C22 ◁ C2×#41 ◁ #537

Complements

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

NH ≅ G/Ntype
1. #19152162C2semidirect
2. #19151936C2semidirect
3. #19151919C2semidirect
4. #19151916C2semidirect
5. #19151911C2semidirect
6. #19151849C2semidirect
7. #19151846C2semidirect
8. #19151832C2semidirect
9. #19151829C2semidirect
10. #19151748C2semidirect
11. #19151743C2semidirect
12. #19151743C2semidirect
13. #19151731C2semidirect
14. #19151565C2semidirect
15. #537×C89C2semidirect
21. C2×#13083558C22semidirect
22. C22×#10623494C22semidirect
32. #15667945C22semidirect
33. #15667945C22semidirect
34. #15667943C22semidirect
35. #15667943C22semidirect
36. #15667936C22semidirect
37. #15667936C22semidirect
38. #15667933C22semidirect
39. #15667933C22semidirect
46. C22⋊#10623494C22semidirect
47. C22⋊#10623494C22semidirect
49. C2×#41×C89C22semidirect
52. C22⋊Q8×C89C22semidirect
57. #121×C89C22semidirect
58. C2×C4⋊C4×C89C22semidirect
204. C89#3198semidirect
205. #537D89semidirect
221. C2×#41C2×D89semidirect
233. C22⋊Q8C2×D89semidirect
242. #121C2×D89semidirect
246. C2×C4⋊C4C2×D89semidirect

Maximal subgroups

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

subgroupindex
#191521622
#191519362
#191519192
#191519162
#191519112
#191518492
#191518462
#191518322
#191518292
#191517482
#191517432
#191517312
#191515652
#537×C892
#319889