Finite Group Databasebeta

← #26031346

Subgroups — #26031346

Order 11392.

408 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19152219C211yesmaximal, characteristic, complemented
2#19151985C211yesmaximal, characteristic, complemented
3#19151980C211yesmaximal, characteristic, complemented
4#19151957C211yesmaximal, characteristic, complemented
5#19151944C211yesmaximal, characteristic, complemented
6#19151817C211yesmaximal, characteristic, complemented
7#19151810C211yesmaximal, characteristic, complemented
8#19151795C211yesmaximal, characteristic, complemented
9#19151790C211yesmaximal, characteristic, complemented
10#19151760C211yesmaximal, characteristic, complemented
11#19151749C211yesmaximal, characteristic, complemented
12#19151743C211yesmaximal, characteristic, complemented
13#19151732C211yesmaximal, characteristic, complemented
14#19151659C211yesmaximal, characteristic, complemented
15#535×C89C211yesmaximal, characteristic, complemented
16C2×#13083564C2211yescharacteristic, complemented
17C2×#13083562C2211yescharacteristic
18C2×#13083562C2211yescharacteristic
19C2×#13083562C2211yescharacteristic, complemented
20C2×#13083561C2211yescharacteristic, complemented
21C2×#13083559C2211yescharacteristic
22C2×#13083559C2211yescharacteristic
23C2×#13083559C2211yescharacteristic, complemented
24#15668012C2211yescharacteristic, complemented
25#15668007—21no—
26#15668000C2211yescharacteristic, complemented
27#15667998—21no—
28#15667994—21no—
29#15667991C2211yescharacteristic
30#15667990—21no—
31#15667986C2211yescharacteristic
32C4×Dic178C2211yescharacteristic, complemented
33C4×D356C2211yescharacteristic, complemented
34C4⋊#10623494C2211yescharacteristic, complemented
35C4⋊#10623494C2211yescharacteristic, complemented
36#15667936C2211yescharacteristic, complemented
37#15667936C2211yescharacteristic, complemented
38#15667933C2211yescharacteristic
39#15667933C2211yescharacteristic
40#15667933C2211yescharacteristic
41#15667933C2211yescharacteristic
42#15667933C2211yescharacteristic, complemented
43#15667933C2211yescharacteristic, complemented
44C22⋊#10623494C2211yescharacteristic
45C22⋊#10623494C2211yescharacteristic
46#15667923C2211yescharacteristic, complemented
47C4×#10623494C2211yescharacteristic, complemented
48C2×#41×C89C2211yescharacteristic
49C22×D4×C89C2211yescharacteristic
50#127×C89C2211yescharacteristic
51#127×C89C2211yescharacteristic
52#124×C89C2211yescharacteristic
53#124×C89C2211yescharacteristic
54#121×C89—21no—
55#121×C89—21no—
56#120×C89—21no—
57#120×C89—21no—
58#117×C89C2211yescharacteristic
59C2×Dic178—21no—
60C2×Dic178C2311yescharacteristic
61C2×D356C2311yescharacteristic
62C2×C22⋊D89—21no—
63C2×C4×D89—21no—
64#13083564—41no—
65#13083562—41no—
66#13083562—41no—
67#13083562—41no—
68#13083561—41no—
69#13083559—41no—
70#13083559—41no—
71#13083559—41no—
72C2×#10623494C2311yescharacteristic
73C2×#10623494C2311yescharacteristic
74C2×#10623494C2311yescharacteristic
75C2×#10623494C2311yescharacteristic
76C4⋊Dic89—21no—
77C4⋊Dic89C2311yescharacteristic
78C4⋊Dic89C2311yescharacteristic
79#13083553—21no—
80#13083553—21no—
81C22⋊Dic89—21no—
82#13083551—21no—
83#13083551—21no—
84#13083551—21no—
85#13083551—21no—
86C4×Dic89—21no—
87C24×C89—21no—
88#41×C89—41no—
89#41×C89—41no—
90C2×Q8×C89C2311yescharacteristic
91C2×D4×C89—21no—
92C2×D4×C89—21no—
93C2×D4×C89—21no—
94C2×D4×C89—21no—
95C2×D4×C89—21no—
96C2×D4×C89—21no—
97C2×D4×C89—41no—
98C2×D4×C89—41no—
99C2×D4×C89C2311yescharacteristic
100C2×D4×C89C2311yescharacteristic
101C2×D4×C89C2311yescharacteristic
102C22×C4×C89—21no—
103C22×C4×C89C2311yescharacteristic
104C4⋊C4×C89D411yescharacteristic
105C4⋊C4×C89D411yescharacteristic
106C22⋊C4×C89—21no—
107C22⋊C4×C89—21no—
108C22⋊C4×C89—21no—
109C22⋊C4×C89—21no—
110C22⋊C4×C89D411yescharacteristic
111C22⋊C4×C89D411yescharacteristic
112C42×C89C2311yescharacteristic
113C42×C89C2311yescharacteristic
114C23×C89—21no—
115C23×C89—21no—
116C23×C89—21no—
117C23×C89—42no—
118C23×C89—81no—
119C23×C89—81no—
120C23×C89C2×D411yescharacteristic
121C22×D89—21no—
122Q8×C89—21no—
123Q8×C89—21no—
124D4×C89—21no—
125D4×C89—21no—
126D4×C89—21no—
127D4×C89—21no—
128D4×C89—21no—
129D4×C89—21no—
130D4×C89—42no—
131D4×C89—42no—
132D4×C89—81no—
133D4×C89—81no—
134D4×C89—81no—
135D4×C89—81no—
136C2×C4×C89—21no—
137C2×C4×C89—21no—
138C2×C4×C89—21no—
139C2×C4×C89—42no—
140C2×C4×C89C2×D411yescharacteristic
141C2×C4×C89C2×D411yescharacteristic
142C2×C4×C89C2×D411yescharacteristic
143C2×C4×C89C2×D411yescharacteristic
144C2×C4×C89C2×D411yescharacteristic
145C2×C4×C89C2411yescharacteristic
146C22⋊D89—81no—
147C2×Dic89—21no—
148C2×Dic89—21no—
149C2×Dic89—21no—
150D356—21no—
151D356—21no—
152C4×D89—81no—
153Dic178—21no—
154Dic178—21no—
155Dic178—81no—
156#10623494—21no—
157#10623494—21no—
158#10623494—21no—
159#10623494—21no—
160C22×C89—21no—
161C22×C89—21no—
162C22×C89—21no—
163C22×C89—41no—
164C22×C89—41no—
165C22×C89—41no—
166C22×C89—41no—
167C22×C89—41no—
168C22×C89—41no—
169C22×C89—41no—
170C22×C89—41no—
171C22×C89—41no—
172C22×C89—84no—
173C22×C89C22×D411yescharacteristic
174C2×D89—41no—
175C2×D89—41no—
176C2×D89—41no—
177C4×C89—21no—
178C4×C89—21no—
179C4×C89—21no—
180C4×C89—21no—
181C4×C89—21no—
182C4×C89—41no—
183C4×C89H(5,𝔽2)11yescharacteristic
184C4×C89H(5,𝔽2)11yescharacteristic
185Dic89—41no—
186Dic89—41no—
187Dic89—41no—
188C2×C89—41no—
189C2×C89—81no—
190C2×C89—81no—
191C2×C89—81no—
192C2×C89#53511yescharacteristic
193C2×C89#57611yescharacteristic
194C2×C89#57711yescharacteristic
195D89—81no—
196#3224—891nomaximal, Sylow
197C89#322411yescharacteristic, complemented, Sylow
198#542—891no—
199#535D8911yescharacteristic, complemented
200#496—891no—
201#495—891no—
202#489—891no—
203#486—891no—
204#464—891no—
205#463—891no—
206#460—891no—
207#459—891no—
208#452—891no—
209#450—891no—
210#449—891no—
211#447—891no—
212#433—891no—
213C2×#41C2×D8911yescharacteristic
214C22×D4C2×D8911yescharacteristic
215C2×Q16—891no—
216C2×SD16—891no—
217C2×SD16—891no—
218C2×SD16—891no—
219C2×SD16—891no—
220C2×D8—891no—
221C2×D8—891no—
222C2×D8—891no—
223C4⋊Q8—891no—
224#127C2×D8911yescharacteristic
225#127C2×D8911yescharacteristic
226#126—1781no—
227#124—891no—
228#124—1781no—
229#124C2×D8911yescharacteristic
230#124C2×D8911yescharacteristic
231#123—1781no—
232C22⋊Q8—891no—
233C22⋊Q8—1781no—
234#121—21no—
235#121—21no—
236#121—891no—
237#120—21no—
238#120—21no—
239C4×Q8—891no—
240C4×D4—891no—
241#117C2×D8911yescharacteristic
242C4⋊C8—891no—
243C4⋊C8—891no—
244#103—891no—
245#103—891no—
246#102—891no—
247#102—891no—
248#102—891no—
249#102—891no—
250#102—891no—
251#102—891no—
252C22⋊C8—891no—
253C22⋊C8—891no—
254#97—891no—
255C4×C8—891no—
256C24—21no—
257#41—41no—
258#41—41no—
259C2×Q8—891no—
260C2×Q8—1781no—
261C2×Q8C22×D8911yescharacteristic
262C2×D4—21no—
263C2×D4—21no—
264C2×D4—21no—
265C2×D4—21no—
266C2×D4—21no—
267C2×D4—21no—
268C2×D4—41no—
269C2×D4—41no—
270C2×D4—891no—
271C2×D4—1781no—
272C2×D4C22×D8911yescharacteristic
273C2×D4C22×D8911yescharacteristic
274C2×D4C22×D8911yescharacteristic
275C22×C4—21no—
276C22×C4—1781no—
277C22×C4C22×D8911yescharacteristic
278Q16—3561no—
279SD16—3561no—
280SD16—3561no—
281SD16—3561no—
282SD16—3561no—
283D8—3561no—
284D8—3561no—
285D8—3561no—
286C2×C8—891no—
287C2×C8—891no—
288C2×C8—891no—
289C2×C8—891no—
290C4⋊C4—891no—
291C4⋊C4—891no—
292C4⋊C4—1781no—
293C4⋊C4—1781no—
294C4⋊C4—1781no—
295C4⋊C4C22⋊D8911yescharacteristic
296C4⋊C4C22⋊D8911yescharacteristic
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—21no—
300C22⋊C4—21no—
301C22⋊C4—1781no—
302C22⋊C4—1781no—
303C22⋊C4—1781no—
304C22⋊C4—1781no—
305C22⋊C4—1781no—
306C22⋊C4C22⋊D8911yescharacteristic
307C22⋊C4C22⋊D8911yescharacteristic
308C42—1781no—
309C42C22×D8911yescharacteristic
310C42C22×D8911yescharacteristic
311C23—21no—
312C23—21no—
313C23—21no—
314C23—42no—
315C23—81no—
316C23—81no—
317C23—1781no—
318C23C2×C22⋊D8911yescharacteristic
319Q8—21no—
320Q8—21no—
321Q8—1781no—
322Q8—1781no—
323Q8—7121no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—21no—
328D4—21no—
329D4—21no—
330D4—42no—
331D4—42no—
332D4—81no—
333D4—81no—
334D4—81no—
335D4—81no—
336D4—1781no—
337D4—1781no—
338D4—7121no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—42no—
343C2×C4—1781no—
344C2×C4—1781no—
345C2×C4—1781no—
346C2×C4—7121no—
347C2×C4C2×C22⋊D8911yescharacteristic
348C2×C4C2×C22⋊D8911yescharacteristic
349C2×C4C2×C22⋊D8911yescharacteristic
350C2×C4C2×C22⋊D8911yescharacteristic
351C2×C4C2×C22⋊D8911yescharacteristic
352C2×C4C23×D8911yescharacteristic
353C8—1781no—
354C8—1781no—
355C8—1781no—
356C8—1781no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—84no—
370C22—3561no—
371C22—3561no—
372C22—3561no—
373C22C22×C22⋊D8911yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—21no—
378C4—21no—
379C4—41no—
380C4—3561no—
381C4—3561no—
382C4—3561no—
383C4#1566805711yescharacteristic
384C4#1566805711yescharacteristic
385C2—41no—
386C2—81no—
387C2—81no—
388C2—81no—
389C2—7121no—
390C2#1915216511yescharacteristic
391C2#1915240111yescharacteristic
392C2#1915240911yescharacteristic
subgroupG/H
centerC22C22×C22⋊D89
commutator, cosocleC2×C4×C89C24
FrattiniC2×C4C23×D89
Fitting#535×C89C2
socleC22×C89C22×D4
hypercenter#535D89
hypocenterC89#3224
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C22 ◁ #117 ◁ #535

Complements

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

NH ≅ G/Ntype
1. #19152219C2semidirect
2. #19151985C2semidirect
3. #19151980C2semidirect
4. #19151957C2semidirect
5. #19151944C2semidirect
6. #19151817C2semidirect
7. #19151810C2semidirect
8. #19151795C2semidirect
9. #19151790C2semidirect
10. #19151760C2semidirect
11. #19151749C2semidirect
12. #19151743C2semidirect
13. #19151732C2semidirect
14. #19151659C2semidirect
15. #535×C89C2semidirect
16. C2×#13083564C22semidirect
19. C2×#13083562C22semidirect
20. C2×#13083561C22semidirect
23. C2×#13083559C22semidirect
24. #15668012C22semidirect
26. #15668000C22semidirect
32. C4×Dic178C22semidirect
33. C4×D356C22semidirect
34. C4⋊#10623494C22semidirect
35. C4⋊#10623494C22semidirect
36. #15667936C22semidirect
37. #15667936C22semidirect
42. #15667933C22semidirect
43. #15667933C22semidirect
46. #15667923C22semidirect
47. C4×#10623494C22semidirect
197. C89#3224semidirect
199. #535D89semidirect

Maximal subgroups

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

subgroupindex
#191522192
#191519852
#191519802
#191519572
#191519442
#191518172
#191518102
#191517952
#191517902
#191517602
#191517492
#191517432
#191517322
#191516592
#535×C892
#322489