Finite Group Databasebeta

← #14909108

Subgroups — #14909108

Order 2816.

602 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079152C211yesmaximal, characteristic, complemented
2#13079103C211yesmaximal, characteristic
3#13070856C212yesmaximal, complemented
4#13070854C212yesmaximal, complemented
5#13070849C212yesmaximal, complemented
6#13070838C212yesmaximal, complemented
7#13070333C211yesmaximal, characteristic, complemented
8#13070323C211yesmaximal, characteristic, complemented
9C2×#10622129C211yesmaximal, characteristic, complemented
10#13070215C211yesmaximal, characteristic, complemented
11C11×#2139C211yesmaximal, characteristic, complemented
12C2×C11×#135C2211yescharacteristic
13#10623361—21no—
14C2×#67002—21no—
15C22×D88C2211yescharacteristic
16#10623031—21no—
17C2×C11×M32C2211yescharacteristic
18C2×C11×#107C2211yescharacteristic
19#10622804C2212yes—
20#10622789—22no—
21#10622764C2212yes—
22#10622719C2211yescharacteristic
23#10622714C2211yescharacteristic
24C22×C11⋊C16C2211yescharacteristic
25#10622577—21no—
26#10622491C2212yescomplemented
27#10622489—22no—
28#10622487C2212yescomplemented
29C11×#358C2212yescomplemented
30C11×#357C2212yescomplemented
31#10622202C2211yescharacteristic, complemented
32#10622202C2211yescharacteristic, complemented
33#10622200C2211yescharacteristic, complemented
34#10622200C2211yescharacteristic, complemented
35#10622147C2212yes—
36#10622147C2212yes—
37#10622140C2212yescomplemented
38C16×Dic11C2212yescomplemented
39#10622129C2212yes—
40#10622129C2212yes—
41C2×C11×#41—21no—
42C22×D44—21no—
43C11×#135—22no—
44C11×#135—22no—
45C2×C11×Q16C2311yescharacteristic
46C2×C11×SD16—21no—
47C2×C11×D8C2311yescharacteristic
48C22×C8×C11C2311yescharacteristic
49C2×C11×C4⋊C4—21no—
50#67002—44no—
51#67000—22no—
52C2×#4325—22no—
53#66993—22no—
54#66990—42no—
55C2×#4323—22no—
56#66983—41no—
57#66983—41no—
58#66979—21no—
59#66979D411yescharacteristic
60#66977—42no—
61C2×#4318D411yescharacteristic
62C2×D88—22no—
63C2×D88—22no—
64C2×D88—21no—
65C2×D88C2312yes—
66#66943—22no—
67#66943—41no—
68#66941—22no—
69#66941—41no—
70C11×M32—22no—
71C2×C11×C16C2312yes—
72C11×#107—21no—
73C11×#107C2312yes—
74#66882C2311yescharacteristic
75#66882C2311yescharacteristic
76#66881—21no—
77#66879D412yes—
78C8×Dic11C2312yes—
79C2×C11⋊C16—22no—
80C2×C11⋊C16C2311yescharacteristic
81C2×C11⋊C16C2311yescharacteristic
82#66872—22no—
83#66871—22no—
84#33702—111nomaximal, Sylow
85C23×D11—41no—
86C11×#41—42no—
87C11×#41—42no—
88C2×Q8×C11—21no—
89C2×D4×C11—21no—
90C2×D4×C11—41no—
91C22×C4×C11—41no—
92C22×C4×C11—41no—
93C22×C4×C11C2×D411yescharacteristic
94C2×C22⋊D11—42no—
95C2×C22⋊D11—42no—
96C2×D44—22no—
97C2×D44—42no—
98C2×D44—41no—
99C2×D44—42no—
100C2×Dic22—42no—
101C11×Q16—21no—
102C11×Q16—21no—
103C11×SD16—42no—
104C11×D8—21no—
105C11×D8—21no—
106C2×C8×C11C2×D411yescharacteristic
107C2×C8×C11#4112yes—
108C2×C8×C11#4112yes—
109C2×C8×C11C2411yescharacteristic
110C11×C4⋊C4—22no—
111C11×C4⋊C4—41no—
112C22⋊Dic11—41no—
113C22⋊Dic11D812yes—
114#4325—44no—
115#4323—44no—
116(C2×D11)⋊C4—42no—
117(C2×D11)⋊C4—42no—
118C4⋊Dic11—21no—
119C4⋊Dic11—21no—
120C4⋊Dic11—42no—
121C4⋊Dic11D811yescharacteristic
122C4⋊Dic11D811yescharacteristic
123Dic11⋊C4—42no—
124Dic11⋊C4—42no—
125C4×Dic11—41no—
126C4×Dic11C2×D412yes—
127#4318SD1614yes—
128C2×C11⋊C8C2×D412yes—
129D88—22no—
130D88—22no—
131D88—42no—
132C11×C16—22no—
133C11⋊C16—21no—
134C11⋊C16—21no—
135#3164—111no—
136#3155—111no—
137#2244—112no—
138#2243—112no—
139#2242—112no—
140#2240—112no—
141#2140—111no—
142#2139D1111yescharacteristic, complemented
143#2138—111no—
144C2×#357—111no—
145#2108—111no—
146C23×C11—41no—
147C23×C11C2×D811yescharacteristic
148C22×D11—42no—
149C22×D11—82no—
150C22×D11—161no—
151C22×D11—161no—
152Q8×C11—41no—
153Q8×C11—41no—
154D4×C11—41no—
155D4×C11—41no—
156D4×C11—82no—
157C2×C4×C11—42no—
158C2×C4×C11—41no—
159C2×C4×C11—82no—
160C2×C4×C11—161no—
161C2×C4×C11#12412yes—
162C2×C4×C11C2×D811yescharacteristic
163C2×C4×C11C2×SD1612yes—
164C2×C4×C11C22×D411yescharacteristic
165C22⋊D11—162no—
166C22⋊D11—162no—
167C2×Dic11—41no—
168C2×Dic11—41no—
169C2×Dic11C2×D812yes—
170C2×Dic11C2×D812yes—
171D44—42no—
172D44—42no—
173D44—82no—
174Dic22—162no—
175C8×C11#12412yes—
176C8×C11C2×#4111yescharacteristic
177C8×C11C2×#4111yescharacteristic
178C11⋊C8C2×SD1614yes—
179C2×AGL(1,ℤ/8)—221no—
180C2×#135C2×D1111yescharacteristic
181C22×D8—111no—
182#544—221no—
183#535—221no—
184C2×M32C2×D1111yescharacteristic
185C22×C16—111no—
186#501—222no—
187#500—112no—
188#499—112no—
189#496—222no—
190#495—112no—
191#493—112no—
192#428—221no—
193#427—111no—
194C2×#107C2×D1111yescharacteristic
195#405—111no—
196#358—111no—
197#358—111no—
198#358C2×D1112yescomplemented
199#357—111no—
200#357—111no—
201#357—112no—
202#357—112no—
203#357—112no—
204#357—112no—
205#357C2×D1112yescomplemented
206#346—112no—
207C4×C16—112no—
208C22×C11—21no—
209C22×C11—21no—
210C22×C11—81no—
211C22×C11—81no—
212C22×C11—81no—
213C22×C11#48612yes—
214C22×C11C22×D811yescharacteristic
215C2×D11—82no—
216C2×D11—82no—
217C2×D11—82no—
218C2×D11—164no—
219C4×C11—81no—
220C4×C11—82no—
221C4×C11#48612yes—
222C4×C11C2×#12411yescharacteristic
223C4×C11C22×SD1611yescharacteristic
224Dic11—22no—
225Dic11—22no—
226Dic11—81no—
227Dic11—81no—
228C2×#41—21no—
229C22×D4—221no—
230AGL(1,ℤ/8)—444no—
231#135—22no—
232#135—22no—
233C2×Q16C22×D1111yescharacteristic
234C2×SD16—21no—
235C2×SD16—222no—
236C2×D8—112no—
237C2×D8—222no—
238C2×D8—222no—
239C2×D8—221no—
240C2×D8—222no—
241C2×D8C22×D1111yescharacteristic
242C2×M16—111no—
243C22×C8C22×D1111yescharacteristic
244C4⋊Q8—222no—
245C4⋊Q8—441no—
246#127—222no—
247#125—222no—
248#125—441no—
249#124—222no—
250C22⋊Q8—442no—
251#121—441no—
252#121—441no—
253#120—442no—
254#117—111no—
255#117—221no—
256C2×C4⋊C4—21no—
257M32—22no—
258C2×C16—111no—
259C2×C16—111no—
260C2×C16—222no—
261C2×C16C22×D1112yes—
262#107—21no—
263#107—111no—
264#107—111no—
265#107—222no—
266#107C22×D1112yes—
267#106—222no—
268#106—221no—
269#97—112no—
270C4×C8—112no—
271C2×C11—22no—
272C2×C11—161no—
273C2×C11C2×#48611yescharacteristic
274C2×C11#341511yescharacteristic
275C2×C11#341611yescharacteristic
276D11—162no—
277C24—441no—
278#41—42no—
279#41—42no—
280C2×Q8—21no—
281C2×Q8—442no—
282C2×D4—21no—
283C2×D4—41no—
284C2×D4—222no—
285C2×D4—442no—
286C2×D4—442no—
287C2×D4—442no—
288C2×D4—441no—
289C2×D4—442no—
290C22×C4—41no—
291C22×C4—41no—
292C22×C4D4×D1111yescharacteristic
293Q16—21no—
294Q16—21no—
295SD16—42no—
296SD16—444no—
297D8—21no—
298D8—21no—
299D8—222no—
300D8—222no—
301D8—444no—
302D8—442no—
303M16—114no—
304C2×C8—112no—
305C2×C8#433912yes—
306C2×C8D4×D1111yescharacteristic
307C2×C8#434112yes—
308C2×C8C23×D1111yescharacteristic
309C4⋊C4—22no—
310C4⋊C4—41no—
311C4⋊C4—111no—
312C4⋊C4—111no—
313C4⋊C4—221no—
314C4⋊C4—221no—
315C4⋊C4—442no—
316C4⋊C4—442no—
317C4⋊C4—442no—
318C22⋊C4—112no—
319C22⋊C4—442no—
320C22⋊C4—442no—
321C22⋊C4—441no—
322C42—112no—
323C42—441no—
324C16—22no—
325C16—221no—
326C16—221no—
327C11#3370211yescharacteristic, complemented, Sylow
328C23—41no—
329C23—442no—
330C23—882no—
331C23—1761no—
332C23—1761no—
333C23D8×D1111yescharacteristic
334Q8—41no—
335Q8—41no—
336Q8—1762no—
337D4—41no—
338D4—41no—
339D4—82no—
340D4—442no—
341D4—442no—
342D4—882no—
343D4—1762no—
344D4—1762no—
345C2×C4—41no—
346C2×C4—42no—
347C2×C4—82no—
348C2×C4—112no—
349C2×C4—112no—
350C2×C4—161no—
351C2×C4—441no—
352C2×C4—441no—
353C2×C4#6693812yes—
354C2×C4D8×D1111yescharacteristic
355C2×C4SD16×D1112yes—
356C2×C4C2×D4×D1111yescharacteristic
357C8—114no—
358C8#6693812yes—
359C8C2×#433911yescharacteristic
360C8C2×#434111yescharacteristic
361C22—21no—
362C22—21no—
363C22—81no—
364C22—81no—
365C22—81no—
366C22—882no—
367C22—882no—
368C22—882no—
369C22—1764no—
370C22#1062237312yes—
371C22C2×D8×D1111yescharacteristic
372C4—81no—
373C4—82no—
374C4—222no—
375C4—222no—
376C4—881no—
377C4—881no—
378C4#1062237312yes—
379C4C2×#6693811yescharacteristic
380C4C2×SD16×D1111yescharacteristic
381C2—22no—
382C2—161no—
383C2—1762no—
384C2C2×#1062237311yescharacteristic
385C2#1308175611yescharacteristic
386C2#1308176111yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2139C2
socleC22×C11C22×D8
prime radical#13079103C2
hypercenter#2139D11
hypocenterC11#33702
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2139

Complements

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

NH ≅ G/Ntype
1. #13079152C2semidirect
3. #13070856C2semidirect
4. #13070854C2semidirect
5. #13070849C2semidirect
6. #13070838C2semidirect
7. #13070333C2semidirect
8. #13070323C2semidirect
9. C2×#10622129C2semidirect
10. #13070215C2semidirect
11. C11×#2139C2semidirect
26. #10622491C22semidirect
28. #10622487C22semidirect
29. C11×#358C22semidirect
30. C11×#357C22semidirect
31. #10622202C22semidirect
32. #10622202C22semidirect
33. #10622200C22semidirect
34. #10622200C22semidirect
37. #10622140C22semidirect
38. C16×Dic11C22semidirect
142. #2139D11semidirect
198. #358C2×D11semidirect
205. #357C2×D11semidirect
327. C11#33702semidirect

Maximal subgroups

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

subgroupindex
#130791522
#130791032
#130708562
#130708542
#130708492
#130708382
#130703332
#130703232
C2×#106221292
#130702152
C11×#21392
#3370211