Finite Group Databasebeta

← #14909101

Subgroups — #14909101

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#13079156C211yesmaximal, characteristic, complemented
2#13079097C211yesmaximal, characteristic
3#13070856C212yesmaximal, complemented
4#13070851C212yesmaximal, complemented
5#13070846C212yesmaximal, complemented
6#13070838C212yesmaximal, complemented
7#13070329C211yesmaximal, characteristic, complemented
8#13070321C211yesmaximal, characteristic, complemented
9C2×#10622200C211yesmaximal, characteristic, complemented
10#13070215C211yesmaximal, characteristic, complemented
11C11×#2140C211yesmaximal, characteristic, complemented
12C22×C11×D8C2211yescharacteristic
13#10623336—21no—
14C2×#66985—21no—
15C2×#66957C2211yescharacteristic
16#10623050—21no—
17C2×C11×M32C2211yescharacteristic
18C11×#427C2211yescharacteristic
19#10622768C2212yes—
20#10622767—22no—
21#10622764C2212yes—
22C2×#66882C2211yescharacteristic
23#10622714C2211yescharacteristic
24C22×C11⋊C16C2211yescharacteristic
25#10622608—21no—
26#10622491C2212yescomplemented
27#10622487C2212yescomplemented
28#10622469—22no—
29C11×#357C2212yes—
30C11×#357C2212yes—
31#10622200C2212yes—
32#10622200C2212yes—
33#10622147C2212yescomplemented
34#10622141C2212yescomplemented
35#10622140C2212yescomplemented
36C16×Dic11C2212yescomplemented
37#10622130C2211yescharacteristic, complemented
38#10622130C2211yescharacteristic, complemented
39#10622129C2211yescharacteristic, complemented
40#10622129C2211yescharacteristic, complemented
41C22×D4×C11—21no—
42C2×#4339—21no—
43C2×C11×D8—21no—
44C2×C11×D8—22no—
45C2×C11×D8—22no—
46C2×C11×D8C2312yes—
47C22×C8×C11C2311yescharacteristic
48C11×#117—21no—
49#67006—42no—
50#66993—22no—
51#66991—41no—
52#66991—41no—
53#66989—22no—
54C2×#4324—22no—
55#66985—44no—
56C2×#4323—22no—
57#66979D411yescharacteristic
58C2×C4⋊Dic11—21no—
59C2×#4318D411yescharacteristic
60C2×Dic44C2311yescharacteristic
61#66957—22no—
62#66957—22no—
63C2×D88C2311yescharacteristic
64C2×#4314—21no—
65#66943—22no—
66#66941—22no—
67#66931—42no—
68#66923—41no—
69#66922—41no—
70C11×M32—22no—
71C2×C11×C16C2312yes—
72C11×#107C2311yescharacteristic
73C11×#107C2311yescharacteristic
74C11×#106—21no—
75#66882—21no—
76#66882C2312yes—
77#66879D412yes—
78C8×Dic11C2312yes—
79C2×C11⋊C16—22no—
80C2×C11⋊C16C2311yescharacteristic
81C2×C11⋊C16C2311yescharacteristic
82#66872—22no—
83#66871—22no—
84#33702—111nomaximal, Sylow
85C24×C11—41no—
86C2×D4×C11—22no—
87C2×D4×C11—42no—
88C2×D4×C11—41no—
89C2×D4×C11—42no—
90C22×C4×C11C2×D411yescharacteristic
91C2×C22⋊D11—42no—
92C2×C22⋊D11—42no—
93C2×C22⋊D11—41no—
94C22×Dic11—41no—
95#4339—42no—
96#4339—42no—
97C2×D44—21no—
98C2×C4×D11—41no—
99C2×Dic22—21no—
100C2×Dic22—42no—
101C11×D8—22no—
102C11×D8—22no—
103C11×D8—42no—
104C2×C8×C11C2×D411yescharacteristic
105C2×C8×C11#4112yes—
106C2×C8×C11#4112yes—
107C2×C8×C11C2411yescharacteristic
108C11×C4⋊C4—21no—
109C11×C4⋊C4—21no—
110C11×C22⋊C4—41no—
111C42×C11—41no—
112C22⋊Dic11—42no—
113C22⋊Dic11—42no—
114C22⋊Dic11D812yes—
115#4324—44no—
116#4323—44no—
117C4⋊Dic11—22no—
118C4⋊Dic11—42no—
119C4⋊Dic11—41no—
120C4⋊Dic11D811yescharacteristic
121C4⋊Dic11D811yescharacteristic
122Dic11⋊C4—42no—
123Dic11⋊C4—42no—
124C4×Dic11C2×D412yes—
125#4318SD1614yes—
126C2×C11⋊C8C2×D412yes—
127Dic44—21no—
128Dic44—21no—
129D88—21no—
130D88—21no—
131#4314—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#2140D1111yescharacteristic, complemented
142#2139—111no—
143#2138—111no—
144C2×#357—111no—
145#2108—111no—
146C23×C11—42no—
147C23×C11—82no—
148C23×C11—161no—
149C23×C11—161no—
150C23×C11C2×D811yescharacteristic
151C22×D11—41no—
152D4×C11—42no—
153D4×C11—42no—
154D4×C11—82no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11#12412yes—
158C2×C4×C11C2×D811yescharacteristic
159C2×C4×C11C2×SD1612yes—
160C2×C4×C11C22×D411yescharacteristic
161C22⋊D11—82no—
162C22⋊D11—162no—
163C22⋊D11—162no—
164C2×Dic11—42no—
165C2×Dic11—41no—
166C2×Dic11—161no—
167C2×Dic11C2×D812yes—
168C2×Dic11C2×D812yes—
169D44—41no—
170D44—41no—
171C4×D11—82no—
172Dic22—41no—
173Dic22—41no—
174Dic22—162no—
175C8×C11#12412yes—
176C8×C11C2×#4111yescharacteristic
177C8×C11C2×#4111yescharacteristic
178C11⋊C8C2×SD1614yes—
179C2×AGL(1,ℤ/8)—221no—
180C2×#135—111no—
181C22×D8C2×D1111yescharacteristic
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#427C2×D1111yescharacteristic
194C2×#107—111no—
195#405—111no—
196#358—112no—
197#358—111no—
198#358—111no—
199#357—112no—
200#357—112no—
201#357—112no—
202#357—111no—
203#357—111no—
204#357C2×D1112yes—
205#357C2×D1112yes—
206#346—112no—
207C4×C16—112no—
208C22×C11—21no—
209C22×C11—21no—
210C22×C11—82no—
211C22×C11—82no—
212C22×C11—82no—
213C22×C11—164no—
214C22×C11#48612yes—
215C22×C11C22×D811yescharacteristic
216C2×D11—81no—
217C2×D11—81no—
218C2×D11—81no—
219C4×C11—81no—
220C4×C11—81no—
221C4×C11#48612yes—
222C4×C11C2×#12411yescharacteristic
223C4×C11C22×SD1611yescharacteristic
224Dic11—22no—
225Dic11—22no—
226Dic11—81no—
227Dic11—82no—
228C2×#41—221no—
229C22×D4—21no—
230AGL(1,ℤ/8)—444no—
231#135—222no—
232#135—222no—
233C2×Q16—111no—
234C2×SD16—222no—
235C2×SD16—221no—
236C2×D8—22no—
237C2×D8—21no—
238C2×D8—22no—
239C2×D8—111no—
240C2×D8—222no—
241C2×D8C22×D1112yes—
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—21no—
255#117—111no—
256C2×C4⋊C4—221no—
257M32—22no—
258C2×C16—111no—
259C2×C16—111no—
260C2×C16—222no—
261C2×C16C22×D1112yes—
262#107—112no—
263#107—222no—
264#107—221no—
265#107C22×D1111yescharacteristic
266#107C22×D1111yescharacteristic
267#106—21no—
268#106—222no—
269#97—112no—
270C4×C8—112no—
271C2×C11—22no—
272C2×C11—162no—
273C2×C11C2×#48611yescharacteristic
274C2×C11#341511yescharacteristic
275C2×C11#341611yescharacteristic
276D11—161no—
277C24—41no—
278#41—442no—
279#41—442no—
280C2×Q8—221no—
281C2×Q8—442no—
282C2×D4—22no—
283C2×D4—42no—
284C2×D4—41no—
285C2×D4—42no—
286C2×D4—221no—
287C2×D4—442no—
288C2×D4—442no—
289C2×D4—441no—
290C22×C4—441no—
291C22×C4—441no—
292C22×C4D4×D1111yescharacteristic
293Q16—221no—
294Q16—221no—
295SD16—444no—
296SD16—442no—
297D8—22no—
298D8—22no—
299D8—42no—
300D8—221no—
301D8—221no—
302D8—444no—
303M16—114no—
304C2×C8—112no—
305C2×C8#433912yes—
306C2×C8D4×D1111yescharacteristic
307C2×C8#434112yes—
308C2×C8C23×D1111yescharacteristic
309C4⋊C4—21no—
310C4⋊C4—21no—
311C4⋊C4—111no—
312C4⋊C4—111no—
313C4⋊C4—222no—
314C4⋊C4—442no—
315C4⋊C4—442no—
316C4⋊C4—442no—
317C4⋊C4—441no—
318C22⋊C4—41no—
319C22⋊C4—112no—
320C22⋊C4—442no—
321C22⋊C4—442no—
322C42—41no—
323C42—112no—
324C16—22no—
325C16—221no—
326C16—221no—
327C11#3370211yescharacteristic, complemented, Sylow
328C23—42no—
329C23—82no—
330C23—161no—
331C23—161no—
332C23—441no—
333C23D8×D1111yescharacteristic
334Q8—441no—
335Q8—441no—
336Q8—1762no—
337D4—42no—
338D4—42no—
339D4—82no—
340D4—441no—
341D4—441no—
342D4—882no—
343D4—1762no—
344D4—1762no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—112no—
348C2×C4—112no—
349C2×C4—441no—
350C2×C4—442no—
351C2×C4—882no—
352C2×C4—1761no—
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—82no—
364C22—82no—
365C22—82no—
366C22—164no—
367C22—881no—
368C22—881no—
369C22—881no—
370C22#1062237312yes—
371C22C2×D8×D1111yescharacteristic
372C4—81no—
373C4—81no—
374C4—222no—
375C4—222no—
376C4—881no—
377C4—882no—
378C4#1062237312yes—
379C4C2×#6693811yescharacteristic
380C4C2×SD16×D1111yescharacteristic
381C2—22no—
382C2—162no—
383C2—1761no—
384C2C2×#1062237311yescharacteristic
385C2#1308175611yescharacteristic
386C2#1308176211yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2140C2
socleC22×C11C22×D8
prime radical#13079097C2
hypercenter#2140D11
hypocenterC11#33702
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2140

Complements

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

NH ≅ G/Ntype
1. #13079156C2semidirect
3. #13070856C2semidirect
4. #13070851C2semidirect
5. #13070846C2semidirect
6. #13070838C2semidirect
7. #13070329C2semidirect
8. #13070321C2semidirect
9. C2×#10622200C2semidirect
10. #13070215C2semidirect
11. C11×#2140C2semidirect
26. #10622491C22semidirect
27. #10622487C22semidirect
33. #10622147C22semidirect
34. #10622141C22semidirect
35. #10622140C22semidirect
36. C16×Dic11C22semidirect
37. #10622130C22semidirect
38. #10622130C22semidirect
39. #10622129C22semidirect
40. #10622129C22semidirect
141. #2140D11semidirect
327. C11#33702semidirect

Maximal subgroups

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

subgroupindex
#130791562
#130790972
#130708562
#130708512
#130708462
#130708382
#130703292
#130703212
C2×#106222002
#130702152
C11×#21402
#3370211