Finite Group Databasebeta

← #14909107

Subgroups — #14909107

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#13079155C211yesmaximal, characteristic, complemented
2#13079102C211yesmaximal, characteristic
3#13070858C212yesmaximal, complemented
4#13070853C212yesmaximal, complemented
5#13070848C212yesmaximal, complemented
6#13070840C212yesmaximal, complemented
7#13070333C211yesmaximal, characteristic, complemented
8#13070329C211yesmaximal, characteristic, complemented
9#13070324C211yesmaximal, characteristic, complemented
10C2×#10622147C211yesmaximal, characteristic, complemented
11C11×#2108C211yesmaximal, characteristic, complemented
12C2×#66961—21no—
13C2×#66957C2211yescharacteristic
14C22×D88C2211yescharacteristic
15#10623056—21no—
16#10623050—21no—
17C2×C11×M32C2211yescharacteristic
18C22×C11×C16C2211yescharacteristic
19C11×#405C2211yescharacteristic
20#10622734—21no—
21#10622719C2211yescharacteristic
22C2×#66882C2211yescharacteristic
23#10622325—22no—
24#10622315—22no—
25#10622309C2212yes—
26#10622308C2212yes—
27#10622296C2212yescomplemented
28#10622295C2212yescomplemented
29C11×#346C2212yescomplemented
30C4×C11×C16C2212yescomplemented
31#10622147C2212yes—
32#10622147C2212yes—
33#10622147C2212yes—
34#10622147C2212yes—
35#10622147C2211yescharacteristic, complemented
36#10622147C2212yescomplemented
37#10622147C2211yescharacteristic, complemented
38#10622141C2211yescharacteristic, complemented
39#10622141C2212yescomplemented
40#10622141C2211yescharacteristic, complemented
41C2×#4339—21no—
42C22×D44—21no—
43C2×C11×M16D411yescharacteristic
44C22×C8×C11C2311yescharacteristic
45C11×#117D411yescharacteristic
46#66979—21no—
47C2×C4⋊Dic11—21no—
48#66961—44no—
49C2×Dic44C2311yescharacteristic
50#66957—22no—
51#66957—22no—
52C2×D88—22no—
53C2×D88—22no—
54C2×D88—21no—
55C2×D88—22no—
56C2×D88C2312yes—
57C2×D88C2311yescharacteristic
58C2×#4314—21no—
59C2×#4314—22no—
60#66948—41no—
61#66948—41no—
62#66943—41no—
63#66941—41no—
64#66935—42no—
65#66931—42no—
66#66928—22no—
67#66927—22no—
68#66923—22no—
69#66922—22no—
70C11×M32—22no—
71C2×C11×C16—22no—
72C2×C11×C16C2311yescharacteristic
73C2×C11×C16C2311yescharacteristic
74C2×C11×C16C2312yes—
75C11×#97D412yes—
76C4×C8×C11C2312yes—
77#66882—22no—
78#66882—21no—
79#66882C2311yescharacteristic
80#66882C2312yes—
81#66882C2311yescharacteristic
82#66881—22no—
83#66881—21no—
84#33702—111nomaximal, Sylow
85C23×D11—41no—
86C22×C4×C11C2×D411yescharacteristic
87C2×C22⋊D11—41no—
88C22×Dic11—41no—
89#4339—42no—
90#4339—42no—
91C2×D44—21no—
92C2×D44—22no—
93C2×D44—42no—
94C2×D44—41no—
95C2×D44—42no—
96C2×D44—42no—
97C2×D44—42no—
98C2×C4×D11—41no—
99C2×Dic22—21no—
100C2×Dic22—42no—
101C11×M16SD1614yes—
102C2×C8×C11C2×D411yescharacteristic
103C2×C8×C11C2×D412yes—
104C2×C8×C11#4112yes—
105C2×C8×C11#4112yes—
106C2×C8×C11C2411yescharacteristic
107C11×C4⋊C4D811yescharacteristic
108C11×C4⋊C4D811yescharacteristic
109C11×C22⋊C4D812yes—
110C42×C11C2×D412yes—
111C22⋊Dic11—41no—
112(C2×D11)⋊C4—42no—
113(C2×D11)⋊C4—42no—
114C4⋊Dic11—21no—
115C4⋊Dic11—21no—
116C4⋊Dic11—22no—
117C4⋊Dic11—42no—
118C4⋊Dic11—41no—
119Dic11⋊C4—42no—
120Dic11⋊C4—42no—
121C4×Dic11—41no—
122Dic44—21no—
123Dic44—21no—
124D88—22no—
125D88—22no—
126D88—21no—
127D88—21no—
128D88—42no—
129D88—44no—
130#4314—42no—
131#4314—44no—
132C11×C16—21no—
133C11×C16—21no—
134C11×C16—22no—
135#3164—111no—
136#3155—111no—
137#2244—112no—
138#2243—112no—
139#2242—112no—
140#2240—112no—
141#2140—111no—
142#2139—111no—
143#2138—111no—
144C2×#357—111no—
145#2108D1111yescharacteristic, complemented
146C23×C11C2×D811yescharacteristic
147C22×D11—42no—
148C22×D11—41no—
149C22×D11—82no—
150C22×D11—161no—
151C22×D11—161no—
152C2×C4×C11#12412yes—
153C2×C4×C11C2×D812yes—
154C2×C4×C11C2×D812yes—
155C2×C4×C11C2×D811yescharacteristic
156C2×C4×C11C2×SD1612yes—
157C2×C4×C11C22×D411yescharacteristic
158C22⋊D11—82no—
159C2×Dic11—41no—
160C2×Dic11—41no—
161C2×Dic11—42no—
162C2×Dic11—41no—
163C2×Dic11—161no—
164D44—41no—
165D44—42no—
166D44—42no—
167D44—41no—
168D44—82no—
169D44—162no—
170D44—162no—
171C4×D11—82no—
172Dic22—41no—
173Dic22—41no—
174Dic22—162no—
175C8×C11#12412yes—
176C8×C11C2×SD1614yes—
177C8×C11C2×#4111yescharacteristic
178C8×C11C2×#4111yescharacteristic
179C2×AGL(1,ℤ/8)—221no—
180C2×#135—111no—
181C22×D8—111no—
182#544—221no—
183#535—221no—
184C2×M32C2×D1111yescharacteristic
185C22×C16C2×D1111yescharacteristic
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×#107—111no—
195#405C2×D1111yescharacteristic
196#358—111no—
197#358—111no—
198#358—112no—
199#357—112no—
200#357—112no—
201#357—111no—
202#357—111no—
203#357—112no—
204#357—112no—
205#357—112no—
206#346C2×D1112yescomplemented
207C4×C16C2×D1112yescomplemented
208C22×C11—21no—
209C22×C11—21no—
210C22×C11#48612yes—
211C22×C11C22×D811yescharacteristic
212C2×D11—82no—
213C2×D11—81no—
214C2×D11—82no—
215C2×D11—81no—
216C2×D11—82no—
217C2×D11—81no—
218C2×D11—164no—
219C4×C11—22no—
220C4×C11—22no—
221C4×C11#48612yes—
222C4×C11C2×#12411yescharacteristic
223C4×C11C22×SD1611yescharacteristic
224Dic11—81no—
225Dic11—81no—
226Dic11—82no—
227Dic11—81no—
228C2×#41—221no—
229C22×D4—221no—
230AGL(1,ℤ/8)—444no—
231#135—222no—
232#135—222no—
233C2×Q16—111no—
234C2×SD16—221no—
235C2×SD16—222no—
236C2×D8—112no—
237C2×D8—111no—
238C2×D8—221no—
239C2×D8—222no—
240C2×D8—222no—
241C2×D8—222no—
242C2×M16D4411yescharacteristic
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—221no—
255#117D4411yescharacteristic
256C2×C4⋊C4—221no—
257M32—22no—
258C2×C16—22no—
259C2×C16C22×D1111yescharacteristic
260C2×C16C22×D1112yes—
261C2×C16C22×D1111yescharacteristic
262#107—112no—
263#107—111no—
264#107—111no—
265#107—221no—
266#107—222no—
267#106—221no—
268#106—222no—
269#97D4412yes—
270C4×C8C22×D1112yes—
271C2×C11—22no—
272C2×C11C2×#48611yescharacteristic
273C2×C11#341511yescharacteristic
274C2×C11#341611yescharacteristic
275D11—161no—
276D11—162no—
277C24—441no—
278#41—442no—
279#41—442no—
280C2×Q8—221no—
281C2×Q8—442no—
282C2×D4—222no—
283C2×D4—221no—
284C2×D4—441no—
285C2×D4—442no—
286C2×D4—442no—
287C2×D4—441no—
288C2×D4—442no—
289C2×D4—442no—
290C22×C4—441no—
291C22×C4—441no—
292C22×C4C2×D4411yescharacteristic
293Q16—221no—
294Q16—221no—
295SD16—442no—
296SD16—444no—
297D8—222no—
298D8—222no—
299D8—221no—
300D8—221no—
301D8—442no—
302D8—444no—
303M16#431414yes—
304C2×C8C2×D4411yescharacteristic
305C2×C8C2×D4412yes—
306C2×C8#433912yes—
307C2×C8#433912yes—
308C2×C8C23×D1111yescharacteristic
309C4⋊C4—221no—
310C4⋊C4—222no—
311C4⋊C4—221no—
312C4⋊C4—441no—
313C4⋊C4—442no—
314C4⋊C4—442no—
315C4⋊C4—442no—
316C4⋊C4D8811yescharacteristic
317C4⋊C4D8811yescharacteristic
318C22⋊C4—441no—
319C22⋊C4—442no—
320C22⋊C4—442no—
321C22⋊C4D8812yes—
322C42—441no—
323C42C2×D4412yes—
324C16—21no—
325C16—21no—
326C16—22no—
327C11#3370211yescharacteristic, complemented, Sylow
328C23—442no—
329C23—441no—
330C23—882no—
331C23—1761no—
332C23—1761no—
333C23C2×D8811yescharacteristic
334Q8—441no—
335Q8—441no—
336Q8—1762no—
337D4—442no—
338D4—441no—
339D4—441no—
340D4—442no—
341D4—882no—
342D4—882no—
343D4—1762no—
344D4—1762no—
345C2×C4—441no—
346C2×C4—441no—
347C2×C4—441no—
348C2×C4—442no—
349C2×C4—882no—
350C2×C4—1761no—
351C2×C4#6692812yes—
352C2×C4C2×#431412yes—
353C2×C4C2×D8812yes—
354C2×C4C2×D8812yes—
355C2×C4C2×D8811yescharacteristic
356C2×C4C22×D4411yescharacteristic
357C8#6692812yes—
358C8C2×#431414yes—
359C8C2×#433911yescharacteristic
360C8C2×#433911yescharacteristic
361C22—21no—
362C22—21no—
363C22—881no—
364C22—882no—
365C22—881no—
366C22—882no—
367C22—881no—
368C22—882no—
369C22—1764no—
370C22#1062230712yes—
371C22C22×D8811yescharacteristic
372C4—22no—
373C4—22no—
374C4—881no—
375C4—882no—
376C4—881no—
377C4—881no—
378C4#1062230712yes—
379C4C2×#6692811yescharacteristic
380C4C22×#431411yescharacteristic
381C2—22no—
382C2—1762no—
383C2—1761no—
384C2C2×#1062230711yescharacteristic
385C2#1308175711yescharacteristic
386C2#1308176411yescharacteristic
subgroupG/H
centerC22C22×D88
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2108C2
socleC22×C11C22×D8
prime radical#13079102C2
hypercenter#2108D11
hypocenterC11#33702
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #117 ◁ #405 ◁ #2108

Complements

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

NH ≅ G/Ntype
1. #13079155C2semidirect
3. #13070858C2semidirect
4. #13070853C2semidirect
5. #13070848C2semidirect
6. #13070840C2semidirect
7. #13070333C2semidirect
8. #13070329C2semidirect
9. #13070324C2semidirect
10. C2×#10622147C2semidirect
11. C11×#2108C2semidirect
27. #10622296C22semidirect
28. #10622295C22semidirect
29. C11×#346C22semidirect
30. C4×C11×C16C22semidirect
35. #10622147C22semidirect
36. #10622147C22semidirect
37. #10622147C22semidirect
38. #10622141C22semidirect
39. #10622141C22semidirect
40. #10622141C22semidirect
145. #2108D11semidirect
206. #346C2×D11semidirect
207. C4×C16C2×D11semidirect
327. C11#33702semidirect

Maximal subgroups

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

subgroupindex
#130791552
#130791022
#130708582
#130708532
#130708482
#130708402
#130703332
#130703292
#130703242
C2×#106221472
C11×#21082
#3370211