Finite Group Databasebeta

← #14909795

Subgroups — #14909795

Order 2816.

618 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#13079102C211yesmaximal, characteristic, complemented
2#13070880C211yesmaximal, characteristic, complemented
3#13070865C211yesmaximal, characteristic, complemented
4#13070859C211yesmaximal, characteristic, complemented
5#13070850C211yesmaximal, characteristic, complemented
6#13070671C212yesmaximal, complemented
7#13070651C212yesmaximal, complemented
8#13070537C212yesmaximal, complemented
9#13070527C212yesmaximal, complemented
10#13070423C211yesmaximal, characteristic, complemented
11C11×#3176C211yesmaximal, characteristic, complemented
12C11×#540—21no—
13C2×#66961—21no—
14C2×#66957C2211yescharacteristic
15C22×D88C2211yescharacteristic
16#10623056—21no—
17C11×#499C2211yescharacteristic, complemented
18C11×#493C2211yescharacteristic, complemented
19C11×#490—21no—
20C11×#469—21no—
21C11×#466C2212yes—
22C11×#442—21no—
23C4×C11×D8C2212yescomplemented
24C11×#405C2211yescharacteristic
25C2×#66891C2212yescomplemented
26C2×#66890C2212yes—
27C2×#66890C2212yes—
28C2×#66890C2212yescomplemented
29#10622325—21no—
30#10622325—21no—
31#10622309C2211yescharacteristic
32#10622309C2211yescharacteristic
33#10622308C2211yescharacteristic
34#10622308C2211yescharacteristic
35C22⋊(C11⋊C16)C2212yes—
36#10622130C2212yescomplemented
37#10622129C2212yes—
38#10622129C2212yes—
39#10622129C2212yescomplemented
40C4⋊(C11⋊C16)C2212yescomplemented
41#10622099C2211yescharacteristic, complemented
42C4×C11⋊C16C2211yescharacteristic, complemented
43C2×#4339—21no—
44C22×D44—21no—
45C2×C11×D8—21no—
46C2×C11×D8C2312yes—
47C2×C11×M16D411yescharacteristic
48C22×C8×C11C2311yescharacteristic
49C11×#127—21no—
50C11×#125—21no—
51C11×#123—42no—
52C11×#121—22no—
53C11×#121—42no—
54C4×D4×C11—22no—
55C11×#117D411yescharacteristic
56#66961—44no—
57C2×Dic44C2311yescharacteristic
58#66957—42no—
59C2×D88—21no—
60C2×D88—21no—
61C2×D88—21no—
62C2×D88—42no—
63C2×D88C2311yescharacteristic
64C2×D88C2311yescharacteristic
65C2×D88C2311yescharacteristic
66C2×#4314—21no—
67C2×#4314—21no—
68C2×#4314—21no—
69#66948—42no—
70#66935—42no—
71#66928—21no—
72#66928—21no—
73#66927—21no—
74#66927—21no—
75C11×#107C2312yes—
76C11×#106—21no—
77C11×#102—22no—
78C11×#102—22no—
79C11×#97D411yescharacteristic
80C11×#97D411yescharacteristic
81C4×C8×C11C2311yescharacteristic
82C4×C8×C11C2311yescharacteristic
83#66891—42no—
84#66890—42no—
85#66890—42no—
86#66890—42no—
87C2×C11⋊C16C2312yes—
88C2×C11⋊C16C2312yes—
89#33786—111nomaximal, Sylow
90C23×D11—41no—
91C2×D4×C11—22no—
92C2×D4×C11—42no—
93C2×D4×C11—42no—
94C22×C4×C11—42no—
95C22×C4×C11C2×D411yescharacteristic
96C2×C22⋊D11—41no—
97#4339—42no—
98#4339—42no—
99C2×D44—21no—
100C2×D44—21no—
101C2×D44—21no—
102C2×D44—42no—
103C2×D44—42no—
104C2×D44—41no—
105C2×D44—42no—
106C2×D44—42no—
107C2×C4×D11—41no—
108C2×Dic22—21no—
109C11×D8—22no—
110C11×D8—22no—
111C11×D8—42no—
112C11×M16—22no—
113C2×C8×C11—22no—
114C2×C8×C11C2×D411yescharacteristic
115C2×C8×C11C2×D411yescharacteristic
116C2×C8×C11C2×D411yescharacteristic
117C2×C8×C11C2411yescharacteristic
118C11×C4⋊C4—22no—
119C11×C4⋊C4—42no—
120C11×C4⋊C4D812yes—
121C11×C22⋊C4—42no—
122C11×C22⋊C4—42no—
123C11×C22⋊C4D812yes—
124C42×C11C2×D411yescharacteristic
125C42×C11C2×D411yescharacteristic
126(C2×D11)⋊C4—42no—
127(C2×D11)⋊C4—42no—
128Dic44—22no—
129D88—22no—
130D88—22no—
131D88—22no—
132D88—42no—
133D88—42no—
134D88—42no—
135#4314—42no—
136#4314—42no—
137#4314—42no—
138C11⋊C16—22no—
139C11⋊C16—22no—
140#3176D1111yescharacteristic, complemented
141#3155—111no—
142#2250—111no—
143#2246—111no—
144#2244—111no—
145#2242—111no—
146#2210—112no—
147#2206—112no—
148#2186—112no—
149#2184—112no—
150#2164—111no—
151C23×C11—42no—
152C23×C11C2×D811yescharacteristic
153C22×D11—41no—
154C22×D11—41no—
155C22×D11—41no—
156C22×D11—82no—
157C22×D11—162no—
158D4×C11—42no—
159D4×C11—42no—
160D4×C11—162no—
161D4×C11—162no—
162C2×C4×C11—21no—
163C2×C4×C11—21no—
164C2×C4×C11—42no—
165C2×C4×C11—162no—
166C2×C4×C11C2×D812yes—
167C2×C4×C11C2×D812yes—
168C2×C4×C11C2×D811yescharacteristic
169C2×C4×C11C22×D411yescharacteristic
170C22⋊D11—82no—
171C2×Dic11—41no—
172D44—41no—
173D44—41no—
174D44—41no—
175D44—41no—
176D44—41no—
177D44—41no—
178D44—82no—
179D44—162no—
180D44—162no—
181C4×D11—82no—
182Dic22—41no—
183Dic22—41no—
184C8×C11—21no—
185C8×C11—21no—
186C8×C11AGL(1,ℤ/8)12yes—
187C8×C11H(5,𝔽2)12yes—
188C2×AGL(1,ℤ/8)—221no—
189C2×#135—111no—
190C22×D8—111no—
191#540—21no—
192#535—221no—
193C2×SD32—112no—
194C2×D16—112no—
195C2×D16—112no—
196C2×D16—112no—
197#499C2×D1111yescharacteristic, complemented
198#496—221no—
199#496—221no—
200#495—111no—
201#495—111no—
202#493—111no—
203#493—111no—
204#493C2×D1111yescharacteristic, complemented
205#490—21no—
206#469—21no—
207#466C2×D1112yes—
208#442—21no—
209C4×D8C2×D1112yescomplemented
210#405C2×D1111yescharacteristic
211C4⋊C16—112no—
212#358—112no—
213#357—112no—
214#357—112no—
215#357—112no—
216C22⋊C16—112no—
217#346—111no—
218C4×C16—111no—
219C22×C11—22no—
220C22×C11—21no—
221C22×C11—82no—
222C22×C11—82no—
223C22×C11—82no—
224C22×C11C22×D811yescharacteristic
225C2×D11—82no—
226C2×D11—82no—
227C2×D11—82no—
228C2×D11—81no—
229C2×D11—81no—
230C2×D11—81no—
231C2×D11—164no—
232C4×C11—22no—
233C4×C11—22no—
234C4×C11—21no—
235C4×C11—82no—
236C4×C11#53511yescharacteristic
237C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
238Dic11—81no—
239C2×#41—221no—
240C22×D4—221no—
241AGL(1,ℤ/8)—444no—
242#135—442no—
243C2×Q16—111no—
244C2×SD16—221no—
245C2×SD16—221no—
246C2×SD16—221no—
247C2×D8—21no—
248C2×D8—111no—
249C2×D8—111no—
250C2×D8—111no—
251C2×D8—221no—
252C2×D8—221no—
253C2×D8—221no—
254C2×D8—442no—
255C2×D8C22×D1112yes—
256C2×M16C22⋊D1111yescharacteristic
257C22×C8C22×D1111yescharacteristic
258#127—21no—
259#127—221no—
260#127—221no—
261#125—21no—
262#124—221no—
263#124—221no—
264#123—42no—
265#121—22no—
266#121—42no—
267#121—442no—
268#120—442no—
269C4×D4—22no—
270#117C22⋊D1111yescharacteristic
271SD32—442no—
272D16—442no—
273D16—442no—
274D16—442no—
275C2×C16—112no—
276C2×C16—112no—
277#107C22×D1112yes—
278#106—21no—
279#102—22no—
280#102—22no—
281#97C22⋊D1111yescharacteristic
282#97C22⋊D1111yescharacteristic
283C4×C8C22×D1111yescharacteristic
284C4×C8C22×D1111yescharacteristic
285C2×C11—41no—
286C2×C11—162no—
287C2×C11#320511yescharacteristic
288C2×C11#341512yes—
289D11—161no—
290D11—161no—
291D11—161no—
292C24—441no—
293#41—442no—
294#41—442no—
295C2×Q8—221no—
296C2×D4—22no—
297C2×D4—42no—
298C2×D4—42no—
299C2×D4—221no—
300C2×D4—221no—
301C2×D4—221no—
302C2×D4—442no—
303C2×D4—442no—
304C2×D4—441no—
305C2×D4—441no—
306C2×D4—442no—
307C2×D4—442no—
308C22×C4—42no—
309C22×C4—441no—
310C22×C4C2×C22⋊D1111yescharacteristic
311Q16—222no—
312SD16—442no—
313SD16—442no—
314SD16—442no—
315D8—22no—
316D8—22no—
317D8—42no—
318D8—222no—
319D8—222no—
320D8—222no—
321D8—442no—
322D8—442no—
323D8—442no—
324M16—22no—
325C2×C8—22no—
326C2×C8C2×C22⋊D1111yescharacteristic
327C2×C8C2×C22⋊D1111yescharacteristic
328C2×C8C2×C22⋊D1111yescharacteristic
329C2×C8C23×D1111yescharacteristic
330C4⋊C4—22no—
331C4⋊C4—42no—
332C4⋊C4#432312yes—
333C22⋊C4—42no—
334C22⋊C4—42no—
335C22⋊C4—442no—
336C22⋊C4—442no—
337C22⋊C4#432312yes—
338C42C2×C22⋊D1111yescharacteristic
339C42C2×C22⋊D1111yescharacteristic
340C16—222no—
341C16—222no—
342C11#3378611yescharacteristic, complemented, Sylow
343C23—42no—
344C23—441no—
345C23—441no—
346C23—441no—
347C23—882no—
348C23—1762no—
349C23C2×#432311yescharacteristic
350Q8—441no—
351Q8—441no—
352D4—42no—
353D4—42no—
354D4—162no—
355D4—162no—
356D4—441no—
357D4—441no—
358D4—441no—
359D4—441no—
360D4—441no—
361D4—441no—
362D4—882no—
363D4—882no—
364D4—1762no—
365D4—1762no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—42no—
369C2×C4—162no—
370C2×C4—441no—
371C2×C4—882no—
372C2×C4C2×#432312yes—
373C2×C4C2×#432312yes—
374C2×C4C2×#432311yescharacteristic
375C2×C4C22×C22⋊D1111yescharacteristic
376C8—21no—
377C8—21no—
378C8#6700212yes—
379C8#6704212yes—
380C22—22no—
381C22—21no—
382C22—82no—
383C22—82no—
384C22—82no—
385C22—882no—
386C22—882no—
387C22—882no—
388C22—881no—
389C22—881no—
390C22—881no—
391C22—1764no—
392C22C22×#432311yescharacteristic
393C4—22no—
394C4—22no—
395C4—21no—
396C4—82no—
397C4—881no—
398C4C2×#6700211yescharacteristic
399C4#1062336111yescharacteristic
400C2—41no—
401C2—162no—
402C2—1761no—
403C2—1761no—
404C2—1761no—
405C2#1307953111yescharacteristic
406C2#1308175512yes—
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3176C2
socleC22×C11C22×D8
hypercenter#3176D11
hypocenterC11#33786
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #117 ◁ #405 ◁ #3176

Complements

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

NH ≅ G/Ntype
1. #13079102C2semidirect
2. #13070880C2semidirect
3. #13070865C2semidirect
4. #13070859C2semidirect
5. #13070850C2semidirect
6. #13070671C2semidirect
7. #13070651C2semidirect
8. #13070537C2semidirect
9. #13070527C2semidirect
10. #13070423C2semidirect
11. C11×#3176C2semidirect
17. C11×#499C22semidirect
18. C11×#493C22semidirect
23. C4×C11×D8C22semidirect
25. C2×#66891C22semidirect
28. C2×#66890C22semidirect
36. #10622130C22semidirect
39. #10622129C22semidirect
40. C4⋊(C11⋊C16)C22semidirect
41. #10622099C22semidirect
42. C4×C11⋊C16C22semidirect
140. #3176D11semidirect
197. #499C2×D11semidirect
204. #493C2×D11semidirect
209. C4×D8C2×D11semidirect
342. C11#33786semidirect

Maximal subgroups

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

subgroupindex
#130791022
#130708802
#130708652
#130708592
#130708502
#130706712
#130706512
#130705372
#130705272
#130704232
C11×#31762
#3378611