Finite Group Databasebeta

← #14909548

Subgroups — #14909548

Order 2816.

688 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
1C2×#10622728C211yesmaximal, characteristic, complemented
2#13070801C212yesmaximal, complemented
3#13070799C212yesmaximal, complemented
4#13070717C214yesmaximal, complemented
5#13070528C212yesmaximal, complemented
6#13070527C212yesmaximal, complemented
7#13070227C211yesmaximal, characteristic, complemented
8C2×C11×#466C211yesmaximal, characteristic, complemented
9C22×C11×D8C2211yescharacteristic, complemented
10C23×C8×C11C2211yescharacteristic
11C2×C11×#121—21no—
12C2×#66983—21no—
13C22×D88C2211yescharacteristic, complemented
14C11×#466—21no—
15C11×#466—21no—
16C11×#466C2212yes—
17C11×#466C2212yescomplemented
18C2×C11×#107C2211yescharacteristic, complemented
19C2×C11×#102—21no—
20C2×#66890C2214yescomplemented
21#10622728—21no—
22#10622728—21no—
23#10622728C2212yes—
24#10622728C2212yescomplemented
25C2×#66885—21no—
26C2×#66882C2211yescharacteristic, complemented
27C2×#66876C2212yescomplemented
28#10622200C2214yescomplemented
29C22⋊(C11⋊C16)C2212yescomplemented
30C22⋊(C11⋊C16)C2212yescomplemented
31#10622129C2214yescomplemented
32#10622128C2214yescomplemented
33C22×D4×C11—21no—
34C22×D4×C11—41no—
35C23×C4×C11D411yescharacteristic
36C22×C22⋊D11—41no—
37C22×D44—21no—
38C2×C11×D8—21no—
39C2×C11×D8—42no—
40C2×C11×D8C2312yes—
41C22×C8×C11—42no—
42C22×C8×C11D411yescharacteristic
43C22×C8×C11D411yescharacteristic
44C22×C8×C11D411yescharacteristic
45C22×C8×C11C2311yescharacteristic
46C22×C8×C11C2311yescharacteristic
47C22×C8×C11C2311yescharacteristic
48C11×#121—22no—
49C11×#121—22no—
50C11×#121—41no—
51C11×#121—41no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C22⋊C4—41no—
54#66983—22no—
55#66983—22no—
56#66983—41no—
57#66983—41no—
58C2×(C2×D11)⋊C4—41no—
59C2×C4⋊Dic11—21no—
60C2×D88—21no—
61C2×D88—42no—
62C2×D88C2312yes—
63C11×#107—21no—
64C11×#107C2312yes—
65C11×#102—22no—
66C11×#102—22no—
67#66890—44no—
68#66885—22no—
69#66885—22no—
70#66882—21no—
71#66882C2312yes—
72#66876—42no—
73C2×C11⋊C16C2314yes—
74#33758—111nomaximal, Sylow
75C24×C11—41no—
76C24×C11D811yescharacteristic
77C23×D11—41no—
78C2×D4×C11—22no—
79C2×D4×C11—42no—
80C2×D4×C11—42no—
81C2×D4×C11—42no—
82C2×D4×C11—42no—
83C2×D4×C11—41no—
84C2×D4×C11—84no—
85C22×C4×C11—41no—
86C22×C4×C11—41no—
87C22×C4×C11—41no—
88C22×C4×C11D811yescharacteristic
89C22×C4×C11D811yescharacteristic
90C22×C4×C11D811yescharacteristic
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11C2×D411yescharacteristic
94C2×C22⋊D11—42no—
95C2×C22⋊D11—42no—
96C2×C22⋊D11—84no—
97C22×Dic11—41no—
98C2×D44—22no—
99C2×D44—42no—
100C2×D44—42no—
101C2×D44—41no—
102C11×D8—24no—
103C11×D8—42no—
104C2×C8×C11—22no—
105C2×C8×C11—22no—
106C2×C8×C11—22no—
107C2×C8×C11—41no—
108C2×C8×C11—41no—
109C2×C8×C11—41no—
110C2×C8×C11C2×D411yescharacteristic
111C2×C8×C11C2×D411yescharacteristic
112C2×C8×C11C2×D411yescharacteristic
113C2×C8×C11C2411yescharacteristic
114C11×C4⋊C4—22no—
115C11×C4⋊C4—41no—
116C11×C22⋊C4—42no—
117C11×C22⋊C4—42no—
118(C2×D11)⋊C4—42no—
119(C2×D11)⋊C4—42no—
120C4⋊Dic11—22no—
121C4⋊Dic11—41no—
122D88—24no—
123D88—42no—
124C11⋊C16—24no—
125C2×#466—111no—
126C2×#466D1111yescharacteristic, complemented
127#2233—112no—
128#2233—112no—
129#2218—114no—
130#2184—112no—
131#2184—112no—
132#2112—111no—
133C23×C11—22no—
134C23×C11—22no—
135C23×C11—41no—
136C23×C11—42no—
137C23×C11—82no—
138C23×C11—82no—
139C23×C11—82no—
140C23×C11C2×D811yescharacteristic
141C23×C11C2×D811yescharacteristic
142C23×C11C2×D811yescharacteristic
143C22×D11—42no—
144C22×D11—82no—
145C22×D11—82no—
146C22×D11—82no—
147D4×C11—42no—
148D4×C11—42no—
149D4×C11—82no—
150D4×C11—84no—
151D4×C11—84no—
152C2×C4×C11—21no—
153C2×C4×C11—21no—
154C2×C4×C11—21no—
155C2×C4×C11—21no—
156C2×C4×C11—21no—
157C2×C4×C11—21no—
158C2×C4×C11—41no—
159C2×C4×C11—41no—
160C2×C4×C11—41no—
161C2×C4×C11—42no—
162C2×C4×C11—82no—
163C2×C4×C11C2×D811yescharacteristic
164C2×C4×C11C2×D811yescharacteristic
165C2×C4×C11C2×D811yescharacteristic
166C2×C4×C11C22×D411yescharacteristic
167C22⋊D11—84no—
168C22⋊D11—84no—
169C2×Dic11—42no—
170C2×Dic11—82no—
171D44—42no—
172D44—42no—
173D44—82no—
174C8×C11—21no—
175C8×C11—21no—
176C8×C11—21no—
177C8×C11H(5,𝔽2)12yes—
178C22×D8—111no—
179C22×D8C2×D1111yescharacteristic, complemented
180C23×C8C2×D1111yescharacteristic
181C2×#121—21no—
182C2×#121—221no—
183C2×D16—114no—
184C2×M32—112no—
185#466—21no—
186#466—21no—
187#466—112no—
188#466—112no—
189#466—221no—
190#466—221no—
191#466C2×D1112yes—
192#466C2×D1112yescomplemented
193C2×#107—111no—
194C2×#107C2×D1111yescharacteristic, complemented
195C2×#102—21no—
196C2×#102—221no—
197#367—114no—
198#357—114no—
199#357—114no—
200C22⋊C16—112no—
201C22⋊C16—112no—
202C22×C11—21no—
203C22×C11—21no—
204C22×C11—21no—
205C22×C11—21no—
206C22×C11—21no—
207C22×C11—21no—
208C22×C11—21no—
209C22×C11—44no—
210C22×C11—82no—
211C22×C11—82no—
212C22×C11—82no—
213C22×C11—164no—
214C22×C11#50912yes—
215C22×C11#50912yes—
216C22×C11C22×D811yescharacteristic
217C2×D11—82no—
218C2×D11—82no—
219C2×D11—82no—
220C2×D11—164no—
221C4×C11—21no—
222C4×C11—21no—
223C4×C11—21no—
224C4×C11—82no—
225C4×C11#53411yescharacteristic
226C4×C11#57511yescharacteristic
227Dic11—82no—
228C22×D4—21no—
229C22×D4—41no—
230C22×D4—221no—
231C22×D4—441no—
232C23×C4C22⋊D1111yescharacteristic
233C2×D8—21no—
234C2×D8—42no—
235C2×D8—112no—
236C2×D8—221no—
237C2×D8—442no—
238C2×D8C22×D1112yes—
239C22×C8—42no—
240C22×C8C22⋊D1111yescharacteristic
241C22×C8C22⋊D1111yescharacteristic
242C22×C8C22⋊D1111yescharacteristic
243C22×C8C22×D1111yescharacteristic
244C22×C8C22×D1111yescharacteristic
245C22×C8C22×D1111yescharacteristic
246#121—22no—
247#121—22no—
248#121—41no—
249#121—41no—
250#121—222no—
251#121—222no—
252#121—441no—
253#121—441no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—221no—
256C2×C22⋊C4—41no—
257C2×C22⋊C4—441no—
258D16—444no—
259M32—442no—
260C2×C16—114no—
261#107—21no—
262#107—112no—
263#107—221no—
264#107C22×D1112yes—
265#102—22no—
266#102—22no—
267#102—222no—
268#102—222no—
269C2×C11—22no—
270C2×C11—22no—
271C2×C11—41no—
272C2×C11—162no—
273C2×C11#318611yescharacteristic
274C2×C11C2×#50911yescharacteristic
275C2×C11C2×#50911yescharacteristic
276D11—162no—
277C24—41no—
278C24—441no—
279C24#432311yescharacteristic
280C2×D4—22no—
281C2×D4—42no—
282C2×D4—42no—
283C2×D4—42no—
284C2×D4—42no—
285C2×D4—41no—
286C2×D4—84no—
287C2×D4—222no—
288C2×D4—442no—
289C2×D4—442no—
290C2×D4—442no—
291C2×D4—442no—
292C2×D4—441no—
293C2×D4—884no—
294C22×C4—41no—
295C22×C4—41no—
296C22×C4—41no—
297C22×C4—441no—
298C22×C4#432311yescharacteristic
299C22×C4#432311yescharacteristic
300C22×C4#432311yescharacteristic
301C22×C4C2×C22⋊D1111yescharacteristic
302C22×C4C2×C22⋊D1111yescharacteristic
303C22×C4C2×C22⋊D1111yescharacteristic
304D8—24no—
305D8—42no—
306D8—224no—
307D8—442no—
308C2×C8—22no—
309C2×C8—22no—
310C2×C8—22no—
311C2×C8—41no—
312C2×C8—41no—
313C2×C8—41no—
314C2×C8C2×C22⋊D1111yescharacteristic
315C2×C8C2×C22⋊D1111yescharacteristic
316C2×C8C2×C22⋊D1111yescharacteristic
317C2×C8C23×D1111yescharacteristic
318C4⋊C4—22no—
319C4⋊C4—41no—
320C4⋊C4—222no—
321C4⋊C4—441no—
322C22⋊C4—42no—
323C22⋊C4—42no—
324C22⋊C4—442no—
325C22⋊C4—442no—
326C16—224no—
327C11#3375811yescharacteristic, complemented, Sylow
328C23—22no—
329C23—22no—
330C23—41no—
331C23—42no—
332C23—82no—
333C23—82no—
334C23—82no—
335C23—442no—
336C23—882no—
337C23—882no—
338C23—882no—
339C23C2×#432311yescharacteristic
340C23C2×#432311yescharacteristic
341C23C2×#432311yescharacteristic
342D4—42no—
343D4—42no—
344D4—82no—
345D4—84no—
346D4—84no—
347D4—442no—
348D4—442no—
349D4—882no—
350D4—884no—
351D4—884no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—42no—
362C2×C4—82no—
363C2×C4—442no—
364C2×C4—882no—
365C2×C4C2×#432311yescharacteristic
366C2×C4C2×#432311yescharacteristic
367C2×C4C2×#432311yescharacteristic
368C2×C4C22×C22⋊D1111yescharacteristic
369C8—21no—
370C8—21no—
371C8—21no—
372C8#6703712yes—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22—44no—
381C22—82no—
382C22—82no—
383C22—82no—
384C22—164no—
385C22—882no—
386C22—882no—
387C22—882no—
388C22—1764no—
389C22#1062276012yes—
390C22#1062280612yes—
391C22C22×#432311yescharacteristic
392C4—21no—
393C4—21no—
394C4—21no—
395C4—82no—
396C4—882no—
397C4#1062333511yescharacteristic
398C4#1062335311yescharacteristic
399C2—22no—
400C2—22no—
401C2—41no—
402C2—162no—
403C2—1762no—
404C2#1307936411yescharacteristic
405C2C2×#1062280611yescharacteristic
406C2C2×#1062276011yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC2×C11×#466C2
socleC22×C11C22×D8
hypercenterC2×#466D11
hypocenterC11#33758
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C23×C8 ◁ C2×#466

Complements

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

NH ≅ G/Ntype
1. C2×#10622728C2semidirect
2. #13070801C2semidirect
3. #13070799C2semidirect
4. #13070717C2semidirect
5. #13070528C2semidirect
6. #13070527C2semidirect
7. #13070227C2semidirect
8. C2×C11×#466C2semidirect
9. C22×C11×D8C22semidirect
13. C22×D88C22semidirect
17. C11×#466C22semidirect
18. C2×C11×#107C22semidirect
20. C2×#66890C22semidirect
24. #10622728C22semidirect
26. C2×#66882C22semidirect
27. C2×#66876C22semidirect
28. #10622200C22semidirect
29. C22⋊(C11⋊C16)C22semidirect
30. C22⋊(C11⋊C16)C22semidirect
31. #10622129C22semidirect
32. #10622128C22semidirect
126. C2×#466D11semidirect
179. C22×D8C2×D11semidirect
192. #466C2×D11semidirect
194. C2×#107C2×D11semidirect
327. C11#33758semidirect

Maximal subgroups

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

subgroupindex
C2×#106227282
#130708012
#130707992
#130707172
#130705282
#130705272
#130702272
C2×C11×#4662
#3375811