Finite Group Databasebeta

← #14911110

Subgroups — #14911110

Order 2816.

590 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13080964C211yesmaximal, characteristic, complemented
2#13070839C211yesmaximal, characteristic, complemented
3#13070799C212yesmaximal, complemented
4#13070758C211yesmaximal, characteristic, complemented
5#13070717C212yesmaximal, complemented
6#13070648C211yesmaximal, characteristic, complemented
7#13070539C212yesmaximal, complemented
8C4×#66892C211yesmaximal, characteristic, complemented
9#13070448C211yesmaximal, characteristic, complemented
10#13070328C212yesmaximal, complemented
11C11×#3287C211yesmaximal, characteristic, complemented
12C2×C11×#135C2212yes—
13C11×#550—21no—
14#10623086—21no—
15C11×#493C2211yescharacteristic
16C11×#466C2212yes—
17C11×#460—21no—
18C11×#449—22no—
19C4×C11×Q16C2211yescharacteristic
20C8×D4×C11C2211yescharacteristic
21C2×#66892C2211yescharacteristic
22C2×#66890C2212yes—
23#10622728C2212yes—
24C2×#66882C2212yes—
25C2×#66876C2212yes—
26#10622459—21no—
27#10622349—22no—
28C4×D88C2211yescharacteristic
29#10622295C2211yescharacteristic
30#10622202C2211yescharacteristic
31#10622202C2212yes—
32#10622200C2212yes—
33#10622200C2212yes—
34#10622200C2212yes—
35C22⋊(C11⋊C16)C2212yes—
36#10622129C2211yescharacteristic
37#10622128C2212yes—
38#10622128C2211yescharacteristic
39C4⋊(C11⋊C16)C2211yescharacteristic
40C4×C11⋊C16C2211yescharacteristic
41C2×C11×#41—22no—
42C2×#4341—41no—
43C11×#135—24no—
44C11×#135—42no—
45C2×C11×Q16C2311yescharacteristic
46C2×C11×SD16—22no—
47C2×C11×D8—21no—
48C2×C11×D8C2312yes—
49C22×C8×C11C2312yes—
50C11×#127—21no—
51C11×#127—41no—
52C11×#121—22no—
53C11×#121—42no—
54C4×Q8×C11—21no—
55C4×D4×C11—41no—
56C4×D4×C11D411yescharacteristic
57#66983—22no—
58C2×C4⋊Dic11—22no—
59C2×D88C2311yescharacteristic
60#66950—41no—
61#66939—42no—
62C4×D44—21no—
63#66922—21no—
64C11×#107C2311yescharacteristic
65C11×C4⋊C8D411yescharacteristic
66C11×#103—21no—
67C11×#102—22no—
68C11×C22⋊C8D412yes—
69C4×C8×C11C2311yescharacteristic
70#66892—22no—
71#66890—42no—
72#66885—22no—
73#66885—21no—
74#66882—21no—
75#66882—22no—
76#66882C2312yes—
77#66882C2311yescharacteristic
78#66876—42no—
79C2×C11⋊C16C2312yes—
80C2×C11⋊C16C2311yescharacteristic
81C2×C11⋊C16C2311yescharacteristic
82#33899—111nomaximal, Sylow
83C11×#41—44no—
84C11×#41—82no—
85C2×Q8×C11—21no—
86C2×D4×C11—22no—
87C2×D4×C11—42no—
88C2×D4×C11—42no—
89C2×D4×C11—41no—
90C2×D4×C11—41no—
91C2×D4×C11D811yescharacteristic
92C22×C4×C11—42no—
93C22×C4×C11C2×D412yes—
94C2×C22⋊D11—42no—
95C22×Dic11—42no—
96#4341—84no—
97C2×D44—21no—
98C2×C4×D11—41no—
99C2×Dic22—41no—
100C11×Q16—21no—
101C11×Q16#4112yescomplemented
102C11×SD16—44no—
103C11×D8—22no—
104C11×D8—22no—
105C11×D8—81no—
106C2×C8×C11—22no—
107C2×C8×C11—22no—
108C2×C8×C11C2×D411yescharacteristic
109C2×C8×C11C2×D412yes—
110C2×C8×C11C2411yescharacteristic
111C11×C4⋊C4—21no—
112C11×C4⋊C4—41no—
113C11×C4⋊C4D811yescharacteristic
114C11×C22⋊C4—42no—
115C11×C22⋊C4D812yes—
116C42×C11—41no—
117C42×C11C2×D411yescharacteristic
118(C2×D11)⋊C4—41no—
119(C2×D11)⋊C4—42no—
120C4⋊Dic11—22no—
121C4⋊Dic11—21no—
122C4⋊Dic11—41no—
123C4⋊Dic11—42no—
124D88—21no—
125D88—21no—
126C11⋊C16—21no—
127C11⋊C16—21no—
128C11⋊C16—22no—
129#3334—111no—
130#3287D1111yescharacteristic, complemented
131#2240—111no—
132#2233—112no—
133#2225—111no—
134#2218—112no—
135#2206—111no—
136#2186—112no—
137C4×SD32—111no—
138#2169—111no—
139#2139—112no—
140C23×C11—42no—
141C23×C11C2×D812yes—
142C22×D11—41no—
143Q8×C11—22no—
144Q8×C11—41no—
145D4×C11—22no—
146D4×C11—42no—
147D4×C11—42no—
148D4×C11—84no—
149D4×C11—82no—
150D4×C11—161no—
151D4×C11—162no—
152C2×C4×C11—22no—
153C2×C4×C11—22no—
154C2×C4×C11—41no—
155C2×C4×C11—41no—
156C2×C4×C11—84no—
157C2×C4×C11C2×D811yescharacteristic
158C2×C4×C11C2×D812yes—
159C2×C4×C11C2×D811yescharacteristic
160C2×C4×C11C22×D411yescharacteristic
161C22⋊D11—84no—
162C2×Dic11—42no—
163C2×Dic11—41no—
164C2×Dic11—84no—
165D44—41no—
166D44—41no—
167C4×D11—82no—
168Dic22—82no—
169C8×C11—22no—
170C8×C11—21no—
171C8×C11C2×#4111yescharacteristic
172C8×C11H(5,𝔽2)11yescharacteristic
173C2×#135C2×D1112yes—
174#550—21no—
175#547—221no—
176C2×SD32—111no—
177C2×D16—112no—
178C2×M32—112no—
179#500—111no—
180#493C2×D1111yescharacteristic
181#480—222no—
182#474—221no—
183#466—112no—
184#466C2×D1112yes—
185#460—21no—
186#449—22no—
187C4×Q16C2×D1111yescharacteristic
188C4×D8—111no—
189C8×D4C2×D1111yescharacteristic
190C2×#107—112no—
191#367—111no—
192#367—112no—
193C4⋊C16—111no—
194#358—111no—
195#358—112no—
196#357—112no—
197#357—112no—
198#357—112no—
199#357—111no—
200C22⋊C16—112no—
201C4×C16—111no—
202C22×C11—22no—
203C22×C11—22no—
204C22×C11—22no—
205C22×C11—82no—
206C22×C11—82no—
207C22×C11—82no—
208C22×C11C22×D811yescharacteristic
209C2×D11—81no—
210C2×D11—81no—
211C2×D11—81no—
212C4×C11—21no—
213C4×C11—22no—
214C4×C11—42no—
215C4×C11—81no—
216C4×C11#50912yes—
217C4×C11#54611yescharacteristic
218C4×C11#57711yescharacteristic
219Dic11—82no—
220Dic11—81no—
221C2×#41—22no—
222C2×#41—441no—
223#135—24no—
224#135—42no—
225C2×Q16C22×D1111yescharacteristic
226C2×SD16—22no—
227C2×D8—21no—
228C2×D8—111no—
229C2×D8C22×D1112yes—
230C22×C8C22×D1112yes—
231C4⋊Q8—221no—
232#127—21no—
233#127—41no—
234#123—442no—
235C22⋊Q8—441no—
236#121—22no—
237#121—42no—
238#121—222no—
239C4×Q8—21no—
240C4×D4—41no—
241C4×D4—221no—
242C4×D4C22⋊D1111yescharacteristic
243C2×C4⋊C4—222no—
244SD32—222no—
245D16—442no—
246M32—442no—
247C2×C16—111no—
248C2×C16—111no—
249C2×C16—112no—
250#107—111no—
251#107—112no—
252#107—222no—
253#107—221no—
254#107C22×D1111yescharacteristic
255C4⋊C8C22⋊D1111yescharacteristic
256#103—21no—
257#102—22no—
258#102—221no—
259#102—222no—
260C22⋊C8C22⋊D1112yes—
261C4×C8C22×D1111yescharacteristic
262C2×C11—42no—
263C2×C11—162no—
264C2×C11#329411yescharacteristic
265C2×C11C2×#50911yescharacteristic
266C2×C11#341611yescharacteristic
267D11—161no—
268#41—44no—
269#41—82no—
270#41—884no—
271C2×Q8—21no—
272C2×Q8—441no—
273C2×D4—22no—
274C2×D4—42no—
275C2×D4—42no—
276C2×D4—41no—
277C2×D4—41no—
278C2×D4—221no—
279C2×D4—442no—
280C2×D4#432311yescharacteristic
281C22×C4—42no—
282C22×C4—442no—
283C22×C4—441no—
284C22×C4C2×C22⋊D1112yes—
285Q16—21no—
286Q16#434112yescomplemented
287SD16—44no—
288D8—22no—
289D8—22no—
290D8—81no—
291D8—221no—
292D8—221no—
293C2×C8—22no—
294C2×C8—22no—
295C2×C8C2×C22⋊D1111yescharacteristic
296C2×C8C2×C22⋊D1112yes—
297C2×C8C23×D1111yescharacteristic
298C4⋊C4—21no—
299C4⋊C4—41no—
300C4⋊C4—221no—
301C4⋊C4—222no—
302C4⋊C4—442no—
303C4⋊C4—441no—
304C4⋊C4#432311yescharacteristic
305C22⋊C4—42no—
306C22⋊C4—441no—
307C22⋊C4—442no—
308C22⋊C4#432312yes—
309C42—41no—
310C42C2×C22⋊D1111yescharacteristic
311C16—221no—
312C16—221no—
313C16—222no—
314C11#3389911yescharacteristic, complemented, Sylow
315C23—42no—
316C23—441no—
317C23C2×#432312yes—
318Q8—22no—
319Q8—41no—
320Q8—882no—
321D4—22no—
322D4—42no—
323D4—42no—
324D4—84no—
325D4—82no—
326D4—161no—
327D4—162no—
328D4—441no—
329D4—441no—
330D4—884no—
331C2×C4—22no—
332C2×C4—22no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—84no—
336C2×C4—441no—
337C2×C4—442no—
338C2×C4—884no—
339C2×C4—882no—
340C2×C4C2×#432311yescharacteristic
341C2×C4C2×#432312yes—
342C2×C4C2×#432311yescharacteristic
343C2×C4C22×C22⋊D1111yescharacteristic
344C8—22no—
345C8—21no—
346C8C2×#434111yescharacteristic
347C8#6703711yescharacteristic
348C22—22no—
349C22—22no—
350C22—22no—
351C22—82no—
352C22—82no—
353C22—82no—
354C22—881no—
355C22—881no—
356C22—881no—
357C22C22×#432311yescharacteristic
358C4—22no—
359C4—21no—
360C4—42no—
361C4—81no—
362C4—881no—
363C4—882no—
364C4#1062280612yes—
365C4#1062333711yescharacteristic
366C4#1062336711yescharacteristic
367C2—42no—
368C2—162no—
369C2—1761no—
370C2#1308042911yescharacteristic
371C2C2×#1062280611yescharacteristic
372C2#1308176311yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3287C2
socleC22×C11C22×D8
hypercenter#3287D11
hypocenterC11#33899
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #3287

Complements

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

NH ≅ G/Ntype
1. #13080964C2semidirect
2. #13070839C2semidirect
3. #13070799C2semidirect
4. #13070758C2semidirect
5. #13070717C2semidirect
6. #13070648C2semidirect
7. #13070539C2semidirect
8. C4×#66892C2semidirect
9. #13070448C2semidirect
10. #13070328C2semidirect
11. C11×#3287C2semidirect
101. C11×Q16#41semidirect
130. #3287D11semidirect
286. Q16#4341semidirect
314. C11#33899semidirect

Maximal subgroups

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

subgroupindex
#130809642
#130708392
#130707992
#130707582
#130707172
#130706482
#130705392
C4×#668922
#130704482
#130703282
C11×#32872
#3389911