Finite Group Databasebeta

← #14911112

Subgroups — #14911112

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#13080965C211yesmaximal, characteristic, complemented
2#13080375C211yesmaximal, characteristic, complemented
3#13070840C211yesmaximal, characteristic, complemented
4#13070803C212yesmaximal, complemented
5#13070758C211yesmaximal, characteristic, complemented
6#13070718C212yesmaximal, complemented
7#13070651C211yesmaximal, characteristic, complemented
8#13070538C212yesmaximal, complemented
9#13070449C211yesmaximal, characteristic, complemented
10#13070327C212yesmaximal, complemented
11C4×C11×SD32C211yesmaximal, characteristic, complemented
12C2×#66972C2212yes—
13#10623108—21no—
14#10623082—21no—
15C2×C11×SD32C2211yescharacteristic
16C4×C11×Q16C2211yescharacteristic
17C4×C11×D8C2211yescharacteristic
18#10622770C2212yes—
19C2×#66890C2212yes—
20#10622640—21no—
21#10622620—21no—
22C2×#66862C2212yes—
23#10622496C2212yes—
24D11×#107C2212yes—
25#10622424—22no—
26#10622387—22no—
27#10622308C2211yescharacteristic
28C8×D44C2211yescharacteristic
29#10622295C2211yescharacteristic
30C11×#367C2211yescharacteristic
31C11×#358C2211yescharacteristic
32C11×#357C2211yescharacteristic
33C4×C11×C16C2211yescharacteristic
34#10622202C2212yes—
35#10622147C2212yes—
36#10622147C2212yes—
37(C2×D11)⋊C16C2212yes—
38#10622129C2212yes—
39#10622128C2212yes—
40C4⋊(C11⋊C16)C2211yescharacteristic
41C2×#4343—22no—
42C2×#4339—41no—
43C2×C11×Q16C2311yescharacteristic
44C2×C11×D8C2311yescharacteristic
45C4×Q8×C11—21no—
46C4×D4×C11—21no—
47C2×#4325—22no—
48#66991—22no—
49#66977—41no—
50#66972—24no—
51#66972—42no—
52C2×D88—21no—
53C2×D88C2312yes—
54C2×C8×D11C2312yes—
55#66948—22no—
56#66948—42no—
57C4⋊C4×D11—22no—
58#66936—42no—
59#66927—21no—
60#66927—41no—
61C4×D44—41no—
62C4×D44D411yescharacteristic
63#66922—21no—
64C11×SD32—22no—
65C2×C11×C16C2311yescharacteristic
66C2×C11×C16C2311yescharacteristic
67C11×#107C2311yescharacteristic
68C11×#107C2311yescharacteristic
69C11×#103—21no—
70C11×#102—21no—
71C4×C8×C11C2311yescharacteristic
72#66896—22no—
73#66890—42no—
74(C2×D11)⋊C8D412yes—
75#66882—21no—
76#66882C2312yes—
77C2×C11⋊C16C2312yes—
78#66873—22no—
79#66871—22no—
80C4⋊(C11⋊C8)D411yescharacteristic
81#66862—42no—
82#33899—111nomaximal, Sylow
83C2×Q8×C11—21no—
84C2×D4×C11—21no—
85C22×C4×C11—41no—
86C2×C22⋊D11—42no—
87#4343—44no—
88#4343—82no—
89#4339—84no—
90C2×D44—22no—
91C2×D44—42no—
92C2×D44—42no—
93C2×D44—41no—
94C2×D44—41no—
95C2×D44D811yescharacteristic
96C2×C4×D11—42no—
97C2×C4×D11—42no—
98C2×C4×D11C2×D412yes—
99C2×Dic22—41no—
100C11×Q16—21no—
101C11×Q16#4112yescomplemented
102C11×D8—21no—
103C11×D8—21no—
104C2×C8×C11C2×D411yescharacteristic
105C2×C8×C11C2411yescharacteristic
106C11×C4⋊C4—21no—
107C11×C4⋊C4—21no—
108C11×C4⋊C4—41no—
109C11×C22⋊C4—41no—
110C42×C11—41no—
111C42×C11C2×D411yescharacteristic
112C22⋊Dic11—42no—
113#4325—44no—
114(C2×D11)⋊C4—42no—
115(C2×D11)⋊C4D812yes—
116C4⋊Dic11—22no—
117C4⋊Dic11—41no—
118C4⋊Dic11D811yescharacteristic
119Dic11⋊C4—42no—
120C2×C11⋊C8C2×D412yes—
121D88—22no—
122D88—22no—
123D88—81no—
124C8×D11—22no—
125C8×D11—22no—
126C11×C16—21no—
127C11×C16—21no—
128C11⋊C16—22no—
129#3334—111no—
130#3287—111no—
131#2240—111no—
132#2233—112no—
133#2225—111no—
134#2218—112no—
135#2206—111no—
136#2186—112no—
137C4×SD32D1111yescharacteristic, complemented
138#2169—111no—
139#2139—112no—
140C23×C11—41no—
141C22×D11—42no—
142C22×D11C2×D812yes—
143Q8×C11—22no—
144Q8×C11—41no—
145D4×C11—41no—
146D4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11—82no—
151C2×C4×C11C2×D811yescharacteristic
152C2×C4×C11C2×D811yescharacteristic
153C2×C4×C11C22×D411yescharacteristic
154C22⋊D11—84no—
155C2×Dic11—42no—
156C2×Dic11C2×D812yes—
157D44—22no—
158D44—42no—
159D44—42no—
160D44—84no—
161D44—82no—
162D44—161no—
163D44—162no—
164C4×D11—22no—
165C4×D11—22no—
166C4×D11—84no—
167C4×D11—84no—
168Dic22—82no—
169C8×C11—21no—
170C8×C11C2×#4111yescharacteristic
171C8×C11H(5,𝔽2)11yescharacteristic
172C11⋊C8—22no—
173C2×#135—112no—
174#550—221no—
175#547—221no—
176C2×SD32C2×D1111yescharacteristic
177C2×D16—112no—
178C2×M32—112no—
179#500—111no—
180#493—111no—
181#480—222no—
182#474—221no—
183#466—112no—
184#466—112no—
185#460—221no—
186#449—222no—
187C4×Q16C2×D1111yescharacteristic
188C4×D8C2×D1111yescharacteristic
189C8×D4—111no—
190C2×#107—112no—
191#367—112no—
192#367C2×D1111yescharacteristic
193C4⋊C16—111no—
194#358—112no—
195#358C2×D1111yescharacteristic
196#357—112no—
197#357—112no—
198#357—112no—
199#357C2×D1111yescharacteristic
200C22⋊C16—112no—
201C4×C16C2×D1111yescharacteristic
202C22×C11—81no—
203C22×C11—81no—
204C22×C11—81no—
205C22×C11C22×D811yescharacteristic
206C2×D11—22no—
207C2×D11—22no—
208C2×D11—22no—
209C2×D11—82no—
210C2×D11—82no—
211C2×D11—82no—
212C4×C11—21no—
213C4×C11—42no—
214C4×C11—81no—
215C4×C11—81no—
216C4×C11#50912yes—
217C4×C11#54611yescharacteristic
218C4×C11#57711yescharacteristic
219Dic11—22no—
220Dic11—82no—
221C2×#41—222no—
222C2×#41—441no—
223#135—224no—
224#135—442no—
225C2×Q16C22×D1111yescharacteristic
226C2×SD16—222no—
227C2×D8—112no—
228C2×D8—221no—
229C2×D8C22×D1111yescharacteristic
230C22×C8—112no—
231C4⋊Q8—221no—
232#127—221no—
233#127—441no—
234#123—442no—
235C22⋊Q8—441no—
236#121—222no—
237#121—222no—
238#121—442no—
239C4×Q8—21no—
240C4×D4—21no—
241C4×D4—111no—
242C4×D4—441no—
243C2×C4⋊C4—222no—
244SD32—22no—
245D16—442no—
246M32—442no—
247C2×C16—112no—
248C2×C16C22×D1111yescharacteristic
249C2×C16C22×D1111yescharacteristic
250#107—112no—
251#107—222no—
252#107—221no—
253#107C22×D1111yescharacteristic
254#107C22×D1111yescharacteristic
255C4⋊C8—111no—
256#103—21no—
257#102—21no—
258#102—222no—
259#102—222no—
260C22⋊C8—112no—
261C4×C8C22×D1111yescharacteristic
262C2×C11—161no—
263C2×C11#329411yescharacteristic
264C2×C11C2×#50911yescharacteristic
265C2×C11#341611yescharacteristic
266D11—42no—
267D11—162no—
268#41—444no—
269#41—884no—
270#41—882no—
271C2×Q8—21no—
272C2×Q8—441no—
273C2×D4—21no—
274C2×D4—111no—
275C2×D4—222no—
276C2×D4—442no—
277C2×D4—442no—
278C2×D4—442no—
279C2×D4—441no—
280C2×D4—441no—
281C22×C4—41no—
282C22×C4—112no—
283C22×C4—442no—
284C22×C4—442no—
285Q16—21no—
286Q16#433912yescomplemented
287SD16—444no—
288D8—21no—
289D8—21no—
290D8—222no—
291D8—222no—
292D8—881no—
293C2×C8—112no—
294C2×C8—222no—
295C2×C8—222no—
296C2×C8D4×D1111yescharacteristic
297C2×C8C23×D1111yescharacteristic
298C4⋊C4—21no—
299C4⋊C4—21no—
300C4⋊C4—41no—
301C4⋊C4—111no—
302C4⋊C4—222no—
303C4⋊C4—442no—
304C4⋊C4—441no—
305C22⋊C4—41no—
306C22⋊C4—112no—
307C22⋊C4—442no—
308C22⋊C4—442no—
309C42—41no—
310C42D4×D1111yescharacteristic
311C16—21no—
312C16—21no—
313C16—222no—
314C11#3389911yescharacteristic, complemented, Sylow
315C23—41no—
316C23—112no—
317C23—442no—
318Q8—22no—
319Q8—41no—
320Q8—882no—
321D4—41no—
322D4—41no—
323D4—222no—
324D4—442no—
325D4—442no—
326D4—884no—
327D4—884no—
328D4—882no—
329D4—1761no—
330D4—1762no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—82no—
335C2×C4—112no—
336C2×C4—222no—
337C2×C4—222no—
338C2×C4—442no—
339C2×C4—884no—
340C2×C4—884no—
341C2×C4D8×D1111yescharacteristic
342C2×C4D8×D1111yescharacteristic
343C2×C4C2×D4×D1111yescharacteristic
344C8—21no—
345C8—222no—
346C8C2×#433911yescharacteristic
347C8#6704211yescharacteristic
348C22—81no—
349C22—81no—
350C22—81no—
351C22—222no—
352C22—222no—
353C22—222no—
354C22—882no—
355C22—882no—
356C22—882no—
357C22C2×D8×D1111yescharacteristic
358C4—21no—
359C4—42no—
360C4—81no—
361C4—81no—
362C4—222no—
363C4—882no—
364C4#1062252712yes—
365C4#1062308111yescharacteristic
366C4#1062330111yescharacteristic
367C2—161no—
368C2—442no—
369C2—1762no—
370C2#1308043111yescharacteristic
371C2C2×#1062252711yescharacteristic
372C2#1308175911yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC4×C11×SD32C2
socleC22×C11C22×D8
hypercenterC4×SD32D11
hypocenterC11#33899
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ C4×SD32

Complements

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

NH ≅ G/Ntype
1. #13080965C2semidirect
2. #13080375C2semidirect
3. #13070840C2semidirect
4. #13070803C2semidirect
5. #13070758C2semidirect
6. #13070718C2semidirect
7. #13070651C2semidirect
8. #13070538C2semidirect
9. #13070449C2semidirect
10. #13070327C2semidirect
11. C4×C11×SD32C2semidirect
101. C11×Q16#41semidirect
137. C4×SD32D11semidirect
286. Q16#4339semidirect
314. C11#33899semidirect

Maximal subgroups

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

subgroupindex
#130809652
#130803752
#130708402
#130708032
#130707582
#130707182
#130706512
#130705382
#130704492
#130703272
C4×C11×SD322
#3389911