Finite Group Databasebeta

← #14910727

Subgroups — #14910727

Order 2816.

568 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13080376C211yesmaximal, characteristic, complemented
2#13070841C211yesmaximal, characteristic, complemented
3#13070807C212yesmaximal, complemented
4#13070765C211yesmaximal, characteristic, complemented
5#13070700C212yesmaximal, complemented
6#13070651C211yesmaximal, characteristic, complemented
7#13070537C212yesmaximal, complemented
8C4×#66891C211yesmaximal, characteristic, complemented
9D4×C11⋊C16C211yesmaximal, characteristic, complemented
10#13070321C212yesmaximal, complemented
11C11×#3341C211yesmaximal, characteristic, complemented
12C11×#555—21no—
13C2×#66957C2212yes—
14#10623084—21no—
15C11×#500C2211yescharacteristic
16C11×#482—22no—
17C11×#476—21no—
18C11×#466C2212yes—
19C4×C11×D8C2211yescharacteristic
20C8×D4×C11C2211yescharacteristic
21C11×#427C2212yes—
22C2×#66891C2211yescharacteristic
23C2×#66890C2212yes—
24#10622728C2212yes—
25C22×C11⋊C16C2212yes—
26#10622461—21no—
27#10622347—22no—
28C4×Dic44C2211yescharacteristic
29#10622308C2211yescharacteristic
30#10622200C2211yescharacteristic
31C22⋊(C11⋊C16)C2212yes—
32#10622130C2211yescharacteristic
33#10622130C2212yes—
34#10622129C2212yes—
35#10622129C2212yes—
36#10622129C2212yes—
37#10622128C2211yescharacteristic
38#10622127C2212yes—
39C4⋊(C11⋊C16)C2211yescharacteristic
40C4×C11⋊C16C2211yescharacteristic
41C2×#4339—22no—
42C2×C11×D8C2311yescharacteristic
43C22×C8×C11C2312yes—
44C11×C4⋊Q8—21no—
45C11×#124—42no—
46C11×#121—22no—
47C11×#121—41no—
48C4×D4×C11—21no—
49C4×D4×C11D411yescharacteristic
50C11×#117—22no—
51C11×#117—41no—
52#66993—41no—
53#66983—22no—
54C2×Dic44C2311yescharacteristic
55#66957—24no—
56#66957—42no—
57C2×D88—21no—
58C2×D88C2312yes—
59C2×#4314—22no—
60#66946—41no—
61#66937—42no—
62#66927—21no—
63C4×Dic22—21no—
64C11×#107—21no—
65C11×#107C2312yes—
66C11×#107C2311yescharacteristic
67C11×#106—22no—
68C11×C4⋊C8D411yescharacteristic
69C11×#102—21no—
70C11×#102—22no—
71C11×C22⋊C8D412yes—
72C4×C8×C11C2311yescharacteristic
73#66891—22no—
74#66890—42no—
75#66885—22no—
76#66882C2311yescharacteristic
77#66880—21no—
78C2×C11⋊C16—42no—
79C2×C11⋊C16C2312yes—
80C2×C11⋊C16C2311yescharacteristic
81C2×C11⋊C16C2311yescharacteristic
82#33872—111nomaximal, Sylow
83C2×Q8×C11—41no—
84C2×D4×C11—21no—
85C2×D4×C11—42no—
86C2×D4×C11D811yescharacteristic
87C22×C4×C11—41no—
88C22×C4×C11C2×D412yes—
89C2×C22⋊D11—42no—
90C2×C22⋊D11—42no—
91#4339—44no—
92#4339—82no—
93C2×D44—22no—
94C2×D44—41no—
95C2×D44—41no—
96C2×C4×D11—42no—
97C2×Dic22—21no—
98C11×D8—21no—
99C11×D8—21no—
100C2×C8×C11—22no—
101C2×C8×C11—22no—
102C2×C8×C11C2×D411yescharacteristic
103C2×C8×C11C2×D412yes—
104C2×C8×C11C2411yescharacteristic
105C11×C4⋊C4—21no—
106C11×C4⋊C4—22no—
107C11×C4⋊C4—41no—
108C11×C4⋊C4D811yescharacteristic
109C11×C22⋊C4—42no—
110C11×C22⋊C4—42no—
111C11×C22⋊C4—41no—
112C11×C22⋊C4D812yes—
113C42×C11—42no—
114C42×C11C2×D411yescharacteristic
115(C2×D11)⋊C4—42no—
116C4⋊Dic11—21no—
117Dic11⋊C4—41no—
118C4×Dic11—41no—
119Dic44—21no—
120Dic44#4112yes—
121D88—22no—
122D88—22no—
123D88—81no—
124#4314—44no—
125C11⋊C16—21no—
126C11⋊C16—21no—
127C11⋊C16—22no—
128#3341D1111yescharacteristic, complemented
129#3287—111no—
130#2240—111no—
131#2234—112no—
132#2227—111no—
133#2215—112no—
134#2206—111no—
135#2186—112no—
136C4×SD32—111no—
137D4×C16—111no—
138#2138—112no—
139C23×C11—41no—
140C23×C11C2×D812yes—
141C22×D11—42no—
142Q8×C11—161no—
143D4×C11—22no—
144D4×C11—41no—
145D4×C11—41no—
146D4×C11—162no—
147C2×C4×C11—22no—
148C2×C4×C11—22no—
149C2×C4×C11—41no—
150C2×C4×C11—42no—
151C2×C4×C11—82no—
152C2×C4×C11C2×D811yescharacteristic
153C2×C4×C11C2×D812yes—
154C2×C4×C11C2×D811yescharacteristic
155C2×C4×C11C22×D411yescharacteristic
156C22⋊D11—84no—
157C22⋊D11—162no—
158C2×Dic11—41no—
159C2×Dic11—41no—
160D44—42no—
161D44—42no—
162D44—82no—
163D44—161no—
164C4×D11—84no—
165Dic22—22no—
166Dic22—41no—
167C8×C11—22no—
168C8×C11—21no—
169C8×C11C2×#4111yescharacteristic
170C8×C11H(5,𝔽2)11yescharacteristic
171C2×#135—112no—
172#555—21no—
173#550—221no—
174C2×SD32—111no—
175C2×D16—112no—
176C22×C16—112no—
177#500C2×D1111yescharacteristic
178#493—111no—
179#482—22no—
180#476—21no—
181#466—112no—
182#466C2×D1112yes—
183#460—221no—
184#449—222no—
185C4×Q16—111no—
186C4×D8C2×D1111yescharacteristic
187C8×D4C2×D1111yescharacteristic
188#427C2×D1112yes—
189#367—111no—
190#366—112no—
191C4⋊C16—111no—
192#358—111no—
193#358—112no—
194#357—111no—
195#357—112no—
196#357—112no—
197#357—112no—
198C22⋊C16—112no—
199C4×C16—111no—
200C22×C11—22no—
201C22×C11—22no—
202C22×C11—22no—
203C22×C11—81no—
204C22×C11—81no—
205C22×C11—81no—
206C22×C11C22×D811yescharacteristic
207C2×D11—82no—
208C2×D11—82no—
209C2×D11—82no—
210C4×C11—21no—
211C4×C11—22no—
212C4×C11—81no—
213C4×C11—82no—
214C4×C11#50812yes—
215C4×C11#54611yescharacteristic
216C4×C11#57711yescharacteristic
217Dic11—42no—
218Dic11—81no—
219C2×#41—222no—
220#135—224no—
221#135—442no—
222C2×Q16—111no—
223C2×SD16—222no—
224C2×D8—112no—
225C2×D8—221no—
226C2×D8C22×D1111yescharacteristic
227C22×C8C22×D1112yes—
228C4⋊Q8—21no—
229#127—221no—
230#127—441no—
231#124—42no—
232#121—22no—
233#121—41no—
234#121—222no—
235#121—442no—
236C4×Q8—221no—
237C4×D4—21no—
238C4×D4—441no—
239C4×D4C22⋊D1111yescharacteristic
240#117—22no—
241#117—41no—
242SD32—222no—
243D16—442no—
244C2×C16—111no—
245C2×C16—111no—
246C2×C16—112no—
247C2×C16—442no—
248#107—21no—
249#107—111no—
250#107C22×D1112yes—
251#107C22×D1111yescharacteristic
252#106—22no—
253C4⋊C8C22⋊D1111yescharacteristic
254#103—221no—
255#102—21no—
256#102—22no—
257#102—222no—
258C22⋊C8C22⋊D1112yes—
259C4×C8C22×D1111yescharacteristic
260C2×C11—42no—
261C2×C11—161no—
262C2×C11#329411yescharacteristic
263C2×C11C2×#50811yescharacteristic
264C2×C11#341511yescharacteristic
265D11—162no—
266#41—444no—
267#41—882no—
268C2×Q8—41no—
269C2×Q8—221no—
270C2×D4—21no—
271C2×D4—42no—
272C2×D4—222no—
273C2×D4—442no—
274C2×D4—442no—
275C2×D4—441no—
276C2×D4—441no—
277C2×D4#432311yescharacteristic
278C22×C4—41no—
279C22×C4—442no—
280C22×C4C2×C22⋊D1112yes—
281Q16—112no—
282Q16—221no—
283SD16—444no—
284D8—21no—
285D8—21no—
286D8—222no—
287D8—222no—
288D8—881no—
289C2×C8—22no—
290C2×C8—22no—
291C2×C8C2×C22⋊D1111yescharacteristic
292C2×C8C2×C22⋊D1112yes—
293C2×C8C23×D1111yescharacteristic
294C4⋊C4—21no—
295C4⋊C4—22no—
296C4⋊C4—41no—
297C4⋊C4—221no—
298C4⋊C4—441no—
299C4⋊C4#432311yescharacteristic
300C22⋊C4—42no—
301C22⋊C4—42no—
302C22⋊C4—41no—
303C22⋊C4—442no—
304C22⋊C4#432312yes—
305C42—42no—
306C42—441no—
307C42C2×C22⋊D1111yescharacteristic
308C16—221no—
309C16—221no—
310C16—222no—
311C11#3387211yescharacteristic, complemented, Sylow
312C23—41no—
313C23—442no—
314C23C2×#432312yes—
315Q8—161no—
316Q8—222no—
317Q8—441no—
318D4—22no—
319D4—41no—
320D4—41no—
321D4—162no—
322D4—442no—
323D4—442no—
324D4—884no—
325D4—882no—
326D4—1761no—
327D4—1762no—
328C2×C4—22no—
329C2×C4—22no—
330C2×C4—41no—
331C2×C4—42no—
332C2×C4—82no—
333C2×C4—441no—
334C2×C4—441no—
335C2×C4—884no—
336C2×C4C2×#432312yes—
337C2×C4C2×#432311yescharacteristic
338C2×C4C2×#432311yescharacteristic
339C2×C4C22×C22⋊D1111yescharacteristic
340C8—22no—
341C8—21no—
342C8#41×D1111yescharacteristic
343C8#6704211yescharacteristic
344C22—22no—
345C22—22no—
346C22—22no—
347C22—81no—
348C22—81no—
349C22—81no—
350C22—882no—
351C22—882no—
352C22—882no—
353C22C22×#432311yescharacteristic
354C4—22no—
355C4—21no—
356C4—81no—
357C4—82no—
358C4—442no—
359C4—881no—
360C4#1062280712yes—
361C4#1062336011yescharacteristic
362C4#1062336811yescharacteristic
363C2—42no—
364C2—161no—
365C2—1762no—
366C2#1308042311yescharacteristic
367C2C2×#1062280711yescharacteristic
368C2#1308175511yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3341C2
socleC22×C11C22×D8
hypercenter#3341D11
hypocenterC11#33872
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #3341

Complements

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

NH ≅ G/Ntype
1. #13080376C2semidirect
2. #13070841C2semidirect
3. #13070807C2semidirect
4. #13070765C2semidirect
5. #13070700C2semidirect
6. #13070651C2semidirect
7. #13070537C2semidirect
8. C4×#66891C2semidirect
9. D4×C11⋊C16C2semidirect
10. #13070321C2semidirect
11. C11×#3341C2semidirect
128. #3341D11semidirect
311. C11#33872semidirect

Maximal subgroups

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

subgroupindex
#130803762
#130708412
#130708072
#130707652
#130707002
#130706512
#130705372
C4×#668912
D4×C11⋊C162
#130703212
C11×#33412
#3387211