Finite Group Databasebeta

← #14910733

Subgroups — #14910733

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#13081039C211yesmaximal, characteristic, complemented
2#13070839C211yesmaximal, characteristic, complemented
3#13070804C212yesmaximal, complemented
4#13070768C211yesmaximal, characteristic, complemented
5#13070700C212yesmaximal, complemented
6#13070648C211yesmaximal, characteristic, complemented
7#13070539C212yesmaximal, complemented
8C4×#66892C211yesmaximal, characteristic, complemented
9D4×C11⋊C16C211yesmaximal, characteristic, complemented
10#13070323C212yesmaximal, complemented
11C11×#3287C211yesmaximal, characteristic, complemented
12C2×C11×#135C2212yes—
13C11×#550—21no—
14#10623094—21no—
15C11×#493C2211yescharacteristic
16C11×#466C2212yes—
17C11×#460—21no—
18C11×#449—22no—
19C4×C11×Q16C2211yescharacteristic
20C8×D4×C11C2211yescharacteristic
21C2×#66892C2211yescharacteristic
22C2×#66890C2212yes—
23#10622728C2212yes—
24#10622719C2212yes—
25C22×C11⋊C16C2212yes—
26#10622455—21no—
27#10622350—22no—
28C4×D88C2211yescharacteristic
29#10622295C2211yescharacteristic
30#10622202C2211yescharacteristic
31#10622202C2212yes—
32#10622200C2212yes—
33#10622200C2212yes—
34#10622200C2212yes—
35C22⋊(C11⋊C16)C2212yes—
36#10622129C2211yescharacteristic
37#10622128C2211yescharacteristic
38#10622127C2212yes—
39C4⋊(C11⋊C16)C2211yescharacteristic
40C4×C11⋊C16C2211yescharacteristic
41C2×C11×#41—22no—
42C11×#135—24no—
43C11×#135—42no—
44C2×C11×Q16C2311yescharacteristic
45C2×C11×SD16—22no—
46C2×C11×D8—21no—
47C2×C11×D8C2312yes—
48C22×C8×C11C2312yes—
49C11×#127—21no—
50C11×#127—41no—
51C11×#121—22no—
52C11×#121—42no—
53C4×Q8×C11—21no—
54C4×D4×C11—41no—
55C4×D4×C11D411yescharacteristic
56#66991—41no—
57#66983—22no—
58#66979—22no—
59C2×D88C2311yescharacteristic
60#66945—41no—
61#66938—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#66882C2312yes—
76#66882C2311yescharacteristic
77#66881—22no—
78C2×C11⋊C16—42no—
79C2×C11⋊C16C2312yes—
80C2×C11⋊C16C2311yescharacteristic
81C2×C11⋊C16C2311yescharacteristic
82#33872—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—
95C2×D44—21no—
96C2×C4×D11—41no—
97C2×Dic22—41no—
98C11×Q16—21no—
99C11×Q16#4112yes—
100C11×SD16—44no—
101C11×D8—22no—
102C11×D8—22no—
103C11×D8—81no—
104C2×C8×C11—22no—
105C2×C8×C11—22no—
106C2×C8×C11C2×D412yes—
107C2×C8×C11C2×D411yescharacteristic
108C2×C8×C11C2411yescharacteristic
109C11×C4⋊C4—21no—
110C11×C4⋊C4—41no—
111C11×C4⋊C4D811yescharacteristic
112C11×C22⋊C4—42no—
113C11×C22⋊C4D812yes—
114C42×C11—41no—
115C42×C11C2×D411yescharacteristic
116C22⋊Dic11—42no—
117(C2×D11)⋊C4—41no—
118(C2×D11)⋊C4—42no—
119C4⋊Dic11—21no—
120C4⋊Dic11—22no—
121C4⋊Dic11—41no—
122C4×Dic11—42no—
123D88—21no—
124D88—21no—
125C11⋊C16—21no—
126C11⋊C16—21no—
127C11⋊C16—22no—
128#3341—111no—
129#3287D1111yescharacteristic, complemented
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—42no—
140C23×C11C2×D812yes—
141C22×D11—41no—
142Q8×C11—22no—
143Q8×C11—41no—
144D4×C11—22no—
145D4×C11—42no—
146D4×C11—42no—
147D4×C11—84no—
148D4×C11—82no—
149D4×C11—161no—
150D4×C11—162no—
151C2×C4×C11—22no—
152C2×C4×C11—22no—
153C2×C4×C11—41no—
154C2×C4×C11—41no—
155C2×C4×C11—84no—
156C2×C4×C11C2×D812yes—
157C2×C4×C11C2×D811yescharacteristic
158C2×C4×C11C2×D811yescharacteristic
159C2×C4×C11C22×D411yescharacteristic
160C22⋊D11—162no—
161C2×Dic11—41no—
162C2×Dic11—42no—
163D44—41no—
164D44—41no—
165C4×D11—82no—
166Dic22—161no—
167C8×C11—22no—
168C8×C11—21no—
169C8×C11C2×#4111yescharacteristic
170C8×C11H(5,𝔽2)11yescharacteristic
171C2×#135C2×D1112yes—
172#555—221no—
173#550—21no—
174C2×SD32—111no—
175C2×D16—112no—
176C22×C16—112no—
177#500—111no—
178#493C2×D1111yescharacteristic
179#482—222no—
180#476—221no—
181#466—112no—
182#466C2×D1112yes—
183#460—21no—
184#449—22no—
185C4×Q16C2×D1111yescharacteristic
186C4×D8—111no—
187C8×D4C2×D1111yescharacteristic
188#427—112no—
189#367—111no—
190#366—112no—
191C4⋊C16—111no—
192#358—111no—
193#358—112no—
194#357—112no—
195#357—112no—
196#357—112no—
197#357—111no—
198C22⋊C16—112no—
199C4×C16—111no—
200C22×C11—22no—
201C22×C11—22no—
202C22×C11—22no—
203C22×C11—82no—
204C22×C11—82no—
205C22×C11—82no—
206C22×C11C22×D811yescharacteristic
207C2×D11—81no—
208C2×D11—81no—
209C2×D11—81no—
210C4×C11—21no—
211C4×C11—22no—
212C4×C11—42no—
213C4×C11—81no—
214C4×C11#50812yes—
215C4×C11#54611yescharacteristic
216C4×C11#57711yescharacteristic
217Dic11—81no—
218Dic11—82no—
219C2×#41—22no—
220#135—24no—
221#135—42no—
222C2×Q16C22×D1111yescharacteristic
223C2×SD16—22no—
224C2×D8—21no—
225C2×D8—111no—
226C2×D8C22×D1112yes—
227C22×C8C22×D1112yes—
228C4⋊Q8—221no—
229#127—21no—
230#127—41no—
231#124—442no—
232#121—22no—
233#121—42no—
234#121—222no—
235#121—441no—
236C4×Q8—21no—
237C4×D4—41no—
238C4×D4—221no—
239C4×D4C22⋊D1111yescharacteristic
240#117—222no—
241#117—441no—
242SD32—222no—
243D16—442no—
244C2×C16—111no—
245C2×C16—111no—
246C2×C16—112no—
247C2×C16—442no—
248#107—112no—
249#107—111no—
250#107—221no—
251#107C22×D1111yescharacteristic
252#106—222no—
253C4⋊C8C22⋊D1111yescharacteristic
254#103—21no—
255#102—22no—
256#102—221no—
257#102—222no—
258C22⋊C8C22⋊D1112yes—
259C4×C8C22×D1111yescharacteristic
260C2×C11—42no—
261C2×C11—162no—
262C2×C11#329411yescharacteristic
263C2×C11C2×#50811yescharacteristic
264C2×C11#341511yescharacteristic
265D11—161no—
266#41—44no—
267#41—82no—
268C2×Q8—21no—
269C2×Q8—441no—
270C2×D4—22no—
271C2×D4—42no—
272C2×D4—42no—
273C2×D4—41no—
274C2×D4—41no—
275C2×D4—221no—
276C2×D4—442no—
277C2×D4#432311yescharacteristic
278C22×C4—42no—
279C22×C4—441no—
280C22×C4C2×C22⋊D1112yes—
281Q16—21no—
282Q16#434112yes—
283SD16—44no—
284D8—22no—
285D8—22no—
286D8—81no—
287D8—221no—
288D8—221no—
289C2×C8—22no—
290C2×C8—22no—
291C2×C8C2×C22⋊D1111yescharacteristic
292C2×C8C2×C22⋊D1112yes—
293C2×C8C23×D1111yescharacteristic
294C4⋊C4—21no—
295C4⋊C4—41no—
296C4⋊C4—221no—
297C4⋊C4—222no—
298C4⋊C4—441no—
299C4⋊C4#432311yescharacteristic
300C22⋊C4—42no—
301C22⋊C4—442no—
302C22⋊C4—442no—
303C22⋊C4—441no—
304C22⋊C4#432312yes—
305C42—41no—
306C42—442no—
307C42C2×C22⋊D1111yescharacteristic
308C16—221no—
309C16—221no—
310C16—222no—
311C11#3387211yescharacteristic, complemented, Sylow
312C23—42no—
313C23—441no—
314C23C2×#432312yes—
315Q8—22no—
316Q8—41no—
317Q8—1761no—
318D4—22no—
319D4—42no—
320D4—42no—
321D4—84no—
322D4—82no—
323D4—161no—
324D4—162no—
325D4—441no—
326D4—441no—
327D4—1762no—
328C2×C4—22no—
329C2×C4—22no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—84no—
333C2×C4—441no—
334C2×C4—442no—
335C2×C4—882no—
336C2×C4C2×#432312yes—
337C2×C4C2×#432311yescharacteristic
338C2×C4C2×#432311yescharacteristic
339C2×C4C22×C22⋊D1111yescharacteristic
340C8—22no—
341C8—21no—
342C8C2×#434111yescharacteristic
343C8#6703711yescharacteristic
344C22—22no—
345C22—22no—
346C22—22no—
347C22—82no—
348C22—82no—
349C22—82no—
350C22—881no—
351C22—881no—
352C22—881no—
353C22C22×#432311yescharacteristic
354C4—22no—
355C4—21no—
356C4—42no—
357C4—81no—
358C4—881no—
359C4—882no—
360C4#1062280712yes—
361C4#1062333711yescharacteristic
362C4#1062336711yescharacteristic
363C2—42no—
364C2—162no—
365C2—1761no—
366C2#1308042911yescharacteristic
367C2C2×#1062280711yescharacteristic
368C2#1308175511yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3287C2
socleC22×C11C22×D8
hypercenter#3287D11
hypocenterC11#33872
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. #13081039C2semidirect
2. #13070839C2semidirect
3. #13070804C2semidirect
4. #13070768C2semidirect
5. #13070700C2semidirect
6. #13070648C2semidirect
7. #13070539C2semidirect
8. C4×#66892C2semidirect
9. D4×C11⋊C16C2semidirect
10. #13070323C2semidirect
11. C11×#3287C2semidirect
129. #3287D11semidirect
311. C11#33872semidirect

Maximal subgroups

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

subgroupindex
#130810392
#130708392
#130708042
#130707682
#130707002
#130706482
#130705392
C4×#668922
D4×C11⋊C162
#130703232
C11×#32872
#3387211