Finite Group Databasebeta

← #14655880

Subgroups — #14655880

Order 2816.

524 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 524 conjugacy classes of subgroups — too many to draw. Only its 103 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079928C211yesmaximal, characteristic
2#13079543C211yesmaximal, characteristic
3#13079163C211yesmaximal, characteristic, complemented
4#13069564C211yesmaximal, characteristic, complemented
5#13069534C211yesmaximal, characteristic
6#13066465C211yesmaximal, characteristic, complemented
7C11×#1503C211yesmaximal, characteristic, complemented
8C11×#533C2211yescharacteristic
9#10623008C2211yescharacteristic
10C2×#66922C2211yescharacteristic
11C11×#431C2211yescharacteristic
12C4×C11×C4⋊C4C2211yescharacteristic
13#10622697—21no—
14#10622696—21no—
15#10622692—21no—
16#10622691—21no—
17#10622678—22no—
18#10622661—22no—
19#10622640—21no—
20#10622633—21no—
21#10622608—22no—
22C2×#66869—22no—
23C2×C4⋊(C11⋊C8)C2211yescharacteristic
24C4×#4318C2211yescharacteristic
25#10622454—22no—
26#10622351—22no—
27#10622306—21no—
28#10622294—21no—
29C11×#328—22no—
30#10622167—22no—
31C2×#4339—21no—
32C22×Dic22—21no—
33C11×C4⋊Q8D411yescharacteristic
34C11×C4⋊Q8D411yescharacteristic
35C11×#125—21no—
36C11×C22⋊Q8—21no—
37C11×C22⋊Q8—21no—
38C4×Q8×C11—21no—
39C4×Q8×C11—21no—
40C11×#117—21no—
41C2×C11×C4⋊C4—21no—
42C2×C42×C11—21no—
43C2×C42×C11C2311yescharacteristic
44C2×#4325—22no—
45#66983—21no—
46#66983—21no—
47C2×C4⋊Dic11—21no—
48C2×C4⋊Dic11—21no—
49C2×#4318D412yes—
50C22×C11⋊C8D412yes—
51C2×#4314—24no—
52#66928—21no—
53#66927D411yescharacteristic
54C4×D44—21no—
55C4×D44—21no—
56#66922—21no—
57#66922—21no—
58#66922—21no—
59#66922D412yes—
60#66922D411yescharacteristic
61C11×C4⋊C8—21no—
62C11×C22⋊C8D412yes—
63C4×C8×C11—21no—
64C11×#95—21no—
65#66899—22no—
66#66880—24no—
67#66873—22no—
68#66872—24no—
69#66872—22no—
70#66871—24no—
71#66869—44no—
72C4⋊(C11⋊C8)—21no—
73C4⋊(C11⋊C8)—21no—
74#66867—21no—
75C4×C11⋊C8—21no—
76#10197—111nomaximal, Sylow
77C2×Q8×C11—21no—
78C2×Q8×C11—21no—
79C22×C4×C11—41no—
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11C2×D411yescharacteristic
83C2×C22⋊D11—41no—
84C22×Dic11—41no—
85#4339—42no—
86#4339—42no—
87C2×D44—21no—
88C2×D44—21no—
89C2×D44—21no—
90C2×C4×D11—41no—
91C2×Dic22—22no—
92C2×Dic22—21no—
93C2×Dic22—41no—
94C2×Dic22—82no—
95C2×C8×C11—22no—
96C11×C4⋊C4—22no—
97C11×C4⋊C4—21no—
98C11×C4⋊C4—21no—
99C11×C4⋊C4—21no—
100C11×C4⋊C4—21no—
101C11×C4⋊C4—41no—
102C11×C4⋊C4—41no—
103C11×C4⋊C4—41no—
104C11×C22⋊C4—41no—
105C42×C11—41no—
106C42×C11—42no—
107C42×C11C2×D411yescharacteristic
108C42×C11C2×D411yescharacteristic
109C42×C11C2×D411yescharacteristic
110C42×C11#4111yescharacteristic
111#4325—82no—
112(C2×D11)⋊C4—41no—
113(C2×D11)⋊C4—41no—
114C4⋊Dic11—22no—
115C4⋊Dic11—21no—
116C4⋊Dic11—21no—
117C4⋊Dic11—22no—
118C4⋊Dic11—41no—
119C4⋊Dic11—41no—
120#4318—22no—
121#4318SD1614yescomplemented
122C2×C11⋊C8—22no—
123C2×C11⋊C8—22no—
124C2×C11⋊C8—42no—
125#4314—84no—
126#3246—111no—
127#3206—111no—
128#3165—111no—
129#1987—111no—
130#1980—111no—
131#1503D1111yescharacteristic, complemented
132#1283—111no—
133C23×C11#12711yescharacteristic
134C22×D11—41no—
135Q8×C11—41no—
136Q8×C11—41no—
137Q8×C11—81no—
138C2×C4×C11—21no—
139C2×C4×C11—21no—
140C2×C4×C11—41no—
141C2×C4×C11—42no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—81no—
145C2×C4×C11—81no—
146C2×C4×C11#12011yescharacteristic
147C2×C4×C11#12011yescharacteristic
148C2×C4×C11#12011yescharacteristic
149C2×C4×C11#12111yescharacteristic
150C2×C4×C11#12111yescharacteristic
151C2×C4×C11#12111yescharacteristic
152C2×C4×C11C2×SD1612yes—
153C2×C4×C11#13712yes—
154C22⋊D11—81no—
155C22⋊D11—81no—
156C2×Dic11—42no—
157C2×Dic11—41no—
158C2×Dic11—82no—
159D44—42no—
160D44—41no—
161D44—41no—
162D44—42no—
163C4×D11—82no—
164Dic22—44no—
165Dic22—42no—
166Dic22—82no—
167C8×C11—42no—
168C11⋊C8—24no—
169C11⋊C8—42no—
170#533C2×D1111yescharacteristic
171#532—111no—
172C2×C4⋊Q8—111no—
173#501—222no—
174#500—221no—
175#498—221no—
176#492—221no—
177#487—221no—
178#476—221no—
179#475—221no—
180#465—222no—
181#461—222no—
182#461—221no—
183#460—221no—
184#448—222no—
185#431C2×D1111yescharacteristic
186#428—222no—
187C2×C4⋊C8—111no—
188C2×#104—222no—
189C4×M16—111no—
190C4×C4⋊C4C2×D1111yescharacteristic
191#340—222no—
192#328—22no—
193C22×C11—21no—
194C22×C11—21no—
195C22×C11#39211yescharacteristic
196C22×C11#49211yescharacteristic
197C22×C11#49711yescharacteristic
198C2×D11—81no—
199C2×D11—81no—
200C2×D11—81no—
201C4×C11—21no—
202C4×C11—21no—
203C4×C11—21no—
204C4×C11—82no—
205C4×C11—81no—
206C4×C11—81no—
207C4×C11#44812yes—
208C4×C11#45511yescharacteristic
209C4×C11#45611yescharacteristic
210C4×C11#46112yes—
211Dic11—82no—
212Dic11—81no—
213C2×#41—221no—
214C22×Q8—221no—
215C2×SD16—224no—
216C2×SD16—222no—
217C2×M16—112no—
218C22×C8—112no—
219C4⋊Q8—112no—
220C4⋊Q8—111no—
221C4⋊Q8—221no—
222C4⋊Q8—221no—
223C4⋊Q8—221no—
224C4⋊Q8D4411yescharacteristic
225C4⋊Q8D4411yescharacteristic
226#127—111no—
227#125—21no—
228#124—221no—
229C22⋊Q8—21no—
230C22⋊Q8—21no—
231#121—221no—
232#121—221no—
233C4×Q8—21no—
234C4×Q8—21no—
235C4×D4—221no—
236C4×D4—221no—
237#117—21no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—221no—
240C2×C4⋊C4—221no—
241C2×C42—21no—
242C2×C42C22×D1111yescharacteristic
243#107—224no—
244#106—224no—
245#106—222no—
246C4⋊C8—21no—
247C4⋊C8—221no—
248C4⋊C8—221no—
249#104—444no—
250#103—224no—
251#103—222no—
252#102—222no—
253C22⋊C8C22⋊D1112yes—
254#97—221no—
255C4×C8—21no—
256C4×C8—221no—
257#95—21no—
258C2×C11—21no—
259C2×C11—21no—
260C2×C11#200711yescharacteristic
261C2×C11#200811yescharacteristic
262C2×C11#201311yescharacteristic
263D11—161no—
264#41—442no—
265#41—442no—
266C2×Q8—21no—
267C2×Q8—21no—
268C2×Q8—221no—
269C2×Q8—222no—
270C2×Q8—441no—
271C2×Q8—882no—
272C2×D4—221no—
273C2×D4—221no—
274C2×D4—221no—
275C2×D4—441no—
276C22×C4—41no—
277C22×C4—441no—
278C22×C4—441no—
279C22×C4D4×D1111yescharacteristic
280C22×C4D4×D1111yescharacteristic
281C22×C4C2×C22⋊D1111yescharacteristic
282SD16—884no—
283SD16—882no—
284M16—114no—
285M16—222no—
286C2×C8—22no—
287C2×C8—222no—
288C2×C8—222no—
289C2×C8—442no—
290C4⋊C4—22no—
291C4⋊C4—21no—
292C4⋊C4—21no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—41no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C4⋊C4—221no—
299C4⋊C4—222no—
300C4⋊C4—222no—
301C4⋊C4—221no—
302C4⋊C4—441no—
303C4⋊C4—441no—
304C22⋊C4—41no—
305C22⋊C4—441no—
306C22⋊C4—441no—
307C42—41no—
308C42—42no—
309C42C2×D4411yescharacteristic
310C42#433911yescharacteristic
311C42D4×D1111yescharacteristic
312C42D4×D1111yescharacteristic
313C11#1019711yescharacteristic, complemented, Sylow
314C23—441no—
315C23#6699311yescharacteristic
316Q8—41no—
317Q8—41no—
318Q8—81no—
319Q8—444no—
320Q8—442no—
321Q8—882no—
322D4—442no—
323D4—442no—
324D4—441no—
325D4—441no—
326D4—881no—
327D4—881no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—41no—
331C2×C4—42no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—81no—
335C2×C4—81no—
336C2×C4—441no—
337C2×C4—442no—
338C2×C4—882no—
339C2×C4—882no—
340C2×C4#6693511yescharacteristic
341C2×C4#6693511yescharacteristic
342C2×C4#6693711yescharacteristic
343C2×C4#6693711yescharacteristic
344C2×C4SD16×D1112yes—
345C2×C4#6697112yes—
346C2×C4#6698311yescharacteristic
347C2×C4#6699011yescharacteristic
348C8—42no—
349C8—224no—
350C8—442no—
351C22—21no—
352C22—21no—
353C22—881no—
354C22—881no—
355C22—881no—
356C22#1062257311yescharacteristic
357C22#1062278811yescharacteristic
358C22#1062280311yescharacteristic
359C4—21no—
360C4—21no—
361C4—21no—
362C4—82no—
363C4—81no—
364C4—81no—
365C4—882no—
366C4—881no—
367C4#1062241912yes—
368C4#1062243112yes—
369C4#1062243811yescharacteristic
370C4#1062243911yescharacteristic
371C2—21no—
372C2—21no—
373C2—1761no—
374C2#1306966411yescharacteristic
375C2#1306966811yescharacteristic
376C2#1306970011yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1503C2
socleC22×C11#392
prime radical#10623008C22
hypercenter#1503D11
hypocenterC11#10197
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1503

Complements

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

NH ≅ G/Ntype
3. #13079163C2semidirect
4. #13069564C2semidirect
6. #13066465C2semidirect
7. C11×#1503C2semidirect
121. #4318SD16semidirect
131. #1503D11semidirect
313. C11#10197semidirect

Maximal subgroups

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

subgroupindex
#130799282
#130795432
#130791632
#130695642
#130695342
#130664652
C11×#15032
#1019711