Finite Group Databasebeta

← #14655877

Subgroups — #14655877

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#13079933C211yesmaximal, characteristic
2#13079541C211yesmaximal, characteristic
3#13079158C211yesmaximal, characteristic, complemented
4#13069534C211yesmaximal, characteristic
5#13067114C211yesmaximal, characteristic, complemented
6#13066466C211yesmaximal, characteristic, complemented
7C11×#1987C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8C2211yescharacteristic
9#10623008C2211yescharacteristic
10#10623001C2211yescharacteristic
11C2×C11×C4⋊C8C2211yescharacteristic
12C4×C11×C4⋊C4C2211yescharacteristic
13#10622840—22no—
14#10622727—22no—
15#10622698—21no—
16#10622696—22no—
17#10622694—21no—
18#10622693—22no—
19#10622692—21no—
20#10622691—21no—
21#10622577—22no—
22C2×#66869—22no—
23#10622538C2211yescharacteristic
24C4×#4318C2211yescharacteristic
25#10622464—21no—
26#10622461—21no—
27#10622455—21no—
28#10622454—21no—
29C11×#340—22no—
30#10622090—22no—
31C22×Q8×C11—21no—
32C2×#4339—21no—
33C22×C8×C11D412yes—
34C11×C4⋊Q8—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8D412yes—
38C2×C11×C4⋊C4—21no—
39C2×C11×C4⋊C4—21no—
40C2×C11×C4⋊C4—21no—
41C2×C42×C11—21no—
42C2×C42×C11C2311yescharacteristic
43C2×#4325—24no—
44#66983—21no—
45#66983—21no—
46#66979—21no—
47#66977—21no—
48#66977—21no—
49C2×#4318D412yes—
50C2×#4314—22no—
51#66928—21no—
52#66927D411yescharacteristic
53C4×D44—21no—
54C4×D44—21no—
55#66923—21no—
56#66922D411yescharacteristic
57#66922D411yescharacteristic
58#66922D411yescharacteristic
59C4×Dic22—21no—
60C4×Dic22—21no—
61C11×C4⋊C8—21no—
62C11×C4⋊C8—21no—
63C11×#95—21no—
64#66899—24no—
65C22⋊(C11⋊C8)D412yes—
66#66885—22no—
67#66881—22no—
68#66880—22no—
69#66872—24no—
70#66871—24no—
71#66869—44no—
72C4⋊(C11⋊C8)—21no—
73#66867—21no—
74C4×C11⋊C8—21no—
75C4×C11⋊C8—21no—
76#10197—111nomaximal, Sylow
77C2×Q8×C11—22no—
78C2×Q8×C11—41no—
79C2×Q8×C11—82no—
80C22×C4×C11—41no—
81C22×C4×C11—41no—
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C2×C22⋊D11—41no—
86#4339—42no—
87#4339—42no—
88C2×D44—21no—
89C2×D44—21no—
90C2×D44—21no—
91C2×C4×D11—41no—
92C2×Dic22—21no—
93C2×Dic22—21no—
94C2×Dic22—21no—
95C2×C8×C11—22no—
96C2×C8×C11—42no—
97C11×C4⋊C4—22no—
98C11×C4⋊C4—22no—
99C11×C4⋊C4—22no—
100C11×C4⋊C4—41no—
101C11×C4⋊C4—41no—
102C11×C4⋊C4—41no—
103C42×C11—42no—
104C42×C11C2×D411yescharacteristic
105C42×C11C2×D411yescharacteristic
106C42×C11C2×D411yescharacteristic
107C42×C11#4111yescharacteristic
108C22⋊Dic11—41no—
109#4325—84no—
110(C2×D11)⋊C4—41no—
111(C2×D11)⋊C4—41no—
112C4⋊Dic11—21no—
113C4⋊Dic11—21no—
114C4⋊Dic11—21no—
115C4⋊Dic11—21no—
116C4⋊Dic11—21no—
117C4⋊Dic11—21no—
118Dic11⋊C4—41no—
119Dic11⋊C4—41no—
120C4×Dic11—41no—
121#4318—22no—
122#4318SD1614yescomplemented
123C2×C11⋊C8—22no—
124C2×C11⋊C8—22no—
125#4314—82no—
126#3246—111no—
127#3206—111no—
128#3165—111no—
129#1987D1111yescharacteristic, complemented
130#1980—111no—
131#1503—111no—
132#1283—111no—
133C23×C11#12711yescharacteristic
134C22×D11—41no—
135Q8×C11—44no—
136Q8×C11—82no—
137C2×C4×C11—21no—
138C2×C4×C11—21no—
139C2×C4×C11—41no—
140C2×C4×C11—42no—
141C2×C4×C11—42no—
142C2×C4×C11—81no—
143C2×C4×C11—82no—
144C2×C4×C11—81no—
145C2×C4×C11#12011yescharacteristic
146C2×C4×C11#12011yescharacteristic
147C2×C4×C11#12011yescharacteristic
148C2×C4×C11#12111yescharacteristic
149C2×C4×C11#12111yescharacteristic
150C2×C4×C11#12111yescharacteristic
151C2×C4×C11C2×SD1612yes—
152C2×C4×C11#13712yes—
153C22⋊D11—81no—
154C22⋊D11—81no—
155C2×Dic11—41no—
156C2×Dic11—41no—
157C2×Dic11—41no—
158D44—42no—
159D44—41no—
160D44—41no—
161D44—42no—
162C4×D11—82no—
163Dic22—41no—
164Dic22—41no—
165Dic22—42no—
166Dic22—81no—
167C8×C11—42no—
168C11⋊C8—24no—
169C11⋊C8—42no—
170#533—111no—
171#532—111no—
172C2×C4⋊Q8C2×D1111yescharacteristic
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—221no—
182#461—222no—
183#460—221no—
184#448—222no—
185#431—111no—
186#428—222no—
187C2×C4⋊C8C2×D1111yescharacteristic
188C2×#104—222no—
189C4×M16—111no—
190C4×C4⋊C4C2×D1111yescharacteristic
191#340—22no—
192#328—222no—
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—82no—
206C4×C11#44812yes—
207C4×C11#45511yescharacteristic
208C4×C11#45611yescharacteristic
209C4×C11#46112yes—
210Dic11—81no—
211Dic11—81no—
212Dic11—81no—
213C2×#41—221no—
214C22×Q8—21no—
215C2×SD16—222no—
216C2×SD16—224no—
217C2×M16—112no—
218C22×C8C22⋊D1112yes—
219C4⋊Q8—21no—
220C4⋊Q8—21no—
221C4⋊Q8—21no—
222C4⋊Q8—111no—
223C4⋊Q8—111no—
224C4⋊Q8—111no—
225C4⋊Q8D4412yes—
226#127—111no—
227#125—221no—
228#124—221no—
229C22⋊Q8—221no—
230C22⋊Q8—221no—
231#121—221no—
232#121—221no—
233C4×Q8—221no—
234C4×Q8—221no—
235C4×D4—221no—
236C4×D4—221no—
237#117—221no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—21no—
241C2×C42—21no—
242C2×C42C22×D1111yescharacteristic
243#107—224no—
244#106—224no—
245#106—222no—
246C4⋊C8—21no—
247C4⋊C8—21no—
248C4⋊C8—221no—
249#104—444no—
250#103—222no—
251#103—224no—
252#102—222no—
253C22⋊C8—112no—
254#97—221no—
255C4×C8—221no—
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—22no—
267C2×Q8—41no—
268C2×Q8—82no—
269C2×Q8—221no—
270C2×Q8—221no—
271C2×Q8—221no—
272C2×D4—221no—
273C2×D4—221no—
274C2×D4—221no—
275C2×D4—441no—
276C22×C4—41no—
277C22×C4—41no—
278C22×C4—441no—
279C22×C4D4×D1111yescharacteristic
280C22×C4D4×D1111yescharacteristic
281C22×C4C2×C22⋊D1111yescharacteristic
282SD16—882no—
283SD16—884no—
284M16—114no—
285M16—222no—
286C2×C8—22no—
287C2×C8—42no—
288C2×C8—222no—
289C2×C8—222no—
290C4⋊C4—22no—
291C4⋊C4—22no—
292C4⋊C4—22no—
293C4⋊C4—41no—
294C4⋊C4—41no—
295C4⋊C4—41no—
296C4⋊C4—221no—
297C4⋊C4—221no—
298C4⋊C4—221no—
299C4⋊C4—221no—
300C4⋊C4—221no—
301C4⋊C4—221no—
302C4⋊C4—441no—
303C4⋊C4—441no—
304C22⋊C4—441no—
305C22⋊C4—441no—
306C22⋊C4—441no—
307C42—42no—
308C42—441no—
309C42C2×D4411yescharacteristic
310C42#433911yescharacteristic
311C42D4×D1111yescharacteristic
312C42D4×D1111yescharacteristic
313C11#1019711yescharacteristic, complemented, Sylow
314C23—441no—
315C23#6699311yescharacteristic
316Q8—44no—
317Q8—82no—
318Q8—441no—
319Q8—442no—
320Q8—441no—
321Q8—881no—
322D4—442no—
323D4—441no—
324D4—442no—
325D4—441no—
326D4—881no—
327D4—881no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—41no—
331C2×C4—42no—
332C2×C4—42no—
333C2×C4—81no—
334C2×C4—82no—
335C2×C4—81no—
336C2×C4—441no—
337C2×C4—441no—
338C2×C4—441no—
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—82no—
364C4—881no—
365C4—881no—
366C4—881no—
367C4#1062241912yes—
368C4#1062243112yes—
369C4#1062267411yescharacteristic
370C4#1062270811yescharacteristic
371C2—21no—
372C2—21no—
373C2—1761no—
374C2#1306966211yescharacteristic
375C2#1306967111yescharacteristic
376C2#1306970011yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1987C2
socleC22×C11#392
prime radical#10623008C22
hypercenter#1987D11
hypocenterC11#10197
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1987

Complements

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

NH ≅ G/Ntype
3. #13079158C2semidirect
5. #13067114C2semidirect
6. #13066466C2semidirect
7. C11×#1987C2semidirect
122. #4318SD16semidirect
129. #1987D11semidirect
313. C11#10197semidirect

Maximal subgroups

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

subgroupindex
#130799332
#130795412
#130791582
#130695342
#130671142
#130664662
C11×#19872
#1019711