Finite Group Databasebeta

← #14655878

Subgroups — #14655878

Order 2816.

524 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 524 conjugacy classes of subgroups — too many to draw. Only its 105 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#13079538C211yesmaximal, characteristic
2#13079163C211yesmaximal, characteristic, complemented
3#13069563C211yesmaximal, characteristic, complemented
4#13069536C211yesmaximal, characteristic
5#13067115C211yesmaximal, characteristic, complemented
6#13066466C211yesmaximal, characteristic, complemented
7C11×#3246C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9C11×#532C2211yescharacteristic
10C2×#66922C2211yescharacteristic
11C11×#476—21no—
12C11×#475—21no—
13C11×#465—22no—
14C11×#461—21no—
15C11×#460—21no—
16C2×C11×C4⋊C8C2211yescharacteristic
17C2×#66901—22no—
18#10622706—21no—
19#10622692—21no—
20#10622691—21no—
21#10622689—21no—
22#10622678—22no—
23#10622653—22no—
24#10622632—22no—
25#10622608—22no—
26C4×C4⋊Dic11C2211yescharacteristic
27#10622538C2211yescharacteristic
28C4×#4318C2211yescharacteristic
29#10622189—22no—
30#10622176—22no—
31C2×C11×#41—21no—
32C22×Dic22—21no—
33C2×C11×SD16—22no—
34C22×C8×C11D412yes—
35C11×C4⋊Q8D411yescharacteristic
36C11×C4⋊Q8D411yescharacteristic
37C11×C4⋊Q8D411yescharacteristic
38C11×#127D411yescharacteristic
39C11×#125—21no—
40C11×#124—21no—
41C11×C22⋊Q8—21no—
42C11×C22⋊Q8—21no—
43C11×#121—21no—
44C11×#121—21no—
45C4×Q8×C11—21no—
46C4×Q8×C11—21no—
47C4×D4×C11—21no—
48C4×D4×C11—21no—
49C11×#117—21no—
50C2×C42×C11C2311yescharacteristic
51C2×#4324—24no—
52C2×C4⋊Dic11—21no—
53C2×C4⋊Dic11—21no—
54C2×C4⋊Dic11—21no—
55C2×C4×Dic11—21no—
56C2×#4318D412yes—
57#66922—21no—
58#66922—21no—
59#66922—21no—
60#66922D412yes—
61C11×#106—22no—
62C11×C4⋊C8—21no—
63C11×C4⋊C8—21no—
64C11×#103—22no—
65C11×#102—22no—
66#66901—44no—
67C11⋊#95—21no—
68C22⋊(C11⋊C8)D412yes—
69#66874—24no—
70#66872—24no—
71#66871—24no—
72C4⋊(C11⋊C8)—21no—
73#66867—21no—
74C4×C11⋊C8—21no—
75C4×C11⋊C8—21no—
76#10197—111nomaximal, Sylow
77C11×#41—42no—
78C11×#41—42no—
79C2×Q8×C11—21no—
80C2×Q8×C11—21no—
81C2×Q8×C11—21no—
82C2×D4×C11—21no—
83C2×D4×C11—21no—
84C2×D4×C11—21no—
85C2×D4×C11—41no—
86C22×C4×C11—41no—
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11C2×D411yescharacteristic
90C22×Dic11—41no—
91C22×Dic11—41no—
92C2×Dic22—22no—
93C2×Dic22—41no—
94C2×Dic22—82no—
95C11×SD16—82no—
96C2×C8×C11—22no—
97C2×C8×C11—42no—
98C11×C4⋊C4—21no—
99C11×C4⋊C4—21no—
100C11×C4⋊C4—21no—
101C11×C4⋊C4—21no—
102C11×C4⋊C4—21no—
103C11×C4⋊C4—21no—
104C11×C4⋊C4—41no—
105C11×C4⋊C4—41no—
106C11×C22⋊C4—41no—
107C11×C22⋊C4—41no—
108C11×C22⋊C4—41no—
109C42×C11—41no—
110C42×C11C2×D411yescharacteristic
111C42×C11C2×D411yescharacteristic
112C42×C11C2×D411yescharacteristic
113C42×C11#4111yescharacteristic
114#4324—84no—
115C4⋊Dic11—22no—
116C4⋊Dic11—22no—
117C4⋊Dic11—22no—
118C4⋊Dic11—41no—
119C4⋊Dic11—41no—
120C4⋊Dic11—41no—
121C4×Dic11—42no—
122#4318—22no—
123#4318SD1614yescomplemented
124C2×C11⋊C8—22no—
125C2×C11⋊C8—22no—
126#3246D1111yescharacteristic
127#3206—111no—
128#3165—111no—
129#1987—111no—
130#1980—111no—
131#1503—111no—
132#1283—111no—
133C23×C11—41no—
134C23×C11#12711yescharacteristic
135Q8×C11—41no—
136Q8×C11—41no—
137Q8×C11—42no—
138Q8×C11—81no—
139D4×C11—42no—
140D4×C11—41no—
141D4×C11—41no—
142D4×C11—42no—
143D4×C11—81no—
144D4×C11—81no—
145C2×C4×C11—21no—
146C2×C4×C11—21no—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11—82no—
152C2×C4×C11#12011yescharacteristic
153C2×C4×C11#12011yescharacteristic
154C2×C4×C11#12011yescharacteristic
155C2×C4×C11#12111yescharacteristic
156C2×C4×C11#12111yescharacteristic
157C2×C4×C11#12111yescharacteristic
158C2×C4×C11C2×SD1612yes—
159C2×C4×C11#13712yes—
160C2×Dic11—42no—
161C2×Dic11—42no—
162C2×Dic11—82no—
163C2×Dic11—81no—
164C2×Dic11—81no—
165Dic22—44no—
166Dic22—82no—
167C8×C11—42no—
168C11⋊C8—24no—
169C11⋊C8—42no—
170#533C2×D1111yescharacteristic
171#532C2×D1111yescharacteristic
172C2×C4⋊Q8—111no—
173#501—222no—
174#500—221no—
175#498—221no—
176#492—221no—
177#487—221no—
178#476—21no—
179#475—21no—
180#465—22no—
181#461—21no—
182#461—222no—
183#460—21no—
184#448—222no—
185#431—111no—
186#428—222no—
187C2×C4⋊C8C2×D1111yescharacteristic
188C2×#104—222no—
189C4×M16—111no—
190C4×C4⋊C4—111no—
191#340—222no—
192#328—222no—
193C22×C11—21no—
194C22×C11—21no—
195C22×C11—81no—
196C22×C11—81no—
197C22×C11—81no—
198C22×C11#39211yescharacteristic
199C22×C11#49211yescharacteristic
200C22×C11#49711yescharacteristic
201C4×C11—21no—
202C4×C11—21no—
203C4×C11—21no—
204C4×C11—81no—
205C4×C11—81no—
206C4×C11—81no—
207C4×C11#44812yes—
208C4×C11#45511yescharacteristic
209C4×C11#45611yescharacteristic
210C4×C11#46112yes—
211Dic11—82no—
212Dic11—82no—
213C2×#41—21no—
214C22×Q8—221no—
215C2×SD16—22no—
216C2×SD16—224no—
217C2×M16—112no—
218C22×C8C22⋊D1112yes—
219C4⋊Q8—112no—
220C4⋊Q8—221no—
221C4⋊Q8—221no—
222C4⋊Q8—221no—
223C4⋊Q8C22⋊D1111yescharacteristic
224C4⋊Q8C22⋊D1111yescharacteristic
225C4⋊Q8C22⋊D1111yescharacteristic
226#127C22⋊D1111yescharacteristic
227#125—21no—
228#124—21no—
229C22⋊Q8—21no—
230C22⋊Q8—21no—
231#121—21no—
232#121—21no—
233C4×Q8—21no—
234C4×Q8—21no—
235C4×D4—21no—
236C4×D4—21no—
237#117—21no—
238C2×C4⋊C4—221no—
239C2×C4⋊C4—221no—
240C2×C4⋊C4—221no—
241C2×C42—221no—
242C2×C42C22×D1111yescharacteristic
243#107—224no—
244#106—22no—
245#106—224no—
246C4⋊C8—21no—
247C4⋊C8—21no—
248C4⋊C8—221no—
249#104—444no—
250#103—22no—
251#103—224no—
252#102—22no—
253C22⋊C8—112no—
254#97—221no—
255C4×C8—221no—
256C4×C8—221no—
257#95—221no—
258C2×C11—21no—
259C2×C11—21no—
260C2×C11—161no—
261C2×C11#200711yescharacteristic
262C2×C11#200811yescharacteristic
263C2×C11#201311yescharacteristic
264#41—42no—
265#41—42no—
266C2×Q8—21no—
267C2×Q8—21no—
268C2×Q8—21no—
269C2×Q8—222no—
270C2×Q8—441no—
271C2×Q8—882no—
272C2×D4—21no—
273C2×D4—21no—
274C2×D4—21no—
275C2×D4—41no—
276C22×C4—41no—
277C22×C4—441no—
278C22×C4—441no—
279C22×C4D4×D1111yescharacteristic
280C22×C4D4×D1111yescharacteristic
281C22×C4C2×C22⋊D1111yescharacteristic
282SD16—82no—
283SD16—884no—
284M16—114no—
285M16—222no—
286C2×C8—22no—
287C2×C8—42no—
288C2×C8—222no—
289C2×C8—222no—
290C4⋊C4—21no—
291C4⋊C4—21no—
292C4⋊C4—21no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C4⋊C4—222no—
299C4⋊C4—222no—
300C4⋊C4—222no—
301C4⋊C4—441no—
302C4⋊C4—441no—
303C4⋊C4—441no—
304C22⋊C4—41no—
305C22⋊C4—41no—
306C22⋊C4—41no—
307C42—41no—
308C42—442no—
309C42D4×D1111yescharacteristic
310C42#434111yescharacteristic
311C42C2×C22⋊D1111yescharacteristic
312C42C2×C22⋊D1111yescharacteristic
313C11#1019711yescharacteristic, complemented, Sylow
314C23—41no—
315C23#6699311yescharacteristic
316Q8—42no—
317Q8—41no—
318Q8—41no—
319Q8—81no—
320Q8—444no—
321Q8—882no—
322D4—42no—
323D4—42no—
324D4—41no—
325D4—41no—
326D4—81no—
327D4—81no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—82no—
335C2×C4—442no—
336C2×C4—442no—
337C2×C4—882no—
338C2×C4—881no—
339C2×C4—881no—
340C2×C4SD16×D1112yes—
341C2×C4#6696812yes—
342C2×C4#6699011yescharacteristic
343C2×C4#6699011yescharacteristic
344C2×C4#6699111yescharacteristic
345C2×C4#6699211yescharacteristic
346C2×C4#6699211yescharacteristic
347C2×C4#6700611yescharacteristic
348C8—42no—
349C8—224no—
350C8—442no—
351C22—21no—
352C22—21no—
353C22—81no—
354C22—81no—
355C22—81no—
356C22#1062278011yescharacteristic
357C22#1062278811yescharacteristic
358C22#1062283611yescharacteristic
359C4—21no—
360C4—21no—
361C4—21no—
362C4—81no—
363C4—81no—
364C4—81no—
365C4—882no—
366C4—882no—
367C4#1062277512yes—
368C4#1062278312yes—
369C4#1062285511yescharacteristic
370C4#1062285911yescharacteristic
371C2—21no—
372C2—21no—
373C2—161no—
374C2#1306966311yescharacteristic
375C2#1306966611yescharacteristic
376C2#1306969711yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3246C2
socleC22×C11#392
prime radicalC11×#532C22
hypercenter#3246D11
hypocenterC11#10197
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3246

Complements

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

NH ≅ G/Ntype
2. #13079163C2semidirect
3. #13069563C2semidirect
5. #13067115C2semidirect
6. #13066466C2semidirect
123. #4318SD16semidirect
313. C11#10197semidirect

Maximal subgroups

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

subgroupindex
#130795382
#130791632
#130695632
#130695362
#130671152
#130664662
C11×#32462
#1019711