Finite Group Databasebeta

← #14655875

Subgroups — #14655875

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#13079932C211yesmaximal, characteristic
2#13079158C211yesmaximal, characteristic, complemented
3#13069565C211yesmaximal, characteristic, complemented
4#13069536C211yesmaximal, characteristic
5#13067116C211yesmaximal, characteristic, complemented
6#13066465C211yesmaximal, characteristic, complemented
7C11×#3206C211yesmaximal, characteristic
8C11×#532C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10#10623001C2211yescharacteristic
11C11×#492—21no—
12C11×#487—21no—
13C11×#461—22no—
14C11×#448—22no—
15C11×#431C2211yescharacteristic
16C2×#66901—22no—
17#10622707—21no—
18#10622693—22no—
19#10622692—21no—
20#10622691—21no—
21#10622688—21no—
22#10622654—22no—
23#10622632—21no—
24#10622621—21no—
25#10622577—22no—
26C4×C4⋊Dic11C2211yescharacteristic
27C2×C4⋊(C11⋊C8)C2211yescharacteristic
28C4×#4318C2211yescharacteristic
29#10622167—22no—
30#10622105—22no—
31C2×C11×#41—21no—
32C22×Q8×C11—21no—
33C2×C11×SD16—24no—
34C11×C4⋊Q8—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8D412yes—
38C11×C4⋊Q8D411yescharacteristic
39C11×#127D411yescharacteristic
40C11×#124—21no—
41C11×#121—21no—
42C11×#121—21no—
43C4×D4×C11—21no—
44C4×D4×C11—21no—
45C2×C11×C4⋊C4—21no—
46C2×C11×C4⋊C4—21no—
47C2×C42×C11C2311yescharacteristic
48C2×#4324—22no—
49#66979—21no—
50C2×C4⋊Dic11—21no—
51#66977—21no—
52#66977—21no—
53C2×C4×Dic11—21no—
54C2×#4318D412yes—
55C22×C11⋊C8D412yes—
56#66923—21no—
57#66922D411yescharacteristic
58#66922D411yescharacteristic
59C4×Dic22—21no—
60C4×Dic22—21no—
61C11×C4⋊C8—21no—
62C11×#103—24no—
63C11×C22⋊C8D412yes—
64C4×C8×C11—21no—
65#66901—44no—
66#66896—22no—
67C11⋊#95—21no—
68#66874—22no—
69#66872—24no—
70#66872—22no—
71#66871—24no—
72C4⋊(C11⋊C8)—21no—
73C4⋊(C11⋊C8)—21no—
74#66867—21no—
75C4×C11⋊C8—21no—
76#10197—111nomaximal, Sylow
77C11×#41—42no—
78C11×#41—42no—
79C2×Q8×C11—22no—
80C2×Q8×C11—21no—
81C2×Q8×C11—41no—
82C2×Q8×C11—82no—
83C2×D4×C11—21no—
84C2×D4×C11—21no—
85C2×D4×C11—21no—
86C2×D4×C11—41no—
87C22×C4×C11—41no—
88C22×C4×C11—41no—
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11C2×D411yescharacteristic
92C22×Dic11—41no—
93C2×Dic22—21no—
94C2×Dic22—21no—
95C11×SD16—84no—
96C2×C8×C11—22no—
97C11×C4⋊C4—22no—
98C11×C4⋊C4—21no—
99C11×C4⋊C4—21no—
100C11×C4⋊C4—22no—
101C11×C4⋊C4—41no—
102C11×C4⋊C4—41no—
103C11×C22⋊C4—41no—
104C11×C22⋊C4—41no—
105C42×C11C2×D411yescharacteristic
106C42×C11C2×D411yescharacteristic
107C42×C11C2×D411yescharacteristic
108C42×C11#4111yescharacteristic
109C22⋊Dic11—41no—
110#4324—82no—
111C4⋊Dic11—22no—
112C4⋊Dic11—21no—
113C4⋊Dic11—21no—
114C4⋊Dic11—21no—
115C4⋊Dic11—21no—
116C4⋊Dic11—41no—
117Dic11⋊C4—41no—
118Dic11⋊C4—41no—
119C4×Dic11—41no—
120C4×Dic11—42no—
121#4318—22no—
122#4318SD1614yescomplemented
123C2×C11⋊C8—22no—
124C2×C11⋊C8—22no—
125C2×C11⋊C8—42no—
126#3246—111no—
127#3206D1111yescharacteristic
128#3165—111no—
129#1987—111no—
130#1980—111no—
131#1503—111no—
132#1283—111no—
133C23×C11—41no—
134C23×C11#12711yescharacteristic
135Q8×C11—44no—
136Q8×C11—42no—
137Q8×C11—82no—
138D4×C11—42no—
139D4×C11—41no—
140D4×C11—41no—
141D4×C11—42no—
142D4×C11—81no—
143D4×C11—81no—
144C2×C4×C11—21no—
145C2×C4×C11—21no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11—42no—
149C2×C4×C11—82no—
150C2×C4×C11—82no—
151C2×C4×C11#12011yescharacteristic
152C2×C4×C11#12011yescharacteristic
153C2×C4×C11#12011yescharacteristic
154C2×C4×C11#12111yescharacteristic
155C2×C4×C11#12111yescharacteristic
156C2×C4×C11#12111yescharacteristic
157C2×C4×C11C2×SD1612yes—
158C2×C4×C11#13712yes—
159C2×Dic11—42no—
160C2×Dic11—41no—
161C2×Dic11—41no—
162C2×Dic11—81no—
163C2×Dic11—81no—
164Dic22—41no—
165Dic22—41no—
166Dic22—81no—
167C8×C11—42no—
168C11⋊C8—24no—
169C11⋊C8—42no—
170#533—111no—
171#532C2×D1111yescharacteristic
172C2×C4⋊Q8C2×D1111yescharacteristic
173#501—222no—
174#500—221no—
175#498—221no—
176#492—21no—
177#487—21no—
178#476—221no—
179#475—221no—
180#465—222no—
181#461—22no—
182#461—221no—
183#460—221no—
184#448—22no—
185#431C2×D1111yescharacteristic
186#428—222no—
187C2×C4⋊C8—111no—
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—82no—
205C4×C11—81no—
206C4×C11#44812yes—
207C4×C11#45511yescharacteristic
208C4×C11#45611yescharacteristic
209C4×C11#46112yes—
210Dic11—82no—
211Dic11—81no—
212Dic11—81no—
213C2×#41—21no—
214C22×Q8—21no—
215C2×SD16—24no—
216C2×SD16—222no—
217C2×M16—112no—
218C22×C8—112no—
219C4⋊Q8—21no—
220C4⋊Q8—21no—
221C4⋊Q8—21no—
222C4⋊Q8—111no—
223C4⋊Q8—111no—
224C4⋊Q8C22⋊D1112yes—
225C4⋊Q8C22⋊D1111yescharacteristic
226#127C22⋊D1111yescharacteristic
227#125—221no—
228#124—21no—
229C22⋊Q8—221no—
230C22⋊Q8—221no—
231#121—21no—
232#121—21no—
233C4×Q8—221no—
234C4×Q8—221no—
235C4×D4—21no—
236C4×D4—21no—
237#117—221no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—221no—
241C2×C42—221no—
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—24no—
251#103—222no—
252#102—222no—
253C22⋊C8C22⋊D1112yes—
254#97—221no—
255C4×C8—21no—
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—22no—
268C2×Q8—41no—
269C2×Q8—82no—
270C2×Q8—221no—
271C2×Q8—221no—
272C2×D4—21no—
273C2×D4—21no—
274C2×D4—21no—
275C2×D4—41no—
276C22×C4—41no—
277C22×C4—41no—
278C22×C4—441no—
279C22×C4D4×D1111yescharacteristic
280C22×C4D4×D1111yescharacteristic
281C22×C4C2×C22⋊D1111yescharacteristic
282SD16—84no—
283SD16—882no—
284M16—114no—
285M16—222no—
286C2×C8—22no—
287C2×C8—222no—
288C2×C8—222no—
289C2×C8—442no—
290C4⋊C4—21no—
291C4⋊C4—22no—
292C4⋊C4—22no—
293C4⋊C4—21no—
294C4⋊C4—41no—
295C4⋊C4—41no—
296C4⋊C4—222no—
297C4⋊C4—221no—
298C4⋊C4—221no—
299C4⋊C4—221no—
300C4⋊C4—221no—
301C4⋊C4—441no—
302C4⋊C4—441no—
303C4⋊C4—441no—
304C22⋊C4—41no—
305C22⋊C4—41no—
306C22⋊C4—441no—
307C42—441no—
308C42—442no—
309C42D4×D1111yescharacteristic
310C42#434111yescharacteristic
311C42C2×C22⋊D1111yescharacteristic
312C42C2×C22⋊D1111yescharacteristic
313C11#1019711yescharacteristic, complemented, Sylow
314C23—41no—
315C23#6699311yescharacteristic
316Q8—44no—
317Q8—42no—
318Q8—82no—
319Q8—441no—
320Q8—441no—
321Q8—881no—
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—42no—
333C2×C4—82no—
334C2×C4—82no—
335C2×C4—442no—
336C2×C4—441no—
337C2×C4—441no—
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—82no—
363C4—81no—
364C4—882no—
365C4—881no—
366C4—881no—
367C4#1062277512yes—
368C4#1062278312yes—
369C4#1062281511yescharacteristic
370C4#1062281811yescharacteristic
371C2—21no—
372C2—21no—
373C2—161no—
374C2#1306966111yescharacteristic
375C2#1306966911yescharacteristic
376C2#1306969711yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3206C2
socleC22×C11#392
prime radicalC11×#532C22
hypercenter#3206D11
hypocenterC11#10197
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3206

Complements

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

NH ≅ G/Ntype
2. #13079158C2semidirect
3. #13069565C2semidirect
5. #13067116C2semidirect
6. #13066465C2semidirect
122. #4318SD16semidirect
313. C11#10197semidirect

Maximal subgroups

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

subgroupindex
#130799322
#130791582
#130695652
#130695362
#130671162
#130664652
C11×#32062
#1019711