Finite Group Databasebeta

← #14655876

Subgroups — #14655876

Order 2816.

524 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 524 conjugacy classes of subgroups — too many to draw. Only its 109 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#13079541C211yesmaximal, characteristic
3#13069565C211yesmaximal, characteristic, complemented
4#13069535C211yesmaximal, characteristic
5#13067115C211yesmaximal, characteristic, complemented
6#13066467C211yesmaximal, characteristic, complemented
7C11×#3165C211yesmaximal, characteristic, complemented
8C11×#533C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10#10623008C2211yescharacteristic
11C11×#501—22no—
12C11×#500—21no—
13C11×#498—21no—
14C11×#428—22no—
15C4×C11×M16C2211yescharacteristic
16#10622840—22no—
17C2×#66889—22no—
18#10622698—21no—
19#10622697—21no—
20#10622696—21no—
21#10622696—22no—
22#10622694—21no—
23#10622661—22no—
24#10622640—21no—
25#10622633—21no—
26C4×C4⋊Dic11C2211yescharacteristic
27#10622538C2211yescharacteristic
28C2×C4⋊(C11⋊C8)C2211yescharacteristic
29#10622176—22no—
30#10622167—22no—
31C22×Q8×C11—21no—
32C2×#4339—21no—
33C2×C11×M16D412yes—
34C11×C4⋊Q8—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8D411yescharacteristic
38C11×C4⋊Q8D411yescharacteristic
39C11×C4⋊Q8D412yes—
40C11×#125—21no—
41C11×C22⋊Q8—21no—
42C11×C22⋊Q8—21no—
43C4×Q8×C11—21no—
44C4×Q8×C11—21no—
45C11×#117—21no—
46C2×C11×C4⋊C4—21no—
47C2×C11×C4⋊C4—21no—
48C2×C42×C11C2311yescharacteristic
49C2×#4325—24no—
50C2×#4325—22no—
51#66983—21no—
52#66983—21no—
53C2×C4⋊Dic11—21no—
54C2×C4×Dic11—21no—
55C22×C11⋊C8D412yes—
56#66928—21no—
57#66927D411yescharacteristic
58C4×D44—21no—
59C4×D44—21no—
60#66922D411yescharacteristic
61C11×#107—24no—
62C11×#106—24no—
63C11×#97—21no—
64C4×C8×C11—21no—
65#66899—24no—
66#66899—22no—
67C11⋊#95—21no—
68C22⋊(C11⋊C8)D412yes—
69#66889—44no—
70#66873—22no—
71#66872—22no—
72C4⋊(C11⋊C8)—21no—
73C4⋊(C11⋊C8)—21no—
74C4⋊(C11⋊C8)—21no—
75C4×C11⋊C8—21no—
76#10197—111nomaximal, Sylow
77C2×Q8×C11—21no—
78C2×Q8×C11—22no—
79C2×Q8×C11—21no—
80C2×Q8×C11—41no—
81C2×Q8×C11—82no—
82C22×C4×C11—41no—
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11C2×D411yescharacteristic
86C2×C22⋊D11—41no—
87C22×Dic11—41no—
88#4339—42no—
89#4339—42no—
90C2×D44—21no—
91C2×D44—21no—
92C2×D44—21no—
93C2×C4×D11—41no—
94C2×Dic22—21no—
95C11×M16—22no—
96C11×M16SD1614yescomplemented
97C2×C8×C11—22no—
98C11×C4⋊C4—21no—
99C11×C4⋊C4—21no—
100C11×C4⋊C4—22no—
101C11×C4⋊C4—21no—
102C11×C4⋊C4—22no—
103C11×C4⋊C4—21no—
104C11×C4⋊C4—41no—
105C11×C4⋊C4—41no—
106C11×C4⋊C4—41no—
107C11×C4⋊C4—41no—
108C11×C22⋊C4—41no—
109C42×C11—41no—
110C42×C11C2×D411yescharacteristic
111C42×C11C2×D411yescharacteristic
112C42×C11C2×D411yescharacteristic
113C42×C11#4111yescharacteristic
114#4325—84no—
115#4325—82no—
116(C2×D11)⋊C4—41no—
117(C2×D11)⋊C4—41no—
118C4⋊Dic11—22no—
119C4⋊Dic11—21no—
120C4⋊Dic11—21no—
121C4⋊Dic11—41no—
122C4×Dic11—42no—
123C2×C11⋊C8—22no—
124C2×C11⋊C8—22no—
125C2×C11⋊C8—42no—
126#3246—111no—
127#3206—111no—
128#3165D1111yescharacteristic, complemented
129#1987—111no—
130#1980—111no—
131#1503—111no—
132#1283—111no—
133C23×C11#12711yescharacteristic
134C22×D11—41no—
135Q8×C11—44no—
136Q8×C11—41no—
137Q8×C11—41no—
138Q8×C11—81no—
139Q8×C11—82no—
140C2×C4×C11—21no—
141C2×C4×C11—21no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—42no—
146C2×C4×C11—82no—
147C2×C4×C11#12011yescharacteristic
148C2×C4×C11#12011yescharacteristic
149C2×C4×C11#12011yescharacteristic
150C2×C4×C11#12111yescharacteristic
151C2×C4×C11#12111yescharacteristic
152C2×C4×C11#12111yescharacteristic
153C2×C4×C11C2×SD1612yes—
154C2×C4×C11#13712yes—
155C22⋊D11—81no—
156C22⋊D11—81no—
157C2×Dic11—42no—
158C2×Dic11—41no—
159C2×Dic11—81no—
160C2×Dic11—81no—
161D44—42no—
162D44—41no—
163D44—41no—
164D44—42no—
165C4×D11—82no—
166Dic22—42no—
167C8×C11—24no—
168C11⋊C8—42no—
169C11⋊C8—42no—
170#533C2×D1111yescharacteristic
171#532—111no—
172C2×C4⋊Q8C2×D1111yescharacteristic
173#501—22no—
174#500—21no—
175#498—21no—
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#431—111no—
186#428—22no—
187C2×C4⋊C8—111no—
188C2×#104—222no—
189C4×M16C2×D1111yescharacteristic
190C4×C4⋊C4—111no—
191#340—222no—
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—81no—
205C4×C11—82no—
206C4×C11—81no—
207C4×C11#44812yes—
208C4×C11#45511yescharacteristic
209C4×C11#45611yescharacteristic
210C4×C11#46112yes—
211Dic11—82no—
212Dic11—81no—
213C2×#41—221no—
214C22×Q8—21no—
215C2×SD16—224no—
216C2×SD16—222no—
217C2×M16C22⋊D1112yes—
218C22×C8—112no—
219C4⋊Q8—21no—
220C4⋊Q8—21no—
221C4⋊Q8—21no—
222C4⋊Q8—111no—
223C4⋊Q8C22⋊D1112yes—
224C4⋊Q8C22⋊D1111yescharacteristic
225C4⋊Q8C22⋊D1111yescharacteristic
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—21no—
240C2×C4⋊C4—221no—
241C2×C42—221no—
242C2×C42C22×D1111yescharacteristic
243#107—24no—
244#106—24no—
245#106—222no—
246C4⋊C8—221no—
247C4⋊C8—221no—
248C4⋊C8—221no—
249#104—444no—
250#103—224no—
251#103—222no—
252#102—222no—
253C22⋊C8—112no—
254#97—21no—
255C4×C8—21no—
256C4×C8—221no—
257#95—221no—
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—22no—
268C2×Q8—21no—
269C2×Q8—41no—
270C2×Q8—82no—
271C2×Q8—221no—
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—22no—
285M16#432514yescomplemented
286C2×C8—22no—
287C2×C8—222no—
288C2×C8—222no—
289C2×C8—442no—
290C4⋊C4—21no—
291C4⋊C4—22no—
292C4⋊C4—21no—
293C4⋊C4—21no—
294C4⋊C4—22no—
295C4⋊C4—21no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C4⋊C4—41no—
299C4⋊C4—41no—
300C4⋊C4—222no—
301C4⋊C4—221no—
302C4⋊C4—221no—
303C4⋊C4—441no—
304C22⋊C4—41no—
305C22⋊C4—441no—
306C22⋊C4—441no—
307C42—41no—
308C42—442no—
309C42D4×D1111yescharacteristic
310C42#434111yescharacteristic
311C42C2×C22⋊D1111yescharacteristic
312C42C2×C22⋊D1111yescharacteristic
313C11#1019711yescharacteristic, complemented, Sylow
314C23—441no—
315C23#6699311yescharacteristic
316Q8—44no—
317Q8—41no—
318Q8—41no—
319Q8—81no—
320Q8—82no—
321Q8—442no—
322D4—442no—
323D4—441no—
324D4—441no—
325D4—442no—
326D4—881no—
327D4—881no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—42no—
334C2×C4—82no—
335C2×C4—442no—
336C2×C4—441no—
337C2×C4—881no—
338C2×C4—881no—
339C2×C4—882no—
340C2×C4#6699011yescharacteristic
341C2×C4#6699011yescharacteristic
342C2×C4#6699111yescharacteristic
343C2×C4#6699211yescharacteristic
344C2×C4#6699211yescharacteristic
345C2×C4C2×#432512yes—
346C2×C4#6699512yes—
347C2×C4#6700611yescharacteristic
348C8—24no—
349C8—442no—
350C8—442no—
351C22—21no—
352C22—21no—
353C22—881no—
354C22—881no—
355C22—881no—
356C22#1062269811yescharacteristic
357C22#1062269911yescharacteristic
358C22#1062283611yescharacteristic
359C4—21no—
360C4—21no—
361C4—21no—
362C4—81no—
363C4—82no—
364C4—81no—
365C4—882no—
366C4—881no—
367C4#1062269612yes—
368C4#1062281511yescharacteristic
369C4#1062281811yescharacteristic
370C4#1062284012yes—
371C2—21no—
372C2—21no—
373C2—1761no—
374C2#1306966111yescharacteristic
375C2#1306966711yescharacteristic
376C2#1306969911yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3165C2
socleC22×C11#392
prime radical#10623008C22
hypercenter#3165D11
hypocenterC11#10197
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3165

Complements

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

NH ≅ G/Ntype
3. #13069565C2semidirect
5. #13067115C2semidirect
6. #13066467C2semidirect
7. C11×#3165C2semidirect
96. C11×M16SD16semidirect
128. #3165D11semidirect
285. M16#4325semidirect
313. C11#10197semidirect

Maximal subgroups

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

subgroupindex
#130799282
#130795412
#130695652
#130695352
#130671152
#130664672
C11×#31652
#1019711