Finite Group Databasebeta

← #14655351

Subgroups — #14655351

Order 2816.

476 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 81 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#13079802C211yesmaximal, characteristic, complemented
2#13079016C211yesmaximal, characteristic, complemented
3#13067085C211yesmaximal, characteristic, complemented
4#13067033C211yesmaximal, characteristic, complemented
5#13066973C211yesmaximal, characteristic, complemented
6#13066489C211yesmaximal, characteristic, complemented
7C11×#3214C211yesmaximal, characteristic
8C11×#532C2211yescharacteristic
9C11×#532C2211yescharacteristic
10C2×#66923C2211yescharacteristic
11C11×#496—21no—
12C11×#489—21no—
13C11×#461—21no—
14C11×#459—21no—
15C11×#449—22no—
16C11×#432C2211yescharacteristic
17#10622845—21no—
18#10622845—21no—
19#10622695—21no—
20#10622693—21no—
21#10622684—21no—
22#10622684—21no—
23#10622669—22no—
24#10622647—21no—
25#10622646—21no—
26#10622622—22no—
27#10622539C2211yescharacteristic
28#10622538C2211yescharacteristic
29C4×#4318C2211yescharacteristic
30D4⋊(C11⋊C8)—22no—
31D4⋊(C11⋊C8)—22no—
32#10622107—22no—
33C2×C11×#41—21no—
34C2×C11×#41—21no—
35C2×C11×SD16—22no—
36C2×C11×D8—22no—
37C11×C4⋊Q8D411yescharacteristic
38C11×C4⋊Q8D411yescharacteristic
39C11×#127D411yescharacteristic
40C11×#127D411yescharacteristic
41C11×#124—21no—
42C11×#124—21no—
43C11×#121—21no—
44C11×#121—21no—
45C11×#121—21no—
46C11×#121—21no—
47C4×D4×C11—21no—
48C4×D4×C11—21no—
49C4×D4×C11—21no—
50C4×D4×C11—21no—
51C2×C42×C11C2311yescharacteristic
52C2×C4⋊Dic11D411yescharacteristic
53C2×C4⋊Dic11D411yescharacteristic
54C2×Dic11⋊C4—21no—
55C2×Dic11⋊C4—21no—
56C2×#4318—21no—
57#66923—21no—
58#66923—21no—
59#66923—21no—
60#66923—21no—
61C11×C4⋊C8—21no—
62C11×#103—22no—
63C11×#102—22no—
64C11×C22⋊C8D412yes—
65C11×#97—21no—
66#66899—22no—
67#66899—22no—
68#66896—22no—
69#66896—22no—
70#66896—22no—
71#66896—22no—
72C22⋊(C11⋊C8)—21no—
73C22⋊(C11⋊C8)—21no—
74#66872—22no—
75#66871—22no—
76C4⋊(C11⋊C8)—21no—
77C4⋊(C11⋊C8)D412yes—
78#66867—21no—
79#66867—21no—
80C4×C11⋊C8—21no—
81C4×C11⋊C8D412yes—
82#10122—111nomaximal, Sylow
83C11×#41—44no—
84C11×#41—82no—
85C2×Q8×C11—21no—
86C2×Q8×C11—21no—
87C2×D4×C11—21no—
88C2×D4×C11—21no—
89C2×D4×C11—21no—
90C2×D4×C11—21no—
91C2×D4×C11—21no—
92C2×D4×C11—21no—
93C2×D4×C11—41no—
94C2×D4×C11—41no—
95C22×C4×C11—41no—
96C22×C4×C11—41no—
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11#4111yescharacteristic
100C22×Dic11—21no—
101C22×Dic11—21no—
102C11×SD16—82no—
103C11×D8—82no—
104C2×C8×C11—22no—
105C11×C4⋊C4—21no—
106C11×C4⋊C4—21no—
107C11×C4⋊C4—21no—
108C11×C4⋊C4—21no—
109C11×C22⋊C4—41no—
110C11×C22⋊C4—41no—
111C11×C22⋊C4—41no—
112C11×C22⋊C4—41no—
113C42×C11C2×D411yescharacteristic
114C42×C11C2×D411yescharacteristic
115C42×C11C2×D411yescharacteristic
116C42×C11C2×D411yescharacteristic
117C4⋊Dic11—21no—
118C4⋊Dic11—21no—
119C4⋊Dic11—21no—
120C4⋊Dic11—21no—
121Dic11⋊C4—41no—
122Dic11⋊C4—41no—
123Dic11⋊C4—41no—
124Dic11⋊C4—41no—
125#4318—42no—
126C2×C11⋊C8—22no—
127C2×C11⋊C8—22no—
128C2×C11⋊C8—41no—
129#3234—111no—
130#3214D1111yescharacteristic
131#3142—111no—
132#1496—111no—
133#1484—111no—
134#1470—111no—
135#1291—111no—
136C23×C11—41no—
137C23×C11—41no—
138C23×C11#12111yescharacteristic
139Q8×C11—42no—
140Q8×C11—42no—
141D4×C11—41no—
142D4×C11—42no—
143D4×C11—41no—
144D4×C11—42no—
145D4×C11—42no—
146D4×C11—42no—
147D4×C11—42no—
148D4×C11—82no—
149D4×C11—82no—
150C2×C4×C11—22no—
151C2×C4×C11—41no—
152C2×C4×C11—41no—
153C2×C4×C11—41no—
154C2×C4×C11—41no—
155C2×C4×C11—82no—
156C2×C4×C11—82no—
157C2×C4×C11#12011yescharacteristic
158C2×C4×C11#12011yescharacteristic
159C2×C4×C11#12011yescharacteristic
160C2×C4×C11#12111yescharacteristic
161C2×C4×C11#12111yescharacteristic
162C2×C4×C11#12711yescharacteristic
163C2×Dic11—42no—
164C2×Dic11—41no—
165C2×Dic11—41no—
166C2×Dic11—81no—
167C8×C11—42no—
168C11⋊C8—42no—
169C11⋊C8—42no—
170C11⋊C8—81no—
171#532C2×D1111yescharacteristic
172#532C2×D1111yescharacteristic
173C2×#125—111no—
174#501—221no—
175#496—21no—
176#491—221no—
177#490—221no—
178#490—221no—
179#489—21no—
180#488—222no—
181#481—221no—
182#480—221no—
183#478—222no—
184#461—21no—
185#459—21no—
186#449—22no—
187#432—111no—
188#432C2×D1111yescharacteristic
189#431—111no—
190#417—221no—
191#417—221no—
192C4×M16—111no—
193D4⋊C8—222no—
194D4⋊C8—222no—
195#324—222no—
196C22×C11—21no—
197C22×C11—21no—
198C22×C11—21no—
199C22×C11—81no—
200C22×C11—81no—
201C22×C11—81no—
202C22×C11—81no—
203C22×C11—81no—
204C22×C11—81no—
205C22×C11#39211yescharacteristic
206C4×C11—21no—
207C4×C11—21no—
208C4×C11—21no—
209C4×C11—21no—
210C4×C11—21no—
211C4×C11—81no—
212C4×C11—81no—
213C4×C11#45412yes—
214Dic11—81no—
215Dic11—81no—
216C2×#41—21no—
217C2×#41—21no—
218C2×SD16—22no—
219C2×D8—22no—
220C2×M16—221no—
221C4⋊Q8C22⋊D1111yescharacteristic
222C4⋊Q8C22⋊D1111yescharacteristic
223#127C22⋊D1111yescharacteristic
224#127C22⋊D1111yescharacteristic
225#125—221no—
226#125—221no—
227#125—221no—
228#125—221no—
229#124—21no—
230#124—21no—
231#121—21no—
232#121—21no—
233#121—21no—
234#121—21no—
235C4×D4—21no—
236C4×D4—21no—
237C4×D4—21no—
238C4×D4—21no—
239C2×C4⋊C4—111no—
240C2×C4⋊C4—111no—
241C2×C4⋊C4—221no—
242C2×C4⋊C4—221no—
243C2×C42C22×D1111yescharacteristic
244#107—222no—
245#106—222no—
246C4⋊C8—21no—
247C4⋊C8—112no—
248C4⋊C8—221no—
249#103—22no—
250#103—222no—
251#103—222no—
252#102—22no—
253#102—222no—
254#102—222no—
255#102—222no—
256#102—222no—
257C22⋊C8—221no—
258C22⋊C8—221no—
259C22⋊C8C22⋊D1112yes—
260#97—21no—
261#97—221no—
262#97—221no—
263C4×C8—112no—
264C4×C8—221no—
265C2×C11—41no—
266C2×C11—161no—
267C2×C11—161no—
268C2×C11#200311yescharacteristic
269C2×C11#200811yescharacteristic
270C2×C11#201711yescharacteristic
271#41—44no—
272#41—82no—
273C2×Q8—21no—
274C2×Q8—21no—
275C2×D4—21no—
276C2×D4—21no—
277C2×D4—21no—
278C2×D4—21no—
279C2×D4—21no—
280C2×D4—21no—
281C2×D4—41no—
282C2×D4—41no—
283C22×C4—41no—
284C22×C4—41no—
285C22×C4—221no—
286C22×C4—221no—
287C22×C4D4×D1111yescharacteristic
288C22×C4#434111yescharacteristic
289C22×C4C2×C22⋊D1111yescharacteristic
290SD16—82no—
291D8—82no—
292M16—442no—
293C2×C8—22no—
294C2×C8—222no—
295C2×C8—222no—
296C2×C8—441no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—21no—
300C4⋊C4—21no—
301C4⋊C4—221no—
302C4⋊C4—221no—
303C4⋊C4—221no—
304C4⋊C4—221no—
305C4⋊C4—441no—
306C4⋊C4—441no—
307C4⋊C4—441no—
308C4⋊C4—441no—
309C22⋊C4—41no—
310C22⋊C4—41no—
311C22⋊C4—41no—
312C22⋊C4—41no—
313C42D4×D1111yescharacteristic
314C42D4×D1111yescharacteristic
315C42C2×C22⋊D1111yescharacteristic
316C42C2×C22⋊D1111yescharacteristic
317C11#1012211yescharacteristic, complemented, Sylow
318C23—41no—
319C23—41no—
320C23#6699111yescharacteristic
321Q8—42no—
322Q8—42no—
323D4—41no—
324D4—42no—
325D4—41no—
326D4—42no—
327D4—42no—
328D4—42no—
329D4—42no—
330D4—82no—
331D4—82no—
332C2×C4—22no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—82no—
338C2×C4—82no—
339C2×C4—442no—
340C2×C4—441no—
341C2×C4—441no—
342C2×C4—881no—
343C2×C4#6699011yescharacteristic
344C2×C4#6699011yescharacteristic
345C2×C4#6699211yescharacteristic
346C2×C4#6699211yescharacteristic
347C2×C4#6699311yescharacteristic
348C2×C4#6700611yescharacteristic
349C8—42no—
350C8—442no—
351C8—442no—
352C8—881no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—81no—
357C22—81no—
358C22—81no—
359C22—81no—
360C22—81no—
361C22—81no—
362C22#1062283611yescharacteristic
363C4—21no—
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—81no—
369C4—81no—
370C4—881no—
371C4—881no—
372C4#1062281412yes—
373C2—41no—
374C2—161no—
375C2—161no—
376C2#1306963511yescharacteristic
377C2#1306966911yescharacteristic
378C2#1306971911yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
Fitting, prime radicalC11×#3214C2
socleC22×C11#392
hypercenter#3214D11
hypocenterC11#10122
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3214

Complements

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

NH ≅ G/Ntype
1. #13079802C2semidirect
2. #13079016C2semidirect
3. #13067085C2semidirect
4. #13067033C2semidirect
5. #13066973C2semidirect
6. #13066489C2semidirect
317. C11#10122semidirect

Maximal subgroups

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

subgroupindex
#130798022
#130790162
#130670852
#130670332
#130669732
#130664892
C11×#32142
#1012211