Finite Group Databasebeta

← #14654656

Subgroups — #14654656

Order 2816.

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

normal subgroups only

This group has 540 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#13079019C211yesmaximal, characteristic, complemented
2#13078707C211yesmaximal, characteristic
3#13067243C211yesmaximal, characteristic, complemented
4#13067162C211yesmaximal, characteristic, complemented
5#13067059C211yesmaximal, characteristic, complemented
6#13066480C211yesmaximal, characteristic, complemented
7C11×#2633C211yesmaximal, characteristic, complemented
8C2×C11×#125C2211yescharacteristic
9C2×C4×D4×C11C2211yescharacteristic
10#10623008C2211yescharacteristic
11C11×#399—21no—
12C11×#398—21no—
13C11×#397—21no—
14C11×#394—21no—
15C11×#385—22no—
16C11×#383C2211yescharacteristic
17#10622830—21no—
18#10622682—21no—
19#10622681—22no—
20#10622680—21no—
21#10622628—21no—
22#10622627—22no—
23#10622621—21no—
24#10622581—21no—
25#10622579—21no—
26#10622579—21no—
27#10622539C2211yescharacteristic
28#10622539C2211yescharacteristic
29C4×#4318C2211yescharacteristic
30#10622181—22no—
31D4⋊(C11⋊C8)—22no—
32#10622089—22no—
33C22×D4×C11D411yescharacteristic
34C23×C4×C11—21no—
35C2×#4339—21no—
36C11×#125—21no—
37C11×#125—21no—
38C11×#125—21no—
39C11×#125—21no—
40C4×D4×C11—21no—
41C4×D4×C11—21no—
42C4×D4×C11—21no—
43C4×D4×C11—21no—
44C2×C11×C4⋊C4—21no—
45C2×C11×C4⋊C4—21no—
46C2×C11×C4⋊C4—22no—
47C2×C11×C4⋊C4D411yescharacteristic
48C2×C11×C4⋊C4D411yescharacteristic
49C2×C11×C4⋊C4D411yescharacteristic
50C2×C11×C22⋊C4—22no—
51C2×C11×C22⋊C4—21no—
52C2×C11×C22⋊C4—22no—
53C2×C42×C11C2311yescharacteristic
54C2×#4323—22no—
55#66983—21no—
56#66983—21no—
57C2×#4318—21no—
58#66928—21no—
59#66927D411yescharacteristic
60C4×D44—21no—
61C4×D44—21no—
62#66922D411yescharacteristic
63C11×#95—22no—
64C11×#95—21no—
65C11×#95—21no—
66C11×#95D412yes—
67#66896—22no—
68C22⋊(C11⋊C8)—21no—
69C22⋊(C11⋊C8)—21no—
70#66874—22no—
71#66874—22no—
72#66873—22no—
73#66873—22no—
74#66873—22no—
75#66872—22no—
76C4⋊(C11⋊C8)—21no—
77C4⋊(C11⋊C8)—21no—
78#66867—21no—
79#66867—21no—
80#66867D412yes—
81C4×C11⋊C8D412yes—
82#10019—111nomaximal, Sylow
83C24×C11—21no—
84C2×D4×C11—21no—
85C2×D4×C11—21no—
86C2×D4×C11—42no—
87C22×C4×C11—22no—
88C22×C4×C11—21no—
89C22×C4×C11—21no—
90C22×C4×C11—21no—
91C22×C4×C11—41no—
92C22×C4×C11—41no—
93C22×C4×C11—82no—
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11C2×D411yescharacteristic
97C2×C22⋊D11—41no—
98#4339—44no—
99C2×D44—21no—
100C2×D44—21no—
101C2×D44—21no—
102C2×C4×D11—41no—
103C2×Dic22—21no—
104C11×C4⋊C4—21no—
105C11×C4⋊C4—21no—
106C11×C4⋊C4—21no—
107C11×C4⋊C4—21no—
108C11×C4⋊C4—21no—
109C11×C4⋊C4—21no—
110C11×C4⋊C4—41no—
111C11×C4⋊C4—41no—
112C11×C4⋊C4—41no—
113C11×C4⋊C4—41no—
114C11×C4⋊C4—82no—
115C11×C22⋊C4—44no—
116C11×C22⋊C4—41no—
117C11×C22⋊C4—41no—
118C11×C22⋊C4—82no—
119C42×C11C2×D411yescharacteristic
120C42×C11C2×D411yescharacteristic
121C42×C11C2×D411yescharacteristic
122C42×C11#4111yescharacteristic
123#4323—44no—
124(C2×D11)⋊C4—41no—
125(C2×D11)⋊C4—41no—
126C4⋊Dic11—21no—
127C4⋊Dic11—21no—
128#4318—42no—
129C2×C11⋊C8—22no—
130C2×C11⋊C8—22no—
131C2×C11⋊C8—41no—
132#3142—111no—
133#3109—111no—
134#2633D1111yescharacteristic, complemented
135#1534—111no—
136#1514—111no—
137#1490—111no—
138#1288—111no—
139C23×C11—22no—
140C23×C11—42no—
141C23×C11—41no—
142C23×C11—41no—
143C23×C11—42no—
144C23×C11#12011yescharacteristic
145C22×D11—41no—
146D4×C11—22no—
147D4×C11—22no—
148D4×C11—41no—
149D4×C11—41no—
150C2×C4×C11—22no—
151C2×C4×C11—41no—
152C2×C4×C11—41no—
153C2×C4×C11—42no—
154C2×C4×C11—42no—
155C2×C4×C11—41no—
156C2×C4×C11—42no—
157C2×C4×C11—41no—
158C2×C4×C11—42no—
159C2×C4×C11—41no—
160C2×C4×C11—41no—
161C2×C4×C11—41no—
162C2×C4×C11—42no—
163C2×C4×C11—82no—
164C2×C4×C11—82no—
165C2×C4×C11#12011yescharacteristic
166C2×C4×C11#12011yescharacteristic
167C2×C4×C11#12111yescharacteristic
168C2×C4×C11#12111yescharacteristic
169C2×C4×C11#12111yescharacteristic
170C2×C4×C11#12711yescharacteristic
171C22⋊D11—82no—
172C2×Dic11—41no—
173D44—42no—
174D44—42no—
175D44—81no—
176C4×D11—82no—
177Dic22—42no—
178C11⋊C8—42no—
179C11⋊C8—42no—
180C11⋊C8—81no—
181#532—111no—
182C2×#125C2×D1111yescharacteristic
183C2×C4×D4C2×D1111yescharacteristic
184#491—221no—
185#490—221no—
186#488—222no—
187#481—221no—
188#476—221no—
189#459—221no—
190#447—221no—
191#442—222no—
192#432—111no—
193#432—111no—
194#417—221no—
195#417—221no—
196C4×M16—111no—
197#399—21no—
198#398—21no—
199#397—21no—
200#394—21no—
201#385—22no—
202#383C2×D1111yescharacteristic
203#330—222no—
204#327—222no—
205D4⋊C8—222no—
206C22×C11—21no—
207C22×C11—21no—
208C22×C11—44no—
209C22×C11—42no—
210C22×C11—82no—
211C22×C11—81no—
212C22×C11—81no—
213C22×C11#39211yescharacteristic
214C22×C11#45412yes—
215C2×D11—81no—
216C2×D11—81no—
217C2×D11—81no—
218C4×C11—21no—
219C4×C11—21no—
220C4×C11—21no—
221C4×C11—21no—
222C4×C11—21no—
223C4×C11—21no—
224C4×C11—82no—
225C4×C11—81no—
226C4×C11—81no—
227C4×C11—81no—
228Dic11—81no—
229C2×#41—221no—
230C22×D4C22⋊D1111yescharacteristic
231C23×C4—21no—
232C2×D8—222no—
233C2×M16—221no—
234C4⋊Q8—111no—
235#127—111no—
236#125—21no—
237#125—21no—
238#125—21no—
239#125—21no—
240#124—221no—
241#121—221no—
242#121—221no—
243C4×D4—21no—
244C4×D4—21no—
245C4×D4—21no—
246C4×D4—21no—
247C4×D4—221no—
248C4×D4—221no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—22no—
252C2×C4⋊C4C22⋊D1111yescharacteristic
253C2×C4⋊C4C22⋊D1111yescharacteristic
254C2×C4⋊C4C22⋊D1111yescharacteristic
255C2×C22⋊C4—22no—
256C2×C22⋊C4—21no—
257C2×C22⋊C4—22no—
258C2×C42C22×D1111yescharacteristic
259#106—222no—
260C4⋊C8—221no—
261C4⋊C8—221no—
262#103—222no—
263#103—222no—
264#102—222no—
265#102—222no—
266#102—222no—
267#102—222no—
268C22⋊C8—221no—
269C22⋊C8—221no—
270#97—112no—
271#97—221no—
272#97—221no—
273C4×C8—112no—
274#95—22no—
275#95—21no—
276#95—21no—
277#95C22⋊D1112yes—
278C2×C11—22no—
279C2×C11—82no—
280C2×C11#200311yescharacteristic
281C2×C11#200811yescharacteristic
282C2×C11#201011yescharacteristic
283D11—161no—
284C24—21no—
285#41—444no—
286C2×Q8—221no—
287C2×D4—21no—
288C2×D4—21no—
289C2×D4—42no—
290C2×D4—221no—
291C2×D4—221no—
292C2×D4—221no—
293C2×D4—441no—
294C22×C4—22no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—41no—
299C22×C4—41no—
300C22×C4—82no—
301C22×C4—441no—
302C22×C4C2×C22⋊D1111yescharacteristic
303C22×C4C2×C22⋊D1111yescharacteristic
304C22×C4C2×C22⋊D1111yescharacteristic
305D8—444no—
306M16—442no—
307C2×C8—222no—
308C2×C8—222no—
309C2×C8—441no—
310C4⋊C4—21no—
311C4⋊C4—21no—
312C4⋊C4—21no—
313C4⋊C4—21no—
314C4⋊C4—21no—
315C4⋊C4—21no—
316C4⋊C4—41no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C4⋊C4—82no—
321C4⋊C4—221no—
322C4⋊C4—221no—
323C22⋊C4—44no—
324C22⋊C4—41no—
325C22⋊C4—41no—
326C22⋊C4—82no—
327C22⋊C4—441no—
328C22⋊C4—441no—
329C42D4×D1111yescharacteristic
330C42D4×D1111yescharacteristic
331C42D4×D1111yescharacteristic
332C42#434111yescharacteristic
333C11#1001911yescharacteristic, complemented, Sylow
334C23—22no—
335C23—42no—
336C23—41no—
337C23—41no—
338C23—42no—
339C23—441no—
340C23#6700611yescharacteristic
341Q8—442no—
342D4—22no—
343D4—22no—
344D4—41no—
345D4—41no—
346D4—442no—
347D4—442no—
348D4—881no—
349D4—882no—
350C2×C4—22no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—42no—
354C2×C4—42no—
355C2×C4—41no—
356C2×C4—42no—
357C2×C4—41no—
358C2×C4—42no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—42no—
363C2×C4—82no—
364C2×C4—82no—
365C2×C4—441no—
366C2×C4—882no—
367C2×C4#6699011yescharacteristic
368C2×C4#6699011yescharacteristic
369C2×C4#6699111yescharacteristic
370C2×C4#6699211yescharacteristic
371C2×C4#6699211yescharacteristic
372C2×C4#6699311yescharacteristic
373C8—442no—
374C8—442no—
375C8—881no—
376C22—21no—
377C22—21no—
378C22—44no—
379C22—42no—
380C22—82no—
381C22—81no—
382C22—81no—
383C22—881no—
384C22—881no—
385C22—881no—
386C22#1062283611yescharacteristic
387C22#1062285812yes—
388C4—21no—
389C4—21no—
390C4—21no—
391C4—21no—
392C4—21no—
393C4—21no—
394C4—82no—
395C4—81no—
396C4—81no—
397C4—81no—
398C4—881no—
399C2—22no—
400C2—82no—
401C2—1761no—
402C2#1306963611yescharacteristic
403C2#1306966911yescharacteristic
404C2#1306968111yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#2633C2
socleC22×C11#392
prime radical#13078707C2
hypercenter#2633D11
hypocenterC11#10019
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2633

Complements

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

NH ≅ G/Ntype
1. #13079019C2semidirect
3. #13067243C2semidirect
4. #13067162C2semidirect
5. #13067059C2semidirect
6. #13066480C2semidirect
7. C11×#2633C2semidirect
134. #2633D11semidirect
333. C11#10019semidirect

Maximal subgroups

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

subgroupindex
#130790192
#130787072
#130672432
#130671622
#130670592
#130664802
C11×#26332
#1001911