Finite Group Databasebeta

← #14649693

Subgroups — #14649693

Order 2816.

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

normal subgroups only

This group has 494 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#13078415C211yesmaximal, characteristic
2#13071587C211yesmaximal, characteristic
3#13067181C211yesmaximal, characteristic, complemented
4#13067114C211yesmaximal, characteristic, complemented
5#13067008C211yesmaximal, characteristic
6#13066476C211yesmaximal, characteristic, complemented
7C11×#1303C211yesmaximal, characteristic, complemented
8C2×C4×D44C2211yescharacteristic
9#10623001C2211yescharacteristic
10C11×#431C2211yescharacteristic
11C11×#423C2211yescharacteristic
12C4×C11×C4⋊C4C2211yescharacteristic
13#10622744—21no—
14#10622734—21no—
15#10622603—22no—
16#10622552—21no—
17#10622549C2211yescharacteristic
18C4×C4⋊Dic11—21no—
19#10622538C2211yescharacteristic
20#10622460—22no—
21#10622459C412yescomplemented
22#10622455C412yescomplemented
23#10622279—21no—
24#10622277—21no—
25#10622105—22no—
26#10622097—22no—
27#10622090—21no—
28#10622090—21no—
29C22×D44D411yescharacteristic
30C22×C4×D11—21no—
31C2×C11×M16—21no—
32C2×C11×C4⋊C4—21no—
33C2×C42×C11—21no—
34C2×C42×C11C2311yescharacteristic
35C2×(C2×D11)⋊C4—21no—
36C2×(C2×D11)⋊C4—22no—
37C2×(C2×D11)⋊C4—22no—
38#66979—21no—
39C2×C4⋊Dic11—21no—
40C2×C4⋊Dic11D411yescharacteristic
41#66977—21no—
42#66977—21no—
43C2×C4×Dic11—22no—
44C4×D44—21no—
45C4×D44—21no—
46C4×D44C2×C412yes—
47C4×D44D412yes—
48#66923—21no—
49#66922C2×C411yescharacteristic
50#66922C2×C411yescharacteristic
51C4×Dic22—21no—
52C4×Dic22—21no—
53C11×C4⋊C8—21no—
54C11×C4⋊C8—21no—
55C11×C4⋊C8C2×C412yes—
56C11×C22⋊C8—21no—
57C4×C8×C11—21no—
58C11×#95D411yescharacteristic
59C11×#95D411yescharacteristic
60C11⋊#95—22no—
61C11⋊#95—21no—
62C11⋊#95D412yes—
63C22⋊(C11⋊C8)—21no—
64#66885—22no—
65#66885—22no—
66#66882—22no—
67#66881—22no—
68C4⋊(C11⋊C8)—21no—
69C4×C11⋊C8—21no—
70#9177—111nomaximal, Sylow
71C23×D11—21no—
72C22×C4×C11—21no—
73C22×C4×C11—21no—
74C22×C4×C11C2×D411yescharacteristic
75C22×C4×C11C2×D411yescharacteristic
76C22×C4×C11C2×D411yescharacteristic
77C22×Dic11—21no—
78C22×Dic11—22no—
79C2×D44—21no—
80C2×D44—21no—
81C2×D44—21no—
82C2×D44—21no—
83C2×D44—21no—
84C2×D44C22⋊C412yes—
85C2×C4×D11—22no—
86C2×C4×D11—22no—
87C2×C4×D11—82no—
88C2×Dic22—21no—
89C2×Dic22—21no—
90C11×M16—41no—
91C11×M16—41no—
92C2×C8×C11—22no—
93C2×C8×C11—41no—
94C11×C4⋊C4—42no—
95C42×C11—41no—
96C42×C11—41no—
97C42×C11C22×C411yescharacteristic
98C42×C11C2×D411yescharacteristic
99C42×C11#4111yescharacteristic
100C42×C11#4111yescharacteristic
101C22⋊Dic11—41no—
102(C2×D11)⋊C4—22no—
103(C2×D11)⋊C4—22no—
104(C2×D11)⋊C4—44no—
105(C2×D11)⋊C4—82no—
106C4⋊Dic11—21no—
107C4⋊Dic11—21no—
108C4⋊Dic11—21no—
109C4⋊Dic11—21no—
110C4⋊Dic11—21no—
111C4⋊Dic11—41no—
112C4⋊Dic11—41no—
113C4⋊Dic11C22⋊C412yes—
114Dic11⋊C4—41no—
115Dic11⋊C4—41no—
116C4×Dic11—41no—
117C4×Dic11—82no—
118C2×C11⋊C8—41no—
119#3077—111no—
120#2357—111no—
121#1518—111no—
122#1503—111no—
123#1478—111no—
124#1303D1111yescharacteristic, complemented
125#1286—111no—
126C23×C11#12011yescharacteristic
127C22×D11—22no—
128C22×D11—42no—
129C22×D11—42no—
130C22×D11—41no—
131C22×D11—41no—
132C2×C4×C11—22no—
133C2×C4×C11—41no—
134C2×C4×C11—41no—
135C2×C4×C11—41no—
136C2×C4×C11—41no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11C2×C22⋊C411yescharacteristic
141C2×C4×C11C4×D411yescharacteristic
142C2×C4×C11C4×D411yescharacteristic
143C2×C4×C11#12111yescharacteristic
144C2×C4×C11#12111yescharacteristic
145C2×C4×C11#12311yescharacteristic
146C2×C4×C11#13511yescharacteristic
147C2×C4×C11#13511yescharacteristic
148C2×C4×C11#13711yescharacteristic
149C2×C4×C11#13711yescharacteristic
150C2×Dic11—22no—
151C2×Dic11—42no—
152C2×Dic11—42no—
153C2×Dic11—42no—
154C2×Dic11—41no—
155C2×Dic11—41no—
156C2×Dic11—42no—
157D44—22no—
158D44—22no—
159D44—41no—
160D44—41no—
161C4×D11—82no—
162C4×D11—82no—
163Dic22—81no—
164Dic22—81no—
165C8×C11—42no—
166C8×C11—81no—
167C11⋊C8—81no—
168#533—111no—
169C2×C4×D4—111no—
170#478—222no—
171#476—112no—
172#474—112no—
173#431—111no—
174#431C2×D1111yescharacteristic
175#428—221no—
176#423C2×D1111yescharacteristic
177#418—221no—
178#390—221no—
179#388—222no—
180#382—111no—
181#381—221no—
182C4×C4⋊C4—221no—
183C4×C4⋊C4C2×D1111yescharacteristic
184C4×C22⋊C4—221no—
185#328—222no—
186#328—221no—
187#328—221no—
188D4⋊C8—222no—
189C22×C11—21no—
190C22×C11—21no—
191C22×C11#38611yescharacteristic
192C22×C11#45211yescharacteristic
193C22×C11#45211yescharacteristic
194C2×D11—42no—
195C2×D11—42no—
196C2×D11—42no—
197C2×D11—82no—
198C2×D11—82no—
199C4×C11—21no—
200C4×C11—21no—
201C4×C11—21no—
202C4×C11—21no—
203C4×C11—42no—
204C4×C11—81no—
205C4×C11#41611yescharacteristic
206C4×C11#41911yescharacteristic
207C4×C11#48511yescharacteristic
208C4×C11#48511yescharacteristic
209Dic11—42no—
210Dic11—82no—
211Dic11—81no—
212Dic11—81no—
213C22×D4—111no—
214C23×C4—221no—
215C2×M16—21no—
216C4⋊Q8—111no—
217C4⋊Q8—111no—
218#125—221no—
219C22⋊Q8—221no—
220C22⋊Q8—221no—
221C4×Q8—221no—
222C4×Q8—221no—
223C4×D4—112no—
224C4×D4—112no—
225C4×D4—221no—
226C4×D4—221no—
227#117—221no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—111no—
230C2×C4⋊C4—221no—
231C2×C22⋊C4—221no—
232C2×C22⋊C4—222no—
233C2×C22⋊C4—222no—
234C2×C42—21no—
235C2×C42—222no—
236C2×C42C22×D1111yescharacteristic
237#107—222no—
238#106—222no—
239C4⋊C8—21no—
240C4⋊C8—21no—
241C4⋊C8—221no—
242C4⋊C8C4×D1112yes—
243#102—222no—
244#102—222no—
245C22⋊C8—21no—
246C22⋊C8—221no—
247C4×C8—21no—
248C4×C8—221no—
249#95—112no—
250#95—222no—
251#95—221no—
252#95D4411yescharacteristic
253#95D4411yescharacteristic
254C2×C11—21no—
255C2×C11—21no—
256C2×C11#187311yescharacteristic
257C2×C11#190411yescharacteristic
258C2×C11#190611yescharacteristic
259D11—82no—
260C24—221no—
261C2×Q8—221no—
262C2×Q8—221no—
263C2×D4—112no—
264C2×D4—221no—
265C2×D4—221no—
266C2×D4—221no—
267C2×D4—221no—
268C2×D4—221no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—221no—
272C22×C4—222no—
273C22×C4—222no—
274C22×C4—222no—
275C22×C4—882no—
276C22×C4C2×D4411yescharacteristic
277C22×C4D4×D1111yescharacteristic
278C22×C4D4×D1111yescharacteristic
279M16—41no—
280M16—41no—
281C2×C8—22no—
282C2×C8—41no—
283C2×C8—441no—
284C4⋊C4—42no—
285C4⋊C4—112no—
286C4⋊C4—221no—
287C4⋊C4—221no—
288C4⋊C4—221no—
289C4⋊C4—221no—
290C4⋊C4—221no—
291C4⋊C4—441no—
292C4⋊C4—441no—
293C4⋊C4—441no—
294C4⋊C4—441no—
295C22⋊C4—222no—
296C22⋊C4—222no—
297C22⋊C4—444no—
298C22⋊C4—441no—
299C22⋊C4—882no—
300C42—41no—
301C42—41no—
302C42—441no—
303C42—882no—
304C42C2×C4×D1111yescharacteristic
305C42#433911yescharacteristic
306C42D4×D1111yescharacteristic
307C42#434311yescharacteristic
308C11#917711yescharacteristic, complemented, Sylow
309C23—222no—
310C23—442no—
311C23—442no—
312C23—441no—
313C23—441no—
314C23#6693511yescharacteristic
315Q8—881no—
316Q8—881no—
317D4—222no—
318D4—222no—
319D4—441no—
320D4—441no—
321C2×C4—22no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—222no—
330C2×C4—442no—
331C2×C4—442no—
332C2×C4—442no—
333C2×C4—441no—
334C2×C4—441no—
335C2×C4—442no—
336C2×C4—882no—
337C2×C4—882no—
338C2×C4C4×D4411yescharacteristic
339C2×C4C22⋊C4×D1111yescharacteristic
340C2×C4#6693711yescharacteristic
341C2×C4#6694611yescharacteristic
342C2×C4#6694711yescharacteristic
343C2×C4#6694811yescharacteristic
344C2×C4#6696511yescharacteristic
345C2×C4#6696811yescharacteristic
346C2×C4#6696911yescharacteristic
347C2×C4#6697111yescharacteristic
348C8—42no—
349C8—81no—
350C8—881no—
351C22—21no—
352C22—21no—
353C22—442no—
354C22—442no—
355C22—442no—
356C22—882no—
357C22—882no—
358C22#1062227811yescharacteristic
359C22#1062239611yescharacteristic
360C22#1062242311yescharacteristic
361C4—21no—
362C4—21no—
363C4—21no—
364C4—21no—
365C4—42no—
366C4—81no—
367C4—442no—
368C4—882no—
369C4—881no—
370C4—881no—
371C4#1062238511yescharacteristic
372C4#1062241511yescharacteristic
373C4#1062248011yescharacteristic
374C4#1062250111yescharacteristic
375C2—21no—
376C2—21no—
377C2—882no—
378C2#1306892711yescharacteristic
379C2#1306910211yescharacteristic
380C2#1306911611yescharacteristic
subgroupG/H
centerC22#10622278
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1303C2
socleC22×C11#386
prime radicalC22×D44D4
cosocleC2×C42×C11C23
hypercenter#1303D11
hypocenterC11#9177
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1303

Complements

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

NH ≅ G/Ntype
3. #13067181C2semidirect
4. #13067114C2semidirect
6. #13066476C2semidirect
7. C11×#1303C2semidirect
21. #10622459C4semidirect
22. #10622455C4semidirect
124. #1303D11semidirect
308. C11#9177semidirect

Maximal subgroups

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

subgroupindex
#130784152
#130715872
#130671812
#130671142
#130670082
#130664762
C11×#13032
#917711