Finite Group Databasebeta

← #14650720

Subgroups — #14650720

Order 2816.

482 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 482 conjugacy classes of subgroups — too many to draw. Only its 93 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#13078734C211yesmaximal, characteristic
2#13071262C211yesmaximal, characteristic, complemented
3#13067124C211yesmaximal, characteristic
4#13067064C211yesmaximal, characteristic, complemented
5#13066510C211yesmaximal, characteristic, complemented
6#13066472C211yesmaximal, characteristic, complemented
7C11×#1980C211yesmaximal, characteristic
8C11×#532C2211yescharacteristic
9C2×C4×Dic22C2211yescharacteristic
10C2×C11×#104—22no—
11C4×C11×M16C2211yescharacteristic
12C4×C11×C4⋊C4C2211yescharacteristic
13#10622704C412yescomplemented
14#10622688C412yescomplemented
15#10622653—21no—
16#10622646—21no—
17#10622631—22no—
18#10622587—21no—
19#10622586—21no—
20#10622546—22no—
21#10622545C2211yescharacteristic
22#10622539C2211yescharacteristic
23#10622539C2211yescharacteristic
24#10622264—21no—
25#10622263—21no—
26#10622175—21no—
27#10622175—21no—
28#10622094—22no—
29C2×C11×#41—21no—
30C22×Dic22D411yescharacteristic
31C2×C11×M16—21no—
32C11×C4⋊Q8C2×C411yescharacteristic
33C11×#127C2×C411yescharacteristic
34C11×#124—21no—
35C11×#121—21no—
36C11×#121—21no—
37C4×D4×C11—21no—
38C4×D4×C11—21no—
39C2×C11×C4⋊C4—21no—
40C2×C42×C11D412yes—
41C2×C42×C11C2311yescharacteristic
42C2×#4324—22no—
43C2×C4⋊Dic11D411yescharacteristic
44C2×Dic11⋊C4—21no—
45C2×Dic11⋊C4—22no—
46C2×C4×Dic11—21no—
47C2×C4×Dic11—21no—
48C4×Dic22—21no—
49C4×Dic22—21no—
50C4×Dic22C2×C412yes—
51C4×Dic22D412yes—
52C11×#104—44no—
53C11×#97—21no—
54C4×C8×C11—21no—
55C11×#95—21no—
56#66896—22no—
57C11⋊#95—22no—
58C11⋊#95—22no—
59C11⋊#95—22no—
60C11⋊#95—21no—
61C11⋊#95D411yescharacteristic
62C11⋊#95D411yescharacteristic
63C22⋊(C11⋊C8)—21no—
64C22⋊(C11⋊C8)—21no—
65#66874—22no—
66#66871—22no—
67C4⋊(C11⋊C8)—21no—
68C4⋊(C11⋊C8)C2×C412yes—
69#66867—21no—
70#66867—21no—
71#9330—111nomaximal, Sylow
72C11×#41—42no—
73C11×#41—42no—
74C2×Q8×C11—21no—
75C2×D4×C11—21no—
76C2×D4×C11—21no—
77C2×D4×C11—21no—
78C2×D4×C11—41no—
79C22×C4×C11—22no—
80C22×C4×C11—41no—
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11C2×D411yescharacteristic
84C22×Dic11—21no—
85C22×Dic11—21no—
86C22×Dic11—21no—
87C22×Dic11—21no—
88C2×Dic22—21no—
89C2×Dic22—42no—
90C2×Dic22C22⋊C412yes—
91C11×M16—22no—
92C11×M16—41no—
93C2×C8×C11—41no—
94C11×C4⋊C4—21no—
95C11×C4⋊C4—21no—
96C11×C4⋊C4—42no—
97C11×C22⋊C4—41no—
98C11×C22⋊C4—41no—
99C42×C11—42no—
100C42×C11C22×C411yescharacteristic
101C42×C11C2×D411yescharacteristic
102C42×C11#4111yescharacteristic
103C42×C11#4111yescharacteristic
104#4324—44no—
105C4⋊Dic11—21no—
106C4⋊Dic11C22⋊C412yes—
107Dic11⋊C4—22no—
108Dic11⋊C4—22no—
109Dic11⋊C4—82no—
110C4×Dic11—22no—
111C4×Dic11—22no—
112C4×Dic11—42no—
113C2×C11⋊C8—22no—
114C2×C11⋊C8—41no—
115#3112—111no—
116#2320—111no—
117#1980D1111yescharacteristic
118#1505—111no—
119#1491—111no—
120#1300—111no—
121#1285—111no—
122C23×C11—41no—
123C23×C11#12011yescharacteristic
124Q8×C11—42no—
125D4×C11—42no—
126D4×C11—42no—
127D4×C11—81no—
128D4×C11—81no—
129D4×C11—81no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—22no—
133C2×C4×C11—41no—
134C2×C4×C11—42no—
135C2×C4×C11—42no—
136C2×C4×C11—41no—
137C2×C4×C11—42no—
138C2×C4×C11—82no—
139C2×C4×C11C2×C22⋊C411yescharacteristic
140C2×C4×C11C4×D411yescharacteristic
141C2×C4×C11C4×D411yescharacteristic
142C2×C4×C11#12111yescharacteristic
143C2×C4×C11#12111yescharacteristic
144C2×C4×C11#12311yescharacteristic
145C2×Dic11—22no—
146C2×Dic11—22no—
147C2×Dic11—42no—
148C2×Dic11—41no—
149C2×Dic11—41no—
150C2×Dic11—41no—
151C2×Dic11—41no—
152C2×Dic11—41no—
153C2×Dic11—41no—
154C2×Dic11—41no—
155C2×Dic11—41no—
156Dic22—22no—
157Dic22—22no—
158Dic22—42no—
159C8×C11—42no—
160C11⋊C8—42no—
161C11⋊C8—81no—
162#532C2×D1111yescharacteristic
163C2×C4×Q8—111no—
164#480—221no—
165#477—112no—
166#460—112no—
167#448—221no—
168#440—222no—
169#432—111no—
170#432—111no—
171C2×#104—22no—
172C4×M16C2×D1111yescharacteristic
173#391—221no—
174#389—221no—
175#387—222no—
176#383—221no—
177#382—221no—
178C4×C4⋊C4C2×D1111yescharacteristic
179#376—111no—
180#327—221no—
181#327—221no—
182Q8⋊C8—222no—
183C22×C11—21no—
184C22×C11—21no—
185C22×C11—81no—
186C22×C11—81no—
187C22×C11—81no—
188C22×C11#38611yescharacteristic
189C22×C11#45311yescharacteristic
190C22×C11#45411yescharacteristic
191C4×C11—21no—
192C4×C11—21no—
193C4×C11—21no—
194C4×C11—21no—
195C4×C11—21no—
196C4×C11—82no—
197C4×C11—81no—
198C4×C11#42112yes—
199Dic11—42no—
200Dic11—42no—
201Dic11—81no—
202Dic11—81no—
203C2×#41—21no—
204C22×Q8—111no—
205C2×SD16—222no—
206C2×M16—21no—
207C4⋊Q8C4×D1111yescharacteristic
208#127C4×D1111yescharacteristic
209#124—21no—
210#121—21no—
211#121—21no—
212C4×Q8—112no—
213C4×Q8—112no—
214C4×Q8—221no—
215C4×Q8—221no—
216C4×D4—21no—
217C4×D4—21no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—111no—
220C2×C4⋊C4—221no—
221C2×C4⋊C4—222no—
222C2×C42—221no—
223C2×C42—221no—
224C2×C42C22⋊D1112yes—
225C2×C42C22×D1111yescharacteristic
226#107—222no—
227C4⋊C8—112no—
228C4⋊C8—221no—
229#104—44no—
230#103—222no—
231#102—222no—
232C22⋊C8—221no—
233C22⋊C8—221no—
234#97—21no—
235#97—221no—
236#97—221no—
237C4×C8—21no—
238#95—21no—
239#95—111no—
240#95—111no—
241#95—222no—
242#95—222no—
243#95—222no—
244#95—221no—
245C2×C11—21no—
246C2×C11—21no—
247C2×C11—161no—
248C2×C11#188311yescharacteristic
249C2×C11#189711yescharacteristic
250C2×C11#190511yescharacteristic
251#41—42no—
252#41—42no—
253C2×Q8—21no—
254C2×Q8—112no—
255C2×Q8—221no—
256C2×Q8—442no—
257C2×D4—21no—
258C2×D4—21no—
259C2×D4—21no—
260C2×D4—41no—
261C22×C4—22no—
262C22×C4—41no—
263C22×C4—221no—
264C22×C4—221no—
265C22×C4—221no—
266C22×C4—221no—
267C22×C4D4×D1111yescharacteristic
268C22×C4D4×D1111yescharacteristic
269C22×C4C2×C22⋊D1111yescharacteristic
270SD16—444no—
271M16—22no—
272M16—41no—
273C2×C8—41no—
274C2×C8—222no—
275C2×C8—441no—
276C4⋊C4—21no—
277C4⋊C4—21no—
278C4⋊C4—42no—
279C4⋊C4—112no—
280C4⋊C4—221no—
281C4⋊C4—222no—
282C4⋊C4—222no—
283C4⋊C4—882no—
284C22⋊C4—41no—
285C22⋊C4—41no—
286C42—42no—
287C42—222no—
288C42—222no—
289C42—442no—
290C42C2×C4×D1111yescharacteristic
291C42#433911yescharacteristic
292C42D4×D1111yescharacteristic
293C42#434111yescharacteristic
294C11#933011yescharacteristic, complemented, Sylow
295C23—41no—
296C23#6699011yescharacteristic
297Q8—42no—
298Q8—222no—
299Q8—222no—
300Q8—442no—
301D4—42no—
302D4—42no—
303D4—81no—
304D4—81no—
305D4—81no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—22no—
309C2×C4—41no—
310C2×C4—42no—
311C2×C4—42no—
312C2×C4—41no—
313C2×C4—42no—
314C2×C4—82no—
315C2×C4—222no—
316C2×C4—222no—
317C2×C4—442no—
318C2×C4—441no—
319C2×C4—441no—
320C2×C4—441no—
321C2×C4—441no—
322C2×C4—441no—
323C2×C4—441no—
324C2×C4—441no—
325C2×C4—441no—
326C2×C4C22⋊C4×D1111yescharacteristic
327C2×C4(C22⋊D11)⋊C411yescharacteristic
328C2×C4#6693611yescharacteristic
329C2×C4#6693711yescharacteristic
330C2×C4C4×C22⋊D1111yescharacteristic
331C2×C4#6699111yescharacteristic
332C8—42no—
333C8—442no—
334C8—881no—
335C22—21no—
336C22—21no—
337C22—81no—
338C22—81no—
339C22—81no—
340C22#1062256911yescharacteristic
341C22#1062267511yescharacteristic
342C22#1062269011yescharacteristic
343C4—21no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—82no—
349C4—81no—
350C4—442no—
351C4—442no—
352C4—881no—
353C4—881no—
354C4#1062243412yes—
355C2—21no—
356C2—21no—
357C2—161no—
358C2#1306899511yescharacteristic
359C2#1306906111yescharacteristic
360C2#1306910711yescharacteristic
subgroupG/H
centerC22#10622569
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1980C2
socleC22×C11#386
prime radicalC11×#532C22
cosocleC2×C42×C11C23
hypercenter#1980D11
hypocenterC11#9330
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1980

Complements

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

NH ≅ G/Ntype
2. #13071262C2semidirect
4. #13067064C2semidirect
5. #13066510C2semidirect
6. #13066472C2semidirect
13. #10622704C4semidirect
14. #10622688C4semidirect
294. C11#9330semidirect

Maximal subgroups

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

subgroupindex
#130787342
#130712622
#130671242
#130670642
#130665102
#130664722
C11×#19802
#933011