Finite Group Databasebeta

← #14651069

Subgroups — #14651069

Order 2816.

424 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 103 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#13071422C211yesmaximal, characteristic
2#13069561C211yesmaximal, characteristic
3#13067218C211yesmaximal, characteristic
4#13067167C211yesmaximal, characteristic
5#13066482C211yesmaximal, characteristic
6#13066471C211yesmaximal, characteristic
7C11×#3236C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9C2×C11×#125C2211yescharacteristic
10C11×#501C412yescomplemented
11C11×#491C412yescomplemented
12C11×#484—21no—
13C11×#483—21no—
14C11×#479—22no—
15C11×#432C2211yescharacteristic
16#10622598—21no—
17#10622594—21no—
18#10622594—21no—
19#10622594—21no—
20#10622594—21no—
21C4⋊C4×Dic11—21no—
22#10622550C2211yescharacteristic
23C4×C4⋊Dic11C2211yescharacteristic
24#10622539C2211yescharacteristic
25C4×#4318C2211yescharacteristic
26#10622181—22no—
27#10622176—21no—
28#10622176—21no—
29#10622170—21no—
30#10622170—21no—
31C11×C4⋊Q8C2×C411yescharacteristic
32C11×C4⋊Q8C2×C411yescharacteristic
33C11×#125—21no—
34C11×#125—21no—
35C11×#125—21no—
36C11×#125C2×C412yes—
37C11×#125D412yes—
38C11×C22⋊Q8—21no—
39C11×C22⋊Q8—21no—
40C4×Q8×C11—21no—
41C4×Q8×C11—21no—
42C11×#117—21no—
43C2×C11×C4⋊C4—21no—
44C2×C11×C4⋊C4—21no—
45C2×C11×C4⋊C4D411yescharacteristic
46C2×C11×C4⋊C4D411yescharacteristic
47C2×C42×C11C2311yescharacteristic
48C2×C4⋊Dic11—21no—
49C2×C4⋊Dic11—21no—
50C2×C4⋊Dic11—21no—
51C2×C4×Dic11—21no—
52C2×C4×Dic11—21no—
53C2×C4×Dic11D411yescharacteristic
54C2×C4×Dic11D411yescharacteristic
55C2×#4318—21no—
56C11×#107—22no—
57C11×#106—22no—
58C11×C4⋊C8—21no—
59C11×#103—22no—
60C11×#103—22no—
61C11×C22⋊C8—21no—
62C11×#97C2×C412yes—
63C11⋊#95—21no—
64C11⋊#95—21no—
65C11⋊#95—21no—
66C11⋊#95—21no—
67C11⋊#95—21no—
68C11⋊#95—21no—
69C11⋊#95—21no—
70C11⋊#95D411yescharacteristic
71C11⋊#95D411yescharacteristic
72C22⋊(C11⋊C8)—21no—
73C4⋊(C11⋊C8)—21no—
74#66867—21no—
75#66867—21no—
76C4×C11⋊C8—21no—
77#9380—111nomaximal, Sylow
78C2×Q8×C11—21no—
79C2×Q8×C11—21no—
80C22×C4×C11—21no—
81C22×C4×C11—21no—
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C22×Dic11—21no—
86C22×Dic11—21no—
87C22×Dic11—21no—
88C22×Dic11—21no—
89C2×C8×C11—22no—
90C11×C4⋊C4—22no—
91C11×C4⋊C4—22no—
92C11×C4⋊C4—22no—
93C11×C4⋊C4—22no—
94C11×C4⋊C4—21no—
95C11×C4⋊C4—21no—
96C11×C4⋊C4—21no—
97C11×C4⋊C4—21no—
98C11×C4⋊C4—21no—
99C11×C4⋊C4—21no—
100C11×C4⋊C4—41no—
101C11×C4⋊C4—41no—
102C11×C4⋊C4C22⋊C412yes—
103C11×C4⋊C4C22⋊C412yes—
104C11×C22⋊C4—41no—
105C42×C11—41no—
106C42×C11C22×C411yescharacteristic
107C42×C11C2×D411yescharacteristic
108C42×C11#4111yescharacteristic
109C42×C11#4111yescharacteristic
110C4⋊Dic11—42no—
111C4⋊Dic11—42no—
112C4⋊Dic11—81no—
113C4×Dic11—41no—
114C4×Dic11—41no—
115C4×Dic11—42no—
116C4×Dic11—81no—
117#4318—22no—
118#4318—41no—
119C2×C11⋊C8—41no—
120C2×C11⋊C8—41no—
121#3236D1111yescharacteristic
122#2336—111no—
123#1986—111no—
124#1528—111no—
125#1515—111no—
126#1288—111no—
127#1285—111no—
128C23×C11#12011yescharacteristic
129Q8×C11—42no—
130Q8×C11—81no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—22no—
134C2×C4×C11—22no—
135C2×C4×C11—41no—
136C2×C4×C11—41no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11C2×C22⋊C411yescharacteristic
144C2×C4×C11C4×D411yescharacteristic
145C2×C4×C11C4×D411yescharacteristic
146C2×C4×C11#12111yescharacteristic
147C2×C4×C11#12111yescharacteristic
148C2×C4×C11#12311yescharacteristic
149C2×Dic11—22no—
150C2×Dic11—41no—
151C2×Dic11—41no—
152C2×Dic11—41no—
153C2×Dic11—41no—
154C2×Dic11—41no—
155C2×Dic11—41no—
156C2×Dic11—41no—
157C2×Dic11—41no—
158C2×Dic11—41no—
159C2×Dic11—41no—
160C2×Dic11—41no—
161C8×C11—42no—
162C11⋊C8—42no—
163C11⋊C8—81no—
164#533C2×D1111yescharacteristic
165C2×#125C2×D1111yescharacteristic
166#501Dic1112yescomplemented
167#491Dic1112yescomplemented
168#484—21no—
169#483—21no—
170#479—22no—
171#432—111no—
172#432C2×D1111yescharacteristic
173C4×M16—111no—
174#389—221no—
175#387—221no—
176#387—221no—
177#387—221no—
178#387—221no—
179#383—111no—
180C4×C4⋊C4—111no—
181C4×C4⋊C4—221no—
182#339—221no—
183#339—221no—
184#330—222no—
185#328—221no—
186#328—221no—
187C22×C11—21no—
188C22×C11—21no—
189C22×C11#38611yescharacteristic
190C22×C11#45511yescharacteristic
191C22×C11#45611yescharacteristic
192C4×C11—21no—
193C4×C11—21no—
194C4×C11—21no—
195C4×C11—21no—
196C4×C11—21no—
197C4×C11—21no—
198C4×C11—42no—
199C4×C11—42no—
200C4×C11—81no—
201C4×C11—81no—
202Dic11—42no—
203Dic11—81no—
204Dic11—81no—
205Dic11—81no—
206C2×M16—221no—
207C4⋊Q8C2×Dic1111yescharacteristic
208C4⋊Q8C2×Dic1111yescharacteristic
209#125—21no—
210#125—21no—
211#125—21no—
212#125C2×Dic1112yes—
213#125C22⋊D1112yes—
214C22⋊Q8—21no—
215C22⋊Q8—21no—
216C4×Q8—21no—
217C4×Q8—21no—
218#117—21no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—221no—
222C2×C4⋊C4—221no—
223C2×C4⋊C4—221no—
224C2×C4⋊C4C22⋊D1111yescharacteristic
225C2×C4⋊C4C22⋊D1111yescharacteristic
226C2×C42—111no—
227C2×C42—111no—
228C2×C42—221no—
229C2×C42—221no—
230C2×C42C22×D1111yescharacteristic
231#107—22no—
232#106—22no—
233C4⋊C8—21no—
234C4⋊C8—221no—
235#103—22no—
236#103—22no—
237C22⋊C8—21no—
238C22⋊C8—221no—
239#97—221no—
240#97—221no—
241#97C2×Dic1112yes—
242C4×C8—221no—
243#95—111no—
244#95—111no—
245#95—221no—
246#95—221no—
247#95—221no—
248#95—221no—
249#95—221no—
250#95—221no—
251#95—221no—
252C2×C11—21no—
253C2×C11—21no—
254C2×C11#188211yescharacteristic
255C2×C11#190611yescharacteristic
256C2×C11#191211yescharacteristic
257C2×Q8—21no—
258C2×Q8—21no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—221no—
262C22×C4—221no—
263C22×C4—221no—
264C22×C4—221no—
265C22×C4D4×D1111yescharacteristic
266C22×C4D4×D1111yescharacteristic
267C22×C4C2×C22⋊D1111yescharacteristic
268M16—222no—
269M16—441no—
270C2×C8—22no—
271C2×C8—441no—
272C2×C8—441no—
273C4⋊C4—22no—
274C4⋊C4—22no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—22no—
278C4⋊C4—22no—
279C4⋊C4—21no—
280C4⋊C4—21no—
281C4⋊C4—21no—
282C4⋊C4—21no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—442no—
286C4⋊C4—442no—
287C4⋊C4—881no—
288C4⋊C4C22⋊Dic1112yes—
289C4⋊C4C22⋊Dic1112yes—
290C22⋊C4—41no—
291C42—41no—
292C42—441no—
293C42—441no—
294C42—442no—
295C42—881no—
296C42#434111yescharacteristic
297C42#434111yescharacteristic
298C42C22×Dic1111yescharacteristic
299C42C2×C22⋊D1111yescharacteristic
300C11#938011yescharacteristic, complemented, Sylow
301C23#6699011yescharacteristic
302Q8—42no—
303Q8—81no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—222no—
317C2×C4—441no—
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×C4—441no—
327C2×C4—441no—
328C2×C4D4×Dic1111yescharacteristic
329C2×C4D4×Dic1111yescharacteristic
330C2×C4#6698811yescharacteristic
331C2×C4#6699211yescharacteristic
332C2×C4#6699211yescharacteristic
333C2×C4C2×C22⋊Dic1111yescharacteristic
334C8—42no—
335C8—442no—
336C8—881no—
337C22—21no—
338C22—21no—
339C22#1062281511yescharacteristic
340C22#1062281811yescharacteristic
341C22#1062283311yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—42no—
349C4—42no—
350C4—81no—
351C4—81no—
352C4—442no—
353C4—881no—
354C4—881no—
355C4—881no—
356C2—21no—
357C2—21no—
358C2#1306898711yescharacteristic
359C2#1306911911yescharacteristic
360C2#1306915411yescharacteristic
subgroupG/H
centerC22#10622833
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#3236C2
socleC22×C11#386
prime radicalC23×C11#120
cosocleC2×C42×C11C23
hypercenter#3236D11
hypocenterC11#9380
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3236

Complements

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

NH ≅ G/Ntype
10. C11×#501C4semidirect
11. C11×#491C4semidirect
166. #501Dic11semidirect
167. #491Dic11semidirect
300. C11#9380semidirect

Maximal subgroups

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

subgroupindex
#130714222
#130695612
#130672182
#130671672
#130664822
#130664712
C11×#32362
#938011