Finite Group Databasebeta

← #14654667

Subgroups — #14654667

Order 2816.

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

normal subgroups only

This group has 492 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#13079016C211yesmaximal, characteristic
2#13074492C211yesmaximal, characteristic, complemented
3#13067242C211yesmaximal, characteristic, complemented
4#13067163C211yesmaximal, characteristic
5#13067063C211yesmaximal, characteristic, complemented
6#13066482C211yesmaximal, characteristic, complemented
7C11×#3112C211yesmaximal, characteristic
8C11×#532C2211yescharacteristic
9C2×C4×Q8×C11C2211yescharacteristic
10C2×#66923C2211yescharacteristic
11C11×#480—21no—
12C11×#477—21no—
13C11×#460—21no—
14C11×#448—21no—
15C11×#440—22no—
16C11×#432C2211yescharacteristic
17#10622845—21no—
18#10622845—21no—
19#10622842—21no—
20#10622695—21no—
21#10622684—21no—
22#10622669—22no—
23#10622599—21no—
24#10622596—21no—
25#10622595—21no—
26#10622550C2211yescharacteristic
27#10622546—22no—
28#10622539C2211yescharacteristic
29C4×#4318C2211yescharacteristic
30#10622175—22no—
31Q8⋊(C11⋊C8)—22no—
32#10622103—22no—
33C2×C11×#41—21no—
34C22×Q8×C11D411yescharacteristic
35C2×C11×SD16—22no—
36C11×C4⋊Q8D411yescharacteristic
37C11×#127D411yescharacteristic
38C11×#124—21no—
39C11×#121—21no—
40C11×#121—21no—
41C4×Q8×C11—21no—
42C4×Q8×C11—21no—
43C4×Q8×C11—21no—
44C4×Q8×C11—21no—
45C4×D4×C11—21no—
46C4×D4×C11—21no—
47C2×C11×C4⋊C4—21no—
48C2×C11×C4⋊C4D411yescharacteristic
49C2×C42×C11—21no—
50C2×C42×C11C2311yescharacteristic
51C2×C4⋊Dic11D411yescharacteristic
52C2×C4⋊Dic11D411yescharacteristic
53C2×Dic11⋊C4—22no—
54C2×Dic11⋊C4—21no—
55C2×Dic11⋊C4—21no—
56C2×#4318—21no—
57#66923—21no—
58#66923—21no—
59#66923—21no—
60#66923—21no—
61C11×#107—22no—
62C11×C4⋊C8—21no—
63C11×#103—22no—
64C11×#102—22no—
65C11×C22⋊C8—21no—
66C11×#97D412yes—
67#66899—22no—
68#66899—22no—
69#66896—22no—
70#66896—22no—
71C11⋊#95—22no—
72C11⋊#95—22no—
73C11⋊#95—22no—
74C11⋊#95—21no—
75C11⋊#95—21no—
76C11⋊#95D412yes—
77C22⋊(C11⋊C8)—21no—
78C4⋊(C11⋊C8)—21no—
79#66867—21no—
80#66867—21no—
81C4×C11⋊C8D412yes—
82#10021—111nomaximal, Sylow
83C11×#41—44no—
84C2×Q8×C11—21no—
85C2×Q8×C11—21no—
86C2×Q8×C11—21no—
87C2×Q8×C11—42no—
88C2×D4×C11—21no—
89C2×D4×C11—21no—
90C2×D4×C11—21no—
91C2×D4×C11—41no—
92C22×C4×C11—21no—
93C22×C4×C11—21no—
94C22×C4×C11—41no—
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11C2×D411yescharacteristic
98C22×Dic11—22no—
99C22×Dic11—21no—
100C22×Dic11—21no—
101C11×SD16—44no—
102C2×C8×C11—22no—
103C11×C4⋊C4—21no—
104C11×C4⋊C4—21no—
105C11×C4⋊C4—21no—
106C11×C4⋊C4—21no—
107C11×C4⋊C4—41no—
108C11×C4⋊C4—41no—
109C11×C22⋊C4—41no—
110C11×C22⋊C4—41no—
111C42×C11—41no—
112C42×C11—41no—
113C42×C11C2×D411yescharacteristic
114C42×C11C2×D411yescharacteristic
115C42×C11C2×D411yescharacteristic
116C42×C11#4111yescharacteristic
117C4⋊Dic11—21no—
118C4⋊Dic11—21no—
119C4⋊Dic11—21no—
120C4⋊Dic11—21no—
121Dic11⋊C4—44no—
122Dic11⋊C4—41no—
123Dic11⋊C4—41no—
124Dic11⋊C4—41no—
125Dic11⋊C4—41no—
126#4318—42no—
127C2×C11⋊C8—22no—
128C2×C11⋊C8—41no—
129#3142—111no—
130#3112D1111yescharacteristic
131#2634—111no—
132#1534—111no—
133#1514—111no—
134#1491—111no—
135#1288—111no—
136C23×C11—41no—
137C23×C11#12011yescharacteristic
138Q8×C11—22no—
139Q8×C11—22no—
140Q8×C11—41no—
141Q8×C11—41no—
142Q8×C11—42no—
143D4×C11—42no—
144D4×C11—42no—
145D4×C11—81no—
146D4×C11—82no—
147C2×C4×C11—22no—
148C2×C4×C11—22no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11—41no—
152C2×C4×C11—41no—
153C2×C4×C11—41no—
154C2×C4×C11—41no—
155C2×C4×C11—42no—
156C2×C4×C11—82no—
157C2×C4×C11#12011yescharacteristic
158C2×C4×C11#12011yescharacteristic
159C2×C4×C11#12111yescharacteristic
160C2×C4×C11#12111yescharacteristic
161C2×C4×C11#12111yescharacteristic
162C2×C4×C11#12711yescharacteristic
163C2×Dic11—42no—
164C2×Dic11—42no—
165C2×Dic11—42no—
166C2×Dic11—42no—
167C2×Dic11—41no—
168C2×Dic11—41no—
169C2×Dic11—42no—
170C8×C11—42no—
171C11⋊C8—42no—
172C11⋊C8—81no—
173#532C2×D1111yescharacteristic
174C2×#125—111no—
175C2×C4×Q8C2×D1111yescharacteristic
176#491—221no—
177#490—221no—
178#488—222no—
179#480—21no—
180#477—21no—
181#460—21no—
182#448—21no—
183#440—22no—
184#432—111no—
185#432C2×D1111yescharacteristic
186#417—221no—
187#417—221no—
188C4×M16—111no—
189#400—221no—
190#400—221no—
191#398—221no—
192#395—221no—
193#387—222no—
194#383—111no—
195#330—222no—
196#327—222no—
197Q8⋊C8—222no—
198C22×C11—21no—
199C22×C11—21no—
200C22×C11—81no—
201C22×C11—81no—
202C22×C11—81no—
203C22×C11#39211yescharacteristic
204C22×C11#45412yes—
205C4×C11—21no—
206C4×C11—21no—
207C4×C11—21no—
208C4×C11—21no—
209C4×C11—21no—
210C4×C11—21no—
211C4×C11—42no—
212C4×C11—81no—
213C4×C11—81no—
214Dic11—82no—
215Dic11—81no—
216Dic11—81no—
217C2×#41—21no—
218C22×Q8C22⋊D1111yescharacteristic
219C2×SD16—22no—
220C2×M16—221no—
221C4⋊Q8C22⋊D1111yescharacteristic
222#127C22⋊D1111yescharacteristic
223#125—221no—
224#125—221no—
225#125—221no—
226#125—221no—
227#124—21no—
228#121—21no—
229#121—21no—
230C4×Q8—21no—
231C4×Q8—21no—
232C4×Q8—21no—
233C4×Q8—21no—
234C4×D4—21no—
235C4×D4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—111no—
238C2×C4⋊C4—111no—
239C2×C4⋊C4—222no—
240C2×C4⋊C4—221no—
241C2×C4⋊C4—221no—
242C2×C4⋊C4C22⋊D1111yescharacteristic
243C2×C42—21no—
244C2×C42C22×D1111yescharacteristic
245#107—22no—
246C4⋊C8—21no—
247C4⋊C8—221no—
248#103—22no—
249#103—222no—
250#103—222no—
251#102—22no—
252#102—222no—
253#102—222no—
254C22⋊C8—21no—
255C22⋊C8—221no—
256#97—221no—
257#97—221no—
258#97C22⋊D1112yes—
259C4×C8—112no—
260#95—112no—
261#95—222no—
262#95—222no—
263#95—222no—
264#95—221no—
265#95—221no—
266C2×C11—22no—
267C2×C11—161no—
268C2×C11#200311yescharacteristic
269C2×C11#200911yescharacteristic
270C2×C11#201011yescharacteristic
271#41—44no—
272C2×Q8—21no—
273C2×Q8—21no—
274C2×Q8—21no—
275C2×Q8—42no—
276C2×D4—21no—
277C2×D4—21no—
278C2×D4—21no—
279C2×D4—41no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—41no—
283C22×C4—222no—
284C22×C4—221no—
285C22×C4—221no—
286C22×C4D4×D1111yescharacteristic
287C22×C4D4×D1111yescharacteristic
288C22×C4C2×C22⋊D1111yescharacteristic
289SD16—44no—
290M16—442no—
291C2×C8—22no—
292C2×C8—222no—
293C2×C8—441no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—41no—
299C4⋊C4—41no—
300C4⋊C4—221no—
301C4⋊C4—221no—
302C4⋊C4—221no—
303C4⋊C4—221no—
304C4⋊C4—444no—
305C4⋊C4—441no—
306C4⋊C4—441no—
307C4⋊C4—441no—
308C4⋊C4—441no—
309C22⋊C4—41no—
310C22⋊C4—41no—
311C42—41no—
312C42—41no—
313C42D4×D1111yescharacteristic
314C42#434111yescharacteristic
315C42C2×C22⋊D1111yescharacteristic
316C42C2×C22⋊D1111yescharacteristic
317C11#1002111yescharacteristic, complemented, Sylow
318C23—41no—
319C23#6699011yescharacteristic
320Q8—22no—
321Q8—22no—
322Q8—41no—
323Q8—41no—
324Q8—42no—
325D4—42no—
326D4—42no—
327D4—81no—
328D4—82no—
329C2×C4—22no—
330C2×C4—22no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—42no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—82no—
339C2×C4—442no—
340C2×C4—442no—
341C2×C4—442no—
342C2×C4—442no—
343C2×C4—442no—
344C2×C4—441no—
345C2×C4—441no—
346C2×C4#6699011yescharacteristic
347C2×C4#6699111yescharacteristic
348C2×C4#6699211yescharacteristic
349C2×C4#6699211yescharacteristic
350C2×C4#6699311yescharacteristic
351C2×C4#6700611yescharacteristic
352C8—42no—
353C8—442no—
354C8—881no—
355C22—21no—
356C22—21no—
357C22—81no—
358C22—81no—
359C22—81no—
360C22#1062281412yes—
361C22#1062283611yescharacteristic
362C4—21no—
363C4—21no—
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—42no—
369C4—81no—
370C4—81no—
371C4—882no—
372C4—881no—
373C4—881no—
374C2—22no—
375C2—161no—
376C2#1306963511yescharacteristic
377C2#1306967411yescharacteristic
378C2#1306968111yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3112C2
socleC22×C11#392
prime radicalC11×#532C22
hypercenter#3112D11
hypocenterC11#10021
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3112

Complements

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

NH ≅ G/Ntype
2. #13074492C2semidirect
3. #13067242C2semidirect
5. #13067063C2semidirect
6. #13066482C2semidirect
317. C11#10021semidirect

Maximal subgroups

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

subgroupindex
#130790162
#130744922
#130672422
#130671632
#130670632
#130664822
C11×#31122
#1002111