Finite Group Databasebeta

← #14651083

Subgroups — #14651083

Order 2816.

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

normal subgroups only

This group has 462 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, complemented
2#13069536C211yesmaximal, characteristic
3#13067218C211yesmaximal, characteristic, complemented
4#13067163C211yesmaximal, characteristic
5#13066482C211yesmaximal, characteristic, complemented
6#13066471C211yesmaximal, characteristic, complemented
7C11×#3234C211yesmaximal, characteristic
8C11×#532C2211yescharacteristic
9C2×C11×#125C2211yescharacteristic
10C11×#501C412yescomplemented
11C11×#490C412yescomplemented
12C11×#481—21no—
13C11×#480—21no—
14C11×#478—22no—
15C11×#432C2211yescharacteristic
16C2×#66901—21no—
17C2×#66901—21no—
18#10622598—21no—
19#10622594—21no—
20#10622594—21no—
21#10622594—21no—
22#10622594—21no—
23C4⋊C4×Dic11—21no—
24#10622550C2211yescharacteristic
25C4×C4⋊Dic11C2211yescharacteristic
26#10622539C2211yescharacteristic
27C4×#4318C2211yescharacteristic
28#10622181—22no—
29#10622175—21no—
30#10622175—21no—
31C2×C11×#41—21no—
32C11×C4⋊Q8C2×C411yescharacteristic
33C11×#127C2×C411yescharacteristic
34C11×#125—21no—
35C11×#125—21no—
36C11×#125C2×C412yes—
37C11×#125D412yes—
38C11×#124—21no—
39C11×#121—21no—
40C11×#121—21no—
41C4×D4×C11—21no—
42C4×D4×C11—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×#102—22no—
60C11×#102—22no—
61C11×C22⋊C8—21no—
62C11×#97C2×C412yes—
63#66901—42no—
64#66901—42no—
65C11⋊#95—21no—
66C11⋊#95—21no—
67C11⋊#95—21no—
68C11⋊#95—21no—
69C11⋊#95—21no—
70C11⋊#95—21no—
71C11⋊#95—21no—
72C11⋊#95D411yescharacteristic
73C11⋊#95D411yescharacteristic
74C22⋊(C11⋊C8)—21no—
75C4⋊(C11⋊C8)—21no—
76#66867—21no—
77#66867—21no—
78C4×C11⋊C8—21no—
79#9382—111nomaximal, Sylow
80C11×#41—41no—
81C11×#41—41no—
82C11×#41—41no—
83C11×#41—41no—
84C2×Q8×C11—21no—
85C2×D4×C11—21no—
86C2×D4×C11—21no—
87C2×D4×C11—21no—
88C2×D4×C11—41no—
89C22×C4×C11—21no—
90C22×C4×C11—21no—
91C22×C4×C11—41no—
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11C2×D411yescharacteristic
95C22×Dic11—21no—
96C22×Dic11—21no—
97C22×Dic11—21no—
98C22×Dic11—21no—
99C2×C8×C11—22no—
100C11×C4⋊C4—22no—
101C11×C4⋊C4—22no—
102C11×C4⋊C4—22no—
103C11×C4⋊C4—22no—
104C11×C4⋊C4—21no—
105C11×C4⋊C4—21no—
106C11×C4⋊C4—21no—
107C11×C4⋊C4—21no—
108C11×C4⋊C4C22⋊C412yes—
109C11×C4⋊C4C22⋊C412yes—
110C11×C22⋊C4—41no—
111C11×C22⋊C4—41no—
112C42×C11C22×C411yescharacteristic
113C42×C11C2×D411yescharacteristic
114C42×C11#4111yescharacteristic
115C42×C11#4111yescharacteristic
116C4⋊Dic11—42no—
117C4⋊Dic11—42no—
118C4⋊Dic11—81no—
119C4×Dic11—41no—
120C4×Dic11—41no—
121C4×Dic11—42no—
122C4×Dic11—81no—
123#4318—22no—
124#4318—41no—
125C2×C11⋊C8—41no—
126C2×C11⋊C8—41no—
127#3234D1111yescharacteristic
128#2336—111no—
129#1980—111no—
130#1528—111no—
131#1514—111no—
132#1288—111no—
133#1285—111no—
134C23×C11—41no—
135C23×C11#12011yescharacteristic
136Q8×C11—41no—
137Q8×C11—41no—
138D4×C11—42no—
139D4×C11—41no—
140D4×C11—41no—
141D4×C11—81no—
142D4×C11—81no—
143D4×C11—81no—
144C2×C4×C11—21no—
145C2×C4×C11—21no—
146C2×C4×C11—22no—
147C2×C4×C11—22no—
148C2×C4×C11—41no—
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—81no—
156C2×C4×C11—81no—
157C2×C4×C11C2×C22⋊C411yescharacteristic
158C2×C4×C11C4×D411yescharacteristic
159C2×C4×C11C4×D411yescharacteristic
160C2×C4×C11#12111yescharacteristic
161C2×C4×C11#12111yescharacteristic
162C2×C4×C11#12311yescharacteristic
163C2×Dic11—22no—
164C2×Dic11—41no—
165C2×Dic11—41no—
166C2×Dic11—41no—
167C2×Dic11—41no—
168C2×Dic11—41no—
169C2×Dic11—41no—
170C2×Dic11—41no—
171C2×Dic11—41no—
172C2×Dic11—41no—
173C2×Dic11—41no—
174C2×Dic11—41no—
175C8×C11—42no—
176C11⋊C8—42no—
177C11⋊C8—81no—
178#532C2×D1111yescharacteristic
179C2×#125C2×D1111yescharacteristic
180#501Dic1112yescomplemented
181#490Dic1112yescomplemented
182#481—21no—
183#480—21no—
184#478—22no—
185#432—111no—
186#432C2×D1111yescharacteristic
187C2×#104—221no—
188C2×#104—221no—
189C4×M16—111no—
190#389—221no—
191#387—221no—
192#387—221no—
193#387—221no—
194#387—221no—
195#383—111no—
196C4×C4⋊C4—111no—
197C4×C4⋊C4—221no—
198#330—222no—
199#327—221no—
200#327—221no—
201C22×C11—21no—
202C22×C11—21no—
203C22×C11—81no—
204C22×C11—81no—
205C22×C11—81no—
206C22×C11#38611yescharacteristic
207C22×C11#45311yescharacteristic
208C22×C11#45411yescharacteristic
209C4×C11—21no—
210C4×C11—21no—
211C4×C11—21no—
212C4×C11—21no—
213C4×C11—21no—
214C4×C11—21no—
215C4×C11—42no—
216C4×C11—42no—
217C4×C11—81no—
218Dic11—42no—
219Dic11—81no—
220Dic11—81no—
221Dic11—81no—
222C2×#41—21no—
223C2×M16—221no—
224C4⋊Q8C2×Dic1111yescharacteristic
225#127C2×Dic1111yescharacteristic
226#125—21no—
227#125—21no—
228#125C2×Dic1112yes—
229#125C22⋊D1112yes—
230#124—21no—
231#121—21no—
232#121—21no—
233C4×D4—21no—
234C4×D4—21no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—221no—
238C2×C4⋊C4—221no—
239C2×C4⋊C4—221no—
240C2×C4⋊C4C22⋊D1111yescharacteristic
241C2×C4⋊C4C22⋊D1111yescharacteristic
242C2×C42—111no—
243C2×C42—111no—
244C2×C42—221no—
245C2×C42—221no—
246C2×C42C22×D1111yescharacteristic
247#107—22no—
248#106—22no—
249C4⋊C8—21no—
250C4⋊C8—221no—
251#104—442no—
252#104—442no—
253#102—22no—
254#102—22no—
255C22⋊C8—21no—
256C22⋊C8—221no—
257#97—221no—
258#97—221no—
259#97C2×Dic1112yes—
260C4×C8—221no—
261#95—111no—
262#95—111no—
263#95—221no—
264#95—221no—
265#95—221no—
266#95—221no—
267#95—221no—
268#95—221no—
269#95—221no—
270C2×C11—21no—
271C2×C11—21no—
272C2×C11—161no—
273C2×C11#188311yescharacteristic
274C2×C11#190611yescharacteristic
275C2×C11#191211yescharacteristic
276#41—41no—
277#41—41no—
278#41—41no—
279#41—41no—
280C2×Q8—21no—
281C2×D4—21no—
282C2×D4—21no—
283C2×D4—21no—
284C2×D4—41no—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—41no—
288C22×C4—221no—
289C22×C4—221no—
290C22×C4—221no—
291C22×C4—221no—
292C22×C4D4×D1111yescharacteristic
293C22×C4D4×D1111yescharacteristic
294C22×C4C2×C22⋊D1111yescharacteristic
295M16—222no—
296M16—441no—
297C2×C8—22no—
298C2×C8—441no—
299C2×C8—441no—
300C4⋊C4—22no—
301C4⋊C4—22no—
302C4⋊C4—21no—
303C4⋊C4—21no—
304C4⋊C4—22no—
305C4⋊C4—22no—
306C4⋊C4—21no—
307C4⋊C4—21no—
308C4⋊C4—442no—
309C4⋊C4—442no—
310C4⋊C4—881no—
311C4⋊C4C22⋊Dic1112yes—
312C4⋊C4C22⋊Dic1112yes—
313C22⋊C4—41no—
314C22⋊C4—41no—
315C42—441no—
316C42—441no—
317C42—442no—
318C42—881no—
319C42#434111yescharacteristic
320C42#434111yescharacteristic
321C42C22×Dic1111yescharacteristic
322C42C2×C22⋊D1111yescharacteristic
323C11#938211yescharacteristic, complemented, Sylow
324C23—41no—
325C23#6699011yescharacteristic
326Q8—41no—
327Q8—41no—
328D4—42no—
329D4—41no—
330D4—41no—
331D4—81no—
332D4—81no—
333D4—81no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—22no—
337C2×C4—22no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—81no—
346C2×C4—81no—
347C2×C4—222no—
348C2×C4—441no—
349C2×C4—441no—
350C2×C4—441no—
351C2×C4—441no—
352C2×C4—441no—
353C2×C4—441no—
354C2×C4—441no—
355C2×C4—441no—
356C2×C4—441no—
357C2×C4—441no—
358C2×C4—441no—
359C2×C4D4×Dic1111yescharacteristic
360C2×C4D4×Dic1111yescharacteristic
361C2×C4#6698811yescharacteristic
362C2×C4#6699211yescharacteristic
363C2×C4#6699211yescharacteristic
364C2×C4C2×C22⋊Dic1111yescharacteristic
365C8—42no—
366C8—442no—
367C8—881no—
368C22—21no—
369C22—21no—
370C22—81no—
371C22—81no—
372C22—81no—
373C22#1062281111yescharacteristic
374C22#1062281411yescharacteristic
375C22#1062283311yescharacteristic
376C4—21no—
377C4—21no—
378C4—21no—
379C4—21no—
380C4—21no—
381C4—21no—
382C4—42no—
383C4—42no—
384C4—81no—
385C4—442no—
386C4—881no—
387C4—881no—
388C4—881no—
389C2—21no—
390C2—21no—
391C2—161no—
392C2#1306899411yescharacteristic
393C2#1306911911yescharacteristic
394C2#1306915411yescharacteristic
subgroupG/H
centerC22#10622833
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#3234C2
socleC22×C11#386
prime radicalC11×#532C22
cosocleC2×C42×C11C23
hypercenter#3234D11
hypocenterC11#9382
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3234

Complements

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

NH ≅ G/Ntype
1. #13071422C2semidirect
3. #13067218C2semidirect
5. #13066482C2semidirect
6. #13066471C2semidirect
10. C11×#501C4semidirect
11. C11×#490C4semidirect
180. #501Dic11semidirect
181. #490Dic11semidirect
323. C11#9382semidirect

Maximal subgroups

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

subgroupindex
#130714222
#130695362
#130672182
#130671632
#130664822
#130664712
C11×#32342
#938211