Finite Group Databasebeta

← #14656950

Subgroups — #14656950

Order 2816.

398 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 73 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#13074259C211yesmaximal, characteristic, complemented
2#13069534C211yesmaximal, characteristic
3#13067164C211yesmaximal, characteristic
4#13067125C211yesmaximal, characteristic
5#13066508C211yesmaximal, characteristic, complemented
6#13066482C211yesmaximal, characteristic, complemented
7C11×#1285C211yesmaximal, characteristic, complemented
8#10623008C2211yescharacteristic
9C11×#432C2211yescharacteristic
10C11×#432C2211yescharacteristic
11C4×C11×C4⋊C4C2211yescharacteristic
12#10622599—21no—
13#10622592—21no—
14#10622550C2211yescharacteristic
15#10622546—21no—
16#10622545C2211yescharacteristic
17#10622542—21no—
18C2×#66869—21no—
19C2×#66869—21no—
20C4×#4318C2211yescharacteristic
21#10622267—21no—
22#10622259—21no—
23#10622108—21no—
24#10622108—21no—
25#10622108—21no—
26#10622108—21no—
27C2×#4339—21no—
28C22×Dic22—21no—
29C2×C11×C4⋊C4—21no—
30C2×C42×C11D411yescharacteristic
31C2×C42×C11D411yescharacteristic
32C2×C42×C11C2311yescharacteristic
33#66983—21no—
34#66983—21no—
35C2×C4⋊Dic11—21no—
36C2×Dic11⋊C4—21no—
37C2×Dic11⋊C4—21no—
38C2×C4×Dic11—21no—
39C2×#4318—21no—
40#66928—21no—
41#66927Q811yescharacteristic, complemented
42C4×D44—21no—
43C4×D44—21no—
44#66922Q811yescharacteristic, complemented
45C11×C4⋊C8—21no—
46C11×C4⋊C8—21no—
47C11×C22⋊C8—21no—
48C11×C22⋊C8—21no—
49C11×#97—21no—
50C11×#97—21no—
51C11×#95—21no—
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95—21no—
57C11⋊#95—21no—
58C11⋊#95—21no—
59C11⋊#95D411yescharacteristic
60C11⋊#95D411yescharacteristic
61C11⋊#95D411yescharacteristic
62C11⋊#95D411yescharacteristic
63#66869—42no—
64#66869—42no—
65#66867—21no—
66C4×C11⋊C8—21no—
67#10378—111nomaximal, Sylow
68C22×C4×C11—21no—
69C22×C4×C11—21no—
70C22×C4×C11C2×D411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C22×C4×C11C2×D411yescharacteristic
73C2×C22⋊D11—41no—
74C22×Dic11—21no—
75C22×Dic11—21no—
76C22×Dic11—21no—
77C22×Dic11—21no—
78#4339—41no—
79#4339—41no—
80#4339—41no—
81#4339—41no—
82C2×D44—21no—
83C2×D44—21no—
84C2×D44—21no—
85C2×C4×D11—41no—
86C2×Dic22—21no—
87C2×Dic22—42no—
88C2×Dic22—42no—
89C2×Dic22—81no—
90C2×C8×C11—41no—
91C2×C8×C11—41no—
92C11×C4⋊C4—42no—
93C42×C11—41no—
94C42×C11—41no—
95C42×C11C2×Q811yescharacteristic
96C42×C11#4111yescharacteristic
97C42×C11#4111yescharacteristic
98C42×C11#4111yescharacteristic
99(C2×D11)⋊C4—41no—
100(C2×D11)⋊C4—41no—
101C4⋊Dic11—21no—
102C4⋊Dic11—21no—
103C4⋊Dic11—42no—
104Dic11⋊C4—42no—
105Dic11⋊C4—81no—
106C4×Dic11—42no—
107#4318—22no—
108#4318—41no—
109C2×C11⋊C8—41no—
110#2605—111no—
111#1980—111no—
112#1514—111no—
113#1505—111no—
114#1300—111no—
115#1288—111no—
116#1285D1111yescharacteristic, complemented
117C23×C11#12011yescharacteristic
118C22×D11—41no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—22no—
122C2×C4×C11—41no—
123C2×C4×C11—41no—
124C2×C4×C11—41no—
125C2×C4×C11—41no—
126C2×C4×C11—41no—
127C2×C4×C11—41no—
128C2×C4×C11—41no—
129C2×C4×C11C22⋊Q811yescharacteristic
130C2×C4×C11C22⋊Q811yescharacteristic
131C2×C4×C11C22⋊Q811yescharacteristic
132C2×C4×C11#12411yescharacteristic
133C2×C4×C11#12411yescharacteristic
134C2×C4×C11#12411yescharacteristic
135C22⋊D11—81no—
136C22⋊D11—81no—
137C2×Dic11—22no—
138C2×Dic11—41no—
139C2×Dic11—41no—
140C2×Dic11—41no—
141C2×Dic11—41no—
142C2×Dic11—41no—
143C2×Dic11—41no—
144C2×Dic11—41no—
145C2×Dic11—41no—
146C2×Dic11—41no—
147C2×Dic11—41no—
148C2×Dic11—41no—
149C2×Dic11—41no—
150D44—41no—
151D44—41no—
152D44—81no—
153D44—81no—
154C4×D11—81no—
155C4×D11—81no—
156Dic22—41no—
157Dic22—41no—
158Dic22—84no—
159C8×C11—81no—
160C8×C11—81no—
161C11⋊C8—42no—
162#532—111no—
163#432C2×D1111yescharacteristic
164#432C2×D1111yescharacteristic
165C2×#104—221no—
166C2×#104—221no—
167C4×M16—111no—
168#400—221no—
169#395—221no—
170#391—221no—
171#391—221no—
172#387—221no—
173#387—221no—
174#383—111no—
175C4×C4⋊C4C2×D1111yescharacteristic
176#376—111no—
177#327—221no—
178#327—221no—
179#327—221no—
180#327—221no—
181C22×C11—21no—
182C22×C11—21no—
183C22×C11#39311yescharacteristic
184C22×C11#45311yescharacteristic
185C22×C11#45411yescharacteristic
186C2×D11—81no—
187C2×D11—81no—
188C2×D11—81no—
189C4×C11—21no—
190C4×C11—21no—
191C4×C11—21no—
192C4×C11—21no—
193C4×C11—21no—
194C4×C11—21no—
195C4×C11—42no—
196C4×C11—81no—
197Dic11—42no—
198Dic11—81no—
199Dic11—81no—
200Dic11—81no—
201Dic11—81no—
202C2×#41—221no—
203C22×Q8—221no—
204C2×M16—221no—
205C4⋊Q8—111no—
206#127—111no—
207#124—221no—
208#121—221no—
209#121—221no—
210C4×D4—221no—
211C4×D4—221no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—221no—
214C2×C4⋊C4—221no—
215C2×C4⋊C4—221no—
216C2×C42—221no—
217C2×C42D4411yescharacteristic
218C2×C42D4411yescharacteristic
219C2×C42C22×D1111yescharacteristic
220C4⋊C8—21no—
221C4⋊C8—21no—
222#104—442no—
223#104—442no—
224C22⋊C8—21no—
225C22⋊C8—21no—
226#97—21no—
227#97—21no—
228#97—221no—
229C4×C8—221no—
230#95—21no—
231#95—111no—
232#95—111no—
233#95—111no—
234#95—111no—
235#95—221no—
236#95—221no—
237#95—221no—
238#95—221no—
239#95—221no—
240#95—221no—
241#95—221no—
242C2×C11—21no—
243C2×C11—21no—
244C2×C11#202711yescharacteristic
245C2×C11#203111yescharacteristic
246C2×C11#203111yescharacteristic
247D11—161no—
248#41—441no—
249#41—441no—
250#41—441no—
251#41—441no—
252C2×Q8—221no—
253C2×Q8—442no—
254C2×Q8—442no—
255C2×Q8—881no—
256C2×D4—221no—
257C2×D4—221no—
258C2×D4—221no—
259C2×D4—441no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—221no—
263C22×C4—221no—
264C22×C4—221no—
265C22×C4—221no—
266C22×C4—441no—
267C22×C4C2×D4411yescharacteristic
268C22×C4D4×D1111yescharacteristic
269C22×C4D4×D1111yescharacteristic
270M16—222no—
271M16—441no—
272C2×C8—41no—
273C2×C8—41no—
274C2×C8—441no—
275C4⋊C4—42no—
276C4⋊C4—221no—
277C4⋊C4—221no—
278C4⋊C4—442no—
279C4⋊C4—442no—
280C4⋊C4—881no—
281C22⋊C4—441no—
282C22⋊C4—441no—
283C42—41no—
284C42—41no—
285C42—442no—
286C42#433911yescharacteristic
287C42#433911yescharacteristic
288C42#434111yescharacteristic
289C42Q8×D1111yescharacteristic
290C11#1037811yescharacteristic, complemented, Sylow
291C23—441no—
292C23#6693511yescharacteristic
293Q8—441no—
294Q8—441no—
295Q8—884no—
296D4—441no—
297D4—441no—
298D4—881no—
299D4—881no—
300D4—881no—
301D4—881no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—22no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—222no—
313C2×C4—441no—
314C2×C4—441no—
315C2×C4—441no—
316C2×C4—441no—
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—881no—
326C2×C4—881no—
327C2×C4#6692811yescharacteristic
328C2×C4#6693811yescharacteristic
329C2×C4#6693811yescharacteristic
330C2×C4#6694911yescharacteristic
331C2×C4#6694911yescharacteristic
332C2×C4#6695011yescharacteristic
333C8—81no—
334C8—81no—
335C8—442no—
336C22—21no—
337C22—21no—
338C22—881no—
339C22—881no—
340C22—881no—
341C22#1062228611yescharacteristic
342C22#1062236011yescharacteristic
343C22#1062236611yescharacteristic
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—21no—
350C4—42no—
351C4—81no—
352C4—442no—
353C4—881no—
354C4—881no—
355C4—881no—
356C4—881no—
357C2—21no—
358C2—21no—
359C2—1761no—
360C2#1306977311yescharacteristic
361C2#1306978711yescharacteristic
362C2#1306978911yescharacteristic
subgroupG/H
centerC22#10622286
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1285C2
socleC22×C11#393
prime radical#10623008C22
hypercenter#1285D11
hypocenterC11#10378
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1285

Complements

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

NH ≅ G/Ntype
1. #13074259C2semidirect
5. #13066508C2semidirect
6. #13066482C2semidirect
7. C11×#1285C2semidirect
41. #66927Q8semidirect
44. #66922Q8semidirect
116. #1285D11semidirect
290. C11#10378semidirect

Maximal subgroups

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

subgroupindex
#130742592
#130695342
#130671642
#130671252
#130665082
#130664822
C11×#12852
#1037811