Finite Group Databasebeta

← #14655136

Subgroups — #14655136

Order 2816.

560 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 560 conjugacy classes of subgroups — too many to draw. Only its 85 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#13079806C211yesmaximal, characteristic
2#13079073C211yesmaximal, characteristic
3#13067342C211yesmaximal, characteristic, complemented
4#13067218C211yesmaximal, characteristic, complemented
5#13067123C211yesmaximal, characteristic
6#13066509C211yesmaximal, characteristic, complemented
7C11×#2660C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×C11×#125C2211yescharacteristic
10C2×#66995—22no—
11#10623008C2211yescharacteristic
12C11×#398—22no—
13C11×#395—22no—
14C11×#384—21no—
15C11×#382—21no—
16C11×#376C2211yescharacteristic
17#10622705—21no—
18#10622699—22no—
19#10622698—21no—
20#10622680—21no—
21#10622679—22no—
22#10622678—21no—
23#10622581—21no—
24#10622580—21no—
25#10622539C2211yescharacteristic
26#10622539C2211yescharacteristic
27C4×#4318C2211yescharacteristic
28#10622184—22no—
29#10622181—22no—
30#10622089—22no—
31C22×Q8×C11D412yes—
32C2×#4339—21no—
33C11×C4⋊Q8—21no—
34C11×C4⋊Q8—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×#125—21no—
38C11×#125—21no—
39C11×#125—21no—
40C11×#125—21no—
41C2×C11×C4⋊C4—21no—
42C2×C11×C4⋊C4—21no—
43C2×C11×C4⋊C4—21no—
44C2×C11×C4⋊C4—21no—
45C2×C11×C4⋊C4—24no—
46C2×C11×C4⋊C4D411yescharacteristic
47C2×C11×C4⋊C4D411yescharacteristic
48C2×C42×C11—21no—
49C2×C42×C11C2311yescharacteristic
50C2×#4326—24no—
51#66995—48no—
52C2×#4325—24no—
53#66983—21no—
54#66983—21no—
55C2×#4318—21no—
56#66928—21no—
57#66927D411yescharacteristic
58C4×D44—21no—
59C4×D44—21no—
60#66922D411yescharacteristic
61C11×#95—24no—
62C11×#95—21no—
63C11×#95D412yes—
64C22⋊(C11⋊C8)—21no—
65C22⋊(C11⋊C8)—21no—
66#66873—22no—
67#66873—22no—
68#66872—22no—
69#66871—22no—
70C4⋊(C11⋊C8)—21no—
71C4⋊(C11⋊C8)D412yes—
72#66867—21no—
73#66867—21no—
74#66867D412yes—
75C4×C11⋊C8—21no—
76#10091—111nomaximal, Sylow
77C2×Q8×C11—22no—
78C2×Q8×C11—22no—
79C2×Q8×C11—44no—
80C22×C4×C11—22no—
81C22×C4×C11—21no—
82C22×C4×C11—22no—
83C22×C4×C11—21no—
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11C2×D411yescharacteristic
87C2×C22⋊D11—41no—
88#4339—44no—
89C2×D44—21no—
90C2×D44—21no—
91C2×D44—21no—
92C2×C4×D11—41no—
93C2×Dic22—21no—
94C11×C4⋊C4—21no—
95C11×C4⋊C4—21no—
96C11×C4⋊C4—21no—
97C11×C4⋊C4—21no—
98C11×C4⋊C4—41no—
99C11×C4⋊C4—41no—
100C11×C4⋊C4—41no—
101C11×C4⋊C4—41no—
102C11×C4⋊C4—41no—
103C11×C4⋊C4—41no—
104C11×C4⋊C4—41no—
105C11×C4⋊C4—41no—
106C11×C4⋊C4—84no—
107C42×C11—24no—
108C42×C11C2×D411yescharacteristic
109C42×C11C2×D411yescharacteristic
110C42×C11C2×D411yescharacteristic
111C42×C11#4111yescharacteristic
112#4326—48no—
113#4325—48no—
114(C2×D11)⋊C4—41no—
115(C2×D11)⋊C4—41no—
116C4⋊Dic11—21no—
117C4⋊Dic11—21no—
118#4318—24no—
119C2×C11⋊C8—22no—
120C2×C11⋊C8—22no—
121C2×C11⋊C8—41no—
122#3234—111no—
123#3152—111no—
124#2660D1111yescharacteristic, complemented
125#1558—111no—
126#1528—111no—
127#1505—111no—
128#1300—111no—
129C23×C11#12011yescharacteristic
130C22×D11—41no—
131Q8×C11—44no—
132Q8×C11—82no—
133C2×C4×C11—22no—
134C2×C4×C11—22no—
135C2×C4×C11—24no—
136C2×C4×C11—41no—
137C2×C4×C11—42no—
138C2×C4×C11—42no—
139C2×C4×C11—42no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—42no—
143C2×C4×C11—42no—
144C2×C4×C11—44no—
145C2×C4×C11#12011yescharacteristic
146C2×C4×C11#12011yescharacteristic
147C2×C4×C11#12111yescharacteristic
148C2×C4×C11#12111yescharacteristic
149C2×C4×C11#12111yescharacteristic
150C2×C4×C11#12711yescharacteristic
151C22⋊D11—82no—
152C2×Dic11—41no—
153D44—42no—
154D44—42no—
155D44—81no—
156C4×D11—82no—
157Dic22—42no—
158C11⋊C8—24no—
159C11⋊C8—42no—
160C11⋊C8—81no—
161C2×#137—222no—
162#532—111no—
163C2×C4⋊Q8C2×D1111yescharacteristic
164C2×#125C2×D1111yescharacteristic
165#501—221no—
166#497—222no—
167#494—221no—
168#492—221no—
169#490—221no—
170#481—221no—
171#480—221no—
172#478—222no—
173#432—111no—
174#432—111no—
175C4×M16—111no—
176#398—22no—
177#395—22no—
178#384—21no—
179#382—21no—
180#376C2×D1111yescharacteristic
181#333—222no—
182#330—222no—
183#327—222no—
184C22×C11—21no—
185C22×C11—21no—
186C22×C11#39211yescharacteristic
187C22×C11#45312yes—
188C2×D11—81no—
189C2×D11—81no—
190C2×D11—81no—
191C4×C11—21no—
192C4×C11—21no—
193C4×C11—21no—
194C4×C11—21no—
195C4×C11—21no—
196C4×C11—44no—
197C4×C11—81no—
198C4×C11—82no—
199C4×C11—81no—
200C4×C11#45612yes—
201Dic11—81no—
202C2×#41—221no—
203C22×Q8C22⋊D1112yes—
204#137—448no—
205C2×Q16—224no—
206C2×SD16—224no—
207C2×M16—221no—
208C4⋊Q8—21no—
209C4⋊Q8—21no—
210C4⋊Q8—21no—
211C4⋊Q8—21no—
212C4⋊Q8—111no—
213#127—111no—
214#125—21no—
215#125—21no—
216#125—21no—
217#125—21no—
218#124—221no—
219#121—221no—
220#121—221no—
221C4×D4—221no—
222C4×D4—221no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—24no—
228C2×C4⋊C4C22⋊D1111yescharacteristic
229C2×C4⋊C4C22⋊D1111yescharacteristic
230C2×C42—21no—
231C2×C42C22×D1111yescharacteristic
232#107—222no—
233#106—222no—
234C4⋊C8—112no—
235C4⋊C8—221no—
236#102—222no—
237#102—222no—
238C22⋊C8—221no—
239C22⋊C8—221no—
240#97—112no—
241#97—221no—
242#97—221no—
243C4×C8—221no—
244#95—24no—
245#95—21no—
246#95C22⋊D1112yes—
247C2×C11—22no—
248C2×C11#200211yescharacteristic
249C2×C11#200511yescharacteristic
250C2×C11#200911yescharacteristic
251D11—161no—
252#41—444no—
253C2×Q8—22no—
254C2×Q8—22no—
255C2×Q8—44no—
256C2×Q8—221no—
257C2×D4—221no—
258C2×D4—221no—
259C2×D4—221no—
260C2×D4—441no—
261C22×C4—22no—
262C22×C4—21no—
263C22×C4—22no—
264C22×C4—21no—
265C22×C4—441no—
266C22×C4C2×C22⋊D1111yescharacteristic
267C22×C4C2×C22⋊D1111yescharacteristic
268C22×C4C2×C22⋊D1111yescharacteristic
269Q16—448no—
270SD16—448no—
271M16—224no—
272C2×C8—222no—
273C2×C8—222no—
274C2×C8—441no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—21no—
278C4⋊C4—21no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—41no—
286C4⋊C4—41no—
287C4⋊C4—84no—
288C4⋊C4—221no—
289C4⋊C4—221no—
290C22⋊C4—441no—
291C22⋊C4—441no—
292C42—24no—
293C42D4×D1111yescharacteristic
294C42D4×D1111yescharacteristic
295C42D4×D1111yescharacteristic
296C42#434111yescharacteristic
297C11#1009111yescharacteristic, complemented, Sylow
298C23—441no—
299C23#6700611yescharacteristic
300Q8—44no—
301Q8—82no—
302Q8—442no—
303D4—442no—
304D4—442no—
305D4—881no—
306D4—882no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—24no—
310C2×C4—41no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4—44no—
319C2×C4—441no—
320C2×C4—882no—
321C2×C4#6699011yescharacteristic
322C2×C4#6699011yescharacteristic
323C2×C4#6699111yescharacteristic
324C2×C4#6699211yescharacteristic
325C2×C4#6699211yescharacteristic
326C2×C4#6699311yescharacteristic
327C8—224no—
328C8—442no—
329C8—881no—
330C22—21no—
331C22—21no—
332C22—881no—
333C22—881no—
334C22—881no—
335C22#1062283611yescharacteristic
336C22#1062285412yes—
337C4—21no—
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—44no—
343C4—82no—
344C4—81no—
345C4—81no—
346C4—881no—
347C4#1062270812yes—
348C2—22no—
349C2—1761no—
350C2#1306962911yescharacteristic
351C2#1306965211yescharacteristic
352C2#1306967611yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#2660C2
socleC22×C11#392
prime radical#10623008C22
hypercenter#2660D11
hypocenterC11#10091
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2660

Complements

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

NH ≅ G/Ntype
3. #13067342C2semidirect
4. #13067218C2semidirect
6. #13066509C2semidirect
7. C11×#2660C2semidirect
124. #2660D11semidirect
297. C11#10091semidirect

Maximal subgroups

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

subgroupindex
#130798062
#130790732
#130673422
#130672182
#130671232
#130665092
C11×#26602
#1009111