Finite Group Databasebeta

← #14655892

Subgroups — #14655892

Order 2816.

486 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 105 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#13079561C211yesmaximal, characteristic
2#13079163C211yesmaximal, characteristic
3#13069563C211yesmaximal, characteristic
4#13069561C211yesmaximal, characteristic
5#13067115C211yesmaximal, characteristic
6#13066466C211yesmaximal, characteristic
7C11×#3249C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9C11×#533C2211yescharacteristic
10C2×#66922C2211yescharacteristic
11C11×#477—21no—
12C11×#477—21no—
13C11×#467—22no—
14C11×#462—21no—
15C11×#462—21no—
16C2×C11×C4⋊C8C2211yescharacteristic
17#10622706—21no—
18#10622705—21no—
19#10622692—21no—
20#10622691—21no—
21#10622678—22no—
22#10622663—22no—
23#10622644—22no—
24#10622608—22no—
25C4×C4⋊Dic11C2211yescharacteristic
26#10622538C2211yescharacteristic
27C4×#4318C2211yescharacteristic
28#10622189—22no—
29#10622176—22no—
30#10622170—22no—
31C22×Dic22—21no—
32C2×C11×Q16—22no—
33C22×C8×C11D412yes—
34C11×C4⋊Q8D411yescharacteristic
35C11×C4⋊Q8D411yescharacteristic
36C11×C4⋊Q8D411yescharacteristic
37C11×C4⋊Q8D411yescharacteristic
38C11×#125—21no—
39C11×#125—21no—
40C11×C22⋊Q8—21no—
41C11×C22⋊Q8—21no—
42C11×C22⋊Q8—21no—
43C11×C22⋊Q8—21no—
44C4×Q8×C11—21no—
45C4×Q8×C11—21no—
46C4×Q8×C11—21no—
47C4×Q8×C11—21no—
48C11×#117—21no—
49C11×#117—21no—
50C2×C42×C11C2311yescharacteristic
51C2×#4326—24no—
52C2×C4⋊Dic11—21no—
53C2×C4⋊Dic11—21no—
54C2×C4⋊Dic11—21no—
55C2×C4×Dic11—21no—
56C2×#4318D412yes—
57#66922—21no—
58#66922—21no—
59#66922—21no—
60#66922D412yes—
61C11×#107—22no—
62C11×C4⋊C8—21no—
63C11×C4⋊C8—21no—
64C11×#103—22no—
65C11×#103—22no—
66C11⋊#95—21no—
67C22⋊(C11⋊C8)D412yes—
68#66874—24no—
69#66872—24no—
70#66871—24no—
71C4⋊(C11⋊C8)—21no—
72#66867—21no—
73C4×C11⋊C8—21no—
74C4×C11⋊C8—21no—
75#10199—111nomaximal, Sylow
76C2×Q8×C11—21no—
77C2×Q8×C11—21no—
78C2×Q8×C11—21no—
79C2×Q8×C11—21no—
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11C2×D411yescharacteristic
83C22×Dic11—41no—
84C22×Dic11—41no—
85C2×Dic22—22no—
86C2×Dic22—41no—
87C2×Dic22—82no—
88C11×Q16—82no—
89C2×C8×C11—22no—
90C2×C8×C11—42no—
91C11×C4⋊C4—21no—
92C11×C4⋊C4—21no—
93C11×C4⋊C4—21no—
94C11×C4⋊C4—21no—
95C11×C4⋊C4—21no—
96C11×C4⋊C4—21no—
97C11×C4⋊C4—21no—
98C11×C4⋊C4—21no—
99C11×C4⋊C4—41no—
100C11×C4⋊C4—41no—
101C11×C4⋊C4—41no—
102C11×C4⋊C4—41no—
103C11×C22⋊C4—41no—
104C11×C22⋊C4—41no—
105C42×C11—41no—
106C42×C11—41no—
107C42×C11C2×D411yescharacteristic
108C42×C11C2×D411yescharacteristic
109C42×C11C2×D411yescharacteristic
110C42×C11#4111yescharacteristic
111#4326—84no—
112C4⋊Dic11—22no—
113C4⋊Dic11—22no—
114C4⋊Dic11—22no—
115C4⋊Dic11—41no—
116C4⋊Dic11—41no—
117C4⋊Dic11—41no—
118C4×Dic11—42no—
119#4318—22no—
120#4318Q1614yescomplemented
121C2×C11⋊C8—22no—
122C2×C11⋊C8—22no—
123#3249D1111yescharacteristic
124#3209—111no—
125#3165—111no—
126#1987—111no—
127#1986—111no—
128#1503—111no—
129#1283—111no—
130C23×C11#12711yescharacteristic
131Q8×C11—42no—
132Q8×C11—41no—
133Q8×C11—41no—
134Q8×C11—41no—
135Q8×C11—41no—
136Q8×C11—81no—
137C2×C4×C11—21no—
138C2×C4×C11—21no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11#12011yescharacteristic
145C2×C4×C11#12011yescharacteristic
146C2×C4×C11#12011yescharacteristic
147C2×C4×C11#12111yescharacteristic
148C2×C4×C11#12111yescharacteristic
149C2×C4×C11#12111yescharacteristic
150C2×C4×C11C2×Q1612yes—
151C2×C4×C11#13712yes—
152C2×Dic11—42no—
153C2×Dic11—42no—
154C2×Dic11—82no—
155C2×Dic11—81no—
156C2×Dic11—81no—
157Dic22—44no—
158Dic22—82no—
159C8×C11—42no—
160C11⋊C8—24no—
161C11⋊C8—42no—
162#533C2×D1111yescharacteristic
163#533C2×D1111yescharacteristic
164C2×C4⋊Q8—111no—
165#501—222no—
166#500—221no—
167#498—221no—
168#494—221no—
169#487—221no—
170#477—21no—
171#477—21no—
172#467—22no—
173#462—21no—
174#462—21no—
175#462—222no—
176#451—222no—
177#431—111no—
178#428—222no—
179C2×C4⋊C8C2×D1111yescharacteristic
180C4×M16—111no—
181C4×C4⋊C4—111no—
182#340—222no—
183#339—222no—
184#328—222no—
185C22×C11—21no—
186C22×C11—21no—
187C22×C11#39211yescharacteristic
188C22×C11#49411yescharacteristic
189C22×C11#49711yescharacteristic
190C4×C11—21no—
191C4×C11—21no—
192C4×C11—21no—
193C4×C11—81no—
194C4×C11—81no—
195C4×C11—81no—
196C4×C11—81no—
197C4×C11#45112yes—
198C4×C11#45511yescharacteristic
199C4×C11#45611yescharacteristic
200C4×C11#46212yes—
201Dic11—82no—
202Dic11—82no—
203C22×Q8—221no—
204C2×Q16—22no—
205C2×Q16—224no—
206C2×M16—112no—
207C22×C8C22⋊D1112yes—
208C4⋊Q8—112no—
209C4⋊Q8—221no—
210C4⋊Q8—221no—
211C4⋊Q8—221no—
212C4⋊Q8C22⋊D1111yescharacteristic
213C4⋊Q8C22⋊D1111yescharacteristic
214C4⋊Q8C22⋊D1111yescharacteristic
215C4⋊Q8C22⋊D1111yescharacteristic
216#125—21no—
217#125—21no—
218C22⋊Q8—21no—
219C22⋊Q8—21no—
220C22⋊Q8—21no—
221C22⋊Q8—21no—
222C4×Q8—21no—
223C4×Q8—21no—
224C4×Q8—21no—
225C4×Q8—21no—
226#117—21no—
227#117—21no—
228C2×C4⋊C4—221no—
229C2×C4⋊C4—221no—
230C2×C4⋊C4—221no—
231C2×C42—221no—
232C2×C42C22×D1111yescharacteristic
233#107—22no—
234#107—224no—
235#106—224no—
236C4⋊C8—21no—
237C4⋊C8—21no—
238C4⋊C8—221no—
239#103—22no—
240#103—22no—
241#103—224no—
242C22⋊C8—112no—
243#97—221no—
244C4×C8—221no—
245C4×C8—221no—
246#95—221no—
247C2×C11—21no—
248C2×C11—21no—
249C2×C11#200711yescharacteristic
250C2×C11#200811yescharacteristic
251C2×C11#201611yescharacteristic
252C2×Q8—21no—
253C2×Q8—21no—
254C2×Q8—21no—
255C2×Q8—21no—
256C2×Q8—222no—
257C2×Q8—441no—
258C2×Q8—882no—
259C22×C4—441no—
260C22×C4—441no—
261C22×C4D4×D1111yescharacteristic
262C22×C4D4×D1111yescharacteristic
263C22×C4C2×C22⋊D1111yescharacteristic
264Q16—82no—
265Q16—884no—
266M16—114no—
267M16—222no—
268C2×C8—22no—
269C2×C8—42no—
270C2×C8—222no—
271C2×C8—222no—
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—21no—
278C4⋊C4—21no—
279C4⋊C4—21no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—222no—
285C4⋊C4—222no—
286C4⋊C4—222no—
287C4⋊C4—441no—
288C4⋊C4—441no—
289C4⋊C4—441no—
290C22⋊C4—41no—
291C22⋊C4—41no—
292C42—41no—
293C42—41no—
294C42—442no—
295C42D4×D1111yescharacteristic
296C42#434111yescharacteristic
297C42C2×C22⋊D1111yescharacteristic
298C42C2×C22⋊D1111yescharacteristic
299C11#1019911yescharacteristic, complemented, Sylow
300C23#6699311yescharacteristic
301Q8—42no—
302Q8—41no—
303Q8—41no—
304Q8—41no—
305Q8—41no—
306Q8—81no—
307Q8—444no—
308Q8—882no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—442no—
317C2×C4—442no—
318C2×C4—882no—
319C2×C4—881no—
320C2×C4—881no—
321C2×C4Q16×D1112yes—
322C2×C4#6697112yes—
323C2×C4#6699011yescharacteristic
324C2×C4#6699011yescharacteristic
325C2×C4#6699111yescharacteristic
326C2×C4#6699211yescharacteristic
327C2×C4#6699211yescharacteristic
328C2×C4#6700611yescharacteristic
329C8—42no—
330C8—224no—
331C8—442no—
332C22—21no—
333C22—21no—
334C22#1062279411yescharacteristic
335C22#1062280311yescharacteristic
336C22#1062283611yescharacteristic
337C4—21no—
338C4—21no—
339C4—21no—
340C4—81no—
341C4—81no—
342C4—81no—
343C4—81no—
344C4—882no—
345C4—882no—
346C4#1062279512yes—
347C4#1062279912yes—
348C4#1062285511yescharacteristic
349C4#1062285911yescharacteristic
350C2—21no—
351C2—21no—
352C2#1306966311yescharacteristic
353C2#1306966611yescharacteristic
354C2#1306971411yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3249C2
socleC22×C11#392
prime radicalC23×C11#127
hypercenter#3249D11
hypocenterC11#10199
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3249

Complements

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

NH ≅ G/Ntype
120. #4318Q16semidirect
299. C11#10199semidirect

Maximal subgroups

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

subgroupindex
#130795612
#130791632
#130695632
#130695612
#130671152
#130664662
C11×#32492
#1019911