Finite Group Databasebeta

← #14655178

Subgroups — #14655178

Order 2816.

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

normal subgroups only

This group has 542 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#13079822C211yesmaximal, characteristic, complemented
2#13078990C211yesmaximal, characteristic
3#13067330C211yesmaximal, characteristic
4#13067218C211yesmaximal, characteristic, complemented
5#13067127C211yesmaximal, characteristic, complemented
6#13066509C211yesmaximal, characteristic, complemented
7C11×#2641C211yesmaximal, characteristic
8C2×C11×#127C2211yescharacteristic
9C2×C11×#125C2211yescharacteristic
10#10623001C2211yescharacteristic
11C11×#394—22no—
12C11×#394—22no—
13C11×#390—21no—
14C11×#390—21no—
15C11×#376C2211yescharacteristic
16#10622828—22no—
17#10622684—22no—
18#10622683—21no—
19#10622683—21no—
20#10622682—21no—
21#10622678—21no—
22#10622676—22no—
23#10622584—21no—
24#10622583—21no—
25#10622539C2211yescharacteristic
26#10622539C2211yescharacteristic
27C4×#4318C2211yescharacteristic
28#10622182—22no—
29#10622181—22no—
30#10622090—22no—
31C22×D4×C11—21no—
32C22×D4×C11—21no—
33C22×D4×C11D412yes—
34C11×#127—21no—
35C11×#127—21no—
36C11×#127—21no—
37C11×#127—21no—
38C11×#125—21no—
39C11×#125—21no—
40C11×#125—21no—
41C11×#125—21no—
42C2×C11×C4⋊C4—21no—
43C2×C11×C4⋊C4—21no—
44C2×C11×C4⋊C4D411yescharacteristic
45C2×C11×C4⋊C4D411yescharacteristic
46C2×C11×C22⋊C4—24no—
47C2×C11×C22⋊C4—24no—
48C2×C42×C11—21no—
49C2×C42×C11C2311yescharacteristic
50#66979—21no—
51#66977—21no—
52#66977—21no—
53C2×#4318—21no—
54#66923—21no—
55#66922D411yescharacteristic
56#66922D411yescharacteristic
57C4×Dic22—21no—
58C4×Dic22—21no—
59C11×#95—21no—
60C11×#95D412yes—
61#66896—24no—
62#66896—24no—
63C22⋊(C11⋊C8)—21no—
64C22⋊(C11⋊C8)—21no—
65#66874—22no—
66#66874—22no—
67#66872—22no—
68#66871—22no—
69C4⋊(C11⋊C8)—21no—
70C4⋊(C11⋊C8)D412yes—
71#66867—21no—
72#66867—21no—
73#66867D412yes—
74C4×C11⋊C8—21no—
75#10097—111nomaximal, Sylow
76C24×C11—22no—
77C2×D4×C11—22no—
78C2×D4×C11—22no—
79C2×D4×C11—44no—
80C2×D4×C11—44no—
81C2×D4×C11—41no—
82C2×D4×C11—41no—
83C2×D4×C11—41no—
84C2×D4×C11—41no—
85C2×D4×C11—82no—
86C22×C4×C11—22no—
87C22×C4×C11—21no—
88C22×C4×C11—21no—
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11C2×D411yescharacteristic
92C2×Dic22—21no—
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×C22⋊C4—84no—
103C11×C22⋊C4—84no—
104C42×C11—42no—
105C42×C11C2×D411yescharacteristic
106C42×C11C2×D411yescharacteristic
107C42×C11C2×D411yescharacteristic
108C42×C11#4111yescharacteristic
109C22⋊Dic11—41no—
110C4⋊Dic11—21no—
111C4⋊Dic11—21no—
112C4⋊Dic11—21no—
113C4⋊Dic11—21no—
114Dic11⋊C4—41no—
115Dic11⋊C4—41no—
116C4×Dic11—41no—
117#4318—42no—
118C2×C11⋊C8—22no—
119C2×C11⋊C8—22no—
120C2×C11⋊C8—41no—
121#3236—111no—
122#3138—111no—
123#2641D1111yescharacteristic
124#1555—111no—
125#1528—111no—
126#1506—111no—
127#1300—111no—
128C23×C11—44no—
129C23×C11—44no—
130C23×C11—42no—
131C23×C11—44no—
132C23×C11#12011yescharacteristic
133D4×C11—44no—
134D4×C11—82no—
135D4×C11—82no—
136D4×C11—82no—
137D4×C11—82no—
138D4×C11—82no—
139C2×C4×C11—22no—
140C2×C4×C11—22no—
141C2×C4×C11—41no—
142C2×C4×C11—42no—
143C2×C4×C11—42no—
144C2×C4×C11—42no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11—42no—
148C2×C4×C11—42no—
149C2×C4×C11#12011yescharacteristic
150C2×C4×C11#12011yescharacteristic
151C2×C4×C11#12111yescharacteristic
152C2×C4×C11#12111yescharacteristic
153C2×C4×C11#12111yescharacteristic
154C2×C4×C11#12711yescharacteristic
155C2×Dic11—41no—
156C2×Dic11—41no—
157Dic22—42no—
158Dic22—81no—
159C11⋊C8—42no—
160C11⋊C8—42no—
161C11⋊C8—81no—
162#533—111no—
163C2×#127C2×D1111yescharacteristic
164C2×#125C2×D1111yescharacteristic
165#501—221no—
166#491—221no—
167#490—222no—
168#486—221no—
169#486—221no—
170#484—221no—
171#483—221no—
172#479—222no—
173#432—111no—
174#432—111no—
175#418—222no—
176C4×M16—111no—
177#394—22no—
178#394—22no—
179#390—21no—
180#390—21no—
181#376C2×D1111yescharacteristic
182#331—222no—
183#330—222no—
184#328—222no—
185C22×C11—21no—
186C22×C11—21no—
187C22×C11—88no—
188C22×C11—82no—
189C22×C11—82no—
190C22×C11—82no—
191C22×C11#39211yescharacteristic
192C22×C11#45512yes—
193C4×C11—21no—
194C4×C11—21no—
195C4×C11—21no—
196C4×C11—21no—
197C4×C11—21no—
198C4×C11—82no—
199C4×C11—81no—
200C4×C11—81no—
201C4×C11#45412yes—
202Dic11—81no—
203Dic11—81no—
204C22×D4—21no—
205C22×D4—21no—
206C22×D4C22⋊D1112yes—
207C2×M16—221no—
208C4⋊Q8—111no—
209C4⋊Q8—111no—
210#127—21no—
211#127—21no—
212#127—21no—
213#127—21no—
214#125—21no—
215#125—21no—
216#125—21no—
217#125—21no—
218#125—221no—
219C22⋊Q8—221no—
220C22⋊Q8—221no—
221C4×Q8—221no—
222C4×Q8—221no—
223#117—221no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4C22⋊D1111yescharacteristic
227C2×C4⋊C4C22⋊D1111yescharacteristic
228C2×C22⋊C4—24no—
229C2×C22⋊C4—24no—
230C2×C42—21no—
231C2×C42C22×D1111yescharacteristic
232#107—222no—
233#106—222no—
234C4⋊C8—112no—
235C4⋊C8—221no—
236#103—222no—
237#103—222no—
238#102—224no—
239#102—224no—
240C22⋊C8—221no—
241C22⋊C8—221no—
242#97—112no—
243#97—221no—
244#97—221no—
245C4×C8—221no—
246#95—21no—
247#95C22⋊D1112yes—
248C2×C11—22no—
249C2×C11—162no—
250C2×C11#200311yescharacteristic
251C2×C11#200411yescharacteristic
252C2×C11#200811yescharacteristic
253C24—22no—
254C2×Q8—221no—
255C2×Q8—221no—
256C2×D4—22no—
257C2×D4—22no—
258C2×D4—44no—
259C2×D4—44no—
260C2×D4—41no—
261C2×D4—41no—
262C2×D4—41no—
263C2×D4—41no—
264C2×D4—82no—
265C22×C4—22no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4C2×C22⋊D1111yescharacteristic
269C22×C4C2×C22⋊D1111yescharacteristic
270C22×C4C2×C22⋊D1111yescharacteristic
271M16—442no—
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—221no—
284C4⋊C4—221no—
285C4⋊C4—221no—
286C4⋊C4—221no—
287C4⋊C4—441no—
288C4⋊C4—441no—
289C22⋊C4—84no—
290C22⋊C4—84no—
291C22⋊C4—441no—
292C42—42no—
293C42—441no—
294C42D4×D1111yescharacteristic
295C42D4×D1111yescharacteristic
296C42D4×D1111yescharacteristic
297C42#434111yescharacteristic
298C11#1009711yescharacteristic, complemented, Sylow
299C23—44no—
300C23—44no—
301C23—42no—
302C23—44no—
303C23#6700611yescharacteristic
304Q8—442no—
305Q8—881no—
306D4—44no—
307D4—82no—
308D4—82no—
309D4—82no—
310D4—82no—
311D4—82no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—41no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—441no—
323C2×C4—441no—
324C2×C4#6699011yescharacteristic
325C2×C4#6699011yescharacteristic
326C2×C4#6699111yescharacteristic
327C2×C4#6699211yescharacteristic
328C2×C4#6699211yescharacteristic
329C2×C4#6699311yescharacteristic
330C8—442no—
331C8—442no—
332C8—881no—
333C22—21no—
334C22—21no—
335C22—88no—
336C22—82no—
337C22—82no—
338C22—82no—
339C22#1062283611yescharacteristic
340C22#1062285512yes—
341C4—21no—
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—82no—
347C4—81no—
348C4—81no—
349C4—881no—
350C4—881no—
351C4#1062267512yes—
352C2—22no—
353C2—162no—
354C2#1306963811yescharacteristic
355C2#1306964311yescharacteristic
356C2#1306966911yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#2641C2
socleC22×C11#392
prime radicalC2×C11×#127C22
hypercenter#2641D11
hypocenterC11#10097
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2641

Complements

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

NH ≅ G/Ntype
1. #13079822C2semidirect
4. #13067218C2semidirect
5. #13067127C2semidirect
6. #13066509C2semidirect
298. C11#10097semidirect

Maximal subgroups

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

subgroupindex
#130798222
#130789902
#130673302
#130672182
#130671272
#130665092
C11×#26412
#1009711