Finite Group Databasebeta

← #14655486

Subgroups — #14655486

Order 2816.

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

normal subgroups only

This group has 472 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#13079757C211yesmaximal, characteristic, complemented
2C2×#10622668C211yesmaximal, characteristic
3#13067341C211yesmaximal, characteristic, complemented
4#13067231C211yesmaximal, characteristic, complemented
5#13066968C211yesmaximal, characteristic
6#13066514C211yesmaximal, characteristic, complemented
7C11×#3215C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9C2×C11×#124C2211yescharacteristic
10C2×#66922C2211yescharacteristic
11C11×#497—21no—
12C11×#489—21no—
13C11×#464—22no—
14C11×#451—21no—
15C11×#450—21no—
16C11×#432C2211yescharacteristic
17C2×#66899—21no—
18C2×#66896—21no—
19#10622694—21no—
20#10622692—21no—
21#10622668—22no—
22#10622668—22no—
23#10622656—22no—
24#10622633—22no—
25#10622539C2211yescharacteristic
26#10622538C2211yescharacteristic
27C2×#66867C2211yescharacteristic
28#10622181—22no—
29#10622163—22no—
30#10622119—22no—
31C22×Q8×C11D411yescharacteristic
32C22×D4×C11D411yescharacteristic
33C22×Dic22—21no—
34C2×C11×Q16—22no—
35C2×C11×SD16—22no—
36C11×C4⋊Q8D411yescharacteristic
37C11×C4⋊Q8D411yescharacteristic
38C11×#125—21no—
39C11×#124—21no—
40C11×#124—21no—
41C11×#124—21no—
42C11×#124—21no—
43C11×C22⋊Q8—21no—
44C11×C22⋊Q8—21no—
45C4×Q8×C11—21no—
46C4×Q8×C11—21no—
47C11×#117—21no—
48C2×C11×C22⋊C4—21no—
49C2×C11×C22⋊C4—21no—
50C2×C42×C11C2311yescharacteristic
51C2×C4⋊Dic11—21no—
52C2×C4⋊Dic11—21no—
53C22×C11⋊C8—21no—
54#66922—21no—
55#66922—21no—
56#66922—21no—
57#66922D412yes—
58C11×C4⋊C8D412yes—
59C11×#103—22no—
60C11×#102—22no—
61C11×C22⋊C8—21no—
62C11×#97—21no—
63#66899—24no—
64#66899—24no—
65#66896—24no—
66C22⋊(C11⋊C8)—21no—
67C22⋊(C11⋊C8)D412yes—
68#66872—24no—
69C4⋊(C11⋊C8)—21no—
70C4⋊(C11⋊C8)—21no—
71#66867—21no—
72#66867—21no—
73#66867D412yes—
74C4×C11⋊C8—21no—
75#10141—111nomaximal, Sylow
76C24×C11—21no—
77C2×Q8×C11—21no—
78C2×Q8×C11—21no—
79C2×Q8×C11—21no—
80C2×Q8×C11—21no—
81C2×Q8×C11—42no—
82C2×D4×C11—21no—
83C2×D4×C11—21no—
84C2×D4×C11—42no—
85C22×C4×C11—21no—
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11#4111yescharacteristic
89C22×Dic11—41no—
90C2×Dic22—22no—
91C2×Dic22—41no—
92C2×Dic22—82no—
93C11×Q16—82no—
94C11×SD16—82no—
95C2×C8×C11—22no—
96C11×C4⋊C4—21no—
97C11×C4⋊C4—21no—
98C11×C4⋊C4—21no—
99C11×C4⋊C4—21no—
100C11×C4⋊C4—41no—
101C11×C4⋊C4—41no—
102C11×C22⋊C4—41no—
103C11×C22⋊C4—41no—
104C11×C22⋊C4—41no—
105C11×C22⋊C4—41no—
106C11×C22⋊C4—41no—
107C42×C11—41no—
108C42×C11C2×D411yescharacteristic
109C42×C11C2×D411yescharacteristic
110C42×C11C2×D411yescharacteristic
111C42×C11C2×D411yescharacteristic
112C4⋊Dic11—22no—
113C4⋊Dic11—22no—
114C4⋊Dic11—41no—
115C4⋊Dic11—41no—
116C2×C11⋊C8—22no—
117C2×C11⋊C8—22no—
118C2×C11⋊C8—42no—
119C2×C11⋊C8—41no—
120#3229—111no—
121#3215D1111yescharacteristic
122C2×#489—111no—
123#1558—111no—
124#1531—111no—
125#1469—111no—
126#1302—111no—
127C23×C11—41no—
128C23×C11—42no—
129C23×C11—81no—
130C23×C11—81no—
131C23×C11#12111yescharacteristic
132Q8×C11—42no—
133Q8×C11—42no—
134Q8×C11—42no—
135Q8×C11—42no—
136D4×C11—42no—
137D4×C11—42no—
138C2×C4×C11—22no—
139C2×C4×C11—22no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—81no—
145C2×C4×C11#12011yescharacteristic
146C2×C4×C11#12011yescharacteristic
147C2×C4×C11#12011yescharacteristic
148C2×C4×C11#12111yescharacteristic
149C2×C4×C11#12111yescharacteristic
150C2×C4×C11#12711yescharacteristic
151C2×Dic11—42no—
152C2×Dic11—82no—
153Dic22—82no—
154Dic22—82no—
155C8×C11—42no—
156C11⋊C8—42no—
157C11⋊C8—42no—
158C11⋊C8—81no—
159#533C2×D1111yescharacteristic
160C2×C4⋊Q8—111no—
161C2×#124C2×D1111yescharacteristic
162#498—221no—
163#497—21no—
164#489—21no—
165#489—222no—
166#489—222no—
167#487—221no—
168#483—222no—
169#475—222no—
170#464—22no—
171#451—21no—
172#450—21no—
173#432—111no—
174#432C2×D1111yescharacteristic
175#431—111no—
176C2×#103—221no—
177C2×#102—221no—
178C2×#97—111no—
179#333—222no—
180#330—222no—
181#323—222no—
182C22×C11—21no—
183C22×C11—21no—
184C22×C11—81no—
185C22×C11—81no—
186C22×C11—81no—
187C22×C11—162no—
188C22×C11#39211yescharacteristic
189C22×C11#47112yes—
190C4×C11—21no—
191C4×C11—21no—
192C4×C11—21no—
193C4×C11—21no—
194C4×C11—21no—
195C4×C11—81no—
196C4×C11—81no—
197C4×C11—81no—
198C4×C11#45512yes—
199Dic11—82no—
200C22×Q8—221no—
201C22×Q8C22⋊D1111yescharacteristic
202C22×D4C22⋊D1111yescharacteristic
203C2×Q16—22no—
204C2×SD16—22no—
205C22×C8—221no—
206C4⋊Q8—112no—
207C4⋊Q8—221no—
208C4⋊Q8—221no—
209C4⋊Q8—221no—
210C4⋊Q8C22⋊D1111yescharacteristic
211C4⋊Q8C22⋊D1111yescharacteristic
212#125—21no—
213#124—21no—
214#124—21no—
215#124—21no—
216#124—21no—
217C22⋊Q8—21no—
218C22⋊Q8—21no—
219C4×Q8—21no—
220C4×Q8—21no—
221#117—21no—
222C2×C4⋊C4—221no—
223C2×C4⋊C4—221no—
224C2×C22⋊C4—21no—
225C2×C22⋊C4—21no—
226C2×C42C22×D1111yescharacteristic
227#106—224no—
228C4⋊C8—221no—
229C4⋊C8—221no—
230C4⋊C8C22⋊D1112yes—
231#103—22no—
232#103—224no—
233#103—224no—
234#102—22no—
235#102—224no—
236C22⋊C8—21no—
237C22⋊C8—112no—
238C22⋊C8—221no—
239#97—21no—
240#97—112no—
241#97—221no—
242#97—221no—
243C4×C8—221no—
244C2×C11—22no—
245C2×C11—161no—
246C2×C11#200411yescharacteristic
247C2×C11#200911yescharacteristic
248C2×C11#201911yescharacteristic
249C24—21no—
250C2×Q8—21no—
251C2×Q8—21no—
252C2×Q8—21no—
253C2×Q8—21no—
254C2×Q8—42no—
255C2×Q8—222no—
256C2×Q8—441no—
257C2×Q8—882no—
258C2×D4—21no—
259C2×D4—21no—
260C2×D4—42no—
261C22×C4—21no—
262C22×C4—441no—
263C22×C4D4×D1111yescharacteristic
264C22×C4#434111yescharacteristic
265C22×C4C2×C22⋊D1111yescharacteristic
266Q16—82no—
267SD16—82no—
268C2×C8—22no—
269C2×C8—222no—
270C2×C8—222no—
271C2×C8—442no—
272C2×C8—441no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—222no—
280C4⋊C4—222no—
281C4⋊C4—441no—
282C4⋊C4—441no—
283C22⋊C4—41no—
284C22⋊C4—41no—
285C22⋊C4—41no—
286C22⋊C4—41no—
287C22⋊C4—41no—
288C42—41no—
289C42D4×D1111yescharacteristic
290C42D4×D1111yescharacteristic
291C42C2×C22⋊D1111yescharacteristic
292C42C2×C22⋊D1111yescharacteristic
293C11#1014111yescharacteristic, complemented, Sylow
294C23—41no—
295C23—42no—
296C23—81no—
297C23—81no—
298C23#6699211yescharacteristic
299Q8—42no—
300Q8—42no—
301Q8—42no—
302Q8—42no—
303Q8—882no—
304Q8—882no—
305D4—42no—
306D4—42no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—81no—
314C2×C4—442no—
315C2×C4—882no—
316C2×C4#6699011yescharacteristic
317C2×C4#6699011yescharacteristic
318C2×C4#6699111yescharacteristic
319C2×C4#6699211yescharacteristic
320C2×C4#6699311yescharacteristic
321C2×C4#6700611yescharacteristic
322C8—42no—
323C8—442no—
324C8—442no—
325C8—881no—
326C22—21no—
327C22—21no—
328C22—81no—
329C22—81no—
330C22—81no—
331C22—162no—
332C22#1062281612yes—
333C22#1062283611yescharacteristic
334C4—21no—
335C4—21no—
336C4—21no—
337C4—21no—
338C4—21no—
339C4—81no—
340C4—81no—
341C4—81no—
342C4—882no—
343C4#1062285512yes—
344C2—22no—
345C2—161no—
346C2#1306964311yescharacteristic
347C2#1306967311yescharacteristic
348C2#1306972711yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3215C2
socleC22×C11#392
prime radicalC22×D4×C11D4
hypercenter#3215D11
hypocenterC11#10141
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3215

Complements

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

NH ≅ G/Ntype
1. #13079757C2semidirect
3. #13067341C2semidirect
4. #13067231C2semidirect
6. #13066514C2semidirect
293. C11#10141semidirect

Maximal subgroups

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

subgroupindex
#130797572
C2×#106226682
#130673412
#130672312
#130669682
#130665142
C11×#32152
#1014111