Finite Group Databasebeta

← #14657524

Subgroups — #14657524

Order 2816.

420 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 91 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#13078090C211yesmaximal, characteristic
2#13068628C211yesmaximal, characteristic, complemented
3#13067392C211yesmaximal, characteristic, complemented
4#13067263C211yesmaximal, characteristic
5#13067175C211yesmaximal, characteristic
6#13066939C211yesmaximal, characteristic, complemented
7C11×#1286C211yesmaximal, characteristic, complemented
8C2×#66962—21no—
9#10623008C2211yescharacteristic
10C2×C4×Dic22C2211yescharacteristic
11C11×#431C2211yescharacteristic
12C11×#423C2211yescharacteristic
13C11×#382C2211yescharacteristic
14#10622746—21no—
15C2×#66874—21no—
16#10622538C2211yescharacteristic
17C2×C4⋊(C11⋊C8)C2211yescharacteristic
18#10622462—21no—
19#10622461—21no—
20#10622458—22no—
21#10622167—21no—
22#10622124—21no—
23#10622123—21no—
24#10622117—22no—
25#10622107—22no—
26#10622089—22no—
27C2×#4339—21no—
28C22×Dic22D411yescharacteristic
29C2×C11×M16—21no—
30C2×C11×C4⋊C4—21no—
31C2×C42×C11C2311yescharacteristic
32#66983—21no—
33#66983—21no—
34C2×C4⋊Dic11D411yescharacteristic
35C2×Dic11⋊C4—21no—
36C2×C4×Dic11—21no—
37C22×C11⋊C8—21no—
38#66962—42no—
39#66962—42no—
40C2×Dic44—22no—
41C2×#4314—22no—
42#66928—21no—
43#66927D411yescharacteristic
44C4×D44—21no—
45C4×D44—21no—
46#66922D411yescharacteristic
47C4×Dic22—21no—
48C4×Dic22—21no—
49C4×Dic22—21no—
50C4×Dic22—21no—
51C11×C4⋊C8—21no—
52C11×C4⋊C8—21no—
53C11×C4⋊C8D412yes—
54C11×C22⋊C8—21no—
55C4×C8×C11—21no—
56C11×#95—21no—
57C11×#95—21no—
58C22⋊(C11⋊C8)D412yes—
59#66885—22no—
60#66880—22no—
61#66874—42no—
62C4⋊(C11⋊C8)—21no—
63C4⋊(C11⋊C8)—21no—
64C4⋊(C11⋊C8)—21no—
65C4×C11⋊C8—21no—
66#10466—111nomaximal, Sylow
67C22×C4×C11—41no—
68C22×C4×C11C2×D411yescharacteristic
69C22×C4×C11C2×D411yescharacteristic
70C22×C4×C11#4111yescharacteristic
71C2×C22⋊D11—41no—
72C22×Dic11—21no—
73C22×Dic11—21no—
74#4339—41no—
75#4339—41no—
76#4339—41no—
77#4339—41no—
78C2×D44—21no—
79C2×D44—21no—
80C2×D44—21no—
81C2×C4×D11—41no—
82C2×Dic22—21no—
83C2×Dic22—21no—
84C2×Dic22—21no—
85C2×Dic22—21no—
86C2×Dic22—21no—
87C2×Dic22—21no—
88C2×Dic22D812yes—
89C11×M16—41no—
90C11×M16—41no—
91C2×C8×C11—22no—
92C2×C8×C11—41no—
93C11×C4⋊C4—41no—
94C11×C4⋊C4—41no—
95C42×C11C2×D411yescharacteristic
96C42×C11C2×D411yescharacteristic
97C42×C11#4111yescharacteristic
98C42×C11#4111yescharacteristic
99(C2×D11)⋊C4—41no—
100(C2×D11)⋊C4—41no—
101C4⋊Dic11—21no—
102C4⋊Dic11—21no—
103C4⋊Dic11—21no—
104C4⋊Dic11—21no—
105Dic11⋊C4—41no—
106Dic11⋊C4—41no—
107C4×Dic11—41no—
108C4×Dic11—41no—
109C2×C11⋊C8—22no—
110C2×C11⋊C8—41no—
111C2×C11⋊C8—41no—
112C2×C11⋊C8—41no—
113Dic44—44no—
114#4314—44no—
115#3037—111no—
116#1805—111no—
117#1571—111no—
118#1540—111no—
119#1517—111no—
120#1461—111no—
121#1286D1111yescharacteristic, complemented
122C23×C11#12111yescharacteristic
123C22×D11—41no—
124C2×C4×C11—41no—
125C2×C4×C11—41no—
126C2×C4×C11—81no—
127C2×C4×C11—81no—
128C2×C4×C11—81no—
129C2×C4×C11#12011yescharacteristic
130C2×C4×C11#12111yescharacteristic
131C2×C4×C11#12111yescharacteristic
132C2×C4×C11#12311yescharacteristic
133C2×C4×C11#12311yescharacteristic
134C2×C4×C11#12411yescharacteristic
135C2×C4×C11C2×D811yescharacteristic
136C2×C4×C11#13511yescharacteristic
137C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
138C2×C4×C11#13711yescharacteristic
139C22⋊D11—81no—
140C22⋊D11—81no—
141C2×Dic11—22no—
142C2×Dic11—41no—
143C2×Dic11—41no—
144C2×Dic11—41no—
145C2×Dic11—41no—
146C2×Dic11—81no—
147D44—41no—
148D44—41no—
149D44—81no—
150D44—81no—
151C4×D11—81no—
152C4×D11—81no—
153Dic22—22no—
154Dic22—22no—
155Dic22—41no—
156Dic22—41no—
157Dic22—41no—
158Dic22—41no—
159C8×C11—42no—
160C8×C11—81no—
161C11⋊C8—42no—
162C11⋊C8—81no—
163C2×#137—221no—
164#532—111no—
165C2×C4×Q8—111no—
166#464—222no—
167#462—221no—
168#460—221no—
169#431—111no—
170#431C2×D1111yescharacteristic
171#423C2×D1111yescharacteristic
172C2×C4⋊C8—111no—
173#417—221no—
174C2×#103—221no—
175#382C2×D1111yescharacteristic
176#340—221no—
177#335—222no—
178#332—221no—
179#331—221no—
180#327—222no—
181#324—222no—
182C22×C11—21no—
183C22×C11—21no—
184C22×C11#39411yescharacteristic
185C22×C11#46611yescharacteristic
186C22×C11#46811yescharacteristic
187C2×D11—81no—
188C2×D11—81no—
189C2×D11—81no—
190C4×C11—21no—
191C4×C11—21no—
192C4×C11—21no—
193C4×C11—21no—
194C4×C11—161no—
195C4×C11#44711yescharacteristic
196C4×C11#45211yescharacteristic
197C4×C11#48011yescharacteristic
198C4×C11#48211yescharacteristic
199Dic11—42no—
200Dic11—81no—
201Dic11—81no—
202C2×#41—221no—
203C22×Q8—111no—
204#137—442no—
205#137—442no—
206C2×Q16—222no—
207C2×SD16—222no—
208C2×M16—21no—
209C22×C8—221no—
210C4⋊Q8—111no—
211#127—111no—
212#124—221no—
213#121—221no—
214#121—221no—
215C4×Q8—221no—
216C4×Q8—221no—
217C4×Q8—221no—
218C4×Q8—221no—
219C4×D4—221no—
220C4×D4—221no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—111no—
223C2×C4⋊C4—221no—
224C2×C42—221no—
225C2×C42C22×D1111yescharacteristic
226C4⋊C8—21no—
227C4⋊C8—21no—
228C4⋊C8—221no—
229C4⋊C8—221no—
230C4⋊C8—221no—
231C4⋊C8D4412yes—
232#103—222no—
233#103—442no—
234#102—222no—
235C22⋊C8—21no—
236C22⋊C8—112no—
237C4×C8—21no—
238C4×C8—221no—
239#95—21no—
240#95—21no—
241C2×C11—21no—
242C2×C11—21no—
243C2×C11#203311yescharacteristic
244C2×C11#204911yescharacteristic
245C2×C11#205311yescharacteristic
246D11—161no—
247#41—441no—
248#41—441no—
249#41—441no—
250#41—441no—
251C2×Q8—112no—
252C2×Q8—221no—
253C2×Q8—221no—
254C2×Q8—221no—
255C2×Q8—221no—
256C2×Q8—221no—
257C2×Q8—221no—
258C2×D4—221no—
259C2×D4—221no—
260C2×D4—221no—
261C2×D4—441no—
262C22×C4—41no—
263C22×C4—221no—
264C22×C4—221no—
265C22×C4—441no—
266C22×C4#433911yescharacteristic
267C22×C4D4×D1111yescharacteristic
268C22×C4D4×D1111yescharacteristic
269Q16—444no—
270SD16—444no—
271M16—41no—
272M16—41no—
273C2×C8—22no—
274C2×C8—41no—
275C2×C8—222no—
276C2×C8—441no—
277C2×C8—441no—
278C2×C8—441no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—221no—
282C4⋊C4—221no—
283C4⋊C4—221no—
284C4⋊C4—221no—
285C4⋊C4—441no—
286C4⋊C4—441no—
287C22⋊C4—441no—
288C22⋊C4—441no—
289C42—441no—
290C42—441no—
291C42C2×D4411yescharacteristic
292C42#433911yescharacteristic
293C42D4×D1111yescharacteristic
294C42#434311yescharacteristic
295C11#1046611yescharacteristic, complemented, Sylow
296C23—441no—
297C23#6693711yescharacteristic
298Q8—222no—
299Q8—222no—
300Q8—441no—
301Q8—441no—
302Q8—441no—
303Q8—441no—
304D4—441no—
305D4—441no—
306D4—881no—
307D4—881no—
308D4—881no—
309D4—881no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—81no—
313C2×C4—81no—
314C2×C4—81no—
315C2×C4—222no—
316C2×C4—441no—
317C2×C4—441no—
318C2×C4—441no—
319C2×C4—441no—
320C2×C4—881no—
321C2×C4—881no—
322C2×C4—881no—
323C2×C4#6692811yescharacteristic
324C2×C4#6693511yescharacteristic
325C2×C4#6693711yescharacteristic
326C2×C4#6694711yescharacteristic
327C2×C4#6694711yescharacteristic
328C2×C4#6694811yescharacteristic
329C2×C4D8×D1111yescharacteristic
330C2×C4#6696711yescharacteristic
331C2×C4#6696911yescharacteristic
332C2×C4#6697111yescharacteristic
333C8—42no—
334C8—81no—
335C8—442no—
336C8—881no—
337C22—21no—
338C22—21no—
339C22—881no—
340C22—881no—
341C22—881no—
342C22#1062228511yescharacteristic
343C22#1062238811yescharacteristic
344C22#1062242511yescharacteristic
345C4—21no—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—161no—
350C4—442no—
351C4—881no—
352C4—881no—
353C4#1062238611yescharacteristic
354C4#1062242311yescharacteristic
355C4#1062247911yescharacteristic
356C4#1062249511yescharacteristic
357C2—21no—
358C2—21no—
359C2—1761no—
360C2#1306980111yescharacteristic
361C2#1306989911yescharacteristic
362C2#1306992311yescharacteristic
subgroupG/H
centerC22#10622285
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1286C2
socleC22×C11#394
prime radical#10623008C22
hypercenter#1286D11
hypocenterC11#10466
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1286

Complements

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

NH ≅ G/Ntype
2. #13068628C2semidirect
3. #13067392C2semidirect
6. #13066939C2semidirect
7. C11×#1286C2semidirect
121. #1286D11semidirect
295. C11#10466semidirect

Maximal subgroups

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

subgroupindex
#130780902
#130686282
#130673922
#130672632
#130671752
#130669392
C11×#12862
#1046611