Finite Group Databasebeta

← #14650508

Subgroups — #14650508

Order 2816.

508 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 508 conjugacy classes of subgroups — too many to draw. Only its 107 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#13079739C211yesmaximal, characteristic
2#13071333C211yesmaximal, characteristic, complemented
3#13069447C211yesmaximal, characteristic
4#13067289C211yesmaximal, characteristic, complemented
5#13067175C211yesmaximal, characteristic
6#13066444C211yesmaximal, characteristic, complemented
7C11×#1286C211yesmaximal, characteristic, complemented
8C2×#66940—21no—
9#10623008C2211yescharacteristic
10C2×#66922C2211yescharacteristic
11C11×#431C2211yescharacteristic
12C11×#423C2211yescharacteristic
13C11×#382C2211yescharacteristic
14C2×#66889—21no—
15C2×#66889—21no—
16#10622587—21no—
17#10622545C2211yescharacteristic
18#10622538C2211yescharacteristic
19#10622459—22no—
20#10622349—22no—
21#10622307C412yescomplemented
22#10622295C412yescomplemented
23#10622267—22no—
24#10622267—22no—
25#10622120—22no—
26#10622089—22no—
27C2×#4339—21no—
28C22×Dic22—21no—
29C2×C11×M16—21no—
30C2×C11×C4⋊C4—21no—
31C2×C42×C11C2311yescharacteristic
32#66983—21no—
33#66983—21no—
34C2×C4⋊Dic11—21no—
35C2×C4⋊Dic11D412yes—
36C2×Dic11⋊C4—22no—
37C2×C4×Dic11—22no—
38C2×C4×Dic11D411yescharacteristic
39C2×C4×Dic11D411yescharacteristic
40#66940—42no—
41#66940—42no—
42#66928—21no—
43#66927C2×C411yescharacteristic
44C4×D44—21no—
45C4×D44—21no—
46#66922—21no—
47#66922—21no—
48#66922C2×C411yescharacteristic
49#66922C2×C412yes—
50#66922D412yes—
51C11×C4⋊C8—21no—
52C11×C4⋊C8—21no—
53C11×C4⋊C8—21no—
54C11×C22⋊C8—21no—
55C4×C8×C11C2×C412yes—
56C11×#95—21no—
57C11×#95D412yes—
58C11⋊#95—24no—
59C11⋊#95—21no—
60C11⋊#95—21no—
61C22⋊(C11⋊C8)—21no—
62#66889—42no—
63#66889—42no—
64#66885—24no—
65#66882—24no—
66C4⋊(C11⋊C8)—21no—
67C4×C11⋊C8—21no—
68#9300—111nomaximal, Sylow
69C22×C4×C11—22no—
70C22×C4×C11C2×D411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C22×C4×C11C2×D411yescharacteristic
73C2×C22⋊D11—41no—
74C22×Dic11—21no—
75C22×Dic11—22no—
76C22×Dic11—21no—
77#4339—41no—
78#4339—41no—
79#4339—41no—
80#4339—41no—
81C2×D44—21no—
82C2×D44—21no—
83C2×D44—21no—
84C2×C4×D11—41no—
85C2×Dic22—22no—
86C2×Dic22—21no—
87C2×Dic22—22no—
88C2×Dic22—41no—
89C2×Dic22—41no—
90C2×Dic22—41no—
91C2×Dic22—41no—
92C11×M16—41no—
93C11×M16—41no—
94C2×C8×C11—22no—
95C2×C8×C11—41no—
96C11×C4⋊C4—41no—
97C11×C4⋊C4—41no—
98C42×C11C22×C411yescharacteristic
99C42×C11C2×D411yescharacteristic
100C42×C11#4111yescharacteristic
101C42×C11#4111yescharacteristic
102(C2×D11)⋊C4—41no—
103(C2×D11)⋊C4—41no—
104C4⋊Dic11—21no—
105C4⋊Dic11—22no—
106C4⋊Dic11—21no—
107C4⋊Dic11—22no—
108C4⋊Dic11—22no—
109C4⋊Dic11C22⋊C414yes—
110Dic11⋊C4—44no—
111C4×Dic11—21no—
112C4×Dic11—21no—
113C4×Dic11—21no—
114C4×Dic11—44no—
115C4×Dic11D812yes—
116C2×C11⋊C8—41no—
117#3226—111no—
118#2327—111no—
119#1963—111no—
120#1546—111no—
121#1517—111no—
122#1286D1111yescharacteristic, complemented
123#1274—111no—
124C23×C11#12011yescharacteristic
125C22×D11—41no—
126C2×C4×C11—41no—
127C2×C4×C11—41no—
128C2×C4×C11—42no—
129C2×C4×C11—42no—
130C2×C4×C11—42no—
131C2×C4×C11C2×C22⋊C411yescharacteristic
132C2×C4×C11C4×D411yescharacteristic
133C2×C4×C11C4×D411yescharacteristic
134C2×C4×C11#12111yescharacteristic
135C2×C4×C11#12111yescharacteristic
136C2×C4×C11#12311yescharacteristic
137C2×C4×C11C2×D811yescharacteristic
138C2×C4×C11#13511yescharacteristic
139C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
140C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
141C22⋊D11—81no—
142C22⋊D11—81no—
143C2×Dic11—24no—
144C2×Dic11—22no—
145C2×Dic11—41no—
146C2×Dic11—41no—
147C2×Dic11—42no—
148C2×Dic11—42no—
149C2×Dic11—41no—
150C2×Dic11—41no—
151C2×Dic11—41no—
152C2×Dic11—41no—
153D44—42no—
154D44—41no—
155D44—41no—
156D44—81no—
157C4×D11—81no—
158C4×D11—81no—
159Dic22—42no—
160Dic22—42no—
161Dic22—42no—
162Dic22—42no—
163Dic22—41no—
164Dic22—41no—
165C8×C11—42no—
166C8×C11—81no—
167C11⋊C8—81no—
168#532—111no—
169C2×C4⋊Q8—111no—
170C2×C4×Q8—221no—
171#500—112no—
172#486—112no—
173#480—222no—
174#474—222no—
175#431—111no—
176#431C2×D1111yescharacteristic
177#423C2×D1111yescharacteristic
178C2×#104—221no—
179C2×#104—221no—
180#391—221no—
181#387—222no—
182#387—222no—
183#382C2×D1111yescharacteristic
184#376—111no—
185#332—222no—
186#327—222no—
187C22×C11—21no—
188C22×C11—21no—
189C22×C11#38611yescharacteristic
190C22×C11#44711yescharacteristic
191C22×C11#44911yescharacteristic
192C2×D11—81no—
193C2×D11—81no—
194C2×D11—81no—
195C4×C11—21no—
196C4×C11—21no—
197C4×C11—21no—
198C4×C11—21no—
199C4×C11—82no—
200C4×C11C4×D811yescharacteristic
201C4×C11#44211yescharacteristic
202C4×C11#45911yescharacteristic
203C4×C11#46311yescharacteristic
204Dic11—42no—
205Dic11—44no—
206Dic11—81no—
207Dic11—81no—
208C2×#41—221no—
209C22×Q8—221no—
210C2×M16—21no—
211C4⋊Q8—112no—
212C4⋊Q8—111no—
213C4⋊Q8—112no—
214C4⋊Q8—221no—
215C4⋊Q8—221no—
216#127—111no—
217#124—221no—
218#121—221no—
219#121—221no—
220C4×Q8—442no—
221C4×Q8—442no—
222C4×D4—221no—
223C4×D4—221no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—112no—
226C2×C4⋊C4—221no—
227C2×C4⋊C4—222no—
228C2×C42—111no—
229C2×C42—111no—
230C2×C42—222no—
231C2×C42C22×D1111yescharacteristic
232#107—224no—
233C4⋊C8—21no—
234C4⋊C8—21no—
235C4⋊C8—21no—
236C4⋊C8—221no—
237#104—442no—
238#104—442no—
239#102—224no—
240C22⋊C8—21no—
241C22⋊C8—221no—
242C4×C8—221no—
243C4×C8C4×D1112yes—
244#95—21no—
245#95—224no—
246#95—221no—
247#95—221no—
248#95D4412yes—
249C2×C11—21no—
250C2×C11—21no—
251C2×C11#187911yescharacteristic
252C2×C11#190511yescharacteristic
253C2×C11#191211yescharacteristic
254D11—161no—
255#41—441no—
256#41—441no—
257#41—441no—
258#41—441no—
259C2×Q8—222no—
260C2×Q8—222no—
261C2×Q8—221no—
262C2×Q8—441no—
263C2×Q8—441no—
264C2×Q8—441no—
265C2×Q8—441no—
266C2×D4—221no—
267C2×D4—221no—
268C2×D4—221no—
269C2×D4—441no—
270C22×C4—22no—
271C22×C4—221no—
272C22×C4—222no—
273C22×C4—221no—
274C22×C4—441no—
275C22×C4C2×D4411yescharacteristic
276C22×C4D4×D1111yescharacteristic
277C22×C4D4×D1111yescharacteristic
278M16—41no—
279M16—41no—
280C2×C8—22no—
281C2×C8—41no—
282C2×C8—441no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—114no—
286C4⋊C4—222no—
287C4⋊C4—222no—
288C4⋊C4—222no—
289C4⋊C4—221no—
290C4⋊C4—221no—
291C4⋊C4—444no—
292C22⋊C4—441no—
293C22⋊C4—441no—
294C42—112no—
295C42—221no—
296C42—221no—
297C42—221no—
298C42—444no—
299C42C2×C4×D1111yescharacteristic
300C42#433911yescharacteristic
301C42D4×D1111yescharacteristic
302C42#434311yescharacteristic
303C11#930011yescharacteristic, complemented, Sylow
304C23—441no—
305C23#6693511yescharacteristic
306Q8—442no—
307Q8—442no—
308Q8—442no—
309Q8—442no—
310Q8—441no—
311Q8—441no—
312D4—442no—
313D4—441no—
314D4—441no—
315D4—881no—
316D4—881no—
317D4—881no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—224no—
324C2×C4—222no—
325C2×C4—441no—
326C2×C4—441no—
327C2×C4—442no—
328C2×C4—442no—
329C2×C4—441no—
330C2×C4—441no—
331C2×C4—441no—
332C2×C4—441no—
333C2×C4—881no—
334C2×C4—881no—
335C2×C4C4×D4411yescharacteristic
336C2×C4C22⋊C4×D1111yescharacteristic
337C2×C4#6693711yescharacteristic
338C2×C4#6694611yescharacteristic
339C2×C4#6694711yescharacteristic
340C2×C4#6694811yescharacteristic
341C2×C4D8×D1111yescharacteristic
342C2×C4#6696711yescharacteristic
343C2×C4#6696711yescharacteristic
344C2×C4#6697211yescharacteristic
345C8—42no—
346C8—81no—
347C8—881no—
348C22—21no—
349C22—21no—
350C22—881no—
351C22—881no—
352C22—881no—
353C22#1062227811yescharacteristic
354C22#1062238611yescharacteristic
355C22#1062242411yescharacteristic
356C4—21no—
357C4—21no—
358C4—21no—
359C4—21no—
360C4—82no—
361C4—442no—
362C4—444no—
363C4—881no—
364C4—881no—
365C4#1062239911yescharacteristic
366C4#1062243211yescharacteristic
367C4#1062248211yescharacteristic
368C4#1062248511yescharacteristic
369C2—21no—
370C2—21no—
371C2—1761no—
372C2#1306896511yescharacteristic
373C2#1306910911yescharacteristic
374C2#1306915211yescharacteristic
subgroupG/H
centerC22#10622278
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1286C2
socleC22×C11#386
prime radical#10623008C22
cosocleC2×C42×C11C23
hypercenter#1286D11
hypocenterC11#9300
LCSG ▷ 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. #13071333C2semidirect
4. #13067289C2semidirect
6. #13066444C2semidirect
7. C11×#1286C2semidirect
21. #10622307C4semidirect
22. #10622295C4semidirect
122. #1286D11semidirect
303. C11#9300semidirect

Maximal subgroups

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

subgroupindex
#130797392
#130713332
#130694472
#130672892
#130671752
#130664442
C11×#12862
#930011