Finite Group Databasebeta

← #14650504

Subgroups — #14650504

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#13079734C211yesmaximal, characteristic
2#13071333C211yesmaximal, characteristic, complemented
3#13069449C211yesmaximal, characteristic
4#13067287C211yesmaximal, characteristic, complemented
5#13066474C211yesmaximal, characteristic, complemented
6#13066444C211yesmaximal, characteristic, complemented
7C11×#1517C211yesmaximal, characteristic
8C11×#532C2211yescharacteristic
9C2×#66940—21no—
10C2×#66922C2211yescharacteristic
11C11×#431C2211yescharacteristic
12C11×#382C2211yescharacteristic
13C2×#66901—21no—
14C2×#66901—21no—
15#10622691C412yescomplemented
16#10622683C412yescomplemented
17#10622646—22no—
18#10622620—22no—
19#10622587—21no—
20#10622545C2211yescharacteristic
21#10622538C2211yescharacteristic
22#10622537C2211yescharacteristic
23#10622267—22no—
24#10622267—22no—
25C11×#327—22no—
26#10622124—22no—
27C2×C11×#41—21no—
28C22×Dic22—21no—
29C11×C4⋊Q8C2×C411yescharacteristic
30C11×#127C2×C411yescharacteristic
31C11×#124—21no—
32C11×#121—21no—
33C11×#121—21no—
34C4×D4×C11—21no—
35C4×D4×C11—21no—
36C2×C11×C4⋊C4—21no—
37C2×C42×C11C2311yescharacteristic
38C2×C4⋊Dic11—21no—
39C2×C4⋊Dic11D412yes—
40C2×Dic11⋊C4—22no—
41C2×C4×Dic11—22no—
42C2×C4×Dic11D411yescharacteristic
43C2×C4×Dic11D411yescharacteristic
44C2×#4318—21no—
45#66940—42no—
46#66940—42no—
47#66922—21no—
48#66922—21no—
49#66922C2×C412yes—
50#66922D412yes—
51C11×C4⋊C8—21no—
52C11×C22⋊C8—21no—
53C4×C8×C11—21no—
54C11×#95—21no—
55C11×#95D412yes—
56#66901—42no—
57#66901—42no—
58#66896—24no—
59C11⋊#95—24no—
60C11⋊#95—21no—
61C11⋊#95—21no—
62C22⋊(C11⋊C8)—21no—
63#66871—24no—
64C4⋊(C11⋊C8)—21no—
65C4⋊(C11⋊C8)—21no—
66C4⋊(C11⋊C8)—21no—
67C4×C11⋊C8C2×C412yes—
68#9300—111nomaximal, Sylow
69C11×#41—41no—
70C11×#41—41no—
71C11×#41—41no—
72C11×#41—41no—
73C2×Q8×C11—21no—
74C2×D4×C11—21no—
75C2×D4×C11—21no—
76C2×D4×C11—21no—
77C2×D4×C11—41no—
78C22×C4×C11—22no—
79C22×C4×C11—41no—
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11C2×D411yescharacteristic
83C22×Dic11—21no—
84C22×Dic11—22no—
85C22×Dic11—21no—
86C2×Dic22—22no—
87C2×Dic22—22no—
88C2×Dic22—41no—
89C2×Dic22—41no—
90C2×Dic22—41no—
91C2×Dic22—41no—
92C2×C8×C11—41no—
93C11×C4⋊C4—21no—
94C11×C4⋊C4—21no—
95C11×C4⋊C4—41no—
96C11×C4⋊C4—41no—
97C11×C22⋊C4—41no—
98C11×C22⋊C4—41no—
99C42×C11C22×C411yescharacteristic
100C42×C11C2×D411yescharacteristic
101C42×C11#4111yescharacteristic
102C42×C11#4111yescharacteristic
103C4⋊Dic11—22no—
104C4⋊Dic11—22no—
105C4⋊Dic11—22no—
106C4⋊Dic11C22⋊C414yes—
107Dic11⋊C4—44no—
108C4×Dic11—21no—
109C4×Dic11—21no—
110C4×Dic11—21no—
111C4×Dic11—44no—
112C4×Dic11D812yes—
113#4318—41no—
114#4318—41no—
115C2×C11⋊C8—22no—
116C2×C11⋊C8—41no—
117#3226—111no—
118#2327—111no—
119#1963—111no—
120#1546—111no—
121#1517D1111yescharacteristic
122#1286—111no—
123#1274—111no—
124C23×C11—41no—
125C23×C11#12011yescharacteristic
126Q8×C11—41no—
127Q8×C11—41no—
128D4×C11—42no—
129D4×C11—41no—
130D4×C11—41no—
131D4×C11—81no—
132D4×C11—81no—
133D4×C11—81no—
134C2×C4×C11—41no—
135C2×C4×C11—41no—
136C2×C4×C11—42no—
137C2×C4×C11—42no—
138C2×C4×C11—41no—
139C2×C4×C11—42no—
140C2×C4×C11—81no—
141C2×C4×C11—81no—
142C2×C4×C11C2×C22⋊C411yescharacteristic
143C2×C4×C11C4×D411yescharacteristic
144C2×C4×C11C4×D411yescharacteristic
145C2×C4×C11#12111yescharacteristic
146C2×C4×C11#12111yescharacteristic
147C2×C4×C11#12311yescharacteristic
148C2×C4×C11C2×D811yescharacteristic
149C2×C4×C11#13511yescharacteristic
150C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
151C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
152C2×Dic11—24no—
153C2×Dic11—22no—
154C2×Dic11—41no—
155C2×Dic11—41no—
156C2×Dic11—42no—
157C2×Dic11—42no—
158C2×Dic11—41no—
159C2×Dic11—41no—
160C2×Dic11—41no—
161Dic22—42no—
162Dic22—42no—
163Dic22—42no—
164Dic22—42no—
165C8×C11—81no—
166C11⋊C8—42no—
167C11⋊C8—81no—
168#532C2×D1111yescharacteristic
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#423—111no—
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—22no—
187C22×C11—21no—
188C22×C11—21no—
189C22×C11—81no—
190C22×C11—81no—
191C22×C11—81no—
192C22×C11#38611yescharacteristic
193C22×C11#44711yescharacteristic
194C22×C11#44911yescharacteristic
195C4×C11—21no—
196C4×C11—21no—
197C4×C11—21no—
198C4×C11—21no—
199C4×C11—82no—
200C4×C11—81no—
201C4×C11C4×D811yescharacteristic
202C4×C11#44211yescharacteristic
203C4×C11#45911yescharacteristic
204C4×C11#46311yescharacteristic
205Dic11—42no—
206Dic11—44no—
207Dic11—81no—
208C2×#41—21no—
209C22×Q8—221no—
210C2×M16—221no—
211C4⋊Q8—112no—
212C4⋊Q8—112no—
213C4⋊Q8—221no—
214C4⋊Q8—221no—
215C4⋊Q8C4×D1111yescharacteristic
216#127C4×D1111yescharacteristic
217#124—21no—
218#121—21no—
219#121—21no—
220C4×Q8—442no—
221C4×Q8—442no—
222C4×D4—21no—
223C4×D4—21no—
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—221no—
235C4⋊C8—221no—
236C4⋊C8—221no—
237#104—442no—
238#104—442no—
239#102—224no—
240C22⋊C8—21no—
241C22⋊C8—221no—
242C4×C8—21no—
243C4×C8—112no—
244#95—21no—
245#95—224no—
246#95—221no—
247#95—221no—
248#95C22⋊D1112yes—
249C2×C11—21no—
250C2×C11—21no—
251C2×C11—161no—
252C2×C11#187911yescharacteristic
253C2×C11#190511yescharacteristic
254C2×C11#191211yescharacteristic
255#41—41no—
256#41—41no—
257#41—41no—
258#41—41no—
259C2×Q8—21no—
260C2×Q8—222no—
261C2×Q8—222no—
262C2×Q8—441no—
263C2×Q8—441no—
264C2×Q8—441no—
265C2×Q8—441no—
266C2×D4—21no—
267C2×D4—21no—
268C2×D4—21no—
269C2×D4—41no—
270C22×C4—22no—
271C22×C4—41no—
272C22×C4—221no—
273C22×C4—222no—
274C22×C4—221no—
275C22×C4D4×D1111yescharacteristic
276C22×C4D4×D1111yescharacteristic
277C22×C4C2×C22⋊D1111yescharacteristic
278M16—441no—
279M16—441no—
280C2×C8—41no—
281C2×C8—222no—
282C2×C8—441no—
283C4⋊C4—21no—
284C4⋊C4—21no—
285C4⋊C4—41no—
286C4⋊C4—41no—
287C4⋊C4—114no—
288C4⋊C4—222no—
289C4⋊C4—222no—
290C4⋊C4—222no—
291C4⋊C4—444no—
292C22⋊C4—41no—
293C22⋊C4—41no—
294C42—112no—
295C42—221no—
296C42—221no—
297C42—221no—
298C42—444no—
299C42C2×C4×D1111yescharacteristic
300C42#433911yescharacteristic
301C42D4×D1111yescharacteristic
302C42#434111yescharacteristic
303C11#930011yescharacteristic, complemented, Sylow
304C23—41no—
305C23#6699011yescharacteristic
306Q8—41no—
307Q8—41no—
308Q8—442no—
309Q8—442no—
310Q8—442no—
311Q8—442no—
312D4—42no—
313D4—41no—
314D4—41no—
315D4—81no—
316D4—81no—
317D4—81no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—41no—
324C2×C4—81no—
325C2×C4—81no—
326C2×C4—222no—
327C2×C4—224no—
328C2×C4—441no—
329C2×C4—441no—
330C2×C4—442no—
331C2×C4—442no—
332C2×C4—441no—
333C2×C4—441no—
334C2×C4—441no—
335C2×C4C22⋊C4×D1111yescharacteristic
336C2×C4(C22⋊D11)⋊C411yescharacteristic
337C2×C4#6693611yescharacteristic
338C2×C4#6693711yescharacteristic
339C2×C4D8×D1111yescharacteristic
340C2×C4#6696411yescharacteristic
341C2×C4#6696711yescharacteristic
342C2×C4#6696911yescharacteristic
343C2×C4C4×C22⋊D1111yescharacteristic
344C2×C4#6699111yescharacteristic
345C8—81no—
346C8—442no—
347C8—881no—
348C22—21no—
349C22—21no—
350C22—81no—
351C22—81no—
352C22—81no—
353C22#1062256911yescharacteristic
354C22#1062276911yescharacteristic
355C22#1062278511yescharacteristic
356C4—21no—
357C4—21no—
358C4—21no—
359C4—21no—
360C4—82no—
361C4—81no—
362C4—442no—
363C4—444no—
364C4—881no—
365C4#1062236911yescharacteristic
366C4#1062239811yescharacteristic
367C4#1062239911yescharacteristic
368C4#1062240011yescharacteristic
369C2—21no—
370C2—21no—
371C2—161no—
372C2#1306896111yescharacteristic
373C2#1306911311yescharacteristic
374C2#1306915011yescharacteristic
subgroupG/H
centerC22#10622569
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1517C2
socleC22×C11#386
prime radicalC11×#532C22
cosocleC2×C42×C11C23
hypercenter#1517D11
hypocenterC11#9300
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1517

Complements

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

NH ≅ G/Ntype
2. #13071333C2semidirect
4. #13067287C2semidirect
5. #13066474C2semidirect
6. #13066444C2semidirect
15. #10622691C4semidirect
16. #10622683C4semidirect
303. C11#9300semidirect

Maximal subgroups

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

subgroupindex
#130797342
#130713332
#130694492
#130672872
#130664742
#130664442
C11×#15172
#930011