Finite Group Databasebeta

← #14652920

Subgroups — #14652920

Order 2816.

468 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079175C211yesmaximal, characteristic
2#13069559C211yesmaximal, characteristic, complemented
3#13069534C211yesmaximal, characteristic
4#13067114C211yesmaximal, characteristic, complemented
5#13067110C211yesmaximal, characteristic
6C8×#4318C211yesmaximal, characteristic, complemented
7C4×C11×#106C211yesmaximal, characteristic, complemented
8#10623008C2211yescharacteristic
9#10623001C2211yescharacteristic
10C2×C11×#106—21no—
11C2×C4×C8×C11C2211yescharacteristic
12C4×C11×C4⋊C4C2211yescharacteristic
13C4×C11×C4⋊C4C2211yescharacteristic
14#10622727—21no—
15#10622727—21no—
16C2×#66869—22no—
17#10622538C2211yescharacteristic
18C4×#4318C2211yescharacteristic
19#10622307C411yescharacteristic, complemented
20#10622306C411yescharacteristic, complemented
21C4×#4314—21no—
22C4×#4314—21no—
23#10622294C411yescharacteristic, complemented
24#10622293C411yescharacteristic, complemented
25C11×#340—21no—
26#10622161—22no—
27#10622092—21no—
28C8×C11⋊C8—21no—
29#10622090—22no—
30#10622089—22no—
31C2×#4339—21no—
32C22×C8×C11D411yescharacteristic
33C22×C8×C11D411yescharacteristic
34C2×C11×C4⋊C4—21no—
35C2×C11×C4⋊C4—21no—
36C2×C42×C11—21no—
37C2×C42×C11—21no—
38C2×C42×C11C2311yescharacteristic
39#66983—21no—
40#66983—21no—
41#66979—21no—
42#66977—21no—
43#66977—21no—
44C2×#4318D412yes—
45C2×#4314—21no—
46C2×#4314—21no—
47#66928—21no—
48#66927C2×C411yescharacteristic
49C4×D44—21no—
50C4×D44—21no—
51#66923—21no—
52#66922C2×C411yescharacteristic
53#66922C2×C411yescharacteristic
54#66922C2×C411yescharacteristic
55C4×Dic22—21no—
56C4×Dic22—21no—
57C11×#106—24no—
58C4×C8×C11C2×C411yescharacteristic
59C4×C8×C11C2×C411yescharacteristic
60C4×C8×C11D411yescharacteristic
61C4×C8×C11D411yescharacteristic
62C11×#95—21no—
63C11×#95—21no—
64C22⋊(C11⋊C8)D412yes—
65#66885—21no—
66#66885—21no—
67#66881—21no—
68#66881—21no—
69#66880—21no—
70#66880—21no—
71#66869—44no—
72C4⋊(C11⋊C8)—21no—
73#66867—21no—
74C4×C11⋊C8—21no—
75C4×C11⋊C8—21no—
76#9717—111nomaximal, Sylow
77C22×C4×C11—41no—
78C22×C4×C11—41no—
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C2×C22⋊D11—41no—
83#4339—42no—
84#4339—42no—
85C2×D44—21no—
86C2×D44—21no—
87C2×D44—21no—
88C2×C4×D11—41no—
89C2×Dic22—21no—
90C2×Dic22—21no—
91C2×Dic22—21no—
92C2×C8×C11—22no—
93C2×C8×C11—41no—
94C2×C8×C11C22⋊C411yescharacteristic
95C2×C8×C11C22⋊C411yescharacteristic
96C2×C8×C11C22⋊C411yescharacteristic
97C2×C8×C11C22⋊C411yescharacteristic
98C11×C4⋊C4—22no—
99C11×C4⋊C4—22no—
100C11×C4⋊C4—41no—
101C11×C4⋊C4—41no—
102C42×C11—42no—
103C42×C11—42no—
104C42×C11C22×C411yescharacteristic
105C42×C11C2×D411yescharacteristic
106C42×C11#4111yescharacteristic
107C42×C11#4111yescharacteristic
108C22⋊Dic11—41no—
109(C2×D11)⋊C4—41no—
110(C2×D11)⋊C4—41no—
111C4⋊Dic11—21no—
112C4⋊Dic11—21no—
113C4⋊Dic11—21no—
114C4⋊Dic11—21no—
115C4⋊Dic11—21no—
116C4⋊Dic11—21no—
117Dic11⋊C4—41no—
118Dic11⋊C4—41no—
119C4×Dic11—41no—
120#4318—22no—
121#4318SD1614yescomplemented
122C2×C11⋊C8—22no—
123C2×C11⋊C8—22no—
124#4314—42no—
125#4314—42no—
126#3167—111no—
127#1986—111no—
128#1980—111no—
129C4×#106D1111yescharacteristic, complemented
130#1503—111no—
131#1502—111no—
132C8×M16—111no—
133C23×C11#12711yescharacteristic
134C22×D11—41no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—41no—
138C2×C4×C11—42no—
139C2×C4×C11—42no—
140C2×C4×C11—81no—
141C2×C4×C11—81no—
142C2×C4×C11—81no—
143C2×C4×C11—81no—
144C2×C4×C11C2×C22⋊C411yescharacteristic
145C2×C4×C11C4×D411yescharacteristic
146C2×C4×C11C4×D411yescharacteristic
147C2×C4×C11#12111yescharacteristic
148C2×C4×C11#12111yescharacteristic
149C2×C4×C11#12411yescharacteristic
150C2×C4×C11C2×SD1612yes—
151C2×C4×C11#13512yes—
152C22⋊D11—81no—
153C22⋊D11—81no—
154C2×Dic11—41no—
155C2×Dic11—41no—
156C2×Dic11—41no—
157D44—41no—
158D44—41no—
159D44—42no—
160D44—81no—
161C4×D11—82no—
162Dic22—41no—
163Dic22—41no—
164Dic22—42no—
165Dic22—81no—
166C8×C11—21no—
167C8×C11—21no—
168C8×C11—21no—
169C8×C11#10412yescomplemented
170C11⋊C8—24no—
171C11⋊C8—42no—
172#533—111no—
173#532—111no—
174#498—111no—
175#492—111no—
176#487—111no—
177#486—111no—
178#465—221no—
179#465—221no—
180C4×SD16—221no—
181C4×SD16—221no—
182#431—111no—
183C2×#106—21no—
184C2×#104—222no—
185C4×M16—111no—
186C2×C4×C8C2×D1111yescharacteristic
187C4×C4⋊C4C2×D1111yescharacteristic
188C4×C4⋊C4C2×D1111yescharacteristic
189#340—21no—
190#339—222no—
191#328—222no—
192#327—222no—
193#322—221no—
194C82—221no—
195C22×C11—21no—
196C22×C11—21no—
197C22×C11#39011yescharacteristic
198C22×C11#49211yescharacteristic
199C22×C11#49511yescharacteristic
200C2×D11—81no—
201C2×D11—81no—
202C2×D11—81no—
203C4×C11—21no—
204C4×C11—21no—
205C4×C11—21no—
206C4×C11—82no—
207C4×C11—82no—
208C4×C11C2×#10411yescharacteristic
209C4×C11#42111yescharacteristic
210C4×C11C4×SD1612yes—
211C4×C11#46512yes—
212Dic11—81no—
213Dic11—81no—
214Dic11—81no—
215C2×#41—221no—
216C2×SD16—221no—
217C2×SD16—221no—
218C2×M16—112no—
219C22×C8C22⋊D1111yescharacteristic
220C22×C8C22⋊D1111yescharacteristic
221C4⋊Q8—111no—
222C4⋊Q8—111no—
223C4⋊Q8—111no—
224#127—111no—
225#125—221no—
226#124—221no—
227C22⋊Q8—221no—
228C22⋊Q8—221no—
229#121—221no—
230#121—221no—
231C4×Q8—221no—
232C4×Q8—221no—
233C4×D4—221no—
234C4×D4—221no—
235#117—221no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—21no—
238C2×C42—21no—
239C2×C42—21no—
240C2×C42C22×D1111yescharacteristic
241#106—24no—
242#106—221no—
243#106—221no—
244C4⋊C8—221no—
245#104—444no—
246#103—221no—
247#103—221no—
248#102—221no—
249#102—221no—
250C22⋊C8—112no—
251#97—221no—
252C4×C8—221no—
253C4×C8—221no—
254C4×C8C4×D1111yescharacteristic
255C4×C8C4×D1111yescharacteristic
256C4×C8D4411yescharacteristic
257C4×C8D4411yescharacteristic
258#95—21no—
259#95—21no—
260C2×C11—21no—
261C2×C11—21no—
262C2×C11#196811yescharacteristic
263C2×C11#197611yescharacteristic
264C2×C11#198011yescharacteristic
265D11—161no—
266#41—442no—
267#41—442no—
268C2×Q8—221no—
269C2×Q8—221no—
270C2×Q8—221no—
271C2×D4—221no—
272C2×D4—221no—
273C2×D4—221no—
274C2×D4—441no—
275C22×C4—41no—
276C22×C4—41no—
277C22×C4—441no—
278C22×C4D4×D1111yescharacteristic
279C22×C4D4×D1111yescharacteristic
280C22×C4C2×C22⋊D1111yescharacteristic
281SD16—442no—
282SD16—442no—
283M16—114no—
284M16—222no—
285C2×C8—22no—
286C2×C8—41no—
287C2×C8—222no—
288C2×C8—222no—
289C2×C8(C2×D11)⋊C411yescharacteristic
290C2×C8(C2×D11)⋊C411yescharacteristic
291C2×C8(C2×D11)⋊C411yescharacteristic
292C2×C8(C2×D11)⋊C411yescharacteristic
293C4⋊C4—22no—
294C4⋊C4—22no—
295C4⋊C4—41no—
296C4⋊C4—41no—
297C4⋊C4—221no—
298C4⋊C4—221no—
299C4⋊C4—221no—
300C4⋊C4—221no—
301C4⋊C4—221no—
302C4⋊C4—221no—
303C4⋊C4—441no—
304C4⋊C4—441no—
305C22⋊C4—441no—
306C22⋊C4—441no—
307C22⋊C4—441no—
308C42—42no—
309C42—42no—
310C42—441no—
311C42C2×C4×D1111yescharacteristic
312C42C2×D4411yescharacteristic
313C42#434311yescharacteristic
314C42#434311yescharacteristic
315C11#971711yescharacteristic, complemented, Sylow
316C23—441no—
317C23#6699311yescharacteristic
318Q8—442no—
319Q8—441no—
320Q8—441no—
321Q8—881no—
322D4—442no—
323D4—441no—
324D4—441no—
325D4—881no—
326D4—881no—
327D4—881no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—41no—
331C2×C4—42no—
332C2×C4—42no—
333C2×C4—81no—
334C2×C4—81no—
335C2×C4—81no—
336C2×C4—81no—
337C2×C4—441no—
338C2×C4—441no—
339C2×C4—441no—
340C2×C4—882no—
341C2×C4#6694611yescharacteristic
342C2×C4#6694611yescharacteristic
343C2×C4#6694811yescharacteristic
344C2×C4#6694811yescharacteristic
345C2×C4SD16×D1112yes—
346C2×C4#6696912yes—
347C2×C4C2×(C2×D11)⋊C411yescharacteristic
348C2×C4#6700011yescharacteristic
349C8—21no—
350C8—21no—
351C8—21no—
352C8—224no—
353C8—442no—
354C8#6686912yescomplemented
355C22—21no—
356C22—21no—
357C22—881no—
358C22—881no—
359C22—881no—
360C22#1062260111yescharacteristic
361C22#1062278111yescharacteristic
362C22#1062278811yescharacteristic
363C4—21no—
364C4—21no—
365C4—21no—
366C4—82no—
367C4—82no—
368C4—881no—
369C4—881no—
370C4—881no—
371C4#1062246512yes—
372C4#1062247712yes—
373C4C2×#6686911yescharacteristic
374C4#1062261811yescharacteristic
375C2—21no—
376C2—21no—
377C2—1761no—
378C2#1306946811yescharacteristic
379C2#1306951211yescharacteristic
380C2#1306953411yescharacteristic
subgroupG/H
centerC2×C4#66948
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC4×C11×#106C2
socleC22×C11#390
prime radical#10623008C22
cosocleC2×C42×C11C23
hypercenterC4×#106D11
hypocenterC11#9717
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#106

Complements

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

NH ≅ G/Ntype
2. #13069559C2semidirect
4. #13067114C2semidirect
6. C8×#4318C2semidirect
7. C4×C11×#106C2semidirect
19. #10622307C4semidirect
20. #10622306C4semidirect
23. #10622294C4semidirect
24. #10622293C4semidirect
121. #4318SD16semidirect
129. C4×#106D11semidirect
169. C8×C11#104semidirect
315. C11#9717semidirect
354. C8#66869semidirect

Maximal subgroups

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

subgroupindex
#130791752
#130695592
#130695342
#130671142
#130671102
C8×#43182
C4×C11×#1062
#971711