Finite Group Databasebeta

← #14658482

Subgroups — #14658482

Order 2816.

418 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#13069409C211yesmaximal, characteristic
2#13068775C211yesmaximal, characteristic, complemented
3#13068617C211yesmaximal, characteristic
4#13068613C211yesmaximal, characteristic
5#13066500C211yesmaximal, characteristic, complemented
6#13066450C211yesmaximal, characteristic, complemented
7C11×#1296C211yesmaximal, characteristic, complemented
8C2×C4×D44C2211yescharacteristic
9C2×C11×C4⋊C8C2211yescharacteristic
10C2×C11×C4⋊C8C2211yescharacteristic
11C11×#384C2211yescharacteristic
12C2×#66885—21no—
13C2×(C2×D11)⋊C8—21no—
14C2×(C2×D11)⋊C8—21no—
15C2×#66873—21no—
16C2×#66871—21no—
17C2×#66871—21no—
18#10622548C2211yescharacteristic
19C2×C4⋊(C11⋊C8)C2211yescharacteristic
20C2×C4×C11⋊C8C2211yescharacteristic
21#10622189—21no—
22#10622167—21no—
23C22×D44D411yescharacteristic
24C22×C4×D11—21no—
25C22×C8×C11—21no—
26C22×C8×C11—21no—
27C2×C11×C4⋊C4—21no—
28C2×C11×C4⋊C4—21no—
29C2×C11×C4⋊C4—21no—
30C2×C42×C11C2311yescharacteristic
31C2×(C2×D11)⋊C4—21no—
32C2×C4⋊Dic11—21no—
33C2×C4⋊Dic11—21no—
34C2×C4⋊Dic11—21no—
35C2×C4⋊Dic11D411yescharacteristic
36C22×C11⋊C8—21no—
37C22×C11⋊C8D411yescharacteristic
38C22×C11⋊C8D411yescharacteristic
39C4×D44—21no—
40C4×D44—21no—
41C4×D44—21no—
42C4×D44—21no—
43C11×C4⋊C8—21no—
44C11×C4⋊C8—21no—
45C11×C4⋊C8—21no—
46C11×C4⋊C8—21no—
47#66885—42no—
48(C2×D11)⋊C8—42no—
49(C2×D11)⋊C8—42no—
50#66873—42no—
51#66871—42no—
52#66871—42no—
53C4⋊(C11⋊C8)—21no—
54C4⋊(C11⋊C8)—21no—
55C4×C11⋊C8—21no—
56C4×C11⋊C8—21no—
57#10616—111nomaximal, Sylow
58C23×D11—21no—
59C22×C4×C11—41no—
60C22×C4×C11C2×D411yescharacteristic
61C22×C4×C11C2×D411yescharacteristic
62C22×C4×C11#4111yescharacteristic
63C22×Dic11—21no—
64C22×Dic11—41no—
65C2×D44—21no—
66C2×D44—21no—
67C2×D44—21no—
68C2×D44—21no—
69C2×D44—21no—
70C2×D44Q1612yes—
71C2×C4×D11—41no—
72C2×C4×D11—41no—
73C2×C4×D11—41no—
74C2×C4×D11—41no—
75C2×C4×D11—41no—
76C2×C4×D11—41no—
77C2×C8×C11—41no—
78C2×C8×C11—41no—
79C2×C8×C11—41no—
80C2×C8×C11—41no—
81C2×C8×C11—41no—
82C2×C8×C11—41no—
83C11×C4⋊C4—41no—
84C11×C4⋊C4—41no—
85C11×C4⋊C4—41no—
86C11×C4⋊C4—41no—
87C11×C4⋊C4—81no—
88C42×C11#4111yescharacteristic
89C42×C11#4111yescharacteristic
90C42×C11#4111yescharacteristic
91C42×C11#4111yescharacteristic
92(C2×D11)⋊C4—41no—
93(C2×D11)⋊C4—41no—
94C4⋊Dic11—21no—
95C4⋊Dic11—21no—
96C4⋊Dic11—41no—
97C4⋊Dic11—41no—
98C4⋊Dic11—41no—
99C4⋊Dic11—41no—
100C4⋊Dic11—81no—
101C2×C11⋊C8—21no—
102C2×C11⋊C8—21no—
103C2×C11⋊C8—21no—
104C2×C11⋊C8—21no—
105C2×C11⋊C8—41no—
106C2×C11⋊C8—41no—
107C2×C11⋊C8—41no—
108C2×C11⋊C8D812yes—
109C2×C11⋊C8SD1612yes—
110#1954—111no—
111#1845—111no—
112#1802—111no—
113#1802—111no—
114#1296—111no—
115#1296D1111yescharacteristic, complemented
116#1277—111no—
117C23×C11#12111yescharacteristic
118C22×D11—22no—
119C22×D11—41no—
120C22×D11—41no—
121C22×D11—41no—
122C22×D11—41no—
123C22×D11—41no—
124C22×D11—41no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—81no—
128C2×C4×C11—81no—
129C2×C4×C11—81no—
130C2×C4×C11#12311yescharacteristic
131C2×C4×C11#12311yescharacteristic
132C2×C4×C11#12311yescharacteristic
133C2×C4×C11#12411yescharacteristic
134C2×C4×C11#12611yescharacteristic
135C2×C4×C11#12611yescharacteristic
136C2×C4×C11C2×D811yescharacteristic
137C2×C4×C11C2×SD1611yescharacteristic
138C2×C4×C11C2×Q1611yescharacteristic
139C2×C4×C11#13511yescharacteristic
140C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
141C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
142C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
143C2×C4×C11#13711yescharacteristic
144C2×Dic11—41no—
145C2×Dic11—41no—
146C2×Dic11—41no—
147C2×Dic11—81no—
148C2×Dic11—81no—
149C2×Dic11—81no—
150D44—22no—
151D44—22no—
152D44—41no—
153D44—41no—
154C4×D11—81no—
155C4×D11—81no—
156C4×D11—81no—
157C4×D11—81no—
158C8×C11—81no—
159C8×C11—81no—
160C11⋊C8—22no—
161C11⋊C8—22no—
162C11⋊C8—81no—
163C2×C4×D4—111no—
164C2×#107—221no—
165C2×#107—221no—
166C2×C4⋊C8—111no—
167C2×C4⋊C8C2×D1111yescharacteristic
168C2×C4⋊C8C2×D1111yescharacteristic
169C2×#102—221no—
170C2×#102—221no—
171C2×C22⋊C8—221no—
172C2×C22⋊C8—221no—
173C2×C4×C8—111no—
174#384—111no—
175#384C2×D1111yescharacteristic
176#340—221no—
177#340—221no—
178C22×C11#39711yescharacteristic
179C22×C11#45911yescharacteristic
180C22×C11#46111yescharacteristic
181C22×C11#46711yescharacteristic
182C22×C11#46911yescharacteristic
183C22×C11#47211yescharacteristic
184C22×C11#47311yescharacteristic
185C2×D11—42no—
186C2×D11—42no—
187C2×D11—42no—
188C2×D11—81no—
189C2×D11—81no—
190C2×D11—81no—
191C2×D11—81no—
192C4×C11—21no—
193C4×C11—21no—
194C4×C11—161no—
195C4×C11#48011yescharacteristic
196C4×C11#48111yescharacteristic
197C4×C11#48211yescharacteristic
198C4×C11#48211yescharacteristic
199C4×C11#48411yescharacteristic
200C4×C11#48411yescharacteristic
201C4×C11#48611yescharacteristic
202C4×C11#48911yescharacteristic
203Dic11—81no—
204Dic11—161no—
205C22×D4—111no—
206C23×C4—221no—
207C22×C8—21no—
208C22×C8—21no—
209C22×C8—111no—
210C22×C8—111no—
211C22×C8—221no—
212C4×D4—221no—
213C4×D4—221no—
214C4×D4—221no—
215C4×D4—221no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—111no—
220C2×C4⋊C4—221no—
221C2×C4⋊C4—221no—
222C2×C4⋊C4—221no—
223C2×C22⋊C4—221no—
224C2×C42C22×D1111yescharacteristic
225#107—442no—
226#107—442no—
227C4⋊C8—21no—
228C4⋊C8—21no—
229C4⋊C8—21no—
230C4⋊C8—21no—
231C4⋊C8—221no—
232C4⋊C8—221no—
233#102—442no—
234#102—442no—
235C22⋊C8—442no—
236C22⋊C8—442no—
237C4×C8—221no—
238C4×C8—221no—
239C2×C11#166911yescharacteristic
240C2×C11#167511yescharacteristic
241C2×C11#168711yescharacteristic
242C2×C11#169311yescharacteristic
243C2×C11#207111yescharacteristic
244C2×C11#207611yescharacteristic
245C2×C11#207811yescharacteristic
246D11—82no—
247C24—221no—
248C2×D4—112no—
249C2×D4—221no—
250C2×D4—221no—
251C2×D4—221no—
252C2×D4—221no—
253C2×D4—221no—
254C22×C4—41no—
255C22×C4—221no—
256C22×C4—441no—
257C22×C4—441no—
258C22×C4—441no—
259C22×C4—441no—
260C22×C4—441no—
261C22×C4—441no—
262C22×C4—441no—
263C22×C4#433911yescharacteristic
264C22×C4D4×D1111yescharacteristic
265C22×C4D4×D1111yescharacteristic
266C2×C8—41no—
267C2×C8—41no—
268C2×C8—41no—
269C2×C8—41no—
270C2×C8—41no—
271C2×C8—41no—
272C2×C8—112no—
273C2×C8—112no—
274C2×C8—221no—
275C2×C8—221no—
276C2×C8—221no—
277C2×C8—221no—
278C2×C8—441no—
279C2×C8—441no—
280C2×C8—441no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—81no—
286C4⋊C4—221no—
287C4⋊C4—221no—
288C4⋊C4—441no—
289C4⋊C4—441no—
290C4⋊C4—441no—
291C4⋊C4—441no—
292C4⋊C4—881no—
293C22⋊C4—441no—
294C22⋊C4—441no—
295C42#433911yescharacteristic
296C42#433911yescharacteristic
297C42#434111yescharacteristic
298C42#434311yescharacteristic
299C11#1061611yescharacteristic, complemented, Sylow
300C23—222no—
301C23—441no—
302C23—441no—
303C23—441no—
304C23—441no—
305C23—441no—
306C23—441no—
307C23#6693711yescharacteristic
308D4—222no—
309D4—222no—
310D4—441no—
311D4—441no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—81no—
315C2×C4—81no—
316C2×C4—81no—
317C2×C4—441no—
318C2×C4—441no—
319C2×C4—441no—
320C2×C4—881no—
321C2×C4—881no—
322C2×C4—881no—
323C2×C4—881no—
324C2×C4—881no—
325C2×C4—881no—
326C2×C4—881no—
327C2×C4#6692911yescharacteristic
328C2×C4#6693611yescharacteristic
329C2×C4#6693811yescharacteristic
330C2×C4#6694711yescharacteristic
331C2×C4#6694711yescharacteristic
332C2×C4#6695111yescharacteristic
333C2×C4D8×D1111yescharacteristic
334C2×C4#6696411yescharacteristic
335C2×C4SD16×D1111yescharacteristic
336C2×C4#6696711yescharacteristic
337C2×C4#6696711yescharacteristic
338C2×C4#6696911yescharacteristic
339C2×C4Q16×D1111yescharacteristic
340C2×C4#6697111yescharacteristic
341C8—81no—
342C8—81no—
343C8—222no—
344C8—222no—
345C8—881no—
346C22—442no—
347C22—442no—
348C22—442no—
349C22—881no—
350C22—881no—
351C22—881no—
352C22—881no—
353C22#1062228811yescharacteristic
354C22#1062236211yescharacteristic
355C22#1062236811yescharacteristic
356C22#1062239511yescharacteristic
357C22#1062239911yescharacteristic
358C22#1062242611yescharacteristic
359C22#1062243111yescharacteristic
360C4—21no—
361C4—21no—
362C4—161no—
363C4—881no—
364C4—1761no—
365C4#1062237311yescharacteristic
366C4#1062239211yescharacteristic
367C4#1062240811yescharacteristic
368C4#1062242211yescharacteristic
369C4#1062247611yescharacteristic
370C4#1062247911yescharacteristic
371C4#1062249511yescharacteristic
372C4#1062249711yescharacteristic
373C2—882no—
374C2#1306798011yescharacteristic
375C2#1306801411yescharacteristic
376C2#1306809411yescharacteristic
377C2#1306812811yescharacteristic
378C2#1307002311yescharacteristic
379C2#1307004811yescharacteristic
380C2#1307006011yescharacteristic
subgroupG/H
centerC23#66937
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1296C2
socleC23×C11#121
prime radicalC22×D44D4
hypercenter#1296D11
hypocenterC11#10616
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
2. #13068775C2semidirect
5. #13066500C2semidirect
6. #13066450C2semidirect
7. C11×#1296C2semidirect
115. #1296D11semidirect
299. C11#10616semidirect

Maximal subgroups

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

subgroupindex
#130694092
#130687752
#130686172
#130686132
#130665002
#130664502
C11×#12962
#1061611