Finite Group Databasebeta

← #14652154

Subgroups — #14652154

Order 2816.

454 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13069542C211yesmaximal, characteristic
2#13069421C211yesmaximal, characteristic
3#13069372C211yesmaximal, characteristic, complemented
4#13068486C211yesmaximal, characteristic, complemented
5C2×#10622123C211yesmaximal, characteristic
6#13066450C211yesmaximal, characteristic, complemented
7C11×#1296C211yesmaximal, characteristic, complemented
8C2×#66927C2211yescharacteristic
9C2×C11×C4⋊C8C2211yescharacteristic
10C2×C11×C4⋊C8C2211yescharacteristic
11C11×#384C2211yescharacteristic
12C2×#66885—21no—
13C2×#66885—21no—
14C2×#66879—21no—
15C2×#66873—21no—
16C2×#66873—21no—
17C2×#66871—21no—
18C4×C4⋊Dic11C2211yescharacteristic
19C2×C4⋊(C11⋊C8)C2211yescharacteristic
20C2×C4×C11⋊C8C2211yescharacteristic
21#10622188—21no—
22#10622167—21no—
23#10622123C414yescomplemented
24C22×D44—21no—
25C22×D44—21no—
26C22×D44—21no—
27C22×C8×C11—21no—
28C22×C8×C11—21no—
29C2×C11×C4⋊C4—21no—
30C2×C11×C4⋊C4—21no—
31C2×C11×C4⋊C4—21no—
32C2×C42×C11C2311yescharacteristic
33C2×C4⋊Dic11D411yescharacteristic
34C2×C4⋊Dic11D411yescharacteristic
35C2×C4×Dic11—21no—
36C22×C11⋊C8—21no—
37C22×C11⋊C8D411yescharacteristic
38C22×C11⋊C8D411yescharacteristic
39#66927—21no—
40#66927—21no—
41#66927—21no—
42#66927C2×C412yes—
43C11×C4⋊C8—21no—
44C11×C4⋊C8—21no—
45C11×C4⋊C8—21no—
46C11×C4⋊C8C2×C412yes—
47C11⋊#95—21no—
48#66885—42no—
49#66885—42no—
50#66879—42no—
51#66873—42no—
52#66873—42no—
53#66871—42no—
54C4⋊(C11⋊C8)—21no—
55C4⋊(C11⋊C8)C2×C412yes—
56C4×C11⋊C8—21no—
57C4×C11⋊C8—21no—
58#9571—111nomaximal, Sylow
59C23×D11—41no—
60C22×C4×C11—41no—
61C22×C4×C11C2×D411yescharacteristic
62C22×C4×C11C2×D411yescharacteristic
63C22×C4×C11#4111yescharacteristic
64C22×Dic11—21no—
65C22×Dic11—21no—
66C2×D44—22no—
67C2×D44—22no—
68C2×D44—22no—
69C2×D44—41no—
70C2×D44—41no—
71C2×D44—41no—
72C2×D44—41no—
73C2×D44—41no—
74C2×D44—41no—
75C2×D44—41no—
76C2×D44—41no—
77C2×D44—41no—
78C2×D44—41no—
79C2×D44—41no—
80C2×D44—81no—
81C2×D44—81no—
82C2×C8×C11—22no—
83C2×C8×C11—41no—
84C2×C8×C11—41no—
85C2×C8×C11—41no—
86C2×C8×C11—41no—
87C2×C8×C11—41no—
88C11×C4⋊C4—41no—
89C11×C4⋊C4—41no—
90C11×C4⋊C4—41no—
91C11×C4⋊C4—41no—
92C11×C4⋊C4—81no—
93C42×C11C22×C411yescharacteristic
94C42×C11#4111yescharacteristic
95C42×C11#4111yescharacteristic
96C42×C11#4111yescharacteristic
97C4⋊Dic11—21no—
98C4⋊Dic11—21no—
99C4⋊Dic11—21no—
100C4⋊Dic11—21no—
101C4×Dic11—41no—
102C4×Dic11—41no—
103C2×C11⋊C8—22no—
104C2×C11⋊C8—21no—
105C2×C11⋊C8—21no—
106C2×C11⋊C8—21no—
107C2×C11⋊C8—21no—
108C2×C11⋊C8—21no—
109C2×C11⋊C8—41no—
110C2×C11⋊C8—41no—
111C2×C11⋊C8D812yes—
112#1982—111no—
113#1957—111no—
114#1947—111no—
115#1770—111no—
116C2×#331—111no—
117#1296D1111yescharacteristic, complemented
118#1277—111no—
119C23×C11#12111yescharacteristic
120C22×D11—42no—
121C22×D11—81no—
122C22×D11—81no—
123C22×D11—81no—
124C22×D11—81no—
125C22×D11—81no—
126C22×D11—81no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—81no—
130C2×C4×C11—81no—
131C2×C4×C11—81no—
132C2×C4×C11#11711yescharacteristic
133C2×C4×C11C4×D411yescharacteristic
134C2×C4×C11C4×D411yescharacteristic
135C2×C4×C11#12311yescharacteristic
136C2×C4×C11#12411yescharacteristic
137C2×C4×C11#12611yescharacteristic
138C2×C4×C11C2×D811yescharacteristic
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×C11AGL(1,ℤ/8)11yescharacteristic
144C2×C4×C11#13711yescharacteristic
145C2×C4×C11#13711yescharacteristic
146C2×Dic11—41no—
147C2×Dic11—41no—
148C2×Dic11—41no—
149C2×Dic11—41no—
150C2×Dic11—41no—
151C2×Dic11—41no—
152D44—42no—
153D44—42no—
154D44—42no—
155D44—42no—
156D44—82no—
157D44—82no—
158D44—81no—
159D44—81no—
160D44—81no—
161D44—81no—
162C8×C11—42no—
163C8×C11—81no—
164C11⋊C8—22no—
165C11⋊C8—42no—
166C11⋊C8—41no—
167C2×#127—111no—
168C2×#107—221no—
169C2×C4⋊C8—111no—
170C2×C4⋊C8C2×D1111yescharacteristic
171C2×C4⋊C8C2×D1111yescharacteristic
172C2×#102—221no—
173C2×#102—221no—
174C2×#102—221no—
175C2×#102—221no—
176C2×#97—221no—
177C2×C4×C8—111no—
178#384C2×D1111yescharacteristic
179C4×C4⋊C4—111no—
180#340—221no—
181#336—221no—
182#331—114no—
183C22×C11#38811yescharacteristic
184C22×C11#45911yescharacteristic
185C22×C11#46411yescharacteristic
186C22×C11#46811yescharacteristic
187C22×C11#46911yescharacteristic
188C22×C11#47111yescharacteristic
189C22×C11#47211yescharacteristic
190C2×D11—82no—
191C2×D11—82no—
192C2×D11—82no—
193C2×D11—161no—
194C2×D11—161no—
195C2×D11—161no—
196C2×D11—161no—
197C4×C11—21no—
198C4×C11—21no—
199C4×C11—161no—
200C4×C11C4×D811yescharacteristic
201C4×C11#44011yescharacteristic
202C4×C11#44011yescharacteristic
203C4×C11#44211yescharacteristic
204C4×C11#48011yescharacteristic
205C4×C11#48211yescharacteristic
206C4×C11#48911yescharacteristic
207C4×C11#49011yescharacteristic
208Dic11—81no—
209Dic11—81no—
210C22×D4—221no—
211C22×D4—221no—
212C22×D4—221no—
213C22×C8—21no—
214C22×C8—21no—
215C22×C8—111no—
216C22×C8—111no—
217C22×C8—221no—
218#127—112no—
219#127—221no—
220#127—221no—
221#127—221no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—111no—
226C2×C4⋊C4—111no—
227C2×C42—221no—
228C2×C42C22×D1111yescharacteristic
229#107—442no—
230C4⋊C8—21no—
231C4⋊C8—21no—
232C4⋊C8—21no—
233C4⋊C8—112no—
234C4⋊C8—221no—
235C4⋊C8C4×D1112yes—
236#102—442no—
237#102—442no—
238#102—442no—
239#102—442no—
240#97—442no—
241C4×C8—221no—
242C4×C8—221no—
243#95—221no—
244C2×C11#168511yescharacteristic
245C2×C11#168711yescharacteristic
246C2×C11#169811yescharacteristic
247C2×C11#170211yescharacteristic
248C2×C11#192511yescharacteristic
249C2×C11#193111yescharacteristic
250C2×C11#193611yescharacteristic
251D11—162no—
252C24—441no—
253C2×D4—222no—
254C2×D4—222no—
255C2×D4—222no—
256C2×D4—441no—
257C2×D4—441no—
258C2×D4—441no—
259C2×D4—441no—
260C2×D4—441no—
261C2×D4—441no—
262C2×D4—441no—
263C2×D4—441no—
264C2×D4—441no—
265C2×D4—441no—
266C2×D4—441no—
267C2×D4—881no—
268C2×D4—881no—
269C22×C4—41no—
270C22×C4—221no—
271C22×C4—221no—
272C22×C4#433911yescharacteristic
273C22×C4D4×D1111yescharacteristic
274C22×C4D4×D1111yescharacteristic
275C2×C8—22no—
276C2×C8—41no—
277C2×C8—41no—
278C2×C8—41no—
279C2×C8—41no—
280C2×C8—41no—
281C2×C8—112no—
282C2×C8—221no—
283C2×C8—221no—
284C2×C8—222no—
285C2×C8—221no—
286C2×C8—221no—
287C2×C8—221no—
288C2×C8—441no—
289C2×C8—441no—
290C4⋊C4—41no—
291C4⋊C4—41no—
292C4⋊C4—41no—
293C4⋊C4—41no—
294C4⋊C4—81no—
295C4⋊C4—221no—
296C4⋊C4—221no—
297C4⋊C4—221no—
298C4⋊C4—221no—
299C42—441no—
300C42—441no—
301C42C2×C4×D1111yescharacteristic
302C42#433911yescharacteristic
303C42#434111yescharacteristic
304C42#434311yescharacteristic
305C11#957111yescharacteristic, complemented, Sylow
306C23—442no—
307C23—881no—
308C23—881no—
309C23—881no—
310C23—881no—
311C23—881no—
312C23—881no—
313C23#6693711yescharacteristic
314D4—442no—
315D4—442no—
316D4—442no—
317D4—442no—
318D4—882no—
319D4—882no—
320D4—881no—
321D4—881no—
322D4—881no—
323D4—881no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—81no—
327C2×C4—81no—
328C2×C4—81no—
329C2×C4—441no—
330C2×C4—441no—
331C2×C4—441no—
332C2×C4—441no—
333C2×C4—441no—
334C2×C4—441no—
335C2×C4#6692511yescharacteristic
336C2×C4(C22⋊D11)⋊C411yescharacteristic
337C2×C4#6693811yescharacteristic
338C2×C4#6694611yescharacteristic
339C2×C4#6694711yescharacteristic
340C2×C4#6695111yescharacteristic
341C2×C4D8×D1111yescharacteristic
342C2×C4#6696411yescharacteristic
343C2×C4#6696711yescharacteristic
344C2×C4#6696711yescharacteristic
345C2×C4#6696711yescharacteristic
346C2×C4#6696911yescharacteristic
347C2×C4#6697111yescharacteristic
348C2×C4#6697111yescharacteristic
349C8—42no—
350C8—81no—
351C8—222no—
352C8—441no—
353C8—442no—
354C22—882no—
355C22—882no—
356C22—882no—
357C22—1761no—
358C22—1761no—
359C22—1761no—
360C22—1761no—
361C22#1062228211yescharacteristic
362C22#1062236211yescharacteristic
363C22#1062236711yescharacteristic
364C22#1062239511yescharacteristic
365C22#1062239911yescharacteristic
366C22#1062241111yescharacteristic
367C22#1062242511yescharacteristic
368C4—21no—
369C4—21no—
370C4—161no—
371C4—881no—
372C4—881no—
373C4#1062236911yescharacteristic
374C4#1062237711yescharacteristic
375C4#1062240811yescharacteristic
376C4#1062243011yescharacteristic
377C4#1062247911yescharacteristic
378C4#1062248211yescharacteristic
379C4#1062249511yescharacteristic
380C4#1062250211yescharacteristic
381C2—1762no—
382C2#1306808411yescharacteristic
383C2#1306809411yescharacteristic
384C2#1306815911yescharacteristic
385C2#1306818711yescharacteristic
386C2#1306923411yescharacteristic
387C2#1306927611yescharacteristic
388C2#1306931111yescharacteristic
subgroupG/H
centerC23#66937
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1296C2
socleC23×C11#121
prime radicalC2×#66927C22
cosocleC2×C42×C11C23
hypercenter#1296D11
hypocenterC11#9571
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
3. #13069372C2semidirect
4. #13068486C2semidirect
6. #13066450C2semidirect
7. C11×#1296C2semidirect
23. #10622123C4semidirect
117. #1296D11semidirect
305. C11#9571semidirect

Maximal subgroups

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

subgroupindex
#130695422
#130694212
#130693722
#130684862
C2×#106221232
#130664502
C11×#12962
#957111