Finite Group Databasebeta

← #14652155

Subgroups — #14652155

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#13069543C211yesmaximal, characteristic
2#13069421C211yesmaximal, characteristic
3#13068485C211yesmaximal, characteristic, complemented
4C2×#10622123C211yesmaximal, characteristic
5#13066499C211yesmaximal, characteristic, complemented
6#13066450C211yesmaximal, characteristic, complemented
7C11×#1947C211yesmaximal, characteristic, complemented
8C2×#66927C2211yescharacteristic
9C2×C11×#107—21no—
10C2×C11×C4⋊C8C2211yescharacteristic
11C11×#384C2211yescharacteristic
12C4×C11×C4⋊C4C2211yescharacteristic
13C2×#66873—21no—
14C2×#66873—21no—
15C2×#66873—21no—
16C2×#66873—21no—
17C2×C4⋊(C11⋊C8)C2211yescharacteristic
18C2×C4⋊(C11⋊C8)C2211yescharacteristic
19C2×#66867—21no—
20C2×C4×C11⋊C8C2211yescharacteristic
21C11×#340—21no—
22#10622162—21no—
23#10622123C414yescomplemented
24C22×D44—21no—
25C22×D44—21no—
26C22×D44—21no—
27C22×C8×C11—21no—
28C2×C11×C4⋊C4—21no—
29C2×C11×C4⋊C4—21no—
30C2×C11×C4⋊C4—21no—
31C2×C11×C4⋊C4D411yescharacteristic
32C2×C11×C4⋊C4D411yescharacteristic
33C2×C42×C11—21no—
34C2×C42×C11C2311yescharacteristic
35C22×C11⋊C8—21no—
36C22×C11⋊C8—21no—
37C22×C11⋊C8D411yescharacteristic
38C22×C11⋊C8D411yescharacteristic
39#66927—21no—
40#66927—21no—
41#66927—21no—
42#66927C2×C412yes—
43C11×#107—42no—
44C11×C4⋊C8—21no—
45C11×C4⋊C8C2×C412yes—
46C11×#95—21no—
47#66873—42no—
48#66873—42no—
49#66873—42no—
50#66873—42no—
51C4⋊(C11⋊C8)—21no—
52C4⋊(C11⋊C8)—21no—
53C4⋊(C11⋊C8)—21no—
54C4⋊(C11⋊C8)C2×C412yes—
55#66867—42no—
56C4×C11⋊C8—21no—
57C4×C11⋊C8—21no—
58#9571—111nomaximal, Sylow
59C23×D11—41no—
60C22×C4×C11—21no—
61C22×C4×C11—21no—
62C22×C4×C11—41no—
63C22×C4×C11C2×D411yescharacteristic
64C22×C4×C11C2×D411yescharacteristic
65C22×C4×C11#4111yescharacteristic
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—
85C11×C4⋊C4—21no—
86C11×C4⋊C4—21no—
87C11×C4⋊C4—21no—
88C11×C4⋊C4—21no—
89C11×C4⋊C4—41no—
90C11×C4⋊C4—41no—
91C11×C4⋊C4—41no—
92C11×C4⋊C4—41no—
93C11×C4⋊C4—81no—
94C42×C11—41no—
95C42×C11—41no—
96C42×C11C22×C411yescharacteristic
97C42×C11#4111yescharacteristic
98C42×C11#4111yescharacteristic
99C42×C11#4111yescharacteristic
100C2×C11⋊C8—22no—
101C2×C11⋊C8—21no—
102C2×C11⋊C8—21no—
103C2×C11⋊C8—21no—
104C2×C11⋊C8—21no—
105C2×C11⋊C8—21no—
106C2×C11⋊C8—41no—
107C2×C11⋊C8—41no—
108C2×C11⋊C8—41no—
109C2×C11⋊C8—41no—
110C2×C11⋊C8—41no—
111C2×C11⋊C8D812yes—
112#1982—111no—
113#1957—111no—
114#1947D1111yescharacteristic, complemented
115#1770—111no—
116C2×#331—111no—
117#1296—111no—
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—41no—
130C2×C4×C11—41no—
131C2×C4×C11—41no—
132C2×C4×C11—41no—
133C2×C4×C11—41no—
134C2×C4×C11—41no—
135C2×C4×C11—81no—
136C2×C4×C11—81no—
137C2×C4×C11—81no—
138C2×C4×C11#11711yescharacteristic
139C2×C4×C11C4×D411yescharacteristic
140C2×C4×C11C4×D411yescharacteristic
141C2×C4×C11#12311yescharacteristic
142C2×C4×C11#12411yescharacteristic
143C2×C4×C11#12611yescharacteristic
144C2×C4×C11C2×D811yescharacteristic
145C2×C4×C11#13511yescharacteristic
146C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
147C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
148C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
149C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
150C2×C4×C11#13711yescharacteristic
151C2×C4×C11#13711yescharacteristic
152D44—42no—
153D44—42no—
154D44—42no—
155D44—42no—
156D44—82no—
157D44—82no—
158D44—81no—
159D44—81no—
160D44—81no—
161D44—81no—
162C8×C11—42no—
163C11⋊C8—22no—
164C11⋊C8—42no—
165C11⋊C8—41no—
166C11⋊C8—81no—
167C2×#127—111no—
168C2×#107—21no—
169C2×C4⋊C8—111no—
170C2×C4⋊C8—111no—
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⋊C4C2×D1111yescharacteristic
180#340—21no—
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—81no—
200C4×C11—81no—
201C4×C11—161no—
202C4×C11C4×D811yescharacteristic
203C4×C11#44011yescharacteristic
204C4×C11#44011yescharacteristic
205C4×C11#44211yescharacteristic
206C4×C11#48011yescharacteristic
207C4×C11#48211yescharacteristic
208C4×C11#48911yescharacteristic
209C4×C11#49011yescharacteristic
210C22×D4—221no—
211C22×D4—221no—
212C22×D4—221no—
213C22×C8—21no—
214C22×C8—111no—
215C22×C8—111no—
216C22×C8—221no—
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⋊C4C22⋊D1111yescharacteristic
226C2×C4⋊C4C22⋊D1111yescharacteristic
227C2×C42—21no—
228C2×C42C22×D1111yescharacteristic
229#107—42no—
230C4⋊C8—21no—
231C4⋊C8—112no—
232C4⋊C8—221no—
233C4⋊C8—221no—
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—21no—
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—21no—
270C22×C4—21no—
271C22×C4—41no—
272C22×C4D4×D1111yescharacteristic
273C22×C4#434111yescharacteristic
274C22×C4C2×C22⋊D1111yescharacteristic
275C2×C8—22no—
276C2×C8—41no—
277C2×C8—41no—
278C2×C8—112no—
279C2×C8—221no—
280C2×C8—221no—
281C2×C8—222no—
282C2×C8—221no—
283C2×C8—221no—
284C2×C8—221no—
285C2×C8—441no—
286C2×C8—441no—
287C2×C8—441no—
288C2×C8—441no—
289C2×C8—441no—
290C4⋊C4—21no—
291C4⋊C4—21no—
292C4⋊C4—21no—
293C4⋊C4—21no—
294C4⋊C4—41no—
295C4⋊C4—41no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C4⋊C4—81no—
299C42—41no—
300C42—41no—
301C42C2×C4×D1111yescharacteristic
302C42#433911yescharacteristic
303C42#434311yescharacteristic
304C42#434311yescharacteristic
305C11#957111yescharacteristic, complemented, Sylow
306C23—442no—
307C23—881no—
308C23—881no—
309C23—881no—
310C23—881no—
311C23—881no—
312C23—881no—
313C23#6699211yescharacteristic
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—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—81no—
333C2×C4—81no—
334C2×C4—81no—
335C2×C4#6694511yescharacteristic
336C2×C4#6694611yescharacteristic
337C2×C4#6694711yescharacteristic
338C2×C4#6695111yescharacteristic
339C2×C4D8×D1111yescharacteristic
340C2×C4#6696411yescharacteristic
341C2×C4#6697111yescharacteristic
342C2×C4#6697211yescharacteristic
343C2×C4C4×C22⋊D1111yescharacteristic
344C2×C4#6698511yescharacteristic
345C2×C4#6699511yescharacteristic
346C2×C4#6700011yescharacteristic
347C2×C4#6700211yescharacteristic
348C2×C4#6700211yescharacteristic
349C8—42no—
350C8—222no—
351C8—442no—
352C8—441no—
353C8—881no—
354C22—882no—
355C22—882no—
356C22—882no—
357C22—1761no—
358C22—1761no—
359C22—1761no—
360C22—1761no—
361C22#1062260311yescharacteristic
362C22#1062265211yescharacteristic
363C22#1062266211yescharacteristic
364C22#1062276311yescharacteristic
365C22#1062279811yescharacteristic
366C22#1062281211yescharacteristic
367C22#1062281611yescharacteristic
368C4—21no—
369C4—21no—
370C4—81no—
371C4—81no—
372C4—161no—
373C4#1062248511yescharacteristic
374C4#1062249511yescharacteristic
375C4#1062249811yescharacteristic
376C4#1062250211yescharacteristic
377C4#1062262711yescharacteristic
378C4#1062263911yescharacteristic
379C4#1062268011yescharacteristic
380C4#1062270211yescharacteristic
381C2—1762no—
382C2#1306808311yescharacteristic
383C2#1306809311yescharacteristic
384C2#1306815811yescharacteristic
385C2#1306818611yescharacteristic
386C2#1306923511yescharacteristic
387C2#1306927711yescharacteristic
388C2#1306931211yescharacteristic
subgroupG/H
centerC23#66992
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1947C2
socleC23×C11#121
prime radicalC2×#66927C22
cosocleC2×C42×C11C23
hypercenter#1947D11
hypocenterC11#9571
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1947

Complements

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

NH ≅ G/Ntype
3. #13068485C2semidirect
5. #13066499C2semidirect
6. #13066450C2semidirect
7. C11×#1947C2semidirect
23. #10622123C4semidirect
114. #1947D11semidirect
305. C11#9571semidirect

Maximal subgroups

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

subgroupindex
#130695432
#130694212
#130684852
C2×#106221232
#130664992
#130664502
C11×#19472
#957111