Finite Group Databasebeta

← #14652153

Subgroups — #14652153

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#13069544C211yesmaximal, characteristic
2#13069372C211yesmaximal, characteristic, complemented
3#13068483C211yesmaximal, characteristic, complemented
4C2×#10622182C211yesmaximal, characteristic
5#13066499C211yesmaximal, characteristic, complemented
6#13066451C211yesmaximal, characteristic, complemented
7C11×#1957C211yesmaximal, characteristic
8C2×C11×#127C2211yescharacteristic
9C2×C11×#102—21no—
10C2×C11×#102—21no—
11C2×C4×C8×C11C2211yescharacteristic
12C11×#384C2211yescharacteristic
13C2×#66896—21no—
14C2×#66896—21no—
15C2×#66879—21no—
16C2×#66871—21no—
17C4×C4⋊Dic11C2211yescharacteristic
18C2×C4⋊(C11⋊C8)C2211yescharacteristic
19C2×C4⋊(C11⋊C8)C2211yescharacteristic
20C2×C4⋊(C11⋊C8)C2211yescharacteristic
21#10622188—21no—
22#10622182C414yescomplemented
23#10622167—21no—
24C22×D4×C11—21no—
25C22×D4×C11—21no—
26C22×D4×C11—21no—
27C22×C8×C11D411yescharacteristic
28C22×C8×C11D411yescharacteristic
29C11×#127—21no—
30C11×#127—21no—
31C11×#127—21no—
32C11×#127C2×C412yes—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4—21no—
35C2×C11×C4⋊C4—21no—
36C2×C42×C11C2311yescharacteristic
37C2×C4⋊Dic11D411yescharacteristic
38C2×C4⋊Dic11D411yescharacteristic
39C2×C4×Dic11—21no—
40C22×C11⋊C8—21no—
41C22×C11⋊C8—21no—
42C22×C11⋊C8—21no—
43C11×#102—42no—
44C11×#102—42no—
45C4×C8×C11—21no—
46C4×C8×C11—21no—
47#66896—42no—
48#66896—42no—
49C11⋊#95—21no—
50#66879—42no—
51#66871—42no—
52C4⋊(C11⋊C8)—21no—
53C4⋊(C11⋊C8)—21no—
54C4⋊(C11⋊C8)—21no—
55C4⋊(C11⋊C8)—21no—
56C4⋊(C11⋊C8)C2×C412yes—
57C4⋊(C11⋊C8)C2×C412yes—
58#9571—111nomaximal, Sylow
59C24×C11—41no—
60C2×D4×C11—22no—
61C2×D4×C11—22no—
62C2×D4×C11—22no—
63C2×D4×C11—41no—
64C2×D4×C11—41no—
65C2×D4×C11—41no—
66C2×D4×C11—41no—
67C2×D4×C11—41no—
68C2×D4×C11—41no—
69C2×D4×C11—41no—
70C2×D4×C11—41no—
71C2×D4×C11—41no—
72C2×D4×C11—41no—
73C2×D4×C11—41no—
74C2×D4×C11—81no—
75C2×D4×C11—81no—
76C22×C4×C11—41no—
77C22×C4×C11C2×D411yescharacteristic
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11#4111yescharacteristic
80C22×Dic11—21no—
81C22×Dic11—21no—
82C2×C8×C11—21no—
83C2×C8×C11—21no—
84C2×C8×C11—21no—
85C2×C8×C11—21no—
86C2×C8×C11—21no—
87C2×C8×C11D812yes—
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—22no—
105C2×C11⋊C8—41no—
106C2×C11⋊C8—41no—
107C2×C11⋊C8—41no—
108C2×C11⋊C8—41no—
109C2×C11⋊C8—41no—
110C2×C11⋊C8—41no—
111C2×C11⋊C8—41no—
112#1982—111no—
113#1957D1111yescharacteristic
114#1947—111no—
115#1770—111no—
116C2×#331—111no—
117#1296—111no—
118#1277—111no—
119C23×C11—42no—
120C23×C11—81no—
121C23×C11—81no—
122C23×C11—81no—
123C23×C11—81no—
124C23×C11—81no—
125C23×C11—81no—
126C23×C11#12111yescharacteristic
127D4×C11—42no—
128D4×C11—42no—
129D4×C11—42no—
130D4×C11—42no—
131D4×C11—82no—
132D4×C11—82no—
133D4×C11—81no—
134D4×C11—81no—
135D4×C11—81no—
136D4×C11—81no—
137C2×C4×C11—21no—
138C2×C4×C11—21no—
139C2×C4×C11—81no—
140C2×C4×C11—81no—
141C2×C4×C11—81no—
142C2×C4×C11#11711yescharacteristic
143C2×C4×C11C4×D411yescharacteristic
144C2×C4×C11C4×D411yescharacteristic
145C2×C4×C11#12311yescharacteristic
146C2×C4×C11#12411yescharacteristic
147C2×C4×C11#12611yescharacteristic
148C2×C4×C11C2×D811yescharacteristic
149C2×C4×C11#13511yescharacteristic
150C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
151C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
152C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
153C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
154C2×C4×C11#13711yescharacteristic
155C2×C4×C11#13711yescharacteristic
156C2×Dic11—41no—
157C2×Dic11—41no—
158C2×Dic11—41no—
159C2×Dic11—41no—
160C2×Dic11—41no—
161C2×Dic11—41no—
162C8×C11—22no—
163C8×C11—41no—
164C11⋊C8—42no—
165C11⋊C8—42no—
166C11⋊C8—81no—
167C2×#127C2×D1111yescharacteristic
168C2×#107—221no—
169C2×C4⋊C8—111no—
170C2×C4⋊C8—111no—
171C2×C4⋊C8—111no—
172C2×#102—21no—
173C2×#102—21no—
174C2×#102—221no—
175C2×#102—221no—
176C2×#97—221no—
177C2×C4×C8C2×D1111yescharacteristic
178#384C2×D1111yescharacteristic
179C4×C4⋊C4—111no—
180#340—221no—
181#336—221no—
182#331—114no—
183C22×C11—82no—
184C22×C11—82no—
185C22×C11—82no—
186C22×C11—161no—
187C22×C11—161no—
188C22×C11—161no—
189C22×C11—161no—
190C22×C11#38811yescharacteristic
191C22×C11#45911yescharacteristic
192C22×C11#46411yescharacteristic
193C22×C11#46811yescharacteristic
194C22×C11#46911yescharacteristic
195C22×C11#47111yescharacteristic
196C22×C11#47211yescharacteristic
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—21no—
211C22×D4—21no—
212C22×D4—21no—
213C22×C8—221no—
214C22×C8—221no—
215C22×C8—221no—
216C22×C8C22⋊D1111yescharacteristic
217C22×C8C22⋊D1111yescharacteristic
218#127—21no—
219#127—21no—
220#127—21no—
221#127C4×D1112yes—
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—112no—
231C4⋊C8—112no—
232C4⋊C8—221no—
233C4⋊C8—221no—
234C4⋊C8—221no—
235C4⋊C8—221no—
236#102—42no—
237#102—42no—
238#102—442no—
239#102—442no—
240#97—442no—
241C4×C8—21no—
242C4×C8—21no—
243#95—221no—
244C2×C11—162no—
245C2×C11#168511yescharacteristic
246C2×C11#168711yescharacteristic
247C2×C11#169811yescharacteristic
248C2×C11#170211yescharacteristic
249C2×C11#192511yescharacteristic
250C2×C11#193111yescharacteristic
251C2×C11#193611yescharacteristic
252C24—41no—
253C2×D4—22no—
254C2×D4—22no—
255C2×D4—22no—
256C2×D4—41no—
257C2×D4—41no—
258C2×D4—41no—
259C2×D4—41no—
260C2×D4—41no—
261C2×D4—41no—
262C2×D4—41no—
263C2×D4—41no—
264C2×D4—41no—
265C2×D4—41no—
266C2×D4—41no—
267C2×D4—81no—
268C2×D4—81no—
269C22×C4—41no—
270C22×C4—221no—
271C22×C4—221no—
272C22×C4D4×D1111yescharacteristic
273C22×C4#434111yescharacteristic
274C22×C4C2×C22⋊D1111yescharacteristic
275C2×C8—21no—
276C2×C8—21no—
277C2×C8—21no—
278C2×C8—21no—
279C2×C8—21no—
280C2×C8—222no—
281C2×C8—222no—
282C2×C8—441no—
283C2×C8—441no—
284C2×C8—441no—
285C2×C8—441no—
286C2×C8—441no—
287C2×C8—441no—
288C2×C8—441no—
289C2×C8#432312yes—
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#434111yescharacteristic
305C11#957111yescharacteristic, complemented, Sylow
306C23—42no—
307C23—81no—
308C23—81no—
309C23—81no—
310C23—81no—
311C23—81no—
312C23—81no—
313C23#6699111yescharacteristic
314D4—42no—
315D4—42no—
316D4—42no—
317D4—42no—
318D4—82no—
319D4—82no—
320D4—81no—
321D4—81no—
322D4—81no—
323D4—81no—
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#6693011yescharacteristic
336C2×C4#6693211yescharacteristic
337C2×C4(C22⋊D11)⋊C411yescharacteristic
338C2×C4#6693811yescharacteristic
339C2×C4#6696411yescharacteristic
340C2×C4#6696411yescharacteristic
341C2×C4#6696711yescharacteristic
342C2×C4#6696811yescharacteristic
343C2×C4C4×C22⋊D1111yescharacteristic
344C2×C4C2×#432311yescharacteristic
345C2×C4#6698511yescharacteristic
346C2×C4#6698811yescharacteristic
347C2×C4#6700311yescharacteristic
348C2×C4#6700411yescharacteristic
349C8—22no—
350C8—41no—
351C8—442no—
352C8—442no—
353C8—881no—
354C22—82no—
355C22—82no—
356C22—82no—
357C22—161no—
358C22—161no—
359C22—161no—
360C22—161no—
361C22#1062255711yescharacteristic
362C22#1062266711yescharacteristic
363C22#1062268511yescharacteristic
364C22#1062277211yescharacteristic
365C22#1062277311yescharacteristic
366C22#1062278711yescharacteristic
367C22#1062279011yescharacteristic
368C4—21no—
369C4—21no—
370C4—161no—
371C4—881no—
372C4—881no—
373C4#1062237011yescharacteristic
374C4#1062237711yescharacteristic
375C4#1062237811yescharacteristic
376C4#1062239811yescharacteristic
377C4C4×#432311yescharacteristic
378C4#1062263111yescharacteristic
379C4#1062264611yescharacteristic
380C4#1062264811yescharacteristic
381C2—162no—
382C2#1306807811yescharacteristic
383C2#1306809211yescharacteristic
384C2#1306815311yescharacteristic
385C2#1306818111yescharacteristic
386C2#1306923311yescharacteristic
387C2#1306927511yescharacteristic
388C2#1306931011yescharacteristic
subgroupG/H
centerC23#66991
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1957C2
socleC23×C11#121
prime radicalC2×C11×#127C22
cosocleC2×C42×C11C23
hypercenter#1957D11
hypocenterC11#9571
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1957

Complements

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

NH ≅ G/Ntype
2. #13069372C2semidirect
3. #13068483C2semidirect
5. #13066499C2semidirect
6. #13066451C2semidirect
22. #10622182C4semidirect
305. C11#9571semidirect

Maximal subgroups

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

subgroupindex
#130695442
#130693722
#130684832
C2×#106221822
#130664992
#130664512
C11×#19572
#957111