Finite Group Databasebeta

← #14647152

Subgroups — #14647152

Order 2816.

544 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071014C211yesmaximal, characteristic
2#13068684C211yesmaximal, characteristic
3#13066495C212yesmaximal
4#13066495C212yesmaximal
5C11×#1434C211yesmaximal, characteristic
6C22×C42×C11C2211yescharacteristic
7C2×C11×#95—21no—
8C2×C11×#95—21no—
9C2×C11×#95C2212yes—
10#10622825C2211yescharacteristic
11#10622825C2211yescharacteristic
12#10622824—21no—
13C4×C22⋊Dic11—21no—
14C2×C22⋊(C11⋊C8)C2212yes—
15#10622550—21no—
16#10622549C411yescharacteristic, complemented
17#10622549C411yescharacteristic, complemented
18C4×C4⋊Dic11C411yescharacteristic, complemented
19C4×C4⋊Dic11C411yescharacteristic, complemented
20#10622545—21no—
21#10622162—21no—
22#10622162—21no—
23C23×C4×C11—22no—
24C23×C4×C11D411yescharacteristic
25C23×C4×C11D411yescharacteristic
26C23×C4×C11C2311yescharacteristic
27C2×C42×C11—24no—
28C2×C42×C11C2×C411yescharacteristic
29C2×C42×C11C2×C411yescharacteristic
30C2×C42×C11D411yescharacteristic
31C2×C42×C11D411yescharacteristic
32C2×C22⋊Dic11—21no—
33C2×C22⋊Dic11—21no—
34C2×C4⋊Dic11C2×C411yescharacteristic
35C2×C4⋊Dic11C2×C411yescharacteristic
36C2×C4⋊Dic11C2×C411yescharacteristic
37C2×C4⋊Dic11C2×C411yescharacteristic
38C2×C4×Dic11—21no—
39C2×C4×Dic11—21no—
40C22×C11⋊C8—22no—
41C11×#95—24no—
42C11×#95—24no—
43C11×#95—42no—
44C11⋊#95—21no—
45C11⋊#95—21no—
46C11⋊#95—21no—
47C11⋊#95—21no—
48C11⋊#95—21no—
49C11⋊#95—21no—
50C11⋊#95—21no—
51C11⋊#95—21no—
52C22⋊(C11⋊C8)—24no—
53#8714—111nomaximal, Sylow
54C24×C11C2×D411yescharacteristic
55C22×C4×C11—22no—
56C22×C4×C11—22no—
57C22×C4×C11—22no—
58C22×C4×C11—21no—
59C22×C4×C11—21no—
60C22×C4×C11—22no—
61C22×C4×C11—24no—
62C22×C4×C11—41no—
63C22×C4×C11—41no—
64C22×C4×C11—41no—
65C22×C4×C11—42no—
66C22×C4×C11—42no—
67C22×C4×C11—42no—
68C22×C4×C11—42no—
69C22×C4×C11—42no—
70C22×C4×C11—42no—
71C22×C4×C11C22⋊C411yescharacteristic
72C22×C4×C11C22⋊C411yescharacteristic
73C22×C4×C11C22⋊C411yescharacteristic
74C22×C4×C11C22⋊C411yescharacteristic
75C22×C4×C11C22×C411yescharacteristic
76C22×C4×C11C2×D411yescharacteristic
77C22×C4×C11#4114yes—
78C22×Dic11—21no—
79C22×Dic11—21no—
80C22×Dic11—21no—
81C22×Dic11—21no—
82C42×C11—22no—
83C42×C11—22no—
84C42×C11—22no—
85C42×C11—22no—
86C22⋊Dic11—42no—
87C22⋊Dic11—41no—
88C22⋊Dic11—41no—
89C4⋊Dic11—41no—
90C4⋊Dic11—41no—
91C4⋊Dic11—41no—
92C4⋊Dic11—41no—
93C4×Dic11—42no—
94C4×Dic11—42no—
95C2×C11⋊C8—42no—
96C2×C11⋊C8—42no—
97C2×C11⋊C8—42no—
98#2283—111no—
99#1817—111no—
100#1434D1111yescharacteristic
101#1294—112no—
102#1294—112no—
103C23×C11—21no—
104C23×C11—21no—
105C23×C11—21no—
106C23×C11—21no—
107C23×C11C2×C22⋊C411yescharacteristic
108C23×C11#12312yes—
109C23×C11#13512yes—
110C23×C11AGL(1,ℤ/8)11yescharacteristic
111C23×C11#13711yescharacteristic
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—44no—
128C2×C4×C11—44no—
129C2×C4×C11—42no—
130C2×C4×C11—42no—
131C2×C4×C11—44no—
132C2×C4×C11—44no—
133C2×C4×C11—44no—
134C2×C4×C11—82no—
135C2×C4×C11—82no—
136C2×C4×C11—82no—
137C2×C4×C11—82no—
138C2×C4×C11#10412yes—
139C2×C4×C11#11712yes—
140C2×C4×C11#12312yes—
141C2×Dic11—41no—
142C2×Dic11—41no—
143C2×Dic11—41no—
144C2×Dic11—41no—
145C2×Dic11—41no—
146C2×Dic11—41no—
147C2×Dic11—41no—
148C2×Dic11—41no—
149C2×Dic11—41no—
150C2×Dic11—41no—
151C2×Dic11—41no—
152C2×Dic11—41no—
153C11⋊C8—82no—
154C22×C42C2×D1111yescharacteristic
155C2×C22⋊C8—112no—
156#383—221no—
157#382—111no—
158#382—111no—
159#381—221no—
160#380—111no—
161#380—111no—
162C4×C4⋊C4—111no—
163C4×C4⋊C4—111no—
164C4×C22⋊C4—221no—
165#376—221no—
166C2×#95—21no—
167C2×#95—21no—
168C2×#95C2×D1112yes—
169#336—221no—
170#336—221no—
171C22×C11—22no—
172C22×C11—22no—
173C22×C11—22no—
174C22×C11—21no—
175C22×C11—21no—
176C22×C11—21no—
177C22×C11—21no—
178C22×C11—22no—
179C22×C11#38111yescharacteristic
180C22×C11#41011yescharacteristic
181C22×C11#41011yescharacteristic
182C22×C11#41611yescharacteristic
183C22×C11#41711yescharacteristic
184C22×C11C2×#10411yescharacteristic
185C22×C11#42111yescharacteristic
186C22×C11#48212yes—
187C22×C11#48512yes—
188C4×C11—22no—
189C4×C11—22no—
190C4×C11—22no—
191C4×C11—41no—
192C4×C11—41no—
193C4×C11—41no—
194C4×C11—84no—
195Dic11—81no—
196Dic11—81no—
197Dic11—81no—
198Dic11—81no—
199C23×C4—22no—
200C23×C4C22⋊D1111yescharacteristic
201C23×C4C22⋊D1111yescharacteristic
202C23×C4C22×D1111yescharacteristic
203C22×C8—222no—
204C2×C4⋊C4—111no—
205C2×C4⋊C4—111no—
206C2×C4⋊C4—111no—
207C2×C4⋊C4—111no—
208C2×C22⋊C4—221no—
209C2×C22⋊C4—221no—
210C2×C42—24no—
211C2×C42—221no—
212C2×C42—221no—
213C2×C42C4×D1111yescharacteristic
214C2×C42C4×D1111yescharacteristic
215C2×C42D4411yescharacteristic
216C2×C42D4411yescharacteristic
217C22⋊C8—224no—
218#95—24no—
219#95—24no—
220#95—42no—
221#95—221no—
222#95—221no—
223#95—221no—
224#95—221no—
225#95—221no—
226#95—221no—
227#95—221no—
228#95—221no—
229C2×C11—22no—
230C2×C11—22no—
231C2×C11#150011yescharacteristic
232C2×C11#150911yescharacteristic
233C2×C11#151211yescharacteristic
234C2×C11#152111yescharacteristic
235C2×C11#182011yescharacteristic
236C2×C11#182511yescharacteristic
237C2×C11#182611yescharacteristic
238C24C2×C22⋊D1111yescharacteristic
239C22×C4—21no—
240C22×C4—22no—
241C22×C4—22no—
242C22×C4—21no—
243C22×C4—22no—
244C22×C4—22no—
245C22×C4—24no—
246C22×C4—41no—
247C22×C4—41no—
248C22×C4—41no—
249C22×C4—42no—
250C22×C4—42no—
251C22×C4—42no—
252C22×C4—42no—
253C22×C4—42no—
254C22×C4—42no—
255C22×C4—221no—
256C22×C4—221no—
257C22×C4—221no—
258C22×C4—221no—
259C22×C4(C2×D11)⋊C411yescharacteristic
260C22×C4(C2×D11)⋊C411yescharacteristic
261C22×C4(C2×D11)⋊C411yescharacteristic
262C22×C4(C2×D11)⋊C411yescharacteristic
263C22×C4C2×C4×D1111yescharacteristic
264C22×C4C2×D4411yescharacteristic
265C22×C4#434114yes—
266C2×C8—442no—
267C2×C8—442no—
268C2×C8—442no—
269C4⋊C4—441no—
270C4⋊C4—441no—
271C4⋊C4—441no—
272C4⋊C4—441no—
273C22⋊C4—441no—
274C22⋊C4—441no—
275C22⋊C4—442no—
276C42—22no—
277C42—22no—
278C42—22no—
279C42—22no—
280C42—442no—
281C42—442no—
282C11#871411yescharacteristic, complemented, Sylow
283C23—21no—
284C23—21no—
285C23—21no—
286C23—21no—
287C23C2×(C2×D11)⋊C411yescharacteristic
288C23#6698511yescharacteristic
289C23#6698812yes—
290C23#6699511yescharacteristic
291C23#6700312yes—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—44no—
308C2×C4—44no—
309C2×C4—42no—
310C2×C4—42no—
311C2×C4—44no—
312C2×C4—44no—
313C2×C4—44no—
314C2×C4—82no—
315C2×C4—82no—
316C2×C4—82no—
317C2×C4—82no—
318C2×C4—441no—
319C2×C4—441no—
320C2×C4—441no—
321C2×C4—441no—
322C2×C4—441no—
323C2×C4—441no—
324C2×C4—441no—
325C2×C4—441no—
326C2×C4—441no—
327C2×C4—441no—
328C2×C4—441no—
329C2×C4—441no—
330C2×C4#6686912yes—
331C2×C4#6693012yes—
332C2×C4#6693912yes—
333C8—882no—
334C22—22no—
335C22—21no—
336C22—21no—
337C22—21no—
338C22—21no—
339C22—22no—
340C22—22no—
341C22—22no—
342C22C2×#6686911yescharacteristic
343C22#1062255611yescharacteristic
344C22#1062257911yescharacteristic
345C22#1062261511yescharacteristic
346C22#1062261811yescharacteristic
347C22#1062261911yescharacteristic
348C22#1062261911yescharacteristic
349C22#1062264812yes—
350C22#1062265812yes—
351C4—22no—
352C4—22no—
353C4—22no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—84no—
358C4—881no—
359C4—881no—
360C4—881no—
361C4—881no—
362C2—22no—
363C2—22no—
364C2#1306710011yescharacteristic
365C2#1306713911yescharacteristic
366C2#1306715211yescharacteristic
367C2#1306719111yescharacteristic
368C2#1306869111yescharacteristic
369C2#1306870811yescharacteristic
370C2#1306871611yescharacteristic
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1434C2
socleC23×C11C2×C22⋊C4
prime radicalC24×C11C2×D4
cosocleC23×C4×C11C23
hypercenter#1434D11
hypocenterC11#8714
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1434

Complements

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

NH ≅ G/Ntype
16. #10622549C4semidirect
17. #10622549C4semidirect
18. C4×C4⋊Dic11C4semidirect
19. C4×C4⋊Dic11C4semidirect
282. C11#8714semidirect

Maximal subgroups

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

subgroupindex
#130710142
#130686842
#130664952
C11×#14342
#871411