Finite Group Databasebeta

← #14653841

Subgroups — #14653841

Order 2816.

654 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076968C211yesmaximal, characteristic
2C4×C22⋊(C11⋊C8)C211yesmaximal, characteristic
3#13066495C214yesmaximal
4C11×C4⋊#95C211yesmaximal, characteristic
5C22×C11×C4⋊C4—21no—
6C22×C42×C11C2211yescharacteristic
7C2×#66977—21no—
8C2×#66922C411yescharacteristic, complemented
9C2×C11×#95—21no—
10C2×C11×#95C2212yes—
11#10622825—21no—
12#10622825C2212yes—
13C2×C22⋊(C11⋊C8)C2212yes—
14#10622548C411yescharacteristic, complemented
15#10622542—21no—
16#10622541—21no—
17#10622541C412yescomplemented
18C2×C4×C11⋊C8—21no—
19#10622162—21no—
20C23×C4×C11—22no—
21C23×C4×C11D411yescharacteristic
22C23×C4×C11D411yescharacteristic
23C23×C4×C11C2311yescharacteristic
24C22×Dic22—21no—
25C2×C11×C4⋊C4—24no—
26C2×C11×C4⋊C4—42no—
27C2×C11×C4⋊C4—42no—
28C2×C42×C11—42no—
29C2×C42×C11C2×C411yescharacteristic
30C2×C42×C11C2×C411yescharacteristic
31C2×C42×C11D411yescharacteristic
32C2×C42×C11D411yescharacteristic
33C2×C22⋊Dic11—22no—
34C2×C4⋊Dic11—21no—
35C2×C4⋊Dic11—21no—
36C2×C4⋊Dic11—21no—
37C2×C4⋊Dic11C2×C412yes—
38C2×C4⋊Dic11C2×C412yes—
39#66977—42no—
40#66977—42no—
41C2×Dic11⋊C4—22no—
42C22×C11⋊C8—22no—
43#66922—42no—
44C11×#95—24no—
45C11×#95—42no—
46C11⋊#95—22no—
47C11⋊#95—22no—
48C22⋊(C11⋊C8)—22no—
49C22⋊(C11⋊C8)Q814yescomplemented
50C4×C11⋊C8—42no—
51#9885—111nomaximal, Sylow
52C24×C11C2×D411yescharacteristic
53C22×C4×C11—22no—
54C22×C4×C11—22no—
55C22×C4×C11—24no—
56C22×C4×C11—41no—
57C22×C4×C11—41no—
58C22×C4×C11—41no—
59C22×C4×C11—41no—
60C22×C4×C11—42no—
61C22×C4×C11—42no—
62C22×C4×C11—42no—
63C22×C4×C11—42no—
64C22×C4×C11—42no—
65C22×C4×C11—42no—
66C22×C4×C11C22⋊C411yescharacteristic
67C22×C4×C11C22⋊C411yescharacteristic
68C22×C4×C11C22⋊C411yescharacteristic
69C22×C4×C11C22⋊C411yescharacteristic
70C22×C4×C11D812yes—
71C22×C4×C11SD1612yes—
72C22×C4×C11SD1612yes—
73C22×C4×C11Q1612yes—
74C22×C4×C11C22×C411yescharacteristic
75C22×C4×C11C2×D411yescharacteristic
76C22×C4×C11C2×Q812yes—
77C22×C4×C11#4112yes—
78C22×Dic11—22no—
79C22×Dic11—22no—
80C2×Dic22—42no—
81C2×Dic22—42no—
82C2×Dic22—42no—
83C11×C4⋊C4—48no—
84C42×C11—22no—
85C42×C11—22no—
86C42×C11—41no—
87C42×C11—41no—
88C22⋊Dic11—42no—
89C22⋊Dic11—42no—
90C4⋊Dic11—42no—
91C4⋊Dic11—42no—
92C4⋊Dic11—42no—
93C4⋊Dic11—42no—
94C4⋊Dic11—42no—
95Dic11⋊C4—44no—
96C2×C11⋊C8—24no—
97C2×C11⋊C8—42no—
98C2×C11⋊C8—42no—
99#2857—111no—
100C4×C22⋊C8—111no—
101C4⋊#95D1111yescharacteristic
102#1294—114no—
103C23×C11—21no—
104C23×C11—21no—
105C23×C11—21no—
106C23×C11—21no—
107C23×C11C2×C22⋊C411yescharacteristic
108C23×C11#12411yescharacteristic
109C23×C11C4⋊Q811yescharacteristic
110C23×C11C2×D811yescharacteristic
111C23×C11C2×SD1611yescharacteristic
112C23×C11C2×SD1611yescharacteristic
113C23×C11C2×Q1611yescharacteristic
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—24no—
125C2×C4×C11—24no—
126C2×C4×C11—42no—
127C2×C4×C11—42no—
128C2×C4×C11—42no—
129C2×C4×C11—42no—
130C2×C4×C11—44no—
131C2×C4×C11—44no—
132C2×C4×C11—44no—
133C2×C4×C11—82no—
134C2×C4×C11—82no—
135C2×C4×C11—82no—
136C2×C4×C11—82no—
137C2×C4×C11#9912yes—
138C2×C4×C11#10212yes—
139C2×C4×C11#10212yes—
140C2×C4×C11#10312yes—
141C2×C4×C11#10312yes—
142C2×C4×C11#10412yes—
143C2×C4×C11C4×Q812yes—
144C2×C4×C11C22⋊Q812yes—
145C2×Dic11—42no—
146C2×Dic11—42no—
147C2×Dic11—42no—
148C2×Dic11—42no—
149C2×Dic11—42no—
150C2×Dic11—42no—
151Dic22—84no—
152C11⋊C8—44no—
153C2×C4⋊Q8—111no—
154C2×C22⋊Q8—221no—
155C22×C4⋊C4—21no—
156C22×C42C2×D1111yescharacteristic
157C2×C22⋊C8—112no—
158C2×C4×C8—221no—
159#391—221no—
160#389—112no—
161#389—221no—
162#384—111no—
163#380—112no—
164#380—221no—
165C2×#95—21no—
166C2×#95C2×D1112yes—
167#336—221no—
168C22×C11—21no—
169C22×C11—21no—
170C22×C11—21no—
171C22×C11—21no—
172C22×C11—21no—
173C22×C11—21no—
174C22×C11—21no—
175C22×C11—21no—
176C22×C11—21no—
177C22×C11—21no—
178C22×C11—21no—
179C22×C11—21no—
180C22×C11#39111yescharacteristic
181C22×C11C2×#9911yescharacteristic
182C22×C11#41011yescharacteristic
183C22×C11C2×#10211yescharacteristic
184C22×C11C2×#10311yescharacteristic
185C22×C11C2×#10411yescharacteristic
186C22×C11#42111yescharacteristic
187C22×C11#48611yescharacteristic
188C22×C11#48711yescharacteristic
189C22×C11#49811yescharacteristic
190C22×C11#50011yescharacteristic
191C4×C11—22no—
192C4×C11—22no—
193C4×C11—22no—
194C4×C11—22no—
195C4×C11—22no—
196C4×C11—84no—
197C4×C11#32714yes—
198Dic11—82no—
199Dic11—82no—
200C22×Q8—221no—
201C23×C4—22no—
202C23×C4C22⋊D1111yescharacteristic
203C23×C4C22⋊D1111yescharacteristic
204C23×C4C22×D1111yescharacteristic
205C22×C8—222no—
206C4⋊Q8—442no—
207C22⋊Q8—442no—
208C22⋊Q8—442no—
209C2×C4⋊C4—24no—
210C2×C4⋊C4—42no—
211C2×C4⋊C4—42no—
212C2×C4⋊C4—112no—
213C2×C4⋊C4—112no—
214C2×C4⋊C4—221no—
215C2×C4⋊C4—222no—
216C2×C4⋊C4—221no—
217C2×C4⋊C4—221no—
218C2×C22⋊C4—222no—
219C2×C42—42no—
220C2×C42C4×D1111yescharacteristic
221C2×C42C4×D1111yescharacteristic
222C2×C42D4411yescharacteristic
223C2×C42D4411yescharacteristic
224C22⋊C8—114no—
225C22⋊C8—222no—
226C4×C8—442no—
227#95—24no—
228#95—42no—
229#95—222no—
230#95—222no—
231C2×C11—21no—
232C2×C11—21no—
233C2×C11—21no—
234C2×C11—21no—
235C2×C11C2×#32711yescharacteristic
236C2×C11#150311yescharacteristic
237C2×C11#151711yescharacteristic
238C2×C11#152011yescharacteristic
239C2×C11#198611yescharacteristic
240C2×C11#199011yescharacteristic
241C2×C11#199611yescharacteristic
242C24C2×C22⋊D1111yescharacteristic
243C2×Q8—442no—
244C2×Q8—442no—
245C2×Q8—442no—
246C22×C4—22no—
247C22×C4—22no—
248C22×C4—24no—
249C22×C4—41no—
250C22×C4—41no—
251C22×C4—41no—
252C22×C4—41no—
253C22×C4—42no—
254C22×C4—42no—
255C22×C4—42no—
256C22×C4—42no—
257C22×C4—42no—
258C22×C4—42no—
259C22×C4—222no—
260C22×C4—222no—
261C22×C4(C2×D11)⋊C411yescharacteristic
262C22×C4(C2×D11)⋊C411yescharacteristic
263C22×C4(C2×D11)⋊C411yescharacteristic
264C22×C4(C2×D11)⋊C411yescharacteristic
265C22×C4#432312yes—
266C22×C4#432412yes—
267C22×C4#432512yes—
268C22×C4#432612yes—
269C22×C4C2×C4×D1111yescharacteristic
270C22×C4C2×D4411yescharacteristic
271C22×C4#434112yes—
272C22×C4Q8×D1112yes—
273C2×C8—224no—
274C2×C8—442no—
275C2×C8—442no—
276C4⋊C4—48no—
277C4⋊C4—442no—
278C4⋊C4—442no—
279C4⋊C4—442no—
280C4⋊C4—442no—
281C4⋊C4—444no—
282C4⋊C4—442no—
283C22⋊C4—442no—
284C22⋊C4—442no—
285C42—22no—
286C42—22no—
287C42—41no—
288C42—41no—
289C11#988511yescharacteristic, complemented, Sylow
290C23—21no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23C2×(C2×D11)⋊C411yescharacteristic
295C23C2×#432311yescharacteristic
296C23C2×#432411yescharacteristic
297C23#6698911yescharacteristic
298C23C2×#432511yescharacteristic
299C23C2×#432611yescharacteristic
300C23#6699711yescharacteristic
301Q8—884no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—24no—
313C2×C4—24no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4—44no—
319C2×C4—44no—
320C2×C4—44no—
321C2×C4—82no—
322C2×C4—82no—
323C2×C4—82no—
324C2×C4—82no—
325C2×C4—442no—
326C2×C4—442no—
327C2×C4—442no—
328C2×C4—442no—
329C2×C4—442no—
330C2×C4—442no—
331C2×C4#6686912yes—
332C2×C4#6687012yes—
333C2×C4#6687312yes—
334C2×C4#6687312yes—
335C2×C4#6687412yes—
336C2×C4#6687412yes—
337C2×C4#6694012yes—
338C2×C4#6695012yes—
339C8—444no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22C2×#6686911yescharacteristic
353C22C2×#6687011yescharacteristic
354C22C2×#6687311yescharacteristic
355C22C2×#6687411yescharacteristic
356C22#1062258711yescharacteristic
357C22#1062261811yescharacteristic
358C22#1062261911yescharacteristic
359C22#1062268311yescharacteristic
360C22#1062269111yescharacteristic
361C22#1062269211yescharacteristic
362C22#1062269411yescharacteristic
363C4—22no—
364C4—22no—
365C4—22no—
366C4—22no—
367C4—22no—
368C4—84no—
369C4—882no—
370C4—882no—
371C4#1062208914yes—
372C2—21no—
373C2—21no—
374C2—21no—
375C2—21no—
376C2C2×#1062208911yescharacteristic
377C2#1306711411yescharacteristic
378C2#1306717511yescharacteristic
379C2#1306718711yescharacteristic
380C2#1306955911yescharacteristic
381C2#1306957611yescharacteristic
382C2#1306960011yescharacteristic
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×C4⋊#95C2
socleC23×C11C2×C22⋊C4
prime radicalC24×C11C2×D4
cosocleC23×C4×C11C23
hypercenterC4⋊#95D11
hypocenterC11#9885
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
8. C2×#66922C4semidirect
14. #10622548C4semidirect
17. #10622541C4semidirect
49. C22⋊(C11⋊C8)Q8semidirect
289. C11#9885semidirect

Maximal subgroups

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

subgroupindex
#130769682
C4×C22⋊(C11⋊C8)2
#130664952
C11×C4⋊#952
#988511