Finite Group Databasebeta

← #14652824

Subgroups — #14652824

Order 2816.

602 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076972C211yesmaximal, characteristic
2#13068732C211yesmaximal, characteristic, complemented
3C4⋊C8×Dic11C211yesmaximal, characteristic, complemented
4C2×#10622120C211yesmaximal, characteristic, complemented
5C2×#10622124C211yesmaximal, characteristic, complemented
6C2×#10622182C211yesmaximal, characteristic
7C2×C11×#331C211yesmaximal, characteristic
8C2×C11×#127C2211yescharacteristic
9C2×#66989—21no—
10C2×#66989—21no—
11C2×#66922C2211yescharacteristic
12C2×C11×C4⋊C8C2211yescharacteristic
13C2×C11×C4⋊C8C2211yescharacteristic
14#10622834—22no—
15#10622834C414yes—
16C2×C8×Dic11—21no—
17C42×Dic11C2211yescharacteristic
18C2×C4⋊(C11⋊C8)C2211yescharacteristic
19C2×C4⋊(C11⋊C8)C2211yescharacteristic
20C11×#331—22no—
21#10622188—21no—
22#10622188—22no—
23#10622182—22no—
24#10622124—22no—
25#10622120—22no—
26C22×D4×C11—21no—
27C22×D4×C11—21no—
28C22×D4×C11C2×C412yes—
29C22×Dic22—21no—
30C22×C8×C11—21no—
31C22×C8×C11—21no—
32C11×#127—21no—
33C11×#127—21no—
34C11×#127—21no—
35C11×#127—21no—
36C2×C42×C11C2311yescharacteristic
37C2×C22⋊Dic11—24no—
38C2×C22⋊Dic11—24no—
39#66989—42no—
40#66989—42no—
41#66989—42no—
42#66989—42no—
43C2×C4⋊Dic11—21no—
44C2×C4⋊Dic11C2×C412yes—
45C2×C4×Dic11C2×C412yes—
46C2×C4×Dic11D411yescharacteristic
47C2×C4×Dic11D412yes—
48C2×C4×Dic11D411yescharacteristic
49C22×C11⋊C8—21no—
50C22×C11⋊C8—21no—
51#66922—21no—
52#66922—21no—
53#66922—21no—
54#66922—21no—
55C11×C4⋊C8—21no—
56C11×C4⋊C8—21no—
57C11×C4⋊C8—21no—
58C11×C4⋊C8D412yes—
59C8×Dic11—42no—
60C4⋊(C11⋊C8)—21no—
61C4⋊(C11⋊C8)—21no—
62C4⋊(C11⋊C8)—21no—
63C4⋊(C11⋊C8)D412yes—
64#9696—111nomaximal, Sylow
65C24×C11—22no—
66C2×D4×C11—22no—
67C2×D4×C11—22no—
68C2×D4×C11—44no—
69C2×D4×C11—41no—
70C2×D4×C11—41no—
71C2×D4×C11—41no—
72C2×D4×C11—41no—
73C2×D4×C11—41no—
74C2×D4×C11—41no—
75C2×D4×C11—42no—
76C2×D4×C11—42no—
77C2×D4×C11—41no—
78C2×D4×C11—41no—
79C22×C4×C11C22×C411yescharacteristic
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C22×Dic11—22no—
83C22×Dic11C22⋊C412yes—
84C22×Dic11C22⋊C412yes—
85C2×Dic22—41no—
86C2×Dic22—41no—
87C2×Dic22—41no—
88C2×Dic22—41no—
89C2×Dic22—41no—
90C2×Dic22—41no—
91C2×C8×C11—22no—
92C2×C8×C11—41no—
93C2×C8×C11—41no—
94C2×C8×C11—42no—
95C2×C8×C11—41no—
96C42×C11C2×D411yescharacteristic
97C42×C11C2×D411yescharacteristic
98C42×C11#4111yescharacteristic
99C42×C11#4111yescharacteristic
100C22⋊Dic11—48no—
101C22⋊Dic11—48no—
102C4⋊Dic11—22no—
103C4⋊Dic11—22no—
104C4⋊Dic11—41no—
105C4⋊Dic11—41no—
106C4×Dic11—22no—
107C4×Dic11—22no—
108C4×Dic11—21no—
109C4×Dic11—21no—
110C4×Dic11—42no—
111C4×Dic11D812yes—
112C4×Dic11SD1612yes—
113C2×C11⋊C8—22no—
114C2×C11⋊C8—41no—
115C2×C11⋊C8—41no—
116C2×C11⋊C8—42no—
117C2×C11⋊C8—41no—
118#2858—111no—
119#1831—111no—
120C4×C4⋊C8—111no—
121C2×#332—111no—
122C2×#332—111no—
123C2×#331—111no—
124C2×#331D1111yescharacteristic
125C23×C11—42no—
126C23×C11—44no—
127C23×C11—42no—
128C23×C11—44no—
129C23×C11—42no—
130C23×C11C2×C22⋊C411yescharacteristic
131D4×C11—82no—
132D4×C11—82no—
133D4×C11—81no—
134D4×C11—81no—
135D4×C11—81no—
136D4×C11—81no—
137D4×C11—82no—
138D4×C11—81no—
139D4×C11—81no—
140C2×C4×C11—22no—
141C2×C4×C11C4×D411yescharacteristic
142C2×C4×C11C4×D411yescharacteristic
143C2×C4×C11#12111yescharacteristic
144C2×C4×C11#12111yescharacteristic
145C2×C4×C11#12411yescharacteristic
146C2×C4×C11#12711yescharacteristic
147C2×C4×C11C2×D811yescharacteristic
148C2×C4×C11C2×SD1611yescharacteristic
149C2×C4×C11#13512yes—
150C2×C4×C11#13512yes—
151C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
152C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
153C2×Dic11—22no—
154C2×Dic11—22no—
155C2×Dic11—22no—
156C2×Dic11—22no—
157C2×Dic11—22no—
158C2×Dic11—42no—
159C2×Dic11—42no—
160C2×Dic11—42no—
161C2×Dic11#10214yes—
162Dic22—81no—
163Dic22—81no—
164Dic22—81no—
165Dic22—81no—
166C8×C11—42no—
167C8×C11—81no—
168C11⋊C8—42no—
169C11⋊C8—81no—
170C2×C4⋊Q8—111no—
171C2×#127C2×D1111yescharacteristic
172C2×#124—221no—
173C2×#124—221no—
174C2×C4⋊C8—111no—
175C2×C4⋊C8—111no—
176C2×C4⋊C8C2×D1111yescharacteristic
177C2×C4⋊C8C2×D1111yescharacteristic
178C2×C4×C8—221no—
179#390—114no—
180#390—222no—
181C43—111no—
182#336—222no—
183#336—221no—
184#332—222no—
185#332—222no—
186#331—22no—
187#331—222no—
188C22×C11—84no—
189C22×C11—84no—
190C22×C11—82no—
191C22×C11—82no—
192C22×C11—82no—
193C22×C11#39011yescharacteristic
194C22×C11#41312yes—
195C22×C11C2×#10211yescharacteristic
196C22×C11#41612yes—
197C22×C11#41811yescharacteristic
198C4×C11—21no—
199C4×C11—21no—
200C4×C11#45911yescharacteristic
201C4×C11#45911yescharacteristic
202C4×C11#46011yescharacteristic
203C4×C11#46011yescharacteristic
204C4×C11#48812yes—
205C4×C11#49511yescharacteristic
206C4×C11#49511yescharacteristic
207Dic11—24no—
208Dic11—42no—
209Dic11—82no—
210C22×Q8—221no—
211C22×D4—21no—
212C22×D4—21no—
213C22×D4C4×D1112yes—
214C22×C8—21no—
215C22×C8—21no—
216C22×C8—221no—
217C22×C8—221no—
218C4⋊Q8—221no—
219C4⋊Q8—221no—
220C4⋊Q8—221no—
221C4⋊Q8—221no—
222#127—21no—
223#127—21no—
224#127—21no—
225#127—21no—
226#124—442no—
227#124—442no—
228#124—442no—
229#124—442no—
230C2×C4⋊C4—112no—
231C2×C4⋊C4—221no—
232C2×C22⋊C4—224no—
233C2×C22⋊C4—224no—
234C2×C42—111no—
235C2×C42—111no—
236C2×C42—112no—
237C2×C42—112no—
238C2×C42C22×D1111yescharacteristic
239C4⋊C8—21no—
240C4⋊C8—21no—
241C4⋊C8—21no—
242C4⋊C8—112no—
243C4⋊C8—221no—
244C4⋊C8—221no—
245C4⋊C8—221no—
246C4⋊C8C22⋊D1112yes—
247C4×C8—442no—
248C2×C11—162no—
249C2×C11#154012yes—
250C2×C11#155312yes—
251C2×C11#195811yescharacteristic
252C2×C11#196711yescharacteristic
253C2×C11#198211yescharacteristic
254C24—22no—
255C2×Q8—441no—
256C2×Q8—441no—
257C2×Q8—441no—
258C2×Q8—441no—
259C2×Q8—441no—
260C2×Q8—441no—
261C2×D4—22no—
262C2×D4—22no—
263C2×D4—44no—
264C2×D4—41no—
265C2×D4—41no—
266C2×D4—41no—
267C2×D4—41no—
268C2×D4—42no—
269C2×D4—41no—
270C2×D4—41no—
271C2×D4—42no—
272C2×D4—41no—
273C2×D4—41no—
274C22×C4—112no—
275C22×C4—112no—
276C22×C4—222no—
277C22×C4C2×C4×D1111yescharacteristic
278C22×C4D4×D1111yescharacteristic
279C22×C4D4×D1111yescharacteristic
280C2×C8—22no—
281C2×C8—41no—
282C2×C8—41no—
283C2×C8—42no—
284C2×C8—41no—
285C2×C8—222no—
286C2×C8—441no—
287C2×C8—441no—
288C2×C8—442no—
289C2×C8—441no—
290C4⋊C4—222no—
291C4⋊C4—222no—
292C4⋊C4—441no—
293C4⋊C4—441no—
294C22⋊C4—448no—
295C22⋊C4—448no—
296C42—112no—
297C42—112no—
298C42—221no—
299C42—222no—
300C42—221no—
301C42—222no—
302C42—442no—
303C42#433911yescharacteristic
304C42D4×D1111yescharacteristic
305C42#434111yescharacteristic
306C42C2×C22⋊D1111yescharacteristic
307C11#969611yescharacteristic, complemented, Sylow
308C23—42no—
309C23—44no—
310C23—42no—
311C23—42no—
312C23—44no—
313C23C22⋊C4×D1111yescharacteristic
314Q8—881no—
315Q8—881no—
316Q8—881no—
317Q8—881no—
318D4—82no—
319D4—82no—
320D4—81no—
321D4—81no—
322D4—81no—
323D4—81no—
324D4—81no—
325D4—82no—
326D4—81no—
327C2×C4—22no—
328C2×C4—114no—
329C2×C4—222no—
330C2×C4—222no—
331C2×C4—222no—
332C2×C4—222no—
333C2×C4—222no—
334C2×C4—442no—
335C2×C4—442no—
336C2×C4—442no—
337C2×C4(C22⋊D11)⋊C411yescharacteristic
338C2×C4#6693711yescharacteristic
339C2×C4#6693811yescharacteristic
340C2×C4D8×D1111yescharacteristic
341C2×C4#6696411yescharacteristic
342C2×C4#6696512yes—
343C2×C4SD16×D1111yescharacteristic
344C2×C4#6696711yescharacteristic
345C2×C4#6696912yes—
346C2×C4C4×C22⋊D1111yescharacteristic
347C2×C4#6699211yescharacteristic
348C2×C4#6699311yescharacteristic
349C8—42no—
350C8—81no—
351C8—442no—
352C8—881no—
353C22—84no—
354C22—82no—
355C22—82no—
356C22—82no—
357C22—84no—
358C22#1062235812yes—
359C22D11×#10211yescharacteristic
360C22#1062238311yescharacteristic
361C22#1062238512yes—
362C22#1062257011yescharacteristic
363C4—21no—
364C4—21no—
365C4—224no—
366C4—442no—
367C4—882no—
368C4#1062237511yescharacteristic
369C4#1062238112yes—
370C4#1062239911yescharacteristic
371C4#1062276311yescharacteristic
372C4#1062276811yescharacteristic
373C4#1062277611yescharacteristic
374C4#1062278111yescharacteristic
375C2—162no—
376C2#1306726212yes—
377C2#1306731812yes—
378C2#1306942611yescharacteristic
379C2#1306946211yescharacteristic
380C2#1306954111yescharacteristic
subgroupG/H
centerC23C22⋊C4×D11
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC2×C11×#331C2
socleC23×C11C2×C22⋊C4
prime radicalC2×C11×#127C22
cosocleC2×C42×C11C23
hypercenterC2×#331D11
hypocenterC11#9696
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#331

Complements

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

NH ≅ G/Ntype
2. #13068732C2semidirect
3. C4⋊C8×Dic11C2semidirect
4. C2×#10622120C2semidirect
5. C2×#10622124C2semidirect
307. C11#9696semidirect

Maximal subgroups

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

subgroupindex
#130769722
#130687322
C4⋊C8×Dic112
C2×#106221202
C2×#106221242
C2×#106221822
C2×C11×#3312
#969611