Finite Group Databasebeta

← #14684825

Subgroups — #14684825

Order 2816.

1334 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66943C211yesmaximal, characteristic
2C2×#10622263C211yesmaximal, characteristic
3C2×#10622263C211yesmaximal, characteristic
4#13066885C211yesmaximal, characteristic
5#13066884C211yesmaximal, characteristic
6#13066883C211yesmaximal, characteristic
7#13066868C214yesmaximal
8#13066867C214yesmaximal
9C11×#1445C211yesmaximal, characteristic
10C22×C11×C4⋊C4C2211yescharacteristic
11C22×C4⋊Dic11C2212yes—
12C22×C4⋊Dic11C2211yescharacteristic
13C22×Dic11⋊C4C2212yes—
14C22×Dic11⋊C4C2212yes—
15C22×Dic11⋊C4C2212yes—
16C22×C4×Dic11C2211yescharacteristic
17C2×#66943—24no—
18C2×#66943—24no—
19C2×#66943C418yescomplemented
20C2×C11×#95C2211yescharacteristic
21C2×C11×#95C2211yescharacteristic
22C2×C11×#95C2214yes—
23C2×C11⋊#95C2212yes—
24C2×C11⋊#95C2212yes—
25C2×C11⋊#95C2211yescharacteristic
26C2×C11⋊#95C2211yescharacteristic
27C2×C11⋊#95C2214yes—
28C2×C11⋊#95C2214yes—
29C2×C11⋊#95C2214yes—
30#10622263—24no—
31#10622263—24no—
32C23×C4×C11C2312yes—
33C23×C4×C11C2312yes—
34C23×C4×C11C2312yes—
35C23×C4×C11C2311yescharacteristic
36C23×Dic11C2312yes—
37C23×Dic11C2312yes—
38C23×Dic11C2312yes—
39C23×Dic11C2311yescharacteristic
40C23×Dic11C2311yescharacteristic
41C2×C11×C4⋊C4—22no—
42C2×C11×C4⋊C4—22no—
43C2×C11×C4⋊C4C2×C414yes—
44C2×C4⋊Dic11—22no—
45C2×C4⋊Dic11—22no—
46C2×C4⋊Dic11—24no—
47C2×C4⋊Dic11—24no—
48C2×C4⋊Dic11C2×C418yes—
49C2×C4⋊Dic11C2×C414yes—
50C2×Dic11⋊C4—24no—
51C2×Dic11⋊C4—24no—
52C2×Dic11⋊C4—24no—
53C2×Dic11⋊C4—24no—
54C2×Dic11⋊C4—44no—
55C2×Dic11⋊C4—44no—
56C2×Dic11⋊C4C2×C418yes—
57C2×C4×Dic11C2×C414yes—
58C2×C4×Dic11D414yes—
59C2×C4×Dic11D414yes—
60#66943—232no—
61C11×#95—22no—
62C11×#95—22no—
63C11×#95—44no—
64C11⋊#95—22no—
65C11⋊#95—22no—
66C11⋊#95—24no—
67C11⋊#95—24no—
68C11⋊#95—44no—
69C11⋊#95—44no—
70C11⋊#95—44no—
71#14664—111nomaximal, Sylow
72C24×C11C2411yescharacteristic
73C22×C4×C11—24no—
74C22×C4×C11—22no—
75C22×C4×C11—22no—
76C22×C4×C11—24no—
77C22×C4×C11—24no—
78C22×C4×C11—22no—
79C22×C4×C11—22no—
80C22×C4×C11—22no—
81C22×C4×C11—24no—
82C22×C4×C11—22no—
83C22×C4×C11—24no—
84C22×C4×C11—24no—
85C22×C4×C11—24no—
86C22×C4×C11—22no—
87C22×C4×C11—22no—
88C22×C4×C11C22×C414yes—
89C22×C4×C11C22×C412yes—
90C22×C4×C11C2×D412yes—
91C22×C4×C11C2×D412yes—
92C22×Dic11—22no—
93C22×Dic11—22no—
94C22×Dic11—22no—
95C22×Dic11—22no—
96C22×Dic11—22no—
97C22×Dic11—22no—
98C22×Dic11—24no—
99C22×Dic11—22no—
100C22×Dic11—22no—
101C22×Dic11—24no—
102C22×Dic11—24no—
103C22×Dic11—22no—
104C22×Dic11—22no—
105C22×Dic11—24no—
106C22×Dic11—22no—
107C22×Dic11—24no—
108C22×Dic11—24no—
109C22×Dic11—22no—
110C22×Dic11C22×C414yes—
111C22×Dic11C22×C412yes—
112C22×Dic11C22×C412yes—
113C22×Dic11C2×D412yes—
114C22×Dic11C2×D412yes—
115C22×Dic11C2×D412yes—
116C22×Dic11C2×D412yes—
117C11×C4⋊C4—28no—
118C4⋊Dic11—216no—
119C4⋊Dic11—28no—
120Dic11⋊C4—216no—
121Dic11⋊C4—48no—
122Dic11⋊C4—48no—
123C4×Dic11C22⋊C4116yes—
124C22×#125—111no—
125C2×#382—111no—
126C2×#382—111no—
127#1445—111no—
128#1445—111no—
129#1445—111no—
130#1445D1111yescharacteristic
131#1441—114no—
132#1441—114no—
133C23×C11C23×C411yescharacteristic
134C23×C11C22×D411yescharacteristic
135C23×C11C22×D411yescharacteristic
136C23×C11H(5,𝔽2)12yes—
137C23×C11H(5,𝔽2)12yes—
138C23×C112−1+412yes—
139C23×C112−1+414yes—
140C23×C112−1+412yes—
141C2×C4×C11—24no—
142C2×C4×C11—24no—
143C2×C4×C11—24no—
144C2×C4×C11—24no—
145C2×C4×C11—28no—
146C2×C4×C11—42no—
147C2×C4×C11—42no—
148C2×C4×C11—44no—
149C2×C4×C11—42no—
150C2×C4×C11—42no—
151C2×C4×C11—42no—
152C2×C4×C11—42no—
153C2×C4×C11—42no—
154C2×C4×C11—42no—
155C2×C4×C11—44no—
156C2×C4×C11—44no—
157C2×C4×C11—44no—
158C2×C4×C11—44no—
159C2×C4×C11C2×C22⋊C414yes—
160C2×Dic11—24no—
161C2×Dic11—24no—
162C2×Dic11—22no—
163C2×Dic11—22no—
164C2×Dic11—22no—
165C2×Dic11—22no—
166C2×Dic11—24no—
167C2×Dic11—24no—
168C2×Dic11—24no—
169C2×Dic11—28no—
170C2×Dic11—42no—
171C2×Dic11—42no—
172C2×Dic11—44no—
173C2×Dic11—42no—
174C2×Dic11—42no—
175C2×Dic11—42no—
176C2×Dic11—42no—
177C2×Dic11—42no—
178C2×Dic11—42no—
179C2×Dic11—44no—
180C2×Dic11—44no—
181C2×Dic11—44no—
182C2×Dic11—44no—
183C2×Dic11C2×C22⋊C414yes—
184C2×Dic11C2×C22⋊C414yes—
185C2×#125—118no—
186C2×#125—224no—
187C2×#125—224no—
188C22×C4⋊C4—112no—
189C22×C4⋊C4—112no—
190C22×C4⋊C4—111no—
191C22×C4⋊C4—112no—
192C22×C4⋊C4—112no—
193C22×C4⋊C4C2×D1111yescharacteristic
194C22×C42—111no—
195#382—224no—
196#382—224no—
197C2×#95—112no—
198C2×#95—112no—
199C2×#95—111no—
200C2×#95—111no—
201C2×#95—114no—
202C2×#95—114no—
203C2×#95—114no—
204C2×#95C2×D1111yescharacteristic
205C2×#95C2×D1111yescharacteristic
206C2×#95C2×D1114yes—
207C22×C11C22×C22⋊C411yescharacteristic
208C22×C11#51912yes—
209C22×C11#52012yes—
210C22×C11#52012yes—
211C22×C11#53511yescharacteristic
212C22×C11#53511yescharacteristic
213C22×C11#53611yescharacteristic
214C22×C11#53612yes—
215C22×C11#53612yes—
216C22×C11#53611yescharacteristic
217C22×C11#53712yes—
218C22×C11#53712yes—
219C22×C11#56214yes—
220C22×C11#56314yes—
221C22×C11#56314yes—
222C22×C11#56414yes—
223C4×C11—24no—
224C4×C11—44no—
225C4×C11—82no—
226C4×C11—82no—
227Dic11—24no—
228Dic11—24no—
229Dic11—44no—
230Dic11—82no—
231Dic11—82no—
232C23×C4—111no—
233C23×C4—111no—
234C23×C4—112no—
235C23×C4—112no—
236C23×C4—112no—
237C23×C4C22×D1112yes—
238C23×C4C22×D1112yes—
239C23×C4C22×D1112yes—
240C23×C4C22×D1111yescharacteristic
241#125—2232no—
242C2×C4⋊C4—22no—
243C2×C4⋊C4—22no—
244C2×C4⋊C4—118no—
245C2×C4⋊C4—118no—
246C2×C4⋊C4—114no—
247C2×C4⋊C4—224no—
248C2×C4⋊C4—224no—
249C2×C4⋊C4—224no—
250C2×C4⋊C4—224no—
251C2×C4⋊C4—222no—
252C2×C4⋊C4—222no—
253C2×C4⋊C4—224no—
254C2×C4⋊C4—224no—
255C2×C4⋊C4—444no—
256C2×C4⋊C4—444no—
257C2×C4⋊C4C4×D1114yes—
258C2×C42—114no—
259C2×C42—114no—
260C2×C42—114no—
261#95—22no—
262#95—22no—
263#95—44no—
264#95—224no—
265#95—224no—
266#95—222no—
267#95—222no—
268#95—444no—
269#95—444no—
270#95—444no—
271C2×C11#231011yescharacteristic
272C2×C11#231111yescharacteristic
273C2×C11#231111yescharacteristic
274C2×C11#238214yes—
275C2×C11#282012yes—
276C2×C11#282012yes—
277C2×C11#282212yes—
278C2×C11#282212yes—
279C24C23×D1111yescharacteristic
280C22×C4—24no—
281C22×C4—22no—
282C22×C4—22no—
283C22×C4—24no—
284C22×C4—24no—
285C22×C4—22no—
286C22×C4—22no—
287C22×C4—22no—
288C22×C4—24no—
289C22×C4—22no—
290C22×C4—22no—
291C22×C4—24no—
292C22×C4—22no—
293C22×C4—24no—
294C22×C4—24no—
295C22×C4—112no—
296C22×C4—112no—
297C22×C4—112no—
298C22×C4—112no—
299C22×C4—112no—
300C22×C4—112no—
301C22×C4—114no—
302C22×C4—222no—
303C22×C4—222no—
304C22×C4—222no—
305C22×C4—222no—
306C22×C4—222no—
307C22×C4—222no—
308C22×C4—224no—
309C22×C4—224no—
310C22×C4—222no—
311C22×C4—222no—
312C22×C4—222no—
313C22×C4—224no—
314C22×C4—222no—
315C22×C4—222no—
316C22×C4—224no—
317C22×C4—222no—
318C22×C4—224no—
319C22×C4—224no—
320C22×C4C2×C4×D1114yes—
321C22×C4C2×C4×D1112yes—
322C22×C4D4×D1112yes—
323C22×C4D4×D1112yes—
324C4⋊C4—28no—
325C4⋊C4—2216no—
326C4⋊C4—2216no—
327C4⋊C4—228no—
328C4⋊C4—448no—
329C4⋊C4—448no—
330C42—1116no—
331C11#1466411yescharacteristic, complemented, Sylow
332C23C22×C4×D1111yescharacteristic
333C23C2×D4×D1111yescharacteristic
334C23C2×D4×D1111yescharacteristic
335C23#6703712yes—
336C23#6704012yes—
337C23#6704212yes—
338C23#6704312yes—
339C23#6704314yes—
340C2×C4—24no—
341C2×C4—24no—
342C2×C4—24no—
343C2×C4—24no—
344C2×C4—28no—
345C2×C4—42no—
346C2×C4—44no—
347C2×C4—42no—
348C2×C4—44no—
349C2×C4—42no—
350C2×C4—42no—
351C2×C4—42no—
352C2×C4—44no—
353C2×C4—42no—
354C2×C4—42no—
355C2×C4—44no—
356C2×C4—44no—
357C2×C4—42no—
358C2×C4—114no—
359C2×C4—114no—
360C2×C4—222no—
361C2×C4—222no—
362C2×C4—224no—
363C2×C4—224no—
364C2×C4—224no—
365C2×C4—224no—
366C2×C4—222no—
367C2×C4—222no—
368C2×C4—224no—
369C2×C4—228no—
370C2×C4—442no—
371C2×C4—444no—
372C2×C4—442no—
373C2×C4—444no—
374C2×C4—442no—
375C2×C4—442no—
376C2×C4—442no—
377C2×C4—444no—
378C2×C4—442no—
379C2×C4—442no—
380C2×C4—444no—
381C2×C4—444no—
382C2×C4—442no—
383C2×C4C22⋊C4×D1114yes—
384C22C2×C22⋊C4×D1111yescharacteristic
385C22#1062304712yes—
386C22#1062307712yes—
387C22#1062310512yes—
388C22#1062313912yes—
389C22#1062316012yes—
390C22#1062317714yes—
391C22#1062317912yes—
392C22#1062317912yes—
393C22#1062319814yes—
394C22#1062320511yescharacteristic
395C22#1062320611yescharacteristic
396C22C11⋊#56414yes—
397C22#1062324314yes—
398C22#1062324611yescharacteristic
399C22#1062325511yescharacteristic
400C4—24no—
401C4—44no—
402C4—82no—
403C4—82no—
404C4—224no—
405C4—224no—
406C4—444no—
407C4—882no—
408C4—882no—
409C2#1307120111yescharacteristic
410C2#1307120611yescharacteristic
411C2#1307120711yescharacteristic
412C2#1307179914yes—
413C2#1307667012yes—
414C2#1307667212yes—
415C2#1307668512yes—
416C2#1307668612yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1445C2
socle, prime radical, cosocleC24×C11C24
hypercenter#1445D11
hypocenterC11#14664
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1445

Complements

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

NH ≅ G/Ntype
19. C2×#66943C4semidirect
331. C11#14664semidirect

Maximal subgroups

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

subgroupindex
C22×#669432
C2×#106222632
#130668852
#130668842
#130668832
#130668682
#130668672
C11×#14452
#1466411