Finite Group Databasebeta

← #14676168

Subgroups — #14676168

Order 2816.

2166 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622825C211yesmaximal, characteristic
2C2×C4×C22⋊Dic11C211yesmaximal, characteristic
3#13066869C214yesmaximal, complemented
4#13066848C214yesmaximal, complemented
5#13066839C212yesmaximal
6#13066839C212yesmaximal
7C23×C11×C4⋊C4C211yesmaximal, characteristic
8C24×C4×C11C2211yescharacteristic
9C24×C4×C11C2211yescharacteristic
10C24×C4×C11C2211yescharacteristic
11C22×C11×C4⋊C4—24no—
12C22×C11×C4⋊C4—24no—
13C22×C11×C4⋊C4C418yescomplemented
14C22×C11×C4⋊C4C2212yes—
15C22×C11×C4⋊C4C2212yes—
16C22×C22⋊Dic11C2212yes—
17C22×C22⋊Dic11C2212yes—
18C22×C4⋊Dic11C2212yes—
19C22×C4×Dic11C2212yes—
20#10622825—24no—
21C4×C22⋊Dic11—24no—
22C2×C11⋊#95C2218yes—
23C2×C11⋊#95C2212yes—
24C2×C11⋊#95C2212yes—
25C2×C11⋊#95C2218yes—
26C25×C11C2311yescharacteristic
27C23×C4×C11—22no—
28C23×C4×C11—22no—
29C23×C4×C11—28no—
30C23×C4×C11—22no—
31C23×C4×C11—22no—
32C23×C4×C11—44no—
33C23×C4×C11—44no—
34C23×C4×C11C2×C414yes—
35C23×C4×C11C2×C414yes—
36C23×C4×C11C2×C414yes—
37C23×C4×C11D414yes—
38C23×C4×C11D414yes—
39C23×C4×C11C2312yes—
40C23×C4×C11C2311yescharacteristic
41C23×C4×C11C2311yescharacteristic
42C23×C4×C11C2312yes—
43C23×Dic11C2314yes—
44C23×Dic11C2314yes—
45C2×C11×C4⋊C4—232no—
46C2×C11×C4⋊C4—24no—
47C2×C11×C4⋊C4—24no—
48C2×C11×C4⋊C4—24no—
49C2×C11×C4⋊C4—24no—
50C2×C11×C4⋊C4C2×C418yes—
51C2×C11×C4⋊C4C2×C418yes—
52C2×C22⋊Dic11—24no—
53C2×C22⋊Dic11—24no—
54C2×C22⋊Dic11—24no—
55C2×C22⋊Dic11—28no—
56C2×C22⋊Dic11Q818yes—
57C2×C4⋊Dic11—24no—
58C2×C4⋊Dic11—44no—
59C2×C4×Dic11—24no—
60C2×C4×Dic11—44no—
61C11⋊#95—24no—
62C11⋊#95—24no—
63C11⋊#95—216no—
64C11⋊#95—48no—
65#13923—111nomaximal, Sylow
66C24×C11—24no—
67C24×C11—24no—
68C24×C11C22×C412yes—
69C24×C11C2×D412yes—
70C24×C11C2×D412yes—
71C24×C11C2×Q814yes—
72C24×C11#4114yes—
73C24×C11C2411yescharacteristic
74C22×C4×C11—216no—
75C22×C4×C11—216no—
76C22×C4×C11—28no—
77C22×C4×C11—22no—
78C22×C4×C11—22no—
79C22×C4×C11—24no—
80C22×C4×C11—24no—
81C22×C4×C11—24no—
82C22×C4×C11—216no—
83C22×C4×C11—28no—
84C22×C4×C11—22no—
85C22×C4×C11—22no—
86C22×C4×C11—28no—
87C22×C4×C11—48no—
88C22×C4×C11—48no—
89C22×C4×C11—48no—
90C22×C4×C11—48no—
91C22×C4×C11—48no—
92C22×C4×C11—48no—
93C22×C4×C11C22⋊C4116yes—
94C22×C4×C11C22×C414yes—
95C22×C4×C11C22×C412yes—
96C22×C4×C11C22×C412yes—
97C22×C4×C11C22×C414yes—
98C22×C4×C11C2×D412yes—
99C22×C4×C11C2×D412yes—
100C22×C4×C11C2×D412yes—
101C22×C4×C11C2×D412yes—
102C22×C4×C11#4118yes—
103C22×Dic11—24no—
104C22×Dic11—24no—
105C22×Dic11—28no—
106C22×Dic11—24no—
107C22×Dic11—28no—
108C22×Dic11—28no—
109C22×Dic11—28no—
110C22×Dic11—28no—
111C22×Dic11C2×Q818yes—
112C11×C4⋊C4—216no—
113C11×C4⋊C4—216no—
114C22⋊Dic11—216no—
115C22⋊Dic11—48no—
116C4⋊Dic11—48no—
117C4×Dic11—48no—
118C23×C4⋊C4D1111yescharacteristic
119C2×#380—111no—
120C2×C4×C22⋊C4—111no—
121#1441—114no—
122#1436—114no—
123C22⋊#95—112no—
124C22⋊#95—112no—
125C23×C11—24no—
126C23×C11—24no—
127C23×C11—24no—
128C23×C11—24no—
129C23×C11—24no—
130C23×C11—24no—
131C23×C11—216no—
132C23×C11—216no—
133C23×C11C2×C22⋊C414yes—
134C23×C11C4×Q818yes—
135C23×C11C22⋊Q818yes—
136C23×C11#12414yes—
137C23×C11C4⋊Q814yes—
138C23×C11C23×C411yescharacteristic
139C23×C11C22×D411yescharacteristic
140C23×C11C22×D411yescharacteristic
141C23×C11C22×Q812yes—
142C23×C11C2×#4114yes—
143C23×C11C2×#4112yes—
144C23×C11H(5,𝔽2)14yes—
145C2×C4×C11—232no—
146C2×C4×C11—24no—
147C2×C4×C11—24no—
148C2×C4×C11—24no—
149C2×C4×C11—24no—
150C2×C4×C11—28no—
151C2×C4×C11—28no—
152C2×C4×C11—24no—
153C2×C4×C11—24no—
154C2×C4×C11—24no—
155C2×C4×C11—24no—
156C2×C4×C11—24no—
157C2×C4×C11—28no—
158C2×C4×C11—416no—
159C2×C4×C11—416no—
160C2×C4×C11—44no—
161C2×C4×C11—44no—
162C2×C4×C11C2×C22⋊C414yes—
163C2×C4×C11C2×C22⋊C414yes—
164C2×C4×C11#11718yes—
165C2×Dic11—28no—
166C2×Dic11—216no—
167C2×Dic11—44no—
168C2×Dic11—44no—
169C2×Dic11—48no—
170C2×Dic11—44no—
171C2×Dic11—44no—
172C2×Dic11—44no—
173C2×Dic11—416no—
174C24×C4C2×D1111yescharacteristic
175C24×C4C2×D1111yescharacteristic
176C24×C4C2×D1111yescharacteristic
177C22×C4⋊C4—24no—
178C22×C4⋊C4—24no—
179C22×C4⋊C4—112no—
180C22×C4⋊C4Dic1118yescomplemented
181C22×C4⋊C4C2×D1112yes—
182C22×C4⋊C4C2×D1112yes—
183C22×C22⋊C4—112no—
184C22×C22⋊C4—112no—
185C22×C42—112no—
186#380—224no—
187C4×C22⋊C4—224no—
188C2×#95—118no—
189C2×#95—112no—
190C2×#95—112no—
191C2×#95—118no—
192C22×C11—24no—
193C22×C11—216no—
194C22×C11—28no—
195C22×C11—28no—
196C22×C11—216no—
197C22×C11—24no—
198C22×C11#39118yes—
199C22×C11C22×C22⋊C411yescharacteristic
200C22×C11C2×#11712yes—
201C22×C11C2×C4×Q812yes—
202C22×C11#51812yes—
203C22×C11C2×C22⋊Q812yes—
204C22×C11#52512yes—
205C22×C11#52512yes—
206C22×C11C2×#12411yescharacteristic
207C22×C11C2×C4⋊Q811yescharacteristic
208C22×C11#53412yes—
209C22×C11#53412yes—
210C22×C11#55318yes—
211C22×C11#55418yes—
212C4×C11—24no—
213C4×C11—24no—
214C4×C11—28no—
215C4×C11—44no—
216Dic11—48no—
217Dic11—84no—
218C25C22×D1111yescharacteristic
219C23×C4—22no—
220C23×C4—22no—
221C23×C4—28no—
222C23×C4—22no—
223C23×C4—22no—
224C23×C4—44no—
225C23×C4—44no—
226C23×C4—114no—
227C23×C4—114no—
228C23×C4C2×Dic1114yes—
229C23×C4C2×Dic1114yes—
230C23×C4C2×Dic1114yes—
231C23×C4C22⋊D1114yes—
232C23×C4C22⋊D1114yes—
233C23×C4C22×D1112yes—
234C23×C4C22×D1112yes—
235C23×C4C22×D1111yescharacteristic
236C23×C4C22×D1111yescharacteristic
237C2×C4⋊C4—232no—
238C2×C4⋊C4—24no—
239C2×C4⋊C4—24no—
240C2×C4⋊C4—24no—
241C2×C4⋊C4—24no—
242C2×C4⋊C4—224no—
243C2×C4⋊C4—444no—
244C2×C4⋊C4C2×Dic1118yes—
245C2×C4⋊C4C2×Dic1118yes—
246C2×C22⋊C4—118no—
247C2×C22⋊C4—224no—
248C2×C22⋊C4—224no—
249C2×C22⋊C4—228no—
250C2×C22⋊C4—224no—
251C2×C42—224no—
252C2×C42—444no—
253#95—2216no—
254#95—224no—
255#95—224no—
256#95—448no—
257C2×C11—28no—
258C2×C11#228011yescharacteristic
259C2×C11C2×#39111yescharacteristic
260C2×C11#230811yescharacteristic
261C2×C11#234514yes—
262C2×C11#257914yes—
263C2×C11#258312yes—
264C2×C11#259112yes—
265C24—24no—
266C24—24no—
267C24Q8×D1114yes—
268C24#434314yes—
269C24C22×Dic1112yes—
270C24C2×C22⋊D1112yes—
271C24C2×C22⋊D1112yes—
272C24C23×D1111yescharacteristic
273C22×C4—216no—
274C22×C4—216no—
275C22×C4—28no—
276C22×C4—24no—
277C22×C4—24no—
278C22×C4—24no—
279C22×C4—22no—
280C22×C4—22no—
281C22×C4—216no—
282C22×C4—28no—
283C22×C4—28no—
284C22×C4—22no—
285C22×C4—22no—
286C22×C4—48no—
287C22×C4—48no—
288C22×C4—48no—
289C22×C4—48no—
290C22×C4—48no—
291C22×C4—48no—
292C22×C4—118no—
293C22×C4—228no—
294C22×C4—228no—
295C22×C4—224no—
296C22×C4—224no—
297C22×C4—228no—
298C22×C4—228no—
299C22×C4—228no—
300C22×C4—224no—
301C22×C4C22⋊Dic11116yes—
302C22×C4#433918yes—
303C22×C4C22×Dic1114yes—
304C22×C4C22×Dic1114yes—
305C22×C4C22×Dic1112yes—
306C22×C4C22×Dic1112yes—
307C22×C4C2×C22⋊D1112yes—
308C22×C4C2×C22⋊D1112yes—
309C22×C4C2×C22⋊D1112yes—
310C22×C4C2×C22⋊D1112yes—
311C4⋊C4—216no—
312C4⋊C4—216no—
313C4⋊C4—448no—
314C22⋊C4—2216no—
315C22⋊C4—448no—
316C42—448no—
317C11#1392311yescharacteristic, complemented, Sylow
318C23—216no—
319C23—216no—
320C23—24no—
321C23—24no—
322C23—24no—
323C23—24no—
324C23—24no—
325C23—24no—
326C23#6699714yes—
327C23Q8×Dic1118yes—
328C23#6699918yes—
329C23#6700014yes—
330C23C2×C22⋊Dic1114yes—
331C23C2×#433914yes—
332C23#6703714yes—
333C23C2×Q8×D1112yes—
334C23C2×#434312yes—
335C23C23×Dic1111yescharacteristic
336C23C22×C22⋊D1111yescharacteristic
337C23C22×C22⋊D1111yescharacteristic
338C2×C4—232no—
339C2×C4—24no—
340C2×C4—28no—
341C2×C4—28no—
342C2×C4—24no—
343C2×C4—24no—
344C2×C4—24no—
345C2×C4—24no—
346C2×C4—24no—
347C2×C4—24no—
348C2×C4—24no—
349C2×C4—28no—
350C2×C4—24no—
351C2×C4—416no—
352C2×C4—416no—
353C2×C4—44no—
354C2×C4—44no—
355C2×C4—2216no—
356C2×C4—228no—
357C2×C4—448no—
358C2×C4—444no—
359C2×C4—444no—
360C2×C4—4416no—
361C2×C4—444no—
362C2×C4—444no—
363C2×C4—444no—
364C2×C4#6697918yes—
365C2×C4C2×C22⋊Dic1114yes—
366C2×C4C2×C22⋊Dic1114yes—
367C22—216no—
368C22—28no—
369C22—24no—
370C22—216no—
371C22—24no—
372C22—28no—
373C22#1062284318yes—
374C22#1062304218yes—
375C22#1062304518yes—
376C22C2×#6697912yes—
377C22#1062332212yes—
378C22#1062332212yes—
379C22#1062332912yes—
380C22#1062333512yes—
381C22#1062333512yes—
382C22C2×#6699711yescharacteristic
383C22C2×Q8×Dic1112yes—
384C22C2×#6699912yes—
385C22C2×#6700011yescharacteristic
386C22C22×C22⋊Dic1111yescharacteristic
387C4—24no—
388C4—24no—
389C4—28no—
390C4—44no—
391C4—448no—
392C4—884no—
393C2—28no—
394C2#1307099911yescharacteristic
395C2C2×#1062284311yescharacteristic
396C2#1307119411yescharacteristic
397C2#1307149314yes—
398C2#1307396314yes—
399C2#1307399612yes—
400C2#1307409612yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC23×C11×C4⋊C4C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenterC23×C4⋊C4D11
hypocenterC11#13923
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C23×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #13066869C2semidirect
4. #13066848C2semidirect
13. C22×C11×C4⋊C4C4semidirect
180. C22×C4⋊C4Dic11semidirect
317. C11#13923semidirect

Maximal subgroups

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

subgroupindex
C2×#106228252
C2×C4×C22⋊Dic112
#130668692
#130668482
#130668392
C23×C11×C4⋊C42
#1392311