Finite Group Databasebeta

← #14675232

Subgroups — #14675232

Order 2816.

1486 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622550C211yesmaximal, characteristic
2C2×C4×C4⋊Dic11C211yesmaximal, characteristic
3#13066850C214yesmaximal
4#13066843C212yesmaximal
5#13066841C212yesmaximal
6C4×C11⋊#95C212yesmaximal
7#95×Dic11C212yesmaximal
8C2×C11×#376C211yesmaximal, characteristic
9C22×C42×C11C2212yes—
10C22×C42×C11C2211yescharacteristic
11C22×C4⋊Dic11C2212yes—
12C22×C4×Dic11C2214yes—
13C22×C4×Dic11C2212yes—
14C11×#376C418yescomplemented
15C2×C11×#95C2211yescharacteristic
16C2×C11×#95C2211yescharacteristic
17C2×C11×#95C2212yes—
18C2×C11⋊#95C2214yes—
19C2×C11⋊#95C2214yes—
20C2×C11⋊#95C2214yes—
21C2×C11⋊#95C2212yes—
22C2×C11⋊#95C2211yescharacteristic
23C2×C11⋊#95C2212yes—
24C2×C11⋊#95C2211yescharacteristic
25C2×C11⋊#95C2212yes—
26#10622550C418yescomplemented
27C4×C4⋊Dic11C418yescomplemented
28C23×C4×C11C2312yes—
29C23×C4×C11C2311yescharacteristic
30C23×C4×C11C2311yescharacteristic
31C23×C4×C11C2311yescharacteristic
32C23×C4×C11C2312yes—
33C23×Dic11C2312yes—
34C23×Dic11C2314yes—
35C23×Dic11C2312yes—
36C2×C42×C11—28no—
37C2×C42×C11C2×C414yes—
38C2×C42×C11C2×C414yes—
39C2×C42×C11C2×C418yes—
40C2×C42×C11C2×C414yes—
41C2×C4⋊Dic11—24no—
42C2×C4⋊Dic11—24no—
43C2×C4⋊Dic11C2×C418yes—
44C2×C4×Dic11—28no—
45C2×C4×Dic11—28no—
46C2×C4×Dic11—44no—
47C2×C4×Dic11—44no—
48C2×C4×Dic11C2×C418yes—
49C11×#95C2×C414yes—
50C11×#95C2×C418yes—
51C11×#95C2×C414yes—
52C11⋊#95—28no—
53C11⋊#95—28no—
54C11⋊#95—44no—
55C11⋊#95C2×C414yes—
56C11⋊#95C2×C414yes—
57C11⋊#95C2×C418yes—
58C11⋊#95C2×C418yes—
59C11⋊#95C2×C418yes—
60#13806—111nomaximal, Sylow
61C24×C11C2411yescharacteristic
62C22×C4×C11—24no—
63C22×C4×C11—22no—
64C22×C4×C11—22no—
65C22×C4×C11—24no—
66C22×C4×C11—22no—
67C22×C4×C11—22no—
68C22×C4×C11—22no—
69C22×C4×C11—22no—
70C22×C4×C11—24no—
71C22×C4×C11—24no—
72C22×C4×C11—22no—
73C22×C4×C11—22no—
74C22×C4×C11C22×C414yes—
75C22×C4×C11C22×C412yes—
76C22×C4×C11C22×C412yes—
77C22×C4×C11C22×C412yes—
78C22×C4×C11C22×C412yes—
79C22×C4×C11C22×C412yes—
80C22×C4×C11C22×C412yes—
81C22×C4×C11C22×C412yes—
82C22×C4×C11C22×C412yes—
83C22×C4×C11C22×C412yes—
84C22×C4×C11C22×C414yes—
85C22×C4×C11#4118yes—
86C22×Dic11—24no—
87C22×Dic11—24no—
88C22×Dic11—24no—
89C22×Dic11—24no—
90C22×Dic11—24no—
91C22×Dic11—24no—
92C22×Dic11—22no—
93C22×Dic11—22no—
94C22×Dic11—24no—
95C22×Dic11—24no—
96C22×Dic11—24no—
97C22×Dic11—24no—
98C22×Dic11C22×C418yes—
99C22×Dic11C22×C414yes—
100C22×Dic11C22×C414yes—
101C22×Dic11#4114yes—
102C22×Dic11#4114yes—
103C42×C11—216no—
104C42×C11C42116yescomplemented
105C4⋊Dic11—216no—
106C4×Dic11—48no—
107C4×Dic11—416no—
108C2×#383—111no—
109C2×C4×C4⋊C4—111no—
110C2×#376D1111yescharacteristic
111#1436—114no—
112#1434—112no—
113#1434—112no—
114C4×#95—112no—
115C4×#95—112no—
116C23×C11C23×C411yescharacteristic
117C23×C11C23×C411yescharacteristic
118C23×C11C23×C411yescharacteristic
119C23×C11C2×#4114yes—
120C23×C11C2×#4112yes—
121C23×C11C2×#4112yes—
122C23×C11H(5,𝔽2)12yes—
123C23×C112−1+412yes—
124C2×C4×C11—24no—
125C2×C4×C11—24no—
126C2×C4×C11—24no—
127C2×C4×C11—24no—
128C2×C4×C11—24no—
129C2×C4×C11—24no—
130C2×C4×C11—22no—
131C2×C4×C11—22no—
132C2×C4×C11—22no—
133C2×C4×C11—22no—
134C2×C4×C11—24no—
135C2×C4×C11—24no—
136C2×C4×C11—24no—
137C2×C4×C11—28no—
138C2×C4×C11—28no—
139C2×C4×C11—24no—
140C2×C4×C11—24no—
141C2×C4×C11—24no—
142C2×C4×C11—44no—
143C2×C4×C11—44no—
144C2×C4×C11C2×C4214yes—
145C2×C4×C11C2×C4214yes—
146C2×C4×C11C2×C4214yes—
147C2×C4×C11#11718yes—
148C2×Dic11—24no—
149C2×Dic11—24no—
150C2×Dic11—28no—
151C2×Dic11—28no—
152C2×Dic11—24no—
153C2×Dic11—24no—
154C2×Dic11—28no—
155C2×Dic11—28no—
156C2×Dic11—24no—
157C2×Dic11—28no—
158C2×Dic11—44no—
159C2×Dic11—44no—
160C2×Dic11—44no—
161C2×Dic11—44no—
162C2×Dic11—44no—
163C2×Dic11—44no—
164C2×Dic11#11718yes—
165C22×C4⋊C4—112no—
166C22×C42—112no—
167C22×C42—114no—
168C22×C42C2×D1112yes—
169C22×C42C2×D1111yescharacteristic
170#383—118no—
171C4×C4⋊C4—118no—
172#376Dic1118yescomplemented
173C2×#95—111no—
174C2×#95—112no—
175C2×#95—112no—
176C2×#95—111no—
177C2×#95—112no—
178C2×#95—114no—
179C2×#95—114no—
180C2×#95—114no—
181C2×#95C2×D1111yescharacteristic
182C2×#95C2×D1111yescharacteristic
183C2×#95C2×D1112yes—
184C22×C11C22×C4211yescharacteristic
185C22×C11C2×#11712yes—
186C22×C11C2×#11712yes—
187C22×C11C4×#4112yes—
188C22×C11C4×#4112yes—
189C22×C11C4×#4112yes—
190C22×C11C4×#4111yescharacteristic
191C22×C11C4×#4111yescharacteristic
192C22×C11#51811yescharacteristic
193C22×C11#51911yescharacteristic
194C22×C11#52012yes—
195C22×C11#52012yes—
196C22×C11#55114yes—
197C22×C11#55214yes—
198C22×C11#55314yes—
199C22×C11#55614yes—
200C4×C11—28no—
201C4×C11—24no—
202C4×C11—24no—
203C4×C11—24no—
204C4×C11—44no—
205Dic11—28no—
206Dic11—44no—
207Dic11—48no—
208C23×C4—112no—
209C23×C4—112no—
210C23×C4—114no—
211C23×C4C22×D1112yes—
212C23×C4C22×D1111yescharacteristic
213C23×C4C22×D1111yescharacteristic
214C23×C4C22×D1111yescharacteristic
215C23×C4C22×D1112yes—
216C2×C4⋊C4—118no—
217C2×C4⋊C4—224no—
218C2×C4⋊C4—224no—
219C2×C42—28no—
220C2×C42—118no—
221C2×C42—228no—
222C2×C42—228no—
223C2×C42—444no—
224C2×C42—444no—
225C2×C42C4×D1114yes—
226C2×C42C4×D1114yes—
227C2×C42C2×Dic1118yes—
228C2×C42C2×Dic1114yes—
229#95—114no—
230#95—114no—
231#95—118no—
232#95—118no—
233#95—118no—
234#95—228no—
235#95—228no—
236#95—444no—
237#95C2×Dic1114yes—
238#95C2×Dic1118yes—
239#95C2×Dic1114yes—
240C2×C11C4×#11711yescharacteristic
241C2×C11C4×#11711yescharacteristic
242C2×C11#227411yescharacteristic
243C2×C11#234312yes—
244C2×C11#234712yes—
245C2×C11#235312yes—
246C2×C11#235612yes—
247C2×C11#237314yes—
248C24C23×D1111yescharacteristic
249C22×C4—24no—
250C22×C4—24no—
251C22×C4—22no—
252C22×C4—22no—
253C22×C4—22no—
254C22×C4—22no—
255C22×C4—22no—
256C22×C4—22no—
257C22×C4—24no—
258C22×C4—24no—
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—114no—
262C22×C4—114no—
263C22×C4—114no—
264C22×C4—118no—
265C22×C4—114no—
266C22×C4—224no—
267C22×C4—224no—
268C22×C4—224no—
269C22×C4—224no—
270C22×C4—224no—
271C22×C4—224no—
272C22×C4—224no—
273C22×C4—222no—
274C22×C4—222no—
275C22×C4—224no—
276C22×C4—224no—
277C22×C4—224no—
278C22×C4C2×C4×D1112yes—
279C22×C4C2×C4×D1112yes—
280C22×C4C2×C4×D1112yes—
281C22×C4C2×C4×D1112yes—
282C22×C4C2×C4×D1112yes—
283C22×C4C2×C4×D1112yes—
284C22×C4#433918yes—
285C22×C4C22×Dic1114yes—
286C22×C4C22×Dic1112yes—
287C22×C4C22×Dic1112yes—
288C22×C4C22×Dic1112yes—
289C22×C4C22×Dic1114yes—
290C4⋊C4—2216no—
291C42—216no—
292C42—448no—
293C42—4416no—
294C42C4×Dic11116yescomplemented
295C11#1380611yescharacteristic, complemented, Sylow
296C23C22×C4×D1111yescharacteristic
297C23C22×C4×D1111yescharacteristic
298C23C2×#433914yes—
299C23#41×D1112yes—
300C23#41×D1112yes—
301C23#6704212yes—
302C23#6704312yes—
303C23C23×Dic1111yescharacteristic
304C2×C4—24no—
305C2×C4—24no—
306C2×C4—22no—
307C2×C4—24no—
308C2×C4—22no—
309C2×C4—24no—
310C2×C4—24no—
311C2×C4—28no—
312C2×C4—24no—
313C2×C4—28no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—24no—
317C2×C4—24no—
318C2×C4—24no—
319C2×C4—24no—
320C2×C4—24no—
321C2×C4—24no—
322C2×C4—44no—
323C2×C4—44no—
324C2×C4—118no—
325C2×C4—224no—
326C2×C4—224no—
327C2×C4—228no—
328C2×C4—228no—
329C2×C4—228no—
330C2×C4—224no—
331C2×C4—224no—
332C2×C4—224no—
333C2×C4—228no—
334C2×C4—228no—
335C2×C4—444no—
336C2×C4—444no—
337C2×C4—444no—
338C2×C4—444no—
339C2×C4—444no—
340C2×C4—444no—
341C2×C4C2×C4×Dic1114yes—
342C2×C4C2×C4×Dic1114yes—
343C2×C4C2×C4×Dic1114yes—
344C2×C4#6697918yes—
345C22C4×#433912yes—
346C22C4×#433912yes—
347C22#1062304711yescharacteristic
348C22D11×#11712yes—
349C22#1062305211yescharacteristic
350C22#1062305312yes—
351C22#1062305412yes—
352C22#1062305814yes—
353C22#1062306114yes—
354C22#1062306214yes—
355C22#1062306414yes—
356C22C22×C4×Dic1111yescharacteristic
357C22C2×#6697912yes—
358C22#41×Dic1111yescharacteristic
359C22#41×Dic1111yescharacteristic
360C22#1062335812yes—
361C4—24no—
362C4—24no—
363C4—28no—
364C4—24no—
365C4—44no—
366C4—228no—
367C4—448no—
368C4—444no—
369C2C4×#6697911yescharacteristic
370C2#117×Dic1111yescharacteristic
371C2#1307097211yescharacteristic
372C2#1307147612yes—
373C2#1307150912yes—
374C2#1307155712yes—
375C2#1307158212yes—
376C2#1307173614yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC22×C11C22×C42
FittingC2×C11×#376C2
socle, prime radical, cosocleC24×C11C24
hypercenterC2×#376D11
hypocenterC11#13806
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#376

Complements

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

NH ≅ G/Ntype
14. C11×#376C4semidirect
26. #10622550C4semidirect
27. C4×C4⋊Dic11C4semidirect
104. C42×C11C42semidirect
172. #376Dic11semidirect
294. C42C4×Dic11semidirect
295. C11#13806semidirect

Maximal subgroups

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

subgroupindex
C2×#106225502
C2×C4×C4⋊Dic112
#130668502
#130668432
#130668412
C4×C11⋊#952
#95×Dic112
C2×C11×#3762
#1380611