Finite Group Databasebeta

← #14675540

Subgroups — #14675540

Order 2816.

2118 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C4⋊Dic11C212yesmaximal, complemented
2C2×C4×C22⋊Dic11C212yesmaximal
3#13066869C214yesmaximal, complemented
4#13066861C214yesmaximal
5C4×C11⋊#95C212yesmaximal, complemented
6C22×C11×#117C211yesmaximal, characteristic
7C24×C4×C11C2211yescharacteristic
8C2×C11×#117—28no—
9C2×C11×#117C418yescomplemented
10C22×C11×C4⋊C4C2212yes—
11C22×C11×C22⋊C4C2212yes—
12C22×C42×C11C2211yescharacteristic
13C22×C42×C11C2211yescharacteristic
14C22×C22⋊Dic11C2214yes—
15C22×C4⋊Dic11C2214yes—
16C22×C4×Dic11C2214yes—
17C4×C22⋊Dic11—28no—
18C2×C11⋊#95C2218yes—
19C2×C11⋊#95C2214yes—
20C2×C11⋊#95C2214yes—
21C4×C4⋊Dic11—28no—
22C25×C11C2311yescharacteristic
23C23×C4×C11—24no—
24C23×C4×C11—24no—
25C23×C4×C11C2×C414yes—
26C23×C4×C11D414yes—
27C23×C4×C11Q814yes—
28C23×C4×C11C2312yes—
29C23×C4×C11C2312yes—
30C23×C4×C11C2311yescharacteristic
31C23×C4×C11C2311yescharacteristic
32C23×Dic11C2318yes—
33C11×#117—232no—
34C2×C11×C4⋊C4—24no—
35C2×C11×C4⋊C4—24no—
36C2×C11×C4⋊C4C2×C418yes—
37C2×C11×C22⋊C4—24no—
38C2×C11×C22⋊C4—24no—
39C2×C11×C22⋊C4C2×C418yes—
40C2×C42×C11—24no—
41C2×C42×C11C2×C414yes—
42C2×C42×C11C2×C414yes—
43C2×C42×C11D418yes—
44C2×C22⋊Dic11—28no—
45C2×C22⋊Dic11—216no—
46C2×C4⋊Dic11—28no—
47C2×C4⋊Dic11—216no—
48C2×C4×Dic11—28no—
49C2×C4×Dic11—28no—
50C2×C4×Dic11—28no—
51C11⋊#95—28no—
52C11⋊#95—28no—
53C11⋊#95—216no—
54#13852—111nomaximal, Sylow
55C24×C11—22no—
56C24×C11—28no—
57C24×C11—22no—
58C24×C11C22×C412yes—
59C24×C11C2×D412yes—
60C24×C11C2×Q812yes—
61C24×C11C2411yescharacteristic
62C22×C4×C11—22no—
63C22×C4×C11—28no—
64C22×C4×C11—22no—
65C22×C4×C11—28no—
66C22×C4×C11—28no—
67C22×C4×C11—216no—
68C22×C4×C11—216no—
69C22×C4×C11—22no—
70C22×C4×C11—22no—
71C22×C4×C11—28no—
72C22×C4×C11C4⋊C4116yescomplemented
73C22×C4×C11C22×C414yes—
74C22×C4×C11C22×C414yes—
75C22×C4×C11C22×C412yes—
76C22×C4×C11C22×C412yes—
77C22×C4×C11C2×D414yes—
78C22×C4×C11C2×D414yes—
79C22×C4×C11C2×D412yes—
80C22×C4×C11C2×D414yes—
81C22×C4×C11C2×D412yes—
82C22×C4×C11C2×Q812yes—
83C22×C4×C11C2×Q812yes—
84C22×C4×C11#4114yes—
85C22×Dic11—28no—
86C22×Dic11—28no—
87C22×Dic11—28no—
88C22×Dic11—28no—
89C22×Dic11—28no—
90C22×Dic11—28no—
91C22×Dic11#41116yes—
92C11×C4⋊C4—216no—
93C11×C22⋊C4—216no—
94C42×C11—28no—
95C42×C11C22⋊C4116yescomplemented
96C22⋊Dic11—232no—
97C4⋊Dic11—232no—
98C4×Dic11—416no—
99C22×#117D1111yescharacteristic
100C2×C4×C4⋊C4—112no—
101C2×C4×C22⋊C4—112no—
102#1441—114no—
103#1439—114no—
104C4×#95—112no—
105C23×C11—22no—
106C23×C11—22no—
107C23×C11—28no—
108C23×C11—24no—
109C23×C11—24no—
110C23×C11—28no—
111C23×C11—28no—
112C23×C11—44no—
113C23×C11—48no—
114C23×C11—44no—
115C23×C11C2×C4⋊C414yes—
116C23×C11C23×C411yescharacteristic
117C23×C11C22×D411yescharacteristic
118C23×C11C22×D412yes—
119C23×C11C22×Q811yescharacteristic
120C23×C11C2×#4112yes—
121C23×C11C2×#4118yes—
122C2×C4×C11—22no—
123C2×C4×C11—22no—
124C2×C4×C11—28no—
125C2×C4×C11—24no—
126C2×C4×C11—24no—
127C2×C4×C11—28no—
128C2×C4×C11—28no—
129C2×C4×C11—232no—
130C2×C4×C11—24no—
131C2×C4×C11—28no—
132C2×C4×C11—44no—
133C2×C4×C11—44no—
134C2×C4×C11C2×C22⋊C418yes—
135C2×C4×C11C2×C22⋊C414yes—
136C2×C4×C11C2×C4⋊C414yes—
137C2×C4×C11C2×C4⋊C414yes—
138C2×C4×C11#11714yes—
139C2×C4×C11#12118yes—
140C2×C4×C11C22⋊Q818yes—
141C2×Dic11—216no—
142C2×Dic11—216no—
143C2×Dic11—216no—
144C2×Dic11—48no—
145C2×Dic11—48no—
146C2×Dic11—48no—
147C2×Dic11—48no—
148C24×C4C2×D1111yescharacteristic
149C2×#117—28no—
150C2×#117Dic1118yescomplemented
151C22×C4⋊C4—114no—
152C22×C4⋊C4C2×D1112yes—
153C22×C22⋊C4—114no—
154C22×C22⋊C4C2×D1112yes—
155C22×C42—114no—
156C22×C42C2×D1111yescharacteristic
157C22×C42C2×D1111yescharacteristic
158C4×C4⋊C4—228no—
159C4×C22⋊C4—228no—
160C2×#95—118no—
161C2×#95—114no—
162C2×#95—114no—
163C22×C11—24no—
164C22×C11—28no—
165C22×C11—48no—
166C22×C11—48no—
167C22×C11—44no—
168C22×C11—44no—
169C22×C11C22×C22⋊C411yescharacteristic
170C22×C11C22×C4⋊C411yescharacteristic
171C22×C11C2×#11711yescharacteristic
172C22×C11C4×#4114yes—
173C22×C11C2×#12112yes—
174C22×C11C2×C22⋊Q812yes—
175C22×C11#52514yes—
176C22×C11#52514yes—
177C22×C11#52918yes—
178C22×C11#53214yes—
179C22×C11#53314yes—
180C4×C11—24no—
181C4×C11—28no—
182C4×C11—44no—
183C4×C11#38018yes—
184Dic11—416no—
185C25C22×D1111yescharacteristic
186C23×C4—24no—
187C23×C4—24no—
188C23×C4—118no—
189C23×C4Dic2214yes—
190C23×C4D4414yes—
191C23×C4C2×Dic1114yes—
192C23×C4C22×D1112yes—
193C23×C4C22×D1111yescharacteristic
194C23×C4C22×D1112yes—
195C23×C4C22×D1111yescharacteristic
196#117—232no—
197C2×C4⋊C4—24no—
198C2×C4⋊C4—24no—
199C2×C4⋊C4—2216no—
200C2×C4⋊C4—228no—
201C2×C4⋊C4C2×Dic1118yes—
202C2×C22⋊C4—24no—
203C2×C22⋊C4—24no—
204C2×C22⋊C4—2216no—
205C2×C22⋊C4—228no—
206C2×C22⋊C4C2×Dic1118yes—
207C2×C42—24no—
208C2×C42—228no—
209C2×C42—228no—
210C2×C42—228no—
211C2×C42C2×Dic1114yes—
212C2×C42C2×Dic1114yes—
213C2×C42C22⋊D1118yes—
214#95—2216no—
215#95—228no—
216#95—228no—
217C2×C11—44no—
218C2×C11C2×#38011yescharacteristic
219C2×C11#229612yes—
220C2×C11#229712yes—
221C2×C11#229812yes—
222C2×C11#239214yes—
223C2×C11#239614yes—
224C24—22no—
225C24—28no—
226C24—22no—
227C24C2×Dic2212yes—
228C24C2×D4412yes—
229C24C22×Dic1112yes—
230C24C23×D1111yescharacteristic
231C22×C4—22no—
232C22×C4—28no—
233C22×C4—22no—
234C22×C4—216no—
235C22×C4—28no—
236C22×C4—216no—
237C22×C4—28no—
238C22×C4—28no—
239C22×C4—22no—
240C22×C4—22no—
241C22×C4—1116no—
242C22×C4—228no—
243C22×C4—228no—
244C22×C4—228no—
245C22×C4—228no—
246C22×C4—228no—
247C22×C4—228no—
248C22×C4C4⋊Dic11116yescomplemented
249C22×C4C2×Dic2212yes—
250C22×C4C2×Dic2212yes—
251C22×C4C2×D4412yes—
252C22×C4C2×D4412yes—
253C22×C4#433914yes—
254C22×C4C22×Dic1114yes—
255C22×C4C22×Dic1112yes—
256C22×C4C22×Dic1114yes—
257C22×C4C22×Dic1112yes—
258C22×C4C2×C22⋊D1114yes—
259C22×C4C2×C22⋊D1114yes—
260C22×C4C2×C22⋊D1114yes—
261C4⋊C4—216no—
262C4⋊C4—2232no—
263C22⋊C4—216no—
264C22⋊C4—2232no—
265C42—28no—
266C42—4416no—
267C42C22⋊Dic11116yescomplemented
268C11#1385211yescharacteristic, complemented, Sylow
269C23—28no—
270C23—28no—
271C23—24no—
272C23—22no—
273C23—24no—
274C23—28no—
275C23—22no—
276C23—48no—
277C23—44no—
278C23—44no—
279C23C2×C4⋊Dic1114yes—
280C23C22×Dic2211yescharacteristic
281C23C22×D4411yescharacteristic
282C23C2×#433912yes—
283C23#41×D1118yes—
284C23C23×Dic1111yescharacteristic
285C23C22×C22⋊D1112yes—
286C2×C4—24no—
287C2×C4—22no—
288C2×C4—24no—
289C2×C4—28no—
290C2×C4—28no—
291C2×C4—28no—
292C2×C4—22no—
293C2×C4—232no—
294C2×C4—28no—
295C2×C4—24no—
296C2×C4—44no—
297C2×C4—44no—
298C2×C4—2216no—
299C2×C4—2216no—
300C2×C4—2216no—
301C2×C4—448no—
302C2×C4—448no—
303C2×C4—448no—
304C2×C4—448no—
305C2×C4#6697718yes—
306C2×C4C2×C4⋊Dic1114yes—
307C2×C4C2×C4⋊Dic1114yes—
308C2×C4#6697914yes—
309C2×C4#6698318yes—
310C2×C4C2×C22⋊Dic1118yes—
311C2×C4C2×C22⋊Dic1114yes—
312C22—24no—
313C22—28no—
314C22—44no—
315C22—44no—
316C22—48no—
317C22—48no—
318C22#1062304814yes—
319C22#1062305514yes—
320C22#1062305918yes—
321C22C2×#6697712yes—
322C22C22×C4⋊Dic1111yescharacteristic
323C22C2×#6697911yescharacteristic
324C22C2×#6698312yes—
325C22#41×Dic1114yes—
326C22#1062335914yes—
327C22#1062336314yes—
328C22C22×C22⋊Dic1111yescharacteristic
329C4—28no—
330C4—24no—
331C4—44no—
332C4—4416no—
333C4#1062282518yes—
334C2—44no—
335C2C2×#1062282511yescharacteristic
336C2#1307110012yes—
337C2#1307110712yes—
338C2#1307111412yes—
339C2#1307185214yes—
340C2#1307188414yes—
subgroupG/H
centerC23×C4C22×D11
commutatorC23×C11C23×C4
FrattiniC24C23×D11
FittingC22×C11×#117C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenterC22×#117D11
hypocenterC11#13852
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23×C4 ◁ C22×#117

Complements

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

NH ≅ G/Ntype
1. C2×C4×C4⋊Dic11C2semidirect
3. #13066869C2semidirect
5. C4×C11⋊#95C2semidirect
9. C2×C11×#117C4semidirect
72. C22×C4×C11C4⋊C4semidirect
95. C42×C11C22⋊C4semidirect
150. C2×#117Dic11semidirect
248. C22×C4C4⋊Dic11semidirect
267. C42C22⋊Dic11semidirect
268. C11#13852semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C4⋊Dic112
C2×C4×C22⋊Dic112
#130668692
#130668612
C4×C11⋊#952
C22×C11×#1172
#1385211