Finite Group Databasebeta

← #14912181

Subgroups — #14912181

Order 2816.

2782 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×C4×#4339C211yesmaximal, characteristic
2#13071113C214yesmaximal, complemented
3#13071106C212yesmaximal
4#13071099C212yesmaximal, complemented
5#13071093C214yesmaximal, complemented
6#13071080C214yesmaximal, complemented
7#13071059C218yesmaximal, complemented
8C4×#66925C214yesmaximal, complemented
9C4×#66979C211yesmaximal, characteristic, complemented
10C2×C43×C11C211yesmaximal, characteristic, complemented
11C22×#4339C2211yescharacteristic
12C22×C42×C11C2212yes—
13C22×C42×C11C2214yes—
14C22×C42×C11C2211yescharacteristic
15C2×C4×C22⋊D11C2214yes—
16C2×#66979C2212yes—
17C2×#66979C2211yescharacteristic
18C4×#4339C4116yescomplemented
19C2×C4×D44C2212yes—
20C2×#66925C2218yes—
21C2×#66925C2212yes—
22C2×C42×D11C2212yes—
23C2×C4×Dic22C2212yes—
24C43×C11C2212yes—
25C43×C11C2212yes—
26C43×C11C2214yes—
27#10622826C2218yes—
28#10622823C2218yes—
29C4×C22⋊Dic11C2214yes—
30#10622553C22116yes—
31#10622552C2214yes—
32C4×(C2×D11)⋊C4C2218yes—
33C4×(C2×D11)⋊C4C2218yes—
34C4×C4⋊Dic11C2214yes—
35#10622546C22116yes—
36#10622545C2212yes—
37#10622545C2218yes—
38C4×Dic11⋊C4C2218yes—
39C4×Dic11⋊C4C2218yes—
40C42×Dic11C2212yes—
41#10622542C2214yes—
42#10622541C2218yes—
43C23×C4×C11C2314yes—
44C23×C4×C11C2312yes—
45C23×C4×C11C2311yescharacteristic
46C22×C22⋊D11C2312yes—
47C2×#4339—28no—
48C2×#4339C2×C418yes—
49C22×D44C2311yescharacteristic
50C22×C4×D11C2314yes—
51C22×C4×D11C2312yes—
52C22×Dic22C2311yescharacteristic
53C2×C42×C11—28no—
54C2×C42×C11—216no—
55C2×C42×C11C2×C418yes—
56C2×C42×C11C2314yes—
57C2×C42×C11C2314yes—
58C2×C42×C11C2314yes—
59C2×C42×C11C2318yes—
60C2×C42×C11C2312yes—
61C2×C42×C11C2311yescharacteristic
62C2×C42×C11C2314yes—
63C2×C42×C11C2311yescharacteristic
64C2×C22⋊Dic11C2314yes—
65C2×C22⋊Dic11C2312yes—
66C4×C22⋊D11C2×C4132yes—
67C2×(C2×D11)⋊C4C23116yes—
68C2×(C2×D11)⋊C4C2314yes—
69#66979—28no—
70#66979C2×C418yes—
71C2×C4⋊Dic11C2314yes—
72C2×C4⋊Dic11C2312yes—
73C2×Dic11⋊C4C23116yes—
74C2×Dic11⋊C4C2314yes—
75C2×C4×Dic11C2318yes—
76C2×C4×Dic11C2314yes—
77C2×C4×Dic11C2314yes—
78C2×C4×Dic11C2312yes—
79C4×D44C2×C4116yescomplemented
80#66925—232no—
81#66925C2×C4116yescomplemented
82C42×D11C2×C4116yescomplemented
83C4×Dic22C2×C4116yescomplemented
84C11⋊#95C23116yes—
85C11⋊#95C23116yes—
86C11⋊#95C2318yes—
87#34026—111nomaximal, Sylow
88C24×C11C2411yescharacteristic
89C23×D11C2412yes—
90C22×C4×C11—28no—
91C22×C4×C11—216no—
92C22×C4×C11—28no—
93C22×C4×C11C22×C418yes—
94C22×C4×C11C22×C414yes—
95C22×C4×C11#4118yes—
96C22×C4×C11C2412yes—
97C22×C4×C11C2418yes—
98C22×C4×C11C2411yescharacteristic
99C22×C4×C11C2412yes—
100C22×C4×C11C2411yescharacteristic
101C2×C22⋊D11—28no—
102C2×C22⋊D11C22×C418yes—
103C22×Dic11C2418yes—
104C22×Dic11C2412yes—
105C22×Dic11C2414yes—
106#4339—232no—
107C2×D44—24no—
108C2×D44C22×C414yes—
109C2×C4×D11—216no—
110C2×C4×D11—28no—
111C2×C4×D11C22×C418yes—
112C2×C4×D11C22×C4116yes—
113C2×Dic22—24no—
114C2×Dic22C22×C414yes—
115C42×C11—216no—
116C42×C11—28no—
117C42×C11—28no—
118C42×C11—28no—
119C42×C11C22×C418yes—
120C42×C11C22×C414yes—
121C42×C11C22×C414yes—
122C42×C11#41116yescomplemented
123C22⋊Dic11—28no—
124C22⋊Dic11C22×C418yes—
125(C2×D11)⋊C4—232no—
126(C2×D11)⋊C4C22×C4116yes—
127C4⋊Dic11—28no—
128C4⋊Dic11C22×C418yes—
129Dic11⋊C4—232no—
130Dic11⋊C4C22×C4116yes—
131C4×Dic11—216no—
132C4×Dic11—28no—
133C4×Dic11C22×C4116yes—
134C4×Dic11C22×C418yes—
135C2×C4×#41—111no—
136#2298—114no—
137#2297—112no—
138#2296—112no—
139#2295—114no—
140#2293—114no—
141#2290—118no—
142C4×#117—111no—
143C4×#117—114no—
144C2×C43D1111yescharacteristic, complemented
145C23×C11—24no—
146C23×C11C23×C412yes—
147C23×C11C2×#4114yes—
148C23×C11C2511yescharacteristic
149C22×D11—28no—
150C22×D11—24no—
151C22×D11C23×C414yes—
152C2×C4×C11—232no—
153C2×C4×C11—24no—
154C2×C4×C11—28no—
155C2×C4×C11—28no—
156C2×C4×C11—216no—
157C2×C4×C11#117116yescomplemented
158C2×C4×C11C23×C414yes—
159C2×C4×C11C23×C412yes—
160C2×C4×C11C23×C412yes—
161C2×C4×C11C23×C414yes—
162C2×C4×C11C2×#41116yes—
163C2×C4×C11C2×#4114yes—
164C2×C4×C11C2×#4114yes—
165C2×C4×C11C2×#4118yes—
166C22⋊D11—216no—
167C2×Dic11—28no—
168C2×Dic11—24no—
169C2×Dic11—216no—
170C2×Dic11—28no—
171C2×Dic11C23×C414yes—
172C2×Dic11C23×C418yes—
173D44—28no—
174C4×D11—216no—
175C4×D11—232no—
176Dic22—28no—
177C22×#41—111no—
178C4×#41—1116no—
179C2×C4×Q8—112no—
180C2×C4×D4—114no—
181C2×C4×D4—112no—
182C2×#117—111no—
183C2×#117—112no—
184C2×#117—112no—
185C2×#117—118no—
186C22×C42—112no—
187C22×C42C2×D1114yes—
188C22×C42C2×D1112yes—
189C22×C42C2×D1111yescharacteristic
190#391—114no—
191#390—114no—
192#389—118no—
193#388—1116no—
194#387—1116no—
195#386—118no—
196#385—118no—
197C4×C4⋊C4—118no—
198C4×C4⋊C4—118no—
199C4×C4⋊C4—114no—
200C4×C22⋊C4—114no—
201C4×C22⋊C4—118no—
202C4×C22⋊C4—118no—
203#376—118no—
204#376—112no—
205C43—112no—
206C43C2×D1114yes—
207C43C2×D1112yes—
208C43C2×D1112yes—
209C22×C11—24no—
210C22×C11—28no—
211C22×C11C2×#11714yes—
212C22×C11C24×C411yescharacteristic
213C22×C11C22×#4112yes—
214C22×C11C22×#4114yes—
215C2×D11—24no—
216C2×D11—28no—
217C2×D11—48no—
218C4×C11—24no—
219C4×C11—216no—
220C4×C11C2×#11714yes—
221C4×C11C2×#11714yes—
222C4×C11C4×#4118yes—
223Dic11—24no—
224Dic11—28no—
225Dic11—48no—
226C2×#41—118no—
227C2×#41—228no—
228C22×Q8—111no—
229C22×D4—112no—
230C22×D4—111no—
231C23×C4—114no—
232C23×C4—112no—
233C23×C4C22×D1114yes—
234C23×C4C22×D1112yes—
235C23×C4C22×D1111yescharacteristic
236C4×Q8—1116no—
237C4×D4—1132no—
238C4×D4—1116no—
239#117—118no—
240#117—1116no—
241#117—228no—
242#117—2232no—
243C2×C4⋊C4—114no—
244C2×C4⋊C4—112no—
245C2×C4⋊C4—1116no—
246C2×C4⋊C4—114no—
247C2×C22⋊C4—112no—
248C2×C22⋊C4—114no—
249C2×C22⋊C4—114no—
250C2×C22⋊C4—1116no—
251C2×C42—28no—
252C2×C42—216no—
253C2×C42—112no—
254C2×C42—114no—
255C2×C42—1116no—
256C2×C42—114no—
257C2×C42—118no—
258C2×C42C4×D1118yes—
259C2×C42C22×D1114yes—
260C2×C42C22×D1114yes—
261C2×C42C22×D1118yes—
262C2×C42C22×D1114yes—
263C2×C42C22×D1111yescharacteristic
264C2×C42C22×D1112yes—
265C2×C42C22×D1114yes—
266C2×C42C22×D1111yescharacteristic
267#95—1116no—
268#95—1116no—
269#95—118no—
270C2×C11—24no—
271C2×C11C22×#11711yescharacteristic
272C2×C11C2×C4×#4112yes—
273C2×C11#344414yes—
274D11—44no—
275C24—112no—
276C24C23×D1111yescharacteristic
277#41—2232no—
278C2×Q8—114no—
279C2×Q8—224no—
280C2×D4—118no—
281C2×D4—114no—
282C2×D4—228no—
283C2×D4—224no—
284C22×C4—28no—
285C22×C4—216no—
286C22×C4—28no—
287C22×C4—112no—
288C22×C4—114no—
289C22×C4—118no—
290C22×C4—1116no—
291C22×C4—118no—
292C22×C4—2216no—
293C22×C4—228no—
294C22×C4C2×C4×D1118yes—
295C22×C4C2×C4×D1114yes—
296C22×C4#433918yes—
297C22×C4C23×D1112yes—
298C22×C4C23×D1118yes—
299C22×C4C23×D1111yescharacteristic
300C22×C4C23×D1112yes—
301C22×C4C23×D1111yescharacteristic
302C4⋊C4—1116no—
303C4⋊C4—118no—
304C4⋊C4—2232no—
305C4⋊C4—228no—
306C22⋊C4—118no—
307C22⋊C4—1116no—
308C22⋊C4—228no—
309C22⋊C4—2232no—
310C42—216no—
311C42—28no—
312C42—28no—
313C42—28no—
314C42—118no—
315C42—1116no—
316C42—228no—
317C42—2216no—
318C42C2×C4×D1114yes—
319C42C2×C4×D1114yes—
320C42C2×C4×D1118yes—
321C42#4339116yescomplemented
322C11#3402611yescharacteristic, complemented, Sylow
323C23—24no—
324C23—114no—
325C23—228no—
326C23—224no—
327C23C22×C4×D1112yes—
328C23C2×#433914yes—
329C23C24×D1111yescharacteristic
330Q8—228no—
331D4—2216no—
332D4—228no—
333C2×C4—232no—
334C2×C4—28no—
335C2×C4—28no—
336C2×C4—24no—
337C2×C4—216no—
338C2×C4—118no—
339C2×C4—114no—
340C2×C4—228no—
341C2×C4—224no—
342C2×C4—2216no—
343C2×C4—2232no—
344C2×C4—228no—
345C2×C4—2216no—
346C2×C4#66925116yescomplemented
347C2×C4C22×C4×D1114yes—
348C2×C4C22×C4×D1112yes—
349C2×C4C22×C4×D1112yes—
350C2×C4C22×C4×D1114yes—
351C2×C4C2×#4339116yes—
352C2×C4C2×#433914yes—
353C2×C4C2×#433914yes—
354C2×C4C2×#433918yes—
355C22—28no—
356C22—24no—
357C22—224no—
358C22—228no—
359C22—448no—
360C22C2×#6692514yes—
361C22C23×C4×D1111yescharacteristic
362C22C22×#433912yes—
363C22C22×#433914yes—
364C4—216no—
365C4—24no—
366C4—224no—
367C4—228no—
368C4—448no—
369C4C2×#6692514yes—
370C4C2×#6692514yes—
371C4C4×#433918yes—
372C2—24no—
373C2—444no—
374C2C22×#6692511yescharacteristic
375C2C2×C4×#433912yes—
376C2#1308191214yes—
subgroupG/H
centerC2×C42C22×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC2×C43×C11C2
socle, cosocleC23×C11C25
prime radicalC22×#4339C22
hypercenterC2×C43D11
hypocenterC11#34026
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C42 ◁ C2×C43

Complements

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

NH ≅ G/Ntype
2. #13071113C2semidirect
4. #13071099C2semidirect
5. #13071093C2semidirect
6. #13071080C2semidirect
7. #13071059C2semidirect
8. C4×#66925C2semidirect
9. C4×#66979C2semidirect
10. C2×C43×C11C2semidirect
18. C4×#4339C4semidirect
79. C4×D44C2×C4semidirect
81. #66925C2×C4semidirect
82. C42×D11C2×C4semidirect
83. C4×Dic22C2×C4semidirect
122. C42×C11#41semidirect
144. C2×C43D11semidirect
157. C2×C4×C11#117semidirect
321. C42#4339semidirect
322. C11#34026semidirect
346. C2×C4#66925semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#43392
#130711132
#130711062
#130710992
#130710932
#130710802
#130710592
C4×#669252
C4×#669792
C2×C43×C112
#3402611