Finite Group Databasebeta

← #117×#1057 #16797268

Subgroups — #117×#1057 #16797268

Order 3328.

1174 conjugacy classes of subgroups.

The subgroup lattice has 318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719119C211yesmaximal, characteristic
2C22×C4×#1057C211yesmaximal, characteristic
3C4⋊C4×#1057C214yesmaximal, complemented
4C22⋊C4×#1057C214yesmaximal
5#13130550C212yesmaximal, complemented
6C42×#1057C212yesmaximal, complemented
7#117×Dic13C211yesmaximal, characteristic
8C23×#1057C2212yes—
9C2×C13×#117C411yescharacteristic
10C2×#88180C411yescharacteristic
11C22×C4×Dic13C2211yescharacteristic
12C2×C22⋊#1057C2212yes—
13#11719119C418yescomplemented
14C2×C4⋊#1057C2212yes—
15C2×C4×#1057C418yescomplemented
16C2×C4×#1057C2218yes—
17C2×C4×#1057C2211yescharacteristic
18C2×C4×#1057C2212yes—
19C2×C4×#1057C2212yes—
20C2×C4×#1057C2211yescharacteristic
21C4⋊C4×Dic13C412yes—
22C4⋊C4×Dic13C2212yes—
23C22⋊C4×Dic13C412yes—
24C22⋊C4×Dic13C2212yes—
25#11718593C412yes—
26C42×Dic13C2212yes—
27#11718290C2218yes—
28C23×C4×C13C2×C411yescharacteristic
29C23×Dic13C2×C411yescharacteristic
30C23×Dic13C2311yescharacteristic
31C22×#1057—28no—
32C22×#1057C2×C418yes—
33C22×#1057C2314yes—
34C22×#1057C2312yes—
35C22×#1057C2312yes—
36C13×#117C818yescomplemented
37C2×C13×C4⋊C4C2×C412yes—
38C2×C13×C22⋊C4C2×C412yes—
39C2×C42×C13C2×C412yes—
40C2×C22⋊Dic13C2×C412yes—
41#88180C818yescomplemented
42C2×C4⋊Dic13C2×C412yes—
43C2×C4×Dic13C2×C414yes—
44C2×C4×Dic13C2×C411yescharacteristic
45C2×C4×Dic13C2×C411yescharacteristic
46C2×C4×Dic13C2×C414yes—
47C2×C4×Dic13C2×C414yes—
48C2×C4×Dic13C2×C412yes—
49C2×C4×Dic13C2314yes—
50C2×C4×Dic13C2311yescharacteristic
51C2×C4×Dic13C2311yescharacteristic
52C22⋊#1057C2×C418yes—
53C4⋊#1057C2×C418yes—
54C4×#1057—216no—
55C4×#1057C2×C414yes—
56C4×#1057C2×C418yes—
57C4×#1057C2×C414yes—
58C4×#1057C2×C418yes—
59#88071C2×C414yes—
60#88071C2×C414yes—
61C8×#117—131nomaximal, Sylow
62C24×C13C22×C411yescharacteristic
63C22×C4×C13C4214yes—
64C22×C4×C13C2×C814yes—
65C22×C4×C13C2×C814yes—
66C22×C4×C13C22×C414yes—
67C22×C4×C13C22×C411yescharacteristic
68C22×C4×C13C22×C411yescharacteristic
69C22×Dic13—24no—
70C22×Dic13—24no—
71C22×Dic13C4214yes—
72C22×Dic13C22×C411yescharacteristic
73C22×Dic13C22×C411yescharacteristic
74C22×Dic13C22×C412yes—
75C22×Dic13C22×C412yes—
76C22×Dic13C22×C414yes—
77C22×Dic13C22×C411yescharacteristic
78C22×Dic13C2411yescharacteristic
79C2×#1057—28no—
80C2×#1057—24no—
81C2×#1057—216no—
82C2×#1057C22×C414yes—
83C2×#1057C22×C418yes—
84C2×#1057C22×C414yes—
85C2×#1057#4118yes—
86C13×C4⋊C4C2×C818yescomplemented
87C13×C22⋊C4C2×C818yes—
88C42×C13C2×C818yescomplemented
89C22⋊Dic13C2×C818yes—
90C4⋊Dic13C2×C818yescomplemented
91C4×Dic13—28no—
92C4×Dic13—28no—
93C4×Dic13C4214yes—
94C4×Dic13C4214yes—
95C4×Dic13C2×C818yescomplemented
96C4×Dic13C22×C412yes—
97C4×Dic13C22×C412yes—
98C4×Dic13C22×C412yes—
99C4×Dic13C22×C412yes—
100C2×#431—131no—
101C22×C4×C8—131no—
102C4×#117—131no—
103C8×C4⋊C4—134no—
104C8×C22⋊C4—134no—
105#1744—132no—
106C42×C8—132no—
107C23×C13—22no—
108C23×C13—22no—
109C23×C13C2×C4212yes—
110C23×C13C22×C812yes—
111C23×C13C22×C812yes—
112C23×C13C23×C411yescharacteristic
113C2×C4×C13—24no—
114C2×C4×C13—24no—
115C2×C4×C13C4×C8116yescomplemented
116C2×C4×C13C2×C4212yes—
117C2×C4×C13C2×C4212yes—
118C2×C4×C13C22×C818yes—
119C2×C4×C13C22×C812yes—
120C2×C4×C13C22×C812yes—
121C2×C4×C13C22×C812yes—
122C2×C4×C13C22×C812yes—
123C2×Dic13—24no—
124C2×Dic13—22no—
125C2×Dic13—24no—
126C2×Dic13—22no—
127C2×Dic13—24no—
128C2×Dic13—24no—
129C2×Dic13—28no—
130C2×Dic13C2×C4212yes—
131C2×Dic13C2×C4212yes—
132C2×Dic13C2×C4212yes—
133C2×Dic13C22×C818yes—
134C2×Dic13#13114yes—
135C2×Dic13C23×C411yescharacteristic
136C2×Dic13C23×C411yescharacteristic
137C2×Dic13C2×#4114yes—
138#1057—24no—
139#1057—28no—
140#1057#11718yesdirect product factor
141C23×C8—132no—
142C2×#117—131no—
143C2×#117#26111yescharacteristic
144C22×C42—131no—
145#431—138no—
146C2×C4⋊C8—132no—
147C2×C22⋊C8—132no—
148C2×C4×C8—131no—
149C2×C4×C8—138no—
150C2×C4×C8—131no—
151C2×C4×C8—132no—
152C2×C4×C8—132no—
153C2×C4×C8—138no—
154C4×C4⋊C4—132no—
155C4×C4⋊C4—132no—
156C4×C22⋊C4—132no—
157C4×C22⋊C4—132no—
158#376—132no—
159C43—132no—
160#336—138no—
161C22×C13—22no—
162C22×C13—24no—
163C22×C13—24no—
164C22×C13—22no—
165C22×C13C2×C4×C814yes—
166C22×C13C22×C4211yescharacteristic
167C22×C13C4×#4112yes—
168C22×C13C23×C811yescharacteristic
169C22×C13C23×C811yescharacteristic
170C22×C13C2×#13112yes—
171C4×C13—28no—
172C4×C13C2×C4×C814yes—
173C4×C13C2×C4×C814yes—
174Dic13—22no—
175Dic13—28no—
176Dic13—22no—
177Dic13#40514yes—
178Dic13C2×#11712yes—
179Dic13C4×#4112yes—
180C23×C4—131no—
181C23×C4—131no—
182C23×C4C2×#26111yescharacteristic
183C22×C8—132no—
184C22×C8—132no—
185C22×C8—138no—
186C22×C8—134no—
187C22×C8—268no—
188#117—138no—
189#117#105718yesdirect product factor
190C2×C4⋊C4—132no—
191C2×C4⋊C4C2×#26112yes—
192C2×C22⋊C4—132no—
193C2×C22⋊C4C2×#26112yes—
194C2×C42—134no—
195C2×C42—134no—
196C2×C42—131no—
197C2×C42—131no—
198C2×C42—132no—
199C2×C42—131no—
200C2×C42—131no—
201C2×C42—134no—
202C2×C42—134no—
203C2×C42C2×#26112yes—
204C4⋊C8—138no—
205C22⋊C8—138no—
206C4×C8—134no—
207C4×C8—138no—
208C4×C8—134no—
209C4×C8—138no—
210C4×C8—2616no—
211#95—134no—
212#95—134no—
213C2×C13—24no—
214C2×C13C4×#11711yescharacteristic
215C2×C13C22×C4×C811yescharacteristic
216C2×C13C2×#40511yescharacteristic
217C2×C13C8×#4112yes—
218C2×C13C8×#4112yes—
219C24C22×#26111yescharacteristic
220C22×C4—131no—
221C22×C4—131no—
222C22×C4—132no—
223C22×C4—132no—
224C22×C4—134no—
225C22×C4—131no—
226C22×C4—131no—
227C22×C4—134no—
228C22×C4—264no—
229C22×C4—264no—
230C22×C4D13⋊C814yes—
231C22×C4C4×#26114yes—
232C22×C4C2×#105714yes—
233C22×C4C22×#26114yes—
234C22×C4C22×#26111yescharacteristic
235C22×C4C22×#26111yescharacteristic
236C2×C8—134no—
237C2×C8—138no—
238C2×C8—134no—
239C2×C8—138no—
240C2×C8—2616no—
241C2×C8—268no—
242C2×C8—264no—
243C4⋊C4—138no—
244C4⋊C4C2×#105718yescomplemented
245C22⋊C4—138no—
246C22⋊C4C2×#105718yes—
247C42—138no—
248C42—132no—
249C42—132no—
250C42—132no—
251C42—132no—
252C42—134no—
253C42—134no—
254C42—268no—
255C42—268no—
256C42C2×#105718yescomplemented
257C13C8×#11711yescharacteristic, complemented, Sylow
258C23—22no—
259C23—22no—
260C23C2×D13⋊C812yes—
261C23C2×C4×#26112yes—
262C23C22×#105712yes—
263C23C23×#26111yescharacteristic
264C2×C4—24no—
265C2×C4—24no—
266C2×C4—131no—
267C2×C4—131no—
268C2×C4—132no—
269C2×C4—134no—
270C2×C4—134no—
271C2×C4—138no—
272C2×C4—132no—
273C2×C4—132no—
274C2×C4—264no—
275C2×C4—264no—
276C2×C4—268no—
277C2×C4—264no—
278C2×C4—262no—
279C2×C4—264no—
280C2×C4—262no—
281C2×C4C4×#1057116yescomplemented
282C2×C4C2×D13⋊C812yes—
283C2×C4C2×D13⋊C812yes—
284C2×C4C2×C4×#26112yes—
285C2×C4C2×C4×#26112yes—
286C2×C4C22×#105718yes—
287C2×C4C22×#105712yes—
288C2×C4C22×#105712yes—
289C8—138no—
290C8—264no—
291C8—268no—
292C22—22no—
293C22—24no—
294C22—24no—
295C22—22no—
296C22C2×C4×#105714yes—
297C22C22×D13⋊C811yescharacteristic
298C22C22×C4×#26111yescharacteristic
299C22D13⋊#13112yes—
300C22#41×#26112yes—
301C22C23×#105711yescharacteristic
302C4—28no—
303C4—132no—
304C4—132no—
305C4—134no—
306C4—262no—
307C4—268no—
308C4—262no—
309C4C2×C4×#105714yes—
310C4C2×C4×#105714yes—
311C2—24no—
312C2#117×#26111yescharacteristic
313C2C22×C4×#105711yescharacteristic
314C2#1313139611yescharacteristic
315C2#41×#105712yes—
316C2#1313164012yes—
subgroupG/H
centerC22×C4C22×#261
commutatorC2×C13C22×C4×C8
FrattiniC23C23×#261
FittingC2×C13×#117C4
socleC23×C13C23×C4
prime radicalC24×C13C22×C4
cosocleC22×Dic13C24
hypercenterC2×#117#261
hypocenterC13C8×#117
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
3. C4⋊C4×#1057C2semidirect
5. #13130550C2semidirect
6. C42×#1057C2semidirect
13. #11719119C4semidirect
15. C2×C4×#1057C4semidirect
36. C13×#117C8semidirect
41. #88180C8semidirect
86. C13×C4⋊C4C2×C8semidirect
88. C42×C13C2×C8semidirect
90. C4⋊Dic13C2×C8semidirect
95. C4×Dic13C2×C8semidirect
115. C2×C4×C13C4×C8semidirect
140. #1057#117direct (N × H)
189. #117#1057direct (N × H)
244. C4⋊C4C2×#1057semidirect
256. C42C2×#1057semidirect
257. C13C8×#117semidirect
281. C2×C4C4×#1057semidirect

Maximal subgroups

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

subgroupindex
C2×#117191192
C22×C4×#10572
C4⋊C4×#10572
C22⋊C4×#10572
#131305502
C42×#10572
#117×Dic132
C8×#11713