Finite Group Databasebeta

← #16797530

Subgroups — #16797530

Order 3328.

1010 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719130C212yesmaximal
2#13130635C218yesmaximal, complemented
3#13130562C212yesmaximal
4C4×C22⋊#1057C212yesmaximal
5C2×#11718310C211yesmaximal, characteristic
6C22×#6101C411yescharacteristic
7C22×#6101C411yescharacteristic
8C22×C4×Dic13C2211yescharacteristic
9C22×C4×Dic13C2211yescharacteristic
10C22×C4×Dic13C2211yescharacteristic
11C2×C22⋊#1057C2214yes—
12#11719130C4116yescomplemented
13C2×#88110C2214yes—
14C2×#88110C2214yes—
15C2×C4⋊#1057C2214yes—
16C2×C4×#1057C2214yes—
17C2×C13×#95C411yescharacteristic
18C2×#88071C411yescharacteristic
19#11718310C414yes—
20#11718310C2214yes—
21#11718290C2214yes—
22#11718290C2214yes—
23C23×C4×C13C2×C411yescharacteristic
24C23×C4×C13C2×C411yescharacteristic
25C23×C4×C13C2×C411yescharacteristic
26C23×Dic13C2×C411yescharacteristic
27C23×Dic13C2×C411yescharacteristic
28C23×Dic13C2×C411yescharacteristic
29C23×Dic13C2311yescharacteristic
30C22×#1057C2318yes—
31C2×#6101—24no—
32C2×#6101—24no—
33C2×#6101C2×C414yes—
34C2×#6101C2×C414yes—
35C2×C4×Dic13—42no—
36C2×C4×Dic13—42no—
37C2×C4×Dic13C2×C412yes—
38C2×C4×Dic13C2×C412yes—
39C2×C4×Dic13C2×C412yes—
40C2×C4×Dic13C2×C418yes—
41C2×C4×Dic13C2312yes—
42C2×C4×Dic13C2312yes—
43C2×C4×Dic13C2312yes—
44C22⋊#1057C2×C4116yes—
45#88110—44no—
46#88110C2×C4116yescomplemented
47C4⋊#1057C2×C4116yescomplemented
48C4×#1057—44no—
49C13×#95C2×C414yes—
50#88071C2×C414yes—
51#20534—131nomaximal, Sylow
52C24×C13C22×C411yescharacteristic
53C22×C4×C13—22no—
54C22×C4×C13—41no—
55C22×C4×C13—41no—
56C22×C4×C13—41no—
57C22×C4×C13—41no—
58C22×C4×C13—41no—
59C22×C4×C13—41no—
60C22×C4×C13C4214yes—
61C22×C4×C13M1614yes—
62C22×C4×C13C22×C412yes—
63C22×C4×C13C22×C412yes—
64C22×C4×C13C22×C412yes—
65C22×Dic13—22no—
66C22×Dic13—22no—
67C22×Dic13—22no—
68C22×Dic13—22no—
69C22×Dic13—22no—
70C22×Dic13—41no—
71C22×Dic13—41no—
72C22×Dic13—41no—
73C22×Dic13—41no—
74C22×Dic13C4214yes—
75C22×Dic13M1614yes—
76C22×Dic13C22×C412yes—
77C22×Dic13C22×C411yescharacteristic
78C22×Dic13C22×C412yes—
79C22×Dic13C22×C414yes—
80C22×Dic13C22×C412yes—
81C22×Dic13C2411yescharacteristic
82C2×#1057—28no—
83C2×#1057—28no—
84C2×#1057C22×C4116yes—
85#6101—28no—
86#6101—28no—
87C4×Dic13—24no—
88C4×Dic13—24no—
89C4×Dic13—42no—
90C4×Dic13—42no—
91C4×Dic13C4218yes—
92C4×Dic13C22×C414yes—
93C4×Dic13C22×C414yes—
94C2×#432—132no—
95C2×C4×C4⋊C4—131no—
96#1771—138no—
97#1749—132no—
98C4×C22⋊C8—132no—
99C23×C13—21no—
100C23×C13—21no—
101C23×C13—21no—
102C23×C13—21no—
103C23×C13C2×C4212yes—
104C23×C13C2×M1612yes—
105C23×C13C2×M1612yes—
106C23×C13C23×C411yescharacteristic
107C2×C4×C13—22no—
108C2×C4×C13—22no—
109C2×C4×C13—22no—
110C2×C4×C13—22no—
111C2×C4×C13—22no—
112C2×C4×C13—22no—
113C2×C4×C13—22no—
114C2×C4×C13—44no—
115C2×C4×C13—44no—
116C2×C4×C13—44no—
117C2×C4×C13C2×C4214yes—
118C2×C4×C13C2×M1614yes—
119C2×Dic13—22no—
120C2×Dic13—21no—
121C2×Dic13—21no—
122C2×Dic13—22no—
123C2×Dic13—22no—
124C2×Dic13—22no—
125C2×Dic13—28no—
126C2×Dic13—28no—
127C2×Dic13—22no—
128C2×Dic13—22no—
129C2×Dic13—22no—
130C2×Dic13—44no—
131C2×Dic13—44no—
132C2×Dic13C2×C4212yes—
133C2×Dic13C2×C4214yes—
134C2×Dic13C2×M1614yes—
135C2×Dic13C23×C412yes—
136C2×Dic13H(5,𝔽2)12yes—
137C2×Dic132−1+412yes—
138#1057—216no—
139C22×C4⋊C4—131no—
140C22×C4⋊C4—131no—
141C22×C42—131no—
142C22×C42—131no—
143C22×C42—131no—
144#432—1316no—
145C2×C4⋊C8—134no—
146C2×C22⋊C8—134no—
147C2×#97—134no—
148C2×#97—134no—
149C2×C4×C8—134no—
150C4×C4⋊C4—134no—
151C4×C4⋊C4—134no—
152C2×#95—131no—
153C2×#95#26111yescharacteristic
154#336—134no—
155#336—134no—
156C22×C13—22no—
157C22×C13—22no—
158C22×C13—22no—
159C22×C13—22no—
160C22×C13—22no—
161C22×C13—22no—
162C22×C13C4×M1614yes—
163C22×C13C22×C4211yescharacteristic
164C22×C13#51811yescharacteristic
165C22×C13#51911yescharacteristic
166C22×C13C22×M1611yescharacteristic
167C22×C13C22×M1611yescharacteristic
168C22×C13#56811yescharacteristic
169C22×C13#56811yescharacteristic
170C4×C13—24no—
171C4×C13—24no—
172C4×C13—42no—
173Dic13—24no—
174Dic13—24no—
175Dic13—22no—
176Dic13—42no—
177Dic13#52014yes—
178C23×C4—131no—
179C23×C4—131no—
180C23×C4—131no—
181C23×C4—131no—
182C23×C4C2×#26111yescharacteristic
183C23×C4C2×#26111yescharacteristic
184C23×C4C2×#26111yescharacteristic
185C22×C8—138no—
186C2×C4⋊C4—134no—
187C2×C4⋊C4—134no—
188C2×C4⋊C4—264no—
189C2×C4⋊C4—264no—
190C2×C42—138no—
191C2×C42—132no—
192C2×C42—132no—
193C2×C42—132no—
194C2×C42—132no—
195C2×C42—132no—
196C2×C42—132no—
197C2×C42—522no—
198C2×C42—522no—
199C4⋊C8—1316no—
200C22⋊C8—1316no—
201#97—1316no—
202#97—524no—
203C4×C8—524no—
204#95—134no—
205#95C2×#26114yes—
206C2×C13—24no—
207C2×C13#227411yescharacteristic
208C2×C13C2×C4×M1611yescharacteristic
209C2×C13#287311yescharacteristic
210C2×C13#297311yescharacteristic
211C2×C13#297311yescharacteristic
212C2×C13#298311yescharacteristic
213C2×C13#298311yescharacteristic
214C24C22×#26111yescharacteristic
215C22×C4—22no—
216C22×C4—41no—
217C22×C4—41no—
218C22×C4—41no—
219C22×C4—41no—
220C22×C4—41no—
221C22×C4—41no—
222C22×C4—131no—
223C22×C4—134no—
224C22×C4—134no—
225C22×C4—132no—
226C22×C4—131no—
227C22×C4—132no—
228C22×C4—134no—
229C22×C4—132no—
230C22×C4—262no—
231C22×C4—262no—
232C22×C4—262no—
233C22×C4—262no—
234C22×C4—262no—
235C22×C4—521no—
236C22×C4—521no—
237C22×C4—521no—
238C22×C4—521no—
239C22×C4#611814yes—
240C22×C4C4×#26114yes—
241C22×C4C22×#26112yes—
242C22×C4C22×#26112yes—
243C22×C4C22×#26112yes—
244C2×C8—1316no—
245C2×C8—268no—
246C2×C8—268no—
247C4⋊C4—268no—
248C4⋊C4—268no—
249C42—134no—
250C42—134no—
251C42—138no—
252C42—264no—
253C42—264no—
254C42—522no—
255C42—522no—
256C13#2053411yescharacteristic, complemented, Sylow
257C23—21no—
258C23—21no—
259C23—21no—
260C23—21no—
261C23C2×#611812yes—
262C23D13⋊M1612yes—
263C23C2×C4×#26112yes—
264C23C23×#26111yescharacteristic
265C2×C4—22no—
266C2×C4—22no—
267C2×C4—22no—
268C2×C4—22no—
269C2×C4—22no—
270C2×C4—22no—
271C2×C4—22no—
272C2×C4—44no—
273C2×C4—44no—
274C2×C4—44no—
275C2×C4—132no—
276C2×C4—132no—
277C2×C4—132no—
278C2×C4—134no—
279C2×C4—132no—
280C2×C4—134no—
281C2×C4—268no—
282C2×C4—268no—
283C2×C4—262no—
284C2×C4—262no—
285C2×C4—262no—
286C2×C4—262no—
287C2×C4—261no—
288C2×C4—261no—
289C2×C4—262no—
290C2×C4—262no—
291C2×C4—262no—
292C2×C4—524no—
293C2×C4—524no—
294C2×C4C2×#611814yes—
295C2×C4C2×C4×#26114yes—
296C8—2616no—
297C22—22no—
298C22—22no—
299C22—22no—
300C22—22no—
301C22—22no—
302C22—22no—
303C22C4×#611814yes—
304C22C22×#611811yescharacteristic
305C22C2×D13⋊M1611yescharacteristic
306C22C22×C4×#26111yescharacteristic
307C22#1171962111yescharacteristic
308C22#1171962111yescharacteristic
309C22#1171962311yescharacteristic
310C22#1171962711yescharacteristic
311C4—24no—
312C4—24no—
313C4—42no—
314C4—134no—
315C4—262no—
316C4—264no—
317C4—264no—
318C4—522no—
319C2—24no—
320C2#1313127411yescharacteristic
321C2C2×C4×#611811yescharacteristic
322C2#1313140011yescharacteristic
323C2#1313168911yescharacteristic
324C2#1313169011yescharacteristic
325C2#1313173411yescharacteristic
326C2#1313173511yescharacteristic
subgroupG/H
center, FrattiniC23C23×#261
commutatorC22×C13C22×C42
FittingC2×C13×#95C4
socleC23×C13C23×C4
prime radicalC24×C13C22×C4
cosocleC22×Dic13C24
hypercenterC2×#95#261
hypocenterC13#20534
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
2. #13130635C2semidirect
12. #11719130C4semidirect
46. #88110C2×C4semidirect
47. C4⋊#1057C2×C4semidirect
256. C13#20534semidirect

Maximal subgroups

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

subgroupindex
C2×#117191302
#131306352
#131305622
C4×C22⋊#10572
C2×#117183102
#2053413