Finite Group Databasebeta

← #15757432

Subgroups — #15757432

Order 3328.

356 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 356 conjugacy classes of subgroups — too many to draw. Only its 97 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123937C211yesmaximal, characteristic
2#13115812C211yesmaximal, characteristic
3#13113627C211yesmaximal, characteristic
4#13113500C211yesmaximal, characteristic
5#13112668C211yesmaximal, characteristic
6#13112668C211yesmaximal, characteristic
7C13×#1574C211yesmaximal, characteristic
8#11719175C2211yescharacteristic
9C13×#431C2211yescharacteristic
10C13×#431C2211yescharacteristic
11C13×#423C2211yescharacteristic
12C42×Dic13C2211yescharacteristic
13#11718586C2211yescharacteristic
14#11718586C2211yescharacteristic
15#11718492—21no—
16#11718491—21no—
17#11718381—22no—
18#11718340—21no—
19C8×Dic26—21no—
20C13×#335—21no—
21C13×#334—21no—
22#11718147—22no—
23#11718078C411yescharacteristic, complemented
24#11718078C411yescharacteristic, complemented
25#11718074C411yescharacteristic, complemented
26#11718074C411yescharacteristic, complemented
27#11718072—21no—
28#11718071—21no—
29C2×C13×M16—21no—
30C2×C42×C13C2311yescharacteristic
31#88180D412yes—
32#88178—21no—
33#88178—21no—
34C2×C4×Dic13—21no—
35C2×C4×Dic13—21no—
36C2×C4×Dic13—21no—
37#88124Q812yes—
38#88123C2×C411yescharacteristic
39#88123C2×C411yescharacteristic
40C4×Dic26—21no—
41C4×Dic26—21no—
42C13×C4⋊C8—21no—
43C13×C4⋊C8—21no—
44C13×C4⋊C8C2×C411yescharacteristic
45C13×C4⋊C8C2×C411yescharacteristic
46C13×C4⋊C8D411yescharacteristic
47C13×C4⋊C8D411yescharacteristic
48C13×C22⋊C8—21no—
49C13×C22⋊C8—21no—
50C4×C8×C13—21no—
51C4×C8×C13—21no—
52C22⋊#1055—21no—
53C22⋊#1055—21no—
54#88055—22no—
55#88054—22no—
56#88054—22no—
57C8×Dic13—22no—
58C4⋊#1055C2×C411yescharacteristic
59C4⋊#1055C2×C411yescharacteristic
60C4⋊#1055D411yescharacteristic
61C4⋊#1055D411yescharacteristic
62C4×#1055—21no—
63C4×#1055—21no—
64#8936—131nomaximal, Sylow
65C22×C4×C13C2×D411yescharacteristic
66C22×C4×C13#4111yescharacteristic
67C22×C4×C13#4111yescharacteristic
68C22×Dic13—41no—
69C2×Dic26—21no—
70C2×Dic26—21no—
71C13×M16—42no—
72C2×C8×C13—21no—
73C2×C8×C13—21no—
74C2×C8×C13—21no—
75C2×C8×C13—21no—
76C2×C8×C13—41no—
77C42×C13C22×C411yescharacteristic
78C42×C13C2×D411yescharacteristic
79C42×C13C2×D411yescharacteristic
80C42×C13C2×Q811yescharacteristic
81C22⋊Dic13—22no—
82C4⋊Dic13—21no—
83C4⋊Dic13—21no—
84C4⋊Dic13C4⋊C412yes—
85C4⋊Dic13C4⋊C412yes—
86#6101—22no—
87#6101—22no—
88C4×Dic13—22no—
89C4×Dic13—22no—
90C4×Dic13—22no—
91C4×Dic13—22no—
92C4×Dic13—41no—
93C4×Dic13—41no—
94C4×Dic13—41no—
95C2×#1055—21no—
96C2×#1055—21no—
97C2×#1055—21no—
98C2×#1055—21no—
99#2986—131no—
100#1994—131no—
101#1574—131no—
102#1574D1311yescharacteristic
103#1544—131no—
104#1276—131no—
105#1276—131no—
106C23×C13#12311yescharacteristic
107C2×C4×C13—21no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13C2×C4⋊C411yescharacteristic
114C2×C4×C13C4×D411yescharacteristic
115C2×C4×C13C4×D411yescharacteristic
116C2×C4×C13#12011yescharacteristic
117C2×C4×C13C22⋊Q811yescharacteristic
118C2×C4×C13C22⋊Q811yescharacteristic
119C2×Dic13—22no—
120C2×Dic13—22no—
121C2×Dic13—42no—
122C2×Dic13—42no—
123C2×Dic13—42no—
124Dic26—41no—
125Dic26—41no—
126Dic26—41no—
127Dic26—41no—
128C8×C13—41no—
129C8×C13—41no—
130C8×C13—41no—
131C8×C13—41no—
132C8×C13—81no—
133#1055—41no—
134#1055—41no—
135#1055—41no—
136#1055—41no—
137#533—131no—
138#446—261no—
139#446—261no—
140C8×Q8—261no—
141C8×Q8—261no—
142#433—262no—
143#431—131no—
144#431—131no—
145#431C2×D1311yescharacteristic
146#431C2×D1311yescharacteristic
147#423C2×D1311yescharacteristic
148C43—131no—
149#339—262no—
150#335—21no—
151#335—261no—
152#334—21no—
153#334—261no—
154#332—131no—
155#332—131no—
156#332—131no—
157#332—131no—
158C22×C13—21no—
159C22×C13—21no—
160C22×C13—21no—
161C22×C13#38511yescharacteristic
162C4×C13—21no—
163C4×C13—21no—
164C4×C13—21no—
165C4×C13#44311yescharacteristic
166C4×C13#44311yescharacteristic
167C4×C13#44411yescharacteristic
168C4×C13#44411yescharacteristic
169C4×C13#45411yescharacteristic
170C4×C13#45611yescharacteristic
171Dic13—44no—
172Dic13—42no—
173Dic13—42no—
174C2×M16—21no—
175C4⋊Q8—131no—
176C4⋊Q8—131no—
177#125—132no—
178C22⋊Q8—261no—
179C22⋊Q8—261no—
180C4×Q8—261no—
181C4×Q8—261no—
182#117—132no—
183C2×C42—261no—
184C2×C42—261no—
185C2×C42—261no—
186C2×C42C22×D1311yescharacteristic
187C4⋊C8—21no—
188C4⋊C8—21no—
189C4⋊C8—131no—
190C4⋊C8—131no—
191C4⋊C8—131no—
192C4⋊C8—131no—
193C4⋊C8—262no—
194C4⋊C8—262no—
195C4⋊C8C4×D1311yescharacteristic
196C4⋊C8C4×D1311yescharacteristic
197C4⋊C8C22⋊D1311yescharacteristic
198C4⋊C8C22⋊D1311yescharacteristic
199C22⋊C8—21no—
200C22⋊C8—21no—
201C22⋊C8—261no—
202C22⋊C8—261no—
203#97—262no—
204C4×C8—21no—
205C4×C8—21no—
206C4×C8—262no—
207C4×C8—261no—
208C4×C8—261no—
209C2×C13—41no—
210C2×C13#185711yescharacteristic
211C2×C13#186611yescharacteristic
212C2×C13#186611yescharacteristic
213C2×Q8—261no—
214C2×Q8—261no—
215C22×C4—521no—
216C22×C4#612711yescharacteristic
217C22×C4D4×D1311yescharacteristic
218C22×C4#613111yescharacteristic
219M16—42no—
220C2×C8—21no—
221C2×C8—21no—
222C2×C8—21no—
223C2×C8—21no—
224C2×C8—41no—
225C2×C8—261no—
226C2×C8—261no—
227C2×C8—261no—
228C2×C8—261no—
229C4⋊C4—132no—
230C4⋊C4—132no—
231C4⋊C4—261no—
232C4⋊C4—262no—
233C4⋊C4—261no—
234C4⋊C4—262no—
235C22⋊C4—262no—
236C42—262no—
237C42—262no—
238C42—262no—
239C42—262no—
240C42—521no—
241C42—521no—
242C42—521no—
243C42C2×C4×D1311yescharacteristic
244C42D4×D1311yescharacteristic
245C42Q8×D1311yescharacteristic
246C42C2×C22⋊D1311yescharacteristic
247C13#893611yescharacteristic, complemented, Sylow
248C23#8814811yescharacteristic
249Q8—521no—
250Q8—521no—
251Q8—521no—
252Q8—521no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—262no—
260C2×C4—262no—
261C2×C4—522no—
262C2×C4—522no—
263C2×C4—522no—
264C2×C4C4⋊C4×D1311yescharacteristic
265C2×C4#8814711yescharacteristic
266C2×C4#8815011yescharacteristic
267C2×C4C4×C22⋊D1311yescharacteristic
268C2×C4#8819111yescharacteristic
269C2×C4#8820011yescharacteristic
270C8—41no—
271C8—41no—
272C8—41no—
273C8—41no—
274C8—81no—
275C8—521no—
276C8—521no—
277C8—521no—
278C8—521no—
279C22—21no—
280C22—21no—
281C22—21no—
282C22#1171865011yescharacteristic
283C4—21no—
284C4—21no—
285C4—21no—
286C4—524no—
287C4—522no—
288C4—522no—
289C4#1171855511yescharacteristic
290C4#1171855611yescharacteristic
291C4#1171880511yescharacteristic
292C4#1171880611yescharacteristic
293C4#1171886211yescharacteristic
294C4#1171886611yescharacteristic
295C2—41no—
296C2#1311504911yescharacteristic
297C2#1311510811yescharacteristic
298C2#1311511011yescharacteristic
subgroupG/H
centerC2×C4#88191
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1574C2
socleC22×C13#385
prime radicalC23×C13#123
cosocleC2×C42×C13C23
hypercenter#1574D13
hypocenterC13#8936
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1574

Complements

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

NH ≅ G/Ntype
23. #11718078C4semidirect
24. #11718078C4semidirect
25. #11718074C4semidirect
26. #11718074C4semidirect
247. C13#8936semidirect

Maximal subgroups

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

subgroupindex
#131239372
#131158122
#131136272
#131135002
#131126682
C13×#15742
#893613