Finite Group Databasebeta

← #16787812

Subgroups — #16787812

Order 3328.

358 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 68 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
1C4×#88113C211yesmaximal, characteristic
2#13130078C211yesmaximal, characteristic
3#13129835C212yesmaximal
4#13129820C212yesmaximal
5#13120713C211yesmaximal, characteristic
6C2×C13×#125C411yescharacteristic
7C2×C4×Dic26C2211yescharacteristic
8C2×#88113—21no—
9#11719125—21no—
10C4×#6122—21no—
11#11718647—21no—
12#11718643C411yescharacteristic
13#11718643C2211yescharacteristic
14#11718641C411yescharacteristic
15#11718641C2211yescharacteristic
16#11718640—21no—
17#11718639—21no—
18#11718639—21no—
19#11718598C411yescharacteristic
20#11718291C2212yes—
21#11718286C2212yes—
22#11718285—21no—
23C22×Dic26D411yescharacteristic
24C2×#6122—22no—
25C13×#125—41no—
26C13×#125—41no—
27C2×C13×C4⋊C4—21no—
28C2×C13×C4⋊C4—21no—
29C2×C13×C4⋊C4C2×C411yescharacteristic
30C2×C13×C4⋊C4C2×C411yescharacteristic
31C2×C42×C13C2×C411yescharacteristic
32C2×C4⋊Dic13D411yescharacteristic
33C2×#6101—21no—
34C2×#6101—21no—
35C2×#6101C2×C411yescharacteristic
36C2×#6101C2311yescharacteristic
37C2×C4×Dic13D411yescharacteristic
38C2×C4×Dic13D411yescharacteristic
39C4×Dic26—41no—
40C4×Dic26—41no—
41C22⋊#1057—22no—
42#88113—24no—
43#88112—41no—
44#88110—41no—
45C4×#1057—41no—
46C4×#1057—41no—
47#88071—21no—
48#88071—21no—
49#88071—21no—
50#88071—21no—
51#88071—21no—
52#88071—21no—
53#88071—21no—
54#88071—21no—
55#88071C2×C411yescharacteristic
56#88071C2×C411yescharacteristic
57#11740—131nomaximal, Sylow
58C22×C4×C13—21no—
59C22×C4×C13—21no—
60C22×C4×C13C22⋊C411yescharacteristic
61C22×C4×C13C22⋊C411yescharacteristic
62C22×C4×C13C22×C411yescharacteristic
63C22×Dic13—21no—
64C22×Dic13—21no—
65C22×Dic13C22⋊C411yescharacteristic
66C22×Dic13C22⋊C411yescharacteristic
67C22×Dic13C2×D411yescharacteristic
68C22×Dic13C2×D411yescharacteristic
69C2×Dic26—22no—
70C2×Dic26—22no—
71C2×Dic26—41no—
72#6122—24no—
73#6122—42no—
74C2×#1057—42no—
75C2×#1057—42no—
76C13×C4⋊C4—41no—
77C13×C4⋊C4—41no—
78C13×C4⋊C4—42no—
79C13×C4⋊C4—41no—
80C13×C4⋊C4—41no—
81C42×C13—21no—
82C42×C13—21no—
83C4⋊Dic13—41no—
84#6101—41no—
85#6101—41no—
86#6101—42no—
87#6101—42no—
88C4×Dic13—21no—
89C4×Dic13—21no—
90C4×Dic13—21no—
91C4×Dic13—21no—
92#2634—131no—
93C4×#101—131no—
94#1461—131no—
95#1353—132no—
96#1346—132no—
97C23×C13C2×C22⋊C411yescharacteristic
98C2×C4×C13—21no—
99C2×C4×C13—21no—
100C2×C4×C13—21no—
101C2×C4×C13—21no—
102C2×C4×C13—41no—
103C2×C4×C13—41no—
104C2×C4×C13—42no—
105C2×C4×C13—41no—
106C2×C4×C13—41no—
107C2×C4×C13—41no—
108C2×C4×C13—41no—
109C2×C4×C13#9911yescharacteristic
110C2×C4×C13#9911yescharacteristic
111C2×Dic13—21no—
112C2×Dic13—21no—
113C2×Dic13—21no—
114C2×Dic13—21no—
115C2×Dic13—21no—
116C2×Dic13—21no—
117C2×Dic13—41no—
118C2×Dic13—41no—
119C2×Dic13—41no—
120C2×Dic13—41no—
121C2×Dic13—41no—
122C2×Dic13—41no—
123C2×Dic13—41no—
124C2×Dic13—41no—
125C2×Dic13#10412yes—
126C2×Dic13#13512yes—
127Dic26—44no—
128#1057—44no—
129#1057—82no—
130C2×#125#26111yescharacteristic
131C2×C4×Q8—131no—
132#431—261no—
133C2×#101—261no—
134C4×M16—261no—
135#400—131no—
136#400—131no—
137#400—261no—
138#398—131no—
139#398—131no—
140#395—261no—
141#387—261no—
142#387—261no—
143#383—131no—
144#343—132no—
145#324—132no—
146#324—261no—
147C22×C13—21no—
148C22×C13—21no—
149C22×C13C2×#9911yescharacteristic
150C22×C13#41611yescharacteristic
151C22×C13C2×#10411yescharacteristic
152C4×C13—21no—
153C4×C13—21no—
154C4×C13—41no—
155C4×C13—41no—
156C4×C13—81no—
157C4×C13—81no—
158Dic13—22no—
159Dic13—22no—
160Dic13—41no—
161Dic13—41no—
162Dic13—81no—
163Dic13—81no—
164C22×Q8—131no—
165C2×M16—262no—
166#125—41no—
167#125—41no—
168C4×Q8—521no—
169C4×Q8—521no—
170C2×C4⋊C4—21no—
171C2×C4⋊C4—21no—
172C2×C4⋊C4—131no—
173C2×C4⋊C4—131no—
174C2×C4⋊C4—131no—
175C2×C4⋊C4—261no—
176C2×C4⋊C4—261no—
177C2×C4⋊C4C2×#26111yescharacteristic
178C2×C4⋊C4C2×#26111yescharacteristic
179C2×C42—131no—
180C2×C42—131no—
181C2×C42C2×#26111yescharacteristic
182C4⋊C8—521no—
183#101—264no—
184C22⋊C8—262no—
185#97—521no—
186C4×C8—521no—
187C4×C8—521no—
188#95—131no—
189#95—131no—
190#95—261no—
191#95—261no—
192#95—261no—
193#95—261no—
194#95—261no—
195#95—261no—
196#95—261no—
197#95—261no—
198C2×C13—21no—
199C2×C13—21no—
200C2×C13#150111yescharacteristic
201C2×C13#212311yescharacteristic
202C2×C13#213311yescharacteristic
203C2×Q8—262no—
204C2×Q8—262no—
205C2×Q8—521no—
206C22×C4—21no—
207C22×C4—21no—
208C22×C4—131no—
209C22×C4—131no—
210C22×C4—131no—
211C22×C4—131no—
212C22×C4—261no—
213C22×C4—261no—
214C22×C4C22⋊#26111yescharacteristic
215C22×C4C22⋊#26111yescharacteristic
216C22×C4C22×#26111yescharacteristic
217M16—264no—
218M16—522no—
219C2×C8—522no—
220C2×C8—522no—
221C4⋊C4—41no—
222C4⋊C4—41no—
223C4⋊C4—42no—
224C4⋊C4—41no—
225C4⋊C4—41no—
226C4⋊C4—521no—
227C4⋊C4—521no—
228C4⋊C4—521no—
229C4⋊C4—522no—
230C4⋊C4—522no—
231C42—21no—
232C42—21no—
233C42—261no—
234C42—261no—
235C42—261no—
236C42—261no—
237C13#1174011yescharacteristic, complemented, Sylow
238C23C2×C22⋊#26111yescharacteristic
239Q8—524no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—42no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—132no—
252C2×C4—132no—
253C2×C4—261no—
254C2×C4—261no—
255C2×C4—261no—
256C2×C4—261no—
257C2×C4—261no—
258C2×C4—261no—
259C2×C4—521no—
260C2×C4—521no—
261C2×C4—521no—
262C2×C4—521no—
263C2×C4—521no—
264C2×C4—521no—
265C2×C4—521no—
266C2×C4—521no—
267C2×C4#8811911yescharacteristic
268C2×C4#8811911yescharacteristic
269C8—524no—
270C8—1042no—
271C22—21no—
272C22—21no—
273C22D13⋊#10411yescharacteristic
274C22#1171916511yescharacteristic
275C22C2×#8811911yescharacteristic
276C4—21no—
277C4—21no—
278C4—41no—
279C4—41no—
280C4—81no—
281C4—81no—
282C4—262no—
283C4—262no—
284C4—521no—
285C4—521no—
286C4—1041no—
287C4—1041no—
288C2—21no—
289C2—21no—
290C2#1313021111yescharacteristic
291C2#1313109811yescharacteristic
292C2#1313113111yescharacteristic
subgroupG/H
centerC22C2×#88119
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC2×C13×#125C4
socleC22×C13C2×#99
prime radicalC23×C13C2×C22⋊C4
cosocleC2×#6101C23
hypercenterC2×#125#261
hypocenterC13#11740
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
237. C13#11740semidirect

Maximal subgroups

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

subgroupindex
C4×#881132
#131300782
#131298352
#131298202
#131207132
#1174013