Finite Group Databasebeta

← #15754482

Subgroups — #15754482

Order 3328.

686 conjugacy classes of subgroups; only the 167 normal subgroups are shown.

normal subgroups only

This group has 686 conjugacy classes of subgroups — too many to draw. Only its 167 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#13115773C211yesmaximal, characteristic
2#13114832C211yesmaximal, characteristic
3#13113526C212yesmaximal
4#13113291C212yesmaximal
5C13×#3502C211yesmaximal, characteristic
6Q82×C13—22no—
7C13×#557—22no—
8C13×#557—24no—
9C13×#544—21no—
10C13×#544C414yes—
11C13×#533—22no—
12C13×#533C2212yes—
13C13×#519—21no—
14C2×C4×Q8×C13C2211yescharacteristic
15C2×#88076—21no—
16#11718585C2212yes—
17C2×C4⋊#1055C2211yescharacteristic
18C2×C4×#1055C2211yescharacteristic
19#11718139—22no—
20#11718138—22no—
21Q8⋊#1055—24no—
22#11718122—21no—
23#11718116—22no—
24C22×Q8×C13D411yescharacteristic
25C13×C4⋊Q8—22no—
26C13×C4⋊Q8—22no—
27C13×C4⋊Q8—24no—
28C13×C4⋊Q8—28no—
29C13×C4⋊Q8D412yes—
30C13×C4⋊Q8D412yes—
31C13×#125—24no—
32C13×#125—24no—
33C13×#125—28no—
34C13×#125—22no—
35C13×C22⋊Q8—24no—
36C13×C22⋊Q8—22no—
37C13×C22⋊Q8C2×C414yes—
38C4×Q8×C13—24no—
39C4×Q8×C13—24no—
40C4×Q8×C13—24no—
41C4×Q8×C13—24no—
42C4×Q8×C13—22no—
43C4×Q8×C13—22no—
44C4×Q8×C13—22no—
45C4×Q8×C13D414yes—
46C13×#117—24no—
47C13×#117—22no—
48C2×C13×C4⋊C4C2×C412yes—
49C2×C13×C4⋊C4D411yescharacteristic
50C2×C42×C13D412yes—
51C2×C42×C13C2311yescharacteristic
52C2×#6099—22no—
53C22×#1055—21no—
54C22×#1055—21no—
55#88076—42no—
56C4⋊#1055—22no—
57C4⋊#1055—22no—
58C4⋊#1055—22no—
59C4×#1055—22no—
60#8356—131nomaximal, Sylow
61C2×Q8×C13—24no—
62C2×Q8×C13—22no—
63C2×Q8×C13—22no—
64C2×Q8×C13—22no—
65C2×Q8×C13C22⋊C414yes—
66C2×Q8×C13SD1612yes—
67C2×Q8×C13Q1612yes—
68C22×C4×C13C22⋊C412yes—
69C22×C4×C13C22⋊C412yes—
70C22×C4×C13C22×C411yescharacteristic
71C22×C4×C13C2×D411yescharacteristic
72C22×C4×C13C2×D411yescharacteristic
73C13×C4⋊C4—24no—
74C13×C4⋊C4—24no—
75C13×C4⋊C4—24no—
76C13×C4⋊C4—28no—
77C13×C4⋊C4—24no—
78C13×C4⋊C4—24no—
79C13×C4⋊C4—22no—
80C13×C4⋊C4—22no—
81C13×C4⋊C4—22no—
82C13×C4⋊C4—22no—
83C13×C4⋊C4—24no—
84C13×C4⋊C4C22⋊C414yes—
85C13×C22⋊C4—24no—
86C42×C13—28no—
87C42×C13—22no—
88C42×C13—22no—
89C42×C13—24no—
90C42×C13C2×D412yes—
91C42×C13C2×D412yes—
92#6099—42no—
93#6099—42no—
94C2×#1055—22no—
95C2×#1055—41no—
96C2×#1055—41no—
97C2×#1055—42no—
98C2×#1055—41no—
99C2×#1055—42no—
100#3502D1311yescharacteristic
101#1984—131no—
102#1801—131no—
103#1550—132no—
104#1493—132no—
105C23×C13C2×C22⋊C411yescharacteristic
106Q8×C13—24no—
107Q8×C13—24no—
108Q8×C13—44no—
109Q8×C13—42no—
110Q8×C13—42no—
111Q8×C13—84no—
112C2×C4×C13—22no—
113C2×C4×C13—22no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—24no—
117C2×C4×C13—24no—
118C2×C4×C13—22no—
119C2×C4×C13—41no—
120C2×C4×C13—42no—
121C2×C4×C13#10314yes—
122C2×C4×C13C2×C22⋊C412yes—
123C2×C4×C13#12011yescharacteristic
124C2×C4×C13#12012yes—
125C2×C4×C13#12011yescharacteristic
126C2×C4×C13C2×SD1611yescharacteristic
127C2×C4×C13C2×Q1611yescharacteristic
128C2×C4×C13#13712yes—
129#1055—42no—
130#1055—82no—
131#1055—81no—
132Q82—22no—
133#557—22no—
134#557—24no—
135#544—21no—
136#544Dic1314yes—
137#533—22no—
138#533C2×D1312yes—
139#519—21no—
140C2×C4×Q8C2×D1311yescharacteristic
141#423—132no—
142C2×C4⋊C8—131no—
143C2×#101—261no—
144C2×C4×C8—131no—
145#343—261no—
146#336—262no—
147#333—262no—
148#332—262no—
149Q8⋊C8—264no—
150C22×C13—21no—
151C22×C13—21no—
152C22×C13#37911yescharacteristic
153C22×C13C2×#10311yescharacteristic
154C22×C13#41911yescharacteristic
155C4×C13—21no—
156C4×C13—24no—
157C4×C13—22no—
158C4×C13—44no—
159C4×C13—42no—
160C4×C13—44no—
161C4×C13#44812yes—
162C4×C13#45112yes—
163C4×C13#45411yescharacteristic
164C4×C13#45611yescharacteristic
165C22×Q8C22⋊D1311yescharacteristic
166C2×M16—262no—
167C22×C8—261no—
168C22×C8—261no—
169C4⋊Q8—22no—
170C4⋊Q8—22no—
171C4⋊Q8—24no—
172C4⋊Q8—28no—
173C4⋊Q8C22⋊D1312yes—
174C4⋊Q8C22⋊D1312yes—
175#125—24no—
176#125—24no—
177#125—28no—
178#125—22no—
179C22⋊Q8—24no—
180C22⋊Q8—22no—
181C22⋊Q8C2×Dic1314yes—
182C4×Q8—24no—
183C4×Q8—24no—
184C4×Q8—24no—
185C4×Q8—24no—
186C4×Q8—22no—
187C4×Q8—22no—
188C4×Q8—22no—
189C4×Q8C22⋊D1314yes—
190#117—24no—
191#117—22no—
192C2×C4⋊C4C2×Dic1312yes—
193C2×C4⋊C4C22⋊D1311yescharacteristic
194C2×C42C22⋊D1312yes—
195C2×C42C22×D1311yescharacteristic
196C4⋊C8—262no—
197C4⋊C8—262no—
198C4⋊C8—262no—
199#101—522no—
200C4×C8—262no—
201C2×C13—21no—
202C2×C13—21no—
203C2×C13#178711yescharacteristic
204C2×C13#179111yescharacteristic
205C2×C13#179311yescharacteristic
206C2×Q8—24no—
207C2×Q8—22no—
208C2×Q8—22no—
209C2×Q8—22no—
210C2×Q8#610612yes—
211C2×Q8#610712yes—
212C2×Q8C22⋊Dic1314yes—
213C22×C4C22⋊Dic1312yes—
214C22×C4C22⋊Dic1312yes—
215C22×C4C22×Dic1311yescharacteristic
216C22×C4C2×C22⋊D1311yescharacteristic
217C22×C4C2×C22⋊D1311yescharacteristic
218M16—522no—
219M16—522no—
220C2×C8—262no—
221C2×C8—521no—
222C2×C8—521no—
223C2×C8—522no—
224C2×C8—521no—
225C2×C8—522no—
226C4⋊C4—24no—
227C4⋊C4—24no—
228C4⋊C4—24no—
229C4⋊C4—28no—
230C4⋊C4—24no—
231C4⋊C4—24no—
232C4⋊C4—22no—
233C4⋊C4—22no—
234C4⋊C4—22no—
235C4⋊C4—22no—
236C4⋊C4—24no—
237C4⋊C4C22⋊Dic1314yes—
238C22⋊C4—24no—
239C42—28no—
240C42—22no—
241C42—22no—
242C42—24no—
243C42C2×C22⋊D1312yes—
244C42C2×C22⋊D1312yes—
245C13#835611yescharacteristic, complemented, Sylow
246C23C2×C22⋊Dic1311yescharacteristic
247Q8—24no—
248Q8—24no—
249Q8—44no—
250Q8—42no—
251Q8—42no—
252Q8—84no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—24no—
258C2×C4—24no—
259C2×C4—22no—
260C2×C4—41no—
261C2×C4—42no—
262C2×C4#8807514yes—
263C2×C4C2×#610611yescharacteristic
264C2×C4#8819612yes—
265C2×C4C2×#610711yescharacteristic
266C2×C4C2×C22⋊Dic1312yes—
267C2×C4#8820711yescharacteristic
268C2×C4#8820712yes—
269C2×C4#8820711yescharacteristic
270C8—522no—
271C8—1042no—
272C8—1041no—
273C22—21no—
274C22—21no—
275C22C2×#8807511yescharacteristic
276C22#1171888611yescharacteristic
277C22#1171890811yescharacteristic
278C4—24no—
279C4—22no—
280C4—21no—
281C4—42no—
282C4—44no—
283C4—44no—
284C4#1171888812yes—
285C4#1171888912yes—
286C4#1171890611yescharacteristic
287C4#1171890711yescharacteristic
288C2—21no—
289C2—21no—
290C2#1311477111yescharacteristic
291C2#1311478711yescharacteristic
292C2#1311479511yescharacteristic
subgroupG/H
centerC22#11718908
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#3502C2
socleC22×C13#379
prime radicalC23×C13C2×C22⋊C4
cosocleC2×C42×C13C23
hypercenter#3502D13
hypocenterC13#8356
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3502

Complements

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

NH ≅ G/Ntype
245. C13#8356semidirect

Maximal subgroups

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

subgroupindex
#131157732
#131148322
#131135262
#131132912
C13×#35022
#835613