Finite Group Databasebeta

← #15758917

Subgroups — #15758917

Order 3328.

436 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 103 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#13120712C211yesmaximal, characteristic
2C4×#88076C211yesmaximal, characteristic
3#13113439C212yesmaximal
4#13112702C212yesmaximal
5C13×#2983C211yesmaximal, characteristic
6C2×C4×Q8×C13C2211yescharacteristic
7C2×#88124C2211yescharacteristic
8C13×#446—24no—
9C13×#432—21no—
10C13×#432C2212yes—
11C13×#431—21no—
12#11718890—21no—
13C2×#88076—21no—
14#11718647C411yescharacteristic
15#11718647C411yescharacteristic
16#11718644C411yescharacteristic
17#11718644C411yescharacteristic
18#11718643—21no—
19#11718598C2211yescharacteristic
20#11718594—21no—
21#11718594—21no—
22C4×#6099C2212yes—
23#11718122—21no—
24#11718057—24no—
25C22×Q8×C13D411yescharacteristic
26C4×Q8×C13—22no—
27C4×Q8×C13—22no—
28C2×C13×C4⋊C4C2×C411yescharacteristic
29C2×C13×C4⋊C4C2×C411yescharacteristic
30C2×C13×C4⋊C4D411yescharacteristic
31C2×C42×C13D411yescharacteristic
32C2×C42×C13D411yescharacteristic
33C2×C42×C13C2311yescharacteristic
34C2×C4⋊Dic13C2×C411yescharacteristic
35C2×C4⋊Dic13C2×C411yescharacteristic
36C2×#6101—21no—
37C2×#6101—21no—
38C2×#6101—21no—
39C2×#6101—21no—
40C2×#6099—22no—
41#88124—22no—
42#88124—22no—
43C13×C4⋊C8—22no—
44C13×C4⋊C8—22no—
45C13×C4⋊C8—22no—
46C13×C22⋊C8—22no—
47C13×#97—22no—
48C13×#97D414yes—
49C4×C8×C13—22no—
50#88076—24no—
51#88071—21no—
52#88071—21no—
53#88071—21no—
54#88071—21no—
55#88071—21no—
56#88071—21no—
57#88071—21no—
58#88071—21no—
59#88071C2×C411yescharacteristic
60#88071C2×C411yescharacteristic
61#88043—22no—
62C4×#1055—22no—
63#9190—131nomaximal, Sylow
64C2×Q8×C13—22no—
65C2×Q8×C13—22no—
66C2×Q8×C13—41no—
67C22×C4×C13C22⋊C411yescharacteristic
68C22×C4×C13C22⋊C411yescharacteristic
69C22×C4×C13C22⋊C411yescharacteristic
70C22×C4×C13C22⋊C411yescharacteristic
71C22×C4×C13C22×C411yescharacteristic
72C22×C4×C13C2×D411yescharacteristic
73C22×C4×C13C2×D411yescharacteristic
74C22×Dic13—21no—
75C22×Dic13—21no—
76C22×Dic13—21no—
77C22×Dic13—21no—
78C2×C8×C13—24no—
79C13×C4⋊C4—22no—
80C13×C4⋊C4—22no—
81C13×C4⋊C4—22no—
82C42×C13—21no—
83C42×C13—21no—
84C42×C13—21no—
85C42×C13—21no—
86C42×C13C2×D412yes—
87C42×C13#4112yes—
88C4⋊Dic13—22no—
89C4⋊Dic13—22no—
90#6101—42no—
91#6101—42no—
92#6101—41no—
93#6101—42no—
94#6101—41no—
95#6099—24no—
96#6099—42no—
97C2×#1055—42no—
98#2983D1311yescharacteristic
99#2634—131no—
100C4×#101—131no—
101#1528—132no—
102#1288—132no—
103C23×C13C2×C22⋊C411yescharacteristic
104Q8×C13—44no—
105C2×C4×C13—21no—
106C2×C4×C13—21no—
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×C13—21no—
114C2×C4×C13—41no—
115C2×C4×C13—41no—
116C2×C4×C13—41no—
117C2×C4×C13—41no—
118C2×C4×C13#10412yes—
119C2×C4×C13C4×D412yes—
120C2×C4×C13#12011yescharacteristic
121C2×C4×C13#12112yes—
122C2×C4×C13#12311yescharacteristic
123C2×Dic13—41no—
124C2×Dic13—41no—
125C2×Dic13—41no—
126C2×Dic13—41no—
127C2×Dic13—42no—
128C2×Dic13—41no—
129C2×Dic13—41no—
130C2×Dic13—41no—
131C2×Dic13—41no—
132C2×Dic13—41no—
133C2×Dic13—41no—
134C8×C13—44no—
135#1055—44no—
136C2×#125—131no—
137C2×C4×Q8C2×D1311yescharacteristic
138#446—24no—
139#432—21no—
140#432C2×D1312yes—
141#431—21no—
142C2×#101—261no—
143C4×M16—132no—
144#400—131no—
145#400—131no—
146#400—261no—
147#398—131no—
148#398—131no—
149#395—261no—
150#387—261no—
151#387—261no—
152#383—131no—
153#343—261no—
154#330—264no—
155C22×C13—21no—
156C22×C13—21no—
157C22×C13#38611yescharacteristic
158C22×C13C2×#10411yescharacteristic
159C22×C13#42111yescharacteristic
160C4×C13—22no—
161C4×C13—22no—
162C4×C13—21no—
163C4×C13—21no—
164C4×C13—22no—
165C4×C13—41no—
166C4×C13—41no—
167C4×C13—41no—
168Dic13—81no—
169Dic13—81no—
170Dic13—81no—
171Dic13—81no—
172C22×Q8D5211yescharacteristic
173C2×M16—262no—
174#125—262no—
175#125—262no—
176C4×Q8—22no—
177C4×Q8—22no—
178C2×C4⋊C4—131no—
179C2×C4⋊C4—131no—
180C2×C4⋊C4—261no—
181C2×C4⋊C4—261no—
182C2×C4⋊C4—261no—
183C2×C4⋊C4—261no—
184C2×C4⋊C4C4×D1311yescharacteristic
185C2×C4⋊C4C4×D1311yescharacteristic
186C2×C4⋊C4D5211yescharacteristic
187C2×C42C22⋊D1311yescharacteristic
188C2×C42C22⋊D1311yescharacteristic
189C2×C42C22×D1311yescharacteristic
190C4⋊C8—22no—
191C4⋊C8—22no—
192C4⋊C8—22no—
193#101—264no—
194C22⋊C8—22no—
195#97—22no—
196#97—262no—
197#97C22⋊D1314yes—
198C4×C8—22no—
199C4×C8—262no—
200#95—131no—
201#95—131no—
202#95—261no—
203#95—261no—
204#95—261no—
205#95—261no—
206#95—261no—
207#95—261no—
208#95—261no—
209#95—261no—
210C2×C13—21no—
211C2×C13—21no—
212C2×C13#187111yescharacteristic
213C2×C13#191211yescharacteristic
214C2×C13#191511yescharacteristic
215C2×Q8—22no—
216C2×Q8—22no—
217C2×Q8—41no—
218C22×C4—261no—
219C22×C4—261no—
220C22×C4—261no—
221C22×C4—261no—
222C22×C4#610311yescharacteristic
223C22×C4#610311yescharacteristic
224C22×C4#610311yescharacteristic
225C22×C4#610311yescharacteristic
226C22×C4C2×C4×D1311yescharacteristic
227C22×C4C2×D5211yescharacteristic
228C22×C4C2×C22⋊D1311yescharacteristic
229M16—264no—
230M16—522no—
231C2×C8—24no—
232C2×C8—522no—
233C4⋊C4—22no—
234C4⋊C4—22no—
235C4⋊C4—22no—
236C4⋊C4—262no—
237C4⋊C4—262no—
238C4⋊C4—522no—
239C4⋊C4—522no—
240C4⋊C4—521no—
241C4⋊C4—522no—
242C4⋊C4—521no—
243C42—21no—
244C42—21no—
245C42—21no—
246C42—21no—
247C42#612712yes—
248C42C2×C22⋊D1312yes—
249C13#919011yescharacteristic, complemented, Sylow
250C23C2×#610311yescharacteristic
251Q8—44no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—521no—
266C2×C4—521no—
267C2×C4—521no—
268C2×C4—521no—
269C2×C4—522no—
270C2×C4—521no—
271C2×C4—521no—
272C2×C4—521no—
273C2×C4—521no—
274C2×C4—521no—
275C2×C4—521no—
276C2×C4#8806512yes—
277C2×C4C4×C22⋊D1312yes—
278C2×C4#8818311yescharacteristic
279C2×C4#8818412yes—
280C2×C4#8820711yescharacteristic
281C8—44no—
282C8—524no—
283C22—21no—
284C22—21no—
285C22C2×#8806511yescharacteristic
286C22#1171880011yescharacteristic
287C22#1171887411yescharacteristic
288C4—22no—
289C4—22no—
290C4—21no—
291C4—21no—
292C4—22no—
293C4—41no—
294C4—41no—
295C4—41no—
296C4—1041no—
297C4—1041no—
298C4—1041no—
299C4—1041no—
300C2—21no—
301C2—21no—
302C2#1311513811yescharacteristic
303C2#1311537311yescharacteristic
304C2#1311538811yescharacteristic
subgroupG/H
centerC22#11718874
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#2983C2
socleC22×C13#386
prime radicalC23×C13C2×C22⋊C4
cosocleC2×C42×C13C23
hypercenter#2983D13
hypocenterC13#9190
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2983

Complements

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

NH ≅ G/Ntype
249. C13#9190semidirect

Maximal subgroups

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

subgroupindex
#131207122
C4×#880762
#131134392
#131127022
C13×#29832
#919013