Finite Group Databasebeta

← #16790033

Subgroups — #16790033

Order 3328.

432 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 86 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
1C2×#11718301C212yesmaximal
2#13130702C212yesmaximal
3#13129934C212yesmaximal
4#13117552C211yesmaximal, characteristic
5C2×C4×Q8×C13C411yescharacteristic
6C2×#88198C2211yescharacteristic
7C2×C4×Dic26C2211yescharacteristic
8C2×#88113C2214yes—
9#11719129—22no—
10#11718891C411yescharacteristic
11#11718639—22no—
12#11718638C411yescharacteristic
13#11718635C2211yescharacteristic
14#11718594—22no—
15#11718593C411yescharacteristic
16#11718301—24no—
17#11718291—22no—
18C22×Q8×C13C2×C411yescharacteristic
19C22×Dic26C2311yescharacteristic
20C2×#6122—24no—
21C4×Q8×C13—42no—
22C2×C13×C4⋊C4—21no—
23C2×C13×C4⋊C4C2×C411yescharacteristic
24C2×C42×C13—21no—
25C2×C42×C13C2×C411yescharacteristic
26#88198—22no—
27#88198D412yes—
28#88198Q812yes—
29C2×C4⋊Dic13C2×C411yescharacteristic
30C2×#6101—22no—
31C2×#6101D412yes—
32C2×C4×Dic13C2×C411yescharacteristic
33C2×C4×Dic13C2×C411yescharacteristic
34C2×C4×Dic13D412yes—
35C4×Dic26—42no—
36#88113—24no—
37#88113—24no—
38#88112—42no—
39C4⋊#1057—42no—
40#88071—21no—
41#88071—21no—
42#88071—22no—
43#88071—22no—
44#88071—22no—
45#12804—131nomaximal, Sylow
46C2×Q8×C13—21no—
47C2×Q8×C13—41no—
48C2×Q8×C13—41no—
49C2×Q8×C13C4⋊C412yes—
50C22×C4×C13—21no—
51C22×C4×C13—21no—
52C22×C4×C13C22⋊C411yescharacteristic
53C22×C4×C13C22⋊C411yescharacteristic
54C22×C4×C13C22×C411yescharacteristic
55C22×Dic13—21no—
56C22×Dic13—21no—
57C22×Dic13C22⋊C412yes—
58C22×Dic13C2×D412yes—
59C2×Dic26—41no—
60C2×Dic26—41no—
61C2×Dic26C2×D411yescharacteristic
62C2×Dic26C2×Q811yescharacteristic
63C2×Dic26#4112yes—
64#6122—44no—
65#6122—44no—
66C2×#1057—44no—
67C13×C4⋊C4—41no—
68C13×C4⋊C4—42no—
69C42×C13—22no—
70C42×C13—42no—
71C4⋊Dic13—41no—
72#6101—24no—
73#6101—24no—
74#6101—42no—
75C4×Dic13—22no—
76C4×Dic13—22no—
77C4×Dic13—21no—
78C4×Dic13—41no—
79C4×Dic13C4⋊C412yes—
80#2327—131no—
81C2×#356—132no—
82#1801—132no—
83#1394—132no—
84C23×C13C2×C22⋊C411yescharacteristic
85Q8×C13—42no—
86Q8×C13—42no—
87C2×C4×C13—21no—
88C2×C4×C13—21no—
89C2×C4×C13—22no—
90C2×C4×C13—21no—
91C2×C4×C13—41no—
92C2×C4×C13—41no—
93C2×C4×C13—41no—
94C2×C4×C13—41no—
95C2×C4×C13—42no—
96C2×C4×C13—41no—
97C2×C4×C13#9912yes—
98C2×C4×C13C2×C4⋊C411yescharacteristic
99C2×C4×C13#11711yescharacteristic
100C2×Dic13—22no—
101C2×Dic13—22no—
102C2×Dic13—22no—
103C2×Dic13—22no—
104C2×Dic13—41no—
105C2×Dic13—41no—
106C2×Dic13—42no—
107C2×Dic13—41no—
108C2×Dic13—41no—
109C2×Dic13—41no—
110C2×Dic13#12112yes—
111C2×Dic13C22⋊Q812yes—
112Dic26—41no—
113Dic26—41no—
114Dic26—42no—
115#1057—84no—
116C2×C4⋊Q8—131no—
117C2×C4×Q8—131no—
118C2×C4×Q8#26111yescharacteristic
119#423—262no—
120C2×#101—134no—
121#391—131no—
122#391—131no—
123#387—262no—
124#387—262no—
125#382—131no—
126#376—131no—
127#356—264no—
128#343—262no—
129C22×C13—21no—
130C22×C13—21no—
131C22×C13#38011yescharacteristic
132C22×C13C2×#9911yescharacteristic
133C22×C13#41011yescharacteristic
134C4×C13—21no—
135C4×C13—21no—
136C4×C13—22no—
137C4×C13—42no—
138C4×C13—41no—
139C4×C13—81no—
140Dic13—22no—
141Dic13—22no—
142Dic13—42no—
143Dic13—42no—
144Dic13—81no—
145C22×Q8—131no—
146C22×Q8C2×#26111yescharacteristic
147C2×M16—264no—
148C4⋊Q8—132no—
149C4⋊Q8—132no—
150C4⋊Q8—262no—
151C4×Q8—42no—
152C4×Q8—522no—
153C2×C4⋊C4—21no—
154C2×C4⋊C4—132no—
155C2×C4⋊C4—131no—
156C2×C4⋊C4—262no—
157C2×C4⋊C4C2×#26111yescharacteristic
158C2×C42—21no—
159C2×C42—131no—
160C2×C42—132no—
161C2×C42—131no—
162C2×C42C2×#26111yescharacteristic
163C4⋊C8—522no—
164C4⋊C8—522no—
165#101—264no—
166#101—264no—
167#95—262no—
168#95—262no—
169#95—262no—
170#95—261no—
171#95—261no—
172C2×C13—21no—
173C2×C13—21no—
174C2×C13#179911yescharacteristic
175C2×C13#213311yescharacteristic
176C2×C13#213511yescharacteristic
177C2×Q8—21no—
178C2×Q8—41no—
179C2×Q8—41no—
180C2×Q8—131no—
181C2×Q8—131no—
182C2×Q8—132no—
183C2×Q8—521no—
184C2×Q8—521no—
185C2×Q8C4⋊#26112yes—
186C22×C4—21no—
187C22×C4—21no—
188C22×C4—132no—
189C22×C4—132no—
190C22×C4—261no—
191C22×C4—261no—
192C22×C4C22⋊#26111yescharacteristic
193C22×C4C22⋊#26111yescharacteristic
194C22×C4C22×#26111yescharacteristic
195M16—524no—
196M16—524no—
197C2×C8—524no—
198C4⋊C4—41no—
199C4⋊C4—42no—
200C4⋊C4—264no—
201C4⋊C4—264no—
202C4⋊C4—522no—
203C4⋊C4—521no—
204C42—22no—
205C42—42no—
206C42—132no—
207C42—262no—
208C42—262no—
209C42—261no—
210C42—521no—
211C13#1280411yescharacteristic, complemented, Sylow
212C23C2×C22⋊#26111yescharacteristic
213Q8—42no—
214Q8—42no—
215Q8—521no—
216Q8—521no—
217Q8—522no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—22no—
221C2×C4—21no—
222C2×C4—41no—
223C2×C4—41no—
224C2×C4—41no—
225C2×C4—41no—
226C2×C4—42no—
227C2×C4—41no—
228C2×C4—132no—
229C2×C4—132no—
230C2×C4—262no—
231C2×C4—262no—
232C2×C4—262no—
233C2×C4—262no—
234C2×C4—521no—
235C2×C4—521no—
236C2×C4—522no—
237C2×C4—521no—
238C2×C4—521no—
239C2×C4—521no—
240C2×C4#8811912yes—
241C2×C4C2×C4⋊#26111yescharacteristic
242C2×C4#8823711yescharacteristic
243C8—1044no—
244C22—21no—
245C22—21no—
246C22#1171911611yescharacteristic
247C22#1171913611yescharacteristic
248C22C2×#8811911yescharacteristic
249C4—22no—
250C4—21no—
251C4—21no—
252C4—41no—
253C4—42no—
254C4—81no—
255C4—262no—
256C4—262no—
257C4—522no—
258C4—522no—
259C4—1041no—
260C2—21no—
261C2—21no—
262C2#1313069611yescharacteristic
263C2#1313113111yescharacteristic
264C2#1313113811yescharacteristic
subgroupG/H
centerC22C2×#88119
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC2×C4×Q8×C13C4
socleC22×C13C2×#99
prime radicalC23×C13C2×C22⋊C4
cosocleC22×Dic26C23
hypercenterC2×C4×Q8#261
hypocenterC13#12804
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
211. C13#12804semidirect

Maximal subgroups

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

subgroupindex
C2×#117183012
#131307022
#131299342
#131175522
#1280413