Finite Group Databasebeta

← #15778922

Subgroups — #15778922

Order 3328.

468 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 123 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×#11718140C212yesmaximal
2#13114832C212yesmaximal
3#13112963C212yesmaximal
4C4×C13×C4⋊Q8C211yesmaximal, characteristic
5C2×C13×C4⋊Q8C2211yescharacteristic
6C2×C4×Q8×C13C411yescharacteristic
7C2×C4×Q8×C13C2211yescharacteristic
8C13×#391C411yescharacteristic
9C13×#391C2211yescharacteristic
10C13×#389—22no—
11C13×#384C411yescharacteristic
12C4×C13×C4⋊C4—22no—
13C43×C13C411yescharacteristic
14C2×#88076C2214yes—
15#11718585—22no—
16#11718140—24no—
17#11718122—22no—
18C22×Q8×C13C2×C411yescharacteristic
19C22×Q8×C13C2311yescharacteristic
20C13×C4⋊Q8—22no—
21C13×C4⋊Q8D412yes—
22C13×C4⋊Q8Q812yes—
23C4×Q8×C13—41no—
24C4×Q8×C13—41no—
25C4×Q8×C13—41no—
26C4×Q8×C13—41no—
27C2×C13×C4⋊C4—22no—
28C2×C13×C4⋊C4—22no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4C2×C411yescharacteristic
31C2×C13×C4⋊C4C2×C411yescharacteristic
32C2×C13×C4⋊C4D412yes—
33C2×C42×C13—21no—
34C2×C42×C13—21no—
35C2×C42×C13—21no—
36C2×C42×C13C2×C411yescharacteristic
37C2×C42×C13C2×C411yescharacteristic
38C2×C42×C13C2×C411yescharacteristic
39C2×C42×C13D412yes—
40C2×#6099—24no—
41C13×#95—22no—
42C13×#95—22no—
43#88076—24no—
44#88076—24no—
45C4⋊#1055—42no—
46C4⋊#1055—42no—
47#12802—131nomaximal, Sylow
48C2×Q8×C13—21no—
49C2×Q8×C13—41no—
50C2×Q8×C13—41no—
51C2×Q8×C13—41no—
52C2×Q8×C13—41no—
53C2×Q8×C13C4⋊C412yes—
54C2×Q8×C13C2×D411yescharacteristic
55C2×Q8×C13C2×Q811yescharacteristic
56C2×Q8×C13#4112yes—
57C22×C4×C13—21no—
58C22×C4×C13—21no—
59C22×C4×C13—21no—
60C22×C4×C13—21no—
61C22×C4×C13C22⋊C412yes—
62C22×C4×C13C22⋊C411yescharacteristic
63C22×C4×C13C22⋊C411yescharacteristic
64C22×C4×C13C22×C411yescharacteristic
65C22×C4×C13C2×D412yes—
66C13×C4⋊C4—24no—
67C13×C4⋊C4—24no—
68C13×C4⋊C4—41no—
69C13×C4⋊C4—42no—
70C13×C4⋊C4—41no—
71C13×C4⋊C4—44no—
72C13×C4⋊C4—42no—
73C42×C13—24no—
74C42×C13—21no—
75C42×C13—21no—
76C42×C13—22no—
77C42×C13—22no—
78C42×C13—21no—
79C42×C13—41no—
80C42×C13—42no—
81C42×C13—41no—
82C42×C13—41no—
83C42×C13C4⋊C412yes—
84#6099—44no—
85#6099—44no—
86C2×#1055—44no—
87C4×C4⋊Q8D1311yescharacteristic
88C2×#356—132no—
89#1801—132no—
90#1394—132no—
91C23×C13C2×C22⋊C411yescharacteristic
92Q8×C13—41no—
93Q8×C13—41no—
94Q8×C13—42no—
95Q8×C13—42no—
96Q8×C13—42no—
97C2×C4×C13—22no—
98C2×C4×C13—22no—
99C2×C4×C13—22no—
100C2×C4×C13—22no—
101C2×C4×C13—21no—
102C2×C4×C13—22no—
103C2×C4×C13—21no—
104C2×C4×C13—22no—
105C2×C4×C13—22no—
106C2×C4×C13—22no—
107C2×C4×C13—21no—
108C2×C4×C13—22no—
109C2×C4×C13—41no—
110C2×C4×C13—41no—
111C2×C4×C13—41no—
112C2×C4×C13—41no—
113C2×C4×C13—41no—
114C2×C4×C13—42no—
115C2×C4×C13—42no—
116C2×C4×C13—41no—
117C2×C4×C13#9911yescharacteristic
118C2×C4×C13#9911yescharacteristic
119C2×C4×C13C2×C4⋊C411yescharacteristic
120C2×C4×C13#11711yescharacteristic
121C2×C4×C13#12112yes—
122C2×C4×C13C22⋊Q812yes—
123#1055—84no—
124C2×C4⋊Q8C2×D1311yescharacteristic
125C2×C4×Q8Dic1311yescharacteristic
126C2×C4×Q8C2×D1311yescharacteristic
127#423—262no—
128C2×#101—134no—
129#391Dic1311yescharacteristic
130#391C2×D1311yescharacteristic
131#389—22no—
132#384Dic1311yescharacteristic
133C4×C4⋊C4—22no—
134C43Dic1311yescharacteristic
135#356—264no—
136#343—262no—
137C22×C13—21no—
138C22×C13—21no—
139C22×C13#38011yescharacteristic
140C22×C13C2×#9911yescharacteristic
141C22×C13#41011yescharacteristic
142C4×C13—24no—
143C4×C13—22no—
144C4×C13—21no—
145C4×C13—21no—
146C4×C13—22no—
147C4×C13—21no—
148C4×C13—42no—
149C4×C13—42no—
150C4×C13—41no—
151C4×C13—42no—
152C4×C13—81no—
153C4×C13#35612yescomplemented
154C22×Q8C2×Dic1311yescharacteristic
155C22×Q8C22×D1311yescharacteristic
156C2×M16—264no—
157C4⋊Q8—22no—
158C4⋊Q8Dic2612yes—
159C4⋊Q8D5212yes—
160C4×Q8—41no—
161C4×Q8—41no—
162C4×Q8—41no—
163C4×Q8—41no—
164C2×C4⋊C4—22no—
165C2×C4⋊C4—21no—
166C2×C4⋊C4—22no—
167C2×C4⋊C4C2×Dic1311yescharacteristic
168C2×C4⋊C4C2×Dic1311yescharacteristic
169C2×C4⋊C4C22⋊D1312yes—
170C2×C42—21no—
171C2×C42—21no—
172C2×C42—21no—
173C2×C42C2×Dic1311yescharacteristic
174C2×C42C2×Dic1311yescharacteristic
175C2×C42C2×Dic1311yescharacteristic
176C2×C42C22⋊D1312yes—
177C4⋊C8—522no—
178C4⋊C8—522no—
179#101—264no—
180#101—264no—
181#95—22no—
182#95—22no—
183C2×C13—21no—
184C2×C13—21no—
185C2×C13#179911yescharacteristic
186C2×C13C2×#35611yescharacteristic
187C2×C13#213211yescharacteristic
188C2×Q8—21no—
189C2×Q8—41no—
190C2×Q8—41no—
191C2×Q8—41no—
192C2×Q8—41no—
193C2×Q8C4⋊Dic1312yes—
194C2×Q8C2×Dic2611yescharacteristic
195C2×Q8C2×D5211yescharacteristic
196C2×Q8#612712yes—
197C22×C4—21no—
198C22×C4—21no—
199C22×C4—21no—
200C22×C4—21no—
201C22×C4C22⋊Dic1312yes—
202C22×C4C22⋊Dic1311yescharacteristic
203C22×C4C22⋊Dic1311yescharacteristic
204C22×C4C22×Dic1311yescharacteristic
205C22×C4C2×C22⋊D1312yes—
206M16—524no—
207M16—524no—
208C2×C8—524no—
209C4⋊C4—24no—
210C4⋊C4—24no—
211C4⋊C4—41no—
212C4⋊C4—42no—
213C4⋊C4—41no—
214C4⋊C4—42no—
215C4⋊C4—44no—
216C42—24no—
217C42—22no—
218C42—22no—
219C42—21no—
220C42—21no—
221C42—21no—
222C42—41no—
223C42—42no—
224C42—41no—
225C42—41no—
226C42C4⋊Dic1312yes—
227C13#1280211yescharacteristic, complemented, Sylow
228C23C2×C22⋊Dic1311yescharacteristic
229Q8—41no—
230Q8—41no—
231Q8—42no—
232Q8—42no—
233Q8—42no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—21no—
238C2×C4—22no—
239C2×C4—21no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—22no—
244C2×C4—21no—
245C2×C4—22no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—42no—
252C2×C4—42no—
253C2×C4—41no—
254C2×C4#8807411yescharacteristic
255C2×C4#8807411yescharacteristic
256C2×C4#8817812yes—
257C2×C4C2×C4⋊Dic1311yescharacteristic
258C2×C4#8818011yescharacteristic
259C2×C4#8818412yes—
260C8—1044no—
261C22—21no—
262C22—21no—
263C22#1171887311yescharacteristic
264C22C2×#8807411yescharacteristic
265C22#1171890111yescharacteristic
266C4—24no—
267C4—21no—
268C4—22no—
269C4—22no—
270C4—21no—
271C4—21no—
272C4—42no—
273C4—41no—
274C4—42no—
275C4—42no—
276C4—81no—
277C4#1171814012yescomplemented
278C2—21no—
279C2—21no—
280C2#1311482411yescharacteristic
281C2C2×#1171814011yescharacteristic
282C2#1311652111yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC22×Q8C22×D13
FittingC4×C13×C4⋊Q8C2
socleC22×C13C2×#99
prime radicalC23×C13C2×C22⋊C4
cosocleC22×Q8×C13C23
hypercenterC4×C4⋊Q8D13
hypocenterC13#12802
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ C4×C4⋊Q8

Complements

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

NH ≅ G/Ntype
153. C4×C13#356semidirect
227. C13#12802semidirect
277. C4#11718140semidirect

Maximal subgroups

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

subgroupindex
C2×#117181402
#131148322
#131129632
C4×C13×C4⋊Q82
#1280213