Finite Group Databasebeta

← #16786933

Subgroups — #16786933

Order 3328.

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

normal subgroups only

This group has 368 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
1#13131072C212yesmaximal, complemented
2#13129785C212yesmaximal, complemented
3#13129769C212yesmaximal, complemented
4#13123542C211yesmaximal, characteristic
5#11719533C411yescharacteristic
6C2×#88202C2211yescharacteristic
7C22×#6094C411yescharacteristic
8C2×#88106—22no—
9C13×#408C411yescharacteristic
10#11718787C2211yescharacteristic
11#11718783C411yescharacteristic
12#11718763C2211yescharacteristic
13#11718391—22no—
14#11718390—22no—
15#11718284—22no—
16#11718284C2214yes—
17C2×C13×#41C2×C411yescharacteristic
18C22×C4×D13C2×C411yescharacteristic
19C2×C13×M16C2×C411yescharacteristic
20C22×C8×C13C2×C411yescharacteristic
21#88202—42no—
22#88200—21no—
23#88192—21no—
24#88191C812yes—
25#88189C812yes—
26C4×C22⋊D13—22no—
27#88180C2×C411yescharacteristic
28C2×#6099D412yes—
29C2×#6099C2311yescharacteristic
30C22×#1055C2×C411yescharacteristic
31C22×#1055D412yes—
32C2×#6094—21no—
33C2×#6094—21no—
34C2×#6094—42no—
35#88106—24no—
36#88106—42no—
37C2×#6092—42no—
38C13×C22⋊C8—22no—
39#88060—22no—
40#88055—21no—
41#88054—22no—
42C8×Dic13—21no—
43#11484—131nomaximal, Sylow
44C23×D13C2×C811yescharacteristic
45C13×#41—41no—
46C13×#41—41no—
47C2×Q8×C13M1611yescharacteristic
48C2×D4×C13C2×C812yes—
49C2×D4×C13M1611yescharacteristic
50C22×C4×C13C22⋊C412yes—
51C22×C4×C13C22×C411yescharacteristic
52C2×C22⋊D13—22no—
53C22×Dic13C2×C811yescharacteristic
54C2×C4×D13—21no—
55C2×C4×D13—21no—
56C2×C4×D13—41no—
57C2×C4×D13—41no—
58C13×M16—41no—
59C2×C8×C13—21no—
60C2×C8×C13—21no—
61C2×C8×C13—41no—
62C22⋊Dic13—22no—
63C22⋊Dic13C2×C812yes—
64#6103—22no—
65C4⋊Dic13—21no—
66#6101—22no—
67C4×Dic13—21no—
68#6099—42no—
69#6099—41no—
70C2×#1055—22no—
71C2×#1055—22no—
72C2×#1055—22no—
73C2×#1055C22⋊C411yescharacteristic
74C2×#1055C22⋊C411yescharacteristic
75C2×#1055C2×D412yes—
76#6094—42no—
77#6094—42no—
78#6092—44no—
79#2930—131no—
80#2115—132no—
81#1328—132no—
82#1320—132no—
83C23×C13C22⋊C812yes—
84C23×C13C22×C811yescharacteristic
85C22×D13—21no—
86C22×D13—41no—
87C22×D13—81no—
88Q8×C13—41no—
89D4×C13—42no—
90D4×C13—41no—
91C2×C4×C13—21no—
92C2×C4×C13—22no—
93C2×C4×C13—21no—
94C2×C4×C13—22no—
95C2×C4×C13C22⋊C812yes—
96C2×C4×C13C2×C22⋊C411yescharacteristic
97C2×C4×C13C2×M1611yescharacteristic
98C22⋊D13—82no—
99C2×Dic13—22no—
100C2×Dic13—21no—
101C2×Dic13—41no—
102C4×D13—42no—
103C4×D13—41no—
104C4×D13—41no—
105C8×C13—41no—
106C8×C13—41no—
107#1055—22no—
108#1055—21no—
109#1055#9912yes—
110C2×#131—131no—
111C22×M16—131no—
112#525—131no—
113C2×M32—262no—
114#436—262no—
115#435—262no—
116#424—131no—
117#408#26111yescharacteristic
118#407—131no—
119#405—131no—
120#349—134no—
121#349—262no—
122C22×C13—21no—
123C22×C13—22no—
124C22×C13—42no—
125C22×C13—41no—
126C22×C13C2×C22⋊C811yescharacteristic
127C2×D13—41no—
128C2×D13—41no—
129C2×D13—41no—
130C2×D13—82no—
131C4×C13—21no—
132C4×C13—22no—
133C4×C13C2×#9911yescharacteristic
134C4×C13#41311yescharacteristic
135Dic13—42no—
136Dic13—41no—
137C2×#41C2×#26111yescharacteristic
138C23×C4—131no—
139#131—522no—
140C2×M16—132no—
141C2×M16—131no—
142C2×M16—261no—
143C2×M16—261no—
144C2×M16—522no—
145C2×M16C2×#26111yescharacteristic
146C22×C8—132no—
147C22×C8—131no—
148C22×C8C2×#26111yescharacteristic
149#123—132no—
150C22⋊Q8—261no—
151#121—261no—
152#120—132no—
153C4×D4—262no—
154#117—131no—
155M32—264no—
156M32—522no—
157C2×C16—522no—
158C4⋊C8—262no—
159C22⋊C8—22no—
160C22⋊C8—262no—
161#97—261no—
162C4×C8—261no—
163C2×C13—21no—
164C2×C13—41no—
165C2×C13—42no—
166C2×C13#145911yescharacteristic
167D13—81no—
168C24—131no—
169#41—41no—
170#41—41no—
171C2×Q8#611811yescharacteristic
172C2×D4—262no—
173C2×D4D13⋊C812yes—
174C2×D4#611811yescharacteristic
175C22×C4—131no—
176C22×C4—261no—
177C22×C4—261no—
178C22×C4—521no—
179C22×C4—521no—
180C22×C4C22⋊#26112yes—
181C22×C4C22×#26111yescharacteristic
182M16—41no—
183M16—522no—
184M16—522no—
185M16—521no—
186M16—522no—
187C2×C8—21no—
188C2×C8—21no—
189C2×C8—41no—
190C2×C8—131no—
191C2×C8—131no—
192C2×C8—132no—
193C2×C8—262no—
194C2×C8—262no—
195C2×C8—262no—
196C4⋊C4—262no—
197C4⋊C4—261no—
198C22⋊C4—132no—
199C22⋊C4—262no—
200C22⋊C4—262no—
201C42—261no—
202C16—524no—
203C13#1148411yescharacteristic, complemented, Sylow
204C23—261no—
205C23—521no—
206C23—1041no—
207C23#8811112yes—
208C23C2×D13⋊C811yescharacteristic
209Q8—41no—
210D4—42no—
211D4—41no—
212D4—1042no—
213C2×C4—21no—
214C2×C4—22no—
215C2×C4—21no—
216C2×C4—22no—
217C2×C4—262no—
218C2×C4—261no—
219C2×C4—522no—
220C2×C4—521no—
221C2×C4—521no—
222C2×C4—521no—
223C2×C4#8811112yes—
224C2×C4C2×#611811yescharacteristic
225C2×C4C2×C22⋊#26111yescharacteristic
226C8—41no—
227C8—41no—
228C8—132no—
229C8—262no—
230C8—261no—
231C22—21no—
232C22—22no—
233C22—42no—
234C22—41no—
235C22—521no—
236C22—521no—
237C22—521no—
238C22—1042no—
239C22C2×#8811111yescharacteristic
240C4—21no—
241C4—22no—
242C4—522no—
243C4—521no—
244C4D13⋊#9911yescharacteristic
245C4#1171914811yescharacteristic
246C2—21no—
247C2—41no—
248C2—42no—
249C2—1041no—
250C2#1313007411yescharacteristic
subgroupG/H
centerC4D13⋊#99
commutatorC23×C13C22×C8
FrattiniC22×C4C22×#261
FittingC13×#408C4
socleC2×C13#1459
prime radical#11719533C4
cosocleC2×#6099C23
hypercenter#408#261
hypocenterC13#11484
LCSG ▷ C23×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41 ◁ #408

Complements

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

NH ≅ G/Ntype
1. #13131072C2semidirect
2. #13129785C2semidirect
3. #13129769C2semidirect
203. C13#11484semidirect

Maximal subgroups

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

subgroupindex
#131310722
#131297852
#131297692
#131235422
#1148413