Finite Group Databasebeta

← #16789394

Subgroups — #16789394

Order 3328.

382 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 110 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×#11719096C211yesmaximal, characteristic
2#13131056C212yesmaximal, complemented
3#13130592C211yesmaximal, characteristic
4#13129892C212yesmaximal, complemented
5#13116455C211yesmaximal, characteristic
6C2×#88161C2211yescharacteristic
7#11719132C411yescharacteristic
8#11719116C411yescharacteristic
9C2×#88106C411yescharacteristic, complemented
10C22×#6092C411yescharacteristic, complemented
11#11719096—22no—
12#11719096—22no—
13#11719089C2212yes—
14C2×#88098C411yescharacteristic, complemented
15C2×#88098C2211yescharacteristic
16C2×D13⋊C16C411yescharacteristic, complemented
17C2×D13⋊C16C2211yescharacteristic
18D13×M32C2212yes—
19#11718266C412yes—
20#11718218—22no—
21#11718217—22no—
22C13×#349C411yescharacteristic, complemented
23#11718145C411yescharacteristic, complemented
24#11718106C412yescomplemented
25C2×#6127C2×C411yescharacteristic
26#88237C2×C412yes—
27D13⋊M16C2×C412yes—
28C2×C13×M16C2×C411yescharacteristic
29C22×#1055C2×C411yescharacteristic
30#88161—22no—
31#88161—22no—
32C2×#6094C2×C411yescharacteristic
33C2×#6094C2×C411yescharacteristic
34C2×C8×D13C2×C411yescharacteristic
35C2×C8×D13C2311yescharacteristic
36#88121—21no—
37#88119—21no—
38#88113—21no—
39#88107—21no—
40#88106—22no—
41C2×#6092—21no—
42C2×#6092—21no—
43C2×#6092C2×C411yescharacteristic
44C2×#6092C2×C411yescharacteristic
45C2×#6092C2×C411yescharacteristic
46C2×#6092C2×C411yescharacteristic
47#88100—22no—
48C8×#261—22no—
49#88098—21no—
50#88098—21no—
51#88098D412yes—
52#88098D412yes—
53D13⋊C16—22no—
54D13⋊C16—22no—
55C13×M32C2×C412yes—
56#88052C2×C412yes—
57#88038—22no—
58C16×D13—22no—
59#12617—131nomaximal, Sylow
60C22×C4×C13C4211yescharacteristic
61C2×C22⋊D13M1611yescharacteristic
62C2×C22⋊D13M1611yescharacteristic
63#6127—22no—
64#6127—22no—
65C2×D52M1611yescharacteristic
66C2×C4×D13C4211yescharacteristic
67C2×C4×D13C22×C411yescharacteristic
68C2×Dic26M1611yescharacteristic
69C22⋊#261—22no—
70#6122—22no—
71C4⋊#261—22no—
72C4×#261—22no—
73#6118—22no—
74D13⋊C8—22no—
75C13×M16—22no—
76C2×C8×C13C4211yescharacteristic
77C2×C8×C13C22×C411yescharacteristic
78C2×#1055—21no—
79C2×#1055—21no—
80C2×#1055C4211yescharacteristic
81C2×#1055C22×C411yescharacteristic
82#6094—22no—
83#6094—22no—
84C8×D13—21no—
85C8×D13—21no—
86C8×D13C2×D412yes—
87C8×D13#4112yes—
88#6092—21no—
89#6092—21no—
90#6092C22⋊C412yes—
91#6092C22⋊C411yescharacteristic
92#6092C22⋊C411yescharacteristic
93C13×C16—22no—
94#6090—22no—
95C2×#504—131no—
96#2115—131no—
97#2110—132no—
98#1757—131no—
99#1379—132no—
100C23×C13#9711yescharacteristic
101C22×D13#9711yescharacteristic
102C22×D13C2×M1611yescharacteristic
103C2×#261—42no—
104C2×C4×C13—21no—
105C2×C4×C13—21no—
106C2×C4×C13#9711yescharacteristic
107C2×C4×C13C2×C4211yescharacteristic
108C22⋊D13—22no—
109C22⋊D13—22no—
110C2×Dic13#9711yescharacteristic
111C2×Dic13C2×M1611yescharacteristic
112D52—22no—
113C4×D13—21no—
114C4×D13—21no—
115C4×D13C4×D412yes—
116C4×D13#13112yes—
117Dic26—22no—
118#1057—42no—
119C8×C13—21no—
120C8×C13C4×D412yes—
121#1055—21no—
122#1055C2×C22⋊C411yescharacteristic
123#1055#11711yescharacteristic
124C2×#131—131no—
125#504—262no—
126#504—262no—
127C2×M32—131no—
128C2×M32—131no—
129C2×M32—131no—
130C2×M32—132no—
131C22×C16—131no—
132C22×C16—131no—
133C22×C16—131no—
134#413—131no—
135#410—131no—
136#405—132no—
137#349—131no—
138#349—132no—
139#349#26111yescharacteristic, complemented
140#347—262no—
141#347—262no—
142#344—132no—
143C22×C13—21no—
144C22×C13—41no—
145C22×C13C2×#9711yescharacteristic
146C2×D13—21no—
147C2×D13—41no—
148C2×D13—41no—
149C2×D13#43512yes—
150#261—82no—
151C4×C13—21no—
152C4×C13C4×C22⋊C411yescharacteristic
153C4×C13#40511yescharacteristic
154Dic13—21no—
155Dic13#43512yes—
156C2×#41—131no—
157#131—262no—
158#131—262no—
159C2×M16—131no—
160C2×M16—131no—
161C2×M16—132no—
162C2×M16C2×#26111yescharacteristic
163C22×C8—131no—
164C22×C8—131no—
165C22×C8—131no—
166#117—132no—
167M32—132no—
168M32—132no—
169M32—132no—
170M32—262no—
171M32—261no—
172M32—261no—
173M32—262no—
174M32C2×#26112yes—
175C2×C16—131no—
176C2×C16—131no—
177C2×C16—131no—
178C2×C16—131no—
179C2×C16—262no—
180C2×C16—262no—
181C2×C16—261no—
182C2×C16—261no—
183C2×C16—262no—
184#101—261no—
185#100—261no—
186#99—261no—
187#99—261no—
188#97—262no—
189C4×C8—262no—
190C2×C13—21no—
191C2×C13—41no—
192C2×C13#175211yescharacteristic
193D13—22no—
194D13—41no—
195#41—262no—
196#41—262no—
197C2×Q8—131no—
198C2×D4—131no—
199C2×D4—131no—
200C2×D4—131no—
201C22×C4—131no—
202C22×C4—131no—
203C22×C4C4×#26111yescharacteristic
204M16—22no—
205M16—262no—
206M16—262no—
207M16—262no—
208M16—262no—
209C2×C8—131no—
210C2×C8—132no—
211C2×C8—132no—
212C2×C8—131no—
213C2×C8—261no—
214C2×C8—261no—
215C2×C8—261no—
216C2×C8—261no—
217C2×C8—262no—
218C2×C8C4×#26111yescharacteristic
219C2×C8C22×#26111yescharacteristic
220C4⋊C4—262no—
221C22⋊C4—262no—
222C42—262no—
223C16—22no—
224C16—132no—
225C16—131no—
226C16—131no—
227C16—261no—
228C16—261no—
229C16—262no—
230C13#1261711yescharacteristic, complemented, Sylow
231C23—131no—
232C23—131no—
233C23#8810011yescharacteristic
234Q8—262no—
235D4—262no—
236D4—262no—
237D4—262no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—131no—
241C2×C4—132no—
242C2×C4—132no—
243C2×C4—131no—
244C2×C4—261no—
245C2×C4—261no—
246C2×C4—522no—
247C2×C4#8810011yescharacteristic
248C2×C4C2×C4×#26111yescharacteristic
249C8—21no—
250C8—131no—
251C8—131no—
252C8—261no—
253C8—522no—
254C8D4×#26112yes—
255C22—21no—
256C22—41no—
257C22—132no—
258C22—261no—
259C22—521no—
260C22—521no—
261C22C2×#8810011yescharacteristic
262C4—21no—
263C4—132no—
264C4—261no—
265C4—1042no—
266C4C22⋊C4×#26111yescharacteristic
267C4#1171909911yescharacteristic
268C2—21no—
269C2—41no—
270C2—262no—
271C2—521no—
272C2#1313057511yescharacteristic
subgroupG/H
centerC4C22⋊C4×#261
commutatorC2×C4×C13C2×C42
FrattiniC2×C8C22×#261
FittingC13×#349C4
socleC2×C13#1752
prime radicalC2×#6127C2×C4
cosocleC2×C8×D13C23
hypercenter#349#261
hypocenterC13#12617
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C2×C8 ◁ #349

Complements

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

NH ≅ G/Ntype
2. #13131056C2semidirect
4. #13129892C2semidirect
9. C2×#88106C4semidirect
10. C22×#6092C4semidirect
14. C2×#88098C4semidirect
16. C2×D13⋊C16C4semidirect
22. C13×#349C4semidirect
23. #11718145C4semidirect
24. #11718106C4semidirect
139. #349#261semidirect
230. C13#12617semidirect

Maximal subgroups

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

subgroupindex
C2×#117190962
#131310562
#131305922
#131298922
#131164552
#1261713