Finite Group Databasebeta

← #16788558

Subgroups — #16788558

Order 3328.

394 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 92 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#13131195C211yesmaximal, characteristic
2#13130395C211yesmaximal, characteristic
3#13129851C214yesmaximal, complemented
4D13×#494C211yesmaximal, characteristic
5C2×Q16×D13—21no—
6C2×Q16×D13C412yes—
7D13×C4⋊Q8—21no—
8#11719052—21no—
9C13×#494C411yescharacteristic
10#11718842—21no—
11#11718842C2212yes—
12#11718753—21no—
13#11718360C411yescharacteristic
14C4×C8×D13C2211yescharacteristic
15#11718260C2212yes—
16#11718259—21no—
17#11718256—21no—
18#11718256C2212yes—
19C4×#6092—21no—
20C2×Q8×D13—22no—
21C2×#6118—41no—
22C2×C13×Q16—21no—
23C2×C13×Q16C2×C412yes—
24C13×C4⋊Q8—21no—
25#88198—22no—
26C2×#6107—22no—
27C2×#6107—22no—
28Q16×D13—44no—
29Q16×D13—44no—
30C2×Dic52—21no—
31C2×Dic52C2×C412yes—
32C2×C8×D13C2×C411yescharacteristic
33C2×C8×D13D411yescharacteristic
34C4⋊C4×D13—41no—
35C4⋊C4×D13—41no—
36#88142—41no—
37#88142—41no—
38C42×D13D411yescharacteristic
39#88123—21no—
40C4⋊#1057—22no—
41C4⋊#1057—41no—
42C2×#6092—22no—
43C4×C8×C13C2×C411yescharacteristic
44C8×Dic13D411yescharacteristic
45C8×Dic13C2311yescharacteristic
46C4×#1055D411yescharacteristic
47#11962—131nomaximal, Sylow
48C2×Q8×C13—22no—
49Q8×D13—44no—
50Q8×D13—44no—
51C2×C4×D13—42no—
52C2×C4×D13C22⋊C411yescharacteristic
53C2×C4×D13D811yescharacteristic
54C2×C4×D13SD1611yescharacteristic
55C2×Dic26—22no—
56C2×Dic26—42no—
57C2×#1057—42no—
58#6118—82no—
59C13×Q16—42no—
60C13×Q16—42no—
61C2×C8×C13C22⋊C411yescharacteristic
62C2×C8×C13C22×C411yescharacteristic
63C13×C4⋊C4—41no—
64C13×C4⋊C4—41no—
65C42×C13C22⋊C411yescharacteristic
66#6107—44no—
67#6107—44no—
68C4⋊Dic13—41no—
69C4⋊Dic13—41no—
70#6101—42no—
71#6101—42no—
72C4×Dic13D811yescharacteristic
73C4×Dic13SD1611yescharacteristic
74C4×Dic13C2×D411yescharacteristic
75C2×#1055C22⋊C411yescharacteristic
76C2×#1055C2×D411yescharacteristic
77Dic52—42no—
78Dic52—42no—
79C8×D13—22no—
80C8×D13—22no—
81#6092—42no—
82C2×#494—131no—
83#2162—131no—
84#1567—131no—
85#1362—134no—
86C22×D13#10211yescharacteristic
87Q8×C13—42no—
88Q8×C13—42no—
89C2×C4×C13—42no—
90C2×C4×C13#10211yescharacteristic
91C2×C4×C13#10211yescharacteristic
92C2×C4×C13C2×C22⋊C411yescharacteristic
93C2×Dic13—42no—
94C2×Dic13#10211yescharacteristic
95C2×Dic13C2×D811yescharacteristic
96C2×Dic13C2×SD1611yescharacteristic
97C4×D13—22no—
98C4×D13—21no—
99C4×D13—21no—
100C4×D13—84no—
101C4×D13SD3212yes—
102C4×D13Q3212yes—
103Dic26—42no—
104Dic26—42no—
105Dic26—84no—
106#1057—82no—
107C8×C13—21no—
108C8×C13—21no—
109#1055#10012yes—
110#1055AGL(1,ℤ/8)12yes—
111C22×Q16—132no—
112C22×Q16—261no—
113C2×C4⋊Q8—261no—
114#494—132no—
115#494—131no—
116#494—261no—
117#494—261no—
118#494#26111yescharacteristic
119#423—261no—
120C2×C4×C8—131no—
121C4⋊C16—132no—
122C22⋊C16—261no—
123C4×C16—261no—
124#335—132no—
125#335—261no—
126C22×C13C2×#10211yescharacteristic
127C2×D13—21no—
128C2×D13—21no—
129C2×D13#35812yes—
130C4×C13—82no—
131C4×C13#35812yes—
132C4×C13#36212yes—
133C4×C13C2×#10011yescharacteristic
134C4×C13#41811yescharacteristic
135Dic13—21no—
136Dic13—21no—
137Dic13—82no—
138Dic13C2×SD3211yescharacteristic
139Dic13C2×Q3211yescharacteristic
140C22×Q8—262no—
141C2×Q16—21no—
142C2×Q16—132no—
143C2×Q16—262no—
144C2×Q16—262no—
145C2×Q16—261no—
146C2×Q16—524no—
147C2×Q16—524no—
148C2×Q16C2×#26112yes—
149C2×M16—521no—
150C22×C8—131no—
151C22×C8—131no—
152C4⋊Q8—21no—
153C4⋊Q8—262no—
154C4⋊Q8—261no—
155C4⋊Q8—521no—
156C4⋊Q8—521no—
157C2×C4⋊C4—521no—
158C2×C4⋊C4—521no—
159C2×C42—131no—
160C2×C16—262no—
161C4⋊C8—262no—
162C4⋊C8—521no—
163C4×C8—131no—
164C4×C8—131no—
165C4×C8—131no—
166C4×C8C2×#26111yescharacteristic
167C2×C13#154511yescharacteristic
168C2×C13C2×#35811yescharacteristic
169C2×C13C2×#36211yescharacteristic
170D13—22no—
171C2×Q8—22no—
172C2×Q8—262no—
173C2×Q8—522no—
174C2×Q8—524no—
175C2×Q8—524no—
176C22×C4—131no—
177C22×C4—131no—
178C22×C4—131no—
179C22×C4—522no—
180Q16—42no—
181Q16—42no—
182Q16—522no—
183Q16—522no—
184Q16—524no—
185Q16—524no—
186M16—1042no—
187C2×C8—131no—
188C2×C8—131no—
189C2×C8—262no—
190C2×C8—262no—
191C2×C8—522no—
192C2×C8C22⋊#26111yescharacteristic
193C2×C8C22×#26111yescharacteristic
194C4⋊C4—41no—
195C4⋊C4—41no—
196C4⋊C4—522no—
197C4⋊C4—522no—
198C4⋊C4—521no—
199C4⋊C4—521no—
200C42—131no—
201C42—131no—
202C42—131no—
203C42C22⋊#26111yescharacteristic
204C16—522no—
205C13#1196211yescharacteristic, complemented, Sylow
206C23—131no—
207Q8—42no—
208Q8—42no—
209Q8—522no—
210Q8—522no—
211Q8—1044no—
212C2×C4—42no—
213C2×C4—131no—
214C2×C4—132no—
215C2×C4—132no—
216C2×C4—131no—
217C2×C4—131no—
218C2×C4—262no—
219C2×C4—261no—
220C2×C4—261no—
221C2×C4—522no—
222C2×C4—1044no—
223C2×C4#8811511yescharacteristic
224C2×C4#8811511yescharacteristic
225C2×C4C2×C22⋊#26111yescharacteristic
226C8—21no—
227C8—21no—
228C8—132no—
229C8—132no—
230C8—1042no—
231C22—132no—
232C22—261no—
233C22—261no—
234C22C2×#8811511yescharacteristic
235C4—82no—
236C4—131no—
237C4—131no—
238C4—261no—
239C4—261no—
240C4—1042no—
241C4#1171828012yes—
242C4#1171828212yes—
243C4#1171913811yescharacteristic
244C4D13⋊#10011yescharacteristic
245C2—262no—
246C2#1313034411yescharacteristic
247C2C2×#1171828011yescharacteristic
248C2C2×#1171828211yescharacteristic
subgroupG/H
centerC22C2×#88115
commutatorC2×C8×C13C22×C4
FrattiniC2×C8C22×#261
FittingC13×#494C4
socleC22×C13C2×#102
prime radicalC22×D13#102
cosocleC8×Dic13C23
hypercenter#494#261
hypocenterC13#11962
LCSG ▷ C2×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #494

Complements

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

NH ≅ G/Ntype
3. #13129851C2semidirect
205. C13#11962semidirect

Maximal subgroups

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

subgroupindex
#131311952
#131303952
#131298512
D13×#4942
#1196213