Finite Group Databasebeta

← #16778041

Subgroups — #16778041

Order 3328.

262 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 46 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×#11718301C211yesmaximal, characteristic
2#13130369C211yesmaximal, characteristic
3#13115227C211yesmaximal, characteristic
4#11719517C411yescharacteristic
5C2×#88198C2211yescharacteristic
6C2×#88113—21no—
7#11719128—21no—
8C2×C13×#101C411yescharacteristic
9#11718781—21no—
10#11718303—21no—
11#11718303C412yescomplemented
12#11718301—21no—
13#11718301C412yescomplemented
14#11718147—21no—
15C22×Q8×C13C2×C411yescharacteristic
16C22×Dic26D411yescharacteristic
17C2×#6122—41no—
18C2×C13×M16—21no—
19Q8×Dic13—42no—
20#88198—41no—
21#88198C2×C411yescharacteristic
22#88198C2×C411yescharacteristic
23#88198D411yescharacteristic
24#88198Q811yescharacteristic
25#88180—21no—
26#88180—41no—
27C2×#6101—41no—
28C2×C4×Dic13D411yescharacteristic
29C22⋊#1057—41no—
30#88113—22no—
31#88113—41no—
32#88112—22no—
33#88110—41no—
34C13×#101—41no—
35#88056—42no—
36#7483—131nomaximal, Sylow
37C2×Q8×C13—21no—
38C2×Q8×C13—41no—
39C2×Q8×C13—41no—
40C2×Q8×C13C4211yescharacteristic
41C2×Q8×C13C4⋊C411yescharacteristic
42C22×C4×C13—21no—
43C22×C4×C13C22⋊C411yescharacteristic
44C22×Dic13—21no—
45C22×Dic13—21no—
46C2×Dic26—21no—
47C2×Dic26—41no—
48C2×Dic26—41no—
49C2×Dic26C22⋊C411yescharacteristic
50C2×Dic26C4⋊C411yescharacteristic
51#6122—42no—
52#6122—81no—
53C2×#1057—42no—
54C2×#1057—81no—
55C13×M16—41no—
56C13×M16—41no—
57C2×C8×C13—41no—
58C22⋊Dic13—41no—
59C4⋊Dic13—22no—
60C4⋊Dic13—42no—
61#6101—41no—
62#6101—41no—
63#6101—41no—
64#6101—41no—
65C4×Dic13—21no—
66C4×Dic13—41no—
67C4×Dic13—42no—
68C4×Dic13C22⋊C411yescharacteristic
69C4×Dic13C4⋊C411yescharacteristic
70C2×#356—131no—
71#1886—131no—
72#1558—131no—
73C23×C13#9911yescharacteristic
74Q8×C13—42no—
75Q8×C13—41no—
76Q8×C13—41no—
77C2×C4×C13—21no—
78C2×C4×C13—21no—
79C2×C4×C13—21no—
80C2×C4×C13—21no—
81C2×C4×C13—41no—
82C2×C4×C13—41no—
83C2×C4×C13#9511yescharacteristic
84C2×C4×C13#9911yescharacteristic
85C2×Dic13—21no—
86C2×Dic13—21no—
87C2×Dic13—21no—
88C2×Dic13—21no—
89C2×Dic13—42no—
90C2×Dic13—41no—
91C2×Dic13—41no—
92C2×Dic13—42no—
93Dic26—41no—
94Dic26—41no—
95Dic26—81no—
96#1057—82no—
97#1057—82no—
98C8×C13—81no—
99C2×C4⋊Q8—131no—
100#519—131no—
101#432—261no—
102#419—261no—
103C2×#101—261no—
104C2×#101#26111yescharacteristic
105#356—132no—
106#356—261no—
107#339—261no—
108#333—132no—
109#333—261no—
110C22×C13—41no—
111C22×C13#34211yescharacteristic
112C22×C13AΣL(1,𝔽16)11yescharacteristic
113C22×C13#35211yescharacteristic
114C4×C13—21no—
115C4×C13—21no—
116C4×C13—41no—
117C4×C13—41no—
118Dic13—22no—
119Dic13—41no—
120Dic13—41no—
121Dic13—41no—
122Dic13—82no—
123C22×Q8—131no—
124C22×Q8C2×#26111yescharacteristic
125C2×M16—21no—
126C2×M16—521no—
127C4⋊Q8—131no—
128C4⋊Q8—131no—
129C4⋊Q8—131no—
130C4⋊Q8—131no—
131C4⋊Q8—521no—
132C4×Q8—522no—
133#117—261no—
134#117—521no—
135C2×C4⋊C4—521no—
136C2×C42—131no—
137C4⋊C8—262no—
138#103—522no—
139#101—41no—
140#101—262no—
141#101—521no—
142C22⋊C8—521no—
143#97—521no—
144C2×C13—21no—
145C2×C13—21no—
146C2×C13—21no—
147C2×C13#139011yescharacteristic
148C2×Q8—21no—
149C2×Q8—41no—
150C2×Q8—41no—
151C2×Q8—131no—
152C2×Q8—131no—
153C2×Q8—261no—
154C2×Q8—521no—
155C2×Q8—521no—
156C2×Q8C4×#26111yescharacteristic
157C2×Q8C4⋊#26111yescharacteristic
158C22×C4—21no—
159C22×C4—261no—
160C22×C4—261no—
161C22×C4C22⋊#26111yescharacteristic
162M16—41no—
163M16—41no—
164M16—522no—
165M16—1041no—
166C2×C8—41no—
167C2×C8—522no—
168C2×C8—1041no—
169C4⋊C4—262no—
170C4⋊C4—521no—
171C4⋊C4—521no—
172C4⋊C4—521no—
173C4⋊C4—521no—
174C4⋊C4—522no—
175C22⋊C4—521no—
176C42—131no—
177C42—131no—
178C42—261no—
179C42—521no—
180C42—522no—
181C13#748311yescharacteristic, complemented, Sylow
182C23#8810711yescharacteristic
183Q8—41no—
184Q8—41no—
185Q8—42no—
186Q8—521no—
187Q8—521no—
188Q8—1041no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—41no—
194C2×C4—41no—
195C2×C4—261no—
196C2×C4—261no—
197C2×C4—261no—
198C2×C4—261no—
199C2×C4—522no—
200C2×C4—521no—
201C2×C4—521no—
202C2×C4—522no—
203C2×C4(C2×#261)⋊C411yescharacteristic
204C2×C4#8811911yescharacteristic
205C8—81no—
206C8—1042no—
207C8—1042no—
208C22—41no—
209C22#1171823611yescharacteristic
210C22#1171823711yescharacteristic
211C22#1171828911yescharacteristic
212C4—21no—
213C4—21no—
214C4—41no—
215C4—41no—
216C4—262no—
217C4—521no—
218C4—521no—
219C4—521no—
220C4—1042no—
221C2—21no—
222C2—21no—
223C2—21no—
224C2#1312992111yescharacteristic
subgroupG/H
centerC2#13129921
commutatorC2×Q8×C13C42
FrattiniC22×Q8C2×#261
FittingC2×C13×#101C4
socleC2×C13#1390
prime radicalC23×C13#99
cosocleC2×#88198C22
hypercenterC2×#101#261
hypocenterC13#7483
LCSG ▷ C2×Q8×C13 ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C23 ◁ C22×C4 ◁ C22×Q8 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
11. #11718303C4semidirect
13. #11718301C4semidirect
181. C13#7483semidirect

Maximal subgroups

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

subgroupindex
C2×#117183012
#131303692
#131152272
#748313