Finite Group Databasebeta

← #16787590

Subgroups — #16787590

Order 3328.

316 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 82 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#13131043C211yesmaximal, characteristic
2#13130397C211yesmaximal, characteristic
3#13129792C214yesmaximal, complemented
4#13125420C211yesmaximal, characteristic
5#11719433—21no—
6C2×#88098—21no—
7#11719054—21no—
8C13×#494C411yescharacteristic
9#11718849—21no—
10#11718849C412yes—
11Q16×Dic13—21no—
12Q16×Dic13C2212yes—
13#11718742—21no—
14C4×C8×D13C2211yescharacteristic
15#11718343C411yescharacteristic
16#11718257C2212yes—
17#11718254C2212yes—
18#11718253—21no—
19#11718231—21no—
20C2×C13×Q16—21no—
21C2×C13×Q16C2×C412yes—
22C13×C4⋊Q8—21no—
23#88200—22no—
24Q8×Dic13—22no—
25C2×C8×D13C2×C411yescharacteristic
26C2×C8×D13D411yescharacteristic
27#88151—41no—
28#88146—41no—
29#88144—41no—
30#88141—41no—
31C42×D13D411yescharacteristic
32#88123—21no—
33#88111—41no—
34#88110—41no—
35C4⋊#1057—22no—
36C2×#6092—22no—
37#88098—24no—
38C4×C8×C13C2×C411yescharacteristic
39#88075—22no—
40#88075—22no—
41#88058—21no—
42#88058C2×C412yes—
43C8×Dic13D411yescharacteristic
44C8×Dic13C2311yescharacteristic
45C4×#1055D411yescharacteristic
46#11676—131nomaximal, Sylow
47C2×Q8×C13—22no—
48C2×C4×D13C22⋊C411yescharacteristic
49C2×C4×D13D811yescharacteristic
50C2×C4×D13SD1611yescharacteristic
51C2×Dic26—41no—
52C2×#1057—42no—
53C13×Q16—24no—
54C13×Q16—42no—
55C2×C8×C13C22⋊C411yescharacteristic
56C2×C8×C13C22×C411yescharacteristic
57C13×C4⋊C4—41no—
58C13×C4⋊C4—41no—
59C42×C13C22⋊C411yescharacteristic
60#6103—42no—
61C4⋊Dic13—22no—
62C4⋊Dic13—41no—
63C4⋊Dic13—42no—
64#6101—42no—
65C4×Dic13—42no—
66C4×Dic13D811yescharacteristic
67C4×Dic13SD1611yescharacteristic
68C4×Dic13C2×D411yescharacteristic
69C2×#1055C22⋊C411yescharacteristic
70C2×#1055C2×D411yescharacteristic
71C8×D13—22no—
72C8×D13—22no—
73#6092—24no—
74#3170—131no—
75C4×M32—131no—
76#1568—131no—
77#1332—134no—
78C22×D13#10211yescharacteristic
79Q8×C13—42no—
80Q8×C13—42no—
81C2×C4×C13—42no—
82C2×C4×C13#10211yescharacteristic
83C2×C4×C13#10211yescharacteristic
84C2×C4×C13C2×C22⋊C411yescharacteristic
85C2×Dic13—42no—
86C2×Dic13#10211yescharacteristic
87C2×Dic13C2×D811yescharacteristic
88C2×Dic13C2×SD1611yescharacteristic
89C4×D13—21no—
90C4×D13—21no—
91C4×D13—22no—
92C4×D13—41no—
93Dic26—82no—
94#1057—82no—
95C8×C13#10412yes—
96C8×C13#13112yes—
97#1055—21no—
98#1055—21no—
99#533—261no—
100C2×M32—261no—
101#500—131no—
102#494#26111yescharacteristic
103#487—261no—
104#467—132no—
105#467—261no—
106C4×Q16—132no—
107C4×Q16—261no—
108#432—261no—
109C2×C4×C8—131no—
110#346—261no—
111C4×C16—132no—
112#335—132no—
113#334—261no—
114C22×C13C2×#10211yescharacteristic
115C2×D13—21no—
116C2×D13—21no—
117C2×D13—21no—
118C4×C13—21no—
119C4×C13—21no—
120C4×C13—82no—
121C4×C13#40811yescharacteristic
122C4×C13C2×#10411yescharacteristic
123Dic13—21no—
124Dic13—21no—
125Dic13—82no—
126Dic13#51012yes—
127C2×Q16—21no—
128C2×Q16C2×#26112yes—
129C22×C8—131no—
130C22×C8—131no—
131C4⋊Q8—21no—
132C4⋊Q8—261no—
133#125—521no—
134C22⋊Q8—262no—
135C22⋊Q8—521no—
136C4×Q8—262no—
137C4×Q8—521no—
138#117—521no—
139C2×C42—131no—
140M32—264no—
141C2×C16—262no—
142#107—132no—
143#107—261no—
144C4⋊C8—262no—
145#103—262no—
146#103—262no—
147C22⋊C8—521no—
148#97—521no—
149C4×C8—131no—
150C4×C8—131no—
151C4×C8—131no—
152C4×C8C2×#26111yescharacteristic
153C2×C13#149211yescharacteristic
154C2×C13#214111yescharacteristic
155C2×C13#214311yescharacteristic
156D13—41no—
157C2×Q8—22no—
158C2×Q8—521no—
159C22×C4—131no—
160C22×C4—131no—
161C22×C4—131no—
162Q16—24no—
163Q16—42no—
164C2×C8—131no—
165C2×C8—131no—
166C2×C8—262no—
167C2×C8—262no—
168C2×C8—522no—
169C2×C8C22⋊#26111yescharacteristic
170C2×C8C22×#26111yescharacteristic
171C4⋊C4—41no—
172C4⋊C4—41no—
173C4⋊C4—262no—
174C4⋊C4—522no—
175C4⋊C4—522no—
176C4⋊C4—521no—
177C22⋊C4—522no—
178C42—131no—
179C42—131no—
180C42—131no—
181C42—522no—
182C42C22⋊#26111yescharacteristic
183C16—264no—
184C13#1167611yescharacteristic, complemented, Sylow
185C23—131no—
186Q8—42no—
187Q8—42no—
188Q8—1042no—
189C2×C4—42no—
190C2×C4—131no—
191C2×C4—131no—
192C2×C4—131no—
193C2×C4—262no—
194C2×C4—261no—
195C2×C4—261no—
196C2×C4—521no—
197C2×C4—522no—
198C2×C4#8811511yescharacteristic
199C2×C4#8811511yescharacteristic
200C2×C4C2×C22⋊#26111yescharacteristic
201C8—261no—
202C8—261no—
203C8—1042no—
204C8#8811612yes—
205C8#8823812yes—
206C22—261no—
207C22—261no—
208C22—261no—
209C22C2×#8811511yescharacteristic
210C4—21no—
211C4—21no—
212C4—82no—
213C4—132no—
214C4—261no—
215C4—261no—
216C4—1042no—
217C4C2×#8811611yescharacteristic
218C4#1171914711yescharacteristic
219C2—521no—
220C2#1313018211yescharacteristic
221C2#1313114611yescharacteristic
222C2#1313115211yescharacteristic
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#11676
LCSG ▷ C2×C8×C13 ▷ 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. #13129792C2semidirect
184. C13#11676semidirect

Maximal subgroups

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

subgroupindex
#131310432
#131303972
#131297922
#131254202
#1167613