Finite Group Databasebeta

← #16790827

Subgroups — #16790827

Order 3328.

262 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 84 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×#11718223C211yesmaximal, characteristic
2#13131044C211yesmaximal, characteristic
3#13130956C212yesmaximal
4#13129915C212yesmaximal
5D13×#368C211yesmaximal, characteristic
6#11719100—22no—
7C2×#88104C2212yes—
8#11719089C2211yescharacteristic
9D13⋊M32C2211yescharacteristic
10C2×C16×D13C2211yescharacteristic
11D13×#108C2212yes—
12#11718274—22no—
13#11718223—21no—
14#11718223—21no—
15#11718216—21no—
16C16×#261—21no—
17C13×#368C411yescharacteristic, complemented
18#11718098C411yescharacteristic, complemented
19#11718085C412yescomplemented
20#88237D411yescharacteristic
21D13⋊M16D411yescharacteristic
22C2×#6118—22no—
23M16×D13—22no—
24C2×C8×D13C2311yescharacteristic
25#88106—21no—
26#88104—22no—
27#88104—22no—
28#88104—42no—
29#88103—42no—
30#88100—21no—
31C8×#261—21no—
32#88098Q812yes—
33D13⋊C16—21no—
34C2×C13×C16C2×C411yescharacteristic
35C13×#108C2×C412yes—
36#88062—22no—
37#88059C2×C412yes—
38C2×#6090C2×C411yescharacteristic
39C16×D13D411yescharacteristic
40C16×D13D411yescharacteristic
41C16×D13Q811yescharacteristic
42C16×D13Q811yescharacteristic
43#13173—131nomaximal, Sylow
44C2×C4×D13C2×D411yescharacteristic
45C22⋊#261Q1612yes—
46#6122—21no—
47C2×#1057—42no—
48C4⋊#261—21no—
49C4×#261—21no—
50#6118—42no—
51#6118—42no—
52#6118D811yescharacteristic
53#6118D811yescharacteristic
54D13⋊C8—21no—
55C13×M16—22no—
56C2×C8×C13C22×C411yescharacteristic
57#6099—22no—
58C2×#1055#4111yescharacteristic
59#6094—42no—
60C8×D13—42no—
61C8×D13C2×D411yescharacteristic
62C8×D13C2×Q811yescharacteristic
63C8×D13C2×Q811yescharacteristic
64C8×D13#4111yescharacteristic
65#6092—22no—
66C13×C16C4⋊C411yescharacteristic
67C13×C16C4⋊C411yescharacteristic
68#6090C4⋊C411yescharacteristic
69#6090C4⋊C411yescharacteristic
70C2×#368—131no—
71C2×#368—131no—
72#2108—131no—
73#1953—132no—
74#1388—132no—
75C22×D13C2×Q1611yescharacteristic
76C2×#261—22no—
77C2×C4×C13C4×D411yescharacteristic
78C2×Dic13#13511yescharacteristic
79C4×D13#12111yescharacteristic
80C4×D13C4⋊Q811yescharacteristic
81C4×D13C2×D811yescharacteristic
82C4×D13#13511yescharacteristic
83#1057—21no—
84#1057—21no—
85#1057—82no—
86C8×C13—42no—
87C8×C13C2×C4⋊C411yescharacteristic
88C8×C13C4×Q811yescharacteristic
89#1055—42no—
90#1055C22⋊Q811yescharacteristic
91#1055#12511yescharacteristic
92C2×M32—131no—
93C22×C16—131no—
94#430—262no—
95C2×#108—132no—
96C2×#108—132no—
97#405—131no—
98#368—131no—
99#368—132no—
100#368—261no—
101#368—261no—
102#368#26111yescharacteristic, complemented
103#346—261no—
104C4×C16—261no—
105#344—262no—
106C22×C13C4×Q1611yescharacteristic
107C2×D13—41no—
108C2×D13#46711yescharacteristic
109C2×D13#50011yescharacteristic
110#261—42no—
111C4×C13#38911yescharacteristic
112C4×C13C4×D811yescharacteristic
113Dic13#46611yescharacteristic
114Dic13#49911yescharacteristic
115C2×M16—131no—
116C2×M16—262no—
117C2×M16—262no—
118C22×C8—131no—
119#117—131no—
120M32—132no—
121M32—261no—
122C2×C16—131no—
123C2×C16—131no—
124C2×C16—131no—
125C2×C16—131no—
126C2×C16—131no—
127C2×C16—261no—
128C2×C16C2×#26111yescharacteristic
129#108—132no—
130#108—262no—
131#108—262no—
132#108—262no—
133#108—522no—
134#108—522no—
135#108C2×#26112yes—
136#97—261no—
137C4×C8—261no—
138C2×C13—21no—
139C2×C13#194211yescharacteristic
140D13—21no—
141D13—21no—
142C22×C4—131no—
143M16—22no—
144M16—131no—
145M16—131no—
146M16—261no—
147M16—262no—
148M16—522no—
149M16—522no—
150M16—522no—
151C2×C8—131no—
152C2×C8—131no—
153C2×C8—131no—
154C2×C8—131no—
155C2×C8—131no—
156C2×C8—261no—
157C2×C8—522no—
158C2×C8—522no—
159C2×C8C22×#26111yescharacteristic
160C4⋊C4—261no—
161C22⋊C4—132no—
162C42—261no—
163C16—131no—
164C16—131no—
165C16—262no—
166C16C4⋊#26111yescharacteristic
167C16C4⋊#26111yescharacteristic
168C13#1317311yescharacteristic, complemented, Sylow
169C23—131no—
170C2×C4—131no—
171C2×C4—131no—
172C2×C4—131no—
173C2×C4—131no—
174C2×C4—131no—
175C2×C4—262no—
176C2×C4D4×#26111yescharacteristic
177C8—42no—
178C8—131no—
179C8—131no—
180C8—261no—
181C8—261no—
182C8—522no—
183C8—1042no—
184C8C2×C4⋊#26111yescharacteristic
185C8Q8×#26111yescharacteristic
186C22—131no—
187C22—131no—
188C22—521no—
189C22Q16×#26111yescharacteristic
190C4—131no—
191C4—131no—
192C4—522no—
193C4#1171908311yescharacteristic
194C4D8×#26111yescharacteristic
195C2—21no—
196C2—261no—
197C2—261no—
198C2#1313094011yescharacteristic
subgroupG/H
centerC2#13130940
commutatorC2×C8×C13C22×C4
FrattiniC2×C8C22×#261
FittingC13×#368C4
socleC2×C13#1942
prime radicalC22×D13C2×Q16
cosocleC2×C8×D13C23
hypercenter#368#261
hypocenterC13#13173
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #368

Complements

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

NH ≅ G/Ntype
17. C13×#368C4semidirect
18. #11718098C4semidirect
19. #11718085C4semidirect
102. #368#261semidirect
168. C13#13173semidirect

Maximal subgroups

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

subgroupindex
C2×#117182232
#131310442
#131309562
#131299152
D13×#3682
#1317313