Finite Group Databasebeta

← #16790828

Subgroups — #16790828

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×#11718224C211yesmaximal, 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#11718224—21no—
14#11718224—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#6118D812yes—
53D13⋊C8—21no—
54C13×M16—22no—
55C2×C8×C13C22×C411yescharacteristic
56#6099—22no—
57C2×#1055#4111yescharacteristic
58#6094—42no—
59C8×D13—42no—
60C8×D13C2×D411yescharacteristic
61C8×D13C2×Q811yescharacteristic
62C8×D13C2×Q811yescharacteristic
63C8×D13#4111yescharacteristic
64#6092—22no—
65C13×C16C4⋊C411yescharacteristic
66C13×C16C4⋊C411yescharacteristic
67#6090C4⋊C411yescharacteristic
68#6090C4⋊C411yescharacteristic
69C2×#368—131no—
70C2×#368—131no—
71#2108—131no—
72#1953—132no—
73#1388—132no—
74C22×D13C2×Q1611yescharacteristic
75C2×#261—22no—
76C2×C4×C13C4×D411yescharacteristic
77C2×Dic13#13511yescharacteristic
78C4×D13#12111yescharacteristic
79C4×D13C4⋊Q811yescharacteristic
80C4×D13C2×D811yescharacteristic
81C4×D13#13511yescharacteristic
82#1057—22no—
83#1057—82no—
84C8×C13—42no—
85C8×C13C2×C4⋊C411yescharacteristic
86C8×C13C4×Q811yescharacteristic
87#1055—42no—
88#1055C22⋊Q811yescharacteristic
89#1055#12511yescharacteristic
90C2×M32—131no—
91C22×C16—131no—
92#430—262no—
93C2×#108—132no—
94C2×#108—132no—
95#405—131no—
96#368—131no—
97#368—132no—
98#368—261no—
99#368—261no—
100#368#26111yescharacteristic, complemented
101#346—261no—
102C4×C16—261no—
103#344—262no—
104C22×C13C4×Q1611yescharacteristic
105C2×D13—41no—
106C2×D13#46711yescharacteristic
107C2×D13#50011yescharacteristic
108#261—42no—
109C4×C13#38911yescharacteristic
110C4×C13C4×D811yescharacteristic
111Dic13#46611yescharacteristic
112Dic13#49911yescharacteristic
113C2×M16—131no—
114C2×M16—262no—
115C2×M16—262no—
116C22×C8—131no—
117#117—131no—
118M32—132no—
119M32—261no—
120C2×C16—131no—
121C2×C16—131no—
122C2×C16—131no—
123C2×C16—131no—
124C2×C16—131no—
125C2×C16—261no—
126C2×C16C2×#26111yescharacteristic
127#108—132no—
128#108—262no—
129#108—262no—
130#108—262no—
131#108—522no—
132#108—522no—
133#108C2×#26112yes—
134#97—261no—
135C4×C8—261no—
136C2×C13—21no—
137C2×C13#194211yescharacteristic
138D13—21no—
139D13—21no—
140C22×C4—131no—
141M16—22no—
142M16—132no—
143M16—261no—
144M16—262no—
145M16—522no—
146M16—522no—
147M16—522no—
148C2×C8—131no—
149C2×C8—131no—
150C2×C8—131no—
151C2×C8—131no—
152C2×C8—131no—
153C2×C8—261no—
154C2×C8—522no—
155C2×C8—522no—
156C2×C8C22×#26111yescharacteristic
157C4⋊C4—261no—
158C22⋊C4—132no—
159C42—261no—
160C16—131no—
161C16—131no—
162C16—262no—
163C16C4⋊#26111yescharacteristic
164C16C4⋊#26111yescharacteristic
165C13#1317311yescharacteristic, complemented, Sylow
166C23—131no—
167C2×C4—131no—
168C2×C4—131no—
169C2×C4—131no—
170C2×C4—131no—
171C2×C4—131no—
172C2×C4—262no—
173C2×C4D4×#26111yescharacteristic
174C8—42no—
175C8—131no—
176C8—131no—
177C8—262no—
178C8—522no—
179C8—1042no—
180C8C2×C4⋊#26111yescharacteristic
181C8Q8×#26111yescharacteristic
182C22—131no—
183C22—131no—
184C22—521no—
185C22Q16×#26111yescharacteristic
186C4—131no—
187C4—131no—
188C4—522no—
189C4#1171908311yescharacteristic
190C4D8×#26111yescharacteristic
191C2—21no—
192C2—261no—
193C2—261no—
194C2#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
100. #368#261semidirect
165. C13#13173semidirect

Maximal subgroups

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

subgroupindex
C2×#117182242
#131310442
#131309562
#131299152
D13×#3682
#1317313