Finite Group Databasebeta

← #16788433

Subgroups — #16788433

Order 3328.

272 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 62 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#13131211C211yesmaximal, characteristic
2#13131058C211yesmaximal, characteristic
3#13129841C214yesmaximal, complemented
4#13125492C211yesmaximal, characteristic
5#11719436C412yes—
6D13⋊M32—21no—
7C13×#494C411yescharacteristic
8#11718850—21no—
9#11718849—21no—
10#11718845—21no—
11Q16×Dic13—21no—
12#11718743C2212yes—
13#11718350C2211yescharacteristic
14#11718344C411yescharacteristic
15#11718263—21no—
16#11718262—21no—
17#11718261—21no—
18#11718232C2212yes—
19#11718232C2212yes—
20C2×C13×Q16—21no—
21C2×C13×Q16—21no—
22C13×C4⋊Q8C2×C412yes—
23#88200—22no—
24Q8×Dic13—22no—
25C2×#6094D411yescharacteristic
26C2×C8×D13D411yescharacteristic
27#88152—42no—
28#88143—42no—
29#88126C2×C411yescharacteristic
30#88124C2×C412yes—
31#88106—22no—
32#88106—22no—
33#88098—22no—
34D13⋊C16—22no—
35C4×C8×C13C2×C411yescharacteristic
36#88075—22no—
37#88075—22no—
38#88058—21no—
39#88057—21no—
40#88055D411yescharacteristic
41C8×Dic13D411yescharacteristic
42#88043C2311yescharacteristic
43#11914—131nomaximal, Sylow
44C2×Q8×C13—22no—
45C2×C4×D13C22⋊C411yescharacteristic
46C13×Q16—42no—
47C13×Q16—41no—
48C13×Q16—41no—
49C2×C8×C13C22⋊C411yescharacteristic
50C2×C8×C13C22⋊C411yescharacteristic
51C13×C4⋊C4—42no—
52C42×C13C22×C411yescharacteristic
53#6103—21no—
54#6103—42no—
55C4⋊Dic13—22no—
56C4⋊Dic13—42no—
57#6101—21no—
58#6101—42no—
59#6101—42no—
60C4×Dic13—42no—
61C4×Dic13C22⋊C411yescharacteristic
62C2×#1055C2×D411yescharacteristic
63C2×#1055C2×D411yescharacteristic
64#6094—41no—
65C8×D13—21no—
66C8×D13—21no—
67#6092—24no—
68#6092—42no—
69#3177—131no—
70#2166—131no—
71#2110—131no—
72#1356—134no—
73C22×D13#10011yescharacteristic
74Q8×C13—42no—
75Q8×C13—42no—
76C2×C4×C13—21no—
77C2×C4×C13—42no—
78C2×C4×C13C2×C22⋊C411yescharacteristic
79C2×Dic13—21no—
80C2×Dic13—42no—
81C2×Dic13#10011yescharacteristic
82C4×D13—21no—
83C4×D13—21no—
84C8×C13—21no—
85C8×C13#10411yescharacteristic
86C8×C13#10411yescharacteristic
87#1055—21no—
88#1055—21no—
89#541—132no—
90C2×M32—261no—
91#499—131no—
92#494#26111yescharacteristic
93#491—132no—
94#470—261no—
95#467—261no—
96#441—261no—
97C4×Q16—261no—
98#405—131no—
99#364—261no—
100#349—261no—
101#347—132no—
102#347—132no—
103#347—261no—
104C22×C13C2×#10011yescharacteristic
105C2×D13—21no—
106C2×D13—41no—
107C4×C13—41no—
108C4×C13—82no—
109C4×C13C2×#10411yescharacteristic
110C4×C13#42111yescharacteristic
111Dic13—21no—
112Dic13—41no—
113Dic13—82no—
114C2×Q16—21no—
115C2×Q16—21no—
116C2×M16—131no—
117C22×C8—131no—
118C4⋊Q8C2×#26112yes—
119#126—522no—
120#125—132no—
121#125—522no—
122C22⋊Q8—262no—
123C4×Q8—262no—
124#117—131no—
125M32—262no—
126M32—262no—
127M32—262no—
128C2×C16—262no—
129#107—261no—
130#106—261no—
131#103—262no—
132#103—262no—
133#97—131no—
134#97—131no—
135C4×C8—131no—
136C4×C8C2×#26111yescharacteristic
137C2×C13—21no—
138C2×C13#153011yescharacteristic
139D13—41no—
140C2×Q8—22no—
141C22×C4—131no—
142Q16—42no—
143Q16—41no—
144Q16—41no—
145M16—521no—
146C2×C8—131no—
147C2×C8—131no—
148C2×C8—261no—
149C2×C8—261no—
150C2×C8C22⋊#26111yescharacteristic
151C2×C8C22⋊#26111yescharacteristic
152C4⋊C4—42no—
153C4⋊C4—261no—
154C4⋊C4—262no—
155C4⋊C4—522no—
156C4⋊C4—522no—
157C4⋊C4—522no—
158C22⋊C4—261no—
159C22⋊C4—522no—
160C42—131no—
161C42—522no—
162C42C22×#26111yescharacteristic
163C16—264no—
164C16—522no—
165C13#1191411yescharacteristic, complemented, Sylow
166C23—131no—
167Q8—42no—
168Q8—42no—
169C2×C4—21no—
170C2×C4—42no—
171C2×C4—131no—
172C2×C4—261no—
173C2×C4—261no—
174C2×C4—261no—
175C2×C4—522no—
176C2×C4C2×C22⋊#26111yescharacteristic
177C8—21no—
178C8—261no—
179C8—261no—
180C8#8811611yescharacteristic
181C8#8811611yescharacteristic
182C22—261no—
183C22—521no—
184C22D13⋊#10011yescharacteristic
185C4—41no—
186C4—82no—
187C4—261no—
188C4—521no—
189C4—1042no—
190C4C2×#8811611yescharacteristic
191C4#1171914011yescharacteristic
192C2—21no—
193C2—521no—
194C2#1313030611yescharacteristic
subgroupG/H
centerC2#13130306
commutatorC42×C13C22×C4
FrattiniC42C22×#261
FittingC13×#494C4
socleC2×C13#1530
prime radicalC22×D13#100
cosocle#88043C23
hypercenter#494#261
hypocenterC13#11914
LCSG ▷ C42×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #494

Complements

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

NH ≅ G/Ntype
3. #13129841C2semidirect
165. C13#11914semidirect

Maximal subgroups

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

subgroupindex
#131312112
#131310582
#131298412
#131254922
#1191413