Finite Group Databasebeta

← #46836899

Subgroups — #46836899

Order 34688.

314 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 85 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#31774471C211yesmaximal, characteristic
2#31774375C211yesmaximal, characteristic, complemented
3#31773913C212yesmaximal
4#31773654C212yesmaximal, complemented
5C2×#101×C271C211yesmaximal, characteristic, complemented
6C2×#16864654C2211yescharacteristic
7#22576158C412yescomplemented
8#22576149C412yescomplemented
9#22576143—22no—
10#22576136—22no—
11Q8×Dic271—24no—
12#22576119—22no—
13#22576119C2211yescharacteristic
14#22576119C2212yes—
15#22576086—24no—
16C22×Q8×C271C2211yescharacteristic
17C2×M16×C271C2212yes—
18#101×C271—22no—
19#16864654—22no—
20#16864654—22no—
21C2×Dic542C2×C411yescharacteristic
22C2×D1084C2×C411yescharacteristic
23C2×C22⋊D271—21no—
24C2×C4×D271—21no—
25C4⋊Dic271—24no—
26C4⋊Dic271—21no—
27C4⋊Dic271—22no—
28Dic271⋊C4—24no—
29C22⋊Dic271—21no—
30C22⋊Dic271—22no—
31(C2×D271)⋊C4—24no—
32C4×Dic271—24no—
33C4×Dic271C2×C412yes—
34C4×Dic271D414yes—
35C2×Q8×C271—22no—
36C2×Q8×C271—22no—
37C2×Q8×C271C2×C412yes—
38C2×Q8×C271D412yes—
39C22×C4×C271D412yes—
40C22×C4×C271C2311yescharacteristic
41M16×C271—22no—
42M16×C271—22no—
43C2×C8×C271—22no—
44C22×D271—21no—
45Dic542—22no—
46D1084—22no—
47C22⋊D271—41no—
48C22⋊D271—41no—
49C2×Dic271—22no—
50C2×Dic271—21no—
51C2×Dic271—24no—
52C4×D271—42no—
53C23×C271C2×D411yescharacteristic
54Q8×C271—24no—
55Q8×C271—24no—
56C2×C4×C271—22no—
57C2×C4×C271—22no—
58C2×C4×C271C22⋊C414yes—
59C2×C4×C271C22×C411yescharacteristic
60C2×C4×C271C2×D412yes—
61C2×C4×C271C2×D411yescharacteristic
62C2×C4×C271#4112yes—
63C8×C271—42no—
64C22×C271—41no—
65C22×C271C2×C22⋊C411yescharacteristic
66C22×C271#12011yescharacteristic
67C22×C271#12311yescharacteristic
68C2×D271—42no—
69C2×D271—41no—
70C4×C271—24no—
71C4×C271C4×D412yes—
72C4×C271#12112yes—
73Dic271—44no—
74Dic271—42no—
75Dic271—41no—
76C2×C271—21no—
77C2×C271—21no—
78C2×C271—21no—
79C2×C271#38611yescharacteristic
80D271—81no—
81C271#191211yescharacteristic, complemented, Sylow
82#1912—2711nomaximal, Sylow
83#536—2711no—
84#519—2711no—
85#421—2712no—
86C2×#101D27111yescharacteristic, complemented
87H(3,ℤ/4)—2712no—
88C2×#41—2711no—
89C22×Q8C2×D27111yescharacteristic
90C2×M16C2×D27112yes—
91C4⋊Q8—2712no—
92#124—2712no—
93#123—5422no—
94C22⋊Q8—5422no—
95C4×Q8—5424no—
96#117—2712no—
97#117—2711no—
98#117—5422no—
99#104—5424no—
100#101—22no—
101#41—5422no—
102#41—5422no—
103C2×Q8—22no—
104C2×Q8—22no—
105C2×Q8—2711no—
106C2×Q8C4×D27112yes—
107C2×Q8C22⋊D27112yes—
108C2×D4—2711no—
109C2×D4—5421no—
110C22×C4—5421no—
111C22×C4D108412yes—
112C22×C4C22×D27111yescharacteristic
113M16—22no—
114M16—22no—
115C2×C8—22no—
116C4⋊C4—5424no—
117C4⋊C4—5424no—
118C4⋊C4—5422no—
119C4⋊C4—5421no—
120C22⋊C4—5422no—
121C22⋊C4—5421no—
122C22⋊C4—5424no—
123C42—2712no—
124C42—2714no—
125C42—5424no—
126C23—5421no—
127C23C2×D108411yescharacteristic
128Q8—24no—
129Q8—24no—
130Q8—5422no—
131D4—5422no—
132D4—10841no—
133D4—10841no—
134C2×C4—22no—
135C2×C4—22no—
136C2×C4—5424no—
137C2×C4—5422no—
138C2×C4—5421no—
139C2×C4—10842no—
140C2×C4(C2×D271)⋊C414yes—
141C2×C4C2×C4×D27111yescharacteristic
142C2×C4D4×D27112yes—
143C2×C4C2×C22⋊D27111yescharacteristic
144C2×C4#1686465312yes—
145C8—42no—
146C22—41no—
147C22—10842no—
148C22—10841no—
149C22C2×(C2×D271)⋊C411yescharacteristic
150C22#2257613011yescharacteristic
151C22#2257614411yescharacteristic
152C4—24no—
153C4—10844no—
154C4—10842no—
155C4—10841no—
156C4(C22⋊D271)⋊C412yes—
157C4#2257613212yes—
158C2—21no—
159C2—21no—
160C2—21no—
161C2—21681no—
162C2#3177377411yescharacteristic
subgroupG/H
centerC2#31773774
commutatorC2×C4×C271C22×C4
FrattiniC22×C4C22×D271
FittingC2×#101×C271C2
socleC2×C271#386
prime radicalC2×#16864654C22
cosocleC22×C4×C271C23
hypercenterC2×#101D271
hypocenterC271#1912
LCSG ▷ C2×C4×C271 ▷ C2×C271 ▷ C271
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
2. #31774375C2semidirect
4. #31773654C2semidirect
5. C2×#101×C271C2semidirect
7. #22576158C4semidirect
8. #22576149C4semidirect
81. C271#1912semidirect
86. C2×#101D271semidirect

Maximal subgroups

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

subgroupindex
#317744712
#317743752
#317739132
#317736542
C2×#101×C2712
#1912271