Finite Group Databasebeta

← #17948790

Subgroups — #17948790

Order 4352.

180 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 180 conjugacy classes of subgroups — too many to draw. Only its 44 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#14544715C211yesmaximal, characteristic
2#14544004C211yesmaximal, characteristic
3#14530594C211yesmaximal, characteristic
4#11763828—21no—
5#11763691—21no—
6#11763680—21no—
7#11763678C411yescharacteristic
8#11763677C411yescharacteristic
9#11763651—21no—
10#11763650C411yescharacteristic, complemented
11C8×#3624C411yescharacteristic, complemented
12#11762761C2211yescharacteristic
13#11762629—21no—
14#11762590—21no—
15#11762587C411yescharacteristic, complemented
16C17×#347C411yescharacteristic, complemented
17#10587677—21no—
18D17⋊M16—21no—
19C2×#63218C2×C411yescharacteristic
20C2×#63218D411yescharacteristic
21C42×D17D411yescharacteristic
22#10587543—22no—
23C4⋊#3624—22no—
24C4×#3624—21no—
25C4×#3624—21no—
26C17×M32—21no—
27C17×#97C2×C411yescharacteristic
28C8×Dic17C2×C411yescharacteristic
29C8×Dic17D411yescharacteristic
30#10587483—21no—
31#10587474Q811yescharacteristic
32C2×C4×D17—21no—
33C2×C4×D17C22⋊C411yescharacteristic
34C22⋊#595—41no—
35#63247—41no—
36C2×#3624—22no—
37C2×#3624—22no—
38C4⋊#595—41no—
39C4×#595—41no—
40#63243—41no—
41#63242—41no—
42C2×C8×C17C4211yescharacteristic
43C2×C8×C17C22⋊C411yescharacteristic
44C42×C17C4⋊C411yescharacteristic
45C4×Dic17—21no—
46C4×Dic17C22⋊C411yescharacteristic
47C2×#3622C4⋊C411yescharacteristic
48C2×#3622C4⋊C411yescharacteristic
49#63218—41no—
50#63218—41no—
51C16×C17—41no—
52#63214—41no—
53#7226—171nomaximal, Sylow
54C22×D17#10411yescharacteristic
55C2×#595—81no—
56C2×C4×C17—21no—
57C2×C4×C17#9511yescharacteristic
58C2×Dic17—21no—
59C2×Dic17#10411yescharacteristic
60C4×D17—21no—
61C4×D17—21no—
62C4×D17—42no—
63#3624—42no—
64#3624—42no—
65#3624—81no—
66C8×C17—21no—
67C8×C17—21no—
68#3622—21no—
69#3622—21no—
70#2165—171no—
71#1841—171no—
72#1453—171no—
73C22×C17#33911yescharacteristic
74C2×D17—21no—
75C2×D17—41no—
76#595—161no—
77C4×C17—41no—
78C4×C17H(3,ℤ/4)11yescharacteristic
79C4×C17#34411yescharacteristic
80Dic17—22no—
81Dic17—21no—
82#431—341no—
83C4×M16—171no—
84#364—341no—
85#349—341no—
86#347—171no—
87#347#59511yescharacteristic, complemented
88#344—341no—
89#339—341no—
90#338—171no—
91H(3,ℤ/4)—171no—
92#322—171no—
93#322—341no—
94C82—171no—
95C2×C17—21no—
96C2×C17#128811yescharacteristic
97D17—41no—
98C2×M16—171no—
99C2×M16—171no—
100C2×M16—341no—
101#117—341no—
102C2×C42—171no—
103M32—21no—
104M32—341no—
105C4⋊C8—342no—
106C22⋊C8—342no—
107#97—171no—
108#97C2×#59511yescharacteristic
109C4×C8—171no—
110C4×C8—171no—
111C4×C8—341no—
112C4×C8—341no—
113C17#722611yescharacteristic, complemented, Sylow
114C22×C4—171no—
115C22×C4—341no—
116M16—681no—
117M16—681no—
118M16—681no—
119M16—681no—
120C2×C8—171no—
121C2×C8—171no—
122C2×C8—342no—
123C2×C8—342no—
124C2×C8—681no—
125C2×C8C4×#59511yescharacteristic
126C2×C8C22⋊#59511yescharacteristic
127C4⋊C4—681no—
128C22⋊C4—681no—
129C42—171no—
130C42—341no—
131C42—681no—
132C42C4⋊#59511yescharacteristic
133C16—41no—
134C16—681no—
135C23—171no—
136C2×C4—21no—
137C2×C4—171no—
138C2×C4—341no—
139C2×C4—341no—
140C2×C4—341no—
141C2×C4—682no—
142C2×C4—1361no—
143C2×C4(C2×#595)⋊C411yescharacteristic
144C8—21no—
145C8—21no—
146C8—341no—
147C8—341no—
148C8—682no—
149C8—682no—
150C8—1361no—
151C22—341no—
152C22—681no—
153C22#1176368111yescharacteristic
154C4—41no—
155C4—2721no—
156C4—342no—
157C4—341no—
158C4#1176367611yescharacteristic
159C4#1176369211yescharacteristic
160C2—21no—
161C2—681no—
162C2#1454364511yescharacteristic
subgroupG/H
centerC4#11763676
commutatorC2×C8×C17C42
Frattini#97C2×#595
FittingC17×#347C4
socleC2×C17#1288
prime radicalC22×D17#104
cosocle#11762761C22
hypercenter#347#595
hypocenterC17#7226
LCSG ▷ C2×C8×C17 ▷ C4×C17 ▷ C17
UCSC1 ◁ C4 ◁ C2×C8 ◁ #347

Complements

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

NH ≅ G/Ntype
10. #11763650C4semidirect
11. C8×#3624C4semidirect
15. #11762587C4semidirect
16. C17×#347C4semidirect
87. #347#595semidirect
113. C17#7226semidirect

Maximal subgroups

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

subgroupindex
#145447152
#145440042
#145305942
#722617