Finite Group Databasebeta

← #17948785

Subgroups — #17948785

Order 4352.

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

normal subgroups only

This group has 192 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#14544008C211yesmaximal, characteristic
3#14530594C211yesmaximal, characteristic
4C4×#63243—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×#63243—22no—
20C2×#63218C2×C411yescharacteristic
21C2×#63218D411yescharacteristic
22C42×D17D411yescharacteristic
23#10587542—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—44no—
41#63243—41no—
42#63242—41no—
43C2×C8×C17C4211yescharacteristic
44C2×C8×C17C22⋊C411yescharacteristic
45C42×C17C4⋊C411yescharacteristic
46C4×Dic17—21no—
47C4×Dic17C22⋊C411yescharacteristic
48C2×#3622C4⋊C411yescharacteristic
49C2×#3622C4⋊C411yescharacteristic
50#63218—41no—
51#63218—41no—
52C16×C17—41no—
53#63214—41no—
54#7225—171nomaximal, Sylow
55C22×D17#10411yescharacteristic
56C2×#595—81no—
57C2×C4×C17—21no—
58C2×C4×C17#9511yescharacteristic
59C2×Dic17—21no—
60C2×Dic17#10411yescharacteristic
61C4×D17—21no—
62C4×D17—21no—
63C4×D17—42no—
64#3624—24no—
65#3624—42no—
66#3624—81no—
67C8×C17—21no—
68C8×C17—21no—
69#3622—21no—
70#3622—21no—
71#2165—171no—
72#1841—171no—
73#1455—171no—
74C22×C17#33911yescharacteristic
75C2×D17—21no—
76C2×D17—41no—
77#595—161no—
78C4×C17—41no—
79C4×C17H(3,ℤ/4)11yescharacteristic
80C4×C17#34411yescharacteristic
81Dic17—22no—
82Dic17—21no—
83C4×M16—171no—
84C4×M16—341no—
85#364—341no—
86#349—341no—
87#347—171no—
88#347#59511yescharacteristic, complemented
89#344—341no—
90#339—341no—
91#338—171no—
92H(3,ℤ/4)—171no—
93#322—171no—
94#322—341no—
95C82—171no—
96C2×C17—21no—
97C2×C17#128811yescharacteristic
98D17—41no—
99C2×M16—171no—
100C2×M16—171no—
101C2×M16—342no—
102C2×M16—341no—
103#117—341no—
104C2×C42—171no—
105M32—21no—
106M32—341no—
107#97—171no—
108#97—342no—
109#97C2×#59511yescharacteristic
110C4×C8—171no—
111C4×C8—171no—
112C4×C8—341no—
113C4×C8—341no—
114C17#722511yescharacteristic, complemented, Sylow
115C22×C4—171no—
116C22×C4—341no—
117M16—681no—
118M16—681no—
119M16—684no—
120M16—681no—
121M16—681no—
122C2×C8—171no—
123C2×C8—171no—
124C2×C8—342no—
125C2×C8—342no—
126C2×C8—681no—
127C2×C8C4×#59511yescharacteristic
128C2×C8C22⋊#59511yescharacteristic
129C4⋊C4—681no—
130C22⋊C4—681no—
131C42—171no—
132C42—341no—
133C42—681no—
134C42C4⋊#59511yescharacteristic
135C16—41no—
136C16—681no—
137C23—171no—
138C2×C4—21no—
139C2×C4—171no—
140C2×C4—341no—
141C2×C4—341no—
142C2×C4—341no—
143C2×C4—682no—
144C2×C4—1361no—
145C2×C4(C2×#595)⋊C411yescharacteristic
146C8—21no—
147C8—21no—
148C8—344no—
149C8—341no—
150C8—341no—
151C8—682no—
152C8—1361no—
153C22—341no—
154C22—681no—
155C22#1176368111yescharacteristic
156C4—41no—
157C4—2721no—
158C4—342no—
159C4—341no—
160C4#1176367611yescharacteristic
161C4#1176369211yescharacteristic
162C2—21no—
163C2—681no—
164C2#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#7225
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
88. #347#595semidirect
114. C17#7225semidirect

Maximal subgroups

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

subgroupindex
#145447152
#145440082
#145305942
#722517