Finite Group Databasebeta

← #17949338

Subgroups — #17949338

Order 4352.

194 conjugacy classes of subgroups; only the 36 normal subgroups are shown.

normal subgroups only

This group has 194 conjugacy classes of subgroups — too many to draw. Only its 36 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#14543881C211yesmaximal, characteristic
2#14543715C211yesmaximal, characteristic
3#14530328C211yesmaximal, characteristic
4C2×#10587545—21no—
5#11763654—21no—
6C2×#10587479—21no—
7C2×#10587481—21no—
8#11762715C2211yescharacteristic
9#11762564C411yescharacteristic
10C17×#384C411yescharacteristic
11C22×Dic34D411yescharacteristic
12C2×#63247—41no—
13C2×C4⋊C4×C17—21no—
14C2×C4⋊C4×C17—41no—
15C2×C42×C17C2×C411yescharacteristic
16C2×C4⋊Dic17D411yescharacteristic
17C22×#3622—21no—
18C22⋊#3624—41no—
19#10587545—22no—
20#10587545—41no—
21#10587502—41no—
22#10587481—42no—
23#10587479—42no—
24C22×C4×C17—21no—
25C22×C4×C17—41no—
26C22×C4×C17C22⋊C411yescharacteristic
27C22×Dic17—21no—
28C22×Dic17—21no—
29C2×Dic34—21no—
30C2×Dic34—41no—
31C2×Dic34—41no—
32C2×Dic34SD1611yescharacteristic
33C2×Dic34Q1611yescharacteristic
34#63247—42no—
35#63247—81no—
36C2×#3624—81no—
37C2×#3624—81no—
38C4⋊C4×C17—41no—
39C4⋊C4×C17—41no—
40C4⋊C4×C17—82no—
41C42×C17—41no—
42C4⋊Dic17—41no—
43C2×#3622—22no—
44C2×#3622—41no—
45C2×#3622—41no—
46#7437—171nomaximal, Sylow
47C23×C17#9911yescharacteristic
48C2×C4×C17—21no—
49C2×C4×C17—21no—
50C2×C4×C17—22no—
51C2×C4×C17—41no—
52C2×C4×C17—41no—
53C2×C4×C17—82no—
54C2×C4×C17—81no—
55C2×C4×C17#10311yescharacteristic
56C2×C4×C17#10411yescharacteristic
57C2×Dic17—21no—
58C2×Dic17—21no—
59C2×Dic17—41no—
60C2×Dic17—41no—
61C2×Dic17—41no—
62C2×Dic17—81no—
63Dic34—41no—
64Dic34—41no—
65Dic34—81no—
66#3624—82no—
67#3624—161no—
68#3622—42no—
69#2096—171no—
70#1394—171no—
71#1319—171no—
72C22×C17—21no—
73C22×C17—21no—
74C22×C17#32811yescharacteristic
75C22×C17#35211yescharacteristic
76C22×C17#35311yescharacteristic
77C4×C17—21no—
78C4×C17—21no—
79C4×C17—42no—
80C4×C17—161no—
81Dic17—41no—
82Dic17—41no—
83Dic17—81no—
84C2×#106—341no—
85C2×#103—341no—
86C2×#101—341no—
87#391—171no—
88#384#59511yescharacteristic
89#336—171no—
90#324—341no—
91C2×C17—21no—
92C2×C17—21no—
93C2×C17#135211yescharacteristic
94C2×C17#140711yescharacteristic
95C2×C17#141011yescharacteristic
96C22×Q8—171no—
97C2×M16—681no—
98C22×C8—341no—
99C2×C4⋊C4—21no—
100C2×C4⋊C4—41no—
101C2×C4⋊C4—171no—
102C2×C42C2×#59511yescharacteristic
103#106—682no—
104#103—682no—
105#101—342no—
106#101—681no—
107C22⋊C8—681no—
108#95—681no—
109C17#743711yescharacteristic, complemented, Sylow
110C2×Q8—171no—
111C2×Q8—171no—
112C2×Q8—341no—
113C2×Q8—681no—
114C2×Q8—681no—
115C22×C4—21no—
116C22×C4—41no—
117C22×C4—341no—
118C22×C4—341no—
119C22×C4C22⋊#59511yescharacteristic
120M16—682no—
121M16—1361no—
122C2×C8—342no—
123C2×C8—681no—
124C2×C8—681no—
125C2×C8—1361no—
126C2×C8—1361no—
127C4⋊C4—41no—
128C4⋊C4—41no—
129C4⋊C4—82no—
130C4⋊C4—681no—
131C42—41no—
132C23#1058755111yescharacteristic
133Q8—681no—
134Q8—681no—
135Q8—1361no—
136C2×C4—21no—
137C2×C4—21no—
138C2×C4—22no—
139C2×C4—41no—
140C2×C4—41no—
141C2×C4—82no—
142C2×C4—81no—
143C2×C4—341no—
144C2×C4—341no—
145C2×C4—681no—
146C2×C4—681no—
147C2×C4—681no—
148C2×C4—1361no—
149C2×C4#1058754911yescharacteristic
150C2×C4#1058755011yescharacteristic
151C8—2721no—
152C8—682no—
153C8—1362no—
154C22—21no—
155C22—21no—
156C22#1176366311yescharacteristic
157C22#1176371111yescharacteristic
158C22#1176371311yescharacteristic
159C4—21no—
160C4—21no—
161C4—42no—
162C4—161no—
163C4—681no—
164C4—681no—
165C4—1361no—
166C2—21no—
167C2—21no—
168C2#1454378111yescharacteristic
169C2#1454391311yescharacteristic
170C2#1454391911yescharacteristic
subgroupG/H
centerC22#11763713
commutatorC2×C42×C17C2×C4
FrattiniC2×C42C2×#595
FittingC17×#384C4
socleC22×C17#353
prime radicalC23×C17#99
cosocle#11762715C22
hypercenter#384#595
hypocenterC17#7437
LCSG ▷ C2×C42×C17 ▷ C22×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×C42 ◁ #384

Complements

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

NH ≅ G/Ntype
109. C17#7437semidirect

Maximal subgroups

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

subgroupindex
#145438812
#145437152
#145303282
#743717