Finite Group Databasebeta

← #17948370

Subgroups — #17948370

Order 4352.

218 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 42 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#14543705C211yesmaximal, characteristic
2#14543647C211yesmaximal, characteristic
3#14530213C211yesmaximal, characteristic
4#11763751—21no—
5C22⋊#63216—21no—
6C2×#10587491C2211yescharacteristic
7#11762666—21no—
8#11762572C411yescharacteristic, complemented
9#11762571—21no—
10C2×C17×#107C411yescharacteristic, complemented
11C22×C4×D17D411yescharacteristic
12C2×C22⋊#595—41no—
13C2×C4⋊#595—41no—
14C22×C8×C17C2×C411yescharacteristic
15C2×C4⋊C4×C17—21no—
16C2×#63227—41no—
17C2×C4⋊Dic17—21no—
18C22×#3622D411yescharacteristic
19(C2×#595)⋊C4—22no—
20C2×#63216—41no—
21C17×#107—41no—
22#10587502—41no—
23#10587491—41no—
24C23×D17D811yescharacteristic
25C22×#595—42no—
26C22×C4×C17—41no—
27C22×C4×C17C22⋊C411yescharacteristic
28C22×Dic17—41no—
29C22×Dic17SD1611yescharacteristic
30C2×C4×D17—21no—
31C2×C4×D17—21no—
32C2×C4×D17—41no—
33C2×C4×D17—41no—
34C22⋊#595—81no—
35C22⋊#595—81no—
36C4⋊#595—81no—
37C4⋊#595—81no—
38C2×C8×C17—21no—
39C2×C8×C17—41no—
40C4⋊C4×C17—41no—
41C4⋊C4×C17—41no—
42#63227—82no—
43C4⋊Dic17—41no—
44C4⋊Dic17—41no—
45C2×#3622—21no—
46C2×#3622—41no—
47#63216—81no—
48#7077—171nomaximal, Sylow
49C23×C17#10211yescharacteristic
50C22×D17—21no—
51C22×D17—21no—
52C22×D17—41no—
53C22×D17—41no—
54C22×D17SD3211yescharacteristic
55C22×D17Q3211yescharacteristic
56C2×#595—82no—
57C2×#595—82no—
58C2×#595—82no—
59C2×C4×C17—21no—
60C2×C4×C17—21no—
61C2×C4×C17—81no—
62C2×C4×C17—81no—
63C2×C4×C17—81no—
64C2×C4×C17#9911yescharacteristic
65C2×C4×C17#10411yescharacteristic
66C2×Dic17—21no—
67C2×Dic17—41no—
68C2×Dic17—81no—
69C2×Dic17—81no—
70C2×Dic17—81no—
71C4×D17—41no—
72C4×D17—41no—
73C4×D17—81no—
74C8×C17—41no—
75#3622—41no—
76#2076—171no—
77#1314—171no—
78#1289—171no—
79C22×C17—21no—
80C22×C17—21no—
81C22×C17#32711yescharacteristic
82C22×C17#35811yescharacteristic
83C22×C17#36011yescharacteristic
84C2×D17—21no—
85C2×D17—21no—
86C2×D17—41no—
87C2×D17—41no—
88C2×D17—41no—
89C2×D17—41no—
90C2×D17—81no—
91#595—162no—
92C4×C17—21no—
93C4×C17—161no—
94C4×C17#35211yescharacteristic
95C4×C17#35411yescharacteristic
96Dic17—41no—
97Dic17—161no—
98C2×#107#59511yescharacteristic, complemented
99C2×C22⋊C8—171no—
100#380—341no—
101#380—341no—
102C22⋊C16—341no—
103#340—171no—
104#340—341no—
105C2×C17—21no—
106C2×C17—21no—
107C2×C17#133911yescharacteristic
108C2×C17#134411yescharacteristic
109C2×C17#134811yescharacteristic
110D17—41no—
111D17—41no—
112C23×C4—171no—
113C22×C8—171no—
114C22×C8C2×#59511yescharacteristic
115C2×C4⋊C4—21no—
116C2×C4⋊C4—341no—
117C2×C4⋊C4—681no—
118C2×C22⋊C4—681no—
119C2×C22⋊C4—681no—
120C2×C16—681no—
121#107—41no—
122C22⋊C8—681no—
123#95—342no—
124#95—681no—
125C17#707711yescharacteristic, complemented, Sylow
126C24—171no—
127C22×C4—41no—
128C22×C4—171no—
129C22×C4—341no—
130C22×C4—341no—
131C22×C4—681no—
132C22×C4—681no—
133C22×C4—682no—
134C22×C4—681no—
135C22×C4C22⋊#59511yescharacteristic
136C2×C8—21no—
137C2×C8—41no—
138C2×C8—341no—
139C2×C8—681no—
140C4⋊C4—41no—
141C4⋊C4—41no—
142C4⋊C4—681no—
143C4⋊C4—681no—
144C4⋊C4—1361no—
145C4⋊C4—1361no—
146C22⋊C4—1362no—
147C22⋊C4—1361no—
148C22⋊C4—1361no—
149C16—1361no—
150C23—171no—
151C23—171no—
152C23—341no—
153C23—341no—
154C23—681no—
155C23—681no—
156C23#1058754711yescharacteristic
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—81no—
160C2×C4—81no—
161C2×C4—81no—
162C2×C4—341no—
163C2×C4—681no—
164C2×C4—681no—
165C2×C4—681no—
166C2×C4—1361no—
167C2×C4—1361no—
168C2×C4—1361no—
169C2×C4—1362no—
170C2×C4—1362no—
171C2×C4—1362no—
172C2×C4—1361no—
173C2×C4#1058754811yescharacteristic
174C2×C4#1058755111yescharacteristic
175C8—41no—
176C8—681no—
177C22—21no—
178C22—21no—
179C22—341no—
180C22—341no—
181C22—681no—
182C22—681no—
183C22—681no—
184C22—681no—
185C22—1361no—
186C22#1176366011yescharacteristic
187C22#1176372211yescharacteristic
188C22#1176372611yescharacteristic
189C4—21no—
190C4—161no—
191C4—2721no—
192C4—2722no—
193C4—681no—
194C4#1176371111yescharacteristic
195C4#1176371511yescharacteristic
196C2—21no—
197C2—21no—
198C2—681no—
199C2—681no—
200C2#1454375411yescharacteristic
201C2#1454376411yescharacteristic
202C2#1454377211yescharacteristic
subgroupG/H
centerC22#11763660
commutatorC22×C8×C17C2×C4
FrattiniC22×C8C2×#595
FittingC2×C17×#107C4
socleC22×C17#327
prime radicalC23×D17D8
cosocleC2×#10587491C22
hypercenterC2×#107#595
hypocenterC17#7077
LCSG ▷ C22×C8×C17 ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
8. #11762572C4semidirect
10. C2×C17×#107C4semidirect
98. C2×#107#595semidirect
125. C17#7077semidirect

Maximal subgroups

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

subgroupindex
#145437052
#145436472
#145302132
#707717