Finite Group Databasebeta

← #17948374

Subgroups — #17948374

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#14530208C211yesmaximal, 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—81no—
43#63227—81no—
44C4⋊Dic17—41no—
45C4⋊Dic17—41no—
46C2×#3622—21no—
47C2×#3622—41no—
48#63216—81no—
49#7079—171nomaximal, Sylow
50C23×C17#10211yescharacteristic
51C22×D17—21no—
52C22×D17—21no—
53C22×D17—41no—
54C22×D17—41no—
55C22×D17D1611yescharacteristic
56C22×D17SD3211yescharacteristic
57C2×#595—82no—
58C2×#595—82no—
59C2×#595—82no—
60C2×C4×C17—21no—
61C2×C4×C17—21no—
62C2×C4×C17—81no—
63C2×C4×C17—81no—
64C2×C4×C17—81no—
65C2×C4×C17#9911yescharacteristic
66C2×C4×C17#10411yescharacteristic
67C2×Dic17—21no—
68C2×Dic17—41no—
69C2×Dic17—81no—
70C2×Dic17—81no—
71C2×Dic17—81no—
72C4×D17—41no—
73C4×D17—41no—
74C4×D17—81no—
75C8×C17—41no—
76#3622—41no—
77#2075—171no—
78#1314—171no—
79#1289—171no—
80C22×C17—21no—
81C22×C17—21no—
82C22×C17#32711yescharacteristic
83C22×C17#35711yescharacteristic
84C22×C17#36011yescharacteristic
85C2×D17—21no—
86C2×D17—21no—
87C2×D17—41no—
88C2×D17—41no—
89C2×D17—41no—
90C2×D17—41no—
91C2×D17—81no—
92#595—162no—
93C4×C17—21no—
94C4×C17—161no—
95C4×C17#35211yescharacteristic
96C4×C17#35411yescharacteristic
97Dic17—41no—
98Dic17—161no—
99C2×#107#59511yescharacteristic, complemented
100C2×C22⋊C8—171no—
101#380—341no—
102#380—341no—
103C22⋊C16—341no—
104#340—171no—
105#340—341no—
106C2×C17—21no—
107C2×C17—21no—
108C2×C17#134011yescharacteristic
109C2×C17#134411yescharacteristic
110C2×C17#134711yescharacteristic
111D17—41no—
112D17—41no—
113C23×C4—171no—
114C22×C8—171no—
115C22×C8C2×#59511yescharacteristic
116C2×C4⋊C4—21no—
117C2×C4⋊C4—341no—
118C2×C4⋊C4—681no—
119C2×C22⋊C4—681no—
120C2×C22⋊C4—681no—
121C2×C16—681no—
122#107—41no—
123C22⋊C8—681no—
124#95—342no—
125#95—681no—
126C17#707911yescharacteristic, complemented, Sylow
127C24—171no—
128C22×C4—41no—
129C22×C4—171no—
130C22×C4—341no—
131C22×C4—341no—
132C22×C4—681no—
133C22×C4—681no—
134C22×C4—682no—
135C22×C4—681no—
136C22×C4C22⋊#59511yescharacteristic
137C2×C8—21no—
138C2×C8—41no—
139C2×C8—341no—
140C2×C8—681no—
141C4⋊C4—41no—
142C4⋊C4—41no—
143C4⋊C4—681no—
144C4⋊C4—681no—
145C4⋊C4—1361no—
146C4⋊C4—1361no—
147C22⋊C4—1361no—
148C22⋊C4—1361no—
149C22⋊C4—1361no—
150C22⋊C4—1361no—
151C16—1361no—
152C23—171no—
153C23—171no—
154C23—341no—
155C23—341no—
156C23—681no—
157C23—681no—
158C23#1058754711yescharacteristic
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—81no—
162C2×C4—81no—
163C2×C4—81no—
164C2×C4—341no—
165C2×C4—681no—
166C2×C4—681no—
167C2×C4—681no—
168C2×C4—1361no—
169C2×C4—1361no—
170C2×C4—1361no—
171C2×C4—1362no—
172C2×C4—1362no—
173C2×C4—1362no—
174C2×C4—1361no—
175C2×C4#1058754811yescharacteristic
176C2×C4#1058755111yescharacteristic
177C8—41no—
178C8—681no—
179C22—21no—
180C22—21no—
181C22—341no—
182C22—341no—
183C22—681no—
184C22—681no—
185C22—681no—
186C22—681no—
187C22—1361no—
188C22#1176366011yescharacteristic
189C22#1176372111yescharacteristic
190C22#1176372511yescharacteristic
191C4—21no—
192C4—161no—
193C4—2721no—
194C4—2722no—
195C4—681no—
196C4#1176371111yescharacteristic
197C4#1176371511yescharacteristic
198C2—21no—
199C2—21no—
200C2—681no—
201C2—681no—
202C2#1454375611yescharacteristic
203C2#1454376411yescharacteristic
204C2#1454377011yescharacteristic
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#7079
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
99. C2×#107#595semidirect
126. C17#7079semidirect

Maximal subgroups

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

subgroupindex
#145437052
#145436472
#145302082
#707917