Finite Group Databasebeta

← #17956364

Subgroups — #17956364

Order 4352.

542 conjugacy classes of subgroups; only the 132 normal subgroups are shown.

normal subgroups only

This group has 542 conjugacy classes of subgroups — too many to draw. Only its 132 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#14544965C214yesmaximal
2#14544719C211yesmaximal, characteristic
3#14543978C211yesmaximal, characteristic
4D17×#494C211yesmaximal, characteristic
5C2×#10587533—22no—
6C4×#63242C2212yes—
7#11763755C2212yes—
8#11763682—28no—
9#11763650—22no—
10C2×Q16×D17—22no—
11C4⋊Q8×D17C2212yes—
12#11763189C411yescharacteristic, complemented
13#11763188C412yescomplemented
14#11763187—22no—
15C4×C8×D17C2211yescharacteristic
16C17×#494C411yescharacteristic, complemented
17C2×Q8×D17—22no—
18C2×C4⋊#595—22no—
19C2×C4⋊#595—24no—
20C2×#63242D414yes—
21C2×Q16×C17—22no—
22C17×C4⋊Q8C2×C412yes—
23#10587630—22no—
24C2×#63231—24no—
25Q16×D17—44no—
26Q16×D17—44no—
27C2×Dic68—22no—
28C2×C8×D17D412yes—
29C4⋊C4×D17—24no—
30#10587574—24no—
31C42×D17C2311yescharacteristic
32#10587555C2×C412yes—
33C4×#3624—22no—
34C4×#3624—22no—
35#10587533—44no—
36C4×C8×C17C2×C411yescharacteristic
37C8×Dic17D412yes—
38C4×#3622C2×C411yescharacteristic
39C22×#595—42no—
40C2×Q8×C17—22no—
41Q8×D17—44no—
42Q8×D17—44no—
43C2×C4×D17—42no—
44C2×C4×D17C2×D411yescharacteristic
45C2×C4×D17C2×D412yes—
46C2×Dic34—22no—
47C2×Dic34—42no—
48C2×#3624—24no—
49C4⋊#595—44no—
50C4⋊#595—48no—
51#63242—28no—
52Q16×C17—44no—
53C2×C8×C17C22⋊C412yes—
54C4⋊C4×C17—24no—
55C42×C17C22×C411yescharacteristic
56#63231—48no—
57C4⋊Dic17—24no—
58#63225—44no—
59C4×Dic17C2×D411yescharacteristic
60C4×Dic17#4112yes—
61C2×#3622C22⋊C412yes—
62Dic68—44no—
63C8×D17D814yes—
64C8×D17SD1614yes—
65#9839—171nomaximal, Sylow
66C22×D17#12711yescharacteristic
67C2×#595—82no—
68C2×#595—84no—
69Q8×C17—44no—
70C2×C4×C17—42no—
71C2×C4×C17C2×C22⋊C411yescharacteristic
72C2×C4×C17C4×D412yes—
73C2×Dic17—42no—
74C2×Dic17#12112yes—
75C2×Dic17#12411yescharacteristic
76C4×D17—82no—
77C4×D17—82no—
78C4×D17C2×D812yes—
79C4×D17C2×SD1612yes—
80C4×D17#13718yes—
81Dic34—44no—
82Dic34—84no—
83#3624—44no—
84C8×C17#10214yes—
85#3622#10214yes—
86C2×#494—171no—
87#1990—174no—
88#1844—171no—
89C2×#322—171no—
90C22×C17#39011yescharacteristic
91C2×D17#49211yescharacteristic
92C2×D17#49311yescharacteristic
93C2×D17#49714yes—
94#595—162no—
95C4×C17—82no—
96C4×C17C2×#10212yes—
97C4×C17#44114yes—
98Dic17—82no—
99Dic17#47014yes—
100Dic17#48612yes—
101C22×Q16—342no—
102C2×C4⋊Q8—172no—
103#494—172no—
104#494—171no—
105#494—342no—
106#494#59511yescharacteristic, complemented
107C2×#106—342no—
108C2×C4×C8—171no—
109C2×C4×C8—172no—
110#384—172no—
111#340—348no—
112#322—342no—
113C2×C17#195711yescharacteristic
114C2×C17#197112yes—
115D17#171612yes—
116D17#172212yes—
117C22×Q8—342no—
118C2×Q16—22no—
119C2×Q16—344no—
120C2×Q16—342no—
121C2×Q16—684no—
122C2×Q16—684no—
123C22×C8—172no—
124C22×C8—174no—
125C4⋊Q8—172no—
126C4⋊Q8—344no—
127C4⋊Q8—342no—
128C4⋊Q8C2×#59512yes—
129C2×C4⋊C4—344no—
130C2×C4⋊C4—344no—
131C2×C4⋊C4—342no—
132C2×C42—171no—
133#106—684no—
134C4×C8—172no—
135C4×C8—171no—
136C4×C8—342no—
137C4×C8—342no—
138C4×C8C2×#59511yescharacteristic
139C17#983911yescharacteristic, complemented, Sylow
140C2×Q8—22no—
141C2×Q8—342no—
142C2×Q8—682no—
143C2×Q8—684no—
144C2×Q8—684no—
145C22×C4—172no—
146C22×C4—171no—
147C22×C4—682no—
148C22×C4—682no—
149Q16—44no—
150Q16—688no—
151Q16—684no—
152C2×C8—172no—
153C2×C8—174no—
154C2×C8—174no—
155C2×C8—348no—
156C2×C8—344no—
157C2×C8C22⋊#59512yes—
158C4⋊C4—24no—
159C4⋊C4—344no—
160C4⋊C4—684no—
161C4⋊C4—684no—
162C4⋊C4—688no—
163C42—172no—
164C42—171no—
165C42C22×#59511yescharacteristic
166C23—171no—
167Q8—44no—
168Q8—684no—
169Q8—1364no—
170C2×C4—42no—
171C2×C4—172no—
172C2×C4—171no—
173C2×C4—172no—
174C2×C4—172no—
175C2×C4—178no—
176C2×C4—682no—
177C2×C4—1362no—
178C2×C4—1362no—
179C2×C4—1362no—
180C2×C4—1364no—
181C2×C4D4×#59512yes—
182C2×C4C2×C22⋊#59511yescharacteristic
183C8—174no—
184C8—684no—
185C8#1058754714yes—
186C22—171no—
187C22—171no—
188C22—174no—
189C22#1176376111yescharacteristic
190C4—82no—
191C4—2722no—
192C4—172no—
193C4—174no—
194C4—1362no—
195C4C2×#1058754712yes—
196C4#1176384914yes—
197C2—172no—
198C2—172no—
199C2#1454491211yescharacteristic
200C2#1454493212yes—
subgroupG/H
centerC22#11763761
commutatorC42×C17C22×C4
FrattiniC42C22×#595
FittingC17×#494C4
socleC22×C17#390
prime radicalC22×D17#127
cosocleC42×D17C23
hypercenter#494#595
hypocenterC17#9839
LCSG ▷ C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C42 ◁ #494

Complements

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

NH ≅ G/Ntype
12. #11763189C4semidirect
13. #11763188C4semidirect
16. C17×#494C4semidirect
106. #494#595semidirect
139. C17#9839semidirect

Maximal subgroups

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

subgroupindex
#145449652
#145447192
#145439782
D17×#4942
#983917