Finite Group Databasebeta

← #17949197

Subgroups — #17949197

Order 4352.

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

normal subgroups only

This group has 202 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#14543714C211yesmaximal, characteristic
2#14543604C211yesmaximal, characteristic
3#14529001C211yesmaximal, characteristic
4#11763675—21no—
5#11763654—21no—
6#11763287C411yescharacteristic
7#11762851—21no—
8#11762716C2211yescharacteristic
9#11762570—21no—
10C2×C17×#101C411yescharacteristic
11C22×Q8×C17C2×C411yescharacteristic
12C22×#3624—41no—
13C2×M16×C17—21no—
14Q8×Dic17—41no—
15Q8×Dic17—41no—
16#10587612—21no—
17#10587612—41no—
18C2×C4⋊Dic17D411yescharacteristic
19C2×C4×Dic17D411yescharacteristic
20C22⋊#3624—41no—
21C17×#101—21no—
22C17×#101C812yescomplemented
23#10587502—41no—
24#10587489—41no—
25#10587488—41no—
26C2×Q8×C17—21no—
27C2×Q8×C17—41no—
28C2×Q8×C17—41no—
29C2×Q8×C17C2×C811yescharacteristic
30C2×Q8×C17M1611yescharacteristic
31C22×C4×C17—21no—
32C22×C4×C17C22⋊C411yescharacteristic
33C22×Dic17—21no—
34C22×Dic17—21no—
35C2×#3624—42no—
36C2×#3624—81no—
37C2×#3624—81no—
38C2×#3624—81no—
39M16×C17—22no—
40M16×C17—41no—
41C2×C8×C17—41no—
42C22⋊Dic17—41no—
43C4⋊Dic17—21no—
44C4⋊Dic17—21no—
45C4⋊Dic17—41no—
46C4⋊Dic17—41no—
47C4⋊Dic17—41no—
48C4×Dic17—41no—
49C4×Dic17—42no—
50C4×Dic17—41no—
51#7376—171nomaximal, Sylow
52C23×C17#9911yescharacteristic
53Q8×C17—41no—
54Q8×C17—41no—
55Q8×C17—42no—
56C2×C4×C17—21no—
57C2×C4×C17—21no—
58C2×C4×C17—21no—
59C2×C4×C17—21no—
60C2×C4×C17—41no—
61C2×C4×C17—41no—
62C2×C4×C17C22⋊C811yescharacteristic
63C2×C4×C17#10111yescharacteristic
64C2×Dic17—21no—
65C2×Dic17—21no—
66C2×Dic17—41no—
67C2×Dic17—41no—
68C2×Dic17—41no—
69C2×Dic17—41no—
70C2×Dic17—41no—
71C2×Dic17—81no—
72#3624—82no—
73#3624—161no—
74C8×C17—42no—
75#1857—171no—
76#1319—171no—
77#1272—171no—
78C22×C17—21no—
79C22×C17—21no—
80C22×C17#32411yescharacteristic
81C22×C17AΣL(1,𝔽16)11yescharacteristic
82C22×C17#35211yescharacteristic
83C4×C17—21no—
84C4×C17—21no—
85C4×C17—41no—
86C4×C17—41no—
87Dic17—41no—
88Dic17—41no—
89Dic17—81no—
90Dic17—81no—
91Dic17—81no—
92#519—171no—
93#428—341no—
94C2×#101#59511yescharacteristic
95#391—171no—
96#339—341no—
97#336—341no—
98#324—341no—
99C2×C17—21no—
100C2×C17—21no—
101C2×C17#132611yescharacteristic
102C2×C17#140411yescharacteristic
103C2×C17#140511yescharacteristic
104C22×Q8C2×#59511yescharacteristic
105C2×M16—21no—
106C22×C8—681no—
107C4×Q8—681no—
108C4×Q8—681no—
109#117—341no—
110#117—681no—
111C2×C4⋊C4—171no—
112C2×C42—171no—
113#107—681no—
114#106—681no—
115#101—21no—
116#101#362412yescomplemented
117C22⋊C8—681no—
118#95—681no—
119C17#737611yescharacteristic, complemented, Sylow
120C2×Q8—21no—
121C2×Q8—41no—
122C2×Q8—41no—
123C2×Q8C2×#362411yescharacteristic
124C2×Q8#6324711yescharacteristic
125C22×C4—21no—
126C22×C4—341no—
127C22×C4—341no—
128C22×C4C22⋊#59511yescharacteristic
129M16—22no—
130M16—41no—
131C2×C8—41no—
132C2×C8—682no—
133C2×C8—1361no—
134C2×C8—1361no—
135C2×C8—1361no—
136C4⋊C4—341no—
137C4⋊C4—341no—
138C4⋊C4—681no—
139C4⋊C4—681no—
140C4⋊C4—681no—
141C22⋊C4—681no—
142C42—681no—
143C42—681no—
144C42—682no—
145C23#1058753911yescharacteristic
146Q8—41no—
147Q8—41no—
148Q8—42no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—341no—
156C2×C4—341no—
157C2×C4—681no—
158C2×C4—681no—
159C2×C4—681no—
160C2×C4—681no—
161C2×C4—681no—
162C2×C4—1361no—
163C2×C4#1058754511yescharacteristic
164C2×C4C22⋊#362411yescharacteristic
165C8—42no—
166C8—2721no—
167C8—1362no—
168C22—21no—
169C22—21no—
170C22#1176365411yescharacteristic
171C22#1176371011yescharacteristic
172C22#1176371211yescharacteristic
173C4—21no—
174C4—21no—
175C4—41no—
176C4—41no—
177C4—681no—
178C4—681no—
179C4—1361no—
180C4—1361no—
181C4—1361no—
182C2—21no—
183C2—21no—
184C2#1454372811yescharacteristic
185C2#1454390811yescharacteristic
186C2#1454391011yescharacteristic
subgroupG/H
centerC22#11763710
commutatorC2×Q8×C17C2×C8
FrattiniC22×Q8C2×#595
FittingC2×C17×#101C4
socleC22×C17AΣL(1,𝔽16)
prime radicalC23×C17#99
cosocle#11762716C22
hypercenterC2×#101#595
hypocenterC17#7376
LCSG ▷ C2×Q8×C17 ▷ C2×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C22×Q8 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
22. C17×#101C8semidirect
116. #101#3624semidirect
119. C17#7376semidirect

Maximal subgroups

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

subgroupindex
#145437142
#145436042
#145290012
#737617