Finite Group Databasebeta

← #17949083

Subgroups — #17949083

Order 4352.

244 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 244 conjugacy classes of subgroups — too many to draw. Only its 50 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#14544035C211yesmaximal, characteristic
2#14544035C211yesmaximal, characteristic
3#14528853C211yesmaximal, characteristic
4#11763829—21no—
5#11763829—21no—
6#11763654C412yes—
7#11763654C412yes—
8#11763652—21no—
9#11763652—21no—
10C2×#10587612C2211yescharacteristic
11C2×C22⋊#3622C411yescharacteristic
12#11762563—21no—
13#11762563—21no—
14C2×C17×C22⋊C8C411yescharacteristic
15C23×C4×C17C2×C411yescharacteristic
16C22×C8×C17—21no—
17C2×C22⋊Dic17D411yescharacteristic
18C2×C22⋊Dic17Q811yescharacteristic
19#10587612—41no—
20#10587612—41no—
21C2×C4⋊Dic17C2×C411yescharacteristic
22C2×C4⋊Dic17C2×C411yescharacteristic
23C2×C4×Dic17D411yescharacteristic
24C2×C4×Dic17D411yescharacteristic
25C22×#3622—21no—
26C22⋊#3624—22no—
27C22⋊#3624—22no—
28#10587544—41no—
29#10587544—41no—
30#10587542—41no—
31#10587542—41no—
32C17×C22⋊C8—41no—
33C22⋊#3622—41no—
34C24×C17C4⋊C411yescharacteristic
35C22×C4×C17—21no—
36C22×C4×C17—21no—
37C22×C4×C17—42no—
38C22×C4×C17C4211yescharacteristic
39C22×C4×C17C22⋊C411yescharacteristic
40C22×Dic17C22⋊C411yescharacteristic
41C22×Dic17C22⋊C411yescharacteristic
42C22×Dic17C4⋊C411yescharacteristic
43C22×Dic17C4⋊C411yescharacteristic
44C2×#3624—42no—
45C2×#3624—42no—
46C2×C8×C17—42no—
47C2×C8×C17—41no—
48C22⋊Dic17—41no—
49C22⋊Dic17—41no—
50C4⋊Dic17—41no—
51C4⋊Dic17—41no—
52C4×Dic17—21no—
53C4×Dic17—21no—
54C4×Dic17—21no—
55C4×Dic17—21no—
56C2×#3622—42no—
57C2×#3622—41no—
58#7327—171nomaximal, Sylow
59C23×C17—21no—
60C23×C17—22no—
61C23×C17—41no—
62C23×C17—41no—
63C23×C17#9511yescharacteristic
64C2×C4×C17—22no—
65C2×C4×C17—21no—
66C2×C4×C17—22no—
67C2×C4×C17—42no—
68C2×C4×C17—42no—
69C2×C4×C17#9911yescharacteristic
70C2×C4×C17#9911yescharacteristic
71C2×Dic17—21no—
72C2×Dic17—21no—
73C2×Dic17—21no—
74C2×Dic17—21no—
75C2×Dic17—41no—
76C2×Dic17—41no—
77C2×Dic17—41no—
78C2×Dic17—41no—
79#3624—82no—
80#3624—82no—
81C8×C17—81no—
82#3622—81no—
83#1818—171no—
84#1464—171no—
85#1464—171no—
86C22×C17—21no—
87C22×C17—21no—
88C22×C17—41no—
89C22×C17—41no—
90C22×C17—41no—
91C22×C17—82no—
92C22×C17#34211yescharacteristic
93C22×C17#34412yes—
94C4×C17—21no—
95C4×C17—21no—
96C4×C17—41no—
97Dic17—41no—
98Dic17—41no—
99Dic17—41no—
100Dic17—41no—
101C2×#117—171no—
102#432—341no—
103#432—341no—
104C2×C22⋊C8—171no—
105C2×C22⋊C8#59511yescharacteristic
106#336—341no—
107#336—341no—
108#324—172no—
109#324—172no—
110#323—341no—
111#323—341no—
112C2×C17—22no—
113C2×C17—81no—
114C2×C17#130611yescharacteristic
115C2×C17#139511yescharacteristic
116C2×C17#139511yescharacteristic
117C23×C4C2×#59511yescharacteristic
118C22×C8—21no—
119C22×C8—341no—
120#117—681no—
121#117—681no—
122C2×C4⋊C4—171no—
123C2×C4⋊C4—171no—
124C2×C22⋊C4—171no—
125C2×C22⋊C4—171no—
126C2×C42—171no—
127C2×C42—171no—
128C4⋊C8—681no—
129C4⋊C8—681no—
130C22⋊C8—41no—
131C22⋊C8—342no—
132C22⋊C8—342no—
133C22⋊C8—681no—
134#97—681no—
135#97—681no—
136C17#732711yescharacteristic, complemented, Sylow
137C24C4⋊#59511yescharacteristic
138C22×C4—21no—
139C22×C4—21no—
140C22×C4—42no—
141C22×C4—171no—
142C22×C4—171no—
143C22×C4—171no—
144C22×C4—171no—
145C22×C4C4×#59511yescharacteristic
146C22×C4C22⋊#59511yescharacteristic
147C2×C8—42no—
148C2×C8—41no—
149C2×C8—682no—
150C2×C8—682no—
151C2×C8—682no—
152C2×C8—681no—
153C4⋊C4—681no—
154C4⋊C4—681no—
155C22⋊C4—681no—
156C22⋊C4—681no—
157C42—341no—
158C42—341no—
159C42—341no—
160C42—341no—
161C23—21no—
162C23—22no—
163C23—41no—
164C23—41no—
165C23(C2×#595)⋊C411yescharacteristic
166C2×C4—22no—
167C2×C4—21no—
168C2×C4—22no—
169C2×C4—42no—
170C2×C4—42no—
171C2×C4—341no—
172C2×C4—341no—
173C2×C4—341no—
174C2×C4—341no—
175C2×C4—681no—
176C2×C4—681no—
177C2×C4—681no—
178C2×C4—681no—
179C2×C4#1058753911yescharacteristic
180C2×C4#1058755111yescharacteristic
181C8—81no—
182C8—1361no—
183C8—1362no—
184C8—1362no—
185C22—21no—
186C22—21no—
187C22—41no—
188C22—41no—
189C22—41no—
190C22—82no—
191C22#1176368711yescharacteristic
192C22#1176369012yes—
193C4—21no—
194C4—21no—
195C4—41no—
196C4—681no—
197C4—681no—
198C4—681no—
199C4—681no—
200C2—22no—
201C2—81no—
202C2#1454368711yescharacteristic
203C2#1454388411yescharacteristic
204C2#1454388511yescharacteristic
subgroupG/H
centerC22#11763687
commutatorC22×C4×C17C42
FrattiniC23×C4C2×#595
FittingC2×C17×C22⋊C8C4
socleC22×C17#342
prime radicalC24×C17C4⋊C4
cosocleC2×#10587612C22
hypercenterC2×C22⋊C8#595
hypocenterC17#7327
LCSG ▷ C22×C4×C17 ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
136. C17#7327semidirect

Maximal subgroups

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

subgroupindex
#145440352
#145288532
#732717