Finite Group Databasebeta

← #17948895

Subgroups — #17948895

Order 4352.

336 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 68 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#14544664C211yesmaximal, characteristic
2#14544470C211yesmaximal, characteristic
3D17×C22⋊C16C211yesmaximal, characteristic
4C2×#10587677—21no—
5C2×#10587536C412yescomplemented
6#11763780—21no—
7#11763685—21no—
8#11763683—21no—
9#11763683C412yes—
10C22×C8×D17C2211yescharacteristic
11C2×C16×D17—21no—
12C22⋊#63214C411yescharacteristic, complemented
13#11762588—21no—
14C17×C22⋊C16C411yescharacteristic, complemented
15C22×C4×D17D411yescharacteristic
16C2×C22⋊#595—41no—
17#10587677—24no—
18#10587677—42no—
19C2×C4⋊#595—22no—
20C2×C4×#595—41no—
21C2×#63243—22no—
22C22×C8×C17C2×C411yescharacteristic
23C22×#3622Q811yescharacteristic
24C2×C8×D17—42no—
25C2×C8×D17C2×C411yescharacteristic
26C2×C8×D17C2×C411yescharacteristic
27C2×C8×D17D411yescharacteristic
28C2×C8×D17D411yescharacteristic
29C22⋊#3624—41no—
30#10587543—41no—
31#10587536—42no—
32C2×C16×C17—21no—
33C2×#63214—21no—
34C16×D17—42no—
35C23×D17SD1611yescharacteristic
36C22×#595—42no—
37C22×C4×C17C4⋊C411yescharacteristic
38C22×Dic17SD1611yescharacteristic
39C2×C4×D17—22no—
40C2×C4×D17—22no—
41C2×C4×D17C22⋊C411yescharacteristic
42C2×C4×D17C22⋊C411yescharacteristic
43C2×C4×D17D811yescharacteristic
44C2×C4×D17Q1611yescharacteristic
45C22⋊#595—44no—
46C2×#3624—42no—
47C4⋊#595—24no—
48C4⋊#595—42no—
49C4×#595—44no—
50#63243—42no—
51#63243—42no—
52C2×C8×C17—41no—
53C2×C8×C17C4211yescharacteristic
54C2×C8×C17C22⋊C411yescharacteristic
55C2×#3622—41no—
56C2×#3622C4⋊C411yescharacteristic
57C2×#3622C4⋊C411yescharacteristic
58C8×D17—22no—
59C8×D17—22no—
60C8×D17—41no—
61C8×D17—41no—
62C16×C17—41no—
63#63214—41no—
64#7260—171nomaximal, Sylow
65C23×C17#10611yescharacteristic
66C22×D17—22no—
67C22×D17—22no—
68C22×D17—41no—
69C22×D17#10211yescharacteristic
70C22×D17#10311yescharacteristic
71C2×#595—44no—
72C2×#595—82no—
73C2×#595—82no—
74C2×C4×C17—21no—
75C2×C4×C17—21no—
76C2×C4×C17#9511yescharacteristic
77C2×C4×C17#10711yescharacteristic
78C2×Dic17—22no—
79C2×Dic17#10211yescharacteristic
80C2×Dic17#10311yescharacteristic
81C4×D17—22no—
82C4×D17—21no—
83C4×D17—21no—
84C4×D17—22no—
85C4×D17#9912yes—
86C4×D17#10412yes—
87#3624—82no—
88C8×C17—21no—
89C8×C17—21no—
90#3622—21no—
91#3622—21no—
92C2×C22⋊C16—171no—
93#1810—171no—
94#1735—171no—
95C22×C17—21no—
96C22×C17—21no—
97C22×C17—21no—
98C22×C17#34011yescharacteristic
99C2×D17—21no—
100C2×D17—21no—
101C2×D17—21no—
102C2×D17—21no—
103C2×D17—44no—
104C2×D17#32812yes—
105C2×D17#35912yes—
106#595—84no—
107C4×C17—21no—
108C4×C17#33911yescharacteristic
109C4×C17#34211yescharacteristic
110Dic17—21no—
111Dic17#32712yes—
112C23×C8—171no—
113C2×#117—341no—
114C22×C16—341no—
115C2×#108—172no—
116#407—341no—
117C22⋊C16—171no—
118C22⋊C16—341no—
119C22⋊C16#59511yescharacteristic, complemented
120#341—341no—
121#340—172no—
122#340—341no—
123C2×C17—41no—
124C2×C17#129411yescharacteristic
125C2×C17#138211yescharacteristic
126C2×C17#138911yescharacteristic
127D17—22no—
128D17—22no—
129C23×C4—171no—
130C2×M16—342no—
131C22×C8—171no—
132C22×C8—171no—
133C22×C8—171no—
134C22×C8—171no—
135C22×C8—171no—
136C22×C8—682no—
137C22×C8C2×#59511yescharacteristic
138#117—344no—
139#117—682no—
140C2×C4⋊C4—342no—
141C2×C22⋊C4—681no—
142C2×C42—681no—
143C2×C16—21no—
144C2×C16—341no—
145C2×C16—682no—
146#108—682no—
147C22⋊C8—681no—
148C22⋊C8—681no—
149C17#726011yescharacteristic, complemented, Sylow
150C24—171no—
151C22×C4—171no—
152C22×C4—171no—
153C22×C4—171no—
154C22×C4—171no—
155C22×C4—171no—
156C22×C4—342no—
157C22×C4—342no—
158C22×C4—682no—
159C22×C4C4⋊#59511yescharacteristic
160M16—682no—
161M16—682no—
162C2×C8—41no—
163C2×C8—171no—
164C2×C8—171no—
165C2×C8—342no—
166C2×C8—342no—
167C2×C8—681no—
168C2×C8—681no—
169C2×C8—681no—
170C2×C8—682no—
171C2×C8C4×#59511yescharacteristic
172C2×C8C22⋊#59511yescharacteristic
173C4⋊C4—344no—
174C4⋊C4—682no—
175C22⋊C4—684no—
176C42—684no—
177C16—41no—
178C16—681no—
179C23—171no—
180C23—171no—
181C23—342no—
182C23—342no—
183C23—681no—
184C23#1058753311yescharacteristic
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—171no—
188C2×C4—172no—
189C2×C4—172no—
190C2×C4—171no—
191C2×C4—342no—
192C2×C4—342no—
193C2×C4—342no—
194C2×C4—341no—
195C2×C4—341no—
196C2×C4—684no—
197C2×C4—1362no—
198C2×C4—1362no—
199C2×C4#1058753411yescharacteristic
200C2×C4(C2×#595)⋊C411yescharacteristic
201C8—21no—
202C8—21no—
203C8—341no—
204C8—341no—
205C8—1362no—
206C22—21no—
207C22—21no—
208C22—21no—
209C22—172no—
210C22—172no—
211C22—341no—
212C22—341no—
213C22—341no—
214C22—341no—
215C22—684no—
216C22#1176368311yescharacteristic
217C4—21no—
218C4—172no—
219C4—341no—
220C4—1364no—
221C4#1176368111yescharacteristic
222C4#1176368611yescharacteristic
223C2—41no—
224C2—342no—
225C2—342no—
226C2#1454365911yescharacteristic
227C2#1454384611yescharacteristic
228C2#1454386511yescharacteristic
subgroupG/H
centerC22#11763683
commutatorC2×C8×C17C42
FrattiniC22×C8C2×#595
FittingC17×C22⋊C16C4
socleC22×C17#340
prime radicalC23×D17SD16
cosocleC22×C8×D17C22
hypercenterC22⋊C16#595
hypocenterC17#7260
LCSG ▷ C2×C8×C17 ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C22⋊C16

Complements

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

NH ≅ G/Ntype
5. C2×#10587536C4semidirect
12. C22⋊#63214C4semidirect
14. C17×C22⋊C16C4semidirect
119. C22⋊C16#595semidirect
149. C17#7260semidirect

Maximal subgroups

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

subgroupindex
#145446642
#145444702
D17×C22⋊C162
#726017