Finite Group Databasebeta

← #17948900

Subgroups — #17948900

Order 4352.

352 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 352 conjugacy classes of subgroups — too many to draw. Only its 70 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#14545012C211yesmaximal, characteristic
2#14544660C211yesmaximal, characteristic
3#14528499C211yesmaximal, characteristic
4C2×#10587530—21no—
5C2×#10587533C412yescomplemented
6#11763751—21no—
7#11763704C412yescomplemented
8C22⋊#63216—21no—
9#11763683—21no—
10C22×C8×D17C2211yescharacteristic
11C2×#10587578—21no—
12#11762572C411yescharacteristic, complemented
13#11762571—21no—
14C17×#340C411yescharacteristic, complemented
15C22×C4×D17D411yescharacteristic
16C2×C22⋊#595—41no—
17C2×C4⋊#595—22no—
18C22×C8×C17C2×C411yescharacteristic
19C2×C4⋊C4×C17—21no—
20C2×#63227—41no—
21C2×C4⋊Dic17—21no—
22C2×C4×Dic17—41no—
23C22×#3622D411yescharacteristic
24C2×C8×D17—42no—
25C2×C8×D17C2×C411yescharacteristic
26C2×C8×D17C2×C411yescharacteristic
27C2×C8×D17D411yescharacteristic
28C2×C8×D17Q811yescharacteristic
29#10587578—24no—
30#10587578—42no—
31(C2×#595)⋊C4—41no—
32C2×#63216—22no—
33#10587533—42no—
34#10587530—42no—
35C23×D17D811yescharacteristic
36C22×#595—42no—
37C22×C4×C17—41no—
38C22×C4×C17C22⋊C411yescharacteristic
39C22×Dic17—41no—
40C22×Dic17SD1611yescharacteristic
41C2×C4×D17—22no—
42C2×C4×D17—22no—
43C2×C4×D17C22⋊C411yescharacteristic
44C2×C4×D17C4⋊C411yescharacteristic
45C2×C4×D17SD1611yescharacteristic
46C2×C4×D17Q1611yescharacteristic
47C22⋊#595—81no—
48C22⋊#595—81no—
49C4⋊#595—42no—
50C4⋊#595—42no—
51C2×C8×C17—41no—
52C2×C8×C17C4211yescharacteristic
53C2×C8×C17C4⋊C411yescharacteristic
54C4⋊C4×C17—22no—
55C4⋊C4×C17—41no—
56#63227—44no—
57C4⋊Dic17—22no—
58C4⋊Dic17—41no—
59C4×Dic17—44no—
60C2×#3622—41no—
61C2×#3622C22⋊C411yescharacteristic
62C2×#3622C4⋊C411yescharacteristic
63C8×D17—22no—
64C8×D17—22no—
65C8×D17—41no—
66C8×D17—41no—
67#63216—42no—
68#7262—171nomaximal, Sylow
69C23×C17#10211yescharacteristic
70C22×D17—21no—
71C22×D17—21no—
72C22×D17—22no—
73C22×D17—41no—
74C22×D17#10211yescharacteristic
75C22×D17#10711yescharacteristic
76C2×#595—82no—
77C2×#595—82no—
78C2×#595—82no—
79C2×C4×C17—21no—
80C2×C4×C17—21no—
81C2×C4×C17—42no—
82C2×C4×C17—81no—
83C2×C4×C17—81no—
84C2×C4×C17#9511yescharacteristic
85C2×C4×C17#10311yescharacteristic
86C2×Dic17—22no—
87C2×Dic17—42no—
88C2×Dic17—81no—
89C2×Dic17—81no—
90C2×Dic17#10311yescharacteristic
91C2×Dic17#10611yescharacteristic
92C4×D17—22no—
93C4×D17—21no—
94C4×D17—21no—
95C4×D17—22no—
96C4×D17#9912yes—
97C4×D17#10412yes—
98C8×C17—21no—
99C8×C17—21no—
100#3622—21no—
101#3622—21no—
102#2112—171no—
103#1807—171no—
104#1735—171no—
105C22×C17—21no—
106C22×C17—21no—
107C22×C17#34011yescharacteristic
108C22×C17#36011yescharacteristic
109C22×C17#36011yescharacteristic
110C2×D17—21no—
111C2×D17—21no—
112C2×D17—21no—
113C2×D17—21no—
114C2×D17—21no—
115C2×D17—42no—
116C2×D17—42no—
117C2×D17#32712yes—
118#595—162no—
119C4×C17—21no—
120C4×C17—82no—
121C4×C17#33911yescharacteristic
122C4×C17#34211yescharacteristic
123Dic17—21no—
124Dic17—82no—
125Dic17#32812yes—
126C23×C8—171no—
127C2×#117—341no—
128C2×M32—341no—
129C2×#106—172no—
130#380—341no—
131C22⋊C16—172no—
132C22⋊C16—341no—
133#340—171no—
134#340—341no—
135#340—341no—
136#340#59511yescharacteristic, complemented
137C2×C17—21no—
138C2×C17—21no—
139C2×C17#129411yescharacteristic
140C2×C17#138411yescharacteristic
141C2×C17#138611yescharacteristic
142D17—22no—
143D17—41no—
144C23×C4—171no—
145C22×C8—171no—
146C22×C8—171no—
147C22×C8—171no—
148C22×C8—171no—
149C22×C8—171no—
150C22×C8—682no—
151C22×C8C2×#59511yescharacteristic
152#117—344no—
153#117—682no—
154C2×C4⋊C4—21no—
155C2×C4⋊C4—341no—
156C2×C4⋊C4—342no—
157C2×C22⋊C4—681no—
158C2×C22⋊C4—681no—
159C2×C42—681no—
160M32—682no—
161C2×C16—342no—
162#106—682no—
163#95—681no—
164C17#726211yescharacteristic, complemented, Sylow
165C24—171no—
166C22×C4—41no—
167C22×C4—171no—
168C22×C4—171no—
169C22×C4—171no—
170C22×C4—171no—
171C22×C4—171no—
172C22×C4—342no—
173C22×C4—342no—
174C22×C4—681no—
175C22×C4—682no—
176C22×C4C22⋊#59511yescharacteristic
177C2×C8—41no—
178C2×C8—171no—
179C2×C8—171no—
180C2×C8—342no—
181C2×C8—342no—
182C2×C8—681no—
183C2×C8—681no—
184C2×C8—681no—
185C2×C8C4×#59511yescharacteristic
186C2×C8C4⋊#59511yescharacteristic
187C4⋊C4—22no—
188C4⋊C4—41no—
189C4⋊C4—342no—
190C4⋊C4—681no—
191C4⋊C4—682no—
192C4⋊C4—682no—
193C22⋊C4—684no—
194C22⋊C4—1361no—
195C22⋊C4—1361no—
196C42—684no—
197C16—682no—
198C23—171no—
199C23—171no—
200C23—342no—
201C23—341no—
202C23—341no—
203C23—681no—
204C23#1058754711yescharacteristic
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—42no—
208C2×C4—81no—
209C2×C4—81no—
210C2×C4—171no—
211C2×C4—172no—
212C2×C4—172no—
213C2×C4—171no—
214C2×C4—342no—
215C2×C4—342no—
216C2×C4—342no—
217C2×C4—341no—
218C2×C4—341no—
219C2×C4—682no—
220C2×C4—1362no—
221C2×C4—1362no—
222C2×C4—1362no—
223C2×C4—1361no—
224C2×C4—1361no—
225C2×C4(C2×#595)⋊C411yescharacteristic
226C2×C4#1058754911yescharacteristic
227C8—21no—
228C8—21no—
229C8—341no—
230C8—341no—
231C22—21no—
232C22—21no—
233C22—172no—
234C22—341no—
235C22—341no—
236C22—341no—
237C22—341no—
238C22—341no—
239C22—682no—
240C22—682no—
241C22#1176368211yescharacteristic
242C22#1176372511yescharacteristic
243C22#1176372611yescharacteristic
244C4—21no—
245C4—82no—
246C4—2722no—
247C4—172no—
248C4—341no—
249C4—1362no—
250C4#1176368011yescharacteristic
251C4#1176368611yescharacteristic
252C2—21no—
253C2—21no—
254C2—342no—
255C2—681no—
256C2#1454365811yescharacteristic
257C2#1454385111yescharacteristic
258C2#1454385511yescharacteristic
subgroupG/H
centerC22#11763682
commutatorC2×C8×C17C42
FrattiniC22×C8C2×#595
FittingC17×#340C4
socleC22×C17#340
prime radicalC23×D17D8
cosocleC22×C8×D17C22
hypercenter#340#595
hypocenterC17#7262
LCSG ▷ C2×C8×C17 ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #340

Complements

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

NH ≅ G/Ntype
5. C2×#10587533C4semidirect
7. #11763704C4semidirect
12. #11762572C4semidirect
14. C17×#340C4semidirect
136. #340#595semidirect
164. C17#7262semidirect

Maximal subgroups

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

subgroupindex
#145450122
#145446602
#145284992
#726217