Finite Group Databasebeta

← #17962663

Subgroups — #17962663

Order 4352.

416 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 60 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#14545057C212yesmaximal, complemented
2#14543918C212yesmaximal, complemented
3#14543916C212yesmaximal, complemented
4#14539212C211yesmaximal, characteristic
5#11763788—22no—
6#11763716—22no—
7#11763714C2214yes—
8C2×#10587590—22no—
9#11763359C411yescharacteristic, complemented
10#11763359C2211yescharacteristic
11#11763193—22no—
12#11763189C411yescharacteristic, complemented
13#11763186C2211yescharacteristic
14#11763182C411yescharacteristic, complemented
15#11763182C2211yescharacteristic
16C2×C4×C8×C17C411yescharacteristic, complemented
17C2×#63252—21no—
18C2×#63252D412yes—
19#10587677—42no—
20C22×C8×C17—21no—
21C2×C42×C17C2×C411yescharacteristic
22#10587616—41no—
23#10587616—41no—
24C2×Dic68—22no—
25#10587590—44no—
26#10587590—44no—
27C2×D136—22no—
28C2×#63219—22no—
29C2×#63219—22no—
30#10587561—21no—
31#10587561D412yes—
32#10587560C2×C411yescharacteristic
33#10587560C2311yescharacteristic
34C4×D68—41no—
35C4×D68—41no—
36#10587555C2×C411yescharacteristic
37#10587555C2×C411yescharacteristic
38#10587551—42no—
39#10587539—24no—
40C4×C8×C17—21no—
41C4×C8×C17C2×C411yescharacteristic
42C4×C8×C17C2×C411yescharacteristic
43C22×C4×C17—21no—
44C22×C4×C17C22⋊C411yescharacteristic
45C2×C22⋊D17—22no—
46C2×C22⋊D17—41no—
47#63252—42no—
48#63252—42no—
49#63252—42no—
50#63252—42no—
51C2×D68—21no—
52C2×D68—41no—
53C2×D68—41no—
54C2×D68C2×D412yes—
55C2×C4×D17—22no—
56C2×C4×D17—41no—
57C2×Dic34—21no—
58C2×Dic34C22⋊C412yes—
59C22⋊#595—44no—
60C4⋊#595—82no—
61C4×#595—82no—
62C2×C8×C17—22no—
63C2×C8×C17—22no—
64C2×C8×C17—21no—
65C2×C8×C17—21no—
66C42×C17—21no—
67C42×C17C22⋊C411yescharacteristic
68C42×C17C22×C411yescharacteristic
69#63227—42no—
70#63227—42no—
71C4⋊Dic17—41no—
72C4⋊Dic17—41no—
73Dic68—44no—
74D136—44no—
75#63219—44no—
76#63219—44no—
77#13583—171nomaximal, Sylow
78C23×C17#9911yescharacteristic
79C22×D17—22no—
80C22×D17—41no—
81C2×#595—84no—
82C2×C4×C17—21no—
83C2×C4×C17—21no—
84C2×C4×C17—21no—
85C2×C4×C17—21no—
86C2×C4×C17—42no—
87C2×C4×C17#9911yescharacteristic
88C2×C4×C17C2×C22⋊C411yescharacteristic
89C22⋊D17—82no—
90C22⋊D17—82no—
91C2×Dic17—22no—
92C2×Dic17—41no—
93D68—42no—
94D68—42no—
95D68—82no—
96D68—82no—
97C4×D17—42no—
98C4×D17—42no—
99C4×D17—81no—
100C4×D17—81no—
101Dic34—42no—
102Dic34—42no—
103C8×C17—22no—
104C8×C17—22no—
105#3147—171no—
106#2126—172no—
107#1409—172no—
108#1408—172no—
109C22×C17—21no—
110C22×C17—41no—
111C22×C17C2×#9911yescharacteristic
112C2×D17—42no—
113C2×D17—82no—
114C2×D17—82no—
115C2×D17—81no—
116#595—164no—
117C4×C17—22no—
118C4×C17—21no—
119C4×C17—41no—
120C4×C17#35311yescharacteristic
121C4×C17#35311yescharacteristic
122Dic17—42no—
123Dic17—81no—
124C2×#135—342no—
125#532—171no—
126#532—171no—
127#495—342no—
128#494—171no—
129#493—171no—
130#492—171no—
131#492—171no—
132#410—342no—
133C2×C4×C8#59511yescharacteristic, complemented
134#354—342no—
135#353—174no—
136C2×C17—21no—
137C2×C17—41no—
138C2×C17C2×#35311yescharacteristic
139D17—82no—
140D17—161no—
141C2×#41—172no—
142C2×#41—341no—
143#135—684no—
144#135—684no—
145C2×Q16—342no—
146C2×SD16—342no—
147C2×SD16—342no—
148C2×D8—342no—
149C22×C8—21no—
150C4⋊Q8—171no—
151C4⋊Q8—171no—
152#127—171no—
153#127—171no—
154#124—172no—
155#124—341no—
156#121—681no—
157#121—681no—
158C4×D4—681no—
159C4×D4—681no—
160#117—682no—
161C2×C42C2×#59511yescharacteristic
162#99—344no—
163#99—682no—
164C4×C8—21no—
165C4×C8C2×#59511yescharacteristic
166C4×C8C2×#59511yescharacteristic
167C17#1358311yescharacteristic, complemented, Sylow
168#41—682no—
169#41—682no—
170#41—682no—
171#41—682no—
172C2×Q8—172no—
173C2×Q8—341no—
174C2×D4—172no—
175C2×D4—342no—
176C2×D4—341no—
177C2×D4—681no—
178C2×D4—681no—
179C2×D4—681no—
180C22×C4—21no—
181C22×C4—342no—
182C22×C4—681no—
183C22×C4C22⋊#59511yescharacteristic
184Q16—684no—
185SD16—684no—
186SD16—684no—
187D8—684no—
188C2×C8—22no—
189C2×C8—22no—
190C2×C8—21no—
191C2×C8—21no—
192C4⋊C4—681no—
193C4⋊C4—681no—
194C4⋊C4—1362no—
195C22⋊C4—682no—
196C22⋊C4—682no—
197C22⋊C4—684no—
198C42—21no—
199C42—1362no—
200C42C22⋊#59511yescharacteristic
201C42C22×#59511yescharacteristic
202C23—342no—
203C23—681no—
204C23#1058753911yescharacteristic
205Q8—682no—
206Q8—682no—
207D4—682no—
208D4—682no—
209D4—1362no—
210D4—1362no—
211D4—1362no—
212D4—1362no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—42no—
218C2×C4—342no—
219C2×C4—682no—
220C2×C4—682no—
221C2×C4—681no—
222C2×C4—1364no—
223C2×C4—1361no—
224C2×C4—1361no—
225C2×C4#1058753911yescharacteristic
226C2×C4C2×C22⋊#59511yescharacteristic
227C8—22no—
228C8—22no—
229C22—21no—
230C22—41no—
231C22—682no—
232C22—1362no—
233C22—1362no—
234C22—1361no—
235C22C2×#1058753911yescharacteristic
236C4—22no—
237C4—21no—
238C4—41no—
239C4—2724no—
240C4—682no—
241C4—1361no—
242C4#1176371411yescharacteristic
243C4#1176371411yescharacteristic
244C2—21no—
245C2—41no—
246C2—2721no—
247C2—1362no—
248C2C2×#1176371411yescharacteristic
subgroupG/H
centerC4#11763714
commutatorC42×C17C22×C4
FrattiniC42C22×#595
FittingC2×C4×C8×C17C4
socleC2×C17C2×#353
prime radical#14539212C2
cosocle#10587560C23
hypercenterC2×C4×C8#595
hypocenterC17#13583
LCSG ▷ C42×C17 ▷ C2×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×C8

Complements

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

NH ≅ G/Ntype
1. #14545057C2semidirect
2. #14543918C2semidirect
3. #14543916C2semidirect
9. #11763359C4semidirect
12. #11763189C4semidirect
14. #11763182C4semidirect
16. C2×C4×C8×C17C4semidirect
133. C2×C4×C8#595semidirect
167. C17#13583semidirect

Maximal subgroups

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

subgroupindex
#145450572
#145439182
#145439162
#145392122
#1358317