Finite Group Databasebeta

← #17949671

Subgroups — #17949671

Order 4352.

528 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 118 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#14544498C212yesmaximal, complemented
2#14543605C212yesmaximal, complemented
3#14543601C212yesmaximal
4#14531323C211yesmaximal, characteristic
5C2×C4×#3624—22no—
6#11763675—22no—
7#11763675C2214yes—
8C2×#10587561C411yescharacteristic
9C2×#10587573C411yescharacteristic
10C2×#10587579C411yescharacteristic
11#11762714C2211yescharacteristic
12#11762710C2211yescharacteristic
13#11762698—22no—
14#11762656—22no—
15C42×Dic17C2211yescharacteristic
16C17×#382C411yescharacteristic
17C22×D68C2×C411yescharacteristic
18C22×C4×D17—21no—
19C22×Dic34C2×C411yescharacteristic
20C22×#3624—24no—
21C2×C4⋊C4×C17C2×C411yescharacteristic
22C2×C4⋊C4×C17C2×C411yescharacteristic
23C2×C42×C17C2×C411yescharacteristic
24C2×#63227—22no—
25C2×#63227—21no—
26C2×#63227—22no—
27C2×#63225—21no—
28C2×C4×Dic17—21no—
29C2×C4×Dic17C2×C411yescharacteristic
30C2×C4×Dic17D412yes—
31C2×C4×Dic17D412yes—
32C2×C4×Dic17C2311yescharacteristic
33#10587579—42no—
34#10587573—42no—
35#10587561—22no—
36#10587561C814yescomplemented
37C4×#3624—28no—
38C17×#95—22no—
39#10587502—22no—
40C23×D17—21no—
41C22×C4×C17—21no—
42C22×C4×C17—21no—
43C22×C4×C17C22⋊C412yes—
44C22×C4×C17C22×C411yescharacteristic
45C22×Dic17—21no—
46C22×Dic17C22⋊C411yescharacteristic
47C22×Dic17C22⋊C411yescharacteristic
48C22×Dic17C2×D412yes—
49C2×D68—21no—
50C2×D68—41no—
51C2×D68—41no—
52C2×D68C2×C812yes—
53C2×C4×D17—42no—
54C2×C4×D17—44no—
55C2×Dic34—21no—
56C2×Dic34—41no—
57C2×Dic34—41no—
58C2×Dic34C2×C812yes—
59C2×#3624—28no—
60C2×#3624—44no—
61C2×#3624—44no—
62C4⋊C4×C17—41no—
63C4⋊C4×C17—41no—
64C42×C17C2×C812yes—
65C42×C17M1612yes—
66#63227—28no—
67#63227—42no—
68#63227—44no—
69#63225—42no—
70C4×Dic17—22no—
71C4×Dic17—24no—
72C4×Dic17—24no—
73C4×Dic17—41no—
74C4×Dic17—42no—
75#7567—171nomaximal, Sylow
76C23×C17C2×C22⋊C411yescharacteristic
77C22×D17—22no—
78C22×D17—41no—
79C22×D17—41no—
80C22×D17—42no—
81C22×D17—42no—
82C2×C4×C17—21no—
83C2×C4×C17—21no—
84C2×C4×C17—22no—
85C2×C4×C17—22no—
86C2×C4×C17—41no—
87C2×C4×C17—41no—
88C2×C4×C17—42no—
89C2×C4×C17—42no—
90C2×C4×C17C22⋊C814yes—
91C2×C4×C17C22×C811yescharacteristic
92C2×C4×C17C2×M1611yescharacteristic
93C2×Dic17—22no—
94C2×Dic17—22no—
95C2×Dic17—22no—
96C2×Dic17—21no—
97C2×Dic17—22no—
98C2×Dic17—41no—
99C2×Dic17—41no—
100C2×Dic17#10012yes—
101C2×Dic17#10414yes—
102C2×Dic17#13514yes—
103D68—42no—
104D68—42no—
105C4×D17—84no—
106Dic34—42no—
107Dic34—42no—
108#3624—48no—
109C4×#124—171no—
110#1744—172no—
111#1272—172no—
112#1270—172no—
113C22×C17C2×C22⋊C811yescharacteristic
114C22×C17#41011yescharacteristic
115C22×C17C2×#10011yescharacteristic
116C22×C17#41612yes—
117C22×C17C2×#10412yes—
118C2×D17—42no—
119C2×D17—44no—
120C2×D17—81no—
121C2×D17—82no—
122C2×D17—81no—
123C4×C17—21no—
124C4×C17—21no—
125C4×C17—24no—
126C4×C17—81no—
127C4×C17—81no—
128Dic17—24no—
129Dic17—41no—
130Dic17—42no—
131Dic17#32914yes—
132C2×#124—171no—
133C2×C4×Q8—171no—
134C2×C4×D4—171no—
135C2×C4×C8—342no—
136#391—171no—
137#390—171no—
138#388—342no—
139#382#59511yescharacteristic
140C4×C22⋊C4—342no—
141C43—171no—
142#336—174no—
143#336—342no—
144C2×C17#146011yescharacteristic
145C2×C17#147612yes—
146C2×C17#150012yes—
147C2×C17C2×#32911yescharacteristic
148C2×C17#154311yescharacteristic
149D17—82no—
150C22×Q8—171no—
151C22×D4—171no—
152C23×C4—341no—
153C22×C8—344no—
154#124—174no—
155#124—342no—
156C4×Q8—682no—
157C4×D4—682no—
158C2×C4⋊C4—341no—
159C2×C4⋊C4C2×#59511yescharacteristic
160C2×C4⋊C4C2×#59511yescharacteristic
161C2×C22⋊C4—342no—
162C2×C22⋊C4—341no—
163C2×C22⋊C4—342no—
164C2×C42—172no—
165C2×C42—172no—
166C2×C42—171no—
167C2×C42—171no—
168C2×C42—341no—
169C2×C42C2×#59511yescharacteristic
170C4×C8—348no—
171#95—22no—
172#95—342no—
173C17#756711yescharacteristic, complemented, Sylow
174C24—341no—
175C2×Q8—172no—
176C2×Q8—341no—
177C2×Q8—681no—
178C2×Q8—681no—
179C2×D4—172no—
180C2×D4—341no—
181C2×D4—681no—
182C2×D4—681no—
183C22×C4—21no—
184C22×C4—21no—
185C22×C4—171no—
186C22×C4—172no—
187C22×C4—171no—
188C22×C4—341no—
189C22×C4—682no—
190C22×C4—684no—
191C22×C4C22⋊#59512yes—
192C22×C4C22×#59511yescharacteristic
193C2×C8—348no—
194C2×C8—684no—
195C2×C8—684no—
196C4⋊C4—41no—
197C4⋊C4—41no—
198C4⋊C4—682no—
199C22⋊C4—348no—
200C22⋊C4—684no—
201C22⋊C4—682no—
202C42—344no—
203C42—342no—
204C42—344no—
205C42—681no—
206C42—682no—
207C42#6324212yes—
208C42#6324312yes—
209C23—342no—
210C23—681no—
211C23—681no—
212C23—682no—
213C23—682no—
214C23C2×C22⋊#59511yescharacteristic
215Q8—682no—
216Q8—682no—
217D4—682no—
218D4—682no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—41no—
224C2×C4—41no—
225C2×C4—42no—
226C2×C4—42no—
227C2×C4—172no—
228C2×C4—174no—
229C2×C4—174no—
230C2×C4—342no—
231C2×C4—342no—
232C2×C4—342no—
233C2×C4—341no—
234C2×C4—342no—
235C2×C4—681no—
236C2×C4—681no—
237C2×C4—1364no—
238C2×C4#1058754314yes—
239C2×C4C2×#6324211yescharacteristic
240C2×C4C2×#6324311yescharacteristic
241C8—688no—
242C22—682no—
243C22—684no—
244C22—1362no—
245C22—1361no—
246C22—1361no—
247C22C2×#1058754311yescharacteristic
248C22#1176379011yescharacteristic
249C22D17⋊#10011yescharacteristic
250C22#1176379912yes—
251C22D17⋊#10412yes—
252C4—21no—
253C4—21no—
254C4—24no—
255C4—81no—
256C4—81no—
257C4—174no—
258C4—344no—
259C4—682no—
260C4—681no—
261C2—1362no—
262C2#1454402511yescharacteristic
263C2#1454407712yes—
264C2#1454415812yes—
265C2D17⋊#32911yescharacteristic
266C2#1454428811yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutatorC2×C4×C17C22×C8
FrattiniC22×C4C22×#595
FittingC17×#382C4
socleC23×C17C2×C22⋊C4
prime radicalC22×D68C2×C4
cosocleC2×C4×Dic17C23
hypercenter#382#595
hypocenterC17#7567
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #382

Complements

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

NH ≅ G/Ntype
1. #14544498C2semidirect
2. #14543605C2semidirect
36. #10587561C8semidirect
173. C17#7567semidirect

Maximal subgroups

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

subgroupindex
#145444982
#145436052
#145436012
#145313232
#756717