Finite Group Databasebeta

← #17949911

Subgroups — #17949911

Order 4352.

520 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 98 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#14544569C212yesmaximal, complemented
2#14543605C212yesmaximal, complemented
3#14543601C212yesmaximal
4#14531323C211yesmaximal, characteristic
5C2×#10587544—22no—
6C2×#10587542—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#10587561—22no—
37#10587544—28no—
38#10587542—44no—
39C17×#95—22no—
40#10587502—22no—
41C23×D17—21no—
42C22×C4×C17—21no—
43C22×C4×C17—21no—
44C22×C4×C17C22⋊C412yes—
45C22×C4×C17C22×C411yescharacteristic
46C22×Dic17—21no—
47C22×Dic17C22⋊C411yescharacteristic
48C22×Dic17C22⋊C411yescharacteristic
49C22×Dic17C2×D412yes—
50C2×D68—21no—
51C2×D68—41no—
52C2×D68—41no—
53C2×D68M1612yes—
54C2×C4×D17—42no—
55C2×C4×D17—44no—
56C2×Dic34—21no—
57C2×Dic34—41no—
58C2×Dic34—41no—
59C2×Dic34M1612yes—
60C2×#3624—28no—
61C2×#3624—44no—
62C2×#3624—44no—
63C4⋊C4×C17—41no—
64C4⋊C4×C17—41no—
65C42×C17—21no—
66C42×C17—21no—
67#63227—28no—
68#63227—42no—
69#63227—42no—
70#63227—42no—
71#63225—42no—
72C4×Dic17—22no—
73C4×Dic17—24no—
74C4×Dic17—22no—
75C4×Dic17—22no—
76C4×Dic17—41no—
77C4×Dic17—42no—
78#7635—171nomaximal, Sylow
79C23×C17C2×C22⋊C411yescharacteristic
80C22×D17—22no—
81C22×D17—41no—
82C22×D17—41no—
83C22×D17—42no—
84C22×D17—42no—
85C2×C4×C17—21no—
86C2×C4×C17—21no—
87C2×C4×C17—22no—
88C2×C4×C17—22no—
89C2×C4×C17—22no—
90C2×C4×C17—41no—
91C2×C4×C17—41no—
92C2×C4×C17—42no—
93C2×C4×C17—42no—
94C2×C4×C17C2×M1611yescharacteristic
95C2×C4×C17C2×M1611yescharacteristic
96C2×Dic17—22no—
97C2×Dic17—22no—
98C2×Dic17—22no—
99C2×Dic17—21no—
100C2×Dic17—22no—
101C2×Dic17—41no—
102C2×Dic17—41no—
103C2×Dic17#10012yes—
104C2×Dic17#10414yes—
105C2×Dic17AGL(1,ℤ/8)12yes—
106C2×Dic17#13712yes—
107D68—42no—
108D68—42no—
109C4×D17—84no—
110Dic34—42no—
111Dic34—42no—
112#3624—48no—
113C4×#124—171no—
114#1767—172no—
115#1272—172no—
116#1270—172no—
117C22×C17#40711yescharacteristic
118C22×C17#41011yescharacteristic
119C22×C17C2×#10011yescharacteristic
120C22×C17#41712yes—
121C22×C17C2×#10412yes—
122C2×D17—42no—
123C2×D17—44no—
124C2×D17—81no—
125C2×D17—82no—
126C2×D17—81no—
127C4×C17—21no—
128C4×C17—21no—
129C4×C17—42no—
130C4×C17—81no—
131C4×C17—81no—
132Dic17—22no—
133Dic17—22no—
134Dic17—41no—
135Dic17—42no—
136Dic17#32914yes—
137C2×#124—171no—
138C2×C4×Q8—171no—
139C2×C4×D4—171no—
140C2×C4⋊C8—342no—
141C2×#97—342no—
142#391—171no—
143#390—171no—
144#388—342no—
145#382#59511yescharacteristic
146C4×C22⋊C4—342no—
147C43—171no—
148#336—174no—
149C2×C17#146611yescharacteristic
150C2×C17#148912yes—
151C2×C17#150912yes—
152C2×C17C2×#32911yescharacteristic
153C2×C17#156011yescharacteristic
154D17—82no—
155C22×Q8—171no—
156C22×D4—171no—
157C23×C4—341no—
158C22×C8—344no—
159#124—342no—
160#124—342no—
161C4×Q8—682no—
162C4×D4—682no—
163C2×C4⋊C4—341no—
164C2×C4⋊C4C2×#59511yescharacteristic
165C2×C4⋊C4C2×#59511yescharacteristic
166C2×C22⋊C4—342no—
167C2×C22⋊C4—341no—
168C2×C22⋊C4—342no—
169C2×C42—172no—
170C2×C42—172no—
171C2×C42—171no—
172C2×C42—171no—
173C2×C42—341no—
174C2×C42C2×#59511yescharacteristic
175C4⋊C8—348no—
176#97—684no—
177#95—22no—
178#95—342no—
179C17#763511yescharacteristic, complemented, Sylow
180C24—341no—
181C2×Q8—172no—
182C2×Q8—341no—
183C2×Q8—681no—
184C2×Q8—681no—
185C2×D4—172no—
186C2×D4—341no—
187C2×D4—681no—
188C2×D4—681no—
189C22×C4—21no—
190C22×C4—21no—
191C22×C4—171no—
192C22×C4—172no—
193C22×C4—171no—
194C22×C4—341no—
195C22×C4—682no—
196C22×C4—684no—
197C22×C4C22⋊#59512yes—
198C22×C4C22×#59511yescharacteristic
199C2×C8—348no—
200C2×C8—684no—
201C2×C8—684no—
202C4⋊C4—41no—
203C4⋊C4—41no—
204C4⋊C4—682no—
205C22⋊C4—348no—
206C22⋊C4—682no—
207C22⋊C4—682no—
208C22⋊C4—682no—
209C42—21no—
210C42—21no—
211C42—342no—
212C42—344no—
213C42—342no—
214C42—342no—
215C42—681no—
216C42—682no—
217C23—342no—
218C23—681no—
219C23—681no—
220C23—682no—
221C23—682no—
222C23C2×C22⋊#59511yescharacteristic
223Q8—682no—
224Q8—682no—
225D4—682no—
226D4—682no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—41no—
233C2×C4—41no—
234C2×C4—42no—
235C2×C4—42no—
236C2×C4—172no—
237C2×C4—174no—
238C2×C4—172no—
239C2×C4—172no—
240C2×C4—342no—
241C2×C4—342no—
242C2×C4—342no—
243C2×C4—341no—
244C2×C4—342no—
245C2×C4—681no—
246C2×C4—681no—
247C2×C4—1364no—
248C2×C4D17⋊M1611yescharacteristic
249C2×C4D17⋊M1611yescharacteristic
250C8—688no—
251C22—682no—
252C22—684no—
253C22—1362no—
254C22—1361no—
255C22—1361no—
256C22#1176378111yescharacteristic
257C22#1176379011yescharacteristic
258C22D17⋊#10011yescharacteristic
259C22#1176380012yes—
260C22D17⋊#10412yes—
261C4—21no—
262C4—21no—
263C4—42no—
264C4—81no—
265C4—81no—
266C4—174no—
267C4—342no—
268C4—342no—
269C4—682no—
270C4—681no—
271C2—1362no—
272C2#1454404511yescharacteristic
273C2#1454412112yes—
274C2#1454418712yes—
275C2D17⋊#32911yescharacteristic
276C2#1454432211yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC17×#382C4
socleC23×C17C2×C22⋊C4
prime radicalC22×D68C2×C4
cosocleC2×C4×Dic17C23
hypercenter#382#595
hypocenterC17#7635
LCSG ▷ C22×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. #14544569C2semidirect
2. #14543605C2semidirect
179. C17#7635semidirect

Maximal subgroups

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

subgroupindex
#145445692
#145436052
#145436012
#145313232
#763517