Finite Group Databasebeta

← #17958200

Subgroups — #17958200

Order 4352.

462 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 90 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#14544018C212yesmaximal
2#14543726C212yesmaximal, complemented
3#14543725C212yesmaximal, complemented
4#14531189C211yesmaximal, characteristic
5#11763826—22no—
6#11763654C2214yes—
7#11763653—22no—
8C2×#10587578C411yescharacteristic
9C2×#10587578C2211yescharacteristic
10C2×C42×D17C411yescharacteristic
11#11762679C2211yescharacteristic
12#11762674C411yescharacteristic
13#11762674C2211yescharacteristic
14#11762666—22no—
15C4⋊C4×Dic17—22no—
16C17×#384C411yescharacteristic
17C22×C4×D17—21no—
18C22×C4×D17C2×C411yescharacteristic
19C2×C4⋊C4×C17—22no—
20C2×C4⋊C4×C17C2×C411yescharacteristic
21C2×C4⋊C4×C17C2×C411yescharacteristic
22C2×C42×C17C2×C411yescharacteristic
23C2×#63227—21no—
24C2×#63227D412yes—
25C2×C4⋊Dic17—22no—
26C2×C4⋊Dic17C2×C411yescharacteristic
27C2×C4⋊Dic17C2311yescharacteristic
28C2×C4×Dic17—21no—
29C2×C4×Dic17—21no—
30C2×C4×Dic17C2×C411yescharacteristic
31C2×C4×Dic17D412yes—
32#10587578—41no—
33#10587578—41no—
34#10587578—41no—
35#10587578—41no—
36C42×D17—22no—
37C42×D17C814yescomplemented
38C22⋊#3624—24no—
39#10587544—42no—
40C4×#3624—42no—
41#10587502—22no—
42#10587502—22no—
43C23×D17C22⋊C411yescharacteristic
44C22×C4×C17—21no—
45C22×C4×C17—21no—
46C22×C4×C17C22⋊C412yes—
47C22×C4×C17C22×C411yescharacteristic
48C22×Dic17—21no—
49C22×Dic17—21no—
50C22×Dic17C22⋊C411yescharacteristic
51C22×Dic17C2×D412yes—
52C2×C4×D17—21no—
53C2×C4×D17—21no—
54C2×C4×D17—22no—
55C2×C4×D17—24no—
56C2×C4×D17—42no—
57C2×C4×D17—42no—
58C2×C4×D17C2×C812yes—
59C2×C4×D17M1612yes—
60C2×#3624—44no—
61C4⋊C4×C17—41no—
62C4⋊C4×C17—41no—
63C4⋊C4×C17—44no—
64C42×C17—21no—
65C42×C17C2×C812yes—
66#63227—42no—
67#63227—42no—
68C4⋊Dic17—41no—
69C4⋊Dic17—44no—
70C4⋊Dic17—41no—
71C4×Dic17—21no—
72C4×Dic17—24no—
73C4×Dic17—22no—
74C4×Dic17—22no—
75C4×Dic17—41no—
76C4×Dic17—41no—
77C4×Dic17C2×C812yes—
78#11447—171nomaximal, Sylow
79C23×C17C2×C22⋊C411yescharacteristic
80C22×D17—21no—
81C22×D17—21no—
82C22×D17—41no—
83C22×D17—41no—
84C22×D17C22⋊C812yes—
85C2×C4×C17—22no—
86C2×C4×C17—22no—
87C2×C4×C17—22no—
88C2×C4×C17—21no—
89C2×C4×C17—21no—
90C2×C4×C17—22no—
91C2×C4×C17—42no—
92C2×C4×C17—42no—
93C2×C4×C17—41no—
94C2×C4×C17C22×C811yescharacteristic
95C2×C4×C17C2×M1611yescharacteristic
96C2×Dic17—22no—
97C2×Dic17—22no—
98C2×Dic17—41no—
99C2×Dic17—41no—
100C2×Dic17—42no—
101C2×Dic17—42no—
102C2×Dic17—41no—
103C2×Dic17C22⋊C812yes—
104C2×Dic17#9911yescharacteristic
105C2×Dic17#9911yescharacteristic
106C2×Dic17#10112yes—
107C4×D17—22no—
108C4×D17—22no—
109C4×D17—22no—
110C4×D17—22no—
111C4×D17—48no—
112#3624—84no—
113#2285—171no—
114#1458—172no—
115#1325—172no—
116#1324—172no—
117C22×C17—21no—
118C22×C17—21no—
119C22×C17C2×C22⋊C811yescharacteristic
120C22×C17C2×#9911yescharacteristic
121C22×C17C2×#10111yescharacteristic
122C2×D17—22no—
123C2×D17—42no—
124C2×D17—41no—
125C2×D17—41no—
126C2×D17—42no—
127C4×C17—24no—
128C4×C17—21no—
129C4×C17—21no—
130C4×C17—42no—
131C4×C17—81no—
132Dic17—42no—
133Dic17—42no—
134Dic17—81no—
135Dic17#32412yes—
136Dic17#32412yes—
137C2×#117—171no—
138C2×#117—171no—
139C22×C42—171no—
140#431—342no—
141#384—171no—
142#384#59511yescharacteristic
143#382—171no—
144#382—171no—
145#380—342no—
146C4×C4⋊C4—342no—
147#324—174no—
148#323—342no—
149C2×C17—21no—
150C2×C17—21no—
151C2×C17C2×#32411yescharacteristic
152C2×C17#212611yescharacteristic
153C2×C17#213211yescharacteristic
154D17—42no—
155C23×C4—171no—
156C23×C4—341no—
157#117—681no—
158#117—681no—
159#117—681no—
160#117—681no—
161C2×C4⋊C4—22no—
162C2×C4⋊C4—171no—
163C2×C4⋊C4—171no—
164C2×C4⋊C4—342no—
165C2×C4⋊C4C2×#59511yescharacteristic
166C2×C4⋊C4C2×#59511yescharacteristic
167C2×C22⋊C4—172no—
168C2×C22⋊C4—341no—
169C2×C42—171no—
170C2×C42—174no—
171C2×C42—172no—
172C2×C42—342no—
173C2×C42—341no—
174C2×C42—341no—
175C2×C42C2×#59511yescharacteristic
176C4⋊C8—682no—
177C22⋊C8—344no—
178C4×C8—682no—
179#95—342no—
180#95—342no—
181C17#1144711yescharacteristic, complemented, Sylow
182C24—171no—
183C22×C4—21no—
184C22×C4—21no—
185C22×C4—171no—
186C22×C4—172no—
187C22×C4—172no—
188C22×C4—172no—
189C22×C4—341no—
190C22×C4—341no—
191C22×C4—342no—
192C22×C4—344no—
193C22×C4—341no—
194C22×C4—341no—
195C22×C4—682no—
196C22×C4—682no—
197C22×C4C22⋊#59512yes—
198C22×C4C22×#59511yescharacteristic
199C2×C8—684no—
200C4⋊C4—41no—
201C4⋊C4—41no—
202C4⋊C4—44no—
203C4⋊C4—681no—
204C4⋊C4—681no—
205C4⋊C4—684no—
206C22⋊C4—682no—
207C22⋊C4—682no—
208C42—21no—
209C42—172no—
210C42—342no—
211C42—342no—
212C42—344no—
213C42—341no—
214C42—681no—
215C42—681no—
216C42#6324212yes—
217C23—172no—
218C23—341no—
219C23—341no—
220C23—681no—
221C23—681no—
222C23C2×C22⋊#59511yescharacteristic
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—22no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4—41no—
232C2×C4—172no—
233C2×C4—171no—
234C2×C4—171no—
235C2×C4—172no—
236C2×C4—342no—
237C2×C4—342no—
238C2×C4—342no—
239C2×C4—342no—
240C2×C4—342no—
241C2×C4—342no—
242C2×C4—688no—
243C2×C4—681no—
244C2×C4—681no—
245C2×C4—682no—
246C2×C4—682no—
247C2×C4—681no—
248C2×C4C2×#6324211yescharacteristic
249C2×C4D17⋊M1611yescharacteristic
250C8—1364no—
251C22—21no—
252C22—21no—
253C22—342no—
254C22—682no—
255C22—682no—
256C22—681no—
257C22—681no—
258C22#1176377711yescharacteristic
259C22D17⋊#9911yescharacteristic
260C22D17⋊#10111yescharacteristic
261C4—24no—
262C4—21no—
263C4—21no—
264C4—42no—
265C4—81no—
266C4—172no—
267C4—172no—
268C4—682no—
269C4—682no—
270C4—1361no—
271C2—21no—
272C2—21no—
273C2—682no—
274C2#1454401311yescharacteristic
275C2#1454505811yescharacteristic
276C2#1454507611yescharacteristic
subgroupG/H
centerC22D17⋊#99
commutatorC2×C4×C17C22×C8
FrattiniC22×C4C22×#595
FittingC17×#384C4
socleC22×C17C2×#99
prime radicalC23×D17C22⋊C4
cosocleC2×C4⋊Dic17C23
hypercenter#384#595
hypocenterC17#11447
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #384

Complements

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

NH ≅ G/Ntype
2. #14543726C2semidirect
3. #14543725C2semidirect
37. C42×D17C8semidirect
181. C17#11447semidirect

Maximal subgroups

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

subgroupindex
#145440182
#145437262
#145437252
#145311892
#1144717