Finite Group Databasebeta

← #17958197

Subgroups — #17958197

Order 4352.

462 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 112 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#14544015C212yesmaximal
2#14543726C212yesmaximal, complemented
3#14543724C212yesmaximal, complemented
4#14531191C211yesmaximal, characteristic
5#11763825—22no—
6#11763654C2214yes—
7#11763652—22no—
8C2×#10587612C411yescharacteristic
9C2×#10587612C2211yescharacteristic
10#11762679C411yescharacteristic
11#11762679C2211yescharacteristic
12#11762675C411yescharacteristic
13#11762675C2211yescharacteristic
14#11762669—22no—
15C4×C4⋊Dic17—22no—
16C22×C42×C17C411yescharacteristic
17C23×C4×C17—21no—
18C23×C4×C17C2×C411yescharacteristic
19C2×C42×C17—21no—
20C2×C42×C17—22no—
21C2×C42×C17C814yescomplemented
22C2×C42×C17C2×C411yescharacteristic
23C2×C42×C17C2×C411yescharacteristic
24C2×C22⋊Dic17—21no—
25C2×C22⋊Dic17D412yes—
26#10587612—41no—
27#10587612—41no—
28#10587612—41no—
29#10587612—41no—
30C2×C4⋊Dic17—22no—
31C2×C4⋊Dic17—22no—
32C2×C4⋊Dic17C2×C411yescharacteristic
33C2×C4⋊Dic17C2×C411yescharacteristic
34C2×C4⋊Dic17C2×C411yescharacteristic
35C2×C4⋊Dic17C2311yescharacteristic
36C2×C4×Dic17—21no—
37C2×C4×Dic17D412yes—
38C22⋊#3624—24no—
39C4⋊#3624—42no—
40C4×#3624—42no—
41#10587502—22no—
42#10587502—22no—
43C24×C17C22⋊C411yescharacteristic
44C22×C4×C17—21no—
45C22×C4×C17—21no—
46C22×C4×C17—21no—
47C22×C4×C17—22no—
48C22×C4×C17—24no—
49C22×C4×C17—21no—
50C22×C4×C17—42no—
51C22×C4×C17—42no—
52C22×C4×C17C22⋊C411yescharacteristic
53C22×C4×C17C2×C812yes—
54C22×C4×C17M1612yes—
55C22×C4×C17C22×C411yescharacteristic
56C22×Dic17—21no—
57C22×Dic17—21no—
58C22×Dic17C22⋊C412yes—
59C22×Dic17C2×D412yes—
60C2×#3624—44no—
61C42×C17—24no—
62C42×C17—21no—
63C42×C17—21no—
64C42×C17C2×C812yes—
65C42×C17C2×C812yes—
66C22⋊Dic17—42no—
67C22⋊Dic17—42no—
68C4⋊Dic17—41no—
69C4⋊Dic17—41no—
70C4⋊Dic17—44no—
71C4⋊Dic17—44no—
72C4⋊Dic17—41no—
73C4⋊Dic17—41no—
74C4×Dic17—22no—
75C4×Dic17—22no—
76C4×Dic17—41no—
77C4×Dic17—41no—
78#11447—171nomaximal, Sylow
79C23×C17—21no—
80C23×C17—21no—
81C23×C17—41no—
82C23×C17—41no—
83C23×C17C22⋊C812yes—
84C23×C17C2×C22⋊C411yescharacteristic
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—22no—
92C2×C4×C17—22no—
93C2×C4×C17—22no—
94C2×C4×C17—22no—
95C2×C4×C17—48no—
96C2×C4×C17—41no—
97C2×C4×C17—41no—
98C2×C4×C17C22⋊C812yes—
99C2×C4×C17#9911yescharacteristic
100C2×C4×C17#9911yescharacteristic
101C2×C4×C17#10112yes—
102C2×C4×C17C22×C811yescharacteristic
103C2×C4×C17C2×M1611yescharacteristic
104C2×Dic17—22no—
105C2×Dic17—22no—
106C2×Dic17—42no—
107C2×Dic17—42no—
108C2×Dic17—42no—
109C2×Dic17—42no—
110C2×Dic17—41no—
111C2×Dic17—41no—
112#3624—84no—
113#2285—171no—
114#1458—172no—
115#1325—172no—
116#1324—172no—
117C22×C17—21no—
118C22×C17—21no—
119C22×C17—22no—
120C22×C17—42no—
121C22×C17—42no—
122C22×C17—41no—
123C22×C17—41no—
124C22×C17C2×C22⋊C811yescharacteristic
125C22×C17C2×#9911yescharacteristic
126C22×C17C2×#10111yescharacteristic
127C4×C17—24no—
128C4×C17—21no—
129C4×C17—21no—
130C4×C17—42no—
131C4×C17#32412yes—
132C4×C17#32412yes—
133Dic17—42no—
134Dic17—42no—
135Dic17—81no—
136Dic17—81no—
137C2×#117—171no—
138C2×#117—171no—
139C22×C42#59511yescharacteristic
140#431—342no—
141#384—171no—
142#384—171no—
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×C17—42no—
152C2×C17C2×#32411yescharacteristic
153C2×C17#212611yescharacteristic
154C2×C17#213211yescharacteristic
155C23×C4—21no—
156C23×C4C2×#59511yescharacteristic
157#117—681no—
158#117—681no—
159#117—681no—
160#117—681no—
161C2×C4⋊C4—171no—
162C2×C4⋊C4—171no—
163C2×C4⋊C4—171no—
164C2×C4⋊C4—171no—
165C2×C4⋊C4—342no—
166C2×C4⋊C4—342no—
167C2×C22⋊C4—172no—
168C2×C22⋊C4—341no—
169C2×C42—22no—
170C2×C42—21no—
171C2×C42—172no—
172C2×C42—341no—
173C2×C42#362414yescomplemented
174C2×C42C2×#59511yescharacteristic
175C2×C42C2×#59511yescharacteristic
176C4⋊C8—682no—
177C22⋊C8—344no—
178C4×C8—682no—
179#95—342no—
180#95—342no—
181C17#1144711yescharacteristic, complemented, Sylow
182C24C22⋊#59511yescharacteristic
183C22×C4—21no—
184C22×C4—21no—
185C22×C4—21no—
186C22×C4—22no—
187C22×C4—21no—
188C22×C4—24no—
189C22×C4—42no—
190C22×C4—42no—
191C22×C4—172no—
192C22×C4—172no—
193C22×C4—341no—
194C22×C4—341no—
195C22×C4C2×#362412yes—
196C22×C4#6324712yes—
197C22×C4C22⋊#59511yescharacteristic
198C22×C4C22×#59511yescharacteristic
199C2×C8—684no—
200C4⋊C4—681no—
201C4⋊C4—681no—
202C4⋊C4—681no—
203C4⋊C4—681no—
204C4⋊C4—684no—
205C4⋊C4—684no—
206C22⋊C4—682no—
207C22⋊C4—682no—
208C42—21no—
209C42—21no—
210C42—24no—
211C42—342no—
212C42—342no—
213C42—681no—
214C42—681no—
215C42C2×#362412yes—
216C42C2×#362412yes—
217C23—21no—
218C23—21no—
219C23—41no—
220C23—41no—
221C23C22⋊#362412yes—
222C23C2×C22⋊#59511yescharacteristic
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—48no—
234C2×C4—41no—
235C2×C4—41no—
236C2×C4—342no—
237C2×C4—342no—
238C2×C4—682no—
239C2×C4—682no—
240C2×C4—682no—
241C2×C4—682no—
242C2×C4—681no—
243C2×C4—681no—
244C2×C4#1058753911yescharacteristic
245C2×C4#1058753911yescharacteristic
246C2×C4#1058754512yes—
247C2×C4C22⋊#362412yes—
248C2×C4C22×#362411yescharacteristic
249C2×C4C2×#6324711yescharacteristic
250C8—1364no—
251C22—21no—
252C22—21no—
253C22—22no—
254C22—42no—
255C22—42no—
256C22—41no—
257C22—41no—
258C22C2×C22⋊#362411yescharacteristic
259C22C2×#1058753911yescharacteristic
260C22C2×#1058754511yescharacteristic
261C4—24no—
262C4—21no—
263C4—21no—
264C4—42no—
265C4—682no—
266C4—682no—
267C4—1361no—
268C4—1361no—
269C4#1176365412yes—
270C4#1176365412yes—
271C2—21no—
272C2—21no—
273C2—42no—
274C2C2×#1176365411yescharacteristic
275C2#1454505711yescharacteristic
276C2#1454507711yescharacteristic
subgroupG/H
centerC2×C4#10587539
commutatorC2×C4×C17C22×C8
FrattiniC22×C4C22×#595
FittingC22×C42×C17C4
socleC22×C17C2×#99
prime radicalC24×C17C22⋊C4
cosocleC2×C4⋊Dic17C23
hypercenterC22×C42#595
hypocenterC17#11447
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C23×C4 ◁ C22×C42

Complements

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

NH ≅ G/Ntype
2. #14543726C2semidirect
3. #14543724C2semidirect
21. C2×C42×C17C8semidirect
173. C2×C42#3624semidirect
181. C17#11447semidirect

Maximal subgroups

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

subgroupindex
#145440152
#145437262
#145437242
#145311912
#1144717