Finite Group Databasebeta

← #17958199

Subgroups — #17958199

Order 4352.

462 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 104 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#14543727C212yesmaximal, complemented
3#14543725C212yesmaximal, complemented
4#14531187C211yesmaximal, characteristic
5#11763825—22no—
6#11763654C2214yes—
7#11763652—22no—
8C2×#10587612C2211yescharacteristic
9C22×C4×Dic17C411yescharacteristic
10#11762678C411yescharacteristic
11#11762678C2211yescharacteristic
12#11762674C411yescharacteristic
13#11762674C2211yescharacteristic
14#11762667—22no—
15C4×#63225—22no—
16C2×C17×#117C411yescharacteristic
17C23×C4×C17C2×C411yescharacteristic
18C23×Dic17—21no—
19C17×#117—41no—
20C17×#117—41no—
21C2×C4⋊C4×C17C2×C411yescharacteristic
22C2×C4⋊C4×C17C2×C411yescharacteristic
23C2×C22⋊C4×C17—21no—
24C2×C42×C17—21no—
25C2×C22⋊Dic17D412yes—
26#10587612—41no—
27#10587612—41no—
28C2×C4⋊Dic17C2×C411yescharacteristic
29C2×C4⋊Dic17C2311yescharacteristic
30C2×#63225—22no—
31C2×#63225—22no—
32C2×C4×Dic17—21no—
33C2×C4×Dic17—22no—
34C2×C4×Dic17C814yescomplemented
35C2×C4×Dic17C2×C411yescharacteristic
36C2×C4×Dic17C2×C411yescharacteristic
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—22no—
47C22×C4×C17—21no—
48C22×C4×C17—21no—
49C22×C4×C17C22⋊C411yescharacteristic
50C22×C4×C17C2×C812yes—
51C22×C4×C17M1612yes—
52C22×C4×C17C22×C411yescharacteristic
53C22×Dic17—21no—
54C22×Dic17—24no—
55C22×Dic17—21no—
56C22×Dic17—42no—
57C22×Dic17—42no—
58C22×Dic17C22⋊C412yes—
59C22×Dic17C2×D412yes—
60C2×#3624—44no—
61C4⋊C4×C17—41no—
62C4⋊C4×C17—41no—
63C22⋊C4×C17—42no—
64C42×C17—41no—
65C42×C17—41no—
66C22⋊Dic17—42no—
67C4⋊Dic17—41no—
68C4⋊Dic17—41no—
69#63225—44no—
70#63225—44no—
71C4×Dic17—24no—
72C4×Dic17—22no—
73C4×Dic17—22no—
74C4×Dic17—21no—
75C4×Dic17—21no—
76C4×Dic17C2×C812yes—
77C4×Dic17C2×C812yes—
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—21no—
86C2×C4×C17—21no—
87C2×C4×C17—22no—
88C2×C4×C17—22no—
89C2×C4×C17—22no—
90C2×C4×C17—22no—
91C2×C4×C17—42no—
92C2×C4×C17—42no—
93C2×C4×C17—41no—
94C2×C4×C17—41no—
95C2×C4×C17C22⋊C812yes—
96C2×C4×C17#9911yescharacteristic
97C2×C4×C17#9911yescharacteristic
98C2×C4×C17#10112yes—
99C2×C4×C17C22×C811yescharacteristic
100C2×C4×C17C2×M1611yescharacteristic
101C2×Dic17—22no—
102C2×Dic17—22no—
103C2×Dic17—22no—
104C2×Dic17—22no—
105C2×Dic17—22no—
106C2×Dic17—22no—
107C2×Dic17—48no—
108C2×Dic17—41no—
109C2×Dic17—41no—
110C2×Dic17—42no—
111C2×Dic17—42no—
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—21no—
128C4×C17—21no—
129C4×C17—81no—
130C4×C17—81no—
131C4×C17#32412yes—
132C4×C17#32412yes—
133Dic17—24no—
134Dic17—42no—
135Dic17—42no—
136Dic17—42no—
137C2×#117—171no—
138C2×#117#59511yescharacteristic
139C22×C42—171no—
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—341no—
156C23×C4C2×#59511yescharacteristic
157#117—41no—
158#117—41no—
159#117—681no—
160#117—681no—
161C2×C4⋊C4—171no—
162C2×C4⋊C4—171no—
163C2×C4⋊C4—342no—
164C2×C4⋊C4—342no—
165C2×C4⋊C4C2×#59511yescharacteristic
166C2×C4⋊C4C2×#59511yescharacteristic
167C2×C22⋊C4—21no—
168C2×C22⋊C4—172no—
169C2×C42—21no—
170C2×C42—174no—
171C2×C42—171no—
172C2×C42—171no—
173C2×C42—172no—
174C2×C42—342no—
175C2×C42—341no—
176C4⋊C8—682no—
177C22⋊C8—344no—
178C4×C8—682no—
179#95—342no—
180#95—342no—
181C17#1144711yescharacteristic, complemented, Sylow
182C24C22⋊#59511yescharacteristic
183C22×C4—22no—
184C22×C4—21no—
185C22×C4—21no—
186C22×C4—21no—
187C22×C4—21no—
188C22×C4—172no—
189C22×C4—172no—
190C22×C4—341no—
191C22×C4—341no—
192C22×C4—344no—
193C22×C4—682no—
194C22×C4—682no—
195C22×C4#6324212yes—
196C22×C4#6324312yes—
197C22×C4C22⋊#59511yescharacteristic
198C22×C4C22×#59511yescharacteristic
199C2×C8—684no—
200C4⋊C4—41no—
201C4⋊C4—41no—
202C4⋊C4—681no—
203C4⋊C4—681no—
204C4⋊C4—684no—
205C4⋊C4—684no—
206C22⋊C4—42no—
207C22⋊C4—682no—
208C42—41no—
209C42—41no—
210C42—172no—
211C42—172no—
212C42—341no—
213C42—341no—
214C42—344no—
215C42—342no—
216C42—342no—
217C23—21no—
218C23—21no—
219C23—41no—
220C23—41no—
221C23#1058754312yes—
222C23C2×C22⋊#59511yescharacteristic
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4—41no—
232C2×C4—41no—
233C2×C4—342no—
234C2×C4—342no—
235C2×C4—342no—
236C2×C4—342no—
237C2×C4—342no—
238C2×C4—342no—
239C2×C4—688no—
240C2×C4—681no—
241C2×C4—681no—
242C2×C4—682no—
243C2×C4—682no—
244C2×C4#1058754312yes—
245C2×C4#1058754512yes—
246C2×C4#1058755111yescharacteristic
247C2×C4#1058755111yescharacteristic
248C2×C4C2×#6324211yescharacteristic
249C2×C4C2×#6324311yescharacteristic
250C8—1364no—
251C22—21no—
252C22—21no—
253C22—22no—
254C22—42no—
255C22—42no—
256C22—41no—
257C22—41no—
258C22C2×#1058754311yescharacteristic
259C22C2×#1058755111yescharacteristic
260C22C2×#1058754511yescharacteristic
261C4—21no—
262C4—21no—
263C4—81no—
264C4—81no—
265C4—344no—
266C4—682no—
267C4—682no—
268C4—682no—
269C4#1176365512yes—
270C4#1176365512yes—
271C2—21no—
272C2—21no—
273C2—42no—
274C2C2×#1176365511yescharacteristic
275C2#1454505511yescharacteristic
276C2#1454507511yescharacteristic
subgroupG/H
centerC2×C4#10587551
commutatorC2×C4×C17C22×C8
FrattiniC22×C4C22×#595
FittingC2×C17×#117C4
socleC22×C17C2×#99
prime radicalC24×C17C22⋊C4
cosocleC2×C4⋊Dic17C23
hypercenterC2×#117#595
hypocenterC17#11447
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. #14543727C2semidirect
3. #14543725C2semidirect
34. C2×C4×Dic17C8semidirect
181. C17#11447semidirect

Maximal subgroups

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

subgroupindex
#145440152
#145437272
#145437252
#145311872
#1144717