Finite Group Databasebeta

← #16937326

Subgroups — #16937326

Order 4352.

500 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 109 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#14528872C212yesmaximal
2#14527053C211yesmaximal, characteristic
3#14526662C212yesmaximal
4#14526627C211yesmaximal, characteristic
5C17×#2646C211yesmaximal, characteristic
6C22×C4⋊Dic17C2211yescharacteristic
7C2×C22⋊#3622C2212yes—
8C2×#10587502—22no—
9C2×#10587502C2211yescharacteristic
10#11762571—22no—
11#11762571—22no—
12C17×#400—22no—
13C17×#398—22no—
14C17×#385—22no—
15C17×#380C2212yes—
16C2×C17×#95C2211yescharacteristic
17C23×C4×C17D412yes—
18C23×C4×C17C2311yescharacteristic
19C23×Dic17—21no—
20C23×Dic17—21no—
21C2×C4⋊C4×C17—22no—
22C2×C4⋊C4×C17—22no—
23C2×C4⋊C4×C17D412yes—
24C2×C4⋊C4×C17D412yes—
25C2×C22⋊C4×C17—22no—
26C2×C4⋊Dic17—21no—
27C2×C4⋊Dic17—22no—
28C2×C4⋊Dic17—22no—
29C2×C4⋊Dic17Q812yes—
30C22×#3622—22no—
31C17×#95—22no—
32C17×#95—22no—
33C17×#95—22no—
34C17×#95—22no—
35#10587502—22no—
36#10587502—44no—
37C22⋊#3622—22no—
38C22⋊#3622—22no—
39C24×C17C2×D411yescharacteristic
40C22×C4×C17—22no—
41C22×C4×C17—22no—
42C22×C4×C17—22no—
43C22×C4×C17—22no—
44C22×C4×C17—22no—
45C22×C4×C17—42no—
46C22×C4×C17—42no—
47C22×C4×C17—42no—
48C22×C4×C17C2×D412yes—
49C22×C4×C17C2×Q811yescharacteristic
50C22×C4×C17#4112yes—
51C22×C4×C17#4111yescharacteristic
52C22×Dic17—22no—
53C22×Dic17—22no—
54C22×Dic17—41no—
55C22×Dic17—42no—
56C22×Dic17—42no—
57C22×Dic17—42no—
58C22×Dic17—41no—
59C22×Dic17—41no—
60C22×Dic17—41no—
61C22×Dic17—42no—
62C4⋊C4×C17—42no—
63C4⋊C4×C17—42no—
64C4⋊C4×C17—82no—
65C4⋊C4×C17—82no—
66C22⋊C4×C17—42no—
67C22⋊C4×C17—42no—
68C4⋊Dic17—24no—
69C4⋊Dic17—42no—
70C2×#3622—42no—
71C2×#3622—42no—
72C2×#3622—42no—
73#10347—171nomaximal, Sylow
74C23×C17—21no—
75C23×C17—21no—
76C23×C17—22no—
77C23×C17#12011yescharacteristic
78C23×C17C22⋊Q811yescharacteristic
79C23×C17#12411yescharacteristic
80C23×C17#13512yes—
81C23×C17#13712yes—
82C2×C4×C17—22no—
83C2×C4×C17—22no—
84C2×C4×C17—41no—
85C2×C4×C17—41no—
86C2×C4×C17—42no—
87C2×C4×C17—44no—
88C2×C4×C17—42no—
89C2×C4×C17—42no—
90C2×C4×C17—42no—
91C2×C4×C17—42no—
92C2×C4×C17—42no—
93C2×C4×C17—42no—
94C2×C4×C17—42no—
95C2×C4×C17—42no—
96C2×C4×C17—42no—
97C2×C4×C17—82no—
98C2×C4×C17C22⋊Q812yes—
99C2×C4×C17#12412yes—
100C2×Dic17—44no—
101C2×Dic17—42no—
102C2×Dic17—44no—
103C2×Dic17—42no—
104C2×Dic17—82no—
105C2×Dic17—81no—
106C2×Dic17—82no—
107C2×Dic17—81no—
108C2×Dic17—81no—
109C2×Dic17—81no—
110#3622—82no—
111#2646D1711yescharacteristic
112#1824—172no—
113#1445—171no—
114#1294—172no—
115#1280—171no—
116C22×C17—22no—
117C22×C17—22no—
118C22×C17—22no—
119C22×C17—22no—
120C22×C17—21no—
121C22×C17—21no—
122C22×C17—21no—
123C22×C17—21no—
124C22×C17#39311yescharacteristic
125C22×C17#45212yes—
126C22×C17#45311yescharacteristic
127C22×C17#45411yescharacteristic
128C22×C17#45812yes—
129C22×C17#47912yes—
130C22×C17#48811yescharacteristic
131C22×C17#49111yescharacteristic
132C4×C17—22no—
133C4×C17—22no—
134C4×C17—82no—
135C4×C17—82no—
136C4×C17—82no—
137Dic17—82no—
138Dic17—82no—
139C22×C4⋊C4—171no—
140C2×C22⋊C8—172no—
141#400—22no—
142#398—22no—
143#385—22no—
144#380C2×D1712yes—
145C2×#95—171no—
146C2×#95—342no—
147C2×#95C2×D1711yescharacteristic
148#340—342no—
149#340—342no—
150C2×C17—21no—
151C2×C17—22no—
152C2×C17—21no—
153C2×C17#161512yes—
154C2×C17#161812yes—
155C2×C17#202611yescharacteristic
156C2×C17#202711yescharacteristic
157C2×C17#203011yescharacteristic
158C23×C4—341no—
159C23×C4—341no—
160C23×C4C22⋊D1712yes—
161C23×C4C22×D1711yescharacteristic
162C22×C8—342no—
163C2×C4⋊C4—22no—
164C2×C4⋊C4—22no—
165C2×C4⋊C4—172no—
166C2×C4⋊C4—342no—
167C2×C4⋊C4—342no—
168C2×C4⋊C4—341no—
169C2×C4⋊C4C22⋊D1712yes—
170C2×C4⋊C4C22⋊D1712yes—
171C2×C22⋊C4—22no—
172C22⋊C8—342no—
173C22⋊C8—342no—
174#95—22no—
175#95—22no—
176#95—22no—
177#95—22no—
178#95—342no—
179#95—684no—
180C17#1034711yescharacteristic, complemented, Sylow
181C24C2×C22⋊D1711yescharacteristic
182C22×C4—22no—
183C22×C4—22no—
184C22×C4—22no—
185C22×C4—22no—
186C22×C4—22no—
187C22×C4—42no—
188C22×C4—42no—
189C22×C4—42no—
190C22×C4—342no—
191C22×C4—342no—
192C22×C4—682no—
193C22×C4—681no—
194C22×C4—682no—
195C22×C4—682no—
196C22×C4—681no—
197C22×C4—681no—
198C22×C4—682no—
199C22×C4—681no—
200C22×C4Q8×D1711yescharacteristic
201C22×C4#6325612yes—
202C22×C4#6325611yescharacteristic
203C22×C4C2×C22⋊D1712yes—
204C2×C8—682no—
205C2×C8—682no—
206C2×C8—682no—
207C4⋊C4—42no—
208C4⋊C4—42no—
209C4⋊C4—82no—
210C4⋊C4—82no—
211C4⋊C4—344no—
212C4⋊C4—682no—
213C22⋊C4—42no—
214C22⋊C4—42no—
215C23—21no—
216C23—21no—
217C23—22no—
218C23#1058763211yescharacteristic
219C23#1058763311yescharacteristic
220C23#1058763612yes—
221C23#1058763712yes—
222C23#1058763911yescharacteristic
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—42no—
228C2×C4—44no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4—42no—
232C2×C4—42no—
233C2×C4—42no—
234C2×C4—42no—
235C2×C4—42no—
236C2×C4—42no—
237C2×C4—42no—
238C2×C4—82no—
239C2×C4—684no—
240C2×C4—682no—
241C2×C4—684no—
242C2×C4—682no—
243C2×C4—1362no—
244C2×C4—1361no—
245C2×C4—1362no—
246C2×C4—1361no—
247C2×C4—1361no—
248C2×C4—1361no—
249C2×C4#1058763212yes—
250C2×C4#1058763312yes—
251C8—1362no—
252C22—22no—
253C22—22no—
254C22—22no—
255C22—22no—
256C22—21no—
257C22—21no—
258C22—21no—
259C22—21no—
260C22#1176272011yescharacteristic
261C22#1176297112yes—
262C22#1176297711yescharacteristic
263C22#1176298211yescharacteristic
264C22#1176299912yes—
265C22#1176311312yes—
266C22#1176316611yescharacteristic
267C22#1176317911yescharacteristic
268C4—22no—
269C4—22no—
270C4—82no—
271C4—82no—
272C4—82no—
273C4—1362no—
274C4—1362no—
275C2—21no—
276C2—22no—
277C2—21no—
278C2#1452781512yes—
279C2#1452783212yes—
280C2#1452993211yescharacteristic
281C2#1452993711yescharacteristic
282C2#1452995011yescharacteristic
subgroupG/H
centerC23#10587639
commutator, cosocleC23×C4×C17C23
FrattiniC23×C4C22×D17
FittingC17×#2646C2
socleC23×C17#120
prime radicalC24×C17C2×D4
hypercenter#2646D17
hypocenterC17#10347
LCSG ▷ C23×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2646

Complements

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

NH ≅ G/Ntype
180. C17#10347semidirect

Maximal subgroups

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

subgroupindex
#145288722
#145270532
#145266622
#145266272
C17×#26462
#1034717