Finite Group Databasebeta

← #17949967

Subgroups — #17949967

Order 4352.

456 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 118 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#14544700C211yesmaximal, characteristic
2#14544700C211yesmaximal, characteristic
3#14543602C214yesmaximal
4C4⋊Q8×Dic17C211yesmaximal, characteristic
5C2×#10587544—21no—
6C2×#10587544—21no—
7#11763675—21no—
8#11763675—21no—
9#11763675C2212yes—
10#11763675C2212yes—
11C2×Q8×Dic17—21no—
12#11762716—21no—
13#11762708—21no—
14#11762708C2212yes—
15#11762679C411yescharacteristic
16C4⋊C4×Dic17—21no—
17C4⋊C4×Dic17C412yes—
18C42×Dic17C2211yescharacteristic
19C2×C17×C4⋊Q8C411yescharacteristic
20C22×Q8×C17—21no—
21C22×#3624—22no—
22C22×#3624—22no—
23C17×C4⋊Q8—24no—
24C2×C4⋊C4×C17—21no—
25C2×C4⋊C4×C17C2×C412yes—
26C2×C42×C17C2×C411yescharacteristic
27Q8×Dic17—42no—
28Q8×Dic17—42no—
29C2×C4⋊Dic17—21no—
30C2×C4⋊Dic17—21no—
31C2×C4⋊Dic17—22no—
32C2×C4⋊Dic17C2×C412yes—
33C2×C4×Dic17—22no—
34C2×C4×Dic17C2×C411yescharacteristic
35C2×C4×Dic17D411yescharacteristic
36C2×C4×Dic17D411yescharacteristic
37C2×C4×Dic17D411yescharacteristic
38C2×C4×Dic17D411yescharacteristic
39C2×C4×Dic17C2311yescharacteristic
40#10587544—42no—
41#10587544—42no—
42#10587502—22no—
43#10587502—22no—
44C2×Q8×C17—24no—
45C2×Q8×C17—42no—
46C2×Q8×C17—42no—
47C22×C4×C17—22no—
48C22×C4×C17C22⋊C411yescharacteristic
49C22×C4×C17C22⋊C411yescharacteristic
50C22×C4×C17C22×C411yescharacteristic
51C22×Dic17—22no—
52C22×Dic17C22⋊C411yescharacteristic
53C22×Dic17C22⋊C411yescharacteristic
54C22×Dic17C2×D411yescharacteristic
55C22×Dic17C2×D411yescharacteristic
56C2×#3624—42no—
57C2×#3624—42no—
58C2×#3624—42no—
59C2×#3624—42no—
60C2×#3624—42no—
61C2×#3624—42no—
62C4⋊C4×C17—24no—
63C4⋊C4×C17—22no—
64C4⋊C4×C17M1614yes—
65C42×C17—22no—
66C4⋊Dic17—42no—
67C4⋊Dic17—42no—
68C4⋊Dic17—42no—
69C4⋊Dic17—42no—
70C4⋊Dic17—42no—
71C4×Dic17—22no—
72C4×Dic17—41no—
73C4×Dic17—41no—
74C4×Dic17—41no—
75C4×Dic17—44no—
76C4×Dic17D812yes—
77C4×Dic17SD1612yes—
78C4×Dic17SD1612yes—
79C4×Dic17Q1612yes—
80#7652—171nomaximal, Sylow
81C23×C17C2×C22⋊C411yescharacteristic
82Q8×C17—48no—
83C2×C4×C17—21no—
84C2×C4×C17—21no—
85C2×C4×C17—21no—
86C2×C4×C17—21no—
87C2×C4×C17—21no—
88C2×C4×C17—21no—
89C2×C4×C17—24no—
90C2×C4×C17—42no—
91C2×C4×C17—42no—
92C2×C4×C17#10212yes—
93C2×C4×C17#10312yes—
94C2×C4×C17C2×M1612yes—
95C2×Dic17—21no—
96C2×Dic17—21no—
97C2×Dic17—21no—
98C2×Dic17—21no—
99C2×Dic17—21no—
100C2×Dic17—21no—
101C2×Dic17—21no—
102C2×Dic17—42no—
103C2×Dic17—42no—
104C2×Dic17—42no—
105C2×Dic17#10112yes—
106C2×Dic17#10212yes—
107C2×Dic17#10312yes—
108C2×Dic17C2×D811yescharacteristic
109C2×Dic17C2×SD1611yescharacteristic
110C2×Dic17C2×SD1611yescharacteristic
111C2×Dic17C2×Q1611yescharacteristic
112#3624—82no—
113#3624—82no—
114C4×C4⋊Q8—171no—
115#1831—171no—
116#1831—171no—
117#1271—174no—
118C22×C17#40711yescharacteristic
119C22×C17#41011yescharacteristic
120C22×C17C2×#10111yescharacteristic
121C22×C17C2×#10211yescharacteristic
122C22×C17C2×#10311yescharacteristic
123C22×C17#42111yescharacteristic
124C22×C17#42111yescharacteristic
125C4×C17—22no—
126C4×C17—22no—
127C4×C17—22no—
128C4×C17—44no—
129Dic17—21no—
130Dic17—21no—
131Dic17—21no—
132Dic17—21no—
133Dic17—41no—
134Dic17—82no—
135Dic17#33214yes—
136C2×C4⋊Q8#59511yescharacteristic
137C2×C4×Q8—341no—
138C2×C4⋊C8—341no—
139C2×C4⋊C8—341no—
140#391—341no—
141#389—172no—
142#389—341no—
143#384—171no—
144C4×C4⋊C4—172no—
145C4×C4⋊C4—341no—
146C43—171no—
147#336—172no—
148#336—172no—
149#336—341no—
150#336—341no—
151C2×C17#146711yescharacteristic
152C2×C17#148611yescharacteristic
153C2×C17#148711yescharacteristic
154C2×C17#151711yescharacteristic
155C2×C17#151811yescharacteristic
156C2×C17#153711yescharacteristic
157C2×C17C2×#33211yescharacteristic
158C22×Q8—21no—
159C22×C8—342no—
160C22×C8—342no—
161C4⋊Q8—24no—
162C4×Q8—682no—
163C4×Q8—682no—
164C2×C4⋊C4—21no—
165C2×C4⋊C4—172no—
166C2×C4⋊C4—342no—
167C2×C4⋊C4—341no—
168C2×C4⋊C4—341no—
169C2×C4⋊C4C2×#59512yes—
170C2×C42—171no—
171C2×C42—171no—
172C2×C42—171no—
173C2×C42—171no—
174C2×C42—171no—
175C2×C42—171no—
176C2×C42—342no—
177C2×C42C2×#59511yescharacteristic
178C4⋊C8—682no—
179C4⋊C8—682no—
180#95—342no—
181#95—342no—
182C17#765211yescharacteristic, complemented, Sylow
183C2×Q8—24no—
184C2×Q8—42no—
185C2×Q8—42no—
186C22×C4—22no—
187C22×C4—171no—
188C22×C4—171no—
189C22×C4—171no—
190C22×C4—171no—
191C22×C4—342no—
192C22×C4C22⋊#59511yescharacteristic
193C22×C4C22⋊#59511yescharacteristic
194C22×C4C22×#59511yescharacteristic
195C2×C8—682no—
196C2×C8—682no—
197C2×C8—682no—
198C2×C8—682no—
199C2×C8—682no—
200C2×C8—682no—
201C4⋊C4—24no—
202C4⋊C4—22no—
203C4⋊C4—682no—
204C4⋊C4—682no—
205C4⋊C4—682no—
206C4⋊C4—682no—
207C4⋊C4—682no—
208C4⋊C4#6324714yes—
209C42—22no—
210C42—172no—
211C42—172no—
212C42—172no—
213C42—172no—
214C42—342no—
215C42—681no—
216C42—681no—
217C42—681no—
218C42—684no—
219C23C2×C22⋊#59511yescharacteristic
220Q8—48no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—24no—
228C2×C4—42no—
229C2×C4—42no—
230C2×C4—172no—
231C2×C4—172no—
232C2×C4—172no—
233C2×C4—171no—
234C2×C4—171no—
235C2×C4—171no—
236C2×C4—171no—
237C2×C4—341no—
238C2×C4—341no—
239C2×C4—341no—
240C2×C4—341no—
241C2×C4—341no—
242C2×C4—341no—
243C2×C4—341no—
244C2×C4—682no—
245C2×C4—682no—
246C2×C4—682no—
247C2×C4#1058754712yes—
248C2×C4#1058754912yes—
249C2×C4C2×#6324712yes—
250C8—1362no—
251C8—1362no—
252C22#1176377911yescharacteristic
253C22#1176379011yescharacteristic
254C22D17⋊#10111yescharacteristic
255C22C2×#1058754711yescharacteristic
256C22C2×#1058754911yescharacteristic
257C22#1176380711yescharacteristic
258C22#1176380811yescharacteristic
259C4—22no—
260C4—22no—
261C4—22no—
262C4—44no—
263C4—174no—
264C4—341no—
265C4—341no—
266C4—341no—
267C4—341no—
268C4—681no—
269C4—1362no—
270C2#1454404711yescharacteristic
271C2#1454410911yescharacteristic
272C2#1454411211yescharacteristic
273C2#1454421511yescharacteristic
274C2#1454421611yescharacteristic
275C2#1454427611yescharacteristic
276C2D17⋊#33211yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC2×C17×C4⋊Q8C4
socle, prime radicalC23×C17C2×C22⋊C4
cosocleC2×C4×Dic17C23
hypercenterC2×C4⋊Q8#595
hypocenterC17#7652
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
182. C17#7652semidirect

Maximal subgroups

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

subgroupindex
#145447002
#145436022
C4⋊Q8×Dic172
#765217