Finite Group Databasebeta

← #17962530

Subgroups — #17962530

Order 4352.

420 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 84 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#14544650C211yesmaximal, characteristic
2C4×#10587545C211yesmaximal, characteristic
3#14543882C214yesmaximal
4#14533993C211yesmaximal, characteristic
5#11763812—21no—
6C2×#10587545C2212yes—
7C2×#10587545C2212yes—
8C4×#63247—21no—
9#11763689—21no—
10#11763689—21no—
11C2×C4×Dic34C2211yescharacteristic
12#11762728—21no—
13#11762728—21no—
14#11762714C2212yes—
15#11762705—21no—
16#11762705—21no—
17#11762678C412yes—
18C4×C4⋊Dic17C411yescharacteristic
19C2×C17×C4⋊Q8C411yescharacteristic
20C22×Q8×C17—21no—
21C22×Dic34C2311yescharacteristic
22C2×#63247—22no—
23C2×#63247—22no—
24C17×C4⋊Q8—41no—
25C17×C4⋊Q8—41no—
26C2×C4⋊C4×C17—21no—
27C2×C4⋊C4×C17C2×C412yes—
28C2×C42×C17C2×C411yescharacteristic
29C2×C4⋊Dic17—21no—
30C2×C4⋊Dic17C2×C411yescharacteristic
31C2×#63225—22no—
32C2×#63225—22no—
33C2×#63225D411yescharacteristic
34C2×#63225D411yescharacteristic
35C2×C4×Dic17C2×C412yes—
36C2×C4×Dic17D411yescharacteristic
37C2×C4×Dic17D411yescharacteristic
38C4×Dic34—41no—
39C4×Dic34—41no—
40#10587545—22no—
41#10587545—24no—
42#10587545Q814yescomplemented
43#10587544—41no—
44#10587542—41no—
45C4⋊#3624—41no—
46C4×#3624—41no—
47#10587502—21no—
48#10587502—22no—
49#10587502—22no—
50C2×Q8×C17—42no—
51C2×Q8×C17—82no—
52C22×C4×C17—22no—
53C22×C4×C17C22⋊C411yescharacteristic
54C22×C4×C17C22⋊C411yescharacteristic
55C22×C4×C17C22×C411yescharacteristic
56C22×Dic17—22no—
57C22×Dic17C22⋊C411yescharacteristic
58C22×Dic17C22⋊C411yescharacteristic
59C22×Dic17C2×D411yescharacteristic
60C22×Dic17C2×D411yescharacteristic
61C2×Dic34—41no—
62C2×Dic34—41no—
63C2×Dic34C2×Q812yes—
64C2×Dic34#4112yes—
65#63247—24no—
66#63247—42no—
67#63247—42no—
68#63247—42no—
69C2×#3624—42no—
70C2×#3624—42no—
71C4⋊C4×C17—42no—
72C4⋊C4×C17—41no—
73C4⋊C4×C17—41no—
74C42×C17—21no—
75C42×C17—21no—
76C4⋊Dic17—24no—
77C4⋊Dic17—41no—
78#63225—41no—
79#63225—41no—
80#63225—82no—
81#63225—82no—
82C4×Dic17—21no—
83C4×Dic17—21no—
84C4×Dic17—21no—
85C4×Dic17—21no—
86C4×Dic17—42no—
87#13302—171nomaximal, Sylow
88C23×C17C2×C22⋊C411yescharacteristic
89Q8×C17—84no—
90C2×C4×C17—21no—
91C2×C4×C17—21no—
92C2×C4×C17—22no—
93C2×C4×C17—21no—
94C2×C4×C17—41no—
95C2×C4×C17—42no—
96C2×C4×C17—42no—
97C2×C4×C17—42no—
98C2×C4×C17#9911yescharacteristic
99C2×C4×C17#9911yescharacteristic
100C2×C4×C17C4×Q812yes—
101C2×Dic17—21no—
102C2×Dic17—21no—
103C2×Dic17—21no—
104C2×Dic17—21no—
105C2×Dic17—24no—
106C2×Dic17—21no—
107C2×Dic17—21no—
108C2×Dic17—42no—
109C2×Dic17—42no—
110C2×Dic17—41no—
111C2×Dic17—41no—
112C2×Dic17C22⋊Q812yes—
113C2×Dic17#12411yescharacteristic
114C2×Dic17C4⋊Q811yescharacteristic
115Dic34—42no—
116Dic34—42no—
117#3624—44no—
118#3624—82no—
119#2567—171no—
120#1801—171no—
121C4×#101—171no—
122#1394—174no—
123C22×C17—21no—
124C22×C17—21no—
125C22×C17#39111yescharacteristic
126C22×C17C2×#9911yescharacteristic
127C22×C17#41011yescharacteristic
128C4×C17—21no—
129C4×C17—22no—
130C4×C17—41no—
131C4×C17—82no—
132C4×C17#35612yes—
133Dic17—22no—
134Dic17—21no—
135Dic17—21no—
136Dic17—44no—
137Dic17—41no—
138Dic17—41no—
139C2×C4⋊Q8#59511yescharacteristic
140C2×C4×Q8—171no—
141#423—341no—
142C2×#101—172no—
143C2×#101—172no—
144C4×M16—341no—
145#395—341no—
146#395—341no—
147#391—172no—
148#389—341no—
149#389—341no—
150#384—172no—
151C4×C4⋊C4—171no—
152#343—341no—
153#343—341no—
154C2×C17—21no—
155C2×C17—21no—
156C2×C17#199611yescharacteristic
157C2×C17C2×#35611yescharacteristic
158C2×C17#213411yescharacteristic
159C22×Q8—21no—
160C22×Q8—171no—
161C2×M16—342no—
162C2×M16—342no—
163C4⋊Q8—41no—
164C4⋊Q8—41no—
165C4×Q8—681no—
166C4×Q8—681no—
167C2×C4⋊C4—21no—
168C2×C4⋊C4—171no—
169C2×C4⋊C4—171no—
170C2×C4⋊C4—171no—
171C2×C4⋊C4—341no—
172C2×C4⋊C4—342no—
173C2×C4⋊C4—342no—
174C2×C4⋊C4C2×#59512yes—
175C2×C42—171no—
176C2×C42—171no—
177C2×C42—172no—
178C2×C42C2×#59511yescharacteristic
179C4⋊C8—681no—
180C4⋊C8—681no—
181#101—174no—
182#101—342no—
183#101—344no—
184#97—681no—
185C4×C8—681no—
186#95—342no—
187#95—342no—
188#95—341no—
189C17#1330211yescharacteristic, complemented, Sylow
190C2×Q8—42no—
191C2×Q8—82no—
192C2×Q8—172no—
193C2×Q8—172no—
194C2×Q8—681no—
195C2×Q8—681no—
196C22×C4—22no—
197C22×C4—171no—
198C22×C4—171no—
199C22×C4—171no—
200C22×C4—171no—
201C22×C4—342no—
202C22×C4C22⋊#59511yescharacteristic
203C22×C4C22⋊#59511yescharacteristic
204C22×C4C22×#59511yescharacteristic
205M16—344no—
206M16—682no—
207M16—682no—
208M16—682no—
209C2×C8—682no—
210C2×C8—682no—
211C4⋊C4—42no—
212C4⋊C4—41no—
213C4⋊C4—41no—
214C4⋊C4—344no—
215C4⋊C4—681no—
216C4⋊C4—681no—
217C4⋊C4—681no—
218C4⋊C4—1362no—
219C4⋊C4—1362no—
220C42—21no—
221C42—21no—
222C42—341no—
223C42—341no—
224C42—341no—
225C42—341no—
226C42—682no—
227C23C2×C22⋊#59511yescharacteristic
228Q8—84no—
229Q8—682no—
230Q8—682no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—22no—
234C2×C4—21no—
235C2×C4—41no—
236C2×C4—42no—
237C2×C4—42no—
238C2×C4—42no—
239C2×C4—172no—
240C2×C4—171no—
241C2×C4—171no—
242C2×C4—341no—
243C2×C4—341no—
244C2×C4—341no—
245C2×C4—341no—
246C2×C4—344no—
247C2×C4—341no—
248C2×C4—341no—
249C2×C4—682no—
250C2×C4—682no—
251C2×C4—681no—
252C2×C4—681no—
253C2×C4#1058755111yescharacteristic
254C2×C4#1058755111yescharacteristic
255C2×C4Q8×#59512yes—
256C8—684no—
257C8—1362no—
258C22—21no—
259C22—21no—
260C22(C2×#595)⋊Q811yescharacteristic
261C22C2×#1058755111yescharacteristic
262C22#1176379011yescharacteristic
263C4—22no—
264C4—21no—
265C4—41no—
266C4—82no—
267C4—342no—
268C4—341no—
269C4—341no—
270C4—684no—
271C4—681no—
272C4—681no—
273C4#1176371912yes—
274C2—21no—
275C2—21no—
276C2#1454497311yescharacteristic
277C2C2×#1176371911yescharacteristic
278C2#1454508311yescharacteristic
subgroupG/H
centerC22C2×#10587551
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC2×C17×C4⋊Q8C4
socleC22×C17C2×#99
prime radicalC23×C17C2×C22⋊C4
cosocleC22×Dic34C23
hypercenterC2×C4⋊Q8#595
hypocenterC17#13302
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
42. #10587545Q8semidirect
189. C17#13302semidirect

Maximal subgroups

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

subgroupindex
#145446502
C4×#105875452
#145438822
#145339932
#1330217