Finite Group Databasebeta

← #17961431

Subgroups — #17961431

Order 4352.

468 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 90 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
1C2×#11763720C212yesmaximal
2#14544650C212yesmaximal
3#14543881C212yesmaximal
4C4×#10587555C211yesmaximal, characteristic
5#11763812—22no—
6C2×#10587545C2214yes—
7#11763720—24no—
8#11763689—22no—
9C2×#10587555C2211yescharacteristic
10C2×C4×Dic34C411yescharacteristic
11C2×C4×Dic34C2211yescharacteristic
12#11762715C411yescharacteristic
13#11762715C2211yescharacteristic
14#11762707—22no—
15#11762679C411yescharacteristic
16C4×C4⋊Dic17—22no—
17C43×C17C411yescharacteristic
18C22×Dic34C2×C411yescharacteristic
19C22×Dic34C2311yescharacteristic
20C2×#63247—24no—
21C2×C42×C17—21no—
22C2×C42×C17—21no—
23C2×C42×C17C2×C411yescharacteristic
24C2×C42×C17C2×C411yescharacteristic
25C2×C42×C17C2×C411yescharacteristic
26C2×C4⋊Dic17—22no—
27C2×C4⋊Dic17—22no—
28C2×C4⋊Dic17C2×C411yescharacteristic
29C2×C4⋊Dic17C2×C411yescharacteristic
30C2×#63225—21no—
31C2×#63225D412yes—
32C2×C4×Dic17—21no—
33C2×C4×Dic17D412yes—
34#10587555—22no—
35#10587555D412yes—
36#10587555Q812yes—
37C4×Dic34—41no—
38C4×Dic34—41no—
39C4×Dic34—41no—
40C4×Dic34—41no—
41#10587545—24no—
42#10587545—24no—
43#10587544—42no—
44C4⋊#3624—42no—
45#10587502—22no—
46#10587502—22no—
47C22×C4×C17—21no—
48C22×C4×C17—21no—
49C22×C4×C17C22⋊C411yescharacteristic
50C22×C4×C17C22⋊C411yescharacteristic
51C22×C4×C17C22×C411yescharacteristic
52C22×Dic17—21no—
53C22×Dic17—21no—
54C22×Dic17C22⋊C412yes—
55C22×Dic17C2×D412yes—
56C2×Dic34—21no—
57C2×Dic34—41no—
58C2×Dic34—41no—
59C2×Dic34—41no—
60C2×Dic34—41no—
61C2×Dic34C4⋊C412yes—
62C2×Dic34C2×D411yescharacteristic
63C2×Dic34C2×Q811yescharacteristic
64C2×Dic34#4112yes—
65#63247—44no—
66#63247—44no—
67C2×#3624—44no—
68C42×C17—24no—
69C42×C17—21no—
70C42×C17—21no—
71C42×C17—21no—
72C42×C17—41no—
73C42×C17—42no—
74C42×C17C4⋊C412yes—
75C4⋊Dic17—24no—
76C4⋊Dic17—24no—
77C4⋊Dic17—41no—
78C4⋊Dic17—44no—
79C4⋊Dic17—41no—
80#63225—42no—
81#63225—42no—
82C4×Dic17—22no—
83C4×Dic17—22no—
84C4×Dic17—41no—
85C4×Dic17—41no—
86#12802—171nomaximal, Sylow
87C23×C17C2×C22⋊C411yescharacteristic
88C2×C4×C17—22no—
89C2×C4×C17—22no—
90C2×C4×C17—22no—
91C2×C4×C17—21no—
92C2×C4×C17—21no—
93C2×C4×C17—22no—
94C2×C4×C17—22no—
95C2×C4×C17—21no—
96C2×C4×C17—41no—
97C2×C4×C17—41no—
98C2×C4×C17—41no—
99C2×C4×C17#9911yescharacteristic
100C2×C4×C17#9911yescharacteristic
101C2×C4×C17C2×C4⋊C411yescharacteristic
102C2×C4×C17#11711yescharacteristic
103C2×Dic17—22no—
104C2×Dic17—22no—
105C2×Dic17—22no—
106C2×Dic17—22no—
107C2×Dic17—41no—
108C2×Dic17—41no—
109C2×Dic17—42no—
110C2×Dic17—42no—
111C2×Dic17—41no—
112C2×Dic17#12112yes—
113C2×Dic17C22⋊Q812yes—
114Dic34—41no—
115Dic34—41no—
116Dic34—42no—
117Dic34—42no—
118Dic34—42no—
119#3624—84no—
120C4×C4⋊Q8—171no—
121C2×#356—172no—
122#1801—172no—
123#1394—172no—
124C22×C17—21no—
125C22×C17—21no—
126C22×C17#38011yescharacteristic
127C22×C17C2×#9911yescharacteristic
128C22×C17#41011yescharacteristic
129C4×C17—24no—
130C4×C17—21no—
131C4×C17—21no—
132C4×C17—21no—
133C4×C17—42no—
134C4×C17—41no—
135C4×C17#35612yescomplemented
136Dic17—22no—
137Dic17—22no—
138Dic17—42no—
139Dic17—42no—
140Dic17—81no—
141C2×C4⋊Q8—171no—
142C2×C4×Q8—171no—
143C2×C4×Q8—171no—
144#423—342no—
145C2×#101—174no—
146#391—171no—
147#391—171no—
148#389—342no—
149#384—171no—
150C4×C4⋊C4—342no—
151C43#59511yescharacteristic
152#356—344no—
153#343—342no—
154C2×C17—21no—
155C2×C17—21no—
156C2×C17#179911yescharacteristic
157C2×C17C2×#35611yescharacteristic
158C2×C17#213211yescharacteristic
159C22×Q8—171no—
160C22×Q8—171no—
161C2×M16—344no—
162C4⋊Q8—172no—
163C4⋊Q8—172no—
164C4⋊Q8—342no—
165C4×Q8—681no—
166C4×Q8—681no—
167C4×Q8—681no—
168C4×Q8—681no—
169C2×C4⋊C4—172no—
170C2×C4⋊C4—171no—
171C2×C4⋊C4—171no—
172C2×C4⋊C4—342no—
173C2×C4⋊C4—342no—
174C2×C4⋊C4—341no—
175C2×C42—21no—
176C2×C42—21no—
177C2×C42—172no—
178C2×C42—341no—
179C2×C42C2×#59511yescharacteristic
180C2×C42C2×#59511yescharacteristic
181C2×C42C2×#59511yescharacteristic
182C4⋊C8—682no—
183C4⋊C8—682no—
184#101—344no—
185#101—344no—
186#95—342no—
187#95—342no—
188C17#1280211yescharacteristic, complemented, Sylow
189C2×Q8—171no—
190C2×Q8—171no—
191C2×Q8—172no—
192C2×Q8—172no—
193C2×Q8—341no—
194C2×Q8—681no—
195C2×Q8—681no—
196C2×Q8—681no—
197C2×Q8—681no—
198C22×C4—21no—
199C22×C4—21no—
200C22×C4—172no—
201C22×C4—172no—
202C22×C4—341no—
203C22×C4—341no—
204C22×C4C22⋊#59511yescharacteristic
205C22×C4C22⋊#59511yescharacteristic
206C22×C4C22×#59511yescharacteristic
207M16—684no—
208M16—684no—
209C2×C8—684no—
210C4⋊C4—344no—
211C4⋊C4—344no—
212C4⋊C4—682no—
213C4⋊C4—681no—
214C4⋊C4—681no—
215C4⋊C4—682no—
216C4⋊C4—684no—
217C42—24no—
218C42—21no—
219C42—21no—
220C42—21no—
221C42—41no—
222C42—42no—
223C42—342no—
224C42—342no—
225C42—681no—
226C42—681no—
227C42C4⋊#59512yes—
228C23C2×C22⋊#59511yescharacteristic
229Q8—681no—
230Q8—681no—
231Q8—682no—
232Q8—682no—
233Q8—682no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—21no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—172no—
246C2×C4—172no—
247C2×C4—342no—
248C2×C4—342no—
249C2×C4—342no—
250C2×C4—342no—
251C2×C4—681no—
252C2×C4—681no—
253C2×C4—682no—
254C2×C4—682no—
255C2×C4—681no—
256C2×C4#1058753911yescharacteristic
257C2×C4#1058753911yescharacteristic
258C2×C4C2×C4⋊#59511yescharacteristic
259C2×C4#1058767711yescharacteristic
260C8—1364no—
261C22—21no—
262C22—21no—
263C22#1176375111yescharacteristic
264C22C2×#1058753911yescharacteristic
265C22#1176378811yescharacteristic
266C4—24no—
267C4—21no—
268C4—21no—
269C4—21no—
270C4—42no—
271C4—41no—
272C4—342no—
273C4—342no—
274C4—682no—
275C4—682no—
276C4—1361no—
277C4#1176372012yescomplemented
278C2—21no—
279C2—21no—
280C2#1454464511yescharacteristic
281C2C2×#1176372011yescharacteristic
282C2#1454507711yescharacteristic
subgroupG/H
centerC22C2×#10587539
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC43×C17C4
socleC22×C17C2×#99
prime radicalC23×C17C2×C22⋊C4
cosocleC22×Dic34C23
hypercenterC43#595
hypocenterC17#12802
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ C43

Complements

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

NH ≅ G/Ntype
135. C4×C17#356semidirect
188. C17#12802semidirect
277. C4#11763720semidirect

Maximal subgroups

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

subgroupindex
C2×#117637202
#145446502
#145438812
C4×#105875552
#1280217