Finite Group Databasebeta

← #17961433

Subgroups — #17961433

Order 4352.

468 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 86 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#14544651C212yesmaximal
3#14543882C212yesmaximal
4#14531351C211yesmaximal, characteristic
5#11763812—22no—
6C2×#10587545C2214yes—
7#11763720—24no—
8#11763689—22no—
9C2×#10587555C2211yescharacteristic
10C2×#10587573C411yescharacteristic
11C2×#10587573C2211yescharacteristic
12#11762714C411yescharacteristic
13#11762714C2211yescharacteristic
14#11762705—22no—
15C4⋊C4×Dic17—22no—
16C42×Dic17C411yescharacteristic
17C17×#384C411yescharacteristic
18C22×Dic34C2×C411yescharacteristic
19C22×Dic34C2311yescharacteristic
20C2×#63247—24no—
21C2×C4⋊C4×C17—22no—
22C2×C4⋊C4×C17C2×C411yescharacteristic
23C2×C4⋊C4×C17C2×C411yescharacteristic
24C2×C42×C17C2×C411yescharacteristic
25C2×C4⋊Dic17—22no—
26C2×#63225—21no—
27C2×#63225D412yes—
28C2×C4×Dic17—21no—
29C2×C4×Dic17—21no—
30C2×C4×Dic17—21no—
31C2×C4×Dic17C2×C411yescharacteristic
32C2×C4×Dic17C2×C411yescharacteristic
33C2×C4×Dic17D412yes—
34#10587573—41no—
35#10587573—41no—
36#10587573—41no—
37#10587573—41no—
38#10587555—22no—
39#10587555D412yes—
40#10587555Q812yes—
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⋊C412yes—
50C22×C4×C17C22×C411yescharacteristic
51C22×Dic17—21no—
52C22×Dic17—21no—
53C22×Dic17C22⋊C411yescharacteristic
54C22×Dic17C22⋊C411yescharacteristic
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—
68C4⋊C4×C17—41no—
69C4⋊C4×C17—41no—
70C4⋊C4×C17—44no—
71C42×C17—21no—
72C42×C17C4⋊C412yes—
73C4⋊Dic17—24no—
74C4⋊Dic17—24no—
75#63225—42no—
76#63225—42no—
77C4×Dic17—24no—
78C4×Dic17—22no—
79C4×Dic17—22no—
80C4×Dic17—21no—
81C4×Dic17—21no—
82C4×Dic17—42no—
83C4×Dic17—41no—
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—42no—
95C2×C4×C17—42no—
96C2×C4×C17—41no—
97C2×C4×C17C2×C4⋊C411yescharacteristic
98C2×C4×C17#11711yescharacteristic
99C2×Dic17—22no—
100C2×Dic17—22no—
101C2×Dic17—22no—
102C2×Dic17—22no—
103C2×Dic17—22no—
104C2×Dic17—21no—
105C2×Dic17—41no—
106C2×Dic17—41no—
107C2×Dic17—41no—
108C2×Dic17—41no—
109C2×Dic17—41no—
110C2×Dic17#9911yescharacteristic
111C2×Dic17#9911yescharacteristic
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—42no—
133C4×C17—81no—
134Dic17—22no—
135Dic17—22no—
136Dic17—21no—
137Dic17—42no—
138Dic17—42no—
139Dic17—41no—
140Dic17#35612yescomplemented
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#59511yescharacteristic
150C4×C4⋊C4—342no—
151C43—171no—
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—22no—
170C2×C4⋊C4—172no—
171C2×C4⋊C4—342no—
172C2×C4⋊C4—341no—
173C2×C4⋊C4C2×#59511yescharacteristic
174C2×C4⋊C4C2×#59511yescharacteristic
175C2×C42—172no—
176C2×C42—171no—
177C2×C42—171no—
178C2×C42—341no—
179C2×C42—341no—
180C2×C42—341no—
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—171no—
201C22×C4—172no—
202C22×C4—171no—
203C22×C4—341no—
204C22×C4—341no—
205C22×C4C22⋊#59512yes—
206C22×C4C22×#59511yescharacteristic
207M16—684no—
208M16—684no—
209C2×C8—684no—
210C4⋊C4—41no—
211C4⋊C4—41no—
212C4⋊C4—44no—
213C4⋊C4—344no—
214C4⋊C4—344no—
215C4⋊C4—682no—
216C4⋊C4—682no—
217C42—21no—
218C42—342no—
219C42—342no—
220C42—341no—
221C42—341no—
222C42—344no—
223C42—681no—
224C42—682no—
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—42no—
241C2×C4—42no—
242C2×C4—41no—
243C2×C4—171no—
244C2×C4—172no—
245C2×C4—172no—
246C2×C4—171no—
247C2×C4—342no—
248C2×C4—342no—
249C2×C4—342no—
250C2×C4—342no—
251C2×C4—342no—
252C2×C4—341no—
253C2×C4—681no—
254C2×C4—681no—
255C2×C4—681no—
256C2×C4—681no—
257C2×C4—681no—
258C2×C4C2×C4⋊#59511yescharacteristic
259C2×C4#1058767711yescharacteristic
260C8—1364no—
261C22—21no—
262C22—21no—
263C22#1176375111yescharacteristic
264C22D17⋊#9911yescharacteristic
265C22#1176379011yescharacteristic
266C4—24no—
267C4—21no—
268C4—21no—
269C4—42no—
270C4—81no—
271C4—172no—
272C4—342no—
273C4—342no—
274C4—341no—
275C4—682no—
276C4—682no—
277C4—681no—
278C2—21no—
279C2—21no—
280C2#1454464711yescharacteristic
281C2D17⋊#35611yescharacteristic
282C2#1454507611yescharacteristic
subgroupG/H
centerC22D17⋊#99
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC17×#384C4
socleC22×C17C2×#99
prime radicalC23×C17C2×C22⋊C4
cosocleC22×Dic34C23
hypercenter#384#595
hypocenterC17#12802
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #384

Complements

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

NH ≅ G/Ntype
140. Dic17#356semidirect
188. C17#12802semidirect

Maximal subgroups

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

subgroupindex
C2×#117637202
#145446512
#145438822
#145313512
#1280217