Finite Group Databasebeta

← #17958127

Subgroups — #17958127

Order 4352.

678 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 678 conjugacy classes of subgroups — too many to draw. Only its 112 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#14544015C212yesmaximal, complemented
2#14543710C212yesmaximal, complemented
3#14543708C212yesmaximal
4#14531167C211yesmaximal, characteristic
5#11763825—22no—
6#11763654—22no—
7#11763652C2214yes—
8C2×#10587612C411yescharacteristic
9C2×#10587612C2211yescharacteristic
10#11762672C411yescharacteristic
11#11762672C2211yescharacteristic
12#11762669—22no—
13#11762665C411yescharacteristic
14#11762665C2211yescharacteristic
15C4×C22⋊Dic17—22no—
16C24×C4×C17C411yescharacteristic
17C25×C17C2×C411yescharacteristic
18C23×C4×C17—21no—
19C23×C4×C17—21no—
20C23×C4×C17—22no—
21C23×C4×C17—41no—
22C23×C4×C17—41no—
23C23×C4×C17—42no—
24C23×C4×C17C814yescomplemented
25C23×C4×C17C2×C411yescharacteristic
26C23×C4×C17C2×C411yescharacteristic
27C2×C22⋊Dic17—22no—
28C2×C22⋊Dic17—22no—
29C2×C22⋊Dic17C2×C411yescharacteristic
30C2×C22⋊Dic17C2×C411yescharacteristic
31C2×C22⋊Dic17C2×C411yescharacteristic
32C2×C22⋊Dic17C2311yescharacteristic
33#10587612—41no—
34#10587612—41no—
35#10587612—42no—
36C2×C4⋊Dic17—21no—
37C2×C4⋊Dic17D412yes—
38C2×C4×Dic17—21no—
39C2×C4×Dic17D412yes—
40C22⋊#3624—24no—
41C4⋊#3624—42no—
42C4×#3624—42no—
43#10587502—22no—
44#10587502—22no—
45C24×C17—21no—
46C24×C17—21no—
47C24×C17—41no—
48C24×C17—41no—
49C24×C17—44no—
50C24×C17C2×C812yes—
51C24×C17C22×C411yescharacteristic
52C22×C4×C17—21no—
53C22×C4×C17—21no—
54C22×C4×C17—22no—
55C22×C4×C17—21no—
56C22×C4×C17—21no—
57C22×C4×C17—24no—
58C22×C4×C17—24no—
59C22×C4×C17—42no—
60C22×C4×C17—42no—
61C22×C4×C17—44no—
62C22×C4×C17—44no—
63C22×C4×C17—44no—
64C22×C4×C17—44no—
65C22×C4×C17—41no—
66C22×C4×C17—41no—
67C22×C4×C17—42no—
68C22×C4×C17—41no—
69C22×C4×C17—41no—
70C22×C4×C17C22⋊C411yescharacteristic
71C22×C4×C17C22⋊C411yescharacteristic
72C22×C4×C17C2×C812yes—
73C22×C4×C17C2×C812yes—
74C22×C4×C17M1612yes—
75C22×Dic17—21no—
76C22×Dic17—21no—
77C22×Dic17C22⋊C412yes—
78C22×Dic17C2×D412yes—
79C2×#3624—44no—
80C22⋊Dic17—41no—
81C22⋊Dic17—41no—
82C22⋊Dic17—44no—
83C22⋊Dic17—44no—
84C22⋊Dic17—41no—
85C22⋊Dic17—41no—
86C4⋊Dic17—42no—
87C4⋊Dic17—42no—
88C4×Dic17—22no—
89C4×Dic17—22no—
90C4×Dic17—42no—
91#11425—171nomaximal, Sylow
92C23×C17—24no—
93C23×C17—22no—
94C23×C17—21no—
95C23×C17—21no—
96C23×C17—42no—
97C23×C17—44no—
98C23×C17—42no—
99C23×C17—42no—
100C23×C17—42no—
101C23×C17—44no—
102C23×C17—44no—
103C23×C17—48no—
104C23×C17—44no—
105C23×C17—41no—
106C23×C17—41no—
107C23×C17C2×C22⋊C411yescharacteristic
108C23×C17C22×C811yescharacteristic
109C23×C17C2×M1611yescharacteristic
110C2×C4×C17—21no—
111C2×C4×C17—21no—
112C2×C4×C17—22no—
113C2×C4×C17—22no—
114C2×C4×C17—22no—
115C2×C4×C17—22no—
116C2×C4×C17—22no—
117C2×C4×C17—48no—
118C2×C4×C17—42no—
119C2×C4×C17—41no—
120C2×C4×C17—41no—
121C2×C4×C17—44no—
122C2×C4×C17—44no—
123C2×C4×C17—42no—
124C2×C4×C17C22⋊C812yes—
125C2×C4×C17C22⋊C812yes—
126C2×C4×C17#9911yescharacteristic
127C2×C4×C17#9911yescharacteristic
128C2×C4×C17#10012yes—
129C2×Dic17—22no—
130C2×Dic17—22no—
131C2×Dic17—42no—
132C2×Dic17—42no—
133C2×Dic17—42no—
134C2×Dic17—42no—
135C2×Dic17—41no—
136C2×Dic17—41no—
137#3624—84no—
138#2280—171no—
139#1458—172no—
140#1317—172no—
141#1316—172no—
142C22×C17—22no—
143C22×C17—24no—
144C22×C17—21no—
145C22×C17—21no—
146C22×C17—41no—
147C22×C17—41no—
148C22×C17—44no—
149C22×C17—42no—
150C22×C17—42no—
151C22×C17—44no—
152C22×C17—44no—
153C22×C17—48no—
154C22×C17—44no—
155C22×C17—42no—
156C22×C17—42no—
157C22×C17C2×C22⋊C811yescharacteristic
158C22×C17C2×#9911yescharacteristic
159C22×C17C2×#10011yescharacteristic
160C4×C17—22no—
161C4×C17—42no—
162C4×C17#32312yes—
163C4×C17#32312yes—
164Dic17—42no—
165Dic17—42no—
166Dic17—81no—
167Dic17—81no—
168C24×C4#59511yescharacteristic
169C2×#117—171no—
170C2×#117—171no—
171#431—342no—
172#381—171no—
173#381—171no—
174#380—342no—
175#379—171no—
176#379—171no—
177C4×C22⋊C4—342no—
178#324—342no—
179#323—174no—
180C2×C17—21no—
181C2×C17—21no—
182C2×C17—44no—
183C2×C17—41no—
184C2×C17—41no—
185C2×C17C2×#32311yescharacteristic
186C2×C17#212012yes—
187C25C2×#59511yescharacteristic
188C23×C4—22no—
189C23×C4—21no—
190C23×C4—21no—
191C23×C4—41no—
192C23×C4—41no—
193C23×C4—42no—
194C23×C4#362414yescomplemented
195C23×C4C2×#59511yescharacteristic
196C23×C4C2×#59511yescharacteristic
197#117—681no—
198#117—681no—
199#117—682no—
200C2×C4⋊C4—172no—
201C2×C4⋊C4—341no—
202C2×C22⋊C4—171no—
203C2×C22⋊C4—171no—
204C2×C22⋊C4—171no—
205C2×C22⋊C4—171no—
206C2×C22⋊C4—342no—
207C2×C22⋊C4—342no—
208C2×C42—172no—
209C2×C42—341no—
210C4⋊C8—682no—
211C22⋊C8—344no—
212C4×C8—682no—
213#95—342no—
214#95—342no—
215C17#1142511yescharacteristic, complemented, Sylow
216C24—21no—
217C24—21no—
218C24—41no—
219C24—41no—
220C24—44no—
221C24C2×#362412yes—
222C24C22×#59511yescharacteristic
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—22no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—24no—
229C22×C4—24no—
230C22×C4—42no—
231C22×C4—42no—
232C22×C4—44no—
233C22×C4—44no—
234C22×C4—44no—
235C22×C4—44no—
236C22×C4—41no—
237C22×C4—41no—
238C22×C4—42no—
239C22×C4—41no—
240C22×C4—41no—
241C22×C4—172no—
242C22×C4—172no—
243C22×C4—341no—
244C22×C4—341no—
245C22×C4C2×#362412yes—
246C22×C4C2×#362412yes—
247C22×C4#6324712yes—
248C22×C4C22⋊#59511yescharacteristic
249C22×C4C22⋊#59511yescharacteristic
250C2×C8—684no—
251C4⋊C4—682no—
252C4⋊C4—682no—
253C22⋊C4—681no—
254C22⋊C4—681no—
255C22⋊C4—684no—
256C22⋊C4—684no—
257C22⋊C4—681no—
258C22⋊C4—681no—
259C42—342no—
260C42—342no—
261C42—682no—
262C23—24no—
263C23—22no—
264C23—21no—
265C23—21no—
266C23—42no—
267C23—44no—
268C23—42no—
269C23—42no—
270C23—42no—
271C23—44no—
272C23—44no—
273C23—48no—
274C23—44no—
275C23—41no—
276C23—41no—
277C23C22×#362411yescharacteristic
278C23C2×#6324711yescharacteristic
279C23C2×C22⋊#59511yescharacteristic
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—22no—
283C2×C4—22no—
284C2×C4—22no—
285C2×C4—22no—
286C2×C4—22no—
287C2×C4—48no—
288C2×C4—42no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—44no—
292C2×C4—44no—
293C2×C4—42no—
294C2×C4—342no—
295C2×C4—342no—
296C2×C4—682no—
297C2×C4—682no—
298C2×C4—682no—
299C2×C4—682no—
300C2×C4—681no—
301C2×C4—681no—
302C2×C4#1058755111yescharacteristic
303C2×C4#1058755111yescharacteristic
304C2×C4C22⋊#362412yes—
305C2×C4C22⋊#362412yes—
306C2×C4#1058755312yes—
307C8—1364no—
308C22—22no—
309C22—24no—
310C22—21no—
311C22—21no—
312C22—41no—
313C22—41no—
314C22—44no—
315C22—42no—
316C22—42no—
317C22—44no—
318C22—44no—
319C22—48no—
320C22—42no—
321C22—44no—
322C22—42no—
323C22C2×C22⋊#362411yescharacteristic
324C22C2×#1058755111yescharacteristic
325C22C2×#1058755311yescharacteristic
326C4—22no—
327C4—42no—
328C4—682no—
329C4—682no—
330C4—1361no—
331C4—1361no—
332C4#1176365212yes—
333C4#1176365212yes—
334C2—21no—
335C2—21no—
336C2—44no—
337C2—41no—
338C2—41no—
339C2C2×#1176365211yescharacteristic
340C2#1454503512yes—
subgroupG/H
centerC2×C4#10587551
commutatorC23×C17C22×C8
FrattiniC24C22×#595
FittingC24×C4×C17C4
socleC22×C17C2×#99
prime radicalC25×C17C2×C4
cosocleC2×C22⋊Dic17C23
hypercenterC24×C4#595
hypocenterC17#11425
LCSG ▷ C23×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C23×C4 ◁ C24×C4

Complements

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

NH ≅ G/Ntype
1. #14544015C2semidirect
2. #14543710C2semidirect
24. C23×C4×C17C8semidirect
194. C23×C4#3624semidirect
215. C17#11425semidirect

Maximal subgroups

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

subgroupindex
#145440152
#145437102
#145437082
#145311672
#1142517