Finite Group Databasebeta

← #16924453

Subgroups — #16924453

Order 4352.

604 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14537417C211yesmaximal, characteristic
2#14531182C211yesmaximal, characteristic
3#14526670C214yesmaximal
4C17×#2283C211yesmaximal, characteristic
5#11762866—21no—
6#11762866—21no—
7#11762862—21no—
8#11762862—21no—
9#11762833C412yescomplemented
10#11762773C2212yes—
11C4×#63223C412yescomplemented
12#11762677C412yescomplemented
13#11762675C412yescomplemented
14#11762672—21no—
15#11762669—21no—
16C4×C4⋊Dic17—21no—
17C4×C22⋊Dic17C2212yes—
18#11762655—21no—
19C22×C42×C17C2211yescharacteristic
20C17×#383C412yescomplemented
21C17×#382C412yescomplemented
22C17×#381—21no—
23C17×#380—21no—
24C4×C4⋊C4×C17—21no—
25C4×C22⋊C4×C17C2212yes—
26C17×#376—21no—
27C23×C4×C17D411yescharacteristic
28C23×C4×C17D411yescharacteristic
29C23×C4×C17C2311yescharacteristic
30C2×C4⋊C4×C17—22no—
31C2×C22⋊C4×C17—22no—
32C2×C42×C17—22no—
33C2×C42×C17C2×C411yescharacteristic
34C2×C42×C17C2×C411yescharacteristic
35C2×C42×C17C2×C411yescharacteristic
36C2×C42×C17C2×C411yescharacteristic
37C2×C42×C17C2×C411yescharacteristic
38C2×C42×C17C2×C411yescharacteristic
39C2×C42×C17D411yescharacteristic
40C2×C42×C17D411yescharacteristic
41C2×C42×C17D411yescharacteristic
42C2×C42×C17D411yescharacteristic
43C2×C42×C17Q811yescharacteristic
44C2×C42×C17Q811yescharacteristic
45C2×C22⋊Dic17—22no—
46C2×C4⋊Dic17—22no—
47C2×C4×Dic17—22no—
48C2×#63223C2×C414yes—
49C17×#95—22no—
50C17×#95—22no—
51C17×#95—22no—
52C17×#95C2×C414yes—
53#10587502—22no—
54#10587502—22no—
55#10587502—22no—
56#10587502C2×C414yes—
57C22⋊#3622—22no—
58C22⋊#3622—22no—
59C4⋊#3622—22no—
60C4⋊#3622—22no—
61#10587474—22no—
62C4×#3622—22no—
63C24×C17C2×D411yescharacteristic
64C22×C4×C17—24no—
65C22×C4×C17—42no—
66C22×C4×C17—42no—
67C22×C4×C17—42no—
68C22×C4×C17C22⋊C411yescharacteristic
69C22×C4×C17C22⋊C411yescharacteristic
70C22×C4×C17C22⋊C411yescharacteristic
71C22×C4×C17C22⋊C411yescharacteristic
72C22×C4×C17C22⋊C411yescharacteristic
73C22×C4×C17C22⋊C411yescharacteristic
74C22×C4×C17C22⋊C411yescharacteristic
75C22×C4×C17C22⋊C411yescharacteristic
76C22×C4×C17C4⋊C411yescharacteristic
77C22×C4×C17C4⋊C411yescharacteristic
78C22×C4×C17C4⋊C411yescharacteristic
79C22×C4×C17C4⋊C411yescharacteristic
80C22×C4×C17C22×C411yescharacteristic
81C22×C4×C17C22×C411yescharacteristic
82C22×C4×C17C22×C411yescharacteristic
83C22×C4×C17C2×D411yescharacteristic
84C22×C4×C17C2×D411yescharacteristic
85C22×C4×C17C2×Q811yescharacteristic
86C22×Dic17—24no—
87C4⋊C4×C17—44no—
88C22⋊C4×C17—44no—
89C42×C17—44no—
90C42×C17C4211yescharacteristic
91C42×C17C4211yescharacteristic
92C42×C17C4211yescharacteristic
93C42×C17C4211yescharacteristic
94C42×C17C22⋊C411yescharacteristic
95C42×C17C22⋊C411yescharacteristic
96C42×C17C22⋊C411yescharacteristic
97C42×C17C22⋊C411yescharacteristic
98C42×C17C4⋊C411yescharacteristic
99C42×C17C4⋊C411yescharacteristic
100C42×C17C4⋊C411yescharacteristic
101C42×C17C4⋊C411yescharacteristic
102C42×C17C4⋊C411yescharacteristic
103C42×C17C4⋊C411yescharacteristic
104C42×C17C4⋊C411yescharacteristic
105C42×C17C4⋊C411yescharacteristic
106C22⋊Dic17—44no—
107C4⋊Dic17—44no—
108C4×Dic17—44no—
109#63223—44no—
110C2×#3622—24no—
111#8050—171nomaximal, Sylow
112C23×C17—22no—
113C23×C17—22no—
114C23×C17—41no—
115C23×C17C2×C22⋊C411yescharacteristic
116C23×C17C2×C22⋊C411yescharacteristic
117C23×C17C2×C4⋊C411yescharacteristic
118C2×C4×C17—22no—
119C2×C4×C17—22no—
120C2×C4×C17—22no—
121C2×C4×C17—22no—
122C2×C4×C17—22no—
123C2×C4×C17—22no—
124C2×C4×C17—22no—
125C2×C4×C17—41no—
126C2×C4×C17—41no—
127C2×C4×C17—41no—
128C2×C4×C17—41no—
129C2×C4×C17—41no—
130C2×C4×C17—41no—
131C2×C4×C17—41no—
132C2×C4×C17—41no—
133C2×C4×C17—41no—
134C2×C4×C17—41no—
135C2×C4×C17—41no—
136C2×C4×C17—44no—
137C2×C4×C17—44no—
138C2×C4×C17—44no—
139C2×C4×C17#9511yescharacteristic
140C2×C4×C17#9511yescharacteristic
141C2×C4×C17#9511yescharacteristic
142C2×C4×C17#9511yescharacteristic
143C2×C4×C17#9511yescharacteristic
144C2×C4×C17#9511yescharacteristic
145C2×C4×C17#9511yescharacteristic
146C2×C4×C17#9511yescharacteristic
147C2×C4×C17C2×C4211yescharacteristic
148C2×C4×C17C2×C22⋊C411yescharacteristic
149C2×C4×C17C2×C4⋊C411yescharacteristic
150C2×C4×C17C2×C4⋊C411yescharacteristic
151C2×Dic17—44no—
152C2×Dic17—44no—
153C2×Dic17—44no—
154#3622—44no—
155#2920—171no—
156#2283—171no—
157#2283D1711yescharacteristic
158#1297—174no—
159C22×C17—21no—
160C22×C17—21no—
161C22×C17—21no—
162C22×C17—21no—
163C22×C17—21no—
164C22×C17—21no—
165C22×C17—21no—
166C22×C17—44no—
167C22×C17C2×#9511yescharacteristic
168C22×C17#42112yes—
169C22×C17#42112yes—
170C4×C17—21no—
171C4×C17—21no—
172C4×C17—21no—
173C4×C17—21no—
174C4×C17—21no—
175C4×C17—21no—
176C4×C17—21no—
177C4×C17—21no—
178C4×C17—21no—
179C4×C17—21no—
180C4×C17—21no—
181C4×C17—84no—
182C4×C17#41012yes—
183Dic17—84no—
184C22×C42C2×D1711yescharacteristic
185#432—341no—
186#432—341no—
187#431—341no—
188#431—341no—
189#423—172no—
190#407—172no—
191C4×M16—172no—
192#383—172no—
193#383Dic1712yescomplemented
194#382—172no—
195#382Dic1712yescomplemented
196#381—21no—
197#381—341no—
198#380—21no—
199#380—341no—
200C4×C4⋊C4—21no—
201C4×C4⋊C4—341no—
202C4×C22⋊C4—172no—
203C4×C22⋊C4C2×D1712yes—
204#376—21no—
205#376—341no—
206C2×C17—22no—
207C2×C17—22no—
208C2×C17—41no—
209C2×C17#173311yescharacteristic
210C2×C17#173311yescharacteristic
211C2×C17#174011yescharacteristic
212C23×C4C22⋊D1711yescharacteristic
213C23×C4C22⋊D1711yescharacteristic
214C23×C4C22×D1711yescharacteristic
215C2×M16—174no—
216C2×C4⋊C4—22no—
217C2×C4⋊C4—342no—
218C2×C22⋊C4—22no—
219C2×C22⋊C4—342no—
220C2×C42—22no—
221C2×C42—342no—
222C2×C42Dic3411yescharacteristic
223C2×C42Dic3411yescharacteristic
224C2×C42C4×D1711yescharacteristic
225C2×C42C4×D1711yescharacteristic
226C2×C42C4×D1711yescharacteristic
227C2×C42C4×D1711yescharacteristic
228C2×C42D6811yescharacteristic
229C2×C42D6811yescharacteristic
230C2×C42C2×Dic1711yescharacteristic
231C2×C42C2×Dic1711yescharacteristic
232C2×C42C22⋊D1711yescharacteristic
233C2×C42C22⋊D1711yescharacteristic
234C4⋊C8—342no—
235C4⋊C8—342no—
236C22⋊C8—342no—
237C22⋊C8—342no—
238#97—342no—
239C4×C8—342no—
240#95—22no—
241#95—22no—
242#95—22no—
243#95—174no—
244#95—342no—
245#95—342no—
246#95—342no—
247#95C2×Dic1714yes—
248C17#805011yescharacteristic, complemented, Sylow
249C24C2×C22⋊D1711yescharacteristic
250C22×C4—24no—
251C22×C4—42no—
252C22×C4—42no—
253C22×C4—42no—
254C22×C4—344no—
255C22×C4#6322511yescharacteristic
256C22×C4#6322511yescharacteristic
257C22×C4#6322511yescharacteristic
258C22×C4#6322511yescharacteristic
259C22×C4#6322711yescharacteristic
260C22×C4#6322711yescharacteristic
261C22×C4#6322711yescharacteristic
262C22×C4#6322711yescharacteristic
263C22×C4C22⋊Dic1711yescharacteristic
264C22×C4C22⋊Dic1711yescharacteristic
265C22×C4C22⋊Dic1711yescharacteristic
266C22×C4C22⋊Dic1711yescharacteristic
267C22×C4C2×Dic3411yescharacteristic
268C22×C4C2×C4×D1711yescharacteristic
269C22×C4C2×C4×D1711yescharacteristic
270C22×C4C2×D6811yescharacteristic
271C22×C4C22×Dic1711yescharacteristic
272C22×C4C2×C22⋊D1711yescharacteristic
273M16—684no—
274C2×C8—344no—
275C4⋊C4—44no—
276C4⋊C4—684no—
277C22⋊C4—44no—
278C22⋊C4—684no—
279C42—44no—
280C42—684no—
281C42C4×Dic1711yescharacteristic
282C42C4×Dic1711yescharacteristic
283C42C4×Dic1711yescharacteristic
284C42C4×Dic1711yescharacteristic
285C42#6322511yescharacteristic
286C42#6322511yescharacteristic
287C42#6322511yescharacteristic
288C42#6322511yescharacteristic
289C42C4⋊Dic1711yescharacteristic
290C42C4⋊Dic1711yescharacteristic
291C42C4⋊Dic1711yescharacteristic
292C42C4⋊Dic1711yescharacteristic
293C42#6322711yescharacteristic
294C42#6322711yescharacteristic
295C42#6322711yescharacteristic
296C42#6322711yescharacteristic
297C23—22no—
298C23—22no—
299C23—41no—
300C23C2×#6322511yescharacteristic
301C23C2×#6322711yescharacteristic
302C23C2×C22⋊Dic1711yescharacteristic
303C2×C4—22no—
304C2×C4—22no—
305C2×C4—22no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—44no—
322C2×C4—44no—
323C2×C4—44no—
324C2×C4—684no—
325C2×C4—684no—
326C2×C4—684no—
327C2×C4#1058750211yescharacteristic
328C2×C4#1058750211yescharacteristic
329C2×C4#1058750211yescharacteristic
330C2×C4#1058750211yescharacteristic
331C2×C4#1058750211yescharacteristic
332C2×C4#1058750211yescharacteristic
333C2×C4#1058750211yescharacteristic
334C2×C4#1058750211yescharacteristic
335C2×C4C2×C4×Dic1711yescharacteristic
336C2×C4C2×#6322511yescharacteristic
337C2×C4C2×C4⋊Dic1711yescharacteristic
338C2×C4C2×#6322711yescharacteristic
339C8—684no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—44no—
348C22C2×#1058750211yescharacteristic
349C22#1176282612yes—
350C22#1176282712yes—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—21no—
355C4—21no—
356C4—21no—
357C4—21no—
358C4—21no—
359C4—21no—
360C4—21no—
361C4—21no—
362C4—84no—
363C4—1364no—
364C4#1176278212yes—
365C2—22no—
366C2—22no—
367C2—41no—
368C2#1452849311yescharacteristic
369C2#1452849411yescharacteristic
370C2#1452851611yescharacteristic
subgroupG/H
centerC2×C4C2×#63227
commutatorC2×C4×C17C2×C42
FrattiniC23×C4C22×D17
FittingC17×#2283C2
socleC22×C17C2×#95
prime radicalC24×C17C2×D4
cosocleC23×C4×C17C23
hypercenter#2283D17
hypocenterC17#8050
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C22×C42 ◁ #2283

Complements

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

NH ≅ G/Ntype
9. #11762833C4semidirect
11. C4×#63223C4semidirect
12. #11762677C4semidirect
13. #11762675C4semidirect
20. C17×#383C4semidirect
21. C17×#382C4semidirect
193. #383Dic17semidirect
195. #382Dic17semidirect
248. C17#8050semidirect

Maximal subgroups

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

subgroupindex
#145374172
#145311822
#145266702
C17×#22832
#805017