Finite Group Databasebeta

← #16932118

Subgroups — #16932118

Order 4352.

576 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 576 conjugacy classes of subgroups — too many to draw. Only its 119 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#14533092C211yesmaximal, characteristic
2#14528871C212yesmaximal, complemented
3#14528772C211yesmaximal, characteristic
4#14526652C212yesmaximal, complemented
5C17×#2973C211yesmaximal, characteristic
6C2×#10587621—21no—
7C22×C4⋊Dic17C2211yescharacteristic
8C2×#10587505—21no—
9#11762739C412yescomplemented
10#11762734C412yescomplemented
11#11762707—21no—
12#11762670—21no—
13#11762669—21no—
14#11762669C2212yes—
15#11762669C2211yescharacteristic
16#11762576—21no—
17#11762572—24no—
18C2×C4×D4×C17C2211yescharacteristic
19C17×#435—24no—
20C17×#432—21no—
21C17×#407—21no—
22C2×C17×C22⋊C8C2212yes—
23C22×D4×C17D411yescharacteristic
24C23×C4×C17D411yescharacteristic
25C23×C4×C17C2311yescharacteristic
26C23×Dic17—21no—
27C2×M16×C17—22no—
28C22×C8×C17D414yes—
29C4×D4×C17—22no—
30C4×D4×C17—22no—
31C2×C4⋊C4×C17C2×C411yescharacteristic
32C2×C22⋊C4×C17C2×C411yescharacteristic
33C2×C22⋊C4×C17D411yescharacteristic
34C2×C42×C17D411yescharacteristic
35C2×C22⋊Dic17—22no—
36C2×C22⋊Dic17—21no—
37C2×C22⋊Dic17—22no—
38#10587621—44no—
39C2×C4⋊Dic17—21no—
40C2×C4⋊Dic17—21no—
41C2×C4⋊Dic17—22no—
42C2×C4⋊Dic17—22no—
43C2×C4⋊Dic17—22no—
44C2×C4⋊Dic17C2×C412yes—
45C2×#63225—22no—
46C17×C4⋊C8—22no—
47C17×C22⋊C8—22no—
48C17×C22⋊C8—22no—
49C17×C22⋊C8—22no—
50C17×#97—22no—
51#10587505—42no—
52#10587502—22no—
53#10587502—22no—
54#10587502—22no—
55#10587502C2×C412yes—
56C24×C17C22⋊C411yescharacteristic
57C24×C17C2×D411yescharacteristic
58C2×D4×C17—22no—
59C2×D4×C17—21no—
60C2×D4×C17—22no—
61C2×D4×C17—21no—
62C22×C4×C17—21no—
63C22×C4×C17—21no—
64C22×C4×C17—42no—
65C22×C4×C17—42no—
66C22×C4×C17C22⋊C411yescharacteristic
67C22×C4×C17C22⋊C411yescharacteristic
68C22×C4×C17C22⋊C411yescharacteristic
69C22×C4×C17C22×C411yescharacteristic
70C22×C4×C17C2×D412yes—
71C22×C4×C17C2×D411yescharacteristic
72C22×C4×C17#4112yes—
73C22×Dic17—22no—
74C22×Dic17—22no—
75C22×Dic17—42no—
76C22×Dic17—41no—
77C22×Dic17—42no—
78C22×Dic17—41no—
79C22×Dic17—42no—
80M16×C17—82no—
81C2×C8×C17—24no—
82C2×C8×C17—44no—
83C4⋊C4×C17—22no—
84C22⋊C4×C17—22no—
85C22⋊C4×C17—22no—
86C42×C17—21no—
87C42×C17—21no—
88C22⋊Dic17—44no—
89C22⋊Dic17—42no—
90C22⋊Dic17—42no—
91C22⋊Dic17—42no—
92C4⋊Dic17—24no—
93C4⋊Dic17—42no—
94C4⋊Dic17—41no—
95C4⋊Dic17—41no—
96C4⋊Dic17—44no—
97#63225—44no—
98#9474—171nomaximal, Sylow
99C23×C17—21no—
100C23×C17—21no—
101C23×C17—21no—
102C23×C17—41no—
103C23×C17—41no—
104C23×C17—41no—
105C23×C17—41no—
106C23×C17C2×C22⋊C411yescharacteristic
107C23×C17#12112yes—
108C23×C17AGL(1,ℤ/8)11yescharacteristic
109C23×C17AGL(1,ℤ/8)12yes—
110C23×C17#13711yescharacteristic
111D4×C17—42no—
112D4×C17—42no—
113C2×C4×C17—24no—
114C2×C4×C17—22no—
115C2×C4×C17—21no—
116C2×C4×C17—21no—
117C2×C4×C17—21no—
118C2×C4×C17—21no—
119C2×C4×C17—21no—
120C2×C4×C17—41no—
121C2×C4×C17—42no—
122C2×C4×C17—42no—
123C2×C4×C17—41no—
124C2×C4×C17—41no—
125C2×C4×C17—81no—
126C2×C4×C17C4×D412yes—
127C2×C4×C17#12011yescharacteristic
128C2×C4×C17#12311yescharacteristic
129C2×Dic17—42no—
130C2×Dic17—42no—
131C2×Dic17—42no—
132C2×Dic17—42no—
133C2×Dic17—42no—
134C2×Dic17—42no—
135C2×Dic17—82no—
136C2×Dic17—82no—
137C2×Dic17—82no—
138C2×Dic17—82no—
139C2×Dic17—82no—
140C8×C17—44no—
141#2973D1711yescharacteristic
142#2486—171no—
143#1823—172no—
144#1799—171no—
145#1289—172no—
146C22×C17—21no—
147C22×C17—22no—
148C22×C17—21no—
149C22×C17—22no—
150C22×C17—42no—
151C22×C17—41no—
152C22×C17—41no—
153C22×C17—42no—
154C22×C17—41no—
155C22×C17—41no—
156C22×C17—41no—
157C22×C17—81no—
158C22×C17#38611yescharacteristic
159C22×C17#41711yescharacteristic
160C22×C17#41811yescharacteristic
161C22×C17#46812yes—
162C22×C17#46912yes—
163C4×C17—21no—
164C4×C17—22no—
165C4×C17—41no—
166C4×C17—41no—
167C4×C17—41no—
168C4×C17#45812yes—
169Dic17—82no—
170Dic17—82no—
171Dic17—162no—
172C2×#123—341no—
173C2×C4×D4C2×D1711yescharacteristic
174C22×C4⋊C4—171no—
175#435—24no—
176#432—21no—
177C2×#99—341no—
178#407—21no—
179C2×C22⋊C8C2×D1712yes—
180#398—172no—
181#397—172no—
182#389—341no—
183#381—341no—
184#380—171no—
185#380—172no—
186#380—341no—
187#342—341no—
188#340—344no—
189C2×C17—21no—
190C2×C17—22no—
191C2×C17—21no—
192C2×C17—22no—
193C2×C17—81no—
194C2×C17#189011yescharacteristic
195C2×C17#189511yescharacteristic
196C2×C17#190911yescharacteristic
197C22×D4D6811yescharacteristic
198C23×C4—341no—
199C23×C4C22⋊D1711yescharacteristic
200C23×C4C22×D1711yescharacteristic
201C2×M16—22no—
202C22×C8C22⋊D1714yes—
203#123—684no—
204C4×D4—22no—
205C4×D4—22no—
206C2×C4⋊C4—172no—
207C2×C4⋊C4—342no—
208C2×C4⋊C4—342no—
209C2×C4⋊C4—341no—
210C2×C4⋊C4—341no—
211C2×C4⋊C4—342no—
212C2×C4⋊C4—342no—
213C2×C4⋊C4C4×D1711yescharacteristic
214C2×C22⋊C4—341no—
215C2×C22⋊C4—342no—
216C2×C22⋊C4—342no—
217C2×C22⋊C4C4×D1711yescharacteristic
218C2×C22⋊C4D6811yescharacteristic
219C2×C42C22⋊D1711yescharacteristic
220C4⋊C8—22no—
221#99—682no—
222C22⋊C8—22no—
223C22⋊C8—22no—
224C22⋊C8—22no—
225#97—22no—
226#95—172no—
227#95—342no—
228#95—342no—
229#95—342no—
230C17#947411yescharacteristic, complemented, Sylow
231C24#6322711yescharacteristic
232C24C2×D6811yescharacteristic
233C2×D4—21no—
234C2×D4—22no—
235C2×D4—21no—
236C2×D4—22no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—42no—
240C22×C4—42no—
241C22×C4—342no—
242C22×C4—342no—
243C22×C4—682no—
244C22×C4—681no—
245C22×C4—681no—
246C22×C4—682no—
247C22×C4—682no—
248C22×C4#6322711yescharacteristic
249C22×C4#6322711yescharacteristic
250C22×C4#6322711yescharacteristic
251C22×C4C2×C4×D1711yescharacteristic
252C22×C4#6325212yes—
253C22×C4C2×C22⋊D1712yes—
254C22×C4C2×C22⋊D1711yescharacteristic
255M16—82no—
256C2×C8—24no—
257C2×C8—44no—
258C4⋊C4—22no—
259C4⋊C4—344no—
260C4⋊C4—684no—
261C4⋊C4—682no—
262C4⋊C4—684no—
263C4⋊C4—681no—
264C4⋊C4—681no—
265C22⋊C4—22no—
266C22⋊C4—22no—
267C22⋊C4—684no—
268C22⋊C4—682no—
269C22⋊C4—682no—
270C22⋊C4—682no—
271C42—21no—
272C42—21no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23—41no—
277C23—41no—
278C23—41no—
279C23—41no—
280C23#1058759412yes—
281C23#1058759411yescharacteristic
282C23#1058759511yescharacteristic
283C23C2×#6322711yescharacteristic
284C23#1058761612yes—
285D4—42no—
286D4—42no—
287C2×C4—24no—
288C2×C4—22no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—41no—
295C2×C4—42no—
296C2×C4—42no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—81no—
300C2×C4—682no—
301C2×C4—682no—
302C2×C4—682no—
303C2×C4—682no—
304C2×C4—682no—
305C2×C4—682no—
306C2×C4—1362no—
307C2×C4—1362no—
308C2×C4—1362no—
309C2×C4—1362no—
310C2×C4—1362no—
311C2×C4C4×C22⋊D1712yes—
312C2×C4#1058761511yescharacteristic
313C2×C4#1058763911yescharacteristic
314C8—44no—
315C22—21no—
316C22—22no—
317C22—21no—
318C22—22no—
319C22—41no—
320C22—42no—
321C22—41no—
322C22—42no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—81no—
327C22#1176268811yescharacteristic
328C22#1176281111yescharacteristic
329C22#1176281511yescharacteristic
330C22#1176305512yes—
331C22#1176306212yes—
332C4—21no—
333C4—22no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—2722no—
338C4—1362no—
339C4—1362no—
340C4#1176299912yes—
341C2—22no—
342C2—21no—
343C2—21no—
344C2—22no—
345C2—81no—
346C2#1452919711yescharacteristic
347C2#1452922211yescharacteristic
348C2#1452930611yescharacteristic
subgroupG/H
centerC22#11762688
commutatorC22×C4×C17C22×C4
FrattiniC23×C4C22×D17
FittingC17×#2973C2
socleC22×C17#386
prime radicalC22×D4×C17D4
cosocleC23×C4×C17C23
hypercenter#2973D17
hypocenterC17#9474
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2973

Complements

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

NH ≅ G/Ntype
2. #14528871C2semidirect
4. #14526652C2semidirect
9. #11762739C4semidirect
10. #11762734C4semidirect
230. C17#9474semidirect

Maximal subgroups

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

subgroupindex
#145330922
#145288712
#145287722
#145266522
C17×#29732
#947417