Finite Group Databasebeta

← #17950964

Subgroups — #17950964

Order 4352.

986 conjugacy classes of subgroups; only the 158 normal subgroups are shown.

normal subgroups only

This group has 986 conjugacy classes of subgroups — too many to draw. Only its 158 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#14545228C212yesmaximal
2#14543647C214yesmaximal, complemented
3C2×C22⋊C8×D17C211yesmaximal, characteristic
4C2×#10587677—22no—
5#11763752C414yescomplemented
6#11763751—22no—
7#11763751C2214yes—
8#11763750—22no—
9C4×C22⋊#595—22no—
10C4×C22⋊#595C414yescomplemented
11C23×C4×D17C2211yescharacteristic
12C22×C8×D17C412yescomplemented
13C2×C22⋊#3622C411yescharacteristic, complemented
14C2×#10587491C2212yes—
15C22⋊C8×D17—22no—
16C22⋊C8×D17—22no—
17C2×C17×C22⋊C8C411yescharacteristic, complemented
18C24×D17D411yescharacteristic
19C23×C4×C17C2×C411yescharacteristic
20C23×Dic17Q811yescharacteristic
21C22×C4×D17—44no—
22C22×C4×D17C2×C411yescharacteristic
23C22×C4×D17C2×C412yes—
24C22×C4×D17C2×C412yes—
25C22×C4×D17D412yes—
26C22×C4×D17D411yescharacteristic
27C22×C4×D17D412yes—
28C22×C4×D17Q811yescharacteristic
29C22×C4×D17C2311yescharacteristic
30C2×C22⋊#595—24no—
31C2×C22⋊#595—24no—
32C2×C22⋊#595—24no—
33#10587677—48no—
34C2×C4⋊#595—24no—
35C2×C4×#595—24no—
36C22×C8×C17C2×C412yes—
37C22×#3622C2×C412yes—
38C2×C8×D17—22no—
39C2×C8×D17—22no—
40C2×C8×D17—44no—
41(C2×#595)⋊C4—24no—
42(C2×#595)⋊C4C2×C418yes—
43C17×C22⋊C8—22no—
44C22⋊#3622—22no—
45#10587491—24no—
46C24×C17C4⋊C411yescharacteristic
47C23×D17—24no—
48C23×D17—42no—
49C23×D17—42no—
50C23×D17C22⋊C412yes—
51C23×D17C22⋊C412yes—
52C23×D17C4⋊C411yescharacteristic
53C23×D17C2×D411yescharacteristic
54C22×#595—28no—
55C22×C4×C17—42no—
56C22×C4×C17C4212yes—
57C22×C4×C17C22⋊C412yes—
58C22×C4×C17C4⋊C411yescharacteristic
59C22×C4×C17C22×C411yescharacteristic
60C22×Dic17—42no—
61C22×Dic17C4⋊C411yescharacteristic
62C22×Dic17C4⋊C412yes—
63C22×Dic17C4⋊C412yes—
64C22×Dic17C2×Q811yescharacteristic
65C2×C4×D17—28no—
66C2×C4×D17—24no—
67C2×C4×D17—44no—
68C2×C4×D17—42no—
69C2×C4×D17—44no—
70C2×C4×D17—42no—
71C2×C4×D17—44no—
72C2×C4×D17—42no—
73C2×C4×D17C4211yescharacteristic
74C2×C4×D17C4211yescharacteristic
75C2×C4×D17C22⋊C412yes—
76C2×C4×D17C22⋊C411yescharacteristic
77C2×C4×D17C22⋊C412yes—
78C2×C4×D17C22⋊C411yescharacteristic
79C2×C4×D17C4⋊C412yes—
80C2×C4×D17C4⋊C412yes—
81C2×C4×D17C22×C412yes—
82C2×C4×D17C2×D412yes—
83C22⋊#595—48no—
84C22⋊#595—48no—
85C22⋊#595—48no—
86C4⋊#595—48no—
87C4×#595—48no—
88C2×C8×C17—22no—
89C2×C8×C17—42no—
90C2×#3622—22no—
91C2×#3622—42no—
92C8×D17—44no—
93C8×D17—44no—
94#7982—171nomaximal, Sylow
95C23×C17—22no—
96C23×C17—41no—
97C23×C17—41no—
98C23×C17#9512yes—
99C23×C17C2×C4⋊C411yescharacteristic
100C22×D17—22no—
101C22×D17—22no—
102C22×D17—22no—
103C22×D17—24no—
104C22×D17—24no—
105C22×D17—24no—
106C22×D17—24no—
107C22×D17—42no—
108C22×D17—41no—
109C22×D17—42no—
110C22×D17—41no—
111C22×D17—416no—
112C22×D17#9511yescharacteristic
113C22×D17#9511yescharacteristic
114C22×D17C2×C22⋊C412yes—
115C22×D17#13514yes—
116C2×#595—48no—
117C2×#595—48no—
118C2×#595—48no—
119C2×C4×C17—22no—
120C2×C4×C17—24no—
121C2×C4×C17—42no—
122C2×C4×C17—41no—
123C2×C4×C17#9512yes—
124C2×C4×C17C2×C4211yescharacteristic
125C2×C4×C17C2×C22⋊C411yescharacteristic
126C2×Dic17—22no—
127C2×Dic17—24no—
128C2×Dic17—42no—
129C2×Dic17—41no—
130C2×Dic17#9511yescharacteristic
131C2×Dic17#9511yescharacteristic
132C2×Dic17C2×C4⋊C412yes—
133C4×D17—22no—
134C4×D17—24no—
135C4×D17—24no—
136C4×D17—22no—
137C4×D17—24no—
138C4×D17—22no—
139C4×D17—42no—
140C4×D17—42no—
141C4×D17—42no—
142C4×D17#9914yes—
143C8×C17—42no—
144#3622—42no—
145C22×C22⋊C8—171no—
146#2280—172no—
147#1289—174no—
148C22×C17—21no—
149C22×C17—21no—
150C22×C17—22no—
151C22×C17—22no—
152C22×C17—22no—
153C22×C17—44no—
154C22×C17C2×#9511yescharacteristic
155C22×C17#42712yes—
156C2×D17—28no—
157C2×D17—22no—
158C2×D17—21no—
159C2×D17—21no—
160C2×D17—21no—
161C2×D17—22no—
162C2×D17—21no—
163C2×D17—44no—
164C2×D17—48no—
165C2×D17—48no—
166C2×D17H(3,ℤ/4)12yes—
167C2×D17#34212yes—
168C2×D17#41614yes—
169#595—88no—
170C4×C17—22no—
171C4×C17—21no—
172C4×C17C2×#9912yes—
173Dic17—21no—
174Dic17—22no—
175Dic17#34212yes—
176C24×C4—171no—
177C23×C8—172no—
178C2×#117—342no—
179C2×C22⋊C8—171no—
180C2×C22⋊C8—172no—
181C2×C22⋊C8—342no—
182C2×C22⋊C8—342no—
183C2×C22⋊C8#59511yescharacteristic, complemented
184#381—174no—
185#380—174no—
186#380—342no—
187#379—342no—
188C4×C22⋊C4—174no—
189C4×C22⋊C4—342no—
190C2×C17—22no—
191C2×C17—42no—
192C2×C17C2×H(3,ℤ/4)11yescharacteristic
193C2×C17#173511yescharacteristic
194C2×C17C2×#34211yescharacteristic
195D17—24no—
196D17—22no—
197D17—22no—
198C25—171no—
199C23×C4—171no—
200C23×C4—172no—
201C23×C4—171no—
202C23×C4—172no—
203C23×C4—172no—
204C23×C4—171no—
205C23×C4—171no—
206C23×C4—172no—
207C23×C4—171no—
208C23×C4—684no—
209C23×C4C2×#59511yescharacteristic
210C22×C8—172no—
211C22×C8—342no—
212C22×C8—342no—
213C22×C8—684no—
214C22×C8C2×#59512yes—
215#117—688no—
216C2×C4⋊C4—344no—
217C2×C22⋊C4—344no—
218C2×C22⋊C4—344no—
219C2×C22⋊C4—344no—
220C2×C42—344no—
221C22⋊C8—22no—
222C22⋊C8—344no—
223C22⋊C8—342no—
224#95—178no—
225#95—344no—
226C17#798211yescharacteristic, complemented, Sylow
227C24—171no—
228C24—171no—
229C24—172no—
230C24—172no—
231C24—344no—
232C24—682no—
233C24—682no—
234C24C4⋊#59511yescharacteristic
235C22×C4—42no—
236C22×C4—171no—
237C22×C4—171no—
238C22×C4—172no—
239C22×C4—171no—
240C22×C4—172no—
241C22×C4—171no—
242C22×C4—171no—
243C22×C4—171no—
244C22×C4—172no—
245C22×C4—172no—
246C22×C4—172no—
247C22×C4—172no—
248C22×C4—172no—
249C22×C4—172no—
250C22×C4—348no—
251C22×C4—344no—
252C22×C4—348no—
253C22×C4—682no—
254C22×C4—684no—
255C22×C4—684no—
256C22×C4—682no—
257C22×C4—684no—
258C22×C4—682no—
259C22×C4—682no—
260C22×C4C4×#59512yes—
261C22×C4C4⋊#59511yescharacteristic
262C22×C4C22⋊#59512yes—
263C22×C4C22×#59511yescharacteristic
264C2×C8—22no—
265C2×C8—42no—
266C2×C8—342no—
267C2×C8—684no—
268C2×C8—684no—
269C2×C8—682no—
270C4⋊C4—688no—
271C22⋊C4—688no—
272C22⋊C4—688no—
273C22⋊C4—688no—
274C42—688no—
275C23—22no—
276C23—41no—
277C23—41no—
278C23—172no—
279C23—171no—
280C23—171no—
281C23—174no—
282C23—342no—
283C23—342no—
284C23—344no—
285C23—344no—
286C23—344no—
287C23—344no—
288C23—342no—
289C23—681no—
290C23—682no—
291C23—681no—
292C23—682no—
293C23—6816no—
294C23(C2×#595)⋊C412yes—
295C23C2×C4⋊#59511yescharacteristic
296C2×C4—22no—
297C2×C4—24no—
298C2×C4—42no—
299C2×C4—41no—
300C2×C4—171no—
301C2×C4—174no—
302C2×C4—171no—
303C2×C4—172no—
304C2×C4—344no—
305C2×C4—342no—
306C2×C4—342no—
307C2×C4—344no—
308C2×C4—342no—
309C2×C4—344no—
310C2×C4—344no—
311C2×C4—342no—
312C2×C4—682no—
313C2×C4—682no—
314C2×C4—682no—
315C2×C4—681no—
316C2×C4—682no—
317C2×C4—688no—
318C2×C4—688no—
319C2×C4—688no—
320C2×C4(C2×#595)⋊C412yes—
321C2×C4C2×C4×#59511yescharacteristic
322C2×C4C2×C22⋊#59511yescharacteristic
323C8—42no—
324C8—682no—
325C22—21no—
326C22—21no—
327C22—22no—
328C22—22no—
329C22—22no—
330C22—44no—
331C22—172no—
332C22—174no—
333C22—172no—
334C22—348no—
335C22—342no—
336C22—341no—
337C22—341no—
338C22—341no—
339C22—342no—
340C22—341no—
341C22—684no—
342C22—688no—
343C22—688no—
344C22C2×(C2×#595)⋊C411yescharacteristic
345C22#1176381912yes—
346C4—21no—
347C4—22no—
348C4—172no—
349C4—341no—
350C4—342no—
351C4—1368no—
352C4D17⋊#9912yes—
353C2—22no—
354C2—42no—
355C2—344no—
356C2—342no—
357C2—342no—
358C2#1454445611yescharacteristic
359C2#1454447011yescharacteristic
360C2#1454448111yescharacteristic
subgroupG/H
centerC22C2×(C2×#595)⋊C4
commutatorC2×C4×C17C2×C42
FrattiniC22×C4C22×#595
FittingC2×C17×C22⋊C8C4
socleC22×C17C2×#95
prime radicalC24×D17D4
cosocleC22×C4×D17C23
hypercenterC2×C22⋊C8#595
hypocenterC17#7982
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. #14543647C2semidirect
5. #11763752C4semidirect
10. C4×C22⋊#595C4semidirect
12. C22×C8×D17C4semidirect
13. C2×C22⋊#3622C4semidirect
17. C2×C17×C22⋊C8C4semidirect
183. C2×C22⋊C8#595semidirect
226. C17#7982semidirect

Maximal subgroups

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

subgroupindex
#145452282
#145436472
C2×C22⋊C8×D172
#798217