Finite Group Databasebeta

← #17951543

Subgroups — #17951543

Order 4352.

994 conjugacy classes of subgroups; only the 156 normal subgroups are shown.

normal subgroups only

This group has 994 conjugacy classes of subgroups — too many to draw. Only its 156 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#14543683C214yesmaximal
3#14531163C211yesmaximal, characteristic
4C2×#10587677—22no—
5#11763752—22no—
6#11763751—22no—
7#11763751C414yescomplemented
8#11763750C2214yes—
9C4×C22⋊#595—22no—
10C4×C22⋊#595C414yescomplemented
11C23×C4×D17C2211yescharacteristic
12C2×#10587612C411yescharacteristic, complemented
13#11762670C412yescomplemented
14#11762666—22no—
15#11762664C2212yes—
16C4×#63227—22no—
17C2×C17×#117C411yescharacteristic, complemented
18C24×D17C2311yescharacteristic
19C23×C4×C17C2×C411yescharacteristic
20C23×Dic17C2×C411yescharacteristic
21C22×C4×D17—42no—
22C22×C4×D17—42no—
23C22×C4×D17C2×C412yes—
24C22×C4×D17C2×C412yes—
25C22×C4×D17D412yes—
26C22×C4×D17D411yescharacteristic
27C22×C4×D17D411yescharacteristic
28C22×C4×D17D412yes—
29C22×C4×D17Q811yescharacteristic
30C22×C4×D17Q811yescharacteristic
31C2×C22⋊#595—24no—
32C2×C22⋊#595—24no—
33C2×C22⋊#595C2×C418yes—
34#10587677—44no—
35#10587677—44no—
36C2×C4⋊#595—24no—
37C2×C4×#595—24no—
38C17×#117—42no—
39C2×C4⋊C4×C17—21no—
40C2×C22⋊C4×C17C2×C412yes—
41C2×C42×C17—21no—
42C2×C22⋊Dic17C2×C412yes—
43C2×#63227—24no—
44#10587612—42no—
45C2×C4⋊Dic17—21no—
46C2×C4×Dic17—21no—
47(C2×#595)⋊C4—24no—
48(C2×#595)⋊C4—24no—
49#10587502—24no—
50C24×C17C22×C411yescharacteristic
51C23×D17—44no—
52C23×D17—41no—
53C23×D17—41no—
54C23×D17C22×C412yes—
55C23×D17C2×D411yescharacteristic
56C23×D17C2×D412yes—
57C23×D17C2×Q811yescharacteristic
58C22×#595—28no—
59C22×C4×C17—22no—
60C22×C4×C17—22no—
61C22×C4×C17—22no—
62C22×C4×C17C4211yescharacteristic
63C22×C4×C17C4211yescharacteristic
64C22×C4×C17C22⋊C411yescharacteristic
65C22×C4×C17C22⋊C411yescharacteristic
66C22×C4×C17C4⋊C411yescharacteristic
67C22×C4×C17C4⋊C411yescharacteristic
68C22×Dic17—22no—
69C22×Dic17—41no—
70C22×Dic17—41no—
71C22×Dic17C4212yes—
72C22×Dic17C22⋊C412yes—
73C22×Dic17C4⋊C411yescharacteristic
74C22×Dic17C4⋊C411yescharacteristic
75C2×C4×D17—24no—
76C2×C4×D17—24no—
77C2×C4×D17—44no—
78C2×C4×D17—44no—
79C2×C4×D17—42no—
80C2×C4×D17—42no—
81C2×C4×D17—42no—
82C2×C4×D17—42no—
83C2×C4×D17—42no—
84C2×C4×D17—42no—
85C2×C4×D17C22⋊C412yes—
86C2×C4×D17C22⋊C412yes—
87C2×C4×D17C22⋊C412yes—
88C2×C4×D17C22⋊C412yes—
89C2×C4×D17C4⋊C412yes—
90C2×C4×D17C4⋊C412yes—
91C2×C4×D17C4⋊C412yes—
92C2×C4×D17C4⋊C412yes—
93C22⋊#595—44no—
94C22⋊#595—44no—
95C22⋊#595—48no—
96C22⋊#595—48no—
97C4⋊#595—48no—
98C4×#595—48no—
99C4⋊C4×C17—42no—
100C22⋊C4×C17—42no—
101C42×C17—42no—
102C22⋊Dic17—42no—
103#63227—48no—
104C4⋊Dic17—42no—
105C4×Dic17—42no—
106#8100—171nomaximal, Sylow
107C23×C17—21no—
108C23×C17—21no—
109C23×C17—42no—
110C23×C17C2×C4211yescharacteristic
111C23×C17C2×C22⋊C411yescharacteristic
112C23×C17C2×C4⋊C411yescharacteristic
113C22×D17—22no—
114C22×D17—22no—
115C22×D17—24no—
116C22×D17—24no—
117C22×D17—24no—
118C22×D17—42no—
119C22×D17—41no—
120C22×D17—41no—
121C22×D17—42no—
122C22×D17—42no—
123C22×D17—42no—
124C22×D17—48no—
125C22×D17—48no—
126C22×D17C2×C22⋊C412yes—
127C22×D17C2×C4⋊C412yes—
128C2×#595—48no—
129C2×#595—48no—
130C2×#595—48no—
131C2×C4×C17—21no—
132C2×C4×C17—21no—
133C2×C4×C17—22no—
134C2×C4×C17—22no—
135C2×C4×C17—22no—
136C2×C4×C17—22no—
137C2×C4×C17—44no—
138C2×C4×C17—42no—
139C2×C4×C17#9511yescharacteristic
140C2×C4×C17#9511yescharacteristic
141C2×C4×C17#9511yescharacteristic
142C2×C4×C17#9511yescharacteristic
143C2×C4×C17#9912yes—
144C2×C4×C17#9912yes—
145C2×Dic17—22no—
146C2×Dic17—22no—
147C2×Dic17—42no—
148C2×Dic17—41no—
149C2×Dic17—41no—
150C2×Dic17—44no—
151C2×Dic17—42no—
152C2×Dic17#9512yes—
153C2×Dic17#9512yes—
154C4×D17—24no—
155C4×D17—24no—
156C4×D17—24no—
157C4×D17—24no—
158C4×D17—42no—
159C4×D17—42no—
160C4×D17—42no—
161C4×D17—42no—
162#2280—171no—
163#2280—172no—
164#1304—174no—
165C22×C17—22no—
166C22×C17—21no—
167C22×C17—21no—
168C22×C17—22no—
169C22×C17—22no—
170C22×C17—42no—
171C22×C17—42no—
172C22×C17C2×#9511yescharacteristic
173C22×C17C2×#9911yescharacteristic
174C22×C17C2×#9911yescharacteristic
175C2×D17—22no—
176C2×D17—22no—
177C2×D17—22no—
178C2×D17—22no—
179C2×D17—22no—
180C2×D17—44no—
181C2×D17—44no—
182C2×D17—44no—
183C2×D17—48no—
184C2×D17—44no—
185C2×D17#41014yes—
186#595—88no—
187C4×C17—21no—
188C4×C17—21no—
189C4×C17—82no—
190C4×C17#34212yes—
191C4×C17#34212yes—
192Dic17—22no—
193Dic17—22no—
194Dic17—82no—
195C24×C4—171no—
196C2×#117—171no—
197C2×#117—342no—
198C2×#117#59511yescharacteristic, complemented
199#381—172no—
200#381—342no—
201#380—174no—
202#380—342no—
203#380—342no—
204#379—174no—
205#379—172no—
206C4×C22⋊C4—174no—
207C4×C22⋊C4—342no—
208C4×C22⋊C4—342no—
209C2×C17—21no—
210C2×C17—21no—
211C2×C17—41no—
212C2×C17—41no—
213C2×C17C2×#34211yescharacteristic
214C2×C17#174012yes—
215D17—24no—
216D17—42no—
217C25—171no—
218C23×C4—171no—
219C23×C4—172no—
220C23×C4—172no—
221C23×C4—172no—
222C23×C4—171no—
223C23×C4—171no—
224C23×C4—171no—
225C23×C4—171no—
226C23×C4—172no—
227C23×C4—682no—
228C23×C4—682no—
229C23×C4C2×#59511yescharacteristic
230#117—42no—
231#117—684no—
232#117—684no—
233#117—682no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—344no—
236C2×C4⋊C4—341no—
237C2×C22⋊C4—178no—
238C2×C22⋊C4—172no—
239C2×C22⋊C4—344no—
240C2×C22⋊C4—344no—
241C2×C22⋊C4—344no—
242C2×C22⋊C4C2×#59512yes—
243C2×C42—21no—
244C2×C42—344no—
245C2×C42—341no—
246#95—344no—
247#95—344no—
248#95—344no—
249C17#810011yescharacteristic, complemented, Sylow
250C24—171no—
251C24—172no—
252C24—172no—
253C24—171no—
254C24—681no—
255C24—681no—
256C24—684no—
257C24C22×#59511yescharacteristic
258C22×C4—22no—
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—172no—
262C22×C4—172no—
263C22×C4—171no—
264C22×C4—171no—
265C22×C4—172no—
266C22×C4—172no—
267C22×C4—172no—
268C22×C4—172no—
269C22×C4—172no—
270C22×C4—172no—
271C22×C4—172no—
272C22×C4—172no—
273C22×C4—344no—
274C22×C4—344no—
275C22×C4—348no—
276C22×C4—342no—
277C22×C4—684no—
278C22×C4—684no—
279C22×C4—682no—
280C22×C4—682no—
281C22×C4—682no—
282C22×C4—682no—
283C22×C4—682no—
284C22×C4—682no—
285C22×C4—681no—
286C22×C4—681no—
287C22×C4C4×#59511yescharacteristic
288C22×C4C4×#59511yescharacteristic
289C22×C4C4⋊#59511yescharacteristic
290C22×C4C4⋊#59511yescharacteristic
291C22×C4C22⋊#59511yescharacteristic
292C22×C4C22⋊#59511yescharacteristic
293C4⋊C4—42no—
294C4⋊C4—682no—
295C4⋊C4—688no—
296C22⋊C4—42no—
297C22⋊C4—688no—
298C22⋊C4—688no—
299C22⋊C4—684no—
300C22⋊C4—684no—
301C22⋊C4—682no—
302C22⋊C4—688no—
303C42—42no—
304C42—688no—
305C42—682no—
306C23—21no—
307C23—21no—
308C23—42no—
309C23—172no—
310C23—172no—
311C23—344no—
312C23—344no—
313C23—344no—
314C23—342no—
315C23—342no—
316C23—682no—
317C23—681no—
318C23—681no—
319C23—682no—
320C23—682no—
321C23—682no—
322C23—688no—
323C23—688no—
324C23C2×C4×#59511yescharacteristic
325C23C2×C4⋊#59511yescharacteristic
326C23C2×C22⋊#59511yescharacteristic
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—22no—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—22no—
333C2×C4—44no—
334C2×C4—42no—
335C2×C4—172no—
336C2×C4—172no—
337C2×C4—342no—
338C2×C4—342no—
339C2×C4—344no—
340C2×C4—344no—
341C2×C4—344no—
342C2×C4—344no—
343C2×C4—682no—
344C2×C4—682no—
345C2×C4—682no—
346C2×C4—682no—
347C2×C4—682no—
348C2×C4—681no—
349C2×C4—681no—
350C2×C4—684no—
351C2×C4—688no—
352C2×C4—688no—
353C2×C4—688no—
354C2×C4—682no—
355C2×C4#1058753912yes—
356C2×C4(C2×#595)⋊C411yescharacteristic
357C2×C4(C2×#595)⋊C411yescharacteristic
358C2×C4(C2×#595)⋊C411yescharacteristic
359C2×C4(C2×#595)⋊C411yescharacteristic
360C2×C4#1058755112yes—
361C22—22no—
362C22—21no—
363C22—21no—
364C22—22no—
365C22—22no—
366C22—42no—
367C22—42no—
368C22—174no—
369C22—342no—
370C22—342no—
371C22—342no—
372C22—342no—
373C22—342no—
374C22—684no—
375C22—684no—
376C22—684no—
377C22—688no—
378C22—684no—
379C22C2×(C2×#595)⋊C411yescharacteristic
380C22C2×#1058755111yescharacteristic
381C22C2×#1058753911yescharacteristic
382C4—21no—
383C4—21no—
384C4—82no—
385C4—342no—
386C4—342no—
387C4—1362no—
388C4—1368no—
389C4#1176368712yes—
390C4#1176368712yes—
391C2—21no—
392C2—21no—
393C2—41no—
394C2—41no—
395C2—344no—
396C2—682no—
397C2C2×#1176368711yescharacteristic
398C2#1454448212yes—
subgroupG/H
centerC2×C4(C2×#595)⋊C4
commutatorC23×C17C2×C42
FrattiniC24C22×#595
FittingC2×C17×#117C4
socleC22×C17C2×#95
prime radical, cosocleC24×D17C23
hypercenterC2×#117#595
hypocenterC17#8100
LCSG ▷ C23×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
7. #11763751C4semidirect
10. C4×C22⋊#595C4semidirect
12. C2×#10587612C4semidirect
13. #11762670C4semidirect
17. C2×C17×#117C4semidirect
198. C2×#117#595semidirect
249. C17#8100semidirect

Maximal subgroups

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

subgroupindex
#145452282
#145436832
#145311632
#810017