Finite Group Databasebeta

← #427×#595 #17968598

Subgroups — #427×#595 #17968598

Order 4352.

1182 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763819C211yesmaximal, characteristic
2C22×C8×#595C211yesmaximal, characteristic
3#117×#595C212yesmaximal
4#107×#595C214yesmaximal, complemented
5#106×#595C214yesmaximal, complemented
6#14544469C212yesmaximal
7D17×#427C211yesmaximal, characteristic
8C22×#63242C2211yescharacteristic
9C2×#10587677C2212yes—
10C22×C4×#595C2211yescharacteristic
11#11763819C418yescomplemented
12C2×#10587534C2212yes—
13C2×#10587533C2212yes—
14C2×C8×#595C418yescomplemented
15C2×C8×#595C2212yes—
16C2×C8×#595C2212yes—
17C4⋊C4×#595C2218yes—
18C22⋊C4×#595—24no—
19#11763745—22no—
20C42×#595—22no—
21#11763682C2218yes—
22C22×C8×D17C2211yescharacteristic
23#117×D17C2212yes—
24#11762847C411yescharacteristic, complemented
25#11762846C412yescomplemented
26#11762845C412yescomplemented
27#11762844C412yescomplemented
28#107×D17C2212yes—
29#106×D17C2212yes—
30C17×#427C411yescharacteristic, complemented
31C23×#595D412yes—
32C22×C4×D17C2311yescharacteristic
33C2×C22⋊#595—22no—
34C22×#3624—21no—
35#10587677—24no—
36#10587677C2×C418yes—
37C2×C4⋊#595C2314yes—
38C2×C4×#595—22no—
39C2×C4×#595—28no—
40C2×C4×#595C2×C414yes—
41C2×C4×#595D411yescharacteristic
42C2×C4×#595D411yescharacteristic
43C2×C4×#595Q814yes—
44C2×C4×#595C2312yes—
45C2×#63242—21no—
46C2×#63242—22no—
47C2×#63242C2×C414yes—
48C2×#63242C2312yes—
49C22×C8×C17C2×C411yescharacteristic
50C17×#117C2×C412yes—
51#10587612C2×C412yes—
52C22×#3622C2×C411yescharacteristic
53C2×C8×D17C2×C414yes—
54C2×C8×D17C2×C414yes—
55C2×C8×D17C2×C411yescharacteristic
56C2×C8×D17C2×C411yescharacteristic
57C2×C8×D17C2311yescharacteristic
58C2×C8×D17C2311yescharacteristic
59#10587578C2×C414yes—
60C4⋊C4×D17C2314yes—
61C22⋊C4×D17—22no—
62#10587563—22no—
63#10587558—22no—
64C42×D17—22no—
65(C2×#595)⋊C4—28no—
66#10587534C2×C418yescomplemented
67#10587533C2×C418yescomplemented
68C8×#595C2×C418yes—
69C8×#595C2×C418yes—
70C17×#107C2×C412yescomplemented
71C17×#106C2×C412yescomplemented
72#10587489C2×C412yescomplemented
73#10587488C2×C412yescomplemented
74#10587479C2×C414yescomplemented
75#10587478C2×C414yescomplemented
76C23×D17C2×D411yescharacteristic
77C22×#595—28no—
78C22×#595—24no—
79C22×#595C4⋊C418yes—
80C22×#595C2×D412yes—
81C22×#595C2×D412yes—
82C22×C4×C17C22×C411yescharacteristic
83C22×Dic17#4111yescharacteristic
84C2×C4×D17—24no—
85C2×C4×D17C22×C411yescharacteristic
86C2×C4×D17C22×C412yes—
87C2×C4×D17C22×C412yes—
88C2×C4×D17C2×D411yescharacteristic
89C2×C4×D17C2×Q812yes—
90C2×C4×D17#4111yescharacteristic
91C2×C4×D17#4112yes—
92C2×C4×D17C2411yescharacteristic
93C22⋊#595—28no—
94C2×#3624—24no—
95C2×#3624—22no—
96C4⋊#595—24no—
97C4⋊#595C22×C418yes—
98C4×#595—28no—
99C4×#595—416no—
100C4×#595C4⋊C414yes—
101C4×#595C4⋊C414yes—
102C4×#595C22×C414yes—
103C4×#595C2×Q814yes—
104#63242—24no—
105#63242—22no—
106#63242C22×C414yes—
107C2×C8×C17C4214yescomplemented
108C2×C8×C17C22×C411yescharacteristic
109C2×C8×C17C22×C411yescharacteristic
110C4⋊C4×C17C22×C414yes—
111C22⋊C4×C17—22no—
112C42×C17—22no—
113C22⋊Dic17—22no—
114#63227—24no—
115C4⋊Dic17C22×C414yes—
116#63225—24no—
117C4×Dic17—22no—
118C4×Dic17—24no—
119C2×#3622C4214yescomplemented
120C2×#3622C22×C411yescharacteristic
121C2×#3622C22×C411yescharacteristic
122C8×D17C4214yescomplemented
123C8×D17C4214yescomplemented
124C8×D17C22×C412yes—
125C8×D17C22×C412yes—
126C8×D17C22×C412yes—
127C8×D17C22×C412yes—
128C4×#427—171nomaximal, Sylow
129C23×C17C4×D411yescharacteristic
130C22×D17—24no—
131C22×D17C2×C4⋊C412yes—
132C22×D17C4×D412yes—
133C22×D17C4×D411yescharacteristic
134C22×D17C22×D411yescharacteristic
135C2×#595—24no—
136C2×#595—216no—
137C2×#595—28no—
138C2×#595—48no—
139C2×#595C2×C4⋊C414yes—
140C2×#595C2×C4⋊C414yes—
141C2×#595#13518yes—
142C2×C4×C17—24no—
143C2×C4×C17C2×C4212yes—
144C2×C4×C17C4×D411yescharacteristic
145C2×C4×C17C4×Q812yes—
146C2×C4×C17C23×C411yescharacteristic
147C2×Dic17—24no—
148C2×Dic17#11712yes—
149C2×Dic17C4×D411yescharacteristic
150C2×Dic17C4×Q812yes—
151C2×Dic17C2×#4111yescharacteristic
152C4×D17—48no—
153C4×D17C2×C4212yes—
154C4×D17C2×C4⋊C412yes—
155C4×D17#11712yes—
156C4×D17C4×D412yes—
157C4×D17C4×Q812yes—
158C4×D17C4×Q812yes—
159C4×D17C23×C411yescharacteristic
160C4×D17C23×C411yescharacteristic
161C4×D17C22×Q811yescharacteristic
162C4×D17C2×#4111yescharacteristic
163#3624—24no—
164C8×C17C2×C4212yes—
165C8×C17C2×C4212yes—
166#3622C2×C4212yes—
167#3622C2×C4212yes—
168C2×#427—171no—
169C2×#427—171no—
170C22×C4×C8—171no—
171C4×#117—172no—
172C4×#107—174no—
173C4×#106—174no—
174#1735—172no—
175C22×C17—22no—
176C22×C17C4×C4⋊C412yes—
177C22×C17C2×C4×D411yescharacteristic
178C2×D17—22no—
179C2×D17—24no—
180C2×D17—24no—
181C2×D17C4×C4⋊C412yes—
182C2×D17C22×C4⋊C411yescharacteristic
183C2×D17C2×C4×D411yescharacteristic
184C2×D17C2×#13514yes—
185#595—24no—
186#595—48no—
187#595#42718yesdirect product factor
188C4×C17—44no—
189C4×C17C4×C4⋊C412yes—
190C4×C17C22×C4211yescharacteristic
191C4×C17C2×C4×Q811yescharacteristic
192Dic17—44no—
193Dic17C4×C4⋊C412yes—
194Dic17C2×#11711yescharacteristic
195Dic17C2×C4×Q811yescharacteristic
196C23×C8—171no—
197C23×C8—171no—
198C2×#117—172no—
199C2×#117—172no—
200C22×C42—171no—
201#427—178no—
202#427—171no—
203#427—172no—
204#427—172no—
205#427—172no—
206#427#59511yescharacteristic, direct product factor
207C2×#107—172no—
208C2×#107—172no—
209C2×#106—172no—
210C2×#106—172no—
211C2×C4×C8—178no—
212C2×C4×C8—172no—
213C2×C4×C8—172no—
214C4×C4⋊C4—178no—
215C4×C22⋊C4—344no—
216#376—342no—
217C43—342no—
218#340—178no—
219C2×C17—22no—
220C2×C17C2×C4×C4⋊C411yescharacteristic
221C2×C17C4×#13512yes—
222D17—22no—
223D17C2×#42712yes—
224D17C4×#13512yes—
225C23×C4—171no—
226C23×C4—172no—
227C22×C8—171no—
228C22×C8—174no—
229C22×C8—174no—
230C22×C8—171no—
231C22×C8—171no—
232C22×C8—171no—
233C22×C8—171no—
234C22×C8—174no—
235C22×C8—172no—
236C22×C8—341no—
237C22×C8—342no—
238C22×C8—341no—
239C22×C8C2×#59511yescharacteristic
240#117—178no—
241#117—172no—
242#117—174no—
243#117—342no—
244#117—342no—
245#117—344no—
246#117C2×#59512yes—
247C2×C4⋊C4—174no—
248C2×C4⋊C4—174no—
249C2×C22⋊C4—342no—
250C2×C22⋊C4—342no—
251C2×C42—174no—
252C2×C42—171no—
253C2×C42—171no—
254C2×C42—174no—
255C2×C42—172no—
256C2×C42—342no—
257C2×C42—342no—
258C2×C42—348no—
259#107—178no—
260#107—172no—
261#107—174no—
262#107C2×#59512yescomplemented
263#106—178no—
264#106—172no—
265#106—174no—
266#106C2×#59512yescomplemented
267C4×C8—178no—
268C4×C8—178no—
269#95—348no—
270C17C4×#42711yescharacteristic, complemented, Sylow
271C24—171no—
272C22×C4—172no—
273C22×C4—171no—
274C22×C4—172no—
275C22×C4—172no—
276C22×C4—171no—
277C22×C4—171no—
278C22×C4—172no—
279C22×C4—172no—
280C22×C4—171no—
281C22×C4—171no—
282C22×C4—178no—
283C22×C4—172no—
284C22×C4—344no—
285C22×C4—348no—
286C22×C4—344no—
287C22×C4C22×#59511yescharacteristic
288C2×C8—174no—
289C2×C8—171no—
290C2×C8—171no—
291C2×C8—172no—
292C2×C8—172no—
293C2×C8—172no—
294C2×C8—172no—
295C2×C8—174no—
296C2×C8—174no—
297C2×C8—174no—
298C2×C8—344no—
299C2×C8—342no—
300C2×C8—344no—
301C2×C8—342no—
302C2×C8C4×#59514yescomplemented
303C2×C8C22×#59511yescharacteristic
304C2×C8C22×#59511yescharacteristic
305C4⋊C4—178no—
306C4⋊C4—174no—
307C4⋊C4—344no—
308C4⋊C4—344no—
309C4⋊C4C22×#59514yes—
310C22⋊C4—22no—
311C22⋊C4—344no—
312C22⋊C4—348no—
313C22⋊C4—342no—
314C42—22no—
315C42—174no—
316C42—174no—
317C42—174no—
318C42—174no—
319C42—344no—
320C42—348no—
321C42—342no—
322C42—6816no—
323C23—171no—
324C23—172no—
325C23—172no—
326C23—171no—
327C23—344no—
328C23D4×#59511yescharacteristic
329C2×C4—24no—
330C2×C4—174no—
331C2×C4—178no—
332C2×C4—172no—
333C2×C4—172no—
334C2×C4—171no—
335C2×C4—171no—
336C2×C4—172no—
337C2×C4—172no—
338C2×C4—172no—
339C2×C4—172no—
340C2×C4—171no—
341C2×C4—171no—
342C2×C4—172no—
343C2×C4—171no—
344C2×C4—171no—
345C2×C4—172no—
346C2×C4—174no—
347C2×C4—3416no—
348C2×C4—344no—
349C2×C4—348no—
350C2×C4—344no—
351C2×C4—688no—
352C2×C4—688no—
353C2×C4C2×C4×#59512yes—
354C2×C4D4×#59511yescharacteristic
355C2×C4Q8×#59512yes—
356C2×C4C23×#59511yescharacteristic
357C8—172no—
358C8—172no—
359C8—344no—
360C8C2×C4×#59512yes—
361C8C2×C4×#59512yes—
362C22—22no—
363C22—171no—
364C22—171no—
365C22—174no—
366C22—172no—
367C22—344no—
368C22—344no—
369C22—342no—
370C22C4⋊C4×#59512yes—
371C22C2×D4×#59511yescharacteristic
372C4—44no—
373C4—178no—
374C4—171no—
375C4—171no—
376C4—172no—
377C4—344no—
378C4—688no—
379C4—684no—
380C4C4⋊C4×#59512yes—
381C4C22×C4×#59511yescharacteristic
382C4C2×Q8×#59511yescharacteristic
383C2—22no—
384C2—172no—
385C2—172no—
386C2—342no—
387C2C2×C4⋊C4×#59511yescharacteristic
388C2#135×#59512yes—
subgroupG/H
centerC2×C4D4×#595
commutatorC4×C17C22×C42
FrattiniC2×C4C23×#595
FittingC17×#427C4
socleC22×C17C2×C4×D4
prime radicalC23×D17C2×D4
cosocleC2×C4×D17C24
hypercenter#427#595
hypocenterC17C4×#427
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #427

Complements

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

NH ≅ G/Ntype
4. #107×#595C2semidirect
5. #106×#595C2semidirect
11. #11763819C4semidirect
14. C2×C8×#595C4semidirect
24. #11762847C4semidirect
25. #11762846C4semidirect
26. #11762845C4semidirect
27. #11762844C4semidirect
30. C17×#427C4semidirect
66. #10587534C2×C4semidirect
67. #10587533C2×C4semidirect
70. C17×#107C2×C4semidirect
71. C17×#106C2×C4semidirect
72. #10587489C2×C4semidirect
73. #10587488C2×C4semidirect
74. #10587479C2×C4semidirect
75. #10587478C2×C4semidirect
107. C2×C8×C17C42semidirect
119. C2×#3622C42semidirect
122. C8×D17C42semidirect
123. C8×D17C42semidirect
187. #595#427direct (N × H)
206. #427#595direct (N × H)
262. #107C2×#595semidirect
266. #106C2×#595semidirect
270. C17C4×#427semidirect
302. C2×C8C4×#595semidirect

Maximal subgroups

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

subgroupindex
C2×#117638192
C22×C8×#5952
#117×#5952
#107×#5952
#106×#5952
#145444692
D17×#4272
C4×#42717