Finite Group Databasebeta

← #44487254

Subgroups — #44487254

Order 30592.

612 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#21439946C211yesmaximal, characteristic
2C2×#21439925C211yesmaximal, characteristic, complemented
3C2×C4×C22⋊D239C211yesmaximal, characteristic
4#29504676C211yesmaximal, characteristic, complemented
5#29504672C211yesmaximal, characteristic
6#29504666C211yesmaximal, characteristic, complemented
7#29504665C211yesmaximal, characteristic, complemented
8#29504662C211yesmaximal, characteristic, complemented
9#29504661C211yesmaximal, characteristic, complemented
10#29504646C211yesmaximal, characteristic, complemented
11#29504645C211yesmaximal, characteristic, complemented
12#29504643C211yesmaximal, characteristic, complemented
13#29504641C211yesmaximal, characteristic, complemented
14#29504617C211yesmaximal, characteristic, complemented
15#385×C239C211yesmaximal, characteristic, complemented
16C22×Dic478C2211yescharacteristic
17C22×C22⋊D239C2211yescharacteristic
18C22×C4×D239C2211yescharacteristic
19#21439946C418yescomplemented
20#21439925—24no—
21C4×C22⋊D239—24no—
22C2×C4⋊Dic239C2211yescharacteristic
23C2×Dic239⋊C4C2211yescharacteristic
24C2×Dic239⋊C4C2211yescharacteristic
25C2×Dic239⋊C4C2211yescharacteristic
26C2×Dic239⋊C4C2211yescharacteristic
27C2×Dic239⋊C4C2211yescharacteristic
28C2×C22⋊Dic239C2211yescharacteristic
29C2×C22⋊Dic239C2211yescharacteristic
30C2×C22⋊Dic239C2211yescharacteristic
31C2×(C2×D239)⋊C4C2211yescharacteristic
32C2×(C2×D239)⋊C4C2211yescharacteristic
33C2×(C2×D239)⋊C4C2211yescharacteristic
34C2×(C2×D239)⋊C4C2211yescharacteristic
35C2×(C2×D239)⋊C4C2211yescharacteristic
36C2×C4×Dic239C2211yescharacteristic
37C2×C4×Dic239C2211yescharacteristic
38C2×C4×Dic239C2211yescharacteristic
39C2×C4×Dic239C2211yescharacteristic
40C2×C4×Dic239C2211yescharacteristic
41C239⋊#95C2211yescharacteristic
42C239⋊#95C2211yescharacteristic
43C239⋊#95C2211yescharacteristic
44C239⋊#95C2211yescharacteristic
45C239⋊#95C2211yescharacteristic
46C239⋊#95C2211yescharacteristic
47C23×C4×C239C2211yescharacteristic
48C2×C4⋊C4×C239C2211yescharacteristic
49C2×C4⋊C4×C239C2211yescharacteristic
50C2×C22⋊C4×C239C2211yescharacteristic
51C2×C22⋊C4×C239C2211yescharacteristic
52#95×C239C2211yescharacteristic
53#95×C239C2211yescharacteristic
54C23×D239C2311yescharacteristic
55C2×Dic478—22no—
56C2×Dic478—22no—
57C2×Dic478C2×C414yescomplemented
58C2×C22⋊D239—22no—
59C2×C22⋊D239—22no—
60C2×C22⋊D239C2×C414yes—
61C22×Dic239C2311yescharacteristic
62C22×Dic239C2311yescharacteristic
63C22×Dic239C2311yescharacteristic
64C22×Dic239C2311yescharacteristic
65C22×Dic239C2311yescharacteristic
66C22×Dic239C2311yescharacteristic
67C22×Dic239C2311yescharacteristic
68C2×C4×D239—22no—
69C2×C4×D239—41no—
70C2×C4×D239—41no—
71C4⋊Dic239—41no—
72Dic239⋊C4—22no—
73Dic239⋊C4—22no—
74Dic239⋊C4—22no—
75Dic239⋊C4—41no—
76Dic239⋊C4—41no—
77C22⋊Dic239—22no—
78C22⋊Dic239—41no—
79C22⋊Dic239C2×C414yescomplemented
80(C2×D239)⋊C4—22no—
81(C2×D239)⋊C4—41no—
82(C2×D239)⋊C4—41no—
83(C2×D239)⋊C4C2×C414yescomplemented
84(C2×D239)⋊C4C2×C414yescomplemented
85C4×Dic239—22no—
86C4×Dic239—22no—
87C4×Dic239—22no—
88C4×Dic239C2×C414yescomplemented
89C4×Dic239D414yes—
90C24×C239C2311yescharacteristic
91C22×C4×C239—22no—
92C22×C4×C239—41no—
93C22×C4×C239—41no—
94C22×C4×C239C2311yescharacteristic
95C22×C4×C239C2311yescharacteristic
96C22×C4×C239C2311yescharacteristic
97C22×C4×C239C2311yescharacteristic
98C22×C4×C239C2311yescharacteristic
99C22×C4×C239C2311yescharacteristic
100C4⋊C4×C239—22no—
101C4⋊C4×C239—41no—
102C22⋊C4×C239—41no—
103C22⋊C4×C239C2×C414yescomplemented
104C22×D239—21no—
105C22×D239—21no—
106C22×D239—21no—
107C22×D239—21no—
108C22×D239—21no—
109C22×D239—21no—
110C22×D239C22×C412yes—
111Dic478—28no—
112C22⋊D239—28no—
113C2×Dic239—21no—
114C2×Dic239—21no—
115C2×Dic239—21no—
116C2×Dic239—21no—
117C2×Dic239—21no—
118C2×Dic239—21no—
119C2×Dic239—21no—
120C2×Dic239—21no—
121C2×Dic239—21no—
122C2×Dic239—21no—
123C2×Dic239—21no—
124C2×Dic239—21no—
125C2×Dic239—21no—
126C2×Dic239—21no—
127C2×Dic239—21no—
128C2×Dic239C22×C412yes—
129C2×Dic239C22×C412yes—
130C2×Dic239C22×C412yes—
131C2×Dic239C2×D412yes—
132C2×Dic239C2×D412yes—
133C2×Dic239#4112yes—
134C4×D239—44no—
135C23×C239—21no—
136C23×C239—21no—
137C23×C239—21no—
138C23×C239—21no—
139C23×C239—21no—
140C23×C239—21no—
141C23×C239C22×C412yes—
142C23×C239C2411yescharacteristic
143C2×C4×C239—21no—
144C2×C4×C239—21no—
145C2×C4×C239—21no—
146C2×C4×C239—21no—
147C2×C4×C239—21no—
148C2×C4×C239—21no—
149C2×C4×C239—21no—
150C2×C4×C239—21no—
151C2×C4×C239—21no—
152C2×C4×C239—21no—
153C2×C4×C239—21no—
154C2×C4×C239—21no—
155C2×C4×C239—21no—
156C2×C4×C239—21no—
157C2×C4×C239—21no—
158C2×C4×C239—44no—
159C2×C4×C239C22×C412yes—
160C2×C4×C239C22×C412yes—
161C2×C4×C239C2×D412yes—
162C22×C239—22no—
163C22×C239—22no—
164C22×C239—22no—
165C22×C239—41no—
166C22×C239—41no—
167C22×C239—41no—
168C22×C239—41no—
169C22×C239C23×C411yescharacteristic
170C22×C239C22×D411yescharacteristic
171C22×C239C2×#4111yescharacteristic
172C22×C239H(5,𝔽2)11yescharacteristic
173C22×C239H(5,𝔽2)11yescharacteristic
174C22×C2392−1+411yescharacteristic
175C22×C2392−1+411yescharacteristic
176C2×D239—22no—
177C2×D239—22no—
178C2×D239—22no—
179C2×D239—41no—
180C2×D239—41no—
181C2×D239—41no—
182C2×D239—41no—
183C4×C239—22no—
184C4×C239—22no—
185C4×C239—22no—
186C4×C239—41no—
187C4×C239—41no—
188C4×C239—41no—
189Dic239—22no—
190Dic239—22no—
191Dic239—22no—
192Dic239—41no—
193Dic239—41no—
194Dic239—41no—
195Dic239C4×D414yes—
196C2×C239—42no—
197C2×C239C2×C4×D411yescharacteristic
198C2×C239#52011yescharacteristic
199C2×C239#52011yescharacteristic
200C2×C239#53511yescharacteristic
201C2×C239#53611yescharacteristic
202C2×C239#54211yescharacteristic
203C2×C239#54211yescharacteristic
204D239—42no—
205C239#232611yescharacteristic, complemented, Sylow
206#2326—2391nomaximal, Sylow
207C2×#124—2391no—
208C2×C4×Q8—2391no—
209C2×C4×D4—2391no—
210#391—2391no—
211#390—2391no—
212#388—2391no—
213#388—2391no—
214#388—2391no—
215#388—2391no—
216#385—2391no—
217#385—2391no—
218#385—2391no—
219#385D23911yescharacteristic, complemented
220#384—2391no—
221#376—2391no—
222C22×Q8—2391no—
223C22×D4—2391no—
224C23×C4—2391no—
225C23×C4C2×D23911yescharacteristic
226#124—2398no—
227C4×Q8—4784no—
228C4×D4—4784no—
229C2×C4⋊C4—2391no—
230C2×C4⋊C4—2391no—
231C2×C4⋊C4—2391no—
232C2×C4⋊C4—2391no—
233C2×C4⋊C4—2391no—
234C2×C4⋊C4—2391no—
235C2×C4⋊C4C2×D23911yescharacteristic
236C2×C4⋊C4C2×D23911yescharacteristic
237C2×C22⋊C4—2391no—
238C2×C22⋊C4—2391no—
239C2×C22⋊C4—2391no—
240C2×C22⋊C4—2391no—
241C2×C22⋊C4—2391no—
242C2×C22⋊C4—2391no—
243C2×C22⋊C4—2391no—
244C2×C22⋊C4—2391no—
245C2×C22⋊C4C2×D23911yescharacteristic
246C2×C22⋊C4C2×D23911yescharacteristic
247C2×C42—2391no—
248C2×C42—2391no—
249C2×C42—2391no—
250C2×C42—2391no—
251C2×C42—2391no—
252#95—2391no—
253#95—2391no—
254#95—2391no—
255#95—2391no—
256#95—2391no—
257#95—2391no—
258#95C2×D23911yescharacteristic
259#95C2×D23911yescharacteristic
260C24—2391no—
261C24C22×D23911yescharacteristic
262C2×Q8—4782no—
263C2×Q8—4782no—
264C2×Q8—2394no—
265C2×D4—4782no—
266C2×D4—4782no—
267C2×D4—2394no—
268C22×C4—22no—
269C22×C4—41no—
270C22×C4—41no—
271C22×C4—9561no—
272C22×C4—9561no—
273C22×C4—4782no—
274C22×C4—2391no—
275C22×C4—2391no—
276C22×C4—2391no—
277C22×C4—2391no—
278C22×C4—2391no—
279C22×C4—2391no—
280C22×C4—2391no—
281C22×C4C22×D23911yescharacteristic
282C22×C4C22×D23911yescharacteristic
283C22×C4C22×D23911yescharacteristic
284C22×C4C22×D23911yescharacteristic
285C22×C4C22×D23911yescharacteristic
286C22×C4C22×D23911yescharacteristic
287C4⋊C4—22no—
288C4⋊C4—41no—
289C4⋊C4—9561no—
290C4⋊C4—9561no—
291C4⋊C4—9561no—
292C4⋊C4—4782no—
293C4⋊C4—4782no—
294C4⋊C4—4782no—
295C22⋊C4—41no—
296C22⋊C4—9561no—
297C22⋊C4—9561no—
298C22⋊C4—9561no—
299C22⋊C4—4782no—
300C22⋊C4—4782no—
301C22⋊C4—2394no—
302C22⋊C4—2394no—
303C22⋊C4—2394no—
304C22⋊C4C4×D23914yescomplemented
305C42—4782no—
306C42—4782no—
307C42—4782no—
308C42—2394no—
309C42—2394no—
310C23—21no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—4781no—
317C23—4781no—
318C23—4781no—
319C23—4781no—
320C23—4781no—
321C23—4781no—
322C23—2392no—
323C23C2×C4×D23912yes—
324C23C23×D23911yescharacteristic
325Q8—4788no—
326D4—4788no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—44no—
343C2×C4—9564no—
344C2×C4—4781no—
345C2×C4—4781no—
346C2×C4—4781no—
347C2×C4—4781no—
348C2×C4—4781no—
349C2×C4—4781no—
350C2×C4—4781no—
351C2×C4—4781no—
352C2×C4—4781no—
353C2×C4—4781no—
354C2×C4—4781no—
355C2×C4—4781no—
356C2×C4—4781no—
357C2×C4—4781no—
358C2×C4—4781no—
359C2×C4—2392no—
360C2×C4—2392no—
361C2×C4—2392no—
362C2×C4—2392no—
363C2×C4—2392no—
364C2×C4—2392no—
365C2×C4C2×C4×D23912yes—
366C2×C4C2×C4×D23912yes—
367C2×C4D4×D23912yes—
368C22—22no—
369C22—22no—
370C22—22no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—9561no—
376C22—9561no—
377C22—9561no—
378C22—9561no—
379C22—4782no—
380C22—4782no—
381C22—4782no—
382C22C22×C4×D23911yescharacteristic
383C22C2×D4×D23911yescharacteristic
384C22#41×D23911yescharacteristic
385C22#2144000511yescharacteristic
386C22#2144000511yescharacteristic
387C22#2144000711yescharacteristic
388C22#2144000811yescharacteristic
389C4—22no—
390C4—22no—
391C4—22no—
392C4—41no—
393C4—41no—
394C4—41no—
395C4—9561no—
396C4—9561no—
397C4—9561no—
398C4—4782no—
399C4—4782no—
400C4—4782no—
401C4—2394no—
402C2—42no—
403C2—9562no—
404C2C4×D4×D23911yescharacteristic
405C2#2950525111yescharacteristic
406C2#2950525311yescharacteristic
407C2#2950533711yescharacteristic
408C2#2950534511yescharacteristic
409C2#2950539011yescharacteristic
410C2#2950539211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D239
commutatorC22×C239C23×C4
Fitting#385×C239C2
socle, cosocleC23×C239C24
prime radicalC22×C22⋊D239C22
hypercenter#385D239
hypocenterC239#2326
LCSG ▷ C22×C239 ▷ C239
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
2. C2×#21439925C2semidirect
4. #29504676C2semidirect
6. #29504666C2semidirect
7. #29504665C2semidirect
8. #29504662C2semidirect
9. #29504661C2semidirect
10. #29504646C2semidirect
11. #29504645C2semidirect
12. #29504643C2semidirect
13. #29504641C2semidirect
14. #29504617C2semidirect
15. #385×C239C2semidirect
19. #21439946C4semidirect
57. C2×Dic478C2×C4semidirect
79. C22⋊Dic239C2×C4semidirect
83. (C2×D239)⋊C4C2×C4semidirect
84. (C2×D239)⋊C4C2×C4semidirect
88. C4×Dic239C2×C4semidirect
103. C22⋊C4×C239C2×C4semidirect
205. C239#2326semidirect
219. #385D239semidirect
304. C22⋊C4C4×D239semidirect

Maximal subgroups

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

subgroupindex
C2×#214399462
C2×#214399252
C2×C4×C22⋊D2392
#295046762
#295046722
#295046662
#295046652
#295046622
#295046612
#295046462
#295046452
#295046432
#295046412
#295046172
#385×C2392
#2326239