Finite Group Databasebeta

← #44487703

Subgroups — #44487703

Order 30592.

576 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#21439935C211yesmaximal, characteristic
2#29504674C211yesmaximal, characteristic, complemented
3#29504673C211yesmaximal, characteristic, complemented
4#29504663C211yesmaximal, characteristic, complemented
5#29504661C211yesmaximal, characteristic, complemented
6#29504658C211yesmaximal, characteristic, complemented
7#29504650C211yesmaximal, characteristic, complemented
8#29504650C211yesmaximal, characteristic, complemented
9#29504650C211yesmaximal, characteristic, complemented
10#29504650C211yesmaximal, characteristic, complemented
11#29504646C211yesmaximal, characteristic, complemented
12#29504643C211yesmaximal, characteristic, complemented
13#29504634C211yesmaximal, characteristic, complemented
14#29504631C211yesmaximal, characteristic, complemented
15#387×C239C211yesmaximal, characteristic, complemented
16C22×D956C2211yescharacteristic
17C22×D956C2211yescharacteristic
18C22×D956C2211yescharacteristic
19C22×C4×D239C2211yescharacteristic
20C22×C4×D239C2211yescharacteristic
21C22×C4×D239C2211yescharacteristic
22#21439935C418yescomplemented
23C2×C4⋊Dic239C2211yescharacteristic
24C2×Dic239⋊C4C2211yescharacteristic
25C2×Dic239⋊C4C2211yescharacteristic
26C2×(C2×D239)⋊C4C2211yescharacteristic
27C2×(C2×D239)⋊C4C2211yescharacteristic
28C2×(C2×D239)⋊C4C2211yescharacteristic
29C2×(C2×D239)⋊C4C2211yescharacteristic
30C2×(C2×D239)⋊C4C2211yescharacteristic
31C2×(C2×D239)⋊C4C2211yescharacteristic
32C2×(C2×D239)⋊C4C2211yescharacteristic
33C2×(C2×D239)⋊C4C2211yescharacteristic
34C2×(C2×D239)⋊C4C2211yescharacteristic
35C2×(C2×D239)⋊C4C2211yescharacteristic
36C2×(C2×D239)⋊C4C2211yescharacteristic
37C2×(C2×D239)⋊C4C2211yescharacteristic
38C2×C4×Dic239C2211yescharacteristic
39C239⋊#95C2211yescharacteristic
40C239⋊#95C2211yescharacteristic
41C239⋊#95C2211yescharacteristic
42C239⋊#95C2211yescharacteristic
43C239⋊#95C2211yescharacteristic
44C239⋊#95C2211yescharacteristic
45C2×C4⋊C4×C239C2211yescharacteristic
46C2×C4⋊C4×C239C2211yescharacteristic
47C2×C42×C239C2211yescharacteristic
48#95×C239C2211yescharacteristic
49#95×C239C2211yescharacteristic
50#95×C239C2211yescharacteristic
51#95×C239C2211yescharacteristic
52C23×D239C2311yescharacteristic
53C23×D239C2311yescharacteristic
54C23×D239C2311yescharacteristic
55C2×D956—41no—
56C2×D956—41no—
57C2×D956—41no—
58C2×D956—41no—
59C2×D956—41no—
60C2×D956—41no—
61C2×D956C2×C414yes—
62C2×D956C2×C414yescomplemented
63C2×D956C2×C414yescomplemented
64C22×Dic239C2311yescharacteristic
65C22×Dic239C2311yescharacteristic
66C22×Dic239C2311yescharacteristic
67C22×Dic239C2311yescharacteristic
68C22×Dic239C2311yescharacteristic
69C2×C4×D239—41no—
70C2×C4×D239—41no—
71C2×C4×D239—41no—
72C2×C4×D239—41no—
73C2×C4×D239—41no—
74C2×C4×D239—41no—
75C2×C4×D239—41no—
76C2×C4×D239—41no—
77C2×C4×D239C2×C414yescomplemented
78C4⋊Dic239—41no—
79Dic239⋊C4—41no—
80Dic239⋊C4—41no—
81(C2×D239)⋊C4—41no—
82(C2×D239)⋊C4—41no—
83(C2×D239)⋊C4—41no—
84(C2×D239)⋊C4—41no—
85(C2×D239)⋊C4—41no—
86(C2×D239)⋊C4—41no—
87(C2×D239)⋊C4—41no—
88(C2×D239)⋊C4—41no—
89(C2×D239)⋊C4—41no—
90(C2×D239)⋊C4—41no—
91(C2×D239)⋊C4C2×C414yescomplemented
92(C2×D239)⋊C4C2×C414yescomplemented
93C4×Dic239—41no—
94C22×C4×C239C2311yescharacteristic
95C22×C4×C239C2311yescharacteristic
96C22×C4×C239C2311yescharacteristic
97C22×C4×C239C2311yescharacteristic
98C22×C4×C239C2311yescharacteristic
99C22×C4×C239C2311yescharacteristic
100C22×C4×C239C2311yescharacteristic
101C4⋊C4×C239—41no—
102C4⋊C4×C239C2×C414yescomplemented
103C42×C239—41no—
104C22×D239—21no—
105C22×D239—21no—
106C22×D239—21no—
107C22×D239—21no—
108C22×D239—21no—
109C22×D239—21no—
110C22×D239—21no—
111C22×D239—21no—
112C22×D239—21no—
113C22×D239—21no—
114C22×D239—21no—
115C22×D239—21no—
116C22×D239—21no—
117C22×D239—21no—
118C22×D239—21no—
119C22×D239—21no—
120C22×D239—21no—
121C22×D239—21no—
122C22×D239C22×C412yes—
123C22×D239C22×C412yes—
124C22×D239C22×C412yes—
125D956—44no—
126D956—44no—
127D956—44no—
128C2×Dic239—21no—
129C2×Dic239—21no—
130C2×Dic239—21no—
131C2×Dic239—21no—
132C2×Dic239—21no—
133C2×Dic239—21no—
134C2×Dic239—21no—
135C2×Dic239—21no—
136C2×Dic239—21no—
137C2×Dic239—21no—
138C2×Dic239—21no—
139C2×Dic239—21no—
140C2×Dic239—21no—
141C2×Dic239—21no—
142C2×Dic239C22×C412yes—
143C4×D239—44no—
144C4×D239—44no—
145C4×D239—44no—
146C23×C239C2411yescharacteristic
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—21no—
159C2×C4×C239—21no—
160C2×C4×C239—21no—
161C2×C4×C239—21no—
162C2×C4×C239—21no—
163C2×C4×C239—21no—
164C2×C4×C239—21no—
165C2×C4×C239C22×C412yes—
166C2×C4×C239C22×C412yes—
167C2×C4×C239C22×C412yes—
168C22×C239C23×C411yescharacteristic
169C22×C239H(5,𝔽2)11yescharacteristic
170C22×C239H(5,𝔽2)11yescharacteristic
171C22×C239H(5,𝔽2)11yescharacteristic
172C22×C239H(5,𝔽2)11yescharacteristic
173C22×C239H(5,𝔽2)11yescharacteristic
174C22×C2392−1+411yescharacteristic
175C2×D239—22no—
176C2×D239—22no—
177C2×D239—22no—
178C2×D239—22no—
179C2×D239—22no—
180C2×D239—22no—
181C2×D239—22no—
182C2×D239—22no—
183C2×D239—22no—
184C2×D239—41no—
185C2×D239—41no—
186C2×D239—41no—
187C2×D239—41no—
188C2×D239—41no—
189C2×D239—41no—
190C2×D239—41no—
191C2×D239—41no—
192C2×D239—41no—
193C2×D239—41no—
194C2×D239—41no—
195C2×D239—41no—
196C4×C239—22no—
197C4×C239—22no—
198C4×C239—22no—
199C4×C239—41no—
200C4×C239—41no—
201C4×C239—41no—
202C4×C239—41no—
203Dic239—22no—
204Dic239—41no—
205Dic239—41no—
206Dic239—41no—
207Dic239—41no—
208C2×C239#51811yescharacteristic
209C2×C239#51811yescharacteristic
210C2×C239#52011yescharacteristic
211C2×C239#56011yescharacteristic
212C2×C239#56011yescharacteristic
213C2×C239#56211yescharacteristic
214C2×C239#56211yescharacteristic
215D239—42no—
216D239—42no—
217D239—42no—
218C239#237711yescharacteristic, complemented, Sylow
219#2377—2391nomaximal, Sylow
220C2×#121—2391no—
221#390—2391no—
222#390—2391no—
223#388—2391no—
224#388—2391no—
225#387—2391no—
226#387D23911yescharacteristic, complemented
227#386—2391no—
228#386—2391no—
229#386—2391no—
230#386—2391no—
231#385—2391no—
232#385—2391no—
233#381—2391no—
234#380—2391no—
235C22×D4—2391no—
236C22×D4—2391no—
237C22×D4—2391no—
238C23×C4—2391no—
239C23×C4—2391no—
240C23×C4—2391no—
241#121—2398no—
242C2×C4⋊C4—2391no—
243C2×C4⋊C4—2391no—
244C2×C4⋊C4—2391no—
245C2×C4⋊C4C2×D23911yescharacteristic
246C2×C4⋊C4C2×D23911yescharacteristic
247C2×C22⋊C4—2391no—
248C2×C22⋊C4—2391no—
249C2×C22⋊C4—2391no—
250C2×C22⋊C4—2391no—
251C2×C22⋊C4—2391no—
252C2×C22⋊C4—2391no—
253C2×C22⋊C4—2391no—
254C2×C22⋊C4—2391no—
255C2×C22⋊C4—2391no—
256C2×C22⋊C4—2391no—
257C2×C22⋊C4—2391no—
258C2×C22⋊C4—2391no—
259C2×C42—2391no—
260C2×C42C2×D23911yescharacteristic
261#95—2391no—
262#95—2391no—
263#95—2391no—
264#95—2391no—
265#95—2391no—
266#95—2391no—
267#95C2×D23911yescharacteristic
268#95C2×D23911yescharacteristic
269#95C2×D23911yescharacteristic
270#95C2×D23911yescharacteristic
271C24—2391no—
272C24—2391no—
273C24—2391no—
274C2×D4—9561no—
275C2×D4—9561no—
276C2×D4—9561no—
277C2×D4—9561no—
278C2×D4—9561no—
279C2×D4—9561no—
280C2×D4—2394no—
281C2×D4—2394no—
282C2×D4—2394no—
283C22×C4—9561no—
284C22×C4—9561no—
285C22×C4—9561no—
286C22×C4—9561no—
287C22×C4—9561no—
288C22×C4—9561no—
289C22×C4—9561no—
290C22×C4—9561no—
291C22×C4—2394no—
292C22×C4—2391no—
293C22×C4—2391no—
294C22×C4—2391no—
295C22×C4—2391no—
296C22×C4—2391no—
297C22×C4C22×D23911yescharacteristic
298C22×C4C22×D23911yescharacteristic
299C22×C4C22×D23911yescharacteristic
300C22×C4C22×D23911yescharacteristic
301C22×C4C22×D23911yescharacteristic
302C22×C4C22×D23911yescharacteristic
303C22×C4C22×D23911yescharacteristic
304C4⋊C4—41no—
305C4⋊C4—9561no—
306C4⋊C4—9561no—
307C4⋊C4—9561no—
308C4⋊C4C4×D23914yescomplemented
309C22⋊C4—9561no—
310C22⋊C4—9561no—
311C22⋊C4—9561no—
312C22⋊C4—9561no—
313C22⋊C4—9561no—
314C22⋊C4—9561no—
315C22⋊C4—9561no—
316C22⋊C4—9561no—
317C22⋊C4—9561no—
318C22⋊C4—9561no—
319C22⋊C4—2394no—
320C22⋊C4—2394no—
321C42—41no—
322C42—9561no—
323C23—4781no—
324C23—4781no—
325C23—4781no—
326C23—4781no—
327C23—4781no—
328C23—4781no—
329C23—4781no—
330C23—4781no—
331C23—4781no—
332C23—4781no—
333C23—4781no—
334C23—4781no—
335C23—4781no—
336C23—4781no—
337C23—4781no—
338C23—4781no—
339C23—4781no—
340C23—4781no—
341C23—2392no—
342C23—2392no—
343C23—2392no—
344C23C23×D23911yescharacteristic
345D4—9564no—
346D4—9564no—
347D4—9564no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—9564no—
367C2×C4—9564no—
368C2×C4—9564no—
369C2×C4—4781no—
370C2×C4—4781no—
371C2×C4—4781no—
372C2×C4—4781no—
373C2×C4—4781no—
374C2×C4—4781no—
375C2×C4—4781no—
376C2×C4—4781no—
377C2×C4—4781no—
378C2×C4—4781no—
379C2×C4—4781no—
380C2×C4—4781no—
381C2×C4—4781no—
382C2×C4—4781no—
383C2×C4—2392no—
384C2×C4C2×C4×D23912yes—
385C2×C4C2×C4×D23912yes—
386C2×C4C2×C4×D23912yes—
387C22—9561no—
388C22—9561no—
389C22—9561no—
390C22—9561no—
391C22—9561no—
392C22—9561no—
393C22—9561no—
394C22—9561no—
395C22—9561no—
396C22—9561no—
397C22—9561no—
398C22—9561no—
399C22—4782no—
400C22—4782no—
401C22—4782no—
402C22—4782no—
403C22—4782no—
404C22—4782no—
405C22—4782no—
406C22—4782no—
407C22—4782no—
408C22C22×C4×D23911yescharacteristic
409C22#2144000511yescharacteristic
410C22#2144000611yescharacteristic
411C22#2144000611yescharacteristic
412C22#2144000611yescharacteristic
413C22#2144000611yescharacteristic
414C22#2144000811yescharacteristic
415C4—22no—
416C4—22no—
417C4—22no—
418C4—41no—
419C4—41no—
420C4—41no—
421C4—41no—
422C4—9561no—
423C4—9561no—
424C4—9561no—
425C4—9561no—
426C4—4782no—
427C2—9562no—
428C2—9562no—
429C2—9562no—
430C2#2950524411yescharacteristic
431C2#2950524611yescharacteristic
432C2#2950525411yescharacteristic
433C2#2950551211yescharacteristic
434C2#2950551311yescharacteristic
435C2#2950551811yescharacteristic
436C2#2950552011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D239
commutatorC22×C239C23×C4
Fitting#387×C239C2
socle, cosocleC23×C239C24
prime radicalC2×#21439935C2
hypercenter#387D239
hypocenterC239#2377
LCSG ▷ C22×C239 ▷ C239
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
2. #29504674C2semidirect
3. #29504673C2semidirect
4. #29504663C2semidirect
5. #29504661C2semidirect
6. #29504658C2semidirect
7. #29504650C2semidirect
8. #29504650C2semidirect
9. #29504650C2semidirect
10. #29504650C2semidirect
11. #29504646C2semidirect
12. #29504643C2semidirect
13. #29504634C2semidirect
14. #29504631C2semidirect
15. #387×C239C2semidirect
22. #21439935C4semidirect
62. C2×D956C2×C4semidirect
63. C2×D956C2×C4semidirect
77. C2×C4×D239C2×C4semidirect
91. (C2×D239)⋊C4C2×C4semidirect
92. (C2×D239)⋊C4C2×C4semidirect
102. C4⋊C4×C239C2×C4semidirect
218. C239#2377semidirect
226. #387D239semidirect
308. C4⋊C4C4×D239semidirect

Maximal subgroups

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

subgroupindex
C2×#214399352
#295046742
#295046732
#295046632
#295046612
#295046582
#295046502
#295046462
#295046432
#295046342
#295046312
#387×C2392
#2377239