Finite Group Databasebeta

← #44487550

Subgroups — #44487550

Order 30592.

620 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#21439938C211yesmaximal, characteristic
2C2×#21439925C211yesmaximal, characteristic, complemented
3C2×C4⋊C4×D239C211yesmaximal, characteristic
4#29504676C211yesmaximal, characteristic, complemented
5#29504669C211yesmaximal, characteristic, complemented
6#29504667C211yesmaximal, characteristic, complemented
7#29504658C211yesmaximal, characteristic, complemented
8#29504653C211yesmaximal, characteristic, complemented
9#29504643C211yesmaximal, characteristic
10#29504643C211yesmaximal, characteristic
11C4×Dic239⋊C4C211yesmaximal, characteristic, complemented
12C4×(C2×D239)⋊C4C211yesmaximal, characteristic
13#29504619C211yesmaximal, characteristic
14#29504619C211yesmaximal, characteristic
15#389×C239C211yesmaximal, characteristic, complemented
16C22×Dic478C2211yescharacteristic
17C22×C4×D239C2211yescharacteristic
18C22×C4×D239C2211yescharacteristic
19C22×C4×D239C2211yescharacteristic
20#21439938C418yescomplemented
21#21439925—24no—
22C2×C4⋊Dic239C2211yescharacteristic
23C2×Dic239⋊C4C2211yescharacteristic
24C2×Dic239⋊C4C2211yescharacteristic
25C2×Dic239⋊C4C2211yescharacteristic
26C2×Dic239⋊C4C2211yescharacteristic
27C2×Dic239⋊C4C2211yescharacteristic
28C2×Dic239⋊C4C2211yescharacteristic
29C4⋊C4×D239—24no—
30C2×(C2×D239)⋊C4C2211yescharacteristic
31C2×(C2×D239)⋊C4C2211yescharacteristic
32C2×(C2×D239)⋊C4C2211yescharacteristic
33C2×(C2×D239)⋊C4C2211yescharacteristic
34C2×C4×Dic239C2211yescharacteristic
35C2×C4×Dic239C2211yescharacteristic
36C2×C4×Dic239C2211yescharacteristic
37C2×C4×Dic239C2211yescharacteristic
38C2×C4×Dic239C2211yescharacteristic
39C239⋊#95C2211yescharacteristic
40C239⋊#95C2211yescharacteristic
41C239⋊#95C2211yescharacteristic
42C239⋊#95C2211yescharacteristic
43C239⋊#95C2211yescharacteristic
44C239⋊#95C2211yescharacteristic
45C239⋊#95C2211yescharacteristic
46C239⋊#95C2211yescharacteristic
47C2×C4⋊C4×C239C2211yescharacteristic
48C2×C4⋊C4×C239C2211yescharacteristic
49C2×C4⋊C4×C239C2211yescharacteristic
50C2×C4⋊C4×C239C2211yescharacteristic
51C2×C42×C239C2211yescharacteristic
52#95×C239C2211yescharacteristic
53#95×C239C2211yescharacteristic
54C23×D239C2311yescharacteristic
55C2×Dic478—22no—
56C2×Dic478—22no—
57C2×Dic478C2×C414yescomplemented
58C22×Dic239C2311yescharacteristic
59C22×Dic239C2311yescharacteristic
60C22×Dic239C2311yescharacteristic
61C22×Dic239C2311yescharacteristic
62C22×Dic239C2311yescharacteristic
63C22×Dic239C2311yescharacteristic
64C22×Dic239C2311yescharacteristic
65C2×C4×D239—22no—
66C2×C4×D239—22no—
67C2×C4×D239—22no—
68C2×C4×D239—22no—
69C2×C4×D239—22no—
70C2×C4×D239—22no—
71C2×C4×D239—41no—
72C2×C4×D239—41no—
73C2×C4×D239C2×C414yes—
74C4⋊Dic239—22no—
75Dic239⋊C4—22no—
76Dic239⋊C4—22no—
77Dic239⋊C4—41no—
78Dic239⋊C4C2×C414yescomplemented
79Dic239⋊C4C2×C414yescomplemented
80Dic239⋊C4D414yes—
81(C2×D239)⋊C4—22no—
82(C2×D239)⋊C4C2×C414yes—
83(C2×D239)⋊C4C2×C414yes—
84(C2×D239)⋊C4Q814yescomplemented
85C4×Dic239—22no—
86C4×Dic239—22no—
87C4×Dic239—22no—
88C4×Dic239—22no—
89C4×Dic239—41no—
90C22×C4×C239C2311yescharacteristic
91C22×C4×C239C2311yescharacteristic
92C22×C4×C239C2311yescharacteristic
93C22×C4×C239C2311yescharacteristic
94C22×C4×C239C2311yescharacteristic
95C22×C4×C239C2311yescharacteristic
96C22×C4×C239C2311yescharacteristic
97C4⋊C4×C239—22no—
98C4⋊C4×C239—22no—
99C4⋊C4×C239—41no—
100C4⋊C4×C239C2×C414yescomplemented
101C42×C239—41no—
102C22×D239—21no—
103C22×D239—21no—
104C22×D239—21no—
105C22×D239—21no—
106C22×D239C22×C412yes—
107C22×D239C2×Q812yes—
108C22×D239#4112yes—
109Dic478—28no—
110C2×Dic239—21no—
111C2×Dic239—21no—
112C2×Dic239—21no—
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×Dic239C22×C412yes—
125C2×Dic239C22×C412yes—
126C2×Dic239C22×C412yes—
127C2×Dic239C2×D412yes—
128C2×Dic239C2×D412yes—
129C2×Dic239C2×Q812yes—
130C2×Dic239#4112yes—
131C4×D239—28no—
132C4×D239—44no—
133C4×D239—44no—
134C23×C239C2411yescharacteristic
135C2×C4×C239—21no—
136C2×C4×C239—21no—
137C2×C4×C239—21no—
138C2×C4×C239—21no—
139C2×C4×C239—21no—
140C2×C4×C239—21no—
141C2×C4×C239—21no—
142C2×C4×C239—21no—
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×C239C22×C412yes—
152C2×C4×C239C22×C412yes—
153C2×C4×C239C22×C412yes—
154C2×C4×C239C2×D412yes—
155C2×C4×C239C2×Q812yes—
156C22×C239C23×C411yescharacteristic
157C22×C239C22×D411yescharacteristic
158C22×C239C22×Q811yescharacteristic
159C22×C239C2×#4111yescharacteristic
160C22×C239C2×#4111yescharacteristic
161C22×C239H(5,𝔽2)11yescharacteristic
162C22×C2392−1+411yescharacteristic
163C2×D239—22no—
164C2×D239—22no—
165C2×D239—22no—
166C2×D239—22no—
167C2×D239—22no—
168C2×D239—22no—
169C2×D239C4×Q814yescomplemented
170C4×C239—22no—
171C4×C239—22no—
172C4×C239—22no—
173C4×C239—22no—
174C4×C239—22no—
175C4×C239—41no—
176C4×C239—41no—
177Dic239—22no—
178Dic239—22no—
179Dic239—22no—
180Dic239—22no—
181Dic239—41no—
182Dic239—41no—
183Dic239C4×D414yes—
184C2×C239C2×C4×D411yescharacteristic
185C2×C239C2×C4×Q811yescharacteristic
186C2×C239#52011yescharacteristic
187C2×C239#54611yescharacteristic
188C2×C239D4×Q811yescharacteristic
189C2×C239#55211yescharacteristic
190C2×C239#55411yescharacteristic
191D239—24no—
192C239#236011yescharacteristic, complemented, Sylow
193#2360—2391nomaximal, Sylow
194C2×C22⋊Q8—2391no—
195C2×C4×Q8—2391no—
196C22×C4⋊C4—2391no—
197#391—2391no—
198#389—2391no—
199#389—2391no—
200#389D23911yescharacteristic, complemented
201#387—2391no—
202#387—2391no—
203#385—2391no—
204#385—2391no—
205C4×C4⋊C4—2391no—
206C4×C22⋊C4—2391no—
207C4×C22⋊C4—2391no—
208C4×C22⋊C4—2391no—
209C22×Q8—2391no—
210C23×C4—2391no—
211C23×C4—2391no—
212C23×C4—2391no—
213C22⋊Q8—2398no—
214C4×Q8—4784no—
215C2×C4⋊C4—4784no—
216C2×C4⋊C4—2391no—
217C2×C4⋊C4—2391no—
218C2×C4⋊C4—2391no—
219C2×C4⋊C4—2391no—
220C2×C4⋊C4—2391no—
221C2×C4⋊C4—2391no—
222C2×C4⋊C4—2391no—
223C2×C4⋊C4C2×D23911yescharacteristic
224C2×C4⋊C4C2×D23911yescharacteristic
225C2×C4⋊C4C2×D23911yescharacteristic
226C2×C4⋊C4C2×D23911yescharacteristic
227C2×C22⋊C4—2391no—
228C2×C22⋊C4—2391no—
229C2×C22⋊C4—2391no—
230C2×C22⋊C4—2391no—
231C2×C42—2391no—
232C2×C42—2391no—
233C2×C42—2391no—
234C2×C42—2391no—
235C2×C42—2391no—
236C2×C42C2×D23911yescharacteristic
237#95—2391no—
238#95—2391no—
239#95—2391no—
240#95—2391no—
241#95—2391no—
242#95—2391no—
243#95—2391no—
244#95—2391no—
245#95C2×D23911yescharacteristic
246#95C2×D23911yescharacteristic
247C24—2391no—
248C2×Q8—4782no—
249C2×Q8—4782no—
250C2×Q8—2394no—
251C22×C4—9561no—
252C22×C4—9561no—
253C22×C4—4782no—
254C22×C4—4782no—
255C22×C4—4782no—
256C22×C4—4782no—
257C22×C4—4782no—
258C22×C4—4782no—
259C22×C4—2391no—
260C22×C4—2391no—
261C22×C4—2391no—
262C22×C4—2391no—
263C22×C4—2391no—
264C22×C4—2391no—
265C22×C4—2394no—
266C22×C4—2391no—
267C22×C4C22×D23911yescharacteristic
268C22×C4C22×D23911yescharacteristic
269C22×C4C22×D23911yescharacteristic
270C22×C4C22×D23911yescharacteristic
271C22×C4C22×D23911yescharacteristic
272C22×C4C22×D23911yescharacteristic
273C22×C4C22×D23911yescharacteristic
274C4⋊C4—22no—
275C4⋊C4—22no—
276C4⋊C4—41no—
277C4⋊C4—9561no—
278C4⋊C4—4782no—
279C4⋊C4—4782no—
280C4⋊C4—4782no—
281C4⋊C4—2394no—
282C4⋊C4—2394no—
283C4⋊C4—2394no—
284C4⋊C4C4×D23914yescomplemented
285C22⋊C4—4782no—
286C22⋊C4—2394no—
287C22⋊C4—2394no—
288C22⋊C4—2394no—
289C42—41no—
290C42—9561no—
291C42—4782no—
292C42—4782no—
293C42—4782no—
294C42—4782no—
295C23—4781no—
296C23—4781no—
297C23—4781no—
298C23—4781no—
299C23—2392no—
300C23—2392no—
301C23—2392no—
302C23C23×D23911yescharacteristic
303Q8—4788no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—9564no—
321C2×C4—9564no—
322C2×C4—4788no—
323C2×C4—4781no—
324C2×C4—4781no—
325C2×C4—4781no—
326C2×C4—4781no—
327C2×C4—4781no—
328C2×C4—4781no—
329C2×C4—4781no—
330C2×C4—4781no—
331C2×C4—4781no—
332C2×C4—4781no—
333C2×C4—4781no—
334C2×C4—4781no—
335C2×C4—4781no—
336C2×C4—4781no—
337C2×C4—2392no—
338C2×C4—2392no—
339C2×C4—2392no—
340C2×C4—2392no—
341C2×C4—2392no—
342C2×C4—2392no—
343C2×C4—2392no—
344C2×C4C2×C4×D23912yes—
345C2×C4C2×C4×D23912yes—
346C2×C4C2×C4×D23912yes—
347C2×C4D4×D23912yes—
348C2×C4Q8×D23912yes—
349C22—4782no—
350C22—4782no—
351C22—4782no—
352C22—4782no—
353C22—4782no—
354C22—4782no—
355C22—2394no—
356C22C22×C4×D23911yescharacteristic
357C22C2×D4×D23911yescharacteristic
358C22C2×Q8×D23911yescharacteristic
359C22#41×D23911yescharacteristic
360C22#41×D23911yescharacteristic
361C22#2144000511yescharacteristic
362C22#2144000811yescharacteristic
363C4—22no—
364C4—22no—
365C4—22no—
366C4—22no—
367C4—22no—
368C4—41no—
369C4—41no—
370C4—9561no—
371C4—9561no—
372C4—4782no—
373C4—4782no—
374C4—4782no—
375C4—4782no—
376C4—2394no—
377C2—4784no—
378C2C4×D4×D23911yescharacteristic
379C2C4×Q8×D23911yescharacteristic
380C2#2950525311yescharacteristic
381C2#2950541111yescharacteristic
382C2#2950543711yescharacteristic
383C2#2950545411yescharacteristic
384C2#2950547611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D239
commutatorC22×C239C23×C4
Fitting#389×C239C2
socle, cosocleC23×C239C24
prime radicalC23×D239C23
hypercenter#389D239
hypocenterC239#2360
LCSG ▷ C22×C239 ▷ C239
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
2. C2×#21439925C2semidirect
4. #29504676C2semidirect
5. #29504669C2semidirect
6. #29504667C2semidirect
7. #29504658C2semidirect
8. #29504653C2semidirect
11. C4×Dic239⋊C4C2semidirect
15. #389×C239C2semidirect
20. #21439938C4semidirect
57. C2×Dic478C2×C4semidirect
78. Dic239⋊C4C2×C4semidirect
79. Dic239⋊C4C2×C4semidirect
84. (C2×D239)⋊C4Q8semidirect
100. C4⋊C4×C239C2×C4semidirect
169. C2×D239C4×Q8semidirect
192. C239#2360semidirect
200. #389D239semidirect
284. C4⋊C4C4×D239semidirect

Maximal subgroups

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

subgroupindex
C2×#214399382
C2×#214399252
C2×C4⋊C4×D2392
#295046762
#295046692
#295046672
#295046582
#295046532
#295046432
C4×Dic239⋊C42
C4×(C2×D239)⋊C42
#295046192
#389×C2392
#2360239