Finite Group Databasebeta

← #44487695

Subgroups — #44487695

Order 30592.

512 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#21439945C211yesmaximal, characteristic
2#29504674C211yesmaximal, characteristic
3#29504671C211yesmaximal, characteristic, complemented
4#29504669C211yesmaximal, characteristic, complemented
5#29504664C211yesmaximal, characteristic, complemented
6#29504662C211yesmaximal, characteristic, complemented
7#29504661C211yesmaximal, characteristic, complemented
8#29504661C211yesmaximal, characteristic, complemented
9#29504656C211yesmaximal, characteristic, complemented
10#29504650C211yesmaximal, characteristic
11#29504646C211yesmaximal, characteristic, complemented
12#29504646C211yesmaximal, characteristic, complemented
13#29504631C211yesmaximal, characteristic, complemented
14#29504629C211yesmaximal, characteristic, complemented
15#387×C239C211yesmaximal, characteristic, complemented
16C22×D956C2211yescharacteristic
17C22×C4×D239C2211yescharacteristic
18C22×C4×D239C2211yescharacteristic
19#21439945C418yescomplemented
20C2×C4⋊Dic239C2211yescharacteristic
21C2×C4⋊Dic239C2211yescharacteristic
22C2×C4⋊Dic239C2211yescharacteristic
23C2×Dic239⋊C4C2211yescharacteristic
24C2×Dic239⋊C4C2211yescharacteristic
25C2×Dic239⋊C4C2211yescharacteristic
26C2×Dic239⋊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×C4×Dic239C2211yescharacteristic
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
54C2×D956—41no—
55C2×D956—41no—
56C2×D956C2×C414yes—
57C22×Dic239C2311yescharacteristic
58C22×Dic239C2311yescharacteristic
59C22×Dic239C2311yescharacteristic
60C22×Dic239C2311yescharacteristic
61C22×Dic239C2311yescharacteristic
62C22×Dic239C2311yescharacteristic
63C2×C4×D239—41no—
64C2×C4×D239—41no—
65C2×C4×D239—41no—
66C2×C4×D239—41no—
67C2×C4×D239—41no—
68C2×C4×D239C2×C414yescomplemented
69C4⋊Dic239—41no—
70C4⋊Dic239—41no—
71C4⋊Dic239—41no—
72Dic239⋊C4—41no—
73Dic239⋊C4—41no—
74Dic239⋊C4—41no—
75Dic239⋊C4C2×C414yescomplemented
76(C2×D239)⋊C4—41no—
77(C2×D239)⋊C4—41no—
78(C2×D239)⋊C4—41no—
79(C2×D239)⋊C4—41no—
80(C2×D239)⋊C4—41no—
81(C2×D239)⋊C4—41no—
82(C2×D239)⋊C4—41no—
83(C2×D239)⋊C4C2×C414yes—
84(C2×D239)⋊C4C2×C414yes—
85(C2×D239)⋊C4C2×C414yescomplemented
86C4×Dic239—41no—
87C4×Dic239—41no—
88C22×C4×C239C2311yescharacteristic
89C22×C4×C239C2311yescharacteristic
90C22×C4×C239C2311yescharacteristic
91C22×C4×C239C2311yescharacteristic
92C22×C4×C239C2311yescharacteristic
93C22×C4×C239C2311yescharacteristic
94C22×C4×C239C2311yescharacteristic
95C4⋊C4×C239—41no—
96C4⋊C4×C239C2×C414yescomplemented
97C42×C239—41no—
98C22×D239—21no—
99C22×D239—21no—
100C22×D239—21no—
101C22×D239—21no—
102C22×D239—21no—
103C22×D239—21no—
104C22×D239—21no—
105C22×D239—21no—
106C22×D239—21no—
107C22×D239—21no—
108C22×D239—21no—
109C22×D239—21no—
110C22×D239C22×C412yes—
111C22×D239C22×C412yes—
112D956—44no—
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×Dic239—21no—
129C2×Dic239C22×C412yes—
130C2×Dic239C22×C412yes—
131C4×D239—44no—
132C4×D239—44no—
133C23×C239C2411yescharacteristic
134C2×C4×C239—21no—
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×C239—21no—
152C2×C4×C239C22×C412yes—
153C2×C4×C239C22×C412yes—
154C2×C4×C239C22×C412yes—
155C22×C239C23×C411yescharacteristic
156C22×C239H(5,𝔽2)11yescharacteristic
157C22×C239H(5,𝔽2)11yescharacteristic
158C22×C239H(5,𝔽2)11yescharacteristic
159C22×C239H(5,𝔽2)11yescharacteristic
160C22×C2392−1+411yescharacteristic
161C22×C2392−1+411yescharacteristic
162C2×D239—22no—
163C2×D239—22no—
164C2×D239—22no—
165C2×D239—22no—
166C2×D239—22no—
167C2×D239—22no—
168C2×D239—41no—
169C2×D239—41no—
170C2×D239—41no—
171C2×D239—41no—
172C2×D239—41no—
173C2×D239—41no—
174C2×D239—41no—
175C2×D239—41no—
176C4×C239—22no—
177C4×C239—22no—
178C4×C239—22no—
179C4×C239—41no—
180C4×C239—41no—
181C4×C239—41no—
182C4×C239—41no—
183Dic239—22no—
184Dic239—22no—
185Dic239—41no—
186Dic239—41no—
187Dic239—41no—
188Dic239—41no—
189C2×C239#51811yescharacteristic
190C2×C239#52011yescharacteristic
191C2×C239#52011yescharacteristic
192C2×C239#56011yescharacteristic
193C2×C239#56211yescharacteristic
194C2×C239#56211yescharacteristic
195C2×C239#56311yescharacteristic
196D239—42no—
197D239—42no—
198C239#237611yescharacteristic, complemented, Sylow
199#2376—2391nomaximal, Sylow
200C2×#123—2391no—
201#390—2391no—
202#389—2391no—
203#389—2391no—
204#388—2391no—
205#388—2391no—
206#388—2391no—
207#388—2391no—
208#387—2391no—
209#387D23911yescharacteristic, complemented
210#386—2391no—
211#385—2391no—
212#385—2391no—
213#380—2391no—
214#380—2391no—
215C22×D4—2391no—
216C23×C4—2391no—
217C23×C4—2391no—
218#123—2398no—
219C2×C4⋊C4—2391no—
220C2×C4⋊C4—2391no—
221C2×C4⋊C4—2391no—
222C2×C4⋊C4—2391no—
223C2×C4⋊C4—2391no—
224C2×C4⋊C4—2391no—
225C2×C4⋊C4—2391no—
226C2×C4⋊C4C2×D23911yescharacteristic
227C2×C4⋊C4C2×D23911yescharacteristic
228C2×C22⋊C4—2391no—
229C2×C22⋊C4—2391no—
230C2×C22⋊C4—2391no—
231C2×C22⋊C4—2391no—
232C2×C22⋊C4—2391no—
233C2×C22⋊C4—2391no—
234C2×C22⋊C4—2391no—
235C2×C22⋊C4—2391no—
236C2×C22⋊C4—2391no—
237C2×C22⋊C4—2391no—
238C2×C42—2391no—
239C2×C42—2391no—
240C2×C42C2×D23911yescharacteristic
241#95—2391no—
242#95—2391no—
243#95—2391no—
244#95—2391no—
245#95—2391no—
246#95—2391no—
247#95C2×D23911yescharacteristic
248#95C2×D23911yescharacteristic
249#95C2×D23911yescharacteristic
250#95C2×D23911yescharacteristic
251C24—2391no—
252C24—2391no—
253C2×D4—9561no—
254C2×D4—9561no—
255C2×D4—2394no—
256C22×C4—9561no—
257C22×C4—9561no—
258C22×C4—9561no—
259C22×C4—9561no—
260C22×C4—9561no—
261C22×C4—2394no—
262C22×C4—2391no—
263C22×C4—2391no—
264C22×C4—2391no—
265C22×C4—2391no—
266C22×C4—2391no—
267C22×C4—2391no—
268C22×C4C22×D23911yescharacteristic
269C22×C4C22×D23911yescharacteristic
270C22×C4C22×D23911yescharacteristic
271C22×C4C22×D23911yescharacteristic
272C22×C4C22×D23911yescharacteristic
273C22×C4C22×D23911yescharacteristic
274C22×C4C22×D23911yescharacteristic
275C4⋊C4—41no—
276C4⋊C4—9561no—
277C4⋊C4—9561no—
278C4⋊C4—9561no—
279C4⋊C4—9561no—
280C4⋊C4—9561no—
281C4⋊C4—9561no—
282C4⋊C4—2394no—
283C4⋊C4C4×D23914yescomplemented
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—2394no—
293C22⋊C4—2394no—
294C42—41no—
295C42—9561no—
296C42—9561no—
297C23—4781no—
298C23—4781no—
299C23—4781no—
300C23—4781no—
301C23—4781no—
302C23—4781no—
303C23—4781no—
304C23—4781no—
305C23—4781no—
306C23—4781no—
307C23—4781no—
308C23—4781no—
309C23—2392no—
310C23—2392no—
311C23C23×D23911yescharacteristic
312D4—9564no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—9564no—
332C2×C4—9564no—
333C2×C4—4781no—
334C2×C4—4781no—
335C2×C4—4781no—
336C2×C4—4781no—
337C2×C4—4781no—
338C2×C4—4781no—
339C2×C4—4781no—
340C2×C4—4781no—
341C2×C4—4781no—
342C2×C4—4781no—
343C2×C4—4781no—
344C2×C4—4781no—
345C2×C4—4781no—
346C2×C4—4781no—
347C2×C4—4781no—
348C2×C4—4781no—
349C2×C4—2392no—
350C2×C4—2392no—
351C2×C4C2×C4×D23912yes—
352C2×C4C2×C4×D23912yes—
353C2×C4C2×C4×D23912yes—
354C22—9561no—
355C22—9561no—
356C22—9561no—
357C22—9561no—
358C22—9561no—
359C22—9561no—
360C22—9561no—
361C22—9561no—
362C22—4782no—
363C22—4782no—
364C22—4782no—
365C22—4782no—
366C22—4782no—
367C22—4782no—
368C22C22×C4×D23911yescharacteristic
369C22#2144000511yescharacteristic
370C22#2144000611yescharacteristic
371C22#2144000611yescharacteristic
372C22#2144000611yescharacteristic
373C22#2144000711yescharacteristic
374C22#2144000811yescharacteristic
375C4—22no—
376C4—22no—
377C4—22no—
378C4—41no—
379C4—41no—
380C4—41no—
381C4—41no—
382C4—9561no—
383C4—9561no—
384C4—9561no—
385C4—9561no—
386C4—4782no—
387C4—4782no—
388C2—9562no—
389C2—9562no—
390C2#2950524411yescharacteristic
391C2#2950525211yescharacteristic
392C2#2950525411yescharacteristic
393C2#2950551311yescharacteristic
394C2#2950551811yescharacteristic
395C2#2950551911yescharacteristic
396C2#2950552611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D239
commutatorC22×C239C23×C4
Fitting#387×C239C2
socle, cosocleC23×C239C24
prime radicalC22×D956C22
hypercenter#387D239
hypocenterC239#2376
LCSG ▷ C22×C239 ▷ C239
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
3. #29504671C2semidirect
4. #29504669C2semidirect
5. #29504664C2semidirect
6. #29504662C2semidirect
7. #29504661C2semidirect
8. #29504661C2semidirect
9. #29504656C2semidirect
11. #29504646C2semidirect
12. #29504646C2semidirect
13. #29504631C2semidirect
14. #29504629C2semidirect
15. #387×C239C2semidirect
19. #21439945C4semidirect
68. C2×C4×D239C2×C4semidirect
75. Dic239⋊C4C2×C4semidirect
85. (C2×D239)⋊C4C2×C4semidirect
96. C4⋊C4×C239C2×C4semidirect
198. C239#2376semidirect
209. #387D239semidirect
283. C4⋊C4C4×D239semidirect

Maximal subgroups

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

subgroupindex
C2×#214399452
#295046742
#295046712
#295046692
#295046642
#295046622
#295046612
#295046562
#295046502
#295046462
#295046312
#295046292
#387×C2392
#2376239