Finite Group Databasebeta

← #44487536

Subgroups — #44487536

Order 30592.

652 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#21439943C211yesmaximal, characteristic
2C2×C4×C22⋊D239C211yesmaximal, characteristic
3C2×#21439919C211yesmaximal, characteristic, complemented
4#29504669C211yesmaximal, characteristic, complemented
5#29504664C211yesmaximal, characteristic, complemented
6#29504661C211yesmaximal, characteristic, complemented
7#29504659C211yesmaximal, characteristic, complemented
8#29504654C211yesmaximal, characteristic, complemented
9#29504651C211yesmaximal, characteristic
10#29504646C211yesmaximal, characteristic, complemented
11#29504645C211yesmaximal, characteristic, complemented
12#29504623C211yesmaximal, characteristic, complemented
13C4×C22⋊Dic239C211yesmaximal, characteristic, complemented
14#29504619C211yesmaximal, characteristic, complemented
15C2×#95×C239C211yesmaximal, characteristic, complemented
16C22×C22⋊D239C2211yescharacteristic
17C22×C4×D239C2211yescharacteristic
18#21439943C418yescomplemented
19C4×C22⋊D239—24no—
20#21439919—24no—
21C2×C4⋊Dic239C2211yescharacteristic
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
48C23×C4×C239C2211yescharacteristic
49C23×C4×C239C2211yescharacteristic
50#95×C239C2211yescharacteristic
51#95×C239C2211yescharacteristic
52#95×C239C2211yescharacteristic
53#95×C239C2211yescharacteristic
54C23×D239C2311yescharacteristic
55C2×C22⋊D239—22no—
56C2×C22⋊D239—22no—
57C2×C22⋊D239C2×C414yes—
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—41no—
68C4⋊Dic239—22no—
69C4⋊Dic239—22no—
70Dic239⋊C4—22no—
71Dic239⋊C4—22no—
72Dic239⋊C4—41no—
73Dic239⋊C4C2×C414yescomplemented
74Dic239⋊C4C2×C414yescomplemented
75C22⋊Dic239—22no—
76C22⋊Dic239C2×C414yescomplemented
77C22⋊Dic239D414yes—
78(C2×D239)⋊C4—22no—
79(C2×D239)⋊C4—22no—
80(C2×D239)⋊C4—41no—
81(C2×D239)⋊C4C2×C414yescomplemented
82(C2×D239)⋊C4C2×C414yescomplemented
83C4×Dic239—22no—
84C4×Dic239—22no—
85C4×Dic239—22no—
86C4×Dic239—22no—
87C4×Dic239—41no—
88C24×C239C2311yescharacteristic
89C22×C4×C239—22no—
90C22×C4×C239—22no—
91C22×C4×C239—22no—
92C22×C4×C239—22no—
93C22×C4×C239—22no—
94C22×C4×C239—22no—
95C22×C4×C239—41no—
96C22×C4×C239—41no—
97C22×C4×C239C2×C414yescomplemented
98C22×C4×C239C2311yescharacteristic
99C22×C4×C239C2311yescharacteristic
100C22×C4×C239C2311yescharacteristic
101C22×C4×C239C2311yescharacteristic
102C22×C4×C239C2311yescharacteristic
103C22×C4×C239C2311yescharacteristic
104C22×D239—21no—
105C22×D239—21no—
106C22×D239—21no—
107C22×D239—21no—
108C22×D239—21no—
109C22×D239—21no—
110C22×D239C22×C412yes—
111C22⋊D239—28no—
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×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—
133C4×D239—44no—
134C23×C239—21no—
135C23×C239—21no—
136C23×C239—21no—
137C23×C239—21no—
138C23×C239C22×C412yes—
139C23×C239C2×D412yes—
140C23×C239#4112yes—
141C23×C239C2411yescharacteristic
142C2×C4×C239—28no—
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—44no—
158C2×C4×C239—44no—
159C2×C4×C239C22×C412yes—
160C2×C4×C239C22×C412yes—
161C2×C4×C239#4112yes—
162C2×C4×C239#4112yes—
163C22×C239—22no—
164C22×C239—22no—
165C22×C239—22no—
166C22×C239—22no—
167C22×C239—22no—
168C22×C239—22no—
169C22×C239C4×D414yes—
170C22×C239C23×C411yescharacteristic
171C22×C239C22×D411yescharacteristic
172C22×C239C2×#4111yescharacteristic
173C22×C239C2×#4111yescharacteristic
174C22×C239C2×#4111yescharacteristic
175C22×C239H(5,𝔽2)11yescharacteristic
176C22×C2392−1+411yescharacteristic
177C2×D239—22no—
178C2×D239—22no—
179C2×D239—22no—
180C2×D239—41no—
181C2×D239—41no—
182C2×D239—41no—
183C2×D239—41no—
184C4×C239—22no—
185C4×C239—22no—
186C4×C239—22no—
187C4×C239—22no—
188C4×C239—41no—
189C4×C239—41no—
190Dic239—22no—
191Dic239—22no—
192Dic239—22no—
193Dic239—22no—
194Dic239—22no—
195Dic239—41no—
196Dic239—41no—
197C2×C239—24no—
198C2×C239C2×C4×D411yescharacteristic
199C2×C239C4×#4111yescharacteristic
200C2×C239#52011yescharacteristic
201C2×C239#54611yescharacteristic
202C2×C239#54711yescharacteristic
203C2×C239#55111yescharacteristic
204C2×C239#55211yescharacteristic
205D239—42no—
206C239#235911yescharacteristic, complemented, Sylow
207#2359—2391nomaximal, Sylow
208C2×#123—2391no—
209C2×C4×D4—2391no—
210C2×#117—2391no—
211#389—2391no—
212#388—2391no—
213#388—2391no—
214#387—2391no—
215#387—2391no—
216#386—2391no—
217#385—2391no—
218#385—2391no—
219C4×C4⋊C4—2391no—
220C4×C22⋊C4—2391no—
221C4×C22⋊C4—2391no—
222C2×#95D23911yescharacteristic, complemented
223C22×D4—2391no—
224C23×C4—2391no—
225C23×C4C2×D23911yescharacteristic
226C23×C4C2×D23911yescharacteristic
227C23×C4C2×D23911yescharacteristic
228#123—2398no—
229C4×D4—4784no—
230#117—4784no—
231C2×C4⋊C4—2391no—
232C2×C4⋊C4—2391no—
233C2×C4⋊C4—2391no—
234C2×C4⋊C4—2391no—
235C2×C4⋊C4—2391no—
236C2×C4⋊C4—2391no—
237C2×C4⋊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⋊C4—2391no—
246C2×C42—2391no—
247C2×C42—2391no—
248C2×C42—2391no—
249C2×C42—2391no—
250C2×C42—2391no—
251#95—2391no—
252#95—2391no—
253#95—2391no—
254#95—2391no—
255#95—2391no—
256#95—2391no—
257#95C2×D23911yescharacteristic
258#95C2×D23911yescharacteristic
259#95C2×D23911yescharacteristic
260#95C2×D23911yescharacteristic
261C24—2391no—
262C24C22×D23911yescharacteristic
263C2×D4—4782no—
264C2×D4—4782no—
265C2×D4—2394no—
266C22×C4—22no—
267C22×C4—22no—
268C22×C4—22no—
269C22×C4—22no—
270C22×C4—22no—
271C22×C4—22no—
272C22×C4—41no—
273C22×C4—41no—
274C22×C4—9561no—
275C22×C4—4782no—
276C22×C4—4782no—
277C22×C4—2391no—
278C22×C4—2391no—
279C22×C4—2391no—
280C22×C4—2391no—
281C22×C4—2391no—
282C22×C4—2391no—
283C22×C4—2391no—
284C22×C4C4×D23914yescomplemented
285C22×C4C22×D23911yescharacteristic
286C22×C4C22×D23911yescharacteristic
287C22×C4C22×D23911yescharacteristic
288C22×C4C22×D23911yescharacteristic
289C22×C4C22×D23911yescharacteristic
290C22×C4C22×D23911yescharacteristic
291C4⋊C4—9561no—
292C4⋊C4—4782no—
293C4⋊C4—4782no—
294C4⋊C4—4782no—
295C4⋊C4—4782no—
296C4⋊C4—2394no—
297C4⋊C4—2394no—
298C22⋊C4—9561no—
299C22⋊C4—4782no—
300C22⋊C4—4782no—
301C22⋊C4—4782no—
302C22⋊C4—2394no—
303C22⋊C4—2394no—
304C22⋊C4—2394no—
305C22⋊C4—2394no—
306C42—9561no—
307C42—4782no—
308C42—4782no—
309C42—4782no—
310C42—4782no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—4781no—
316C23—4781no—
317C23—4781no—
318C23—4781no—
319C23—4781no—
320C23—4781no—
321C23—2392no—
322C23C2×C4×D23912yes—
323C23D4×D23912yes—
324C23#1683854712yes—
325C23C23×D23911yescharacteristic
326D4—4788no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—28no—
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—44no—
344C2×C4—9564no—
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—4781no—
360C2×C4—4781no—
361C2×C4—2392no—
362C2×C4—2392no—
363C2×C4—2392no—
364C2×C4—2392no—
365C2×C4—2392no—
366C2×C4C2×C4×D23912yes—
367C2×C4C2×C4×D23912yes—
368C2×C4#1683854812yes—
369C2×C4#1683854812yes—
370C22—22no—
371C22—22no—
372C22—22no—
373C22—22no—
374C22—22no—
375C22—22no—
376C22—9561no—
377C22—9561no—
378C22—9561no—
379C22—9561no—
380C22—4782no—
381C22—4782no—
382C22—4782no—
383C22(C22⋊D239)⋊C414yes—
384C22C22×C4×D23911yescharacteristic
385C22C2×D4×D23911yescharacteristic
386C22C2×#1683854711yescharacteristic
387C22C2×#1683854811yescharacteristic
388C22C2×#1683854811yescharacteristic
389C22#2144000511yescharacteristic
390C22#2144000811yescharacteristic
391C4—22no—
392C4—22no—
393C4—22no—
394C4—22no—
395C4—41no—
396C4—41no—
397C4—9561no—
398C4—9561no—
399C4—4782no—
400C4—4782no—
401C4—4782no—
402C4—4782no—
403C4—4782no—
404C2—24no—
405C2—9562no—
406C2C2×(C22⋊D239)⋊C411yescharacteristic
407C2C4×#1683854811yescharacteristic
408C2#2950525311yescharacteristic
409C2#2950541211yescharacteristic
410C2#2950542311yescharacteristic
411C2#2950544811yescharacteristic
412C2#2950545711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D239
commutatorC22×C239C23×C4
FittingC2×#95×C239C2
socle, cosocleC23×C239C24
prime radicalC22×C22⋊D239C22
hypercenterC2×#95D239
hypocenterC239#2359
LCSG ▷ C22×C239 ▷ C239
UCSC1 ◁ C23 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
3. C2×#21439919C2semidirect
4. #29504669C2semidirect
5. #29504664C2semidirect
6. #29504661C2semidirect
7. #29504659C2semidirect
8. #29504654C2semidirect
10. #29504646C2semidirect
11. #29504645C2semidirect
12. #29504623C2semidirect
13. C4×C22⋊Dic239C2semidirect
14. #29504619C2semidirect
15. C2×#95×C239C2semidirect
18. #21439943C4semidirect
73. Dic239⋊C4C2×C4semidirect
74. Dic239⋊C4C2×C4semidirect
76. C22⋊Dic239C2×C4semidirect
81. (C2×D239)⋊C4C2×C4semidirect
82. (C2×D239)⋊C4C2×C4semidirect
97. C22×C4×C239C2×C4semidirect
206. C239#2359semidirect
222. C2×#95D239semidirect
284. C22×C4C4×D239semidirect

Maximal subgroups

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

subgroupindex
C2×#214399432
C2×C4×C22⋊D2392
C2×#214399192
#295046692
#295046642
#295046612
#295046592
#295046542
#295046512
#295046462
#295046452
#295046232
C4×C22⋊Dic2392
#295046192
C2×#95×C2392
#2359239