Finite Group Databasebeta

← #37582154

Subgroups — #37582154

Order 24448.

492 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD16×D191C211yesmaximal, characteristic, complemented
2C2×#20259328C211yesmaximal, characteristic, complemented
3#27133236C211yesmaximal, characteristic, complemented
4#27133229C211yesmaximal, characteristic
5#27132912C211yesmaximal, characteristic, complemented
6#27132911C211yesmaximal, characteristic, complemented
7#27132908C211yesmaximal, characteristic, complemented
8#27132907C211yesmaximal, characteristic, complemented
9#27132893C211yesmaximal, characteristic, complemented
10#27132892C211yesmaximal, characteristic, complemented
11#27132889C211yesmaximal, characteristic, complemented
12#27132698C211yesmaximal, characteristic, complemented
13#27132670C211yesmaximal, characteristic, complemented
14#27132666C211yesmaximal, characteristic, complemented
15#465×C191C211yesmaximal, characteristic, complemented
16C2×#15690287C2211yescharacteristic
17C2×Q8×D191C2211yescharacteristic
18C2×D4×D191C2211yescharacteristic
19C2×#15690276C2211yescharacteristic
20C2×#15690275C2211yescharacteristic
21C2×#15690274C2211yescharacteristic
22SD16×D191—24no—
23#20259328—24no—
24C2×#15690271C2211yescharacteristic, complemented
25C2×#15690270C2211yescharacteristic
26C2×#15690270C2211yescharacteristic, complemented
27C2×C8×D191C2211yescharacteristic
28C2×C8×D191C2211yescharacteristic, complemented
29#20259321—21no—
30#20259318—21no—
31#20259308—21no—
32#20259308—21no—
33#20259307—21no—
34#20259304—21no—
35#20259302C2211yescharacteristic, complemented
36#20259301C2211yescharacteristic, complemented
37#20259298C2211yescharacteristic, complemented
38#20259297C2211yescharacteristic
39#20259296C2211yescharacteristic
40#20259293C2211yescharacteristic
41#20259292—21no—
42#20259290—21no—
43#20259280C2211yescharacteristic
44#20259280C2211yescharacteristic
45#20259255C2211yescharacteristic, complemented
46#20259255C2211yescharacteristic, complemented
47#20259254C2211yescharacteristic, complemented
48#20259247C2211yescharacteristic, complemented
49#20259246C2211yescharacteristic, complemented
50#20259245C2211yescharacteristic, complemented
51#20259244C2211yescharacteristic
52#20259243C2211yescharacteristic
53#20259242C2211yescharacteristic
54C2×SD16×C191C2211yescharacteristic
55C22×C8×C191C2211yescharacteristic, complemented
56C22⋊Q8×C191C2211yescharacteristic, complemented
57#121×C191C2211yescharacteristic
58#106×C191C2211yescharacteristic, complemented
59#103×C191C2211yescharacteristic, complemented
60#102×C191C2211yescharacteristic
61C23×D191—21no—
62#15690287—22no—
63#15690287—22no—
64C2×Dic382—21no—
65C2×Dic382D411yescharacteristic
66C2×Dic382C2311yescharacteristic
67Q8×D191—22no—
68Q8×D191—22no—
69C2×D764—21no—
70C2×D764D411yescharacteristic
71C2×D764C2311yescharacteristic
72C2×C22⋊D191—21no—
73C2×C22⋊D191—21no—
74C2×C22⋊D191—21no—
75C2×C22⋊D191D411yescharacteristic
76C2×C22⋊D191D411yescharacteristic
77D4×D191—22no—
78D4×D191—22no—
79C2×C4×D191—21no—
80C2×C4×D191C2311yescharacteristic
81C2×C4×D191C2311yescharacteristic
82#15690276—22no—
83#15690275—22no—
84#15690274—22no—
85#15690271—22no—
86#15690270—22no—
87#15690270—22no—
88C2×C191⋊C8C2311yescharacteristic
89C2×C191⋊C8C2311yescharacteristic
90C8×D191—22no—
91C8×D191D414yescomplemented
92C4⋊Dic191—21no—
93C4⋊Dic191C2311yescharacteristic
94C4⋊Dic191C2311yescharacteristic
95Dic191⋊C4—21no—
96Dic191⋊C4—21no—
97C22⋊Dic191—21no—
98C22⋊Dic191—21no—
99(C2×D191)⋊C4—21no—
100(C2×D191)⋊C4—21no—
101(C2×D191)⋊C4—21no—
102(C2×D191)⋊C4—21no—
103(C2×D191)⋊C4—21no—
104(C2×D191)⋊C4—21no—
105C4×Dic191—21no—
106C4×Dic191—21no—
107C2×Q8×C191C2311yescharacteristic
108C2×D4×C191—21no—
109C2×D4×C191C2311yescharacteristic
110C22×C4×C191C2311yescharacteristic
111SD16×C191—22no—
112C2×C8×C191—22no—
113C2×C8×C191C2311yescharacteristic
114C2×C8×C191C2311yescharacteristic
115C4⋊C4×C191—21no—
116C4⋊C4×C191C2311yescharacteristic
117C4⋊C4×C191C2311yescharacteristic
118C22⋊C4×C191—21no—
119C22⋊C4×C191—21no—
120C22×D191—21no—
121C22×D191—42no—
122C22×D191—81no—
123C22×D191—81no—
124C22×D191C2×D411yescharacteristic
125C22×D191C2×D411yescharacteristic
126Dic382—22no—
127Dic382—21no—
128Dic382—21no—
129Dic382—42no—
130D764—22no—
131D764—21no—
132D764—21no—
133D764—81no—
134C22⋊D191—22no—
135C22⋊D191—22no—
136C22⋊D191—42no—
137C22⋊D191—81no—
138C22⋊D191—81no—
139C2×Dic191—21no—
140C2×Dic191—21no—
141C2×Dic191—21no—
142C2×Dic191C2×D411yescharacteristic
143C2×Dic191C2×D411yescharacteristic
144C4×D191—21no—
145C4×D191—21no—
146C4×D191—42no—
147C4×D191C2×D412yes—
148C4×D191#4112yes—
149C191⋊C8—21no—
150C191⋊C8C2×D412yes—
151C23×C191—21no—
152C23×C191C2×D411yescharacteristic
153Q8×C191—21no—
154Q8×C191—21no—
155D4×C191—21no—
156D4×C191—21no—
157D4×C191—81no—
158C2×C4×C191—21no—
159C2×C4×C191—21no—
160C2×C4×C191—21no—
161C2×C4×C191—21no—
162C2×C4×C191—21no—
163C2×C4×C191C2×D411yescharacteristic
164C2×C4×C191C2411yescharacteristic
165C8×C191—21no—
166C8×C191C2×D412yes—
167C22×C191—21no—
168C22×C191—21no—
169C22×C191—21no—
170C22×C191—41no—
171C22×C191—41no—
172C22×C191—41no—
173C22×C191C22×D411yescharacteristic
174C2×D191—21no—
175C2×D191—21no—
176C2×D191—21no—
177C2×D191—21no—
178C2×D191—21no—
179C2×D191—41no—
180C2×D191—41no—
181C2×D191—41no—
182C2×D191—84no—
183C2×D191#12112yes—
184C4×C191—21no—
185C4×C191—41no—
186C4×C191—41no—
187C4×C191—41no—
188C4×C191C22×D411yescharacteristic
189C4×C191C2×#4111yescharacteristic
190Dic191—21no—
191Dic191—41no—
192Dic191—41no—
193Dic191—41no—
194Dic191#12112yes—
195C2×C191—41no—
196C2×C191—81no—
197C2×C191C2×#12111yescharacteristic
198C2×C191#57711yescharacteristic
199C2×C191#57711yescharacteristic
200D191—22no—
201D191—41no—
202D191—81no—
203C191#305711yescharacteristic, complemented, Sylow
204#3057—1911nomaximal, Sylow
205C22×SD16—1911no—
206C2×#131—1911no—
207#536—1911no—
208#535—1911no—
209#468—1911no—
210#468—1911no—
211#468—1911no—
212#468—1911no—
213#465—1911no—
214#465—1911no—
215#465—1911no—
216#465D19111yescharacteristic, complemented
217#427—1911no—
218#419—1911no—
219#418—1911no—
220C2×#41—1911no—
221C22×Q8—1911no—
222C22×D4—1911no—
223C2×SD16—3824no—
224C2×SD16—1911no—
225C2×SD16—1911no—
226C2×SD16—1911no—
227C2×SD16C2×D19111yescharacteristic
228#131—3824no—
229C2×M16—1911no—
230C2×M16—1911no—
231C2×M16—1911no—
232C22×C8—1911no—
233C22×C8—1911no—
234C22×C8C2×D19111yescharacteristic, complemented
235C4⋊Q8—3821no—
236#127—3821no—
237#124—3821no—
238#124—3821no—
239#123—3821no—
240#123—3821no—
241C22⋊Q8—1911no—
242C22⋊Q8—1911no—
243C22⋊Q8—1911no—
244C22⋊Q8C2×D19111yescharacteristic, complemented
245#121—1911no—
246#121—1911no—
247#121—1911no—
248#121C2×D19111yescharacteristic
249#120—3821no—
250#120—3821no—
251#117—1911no—
252#117—1911no—
253#107—1911no—
254#107—1911no—
255#106—1911no—
256#106C2×D19111yescharacteristic, complemented
257#103—1911no—
258#103—1911no—
259#103—1911no—
260#103C2×D19111yescharacteristic, complemented
261#102—1911no—
262#102—1911no—
263#102—1911no—
264#102C2×D19111yescharacteristic
265C24—3821no—
266#41—3822no—
267#41—3822no—
268C2×Q8—3821no—
269C2×Q8—3822no—
270C2×Q8—3822no—
271C2×Q8—1911no—
272C2×Q8—1911no—
273C2×Q8C22×D19111yescharacteristic
274C2×D4—21no—
275C2×D4—3821no—
276C2×D4—3821no—
277C2×D4—3821no—
278C2×D4—3822no—
279C2×D4—3822no—
280C2×D4—3821no—
281C2×D4—1911no—
282C2×D4—1911no—
283C2×D4—1911no—
284C2×D4—1911no—
285C2×D4C22×D19111yescharacteristic
286C22×C4—3821no—
287C22×C4—1911no—
288C22×C4—1911no—
289C22×C4C22×D19111yescharacteristic
290SD16—22no—
291SD16—3822no—
292SD16—3822no—
293SD16—3822no—
294M16—3822no—
295M16—3822no—
296M16—3822no—
297C2×C8—22no—
298C2×C8—3822no—
299C2×C8—1911no—
300C2×C8—1911no—
301C2×C8—1914no—
302C2×C8C22×D19111yescharacteristic
303C2×C8C22×D19111yescharacteristic
304C4⋊C4—21no—
305C4⋊C4—3821no—
306C4⋊C4—3821no—
307C4⋊C4—3821no—
308C4⋊C4—1911no—
309C4⋊C4—1911no—
310C4⋊C4C22×D19111yescharacteristic
311C4⋊C4C22×D19111yescharacteristic
312C22⋊C4—21no—
313C22⋊C4—21no—
314C22⋊C4—3821no—
315C22⋊C4—3821no—
316C22⋊C4—3821no—
317C22⋊C4—3821no—
318C22⋊C4—3821no—
319C22⋊C4—3821no—
320C22⋊C4—3821no—
321C22⋊C4—3821no—
322C42—3821no—
323C42—3821no—
324C23—21no—
325C23—3821no—
326C23—1911no—
327C23—1911no—
328C23—15281no—
329C23—15281no—
330C23—7642no—
331C23D4×D19111yescharacteristic
332Q8—21no—
333Q8—21no—
334Q8—3822no—
335Q8—3821no—
336Q8—3821no—
337Q8—7642no—
338D4—21no—
339D4—21no—
340D4—81no—
341D4—3822no—
342D4—3822no—
343D4—3822no—
344D4—3821no—
345D4—3821no—
346D4—15281no—
347D4—15281no—
348D4—15281no—
349D4—7642no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—3821no—
356C2×C4—3821no—
357C2×C4—3821no—
358C2×C4—3821no—
359C2×C4—3821no—
360C2×C4—1911no—
361C2×C4—1911no—
362C2×C4—1912no—
363C2×C4—1912no—
364C2×C4—7642no—
365C2×C4D4×D19111yescharacteristic
366C2×C4C23×D19111yescharacteristic
367C8—21no—
368C8—3821no—
369C8—1912no—
370C8D4×D19112yes—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—3821no—
378C22—3821no—
379C22—3821no—
380C22—3821no—
381C22—3821no—
382C22—1912no—
383C22—15284no—
384C22—7641no—
385C22—7641no—
386C22—7641no—
387C22C2×D4×D19111yescharacteristic
388C4—21no—
389C4—41no—
390C4—41no—
391C4—41no—
392C4—3821no—
393C4—1912no—
394C4—7641no—
395C4—7641no—
396C4—7641no—
397C4C2×D4×D19111yescharacteristic
398C4#41×D19111yescharacteristic
399C2—41no—
400C2—81no—
401C2—3822no—
402C2—15281no—
403C2—7641no—
404C2#121×D19111yescharacteristic
405C2#2713346911yescharacteristic
406C2#2713347011yescharacteristic
subgroupG/H
centerC22C2×D4×D191
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
Fitting#465×C191C2
socleC22×C191C22×D4
prime radical#27133229C2
hypercenter#465D191
hypocenterC191#3057
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. C2×SD16×D191C2semidirect
2. C2×#20259328C2semidirect
3. #27133236C2semidirect
5. #27132912C2semidirect
6. #27132911C2semidirect
7. #27132908C2semidirect
8. #27132907C2semidirect
9. #27132893C2semidirect
10. #27132892C2semidirect
11. #27132889C2semidirect
12. #27132698C2semidirect
13. #27132670C2semidirect
14. #27132666C2semidirect
15. #465×C191C2semidirect
24. C2×#15690271C22semidirect
26. C2×#15690270C22semidirect
28. C2×C8×D191C22semidirect
35. #20259302C22semidirect
36. #20259301C22semidirect
37. #20259298C22semidirect
45. #20259255C22semidirect
46. #20259255C22semidirect
47. #20259254C22semidirect
48. #20259247C22semidirect
49. #20259246C22semidirect
50. #20259245C22semidirect
55. C22×C8×C191C22semidirect
56. C22⋊Q8×C191C22semidirect
58. #106×C191C22semidirect
59. #103×C191C22semidirect
91. C8×D191D4semidirect
203. C191#3057semidirect
216. #465D191semidirect
234. C22×C8C2×D191semidirect
244. C22⋊Q8C2×D191semidirect
256. #106C2×D191semidirect
260. #103C2×D191semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×D1912
C2×#202593282
#271332362
#271332292
#271329122
#271329112
#271329082
#271329072
#271328932
#271328922
#271328892
#271326982
#271326702
#271326662
#465×C1912
#3057191