Finite Group Databasebeta

← #37582096

Subgroups — #37582096

Order 24448.

520 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×#20259343C211yesmaximal, characteristic, complemented
2C22×C8×D191C211yesmaximal, characteristic, complemented
3#27133176C211yesmaximal, characteristic, complemented
4#27133173C211yesmaximal, characteristic, complemented
5#27132903C211yesmaximal, characteristic, complemented
6#27132902C211yesmaximal, characteristic, complemented
7#27132898C211yesmaximal, characteristic, complemented
8#27132897C211yesmaximal, characteristic, complemented
9#27132893C211yesmaximal, characteristic, complemented
10#27132892C211yesmaximal, characteristic, complemented
11#27132889C211yesmaximal, characteristic, complemented
12#27132698C211yesmaximal, characteristic, complemented
13#27132658C211yesmaximal, characteristic, complemented
14#27132656C211yesmaximal, characteristic, complemented
15#465×C191C211yesmaximal, characteristic, complemented
16C2×#15690288C2211yescharacteristic
17C2×#15690286C2211yescharacteristic
18C22×C4×D191C2211yescharacteristic
19#20259343—24no—
20C2×#15690277C2211yescharacteristic, complemented
21C2×#15690276C2211yescharacteristic, complemented
22C2×#15690272C2211yescharacteristic, complemented
23C22×C191⋊C8C2211yescharacteristic
24C2×C8×D191—24no—
25C2×C8×D191C2211yescharacteristic
26C2×C8×D191C2211yescharacteristic
27C2×C8×D191C2211yescharacteristic
28C2×C8×D191C2211yescharacteristic
29#20259307—21no—
30#20259304—21no—
31#20259302C2211yescharacteristic
32#20259301C2211yescharacteristic
33#20259298C2211yescharacteristic
34#20259297C2211yescharacteristic
35#20259296C2211yescharacteristic
36#20259293C2211yescharacteristic
37#20259292—21no—
38#20259290—21no—
39D4×Dic191—21no—
40#20259284—21no—
41(C22⋊D191)⋊C4—21no—
42(C22⋊D191)⋊C4—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, complemented
52#20259243C2211yescharacteristic, complemented
53#20259242C2211yescharacteristic, complemented
54C2×SD16×C191C2211yescharacteristic, complemented
55C22×C8×C191C2211yescharacteristic
56C22⋊Q8×C191C2211yescharacteristic
57#121×C191C2211yescharacteristic
58#106×C191C2211yescharacteristic, complemented
59#103×C191C2211yescharacteristic, complemented
60#102×C191C2211yescharacteristic, complemented
61C23×D191D411yescharacteristic
62#15690288—22no—
63#15690288—22no—
64#15690286—22no—
65#15690286—22no—
66C2×Dic382C2311yescharacteristic
67C2×D764—21no—
68C2×D764—21no—
69C2×D764C2311yescharacteristic
70C2×C22⋊D191—21no—
71C2×C22⋊D191—21no—
72C2×C22⋊D191—21no—
73C22×Dic191—21no—
74C22×Dic191D411yescharacteristic
75C2×C4×D191—22no—
76C2×C4×D191—22no—
77C2×C4×D191—21no—
78C2×C4×D191D411yescharacteristic
79C2×C4×D191D411yescharacteristic
80C2×C4×D191C2311yescharacteristic
81C2×C4×D191C2311yescharacteristic
82#15690277—22no—
83#15690276—22no—
84#15690272—22no—
85C2×C191⋊C8—22no—
86C2×C191⋊C8C2311yescharacteristic
87C2×C191⋊C8C2311yescharacteristic
88C8×D191—22no—
89C8×D191—22no—
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—22no—
121C22×D191—22no—
122C22×D191—22no—
123C22×D191—21no—
124C22×D191C2×D411yescharacteristic
125C22×D191C2×D411yescharacteristic
126Dic382—21no—
127Dic382—21no—
128D764—21no—
129D764—21no—
130D764—42no—
131D764—42no—
132C22⋊D191—42no—
133C22⋊D191—42no—
134C22⋊D191—42no—
135C2×Dic191—22no—
136C2×Dic191—21no—
137C2×Dic191—21no—
138C2×Dic191—21no—
139C2×Dic191—42no—
140C2×Dic191C2×D411yescharacteristic
141C2×Dic191C2×D411yescharacteristic
142C4×D191—22no—
143C4×D191—21no—
144C4×D191—21no—
145C4×D191—22no—
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—42no—
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—41no—
170C22×C191—41no—
171C22×C191—41no—
172C22×C191#13512yescomplemented
173C22×C191C22×D411yescharacteristic
174C2×D191—28no—
175C2×D191—21no—
176C2×D191—21no—
177C2×D191—21no—
178C2×D191—21no—
179C2×D191—41no—
180C2×D191—41no—
181C2×D191—41no—
182C2×D191#12112yes—
183C2×D191#13512yescomplemented
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—22no—
196C2×C191—81no—
197C2×C191C2×#12111yescharacteristic
198C2×C191C2×#13511yescharacteristic
199C2×C191C2×#13511yescharacteristic
200D191—22no—
201D191—22no—
202D191—81no—
203C191#305011yescharacteristic, complemented, Sylow
204#3050—1911nomaximal, Sylow
205C2×#135—1911no—
206C23×C8—1911no—
207#525—1911no—
208#525—1911no—
209#467—1911no—
210#467—1911no—
211#466—1911no—
212#466—1911no—
213#465—1911no—
214#465—1911no—
215#465—1911no—
216#465D19111yescharacteristic, complemented
217#427—1911no—
218#416—1911no—
219#416—1911no—
220C2×#41—1911no—
221C2×#41—1911no—
222C23×C4—1911no—
223#135—3824no—
224C2×Q16—1911no—
225C2×SD16—1911no—
226C2×SD16C2×D19111yescharacteristic, complemented
227C2×D8—1911no—
228C22×C8—3824no—
229C22×C8—1911no—
230C22×C8—1911no—
231C22×C8—1911no—
232C22×C8—1911no—
233C22×C8—1911no—
234C22×C8C2×D19111yescharacteristic
235#123—3821no—
236#123—3821no—
237C22⋊Q8—1911no—
238C22⋊Q8—1911no—
239C22⋊Q8—1911no—
240C22⋊Q8C2×D19111yescharacteristic
241#121—1911no—
242#121—1911no—
243#121—1911no—
244#121C2×D19111yescharacteristic
245#120—3821no—
246#120—3821no—
247C4×D4—3821no—
248C4×D4—3821no—
249C4×D4—3821no—
250C4×D4—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, complemented
265C24—1911no—
266#41—3822no—
267#41—3822no—
268#41—3822no—
269#41—3822no—
270C2×Q8—1911no—
271C2×Q8C22×D19111yescharacteristic
272C2×D4—21no—
273C2×D4—3821no—
274C2×D4—3821no—
275C2×D4—3821no—
276C2×D4—3821no—
277C2×D4—3821no—
278C2×D4—1911no—
279C2×D4C22×D19111yescharacteristic
280C22×C4—3822no—
281C22×C4—3822no—
282C22×C4—3821no—
283C22×C4—3821no—
284C22×C4—1911no—
285C22×C4—1911no—
286C22×C4—1911no—
287C22×C4—1911no—
288C22×C4—1911no—
289C22×C4C22×D19111yescharacteristic
290Q16—3822no—
291SD16—22no—
292SD16—3822no—
293D8—3822no—
294C2×C8—22no—
295C2×C8—3822no—
296C2×C8—3822no—
297C2×C8—3822no—
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—3822no—
326C23—3822no—
327C23—3822no—
328C23—3821no—
329C23—1911no—
330C23—1911no—
331C23D4×D19111yescharacteristic
332Q8—21no—
333Q8—21no—
334Q8—3821no—
335Q8—3821no—
336D4—21no—
337D4—21no—
338D4—42no—
339D4—3821no—
340D4—3821no—
341D4—7642no—
342D4—7642no—
343D4—7642no—
344D4—7642no—
345D4—7642no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—3822no—
352C2×C4—3822no—
353C2×C4—3822no—
354C2×C4—3821no—
355C2×C4—3821no—
356C2×C4—3821no—
357C2×C4—3821no—
358C2×C4—3821no—
359C2×C4—1911no—
360C2×C4—1911no—
361C2×C4—1912no—
362C2×C4—1912no—
363C2×C4—7642no—
364C2×C4—7642no—
365C2×C4D4×D19111yescharacteristic
366C2×C4C23×D19111yescharacteristic
367C8—21no—
368C8—3821no—
369C8—1912no—
370C8D4×D19112yes—
371C22—21no—
372C22—21no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—3828no—
377C22—3821no—
378C22—3821no—
379C22—3821no—
380C22—3821no—
381C22—1912no—
382C22—1912no—
383C22—7641no—
384C22—7641no—
385C22—7641no—
386C22#2025934312yescomplemented
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—22no—
400C2—81no—
401C2—3822no—
402C2—3822no—
403C2—15281no—
404C2#121×D19111yescharacteristic
405C2#135×D19111yescharacteristic
406C2C2×#2025934311yescharacteristic
subgroupG/H
centerC22C2×D4×D191
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
Fitting#465×C191C2
socleC22×C191C22×D4
hypercenter#465D191
hypocenterC191#3050
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×#20259343C2semidirect
2. C22×C8×D191C2semidirect
3. #27133176C2semidirect
4. #27133173C2semidirect
5. #27132903C2semidirect
6. #27132902C2semidirect
7. #27132898C2semidirect
8. #27132897C2semidirect
9. #27132893C2semidirect
10. #27132892C2semidirect
11. #27132889C2semidirect
12. #27132698C2semidirect
13. #27132658C2semidirect
14. #27132656C2semidirect
15. #465×C191C2semidirect
20. C2×#15690277C22semidirect
21. C2×#15690276C22semidirect
22. C2×#15690272C22semidirect
45. #20259255C22semidirect
46. #20259255C22semidirect
47. #20259254C22semidirect
48. #20259247C22semidirect
49. #20259246C22semidirect
50. #20259245C22semidirect
51. #20259244C22semidirect
52. #20259243C22semidirect
53. #20259242C22semidirect
54. C2×SD16×C191C22semidirect
58. #106×C191C22semidirect
59. #103×C191C22semidirect
60. #102×C191C22semidirect
91. C8×D191D4semidirect
172. C22×C191#135semidirect
183. C2×D191#135semidirect
203. C191#3050semidirect
216. #465D191semidirect
226. C2×SD16C2×D191semidirect
256. #106C2×D191semidirect
260. #103C2×D191semidirect
264. #102C2×D191semidirect
386. C22#20259343semidirect

Maximal subgroups

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

subgroupindex
C2×#202593432
C22×C8×D1912
#271331762
#271331732
#271329032
#271329022
#271328982
#271328972
#271328932
#271328922
#271328892
#271326982
#271326582
#271326562
#465×C1912
#3050191