Finite Group Databasebeta

← #14577023

Subgroups — #14577023

Order 2432.

1040 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11927167C212yesmaximal, complemented
2#11927161C212yesmaximal, complemented
3#11927154C212yesmaximal, complemented
4#11927147C212yesmaximal, complemented
5#11927138C214yesmaximal, complemented
6#11927129C214yesmaximal, complemented
7#11927097C211yesmaximal, characteristic, complemented
8#11927090C211yesmaximal, characteristic, complemented
9#11927076C214yesmaximal, complemented
10#11927074C214yesmaximal, complemented
11#11927055C211yesmaximal, characteristic, complemented
12#41×Dic19C211yesmaximal, characteristic, complemented
13#11927012C211yesmaximal, characteristic, complemented
14C2×#10597372C211yesmaximal, characteristic, complemented
15C19×#525C211yesmaximal, characteristic, complemented
16C2×#41×C19C2211yescharacteristic
17C23×C4×C19C2211yescharacteristic
18C2×#64541C2211yescharacteristic
19C19×#123C2212yes—
20C19×C22⋊Q8C2212yes—
21C19×#121C2212yes—
22C19×#120C2212yes—
23C4×D4×C19C2214yes—
24C19×#117C2211yescharacteristic
25#10597399C2212yes—
26C2×C22⋊Dic19C2212yes—
27#10597393C2211yescharacteristic, complemented
28Q8×Dic19C2212yescomplemented
29#10597390C2211yescharacteristic, complemented
30#10597386C2211yescharacteristic, complemented
31#10597385C2214yes—
32#10597385C2214yes—
33#10597384C2214yes—
34#10597382C2214yes—
35#10597382C2211yescharacteristic, complemented
36#10597381C2214yes—
37D4×Dic19C2214yes—
38D4×Dic19C2212yescomplemented
39#10597376C2212yes—
40#10597375C2212yes—
41C4×C22⋊D19C2214yes—
42C4×C22⋊D19C2214yescomplemented
43#10597372C2211yescharacteristic
44#10597372C2212yes—
45#10597372C2212yes—
46#10597372C2212yes—
47#10597372C2212yes—
48#10597372C2212yescomplemented
49C2×C4⋊Dic19C2212yes—
50#10597370C2212yes—
51C2×C4×Dic19C2211yescharacteristic
52C2×C4×Dic19C2211yescharacteristic
53C2×C4×Dic19C2212yescomplemented
54#10597344C2214yescomplemented
55#10597343C2214yescomplemented
56#10597339C2212yescomplemented
57#10597336C2214yescomplemented
58#10597336C2212yescomplemented
59#10597335C2214yescomplemented
60#10597334C2212yescomplemented
61#10597333C2212yescomplemented
62#10597332C2214yescomplemented
63#10597331C2214yes—
64#10597329C2214yes—
65#10597329C2214yescomplemented
66(C22⋊D19)⋊C4C2214yes—
67#10597325C2214yes—
68#10597325C2214yes—
69#10597325C2214yescomplemented
70#10597324C2214yes—
71#10597324C2214yescomplemented
72#10597318C2212yescomplemented
73C42×D19C2212yescomplemented
74C4×Dic38C2214yescomplemented
75C24×C19C2311yescharacteristic
76#41×C19—24no—
77C2×Q8×C19C2311yescharacteristic
78C2×D4×C19C2312yes—
79C2×D4×C19C2311yescharacteristic
80C2×D4×C19C2314yes—
81C22×C4×C19—24no—
82C22×C4×C19C2312yes—
83C22×C4×C19C2312yes—
84C22×C4×C19C2312yes—
85C22×C4×C19C2311yescharacteristic
86C22×C4×C19C2311yescharacteristic
87C2×C22⋊D19C2312yes—
88C2×C22⋊D19C2314yes—
89C2×C22⋊D19C2314yes—
90C22×Dic19C2312yes—
91C22×Dic19C2314yes—
92C22×Dic19C2312yes—
93#64541—24no—
94C2×D76C2311yescharacteristic
95C2×C4×D19C2312yes—
96C2×C4×D19C2314yes—
97C2×Dic38C2311yescharacteristic
98C2×Dic38C2314yes—
99C4⋊C4×C19C2312yes—
100C4⋊C4×C19C2314yes—
101C22⋊C4×C19C2312yes—
102C22⋊C4×C19C2314yes—
103C22⋊C4×C19C2314yes—
104C42×C19C2312yes—
105C22⋊Dic19C2312yes—
106C22⋊Dic19C2314yes—
107C22⋊Dic19C2312yes—
108C22⋊Dic19C2314yes—
109C22⋊Dic19C2314yes—
110C22⋊Dic19C2312yes—
111C22⋊Dic19C2312yes—
112C22⋊Dic19C2312yes—
113(C2×D19)⋊C4C2314yes—
114(C2×D19)⋊C4C2314yes—
115(C2×D19)⋊C4C2314yes—
116C4⋊Dic19C2312yes—
117C4⋊Dic19C2314yes—
118C4⋊Dic19C2314yes—
119C4⋊Dic19C2312yes—
120C4⋊Dic19C2312yes—
121C4⋊Dic19C2312yes—
122C4⋊Dic19C2312yes—
123Dic19⋊C4C2314yes—
124Dic19⋊C4C2314yes—
125Dic19⋊C4C2314yes—
126Dic19⋊C4C2314yes—
127Dic19⋊C4C2314yes—
128C4×Dic19C2314yes—
129C4×Dic19C2312yes—
130C4×Dic19C2314yes—
131C4×Dic19C2311yescharacteristic
132C4×Dic19C2311yescharacteristic
133C4×Dic19C2312yes—
134C4×Dic19C2312yes—
135C4×Dic19C2311yescharacteristic
136C4×Dic19C2311yescharacteristic
137C23×C19—22no—
138C23×C19—42no—
139C23×C19C2412yes—
140C23×C19C2412yes—
141C23×C19C2411yescharacteristic
142C22×D19C2412yes—
143Q8×C19—22no—
144D4×C19—24no—
145D4×C19—22no—
146D4×C19—44no—
147C2×C4×C19—22no—
148C2×C4×C19—24no—
149C2×C4×C19—24no—
150C2×C4×C19—24no—
151C2×C4×C19#4114yes—
152C2×C4×C19C2412yes—
153C2×C4×C19C2414yes—
154C2×C4×C19C2412yes—
155C2×C4×C19C2411yescharacteristic
156C2×C4×C19C2411yescharacteristic
157C22⋊D19—24no—
158C22⋊D19—44no—
159C22⋊D19—44no—
160C2×Dic19—42no—
161C2×Dic19—44no—
162C2×Dic19—42no—
163C2×Dic19C2412yes—
164C2×Dic19C2412yes—
165C2×Dic19C2412yes—
166C2×Dic19C2412yes—
167C2×Dic19C2414yes—
168C2×Dic19C2412yes—
169D76—22no—
170C4×D19—24no—
171C4×D19—44no—
172Dic38—22no—
173Dic38—44no—
174#3455—191nomaximal, Sylow
175C22×C19—22no—
176C22×C19—22no—
177C22×C19—22no—
178C22×C19—24no—
179C22×C19—22no—
180C22×C19—22no—
181C22×C19—44no—
182C22×C19C2×#4112yes—
183C22×C19C2511yescharacteristic
184C2×D19—22no—
185C2×D19—24no—
186C4×C19—22no—
187C4×C19—22no—
188C4×C19—24no—
189C4×C19C2×#4112yes—
190C4×C19C2×#4112yes—
191Dic19—22no—
192Dic19—22no—
193Dic19—24no—
194Dic19—22no—
195Dic19—22no—
196Dic19—22no—
197#542—192no—
198#542—192no—
199#541—192no—
200#540—192no—
201#539—194no—
202#538—194no—
203#533—191no—
204#532—191no—
205#529—194no—
206#529—194no—
207#525—191no—
208#525D1911yescharacteristic, complemented
209C4×#41—191no—
210C4×#41—191no—
211C2×#117—191no—
212C2×C19—22no—
213C2×C19—42no—
214C2×C19—42no—
215C2×C19C22×#4111yescharacteristic
216C2×C19#58512yes—
217D19—42no—
218C2×#41—191no—
219C2×#41C2×D1911yescharacteristic
220C23×C4C2×D1911yescharacteristic
221C4⋊Q8—191no—
222C4⋊Q8—192no—
223#127—191no—
224#126—194no—
225#126—194no—
226#126—194no—
227#126—194no—
228#125—194no—
229#125—194no—
230#125—192no—
231#124—191no—
232#124—194no—
233#124—191no—
234#124—194no—
235#123—194no—
236#123—192no—
237#123—194no—
238#123—194no—
239#123—194no—
240#123C2×D1912yes—
241C22⋊Q8—192no—
242C22⋊Q8—194no—
243C22⋊Q8—194no—
244C22⋊Q8—194no—
245C22⋊Q8C2×D1912yes—
246#121—194no—
247#121—194no—
248#121—194no—
249#121—192no—
250#121C2×D1912yes—
251#120—192no—
252#120C2×D1912yes—
253C4×Q8—192no—
254C4×Q8—192no—
255C4×Q8—194no—
256C4×D4—194no—
257C4×D4—192no—
258C4×D4—194no—
259C4×D4—194no—
260C4×D4—192no—
261C4×D4—194no—
262C4×D4C2×D1914yes—
263#117—192no—
264#117—192no—
265#117—192no—
266#117—192no—
267#117—191no—
268#117—192no—
269#117—192no—
270#117C2×D1911yescharacteristic
271C2×C4⋊C4—192no—
272C2×C22⋊C4—192no—
273C2×C42—191no—
274C2×C42—191no—
275C2×C42—192no—
276C2×C42—192no—
277C19#345511yescharacteristic, complemented, Sylow
278C24C22×D1911yescharacteristic
279#41—24no—
280#41—384no—
281C2×Q8—191no—
282C2×Q8—194no—
283C2×Q8C22×D1911yescharacteristic
284C2×D4—192no—
285C2×D4—194no—
286C2×D4—194no—
287C2×D4—191no—
288C2×D4C22×D1912yes—
289C2×D4C22×D1911yescharacteristic
290C2×D4C22×D1914yes—
291C22×C4—24no—
292C22×C4—192no—
293C22×C4—192no—
294C22×C4—194no—
295C22×C4—192no—
296C22×C4—194no—
297C22×C4C22×D1911yescharacteristic
298C22×C4C22×D1912yes—
299C22×C4C22×D1912yes—
300C22×C4C22×D1912yes—
301C22×C4C22×D1911yescharacteristic
302C4⋊C4—194no—
303C4⋊C4—194no—
304C4⋊C4—194no—
305C4⋊C4—194no—
306C4⋊C4—194no—
307C4⋊C4—192no—
308C4⋊C4—192no—
309C4⋊C4—192no—
310C4⋊C4—192no—
311C4⋊C4—192no—
312C4⋊C4—194no—
313C4⋊C4—194no—
314C4⋊C4C22×D1912yes—
315C4⋊C4C22×D1914yes—
316C22⋊C4—192no—
317C22⋊C4—192no—
318C22⋊C4—192no—
319C22⋊C4—192no—
320C22⋊C4—192no—
321C22⋊C4—194no—
322C22⋊C4—194no—
323C22⋊C4—194no—
324C22⋊C4—194no—
325C22⋊C4—194no—
326C22⋊C4—194no—
327C22⋊C4C22×D1912yes—
328C22⋊C4C22×D1914yes—
329C22⋊C4C22×D1914yes—
330C42—192no—
331C42—191no—
332C42—191no—
333C42—194no—
334C42—194no—
335C42—191no—
336C42—191no—
337C42—192no—
338C42—192no—
339C42C22×D1912yes—
340C23—22no—
341C23—42no—
342C23—192no—
343C23C23×D1912yes—
344C23C23×D1912yes—
345C23C23×D1911yescharacteristic
346Q8—22no—
347Q8—382no—
348Q8—764no—
349D4—24no—
350D4—22no—
351D4—44no—
352D4—384no—
353D4—382no—
354D4—764no—
355D4—764no—
356C2×C4—22no—
357C2×C4—24no—
358C2×C4—24no—
359C2×C4—24no—
360C2×C4—192no—
361C2×C4—192no—
362C2×C4—192no—
363C2×C4—192no—
364C2×C4—194no—
365C2×C4—192no—
366C2×C4—384no—
367C2×C4—764no—
368C2×C4—762no—
369C2×C4—764no—
370C2×C4—762no—
371C2×C4#6454314yes—
372C2×C4C23×D1912yes—
373C2×C4C23×D1914yes—
374C2×C4C23×D1912yes—
375C2×C4C23×D1911yescharacteristic
376C2×C4C23×D1911yescharacteristic
377C22—22no—
378C22—22no—
379C22—22no—
380C22—24no—
381C22—22no—
382C22—22no—
383C22—44no—
384C22—382no—
385C22—384no—
386C22C2×#6454312yes—
387C22C24×D1911yescharacteristic
388C4—22no—
389C4—22no—
390C4—24no—
391C4—382no—
392C4—382no—
393C4—382no—
394C4—382no—
395C4—384no—
396C4—382no—
397C4C2×#6454312yes—
398C4C2×#6454312yes—
399C2—22no—
400C2—42no—
401C2—42no—
402C2—762no—
403C2C22×#6454311yescharacteristic
404C2#1192738012yes—
subgroupG/H
centerC2×C4C23×D19
commutator, socle, cosocleC22×C19C25
FrattiniC22C24×D19
FittingC19×#525C2
hypercenter#525D19
hypocenterC19#3455
LCSG ▷ C22×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. #11927167C2semidirect
2. #11927161C2semidirect
3. #11927154C2semidirect
4. #11927147C2semidirect
5. #11927138C2semidirect
6. #11927129C2semidirect
7. #11927097C2semidirect
8. #11927090C2semidirect
9. #11927076C2semidirect
10. #11927074C2semidirect
11. #11927055C2semidirect
12. #41×Dic19C2semidirect
13. #11927012C2semidirect
14. C2×#10597372C2semidirect
15. C19×#525C2semidirect
27. #10597393C22semidirect
28. Q8×Dic19C22semidirect
29. #10597390C22semidirect
30. #10597386C22semidirect
35. #10597382C22semidirect
38. D4×Dic19C22semidirect
42. C4×C22⋊D19C22semidirect
48. #10597372C22semidirect
53. C2×C4×Dic19C22semidirect
54. #10597344C22semidirect
55. #10597343C22semidirect
56. #10597339C22semidirect
57. #10597336C22semidirect
58. #10597336C22semidirect
59. #10597335C22semidirect
60. #10597334C22semidirect
61. #10597333C22semidirect
62. #10597332C22semidirect
65. #10597329C22semidirect
69. #10597325C22semidirect
71. #10597324C22semidirect
72. #10597318C22semidirect
73. C42×D19C22semidirect
74. C4×Dic38C22semidirect
208. #525D19semidirect
277. C19#3455semidirect

Maximal subgroups

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

subgroupindex
#119271672
#119271612
#119271542
#119271472
#119271382
#119271292
#119270972
#119270902
#119270762
#119270742
#119270552
#41×Dic192
#119270122
C2×#105973722
C19×#5252
#345519