Finite Group Databasebeta

← #14575446

Subgroups — #14575446

Order 2432.

494 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11927195C211yesmaximal, characteristic, complemented
2#11927178C211yesmaximal, characteristic, complemented
3#11926889C211yesmaximal, characteristic, complemented
4#11926859C211yesmaximal, characteristic, complemented
5#11926823C211yesmaximal, characteristic, complemented
6#11926781C211yesmaximal, characteristic, complemented
7#11926778C211yesmaximal, characteristic, complemented
8#11926738C211yesmaximal, characteristic, complemented
9#11926680C211yesmaximal, characteristic, complemented
10#11926679C211yesmaximal, characteristic, complemented
11#11926626C211yesmaximal, characteristic, complemented
12(C22⋊D19)⋊C8C211yesmaximal, characteristic, complemented
13C2×#10597266C211yesmaximal, characteristic, complemented
14#102×D19C211yesmaximal, characteristic, complemented
15C19×#480C211yesmaximal, characteristic, complemented
16C2×D4×D19—21no—
17C2×D4×D19C2211yescharacteristic
18C2×#64541—21no—
19C22×D76C2211yescharacteristic
20C19×#121C2211yescharacteristic
21C2×C4⋊C4×C19C2211yescharacteristic, complemented
22#10597386C2211yescharacteristic
23#10597383—21no—
24C2×#64525C2211yescharacteristic, complemented
25#10597376C2211yescharacteristic, complemented
26#10597375—21no—
27C4×C22⋊D19C2211yescharacteristic
28C22×C19⋊C8C2211yescharacteristic, complemented
29C2×D152C2211yescharacteristic
30C2×D152C2211yescharacteristic, complemented
31C2×C8×D19C2211yescharacteristic, complemented
32#10597342—21no—
33#10597341C2211yescharacteristic
34#10597341C2211yescharacteristic, complemented
35#10597340—21no—
36#10597339C2211yescharacteristic
37#10597339C2211yescharacteristic, complemented
38C4⋊C4×D19C2211yescharacteristic, complemented
39#10597334C2211yescharacteristic, complemented
40#10597330—21no—
41#10597328—21no—
42C19×#107C2211yescharacteristic, complemented
43C19×#107C2211yescharacteristic, complemented
44C19×#102C2211yescharacteristic, complemented
45C19×#102C2211yescharacteristic, complemented
46C19×C22⋊C8C2211yescharacteristic, complemented
47#10597289C2211yescharacteristic, complemented
48#10597278C2211yescharacteristic
49#10597278C2211yescharacteristic, complemented
50(C2×D19)⋊C8C2211yescharacteristic, complemented
51Dic19⋊C8C2211yescharacteristic, complemented
52C8×Dic19C2211yescharacteristic, complemented
53#10597266C2211yescharacteristic
54#10597266C2211yescharacteristic
55#10597266C2211yescharacteristic, complemented
56#10597266C2211yescharacteristic, complemented
57#10597266C2211yescharacteristic, complemented
58#10597264C2211yescharacteristic, complemented
59C23×D19—21no—
60C23×D19—21no—
61C2×D4×C19—21no—
62C2×D4×C19C2311yescharacteristic
63C22×C4×C19—21no—
64C22×C4×C19C2311yescharacteristic
65C2×C22⋊D19—21no—
66C2×C22⋊D19—21no—
67C2×C22⋊D19—21no—
68C2×C22⋊D19—21no—
69C2×C22⋊D19D411yescharacteristic
70D4×D19—22no—
71D4×D19—41no—
72D4×D19—44no—
73#64541—44no—
74C2×D76—22no—
75C2×D76—21no—
76C2×D76—21no—
77C2×D76—21no—
78C2×D76—41no—
79C2×D76C2311yescharacteristic
80C2×D76C2311yescharacteristic
81C2×D76C2311yescharacteristic
82C2×C4×D19—21no—
83C2×C4×D19—21no—
84C2×C4×D19—21no—
85C2×C4×D19C2311yescharacteristic
86C2×Dic38—21no—
87C2×C8×C19C2311yescharacteristic
88C2×C8×C19C2311yescharacteristic
89C4⋊C4×C19—21no—
90C4⋊C4×C19C2311yescharacteristic
91C4⋊C4×C19C2311yescharacteristic
92C4⋊C4×C19C2311yescharacteristic
93C22⋊C4×C19—21no—
94C22⋊Dic19D411yescharacteristic
95#64525—41no—
96(C2×D19)⋊C4—21no—
97(C2×D19)⋊C4—21no—
98(C2×D19)⋊C4—21no—
99(C2×D19)⋊C4—21no—
100(C2×D19)⋊C4—21no—
101(C2×D19)⋊C4D411yescharacteristic
102C4⋊Dic19C2311yescharacteristic
103Dic19⋊C4—21no—
104Dic19⋊C4—21no—
105Dic19⋊C4D411yescharacteristic
106C4×Dic19C2311yescharacteristic
107C2×C19⋊C8—41no—
108C2×C19⋊C8C2311yescharacteristic
109C2×C19⋊C8C2311yescharacteristic
110D152—22no—
111D152—41no—
112C8×D19—41no—
113C23×C19—21no—
114C23×C19C2×D411yescharacteristic
115C22×D19—21no—
116C22×D19—21no—
117C22×D19—21no—
118C22×D19—42no—
119C22×D19—42no—
120C22×D19—42no—
121C22×D19—42no—
122C22×D19—81no—
123C22×D19—81no—
124C22×D19C2×D411yescharacteristic
125D4×C19—21no—
126D4×C19—21no—
127D4×C19—42no—
128C2×C4×C19—21no—
129C2×C4×C19—21no—
130C2×C4×C19—21no—
131C2×C4×C19—21no—
132C2×C4×C19—21no—
133C2×C4×C19—42no—
134C2×C4×C19C2×D411yescharacteristic
135C2×C4×C19C2411yescharacteristic
136C22⋊D19—42no—
137C22⋊D19—42no—
138C22⋊D19—42no—
139C22⋊D19—81no—
140C22⋊D19D814yescomplemented
141C2×Dic19—21no—
142C2×Dic19C2×D411yescharacteristic
143C2×Dic19C2×D411yescharacteristic
144C2×Dic19C2×D411yescharacteristic
145D76—21no—
146D76—21no—
147D76—21no—
148D76—21no—
149D76—21no—
150D76—42no—
151D76—42no—
152D76—42no—
153D76#4112yescomplemented
154C4×D19—21no—
155C4×D19—21no—
156C4×D19—42no—
157C4×D19—42no—
158C4×D19—42no—
159Dic38—42no—
160C8×C19—21no—
161C8×C19—21no—
162C19⋊C8—21no—
163C19⋊C8—21no—
164#3294—191nomaximal, Sylow
165C22×C19—21no—
166C22×C19—21no—
167C22×C19—41no—
168C22×C19—41no—
169C22×C19—41no—
170C22×C19C2×D812yes—
171C22×C19C22×D411yescharacteristic
172C2×D19—21no—
173C2×D19—21no—
174C2×D19—22no—
175C2×D19—41no—
176C2×D19—41no—
177C2×D19—41no—
178C2×D19—41no—
179C2×D19—41no—
180C2×D19—41no—
181C2×D19—41no—
182C2×D19—41no—
183C2×D19—84no—
184C2×D19—84no—
185C2×D19C2×D812yes—
186C4×C19—21no—
187C4×C19—41no—
188C4×C19—41no—
189C4×C19—41no—
190C4×C19C2×#4111yescharacteristic
191C4×C19H(5,𝔽2)11yescharacteristic
192Dic19—21no—
193Dic19—21no—
194Dic19—41no—
195Dic19C2×D812yes—
196#547—191no—
197D42—191no—
198#486—191no—
199#480—191no—
200#480D1911yescharacteristic, complemented
201#474—191no—
202#466—191no—
203#466—191no—
204#459—191no—
205#447—191no—
206#447—191no—
207C4×D8—191no—
208C8×D4—191no—
209C2×#102—191no—
210C2×#102—191no—
211C2×C19—22no—
212C2×C19—81no—
213C2×C19#54611yescharacteristic
214C2×C19C22×D811yescharacteristic
215C2×C19#57711yescharacteristic
216D19—22no—
217D19—42no—
218D19—81no—
219D19—81no—
220C2×#41—381no—
221C22×D4—191no—
222C22×D4—191no—
223C22×D4—381no—
224C2×D8—191no—
225C2×D8—191no—
226C2×D8—191no—
227C22×C8—191no—
228C22×C8—191no—
229C4⋊Q8—191no—
230#127—191no—
231#123—381no—
232#123—381no—
233C22⋊Q8—381no—
234#121—191no—
235#121—191no—
236#121—191no—
237#121—381no—
238#121C2×D1911yescharacteristic
239#120—381no—
240#120—381no—
241C4×D4—191no—
242C4×D4—191no—
243C4×D4—191no—
244C2×C4⋊C4—191no—
245C2×C4⋊C4C2×D1911yescharacteristic, complemented
246#107—191no—
247#107C2×D1911yescharacteristic, complemented
248#107C2×D1911yescharacteristic, complemented
249C4⋊C8—191no—
250#102—191no—
251#102—191no—
252#102—191no—
253#102—191no—
254#102—191no—
255#102—191no—
256#102—191no—
257#102—191no—
258#102C2×D1911yescharacteristic, complemented
259#102C2×D1911yescharacteristic, complemented
260C22⋊C8—191no—
261C22⋊C8C2×D1911yescharacteristic, complemented
262C4×C8—191no—
263C19#329411yescharacteristic, complemented, Sylow
264C24—381no—
265C24—381no—
266#41—764no—
267C2×Q8—381no—
268C2×D4—21no—
269C2×D4—191no—
270C2×D4—191no—
271C2×D4—191no—
272C2×D4—191no—
273C2×D4—382no—
274C2×D4—381no—
275C2×D4—381no—
276C2×D4—381no—
277C2×D4—381no—
278C2×D4—381no—
279C2×D4—382no—
280C2×D4—381no—
281C2×D4—381no—
282C2×D4—761no—
283C2×D4—761no—
284C2×D4—764no—
285C2×D4C22×D1911yescharacteristic
286C22×C4—21no—
287C22×C4—191no—
288C22×C4—381no—
289C22×C4—381no—
290C22×C4—381no—
291C22×C4C22×D1911yescharacteristic
292D8—382no—
293D8—761no—
294D8—761no—
295C2×C8—191no—
296C2×C8—191no—
297C2×C8—761no—
298C2×C8—761no—
299C2×C8C22×D1911yescharacteristic
300C2×C8C22×D1911yescharacteristic
301C4⋊C4—21no—
302C4⋊C4—191no—
303C4⋊C4—191no—
304C4⋊C4—381no—
305C4⋊C4—381no—
306C4⋊C4C22×D1911yescharacteristic
307C4⋊C4C22×D1911yescharacteristic
308C4⋊C4C22×D1911yescharacteristic
309C22⋊C4—21no—
310C22⋊C4—191no—
311C22⋊C4—191no—
312C22⋊C4—381no—
313C22⋊C4—381no—
314C22⋊C4—381no—
315C22⋊C4—381no—
316C22⋊C4—381no—
317C42—191no—
318C23—21no—
319C23—191no—
320C23—381no—
321C23—381no—
322C23—381no—
323C23—762no—
324C23—762no—
325C23—762no—
326C23—762no—
327C23—1521no—
328C23—1521no—
329C23D4×D1911yescharacteristic
330Q8—762no—
331D4—21no—
332D4—21no—
333D4—42no—
334D4—194no—
335D4—192no—
336D4—381no—
337D4—381no—
338D4—381no—
339D4—381no—
340D4—381no—
341D4—762no—
342D4—762no—
343D4—762no—
344D4—762no—
345D4—762no—
346D4—762no—
347D4—1521no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—42no—
354C2×C4—191no—
355C2×C4—191no—
356C2×C4—191no—
357C2×C4—381no—
358C2×C4—381no—
359C2×C4—381no—
360C2×C4—762no—
361C2×C4—762no—
362C2×C4—762no—
363C2×C4D4×D1911yescharacteristic
364C2×C4C23×D1911yescharacteristic
365C8—21no—
366C8—21no—
367C8—381no—
368C8—381no—
369C22—21no—
370C22—21no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—192no—
375C22—381no—
376C22—381no—
377C22—382no—
378C22—761no—
379C22—761no—
380C22—761no—
381C22—761no—
382C22—761no—
383C22—761no—
384C22—761no—
385C22—761no—
386C22—1524no—
387C22—1524no—
388C22D8×D1912yes—
389C22C2×D4×D1911yescharacteristic
390C4—21no—
391C4—41no—
392C4—41no—
393C4—41no—
394C4—192no—
395C4—381no—
396C4—381no—
397C4—761no—
398C4#41×D1911yescharacteristic
399C4#1059743511yescharacteristic
400C2—22no—
401C2—81no—
402C2—382no—
403C2—762no—
404C2—1521no—
405C2—1521no—
406C2#1192718611yescharacteristic
407C2C2×D8×D1911yescharacteristic
408C2#1192735311yescharacteristic
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#480C2
socleC22×C19C22×D4
hypercenter#480D19
hypocenterC19#3294
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
1. #11927195C2semidirect
2. #11927178C2semidirect
3. #11926889C2semidirect
4. #11926859C2semidirect
5. #11926823C2semidirect
6. #11926781C2semidirect
7. #11926778C2semidirect
8. #11926738C2semidirect
9. #11926680C2semidirect
10. #11926679C2semidirect
11. #11926626C2semidirect
12. (C22⋊D19)⋊C8C2semidirect
13. C2×#10597266C2semidirect
14. #102×D19C2semidirect
15. C19×#480C2semidirect
21. C2×C4⋊C4×C19C22semidirect
24. C2×#64525C22semidirect
25. #10597376C22semidirect
28. C22×C19⋊C8C22semidirect
30. C2×D152C22semidirect
31. C2×C8×D19C22semidirect
34. #10597341C22semidirect
37. #10597339C22semidirect
38. C4⋊C4×D19C22semidirect
39. #10597334C22semidirect
42. C19×#107C22semidirect
43. C19×#107C22semidirect
44. C19×#102C22semidirect
45. C19×#102C22semidirect
46. C19×C22⋊C8C22semidirect
47. #10597289C22semidirect
49. #10597278C22semidirect
50. (C2×D19)⋊C8C22semidirect
51. Dic19⋊C8C22semidirect
52. C8×Dic19C22semidirect
55. #10597266C22semidirect
56. #10597266C22semidirect
57. #10597266C22semidirect
58. #10597264C22semidirect
140. C22⋊D19D8semidirect
153. D76#41semidirect
200. #480D19semidirect
245. C2×C4⋊C4C2×D19semidirect
247. #107C2×D19semidirect
248. #107C2×D19semidirect
258. #102C2×D19semidirect
259. #102C2×D19semidirect
261. C22⋊C8C2×D19semidirect
263. C19#3294semidirect

Maximal subgroups

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

subgroupindex
#119271952
#119271782
#119268892
#119268592
#119268232
#119267812
#119267782
#119267382
#119266802
#119266792
#119266262
(C22⋊D19)⋊C82
C2×#105972662
#102×D192
C19×#4802
#329419