Finite Group Databasebeta

← #14573459

Subgroups — #14573459

Order 2432.

398 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11927171C211yesmaximal, characteristic, complemented
2#11927016C211yesmaximal, characteristic
3#11926847C211yesmaximal, characteristic, complemented
4#11926845C211yesmaximal, characteristic, complemented
5#11926844C211yesmaximal, characteristic, complemented
6#11926842C211yesmaximal, characteristic, complemented
7#11926832C211yesmaximal, characteristic, complemented
8#11926831C211yesmaximal, characteristic, complemented
9#11926823C211yesmaximal, characteristic, complemented
10#11926585C211yesmaximal, characteristic, complemented
11#11926581C211yesmaximal, characteristic, complemented
12#11926569C211yesmaximal, characteristic, complemented
13#11926547C211yesmaximal, characteristic
14#102×D19C211yesmaximal, characteristic
15C19×#474C211yesmaximal, characteristic, complemented
16C2×D4×D19C2211yescharacteristic
17C19×C4⋊Q8C2211yescharacteristic, complemented
18C4×D4×C19C2211yescharacteristic
19#10597392—21no—
20#10597390—21no—
21D4×Dic19C2211yescharacteristic
22C4×C22⋊D19—21no—
23C2×(C2×D19)⋊C4—21no—
24C2×#64515C2211yescharacteristic
25C2×C8×D19C2211yescharacteristic
26#10597342—21no—
27#10597339C2211yescharacteristic
28#10597338C2211yescharacteristic
29#10597338C2211yescharacteristic
30C4⋊C4×D19C2211yescharacteristic
31#10597336C2211yescharacteristic, complemented
32#10597335—21no—
33#10597334C2211yescharacteristic, complemented
34(C22⋊D19)⋊C4—21no—
35C22⋊C4×D19—21no—
36C4×D76C2211yescharacteristic
37#10597318C2211yescharacteristic
38#10597316C2211yescharacteristic, complemented
39C19×#107C2211yescharacteristic, complemented
40C19×#107C2211yescharacteristic, complemented
41C19×C4⋊C8C2211yescharacteristic, complemented
42C19×#102C2211yescharacteristic
43C19×#102C2211yescharacteristic
44#10597289C2211yescharacteristic
45#10597289C2211yescharacteristic
46#10597278C2211yescharacteristic
47#10597278C2211yescharacteristic
48#10597275C2211yescharacteristic, complemented
49#10597274C2211yescharacteristic, complemented
50Dic19⋊C8C2211yescharacteristic, complemented
51Dic19⋊C8C2211yescharacteristic, complemented
52#10597266C2211yescharacteristic
53#10597266C2211yescharacteristic
54#10597265C2211yescharacteristic, complemented
55#10597265C2211yescharacteristic, complemented
56#10597265C2211yescharacteristic, complemented
57#10597264C2211yescharacteristic, complemented
58C4⋊(C19⋊C8)C2211yescharacteristic, complemented
59C23×D19—21no—
60C2×Q8×C19—21no—
61C2×D4×C19C2311yescharacteristic
62C22×C4×C19—21no—
63C2×C22⋊D19—21no—
64C22×Dic19—21no—
65D4×D19—22no—
66D4×D19Q814yescomplemented
67C2×D76C2311yescharacteristic
68C2×C4×D19—21no—
69C2×C4×D19—21no—
70C2×C4×D19—21no—
71C2×C4×D19C2311yescharacteristic
72C2×Dic38—21no—
73C2×C8×C19C2311yescharacteristic
74C2×C8×C19C2311yescharacteristic
75C4⋊C4×C19—21no—
76C4⋊C4×C19C2311yescharacteristic
77C4⋊C4×C19C2311yescharacteristic
78C4⋊C4×C19C2311yescharacteristic
79C22⋊C4×C19—21no—
80C42×C19C2311yescharacteristic
81C22⋊Dic19—21no—
82(C2×D19)⋊C4—21no—
83(C2×D19)⋊C4—21no—
84(C2×D19)⋊C4—21no—
85(C2×D19)⋊C4—21no—
86(C2×D19)⋊C4D411yescharacteristic
87(C2×D19)⋊C4D411yescharacteristic
88C4⋊Dic19—21no—
89C4⋊Dic19C2311yescharacteristic
90C4⋊Dic19C2311yescharacteristic
91C4⋊Dic19C2311yescharacteristic
92Dic19⋊C4—21no—
93Dic19⋊C4—21no—
94Dic19⋊C4—21no—
95Dic19⋊C4—21no—
96Dic19⋊C4—21no—
97Dic19⋊C4D411yescharacteristic
98Dic19⋊C4D411yescharacteristic
99C4×Dic19—21no—
100C4×Dic19—21no—
101C4×Dic19C2311yescharacteristic
102C2×C19⋊C8C2311yescharacteristic
103C2×C19⋊C8C2311yescharacteristic
104#64515—22no—
105C8×D19—22no—
106C23×C19—21no—
107C22×D19—21no—
108C22×D19—24no—
109C22×D19—81no—
110C22×D19—81no—
111C22×D19C2×D411yescharacteristic
112Q8×C19—81no—
113D4×C19—21no—
114D4×C19C2×Q812yes—
115C2×C4×C19—21no—
116C2×C4×C19—21no—
117C2×C4×C19—21no—
118C2×C4×C19—81no—
119C2×C4×C19C2×D411yescharacteristic
120C2×C4×C19C2×D411yescharacteristic
121C2×C4×C19C2411yescharacteristic
122C22⋊D19—24no—
123C2×Dic19—21no—
124C2×Dic19—21no—
125C2×Dic19—21no—
126C2×Dic19—81no—
127C2×Dic19C2×D411yescharacteristic
128C2×Dic19C2×D411yescharacteristic
129C2×Dic19C2×D411yescharacteristic
130D76—21no—
131D76C2×Q812yes—
132C4×D19—81no—
133C4×D19—81no—
134C4×D19—81no—
135C4×D19C2×Q812yes—
136C4×D19#4112yes—
137Dic38—81no—
138C8×C19—21no—
139C8×C19—21no—
140C19⋊C8—21no—
141C19⋊C8—21no—
142#3081—191nomaximal, Sylow
143C22×C19—22no—
144C22×C19—41no—
145C22×C19—41no—
146C22×C19C22×D411yescharacteristic
147C2×D19—21no—
148C2×D19—21no—
149C2×D19—22no—
150C2×D19—41no—
151C2×D19—41no—
152C2×D19—84no—
153C2×D19C22⋊Q812yes—
154C4×C19—21no—
155C4×C19—21no—
156C4×C19—41no—
157C4×C19—41no—
158C4×C19—41no—
159C4×C19C22×Q811yescharacteristic
160C4×C19C2×#4111yescharacteristic
161Dic19—21no—
162Dic19—21no—
163Dic19—41no—
164Dic19—41no—
165Dic19—41no—
166Dic19C22⋊Q812yes—
167#544—191no—
168#518—191no—
169#478—191no—
170#478—191no—
171#478—191no—
172#478—191no—
173#476—191no—
174#476—191no—
175#474—191no—
176#474D1911yescharacteristic, complemented
177#428—191no—
178#427—191no—
179#424—191no—
180#418—191no—
181C2×#102—191no—
182C2×C19—42no—
183C2×C19C2×C22⋊Q811yescharacteristic
184C2×C19#57611yescharacteristic
185C2×C19#57711yescharacteristic
186D19—22no—
187D19—42no—
188C22×D4—191no—
189C2×M16—191no—
190C22×C8—191no—
191C4⋊Q8—191no—
192C4⋊Q8—381no—
193C4⋊Q8C2×D1911yescharacteristic, complemented
194#125—191no—
195#125—191no—
196#125—381no—
197C22⋊Q8—381no—
198C22⋊Q8—381no—
199C4×D4—191no—
200C4×D4—191no—
201C4×D4—191no—
202C4×D4—381no—
203C4×D4—381no—
204C4×D4C2×D1911yescharacteristic
205#117—191no—
206#117—191no—
207#117—191no—
208C2×C4⋊C4—191no—
209C2×C22⋊C4—381no—
210C2×C22⋊C4—381no—
211#107—191no—
212#107—191no—
213#107C2×D1911yescharacteristic, complemented
214#107C2×D1911yescharacteristic, complemented
215#106—191no—
216#106—191no—
217#106—191no—
218#106—191no—
219C4⋊C8—191no—
220C4⋊C8—191no—
221C4⋊C8—191no—
222C4⋊C8C2×D1911yescharacteristic, complemented
223#102—191no—
224#102—191no—
225#102—191no—
226#102—191no—
227#102—191no—
228#102—191no—
229#102C2×D1911yescharacteristic
230#102C2×D1911yescharacteristic
231C19#308111yescharacteristic, complemented, Sylow
232C24—381no—
233C2×Q8—21no—
234C2×Q8—381no—
235C2×D4—194no—
236C2×D4—191no—
237C2×D4—382no—
238C2×D4—381no—
239C2×D4C22×D1911yescharacteristic
240C22×C4—21no—
241C22×C4—191no—
242C22×C4—381no—
243C22×C4—381no—
244C22×C4—381no—
245C22×C4—381no—
246M16—382no—
247C2×C8—191no—
248C2×C8—191no—
249C2×C8—382no—
250C2×C8C22×D1911yescharacteristic
251C2×C8C22×D1911yescharacteristic
252C4⋊C4—21no—
253C4⋊C4—191no—
254C4⋊C4—191no—
255C4⋊C4—191no—
256C4⋊C4—191no—
257C4⋊C4—191no—
258C4⋊C4—381no—
259C4⋊C4—381no—
260C4⋊C4—381no—
261C4⋊C4—381no—
262C4⋊C4—381no—
263C4⋊C4—381no—
264C4⋊C4C22×D1911yescharacteristic
265C4⋊C4C22×D1911yescharacteristic
266C4⋊C4C22×D1911yescharacteristic
267C22⋊C4—21no—
268C22⋊C4—191no—
269C22⋊C4—191no—
270C22⋊C4—381no—
271C22⋊C4—381no—
272C22⋊C4—381no—
273C22⋊C4—381no—
274C22⋊C4—381no—
275C42—191no—
276C42—381no—
277C42—381no—
278C42C22×D1911yescharacteristic
279C23—21no—
280C23—191no—
281C23—384no—
282C23—381no—
283C23—1521no—
284C23—1521no—
285Q8—81no—
286Q8—1521no—
287D4—21no—
288D4—192no—
289D4—384no—
290D4—381no—
291D4Q8×D1912yes—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—81no—
296C2×C4—191no—
297C2×C4—192no—
298C2×C4—192no—
299C2×C4—191no—
300C2×C4—191no—
301C2×C4—381no—
302C2×C4—381no—
303C2×C4—381no—
304C2×C4—1521no—
305C2×C4—1521no—
306C2×C4—1521no—
307C2×C4—1521no—
308C2×C4D4×D1911yescharacteristic
309C2×C4D4×D1911yescharacteristic
310C2×C4C23×D1911yescharacteristic
311C8—21no—
312C8—21no—
313C8—381no—
314C8—381no—
315C22—22no—
316C22—41no—
317C22—41no—
318C22—192no—
319C22—381no—
320C22—381no—
321C22—382no—
322C22—761no—
323C22—761no—
324C22—1524no—
325C22C2×D4×D1911yescharacteristic
326C4—21no—
327C4—21no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—192no—
332C4—381no—
333C4—381no—
334C4—761no—
335C4—761no—
336C4—761no—
337C4C2×Q8×D1911yescharacteristic
338C4#41×D1911yescharacteristic
339C2—42no—
340C2—382no—
341C2—762no—
342C2C22⋊Q8×D1911yescharacteristic
343C2#1192734511yescharacteristic
344C2#1192735311yescharacteristic
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#474C2
socleC22×C19C22×D4
prime radicalC2×D4×D19C22
hypercenter#474D19
hypocenterC19#3081
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #11927171C2semidirect
3. #11926847C2semidirect
4. #11926845C2semidirect
5. #11926844C2semidirect
6. #11926842C2semidirect
7. #11926832C2semidirect
8. #11926831C2semidirect
9. #11926823C2semidirect
10. #11926585C2semidirect
11. #11926581C2semidirect
12. #11926569C2semidirect
15. C19×#474C2semidirect
17. C19×C4⋊Q8C22semidirect
31. #10597336C22semidirect
33. #10597334C22semidirect
38. #10597316C22semidirect
39. C19×#107C22semidirect
40. C19×#107C22semidirect
41. C19×C4⋊C8C22semidirect
48. #10597275C22semidirect
49. #10597274C22semidirect
50. Dic19⋊C8C22semidirect
51. Dic19⋊C8C22semidirect
54. #10597265C22semidirect
55. #10597265C22semidirect
56. #10597265C22semidirect
57. #10597264C22semidirect
58. C4⋊(C19⋊C8)C22semidirect
66. D4×D19Q8semidirect
176. #474D19semidirect
193. C4⋊Q8C2×D19semidirect
213. #107C2×D19semidirect
214. #107C2×D19semidirect
222. C4⋊C8C2×D19semidirect
231. C19#3081semidirect

Maximal subgroups

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

subgroupindex
#119271712
#119270162
#119268472
#119268452
#119268442
#119268422
#119268322
#119268312
#119268232
#119265852
#119265812
#119265692
#119265472
#102×D192
C19×#4742
#308119