Finite Group Databasebeta

← #14572291

Subgroups — #14572291

Order 2432.

402 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#117×D19C211yesmaximal, characteristic
2#11926605C211yesmaximal, characteristic, complemented
3#11926602C211yesmaximal, characteristic, complemented
4#11926602C211yesmaximal, characteristic, complemented
5#11926600C211yesmaximal, characteristic, complemented
6#11926599C211yesmaximal, characteristic, complemented
7#11926596C211yesmaximal, characteristic, complemented
8#11926595C211yesmaximal, characteristic, complemented
9#11926569C211yesmaximal, characteristic, complemented
10#11926569C211yesmaximal, characteristic, complemented
11#11926506C211yesmaximal, characteristic
12C22⋊C8×D19C211yesmaximal, characteristic
13#11926501C211yesmaximal, characteristic, complemented
14#11926498C211yesmaximal, characteristic, complemented
15C19×#433C211yesmaximal, characteristic, complemented
16C22×C4×D19C2211yescharacteristic
17C19×#117C2211yescharacteristic
18#10597372C2211yescharacteristic
19C2×#64515C2211yescharacteristic
20C2×#64515C2211yescharacteristic
21C2×C8×D19C2211yescharacteristic
22C2×C8×D19C2211yescharacteristic
23#10597338C411yescharacteristic
24#10597338C411yescharacteristic
25C4⋊C4×D19C411yescharacteristic
26C4⋊C4×D19C411yescharacteristic
27C22⋊C4×D19C411yescharacteristic
28C22⋊C4×D19C411yescharacteristic
29#10597323C411yescharacteristic
30#10597323C411yescharacteristic
31#10597318C2211yescharacteristic
32#10597318C2211yescharacteristic
33C42×D19C2211yescharacteristic
34C42×D19C2211yescharacteristic
35C19×C4⋊C8C2211yescharacteristic, complemented
36C19×C4⋊C8C2211yescharacteristic, complemented
37C19×C22⋊C8C2211yescharacteristic
38C19×C22⋊C8C2211yescharacteristic
39C19×#97C2211yescharacteristic, complemented
40C4×C8×C19C2211yescharacteristic, complemented
41C22⋊(C19⋊C8)C2211yescharacteristic
42C22⋊(C19⋊C8)C2211yescharacteristic
43(C2×D19)⋊C8C2211yescharacteristic
44(C2×D19)⋊C8C2211yescharacteristic
45(C2×D19)⋊C8C2211yescharacteristic
46(C2×D19)⋊C8C2211yescharacteristic
47#10597272C2211yescharacteristic, complemented
48#10597272C2211yescharacteristic, complemented
49Dic19⋊C8C2211yescharacteristic, complemented
50Dic19⋊C8C2211yescharacteristic, complemented
51Dic19⋊C8C2211yescharacteristic, complemented
52Dic19⋊C8C2211yescharacteristic, complemented
53C8×Dic19C2211yescharacteristic, complemented
54C8×Dic19C2211yescharacteristic, complemented
55C4⋊(C19⋊C8)C2211yescharacteristic, complemented
56C4⋊(C19⋊C8)C2211yescharacteristic, complemented
57#10597260C2211yescharacteristic, complemented
58C4×C19⋊C8C2211yescharacteristic, complemented
59C23×D19C2×C411yescharacteristic
60C22×C4×C19C2311yescharacteristic
61C22×Dic19C2×C411yescharacteristic
62C2×C4×D19—22no—
63C2×C4×D19—22no—
64C2×C4×D19C2×C411yescharacteristic
65C2×C4×D19C2×C411yescharacteristic
66C2×C4×D19C2×C411yescharacteristic
67C2×C4×D19C2×C411yescharacteristic
68C2×C4×D19C2×C411yescharacteristic
69C2×C4×D19C2×C411yescharacteristic
70C2×C4×D19C2311yescharacteristic
71C2×C4×D19C2311yescharacteristic
72C2×C8×C19C2311yescharacteristic
73C2×C8×C19C2311yescharacteristic
74C2×C8×C19C2311yescharacteristic
75C2×C8×C19C2311yescharacteristic
76C4⋊C4×C19C2×C411yescharacteristic
77C4⋊C4×C19C2×C411yescharacteristic
78C22⋊C4×C19C2×C411yescharacteristic
79C22⋊C4×C19C2×C411yescharacteristic
80C42×C19C2311yescharacteristic
81C42×C19C2311yescharacteristic
82C22⋊Dic19C2×C411yescharacteristic
83C22⋊Dic19C2×C411yescharacteristic
84(C2×D19)⋊C4C2×C411yescharacteristic
85(C2×D19)⋊C4C2×C411yescharacteristic
86(C2×D19)⋊C4C2×C411yescharacteristic
87(C2×D19)⋊C4C2×C411yescharacteristic
88C4⋊Dic19C2×C411yescharacteristic
89C4⋊Dic19C2×C411yescharacteristic
90Dic19⋊C4C2×C411yescharacteristic
91Dic19⋊C4C2×C411yescharacteristic
92Dic19⋊C4C2×C411yescharacteristic
93Dic19⋊C4C2×C411yescharacteristic
94C4×Dic19C2×C411yescharacteristic
95C4×Dic19C2×C411yescharacteristic
96C4×Dic19C2×C411yescharacteristic
97C4×Dic19C2×C411yescharacteristic
98C4×Dic19C2311yescharacteristic
99C4×Dic19C2311yescharacteristic
100C2×C19⋊C8C2311yescharacteristic
101C2×C19⋊C8C2311yescharacteristic
102C2×C19⋊C8C2311yescharacteristic
103C2×C19⋊C8C2311yescharacteristic
104#64515—22no—
105#64515—22no—
106C8×D19—22no—
107C8×D19—22no—
108C23×C19C22×C411yescharacteristic
109C22×D19—22no—
110C22×D19—22no—
111C22×D19—41no—
112C22×D19C22×C411yescharacteristic
113C22×D19C22×C411yescharacteristic
114C2×C4×C19—21no—
115C2×C4×C19—21no—
116C2×C4×C19C22×C411yescharacteristic
117C2×C4×C19C22×C411yescharacteristic
118C2×C4×C19C22×C411yescharacteristic
119C2×C4×C19C22×C411yescharacteristic
120C2×C4×C19C22×C411yescharacteristic
121C2×C4×C19C2411yescharacteristic
122C2×Dic19—22no—
123C2×Dic19C22×C411yescharacteristic
124C2×Dic19C22×C411yescharacteristic
125C2×Dic19C22×C411yescharacteristic
126C2×Dic19C22×C411yescharacteristic
127C2×Dic19C22×C411yescharacteristic
128C2×Dic19C22×C411yescharacteristic
129C4×D19—22no—
130C4×D19—22no—
131C4×D19—22no—
132C4×D19—21no—
133C4×D19—21no—
134C4×D19—22no—
135C4×D19—41no—
136C4×D19—41no—
137C4×D19#4112yes—
138C4×D19#4112yes—
139C8×C19—21no—
140C8×C19—21no—
141C8×C19—21no—
142C8×C19—21no—
143C19⋊C8—21no—
144C19⋊C8—21no—
145C19⋊C8—21no—
146C19⋊C8—21no—
147#2924—191nomaximal, Sylow
148C22×C19—21no—
149C22×C19—21no—
150C22×C19—21no—
151C22×C19C23×C411yescharacteristic
152C2×D19—21no—
153C2×D19—21no—
154C2×D19—21no—
155C2×D19—21no—
156C2×D19—44no—
157C2×D19#11712yes—
158C2×D19#13112yes—
159C4×C19—21no—
160C4×C19—21no—
161C4×C19—21no—
162C4×C19—21no—
163C4×C19—21no—
164C4×C19C2×#4111yescharacteristic
165C4×C19C2×#4111yescharacteristic
166Dic19—21no—
167Dic19—21no—
168Dic19—21no—
169Dic19—21no—
170Dic19—21no—
171Dic19#11712yes—
172C2×#117—191no—
173#433—191no—
174#433—191no—
175#433—191no—
176#433D1911yescharacteristic, complemented
177#432—191no—
178#432—191no—
179#431—191no—
180#431—191no—
181#424—191no—
182#424—191no—
183#407—191no—
184C2×C22⋊C8—191no—
185#405—191no—
186#405—191no—
187C2×C19—41no—
188C2×C19C2×#11711yescharacteristic
189C2×C19C2×#13111yescharacteristic
190C2×C19#56811yescharacteristic
191D19—22no—
192D19—22no—
193C23×C4—191no—
194C2×M16—191no—
195C2×M16—191no—
196C22×C8—191no—
197C22×C8—191no—
198#117—191no—
199#117—191no—
200#117—191no—
201#117—191no—
202#117—191no—
203#117—191no—
204#117—191no—
205#117C2×D1911yescharacteristic
206C2×C4⋊C4—191no—
207C2×C4⋊C4—191no—
208C2×C22⋊C4—191no—
209C2×C22⋊C4—191no—
210C2×C42—191no—
211C2×C42—191no—
212C4⋊C8—191no—
213C4⋊C8—191no—
214C4⋊C8—191no—
215C4⋊C8—191no—
216C4⋊C8—191no—
217C4⋊C8—191no—
218C4⋊C8C2×D1911yescharacteristic, complemented
219C4⋊C8C2×D1911yescharacteristic, complemented
220C22⋊C8—191no—
221C22⋊C8—191no—
222C22⋊C8—191no—
223C22⋊C8—191no—
224C22⋊C8—191no—
225C22⋊C8—191no—
226C22⋊C8C2×D1911yescharacteristic
227C22⋊C8C2×D1911yescharacteristic
228#97—191no—
229#97—191no—
230#97—191no—
231#97C2×D1911yescharacteristic, complemented
232C4×C8—191no—
233C4×C8—191no—
234C4×C8—191no—
235C4×C8C2×D1911yescharacteristic, complemented
236C19#292411yescharacteristic, complemented, Sylow
237C24—191no—
238C22×C4—191no—
239C22×C4—191no—
240C22×C4—191no—
241C22×C4—191no—
242C22×C4—191no—
243C22×C4—191no—
244C22×C4—191no—
245C22×C4—191no—
246C22×C4—191no—
247C22×C4—382no—
248C22×C4—382no—
249C22×C4C22×D1911yescharacteristic
250M16—382no—
251M16—382no—
252C2×C8—191no—
253C2×C8—191no—
254C2×C8—191no—
255C2×C8—191no—
256C2×C8—382no—
257C2×C8—382no—
258C2×C8C22×D1911yescharacteristic
259C2×C8C22×D1911yescharacteristic
260C2×C8C22×D1911yescharacteristic
261C2×C8C22×D1911yescharacteristic
262C4⋊C4—191no—
263C4⋊C4—191no—
264C4⋊C4—191no—
265C4⋊C4—191no—
266C4⋊C4—191no—
267C4⋊C4—191no—
268C4⋊C4C4×D1911yescharacteristic
269C4⋊C4C4×D1911yescharacteristic
270C22⋊C4—191no—
271C22⋊C4—191no—
272C22⋊C4—191no—
273C22⋊C4—191no—
274C22⋊C4—191no—
275C22⋊C4—191no—
276C22⋊C4C4×D1911yescharacteristic
277C22⋊C4C4×D1911yescharacteristic
278C42—191no—
279C42—191no—
280C42—191no—
281C42—191no—
282C42—191no—
283C42—191no—
284C42C22×D1911yescharacteristic
285C42C22×D1911yescharacteristic
286C23—191no—
287C23—191no—
288C23—382no—
289C23—382no—
290C23—761no—
291C23C2×C4×D1911yescharacteristic
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—191no—
295C2×C4—192no—
296C2×C4—192no—
297C2×C4—191no—
298C2×C4—191no—
299C2×C4—191no—
300C2×C4—191no—
301C2×C4—191no—
302C2×C4—382no—
303C2×C4—382no—
304C2×C4—382no—
305C2×C4—382no—
306C2×C4—382no—
307C2×C4—381no—
308C2×C4—381no—
309C2×C4—761no—
310C2×C4—761no—
311C2×C4C2×C4×D1911yescharacteristic
312C2×C4C2×C4×D1911yescharacteristic
313C2×C4C2×C4×D1911yescharacteristic
314C2×C4C2×C4×D1911yescharacteristic
315C2×C4C2×C4×D1911yescharacteristic
316C2×C4C23×D1911yescharacteristic
317C8—21no—
318C8—21no—
319C8—21no—
320C8—21no—
321C8—381no—
322C8—381no—
323C8—381no—
324C8—381no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—192no—
329C22—192no—
330C22—381no—
331C22—381no—
332C22—381no—
333C22—381no—
334C22—764no—
335C22C22×C4×D1911yescharacteristic
336C4—21no—
337C4—21no—
338C4—21no—
339C4—21no—
340C4—21no—
341C4—192no—
342C4—381no—
343C4—381no—
344C4—381no—
345C4—381no—
346C4—381no—
347C4#41×D1911yescharacteristic
348C4#41×D1911yescharacteristic
349C2—41no—
350C2—382no—
351C2—382no—
352C2#117×D1911yescharacteristic
353C2#131×D1911yescharacteristic
354C2#1192730911yescharacteristic
subgroupG/H
center, FrattiniC2×C4C23×D19
commutator, socleC22×C19C23×C4
FittingC19×#433C2
prime radicalC23×D19C2×C4
cosocleC2×C4×C19C24
hypercenter#433D19
hypocenterC19#2924
LCSG ▷ C22×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ #433

Complements

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

NH ≅ G/Ntype
2. #11926605C2semidirect
3. #11926602C2semidirect
4. #11926602C2semidirect
5. #11926600C2semidirect
6. #11926599C2semidirect
7. #11926596C2semidirect
8. #11926595C2semidirect
9. #11926569C2semidirect
10. #11926569C2semidirect
13. #11926501C2semidirect
14. #11926498C2semidirect
15. C19×#433C2semidirect
35. C19×C4⋊C8C22semidirect
36. C19×C4⋊C8C22semidirect
39. C19×#97C22semidirect
40. C4×C8×C19C22semidirect
47. #10597272C22semidirect
48. #10597272C22semidirect
49. Dic19⋊C8C22semidirect
50. Dic19⋊C8C22semidirect
51. Dic19⋊C8C22semidirect
52. Dic19⋊C8C22semidirect
53. C8×Dic19C22semidirect
54. C8×Dic19C22semidirect
55. C4⋊(C19⋊C8)C22semidirect
56. C4⋊(C19⋊C8)C22semidirect
57. #10597260C22semidirect
58. C4×C19⋊C8C22semidirect
176. #433D19semidirect
218. C4⋊C8C2×D19semidirect
219. C4⋊C8C2×D19semidirect
231. #97C2×D19semidirect
235. C4×C8C2×D19semidirect
236. C19#2924semidirect

Maximal subgroups

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

subgroupindex
#117×D192
#119266052
#119266022
#119266002
#119265992
#119265962
#119265952
#119265692
#119265062
C22⋊C8×D192
#119265012
#119264982
C19×#4332
#292419