Finite Group Databasebeta

← #14573239

Subgroups — #14573239

Order 2432.

500 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×#10597362C211yesmaximal, characteristic, complemented
2C2×M16×D19C211yesmaximal, characteristic, complemented
3#11927057C211yesmaximal, characteristic, complemented
4#11927054C211yesmaximal, characteristic, complemented
5#11926801C211yesmaximal, characteristic, complemented
6#11926800C211yesmaximal, characteristic, complemented
7#11926796C211yesmaximal, characteristic, complemented
8#11926795C211yesmaximal, characteristic, complemented
9#11926791C211yesmaximal, characteristic, complemented
10#11926790C211yesmaximal, characteristic, complemented
11#11926787C211yesmaximal, characteristic, complemented
12#11926581C211yesmaximal, characteristic, complemented
13#11926539C211yesmaximal, characteristic, complemented
14#11926537C211yesmaximal, characteristic, complemented
15C19×#468C211yesmaximal, characteristic, complemented
16C2×#64545C2211yescharacteristic
17C2×#64543C2211yescharacteristic
18C22×C4×D19C2211yescharacteristic
19C2×SD16×C19C2211yescharacteristic, complemented
20C2×M16×C19C2211yescharacteristic
21C19×C22⋊Q8C2211yescharacteristic
22C19×#121C2211yescharacteristic
23#10597392C2211yescharacteristic
24C2×#64528C2211yescharacteristic, complemented
25#10597384C2211yescharacteristic
26#10597383—21no—
27D4×Dic19—21no—
28C2×#64525C2211yescharacteristic, complemented
29#10597376C2211yescharacteristic
30#10597370C2211yescharacteristic
31C2×#64520C2211yescharacteristic
32#10597362—24no—
33M16×D19—24no—
34C2×#64516C2211yescharacteristic, complemented
35C2×#64515C2211yescharacteristic
36C2×#64515C2211yescharacteristic
37C2×C8×D19C2211yescharacteristic
38C2×C8×D19C2211yescharacteristic
39#10597343C2211yescharacteristic
40#10597341C2211yescharacteristic
41#10597340—21no—
42#10597339—21no—
43#10597338C2211yescharacteristic
44#10597338C2211yescharacteristic
45#10597329—21no—
46#10597328—21no—
47(C22⋊D19)⋊C4—21no—
48(C22⋊D19)⋊C4—21no—
49C19×#107C2211yescharacteristic, complemented
50C19×#103C2211yescharacteristic, complemented
51C19×#102C2211yescharacteristic, complemented
52#10597292C2211yescharacteristic, complemented
53#10597289C2211yescharacteristic, complemented
54#10597278C2211yescharacteristic, complemented
55#10597275C2211yescharacteristic, complemented
56#10597273C2211yescharacteristic, complemented
57#10597267C2211yescharacteristic, complemented
58#10597266C2211yescharacteristic, complemented
59#10597265C2211yescharacteristic, complemented
60#10597265C2211yescharacteristic, complemented
61C23×D19D411yescharacteristic
62C2×Q8×C19C2311yescharacteristic
63C2×D4×C19—21no—
64C2×D4×C19C2311yescharacteristic
65C22×C4×C19C2311yescharacteristic
66C2×C22⋊D19—21no—
67C2×C22⋊D19—21no—
68C2×C22⋊D19—21no—
69C22×Dic19—21no—
70C22×Dic19D411yescharacteristic
71#64545—22no—
72#64545—22no—
73#64543—22no—
74#64543—22no—
75C2×D76—21no—
76C2×D76—21no—
77C2×D76C2311yescharacteristic
78C2×C4×D19—22no—
79C2×C4×D19—22no—
80C2×C4×D19—21no—
81C2×C4×D19D411yescharacteristic
82C2×C4×D19D411yescharacteristic
83C2×C4×D19C2311yescharacteristic
84C2×C4×D19C2311yescharacteristic
85C2×Dic38C2311yescharacteristic
86SD16×C19—22no—
87M16×C19—22no—
88C2×C8×C19C2311yescharacteristic
89C2×C8×C19C2311yescharacteristic
90C4⋊C4×C19—21no—
91C4⋊C4×C19C2311yescharacteristic
92C4⋊C4×C19C2311yescharacteristic
93C22⋊C4×C19—21no—
94C22⋊C4×C19—21no—
95C22⋊Dic19—21no—
96C22⋊Dic19—21no—
97#64528—22no—
98#64525—22no—
99(C2×D19)⋊C4—21no—
100(C2×D19)⋊C4—21no—
101(C2×D19)⋊C4—21no—
102(C2×D19)⋊C4—21no—
103(C2×D19)⋊C4—21no—
104(C2×D19)⋊C4—21no—
105C4⋊Dic19—21no—
106C4⋊Dic19C2311yescharacteristic
107C4⋊Dic19C2311yescharacteristic
108Dic19⋊C4—21no—
109Dic19⋊C4—21no—
110C4×Dic19—21no—
111C4×Dic19—21no—
112#64520—22no—
113C2×C19⋊C8C2311yescharacteristic
114C2×C19⋊C8C2311yescharacteristic
115#64516—22no—
116#64515—22no—
117#64515—22no—
118C8×D19—22no—
119C8×D19D414yescomplemented
120C23×C19—21no—
121C23×C19C2×D411yescharacteristic
122C22×D19—22no—
123C22×D19—21no—
124C22×D19—41no—
125C22×D19—41no—
126C22×D19C2×D411yescharacteristic
127C22×D19C2×D411yescharacteristic
128Q8×C19—21no—
129Q8×C19—21no—
130D4×C19—21no—
131D4×C19—21no—
132D4×C19—42no—
133C2×C4×C19—21no—
134C2×C4×C19—21no—
135C2×C4×C19—21no—
136C2×C4×C19—21no—
137C2×C4×C19—21no—
138C2×C4×C19C2×D411yescharacteristic
139C2×C4×C19C2411yescharacteristic
140C22⋊D19—42no—
141C22⋊D19—42no—
142C22⋊D19—42no—
143C2×Dic19—22no—
144C2×Dic19—21no—
145C2×Dic19—21no—
146C2×Dic19—21no—
147C2×Dic19—42no—
148C2×Dic19C2×D411yescharacteristic
149C2×Dic19C2×D411yescharacteristic
150D76—21no—
151D76—21no—
152D76—42no—
153D76—42no—
154C4×D19—22no—
155C4×D19—21no—
156C4×D19—21no—
157C4×D19—22no—
158C4×D19—42no—
159C4×D19C2×D412yes—
160C4×D19#4112yes—
161Dic38—21no—
162Dic38—21no—
163C8×C19—21no—
164C8×C19C2×D412yes—
165C19⋊C8—21no—
166C19⋊C8C2×D412yes—
167#3054—191nomaximal, Sylow
168C22×C19—21no—
169C22×C19—21no—
170C22×C19—21no—
171C22×C19—41no—
172C22×C19—41no—
173C22×C19—41no—
174C22×C19C22×D411yescharacteristic
175C2×D19—21no—
176C2×D19—21no—
177C2×D19—21no—
178C2×D19—21no—
179C2×D19—21no—
180C2×D19—44no—
181C2×D19—41no—
182C2×D19—41no—
183C2×D19—41no—
184C2×D19#12112yes—
185C4×C19—21no—
186C4×C19—41no—
187C4×C19—41no—
188C4×C19—41no—
189C4×C19C22×D411yescharacteristic
190C4×C19C2×#4111yescharacteristic
191Dic19—21no—
192Dic19—41no—
193Dic19—41no—
194Dic19—41no—
195Dic19#12112yes—
196C2×#135—191no—
197C22×M16—191no—
198#525—191no—
199#525—191no—
200#470—191no—
201#470—191no—
202#469—191no—
203#469—191no—
204#468—191no—
205#468—191no—
206#468—191no—
207#468D1911yescharacteristic, complemented
208#427—191no—
209#416—191no—
210#416—191no—
211C2×C19—41no—
212C2×C19—81no—
213C2×C19C2×#12111yescharacteristic
214C2×C19#57511yescharacteristic
215C2×C19#57511yescharacteristic
216D19—22no—
217D19—41no—
218D19—81no—
219C2×#41—191no—
220C2×#41—191no—
221C23×C4—191no—
222#135—384no—
223C2×Q16—191no—
224C2×SD16—191no—
225C2×SD16C2×D1911yescharacteristic, complemented
226C2×D8—191no—
227C2×M16—191no—
228C2×M16—191no—
229C2×M16—191no—
230C2×M16—384no—
231C2×M16C2×D1911yescharacteristic
232C22×C8—191no—
233C22×C8—191no—
234#123—381no—
235#123—381no—
236C22⋊Q8—191no—
237C22⋊Q8—191no—
238C22⋊Q8—191no—
239C22⋊Q8C2×D1911yescharacteristic
240#121—191no—
241#121—191no—
242#121—191no—
243#121C2×D1911yescharacteristic
244#120—381no—
245#120—381no—
246C4×D4—381no—
247C4×D4—381no—
248C4×D4—381no—
249C4×D4—381no—
250#117—191no—
251#117—191no—
252#107—191no—
253#107C2×D1911yescharacteristic, complemented
254#106—191no—
255#106—191no—
256#103—191no—
257#103—191no—
258#103—191no—
259#103C2×D1911yescharacteristic, complemented
260#102—191no—
261#102—191no—
262#102—191no—
263#102C2×D1911yescharacteristic, complemented
264C19#305411yescharacteristic, complemented, Sylow
265C24—191no—
266#41—382no—
267#41—382no—
268#41—382no—
269#41—382no—
270C2×Q8—191no—
271C2×Q8C22×D1911yescharacteristic
272C2×D4—21no—
273C2×D4—191no—
274C2×D4—381no—
275C2×D4—381no—
276C2×D4—381no—
277C2×D4—381no—
278C2×D4—381no—
279C2×D4C22×D1911yescharacteristic
280C22×C4—191no—
281C22×C4—191no—
282C22×C4—191no—
283C22×C4—191no—
284C22×C4—191no—
285C22×C4—382no—
286C22×C4—382no—
287C22×C4—381no—
288C22×C4—381no—
289C22×C4C22×D1911yescharacteristic
290Q16—382no—
291SD16—22no—
292SD16—382no—
293D8—382no—
294M16—22no—
295M16—382no—
296M16—382no—
297M16—382no—
298C2×C8—191no—
299C2×C8—194no—
300C2×C8—191no—
301C2×C8—382no—
302C2×C8C22×D1911yescharacteristic
303C2×C8C22×D1911yescharacteristic
304C4⋊C4—21no—
305C4⋊C4—191no—
306C4⋊C4—191no—
307C4⋊C4—381no—
308C4⋊C4—381no—
309C4⋊C4—381no—
310C4⋊C4C22×D1911yescharacteristic
311C4⋊C4C22×D1911yescharacteristic
312C22⋊C4—21no—
313C22⋊C4—21no—
314C22⋊C4—381no—
315C22⋊C4—381no—
316C22⋊C4—381no—
317C22⋊C4—381no—
318C22⋊C4—381no—
319C22⋊C4—381no—
320C22⋊C4—381no—
321C22⋊C4—381no—
322C42—381no—
323C42—381no—
324C23—21no—
325C23—191no—
326C23—191no—
327C23—382no—
328C23—381no—
329C23—761no—
330C23—761no—
331C23D4×D1911yescharacteristic
332Q8—21no—
333Q8—21no—
334Q8—381no—
335Q8—381no—
336D4—21no—
337D4—21no—
338D4—42no—
339D4—381no—
340D4—381no—
341D4—762no—
342D4—762no—
343D4—762no—
344D4—762no—
345D4—762no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—191no—
352C2×C4—192no—
353C2×C4—192no—
354C2×C4—191no—
355C2×C4—382no—
356C2×C4—382no—
357C2×C4—382no—
358C2×C4—381no—
359C2×C4—381no—
360C2×C4—381no—
361C2×C4—381no—
362C2×C4—381no—
363C2×C4—762no—
364C2×C4—762no—
365C2×C4D4×D1911yescharacteristic
366C2×C4C23×D1911yescharacteristic
367C8—21no—
368C8—192no—
369C8—381no—
370C8D4×D1912yes—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—192no—
378C22—381no—
379C22—381no—
380C22—381no—
381C22—381no—
382C22—381no—
383C22—764no—
384C22—761no—
385C22—761no—
386C22—761no—
387C22C2×D4×D1911yescharacteristic
388C4—21no—
389C4—41no—
390C4—41no—
391C4—41no—
392C4—192no—
393C4—381no—
394C4—761no—
395C4—761no—
396C4—761no—
397C4C2×D4×D1911yescharacteristic
398C4#41×D1911yescharacteristic
399C2—41no—
400C2—81no—
401C2—382no—
402C2—761no—
403C2—1521no—
404C2#121×D1911yescharacteristic
405C2#1192734011yescharacteristic
406C2#1192734311yescharacteristic
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#468C2
socleC22×C19C22×D4
hypercenter#468D19
hypocenterC19#3054
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. C2×#10597362C2semidirect
2. C2×M16×D19C2semidirect
3. #11927057C2semidirect
4. #11927054C2semidirect
5. #11926801C2semidirect
6. #11926800C2semidirect
7. #11926796C2semidirect
8. #11926795C2semidirect
9. #11926791C2semidirect
10. #11926790C2semidirect
11. #11926787C2semidirect
12. #11926581C2semidirect
13. #11926539C2semidirect
14. #11926537C2semidirect
15. C19×#468C2semidirect
19. C2×SD16×C19C22semidirect
24. C2×#64528C22semidirect
28. C2×#64525C22semidirect
34. C2×#64516C22semidirect
49. C19×#107C22semidirect
50. C19×#103C22semidirect
51. C19×#102C22semidirect
52. #10597292C22semidirect
53. #10597289C22semidirect
54. #10597278C22semidirect
55. #10597275C22semidirect
56. #10597273C22semidirect
57. #10597267C22semidirect
58. #10597266C22semidirect
59. #10597265C22semidirect
60. #10597265C22semidirect
119. C8×D19D4semidirect
207. #468D19semidirect
225. C2×SD16C2×D19semidirect
253. #107C2×D19semidirect
259. #103C2×D19semidirect
263. #102C2×D19semidirect
264. C19#3054semidirect

Maximal subgroups

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

subgroupindex
C2×#105973622
C2×M16×D192
#119270572
#119270542
#119268012
#119268002
#119267962
#119267952
#119267912
#119267902
#119267872
#119265812
#119265392
#119265372
C19×#4682
#305419