Finite Group Databasebeta

← #14575151

Subgroups — #14575151

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
1C2×#10597361C211yesmaximal, characteristic, complemented
2C2×SD16×D19C211yesmaximal, characteristic, complemented
3#11927209C211yesmaximal, characteristic, complemented
4#11927189C211yesmaximal, characteristic
5#11926936C211yesmaximal, characteristic, complemented
6#11926793C211yesmaximal, characteristic, complemented
7#11926784C211yesmaximal, characteristic, complemented
8#11926767C211yesmaximal, characteristic, complemented
9#11926703C211yesmaximal, characteristic, complemented
10#11926701C211yesmaximal, characteristic, complemented
11#11926693C211yesmaximal, characteristic, complemented
12#11926684C211yesmaximal, characteristic, complemented
13#11926644C211yesmaximal, characteristic, complemented
14#11926614C211yesmaximal, characteristic, complemented
15C19×#461C211yesmaximal, characteristic, complemented
16C2×Q8×D19C2211yescharacteristic
17C2×Q8×D19C2211yescharacteristic, complemented
18C2×#64543C2211yescharacteristic
19C2×D4×D19C2211yescharacteristic
20C2×SD16×C19C2211yescharacteristic
21C2×SD16×C19C2211yescharacteristic
22C19×C4⋊Q8C2211yescharacteristic, complemented
23C4×D4×C19C2211yescharacteristic
24#10597392C2211yescharacteristic
25#10597392C2211yescharacteristic, complemented
26C2×#64528C2211yescharacteristic, complemented
27C2×#64528C2211yescharacteristic, complemented
28C2×#64527C2211yescharacteristic
29C2×#64527C2211yescharacteristic
30C2×#64526C2211yescharacteristic
31#10597376—21no—
32C2×(C2×D19)⋊C4—21no—
33#10597361—24no—
34SD16×D19—24no—
35C2×Dic76C2211yescharacteristic, complemented
36C2×#64516C2211yescharacteristic
37C2×#64515C2211yescharacteristic, complemented
38C2×C8×D19C2211yescharacteristic
39#10597343C2211yescharacteristic
40#10597342—21no—
41#10597342—21no—
42#10597341C2211yescharacteristic
43#10597339—21no—
44#10597334—21no—
45#10597332—21no—
46#10597328—21no—
47#10597321C2211yescharacteristic
48C4×D76C2211yescharacteristic
49C4×Dic38C2211yescharacteristic, complemented
50C19×C4⋊C8C2211yescharacteristic, complemented
51C19×#103C2211yescharacteristic, complemented
52C19×#103C2211yescharacteristic, complemented
53#10597289C2211yescharacteristic
54#10597278C2211yescharacteristic
55(C2×D19)⋊C8C2211yescharacteristic
56(C2×D19)⋊C8C2211yescharacteristic, complemented
57#10597273C2211yescharacteristic, complemented
58#10597267C2211yescharacteristic, complemented
59#10597264C2211yescharacteristic, complemented
60#10597260C2211yescharacteristic, complemented
61C23×D19—21no—
62C2×Q8×C19C2311yescharacteristic
63C2×Q8×C19C2311yescharacteristic
64C2×D4×C19C2311yescharacteristic
65C22×C4×C19—21no—
66C2×C22⋊D19—21no—
67C2×C22⋊D19—21no—
68C22×Dic19—21no—
69Q8×D19—22no—
70Q8×D19—22no—
71Q8×D19—41no—
72Q8×D19—41no—
73#64543—22no—
74#64543—41no—
75D4×D19—22no—
76D4×D19—41no—
77C2×D76—21no—
78C2×D76D411yescharacteristic
79C2×D76C2311yescharacteristic
80C2×C4×D19—21no—
81C2×C4×D19—21no—
82C2×C4×D19C2311yescharacteristic
83C2×C4×D19C2311yescharacteristic
84C2×Dic38—21no—
85C2×Dic38—21no—
86C2×Dic38C2311yescharacteristic
87C2×Dic38C2311yescharacteristic
88SD16×C19—22no—
89SD16×C19—22no—
90C2×C8×C19C2311yescharacteristic
91C2×C8×C19C2311yescharacteristic
92C4⋊C4×C19—21no—
93C4⋊C4×C19—21no—
94C4⋊C4×C19C2311yescharacteristic
95C22⋊C4×C19—21no—
96C42×C19C2311yescharacteristic
97#64528—22no—
98#64528—41no—
99#64527—22no—
100#64527—41no—
101#64526D414yescomplemented
102(C2×D19)⋊C4—21no—
103(C2×D19)⋊C4—21no—
104(C2×D19)⋊C4—21no—
105(C2×D19)⋊C4—21no—
106(C2×D19)⋊C4—21no—
107(C2×D19)⋊C4—21no—
108(C2×D19)⋊C4D411yescharacteristic
109(C2×D19)⋊C4D411yescharacteristic
110C4⋊Dic19—21no—
111C4⋊Dic19D411yescharacteristic
112C4⋊Dic19C2311yescharacteristic
113Dic19⋊C4—21no—
114Dic19⋊C4—21no—
115Dic19⋊C4—21no—
116C4×Dic19—21no—
117C2×C19⋊C8C2311yescharacteristic
118C2×C19⋊C8C2311yescharacteristic
119Dic76—22no—
120#64516—22no—
121#64515—22no—
122C8×D19—22no—
123C23×C19—21no—
124C22×D19—21no—
125C22×D19—42no—
126C22×D19—42no—
127C22×D19—81no—
128C22×D19C2×D411yescharacteristic
129C22×D19C2×D411yescharacteristic
130Q8×C19—21no—
131Q8×C19—21no—
132Q8×C19—21no—
133Q8×C19—21no—
134D4×C19—21no—
135D4×C19C2×D412yes—
136C2×C4×C19—21no—
137C2×C4×C19—21no—
138C2×C4×C19—21no—
139C2×C4×C19—81no—
140C2×C4×C19C2×D411yescharacteristic
141C2×C4×C19C2×D411yescharacteristic
142C2×C4×C19C2411yescharacteristic
143C22⋊D19—42no—
144C22⋊D19—42no—
145C2×Dic19—21no—
146C2×Dic19—21no—
147C2×Dic19—21no—
148C2×Dic19—42no—
149C2×Dic19C2×D411yescharacteristic
150C2×Dic19C2×D411yescharacteristic
151D76—22no—
152D76—21no—
153D76—21no—
154D76—81no—
155C4×D19—21no—
156C4×D19—21no—
157C4×D19—21no—
158C4×D19—21no—
159C4×D19—42no—
160C4×D19—42no—
161Dic38—21no—
162Dic38—21no—
163Dic38—21no—
164Dic38—42no—
165Dic38—42no—
166Dic38C2×D412yes—
167C8×C19—21no—
168C8×C19—21no—
169C19⋊C8—21no—
170C19⋊C8C2×D412yes—
171#3266—191nomaximal, Sylow
172C22×C19—22no—
173C22×C19—41no—
174C22×C19—41no—
175C22×C19C22×D411yescharacteristic
176C2×D19—21no—
177C2×D19—21no—
178C2×D19—21no—
179C2×D19—21no—
180C2×D19—21no—
181C2×D19—41no—
182C2×D19—41no—
183C2×D19—41no—
184C2×D19—84no—
185C2×D19#13712yescomplemented
186C4×C19—21no—
187C4×C19—21no—
188C4×C19—41no—
189C4×C19—41no—
190C4×C19—41no—
191C4×C19C22×D411yescharacteristic
192C4×C19H(5,𝔽2)11yescharacteristic
193Dic19—22no—
194Dic19—21no—
195Dic19—21no—
196Dic19—41no—
197Dic19—41no—
198C2×#137—191no—
199C22×SD16—191no—
200D4×Q8—191no—
201#546—191no—
202#497—191no—
203#468—191no—
204#467—191no—
205#464—191no—
206#461D1911yescharacteristic, complemented
207#452—191no—
208#451—191no—
209#450—191no—
210#448—191no—
211#440—191no—
212#435—191no—
213C2×C19—42no—
214C2×C19D4211yescharacteristic
215C2×C19C2×#13711yescharacteristic
216C2×C19#57711yescharacteristic
217D19—22no—
218D19—41no—
219D19—81no—
220C2×#41—191no—
221C22×Q8—191no—
222C22×Q8—191no—
223C22×D4—191no—
224#137—384no—
225C2×Q16—191no—
226C2×Q16—191no—
227C2×Q16—191no—
228C2×SD16—191no—
229C2×SD16—191no—
230C2×SD16—191no—
231C2×SD16—191no—
232C2×SD16—384no—
233C2×SD16C2×D1911yescharacteristic
234C2×SD16C2×D1911yescharacteristic
235C2×M16—191no—
236C22×C8—191no—
237C4⋊Q8—381no—
238C4⋊Q8C2×D1911yescharacteristic, complemented
239#124—191no—
240#123—381no—
241C22⋊Q8—191no—
242C22⋊Q8—191no—
243C22⋊Q8—191no—
244C22⋊Q8—381no—
245C22⋊Q8—381no—
246#121—191no—
247#121—381no—
248#120—381no—
249C4×Q8—191no—
250C4×D4—191no—
251C4×D4—381no—
252C4×D4C2×D1911yescharacteristic
253C2×C22⋊C4—381no—
254#107—191no—
255C4⋊C8C2×D1911yescharacteristic, complemented
256#103—191no—
257#103—191no—
258#103C2×D1911yescharacteristic, complemented
259#103C2×D1911yescharacteristic, complemented
260#102—191no—
261#102—191no—
262C22⋊C8—191no—
263C22⋊C8—191no—
264#97—191no—
265C19#326611yescharacteristic, complemented, Sylow
266C24—381no—
267#41—382no—
268#41—761no—
269C2×Q8—191no—
270C2×Q8—191no—
271C2×Q8—381no—
272C2×Q8—381no—
273C2×Q8—382no—
274C2×Q8—382no—
275C2×Q8—761no—
276C2×Q8—761no—
277C2×Q8C22×D1911yescharacteristic
278C2×Q8C22×D1911yescharacteristic
279C2×D4—191no—
280C2×D4—191no—
281C2×D4—381no—
282C2×D4—381no—
283C2×D4—382no—
284C2×D4—381no—
285C2×D4—761no—
286C2×D4C22×D1911yescharacteristic
287C22×C4—21no—
288C22×C4—191no—
289C22×C4—191no—
290C22×C4—381no—
291C22×C4—381no—
292C22×C4—381no—
293Q16—382no—
294Q16—382no—
295Q16—761no—
296SD16—22no—
297SD16—22no—
298SD16—194no—
299SD16—382no—
300SD16—382no—
301SD16—761no—
302M16—382no—
303C2×C8—191no—
304C2×C8—191no—
305C2×C8—382no—
306C2×C8C22×D1911yescharacteristic
307C2×C8C22×D1911yescharacteristic
308C4⋊C4—21no—
309C4⋊C4—21no—
310C4⋊C4—191no—
311C4⋊C4—191no—
312C4⋊C4—381no—
313C4⋊C4—381no—
314C4⋊C4—381no—
315C4⋊C4—381no—
316C4⋊C4C22×D1911yescharacteristic
317C22⋊C4—21no—
318C22⋊C4—191no—
319C22⋊C4—191no—
320C22⋊C4—381no—
321C22⋊C4—381no—
322C22⋊C4—381no—
323C22⋊C4—381no—
324C22⋊C4—381no—
325C22⋊C4—381no—
326C42—381no—
327C42C22×D1911yescharacteristic
328C23—21no—
329C23—191no—
330C23—191no—
331C23—381no—
332C23—762no—
333C23—762no—
334C23—1521no—
335Q8—21no—
336Q8—21no—
337Q8—21no—
338Q8—21no—
339Q8—192no—
340Q8—381no—
341Q8—381no—
342Q8—381no—
343Q8—762no—
344Q8—762no—
345D4—21no—
346D4—382no—
347D4—381no—
348D4—381no—
349D4—762no—
350D4—762no—
351D4—1521no—
352D4D4×D1912yes—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—81no—
357C2×C4—191no—
358C2×C4—191no—
359C2×C4—381no—
360C2×C4—381no—
361C2×C4—381no—
362C2×C4—381no—
363C2×C4—381no—
364C2×C4—381no—
365C2×C4—381no—
366C2×C4—762no—
367C2×C4—762no—
368C2×C4—762no—
369C2×C4D4×D1911yescharacteristic
370C2×C4D4×D1911yescharacteristic
371C2×C4C23×D1911yescharacteristic
372C8—21no—
373C8—21no—
374C8—192no—
375C8—381no—
376C22—22no—
377C22—41no—
378C22—41no—
379C22—192no—
380C22—381no—
381C22—381no—
382C22—381no—
383C22—381no—
384C22—381no—
385C22—761no—
386C22—761no—
387C22—761no—
388C22—1524no—
389C22C2×D4×D1911yescharacteristic
390C4—21no—
391C4—21no—
392C4—41no—
393C4—41no—
394C4—41no—
395C4—381no—
396C4—381no—
397C4—382no—
398C4—761no—
399C4—761no—
400C4C2×D4×D1911yescharacteristic
401C4#1059743511yescharacteristic
402C2—42no—
403C2—382no—
404C2—761no—
405C2—1521no—
406C2#1192717811yescharacteristic
407C2#137×D1911yescharacteristic
408C2#1192735011yescharacteristic
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#461C2
socleC22×C19C22×D4
prime radical#11927189C2
hypercenter#461D19
hypocenterC19#3266
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
1. C2×#10597361C2semidirect
2. C2×SD16×D19C2semidirect
3. #11927209C2semidirect
5. #11926936C2semidirect
6. #11926793C2semidirect
7. #11926784C2semidirect
8. #11926767C2semidirect
9. #11926703C2semidirect
10. #11926701C2semidirect
11. #11926693C2semidirect
12. #11926684C2semidirect
13. #11926644C2semidirect
14. #11926614C2semidirect
15. C19×#461C2semidirect
17. C2×Q8×D19C22semidirect
22. C19×C4⋊Q8C22semidirect
25. #10597392C22semidirect
26. C2×#64528C22semidirect
27. C2×#64528C22semidirect
35. C2×Dic76C22semidirect
37. C2×#64515C22semidirect
49. C4×Dic38C22semidirect
50. C19×C4⋊C8C22semidirect
51. C19×#103C22semidirect
52. C19×#103C22semidirect
56. (C2×D19)⋊C8C22semidirect
57. #10597273C22semidirect
58. #10597267C22semidirect
59. #10597264C22semidirect
60. #10597260C22semidirect
101. #64526D4semidirect
185. C2×D19#137semidirect
206. #461D19semidirect
238. C4⋊Q8C2×D19semidirect
255. C4⋊C8C2×D19semidirect
258. #103C2×D19semidirect
259. #103C2×D19semidirect
265. C19#3266semidirect

Maximal subgroups

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

subgroupindex
C2×#105973612
C2×SD16×D192
#119272092
#119271892
#119269362
#119267932
#119267842
#119267672
#119267032
#119267012
#119266932
#119266842
#119266442
#119266142
C19×#4612
#326619