Finite Group Databasebeta

← #14574481

Subgroups — #14574481

Order 2432.

422 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
1#11927108C211yesmaximal, characteristic, complemented
2#11926882C211yesmaximal, characteristic, complemented
3#11926865C211yesmaximal, characteristic, complemented
4#11926862C211yesmaximal, characteristic, complemented
5#11926857C211yesmaximal, characteristic, complemented
6#11926795C211yesmaximal, characteristic, complemented
7#11926792C211yesmaximal, characteristic, complemented
8#11926778C211yesmaximal, characteristic, complemented
9#11926775C211yesmaximal, characteristic, complemented
10#11926694C211yesmaximal, characteristic, complemented
11#11926689C211yesmaximal, characteristic, complemented
12#11926689C211yesmaximal, characteristic, complemented
13#11926677C211yesmaximal, characteristic, complemented
14#11926511C211yesmaximal, characteristic, complemented
15C19×#537C211yesmaximal, characteristic, complemented
16C2×#41×C19C2211yescharacteristic
17C2×#41×C19C2211yescharacteristic, complemented
18C22×D76C2211yescharacteristic
19C19×C22⋊Q8—21no—
20C19×C22⋊Q8C2211yescharacteristic
21C19×C22⋊Q8C2211yescharacteristic, complemented
22C19×#121—21no—
23C19×#121—21no—
24C19×#121—21no—
25C19×#121C2211yescharacteristic
26C19×#121C2211yescharacteristic, complemented
27C2×C4⋊C4×C19C2211yescharacteristic, complemented
28#10597393—21no—
29C2×#64527C2211yescharacteristic
30C2×#64527C2211yescharacteristic
31#10597386—21no—
32#10597383—21no—
33#10597383—21no—
34C2×#64525C2211yescharacteristic
35C2×#64525C2211yescharacteristic
36#10597376C2211yescharacteristic
37#10597376C2211yescharacteristic
38#10597376C2211yescharacteristic
39#10597376C2211yescharacteristic
40#10597372C2211yescharacteristic
41C2×#64520C2211yescharacteristic, complemented
42C22×C19⋊C8C2211yescharacteristic, complemented
43#10597292C2211yescharacteristic, complemented
44#10597292C2211yescharacteristic, complemented
45#10597289C2211yescharacteristic, complemented
46#10597289C2211yescharacteristic, complemented
47C22⋊(C19⋊C8)C2211yescharacteristic
48C22⋊(C19⋊C8)C2211yescharacteristic
49C22⋊(C19⋊C8)C2211yescharacteristic, complemented
50C22⋊(C19⋊C8)C2211yescharacteristic, complemented
51#10597266C2211yescharacteristic
52#10597266C2211yescharacteristic
53#10597266C2211yescharacteristic
54#10597266C2211yescharacteristic
55#10597265C2211yescharacteristic, complemented
56#10597265C2211yescharacteristic, complemented
57#10597264C2211yescharacteristic, complemented
58#10597264C2211yescharacteristic, complemented
59C23×D19—21no—
60#41×C19—41no—
61#41×C19—41no—
62#41×C19—41no—
63#41×C19—41no—
64C2×Q8×C19D411yescharacteristic
65C2×Q8×C19C2311yescharacteristic
66C2×D4×C19—21no—
67C2×D4×C19—21no—
68C2×D4×C19—21no—
69C2×D4×C19D411yescharacteristic
70C2×D4×C19D411yescharacteristic
71C2×D4×C19D411yescharacteristic
72C2×D4×C19C2311yescharacteristic
73C22×C4×C19—21no—
74C22×C4×C19—21no—
75C22×C4×C19C2311yescharacteristic
76C22×C4×C19C2311yescharacteristic
77C22×C4×C19C2311yescharacteristic
78C2×C22⋊D19—21no—
79C2×C22⋊D19—21no—
80C2×C22⋊D19—21no—
81C2×C22⋊D19—21no—
82C2×D76—21no—
83C2×D76—41no—
84C2×D76—41no—
85C2×D76C2311yescharacteristic
86C2×D76C2311yescharacteristic
87C4⋊C4×C19—21no—
88C4⋊C4×C19—21no—
89C4⋊C4×C19—21no—
90C4⋊C4×C19C2311yescharacteristic
91C4⋊C4×C19C2311yescharacteristic
92C22⋊C4×C19—21no—
93C22⋊C4×C19—21no—
94C22⋊C4×C19—21no—
95C22⋊C4×C19—21no—
96C22⋊Dic19—21no—
97#64527—41no—
98#64527—41no—
99#64525—41no—
100#64525—41no—
101(C2×D19)⋊C4—21no—
102(C2×D19)⋊C4—21no—
103(C2×D19)⋊C4—21no—
104(C2×D19)⋊C4—21no—
105C4⋊Dic19C2311yescharacteristic
106C4⋊Dic19C2311yescharacteristic
107C4×Dic19—21no—
108#64520—41no—
109C2×C19⋊C8—41no—
110C2×C19⋊C8C2311yescharacteristic
111C2×C19⋊C8C2311yescharacteristic
112C2×C19⋊C8C2311yescharacteristic
113C2×C19⋊C8C2311yescharacteristic
114C23×C19—21no—
115C23×C19C2×D411yescharacteristic
116C23×C19C2×D411yescharacteristic
117C23×C19C2×D411yescharacteristic
118C22×D19—21no—
119C22×D19—21no—
120C22×D19—42no—
121C22×D19—81no—
122C22×D19—81no—
123Q8×C19—21no—
124Q8×C19—21no—
125Q8×C19—41no—
126D4×C19—21no—
127D4×C19—21no—
128D4×C19—41no—
129D4×C19—41no—
130D4×C19—41no—
131D4×C19—42no—
132D4×C19—81no—
133D4×C19—81no—
134C2×C4×C19—21no—
135C2×C4×C19—21no—
136C2×C4×C19—21no—
137C2×C4×C19—21no—
138C2×C4×C19—21no—
139C2×C4×C19—21no—
140C2×C4×C19—21no—
141C2×C4×C19—21no—
142C2×C4×C19—21no—
143C2×C4×C19—42no—
144C2×C4×C19—81no—
145C2×C4×C19C2×D411yescharacteristic
146C2×C4×C19C2×D411yescharacteristic
147C2×C4×C19C2×D411yescharacteristic
148C2×C4×C19C2411yescharacteristic
149C22⋊D19—81no—
150C22⋊D19—81no—
151C22⋊D19—81no—
152C22⋊D19—81no—
153C2×Dic19—21no—
154C2×Dic19—21no—
155D76—21no—
156D76—21no—
157D76—21no—
158D76—21no—
159D76—42no—
160C19⋊C8—21no—
161C19⋊C8—21no—
162C19⋊C8—21no—
163C19⋊C8—21no—
164#3198—191nomaximal, Sylow
165C22×C19—21no—
166C22×C19—21no—
167C22×C19—21no—
168C22×C19—21no—
169C22×C19—21no—
170C22×C19—21no—
171C22×C19—21no—
172C22×C19—21no—
173C22×C19—21no—
174C22×C19—41no—
175C22×C19—41no—
176C22×C19—41no—
177C22×C19C22×D411yescharacteristic
178C2×D19—41no—
179C2×D19—41no—
180C2×D19—41no—
181C2×D19—41no—
182C2×D19—41no—
183C2×D19—41no—
184C2×D19—84no—
185C4×C19—21no—
186C4×C19—21no—
187C4×C19—21no—
188C4×C19—41no—
189C4×C19—41no—
190C4×C19—41no—
191C4×C19H(5,𝔽2)11yescharacteristic
192C4×C19H(5,𝔽2)11yescharacteristic
193Dic19—41no—
194Dic19—41no—
195#537D1911yescharacteristic, complemented
196#535—191no—
197#485—191no—
198#482—191no—
199#481—191no—
200#480—191no—
201#469—191no—
202#468—191no—
203#466—191no—
204#465—191no—
205#450—191no—
206#449—191no—
207#449—191no—
208#447—191no—
209#408—191no—
210C2×C19—41no—
211C2×C19—41no—
212C2×C19—41no—
213C2×C19—81no—
214C2×C19#53411yescharacteristic
215C2×C19#57611yescharacteristic
216C2×C19#57711yescharacteristic
217D19—81no—
218D19—81no—
219C2×#41C2×D1911yescharacteristic
220C2×#41C2×D1911yescharacteristic, complemented
221C22×D4—191no—
222C2×SD16—191no—
223C2×SD16—191no—
224C2×D8—191no—
225C2×D8—191no—
226C2×M16—191no—
227C22×C8—191no—
228#127—381no—
229#124—381no—
230C22⋊Q8—21no—
231C22⋊Q8C2×D1911yescharacteristic
232C22⋊Q8C2×D1911yescharacteristic, complemented
233#121—21no—
234#121—21no—
235#121—21no—
236#121—191no—
237#121—191no—
238#121—191no—
239#121—191no—
240#121C2×D1911yescharacteristic
241#121C2×D1911yescharacteristic, complemented
242#120—381no—
243#120—381no—
244#117—191no—
245C2×C4⋊C4C2×D1911yescharacteristic, complemented
246#107—191no—
247#107—191no—
248#106—191no—
249#106—191no—
250#103—191no—
251#103—191no—
252#102—191no—
253#102—191no—
254#102—191no—
255#102—191no—
256#102—191no—
257#102—191no—
258C22⋊C8—191no—
259C22⋊C8—191no—
260C22⋊C8—191no—
261C22⋊C8—191no—
262C19#319811yescharacteristic, complemented, Sylow
263C24—381no—
264#41—41no—
265#41—41no—
266#41—41no—
267#41—41no—
268C2×Q8C22⋊D1911yescharacteristic
269C2×Q8C22×D1911yescharacteristic
270C2×D4—21no—
271C2×D4—21no—
272C2×D4—21no—
273C2×D4—191no—
274C2×D4—191no—
275C2×D4—381no—
276C2×D4—381no—
277C2×D4—381no—
278C2×D4—381no—
279C2×D4—381no—
280C2×D4—761no—
281C2×D4—761no—
282C2×D4C22⋊D1911yescharacteristic
283C2×D4C22⋊D1911yescharacteristic
284C2×D4C22⋊D1911yescharacteristic
285C2×D4C22×D1911yescharacteristic
286C22×C4—21no—
287C22×C4—21no—
288C22×C4C22×D1911yescharacteristic
289C22×C4C22×D1911yescharacteristic
290C22×C4C22×D1911yescharacteristic
291SD16—761no—
292SD16—761no—
293D8—761no—
294D8—761no—
295M16—761no—
296C2×C8—191no—
297C2×C8—191no—
298C2×C8—191no—
299C2×C8—191no—
300C2×C8—761no—
301C4⋊C4—21no—
302C4⋊C4—21no—
303C4⋊C4—21no—
304C4⋊C4—191no—
305C4⋊C4—191no—
306C4⋊C4C22×D1911yescharacteristic
307C4⋊C4C22×D1911yescharacteristic
308C22⋊C4—21no—
309C22⋊C4—21no—
310C22⋊C4—21no—
311C22⋊C4—21no—
312C22⋊C4—381no—
313C22⋊C4—381no—
314C22⋊C4—381no—
315C22⋊C4—381no—
316C22⋊C4—381no—
317C42—381no—
318C23—21no—
319C23—381no—
320C23—381no—
321C23—762no—
322C23—1521no—
323C23—1521no—
324C23C2×C22⋊D1911yescharacteristic
325C23C2×C22⋊D1911yescharacteristic
326C23C2×C22⋊D1911yescharacteristic
327Q8—21no—
328Q8—21no—
329Q8—41no—
330D4—21no—
331D4—21no—
332D4—41no—
333D4—41no—
334D4—41no—
335D4—42no—
336D4—81no—
337D4—81no—
338D4—381no—
339D4—381no—
340D4—381no—
341D4—381no—
342D4—762no—
343D4—1521no—
344D4—1521no—
345D4—1521no—
346D4—1521no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—42no—
357C2×C4—81no—
358C2×C4—381no—
359C2×C4—381no—
360C2×C4C2×C22⋊D1911yescharacteristic
361C2×C4C2×C22⋊D1911yescharacteristic
362C2×C4C2×C22⋊D1911yescharacteristic
363C2×C4C23×D1911yescharacteristic
364C8—381no—
365C8—381no—
366C8—381no—
367C8—381no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—761no—
381C22—761no—
382C22—761no—
383C22—761no—
384C22—761no—
385C22—761no—
386C22—1524no—
387C22C22×C22⋊D1911yescharacteristic
388C4—21no—
389C4—21no—
390C4—21no—
391C4—41no—
392C4—41no—
393C4—41no—
394C4—761no—
395C4—761no—
396C4#1059743011yescharacteristic
397C4#1059743011yescharacteristic
398C2—41no—
399C2—41no—
400C2—41no—
401C2—81no—
402C2—1521no—
403C2—1521no—
404C2#1192710311yescharacteristic
405C2#1192734711yescharacteristic
406C2#1192735211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#537C2
socleC22×C19C22×D4
hypercenter#537D19
hypocenterC19#3198
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×#41 ◁ #537

Complements

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

NH ≅ G/Ntype
1. #11927108C2semidirect
2. #11926882C2semidirect
3. #11926865C2semidirect
4. #11926862C2semidirect
5. #11926857C2semidirect
6. #11926795C2semidirect
7. #11926792C2semidirect
8. #11926778C2semidirect
9. #11926775C2semidirect
10. #11926694C2semidirect
11. #11926689C2semidirect
12. #11926689C2semidirect
13. #11926677C2semidirect
14. #11926511C2semidirect
15. C19×#537C2semidirect
17. C2×#41×C19C22semidirect
21. C19×C22⋊Q8C22semidirect
26. C19×#121C22semidirect
27. C2×C4⋊C4×C19C22semidirect
41. C2×#64520C22semidirect
42. C22×C19⋊C8C22semidirect
43. #10597292C22semidirect
44. #10597292C22semidirect
45. #10597289C22semidirect
46. #10597289C22semidirect
49. C22⋊(C19⋊C8)C22semidirect
50. C22⋊(C19⋊C8)C22semidirect
55. #10597265C22semidirect
56. #10597265C22semidirect
57. #10597264C22semidirect
58. #10597264C22semidirect
195. #537D19semidirect
220. C2×#41C2×D19semidirect
232. C22⋊Q8C2×D19semidirect
241. #121C2×D19semidirect
245. C2×C4⋊C4C2×D19semidirect
262. C19#3198semidirect

Maximal subgroups

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

subgroupindex
#119271082
#119268822
#119268652
#119268622
#119268572
#119267952
#119267922
#119267782
#119267752
#119266942
#119266892
#119266772
#119265112
C19×#5372
#319819