Finite Group Databasebeta

← #14574480

Subgroups — #14574480

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#11927123C211yesmaximal, characteristic, complemented
2#11927110C211yesmaximal, characteristic, complemented
3#11926887C211yesmaximal, characteristic, complemented
4#11926867C211yesmaximal, characteristic, complemented
5#11926861C211yesmaximal, characteristic, complemented
6#11926859C211yesmaximal, characteristic, complemented
7#11926795C211yesmaximal, characteristic, complemented
8#11926788C211yesmaximal, characteristic, complemented
9#11926773C211yesmaximal, characteristic, complemented
10#11926696C211yesmaximal, characteristic, complemented
11#11926690C211yesmaximal, characteristic, complemented
12#11926686C211yesmaximal, characteristic, complemented
13#11926676C211yesmaximal, characteristic, complemented
14#11926510C211yesmaximal, characteristic, complemented
15C19×#466C211yesmaximal, characteristic, complemented
16C2×#64543C2211yescharacteristic, complemented
17C2×D4×D19C2211yescharacteristic
18C2×#64541C2211yescharacteristic
19C2×D8×C19C2211yescharacteristic
20C22×C8×C19C2211yescharacteristic, complemented
21C19×#121C2211yescharacteristic
22C19×#121C2211yescharacteristic, complemented
23#10597386—21no—
24#10597385—21no—
25#10597384—21no—
26#10597384C2211yescharacteristic
27#10597384C2211yescharacteristic
28#10597383—21no—
29C2×#64526C2211yescharacteristic
30C2×#64525C2211yescharacteristic
31#10597376C2211yescharacteristic
32#10597370C2211yescharacteristic, complemented
33C2×#64520C2211yescharacteristic, complemented
34C2×#64516C2211yescharacteristic
35#10597343C2211yescharacteristic
36#10597341C2211yescharacteristic
37#10597338C2211yescharacteristic
38C4⋊C4×D19C2211yescharacteristic, complemented
39#10597331—21no—
40#10597330—21no—
41#10597328—21no—
42#10597324—21no—
43C19×#107C2211yescharacteristic, complemented
44C19×#102C2211yescharacteristic
45C19×#102C2211yescharacteristic, complemented
46#10597289C2211yescharacteristic
47#10597289C2211yescharacteristic, complemented
48#10597278C2211yescharacteristic
49(C2×D19)⋊C8C2211yescharacteristic
50(C2×D19)⋊C8C2211yescharacteristic
51(C2×D19)⋊C8C2211yescharacteristic, complemented
52(C2×D19)⋊C8C2211yescharacteristic, complemented
53#10597274C2211yescharacteristic, complemented
54#10597273C2211yescharacteristic, complemented
55#10597267C2211yescharacteristic, complemented
56#10597266C2211yescharacteristic
57#10597265C2211yescharacteristic, complemented
58#10597264C2211yescharacteristic, complemented
59C23×D19—21no—
60C2×D4×C19—21no—
61C2×D4×C19—21no—
62C2×D4×C19C2311yescharacteristic
63C2×D4×C19C2311yescharacteristic
64C22×C4×C19C2311yescharacteristic
65C2×C22⋊D19—21no—
66C2×C22⋊D19—21no—
67C2×C22⋊D19—21no—
68C2×C22⋊D19—21no—
69C2×C22⋊D19—21no—
70C2×C22⋊D19D411yescharacteristic
71C2×C22⋊D19D411yescharacteristic
72C22×Dic19—21no—
73#64543—41no—
74#64543—41no—
75D4×D19—41no—
76D4×D19—41no—
77#64541—41no—
78#64541—41no—
79C2×D76—21no—
80C2×D76D411yescharacteristic
81C2×D76C2311yescharacteristic
82C2×C4×D19—21no—
83C2×C4×D19C2311yescharacteristic
84C2×C4×D19C2311yescharacteristic
85C2×Dic38D411yescharacteristic
86C2×Dic38C2311yescharacteristic
87D8×C19—41no—
88C2×C8×C19—41no—
89C2×C8×C19C2311yescharacteristic
90C2×C8×C19C2311yescharacteristic
91C4⋊C4×C19C2311yescharacteristic
92C4⋊C4×C19C2311yescharacteristic
93C22⋊C4×C19—21no—
94C22⋊C4×C19—21no—
95C22⋊Dic19—21no—
96C22⋊Dic19—21no—
97C22⋊Dic19—21no—
98#64526—41no—
99#64525—41no—
100(C2×D19)⋊C4—21no—
101(C2×D19)⋊C4—21no—
102(C2×D19)⋊C4—21no—
103(C2×D19)⋊C4—21no—
104C4⋊Dic19—21no—
105C4⋊Dic19C2311yescharacteristic
106C4⋊Dic19C2311yescharacteristic
107Dic19⋊C4—21no—
108Dic19⋊C4—21no—
109C4×Dic19—21no—
110#64520—41no—
111C2×C19⋊C8C2311yescharacteristic
112C2×C19⋊C8C2311yescharacteristic
113#64516—41no—
114C23×C19—21no—
115C23×C19—21no—
116C23×C19C2×D411yescharacteristic
117C22×D19—21no—
118C22×D19—42no—
119C22×D19—81no—
120C22×D19—81no—
121C22×D19C2×D411yescharacteristic
122C22×D19C2×D411yescharacteristic
123D4×C19—21no—
124D4×C19—21no—
125D4×C19—21no—
126D4×C19—21no—
127D4×C19—81no—
128D4×C19—81no—
129C2×C4×C19—21no—
130C2×C4×C19—21no—
131C2×C4×C19—21no—
132C2×C4×C19—21no—
133C2×C4×C19C2×D411yescharacteristic
134C2×C4×C19C2411yescharacteristic
135C22⋊D19—41no—
136C22⋊D19—41no—
137C22⋊D19—42no—
138C22⋊D19—42no—
139C22⋊D19—81no—
140C22⋊D19—81no—
141C22⋊D19—81no—
142C2×Dic19—21no—
143C2×Dic19—21no—
144C2×Dic19—21no—
145C2×Dic19—42no—
146C2×Dic19C2×D411yescharacteristic
147C2×Dic19C2×D411yescharacteristic
148D76—21no—
149D76—21no—
150D76—41no—
151D76—81no—
152C4×D19—21no—
153C4×D19—21no—
154C4×D19—21no—
155C4×D19—21no—
156C4×D19—81no—
157Dic38—21no—
158Dic38—21no—
159Dic38—41no—
160C8×C19—21no—
161C8×C19—21no—
162C19⋊C8—21no—
163C19⋊C8—21no—
164#3198—191nomaximal, Sylow
165C22×C19—21no—
166C22×C19—21no—
167C22×C19—21no—
168C22×C19—41no—
169C22×C19—41no—
170C22×C19—41no—
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—21no—
181C2×D19—41no—
182C2×D19—41no—
183C2×D19—41no—
184C2×D19—84no—
185C4×C19—21no—
186C4×C19—41no—
187C4×C19—41no—
188C4×C19H(5,𝔽2)11yescharacteristic
189C4×C19H(5,𝔽2)11yescharacteristic
190Dic19—21no—
191Dic19—21no—
192Dic19—41no—
193Dic19—41no—
194Dic19—41no—
195#537—191no—
196#535—191no—
197#485—191no—
198#482—191no—
199#481—191no—
200#480—191no—
201#469—191no—
202#468—191no—
203#466D1911yescharacteristic, complemented
204#465—191no—
205#450—191no—
206#449—191no—
207#449—191no—
208#447—191no—
209#408—191no—
210C2×C19—41no—
211C2×C19—81no—
212C2×C19—81no—
213C2×C19#53411yescharacteristic
214C2×C19#57611yescharacteristic
215C2×C19#57711yescharacteristic
216D19—41no—
217D19—41no—
218D19—81no—
219C2×#41—191no—
220C2×#41—191no—
221C22×D4—191no—
222C2×SD16—191no—
223C2×SD16—191no—
224C2×D8—191no—
225C2×D8C2×D1911yescharacteristic
226C2×M16—191no—
227C22×C8C2×D1911yescharacteristic, complemented
228#127—381no—
229#124—381no—
230C22⋊Q8—191no—
231C22⋊Q8—191no—
232C22⋊Q8—381no—
233#121—191no—
234#121—191no—
235#121—191no—
236#121—191no—
237#121—381no—
238#121—381no—
239#121—381no—
240#121C2×D1911yescharacteristic
241#121C2×D1911yescharacteristic, complemented
242#120—381no—
243#120—381no—
244#117—191no—
245C2×C4⋊C4—191no—
246#107—191no—
247#107C2×D1911yescharacteristic, complemented
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#102C2×D1911yescharacteristic
257#102C2×D1911yescharacteristic, complemented
258C22⋊C8—191no—
259C22⋊C8—191no—
260C22⋊C8—191no—
261C22⋊C8—191no—
262C19#319811yescharacteristic, complemented, Sylow
263C24—381no—
264#41—761no—
265#41—761no—
266#41—761no—
267#41—761no—
268C2×Q8—191no—
269C2×Q8—191no—
270C2×D4—21no—
271C2×D4—21no—
272C2×D4—191no—
273C2×D4—191no—
274C2×D4—191no—
275C2×D4—191no—
276C2×D4—381no—
277C2×D4—381no—
278C2×D4—381no—
279C2×D4—381no—
280C2×D4—381no—
281C2×D4—381no—
282C2×D4—761no—
283C2×D4—761no—
284C2×D4C22×D1911yescharacteristic
285C2×D4C22×D1911yescharacteristic
286C22×C4—191no—
287C22×C4—191no—
288C22×C4—381no—
289C22×C4—381no—
290C22×C4C22×D1911yescharacteristic
291SD16—761no—
292SD16—761no—
293D8—41no—
294D8—761no—
295M16—761no—
296C2×C8—41no—
297C2×C8—191no—
298C2×C8—191no—
299C2×C8C22×D1911yescharacteristic
300C2×C8C22×D1911yescharacteristic
301C4⋊C4—191no—
302C4⋊C4—191no—
303C4⋊C4—381no—
304C4⋊C4—381no—
305C4⋊C4—381no—
306C4⋊C4C22×D1911yescharacteristic
307C4⋊C4C22×D1911yescharacteristic
308C22⋊C4—21no—
309C22⋊C4—21no—
310C22⋊C4—381no—
311C22⋊C4—381no—
312C22⋊C4—381no—
313C22⋊C4—381no—
314C22⋊C4—381no—
315C22⋊C4—381no—
316C22⋊C4—381no—
317C42—381no—
318C23—21no—
319C23—21no—
320C23—191no—
321C23—191no—
322C23—381no—
323C23—762no—
324C23—1521no—
325C23—1521no—
326C23D4×D1911yescharacteristic
327Q8—381no—
328Q8—381no—
329Q8—761no—
330D4—21no—
331D4—21no—
332D4—21no—
333D4—21no—
334D4—81no—
335D4—81no—
336D4—381no—
337D4—381no—
338D4—761no—
339D4—761no—
340D4—761no—
341D4—762no—
342D4—762no—
343D4—1521no—
344D4—1521no—
345D4—1521no—
346D4—1521no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—191no—
352C2×C4—191no—
353C2×C4—381no—
354C2×C4—381no—
355C2×C4—381no—
356C2×C4—381no—
357C2×C4—381no—
358C2×C4—381no—
359C2×C4—381no—
360C2×C4—762no—
361C2×C4—1521no—
362C2×C4D4×D1911yescharacteristic
363C2×C4C23×D1911yescharacteristic
364C8—21no—
365C8—21no—
366C8—381no—
367C8—381no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—381no—
378C22—381no—
379C22—381no—
380C22—381no—
381C22—381no—
382C22—381no—
383C22—761no—
384C22—761no—
385C22—761no—
386C22—1524no—
387C22C2×D4×D1911yescharacteristic
388C4—21no—
389C4—41no—
390C4—41no—
391C4—381no—
392C4—381no—
393C4—761no—
394C4—761no—
395C4—761no—
396C4#1059743011yescharacteristic
397C4#1059743511yescharacteristic
398C2—41no—
399C2—81no—
400C2—81no—
401C2—761no—
402C2—761no—
403C2—1521no—
404C2#1192710211yescharacteristic
405C2#1192734511yescharacteristic
406C2#1192735111yescharacteristic
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#466C2
socleC22×C19C22×D4
hypercenter#466D19
hypocenterC19#3198
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C22×C4 ◁ #466

Complements

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

NH ≅ G/Ntype
1. #11927123C2semidirect
2. #11927110C2semidirect
3. #11926887C2semidirect
4. #11926867C2semidirect
5. #11926861C2semidirect
6. #11926859C2semidirect
7. #11926795C2semidirect
8. #11926788C2semidirect
9. #11926773C2semidirect
10. #11926696C2semidirect
11. #11926690C2semidirect
12. #11926686C2semidirect
13. #11926676C2semidirect
14. #11926510C2semidirect
15. C19×#466C2semidirect
16. C2×#64543C22semidirect
20. C22×C8×C19C22semidirect
22. C19×#121C22semidirect
32. #10597370C22semidirect
33. C2×#64520C22semidirect
38. C4⋊C4×D19C22semidirect
43. C19×#107C22semidirect
45. C19×#102C22semidirect
47. #10597289C22semidirect
51. (C2×D19)⋊C8C22semidirect
52. (C2×D19)⋊C8C22semidirect
53. #10597274C22semidirect
54. #10597273C22semidirect
55. #10597267C22semidirect
57. #10597265C22semidirect
58. #10597264C22semidirect
203. #466D19semidirect
227. C22×C8C2×D19semidirect
241. #121C2×D19semidirect
247. #107C2×D19semidirect
257. #102C2×D19semidirect
262. C19#3198semidirect

Maximal subgroups

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

subgroupindex
#119271232
#119271102
#119268872
#119268672
#119268612
#119268592
#119267952
#119267882
#119267732
#119266962
#119266902
#119266862
#119266762
#119265102
C19×#4662
#319819