Finite Group Databasebeta

← #14574684

Subgroups — #14574684

Order 2432.

420 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11927145C211yesmaximal, characteristic, complemented
2#11927107C211yesmaximal, characteristic, complemented
3#11926932C211yesmaximal, characteristic, complemented
4#11926919C211yesmaximal, characteristic, complemented
5#11926907C211yesmaximal, characteristic, complemented
6#11926897C211yesmaximal, characteristic, complemented
7#11926760C211yesmaximal, characteristic, complemented
8#11926759C211yesmaximal, characteristic, complemented
9#11926736C211yesmaximal, characteristic, complemented
10#11926690C211yesmaximal, characteristic, complemented
11#11926686C211yesmaximal, characteristic, complemented
12#11926679C211yesmaximal, characteristic, complemented
13#11926676C211yesmaximal, characteristic, complemented
14#11926604C211yesmaximal, characteristic, complemented
15C19×#459C211yesmaximal, characteristic, complemented
16C2×#64543C2211yescharacteristic
17C2×D4×D19C2211yescharacteristic
18C2×D8×C19C2211yescharacteristic
19C2×D8×C19C2211yescharacteristic, complemented
20C19×#127C2211yescharacteristic
21C4×D4×C19C2211yescharacteristic, complemented
22#10597386C2211yescharacteristic
23#10597386C2211yescharacteristic, complemented
24#10597385—21no—
25#10597385—21no—
26#10597384C2211yescharacteristic
27#10597383—21no—
28#10597383—21no—
29#10597382C2211yescharacteristic
30C2×#64526C2211yescharacteristic, complemented
31C2×#64525C2211yescharacteristic
32C2×#64525C2211yescharacteristic
33C2×#64525C2211yescharacteristic, complemented
34#10597376—21no—
35#10597375—21no—
36C2×D152C2211yescharacteristic
37C2×#64516C2211yescharacteristic, complemented
38#10597341C2211yescharacteristic
39#10597336C2211yescharacteristic, complemented
40#10597330—21no—
41#10597329—21no—
42#10597321C2211yescharacteristic
43C4×D76C2211yescharacteristic, complemented
44#10597318C2211yescharacteristic
45C19×C4⋊C8C2211yescharacteristic, complemented
46C19×#102C2211yescharacteristic
47C19×#102C2211yescharacteristic, complemented
48#10597289C2211yescharacteristic
49#10597289C2211yescharacteristic, complemented
50#10597278C2211yescharacteristic
51(C2×D19)⋊C8C2211yescharacteristic
52(C2×D19)⋊C8C2211yescharacteristic
53#10597273C2211yescharacteristic, complemented
54#10597272C2211yescharacteristic, complemented
55C8×Dic19C2211yescharacteristic, complemented
56#10597267C2211yescharacteristic, complemented
57#10597266C2211yescharacteristic
58C4⋊(C19⋊C8)C2211yescharacteristic, complemented
59C23×D19—21no—
60C2×D4×C19—21no—
61C2×D4×C19—21no—
62C2×D4×C19C2311yescharacteristic
63C2×D4×C19C2311yescharacteristic
64C2×D4×C19C2311yescharacteristic
65C22×C4×C19—21no—
66C2×C22⋊D19—21no—
67C2×C22⋊D19—21no—
68C2×C22⋊D19—21no—
69C2×C22⋊D19—21no—
70C2×C22⋊D19—21no—
71C2×C22⋊D19—21no—
72C2×C22⋊D19—21no—
73C22×Dic19—21no—
74#64543—41no—
75#64543—41no—
76D4×D19—41no—
77D4×D19—41no—
78C2×D76—21no—
79C2×D76C2311yescharacteristic
80C2×D76C2311yescharacteristic
81C2×C4×D19—21no—
82C2×C4×D19C2311yescharacteristic
83C2×Dic38C2311yescharacteristic
84D8×C19—41no—
85D8×C19—41no—
86C2×C8×C19C2311yescharacteristic
87C2×C8×C19C2311yescharacteristic
88C4⋊C4×C19C2311yescharacteristic
89C22⋊C4×C19—21no—
90C42×C19C2311yescharacteristic
91C22⋊Dic19—21no—
92C22⋊Dic19—21no—
93C22⋊Dic19—21no—
94#64526—41no—
95#64525—41no—
96#64525—41no—
97#64525—41no—
98(C2×D19)⋊C4—21no—
99(C2×D19)⋊C4—21no—
100(C2×D19)⋊C4—21no—
101(C2×D19)⋊C4—21no—
102(C2×D19)⋊C4D411yescharacteristic
103(C2×D19)⋊C4D411yescharacteristic
104C4⋊Dic19—21no—
105C4⋊Dic19C2311yescharacteristic
106Dic19⋊C4—21no—
107Dic19⋊C4D411yescharacteristic
108Dic19⋊C4D411yescharacteristic
109C4×Dic19C2311yescharacteristic
110C2×C19⋊C8C2311yescharacteristic
111C2×C19⋊C8C2311yescharacteristic
112D152—41no—
113#64516—41no—
114C23×C19—21no—
115C23×C19—21no—
116C23×C19—21no—
117C22×D19—21no—
118C22×D19—21no—
119C22×D19—42no—
120C22×D19—81no—
121C22×D19—81no—
122C22×D19C2×D411yescharacteristic
123D4×C19—21no—
124D4×C19—21no—
125D4×C19—21no—
126D4×C19—21no—
127D4×C19—21no—
128D4×C19—21no—
129D4×C19—81no—
130D4×C19—81no—
131C2×C4×C19—21no—
132C2×C4×C19—81no—
133C2×C4×C19C2×D411yescharacteristic
134C2×C4×C19C2×D411yescharacteristic
135C2×C4×C19C2411yescharacteristic
136C22⋊D19—42no—
137C22⋊D19—42no—
138C22⋊D19—81no—
139C22⋊D19—81no—
140C22⋊D19—81no—
141C22⋊D19—81no—
142C22⋊D19—81no—
143C2×Dic19—21no—
144C2×Dic19—21no—
145C2×Dic19—42no—
146C2×Dic19C2×D411yescharacteristic
147C2×Dic19C2×D411yescharacteristic
148C2×Dic19C2×D411yescharacteristic
149D76—21no—
150D76—21no—
151D76—21no—
152D76—21no—
153D76—81no—
154C4×D19—21no—
155C4×D19—21no—
156C4×D19—81no—
157Dic38—21no—
158Dic38—21no—
159C8×C19—21no—
160C8×C19—21no—
161C19⋊C8—21no—
162C19⋊C8—21no—
163#3220—191nomaximal, Sylow
164C22×C19—41no—
165C22×C19—41no—
166C22×C19—41no—
167C22×C19—41no—
168C22×C19—41no—
169C22×C19—41no—
170C22×C19—41no—
171C22×C19—41no—
172C22×C19—41no—
173C22×C19C22×D411yescharacteristic
174C2×D19—21no—
175C2×D19—21no—
176C2×D19—21no—
177C2×D19—41no—
178C2×D19—41no—
179C2×D19—41no—
180C2×D19—41no—
181C2×D19—41no—
182C2×D19—41no—
183C2×D19—84no—
184C4×C19—21no—
185C4×C19—21no—
186C4×C19—41no—
187C4×C19H(5,𝔽2)11yescharacteristic
188C4×C19H(5,𝔽2)11yescharacteristic
189Dic19—21no—
190Dic19—21no—
191Dic19—21no—
192Dic19—41no—
193Dic19—41no—
194#540—191no—
195#535—191no—
196#496—191no—
197#493—191no—
198#490—191no—
199#488—191no—
200#463—191no—
201#463—191no—
202#459—191no—
203#459D1911yescharacteristic, complemented
204#449—191no—
205#449—191no—
206#447—191no—
207#447—191no—
208#433—191no—
209C2×C19—81no—
210C2×C19—81no—
211C2×C19—81no—
212C2×C19#53511yescharacteristic
213C2×C19#57611yescharacteristic
214C2×C19#57611yescharacteristic
215D19—41no—
216D19—81no—
217D19—81no—
218C2×#41—191no—
219C22×D4—191no—
220C2×SD16—191no—
221C2×SD16—191no—
222C2×D8—191no—
223C2×D8—191no—
224C2×D8—191no—
225C2×D8—191no—
226C2×D8C2×D1911yescharacteristic
227C2×D8C2×D1911yescharacteristic, complemented
228#127—191no—
229#127—191no—
230#127C2×D1911yescharacteristic
231#125—191no—
232#124—191no—
233#124—191no—
234#123—381no—
235#123—381no—
236#121—191no—
237#121—191no—
238#121—381no—
239#121—381no—
240#121—381no—
241#121—381no—
242#120—381no—
243#120—381no—
244C4×D4—191no—
245C4×D4C2×D1911yescharacteristic, complemented
246#117—191no—
247C4⋊C8—191no—
248C4⋊C8C2×D1911yescharacteristic, complemented
249#103—191no—
250#103—191no—
251#102—191no—
252#102—191no—
253#102—191no—
254#102—191no—
255#102C2×D1911yescharacteristic
256#102C2×D1911yescharacteristic, complemented
257C22⋊C8—191no—
258C22⋊C8—191no—
259#97—191no—
260C4×C8—191no—
261C19#322011yescharacteristic, complemented, Sylow
262C24—381no—
263#41—761no—
264#41—761no—
265C2×Q8—191no—
266C2×D4—21no—
267C2×D4—21no—
268C2×D4—191no—
269C2×D4—191no—
270C2×D4—381no—
271C2×D4—381no—
272C2×D4—381no—
273C2×D4—381no—
274C2×D4—381no—
275C2×D4—381no—
276C2×D4—381no—
277C2×D4—381no—
278C2×D4—761no—
279C2×D4—761no—
280C2×D4C22×D1911yescharacteristic
281C2×D4C22×D1911yescharacteristic
282C2×D4C22×D1911yescharacteristic
283C22×C4—21no—
284C22×C4—191no—
285C22×C4—381no—
286C22×C4—381no—
287SD16—761no—
288SD16—761no—
289D8—41no—
290D8—41no—
291D8—761no—
292D8—761no—
293D8—761no—
294D8—761no—
295C2×C8—191no—
296C2×C8—191no—
297C2×C8C22×D1911yescharacteristic
298C2×C8C22×D1911yescharacteristic
299C4⋊C4—191no—
300C4⋊C4—191no—
301C4⋊C4—191no—
302C4⋊C4—381no—
303C4⋊C4—381no—
304C4⋊C4C22×D1911yescharacteristic
305C22⋊C4—21no—
306C22⋊C4—191no—
307C22⋊C4—191no—
308C22⋊C4—381no—
309C22⋊C4—381no—
310C22⋊C4—381no—
311C22⋊C4—381no—
312C22⋊C4—381no—
313C22⋊C4—381no—
314C22⋊C4—381no—
315C42—191no—
316C42C22×D1911yescharacteristic
317C23—21no—
318C23—21no—
319C23—21no—
320C23—191no—
321C23—381no—
322C23—381no—
323C23—762no—
324C23—1521no—
325C23—1521no—
326Q8—381no—
327Q8—381no—
328D4—21no—
329D4—21no—
330D4—21no—
331D4—21no—
332D4—21no—
333D4—21no—
334D4—81no—
335D4—81no—
336D4—381no—
337D4—381no—
338D4—381no—
339D4—381no—
340D4—762no—
341D4—762no—
342D4—1521no—
343D4—1521no—
344D4—1521no—
345D4—1521no—
346D4—1521no—
347D4—1521no—
348C2×C4—21no—
349C2×C4—81no—
350C2×C4—191no—
351C2×C4—191no—
352C2×C4—191no—
353C2×C4—381no—
354C2×C4—381no—
355C2×C4—381no—
356C2×C4—381no—
357C2×C4—762no—
358C2×C4—1521no—
359C2×C4D4×D1911yescharacteristic
360C2×C4D4×D1911yescharacteristic
361C2×C4C23×D1911yescharacteristic
362C8—21no—
363C8—21no—
364C8—381no—
365C8—381no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—381no—
376C22—381no—
377C22—381no—
378C22—761no—
379C22—761no—
380C22—761no—
381C22—761no—
382C22—761no—
383C22—761no—
384C22—1524no—
385C22C2×D4×D1911yescharacteristic
386C4—21no—
387C4—21no—
388C4—41no—
389C4—381no—
390C4—381no—
391C4—381no—
392C4—761no—
393C4—761no—
394C4#1059743011yescharacteristic
395C4#1059743511yescharacteristic
396C2—81no—
397C2—81no—
398C2—81no—
399C2—761no—
400C2—1521no—
401C2—1521no—
402C2#1192711011yescharacteristic
403C2#1192734511yescharacteristic
404C2#1192734811yescharacteristic
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#459C2
socleC22×C19C22×D4
hypercenter#459D19
hypocenterC19#3220
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #11927145C2semidirect
2. #11927107C2semidirect
3. #11926932C2semidirect
4. #11926919C2semidirect
5. #11926907C2semidirect
6. #11926897C2semidirect
7. #11926760C2semidirect
8. #11926759C2semidirect
9. #11926736C2semidirect
10. #11926690C2semidirect
11. #11926686C2semidirect
12. #11926679C2semidirect
13. #11926676C2semidirect
14. #11926604C2semidirect
15. C19×#459C2semidirect
19. C2×D8×C19C22semidirect
21. C4×D4×C19C22semidirect
23. #10597386C22semidirect
30. C2×#64526C22semidirect
33. C2×#64525C22semidirect
37. C2×#64516C22semidirect
39. #10597336C22semidirect
43. C4×D76C22semidirect
45. C19×C4⋊C8C22semidirect
47. C19×#102C22semidirect
49. #10597289C22semidirect
53. #10597273C22semidirect
54. #10597272C22semidirect
55. C8×Dic19C22semidirect
56. #10597267C22semidirect
58. C4⋊(C19⋊C8)C22semidirect
203. #459D19semidirect
227. C2×D8C2×D19semidirect
245. C4×D4C2×D19semidirect
248. C4⋊C8C2×D19semidirect
256. #102C2×D19semidirect
261. C19#3220semidirect

Maximal subgroups

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

subgroupindex
#119271452
#119271072
#119269322
#119269192
#119269072
#119268972
#119267602
#119267592
#119267362
#119266902
#119266862
#119266792
#119266762
#119266042
C19×#4592
#322019