Finite Group Databasebeta

← #14574734

Subgroups — #14574734

Order 2432.

408 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11927166C211yesmaximal, characteristic, complemented
2#11927107C211yesmaximal, characteristic, complemented
3#11926930C211yesmaximal, characteristic, complemented
4#11926925C211yesmaximal, characteristic, complemented
5#11926902C211yesmaximal, characteristic, complemented
6#11926889C211yesmaximal, characteristic, complemented
7#11926766C211yesmaximal, characteristic, complemented
8#11926760C211yesmaximal, characteristic, complemented
9#11926736C211yesmaximal, characteristic, complemented
10#11926703C211yesmaximal, characteristic, complemented
11#11926693C211yesmaximal, characteristic, complemented
12#11926690C211yesmaximal, characteristic, complemented
13#11926679C211yesmaximal, characteristic, complemented
14#11926604C211yesmaximal, characteristic, complemented
15C19×#460C211yesmaximal, characteristic, complemented
16C2×#64543C2211yescharacteristic
17C2×D4×D19C2211yescharacteristic
18C2×SD16×C19C2211yescharacteristic
19C2×SD16×C19C2211yescharacteristic, complemented
20C19×#127C2211yescharacteristic
21C4×Q8×C19C2211yescharacteristic, complemented
22#10597393C2211yescharacteristic, complemented
23#10597392C2211yescharacteristic
24C2×#64528C2211yescharacteristic, complemented
25C2×#64527C2211yescharacteristic
26#10597386C2211yescharacteristic
27#10597385—21no—
28#10597385—21no—
29#10597383—21no—
30#10597383—21no—
31#10597382C2211yescharacteristic
32C2×#64525C2211yescharacteristic
33C2×#64525C2211yescharacteristic, complemented
34C2×D152C2211yescharacteristic
35C2×#64516C2211yescharacteristic, complemented
36#10597342—21no—
37#10597341C2211yescharacteristic
38#10597340—21no—
39#10597334C2211yescharacteristic, complemented
40#10597322—21no—
41#10597321—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×Q8×C19C2311yescharacteristic
61C2×D4×C19—21no—
62C2×D4×C19—21no—
63C2×D4×C19C2311yescharacteristic
64C2×D4×C19C2311yescharacteristic
65C2×C22⋊D19—21no—
66C2×C22⋊D19—21no—
67C2×C22⋊D19—21no—
68C2×C22⋊D19—21no—
69C22×Dic19—21no—
70#64543—41no—
71#64543—41no—
72D4×D19—41no—
73D4×D19—41no—
74C2×D76—21no—
75C2×D76C2311yescharacteristic
76C2×D76C2311yescharacteristic
77C2×C4×D19—21no—
78C2×C4×D19C2311yescharacteristic
79C2×Dic38—21no—
80C2×Dic38C2311yescharacteristic
81SD16×C19—41no—
82SD16×C19—41no—
83C2×C8×C19C2311yescharacteristic
84C2×C8×C19C2311yescharacteristic
85C4⋊C4×C19—21no—
86C4⋊C4×C19C2311yescharacteristic
87C42×C19—21no—
88C42×C19C2311yescharacteristic
89C22⋊Dic19—21no—
90C22⋊Dic19—21no—
91#64528—41no—
92#64527—41no—
93#64525—41no—
94#64525—41no—
95(C2×D19)⋊C4—21no—
96(C2×D19)⋊C4—21no—
97(C2×D19)⋊C4—21no—
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⋊Dic19C2311yescharacteristic
105Dic19⋊C4—21no—
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—
116C22×D19—21no—
117C22×D19—21no—
118C22×D19—42no—
119C22×D19—81no—
120C22×D19—81no—
121C22×D19C2×D411yescharacteristic
122Q8×C19—21no—
123Q8×C19—21no—
124D4×C19—21no—
125D4×C19—21no—
126D4×C19—21no—
127D4×C19—21no—
128D4×C19—81no—
129D4×C19—81no—
130C2×C4×C19—21no—
131C2×C4×C19—21no—
132C2×C4×C19C2×D411yescharacteristic
133C2×C4×C19C2×D411yescharacteristic
134C2×C4×C19C2411yescharacteristic
135C22⋊D19—42no—
136C22⋊D19—42no—
137C22⋊D19—81no—
138C22⋊D19—81no—
139C2×Dic19—21no—
140C2×Dic19—21no—
141C2×Dic19—42no—
142C2×Dic19C2×D411yescharacteristic
143C2×Dic19C2×D411yescharacteristic
144C2×Dic19C2×D411yescharacteristic
145D76—21no—
146D76—21no—
147D76—21no—
148D76—21no—
149D76—81no—
150C4×D19—21no—
151C4×D19—21no—
152C4×D19—81no—
153Dic38—21no—
154Dic38—21no—
155Dic38—81no—
156C8×C19—21no—
157C8×C19—21no—
158C19⋊C8—21no—
159C19⋊C8—21no—
160#3224—191nomaximal, Sylow
161C22×C19—41no—
162C22×C19—41no—
163C22×C19—41no—
164C22×C19—41no—
165C22×C19—41no—
166C22×C19—41no—
167C22×C19C22×D411yescharacteristic
168C2×D19—21no—
169C2×D19—21no—
170C2×D19—21no—
171C2×D19—41no—
172C2×D19—41no—
173C2×D19—41no—
174C2×D19—41no—
175C2×D19—41no—
176C2×D19—41no—
177C2×D19—84no—
178C4×C19—21no—
179C4×C19—21no—
180C4×C19—41no—
181C4×C19—41no—
182C4×C19H(5,𝔽2)11yescharacteristic
183C4×C19H(5,𝔽2)11yescharacteristic
184Dic19—21no—
185Dic19—21no—
186Dic19—21no—
187Dic19—41no—
188Dic19—41no—
189#542—191no—
190#535—191no—
191#496—191no—
192#495—191no—
193#489—191no—
194#486—191no—
195#464—191no—
196#463—191no—
197#460D1911yescharacteristic, complemented
198#459—191no—
199#452—191no—
200#450—191no—
201#449—191no—
202#447—191no—
203#433—191no—
204C2×C19—81no—
205C2×C19—81no—
206C2×C19#53511yescharacteristic
207C2×C19#57611yescharacteristic
208C2×C19#57711yescharacteristic
209D19—41no—
210D19—81no—
211D19—81no—
212C2×#41—191no—
213C22×D4—191no—
214C2×Q16—191no—
215C2×SD16—191no—
216C2×SD16—191no—
217C2×SD16C2×D1911yescharacteristic
218C2×SD16C2×D1911yescharacteristic, complemented
219C2×D8—191no—
220C2×D8—191no—
221C2×D8—191no—
222C4⋊Q8—191no—
223#127—191no—
224#127C2×D1911yescharacteristic
225#126—381no—
226#124—191no—
227#124—191no—
228#124—191no—
229#124—381no—
230#123—381no—
231C22⋊Q8—191no—
232C22⋊Q8—381no—
233#121—191no—
234#121—381no—
235#121—381no—
236#120—381no—
237#120—381no—
238C4×Q8C2×D1911yescharacteristic, complemented
239C4×D4—191no—
240#117—191no—
241C4⋊C8—191no—
242C4⋊C8C2×D1911yescharacteristic, complemented
243#103—191no—
244#103—191no—
245#102—191no—
246#102—191no—
247#102—191no—
248#102—191no—
249#102C2×D1911yescharacteristic
250#102C2×D1911yescharacteristic, complemented
251C22⋊C8—191no—
252C22⋊C8—191no—
253#97—191no—
254C4×C8—191no—
255C19#322411yescharacteristic, complemented, Sylow
256C24—381no—
257#41—761no—
258#41—761no—
259C2×Q8—191no—
260C2×Q8—381no—
261C2×Q8C22×D1911yescharacteristic
262C2×D4—21no—
263C2×D4—21no—
264C2×D4—191no—
265C2×D4—191no—
266C2×D4—381no—
267C2×D4—381no—
268C2×D4—381no—
269C2×D4—381no—
270C2×D4—381no—
271C2×D4—761no—
272C2×D4—761no—
273C2×D4C22×D1911yescharacteristic
274C2×D4C22×D1911yescharacteristic
275C22×C4—191no—
276C22×C4—381no—
277C22×C4—381no—
278Q16—761no—
279SD16—41no—
280SD16—41no—
281SD16—761no—
282SD16—761no—
283D8—761no—
284D8—761no—
285D8—761no—
286C2×C8—191no—
287C2×C8—191no—
288C2×C8C22×D1911yescharacteristic
289C2×C8C22×D1911yescharacteristic
290C4⋊C4—21no—
291C4⋊C4—191no—
292C4⋊C4—191no—
293C4⋊C4—191no—
294C4⋊C4—381no—
295C4⋊C4—381no—
296C4⋊C4C22×D1911yescharacteristic
297C22⋊C4—191no—
298C22⋊C4—191no—
299C22⋊C4—381no—
300C22⋊C4—381no—
301C22⋊C4—381no—
302C22⋊C4—381no—
303C22⋊C4—381no—
304C22⋊C4—381no—
305C22⋊C4—381no—
306C22⋊C4—381no—
307C22⋊C4—381no—
308C42—21no—
309C42—191no—
310C42C22×D1911yescharacteristic
311C23—21no—
312C23—21no—
313C23—191no—
314C23—381no—
315C23—381no—
316C23—762no—
317C23—1521no—
318C23—1521no—
319Q8—21no—
320Q8—21no—
321Q8—381no—
322Q8—381no—
323Q8—1521no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—21no—
328D4—81no—
329D4—81no—
330D4—381no—
331D4—381no—
332D4—381no—
333D4—381no—
334D4—762no—
335D4—762no—
336D4—1521no—
337D4—1521no—
338D4—1521no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—191no—
342C2×C4—191no—
343C2×C4—191no—
344C2×C4—381no—
345C2×C4—381no—
346C2×C4—381no—
347C2×C4—381no—
348C2×C4—762no—
349C2×C4—1521no—
350C2×C4D4×D1911yescharacteristic
351C2×C4D4×D1911yescharacteristic
352C2×C4C23×D1911yescharacteristic
353C8—21no—
354C8—21no—
355C8—381no—
356C8—381no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—381no—
364C22—381no—
365C22—381no—
366C22—761no—
367C22—761no—
368C22—761no—
369C22—761no—
370C22—761no—
371C22—761no—
372C22—1524no—
373C22C2×D4×D1911yescharacteristic
374C4—21no—
375C4—21no—
376C4—41no—
377C4—41no—
378C4—381no—
379C4—381no—
380C4—381no—
381C4—761no—
382C4—761no—
383C4#1059743011yescharacteristic
384C4#1059743511yescharacteristic
385C2—81no—
386C2—81no—
387C2—761no—
388C2—1521no—
389C2—1521no—
390C2#1192711011yescharacteristic
391C2#1192734811yescharacteristic
392C2#1192735011yescharacteristic
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#460C2
socleC22×C19C22×D4
hypercenter#460D19
hypocenterC19#3224
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
1. #11927166C2semidirect
2. #11927107C2semidirect
3. #11926930C2semidirect
4. #11926925C2semidirect
5. #11926902C2semidirect
6. #11926889C2semidirect
7. #11926766C2semidirect
8. #11926760C2semidirect
9. #11926736C2semidirect
10. #11926703C2semidirect
11. #11926693C2semidirect
12. #11926690C2semidirect
13. #11926679C2semidirect
14. #11926604C2semidirect
15. C19×#460C2semidirect
19. C2×SD16×C19C22semidirect
21. C4×Q8×C19C22semidirect
22. #10597393C22semidirect
24. C2×#64528C22semidirect
33. C2×#64525C22semidirect
35. C2×#64516C22semidirect
39. #10597334C22semidirect
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
197. #460D19semidirect
218. C2×SD16C2×D19semidirect
238. C4×Q8C2×D19semidirect
242. C4⋊C8C2×D19semidirect
250. #102C2×D19semidirect
255. C19#3224semidirect

Maximal subgroups

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

subgroupindex
#119271662
#119271072
#119269302
#119269252
#119269022
#119268892
#119267662
#119267602
#119267362
#119267032
#119266932
#119266902
#119266792
#119266042
C19×#4602
#322419