Finite Group Databasebeta

← #14574731

Subgroups — #14574731

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#11927165C211yesmaximal, characteristic, complemented
2#11927113C211yesmaximal, characteristic, complemented
3#11926933C211yesmaximal, characteristic, complemented
4#11926928C211yesmaximal, characteristic, complemented
5#11926904C211yesmaximal, characteristic, complemented
6#11926891C211yesmaximal, characteristic, complemented
7#11926767C211yesmaximal, characteristic, complemented
8#11926760C211yesmaximal, characteristic, complemented
9#11926745C211yesmaximal, characteristic, complemented
10#11926740C211yesmaximal, characteristic, complemented
11#11926708C211yesmaximal, characteristic, complemented
12#11926697C211yesmaximal, characteristic, complemented
13#11926691C211yesmaximal, characteristic, complemented
14#11926680C211yesmaximal, characteristic, complemented
15C19×#433C211yesmaximal, characteristic, complemented
16C2×#64541C2211yescharacteristic
17C22×D76C2211yescharacteristic
18C19×#117C2211yescharacteristic
19#10597376C2211yescharacteristic
20#10597370C2211yescharacteristic
21C2×Dic76C2211yescharacteristic, complemented
22C2×D152C2211yescharacteristic
23C2×D152C2211yescharacteristic
24C2×D152C2211yescharacteristic, complemented
25C2×#64516C2211yescharacteristic
26C2×#64516C2211yescharacteristic
27C2×#64516C2211yescharacteristic, complemented
28C2×#64516C2211yescharacteristic, complemented
29#10597344—21no—
30#10597342—21no—
31#10597341—21no—
32#10597341—21no—
33#10597331—21no—
34#10597329—21no—
35#10597328—21no—
36#10597328—21no—
37#10597321C2211yescharacteristic
38#10597321C2211yescharacteristic
39#10597321C2211yescharacteristic, complemented
40#10597320C2211yescharacteristic
41#10597320C2211yescharacteristic
42C4×D76C2211yescharacteristic, complemented
43#10597315C2211yescharacteristic, complemented
44C4×Dic38C2211yescharacteristic, complemented
45C19×C4⋊C8C2211yescharacteristic, complemented
46C19×C4⋊C8C2211yescharacteristic, complemented
47C19×C22⋊C8C2211yescharacteristic
48C19×C22⋊C8C2211yescharacteristic
49C19×#97C2211yescharacteristic, complemented
50C4×C8×C19C2211yescharacteristic, complemented
51#10597278C2211yescharacteristic
52#10597278C2211yescharacteristic
53#10597278C2211yescharacteristic
54#10597278C2211yescharacteristic
55#10597278C2211yescharacteristic, complemented
56#10597278C2211yescharacteristic, complemented
57#10597273C2211yescharacteristic, complemented
58#10597273C2211yescharacteristic, complemented
59C23×D19—21no—
60C22×C4×C19C2311yescharacteristic
61C2×C22⋊D19—21no—
62C2×C22⋊D19—21no—
63#64541—41no—
64#64541—41no—
65C2×D76—21no—
66C2×D76—21no—
67C2×D76—21no—
68C2×D76—21no—
69C2×D76—21no—
70C2×D76—41no—
71C2×D76—41no—
72C2×D76C2311yescharacteristic
73C2×D76C2311yescharacteristic
74C2×D76C2311yescharacteristic
75C2×D76C2311yescharacteristic
76C2×C4×D19—21no—
77C2×C4×D19—21no—
78C2×Dic38—21no—
79C2×Dic38C2311yescharacteristic
80C2×Dic38C2311yescharacteristic
81C2×C8×C19C2311yescharacteristic
82C2×C8×C19C2311yescharacteristic
83C2×C8×C19C2311yescharacteristic
84C2×C8×C19C2311yescharacteristic
85C4⋊C4×C19D411yescharacteristic
86C4⋊C4×C19D411yescharacteristic
87C22⋊C4×C19D411yescharacteristic
88C22⋊C4×C19D411yescharacteristic
89C42×C19C2311yescharacteristic
90C42×C19C2311yescharacteristic
91C22⋊Dic19—21no—
92(C2×D19)⋊C4—21no—
93(C2×D19)⋊C4—21no—
94(C2×D19)⋊C4—21no—
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—
100C4⋊Dic19—21no—
101C4⋊Dic19C2311yescharacteristic
102C4⋊Dic19C2311yescharacteristic
103Dic19⋊C4—21no—
104Dic19⋊C4—21no—
105C4×Dic19—21no—
106Dic76—41no—
107D152—41no—
108D152—41no—
109D152—41no—
110#64516—41no—
111#64516—41no—
112#64516—41no—
113#64516—41no—
114C23×C19C2×D411yescharacteristic
115C22×D19—21no—
116C22×D19—21no—
117C22×D19—21no—
118C22×D19—21no—
119C22×D19—42no—
120C22×D19—81no—
121C22×D19—81no—
122C2×C4×C19—21no—
123C2×C4×C19—21no—
124C2×C4×C19C2×D411yescharacteristic
125C2×C4×C19C2×D411yescharacteristic
126C2×C4×C19C2×D411yescharacteristic
127C2×C4×C19C2×D411yescharacteristic
128C2×C4×C19C2×D411yescharacteristic
129C2×C4×C19C2411yescharacteristic
130C22⋊D19—42no—
131C22⋊D19—81no—
132C2×Dic19—21no—
133C2×Dic19—21no—
134C2×Dic19—21no—
135C2×Dic19—21no—
136D76—21no—
137D76—21no—
138D76—21no—
139D76—21no—
140D76—21no—
141D76—21no—
142D76—21no—
143D76—21no—
144D76—42no—
145D76—81no—
146D76—81no—
147D76—81no—
148D76—81no—
149C4×D19—42no—
150C4×D19—81no—
151Dic38—21no—
152Dic38—21no—
153Dic38—21no—
154Dic38—21no—
155Dic38—81no—
156C8×C19—21no—
157C8×C19—21no—
158C8×C19—21no—
159C8×C19—21no—
160#3224—191nomaximal, Sylow
161C22×C19—21no—
162C22×C19—21no—
163C22×C19—21no—
164C22×C19C22×D411yescharacteristic
165C2×D19—41no—
166C2×D19—41no—
167C2×D19—41no—
168C2×D19—41no—
169C2×D19—41no—
170C2×D19—41no—
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—21no—
181C4×C19—21no—
182C4×C19—21no—
183C4×C19H(5,𝔽2)11yescharacteristic
184C4×C19H(5,𝔽2)11yescharacteristic
185Dic19—41no—
186Dic19—41no—
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#460—191no—
198#459—191no—
199#452—191no—
200#450—191no—
201#449—191no—
202#447—191no—
203#433D1911yescharacteristic, complemented
204C2×C19—41no—
205C2×C19#53511yescharacteristic
206C2×C19#57611yescharacteristic
207C2×C19#57711yescharacteristic
208D19—81no—
209D19—81no—
210D19—81no—
211D19—81no—
212C2×#41—191no—
213C22×D4—191no—
214C2×Q16—191no—
215C2×SD16—191no—
216C2×SD16—191no—
217C2×SD16—191no—
218C2×SD16—191no—
219C2×D8—191no—
220C2×D8—191no—
221C2×D8—191no—
222C4⋊Q8—191no—
223#127—191no—
224#127—191no—
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×Q8—191no—
239C4×D4—191no—
240#117C2×D1911yescharacteristic
241C4⋊C8C2×D1911yescharacteristic, complemented
242C4⋊C8C2×D1911yescharacteristic, complemented
243#103—191no—
244#103—191no—
245#102—191no—
246#102—191no—
247#102—191no—
248#102—191no—
249#102—191no—
250#102—191no—
251C22⋊C8C2×D1911yescharacteristic
252C22⋊C8C2×D1911yescharacteristic
253#97C2×D1911yescharacteristic, complemented
254C4×C8C2×D1911yescharacteristic, complemented
255C19#322411yescharacteristic, complemented, Sylow
256C24—381no—
257#41—761no—
258#41—761no—
259C2×Q8—191no—
260C2×Q8—191no—
261C2×Q8—381no—
262C2×D4—191no—
263C2×D4—191no—
264C2×D4—191no—
265C2×D4—191no—
266C2×D4—381no—
267C2×D4—381no—
268C2×D4—381no—
269C2×D4—381no—
270C2×D4—381no—
271C2×D4—381no—
272C2×D4—381no—
273C2×D4—761no—
274C2×D4—761no—
275C22×C4—381no—
276C22×C4—381no—
277C22×C4C22×D1911yescharacteristic
278Q16—761no—
279SD16—761no—
280SD16—761no—
281SD16—761no—
282SD16—761no—
283D8—761no—
284D8—761no—
285D8—761no—
286C2×C8C22×D1911yescharacteristic
287C2×C8C22×D1911yescharacteristic
288C2×C8C22×D1911yescharacteristic
289C2×C8C22×D1911yescharacteristic
290C4⋊C4—191no—
291C4⋊C4—191no—
292C4⋊C4—381no—
293C4⋊C4—381no—
294C4⋊C4—381no—
295C4⋊C4D7611yescharacteristic
296C4⋊C4D7611yescharacteristic
297C22⋊C4—381no—
298C22⋊C4—381no—
299C22⋊C4—381no—
300C22⋊C4—381no—
301C22⋊C4—381no—
302C22⋊C4—381no—
303C22⋊C4—381no—
304C22⋊C4—381no—
305C22⋊C4—381no—
306C22⋊C4D7611yescharacteristic
307C22⋊C4D7611yescharacteristic
308C42—381no—
309C42C22×D1911yescharacteristic
310C42C22×D1911yescharacteristic
311C23—381no—
312C23—381no—
313C23—381no—
314C23—381no—
315C23—762no—
316C23—1521no—
317C23—1521no—
318C23C2×D7611yescharacteristic
319Q8—381no—
320Q8—381no—
321Q8—381no—
322Q8—381no—
323Q8—1521no—
324D4—381no—
325D4—381no—
326D4—381no—
327D4—381no—
328D4—381no—
329D4—381no—
330D4—381no—
331D4—381no—
332D4—762no—
333D4—762no—
334D4—1521no—
335D4—1521no—
336D4—1521no—
337D4—1521no—
338D4—1521no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—381no—
342C2×C4—381no—
343C2×C4—381no—
344C2×C4—381no—
345C2×C4—762no—
346C2×C4—1521no—
347C2×C4C2×D7611yescharacteristic
348C2×C4C2×D7611yescharacteristic
349C2×C4C2×D7611yescharacteristic
350C2×C4C2×D7611yescharacteristic
351C2×C4C2×D7611yescharacteristic
352C2×C4C23×D1911yescharacteristic
353C8—21no—
354C8—21no—
355C8—21no—
356C8—21no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—761no—
361C22—761no—
362C22—761no—
363C22—761no—
364C22—761no—
365C22—761no—
366C22—761no—
367C22—761no—
368C22—761no—
369C22—761no—
370C22—761no—
371C22—761no—
372C22—1524no—
373C22C22×D7611yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—21no—
378C4—21no—
379C4—761no—
380C4—761no—
381C4—761no—
382C4—761no—
383C4#1059743511yescharacteristic
384C4#1059743511yescharacteristic
385C2—41no—
386C2—1521no—
387C2—1521no—
388C2—1521no—
389C2—1521no—
390C2#1192711311yescharacteristic
391C2#1192734911yescharacteristic
392C2#1192735611yescharacteristic
subgroupG/H
centerC22C22×D76
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#433C2
socleC22×C19C22×D4
hypercenter#433D19
hypocenterC19#3224
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #11927165C2semidirect
2. #11927113C2semidirect
3. #11926933C2semidirect
4. #11926928C2semidirect
5. #11926904C2semidirect
6. #11926891C2semidirect
7. #11926767C2semidirect
8. #11926760C2semidirect
9. #11926745C2semidirect
10. #11926740C2semidirect
11. #11926708C2semidirect
12. #11926697C2semidirect
13. #11926691C2semidirect
14. #11926680C2semidirect
15. C19×#433C2semidirect
21. C2×Dic76C22semidirect
24. C2×D152C22semidirect
27. C2×#64516C22semidirect
28. C2×#64516C22semidirect
39. #10597321C22semidirect
42. C4×D76C22semidirect
43. #10597315C22semidirect
44. C4×Dic38C22semidirect
45. C19×C4⋊C8C22semidirect
46. C19×C4⋊C8C22semidirect
49. C19×#97C22semidirect
50. C4×C8×C19C22semidirect
55. #10597278C22semidirect
56. #10597278C22semidirect
57. #10597273C22semidirect
58. #10597273C22semidirect
203. #433D19semidirect
241. C4⋊C8C2×D19semidirect
242. C4⋊C8C2×D19semidirect
253. #97C2×D19semidirect
254. C4×C8C2×D19semidirect
255. C19#3224semidirect

Maximal subgroups

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

subgroupindex
#119271652
#119271132
#119269332
#119269282
#119269042
#119268912
#119267672
#119267602
#119267452
#119267402
#119267082
#119266972
#119266912
#119266802
C19×#4332
#322419