Finite Group Databasebeta

← #14575152

Subgroups — #14575152

Order 2432.

494 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10597355C211yesmaximal, characteristic, complemented
2C2×SD16×D19C211yesmaximal, characteristic, complemented
3#11927207C211yesmaximal, characteristic, complemented
4#11927191C211yesmaximal, characteristic
5#11926935C211yesmaximal, characteristic, complemented
6#11926786C211yesmaximal, characteristic, complemented
7#11926765C211yesmaximal, characteristic, complemented
8#11926748C211yesmaximal, characteristic, complemented
9#11926704C211yesmaximal, characteristic, complemented
10#11926701C211yesmaximal, characteristic, complemented
11#11926696C211yesmaximal, characteristic, complemented
12#11926682C211yesmaximal, characteristic, complemented
13#11926643C211yesmaximal, characteristic, complemented
14#11926613C211yesmaximal, characteristic, complemented
15C19×#468C211yesmaximal, characteristic, complemented
16C2×Q8×D19C2211yescharacteristic
17C2×D4×D19C2211yescharacteristic
18C2×#64541C2211yescharacteristic
19C22×Dic38C2211yescharacteristic, complemented
20C2×SD16×C19C2211yescharacteristic
21C2×M16×C19C2211yescharacteristic, complemented
22C19×C22⋊Q8C2211yescharacteristic, complemented
23C19×#121C2211yescharacteristic
24#10597390C2211yescharacteristic, complemented
25C2×#64528C2211yescharacteristic, complemented
26C2×#64527C2211yescharacteristic
27#10597384—21no—
28#10597383—21no—
29#10597382C2211yescharacteristic
30C2×#64526C2211yescharacteristic
31C2×#64526C2211yescharacteristic
32C4×C22⋊D19C2211yescharacteristic
33SD16×D19—24no—
34#10597355—24no—
35C2×Dic76C2211yescharacteristic, complemented
36C2×Dic76C2211yescharacteristic, complemented
37C2×#64516C2211yescharacteristic
38C2×#64516C2211yescharacteristic
39C2×C8×D19C2211yescharacteristic
40#10597343C2211yescharacteristic
41#10597343C2211yescharacteristic
42#10597342—21no—
43#10597339C2211yescharacteristic
44#10597334—21no—
45#10597333C2211yescharacteristic, complemented
46#10597329—21no—
47(C22⋊D19)⋊C4—21no—
48C22⋊C4×D19—21no—
49#10597324—21no—
50C19×#107C2211yescharacteristic, complemented
51C19×#103C2211yescharacteristic, complemented
52C19×#102C2211yescharacteristic
53C22⋊(C19⋊C8)C2211yescharacteristic, complemented
54(C2×D19)⋊C8C2211yescharacteristic
55#10597272C2211yescharacteristic, complemented
56Dic19⋊C8C2211yescharacteristic, complemented
57#10597267C2211yescharacteristic, complemented
58#10597267C2211yescharacteristic, complemented
59#10597267C2211yescharacteristic, complemented
60#10597266C2211yescharacteristic
61C23×D19—21no—
62C2×Q8×C19C2311yescharacteristic
63C2×D4×C19—21no—
64C2×D4×C19C2311yescharacteristic
65C22×C4×C19C2311yescharacteristic
66C2×C22⋊D19—21no—
67C2×C22⋊D19—21no—
68C2×C22⋊D19D411yescharacteristic
69C22×Dic19—21no—
70Q8×D19—22no—
71Q8×D19—41no—
72D4×D19—22no—
73D4×D19—41no—
74#64541—22no—
75#64541—41no—
76C2×D76C2311yescharacteristic
77C2×C4×D19—21no—
78C2×C4×D19—21no—
79C2×C4×D19—21no—
80C2×C4×D19C2311yescharacteristic
81C2×Dic38—22no—
82C2×Dic38—21no—
83C2×Dic38—21no—
84C2×Dic38—41no—
85C2×Dic38C2311yescharacteristic
86C2×Dic38C2311yescharacteristic
87C2×Dic38C2311yescharacteristic
88SD16×C19—22no—
89M16×C19—22no—
90C2×C8×C19C2311yescharacteristic
91C2×C8×C19C2311yescharacteristic
92C4⋊C4×C19—21no—
93C4⋊C4×C19C2311yescharacteristic
94C4⋊C4×C19C2311yescharacteristic
95C22⋊C4×C19—21no—
96C22⋊C4×C19—21no—
97C22⋊Dic19—21no—
98C22⋊Dic19—21no—
99C22⋊Dic19D411yescharacteristic
100#64528—41no—
101#64527—22no—
102#64526—22no—
103#64526—41no—
104(C2×D19)⋊C4—21no—
105(C2×D19)⋊C4—21no—
106(C2×D19)⋊C4—21no—
107(C2×D19)⋊C4D411yescharacteristic
108C4⋊Dic19—21no—
109C4⋊Dic19—21no—
110Dic19⋊C4—21no—
111Dic19⋊C4—21no—
112Dic19⋊C4—21no—
113Dic19⋊C4D411yescharacteristic
114C4×Dic19—21no—
115C4×Dic19C2311yescharacteristic
116C2×C19⋊C8C2311yescharacteristic
117C2×C19⋊C8C2311yescharacteristic
118Dic76—22no—
119Dic76—22no—
120#64516—22no—
121#64516D414yescomplemented
122C8×D19—22no—
123C23×C19—21no—
124C23×C19C2×D411yescharacteristic
125C22×D19—21no—
126C22×D19—42no—
127C22×D19—42no—
128C22×D19—81no—
129C22×D19C2×D411yescharacteristic
130Q8×C19—21no—
131Q8×C19—21no—
132D4×C19—21no—
133D4×C19—21no—
134D4×C19—81no—
135C2×C4×C19—21no—
136C2×C4×C19—21no—
137C2×C4×C19—21no—
138C2×C4×C19—21no—
139C2×C4×C19—21no—
140C2×C4×C19C2×D411yescharacteristic
141C2×C4×C19C2411yescharacteristic
142C22⋊D19—22no—
143C22⋊D19—42no—
144C22⋊D19—42no—
145C2×Dic19—21no—
146C2×Dic19—21no—
147C2×Dic19—21no—
148C2×Dic19—42no—
149C2×Dic19C2×D411yescharacteristic
150C2×Dic19C2×D411yescharacteristic
151C2×Dic19C2×D411yescharacteristic
152D76—21no—
153D76C2×D412yes—
154C4×D19—21no—
155C4×D19—21no—
156C4×D19—42no—
157C4×D19—42no—
158C4×D19—81no—
159Dic38—21no—
160Dic38—21no—
161Dic38—21no—
162Dic38—21no—
163Dic38—21no—
164Dic38—42no—
165Dic38—42no—
166Dic38C2×D412yes—
167C8×C19—21no—
168C8×C19C2×D412yes—
169C19⋊C8—21no—
170C19⋊C8—21no—
171#3266—191nomaximal, Sylow
172C22×C19—21no—
173C22×C19—21no—
174C22×C19—21no—
175C22×C19—41no—
176C22×C19—41no—
177C22×C19—41no—
178C22×C19C22×D411yescharacteristic
179C2×D19—21no—
180C2×D19—21no—
181C2×D19—22no—
182C2×D19—41no—
183C2×D19—41no—
184C2×D19—84no—
185C2×D19#13712yescomplemented
186C4×C19—21no—
187C4×C19—41no—
188C4×C19—41no—
189C4×C19—41no—
190C4×C19C22×D411yescharacteristic
191C4×C19H(5,𝔽2)11yescharacteristic
192Dic19—22no—
193Dic19—21no—
194Dic19—21no—
195Dic19—21no—
196Dic19—41no—
197Dic19—41no—
198C2×#137—191no—
199C22×SD16—191no—
200D4×Q8—191no—
201#546—191no—
202#497—191no—
203#468D1911yescharacteristic, complemented
204#467—191no—
205#464—191no—
206#461—191no—
207#452—191no—
208#451—191no—
209#450—191no—
210#448—191no—
211#440—191no—
212#435—191no—
213C2×C19—41no—
214C2×C19—81no—
215C2×C19D4211yescharacteristic
216C2×C19C2×#13711yescharacteristic
217C2×C19#57711yescharacteristic
218D19—22no—
219D19—42no—
220C2×#41—191no—
221C22×Q8—191no—
222C22×Q8—191no—
223C22×D4—191no—
224#137—384no—
225C2×Q16—191no—
226C2×Q16—191no—
227C2×Q16—191no—
228C2×SD16—191no—
229C2×SD16—191no—
230C2×SD16—191no—
231C2×SD16—191no—
232C2×SD16—191no—
233C2×SD16—384no—
234C2×SD16C2×D1911yescharacteristic
235C2×M16C2×D1911yescharacteristic, complemented
236C22×C8—191no—
237C4⋊Q8—191no—
238C4⋊Q8—381no—
239#124—191no—
240#123—381no—
241C22⋊Q8—191no—
242C22⋊Q8—191no—
243C22⋊Q8—381no—
244C22⋊Q8—381no—
245C22⋊Q8C2×D1911yescharacteristic, complemented
246#121—381no—
247#121C2×D1911yescharacteristic
248#120—381no—
249C4×Q8—191no—
250C4×D4—191no—
251C4×D4—191no—
252C4×D4—381no—
253C2×C22⋊C4—381no—
254#107C2×D1911yescharacteristic, complemented
255C4⋊C8—191no—
256#103—191no—
257#103—191no—
258#103—191no—
259#103C2×D1911yescharacteristic, complemented
260#102—191no—
261#102C2×D1911yescharacteristic
262C22⋊C8—191no—
263C22⋊C8—191no—
264#97—191no—
265C19#326611yescharacteristic, complemented, Sylow
266C24—381no—
267#41—382no—
268#41—761no—
269C2×Q8—191no—
270C2×Q8—191no—
271C2×Q8—191no—
272C2×Q8—381no—
273C2×Q8—382no—
274C2×Q8—381no—
275C2×Q8—382no—
276C2×Q8—761no—
277C2×Q8—761no—
278C2×Q8C22×D1911yescharacteristic
279C2×D4—21no—
280C2×D4—191no—
281C2×D4—191no—
282C2×D4—381no—
283C2×D4—382no—
284C2×D4—381no—
285C2×D4—761no—
286C2×D4C22×D1911yescharacteristic
287C22×C4—191no—
288C22×C4—381no—
289C22×C4—381no—
290C22×C4—381no—
291C22×C4—381no—
292C22×C4C22×D1911yescharacteristic
293Q16—382no—
294Q16—382no—
295Q16—761no—
296SD16—22no—
297SD16—194no—
298SD16—382no—
299SD16—382no—
300SD16—382no—
301SD16—761no—
302M16—22no—
303C2×C8—191no—
304C2×C8—191no—
305C2×C8—382no—
306C2×C8C22×D1911yescharacteristic
307C2×C8C22×D1911yescharacteristic
308C4⋊C4—21no—
309C4⋊C4—191no—
310C4⋊C4—381no—
311C4⋊C4—381no—
312C4⋊C4—381no—
313C4⋊C4—381no—
314C4⋊C4—381no—
315C4⋊C4C22×D1911yescharacteristic
316C4⋊C4C22×D1911yescharacteristic
317C22⋊C4—21no—
318C22⋊C4—21no—
319C22⋊C4—191no—
320C22⋊C4—191no—
321C22⋊C4—381no—
322C22⋊C4—381no—
323C22⋊C4—381no—
324C22⋊C4—381no—
325C22⋊C4—381no—
326C42—191no—
327C42—381no—
328C23—21no—
329C23—191no—
330C23—381no—
331C23—762no—
332C23—762no—
333C23—1521no—
334C23D4×D1911yescharacteristic
335Q8—21no—
336Q8—21no—
337Q8—192no—
338Q8—381no—
339Q8—381no—
340Q8—381no—
341Q8—381no—
342Q8—381no—
343Q8—762no—
344Q8—762no—
345D4—21no—
346D4—21no—
347D4—81no—
348D4—192no—
349D4—382no—
350D4—381no—
351D4—762no—
352D4—762no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—191no—
359C2×C4—191no—
360C2×C4—191no—
361C2×C4—381no—
362C2×C4—381no—
363C2×C4—381no—
364C2×C4—381no—
365C2×C4—381no—
366C2×C4—762no—
367C2×C4—762no—
368C2×C4—762no—
369C2×C4—1521no—
370C2×C4D4×D1911yescharacteristic
371C2×C4C23×D1911yescharacteristic
372C8—21no—
373C8—381no—
374C8—381no—
375C8D4×D1912yes—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—192no—
383C22—381no—
384C22—381no—
385C22—382no—
386C22—761no—
387C22—761no—
388C22—1524no—
389C22C2×D4×D1911yescharacteristic
390C4—21no—
391C4—41no—
392C4—41no—
393C4—41no—
394C4—381no—
395C4—381no—
396C4—381no—
397C4—382no—
398C4—761no—
399C4—761no—
400C4C2×D4×D1911yescharacteristic
401C4#1059743511yescharacteristic
402C2—41no—
403C2—81no—
404C2—382no—
405C2—762no—
406C2#1192717811yescharacteristic
407C2#137×D1911yescharacteristic
408C2#1192735411yescharacteristic
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#468C2
socleC22×C19C22×D4
prime radical#11927191C2
hypercenter#468D19
hypocenterC19#3266
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. C2×#10597355C2semidirect
2. C2×SD16×D19C2semidirect
3. #11927207C2semidirect
5. #11926935C2semidirect
6. #11926786C2semidirect
7. #11926765C2semidirect
8. #11926748C2semidirect
9. #11926704C2semidirect
10. #11926701C2semidirect
11. #11926696C2semidirect
12. #11926682C2semidirect
13. #11926643C2semidirect
14. #11926613C2semidirect
15. C19×#468C2semidirect
19. C22×Dic38C22semidirect
21. C2×M16×C19C22semidirect
22. C19×C22⋊Q8C22semidirect
24. #10597390C22semidirect
25. C2×#64528C22semidirect
35. C2×Dic76C22semidirect
36. C2×Dic76C22semidirect
45. #10597333C22semidirect
50. C19×#107C22semidirect
51. C19×#103C22semidirect
53. C22⋊(C19⋊C8)C22semidirect
55. #10597272C22semidirect
56. Dic19⋊C8C22semidirect
57. #10597267C22semidirect
58. #10597267C22semidirect
59. #10597267C22semidirect
121. #64516D4semidirect
185. C2×D19#137semidirect
203. #468D19semidirect
235. C2×M16C2×D19semidirect
245. C22⋊Q8C2×D19semidirect
254. #107C2×D19semidirect
259. #103C2×D19semidirect
265. C19#3266semidirect

Maximal subgroups

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

subgroupindex
C2×#105973552
C2×SD16×D192
#119272072
#119271912
#119269352
#119267862
#119267652
#119267482
#119267042
#119267012
#119266962
#119266822
#119266432
#119266132
C19×#4682
#326619