Finite Group Databasebeta

← #14575147

Subgroups — #14575147

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×#10597361C211yesmaximal, characteristic, complemented
2C2×SD16×D19C211yesmaximal, characteristic, complemented
3Q8×D76C211yesmaximal, characteristic, complemented
4#11927189C211yesmaximal, characteristic
5#11926938C211yesmaximal, characteristic, complemented
6#11926791C211yesmaximal, characteristic, complemented
7#11926786C211yesmaximal, characteristic, complemented
8#11926766C211yesmaximal, characteristic, complemented
9#11926749C211yesmaximal, characteristic, complemented
10#11926707C211yesmaximal, characteristic, complemented
11#11926701C211yesmaximal, characteristic, complemented
12#11926696C211yesmaximal, characteristic, complemented
13#11926684C211yesmaximal, characteristic, complemented
14#11926617C211yesmaximal, characteristic, complemented
15C19×#440C211yesmaximal, characteristic, complemented
16C2×Q8×D19C2211yescharacteristic
17C2×Q8×D19C2211yescharacteristic, complemented
18C2×#64543C2211yescharacteristic
19C2×D4×D19C2211yescharacteristic
20C2×SD16×C19C2211yescharacteristic
21C4×Q8×C19C2211yescharacteristic, complemented
22C4×D4×C19C2211yescharacteristic
23C2×#64528C2211yescharacteristic, complemented
24C2×#64527C2211yescharacteristic
25C2×#64526C2211yescharacteristic
26C2×#64526C2211yescharacteristic
27#10597376—21no—
28C2×(C2×D19)⋊C4—21no—
29#10597361—24no—
30SD16×D19—24no—
31C2×Dic76C2211yescharacteristic, complemented
32C2×Dic76C2211yescharacteristic, complemented
33C2×#64516C2211yescharacteristic
34C2×#64516C2211yescharacteristic
35C2×#64515C2211yescharacteristic, complemented
36C2×C8×D19C2211yescharacteristic
37#10597343—21no—
38#10597343—21no—
39#10597343C2211yescharacteristic
40#10597343C2211yescharacteristic
41#10597343C2211yescharacteristic, complemented
42#10597341C2211yescharacteristic
43#10597332—21no—
44#10597328—21no—
45#10597321C2211yescharacteristic
46C4×D76—21no—
47C4×D76C2211yescharacteristic
48#10597315—21no—
49#10597315C2211yescharacteristic, complemented
50C19×#107C2211yescharacteristic, complemented
51C19×#103C2211yescharacteristic, complemented
52C19×#102C2211yescharacteristic
53C19×#97C2211yescharacteristic, complemented
54(C2×D19)⋊C8C2211yescharacteristic
55(C2×D19)⋊C8C2211yescharacteristic, complemented
56#10597267C2211yescharacteristic, complemented
57#10597267C2211yescharacteristic, complemented
58#10597267C2211yescharacteristic, complemented
59#10597266C2211yescharacteristic
60C4⋊(C19⋊C8)C2211yescharacteristic, complemented
61C23×D19—21no—
62C2×Q8×C19C2311yescharacteristic
63C2×D4×C19C2311yescharacteristic
64C22×C4×C19—21no—
65C2×C22⋊D19—21no—
66C2×C22⋊D19—21no—
67C22×Dic19—21no—
68Q8×D19—22no—
69Q8×D19—22no—
70Q8×D19—41no—
71Q8×D19—41no—
72#64543—22no—
73#64543—41no—
74D4×D19—22no—
75D4×D19—41no—
76C2×D76—21no—
77C2×D76D411yescharacteristic
78C2×D76C2311yescharacteristic
79C2×C4×D19—21no—
80C2×C4×D19—21no—
81C2×C4×D19C2311yescharacteristic
82C2×C4×D19C2311yescharacteristic
83C2×Dic38—21no—
84C2×Dic38—21no—
85C2×Dic38C2311yescharacteristic
86C2×Dic38C2311yescharacteristic
87C2×Dic38C2311yescharacteristic
88SD16×C19D414yescomplemented
89C2×C8×C19C2311yescharacteristic
90C2×C8×C19C2311yescharacteristic
91C4⋊C4×C19—21no—
92C4⋊C4×C19C2311yescharacteristic
93C4⋊C4×C19C2311yescharacteristic
94C22⋊C4×C19—21no—
95C42×C19—21no—
96C42×C19C2311yescharacteristic
97#64528—22no—
98#64527—22no—
99#64526—22no—
100#64526—22no—
101(C2×D19)⋊C4—21no—
102(C2×D19)⋊C4—21no—
103(C2×D19)⋊C4—21no—
104(C2×D19)⋊C4—21no—
105(C2×D19)⋊C4—21no—
106(C2×D19)⋊C4—21no—
107(C2×D19)⋊C4D411yescharacteristic
108(C2×D19)⋊C4D411yescharacteristic
109C4⋊Dic19—21no—
110C4⋊Dic19—21no—
111C4⋊Dic19—21no—
112C4⋊Dic19—21no—
113C4⋊Dic19—21no—
114C4⋊Dic19D411yescharacteristic
115C2×C19⋊C8C2311yescharacteristic
116C2×C19⋊C8C2311yescharacteristic
117Dic76—22no—
118Dic76—41no—
119#64516—22no—
120#64516—41no—
121#64515—22no—
122C8×D19—22no—
123C23×C19—21no—
124C22×D19—21no—
125C22×D19—42no—
126C22×D19—42no—
127C22×D19—81no—
128C22×D19C2×D411yescharacteristic
129C22×D19C2×D411yescharacteristic
130Q8×C19—21no—
131Q8×C19C2×D412yes—
132D4×C19—21no—
133D4×C19C2×D412yes—
134C2×C4×C19—21no—
135C2×C4×C19—21no—
136C2×C4×C19—21no—
137C2×C4×C19—81no—
138C2×C4×C19C2×D411yescharacteristic
139C2×C4×C19C2×D411yescharacteristic
140C2×C4×C19C2411yescharacteristic
141C22⋊D19—42no—
142C22⋊D19—42no—
143C2×Dic19—21no—
144C2×Dic19—21no—
145C2×Dic19—21no—
146C2×Dic19—42no—
147C2×Dic19C2×D411yescharacteristic
148C2×Dic19C2×D411yescharacteristic
149D76—22no—
150D76—21no—
151D76—21no—
152D76—81no—
153C4×D19—21no—
154C4×D19—21no—
155C4×D19—21no—
156C4×D19—21no—
157C4×D19—42no—
158C4×D19—42no—
159Dic38—21no—
160Dic38—21no—
161Dic38—21no—
162Dic38—21no—
163Dic38—21no—
164Dic38—21no—
165Dic38—42no—
166Dic38—42no—
167C8×C19—21no—
168C8×C19C2×D412yes—
169C19⋊C8—21no—
170C19⋊C8—21no—
171#3266—191nomaximal, Sylow
172C22×C19—22no—
173C22×C19—41no—
174C22×C19—41no—
175C22×C19C22×D411yescharacteristic
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—
185C2×D19#13712yescomplemented
186C4×C19—22no—
187C4×C19—21no—
188C4×C19—21no—
189C4×C19—41no—
190C4×C19—41no—
191C4×C19C22×D411yescharacteristic
192C4×C19H(5,𝔽2)11yescharacteristic
193Dic19—21no—
194Dic19—21no—
195Dic19—41no—
196Dic19—41no—
197Dic19—41no—
198C2×#137—191no—
199C22×SD16—191no—
200D4×Q8—191no—
201#546—191no—
202#497—191no—
203#468—191no—
204#467—191no—
205#464—191no—
206#461—191no—
207#452—191no—
208#451—191no—
209#450—191no—
210#448—191no—
211#440D1911yescharacteristic, complemented
212#435—191no—
213C2×C19—42no—
214C2×C19D4211yescharacteristic
215C2×C19C2×#13711yescharacteristic
216C2×C19#57711yescharacteristic
217D19—22no—
218D19—41no—
219D19—81no—
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×M16—191no—
236C22×C8—191no—
237C4⋊Q8—191no—
238C4⋊Q8—381no—
239#124—191no—
240#123—381no—
241C22⋊Q8—191no—
242C22⋊Q8—191no—
243C22⋊Q8—191no—
244C22⋊Q8—381no—
245C22⋊Q8—381no—
246#121—191no—
247#121—381no—
248#120—381no—
249C4×Q8C2×D1911yescharacteristic, complemented
250C4×D4—191no—
251C4×D4—381no—
252C4×D4C2×D1911yescharacteristic
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#97C2×D1911yescharacteristic, complemented
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—381no—
274C2×Q8—382no—
275C2×Q8—382no—
276C2×Q8—761no—
277C2×Q8—761no—
278C2×Q8C22×D1911yescharacteristic
279C2×D4—191no—
280C2×D4—191no—
281C2×D4—381no—
282C2×D4—381no—
283C2×D4—382no—
284C2×D4—381no—
285C2×D4—761no—
286C2×D4C22×D1911yescharacteristic
287C22×C4—21no—
288C22×C4—191no—
289C22×C4—191no—
290C22×C4—381no—
291C22×C4—381no—
292C22×C4—381no—
293Q16—382no—
294Q16—382no—
295Q16—761no—
296SD16—382no—
297SD16—382no—
298SD16—382no—
299SD16—382no—
300SD16—761no—
301SD16D7614yescomplemented
302M16—382no—
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—191no—
319C22⋊C4—191no—
320C22⋊C4—381no—
321C22⋊C4—381no—
322C22⋊C4—381no—
323C22⋊C4—381no—
324C22⋊C4—381no—
325C22⋊C4—381no—
326C42—21no—
327C42C22×D1911yescharacteristic
328C23—21no—
329C23—191no—
330C23—191no—
331C23—381no—
332C23—762no—
333C23—762no—
334C23—1521no—
335Q8—21no—
336Q8—381no—
337Q8—381no—
338Q8—381no—
339Q8—381no—
340Q8—381no—
341Q8—381no—
342Q8—762no—
343Q8—762no—
344Q8C2×D7612yes—
345D4—21no—
346D4—382no—
347D4—381no—
348D4—381no—
349D4—762no—
350D4—762no—
351D4—1521no—
352D4C2×D7612yes—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—81no—
357C2×C4—191no—
358C2×C4—191no—
359C2×C4—381no—
360C2×C4—381no—
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×C4D4×D1911yescharacteristic
370C2×C4D4×D1911yescharacteristic
371C2×C4C23×D1911yescharacteristic
372C8—21no—
373C8—381no—
374C8—381no—
375C8C2×D7612yes—
376C22—22no—
377C22—41no—
378C22—41no—
379C22—192no—
380C22—381no—
381C22—381no—
382C22—381no—
383C22—381no—
384C22—381no—
385C22—761no—
386C22—761no—
387C22—761no—
388C22—1524no—
389C22C2×D4×D1911yescharacteristic
390C4—21no—
391C4—21no—
392C4—22no—
393C4—41no—
394C4—41no—
395C4—381no—
396C4—381no—
397C4—761no—
398C4—761no—
399C4—761no—
400C4C22×D7611yescharacteristic
401C4#1059743511yescharacteristic
402C2—42no—
403C2—382no—
404C2—761no—
405C2—1521no—
406C2D4×D7611yescharacteristic
407C2#137×D1911yescharacteristic
408C2#1192735411yescharacteristic
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#440C2
socleC22×C19C22×D4
prime radical#11927189C2
hypercenter#440D19
hypocenterC19#3266
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. C2×#10597361C2semidirect
2. C2×SD16×D19C2semidirect
3. Q8×D76C2semidirect
5. #11926938C2semidirect
6. #11926791C2semidirect
7. #11926786C2semidirect
8. #11926766C2semidirect
9. #11926749C2semidirect
10. #11926707C2semidirect
11. #11926701C2semidirect
12. #11926696C2semidirect
13. #11926684C2semidirect
14. #11926617C2semidirect
15. C19×#440C2semidirect
17. C2×Q8×D19C22semidirect
21. C4×Q8×C19C22semidirect
23. C2×#64528C22semidirect
31. C2×Dic76C22semidirect
32. C2×Dic76C22semidirect
35. C2×#64515C22semidirect
41. #10597343C22semidirect
49. #10597315C22semidirect
50. C19×#107C22semidirect
51. C19×#103C22semidirect
53. C19×#97C22semidirect
55. (C2×D19)⋊C8C22semidirect
56. #10597267C22semidirect
57. #10597267C22semidirect
58. #10597267C22semidirect
60. C4⋊(C19⋊C8)C22semidirect
88. SD16×C19D4semidirect
185. C2×D19#137semidirect
211. #440D19semidirect
249. C4×Q8C2×D19semidirect
254. #107C2×D19semidirect
259. #103C2×D19semidirect
264. #97C2×D19semidirect
265. C19#3266semidirect
301. SD16D76semidirect

Maximal subgroups

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

subgroupindex
C2×#105973612
C2×SD16×D192
Q8×D762
#119271892
#119269382
#119267912
#119267862
#119267662
#119267492
#119267072
#119267012
#119266962
#119266842
#119266172
C19×#4402
#326619