Finite Group Databasebeta

← #14575145

Subgroups — #14575145

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
2Q8×C22⋊D19C211yesmaximal, characteristic, complemented
3#11927188C211yesmaximal, characteristic
4#11926935C211yesmaximal, characteristic, complemented
5#11926787C211yesmaximal, characteristic, complemented
6#11926785C211yesmaximal, characteristic, complemented
7#11926764C211yesmaximal, characteristic, complemented
8#11926747C211yesmaximal, characteristic, complemented
9#11926703C211yesmaximal, characteristic, complemented
10#11926700C211yesmaximal, characteristic, complemented
11#11926695C211yesmaximal, characteristic, complemented
12#11926681C211yesmaximal, characteristic, complemented
13#11926645C211yesmaximal, characteristic, complemented
14#11926615C211yesmaximal, characteristic, complemented
15C22×SD16×C19C211yesmaximal, characteristic, complemented
16C22×Q8×C19C2211yescharacteristic
17C22×D4×C19C2211yescharacteristic
18C2×Q8×D19C2211yescharacteristic, complemented
19C2×#64543C2211yescharacteristic
20C2×SD16×C19—24no—
21C2×SD16×C19C2211yescharacteristic
22C2×SD16×C19C2211yescharacteristic
23C2×SD16×C19C2211yescharacteristic
24C2×SD16×C19C2211yescharacteristic
25C22×C8×C19C2211yescharacteristic
26#10597399—21no—
27C2×C22⋊Dic19—21no—
28#10597392—21no—
29#10597392C2211yescharacteristic, complemented
30Q8×Dic19C2211yescharacteristic, complemented
31#10597390—21no—
32#10597390C2211yescharacteristic, complemented
33C2×#64528C2211yescharacteristic, complemented
34C2×#64528C2211yescharacteristic, complemented
35#10597385—21no—
36#10597384C2211yescharacteristic
37#10597382C2211yescharacteristic
38#10597381—21no—
39D4×Dic19C2211yescharacteristic
40C2×#64526C2211yescharacteristic
41C2×#64526C2211yescharacteristic
42C4×C22⋊D19—21no—
43C4×C22⋊D19C2211yescharacteristic
44#10597370—21no—
45#10597370C2211yescharacteristic
46#10597370C2211yescharacteristic
47#10597361—24no—
48C2×Dic76C2211yescharacteristic, complemented
49C2×#64515C2211yescharacteristic, complemented
50#10597292C2211yescharacteristic, complemented
51#10597292C2211yescharacteristic, complemented
52#10597289C2211yescharacteristic
53#10597289C2211yescharacteristic
54C22⋊(C19⋊C8)C2211yescharacteristic
55(C2×D19)⋊C8C2211yescharacteristic, complemented
56#10597275C2211yescharacteristic, complemented
57#10597273C2211yescharacteristic, complemented
58#10597273C2211yescharacteristic, complemented
59#10597272C2211yescharacteristic, complemented
60Dic19⋊C8C2211yescharacteristic, complemented
61C24×C19—21no—
62C2×Q8×C19—21no—
63C2×Q8×C19—22no—
64C2×Q8×C19—41no—
65C2×Q8×C19C2311yescharacteristic
66C2×Q8×C19C2311yescharacteristic
67C2×D4×C19—22no—
68C2×D4×C19—21no—
69C2×D4×C19—41no—
70C2×D4×C19C2311yescharacteristic
71C2×D4×C19C2311yescharacteristic
72C22×C4×C19—21no—
73C22×C4×C19C2311yescharacteristic
74C2×C22⋊D19—21no—
75C2×C22⋊D19—21no—
76C2×C22⋊D19D411yescharacteristic
77C22×Dic19—21no—
78C22×Dic19—21no—
79Q8×D19—22no—
80Q8×D19—41no—
81#64543—22no—
82#64543—41no—
83C2×C4×D19—21no—
84C2×C4×D19C2311yescharacteristic
85C2×Dic38—21no—
86C2×Dic38C2311yescharacteristic
87C2×Dic38C2311yescharacteristic
88SD16×C19—22no—
89SD16×C19—22no—
90SD16×C19—22no—
91SD16×C19D414yescomplemented
92C2×C8×C19—22no—
93C2×C8×C19C2311yescharacteristic
94C2×C8×C19C2311yescharacteristic
95C22⋊Dic19—21no—
96C22⋊Dic19—21no—
97C22⋊Dic19—21no—
98C22⋊Dic19—21no—
99C22⋊Dic19—21no—
100C22⋊Dic19—21no—
101C22⋊Dic19D411yescharacteristic
102#64528—22no—
103#64528—41no—
104#64526—22no—
105#64526—41no—
106(C2×D19)⋊C4—21no—
107(C2×D19)⋊C4D411yescharacteristic
108C4⋊Dic19—21no—
109C4⋊Dic19C2311yescharacteristic
110C4⋊Dic19C2311yescharacteristic
111Dic19⋊C4—21no—
112Dic19⋊C4—21no—
113Dic19⋊C4—21no—
114Dic19⋊C4—21no—
115Dic19⋊C4—21no—
116Dic19⋊C4D411yescharacteristic
117C4×Dic19—21no—
118C4×Dic19C2311yescharacteristic
119C2×C19⋊C8C2311yescharacteristic
120C2×C19⋊C8C2311yescharacteristic
121Dic76—22no—
122#64515—22no—
123C23×C19—21no—
124C23×C19—21no—
125C23×C19—42no—
126C23×C19—42no—
127C23×C19—81no—
128C23×C19C2×D411yescharacteristic
129C22×D19C2×D411yescharacteristic
130Q8×C19—21no—
131Q8×C19—21no—
132Q8×C19—21no—
133Q8×C19—42no—
134Q8×C19C2×D412yes—
135D4×C19—21no—
136D4×C19—21no—
137D4×C19—21no—
138D4×C19—42no—
139D4×C19C2×D412yes—
140C2×C4×C19—21no—
141C2×C4×C19—21no—
142C2×C4×C19—21no—
143C2×C4×C19—21no—
144C2×C4×C19—42no—
145C2×C4×C19C2×D411yescharacteristic
146C2×C4×C19C2411yescharacteristic
147C22⋊D19—22no—
148C22⋊D19—42no—
149C22⋊D19—81no—
150C2×Dic19—21no—
151C2×Dic19—21no—
152C2×Dic19—21no—
153C2×Dic19—21no—
154C2×Dic19—42no—
155C2×Dic19—81no—
156C2×Dic19C2×D411yescharacteristic
157C2×Dic19C2×D411yescharacteristic
158C2×Dic19C2×D411yescharacteristic
159C4×D19—21no—
160C4×D19—21no—
161C4×D19—42no—
162Dic38—21no—
163Dic38—21no—
164Dic38—21no—
165Dic38—21no—
166Dic38—42no—
167C8×C19—21no—
168C8×C19C2×D412yes—
169C19⋊C8—21no—
170C19⋊C8—21no—
171#3266—191nomaximal, Sylow
172C22×C19—21no—
173C22×C19—21no—
174C22×C19—22no—
175C22×C19—41no—
176C22×C19—41no—
177C22×C19—41no—
178C22×C19—41no—
179C22×C19—41no—
180C22×C19—84no—
181C22×C19#13712yescomplemented
182C22×C19C22×D411yescharacteristic
183C2×D19—21no—
184C2×D19—21no—
185C2×D19—21no—
186C4×C19—22no—
187C4×C19—21no—
188C4×C19—41no—
189C4×C19C22×D411yescharacteristic
190C4×C19H(5,𝔽2)11yescharacteristic
191Dic19—21no—
192Dic19—21no—
193Dic19—21no—
194Dic19—41no—
195Dic19—41no—
196Dic19—41no—
197Dic19—41no—
198C2×#137—191no—
199C22×SD16D1911yescharacteristic, complemented
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#440—191no—
212#435—191no—
213C2×C19—22no—
214C2×C19—42no—
215C2×C19—81no—
216C2×C19D4211yescharacteristic
217C2×C19C2×#13711yescharacteristic
218C2×C19#57711yescharacteristic
219D19—41no—
220C2×#41—191no—
221C22×Q8—191no—
222C22×Q8C2×D1911yescharacteristic
223C22×D4C2×D1911yescharacteristic
224#137—384no—
225C2×Q16—191no—
226C2×Q16—191no—
227C2×Q16—191no—
228C2×SD16—24no—
229C2×SD16—191no—
230C2×SD16—191no—
231C2×SD16C2×D1911yescharacteristic
232C2×SD16C2×D1911yescharacteristic
233C2×SD16C2×D1911yescharacteristic
234C2×SD16C2×D1911yescharacteristic
235C2×M16—191no—
236C22×C8C2×D1911yescharacteristic
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×Q8—191no—
250C4×D4—191no—
251C4×D4—191no—
252C4×D4—381no—
253C2×C22⋊C4—381no—
254#107—191no—
255C4⋊C8—191no—
256#103—191no—
257#103—191no—
258#103—191no—
259#103—191no—
260#102—191no—
261#102—191no—
262C22⋊C8—191no—
263C22⋊C8—191no—
264#97—191no—
265C19#326611yescharacteristic, complemented, Sylow
266C24—21no—
267#41—382no—
268#41—761no—
269C2×Q8—21no—
270C2×Q8—22no—
271C2×Q8—41no—
272C2×Q8—191no—
273C2×Q8—191no—
274C2×Q8—381no—
275C2×Q8—382no—
276C2×Q8—761no—
277C2×Q8C22×D1911yescharacteristic
278C2×Q8C22×D1911yescharacteristic
279C2×D4—22no—
280C2×D4—21no—
281C2×D4—41no—
282C2×D4—191no—
283C2×D4—381no—
284C2×D4—381no—
285C2×D4C22×D1911yescharacteristic
286C2×D4C22×D1911yescharacteristic
287C22×C4—21no—
288C22×C4—191no—
289C22×C4—381no—
290C22×C4—381no—
291C22×C4—381no—
292C22×C4C22×D1911yescharacteristic
293Q16—382no—
294Q16—382no—
295Q16—761no—
296SD16—22no—
297SD16—22no—
298SD16—22no—
299SD16—382no—
300SD16—761no—
301SD16C22⋊D1914yescomplemented
302M16—382no—
303C2×C8—22no—
304C2×C8—191no—
305C2×C8—191no—
306C2×C8C22×D1911yescharacteristic
307C2×C8C22×D1911yescharacteristic
308C4⋊C4—191no—
309C4⋊C4—191no—
310C4⋊C4—191no—
311C4⋊C4—381no—
312C4⋊C4—381no—
313C4⋊C4—381no—
314C4⋊C4—381no—
315C4⋊C4—381no—
316C4⋊C4—381no—
317C22⋊C4—191no—
318C22⋊C4—191no—
319C22⋊C4—381no—
320C22⋊C4—381no—
321C22⋊C4—381no—
322C22⋊C4—381no—
323C22⋊C4—381no—
324C22⋊C4—381no—
325C22⋊C4—381no—
326C42—191no—
327C42—381no—
328C23—21no—
329C23—21no—
330C23—42no—
331C23—42no—
332C23—81no—
333C23—191no—
334C23D4×D1911yescharacteristic
335Q8—21no—
336Q8—21no—
337Q8—21no—
338Q8—42no—
339Q8—381no—
340Q8—381no—
341Q8—381no—
342Q8—381no—
343Q8—762no—
344Q8C2×C22⋊D1912yes—
345D4—21no—
346D4—21no—
347D4—21no—
348D4—42no—
349D4—382no—
350D4—762no—
351D4—1521no—
352D4C2×C22⋊D1912yes—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—42no—
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—381no—
367C2×C4—762no—
368C2×C4—762no—
369C2×C4—1521no—
370C2×C4D4×D1911yescharacteristic
371C2×C4C23×D1911yescharacteristic
372C8—21no—
373C8—381no—
374C8—381no—
375C8C2×C22⋊D1912yes—
376C22—21no—
377C22—21no—
378C22—22no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—84no—
385C22—381no—
386C22—381no—
387C22—381no—
388C22#1059736112yescomplemented
389C22C2×D4×D1911yescharacteristic
390C4—21no—
391C4—22no—
392C4—41no—
393C4—381no—
394C4—381no—
395C4—381no—
396C4—761no—
397C4—761no—
398C4—761no—
399C4—761no—
400C4#1059743011yescharacteristic
401C4C22×C22⋊D1911yescharacteristic
402C2—22no—
403C2—42no—
404C2—81no—
405C2—761no—
406C2D4×C22⋊D1911yescharacteristic
407C2C2×#1059736111yescharacteristic
408C2#1192735011yescharacteristic
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC22×SD16×C19C2
socleC22×C19C22×D4
prime radical#11927188C2
hypercenterC22×SD16D19
hypocenterC19#3266
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#10597361C2semidirect
2. Q8×C22⋊D19C2semidirect
4. #11926935C2semidirect
5. #11926787C2semidirect
6. #11926785C2semidirect
7. #11926764C2semidirect
8. #11926747C2semidirect
9. #11926703C2semidirect
10. #11926700C2semidirect
11. #11926695C2semidirect
12. #11926681C2semidirect
13. #11926645C2semidirect
14. #11926615C2semidirect
15. C22×SD16×C19C2semidirect
18. C2×Q8×D19C22semidirect
29. #10597392C22semidirect
30. Q8×Dic19C22semidirect
32. #10597390C22semidirect
33. C2×#64528C22semidirect
34. C2×#64528C22semidirect
48. C2×Dic76C22semidirect
49. C2×#64515C22semidirect
50. #10597292C22semidirect
51. #10597292C22semidirect
55. (C2×D19)⋊C8C22semidirect
56. #10597275C22semidirect
57. #10597273C22semidirect
58. #10597273C22semidirect
59. #10597272C22semidirect
60. Dic19⋊C8C22semidirect
91. SD16×C19D4semidirect
181. C22×C19#137semidirect
199. C22×SD16D19semidirect
265. C19#3266semidirect
301. SD16C22⋊D19semidirect
388. C22#10597361semidirect

Maximal subgroups

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

subgroupindex
C2×#105973612
Q8×C22⋊D192
#119271882
#119269352
#119267872
#119267852
#119267642
#119267472
#119267032
#119267002
#119266952
#119266812
#119266452
#119266152
C22×SD16×C192
#326619