Finite Group Databasebeta

← #14575206

Subgroups — #14575206

Order 2432.

472 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10597388C211yesmaximal, characteristic, complemented
2C22×#64528C211yesmaximal, characteristic, complemented
3#11927203C211yesmaximal, characteristic
4#11926936C211yesmaximal, characteristic, complemented
5#11926800C211yesmaximal, characteristic, complemented
6#11926775C211yesmaximal, characteristic, complemented
7#11926766C211yesmaximal, characteristic, complemented
8#11926751C211yesmaximal, characteristic, complemented
9#11926704C211yesmaximal, characteristic, complemented
10#11926700C211yesmaximal, characteristic, complemented
11#11926699C211yesmaximal, characteristic, complemented
12#11926683C211yesmaximal, characteristic, complemented
13#11926649C211yesmaximal, characteristic, complemented
14#11926616C211yesmaximal, characteristic, complemented
15D4×Q8×C19C211yesmaximal, characteristic, complemented
16C22×Q8×C19C2211yescharacteristic
17C22×Q8×C19C2211yescharacteristic
18C2×#64541C2211yescharacteristic
19C22×Dic38C2211yescharacteristic
20C19×C4⋊Q8—21no—
21C19×C4⋊Q8C2211yescharacteristic
22C19×C22⋊Q8—21no—
23C19×C22⋊Q8—21no—
24C19×C22⋊Q8C2211yescharacteristic
25C19×C22⋊Q8C2211yescharacteristic
26C4×Q8×C19C2211yescharacteristic
27C4×D4×C19—21no—
28C4×D4×C19C2211yescharacteristic
29C2×#64528—24no—
30C2×#64528C2211yescharacteristic
31C2×#64528C2211yescharacteristic
32C2×#64528C2211yescharacteristic
33C2×#64528C2211yescharacteristic
34C2×#64528C2211yescharacteristic
35C2×#64528C2211yescharacteristic
36#10597388—24no—
37C2×#64527C2211yescharacteristic
38C2×#64527C2211yescharacteristic
39C2×#64527C2211yescharacteristic
40#10597385—21no—
41#10597376C2211yescharacteristic
42#10597370C2211yescharacteristic
43C2×#64520C2211yescharacteristic
44C22×C19⋊C8C2211yescharacteristic
45#10597342—21no—
46#10597331—21no—
47(C22⋊D19)⋊C4—21no—
48#10597321C2211yescharacteristic
49C4×Dic38C2211yescharacteristic
50#10597292C2211yescharacteristic
51#10597292C2211yescharacteristic
52#10597292C2211yescharacteristic
53C22⋊(C19⋊C8)C2211yescharacteristic
54C22⋊(C19⋊C8)C2211yescharacteristic
55#10597267C2211yescharacteristic
56#10597267C2211yescharacteristic
57#10597266C2211yescharacteristic
58#10597265C2211yescharacteristic
59C4⋊(C19⋊C8)C2211yescharacteristic
60#10597260C2211yescharacteristic
61C2×Q8×C19—21no—
62C2×Q8×C19—21no—
63C2×Q8×C19—22no—
64C2×Q8×C19—22no—
65C2×Q8×C19—41no—
66C2×Q8×C19—41no—
67C2×Q8×C19C2311yescharacteristic
68C2×Q8×C19C2311yescharacteristic
69C2×Q8×C19C2311yescharacteristic
70C2×D4×C19D411yescharacteristic
71C22×C4×C19—21no—
72C22×C4×C19—21no—
73C22×C4×C19C2311yescharacteristic
74C22×C4×C19C2311yescharacteristic
75C2×C22⋊D19—21no—
76C2×C22⋊D19—21no—
77C22×Dic19—21no—
78#64541—22no—
79#64541—41no—
80C2×D76C2311yescharacteristic
81C2×C4×D19—21no—
82C2×Dic38—22no—
83C2×Dic38—21no—
84C2×Dic38—41no—
85C2×Dic38C2311yescharacteristic
86C2×Dic38C2311yescharacteristic
87C4⋊C4×C19—21no—
88C4⋊C4×C19—21no—
89C4⋊C4×C19—21no—
90C4⋊C4×C19—21no—
91C4⋊C4×C19—21no—
92C4⋊C4×C19D411yescharacteristic
93C4⋊C4×C19C2311yescharacteristic
94C22⋊C4×C19—21no—
95C22⋊C4×C19—21no—
96C22⋊C4×C19D411yescharacteristic
97C22⋊C4×C19D411yescharacteristic
98C42×C19—21no—
99C42×C19C2311yescharacteristic
100C22⋊Dic19—21no—
101#64528—22no—
102#64528—22no—
103#64528—22no—
104#64528—22no—
105#64528—41no—
106#64528D414yescomplemented
107#64527—22no—
108#64527—22no—
109#64527—41no—
110(C2×D19)⋊C4—21no—
111(C2×D19)⋊C4—21no—
112(C2×D19)⋊C4—21no—
113C4⋊Dic19C2311yescharacteristic
114Dic19⋊C4—21no—
115Dic19⋊C4—21no—
116C4×Dic19—21no—
117#64520—22no—
118C2×C19⋊C8—22no—
119C2×C19⋊C8C2311yescharacteristic
120C2×C19⋊C8C2311yescharacteristic
121C2×C19⋊C8C2311yescharacteristic
122C2×C19⋊C8C2311yescharacteristic
123C23×C19C2×D411yescharacteristic
124C23×C19C2×D411yescharacteristic
125C22×D19—21no—
126Q8×C19—21no—
127Q8×C19—21no—
128Q8×C19—21no—
129Q8×C19—21no—
130Q8×C19—21no—
131Q8×C19—42no—
132Q8×C19—42no—
133Q8×C19C2×D412yes—
134D4×C19—22no—
135C2×C4×C19—21no—
136C2×C4×C19—21no—
137C2×C4×C19—21no—
138C2×C4×C19—21no—
139C2×C4×C19—21no—
140C2×C4×C19—21no—
141C2×C4×C19—21no—
142C2×C4×C19—21no—
143C2×C4×C19—42no—
144C2×C4×C19—42no—
145C2×C4×C19C2×D411yescharacteristic
146C2×C4×C19C2×D411yescharacteristic
147C2×C4×C19C2×D411yescharacteristic
148C2×C4×C19C2×D411yescharacteristic
149C2×C4×C19C2411yescharacteristic
150C22⋊D19—42no—
151C22⋊D19—42no—
152C2×Dic19—21no—
153C2×Dic19—21no—
154C2×Dic19—21no—
155C2×Dic19—42no—
156D76—21no—
157D76—21no—
158C4×D19—42no—
159Dic38—21no—
160Dic38—21no—
161Dic38—21no—
162Dic38—42no—
163Dic38C2×D412yes—
164C19⋊C8—21no—
165C19⋊C8—21no—
166C19⋊C8—21no—
167C19⋊C8C2×D412yes—
168#3270—191nomaximal, Sylow
169C22×C19—21no—
170C22×C19—21no—
171C22×C19—21no—
172C22×C19—21no—
173C22×C19—21no—
174C22×C19#13712yescomplemented
175C22×C19C22×D411yescharacteristic
176C2×D19—41no—
177C2×D19—41no—
178C2×D19—41no—
179C4×C19—21no—
180C4×C19—21no—
181C4×C19—22no—
182C4×C19—21no—
183C4×C19—21no—
184C4×C19—41no—
185C4×C19—41no—
186C4×C19—41no—
187C4×C19C22×D411yescharacteristic
188C4×C19H(5,𝔽2)11yescharacteristic
189Dic19—22no—
190Dic19—41no—
191Dic19—41no—
192C2×#137—191no—
193C22×Q16—191no—
194D4×Q8D1911yescharacteristic, complemented
195#548—191no—
196#497—191no—
197#470—191no—
198#465—191no—
199#464—191no—
200#462—191no—
201#452—191no—
202#451—191no—
203#451—191no—
204#448—191no—
205#441—191no—
206#435—191no—
207C2×C19—22no—
208C2×C19—41no—
209C2×C19D4211yescharacteristic
210C2×C19C2×#13711yescharacteristic
211C2×C19#57811yescharacteristic
212D19—81no—
213C2×#41—191no—
214C22×Q8—191no—
215C22×Q8C2×D1911yescharacteristic
216C22×Q8C2×D1911yescharacteristic
217#137—384no—
218C2×Q16—191no—
219C2×Q16—191no—
220C2×Q16—191no—
221C2×Q16—191no—
222C2×Q16—191no—
223C2×Q16—191no—
224C2×Q16—384no—
225C2×SD16—191no—
226C2×SD16—191no—
227C2×SD16—191no—
228C2×M16—191no—
229C22×C8—191no—
230C4⋊Q8—21no—
231C4⋊Q8C2×D1911yescharacteristic
232#124—191no—
233#124—381no—
234C22⋊Q8—21no—
235C22⋊Q8—21no—
236C22⋊Q8—191no—
237C22⋊Q8—381no—
238C22⋊Q8C2×D1911yescharacteristic
239C22⋊Q8C2×D1911yescharacteristic
240#121—191no—
241#121—381no—
242C4×Q8—191no—
243C4×Q8C2×D1911yescharacteristic
244C4×D4—21no—
245C4×D4—381no—
246C4×D4C2×D1911yescharacteristic
247#106—191no—
248C4⋊C8—191no—
249#103—191no—
250#103—191no—
251#103—191no—
252#103—191no—
253#103—191no—
254#102—191no—
255C22⋊C8—191no—
256C22⋊C8—191no—
257#97—191no—
258C19#327011yescharacteristic, complemented, Sylow
259#41—382no—
260#41—761no—
261C2×Q8—21no—
262C2×Q8—21no—
263C2×Q8—22no—
264C2×Q8—22no—
265C2×Q8—41no—
266C2×Q8—41no—
267C2×Q8—191no—
268C2×Q8—191no—
269C2×Q8—382no—
270C2×Q8—381no—
271C2×Q8—761no—
272C2×Q8C22×D1911yescharacteristic
273C2×Q8C22×D1911yescharacteristic
274C2×Q8C22×D1911yescharacteristic
275C2×D4—191no—
276C2×D4—381no—
277C2×D4—381no—
278C2×D4C22⋊D1911yescharacteristic
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—381no—
282C22×C4—381no—
283C22×C4C22×D1911yescharacteristic
284C22×C4C22×D1911yescharacteristic
285Q16—194no—
286Q16—382no—
287Q16—382no—
288Q16—382no—
289Q16—382no—
290Q16—761no—
291SD16—382no—
292SD16—382no—
293SD16—761no—
294M16—382no—
295C2×C8—191no—
296C2×C8—191no—
297C2×C8—191no—
298C2×C8—191no—
299C2×C8—382no—
300C4⋊C4—21no—
301C4⋊C4—21no—
302C4⋊C4—21no—
303C4⋊C4—21no—
304C4⋊C4—21no—
305C4⋊C4—191no—
306C4⋊C4—381no—
307C4⋊C4—381no—
308C4⋊C4C22⋊D1911yescharacteristic
309C4⋊C4C22×D1911yescharacteristic
310C22⋊C4—21no—
311C22⋊C4—21no—
312C22⋊C4—381no—
313C22⋊C4—381no—
314C22⋊C4—381no—
315C22⋊C4—381no—
316C22⋊C4C22⋊D1911yescharacteristic
317C22⋊C4C22⋊D1911yescharacteristic
318C42—21no—
319C42—381no—
320C42C22×D1911yescharacteristic
321C23—381no—
322C23C2×C22⋊D1911yescharacteristic
323C23C2×C22⋊D1911yescharacteristic
324Q8—21no—
325Q8—21no—
326Q8—21no—
327Q8—21no—
328Q8—21no—
329Q8—42no—
330Q8—42no—
331Q8—192no—
332Q8—381no—
333Q8—381no—
334Q8—381no—
335Q8—762no—
336Q8D4×D1912yes—
337D4—22no—
338D4—381no—
339D4—381no—
340D4—762no—
341D4—762no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—42no—
351C2×C4—42no—
352C2×C4—381no—
353C2×C4—381no—
354C2×C4—381no—
355C2×C4—762no—
356C2×C4—762no—
357C2×C4C2×C22⋊D1911yescharacteristic
358C2×C4C2×C22⋊D1911yescharacteristic
359C2×C4C2×C22⋊D1911yescharacteristic
360C2×C4C2×C22⋊D1911yescharacteristic
361C2×C4C23×D1911yescharacteristic
362C8—192no—
363C8—381no—
364C8—381no—
365C8—381no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—761no—
372C22—761no—
373C22—761no—
374C22#1059738812yescomplemented
375C22C22×C22⋊D1911yescharacteristic
376C4—21no—
377C4—21no—
378C4—21no—
379C4—21no—
380C4—22no—
381C4—41no—
382C4—41no—
383C4—41no—
384C4—382no—
385C4—761no—
386C4—761no—
387C4C2×D4×D1911yescharacteristic
388C4#1059743011yescharacteristic
389C2—22no—
390C2—41no—
391C2—1521no—
392C2D4×C22⋊D1911yescharacteristic
393C2C2×#1059738811yescharacteristic
394C2#1192735911yescharacteristic
subgroupG/H
centerC22C22×C22⋊D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingD4×Q8×C19C2
socleC22×C19C22×D4
prime radical#11927203C2
hypercenterD4×Q8D19
hypocenterC19#3270
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C4×D4 ◁ D4×Q8

Complements

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

NH ≅ G/Ntype
1. C2×#10597388C2semidirect
2. C22×#64528C2semidirect
4. #11926936C2semidirect
5. #11926800C2semidirect
6. #11926775C2semidirect
7. #11926766C2semidirect
8. #11926751C2semidirect
9. #11926704C2semidirect
10. #11926700C2semidirect
11. #11926699C2semidirect
12. #11926683C2semidirect
13. #11926649C2semidirect
14. #11926616C2semidirect
15. D4×Q8×C19C2semidirect
106. #64528D4semidirect
174. C22×C19#137semidirect
194. D4×Q8D19semidirect
258. C19#3270semidirect
374. C22#10597388semidirect

Maximal subgroups

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

subgroupindex
C2×#105973882
C22×#645282
#119272032
#119269362
#119268002
#119267752
#119267662
#119267512
#119267042
#119267002
#119266992
#119266832
#119266492
#119266162
D4×Q8×C192
#327019