Finite Group Databasebeta

← #14575275

Subgroups — #14575275

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×#10597361C211yesmaximal, characteristic, complemented
2Q8×C22⋊D19C211yesmaximal, characteristic, complemented
3#11927193C211yesmaximal, characteristic
4#11926922C211yesmaximal, characteristic, complemented
5#11926802C211yesmaximal, characteristic, complemented
6#11926799C211yesmaximal, characteristic, complemented
7#11926752C211yesmaximal, characteristic, complemented
8#11926747C211yesmaximal, characteristic, complemented
9#11926706C211yesmaximal, characteristic, complemented
10#11926703C211yesmaximal, characteristic, complemented
11#11926700C211yesmaximal, characteristic, complemented
12#11926698C211yesmaximal, characteristic, complemented
13SD16×Dic19C211yesmaximal, characteristic, complemented
14#11926620C211yesmaximal, characteristic, complemented
15C2×C19×#137C211yesmaximal, characteristic, complemented
16C2×#41×C19C2211yescharacteristic
17C22×Q8×C19C2211yescharacteristic
18C2×Q8×D19C2211yescharacteristic
19C2×#64543C2211yescharacteristic
20C19×#137—24no—
21C2×Q16×C19C2211yescharacteristic
22C2×Q16×C19C2211yescharacteristic
23C2×SD16×C19C2211yescharacteristic
24C2×SD16×C19C2211yescharacteristic
25C2×M16×C19C2211yescharacteristic
26#10597392—21no—
27#10597392C2211yescharacteristic
28#10597392C2211yescharacteristic
29Q8×Dic19C2211yescharacteristic
30#10597390—21no—
31#10597390C2211yescharacteristic
32#10597390C2211yescharacteristic
33C2×#64528C2211yescharacteristic
34C2×#64528C2211yescharacteristic
35C2×#64528C2211yescharacteristic
36#10597385—21no—
37#10597381—21no—
38D4×Dic19C2211yescharacteristic
39C2×#64526C2211yescharacteristic
40#10597375—21no—
41C4×C22⋊D19—21no—
42C4×C22⋊D19C2211yescharacteristic
43#10597370—21no—
44#10597370C2211yescharacteristic
45#10597370C2211yescharacteristic
46C2×Dic19⋊C4—21no—
47#10597361—24no—
48C2×Dic76C2211yescharacteristic
49C2×#64515C2211yescharacteristic
50#10597292C2211yescharacteristic
51#10597292C2211yescharacteristic
52#10597292C2211yescharacteristic
53#10597289C2211yescharacteristic
54C22⋊(C19⋊C8)C2211yescharacteristic
55(C2×D19)⋊C8C2211yescharacteristic
56#10597274C2211yescharacteristic
57#10597273C2211yescharacteristic
58#10597273C2211yescharacteristic
59Dic19⋊C8C2211yescharacteristic
60C8×Dic19C2211yescharacteristic
61#41×C19—22no—
62#41×C19—41no—
63C2×Q8×C19—21no—
64C2×Q8×C19—22no—
65C2×Q8×C19—41no—
66C2×Q8×C19C2311yescharacteristic
67C2×Q8×C19C2311yescharacteristic
68C2×Q8×C19C2311yescharacteristic
69C2×D4×C19—21no—
70C2×D4×C19C2311yescharacteristic
71C22×C4×C19—21no—
72C22×C4×C19—21no—
73C22×C4×C19C2311yescharacteristic
74C2×C22⋊D19—21no—
75C2×C22⋊D19D411yescharacteristic
76C22×Dic19—21no—
77C22×Dic19—21no—
78Q8×D19—22no—
79Q8×D19—41no—
80#64543—22no—
81#64543—41no—
82C2×C4×D19—21no—
83C2×C4×D19C2311yescharacteristic
84C2×Dic38—21no—
85C2×Dic38C2311yescharacteristic
86C2×Dic38C2311yescharacteristic
87Q16×C19—22no—
88Q16×C19—22no—
89SD16×C19—22no—
90SD16×C19D414yescomplemented
91M16×C19—22no—
92C2×C8×C19C2311yescharacteristic
93C2×C8×C19C2311yescharacteristic
94C22⋊Dic19—21no—
95C22⋊Dic19—21no—
96C22⋊Dic19—21no—
97C22⋊Dic19D411yescharacteristic
98#64528—22no—
99#64528—41no—
100#64528—41no—
101#64526—22no—
102(C2×D19)⋊C4—21no—
103(C2×D19)⋊C4—21no—
104(C2×D19)⋊C4D411yescharacteristic
105C4⋊Dic19—21no—
106C4⋊Dic19C2311yescharacteristic
107C4⋊Dic19C2311yescharacteristic
108Dic19⋊C4—21no—
109Dic19⋊C4—21no—
110Dic19⋊C4—21no—
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×C19C2×D411yescharacteristic
125C22×D19C2×D411yescharacteristic
126Q8×C19—21no—
127Q8×C19—21no—
128Q8×C19—21no—
129Q8×C19—21no—
130Q8×C19—21no—
131Q8×C19—42no—
132Q8×C19C2×D412yes—
133D4×C19—21no—
134D4×C19—42no—
135D4×C19C2×D412yes—
136C2×C4×C19—21no—
137C2×C4×C19—21no—
138C2×C4×C19—21no—
139C2×C4×C19—21no—
140C2×C4×C19—21no—
141C2×C4×C19—42no—
142C2×C4×C19—42no—
143C2×C4×C19C2×D411yescharacteristic
144C2×C4×C19C2411yescharacteristic
145C22⋊D19—22no—
146C22⋊D19—42no—
147C2×Dic19—21no—
148C2×Dic19—21no—
149C2×Dic19—21no—
150C2×Dic19—21no—
151C2×Dic19—42no—
152C2×Dic19—42no—
153C2×Dic19C2×D411yescharacteristic
154C2×Dic19C2×D411yescharacteristic
155C2×Dic19C2×D411yescharacteristic
156C4×D19—21no—
157C4×D19—21no—
158C4×D19—42no—
159Dic38—21no—
160Dic38—21no—
161Dic38—21no—
162Dic38—21no—
163Dic38—42no—
164C8×C19—21no—
165C8×C19C2×D412yes—
166C19⋊C8—21no—
167C19⋊C8—21no—
168#3276—191nomaximal, Sylow
169C22×C19—22no—
170C22×C19—21no—
171C22×C19—21no—
172C22×C19—21no—
173C22×C19—41no—
174C22×C19—41no—
175C22×C19C22×D411yescharacteristic
176C2×D19—21no—
177C2×D19—21no—
178C2×D19—21no—
179C4×C19—22no—
180C4×C19—21no—
181C4×C19—41no—
182C4×C19—41no—
183C4×C19C22×D411yescharacteristic
184C4×C19H(5,𝔽2)11yescharacteristic
185Dic19—21no—
186Dic19—21no—
187Dic19—41no—
188Dic19—41no—
189Dic19—41no—
190Dic19—41no—
191Dic19#13712yescomplemented
192C2×#137—191no—
193C2×#137D1911yescharacteristic, complemented
194D4×Q8—191no—
195#547—191no—
196#494—191no—
197#470—191no—
198#470—191no—
199#462—191no—
200#461—191no—
201#452—191no—
202#452—191no—
203#451—191no—
204#451—191no—
205C4×SD16—191no—
206#436—191no—
207C2×C19—41no—
208C2×C19—42no—
209C2×C19D4211yescharacteristic
210C2×C19C2×#13711yescharacteristic
211C2×C19#57811yescharacteristic
212D19—41no—
213C2×#41—191no—
214C2×#41C2×D1911yescharacteristic
215C22×Q8—191no—
216C22×Q8C2×D1911yescharacteristic
217#137—24no—
218#137—384no—
219C2×Q16—191no—
220C2×Q16—191no—
221C2×Q16—191no—
222C2×Q16—191no—
223C2×Q16C2×D1911yescharacteristic
224C2×Q16C2×D1911yescharacteristic
225C2×SD16—191no—
226C2×SD16C2×D1911yescharacteristic
227C2×SD16C2×D1911yescharacteristic
228C2×M16—191no—
229C2×M16C2×D1911yescharacteristic
230C4⋊Q8—191no—
231C4⋊Q8—191no—
232C4⋊Q8—381no—
233#123—381no—
234#123—381no—
235C22⋊Q8—191no—
236C22⋊Q8—191no—
237C22⋊Q8—191no—
238C22⋊Q8—191no—
239C22⋊Q8—381no—
240C22⋊Q8—381no—
241#121—381no—
242C4×Q8—191no—
243C4×D4—191no—
244C4×D4—191no—
245C4×D4—381no—
246C2×C4⋊C4—381no—
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—
257C4×C8—191no—
258C19#327611yescharacteristic, complemented, Sylow
259#41—22no—
260#41—41no—
261#41—382no—
262#41—761no—
263C2×Q8—21no—
264C2×Q8—22no—
265C2×Q8—41no—
266C2×Q8—191no—
267C2×Q8—191no—
268C2×Q8—381no—
269C2×Q8—382no—
270C2×Q8—761no—
271C2×Q8C22×D1911yescharacteristic
272C2×Q8C22×D1911yescharacteristic
273C2×Q8C22×D1911yescharacteristic
274C2×D4—21no—
275C2×D4—191no—
276C2×D4—381no—
277C2×D4C22×D1911yescharacteristic
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—191no—
281C22×C4—381no—
282C22×C4—381no—
283C22×C4—381no—
284C22×C4C22×D1911yescharacteristic
285Q16—22no—
286Q16—22no—
287Q16—382no—
288Q16—382no—
289Q16—761no—
290Q16—761no—
291SD16—22no—
292SD16—382no—
293SD16C22⋊D1914yescomplemented
294M16—22no—
295M16—382no—
296C2×C8—191no—
297C2×C8—191no—
298C2×C8C22×D1911yescharacteristic
299C2×C8C22×D1911yescharacteristic
300C4⋊C4—191no—
301C4⋊C4—191no—
302C4⋊C4—191no—
303C4⋊C4—381no—
304C4⋊C4—381no—
305C4⋊C4—381no—
306C4⋊C4—381no—
307C4⋊C4—381no—
308C4⋊C4—381no—
309C4⋊C4—381no—
310C4⋊C4—381no—
311C4⋊C4—381no—
312C22⋊C4—191no—
313C22⋊C4—191no—
314C22⋊C4—381no—
315C22⋊C4—381no—
316C22⋊C4—381no—
317C22⋊C4—381no—
318C22⋊C4—381no—
319C42—191no—
320C42—381no—
321C23—21no—
322C23—191no—
323C23D4×D1911yescharacteristic
324Q8—21no—
325Q8—21no—
326Q8—21no—
327Q8—21no—
328Q8—21no—
329Q8—42no—
330Q8—381no—
331Q8—381no—
332Q8—381no—
333Q8—381no—
334Q8—762no—
335Q8C2×C22⋊D1912yes—
336D4—21no—
337D4—42no—
338D4—382no—
339D4—762no—
340D4C2×C22⋊D1912yes—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—42no—
347C2×C4—42no—
348C2×C4—191no—
349C2×C4—191no—
350C2×C4—191no—
351C2×C4—381no—
352C2×C4—381no—
353C2×C4—381no—
354C2×C4—381no—
355C2×C4—381no—
356C2×C4—381no—
357C2×C4—762no—
358C2×C4—762no—
359C2×C4—762no—
360C2×C4D4×D1911yescharacteristic
361C2×C4C23×D1911yescharacteristic
362C8—21no—
363C8—381no—
364C8—381no—
365C8C2×C22⋊D1912yes—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—22no—
370C22—41no—
371C22—41no—
372C22—381no—
373C22—381no—
374C22—381no—
375C22C2×D4×D1911yescharacteristic
376C4—21no—
377C4—22no—
378C4—41no—
379C4—41no—
380C4—192no—
381C4—381no—
382C4—381no—
383C4—761no—
384C4—761no—
385C4—761no—
386C4—761no—
387C4#1059743011yescharacteristic
388C4C22×C22⋊D1911yescharacteristic
389C2—41no—
390C2—42no—
391C2—761no—
392C2D4×C22⋊D1911yescharacteristic
393C2#137×D1911yescharacteristic
394C2#1192736011yescharacteristic
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC2×C19×#137C2
socleC22×C19C22×D4
prime radical#11927193C2
hypercenterC2×#137D19
hypocenterC19#3276
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
1. C2×#10597361C2semidirect
2. Q8×C22⋊D19C2semidirect
4. #11926922C2semidirect
5. #11926802C2semidirect
6. #11926799C2semidirect
7. #11926752C2semidirect
8. #11926747C2semidirect
9. #11926706C2semidirect
10. #11926703C2semidirect
11. #11926700C2semidirect
12. #11926698C2semidirect
13. SD16×Dic19C2semidirect
14. #11926620C2semidirect
15. C2×C19×#137C2semidirect
90. SD16×C19D4semidirect
191. Dic19#137semidirect
193. C2×#137D19semidirect
258. C19#3276semidirect
293. SD16C22⋊D19semidirect

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
#119271932
#119269222
#119268022
#119267992
#119267522
#119267472
#119267062
#119267032
#119267002
#119266982
SD16×Dic192
#119266202
C2×C19×#1372
#327619