Finite Group Databasebeta

← #14575340

Subgroups — #14575340

Order 2432.

504 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10597396C211yesmaximal, characteristic, complemented
2C2×SD16×D19C211yesmaximal, characteristic, complemented
3#11927204C211yesmaximal, characteristic, complemented
4#11927182C211yesmaximal, characteristic, complemented
5#11926929C211yesmaximal, characteristic, complemented
6#11926776C211yesmaximal, characteristic, complemented
7#11926775C211yesmaximal, characteristic, complemented
8#11926769C211yesmaximal, characteristic, complemented
9#11926761C211yesmaximal, characteristic, complemented
10#11926698C211yesmaximal, characteristic, complemented
11#11926691C211yesmaximal, characteristic, complemented
12#11926679C211yesmaximal, characteristic, complemented
13#11926635C211yesmaximal, characteristic, complemented
14(C22⋊D19)⋊C8C211yesmaximal, characteristic, complemented
15C19×#452C211yesmaximal, characteristic, complemented
16C2×#41×C19C2211yescharacteristic
17C2×Q8×D19C2211yescharacteristic
18C2×D4×D19C2211yescharacteristic
19C2×#64541C2211yescharacteristic, complemented
20C2×Q16×C19C2211yescharacteristic, complemented
21C2×SD16×C19C2211yescharacteristic
22C19×C22⋊Q8C2211yescharacteristic, complemented
23#10597396—24no—
24#10597393C2211yescharacteristic
25#10597393C2211yescharacteristic, complemented
26#10597392C2211yescharacteristic
27C2×#64528C2211yescharacteristic, complemented
28C2×#64527C2211yescharacteristic
29C2×#64527C2211yescharacteristic, complemented
30#10597385—21no—
31#10597383—21no—
32D4×Dic19C2211yescharacteristic
33C2×#64526C2211yescharacteristic
34C2×#64525C2211yescharacteristic
35#10597376C2211yescharacteristic
36#10597375—21no—
37C4×C22⋊D19C2211yescharacteristic
38C2×(C2×D19)⋊C4—21no—
39C22×C19⋊C8C2211yescharacteristic, complemented
40SD16×D19—24no—
41C2×D152C2211yescharacteristic
42C2×#64516C2211yescharacteristic
43C2×C8×D19C2211yescharacteristic
44#10597342—21no—
45#10597341C2211yescharacteristic
46#10597339—21no—
47#10597333C2211yescharacteristic, complemented
48#10597331—21no—
49#10597330—21no—
50C19×#103C2211yescharacteristic, complemented
51C19×#102C2211yescharacteristic
52C19×C22⋊C8C2211yescharacteristic, complemented
53#10597292C2211yescharacteristic, complemented
54#10597278C2211yescharacteristic, complemented
55(C2×D19)⋊C8C2211yescharacteristic
56#10597273C2211yescharacteristic, complemented
57Dic19⋊C8C2211yescharacteristic, complemented
58C8×Dic19C2211yescharacteristic, complemented
59#10597266C2211yescharacteristic
60#10597265C2211yescharacteristic, complemented
61C23×D19—21no—
62#41×C19—22no—
63#41×C19—41no—
64C2×Q8×C19C2311yescharacteristic
65C2×Q8×C19C2311yescharacteristic
66C2×D4×C19—21no—
67C2×D4×C19C2311yescharacteristic
68C22×C4×C19—21no—
69C22×C4×C19C2311yescharacteristic
70C2×C22⋊D19—21no—
71C2×C22⋊D19—21no—
72C2×C22⋊D19—21no—
73C2×C22⋊D19D411yescharacteristic
74C22×Dic19—21no—
75Q8×D19—22no—
76Q8×D19—41no—
77D4×D19—22no—
78D4×D19—41no—
79#64541—22no—
80#64541—41no—
81C2×D76—21no—
82C2×D76C2311yescharacteristic
83C2×D76C2311yescharacteristic
84C2×C4×D19—21no—
85C2×C4×D19—21no—
86C2×C4×D19C2311yescharacteristic
87C2×Dic38—21no—
88C2×Dic38C2311yescharacteristic
89Q16×C19—41no—
90SD16×C19—22no—
91C2×C8×C19C2311yescharacteristic
92C2×C8×C19C2311yescharacteristic
93C4⋊C4×C19—21no—
94C4⋊C4×C19C2311yescharacteristic
95C22⋊C4×C19—21no—
96C22⋊Dic19—21no—
97C22⋊Dic19D411yescharacteristic
98#64528—22no—
99#64527—22no—
100#64527—22no—
101#64526D414yescomplemented
102#64525—22no—
103(C2×D19)⋊C4—21no—
104(C2×D19)⋊C4—21no—
105(C2×D19)⋊C4—21no—
106(C2×D19)⋊C4—21no—
107(C2×D19)⋊C4—21no—
108(C2×D19)⋊C4—21no—
109(C2×D19)⋊C4—21no—
110(C2×D19)⋊C4D411yescharacteristic
111C4⋊Dic19C2311yescharacteristic
112Dic19⋊C4—21no—
113Dic19⋊C4—21no—
114Dic19⋊C4D411yescharacteristic
115C4×Dic19—21no—
116C4×Dic19C2311yescharacteristic
117C2×C19⋊C8—22no—
118C2×C19⋊C8C2311yescharacteristic
119C2×C19⋊C8C2311yescharacteristic
120D152—41no—
121#64516—22no—
122C8×D19—22no—
123C23×C19—21no—
124C23×C19C2×D411yescharacteristic
125C22×D19—21no—
126C22×D19—21no—
127C22×D19—42no—
128C22×D19—42no—
129C22×D19—81no—
130C22×D19C2×D411yescharacteristic
131Q8×C19—21no—
132Q8×C19—21no—
133Q8×C19—21no—
134Q8×C19—21no—
135D4×C19—21no—
136D4×C19—42no—
137D4×C19C2×D412yes—
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×C19C2×D411yescharacteristic
145C2×C4×C19C2411yescharacteristic
146C22⋊D19—22no—
147C22⋊D19—42no—
148C22⋊D19—42no—
149C22⋊D19—81no—
150C2×Dic19—21no—
151C2×Dic19—21no—
152C2×Dic19—81no—
153C2×Dic19C2×D411yescharacteristic
154C2×Dic19C2×D411yescharacteristic
155C2×Dic19C2×D411yescharacteristic
156D76—21no—
157D76—21no—
158D76—21no—
159D76—21no—
160D76—42no—
161C4×D19—21no—
162C4×D19—21no—
163C4×D19—42no—
164C4×D19—42no—
165Dic38—21no—
166Dic38—42no—
167Dic38C2×D412yes—
168C8×C19—21no—
169C8×C19—21no—
170C19⋊C8—21no—
171C19⋊C8C2×D412yes—
172#3282—191nomaximal, Sylow
173C22×C19—21no—
174C22×C19—22no—
175C22×C19—21no—
176C22×C19—21no—
177C22×C19—41no—
178C22×C19—41no—
179C22×C19C22×D411yescharacteristic
180C2×D19—21no—
181C2×D19—21no—
182C2×D19—41no—
183C2×D19—41no—
184C2×D19—41no—
185C2×D19—41no—
186C2×D19—41no—
187C2×D19—41no—
188C2×D19—84no—
189C2×D19#13512yescomplemented
190C4×C19—21no—
191C4×C19—41no—
192C4×C19—41no—
193C4×C19—41no—
194C4×C19C22×D411yescharacteristic
195C4×C19H(5,𝔽2)11yescharacteristic
196Dic19—22no—
197Dic19—21no—
198Dic19—21no—
199Dic19—21no—
200Dic19—41no—
201C2×#135—191no—
202C22×SD16—191no—
203#548—191no—
204#546—191no—
205#495—191no—
206#465—191no—
207#465—191no—
208#464—191no—
209#463—191no—
210#452D1911yescharacteristic, complemented
211#451—191no—
212#449—191no—
213#447—191no—
214C4×SD16—191no—
215C8×D4—191no—
216C2×C19—42no—
217C2×C19—41no—
218C2×C19D4211yescharacteristic
219C2×C19C2×#13511yescharacteristic
220C2×C19#57711yescharacteristic
221D19—22no—
222D19—81no—
223D19—81no—
224C2×#41—191no—
225C2×#41C2×D1911yescharacteristic
226C22×Q8—191no—
227C22×D4—191no—
228#135—384no—
229C2×Q16—191no—
230C2×Q16C2×D1911yescharacteristic, complemented
231C2×SD16—191no—
232C2×SD16—191no—
233C2×SD16—191no—
234C2×SD16—191no—
235C2×SD16—384no—
236C2×SD16C2×D1911yescharacteristic
237C2×D8—191no—
238C2×D8—191no—
239C22×C8—191no—
240C22×C8—191no—
241#124—191no—
242#124—191no—
243#124—381no—
244#123—381no—
245C22⋊Q8—191no—
246C22⋊Q8—381no—
247C22⋊Q8C2×D1911yescharacteristic, complemented
248#121—191no—
249#121—191no—
250#121—381no—
251#121—381no—
252#120—381no—
253C4×Q8—191no—
254C4×D4—191no—
255C4×D4—191no—
256C4×D4—381no—
257C2×C22⋊C4—381no—
258#106—191no—
259C4⋊C8—191no—
260#103—191no—
261#103—191no—
262#103C2×D1911yescharacteristic, complemented
263#102—191no—
264#102—191no—
265#102C2×D1911yescharacteristic
266C22⋊C8—191no—
267C22⋊C8C2×D1911yescharacteristic, complemented
268C4×C8—191no—
269C19#328211yescharacteristic, complemented, Sylow
270C24—381no—
271#41—22no—
272#41—41no—
273#41—382no—
274#41—761no—
275C2×Q8—191no—
276C2×Q8—381no—
277C2×Q8—382no—
278C2×Q8—761no—
279C2×Q8C22×D1911yescharacteristic
280C2×Q8C22×D1911yescharacteristic
281C2×D4—21no—
282C2×D4—191no—
283C2×D4—191no—
284C2×D4—191no—
285C2×D4—381no—
286C2×D4—381no—
287C2×D4—382no—
288C2×D4—381no—
289C2×D4—381no—
290C2×D4—761no—
291C2×D4C22×D1911yescharacteristic
292C22×C4—21no—
293C22×C4—191no—
294C22×C4—381no—
295C22×C4—381no—
296C22×C4—381no—
297C22×C4C22×D1911yescharacteristic
298Q16—41no—
299Q16—382no—
300SD16—22no—
301SD16—194no—
302SD16—382no—
303SD16—382no—
304SD16—382no—
305D8—382no—
306D8—761no—
307C2×C8—191no—
308C2×C8—191no—
309C2×C8—382no—
310C2×C8—382no—
311C2×C8C22×D1911yescharacteristic
312C2×C8C22×D1911yescharacteristic
313C4⋊C4—21no—
314C4⋊C4—191no—
315C4⋊C4—191no—
316C4⋊C4—381no—
317C4⋊C4—381no—
318C4⋊C4C22×D1911yescharacteristic
319C22⋊C4—21no—
320C22⋊C4—191no—
321C22⋊C4—191no—
322C22⋊C4—381no—
323C22⋊C4—381no—
324C22⋊C4—381no—
325C22⋊C4—381no—
326C22⋊C4—381no—
327C22⋊C4—381no—
328C22⋊C4—381no—
329C22⋊C4—381no—
330C42—191no—
331C42—381no—
332C23—21no—
333C23—191no—
334C23—381no—
335C23—381no—
336C23—762no—
337C23—762no—
338C23—1521no—
339C23D4×D1911yescharacteristic
340Q8—21no—
341Q8—21no—
342Q8—21no—
343Q8—21no—
344Q8—192no—
345Q8—381no—
346Q8—762no—
347D4—21no—
348D4—42no—
349D4—382no—
350D4—381no—
351D4—381no—
352D4—381no—
353D4—381no—
354D4—762no—
355D4—762no—
356D4—762no—
357D4—1521no—
358D4D4×D1912yes—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—42no—
365C2×C4—191no—
366C2×C4—191no—
367C2×C4—191no—
368C2×C4—381no—
369C2×C4—381no—
370C2×C4—381no—
371C2×C4—381no—
372C2×C4—762no—
373C2×C4—762no—
374C2×C4—1521no—
375C2×C4D4×D1911yescharacteristic
376C2×C4C23×D1911yescharacteristic
377C8—21no—
378C8—21no—
379C8—192no—
380C8—381no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—22no—
385C22—41no—
386C22—41no—
387C22—192no—
388C22—381no—
389C22—381no—
390C22—761no—
391C22—761no—
392C22—761no—
393C22—761no—
394C22—761no—
395C22—761no—
396C22—1524no—
397C22C2×D4×D1911yescharacteristic
398C4—21no—
399C4—41no—
400C4—41no—
401C4—41no—
402C4—381no—
403C4—381no—
404C4—381no—
405C4—382no—
406C4—761no—
407C4C2×D4×D1911yescharacteristic
408C4#1059743011yescharacteristic
409C2—41no—
410C2—42no—
411C2—382no—
412C2—1521no—
413C2—1521no—
414C2#1192717611yescharacteristic
415C2#135×D1911yescharacteristic
416C2#1192735311yescharacteristic
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#452C2
socleC22×C19C22×D4
hypercenter#452D19
hypocenterC19#3282
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
1. C2×#10597396C2semidirect
2. C2×SD16×D19C2semidirect
3. #11927204C2semidirect
4. #11927182C2semidirect
5. #11926929C2semidirect
6. #11926776C2semidirect
7. #11926775C2semidirect
8. #11926769C2semidirect
9. #11926761C2semidirect
10. #11926698C2semidirect
11. #11926691C2semidirect
12. #11926679C2semidirect
13. #11926635C2semidirect
14. (C22⋊D19)⋊C8C2semidirect
15. C19×#452C2semidirect
19. C2×#64541C22semidirect
20. C2×Q16×C19C22semidirect
22. C19×C22⋊Q8C22semidirect
25. #10597393C22semidirect
27. C2×#64528C22semidirect
29. C2×#64527C22semidirect
39. C22×C19⋊C8C22semidirect
47. #10597333C22semidirect
50. C19×#103C22semidirect
52. C19×C22⋊C8C22semidirect
53. #10597292C22semidirect
54. #10597278C22semidirect
56. #10597273C22semidirect
57. Dic19⋊C8C22semidirect
58. C8×Dic19C22semidirect
60. #10597265C22semidirect
101. #64526D4semidirect
189. C2×D19#135semidirect
210. #452D19semidirect
230. C2×Q16C2×D19semidirect
247. C22⋊Q8C2×D19semidirect
262. #103C2×D19semidirect
267. C22⋊C8C2×D19semidirect
269. C19#3282semidirect

Maximal subgroups

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

subgroupindex
C2×#105973962
C2×SD16×D192
#119272042
#119271822
#119269292
#119267762
#119267752
#119267692
#119267612
#119266982
#119266912
#119266792
#119266352
(C22⋊D19)⋊C82
C19×#4522
#328219