Finite Group Databasebeta

← #14575270

Subgroups — #14575270

Order 2432.

498 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×#10597361C211yesmaximal, characteristic, complemented
2C2×#10597378C211yesmaximal, characteristic, complemented
3#11927204C211yesmaximal, characteristic, complemented
4#11927188C211yesmaximal, characteristic, complemented
5#11926925C211yesmaximal, characteristic, complemented
6#11926800C211yesmaximal, characteristic, complemented
7#11926796C211yesmaximal, characteristic, complemented
8#11926765C211yesmaximal, characteristic, complemented
9#11926761C211yesmaximal, characteristic, complemented
10#11926708C211yesmaximal, characteristic, complemented
11#11926690C211yesmaximal, characteristic, complemented
12#11926681C211yesmaximal, characteristic, complemented
13#11926635C211yesmaximal, characteristic, complemented
14#11926619C211yesmaximal, characteristic, complemented
15C19×#450C211yesmaximal, characteristic, complemented
16C22×D4×C19C2211yescharacteristic
17C2×Q8×D19C2211yescharacteristic, complemented
18C2×#64543C2211yescharacteristic
19C2×#64541C2211yescharacteristic
20C2×SD16×C19C2211yescharacteristic
21C2×SD16×C19C2211yescharacteristic
22C19×C22⋊Q8C2211yescharacteristic
23#10597399—21no—
24C2×C22⋊Dic19—21no—
25#10597393C2211yescharacteristic, complemented
26C2×#64528C2211yescharacteristic, complemented
27#10597385—21no—
28#10597384C2211yescharacteristic
29#10597382C2211yescharacteristic
30#10597381—21no—
31D4×Dic19C2211yescharacteristic
32C2×#64526C2211yescharacteristic
33C2×#64526C2211yescharacteristic
34#10597378—24no—
35C2×#64525C2211yescharacteristic
36C2×#64525C2211yescharacteristic
37C4×C22⋊D19C2211yescharacteristic
38#10597370C2211yescharacteristic
39C2×#64520C2211yescharacteristic
40#10597361—24no—
41C2×Dic76C2211yescharacteristic, complemented
42C2×#64516C2211yescharacteristic, complemented
43C2×#64515C2211yescharacteristic, complemented
44#10597342—21no—
45#10597341C2211yescharacteristic, complemented
46#10597339—21no—
47#10597333C2211yescharacteristic, complemented
48#10597331—21no—
49#10597330—21no—
50C19×#102C2211yescharacteristic
51C19×#102C2211yescharacteristic
52C19×C22⋊C8C2211yescharacteristic
53#10597292C2211yescharacteristic, complemented
54#10597278C2211yescharacteristic, complemented
55(C2×D19)⋊C8C2211yescharacteristic, complemented
56#10597273C2211yescharacteristic, complemented
57Dic19⋊C8C2211yescharacteristic, complemented
58C8×Dic19C2211yescharacteristic, complemented
59#10597267C2211yescharacteristic, complemented
60#10597265C2211yescharacteristic, complemented
61C24×C19—21no—
62C2×Q8×C19C2311yescharacteristic
63C2×D4×C19—22no—
64C2×D4×C19—21no—
65C2×D4×C19—41no—
66C2×D4×C19C2311yescharacteristic
67C2×D4×C19C2311yescharacteristic
68C22×C4×C19C2311yescharacteristic
69C2×C22⋊D19—21no—
70C2×C22⋊D19—21no—
71C2×C22⋊D19—21no—
72C2×C22⋊D19D411yescharacteristic
73C22×Dic19—21no—
74C22×Dic19—21no—
75Q8×D19—22no—
76Q8×D19—41no—
77#64543—22no—
78#64543—41no—
79#64541—22no—
80#64541—41no—
81C2×D76—21no—
82C2×D76C2311yescharacteristic
83C2×C4×D19—21no—
84C2×C4×D19—21no—
85C2×C4×D19C2311yescharacteristic
86C2×Dic38—21no—
87C2×Dic38C2311yescharacteristic
88C2×Dic38C2311yescharacteristic
89SD16×C19—22no—
90SD16×C19—41no—
91C2×C8×C19C2311yescharacteristic
92C2×C8×C19C2311yescharacteristic
93C4⋊C4×C19—21no—
94C4⋊C4×C19C2311yescharacteristic
95C22⋊C4×C19—21no—
96C22⋊Dic19—21no—
97C22⋊Dic19—21no—
98C22⋊Dic19—21no—
99C22⋊Dic19—21no—
100C22⋊Dic19—21no—
101C22⋊Dic19D411yescharacteristic
102#64528—22no—
103#64526—22no—
104#64526D414yescomplemented
105#64525—22no—
106#64525—22no—
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
117#64520—22no—
118C2×C19⋊C8C2311yescharacteristic
119C2×C19⋊C8C2311yescharacteristic
120Dic76—22no—
121#64516—41no—
122#64515—22no—
123C23×C19—21no—
124C23×C19—21no—
125C23×C19—42no—
126C23×C19—42no—
127C23×C19—81no—
128C23×C19C2×D411yescharacteristic
129C22×D19—21no—
130C22×D19C2×D411yescharacteristic
131Q8×C19—21no—
132Q8×C19—21no—
133D4×C19—21no—
134D4×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×C19C2×D411yescharacteristic
143C2×C4×C19C2411yescharacteristic
144C22⋊D19—41no—
145C22⋊D19—42no—
146C22⋊D19—42no—
147C22⋊D19—81no—
148C2×Dic19—21no—
149C2×Dic19—21no—
150C2×Dic19—21no—
151C2×Dic19—42no—
152C2×Dic19—81no—
153C2×Dic19C2×D411yescharacteristic
154C2×Dic19C2×D411yescharacteristic
155C2×Dic19C2×D411yescharacteristic
156D76—21no—
157D76—21no—
158D76—42no—
159C4×D19—21no—
160C4×D19—21no—
161C4×D19—42no—
162C4×D19—42no—
163Dic38—21no—
164Dic38—21no—
165Dic38—21no—
166Dic38—42no—
167Dic38C2×D412yes—
168C8×C19—21no—
169C8×C19—21no—
170C19⋊C8—21no—
171C19⋊C8C2×D412yes—
172#3275—191nomaximal, Sylow
173C22×C19—22no—
174C22×C19—21no—
175C22×C19—21no—
176C22×C19—21no—
177C22×C19—41no—
178C22×C19—41no—
179C22×C19—41no—
180C22×C19—41no—
181C22×C19—41no—
182C22×C19—84no—
183C22×C19C22×D411yescharacteristic
184C2×D19—21no—
185C2×D19—21no—
186C2×D19—21no—
187C2×D19—41no—
188C2×D19—41no—
189C2×D19—41no—
190C4×C19—21no—
191C4×C19—41no—
192C4×C19—41no—
193C4×C19C22×D411yescharacteristic
194C4×C19H(5,𝔽2)11yescharacteristic
195Dic19—22no—
196Dic19—21no—
197Dic19—21no—
198Dic19—21no—
199Dic19—41no—
200Dic19—41no—
201C2×#137—191no—
202C2×AGL(1,ℤ/8)—191no—
203#548—191no—
204#546—191no—
205#495—191no—
206#470—191no—
207#469—191no—
208#464—191no—
209#463—191no—
210#452—191no—
211#450D1911yescharacteristic, complemented
212#449—191no—
213#448—191no—
214C4×SD16—191no—
215#436—191no—
216C2×C19—41no—
217C2×C19—42no—
218C2×C19—81no—
219C2×C19D4211yescharacteristic
220C2×C19#57511yescharacteristic
221C2×C19#57711yescharacteristic
222D19—41no—
223D19—81no—
224C2×#41—191no—
225C2×#41—191no—
226C22×Q8—191no—
227C22×D4C2×D1911yescharacteristic
228#137—384no—
229AGL(1,ℤ/8)—384no—
230C2×Q16—191no—
231C2×Q16—191no—
232C2×SD16—191no—
233C2×SD16—191no—
234C2×SD16—191no—
235C2×SD16C2×D1911yescharacteristic
236C2×SD16C2×D1911yescharacteristic
237C2×D8—191no—
238C2×D8—191no—
239C2×M16—191no—
240C2×M16—191no—
241#124—191no—
242#124—191no—
243#124—381no—
244#123—381no—
245C22⋊Q8—191no—
246C22⋊Q8—381no—
247C22⋊Q8C2×D1911yescharacteristic
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#103—191no—
263#102—191no—
264#102C2×D1911yescharacteristic
265#102C2×D1911yescharacteristic
266C22⋊C8—191no—
267C22⋊C8C2×D1911yescharacteristic
268C4×C8—191no—
269C19#327511yescharacteristic, complemented, Sylow
270C24—21no—
271#41—382no—
272#41—382no—
273#41—761no—
274#41—761no—
275C2×Q8—191no—
276C2×Q8—191no—
277C2×Q8—381no—
278C2×Q8—382no—
279C2×Q8—761no—
280C2×Q8C22×D1911yescharacteristic
281C2×D4—22no—
282C2×D4—21no—
283C2×D4—41no—
284C2×D4—191no—
285C2×D4—191no—
286C2×D4—381no—
287C2×D4—381no—
288C2×D4—381no—
289C2×D4—381no—
290C2×D4C22×D1911yescharacteristic
291C2×D4C22×D1911yescharacteristic
292C22×C4—191no—
293C22×C4—381no—
294C22×C4—381no—
295C22×C4—381no—
296C22×C4—381no—
297C22×C4C22×D1911yescharacteristic
298Q16—382no—
299Q16—382no—
300SD16—22no—
301SD16—41no—
302SD16—194no—
303SD16—382no—
304SD16—761no—
305D8—382no—
306D8—382no—
307M16—382no—
308M16—382no—
309C2×C8—191no—
310C2×C8—191no—
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—21no—
334C23—42no—
335C23—42no—
336C23—81no—
337C23—191no—
338C23—381no—
339C23D4×D1911yescharacteristic
340Q8—21no—
341Q8—21no—
342Q8—192no—
343Q8—381no—
344Q8—381no—
345Q8—381no—
346Q8—762no—
347D4—21no—
348D4—21no—
349D4—21no—
350D4—42no—
351D4—381no—
352D4—381no—
353D4—762no—
354D4—761no—
355D4—762no—
356D4—762no—
357D4—1521no—
358D4D4×D1912yes—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—191no—
364C2×C4—191no—
365C2×C4—191no—
366C2×C4—381no—
367C2×C4—381no—
368C2×C4—381no—
369C2×C4—381no—
370C2×C4—381no—
371C2×C4—762no—
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—41no—
388C22—41no—
389C22—41no—
390C22—84no—
391C22—381no—
392C22—381no—
393C22—381no—
394C22—761no—
395C22—761no—
396C22—761no—
397C22C2×D4×D1911yescharacteristic
398C4—21no—
399C4—41no—
400C4—41no—
401C4—381no—
402C4—381no—
403C4—381no—
404C4—382no—
405C4—761no—
406C4—761no—
407C4C2×D4×D1911yescharacteristic
408C4#1059743011yescharacteristic
409C2—41no—
410C2—42no—
411C2—81no—
412C2—761no—
413C2—1521no—
414C2#1192717611yescharacteristic
415C2#1192734011yescharacteristic
416C2#1192735011yescharacteristic
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#450C2
socleC22×C19C22×D4
hypercenter#450D19
hypocenterC19#3275
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. C2×#10597361C2semidirect
2. C2×#10597378C2semidirect
3. #11927204C2semidirect
4. #11927188C2semidirect
5. #11926925C2semidirect
6. #11926800C2semidirect
7. #11926796C2semidirect
8. #11926765C2semidirect
9. #11926761C2semidirect
10. #11926708C2semidirect
11. #11926690C2semidirect
12. #11926681C2semidirect
13. #11926635C2semidirect
14. #11926619C2semidirect
15. C19×#450C2semidirect
17. C2×Q8×D19C22semidirect
25. #10597393C22semidirect
26. C2×#64528C22semidirect
41. C2×Dic76C22semidirect
42. C2×#64516C22semidirect
43. C2×#64515C22semidirect
45. #10597341C22semidirect
47. #10597333C22semidirect
53. #10597292C22semidirect
54. #10597278C22semidirect
55. (C2×D19)⋊C8C22semidirect
56. #10597273C22semidirect
57. Dic19⋊C8C22semidirect
58. C8×Dic19C22semidirect
59. #10597267C22semidirect
60. #10597265C22semidirect
104. #64526D4semidirect
211. #450D19semidirect
269. C19#3275semidirect

Maximal subgroups

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

subgroupindex
C2×#105973612
C2×#105973782
#119272042
#119271882
#119269252
#119268002
#119267962
#119267652
#119267612
#119267082
#119266902
#119266812
#119266352
#119266192
C19×#4502
#327519