Finite Group Databasebeta

← #14575172

Subgroups — #14575172

Order 2432.

510 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10597357C211yesmaximal, characteristic, complemented
2C2×#10597350C211yesmaximal, characteristic, complemented
3#11927212C211yesmaximal, characteristic, complemented
4#11927191C211yesmaximal, characteristic, complemented
5#11926932C211yesmaximal, characteristic, complemented
6#11926791C211yesmaximal, characteristic, complemented
7#11926765C211yesmaximal, characteristic, complemented
8#11926738C211yesmaximal, characteristic, complemented
9#11926707C211yesmaximal, characteristic, complemented
10#11926687C211yesmaximal, characteristic, complemented
11#11926687C211yesmaximal, characteristic, complemented
12#11926679C211yesmaximal, characteristic, complemented
13#11926643C211yesmaximal, characteristic, complemented
14#11926615C211yesmaximal, characteristic, complemented
15C19×#466C211yesmaximal, characteristic, complemented
16C2×#64543C2211yescharacteristic
17C2×D4×D19C2211yescharacteristic
18C2×#64541C2211yescharacteristic
19C2×#64541C2211yescharacteristic, complemented
20C2×D8×C19C2211yescharacteristic
21C22×C8×C19C2211yescharacteristic, complemented
22C19×#121C2211yescharacteristic
23C19×#121C2211yescharacteristic, complemented
24#10597386—21no—
25#10597386C2211yescharacteristic, complemented
26#10597385—21no—
27#10597384—21no—
28#10597383—21no—
29#10597382C2211yescharacteristic
30C2×#64526C2211yescharacteristic
31C2×#64526C2211yescharacteristic, complemented
32C2×#64525C2211yescharacteristic
33C2×#64525C2211yescharacteristic
34C4×C22⋊D19C2211yescharacteristic
35#10597357—24no—
36C2×Dic76C2211yescharacteristic, complemented
37#10597350—24no—
38C2×D152C2211yescharacteristic
39C2×#64516C2211yescharacteristic
40C2×#64516C2211yescharacteristic, complemented
41C2×#64515C2211yescharacteristic
42#10597343C2211yescharacteristic
43#10597341C2211yescharacteristic
44#10597339C2211yescharacteristic
45#10597333C2211yescharacteristic, complemented
46#10597330—21no—
47#10597329—21no—
48(C22⋊D19)⋊C4—21no—
49C22⋊C4×D19—21no—
50C19×#107C2211yescharacteristic, complemented
51C19×#102C2211yescharacteristic
52C19×#102C2211yescharacteristic, complemented
53C22⋊(C19⋊C8)C2211yescharacteristic, complemented
54(C2×D19)⋊C8C2211yescharacteristic
55#10597272C2211yescharacteristic, complemented
56Dic19⋊C8C2211yescharacteristic, complemented
57#10597267C2211yescharacteristic, complemented
58#10597267C2211yescharacteristic, complemented
59#10597266C2211yescharacteristic
60#10597266C2211yescharacteristic, complemented
61C23×D19—21no—
62C2×D4×C19—21no—
63C2×D4×C19—21no—
64C2×D4×C19C2311yescharacteristic
65C2×D4×C19C2311yescharacteristic
66C22×C4×C19C2311yescharacteristic
67C2×C22⋊D19—21no—
68C2×C22⋊D19—21no—
69C2×C22⋊D19—21no—
70C2×C22⋊D19—21no—
71C2×C22⋊D19—21no—
72C2×C22⋊D19—21no—
73C2×C22⋊D19D411yescharacteristic
74C22×Dic19—21no—
75#64543—22no—
76#64543—41no—
77D4×D19—22no—
78D4×D19—41no—
79#64541—22no—
80#64541—22no—
81#64541—41no—
82#64541—41no—
83C2×D76—21no—
84C2×D76C2311yescharacteristic
85C2×D76C2311yescharacteristic
86C2×C4×D19—21no—
87C2×C4×D19—21no—
88C2×C4×D19—21no—
89C2×C4×D19C2311yescharacteristic
90C2×Dic38C2311yescharacteristic
91C2×Dic38C2311yescharacteristic
92D8×C19—22no—
93C2×C8×C19—22no—
94C2×C8×C19C2311yescharacteristic
95C2×C8×C19C2311yescharacteristic
96C4⋊C4×C19C2311yescharacteristic
97C4⋊C4×C19C2311yescharacteristic
98C22⋊C4×C19—21no—
99C22⋊C4×C19—21no—
100C22⋊Dic19—21no—
101C22⋊Dic19—21no—
102C22⋊Dic19D411yescharacteristic
103#64526—22no—
104#64526—41no—
105#64525—22no—
106#64525—41no—
107(C2×D19)⋊C4—21no—
108(C2×D19)⋊C4—21no—
109(C2×D19)⋊C4—21no—
110(C2×D19)⋊C4D411yescharacteristic
111C4⋊Dic19—21no—
112Dic19⋊C4—21no—
113Dic19⋊C4D411yescharacteristic
114C4×Dic19—21no—
115C4×Dic19C2311yescharacteristic
116C2×C19⋊C8C2311yescharacteristic
117C2×C19⋊C8C2311yescharacteristic
118Dic76—22no—
119D152—22no—
120#64516—22no—
121#64516D414yescomplemented
122#64515—22no—
123C23×C19—21no—
124C23×C19—21no—
125C23×C19C2×D411yescharacteristic
126C22×D19—21no—
127C22×D19—21no—
128C22×D19—42no—
129C22×D19—42no—
130C22×D19—81no—
131C22×D19C2×D411yescharacteristic
132D4×C19—21no—
133D4×C19—21no—
134D4×C19—21no—
135D4×C19—21no—
136D4×C19—81no—
137D4×C19—81no—
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—42no—
148C22⋊D19—42no—
149C22⋊D19—42no—
150C22⋊D19—81no—
151C2×Dic19—21no—
152C2×Dic19—21no—
153C2×Dic19—42no—
154C2×Dic19C2×D411yescharacteristic
155C2×Dic19C2×D411yescharacteristic
156C2×Dic19C2×D411yescharacteristic
157D76—21no—
158D76—21no—
159D76—21no—
160D76—81no—
161D76C2×D412yes—
162C4×D19—21no—
163C4×D19—21no—
164C4×D19—42no—
165C4×D19—42no—
166C4×D19—81no—
167Dic38—21no—
168Dic38—21no—
169Dic38—21no—
170Dic38C2×D412yes—
171C8×C19—21no—
172C8×C19C2×D412yes—
173C19⋊C8—21no—
174C19⋊C8—21no—
175#3268—191nomaximal, Sylow
176C22×C19—21no—
177C22×C19—21no—
178C22×C19—21no—
179C22×C19—41no—
180C22×C19—41no—
181C22×C19—41no—
182C22×C19—41no—
183C22×C19—41no—
184C22×C19—41no—
185C22×C19C22×D411yescharacteristic
186C2×D19—21no—
187C2×D19—22no—
188C2×D19—21no—
189C2×D19—21no—
190C2×D19—41no—
191C2×D19—41no—
192C2×D19—41no—
193C2×D19—41no—
194C2×D19—41no—
195C2×D19—84no—
196C4×C19—21no—
197C4×C19—41no—
198C4×C19—41no—
199C4×C19C22×D411yescharacteristic
200C4×C19H(5,𝔽2)11yescharacteristic
201Dic19—22no—
202Dic19—21no—
203Dic19—21no—
204Dic19—21no—
205Dic19—41no—
206C2×AGL(1,ℤ/8)—191no—
207C2×#135—191no—
208#550—191no—
209#546—191no—
210#496—191no—
211#468—191no—
212#466D1911yescharacteristic, complemented
213#464—191no—
214#459—191no—
215#452—191no—
216#449—191no—
217#449—191no—
218#447—191no—
219#440—191no—
220#435—191no—
221C2×C19—41no—
222C2×C19—81no—
223C2×C19—81no—
224C2×C19D4211yescharacteristic
225C2×C19#57511yescharacteristic
226C2×C19#57611yescharacteristic
227D19—41no—
228D19—42no—
229D19—81no—
230C2×#41—191no—
231C2×#41—191no—
232C2×#41—191no—
233C22×D4—191no—
234AGL(1,ℤ/8)—384no—
235#135—384no—
236C2×Q16—191no—
237C2×SD16—191no—
238C2×SD16—191no—
239C2×SD16—191no—
240C2×SD16—191no—
241C2×D8—191no—
242C2×D8—191no—
243C2×D8—191no—
244C2×D8C2×D1911yescharacteristic
245C2×M16—191no—
246C22×C8C2×D1911yescharacteristic, complemented
247#127—191no—
248#127—381no—
249#124—191no—
250#123—381no—
251C22⋊Q8—191no—
252#121—191no—
253#121—381no—
254#121—381no—
255#121—381no—
256#121C2×D1911yescharacteristic
257#121C2×D1911yescharacteristic, complemented
258#120—381no—
259C4×Q8—191no—
260C4×D4—191no—
261C4×D4—191no—
262C4×D4—381no—
263C2×C22⋊C4—381no—
264#107C2×D1911yescharacteristic, complemented
265C4⋊C8—191no—
266#103—191no—
267#103—191no—
268#102—191no—
269#102—191no—
270#102C2×D1911yescharacteristic
271#102C2×D1911yescharacteristic, complemented
272C22⋊C8—191no—
273C22⋊C8—191no—
274#97—191no—
275C19#326811yescharacteristic, complemented, Sylow
276C24—381no—
277#41—382no—
278#41—382no—
279#41—382no—
280#41—761no—
281#41—761no—
282#41—761no—
283C2×Q8—191no—
284C2×Q8—191no—
285C2×D4—21no—
286C2×D4—21no—
287C2×D4—191no—
288C2×D4—191no—
289C2×D4—191no—
290C2×D4—381no—
291C2×D4—381no—
292C2×D4—381no—
293C2×D4—381no—
294C2×D4—382no—
295C2×D4—381no—
296C2×D4—381no—
297C2×D4—381no—
298C2×D4—761no—
299C2×D4C22×D1911yescharacteristic
300C2×D4C22×D1911yescharacteristic
301C22×C4—191no—
302C22×C4—381no—
303C22×C4—381no—
304C22×C4—381no—
305C22×C4—381no—
306C22×C4C22×D1911yescharacteristic
307Q16—382no—
308SD16—194no—
309SD16—382no—
310SD16—382no—
311SD16—761no—
312D8—22no—
313D8—382no—
314D8—382no—
315D8—761no—
316M16—382no—
317C2×C8—22no—
318C2×C8—191no—
319C2×C8—191no—
320C2×C8C22×D1911yescharacteristic
321C2×C8C22×D1911yescharacteristic
322C4⋊C4—191no—
323C4⋊C4—381no—
324C4⋊C4—381no—
325C4⋊C4C22×D1911yescharacteristic
326C4⋊C4C22×D1911yescharacteristic
327C22⋊C4—21no—
328C22⋊C4—21no—
329C22⋊C4—191no—
330C22⋊C4—191no—
331C22⋊C4—381no—
332C22⋊C4—381no—
333C22⋊C4—381no—
334C22⋊C4—381no—
335C22⋊C4—381no—
336C42—191no—
337C42—381no—
338C23—21no—
339C23—21no—
340C23—191no—
341C23—381no—
342C23—381no—
343C23—762no—
344C23—762no—
345C23—1521no—
346C23D4×D1911yescharacteristic
347Q8—192no—
348Q8—381no—
349Q8—381no—
350Q8—381no—
351D4—21no—
352D4—21no—
353D4—21no—
354D4—21no—
355D4—81no—
356D4—81no—
357D4—192no—
358D4—381no—
359D4—381no—
360D4—381no—
361D4—761no—
362D4—762no—
363D4—762no—
364D4—762no—
365D4—762no—
366D4—762no—
367D4—1521no—
368D4—1521no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—191no—
374C2×C4—191no—
375C2×C4—191no—
376C2×C4—381no—
377C2×C4—381no—
378C2×C4—381no—
379C2×C4—381no—
380C2×C4—762no—
381C2×C4—762no—
382C2×C4—762no—
383C2×C4—1521no—
384C2×C4D4×D1911yescharacteristic
385C2×C4C23×D1911yescharacteristic
386C8—21no—
387C8—381no—
388C8—381no—
389C8D4×D1912yes—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—381no—
400C22—381no—
401C22—381no—
402C22—382no—
403C22—761no—
404C22—761no—
405C22—761no—
406C22—761no—
407C22—761no—
408C22—1524no—
409C22C2×D4×D1911yescharacteristic
410C4—21no—
411C4—41no—
412C4—41no—
413C4—381no—
414C4—381no—
415C4—381no—
416C4—382no—
417C4—761no—
418C4C2×D4×D1911yescharacteristic
419C4#1059743511yescharacteristic
420C2—41no—
421C2—81no—
422C2—81no—
423C2—761no—
424C2—762no—
425C2—1521no—
426C2#1192717811yescharacteristic
427C2#1192734111yescharacteristic
428C2#1192734511yescharacteristic
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#466C2
socleC22×C19C22×D4
hypercenter#466D19
hypocenterC19#3268
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C22×C4 ◁ #466

Complements

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

NH ≅ G/Ntype
1. C2×#10597357C2semidirect
2. C2×#10597350C2semidirect
3. #11927212C2semidirect
4. #11927191C2semidirect
5. #11926932C2semidirect
6. #11926791C2semidirect
7. #11926765C2semidirect
8. #11926738C2semidirect
9. #11926707C2semidirect
10. #11926687C2semidirect
11. #11926687C2semidirect
12. #11926679C2semidirect
13. #11926643C2semidirect
14. #11926615C2semidirect
15. C19×#466C2semidirect
19. C2×#64541C22semidirect
21. C22×C8×C19C22semidirect
23. C19×#121C22semidirect
25. #10597386C22semidirect
31. C2×#64526C22semidirect
36. C2×Dic76C22semidirect
40. C2×#64516C22semidirect
45. #10597333C22semidirect
50. C19×#107C22semidirect
52. C19×#102C22semidirect
53. C22⋊(C19⋊C8)C22semidirect
55. #10597272C22semidirect
56. Dic19⋊C8C22semidirect
57. #10597267C22semidirect
58. #10597267C22semidirect
60. #10597266C22semidirect
121. #64516D4semidirect
212. #466D19semidirect
246. C22×C8C2×D19semidirect
257. #121C2×D19semidirect
264. #107C2×D19semidirect
271. #102C2×D19semidirect
275. C19#3268semidirect

Maximal subgroups

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

subgroupindex
C2×#105973572
C2×#105973502
#119272122
#119271912
#119269322
#119267912
#119267652
#119267382
#119267072
#119266872
#119266792
#119266432
#119266152
C19×#4662
#326819