Finite Group Databasebeta

← #14570680

Subgroups — #14570680

Order 2432.

560 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11926473C211yesmaximal, characteristic, complemented
2#11926472C211yesmaximal, characteristic, complemented
3#11926470C211yesmaximal, characteristic, complemented
4#11926457C211yesmaximal, characteristic, complemented
5#11926457C211yesmaximal, characteristic, complemented
6#11926456C211yesmaximal, characteristic, complemented
7#11926435C211yesmaximal, characteristic, complemented
8#11926435C211yesmaximal, characteristic, complemented
9#11926434C211yesmaximal, characteristic, complemented
10#11926433C211yesmaximal, characteristic, complemented
11#11926432C211yesmaximal, characteristic, complemented
12#11926399C211yesmaximal, characteristic
13#11926399C211yesmaximal, characteristic
14#11926399C211yesmaximal, characteristic
15C19×#388C211yesmaximal, characteristic, complemented
16C24×D19C2211yescharacteristic
17C22×Dic38C2211yescharacteristic, complemented
18C2×C4⋊C4×C19C2211yescharacteristic, complemented
19C2×C22⋊C4×C19C2211yescharacteristic
20C2×C22⋊C4×C19C2211yescharacteristic
21C2×C22⋊C4×C19C2211yescharacteristic
22C2×C42×C19C2211yescharacteristic, complemented
23C2×C22⋊Dic19C2211yescharacteristic
24C2×C22⋊Dic19C2211yescharacteristic
25C2×C22⋊Dic19C2211yescharacteristic
26C2×(C2×D19)⋊C4C2211yescharacteristic
27C2×(C2×D19)⋊C4C2211yescharacteristic
28C2×(C2×D19)⋊C4C2211yescharacteristic
29C2×(C2×D19)⋊C4C2211yescharacteristic
30C2×(C2×D19)⋊C4C2211yescharacteristic
31C2×(C2×D19)⋊C4C2211yescharacteristic
32C2×(C2×D19)⋊C4C2211yescharacteristic
33C2×(C2×D19)⋊C4C2211yescharacteristic
34C2×(C2×D19)⋊C4C2211yescharacteristic
35C2×(C2×D19)⋊C4C2211yescharacteristic
36C2×(C2×D19)⋊C4C2211yescharacteristic
37C2×(C2×D19)⋊C4C2211yescharacteristic
38C2×Dic19⋊C4C2211yescharacteristic, complemented
39C2×Dic19⋊C4C2211yescharacteristic, complemented
40C2×C4×Dic19C2211yescharacteristic, complemented
41C19×#95C2211yescharacteristic, complemented
42C19×#95C2211yescharacteristic, complemented
43C19⋊#95C2211yescharacteristic, complemented
44C19⋊#95C2211yescharacteristic, complemented
45C19⋊#95C2211yescharacteristic, complemented
46C19⋊#95C2211yescharacteristic, complemented
47C19⋊#95C2211yescharacteristic, complemented
48C19⋊#95C2211yescharacteristic, complemented
49C19⋊#95C2211yescharacteristic, complemented
50C19⋊#95C2211yescharacteristic, complemented
51C24×C19C2311yescharacteristic
52C23×D19—22no—
53C23×D19—22no—
54C23×D19—22no—
55C23×D19—41no—
56C23×D19—41no—
57C23×D19—41no—
58C23×D19—41no—
59C23×D19C2311yescharacteristic
60C23×D19C2311yescharacteristic
61C22×C4×C19C2311yescharacteristic
62C22×C4×C19C2311yescharacteristic
63C22×C4×C19C2311yescharacteristic
64C22×C4×C19C2311yescharacteristic
65C22×C4×C19C2311yescharacteristic
66C22×C4×C19C2311yescharacteristic
67C22×Dic19C2311yescharacteristic
68C22×Dic19C2311yescharacteristic
69C22×Dic19C2311yescharacteristic
70C22×Dic19C2311yescharacteristic
71C22×Dic19C2311yescharacteristic
72C22×Dic19C2311yescharacteristic
73C2×Dic38—41no—
74C2×Dic38—41no—
75C2×Dic38—41no—
76C4⋊C4×C19—41no—
77C22⋊C4×C19—22no—
78C22⋊C4×C19—41no—
79C22⋊C4×C19—41no—
80C42×C19—41no—
81C22⋊Dic19—22no—
82C22⋊Dic19—41no—
83C22⋊Dic19—41no—
84(C2×D19)⋊C4—22no—
85(C2×D19)⋊C4—22no—
86(C2×D19)⋊C4—22no—
87(C2×D19)⋊C4—22no—
88(C2×D19)⋊C4—41no—
89(C2×D19)⋊C4—41no—
90(C2×D19)⋊C4—41no—
91(C2×D19)⋊C4—41no—
92(C2×D19)⋊C4—41no—
93(C2×D19)⋊C4—41no—
94(C2×D19)⋊C4—41no—
95(C2×D19)⋊C4—41no—
96Dic19⋊C4—41no—
97Dic19⋊C4—41no—
98C4×Dic19—41no—
99C23×C19—21no—
100C23×C19—21no—
101C23×C19—21no—
102C23×C19—21no—
103C23×C19—21no—
104C23×C19—21no—
105C23×C19#4112yes—
106C23×C19C2411yescharacteristic
107C22×D19—21no—
108C22×D19—21no—
109C22×D19—21no—
110C22×D19—21no—
111C22×D19—21no—
112C22×D19—21no—
113C22×D19—21no—
114C22×D19—21no—
115C22×D19—21no—
116C22×D19—21no—
117C22×D19—21no—
118C22×D19—21no—
119C22×D19—44no—
120C22×D19—44no—
121C22×D19—44no—
122C22×D19—44no—
123C22×D19—44no—
124C22×D19—44no—
125C22×D19—44no—
126C22×D19#4112yes—
127C22×D19#4112yes—
128C2×C4×C19—21no—
129C2×C4×C19—21no—
130C2×C4×C19—21no—
131C2×C4×C19—21no—
132C2×C4×C19—21no—
133C2×C4×C19—21no—
134C2×C4×C19—21no—
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—21no—
144C2×C4×C19—21no—
145C2×C4×C19—21no—
146C2×Dic19—21no—
147C2×Dic19—21no—
148C2×Dic19—21no—
149C2×Dic19—21no—
150C2×Dic19—21no—
151C2×Dic19—21no—
152C2×Dic19—21no—
153C2×Dic19—21no—
154C2×Dic19—21no—
155C2×Dic19—21no—
156C2×Dic19—21no—
157C2×Dic19—21no—
158C2×Dic19—21no—
159C2×Dic19—21no—
160C2×Dic19—21no—
161C2×Dic19—21no—
162C2×Dic19—21no—
163C2×Dic19—21no—
164Dic38—44no—
165#2736—191nomaximal, Sylow
166C22×C19—22no—
167C22×C19—22no—
168C22×C19—22no—
169C22×C19—41no—
170C22×C19—41no—
171C22×C19—41no—
172C22×C19—41no—
173C22×C19C2×#4111yescharacteristic
174C22×C19C2×#4111yescharacteristic
175C22×C19C2×#4111yescharacteristic
176C22×C19H(5,𝔽2)11yescharacteristic
177C22×C19H(5,𝔽2)11yescharacteristic
178C22×C19H(5,𝔽2)11yescharacteristic
179C22×C19H(5,𝔽2)11yescharacteristic
180C2×D19—22no—
181C2×D19—22no—
182C2×D19—22no—
183C2×D19—22no—
184C2×D19—22no—
185C2×D19—22no—
186C2×D19—416no—
187C2×D19—41no—
188C2×D19—41no—
189C2×D19—41no—
190C2×D19—41no—
191C2×D19—41no—
192C2×D19—41no—
193C2×D19—41no—
194C2×D19—41no—
195C4×C19—41no—
196C4×C19—41no—
197C4×C19—41no—
198C4×C19—41no—
199C4×C19—41no—
200C4×C19—41no—
201Dic19—41no—
202Dic19—41no—
203Dic19—41no—
204Dic19—41no—
205Dic19—41no—
206Dic19—41no—
207#397—191no—
208#397—191no—
209#397—191no—
210#393—191no—
211#393—191no—
212#393—191no—
213#388—191no—
214#388—191no—
215#388—191no—
216#388—191no—
217#388—191no—
218#388D1911yescharacteristic, complemented
219#379—191no—
220#379—191no—
221#379—191no—
222C2×C19—42no—
223C2×C19#53811yescharacteristic
224C2×C19#53811yescharacteristic
225C2×C19#53811yescharacteristic
226C2×C19#55111yescharacteristic
227C2×C19#55111yescharacteristic
228C2×C19#55111yescharacteristic
229C2×C19H(3,𝔽4)11yescharacteristic
230D19—42no—
231D19—42no—
232C25—191no—
233C22×Q8—191no—
234C2×C4⋊C4—191no—
235C2×C4⋊C4—191no—
236C2×C4⋊C4C2×D1911yescharacteristic, complemented
237C2×C22⋊C4—191no—
238C2×C22⋊C4—191no—
239C2×C22⋊C4—191no—
240C2×C22⋊C4—191no—
241C2×C22⋊C4—191no—
242C2×C22⋊C4—191no—
243C2×C22⋊C4—191no—
244C2×C22⋊C4—191no—
245C2×C22⋊C4—191no—
246C2×C22⋊C4—191no—
247C2×C22⋊C4—191no—
248C2×C22⋊C4—191no—
249C2×C22⋊C4—191no—
250C2×C22⋊C4—191no—
251C2×C22⋊C4—191no—
252C2×C22⋊C4C2×D1911yescharacteristic
253C2×C22⋊C4C2×D1911yescharacteristic
254C2×C22⋊C4C2×D1911yescharacteristic
255C2×C42—191no—
256C2×C42C2×D1911yescharacteristic, complemented
257#95—191no—
258#95—191no—
259#95—191no—
260#95—191no—
261#95—191no—
262#95—191no—
263#95—191no—
264#95—191no—
265#95C2×D1911yescharacteristic, complemented
266#95C2×D1911yescharacteristic, complemented
267C19#273611yescharacteristic, complemented, Sylow
268C24—191no—
269C24—191no—
270C24—382no—
271C24—382no—
272C24—382no—
273C24—761no—
274C24—761no—
275C24—761no—
276C24—761no—
277C24C22×D1911yescharacteristic
278C2×Q8—761no—
279C2×Q8—761no—
280C2×Q8—761no—
281C22×C4—191no—
282C22×C4—191no—
283C22×C4—191no—
284C22×C4—191no—
285C22×C4—191no—
286C22×C4—191no—
287C22×C4C22×D1911yescharacteristic
288C22×C4C22×D1911yescharacteristic
289C22×C4C22×D1911yescharacteristic
290C22×C4C22×D1911yescharacteristic
291C22×C4C22×D1911yescharacteristic
292C22×C4C22×D1911yescharacteristic
293C4⋊C4—41no—
294C4⋊C4—761no—
295C4⋊C4—761no—
296C22⋊C4—22no—
297C22⋊C4—41no—
298C22⋊C4—41no—
299C22⋊C4—382no—
300C22⋊C4—382no—
301C22⋊C4—382no—
302C22⋊C4—382no—
303C22⋊C4—382no—
304C22⋊C4—761no—
305C22⋊C4—761no—
306C22⋊C4—761no—
307C22⋊C4—761no—
308C22⋊C4—761no—
309C22⋊C4—761no—
310C22⋊C4—761no—
311C22⋊C4—761no—
312C22⋊C4—761no—
313C22⋊C4—761no—
314C42—41no—
315C42—761no—
316C23—21no—
317C23—21no—
318C23—21no—
319C23—21no—
320C23—21no—
321C23—21no—
322C23—192no—
323C23—192no—
324C23—381no—
325C23—381no—
326C23—381no—
327C23—381no—
328C23—381no—
329C23—381no—
330C23—381no—
331C23—381no—
332C23—381no—
333C23—381no—
334C23—381no—
335C23—381no—
336C23—764no—
337C23—764no—
338C23—764no—
339C23—764no—
340C23—764no—
341C23—764no—
342C23—764no—
343C23#6454112yes—
344C23C23×D1911yescharacteristic
345Q8—764no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—381no—
365C2×C4—381no—
366C2×C4—381no—
367C2×C4—381no—
368C2×C4—381no—
369C2×C4—381no—
370C2×C4—381no—
371C2×C4—381no—
372C2×C4—381no—
373C2×C4—381no—
374C2×C4—381no—
375C2×C4—381no—
376C2×C4—381no—
377C2×C4—381no—
378C2×C4—381no—
379C2×C4—381no—
380C2×C4—381no—
381C2×C4—381no—
382C22—22no—
383C22—22no—
384C22—22no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—382no—
390C22—382no—
391C22—382no—
392C22—382no—
393C22—382no—
394C22—382no—
395C22—7616no—
396C22—761no—
397C22—761no—
398C22—761no—
399C22—761no—
400C22—761no—
401C22—761no—
402C22—761no—
403C22—761no—
404C22C2×#6454111yescharacteristic
405C22#1059743011yescharacteristic
406C22#1059743011yescharacteristic
407C22#41×D1911yescharacteristic
408C22#41×D1911yescharacteristic
409C22#1059743511yescharacteristic
410C22#1059743511yescharacteristic
411C4—41no—
412C4—41no—
413C4—41no—
414C4—41no—
415C4—41no—
416C4—41no—
417C4—761no—
418C4—761no—
419C4—761no—
420C4—761no—
421C4—761no—
422C4—761no—
423C2—42no—
424C2—762no—
425C2—762no—
426C2#1192712611yescharacteristic
427C2#1192712711yescharacteristic
428C2#1192713011yescharacteristic
429C2#1192721811yescharacteristic
430C2#1192721911yescharacteristic
431C2#1192722311yescharacteristic
432C2#1192728611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC19×#388C2
prime radicalC24×D19C22
hypercenter#388D19
hypocenterC19#2736
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. #11926473C2semidirect
2. #11926472C2semidirect
3. #11926470C2semidirect
4. #11926457C2semidirect
5. #11926457C2semidirect
6. #11926456C2semidirect
7. #11926435C2semidirect
8. #11926435C2semidirect
9. #11926434C2semidirect
10. #11926433C2semidirect
11. #11926432C2semidirect
15. C19×#388C2semidirect
17. C22×Dic38C22semidirect
18. C2×C4⋊C4×C19C22semidirect
22. C2×C42×C19C22semidirect
38. C2×Dic19⋊C4C22semidirect
39. C2×Dic19⋊C4C22semidirect
40. C2×C4×Dic19C22semidirect
41. C19×#95C22semidirect
42. C19×#95C22semidirect
43. C19⋊#95C22semidirect
44. C19⋊#95C22semidirect
45. C19⋊#95C22semidirect
46. C19⋊#95C22semidirect
47. C19⋊#95C22semidirect
48. C19⋊#95C22semidirect
49. C19⋊#95C22semidirect
50. C19⋊#95C22semidirect
218. #388D19semidirect
236. C2×C4⋊C4C2×D19semidirect
256. C2×C42C2×D19semidirect
265. #95C2×D19semidirect
266. #95C2×D19semidirect
267. C19#2736semidirect

Maximal subgroups

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

subgroupindex
#119264732
#119264722
#119264702
#119264572
#119264562
#119264352
#119264342
#119264332
#119264322
#119263992
C19×#3882
#273619