Finite Group Databasebeta

← #14573633

Subgroups — #14573633

Order 2432.

492 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11927091C211yesmaximal, characteristic, complemented
2C4×D4×D19C211yesmaximal, characteristic, complemented
3#11926859C211yesmaximal, characteristic, complemented
4#11926856C211yesmaximal, characteristic, complemented
5#11926823C211yesmaximal, characteristic, complemented
6#11926822C211yesmaximal, characteristic, complemented
7#11926738C211yesmaximal, characteristic, complemented
8#11926737C211yesmaximal, characteristic, complemented
9#11926679C211yesmaximal, characteristic, complemented
10#11926676C211yesmaximal, characteristic, complemented
11C4×D152C211yesmaximal, characteristic, complemented
12C4×#64525C211yesmaximal, characteristic, complemented
13C4×#64525C211yesmaximal, characteristic, complemented
14#11926595C211yesmaximal, characteristic, complemented
15C4×D8×C19C211yesmaximal, characteristic, complemented
16C2×D4×D19C2211yescharacteristic
17C2×#64541—21no—
18C22×C4×D19—21no—
19C2×D8×C19C2211yescharacteristic
20C4×D4×C19C2211yescharacteristic
21C4×D4×C19C2211yescharacteristic, complemented
22#10597386C2211yescharacteristic, complemented
23#10597384C2211yescharacteristic
24D4×Dic19C2211yescharacteristic
25C2×#64525C2211yescharacteristic
26C2×#64525C2211yescharacteristic
27C4×C22⋊D19—21no—
28C4×C22⋊D19—21no—
29C2×D152C2211yescharacteristic
30#10597341C2211yescharacteristic
31#10597339C2211yescharacteristic
32C4⋊C4×D19C2211yescharacteristic
33#10597334C2211yescharacteristic, complemented
34#10597331—21no—
35#10597330—21no—
36(C22⋊D19)⋊C4—21no—
37C22⋊C4×D19—21no—
38C4×D76C2211yescharacteristic
39C4×D76C2211yescharacteristic, complemented
40C42×D19C2211yescharacteristic
41C19×#107C2211yescharacteristic, complemented
42C19×#102C2211yescharacteristic
43C19×#102C2211yescharacteristic, complemented
44C4×C8×C19C2211yescharacteristic, complemented
45#10597289C2211yescharacteristic
46#10597289C2211yescharacteristic, complemented
47#10597278C2211yescharacteristic
48#10597278C2211yescharacteristic, complemented
49(C2×D19)⋊C8C2211yescharacteristic
50(C2×D19)⋊C8C2211yescharacteristic
51#10597275C2211yescharacteristic, complemented
52Dic19⋊C8C2211yescharacteristic, complemented
53Dic19⋊C8C2211yescharacteristic, complemented
54#10597266C2211yescharacteristic
55#10597266C2211yescharacteristic, complemented
56#10597264C2211yescharacteristic, complemented
57#10597264C2211yescharacteristic, complemented
58C4×C19⋊C8C2211yescharacteristic, complemented
59C23×D19—21no—
60C2×D4×C19C2311yescharacteristic
61C2×D4×C19C2311yescharacteristic
62C22×C4×C19—21no—
63C22×C4×C19—21no—
64C2×C22⋊D19—21no—
65C2×C22⋊D19—21no—
66C2×C22⋊D19—21no—
67C2×C22⋊D19—21no—
68C22×Dic19—21no—
69D4×D19—22no—
70D4×D19—22no—
71#64541—44no—
72C2×D76—21no—
73C2×D76C2311yescharacteristic
74C2×D76C2311yescharacteristic
75C2×C4×D19—21no—
76C2×C4×D19—21no—
77C2×C4×D19—21no—
78C2×C4×D19—21no—
79C2×C4×D19—44no—
80C2×C4×D19D411yescharacteristic
81C2×C4×D19D411yescharacteristic
82C2×C4×D19C2311yescharacteristic
83C2×Dic38—21no—
84D8×C19—22no—
85C2×C8×C19C2311yescharacteristic
86C2×C8×C19C2311yescharacteristic
87C4⋊C4×C19C2311yescharacteristic
88C4⋊C4×C19C2311yescharacteristic
89C22⋊C4×C19—21no—
90C22⋊C4×C19—21no—
91C42×C19C2311yescharacteristic
92C22⋊Dic19—21no—
93C22⋊Dic19—21no—
94#64525—22no—
95#64525—22no—
96(C2×D19)⋊C4—21no—
97(C2×D19)⋊C4—21no—
98(C2×D19)⋊C4—21no—
99(C2×D19)⋊C4—21no—
100C4⋊Dic19C2311yescharacteristic
101C4⋊Dic19C2311yescharacteristic
102Dic19⋊C4—21no—
103Dic19⋊C4—21no—
104C4×Dic19D411yescharacteristic
105C4×Dic19D411yescharacteristic
106C4×Dic19C2311yescharacteristic
107C2×C19⋊C8C2311yescharacteristic
108C2×C19⋊C8C2311yescharacteristic
109D152—22no—
110C23×C19—21no—
111C23×C19—21no—
112C22×D19—24no—
113C22×D19—21no—
114C22×D19—21no—
115C22×D19—42no—
116C22×D19—42no—
117C22×D19C2×D411yescharacteristic
118D4×C19—21no—
119D4×C19—21no—
120D4×C19—21no—
121D4×C19#4112yescomplemented
122C2×C4×C19—21no—
123C2×C4×C19—21no—
124C2×C4×C19—42no—
125C2×C4×C19—42no—
126C2×C4×C19C2×D411yescharacteristic
127C2×C4×C19C2×D411yescharacteristic
128C2×C4×C19C2411yescharacteristic
129C22⋊D19—24no—
130C22⋊D19—42no—
131C22⋊D19—42no—
132C22⋊D19—42no—
133C2×Dic19—21no—
134C2×Dic19—21no—
135C2×Dic19—42no—
136C2×Dic19C2×D411yescharacteristic
137C2×Dic19C2×D411yescharacteristic
138C2×Dic19C2×D411yescharacteristic
139D76—21no—
140D76—21no—
141D76—21no—
142D76—42no—
143D76#4112yescomplemented
144C4×D19—21no—
145C4×D19—21no—
146C4×D19—41no—
147C4×D19—42no—
148C4×D19—42no—
149C4×D19—42no—
150C4×D19—42no—
151C4×D19D814yescomplemented
152Dic38—42no—
153C8×C19—21no—
154C8×C19—21no—
155C19⋊C8—21no—
156C19⋊C8—21no—
157#3100—191nomaximal, Sylow
158C22×C19—22no—
159C22×C19—41no—
160C22×C19—41no—
161C22×C19—41no—
162C22×C19—41no—
163C22×C19—41no—
164C22×C19C22×D411yescharacteristic
165C2×D19—21no—
166C2×D19—21no—
167C2×D19—22no—
168C2×D19—48no—
169C2×D19—41no—
170C2×D19—41no—
171C2×D19—41no—
172C2×D19—41no—
173C2×D19—41no—
174C2×D19C2×D812yes—
175C4×C19—21no—
176C4×C19—41no—
177C4×C19—41no—
178C4×C19C2×D812yes—
179C4×C19C2×#4111yescharacteristic
180C4×C19C2×#4111yescharacteristic
181Dic19—21no—
182Dic19—21no—
183Dic19—41no—
184Dic19—41no—
185Dic19C2×D812yes—
186#532—191no—
187C2×C4×D4—191no—
188#480—191no—
189#480—191no—
190#474—191no—
191#474—191no—
192#459—191no—
193#459—191no—
194#447—191no—
195#447—191no—
196C4×D8—191no—
197C4×D8—191no—
198C4×D8—191no—
199C4×D8D1911yescharacteristic, complemented
200#431—191no—
201C2×C19—42no—
202C2×C19—81no—
203C2×C19#52511yescharacteristic
204C2×C19C22×D811yescharacteristic
205C2×C19#57511yescharacteristic
206D19—22no—
207D19—42no—
208D19—81no—
209C2×#41—381no—
210C22×D4—191no—
211C23×C4—381no—
212C2×D8—191no—
213C2×D8—191no—
214C2×D8—191no—
215C2×D8C2×D1911yescharacteristic
216C4⋊Q8—191no—
217#127—191no—
218#124—381no—
219#121—191no—
220#121—191no—
221#121—381no—
222C4×D4—191no—
223C4×D4—191no—
224C4×D4—191no—
225C4×D4—191no—
226C4×D4—381no—
227C4×D4—381no—
228C4×D4—381no—
229C4×D4C2×D1911yescharacteristic
230C4×D4C2×D1911yescharacteristic, complemented
231C2×C4⋊C4—191no—
232C2×C22⋊C4—381no—
233C2×C42—191no—
234#107—191no—
235#107—191no—
236#107—191no—
237#107C2×D1911yescharacteristic, complemented
238C4⋊C8—191no—
239C4⋊C8—191no—
240#102—191no—
241#102—191no—
242#102—191no—
243#102—191no—
244#102—191no—
245#102—191no—
246#102C2×D1911yescharacteristic
247#102C2×D1911yescharacteristic, complemented
248C22⋊C8—191no—
249C22⋊C8—191no—
250C4×C8—191no—
251C4×C8C2×D1911yescharacteristic, complemented
252C19#310011yescharacteristic, complemented, Sylow
253C24—381no—
254#41—764no—
255C2×Q8—381no—
256C2×D4—191no—
257C2×D4—191no—
258C2×D4—381no—
259C2×D4—381no—
260C2×D4—381no—
261C2×D4—381no—
262C2×D4—382no—
263C2×D4—382no—
264C2×D4—381no—
265C2×D4C22×D1911yescharacteristic
266C2×D4C22×D1911yescharacteristic
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—191no—
270C22×C4—191no—
271C22×C4—191no—
272C22×C4—381no—
273C22×C4—381no—
274C22×C4—381no—
275C22×C4—381no—
276C22×C4—381no—
277C22×C4—764no—
278D8—22no—
279D8—382no—
280D8—382no—
281D8—382no—
282C2×C8—191no—
283C2×C8—191no—
284C2×C8C22×D1911yescharacteristic
285C2×C8C22×D1911yescharacteristic
286C4⋊C4—191no—
287C4⋊C4—191no—
288C4⋊C4—381no—
289C4⋊C4—381no—
290C4⋊C4C22×D1911yescharacteristic
291C4⋊C4C22×D1911yescharacteristic
292C22⋊C4—21no—
293C22⋊C4—21no—
294C22⋊C4—381no—
295C22⋊C4—381no—
296C22⋊C4—381no—
297C22⋊C4—381no—
298C22⋊C4—381no—
299C22⋊C4—381no—
300C42—191no—
301C42—191no—
302C42—191no—
303C42C22×D1911yescharacteristic
304C23—21no—
305C23—21no—
306C23—191no—
307C23—384no—
308C23—381no—
309C23—381no—
310C23—762no—
311C23—762no—
312Q8—762no—
313D4—21no—
314D4—21no—
315D4—21no—
316D4—192no—
317D4—384no—
318D4—381no—
319D4—381no—
320D4—381no—
321D4—762no—
322D4—762no—
323D4—762no—
324D4—762no—
325D4#6454112yescomplemented
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—191no—
331C2×C4—194no—
332C2×C4—191no—
333C2×C4—191no—
334C2×C4—381no—
335C2×C4—381no—
336C2×C4—381no—
337C2×C4—381no—
338C2×C4—761no—
339C2×C4—762no—
340C2×C4—762no—
341C2×C4—762no—
342C2×C4—762no—
343C2×C4—762no—
344C2×C4D4×D1911yescharacteristic
345C2×C4D4×D1911yescharacteristic
346C2×C4C23×D1911yescharacteristic
347C8—21no—
348C8—21no—
349C8—381no—
350C8—381no—
351C22—22no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—192no—
358C22—381no—
359C22—381no—
360C22—382no—
361C22—768no—
362C22—761no—
363C22—761no—
364C22—761no—
365C22—761no—
366C22—761no—
367C22C2×D4×D1911yescharacteristic
368C4—21no—
369C4—41no—
370C4—41no—
371C4—192no—
372C4—381no—
373C4—381no—
374C4—761no—
375C4—761no—
376C4D8×D1912yes—
377C4C2×#6454111yescharacteristic
378C4#41×D1911yescharacteristic
379C2—42no—
380C2—81no—
381C2—382no—
382C2—762no—
383C2—1521no—
384C2#1192705311yescharacteristic
385C2C2×D8×D1911yescharacteristic
386C2#1192734111yescharacteristic
subgroupG/H
centerC2×C4D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC4×D8×C19C2
socleC22×C19C22×D4
hypercenterC4×D8D19
hypocenterC19#3100
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #11927091C2semidirect
2. C4×D4×D19C2semidirect
3. #11926859C2semidirect
4. #11926856C2semidirect
5. #11926823C2semidirect
6. #11926822C2semidirect
7. #11926738C2semidirect
8. #11926737C2semidirect
9. #11926679C2semidirect
10. #11926676C2semidirect
11. C4×D152C2semidirect
12. C4×#64525C2semidirect
13. C4×#64525C2semidirect
14. #11926595C2semidirect
15. C4×D8×C19C2semidirect
21. C4×D4×C19C22semidirect
22. #10597386C22semidirect
33. #10597334C22semidirect
39. C4×D76C22semidirect
41. C19×#107C22semidirect
43. C19×#102C22semidirect
44. C4×C8×C19C22semidirect
46. #10597289C22semidirect
48. #10597278C22semidirect
51. #10597275C22semidirect
52. Dic19⋊C8C22semidirect
53. Dic19⋊C8C22semidirect
55. #10597266C22semidirect
56. #10597264C22semidirect
57. #10597264C22semidirect
58. C4×C19⋊C8C22semidirect
121. D4×C19#41semidirect
143. D76#41semidirect
151. C4×D19D8semidirect
199. C4×D8D19semidirect
230. C4×D4C2×D19semidirect
237. #107C2×D19semidirect
247. #102C2×D19semidirect
251. C4×C8C2×D19semidirect
252. C19#3100semidirect
325. D4#64541semidirect

Maximal subgroups

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

subgroupindex
#119270912
C4×D4×D192
#119268592
#119268562
#119268232
#119268222
#119267382
#119267372
#119266792
#119266762
C4×D1522
C4×#645252
#119265952
C4×D8×C192
#310019