Finite Group Databasebeta

← #34079296

Subgroups — #34079296

Order 19328.

406 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752833C211yesmaximal, characteristic, complemented
2#23752686C211yesmaximal, characteristic, complemented
3#23752554C211yesmaximal, characteristic, complemented
4#23752537C211yesmaximal, characteristic, complemented
5#23752503C211yesmaximal, characteristic, complemented
6#23752493C211yesmaximal, characteristic, complemented
7#23752428C211yesmaximal, characteristic, complemented
8#23752428C211yesmaximal, characteristic, complemented
9#23752365C211yesmaximal, characteristic, complemented
10#23752348C211yesmaximal, characteristic
11#23752325C211yesmaximal, characteristic, complemented
12#23752314C211yesmaximal, characteristic, complemented
13C4×#14558993C211yesmaximal, characteristic, complemented
14C4×D1208C211yesmaximal, characteristic, complemented
15#433×C151C211yesmaximal, characteristic, complemented
16C22×D604C2211yescharacteristic
17C2×#14558993C2211yescharacteristic
18C2×#14558993C2211yescharacteristic
19C2×D1208C2211yescharacteristic
20C2×D1208C2211yescharacteristic
21#18012739C2211yescharacteristic, complemented
22#18012734—21no—
23#18012727C2211yescharacteristic, complemented
24#18012725—21no—
25#18012721—21no—
26#18012718C2211yescharacteristic
27#18012717—21no—
28#18012713C2211yescharacteristic
29C4×Dic302C2211yescharacteristic, complemented
30C4×D604C2211yescharacteristic
31C4×D604C2211yescharacteristic
32C4×D604C2211yescharacteristic
33C4×D604C2211yescharacteristic
34C4×D604C2211yescharacteristic, complemented
35#18012701—21no—
36#18012701—21no—
37#18012698C2211yescharacteristic
38C22⋊C4×D151—21no—
39C22⋊C4×D151—21no—
40#18012673C2211yescharacteristic, complemented
41#18012673C2211yescharacteristic, complemented
42#18012671C2211yescharacteristic, complemented
43#18012671C2211yescharacteristic, complemented
44#18012664C2211yescharacteristic, complemented
45#18012664C2211yescharacteristic, complemented
46#18012661C2211yescharacteristic
47#18012661C2211yescharacteristic
48#18012661C2211yescharacteristic
49#18012661C2211yescharacteristic
50#18012661C2211yescharacteristic, complemented
51#18012661C2211yescharacteristic, complemented
52#117×C151C2211yescharacteristic
53C4⋊C8×C151C2211yescharacteristic, complemented
54C4⋊C8×C151C2211yescharacteristic, complemented
55C22⋊C8×C151C2211yescharacteristic
56C22⋊C8×C151C2211yescharacteristic
57#97×C151C2211yescharacteristic, complemented
58C4×C8×C151C2211yescharacteristic, complemented
59C23×D151—21no—
60C2×Dic302—21no—
61C2×Dic302C2311yescharacteristic
62C2×D604—22no—
63C2×D604—22no—
64C2×D604—21no—
65C2×D604C2311yescharacteristic
66C2×D604C2311yescharacteristic
67C2×D604C2311yescharacteristic
68C2×C22⋊D151—21no—
69C2×C4×D151—21no—
70C2×C4×D151—21no—
71C2×C4×D151—21no—
72C2×C4×D151—21no—
73C2×C4×D151—21no—
74#14558993—22no—
75#14558993—22no—
76D1208—22no—
77D1208—22no—
78C4⋊Dic151—21no—
79C4⋊Dic151C2311yescharacteristic
80C4⋊Dic151C2311yescharacteristic
81C4⋊Dic151C2311yescharacteristic
82C4⋊Dic151C2311yescharacteristic
83Dic151⋊C4—21no—
84Dic151⋊C4—21no—
85C22⋊Dic151—21no—
86C22⋊Dic151—21no—
87(C2×D151)⋊C4—21no—
88(C2×D151)⋊C4—21no—
89(C2×D151)⋊C4—21no—
90(C2×D151)⋊C4—21no—
91(C2×D151)⋊C4—21no—
92(C2×D151)⋊C4—21no—
93(C2×D151)⋊C4—21no—
94(C2×D151)⋊C4—21no—
95C4×Dic151—21no—
96C4×Dic151—21no—
97C22×C4×C151C2311yescharacteristic
98C2×C8×C151C2311yescharacteristic
99C2×C8×C151C2311yescharacteristic
100C2×C8×C151C2311yescharacteristic
101C2×C8×C151C2311yescharacteristic
102C4⋊C4×C151D411yescharacteristic
103C4⋊C4×C151D411yescharacteristic
104C22⋊C4×C151D411yescharacteristic
105C22⋊C4×C151D411yescharacteristic
106C42×C151C2311yescharacteristic
107C42×C151C2311yescharacteristic
108C22×D151—21no—
109C22×D151—21no—
110C22×D151—24no—
111C22×D151—21no—
112C22×D151—81no—
113C22×D151—81no—
114Dic302—21no—
115Dic302—21no—
116Dic302—81no—
117D604—24no—
118D604—21no—
119D604—21no—
120D604—21no—
121D604—21no—
122D604#4112yes—
123D604#4112yes—
124C22⋊D151—81no—
125C2×Dic151—21no—
126C2×Dic151—21no—
127C2×Dic151—21no—
128C2×Dic151—21no—
129C2×Dic151—21no—
130C4×D151—81no—
131C4×D151—81no—
132C4×D151—81no—
133C4×D151—81no—
134C4×D151—81no—
135C23×C151C2×D411yescharacteristic
136C2×C4×C151—21no—
137C2×C4×C151—21no—
138C2×C4×C151C2×D411yescharacteristic
139C2×C4×C151C2×D411yescharacteristic
140C2×C4×C151C2×D411yescharacteristic
141C2×C4×C151C2×D411yescharacteristic
142C2×C4×C151C2×D411yescharacteristic
143C2×C4×C151C2411yescharacteristic
144C8×C151—21no—
145C8×C151—21no—
146C8×C151—21no—
147C8×C151—21no—
148C22×C151—21no—
149C22×C151—21no—
150C22×C151—21no—
151C22×C151C22×D411yescharacteristic
152C2×D151—22no—
153C2×D151—22no—
154C2×D151—41no—
155C2×D151—41no—
156C2×D151—41no—
157C2×D151—41no—
158C2×D151—41no—
159C2×D151—41no—
160C2×D151—41no—
161C2×D151—84no—
162C4×C151—21no—
163C4×C151—21no—
164C4×C151—21no—
165C4×C151—21no—
166C4×C151—21no—
167C4×C151C2×#4111yescharacteristic
168C4×C151C2×#4111yescharacteristic
169Dic151—41no—
170Dic151—41no—
171Dic151—41no—
172Dic151—41no—
173Dic151—41no—
174C2×C151—41no—
175C2×C151#52511yescharacteristic
176C2×C151#57611yescharacteristic
177C2×C151#57711yescharacteristic
178D151—42no—
179D151—42no—
180D151—81no—
181C151#311811yescharacteristic, complemented, Sylow
182#3118—1511nomaximal, Sylow
183#542—1511no—
184#518—1511no—
185#485—1511no—
186#482—1511no—
187#476—1511no—
188#474—1511no—
189#463—1511no—
190#463—1511no—
191#450—1511no—
192#447—1511no—
193#442—1511no—
194#440—1511no—
195C4×SD16—1511no—
196C4×D8—1511no—
197#433D15111yescharacteristic, complemented
198C22×D4—1511no—
199C2×SD16—1511no—
200C2×SD16—1511no—
201C2×D8—1511no—
202C2×D8—1511no—
203C4⋊Q8—1511no—
204#126—3021no—
205#124—3021no—
206#124—1511no—
207#123—3021no—
208C22⋊Q8—3021no—
209C22⋊Q8—1511no—
210#121—1511no—
211C4×Q8—1511no—
212C4×D4—3021no—
213C4×D4—3021no—
214C4×D4—1511no—
215C4×D4—1511no—
216C4×D4—1511no—
217C4×D4—1511no—
218C4×D4—1511no—
219#117—1511no—
220#117C2×D15111yescharacteristic
221C2×C22⋊C4—3021no—
222C2×C22⋊C4—3021no—
223#107—1511no—
224#107—1511no—
225#106—1511no—
226#106—1511no—
227C4⋊C8C2×D15111yescharacteristic, complemented
228C4⋊C8C2×D15111yescharacteristic, complemented
229#103—1511no—
230#103—1511no—
231#102—1511no—
232#102—1511no—
233#102—1511no—
234#102—1511no—
235#102—1511no—
236#102—1511no—
237C22⋊C8C2×D15111yescharacteristic
238C22⋊C8C2×D15111yescharacteristic
239#97C2×D15111yescharacteristic, complemented
240C4×C8C2×D15111yescharacteristic, complemented
241C24—3021no—
242C2×Q8—3021no—
243C2×Q8—1511no—
244C2×D4—3022no—
245C2×D4—3022no—
246C2×D4—3021no—
247C2×D4—3021no—
248C2×D4—1511no—
249C2×D4—1511no—
250C2×D4—1511no—
251C22×C4—3021no—
252C22×C4—3021no—
253C22×C4—3021no—
254C22×C4—3021no—
255C22×C4—3021no—
256C22×C4C22×D15111yescharacteristic
257SD16—3022no—
258SD16—3022no—
259D8—3022no—
260D8—3022no—
261C2×C8C22×D15111yescharacteristic
262C2×C8C22×D15111yescharacteristic
263C2×C8C22×D15111yescharacteristic
264C2×C8C22×D15111yescharacteristic
265C4⋊C4—3021no—
266C4⋊C4—3021no—
267C4⋊C4—3021no—
268C4⋊C4—1511no—
269C4⋊C4—1511no—
270C4⋊C4—1511no—
271C4⋊C4—1511no—
272C4⋊C4D60411yescharacteristic
273C4⋊C4D60411yescharacteristic
274C22⋊C4—3021no—
275C22⋊C4—3021no—
276C22⋊C4—3021no—
277C22⋊C4—3021no—
278C22⋊C4—3021no—
279C22⋊C4—3021no—
280C22⋊C4—3021no—
281C22⋊C4—3021no—
282C22⋊C4—3021no—
283C22⋊C4—3021no—
284C22⋊C4D60411yescharacteristic
285C22⋊C4D60411yescharacteristic
286C42—3021no—
287C42—3021no—
288C42C22×D15111yescharacteristic
289C42C22×D15111yescharacteristic
290C23—3024no—
291C23—3021no—
292C23—3021no—
293C23—3021no—
294C23—12081no—
295C23—12081no—
296C23C2×D60411yescharacteristic
297Q8—3021no—
298Q8—3021no—
299Q8—12081no—
300D4—3024no—
301D4—3021no—
302D4—3021no—
303D4—3021no—
304D4—3021no—
305D4—1512no—
306D4—1512no—
307D4—12081no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—3021no—
311C2×C4—3021no—
312C2×C4—3021no—
313C2×C4—3021no—
314C2×C4—3021no—
315C2×C4—12081no—
316C2×C4—12081no—
317C2×C4—12081no—
318C2×C4—12081no—
319C2×C4—12081no—
320C2×C4C2×D60411yescharacteristic
321C2×C4C2×D60411yescharacteristic
322C2×C4C2×D60411yescharacteristic
323C2×C4C2×D60411yescharacteristic
324C2×C4C2×D60411yescharacteristic
325C2×C4C23×D15111yescharacteristic
326C8—21no—
327C8—21no—
328C8—21no—
329C8—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—3022no—
334C22—3022no—
335C22—6041no—
336C22—6041no—
337C22—6041no—
338C22—6041no—
339C22—6041no—
340C22—6041no—
341C22—6041no—
342C22—12084no—
343C22C22×D60411yescharacteristic
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—6041no—
350C4—6041no—
351C4—6041no—
352C4—6041no—
353C4—6041no—
354C4#41×D15111yescharacteristic
355C4#41×D15111yescharacteristic
356C2—41no—
357C2—6042no—
358C2—6042no—
359C2—12081no—
360C2#2375272411yescharacteristic
361C2#2375301711yescharacteristic
362C2#2375302411yescharacteristic
subgroupG/H
centerC22C22×D604
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#433×C151C2
socleC22×C151C22×D4
prime radical#23752348C2
hypercenter#433D151
hypocenterC151#3118
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #23752833C2semidirect
2. #23752686C2semidirect
3. #23752554C2semidirect
4. #23752537C2semidirect
5. #23752503C2semidirect
6. #23752493C2semidirect
7. #23752428C2semidirect
8. #23752428C2semidirect
9. #23752365C2semidirect
11. #23752325C2semidirect
12. #23752314C2semidirect
13. C4×#14558993C2semidirect
14. C4×D1208C2semidirect
15. #433×C151C2semidirect
21. #18012739C22semidirect
23. #18012727C22semidirect
29. C4×Dic302C22semidirect
34. C4×D604C22semidirect
40. #18012673C22semidirect
41. #18012673C22semidirect
42. #18012671C22semidirect
43. #18012671C22semidirect
44. #18012664C22semidirect
45. #18012664C22semidirect
50. #18012661C22semidirect
51. #18012661C22semidirect
53. C4⋊C8×C151C22semidirect
54. C4⋊C8×C151C22semidirect
57. #97×C151C22semidirect
58. C4×C8×C151C22semidirect
181. C151#3118semidirect
197. #433D151semidirect
227. C4⋊C8C2×D151semidirect
228. C4⋊C8C2×D151semidirect
239. #97C2×D151semidirect
240. C4×C8C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237528332
#237526862
#237525542
#237525372
#237525032
#237524932
#237524282
#237523652
#237523482
#237523252
#237523142
C4×#145589932
C4×D12082
#433×C1512
#3118151