Finite Group Databasebeta

← #34079259

Subgroups — #34079259

Order 19328.

430 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752759C211yesmaximal, characteristic, complemented
2C4×#14559005C211yesmaximal, characteristic, complemented
3#23752539C211yesmaximal, characteristic, complemented
4#23752535C211yesmaximal, characteristic, complemented
5#23752495C211yesmaximal, characteristic, complemented
6#23752491C211yesmaximal, characteristic, complemented
7#23752410C211yesmaximal, characteristic, complemented
8#23752406C211yesmaximal, characteristic, complemented
9#23752360C211yesmaximal, characteristic, complemented
10#23752356C211yesmaximal, characteristic, complemented
11#23752325C211yesmaximal, characteristic, complemented
12#23752322C211yesmaximal, characteristic, complemented
13#23752310C211yesmaximal, characteristic, complemented
14#23752267C211yesmaximal, characteristic, complemented
15#440×C151C211yesmaximal, characteristic, complemented
16C2×#14559005C2211yescharacteristic
17C2×#14559004—21no—
18C2×#14558991C2211yescharacteristic
19C2×D1208C2211yescharacteristic
20C2×#14558989C2211yescharacteristic
21#18012738C2211yescharacteristic
22#18012735C2211yescharacteristic
23#18012725—21no—
24#18012714C2211yescharacteristic
25#18012712—21no—
26#18012710C2211yescharacteristic
27Q8×Dic151C2211yescharacteristic
28C4×D604—21no—
29C4×D604C2211yescharacteristic
30C4×D604C2211yescharacteristic
31#18012701—21no—
32#18012701C2211yescharacteristic
33C4×C22⋊D151—21no—
34#18012697—21no—
35#18012697C2211yescharacteristic
36C42×D151—21no—
37C42×D151C2211yescharacteristic
38#18012672C2211yescharacteristic
39#18012671C2211yescharacteristic
40#18012670C2211yescharacteristic
41Dic151⋊C8C2211yescharacteristic
42Dic151⋊C8C2211yescharacteristic
43#18012663C2211yescharacteristic
44#18012661C2211yescharacteristic
45#18012661C2211yescharacteristic
46#18012660C2211yescharacteristic
47#18012659C2211yescharacteristic
48#18012659C2211yescharacteristic
49(C2×D151)⋊C8C2211yescharacteristic
50(C2×D151)⋊C8C2211yescharacteristic
51#18012650C2211yescharacteristic
52C2×SD16×C151C2211yescharacteristic
53C4×Q8×C151C2211yescharacteristic
54C4×D4×C151C2211yescharacteristic
55#107×C151C2211yescharacteristic
56#103×C151C2211yescharacteristic
57#102×C151C2211yescharacteristic
58#97×C151C2211yescharacteristic
59#14559005—22no—
60#14559005—22no—
61#14559004—44no—
62C2×Dic302—21no—
63C2×D604—21no—
64C2×D604—21no—
65C2×D604C2311yescharacteristic
66C2×D604C2311yescharacteristic
67C2×C22⋊D151—21no—
68C2×C22⋊D151—21no—
69C2×C22⋊D151—21no—
70C2×C4×D151—21no—
71C2×C4×D151—21no—
72C2×C4×D151—21no—
73C2×C4×D151—21no—
74C2×C4×D151D411yescharacteristic
75C2×C4×D151D411yescharacteristic
76C2×C4×D151C2311yescharacteristic
77#14558991—22no—
78D1208—22no—
79#14558989—22no—
80C2×C151⋊C8C2311yescharacteristic
81C2×C151⋊C8C2311yescharacteristic
82C4⋊Dic151—21no—
83C4⋊Dic151C2311yescharacteristic
84C4⋊Dic151C2311yescharacteristic
85Dic151⋊C4—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—
92C4×Dic151—21no—
93C4×Dic151—21no—
94C4×Dic151D411yescharacteristic
95C4×Dic151D411yescharacteristic
96C4×Dic151C2311yescharacteristic
97C2×Q8×C151C2311yescharacteristic
98C2×D4×C151C2311yescharacteristic
99C22×C4×C151—21no—
100SD16×C151—22no—
101C2×C8×C151C2311yescharacteristic
102C2×C8×C151C2311yescharacteristic
103C4⋊C4×C151—21no—
104C4⋊C4×C151C2311yescharacteristic
105C4⋊C4×C151C2311yescharacteristic
106C22⋊C4×C151—21no—
107C42×C151—21no—
108C42×C151C2311yescharacteristic
109C22×D151—21no—
110C22×D151—21no—
111C22×D151C2×D411yescharacteristic
112Dic302—42no—
113D604—24no—
114D604—21no—
115D604—21no—
116D604—21no—
117D604—42no—
118D604#4112yescomplemented
119C22⋊D151—42no—
120C22⋊D151—42no—
121C22⋊D151—42no—
122C2×Dic151—21no—
123C2×Dic151—21no—
124C2×Dic151C2×D411yescharacteristic
125C2×Dic151C2×D411yescharacteristic
126C2×Dic151C2×D411yescharacteristic
127C4×D151—24no—
128C4×D151—21no—
129C4×D151—21no—
130C4×D151—22no—
131C4×D151—41no—
132C4×D151—42no—
133C4×D151—42no—
134C4×D151—42no—
135C151⋊C8—21no—
136C151⋊C8—21no—
137C23×C151—21no—
138Q8×C151—21no—
139Q8×C151#4112yescomplemented
140D4×C151—21no—
141D4×C151—21no—
142C2×C4×C151—21no—
143C2×C4×C151—21no—
144C2×C4×C151—21no—
145C2×C4×C151—42no—
146C2×C4×C151C2×D411yescharacteristic
147C2×C4×C151C2×D411yescharacteristic
148C2×C4×C151C2411yescharacteristic
149C8×C151—21no—
150C8×C151—21no—
151C22×C151—41no—
152C22×C151—41no—
153C22×C151—41no—
154C22×C151C22×D411yescharacteristic
155C2×D151—21no—
156C2×D151—22no—
157C2×D151—21no—
158C2×D151—21no—
159C2×D151—41no—
160C2×D151—41no—
161C2×D151—41no—
162C2×D151—41no—
163C2×D151—41no—
164C4×C151—22no—
165C4×C151—21no—
166C4×C151—21no—
167C4×C151—41no—
168C4×C151—41no—
169C4×C151C2×#4111yescharacteristic
170C4×C151C2×#4111yescharacteristic
171Dic151—21no—
172Dic151—21no—
173Dic151—41no—
174Dic151—41no—
175Dic151AGL(1,ℤ/8)12yes—
176C2×C151—81no—
177C2×C151#52511yescharacteristic
178C2×C151C2×AGL(1,ℤ/8)11yescharacteristic
179C2×C151#57511yescharacteristic
180D151—41no—
181D151—42no—
182D151—81no—
183C151#311511yescharacteristic, complemented, Sylow
184#3115—1511nomaximal, Sylow
185#532—1511no—
186C4×#41—1511no—
187#482—1511no—
188#482—1511no—
189#475—1511no—
190#474—1511no—
191#460—1511no—
192#459—1511no—
193#449—1511no—
194#449—1511no—
195#442—1511no—
196#442—1511no—
197#440—1511no—
198#440D15111yescharacteristic, complemented
199#432—1511no—
200C2×#41—3021no—
201C2×#41—1511no—
202C2×SD16—1511no—
203C2×SD16C2×D15111yescharacteristic
204C2×D8—1511no—
205C2×D8—1511no—
206C4⋊Q8—1511no—
207#127—1511no—
208#124—3021no—
209#121—3021no—
210#121—1511no—
211#121—1511no—
212C4×Q8—1511no—
213C4×Q8C2×D15111yescharacteristic
214C4×D4—3021no—
215C4×D4—3021no—
216C4×D4—3021no—
217C4×D4—1511no—
218C4×D4—1511no—
219C4×D4—1511no—
220C4×D4C2×D15111yescharacteristic
221#117—3021no—
222#117—1511no—
223C2×C42—3021no—
224C2×C42—1511no—
225#107—1511no—
226#107C2×D15111yescharacteristic
227#106—1511no—
228#106—1511no—
229C4⋊C8—1511no—
230C4⋊C8—1511no—
231#103—1511no—
232#103C2×D15111yescharacteristic
233#102—1511no—
234#102—1511no—
235#102—1511no—
236#102—1511no—
237#102—1511no—
238#102C2×D15111yescharacteristic
239C22⋊C8—1511no—
240C22⋊C8—1511no—
241#97—1511no—
242#97C2×D15111yescharacteristic
243#41—3022no—
244#41—3022no—
245#41—6044no—
246C2×Q8—3021no—
247C2×Q8C22×D15111yescharacteristic
248C2×D4—3021no—
249C2×D4—3021no—
250C2×D4—3021no—
251C2×D4—3021no—
252C2×D4—3021no—
253C2×D4—1511no—
254C2×D4—1511no—
255C2×D4C22×D15111yescharacteristic
256C22×C4—21no—
257C22×C4—3021no—
258C22×C4—3021no—
259C22×C4—3021no—
260C22×C4—3021no—
261C22×C4—1511no—
262C22×C4—1511no—
263C22×C4—1511no—
264SD16—22no—
265SD16—3022no—
266D8—3022no—
267D8—3022no—
268C2×C8—1511no—
269C2×C8—1511no—
270C2×C8C22×D15111yescharacteristic
271C2×C8C22×D15111yescharacteristic
272C4⋊C4—21no—
273C4⋊C4—3021no—
274C4⋊C4—3021no—
275C4⋊C4—1511no—
276C4⋊C4—1511no—
277C4⋊C4C22×D15111yescharacteristic
278C4⋊C4C22×D15111yescharacteristic
279C22⋊C4—21no—
280C22⋊C4—3021no—
281C22⋊C4—3021no—
282C22⋊C4—3021no—
283C22⋊C4—3021no—
284C22⋊C4—3021no—
285C22⋊C4—3021no—
286C42—21no—
287C42—3021no—
288C42—3021no—
289C42—1511no—
290C42—1511no—
291C42—1511no—
292C42C22×D15111yescharacteristic
293C23—21no—
294C23—3021no—
295C23—3021no—
296C23—1511no—
297Q8—21no—
298Q8—6042no—
299Q8#1455900412yescomplemented
300D4—21no—
301D4—21no—
302D4—3024no—
303D4—3021no—
304D4—3021no—
305D4—3021no—
306D4—6042no—
307D4—6042no—
308D4—6042no—
309D4—6042no—
310D4—1512no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—42no—
315C2×C4—3024no—
316C2×C4—3022no—
317C2×C4—3021no—
318C2×C4—3021no—
319C2×C4—3021no—
320C2×C4—3021no—
321C2×C4—6041no—
322C2×C4—6042no—
323C2×C4—6042no—
324C2×C4—6042no—
325C2×C4—1511no—
326C2×C4—1511no—
327C2×C4—1511no—
328C2×C4D4×D15111yescharacteristic
329C2×C4D4×D15111yescharacteristic
330C2×C4C23×D15111yescharacteristic
331C8—21no—
332C8—21no—
333C8—3021no—
334C8—3021no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—3021no—
339C22—3022no—
340C22—3021no—
341C22—3021no—
342C22—6041no—
343C22—6041no—
344C22—6041no—
345C22—6041no—
346C22—6041no—
347C22C2×D4×D15111yescharacteristic
348C4—22no—
349C4—21no—
350C4—21no—
351C4—41no—
352C4—41no—
353C4—3021no—
354C4—3021no—
355C4—6041no—
356C4—6041no—
357C4—1512no—
358C4#41×D15111yescharacteristic
359C4C2×#1455900411yescharacteristic
360C2—81no—
361C2—6041no—
362C2—6042no—
363C2—12081no—
364C2#2375272111yescharacteristic
365C2AGL(1,ℤ/8)×D15111yescharacteristic
366C2#2375301111yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#440×C151C2
socleC22×C151C22×D4
hypercenter#440D151
hypocenterC151#3115
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. #23752759C2semidirect
2. C4×#14559005C2semidirect
3. #23752539C2semidirect
4. #23752535C2semidirect
5. #23752495C2semidirect
6. #23752491C2semidirect
7. #23752410C2semidirect
8. #23752406C2semidirect
9. #23752360C2semidirect
10. #23752356C2semidirect
11. #23752325C2semidirect
12. #23752322C2semidirect
13. #23752310C2semidirect
14. #23752267C2semidirect
15. #440×C151C2semidirect
118. D604#41semidirect
139. Q8×C151#41semidirect
183. C151#3115semidirect
198. #440D151semidirect
299. Q8#14559004semidirect

Maximal subgroups

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

subgroupindex
#237527592
C4×#145590052
#237525392
#237525352
#237524952
#237524912
#237524102
#237524062
#237523602
#237523562
#237523252
#237523222
#237523102
#237522672
#440×C1512
#3115151