Finite Group Databasebeta

← #34079230

Subgroups — #34079230

Order 19328.

424 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752759C211yesmaximal, characteristic
2C4×Q8×D151C211yesmaximal, characteristic, complemented
3#23752527C211yesmaximal, characteristic, complemented
4#23752524C211yesmaximal, characteristic, complemented
5#23752506C211yesmaximal, characteristic, complemented
6#23752505C211yesmaximal, characteristic, complemented
7#23752411C211yesmaximal, characteristic, complemented
8#23752410C211yesmaximal, characteristic, complemented
9#23752352C211yesmaximal, characteristic, complemented
10#23752349C211yesmaximal, characteristic, complemented
11#23752314C211yesmaximal, characteristic, complemented
12#23752312C211yesmaximal, characteristic, complemented
13#23752310C211yesmaximal, characteristic, complemented
14#23752267C211yesmaximal, characteristic, complemented
15#440×C151C211yesmaximal, characteristic, complemented
16C2×#14559004—21no—
17C2×Q8×D151C2211yescharacteristic
18C2×#14558993C2211yescharacteristic
19C2×#14558992C2211yescharacteristic
20C2×#14558991C2211yescharacteristic
21#18012738C2211yescharacteristic
22#18012735C2211yescharacteristic
23#18012725—21no—
24#18012714C2211yescharacteristic
25#18012712—21no—
26#18012710C2211yescharacteristic
27Q8×Dic151C2211yescharacteristic
28C4×Dic302—21no—
29C4×Dic302C2211yescharacteristic
30#18012704—21no—
31#18012704C2211yescharacteristic
32C4×D604C2211yescharacteristic
33C4×C22⋊D151—21no—
34C4⋊C4×D151—21no—
35C4⋊C4×D151C2211yescharacteristic
36C42×D151—21no—
37C42×D151C2211yescharacteristic
38#18012673C2211yescharacteristic
39#18012672C2211yescharacteristic
40#18012672C2211yescharacteristic
41Dic151⋊C8C2211yescharacteristic
42Dic151⋊C8C2211yescharacteristic
43#18012664C2211yescharacteristic
44#18012663C2211yescharacteristic
45#18012662C2211yescharacteristic
46#18012661C2211yescharacteristic
47#18012660C2211yescharacteristic
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#14559004—44no—
60C2×Dic302—21no—
61C2×Dic302—21no—
62C2×Dic302C2311yescharacteristic
63Q8×D151—22no—
64Q8×D151—22no—
65C2×D604—21no—
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×D151D411yescharacteristic
74C2×C4×D151D411yescharacteristic
75C2×C4×D151C2311yescharacteristic
76#14558993—22no—
77#14558992—22no—
78#14558991—22no—
79C2×C151⋊C8C2311yescharacteristic
80C2×C151⋊C8C2311yescharacteristic
81C4⋊Dic151—21no—
82C4⋊Dic151C2311yescharacteristic
83C4⋊Dic151C2311yescharacteristic
84Dic151⋊C4—21no—
85Dic151⋊C4—21no—
86Dic151⋊C4—21no—
87Dic151⋊C4—21no—
88C22⋊Dic151—21no—
89(C2×D151)⋊C4—21no—
90(C2×D151)⋊C4—21no—
91C4×Dic151—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×D151C2×D411yescharacteristic
111Dic302—24no—
112Dic302—21no—
113Dic302—42no—
114Dic302#4112yescomplemented
115D604—21no—
116D604—21no—
117D604—42no—
118C22⋊D151—42no—
119C22⋊D151—42no—
120C22⋊D151—42no—
121C2×Dic151—21no—
122C2×Dic151—21no—
123C2×Dic151—21no—
124C2×Dic151C2×D411yescharacteristic
125C2×Dic151C2×D411yescharacteristic
126C2×Dic151C2×D411yescharacteristic
127C4×D151—24no—
128C4×D151—22no—
129C4×D151—21no—
130C4×D151—21no—
131C4×D151—22no—
132C4×D151—42no—
133C4×D151—42no—
134C151⋊C8—21no—
135C151⋊C8—21no—
136C23×C151—21no—
137Q8×C151—21no—
138Q8×C151#4112yescomplemented
139D4×C151—21no—
140D4×C151—21no—
141C2×C4×C151—21no—
142C2×C4×C151—21no—
143C2×C4×C151—21no—
144C2×C4×C151—42no—
145C2×C4×C151C2×D411yescharacteristic
146C2×C4×C151C2×D411yescharacteristic
147C2×C4×C151C2411yescharacteristic
148C8×C151—21no—
149C8×C151—21no—
150C22×C151—41no—
151C22×C151—41no—
152C22×C151—41no—
153C22×C151C22×D411yescharacteristic
154C2×D151—21no—
155C2×D151—21no—
156C2×D151—41no—
157C2×D151—41no—
158C2×D151—41no—
159C2×D151AGL(1,ℤ/8)12yes—
160C4×C151—22no—
161C4×C151—21no—
162C4×C151—21no—
163C4×C151—41no—
164C4×C151—41no—
165C4×C151C2×#4111yescharacteristic
166C4×C151C2×#4111yescharacteristic
167Dic151—22no—
168Dic151—21no—
169Dic151—21no—
170Dic151—41no—
171Dic151—41no—
172Dic151#13712yes—
173C2×C151—81no—
174C2×C151#52511yescharacteristic
175C2×C151C2×AGL(1,ℤ/8)11yescharacteristic
176C2×C151C2×#13711yescharacteristic
177D151—22no—
178D151—81no—
179C151#311211yescharacteristic, complemented, Sylow
180#3112—1511nomaximal, Sylow
181#532—1511no—
182C2×C4×Q8—1511no—
183#480—1511no—
184#480—1511no—
185#477—1511no—
186#477—1511no—
187#460—1511no—
188#460—1511no—
189#448—1511no—
190#448—1511no—
191#440—1511no—
192#440—1511no—
193#440—1511no—
194#440D15111yescharacteristic, complemented
195#432—1511no—
196C2×#41—3021no—
197C22×Q8—1511no—
198C2×SD16—1511no—
199C2×SD16—1511no—
200C2×SD16—1511no—
201C2×SD16C2×D15111yescharacteristic
202C4⋊Q8—1511no—
203#127—1511no—
204#124—3021no—
205#121—3021no—
206#121—1511no—
207#121—1511no—
208C4×Q8—3021no—
209C4×Q8—3021no—
210C4×Q8—1511no—
211C4×Q8—1511no—
212C4×Q8—1511no—
213C4×Q8C2×D15111yescharacteristic
214C4×D4—3021no—
215C4×D4—1511no—
216C4×D4C2×D15111yescharacteristic
217C2×C4⋊C4—3021no—
218C2×C4⋊C4—1511no—
219C2×C42—3021no—
220C2×C42—1511no—
221#107—1511no—
222#107—1511no—
223#107—1511no—
224#107C2×D15111yescharacteristic
225C4⋊C8—1511no—
226C4⋊C8—1511no—
227#103—1511no—
228#103—1511no—
229#103—1511no—
230#103C2×D15111yescharacteristic
231#102—1511no—
232#102—1511no—
233#102—1511no—
234#102C2×D15111yescharacteristic
235C22⋊C8—1511no—
236C22⋊C8—1511no—
237#97—1511no—
238#97C2×D15111yescharacteristic
239#41—6044no—
240C2×Q8—3021no—
241C2×Q8—3021no—
242C2×Q8—3022no—
243C2×Q8—3022no—
244C2×Q8—1511no—
245C2×Q8C22×D15111yescharacteristic
246C2×D4—3021no—
247C2×D4—3021no—
248C2×D4—3021no—
249C2×D4—3021no—
250C2×D4—1511no—
251C2×D4C22×D15111yescharacteristic
252C22×C4—21no—
253C22×C4—3021no—
254C22×C4—3021no—
255C22×C4—3021no—
256C22×C4—1511no—
257C22×C4—1511no—
258C22×C4—1511no—
259SD16—22no—
260SD16—3022no—
261SD16—3022no—
262SD16—3022no—
263C2×C8—1511no—
264C2×C8—1511no—
265C2×C8C22×D15111yescharacteristic
266C2×C8C22×D15111yescharacteristic
267C4⋊C4—21no—
268C4⋊C4—3021no—
269C4⋊C4—3021no—
270C4⋊C4—3021no—
271C4⋊C4—3021no—
272C4⋊C4—3021no—
273C4⋊C4—1511no—
274C4⋊C4—1511no—
275C4⋊C4C22×D15111yescharacteristic
276C4⋊C4C22×D15111yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—3021no—
279C22⋊C4—3021no—
280C22⋊C4—3021no—
281C42—21no—
282C42—3021no—
283C42—3021no—
284C42—3021no—
285C42—1511no—
286C42—1511no—
287C42—1511no—
288C42C22×D15111yescharacteristic
289C23—21no—
290C23—3021no—
291C23—1511no—
292Q8—21no—
293Q8—3024no—
294Q8—3021no—
295Q8—6042no—
296Q8—1512no—
297Q8#1455900412yescomplemented
298D4—21no—
299D4—21no—
300D4—3021no—
301D4—3021no—
302D4—6042no—
303D4—6042no—
304D4—6042no—
305D4—6042no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—42no—
310C2×C4—3024no—
311C2×C4—3022no—
312C2×C4—3022no—
313C2×C4—3021no—
314C2×C4—3021no—
315C2×C4—3021no—
316C2×C4—3021no—
317C2×C4—3021no—
318C2×C4—6042no—
319C2×C4—6042no—
320C2×C4—1511no—
321C2×C4—1511no—
322C2×C4—1511no—
323C2×C4D4×D15111yescharacteristic
324C2×C4D4×D15111yescharacteristic
325C2×C4C23×D15111yescharacteristic
326C8—21no—
327C8—21no—
328C8—3021no—
329C8—3021no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—3021no—
334C22—3021no—
335C22—6041no—
336C22—6041no—
337C22—6041no—
338C22—1512no—
339C22C2×D4×D15111yescharacteristic
340C4—22no—
341C4—21no—
342C4—21no—
343C4—41no—
344C4—41no—
345C4—3022no—
346C4—3021no—
347C4—3021no—
348C4—6041no—
349C4—6041no—
350C4—1512no—
351C4#41×D15111yescharacteristic
352C4C2×#1455900411yescharacteristic
353C2—81no—
354C2—3022no—
355C2—12081no—
356C2#2375272111yescharacteristic
357C2AGL(1,ℤ/8)×D15111yescharacteristic
358C2#137×D15111yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#440×C151C2
socleC22×C151C22×D4
prime radical#23752759C2
hypercenter#440D151
hypocenterC151#3112
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
2. C4×Q8×D151C2semidirect
3. #23752527C2semidirect
4. #23752524C2semidirect
5. #23752506C2semidirect
6. #23752505C2semidirect
7. #23752411C2semidirect
8. #23752410C2semidirect
9. #23752352C2semidirect
10. #23752349C2semidirect
11. #23752314C2semidirect
12. #23752312C2semidirect
13. #23752310C2semidirect
14. #23752267C2semidirect
15. #440×C151C2semidirect
114. Dic302#41semidirect
138. Q8×C151#41semidirect
179. C151#3112semidirect
194. #440D151semidirect
297. Q8#14559004semidirect

Maximal subgroups

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

subgroupindex
#237527592
C4×Q8×D1512
#237525272
#237525242
#237525062
#237525052
#237524112
#237524102
#237523522
#237523492
#237523142
#237523122
#237523102
#237522672
#440×C1512
#3112151