Finite Group Databasebeta

← #34077905

Subgroups — #34077905

Order 19328.

492 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
1C2×#18012760C211yesmaximal, characteristic
2C4×#14559005C211yesmaximal, characteristic, complemented
3C4×#14559003C211yesmaximal, characteristic, complemented
4#23752322C211yesmaximal, characteristic, complemented
5#23752321C211yesmaximal, characteristic, complemented
6#23752317C211yesmaximal, characteristic, complemented
7#23752316C211yesmaximal, characteristic, complemented
8#23752314C211yesmaximal, characteristic, complemented
9#23752313C211yesmaximal, characteristic, complemented
10#23752311C211yesmaximal, characteristic, complemented
11#23752249C211yesmaximal, characteristic, complemented
12#23752207C211yesmaximal, characteristic, complemented
13#23752205C211yesmaximal, characteristic, complemented
14#97×D151C211yesmaximal, characteristic, complemented
15#440×C151C211yesmaximal, characteristic, complemented
16C2×#14559005C2211yescharacteristic
17C2×#14559003C2211yescharacteristic
18#18012760C418yescomplemented
19C2×#14558994C2211yescharacteristic
20C2×#14558993C2211yescharacteristic
21C2×#14558989C2211yescharacteristic
22C2×C8×D151C2211yescharacteristic
23C2×C8×D151C2211yescharacteristic
24Q8×Dic151C2211yescharacteristic
25C4×Dic302C2211yescharacteristic
26#18012704C2211yescharacteristic
27C4×D604—21no—
28C4×D604C2211yescharacteristic
29D4×Dic151C2211yescharacteristic
30#18012701—21no—
31#18012701C2211yescharacteristic
32C4×C22⋊D151—21no—
33(C22⋊D151)⋊C4—21no—
34#18012697—21no—
35#18012697C2211yescharacteristic
36#18012697C2211yescharacteristic
37#18012695—21no—
38C2×C4×Dic151—21no—
39C42×D151—21no—
40C42×D151C2211yescharacteristic
41#18012673C2211yescharacteristic
42#18012670C2211yescharacteristic
43#18012670C2211yescharacteristic
44#18012664C2211yescharacteristic
45#18012663C2211yescharacteristic
46#18012662C2211yescharacteristic
47#18012661C2211yescharacteristic
48#18012660C2211yescharacteristic
49#18012659C2211yescharacteristic
50#18012650C2211yescharacteristic
51#18012649C2211yescharacteristic
52#18012649C2211yescharacteristic
53C2×SD16×C151C2211yescharacteristic
54C4×Q8×C151C2211yescharacteristic
55C4×D4×C151C2211yescharacteristic
56#107×C151C2211yescharacteristic
57#103×C151C2211yescharacteristic
58#102×C151C2211yescharacteristic
59#97×C151C2211yescharacteristic
60#14559005—22no—
61#14559005C2×C414yescomplemented
62#14559003—22no—
63#14559003C2×C414yescomplemented
64C2×Dic302C2311yescharacteristic
65C2×D604—21no—
66C2×D604C2311yescharacteristic
67C2×C22⋊D151—21no—
68C22×Dic151—21no—
69C22×Dic151—21no—
70C2×C4×D151—21no—
71C2×C4×D151—21no—
72C2×C4×D151—21no—
73C2×C4×D151D411yescharacteristic
74C2×C4×D151D411yescharacteristic
75C2×C4×D151C2311yescharacteristic
76#14558994C2×C414yescomplemented
77#14558993C2×C414yescomplemented
78#14558989C2×C414yescomplemented
79C2×C151⋊C8C2311yescharacteristic
80C2×C151⋊C8C2311yescharacteristic
81C8×D151—22no—
82C8×D151C2×C414yescomplemented
83C4⋊Dic151—21no—
84C4⋊Dic151C2311yescharacteristic
85C4⋊Dic151C2311yescharacteristic
86Dic151⋊C4—21no—
87Dic151⋊C4—21no—
88C22⋊Dic151—21no—
89(C2×D151)⋊C4—21no—
90(C2×D151)⋊C4—21no—
91(C2×D151)⋊C4—21no—
92(C2×D151)⋊C4—21no—
93C4×Dic151—21no—
94C4×Dic151—21no—
95C4×Dic151—21no—
96C4×Dic151—21no—
97C4×Dic151—21no—
98C4×Dic151D411yescharacteristic
99C4×Dic151D411yescharacteristic
100C4×Dic151C2311yescharacteristic
101C2×Q8×C151C2311yescharacteristic
102C2×D4×C151C2311yescharacteristic
103C22×C4×C151—21no—
104SD16×C151C2×C414yescomplemented
105C2×C8×C151C2311yescharacteristic
106C2×C8×C151C2311yescharacteristic
107C4⋊C4×C151—21no—
108C4⋊C4×C151C2311yescharacteristic
109C4⋊C4×C151C2311yescharacteristic
110C22⋊C4×C151—21no—
111C42×C151—21no—
112C42×C151C2311yescharacteristic
113C22×D151—21no—
114C22×D151C2×D411yescharacteristic
115Dic302—21no—
116Dic302C22×C412yes—
117D604—24no—
118D604—21no—
119D604C22×C412yes—
120C22⋊D151—24no—
121C2×Dic151—21no—
122C2×Dic151—24no—
123C2×Dic151—21no—
124C2×Dic151—21no—
125C2×Dic151—42no—
126C2×Dic151C2×D411yescharacteristic
127C2×Dic151C2×D411yescharacteristic
128C2×Dic151C2×D411yescharacteristic
129C4×D151—24no—
130C4×D151—41no—
131C4×D151—41no—
132C4×D151—42no—
133C4×D151—42no—
134C4×D151C22×C412yes—
135C4×D151#4112yes—
136C151⋊C8—21no—
137C151⋊C8C22×C412yes—
138C23×C151—21no—
139Q8×C151—21no—
140Q8×C151C22×C412yes—
141D4×C151—21no—
142D4×C151C22×C412yes—
143C2×C4×C151—21no—
144C2×C4×C151—21no—
145C2×C4×C151—21no—
146C2×C4×C151—42no—
147C2×C4×C151C2×D411yescharacteristic
148C2×C4×C151C2×D411yescharacteristic
149C2×C4×C151C2411yescharacteristic
150C8×C151—21no—
151C8×C151C22×C412yes—
152C22×C151—22no—
153C22×C151—41no—
154C22×C151—41no—
155C22×C151C22×D411yescharacteristic
156C2×D151—21no—
157C2×D151—21no—
158C2×D151—22no—
159C2×D151—41no—
160C2×D151—41no—
161C2×D151C4×D412yes—
162C4×C151—22no—
163C4×C151—21no—
164C4×C151—21no—
165C4×C151—41no—
166C4×C151—41no—
167C4×C151C23×C411yescharacteristic
168C4×C151C2×#4111yescharacteristic
169Dic151—22no—
170Dic151—21no—
171Dic151—21no—
172Dic151—41no—
173Dic151—41no—
174Dic151C4×D412yes—
175C2×C151—42no—
176C2×C151C2×C4×D411yescharacteristic
177C2×C151#57511yescharacteristic
178C2×C151#57511yescharacteristic
179D151—22no—
180D151—42no—
181C151#294311yescharacteristic, complemented, Sylow
182#2943—1511nomaximal, Sylow
183C2×#135—1511no—
184C4×#41—1511no—
185C4×#41—1511no—
186#442—1511no—
187#442—1511no—
188#441—1511no—
189#441—1511no—
190#440—1511no—
191#440—1511no—
192#440—1511no—
193#440D15111yescharacteristic, complemented
194#427—1511no—
195#416—1511no—
196#416—1511no—
197C2×#97—1511no—
198C2×#41—1511no—
199C2×#41—1511no—
200#135—1518no—
201C2×Q16—1511no—
202C2×SD16—1511no—
203C2×SD16C2×D15111yescharacteristic
204C2×D8—1511no—
205C22×C8—1511no—
206C22×C8—1511no—
207C4×Q8—1511no—
208C4×Q8—1511no—
209C4×Q8—1511no—
210C4×Q8C2×D15111yescharacteristic
211C4×D4—3021no—
212C4×D4—3021no—
213C4×D4—3021no—
214C4×D4—3021no—
215C4×D4—1511no—
216C4×D4—1511no—
217C4×D4—1511no—
218C4×D4C2×D15111yescharacteristic
219#117—3021no—
220#117—3021no—
221#117—1511no—
222#117—1511no—
223C2×C42—3021no—
224C2×C42—3021no—
225C2×C42—1511no—
226#107—1511no—
227#107C2×D15111yescharacteristic
228#106—1511no—
229#106—1511no—
230#103—1511no—
231#103—1511no—
232#103—1511no—
233#103C2×D15111yescharacteristic
234#102—1511no—
235#102—1511no—
236#102—1511no—
237#102C2×D15111yescharacteristic
238#97—1511no—
239#97—1511no—
240#97—1511no—
241#97C2×D15111yescharacteristic
242#41—3022no—
243#41—3022no—
244#41—1514no—
245#41—1514no—
246C2×Q8—1511no—
247C2×Q8C22×D15111yescharacteristic
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—3021no—
257C22×C4—3021no—
258C22×C4—1511no—
259C22×C4—1511no—
260C22×C4—1511no—
261Q16—1514no—
262SD16—1514no—
263SD16C4×D15114yescomplemented
264D8—1514no—
265C2×C8—3022no—
266C2×C8—1511no—
267C2×C8—1511no—
268C2×C8—1514no—
269C2×C8C22×D15111yescharacteristic
270C2×C8C22×D15111yescharacteristic
271C4⋊C4—21no—
272C4⋊C4—3021no—
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—
285C42—21no—
286C42—3021no—
287C42—3021no—
288C42—3021no—
289C42—3021no—
290C42—3021no—
291C42—1511no—
292C42—1511no—
293C42—1511no—
294C42C22×D15111yescharacteristic
295C23—21no—
296C23—3021no—
297C23—1511no—
298Q8—21no—
299Q8—3021no—
300Q8—1512no—
301Q8C2×C4×D15112yes—
302D4—21no—
303D4—3024no—
304D4—3024no—
305D4—3021no—
306D4—1512no—
307D4C2×C4×D15112yes—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—42no—
312C2×C4—3024no—
313C2×C4—3021no—
314C2×C4—3024no—
315C2×C4—3021no—
316C2×C4—3021no—
317C2×C4—6041no—
318C2×C4—6041no—
319C2×C4—6042no—
320C2×C4—6042no—
321C2×C4—6042no—
322C2×C4—1511no—
323C2×C4—1511no—
324C2×C4—1511no—
325C2×C4—1512no—
326C2×C4—1512no—
327C2×C4D4×D15111yescharacteristic
328C2×C4D4×D15111yescharacteristic
329C2×C4C23×D15111yescharacteristic
330C8—21no—
331C8—3021no—
332C8—1512no—
333C8C2×C4×D15112yes—
334C22—22no—
335C22—41no—
336C22—41no—
337C22—3021no—
338C22—3021no—
339C22—3022no—
340C22—6041no—
341C22—6041no—
342C22—1512no—
343C22C2×D4×D15111yescharacteristic
344C4—21no—
345C4—21no—
346C4—22no—
347C4—41no—
348C4—41no—
349C4—3021no—
350C4—3021no—
351C4—3022no—
352C4—6041no—
353C4—6041no—
354C4—1512no—
355C4C22×C4×D15111yescharacteristic
356C4#41×D15111yescharacteristic
357C2—42no—
358C2—3022no—
359C2—6042no—
360C2C4×D4×D15111yescharacteristic
361C2#2375300811yescharacteristic
362C2#2375301111yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutatorC4×C151C23×C4
FrattiniC2×C4C23×D151
Fitting#440×C151C2
socleC22×C151C22×D4
prime radicalC2×#18012760C2
cosocleC2×C4×C151C24
hypercenter#440D151
hypocenterC151#2943
LCSG ▷ 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×#14559005C2semidirect
3. C4×#14559003C2semidirect
4. #23752322C2semidirect
5. #23752321C2semidirect
6. #23752317C2semidirect
7. #23752316C2semidirect
8. #23752314C2semidirect
9. #23752313C2semidirect
10. #23752311C2semidirect
11. #23752249C2semidirect
12. #23752207C2semidirect
13. #23752205C2semidirect
14. #97×D151C2semidirect
15. #440×C151C2semidirect
18. #18012760C4semidirect
61. #14559005C2×C4semidirect
63. #14559003C2×C4semidirect
76. #14558994C2×C4semidirect
77. #14558993C2×C4semidirect
78. #14558989C2×C4semidirect
82. C8×D151C2×C4semidirect
104. SD16×C151C2×C4semidirect
181. C151#2943semidirect
193. #440D151semidirect
263. SD16C4×D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127602
C4×#145590052
C4×#145590032
#237523222
#237523212
#237523172
#237523162
#237523142
#237523132
#237523112
#237522492
#237522072
#237522052
#97×D1512
#440×C1512
#2943151