Finite Group Databasebeta

← #34079698

Subgroups — #34079698

Order 19328.

408 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#23752757C211yesmaximal, characteristic, complemented
2#23752748C211yesmaximal, characteristic, complemented
3#23752620C211yesmaximal, characteristic, complemented
4#23752598C211yesmaximal, characteristic, complemented
5#23752575C211yesmaximal, characteristic, complemented
6#23752573C211yesmaximal, characteristic, complemented
7#23752465C211yesmaximal, characteristic, complemented
8#23752463C211yesmaximal, characteristic, complemented
9#23752460C211yesmaximal, characteristic, complemented
10SD16×Dic151C211yesmaximal, characteristic, complemented
11#23752297C211yesmaximal, characteristic, complemented
12#23752294C211yesmaximal, characteristic, complemented
13#23752292C211yesmaximal, characteristic, complemented
14M16×Dic151C211yesmaximal, characteristic, complemented
15#468×C151C211yesmaximal, characteristic, complemented
16C2×#14559003—21no—
17C2×#14558991C2211yescharacteristic
18C2×D1208C2211yescharacteristic
19C2×#14558989C2211yescharacteristic
20C2×#14558988C2211yescharacteristic
21#18012738C2211yescharacteristic
22#18012735C2211yescharacteristic
23#18012734—21no—
24#18012730C2211yescharacteristic
25#18012728C2211yescharacteristic
26#18012725—21no—
27#18012723—21no—
28#18012713C2211yescharacteristic
29#18012713C2211yescharacteristic
30#18012711—21no—
31Q8×Dic151C2211yescharacteristic
32D4×Dic151C2211yescharacteristic
33#18012701C2211yescharacteristic
34#18012701C2211yescharacteristic
35(C22⋊D151)⋊C4—21no—
36(C22⋊D151)⋊C4—21no—
37#18012697—21no—
38C2×C4×Dic151C2211yescharacteristic
39#18012672C2211yescharacteristic
40#18012671C2211yescharacteristic
41#18012670C2211yescharacteristic
42#18012663C2211yescharacteristic
43#18012661C2211yescharacteristic
44#18012661C2211yescharacteristic
45#18012660C2211yescharacteristic
46#18012659C2211yescharacteristic
47#18012659C2211yescharacteristic
48#18012649C2211yescharacteristic
49#18012649C2211yescharacteristic
50C8×Dic151C2211yescharacteristic
51C8×Dic151C2211yescharacteristic
52C2×SD16×C151C2211yescharacteristic
53C2×M16×C151C2211yescharacteristic
54C22⋊Q8×C151C2211yescharacteristic
55#121×C151C2211yescharacteristic
56#107×C151C2211yescharacteristic
57#103×C151C2211yescharacteristic
58#102×C151C2211yescharacteristic
59#14559003—44no—
60C2×Dic302—21no—
61C2×D604C2311yescharacteristic
62C2×D604C2311yescharacteristic
63C2×C22⋊D151—21no—
64C2×C22⋊D151—21no—
65C2×C22⋊D151—21no—
66C2×C22⋊D151—21no—
67C22×Dic151—21no—
68C22×Dic151D411yescharacteristic
69C22×Dic151D411yescharacteristic
70C2×C4×D151—21no—
71C2×C4×D151—21no—
72#14558991—22no—
73D1208—22no—
74#14558989—22no—
75#14558988—22no—
76C2×C151⋊C8C2311yescharacteristic
77C2×C151⋊C8C2311yescharacteristic
78C4⋊Dic151—21no—
79C4⋊Dic151—21no—
80C4⋊Dic151C2311yescharacteristic
81C4⋊Dic151C2311yescharacteristic
82Dic151⋊C4—21no—
83Dic151⋊C4—21no—
84C22⋊Dic151—21no—
85(C2×D151)⋊C4—21no—
86(C2×D151)⋊C4—21no—
87(C2×D151)⋊C4—21no—
88(C2×D151)⋊C4—21no—
89(C2×D151)⋊C4—21no—
90(C2×D151)⋊C4—21no—
91C4×Dic151—21no—
92C4×Dic151D411yescharacteristic
93C4×Dic151D411yescharacteristic
94C4×Dic151C2311yescharacteristic
95C4×Dic151C2311yescharacteristic
96C2×Q8×C151C2311yescharacteristic
97C2×D4×C151—21no—
98C2×D4×C151C2311yescharacteristic
99C22×C4×C151C2311yescharacteristic
100SD16×C151—22no—
101M16×C151—22no—
102C2×C8×C151C2311yescharacteristic
103C2×C8×C151C2311yescharacteristic
104C4⋊C4×C151—21no—
105C4⋊C4×C151C2311yescharacteristic
106C4⋊C4×C151C2311yescharacteristic
107C22⋊C4×C151—21no—
108C22⋊C4×C151—21no—
109C22×D151—21no—
110C22×D151—21no—
111Dic302—42no—
112D604—21no—
113D604—21no—
114D604—21no—
115D604—21no—
116C22⋊D151—42no—
117C22⋊D151—42no—
118C22⋊D151—42no—
119C22⋊D151—42no—
120C2×Dic151—22no—
121C2×Dic151—21no—
122C2×Dic151—21no—
123C2×Dic151—41no—
124C2×Dic151—42no—
125C2×Dic151C2×D411yescharacteristic
126C2×Dic151C2×D411yescharacteristic
127C2×Dic151C2×D411yescharacteristic
128C2×Dic151C2×D411yescharacteristic
129C4×D151—42no—
130C4×D151—42no—
131C151⋊C8—21no—
132C151⋊C8#4112yescomplemented
133C23×C151—21no—
134C23×C151C2×D411yescharacteristic
135Q8×C151—21no—
136Q8×C151—21no—
137D4×C151—21no—
138D4×C151—21no—
139D4×C151—42no—
140C2×C4×C151—21no—
141C2×C4×C151—21no—
142C2×C4×C151—21no—
143C2×C4×C151—21no—
144C2×C4×C151—21no—
145C2×C4×C151C2×D411yescharacteristic
146C2×C4×C151C2411yescharacteristic
147C8×C151—21no—
148C8×C151#4112yescomplemented
149C22×C151—21no—
150C22×C151—21no—
151C22×C151—21no—
152C22×C151—41no—
153C22×C151—41no—
154C22×C151—41no—
155C22×C151C22×D411yescharacteristic
156C2×D151—41no—
157C2×D151—41no—
158C2×D151—41no—
159C2×D151—41no—
160C2×D151—41no—
161C2×D151—41no—
162C4×C151—21no—
163C4×C151—41no—
164C4×C151—41no—
165C4×C151—41no—
166C4×C151C2×#4111yescharacteristic
167C4×C151C2×#4111yescharacteristic
168Dic151—21no—
169Dic151—21no—
170Dic151—21no—
171Dic151—41no—
172Dic151—41no—
173Dic151AGL(1,ℤ/8)12yes—
174C2×C151—41no—
175C2×C151—81no—
176C2×C151#53211yescharacteristic
177C2×C151C2×AGL(1,ℤ/8)11yescharacteristic
178C2×C151#57511yescharacteristic
179D151—81no—
180D151—81no—
181C151#317111yescharacteristic, complemented, Sylow
182#3171—1511nomaximal, Sylow
183#532—1511no—
184#529—1511no—
185#501—1511no—
186#496—1511no—
187#490—1511no—
188#489—1511no—
189#469—1511no—
190#469—1511no—
191#468—1511no—
192#468D15111yescharacteristic, complemented
193C4×SD16—1511no—
194C4×SD16—1511no—
195C4×D8—1511no—
196C4×D8—1511no—
197C4×M16—1511no—
198C2×#41—3021no—
199C2×SD16—1511no—
200C2×SD16C2×D15111yescharacteristic
201C2×D8—1511no—
202C2×D8—1511no—
203C2×M16—1511no—
204C2×M16C2×D15111yescharacteristic
205C4⋊Q8—1511no—
206#127—1511no—
207#126—3021no—
208#125—1511no—
209#124—3021no—
210#124—1511no—
211#123—3021no—
212C22⋊Q8C2×D15111yescharacteristic
213#121—3021no—
214#121—1511no—
215#121—1511no—
216#121C2×D15111yescharacteristic
217C4×Q8—1511no—
218C4×D4—3021no—
219C4×D4—3021no—
220C4×D4—1511no—
221C4×D4—1511no—
222C4×D4—1511no—
223#117—3021no—
224C2×C42—1511no—
225#107—1511no—
226#107C2×D15111yescharacteristic
227#106—1511no—
228#106—1511no—
229#103—1511no—
230#103C2×D15111yescharacteristic
231#102—1511no—
232#102—1511no—
233#102—1511no—
234#102—1511no—
235#102—1511no—
236#102C2×D15111yescharacteristic
237#97—1511no—
238#97—1511no—
239C4×C8—1511no—
240C4×C8—1511no—
241#41—6044no—
242C2×Q8—3021no—
243C2×Q8C22×D15111yescharacteristic
244C2×D4—21no—
245C2×D4—3021no—
246C2×D4—3021no—
247C2×D4—3021no—
248C2×D4—3021no—
249C2×D4—1511no—
250C2×D4—1511no—
251C2×D4C22×D15111yescharacteristic
252C22×C4—3021no—
253C22×C4—3021no—
254C22×C4—3021no—
255C22×C4—1511no—
256C22×C4—1511no—
257C22×C4C22×D15111yescharacteristic
258SD16—22no—
259SD16—3022no—
260D8—3022no—
261D8—3022no—
262M16—22no—
263M16—3022no—
264C2×C8—1511no—
265C2×C8—1511no—
266C2×C8C22×D15111yescharacteristic
267C2×C8C22×D15111yescharacteristic
268C4⋊C4—21no—
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—21no—
279C22⋊C4—3021no—
280C22⋊C4—3021no—
281C22⋊C4—3021no—
282C22⋊C4—3021no—
283C22⋊C4—3021no—
284C22⋊C4—3021no—
285C22⋊C4—3021no—
286C42—3021no—
287C42—1511no—
288C42—1511no—
289C42—1511no—
290C42—1511no—
291C23—21no—
292C23—3021no—
293C23—3021no—
294C23D4×D15111yescharacteristic
295Q8—21no—
296Q8—21no—
297Q8—6042no—
298D4—21no—
299D4—21no—
300D4—42no—
301D4—3021no—
302D4—3021no—
303D4—3021no—
304D4—3021no—
305D4—6042no—
306D4—6042no—
307D4—6042no—
308D4—6042no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—3022no—
315C2×C4—3021no—
316C2×C4—3021no—
317C2×C4—6042no—
318C2×C4—6042no—
319C2×C4—6041no—
320C2×C4—6042no—
321C2×C4—1511no—
322C2×C4—1511no—
323C2×C4—1511no—
324C2×C4—1511no—
325C2×C4D4×D15111yescharacteristic
326C2×C4C23×D15111yescharacteristic
327C8—21no—
328C8—3021no—
329C8—1512no—
330C8#1455900312yescomplemented
331C22—21no—
332C22—21no—
333C22—21no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—6041no—
338C22—6041no—
339C22—6041no—
340C22—6041no—
341C22—6041no—
342C22—6041no—
343C22C2×D4×D15111yescharacteristic
344C4—21no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—3021no—
349C4—3021no—
350C4—3021no—
351C4—6041no—
352C4—6041no—
353C4—1512no—
354C4#41×D15111yescharacteristic
355C4C2×#1455900311yescharacteristic
356C2—41no—
357C2—81no—
358C2—12081no—
359C2—12081no—
360C2#2375275711yescharacteristic
361C2AGL(1,ℤ/8)×D15111yescharacteristic
362C2#2375301111yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#468×C151C2
socleC22×C151C22×D4
hypercenter#468D151
hypocenterC151#3171
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. #23752757C2semidirect
2. #23752748C2semidirect
3. #23752620C2semidirect
4. #23752598C2semidirect
5. #23752575C2semidirect
6. #23752573C2semidirect
7. #23752465C2semidirect
8. #23752463C2semidirect
9. #23752460C2semidirect
10. SD16×Dic151C2semidirect
11. #23752297C2semidirect
12. #23752294C2semidirect
13. #23752292C2semidirect
14. M16×Dic151C2semidirect
15. #468×C151C2semidirect
132. C151⋊C8#41semidirect
148. C8×C151#41semidirect
181. C151#3171semidirect
192. #468D151semidirect
330. C8#14559003semidirect

Maximal subgroups

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

subgroupindex
#237527572
#237527482
#237526202
#237525982
#237525752
#237525732
#237524652
#237524632
#237524602
SD16×Dic1512
#237522972
#237522942
#237522922
M16×Dic1512
#468×C1512
#3171151