Finite Group Databasebeta

← #34080991

Subgroups — #34080991

Order 19328.

386 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752871C211yesmaximal, characteristic
2#23752569C211yesmaximal, characteristic, complemented
3#23752553C211yesmaximal, characteristic, complemented
4#23752525C211yesmaximal, characteristic, complemented
5#23752516C211yesmaximal, characteristic, complemented
6#23752451C211yesmaximal, characteristic, complemented
7#23752443C211yesmaximal, characteristic, complemented
8#23752434C211yesmaximal, characteristic, complemented
9#23752372C211yesmaximal, characteristic, complemented
10#23752367C211yesmaximal, characteristic, complemented
11C4×#14558994C211yesmaximal, characteristic, complemented
12D4×C151⋊C8C211yesmaximal, characteristic, complemented
13#23752206C211yesmaximal, characteristic, complemented
14C2×#18012662C211yesmaximal, characteristic, complemented
15#552×C151C211yesmaximal, characteristic, complemented
16C2×#14559004C2211yescharacteristic
17C22×Dic302C2211yescharacteristic
18C2×#14558994C2211yescharacteristic
19C2×#14558994C2211yescharacteristic
20C2×#14558991C2211yescharacteristic
21C22×C151⋊C8C2211yescharacteristic
22C22×C151⋊C8C2211yescharacteristic
23#18012727C2211yescharacteristic
24#18012725—21no—
25#18012718C2211yescharacteristic
26#18012717—21no—
27#18012713C2211yescharacteristic
28#18012711—21no—
29C4×Dic302C2211yescharacteristic
30(C22⋊D151)⋊C4—21no—
31#18012672C2211yescharacteristic
32#18012672C2211yescharacteristic
33#18012670C2211yescharacteristic
34C4⋊(C151⋊C8)C2211yescharacteristic
35#18012663C2211yescharacteristic
36#18012662C2211yescharacteristic
37#18012662C2211yescharacteristic
38#18012662C2211yescharacteristic
39#18012662C2211yescharacteristic
40#18012662C2211yescharacteristic
41#18012662C2211yescharacteristic
42#18012659C2211yescharacteristic
43#18012659C2211yescharacteristic
44#18012659C2211yescharacteristic
45C22⋊(C151⋊C8)C2211yescharacteristic
46C22⋊(C151⋊C8)C2211yescharacteristic
47C4×C151⋊C8C2211yescharacteristic
48#126×C151—21no—
49#125×C151—21no—
50#125×C151C2211yescharacteristic
51#123×C151—21no—
52C22⋊Q8×C151C2211yescharacteristic
53C22⋊Q8×C151C2211yescharacteristic
54C4×Q8×C151C2211yescharacteristic
55C4×D4×C151C2211yescharacteristic
56#117×C151—21no—
57#117×C151C2211yescharacteristic
58C2×C4⋊C4×C151C2211yescharacteristic
59#14559004—22no—
60#14559004—41no—
61C2×Dic302—22no—
62C2×Dic302—21no—
63C2×Dic302—41no—
64C2×Dic302C2311yescharacteristic
65C2×Dic302C2311yescharacteristic
66C2×D604C2311yescharacteristic
67C2×C22⋊D151—21no—
68C2×C22⋊D151—21no—
69C22×Dic151—21no—
70C2×C4×D151—21no—
71#14558994—22no—
72#14558994—41no—
73#14558991—41no—
74C2×C151⋊C8—41no—
75C2×C151⋊C8—41no—
76C2×C151⋊C8C2311yescharacteristic
77C2×C151⋊C8C2311yescharacteristic
78C2×C151⋊C8C2311yescharacteristic
79C2×C151⋊C8C2311yescharacteristic
80C4⋊Dic151C2311yescharacteristic
81Dic151⋊C4—21no—
82Dic151⋊C4—21no—
83C22⋊Dic151—21no—
84(C2×D151)⋊C4—21no—
85(C2×D151)⋊C4—21no—
86(C2×D151)⋊C4—21no—
87C4×Dic151—21no—
88C2×Q8×C151C2311yescharacteristic
89C2×D4×C151D411yescharacteristic
90C22×C4×C151—21no—
91C22×C4×C151C2311yescharacteristic
92C22×C4×C151C2311yescharacteristic
93C4⋊C4×C151—21no—
94C4⋊C4×C151—21no—
95C4⋊C4×C151—21no—
96C4⋊C4×C151—21no—
97C4⋊C4×C151—21no—
98C4⋊C4×C151—21no—
99C4⋊C4×C151D411yescharacteristic
100C4⋊C4×C151C2311yescharacteristic
101C4⋊C4×C151C2311yescharacteristic
102C4⋊C4×C151C2311yescharacteristic
103C22⋊C4×C151—21no—
104C22⋊C4×C151—21no—
105C22⋊C4×C151—21no—
106C22⋊C4×C151D411yescharacteristic
107C22⋊C4×C151D411yescharacteristic
108C42×C151—21no—
109C42×C151—21no—
110C42×C151C2311yescharacteristic
111C22×D151—21no—
112Dic302—21no—
113Dic302—21no—
114Dic302—21no—
115Dic302—42no—
116Dic302#4112yes—
117D604—21no—
118D604—21no—
119C22⋊D151—42no—
120C22⋊D151—42no—
121C2×Dic151—21no—
122C2×Dic151—21no—
123C2×Dic151—21no—
124C2×Dic151—42no—
125C4×D151—42no—
126C151⋊C8—21no—
127C151⋊C8—21no—
128C151⋊C8—21no—
129C151⋊C8—21no—
130C23×C151C2×D411yescharacteristic
131C23×C151C2×D411yescharacteristic
132Q8×C151—21no—
133Q8×C151—21no—
134D4×C151—22no—
135C2×C4×C151—21no—
136C2×C4×C151—21no—
137C2×C4×C151—21no—
138C2×C4×C151—21no—
139C2×C4×C151—21no—
140C2×C4×C151—21no—
141C2×C4×C151—21no—
142C2×C4×C151—21no—
143C2×C4×C151—42no—
144C2×C4×C151C2×D411yescharacteristic
145C2×C4×C151C2×D411yescharacteristic
146C2×C4×C151C2×D411yescharacteristic
147C2×C4×C151C2×D411yescharacteristic
148C2×C4×C151C2411yescharacteristic
149C22×C151—21no—
150C22×C151—21no—
151C22×C151—21no—
152C22×C151—21no—
153C22×C151—21no—
154C22×C151#13512yes—
155C22×C151C22×D411yescharacteristic
156C2×D151—41no—
157C2×D151—41no—
158C2×D151—41no—
159C4×C151—21no—
160C4×C151—21no—
161C4×C151—21no—
162C4×C151—21no—
163C4×C151—41no—
164C4×C151—41no—
165C4×C151—41no—
166C4×C151—41no—
167C4×C151C2×#4111yescharacteristic
168C4×C151H(5,𝔽2)11yescharacteristic
169Dic151—22no—
170Dic151—41no—
171Dic151—41no—
172C2×C151—22no—
173C2×C151—41no—
174C2×C151#54611yescharacteristic
175C2×C151C2×#13511yescharacteristic
176C2×C151#57811yescharacteristic
177D151—81no—
178C151#330011yescharacteristic, complemented, Sylow
179#3300—1511nomaximal, Sylow
180#552D15111yescharacteristic, complemented
181#548—1511no—
182#488—1511no—
183#485—1511no—
184#480—1511no—
185#479—1511no—
186#467—1511no—
187#465—1511no—
188#464—1511no—
189#452—1511no—
190#451—1511no—
191C4×Q16—1511no—
192C8×D4—1511no—
193#416—1511no—
194C2×#103—1511no—
195C2×#41—1511no—
196C22×Q8—1511no—
197C2×Q16—1511no—
198C2×Q16—1511no—
199C2×SD16—1511no—
200C22×C8—1511no—
201C22×C8—1511no—
202#126—21no—
203#125—21no—
204#125C2×D15111yescharacteristic
205#124—3021no—
206#124—1511no—
207#123—21no—
208C22⋊Q8—3021no—
209C22⋊Q8—1511no—
210C22⋊Q8C2×D15111yescharacteristic
211C22⋊Q8C2×D15111yescharacteristic
212#121—3021no—
213#121—1511no—
214C4×Q8—1511no—
215C4×Q8C2×D15111yescharacteristic
216C4×D4—3021no—
217C4×D4C2×D15111yescharacteristic
218#117—21no—
219#117C2×D15111yescharacteristic
220C2×C4⋊C4C2×D15111yescharacteristic
221#107—1511no—
222#107—1511no—
223#106—1511no—
224C4⋊C8—1511no—
225#103—1511no—
226#103—1511no—
227#103—1511no—
228#103—1511no—
229#103—1511no—
230#103—1511no—
231#103—1511no—
232#102—1511no—
233#102—1511no—
234#102—1511no—
235C22⋊C8—1511no—
236C22⋊C8—1511no—
237C4×C8—1511no—
238#41—3022no—
239#41—6041no—
240C2×Q8—3022no—
241C2×Q8—3021no—
242C2×Q8—6041no—
243C2×Q8—1511no—
244C2×Q8—1511no—
245C2×Q8C22×D15111yescharacteristic
246C2×D4—3021no—
247C2×D4—3021no—
248C2×D4—1511no—
249C2×D4C22⋊D15111yescharacteristic
250C22×C4—21no—
251C22×C4—3021no—
252C22×C4—3021no—
253C22×C4C22×D15111yescharacteristic
254C22×C4C22×D15111yescharacteristic
255Q16—3022no—
256Q16—6041no—
257SD16—6041no—
258C2×C8—6041no—
259C2×C8—6041no—
260C2×C8—1511no—
261C2×C8—1511no—
262C2×C8—1511no—
263C2×C8—1511no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—3021no—
271C4⋊C4—3021no—
272C4⋊C4—1511no—
273C4⋊C4C22⋊D15111yescharacteristic
274C4⋊C4C22×D15111yescharacteristic
275C4⋊C4C22×D15111yescharacteristic
276C4⋊C4C22×D15111yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—21no—
280C22⋊C4—3021no—
281C22⋊C4—3021no—
282C22⋊C4—3021no—
283C22⋊C4—3021no—
284C22⋊C4C22⋊D15111yescharacteristic
285C22⋊C4C22⋊D15111yescharacteristic
286C42—21no—
287C42—21no—
288C42—3021no—
289C42C22×D15111yescharacteristic
290C23—3021no—
291C23C2×C22⋊D15111yescharacteristic
292C23C2×C22⋊D15111yescharacteristic
293Q8—21no—
294Q8—21no—
295Q8—3021no—
296Q8—3021no—
297Q8—3021no—
298Q8—6042no—
299Q8—1512no—
300D4—22no—
301D4—3021no—
302D4—3021no—
303D4—6042no—
304D4—6042no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—42no—
314C2×C4—3021no—
315C2×C4—3021no—
316C2×C4—3021no—
317C2×C4—6042no—
318C2×C4—6042no—
319C2×C4C2×C22⋊D15111yescharacteristic
320C2×C4C2×C22⋊D15111yescharacteristic
321C2×C4C2×C22⋊D15111yescharacteristic
322C2×C4C2×C22⋊D15111yescharacteristic
323C2×C4C23×D15111yescharacteristic
324C8—3021no—
325C8—3021no—
326C8—3021no—
327C8—3021no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—6041no—
334C22—6041no—
335C22—6041no—
336C22#1801275912yes—
337C22C22×C22⋊D15111yescharacteristic
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—41no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—3022no—
347C4—6041no—
348C4—6041no—
349C4#41×D15111yescharacteristic
350C4#1801278511yescharacteristic
351C2—22no—
352C2—41no—
353C2—12081no—
354C2#2375285011yescharacteristic
355C2C2×#1801275911yescharacteristic
356C2#2375302711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#552×C151C2
socleC22×C151C22×D4
prime radical#23752871C2
hypercenter#552D151
hypocenterC151#3300
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C4×D4 ◁ #552

Complements

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

NH ≅ G/Ntype
2. #23752569C2semidirect
3. #23752553C2semidirect
4. #23752525C2semidirect
5. #23752516C2semidirect
6. #23752451C2semidirect
7. #23752443C2semidirect
8. #23752434C2semidirect
9. #23752372C2semidirect
10. #23752367C2semidirect
11. C4×#14558994C2semidirect
12. D4×C151⋊C8C2semidirect
13. #23752206C2semidirect
14. C2×#18012662C2semidirect
15. #552×C151C2semidirect
178. C151#3300semidirect
180. #552D151semidirect

Maximal subgroups

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

subgroupindex
#237528712
#237525692
#237525532
#237525252
#237525162
#237524512
#237524432
#237524342
#237523722
#237523672
C4×#145589942
D4×C151⋊C82
#237522062
C2×#180126622
#552×C1512
#3300151