Finite Group Databasebeta

← #34081003

Subgroups — #34081003

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#23752904C211yesmaximal, characteristic, complemented
2#23752868C211yesmaximal, characteristic
3#23752565C211yesmaximal, characteristic, complemented
4#23752556C211yesmaximal, characteristic, complemented
5#23752523C211yesmaximal, characteristic, complemented
6#23752522C211yesmaximal, characteristic, complemented
7#23752452C211yesmaximal, characteristic, complemented
8#23752432C211yesmaximal, characteristic, complemented
9#23752371C211yesmaximal, characteristic, complemented
10#23752367C211yesmaximal, characteristic, complemented
11#23752304C211yesmaximal, characteristic, complemented
12C8×C22⋊D151C211yesmaximal, characteristic, complemented
13#23752205C211yesmaximal, characteristic, complemented
14C2×#18012664C211yesmaximal, characteristic, complemented
15#465×C151C211yesmaximal, characteristic, complemented
16C2×#14559003C2211yescharacteristic
17C22×Dic302C2211yescharacteristic
18C2×#14558994C2211yescharacteristic
19C2×#14558994C2211yescharacteristic
20C2×C8×D151C2211yescharacteristic
21#18012734—21no—
22#18012730—21no—
23#18012730C2211yescharacteristic
24#18012726C2211yescharacteristic
25#18012725—21no—
26#18012723—21no—
27#18012719C2211yescharacteristic
28#18012716—21no—
29#18012715C2211yescharacteristic
30#18012711—21no—
31Q8×Dic151C2211yescharacteristic
32#18012704C2211yescharacteristic
33D4×Dic151—21no—
34C4×C22⋊D151C2211yescharacteristic
35#18012697C2211yescharacteristic
36#18012695—21no—
37C2×C4⋊Dic151C2211yescharacteristic
38#18012672C2211yescharacteristic
39#18012672C2211yescharacteristic
40Dic151⋊C8C2211yescharacteristic
41#18012664C2211yescharacteristic
42#18012664C2211yescharacteristic
43#18012664C2211yescharacteristic
44#18012664C2211yescharacteristic
45#18012662C2211yescharacteristic
46#18012662C2211yescharacteristic
47#18012660C2211yescharacteristic
48#18012660C2211yescharacteristic
49C22⋊(C151⋊C8)C2211yescharacteristic
50(C2×D151)⋊C8C2211yescharacteristic
51C8×Dic151C2211yescharacteristic
52C2×SD16×C151C2211yescharacteristic
53C22×C8×C151C2211yescharacteristic
54C22⋊Q8×C151C2211yescharacteristic
55#121×C151C2211yescharacteristic
56#106×C151C2211yescharacteristic
57#103×C151C2211yescharacteristic
58#102×C151C2211yescharacteristic
59#14559003—22no—
60#14559003—41no—
61C2×Dic302—22no—
62C2×Dic302—21no—
63C2×Dic302—41no—
64C2×Dic302C2311yescharacteristic
65C2×Dic302C2311yescharacteristic
66C2×C22⋊D151—21no—
67C2×C22⋊D151D411yescharacteristic
68C22×Dic151—21no—
69C22×Dic151—21no—
70C22×Dic151—21no—
71C2×C4×D151C2311yescharacteristic
72#14558994—22no—
73#14558994—41no—
74C2×C151⋊C8C2311yescharacteristic
75C2×C151⋊C8C2311yescharacteristic
76C8×D151—41no—
77C4⋊Dic151—21no—
78C4⋊Dic151—21no—
79C4⋊Dic151—21no—
80C4⋊Dic151—21no—
81C4⋊Dic151C2311yescharacteristic
82C4⋊Dic151C2311yescharacteristic
83Dic151⋊C4—21no—
84Dic151⋊C4—21no—
85Dic151⋊C4—21no—
86Dic151⋊C4D411yescharacteristic
87C22⋊Dic151—21no—
88C22⋊Dic151—21no—
89C22⋊Dic151D411yescharacteristic
90(C2×D151)⋊C4—21no—
91(C2×D151)⋊C4—21no—
92(C2×D151)⋊C4—21no—
93(C2×D151)⋊C4D411yescharacteristic
94C4×Dic151—21no—
95C4×Dic151—21no—
96C4×Dic151—21no—
97C4×Dic151C2311yescharacteristic
98C2×Q8×C151C2311yescharacteristic
99C2×D4×C151—21no—
100C2×D4×C151C2311yescharacteristic
101C22×C4×C151C2311yescharacteristic
102SD16×C151—41no—
103C2×C8×C151—41no—
104C2×C8×C151C2311yescharacteristic
105C2×C8×C151C2311yescharacteristic
106C4⋊C4×C151—21no—
107C4⋊C4×C151C2311yescharacteristic
108C4⋊C4×C151C2311yescharacteristic
109C22⋊C4×C151—21no—
110C22⋊C4×C151—21no—
111C22×D151C2×D411yescharacteristic
112Dic302—21no—
113Dic302—21no—
114Dic302—21no—
115Dic302—42no—
116Dic302#4112yes—
117C22⋊D151—22no—
118C22⋊D151—42no—
119C2×Dic151—21no—
120C2×Dic151—21no—
121C2×Dic151—21no—
122C2×Dic151—21no—
123C2×Dic151—42no—
124C2×Dic151—42no—
125C2×Dic151—42no—
126C2×Dic151C2×D411yescharacteristic
127C2×Dic151C2×D411yescharacteristic
128C2×Dic151C2×D411yescharacteristic
129C4×D151—21no—
130C4×D151—21no—
131C151⋊C8—21no—
132C151⋊C8—21no—
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—21no—
149C22×C151—21no—
150C22×C151—21no—
151C22×C151—41no—
152C22×C151—41no—
153C22×C151—41no—
154C22×C151#13512yes—
155C22×C151C22×D411yescharacteristic
156C2×D151—21no—
157C2×D151—21no—
158C2×D151—21no—
159C4×C151—21no—
160C4×C151—41no—
161C4×C151—41no—
162C4×C151—41no—
163C4×C151C2×#4111yescharacteristic
164C4×C151H(5,𝔽2)11yescharacteristic
165Dic151—21no—
166Dic151—22no—
167Dic151—21no—
168Dic151—21no—
169Dic151—41no—
170Dic151—41no—
171Dic151—41no—
172C2×C151—22no—
173C2×C151—81no—
174C2×C151#54611yescharacteristic
175C2×C151C2×#13511yescharacteristic
176C2×C151#57811yescharacteristic
177D151—41no—
178C151#330011yescharacteristic, complemented, Sylow
179#3300—1511nomaximal, Sylow
180#552—1511no—
181#548—1511no—
182#488—1511no—
183#485—1511no—
184#480—1511no—
185#479—1511no—
186#467—1511no—
187#465D15111yescharacteristic, complemented
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×SD16C2×D15111yescharacteristic
200C22×C8—1511no—
201C22×C8C2×D15111yescharacteristic
202#126—3021no—
203#125—3021no—
204#125—1511no—
205#124—3021no—
206#124—1511no—
207#123—3021no—
208C22⋊Q8—3021no—
209C22⋊Q8—1511no—
210C22⋊Q8—1511no—
211C22⋊Q8C2×D15111yescharacteristic
212#121—3021no—
213#121C2×D15111yescharacteristic
214C4×Q8—1511no—
215C4×Q8—1511no—
216C4×D4—3021no—
217C4×D4—1511no—
218#117—3021no—
219#117—1511no—
220C2×C4⋊C4—1511no—
221#107—1511no—
222#107—1511no—
223#106C2×D15111yescharacteristic
224C4⋊C8—1511no—
225#103—1511no—
226#103—1511no—
227#103—1511no—
228#103—1511no—
229#103—1511no—
230#103—1511no—
231#103C2×D15111yescharacteristic
232#102—1511no—
233#102—1511no—
234#102C2×D15111yescharacteristic
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—21no—
247C2×D4—3021no—
248C2×D4—1511no—
249C2×D4C22×D15111yescharacteristic
250C22×C4—3021no—
251C22×C4—3021no—
252C22×C4—3021no—
253C22×C4—1511no—
254C22×C4C22×D15111yescharacteristic
255Q16—3022no—
256Q16—6041no—
257SD16—41no—
258C2×C8—41no—
259C2×C8—6041no—
260C2×C8—1511no—
261C2×C8—1511no—
262C2×C8C22×D15111yescharacteristic
263C2×C8C22×D15111yescharacteristic
264C4⋊C4—21no—
265C4⋊C4—3021no—
266C4⋊C4—3021no—
267C4⋊C4—3021no—
268C4⋊C4—3021no—
269C4⋊C4—3021no—
270C4⋊C4—3021no—
271C4⋊C4—3021no—
272C4⋊C4—1511no—
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—1511no—
285C22⋊C4—1511no—
286C42—3021no—
287C42—3021no—
288C42—3021no—
289C42—1511no—
290C23—21no—
291C23—1511no—
292C23D4×D15111yescharacteristic
293Q8—21no—
294Q8—21no—
295Q8—3021no—
296Q8—3021no—
297Q8—3021no—
298Q8—6042no—
299Q8—1512no—
300D4—21no—
301D4—21no—
302D4—42no—
303D4—3022no—
304D4—6042no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—3021no—
311C2×C4—3021no—
312C2×C4—3021no—
313C2×C4—3021no—
314C2×C4—3021no—
315C2×C4—3021no—
316C2×C4—6042no—
317C2×C4—6042no—
318C2×C4—6042no—
319C2×C4—1511no—
320C2×C4—1511no—
321C2×C4—1511no—
322C2×C4D4×D15111yescharacteristic
323C2×C4C23×D15111yescharacteristic
324C8—21no—
325C8—21no—
326C8—3021no—
327C8—3021no—
328C22—21no—
329C22—21no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—3021no—
334C22—3021no—
335C22—3021no—
336C22#1801276012yes—
337C22C2×D4×D15111yescharacteristic
338C4—21no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—3021no—
343C4—3021no—
344C4—3021no—
345C4—3022no—
346C4—6041no—
347C4—6041no—
348C4—6041no—
349C4#41×D15111yescharacteristic
350C4#1801278411yescharacteristic
351C2—22no—
352C2—81no—
353C2—6041no—
354C2#2375285111yescharacteristic
355C2C2×#1801276011yescharacteristic
356C2#2375302611yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#465×C151C2
socleC22×C151C22×D4
prime radical#23752868C2
hypercenter#465D151
hypocenterC151#3300
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. #23752904C2semidirect
3. #23752565C2semidirect
4. #23752556C2semidirect
5. #23752523C2semidirect
6. #23752522C2semidirect
7. #23752452C2semidirect
8. #23752432C2semidirect
9. #23752371C2semidirect
10. #23752367C2semidirect
11. #23752304C2semidirect
12. C8×C22⋊D151C2semidirect
13. #23752205C2semidirect
14. C2×#18012664C2semidirect
15. #465×C151C2semidirect
178. C151#3300semidirect
187. #465D151semidirect

Maximal subgroups

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

subgroupindex
#237529042
#237528682
#237525652
#237525562
#237525232
#237525222
#237524522
#237524322
#237523712
#237523672
#237523042
C8×C22⋊D1512
#237522052
C2×#180126642
#465×C1512
#3300151