Finite Group Databasebeta

← #34080367

Subgroups — #34080367

Order 19328.

332 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752843C211yesmaximal, characteristic, complemented
2#23752815C211yesmaximal, characteristic
3#23752619C211yesmaximal, characteristic, complemented
4#23752612C211yesmaximal, characteristic, complemented
5#23752575C211yesmaximal, characteristic, complemented
6#23752557C211yesmaximal, characteristic, complemented
7#23752537C211yesmaximal, characteristic, complemented
8#23752533C211yesmaximal, characteristic, complemented
9#23752525C211yesmaximal, characteristic, complemented
10#23752514C211yesmaximal, characteristic, complemented
11#23752511C211yesmaximal, characteristic, complemented
12#23752501C211yesmaximal, characteristic, complemented
13#23752490C211yesmaximal, characteristic, complemented
14#23752270C211yesmaximal, characteristic, complemented
15#481×C151C211yesmaximal, characteristic, complemented
16#18012738—21no—
17#18012738C2211yescharacteristic
18#18012738C2211yescharacteristic
19#18012735C2211yescharacteristic
20#18012730—21no—
21#18012730C2211yescharacteristic
22#18012730C2211yescharacteristic
23#18012730C2211yescharacteristic
24#18012723—21no—
25#18012721—21no—
26#18012718—21no—
27#18012718—21no—
28#18012713C2211yescharacteristic
29#18012711—21no—
30#18012710—21no—
31D4×Dic151C2211yescharacteristic
32#18012701C2211yescharacteristic
33#18012698C2211yescharacteristic
34#18012698C2211yescharacteristic
35#18012673C2211yescharacteristic
36#18012672C2211yescharacteristic
37#18012672C2211yescharacteristic
38#18012672C2211yescharacteristic
39#18012671C2211yescharacteristic
40#18012670C2211yescharacteristic
41Dic151⋊C8C2211yescharacteristic
42Dic151⋊C8C2211yescharacteristic
43#18012661C2211yescharacteristic
44#18012661C2211yescharacteristic
45#18012660C2211yescharacteristic
46#18012660C2211yescharacteristic
47#18012659C2211yescharacteristic
48#18012659C2211yescharacteristic
49C22⋊(C151⋊C8)C2211yescharacteristic
50#18012649C2211yescharacteristic
51C8×Dic151C2211yescharacteristic
52#121×C151C2211yescharacteristic
53C2×C4⋊C4×C151C2211yescharacteristic
54#106×C151C2211yescharacteristic
55#106×C151C2211yescharacteristic
56#102×C151C2211yescharacteristic
57#102×C151C2211yescharacteristic
58C22⋊C8×C151C2211yescharacteristic
59C2×Dic302—21no—
60C2×Dic302—21no—
61C2×D604C2311yescharacteristic
62C2×C22⋊D151—21no—
63C2×C22⋊D151—21no—
64C2×C22⋊D151—21no—
65C22×Dic151—21no—
66C2×C4×D151—21no—
67C2×C151⋊C8C2311yescharacteristic
68C2×C151⋊C8C2311yescharacteristic
69C4⋊Dic151—21no—
70C4⋊Dic151—21no—
71C4⋊Dic151—21no—
72C4⋊Dic151D411yescharacteristic
73C4⋊Dic151D411yescharacteristic
74C4⋊Dic151C2311yescharacteristic
75C4⋊Dic151C2311yescharacteristic
76C4⋊Dic151C2311yescharacteristic
77Dic151⋊C4—21no—
78Dic151⋊C4—21no—
79Dic151⋊C4—21no—
80Dic151⋊C4—21no—
81Dic151⋊C4—21no—
82C22⋊Dic151—21no—
83C22⋊Dic151—21no—
84C22⋊Dic151D411yescharacteristic
85C22⋊Dic151D411yescharacteristic
86(C2×D151)⋊C4—21no—
87(C2×D151)⋊C4—21no—
88C4×Dic151—21no—
89C4×Dic151C2311yescharacteristic
90C4×Dic151C2311yescharacteristic
91C2×D4×C151—21no—
92C2×D4×C151C2311yescharacteristic
93C22×C4×C151—21no—
94C22×C4×C151C2311yescharacteristic
95C2×C8×C151C2311yescharacteristic
96C2×C8×C151C2311yescharacteristic
97C4⋊C4×C151—21no—
98C4⋊C4×C151C2311yescharacteristic
99C4⋊C4×C151C2311yescharacteristic
100C4⋊C4×C151C2311yescharacteristic
101C22⋊C4×C151—21no—
102C22×D151—21no—
103Dic302—81no—
104Dic302—81no—
105D604—21no—
106D604—21no—
107C22⋊D151—81no—
108C22⋊D151—81no—
109C22⋊D151—81no—
110C2×Dic151—21no—
111C2×Dic151—21no—
112C2×Dic151—21no—
113C2×Dic151—81no—
114C2×Dic151C2×D411yescharacteristic
115C2×Dic151C2×D411yescharacteristic
116C2×Dic151C2×D411yescharacteristic
117C2×Dic151C2×D411yescharacteristic
118C4×D151—81no—
119C151⋊C8—21no—
120C151⋊C8—21no—
121C23×C151—21no—
122C23×C151C2×D411yescharacteristic
123D4×C151—21no—
124D4×C151—21no—
125D4×C151—81no—
126C2×C4×C151—21no—
127C2×C4×C151—21no—
128C2×C4×C151—21no—
129C2×C4×C151—21no—
130C2×C4×C151—21no—
131C2×C4×C151—81no—
132C2×C4×C151C2×D411yescharacteristic
133C2×C4×C151C2411yescharacteristic
134C8×C151—21no—
135C8×C151—21no—
136C22×C151—21no—
137C22×C151—21no—
138C22×C151—21no—
139C22×C151—41no—
140C22×C151—41no—
141C22×C151—41no—
142C22×C151C22×D411yescharacteristic
143C2×D151—41no—
144C2×D151—41no—
145C2×D151—41no—
146C4×C151—21no—
147C4×C151—41no—
148C4×C151—41no—
149C4×C151—41no—
150C4×C1512−1+411yescharacteristic
151C4×C1512−1+411yescharacteristic
152Dic151—21no—
153Dic151—21no—
154Dic151—21no—
155Dic151—21no—
156Dic151—41no—
157Dic151—41no—
158Dic151—41no—
159C2×C151—41no—
160C2×C151—81no—
161C2×C151#53611yescharacteristic
162C2×C151#57611yescharacteristic
163C2×C151#57711yescharacteristic
164D151—81no—
165C151#324111yescharacteristic, complemented, Sylow
166#3241—1511nomaximal, Sylow
167#544—1511no—
168#540—1511no—
169#501—1511no—
170#499—1511no—
171#490—1511no—
172#486—1511no—
173#482—1511no—
174#482—1511no—
175#481D15111yescharacteristic, complemented
176#480—1511no—
177#478—1511no—
178#478—1511no—
179#476—1511no—
180#474—1511no—
181#433—1511no—
182C4⋊Q8—3021no—
183C4⋊Q8—1511no—
184C4⋊Q8—1511no—
185#127—1511no—
186#125—3021no—
187#125—1511no—
188#125—1511no—
189#125—1511no—
190#123—3021no—
191#123—3021no—
192C22⋊Q8—3021no—
193C22⋊Q8—3021no—
194#121—3021no—
195#121—3021no—
196#121—1511no—
197#121C2×D15111yescharacteristic
198C4×D4—1511no—
199C4×D4—1511no—
200#117—1511no—
201#117—1511no—
202C2×C4⋊C4C2×D15111yescharacteristic
203#107—1511no—
204#107—1511no—
205#107—1511no—
206#107—1511no—
207#106—1511no—
208#106—1511no—
209#106C2×D15111yescharacteristic
210#106C2×D15111yescharacteristic
211C4⋊C8—1511no—
212C4⋊C8—1511no—
213#102—1511no—
214#102—1511no—
215#102—1511no—
216#102—1511no—
217#102—1511no—
218#102—1511no—
219#102C2×D15111yescharacteristic
220#102C2×D15111yescharacteristic
221C22⋊C8—1511no—
222C22⋊C8C2×D15111yescharacteristic
223#97—1511no—
224C4×C8—1511no—
225C2×Q8—3021no—
226C2×Q8—3021no—
227C2×D4—21no—
228C2×D4—3021no—
229C2×D4—3021no—
230C2×D4—3021no—
231C2×D4—1511no—
232C2×D4C22×D15111yescharacteristic
233C22×C4—21no—
234C22×C4—3021no—
235C22×C4—3021no—
236C22×C4C22×D15111yescharacteristic
237C2×C8—1511no—
238C2×C8—1511no—
239C2×C8C22×D15111yescharacteristic
240C2×C8C22×D15111yescharacteristic
241C4⋊C4—21no—
242C4⋊C4—3021no—
243C4⋊C4—3021no—
244C4⋊C4—3021no—
245C4⋊C4—3021no—
246C4⋊C4—3021no—
247C4⋊C4—3021no—
248C4⋊C4—3021no—
249C4⋊C4—3021no—
250C4⋊C4—1511no—
251C4⋊C4—1511no—
252C4⋊C4—1511no—
253C4⋊C4—1511no—
254C4⋊C4—1511no—
255C4⋊C4C22×D15111yescharacteristic
256C4⋊C4C22×D15111yescharacteristic
257C4⋊C4C22×D15111yescharacteristic
258C22⋊C4—21no—
259C22⋊C4—3021no—
260C22⋊C4—3021no—
261C22⋊C4—3021no—
262C22⋊C4—3021no—
263C22⋊C4—1511no—
264C22⋊C4—1511no—
265C42—3021no—
266C42—1511no—
267C42—1511no—
268C23—21no—
269C23—3021no—
270C23D4×D15111yescharacteristic
271Q8—12081no—
272Q8—12081no—
273D4—21no—
274D4—21no—
275D4—81no—
276D4—3021no—
277D4—3021no—
278D4—12081no—
279D4—12081no—
280D4—12081no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—81no—
287C2×C4—3021no—
288C2×C4—3021no—
289C2×C4—3021no—
290C2×C4—1511no—
291C2×C4—1511no—
292C2×C4—1511no—
293C2×C4—1511no—
294C2×C4—12081no—
295C2×C4—12081no—
296C2×C4D4×D15111yescharacteristic
297C2×C4C23×D15111yescharacteristic
298C8—21no—
299C8—21no—
300C8—3021no—
301C8—3021no—
302C22—21no—
303C22—21no—
304C22—21no—
305C22—41no—
306C22—41no—
307C22—41no—
308C22—6041no—
309C22—6041no—
310C22—6041no—
311C22C2×D4×D15111yescharacteristic
312C4—21no—
313C4—41no—
314C4—41no—
315C4—41no—
316C4—3021no—
317C4—3021no—
318C4—3021no—
319C4—3021no—
320C4—6041no—
321C4—6041no—
322C4—6041no—
323C4#1801278611yescharacteristic
324C4#1801278611yescharacteristic
325C2—41no—
326C2—81no—
327C2—12081no—
328C2#2375278411yescharacteristic
329C2#2375301611yescharacteristic
330C2#2375301811yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#481×C151C2
socleC22×C151C22×D4
prime radical#23752815C2
hypercenter#481D151
hypocenterC151#3241
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

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

NH ≅ G/Ntype
1. #23752843C2semidirect
3. #23752619C2semidirect
4. #23752612C2semidirect
5. #23752575C2semidirect
6. #23752557C2semidirect
7. #23752537C2semidirect
8. #23752533C2semidirect
9. #23752525C2semidirect
10. #23752514C2semidirect
11. #23752511C2semidirect
12. #23752501C2semidirect
13. #23752490C2semidirect
14. #23752270C2semidirect
15. #481×C151C2semidirect
165. C151#3241semidirect
175. #481D151semidirect

Maximal subgroups

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

subgroupindex
#237528432
#237528152
#237526192
#237526122
#237525752
#237525572
#237525372
#237525332
#237525252
#237525142
#237525112
#237525012
#237524902
#237522702
#481×C1512
#3241151