Finite Group Databasebeta

← #34081878

Subgroups — #34081878

Order 19328.

344 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752947C211yesmaximal, characteristic
2#23752578C211yesmaximal, characteristic
3#23752574C211yesmaximal, characteristic, complemented
4#23752569C211yesmaximal, characteristic, complemented
5#23752516C211yesmaximal, characteristic, complemented
6#23752509C211yesmaximal, characteristic, complemented
7#23752499C211yesmaximal, characteristic, complemented
8#23752434C211yesmaximal, characteristic, complemented
9#23752434C211yesmaximal, characteristic, complemented
10#23752412C211yesmaximal, characteristic
11#23752343C211yesmaximal, characteristic, complemented
12#23752317C211yesmaximal, characteristic, complemented
13#23752310C211yesmaximal, characteristic, complemented
14C4×#14558991C211yesmaximal, characteristic, complemented
15#557×C151C211yesmaximal, characteristic, complemented
16C2×#14558994C2211yescharacteristic
17C2×#14558991C2211yescharacteristic
18C2×#14558991C2211yescharacteristic
19#18012736C2211yescharacteristic
20#18012728—21no—
21#18012727C2211yescharacteristic
22#18012727C2211yescharacteristic
23#18012724—21no—
24#18012724—21no—
25C4×Dic302C2211yescharacteristic
26C4×D604C2211yescharacteristic
27C4×D604C2211yescharacteristic
28#18012701—21no—
29#18012672C2211yescharacteristic
30#18012670C2211yescharacteristic
31#18012670C2211yescharacteristic
32C4⋊(C151⋊C8)C2211yescharacteristic
33C4⋊(C151⋊C8)C2211yescharacteristic
34C4⋊(C151⋊C8)C2211yescharacteristic
35#18012663C2211yescharacteristic
36#18012662C2211yescharacteristic
37#18012662C2211yescharacteristic
38#18012662C2211yescharacteristic
39#18012659C2211yescharacteristic
40#18012659C2211yescharacteristic
41#18012659C2211yescharacteristic
42#18012659C2211yescharacteristic
43#18012659C2211yescharacteristic
44#18012659C2211yescharacteristic
45#18012650C2211yescharacteristic
46#18012650C2211yescharacteristic
47C4×C151⋊C8C2211yescharacteristic
48C4⋊Q8×C151—21no—
49C4⋊Q8×C151C2211yescharacteristic
50#125×C151—21no—
51#125×C151—21no—
52#125×C151C2211yescharacteristic
53#125×C151C2211yescharacteristic
54C4×Q8×C151—21no—
55C4×Q8×C151C2211yescharacteristic
56C4×Q8×C151C2211yescharacteristic
57C4×Q8×C151C2211yescharacteristic
58C4×Q8×C151C2211yescharacteristic
59C2×Dic302C2311yescharacteristic
60C2×D604—21no—
61C2×D604—21no—
62C2×D604C2311yescharacteristic
63C2×D604C2311yescharacteristic
64C2×C4×D151—21no—
65C2×C4×D151—21no—
66#14558994—22no—
67#14558991—22no—
68#14558991—22no—
69C2×C151⋊C8C2311yescharacteristic
70C2×C151⋊C8C2311yescharacteristic
71C2×C151⋊C8C2311yescharacteristic
72C2×C151⋊C8C2311yescharacteristic
73C4⋊Dic151C2311yescharacteristic
74Dic151⋊C4—21no—
75(C2×D151)⋊C4—21no—
76(C2×D151)⋊C4—21no—
77(C2×D151)⋊C4—21no—
78(C2×D151)⋊C4—21no—
79(C2×D151)⋊C4—21no—
80(C2×D151)⋊C4—21no—
81C4×Dic151—21no—
82C2×Q8×C151—21no—
83C2×Q8×C151D411yescharacteristic
84C2×Q8×C151C2311yescharacteristic
85C4⋊C4×C151—21no—
86C4⋊C4×C151—21no—
87C4⋊C4×C151—21no—
88C4⋊C4×C151—21no—
89C4⋊C4×C151—21no—
90C4⋊C4×C151—21no—
91C4⋊C4×C151—21no—
92C4⋊C4×C151—21no—
93C4⋊C4×C151D411yescharacteristic
94C4⋊C4×C151D411yescharacteristic
95C4⋊C4×C151D411yescharacteristic
96C4⋊C4×C151C2311yescharacteristic
97C4⋊C4×C151C2311yescharacteristic
98C4⋊C4×C151C2311yescharacteristic
99C42×C151—21no—
100C42×C151—21no—
101C42×C151—21no—
102C42×C151C2311yescharacteristic
103C42×C151C2311yescharacteristic
104C42×C151C2311yescharacteristic
105C22×D151—21no—
106C22×D151—21no—
107Dic302—21no—
108Dic302—21no—
109D604—21no—
110D604—21no—
111D604—21no—
112D604—21no—
113D604—42no—
114D604—81no—
115C2×Dic151—21no—
116C2×Dic151—21no—
117C4×D151—81no—
118C4×D151—81no—
119C151⋊C8—21no—
120C151⋊C8—21no—
121C151⋊C8—21no—
122C151⋊C8—21no—
123Q8×C151—21no—
124Q8×C151—41no—
125Q8×C151—42no—
126Q8×C151#4112yes—
127C2×C4×C151—21no—
128C2×C4×C151—21no—
129C2×C4×C151—21no—
130C2×C4×C151—21no—
131C2×C4×C151C2×D411yescharacteristic
132C2×C4×C151C2×D411yescharacteristic
133C2×C4×C151C2×D411yescharacteristic
134C2×C4×C151C2×D411yescharacteristic
135C2×C4×C151C2×D411yescharacteristic
136C2×C4×C151C2×D411yescharacteristic
137C2×C4×C151C2411yescharacteristic
138C22×C151C22×D411yescharacteristic
139C2×D151—41no—
140C2×D151—41no—
141C2×D151—41no—
142C2×D151—41no—
143C2×D151—41no—
144C2×D151—41no—
145C4×C151—22no—
146C4×C151—21no—
147C4×C151—21no—
148C4×C151—21no—
149C4×C151—21no—
150C4×C151—21no—
151C4×C151—21no—
152C4×C151—41no—
153C4×C151—41no—
154C4×C151—41no—
155C4×C151C2×#4111yescharacteristic
156C4×C1512−1+411yescharacteristic
157Dic151—41no—
158Dic151—41no—
159C2×C151#54811yescharacteristic
160C2×C151#57511yescharacteristic
161C2×C151#57711yescharacteristic
162D151—81no—
163D151—81no—
164C151#337111yescharacteristic, complemented, Sylow
165#3371—1511nomaximal, Sylow
166#559—1511no—
167#557D15111yescharacteristic, complemented
168#490—1511no—
169#489—1511no—
170#488—1511no—
171#479—1511no—
172#478—1511no—
173#476—1511no—
174#464—1511no—
175#464—1511no—
176#460—1511no—
177#446—1511no—
178#441—1511no—
179#440—1511no—
180C4×SD16—1511no—
181C2×Q16—1511no—
182C2×SD16—1511no—
183C2×SD16—1511no—
184C4⋊Q8—21no—
185C4⋊Q8C2×D15111yescharacteristic
186#127—1511no—
187#125—21no—
188#125—21no—
189#125C2×D15111yescharacteristic
190#125C2×D15111yescharacteristic
191#124—3021no—
192#124—1511no—
193#124—1511no—
194#123—3021no—
195#123—3021no—
196C4×Q8—21no—
197C4×Q8—1511no—
198C4×Q8C2×D15111yescharacteristic
199C4×Q8C2×D15111yescharacteristic
200C4×Q8C2×D15111yescharacteristic
201C4×Q8C2×D15111yescharacteristic
202C4×D4—3021no—
203C4×D4—1511no—
204C4×D4—1511no—
205#107—1511no—
206#106—1511no—
207#106—1511no—
208C4⋊C8—1511no—
209C4⋊C8—1511no—
210C4⋊C8—1511no—
211#103—1511no—
212#103—1511no—
213#103—1511no—
214#103—1511no—
215#102—1511no—
216#102—1511no—
217#102—1511no—
218#102—1511no—
219#102—1511no—
220#102—1511no—
221#97—1511no—
222#97—1511no—
223C4×C8—1511no—
224C2×Q8—21no—
225C2×Q8—1511no—
226C2×Q8C22⋊D15111yescharacteristic
227C2×Q8C22×D15111yescharacteristic
228C2×D4—3021no—
229C2×D4—3021no—
230C2×D4—1511no—
231C2×D4—1511no—
232C22×C4—3021no—
233C22×C4—3021no—
234Q16—3022no—
235SD16—3022no—
236SD16—3022no—
237C2×C8—1511no—
238C2×C8—1511no—
239C2×C8—1511no—
240C2×C8—1511no—
241C4⋊C4—21no—
242C4⋊C4—21no—
243C4⋊C4—21no—
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—3021no—
250C4⋊C4—1511no—
251C4⋊C4C22⋊D15111yescharacteristic
252C4⋊C4C22⋊D15111yescharacteristic
253C4⋊C4C22⋊D15111yescharacteristic
254C4⋊C4C22×D15111yescharacteristic
255C4⋊C4C22×D15111yescharacteristic
256C4⋊C4C22×D15111yescharacteristic
257C22⋊C4—3021no—
258C22⋊C4—3021no—
259C22⋊C4—3021no—
260C22⋊C4—3021no—
261C22⋊C4—3021no—
262C22⋊C4—3021no—
263C42—21no—
264C42—21no—
265C42—21no—
266C42—3021no—
267C42C22×D15111yescharacteristic
268C42C22×D15111yescharacteristic
269C42C22×D15111yescharacteristic
270C23—3021no—
271C23—3021no—
272Q8—21no—
273Q8—41no—
274Q8—42no—
275Q8—3021no—
276Q8—3021no—
277Q8#1455900512yes—
278D4—3021no—
279D4—3021no—
280D4—3021no—
281D4—3021no—
282D4—6042no—
283D4—12081no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—3021no—
289C2×C4—3021no—
290C2×C4—12081no—
291C2×C4—12081no—
292C2×C4C2×C22⋊D15111yescharacteristic
293C2×C4C2×C22⋊D15111yescharacteristic
294C2×C4C2×C22⋊D15111yescharacteristic
295C2×C4C2×C22⋊D15111yescharacteristic
296C2×C4C2×C22⋊D15111yescharacteristic
297C2×C4C2×C22⋊D15111yescharacteristic
298C2×C4C23×D15111yescharacteristic
299C8—3021no—
300C8—3021no—
301C8—3021no—
302C8—3021no—
303C22—6041no—
304C22—6041no—
305C22—6041no—
306C22—6041no—
307C22—6041no—
308C22—6041no—
309C22C22×C22⋊D15111yescharacteristic
310C4—21no—
311C4—21no—
312C4—21no—
313C4—21no—
314C4—21no—
315C4—21no—
316C4—22no—
317C4—41no—
318C4—41no—
319C4—41no—
320C4—6041no—
321C4—6041no—
322C4C2×#1455900511yescharacteristic
323C4#1801278711yescharacteristic
324C2—12081no—
325C2—12081no—
326C2#2375287311yescharacteristic
327C2#2375301011yescharacteristic
328C2#2375302011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#557×C151C2
socleC22×C151C22×D4
prime radical#18012736C22
hypercenter#557D151
hypocenterC151#3371
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #557

Complements

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

NH ≅ G/Ntype
3. #23752574C2semidirect
4. #23752569C2semidirect
5. #23752516C2semidirect
6. #23752509C2semidirect
7. #23752499C2semidirect
8. #23752434C2semidirect
9. #23752434C2semidirect
11. #23752343C2semidirect
12. #23752317C2semidirect
13. #23752310C2semidirect
14. C4×#14558991C2semidirect
15. #557×C151C2semidirect
164. C151#3371semidirect
167. #557D151semidirect

Maximal subgroups

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

subgroupindex
#237529472
#237525782
#237525742
#237525692
#237525162
#237525092
#237524992
#237524342
#237524122
#237523432
#237523172
#237523102
C4×#145589912
#557×C1512
#3371151