Finite Group Databasebeta

← #34078975

Subgroups — #34078975

Order 19328.

376 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#23752842C211yesmaximal, characteristic, complemented
2#23752694C211yesmaximal, characteristic
3#23752517C211yesmaximal, characteristic, complemented
4#23752515C211yesmaximal, characteristic, complemented
5#23752509C211yesmaximal, characteristic, complemented
6#23752503C211yesmaximal, characteristic, complemented
7#23752501C211yesmaximal, characteristic, complemented
8#23752497C211yesmaximal, characteristic, complemented
9#23752495C211yesmaximal, characteristic, complemented
10#23752253C211yesmaximal, characteristic, complemented
11#106×D151C211yesmaximal, characteristic, complemented
12#23752237C211yesmaximal, characteristic, complemented
13#23752212C211yesmaximal, characteristic
14#23752207C211yesmaximal, characteristic
15#479×C151C211yesmaximal, characteristic, complemented
16C2×#14559005C2211yescharacteristic
17C2×#14558987C2211yescharacteristic
18C2×C8×D151C2211yescharacteristic
19#18012739C2211yescharacteristic
20#18012738—21no—
21#18012738C2211yescharacteristic
22#18012730C2211yescharacteristic
23#18012729—21no—
24#18012719—21no—
25#18012717—21no—
26Q8×Dic151C2211yescharacteristic
27C4×D604—21no—
28C4×D604C2211yescharacteristic
29#18012701—21no—
30#18012701C2211yescharacteristic
31#18012697C2211yescharacteristic
32#18012696—21no—
33#18012696C2211yescharacteristic
34C4⋊C4×D151—21no—
35C4⋊C4×D151C2211yescharacteristic
36C4⋊C4×D151C2211yescharacteristic
37#18012672C2211yescharacteristic
38#18012671C2211yescharacteristic
39#18012671C2211yescharacteristic
40#18012670C2211yescharacteristic
41#18012670C2211yescharacteristic
42#18012670C2211yescharacteristic
43C4⋊(C151⋊C8)C2211yescharacteristic
44Dic151⋊C8C2211yescharacteristic
45Dic151⋊C8C2211yescharacteristic
46#18012663C2211yescharacteristic
47#18012663C2211yescharacteristic
48#18012661C2211yescharacteristic
49#18012661C2211yescharacteristic
50#18012659C2211yescharacteristic
51#18012659C2211yescharacteristic
52#125×C151C2211yescharacteristic
53C4×Q8×C151C2211yescharacteristic
54#107×C151C2211yescharacteristic
55#106×C151C2211yescharacteristic
56C4⋊C8×C151C2211yescharacteristic
57#103×C151C2211yescharacteristic
58#103×C151C2211yescharacteristic
59#14559005—22no—
60#14559005Q814yescomplemented
61C2×Dic302—21no—
62C2×Dic302—21no—
63C2×D604—21no—
64C2×D604C2311yescharacteristic
65C2×C4×D151—21no—
66C2×C4×D151—21no—
67C2×C4×D151—21no—
68C2×C4×D151—21no—
69C2×C4×D151—21no—
70C2×C4×D151C2311yescharacteristic
71#14558987—22no—
72C2×C151⋊C8C2311yescharacteristic
73C2×C151⋊C8C2311yescharacteristic
74C8×D151—22no—
75C4⋊Dic151—21no—
76C4⋊Dic151—21no—
77C4⋊Dic151—21no—
78C4⋊Dic151C2311yescharacteristic
79C4⋊Dic151C2311yescharacteristic
80C4⋊Dic151C2311yescharacteristic
81Dic151⋊C4—21no—
82Dic151⋊C4—21no—
83Dic151⋊C4—21no—
84Dic151⋊C4—21no—
85Dic151⋊C4D411yescharacteristic
86Dic151⋊C4D411yescharacteristic
87(C2×D151)⋊C4—21no—
88(C2×D151)⋊C4—21no—
89(C2×D151)⋊C4—21no—
90(C2×D151)⋊C4D411yescharacteristic
91(C2×D151)⋊C4D411yescharacteristic
92C4×Dic151—21no—
93C4×Dic151—21no—
94C4×Dic151C2311yescharacteristic
95C2×Q8×C151C2311yescharacteristic
96C2×C8×C151C2311yescharacteristic
97C2×C8×C151C2311yescharacteristic
98C4⋊C4×C151—21no—
99C4⋊C4×C151—21no—
100C4⋊C4×C151—21no—
101C4⋊C4×C151C2311yescharacteristic
102C4⋊C4×C151C2311yescharacteristic
103C4⋊C4×C151C2311yescharacteristic
104C42×C151—21no—
105C42×C151C2311yescharacteristic
106C22×D151—21no—
107C22×D151C2×D411yescharacteristic
108Dic302—81no—
109Dic302—81no—
110D604—24no—
111D604—21no—
112D604C2×Q812yes—
113C2×Dic151—21no—
114C2×Dic151—21no—
115C2×Dic151—21no—
116C2×Dic151C2×D411yescharacteristic
117C2×Dic151C2×D411yescharacteristic
118C2×Dic151C2×D411yescharacteristic
119C4×D151—24no—
120C4×D151—81no—
121C4×D151—81no—
122C4×D151—81no—
123C4×D151—81no—
124C4×D151C2×Q812yes—
125C4×D151#4112yes—
126C151⋊C8—21no—
127C151⋊C8—21no—
128Q8×C151—21no—
129Q8×C151C2×Q812yes—
130C2×C4×C151—21no—
131C2×C4×C151—21no—
132C2×C4×C151—21no—
133C2×C4×C151—21no—
134C2×C4×C151C2×D411yescharacteristic
135C2×C4×C151C2×D411yescharacteristic
136C2×C4×C151C2411yescharacteristic
137C8×C151—21no—
138C8×C151—21no—
139C22×C151C22×D411yescharacteristic
140C2×D151—21no—
141C2×D151—21no—
142C2×D151—22no—
143C2×D151—41no—
144C2×D151—41no—
145C2×D151C22⋊Q812yes—
146C4×C151—22no—
147C4×C151—21no—
148C4×C151—21no—
149C4×C151—41no—
150C4×C151—41no—
151C4×C151—41no—
152C4×C151C22×Q811yescharacteristic
153C4×C151C2×#4111yescharacteristic
154Dic151—21no—
155Dic151—21no—
156Dic151—41no—
157Dic151—41no—
158Dic151—41no—
159Dic151C22⋊Q812yes—
160C2×C151C2×C22⋊Q811yescharacteristic
161C2×C151#57711yescharacteristic
162C2×C151#57711yescharacteristic
163D151—22no—
164D151—42no—
165C151#308411yescharacteristic, complemented, Sylow
166#3084—1511nomaximal, Sylow
167#544—1511no—
168#520—1511no—
169#479—1511no—
170#479D15111yescharacteristic, complemented
171#478—1511no—
172#478—1511no—
173#476—1511no—
174#476—1511no—
175#475—1511no—
176#475—1511no—
177#428—1511no—
178C2×#106—1511no—
179#424—1511no—
180#417—1511no—
181#416—1511no—
182C2×#41—1511no—
183C2×M16—1511no—
184C22×C8—1511no—
185C4⋊Q8—3021no—
186C4⋊Q8—1511no—
187C4⋊Q8—1511no—
188#125—3021no—
189#125—1511no—
190#125C2×D15111yescharacteristic
191C22⋊Q8—3021no—
192C22⋊Q8—3021no—
193C4×Q8—1511no—
194C4×Q8C2×D15111yescharacteristic
195C4×D4—3021no—
196C4×D4—3021no—
197C4×D4—1511no—
198C4×D4—1511no—
199#117—3021no—
200#117—1511no—
201#117—1511no—
202C2×C4⋊C4—3021no—
203C2×C4⋊C4—1511no—
204C2×C4⋊C4—1511no—
205#107—1511no—
206#107C2×D15111yescharacteristic
207#106—1511no—
208#106—1511no—
209#106—1511no—
210#106—1511no—
211#106—1511no—
212#106C2×D15111yescharacteristic
213C4⋊C8—1511no—
214C4⋊C8—1511no—
215C4⋊C8—1511no—
216C4⋊C8C2×D15111yescharacteristic
217#103—1511no—
218#103—1511no—
219#103C2×D15111yescharacteristic
220#103C2×D15111yescharacteristic
221#102—1511no—
222#102—1511no—
223#102—1511no—
224#102—1511no—
225#41—3022no—
226#41—1514no—
227C2×Q8—3021no—
228C2×Q8—3021no—
229C2×Q8C22×D15111yescharacteristic
230C2×D4—3021no—
231C2×D4—1511no—
232C22×C4—3021no—
233C22×C4—3021no—
234C22×C4—3021no—
235C22×C4—3021no—
236C22×C4—3021no—
237C22×C4—1511no—
238M16—3022no—
239C2×C8—3022no—
240C2×C8—1511no—
241C2×C8—1511no—
242C2×C8C22×D15111yescharacteristic
243C2×C8C22×D15111yescharacteristic
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—3021no—
248C4⋊C4—3021no—
249C4⋊C4—3021no—
250C4⋊C4—3021no—
251C4⋊C4—3021no—
252C4⋊C4—3021no—
253C4⋊C4—3021no—
254C4⋊C4—1511no—
255C4⋊C4—1511no—
256C4⋊C4—1511no—
257C4⋊C4—1511no—
258C4⋊C4—1511no—
259C4⋊C4C22×D15111yescharacteristic
260C4⋊C4C22×D15111yescharacteristic
261C4⋊C4C22×D15111yescharacteristic
262C22⋊C4—3021no—
263C22⋊C4—3021no—
264C22⋊C4—3021no—
265C22⋊C4—1511no—
266C22⋊C4—1511no—
267C42—21no—
268C42—3021no—
269C42—3021no—
270C42—1511no—
271C42C22×D15111yescharacteristic
272C23—3021no—
273C23—1511no—
274Q8—21no—
275Q8—12081no—
276Q8—12081no—
277Q8Q8×D15112yes—
278D4—3024no—
279D4—3021no—
280D4—1512no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—3024no—
286C2×C4—3021no—
287C2×C4—3021no—
288C2×C4—3021no—
289C2×C4—1511no—
290C2×C4—1511no—
291C2×C4—1511no—
292C2×C4—1512no—
293C2×C4—1512no—
294C2×C4—12081no—
295C2×C4—12081no—
296C2×C4—12081no—
297C2×C4—12081no—
298C2×C4D4×D15111yescharacteristic
299C2×C4D4×D15111yescharacteristic
300C2×C4C23×D15111yescharacteristic
301C8—21no—
302C8—21no—
303C8—3021no—
304C8—3021no—
305C22—3021no—
306C22—3021no—
307C22—3022no—
308C22—6041no—
309C22—6041no—
310C22—1512no—
311C22C2×D4×D15111yescharacteristic
312C4—22no—
313C4—21no—
314C4—21no—
315C4—41no—
316C4—41no—
317C4—41no—
318C4—3021no—
319C4—3021no—
320C4—6041no—
321C4—6041no—
322C4—6041no—
323C4—1512no—
324C4C2×Q8×D15111yescharacteristic
325C4#41×D15111yescharacteristic
326C2—3022no—
327C2—6042no—
328C2C22⋊Q8×D15111yescharacteristic
329C2#2375301911yescharacteristic
330C2#2375302111yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#479×C151C2
socleC22×C151C22×D4
prime radicalC2×#14559005C22
hypercenter#479D151
hypocenterC151#3084
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #479

Complements

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

NH ≅ G/Ntype
1. #23752842C2semidirect
3. #23752517C2semidirect
4. #23752515C2semidirect
5. #23752509C2semidirect
6. #23752503C2semidirect
7. #23752501C2semidirect
8. #23752497C2semidirect
9. #23752495C2semidirect
10. #23752253C2semidirect
11. #106×D151C2semidirect
12. #23752237C2semidirect
15. #479×C151C2semidirect
60. #14559005Q8semidirect
165. C151#3084semidirect
170. #479D151semidirect

Maximal subgroups

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

subgroupindex
#237528422
#237526942
#237525172
#237525152
#237525092
#237525032
#237525012
#237524972
#237524952
#237522532
#106×D1512
#237522372
#237522122
#237522072
#479×C1512
#3084151