Finite Group Databasebeta

← #34080385

Subgroups — #34080385

Order 19328.

308 conjugacy classes of subgroups.

The subgroup lattice has 308 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752839C211yesmaximal, characteristic
2#23752820C211yesmaximal, characteristic
3#23752619C211yesmaximal, characteristic, complemented
4#23752612C211yesmaximal, characteristic, complemented
5#23752579C211yesmaximal, characteristic, complemented
6#23752561C211yesmaximal, characteristic, complemented
7#23752556C211yesmaximal, characteristic
8#23752551C211yesmaximal, characteristic
9#23752546C211yesmaximal, characteristic
10#23752544C211yesmaximal, characteristic
11#23752520C211yesmaximal, characteristic, complemented
12#23752519C211yesmaximal, characteristic, complemented
13#23752504C211yesmaximal, characteristic, complemented
14#23752272C211yesmaximal, characteristic
15#475×C151C211yesmaximal, characteristic, complemented
16#18012738C2211yescharacteristic
17#18012737—21no—
18#18012737C2211yescharacteristic
19#18012734—21no—
20#18012733—21no—
21#18012731—21no—
22#18012731C2211yescharacteristic
23#18012730C2211yescharacteristic
24#18012730C2211yescharacteristic
25#18012729—21no—
26#18012729—21no—
27#18012719C2211yescharacteristic
28#18012717—21no—
29#18012715—21no—
30#18012715C2211yescharacteristic
31C4×Dic302C2211yescharacteristic
32#18012697C2211yescharacteristic
33#18012696C2211yescharacteristic
34C4⋊C4×D151C2211yescharacteristic
35#18012673C2211yescharacteristic
36#18012672C2211yescharacteristic
37#18012672C2211yescharacteristic
38#18012672C2211yescharacteristic
39#18012671C2211yescharacteristic
40#18012670C2211yescharacteristic
41C4⋊(C151⋊C8)C2211yescharacteristic
42#18012664C2211yescharacteristic
43#18012664C2211yescharacteristic
44#18012663C2211yescharacteristic
45#18012663C2211yescharacteristic
46#18012662C2211yescharacteristic
47#18012662C2211yescharacteristic
48(C2×D151)⋊C8C2211yescharacteristic
49(C2×D151)⋊C8C2211yescharacteristic
50#18012649C2211yescharacteristic
51C8×Dic151C2211yescharacteristic
52C4⋊Q8×C151C2211yescharacteristic
53C4×Q8×C151C2211yescharacteristic
54#106×C151C2211yescharacteristic
55#106×C151C2211yescharacteristic
56C4⋊C8×C151C2211yescharacteristic
57#103×C151C2211yescharacteristic
58#103×C151C2211yescharacteristic
59C2×Dic302—21no—
60C2×Dic302C2311yescharacteristic
61C2×C4×D151—21no—
62C2×C4×D151C2311yescharacteristic
63C2×C151⋊C8C2311yescharacteristic
64C2×C151⋊C8C2311yescharacteristic
65C4⋊Dic151—21no—
66C4⋊Dic151—21no—
67C4⋊Dic151—21no—
68C4⋊Dic151C2311yescharacteristic
69C4⋊Dic151C2311yescharacteristic
70C4⋊Dic151C2311yescharacteristic
71Dic151⋊C4—21no—
72Dic151⋊C4—21no—
73Dic151⋊C4—21no—
74Dic151⋊C4—21no—
75Dic151⋊C4—21no—
76Dic151⋊C4—21no—
77Dic151⋊C4—21no—
78Dic151⋊C4—21no—
79Dic151⋊C4—21no—
80Dic151⋊C4—21no—
81Dic151⋊C4D411yescharacteristic
82Dic151⋊C4D411yescharacteristic
83(C2×D151)⋊C4—21no—
84(C2×D151)⋊C4—21no—
85(C2×D151)⋊C4—21no—
86(C2×D151)⋊C4D411yescharacteristic
87(C2×D151)⋊C4D411yescharacteristic
88C4×Dic151—21no—
89C4×Dic151—21no—
90C4×Dic151C2311yescharacteristic
91C2×Q8×C151—21no—
92C2×Q8×C151C2311yescharacteristic
93C2×C8×C151C2311yescharacteristic
94C2×C8×C151C2311yescharacteristic
95C4⋊C4×C151—21no—
96C4⋊C4×C151—21no—
97C4⋊C4×C151C2311yescharacteristic
98C4⋊C4×C151C2311yescharacteristic
99C4⋊C4×C151C2311yescharacteristic
100C42×C151—21no—
101C42×C151C2311yescharacteristic
102C22×D151C2×D411yescharacteristic
103Dic302—21no—
104Dic302—21no—
105Dic302—81no—
106C2×Dic151—21no—
107C2×Dic151—21no—
108C2×Dic151—21no—
109C2×Dic151—21no—
110C2×Dic151C2×D411yescharacteristic
111C2×Dic151C2×D411yescharacteristic
112C2×Dic151C2×D411yescharacteristic
113C4×D151—21no—
114C4×D151—21no—
115C4×D151—81no—
116C151⋊C8—21no—
117C151⋊C8—21no—
118Q8×C151—21no—
119Q8×C151—21no—
120Q8×C151—81no—
121C2×C4×C151—21no—
122C2×C4×C151—21no—
123C2×C4×C151—21no—
124C2×C4×C151—21no—
125C2×C4×C151C2×D411yescharacteristic
126C2×C4×C151C2×D411yescharacteristic
127C2×C4×C151C2411yescharacteristic
128C8×C151—21no—
129C8×C151—21no—
130C22×C151C22×D411yescharacteristic
131C2×D151—21no—
132C2×D151—21no—
133C2×D151—21no—
134C4×C151—21no—
135C4×C151—21no—
136C4×C151—41no—
137C4×C151—41no—
138C4×C151—41no—
139C4×C151—41no—
140C4×C1512−1+411yescharacteristic
141C4×C1512−1+411yescharacteristic
142Dic151—21no—
143Dic151—21no—
144Dic151—21no—
145Dic151—41no—
146Dic151—41no—
147Dic151—41no—
148Dic151—41no—
149C2×C151#53611yescharacteristic
150C2×C151#57711yescharacteristic
151C2×C151#57811yescharacteristic
152D151—41no—
153C151#324211yescharacteristic, complemented, Sylow
154#3242—1511nomaximal, Sylow
155#544—1511no—
156#541—1511no—
157#501—1511no—
158#499—1511no—
159#491—1511no—
160#487—1511no—
161#485—1511no—
162#485—1511no—
163#484—1511no—
164#483—1511no—
165#479—1511no—
166#479—1511no—
167#477—1511no—
168#475D15111yescharacteristic, complemented
169#433—1511no—
170C4⋊Q8—3021no—
171C4⋊Q8—1511no—
172C4⋊Q8—1511no—
173C4⋊Q8C2×D15111yescharacteristic
174#126—3021no—
175#126—3021no—
176#125—3021no—
177#125—3021no—
178#125—3021no—
179#125—1511no—
180#125—1511no—
181#125—1511no—
182C22⋊Q8—3021no—
183C22⋊Q8—3021no—
184C22⋊Q8—1511no—
185C22⋊Q8—1511no—
186C4×Q8—1511no—
187C4×Q8C2×D15111yescharacteristic
188#117—1511no—
189#117—1511no—
190C2×C4⋊C4—1511no—
191#107—1511no—
192#107—1511no—
193#107—1511no—
194#107—1511no—
195#106—1511no—
196#106—1511no—
197#106C2×D15111yescharacteristic
198#106C2×D15111yescharacteristic
199C4⋊C8—1511no—
200C4⋊C8C2×D15111yescharacteristic
201#103—1511no—
202#103—1511no—
203#103—1511no—
204#103—1511no—
205#103—1511no—
206#103—1511no—
207#103C2×D15111yescharacteristic
208#103C2×D15111yescharacteristic
209C22⋊C8—1511no—
210C22⋊C8—1511no—
211#97—1511no—
212C4×C8—1511no—
213C2×Q8—21no—
214C2×Q8—3021no—
215C2×Q8—1511no—
216C2×Q8C22×D15111yescharacteristic
217C22×C4—3021no—
218C22×C4—1511no—
219C2×C8—1511no—
220C2×C8—1511no—
221C2×C8C22×D15111yescharacteristic
222C2×C8C22×D15111yescharacteristic
223C4⋊C4—21no—
224C4⋊C4—21no—
225C4⋊C4—3021no—
226C4⋊C4—3021no—
227C4⋊C4—3021no—
228C4⋊C4—3021no—
229C4⋊C4—3021no—
230C4⋊C4—3021no—
231C4⋊C4—3021no—
232C4⋊C4—3021no—
233C4⋊C4—3021no—
234C4⋊C4—3021no—
235C4⋊C4—3021no—
236C4⋊C4—3021no—
237C4⋊C4—3021no—
238C4⋊C4—1511no—
239C4⋊C4—1511no—
240C4⋊C4—1511no—
241C4⋊C4—1511no—
242C4⋊C4—1511no—
243C4⋊C4C22×D15111yescharacteristic
244C4⋊C4C22×D15111yescharacteristic
245C4⋊C4C22×D15111yescharacteristic
246C22⋊C4—3021no—
247C22⋊C4—3021no—
248C22⋊C4—3021no—
249C22⋊C4—1511no—
250C22⋊C4—1511no—
251C42—21no—
252C42—3021no—
253C42—3021no—
254C42—1511no—
255C42C22×D15111yescharacteristic
256C23—1511no—
257Q8—21no—
258Q8—21no—
259Q8—81no—
260Q8—3021no—
261Q8—3021no—
262Q8—12081no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—3021no—
268C2×C4—3021no—
269C2×C4—3021no—
270C2×C4—3021no—
271C2×C4—3021no—
272C2×C4—3021no—
273C2×C4—1511no—
274C2×C4—1511no—
275C2×C4—1511no—
276C2×C4—12081no—
277C2×C4D4×D15111yescharacteristic
278C2×C4D4×D15111yescharacteristic
279C2×C4C23×D15111yescharacteristic
280C8—21no—
281C8—21no—
282C8—3021no—
283C8—3021no—
284C22—3021no—
285C22—3021no—
286C22—3021no—
287C22C2×D4×D15111yescharacteristic
288C4—21no—
289C4—21no—
290C4—41no—
291C4—41no—
292C4—41no—
293C4—41no—
294C4—3021no—
295C4—3021no—
296C4—3021no—
297C4—6041no—
298C4—6041no—
299C4—6041no—
300C4—6041no—
301C4#1801278611yescharacteristic
302C4#1801278711yescharacteristic
303C2—6041no—
304C2#2375278511yescharacteristic
305C2#2375301811yescharacteristic
306C2#2375302811yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#475×C151C2
socleC22×C151C22×D4
prime radicalC22×D151C2×D4
hypercenter#475D151
hypocenterC151#3242
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
3. #23752619C2semidirect
4. #23752612C2semidirect
5. #23752579C2semidirect
6. #23752561C2semidirect
11. #23752520C2semidirect
12. #23752519C2semidirect
13. #23752504C2semidirect
15. #475×C151C2semidirect
153. C151#3242semidirect
168. #475D151semidirect

Maximal subgroups

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

subgroupindex
#237528392
#237528202
#237526192
#237526122
#237525792
#237525612
#237525562
#237525512
#237525462
#237525442
#237525202
#237525192
#237525042
#237522722
#475×C1512
#3242151