Finite Group Databasebeta

← #34080380

Subgroups — #34080380

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#23752840C211yesmaximal, characteristic
2#23752824C211yesmaximal, characteristic
3#23752621C211yesmaximal, characteristic, complemented
4#23752614C211yesmaximal, characteristic, complemented
5#23752581C211yesmaximal, characteristic, complemented
6#23752563C211yesmaximal, characteristic, complemented
7#23752554C211yesmaximal, characteristic
8#23752554C211yesmaximal, characteristic
9#23752548C211yesmaximal, characteristic
10#23752543C211yesmaximal, characteristic
11#23752520C211yesmaximal, characteristic, complemented
12#23752520C211yesmaximal, characteristic, complemented
13#23752508C211yesmaximal, characteristic, complemented
14#23752498C211yesmaximal, characteristic, complemented
15#433×C151C211yesmaximal, characteristic
16#18012739C2211yescharacteristic
17#18012739C2211yescharacteristic
18#18012739C2211yescharacteristic
19#18012738—21no—
20#18012732—21no—
21#18012732—21no—
22#18012731C2211yescharacteristic
23#18012731C2211yescharacteristic
24#18012731C2211yescharacteristic
25#18012730—21no—
26#18012729—21no—
27#18012729—21no—
28#18012718C2211yescharacteristic
29#18012718C2211yescharacteristic
30#18012716—21no—
31#18012716—21no—
32C4×Dic302C2211yescharacteristic
33C4×Dic302C2211yescharacteristic
34#18012698C2211yescharacteristic
35C2×C4⋊Dic151C2211yescharacteristic
36#18012673C2211yescharacteristic
37#18012673C2211yescharacteristic
38#18012673C2211yescharacteristic
39#18012673C2211yescharacteristic
40#18012671C2211yescharacteristic
41#18012671C2211yescharacteristic
42#18012671C2211yescharacteristic
43#18012671C2211yescharacteristic
44#18012664C2211yescharacteristic
45#18012664C2211yescharacteristic
46#18012664C2211yescharacteristic
47#18012664C2211yescharacteristic
48#18012664C2211yescharacteristic
49#18012664C2211yescharacteristic
50#18012664C2211yescharacteristic
51#18012664C2211yescharacteristic
52#117×C151C2211yescharacteristic
53C4⋊C8×C151C2211yescharacteristic
54C4⋊C8×C151C2211yescharacteristic
55C22⋊C8×C151C2211yescharacteristic
56C22⋊C8×C151C2211yescharacteristic
57#97×C151C2211yescharacteristic
58C4×C8×C151C2211yescharacteristic
59C2×Dic302—21no—
60C2×Dic302—21no—
61C2×Dic302C2311yescharacteristic
62C2×Dic302C2311yescharacteristic
63C22×Dic151—21no—
64C4⋊Dic151—21no—
65C4⋊Dic151—21no—
66C4⋊Dic151—21no—
67C4⋊Dic151—21no—
68C4⋊Dic151—21no—
69C4⋊Dic151C2311yescharacteristic
70C4⋊Dic151C2311yescharacteristic
71C4⋊Dic151C2311yescharacteristic
72C4⋊Dic151C2311yescharacteristic
73C4⋊Dic151C2311yescharacteristic
74C4⋊Dic151C2311yescharacteristic
75Dic151⋊C4—21no—
76Dic151⋊C4—21no—
77Dic151⋊C4—21no—
78Dic151⋊C4—21no—
79Dic151⋊C4—21no—
80Dic151⋊C4—21no—
81Dic151⋊C4—21no—
82Dic151⋊C4—21no—
83Dic151⋊C4—21no—
84Dic151⋊C4—21no—
85C22⋊Dic151—21no—
86C22⋊Dic151—21no—
87C22⋊Dic151—21no—
88C4×Dic151—21no—
89C4×Dic151—21no—
90C4×Dic151—21no—
91C22×C4×C151C2311yescharacteristic
92C2×C8×C151C2311yescharacteristic
93C2×C8×C151C2311yescharacteristic
94C2×C8×C151C2311yescharacteristic
95C2×C8×C151C2311yescharacteristic
96C4⋊C4×C151D411yescharacteristic
97C4⋊C4×C151D411yescharacteristic
98C22⋊C4×C151D411yescharacteristic
99C22⋊C4×C151D411yescharacteristic
100C42×C151C2311yescharacteristic
101C42×C151C2311yescharacteristic
102Dic302—21no—
103Dic302—21no—
104Dic302—21no—
105Dic302—21no—
106Dic302—81no—
107Dic302—81no—
108C2×Dic151—21no—
109C2×Dic151—21no—
110C2×Dic151—21no—
111C2×Dic151—21no—
112C2×Dic151—21no—
113C2×Dic151—21no—
114C2×Dic151—21no—
115C2×Dic151—21no—
116C2×Dic151—81no—
117C23×C151C2×D411yescharacteristic
118C2×C4×C151—21no—
119C2×C4×C151—21no—
120C2×C4×C151C2×D411yescharacteristic
121C2×C4×C151C2×D411yescharacteristic
122C2×C4×C151C2×D411yescharacteristic
123C2×C4×C151C2×D411yescharacteristic
124C2×C4×C151C2×D411yescharacteristic
125C2×C4×C151C2411yescharacteristic
126C8×C151—21no—
127C8×C151—21no—
128C8×C151—21no—
129C8×C151—21no—
130C22×C151—21no—
131C22×C151—21no—
132C22×C151—21no—
133C22×C151C22×D411yescharacteristic
134C4×C151—21no—
135C4×C151—21no—
136C4×C151—21no—
137C4×C151—21no—
138C4×C151—21no—
139C4×C1512−1+411yescharacteristic
140C4×C1512−1+411yescharacteristic
141Dic151—41no—
142Dic151—41no—
143Dic151—41no—
144Dic151—41no—
145Dic151—41no—
146Dic151—41no—
147Dic151—41no—
148Dic151—41no—
149C2×C151—41no—
150C2×C151#53611yescharacteristic
151C2×C151#57711yescharacteristic
152C2×C151#57811yescharacteristic
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#475—1511no—
169#433D15111yescharacteristic
170C4⋊Q8—3021no—
171C4⋊Q8—1511no—
172C4⋊Q8—1511no—
173C4⋊Q8—1511no—
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×Q8—1511no—
188#117—1511no—
189#117C2×D15111yescharacteristic
190C2×C4⋊C4—1511no—
191#107—1511no—
192#107—1511no—
193#107—1511no—
194#107—1511no—
195#106—1511no—
196#106—1511no—
197#106—1511no—
198#106—1511no—
199C4⋊C8C2×D15111yescharacteristic
200C4⋊C8C2×D15111yescharacteristic
201#103—1511no—
202#103—1511no—
203#103—1511no—
204#103—1511no—
205#103—1511no—
206#103—1511no—
207#103—1511no—
208#103—1511no—
209C22⋊C8C2×D15111yescharacteristic
210C22⋊C8C2×D15111yescharacteristic
211#97C2×D15111yescharacteristic
212C4×C8C2×D15111yescharacteristic
213C2×Q8—3021no—
214C2×Q8—3021no—
215C2×Q8—1511no—
216C2×Q8—1511no—
217C22×C4—3021no—
218C22×C4C22×D15111yescharacteristic
219C2×C8C22×D15111yescharacteristic
220C2×C8C22×D15111yescharacteristic
221C2×C8C22×D15111yescharacteristic
222C2×C8C22×D15111yescharacteristic
223C4⋊C4—3021no—
224C4⋊C4—3021no—
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⋊C4—1511no—
244C4⋊C4D60411yescharacteristic
245C4⋊C4D60411yescharacteristic
246C22⋊C4—3021no—
247C22⋊C4—3021no—
248C22⋊C4—3021no—
249C22⋊C4D60411yescharacteristic
250C22⋊C4D60411yescharacteristic
251C42—3021no—
252C42—3021no—
253C42—3021no—
254C42C22×D15111yescharacteristic
255C42C22×D15111yescharacteristic
256C23C2×D60411yescharacteristic
257Q8—3021no—
258Q8—3021no—
259Q8—3021no—
260Q8—3021no—
261Q8—12081no—
262Q8—12081no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—3021no—
266C2×C4—3021no—
267C2×C4—3021no—
268C2×C4—3021no—
269C2×C4—3021no—
270C2×C4—3021no—
271C2×C4—3021no—
272C2×C4—3021no—
273C2×C4—12081no—
274C2×C4C2×D60411yescharacteristic
275C2×C4C2×D60411yescharacteristic
276C2×C4C2×D60411yescharacteristic
277C2×C4C2×D60411yescharacteristic
278C2×C4C2×D60411yescharacteristic
279C2×C4C23×D15111yescharacteristic
280C8—21no—
281C8—21no—
282C8—21no—
283C8—21no—
284C22—21no—
285C22—21no—
286C22—21no—
287C22C22×D60411yescharacteristic
288C4—21no—
289C4—21no—
290C4—21no—
291C4—21no—
292C4—21no—
293C4—6041no—
294C4—6041no—
295C4—6041no—
296C4—6041no—
297C4—6041no—
298C4—6041no—
299C4—6041no—
300C4—6041no—
301C4#1801278611yescharacteristic
302C4#1801278611yescharacteristic
303C2—41no—
304C2#2375278811yescharacteristic
305C2#2375302411yescharacteristic
306C2#2375302911yescharacteristic
subgroupG/H
centerC22C22×D604
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#433×C151C2
socleC22×C151C22×D4
prime radicalC23×C151C2×D4
hypercenter#433D151
hypocenterC151#3242
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
3. #23752621C2semidirect
4. #23752614C2semidirect
5. #23752581C2semidirect
6. #23752563C2semidirect
11. #23752520C2semidirect
12. #23752520C2semidirect
13. #23752508C2semidirect
14. #23752498C2semidirect
153. C151#3242semidirect

Maximal subgroups

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

subgroupindex
#237528402
#237528242
#237526212
#237526142
#237525812
#237525632
#237525542
#237525482
#237525432
#237525202
#237525082
#237524982
#433×C1512
#3242151