Finite Group Databasebeta

← #34080370

Subgroups — #34080370

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#23752839C211yesmaximal, characteristic, complemented
2#23752813C211yesmaximal, characteristic
3#23752620C211yesmaximal, characteristic, complemented
4#23752613C211yesmaximal, characteristic, complemented
5#23752575C211yesmaximal, characteristic, complemented
6#23752557C211yesmaximal, characteristic, complemented
7#23752539C211yesmaximal, characteristic, complemented
8#23752534C211yesmaximal, characteristic, complemented
9#23752529C211yesmaximal, characteristic, complemented
10#23752527C211yesmaximal, characteristic, complemented
11#23752513C211yesmaximal, characteristic, complemented
12#23752512C211yesmaximal, characteristic, complemented
13#23752499C211yesmaximal, characteristic, complemented
14#23752272C211yesmaximal, characteristic, complemented
15#474×C151C211yesmaximal, characteristic, complemented
16#18012738C2211yescharacteristic
17#18012737—21no—
18#18012735C2211yescharacteristic
19#18012731C2211yescharacteristic
20#18012730C2211yescharacteristic
21#18012730C2211yescharacteristic
22#18012729—21no—
23#18012722—21no—
24#18012721—21no—
25#18012717—21no—
26#18012715—21no—
27#18012714C2211yescharacteristic
28#18012713—21no—
29#18012712—21no—
30#18012710C2211yescharacteristic
31C4×D604C2211yescharacteristic
32#18012697C2211yescharacteristic
33#18012696C2211yescharacteristic
34C4⋊C4×D151C2211yescharacteristic
35#18012673C2211yescharacteristic
36#18012672C2211yescharacteristic
37#18012671C2211yescharacteristic
38#18012670C2211yescharacteristic
39#18012670C2211yescharacteristic
40#18012670C2211yescharacteristic
41C4⋊(C151⋊C8)C2211yescharacteristic
42#18012661C2211yescharacteristic
43#18012661C2211yescharacteristic
44#18012660C2211yescharacteristic
45#18012660C2211yescharacteristic
46#18012659C2211yescharacteristic
47#18012659C2211yescharacteristic
48(C2×D151)⋊C8C2211yescharacteristic
49(C2×D151)⋊C8C2211yescharacteristic
50#18012649C2211yescharacteristic
51C8×Dic151C2211yescharacteristic
52C4⋊Q8×C151C2211yescharacteristic
53C4×D4×C151C2211yescharacteristic
54#107×C151C2211yescharacteristic
55#107×C151C2211yescharacteristic
56C4⋊C8×C151C2211yescharacteristic
57#102×C151C2211yescharacteristic
58#102×C151C2211yescharacteristic
59C2×Dic302—21no—
60C2×D604—21no—
61C2×D604C2311yescharacteristic
62C2×C22⋊D151—21no—
63C2×C22⋊D151—21no—
64C2×C22⋊D151—21no—
65C2×C4×D151—21no—
66C2×C4×D151—21no—
67C2×C4×D151C2311yescharacteristic
68C2×C151⋊C8C2311yescharacteristic
69C2×C151⋊C8C2311yescharacteristic
70C4⋊Dic151—21no—
71C4⋊Dic151—21no—
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⋊C4D411yescharacteristic
82Dic151⋊C4D411yescharacteristic
83C22⋊Dic151—21no—
84(C2×D151)⋊C4—21no—
85(C2×D151)⋊C4—21no—
86(C2×D151)⋊C4—21no—
87(C2×D151)⋊C4D411yescharacteristic
88(C2×D151)⋊C4D411yescharacteristic
89C4×Dic151—21no—
90C4×Dic151C2311yescharacteristic
91C2×Q8×C151—21no—
92C2×D4×C151C2311yescharacteristic
93C22×C4×C151—21no—
94C2×C8×C151C2311yescharacteristic
95C2×C8×C151C2311yescharacteristic
96C4⋊C4×C151—21no—
97C4⋊C4×C151C2311yescharacteristic
98C4⋊C4×C151C2311yescharacteristic
99C4⋊C4×C151C2311yescharacteristic
100C22⋊C4×C151—21no—
101C42×C151C2311yescharacteristic
102C22×D151—21no—
103C22×D151C2×D411yescharacteristic
104Dic302—81no—
105D604—21no—
106D604—21no—
107D604—81no—
108C22⋊D151—81no—
109C22⋊D151—81no—
110C22⋊D151—81no—
111C2×Dic151—21no—
112C2×Dic151—21no—
113C2×Dic151—21no—
114C2×Dic151C2×D411yescharacteristic
115C2×Dic151C2×D411yescharacteristic
116C2×Dic151C2×D411yescharacteristic
117C4×D151—21no—
118C4×D151—21no—
119C4×D151—81no—
120C4×D151—81no—
121C151⋊C8—21no—
122C151⋊C8—21no—
123C23×C151—21no—
124Q8×C151—81no—
125D4×C151—21no—
126D4×C151—21no—
127C2×C4×C151—21no—
128C2×C4×C151—21no—
129C2×C4×C151—21no—
130C2×C4×C151—81no—
131C2×C4×C151C2×D411yescharacteristic
132C2×C4×C151C2×D411yescharacteristic
133C2×C4×C151C2411yescharacteristic
134C8×C151—21no—
135C8×C151—21no—
136C22×C151—41no—
137C22×C151—41no—
138C22×C151—41no—
139C22×C151C22×D411yescharacteristic
140C2×D151—21no—
141C2×D151—21no—
142C2×D151—21no—
143C2×D151—41no—
144C2×D151—41no—
145C2×D151—41no—
146C4×C151—21no—
147C4×C151—21no—
148C4×C151—41no—
149C4×C151—41no—
150C4×C151—41no—
151C4×C1512−1+411yescharacteristic
152C4×C1512−1+411yescharacteristic
153Dic151—21no—
154Dic151—21no—
155Dic151—21no—
156Dic151—41no—
157Dic151—41no—
158Dic151—41no—
159C2×C151—81no—
160C2×C151#53611yescharacteristic
161C2×C151#57611yescharacteristic
162C2×C151#57711yescharacteristic
163D151—41no—
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#481—1511no—
176#480—1511no—
177#478—1511no—
178#478—1511no—
179#476—1511no—
180#474D15111yescharacteristic, complemented
181#433—1511no—
182C4⋊Q8—3021no—
183C4⋊Q8—1511no—
184C4⋊Q8C2×D15111yescharacteristic
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#121—1511no—
198C4×D4—1511no—
199C4×D4C2×D15111yescharacteristic
200#117—1511no—
201#117—1511no—
202C2×C4⋊C4—1511no—
203#107—1511no—
204#107—1511no—
205#107C2×D15111yescharacteristic
206#107C2×D15111yescharacteristic
207#106—1511no—
208#106—1511no—
209#106—1511no—
210#106—1511no—
211C4⋊C8—1511no—
212C4⋊C8C2×D15111yescharacteristic
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⋊C8—1511no—
223#97—1511no—
224C4×C8—1511no—
225C2×Q8—21no—
226C2×Q8—3021no—
227C2×D4—3021no—
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×C4—1511no—
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—
267C42C22×D15111yescharacteristic
268C23—21no—
269C23—3021no—
270C23—1511no—
271Q8—81no—
272Q8—12081no—
273D4—21no—
274D4—21no—
275D4—3021no—
276D4—3021no—
277D4—12081no—
278D4—12081no—
279D4—12081no—
280D4—12081no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—81no—
285C2×C4—3021no—
286C2×C4—3021no—
287C2×C4—3021no—
288C2×C4—3021no—
289C2×C4—3021no—
290C2×C4—1511no—
291C2×C4—1511no—
292C2×C4—1511no—
293C2×C4—12081no—
294C2×C4—12081no—
295C2×C4D4×D15111yescharacteristic
296C2×C4D4×D15111yescharacteristic
297C2×C4C23×D15111yescharacteristic
298C8—21no—
299C8—21no—
300C8—3021no—
301C8—3021no—
302C22—41no—
303C22—41no—
304C22—41no—
305C22—3021no—
306C22—3021no—
307C22—3021no—
308C22—6041no—
309C22—6041no—
310C22—6041no—
311C22C2×D4×D15111yescharacteristic
312C4—21no—
313C4—21no—
314C4—41no—
315C4—41no—
316C4—41no—
317C4—3021no—
318C4—3021no—
319C4—3021no—
320C4—6041no—
321C4—6041no—
322C4—6041no—
323C4#1801278611yescharacteristic
324C4#1801278711yescharacteristic
325C2—81no—
326C2—6041no—
327C2—12081no—
328C2#2375278511yescharacteristic
329C2#2375301311yescharacteristic
330C2#2375302111yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#474×C151C2
socleC22×C151C22×D4
prime radical#23752813C2
hypercenter#474D151
hypocenterC151#3241
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #23752839C2semidirect
3. #23752620C2semidirect
4. #23752613C2semidirect
5. #23752575C2semidirect
6. #23752557C2semidirect
7. #23752539C2semidirect
8. #23752534C2semidirect
9. #23752529C2semidirect
10. #23752527C2semidirect
11. #23752513C2semidirect
12. #23752512C2semidirect
13. #23752499C2semidirect
14. #23752272C2semidirect
15. #474×C151C2semidirect
165. C151#3241semidirect
180. #474D151semidirect

Maximal subgroups

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

subgroupindex
#237528392
#237528132
#237526202
#237526132
#237525752
#237525572
#237525392
#237525342
#237525292
#237525272
#237525132
#237525122
#237524992
#237522722
#474×C1512
#3241151