Finite Group Databasebeta

← #34079307

Subgroups — #34079307

Order 19328.

396 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752813C211yesmaximal, characteristic, complemented
2#23752694C211yesmaximal, characteristic, complemented
3#23752529C211yesmaximal, characteristic, complemented
4#23752527C211yesmaximal, characteristic, complemented
5#23752517C211yesmaximal, characteristic, complemented
6#23752515C211yesmaximal, characteristic, complemented
7#23752410C211yesmaximal, characteristic, complemented
8#23752406C211yesmaximal, characteristic, complemented
9#23752360C211yesmaximal, characteristic, complemented
10#23752356C211yesmaximal, characteristic, complemented
11#23752325C211yesmaximal, characteristic, complemented
12C4×#14558991C211yesmaximal, characteristic, complemented
13C4×#14558989C211yesmaximal, characteristic, complemented
14#23752274C211yesmaximal, characteristic, complemented
15#440×C151C211yesmaximal, characteristic, complemented
16C2×#14559005C2211yescharacteristic
17C2×#14558991C2211yescharacteristic
18C2×D1208C2211yescharacteristic
19C2×#14558989C2211yescharacteristic
20#18012735C2211yescharacteristic
21#18012730C2211yescharacteristic
22#18012722—21no—
23#18012721—21no—
24#18012714C2211yescharacteristic
25#18012713—21no—
26#18012712—21no—
27#18012710C2211yescharacteristic
28Q8×Dic151C2211yescharacteristic
29C4×D604—21no—
30C4×D604C2211yescharacteristic
31C4×D604C2211yescharacteristic
32#18012701—21no—
33#18012701C2211yescharacteristic
34#18012696—21no—
35#18012696C2211yescharacteristic
36C4⋊C4×D151—21no—
37C4⋊C4×D151C2211yescharacteristic
38#18012672C2211yescharacteristic
39#18012671C2211yescharacteristic
40#18012670C2211yescharacteristic
41Dic151⋊C8C2211yescharacteristic
42Dic151⋊C8C2211yescharacteristic
43#18012663C2211yescharacteristic
44#18012661C2211yescharacteristic
45#18012661C2211yescharacteristic
46#18012660C2211yescharacteristic
47#18012659C2211yescharacteristic
48#18012659C2211yescharacteristic
49(C2×D151)⋊C8C2211yescharacteristic
50(C2×D151)⋊C8C2211yescharacteristic
51C4×C151⋊C8C2211yescharacteristic
52C2×SD16×C151C2211yescharacteristic
53C4×Q8×C151C2211yescharacteristic
54C4×D4×C151C2211yescharacteristic
55#107×C151C2211yescharacteristic
56#103×C151C2211yescharacteristic
57#102×C151C2211yescharacteristic
58#97×C151C2211yescharacteristic
59#14559005—22no—
60#14559005—22no—
61C2×D604—21no—
62C2×D604—21no—
63C2×D604C2311yescharacteristic
64C2×D604C2311yescharacteristic
65C2×C22⋊D151—21no—
66C2×C22⋊D151—21no—
67C2×C22⋊D151—21no—
68C2×C4×D151—21no—
69C2×C4×D151—21no—
70C2×C4×D151—21no—
71C2×C4×D151—21no—
72C2×C4×D151—21no—
73C2×C4×D151C2311yescharacteristic
74#14558991—22no—
75D1208—22no—
76#14558989—22no—
77C2×C151⋊C8C2311yescharacteristic
78C2×C151⋊C8C2311yescharacteristic
79C4⋊Dic151—21no—
80C4⋊Dic151—21no—
81C4⋊Dic151C2311yescharacteristic
82C4⋊Dic151C2311yescharacteristic
83Dic151⋊C4—21no—
84Dic151⋊C4—21no—
85Dic151⋊C4D411yescharacteristic
86Dic151⋊C4D411yescharacteristic
87C22⋊Dic151—21no—
88(C2×D151)⋊C4—21no—
89(C2×D151)⋊C4—21no—
90(C2×D151)⋊C4—21no—
91(C2×D151)⋊C4—21no—
92(C2×D151)⋊C4D411yescharacteristic
93(C2×D151)⋊C4D411yescharacteristic
94C4×Dic151—21no—
95C4×Dic151C2311yescharacteristic
96C2×Q8×C151C2311yescharacteristic
97C2×D4×C151C2311yescharacteristic
98C22×C4×C151—21no—
99SD16×C151—22no—
100C2×C8×C151C2311yescharacteristic
101C2×C8×C151C2311yescharacteristic
102C4⋊C4×C151—21no—
103C4⋊C4×C151C2311yescharacteristic
104C4⋊C4×C151C2311yescharacteristic
105C22⋊C4×C151—21no—
106C42×C151—21no—
107C42×C151C2311yescharacteristic
108C22×D151—21no—
109C22×D151—21no—
110C22×D151C2×D411yescharacteristic
111D604—24no—
112D604—21no—
113D604—21no—
114D604—21no—
115D604—81no—
116D604#4112yes—
117C22⋊D151—81no—
118C22⋊D151—81no—
119C22⋊D151—81no—
120C2×Dic151—21no—
121C2×Dic151—21no—
122C2×Dic151C2×D411yescharacteristic
123C2×Dic151C2×D411yescharacteristic
124C2×Dic151C2×D411yescharacteristic
125C4×D151—24no—
126C4×D151—21no—
127C4×D151—21no—
128C4×D151—81no—
129C4×D151—81no—
130C4×D151—81no—
131C4×D151—81no—
132C151⋊C8—21no—
133C151⋊C8—21no—
134C23×C151—21no—
135Q8×C151—21no—
136Q8×C151#4112yes—
137D4×C151—21no—
138D4×C151—21no—
139C2×C4×C151—21no—
140C2×C4×C151—21no—
141C2×C4×C151—21no—
142C2×C4×C151—81no—
143C2×C4×C151C2×D411yescharacteristic
144C2×C4×C151C2×D411yescharacteristic
145C2×C4×C151C2411yescharacteristic
146C8×C151—21no—
147C8×C151—21no—
148C22×C151—41no—
149C22×C151—41no—
150C22×C151—41no—
151C22×C151C22×D411yescharacteristic
152C2×D151—21no—
153C2×D151—22no—
154C2×D151—21no—
155C2×D151—21no—
156C2×D151—41no—
157C2×D151—41no—
158C2×D151—41no—
159C2×D151—41no—
160C2×D151—41no—
161C4×C151—22no—
162C4×C151—21no—
163C4×C151—21no—
164C4×C151—41no—
165C4×C151—41no—
166C4×C151C2×#4111yescharacteristic
167C4×C151C2×#4111yescharacteristic
168Dic151—21no—
169Dic151—21no—
170Dic151—21no—
171Dic151—41no—
172Dic151—41no—
173C2×C151—81no—
174C2×C151#52511yescharacteristic
175C2×C151#57611yescharacteristic
176C2×C151#57711yescharacteristic
177D151—41no—
178D151—42no—
179D151—81no—
180C151#311911yescharacteristic, complemented, Sylow
181#3119—1511nomaximal, Sylow
182#540—1511no—
183#520—1511no—
184#481—1511no—
185#480—1511no—
186#479—1511no—
187#478—1511no—
188#460—1511no—
189#459—1511no—
190#449—1511no—
191#449—1511no—
192#442—1511no—
193#440D15111yescharacteristic, complemented
194C4×SD16—1511no—
195C4×D8—1511no—
196#433—1511no—
197C2×#41—1511no—
198C2×SD16—1511no—
199C2×SD16C2×D15111yescharacteristic
200C2×D8—1511no—
201C2×D8—1511no—
202#127—1511no—
203#125—1511no—
204#123—3021no—
205#123—3021no—
206#121—3021no—
207#121—3021no—
208#121—1511no—
209#121—1511no—
210C4×Q8—1511no—
211C4×Q8C2×D15111yescharacteristic
212C4×D4—3021no—
213C4×D4—3021no—
214C4×D4—1511no—
215C4×D4—1511no—
216C4×D4—1511no—
217C4×D4C2×D15111yescharacteristic
218#117—3021no—
219#117—1511no—
220C2×C4⋊C4—3021no—
221C2×C4⋊C4—1511no—
222#107—1511no—
223#107C2×D15111yescharacteristic
224#106—1511no—
225#106—1511no—
226C4⋊C8—1511no—
227C4⋊C8—1511no—
228#103—1511no—
229#103C2×D15111yescharacteristic
230#102—1511no—
231#102—1511no—
232#102—1511no—
233#102—1511no—
234#102—1511no—
235#102C2×D15111yescharacteristic
236C22⋊C8—1511no—
237C22⋊C8—1511no—
238#97C2×D15111yescharacteristic
239C4×C8—1511no—
240#41—3022no—
241#41—3022no—
242C2×Q8C22×D15111yescharacteristic
243C2×D4—3021no—
244C2×D4—3021no—
245C2×D4—3021no—
246C2×D4—3021no—
247C2×D4—3021no—
248C2×D4—1511no—
249C2×D4—1511no—
250C2×D4C22×D15111yescharacteristic
251C22×C4—21no—
252C22×C4—3021no—
253C22×C4—3021no—
254C22×C4—3021no—
255C22×C4—3021no—
256C22×C4—3021no—
257C22×C4—1511no—
258SD16—22no—
259SD16—3022no—
260D8—3022no—
261D8—3022no—
262C2×C8—1511no—
263C2×C8—1511no—
264C2×C8C22×D15111yescharacteristic
265C2×C8C22×D15111yescharacteristic
266C4⋊C4—21no—
267C4⋊C4—3021no—
268C4⋊C4—3021no—
269C4⋊C4—3021no—
270C4⋊C4—3021no—
271C4⋊C4—1511no—
272C4⋊C4—1511no—
273C4⋊C4—1511no—
274C4⋊C4—1511no—
275C4⋊C4C22×D15111yescharacteristic
276C4⋊C4C22×D15111yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—3021no—
279C22⋊C4—3021no—
280C22⋊C4—3021no—
281C22⋊C4—3021no—
282C22⋊C4—3021no—
283C22⋊C4—1511no—
284C22⋊C4—1511no—
285C42—21no—
286C42—3021no—
287C42—1511no—
288C42C22×D15111yescharacteristic
289C23—21no—
290C23—3021no—
291C23—3021no—
292C23—1511no—
293Q8—21no—
294Q8#1455900412yes—
295D4—21no—
296D4—21no—
297D4—3024no—
298D4—3021no—
299D4—3021no—
300D4—3021no—
301D4—1512no—
302D4—12081no—
303D4—12081no—
304D4—12081no—
305D4—12081no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—81no—
310C2×C4—3024no—
311C2×C4—3021no—
312C2×C4—3021no—
313C2×C4—3021no—
314C2×C4—3021no—
315C2×C4—1511no—
316C2×C4—1511no—
317C2×C4—1511no—
318C2×C4—12081no—
319C2×C4—12081no—
320C2×C4—12081no—
321C2×C4—12081no—
322C2×C4D4×D15111yescharacteristic
323C2×C4D4×D15111yescharacteristic
324C2×C4C23×D15111yescharacteristic
325C8—21no—
326C8—21no—
327C8—3021no—
328C8—3021no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—3021no—
333C22—3022no—
334C22—3021no—
335C22—3021no—
336C22—6041no—
337C22—6041no—
338C22—6041no—
339C22—6041no—
340C22—6041no—
341C22C2×D4×D15111yescharacteristic
342C4—22no—
343C4—21no—
344C4—21no—
345C4—41no—
346C4—41no—
347C4—3021no—
348C4—3021no—
349C4—3021no—
350C4—6041no—
351C4—6041no—
352C4#41×D15111yescharacteristic
353C4C2×#1455900411yescharacteristic
354C2—81no—
355C2—6041no—
356C2—6042no—
357C2—12081no—
358C2#2375272111yescharacteristic
359C2#2375301611yescharacteristic
360C2#2375302111yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#440×C151C2
socleC22×C151C22×D4
hypercenter#440D151
hypocenterC151#3119
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. #23752813C2semidirect
2. #23752694C2semidirect
3. #23752529C2semidirect
4. #23752527C2semidirect
5. #23752517C2semidirect
6. #23752515C2semidirect
7. #23752410C2semidirect
8. #23752406C2semidirect
9. #23752360C2semidirect
10. #23752356C2semidirect
11. #23752325C2semidirect
12. C4×#14558991C2semidirect
13. C4×#14558989C2semidirect
14. #23752274C2semidirect
15. #440×C151C2semidirect
180. C151#3119semidirect
193. #440D151semidirect

Maximal subgroups

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

subgroupindex
#237528132
#237526942
#237525292
#237525272
#237525172
#237525152
#237524102
#237524062
#237523602
#237523562
#237523252
C4×#145589912
C4×#145589892
#237522742
#440×C1512
#3119151