Finite Group Databasebeta

← #34081716

Subgroups — #34081716

Order 19328.

360 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752910C211yesmaximal, characteristic, complemented
2#23752909C211yesmaximal, characteristic, complemented
3#23752613C211yesmaximal, characteristic, complemented
4#23752537C211yesmaximal, characteristic, complemented
5#23752534C211yesmaximal, characteristic, complemented
6#23752527C211yesmaximal, characteristic, complemented
7#23752515C211yesmaximal, characteristic, complemented
8#23752514C211yesmaximal, characteristic, complemented
9#23752464C211yesmaximal, characteristic, complemented
10#23752463C211yesmaximal, characteristic, complemented
11#23752292C211yesmaximal, characteristic, complemented
12#23752287C211yesmaximal, characteristic, complemented
13#23752253C211yesmaximal, characteristic, complemented
14#23752252C211yesmaximal, characteristic, complemented
15#480×C151C211yesmaximal, characteristic, complemented
16C2×#14558989C2211yescharacteristic
17C2×#14558988C2211yescharacteristic
18C2×#14558987C2211yescharacteristic
19#18012734—21no—
20#18012732—21no—
21#18012730C2211yescharacteristic
22#18012730C2211yescharacteristic
23#18012724—21no—
24#18012720—21no—
25#18012714C2211yescharacteristic
26#18012713—21no—
27#18012713C2211yescharacteristic
28#18012710—21no—
29#18012710C2211yescharacteristic
30D4×Dic151C2211yescharacteristic
31#18012701C2211yescharacteristic
32C4×C22⋊D151—21no—
33C4×C22⋊D151C2211yescharacteristic
34(C22⋊D151)⋊C4—21no—
35#18012698C2211yescharacteristic
36#18012697C2211yescharacteristic
37C4⋊C4×D151C2211yescharacteristic
38#18012673C2211yescharacteristic
39#18012672C2211yescharacteristic
40#18012672C2211yescharacteristic
41#18012671C2211yescharacteristic
42#18012670C2211yescharacteristic
43#18012670C2211yescharacteristic
44#18012670C2211yescharacteristic
45Dic151⋊C8C2211yescharacteristic
46#18012661C2211yescharacteristic
47#18012661C2211yescharacteristic
48#18012660C2211yescharacteristic
49#18012659C2211yescharacteristic
50(C2×D151)⋊C8C2211yescharacteristic
51C8×Dic151C2211yescharacteristic
52#121×C151C2211yescharacteristic
53C2×C4⋊C4×C151C2211yescharacteristic
54#107×C151C2211yescharacteristic
55#107×C151C2211yescharacteristic
56#102×C151C2211yescharacteristic
57#102×C151C2211yescharacteristic
58C22⋊C8×C151C2211yescharacteristic
59C2×D604—21no—
60C2×D604C2311yescharacteristic
61C2×C22⋊D151—21no—
62C2×C22⋊D151—21no—
63C2×C22⋊D151D411yescharacteristic
64C22×Dic151—21no—
65C2×C4×D151—21no—
66C2×C4×D151—21no—
67C2×C4×D151C2311yescharacteristic
68#14558989—22no—
69#14558988—22no—
70#14558987—22no—
71C2×C151⋊C8C2311yescharacteristic
72C2×C151⋊C8C2311yescharacteristic
73C4⋊Dic151—21no—
74C4⋊Dic151—21no—
75C4⋊Dic151C2311yescharacteristic
76C4⋊Dic151C2311yescharacteristic
77C4⋊Dic151C2311yescharacteristic
78Dic151⋊C4—21no—
79Dic151⋊C4—21no—
80Dic151⋊C4—21no—
81Dic151⋊C4D411yescharacteristic
82C22⋊Dic151—21no—
83C22⋊Dic151—21no—
84C22⋊Dic151—21no—
85C22⋊Dic151D411yescharacteristic
86(C2×D151)⋊C4—21no—
87(C2×D151)⋊C4—21no—
88(C2×D151)⋊C4—21no—
89(C2×D151)⋊C4—21no—
90(C2×D151)⋊C4D411yescharacteristic
91C4×Dic151—21no—
92C4×Dic151—21no—
93C4×Dic151C2311yescharacteristic
94C2×D4×C151—21no—
95C2×D4×C151C2311yescharacteristic
96C22×C4×C151—21no—
97C22×C4×C151C2311yescharacteristic
98C2×C8×C151C2311yescharacteristic
99C2×C8×C151C2311yescharacteristic
100C4⋊C4×C151—21no—
101C4⋊C4×C151C2311yescharacteristic
102C4⋊C4×C151C2311yescharacteristic
103C4⋊C4×C151C2311yescharacteristic
104C22⋊C4×C151—21no—
105C22×D151—21no—
106C22×D151C2×D411yescharacteristic
107D604—21no—
108D604—21no—
109D604—81no—
110C22⋊D151—41no—
111C22⋊D151—42no—
112C22⋊D151—42no—
113C2×Dic151—21no—
114C2×Dic151—21no—
115C2×Dic151—21no—
116C2×Dic151—81no—
117C2×Dic151C2×D411yescharacteristic
118C2×Dic151C2×D411yescharacteristic
119C2×Dic151C2×D411yescharacteristic
120C4×D151—21no—
121C4×D151—21no—
122C4×D151—81no—
123C4×D151—81no—
124C151⋊C8—21no—
125C151⋊C8#4112yes—
126C23×C151—21no—
127C23×C151C2×D411yescharacteristic
128D4×C151—21no—
129D4×C151—21no—
130D4×C151—81no—
131C2×C4×C151—21no—
132C2×C4×C151—21no—
133C2×C4×C151—21no—
134C2×C4×C151—21no—
135C2×C4×C151—21no—
136C2×C4×C151—81no—
137C2×C4×C151C2×D411yescharacteristic
138C2×C4×C151C2411yescharacteristic
139C8×C151—21no—
140C8×C151—21no—
141C22×C151—21no—
142C22×C151—21no—
143C22×C151—21no—
144C22×C151—41no—
145C22×C151—41no—
146C22×C151—41no—
147C22×C151C22×D411yescharacteristic
148C2×D151—21no—
149C2×D151—21no—
150C2×D151—21no—
151C2×D151—41no—
152C2×D151—41no—
153C2×D151—41no—
154C4×C151—21no—
155C4×C151—41no—
156C4×C151—41no—
157C4×C151—41no—
158C4×C151C2×#4111yescharacteristic
159C4×C1512−1+411yescharacteristic
160Dic151—21no—
161Dic151—21no—
162Dic151—21no—
163Dic151—41no—
164Dic151—41no—
165Dic151—41no—
166C2×C151—41no—
167C2×C151—81no—
168C2×C151#54711yescharacteristic
169C2×C151#57511yescharacteristic
170C2×C151#57611yescharacteristic
171D151—41no—
172D151—81no—
173C151#335511yescharacteristic, complemented, Sylow
174#3355—1511nomaximal, Sylow
175#553—1511no—
176#553—1511no—
177#499—1511no—
178#482—1511no—
179#482—1511no—
180#480—1511no—
181#480D15111yescharacteristic, complemented
182#478—1511no—
183#478—1511no—
184#469—1511no—
185#469—1511no—
186C4×D8—1511no—
187#436—1511no—
188#428—1511no—
189#428—1511no—
190C2×D8—1511no—
191C2×M16—1511no—
192C2×M16—1511no—
193#126—3021no—
194#126—3021no—
195#125—1511no—
196#125—1511no—
197#123—3021no—
198#123—3021no—
199#121—3021no—
200#121—3021no—
201#121—1511no—
202#121—1511no—
203#121—1511no—
204#121C2×D15111yescharacteristic
205C4×D4—3021no—
206C4×D4—3021no—
207C4×D4—1511no—
208C4×D4—1511no—
209C4×D4—1511no—
210#117—1511no—
211#117—1511no—
212C2×C4⋊C4—1511no—
213C2×C4⋊C4C2×D15111yescharacteristic
214#107—1511no—
215#107—1511no—
216#107—1511no—
217#107C2×D15111yescharacteristic
218#107C2×D15111yescharacteristic
219#106—1511no—
220#106—1511no—
221#106—1511no—
222#106—1511no—
223C4⋊C8—1511no—
224#102—1511no—
225#102—1511no—
226#102—1511no—
227#102—1511no—
228#102C2×D15111yescharacteristic
229#102C2×D15111yescharacteristic
230C22⋊C8—1511no—
231C22⋊C8C2×D15111yescharacteristic
232C4×C8—1511no—
233C2×D4—21no—
234C2×D4—3021no—
235C2×D4—3021no—
236C2×D4—3021no—
237C2×D4—1511no—
238C2×D4—1511no—
239C2×D4C22×D15111yescharacteristic
240C22×C4—21no—
241C22×C4—3021no—
242C22×C4—3021no—
243C22×C4—3021no—
244C22×C4—1511no—
245C22×C4C22×D15111yescharacteristic
246D8—3022no—
247M16—3022no—
248M16—3022no—
249C2×C8—1511no—
250C2×C8—1511no—
251C2×C8C22×D15111yescharacteristic
252C2×C8C22×D15111yescharacteristic
253C4⋊C4—21no—
254C4⋊C4—3021no—
255C4⋊C4—3021no—
256C4⋊C4—3021no—
257C4⋊C4—3021no—
258C4⋊C4—3021no—
259C4⋊C4—1511no—
260C4⋊C4—1511no—
261C4⋊C4—1511no—
262C4⋊C4—1511no—
263C4⋊C4C22×D15111yescharacteristic
264C4⋊C4C22×D15111yescharacteristic
265C4⋊C4C22×D15111yescharacteristic
266C22⋊C4—21no—
267C22⋊C4—3021no—
268C22⋊C4—3021no—
269C22⋊C4—3021no—
270C22⋊C4—3021no—
271C22⋊C4—3021no—
272C22⋊C4—3021no—
273C22⋊C4—3021no—
274C22⋊C4—1511no—
275C22⋊C4—1511no—
276C42—3021no—
277C42—3021no—
278C42—1511no—
279C23—21no—
280C23—3021no—
281C23—1511no—
282C23D4×D15111yescharacteristic
283D4—21no—
284D4—21no—
285D4—81no—
286D4—3021no—
287D4—3021no—
288D4—6041no—
289D4—6042no—
290D4—6042no—
291D4—12081no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—81no—
298C2×C4—3021no—
299C2×C4—3021no—
300C2×C4—3021no—
301C2×C4—3021no—
302C2×C4—3021no—
303C2×C4—1511no—
304C2×C4—1511no—
305C2×C4—1511no—
306C2×C4—12081no—
307C2×C4—12081no—
308C2×C4—12081no—
309C2×C4D4×D15111yescharacteristic
310C2×C4C23×D15111yescharacteristic
311C8—21no—
312C8—21no—
313C8—3021no—
314C8—1512no—
315C22—21no—
316C22—21no—
317C22—21no—
318C22—41no—
319C22—41no—
320C22—41no—
321C22—3021no—
322C22—3021no—
323C22—3021no—
324C22—6041no—
325C22—6041no—
326C22—6041no—
327C22C2×D4×D15111yescharacteristic
328C4—21no—
329C4—41no—
330C4—41no—
331C4—41no—
332C4—3021no—
333C4—3021no—
334C4—3021no—
335C4—6041no—
336C4—6041no—
337C4—6041no—
338C4#41×D15111yescharacteristic
339C4#1801278611yescharacteristic
340C2—41no—
341C2—81no—
342C2—6041no—
343C2—12081no—
344C2#2375286011yescharacteristic
345C2#2375301111yescharacteristic
346C2#2375301311yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#480×C151C2
socleC22×C151C22×D4
hypercenter#480D151
hypocenterC151#3355
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
1. #23752910C2semidirect
2. #23752909C2semidirect
3. #23752613C2semidirect
4. #23752537C2semidirect
5. #23752534C2semidirect
6. #23752527C2semidirect
7. #23752515C2semidirect
8. #23752514C2semidirect
9. #23752464C2semidirect
10. #23752463C2semidirect
11. #23752292C2semidirect
12. #23752287C2semidirect
13. #23752253C2semidirect
14. #23752252C2semidirect
15. #480×C151C2semidirect
173. C151#3355semidirect
181. #480D151semidirect

Maximal subgroups

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

subgroupindex
#237529102
#237529092
#237526132
#237525372
#237525342
#237525272
#237525152
#237525142
#237524642
#237524632
#237522922
#237522872
#237522532
#237522522
#480×C1512
#3355151