Finite Group Databasebeta

← #34080506

Subgroups — #34080506

Order 19328.

354 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752746C211yesmaximal, characteristic, complemented
2#23752519C211yesmaximal, characteristic, complemented
3#23752516C211yesmaximal, characteristic, complemented
4#23752512C211yesmaximal, characteristic, complemented
5#23752509C211yesmaximal, characteristic, complemented
6#23752468C211yesmaximal, characteristic, complemented
7#23752463C211yesmaximal, characteristic
8#23752460C211yesmaximal, characteristic, complemented
9#23752456C211yesmaximal, characteristic, complemented
10#23752434C211yesmaximal, characteristic, complemented
11#23752431C211yesmaximal, characteristic, complemented
12#23752427C211yesmaximal, characteristic, complemented
13#23752424C211yesmaximal, characteristic, complemented
14#23752236C211yesmaximal, characteristic, complemented
15#529×C151C211yesmaximal, characteristic, complemented
16C2×#14558994C2211yescharacteristic
17C2×#14558992C2211yescharacteristic
18C2×#14558991C2211yescharacteristic
19C2×#14558989C2211yescharacteristic
20C2×#14558988C2211yescharacteristic
21C2×#14558988C2211yescharacteristic
22#18012733—21no—
23#18012731C2211yescharacteristic
24#18012727C2211yescharacteristic
25#18012722—21no—
26#18012718C2211yescharacteristic
27#18012713C2211yescharacteristic
28C4×Dic302C2211yescharacteristic
29C4×D604C2211yescharacteristic
30C4×C22⋊D151—21no—
31#18012696—21no—
32#18012672C2211yescharacteristic
33#18012672C2211yescharacteristic
34#18012670C2211yescharacteristic
35#18012670C2211yescharacteristic
36C4⋊(C151⋊C8)C2211yescharacteristic
37C4⋊(C151⋊C8)C2211yescharacteristic
38C4⋊(C151⋊C8)C2211yescharacteristic
39C4⋊(C151⋊C8)C2211yescharacteristic
40#18012663C2211yescharacteristic
41#18012663C2211yescharacteristic
42#18012662C2211yescharacteristic
43#18012662C2211yescharacteristic
44#18012660C2211yescharacteristic
45#18012660C2211yescharacteristic
46#18012659C2211yescharacteristic
47#18012659C2211yescharacteristic
48#126×C151—21no—
49#125×C151C2211yescharacteristic
50#124×C151C2211yescharacteristic
51#123×C151—21no—
52C22⋊Q8×C151C2211yescharacteristic
53#121×C151C2211yescharacteristic
54C4×Q8×C151C2211yescharacteristic
55C4×D4×C151—21no—
56C4×D4×C151C2211yescharacteristic
57#117×C151—21no—
58C2×C42×C151C2211yescharacteristic
59C2×Dic302C2311yescharacteristic
60C2×D604C2311yescharacteristic
61C2×C22⋊D151—21no—
62C2×C4×D151—21no—
63#14558994—41no—
64#14558992—41no—
65#14558991—41no—
66#14558989—41no—
67#14558988—41no—
68#14558988—41no—
69C2×C151⋊C8C2311yescharacteristic
70C2×C151⋊C8C2311yescharacteristic
71C2×C151⋊C8C2311yescharacteristic
72C2×C151⋊C8C2311yescharacteristic
73C4⋊Dic151C2311yescharacteristic
74C4⋊Dic151C2311yescharacteristic
75Dic151⋊C4—21no—
76Dic151⋊C4—21no—
77Dic151⋊C4—21no—
78Dic151⋊C4—21no—
79C22⋊Dic151—21no—
80(C2×D151)⋊C4—21no—
81(C2×D151)⋊C4—21no—
82(C2×D151)⋊C4—21no—
83(C2×D151)⋊C4—21no—
84C4×Dic151—21no—
85C2×Q8×C151C2311yescharacteristic
86C2×D4×C151—21no—
87C2×D4×C151C2311yescharacteristic
88C22×C4×C151—21no—
89C22×C4×C151D411yescharacteristic
90C22×C4×C151D411yescharacteristic
91C22×C4×C151C2311yescharacteristic
92C4⋊C4×C151—21no—
93C4⋊C4×C151—21no—
94C4⋊C4×C151—21no—
95C4⋊C4×C151—21no—
96C4⋊C4×C151C2311yescharacteristic
97C4⋊C4×C151C2311yescharacteristic
98C22⋊C4×C151—21no—
99C22⋊C4×C151—21no—
100C22⋊C4×C151—21no—
101C22⋊C4×C151—21no—
102C22⋊C4×C151—21no—
103C42×C151—21no—
104C42×C151D411yescharacteristic
105C42×C151D411yescharacteristic
106C42×C151C2311yescharacteristic
107C42×C151C2311yescharacteristic
108C22×D151—21no—
109Dic302—21no—
110Dic302—21no—
111D604—21no—
112D604—21no—
113C22⋊D151—42no—
114C2×Dic151—21no—
115C2×Dic151—21no—
116C2×Dic151—21no—
117C4×D151—42no—
118C151⋊C8—21no—
119C151⋊C8—21no—
120C151⋊C8—21no—
121C151⋊C8—21no—
122C23×C151—21no—
123C23×C151C2×D411yescharacteristic
124Q8×C151—21no—
125Q8×C151—21no—
126D4×C151—21no—
127D4×C151—21no—
128D4×C151—42no—
129C2×C4×C151—21no—
130C2×C4×C151—21no—
131C2×C4×C151—21no—
132C2×C4×C151—21no—
133C2×C4×C151—21no—
134C2×C4×C151—41no—
135C2×C4×C151—41no—
136C2×C4×C151—42no—
137C2×C4×C151C2×D411yescharacteristic
138C2×C4×C151C2×D411yescharacteristic
139C2×C4×C151C2×D411yescharacteristic
140C2×C4×C151C2×D411yescharacteristic
141C2×C4×C151C2×D411yescharacteristic
142C2×C4×C151C2411yescharacteristic
143C22×C151—21no—
144C22×C151—21no—
145C22×C151—21no—
146C22×C151—41no—
147C22×C151—41no—
148C22×C151—41no—
149C22×C151C22×D411yescharacteristic
150C2×D151—41no—
151C2×D151—41no—
152C2×D151—41no—
153C4×C151—21no—
154C4×C151—21no—
155C4×C151—21no—
156C4×C151—21no—
157C4×C151—21no—
158C4×C151—41no—
159C4×C151—41no—
160C4×C151—41no—
161C4×C151H(5,𝔽2)11yescharacteristic
162C4×C1512−1+411yescharacteristic
163Dic151—41no—
164Dic151—41no—
165Dic151—41no—
166C2×C151—41no—
167C2×C151—81no—
168C2×C151#53711yescharacteristic
169C2×C151#57511yescharacteristic
170C2×C151#57511yescharacteristic
171D151—81no—
172C151#325611yescharacteristic, complemented, Sylow
173#3256—1511nomaximal, Sylow
174#529—1511no—
175#529D15111yescharacteristic, complemented
176#479—1511no—
177#479—1511no—
178#478—1511no—
179#478—1511no—
180#470—1511no—
181#469—1511no—
182#468—1511no—
183#468—1511no—
184#464—1511no—
185#464—1511no—
186#463—1511no—
187#463—1511no—
188#423—1511no—
189C2×Q16—1511no—
190C2×SD16—1511no—
191C2×SD16—1511no—
192C2×D8—1511no—
193C2×M16—1511no—
194C2×M16—1511no—
195#126—21no—
196#126—3021no—
197#125—1511no—
198#125C2×D15111yescharacteristic
199#124—1511no—
200#124C2×D15111yescharacteristic
201#123—21no—
202#123—3021no—
203C22⋊Q8—1511no—
204C22⋊Q8C2×D15111yescharacteristic
205#121—1511no—
206#121C2×D15111yescharacteristic
207C4×Q8—1511no—
208C4×Q8C2×D15111yescharacteristic
209C4×D4—21no—
210C4×D4—3021no—
211C4×D4—1511no—
212C4×D4C2×D15111yescharacteristic
213#117—21no—
214#117—3021no—
215C2×C42C2×D15111yescharacteristic
216#107—1511no—
217#107—1511no—
218#106—1511no—
219#106—1511no—
220C4⋊C8—1511no—
221C4⋊C8—1511no—
222C4⋊C8—1511no—
223C4⋊C8—1511no—
224#103—1511no—
225#103—1511no—
226#103—1511no—
227#103—1511no—
228#102—1511no—
229#102—1511no—
230#102—1511no—
231#102—1511no—
232C2×Q8—1511no—
233C2×Q8C22×D15111yescharacteristic
234C2×D4—21no—
235C2×D4—3021no—
236C2×D4—1511no—
237C2×D4C22×D15111yescharacteristic
238C22×C4—21no—
239C22×C4—3021no—
240C22×C4C22⋊D15111yescharacteristic
241C22×C4C22⋊D15111yescharacteristic
242C22×C4C22×D15111yescharacteristic
243Q16—6041no—
244SD16—6041no—
245SD16—6041no—
246D8—6041no—
247M16—6041no—
248M16—6041no—
249C2×C8—1511no—
250C2×C8—1511no—
251C2×C8—1511no—
252C2×C8—1511no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—21no—
257C4⋊C4—3021no—
258C4⋊C4—3021no—
259C4⋊C4—3021no—
260C4⋊C4—3021no—
261C4⋊C4—1511no—
262C4⋊C4—1511no—
263C4⋊C4C22×D15111yescharacteristic
264C4⋊C4C22×D15111yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—21no—
270C22⋊C4—3021no—
271C22⋊C4—3021no—
272C22⋊C4—3021no—
273C22⋊C4—3021no—
274C22⋊C4—3021no—
275C42—21no—
276C42—3021no—
277C42C22⋊D15111yescharacteristic
278C42C22⋊D15111yescharacteristic
279C42C22×D15111yescharacteristic
280C42C22×D15111yescharacteristic
281C23—21no—
282C23—3021no—
283C23C2×C22⋊D15111yescharacteristic
284Q8—21no—
285Q8—21no—
286Q8—3021no—
287Q8—3021no—
288D4—21no—
289D4—21no—
290D4—42no—
291D4—3021no—
292D4—3021no—
293D4—6042no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—42no—
302C2×C4—3021no—
303C2×C4—3021no—
304C2×C4—3021no—
305C2×C4—6042no—
306C2×C4C2×C22⋊D15111yescharacteristic
307C2×C4C2×C22⋊D15111yescharacteristic
308C2×C4C2×C22⋊D15111yescharacteristic
309C2×C4C2×C22⋊D15111yescharacteristic
310C2×C4C2×C22⋊D15111yescharacteristic
311C2×C4C23×D15111yescharacteristic
312C8—3021no—
313C8—3021no—
314C8—3021no—
315C8—3021no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—41no—
320C22—41no—
321C22—41no—
322C22—6041no—
323C22—6041no—
324C22—6041no—
325C22C22×C22⋊D15111yescharacteristic
326C4—21no—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—21no—
331C4—41no—
332C4—41no—
333C4—41no—
334C4—6041no—
335C4—6041no—
336C4—6041no—
337C4#1801278511yescharacteristic
338C4#1801278611yescharacteristic
339C2—41no—
340C2—81no—
341C2—12081no—
342C2#2375279011yescharacteristic
343C2#2375301011yescharacteristic
344C2#2375301011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#529×C151C2
socleC22×C151C22×D4
prime radical#23752463C2
hypercenter#529D151
hypocenterC151#3256
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C2×C42 ◁ #529

Complements

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

NH ≅ G/Ntype
1. #23752746C2semidirect
2. #23752519C2semidirect
3. #23752516C2semidirect
4. #23752512C2semidirect
5. #23752509C2semidirect
6. #23752468C2semidirect
8. #23752460C2semidirect
9. #23752456C2semidirect
10. #23752434C2semidirect
11. #23752431C2semidirect
12. #23752427C2semidirect
13. #23752424C2semidirect
14. #23752236C2semidirect
15. #529×C151C2semidirect
172. C151#3256semidirect
175. #529D151semidirect

Maximal subgroups

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

subgroupindex
#237527462
#237525192
#237525162
#237525122
#237525092
#237524682
#237524632
#237524602
#237524562
#237524342
#237524312
#237524272
#237524242
#237522362
#529×C1512
#3256151