Finite Group Databasebeta

← #34080999

Subgroups — #34080999

Order 19328.

386 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752902C211yesmaximal, characteristic, complemented
2#23752871C211yesmaximal, characteristic
3#23752567C211yesmaximal, characteristic, complemented
4#23752554C211yesmaximal, characteristic, complemented
5#23752526C211yesmaximal, characteristic, complemented
6#23752520C211yesmaximal, characteristic, complemented
7#23752453C211yesmaximal, characteristic, complemented
8#23752441C211yesmaximal, characteristic, complemented
9#23752435C211yesmaximal, characteristic, complemented
10#23752376C211yesmaximal, characteristic, complemented
11#23752370C211yesmaximal, characteristic, complemented
12C4×Dic604C211yesmaximal, characteristic, complemented
13#23752209C211yesmaximal, characteristic, complemented
14C2×#18012664C211yesmaximal, characteristic, complemented
15C8×D4×C151C211yesmaximal, characteristic, complemented
16C2×#14559004C2211yescharacteristic
17C22×Dic302C2211yescharacteristic
18C2×Dic604C2211yescharacteristic
19C2×Dic604C2211yescharacteristic
20C2×#14558993C2211yescharacteristic
21#18012732—21no—
22#18012731C2211yescharacteristic
23#18012729—21no—
24#18012727C2211yescharacteristic
25#18012725—21no—
26#18012720—21no—
27#18012718C2211yescharacteristic
28#18012718C2211yescharacteristic
29#18012718C2211yescharacteristic
30#18012717—21no—
31#18012713C2211yescharacteristic
32#18012711—21no—
33C4×Dic302C2211yescharacteristic
34C4×Dic302C2211yescharacteristic
35(C22⋊D151)⋊C4—21no—
36#18012698C2211yescharacteristic
37#18012695—21no—
38C2×C4⋊Dic151C2211yescharacteristic
39#18012673C2211yescharacteristic
40#18012673C2211yescharacteristic
41#18012671C2211yescharacteristic
42#18012664C2211yescharacteristic
43#18012664C2211yescharacteristic
44#18012664C2211yescharacteristic
45#18012664C2211yescharacteristic
46#18012664C2211yescharacteristic
47#18012664C2211yescharacteristic
48#18012664C2211yescharacteristic
49#18012661C2211yescharacteristic
50#18012661C2211yescharacteristic
51#18012661C2211yescharacteristic
52C22×C8×C151C2211yescharacteristic
53C22×C8×C151C2211yescharacteristic
54C4×D4×C151C2211yescharacteristic
55C4⋊C8×C151C2211yescharacteristic
56C22⋊C8×C151C2211yescharacteristic
57C22⋊C8×C151C2211yescharacteristic
58C4×C8×C151C2211yescharacteristic
59#14559004—22no—
60#14559004—41no—
61C2×Dic302—22no—
62C2×Dic302—21no—
63C2×Dic302—41no—
64C2×Dic302C2311yescharacteristic
65C2×Dic302C2311yescharacteristic
66C2×Dic302C2311yescharacteristic
67C2×D604C2311yescharacteristic
68C2×C22⋊D151—21no—
69C2×C22⋊D151—21no—
70C22×Dic151—21no—
71C22×Dic151—21no—
72C2×C4×D151—21no—
73Dic604—22no—
74Dic604—41no—
75#14558993—41no—
76C4⋊Dic151—21no—
77C4⋊Dic151C2311yescharacteristic
78C4⋊Dic151C2311yescharacteristic
79C4⋊Dic151C2311yescharacteristic
80C4⋊Dic151C2311yescharacteristic
81Dic151⋊C4—21no—
82Dic151⋊C4—21no—
83Dic151⋊C4—21no—
84Dic151⋊C4—21no—
85Dic151⋊C4—21no—
86Dic151⋊C4—21no—
87Dic151⋊C4—21no—
88C22⋊Dic151—21no—
89C22⋊Dic151—21no—
90C22⋊Dic151—21no—
91C22⋊Dic151—21no—
92(C2×D151)⋊C4—21no—
93(C2×D151)⋊C4—21no—
94(C2×D151)⋊C4—21no—
95C4×Dic151—21no—
96C4×Dic151—21no—
97C4×Dic151—21no—
98C2×D4×C151D411yescharacteristic
99C22×C4×C151C2311yescharacteristic
100C22×C4×C151C2311yescharacteristic
101C2×C8×C151—41no—
102C2×C8×C151—41no—
103C2×C8×C151C2311yescharacteristic
104C2×C8×C151C2311yescharacteristic
105C2×C8×C151C2311yescharacteristic
106C2×C8×C151C2311yescharacteristic
107C4⋊C4×C151D411yescharacteristic
108C22⋊C4×C151D411yescharacteristic
109C22⋊C4×C151D411yescharacteristic
110C42×C151C2311yescharacteristic
111C22×D151—21no—
112Dic302—21no—
113Dic302—21no—
114Dic302—21no—
115Dic302—21no—
116Dic302—21no—
117Dic302—42no—
118Dic302#4112yes—
119D604—21no—
120D604—21no—
121C22⋊D151—42no—
122C22⋊D151—42no—
123C2×Dic151—21no—
124C2×Dic151—21no—
125C2×Dic151—21no—
126C2×Dic151—21no—
127C2×Dic151—21no—
128C2×Dic151—21no—
129C2×Dic151—21no—
130C2×Dic151—42no—
131C2×Dic151—42no—
132C4×D151—42no—
133C23×C151C2×D411yescharacteristic
134C23×C151C2×D411yescharacteristic
135D4×C151—22no—
136C2×C4×C151—21no—
137C2×C4×C151—21no—
138C2×C4×C151—21no—
139C2×C4×C151—21no—
140C2×C4×C151C2×D411yescharacteristic
141C2×C4×C151C2×D411yescharacteristic
142C2×C4×C151C2×D411yescharacteristic
143C2×C4×C151C2×D411yescharacteristic
144C2×C4×C151C2411yescharacteristic
145C8×C151—21no—
146C8×C151—21no—
147C8×C151—21no—
148C8×C151—21no—
149C22×C151—21no—
150C22×C151—21no—
151C22×C151—21no—
152C22×C151—21no—
153C22×C151—21no—
154C22×C151#13512yes—
155C22×C151C22×D411yescharacteristic
156C2×D151—41no—
157C2×D151—41no—
158C2×D151—41no—
159C4×C151—21no—
160C4×C151—21no—
161C4×C151—21no—
162C4×C151—21no—
163C4×C151C2×#4111yescharacteristic
164C4×C151H(5,𝔽2)11yescharacteristic
165Dic151—22no—
166Dic151—41no—
167Dic151—41no—
168Dic151—41no—
169Dic151—41no—
170Dic151—41no—
171Dic151—41no—
172C2×C151—22no—
173C2×C151—41no—
174C2×C151#54611yescharacteristic
175C2×C151C2×#13511yescharacteristic
176C2×C151#57811yescharacteristic
177D151—81no—
178C151#330011yescharacteristic, complemented, Sylow
179#3300—1511nomaximal, Sylow
180#552—1511no—
181#548—1511no—
182#488—1511no—
183#485—1511no—
184#480—1511no—
185#479—1511no—
186#467—1511no—
187#465—1511no—
188#464—1511no—
189#452—1511no—
190#451—1511no—
191C4×Q16—1511no—
192C8×D4D15111yescharacteristic, complemented
193#416—1511no—
194C2×#103—1511no—
195C2×#41—1511no—
196C22×Q8—1511no—
197C2×Q16—1511no—
198C2×Q16—1511no—
199C2×SD16—1511no—
200C22×C8C2×D15111yescharacteristic
201C22×C8C2×D15111yescharacteristic
202#126—3021no—
203#125—3021no—
204#125—1511no—
205#124—3021no—
206#124—1511no—
207#123—3021no—
208C22⋊Q8—3021no—
209C22⋊Q8—1511no—
210C22⋊Q8—1511no—
211C22⋊Q8—1511no—
212#121—3021no—
213#121—1511no—
214C4×Q8—1511no—
215C4×Q8—1511no—
216C4×D4—3021no—
217C4×D4C2×D15111yescharacteristic
218#117—3021no—
219#117—1511no—
220C2×C4⋊C4—1511no—
221#107—1511no—
222#107—1511no—
223#106—1511no—
224C4⋊C8C2×D15111yescharacteristic
225#103—1511no—
226#103—1511no—
227#103—1511no—
228#103—1511no—
229#103—1511no—
230#103—1511no—
231#103—1511no—
232#102—1511no—
233#102—1511no—
234#102—1511no—
235C22⋊C8C2×D15111yescharacteristic
236C22⋊C8C2×D15111yescharacteristic
237C4×C8C2×D15111yescharacteristic
238#41—3022no—
239#41—6041no—
240C2×Q8—3022no—
241C2×Q8—3021no—
242C2×Q8—6041no—
243C2×Q8—1511no—
244C2×Q8—1511no—
245C2×Q8—1511no—
246C2×D4—3021no—
247C2×D4—3021no—
248C2×D4—1511no—
249C2×D4D60411yescharacteristic
250C22×C4—3021no—
251C22×C4—3021no—
252C22×C4—3021no—
253C22×C4C22×D15111yescharacteristic
254C22×C4C22×D15111yescharacteristic
255Q16—3022no—
256Q16—6041no—
257SD16—6041no—
258C2×C8—41no—
259C2×C8—41no—
260C2×C8C22×D15111yescharacteristic
261C2×C8C22×D15111yescharacteristic
262C2×C8C22×D15111yescharacteristic
263C2×C8C22×D15111yescharacteristic
264C4⋊C4—3021no—
265C4⋊C4—3021no—
266C4⋊C4—3021no—
267C4⋊C4—3021no—
268C4⋊C4—3021no—
269C4⋊C4—3021no—
270C4⋊C4—3021no—
271C4⋊C4—3021no—
272C4⋊C4—1511no—
273C4⋊C4—1511no—
274C4⋊C4—1511no—
275C4⋊C4—1511no—
276C4⋊C4D60411yescharacteristic
277C22⋊C4—3021no—
278C22⋊C4—3021no—
279C22⋊C4—3021no—
280C22⋊C4—3021no—
281C22⋊C4—3021no—
282C22⋊C4—3021no—
283C22⋊C4—3021no—
284C22⋊C4D60411yescharacteristic
285C22⋊C4D60411yescharacteristic
286C42—3021no—
287C42—3021no—
288C42—3021no—
289C42C22×D15111yescharacteristic
290C23—3021no—
291C23C2×D60411yescharacteristic
292C23C2×D60411yescharacteristic
293Q8—3021no—
294Q8—3021no—
295Q8—3021no—
296Q8—3021no—
297Q8—3021no—
298Q8—6042no—
299Q8—1512no—
300D4—22no—
301D4—3021no—
302D4—3021no—
303D4—6042no—
304D4—6042no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—3021no—
310C2×C4—3021no—
311C2×C4—3021no—
312C2×C4—3021no—
313C2×C4—3021no—
314C2×C4—3021no—
315C2×C4—3021no—
316C2×C4—6042no—
317C2×C4—6042no—
318C2×C4—6042no—
319C2×C4C2×D60411yescharacteristic
320C2×C4C2×D60411yescharacteristic
321C2×C4C2×D60411yescharacteristic
322C2×C4C2×D60411yescharacteristic
323C2×C4C23×D15111yescharacteristic
324C8—21no—
325C8—21no—
326C8—21no—
327C8—21no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—6041no—
334C22—6041no—
335C22—6041no—
336C22#1801276112yes—
337C22C22×D60411yescharacteristic
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—3022no—
343C4—6041no—
344C4—6041no—
345C4—6041no—
346C4—6041no—
347C4—6041no—
348C4—6041no—
349C4#41×D15111yescharacteristic
350C4#1801278411yescharacteristic
351C2—22no—
352C2—41no—
353C2—12081no—
354C2#2375285711yescharacteristic
355C2C2×#1801276111yescharacteristic
356C2#2375302911yescharacteristic
subgroupG/H
centerC22C22×D604
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
FittingC8×D4×C151C2
socleC22×C151C22×D4
prime radical#23752871C2
hypercenterC8×D4D151
hypocenterC151#3300
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
1. #23752902C2semidirect
3. #23752567C2semidirect
4. #23752554C2semidirect
5. #23752526C2semidirect
6. #23752520C2semidirect
7. #23752453C2semidirect
8. #23752441C2semidirect
9. #23752435C2semidirect
10. #23752376C2semidirect
11. #23752370C2semidirect
12. C4×Dic604C2semidirect
13. #23752209C2semidirect
14. C2×#18012664C2semidirect
15. C8×D4×C151C2semidirect
178. C151#3300semidirect
192. C8×D4D151semidirect

Maximal subgroups

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

subgroupindex
#237529022
#237528712
#237525672
#237525542
#237525262
#237525202
#237524532
#237524412
#237524352
#237523762
#237523702
C4×Dic6042
#237522092
C2×#180126642
C8×D4×C1512
#3300151