Finite Group Databasebeta

← #34081006

Subgroups — #34081006

Order 19328.

398 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752871C211yesmaximal, characteristic, complemented
2#23752569C211yesmaximal, characteristic, complemented
3#23752553C211yesmaximal, characteristic, complemented
4#23752530C211yesmaximal, characteristic, complemented
5#23752516C211yesmaximal, characteristic, complemented
6#23752446C211yesmaximal, characteristic, complemented
7#23752439C211yesmaximal, characteristic, complemented
8#23752427C211yesmaximal, characteristic, complemented
9#23752355C211yesmaximal, characteristic, complemented
10#23752350C211yesmaximal, characteristic, complemented
11C4×#14558992C211yesmaximal, characteristic, complemented
12D4×C151⋊C8C211yesmaximal, characteristic, complemented
13#23752206C211yesmaximal, characteristic, complemented
14C2×#18012662C211yesmaximal, characteristic, complemented
15#553×C151C211yesmaximal, characteristic, complemented
16C2×#14559004C2211yescharacteristic
17C22×Dic302C2211yescharacteristic
18C2×#14558992C2211yescharacteristic
19C2×#14558992C2211yescharacteristic
20C2×#14558989C2211yescharacteristic
21C22×C151⋊C8C2211yescharacteristic
22C22×C151⋊C8C2211yescharacteristic
23#18012727C2211yescharacteristic
24#18012725—21no—
25#18012718C2211yescharacteristic
26#18012717—21no—
27#18012713C2211yescharacteristic
28#18012711—21no—
29C4×Dic302C2211yescharacteristic
30(C22⋊D151)⋊C4—21no—
31#18012672C2211yescharacteristic
32#18012670C2211yescharacteristic
33#18012670C2211yescharacteristic
34C4⋊(C151⋊C8)C2211yescharacteristic
35#18012662C2211yescharacteristic
36#18012662C2211yescharacteristic
37#18012662C2211yescharacteristic
38#18012662C2211yescharacteristic
39#18012662C2211yescharacteristic
40#18012662C2211yescharacteristic
41#18012660C2211yescharacteristic
42#18012659C2211yescharacteristic
43#18012659C2211yescharacteristic
44#18012659C2211yescharacteristic
45C22⋊(C151⋊C8)C2211yescharacteristic
46C22⋊(C151⋊C8)C2211yescharacteristic
47C4×C151⋊C8C2211yescharacteristic
48#126×C151—21no—
49#125×C151C2211yescharacteristic
50#123×C151—21no—
51#121×C151—21no—
52#121×C151C2211yescharacteristic
53#121×C151C2211yescharacteristic
54C4×D4×C151—21no—
55C4×D4×C151C2211yescharacteristic
56C4×D4×C151C2211yescharacteristic
57#117×C151C2211yescharacteristic
58C2×C4⋊C4×C151C2211yescharacteristic
59#14559004—22no—
60#14559004—41no—
61C2×Dic302—22no—
62C2×Dic302—21no—
63C2×Dic302—41no—
64C2×Dic302C2311yescharacteristic
65C2×Dic302C2311yescharacteristic
66C2×D604C2311yescharacteristic
67C2×C22⋊D151—21no—
68C2×C22⋊D151—21no—
69C22×Dic151—21no—
70C2×C4×D151—21no—
71#14558992—22no—
72#14558992—41no—
73#14558989—41no—
74C2×C151⋊C8—41no—
75C2×C151⋊C8—41no—
76C2×C151⋊C8C2311yescharacteristic
77C2×C151⋊C8C2311yescharacteristic
78C2×C151⋊C8C2311yescharacteristic
79C2×C151⋊C8C2311yescharacteristic
80C4⋊Dic151C2311yescharacteristic
81Dic151⋊C4—21no—
82Dic151⋊C4—21no—
83C22⋊Dic151—21no—
84(C2×D151)⋊C4—21no—
85(C2×D151)⋊C4—21no—
86(C2×D151)⋊C4—21no—
87C4×Dic151—21no—
88C2×D4×C151—21no—
89C2×D4×C151—21no—
90C2×D4×C151D411yescharacteristic
91C2×D4×C151C2311yescharacteristic
92C22×C4×C151—21no—
93C22×C4×C151—21no—
94C22×C4×C151C2311yescharacteristic
95C22×C4×C151C2311yescharacteristic
96C4⋊C4×C151—21no—
97C4⋊C4×C151—21no—
98C4⋊C4×C151—21no—
99C4⋊C4×C151D411yescharacteristic
100C4⋊C4×C151C2311yescharacteristic
101C4⋊C4×C151C2311yescharacteristic
102C4⋊C4×C151C2311yescharacteristic
103C22⋊C4×C151—21no—
104C22⋊C4×C151—21no—
105C22⋊C4×C151—21no—
106C22⋊C4×C151—21no—
107C22⋊C4×C151D411yescharacteristic
108C22⋊C4×C151D411yescharacteristic
109C42×C151—21no—
110C42×C151C2311yescharacteristic
111C22×D151—21no—
112Dic302—21no—
113Dic302—21no—
114Dic302—21no—
115Dic302—42no—
116Dic302#4112yes—
117D604—21no—
118D604—21no—
119C22⋊D151—42no—
120C22⋊D151—42no—
121C2×Dic151—21no—
122C2×Dic151—21no—
123C2×Dic151—21no—
124C2×Dic151—42no—
125C4×D151—42no—
126C151⋊C8—21no—
127C151⋊C8—21no—
128C151⋊C8—21no—
129C151⋊C8—21no—
130C23×C151—21no—
131C23×C151C2×D411yescharacteristic
132C23×C151C2×D411yescharacteristic
133D4×C151—22no—
134D4×C151—21no—
135D4×C151—21no—
136D4×C151—42no—
137D4×C151—81no—
138C2×C4×C151—21no—
139C2×C4×C151—21no—
140C2×C4×C151—21no—
141C2×C4×C151—21no—
142C2×C4×C151—21no—
143C2×C4×C151—21no—
144C2×C4×C151—21no—
145C2×C4×C151—81no—
146C2×C4×C151—81no—
147C2×C4×C151C2×D411yescharacteristic
148C2×C4×C151C2×D411yescharacteristic
149C2×C4×C151C2×D411yescharacteristic
150C2×C4×C151C2×D411yescharacteristic
151C2×C4×C151C2411yescharacteristic
152C22×C151—21no—
153C22×C151—21no—
154C22×C151—21no—
155C22×C151—21no—
156C22×C151—21no—
157C22×C151—41no—
158C22×C151—41no—
159C22×C151—41no—
160C22×C151#13512yes—
161C22×C151C22×D411yescharacteristic
162C2×D151—41no—
163C2×D151—41no—
164C2×D151—41no—
165C4×C151—21no—
166C4×C151—21no—
167C4×C151—21no—
168C4×C151—21no—
169C4×C151—41no—
170C4×C151—41no—
171C4×C151—41no—
172C4×C151C2×#4111yescharacteristic
173C4×C151H(5,𝔽2)11yescharacteristic
174Dic151—22no—
175Dic151—41no—
176Dic151—41no—
177C2×C151—22no—
178C2×C151—41no—
179C2×C151—81no—
180C2×C151#54611yescharacteristic
181C2×C151C2×#13511yescharacteristic
182C2×C151#57711yescharacteristic
183D151—81no—
184C151#330111yescharacteristic, complemented, Sylow
185#3301—1511nomaximal, Sylow
186#553D15111yescharacteristic, complemented
187#548—1511no—
188#488—1511no—
189#485—1511no—
190#481—1511no—
191#479—1511no—
192#466—1511no—
193#465—1511no—
194#463—1511no—
195#449—1511no—
196#448—1511no—
197C4×SD16—1511no—
198C8×D4—1511no—
199#416—1511no—
200C2×#103—1511no—
201C2×#41—1511no—
202C22×Q8—1511no—
203C2×SD16—1511no—
204C2×SD16—1511no—
205C2×D8—1511no—
206C22×C8—1511no—
207C22×C8—1511no—
208#126—21no—
209#125C2×D15111yescharacteristic
210#124—3021no—
211#124—1511no—
212#123—21no—
213C22⋊Q8—3021no—
214C22⋊Q8—1511no—
215#121—21no—
216#121—3021no—
217#121—1511no—
218#121C2×D15111yescharacteristic
219#121C2×D15111yescharacteristic
220C4×Q8—1511no—
221C4×D4—21no—
222C4×D4—3021no—
223C4×D4C2×D15111yescharacteristic
224C4×D4C2×D15111yescharacteristic
225#117C2×D15111yescharacteristic
226C2×C4⋊C4C2×D15111yescharacteristic
227#107—1511no—
228#106—1511no—
229#106—1511no—
230C4⋊C8—1511no—
231#103—1511no—
232#103—1511no—
233#103—1511no—
234#103—1511no—
235#103—1511no—
236#103—1511no—
237#102—1511no—
238#102—1511no—
239#102—1511no—
240#102—1511no—
241C22⋊C8—1511no—
242C22⋊C8—1511no—
243C4×C8—1511no—
244#41—3022no—
245#41—6041no—
246C2×Q8—3022no—
247C2×Q8—3021no—
248C2×Q8—6041no—
249C2×Q8—1511no—
250C2×Q8—1511no—
251C2×D4—21no—
252C2×D4—21no—
253C2×D4—3021no—
254C2×D4—3021no—
255C2×D4—1511no—
256C2×D4C22⋊D15111yescharacteristic
257C2×D4C22×D15111yescharacteristic
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—3021no—
261C22×C4—3021no—
262C22×C4C22×D15111yescharacteristic
263C22×C4C22×D15111yescharacteristic
264SD16—3022no—
265SD16—6041no—
266D8—6041no—
267C2×C8—6041no—
268C2×C8—6041no—
269C2×C8—1511no—
270C2×C8—1511no—
271C2×C8—1511no—
272C2×C8—1511no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—3021no—
277C4⋊C4—3021no—
278C4⋊C4—1511no—
279C4⋊C4C22⋊D15111yescharacteristic
280C4⋊C4C22×D15111yescharacteristic
281C4⋊C4C22×D15111yescharacteristic
282C4⋊C4C22×D15111yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—3021no—
288C22⋊C4—3021no—
289C22⋊C4—3021no—
290C22⋊C4—3021no—
291C22⋊C4C22⋊D15111yescharacteristic
292C22⋊C4C22⋊D15111yescharacteristic
293C42—21no—
294C42—3021no—
295C42C22×D15111yescharacteristic
296C23—21no—
297C23—3021no—
298C23C2×C22⋊D15111yescharacteristic
299C23C2×C22⋊D15111yescharacteristic
300Q8—3021no—
301Q8—3021no—
302Q8—3021no—
303Q8—6042no—
304Q8—1512no—
305D4—22no—
306D4—21no—
307D4—21no—
308D4—42no—
309D4—81no—
310D4—3021no—
311D4—3021no—
312D4—6042no—
313D4—6042no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—81no—
322C2×C4—81no—
323C2×C4—3021no—
324C2×C4—3021no—
325C2×C4—3021no—
326C2×C4—6042no—
327C2×C4—6042no—
328C2×C4C2×C22⋊D15111yescharacteristic
329C2×C4C2×C22⋊D15111yescharacteristic
330C2×C4C2×C22⋊D15111yescharacteristic
331C2×C4C2×C22⋊D15111yescharacteristic
332C2×C4C23×D15111yescharacteristic
333C8—3021no—
334C8—3021no—
335C8—3021no—
336C8—3021no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—6041no—
346C22—6041no—
347C22—6041no—
348C22#1801275912yes—
349C22C22×C22⋊D15111yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—3022no—
358C4—6041no—
359C4—6041no—
360C4#41×D15111yescharacteristic
361C4#1801278511yescharacteristic
362C2—22no—
363C2—41no—
364C2—81no—
365C2—12081no—
366C2#2375285011yescharacteristic
367C2C2×#1801275911yescharacteristic
368C2#2375302311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#553×C151C2
socleC22×C151C22×D4
hypercenter#553D151
hypocenterC151#3301
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C4×D4 ◁ #553

Complements

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

NH ≅ G/Ntype
1. #23752871C2semidirect
2. #23752569C2semidirect
3. #23752553C2semidirect
4. #23752530C2semidirect
5. #23752516C2semidirect
6. #23752446C2semidirect
7. #23752439C2semidirect
8. #23752427C2semidirect
9. #23752355C2semidirect
10. #23752350C2semidirect
11. C4×#14558992C2semidirect
12. D4×C151⋊C8C2semidirect
13. #23752206C2semidirect
14. C2×#18012662C2semidirect
15. #553×C151C2semidirect
184. C151#3301semidirect
186. #553D151semidirect

Maximal subgroups

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

subgroupindex
#237528712
#237525692
#237525532
#237525302
#237525162
#237524462
#237524392
#237524272
#237523552
#237523502
C4×#145589922
D4×C151⋊C82
#237522062
C2×#180126622
#553×C1512
#3301151