Finite Group Databasebeta

← #34081095

Subgroups — #34081095

Order 19328.

420 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752871C211yesmaximal, characteristic, complemented
2#23752574C211yesmaximal, characteristic, complemented
3#23752547C211yesmaximal, characteristic, complemented
4#23752525C211yesmaximal, characteristic, complemented
5#23752504C211yesmaximal, characteristic, complemented
6#23752456C211yesmaximal, characteristic, complemented
7#23752446C211yesmaximal, characteristic, complemented
8#23752427C211yesmaximal, characteristic, complemented
9#23752355C211yesmaximal, characteristic, complemented
10#23752350C211yesmaximal, characteristic, complemented
11#23752312C211yesmaximal, characteristic, complemented
12#23752284C211yesmaximal, characteristic, complemented
13#23752211C211yesmaximal, characteristic, complemented
14C2×#18012662C211yesmaximal, characteristic, complemented
15#547×C151C211yesmaximal, characteristic, complemented
16C2×#14559004C2211yescharacteristic
17C22×Dic302C2211yescharacteristic
18C2×#14558992C2211yescharacteristic
19C2×#14558992C2211yescharacteristic
20C2×#14558989C2211yescharacteristic
21C2×#14558988C2211yescharacteristic
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#18012672C2211yescharacteristic
33#18012672C2211yescharacteristic
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
47#18012650C2211yescharacteristic
48C2×#41×C151—21no—
49C4⋊Q8×C151C2211yescharacteristic
50#123×C151—21no—
51#123×C151—21no—
52C22⋊Q8×C151—21no—
53#121×C151C2211yescharacteristic
54#121×C151C2211yescharacteristic
55C4×D4×C151C2211yescharacteristic
56C4×D4×C151C2211yescharacteristic
57C2×C4⋊C4×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—
74#14558988—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—
88#41×C151—44no—
89C2×Q8×C151—21no—
90C2×D4×C151—21no—
91C2×D4×C151—21no—
92C2×D4×C151D411yescharacteristic
93C2×D4×C151C2311yescharacteristic
94C22×C4×C151—21no—
95C22×C4×C151—21no—
96C22×C4×C151—21no—
97C22×C4×C151C2311yescharacteristic
98C22×C4×C151C2311yescharacteristic
99C4⋊C4×C151—21no—
100C4⋊C4×C151—21no—
101C4⋊C4×C151—21no—
102C4⋊C4×C151D411yescharacteristic
103C4⋊C4×C151C2311yescharacteristic
104C4⋊C4×C151C2311yescharacteristic
105C4⋊C4×C151C2311yescharacteristic
106C22⋊C4×C151—21no—
107C22⋊C4×C151—21no—
108C22⋊C4×C151—21no—
109C22⋊C4×C151D411yescharacteristic
110C22⋊C4×C151D411yescharacteristic
111C42×C151C2311yescharacteristic
112C22×D151—21no—
113Dic302—21no—
114Dic302—21no—
115Dic302—21no—
116Dic302—42no—
117Dic302#4112yescomplemented
118D604—21no—
119D604—21no—
120C22⋊D151—42no—
121C22⋊D151—42no—
122C2×Dic151—21no—
123C2×Dic151—21no—
124C2×Dic151—21no—
125C2×Dic151—42no—
126C4×D151—42no—
127C151⋊C8—21no—
128C151⋊C8—21no—
129C151⋊C8—21no—
130C151⋊C8—21no—
131C23×C151—21no—
132C23×C151C2×D411yescharacteristic
133C23×C151C2×D411yescharacteristic
134Q8×C151—42no—
135D4×C151—22no—
136D4×C151—21no—
137D4×C151—21no—
138D4×C151—42no—
139D4×C151—42no—
140C2×C4×C151—21no—
141C2×C4×C151—21no—
142C2×C4×C151—21no—
143C2×C4×C151—21no—
144C2×C4×C151—21no—
145C2×C4×C151—21no—
146C2×C4×C151—21no—
147C2×C4×C151—42no—
148C2×C4×C151—42no—
149C2×C4×C151—42no—
150C2×C4×C151C2×D411yescharacteristic
151C2×C4×C151C2×D411yescharacteristic
152C2×C4×C151C2×D411yescharacteristic
153C2×C4×C151C2×D411yescharacteristic
154C2×C4×C151C2411yescharacteristic
155C22×C151—21no—
156C22×C151—21no—
157C22×C151—21no—
158C22×C151—21no—
159C22×C151—21no—
160C22×C151—41no—
161C22×C151—41no—
162C22×C151—41no—
163C22×C151AGL(1,ℤ/8)12yes—
164C22×C151C22×D411yescharacteristic
165C2×D151—41no—
166C2×D151—41no—
167C2×D151—41no—
168C4×C151—21no—
169C4×C151—21no—
170C4×C151—21no—
171C4×C151—21no—
172C4×C151—41no—
173C4×C151—41no—
174C4×C151—41no—
175C4×C151C2×#4111yescharacteristic
176C4×C151H(5,𝔽2)11yescharacteristic
177Dic151—22no—
178Dic151—41no—
179Dic151—41no—
180C2×C151—22no—
181C2×C151—41no—
182C2×C151—81no—
183C2×C151#54611yescharacteristic
184C2×C151C2×AGL(1,ℤ/8)11yescharacteristic
185C2×C151#57811yescharacteristic
186D151—81no—
187C151#330811yescharacteristic, complemented, Sylow
188#3308—1511nomaximal, Sylow
189#548—1511no—
190#547D15111yescharacteristic, complemented
191#489—1511no—
192#484—1511no—
193#480—1511no—
194#477—1511no—
195#468—1511no—
196#466—1511no—
197#463—1511no—
198#449—1511no—
199#448—1511no—
200#440—1511no—
201#435—1511no—
202#417—1511no—
203C2×#103—1511no—
204C2×#41—21no—
205C2×#41—1511no—
206C22×Q8—1511no—
207C2×SD16—1511no—
208C2×SD16—1511no—
209C2×D8—1511no—
210C2×M16—1511no—
211C22×C8—1511no—
212C4⋊Q8C2×D15111yescharacteristic
213#124—3021no—
214#124—1511no—
215#123—21no—
216#123—21no—
217C22⋊Q8—21no—
218C22⋊Q8—3021no—
219C22⋊Q8—1511no—
220#121—3021no—
221#121—1511no—
222#121C2×D15111yescharacteristic
223#121C2×D15111yescharacteristic
224C4×Q8—1511no—
225C4×D4—3021no—
226C4×D4C2×D15111yescharacteristic
227C4×D4C2×D15111yescharacteristic
228C2×C4⋊C4C2×D15111yescharacteristic
229C2×C4⋊C4C2×D15111yescharacteristic
230#107—1511no—
231#107—1511no—
232#107—1511no—
233C4⋊C8—1511no—
234#103—1511no—
235#103—1511no—
236#103—1511no—
237#103—1511no—
238#103—1511no—
239#103—1511no—
240#102—1511no—
241#102—1511no—
242#102—1511no—
243#102—1511no—
244C22⋊C8—1511no—
245C22⋊C8—1511no—
246#97—1511no—
247#41—44no—
248#41—3022no—
249#41—6041no—
250C2×Q8—21no—
251C2×Q8—3022no—
252C2×Q8—3021no—
253C2×Q8—6041no—
254C2×Q8—1511no—
255C2×Q8—1511no—
256C2×D4—21no—
257C2×D4—21no—
258C2×D4—3021no—
259C2×D4—3021no—
260C2×D4—1511no—
261C2×D4C22⋊D15111yescharacteristic
262C2×D4C22×D15111yescharacteristic
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—3021no—
267C22×C4—3021no—
268C22×C4C22×D15111yescharacteristic
269C22×C4C22×D15111yescharacteristic
270SD16—3022no—
271SD16—6041no—
272D8—6041no—
273M16—6041no—
274C2×C8—6041no—
275C2×C8—1511no—
276C2×C8—1511no—
277C2×C8—1511no—
278C2×C8—1511no—
279C4⋊C4—21no—
280C4⋊C4—21no—
281C4⋊C4—21no—
282C4⋊C4—3021no—
283C4⋊C4—3021no—
284C4⋊C4—1511no—
285C4⋊C4C22⋊D15111yescharacteristic
286C4⋊C4C22×D15111yescharacteristic
287C4⋊C4C22×D15111yescharacteristic
288C4⋊C4C22×D15111yescharacteristic
289C22⋊C4—21no—
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—3021no—
293C22⋊C4—3021no—
294C22⋊C4—3021no—
295C22⋊C4—3021no—
296C22⋊C4C22⋊D15111yescharacteristic
297C22⋊C4C22⋊D15111yescharacteristic
298C42—3021no—
299C42C22×D15111yescharacteristic
300C23—21no—
301C23—3021no—
302C23C2×C22⋊D15111yescharacteristic
303C23C2×C22⋊D15111yescharacteristic
304Q8—42no—
305Q8—3021no—
306Q8—3021no—
307Q8—3021no—
308Q8—6042no—
309Q8—1512no—
310D4—22no—
311D4—21no—
312D4—21no—
313D4—42no—
314D4—42no—
315D4—3021no—
316D4—3021no—
317D4—6042no—
318D4—6042no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—3021no—
330C2×C4—3021no—
331C2×C4—3021no—
332C2×C4—6042no—
333C2×C4—6042no—
334C2×C4C2×C22⋊D15111yescharacteristic
335C2×C4C2×C22⋊D15111yescharacteristic
336C2×C4C2×C22⋊D15111yescharacteristic
337C2×C4C2×C22⋊D15111yescharacteristic
338C2×C4C23×D15111yescharacteristic
339C8—3021no—
340C8—3021no—
341C8—3021no—
342C8—3021no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—6041no—
352C22—6041no—
353C22—6041no—
354C22#1801276512yes—
355C22C22×C22⋊D15111yescharacteristic
356C4—21no—
357C4—21no—
358C4—21no—
359C4—21no—
360C4—41no—
361C4—41no—
362C4—41no—
363C4—3022no—
364C4—6041no—
365C4—6041no—
366C4#41×D15111yescharacteristic
367C4#1801278511yescharacteristic
368C2—22no—
369C2—41no—
370C2—81no—
371C2—12081no—
372C2#2375285011yescharacteristic
373C2C2×#1801276511yescharacteristic
374C2#2375302711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#547×C151C2
socleC22×C151C22×D4
hypercenter#547D151
hypocenterC151#3308
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C4×D4 ◁ #547

Complements

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

NH ≅ G/Ntype
1. #23752871C2semidirect
2. #23752574C2semidirect
3. #23752547C2semidirect
4. #23752525C2semidirect
5. #23752504C2semidirect
6. #23752456C2semidirect
7. #23752446C2semidirect
8. #23752427C2semidirect
9. #23752355C2semidirect
10. #23752350C2semidirect
11. #23752312C2semidirect
12. #23752284C2semidirect
13. #23752211C2semidirect
14. C2×#18012662C2semidirect
15. #547×C151C2semidirect
117. Dic302#41semidirect
187. C151#3308semidirect
190. #547D151semidirect

Maximal subgroups

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

subgroupindex
#237528712
#237525742
#237525472
#237525252
#237525042
#237524562
#237524462
#237524272
#237523552
#237523502
#237523122
#237522842
#237522112
C2×#180126622
#547×C1512
#3308151