Finite Group Databasebeta

← #34081110

Subgroups — #34081110

Order 19328.

404 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752883C211yesmaximal, characteristic, complemented
2#23752578C211yesmaximal, characteristic, complemented
3#23752536C211yesmaximal, characteristic, complemented
4#23752525C211yesmaximal, characteristic, complemented
5#23752516C211yesmaximal, characteristic, complemented
6#23752463C211yesmaximal, characteristic, complemented
7#23752446C211yesmaximal, characteristic, complemented
8#23752407C211yesmaximal, characteristic, complemented
9#23752355C211yesmaximal, characteristic, complemented
10#23752355C211yesmaximal, characteristic, complemented
11#23752312C211yesmaximal, characteristic, complemented
12#23752284C211yesmaximal, characteristic, complemented
13#23752211C211yesmaximal, characteristic, complemented
14#23752206C211yesmaximal, characteristic, complemented
15#553×C151C211yesmaximal, characteristic, complemented
16C2×#14559004C2211yescharacteristic
17C2×#14559004C2211yescharacteristic
18C2×#14558992C2211yescharacteristic
19C2×#14558989C2211yescharacteristic
20C2×#14558989C2211yescharacteristic
21C2×#14558988C2211yescharacteristic
22C22×C151⋊C8C2211yescharacteristic
23#18012736C2211yescharacteristic
24#18012735—21no—
25#18012713C2211yescharacteristic
26#18012713C2211yescharacteristic
27#18012712—21no—
28#18012712—21no—
29C4×Dic302C2211yescharacteristic
30#18012701—21no—
31#18012672C2211yescharacteristic
32#18012672C2211yescharacteristic
33#18012670C2211yescharacteristic
34C4⋊(C151⋊C8)C2211yescharacteristic
35#18012662C2211yescharacteristic
36#18012662C2211yescharacteristic
37#18012662C2211yescharacteristic
38#18012660C2211yescharacteristic
39#18012659C2211yescharacteristic
40#18012659C2211yescharacteristic
41#18012659C2211yescharacteristic
42#18012659C2211yescharacteristic
43#18012659C2211yescharacteristic
44#18012659C2211yescharacteristic
45C22⋊(C151⋊C8)C2211yescharacteristic
46C22⋊(C151⋊C8)C2211yescharacteristic
47#18012650C2211yescharacteristic
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—22no—
61#14559004—41no—
62#14559004—41no—
63C2×Dic302C2311yescharacteristic
64C2×D604—21no—
65C2×D604—21no—
66C2×D604C2311yescharacteristic
67C2×D604C2311yescharacteristic
68C2×C22⋊D151—21no—
69C2×C22⋊D151—21no—
70C2×C22⋊D151—21no—
71C2×C22⋊D151—21no—
72C2×C4×D151—21no—
73C2×C4×D151—21no—
74#14558992—22no—
75#14558989—41no—
76#14558989—41no—
77#14558988—41no—
78C2×C151⋊C8—41no—
79C2×C151⋊C8C2311yescharacteristic
80C2×C151⋊C8C2311yescharacteristic
81C2×C151⋊C8C2311yescharacteristic
82C2×C151⋊C8C2311yescharacteristic
83C4⋊Dic151C2311yescharacteristic
84Dic151⋊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—
112C22×D151—21no—
113Dic302—21no—
114Dic302#4112yes—
115D604—21no—
116D604—21no—
117D604—21no—
118D604—21no—
119D604—42no—
120D604—81no—
121C22⋊D151—42no—
122C22⋊D151—42no—
123C22⋊D151—81no—
124C22⋊D151—81no—
125C2×Dic151—21no—
126C2×Dic151—21no—
127C4×D151—42no—
128C4×D151—42no—
129C151⋊C8—21no—
130C151⋊C8—21no—
131C151⋊C8—21no—
132C151⋊C8—21no—
133C23×C151—21no—
134C23×C151C2×D411yescharacteristic
135C23×C151C2×D411yescharacteristic
136D4×C151—21no—
137D4×C151—21no—
138D4×C151—41no—
139D4×C151—42no—
140D4×C151—81no—
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—21no—
148C2×C4×C151—81no—
149C2×C4×C151—81no—
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—21no—
161C22×C151—41no—
162C22×C151—41no—
163C22×C151—41no—
164C22×C151C22×D411yescharacteristic
165C2×D151—41no—
166C2×D151—41no—
167C2×D151—41no—
168C2×D151—41no—
169C2×D151—41no—
170C2×D151—41no—
171C4×C151—21no—
172C4×C151—21no—
173C4×C151—21no—
174C4×C151—21no—
175C4×C151—41no—
176C4×C151—41no—
177C4×C151—41no—
178C4×C151C2×#4111yescharacteristic
179C4×C151H(5,𝔽2)11yescharacteristic
180Dic151—22no—
181Dic151—41no—
182C2×C151—41no—
183C2×C151—41no—
184C2×C151—81no—
185C2×C151#54611yescharacteristic
186C2×C151#57511yescharacteristic
187C2×C151#57611yescharacteristic
188D151—81no—
189D151—81no—
190C151#330911yescharacteristic, complemented, Sylow
191#3309—1511nomaximal, Sylow
192#553D15111yescharacteristic, complemented
193#550—1511no—
194#490—1511no—
195#482—1511no—
196#480—1511no—
197#479—1511no—
198#469—1511no—
199#466—1511no—
200#459—1511no—
201#449—1511no—
202#449—1511no—
203#440—1511no—
204#435—1511no—
205#417—1511no—
206#416—1511no—
207C2×#41—1511no—
208C2×#41—1511no—
209C2×SD16—1511no—
210C2×D8—1511no—
211C2×D8—1511no—
212C2×M16—1511no—
213C22×C8—1511no—
214#127—3021no—
215#127—1511no—
216#126—21no—
217#125C2×D15111yescharacteristic
218#123—21no—
219#121—21no—
220#121—3021no—
221#121—3021no—
222#121—1511no—
223#121—1511no—
224#121C2×D15111yescharacteristic
225#121C2×D15111yescharacteristic
226C4×Q8—1511no—
227C4×D4—21no—
228C4×D4—3021no—
229C4×D4C2×D15111yescharacteristic
230C4×D4C2×D15111yescharacteristic
231#117C2×D15111yescharacteristic
232C2×C4⋊C4C2×D15111yescharacteristic
233#107—1511no—
234#107—1511no—
235#106—1511no—
236C4⋊C8—1511no—
237#103—1511no—
238#103—1511no—
239#103—1511no—
240#102—1511no—
241#102—1511no—
242#102—1511no—
243#102—1511no—
244#102—1511no—
245#102—1511no—
246#102—1511no—
247C22⋊C8—1511no—
248C22⋊C8—1511no—
249#97—1511no—
250#41—3022no—
251#41—3022no—
252#41—6041no—
253#41—6041no—
254C2×Q8—1511no—
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—3021no—
258C2×D4—3021no—
259C2×D4—3021no—
260C2×D4—3021no—
261C2×D4—3021no—
262C2×D4—3021no—
263C2×D4—1511no—
264C2×D4—1511no—
265C2×D4C22⋊D15111yescharacteristic
266C2×D4C22×D15111yescharacteristic
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—3021no—
270C22×C4—3021no—
271C22×C4C22×D15111yescharacteristic
272C22×C4C22×D15111yescharacteristic
273SD16—3022no—
274D8—6041no—
275D8—6041no—
276M16—6041no—
277C2×C8—6041no—
278C2×C8—1511no—
279C2×C8—1511no—
280C2×C8—1511no—
281C2×C8—1511no—
282C4⋊C4—21no—
283C4⋊C4—21no—
284C4⋊C4—21no—
285C4⋊C4—3021no—
286C4⋊C4—1511no—
287C4⋊C4C22⋊D15111yescharacteristic
288C4⋊C4C22×D15111yescharacteristic
289C4⋊C4C22×D15111yescharacteristic
290C4⋊C4C22×D15111yescharacteristic
291C22⋊C4—21no—
292C22⋊C4—21no—
293C22⋊C4—21no—
294C22⋊C4—21no—
295C22⋊C4—3021no—
296C22⋊C4—3021no—
297C22⋊C4C22⋊D15111yescharacteristic
298C22⋊C4C22⋊D15111yescharacteristic
299C42—21no—
300C42—3021no—
301C42C22×D15111yescharacteristic
302C23—21no—
303C23—3021no—
304C23—3021no—
305C23C2×C22⋊D15111yescharacteristic
306C23C2×C22⋊D15111yescharacteristic
307Q8—3021no—
308Q8—1512no—
309D4—21no—
310D4—21no—
311D4—41no—
312D4—42no—
313D4—81no—
314D4—3021no—
315D4—3021no—
316D4—3021no—
317D4—3021no—
318D4—6042no—
319D4—6042no—
320D4—6042no—
321D4—12081no—
322D4—12081no—
323D4—12081no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—81no—
332C2×C4—81no—
333C2×C4—3021no—
334C2×C4—3021no—
335C2×C4—6042no—
336C2×C4—6042no—
337C2×C4C2×C22⋊D15111yescharacteristic
338C2×C4C2×C22⋊D15111yescharacteristic
339C2×C4C2×C22⋊D15111yescharacteristic
340C2×C4C2×C22⋊D15111yescharacteristic
341C2×C4C23×D15111yescharacteristic
342C8—3021no—
343C8—3021no—
344C8—3021no—
345C8—3021no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—6041no—
356C22—6041no—
357C22—6041no—
358C22—6041no—
359C22—6041no—
360C22—6041no—
361C22C22×C22⋊D15111yescharacteristic
362C4—21no—
363C4—21no—
364C4—21no—
365C4—21no—
366C4—41no—
367C4—41no—
368C4—41no—
369C4—3022no—
370C4—6041no—
371C4#41×D15111yescharacteristic
372C4#1801278511yescharacteristic
373C2—41no—
374C2—41no—
375C2—81no—
376C2—12081no—
377C2—12081no—
378C2#2375285011yescharacteristic
379C2#2375301011yescharacteristic
380C2#2375301511yescharacteristic
subgroupG/H
centerC22C22×C22⋊D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#553×C151C2
socleC22×C151C22×D4
hypercenter#553D151
hypocenterC151#3309
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. #23752883C2semidirect
2. #23752578C2semidirect
3. #23752536C2semidirect
4. #23752525C2semidirect
5. #23752516C2semidirect
6. #23752463C2semidirect
7. #23752446C2semidirect
8. #23752407C2semidirect
9. #23752355C2semidirect
10. #23752355C2semidirect
11. #23752312C2semidirect
12. #23752284C2semidirect
13. #23752211C2semidirect
14. #23752206C2semidirect
15. #553×C151C2semidirect
190. C151#3309semidirect
192. #553D151semidirect

Maximal subgroups

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

subgroupindex
#237528832
#237525782
#237525362
#237525252
#237525162
#237524632
#237524462
#237524072
#237523552
#237523122
#237522842
#237522112
#237522062
#553×C1512
#3309151