Finite Group Databasebeta

← #34081058

Subgroups — #34081058

Order 19328.

408 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#23752925C211yesmaximal, characteristic, complemented
2#23752880C211yesmaximal, characteristic, complemented
3#23752557C211yesmaximal, characteristic, complemented
4#23752538C211yesmaximal, characteristic, complemented
5#23752506C211yesmaximal, characteristic, complemented
6#23752449C211yesmaximal, characteristic, complemented
7#23752446C211yesmaximal, characteristic, complemented
8#23752406C211yesmaximal, characteristic, complemented
9#23752359C211yesmaximal, characteristic, complemented
10#23752358C211yesmaximal, characteristic, complemented
11#23752299C211yesmaximal, characteristic, complemented
12(C22⋊D151)⋊C8C211yesmaximal, characteristic, complemented
13#23752206C211yesmaximal, characteristic, complemented
14#23752205C211yesmaximal, characteristic, complemented
15#482×C151C211yesmaximal, characteristic, complemented
16C2×#14559004C2211yescharacteristic
17C2×#14559003C2211yescharacteristic
18C2×#14558993C2211yescharacteristic
19C2×D1208C2211yescharacteristic
20C2×#14558989C2211yescharacteristic
21C22×C151⋊C8C2211yescharacteristic
22C2×C8×D151C2211yescharacteristic
23#18012738C2211yescharacteristic
24#18012735—21no—
25#18012735C2211yescharacteristic
26#18012727—21no—
27#18012725—21no—
28#18012714C2211yescharacteristic
29#18012714C2211yescharacteristic
30#18012713C2211yescharacteristic
31#18012712—21no—
32#18012712—21no—
33#18012711—21no—
34#18012704C2211yescharacteristic
35#18012701C2211yescharacteristic
36C4×C22⋊D151C2211yescharacteristic
37(C22⋊D151)⋊C4—21no—
38#18012697C2211yescharacteristic
39#18012696—21no—
40#18012672C2211yescharacteristic
41Dic151⋊C8C2211yescharacteristic
42#18012664C2211yescharacteristic
43#18012662C2211yescharacteristic
44#18012662C2211yescharacteristic
45#18012661C2211yescharacteristic
46#18012660C2211yescharacteristic
47#18012659C2211yescharacteristic
48#18012659C2211yescharacteristic
49#18012659C2211yescharacteristic
50(C2×D151)⋊C8C2211yescharacteristic
51C8×Dic151C2211yescharacteristic
52#121×C151C2211yescharacteristic
53#117×C151C2211yescharacteristic
54#107×C151C2211yescharacteristic
55#106×C151C2211yescharacteristic
56#102×C151C2211yescharacteristic
57#102×C151C2211yescharacteristic
58C22⋊C8×C151C2211yescharacteristic
59#14559004—22no—
60#14559004—41no—
61#14559003—22no—
62#14559003—41no—
63C2×Dic302—21no—
64C2×Dic302C2311yescharacteristic
65C2×D604—21no—
66C2×D604—21no—
67C2×D604C2311yescharacteristic
68C2×D604C2311yescharacteristic
69C2×C22⋊D151—21no—
70C2×C22⋊D151—21no—
71C2×C22⋊D151—21no—
72C2×C22⋊D151—21no—
73C2×C22⋊D151—21no—
74C2×C22⋊D151D411yescharacteristic
75C22×Dic151—21no—
76C2×C4×D151—21no—
77C2×C4×D151—21no—
78C2×C4×D151C2311yescharacteristic
79#14558993—22no—
80D1208—41no—
81#14558989—41no—
82C2×C151⋊C8—41no—
83C2×C151⋊C8C2311yescharacteristic
84C2×C151⋊C8C2311yescharacteristic
85C8×D151—41no—
86C4⋊Dic151C2311yescharacteristic
87Dic151⋊C4—21no—
88Dic151⋊C4—21no—
89Dic151⋊C4D411yescharacteristic
90C22⋊Dic151D411yescharacteristic
91(C2×D151)⋊C4—21no—
92(C2×D151)⋊C4—21no—
93(C2×D151)⋊C4—21no—
94(C2×D151)⋊C4—21no—
95(C2×D151)⋊C4—21no—
96(C2×D151)⋊C4D411yescharacteristic
97C4×Dic151—21no—
98C4×Dic151—21no—
99C4×Dic151C2311yescharacteristic
100C2×D4×C151—21no—
101C2×D4×C151C2311yescharacteristic
102C22×C4×C151C2311yescharacteristic
103C2×C8×C151C2311yescharacteristic
104C2×C8×C151C2311yescharacteristic
105C4⋊C4×C151C2311yescharacteristic
106C4⋊C4×C151C2311yescharacteristic
107C4⋊C4×C151C2311yescharacteristic
108C22⋊C4×C151—21no—
109C22⋊C4×C151—21no—
110C42×C151—21no—
111C22×D151—21no—
112C22×D151—21no—
113C22×D151C2×D411yescharacteristic
114Dic302—21no—
115Dic302—81no—
116Dic302#4112yes—
117D604—21no—
118D604—21no—
119D604—21no—
120D604—21no—
121D604—81no—
122D604—81no—
123C22⋊D151—22no—
124C22⋊D151—42no—
125C22⋊D151—42no—
126C22⋊D151—42no—
127C22⋊D151—81no—
128C22⋊D151—81no—
129C2×Dic151—21no—
130C2×Dic151—21no—
131C2×Dic151—42no—
132C2×Dic151C2×D411yescharacteristic
133C2×Dic151C2×D411yescharacteristic
134C2×Dic151C2×D411yescharacteristic
135C4×D151—21no—
136C4×D151—21no—
137C4×D151—42no—
138C4×D151—42no—
139C151⋊C8—21no—
140C151⋊C8—21no—
141C23×C151—21no—
142C23×C151C2×D411yescharacteristic
143D4×C151—21no—
144D4×C151—21no—
145D4×C151—81no—
146C2×C4×C151—21no—
147C2×C4×C151—21no—
148C2×C4×C151—21no—
149C2×C4×C151—21no—
150C2×C4×C151—21no—
151C2×C4×C151C2×D411yescharacteristic
152C2×C4×C151C2411yescharacteristic
153C8×C151—21no—
154C8×C151—21no—
155C22×C151—21no—
156C22×C151—21no—
157C22×C151—21no—
158C22×C151—41no—
159C22×C151—41no—
160C22×C151—41no—
161C22×C151C22×D411yescharacteristic
162C2×D151—21no—
163C2×D151—21no—
164C2×D151—21no—
165C2×D151—41no—
166C2×D151—41no—
167C2×D151—41no—
168C2×D151—41no—
169C2×D151—41no—
170C2×D151—41no—
171C4×C151—21no—
172C4×C151—41no—
173C4×C151—41no—
174C4×C151—41no—
175C4×C151C2×#4111yescharacteristic
176C4×C151H(5,𝔽2)11yescharacteristic
177Dic151—21no—
178Dic151—22no—
179Dic151—21no—
180Dic151—41no—
181Dic151#13512yes—
182C2×C151—41no—
183C2×C151—81no—
184C2×C151#54611yescharacteristic
185C2×C151C2×#13511yescharacteristic
186C2×C151#57611yescharacteristic
187D151—41no—
188D151—81no—
189D151—81no—
190C151#330511yescharacteristic, complemented, Sylow
191#3305—1511nomaximal, Sylow
192#555—1511no—
193#550—1511no—
194#486—1511no—
195#482—1511no—
196#482D15111yescharacteristic, complemented
197#477—1511no—
198#466—1511no—
199#466—1511no—
200#459—1511no—
201#449—1511no—
202#449—1511no—
203C4×SD16—1511no—
204C8×D4—1511no—
205#416—1511no—
206#416—1511no—
207C2×#41—1511no—
208C2×#41—1511no—
209C2×SD16—1511no—
210C2×D8—1511no—
211C2×D8—1511no—
212C22×C8—1511no—
213C22×C8—1511no—
214C4⋊Q8—1511no—
215#127—3021no—
216#127—1511no—
217#124—3021no—
218#124—3021no—
219#121—3021no—
220#121—3021no—
221#121—3021no—
222#121—1511no—
223#121—1511no—
224#121—1511no—
225#121C2×D15111yescharacteristic
226C4×Q8—1511no—
227C4×D4—3021no—
228C4×D4—1511no—
229C4×D4—1511no—
230#117—3021no—
231#117—1511no—
232#117C2×D15111yescharacteristic
233#107—1511no—
234#107C2×D15111yescharacteristic
235#106C2×D15111yescharacteristic
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#102C2×D15111yescharacteristic
246#102C2×D15111yescharacteristic
247C22⋊C8—1511no—
248C22⋊C8C2×D15111yescharacteristic
249C4×C8—1511no—
250#41—3022no—
251#41—3022no—
252#41—6041no—
253#41—6041no—
254C2×Q8—3021no—
255C2×Q8—1511no—
256C2×D4—21no—
257C2×D4—3021no—
258C2×D4—3021no—
259C2×D4—3021no—
260C2×D4—3021no—
261C2×D4—3021no—
262C2×D4—3021no—
263C2×D4—3021no—
264C2×D4—1511no—
265C2×D4—1511no—
266C2×D4—1511no—
267C2×D4C22×D15111yescharacteristic
268C22×C4—3021no—
269C22×C4—3021no—
270C22×C4—3021no—
271C22×C4—1511no—
272C22×C4C22×D15111yescharacteristic
273SD16—3022no—
274D8—6041no—
275D8—6041no—
276C2×C8—6041no—
277C2×C8—6041no—
278C2×C8—1511no—
279C2×C8—1511no—
280C2×C8C22×D15111yescharacteristic
281C2×C8C22×D15111yescharacteristic
282C4⋊C4—3021no—
283C4⋊C4—3021no—
284C4⋊C4—1511no—
285C4⋊C4—1511no—
286C4⋊C4C22×D15111yescharacteristic
287C4⋊C4C22×D15111yescharacteristic
288C4⋊C4C22×D15111yescharacteristic
289C22⋊C4—21no—
290C22⋊C4—21no—
291C22⋊C4—3021no—
292C22⋊C4—3021no—
293C22⋊C4—3021no—
294C22⋊C4—3021no—
295C22⋊C4—3021no—
296C22⋊C4—1511no—
297C22⋊C4—1511no—
298C42—21no—
299C42—3021no—
300C42—3021no—
301C42—1511no—
302C23—21no—
303C23—3021no—
304C23—3021no—
305C23—1511no—
306C23D4×D15111yescharacteristic
307Q8—3021no—
308Q8—1512no—
309Q8—12081no—
310D4—21no—
311D4—21no—
312D4—81no—
313D4—3022no—
314D4—3021no—
315D4—3021no—
316D4—3021no—
317D4—3021no—
318D4—6042no—
319D4—6042no—
320D4—6042no—
321D4—12081no—
322D4—12081no—
323D4—12081no—
324D4—12081no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—3021no—
331C2×C4—3021no—
332C2×C4—3021no—
333C2×C4—3021no—
334C2×C4—6042no—
335C2×C4—6042no—
336C2×C4—6042no—
337C2×C4—1511no—
338C2×C4—1511no—
339C2×C4—1511no—
340C2×C4D4×D15111yescharacteristic
341C2×C4C23×D15111yescharacteristic
342C8—21no—
343C8—21no—
344C8—3021no—
345C8—3021no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—3021no—
353C22—3021no—
354C22—3021no—
355C22—6041no—
356C22—6041no—
357C22—6041no—
358C22—6041no—
359C22—6041no—
360C22—6041no—
361C22C2×D4×D15111yescharacteristic
362C4—21no—
363C4—41no—
364C4—41no—
365C4—41no—
366C4—3021no—
367C4—3021no—
368C4—3022no—
369C4—6041no—
370C4—1512no—
371C4#41×D15111yescharacteristic
372C4#1801278511yescharacteristic
373C2—41no—
374C2—81no—
375C2—6041no—
376C2—12081no—
377C2—12081no—
378C2#2375285411yescharacteristic
379C2#135×D15111yescharacteristic
380C2#2375301611yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#482×C151C2
socleC22×C151C22×D4
hypercenter#482D151
hypocenterC151#3305
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
1. #23752925C2semidirect
2. #23752880C2semidirect
3. #23752557C2semidirect
4. #23752538C2semidirect
5. #23752506C2semidirect
6. #23752449C2semidirect
7. #23752446C2semidirect
8. #23752406C2semidirect
9. #23752359C2semidirect
10. #23752358C2semidirect
11. #23752299C2semidirect
12. (C22⋊D151)⋊C8C2semidirect
13. #23752206C2semidirect
14. #23752205C2semidirect
15. #482×C151C2semidirect
190. C151#3305semidirect
196. #482D151semidirect

Maximal subgroups

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

subgroupindex
#237529252
#237528802
#237525572
#237525382
#237525062
#237524492
#237524462
#237524062
#237523592
#237523582
#237522992
(C22⋊D151)⋊C82
#237522062
#237522052
#482×C1512
#3305151