Finite Group Databasebeta

← #34081053

Subgroups — #34081053

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#23752926C211yesmaximal, characteristic, complemented
2#23752881C211yesmaximal, characteristic, complemented
3#23752557C211yesmaximal, characteristic, complemented
4#23752537C211yesmaximal, characteristic, complemented
5#23752535C211yesmaximal, characteristic, complemented
6#23752505C211yesmaximal, characteristic, complemented
7#23752446C211yesmaximal, characteristic, complemented
8#23752445C211yesmaximal, characteristic, complemented
9#23752405C211yesmaximal, characteristic, complemented
10#23752356C211yesmaximal, characteristic, complemented
11SD16×Dic151C211yesmaximal, characteristic, complemented
12(C22⋊D151)⋊C8C211yesmaximal, characteristic, complemented
13#23752208C211yesmaximal, characteristic, complemented
14#23752207C211yesmaximal, characteristic, complemented
15#449×C151C211yesmaximal, characteristic, complemented
16C2×#14559005C2211yescharacteristic
17C2×#14558989C2211yescharacteristic
18C22×C151⋊C8C2211yescharacteristic
19C2×C8×D151C2211yescharacteristic
20#18012738C2211yescharacteristic
21#18012735—21no—
22#18012735C2211yescharacteristic
23#18012726—21no—
24#18012725—21no—
25#18012713—21no—
26#18012713C2211yescharacteristic
27#18012711—21no—
28#18012710—21no—
29#18012710C2211yescharacteristic
30#18012710C2211yescharacteristic
31Q8×Dic151C2211yescharacteristic
32D4×Dic151C2211yescharacteristic
33C4×C22⋊D151—21no—
34C4×C22⋊D151C2211yescharacteristic
35#18012698C2211yescharacteristic
36#18012697C2211yescharacteristic
37#18012695—21no—
38#18012673C2211yescharacteristic
39#18012672C2211yescharacteristic
40#18012671C2211yescharacteristic
41Dic151⋊C8C2211yescharacteristic
42#18012663C2211yescharacteristic
43#18012663C2211yescharacteristic
44#18012661C2211yescharacteristic
45#18012661C2211yescharacteristic
46#18012660C2211yescharacteristic
47#18012660C2211yescharacteristic
48#18012660C2211yescharacteristic
49#18012659C2211yescharacteristic
50(C2×D151)⋊C8C2211yescharacteristic
51C8×Dic151C2211yescharacteristic
52C2×#41×C151C2211yescharacteristic
53C2×SD16×C151C2211yescharacteristic
54C2×D8×C151C2211yescharacteristic
55#121×C151C2211yescharacteristic
56#103×C151C2211yescharacteristic
57#102×C151C2211yescharacteristic
58C22⋊C8×C151C2211yescharacteristic
59#14559005—22no—
60#14559005—41no—
61C2×Dic302—21no—
62C2×D604—21no—
63C2×D604C2311yescharacteristic
64C2×C22⋊D151—21no—
65C2×C22⋊D151—21no—
66C2×C22⋊D151—21no—
67C2×C22⋊D151—21no—
68C2×C22⋊D151—21no—
69C2×C22⋊D151D411yescharacteristic
70C22×Dic151—21no—
71C2×C4×D151—21no—
72C2×C4×D151C2311yescharacteristic
73#14558989—41no—
74C2×C151⋊C8—41no—
75C2×C151⋊C8C2311yescharacteristic
76C2×C151⋊C8C2311yescharacteristic
77C8×D151—41no—
78C4⋊Dic151—21no—
79C4⋊Dic151C2311yescharacteristic
80C4⋊Dic151C2311yescharacteristic
81C4⋊Dic151C2311yescharacteristic
82Dic151⋊C4—21no—
83Dic151⋊C4D411yescharacteristic
84C22⋊Dic151—21no—
85C22⋊Dic151—21no—
86C22⋊Dic151—21no—
87C22⋊Dic151—21no—
88C22⋊Dic151D411yescharacteristic
89(C2×D151)⋊C4—21no—
90(C2×D151)⋊C4—21no—
91(C2×D151)⋊C4D411yescharacteristic
92C4×Dic151—21no—
93C4×Dic151—21no—
94C4×Dic151—21no—
95C4×Dic151C2311yescharacteristic
96#41×C151—22no—
97#41×C151—41no—
98C2×Q8×C151C2311yescharacteristic
99C2×D4×C151—21no—
100C2×D4×C151—21no—
101C2×D4×C151C2311yescharacteristic
102C2×D4×C151C2311yescharacteristic
103C22×C4×C151—21no—
104C22×C4×C151C2311yescharacteristic
105SD16×C151—22no—
106D8×C151—41no—
107C2×C8×C151C2311yescharacteristic
108C2×C8×C151C2311yescharacteristic
109C4⋊C4×C151C2311yescharacteristic
110C22⋊C4×C151—21no—
111C22×D151—21no—
112C22×D151C2×D411yescharacteristic
113Dic302—81no—
114D604—21no—
115D604—21no—
116D604—42no—
117C22⋊D151—22no—
118C22⋊D151—42no—
119C22⋊D151—81no—
120C22⋊D151—81no—
121C22⋊D151—81no—
122C22⋊D151—81no—
123C2×Dic151—21no—
124C2×Dic151—21no—
125C2×Dic151—21no—
126C2×Dic151—42no—
127C2×Dic151C2×D411yescharacteristic
128C2×Dic151C2×D411yescharacteristic
129C2×Dic151C2×D411yescharacteristic
130C4×D151—21no—
131C4×D151—21no—
132C4×D151—42no—
133C151⋊C8—21no—
134C151⋊C8—21no—
135C23×C151—21no—
136C23×C151—21no—
137C23×C151C2×D411yescharacteristic
138Q8×C151—21no—
139Q8×C151#4112yes—
140D4×C151—21no—
141D4×C151—21no—
142D4×C151—21no—
143D4×C151—21no—
144D4×C151—42no—
145D4×C151—81no—
146C2×C4×C151—21no—
147C2×C4×C151—21no—
148C2×C4×C151—21no—
149C2×C4×C151—21no—
150C2×C4×C151—42no—
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×C151—41no—
162C22×C151—41no—
163C22×C151—41no—
164C22×C151C22×D411yescharacteristic
165C2×D151—21no—
166C2×D151—21no—
167C2×D151—21no—
168C2×D151—41no—
169C2×D151—41no—
170C2×D151—41no—
171C4×C151—21no—
172C4×C151—22no—
173C4×C151—41no—
174C4×C151C2×#4111yescharacteristic
175C4×C151H(5,𝔽2)11yescharacteristic
176Dic151—21no—
177Dic151—21no—
178Dic151—41no—
179Dic151—41no—
180Dic151—41no—
181Dic151#13512yes—
182C2×C151—41no—
183C2×C151—81no—
184C2×C151—81no—
185C2×C151#54611yescharacteristic
186C2×C151C2×#13511yescharacteristic
187C2×C151#57611yescharacteristic
188D151—41no—
189D151—81no—
190C151#330511yescharacteristic, complemented, Sylow
191#3305—1511nomaximal, Sylow
192#555—1511no—
193#550—1511no—
194#486—1511no—
195#482—1511no—
196#482—1511no—
197#477—1511no—
198#466—1511no—
199#466—1511no—
200#459—1511no—
201#449—1511no—
202#449D15111yescharacteristic, complemented
203C4×SD16—1511no—
204C8×D4—1511no—
205#416—1511no—
206#416—1511no—
207C2×#41—1511no—
208C2×#41C2×D15111yescharacteristic
209C2×SD16C2×D15111yescharacteristic
210C2×D8—1511no—
211C2×D8C2×D15111yescharacteristic
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#117—1511no—
233#107—1511no—
234#107—1511no—
235#106—1511no—
236C4⋊C8—1511no—
237#103—1511no—
238#103—1511no—
239#103C2×D15111yescharacteristic
240#102—1511no—
241#102—1511no—
242#102—1511no—
243#102—1511no—
244#102—1511no—
245#102—1511no—
246#102C2×D15111yescharacteristic
247C22⋊C8—1511no—
248C22⋊C8C2×D15111yescharacteristic
249C4×C8—1511no—
250#41—22no—
251#41—41no—
252#41—3022no—
253#41—6041no—
254C2×Q8—3021no—
255C2×Q8C22×D15111yescharacteristic
256C2×D4—21no—
257C2×D4—21no—
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×D4C22×D15111yescharacteristic
267C2×D4C22×D15111yescharacteristic
268C22×C4—21no—
269C22×C4—3021no—
270C22×C4—3021no—
271C22×C4—1511no—
272C22×C4C22×D15111yescharacteristic
273SD16—22no—
274D8—41no—
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⋊C4—1511no—
287C4⋊C4—1511no—
288C4⋊C4C22×D15111yescharacteristic
289C22⋊C4—21no—
290C22⋊C4—3021no—
291C22⋊C4—3021no—
292C22⋊C4—3021no—
293C22⋊C4—3021no—
294C22⋊C4—3021no—
295C22⋊C4—3021no—
296C22⋊C4—1511no—
297C22⋊C4—1511no—
298C42—3021no—
299C42—3021no—
300C42—3021no—
301C42—1511no—
302C23—21no—
303C23—21no—
304C23—3021no—
305C23—1511no—
306C23D4×D15111yescharacteristic
307Q8—21no—
308Q8—12081no—
309Q8#1455900312yes—
310D4—21no—
311D4—21no—
312D4—21no—
313D4—21no—
314D4—42no—
315D4—81no—
316D4—3022no—
317D4—3021no—
318D4—3021no—
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—42no—
330C2×C4—3021no—
331C2×C4—3021no—
332C2×C4—3021no—
333C2×C4—3021no—
334C2×C4—3021no—
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—41no—
353C22—41no—
354C22—41no—
355C22—3021no—
356C22—3021no—
357C22—3021no—
358C22—6041no—
359C22—6041no—
360C22—6041no—
361C22C2×D4×D15111yescharacteristic
362C4—21no—
363C4—22no—
364C4—41no—
365C4—3021no—
366C4—3021no—
367C4—6041no—
368C4—6041no—
369C4—6041no—
370C4—1512no—
371C4C2×#1455900311yescharacteristic
372C4#1801278411yescharacteristic
373C2—41no—
374C2—81no—
375C2—81no—
376C2—6041no—
377C2—12081no—
378C2#2375284911yescharacteristic
379C2#135×D15111yescharacteristic
380C2#2375301611yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#449×C151C2
socleC22×C151C22×D4
hypercenter#449D151
hypocenterC151#3305
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #23752926C2semidirect
2. #23752881C2semidirect
3. #23752557C2semidirect
4. #23752537C2semidirect
5. #23752535C2semidirect
6. #23752505C2semidirect
7. #23752446C2semidirect
8. #23752445C2semidirect
9. #23752405C2semidirect
10. #23752356C2semidirect
11. SD16×Dic151C2semidirect
12. (C22⋊D151)⋊C8C2semidirect
13. #23752208C2semidirect
14. #23752207C2semidirect
15. #449×C151C2semidirect
190. C151#3305semidirect
202. #449D151semidirect

Maximal subgroups

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

subgroupindex
#237529262
#237528812
#237525572
#237525372
#237525352
#237525052
#237524462
#237524452
#237524052
#237523562
SD16×Dic1512
(C22⋊D151)⋊C82
#237522082
#237522072
#449×C1512
#3305151