Finite Group Databasebeta

← #34081042

Subgroups — #34081042

Order 19328.

396 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#23752933C211yesmaximal, characteristic, complemented
2#23752881C211yesmaximal, characteristic
3#23752557C211yesmaximal, characteristic, complemented
4#23752537C211yesmaximal, characteristic, complemented
5#23752534C211yesmaximal, characteristic, complemented
6#23752495C211yesmaximal, characteristic, complemented
7#23752443C211yesmaximal, characteristic, complemented
8#23752438C211yesmaximal, characteristic, complemented
9#23752410C211yesmaximal, characteristic, complemented
10#23752373C211yesmaximal, characteristic, complemented
11Q16×Dic151C211yesmaximal, characteristic, complemented
12(C22⋊D151)⋊C8C211yesmaximal, characteristic, complemented
13#23752208C211yesmaximal, characteristic, complemented
14#23752207C211yesmaximal, characteristic, complemented
15#452×C151C211yesmaximal, characteristic, complemented
16C2×#14559005C2211yescharacteristic
17C2×#14558991C2211yescharacteristic
18C22×C151⋊C8C2211yescharacteristic
19C2×C8×D151C2211yescharacteristic
20#18012738C2211yescharacteristic
21#18012735—21no—
22#18012735C2211yescharacteristic
23#18012734—21no—
24#18012732—21no—
25#18012725—21no—
26#18012715C2211yescharacteristic
27#18012713—21no—
28#18012713C2211yescharacteristic
29#18012710—21no—
30#18012710C2211yescharacteristic
31Q8×Dic151C2211yescharacteristic
32Q8×Dic151C2211yescharacteristic
33#18012704—21no—
34C4×C22⋊D151—21no—
35C4×C22⋊D151C2211yescharacteristic
36#18012698C2211yescharacteristic
37#18012697C2211yescharacteristic
38#18012673C2211yescharacteristic
39#18012671C2211yescharacteristic
40#18012670C2211yescharacteristic
41Dic151⋊C8C2211yescharacteristic
42#18012663C2211yescharacteristic
43#18012663C2211yescharacteristic
44#18012663C2211yescharacteristic
45#18012661C2211yescharacteristic
46#18012661C2211yescharacteristic
47#18012660C2211yescharacteristic
48#18012660C2211yescharacteristic
49#18012659C2211yescharacteristic
50(C2×D151)⋊C8C2211yescharacteristic
51C8×Dic151C2211yescharacteristic
52C2×#41×C151C2211yescharacteristic
53C2×Q16×C151C2211yescharacteristic
54C2×SD16×C151C2211yescharacteristic
55C22⋊Q8×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⋊D151D411yescharacteristic
69C2×C4×D151—21no—
70C2×C4×D151C2311yescharacteristic
71#14558991—41no—
72C2×C151⋊C8—41no—
73C2×C151⋊C8C2311yescharacteristic
74C2×C151⋊C8C2311yescharacteristic
75C8×D151—41no—
76C4⋊Dic151—21no—
77C4⋊Dic151—21no—
78C4⋊Dic151C2311yescharacteristic
79C4⋊Dic151C2311yescharacteristic
80C4⋊Dic151C2311yescharacteristic
81Dic151⋊C4—21no—
82Dic151⋊C4—21no—
83Dic151⋊C4D411yescharacteristic
84C22⋊Dic151—21no—
85C22⋊Dic151—21no—
86C22⋊Dic151D411yescharacteristic
87(C2×D151)⋊C4—21no—
88(C2×D151)⋊C4—21no—
89(C2×D151)⋊C4—21no—
90(C2×D151)⋊C4D411yescharacteristic
91C4×Dic151—21no—
92C4×Dic151—21no—
93C4×Dic151—21no—
94C4×Dic151—21no—
95C4×Dic151C2311yescharacteristic
96#41×C151—22no—
97#41×C151—41no—
98C2×Q8×C151C2311yescharacteristic
99C2×Q8×C151C2311yescharacteristic
100C2×D4×C151—21no—
101C2×D4×C151C2311yescharacteristic
102C22×C4×C151—21no—
103C22×C4×C151C2311yescharacteristic
104Q16×C151—22no—
105SD16×C151—41no—
106C2×C8×C151C2311yescharacteristic
107C2×C8×C151C2311yescharacteristic
108C4⋊C4×C151—21no—
109C4⋊C4×C151C2311yescharacteristic
110C22⋊C4×C151—21no—
111C22×D151—21no—
112C22×D151C2×D411yescharacteristic
113Dic302—42no—
114D604—21no—
115D604—21no—
116D604—42no—
117C22⋊D151—22no—
118C22⋊D151—42no—
119C22⋊D151—81no—
120C22⋊D151—81no—
121C22⋊D151—81no—
122C2×Dic151—21no—
123C2×Dic151—21no—
124C2×Dic151—21no—
125C2×Dic151C2×D411yescharacteristic
126C2×Dic151C2×D411yescharacteristic
127C2×Dic151C2×D411yescharacteristic
128C4×D151—21no—
129C4×D151—21no—
130C4×D151—42no—
131C151⋊C8—21no—
132C151⋊C8—21no—
133C23×C151—21no—
134C23×C151C2×D411yescharacteristic
135Q8×C151—21no—
136Q8×C151—21no—
137Q8×C151—21no—
138Q8×C151#4112yes—
139D4×C151—21no—
140D4×C151—21no—
141D4×C151—42no—
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×C151C2×D411yescharacteristic
149C2×C4×C151C2411yescharacteristic
150C8×C151—21no—
151C8×C151—21no—
152C22×C151—21no—
153C22×C151—21no—
154C22×C151—21no—
155C22×C151—41no—
156C22×C151—41no—
157C22×C151—41no—
158C22×C151C22×D411yescharacteristic
159C2×D151—21no—
160C2×D151—21no—
161C2×D151—21no—
162C2×D151—41no—
163C2×D151—41no—
164C2×D151—41no—
165C4×C151—21no—
166C4×C151—22no—
167C4×C151—41no—
168C4×C151—41no—
169C4×C151C2×#4111yescharacteristic
170C4×C151H(5,𝔽2)11yescharacteristic
171Dic151—21no—
172Dic151—21no—
173Dic151—41no—
174Dic151—41no—
175Dic151—41no—
176Dic151#13512yes—
177C2×C151—41no—
178C2×C151—81no—
179C2×C151#54611yescharacteristic
180C2×C151C2×#13511yescharacteristic
181C2×C151#57711yescharacteristic
182D151—41no—
183D151—81no—
184C151#330411yescharacteristic, complemented, Sylow
185#3304—1511nomaximal, Sylow
186#556—1511no—
187#550—1511no—
188#486—1511no—
189#482—1511no—
190#482—1511no—
191#475—1511no—
192#465—1511no—
193#465—1511no—
194#460—1511no—
195#452—1511no—
196#452D15111yescharacteristic, complemented
197C4×Q16—1511no—
198C8×D4—1511no—
199#416—1511no—
200#416—1511no—
201C2×#41—1511no—
202C2×#41C2×D15111yescharacteristic
203C2×Q16C2×D15111yescharacteristic
204C2×SD16—1511no—
205C2×SD16C2×D15111yescharacteristic
206C22×C8—1511no—
207C22×C8—1511no—
208C4⋊Q8—1511no—
209#127—3021no—
210#127—1511no—
211#126—3021no—
212#126—3021no—
213#124—3021no—
214C22⋊Q8—1511no—
215C22⋊Q8C2×D15111yescharacteristic
216#121—3021no—
217#121—3021no—
218#121—1511no—
219#121—1511no—
220C4×Q8—3021no—
221C4×Q8—1511no—
222C4×Q8—1511no—
223C4×D4—3021no—
224C4×D4—1511no—
225#117—1511no—
226#117—1511no—
227#107—1511no—
228#106—1511no—
229#106—1511no—
230C4⋊C8—1511no—
231#103—1511no—
232#103—1511no—
233#103—1511no—
234#103C2×D15111yescharacteristic
235#102—1511no—
236#102—1511no—
237#102—1511no—
238#102—1511no—
239#102—1511no—
240#102C2×D15111yescharacteristic
241C22⋊C8—1511no—
242C22⋊C8C2×D15111yescharacteristic
243C4×C8—1511no—
244#41—22no—
245#41—41no—
246#41—3022no—
247#41—6041no—
248C2×Q8—3021no—
249C2×Q8C22×D15111yescharacteristic
250C2×Q8C22×D15111yescharacteristic
251C2×D4—21no—
252C2×D4—3021no—
253C2×D4—3021no—
254C2×D4—3021no—
255C2×D4—3021no—
256C2×D4—3021no—
257C2×D4—1511no—
258C2×D4—1511no—
259C2×D4C22×D15111yescharacteristic
260C22×C4—21no—
261C22×C4—3021no—
262C22×C4—1511no—
263C22×C4C22×D15111yescharacteristic
264Q16—22no—
265SD16—41no—
266SD16—6041no—
267C2×C8—6041no—
268C2×C8—6041no—
269C2×C8—1511no—
270C2×C8—1511no—
271C2×C8C22×D15111yescharacteristic
272C2×C8C22×D15111yescharacteristic
273C4⋊C4—21no—
274C4⋊C4—3021no—
275C4⋊C4—3021no—
276C4⋊C4—3021no—
277C4⋊C4—3021no—
278C4⋊C4—1511no—
279C4⋊C4—1511no—
280C4⋊C4—1511no—
281C4⋊C4—1511no—
282C4⋊C4C22×D15111yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—3021no—
285C22⋊C4—3021no—
286C22⋊C4—3021no—
287C22⋊C4—3021no—
288C22⋊C4—3021no—
289C22⋊C4—1511no—
290C22⋊C4—1511no—
291C42—3021no—
292C42—3021no—
293C42—3021no—
294C42—3021no—
295C42—1511no—
296C23—21no—
297C23—3021no—
298C23—1511no—
299C23D4×D15111yescharacteristic
300Q8—21no—
301Q8—21no—
302Q8—21no—
303Q8—6042no—
304Q8#1455900312yes—
305D4—21no—
306D4—21no—
307D4—42no—
308D4—3022no—
309D4—3021no—
310D4—3021no—
311D4—6042no—
312D4—6042no—
313D4—12081no—
314D4—12081no—
315D4—12081no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—42no—
322C2×C4—3021no—
323C2×C4—3021no—
324C2×C4—3021no—
325C2×C4—3021no—
326C2×C4—3021no—
327C2×C4—6042no—
328C2×C4—1511no—
329C2×C4—1511no—
330C2×C4—1511no—
331C2×C4D4×D15111yescharacteristic
332C2×C4C23×D15111yescharacteristic
333C8—21no—
334C8—21no—
335C8—3021no—
336C8—3021no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—3021no—
344C22—3021no—
345C22—3021no—
346C22—6041no—
347C22—6041no—
348C22—6041no—
349C22C2×D4×D15111yescharacteristic
350C4—21no—
351C4—22no—
352C4—41no—
353C4—41no—
354C4—3021no—
355C4—3021no—
356C4—6041no—
357C4—6041no—
358C4—6041no—
359C4—1512no—
360C4C2×#1455900311yescharacteristic
361C4#1801278411yescharacteristic
362C2—41no—
363C2—81no—
364C2—6041no—
365C2—12081no—
366C2#2375284911yescharacteristic
367C2#135×D15111yescharacteristic
368C2#2375302111yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#452×C151C2
socleC22×C151C22×D4
prime radical#23752881C2
hypercenter#452D151
hypocenterC151#3304
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
1. #23752933C2semidirect
3. #23752557C2semidirect
4. #23752537C2semidirect
5. #23752534C2semidirect
6. #23752495C2semidirect
7. #23752443C2semidirect
8. #23752438C2semidirect
9. #23752410C2semidirect
10. #23752373C2semidirect
11. Q16×Dic151C2semidirect
12. (C22⋊D151)⋊C8C2semidirect
13. #23752208C2semidirect
14. #23752207C2semidirect
15. #452×C151C2semidirect
184. C151#3304semidirect
196. #452D151semidirect

Maximal subgroups

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

subgroupindex
#237529332
#237528812
#237525572
#237525372
#237525342
#237524952
#237524432
#237524382
#237524102
#237523732
Q16×Dic1512
(C22⋊D151)⋊C82
#237522082
#237522072
#452×C1512
#3304151