Finite Group Databasebeta

← #34079720

Subgroups — #34079720

Order 19328.

362 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752835C211yesmaximal, characteristic, complemented
2#23752829C211yesmaximal, characteristic, complemented
3#23752609C211yesmaximal, characteristic, complemented
4#23752593C211yesmaximal, characteristic, complemented
5#23752573C211yesmaximal, characteristic, complemented
6#23752570C211yesmaximal, characteristic, complemented
7#23752468C211yesmaximal, characteristic, complemented
8#23752463C211yesmaximal, characteristic
9#23752441C211yesmaximal, characteristic, complemented
10#23752321C211yesmaximal, characteristic, complemented
11#23752316C211yesmaximal, characteristic, complemented
12SD16×Dic151C211yesmaximal, characteristic, complemented
13#23752299C211yesmaximal, characteristic, complemented
14#23752167C211yesmaximal, characteristic, complemented
15#465×C151C211yesmaximal, characteristic, complemented
16C2×#14558994C2211yescharacteristic
17C2×#14558993C2211yescharacteristic
18C2×#14558989C2211yescharacteristic
19C2×#14558988C2211yescharacteristic
20#18012738C2211yescharacteristic
21#18012738C2211yescharacteristic
22#18012734—21no—
23#18012732—21no—
24#18012728C2211yescharacteristic
25#18012726—21no—
26#18012726C2211yescharacteristic
27#18012725—21no—
28#18012721—21no—
29#18012720—21no—
30#18012719—21no—
31#18012718C2211yescharacteristic
32#18012716—21no—
33#18012713C2211yescharacteristic
34Q8×Dic151C2211yescharacteristic
35#18012704C2211yescharacteristic
36D4×Dic151C2211yescharacteristic
37#18012701C2211yescharacteristic
38#18012698C2211yescharacteristic
39#18012671C2211yescharacteristic
40#18012670C2211yescharacteristic
41#18012670C2211yescharacteristic
42#18012664C2211yescharacteristic
43#18012663C2211yescharacteristic
44#18012662C2211yescharacteristic
45#18012661C2211yescharacteristic
46#18012660C2211yescharacteristic
47#18012659C2211yescharacteristic
48#18012649C2211yescharacteristic
49#18012649C2211yescharacteristic
50C8×Dic151C2211yescharacteristic
51C8×Dic151C2211yescharacteristic
52C2×SD16×C151C2211yescharacteristic
53C22×C8×C151C2211yescharacteristic
54C22⋊Q8×C151C2211yescharacteristic
55#121×C151C2211yescharacteristic
56#106×C151C2211yescharacteristic
57#103×C151C2211yescharacteristic
58#102×C151C2211yescharacteristic
59C2×Dic302—21no—
60C2×Dic302—21no—
61C2×Dic302C2311yescharacteristic
62C2×D604C2311yescharacteristic
63C2×C22⋊D151—21no—
64C22×Dic151—21no—
65C2×C4×D151—21no—
66#14558994—22no—
67#14558993—22no—
68#14558989—22no—
69#14558988—22no—
70C2×C151⋊C8C2311yescharacteristic
71C2×C151⋊C8C2311yescharacteristic
72C4⋊Dic151—21no—
73C4⋊Dic151D411yescharacteristic
74C4⋊Dic151D411yescharacteristic
75C4⋊Dic151C2311yescharacteristic
76C4⋊Dic151C2311yescharacteristic
77Dic151⋊C4—21no—
78Dic151⋊C4—21no—
79Dic151⋊C4—21no—
80Dic151⋊C4—21no—
81C22⋊Dic151—21no—
82C22⋊Dic151—21no—
83C22⋊Dic151—21no—
84C22⋊Dic151—21no—
85C22⋊Dic151D411yescharacteristic
86C22⋊Dic151D411yescharacteristic
87(C2×D151)⋊C4—21no—
88(C2×D151)⋊C4—21no—
89(C2×D151)⋊C4—21no—
90(C2×D151)⋊C4—21no—
91C4×Dic151—21no—
92C4×Dic151—21no—
93C4×Dic151C2311yescharacteristic
94C4×Dic151C2311yescharacteristic
95C2×Q8×C151C2311yescharacteristic
96C2×D4×C151—21no—
97C2×D4×C151C2311yescharacteristic
98C22×C4×C151C2311yescharacteristic
99SD16×C151—22no—
100C2×C8×C151—22no—
101C2×C8×C151C2311yescharacteristic
102C2×C8×C151C2311yescharacteristic
103C4⋊C4×C151—21no—
104C4⋊C4×C151C2311yescharacteristic
105C4⋊C4×C151C2311yescharacteristic
106C22⋊C4×C151—21no—
107C22⋊C4×C151—21no—
108C22×D151—21no—
109Dic302—21no—
110Dic302—21no—
111Dic302—81no—
112Dic302—81no—
113D604—21no—
114D604—21no—
115C22⋊D151—81no—
116C2×Dic151—21no—
117C2×Dic151—21no—
118C2×Dic151—21no—
119C2×Dic151—81no—
120C2×Dic151C2×D411yescharacteristic
121C2×Dic151C2×D411yescharacteristic
122C2×Dic151C2×D411yescharacteristic
123C2×Dic151C2×D411yescharacteristic
124C4×D151—81no—
125C151⋊C8—21no—
126C151⋊C8#4112yes—
127C23×C151—21no—
128C23×C151C2×D411yescharacteristic
129Q8×C151—21no—
130Q8×C151—21no—
131D4×C151—21no—
132D4×C151—21no—
133D4×C151—81no—
134C2×C4×C151—21no—
135C2×C4×C151—21no—
136C2×C4×C151—21no—
137C2×C4×C151—21no—
138C2×C4×C151—21no—
139C2×C4×C151C2×D411yescharacteristic
140C2×C4×C151C2411yescharacteristic
141C8×C151—21no—
142C8×C151#4112yes—
143C22×C151—21no—
144C22×C151—21no—
145C22×C151—21no—
146C22×C151—41no—
147C22×C151—41no—
148C22×C151—41no—
149C22×C151C22×D411yescharacteristic
150C2×D151—41no—
151C2×D151—41no—
152C2×D151—41no—
153C4×C151—21no—
154C4×C151—41no—
155C4×C151—41no—
156C4×C151—41no—
157C4×C151C2×#4111yescharacteristic
158C4×C151C2×#4111yescharacteristic
159Dic151—21no—
160Dic151—21no—
161Dic151—21no—
162Dic151—21no—
163Dic151—41no—
164Dic151—41no—
165Dic151—41no—
166C2×C151—41no—
167C2×C151—81no—
168C2×C151#53211yescharacteristic
169C2×C151#57711yescharacteristic
170C2×C151#57711yescharacteristic
171D151—81no—
172C151#317311yescharacteristic, complemented, Sylow
173#3173—1511nomaximal, Sylow
174#542—1511no—
175#542—1511no—
176#498—1511no—
177#495—1511no—
178#489—1511no—
179#489—1511no—
180#470—1511no—
181#469—1511no—
182#465—1511no—
183#465D15111yescharacteristic, complemented
184#442—1511no—
185#441—1511no—
186C4×SD16—1511no—
187C4×SD16—1511no—
188#405—1511no—
189C2×Q16—1511no—
190C2×SD16—1511no—
191C2×SD16C2×D15111yescharacteristic
192C2×D8—1511no—
193C2×M16—1511no—
194C22×C8C2×D15111yescharacteristic
195C4⋊Q8—1511no—
196C4⋊Q8—1511no—
197#126—3021no—
198#126—3021no—
199#124—3021no—
200#124—3021no—
201#124—1511no—
202#124—1511no—
203#123—3021no—
204#123—3021no—
205C22⋊Q8—3021no—
206C22⋊Q8—3021no—
207C22⋊Q8—1511no—
208C22⋊Q8C2×D15111yescharacteristic
209#121—1511no—
210#121C2×D15111yescharacteristic
211C4×Q8—1511no—
212C4×Q8—1511no—
213C4×D4—1511no—
214C4×D4—1511no—
215#117—1511no—
216#106—1511no—
217#106—1511no—
218#106—1511no—
219#106C2×D15111yescharacteristic
220#103—1511no—
221#103—1511no—
222#103—1511no—
223#103C2×D15111yescharacteristic
224#102—1511no—
225#102—1511no—
226#102—1511no—
227#102C2×D15111yescharacteristic
228#97—1511no—
229#97—1511no—
230C4×C8—1511no—
231C4×C8—1511no—
232C2×Q8—3021no—
233C2×Q8—3021no—
234C2×Q8—1511no—
235C2×Q8C22×D15111yescharacteristic
236C2×D4—21no—
237C2×D4—3021no—
238C2×D4—1511no—
239C2×D4C22×D15111yescharacteristic
240C22×C4—3021no—
241C22×C4—3021no—
242C22×C4C22×D15111yescharacteristic
243Q16—3022no—
244SD16—22no—
245SD16—3022no—
246D8—3022no—
247M16—3022no—
248C2×C8—22no—
249C2×C8—1511no—
250C2×C8—1511no—
251C2×C8C22×D15111yescharacteristic
252C2×C8C22×D15111yescharacteristic
253C4⋊C4—21no—
254C4⋊C4—3021no—
255C4⋊C4—3021no—
256C4⋊C4—3021no—
257C4⋊C4—3021no—
258C4⋊C4—3021no—
259C4⋊C4—1511no—
260C4⋊C4—1511no—
261C4⋊C4—1511no—
262C4⋊C4—1511no—
263C4⋊C4C22×D15111yescharacteristic
264C4⋊C4C22×D15111yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—3021no—
268C22⋊C4—3021no—
269C22⋊C4—3021no—
270C22⋊C4—3021no—
271C22⋊C4—3021no—
272C22⋊C4—3021no—
273C22⋊C4—3021no—
274C22⋊C4—3021no—
275C22⋊C4—1511no—
276C22⋊C4—1511no—
277C42—3021no—
278C42—3021no—
279C42—1511no—
280C42—1511no—
281C23—21no—
282C23—3021no—
283C23D4×D15111yescharacteristic
284Q8—21no—
285Q8—21no—
286Q8—3021no—
287Q8—3021no—
288Q8—12081no—
289Q8—12081no—
290D4—21no—
291D4—21no—
292D4—81no—
293D4—3021no—
294D4—3021no—
295D4—12081no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—3021no—
302C2×C4—3021no—
303C2×C4—3021no—
304C2×C4—1511no—
305C2×C4—1511no—
306C2×C4—1511no—
307C2×C4—1511no—
308C2×C4—12081no—
309C2×C4—12081no—
310C2×C4D4×D15111yescharacteristic
311C2×C4C23×D15111yescharacteristic
312C8—21no—
313C8—3021no—
314C8—1512no—
315C8#1455900312yes—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—41no—
320C22—41no—
321C22—41no—
322C22—6041no—
323C22—6041no—
324C22—6041no—
325C22C2×D4×D15111yescharacteristic
326C4—21no—
327C4—41no—
328C4—41no—
329C4—41no—
330C4—3021no—
331C4—3021no—
332C4—3021no—
333C4—3021no—
334C4—6041no—
335C4—6041no—
336C4—6041no—
337C4#41×D15111yescharacteristic
338C4C2×#1455900311yescharacteristic
339C2—41no—
340C2—81no—
341C2—12081no—
342C2#2375275711yescharacteristic
343C2#2375301811yescharacteristic
344C2#2375301911yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#465×C151C2
socleC22×C151C22×D4
prime radical#23752463C2
hypercenter#465D151
hypocenterC151#3173
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. #23752835C2semidirect
2. #23752829C2semidirect
3. #23752609C2semidirect
4. #23752593C2semidirect
5. #23752573C2semidirect
6. #23752570C2semidirect
7. #23752468C2semidirect
9. #23752441C2semidirect
10. #23752321C2semidirect
11. #23752316C2semidirect
12. SD16×Dic151C2semidirect
13. #23752299C2semidirect
14. #23752167C2semidirect
15. #465×C151C2semidirect
172. C151#3173semidirect
183. #465D151semidirect

Maximal subgroups

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

subgroupindex
#237528352
#237528292
#237526092
#237525932
#237525732
#237525702
#237524682
#237524632
#237524412
#237523212
#237523162
SD16×Dic1512
#237522992
#237521672
#465×C1512
#3173151