Finite Group Databasebeta

← #34079223

Subgroups — #34079223

Order 19328.

392 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752749C211yesmaximal, characteristic, complemented
2C4×#14559003C211yesmaximal, characteristic, complemented
3#23752552C211yesmaximal, characteristic, complemented
4#23752539C211yesmaximal, characteristic, complemented
5#23752518C211yesmaximal, characteristic, complemented
6#23752510C211yesmaximal, characteristic, complemented
7#23752437C211yesmaximal, characteristic, complemented
8#23752429C211yesmaximal, characteristic, complemented
9#23752371C211yesmaximal, characteristic, complemented
10#23752358C211yesmaximal, characteristic
11#23752322C211yesmaximal, characteristic, complemented
12#23752317C211yesmaximal, characteristic, complemented
13#23752314C211yesmaximal, characteristic, complemented
14#23752267C211yesmaximal, characteristic, complemented
15#440×C151C211yesmaximal, characteristic, complemented
16C2×#14559003C2211yescharacteristic
17C2×#14558994C2211yescharacteristic
18C2×#14558993C2211yescharacteristic
19C2×#14558989C2211yescharacteristic
20#18012734—21no—
21#18012730C2211yescharacteristic
22#18012728C2211yescharacteristic
23#18012724—21no—
24#18012715C2211yescharacteristic
25#18012714C2211yescharacteristic
26C4×Dic302C2211yescharacteristic
27#18012704C2211yescharacteristic
28C4×D604—21no—
29C4×D604C2211yescharacteristic
30D4×Dic151C2211yescharacteristic
31C4×C22⋊D151—21no—
32(C22⋊D151)⋊C4—21no—
33#18012697C2211yescharacteristic
34#18012696—21no—
35#18012695—21no—
36C2×C4×Dic151—21no—
37C42×D151C2211yescharacteristic
38#18012673C2211yescharacteristic
39#18012670C2211yescharacteristic
40#18012670C2211yescharacteristic
41Dic151⋊C8C2211yescharacteristic
42Dic151⋊C8C2211yescharacteristic
43#18012664C2211yescharacteristic
44#18012663C2211yescharacteristic
45#18012662C2211yescharacteristic
46#18012661C2211yescharacteristic
47#18012660C2211yescharacteristic
48#18012659C2211yescharacteristic
49(C2×D151)⋊C8C2211yescharacteristic
50(C2×D151)⋊C8C2211yescharacteristic
51#18012650C2211yescharacteristic
52C2×SD16×C151C2211yescharacteristic
53C4×Q8×C151C2211yescharacteristic
54C4×D4×C151C2211yescharacteristic
55#107×C151C2211yescharacteristic
56#103×C151C2211yescharacteristic
57#102×C151C2211yescharacteristic
58#97×C151C2211yescharacteristic
59#14559003—22no—
60#14559003—22no—
61C2×Dic302C2311yescharacteristic
62C2×D604—21no—
63C2×D604C2311yescharacteristic
64C2×C22⋊D151—21no—
65C22×Dic151—21no—
66C22×Dic151—21no—
67C2×C4×D151—21no—
68C2×C4×D151D411yescharacteristic
69C2×C4×D151D411yescharacteristic
70C2×C4×D151C2311yescharacteristic
71#14558994—22no—
72#14558993—22no—
73#14558989—22no—
74C2×C151⋊C8C2311yescharacteristic
75C2×C151⋊C8C2311yescharacteristic
76C4⋊Dic151—21no—
77C4⋊Dic151C2311yescharacteristic
78C4⋊Dic151C2311yescharacteristic
79Dic151⋊C4—21no—
80Dic151⋊C4—21no—
81Dic151⋊C4—21no—
82Dic151⋊C4—21no—
83C22⋊Dic151—21no—
84(C2×D151)⋊C4—21no—
85(C2×D151)⋊C4—21no—
86(C2×D151)⋊C4—21no—
87(C2×D151)⋊C4—21no—
88(C2×D151)⋊C4—21no—
89(C2×D151)⋊C4—21no—
90C4×Dic151—21no—
91C4×Dic151—21no—
92C4×Dic151—21no—
93C4×Dic151D411yescharacteristic
94C4×Dic151D411yescharacteristic
95C4×Dic151C2311yescharacteristic
96C2×Q8×C151C2311yescharacteristic
97C2×D4×C151C2311yescharacteristic
98C22×C4×C151—21no—
99SD16×C151—22no—
100C2×C8×C151C2311yescharacteristic
101C2×C8×C151C2311yescharacteristic
102C4⋊C4×C151—21no—
103C4⋊C4×C151C2311yescharacteristic
104C4⋊C4×C151C2311yescharacteristic
105C22⋊C4×C151—21no—
106C42×C151—21no—
107C42×C151C2311yescharacteristic
108C22×D151—21no—
109C22×D151C2×D411yescharacteristic
110Dic302—21no—
111Dic302#4112yes—
112D604—21no—
113D604—21no—
114D604—42no—
115C22⋊D151—24no—
116C2×Dic151—24no—
117C2×Dic151—21no—
118C2×Dic151—21no—
119C2×Dic151—21no—
120C2×Dic151—42no—
121C2×Dic151C2×D411yescharacteristic
122C2×Dic151C2×D411yescharacteristic
123C2×Dic151C2×D411yescharacteristic
124C4×D151—21no—
125C4×D151—21no—
126C4×D151—41no—
127C4×D151—41no—
128C4×D151—42no—
129C151⋊C8—21no—
130C151⋊C8—21no—
131C23×C151—21no—
132Q8×C151—21no—
133Q8×C151—21no—
134D4×C151—21no—
135D4×C151#4112yes—
136C2×C4×C151—21no—
137C2×C4×C151—21no—
138C2×C4×C151—21no—
139C2×C4×C151—42no—
140C2×C4×C151C2×D411yescharacteristic
141C2×C4×C151C2×D411yescharacteristic
142C2×C4×C151C2411yescharacteristic
143C8×C151—21no—
144C8×C151—21no—
145C22×C151—22no—
146C22×C151—41no—
147C22×C151—41no—
148C22×C151C22×D411yescharacteristic
149C2×D151—21no—
150C2×D151—21no—
151C2×D151—21no—
152C2×D151—41no—
153C2×D151—41no—
154C2×D151—41no—
155C4×C151—21no—
156C4×C151—21no—
157C4×C151—41no—
158C4×C151—41no—
159C4×C151—41no—
160C4×C151C2×#4111yescharacteristic
161C4×C151C2×#4111yescharacteristic
162Dic151—21no—
163Dic151—22no—
164Dic151—21no—
165Dic151—21no—
166Dic151—41no—
167Dic151—41no—
168C2×C151—42no—
169C2×C151#52511yescharacteristic
170C2×C151#57511yescharacteristic
171C2×C151#57511yescharacteristic
172D151—41no—
173D151—81no—
174C151#311111yescharacteristic, complemented, Sylow
175#3111—1511nomaximal, Sylow
176#529—1511no—
177C4×#41—1511no—
178#485—1511no—
179#482—1511no—
180#479—1511no—
181#478—1511no—
182#464—1511no—
183#463—1511no—
184#452—1511no—
185#449—1511no—
186#442—1511no—
187#441—1511no—
188#440—1511no—
189#440D15111yescharacteristic, complemented
190#432—1511no—
191C2×#41—1511no—
192C2×Q16—1511no—
193C2×SD16—1511no—
194C2×SD16C2×D15111yescharacteristic
195C2×D8—1511no—
196#126—3021no—
197#125—1511no—
198#124—1511no—
199#123—3021no—
200C22⋊Q8—1511no—
201#121—1511no—
202C4×Q8—1511no—
203C4×Q8—1511no—
204C4×Q8C2×D15111yescharacteristic
205C4×D4—3021no—
206C4×D4—3021no—
207C4×D4—3021no—
208C4×D4—1511no—
209C4×D4—1511no—
210C4×D4C2×D15111yescharacteristic
211#117—3021no—
212#117—3021no—
213#117—1511no—
214C2×C42—3021no—
215C2×C42—1511no—
216#107—1511no—
217#107C2×D15111yescharacteristic
218#106—1511no—
219#106—1511no—
220C4⋊C8—1511no—
221C4⋊C8—1511no—
222#103—1511no—
223#103—1511no—
224#103—1511no—
225#103C2×D15111yescharacteristic
226#102—1511no—
227#102—1511no—
228#102—1511no—
229#102C2×D15111yescharacteristic
230C22⋊C8—1511no—
231C22⋊C8—1511no—
232#97—1511no—
233#97C2×D15111yescharacteristic
234#41—3022no—
235#41—3022no—
236C2×Q8—1511no—
237C2×Q8C22×D15111yescharacteristic
238C2×D4—3021no—
239C2×D4—3021no—
240C2×D4—1511no—
241C2×D4C22×D15111yescharacteristic
242C22×C4—21no—
243C22×C4—3021no—
244C22×C4—3021no—
245C22×C4—3021no—
246C22×C4—1511no—
247C22×C4—1511no—
248C22×C4—1511no—
249Q16—3022no—
250SD16—22no—
251SD16—3022no—
252D8—3022no—
253C2×C8—1511no—
254C2×C8—1511no—
255C2×C8C22×D15111yescharacteristic
256C2×C8C22×D15111yescharacteristic
257C4⋊C4—21no—
258C4⋊C4—3021no—
259C4⋊C4—3021no—
260C4⋊C4—3021no—
261C4⋊C4—3021no—
262C4⋊C4—3021no—
263C4⋊C4—1511no—
264C4⋊C4—1511no—
265C4⋊C4C22×D15111yescharacteristic
266C4⋊C4C22×D15111yescharacteristic
267C22⋊C4—21no—
268C22⋊C4—3021no—
269C22⋊C4—3021no—
270C22⋊C4—3021no—
271C22⋊C4—3021no—
272C22⋊C4—3021no—
273C22⋊C4—3021no—
274C22⋊C4—3021no—
275C42—21no—
276C42—3021no—
277C42—3021no—
278C42—3021no—
279C42—1511no—
280C42—1511no—
281C42—1511no—
282C42C22×D15111yescharacteristic
283C23—21no—
284C23—3021no—
285C23—1511no—
286Q8—21no—
287Q8—21no—
288Q8—3021no—
289Q8—1512no—
290D4—21no—
291D4—3024no—
292D4—3021no—
293D4—3021no—
294D4—6042no—
295D4#1455900412yes—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—42no—
300C2×C4—3024no—
301C2×C4—3021no—
302C2×C4—3021no—
303C2×C4—3021no—
304C2×C4—3021no—
305C2×C4—3021no—
306C2×C4—6041no—
307C2×C4—6041no—
308C2×C4—6042no—
309C2×C4—6042no—
310C2×C4—1511no—
311C2×C4—1511no—
312C2×C4—1511no—
313C2×C4D4×D15111yescharacteristic
314C2×C4D4×D15111yescharacteristic
315C2×C4C23×D15111yescharacteristic
316C8—21no—
317C8—21no—
318C8—3021no—
319C8—3021no—
320C22—22no—
321C22—41no—
322C22—41no—
323C22—3021no—
324C22—3021no—
325C22—3021no—
326C22—6041no—
327C22—6041no—
328C22—6041no—
329C22C2×D4×D15111yescharacteristic
330C4—21no—
331C4—21no—
332C4—41no—
333C4—41no—
334C4—41no—
335C4—3021no—
336C4—3022no—
337C4—3021no—
338C4—3021no—
339C4—6041no—
340C4—6041no—
341C4#41×D15111yescharacteristic
342C4C2×#1455900411yescharacteristic
343C2—42no—
344C2—6041no—
345C2—12081no—
346C2#2375272111yescharacteristic
347C2#2375300811yescharacteristic
348C2#2375301111yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#440×C151C2
socleC22×C151C22×D4
prime radical#23752358C2
hypercenter#440D151
hypocenterC151#3111
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. #23752749C2semidirect
2. C4×#14559003C2semidirect
3. #23752552C2semidirect
4. #23752539C2semidirect
5. #23752518C2semidirect
6. #23752510C2semidirect
7. #23752437C2semidirect
8. #23752429C2semidirect
9. #23752371C2semidirect
11. #23752322C2semidirect
12. #23752317C2semidirect
13. #23752314C2semidirect
14. #23752267C2semidirect
15. #440×C151C2semidirect
174. C151#3111semidirect
189. #440D151semidirect

Maximal subgroups

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

subgroupindex
#237527492
C4×#145590032
#237525522
#237525392
#237525182
#237525102
#237524372
#237524292
#237523712
#237523582
#237523222
#237523172
#237523142
#237522672
#440×C1512
#3111151