Finite Group Databasebeta

← #34079825

Subgroups — #34079825

Order 19328.

402 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752766C211yesmaximal, characteristic, complemented
2#23752759C211yesmaximal, characteristic
3#23752616C211yesmaximal, characteristic, complemented
4#23752583C211yesmaximal, characteristic, complemented
5#23752561C211yesmaximal, characteristic, complemented
6#23752557C211yesmaximal, characteristic, complemented
7#23752461C211yesmaximal, characteristic, complemented
8#23752459C211yesmaximal, characteristic, complemented
9#23752457C211yesmaximal, characteristic, complemented
10#23752455C211yesmaximal, characteristic, complemented
11#23752314C211yesmaximal, characteristic, complemented
12#23752312C211yesmaximal, characteristic, complemented
13#23752310C211yesmaximal, characteristic, complemented
14#23752164C211yesmaximal, characteristic, complemented
15#440×C151C211yesmaximal, characteristic, complemented
16C2×#14559004—21no—
17C2×#14558993C2211yescharacteristic
18C2×#14558992C2211yescharacteristic
19C2×#14558991C2211yescharacteristic
20C2×#14558987C2211yescharacteristic
21C2×#14558987C2211yescharacteristic
22#18012738C2211yescharacteristic
23#18012738C2211yescharacteristic
24#18012737C2211yescharacteristic
25#18012735C2211yescharacteristic
26#18012729—21no—
27#18012725—21no—
28#18012719C2211yescharacteristic
29#18012717—21no—
30#18012715C2211yescharacteristic
31#18012714C2211yescharacteristic
32#18012712—21no—
33#18012710C2211yescharacteristic
34C4×Dic302—21no—
35C4×Dic302C2211yescharacteristic
36C4×D604C2211yescharacteristic
37C4×C22⋊D151—21no—
38#18012696—21no—
39C42×D151C2211yescharacteristic
40#18012673C2211yescharacteristic
41#18012672C2211yescharacteristic
42#18012672C2211yescharacteristic
43#18012664C2211yescharacteristic
44#18012663C2211yescharacteristic
45#18012662C2211yescharacteristic
46#18012661C2211yescharacteristic
47#18012660C2211yescharacteristic
48#18012659C2211yescharacteristic
49#18012650C2211yescharacteristic
50C8×Dic151C2211yescharacteristic
51C8×Dic151C2211yescharacteristic
52C2×SD16×C151C2211yescharacteristic
53C4×Q8×C151C2211yescharacteristic
54C4×D4×C151C2211yescharacteristic
55#107×C151C2211yescharacteristic
56#103×C151C2211yescharacteristic
57#102×C151C2211yescharacteristic
58#97×C151C2211yescharacteristic
59#14559004—44no—
60C2×Dic302—21no—
61C2×Dic302—21no—
62C2×Dic302C2311yescharacteristic
63C2×D604—21no—
64C2×D604C2311yescharacteristic
65C2×C22⋊D151—21no—
66C2×C22⋊D151—21no—
67C2×C22⋊D151—21no—
68C2×C4×D151—21no—
69C2×C4×D151D411yescharacteristic
70C2×C4×D151D411yescharacteristic
71C2×C4×D151C2311yescharacteristic
72#14558993—22no—
73#14558992—22no—
74#14558991—22no—
75#14558987—22no—
76#14558987—22no—
77C2×C151⋊C8C2311yescharacteristic
78C2×C151⋊C8C2311yescharacteristic
79C4⋊Dic151—21no—
80C4⋊Dic151C2311yescharacteristic
81C4⋊Dic151C2311yescharacteristic
82Dic151⋊C4—21no—
83Dic151⋊C4—21no—
84Dic151⋊C4—21no—
85Dic151⋊C4—21no—
86Dic151⋊C4—21no—
87Dic151⋊C4—21no—
88C22⋊Dic151—21no—
89(C2×D151)⋊C4—21no—
90(C2×D151)⋊C4—21no—
91(C2×D151)⋊C4—21no—
92(C2×D151)⋊C4—21no—
93C4×Dic151—21no—
94C4×Dic151D411yescharacteristic
95C4×Dic151D411yescharacteristic
96C4×Dic151C2311yescharacteristic
97C2×Q8×C151C2311yescharacteristic
98C2×D4×C151C2311yescharacteristic
99C22×C4×C151—21no—
100SD16×C151—22no—
101C2×C8×C151C2311yescharacteristic
102C2×C8×C151C2311yescharacteristic
103C4⋊C4×C151—21no—
104C4⋊C4×C151C2311yescharacteristic
105C4⋊C4×C151C2311yescharacteristic
106C22⋊C4×C151—21no—
107C42×C151—21no—
108C42×C151C2311yescharacteristic
109C22×D151—21no—
110C22×D151C2×D411yescharacteristic
111Dic302—21no—
112Dic302—21no—
113Dic302—42no—
114Dic302—42no—
115D604—21no—
116D604—21no—
117D604—42no—
118C22⋊D151—42no—
119C22⋊D151—42no—
120C22⋊D151—42no—
121C2×Dic151—21no—
122C2×Dic151—21no—
123C2×Dic151—21no—
124C2×Dic151C2×D411yescharacteristic
125C2×Dic151C2×D411yescharacteristic
126C2×Dic151C2×D411yescharacteristic
127C4×D151—21no—
128C4×D151—21no—
129C4×D151—22no—
130C4×D151—22no—
131C4×D151—42no—
132C151⋊C8—21no—
133C151⋊C8#4112yescomplemented
134C23×C151—21no—
135Q8×C151—21no—
136Q8×C151—21no—
137D4×C151—21no—
138D4×C151—21no—
139C2×C4×C151—21no—
140C2×C4×C151—21no—
141C2×C4×C151—21no—
142C2×C4×C151—42no—
143C2×C4×C151C2×D411yescharacteristic
144C2×C4×C151C2×D411yescharacteristic
145C2×C4×C151C2411yescharacteristic
146C8×C151—21no—
147C8×C151#4112yescomplemented
148C22×C151—41no—
149C22×C151—41no—
150C22×C151—41no—
151C22×C151C22×D411yescharacteristic
152C2×D151—21no—
153C2×D151—21no—
154C2×D151—21no—
155C2×D151—41no—
156C2×D151—41no—
157C2×D151—41no—
158C4×C151—21no—
159C4×C151—21no—
160C4×C151—41no—
161C4×C151—41no—
162C4×C151—41no—
163C4×C151C2×#4111yescharacteristic
164C4×C151C2×#4111yescharacteristic
165Dic151—21no—
166Dic151—41no—
167Dic151—41no—
168Dic151—41no—
169Dic151AGL(1,ℤ/8)12yes—
170Dic151#13712yes—
171C2×C151—81no—
172C2×C151#53211yescharacteristic
173C2×C151C2×AGL(1,ℤ/8)11yescharacteristic
174C2×C151C2×#13711yescharacteristic
175D151—41no—
176D151—81no—
177C151#318211yescharacteristic, complemented, Sylow
178#3182—1511nomaximal, Sylow
179#533—1511no—
180#532—1511no—
181#500—1511no—
182#492—1511no—
183#487—1511no—
184#486—1511no—
185#468—1511no—
186#468—1511no—
187#468—1511no—
188#468—1511no—
189#440—1511no—
190#440—1511no—
191#440—1511no—
192#440D15111yescharacteristic, complemented
193C4×M16—1511no—
194C2×#41—3021no—
195C2×SD16—1511no—
196C2×SD16—1511no—
197C2×SD16—1511no—
198C2×SD16C2×D15111yescharacteristic
199C2×M16—1511no—
200C2×M16—1511no—
201C4⋊Q8—1511no—
202C4⋊Q8—1511no—
203C4⋊Q8—1511no—
204#127—1511no—
205#125—3021no—
206#124—3021no—
207C22⋊Q8—3021no—
208C22⋊Q8—1511no—
209C22⋊Q8—1511no—
210#121—3021no—
211#121—1511no—
212#121—1511no—
213C4×Q8—3021no—
214C4×Q8—1511no—
215C4×Q8C2×D15111yescharacteristic
216C4×D4—3021no—
217C4×D4—1511no—
218C4×D4C2×D15111yescharacteristic
219#117—3021no—
220C2×C42—1511no—
221#107—1511no—
222#107—1511no—
223#107—1511no—
224#107C2×D15111yescharacteristic
225#103—1511no—
226#103—1511no—
227#103—1511no—
228#103C2×D15111yescharacteristic
229#102—1511no—
230#102—1511no—
231#102—1511no—
232#102C2×D15111yescharacteristic
233#97—1511no—
234#97C2×D15111yescharacteristic
235C4×C8—1511no—
236C4×C8—1511no—
237#41—6044no—
238C2×Q8—3021no—
239C2×Q8—3021no—
240C2×Q8—1511no—
241C2×Q8C22×D15111yescharacteristic
242C2×D4—3021no—
243C2×D4—3021no—
244C2×D4—3021no—
245C2×D4—3021no—
246C2×D4—1511no—
247C2×D4C22×D15111yescharacteristic
248C22×C4—21no—
249C22×C4—3021no—
250C22×C4—1511no—
251C22×C4—1511no—
252C22×C4—1511no—
253SD16—22no—
254SD16—3022no—
255SD16—3022no—
256SD16—3022no—
257M16—3022no—
258M16—3022no—
259C2×C8—1511no—
260C2×C8—1511no—
261C2×C8C22×D15111yescharacteristic
262C2×C8C22×D15111yescharacteristic
263C4⋊C4—21no—
264C4⋊C4—3021no—
265C4⋊C4—3021no—
266C4⋊C4—3021no—
267C4⋊C4—3021no—
268C4⋊C4—3021no—
269C4⋊C4—3021no—
270C4⋊C4—3021no—
271C4⋊C4—1511no—
272C4⋊C4—1511no—
273C4⋊C4C22×D15111yescharacteristic
274C4⋊C4C22×D15111yescharacteristic
275C22⋊C4—21no—
276C22⋊C4—3021no—
277C22⋊C4—3021no—
278C22⋊C4—3021no—
279C22⋊C4—3021no—
280C22⋊C4—3021no—
281C42—21no—
282C42—3021no—
283C42—1511no—
284C42—1511no—
285C42—1511no—
286C42C22×D15111yescharacteristic
287C23—21no—
288C23—3021no—
289C23—1511no—
290Q8—21no—
291Q8—21no—
292Q8—3021no—
293Q8—3021no—
294Q8—6042no—
295Q8—6042no—
296D4—21no—
297D4—21no—
298D4—3021no—
299D4—3021no—
300D4—6042no—
301D4—6042no—
302D4—6042no—
303D4—6042no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—42no—
308C2×C4—3022no—
309C2×C4—3022no—
310C2×C4—3021no—
311C2×C4—3021no—
312C2×C4—3021no—
313C2×C4—3021no—
314C2×C4—3021no—
315C2×C4—6042no—
316C2×C4—1511no—
317C2×C4—1511no—
318C2×C4—1511no—
319C2×C4D4×D15111yescharacteristic
320C2×C4D4×D15111yescharacteristic
321C2×C4C23×D15111yescharacteristic
322C8—21no—
323C8—3021no—
324C8—1512no—
325C8#1455900412yescomplemented
326C22—41no—
327C22—41no—
328C22—41no—
329C22—3021no—
330C22—3021no—
331C22—3021no—
332C22—6041no—
333C22—6041no—
334C22—6041no—
335C22C2×D4×D15111yescharacteristic
336C4—21no—
337C4—21no—
338C4—41no—
339C4—41no—
340C4—41no—
341C4—3021no—
342C4—6041no—
343C4—6041no—
344C4—6041no—
345C4—1512no—
346C4—1512no—
347C4#41×D15111yescharacteristic
348C4C2×#1455900411yescharacteristic
349C2—81no—
350C2—6041no—
351C2—12081no—
352C2#2375275911yescharacteristic
353C2AGL(1,ℤ/8)×D15111yescharacteristic
354C2#137×D15111yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#440×C151C2
socleC22×C151C22×D4
prime radical#23752759C2
hypercenter#440D151
hypocenterC151#3182
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. #23752766C2semidirect
3. #23752616C2semidirect
4. #23752583C2semidirect
5. #23752561C2semidirect
6. #23752557C2semidirect
7. #23752461C2semidirect
8. #23752459C2semidirect
9. #23752457C2semidirect
10. #23752455C2semidirect
11. #23752314C2semidirect
12. #23752312C2semidirect
13. #23752310C2semidirect
14. #23752164C2semidirect
15. #440×C151C2semidirect
133. C151⋊C8#41semidirect
147. C8×C151#41semidirect
177. C151#3182semidirect
192. #440D151semidirect
325. C8#14559004semidirect

Maximal subgroups

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

subgroupindex
#237527662
#237527592
#237526162
#237525832
#237525612
#237525572
#237524612
#237524592
#237524572
#237524552
#237523142
#237523122
#237523102
#237521642
#440×C1512
#3182151