Finite Group Databasebeta

← #34079664

Subgroups — #34079664

Order 19328.

412 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#23752764C211yesmaximal, characteristic, complemented
2#23752757C211yesmaximal, characteristic
3#23752609C211yesmaximal, characteristic, complemented
4#23752583C211yesmaximal, characteristic, complemented
5#23752561C211yesmaximal, characteristic, complemented
6#23752557C211yesmaximal, characteristic, complemented
7#23752443C211yesmaximal, characteristic, complemented
8#23752441C211yesmaximal, characteristic, complemented
9#23752439C211yesmaximal, characteristic, complemented
10#23752303C211yesmaximal, characteristic, complemented
11SD16×Dic151C211yesmaximal, characteristic, complemented
12#23752299C211yesmaximal, characteristic, complemented
13#23752297C211yesmaximal, characteristic, complemented
14C2×C8×Dic151C211yesmaximal, characteristic, complemented
15#465×C151C211yesmaximal, characteristic, complemented
16C2×#14559003—21no—
17C2×#14558993C2211yescharacteristic
18C2×#14558992C2211yescharacteristic
19C2×#14558991C2211yescharacteristic
20C22×C151⋊C8C2211yescharacteristic
21#18012738C2211yescharacteristic
22#18012738C2211yescharacteristic
23#18012737C2211yescharacteristic
24#18012735C2211yescharacteristic
25#18012729—21no—
26#18012725—21no—
27#18012718C2211yescharacteristic
28#18012716—21no—
29#18012713C2211yescharacteristic
30#18012711—21no—
31Q8×Dic151C2211yescharacteristic
32#18012704—21no—
33#18012704C2211yescharacteristic
34D4×Dic151C2211yescharacteristic
35#18012701C2211yescharacteristic
36(C22⋊D151)⋊C4—21no—
37#18012695—21no—
38C2×C4×Dic151C2211yescharacteristic
39#18012671C2211yescharacteristic
40#18012670C2211yescharacteristic
41#18012670C2211yescharacteristic
42#18012664C2211yescharacteristic
43#18012663C2211yescharacteristic
44#18012662C2211yescharacteristic
45#18012661C2211yescharacteristic
46#18012660C2211yescharacteristic
47#18012659C2211yescharacteristic
48C8×Dic151C2211yescharacteristic
49C8×Dic151C2211yescharacteristic
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
59#14559003—44no—
60C2×Dic302—21no—
61C2×Dic302—21no—
62C2×Dic302C2311yescharacteristic
63C2×D604C2311yescharacteristic
64C2×C22⋊D151—21no—
65C2×C22⋊D151—21no—
66C2×C22⋊D151—21no—
67C22×Dic151—21no—
68C22×Dic151D411yescharacteristic
69C22×Dic151D411yescharacteristic
70C2×C4×D151—21no—
71#14558993—22no—
72#14558992—22no—
73#14558991—22no—
74C2×C151⋊C8—22no—
75C2×C151⋊C8C2311yescharacteristic
76C2×C151⋊C8C2311yescharacteristic
77C4⋊Dic151—21no—
78C4⋊Dic151C2311yescharacteristic
79C4⋊Dic151C2311yescharacteristic
80Dic151⋊C4—21no—
81Dic151⋊C4—21no—
82Dic151⋊C4—21no—
83Dic151⋊C4—21no—
84Dic151⋊C4—21no—
85Dic151⋊C4—21no—
86C22⋊Dic151—21no—
87C22⋊Dic151—21no—
88(C2×D151)⋊C4—21no—
89(C2×D151)⋊C4—21no—
90C4×Dic151—21no—
91C4×Dic151—21no—
92C4×Dic151D411yescharacteristic
93C4×Dic151D411yescharacteristic
94C4×Dic151C2311yescharacteristic
95C4×Dic151C2311yescharacteristic
96C2×Q8×C151C2311yescharacteristic
97C2×D4×C151—21no—
98C2×D4×C151C2311yescharacteristic
99C22×C4×C151C2311yescharacteristic
100SD16×C151—22no—
101C2×C8×C151—22no—
102C2×C8×C151C2311yescharacteristic
103C2×C8×C151C2311yescharacteristic
104C4⋊C4×C151—21no—
105C4⋊C4×C151C2311yescharacteristic
106C4⋊C4×C151C2311yescharacteristic
107C22⋊C4×C151—21no—
108C22⋊C4×C151—21no—
109C22×D151—21no—
110Dic302—21no—
111Dic302—21no—
112Dic302—42no—
113Dic302—42no—
114D604—21no—
115D604—21no—
116C22⋊D151—42no—
117C22⋊D151—42no—
118C22⋊D151—42no—
119C2×Dic151—22no—
120C2×Dic151—21no—
121C2×Dic151—21no—
122C2×Dic151—21no—
123C2×Dic151—42no—
124C2×Dic151SD1614yescomplemented
125C2×Dic151C2×D411yescharacteristic
126C2×Dic151C2×D411yescharacteristic
127C2×Dic151C2×D411yescharacteristic
128C2×Dic151C2×D411yescharacteristic
129C4×D151—42no—
130C151⋊C8—21no—
131C151⋊C8#4112yescomplemented
132C23×C151—21no—
133C23×C151C2×D411yescharacteristic
134Q8×C151—21no—
135Q8×C151—21no—
136D4×C151—21no—
137D4×C151—21no—
138D4×C151—42no—
139C2×C4×C151—21no—
140C2×C4×C151—21no—
141C2×C4×C151—21no—
142C2×C4×C151—21no—
143C2×C4×C151—21no—
144C2×C4×C151C2×D411yescharacteristic
145C2×C4×C151C2411yescharacteristic
146C8×C151—21no—
147C8×C151#4112yescomplemented
148C22×C151—21no—
149C22×C151—21no—
150C22×C151—41no—
151C22×C151—41no—
152C22×C151—41no—
153C22×C151C2×SD1612yes—
154C22×C151C22×D411yescharacteristic
155C2×D151—41no—
156C2×D151—41no—
157C2×D151—41no—
158C4×C151—21no—
159C4×C151—41no—
160C4×C151—41no—
161C4×C151—41no—
162C4×C151C2×#4111yescharacteristic
163C4×C151C2×#4111yescharacteristic
164Dic151—21no—
165Dic151—41no—
166Dic151—41no—
167Dic151—41no—
168Dic151C2×SD1612yes—
169Dic151C2×SD1612yes—
170Dic151#13512yes—
171C2×C151—22no—
172C2×C151—81no—
173C2×C151#53211yescharacteristic
174C2×C151C22×SD1611yescharacteristic
175C2×C151C2×#13511yescharacteristic
176D151—81no—
177C151#316711yescharacteristic, complemented, Sylow
178#3167—1511nomaximal, Sylow
179#533—1511no—
180#532—1511no—
181#498—1511no—
182#492—1511no—
183#487—1511no—
184#486—1511no—
185#465—1511no—
186#465—1511no—
187#465—1511no—
188#465D15111yescharacteristic, complemented
189C4×SD16—1511no—
190C4×SD16—1511no—
191C4×SD16—1511no—
192C4×SD16—1511no—
193C2×C4×C8—1511no—
194C2×#41—3021no—
195C2×SD16—1511no—
196C2×SD16—1511no—
197C2×SD16—1511no—
198C2×SD16C2×D15111yescharacteristic
199C22×C8—1511no—
200C22×C8C2×D15111yescharacteristic
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⋊Q8C2×D15111yescharacteristic
210#121—3021no—
211#121—1511no—
212#121C2×D15111yescharacteristic
213C4×Q8—3021no—
214C4×Q8—1511no—
215C4×Q8—1511no—
216C4×D4—3021no—
217C4×D4—1511no—
218C4×D4—1511no—
219#117—3021no—
220C2×C42—1511no—
221#106—1511no—
222#106—1511no—
223#106—1511no—
224#106C2×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
233C4×C8—1511no—
234C4×C8—1511no—
235C4×C8—1511no—
236C4×C8—1511no—
237#41—6044no—
238C2×Q8—3021no—
239C2×Q8—3021no—
240C2×Q8—1511no—
241C2×Q8C22×D15111yescharacteristic
242C2×D4—21no—
243C2×D4—3021no—
244C2×D4—3021no—
245C2×D4—3021no—
246C2×D4—1511no—
247C2×D4C22×D15111yescharacteristic
248C22×C4—3021no—
249C22×C4—3021no—
250C22×C4—1511no—
251C22×C4—1511no—
252C22×C4C22×D15111yescharacteristic
253SD16—22no—
254SD16—3022no—
255SD16—3022no—
256SD16—3022no—
257C2×C8—22no—
258C2×C8—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—21no—
277C22⋊C4—3021no—
278C22⋊C4—3021no—
279C22⋊C4—3021no—
280C22⋊C4—3021no—
281C42—3021no—
282C42—3021no—
283C42—1511no—
284C42—1511no—
285C42—1511no—
286C42—1511no—
287C23—21no—
288C23—3021no—
289C23D4×D15111yescharacteristic
290Q8—21no—
291Q8—21no—
292Q8—3021no—
293Q8—3021no—
294Q8—6042no—
295Q8—6042no—
296D4—21no—
297D4—21no—
298D4—42no—
299D4—3021no—
300D4—3021no—
301D4—6042no—
302D4—6042no—
303D4—6042no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—3022no—
310C2×C4—3021no—
311C2×C4—3021no—
312C2×C4—3021no—
313C2×C4—6042no—
314C2×C4—6042no—
315C2×C4—1511no—
316C2×C4—1514no—
317C2×C4—1511no—
318C2×C4—1511no—
319C2×C4—1511no—
320C2×C4D4×D15111yescharacteristic
321C2×C4C23×D15111yescharacteristic
322C8—21no—
323C8—3021no—
324C8—1512no—
325C8#1455900312yescomplemented
326C22—21no—
327C22—21no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—6041no—
332C22—6041no—
333C22—6041no—
334C22SD16×D15112yes—
335C22C2×D4×D15111yescharacteristic
336C4—21no—
337C4—41no—
338C4—41no—
339C4—41no—
340C4—3021no—
341C4—6041no—
342C4—6041no—
343C4—6041no—
344C4—1512no—
345C4—1512no—
346C4—1512no—
347C4#41×D15111yescharacteristic
348C4C2×#1455900311yescharacteristic
349C2—22no—
350C2—81no—
351C2—12081no—
352C2#2375275711yescharacteristic
353C2C2×SD16×D15111yescharacteristic
354C2#135×D15111yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#465×C151C2
socleC22×C151C22×D4
prime radical#23752757C2
hypercenter#465D151
hypocenterC151#3167
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. #23752764C2semidirect
3. #23752609C2semidirect
4. #23752583C2semidirect
5. #23752561C2semidirect
6. #23752557C2semidirect
7. #23752443C2semidirect
8. #23752441C2semidirect
9. #23752439C2semidirect
10. #23752303C2semidirect
11. SD16×Dic151C2semidirect
12. #23752299C2semidirect
13. #23752297C2semidirect
14. C2×C8×Dic151C2semidirect
15. #465×C151C2semidirect
124. C2×Dic151SD16semidirect
131. C151⋊C8#41semidirect
147. C8×C151#41semidirect
177. C151#3167semidirect
188. #465D151semidirect
325. C8#14559003semidirect

Maximal subgroups

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

subgroupindex
#237527642
#237527572
#237526092
#237525832
#237525612
#237525572
#237524432
#237524412
#237524392
#237523032
SD16×Dic1512
#237522992
#237522972
C2×C8×Dic1512
#465×C1512
#3167151