Finite Group Databasebeta

← #34080928

Subgroups — #34080928

Order 19328.

462 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 139 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×D604C211yesmaximal, characteristic
2#23752560C211yesmaximal, characteristic, complemented
3#23752530C212yesmaximal, complemented
4#23752499C211yesmaximal, characteristic, complemented
5#23752443C212yesmaximal, complemented
6#23752412C211yesmaximal, characteristic, complemented
7#23752362C212yesmaximal, complemented
8C4×#14558991C211yesmaximal, characteristic, complemented
9D4×C151⋊C8C211yesmaximal, characteristic, complemented
10C2×#18012659C212yesmaximal, complemented
11#554×C151C211yesmaximal, characteristic, complemented
12C22×D604C2212yes—
13C2×D4×D151—21no—
14C2×#14558991C2211yescharacteristic
15C2×#14558991C2212yescomplemented
16C22×C151⋊C8C2212yescomplemented
17#18012736C2211yescharacteristic
18#18012714—21no—
19#18012713C2212yes—
20#18012709—22no—
21C4×D604C2211yescharacteristic
22#18012670C2212yescomplemented
23#18012670C2211yescharacteristic, complemented
24C4⋊(C151⋊C8)C2211yescharacteristic, complemented
25#18012663C2211yescharacteristic, complemented
26#18012659C2211yescharacteristic
27#18012659C2212yes—
28#18012659C2212yescomplemented
29#18012659C2212yescomplemented
30#18012659C2212yescomplemented
31C22⋊(C151⋊C8)C2212yescomplemented
32C4×C151⋊C8C2211yescharacteristic, complemented
33C4⋊Q8×C151C2211yescharacteristic, complemented
34#125×C151—21no—
35C22⋊Q8×C151—22no—
36C22⋊Q8×C151C2212yescomplemented
37C4×Q8×C151C2211yescharacteristic, complemented
38C4×D4×C151—21no—
39C4×D4×C151C2211yescharacteristic
40C2×C4⋊C4×C151C2212yescomplemented
41C23×D151—22no—
42C2×D604—24no—
43C2×D604—22no—
44C2×D604—21no—
45C2×D604—21no—
46C2×D604—42no—
47C2×D604C2312yes—
48C2×D604C2311yescharacteristic
49C2×C22⋊D151—22no—
50D4×D151—44no—
51C2×C4×D151—21no—
52#14558991—22no—
53#14558991—42no—
54C2×C151⋊C8—42no—
55C2×C151⋊C8C2311yescharacteristic
56C2×C151⋊C8C2312yes—
57C2×C151⋊C8C2311yescharacteristic
58C4⋊Dic151C2311yescharacteristic
59(C2×D151)⋊C4—21no—
60(C2×D151)⋊C4—22no—
61C2×Q8×C151—21no—
62C2×Q8×C151C2311yescharacteristic
63C2×D4×C151D411yescharacteristic
64C22×C4×C151—22no—
65C22×C4×C151C2312yes—
66C4⋊C4×C151—22no—
67C4⋊C4×C151—21no—
68C4⋊C4×C151—21no—
69C4⋊C4×C151—22no—
70C4⋊C4×C151D411yescharacteristic
71C4⋊C4×C151C2311yescharacteristic
72C4⋊C4×C151C2312yes—
73C22⋊C4×C151—22no—
74C22⋊C4×C151D412yes—
75C42×C151—21no—
76C42×C151C2311yescharacteristic
77C22×D151—21no—
78C22×D151—22no—
79C22×D151—44no—
80C22×D151—44no—
81C22×D151—82no—
82D604—22no—
83D604—21no—
84D604—22no—
85D604—44no—
86D604—42no—
87D604—81no—
88D604#4112yes—
89C22⋊D151—44no—
90C2×Dic151—21no—
91C4×D151—42no—
92C151⋊C8—21no—
93C151⋊C8—21no—
94C151⋊C8—22no—
95C23×C151C2×D412yes—
96Q8×C151—21no—
97Q8×C151—21no—
98Q8×C151—81no—
99D4×C151SD1614yescomplemented
100C2×C4×C151—22no—
101C2×C4×C151—22no—
102C2×C4×C151—22no—
103C2×C4×C151—21no—
104C2×C4×C151—21no—
105C2×C4×C151—82no—
106C2×C4×C151C2×D411yescharacteristic
107C2×C4×C151C2×D412yes—
108C2×C4×C151C2×D411yescharacteristic
109C2×C4×C151C2411yescharacteristic
110C22×C151—22no—
111C22×C151—22no—
112C22×C151C2×SD1614yes—
113C22×C151C22×D411yescharacteristic
114C2×D151—22no—
115C2×D151—41no—
116C2×D151—41no—
117C2×D151—42no—
118C2×D151—42no—
119C2×D151—42no—
120C2×D151—88no—
121C4×C151—22no—
122C4×C151—21no—
123C4×C151—41no—
124C4×C151—41no—
125C4×C151—42no—
126C4×C151C2×SD1612yes—
127C4×C151C2×#4111yescharacteristic
128C4×C151H(5,𝔽2)11yescharacteristic
129Dic151—41no—
130C2×C151—24no—
131C2×C151#54611yescharacteristic
132C2×C151C22×SD1611yescharacteristic
133C2×C151#57611yescharacteristic
134D151—42no—
135D151—82no—
136C151#329511yescharacteristic, complemented, Sylow
137#3295—1511nomaximal, Sylow
138#554D15111yescharacteristic, complemented
139D42—1511no—
140#486—1511no—
141#481—1512no—
142#476—1511no—
143#465—1512no—
144#460—1511no—
145#450—1512no—
146C4×SD16—1511no—
147C8×D4—1511no—
148C2×#102—1512no—
149C22×D4—3021no—
150C22×D4—1512no—
151C2×SD16—1511no—
152C2×SD16—1512no—
153C22×C8—1512no—
154C4⋊Q8C2×D15111yescharacteristic, complemented
155#127—1511no—
156#125—21no—
157C22⋊Q8—22no—
158C22⋊Q8C2×D15112yescomplemented
159#121—3021no—
160#121—1512no—
161#120—3022no—
162C4×Q8C2×D15111yescharacteristic, complemented
163C4×D4—21no—
164C4×D4—1511no—
165C4×D4C2×D15111yescharacteristic
166C2×C4⋊C4C2×D15112yescomplemented
167#106—1511no—
168#106—1512no—
169C4⋊C8—1511no—
170#103—1511no—
171#102—1511no—
172#102—1512no—
173#102—1512no—
174#102—1512no—
175#102—1512no—
176C22⋊C8—1512no—
177C4×C8—1511no—
178C24—3022no—
179C2×Q8—21no—
180C2×Q8C22×D15111yescharacteristic
181C2×D4—3024no—
182C2×D4—3022no—
183C2×D4—3022no—
184C2×D4—3021no—
185C2×D4—3021no—
186C2×D4—6042no—
187C2×D4—6044no—
188C2×D4—1512no—
189C2×D4—1511no—
190C2×D4C22⋊D15111yescharacteristic
191C22×C4—22no—
192C22×C4—3021no—
193C22×C4C22×D15112yes—
194SD16—3022no—
195SD16—6042no—
196C2×C8—6042no—
197C2×C8—1511no—
198C2×C8—1511no—
199C2×C8—1512no—
200C4⋊C4—22no—
201C4⋊C4—21no—
202C4⋊C4—21no—
203C4⋊C4—22no—
204C4⋊C4—1511no—
205C4⋊C4C22⋊D15111yescharacteristic
206C4⋊C4C22×D15111yescharacteristic
207C4⋊C4C22×D15112yes—
208C22⋊C4—22no—
209C22⋊C4—3021no—
210C22⋊C4—3022no—
211C22⋊C4C22⋊D15112yes—
212C42—21no—
213C42C22×D15111yescharacteristic
214C23—3021no—
215C23—3022no—
216C23—6044no—
217C23—6044no—
218C23—12082no—
219C23C2×C22⋊D15112yes—
220Q8—21no—
221Q8—21no—
222Q8—81no—
223D4—3022no—
224D4—3021no—
225D4—3022no—
226D4—6044no—
227D4—6044no—
228D4—6042no—
229D4—1512no—
230D4—12081no—
231D4#1455899114yescomplemented
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—22no—
237C2×C4—82no—
238C2×C4—3021no—
239C2×C4—6042no—
240C2×C4C2×C22⋊D15111yescharacteristic
241C2×C4C2×C22⋊D15112yes—
242C2×C4C2×C22⋊D15111yescharacteristic
243C2×C4C23×D15111yescharacteristic
244C8—3021no—
245C8—3021no—
246C8—3022no—
247C22—22no—
248C22—22no—
249C22—3022no—
250C22—6041no—
251C22—6041no—
252C22—6042no—
253C22—6042no—
254C22—6042no—
255C22—12088no—
256C22C2×#1455899114yes—
257C22C22×C22⋊D15111yescharacteristic
258C4—21no—
259C4—22no—
260C4—41no—
261C4—42no—
262C4—41no—
263C4—6041no—
264C4C2×#1455899112yes—
265C4#41×D15111yescharacteristic
266C4#1801278511yescharacteristic
267C2—24no—
268C2—6042no—
269C2—12082no—
270C2#2375285011yescharacteristic
271C2C22×#1455899111yescharacteristic
272C2#2375301511yescharacteristic
subgroupG/H
centerC22C22×C22⋊D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#554×C151C2
socleC22×C151C22×D4
prime radicalD4×D604C2
hypercenter#554D151
hypocenterC151#3295
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C4×D4 ◁ #554

Complements

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

NH ≅ G/Ntype
2. #23752560C2semidirect
3. #23752530C2semidirect
4. #23752499C2semidirect
5. #23752443C2semidirect
6. #23752412C2semidirect
7. #23752362C2semidirect
8. C4×#14558991C2semidirect
9. D4×C151⋊C8C2semidirect
10. C2×#18012659C2semidirect
11. #554×C151C2semidirect
15. C2×#14558991C22semidirect
16. C22×C151⋊C8C22semidirect
22. #18012670C22semidirect
23. #18012670C22semidirect
24. C4⋊(C151⋊C8)C22semidirect
25. #18012663C22semidirect
28. #18012659C22semidirect
29. #18012659C22semidirect
30. #18012659C22semidirect
31. C22⋊(C151⋊C8)C22semidirect
32. C4×C151⋊C8C22semidirect
33. C4⋊Q8×C151C22semidirect
36. C22⋊Q8×C151C22semidirect
37. C4×Q8×C151C22semidirect
40. C2×C4⋊C4×C151C22semidirect
99. D4×C151SD16semidirect
136. C151#3295semidirect
138. #554D151semidirect
154. C4⋊Q8C2×D151semidirect
158. C22⋊Q8C2×D151semidirect
162. C4×Q8C2×D151semidirect
166. C2×C4⋊C4C2×D151semidirect
231. D4#14558991semidirect

Maximal subgroups

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

subgroupindex
D4×D6042
#237525602
#237525302
#237524992
#237524432
#237524122
#237523622
C4×#145589912
D4×C151⋊C82
C2×#180126592
#554×C1512
#3295151