Finite Group Databasebeta

← #34079970

Subgroups — #34079970

Order 19328.

442 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 109 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
1#23752778C212yesmaximal, complemented
2#23752539C212yesmaximal, complemented
3#23752534C212yesmaximal, complemented
4#23752463C212yesmaximal, complemented
5#23752448C211yesmaximal, characteristic, complemented
6#23752347C212yesmaximal, complemented
7#23752344C212yesmaximal, complemented
8#23752178C211yesmaximal, characteristic, complemented
9#466×C151C211yesmaximal, characteristic, complemented
10C2×#14559004C2211yescharacteristic
11C2×D4×D151C2212yescomplemented
12C2×D1208C2211yescharacteristic
13C2×#14558989C2212yes—
14C2×#14558988C2211yescharacteristic, complemented
15#18012735—22no—
16#18012725—22no—
17#18012714C2212yes—
18#18012713C2212yescomplemented
19#18012710C2212yes—
20#18012709—22no—
21#18012707—22no—
22#18012697C2212yescomplemented
23#18012673C2211yescharacteristic, complemented
24#18012670C2212yescomplemented
25#18012661C2212yescomplemented
26#18012660C2212yescomplemented
27#18012659C2212yescomplemented
28(C2×D151)⋊C8C2212yescomplemented
29(C2×D151)⋊C8C2212yescomplemented
30C2×D8×C151C2211yescharacteristic
31C22×C8×C151C2211yescharacteristic, complemented
32#121×C151C2212yescomplemented
33#107×C151C2211yescharacteristic, complemented
34#102×C151C2212yescomplemented
35C23×D151—22no—
36#14559004—41no—
37#14559004—41no—
38C2×Dic302D411yescharacteristic
39C2×D604—22no—
40C2×D604D411yescharacteristic
41C2×D604C2312yes—
42C2×C22⋊D151—22no—
43C2×C22⋊D151—22no—
44C2×C22⋊D151—22no—
45C2×C22⋊D151D412yes—
46D4×D151—42no—
47D4×D151—42no—
48C2×C4×D151C2312yes—
49D1208—41no—
50#14558989—42no—
51#14558988—41no—
52C2×C151⋊C8C2312yes—
53C4⋊Dic151C2312yes—
54C22⋊Dic151—22no—
55(C2×D151)⋊C4—22no—
56(C2×D151)⋊C4—22no—
57(C2×D151)⋊C4—22no—
58C4×Dic151—22no—
59C2×D4×C151—22no—
60C2×D4×C151C2312yes—
61C22×C4×C151C2311yescharacteristic
62D8×C151—41no—
63C2×C8×C151—41no—
64C2×C8×C151C2311yescharacteristic
65C2×C8×C151C2311yescharacteristic
66C4⋊C4×C151C2312yes—
67C22⋊C4×C151—22no—
68C22×D151—22no—
69C22×D151—44no—
70C22×D151—82no—
71C22×D151—82no—
72C22×D151C2×D412yes—
73Dic302—41no—
74D604—22no—
75D604—22no—
76D604—41no—
77D604—82no—
78C22⋊D151—42no—
79C22⋊D151—44no—
80C22⋊D151—82no—
81C22⋊D151—82no—
82C2×Dic151—22no—
83C2×Dic151C2×D412yes—
84C4×D151—22no—
85C4×D151—22no—
86C151⋊C8—22no—
87C23×C151—22no—
88C23×C151C2×D411yescharacteristic
89D4×C151—22no—
90D4×C151—22no—
91D4×C151—82no—
92C2×C4×C151—21no—
93C2×C4×C151—21no—
94C2×C4×C151—22no—
95C2×C4×C151C2×D411yescharacteristic
96C2×C4×C151C2411yescharacteristic
97C8×C151—21no—
98C8×C151—21no—
99C22×C151—21no—
100C22×C151—21no—
101C22×C151—21no—
102C22×C151—42no—
103C22×C151—42no—
104C22×C151—42no—
105C22×C151C22×D411yescharacteristic
106C2×D151—22no—
107C2×D151—22no—
108C2×D151—22no—
109C2×D151—42no—
110C2×D151—42no—
111C2×D151—42no—
112C2×D151—88no—
113C4×C151—21no—
114C4×C151—42no—
115C4×C151H(5,𝔽2)11yescharacteristic
116C4×C151H(5,𝔽2)11yescharacteristic
117Dic151—22no—
118Dic151—42no—
119C2×C151—41no—
120C2×C151—82no—
121C2×C151#53411yescharacteristic
122C2×C151#57611yescharacteristic
123C2×C151#57611yescharacteristic
124D151—42no—
125D151—82no—
126C151#319911yescharacteristic, complemented, Sylow
127#3199—1511nomaximal, Sylow
128#535—1512no—
129#482—1512no—
130#482—1512no—
131#469—1512no—
132#466—1511no—
133#466D15111yescharacteristic, complemented
134#447—1512no—
135#447—1512no—
136#408—1511no—
137C2×#41—1511no—
138C22×D4—1512no—
139C2×D8—1512no—
140C2×D8—1511no—
141C2×D8C2×D15111yescharacteristic
142C2×M16—1511no—
143C22×C8C2×D15111yescharacteristic, complemented
144#127—3022no—
145#124—3022no—
146#121—1512no—
147#121—1512no—
148#121—1512no—
149#121C2×D15112yescomplemented
150#120—3022no—
151#120—3022no—
152#117—1512no—
153#107—1511no—
154#107C2×D15111yescharacteristic, complemented
155#106—1512no—
156#102—1512no—
157#102—1512no—
158#102—1512no—
159#102C2×D15112yescomplemented
160C22⋊C8—1512no—
161C22⋊C8—1512no—
162C24—3022no—
163#41—6041no—
164#41—6041no—
165C2×Q8—1511no—
166C2×D4—22no—
167C2×D4—3022no—
168C2×D4—3022no—
169C2×D4—3022no—
170C2×D4—3022no—
171C2×D4—6042no—
172C2×D4—6042no—
173C2×D4—1512no—
174C2×D4—1511no—
175C2×D4—1512no—
176C2×D4C22×D15112yes—
177C22×C4—1512no—
178C22×C4C22×D15111yescharacteristic
179D8—41no—
180D8—6041no—
181D8—6042no—
182M16—6041no—
183C2×C8—41no—
184C2×C8—1512no—
185C2×C8C22×D15111yescharacteristic
186C2×C8C22×D15111yescharacteristic
187C4⋊C4—1512no—
188C4⋊C4C22×D15112yes—
189C22⋊C4—22no—
190C22⋊C4—3022no—
191C22⋊C4—3022no—
192C22⋊C4—3022no—
193C22⋊C4—3022no—
194C42—3022no—
195C23—22no—
196C23—3022no—
197C23—6044no—
198C23—1512no—
199C23—12082no—
200C23—12082no—
201C23D4×D15111yescharacteristic
202Q8—6041no—
203D4—22no—
204D4—22no—
205D4—82no—
206D4—3022no—
207D4—3022no—
208D4—6041no—
209D4—6042no—
210D4—6044no—
211D4—12082no—
212D4—12082no—
213D4—12082no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—22no—
217C2×C4—3022no—
218C2×C4—3022no—
219C2×C4—3022no—
220C2×C4—1512no—
221C2×C4D4×D15111yescharacteristic
222C2×C4C23×D15111yescharacteristic
223C8—21no—
224C8—21no—
225C8—3022no—
226C22—21no—
227C22—21no—
228C22—21no—
229C22—42no—
230C22—42no—
231C22—42no—
232C22—3022no—
233C22—3022no—
234C22—3022no—
235C22—6042no—
236C22—6042no—
237C22—6042no—
238C22—12088no—
239C22C2×D4×D15111yescharacteristic
240C4—21no—
241C4—42no—
242C4—3022no—
243C4—6042no—
244C4#1801278411yescharacteristic
245C4#1801278511yescharacteristic
246C2—41no—
247C2—82no—
248C2—6042no—
249C2—12082no—
250C2#2375277011yescharacteristic
251C2#2375301311yescharacteristic
252C2#2375301411yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#466×C151C2
socleC22×C151C22×D4
hypercenter#466D151
hypocenterC151#3199
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #466

Complements

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

NH ≅ G/Ntype
1. #23752778C2semidirect
2. #23752539C2semidirect
3. #23752534C2semidirect
4. #23752463C2semidirect
5. #23752448C2semidirect
6. #23752347C2semidirect
7. #23752344C2semidirect
8. #23752178C2semidirect
9. #466×C151C2semidirect
11. C2×D4×D151C22semidirect
14. C2×#14558988C22semidirect
18. #18012713C22semidirect
22. #18012697C22semidirect
23. #18012673C22semidirect
24. #18012670C22semidirect
25. #18012661C22semidirect
26. #18012660C22semidirect
27. #18012659C22semidirect
28. (C2×D151)⋊C8C22semidirect
29. (C2×D151)⋊C8C22semidirect
31. C22×C8×C151C22semidirect
32. #121×C151C22semidirect
33. #107×C151C22semidirect
34. #102×C151C22semidirect
126. C151#3199semidirect
133. #466D151semidirect
143. C22×C8C2×D151semidirect
149. #121C2×D151semidirect
154. #107C2×D151semidirect
159. #102C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237527782
#237525392
#237525342
#237524632
#237524482
#237523472
#237523442
#237521782
#466×C1512
#3199151