Finite Group Databasebeta

← #34078474

Subgroups — #34078474

Order 19328.

698 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 698 conjugacy classes of subgroups — too many to draw. Only its 161 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#23753010C212yesmaximal, complemented
2#23752786C211yesmaximal, characteristic, complemented
3#23752395C214yesmaximal, complemented
4#23752385C214yesmaximal, complemented
5#23752229C212yesmaximal, complemented
6C2×#18012658C211yesmaximal, characteristic, complemented
7C2×2−1+4×C151C211yesmaximal, characteristic, complemented
8C2×#14559004C2211yescharacteristic
9#18012770—22no—
10#18012769C2214yescomplemented
11#18012765—22no—
12#18012764C2214yescomplemented
13#18012759—24no—
14C2×#14558988C2212yes—
15#18012737C2212yescomplemented
16#18012728C2212yescomplemented
17#18012722—22no—
18#18012715—22no—
19#18012698C2211yescharacteristic
20#18012666C2218yescomplemented
21#18012658C2214yescomplemented
222−1+4×C151—24no—
232−1+4×C151—22no—
242−1+4×C151C2214yes—
25C2×#41×C151—22no—
26C2×#41×C151—22no—
27C2×#41×C151C2212yes—
28C22×Q8×C151—22no—
29C22×Q8×C151C2211yescharacteristic
30#14559004—22no—
31#14559004—22no—
32C2×Dic302C2311yescharacteristic
33C2×D604C2311yescharacteristic
34C2×C22⋊D151—21no—
35C2×C4×D151—21no—
36#14558994—24no—
37#14558992—24no—
38#14558991—24no—
39#14558989—24no—
40#14558988—22no—
41#14558988C2314yes—
42C2×C151⋊C8—22no—
43C4⋊Dic151—21no—
44Dic151⋊C4—24no—
45C22⋊Dic151—21no—
46(C2×D151)⋊C4—24no—
47C4×Dic151C2312yes—
48#41×C151—28no—
49#41×C151—28no—
50#41×C151—28no—
51#41×C151—28no—
52#41×C151—22no—
53#41×C151—22no—
54#41×C151D414yes—
55#41×C151C2314yes—
56C2×Q8×C151—22no—
57C2×Q8×C151—28no—
58C2×Q8×C151—28no—
59C2×Q8×C151—22no—
60C2×Q8×C151—22no—
61C2×Q8×C151D412yes—
62C2×Q8×C151D412yes—
63C2×Q8×C151C2312yes—
64C2×D4×C151—22no—
65C2×D4×C151—22no—
66C2×D4×C151D412yes—
67C22×C4×C151—24no—
68C22×C4×C151—22no—
69C22×C4×C151D412yes—
70C22×C4×C151C2311yescharacteristic
71C22×D151—21no—
72Dic302—22no—
73D604—22no—
74C22⋊D151—41no—
75C22⋊D151—41no—
76C2×Dic151—22no—
77C2×Dic151—21no—
78C4×D151—42no—
79C151⋊C8—24no—
80C23×C151—22no—
81C23×C151C2×D411yescharacteristic
82Q8×C151—28no—
83Q8×C151—22no—
84Q8×C151—24no—
85Q8×C151—24no—
86Q8×C151C2×D414yes—
87D4×C151—28no—
88D4×C151—24no—
89D4×C151—24no—
90D4×C151—22no—
91D4×C151C2×D414yes—
92C2×C4×C151—216no—
93C2×C4×C151—22no—
94C2×C4×C151—22no—
95C2×C4×C151—22no—
96C2×C4×C151—24no—
97C2×C4×C151—24no—
98C2×C4×C151C2×D414yes—
99C2×C4×C151C2×D411yescharacteristic
100C2×C4×C151C2×D412yes—
101C2×C4×C151C2×D412yes—
102C2×C4×C151C2411yescharacteristic
103C22×C151—24no—
104C22×C151—41no—
105C22×C151—44no—
106C22×C151#12011yescharacteristic
107C22×C151#12011yescharacteristic
108C22×C151C22×D411yescharacteristic
109C2×D151—42no—
110C2×D151—41no—
111C4×C151—24no—
112C4×C151—24no—
113C4×C151#12012yes—
114C4×C151C22×D412yes—
115Dic151—42no—
116Dic151—41no—
117C2×C151—21no—
118C2×C151—21no—
119C2×C151—21no—
120C2×C151—44no—
121C2×C151C2×#12011yescharacteristic
122D151—81no—
123C151#302011yescharacteristic, complemented, Sylow
124#3020—1511nomaximal, Sylow
125C2×2−1+4D15111yescharacteristic, complemented
126#575—1512no—
127#536—1511no—
128#456—1514no—
129#454—1514no—
130#421—1512no—
131C2×#101—1511no—
1322−1+4—24no—
1332−1+4—22no—
1342−1+4C2×D15114yes—
135C2×#41—22no—
136C2×#41—22no—
137C2×#41—1511no—
138C2×#41C2×D15112yes—
139C22×Q8—22no—
140C22×Q8C2×D15111yescharacteristic
141#137—3022no—
142#137—1514no—
143AGL(1,ℤ/8)—3022no—
144AGL(1,ℤ/8)—1514no—
145#135—3024no—
146C2×M16—1512no—
147C4⋊Q8—1512no—
148#124—1512no—
149#123—3022no—
150C22⋊Q8—3022no—
151#117—1511no—
152#104—1518no—
153#101—1514no—
154#41—28no—
155#41—28no—
156#41—28no—
157#41—28no—
158#41—22no—
159#41—22no—
160#41—3022no—
161#41—3022no—
162#41C22⋊D15114yes—
163#41C22×D15114yes—
164C2×Q8—22no—
165C2×Q8—28no—
166C2×Q8—28no—
167C2×Q8—22no—
168C2×Q8—22no—
169C2×Q8—1511no—
170C2×Q8C22⋊D15112yes—
171C2×Q8C22⋊D15112yes—
172C2×Q8C22×D15112yes—
173C2×D4—22no—
174C2×D4—22no—
175C2×D4—3021no—
176C2×D4—1511no—
177C2×D4C22⋊D15112yes—
178C22×C4—24no—
179C22×C4—22no—
180C22×C4—3021no—
181C22×C4C22⋊D15112yes—
182C22×C4C22×D15111yescharacteristic
183Q16—3024no—
184SD16—3024no—
185SD16—3024no—
186D8—3024no—
187M16—3022no—
188M16—1514no—
189C2×C8—3022no—
190C4⋊C4—3024no—
191C4⋊C4—3021no—
192C22⋊C4—3021no—
193C22⋊C4—3024no—
194C42—1512no—
195C23—22no—
196C23—3021no—
197C23C2×C22⋊D15111yescharacteristic
198Q8—28no—
199Q8—22no—
200Q8—24no—
201Q8—24no—
202Q8—3022no—
203Q8C2×C22⋊D15114yes—
204D4—28no—
205D4—24no—
206D4—24no—
207D4—22no—
208D4—3022no—
209D4—6041no—
210D4—6041no—
211D4C2×C22⋊D15114yes—
212C2×C4—216no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—24no—
217C2×C4—24no—
218C2×C4—3022no—
219C2×C4—3021no—
220C2×C4—6042no—
221C2×C4C2×C22⋊D15114yes—
222C2×C4C2×C22⋊D15111yescharacteristic
223C2×C4C2×C22⋊D15112yes—
224C2×C4C2×C22⋊D15112yes—
225C2×C4C23×D15111yescharacteristic
226C8—3024no—
227C22—24no—
228C22—41no—
229C22—44no—
230C22—6042no—
231C22—6041no—
232C22#1801270811yescharacteristic
233C22#1801270811yescharacteristic
234C22C22×C22⋊D15111yescharacteristic
235C4—24no—
236C4—24no—
237C4—6042no—
238C4—6041no—
239C4#1801270812yes—
240C4C22×C22⋊D15112yes—
241C2—21no—
242C2—21no—
243C2—21no—
244C2—44no—
245C2—12081no—
246C2C2×#1801270811yescharacteristic
subgroupG/H
centerC2C2×#18012708
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
FittingC2×2−1+4×C151C2
socleC2×C151C2×#120
hypercenterC2×2−1+4D151
hypocenterC151#3020
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×2−1+4

Complements

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

NH ≅ G/Ntype
1. #23753010C2semidirect
2. #23752786C2semidirect
3. #23752395C2semidirect
4. #23752385C2semidirect
5. #23752229C2semidirect
6. C2×#18012658C2semidirect
7. C2×2−1+4×C151C2semidirect
10. #18012769C22semidirect
12. #18012764C22semidirect
15. #18012737C22semidirect
16. #18012728C22semidirect
20. #18012666C22semidirect
21. #18012658C22semidirect
123. C151#3020semidirect
125. C2×2−1+4D151semidirect

Maximal subgroups

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

subgroupindex
#237530102
#237527862
#237523952
#237523852
#237522292
C2×#180126582
C2×2−1+4×C1512
#3020151