Finite Group Databasebeta

← #34078473

Subgroups — #34078473

Order 19328.

698 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 698 conjugacy classes of subgroups — too many to draw. Only its 145 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
1C2×#18012787C211yesmaximal, characteristic, complemented
2#23753010C212yesmaximal, complemented
3#23752394C214yesmaximal, complemented
4#23752384C214yesmaximal, complemented
5#23752230C212yesmaximal, complemented
6C2×#18012658C211yesmaximal, characteristic, complemented
7#536×C151C211yesmaximal, characteristic, complemented
8#18012787—24no—
9#18012787—22no—
10#18012787C2214yes—
11C2×#14559005—22no—
12C2×#14559004—22no—
13C2×#14559004C2212yes—
14C2×Q8×D151—22no—
15#18012770C2214yescomplemented
16#18012769—22no—
17#18012765C2214yescomplemented
18#18012764—22no—
19#18012759—24no—
20C2×#14558988C2212yes—
21#18012667C2218yescomplemented
22#18012658C2214yescomplemented
23C2×#41×C151C2211yescharacteristic
24C22×Q8×C151C2211yescharacteristic
25C4⋊Q8×C151C2212yescomplemented
26#124×C151C2212yescomplemented
27#123×C151—22no—
28C22⋊Q8×C151—22no—
29#117×C151C2211yescharacteristic
30#14559005—28no—
31#14559005—28no—
32#14559004—28no—
33#14559004—28no—
34#14559004—22no—
35#14559004—22no—
36#14559004D414yes—
37#14559004C2314yes—
38C2×Dic302—22no—
39C2×Dic302D412yes—
40Q8×D151—28no—
41Q8×D151—28no—
42C2×D604—22no—
43C2×D604D412yes—
44C2×C22⋊D151—22no—
45C2×C4×D151—24no—
46C2×C4×D151—22no—
47#14558994—24no—
48#14558992—24no—
49#14558991—24no—
50#14558989—24no—
51#14558988—22no—
52#14558988C2314yes—
53C2×C151⋊C8—22no—
54#41×C151—22no—
55#41×C151—22no—
56C2×Q8×C151—22no—
57C2×Q8×C151—22no—
58C2×Q8×C151D412yes—
59C2×Q8×C151C2311yescharacteristic
60C2×Q8×C151C2312yes—
61C2×D4×C151—21no—
62C2×D4×C151C2311yescharacteristic
63C22×C4×C151—21no—
64C22×C4×C151D412yes—
65C22×C4×C151C2311yescharacteristic
66C4⋊C4×C151—21no—
67C4⋊C4×C151—24no—
68C22⋊C4×C151—21no—
69C22⋊C4×C151—24no—
70C42×C151C2312yes—
71C22×D151—22no—
72Dic302—28no—
73Dic302—22no—
74Dic302C2×D414yes—
75D604—28no—
76D604—22no—
77D604C2×D414yes—
78C22⋊D151—24no—
79C22⋊D151—24no—
80C2×Dic151—22no—
81C4×D151—216no—
82C4×D151—24no—
83C4×D151—24no—
84C151⋊C8—24no—
85C23×C151—21no—
86C23×C151C2×D411yescharacteristic
87Q8×C151—24no—
88Q8×C151—24no—
89Q8×C151—22no—
90D4×C151—22no—
91D4×C151—41no—
92D4×C151—41no—
93C2×C4×C151—22no—
94C2×C4×C151—22no—
95C2×C4×C151—21no—
96C2×C4×C151—22no—
97C2×C4×C151—42no—
98C2×C4×C151C2×D412yes—
99C2×C4×C151C2×D412yes—
100C2×C4×C151C2×D414yes—
101C2×C4×C151C2×D411yescharacteristic
102C2×C4×C151C2411yescharacteristic
103C22×C151—41no—
104C22×C151—42no—
105C22×C151—41no—
106C22×C151#12011yescharacteristic
107C22×C151#12011yescharacteristic
108C22×C151C22×D411yescharacteristic
109C2×D151—24no—
110C2×D151—44no—
111C4×C151—24no—
112C4×C151—42no—
113C4×C151—41no—
114C4×C151#12012yes—
115C4×C151C22×D412yes—
116Dic151—24no—
117C2×C151—21no—
118C2×C151—21no—
119C2×C151—21no—
120C2×C151—81no—
121C2×C151C2×#12011yescharacteristic
122D151—44no—
123C151#302011yescharacteristic, complemented, Sylow
124#3020—1511nomaximal, Sylow
125C2×2−1+4—1511no—
126#575—1512no—
127#536D15111yescharacteristic, complemented
128#456—1514no—
129#454—1514no—
130#421—1512no—
131C2×#101—1511no—
1322−1+4—3024no—
1332−1+4—3022no—
1342−1+4—1514no—
135C2×#41—3022no—
136C2×#41—3022no—
137C2×#41—1512no—
138C2×#41C2×D15111yescharacteristic
139C22×Q8—3022no—
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⋊Q8C2×D15112yescomplemented
148#124C2×D15112yescomplemented
149#123—22no—
150C22⋊Q8—22no—
151#117C2×D15111yescharacteristic
152#104—1518no—
153#101—1514no—
154#41—22no—
155#41—22no—
156#41—3028no—
157#41—3028no—
158#41—3028no—
159#41—3022no—
160#41—3028no—
161#41—3022no—
162#41—1514no—
163#41—1514no—
164C2×Q8—22no—
165C2×Q8—22no—
166C2×Q8—3022no—
167C2×Q8—3028no—
168C2×Q8—3028no—
169C2×Q8—1512no—
170C2×Q8C22⋊D15112yes—
171C2×Q8C22×D15111yescharacteristic
172C2×Q8C22×D15112yes—
173C2×D4—21no—
174C2×D4—3022no—
175C2×D4—3022no—
176C2×D4—1512no—
177C2×D4C22×D15111yescharacteristic
178C22×C4—21no—
179C22×C4—3024no—
180C22×C4—3022no—
181C22×C4C22⋊D15112yes—
182C22×C4C22×D15111yescharacteristic
183Q16—3024no—
184SD16—3024no—
185SD16—3024no—
186D8—3024no—
187M16—3022no—
188M16—1514no—
189C2×C8—3022no—
190C4⋊C4—21no—
191C4⋊C4—24no—
192C22⋊C4—21no—
193C22⋊C4—24no—
194C42C22×D15112yes—
195C23—21no—
196C23—3022no—
197C23C2×C22⋊D15111yescharacteristic
198Q8—24no—
199Q8—24no—
200Q8—22no—
201Q8—3028no—
202Q8—3022no—
203Q8—1514no—
204D4—22no—
205D4—41no—
206D4—41no—
207D4—3028no—
208D4—3024no—
209D4—3024no—
210D4—3022no—
211D4—1514no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—21no—
216C2×C4—42no—
217C2×C4—30216no—
218C2×C4—3022no—
219C2×C4—3024no—
220C2×C4—3024no—
221C2×C4D4×D15112yes—
222C2×C4D4×D15112yes—
223C2×C4C2×C22⋊D15114yes—
224C2×C4C2×C22⋊D15111yescharacteristic
225C2×C4C23×D15111yescharacteristic
226C8—3024no—
227C22—41no—
228C22—42no—
229C22—41no—
230C22—3024no—
231C22—6044no—
232C22#1801270711yescharacteristic
233C22#1801270711yescharacteristic
234C22C22×C22⋊D15111yescharacteristic
235C4—24no—
236C4—42no—
237C4—41no—
238C4—3024no—
239C4#1801270712yes—
240C4C2×D4×D15112yes—
241C2—21no—
242C2—21no—
243C2—21no—
244C2—81no—
245C2—6044no—
246C2C2×#1801270711yescharacteristic
subgroupG/H
centerC2C2×#18012707
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#536×C151C2
socleC2×C151C2×#120
hypercenter#536D151
hypocenterC151#3020
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2 ◁ C22×C4 ◁ #536

Complements

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

NH ≅ G/Ntype
1. C2×#18012787C2semidirect
2. #23753010C2semidirect
3. #23752394C2semidirect
4. #23752384C2semidirect
5. #23752230C2semidirect
6. C2×#18012658C2semidirect
7. #536×C151C2semidirect
15. #18012770C22semidirect
17. #18012765C22semidirect
21. #18012667C22semidirect
22. #18012658C22semidirect
25. C4⋊Q8×C151C22semidirect
26. #124×C151C22semidirect
123. C151#3020semidirect
127. #536D151semidirect
147. C4⋊Q8C2×D151semidirect
148. #124C2×D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127872
#237530102
#237523942
#237523842
#237522302
C2×#180126582
#536×C1512
#3020151