Finite Group Databasebeta

← #34081763

Subgroups — #34081763

Order 19328.

350 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 117 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#23752936C211yesmaximal, characteristic, complemented
2#23752919C211yesmaximal, characteristic, complemented
3#23752568C212yesmaximal, complemented
4#23752562C211yesmaximal, characteristic, complemented
5#23752517C212yesmaximal, complemented
6#23752503C211yesmaximal, characteristic, complemented
7#23752429C212yesmaximal
8#23752336C211yesmaximal, characteristic, complemented
9SD16×Dic151C212yesmaximal, complemented
10C4×#14558989C211yesmaximal, characteristic
11#461×C151C211yesmaximal, characteristic, complemented
12C2×#14558989C2211yescharacteristic
13#18012739C2211yescharacteristic
14#18012734—22no—
15#18012730C2212yes—
16#18012728C2212yes—
17#18012719—21no—
18#18012718—21no—
19#18012716—22no—
20Q8×Dic151C2212yes—
21C4×Dic302C2211yescharacteristic
22C4×D604C2211yescharacteristic
23D4×Dic151C2212yes—
24#18012697—21no—
25C2×C4⋊Dic151—21no—
26#18012672C2211yescharacteristic
27#18012671C2212yes—
28Dic151⋊C8C2212yes—
29#18012663C2212yes—
30#18012663C2212yes—
31#18012661C2212yes—
32#18012660C2211yescharacteristic
33#18012659C2211yescharacteristic
34C4×C151⋊C8C2211yescharacteristic
35C8×Dic151C2212yes—
36C2×SD16×C151C2212yes—
37C4⋊Q8×C151C2211yescharacteristic
38C4×D4×C151C2211yescharacteristic
39C4⋊C8×C151C2211yescharacteristic
40#103×C151C2212yes—
41C2×Dic302—21no—
42C2×Dic302D411yescharacteristic
43C2×D604C2311yescharacteristic
44C22×Dic151—22no—
45C2×C4×D151—21no—
46#14558989—22no—
47C2×C151⋊C8C2311yescharacteristic
48C2×C151⋊C8C2311yescharacteristic
49C4⋊Dic151—22no—
50C4⋊Dic151—22no—
51C4⋊Dic151—21no—
52C4⋊Dic151D411yescharacteristic
53C4⋊Dic151C2311yescharacteristic
54C4⋊Dic151C2312yes—
55Dic151⋊C4—22no—
56Dic151⋊C4D412yes—
57C22⋊Dic151—22no—
58(C2×D151)⋊C4—22no—
59(C2×D151)⋊C4—22no—
60(C2×D151)⋊C4—21no—
61C4×Dic151—22no—
62C4×Dic151C2312yes—
63C2×Q8×C151C2312yes—
64C2×D4×C151C2311yescharacteristic
65C22×C4×C151—21no—
66SD16×C151—24no—
67C2×C8×C151C2312yes—
68C4⋊C4×C151—21no—
69C4⋊C4×C151—21no—
70C4⋊C4×C151C2311yescharacteristic
71C22⋊C4×C151—21no—
72C42×C151C2311yescharacteristic
73C22×D151—21no—
74Dic302—22no—
75Dic302—81no—
76D604—21no—
77D604—21no—
78C2×Dic151—21no—
79C2×Dic151—22no—
80C2×Dic151—82no—
81C2×Dic151C2×D412yes—
82C2×Dic151C2×D412yes—
83C4×D151—42no—
84C151⋊C8—21no—
85C151⋊C8—21no—
86C23×C151—21no—
87Q8×C151—22no—
88Q8×C151—22no—
89D4×C151—21no—
90D4×C151#4112yes—
91C2×C4×C151—22no—
92C2×C4×C151—21no—
93C2×C4×C151—42no—
94C2×C4×C151C2×D411yescharacteristic
95C2×C4×C151C2×D411yescharacteristic
96C2×C4×C151C2411yescharacteristic
97C8×C151—22no—
98C22×C151—22no—
99C22×C151—41no—
100C22×C151—41no—
101C22×C151C22×D411yescharacteristic
102C2×D151—41no—
103C2×D151—41no—
104C2×D151—41no—
105C4×C151—21no—
106C4×C151—42no—
107C4×C151—41no—
108C4×C151#13512yes—
109C4×C151C2×#4111yescharacteristic
110C4×C1512−1+411yescharacteristic
111Dic151—22no—
112Dic151—22no—
113Dic151—41no—
114Dic151—42no—
115C2×C151—42no—
116C2×C151#54811yescharacteristic
117C2×C151C2×#13511yescharacteristic
118C2×C151#57711yescharacteristic
119D151—81no—
120C151#336011yescharacteristic, complemented, Sylow
121#3360—1511nomaximal, Sylow
122#556—1511no—
123#554—1511no—
124#488—1512no—
125#487—1511no—
126#479—1512no—
127#476—1511no—
128#463—1512no—
129#461D15111yescharacteristic, complemented
130C8×Q8—1511no—
131C4×SD16—1512no—
132C4×D8—1511no—
133C2×SD16C2×D15112yes—
134C2×D8—1511no—
135C4⋊Q8—1511no—
136C4⋊Q8C2×D15111yescharacteristic
137#126—3022no—
138#125—1512no—
139#124—1512no—
140C22⋊Q8—3022no—
141C22⋊Q8—3021no—
142C22⋊Q8—3021no—
143C4×Q8—1512no—
144C4×Q8—1511no—
145C4×D4—1512no—
146C4×D4—1511no—
147C4×D4C2×D15111yescharacteristic
148#117—3021no—
149C2×C4⋊C4—3021no—
150#107—1511no—
151#106—1512no—
152C4⋊C8—1512no—
153C4⋊C8C2×D15111yescharacteristic
154#103—1512no—
155#103—1512no—
156#103C2×D15112yes—
157#102—1511no—
158#102—1512no—
159#102—1511no—
160C4×C8—1512no—
161C4×C8—1511no—
162C2×Q8—3021no—
163C2×Q8—1511no—
164C2×Q8C22×D15112yes—
165C2×D4—1511no—
166C2×D4C22×D15111yescharacteristic
167C22×C4—21no—
168C22×C4—3021no—
169C22×C4—3022no—
170SD16—24no—
171D8—3022no—
172C2×C8—1511no—
173C2×C8—1511no—
174C2×C8C22×D15112yes—
175C4⋊C4—21no—
176C4⋊C4—21no—
177C4⋊C4—3022no—
178C4⋊C4—3022no—
179C4⋊C4—3022no—
180C4⋊C4—3021no—
181C4⋊C4—1512no—
182C4⋊C4—1511no—
183C4⋊C4—1512no—
184C4⋊C4—1511no—
185C4⋊C4C22×D15111yescharacteristic
186C22⋊C4—21no—
187C22⋊C4—3022no—
188C22⋊C4—3022no—
189C22⋊C4—3022no—
190C22⋊C4—3021no—
191C42—3022no—
192C42—1512no—
193C42C22×D15111yescharacteristic
194C23—21no—
195C23—3021no—
196Q8—22no—
197Q8—22no—
198Q8—3022no—
199Q8—12081no—
200D4—21no—
201D4—3021no—
202D4—3021no—
203D4#1455900312yes—
204C2×C4—22no—
205C2×C4—21no—
206C2×C4—42no—
207C2×C4—3021no—
208C2×C4—3022no—
209C2×C4—6042no—
210C2×C4—1512no—
211C2×C4—1512no—
212C2×C4—12082no—
213C2×C4D4×D15111yescharacteristic
214C2×C4D4×D15111yescharacteristic
215C2×C4C23×D15111yescharacteristic
216C8—22no—
217C8—3021no—
218C8—3021no—
219C22—22no—
220C22—41no—
221C22—41no—
222C22—6041no—
223C22—6041no—
224C22—6041no—
225C22C2×D4×D15111yescharacteristic
226C4—21no—
227C4—41no—
228C4—42no—
229C4—3022no—
230C4—3022no—
231C4—6041no—
232C4—6042no—
233C4#1801276012yes—
234C4C2×#1455900311yescharacteristic
235C4#1801278611yescharacteristic
236C2—42no—
237C2—12081no—
238C2#2375286811yescharacteristic
239C2C2×#1801276011yescharacteristic
240C2#2375302111yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#461×C151C2
socleC22×C151C22×D4
prime radicalC2×#14558989C22
hypercenter#461D151
hypocenterC151#3360
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
1. #23752936C2semidirect
2. #23752919C2semidirect
3. #23752568C2semidirect
4. #23752562C2semidirect
5. #23752517C2semidirect
6. #23752503C2semidirect
8. #23752336C2semidirect
9. SD16×Dic151C2semidirect
11. #461×C151C2semidirect
120. C151#3360semidirect
129. #461D151semidirect

Maximal subgroups

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

subgroupindex
#237529362
#237529192
#237525682
#237525622
#237525172
#237525032
#237524292
#237523362
SD16×Dic1512
C4×#145589892
#461×C1512
#3360151