Finite Group Databasebeta

← #34081758

Subgroups — #34081758

Order 19328.

350 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 115 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#23752932C211yesmaximal, characteristic, complemented
2#23752923C211yesmaximal, characteristic, complemented
3#23752565C212yesmaximal, complemented
4#23752564C211yesmaximal, characteristic, complemented
5#23752522C212yesmaximal, complemented
6#23752426C212yesmaximal
7#23752418C211yesmaximal, characteristic, complemented
8#23752336C211yesmaximal, characteristic, complemented
9#23752299C212yesmaximal, complemented
10C4×#14558989C211yesmaximal, characteristic
11#476×C151C211yesmaximal, characteristic, complemented
12C2×#14558993C2212yes—
13C2×#14558989C2211yescharacteristic
14#18012739C2211yescharacteristic
15#18012732—22no—
16#18012730C2212yes—
17#18012726C2212yes—
18#18012719—21no—
19#18012718—21no—
20#18012715—22no—
21C4×Dic302C2211yescharacteristic
22#18012704C2212yes—
23C4×D604C2211yescharacteristic
24#18012701C2212yes—
25#18012698—21no—
26C4⋊C4×D151—21no—
27#18012672C2211yescharacteristic
28Dic151⋊C8C2212yes—
29#18012664C2212yes—
30#18012662C2212yes—
31#18012662C2212yes—
32#18012660C2211yescharacteristic
33#18012659C2211yescharacteristic
34C4×C151⋊C8C2211yescharacteristic
35C8×Dic151C2212yes—
36C4⋊Q8×C151C2211yescharacteristic
37C4×D4×C151C2211yescharacteristic
38#106×C151C2212yes—
39C4⋊C8×C151C2211yescharacteristic
40#102×C151C2212yes—
41C2×Dic302D411yescharacteristic
42C2×Dic302C2312yes—
43C2×D604C2311yescharacteristic
44C2×C4×D151—22no—
45C2×C4×D151—21no—
46#14558993—24no—
47#14558989—22no—
48C2×C151⋊C8C2311yescharacteristic
49C2×C151⋊C8C2311yescharacteristic
50C4⋊Dic151—22no—
51C4⋊Dic151—21no—
52C4⋊Dic151—21no—
53C4⋊Dic151D411yescharacteristic
54C4⋊Dic151C2311yescharacteristic
55Dic151⋊C4—22no—
56Dic151⋊C4—22no—
57Dic151⋊C4D412yes—
58C22⋊Dic151—22no—
59C22⋊Dic151—22no—
60(C2×D151)⋊C4—22no—
61(C2×D151)⋊C4—21no—
62C4×Dic151—22no—
63C4×Dic151C2312yes—
64C2×Q8×C151—21no—
65C2×D4×C151C2311yescharacteristic
66C22×C4×C151—21no—
67C2×C8×C151C2312yes—
68C4⋊C4×C151—21no—
69C4⋊C4×C151C2311yescharacteristic
70C4⋊C4×C151C2312yes—
71C22⋊C4×C151—21no—
72C42×C151C2311yescharacteristic
73C22×D151—21no—
74Dic302—22no—
75Dic302—22no—
76Dic302—22no—
77D604—21no—
78D604#4112yes—
79C2×Dic151—22no—
80C2×Dic151—21no—
81C2×Dic151C2×D412yes—
82C2×Dic151C2×D412yes—
83C4×D151—42no—
84C4×D151—82no—
85C151⋊C8—21no—
86C151⋊C8—21no—
87C23×C151—21no—
88Q8×C151—81no—
89D4×C151—21no—
90D4×C151—21no—
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—41no—
99C22×C151—41no—
100C22×C151—41no—
101C22×C151C22×D411yescharacteristic
102C2×D151—22no—
103C2×D151—41no—
104C2×D151—41no—
105C4×C151—21no—
106C4×C151—41no—
107C4×C151—42no—
108C4×C151#13512yes—
109C4×C151C2×#4111yescharacteristic
110C4×C1512−1+411yescharacteristic
111Dic151—22no—
112Dic151—22no—
113Dic151—42no—
114Dic151—41no—
115C2×C151—81no—
116C2×C151#54811yescharacteristic
117C2×C151C2×#13511yescharacteristic
118C2×C151#57711yescharacteristic
119D151—42no—
120C151#336011yescharacteristic, complemented, Sylow
121#3360—1511nomaximal, Sylow
122#556—1511no—
123#554—1511no—
124#488—1512no—
125#487—1511no—
126#479—1512no—
127#476D15111yescharacteristic, complemented
128#463—1512no—
129#461—1511no—
130C8×Q8—1511no—
131C4×SD16—1512no—
132C4×D8—1511no—
133C2×SD16—1512no—
134C2×D8—1511no—
135C4⋊Q8—1511no—
136C4⋊Q8C2×D15111yescharacteristic
137#126—3022no—
138#125—1512no—
139#124—1512no—
140C22⋊Q8—3021no—
141C22⋊Q8—3021no—
142C22⋊Q8—3022no—
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#106C2×D15112yes—
152C4⋊C8—1512no—
153C4⋊C8C2×D15111yescharacteristic
154#103—1512no—
155#103—1512no—
156#103—1512no—
157#102—1511no—
158#102—1511no—
159#102C2×D15112yes—
160C4×C8—1512no—
161C4×C8—1511no—
162C2×Q8—21no—
163C2×Q8—1512no—
164C2×Q8—1511no—
165C2×D4—1511no—
166C2×D4C22×D15111yescharacteristic
167C22×C4—21no—
168C22×C4—3022no—
169C22×C4—3021no—
170SD16—3024no—
171D8—3022no—
172C2×C8—1511no—
173C2×C8—1511no—
174C2×C8C22×D15112yes—
175C4⋊C4—21no—
176C4⋊C4—3022no—
177C4⋊C4—3022no—
178C4⋊C4—3022no—
179C4⋊C4—3021no—
180C4⋊C4—3021no—
181C4⋊C4—1511no—
182C4⋊C4—1512no—
183C4⋊C4—1511no—
184C4⋊C4C22×D15111yescharacteristic
185C4⋊C4C22×D15112yes—
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—81no—
197Q8—3022no—
198Q8—3022no—
199Q8—3022no—
200D4—21no—
201D4—21no—
202D4—3021no—
203D4—1512no—
204C2×C4—21no—
205C2×C4—22no—
206C2×C4—42no—
207C2×C4—3022no—
208C2×C4—3021no—
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—41no—
220C22—41no—
221C22—41no—
222C22—3022no—
223C22—6041no—
224C22—6041no—
225C22C2×D4×D15111yescharacteristic
226C4—21no—
227C4—41no—
228C4—42no—
229C4—3022no—
230C4—3022no—
231C4—6041no—
232C4—6042no—
233C4#1801276012yes—
234C4#41×D15111yescharacteristic
235C4#1801278711yescharacteristic
236C2—81no—
237C2—6042no—
238C2#2375287211yescharacteristic
239C2C2×#1801276011yescharacteristic
240C2#2375302211yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#476×C151C2
socleC22×C151C22×D4
prime radicalC2×#14558989C22
hypercenter#476D151
hypocenterC151#3360
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
1. #23752932C2semidirect
2. #23752923C2semidirect
3. #23752565C2semidirect
4. #23752564C2semidirect
5. #23752522C2semidirect
7. #23752418C2semidirect
8. #23752336C2semidirect
9. #23752299C2semidirect
11. #476×C151C2semidirect
120. C151#3360semidirect
127. #476D151semidirect

Maximal subgroups

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

subgroupindex
#237529322
#237529232
#237525652
#237525642
#237525222
#237524262
#237524182
#237523362
#237522992
C4×#145589892
#476×C1512
#3360151