Finite Group Databasebeta

← #34081827

Subgroups — #34081827

Order 19328.

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

normal subgroups only

This group has 372 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#23752877C211yesmaximal, characteristic, complemented
3#23752570C212yesmaximal, complemented
4#23752564C211yesmaximal, characteristic, complemented
5#23752506C212yesmaximal, complemented
6#23752426C212yesmaximal
7#23752418C211yesmaximal, characteristic, complemented
8#23752339C211yesmaximal, characteristic, complemented
9#23752311C212yesmaximal, complemented
10C4×#14558989C211yesmaximal, characteristic
11#474×C151C211yesmaximal, characteristic, complemented
12C2×Q8×D151—21no—
13C2×#14558993C2212yes—
14C2×#14558989C2211yescharacteristic
15#18012739C2211yescharacteristic
16#18012738C2212yes—
17#18012732—22no—
18#18012726C2212yes—
19#18012718—21no—
20#18012717—22no—
21#18012715—21no—
22C4×Dic302C2211yescharacteristic
23#18012704C2212yes—
24C4×D604C2211yescharacteristic
25#18012701C2212yes—
26#18012698—21no—
27#18012672C2211yescharacteristic
28Dic151⋊C8C2212yes—
29#18012664C2212yes—
30#18012662C2212yes—
31#18012662C2212yes—
32#18012660C2211yescharacteristic
33#18012659C2211yescharacteristic
34#18012649C2212yes—
35C4×C151⋊C8C2211yescharacteristic
36C4⋊Q8×C151C2211yescharacteristic
37C4×D4×C151C2211yescharacteristic
38#107×C151C2212yes—
39C4⋊C8×C151C2211yescharacteristic
40#102×C151C2212yes—
41C2×Dic302—22no—
42C2×Dic302D411yescharacteristic
43C2×Dic302C2312yes—
44Q8×D151—44no—
45C2×D604C2311yescharacteristic
46C2×C4×D151—22no—
47C2×C4×D151—21no—
48#14558993—24no—
49#14558989—22no—
50C2×C151⋊C8C2311yescharacteristic
51C2×C151⋊C8C2311yescharacteristic
52C4⋊Dic151—21no—
53C4⋊Dic151—21no—
54C4⋊Dic151D411yescharacteristic
55C4⋊Dic151C2311yescharacteristic
56Dic151⋊C4—22no—
57Dic151⋊C4—22no—
58Dic151⋊C4D412yes—
59C22⋊Dic151—22no—
60C22⋊Dic151—22no—
61(C2×D151)⋊C4—22no—
62(C2×D151)⋊C4—21no—
63C4×Dic151—22no—
64C4×Dic151C2312yes—
65C2×Q8×C151—21no—
66C2×D4×C151C2311yescharacteristic
67C22×C4×C151—21no—
68C2×C8×C151C2312yes—
69C4⋊C4×C151—21no—
70C4⋊C4×C151C2311yescharacteristic
71C4⋊C4×C151C2312yes—
72C22⋊C4×C151—21no—
73C42×C151C2311yescharacteristic
74C22×D151—21no—
75Dic302—22no—
76Dic302—22no—
77Dic302—22no—
78Dic302—44no—
79D604—21no—
80D604#4112yes—
81C2×Dic151—22no—
82C2×Dic151—21no—
83C2×Dic151C2×D412yes—
84C2×Dic151C2×D412yes—
85C4×D151—44no—
86C4×D151—42no—
87C151⋊C8—21no—
88C151⋊C8—21no—
89C23×C151—21no—
90Q8×C151—42no—
91D4×C151—21no—
92D4×C151—21no—
93C2×C4×C151—22no—
94C2×C4×C151—21no—
95C2×C4×C151—42no—
96C2×C4×C151C2×D411yescharacteristic
97C2×C4×C151C2×D411yescharacteristic
98C2×C4×C151C2411yescharacteristic
99C8×C151—22no—
100C22×C151—41no—
101C22×C151—41no—
102C22×C151—41no—
103C22×C151C22×D411yescharacteristic
104C2×D151—22no—
105C2×D151—41no—
106C2×D151—41no—
107C4×C151—21no—
108C4×C151—41no—
109C4×C151—42no—
110C4×C151AGL(1,ℤ/8)12yes—
111C4×C151C2×#4111yescharacteristic
112C4×C1512−1+411yescharacteristic
113Dic151—22no—
114Dic151—22no—
115Dic151—42no—
116Dic151—41no—
117C2×C151—81no—
118C2×C151#54811yescharacteristic
119C2×C151C2×AGL(1,ℤ/8)11yescharacteristic
120C2×C151#57811yescharacteristic
121D151—42no—
122C151#336711yescharacteristic, complemented, Sylow
123#3367—1511nomaximal, Sylow
124#556—1511no—
125D4×Q8—1511no—
126#489—1512no—
127#487—1511no—
128#477—1512no—
129#474D15111yescharacteristic, complemented
130#463—1512no—
131#461—1511no—
132#446—1511no—
133#440—1512no—
134C4×D8—1511no—
135C22×Q8—3021no—
136C2×SD16—1512no—
137C2×D8—1511no—
138C4⋊Q8—1512no—
139C4⋊Q8—1511no—
140C4⋊Q8C2×D15111yescharacteristic
141#126—3022no—
142#124—1512no—
143C22⋊Q8—3022no—
144C22⋊Q8—3021no—
145C22⋊Q8—3021no—
146C4×Q8—1512no—
147C4×Q8—1511no—
148C4×D4—1512no—
149C4×D4—1511no—
150C4×D4C2×D15111yescharacteristic
151#117—3021no—
152#107—1511no—
153#107C2×D15112yes—
154C4⋊C8—1512no—
155C4⋊C8C2×D15111yescharacteristic
156#103—1512no—
157#103—1512no—
158#103—1512no—
159#102—1511no—
160#102—1511no—
161#102C2×D15112yes—
162#97—1512no—
163C4×C8—1511no—
164C2×Q8—21no—
165C2×Q8—3022no—
166C2×Q8—6044no—
167C2×Q8—1512no—
168C2×Q8—1511no—
169C2×D4—1511no—
170C2×D4C22×D15111yescharacteristic
171C22×C4—21no—
172C22×C4—3022no—
173C22×C4—3021no—
174SD16—3024no—
175D8—3022no—
176C2×C8—1511no—
177C2×C8—1511no—
178C2×C8C22×D15112yes—
179C4⋊C4—21no—
180C4⋊C4—3022no—
181C4⋊C4—3022no—
182C4⋊C4—3021no—
183C4⋊C4—3021no—
184C4⋊C4—1511no—
185C4⋊C4—1512no—
186C4⋊C4—1511no—
187C4⋊C4C22×D15111yescharacteristic
188C4⋊C4C22×D15112yes—
189C22⋊C4—21no—
190C22⋊C4—3022no—
191C22⋊C4—3022no—
192C22⋊C4—3022no—
193C22⋊C4—3021no—
194C42—3022no—
195C42—1512no—
196C42C22×D15111yescharacteristic
197C23—21no—
198C23—3021no—
199Q8—42no—
200Q8—3022no—
201Q8—3022no—
202Q8—3022no—
203Q8—6044no—
204D4—21no—
205D4—21no—
206D4—3021no—
207D4—1512no—
208C2×C4—21no—
209C2×C4—22no—
210C2×C4—42no—
211C2×C4—3022no—
212C2×C4—3021no—
213C2×C4—6044no—
214C2×C4—6042no—
215C2×C4—1512no—
216C2×C4—1512no—
217C2×C4D4×D15111yescharacteristic
218C2×C4D4×D15111yescharacteristic
219C2×C4C23×D15111yescharacteristic
220C8—22no—
221C8—3021no—
222C8—3021no—
223C22—41no—
224C22—41no—
225C22—41no—
226C22—3022no—
227C22—6041no—
228C22—6041no—
229C22C2×D4×D15111yescharacteristic
230C4—21no—
231C4—41no—
232C4—42no—
233C4—3022no—
234C4—3022no—
235C4—6041no—
236C4—6042no—
237C4#1801276312yes—
238C4#41×D15111yescharacteristic
239C4#1801278711yescharacteristic
240C2—81no—
241C2—6042no—
242C2#2375287211yescharacteristic
243C2C2×#1801276311yescharacteristic
244C2#2375302811yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#474×C151C2
socleC22×C151C22×D4
prime radicalC2×#14558989C22
hypercenter#474D151
hypocenterC151#3367
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #23752932C2semidirect
2. #23752877C2semidirect
3. #23752570C2semidirect
4. #23752564C2semidirect
5. #23752506C2semidirect
7. #23752418C2semidirect
8. #23752339C2semidirect
9. #23752311C2semidirect
11. #474×C151C2semidirect
122. C151#3367semidirect
129. #474D151semidirect

Maximal subgroups

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

subgroupindex
#237529322
#237528772
#237525702
#237525642
#237525062
#237524262
#237524182
#237523392
#237523112
C4×#145589892
#474×C1512
#3367151