Finite Group Databasebeta

← #34069631

Subgroups — #34069631

Order 19328.

312 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 79 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#23752978C211yesmaximal, characteristic
2#23752788C211yesmaximal, characteristic
3#23752222C211yesmaximal, characteristic, complemented
4#23752220C211yesmaximal, characteristic, complemented
5#23752185C211yesmaximal, characteristic
6#23751968C211yesmaximal, characteristic, complemented
7H(3,ℤ/4)×C151C211yesmaximal, characteristic, complemented
8C2×#14559004C2211yescharacteristic
9C22×Dic302C2211yescharacteristic
10#18012747—22no—
11#18012745—22no—
12C2×#14558988C2211yescharacteristic
13M16×D151—22no—
14#18012739C412yescomplemented
15#18012727C412yescomplemented
16#18012723—22no—
17#18012719—22no—
18#18012698C2211yescharacteristic
19#18012664—22no—
20#18012662—22no—
21#18012653—22no—
22C2×M16×C151C2211yescharacteristic
23#117×C151C2211yescharacteristic
24#117×C151C2211yescharacteristic
25#14559004—21no—
26#14559004—21no—
27#14559004—21no—
28#14559004—21no—
29C2×Dic302—21no—
30C2×Dic302—21no—
31C2×Dic302—21no—
32C2×Dic302—21no—
33C2×Dic302—21no—
34C2×Dic302C2×C412yes—
35C2×Dic302C2×C411yescharacteristic
36C2×D604C2×C411yescharacteristic
37C2×C22⋊D151D412yes—
38C22×Dic151—21no—
39C2×C4×D151D412yes—
40#14558988—21no—
41#14558988—21no—
42#14558987—24no—
43C2×C151⋊C8D412yes—
44C8×D151—24no—
45C4⋊Dic151—24no—
46C4⋊Dic151—21no—
47C22⋊Dic151—21no—
48(C2×D151)⋊C4—24no—
49C4×Dic151—21no—
50C22×C4×C151C2311yescharacteristic
51M16×C151—21no—
52M16×C151—21no—
53C2×C8×C151D412yes—
54C4⋊C4×C151—21no—
55C4⋊C4×C151—21no—
56C22⋊C4×C151—21no—
57C22⋊C4×C151—21no—
58C42×C151—21no—
59C42×C151C2×C412yes—
60C22×D151C22⋊C412yes—
61Dic302—21no—
62Dic302—21no—
63Dic302—22no—
64Dic302—22no—
65Dic302—41no—
66Dic302—41no—
67D604—21no—
68D604—21no—
69C22⋊D151—22no—
70C22⋊D151—22no—
71C2×Dic151—22no—
72C2×Dic151—41no—
73C2×Dic151—41no—
74C2×Dic151—41no—
75C2×Dic151C22⋊C412yes—
76C4×D151—22no—
77C4×D151—22no—
78C151⋊C8—22no—
79C23×C151C2×D411yescharacteristic
80C2×C4×C151—22no—
81C2×C4×C151—41no—
82C2×C4×C151C22×C411yescharacteristic
83C2×C4×C151C2×D411yescharacteristic
84C2×C4×C151C2×D411yescharacteristic
85C2×C4×C151C2×D411yescharacteristic
86C2×C4×C151#4111yescharacteristic
87C2×C4×C151#4111yescharacteristic
88C8×C151—22no—
89C22×C151—41no—
90C22×C151C2×C22⋊C411yescharacteristic
91C22×C151#12111yescharacteristic
92C22×C151#12111yescharacteristic
93C2×D151—22no—
94C2×D151—42no—
95C4×C151—42no—
96C4×C151—81no—
97C4×C151C4×D411yescharacteristic
98C4×C151C4×D411yescharacteristic
99C4×C151#12011yescharacteristic
100C4×C151#12311yescharacteristic
101Dic151—22no—
102Dic151—42no—
103Dic151—81no—
104C2×C151—21no—
105C2×C151—21no—
106C2×C151—21no—
107C2×C151#38611yescharacteristic
108D151—42no—
109C151#190911yescharacteristic, complemented, Sylow
110#1909—1511nomaximal, Sylow
111#568—1511no—
112#536—1511no—
113#419—1511no—
114#419—1511no—
115#410—1511no—
116H(3,ℤ/4)—1511no—
117H(3,ℤ/4)D15111yescharacteristic, complemented
118C2×#41—1511no—
119C22×Q8—1511no—
120#131—3022no—
121#131—3022no—
122C2×M16—3022no—
123C2×M16—1511no—
124C2×M16C2×D15111yescharacteristic
125C4⋊Q8—1512no—
126#124—1512no—
127#123—3022no—
128C22⋊Q8—3022no—
129#117—1511no—
130#117C2×D15111yescharacteristic
131#117C2×D15111yescharacteristic
132#103—3022no—
133#103—3022no—
134#99—3022no—
135#41—3021no—
136#41—3021no—
137#41—3021no—
138#41—3021no—
139C2×Q8—3021no—
140C2×Q8—3021no—
141C2×Q8—3021no—
142C2×Q8—3021no—
143C2×Q8—3021no—
144C2×Q8—1512no—
145C2×Q8—1511no—
146C2×D4—1512no—
147C2×D4—1511no—
148C22×C4—3021no—
149C22×C4—1512no—
150C22×C4C22×D15111yescharacteristic
151M16—21no—
152M16—21no—
153M16—3024no—
154M16—3021no—
155M16—3021no—
156C2×C8—3024no—
157C2×C8—1512no—
158C2×C8D60412yes—
159C4⋊C4—21no—
160C4⋊C4—21no—
161C4⋊C4—3024no—
162C4⋊C4—3021no—
163C22⋊C4—21no—
164C22⋊C4—21no—
165C22⋊C4—3024no—
166C22⋊C4—3021no—
167C42—21no—
168C42—3021no—
169C42C4×D15112yes—
170C23—1512no—
171C23D4×D15111yescharacteristic
172Q8—3021no—
173Q8—3021no—
174Q8—3022no—
175Q8—3022no—
176Q8—6041no—
177Q8—6041no—
178D4—3022no—
179D4—3022no—
180D4—3021no—
181D4—3021no—
182C2×C4—22no—
183C2×C4—41no—
184C2×C4—3022no—
185C2×C4—3022no—
186C2×C4—3022no—
187C2×C4—6041no—
188C2×C4—6041no—
189C2×C4—6041no—
190C2×C4—1512no—
191C2×C4C2×C4×D15111yescharacteristic
192C2×C4D4×D15111yescharacteristic
193C2×C4D4×D15111yescharacteristic
194C2×C4C2×D60411yescharacteristic
195C2×C4#1455900411yescharacteristic
196C2×C4#1455900511yescharacteristic
197C8—22no—
198C8—3022no—
199C22—41no—
200C22—3022no—
201C22—6042no—
202C22C22⋊C4×D15111yescharacteristic
203C22#1801271211yescharacteristic
204C22#1801271411yescharacteristic
205C4—42no—
206C4—81no—
207C4—3022no—
208C4—6042no—
209C4—12081no—
210C4#1801270111yescharacteristic
211C4C4×D60411yescharacteristic
212C4#1801270911yescharacteristic
213C4#1801272411yescharacteristic
214C2—21no—
215C2—21no—
216C2—21no—
217C2—6042no—
218C2#2375209011yescharacteristic
subgroupG/H
centerC2#23752090
commutatorC2×C4×C151C22×C4
FrattiniC22×C4C22×D151
FittingH(3,ℤ/4)×C151C2
socleC2×C151#386
prime radicalC2×#14559004C22
cosocleC22×C4×C151C23
hypercenterH(3,ℤ/4)D151
hypocenterC151#1909
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2 ◁ C22×C4 ◁ H(3,ℤ/4)

Complements

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

NH ≅ G/Ntype
3. #23752222C2semidirect
4. #23752220C2semidirect
6. #23751968C2semidirect
7. H(3,ℤ/4)×C151C2semidirect
14. #18012739C4semidirect
15. #18012727C4semidirect
109. C151#1909semidirect
117. H(3,ℤ/4)D151semidirect

Maximal subgroups

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

subgroupindex
#237529782
#237527882
#237522222
#237522202
#237521852
#237519682
H(3,ℤ/4)×C1512
#1909151