Finite Group Databasebeta

← #34069968

Subgroups — #34069968

Order 19328.

312 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 103 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
1C22×#14558994C211yesmaximal, characteristic
2C2×#18012672C211yesmaximal, characteristic
3C2×#18012664C211yesmaximal, characteristic
4C2×C8×Dic151C211yesmaximal, characteristic
5#23752119C211yesmaximal, characteristic
6#23752117C211yesmaximal, characteristic
7C2×#103×C151C211yesmaximal, characteristic
8C22×Dic302C2211yescharacteristic
9C2×#14558994—22no—
10C2×#14558994—22no—
11C2×#14558994C414yescomplemented
12C22×C151⋊C8C2211yescharacteristic
13C2×C4⋊Dic151C2211yescharacteristic
14C2×C4×Dic151C2211yescharacteristic
15#18012672—22no—
16#18012664—22no—
17C8×Dic151—22no—
18C151⋊#95—22no—
19C151⋊#95—22no—
20C22×Q8×C151C2211yescharacteristic
21C22×C8×C151C2211yescharacteristic
22C2×C4⋊C4×C151C2211yescharacteristic
23#103×C151—22no—
24C2×Dic302—21no—
25C2×Dic302—21no—
26C2×Dic302—21no—
27C2×Dic302—21no—
28C2×Dic302—21no—
29C2×Dic302C2×C412yes—
30C22×Dic151—21no—
31C22×Dic151—21no—
32C22×Dic151D412yes—
33#14558994—28no—
34C2×C151⋊C8C2×C412yes—
35C2×C151⋊C8D412yes—
36C2×C151⋊C8D412yes—
37C4⋊Dic151—21no—
38C4⋊Dic151—21no—
39C4×Dic151—21no—
40C4×Dic151—21no—
41C2×Q8×C151—21no—
42C2×Q8×C151—21no—
43C2×Q8×C151—21no—
44C2×Q8×C151—21no—
45C2×Q8×C151—21no—
46C2×Q8×C151C2×C412yes—
47C22×C4×C151—21no—
48C22×C4×C151—21no—
49C22×C4×C151C2311yescharacteristic
50C2×C8×C151—21no—
51C2×C8×C151—21no—
52C2×C8×C151D412yes—
53C4⋊C4×C151—21no—
54C4⋊C4×C151—21no—
55Dic302—22no—
56Dic302—22no—
57Dic302—41no—
58Dic302—41no—
59C2×Dic151—22no—
60C2×Dic151—22no—
61C2×Dic151—22no—
62C2×Dic151—41no—
63C2×Dic151—41no—
64C2×Dic151—41no—
65C2×Dic151—42no—
66C2×Dic151Q1614yescomplemented
67C151⋊C8C22⋊C414yes—
68C23×C151C2×D411yescharacteristic
69Q8×C151—22no—
70Q8×C151—22no—
71Q8×C151—41no—
72Q8×C151—41no—
73C2×C4×C151—22no—
74C2×C4×C151—41no—
75C2×C4×C151—41no—
76C2×C4×C151—41no—
77C2×C4×C151—42no—
78C2×C4×C151C22×C411yescharacteristic
79C2×C4×C151C2×D411yescharacteristic
80C2×C4×C151C2×D411yescharacteristic
81C2×C4×C151C2×D411yescharacteristic
82C2×C4×C151#4111yescharacteristic
83C2×C4×C151#4111yescharacteristic
84C8×C151—22no—
85C22×C151C4×D411yescharacteristic
86C22×C151#12111yescharacteristic
87C22×C151#12711yescharacteristic
88C22×C151C2×Q1612yes—
89C22×C151#13512yes—
90C4×C151—42no—
91C4×C151—81no—
92C4×C151C2×C22⋊C411yescharacteristic
93C4×C151C4×D411yescharacteristic
94C4×C151#12111yescharacteristic
95C4×C151#12411yescharacteristic
96Dic151—24no—
97Dic151—42no—
98Dic151—81no—
99C2×C151#39011yescharacteristic
100C2×C151C4×Q1612yes—
101C2×C151#46712yes—
102C2×C151#49411yescharacteristic
103C2×C151#49511yescharacteristic
104C151#196911yescharacteristic, complemented, Sylow
105#1969—1511nomaximal, Sylow
106C22×Q16—1511no—
107C2×#107—1511no—
108C2×#103—1511no—
109C2×#103D15111yescharacteristic
110C2×C4×C8—1511no—
111#391—1511no—
112#391—1511no—
113C22×Q8—1511no—
114C22×Q8C2×D15111yescharacteristic
115C2×Q16—3022no—
116C2×Q16—3022no—
117C2×Q16—1514no—
118C22×C8—1511no—
119C22×C8C2×D15111yescharacteristic
120C2×C4⋊C4—1511no—
121C2×C4⋊C4C2×D15111yescharacteristic
122C2×C42—1511no—
123#107—3022no—
124#103—22no—
125#103—3022no—
126C4×C8—3022no—
127#95—3022no—
128#95—3022no—
129C2×Q8—21no—
130C2×Q8—21no—
131C2×Q8—21no—
132C2×Q8—21no—
133C2×Q8—21no—
134C2×Q8—3021no—
135C2×Q8—3021no—
136C2×Q8—3021no—
137C2×Q8—3021no—
138C2×Q8—3021no—
139C2×Q8—1512no—
140C2×Q8C4×D15112yes—
141C22×C4—21no—
142C22×C4—21no—
143C22×C4—3021no—
144C22×C4—3021no—
145C22×C4—1512no—
146C22×C4C22×D15111yescharacteristic
147Q16—3028no—
148C2×C8—21no—
149C2×C8—21no—
150C2×C8—1512no—
151C2×C8—1512no—
152C2×C8—1512no—
153C2×C8C22⋊D15112yes—
154C4⋊C4—21no—
155C4⋊C4—21no—
156C4⋊C4—3021no—
157C4⋊C4—3021no—
158C42—3021no—
159C42—3021no—
160C23D4×D15111yescharacteristic
161Q8—22no—
162Q8—22no—
163Q8—41no—
164Q8—41no—
165Q8—3022no—
166Q8—3022no—
167Q8—6041no—
168Q8—6041no—
169C2×C4—22no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—42no—
174C2×C4—3022no—
175C2×C4—3022no—
176C2×C4—3022no—
177C2×C4—6041no—
178C2×C4—6041no—
179C2×C4—6041no—
180C2×C4—6042no—
181C2×C4—1514no—
182C2×C4C2×C4×D15111yescharacteristic
183C2×C4D4×D15111yescharacteristic
184C2×C4D4×D15111yescharacteristic
185C2×C4C2×C22⋊D15111yescharacteristic
186C2×C4#1455900311yescharacteristic
187C2×C4#1455900411yescharacteristic
188C8—22no—
189C8—1514no—
190C22(C22⋊D151)⋊C411yescharacteristic
191C22#1801271211yescharacteristic
192C22#1801273511yescharacteristic
193C22Q16×D15112yes—
194C22#1801276012yes—
195C4—42no—
196C4—81no—
197C4—3024no—
198C4—6042no—
199C4—12081no—
200C4C22⋊C4×D15111yescharacteristic
201C4C4×C22⋊D15111yescharacteristic
202C4#1801271111yescharacteristic
203C4#1801272511yescharacteristic
204C2#2375211211yescharacteristic
205C2#2375230412yes—
206C2#2375245212yes—
207C2#2375259011yescharacteristic
208C2#2375259311yescharacteristic
subgroupG/H
centerC23D4×D151
commutatorC2×C4×C151C22×C4
FrattiniC22×C4C22×D151
FittingC2×#103×C151C2
socle, prime radicalC23×C151C2×D4
cosocleC22×C4×C151C23
hypercenterC2×#103D151
hypocenterC151#1969
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
11. C2×#14558994C4semidirect
66. C2×Dic151Q16semidirect
104. C151#1969semidirect

Maximal subgroups

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

subgroupindex
C22×#145589942
C2×#180126722
C2×#180126642
C2×C8×Dic1512
#237521192
#237521172
C2×#103×C1512
#1969151