Finite Group Databasebeta

← #34070340

Subgroups — #34070340

Order 19328.

290 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 67 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#23752793C211yesmaximal, characteristic
2C2×#18012665C212yesmaximal, complemented
3#23752214C212yesmaximal, complemented
4#23752077C211yesmaximal, characteristic, complemented
5#343×C151C211yesmaximal, characteristic, complemented
6C2×#14559004C2212yes—
7#18012719—22no—
8#18012714—22no—
9#18012713—22no—
10C2×C4⋊Dic151C2211yescharacteristic
11C2×C4×Dic151C2211yescharacteristic
12#18012665—24no—
13#18012664—22no—
14#18012661—22no—
15C151⋊#95—22no—
16C2×M16×C151C2212yes—
17C2×C4⋊C4×C151C2211yescharacteristic
18#14559004—22no—
19#14559004—22no—
20#14559004—22no—
21#14559004—22no—
22C2×Dic302D412yes—
23C2×D604—22no—
24C2×D604D412yes—
25C2×C22⋊D151—22no—
26C22×Dic151—21no—
27C22×Dic151—21no—
28C2×C4×D151—22no—
29C4⋊Dic151—22no—
30C4⋊Dic151—22no—
31(C2×D151)⋊C4—24no—
32C4×Dic151—21no—
33C4×Dic151D412yescomplemented
34C22×C4×C151D412yes—
35C22×C4×C151C2311yescharacteristic
36M16×C151—22no—
37M16×C151—22no—
38C2×C8×C151—22no—
39C4⋊C4×C151—22no—
40C22×D151—22no—
41Dic302—22no—
42Dic302—22no—
43D604—22no—
44D604—22no—
45D604—82no—
46C22⋊D151—42no—
47C22⋊D151—42no—
48C2×Dic151—22no—
49C2×Dic151—22no—
50C2×Dic151—41no—
51C2×Dic151—41no—
52C2×Dic151—42no—
53C2×Dic151—41no—
54C4×D151—42no—
55C4×D151—42no—
56C23×C151C2×D411yescharacteristic
57C2×C4×C151—22no—
58C2×C4×C151—42no—
59C2×C4×C151C2×D411yescharacteristic
60C2×C4×C151C2×D412yes—
61C2×C4×C151#4112yes—
62C2×C4×C151#4111yescharacteristic
63C8×C151—42no—
64C22×C151—21no—
65C22×C151—21no—
66C22×C151#12011yescharacteristic
67C22×C151#12111yescharacteristic
68C22×C151#12411yescharacteristic
69C2×D151—42no—
70C2×D151—42no—
71C2×D151—42no—
72C4×C151—42no—
73C4×C151#12112yes—
74C4×C151#12312yes—
75Dic151—42no—
76Dic151—42no—
77Dic151—81no—
78C2×C151—21no—
79C2×C151—21no—
80C2×C151#39411yescharacteristic
81C2×C151#45411yescharacteristic
82C2×C151#45511yescharacteristic
83D151—82no—
84C151#204011yescharacteristic, complemented, Sylow
85#2040—1511nomaximal, Sylow
86#537—1511no—
87C2×#104—1512no—
88#417—1512no—
89#382—1511no—
90#343D15111yescharacteristic, complemented
91C2×#41—1512no—
92C2×M16C2×D15112yes—
93C22⋊Q8—3022no—
94#121—3022no—
95#121—3022no—
96C2×C4⋊C4—1511no—
97C2×C4⋊C4C2×D15111yescharacteristic
98C2×C42—1511no—
99#104—3024no—
100#103—3022no—
101#102—3022no—
102#95—3022no—
103#41—3022no—
104#41—3022no—
105#41—3022no—
106#41—3022no—
107C2×Q8—1512no—
108C2×D4—3022no—
109C2×D4—3022no—
110C2×D4—1512no—
111C22×C4—3021no—
112C22×C4—3022no—
113C22×C4—3021no—
114C22×C4D60412yes—
115C22×C4C22×D15111yescharacteristic
116M16—22no—
117M16—22no—
118C2×C8—22no—
119C4⋊C4—22no—
120C4⋊C4—3022no—
121C4⋊C4—3022no—
122C22⋊C4—3024no—
123C42—3021no—
124C42—1512no—
125C23—3022no—
126C23C2×D60411yescharacteristic
127Q8—3022no—
128Q8—3022no—
129D4—3022no—
130D4—3022no—
131D4—6042no—
132D4—6042no—
133D4—12082no—
134C2×C4—22no—
135C2×C4—42no—
136C2×C4—3022no—
137C2×C4—3022no—
138C2×C4—6041no—
139C2×C4—6041no—
140C2×C4—6042no—
141C2×C4—6042no—
142C2×C4—6042no—
143C2×C4—6041no—
144C2×C4D4×D15111yescharacteristic
145C2×C4D4×D15112yes—
146C2×C4#1455900412yes—
147C2×C4#1455900511yescharacteristic
148C8—42no—
149C22—21no—
150C22—21no—
151C22—6042no—
152C22—6042no—
153C22—6042no—
154C22#1801270911yescharacteristic
155C22#1801271411yescharacteristic
156C22#1801272711yescharacteristic
157C4—42no—
158C4—6042no—
159C4—6042no—
160C4—12081no—
161C4#1801271212yes—
162C4#1801272412yes—
163C2—21no—
164C2—21no—
165C2—12082no—
166C2#2375213011yescharacteristic
167C2#2375238711yescharacteristic
168C2#2375239211yescharacteristic
subgroupG/H
centerC22#18012709
commutator, cosocleC22×C4×C151C23
FrattiniC22×C4C22×D151
Fitting#343×C151C2
socleC22×C151#120
prime radical#23752793C2
hypercenter#343D151
hypocenterC151#2040
LCSG ▷ C22×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
2. C2×#18012665C2semidirect
3. #23752214C2semidirect
4. #23752077C2semidirect
5. #343×C151C2semidirect
33. C4×Dic151D4semidirect
84. C151#2040semidirect
90. #343D151semidirect

Maximal subgroups

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

subgroupindex
#237527932
C2×#180126652
#237522142
#237520772
#343×C1512
#2040151