Finite Group Databasebeta

← #34069528

Subgroups — #34069528

Order 19328.

342 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 89 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#23752719C211yesmaximal, characteristic
2#23752196C211yesmaximal, characteristic, complemented
3#23752175C212yesmaximal, complemented
4#23751983C212yesmaximal, complemented
5#568×C151C211yesmaximal, characteristic, complemented
6C22×C4×D151C2211yescharacteristic
7C2×#14558988C2212yes—
8#18012720C412yes—
9#18012715—21no—
10#18012710—21no—
11#18012707C412yes—
12C4×C22⋊D151—22no—
13#18012698C2211yescharacteristic
14#18012658—21no—
15#18012656—21no—
16(C2×D151)⋊C8—24no—
17C2×#41×C151C2211yescharacteristic
18#131×C151—24no—
19C2×M16×C151—22no—
20C2×M16×C151C2212yes—
21C23×D151C2×C411yescharacteristic
22C2×C22⋊D151—22no—
23C22×Dic151C2×C411yescharacteristic
24C2×C4×D151—21no—
25C2×C4×D151—21no—
26C2×C4×D151—22no—
27C2×C4×D151—22no—
28#14558988—22no—
29#14558988—22no—
30C2×C151⋊C8—22no—
31C4⋊Dic151—21no—
32Dic151⋊C4—22no—
33C22⋊Dic151—22no—
34C22⋊Dic151C2×C412yes—
35(C2×D151)⋊C4—22no—
36C4×Dic151—21no—
37#41×C151—22no—
38#41×C151—22no—
39C2×Q8×C151D411yescharacteristic
40C2×D4×C151C2×C412yes—
41C2×D4×C151D411yescharacteristic
42C22×C4×C151D412yes—
43C22×C4×C151C2311yescharacteristic
44M16×C151—24no—
45M16×C151—22no—
46M16×C151—22no—
47C2×C8×C151—24no—
48C2×C8×C151D414yescomplemented
49C22×D151—21no—
50C22×D151—22no—
51C22×D151—42no—
52C22⋊D151—44no—
53C2×Dic151—22no—
54C2×Dic151—21no—
55C2×Dic151—22no—
56C4×D151—41no—
57C4×D151—42no—
58C4×D151—41no—
59C151⋊C8—42no—
60C23×C151C22⋊C412yes—
61C23×C151C22×C411yescharacteristic
62Q8×C151—22no—
63D4×C151—24no—
64D4×C151—22no—
65C2×C4×C151—22no—
66C2×C4×C151—22no—
67C2×C4×C151C22⋊C412yes—
68C2×C4×C151C2×D412yes—
69C2×C4×C151C2×D411yescharacteristic
70C2×C4×C151C2×D411yescharacteristic
71C2×C4×C151#4112yes—
72C8×C151—24no—
73C22×C151—22no—
74C22×C151—41no—
75C22×C151—42no—
76C22×C151C2×C22⋊C411yescharacteristic
77C22×C151C4×D412yes—
78C2×D151—22no—
79C2×D151—24no—
80C2×D151—41no—
81C2×D151—42no—
82C2×D151—41no—
83C4×C151—22no—
84C4×C151#12011yescharacteristic
85C4×C151#12112yes—
86C4×C151#12311yescharacteristic
87Dic151—42no—
88Dic151—41no—
89C2×C151—21no—
90C2×C151—22no—
91C2×C151—42no—
92C2×C151#38611yescharacteristic
93D151—42no—
94C151#189111yescharacteristic, complemented, Sylow
95#1891—1511nomaximal, Sylow
96#568D15111yescharacteristic, complemented
97#525—1511no—
98#413—1511no—
99#407—1512no—
100#344—1512no—
101C2×#41C2×D15111yescharacteristic
102C23×C4—1511no—
103#131—24no—
104C2×M16—22no—
105C2×M16—1512no—
106C2×M16C2×D15112yes—
107#123—1512no—
108C22⋊Q8—3021no—
109#121—3021no—
110#120—1512no—
111C4×D4—3022no—
112#117—1511no—
113#101—3021no—
114#100—3021no—
115C22⋊C8—3024no—
116C24—1511no—
117#41—22no—
118#41—22no—
119C2×Q8D60411yescharacteristic
120C2×D4—3022no—
121C2×D4C4×D15112yes—
122C2×D4D60411yescharacteristic
123C22×C4—3022no—
124C22×C4—3021no—
125C22×C4—3021no—
126C22×C4—3022no—
127C22×C4—1511no—
128C22×C4C22⋊D15112yes—
129C22×C4C22×D15111yescharacteristic
130M16—24no—
131M16—22no—
132M16—22no—
133M16—3022no—
134M16—3022no—
135C2×C8—24no—
136C2×C8—3022no—
137C2×C8C22⋊D15114yescomplemented
138C4⋊C4—3022no—
139C4⋊C4—3021no—
140C22⋊C4—3022no—
141C22⋊C4—3022no—
142C22⋊C4—1512no—
143C42—3021no—
144C23—3021no—
145C23—3022no—
146C23—6042no—
147C23(C2×D151)⋊C412yes—
148C23C2×C4×D15111yescharacteristic
149Q8—22no—
150D4—24no—
151D4—22no—
152D4—6044no—
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—3022no—
156C2×C4—3021no—
157C2×C4—3022no—
158C2×C4—6041no—
159C2×C4—6042no—
160C2×C4—6041no—
161C2×C4(C2×D151)⋊C412yes—
162C2×C4C2×C22⋊D15112yes—
163C2×C4C2×C22⋊D15111yescharacteristic
164C2×C4C2×D60411yescharacteristic
165C2×C4#1455900412yes—
166C8—24no—
167C8—6042no—
168C22—22no—
169C22—41no—
170C22—42no—
171C22—3022no—
172C22—3024no—
173C22—6041no—
174C22—6042no—
175C22—6041no—
176C22C2×(C2×D151)⋊C411yescharacteristic
177C22C4×C22⋊D15112yes—
178C4—22no—
179C4—6042no—
180C4—6041no—
181C4#1801270811yescharacteristic
182C4#1801271312yes—
183C4#1801272211yescharacteristic
184C2—21no—
185C2—22no—
186C2—42no—
187C2—6042no—
188C2#2375209111yescharacteristic
subgroupG/H
centerC4#18012708
commutatorC23×C151C22×C4
FrattiniC22×C4C22×D151
Fitting#568×C151C2
socleC2×C151#386
prime radical#23752719C2
cosocleC22×C4×C151C23
hypercenter#568D151
hypocenterC151#1891
LCSG ▷ C23×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C4 ◁ C22×C4 ◁ #568

Complements

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

NH ≅ G/Ntype
2. #23752196C2semidirect
3. #23752175C2semidirect
4. #23751983C2semidirect
5. #568×C151C2semidirect
48. C2×C8×C151D4semidirect
94. C151#1891semidirect
96. #568D151semidirect
137. C2×C8C22⋊D151semidirect

Maximal subgroups

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

subgroupindex
#237527192
#237521962
#237521752
#237519832
#568×C1512
#1891151