Finite Group Databasebeta

← #34079401

Subgroups — #34079401

Order 19328.

382 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 125 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#23752817C211yesmaximal, characteristic
2#23752536C212yesmaximal, complemented
3#23752519C212yesmaximal, complemented
4#23752412C212yesmaximal, complemented
5#23752351C212yesmaximal, complemented
6#23752310C212yesmaximal, complemented
7C4×#14558991C212yesmaximal, complemented
8#23752273C211yesmaximal, characteristic, complemented
9#519×C151C211yesmaximal, characteristic, complemented
10C2×#14558991C2212yes—
11C2×#14558991C2212yes—
12#18012736C2211yescharacteristic
13#18012731C2211yescharacteristic
14#18012724—22no—
15#18012713C2212yes—
16#18012712—22no—
17C4×D604C2212yes—
18#18012672C2212yes—
19#18012670C2212yes—
20C4⋊(C151⋊C8)C2212yes—
21#18012663C2212yes—
22#18012663C2212yes—
23#18012659C2212yes—
24#18012659C2212yes—
25C22⋊(C151⋊C8)C2212yes—
26#18012650C2211yescharacteristic
27C4×C151⋊C8C2211yescharacteristic
28C22×Q8×C151C2211yescharacteristic
29C4×Q8×C151—22no—
30C4×Q8×C151C2212yes—
31C4×Q8×C151C2212yes—
32#117×C151—22no—
33#117×C151C2211yescharacteristic
34#117×C151C2211yescharacteristic
35C2×D604—22no—
36C2×D604C2312yes—
37C2×C22⋊D151—22no—
38C2×C4×D151—22no—
39#14558991—24no—
40#14558991—24no—
41C2×C151⋊C8C2312yes—
42C2×C151⋊C8C2312yes—
43C4⋊Dic151C2312yes—
44Dic151⋊C4—22no—
45(C2×D151)⋊C4—22no—
46(C2×D151)⋊C4—22no—
47C2×Q8×C151—24no—
48C2×Q8×C151—21no—
49C2×Q8×C151C2312yes—
50C22×C4×C151—21no—
51C22×C4×C151C2311yescharacteristic
52C4⋊C4×C151—22no—
53C4⋊C4×C151—22no—
54C4⋊C4×C151D412yes—
55C4⋊C4×C151C2312yes—
56C22⋊C4×C151—21no—
57C22⋊C4×C151D412yes—
58C42×C151—22no—
59C42×C151—22no—
60C42×C151—21no—
61C42×C151C2311yescharacteristic
62C42×C151C2311yescharacteristic
63C22×D151—22no—
64D604—22no—
65D604—22no—
66D604—82no—
67C22⋊D151—82no—
68C2×Dic151—22no—
69C4×D151—82no—
70C151⋊C8—22no—
71C151⋊C8—22no—
72C23×C151C2×D411yescharacteristic
73Q8×C151—24no—
74Q8×C151—22no—
75Q8×C151#4114yes—
76C2×C4×C151—24no—
77C2×C4×C151—22no—
78C2×C4×C151—22no—
79C2×C4×C151—22no—
80C2×C4×C151C2×D411yescharacteristic
81C2×C4×C151C2×D412yes—
82C2×C4×C151C2×D412yes—
83C2×C4×C151C2411yescharacteristic
84C22×C151—21no—
85C22×C151—22no—
86C22×C151C22×D411yescharacteristic
87C2×D151—42no—
88C2×D151—42no—
89C2×D151—42no—
90C4×C151—24no—
91C4×C151—21no—
92C4×C151—22no—
93C4×C151—22no—
94C4×C151—42no—
95C4×C151C2×#4112yes—
96Dic151—42no—
97C2×C151—41no—
98C2×C151#52511yescharacteristic
99C2×C151#57712yes—
100D151—82no—
101C151#312611yescharacteristic, complemented, Sylow
102#3126—1511nomaximal, Sylow
103#540—1511no—
104#519D15111yescharacteristic, complemented
105#482—1512no—
106#479—1512no—
107#460—1512no—
108#448—1512no—
109#440—1512no—
110C4×SD16—1512no—
111#433—1511no—
112C22×Q8C2×D15111yescharacteristic
113C2×SD16—1512no—
114C2×SD16—1512no—
115#127—1511no—
116#125—1511no—
117#123—3022no—
118#121—3022no—
119#121—1512no—
120C4×Q8—22no—
121C4×Q8C2×D15112yes—
122C4×Q8C2×D15112yes—
123C4×D4—1512no—
124#117—22no—
125#117C2×D15111yescharacteristic
126#117C2×D15111yescharacteristic
127#107—1512no—
128#106—1512no—
129C4⋊C8—1512no—
130#103—1512no—
131#103—1512no—
132#102—1512no—
133#102—1512no—
134C22⋊C8—1512no—
135#97—1511no—
136C4×C8—1511no—
137C2×Q8—24no—
138C2×Q8—21no—
139C2×Q8C22×D15112yes—
140C2×D4—3022no—
141C2×D4—3022no—
142C2×D4—1512no—
143C22×C4—21no—
144C22×C4—3022no—
145C22×C4C22×D15111yescharacteristic
146SD16—3024no—
147SD16—3024no—
148C2×C8—1512no—
149C2×C8—1512no—
150C4⋊C4—22no—
151C4⋊C4—22no—
152C4⋊C4—3022no—
153C4⋊C4—1512no—
154C4⋊C4C22⋊D15112yes—
155C4⋊C4C22×D15112yes—
156C22⋊C4—21no—
157C22⋊C4—3022no—
158C22⋊C4—3022no—
159C22⋊C4C22⋊D15112yes—
160C42—22no—
161C42—22no—
162C42—21no—
163C42C22×D15111yescharacteristic
164C42C22×D15111yescharacteristic
165C23—3022no—
166C23C2×C22⋊D15111yescharacteristic
167Q8—24no—
168Q8—22no—
169Q8#1455900414yes—
170D4—3022no—
171D4—3022no—
172D4—12082no—
173D4—12082no—
174C2×C4—24no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—3022no—
179C2×C4—12082no—
180C2×C4C2×C22⋊D15112yes—
181C2×C4C2×C22⋊D15112yes—
182C2×C4C2×C22⋊D15111yescharacteristic
183C2×C4C23×D15111yescharacteristic
184C8—3022no—
185C8—3022no—
186C22—21no—
187C22—22no—
188C22—6042no—
189C22—6042no—
190C22—6042no—
191C22C22×C22⋊D15111yescharacteristic
192C4—24no—
193C4—21no—
194C4—22no—
195C4—22no—
196C4—42no—
197C4—6042no—
198C4C2×#1455900412yes—
199C2—41no—
200C2—12082no—
201C2#2375272311yescharacteristic
202C2#2375302012yes—
subgroupG/H
centerC22C22×C22⋊D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#519×C151C2
socleC22×C151C22×D4
prime radical#23752817C2
hypercenter#519D151
hypocenterC151#3126
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ #117 ◁ #519

Complements

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

NH ≅ G/Ntype
2. #23752536C2semidirect
3. #23752519C2semidirect
4. #23752412C2semidirect
5. #23752351C2semidirect
6. #23752310C2semidirect
7. C4×#14558991C2semidirect
8. #23752273C2semidirect
9. #519×C151C2semidirect
101. C151#3126semidirect
104. #519D151semidirect

Maximal subgroups

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

subgroupindex
#237528172
#237525362
#237525192
#237524122
#237523512
#237523102
C4×#145589912
#237522732
#519×C1512
#3126151