Finite Group Databasebeta

← #34070152

Subgroups — #34070152

Order 19328.

406 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 75 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
1C2×#18012764C212yesmaximal, complemented
2C2×#18012666C212yesmaximal, complemented
3#23752113C211yesmaximal, characteristic, complemented
4#23751981C211yesmaximal, characteristic, complemented
5#537×C151C211yesmaximal, characteristic, complemented
6C22×D604C2211yescharacteristic
7#18012764—24no—
8#18012764—24no—
9C2×#14558991—22no—
10C2×#14558989—22no—
11C2×#14558988C2212yes—
12C2×(C2×D151)⋊C4—22no—
13C2×C4×Dic151C2211yescharacteristic
14#18012666—24no—
15C2×#41×C151C2212yes—
16C22⋊Q8×C151—22no—
17#121×C151—22no—
18#121×C151—22no—
19C2×C4⋊C4×C151C2211yescharacteristic
20C23×D151—21no—
21C2×D604—22no—
22C2×D604—22no—
23C2×D604—21no—
24C2×D604D412yescomplemented
25C22×Dic151—21no—
26#14558991—28no—
27#14558989—28no—
28#14558988—22no—
29#14558988D414yescomplemented
30C2×C151⋊C8—22no—
31(C2×D151)⋊C4—44no—
32C4×Dic151—22no—
33#41×C151—22no—
34#41×C151—22no—
35#41×C151—22no—
36#41×C151—22no—
37C2×Q8×C151D412yes—
38C2×D4×C151—22no—
39C2×D4×C151—22no—
40C2×D4×C151D412yes—
41C22×C4×C151—22no—
42C22×C4×C151D412yes—
43C22×C4×C151C2311yescharacteristic
44C4⋊C4×C151—22no—
45C4⋊C4×C151—22no—
46C22⋊C4×C151—24no—
47C22×D151—22no—
48C22×D151—42no—
49C22×D151—42no—
50C22×D151—41no—
51C22×D151—41no—
52D604—24no—
53D604—42no—
54C2×Dic151—22no—
55C2×Dic151—41no—
56C2×Dic151—41no—
57C151⋊C8—24no—
58C23×C151—22no—
59C23×C151C2×D411yescharacteristic
60Q8×C151—22no—
61Q8×C151—22no—
62D4×C151—22no—
63D4×C151—22no—
64D4×C151—42no—
65D4×C151—42no—
66D4×C151—82no—
67C2×C4×C151—22no—
68C2×C4×C151—22no—
69C2×C4×C151—42no—
70C2×C4×C151—42no—
71C2×C4×C151—42no—
72C2×C4×C151C2×D411yescharacteristic
73C2×C4×C151C2×D412yes—
74C2×C4×C151C2×D412yes—
75C2×C4×C151#4111yescharacteristic
76C22×C151—21no—
77C22×C151—21no—
78C22×C151—42no—
79C22×C151—42no—
80C22×C151—42no—
81C22×C151#12011yescharacteristic
82C22×C151#12111yescharacteristic
83C22×C151#12711yescharacteristic
84C2×D151—44no—
85C2×D151—42no—
86C2×D151—82no—
87C2×D151—81no—
88C2×D151—81no—
89C4×C151—42no—
90C4×C151—42no—
91C4×C151#12012yes—
92C4×C151#12112yes—
93Dic151—42no—
94C2×C151—21no—
95C2×C151—21no—
96C2×C151—82no—
97C2×C151#39211yescharacteristic
98C2×C151#45311yescharacteristic
99C2×C151#45411yescharacteristic
100D151—82no—
101C151#200611yescharacteristic, complemented, Sylow
102#2006—1511nomaximal, Sylow
103C2×AGL(1,ℤ/8)—1512no—
104#537D15111yescharacteristic, complemented
105C2×#104—1512no—
106#390—1511no—
107#343—1511no—
108C2×#41C2×D15112yes—
109C22×D4—1511no—
110AGL(1,ℤ/8)—3024no—
111AGL(1,ℤ/8)—3024no—
112C2×SD16—3022no—
113C2×D8—3022no—
114C2×M16—1512no—
115C22⋊Q8—22no—
116#121—22no—
117#121—22no—
118C2×C4⋊C4C2×D15111yescharacteristic
119C2×C22⋊C4—3022no—
120C2×C42—1511no—
121#104—3024no—
122C24—3021no—
123#41—22no—
124#41—22no—
125#41—22no—
126#41—22no—
127C2×Q8C22⋊D15112yes—
128C2×D4—22no—
129C2×D4—22no—
130C2×D4—3022no—
131C2×D4—3022no—
132C2×D4—3021no—
133C2×D4—1512no—
134C2×D4C22⋊D15112yes—
135C22×C4—22no—
136C22×C4—3021no—
137C22×C4C22⋊D15112yes—
138C22×C4C22×D15111yescharacteristic
139SD16—3028no—
140D8—3028no—
141M16—3022no—
142M16—1514no—
143C2×C8—3022no—
144C4⋊C4—22no—
145C4⋊C4—22no—
146C22⋊C4—24no—
147C22⋊C4—6044no—
148C42—3022no—
149C23—22no—
150C23—3022no—
151C23—6042no—
152C23—6042no—
153C23—6041no—
154C23—6041no—
155C23C2×C22⋊D15111yescharacteristic
156Q8—22no—
157Q8—22no—
158D4—22no—
159D4—22no—
160D4—42no—
161D4—42no—
162D4—82no—
163D4—3024no—
164D4—6042no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—42no—
168C2×C4—42no—
169C2×C4—42no—
170C2×C4—3022no—
171C2×C4—6041no—
172C2×C4—6041no—
173C2×C4D4×D15111yescharacteristic
174C2×C4D4×D15112yes—
175C2×C4C2×C22⋊D15112yes—
176C2×C4#1455900311yescharacteristic
177C8—3024no—
178C22—21no—
179C22—21no—
180C22—42no—
181C22—42no—
182C22—42no—
183C22—6044no—
184C22—6042no—
185C22—12082no—
186C22—12081no—
187C22—12081no—
188C22#1801270811yescharacteristic
189C22#1801271011yescharacteristic
190C22#1801273511yescharacteristic
191C4—42no—
192C4—42no—
193C4—6042no—
194C4#1801270712yes—
195C4#1801271112yes—
196C2—21no—
197C2—21no—
198C2—82no—
199C2—12082no—
200C2#2375212011yescharacteristic
201C2#2375238011yescharacteristic
202C2#2375238511yescharacteristic
subgroupG/H
centerC22#18012708
commutator, cosocleC22×C4×C151C23
FrattiniC22×C4C22×D151
Fitting#537×C151C2
socleC22×C151#120
hypercenter#537D151
hypocenterC151#2006
LCSG ▷ C22×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #537

Complements

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

NH ≅ G/Ntype
1. C2×#18012764C2semidirect
2. C2×#18012666C2semidirect
3. #23752113C2semidirect
4. #23751981C2semidirect
5. #537×C151C2semidirect
24. C2×D604D4semidirect
29. #14558988D4semidirect
101. C151#2006semidirect
104. #537D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127642
C2×#180126662
#237521132
#237519812
#537×C1512
#2006151