Finite Group Databasebeta

← #34070151

Subgroups — #34070151

Order 19328.

406 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 73 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×#18012765C212yesmaximal, complemented
2#23752793C211yesmaximal, characteristic, complemented
3C2×#18012667C212yesmaximal, complemented
4#23751981C211yesmaximal, characteristic, complemented
5#390×C151C211yesmaximal, characteristic, complemented
6C2×#14559004C2212yes—
7#18012765—24no—
8#18012765—24no—
9C2×#14558992—22no—
10C2×#14558989—22no—
11C2×#14558988C2212yes—
12#18012719—22no—
13#18012714—22no—
14#18012713—22no—
15#18012667—24no—
16C22×D4×C151C2211yescharacteristic
17C2×C4⋊C4×C151C2211yescharacteristic
18C2×C22⋊C4×C151—22no—
19C2×C42×C151C2211yescharacteristic
20#14559004—22no—
21#14559004—22no—
22#14559004—22no—
23#14559004—22no—
24C2×Dic302D412yes—
25C2×D604—22no—
26C2×D604D412yes—
27C2×C22⋊D151—22no—
28C2×C4×D151—22no—
29#14558992—28no—
30#14558989—28no—
31#14558988—22no—
32#14558988D414yescomplemented
33C2×C151⋊C8—22no—
34C4⋊Dic151—22no—
35(C2×D151)⋊C4—24no—
36C24×C151—21no—
37C2×D4×C151—22no—
38C2×D4×C151—22no—
39C2×D4×C151—21no—
40C2×D4×C151D412yescomplemented
41C22×C4×C151—21no—
42C22×C4×C151D412yes—
43C22×C4×C151C2311yescharacteristic
44C4⋊C4×C151—22no—
45C22⋊C4×C151—44no—
46C42×C151—22no—
47C22×D151—22no—
48Dic302—22no—
49Dic302—22no—
50D604—22no—
51D604—22no—
52D604—82no—
53C22⋊D151—42no—
54C22⋊D151—42no—
55C2×Dic151—22no—
56C4×D151—42no—
57C4×D151—42no—
58C151⋊C8—24no—
59C23×C151—22no—
60C23×C151—42no—
61C23×C151—42no—
62C23×C151—41no—
63C23×C151—41no—
64C23×C151C2×D411yescharacteristic
65D4×C151—24no—
66D4×C151—42no—
67C2×C4×C151—22no—
68C2×C4×C151—22no—
69C2×C4×C151—41no—
70C2×C4×C151—41no—
71C2×C4×C151—42no—
72C2×C4×C151C2×D412yes—
73C2×C4×C151C2×D412yes—
74C2×C4×C151C2×D411yescharacteristic
75C2×C4×C151#4111yescharacteristic
76C22×C151—21no—
77C22×C151—21no—
78C22×C151—44no—
79C22×C151—42no—
80C22×C151—82no—
81C22×C151—81no—
82C22×C151—81no—
83C22×C151#12011yescharacteristic
84C22×C151#12111yescharacteristic
85C22×C151#12711yescharacteristic
86C2×D151—42no—
87C2×D151—42no—
88C2×D151—42no—
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#537—1511no—
105C2×#104—1512no—
106#390D15111yescharacteristic, complemented
107#343—1511no—
108C2×#41—1512no—
109C22×D4C2×D15111yescharacteristic
110AGL(1,ℤ/8)—3024no—
111AGL(1,ℤ/8)—3024no—
112C2×SD16—3022no—
113C2×D8—3022no—
114C2×M16—1512no—
115C22⋊Q8—3022no—
116#121—3022no—
117#121—3022no—
118C2×C4⋊C4C2×D15111yescharacteristic
119C2×C22⋊C4—22no—
120C2×C42C2×D15111yescharacteristic
121#104—3024no—
122C24—21no—
123#41—3022no—
124#41—3022no—
125#41—3022no—
126#41—3022no—
127C2×Q8—1512no—
128C2×D4—22no—
129C2×D4—22no—
130C2×D4—21no—
131C2×D4—3022no—
132C2×D4—3022no—
133C2×D4—1512no—
134C2×D4D60412yescomplemented
135C22×C4—21no—
136C22×C4—3022no—
137C22×C4C22⋊D15112yes—
138C22×C4C22×D15111yescharacteristic
139SD16—3028no—
140D8—3028no—
141M16—3022no—
142M16—1514no—
143C2×C8—3022no—
144C4⋊C4—22no—
145C4⋊C4—3022no—
146C22⋊C4—44no—
147C22⋊C4—3024no—
148C42—22no—
149C23—22no—
150C23—42no—
151C23—42no—
152C23—41no—
153C23—41no—
154C23—3022no—
155C23C2×C22⋊D15111yescharacteristic
156Q8—3022no—
157Q8—3022no—
158D4—24no—
159D4—42no—
160D4—3022no—
161D4—3022no—
162D4—6042no—
163D4—6042no—
164D4—12082no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—42no—
170C2×C4—3022no—
171C2×C4—6042no—
172C2×C4—6042no—
173C2×C4D4×D15112yes—
174C2×C4D4×D15112yes—
175C2×C4C2×D60411yescharacteristic
176C2×C4#1455900411yescharacteristic
177C8—3024no—
178C22—21no—
179C22—21no—
180C22—44no—
181C22—42no—
182C22—82no—
183C22—81no—
184C22—81no—
185C22—6042no—
186C22—6042no—
187C22—6042no—
188C22#1801270711yescharacteristic
189C22#1801271311yescharacteristic
190C22#1801273511yescharacteristic
191C4—42no—
192C4—42no—
193C4—6042no—
194C4#1801270912yes—
195C4#1801271212yes—
196C2—21no—
197C2—21no—
198C2—82no—
199C2—12082no—
200C2#2375212111yescharacteristic
201C2#2375237911yescharacteristic
202C2#2375238411yescharacteristic
subgroupG/H
centerC22#18012707
commutator, cosocleC22×C4×C151C23
FrattiniC22×C4C22×D151
Fitting#390×C151C2
socleC22×C151#120
hypercenter#390D151
hypocenterC151#2006
LCSG ▷ C22×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #390

Complements

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

NH ≅ G/Ntype
1. C2×#18012765C2semidirect
2. #23752793C2semidirect
3. C2×#18012667C2semidirect
4. #23751981C2semidirect
5. #390×C151C2semidirect
32. #14558988D4semidirect
40. C2×D4×C151D4semidirect
101. C151#2006semidirect
106. #390D151semidirect
134. C2×D4D604semidirect

Maximal subgroups

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

subgroupindex
C2×#180127652
#237527932
C2×#180126672
#237519812
#390×C1512
#2006151