Finite Group Databasebeta

← C151×#13535 #50318460

Subgroups — C151×#13535 #50318460

Order 38656.

354 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 114 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×#365×C151C212yesmaximal, complemented
2C2×#361×C151C212yesmaximal
3#1972×C151C211yesmaximal, characteristic
4#1849×C151C211yesmaximal, characteristic, complemented
5#1377×C151C211yesmaximal, characteristic, complemented
6C22×D8×C151C2211yescharacteristic
7C2×M32×C151C2212yes—
8C2×#108×C151—21no—
9C2×#108×C151C2212yes—
10C2×#106×C151C2211yescharacteristic
11#423×C151—21no—
12C2×#102×C151—21no—
13C2×#97×C151C2211yescharacteristic
14#390×C151—21no—
15#365×C151—24no—
16#361×C151—24no—
17C22×D4×C151—21no—
18C2×D8×C151—22no—
19C2×D8×C151—22no—
20C2×D8×C151—21no—
21C2×D8×C151Q812yes—
22C2×M16×C151—22no—
23C22×C8×C151D411yescharacteristic
24C22×C8×C151C2311yescharacteristic
25C2×C4⋊C4×C151—21no—
26C2×C22⋊C4×C151—42no—
27C2×C42×C151D411yescharacteristic
28M32×C151—22no—
29M32×C151D414yes—
30C2×C16×C151—22no—
31#108×C151—22no—
32#108×C151—22no—
33#108×C151—42no—
34#106×C151—22no—
35C4⋊C8×C151—42no—
36#102×C151—42no—
37#97×C151—22no—
38C24×C151—41no—
39C2×D4×C151—22no—
40C2×D4×C151—41no—
41C2×D4×C151—41no—
42C2×D4×C151—41no—
43C2×D4×C151—41no—
44C2×D4×C151—41no—
45C22×C4×C151—41no—
46C22×C4×C151SD1612yes—
47C22×C4×C151C2×D411yescharacteristic
48D8×C151—24no—
49D8×C151—42no—
50M16×C151—42no—
51M16×C151—42no—
52C2×C8×C151—21no—
53C2×C8×C151—21no—
54C2×C8×C151—42no—
55C2×C8×C151SD1612yes—
56C2×C8×C151C2×D412yes—
57C2×C8×C151C2×Q811yescharacteristic
58C2×C8×C151#4112yes—
59C2×C8×C151#4111yescharacteristic
60C4⋊C4×C151—41no—
61C4⋊C4×C151—41no—
62C22⋊C4×C151—84no—
63C42×C151—21no—
64C42×C151—21no—
65C16×C151—24no—
66C23×C151—42no—
67C23×C151—82no—
68C23×C151—82no—
69C23×C151—81no—
70C23×C151—81no—
71C23×C151C2×SD1611yescharacteristic
72D4×C151—42no—
73D4×C151—42no—
74D4×C151—81no—
75D4×C151—81no—
76C2×C4×C151—22no—
77C2×C4×C151—42no—
78C2×C4×C151—82no—
79C2×C4×C151—81no—
80C2×C4×C151C22⋊Q811yescharacteristic
81C2×C4×C151#12311yescharacteristic
82C2×C4×C151#12711yescharacteristic
83C2×C4×C151C2×SD1611yescharacteristic
84C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
85C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
86C8×C151—22no—
87C8×C151—82no—
88C8×C151C22⋊Q812yes—
89C8×C151#12312yes—
90C22×C151—22no—
91C22×C151—84no—
92C22×C151—82no—
93C22×C151—161no—
94C22×C151—161no—
95C22×C151—162no—
96C22×C151#47611yescharacteristic
97C22×C151#48111yescharacteristic
98C22×C151#49211yescharacteristic
99C4×C151—42no—
100C4×C151—161no—
101C4×C151#39911yescharacteristic
102C4×C151#47611yescharacteristic
103C4×C151#48111yescharacteristic
104C4×C151#49611yescharacteristic
105C2×C151—21no—
106C2×C151—21no—
107C2×C151—162no—
108C2×C151#209411yescharacteristic
109C2×C151#223812yes—
110#13535C15111yesmaximal, characteristic, direct product factor, Sylow
111C151#1353511yescharacteristic, direct product factor, Sylow
112C2×#365C2×C15112yescomplemented
113C2×#361C2×C15112yes—
114#1972C2×C15111yescharacteristic
115#1849C2×C15111yescharacteristic, complemented
116#1377C2×C15111yescharacteristic, complemented
117C22×D8C22×C15111yescharacteristic
118C2×M32C22×C15112yes—
119C2×#108—21no—
120C2×#108C22×C15112yes—
121C2×#106C22×C15111yescharacteristic
122#423—21no—
123C2×#102—21no—
124C2×#97C22×C15111yescharacteristic
125#390—21no—
126#365—24no—
127#361—24no—
128C22×D4—21no—
129C2×D8—22no—
130C2×D8—21no—
131C2×D8—22no—
132C2×D8Q8×C15112yes—
133C2×M16—22no—
134C22×C8D4×C15111yescharacteristic
135C22×C8C23×C15111yescharacteristic
136C2×C4⋊C4—21no—
137C2×C22⋊C4—42no—
138C2×C42D4×C15111yescharacteristic
139M32—22no—
140M32D4×C15114yes—
141C2×C16—22no—
142#108—22no—
143#108—22no—
144#108—42no—
145#106—22no—
146C4⋊C8—42no—
147#102—42no—
148#97—22no—
149C24—41no—
150C2×D4—22no—
151C2×D4—41no—
152C2×D4—41no—
153C2×D4—41no—
154C2×D4—41no—
155C2×D4—41no—
156C22×C4—41no—
157C22×C4SD16×C15112yes—
158C22×C4C2×D4×C15111yescharacteristic
159D8—24no—
160D8—42no—
161M16—42no—
162M16—42no—
163C2×C8—21no—
164C2×C8—21no—
165C2×C8—42no—
166C2×C8SD16×C15112yes—
167C2×C8C2×D4×C15112yes—
168C2×C8C2×Q8×C15111yescharacteristic
169C2×C8#41×C15112yes—
170C2×C8#41×C15111yescharacteristic
171C4⋊C4—41no—
172C4⋊C4—41no—
173C22⋊C4—84no—
174C42—21no—
175C42—21no—
176C16—24no—
177C23—42no—
178C23—82no—
179C23—82no—
180C23—81no—
181C23—81no—
182C23C2×SD16×C15111yescharacteristic
183D4—42no—
184D4—42no—
185D4—81no—
186D4—81no—
187C2×C4—22no—
188C2×C4—42no—
189C2×C4—82no—
190C2×C4—81no—
191C2×C4C22⋊Q8×C15111yescharacteristic
192C2×C4#123×C15111yescharacteristic
193C2×C4#127×C15111yescharacteristic
194C2×C4C2×SD16×C15111yescharacteristic
195C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
196C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
197C8—22no—
198C8—82no—
199C8C22⋊Q8×C15112yes—
200C8#123×C15112yes—
201C22—22no—
202C22—84no—
203C22—82no—
204C22—161no—
205C22—161no—
206C22—162no—
207C22#476×C15111yescharacteristic
208C22#481×C15111yescharacteristic
209C22#492×C15111yescharacteristic
210C4—42no—
211C4—161no—
212C4#399×C15111yescharacteristic
213C4#476×C15111yescharacteristic
214C4#481×C15111yescharacteristic
215C4#496×C15111yescharacteristic
216C2—21no—
217C2—21no—
218C2—162no—
219C2#2094×C15111yescharacteristic
220C2#2238×C15112yes—
subgroupG/H
center, socleC22×C151#481
commutator, Frattini, cosocleC22×C8C23×C151
prime radicalC22×D8×C151C22
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C22×C4×C151 ◁ C2×#97×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#365×C151C2semidirect
4. #1849×C151C2semidirect
5. #1377×C151C2semidirect
110. #13535C151direct (N × H)
111. C151#13535direct (N × H)
112. C2×#365C2×C151semidirect
115. #1849C2×C151semidirect
116. #1377C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#365×C1512
C2×#361×C1512
#1972×C1512
#1849×C1512
#1377×C1512
#13535151