Finite Group Databasebeta

← C151×#12496 #50317421

Subgroups — C151×#12496 #50317421

Order 38656.

234 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 78 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#2209×C151C211yesmaximal, characteristic, complemented
2#2207×C151C211yesmaximal, characteristic
3#1709×C151C211yesmaximal, characteristic
4#1591×C151C211yesmaximal, characteristic, complemented
5#1367×C151C211yesmaximal, characteristic, complemented
6#1362×C151C211yesmaximal, characteristic, complemented
7#1361×C151C211yesmaximal, characteristic
8C2×Q32×C151—21no—
9C2×SD32×C151—21no—
10#494×C151C2211yescharacteristic
11#493×C151C2211yescharacteristic
12#486×C151—21no—
13#486×C151—21no—
14#446×C151—21no—
15C4×Q16×C151C2211yescharacteristic
16C4⋊C16×C151C2211yescharacteristic
17C4⋊C16×C151C2211yescharacteristic
18#358×C151—21no—
19#357×C151—21no—
20#335×C151C2211yescharacteristic
21Q8⋊C8×C151—21no—
22C82×C151C2211yescharacteristic
23C2×Q16×C151—21no—
24C2×Q16×C151—21no—
25C2×Q16×C151D411yescharacteristic
26C2×D8×C151—21no—
27C2×D8×C151—21no—
28C4⋊Q8×C151—21no—
29#127×C151—21no—
30C4×Q8×C151—21no—
31Q32×C151—42no—
32SD32×C151—42no—
33C2×C16×C151—21no—
34C2×C16×C151—21no—
35#107×C151D411yescharacteristic
36C4⋊C8×C151—21no—
37C4⋊C8×C151—41no—
38#103×C151—21no—
39#102×C151—42no—
40#102×C151—41no—
41#102×C151—41no—
42#97×C151—41no—
43C4×C8×C151D411yescharacteristic
44C4×C8×C151D411yescharacteristic
45C4×C8×C151C2311yescharacteristic
46C2×Q8×C151—21no—
47C2×Q8×C151—41no—
48C2×D4×C151—41no—
49C2×D4×C151—41no—
50C2×D4×C151—41no—
51Q16×C151—21no—
52Q16×C151—21no—
53Q16×C151—41no—
54Q16×C151—41no—
55Q16×C151—81no—
56D8×C151—41no—
57D8×C151—41no—
58D8×C151—81no—
59C2×C8×C151—21no—
60C2×C8×C151—41no—
61C2×C8×C151D811yescharacteristic
62C2×C8×C151D811yescharacteristic
63C2×C8×C151C2×D411yescharacteristic
64C2×C8×C151#4111yescharacteristic
65C4⋊C4×C151—21no—
66C4⋊C4×C151—41no—
67C4⋊C4×C151—41no—
68C4⋊C4×C151—41no—
69C42×C151—41no—
70C42×C151C2×D411yescharacteristic
71C16×C151—41no—
72C16×C151—41no—
73C23×C151—81no—
74Q8×C151—41no—
75Q8×C151—41no—
76Q8×C151—81no—
77Q8×C151—81no—
78D4×C151—82no—
79D4×C151—81no—
80D4×C151—81no—
81D4×C151—81no—
82D4×C151—81no—
83C2×C4×C151—41no—
84C2×C4×C151—41no—
85C2×C4×C151—81no—
86C2×C4×C151#12111yescharacteristic
87C2×C4×C151C2×D811yescharacteristic
88C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
89C8×C151—21no—
90C8×C151—21no—
91C8×C151—21no—
92C8×C151—41no—
93C8×C151—81no—
94C8×C151AGL(1,ℤ/8)11yescharacteristic
95C8×C151AGL(1,ℤ/8)11yescharacteristic
96C22×C151—161no—
97C22×C151—161no—
98C22×C151—161no—
99C22×C151#45911yescharacteristic
100C4×C151—21no—
101C4×C151—81no—
102C4×C151—81no—
103C4×C151—161no—
104C4×C151#46911yescharacteristic
105C4×C151#47211yescharacteristic
106C4×C151#50811yescharacteristic
107C4×C151#51011yescharacteristic
108C2×C151—321no—
109C2×C151#168711yescharacteristic
110C2×C151#221111yescharacteristic
111C2×C151#221211yescharacteristic
112#12496C15111yesmaximal, characteristic, direct product factor, Sylow
113C151#1249611yescharacteristic, direct product factor, Sylow
114#2209C2×C15111yescharacteristic, complemented
115#2207C2×C15111yescharacteristic
116#1709C2×C15111yescharacteristic
117#1591C2×C15111yescharacteristic, complemented
118#1367C2×C15111yescharacteristic, complemented
119#1362C2×C15111yescharacteristic, complemented
120#1361C2×C15111yescharacteristic
121C2×Q32—21no—
122C2×SD32—21no—
123#494C22×C15111yescharacteristic
124#493C22×C15111yescharacteristic
125#486—21no—
126#486—21no—
127#446—21no—
128C4×Q16C22×C15111yescharacteristic
129C4⋊C16C22×C15111yescharacteristic
130C4⋊C16C22×C15111yescharacteristic
131#358—21no—
132#357—21no—
133#335C22×C15111yescharacteristic
134Q8⋊C8—21no—
135C82C22×C15111yescharacteristic
136C2×Q16—21no—
137C2×Q16—21no—
138C2×Q16D4×C15111yescharacteristic
139C2×D8—21no—
140C2×D8—21no—
141C4⋊Q8—21no—
142#127—21no—
143C4×Q8—21no—
144Q32—42no—
145SD32—42no—
146C2×C16—21no—
147C2×C16—21no—
148#107D4×C15111yescharacteristic
149C4⋊C8—21no—
150C4⋊C8—41no—
151#103—21no—
152#102—42no—
153#102—41no—
154#102—41no—
155#97—41no—
156C4×C8D4×C15111yescharacteristic
157C4×C8D4×C15111yescharacteristic
158C4×C8C23×C15111yescharacteristic
159C2×Q8—21no—
160C2×Q8—41no—
161C2×D4—41no—
162C2×D4—41no—
163C2×D4—41no—
164Q16—21no—
165Q16—21no—
166Q16—41no—
167Q16—41no—
168Q16—81no—
169D8—41no—
170D8—41no—
171D8—81no—
172C2×C8—21no—
173C2×C8—41no—
174C2×C8D8×C15111yescharacteristic
175C2×C8D8×C15111yescharacteristic
176C2×C8C2×D4×C15111yescharacteristic
177C2×C8#41×C15111yescharacteristic
178C4⋊C4—21no—
179C4⋊C4—41no—
180C4⋊C4—41no—
181C4⋊C4—41no—
182C42—41no—
183C42C2×D4×C15111yescharacteristic
184C16—41no—
185C16—41no—
186C23—81no—
187Q8—41no—
188Q8—41no—
189Q8—81no—
190Q8—81no—
191D4—82no—
192D4—81no—
193D4—81no—
194D4—81no—
195D4—81no—
196C2×C4—41no—
197C2×C4—41no—
198C2×C4—81no—
199C2×C4#121×C15111yescharacteristic
200C2×C4C2×D8×C15111yescharacteristic
201C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
202C8—21no—
203C8—21no—
204C8—21no—
205C8—41no—
206C8—81no—
207C8AGL(1,ℤ/8)×C15111yescharacteristic
208C8AGL(1,ℤ/8)×C15111yescharacteristic
209C22—161no—
210C22—161no—
211C22—161no—
212C22#459×C15111yescharacteristic
213C4—21no—
214C4—81no—
215C4—81no—
216C4—161no—
217C4#469×C15111yescharacteristic
218C4#472×C15111yescharacteristic
219C4#508×C15111yescharacteristic
220C4#510×C15111yescharacteristic
221C2—321no—
222C2#1687×C15111yescharacteristic
223C2#2211×C15111yescharacteristic
224C2#2212×C15111yescharacteristic
subgroupG/H
center, socleC22×C151#459
commutator, Frattini, cosocleC4×C8C23×C151
prime radical#493×C151C22
LCSG ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C42×C151 ◁ C82×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. #2209×C151C2semidirect
4. #1591×C151C2semidirect
5. #1367×C151C2semidirect
6. #1362×C151C2semidirect
112. #12496C151direct (N × H)
113. C151#12496direct (N × H)
114. #2209C2×C151semidirect
117. #1591C2×C151semidirect
118. #1367C2×C151semidirect
119. #1362C2×C151semidirect

Maximal subgroups

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

subgroupindex
#2209×C1512
#2207×C1512
#1709×C1512
#1591×C1512
#1367×C1512
#1362×C1512
#1361×C1512
#12496151