Finite Group Databasebeta

← C151×#12479 #50317404

Subgroups — C151×#12479 #50317404

Order 38656.

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

normal subgroups only

This group has 216 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#2240×C151C211yesmaximal, characteristic
2#2183×C151C211yesmaximal, characteristic, complemented
3#1674×C151C211yesmaximal, characteristic, complemented
4#1668×C151C211yesmaximal, characteristic
5#1372×C151C211yesmaximal, characteristic, complemented
6#1364×C151C211yesmaximal, characteristic, complemented
7#1361×C151C211yesmaximal, characteristic
8#500×C151C2211yescharacteristic
9#493×C151C2211yescharacteristic
10#462×C151—21no—
11#460×C151—21no—
12C8×Q8×C151C2211yescharacteristic
13C4⋊C16×C151—21no—
14C4⋊C16×C151C2211yescharacteristic
15#357×C151—21no—
16#357×C151—21no—
17#346×C151—21no—
18C4×C16×C151C2211yescharacteristic
19#335×C151C2211yescharacteristic
20#335×C151C2211yescharacteristic
21#332×C151—21no—
22#331×C151—21no—
23C2×Q16×C151—41no—
24C2×SD16×C151—41no—
25C2×D8×C151—21no—
26C2×D8×C151—21no—
27C4⋊Q8×C151—21no—
28#127×C151—21no—
29C4×Q8×C151D411yescharacteristic
30C2×C16×C151—21no—
31C2×C16×C151D411yescharacteristic
32C2×C16×C151D411yescharacteristic
33#107×C151—21no—
34#107×C151—21no—
35C4⋊C8×C151—21no—
36C4⋊C8×C151—21no—
37C4⋊C8×C151—21no—
38C4⋊C8×C151D411yescharacteristic
39#103×C151—41no—
40#102×C151—41no—
41C4×C8×C151—21no—
42C4×C8×C151C2311yescharacteristic
43C2×Q8×C151—41no—
44C2×Q8×C151D811yescharacteristic
45C2×D4×C151—41no—
46C2×D4×C151—41no—
47C2×D4×C151—41no—
48Q16×C151—82no—
49SD16×C151—82no—
50D8×C151—41no—
51D8×C151—41no—
52D8×C151—81no—
53C2×C8×C151—21no—
54C2×C8×C151—41no—
55C2×C8×C151—41no—
56C2×C8×C151C2×D411yescharacteristic
57C2×C8×C151#4111yescharacteristic
58C4⋊C4×C151—21no—
59C4⋊C4×C151—41no—
60C4⋊C4×C151—41no—
61C4⋊C4×C151D811yescharacteristic
62C42×C151—21no—
63C42×C151C2×D411yescharacteristic
64C16×C151—21no—
65C16×C151—21no—
66C16×C151—41no—
67C23×C151—81no—
68Q8×C151—21no—
69Q8×C151—21no—
70Q8×C151—81no—
71Q8×C151—81no—
72D4×C151—81no—
73D4×C151—81no—
74D4×C151—81no—
75D4×C151—81no—
76D4×C151—161no—
77C2×C4×C151—21no—
78C2×C4×C151—21no—
79C2×C4×C151—81no—
80C2×C4×C151#12111yescharacteristic
81C2×C4×C151C2×D811yescharacteristic
82C2×C4×C151#13511yescharacteristic
83C8×C151—21no—
84C8×C151—41no—
85C8×C151—81no—
86C8×C151—81no—
87C8×C151#13511yescharacteristic
88C8×C151#13711yescharacteristic
89C22×C151—161no—
90C22×C151—161no—
91C22×C151—161no—
92C22×C151#46611yescharacteristic
93C4×C151—21no—
94C4×C151—41no—
95C4×C151—41no—
96C4×C151—161no—
97C4×C151#46411yescharacteristic
98C4×C151#47111yescharacteristic
99C4×C151#50911yescharacteristic
100C4×C151#50911yescharacteristic
101C2×C151—321no—
102C2×C151#168211yescharacteristic
103C2×C151#221811yescharacteristic
104C2×C151#222311yescharacteristic
105#12479C15111yesmaximal, characteristic, direct product factor, Sylow
106C151#1247911yescharacteristic, direct product factor, Sylow
107#2240C2×C15111yescharacteristic
108#2183C2×C15111yescharacteristic, complemented
109#1674C2×C15111yescharacteristic, complemented
110#1668C2×C15111yescharacteristic
111#1372C2×C15111yescharacteristic, complemented
112#1364C2×C15111yescharacteristic, complemented
113#1361C2×C15111yescharacteristic
114#500C22×C15111yescharacteristic
115#493C22×C15111yescharacteristic
116#462—21no—
117#460—21no—
118C8×Q8C22×C15111yescharacteristic
119C4⋊C16—21no—
120C4⋊C16C22×C15111yescharacteristic
121#357—21no—
122#357—21no—
123#346—21no—
124C4×C16C22×C15111yescharacteristic
125#335C22×C15111yescharacteristic
126#335C22×C15111yescharacteristic
127#332—21no—
128#331—21no—
129C2×Q16—41no—
130C2×SD16—41no—
131C2×D8—21no—
132C2×D8—21no—
133C4⋊Q8—21no—
134#127—21no—
135C4×Q8D4×C15111yescharacteristic
136C2×C16—21no—
137C2×C16D4×C15111yescharacteristic
138C2×C16D4×C15111yescharacteristic
139#107—21no—
140#107—21no—
141C4⋊C8—21no—
142C4⋊C8—21no—
143C4⋊C8—21no—
144C4⋊C8D4×C15111yescharacteristic
145#103—41no—
146#102—41no—
147C4×C8—21no—
148C4×C8C23×C15111yescharacteristic
149C2×Q8—41no—
150C2×Q8D8×C15111yescharacteristic
151C2×D4—41no—
152C2×D4—41no—
153C2×D4—41no—
154Q16—82no—
155SD16—82no—
156D8—41no—
157D8—41no—
158D8—81no—
159C2×C8—21no—
160C2×C8—41no—
161C2×C8—41no—
162C2×C8C2×D4×C15111yescharacteristic
163C2×C8#41×C15111yescharacteristic
164C4⋊C4—21no—
165C4⋊C4—41no—
166C4⋊C4—41no—
167C4⋊C4D8×C15111yescharacteristic
168C42—21no—
169C42C2×D4×C15111yescharacteristic
170C16—21no—
171C16—21no—
172C16—41no—
173C23—81no—
174Q8—21no—
175Q8—21no—
176Q8—81no—
177Q8—81no—
178D4—81no—
179D4—81no—
180D4—81no—
181D4—81no—
182D4—161no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—81no—
186C2×C4#121×C15111yescharacteristic
187C2×C4C2×D8×C15111yescharacteristic
188C2×C4#135×C15111yescharacteristic
189C8—21no—
190C8—41no—
191C8—81no—
192C8—81no—
193C8#135×C15111yescharacteristic
194C8#137×C15111yescharacteristic
195C22—161no—
196C22—161no—
197C22—161no—
198C22#466×C15111yescharacteristic
199C4—21no—
200C4—41no—
201C4—41no—
202C4—161no—
203C4#464×C15111yescharacteristic
204C4#471×C15111yescharacteristic
205C4#509×C15111yescharacteristic
206C4#509×C15111yescharacteristic
207C2—321no—
208C2#1682×C15111yescharacteristic
209C2#2218×C15111yescharacteristic
210C2#2223×C15111yescharacteristic
subgroupG/H
center, socleC22×C151#466
commutator, Frattini, cosocleC4×C8C23×C151
prime radical#493×C151C22
LCSG ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C42×C151 ◁ C8×Q8×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2183×C151C2semidirect
3. #1674×C151C2semidirect
5. #1372×C151C2semidirect
6. #1364×C151C2semidirect
105. #12479C151direct (N × H)
106. C151#12479direct (N × H)
108. #2183C2×C151semidirect
109. #1674C2×C151semidirect
111. #1372C2×C151semidirect
112. #1364C2×C151semidirect

Maximal subgroups

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

subgroupindex
#2240×C1512
#2183×C1512
#1674×C1512
#1668×C1512
#1372×C1512
#1364×C1512
#1361×C1512
#12479151