Finite Group Databasebeta

← C151×#12435 #50317360

Subgroups — C151×#12435 #50317360

Order 38656.

246 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 82 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#2248×C151C211yesmaximal, characteristic, complemented
2#2169×C151C211yesmaximal, characteristic, complemented
3#1669×C151C211yesmaximal, characteristic, complemented
4#1667×C151C211yesmaximal, characteristic
5#1371×C151C211yesmaximal, characteristic, complemented
6#1362×C151C211yesmaximal, characteristic, complemented
7#1361×C151C211yesmaximal, characteristic, complemented
8C2×SD32×C151—21no—
9C2×SD32×C151—21no—
10C2×M32×C151—21no—
11#494×C151C2211yescharacteristic
12#493×C151C2211yescharacteristic
13#474×C151—21no—
14#459×C151—21no—
15C8×D4×C151C2211yescharacteristic
16C4⋊C16×C151C2211yescharacteristic
17C22⋊C16×C151—21no—
18C4×C16×C151C2211yescharacteristic
19#335×C151C2211yescharacteristic
20#335×C151C2211yescharacteristic
21#332×C151—21no—
22#331×C151—21no—
23C2×Q16×C151—21no—
24C2×Q16×C151—21no—
25C2×D8×C151—21no—
26C2×D8×C151—21no—
27C2×D8×C151—41no—
28C22×C8×C151—21no—
29C4⋊Q8×C151—21no—
30#127×C151—21no—
31C4×D4×C151D411yescharacteristic
32SD32×C151—42no—
33SD32×C151—42no—
34M32×C151—42no—
35C2×C16×C151—21no—
36C2×C16×C151D411yescharacteristic
37C2×C16×C151D411yescharacteristic
38#107×C151—41no—
39C4⋊C8×C151—21no—
40C4⋊C8×C151—21no—
41C4⋊C8×C151D411yescharacteristic
42#102×C151—41no—
43#102×C151—41no—
44C22⋊C8×C151—21no—
45C4×C8×C151C2311yescharacteristic
46C2×Q8×C151—41no—
47C2×D4×C151—41no—
48C2×D4×C151—41no—
49C2×D4×C151—41no—
50C2×D4×C151D811yescharacteristic
51C22×C4×C151—21no—
52Q16×C151—41no—
53Q16×C151—41no—
54Q16×C151—81no—
55D8×C151—41no—
56D8×C151—41no—
57D8×C151—81no—
58D8×C151—82no—
59C2×C8×C151—21no—
60C2×C8×C151—41no—
61C2×C8×C151—41no—
62C2×C8×C151—41no—
63C2×C8×C151—41no—
64C2×C8×C151C2×D411yescharacteristic
65C2×C8×C151#4111yescharacteristic
66C4⋊C4×C151—41no—
67C4⋊C4×C151—41no—
68C4⋊C4×C151D811yescharacteristic
69C22⋊C4×C151—21no—
70C42×C151C2×D411yescharacteristic
71C16×C151—21no—
72C16×C151—41no—
73C16×C151D812yescomplemented
74C23×C151—21no—
75C23×C151—81no—
76Q8×C151—81no—
77Q8×C151—81no—
78D4×C151—21no—
79D4×C151—21no—
80D4×C151—81no—
81D4×C151—81no—
82D4×C151—81no—
83D4×C151—81no—
84D4×C151—161no—
85C2×C4×C151—21no—
86C2×C4×C151—41no—
87C2×C4×C151—41no—
88C2×C4×C151—81no—
89C2×C4×C151#12111yescharacteristic
90C2×C4×C151C2×D811yescharacteristic
91C2×C4×C151#13511yescharacteristic
92C8×C151—21no—
93C8×C151—41no—
94C8×C151—81no—
95C8×C151—81no—
96C8×C151C2×D811yescharacteristic
97C8×C151AGL(1,ℤ/8)11yescharacteristic
98C22×C151—41no—
99C22×C151—41no—
100C22×C151—41no—
101C22×C151—161no—
102C22×C151—161no—
103C22×C151—161no—
104C22×C151#46611yescharacteristic
105C4×C151—21no—
106C4×C151—41no—
107C4×C151—161no—
108C4×C151#45911yescharacteristic
109C4×C151#47211yescharacteristic
110C4×C151#50911yescharacteristic
111C4×C151#51011yescharacteristic
112C2×C151—81no—
113C2×C151—321no—
114C2×C151#166711yescharacteristic
115C2×C151#222011yescharacteristic
116C2×C151#222311yescharacteristic
117#12435C15111yesmaximal, characteristic, direct product factor, Sylow
118C151#1243511yescharacteristic, direct product factor, Sylow
119#2248C2×C15111yescharacteristic, complemented
120#2169C2×C15111yescharacteristic, complemented
121#1669C2×C15111yescharacteristic, complemented
122#1667C2×C15111yescharacteristic
123#1371C2×C15111yescharacteristic, complemented
124#1362C2×C15111yescharacteristic, complemented
125#1361C2×C15111yescharacteristic, complemented
126C2×SD32—21no—
127C2×SD32—21no—
128C2×M32—21no—
129#494C22×C15111yescharacteristic
130#493C22×C15111yescharacteristic
131#474—21no—
132#459—21no—
133C8×D4C22×C15111yescharacteristic
134C4⋊C16C22×C15111yescharacteristic
135C22⋊C16—21no—
136C4×C16C22×C15111yescharacteristic
137#335C22×C15111yescharacteristic
138#335C22×C15111yescharacteristic
139#332—21no—
140#331—21no—
141C2×Q16—21no—
142C2×Q16—21no—
143C2×D8—21no—
144C2×D8—21no—
145C2×D8—41no—
146C22×C8—21no—
147C4⋊Q8—21no—
148#127—21no—
149C4×D4D4×C15111yescharacteristic
150SD32—42no—
151SD32—42no—
152M32—42no—
153C2×C16—21no—
154C2×C16D4×C15111yescharacteristic
155C2×C16D4×C15111yescharacteristic
156#107—41no—
157C4⋊C8—21no—
158C4⋊C8—21no—
159C4⋊C8D4×C15111yescharacteristic
160#102—41no—
161#102—41no—
162C22⋊C8—21no—
163C4×C8C23×C15111yescharacteristic
164C2×Q8—41no—
165C2×D4—41no—
166C2×D4—41no—
167C2×D4—41no—
168C2×D4D8×C15111yescharacteristic
169C22×C4—21no—
170Q16—41no—
171Q16—41no—
172Q16—81no—
173D8—41no—
174D8—41no—
175D8—81no—
176D8—82no—
177C2×C8—21no—
178C2×C8—41no—
179C2×C8—41no—
180C2×C8—41no—
181C2×C8—41no—
182C2×C8C2×D4×C15111yescharacteristic
183C2×C8#41×C15111yescharacteristic
184C4⋊C4—41no—
185C4⋊C4—41no—
186C4⋊C4D8×C15111yescharacteristic
187C22⋊C4—21no—
188C42C2×D4×C15111yescharacteristic
189C16—21no—
190C16—41no—
191C16D8×C15112yescomplemented
192C23—21no—
193C23—81no—
194Q8—81no—
195Q8—81no—
196D4—21no—
197D4—21no—
198D4—81no—
199D4—81no—
200D4—81no—
201D4—81no—
202D4—161no—
203C2×C4—21no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—81no—
207C2×C4#121×C15111yescharacteristic
208C2×C4C2×D8×C15111yescharacteristic
209C2×C4#135×C15111yescharacteristic
210C8—21no—
211C8—41no—
212C8—81no—
213C8—81no—
214C8C2×D8×C15111yescharacteristic
215C8AGL(1,ℤ/8)×C15111yescharacteristic
216C22—41no—
217C22—41no—
218C22—41no—
219C22—161no—
220C22—161no—
221C22—161no—
222C22#466×C15111yescharacteristic
223C4—21no—
224C4—41no—
225C4—161no—
226C4#459×C15111yescharacteristic
227C4#472×C15111yescharacteristic
228C4#509×C15111yescharacteristic
229C4#510×C15111yescharacteristic
230C2—81no—
231C2—321no—
232C2#1667×C15111yescharacteristic
233C2#2220×C15111yescharacteristic
234C2#2223×C15111yescharacteristic
subgroupG/H
center, socleC22×C151#466
commutator, Frattini, cosocleC4×C8C23×C151
prime radical#1667×C151C2
LCSG ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C42×C151 ◁ C8×D4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. #2248×C151C2semidirect
2. #2169×C151C2semidirect
3. #1669×C151C2semidirect
5. #1371×C151C2semidirect
6. #1362×C151C2semidirect
7. #1361×C151C2semidirect
73. C16×C151D8semidirect
117. #12435C151direct (N × H)
118. C151#12435direct (N × H)
119. #2248C2×C151semidirect
120. #2169C2×C151semidirect
121. #1669C2×C151semidirect
123. #1371C2×C151semidirect
124. #1362C2×C151semidirect
125. #1361C2×C151semidirect
191. C16D8×C151semidirect

Maximal subgroups

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

subgroupindex
#2248×C1512
#2169×C1512
#1669×C1512
#1667×C1512
#1371×C1512
#1362×C1512
#1361×C1512
#12435151