Finite Group Databasebeta

← C151×#12406 #50317331

Subgroups — C151×#12406 #50317331

Order 38656.

282 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 282 conjugacy classes of subgroups — too many to draw. Only its 90 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
1Q8×Q16×C151C211yesmaximal, characteristic
2#2254×C151C211yesmaximal, characteristic
3#2225×C151C211yesmaximal, characteristic
4#1674×C151C211yesmaximal, characteristic
5#1365×C151C211yesmaximal, characteristic
6Q8⋊C16×C151C211yesmaximal, characteristic
7#1332×C151C211yesmaximal, characteristic
8Q82×C151—21no—
9#500×C151—21no—
10#500×C151C2211yescharacteristic
11#500×C151C2211yescharacteristic
12#477×C151—22no—
13#477×C151—21no—
14#462×C151—21no—
15C8×Q8×C151C2211yescharacteristic
16C4×Q16×C151—21no—
17C4×Q16×C151C2211yescharacteristic
18#367×C151—21no—
19#367×C151—22no—
20C4⋊C16×C151C2211yescharacteristic
21#358×C151—21no—
22C4×C16×C151C2211yescharacteristic
23#335×C151C2211yescharacteristic
24#332×C151—21no—
25C2×Q16×C151—41no—
26C2×Q16×C151D411yescharacteristic
27C4⋊Q8×C151—22no—
28C4⋊Q8×C151—21no—
29C4⋊Q8×C151—21no—
30C4⋊Q8×C151—42no—
31C4⋊Q8×C151—41no—
32C4×Q8×C151—22no—
33C4×Q8×C151—21no—
34C4×Q8×C151—41no—
35C4×Q8×C151D411yescharacteristic
36C2×C16×C151—21no—
37C2×C16×C151—21no—
38#107×C151—22no—
39#107×C151—21no—
40#107×C151—21no—
41#107×C151—21no—
42#107×C151D411yescharacteristic
43#107×C151D412yes—
44C4⋊C8×C151—21no—
45C4⋊C8×C151—21no—
46C4⋊C8×C151D411yescharacteristic
47#103×C151—22no—
48#103×C151—21no—
49#103×C151—41no—
50C4×C8×C151—21no—
51C4×C8×C151C2311yescharacteristic
52C2×Q8×C151—21no—
53C2×Q8×C151—42no—
54C2×Q8×C151—41no—
55C2×Q8×C151—41no—
56C2×Q8×C151D811yescharacteristic
57Q16×C151—21no—
58Q16×C151—82no—
59Q16×C151Q1612yescomplemented
60C2×C8×C151—21no—
61C2×C8×C151—41no—
62C2×C8×C151C2×D411yescharacteristic
63C2×C8×C151C2×D411yescharacteristic
64C4⋊C4×C151—21no—
65C4⋊C4×C151—22no—
66C4⋊C4×C151—21no—
67C4⋊C4×C151—42no—
68C4⋊C4×C151—42no—
69C4⋊C4×C151—41no—
70C4⋊C4×C151—41no—
71C4⋊C4×C151—41no—
72C4⋊C4×C151—41no—
73C4⋊C4×C151D811yescharacteristic
74C42×C151—21no—
75C42×C151—42no—
76C42×C151—41no—
77C42×C151C2×D411yescharacteristic
78C16×C151—22no—
79C16×C151—41no—
80Q8×C151—21no—
81Q8×C151—22no—
82Q8×C151—41no—
83Q8×C151—81no—
84Q8×C151—81no—
85Q8×C151—161no—
86Q8×C151—162no—
87Q8×C151SD3212yes—
88C2×C4×C151—21no—
89C2×C4×C151—21no—
90C2×C4×C151—41no—
91C2×C4×C151—41no—
92C2×C4×C151—42no—
93C2×C4×C151—81no—
94C2×C4×C151#12011yescharacteristic
95C2×C4×C151C2×D811yescharacteristic
96C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
97C8×C151—21no—
98C8×C151—41no—
99C8×C151—81no—
100C8×C151C2×Q1611yescharacteristic
101C8×C151#13711yescharacteristic
102C22×C151#44711yescharacteristic
103C4×C151—22no—
104C4×C151—21no—
105C4×C151—42no—
106C4×C151—41no—
107C4×C151—82no—
108C4×C151—81no—
109C4×C151—161no—
110C4×C151#45111yescharacteristic
111C4×C151#45611yescharacteristic
112C4×C151C2×SD3211yescharacteristic
113C4×C151#51011yescharacteristic
114C2×C151#164911yescharacteristic
115C2×C151#218511yescharacteristic
116C2×C151#219411yescharacteristic
117#12406C15111yesmaximal, characteristic, direct product factor, Sylow
118C151#1240611yescharacteristic, direct product factor, Sylow
119Q8×Q16C2×C15111yescharacteristic
120#2254C2×C15111yescharacteristic
121#2225C2×C15111yescharacteristic
122#1674C2×C15111yescharacteristic
123#1365C2×C15111yescharacteristic
124Q8⋊C16C2×C15111yescharacteristic
125#1332C2×C15111yescharacteristic
126Q82—21no—
127#500—21no—
128#500C22×C15111yescharacteristic
129#500C22×C15111yescharacteristic
130#477—22no—
131#477—21no—
132#462—21no—
133C8×Q8C22×C15111yescharacteristic
134C4×Q16—21no—
135C4×Q16C22×C15111yescharacteristic
136#367—21no—
137#367—22no—
138C4⋊C16C22×C15111yescharacteristic
139#358—21no—
140C4×C16C22×C15111yescharacteristic
141#335C22×C15111yescharacteristic
142#332—21no—
143C2×Q16—41no—
144C2×Q16D4×C15111yescharacteristic
145C4⋊Q8—22no—
146C4⋊Q8—21no—
147C4⋊Q8—21no—
148C4⋊Q8—42no—
149C4⋊Q8—41no—
150C4×Q8—22no—
151C4×Q8—21no—
152C4×Q8—41no—
153C4×Q8D4×C15111yescharacteristic
154C2×C16—21no—
155C2×C16—21no—
156#107—22no—
157#107—21no—
158#107—21no—
159#107—21no—
160#107D4×C15111yescharacteristic
161#107D4×C15112yes—
162C4⋊C8—21no—
163C4⋊C8—21no—
164C4⋊C8D4×C15111yescharacteristic
165#103—22no—
166#103—21no—
167#103—41no—
168C4×C8—21no—
169C4×C8C23×C15111yescharacteristic
170C2×Q8—21no—
171C2×Q8—42no—
172C2×Q8—41no—
173C2×Q8—41no—
174C2×Q8D8×C15111yescharacteristic
175Q16—21no—
176Q16—82no—
177Q16Q16×C15112yescomplemented
178C2×C8—21no—
179C2×C8—41no—
180C2×C8C2×D4×C15111yescharacteristic
181C2×C8C2×D4×C15111yescharacteristic
182C4⋊C4—21no—
183C4⋊C4—22no—
184C4⋊C4—21no—
185C4⋊C4—42no—
186C4⋊C4—42no—
187C4⋊C4—41no—
188C4⋊C4—41no—
189C4⋊C4—41no—
190C4⋊C4—41no—
191C4⋊C4D8×C15111yescharacteristic
192C42—21no—
193C42—42no—
194C42—41no—
195C42C2×D4×C15111yescharacteristic
196C16—22no—
197C16—41no—
198Q8—21no—
199Q8—22no—
200Q8—41no—
201Q8—81no—
202Q8—81no—
203Q8—161no—
204Q8—162no—
205Q8SD32×C15112yes—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—41no—
209C2×C4—42no—
210C2×C4—41no—
211C2×C4—81no—
212C2×C4#120×C15111yescharacteristic
213C2×C4C2×D8×C15111yescharacteristic
214C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
215C8—21no—
216C8—41no—
217C8—81no—
218C8C2×Q16×C15111yescharacteristic
219C8#137×C15111yescharacteristic
220C22#447×C15111yescharacteristic
221C4—22no—
222C4—21no—
223C4—42no—
224C4—41no—
225C4—82no—
226C4—81no—
227C4—161no—
228C4#451×C15111yescharacteristic
229C4#456×C15111yescharacteristic
230C4C2×SD32×C15111yescharacteristic
231C4#510×C15111yescharacteristic
232C2#1649×C15111yescharacteristic
233C2#2185×C15111yescharacteristic
234C2#2194×C15111yescharacteristic
subgroupG/H
center, socle, prime radicalC22×C151#447
commutator, Frattini, cosocleC4×C8C23×C151
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
59. Q16×C151Q16semidirect
117. #12406C151direct (N × H)
118. C151#12406direct (N × H)
177. Q16Q16×C151semidirect

Maximal subgroups

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

subgroupindex
Q8×Q16×C1512
#2254×C1512
#2225×C1512
#1674×C1512
#1365×C1512
Q8⋊C16×C1512
#1332×C1512
#12406151