Finite Group Databasebeta

← C151×#10613 #50315538

Subgroups — C151×#10613 #50315538

Order 38656.

276 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 98 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#1574×C151C211yesmaximal, characteristic
2#1574×C151C211yesmaximal, characteristic
3#1574×C151C211yesmaximal, characteristic
4#1549×C151C211yesmaximal, characteristic
5#1548×C151C211yesmaximal, characteristic
6#1546×C151C211yesmaximal, characteristic
7#1309×C151C211yesmaximal, characteristic
8C2×C4⋊Q8×C151C2211yescharacteristic
9#431×C151C2211yescharacteristic
10#431×C151C2211yescharacteristic
11#431×C151C2211yescharacteristic
12#423×C151C2211yescharacteristic
13#423×C151C2211yescharacteristic
14#423×C151C2211yescharacteristic
15#335×C151—21no—
16#335×C151—21no—
17#335×C151—21no—
18#334×C151—21no—
19#334×C151—21no—
20#334×C151—21no—
21#333×C151—21no—
22#333×C151—21no—
23#332×C151—21no—
24#332×C151—21no—
25#332×C151—21no—
26#332×C151—21no—
27C22×Q8×C151—21no—
28C2×M16×C151—21no—
29C2×M16×C151—21no—
30C2×M16×C151—21no—
31C4⋊Q8×C151—21no—
32C4⋊Q8×C151—21no—
33C4⋊Q8×C151—21no—
34C4⋊Q8×C151Q812yes—
35C2×C4⋊C4×C151—21no—
36C2×C4⋊C4×C151—21no—
37C2×C42×C151C2311yescharacteristic
38C4⋊C8×C151—21no—
39C4⋊C8×C151—21no—
40C4⋊C8×C151—21no—
41C4⋊C8×C151—21no—
42C4⋊C8×C151—21no—
43C4⋊C8×C151—21no—
44C4⋊C8×C151D411yescharacteristic
45C4⋊C8×C151D411yescharacteristic
46C4⋊C8×C151D411yescharacteristic
47C4⋊C8×C151D411yescharacteristic
48C4⋊C8×C151D411yescharacteristic
49C4⋊C8×C151D411yescharacteristic
50C22⋊C8×C151—21no—
51C22⋊C8×C151—21no—
52C22⋊C8×C151—21no—
53C4×C8×C151—21no—
54C4×C8×C151—21no—
55C4×C8×C151—21no—
56C2×Q8×C151—22no—
57C2×Q8×C151—41no—
58C2×Q8×C151—81no—
59C2×Q8×C151—81no—
60C22×C4×C151—41no—
61C22×C4×C151#4111yescharacteristic
62C22×C4×C151#4111yescharacteristic
63C22×C4×C151#4111yescharacteristic
64M16×C151—81no—
65M16×C151—81no—
66M16×C151—81no—
67C2×C8×C151—21no—
68C2×C8×C151—21no—
69C2×C8×C151—21no—
70C2×C8×C151—21no—
71C2×C8×C151—21no—
72C2×C8×C151—21no—
73C2×C8×C151—41no—
74C2×C8×C151—41no—
75C2×C8×C151—41no—
76C4⋊C4×C151—22no—
77C4⋊C4×C151—22no—
78C4⋊C4×C151—41no—
79C4⋊C4×C151—41no—
80C42×C151C2×D411yescharacteristic
81C42×C151C2×D411yescharacteristic
82C42×C151C2×D411yescharacteristic
83C42×C151C2×Q811yescharacteristic
84C23×C151#12611yescharacteristic
85Q8×C151—82no—
86Q8×C151—81no—
87Q8×C151—81no—
88C2×C4×C151—21no—
89C2×C4×C151—21no—
90C2×C4×C151—21no—
91C2×C4×C151—21no—
92C2×C4×C151—21no—
93C2×C4×C151—21no—
94C2×C4×C151—42no—
95C2×C4×C151—82no—
96C2×C4×C151#12111yescharacteristic
97C2×C4×C151#12111yescharacteristic
98C2×C4×C151#12111yescharacteristic
99C2×C4×C151C22⋊Q811yescharacteristic
100C2×C4×C151C22⋊Q811yescharacteristic
101C2×C4×C151C22⋊Q811yescharacteristic
102C8×C151—41no—
103C8×C151—41no—
104C8×C151—41no—
105C8×C151—41no—
106C8×C151—41no—
107C8×C151—41no—
108C8×C151—81no—
109C8×C151—81no—
110C8×C151—81no—
111C22×C151—21no—
112C22×C151—21no—
113C22×C151—21no—
114C22×C151#39611yescharacteristic
115C4×C151—21no—
116C4×C151—21no—
117C4×C151—21no—
118C4×C151—82no—
119C4×C151#47111yescharacteristic
120C4×C151#47111yescharacteristic
121C4×C151#47111yescharacteristic
122C4×C151#47211yescharacteristic
123C4×C151#47311yescharacteristic
124C4×C151#47311yescharacteristic
125C2×C151—41no—
126C2×C151#206311yescharacteristic
127C2×C151#206411yescharacteristic
128C2×C151#206411yescharacteristic
129#10613C15111yesmaximal, characteristic, direct product factor, Sylow
130C151#1061311yescharacteristic, direct product factor, Sylow
131#1574C2×C15111yescharacteristic
132#1574C2×C15111yescharacteristic
133#1574C2×C15111yescharacteristic
134#1549C2×C15111yescharacteristic
135#1548C2×C15111yescharacteristic
136#1546C2×C15111yescharacteristic
137#1309C2×C15111yescharacteristic
138C2×C4⋊Q8C22×C15111yescharacteristic
139#431C22×C15111yescharacteristic
140#431C22×C15111yescharacteristic
141#431C22×C15111yescharacteristic
142#423C22×C15111yescharacteristic
143#423C22×C15111yescharacteristic
144#423C22×C15111yescharacteristic
145#335—21no—
146#335—21no—
147#335—21no—
148#334—21no—
149#334—21no—
150#334—21no—
151#333—21no—
152#333—21no—
153#332—21no—
154#332—21no—
155#332—21no—
156#332—21no—
157C22×Q8—21no—
158C2×M16—21no—
159C2×M16—21no—
160C2×M16—21no—
161C4⋊Q8—21no—
162C4⋊Q8—21no—
163C4⋊Q8—21no—
164C4⋊Q8Q8×C15112yes—
165C2×C4⋊C4—21no—
166C2×C4⋊C4—21no—
167C2×C42C23×C15111yescharacteristic
168C4⋊C8—21no—
169C4⋊C8—21no—
170C4⋊C8—21no—
171C4⋊C8—21no—
172C4⋊C8—21no—
173C4⋊C8—21no—
174C4⋊C8D4×C15111yescharacteristic
175C4⋊C8D4×C15111yescharacteristic
176C4⋊C8D4×C15111yescharacteristic
177C4⋊C8D4×C15111yescharacteristic
178C4⋊C8D4×C15111yescharacteristic
179C4⋊C8D4×C15111yescharacteristic
180C22⋊C8—21no—
181C22⋊C8—21no—
182C22⋊C8—21no—
183C4×C8—21no—
184C4×C8—21no—
185C4×C8—21no—
186C2×Q8—22no—
187C2×Q8—41no—
188C2×Q8—81no—
189C2×Q8—81no—
190C22×C4—41no—
191C22×C4#41×C15111yescharacteristic
192C22×C4#41×C15111yescharacteristic
193C22×C4#41×C15111yescharacteristic
194M16—81no—
195M16—81no—
196M16—81no—
197C2×C8—21no—
198C2×C8—21no—
199C2×C8—21no—
200C2×C8—21no—
201C2×C8—21no—
202C2×C8—21no—
203C2×C8—41no—
204C2×C8—41no—
205C2×C8—41no—
206C4⋊C4—22no—
207C4⋊C4—22no—
208C4⋊C4—41no—
209C4⋊C4—41no—
210C42C2×D4×C15111yescharacteristic
211C42C2×D4×C15111yescharacteristic
212C42C2×D4×C15111yescharacteristic
213C42C2×Q8×C15111yescharacteristic
214C23#126×C15111yescharacteristic
215Q8—82no—
216Q8—81no—
217Q8—81no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—42no—
225C2×C4—82no—
226C2×C4#121×C15111yescharacteristic
227C2×C4#121×C15111yescharacteristic
228C2×C4#121×C15111yescharacteristic
229C2×C4C22⋊Q8×C15111yescharacteristic
230C2×C4C22⋊Q8×C15111yescharacteristic
231C2×C4C22⋊Q8×C15111yescharacteristic
232C8—41no—
233C8—41no—
234C8—41no—
235C8—41no—
236C8—41no—
237C8—41no—
238C8—81no—
239C8—81no—
240C8—81no—
241C22—21no—
242C22—21no—
243C22—21no—
244C22#396×C15111yescharacteristic
245C4—21no—
246C4—21no—
247C4—21no—
248C4—82no—
249C4#471×C15111yescharacteristic
250C4#471×C15111yescharacteristic
251C4#471×C15111yescharacteristic
252C4#472×C15111yescharacteristic
253C4#473×C15111yescharacteristic
254C4#473×C15111yescharacteristic
255C2—41no—
256C2#2063×C15111yescharacteristic
257C2#2064×C15111yescharacteristic
258C2#2064×C15111yescharacteristic
subgroupG/H
center, socleC22×C151#396
commutator, Frattini, cosocleC2×C42C23×C151
prime radicalC23×C151#126
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
129. #10613C151direct (N × H)
130. C151#10613direct (N × H)

Maximal subgroups

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

subgroupindex
#1574×C1512
#1549×C1512
#1548×C1512
#1546×C1512
#1309×C1512
#10613151