Finite Group Databasebeta

← C151×#10026 #50314951

Subgroups — C151×#10026 #50314951

Order 38656.

564 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 102 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#3245×C151C211yesmaximal, characteristic, complemented
2#3109×C151C212yesmaximal, complemented
3#1955×C151C211yesmaximal, characteristic, complemented
4#1530×C151C212yesmaximal, complemented
5#1290×C151C211yesmaximal, characteristic, complemented
6#532×C151C2212yes—
7C2×C4×D4×C151C2211yescharacteristic
8#481×C151—22no—
9#476×C151—22no—
10#474×C151—22no—
11#466×C151—22no—
12#459×C151—22no—
13#459×C151—22no—
14#447×C151—22no—
15#442×C151—24no—
16#432×C151C2212yes—
17C2×C4⋊C8×C151C2211yescharacteristic
18C2×C22⋊C8×C151—22no—
19C2×#97×C151C2211yescharacteristic
20#329×C151—24no—
21C2×#41×C151—22no—
22C22×D4×C151D411yescharacteristic
23C23×C4×C151—21no—
24C2×D8×C151—24no—
25C2×D8×C151—22no—
26C22×C8×C151—21no—
27C22×C8×C151D412yes—
28C4⋊Q8×C151D412yes—
29#127×C151D412yes—
30#124×C151—22no—
31#121×C151—22no—
32#121×C151—22no—
33C4×D4×C151—22no—
34C4×D4×C151—22no—
35C4×D4×C151—22no—
36C4×D4×C151—22no—
37C2×C4⋊C4×C151D411yescharacteristic
38C2×C22⋊C4×C151—21no—
39C2×C42×C151C2311yescharacteristic
40#107×C151—22no—
41#106×C151—24no—
42C4⋊C8×C151—22no—
43C4⋊C8×C151—22no—
44#102×C151—24no—
45#102×C151—24no—
46#102×C151—24no—
47C22⋊C8×C151—22no—
48C22⋊C8×C151—44no—
49#97×C151—22no—
50#97×C151D414yes—
51C24×C151—21no—
52#41×C151—84no—
53C2×Q8×C151—22no—
54C2×D4×C151—22no—
55C2×D4×C151—22no—
56C2×D4×C151—22no—
57C2×D4×C151—22no—
58C2×D4×C151—42no—
59C2×D4×C151—42no—
60C22×C4×C151—21no—
61C22×C4×C151—42no—
62C22×C4×C151—42no—
63C22×C4×C151—41no—
64C22×C4×C151—42no—
65C22×C4×C151—41no—
66C22×C4×C151C2×D411yescharacteristic
67C22×C4×C151C2×D411yescharacteristic
68C22×C4×C151#4111yescharacteristic
69D8×C151—48no—
70D8×C151—82no—
71C2×C8×C151—22no—
72C2×C8×C151—24no—
73C2×C8×C151—22no—
74C2×C8×C151—41no—
75C2×C8×C151—41no—
76C2×C8×C151—42no—
77C4⋊C4×C151—22no—
78C4⋊C4×C151—22no—
79C4⋊C4×C151—22no—
80C22⋊C4×C151—42no—
81C22⋊C4×C151—42no—
82C22⋊C4×C151—42no—
83C42×C151C2×D412yes—
84C42×C151C2×D412yes—
85C23×C151—22no—
86C23×C151—42no—
87C23×C151—41no—
88C23×C151—41no—
89C23×C151—42no—
90C23×C151—42no—
91C23×C151#12111yescharacteristic
92Q8×C151—82no—
93D4×C151—24no—
94D4×C151—42no—
95D4×C151—44no—
96D4×C151—42no—
97D4×C151—42no—
98D4×C151—82no—
99D4×C151—84no—
100C2×C4×C151—22no—
101C2×C4×C151—21no—
102C2×C4×C151—21no—
103C2×C4×C151—41no—
104C2×C4×C151—42no—
105C2×C4×C151—42no—
106C2×C4×C151—41no—
107C2×C4×C151—84no—
108C2×C4×C151—82no—
109C2×C4×C151—81no—
110C2×C4×C151—81no—
111C2×C4×C151#12012yes—
112C2×C4×C151#12011yescharacteristic
113C2×C4×C151#12112yes—
114C2×C4×C151#12711yescharacteristic
115C8×C151—42no—
116C8×C151—44no—
117C8×C151—42no—
118C22×C151—21no—
119C22×C151—21no—
120C22×C151—44no—
121C22×C151—42no—
122C22×C151—82no—
123C22×C151—81no—
124C22×C151—81no—
125C22×C151—82no—
126C22×C151—82no—
127C22×C151—82no—
128C22×C151#39211yescharacteristic
129C22×C151#47212yes—
130C4×C151—21no—
131C4×C151—22no—
132C4×C151—22no—
133C4×C151—81no—
134C4×C151—82no—
135C4×C151#45311yescharacteristic
136C4×C151#45411yescharacteristic
137C2×C151—22no—
138C2×C151—82no—
139C2×C151—162no—
140C2×C151#200611yescharacteristic
141C2×C151#201011yescharacteristic
142C2×C151#201811yescharacteristic
143#10026C15111yesmaximal, characteristic, direct product factor, Sylow
144C151#1002611yescharacteristic, direct product factor, Sylow
145#3245C2×C15111yescharacteristic, complemented
146#3109C2×C15112yescomplemented
147#1955C2×C15111yescharacteristic, complemented
148#1530C2×C15112yescomplemented
149#1290C2×C15111yescharacteristic, complemented
150#532C22×C15112yes—
151C2×C4×D4C22×C15111yescharacteristic
152#481—22no—
153#476—22no—
154#474—22no—
155#466—22no—
156#459—22no—
157#459—22no—
158#447—22no—
159#442—24no—
160#432C22×C15112yes—
161C2×C4⋊C8C22×C15111yescharacteristic
162C2×C22⋊C8—22no—
163C2×#97C22×C15111yescharacteristic
164#329—24no—
165C2×#41—22no—
166C22×D4D4×C15111yescharacteristic
167C23×C4—21no—
168C2×D8—24no—
169C2×D8—22no—
170C22×C8—21no—
171C22×C8D4×C15112yes—
172C4⋊Q8D4×C15112yes—
173#127D4×C15112yes—
174#124—22no—
175#121—22no—
176#121—22no—
177C4×D4—22no—
178C4×D4—22no—
179C4×D4—22no—
180C4×D4—22no—
181C2×C4⋊C4D4×C15111yescharacteristic
182C2×C22⋊C4—21no—
183C2×C42C23×C15111yescharacteristic
184#107—22no—
185#106—24no—
186C4⋊C8—22no—
187C4⋊C8—22no—
188#102—24no—
189#102—24no—
190#102—24no—
191C22⋊C8—22no—
192C22⋊C8—44no—
193#97—22no—
194#97D4×C15114yes—
195C24—21no—
196#41—84no—
197C2×Q8—22no—
198C2×D4—22no—
199C2×D4—22no—
200C2×D4—22no—
201C2×D4—22no—
202C2×D4—42no—
203C2×D4—42no—
204C22×C4—21no—
205C22×C4—42no—
206C22×C4—42no—
207C22×C4—41no—
208C22×C4—42no—
209C22×C4—41no—
210C22×C4C2×D4×C15111yescharacteristic
211C22×C4C2×D4×C15111yescharacteristic
212C22×C4#41×C15111yescharacteristic
213D8—48no—
214D8—82no—
215C2×C8—22no—
216C2×C8—24no—
217C2×C8—22no—
218C2×C8—41no—
219C2×C8—41no—
220C2×C8—42no—
221C4⋊C4—22no—
222C4⋊C4—22no—
223C4⋊C4—22no—
224C22⋊C4—42no—
225C22⋊C4—42no—
226C22⋊C4—42no—
227C42C2×D4×C15112yes—
228C42C2×D4×C15112yes—
229C23—22no—
230C23—42no—
231C23—41no—
232C23—41no—
233C23—42no—
234C23—42no—
235C23#121×C15111yescharacteristic
236Q8—82no—
237D4—24no—
238D4—42no—
239D4—44no—
240D4—42no—
241D4—42no—
242D4—82no—
243D4—84no—
244C2×C4—22no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—41no—
248C2×C4—42no—
249C2×C4—41no—
250C2×C4—42no—
251C2×C4—82no—
252C2×C4—84no—
253C2×C4—81no—
254C2×C4—81no—
255C2×C4#120×C15112yes—
256C2×C4#120×C15111yescharacteristic
257C2×C4#121×C15112yes—
258C2×C4#127×C15111yescharacteristic
259C8—42no—
260C8—44no—
261C8—42no—
262C22—21no—
263C22—21no—
264C22—44no—
265C22—42no—
266C22—82no—
267C22—81no—
268C22—81no—
269C22—82no—
270C22—82no—
271C22—82no—
272C22#392×C15111yescharacteristic
273C22#472×C15112yes—
274C4—21no—
275C4—22no—
276C4—22no—
277C4—81no—
278C4—82no—
279C4#453×C15111yescharacteristic
280C4#454×C15111yescharacteristic
281C2—22no—
282C2—82no—
283C2—162no—
284C2#2006×C15111yescharacteristic
285C2#2010×C15111yescharacteristic
286C2#2018×C15111yescharacteristic
subgroupG/H
center, socleC22×C151#392
commutator, Frattini, cosocleC2×C42C23×C151
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
1. #3245×C151C2semidirect
2. #3109×C151C2semidirect
3. #1955×C151C2semidirect
4. #1530×C151C2semidirect
5. #1290×C151C2semidirect
143. #10026C151direct (N × H)
144. C151#10026direct (N × H)
145. #3245C2×C151semidirect
146. #3109C2×C151semidirect
147. #1955C2×C151semidirect
148. #1530C2×C151semidirect
149. #1290C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3245×C1512
#3109×C1512
#1955×C1512
#1530×C1512
#1290×C1512
#10026151