Finite Group Databasebeta

← C151×#8774 #50313699

Subgroups — C151×#8774 #50313699

Order 38656.

384 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 114 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#2356×C151C211yesmaximal, characteristic
2C4×#101×C151C211yesmaximal, characteristic
3#1467×C151C211yesmaximal, characteristic
4#1300×C151C212yesmaximal
5#1288×C151C212yesmaximal
6C2×C4×Q8×C151C2211yescharacteristic
7#432×C151C2212yes—
8C2×#101×C151—21no—
9C4×M16×C151C2212yes—
10#391×C151—21no—
11#387×C151—21no—
12#387×C151—21no—
13#383×C151C411yescharacteristic
14#383×C151C2211yescharacteristic
15#382×C151C411yescharacteristic
16C4×C4⋊C4×C151—21no—
17C4×C4⋊C4×C151C411yescharacteristic
18#376×C151C411yescharacteristic
19#376×C151C2211yescharacteristic
20#343×C151—21no—
21#324×C151—21no—
22#324×C151—21no—
23C22×Q8×C151D411yescharacteristic
24C2×M16×C151—22no—
25C4×Q8×C151—22no—
26C4×Q8×C151—22no—
27C2×C4⋊C4×C151—21no—
28C2×C4⋊C4×C151—21no—
29C2×C4⋊C4×C151D411yescharacteristic
30C2×C4⋊C4×C151D411yescharacteristic
31C2×C4⋊C4×C151D411yescharacteristic
32C2×C42×C151—21no—
33C2×C42×C151—21no—
34C2×C42×C151—21no—
35C2×C42×C151C2×C411yescharacteristic
36C2×C42×C151C2×C411yescharacteristic
37C2×C42×C151C2311yescharacteristic
38C4⋊C8×C151—22no—
39#101×C151—24no—
40C22⋊C8×C151—22no—
41#97×C151—22no—
42#97×C151—22no—
43C4×C8×C151—22no—
44#95×C151—21no—
45#95×C151—21no—
46#95×C151—21no—
47#95×C151—21no—
48#95×C151—21no—
49#95×C151—21no—
50#95×C151—21no—
51#95×C151C2×C411yescharacteristic
52#95×C151C2×C411yescharacteristic
53#95×C151C2×C411yescharacteristic
54#95×C151C2×C411yescharacteristic
55C2×Q8×C151—22no—
56C2×Q8×C151—22no—
57C2×Q8×C151—41no—
58C22×C4×C151—21no—
59C22×C4×C151—21no—
60C22×C4×C151—21no—
61C22×C4×C151—21no—
62C22×C4×C151C22⋊C411yescharacteristic
63C22×C4×C151C22⋊C411yescharacteristic
64C22×C4×C151C22⋊C411yescharacteristic
65C22×C4×C151C22⋊C411yescharacteristic
66C22×C4×C151C22×C411yescharacteristic
67C22×C4×C151C2×D411yescharacteristic
68C22×C4×C151C2×D411yescharacteristic
69M16×C151—24no—
70M16×C151—42no—
71C2×C8×C151—42no—
72C2×C8×C151—42no—
73C4⋊C4×C151—22no—
74C4⋊C4×C151—22no—
75C4⋊C4×C151—22no—
76C4⋊C4×C151—42no—
77C4⋊C4×C151—42no—
78C42×C151—21no—
79C42×C151—21no—
80C42×C151—21no—
81C42×C151—21no—
82C42×C151—42no—
83C42×C151—42no—
84C42×C151—42no—
85C42×C151#4112yes—
86C42×C151#4112yes—
87C23×C151C2×C22⋊C411yescharacteristic
88Q8×C151—44no—
89C2×C4×C151—21no—
90C2×C4×C151—21no—
91C2×C4×C151—21no—
92C2×C4×C151—21no—
93C2×C4×C151—22no—
94C2×C4×C151—21no—
95C2×C4×C151—21no—
96C2×C4×C151—21no—
97C2×C4×C151—21no—
98C2×C4×C151—21no—
99C2×C4×C151—41no—
100C2×C4×C151—41no—
101C2×C4×C151—41no—
102C2×C4×C151—41no—
103C2×C4×C151—41no—
104C2×C4×C151—41no—
105C2×C4×C151—41no—
106C2×C4×C151—41no—
107C2×C4×C151—41no—
108C2×C4×C151—41no—
109C2×C4×C151—41no—
110C2×C4×C151—41no—
111C2×C4×C151—41no—
112C2×C4×C151—41no—
113C2×C4×C151—41no—
114C2×C4×C151#10412yes—
115C2×C4×C151#11711yescharacteristic
116C2×C4×C151#11711yescharacteristic
117C2×C4×C151#12312yes—
118C2×C4×C151#12312yes—
119C8×C151—44no—
120C8×C151—82no—
121C22×C151—21no—
122C22×C151—21no—
123C22×C151#38111yescharacteristic
124C22×C151C2×#10411yescharacteristic
125C22×C151#42111yescharacteristic
126C4×C151—22no—
127C4×C151—22no—
128C4×C151—22no—
129C4×C151—21no—
130C4×C151—21no—
131C4×C151—42no—
132C4×C151—41no—
133C4×C151—41no—
134C4×C151—41no—
135C4×C151—81no—
136C4×C151—81no—
137C4×C151—81no—
138C2×C151—21no—
139C2×C151—21no—
140C2×C151#182611yescharacteristic
141C2×C151#182711yescharacteristic
142C2×C151#183011yescharacteristic
143#8774C15111yesmaximal, characteristic, direct product factor, Sylow
144C151#877411yescharacteristic, direct product factor, Sylow
145#2356C2×C15111yescharacteristic
146C4×#101C2×C15111yescharacteristic
147#1467C2×C15111yescharacteristic
148#1300C2×C15112yes—
149#1288C2×C15112yes—
150C2×C4×Q8C22×C15111yescharacteristic
151#432C22×C15112yes—
152C2×#101—21no—
153C4×M16C22×C15112yes—
154#391—21no—
155#387—21no—
156#387—21no—
157#383C4×C15111yescharacteristic
158#383C22×C15111yescharacteristic
159#382C4×C15111yescharacteristic
160C4×C4⋊C4—21no—
161C4×C4⋊C4C4×C15111yescharacteristic
162#376C4×C15111yescharacteristic
163#376C22×C15111yescharacteristic
164#343—21no—
165#324—21no—
166#324—21no—
167C22×Q8D4×C15111yescharacteristic
168C2×M16—22no—
169C4×Q8—22no—
170C4×Q8—22no—
171C2×C4⋊C4—21no—
172C2×C4⋊C4—21no—
173C2×C4⋊C4D4×C15111yescharacteristic
174C2×C4⋊C4D4×C15111yescharacteristic
175C2×C4⋊C4D4×C15111yescharacteristic
176C2×C42—21no—
177C2×C42—21no—
178C2×C42—21no—
179C2×C42C2×C4×C15111yescharacteristic
180C2×C42C2×C4×C15111yescharacteristic
181C2×C42C23×C15111yescharacteristic
182C4⋊C8—22no—
183#101—24no—
184C22⋊C8—22no—
185#97—22no—
186#97—22no—
187C4×C8—22no—
188#95—21no—
189#95—21no—
190#95—21no—
191#95—21no—
192#95—21no—
193#95—21no—
194#95—21no—
195#95C2×C4×C15111yescharacteristic
196#95C2×C4×C15111yescharacteristic
197#95C2×C4×C15111yescharacteristic
198#95C2×C4×C15111yescharacteristic
199C2×Q8—22no—
200C2×Q8—22no—
201C2×Q8—41no—
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—21no—
205C22×C4—21no—
206C22×C4C22⋊C4×C15111yescharacteristic
207C22×C4C22⋊C4×C15111yescharacteristic
208C22×C4C22⋊C4×C15111yescharacteristic
209C22×C4C22⋊C4×C15111yescharacteristic
210C22×C4C22×C4×C15111yescharacteristic
211C22×C4C2×D4×C15111yescharacteristic
212C22×C4C2×D4×C15111yescharacteristic
213M16—24no—
214M16—42no—
215C2×C8—42no—
216C2×C8—42no—
217C4⋊C4—22no—
218C4⋊C4—22no—
219C4⋊C4—22no—
220C4⋊C4—42no—
221C4⋊C4—42no—
222C42—21no—
223C42—21no—
224C42—21no—
225C42—21no—
226C42—42no—
227C42—42no—
228C42—42no—
229C42#41×C15112yes—
230C42#41×C15112yes—
231C23C2×C22⋊C4×C15111yescharacteristic
232Q8—44no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—22no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4#104×C15112yes—
259C2×C4#117×C15111yescharacteristic
260C2×C4#117×C15111yescharacteristic
261C2×C4#123×C15112yes—
262C2×C4#123×C15112yes—
263C8—44no—
264C8—82no—
265C22—21no—
266C22—21no—
267C22#381×C15111yescharacteristic
268C22C2×#104×C15111yescharacteristic
269C22#421×C15111yescharacteristic
270C4—22no—
271C4—22no—
272C4—22no—
273C4—21no—
274C4—21no—
275C4—42no—
276C4—41no—
277C4—41no—
278C4—41no—
279C4—81no—
280C4—81no—
281C4—81no—
282C2—21no—
283C2—21no—
284C2#1826×C15111yescharacteristic
285C2#1827×C15111yescharacteristic
286C2#1830×C15111yescharacteristic
subgroupG/H
center, socleC22×C151#381
commutatorC22×C4C22×C4×C151
Frattini, cosocleC2×C42C23×C151
prime radicalC23×C151C2×C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
143. #8774C151direct (N × H)
144. C151#8774direct (N × H)

Maximal subgroups

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

subgroupindex
#2356×C1512
C4×#101×C1512
#1467×C1512
#1300×C1512
#1288×C1512
#8774151