Finite Group Databasebeta

← C151×#8707 #50313632

Subgroups — C151×#8707 #50313632

Order 38656.

680 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C4⋊C4×C151C211yesmaximal, characteristic
2#1797×C151C211yesmaximal, characteristic
3C4×C22⋊C8×C151C211yesmaximal, characteristic
4#1279×C151C214yesmaximal, complemented
5C22×C4⋊C4×C151C411yescharacteristic
6C22×C4⋊C4×C151C411yescharacteristic
7C22×C42×C151—21no—
8C22×C42×C151C2211yescharacteristic
9C2×C4⋊C8×C151C2212yes—
10C2×C22⋊C8×C151—21no—
11C2×C22⋊C8×C151—21no—
12C2×C4×C8×C151C2212yes—
13C4×C4⋊C4×C151—21no—
14C4×C4⋊C4×C151—21no—
15C4×C4⋊C4×C151C412yes—
16C4×C4⋊C4×C151C2212yes—
17C2×#95×C151—21no—
18#336×C151—21no—
19#336×C151—21no—
20C23×C4×C151—21no—
21C23×C4×C151—21no—
22C23×C4×C151C2×C411yescharacteristic
23C23×C4×C151D411yescharacteristic
24C23×C4×C151D411yescharacteristic
25C22×C8×C151—22no—
26C22×C8×C151—22no—
27C2×C4⋊C4×C151—21no—
28C2×C4⋊C4×C151—21no—
29C2×C4⋊C4×C151—22no—
30C2×C4⋊C4×C151—24no—
31C2×C4⋊C4×C151C814yescomplemented
32C2×C4⋊C4×C151C2×C412yes—
33C2×C4⋊C4×C151C2×C412yes—
34C2×C42×C151—24no—
35C2×C42×C151—22no—
36C2×C42×C151—22no—
37C2×C42×C151—44no—
38C2×C42×C151C2×C411yescharacteristic
39C2×C42×C151D411yescharacteristic
40C2×C42×C151D411yescharacteristic
41C2×C42×C151C2311yescharacteristic
42C4⋊C8×C151—24no—
43C22⋊C8×C151—24no—
44C22⋊C8×C151—42no—
45C4×C8×C151—24no—
46#95×C151—22no—
47#95×C151—22no—
48C24×C151C22⋊C411yescharacteristic
49C22×C4×C151—22no—
50C22×C4×C151—22no—
51C22×C4×C151—22no—
52C22×C4×C151—22no—
53C22×C4×C151—24no—
54C22×C4×C151—24no—
55C22×C4×C151—22no—
56C22×C4×C151—22no—
57C22×C4×C151—22no—
58C22×C4×C151—22no—
59C22×C4×C151—41no—
60C22×C4×C151—42no—
61C22×C4×C151—42no—
62C22×C4×C151—42no—
63C22×C4×C151—42no—
64C22×C4×C151C22⋊C411yescharacteristic
65C22×C4×C151C22⋊C411yescharacteristic
66C22×C4×C151C22⋊C411yescharacteristic
67C22×C4×C151C2×C812yes—
68C22×C4×C151M1612yes—
69C22×C4×C151SD1612yes—
70C22×C4×C151Q1612yes—
71C22×C4×C151C22×C411yescharacteristic
72C22×C4×C151C2×D411yescharacteristic
73C22×C4×C151C2×D411yescharacteristic
74C2×C8×C151—24no—
75C2×C8×C151—42no—
76C2×C8×C151—42no—
77C2×C8×C151—42no—
78C2×C8×C151—42no—
79C2×C8×C151—42no—
80C4⋊C4×C151—24no—
81C4⋊C4×C151—24no—
82C4⋊C4×C151—22no—
83C4⋊C4×C151—22no—
84C4⋊C4×C151C2×C814yes—
85C4⋊C4×C151M1614yes—
86C42×C151—22no—
87C42×C151—22no—
88C42×C151—22no—
89C42×C151—44no—
90C42×C151—44no—
91C42×C151#4114yes—
92C23×C151—21no—
93C23×C151—21no—
94C23×C151—21no—
95C23×C151—21no—
96C23×C151C22⋊C812yes—
97C23×C151#10312yes—
98C23×C151#10412yes—
99C23×C151C2×C22⋊C411yescharacteristic
100C2×C4×C151—21no—
101C2×C4×C151—21no—
102C2×C4×C151—21no—
103C2×C4×C151—21no—
104C2×C4×C151—21no—
105C2×C4×C151—21no—
106C2×C4×C151—24no—
107C2×C4×C151—24no—
108C2×C4×C151—24no—
109C2×C4×C151—24no—
110C2×C4×C151—21no—
111C2×C4×C151—24no—
112C2×C4×C151—24no—
113C2×C4×C151—21no—
114C2×C4×C151—21no—
115C2×C4×C151—44no—
116C2×C4×C151—48no—
117C2×C4×C151—48no—
118C2×C4×C151—42no—
119C2×C4×C151—42no—
120C2×C4×C151—42no—
121C2×C4×C151—42no—
122C2×C4×C151C22⋊C812yes—
123C2×C4×C151#10312yes—
124C2×C4×C151#11712yes—
125C2×C4×C151#12312yes—
126C2×C4×C151#12312yes—
127C2×C4×C151C22×C811yescharacteristic
128C2×C4×C151C2×M1612yes—
129C2×C4×C151C2×M1611yescharacteristic
130C2×C4×C151C2×SD1611yescharacteristic
131C2×C4×C151C2×Q1611yescharacteristic
132C2×C4×C151AGL(1,ℤ/8)12yes—
133C8×C151—44no—
134C8×C151—82no—
135C22×C151—22no—
136C22×C151—22no—
137C22×C151—22no—
138C22×C151—22no—
139C22×C151—22no—
140C22×C151—22no—
141C22×C151Q8⋊C814yes—
142C22×C151#38111yescharacteristic
143C22×C151C2×C22⋊C811yescharacteristic
144C22×C151#40711yescharacteristic
145C22×C151C2×#10311yescharacteristic
146C22×C151#41811yescharacteristic
147C22×C151C2×#10411yescharacteristic
148C22×C151#42111yescharacteristic
149C4×C151—22no—
150C4×C151—22no—
151C4×C151—22no—
152C4×C151—41no—
153C4×C151—44no—
154C4×C151—44no—
155C4×C151#43112yes—
156C4×C151#43212yes—
157C4×C151#48112yes—
158C4×C151#48412yes—
159C2×C151—24no—
160C2×C151C2×Q8⋊C811yescharacteristic
161C2×C151#147811yescharacteristic
162C2×C151#148711yescharacteristic
163C2×C151#149011yescharacteristic
164C2×C151#181711yescharacteristic
165C2×C151#182411yescharacteristic
166C2×C151#182611yescharacteristic
167#8707C15111yesmaximal, characteristic, direct product factor, Sylow
168C151#870711yescharacteristic, direct product factor, Sylow
169C2×C4×C4⋊C4C2×C15111yescharacteristic
170#1797C2×C15111yescharacteristic
171C4×C22⋊C8C2×C15111yescharacteristic
172#1279C2×C15114yescomplemented
173C22×C4⋊C4C4×C15111yescharacteristic
174C22×C4⋊C4C4×C15111yescharacteristic
175C22×C42—21no—
176C22×C42C22×C15111yescharacteristic
177C2×C4⋊C8C22×C15112yes—
178C2×C22⋊C8—21no—
179C2×C22⋊C8—21no—
180C2×C4×C8C22×C15112yes—
181C4×C4⋊C4—21no—
182C4×C4⋊C4—21no—
183C4×C4⋊C4C4×C15112yes—
184C4×C4⋊C4C22×C15112yes—
185C2×#95—21no—
186#336—21no—
187#336—21no—
188C23×C4—21no—
189C23×C4—21no—
190C23×C4C2×C4×C15111yescharacteristic
191C23×C4D4×C15111yescharacteristic
192C23×C4D4×C15111yescharacteristic
193C22×C8—22no—
194C22×C8—22no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—22no—
198C2×C4⋊C4—24no—
199C2×C4⋊C4C8×C15114yescomplemented
200C2×C4⋊C4C2×C4×C15112yes—
201C2×C4⋊C4C2×C4×C15112yes—
202C2×C42—24no—
203C2×C42—22no—
204C2×C42—22no—
205C2×C42—44no—
206C2×C42C2×C4×C15111yescharacteristic
207C2×C42D4×C15111yescharacteristic
208C2×C42D4×C15111yescharacteristic
209C2×C42C23×C15111yescharacteristic
210C4⋊C8—24no—
211C22⋊C8—24no—
212C22⋊C8—42no—
213C4×C8—24no—
214#95—22no—
215#95—22no—
216C24C22⋊C4×C15111yescharacteristic
217C22×C4—22no—
218C22×C4—22no—
219C22×C4—22no—
220C22×C4—22no—
221C22×C4—24no—
222C22×C4—24no—
223C22×C4—22no—
224C22×C4—22no—
225C22×C4—22no—
226C22×C4—22no—
227C22×C4—41no—
228C22×C4—42no—
229C22×C4—42no—
230C22×C4—42no—
231C22×C4—42no—
232C22×C4C22⋊C4×C15111yescharacteristic
233C22×C4C22⋊C4×C15111yescharacteristic
234C22×C4C22⋊C4×C15111yescharacteristic
235C22×C4C2×C8×C15112yes—
236C22×C4M16×C15112yes—
237C22×C4SD16×C15112yes—
238C22×C4Q16×C15112yes—
239C22×C4C22×C4×C15111yescharacteristic
240C22×C4C2×D4×C15111yescharacteristic
241C22×C4C2×D4×C15111yescharacteristic
242C2×C8—24no—
243C2×C8—42no—
244C2×C8—42no—
245C2×C8—42no—
246C2×C8—42no—
247C2×C8—42no—
248C4⋊C4—24no—
249C4⋊C4—24no—
250C4⋊C4—22no—
251C4⋊C4—22no—
252C4⋊C4C2×C8×C15114yes—
253C4⋊C4M16×C15114yes—
254C42—22no—
255C42—22no—
256C42—22no—
257C42—44no—
258C42—44no—
259C42#41×C15114yes—
260C23—21no—
261C23—21no—
262C23—21no—
263C23—21no—
264C23C22⋊C8×C15112yes—
265C23#103×C15112yes—
266C23#104×C15112yes—
267C23C2×C22⋊C4×C15111yescharacteristic
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—24no—
275C2×C4—24no—
276C2×C4—24no—
277C2×C4—24no—
278C2×C4—21no—
279C2×C4—24no—
280C2×C4—24no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—44no—
284C2×C4—48no—
285C2×C4—48no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4C22⋊C8×C15112yes—
291C2×C4#103×C15112yes—
292C2×C4#117×C15112yes—
293C2×C4#123×C15112yes—
294C2×C4#123×C15112yes—
295C2×C4C22×C8×C15111yescharacteristic
296C2×C4C2×M16×C15112yes—
297C2×C4C2×M16×C15111yescharacteristic
298C2×C4C2×SD16×C15111yescharacteristic
299C2×C4C2×Q16×C15111yescharacteristic
300C2×C4AGL(1,ℤ/8)×C15112yes—
301C8—44no—
302C8—82no—
303C22—22no—
304C22—22no—
305C22—22no—
306C22—22no—
307C22—22no—
308C22—22no—
309C22Q8⋊C8×C15114yes—
310C22#381×C15111yescharacteristic
311C22C2×C22⋊C8×C15111yescharacteristic
312C22#407×C15111yescharacteristic
313C22C2×#103×C15111yescharacteristic
314C22#418×C15111yescharacteristic
315C22C2×#104×C15111yescharacteristic
316C22#421×C15111yescharacteristic
317C4—22no—
318C4—22no—
319C4—22no—
320C4—41no—
321C4—44no—
322C4—44no—
323C4#431×C15112yes—
324C4#432×C15112yes—
325C4#481×C15112yes—
326C4#484×C15112yes—
327C2—24no—
328C2C2×Q8⋊C8×C15111yescharacteristic
329C2#1478×C15111yescharacteristic
330C2#1487×C15111yescharacteristic
331C2#1490×C15111yescharacteristic
332C2#1817×C15111yescharacteristic
333C2#1824×C15111yescharacteristic
334C2#1826×C15111yescharacteristic
subgroupG/H
centerC22×C4×C151C2×D4
commutatorC2×C4C22×C8×C151
Frattini, cosocleC2×C42C23×C151
socleC23×C151C2×C22⋊C4
prime radicalC24×C151C22⋊C4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4×C151 ◁ C22×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
4. #1279×C151C2semidirect
31. C2×C4⋊C4×C151C8semidirect
167. #8707C151direct (N × H)
168. C151#8707direct (N × H)
172. #1279C2×C151semidirect
199. C2×C4⋊C4C8×C151semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C4⋊C4×C1512
#1797×C1512
C4×C22⋊C8×C1512
#1279×C1512
#8707151