Finite Group Databasebeta

← C151×#8708 #50313633

Subgroups — C151×#8708 #50313633

Order 38656.

592 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#117×C151C211yesmaximal, characteristic
2#1797×C151C211yesmaximal, characteristic
3C4×C22⋊C8×C151C211yesmaximal, characteristic
4#1279×C151C212yesmaximal, complemented
5#1279×C151C212yesmaximal, complemented
6C2×#117×C151C411yescharacteristic
7C2×#117×C151C411yescharacteristic
8C22×C42×C151C2211yescharacteristic
9C2×C4⋊C8×C151C2212yes—
10C2×C22⋊C8×C151—21no—
11C2×C22⋊C8×C151—21no—
12C2×C4×C8×C151C2212yes—
13C4×C4⋊C4×C151C411yescharacteristic
14C4×C4⋊C4×C151C411yescharacteristic
15C4×C4⋊C4×C151C2211yescharacteristic
16C4×C4⋊C4×C151C2211yescharacteristic
17C4×C22⋊C4×C151—21no—
18C4×C22⋊C4×C151—21no—
19#376×C151—21no—
20C43×C151—21no—
21#336×C151—21no—
22#336×C151—21no—
23C23×C4×C151C2×C411yescharacteristic
24C23×C4×C151D411yescharacteristic
25C23×C4×C151D411yescharacteristic
26C22×C8×C151—22no—
27C22×C8×C151—22no—
28#117×C151—22no—
29#117×C151—22no—
30#117×C151—22no—
31#117×C151C814yescomplemented
32C2×C4⋊C4×C151C2×C411yescharacteristic
33C2×C4⋊C4×C151C2×C411yescharacteristic
34C2×C4⋊C4×C151C2×C411yescharacteristic
35C2×C4⋊C4×C151C2×C411yescharacteristic
36C2×C22⋊C4×C151—21no—
37C2×C22⋊C4×C151—21no—
38C2×C42×C151—21no—
39C2×C42×C151—21no—
40C2×C42×C151—22no—
41C2×C42×C151—22no—
42C2×C42×C151—21no—
43C2×C42×C151—21no—
44C2×C42×C151—21no—
45C2×C42×C151—21no—
46C2×C42×C151C2×C411yescharacteristic
47C2×C42×C151D411yescharacteristic
48C2×C42×C151D411yescharacteristic
49C2×C42×C151C2311yescharacteristic
50C4⋊C8×C151—22no—
51C4⋊C8×C151—22no—
52C22⋊C8×C151—24no—
53C22⋊C8×C151—42no—
54C4×C8×C151—22no—
55C4×C8×C151—22no—
56#95×C151—21no—
57#95×C151—21no—
58#95×C151—21no—
59#95×C151—21no—
60C24×C151C22⋊C411yescharacteristic
61C22×C4×C151—21no—
62C22×C4×C151—21no—
63C22×C4×C151—21no—
64C22×C4×C151—21no—
65C22×C4×C151—21no—
66C22×C4×C151—21no—
67C22×C4×C151—21no—
68C22×C4×C151—21no—
69C22×C4×C151—22no—
70C22×C4×C151—22no—
71C22×C4×C151—22no—
72C22×C4×C151—22no—
73C22×C4×C151—21no—
74C22×C4×C151—21no—
75C22×C4×C151—41no—
76C22×C4×C151C22⋊C411yescharacteristic
77C22×C4×C151C22⋊C411yescharacteristic
78C22×C4×C151C22⋊C411yescharacteristic
79C22×C4×C151C2×C812yes—
80C22×C4×C151M1612yes—
81C22×C4×C151C22×C411yescharacteristic
82C22×C4×C151C2×D411yescharacteristic
83C22×C4×C151C2×D411yescharacteristic
84C2×C8×C151—24no—
85C2×C8×C151—42no—
86C2×C8×C151—42no—
87C2×C8×C151—42no—
88C2×C8×C151—42no—
89C2×C8×C151—42no—
90C4⋊C4×C151—21no—
91C4⋊C4×C151—21no—
92C4⋊C4×C151—21no—
93C4⋊C4×C151—21no—
94C4⋊C4×C151C2×C812yes—
95C4⋊C4×C151C2×C812yes—
96C4⋊C4×C151M1612yes—
97C4⋊C4×C151M1612yes—
98C22⋊C4×C151—24no—
99C22⋊C4×C151—24no—
100C42×C151—24no—
101C42×C151—24no—
102C42×C151—21no—
103C42×C151—21no—
104C42×C151—22no—
105C42×C151—22no—
106C42×C151—42no—
107C42×C151—42no—
108C42×C151—42no—
109C42×C151—41no—
110C42×C151—41no—
111C42×C151#4112yes—
112C42×C151#4112yes—
113C23×C151—21no—
114C23×C151—21no—
115C23×C151—21no—
116C23×C151—21no—
117C23×C151—21no—
118C23×C151—21no—
119C23×C151C22⋊C812yes—
120C23×C151C2×C22⋊C411yescharacteristic
121C2×C4×C151—21no—
122C2×C4×C151—21no—
123C2×C4×C151—21no—
124C2×C4×C151—21no—
125C2×C4×C151—21no—
126C2×C4×C151—21no—
127C2×C4×C151—22no—
128C2×C4×C151—22no—
129C2×C4×C151—22no—
130C2×C4×C151—22no—
131C2×C4×C151—21no—
132C2×C4×C151—22no—
133C2×C4×C151—22no—
134C2×C4×C151—22no—
135C2×C4×C151—22no—
136C2×C4×C151—21no—
137C2×C4×C151—21no—
138C2×C4×C151—44no—
139C2×C4×C151—41no—
140C2×C4×C151—41no—
141C2×C4×C151—41no—
142C2×C4×C151—41no—
143C2×C4×C151—41no—
144C2×C4×C151—41no—
145C2×C4×C151—41no—
146C2×C4×C151—41no—
147C2×C4×C151—42no—
148C2×C4×C151—42no—
149C2×C4×C151C22⋊C812yes—
150C2×C4×C151#10412yes—
151C2×C4×C151#11711yescharacteristic
152C2×C4×C151#11711yescharacteristic
153C2×C4×C151#12312yes—
154C2×C4×C151#12312yes—
155C2×C4×C151C22×C811yescharacteristic
156C2×C4×C151C2×M1611yescharacteristic
157C2×C4×C151C2×M1611yescharacteristic
158C2×C4×C151C2×M1611yescharacteristic
159C2×C4×C151#13512yes—
160C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
161C2×C4×C151#13711yescharacteristic
162C8×C151—44no—
163C8×C151—82no—
164C22×C151—22no—
165C22×C151—22no—
166C22×C151—22no—
167C22×C151—41no—
168C22×C151—41no—
169C22×C151—41no—
170C22×C151—41no—
171C22×C151#38111yescharacteristic
172C22×C151C2×C22⋊C811yescharacteristic
173C22×C151#40711yescharacteristic
174C22×C151#41611yescharacteristic
175C22×C151#41711yescharacteristic
176C22×C151C2×#10411yescharacteristic
177C22×C151#42111yescharacteristic
178C4×C151—22no—
179C4×C151—22no—
180C4×C151—22no—
181C4×C151—41no—
182C4×C151—42no—
183C4×C151—42no—
184C4×C151—42no—
185C4×C151—42no—
186C4×C151#43111yescharacteristic
187C4×C151#43111yescharacteristic
188C4×C151#43211yescharacteristic
189C4×C151#43211yescharacteristic
190C4×C151#48212yes—
191C4×C151#48512yes—
192C2×C151—42no—
193C2×C151#147611yescharacteristic
194C2×C151#147711yescharacteristic
195C2×C151#148811yescharacteristic
196C2×C151#148911yescharacteristic
197C2×C151#181711yescharacteristic
198C2×C151#182511yescharacteristic
199C2×C151#182611yescharacteristic
200#8708C15111yesmaximal, characteristic, direct product factor, Sylow
201C151#870811yescharacteristic, direct product factor, Sylow
202C4×#117C2×C15111yescharacteristic
203#1797C2×C15111yescharacteristic
204C4×C22⋊C8C2×C15111yescharacteristic
205#1279C2×C15112yescomplemented
206#1279C2×C15112yescomplemented
207C2×#117C4×C15111yescharacteristic
208C2×#117C4×C15111yescharacteristic
209C22×C42C22×C15111yescharacteristic
210C2×C4⋊C8C22×C15112yes—
211C2×C22⋊C8—21no—
212C2×C22⋊C8—21no—
213C2×C4×C8C22×C15112yes—
214C4×C4⋊C4C4×C15111yescharacteristic
215C4×C4⋊C4C4×C15111yescharacteristic
216C4×C4⋊C4C22×C15111yescharacteristic
217C4×C4⋊C4C22×C15111yescharacteristic
218C4×C22⋊C4—21no—
219C4×C22⋊C4—21no—
220#376—21no—
221C43—21no—
222#336—21no—
223#336—21no—
224C23×C4C2×C4×C15111yescharacteristic
225C23×C4D4×C15111yescharacteristic
226C23×C4D4×C15111yescharacteristic
227C22×C8—22no—
228C22×C8—22no—
229#117—22no—
230#117—22no—
231#117—22no—
232#117C8×C15114yescomplemented
233C2×C4⋊C4C2×C4×C15111yescharacteristic
234C2×C4⋊C4C2×C4×C15111yescharacteristic
235C2×C4⋊C4C2×C4×C15111yescharacteristic
236C2×C4⋊C4C2×C4×C15111yescharacteristic
237C2×C22⋊C4—21no—
238C2×C22⋊C4—21no—
239C2×C42—21no—
240C2×C42—21no—
241C2×C42—22no—
242C2×C42—22no—
243C2×C42—21no—
244C2×C42—21no—
245C2×C42—21no—
246C2×C42—21no—
247C2×C42C2×C4×C15111yescharacteristic
248C2×C42D4×C15111yescharacteristic
249C2×C42D4×C15111yescharacteristic
250C2×C42C23×C15111yescharacteristic
251C4⋊C8—22no—
252C4⋊C8—22no—
253C22⋊C8—24no—
254C22⋊C8—42no—
255C4×C8—22no—
256C4×C8—22no—
257#95—21no—
258#95—21no—
259#95—21no—
260#95—21no—
261C24C22⋊C4×C15111yescharacteristic
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—22no—
271C22×C4—22no—
272C22×C4—22no—
273C22×C4—22no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—41no—
277C22×C4C22⋊C4×C15111yescharacteristic
278C22×C4C22⋊C4×C15111yescharacteristic
279C22×C4C22⋊C4×C15111yescharacteristic
280C22×C4C2×C8×C15112yes—
281C22×C4M16×C15112yes—
282C22×C4C22×C4×C15111yescharacteristic
283C22×C4C2×D4×C15111yescharacteristic
284C22×C4C2×D4×C15111yescharacteristic
285C2×C8—24no—
286C2×C8—42no—
287C2×C8—42no—
288C2×C8—42no—
289C2×C8—42no—
290C2×C8—42no—
291C4⋊C4—21no—
292C4⋊C4—21no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4C2×C8×C15112yes—
296C4⋊C4C2×C8×C15112yes—
297C4⋊C4M16×C15112yes—
298C4⋊C4M16×C15112yes—
299C22⋊C4—24no—
300C22⋊C4—24no—
301C42—24no—
302C42—24no—
303C42—21no—
304C42—21no—
305C42—22no—
306C42—22no—
307C42—42no—
308C42—42no—
309C42—42no—
310C42—41no—
311C42—41no—
312C42#41×C15112yes—
313C42#41×C15112yes—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—21no—
318C23—21no—
319C23—21no—
320C23C22⋊C8×C15112yes—
321C23C2×C22⋊C4×C15111yescharacteristic
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—22no—
329C2×C4—22no—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—21no—
333C2×C4—22no—
334C2×C4—22no—
335C2×C4—22no—
336C2×C4—22no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—44no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4C22⋊C8×C15112yes—
351C2×C4#104×C15112yes—
352C2×C4#117×C15111yescharacteristic
353C2×C4#117×C15111yescharacteristic
354C2×C4#123×C15112yes—
355C2×C4#123×C15112yes—
356C2×C4C22×C8×C15111yescharacteristic
357C2×C4C2×M16×C15111yescharacteristic
358C2×C4C2×M16×C15111yescharacteristic
359C2×C4C2×M16×C15111yescharacteristic
360C2×C4#135×C15112yes—
361C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
362C2×C4#137×C15111yescharacteristic
363C8—44no—
364C8—82no—
365C22—22no—
366C22—22no—
367C22—22no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22#381×C15111yescharacteristic
373C22C2×C22⋊C8×C15111yescharacteristic
374C22#407×C15111yescharacteristic
375C22#416×C15111yescharacteristic
376C22#417×C15111yescharacteristic
377C22C2×#104×C15111yescharacteristic
378C22#421×C15111yescharacteristic
379C4—22no—
380C4—22no—
381C4—22no—
382C4—41no—
383C4—42no—
384C4—42no—
385C4—42no—
386C4—42no—
387C4#431×C15111yescharacteristic
388C4#431×C15111yescharacteristic
389C4#432×C15111yescharacteristic
390C4#432×C15111yescharacteristic
391C4#482×C15112yes—
392C4#485×C15112yes—
393C2—42no—
394C2#1476×C15111yescharacteristic
395C2#1477×C15111yescharacteristic
396C2#1488×C15111yescharacteristic
397C2#1489×C15111yescharacteristic
398C2#1817×C15111yescharacteristic
399C2#1825×C15111yescharacteristic
400C2#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
5. #1279×C151C2semidirect
31. #117×C151C8semidirect
200. #8708C151direct (N × H)
201. C151#8708direct (N × H)
205. #1279C2×C151semidirect
206. #1279C2×C151semidirect
232. #117C8×C151semidirect

Maximal subgroups

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

subgroupindex
C4×#117×C1512
#1797×C1512
C4×C22⋊C8×C1512
#1279×C1512
#8708151