Finite Group Databasebeta

← C151×#22969 #50327894

Subgroups — C151×#22969 #50327894

Order 38656.

886 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#476×C151C211yesmaximal, characteristic
2#2369×C151C211yesmaximal, characteristic, complemented
3D4×C4⋊C4×C151C211yesmaximal, characteristic
4#1990×C151C211yesmaximal, characteristic, complemented
5#1947×C151C211yesmaximal, characteristic, complemented
6#1944×C151C212yesmaximal, complemented
7#1920×C151C212yesmaximal, complemented
8#1862×C151C212yesmaximal
9#1770×C151C211yesmaximal, characteristic, complemented
10#1762×C151C212yesmaximal
11C4×#102×C151C211yesmaximal, characteristic
12C2×C4⋊Q8×C151C2211yescharacteristic
13C2×C4×D4×C151C2212yes—
14C2×C4×D4×C151C2211yescharacteristic
15C22×C4⋊C4×C151—21no—
16#476×C151C418yescomplemented
17C2×#107×C151C2212yes—
18C2×#106×C151C2212yes—
19C2×C4⋊C8×C151C2211yescharacteristic
20C2×#102×C151C2211yescharacteristic
21C2×#102×C151C2212yes—
22C2×#102×C151C2211yescharacteristic
23C2×#97×C151C2212yes—
24C2×C4×C8×C151C2211yescharacteristic
25#391×C151—22no—
26#389×C151—21no—
27#389×C151C2212yes—
28#389×C151C2212yes—
29#385×C151—22no—
30#384×C151C2211yescharacteristic
31#380×C151—21no—
32C4×C4⋊C4×C151—21no—
33C4×C4⋊C4×C151C2212yes—
34C4×C4⋊C4×C151C2211yescharacteristic
35C4×C4⋊C4×C151C2211yescharacteristic
36#340×C151C2212yes—
37#340×C151C2211yescharacteristic
38#340×C151C2212yes—
39#340×C151C2211yescharacteristic
40#340×C151C2212yes—
41#336×C151C2212yes—
42C22×Q8×C151—21no—
43C22×D4×C151C2311yescharacteristic
44C23×C4×C151—21no—
45C23×C4×C151—22no—
46C22×C8×C151C2311yescharacteristic
47C22×C8×C151C2312yes—
48C22×C8×C151C2311yescharacteristic
49C4⋊Q8×C151—22no—
50C4⋊Q8×C151C2×C414yescomplemented
51C4×D4×C151—24no—
52C4×D4×C151—22no—
53C4×D4×C151—42no—
54C4×D4×C151C2×C414yes—
55C2×C4⋊C4×C151—21no—
56C2×C4⋊C4×C151—21no—
57C2×C4⋊C4×C151—22no—
58C2×C4⋊C4×C151—21no—
59C2×C4⋊C4×C151—22no—
60C2×C4⋊C4×C151—44no—
61C2×C4⋊C4×C151D411yescharacteristic
62C2×C4⋊C4×C151D411yescharacteristic
63C2×C4⋊C4×C151C2312yes—
64C2×C4⋊C4×C151C2311yescharacteristic
65C2×C4⋊C4×C151C2312yes—
66C2×C4⋊C4×C151C2311yescharacteristic
67C2×C4⋊C4×C151C2311yescharacteristic
68C2×C22⋊C4×C151—21no—
69C2×C22⋊C4×C151—22no—
70C2×C42×C151—21no—
71C2×C42×C151—22no—
72C2×C42×C151C2312yes—
73C2×C42×C151C2311yescharacteristic
74#107×C151—42no—
75#106×C151C2×C418yescomplemented
76C4⋊C8×C151C2×C414yescomplemented
77#102×C151—22no—
78#102×C151C2×C418yes—
79#102×C151Q814yescomplemented
80#97×C151—42no—
81C4×C8×C151—22no—
82#95×C151—22no—
83#95×C151—22no—
84#95×C151—21no—
85#95×C151—22no—
86#95×C151D412yes—
87C24×C151—21no—
88C2×Q8×C151—24no—
89C2×Q8×C151—81no—
90C2×Q8×C151—81no—
91C2×D4×C151—21no—
92C2×D4×C151—21no—
93C2×D4×C151—21no—
94C2×D4×C151C22×C412yes—
95C2×D4×C151C2×Q812yes—
96C2×D4×C151#4112yes—
97C22×C4×C151—21no—
98C22×C4×C151—22no—
99C22×C4×C151—21no—
100C22×C4×C151—24no—
101C22×C4×C151—21no—
102C22×C4×C151—22no—
103C22×C4×C151—44no—
104C22×C4×C151—44no—
105C22×C4×C151—42no—
106C22×C4×C151—42no—
107C22×C4×C151—82no—
108C22×C4×C151C2×D412yes—
109C22×C4×C151C2×D412yes—
110C22×C4×C151C2×D411yescharacteristic
111C22×C4×C151C2×D411yescharacteristic
112C22×C4×C151C2411yescharacteristic
113C2×C8×C151—21no—
114C2×C8×C151—21no—
115C2×C8×C151—22no—
116C2×C8×C151—22no—
117C2×C8×C151—21no—
118C2×C8×C151—21no—
119C2×C8×C151—21no—
120C2×C8×C151C22×C414yes—
121C2×C8×C151C2×Q812yes—
122C4⋊C4×C151—24no—
123C4⋊C4×C151—22no—
124C4⋊C4×C151—22no—
125C4⋊C4×C151—21no—
126C4⋊C4×C151—22no—
127C4⋊C4×C151—21no—
128C4⋊C4×C151—21no—
129C4⋊C4×C151—22no—
130C4⋊C4×C151—21no—
131C4⋊C4×C151—22no—
132C4⋊C4×C151—44no—
133C4⋊C4×C151—42no—
134C4⋊C4×C151—81no—
135C4⋊C4×C151—82no—
136C4⋊C4×C151C22×C414yes—
137C4⋊C4×C151C22×C412yes—
138C4⋊C4×C151C2×Q812yes—
139C22⋊C4×C151—24no—
140C22⋊C4×C151—44no—
141C42×C151—22no—
142C42×C151—22no—
143C42×C151—42no—
144C42×C151—82no—
145C42×C151C22×C412yes—
146C42×C151#4112yes—
147C23×C151—22no—
148C23×C151—22no—
149C23×C151—22no—
150C23×C151—41no—
151C23×C151—41no—
152C23×C151—41no—
153C23×C151—41no—
154C23×C151C22×D411yescharacteristic
155Q8×C151—84no—
156D4×C151—22no—
157D4×C151—22no—
158D4×C151—22no—
159D4×C151C4×Q814yes—
160C2×C4×C151—21no—
161C2×C4×C151—21no—
162C2×C4×C151—24no—
163C2×C4×C151—22no—
164C2×C4×C151—22no—
165C2×C4×C151—22no—
166C2×C4×C151—22no—
167C2×C4×C151—22no—
168C2×C4×C151—22no—
169C2×C4×C151—22no—
170C2×C4×C151—22no—
171C2×C4×C151—41no—
172C2×C4×C151—41no—
173C2×C4×C151—41no—
174C2×C4×C151—42no—
175C2×C4×C151—42no—
176C2×C4×C151—41no—
177C2×C4×C151—48no—
178C2×C4×C151—42no—
179C2×C4×C151—41no—
180C2×C4×C151—41no—
181C2×C4×C151—42no—
182C2×C4×C151—41no—
183C2×C4×C151—42no—
184C2×C4×C151—88no—
185C2×C4×C151C4×D412yes—
186C2×C4×C151C4×D412yes—
187C2×C4×C151AGL(1,ℤ/8)12yes—
188C2×C4×C151#13712yes—
189C2×C4×C151C23×C411yescharacteristic
190C2×C4×C151C22×Q811yescharacteristic
191C2×C4×C151C2×#4111yescharacteristic
192C2×C4×C151C2×#4111yescharacteristic
193C2×C4×C151H(5,𝔽2)11yescharacteristic
194C2×C4×C1512−1+411yescharacteristic
195C8×C151—24no—
196C8×C151—22no—
197C8×C151—41no—
198C22×C151—24no—
199C22×C151—42no—
200C22×C151—42no—
201C22×C151—42no—
202C22×C151—42no—
203C22×C151—42no—
204C22×C151—42no—
205C22×C151C2×C4×D411yescharacteristic
206C22×C151#54611yescharacteristic
207C22×C151D4×Q811yescharacteristic
208C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
209C22×C151C2×#13711yescharacteristic
210C22×C151#57611yescharacteristic
211C22×C151#57711yescharacteristic
212C4×C151—22no—
213C4×C151—42no—
214C4×C151—42no—
215C4×C151—42no—
216C4×C151—44no—
217C4×C151—42no—
218C4×C151—81no—
219C4×C151—82no—
220C4×C151#44014yes—
221C4×C151C2×C4×Q811yescharacteristic
222C4×C151#52011yescharacteristic
223C4×C151#55211yescharacteristic
224C4×C151#55411yescharacteristic
225C2×C151—44no—
226C2×C151#236011yescharacteristic
227C2×C151C2×#44011yescharacteristic
228C2×C151#294611yescharacteristic
229C2×C151#332511yescharacteristic
230C2×C151#333111yescharacteristic
231C2×C151#338411yescharacteristic
232C2×C151#338511yescharacteristic
233#22969C15111yesmaximal, characteristic, direct product factor, Sylow
234C151#2296911yescharacteristic, direct product factor, Sylow
235C2×#476C2×C15111yescharacteristic
236#2369C2×C15111yescharacteristic, complemented
237D4×C4⋊C4C2×C15111yescharacteristic
238#1990C2×C15111yescharacteristic, complemented
239#1947C2×C15111yescharacteristic, complemented
240#1944C2×C15112yescomplemented
241#1920C2×C15112yescomplemented
242#1862C2×C15112yes—
243#1770C2×C15111yescharacteristic, complemented
244#1762C2×C15112yes—
245C4×#102C2×C15111yescharacteristic
246C2×C4⋊Q8C22×C15111yescharacteristic
247C2×C4×D4C22×C15112yes—
248C2×C4×D4C22×C15111yescharacteristic
249C22×C4⋊C4—21no—
250#476C4×C15118yescomplemented
251C2×#107C22×C15112yes—
252C2×#106C22×C15112yes—
253C2×C4⋊C8C22×C15111yescharacteristic
254C2×#102C22×C15111yescharacteristic
255C2×#102C22×C15112yes—
256C2×#102C22×C15111yescharacteristic
257C2×#97C22×C15112yes—
258C2×C4×C8C22×C15111yescharacteristic
259#391—22no—
260#389—21no—
261#389C22×C15112yes—
262#389C22×C15112yes—
263#385—22no—
264#384C22×C15111yescharacteristic
265#380—21no—
266C4×C4⋊C4—21no—
267C4×C4⋊C4C22×C15112yes—
268C4×C4⋊C4C22×C15111yescharacteristic
269C4×C4⋊C4C22×C15111yescharacteristic
270#340C22×C15112yes—
271#340C22×C15111yescharacteristic
272#340C22×C15112yes—
273#340C22×C15111yescharacteristic
274#340C22×C15112yes—
275#336C22×C15112yes—
276C22×Q8—21no—
277C22×D4C23×C15111yescharacteristic
278C23×C4—21no—
279C23×C4—22no—
280C22×C8C23×C15111yescharacteristic
281C22×C8C23×C15111yescharacteristic
282C22×C8C23×C15112yes—
283C4⋊Q8—22no—
284C4⋊Q8C2×C4×C15114yescomplemented
285C4×D4—24no—
286C4×D4—22no—
287C4×D4—42no—
288C4×D4C2×C4×C15114yes—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—44no—
295C2×C4⋊C4D4×C15111yescharacteristic
296C2×C4⋊C4D4×C15111yescharacteristic
297C2×C4⋊C4C23×C15112yes—
298C2×C4⋊C4C23×C15111yescharacteristic
299C2×C4⋊C4C23×C15111yescharacteristic
300C2×C4⋊C4C23×C15111yescharacteristic
301C2×C4⋊C4C23×C15112yes—
302C2×C22⋊C4—21no—
303C2×C22⋊C4—22no—
304C2×C42—21no—
305C2×C42—22no—
306C2×C42C23×C15112yes—
307C2×C42C23×C15111yescharacteristic
308#107—42no—
309#106C2×C4×C15118yescomplemented
310C4⋊C8C2×C4×C15114yescomplemented
311#102—22no—
312#102C2×C4×C15118yes—
313#102Q8×C15114yescomplemented
314#97—42no—
315C4×C8—22no—
316#95—22no—
317#95—22no—
318#95—21no—
319#95—22no—
320#95D4×C15112yes—
321C24—21no—
322C2×Q8—24no—
323C2×Q8—81no—
324C2×Q8—81no—
325C2×D4—21no—
326C2×D4—21no—
327C2×D4—21no—
328C2×D4C22×C4×C15112yes—
329C2×D4C2×Q8×C15112yes—
330C2×D4#41×C15112yes—
331C22×C4—21no—
332C22×C4—22no—
333C22×C4—21no—
334C22×C4—24no—
335C22×C4—21no—
336C22×C4—22no—
337C22×C4—44no—
338C22×C4—44no—
339C22×C4—42no—
340C22×C4—42no—
341C22×C4—82no—
342C22×C4C2×D4×C15112yes—
343C22×C4C2×D4×C15112yes—
344C22×C4C2×D4×C15111yescharacteristic
345C22×C4C2×D4×C15111yescharacteristic
346C22×C4C24×C15111yescharacteristic
347C2×C8—21no—
348C2×C8—21no—
349C2×C8—22no—
350C2×C8—22no—
351C2×C8—21no—
352C2×C8—21no—
353C2×C8—21no—
354C2×C8C22×C4×C15114yes—
355C2×C8C2×Q8×C15112yes—
356C4⋊C4—24no—
357C4⋊C4—22no—
358C4⋊C4—22no—
359C4⋊C4—21no—
360C4⋊C4—22no—
361C4⋊C4—21no—
362C4⋊C4—21no—
363C4⋊C4—22no—
364C4⋊C4—21no—
365C4⋊C4—22no—
366C4⋊C4—44no—
367C4⋊C4—42no—
368C4⋊C4—81no—
369C4⋊C4—82no—
370C4⋊C4C22×C4×C15114yes—
371C4⋊C4C22×C4×C15112yes—
372C4⋊C4C2×Q8×C15112yes—
373C22⋊C4—24no—
374C22⋊C4—44no—
375C42—22no—
376C42—22no—
377C42—42no—
378C42—82no—
379C42C22×C4×C15112yes—
380C42#41×C15112yes—
381C23—22no—
382C23—22no—
383C23—22no—
384C23—41no—
385C23—41no—
386C23—41no—
387C23—41no—
388C23C22×D4×C15111yescharacteristic
389Q8—84no—
390D4—22no—
391D4—22no—
392D4—22no—
393D4C4×Q8×C15114yes—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—22no—
397C2×C4—24no—
398C2×C4—22no—
399C2×C4—22no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—22no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—42no—
409C2×C4—41no—
410C2×C4—42no—
411C2×C4—48no—
412C2×C4—42no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—42no—
416C2×C4—41no—
417C2×C4—42no—
418C2×C4—88no—
419C2×C4C4×D4×C15112yes—
420C2×C4C4×D4×C15112yes—
421C2×C4AGL(1,ℤ/8)×C15112yes—
422C2×C4#137×C15112yes—
423C2×C4C23×C4×C15111yescharacteristic
424C2×C4C22×Q8×C15111yescharacteristic
425C2×C4C2×#41×C15111yescharacteristic
426C2×C4C2×#41×C15111yescharacteristic
427C2×C4H(5,𝔽2)×C15111yescharacteristic
428C2×C42−1+4×C15111yescharacteristic
429C8—24no—
430C8—22no—
431C8—41no—
432C22—24no—
433C22—42no—
434C22—42no—
435C22—42no—
436C22—42no—
437C22—42no—
438C22—42no—
439C22C2×C4×D4×C15111yescharacteristic
440C22#546×C15111yescharacteristic
441C22D4×Q8×C15111yescharacteristic
442C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
443C22C2×#137×C15111yescharacteristic
444C22#576×C15111yescharacteristic
445C22#577×C15111yescharacteristic
446C4—22no—
447C4—42no—
448C4—42no—
449C4—44no—
450C4—42no—
451C4—42no—
452C4—82no—
453C4—81no—
454C4#440×C15114yes—
455C4C2×C4×Q8×C15111yescharacteristic
456C4#520×C15111yescharacteristic
457C4#552×C15111yescharacteristic
458C4#554×C15111yescharacteristic
459C2—44no—
460C2#2360×C15111yescharacteristic
461C2C2×#440×C15111yescharacteristic
462C2#2946×C15111yescharacteristic
463C2#3325×C15111yescharacteristic
464C2#3331×C15111yescharacteristic
465C2#3384×C15111yescharacteristic
466C2#3385×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutatorC2×C4C23×C4×C151
Frattini, cosocleC22×C4C24×C151
prime radicalC22×D4×C151C23
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C4×C4⋊C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2369×C151C2semidirect
4. #1990×C151C2semidirect
5. #1947×C151C2semidirect
6. #1944×C151C2semidirect
7. #1920×C151C2semidirect
9. #1770×C151C2semidirect
16. #476×C151C4semidirect
50. C4⋊Q8×C151C2×C4semidirect
75. #106×C151C2×C4semidirect
76. C4⋊C8×C151C2×C4semidirect
79. #102×C151Q8semidirect
233. #22969C151direct (N × H)
234. C151#22969direct (N × H)
236. #2369C2×C151semidirect
238. #1990C2×C151semidirect
239. #1947C2×C151semidirect
240. #1944C2×C151semidirect
241. #1920C2×C151semidirect
243. #1770C2×C151semidirect
250. #476C4×C151semidirect
284. C4⋊Q8C2×C4×C151semidirect
309. #106C2×C4×C151semidirect
310. C4⋊C8C2×C4×C151semidirect
313. #102Q8×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#476×C1512
#2369×C1512
D4×C4⋊C4×C1512
#1990×C1512
#1947×C1512
#1944×C1512
#1920×C1512
#1862×C1512
#1770×C1512
#1762×C1512
C4×#102×C1512
#22969151