Finite Group Databasebeta

← C151×#9253 #50314178

Subgroups — C151×#9253 #50314178

Order 38656.

612 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#459×C151C211yesmaximal, characteristic
2D4×M16×C151C211yesmaximal, characteristic, complemented
3#1965×C151C211yesmaximal, characteristic, complemented
4#1545×C151C211yesmaximal, characteristic, complemented
5#1486×C151C211yesmaximal, characteristic, complemented
6#1292×C151C211yesmaximal, characteristic, complemented
7#1283×C151C211yesmaximal, characteristic, complemented
8C22×D8×C151C412yes—
9C22×M16×C151—21no—
10C2×#127×C151C2211yescharacteristic
11C2×C4×D4×C151C2211yescharacteristic
12#459×C151—21no—
13#459×C151—21no—
14#459×C151—21no—
15#459×C151—21no—
16#436×C151—21no—
17#435×C151—22no—
18C8×D4×C151—21no—
19#431×C151C2211yescharacteristic
20#423×C151C2211yescharacteristic
21#423×C151C2211yescharacteristic
22C2×C4⋊C8×C151C2211yescharacteristic
23C2×#102×C151C412yes—
24C2×#100×C151—21no—
25C2×#100×C151—21no—
26#407×C151—21no—
27C4×M16×C151C2211yescharacteristic
28#331×C151—22no—
29D4⋊C8×C151—21no—
30D4⋊C8×C151—21no—
31C22×D4×C151—21no—
32C22×D4×C151—21no—
33C22×D4×C151C2×C411yescharacteristic
34C22×D4×C151C2×C412yes—
35C23×C4×C151—21no—
36C2×D8×C151—22no—
37C2×D8×C151—22no—
38C2×D8×C151—44no—
39C2×M16×C151—22no—
40C2×M16×C151—21no—
41C2×M16×C151—21no—
42C2×M16×C151—42no—
43C2×M16×C151—42no—
44C2×M16×C151D411yescharacteristic
45C2×M16×C151D411yescharacteristic
46C22×C8×C151—22no—
47C22×C8×C151C2×C412yes—
48#127×C151—21no—
49#127×C151—21no—
50#127×C151—21no—
51#127×C151—21no—
52C4×D4×C151—21no—
53C4×D4×C151—21no—
54C4×D4×C151D411yescharacteristic
55C4×D4×C151D411yescharacteristic
56C4×D4×C151D411yescharacteristic
57C4×D4×C151D411yescharacteristic
58C2×C4⋊C4×C151C2×C411yescharacteristic
59C2×C22⋊C4×C151—21no—
60C2×C42×C151C2311yescharacteristic
61C4⋊C8×C151—21no—
62C4⋊C8×C151—21no—
63C4⋊C8×C151—21no—
64C4⋊C8×C151—21no—
65C4⋊C8×C151—21no—
66C4⋊C8×C151—21no—
67C4⋊C8×C151D412yes—
68#102×C151—22no—
69#102×C151—22no—
70#100×C151—42no—
71#100×C151—42no—
72C22⋊C8×C151—22no—
73C22⋊C8×C151—22no—
74C22⋊C8×C151—21no—
75#97×C151—21no—
76C4×C8×C151—21no—
77C4×C8×C151—21no—
78C24×C151—21no—
79C24×C151—22no—
80C2×D4×C151—22no—
81C2×D4×C151—22no—
82C2×D4×C151—21no—
83C2×D4×C151—22no—
84C2×D4×C151—41no—
85C2×D4×C151—42no—
86C2×D4×C151—42no—
87C2×D4×C151—41no—
88C2×D4×C151—41no—
89C2×D4×C151—41no—
90C2×D4×C151—41no—
91C2×D4×C151—41no—
92C2×D4×C151—41no—
93C2×D4×C151—41no—
94C2×D4×C151—41no—
95C2×D4×C151—82no—
96C2×D4×C151C22⋊C411yescharacteristic
97C2×D4×C151C22⋊C411yescharacteristic
98C22×C4×C151—21no—
99C22×C4×C151—21no—
100C22×C4×C151—21no—
101C22×C4×C151—21no—
102C22×C4×C151—21no—
103C22×C4×C151—41no—
104C22×C4×C151—41no—
105C22×C4×C151—41no—
106C22×C4×C151—41no—
107C22×C4×C151C22×C411yescharacteristic
108C22×C4×C151C2×D411yescharacteristic
109C22×C4×C151#4111yescharacteristic
110D8×C151—44no—
111D8×C151—44no—
112M16×C151—21no—
113M16×C151—21no—
114M16×C151—21no—
115M16×C151—44no—
116M16×C151—41no—
117M16×C151—41no—
118M16×C151—41no—
119M16×C151—41no—
120M16×C151D812yescomplemented
121C2×C8×C151—21no—
122C2×C8×C151—22no—
123C2×C8×C151—21no—
124C2×C8×C151—22no—
125C2×C8×C151—44no—
126C2×C8×C151—42no—
127C2×C8×C151—41no—
128C2×C8×C151—41no—
129C4⋊C4×C151—21no—
130C4⋊C4×C151C22⋊C411yescharacteristic
131C4⋊C4×C151C22⋊C411yescharacteristic
132C22⋊C4×C151—21no—
133C22⋊C4×C151—21no—
134C22⋊C4×C151—21no—
135C22⋊C4×C151—21no—
136C42×C151C2×D411yescharacteristic
137C42×C151C2×D411yescharacteristic
138C42×C151C2×D411yescharacteristic
139C42×C151#4111yescharacteristic
140C23×C151—21no—
141C23×C151—21no—
142C23×C151—42no—
143C23×C151—41no—
144C23×C151—41no—
145C23×C151—42no—
146C23×C151—42no—
147C23×C151—42no—
148C23×C151—81no—
149C23×C151—82no—
150C23×C151—82no—
151C23×C151C4×D411yescharacteristic
152D4×C151—21no—
153D4×C151—21no—
154D4×C151—21no—
155D4×C151—42no—
156D4×C151—42no—
157D4×C151—42no—
158D4×C151—82no—
159D4×C151—82no—
160D4×C151—82no—
161D4×C151—81no—
162D4×C151—81no—
163D4×C151—81no—
164D4×C151—81no—
165D4×C151#10012yescomplemented
166C2×C4×C151—21no—
167C2×C4×C151—21no—
168C2×C4×C151—21no—
169C2×C4×C151—21no—
170C2×C4×C151—41no—
171C2×C4×C151—41no—
172C2×C4×C151—41no—
173C2×C4×C151—41no—
174C2×C4×C151—41no—
175C2×C4×C151—41no—
176C2×C4×C151—41no—
177C2×C4×C151—41no—
178C2×C4×C151—41no—
179C2×C4×C151—41no—
180C2×C4×C151—41no—
181C2×C4×C151C2×C22⋊C411yescharacteristic
182C2×C4×C151C4×D411yescharacteristic
183C2×C4×C151#12011yescharacteristic
184C2×C4×C151#12111yescharacteristic
185C2×C4×C151#12111yescharacteristic
186C2×C4×C151#12311yescharacteristic
187C2×C4×C151C2×D811yescharacteristic
188C2×C4×C151#13511yescharacteristic
189C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
190C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
191C8×C151—22no—
192C8×C151—42no—
193C8×C151—42no—
194C8×C151—41no—
195C8×C151—81no—
196C8×C151—81no—
197C22×C151—21no—
198C22×C151—21no—
199C22×C151—22no—
200C22×C151—41no—
201C22×C151—41no—
202C22×C151—41no—
203C22×C151—41no—
204C22×C151—41no—
205C22×C151—82no—
206C22×C151—82no—
207C22×C151—82no—
208C22×C151—82no—
209C22×C151—82no—
210C22×C151—162no—
211C22×C151—162no—
212C22×C151#38611yescharacteristic
213C22×C151C4×D811yescharacteristic
214C22×C151#44211yescharacteristic
215C4×C151—21no—
216C4×C151—21no—
217C4×C151—21no—
218C4×C151—41no—
219C4×C151—41no—
220C4×C151C2×#10011yescharacteristic
221C4×C151#41311yescharacteristic
222C4×C151#44711yescharacteristic
223C4×C151#44911yescharacteristic
224C4×C151#45911yescharacteristic
225C4×C151#46311yescharacteristic
226C2×C151—21no—
227C2×C151—21no—
228C2×C151—42no—
229C2×C151—81no—
230C2×C151—162no—
231C2×C151#187911yescharacteristic
232C2×C151#190011yescharacteristic
233C2×C151#190311yescharacteristic
234#9253C15111yesmaximal, characteristic, direct product factor, Sylow
235C151#925311yescharacteristic, direct product factor, Sylow
236C2×#459C2×C15111yescharacteristic
237D4×M16C2×C15111yescharacteristic, complemented
238#1965C2×C15111yescharacteristic, complemented
239#1545C2×C15111yescharacteristic, complemented
240#1486C2×C15111yescharacteristic, complemented
241#1292C2×C15111yescharacteristic, complemented
242#1283C2×C15111yescharacteristic, complemented
243C22×D8C4×C15112yes—
244C22×M16—21no—
245C2×#127C22×C15111yescharacteristic
246C2×C4×D4C22×C15111yescharacteristic
247#459—21no—
248#459—21no—
249#459—21no—
250#459—21no—
251#436—21no—
252#435—22no—
253C8×D4—21no—
254#431C22×C15111yescharacteristic
255#423C22×C15111yescharacteristic
256#423C22×C15111yescharacteristic
257C2×C4⋊C8C22×C15111yescharacteristic
258C2×#102C4×C15112yes—
259C2×#100—21no—
260C2×#100—21no—
261#407—21no—
262C4×M16C22×C15111yescharacteristic
263#331—22no—
264D4⋊C8—21no—
265D4⋊C8—21no—
266C22×D4—21no—
267C22×D4—21no—
268C22×D4C2×C4×C15111yescharacteristic
269C22×D4C2×C4×C15112yes—
270C23×C4—21no—
271C2×D8—22no—
272C2×D8—22no—
273C2×D8—44no—
274C2×M16—22no—
275C2×M16—21no—
276C2×M16—21no—
277C2×M16—42no—
278C2×M16—42no—
279C2×M16D4×C15111yescharacteristic
280C2×M16D4×C15111yescharacteristic
281C22×C8—22no—
282C22×C8C2×C4×C15112yes—
283#127—21no—
284#127—21no—
285#127—21no—
286#127—21no—
287C4×D4—21no—
288C4×D4—21no—
289C4×D4D4×C15111yescharacteristic
290C4×D4D4×C15111yescharacteristic
291C4×D4D4×C15111yescharacteristic
292C4×D4D4×C15111yescharacteristic
293C2×C4⋊C4C2×C4×C15111yescharacteristic
294C2×C22⋊C4—21no—
295C2×C42C23×C15111yescharacteristic
296C4⋊C8—21no—
297C4⋊C8—21no—
298C4⋊C8—21no—
299C4⋊C8—21no—
300C4⋊C8—21no—
301C4⋊C8—21no—
302C4⋊C8D4×C15112yes—
303#102—22no—
304#102—22no—
305#100—42no—
306#100—42no—
307C22⋊C8—22no—
308C22⋊C8—22no—
309C22⋊C8—21no—
310#97—21no—
311C4×C8—21no—
312C4×C8—21no—
313C24—21no—
314C24—22no—
315C2×D4—22no—
316C2×D4—22no—
317C2×D4—21no—
318C2×D4—22no—
319C2×D4—41no—
320C2×D4—42no—
321C2×D4—42no—
322C2×D4—41no—
323C2×D4—41no—
324C2×D4—41no—
325C2×D4—41no—
326C2×D4—41no—
327C2×D4—41no—
328C2×D4—41no—
329C2×D4—41no—
330C2×D4—82no—
331C2×D4C22⋊C4×C15111yescharacteristic
332C2×D4C22⋊C4×C15111yescharacteristic
333C22×C4—21no—
334C22×C4—21no—
335C22×C4—21no—
336C22×C4—21no—
337C22×C4—21no—
338C22×C4—41no—
339C22×C4—41no—
340C22×C4—41no—
341C22×C4—41no—
342C22×C4C22×C4×C15111yescharacteristic
343C22×C4C2×D4×C15111yescharacteristic
344C22×C4#41×C15111yescharacteristic
345D8—44no—
346D8—44no—
347M16—21no—
348M16—21no—
349M16—21no—
350M16—44no—
351M16—41no—
352M16—41no—
353M16—41no—
354M16—41no—
355M16D8×C15112yescomplemented
356C2×C8—21no—
357C2×C8—22no—
358C2×C8—21no—
359C2×C8—22no—
360C2×C8—44no—
361C2×C8—42no—
362C2×C8—41no—
363C2×C8—41no—
364C4⋊C4—21no—
365C4⋊C4C22⋊C4×C15111yescharacteristic
366C4⋊C4C22⋊C4×C15111yescharacteristic
367C22⋊C4—21no—
368C22⋊C4—21no—
369C22⋊C4—21no—
370C22⋊C4—21no—
371C42C2×D4×C15111yescharacteristic
372C42C2×D4×C15111yescharacteristic
373C42C2×D4×C15111yescharacteristic
374C42#41×C15111yescharacteristic
375C23—21no—
376C23—21no—
377C23—42no—
378C23—41no—
379C23—41no—
380C23—42no—
381C23—42no—
382C23—42no—
383C23—81no—
384C23—82no—
385C23—82no—
386C23C4×D4×C15111yescharacteristic
387D4—21no—
388D4—21no—
389D4—21no—
390D4—42no—
391D4—42no—
392D4—42no—
393D4—82no—
394D4—82no—
395D4—82no—
396D4—81no—
397D4—81no—
398D4—81no—
399D4—81no—
400D4#100×C15112yescomplemented
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4C2×C22⋊C4×C15111yescharacteristic
417C2×C4C4×D4×C15111yescharacteristic
418C2×C4#120×C15111yescharacteristic
419C2×C4#121×C15111yescharacteristic
420C2×C4#121×C15111yescharacteristic
421C2×C4#123×C15111yescharacteristic
422C2×C4C2×D8×C15111yescharacteristic
423C2×C4#135×C15111yescharacteristic
424C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
425C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
426C8—22no—
427C8—42no—
428C8—42no—
429C8—41no—
430C8—81no—
431C8—81no—
432C22—21no—
433C22—21no—
434C22—22no—
435C22—41no—
436C22—41no—
437C22—41no—
438C22—41no—
439C22—41no—
440C22—82no—
441C22—82no—
442C22—82no—
443C22—82no—
444C22—82no—
445C22—162no—
446C22—162no—
447C22#386×C15111yescharacteristic
448C22C4×D8×C15111yescharacteristic
449C22#442×C15111yescharacteristic
450C4—21no—
451C4—21no—
452C4—21no—
453C4—41no—
454C4—41no—
455C4C2×#100×C15111yescharacteristic
456C4#413×C15111yescharacteristic
457C4#447×C15111yescharacteristic
458C4#449×C15111yescharacteristic
459C4#459×C15111yescharacteristic
460C4#463×C15111yescharacteristic
461C2—21no—
462C2—21no—
463C2—42no—
464C2—81no—
465C2—162no—
466C2#1879×C15111yescharacteristic
467C2#1900×C15111yescharacteristic
468C2#1903×C15111yescharacteristic
subgroupG/H
center, socleC22×C151#386
commutatorC22×C4C22×C4×C151
Frattini, cosocleC2×C42C23×C151
prime radicalC2×#459×C151C2
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
2. D4×M16×C151C2semidirect
3. #1965×C151C2semidirect
4. #1545×C151C2semidirect
5. #1486×C151C2semidirect
6. #1292×C151C2semidirect
7. #1283×C151C2semidirect
120. M16×C151D8semidirect
165. D4×C151#100semidirect
234. #9253C151direct (N × H)
235. C151#9253direct (N × H)
237. D4×M16C2×C151semidirect
238. #1965C2×C151semidirect
239. #1545C2×C151semidirect
240. #1486C2×C151semidirect
241. #1292C2×C151semidirect
242. #1283C2×C151semidirect
355. M16D8×C151semidirect
400. D4#100×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#459×C1512
D4×M16×C1512
#1965×C1512
#1545×C1512
#1486×C1512
#1292×C1512
#1283×C1512
#9253151