Finite Group Databasebeta

← C151×#12793 #50317718

Subgroups — C151×#12793 #50317718

Order 38656.

808 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#120×C151C211yesmaximal, characteristic
2C2×AΣL(1,𝔽16)×C151C212yesmaximal
3#1800×C151C211yesmaximal, characteristic, complemented
4#1799×C151C211yesmaximal, characteristic, complemented
5#1390×C151C212yesmaximal, complemented
6C24×C4×C151C411yescharacteristic, complemented
7C2×#120×C151C2211yescharacteristic
8C2×C4×D4×C151—21no—
9C2×C4×D4×C151C2211yescharacteristic
10#423×C151—21no—
11C2×#100×C151C2212yes—
12C2×#99×C151C2212yes—
13#386×C151—21no—
14#386×C151C2211yescharacteristic
15#385×C151—21no—
16#385×C151C411yescharacteristic, complemented
17#380×C151—21no—
18#379×C151C411yescharacteristic, complemented
19C4×C22⋊C4×C151—21no—
20C4×C22⋊C4×C151C411yescharacteristic, complemented
21AΣL(1,𝔽16)×C151—24no—
22#343×C151—21no—
23#342×C151—21no—
24C25×C151C2×C411yescharacteristic
25C22×D4×C151—21no—
26C22×D4×C151C2311yescharacteristic
27C23×C4×C151—21no—
28C23×C4×C151—21no—
29C23×C4×C151—44no—
30C23×C4×C151—41no—
31C23×C4×C151—41no—
32C23×C4×C151C2×C411yescharacteristic
33C23×C4×C151C2×C411yescharacteristic
34C23×C4×C151D411yescharacteristic
35C2×M16×C151—22no—
36#120×C151—21no—
37#120×C151—21no—
38#120×C151D412yes—
39#120×C151Q812yes—
40C4×D4×C151—41no—
41C4×D4×C151—41no—
42C4×D4×C151—44no—
43C2×C4⋊C4×C151—21no—
44C2×C4⋊C4×C151—41no—
45C2×C4⋊C4×C151D411yescharacteristic
46C2×C22⋊C4×C151—21no—
47C2×C22⋊C4×C151—21no—
48C2×C22⋊C4×C151—21no—
49C2×C22⋊C4×C151—21no—
50C2×C22⋊C4×C151—22no—
51C2×C22⋊C4×C151C2×C411yescharacteristic
52C2×C22⋊C4×C151C2×C411yescharacteristic
53C2×C22⋊C4×C151C2×C411yescharacteristic
54C2×C22⋊C4×C151D411yescharacteristic
55C2×C42×C151—21no—
56C2×C42×C151D411yescharacteristic
57C4⋊C8×C151—41no—
58C4⋊C8×C151—41no—
59#100×C151—22no—
60#100×C151—22no—
61#99×C151—22no—
62#99×C151—22no—
63#95×C151—21no—
64#95×C151—21no—
65#95×C151—21no—
66#95×C151—41no—
67C24×C151—21no—
68C24×C151—21no—
69C24×C151—42no—
70C24×C151—41no—
71C24×C151—42no—
72C24×C151—41no—
73C24×C151C4⋊C412yescomplemented
74C24×C151C22×C411yescharacteristic
75C24×C151C2×D411yescharacteristic
76C2×D4×C151—22no—
77C2×D4×C151—22no—
78C2×D4×C151—41no—
79C2×D4×C151—41no—
80C2×D4×C151—42no—
81C2×D4×C151—42no—
82C2×D4×C151C2×D411yescharacteristic
83C2×D4×C151C2×Q811yescharacteristic
84C2×D4×C151#4111yescharacteristic
85C2×D4×C151#4111yescharacteristic
86C22×C4×C151—24no—
87C22×C4×C151—21no—
88C22×C4×C151—21no—
89C22×C4×C151—21no—
90C22×C4×C151—21no—
91C22×C4×C151—21no—
92C22×C4×C151—21no—
93C22×C4×C151—21no—
94C22×C4×C151—42no—
95C22×C4×C151—42no—
96C22×C4×C151—42no—
97C22×C4×C151—42no—
98C22×C4×C151—42no—
99C22×C4×C151—42no—
100C22×C4×C151—42no—
101C22×C4×C151—44no—
102C22×C4×C151—44no—
103C22×C4×C151—44no—
104C22×C4×C151—41no—
105C22×C4×C151—41no—
106C22×C4×C151—41no—
107C22×C4×C151—44no—
108C22×C4×C151—42no—
109C22×C4×C151C22⋊C411yescharacteristic
110C22×C4×C151C22⋊C411yescharacteristic
111C22×C4×C151C22⋊C411yescharacteristic
112C22×C4×C151C22⋊C411yescharacteristic
113C22×C4×C151C2×D411yescharacteristic
114M16×C151—42no—
115M16×C151—42no—
116C2×C8×C151—42no—
117C4⋊C4×C151—41no—
118C4⋊C4×C151—42no—
119C4⋊C4×C151—82no—
120C22⋊C4×C151—21no—
121C22⋊C4×C151—22no—
122C22⋊C4×C151—22no—
123C22⋊C4×C151—41no—
124C22⋊C4×C151—41no—
125C22⋊C4×C151—42no—
126C22⋊C4×C151—42no—
127C22⋊C4×C151—42no—
128C22⋊C4×C151—41no—
129C22⋊C4×C151—42no—
130C22⋊C4×C151—42no—
131C22⋊C4×C151C4⋊C412yescomplemented
132C42×C151—21no—
133C42×C151—21no—
134C42×C151—42no—
135C23×C151—22no—
136C23×C151—22no—
137C23×C151—22no—
138C23×C151—21no—
139C23×C151—21no—
140C23×C151—21no—
141C23×C151—21no—
142C23×C151—44no—
143C23×C151—42no—
144C23×C151—41no—
145C23×C151—41no—
146C23×C151—41no—
147C23×C151—44no—
148C23×C151—42no—
149C23×C151—41no—
150C23×C151—41no—
151C23×C151—41no—
152C23×C151—42no—
153C23×C151—42no—
154C23×C151—48no—
155C23×C151—42no—
156C23×C151—42no—
157C23×C151—41no—
158C23×C151—41no—
159C23×C151C2×C22⋊C411yescharacteristic
160C23×C151C2×C4⋊C411yescharacteristic
161C23×C151#11711yescharacteristic
162C23×C151#12111yescharacteristic
163C23×C151C22⋊Q811yescharacteristic
164D4×C151—41no—
165D4×C151—41no—
166D4×C151—41no—
167D4×C151—41no—
168D4×C151—44no—
169D4×C151—44no—
170C2×C4×C151—21no—
171C2×C4×C151—21no—
172C2×C4×C151—22no—
173C2×C4×C151—22no—
174C2×C4×C151—22no—
175C2×C4×C151—21no—
176C2×C4×C151—21no—
177C2×C4×C151—21no—
178C2×C4×C151—44no—
179C2×C4×C151—42no—
180C2×C4×C151—41no—
181C2×C4×C151—41no—
182C2×C4×C151—41no—
183C2×C4×C151—48no—
184C2×C4×C151—42no—
185C2×C4×C151—41no—
186C2×C4×C151—42no—
187C2×C4×C151—44no—
188C2×C4×C151—42no—
189C2×C4×C151—41no—
190C2×C4×C151—41no—
191C2×C4×C151—41no—
192C2×C4×C151—42no—
193C2×C4×C151—41no—
194C2×C4×C151—41no—
195C2×C4×C151—41no—
196C2×C4×C151—81no—
197C2×C4×C151—82no—
198C2×C4×C151—82no—
199C2×C4×C151—82no—
200C2×C4×C151#9911yescharacteristic
201C2×C4×C151#9911yescharacteristic
202C2×C4×C151#12111yescharacteristic
203C2×C4×C151C22⋊Q811yescharacteristic
204C8×C151—82no—
205C22×C151—21no—
206C22×C151—21no—
207C22×C151—24no—
208C22×C151—21no—
209C22×C151—21no—
210C22×C151—21no—
211C22×C151—21no—
212C22×C151—41no—
213C22×C151—41no—
214C22×C151—41no—
215C22×C151—41no—
216C22×C151—42no—
217C22×C151—42no—
218C22×C151—42no—
219C22×C151—42no—
220C22×C151—44no—
221C22×C151—44no—
222C22×C151—44no—
223C22×C151—44no—
224C22×C151—42no—
225C22×C151—42no—
226C22×C151—41no—
227C22×C151—41no—
228C22×C151—41no—
229C22×C151—42no—
230C22×C151—41no—
231C22×C151—81no—
232C22×C151#38011yescharacteristic
233C22×C151C2×#9911yescharacteristic
234C22×C151#41011yescharacteristic
235C4×C151—21no—
236C4×C151—21no—
237C4×C151—21no—
238C4×C151—42no—
239C4×C151—42no—
240C4×C151—41no—
241C4×C151—41no—
242C4×C151—41no—
243C4×C151—81no—
244C4×C151—162no—
245C4×C151AΣL(1,𝔽16)12yescomplemented
246C2×C151—21no—
247C2×C151—21no—
248C2×C151—41no—
249C2×C151—44no—
250C2×C151—41no—
251C2×C151—41no—
252C2×C151—41no—
253C2×C151#179911yescharacteristic
254C2×C151C2×AΣL(1,𝔽16)11yescharacteristic
255C2×C151#212011yescharacteristic
256#12793C15111yesmaximal, characteristic, direct product factor, Sylow
257C151#1279311yescharacteristic, direct product factor, Sylow
258C4×#120C2×C15111yescharacteristic
259C2×AΣL(1,𝔽16)C2×C15112yes—
260#1800C2×C15111yescharacteristic, complemented
261#1799C2×C15111yescharacteristic, complemented
262#1390C2×C15112yescomplemented
263C24×C4C4×C15111yescharacteristic, complemented
264C2×#120C22×C15111yescharacteristic
265C2×C4×D4—21no—
266C2×C4×D4C22×C15111yescharacteristic
267#423—21no—
268C2×#100C22×C15112yes—
269C2×#99C22×C15112yes—
270#386—21no—
271#386C22×C15111yescharacteristic
272#385—21no—
273#385C4×C15111yescharacteristic, complemented
274#380—21no—
275#379C4×C15111yescharacteristic, complemented
276C4×C22⋊C4—21no—
277C4×C22⋊C4C4×C15111yescharacteristic, complemented
278AΣL(1,𝔽16)—24no—
279#343—21no—
280#342—21no—
281C25C2×C4×C15111yescharacteristic
282C22×D4—21no—
283C22×D4C23×C15111yescharacteristic
284C23×C4—21no—
285C23×C4—21no—
286C23×C4—44no—
287C23×C4—41no—
288C23×C4—41no—
289C23×C4C2×C4×C15111yescharacteristic
290C23×C4C2×C4×C15111yescharacteristic
291C23×C4D4×C15111yescharacteristic
292C2×M16—22no—
293#120—21no—
294#120—21no—
295#120D4×C15112yes—
296#120Q8×C15112yes—
297C4×D4—41no—
298C4×D4—41no—
299C4×D4—44no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—41no—
302C2×C4⋊C4D4×C15111yescharacteristic
303C2×C22⋊C4—21no—
304C2×C22⋊C4—21no—
305C2×C22⋊C4—21no—
306C2×C22⋊C4—21no—
307C2×C22⋊C4—22no—
308C2×C22⋊C4C2×C4×C15111yescharacteristic
309C2×C22⋊C4C2×C4×C15111yescharacteristic
310C2×C22⋊C4C2×C4×C15111yescharacteristic
311C2×C22⋊C4D4×C15111yescharacteristic
312C2×C42—21no—
313C2×C42D4×C15111yescharacteristic
314C4⋊C8—41no—
315C4⋊C8—41no—
316#100—22no—
317#100—22no—
318#99—22no—
319#99—22no—
320#95—21no—
321#95—21no—
322#95—21no—
323#95—41no—
324C24—21no—
325C24—21no—
326C24—42no—
327C24—41no—
328C24—42no—
329C24—41no—
330C24C4⋊C4×C15112yescomplemented
331C24C22×C4×C15111yescharacteristic
332C24C2×D4×C15111yescharacteristic
333C2×D4—22no—
334C2×D4—22no—
335C2×D4—41no—
336C2×D4—41no—
337C2×D4—42no—
338C2×D4—42no—
339C2×D4C2×D4×C15111yescharacteristic
340C2×D4C2×Q8×C15111yescharacteristic
341C2×D4#41×C15111yescharacteristic
342C2×D4#41×C15111yescharacteristic
343C22×C4—24no—
344C22×C4—21no—
345C22×C4—21no—
346C22×C4—21no—
347C22×C4—21no—
348C22×C4—21no—
349C22×C4—21no—
350C22×C4—21no—
351C22×C4—42no—
352C22×C4—42no—
353C22×C4—42no—
354C22×C4—42no—
355C22×C4—42no—
356C22×C4—42no—
357C22×C4—42no—
358C22×C4—44no—
359C22×C4—44no—
360C22×C4—44no—
361C22×C4—41no—
362C22×C4—41no—
363C22×C4—41no—
364C22×C4—44no—
365C22×C4—42no—
366C22×C4C22⋊C4×C15111yescharacteristic
367C22×C4C22⋊C4×C15111yescharacteristic
368C22×C4C22⋊C4×C15111yescharacteristic
369C22×C4C22⋊C4×C15111yescharacteristic
370C22×C4C2×D4×C15111yescharacteristic
371M16—42no—
372M16—42no—
373C2×C8—42no—
374C4⋊C4—41no—
375C4⋊C4—42no—
376C4⋊C4—82no—
377C22⋊C4—21no—
378C22⋊C4—22no—
379C22⋊C4—22no—
380C22⋊C4—41no—
381C22⋊C4—41no—
382C22⋊C4—42no—
383C22⋊C4—42no—
384C22⋊C4—42no—
385C22⋊C4—41no—
386C22⋊C4—42no—
387C22⋊C4—42no—
388C22⋊C4C4⋊C4×C15112yescomplemented
389C42—21no—
390C42—21no—
391C42—42no—
392C23—22no—
393C23—22no—
394C23—22no—
395C23—21no—
396C23—21no—
397C23—21no—
398C23—21no—
399C23—41no—
400C23—44no—
401C23—42no—
402C23—41no—
403C23—41no—
404C23—41no—
405C23—44no—
406C23—42no—
407C23—41no—
408C23—41no—
409C23—42no—
410C23—42no—
411C23—42no—
412C23—48no—
413C23—42no—
414C23—41no—
415C23—41no—
416C23C2×C22⋊C4×C15111yescharacteristic
417C23C2×C4⋊C4×C15111yescharacteristic
418C23#117×C15111yescharacteristic
419C23#121×C15111yescharacteristic
420C23C22⋊Q8×C15111yescharacteristic
421D4—41no—
422D4—41no—
423D4—41no—
424D4—41no—
425D4—44no—
426D4—44no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—22no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—44no—
436C2×C4—42no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—48no—
441C2×C4—42no—
442C2×C4—41no—
443C2×C4—42no—
444C2×C4—44no—
445C2×C4—42no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—42no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—81no—
454C2×C4—82no—
455C2×C4—82no—
456C2×C4—82no—
457C2×C4#99×C15111yescharacteristic
458C2×C4#99×C15111yescharacteristic
459C2×C4#121×C15111yescharacteristic
460C2×C4C22⋊Q8×C15111yescharacteristic
461C8—82no—
462C22—21no—
463C22—21no—
464C22—24no—
465C22—21no—
466C22—21no—
467C22—21no—
468C22—21no—
469C22—41no—
470C22—41no—
471C22—41no—
472C22—41no—
473C22—42no—
474C22—42no—
475C22—42no—
476C22—42no—
477C22—44no—
478C22—44no—
479C22—44no—
480C22—44no—
481C22—42no—
482C22—41no—
483C22—41no—
484C22—41no—
485C22—42no—
486C22—41no—
487C22—42no—
488C22—81no—
489C22#380×C15111yescharacteristic
490C22C2×#99×C15111yescharacteristic
491C22#410×C15111yescharacteristic
492C4—21no—
493C4—21no—
494C4—21no—
495C4—42no—
496C4—42no—
497C4—41no—
498C4—41no—
499C4—41no—
500C4—81no—
501C4—162no—
502C4AΣL(1,𝔽16)×C15112yescomplemented
503C2—21no—
504C2—21no—
505C2—41no—
506C2—44no—
507C2—41no—
508C2—41no—
509C2—41no—
510C2#1799×C15111yescharacteristic
511C2C2×AΣL(1,𝔽16)×C15111yescharacteristic
512C2#2120×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#99
commutatorC24C22×C4×C151
Frattini, cosocleC22×D4C23×C151
prime radicalC2×#120×C151C22
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C22×C4×C151 ◁ C2×C4×D4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
3. #1800×C151C2semidirect
4. #1799×C151C2semidirect
5. #1390×C151C2semidirect
6. C24×C4×C151C4semidirect
16. #385×C151C4semidirect
18. #379×C151C4semidirect
20. C4×C22⋊C4×C151C4semidirect
73. C24×C151C4⋊C4semidirect
131. C22⋊C4×C151C4⋊C4semidirect
245. C4×C151AΣL(1,𝔽16)semidirect
256. #12793C151direct (N × H)
257. C151#12793direct (N × H)
260. #1800C2×C151semidirect
261. #1799C2×C151semidirect
262. #1390C2×C151semidirect
263. C24×C4C4×C151semidirect
273. #385C4×C151semidirect
275. #379C4×C151semidirect
277. C4×C22⋊C4C4×C151semidirect
330. C24C4⋊C4×C151semidirect
388. C22⋊C4C4⋊C4×C151semidirect
502. C4AΣL(1,𝔽16)×C151semidirect

Maximal subgroups

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

subgroupindex
C4×#120×C1512
C2×AΣL(1,𝔽16)×C1512
#1800×C1512
#1799×C1512
#1390×C1512
#12793151