Finite Group Databasebeta

← C151×#10000 #50314925

Subgroups — C151×#10000 #50314925

Order 38656.

632 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3101×C151C211yesmaximal, characteristic, complemented
2#3077×C151C211yesmaximal, characteristic, complemented
3#2535×C151C211yesmaximal, characteristic
4#1518×C151C211yesmaximal, characteristic, complemented
5#1486×C151C211yesmaximal, characteristic, complemented
6#1478×C151C211yesmaximal, characteristic, complemented
7#1286×C151C211yesmaximal, characteristic, complemented
8#533×C151C2211yescharacteristic
9C2×#121×C151—21no—
10C2×C4×D4×C151C2211yescharacteristic
11C2×C4×D4×C151C2211yescharacteristic
12#483×C151—21no—
13#478×C151—22no—
14#476×C151—21no—
15#476×C151—21no—
16#474×C151—21no—
17#461×C151—21no—
18#450×C151—21no—
19C4×SD16×C151—22no—
20#431×C151C2211yescharacteristic
21#431×C151C2211yescharacteristic
22#428×C151—21no—
23#423×C151C2211yescharacteristic
24#418×C151—21no—
25#397×C151—21no—
26#392×C151—21no—
27#386×C151—22no—
28#382×C151C2211yescharacteristic
29#380×C151—21no—
30#328×C151—22no—
31D4⋊C8×C151—22no—
32D4⋊C8×C151—22no—
33C22×D4×C151—22no—
34C22×D4×C151D411yescharacteristic
35C22×D4×C151D411yescharacteristic
36C23×C4×C151—21no—
37C23×C4×C151—21no—
38C2×SD16×C151—22no—
39C2×M16×C151—21no—
40C4⋊Q8×C151D411yescharacteristic, complemented
41C4⋊Q8×C151D411yescharacteristic, complemented
42#125×C151—21no—
43C22⋊Q8×C151—21no—
44C22⋊Q8×C151—21no—
45#121×C151—42no—
46#121×C151—42no—
47C4×Q8×C151—21no—
48C4×Q8×C151—21no—
49C4×D4×C151—21no—
50C4×D4×C151—21no—
51C4×D4×C151—21no—
52C4×D4×C151—21no—
53C4×D4×C151—21no—
54C4×D4×C151—21no—
55C4×D4×C151—21no—
56C4×D4×C151—21no—
57#117×C151—21no—
58C2×C4⋊C4×C151—21no—
59C2×C4⋊C4×C151D411yescharacteristic
60C2×C4⋊C4×C151D411yescharacteristic
61C2×C22⋊C4×C151—22no—
62C2×C22⋊C4×C151—21no—
63C2×C22⋊C4×C151—21no—
64C2×C22⋊C4×C151—22no—
65C2×C42×C151C2311yescharacteristic
66#107×C151—22no—
67#106×C151—22no—
68#106×C151—22no—
69C4⋊C8×C151—21no—
70C4⋊C8×C151—21no—
71C4⋊C8×C151—21no—
72C4⋊C8×C151D412yescomplemented
73#103×C151—22no—
74#102×C151—22no—
75#102×C151—22no—
76#102×C151—22no—
77C22⋊C8×C151—21no—
78C22⋊C8×C151—21no—
79C4×C8×C151—21no—
80C4×C8×C151D412yescomplemented
81#95×C151—22no—
82#95×C151—21no—
83#95×C151D412yes—
84C24×C151—21no—
85C24×C151—21no—
86C2×Q8×C151—21no—
87C2×Q8×C151—21no—
88C2×D4×C151—21no—
89C2×D4×C151—21no—
90C2×D4×C151—21no—
91C2×D4×C151—21no—
92C2×D4×C151—21no—
93C2×D4×C151—21no—
94C2×D4×C151—21no—
95C2×D4×C151—42no—
96C2×D4×C151—44no—
97C2×D4×C151—44no—
98C2×D4×C151—82no—
99C2×D4×C151SD1612yescomplemented
100C22×C4×C151—22no—
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×C151—41no—
108C22×C4×C151—41no—
109C22×C4×C151—41no—
110C22×C4×C151—41no—
111C22×C4×C151—82no—
112C22×C4×C151C2×D411yescharacteristic
113C22×C4×C151C2×D411yescharacteristic
114C22×C4×C151C2×D411yescharacteristic
115SD16×C151—44no—
116M16×C151—41no—
117M16×C151—41no—
118C2×C8×C151—22no—
119C2×C8×C151—22no—
120C2×C8×C151—41no—
121C4⋊C4×C151—21no—
122C4⋊C4×C151—21no—
123C4⋊C4×C151—21no—
124C4⋊C4×C151—21no—
125C4⋊C4×C151—21no—
126C4⋊C4×C151—21no—
127C4⋊C4×C151—21no—
128C4⋊C4×C151—21no—
129C4⋊C4×C151—41no—
130C4⋊C4×C151—41no—
131C4⋊C4×C151—41no—
132C4⋊C4×C151—41no—
133C22⋊C4×C151—44no—
134C22⋊C4×C151—41no—
135C22⋊C4×C151—41no—
136C22⋊C4×C151—41no—
137C22⋊C4×C151—41no—
138C22⋊C4×C151—41no—
139C22⋊C4×C151—82no—
140C42×C151—41no—
141C42×C151C2×D411yescharacteristic
142C42×C151C2×D411yescharacteristic
143C42×C151C2×D411yescharacteristic
144C42×C151#4111yescharacteristic
145C23×C151—22no—
146C23×C151—22no—
147C23×C151—41no—
148C23×C151—42no—
149C23×C151—42no—
150C23×C151—41no—
151C23×C151—41no—
152C23×C151—41no—
153C23×C151—41no—
154C23×C151—41no—
155C23×C151—41no—
156C23×C151—41no—
157C23×C151#12011yescharacteristic
158Q8×C151—42no—
159Q8×C151—81no—
160D4×C151—22no—
161D4×C151—22no—
162D4×C151—22no—
163D4×C151—22no—
164D4×C151—41no—
165D4×C151—41no—
166D4×C151—41no—
167D4×C151—41no—
168D4×C151—88no—
169C2×C4×C151—41no—
170C2×C4×C151—41no—
171C2×C4×C151—42no—
172C2×C4×C151—42no—
173C2×C4×C151—42no—
174C2×C4×C151—41no—
175C2×C4×C151—41no—
176C2×C4×C151—41no—
177C2×C4×C151—41no—
178C2×C4×C151—41no—
179C2×C4×C151—42no—
180C2×C4×C151—41no—
181C2×C4×C151—82no—
182C2×C4×C151—82no—
183C2×C4×C151—81no—
184C2×C4×C151—81no—
185C2×C4×C151—81no—
186C2×C4×C151—81no—
187C2×C4×C151#12011yescharacteristic
188C2×C4×C151#12011yescharacteristic
189C2×C4×C151#12111yescharacteristic
190C2×C4×C151#12111yescharacteristic
191C2×C4×C151#12111yescharacteristic
192C2×C4×C151#12711yescharacteristic
193C2×C4×C151C2×SD1611yescharacteristic
194C2×C4×C151#13511yescharacteristic
195C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
196C2×C4×C151#13711yescharacteristic
197C8×C151—42no—
198C8×C151—42no—
199C8×C151—81no—
200C22×C151—21no—
201C22×C151—21no—
202C22×C151—42no—
203C22×C151—44no—
204C22×C151—42no—
205C22×C151—42no—
206C22×C151—42no—
207C22×C151—81no—
208C22×C151—82no—
209C22×C151—81no—
210C22×C151—81no—
211C22×C151—81no—
212C22×C151—81no—
213C22×C151—81no—
214C22×C151#39211yescharacteristic
215C22×C151#45011yescharacteristic
216C22×C151#45211yescharacteristic
217C4×C151—21no—
218C4×C151—21no—
219C4×C151—21no—
220C4×C151—21no—
221C4×C151—82no—
222C4×C151—81no—
223C4×C151—81no—
224C4×C151—81no—
225C4×C151—81no—
226C4×C151#44811yescharacteristic
227C4×C151#44911yescharacteristic
228C4×C151#46511yescharacteristic
229C4×C151#46811yescharacteristic
230C2×C151—21no—
231C2×C151—21no—
232C2×C151—82no—
233C2×C151—82no—
234C2×C151#200011yescharacteristic
235C2×C151#200811yescharacteristic
236C2×C151#201011yescharacteristic
237#10000C15111yesmaximal, characteristic, direct product factor, Sylow
238C151#1000011yescharacteristic, direct product factor, Sylow
239#3101C2×C15111yescharacteristic, complemented
240#3077C2×C15111yescharacteristic, complemented
241#2535C2×C15111yescharacteristic
242#1518C2×C15111yescharacteristic, complemented
243#1486C2×C15111yescharacteristic, complemented
244#1478C2×C15111yescharacteristic, complemented
245#1286C2×C15111yescharacteristic, complemented
246#533C22×C15111yescharacteristic
247C2×#121—21no—
248C2×C4×D4C22×C15111yescharacteristic
249C2×C4×D4C22×C15111yescharacteristic
250#483—21no—
251#478—22no—
252#476—21no—
253#476—21no—
254#474—21no—
255#461—21no—
256#450—21no—
257C4×SD16—22no—
258#431C22×C15111yescharacteristic
259#431C22×C15111yescharacteristic
260#428—21no—
261#423C22×C15111yescharacteristic
262#418—21no—
263#397—21no—
264#392—21no—
265#386—22no—
266#382C22×C15111yescharacteristic
267#380—21no—
268#328—22no—
269D4⋊C8—22no—
270D4⋊C8—22no—
271C22×D4—22no—
272C22×D4D4×C15111yescharacteristic
273C22×D4D4×C15111yescharacteristic
274C23×C4—21no—
275C23×C4—21no—
276C2×SD16—22no—
277C2×M16—21no—
278C4⋊Q8D4×C15111yescharacteristic, complemented
279C4⋊Q8D4×C15111yescharacteristic, complemented
280#125—21no—
281C22⋊Q8—21no—
282C22⋊Q8—21no—
283#121—42no—
284#121—42no—
285C4×Q8—21no—
286C4×Q8—21no—
287C4×D4—21no—
288C4×D4—21no—
289C4×D4—21no—
290C4×D4—21no—
291C4×D4—21no—
292C4×D4—21no—
293C4×D4—21no—
294C4×D4—21no—
295#117—21no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4D4×C15111yescharacteristic
298C2×C4⋊C4D4×C15111yescharacteristic
299C2×C22⋊C4—22no—
300C2×C22⋊C4—21no—
301C2×C22⋊C4—21no—
302C2×C22⋊C4—22no—
303C2×C42C23×C15111yescharacteristic
304#107—22no—
305#106—22no—
306#106—22no—
307C4⋊C8—21no—
308C4⋊C8—21no—
309C4⋊C8—21no—
310C4⋊C8D4×C15112yescomplemented
311#103—22no—
312#102—22no—
313#102—22no—
314#102—22no—
315C22⋊C8—21no—
316C22⋊C8—21no—
317C4×C8—21no—
318C4×C8D4×C15112yescomplemented
319#95—22no—
320#95—21no—
321#95D4×C15112yes—
322C24—21no—
323C24—21no—
324C2×Q8—21no—
325C2×Q8—21no—
326C2×D4—21no—
327C2×D4—21no—
328C2×D4—21no—
329C2×D4—21no—
330C2×D4—21no—
331C2×D4—21no—
332C2×D4—21no—
333C2×D4—42no—
334C2×D4—44no—
335C2×D4—44no—
336C2×D4—82no—
337C2×D4SD16×C15112yescomplemented
338C22×C4—22no—
339C22×C4—21no—
340C22×C4—21no—
341C22×C4—41no—
342C22×C4—41no—
343C22×C4—41no—
344C22×C4—41no—
345C22×C4—41no—
346C22×C4—41no—
347C22×C4—41no—
348C22×C4—41no—
349C22×C4—82no—
350C22×C4C2×D4×C15111yescharacteristic
351C22×C4C2×D4×C15111yescharacteristic
352C22×C4C2×D4×C15111yescharacteristic
353SD16—44no—
354M16—41no—
355M16—41no—
356C2×C8—22no—
357C2×C8—22no—
358C2×C8—41no—
359C4⋊C4—21no—
360C4⋊C4—21no—
361C4⋊C4—21no—
362C4⋊C4—21no—
363C4⋊C4—21no—
364C4⋊C4—21no—
365C4⋊C4—21no—
366C4⋊C4—21no—
367C4⋊C4—41no—
368C4⋊C4—41no—
369C4⋊C4—41no—
370C4⋊C4—41no—
371C22⋊C4—44no—
372C22⋊C4—41no—
373C22⋊C4—41no—
374C22⋊C4—41no—
375C22⋊C4—41no—
376C22⋊C4—41no—
377C22⋊C4—82no—
378C42—41no—
379C42C2×D4×C15111yescharacteristic
380C42C2×D4×C15111yescharacteristic
381C42C2×D4×C15111yescharacteristic
382C42#41×C15111yescharacteristic
383C23—22no—
384C23—22no—
385C23—41no—
386C23—42no—
387C23—42no—
388C23—41no—
389C23—41no—
390C23—41no—
391C23—41no—
392C23—41no—
393C23—41no—
394C23—41no—
395C23#120×C15111yescharacteristic
396Q8—42no—
397Q8—81no—
398D4—22no—
399D4—22no—
400D4—22no—
401D4—22no—
402D4—41no—
403D4—41no—
404D4—41no—
405D4—41no—
406D4—88no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—42no—
418C2×C4—41no—
419C2×C4—82no—
420C2×C4—82no—
421C2×C4—81no—
422C2×C4—81no—
423C2×C4—81no—
424C2×C4—81no—
425C2×C4#120×C15111yescharacteristic
426C2×C4#120×C15111yescharacteristic
427C2×C4#121×C15111yescharacteristic
428C2×C4#121×C15111yescharacteristic
429C2×C4#121×C15111yescharacteristic
430C2×C4#127×C15111yescharacteristic
431C2×C4C2×SD16×C15111yescharacteristic
432C2×C4#135×C15111yescharacteristic
433C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
434C2×C4#137×C15111yescharacteristic
435C8—42no—
436C8—42no—
437C8—81no—
438C22—21no—
439C22—21no—
440C22—42no—
441C22—44no—
442C22—42no—
443C22—42no—
444C22—42no—
445C22—81no—
446C22—82no—
447C22—81no—
448C22—81no—
449C22—81no—
450C22—81no—
451C22—81no—
452C22#392×C15111yescharacteristic
453C22#450×C15111yescharacteristic
454C22#452×C15111yescharacteristic
455C4—21no—
456C4—21no—
457C4—21no—
458C4—21no—
459C4—82no—
460C4—81no—
461C4—81no—
462C4—81no—
463C4—81no—
464C4#448×C15111yescharacteristic
465C4#449×C15111yescharacteristic
466C4#465×C15111yescharacteristic
467C4#468×C15111yescharacteristic
468C2—21no—
469C2—21no—
470C2—82no—
471C2—82no—
472C2#2000×C15111yescharacteristic
473C2#2008×C15111yescharacteristic
474C2#2010×C15111yescharacteristic
subgroupG/H
center, socleC22×C151#392
commutator, Frattini, cosocleC2×C42C23×C151
prime radical#2535×C151C2
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3101×C151C2semidirect
2. #3077×C151C2semidirect
4. #1518×C151C2semidirect
5. #1486×C151C2semidirect
6. #1478×C151C2semidirect
7. #1286×C151C2semidirect
40. C4⋊Q8×C151D4semidirect
41. C4⋊Q8×C151D4semidirect
72. C4⋊C8×C151D4semidirect
80. C4×C8×C151D4semidirect
99. C2×D4×C151SD16semidirect
237. #10000C151direct (N × H)
238. C151#10000direct (N × H)
239. #3101C2×C151semidirect
240. #3077C2×C151semidirect
242. #1518C2×C151semidirect
243. #1486C2×C151semidirect
244. #1478C2×C151semidirect
245. #1286C2×C151semidirect
278. C4⋊Q8D4×C151semidirect
279. C4⋊Q8D4×C151semidirect
310. C4⋊C8D4×C151semidirect
318. C4×C8D4×C151semidirect
337. C2×D4SD16×C151semidirect

Maximal subgroups

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

subgroupindex
#3101×C1512
#3077×C1512
#2535×C1512
#1518×C1512
#1486×C1512
#1478×C1512
#1286×C1512
#10000151