Finite Group Databasebeta

← C151×#9942 #50314867

Subgroups — C151×#9942 #50314867

Order 38656.

894 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 894 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3007×C151C211yesmaximal, characteristic, complemented
2#2561×C151C211yesmaximal, characteristic, complemented
3#2404×C151C211yesmaximal, characteristic
4#1789×C151C211yesmaximal, characteristic, complemented
5#1511×C151C211yesmaximal, characteristic, complemented
6#1462×C151C211yesmaximal, characteristic, complemented
7#1284×C151C211yesmaximal, characteristic, complemented
8C22×#41×C151C2211yescharacteristic
9C2×#137×C151—21no—
10C2×C22⋊Q8×C151C2211yescharacteristic
11C2×#120×C151—21no—
12C22×C22⋊C4×C151C2211yescharacteristic
13#452×C151—22no—
14#451×C151—21no—
15#450×C151—21no—
16C2×#104×C151—22no—
17#417×C151—21no—
18#407×C151C2211yescharacteristic
19#407×C151C2211yescharacteristic
20#397×C151—21no—
21#393×C151—21no—
22#393×C151—21no—
23#392×C151—21no—
24#388×C151—22no—
25#386×C151—21no—
26#386×C151—22no—
27#381×C151—21no—
28#381×C151C2211yescharacteristic
29#379×C151—21no—
30C4×C22⋊C4×C151C2211yescharacteristic
31#328×C151—22no—
32#323×C151—22no—
33C25×C151D411yescharacteristic
34C2×#41×C151—21no—
35C2×#41×C151—21no—
36C2×#41×C151—21no—
37C2×#41×C151—21no—
38C2×#41×C151—44no—
39C22×Q8×C151D411yescharacteristic
40C22×Q8×C151D411yescharacteristic, complemented
41C22×D4×C151—22no—
42C22×D4×C151—21no—
43C22×D4×C151D411yescharacteristic
44C23×C4×C151—21no—
45C23×C4×C151D411yescharacteristic
46C23×C4×C151C2311yescharacteristic
47#137×C151—44no—
48C2×Q16×C151—22no—
49C2×SD16×C151—22no—
50C2×M16×C151—21no—
51C2×M16×C151—21no—
52C22⋊Q8×C151—21no—
53C22⋊Q8×C151—21no—
54C22⋊Q8×C151—21no—
55C22⋊Q8×C151—21no—
56#120×C151—44no—
57C2×C4⋊C4×C151—21no—
58C2×C4⋊C4×C151D411yescharacteristic, complemented
59C2×C22⋊C4×C151—22no—
60C2×C22⋊C4×C151—22no—
61C2×C22⋊C4×C151—21no—
62C2×C22⋊C4×C151—21no—
63C2×C22⋊C4×C151—21no—
64C2×C22⋊C4×C151—21no—
65C2×C22⋊C4×C151—21no—
66C2×C22⋊C4×C151—21no—
67C2×C22⋊C4×C151—22no—
68C2×C22⋊C4×C151—22no—
69C2×C22⋊C4×C151—21no—
70C2×C22⋊C4×C151—21no—
71C2×C22⋊C4×C151—21no—
72C2×C42×C151D412yescomplemented
73#104×C151—44no—
74#103×C151—22no—
75#102×C151—22no—
76C22⋊C8×C151—21no—
77C22⋊C8×C151—21no—
78C22⋊C8×C151—21no—
79C22⋊C8×C151D412yescomplemented
80#95×C151—22no—
81#95×C151—22no—
82#95×C151—22no—
83#95×C151—21no—
84#95×C151—21no—
85#95×C151D412yes—
86C24×C151—21no—
87C24×C151—21no—
88C24×C151—21no—
89C24×C151—21no—
90C24×C151—42no—
91C24×C151—42no—
92C24×C151—42no—
93C24×C151C2×D411yescharacteristic
94#41×C151—24no—
95#41×C151—24no—
96#41×C151—42no—
97#41×C151—42no—
98#41×C151—42no—
99#41×C151—42no—
100#41×C151—42no—
101#41×C151—42no—
102C2×Q8×C151—21no—
103C2×Q8×C151—21no—
104C2×Q8×C151—21no—
105C2×Q8×C151—21no—
106C2×Q8×C151—42no—
107C2×Q8×C151—42no—
108C2×D4×C151—24no—
109C2×D4×C151—21no—
110C2×D4×C151—21no—
111C2×D4×C151—42no—
112C2×D4×C151—42no—
113C2×D4×C151—41no—
114C2×D4×C151—41no—
115C2×D4×C151—44no—
116C2×D4×C151—44no—
117C2×D4×C151—82no—
118C22×C4×C151—21no—
119C22×C4×C151—21no—
120C22×C4×C151—22no—
121C22×C4×C151—22no—
122C22×C4×C151—21no—
123C22×C4×C151—21no—
124C22×C4×C151—21no—
125C22×C4×C151—21no—
126C22×C4×C151—42no—
127C22×C4×C151—42no—
128C22×C4×C151—42no—
129C22×C4×C151—41no—
130C22×C4×C151—41no—
131C22×C4×C151—42no—
132C22×C4×C151C2×D411yescharacteristic
133C22×C4×C151C2×D411yescharacteristic
134C22×C4×C151C2×D411yescharacteristic
135C22×C4×C151C2×D411yescharacteristic
136C22×C4×C151C2×D411yescharacteristic
137C22×C4×C151#4111yescharacteristic
138Q16×C151—44no—
139SD16×C151—44no—
140M16×C151—42no—
141M16×C151—42no—
142C2×C8×C151—22no—
143C2×C8×C151—41no—
144C4⋊C4×C151—21no—
145C4⋊C4×C151—21no—
146C4⋊C4×C151—41no—
147C4⋊C4×C151—41no—
148C22⋊C4×C151—44no—
149C22⋊C4×C151—42no—
150C22⋊C4×C151—44no—
151C22⋊C4×C151—42no—
152C22⋊C4×C151—41no—
153C22⋊C4×C151—41no—
154C22⋊C4×C151—41no—
155C22⋊C4×C151—41no—
156C22⋊C4×C151—41no—
157C22⋊C4×C151—41no—
158C22⋊C4×C151—82no—
159C22⋊C4×C151—82no—
160C42×C151—42no—
161C23×C151—22no—
162C23×C151—22no—
163C23×C151—22no—
164C23×C151—22no—
165C23×C151—22no—
166C23×C151—22no—
167C23×C151—41no—
168C23×C151—42no—
169C23×C151—41no—
170C23×C151—41no—
171C23×C151—41no—
172C23×C151—42no—
173C23×C151—41no—
174C23×C151—42no—
175C23×C151—41no—
176C23×C151—41no—
177C23×C151—42no—
178C23×C151—42no—
179C23×C151—42no—
180C23×C151—81no—
181C23×C151—81no—
182C23×C151—88no—
183C23×C151#12011yescharacteristic
184C23×C151#12011yescharacteristic
185C23×C151#12111yescharacteristic
186Q8×C151—22no—
187Q8×C151—22no—
188Q8×C151—41no—
189Q8×C151—41no—
190Q8×C151—42no—
191Q8×C151—81no—
192D4×C151—22no—
193D4×C151—22no—
194D4×C151—41no—
195D4×C151—41no—
196D4×C151—44no—
197D4×C151—44no—
198D4×C151—88no—
199C2×C4×C151—22no—
200C2×C4×C151—22no—
201C2×C4×C151—22no—
202C2×C4×C151—41no—
203C2×C4×C151—41no—
204C2×C4×C151—41no—
205C2×C4×C151—41no—
206C2×C4×C151—44no—
207C2×C4×C151—44no—
208C2×C4×C151—41no—
209C2×C4×C151—41no—
210C2×C4×C151—42no—
211C2×C4×C151—42no—
212C2×C4×C151—42no—
213C2×C4×C151—42no—
214C2×C4×C151—42no—
215C2×C4×C151—42no—
216C2×C4×C151—41no—
217C2×C4×C151—41no—
218C2×C4×C151—41no—
219C2×C4×C151—42no—
220C2×C4×C151—42no—
221C2×C4×C151—42no—
222C2×C4×C151—42no—
223C2×C4×C151—81no—
224C2×C4×C151#12011yescharacteristic
225C2×C4×C151#12111yescharacteristic
226C2×C4×C151#12111yescharacteristic
227C2×C4×C151#12711yescharacteristic
228C8×C151—42no—
229C8×C151—81no—
230C22×C151—21no—
231C22×C151—21no—
232C22×C151—21no—
233C22×C151—21no—
234C22×C151—21no—
235C22×C151—21no—
236C22×C151—21no—
237C22×C151—44no—
238C22×C151—44no—
239C22×C151—44no—
240C22×C151—44no—
241C22×C151—42no—
242C22×C151—42no—
243C22×C151—82no—
244C22×C151—82no—
245C22×C151—82no—
246C22×C151—82no—
247C22×C151—82no—
248C22×C151—81no—
249C22×C151—81no—
250C22×C151—81no—
251C22×C151—81no—
252C22×C151#39211yescharacteristic
253C22×C151#45512yes—
254C22×C151B(4,𝔽2)12yes—
255C4×C151—21no—
256C4×C151—21no—
257C4×C151—21no—
258C4×C151—21no—
259C4×C151—42no—
260C4×C151—82no—
261C4×C151—82no—
262C4×C151—81no—
263C4×C151—81no—
264C4×C151—81no—
265C2×C151—22no—
266C2×C151—22no—
267C2×C151—41no—
268C2×C151—82no—
269C2×C151—82no—
270C2×C151#200411yescharacteristic
271C2×C151#201011yescharacteristic
272C2×C151#202111yescharacteristic
273#9942C15111yesmaximal, characteristic, direct product factor, Sylow
274C151#994211yescharacteristic, direct product factor, Sylow
275#3007C2×C15111yescharacteristic, complemented
276#2561C2×C15111yescharacteristic, complemented
277#2404C2×C15111yescharacteristic
278#1789C2×C15111yescharacteristic, complemented
279#1511C2×C15111yescharacteristic, complemented
280#1462C2×C15111yescharacteristic, complemented
281#1284C2×C15111yescharacteristic, complemented
282C22×#41C22×C15111yescharacteristic
283C2×#137—21no—
284C2×C22⋊Q8C22×C15111yescharacteristic
285C2×#120—21no—
286C22×C22⋊C4C22×C15111yescharacteristic
287#452—22no—
288#451—21no—
289#450—21no—
290C2×#104—22no—
291#417—21no—
292#407C22×C15111yescharacteristic
293#407C22×C15111yescharacteristic
294#397—21no—
295#393—21no—
296#393—21no—
297#392—21no—
298#388—22no—
299#386—21no—
300#386—22no—
301#381—21no—
302#381C22×C15111yescharacteristic
303#379—21no—
304C4×C22⋊C4C22×C15111yescharacteristic
305#328—22no—
306#323—22no—
307C25D4×C15111yescharacteristic
308C2×#41—21no—
309C2×#41—21no—
310C2×#41—21no—
311C2×#41—21no—
312C2×#41—44no—
313C22×Q8D4×C15111yescharacteristic
314C22×Q8D4×C15111yescharacteristic, complemented
315C22×D4—21no—
316C22×D4—22no—
317C22×D4D4×C15111yescharacteristic
318C23×C4—21no—
319C23×C4D4×C15111yescharacteristic
320C23×C4C23×C15111yescharacteristic
321#137—44no—
322C2×Q16—22no—
323C2×SD16—22no—
324C2×M16—21no—
325C2×M16—21no—
326C22⋊Q8—21no—
327C22⋊Q8—21no—
328C22⋊Q8—21no—
329C22⋊Q8—21no—
330#120—44no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4D4×C15111yescharacteristic, complemented
333C2×C22⋊C4—22no—
334C2×C22⋊C4—22no—
335C2×C22⋊C4—21no—
336C2×C22⋊C4—21no—
337C2×C22⋊C4—21no—
338C2×C22⋊C4—21no—
339C2×C22⋊C4—21no—
340C2×C22⋊C4—21no—
341C2×C22⋊C4—21no—
342C2×C22⋊C4—21no—
343C2×C22⋊C4—21no—
344C2×C22⋊C4—22no—
345C2×C22⋊C4—22no—
346C2×C42D4×C15112yescomplemented
347#104—44no—
348#103—22no—
349#102—22no—
350C22⋊C8—21no—
351C22⋊C8—21no—
352C22⋊C8—21no—
353C22⋊C8D4×C15112yescomplemented
354#95—22no—
355#95—22no—
356#95—22no—
357#95—21no—
358#95—21no—
359#95D4×C15112yes—
360C24—21no—
361C24—21no—
362C24—21no—
363C24—21no—
364C24—42no—
365C24—42no—
366C24—42no—
367C24C2×D4×C15111yescharacteristic
368#41—24no—
369#41—24no—
370#41—42no—
371#41—42no—
372#41—42no—
373#41—42no—
374#41—42no—
375#41—42no—
376C2×Q8—21no—
377C2×Q8—21no—
378C2×Q8—21no—
379C2×Q8—21no—
380C2×Q8—42no—
381C2×Q8—42no—
382C2×D4—24no—
383C2×D4—21no—
384C2×D4—21no—
385C2×D4—42no—
386C2×D4—42no—
387C2×D4—41no—
388C2×D4—41no—
389C2×D4—44no—
390C2×D4—44no—
391C2×D4—82no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—42no—
401C22×C4—42no—
402C22×C4—42no—
403C22×C4—41no—
404C22×C4—41no—
405C22×C4—42no—
406C22×C4C2×D4×C15111yescharacteristic
407C22×C4C2×D4×C15111yescharacteristic
408C22×C4C2×D4×C15111yescharacteristic
409C22×C4C2×D4×C15111yescharacteristic
410C22×C4C2×D4×C15111yescharacteristic
411C22×C4#41×C15111yescharacteristic
412Q16—44no—
413SD16—44no—
414M16—42no—
415M16—42no—
416C2×C8—22no—
417C2×C8—41no—
418C4⋊C4—21no—
419C4⋊C4—21no—
420C4⋊C4—41no—
421C4⋊C4—41no—
422C22⋊C4—44no—
423C22⋊C4—42no—
424C22⋊C4—42no—
425C22⋊C4—44no—
426C22⋊C4—41no—
427C22⋊C4—41no—
428C22⋊C4—41no—
429C22⋊C4—41no—
430C22⋊C4—41no—
431C22⋊C4—41no—
432C22⋊C4—82no—
433C22⋊C4—82no—
434C42—42no—
435C23—22no—
436C23—22no—
437C23—22no—
438C23—22no—
439C23—22no—
440C23—22no—
441C23—41no—
442C23—42no—
443C23—41no—
444C23—42no—
445C23—42no—
446C23—41no—
447C23—41no—
448C23—41no—
449C23—41no—
450C23—41no—
451C23—42no—
452C23—42no—
453C23—42no—
454C23—81no—
455C23—81no—
456C23—88no—
457C23#120×C15111yescharacteristic
458C23#120×C15111yescharacteristic
459C23#121×C15111yescharacteristic
460Q8—22no—
461Q8—22no—
462Q8—41no—
463Q8—41no—
464Q8—42no—
465Q8—81no—
466D4—22no—
467D4—22no—
468D4—41no—
469D4—41no—
470D4—44no—
471D4—44no—
472D4—88no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—44no—
481C2×C4—44no—
482C2×C4—41no—
483C2×C4—41no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—81no—
498C2×C4#120×C15111yescharacteristic
499C2×C4#121×C15111yescharacteristic
500C2×C4#121×C15111yescharacteristic
501C2×C4#127×C15111yescharacteristic
502C8—42no—
503C8—81no—
504C22—21no—
505C22—21no—
506C22—21no—
507C22—21no—
508C22—21no—
509C22—21no—
510C22—21no—
511C22—44no—
512C22—44no—
513C22—44no—
514C22—44no—
515C22—42no—
516C22—42no—
517C22—82no—
518C22—82no—
519C22—82no—
520C22—82no—
521C22—82no—
522C22—81no—
523C22—81no—
524C22—81no—
525C22—81no—
526C22#392×C15111yescharacteristic
527C22#455×C15112yes—
528C22B(4,𝔽2)×C15112yes—
529C4—21no—
530C4—21no—
531C4—21no—
532C4—21no—
533C4—42no—
534C4—82no—
535C4—82no—
536C4—81no—
537C4—81no—
538C4—81no—
539C2—22no—
540C2—22no—
541C2—41no—
542C2—82no—
543C2—82no—
544C2#2004×C15111yescharacteristic
545C2#2010×C15111yescharacteristic
546C2#2021×C15111yescharacteristic
subgroupG/H
center, socleC22×C151#392
commutator, Frattini, cosocleC23×C4C23×C151
prime radical#2404×C151C2
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C23×C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3007×C151C2semidirect
2. #2561×C151C2semidirect
4. #1789×C151C2semidirect
5. #1511×C151C2semidirect
6. #1462×C151C2semidirect
7. #1284×C151C2semidirect
40. C22×Q8×C151D4semidirect
58. C2×C4⋊C4×C151D4semidirect
72. C2×C42×C151D4semidirect
79. C22⋊C8×C151D4semidirect
273. #9942C151direct (N × H)
274. C151#9942direct (N × H)
275. #3007C2×C151semidirect
276. #2561C2×C151semidirect
278. #1789C2×C151semidirect
279. #1511C2×C151semidirect
280. #1462C2×C151semidirect
281. #1284C2×C151semidirect
314. C22×Q8D4×C151semidirect
332. C2×C4⋊C4D4×C151semidirect
346. C2×C42D4×C151semidirect
353. C22⋊C8D4×C151semidirect

Maximal subgroups

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

subgroupindex
#3007×C1512
#2561×C1512
#2404×C1512
#1789×C1512
#1511×C1512
#1462×C1512
#1284×C1512
#9942151