Finite Group Databasebeta

← C151×#9940 #50314865

Subgroups — C151×#9940 #50314865

Order 38656.

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

normal subgroups only

This group has 768 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#3094×C151C211yesmaximal, characteristic, complemented
2#2539×C151C211yesmaximal, characteristic
3#2482×C151C211yesmaximal, characteristic, complemented
4#1826×C151C211yesmaximal, characteristic, complemented
5#1510×C151C211yesmaximal, characteristic, complemented
6#1462×C151C211yesmaximal, characteristic, complemented
7#1284×C151C211yesmaximal, characteristic, complemented
8C2×#123×C151—21no—
9C2×#121×C151C2211yescharacteristic
10C2×#120×C151—21no—
11C2×#117×C151C2211yescharacteristic
12C22×C22⋊C4×C151C2211yescharacteristic
13#482×C151—22no—
14#481×C151—21no—
15#480×C151—21no—
16#428×C151—21no—
17#418×C151—21no—
18#407×C151C2211yescharacteristic
19#407×C151C2211yescharacteristic
20#399×C151—21no—
21#399×C151—21no—
22#397×C151—21no—
23#392×C151—21no—
24#390×C151—22no—
25#388×C151—22no—
26#385×C151—21no—
27#381×C151C2211yescharacteristic
28#379×C151—21no—
29C4×C22⋊C4×C151C2211yescharacteristic
30#339×C151—22no—
31#327×C151—22no—
32#323×C151—22no—
33C25×C151D411yescharacteristic
34C22×D4×C151—22no—
35C22×D4×C151—21no—
36C22×D4×C151D411yescharacteristic
37C23×C4×C151D411yescharacteristic
38C23×C4×C151C2311yescharacteristic
39C2×M16×C151—21no—
40C2×M16×C151—21no—
41#123×C151—44no—
42#121×C151—21no—
43#121×C151—21no—
44#121×C151—21no—
45#121×C151—21no—
46#120×C151—44no—
47#117×C151—21no—
48#117×C151—21no—
49#117×C151—21no—
50#117×C151—21no—
51C2×C4⋊C4×C151—22no—
52C2×C4⋊C4×C151—22no—
53C2×C4⋊C4×C151D411yescharacteristic
54C2×C4⋊C4×C151D411yescharacteristic, complemented
55C2×C4⋊C4×C151D411yescharacteristic, complemented
56C2×C22⋊C4×C151—22no—
57C2×C22⋊C4×C151—22no—
58C2×C22⋊C4×C151—22no—
59C2×C22⋊C4×C151—21no—
60C2×C22⋊C4×C151—21no—
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—22no—
67C2×C22⋊C4×C151—21no—
68C2×C22⋊C4×C151—21no—
69C2×C22⋊C4×C151—21no—
70C2×C42×C151—21no—
71C2×C42×C151D412yes—
72#107×C151—22no—
73#106×C151—22no—
74#102×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—21no—
82#95×C151—21no—
83#95×C151D412yescomplemented
84C24×C151—21no—
85C24×C151—21no—
86C24×C151—21no—
87C24×C151—21no—
88C24×C151—42no—
89C24×C151—42no—
90C24×C151—42no—
91C24×C151C2×D411yescharacteristic
92C2×D4×C151—21no—
93C2×D4×C151—21no—
94C2×D4×C151—42no—
95C2×D4×C151—44no—
96C2×D4×C151—42no—
97C2×D4×C151—42no—
98C2×D4×C151—44no—
99C2×D4×C151—41no—
100C2×D4×C151—41no—
101C2×D4×C151—82no—
102C22×C4×C151—22no—
103C22×C4×C151—22no—
104C22×C4×C151—21no—
105C22×C4×C151—21no—
106C22×C4×C151—21no—
107C22×C4×C151—21no—
108C22×C4×C151—21no—
109C22×C4×C151—21no—
110C22×C4×C151—42no—
111C22×C4×C151—42no—
112C22×C4×C151C2×D411yescharacteristic
113C22×C4×C151C2×D411yescharacteristic
114C22×C4×C151C2×D411yescharacteristic
115C22×C4×C151C2×D411yescharacteristic
116C22×C4×C151C2×D411yescharacteristic
117C22×C4×C151#4111yescharacteristic
118M16×C151—42no—
119M16×C151—42no—
120C2×C8×C151—22no—
121C2×C8×C151—41no—
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—44no—
129C4⋊C4×C151—82no—
130C22⋊C4×C151—24no—
131C22⋊C4×C151—44no—
132C22⋊C4×C151—44no—
133C22⋊C4×C151—42no—
134C22⋊C4×C151—44no—
135C22⋊C4×C151—41no—
136C22⋊C4×C151—41no—
137C22⋊C4×C151—41no—
138C22⋊C4×C151—41no—
139C22⋊C4×C151—41no—
140C22⋊C4×C151—41no—
141C22⋊C4×C151—41no—
142C22⋊C4×C151—41no—
143C22⋊C4×C151—82no—
144C42×C151—42no—
145C42×C151—41no—
146C42×C151—41no—
147C23×C151—22no—
148C23×C151—22no—
149C23×C151—22no—
150C23×C151—22no—
151C23×C151—22no—
152C23×C151—41no—
153C23×C151—41no—
154C23×C151—41no—
155C23×C151—42no—
156C23×C151—41no—
157C23×C151—42no—
158C23×C151—41no—
159C23×C151—42no—
160C23×C151—41no—
161C23×C151—41no—
162C23×C151—42no—
163C23×C151—42no—
164C23×C151—41no—
165C23×C151—42no—
166C23×C151—81no—
167C23×C151—81no—
168C23×C151—88no—
169C23×C151#12011yescharacteristic
170C23×C151#12011yescharacteristic
171C23×C151#12111yescharacteristic
172D4×C151—42no—
173D4×C151—81no—
174D4×C151—88no—
175D4×C151—82no—
176D4×C151—82no—
177C2×C4×C151—22no—
178C2×C4×C151—22no—
179C2×C4×C151—24no—
180C2×C4×C151—41no—
181C2×C4×C151—41no—
182C2×C4×C151—41no—
183C2×C4×C151—41no—
184C2×C4×C151—42no—
185C2×C4×C151—42no—
186C2×C4×C151—41no—
187C2×C4×C151—42no—
188C2×C4×C151—42no—
189C2×C4×C151—42no—
190C2×C4×C151—42no—
191C2×C4×C151—41no—
192C2×C4×C151—41no—
193C2×C4×C151—41no—
194C2×C4×C151—41no—
195C2×C4×C151—41no—
196C2×C4×C151—42no—
197C2×C4×C151—42no—
198C2×C4×C151—42no—
199C2×C4×C151—81no—
200C2×C4×C151#12011yescharacteristic
201C2×C4×C151#12111yescharacteristic
202C2×C4×C151#12111yescharacteristic
203C2×C4×C151#12711yescharacteristic
204C8×C151—42no—
205C8×C151—81no—
206C22×C151—21no—
207C22×C151—21no—
208C22×C151—21no—
209C22×C151—21no—
210C22×C151—21no—
211C22×C151—21no—
212C22×C151—21no—
213C22×C151—44no—
214C22×C151—44no—
215C22×C151—44no—
216C22×C151—42no—
217C22×C151—82no—
218C22×C151—82no—
219C22×C151—82no—
220C22×C151—82no—
221C22×C151—82no—
222C22×C151—82no—
223C22×C151—81no—
224C22×C151—81no—
225C22×C151—81no—
226C22×C151—81no—
227C22×C151—81no—
228C22×C151#39211yescharacteristic
229C22×C151#45312yes—
230C22×C151#45812yes—
231C4×C151—21no—
232C4×C151—21no—
233C4×C151—21no—
234C4×C151—21no—
235C4×C151—44no—
236C4×C151—82no—
237C4×C151—81no—
238C4×C151—81no—
239C4×C151—81no—
240C4×C151—81no—
241C2×C151—22no—
242C2×C151—22no—
243C2×C151—41no—
244C2×C151—82no—
245C2×C151—161no—
246C2×C151#200211yescharacteristic
247C2×C151#201011yescharacteristic
248C2×C151#202211yescharacteristic
249#9940C15111yesmaximal, characteristic, direct product factor, Sylow
250C151#994011yescharacteristic, direct product factor, Sylow
251#3094C2×C15111yescharacteristic, complemented
252#2539C2×C15111yescharacteristic
253#2482C2×C15111yescharacteristic, complemented
254#1826C2×C15111yescharacteristic, complemented
255#1510C2×C15111yescharacteristic, complemented
256#1462C2×C15111yescharacteristic, complemented
257#1284C2×C15111yescharacteristic, complemented
258C2×#123—21no—
259C2×#121C22×C15111yescharacteristic
260C2×#120—21no—
261C2×#117C22×C15111yescharacteristic
262C22×C22⋊C4C22×C15111yescharacteristic
263#482—22no—
264#481—21no—
265#480—21no—
266#428—21no—
267#418—21no—
268#407C22×C15111yescharacteristic
269#407C22×C15111yescharacteristic
270#399—21no—
271#399—21no—
272#397—21no—
273#392—21no—
274#390—22no—
275#388—22no—
276#385—21no—
277#381C22×C15111yescharacteristic
278#379—21no—
279C4×C22⋊C4C22×C15111yescharacteristic
280#339—22no—
281#327—22no—
282#323—22no—
283C25D4×C15111yescharacteristic
284C22×D4—21no—
285C22×D4—22no—
286C22×D4D4×C15111yescharacteristic
287C23×C4D4×C15111yescharacteristic
288C23×C4C23×C15111yescharacteristic
289C2×M16—21no—
290C2×M16—21no—
291#123—44no—
292#121—21no—
293#121—21no—
294#121—21no—
295#121—21no—
296#120—44no—
297#117—21no—
298#117—21no—
299#117—21no—
300#117—21no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4D4×C15111yescharacteristic
304C2×C4⋊C4D4×C15111yescharacteristic, complemented
305C2×C4⋊C4D4×C15111yescharacteristic, complemented
306C2×C22⋊C4—21no—
307C2×C22⋊C4—22no—
308C2×C22⋊C4—22no—
309C2×C22⋊C4—22no—
310C2×C22⋊C4—21no—
311C2×C22⋊C4—21no—
312C2×C22⋊C4—21no—
313C2×C22⋊C4—21no—
314C2×C22⋊C4—21no—
315C2×C22⋊C4—21no—
316C2×C22⋊C4—21no—
317C2×C22⋊C4—21no—
318C2×C22⋊C4—21no—
319C2×C22⋊C4—22no—
320C2×C42—21no—
321C2×C42D4×C15112yes—
322#107—22no—
323#106—22no—
324#102—22no—
325#102—22no—
326C22⋊C8—21no—
327C22⋊C8—21no—
328C22⋊C8—21no—
329C22⋊C8D4×C15112yescomplemented
330#95—22no—
331#95—21no—
332#95—21no—
333#95D4×C15112yescomplemented
334C24—21no—
335C24—21no—
336C24—21no—
337C24—21no—
338C24—42no—
339C24—42no—
340C24—42no—
341C24C2×D4×C15111yescharacteristic
342C2×D4—21no—
343C2×D4—21no—
344C2×D4—42no—
345C2×D4—44no—
346C2×D4—42no—
347C2×D4—42no—
348C2×D4—44no—
349C2×D4—41no—
350C2×D4—41no—
351C2×D4—82no—
352C22×C4—22no—
353C22×C4—22no—
354C22×C4—21no—
355C22×C4—21no—
356C22×C4—21no—
357C22×C4—21no—
358C22×C4—21no—
359C22×C4—21no—
360C22×C4—42no—
361C22×C4—42no—
362C22×C4C2×D4×C15111yescharacteristic
363C22×C4C2×D4×C15111yescharacteristic
364C22×C4C2×D4×C15111yescharacteristic
365C22×C4C2×D4×C15111yescharacteristic
366C22×C4C2×D4×C15111yescharacteristic
367C22×C4#41×C15111yescharacteristic
368M16—42no—
369M16—42no—
370C2×C8—22no—
371C2×C8—41no—
372C4⋊C4—21no—
373C4⋊C4—21no—
374C4⋊C4—21no—
375C4⋊C4—21no—
376C4⋊C4—21no—
377C4⋊C4—21no—
378C4⋊C4—44no—
379C4⋊C4—82no—
380C22⋊C4—24no—
381C22⋊C4—44no—
382C22⋊C4—44no—
383C22⋊C4—42no—
384C22⋊C4—44no—
385C22⋊C4—41no—
386C22⋊C4—41no—
387C22⋊C4—41no—
388C22⋊C4—41no—
389C22⋊C4—41no—
390C22⋊C4—41no—
391C22⋊C4—41no—
392C22⋊C4—41no—
393C22⋊C4—82no—
394C42—42no—
395C42—41no—
396C42—41no—
397C23—22no—
398C23—22no—
399C23—22no—
400C23—22no—
401C23—22no—
402C23—41no—
403C23—42no—
404C23—41no—
405C23—41no—
406C23—42no—
407C23—41no—
408C23—41no—
409C23—41no—
410C23—42no—
411C23—41no—
412C23—42no—
413C23—42no—
414C23—41no—
415C23—42no—
416C23—81no—
417C23—81no—
418C23—88no—
419C23#120×C15111yescharacteristic
420C23#120×C15111yescharacteristic
421C23#121×C15111yescharacteristic
422D4—42no—
423D4—81no—
424D4—88no—
425D4—82no—
426D4—82no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—24no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—41no—
437C2×C4—42no—
438C2×C4—42no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—42no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—81no—
450C2×C4#120×C15111yescharacteristic
451C2×C4#121×C15111yescharacteristic
452C2×C4#121×C15111yescharacteristic
453C2×C4#127×C15111yescharacteristic
454C8—42no—
455C8—81no—
456C22—21no—
457C22—21no—
458C22—21no—
459C22—21no—
460C22—21no—
461C22—21no—
462C22—21no—
463C22—44no—
464C22—44no—
465C22—44no—
466C22—42no—
467C22—82no—
468C22—82no—
469C22—82no—
470C22—82no—
471C22—82no—
472C22—82no—
473C22—81no—
474C22—81no—
475C22—81no—
476C22—81no—
477C22—81no—
478C22#392×C15111yescharacteristic
479C22#453×C15112yes—
480C22#458×C15112yes—
481C4—21no—
482C4—21no—
483C4—21no—
484C4—21no—
485C4—44no—
486C4—82no—
487C4—81no—
488C4—81no—
489C4—81no—
490C4—81no—
491C2—22no—
492C2—22no—
493C2—41no—
494C2—82no—
495C2—161no—
496C2#2002×C15111yescharacteristic
497C2#2010×C15111yescharacteristic
498C2#2022×C15111yescharacteristic
subgroupG/H
center, socleC22×C151#392
commutator, Frattini, cosocleC23×C4C23×C151
prime radical#2539×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. #3094×C151C2semidirect
3. #2482×C151C2semidirect
4. #1826×C151C2semidirect
5. #1510×C151C2semidirect
6. #1462×C151C2semidirect
7. #1284×C151C2semidirect
54. C2×C4⋊C4×C151D4semidirect
55. C2×C4⋊C4×C151D4semidirect
79. C22⋊C8×C151D4semidirect
83. #95×C151D4semidirect
249. #9940C151direct (N × H)
250. C151#9940direct (N × H)
251. #3094C2×C151semidirect
253. #2482C2×C151semidirect
254. #1826C2×C151semidirect
255. #1510C2×C151semidirect
256. #1462C2×C151semidirect
257. #1284C2×C151semidirect
304. C2×C4⋊C4D4×C151semidirect
305. C2×C4⋊C4D4×C151semidirect
329. C22⋊C8D4×C151semidirect
333. #95D4×C151semidirect

Maximal subgroups

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

subgroupindex
#3094×C1512
#2539×C1512
#2482×C1512
#1826×C1512
#1510×C1512
#1462×C1512
#1284×C1512
#9940151