Finite Group Databasebeta

← C151×#10908 #50315833

Subgroups — C151×#10908 #50315833

Order 38656.

958 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#106×C151C211yesmaximal, characteristic
2C2×C4×C4⋊C4×C151C211yesmaximal, characteristic
3C2×#340×C151C211yesmaximal, characteristic
4C2×#340×C151C211yesmaximal, characteristic
5C2×#340×C151C211yesmaximal, characteristic
6C2×#336×C151C211yesmaximal, characteristic
7C4⋊#95×C151C211yesmaximal, characteristic
8C23×C8×C151C2211yescharacteristic
9C23×C8×C151C2211yescharacteristic
10C22×C4⋊C4×C151C2211yescharacteristic
11C22×C4⋊C4×C151C2211yescharacteristic
12C22×C4⋊C4×C151C2211yescharacteristic
13C22×C4⋊C4×C151C2211yescharacteristic
14C22×C42×C151—21no—
15C22×C42×C151C2211yescharacteristic
16C2×#106×C151—22no—
17C2×#106×C151—22no—
18C2×#106×C151C414yescomplemented
19C4×C4⋊C4×C151—22no—
20C4×C4⋊C4×C151—22no—
21C2×#95×C151—21no—
22C2×#95×C151—21no—
23C2×#95×C151—21no—
24#340×C151—22no—
25#340×C151—22no—
26#340×C151C414yescomplemented
27#336×C151C414yescomplemented
28C23×C4×C151—21no—
29C23×C4×C151—21no—
30C23×C4×C151—21no—
31C23×C4×C151—21no—
32C23×C4×C151D411yescharacteristic
33C23×C4×C151D411yescharacteristic
34C23×C4×C151C2311yescharacteristic
35C22×C8×C151—21no—
36C22×C8×C151—21no—
37C22×C8×C151—21no—
38C22×C8×C151—21no—
39C22×C8×C151—21no—
40C22×C8×C151—21no—
41C22×C8×C151—21no—
42C22×C8×C151—21no—
43C22×C8×C151—21no—
44C22×C8×C151—21no—
45C22×C8×C151C2×C412yes—
46C22×C8×C151C2×C412yes—
47C22×C8×C151C2×C412yes—
48C22×C8×C151C2×C412yes—
49C2×C4⋊C4×C151—21no—
50C2×C4⋊C4×C151—21no—
51C2×C4⋊C4×C151—21no—
52C2×C4⋊C4×C151—21no—
53C2×C4⋊C4×C151—21no—
54C2×C4⋊C4×C151—21no—
55C2×C4⋊C4×C151—21no—
56C2×C4⋊C4×C151—21no—
57C2×C4⋊C4×C151—21no—
58C2×C4⋊C4×C151—21no—
59C2×C4⋊C4×C151—21no—
60C2×C4⋊C4×C151—21no—
61C2×C4⋊C4×C151—21no—
62C2×C4⋊C4×C151—21no—
63C2×C4⋊C4×C151—21no—
64C2×C4⋊C4×C151—21no—
65C2×C4⋊C4×C151C2×C412yes—
66C2×C4⋊C4×C151C2×C412yes—
67C2×C4⋊C4×C151C2×C412yes—
68C2×C4⋊C4×C151C2×C412yes—
69C2×C4⋊C4×C151D412yes—
70C2×C4⋊C4×C151D412yes—
71C2×C4⋊C4×C151D412yes—
72C2×C4⋊C4×C151Q812yes—
73C2×C42×C151—21no—
74C2×C42×C151—21no—
75C2×C42×C151—21no—
76C2×C42×C151—21no—
77C2×C42×C151—24no—
78C2×C42×C151—42no—
79C2×C42×C151—42no—
80C2×C42×C151C2×C412yes—
81C2×C42×C151Q812yes—
82#106×C151—28no—
83#95×C151—24no—
84#95×C151—42no—
85#95×C151—42no—
86C24×C151C2×D411yescharacteristic
87C22×C4×C151—21no—
88C22×C4×C151—21no—
89C22×C4×C151—21no—
90C22×C4×C151—21no—
91C22×C4×C151—22no—
92C22×C4×C151—22no—
93C22×C4×C151—21no—
94C22×C4×C151—22no—
95C22×C4×C151—22no—
96C22×C4×C151—22no—
97C22×C4×C151—22no—
98C22×C4×C151—21no—
99C22×C4×C151—21no—
100C22×C4×C151—21no—
101C22×C4×C151—21no—
102C22×C4×C151—21no—
103C22×C4×C151—22no—
104C22×C4×C151—22no—
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—41no—
112C22×C4×C151—41no—
113C22×C4×C151—41no—
114C22×C4×C151—41no—
115C22×C4×C151—41no—
116C22×C4×C151—41no—
117C22×C4×C151—41no—
118C22×C4×C151—41no—
119C22×C4×C151—41no—
120C22×C4×C151—41no—
121C22×C4×C151—41no—
122C22×C4×C151—41no—
123C22×C4×C151—41no—
124C22×C4×C151—41no—
125C22×C4×C151C4⋊C412yes—
126C22×C4×C151C4⋊C412yes—
127C22×C4×C151SD1612yes—
128C22×C4×C151SD1612yes—
129C22×C4×C151C22×C411yescharacteristic
130C22×C4×C151C22×C411yescharacteristic
131C22×C4×C151C22×C411yescharacteristic
132C22×C4×C151C2×D411yescharacteristic
133C22×C4×C151C2×D411yescharacteristic
134C22×C4×C151C2×D411yescharacteristic
135C22×C4×C151C2×Q811yescharacteristic
136C22×C4×C151C2×Q811yescharacteristic
137C22×C4×C151#4111yescharacteristic
138C22×C4×C151#4111yescharacteristic
139C22×C4×C151#4111yescharacteristic
140C22×C4×C151#4111yescharacteristic
141C22×C4×C151#4111yescharacteristic
142C22×C4×C151#4111yescharacteristic
143C2×C8×C151—22no—
144C2×C8×C151—22no—
145C2×C8×C151—22no—
146C2×C8×C151—22no—
147C2×C8×C151—22no—
148C2×C8×C151—22no—
149C2×C8×C151—22no—
150C2×C8×C151—22no—
151C2×C8×C151—22no—
152C2×C8×C151—41no—
153C2×C8×C151—41no—
154C2×C8×C151—41no—
155C2×C8×C151—41no—
156C2×C8×C151C4214yescomplemented
157C4⋊C4×C151—22no—
158C4⋊C4×C151—22no—
159C4⋊C4×C151—22no—
160C4⋊C4×C151—22no—
161C4⋊C4×C151—22no—
162C4⋊C4×C151—22no—
163C4⋊C4×C151—22no—
164C4⋊C4×C151—22no—
165C4⋊C4×C151—22no—
166C4⋊C4×C151—22no—
167C4⋊C4×C151—41no—
168C4⋊C4×C151—41no—
169C4⋊C4×C151—41no—
170C4⋊C4×C151—41no—
171C4⋊C4×C151C22⋊C414yes—
172C4⋊C4×C151C4⋊C414yes—
173C42×C151—22no—
174C42×C151—22no—
175C42×C151—22no—
176C42×C151—22no—
177C42×C151—48no—
178C23×C151C2×C4⋊C411yescharacteristic
179C23×C151C4×D411yescharacteristic
180C23×C151C4×D411yescharacteristic
181C23×C151#12011yescharacteristic
182C23×C151#12111yescharacteristic
183C23×C151C22⋊Q811yescharacteristic
184C23×C151#12311yescharacteristic
185C23×C151C2×SD1611yescharacteristic
186C23×C151C2×SD1611yescharacteristic
187C23×C151#13511yescharacteristic
188C23×C151#13511yescharacteristic
189C23×C151AGL(1,ℤ/8)11yescharacteristic
190C23×C151AGL(1,ℤ/8)11yescharacteristic
191C23×C151#13711yescharacteristic
192C23×C151#13711yescharacteristic
193C2×C4×C151—22no—
194C2×C4×C151—22no—
195C2×C4×C151—22no—
196C2×C4×C151—22no—
197C2×C4×C151—22no—
198C2×C4×C151—22no—
199C2×C4×C151—22no—
200C2×C4×C151—24no—
201C2×C4×C151—24no—
202C2×C4×C151—22no—
203C2×C4×C151—22no—
204C2×C4×C151—42no—
205C2×C4×C151—42no—
206C2×C4×C151—42no—
207C2×C4×C151—42no—
208C2×C4×C151—41no—
209C2×C4×C151—42no—
210C2×C4×C151—42no—
211C2×C4×C151—42no—
212C2×C4×C151—41no—
213C2×C4×C151—42no—
214C2×C4×C151—42no—
215C2×C4×C151—42no—
216C2×C4×C151—42no—
217C2×C4×C151—42no—
218C2×C4×C151—41no—
219C2×C4×C151—41no—
220C2×C4×C151—42no—
221C2×C4×C151—42no—
222C2×C4×C151—42no—
223C2×C4×C151—42no—
224C2×C4×C151—42no—
225C2×C4×C151—42no—
226C2×C4×C151—81no—
227C2×C4×C151—81no—
228C2×C4×C151—81no—
229C2×C4×C151—81no—
230C2×C4×C151—81no—
231C2×C4×C151—81no—
232C2×C4×C151—81no—
233C2×C4×C151—81no—
234C2×C4×C151#10614yescomplemented
235C2×C4×C151C2×C4211yescharacteristic
236C2×C4×C151C2×C22⋊C411yescharacteristic
237C2×C4×C151C2×C4⋊C411yescharacteristic
238C2×C4×C151#11711yescharacteristic
239C2×C4×C151#11711yescharacteristic
240C2×C4×C151#11711yescharacteristic
241C2×C4×C151C4×D411yescharacteristic
242C2×C4×C151C4×D411yescharacteristic
243C2×C4×C151C4×D411yescharacteristic
244C2×C4×C151C4×D411yescharacteristic
245C2×C4×C151C4×D411yescharacteristic
246C2×C4×C151C4×D411yescharacteristic
247C2×C4×C151C4×Q811yescharacteristic
248C2×C4×C151C4×Q811yescharacteristic
249C2×C4×C151C4×Q811yescharacteristic
250C2×C4×C151C4×Q811yescharacteristic
251C2×C4×C151#12111yescharacteristic
252C2×C4×C151C22⋊Q811yescharacteristic
253C2×C4×C151C22⋊Q811yescharacteristic
254C2×C4×C151C22⋊Q811yescharacteristic
255C2×C4×C151#12311yescharacteristic
256C2×C4×C151#12311yescharacteristic
257C2×C4×C151#12411yescharacteristic
258C2×C4×C151#12511yescharacteristic
259C2×C4×C151#12511yescharacteristic
260C2×C4×C151#12611yescharacteristic
261C2×C4×C151#12611yescharacteristic
262C2×C4×C151C4⋊Q811yescharacteristic
263C8×C151—24no—
264C8×C151—42no—
265C22×C151C4×C4⋊C411yescharacteristic
266C22×C151#38511yescharacteristic
267C22×C151#38511yescharacteristic
268C22×C151#38611yescharacteristic
269C22×C151#38711yescharacteristic
270C22×C151#38811yescharacteristic
271C22×C151#38911yescharacteristic
272C22×C151C2×#10611yescharacteristic
273C22×C151#42711yescharacteristic
274C22×C151#42811yescharacteristic
275C22×C151#42811yescharacteristic
276C22×C151C4×SD1611yescharacteristic
277C22×C151C4×SD1611yescharacteristic
278C22×C151C4×SD1611yescharacteristic
279C22×C151C4×SD1611yescharacteristic
280C22×C151#44011yescharacteristic
281C22×C151#44011yescharacteristic
282C22×C151#44111yescharacteristic
283C22×C151#44211yescharacteristic
284C22×C151#44811yescharacteristic
285C22×C151#44911yescharacteristic
286C22×C151#45011yescharacteristic
287C22×C151#45211yescharacteristic
288C22×C151#46011yescharacteristic
289C22×C151#46111yescharacteristic
290C22×C151#46311yescharacteristic
291C22×C151#46411yescharacteristic
292C22×C151#47511yescharacteristic
293C22×C151#47611yescharacteristic
294C22×C151#47811yescharacteristic
295C22×C151#47911yescharacteristic
296C22×C151#48111yescharacteristic
297C22×C151#48211yescharacteristic
298C22×C151#48311yescharacteristic
299C22×C151#48511yescharacteristic
300C4×C151—24no—
301C4×C151—42no—
302C4×C151—44no—
303C4×C151—44no—
304C4×C151—82no—
305C4×C151—82no—
306C4×C151C4×C22⋊C411yescharacteristic
307C4×C151C4×C4⋊C411yescharacteristic
308C4×C151#38711yescharacteristic
309C4×C151#38711yescharacteristic
310C4×C151#38711yescharacteristic
311C4×C151#38811yescharacteristic
312C4×C151#38911yescharacteristic
313C4×C151#39111yescharacteristic
314C2×C151#143611yescharacteristic
315C2×C151C4×#10611yescharacteristic
316C2×C151#177611yescharacteristic
317C2×C151#185311yescharacteristic
318C2×C151#185411yescharacteristic
319C2×C151#186411yescharacteristic
320C2×C151#186511yescharacteristic
321C2×C151#187711yescharacteristic
322C2×C151#188011yescharacteristic
323C2×C151#191911yescharacteristic
324C2×C151#192011yescharacteristic
325C2×C151#192611yescharacteristic
326C2×C151#192711yescharacteristic
327C2×C151#194811yescharacteristic
328C2×C151#194911yescharacteristic
329#10908C15111yesmaximal, characteristic, direct product factor, Sylow
330C151#1090811yescharacteristic, direct product factor, Sylow
331C22×#106C2×C15111yescharacteristic
332C2×C4×C4⋊C4C2×C15111yescharacteristic
333C2×#340C2×C15111yescharacteristic
334C2×#340C2×C15111yescharacteristic
335C2×#340C2×C15111yescharacteristic
336C2×#336C2×C15111yescharacteristic
337C4⋊#95C2×C15111yescharacteristic
338C23×C8C22×C15111yescharacteristic
339C23×C8C22×C15111yescharacteristic
340C22×C4⋊C4C22×C15111yescharacteristic
341C22×C4⋊C4C22×C15111yescharacteristic
342C22×C4⋊C4C22×C15111yescharacteristic
343C22×C4⋊C4C22×C15111yescharacteristic
344C22×C42—21no—
345C22×C42C22×C15111yescharacteristic
346C2×#106—22no—
347C2×#106—22no—
348C2×#106C4×C15114yescomplemented
349C4×C4⋊C4—22no—
350C4×C4⋊C4—22no—
351C2×#95—21no—
352C2×#95—21no—
353C2×#95—21no—
354#340—22no—
355#340—22no—
356#340C4×C15114yescomplemented
357#336C4×C15114yescomplemented
358C23×C4—21no—
359C23×C4—21no—
360C23×C4—21no—
361C23×C4—21no—
362C23×C4D4×C15111yescharacteristic
363C23×C4D4×C15111yescharacteristic
364C23×C4C23×C15111yescharacteristic
365C22×C8—21no—
366C22×C8—21no—
367C22×C8—21no—
368C22×C8—21no—
369C22×C8—21no—
370C22×C8—21no—
371C22×C8—21no—
372C22×C8—21no—
373C22×C8—21no—
374C22×C8—21no—
375C22×C8C2×C4×C15112yes—
376C22×C8C2×C4×C15112yes—
377C22×C8C2×C4×C15112yes—
378C22×C8C2×C4×C15112yes—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4C2×C4×C15112yes—
396C2×C4⋊C4C2×C4×C15112yes—
397C2×C4⋊C4C2×C4×C15112yes—
398C2×C4⋊C4C2×C4×C15112yes—
399C2×C4⋊C4D4×C15112yes—
400C2×C4⋊C4D4×C15112yes—
401C2×C4⋊C4D4×C15112yes—
402C2×C4⋊C4Q8×C15112yes—
403C2×C42—21no—
404C2×C42—21no—
405C2×C42—21no—
406C2×C42—21no—
407C2×C42—24no—
408C2×C42—42no—
409C2×C42—42no—
410C2×C42C2×C4×C15112yes—
411C2×C42Q8×C15112yes—
412#106—28no—
413#95—24no—
414#95—42no—
415#95—42no—
416C24C2×D4×C15111yescharacteristic
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—21no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—41no—
436C22×C4—41no—
437C22×C4—41no—
438C22×C4—41no—
439C22×C4—41no—
440C22×C4—41no—
441C22×C4—41no—
442C22×C4—41no—
443C22×C4—41no—
444C22×C4—41no—
445C22×C4—41no—
446C22×C4—41no—
447C22×C4—41no—
448C22×C4—41no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4—41no—
452C22×C4—41no—
453C22×C4—41no—
454C22×C4—41no—
455C22×C4C4⋊C4×C15112yes—
456C22×C4C4⋊C4×C15112yes—
457C22×C4SD16×C15112yes—
458C22×C4SD16×C15112yes—
459C22×C4C22×C4×C15111yescharacteristic
460C22×C4C22×C4×C15111yescharacteristic
461C22×C4C22×C4×C15111yescharacteristic
462C22×C4C2×D4×C15111yescharacteristic
463C22×C4C2×D4×C15111yescharacteristic
464C22×C4C2×D4×C15111yescharacteristic
465C22×C4C2×Q8×C15111yescharacteristic
466C22×C4C2×Q8×C15111yescharacteristic
467C22×C4#41×C15111yescharacteristic
468C22×C4#41×C15111yescharacteristic
469C22×C4#41×C15111yescharacteristic
470C22×C4#41×C15111yescharacteristic
471C22×C4#41×C15111yescharacteristic
472C22×C4#41×C15111yescharacteristic
473C2×C8—22no—
474C2×C8—22no—
475C2×C8—22no—
476C2×C8—22no—
477C2×C8—22no—
478C2×C8—22no—
479C2×C8—22no—
480C2×C8—22no—
481C2×C8—22no—
482C2×C8—41no—
483C2×C8—41no—
484C2×C8—41no—
485C2×C8—41no—
486C2×C8C42×C15114yescomplemented
487C4⋊C4—22no—
488C4⋊C4—22no—
489C4⋊C4—22no—
490C4⋊C4—22no—
491C4⋊C4—22no—
492C4⋊C4—22no—
493C4⋊C4—22no—
494C4⋊C4—22no—
495C4⋊C4—22no—
496C4⋊C4—22no—
497C4⋊C4—41no—
498C4⋊C4—41no—
499C4⋊C4—41no—
500C4⋊C4—41no—
501C4⋊C4C22⋊C4×C15114yes—
502C4⋊C4C4⋊C4×C15114yes—
503C42—22no—
504C42—22no—
505C42—22no—
506C42—22no—
507C42—48no—
508C23C2×C4⋊C4×C15111yescharacteristic
509C23C4×D4×C15111yescharacteristic
510C23C4×D4×C15111yescharacteristic
511C23#120×C15111yescharacteristic
512C23#121×C15111yescharacteristic
513C23C22⋊Q8×C15111yescharacteristic
514C23#123×C15111yescharacteristic
515C23C2×SD16×C15111yescharacteristic
516C23C2×SD16×C15111yescharacteristic
517C23#135×C15111yescharacteristic
518C23#135×C15111yescharacteristic
519C23AGL(1,ℤ/8)×C15111yescharacteristic
520C23AGL(1,ℤ/8)×C15111yescharacteristic
521C23#137×C15111yescharacteristic
522C23#137×C15111yescharacteristic
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—24no—
531C2×C4—24no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—41no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—41no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—81no—
557C2×C4—81no—
558C2×C4—81no—
559C2×C4—81no—
560C2×C4—81no—
561C2×C4—81no—
562C2×C4—81no—
563C2×C4—81no—
564C2×C4#106×C15114yescomplemented
565C2×C4C2×C42×C15111yescharacteristic
566C2×C4C2×C22⋊C4×C15111yescharacteristic
567C2×C4C2×C4⋊C4×C15111yescharacteristic
568C2×C4#117×C15111yescharacteristic
569C2×C4#117×C15111yescharacteristic
570C2×C4#117×C15111yescharacteristic
571C2×C4C4×D4×C15111yescharacteristic
572C2×C4C4×D4×C15111yescharacteristic
573C2×C4C4×D4×C15111yescharacteristic
574C2×C4C4×D4×C15111yescharacteristic
575C2×C4C4×D4×C15111yescharacteristic
576C2×C4C4×D4×C15111yescharacteristic
577C2×C4C4×Q8×C15111yescharacteristic
578C2×C4C4×Q8×C15111yescharacteristic
579C2×C4C4×Q8×C15111yescharacteristic
580C2×C4C4×Q8×C15111yescharacteristic
581C2×C4#121×C15111yescharacteristic
582C2×C4C22⋊Q8×C15111yescharacteristic
583C2×C4C22⋊Q8×C15111yescharacteristic
584C2×C4C22⋊Q8×C15111yescharacteristic
585C2×C4#123×C15111yescharacteristic
586C2×C4#123×C15111yescharacteristic
587C2×C4#124×C15111yescharacteristic
588C2×C4#125×C15111yescharacteristic
589C2×C4#125×C15111yescharacteristic
590C2×C4#126×C15111yescharacteristic
591C2×C4#126×C15111yescharacteristic
592C2×C4C4⋊Q8×C15111yescharacteristic
593C8—24no—
594C8—42no—
595C22C4×C4⋊C4×C15111yescharacteristic
596C22#385×C15111yescharacteristic
597C22#385×C15111yescharacteristic
598C22#386×C15111yescharacteristic
599C22#387×C15111yescharacteristic
600C22#388×C15111yescharacteristic
601C22#389×C15111yescharacteristic
602C22C2×#106×C15111yescharacteristic
603C22#427×C15111yescharacteristic
604C22#428×C15111yescharacteristic
605C22#428×C15111yescharacteristic
606C22C4×SD16×C15111yescharacteristic
607C22C4×SD16×C15111yescharacteristic
608C22C4×SD16×C15111yescharacteristic
609C22C4×SD16×C15111yescharacteristic
610C22#440×C15111yescharacteristic
611C22#440×C15111yescharacteristic
612C22#441×C15111yescharacteristic
613C22#442×C15111yescharacteristic
614C22#448×C15111yescharacteristic
615C22#449×C15111yescharacteristic
616C22#450×C15111yescharacteristic
617C22#452×C15111yescharacteristic
618C22#460×C15111yescharacteristic
619C22#461×C15111yescharacteristic
620C22#463×C15111yescharacteristic
621C22#464×C15111yescharacteristic
622C22#475×C15111yescharacteristic
623C22#476×C15111yescharacteristic
624C22#478×C15111yescharacteristic
625C22#479×C15111yescharacteristic
626C22#481×C15111yescharacteristic
627C22#482×C15111yescharacteristic
628C22#483×C15111yescharacteristic
629C22#485×C15111yescharacteristic
630C4—24no—
631C4—42no—
632C4—44no—
633C4—44no—
634C4—82no—
635C4—82no—
636C4C4×C22⋊C4×C15111yescharacteristic
637C4C4×C4⋊C4×C15111yescharacteristic
638C4#387×C15111yescharacteristic
639C4#387×C15111yescharacteristic
640C4#387×C15111yescharacteristic
641C4#388×C15111yescharacteristic
642C4#389×C15111yescharacteristic
643C4#391×C15111yescharacteristic
644C2#1436×C15111yescharacteristic
645C2C4×#106×C15111yescharacteristic
646C2#1776×C15111yescharacteristic
647C2#1853×C15111yescharacteristic
648C2#1854×C15111yescharacteristic
649C2#1864×C15111yescharacteristic
650C2#1865×C15111yescharacteristic
651C2#1877×C15111yescharacteristic
652C2#1880×C15111yescharacteristic
653C2#1919×C15111yescharacteristic
654C2#1920×C15111yescharacteristic
655C2#1926×C15111yescharacteristic
656C2#1927×C15111yescharacteristic
657C2#1948×C15111yescharacteristic
658C2#1949×C15111yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C151C2×D4
commutatorC2×C4C2×C42×C151
Frattini, cosocleC23×C4C23×C151
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24×C151 ◁ C22×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
18. C2×#106×C151C4semidirect
26. #340×C151C4semidirect
27. #336×C151C4semidirect
156. C2×C8×C151C42semidirect
234. C2×C4×C151#106semidirect
329. #10908C151direct (N × H)
330. C151#10908direct (N × H)
348. C2×#106C4×C151semidirect
356. #340C4×C151semidirect
357. #336C4×C151semidirect
486. C2×C8C42×C151semidirect
564. C2×C4#106×C151semidirect

Maximal subgroups

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

subgroupindex
C22×#106×C1512
C2×C4×C4⋊C4×C1512
C2×#340×C1512
C2×#336×C1512
C4⋊#95×C1512
#10908151