Finite Group Databasebeta

← C151×#22784 #50327709

Subgroups — C151×#22784 #50327709

Order 38656.

740 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2943×C151C211yesmaximal, characteristic
2#2925×C151C211yesmaximal, characteristic, complemented
3#2906×C151C211yesmaximal, characteristic, complemented
4#1938×C151C211yesmaximal, characteristic, complemented
5#1937×C151C211yesmaximal, characteristic, complemented
6#1922×C151C211yesmaximal, characteristic, complemented
7#1922×C151C211yesmaximal, characteristic, complemented
8#1876×C151C211yesmaximal, characteristic
9#1876×C151C211yesmaximal, characteristic
10#1838×C151C211yesmaximal, characteristic, complemented
11#1806×C151C211yesmaximal, characteristic, complemented
12#1806×C151C211yesmaximal, characteristic, complemented
13#1771×C151C211yesmaximal, characteristic, complemented
14#1765×C151C211yesmaximal, characteristic, complemented
15#1764×C151C211yesmaximal, characteristic, complemented
16C2×#135×C151C2211yescharacteristic
17C2×#131×C151C2211yescharacteristic
18C2×#131×C151C2211yescharacteristic
19C4×#41×C151C2211yescharacteristic
20C4×#41×C151C2211yescharacteristic
21#442×C151C411yescharacteristic, complemented
22#442×C151C411yescharacteristic, complemented
23#441×C151C411yescharacteristic, complemented
24#441×C151C411yescharacteristic, complemented
25#440×C151C411yescharacteristic, complemented
26#440×C151C411yescharacteristic, complemented
27#440×C151C411yescharacteristic, complemented
28#440×C151C411yescharacteristic, complemented
29#433×C151—21no—
30#433×C151—21no—
31#432×C151—21no—
32#431×C151—21no—
33#427×C151C2211yescharacteristic
34#424×C151—21no—
35#424×C151—21no—
36#424×C151C2211yescharacteristic
37#424×C151C2211yescharacteristic
38#423×C151—21no—
39#423×C151C2211yescharacteristic
40#423×C151C2211yescharacteristic
41C2×C4⋊C8×C151—21no—
42C2×C4⋊C8×C151C2211yescharacteristic
43C2×#104×C151C2211yescharacteristic
44C2×#104×C151C2211yescharacteristic
45C2×#104×C151C2211yescharacteristic
46C2×#104×C151C2211yescharacteristic
47#416×C151C2211yescharacteristic
48#416×C151C2211yescharacteristic
49#408×C151C2211yescharacteristic
50#408×C151C2211yescharacteristic
51#405×C151C2211yescharacteristic
52#405×C151C2211yescharacteristic
53C2×#97×C151C2211yescharacteristic
54C2×#97×C151C2211yescharacteristic
55C2×C4×C8×C151C2211yescharacteristic
56C4×C4⋊C4×C151C2211yescharacteristic
57#341×C151C2211yescharacteristic
58#341×C151C2211yescharacteristic
59#341×C151C2211yescharacteristic
60#341×C151C2211yescharacteristic
61#339×C151C2211yescharacteristic
62#339×C151C2211yescharacteristic
63#339×C151C2211yescharacteristic
64#339×C151C2211yescharacteristic
65#336×C151C2211yescharacteristic
66#336×C151C2211yescharacteristic
67C2×#41×C151C2311yescharacteristic
68C2×#41×C151C2311yescharacteristic
69#135×C151—22no—
70#135×C151—22no—
71C2×Q16×C151C2×C411yescharacteristic
72C2×SD16×C151C2×C411yescharacteristic
73C2×SD16×C151C2×C411yescharacteristic
74C2×D8×C151C2×C411yescharacteristic
75#131×C151—22no—
76#131×C151—22no—
77#131×C151—41no—
78#131×C151—41no—
79C2×M16×C151—21no—
80C2×M16×C151—21no—
81C2×M16×C151C2311yescharacteristic
82C2×M16×C151C2311yescharacteristic
83C2×M16×C151C2311yescharacteristic
84C2×M16×C151C2311yescharacteristic
85C22×C8×C151—21no—
86C22×C8×C151—21no—
87C22×C8×C151C2311yescharacteristic
88C22×C8×C151C2311yescharacteristic
89C22×C8×C151C2311yescharacteristic
90C22×C8×C151C2311yescharacteristic
91C4×Q8×C151C2×C411yescharacteristic
92C4×Q8×C151C2×C411yescharacteristic
93C4×Q8×C151C2×C411yescharacteristic
94C4×Q8×C151C2×C411yescharacteristic
95C4×D4×C151—21no—
96C4×D4×C151—21no—
97C4×D4×C151—21no—
98C4×D4×C151—21no—
99C4×D4×C151C2×C411yescharacteristic
100C4×D4×C151C2×C411yescharacteristic
101C4×D4×C151C2×C411yescharacteristic
102C4×D4×C151C2×C411yescharacteristic
103#117×C151—21no—
104#117×C151—21no—
105#117×C151C2311yescharacteristic
106#117×C151C2311yescharacteristic
107C2×C4⋊C4×C151—21no—
108C2×C42×C151—21no—
109C2×C42×C151—21no—
110C2×C42×C151C2311yescharacteristic
111C2×C42×C151C2311yescharacteristic
112C2×C42×C151C2311yescharacteristic
113#107×C151C2×C411yescharacteristic
114#107×C151C2×C411yescharacteristic
115#106×C151C2×C411yescharacteristic
116#106×C151C2×C411yescharacteristic
117C4⋊C8×C151—21no—
118C4⋊C8×C151—21no—
119C4⋊C8×C151—21no—
120C4⋊C8×C151—21no—
121C4⋊C8×C151—21no—
122C4⋊C8×C151—21no—
123C4⋊C8×C151—21no—
124C4⋊C8×C151—21no—
125C4⋊C8×C151D411yescharacteristic
126C4⋊C8×C151D411yescharacteristic
127C4⋊C8×C151D411yescharacteristic
128C4⋊C8×C151D411yescharacteristic
129#104×C151—22no—
130#104×C151—22no—
131#104×C151—41no—
132#104×C151—41no—
133#103×C151C2×C411yescharacteristic
134#103×C151C2×C411yescharacteristic
135#103×C151C2×C411yescharacteristic
136#103×C151C2×C411yescharacteristic
137#102×C151C2×C411yescharacteristic
138#102×C151C2×C411yescharacteristic
139#102×C151C2×C411yescharacteristic
140#102×C151C2×C411yescharacteristic
141C22⋊C8×C151—21no—
142C22⋊C8×C151—21no—
143C22⋊C8×C151—21no—
144C22⋊C8×C151—21no—
145#97×C151—21no—
146#97×C151—21no—
147#97×C151—41no—
148#97×C151C2×C411yescharacteristic
149#97×C151C2×C411yescharacteristic
150#97×C151C2×C411yescharacteristic
151#97×C151C2×C411yescharacteristic
152C4×C8×C151—21no—
153C4×C8×C151—21no—
154C4×C8×C151—41no—
155#95×C151—21no—
156#41×C151—21no—
157#41×C151—21no—
158#41×C151—21no—
159#41×C151—21no—
160#41×C151—21no—
161#41×C151—21no—
162#41×C151#4112yes—
163#41×C151#4112yes—
164C2×Q8×C151C22×C411yescharacteristic
165C2×Q8×C151C22×C411yescharacteristic
166C2×D4×C151—21no—
167C2×D4×C151—21no—
168C2×D4×C151C22×C411yescharacteristic
169C2×D4×C151C22×C411yescharacteristic
170C22×C4×C151—21no—
171C22×C4×C151—21no—
172C22×C4×C151—21no—
173C22×C4×C151—21no—
174C22×C4×C151—21no—
175C22×C4×C151—21no—
176C22×C4×C151—21no—
177C22×C4×C151—21no—
178C22×C4×C151#4111yescharacteristic
179C22×C4×C151#4111yescharacteristic
180C22×C4×C151C2411yescharacteristic
181Q16×C151—22no—
182SD16×C151—22no—
183SD16×C151—22no—
184D8×C151—22no—
185M16×C151—21no—
186M16×C151—21no—
187M16×C151—21no—
188M16×C151—21no—
189M16×C151—21no—
190M16×C151—21no—
191M16×C151—21no—
192M16×C151—21no—
193M16×C151—42no—
194M16×C151—42no—
195C2×C8×C151—21no—
196C2×C8×C151—21no—
197C2×C8×C151—21no—
198C2×C8×C151—21no—
199C2×C8×C151—21no—
200C2×C8×C151—21no—
201C2×C8×C151—21no—
202C2×C8×C151—21no—
203C2×C8×C151—21no—
204C2×C8×C151—21no—
205C2×C8×C151—21no—
206C2×C8×C151—21no—
207C2×C8×C151—42no—
208C2×C8×C151—42no—
209C2×C8×C151C22×C411yescharacteristic
210C2×C8×C151C22×C411yescharacteristic
211C2×C8×C151C22×C411yescharacteristic
212C2×C8×C151C22×C411yescharacteristic
213C2×C8×C151C2×D411yescharacteristic
214C2×C8×C151C2×D411yescharacteristic
215C2×C8×C151C2×D411yescharacteristic
216C2×C8×C151C2×D411yescharacteristic
217C4⋊C4×C151—21no—
218C4⋊C4×C151—21no—
219C4⋊C4×C151—21no—
220C4⋊C4×C151—21no—
221C4⋊C4×C151—42no—
222C4⋊C4×C151C22×C411yescharacteristic
223C4⋊C4×C151C22×C411yescharacteristic
224C4⋊C4×C151C22×C411yescharacteristic
225C4⋊C4×C151C22×C411yescharacteristic
226C22⋊C4×C151—21no—
227C22⋊C4×C151—21no—
228C22⋊C4×C151—21no—
229C22⋊C4×C151—21no—
230C22⋊C4×C151—21no—
231C22⋊C4×C151—21no—
232C42×C151—21no—
233C42×C151—21no—
234C42×C151—21no—
235C42×C151—21no—
236C42×C151—21no—
237C42×C151—21no—
238C42×C151—21no—
239C42×C151—21no—
240C42×C151—21no—
241C42×C151—21no—
242C42×C151C22×C411yescharacteristic
243C42×C151C22×C411yescharacteristic
244C42×C151C2×D411yescharacteristic
245C42×C151C2×D411yescharacteristic
246C23×C151—21no—
247C23×C151—21no—
248C23×C151C2×#4111yescharacteristic
249Q8×C151—21no—
250Q8×C151—21no—
251Q8×C151—21no—
252Q8×C151#11712yes—
253D4×C151—22no—
254D4×C151—22no—
255D4×C151—21no—
256D4×C151—21no—
257D4×C151—21no—
258D4×C151—41no—
259D4×C151—41no—
260D4×C151#11712yes—
261C2×C4×C151—21no—
262C2×C4×C151—22no—
263C2×C4×C151—22no—
264C2×C4×C151—22no—
265C2×C4×C151—21no—
266C2×C4×C151—21no—
267C2×C4×C151—21no—
268C2×C4×C151—21no—
269C2×C4×C151—21no—
270C2×C4×C151—41no—
271C2×C4×C151—41no—
272C2×C4×C151—42no—
273C2×C4×C151—42no—
274C2×C4×C151—41no—
275C2×C4×C151—41no—
276C2×C4×C151—41no—
277C2×C4×C151—41no—
278C2×C4×C151—41no—
279C2×C4×C151—41no—
280C2×C4×C151—41no—
281C2×C4×C151—81no—
282C2×C4×C151—81no—
283C2×C4×C151C4×D411yescharacteristic
284C2×C4×C151C4×D411yescharacteristic
285C2×C4×C151C4×D411yescharacteristic
286C2×C4×C151C4×D411yescharacteristic
287C2×C4×C151C23×C411yescharacteristic
288C2×C4×C151C22×D411yescharacteristic
289C2×C4×C151C2×#4111yescharacteristic
290C2×C4×C151C2×#4111yescharacteristic
291C2×C4×C151H(5,𝔽2)11yescharacteristic
292C2×C4×C1512−1+411yescharacteristic
293C8×C151—21no—
294C8×C151—21no—
295C8×C151—21no—
296C8×C151—21no—
297C8×C151—21no—
298C8×C151—21no—
299C8×C151—21no—
300C8×C151—21no—
301C8×C151—41no—
302C8×C151—41no—
303C8×C151—41no—
304C8×C151—41no—
305C22×C151—21no—
306C22×C151—21no—
307C22×C151—22no—
308C22×C151—41no—
309C22×C151—41no—
310C22×C151—41no—
311C22×C151—41no—
312C22×C151—41no—
313C22×C151C2×C4×D411yescharacteristic
314C22×C151#55211yescharacteristic
315C22×C151#55311yescharacteristic
316C4×C151—22no—
317C4×C151—21no—
318C4×C151—21no—
319C4×C151—21no—
320C4×C151—21no—
321C4×C151—42no—
322C4×C151—41no—
323C4×C151—41no—
324C4×C151—41no—
325C4×C151—41no—
326C4×C151—41no—
327C4×C151—81no—
328C4×C151C2×#11711yescharacteristic
329C4×C151#52011yescharacteristic
330C4×C151#54611yescharacteristic
331C4×C151#54811yescharacteristic
332C2×C151—21no—
333C2×C151—21no—
334C2×C151—42no—
335C2×C151—81no—
336C2×C151#235211yescharacteristic
337C2×C151#295511yescharacteristic
338C2×C151#295611yescharacteristic
339#22784C15111yesmaximal, characteristic, direct product factor, Sylow
340C151#2278411yescharacteristic, direct product factor, Sylow
341#2943C2×C15111yescharacteristic
342#2925C2×C15111yescharacteristic, complemented
343#2906C2×C15111yescharacteristic, complemented
344#1938C2×C15111yescharacteristic, complemented
345#1937C2×C15111yescharacteristic, complemented
346#1922C2×C15111yescharacteristic, complemented
347#1922C2×C15111yescharacteristic, complemented
348#1876C2×C15111yescharacteristic
349#1876C2×C15111yescharacteristic
350#1838C2×C15111yescharacteristic, complemented
351#1806C2×C15111yescharacteristic, complemented
352#1806C2×C15111yescharacteristic, complemented
353#1771C2×C15111yescharacteristic, complemented
354#1765C2×C15111yescharacteristic, complemented
355#1764C2×C15111yescharacteristic, complemented
356C2×#135C22×C15111yescharacteristic
357C2×#131C22×C15111yescharacteristic
358C2×#131C22×C15111yescharacteristic
359C4×#41C22×C15111yescharacteristic
360C4×#41C22×C15111yescharacteristic
361#442C4×C15111yescharacteristic, complemented
362#442C4×C15111yescharacteristic, complemented
363#441C4×C15111yescharacteristic, complemented
364#441C4×C15111yescharacteristic, complemented
365#440C4×C15111yescharacteristic, complemented
366#440C4×C15111yescharacteristic, complemented
367#440C4×C15111yescharacteristic, complemented
368#440C4×C15111yescharacteristic, complemented
369#433—21no—
370#433—21no—
371#432—21no—
372#431—21no—
373#427C22×C15111yescharacteristic
374#424—21no—
375#424—21no—
376#424C22×C15111yescharacteristic
377#424C22×C15111yescharacteristic
378#423—21no—
379#423C22×C15111yescharacteristic
380#423C22×C15111yescharacteristic
381C2×C4⋊C8—21no—
382C2×C4⋊C8C22×C15111yescharacteristic
383C2×#104C22×C15111yescharacteristic
384C2×#104C22×C15111yescharacteristic
385C2×#104C22×C15111yescharacteristic
386C2×#104C22×C15111yescharacteristic
387#416C22×C15111yescharacteristic
388#416C22×C15111yescharacteristic
389#408C22×C15111yescharacteristic
390#408C22×C15111yescharacteristic
391#405C22×C15111yescharacteristic
392#405C22×C15111yescharacteristic
393C2×#97C22×C15111yescharacteristic
394C2×#97C22×C15111yescharacteristic
395C2×C4×C8C22×C15111yescharacteristic
396C4×C4⋊C4C22×C15111yescharacteristic
397#341C22×C15111yescharacteristic
398#341C22×C15111yescharacteristic
399#341C22×C15111yescharacteristic
400#341C22×C15111yescharacteristic
401#339C22×C15111yescharacteristic
402#339C22×C15111yescharacteristic
403#339C22×C15111yescharacteristic
404#339C22×C15111yescharacteristic
405#336C22×C15111yescharacteristic
406#336C22×C15111yescharacteristic
407C2×#41C23×C15111yescharacteristic
408C2×#41C23×C15111yescharacteristic
409#135—22no—
410#135—22no—
411C2×Q16C2×C4×C15111yescharacteristic
412C2×SD16C2×C4×C15111yescharacteristic
413C2×SD16C2×C4×C15111yescharacteristic
414C2×D8C2×C4×C15111yescharacteristic
415#131—22no—
416#131—22no—
417#131—41no—
418#131—41no—
419C2×M16—21no—
420C2×M16—21no—
421C2×M16C23×C15111yescharacteristic
422C2×M16C23×C15111yescharacteristic
423C2×M16C23×C15111yescharacteristic
424C2×M16C23×C15111yescharacteristic
425C22×C8—21no—
426C22×C8—21no—
427C22×C8C23×C15111yescharacteristic
428C22×C8C23×C15111yescharacteristic
429C22×C8C23×C15111yescharacteristic
430C22×C8C23×C15111yescharacteristic
431C4×Q8C2×C4×C15111yescharacteristic
432C4×Q8C2×C4×C15111yescharacteristic
433C4×Q8C2×C4×C15111yescharacteristic
434C4×Q8C2×C4×C15111yescharacteristic
435C4×D4—21no—
436C4×D4—21no—
437C4×D4—21no—
438C4×D4—21no—
439C4×D4C2×C4×C15111yescharacteristic
440C4×D4C2×C4×C15111yescharacteristic
441C4×D4C2×C4×C15111yescharacteristic
442C4×D4C2×C4×C15111yescharacteristic
443#117—21no—
444#117—21no—
445#117C23×C15111yescharacteristic
446#117C23×C15111yescharacteristic
447C2×C4⋊C4—21no—
448C2×C42—21no—
449C2×C42—21no—
450C2×C42C23×C15111yescharacteristic
451C2×C42C23×C15111yescharacteristic
452C2×C42C23×C15111yescharacteristic
453#107C2×C4×C15111yescharacteristic
454#107C2×C4×C15111yescharacteristic
455#106C2×C4×C15111yescharacteristic
456#106C2×C4×C15111yescharacteristic
457C4⋊C8—21no—
458C4⋊C8—21no—
459C4⋊C8—21no—
460C4⋊C8—21no—
461C4⋊C8—21no—
462C4⋊C8—21no—
463C4⋊C8—21no—
464C4⋊C8—21no—
465C4⋊C8D4×C15111yescharacteristic
466C4⋊C8D4×C15111yescharacteristic
467C4⋊C8D4×C15111yescharacteristic
468C4⋊C8D4×C15111yescharacteristic
469#104—22no—
470#104—22no—
471#104—41no—
472#104—41no—
473#103C2×C4×C15111yescharacteristic
474#103C2×C4×C15111yescharacteristic
475#103C2×C4×C15111yescharacteristic
476#103C2×C4×C15111yescharacteristic
477#102C2×C4×C15111yescharacteristic
478#102C2×C4×C15111yescharacteristic
479#102C2×C4×C15111yescharacteristic
480#102C2×C4×C15111yescharacteristic
481C22⋊C8—21no—
482C22⋊C8—21no—
483C22⋊C8—21no—
484C22⋊C8—21no—
485#97—21no—
486#97—21no—
487#97—41no—
488#97C2×C4×C15111yescharacteristic
489#97C2×C4×C15111yescharacteristic
490#97C2×C4×C15111yescharacteristic
491#97C2×C4×C15111yescharacteristic
492C4×C8—21no—
493C4×C8—21no—
494C4×C8—41no—
495#95—21no—
496#41—21no—
497#41—21no—
498#41—21no—
499#41—21no—
500#41—21no—
501#41—21no—
502#41#41×C15112yes—
503#41#41×C15112yes—
504C2×Q8C22×C4×C15111yescharacteristic
505C2×Q8C22×C4×C15111yescharacteristic
506C2×D4—21no—
507C2×D4—21no—
508C2×D4C22×C4×C15111yescharacteristic
509C2×D4C22×C4×C15111yescharacteristic
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4#41×C15111yescharacteristic
519C22×C4#41×C15111yescharacteristic
520C22×C4C24×C15111yescharacteristic
521Q16—22no—
522SD16—22no—
523SD16—22no—
524D8—22no—
525M16—21no—
526M16—21no—
527M16—21no—
528M16—21no—
529M16—21no—
530M16—21no—
531M16—21no—
532M16—21no—
533M16—42no—
534M16—42no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—42no—
548C2×C8—42no—
549C2×C8C22×C4×C15111yescharacteristic
550C2×C8C22×C4×C15111yescharacteristic
551C2×C8C22×C4×C15111yescharacteristic
552C2×C8C22×C4×C15111yescharacteristic
553C2×C8C2×D4×C15111yescharacteristic
554C2×C8C2×D4×C15111yescharacteristic
555C2×C8C2×D4×C15111yescharacteristic
556C2×C8C2×D4×C15111yescharacteristic
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—42no—
562C4⋊C4C22×C4×C15111yescharacteristic
563C4⋊C4C22×C4×C15111yescharacteristic
564C4⋊C4C22×C4×C15111yescharacteristic
565C4⋊C4C22×C4×C15111yescharacteristic
566C22⋊C4—21no—
567C22⋊C4—21no—
568C22⋊C4—21no—
569C22⋊C4—21no—
570C22⋊C4—21no—
571C22⋊C4—21no—
572C42—21no—
573C42—21no—
574C42—21no—
575C42—21no—
576C42—21no—
577C42—21no—
578C42—21no—
579C42—21no—
580C42—21no—
581C42—21no—
582C42C22×C4×C15111yescharacteristic
583C42C22×C4×C15111yescharacteristic
584C42C2×D4×C15111yescharacteristic
585C42C2×D4×C15111yescharacteristic
586C23—21no—
587C23—21no—
588C23C2×#41×C15111yescharacteristic
589Q8—21no—
590Q8—21no—
591Q8—21no—
592Q8#117×C15112yes—
593D4—22no—
594D4—22no—
595D4—21no—
596D4—21no—
597D4—21no—
598D4—41no—
599D4—41no—
600D4#117×C15112yes—
601C2×C4—21no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—42no—
613C2×C4—42no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—81no—
622C2×C4—81no—
623C2×C4C4×D4×C15111yescharacteristic
624C2×C4C4×D4×C15111yescharacteristic
625C2×C4C4×D4×C15111yescharacteristic
626C2×C4C4×D4×C15111yescharacteristic
627C2×C4C23×C4×C15111yescharacteristic
628C2×C4C22×D4×C15111yescharacteristic
629C2×C4C2×#41×C15111yescharacteristic
630C2×C4C2×#41×C15111yescharacteristic
631C2×C4H(5,𝔽2)×C15111yescharacteristic
632C2×C42−1+4×C15111yescharacteristic
633C8—21no—
634C8—21no—
635C8—21no—
636C8—21no—
637C8—21no—
638C8—21no—
639C8—21no—
640C8—21no—
641C8—41no—
642C8—41no—
643C8—41no—
644C8—41no—
645C22—21no—
646C22—21no—
647C22—22no—
648C22—41no—
649C22—41no—
650C22—41no—
651C22—41no—
652C22—41no—
653C22C2×C4×D4×C15111yescharacteristic
654C22#552×C15111yescharacteristic
655C22#553×C15111yescharacteristic
656C4—22no—
657C4—21no—
658C4—21no—
659C4—21no—
660C4—21no—
661C4—42no—
662C4—41no—
663C4—41no—
664C4—41no—
665C4—41no—
666C4—41no—
667C4—81no—
668C4C2×#117×C15111yescharacteristic
669C4#520×C15111yescharacteristic
670C4#546×C15111yescharacteristic
671C4#548×C15111yescharacteristic
672C2—21no—
673C2—21no—
674C2—42no—
675C2—81no—
676C2#2352×C15111yescharacteristic
677C2#2955×C15111yescharacteristic
678C2#2956×C15111yescharacteristic
subgroupG/H
centerC2×C4×C151C22×D4
commutatorC2×C4C23×C4×C151
Frattini, cosocleC22×C4C24×C151
socleC22×C151C2×C4×D4
prime radicalC2×#135×C151C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C151 ◁ C2×C4⋊C8×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2925×C151C2semidirect
3. #2906×C151C2semidirect
4. #1938×C151C2semidirect
5. #1937×C151C2semidirect
6. #1922×C151C2semidirect
7. #1922×C151C2semidirect
10. #1838×C151C2semidirect
11. #1806×C151C2semidirect
12. #1806×C151C2semidirect
13. #1771×C151C2semidirect
14. #1765×C151C2semidirect
15. #1764×C151C2semidirect
21. #442×C151C4semidirect
22. #442×C151C4semidirect
23. #441×C151C4semidirect
24. #441×C151C4semidirect
25. #440×C151C4semidirect
26. #440×C151C4semidirect
27. #440×C151C4semidirect
28. #440×C151C4semidirect
339. #22784C151direct (N × H)
340. C151#22784direct (N × H)
342. #2925C2×C151semidirect
343. #2906C2×C151semidirect
344. #1938C2×C151semidirect
345. #1937C2×C151semidirect
346. #1922C2×C151semidirect
347. #1922C2×C151semidirect
350. #1838C2×C151semidirect
351. #1806C2×C151semidirect
352. #1806C2×C151semidirect
353. #1771C2×C151semidirect
354. #1765C2×C151semidirect
355. #1764C2×C151semidirect
361. #442C4×C151semidirect
362. #442C4×C151semidirect
363. #441C4×C151semidirect
364. #441C4×C151semidirect
365. #440C4×C151semidirect
366. #440C4×C151semidirect
367. #440C4×C151semidirect
368. #440C4×C151semidirect

Maximal subgroups

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

subgroupindex
#2943×C1512
#2925×C1512
#2906×C1512
#1938×C1512
#1937×C1512
#1922×C1512
#1876×C1512
#1838×C1512
#1806×C1512
#1771×C1512
#1765×C1512
#1764×C1512
#22784151