Finite Group Databasebeta

← #29700869

Subgroups — #29700869

Order 15616.

1074 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839930C211yesmaximal, characteristic
2#21454654C211yesmaximal, characteristic, complemented
3#21454647C211yesmaximal, characteristic, complemented
4#21454345C211yesmaximal, characteristic, complemented
5#21446623C211yesmaximal, characteristic, complemented
6#21446484C211yesmaximal, characteristic, complemented
7#21446478C211yesmaximal, characteristic, complemented
8#21446327C211yesmaximal, characteristic, complemented
9#21446325C211yesmaximal, characteristic, complemented
10#21446214C211yesmaximal, characteristic, complemented
11#21446045C211yesmaximal, characteristic, complemented
12#21446043C211yesmaximal, characteristic, complemented
13#21445659C211yesmaximal, characteristic, complemented
14#21445654C211yesmaximal, characteristic, complemented
15C61×#2897C211yesmaximal, characteristic, complemented
16C2×#14519802C2211yescharacteristic
17C2×#14519802C2211yescharacteristic
18C2×#14519784C2211yescharacteristic
19C2×#14519773C2211yescharacteristic
20#16840245C2211yescharacteristic
21#16840236C2211yescharacteristic, complemented
22#16839930C418yescomplemented
23#16839872—21no—
24#16839871—21no—
25#16839865—21no—
26#16839860—21no—
27C4×#11758201—21no—
28#16839847—21no—
29C4×#11758199—21no—
30#16839842—21no—
31#16839805C2211yescharacteristic, complemented
32#16839802C2211yescharacteristic, complemented
33C2×#14519704C2211yescharacteristic
34C2×#14519704C2211yescharacteristic
35#16839767—21no—
36#16839767C2211yescharacteristic
37#16839763—21no—
38#16839763C2211yescharacteristic
39#16839758—21no—
40#16839758C2211yescharacteristic
41C2×#14519699C2211yescharacteristic, complemented
42C2×#14519698—21no—
43C2×#14519698C2211yescharacteristic
44C2×#14519697C2211yescharacteristic, complemented
45C2×#14519694C2211yescharacteristic
46C2×#14519693C2211yescharacteristic, complemented
47#16839718C2211yescharacteristic, complemented
48#16839717C2211yescharacteristic, complemented
49C2×C8×Dic61C2211yescharacteristic, complemented
50#16839631C2211yescharacteristic, complemented
51#16839531C2211yescharacteristic, complemented
52#16839530C2211yescharacteristic, complemented
53#16839527C2211yescharacteristic, complemented
54#16839526C2211yescharacteristic, complemented
55#16839523C2211yescharacteristic, complemented
56#16839521C2211yescharacteristic, complemented
57C2×H(5,𝔽2)×C61C2211yescharacteristic
58C2×#131×C61C2211yescharacteristic
59C61×#520C2211yescharacteristic
60C61×#418—21no—
61C61×#418C2211yescharacteristic
62C61×#417—21no—
63C61×#417C2211yescharacteristic
64C61×#416—21no—
65C61×#416C2211yescharacteristic
66C2×#102×C61—21no—
67C2×#102×C61C2211yescharacteristic
68C22×D244C2311yescharacteristic
69C22×C22⋊D61—41no—
70#14519802—22no—
71#14519802—22no—
72#14519802C2×C414yescomplemented
73#14519802C2×C414yescomplemented
74C2×#11758201—21no—
75C2×#11758201—21no—
76C2×#11758199—21no—
77C2×#11758199—21no—
78#14519784—22no—
79#14519784—41no—
80C2×#11758194—21no—
81C2×#11758194C2311yescharacteristic
82C2×#11758194C2311yescharacteristic
83C2×#11758194C2311yescharacteristic
84C22×#92418—21no—
85C22×#92418C2311yescharacteristic
86#14519773—41no—
87#14519773C2×C414yescomplemented
88Q8×Dic61—21no—
89C4×D244—21no—
90C4×D244—21no—
91D4×Dic61—21no—
92D4×Dic61—41no—
93#14519739—21no—
94#14519739—21no—
95#14519736—21no—
96#14519736C2311yescharacteristic
97C2×C4⋊Dic61—21no—
98C2×C4⋊Dic61C2311yescharacteristic
99C2×#11758196—41no—
100C22⋊C4×D61—41no—
101C2×C4×Dic61C2311yescharacteristic
102#14519710—21no—
103#14519710—21no—
104#14519708—21no—
105#14519708—21no—
106#14519704C2×C414yescomplemented
107#14519704C2×C414yescomplemented
108#14519701—21no—
109#14519701D411yescharacteristic, complemented
110#14519701D411yescharacteristic, complemented
111#14519699—21no—
112#14519699—21no—
113#14519698—21no—
114#14519698—21no—
115#14519698—21no—
116#14519698—21no—
117#14519698—21no—
118#14519698D411yescharacteristic, complemented
119#14519698D411yescharacteristic, complemented
120#14519697—21no—
121#14519697—21no—
122#14519694C2×C414yescomplemented
123#14519693—41no—
124#14519688—21no—
125#14519687—21no—
126C4×#92418—21no—
127C8×Dic61—21no—
128C8×Dic61—41no—
129H(5,𝔽2)×C61—22no—
130H(5,𝔽2)×C61—22no—
131H(5,𝔽2)×C61—41no—
132H(5,𝔽2)×C61C2×C414yescomplemented
133C2×#41×C61—21no—
134C2×#41×C61—21no—
135C2×#41×C61C2311yescharacteristic
136C2×#41×C61C2311yescharacteristic
137C22×D4×C61—21no—
138C22×D4×C61—21no—
139C22×D4×C61—41no—
140C22×D4×C61C2311yescharacteristic
141#131×C61—22no—
142#131×C61—41no—
143C2×M16×C61—21no—
144C2×M16×C61C2311yescharacteristic
145C22×C8×C61—21no—
146C22×C8×C61C2311yescharacteristic
147C4×Q8×C61—21no—
148C4×D4×C61—21no—
149C4×D4×C61—41no—
150#117×C61—21no—
151#117×C61C2311yescharacteristic
152C2×C4⋊C4×C61—21no—
153C2×C4⋊C4×C61C2311yescharacteristic
154#103×C61—21no—
155#103×C61D411yescharacteristic, complemented
156#103×C61D411yescharacteristic, complemented
157#102×C61—21no—
158#102×C61—21no—
159#102×C61—21no—
160#102×C61—21no—
161#102×C61—21no—
162#102×C61D411yescharacteristic, complemented
163#102×C61D411yescharacteristic, complemented
164C24×C61—21no—
165C24×C61—41no—
166C23×D61—21no—
167#41×C61—21no—
168#41×C61—21no—
169#41×C61—21no—
170#41×C61—21no—
171#41×C61—24no—
172#41×C61—24no—
173#41×C61—42no—
174#41×C61—42no—
175#41×C61C22×C412yes—
176#41×C61C22×C412yes—
177#41×C61#4112yes—
178#41×C61#4112yes—
179C2×Q8×C61C2×D411yescharacteristic
180C2×Q8×C61C2×D411yescharacteristic
181C2×D4×C61—21no—
182C2×D4×C61—21no—
183C2×D4×C61—24no—
184C2×D4×C61—24no—
185C2×D4×C61—21no—
186C2×D4×C61—21no—
187C2×D4×C61—21no—
188C2×D4×C61—21no—
189C2×D4×C61—21no—
190C2×D4×C61—42no—
191C2×D4×C61—42no—
192C2×D4×C61—41no—
193C2×D4×C61—41no—
194C2×D4×C61—44no—
195C2×D4×C61—44no—
196C2×D4×C61C22×C412yes—
197C2×D4×C61C2×D411yescharacteristic
198C2×D4×C61C2×D411yescharacteristic
199C22×C4×C61—21no—
200C22×C4×C61—21no—
201C22×C4×C61—21no—
202C22×C4×C61—41no—
203C22×C4×C61—41no—
204C22×C4×C61C2411yescharacteristic
205C2×C22⋊D61—44no—
206C2×C22⋊D61—82no—
207C2×C22⋊D61—82no—
208C22×Dic61—21no—
209C22×Dic61—21no—
210C22×Dic61—41no—
211C2×D244—21no—
212C2×D244—21no—
213C2×D244—21no—
214C2×D244—21no—
215C2×D244—21no—
216C2×D244C22×C412yes—
217C2×C4×D61—41no—
218C2×C4×D61—41no—
219M16×C61—21no—
220M16×C61—21no—
221M16×C61—42no—
222C2×C8×C61—21no—
223C2×C8×C61—21no—
224C2×C8×C61—21no—
225C2×C8×C61—42no—
226C2×C8×C61C2×D411yescharacteristic
227C2×C8×C61C2×D411yescharacteristic
228C4⋊C4×C61—21no—
229C4⋊C4×C61—21no—
230C4⋊C4×C61—41no—
231C4⋊C4×C61C2×D411yescharacteristic
232C4⋊C4×C61C2×D411yescharacteristic
233C22⋊C4×C61—21no—
234C22⋊C4×C61—41no—
235C42×C61—21no—
236C42×C61—41no—
237C22⋊Dic61—21no—
238C22⋊Dic61—41no—
239#11758201—24no—
240#11758201—24no—
241#11758199—24no—
242#11758199—24no—
243#11758198—41no—
244#11758198—41no—
245C4⋊Dic61—21no—
246C4⋊Dic61—21no—
247C4⋊Dic61—41no—
248C4⋊Dic61C2×D411yescharacteristic
249C4⋊Dic61C2×D411yescharacteristic
250#11758196—82no—
251C4×Dic61—21no—
252C4×Dic61—21no—
253C4×Dic61—41no—
254C4×Dic61C22×C412yes—
255#11758194—21no—
256#11758194—21no—
257#11758194—21no—
258#11758194—21no—
259#11758194—42no—
260#11758194C22×C412yes—
261#11758194C22×C412yes—
262C2×#92418—21no—
263C2×#92418—21no—
264C2×#92418—21no—
265C2×#92418—21no—
266C2×#92418—21no—
267C2×#92418—42no—
268C2×#92418C2×D411yescharacteristic
269C2×#92418C2×D411yescharacteristic
270C23×C61—21no—
271C23×C61—21no—
272C23×C61—22no—
273C23×C61—44no—
274C23×C61—41no—
275C23×C61—41no—
276C23×C61—81no—
277C23×C61—81no—
278C23×C61—161no—
279C23×C61—161no—
280C23×C61H(5,𝔽2)11yescharacteristic
281C22×D61—22no—
282C22×D61—41no—
283C22×D61—41no—
284C22×D61—81no—
285C22×D61—81no—
286Q8×C61—21no—
287Q8×C61—21no—
288Q8×C61C4×D412yes—
289Q8×C61C4×D412yes—
290D4×C61—22no—
291D4×C61—22no—
292D4×C61—22no—
293D4×C61—22no—
294D4×C61—22no—
295D4×C61—22no—
296D4×C61—21no—
297D4×C61—21no—
298D4×C61—44no—
299D4×C61—44no—
300D4×C61—41no—
301D4×C61—41no—
302D4×C61C4×D412yes—
303D4×C61C4×D412yes—
304C2×C4×C61—21no—
305C2×C4×C61—21no—
306C2×C4×C61—22no—
307C2×C4×C61—22no—
308C2×C4×C61—22no—
309C2×C4×C61—22no—
310C2×C4×C61—21no—
311C2×C4×C61—21no—
312C2×C4×C61—44no—
313C2×C4×C61—41no—
314C2×C4×C61—81no—
315C2×C4×C61—161no—
316C2×C4×C61C23×C411yescharacteristic
317C2×C4×C61C22×D411yescharacteristic
318C2×C4×C61C22×D411yescharacteristic
319C2×C4×C61C2×#4111yescharacteristic
320C2×C4×C61C2×#4111yescharacteristic
321C2×C4×C61H(5,𝔽2)11yescharacteristic
322C22⋊D61—88no—
323C2×Dic61—22no—
324C2×Dic61—22no—
325C2×Dic61—22no—
326C2×Dic61—21no—
327C2×Dic61—21no—
328C2×Dic61—41no—
329C2×Dic61—81no—
330C2×Dic61—161no—
331D244—22no—
332D244—22no—
333D244—41no—
334D244—41no—
335C4×D61—161no—
336C4×D61—161no—
337C8×C61—21no—
338C8×C61—21no—
339C8×C61—41no—
340#92418—22no—
341#92418—22no—
342#92418—21no—
343#92418—21no—
344#92418—41no—
345#22897—611nomaximal, Sylow
346C22×C61—21no—
347C22×C61—21no—
348C22×C61—22no—
349C22×C61—22no—
350C22×C61—41no—
351C22×C61—41no—
352C22×C61—41no—
353C22×C61—41no—
354C22×C61—42no—
355C22×C61—82no—
356C22×C61—81no—
357C22×C61—81no—
358C22×C61—161no—
359C22×C61—164no—
360C22×C61#51811yescharacteristic
361C22×C61D4211yescharacteristic
362C22×C61#55111yescharacteristic
363C2×D61—42no—
364C2×D61—81no—
365C2×D61—81no—
366C2×D61—82no—
367C2×D61—161no—
368C4×C61—22no—
369C4×C61—22no—
370C4×C61—41no—
371C4×C61—41no—
372C4×C61—81no—
373C4×C61C2×C4×D411yescharacteristic
374C4×C61C2×C4×D411yescharacteristic
375C4×C61#54611yescharacteristic
376C4×C61#54611yescharacteristic
377Dic61—24no—
378Dic61—41no—
379Dic61—41no—
380Dic61—81no—
381C2×#453—611no—
382#2946—611no—
383#2946—611no—
384#2897—611no—
385#2897D6111yescharacteristic, complemented
386#1957—611no—
387#1931—611no—
388#1931—611no—
389#1907—611no—
390#1907—611no—
391#1887—611no—
392#1859—611no—
393#1859—611no—
394#1764—611no—
395#1764—611no—
396C2×C61—21no—
397C2×C61—21no—
398C2×C61—42no—
399C2×C61—42no—
400C2×C61—82no—
401C2×C61#235811yescharacteristic
402C2×C61#329111yescharacteristic
403C2×C61#329211yescharacteristic
404D61—82no—
405C2×H(5,𝔽2)C2×D6111yescharacteristic
406C2×AGL(1,ℤ/8)—611no—
407C2×AGL(1,ℤ/8)—611no—
408C2×#131—611no—
409C2×#131C2×D6111yescharacteristic
410C2×#127—611no—
411#520—611no—
412#520C2×D6111yescharacteristic
413#518—611no—
414#453—618no—
415#442—1221no—
416#442—1221no—
417#440—1221no—
418#440—1221no—
419C4×SD16—1221no—
420C4×SD16—1221no—
421C4×D8—1221no—
422C4×D8—1221no—
423#428—611no—
424#428—611no—
425C2×#104—611no—
426C2×#104—611no—
427#418—21no—
428#418—611no—
429#418—1221no—
430#418C2×D6111yescharacteristic
431#417—21no—
432#417—611no—
433#417—1221no—
434#417C2×D6111yescharacteristic
435#416—21no—
436#416—611no—
437#416—1221no—
438#416C2×D6111yescharacteristic
439C2×#102—21no—
440C2×#102—611no—
441C2×#102—611no—
442C2×#102—611no—
443C2×#102—1221no—
444C2×#102C2×D6111yescharacteristic
445C2×#100—611no—
446C2×#100—611no—
447#405—611no—
448#405—611no—
449C2×C4×C8—611no—
450#384—611no—
451#343—611no—
452#343—611no—
453#341—611no—
454#341—611no—
455#339—611no—
456#339—611no—
457C61#2289711yescharacteristic, complemented, Sylow
458H(5,𝔽2)—22no—
459H(5,𝔽2)—22no—
460H(5,𝔽2)—41no—
461H(5,𝔽2)C4×D6114yescomplemented
462C2×#41—21no—
463C2×#41—21no—
464C2×#41C22×D6111yescharacteristic
465C2×#41C22×D6111yescharacteristic
466C22×D4—21no—
467C22×D4—21no—
468C22×D4—41no—
469C22×D4—611no—
470C22×D4—2441no—
471C22×D4C22×D6111yescharacteristic
472AGL(1,ℤ/8)—614no—
473AGL(1,ℤ/8)—614no—
474AGL(1,ℤ/8)—1222no—
475AGL(1,ℤ/8)—1222no—
476C2×SD16—1221no—
477C2×SD16—1221no—
478C2×D8—1221no—
479C2×D8—1221no—
480#131—22no—
481#131—41no—
482#131—1222no—
483#131—2441no—
484C2×M16—21no—
485C2×M16—611no—
486C2×M16—611no—
487C2×M16—611no—
488C2×M16—1221no—
489C2×M16C22×D6111yescharacteristic
490C22×C8—21no—
491C22×C8—611no—
492C22×C8—1221no—
493C22×C8C22×D6111yescharacteristic
494#127—614no—
495#127—2441no—
496C4×Q8—21no—
497C4×Q8—1221no—
498C4×D4—21no—
499C4×D4—41no—
500C4×D4—1221no—
501C4×D4—1221no—
502C4×D4—1221no—
503C4×D4—1221no—
504C4×D4—1221no—
505C4×D4—2441no—
506#117—21no—
507#117—611no—
508#117—1221no—
509#117C22×D6111yescharacteristic
510C2×C4⋊C4—21no—
511C2×C4⋊C4—611no—
512C2×C4⋊C4—1221no—
513C2×C4⋊C4—2441no—
514C2×C4⋊C4C22×D6111yescharacteristic
515C2×C22⋊C4—2441no—
516C2×C42—611no—
517#107—1221no—
518#107—1221no—
519#106—1221no—
520#106—1221no—
521#104—614no—
522#104—614no—
523#103—21no—
524#103—611no—
525#103—611no—
526#103—1221no—
527#103C22⋊D6111yescharacteristic, complemented
528#103C22⋊D6111yescharacteristic, complemented
529#102—21no—
530#102—21no—
531#102—21no—
532#102—21no—
533#102—21no—
534#102—611no—
535#102—611no—
536#102—1221no—
537#102—1221no—
538#102—1221no—
539#102—1221no—
540#102—1221no—
541#102—1221no—
542#102—1221no—
543#102—1221no—
544#102—1221no—
545#102C22⋊D6111yescharacteristic, complemented
546#102C22⋊D6111yescharacteristic, complemented
547#100—614no—
548#100—2441no—
549#97—1221no—
550#97—1221no—
551C4×C8—1221no—
552C4×C8—1221no—
553C4×C8—2441no—
554C24—21no—
555C24—41no—
556C24—1221no—
557#41—21no—
558#41—21no—
559#41—21no—
560#41—21no—
561#41—24no—
562#41—24no—
563#41—42no—
564#41—42no—
565#41C2×C4×D6112yes—
566#41C2×C4×D6112yes—
567#41#1175822212yes—
568#41#1175822412yes—
569C2×Q8D4×D6111yescharacteristic
570C2×Q8C2×C22⋊D6111yescharacteristic
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—24no—
574C2×D4—24no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—42no—
581C2×D4—42no—
582C2×D4—41no—
583C2×D4—41no—
584C2×D4—44no—
585C2×D4—44no—
586C2×D4—612no—
587C2×D4—1221no—
588C2×D4—1221no—
589C2×D4—1221no—
590C2×D4—1221no—
591C2×D4—1221no—
592C2×D4—4882no—
593C2×D4—4882no—
594C2×D4—2444no—
595C2×D4C2×C4×D6112yes—
596C2×D4D4×D6111yescharacteristic
597C2×D4C2×C22⋊D6111yescharacteristic
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—41no—
602C22×C4—41no—
603C22×C4—1221no—
604C22×C4—1221no—
605C22×C4—2441no—
606C22×C4—2441no—
607C22×C4—2441no—
608C22×C4C23×D6111yescharacteristic
609SD16—1224no—
610SD16—1224no—
611D8—1224no—
612D8—1224no—
613M16—21no—
614M16—21no—
615M16—42no—
616M16—612no—
617M16—612no—
618M16—1221no—
619M16—1221no—
620M16—1221no—
621M16—1221no—
622M16—2442no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—42no—
627C2×C8—611no—
628C2×C8—611no—
629C2×C8—1221no—
630C2×C8—1221no—
631C2×C8—1221no—
632C2×C8—1221no—
633C2×C8—1221no—
634C2×C8—2442no—
635C2×C8C2×C22⋊D6111yescharacteristic
636C2×C8C2×C22⋊D6111yescharacteristic
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—41no—
640C4⋊C4—611no—
641C4⋊C4—611no—
642C4⋊C4—1221no—
643C4⋊C4—1221no—
644C4⋊C4—4882no—
645C4⋊C4—2441no—
646C4⋊C4C2×C22⋊D6111yescharacteristic
647C4⋊C4C2×C22⋊D6111yescharacteristic
648C22⋊C4—21no—
649C22⋊C4—41no—
650C22⋊C4—1221no—
651C22⋊C4—2441no—
652C22⋊C4—2441no—
653C22⋊C4—2441no—
654C42—21no—
655C42—41no—
656C42—612no—
657C42—1221no—
658C42—1221no—
659C42—2441no—
660C23—21no—
661C23—21no—
662C23—22no—
663C23—44no—
664C23—41no—
665C23—41no—
666C23—81no—
667C23—81no—
668C23—161no—
669C23—161no—
670C23—1222no—
671C23—4881no—
672C23—4881no—
673C23—2441no—
674C23—2441no—
675C23#1451982211yescharacteristic
676Q8—21no—
677Q8—21no—
678Q8#1451973712yes—
679Q8C4×C22⋊D6112yes—
680D4—22no—
681D4—22no—
682D4—22no—
683D4—22no—
684D4—22no—
685D4—22no—
686D4—21no—
687D4—21no—
688D4—44no—
689D4—44no—
690D4—41no—
691D4—41no—
692D4—1222no—
693D4—1222no—
694D4—4888no—
695D4—2441no—
696D4—2441no—
697D4#1451973712yes—
698D4C4×C22⋊D6112yes—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—44no—
708C2×C4—41no—
709C2×C4—81no—
710C2×C4—161no—
711C2×C4—1222no—
712C2×C4—1222no—
713C2×C4—1222no—
714C2×C4—1221no—
715C2×C4—1221no—
716C2×C4—9761no—
717C2×C4—9761no—
718C2×C4—9761no—
719C2×C4—4881no—
720C2×C4—2441no—
721C2×C4C22×C4×D6111yescharacteristic
722C2×C4C2×D4×D6111yescharacteristic
723C2×C4C22×C22⋊D6111yescharacteristic
724C2×C4C2×#1175822411yescharacteristic
725C2×C4C2×#1175822211yescharacteristic
726C2×C4#1451982211yescharacteristic
727C8—21no—
728C8—21no—
729C8—41no—
730C8—1222no—
731C8—1222no—
732C8—1221no—
733C8—1221no—
734C8—2441no—
735C22—21no—
736C22—21no—
737C22—22no—
738C22—22no—
739C22—41no—
740C22—41no—
741C22—41no—
742C22—41no—
743C22—42no—
744C22—82no—
745C22—81no—
746C22—81no—
747C22—161no—
748C22—164no—
749C22—9761no—
750C22—4882no—
751C22—4881no—
752C22—4881no—
753C22—2442no—
754C22#1684023511yescharacteristic
755C22D4×C22⋊D6111yescharacteristic
756C22#1684043811yescharacteristic
757C4—22no—
758C4—22no—
759C4—41no—
760C4—41no—
761C4—81no—
762C4—1224no—
763C4—4881no—
764C4—2441no—
765C4—2441no—
766C4C2×#1451973711yescharacteristic
767C4C2×C4×C22⋊D6111yescharacteristic
768C4#1684040211yescharacteristic
769C4#1684040611yescharacteristic
770C2—21no—
771C2—21no—
772C2—42no—
773C2—42no—
774C2—82no—
775C2—4882no—
776C2#2144879811yescharacteristic
777C2#2145761011yescharacteristic
778C2#2145761611yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#2897C2
socleC22×C61D42
prime radicalC2×#16839930C2
cosocleC22×C4×C61C24
hypercenter#2897D61
hypocenterC61#22897
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #2897

Complements

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

NH ≅ G/Ntype
2. #21454654C2semidirect
3. #21454647C2semidirect
4. #21454345C2semidirect
5. #21446623C2semidirect
6. #21446484C2semidirect
7. #21446478C2semidirect
8. #21446327C2semidirect
9. #21446325C2semidirect
10. #21446214C2semidirect
11. #21446045C2semidirect
12. #21446043C2semidirect
13. #21445659C2semidirect
14. #21445654C2semidirect
15. C61×#2897C2semidirect
21. #16840236C22semidirect
22. #16839930C4semidirect
31. #16839805C22semidirect
32. #16839802C22semidirect
41. C2×#14519699C22semidirect
44. C2×#14519697C22semidirect
46. C2×#14519693C22semidirect
47. #16839718C22semidirect
48. #16839717C22semidirect
49. C2×C8×Dic61C22semidirect
50. #16839631C22semidirect
51. #16839531C22semidirect
52. #16839530C22semidirect
53. #16839527C22semidirect
54. #16839526C22semidirect
55. #16839523C22semidirect
56. #16839521C22semidirect
72. #14519802C2×C4semidirect
73. #14519802C2×C4semidirect
87. #14519773C2×C4semidirect
106. #14519704C2×C4semidirect
107. #14519704C2×C4semidirect
109. #14519701D4semidirect
110. #14519701D4semidirect
118. #14519698D4semidirect
119. #14519698D4semidirect
122. #14519694C2×C4semidirect
132. H(5,𝔽2)×C61C2×C4semidirect
155. #103×C61D4semidirect
156. #103×C61D4semidirect
162. #102×C61D4semidirect
163. #102×C61D4semidirect
385. #2897D61semidirect
457. C61#22897semidirect
461. H(5,𝔽2)C4×D61semidirect
527. #103C22⋊D61semidirect
528. #103C22⋊D61semidirect
545. #102C22⋊D61semidirect
546. #102C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168399302
#214546542
#214546472
#214543452
#214466232
#214464842
#214464782
#214463272
#214463252
#214462142
#214460452
#214460432
#214456592
#214456542
C61×#28972
#2289761