Finite Group Databasebeta

← #30543586

Subgroups — #30543586

Order 15616.

4810 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×2−1+4×D61C211yesmaximal, characteristic
2C2×#16840527C211yesmaximal, characteristic, complemented
3#21459019C211yesmaximal, characteristic, complemented
4#21454353C211yesmaximal, characteristic, complemented
5#21454352C211yesmaximal, characteristic, complemented
6#21454351C213yesmaximal, complemented
7#21454350C213yesmaximal, complemented
8#21454349C211yesmaximal, characteristic, complemented
9#21454348C213yesmaximal, complemented
10#21454347C213yesmaximal, complemented
11#21454335C213yesmaximal, complemented
12#21454334C213yesmaximal, complemented
13C2×#16839769C213yesmaximal, complemented
14#419×D61C213yesmaximal, complemented
15C61×#2898C211yesmaximal, characteristic, complemented
16C2×#14519825—21no—
17C2×#14519825C2213yes—
18C2×#14519824—23no—
19C2×#14519824C2211yescharacteristic
20C2×#14519824C2213yes—
212−1+4×D61—28no—
222−1+4×D61C4116yescomplemented
23C2×#41×D61—23no—
24C2×#41×D61C2213yes—
25C2×#41×D61C2211yescharacteristic
26C22×Q8×D61—21no—
27C22×Q8×D61C2213yes—
28#16840527—28no—
29C2×#14519785C2213yescomplemented
30C2×#14519784C2211yescharacteristic, complemented
31C2×#14519783C2213yescomplemented
32C22×#11758189C2213yes—
33C2×M16×D61C2213yes—
34#16840245C2211yescharacteristic, complemented
35#16840243C2213yescomplemented
36#16840242C2213yescomplemented
37#16840238—21no—
38#16840234—23no—
39C4×#11758226—21no—
40C4×#11758224—23no—
41C2×#14519735C2213yes—
42#117×D61C2213yes—
43#16839772C2213yescomplemented
44#16839771C2213yescomplemented
45#16839770C2213yescomplemented
46#16839769C2213yes—
47#16839769C2216yes—
48#16839769C2213yes—
49#16839769C2216yescomplemented
50#16839769C2216yescomplemented
51#16839765C2211yescharacteristic
52#16839765C2213yes—
53#16839764C2213yescomplemented
54#16839763C2213yescomplemented
55#16839762C2213yescomplemented
56#16839762C2213yescomplemented
57#16839761C2213yescomplemented
58#16839760C2213yescomplemented
59#16839760C2213yescomplemented
60#16839759C2213yescomplemented
61#16839758C2213yescomplemented
62#16839757C2216yescomplemented
63#16839756C2213yescomplemented
64#16839755C2216yescomplemented
65C2×#14519702C2213yescomplemented
66C2×#14519701C2213yescomplemented
67C2×#14519700C2213yescomplemented
68#103×D61C2216yescomplemented
69#103×D61C2216yescomplemented
70C2×2−1+4×C61C2211yescharacteristic
71C2×#131×C61C2211yescharacteristic, complemented
72C61×#520C2211yescharacteristic, complemented
73C61×#419C2213yescomplemented
74C61×#417C2213yescomplemented
75C61×#416C2213yescomplemented
76C2×#103×C61C2213yescomplemented
77#14519825—216no—
78#14519825—212no—
79#14519825C2×C4124yescomplemented
80#14519824—24no—
81#14519824—248no—
82#14519824—212no—
83#14519824C2×C4124yescomplemented
84#14519824C2×C418yescomplemented
85C2×#11758226—23no—
86C2×#11758226D411yescharacteristic
87C2×#11758226C2313yes—
88C2×#11758222—26no—
89C2×#11758222—23no—
90C2×#11758222—23no—
91C2×#11758222C2313yes—
92C2×#11758222C2313yes—
93C2×#11758224—23no—
94C2×#11758224—26no—
95C2×#11758224—23no—
96C2×#11758224D413yes—
97C2×#11758224C2313yes—
98#41×D61—248no—
99#41×D61—212no—
100#41×D61C2×C418yes—
101#41×D61C2×C4124yescomplemented
102#41×D61D418yes—
103C22×Dic122—23no—
104C22×Dic122—23no—
105C22×Dic122C2313yes—
106C2×Q8×D61—21no—
107C2×Q8×D61—216no—
108C2×Q8×D61—23no—
109C2×Q8×D61—212no—
110C2×Q8×D61—23no—
111C2×Q8×D61—23no—
112C2×Q8×D61C2×C4124yescomplemented
113C2×Q8×D61D411yescharacteristic
114C2×Q8×D61C2316yes—
115C2×Q8×D61C2313yes—
116C2×D4×D61—23no—
117C2×D4×D61D413yes—
118C2×D4×D61C2311yescharacteristic
119C22×C4×D61—23no—
120C22×C4×D61—23no—
121C22×C4×D61C2313yes—
122#14519785—212no—
123#14519784—24no—
124#14519783—212no—
125C2×#11758194C2313yes—
126C2×#11758189—212no—
127C2×#11758189C2313yes—
128C2×#11758189C2311yescharacteristic
129C2×#11758189C2313yes—
130C2×#11758189C2313yes—
131M16×D61—212no—
132C22×#92418C2313yes—
133C2×C8×D61C2316yes—
134Q8×Dic61—21no—
135C4×Dic122—23no—
136#14519742—23no—
137C4×D244—23no—
138D4×Dic61—23no—
139#14519739—23no—
140C4×C22⋊D61—26no—
141#14519737—26no—
142#14519736C2313yes—
143#14519735—23no—
144#14519735—23no—
145#14519735C2311yescharacteristic
146#14519735C2313yes—
147#14519735C2316yes—
148#14519734—23no—
149#14519733—23no—
150C2×C4⋊Dic61C2313yes—
151C4⋊C4×D61C2313yes—
152C4⋊C4×D61C2313yes—
153C2×#11758198—23no—
154C22⋊C4×D61—23no—
155C2×C4×Dic61—23no—
156C42×D61—23no—
157#14519702C2313yes—
158#14519702C2316yes—
159#14519702C2313yes—
160#14519701C2313yes—
161#14519701C2316yes—
162#14519701C2313yes—
163#14519700C2313yes—
164#14519700C2316yes—
165#14519700C2313yes—
166#14519699C2313yes—
167#14519699C2311yescharacteristic
168#14519698C2313yes—
169#14519698C2311yescharacteristic
170#14519697C2311yescharacteristic
171#14519697C2313yes—
1722−1+4×C61—24no—
1732−1+4×C61C2×C418yescomplemented
174C2×#41×C61—23no—
175C2×#41×C61C2313yes—
176C2×#41×C61C2311yescharacteristic
177C22×Q8×C61—21no—
178C22×Q8×C61C2313yes—
179#131×C61—24no—
180C2×M16×C61C2313yes—
181C22×C8×C61C2313yes—
182C4×Q8×C61—21no—
183C4×D4×C61—23no—
184#117×C61C2313yes—
185C2×C4⋊C4×C61C2313yes—
186#103×C61C2313yes—
187#103×C61C2316yes—
188#103×C61C2313yes—
189#102×C61C2313yes—
190#102×C61C2311yescharacteristic
191C23×D61—21no—
192C23×D61C2×D413yes—
193#41×C61—224no—
194#41×C61—26no—
195#41×C61C22×C4112yes—
196#41×C61C22×C414yes—
197#41×C61C2×D414yes—
198C2×Q8×C61—28no—
199C2×Q8×C61—23no—
200C2×Q8×C61—26no—
201C2×Q8×C61C22×C4112yes—
202C2×Q8×C61C2×D411yescharacteristic
203C2×Q8×C61C2413yes—
204C2×D4×C61—23no—
205C2×D4×C61C2×D413yes—
206C2×D4×C61C2411yescharacteristic
207C22×C4×C61—23no—
208C22×C4×C61—23no—
209C22×C4×C61—23no—
210C22×C4×C61C2413yes—
211C2×C22⋊D61—23no—
212C2×C22⋊D61—23no—
213C2×C22⋊D61—21no—
214C2×C22⋊D61C2×D416yes—
215C22×Dic61—23no—
216C22×Dic61—23no—
217C22×Dic61—23no—
218C22×Dic61C2×D413yes—
219#11758226—224no—
220#11758226—26no—
221#11758226C22⋊C418yes—
222#11758226C22×C4112yes—
223Q8×D61—28no—
224Q8×D61—224no—
225Q8×D61—224no—
226Q8×D61—26no—
227Q8×D61—212no—
228Q8×D61—224no—
229Q8×D61C22⋊C418yes—
230Q8×D61C22×C4112yes—
231Q8×D61C22×C4124yes—
232#11758224—224no—
233#11758224—248no—
234#11758224—224no—
235#11758224—26no—
236#11758224C22⋊C4124yes—
237#11758224C22×C4112yes—
238D4×D61—224no—
239D4×D61—22no—
240D4×D61C22⋊C4124yes—
241D4×D61C22×C414yes—
242#11758222—26no—
243#11758222—248no—
244#11758222—224no—
245#11758222—224no—
246#11758222C22×C4112yes—
247#11758222C22×C4112yes—
248#11758222C2×D4112yes—
249C2×D244—23no—
250C2×D244C2×D413yes—
251C2×D244C2411yescharacteristic
252C2×C4×D61—224no—
253C2×C4×D61—23no—
254C2×C4×D61—26no—
255C2×C4×D61—23no—
256C2×C4×D61—23no—
257C2×C4×D61—224no—
258C2×C4×D61—23no—
259C2×C4×D61—23no—
260C2×C4×D61C22×C4112yes—
261C2×C4×D61C2×D413yes—
262C2×C4×D61C2×D413yes—
263C2×C4×D61C2×D4112yes—
264C2×C4×D61C2411yescharacteristic
265C2×C4×D61C2413yes—
266C2×Dic122—23no—
267C2×Dic122—26no—
268C2×Dic122—224no—
269C2×Dic122—23no—
270C2×Dic122—26no—
271C2×Dic122—224no—
272C2×Dic122C22×C4112yes—
273C2×Dic122C2×D413yes—
274C2×Dic122C2413yes—
275M16×C61—26no—
276C2×C8×C61—26no—
277C2×C8×C61C2411yescharacteristic
278C2×C8×C61C2413yes—
279C4⋊C4×C61—23no—
280C4⋊C4×C61C2413yes—
281C4⋊C4×C61C2411yescharacteristic
282C22⋊C4×C61—23no—
283C42×C61—23no—
284C22⋊Dic61—23no—
285#11758198—21no—
286#11758198—23no—
287#11758198—26no—
288C4⋊Dic61—23no—
289C4⋊Dic61C2411yescharacteristic
290C4⋊Dic61C2413yes—
291#11758196—23no—
292#11758196—23no—
293C4×Dic61—23no—
294C4×Dic61—21no—
295C4×Dic61—23no—
296C4×Dic61—26no—
297#11758194—26no—
298C2×#92418—26no—
299C2×#92418C2413yes—
300C2×#92418C2411yescharacteristic
301#11758189—26no—
302#11758189—22no—
303#11758189—26no—
304#11758189—26no—
305C8×D61—212no—
306C23×C61—21no—
307C23×C61C22×D413yes—
308C22×D61—21no—
309C22×D61—24no—
310C22×D61—43no—
311C22×D61—43no—
312C22×D61—42no—
313C22×D61—42no—
314C22×D61C2×C22⋊C4112yes—
315C22×D61C22×D411yescharacteristic
316C22×D61C22×D413yes—
317Q8×C61—212no—
318Q8×C61—23no—
319Q8×C61C2×C22⋊C414yes—
320Q8×C61C23×C416yes—
321D4×C61—212no—
322D4×C61—21no—
323D4×C61C2×C22⋊C4112yes—
324D4×C61C23×C412yes—
325C2×C4×C61—212no—
326C2×C4×C61—23no—
327C2×C4×C61—212no—
328C2×C4×C61—23no—
329C2×C4×C61—21no—
330C2×C4×C61—83no—
331C2×C4×C61C23×C416yes—
332C2×C4×C61C22×D413yes—
333C2×C4×C61C22×D416yes—
334C2×C4×C61C2511yescharacteristic
335C22⋊D61—212no—
336C22⋊D61—212no—
337C22⋊D61—24no—
338C22⋊D61C2×C22⋊C4124yes—
339C2×Dic61—212no—
340C2×Dic61—23no—
341C2×Dic61—212no—
342C2×Dic61—21no—
343C2×Dic61—23no—
344C2×Dic61—83no—
345C2×Dic61C2×C22⋊C4112yes—
346C2×Dic61C22×D411yescharacteristic
347C2×Dic61C22×D413yes—
348D244—212no—
349D244—21no—
350D244C2×C22⋊C4112yes—
351D244C23×C412yes—
352C4×D61—212no—
353C4×D61—224no—
354C4×D61—212no—
355C4×D61—212no—
356C4×D61—83no—
357C4×D61—83no—
358C4×D61C2×C22⋊C4112yes—
359C4×D61C2×C22⋊C4112yes—
360C4×D61C23×C412yes—
361C4×D61C23×C416yes—
362C4×D61C22×D416yes—
363C4×D61C22×D412yes—
364Dic122—212no—
365Dic122—23no—
366Dic122—212no—
367Dic122—224no—
368Dic122C2×C22⋊C4112yes—
369Dic122C23×C416yes—
370C8×C61—23no—
371C8×C61—21no—
372#92418—23no—
373#92418—21no—
374#60088—611nomaximal, Sylow
375C22×C61—23no—
376C22×C61—23no—
377C22×C61—22no—
378C22×C61—41no—
379C22×C61—41no—
380C22×C61C22×C22⋊C416yes—
381C22×C61C23×D411yescharacteristic
382C2×D61—23no—
383C2×D61—23no—
384C2×D61—21no—
385C2×D61—21no—
386C2×D61—22no—
387C2×D61—412no—
388C2×D61—48no—
389C2×D61—41no—
390C2×D61—41no—
391C2×D61C22×C22⋊C412yes—
392C2×D61C22×C22⋊C416yes—
393C4×C61—26no—
394C4×C61—41no—
395C4×C61—43no—
396C4×C61C22×C22⋊C416yes—
397C4×C61C24×C411yescharacteristic
398C4×C61C23×D411yescharacteristic
399Dic61—26no—
400Dic61—41no—
401Dic61—43no—
402Dic61C22×C22⋊C412yes—
403Dic61C22×C22⋊C416yes—
404C22×2−1+4—611no—
405C2×#568—611no—
406#3428—611no—
407#2898—613no—
408#2898—613no—
409#2898—613no—
410#2898—613no—
411#2898—611no—
412#2898—611no—
413#2898—611no—
414#2898D6111yescharacteristic, complemented
415#2896—613no—
416#2896—613no—
417C2×#419—613no—
418C2×#419—613no—
419C2×C61—26no—
420C2×C61—42no—
421C2×C61C23×C22⋊C411yescharacteristic
422C2×C61#358611yescharacteristic
423C2×C61#358611yescharacteristic
424D61—22no—
425D61—26no—
426D61—42no—
427C2×2−1+4—6116no—
428C2×2−1+4—613no—
429C2×2−1+4—611no—
430C2×2−1+4—613no—
431C2×2−1+4—1221no—
432C2×2−1+4—1223no—
433C2×2−1+4—1228no—
434C2×2−1+4C2×D6111yescharacteristic
435C22×#41—611no—
436C22×#41—613no—
437C22×#41—1223no—
438C23×Q8—613no—
439C23×Q8—1221no—
440#568—1228no—
441C2×#131—611no—
442C2×#131—613no—
443C2×#131—613no—
444C2×#131C2×D6111yescharacteristic, complemented
445C22×M16—613no—
446C22×M16—613no—
447#520—611no—
448#520—613no—
449#520—613no—
450#520C2×D6111yescharacteristic, complemented
451#519—1221no—
452#518—1223no—
453C4×#41—1223no—
454C4×#41—1221no—
455C2×#117—613no—
456C2×#117—613no—
457#419—613no—
458#419—613no—
459#419—613no—
460#419—613no—
461#419—616no—
462#419—613no—
463#419—616no—
464#419—616no—
465#419C2×D6113yescomplemented
466#418—613no—
467#418—611no—
468#417—613no—
469#417—613no—
470#417—613no—
471#417—613no—
472#417—613no—
473#417—613no—
474#417—613no—
475#417C2×D6113yescomplemented
476#416—613no—
477#416—613no—
478#416—613no—
479#416—616no—
480#416—616no—
481#416C2×D6113yescomplemented
482C2×#103—613no—
483C2×#103—613no—
484C2×#103—613no—
485C2×#103—616no—
486C2×#103—616no—
487C2×#103C2×D6113yescomplemented
488C61#6008811yescharacteristic, complemented, Sylow
4892−1+4—24no—
4902−1+4—6124no—
4912−1+4—618no—
4922−1+4—6124no—
4932−1+4—12216no—
4942−1+4—12212no—
4952−1+4—12248no—
4962−1+4—12212no—
4972−1+4—1224no—
4982−1+4C4×D6118yescomplemented
499C2×#41—23no—
500C2×#41—618no—
501C2×#41—618no—
502C2×#41—611no—
503C2×#41—613no—
504C2×#41—613no—
505C2×#41—6124no—
506C2×#41—613no—
507C2×#41—613no—
508C2×#41—613no—
509C2×#41—1223no—
510C2×#41—1226no—
511C2×#41—1223no—
512C2×#41—1223no—
513C2×#41—12212no—
514C2×#41—1226no—
515C2×#41—1223no—
516C2×#41—12248no—
517C2×#41—1223no—
518C2×#41C22×D6113yes—
519C2×#41C22×D6111yescharacteristic
520C22×Q8—21no—
521C22×Q8—611no—
522C22×Q8—6124no—
523C22×Q8—613no—
524C22×Q8—616no—
525C22×Q8—613no—
526C22×Q8—1223no—
527C22×Q8—1223no—
528C22×Q8—1223no—
529C22×Q8—1223no—
530C22×Q8—12212no—
531C22×Q8—12216no—
532C22×Q8—1223no—
533C22×Q8—1221no—
534C22×Q8C22×D6113yes—
535C22×D4—613no—
536C22×D4—611no—
537C22×D4—1223no—
538C23×C4—613no—
539C23×C4—1223no—
540C23×C4—1223no—
541#131—24no—
542#131—12212no—
543#131—12212no—
544#131—1224no—
545C2×M16—613no—
546C2×M16—613no—
547C2×M16—611no—
548C2×M16—613no—
549C2×M16—613no—
550C2×M16—12212no—
551C2×M16—12212no—
552C2×M16C22×D6113yes—
553C22×C8—613no—
554C22×C8—616no—
555C22×C8C22×D6113yes—
556C4×Q8—21no—
557C4×Q8—1223no—
558C4×Q8—1223no—
559C4×Q8—1221no—
560C4×D4—23no—
561C4×D4—1223no—
562C4×D4—1226no—
563C4×D4—1223no—
564C4×D4—1226no—
565C4×D4—1223no—
566#117—613no—
567#117—611no—
568#117—613no—
569#117—616no—
570#117—1223no—
571#117—1223no—
572#117—1223no—
573#117—1223no—
574#117C22×D6113yes—
575C2×C4⋊C4—613no—
576C2×C4⋊C4—613no—
577C2×C4⋊C4—613no—
578C2×C4⋊C4C22×D6113yes—
579C2×C22⋊C4—1223no—
580C2×C22⋊C4—1223no—
581C2×C42—1223no—
582C2×C42—1223no—
583#103—613no—
584#103—616no—
585#103—613no—
586#103—613no—
587#103—616no—
588#103—613no—
589#103—613no—
590#103—616no—
591#103—613no—
592#103C22×D6113yes—
593#103C22×D6116yes—
594#103C22×D6113yes—
595#102—613no—
596#102—611no—
597#102—613no—
598#102—611no—
599#102—611no—
600#102—613no—
601#102C22×D6113yes—
602#102C22×D6111yescharacteristic
603C24—613no—
604C24—1221no—
605#41—224no—
606#41—26no—
607#41—618no—
608#41—6124no—
609#41—6112no—
610#41—6112no—
611#41—6112no—
612#41—6112no—
613#41—6112no—
614#41—12224no—
615#41—12248no—
616#41—12224no—
617#41—12224no—
618#41—1226no—
619#41—1226no—
620#41—12248no—
621#41—12224no—
622#41—12224no—
623#41—1226no—
624#41C2×C4×D61112yes—
625#41C2×C4×D6114yes—
626#41D4×D6114yes—
627C2×Q8—28no—
628C2×Q8—23no—
629C2×Q8—26no—
630C2×Q8—618no—
631C2×Q8—613no—
632C2×Q8—6112no—
633C2×Q8—6124no—
634C2×Q8—6112no—
635C2×Q8—613no—
636C2×Q8—1223no—
637C2×Q8—1226no—
638C2×Q8—12224no—
639C2×Q8—12224no—
640C2×Q8—12224no—
641C2×Q8—1226no—
642C2×Q8—12224no—
643C2×Q8—12212no—
644C2×Q8—12224no—
645C2×Q8—1228no—
646C2×Q8—1223no—
647C2×Q8—1226no—
648C2×Q8C2×C4×D61112yes—
649C2×Q8D4×D6111yescharacteristic
650C2×Q8C23×D6113yes—
651C2×D4—23no—
652C2×D4—616no—
653C2×D4—6124no—
654C2×D4—614no—
655C2×D4—613no—
656C2×D4—611no—
657C2×D4—1223no—
658C2×D4—1222no—
659C2×D4—1221no—
660C2×D4—12224no—
661C2×D4—1223no—
662C2×D4—1223no—
663C2×D4D4×D6113yes—
664C2×D4C23×D6111yescharacteristic
665C22×C4—23no—
666C22×C4—23no—
667C22×C4—23no—
668C22×C4—613no—
669C22×C4—6112no—
670C22×C4—613no—
671C22×C4—613no—
672C22×C4—6112no—
673C22×C4—613no—
674C22×C4—611no—
675C22×C4—1223no—
676C22×C4—12224no—
677C22×C4—1223no—
678C22×C4—12224no—
679C22×C4—1226no—
680C22×C4—1223no—
681C22×C4—1223no—
682C22×C4—1223no—
683C22×C4—1223no—
684C22×C4—1223no—
685C22×C4—1223no—
686C22×C4C23×D6113yes—
687M16—26no—
688M16—1222no—
689M16—1226no—
690M16—1226no—
691M16—1226no—
692M16—1226no—
693C2×C8—26no—
694C2×C8—613no—
695C2×C8—611no—
696C2×C8—12212no—
697C2×C8—1226no—
698C2×C8C23×D6113yes—
699C2×C8C23×D6111yescharacteristic
700C4⋊C4—23no—
701C4⋊C4—613no—
702C4⋊C4—611no—
703C4⋊C4—1223no—
704C4⋊C4—1223no—
705C4⋊C4—1223no—
706C4⋊C4C23×D6111yescharacteristic
707C4⋊C4C23×D6113yes—
708C22⋊C4—23no—
709C22⋊C4—1221no—
710C22⋊C4—1223no—
711C22⋊C4—1226no—
712C22⋊C4—1223no—
713C42—23no—
714C42—1221no—
715C42—1223no—
716C42—1226no—
717C42—1223no—
718C23—21no—
719C23—611no—
720C23—613no—
721C23—6112no—
722C23—1224no—
723C23—1221no—
724C23—2443no—
725C23—2443no—
726C23—2442no—
727C23—2442no—
728C23C2×D4×D6113yes—
729Q8—212no—
730Q8—23no—
731Q8—6112no—
732Q8—616no—
733Q8—12212no—
734Q8—12224no—
735Q8—12212no—
736Q8—1223no—
737Q8C22⋊C4×D6114yes—
738Q8C22×C4×D6116yes—
739D4—212no—
740D4—21no—
741D4—6124no—
742D4—6112no—
743D4—612no—
744D4—12212no—
745D4—1224no—
746D4—12212no—
747D4—12212no—
748D4—1221no—
749D4C22⋊C4×D61112yes—
750D4C22×C4×D6112yes—
751C2×C4—212no—
752C2×C4—23no—
753C2×C4—212no—
754C2×C4—21no—
755C2×C4—23no—
756C2×C4—83no—
757C2×C4—6112no—
758C2×C4—611no—
759C2×C4—613no—
760C2×C4—6112no—
761C2×C4—6112no—
762C2×C4—612no—
763C2×C4—616no—
764C2×C4—616no—
765C2×C4—612no—
766C2×C4—12212no—
767C2×C4—12212no—
768C2×C4—12224no—
769C2×C4—12212no—
770C2×C4—12212no—
771C2×C4—1223no—
772C2×C4—12212no—
773C2×C4—1221no—
774C2×C4—1223no—
775C2×C4—4883no—
776C2×C4—4883no—
777C2×C4—4883no—
778C2×C4C22×C4×D6116yes—
779C2×C4C2×D4×D6113yes—
780C2×C4C2×D4×D6116yes—
781C2×C4C24×D6111yescharacteristic
782C8—21no—
783C8—23no—
784C8—1223no—
785C8—1221no—
786C22—23no—
787C22—23no—
788C22—22no—
789C22—41no—
790C22—41no—
791C22—612no—
792C22—616no—
793C22—1223no—
794C22—1221no—
795C22—1223no—
796C22—1221no—
797C22—1222no—
798C22—24412no—
799C22—2448no—
800C22—2441no—
801C22—2441no—
802C22C2×C22⋊C4×D6116yes—
803C22C22×D4×D6111yescharacteristic
804C4—26no—
805C4—43no—
806C4—41no—
807C4—612no—
808C4—616no—
809C4—1226no—
810C4—2441no—
811C4—2443no—
812C4C2×C22⋊C4×D6116yes—
813C4C23×C4×D6111yescharacteristic
814C4C22×D4×D6111yescharacteristic
815C2—26no—
816C2—42no—
817C2—1222no—
818C2—1226no—
819C2—2442no—
820C2C22×C22⋊C4×D6111yescharacteristic
821C2#2146060111yescharacteristic
822C2#2146060411yescharacteristic
subgroupG/H
centerC22C22×D4×D61
commutatorC4×C61C24×C4
FrattiniC2×C4C24×D61
FittingC61×#2898C2
socleC22×C61C23×D4
prime radicalC2×2−1+4×D61C2
cosocleC2×C4×C61C25
hypercenter#2898D61
hypocenterC61#60088
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×#41 ◁ #2898

Complements

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

NH ≅ G/Ntype
2. C2×#16840527C2semidirect
3. #21459019C2semidirect
4. #21454353C2semidirect
5. #21454352C2semidirect
6. #21454351C2semidirect
7. #21454350C2semidirect
8. #21454349C2semidirect
9. #21454348C2semidirect
10. #21454347C2semidirect
11. #21454335C2semidirect
12. #21454334C2semidirect
13. C2×#16839769C2semidirect
14. #419×D61C2semidirect
15. C61×#2898C2semidirect
22. 2−1+4×D61C4semidirect
29. C2×#14519785C22semidirect
30. C2×#14519784C22semidirect
31. C2×#14519783C22semidirect
34. #16840245C22semidirect
35. #16840243C22semidirect
36. #16840242C22semidirect
43. #16839772C22semidirect
44. #16839771C22semidirect
45. #16839770C22semidirect
49. #16839769C22semidirect
50. #16839769C22semidirect
53. #16839764C22semidirect
54. #16839763C22semidirect
55. #16839762C22semidirect
56. #16839762C22semidirect
57. #16839761C22semidirect
58. #16839760C22semidirect
59. #16839760C22semidirect
60. #16839759C22semidirect
61. #16839758C22semidirect
62. #16839757C22semidirect
63. #16839756C22semidirect
64. #16839755C22semidirect
65. C2×#14519702C22semidirect
66. C2×#14519701C22semidirect
67. C2×#14519700C22semidirect
68. #103×D61C22semidirect
69. #103×D61C22semidirect
71. C2×#131×C61C22semidirect
72. C61×#520C22semidirect
73. C61×#419C22semidirect
74. C61×#417C22semidirect
75. C61×#416C22semidirect
76. C2×#103×C61C22semidirect
79. #14519825C2×C4semidirect
83. #14519824C2×C4semidirect
84. #14519824C2×C4semidirect
101. #41×D61C2×C4semidirect
112. C2×Q8×D61C2×C4semidirect
173. 2−1+4×C61C2×C4semidirect
414. #2898D61semidirect
444. C2×#131C2×D61semidirect
450. #520C2×D61semidirect
465. #419C2×D61semidirect
475. #417C2×D61semidirect
481. #416C2×D61semidirect
487. C2×#103C2×D61semidirect
488. C61#60088semidirect
498. 2−1+4C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×2−1+4×D612
C2×#168405272
#214590192
#214543532
#214543522
#214543512
#214543502
#214543492
#214543482
#214543472
#214543352
#214543342
C2×#168397692
#419×D612
C61×#28982
#6008861