Finite Group Databasebeta

← #29681075

Subgroups — #29681075

Order 15616.

1358 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840527C211yesmaximal, characteristic
2C2×#16839809C211yesmaximal, characteristic, complemented
3#21454380C211yesmaximal, characteristic, complemented
4C2×#104×D61C211yesmaximal, characteristic
5#21454334C211yesmaximal, characteristic
6#21446097C211yesmaximal, characteristic, complemented
7#21446096C211yesmaximal, characteristic, complemented
8#21446095C211yesmaximal, characteristic, complemented
9#21446094C211yesmaximal, characteristic, complemented
10#21446093C211yesmaximal, characteristic, complemented
11#21446092C211yesmaximal, characteristic, complemented
12#21446091C211yesmaximal, characteristic, complemented
13#339×D61C211yesmaximal, characteristic, complemented
14#21445511C211yesmaximal, characteristic, complemented
15C61×#1866C211yesmaximal, characteristic, complemented
16C2×#41×D61C2211yescharacteristic
17#16840527—24no—
18#16840527—24no—
19C2×#14519785—21no—
20C2×#14519785C2211yescharacteristic
21C2×#14519784C2211yescharacteristic
22C2×#14519783—21no—
23C2×#14519783C2211yescharacteristic
24C22×#11758189—21no—
25C22×#11758189C2211yescharacteristic
26C22×#11758189C2211yescharacteristic
27C2×M16×D61—21no—
28C2×M16×D61C2211yescharacteristic
29C2×M16×D61C2211yescharacteristic
30#117×D61C2211yescharacteristic
31C2×C42×D61C2211yescharacteristic
32#16839809—24no—
33C2×#14519713C2211yescharacteristic, complemented
34C2×#14519712C2211yescharacteristic, complemented
35C2×#14519712C2211yescharacteristic, complemented
36#16839790C2211yescharacteristic, complemented
37#16839789C2211yescharacteristic, complemented
38#16839788C2211yescharacteristic, complemented
39#16839787—21no—
40#16839787—21no—
41#16839784—21no—
42#16839784—21no—
43C2×#14519705C2211yescharacteristic
44C2×#14519704C2211yescharacteristic
45C2×#14519703C2211yescharacteristic
46#104×D61—24no—
47#16839769C411yescharacteristic, complemented
48#16839769C411yescharacteristic, complemented
49#16839765C411yescharacteristic, complemented
50#16839765C411yescharacteristic, complemented
51#16839762C411yescharacteristic, complemented
52#16839762C411yescharacteristic, complemented
53#16839760C411yescharacteristic, complemented
54#16839760C411yescharacteristic, complemented
55#16839759C2211yescharacteristic
56#16839758C2211yescharacteristic
57#16839756C2211yescharacteristic
58#16839523C2211yescharacteristic, complemented
59#16839522C2211yescharacteristic, complemented
60#16839521C2211yescharacteristic, complemented
61#16839517C2211yescharacteristic, complemented
62#16839516C2211yescharacteristic, complemented
63#16839516C2211yescharacteristic, complemented
64C2×#131×C61C2211yescharacteristic
65C2×#108×C61C2211yescharacteristic, complemented
66C61×#424C2211yescharacteristic, complemented
67C2×#104×C61C2211yescharacteristic
68C61×#416C2211yescharacteristic
69C61×#339C2211yescharacteristic, complemented
70C61×#336C2211yescharacteristic, complemented
71C2×#11758226C2×C411yescharacteristic
72C2×#11758222—21no—
73C2×#11758222C2311yescharacteristic
74C2×#11758224—21no—
75C2×#11758224C2×C411yescharacteristic
76#41×D61—22no—
77#41×D61—22no—
78#41×D61D414yes—
79#41×D61Q814yes—
80C2×Q8×D61C2×C411yescharacteristic
81C2×D4×D61—21no—
82C2×D4×D61C2×C411yescharacteristic
83C22×C4×D61—21no—
84C22×C4×D61—21no—
85C22×C4×D61C2311yescharacteristic
86#14519785—28no—
87#14519785—22no—
88#14519785—22no—
89#14519784—22no—
90#14519784—22no—
91#14519783—28no—
92#14519783—22no—
93#14519783—22no—
94C2×#11758194—21no—
95C2×#11758194C2311yescharacteristic
96C2×#11758194C2311yescharacteristic
97C2×#11758189—28no—
98C2×#11758189—21no—
99C2×#11758189—22no—
100C2×#11758189—22no—
101C2×#11758189—22no—
102C2×#11758189—22no—
103C2×#11758189—21no—
104C2×#11758189—21no—
105C2×#11758189—21no—
106C2×#11758189C2×C411yescharacteristic
107C2×#11758189C2×C411yescharacteristic
108C2×#11758189C2×C411yescharacteristic
109C2×#11758189C2×C411yescharacteristic
110C2×#11758189D411yescharacteristic
111C2×#11758189D411yescharacteristic
112C2×#11758189D411yescharacteristic
113C2×#11758189D411yescharacteristic
114M16×D61—28no—
115M16×D61—22no—
116M16×D61—22no—
117M16×D61—22no—
118M16×D61D414yes—
119C22×#92418—21no—
120C22×#92418C2311yescharacteristic
121C22×#92418C2311yescharacteristic
122C2×C8×D61—21no—
123C2×C8×D61—21no—
124C2×C8×D61—21no—
125C2×C8×D61—21no—
126#14519736C2311yescharacteristic
127#14519735C2×C411yescharacteristic
128#14519735C2×C411yescharacteristic
129#14519734—21no—
130#14519733—21no—
131C4⋊C4×D61C2×C411yescharacteristic
132C4⋊C4×D61C2×C411yescharacteristic
133C22⋊C4×D61—21no—
134C2×C4×Dic61—21no—
135C2×C4×Dic61C2311yescharacteristic
136C42×D61—21no—
137C42×D61—22no—
138C42×D61—22no—
139#14519713—22no—
140#14519712—22no—
141#14519712—22no—
142C4⋊#92418—21no—
143C4⋊#92418—21no—
144#14519706—21no—
145#14519706—21no—
146#14519706—21no—
147#14519706—21no—
148#14519705—22no—
149#14519704—22no—
150#14519703—22no—
151#14519702C2×C411yescharacteristic, complemented
152#14519702C2×C411yescharacteristic, complemented
153#14519701C2×C411yescharacteristic, complemented
154#14519701C2×C411yescharacteristic, complemented
155#14519700C2×C411yescharacteristic, complemented
156#14519700C2×C411yescharacteristic, complemented
157#14519699C2×C411yescharacteristic, complemented
158#14519699C2×C411yescharacteristic, complemented
159#14519698C2×C411yescharacteristic, complemented
160#14519698C2×C411yescharacteristic, complemented
161#14519697C2×C411yescharacteristic, complemented
162#14519697C2×C411yescharacteristic, complemented
163C2×#41×C61C2311yescharacteristic
164#131×C61—22no—
165#131×C61—22no—
166C2×M16×C61—21no—
167C2×M16×C61C2311yescharacteristic
168C2×M16×C61C2311yescharacteristic
169C22×C8×C61—21no—
170C22×C8×C61C2311yescharacteristic
171C22×C8×C61C2311yescharacteristic
172#117×C61C2311yescharacteristic
173C2×C42×C61C2311yescharacteristic
174#108×C61—22no—
175C4⋊C8×C61—21no—
176C4⋊C8×C61—21no—
177#104×C61—22no—
178#103×C61C2×C411yescharacteristic, complemented
179#103×C61C2×C411yescharacteristic, complemented
180#102×C61C2×C411yescharacteristic, complemented
181#102×C61C2×C411yescharacteristic, complemented
182C23×D61—21no—
183C23×D61#4111yescharacteristic
184#41×C61—21no—
185#41×C61—21no—
186#41×C61C2×D412yes—
187#41×C61C2×Q812yes—
188C2×Q8×C61C22×C411yescharacteristic
189C2×D4×C61—21no—
190C2×D4×C61C22×C411yescharacteristic
191C22×C4×C61—21no—
192C22×C4×C61—21no—
193C22×C4×C61C2411yescharacteristic
194C2×C22⋊D61—21no—
195C2×C22⋊D61—21no—
196C2×C22⋊D61—21no—
197C22×Dic61—21no—
198C22×Dic61—21no—
199C22×Dic61#4111yescharacteristic
200#11758226—22no—
201#11758226C4⋊C414yes—
202Q8×D61—22no—
203Q8×D61C4⋊C414yes—
204#11758224—24no—
205#11758224—24no—
206#11758224—22no—
207#11758224C4⋊C414yes—
208D4×D61—24no—
209D4×D61—24no—
210D4×D61—22no—
211D4×D61C4⋊C414yes—
212#11758222—21no—
213#11758222—21no—
214#11758222—24no—
215#11758222—24no—
216#11758222C2×D412yes—
217#11758222C2×Q812yes—
218C2×D244—21no—
219C2×D244C22×C411yescharacteristic
220C2×C4×D61—21no—
221C2×C4×D61—21no—
222C2×C4×D61—21no—
223C2×C4×D61—24no—
224C2×C4×D61—24no—
225C2×C4×D61—21no—
226C2×C4×D61—21no—
227C2×C4×D61—42no—
228C2×C4×D61—42no—
229C2×C4×D61—42no—
230C2×C4×D61C22×C411yescharacteristic
231C2×C4×D61C22×C411yescharacteristic
232C2×C4×D61C2×D412yes—
233C2×C4×D61C2×D412yes—
234C2×C4×D61C2×D411yescharacteristic
235C2×C4×D61C2×D411yescharacteristic
236C2×C4×D61C2×Q812yes—
237C2×C4×D61#4112yes—
238C2×Dic122—21no—
239C2×Dic122C22×C411yescharacteristic
240M16×C61—24no—
241M16×C61—21no—
242M16×C61—21no—
243M16×C61—21no—
244M16×C61C2×D412yes—
245C2×C8×C61—24no—
246C2×C8×C61—21no—
247C2×C8×C61—21no—
248C2×C8×C61—21no—
249C2×C8×C61—21no—
250C2×C8×C61—21no—
251C2×C8×C61—21no—
252C2×C8×C61C22×C411yescharacteristic
253C2×C8×C61C22×C411yescharacteristic
254C2×C8×C61C2×D411yescharacteristic
255C2×C8×C61C2×D411yescharacteristic
256C4⋊C4×C61C22×C411yescharacteristic
257C4⋊C4×C61C22×C411yescharacteristic
258C22⋊C4×C61—21no—
259C42×C61—21no—
260C42×C61—21no—
261C42×C61—21no—
262C22⋊Dic61—21no—
263#11758198—21no—
264#11758198—21no—
265C4⋊Dic61C22×C411yescharacteristic
266C4⋊Dic61C22×C411yescharacteristic
267#11758196—21no—
268#11758196—21no—
269C4×Dic61—21no—
270C4×Dic61—21no—
271C4×Dic61—21no—
272C4×Dic61—21no—
273C4×Dic61—21no—
274C4×Dic61—42no—
275#11758194—24no—
276#11758194—21no—
277#11758194—21no—
278#11758194—21no—
279#11758194C2×D412yes—
280C2×#92418—24no—
281C2×#92418—21no—
282C2×#92418—21no—
283C2×#92418—21no—
284C2×#92418—21no—
285C2×#92418—21no—
286C2×#92418—21no—
287C2×#92418C22×C411yescharacteristic
288C2×#92418C22×C411yescharacteristic
289C2×#92418C2×D411yescharacteristic
290C2×#92418C2×D411yescharacteristic
291#11758189—24no—
292#11758189—24no—
293#11758189—22no—
294#11758189—22no—
295#11758189—22no—
296#11758189—22no—
297#11758189—22no—
298#11758189—24no—
299#11758189—22no—
300#11758189—22no—
301#11758189—22no—
302#11758189—42no—
303C8×D61—24no—
304C8×D61—24no—
305C8×D61—24no—
306C8×D61—42no—
307C23×C61—21no—
308C23×C61C2×#4111yescharacteristic
309C22×D61—21no—
310C22×D61—24no—
311C22×D61—41no—
312C22×D61—41no—
313C22×D61—81no—
314C22×D61—81no—
315C22×D61C4×D411yescharacteristic
316C22×D61C4×D411yescharacteristic
317C22×D61C22⋊Q812yes—
318C22×D61#12312yes—
319Q8×C61—21no—
320Q8×C61C2×C4⋊C412yes—
321D4×C61—22no—
322D4×C61—22no—
323D4×C61—21no—
324D4×C61C2×C4⋊C412yes—
325C2×C4×C61—21no—
326C2×C4×C61—22no—
327C2×C4×C61—22no—
328C2×C4×C61—22no—
329C2×C4×C61—21no—
330C2×C4×C61—21no—
331C2×C4×C61—41no—
332C2×C4×C61—41no—
333C2×C4×C61C23×C411yescharacteristic
334C2×C4×C61C22×D411yescharacteristic
335C2×C4×C61C22×D411yescharacteristic
336C2×C4×C61C22×D411yescharacteristic
337C2×C4×C61C22×Q811yescharacteristic
338C2×C4×C61C2×#4111yescharacteristic
339C22⋊D61—22no—
340C22⋊D61—22no—
341C22⋊D61—24no—
342C22⋊D61—24no—
343C2×Dic61—21no—
344C2×Dic61—24no—
345C2×Dic61—22no—
346C2×Dic61—21no—
347C2×Dic61—21no—
348C2×Dic61—41no—
349C2×Dic61—41no—
350C2×Dic61C4×D411yescharacteristic
351C2×Dic61C4×D411yescharacteristic
352C2×Dic61C22⋊Q812yes—
353C2×Dic61#12312yes—
354D244—24no—
355D244—21no—
356D244C2×C4⋊C412yes—
357C4×D61—24no—
358C4×D61—22no—
359C4×D61—22no—
360C4×D61—24no—
361C4×D61—48no—
362C4×D61—81no—
363C4×D61—81no—
364C4×D61C2×C4⋊C412yes—
365C4×D61C2×C4⋊C412yes—
366C4×D61C4×D412yes—
367C4×D61C4×D412yes—
368C4×D61#12012yes—
369C4×D61#12012yes—
370C4×D61C22⋊Q812yes—
371C4×D61C22⋊Q812yes—
372Dic122—21no—
373Dic122—24no—
374Dic122C2×C4⋊C412yes—
375C8×C61—21no—
376C8×C61—21no—
377C8×C61—22no—
378C8×C61—21no—
379C8×C61—21no—
380C8×C61—41no—
381#92418—21no—
382#92418—21no—
383#92418—22no—
384#92418—21no—
385#92418—21no—
386#92418—41no—
387#20885—611nomaximal, Sylow
388C22×C61—21no—
389C22×C61—21no—
390C22×C61—22no—
391C22×C61—41no—
392C22×C61—41no—
393C22×C61C2×C4×D411yescharacteristic
394C22×C61C2×C22⋊Q811yescharacteristic
395C22×C61C2×#12311yescharacteristic
396C2×D61—21no—
397C2×D61—21no—
398C2×D61—21no—
399C2×D61—21no—
400C2×D61—22no—
401C2×D61—42no—
402C2×D61—42no—
403C2×D61—41no—
404C2×D61—41no—
405C2×D61—84no—
406C2×D61#38512yes—
407C2×D61#38512yes—
408C4×C61—22no—
409C4×C61—42no—
410C4×C61—41no—
411C4×C61—41no—
412C4×C61C22×C4⋊C411yescharacteristic
413C4×C61C2×C4×D411yescharacteristic
414C4×C61C2×#12011yescharacteristic
415C4×C61C2×C22⋊Q811yescharacteristic
416Dic61—22no—
417Dic61—42no—
418Dic61—41no—
419Dic61—41no—
420Dic61#38512yes—
421Dic61#38512yes—
422C2×#568—611no—
423C2×#430—611no—
424#2905—611no—
425C22×#104—611no—
426#2896—611no—
427#1866—611no—
428#1866—611no—
429#1866—611no—
430#1866—611no—
431#1866—611no—
432#1866—611no—
433#1866—611no—
434#1866D6111yescharacteristic, complemented
435C2×#339—611no—
436#1728—611no—
437C2×C61—21no—
438C2×C61—21no—
439C2×C61—42no—
440C2×C61C2×#38511yescharacteristic
441C2×C61#295611yescharacteristic
442C2×C61#295611yescharacteristic
443D61—22no—
444D61—22no—
445D61—42no—
446C22×#41—611no—
447#568—1224no—
448#568—1224no—
449C2×#131—611no—
450C2×#131—611no—
451C2×#131—611no—
452C2×#131—1221no—
453C2×#131—1221no—
454C2×#131C2×D6111yescharacteristic
455C22×M16—611no—
456C22×M16—611no—
457C22×M16—611no—
458C22×M16—611no—
459C22×M16—1221no—
460C22×M16—1221no—
461C2×#117—611no—
462C22×C42—611no—
463#430—1224no—
464C2×#108—611no—
465C2×#108—611no—
466C2×#108—611no—
467C2×#108C2×D6111yescharacteristic, complemented
468#424—611no—
469#424—611no—
470#424—611no—
471#424—1221no—
472#424—1221no—
473#424C2×D6111yescharacteristic, complemented
474#423—1221no—
475#423—1221no—
476C2×#104—611no—
477C2×#104—611no—
478C2×#104—611no—
479C2×#104—1224no—
480C2×#104C2×D6111yescharacteristic
481#419—611no—
482#419—611no—
483#418—611no—
484#418—611no—
485#417—611no—
486#417—611no—
487#417—611no—
488#417—611no—
489#416—611no—
490#416—611no—
491#416—611no—
492#416C2×D6111yescharacteristic
493#339—611no—
494#339—611no—
495#339—611no—
496#339C2×D6111yescharacteristic, complemented
497#336—611no—
498#336—611no—
499#336—611no—
500#336C2×D6111yescharacteristic, complemented
501C61#2088511yescharacteristic, complemented, Sylow
502C2×#41—614no—
503C2×#41—614no—
504C2×#41—611no—
505C2×#41—611no—
506C2×#41—611no—
507C2×#41—1221no—
508C2×#41—1221no—
509C2×#41—1222no—
510C2×#41—1222no—
511C2×#41C22×D6111yescharacteristic
512C22×Q8—611no—
513C22×D4—611no—
514C22×D4—1221no—
515C23×C4—611no—
516C23×C4—1221no—
517C23×C4—1221no—
518#131—22no—
519#131—22no—
520#131—1222no—
521#131—1222no—
522#131—1228no—
523#131—1222no—
524#131—1228no—
525#131—1222no—
526#131—1222no—
527#131—1222no—
528C2×M16—21no—
529C2×M16—611no—
530C2×M16—611no—
531C2×M16—611no—
532C2×M16—611no—
533C2×M16—611no—
534C2×M16—611no—
535C2×M16—611no—
536C2×M16—611no—
537C2×M16—611no—
538C2×M16—614no—
539C2×M16—611no—
540C2×M16—1221no—
541C2×M16—1221no—
542C2×M16—1222no—
543C2×M16—1222no—
544C2×M16—1222no—
545C2×M16—1222no—
546C2×M16—1228no—
547C2×M16—1221no—
548C2×M16—1221no—
549C2×M16—1222no—
550C2×M16—1228no—
551C2×M16—1221no—
552C2×M16—1222no—
553C2×M16—1222no—
554C2×M16C22×D6111yescharacteristic
555C2×M16C22×D6111yescharacteristic
556C22×C8—21no—
557C22×C8—611no—
558C22×C8—611no—
559C22×C8—1221no—
560C22×C8—1221no—
561C22×C8—1221no—
562C22×C8—1221no—
563C22×C8—1221no—
564C22×C8C22×D6111yescharacteristic
565C22×C8C22×D6111yescharacteristic
566#117—611no—
567#117—611no—
568#117—611no—
569#117—1221no—
570#117—1221no—
571#117C22×D6111yescharacteristic
572C2×C4⋊C4—611no—
573C2×C4⋊C4—611no—
574C2×C22⋊C4—1221no—
575C2×C42—611no—
576C2×C42—1221no—
577C2×C42—1222no—
578C2×C42—1222no—
579C2×C42—1221no—
580C2×C42C22×D6111yescharacteristic
581#108—22no—
582#108—1222no—
583#108—1222no—
584#108—1222no—
585C4⋊C8—21no—
586C4⋊C8—21no—
587C4⋊C8—1221no—
588C4⋊C8—1221no—
589C4⋊C8—1221no—
590C4⋊C8—1221no—
591C4⋊C8—1221no—
592C4⋊C8—1221no—
593#104—22no—
594#104—1222no—
595#104—1222no—
596#104—1222no—
597#103—611no—
598#103—611no—
599#103—611no—
600#103—611no—
601#103—611no—
602#103—611no—
603#103C4×D6111yescharacteristic, complemented
604#103C4×D6111yescharacteristic, complemented
605#102—611no—
606#102—611no—
607#102—611no—
608#102—611no—
609#102—611no—
610#102—611no—
611#102C4×D6111yescharacteristic, complemented
612#102C4×D6111yescharacteristic, complemented
613C24—611no—
614C24—1221no—
615#41—21no—
616#41—21no—
617#41—614no—
618#41—614no—
619#41—612no—
620#41—612no—
621#41—1224no—
622#41—1224no—
623#41—1224no—
624#41—1224no—
625#41—1222no—
626#41—1222no—
627#41—1221no—
628#41—1221no—
629#41D4×D6112yes—
630#41Q8×D6112yes—
631C2×Q8—614no—
632C2×Q8—611no—
633C2×Q8—1221no—
634C2×Q8—1222no—
635C2×Q8C2×C4×D6111yescharacteristic
636C2×D4—21no—
637C2×D4—614no—
638C2×D4—611no—
639C2×D4—1221no—
640C2×D4—1222no—
641C2×D4—1221no—
642C2×D4—1224no—
643C2×D4—1224no—
644C2×D4—1221no—
645C2×D4—1221no—
646C2×D4C2×C4×D6111yescharacteristic
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—611no—
650C22×C4—611no—
651C22×C4—611no—
652C22×C4—612no—
653C22×C4—612no—
654C22×C4—611no—
655C22×C4—611no—
656C22×C4—612no—
657C22×C4—612no—
658C22×C4—1224no—
659C22×C4—1221no—
660C22×C4—1224no—
661C22×C4—1221no—
662C22×C4—1221no—
663C22×C4—1221no—
664C22×C4—1221no—
665C22×C4—1221no—
666C22×C4—1221no—
667C22×C4—2442no—
668C22×C4—2442no—
669C22×C4—2442no—
670C22×C4C23×D6111yescharacteristic
671M16—24no—
672M16—21no—
673M16—21no—
674M16—21no—
675M16—612no—
676M16—1222no—
677M16—1222no—
678M16—1222no—
679M16—1222no—
680M16—1222no—
681M16—1224no—
682M16—1222no—
683M16—1222no—
684M16—1222no—
685M16—1224no—
686M16—1224no—
687M16—1224no—
688M16—1221no—
689M16—1221no—
690M16—1221no—
691M16—2442no—
692M16D4×D6112yes—
693C2×C8—24no—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—21no—
700C2×C8—611no—
701C2×C8—611no—
702C2×C8—611no—
703C2×C8—611no—
704C2×C8—1224no—
705C2×C8—1224no—
706C2×C8—1224no—
707C2×C8—1224no—
708C2×C8—1221no—
709C2×C8—1221no—
710C2×C8—1221no—
711C2×C8—1221no—
712C2×C8—1221no—
713C2×C8—1221no—
714C2×C8—2442no—
715C2×C8C2×C4×D6111yescharacteristic
716C2×C8C2×C4×D6111yescharacteristic
717C2×C8D4×D6111yescharacteristic
718C2×C8D4×D6111yescharacteristic
719C4⋊C4—611no—
720C4⋊C4—611no—
721C4⋊C4—1221no—
722C4⋊C4—1221no—
723C4⋊C4C2×C4×D6111yescharacteristic
724C4⋊C4C2×C4×D6111yescharacteristic
725C22⋊C4—21no—
726C22⋊C4—1221no—
727C22⋊C4—1221no—
728C22⋊C4—1221no—
729C42—21no—
730C42—21no—
731C42—21no—
732C42—1221no—
733C42—1221no—
734C42—1221no—
735C42—1221no—
736C42—1221no—
737C42—2442no—
738C23—21no—
739C23—611no—
740C23—611no—
741C23—612no—
742C23—612no—
743C23—1224no—
744C23—1221no—
745C23—4881no—
746C23—4881no—
747C23—2441no—
748C23—2441no—
749C23#41×D6111yescharacteristic
750Q8—21no—
751Q8—612no—
752Q8—1224no—
753Q8—1221no—
754Q8C4⋊C4×D6112yes—
755D4—22no—
756D4—22no—
757D4—21no—
758D4—612no—
759D4—1224no—
760D4—1224no—
761D4—1224no—
762D4—1222no—
763D4—1222no—
764D4—1221no—
765D4C4⋊C4×D6112yes—
766C2×C4—21no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—611no—
775C2×C4—611no—
776C2×C4—612no—
777C2×C4—612no—
778C2×C4—612no—
779C2×C4—612no—
780C2×C4—612no—
781C2×C4—612no—
782C2×C4—612no—
783C2×C4—612no—
784C2×C4—612no—
785C2×C4—612no—
786C2×C4—1224no—
787C2×C4—1224no—
788C2×C4—1224no—
789C2×C4—1221no—
790C2×C4—1222no—
791C2×C4—1222no—
792C2×C4—1222no—
793C2×C4—1221no—
794C2×C4—1221no—
795C2×C4—4881no—
796C2×C4—4881no—
797C2×C4—2448no—
798C2×C4—2441no—
799C2×C4—2441no—
800C2×C4C22×C4×D6111yescharacteristic
801C2×C4C2×D4×D6111yescharacteristic
802C2×C4C2×D4×D6111yescharacteristic
803C2×C4C2×D4×D6111yescharacteristic
804C2×C4C2×Q8×D6111yescharacteristic
805C2×C4#41×D6111yescharacteristic
806C8—21no—
807C8—21no—
808C8—21no—
809C8—22no—
810C8—21no—
811C8—41no—
812C8—1221no—
813C8—1221no—
814C8—1221no—
815C8—1221no—
816C8—1222no—
817C8—2441no—
818C22—21no—
819C22—21no—
820C22—22no—
821C22—41no—
822C22—41no—
823C22—612no—
824C22—612no—
825C22—1221no—
826C22—1221no—
827C22—1221no—
828C22—1221no—
829C22—1222no—
830C22—4884no—
831C22—2442no—
832C22—2442no—
833C22—2441no—
834C22—2441no—
835C22C4×D4×D6111yescharacteristic
836C22C22⋊Q8×D6111yescharacteristic
837C22#123×D6111yescharacteristic
838C4—22no—
839C4—42no—
840C4—41no—
841C4—41no—
842C4—612no—
843C4—612no—
844C4—1222no—
845C4—2442no—
846C4—2441no—
847C4—2441no—
848C4C2×C4⋊C4×D6111yescharacteristic
849C4C4×D4×D6111yescharacteristic
850C4#120×D6111yescharacteristic
851C4C22⋊Q8×D6111yescharacteristic
852C2—21no—
853C2—21no—
854C2—42no—
855C2—1222no—
856C2—1222no—
857C2—2442no—
858C2#385×D6111yescharacteristic
859C2#2145472411yescharacteristic
860C2#2145472711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1866C2
socleC22×C61C2×C4×D4
prime radicalC2×#41×D61C22
cosocleC22×C4×C61C24
hypercenter#1866D61
hypocenterC61#20885
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1866

Complements

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

NH ≅ G/Ntype
2. C2×#16839809C2semidirect
3. #21454380C2semidirect
6. #21446097C2semidirect
7. #21446096C2semidirect
8. #21446095C2semidirect
9. #21446094C2semidirect
10. #21446093C2semidirect
11. #21446092C2semidirect
12. #21446091C2semidirect
13. #339×D61C2semidirect
14. #21445511C2semidirect
15. C61×#1866C2semidirect
33. C2×#14519713C22semidirect
34. C2×#14519712C22semidirect
35. C2×#14519712C22semidirect
36. #16839790C22semidirect
37. #16839789C22semidirect
38. #16839788C22semidirect
47. #16839769C4semidirect
48. #16839769C4semidirect
49. #16839765C4semidirect
50. #16839765C4semidirect
51. #16839762C4semidirect
52. #16839762C4semidirect
53. #16839760C4semidirect
54. #16839760C4semidirect
58. #16839523C22semidirect
59. #16839522C22semidirect
60. #16839521C22semidirect
61. #16839517C22semidirect
62. #16839516C22semidirect
63. #16839516C22semidirect
65. C2×#108×C61C22semidirect
66. C61×#424C22semidirect
69. C61×#339C22semidirect
70. C61×#336C22semidirect
151. #14519702C2×C4semidirect
152. #14519702C2×C4semidirect
153. #14519701C2×C4semidirect
154. #14519701C2×C4semidirect
155. #14519700C2×C4semidirect
156. #14519700C2×C4semidirect
157. #14519699C2×C4semidirect
158. #14519699C2×C4semidirect
159. #14519698C2×C4semidirect
160. #14519698C2×C4semidirect
161. #14519697C2×C4semidirect
162. #14519697C2×C4semidirect
178. #103×C61C2×C4semidirect
179. #103×C61C2×C4semidirect
180. #102×C61C2×C4semidirect
181. #102×C61C2×C4semidirect
434. #1866D61semidirect
467. C2×#108C2×D61semidirect
473. #424C2×D61semidirect
496. #339C2×D61semidirect
500. #336C2×D61semidirect
501. C61#20885semidirect
603. #103C4×D61semidirect
604. #103C4×D61semidirect
611. #102C4×D61semidirect
612. #102C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168405272
C2×#168398092
#214543802
C2×#104×D612
#214543342
#214460972
#214460962
#214460952
#214460942
#214460932
#214460922
#214460912
#339×D612
#214455112
C61×#18662
#2088561