Finite Group Databasebeta

← #30552336

Subgroups — #30552336

Order 15616.

1756 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×#16840317C211yesmaximal, characteristic
2#533×D61C211yesmaximal, characteristic
3#21457034C214yesmaximal, complemented
4#21457026C214yesmaximal, complemented
5#21456981C212yesmaximal, complemented
6#21456979C212yesmaximal, complemented
7#21456971C212yesmaximal, complemented
8#21456964C212yesmaximal, complemented
9#21456361C211yesmaximal, characteristic, complemented
10#21456201C211yesmaximal, characteristic, complemented
11#21456200C211yesmaximal, characteristic, complemented
12#21455769C214yesmaximal
13#21455623C214yesmaximal, complemented
14#21454450C211yesmaximal, characteristic
15C61×#3165C211yesmaximal, characteristic, complemented
16#16840319C2211yescharacteristic
17#16840318C2212yes—
18#16840317—21no—
19#16840317—21no—
20#16840317—21no—
21#16840317—21no—
22#16840317C2212yes—
23#16840317C2212yes—
24#16840317C2212yes—
25#16840317C2212yes—
26#16840317C2211yescharacteristic
27#16840317C2211yescharacteristic
28#16840316—21no—
29#16840316—21no—
30#16840315C2212yes—
31#16840314—21no—
32#16840314—21no—
33C2×#14519777C2211yescharacteristic
34C4⋊Q8×D61C2211yescharacteristic
35C4⋊Q8×D61C2211yescharacteristic
36C2×#14519768—21no—
37#125×D61C2212yes—
38C2×#14519757C2212yes—
39C2×#14519753—21no—
40C22⋊Q8×D61—21no—
41C22⋊Q8×D61—21no—
42C2×Q8×Dic61—21no—
43C2×#14519742C2212yes—
44C4×Q8×D61—21no—
45C4×Q8×D61—21no—
46C2×#14519735—21no—
47#117×D61C2212yes—
48C2×C42×D61C2211yescharacteristic
49#16840168C2214yescomplemented
50#16840165C2212yescomplemented
51#16840158C2212yescomplemented
52#16840132C2214yescomplemented
53#16840131C2214yescomplemented
54#16840114C2212yescomplemented
55#16840114C2212yescomplemented
56#16840113C2212yescomplemented
57#16840113C2212yescomplemented
58#16840106C2218yes—
59#16840105C2218yes—
60#16840099C2218yes—
61#16840094C2218yes—
62#16840072C2218yescomplemented
63#16840068C2218yescomplemented
64#16840056C2218yescomplemented
65#16840046C2218yescomplemented
66#16839817C2212yes—
67#16839817C2212yes—
68#16839813C2212yes—
69#16839813C2212yes—
70#16839802C2214yes—
71#16839785C2212yes—
72#16839772C2214yes—
73#16839770C2214yes—
74#16839725C2212yes—
75C4×#11758194C2211yescharacteristic
76C61×#533C2211yescharacteristic
77C2×C4⋊Q8×C61C2211yescharacteristic
78C61×#501C2214yescomplemented
79C61×#500C2212yescomplemented
80C61×#498C2212yescomplemented
81C61×#428C2214yes—
82C4×M16×C61C2211yescharacteristic
83C22×Dic122C2312yes—
84C2×Q8×D61—21no—
85C2×Q8×D61—21no—
86C22×C4×D61D411yescharacteristic
87C22×C4×D61D411yescharacteristic
88C22×C4×D61C2311yescharacteristic
89C2×#11758194C2312yes—
90#14519777—21no—
91#14519777—21no—
92#14519777C2312yes—
93#14519777C2312yes—
94#14519777C2311yescharacteristic
95#14519777C2311yescharacteristic
96#14519776—21no—
97#14519776—21no—
98#14519776C2312yes—
99#14519776C2312yes—
100#14519775—21no—
101#14519775—21no—
102#14519769C2312yes—
103#14519768—22no—
104#14519768—22no—
105#14519768—22no—
106#14519768—22no—
107#14519768C2312yes—
108#14519768C2312yes—
109#14519767—22no—
110#14519767—22no—
111#14519757—21no—
112#14519757—21no—
113#14519757—22no—
114#14519757—22no—
115#14519757C2314yes—
116#14519757C2314yes—
117#14519756—21no—
118#14519756—21no—
119#14519755—22no—
120#14519755—22no—
121#14519754—22no—
122#14519754—22no—
123#14519753—21no—
124#14519753—21no—
125#14519753—22no—
126#14519753—22no—
127#14519753—22no—
128#14519753—22no—
129Q8×Dic61—21no—
130Q8×Dic61—21no—
131Q8×Dic61—22no—
132Q8×Dic61—22no—
133Q8×Dic61—22no—
134Q8×Dic61—22no—
135C4×Dic122—21no—
136C4×Dic122—21no—
137C4×Dic122—22no—
138C4×Dic122—22no—
139#14519742—21no—
140#14519742—21no—
141#14519742—22no—
142#14519742—22no—
143#14519742—22no—
144#14519742—22no—
145#14519742C2314yes—
146#14519742C2314yes—
147#14519736C2312yes—
148#14519735—22no—
149#14519735—22no—
150#14519735—22no—
151#14519735—22no—
152#14519735C2312yes—
153#14519735C2312yes—
154#14519734—22no—
155#14519733—22no—
156C2×C4⋊Dic61—21no—
157C2×C4⋊Dic61—21no—
158C2×C4⋊Dic61—22no—
159C2×#11758196—22no—
160C4⋊C4×D61—22no—
161C4⋊C4×D61—22no—
162C4⋊C4×D61—21no—
163C4⋊C4×D61—21no—
164C4⋊C4×D61C2312yes—
165C4⋊C4×D61C2312yes—
166C2×#11758198—22no—
167C22⋊C4×D61—22no—
168C2×C4×Dic61—22no—
169C2×C4×Dic61D411yescharacteristic
170C2×C4×Dic61D411yescharacteristic
171C2×C4×Dic61C2311yescharacteristic
172C42×D61—22no—
173C42×D61D411yescharacteristic
174C42×D61D411yescharacteristic
175C42×D61D411yescharacteristic
176C42×D61D411yescharacteristic
177C42×D61C2311yescharacteristic
178C42×D61C2311yescharacteristic
179C42×D61C2311yescharacteristic
180C42×D61C2311yescharacteristic
181#14519710C2318yes—
182#14519708C2318yes—
183#14519706C2314yes—
184#14519706C2314yes—
185#14519702C2318yes—
186#14519702C2318yes—
187#14519700C2318yes—
188#14519700C2318yes—
189#14519689C2314yes—
190#14519689C2314yes—
191#14519688C2312yes—
192C4×#92418C2312yes—
193C22×Q8×C61—21no—
194C2×M16×C61C2312yes—
195C4⋊Q8×C61—21no—
196C4⋊Q8×C61—21no—
197C4⋊Q8×C61C2312yes—
198C4⋊Q8×C61C2312yes—
199C4⋊Q8×C61C2311yescharacteristic
200C4⋊Q8×C61C2311yescharacteristic
201#125×C61C2312yes—
202C22⋊Q8×C61—21no—
203C22⋊Q8×C61—21no—
204C4×Q8×C61—21no—
205C4×Q8×C61—21no—
206#117×C61C2312yes—
207C2×C4⋊C4×C61—21no—
208C2×C4⋊C4×C61C2312yes—
209C2×C42×C61C2311yescharacteristic
210#107×C61C2318yes—
211#106×C61C2318yes—
212#97×C61C2312yes—
213C4×C8×C61C2312yes—
214C23×D61C2×D411yescharacteristic
215C2×Q8×C61—21no—
216C2×Q8×C61—21no—
217C2×Q8×C61—22no—
218C2×Q8×C61—22no—
219C2×Q8×C61—44no—
220C22×C4×C61—22no—
221C22×C4×C61C2×D411yescharacteristic
222C22×C4×C61C2×D411yescharacteristic
223C22×C4×C61C2411yescharacteristic
224C22×Dic61—22no—
225C22×Dic61C2×D411yescharacteristic
226C22×Dic61C2×D411yescharacteristic
227C22×Dic61C2×D411yescharacteristic
228Q8×D61—44no—
229Q8×D61—44no—
230C2×C4×D61—24no—
231C2×C4×D61—24no—
232C2×C4×D61—22no—
233C2×C4×D61—22no—
234C2×C4×D61—42no—
235C2×C4×D61C2×D411yescharacteristic
236C2×C4×D61C2×D411yescharacteristic
237C2×C4×D61C2×D411yescharacteristic
238C2×C4×D61C2×D411yescharacteristic
239C2×C4×D61C2×D411yescharacteristic
240C2×C4×D61C2×D411yescharacteristic
241C2×C4×D61C2×D411yescharacteristic
242C2×C4×D61C2×D411yescharacteristic
243C2×C4×D61C2×D411yescharacteristic
244C2×C4×D61C2×D411yescharacteristic
245C2×C4×D61C2411yescharacteristic
246C2×C4×D61C2411yescharacteristic
247C2×Dic122—28no—
248C2×Dic122—21no—
249C2×Dic122—21no—
250C2×Dic122—22no—
251C2×Dic122—22no—
252C2×Dic122—22no—
253C2×Dic122C2414yes—
254M16×C61—24no—
255C2×C8×C61C2414yes—
256C4⋊C4×C61—22no—
257C4⋊C4×C61—22no—
258C4⋊C4×C61—22no—
259C4⋊C4×C61—22no—
260C4⋊C4×C61—22no—
261C4⋊C4×C61—21no—
262C4⋊C4×C61—21no—
263C4⋊C4×C61C2412yes—
264C4⋊C4×C61C2414yes—
265C4⋊C4×C61C2412yes—
266C22⋊C4×C61—22no—
267C42×C61—22no—
268C42×C61C2×D411yescharacteristic
269C42×C61C2×D411yescharacteristic
270C42×C61C2411yescharacteristic
271C42×C61C2411yescharacteristic
272C22⋊Dic61—22no—
273#11758198—22no—
274#11758198—22no—
275#11758198—24no—
276#11758198—24no—
277C4⋊Dic61—21no—
278C4⋊Dic61—21no—
279C4⋊Dic61—22no—
280C4⋊Dic61—22no—
281C4⋊Dic61—22no—
282C4⋊Dic61—22no—
283C4⋊Dic61—22no—
284C4⋊Dic61—22no—
285C4⋊Dic61—24no—
286C4⋊Dic61—24no—
287C4⋊Dic61C2412yes—
288C4⋊Dic61C2412yes—
289#11758196—22no—
290#11758196—22no—
291#11758196—22no—
292#11758196—22no—
293#11758196—22no—
294#11758196—22no—
295#11758196—22no—
296#11758196—22no—
297#11758196—24no—
298#11758196—24no—
299C4×Dic61—22no—
300C4×Dic61—22no—
301C4×Dic61—22no—
302C4×Dic61—24no—
303C4×Dic61—24no—
304C4×Dic61C2×D411yescharacteristic
305C4×Dic61C2×D411yescharacteristic
306C4×Dic61C2×D411yescharacteristic
307C4×Dic61C2×D411yescharacteristic
308C4×Dic61C2×D411yescharacteristic
309C4×Dic61C2×D411yescharacteristic
310C4×Dic61C2×D411yescharacteristic
311C4×Dic61C2×D411yescharacteristic
312C4×Dic61C2×D411yescharacteristic
313C4×Dic61C2×D411yescharacteristic
314C4×Dic61C2411yescharacteristic
315C4×Dic61C2411yescharacteristic
316#11758194—24no—
317C2×#92418C2414yes—
318C23×C61C22×D411yescharacteristic
319C22×D61—22no—
320C22×D61—22no—
321C22×D61—41no—
322C22×D61C22×D411yescharacteristic
323C22×D61C22×D411yescharacteristic
324Q8×C61—44no—
325Q8×C61—42no—
326Q8×C61—42no—
327Q8×C61—44no—
328C2×C4×C61—22no—
329C2×C4×C61—22no—
330C2×C4×C61—24no—
331C2×C4×C61—22no—
332C2×C4×C61—22no—
333C2×C4×C61—44no—
334C2×C4×C61C22×D411yescharacteristic
335C2×C4×C61C22×D411yescharacteristic
336C2×C4×C61C22×D411yescharacteristic
337C2×C4×C61C22×D411yescharacteristic
338C2×C4×C61C22×D411yescharacteristic
339C2×C4×C612−1+414yes—
340C2×C4×C61C2511yescharacteristic
341C2×Dic61—22no—
342C2×Dic61—22no—
343C2×Dic61—22no—
344C2×Dic61—22no—
345C2×Dic61—24no—
346C2×Dic61—41no—
347C2×Dic61—44no—
348C2×Dic61C22×D411yescharacteristic
349C2×Dic61C22×D411yescharacteristic
350C2×Dic61C22×D411yescharacteristic
351C2×Dic61C22×D411yescharacteristic
352C2×Dic61C22×D411yescharacteristic
353C2×Dic61C22×D411yescharacteristic
354C4×D61—22no—
355C4×D61—22no—
356C4×D61—22no—
357C4×D61—22no—
358C4×D61—22no—
359C4×D61—22no—
360C4×D61—22no—
361C4×D61—22no—
362C4×D61—22no—
363C4×D61—41no—
364C4×D61—41no—
365C4×D61—44no—
366C4×D61—44no—
367C4×D61#13714yes—
368Dic122—28no—
369Dic122—44no—
370Dic122—44no—
371Dic122—42no—
372Dic122—42no—
373Dic122—44no—
374C8×C61—24no—
375#92418—24no—
376#60865—611nomaximal, Sylow
377C22×C61—21no—
378C22×C61—21no—
379C22×C61#53612yes—
380C22×C61C23×D411yescharacteristic
381C2×D61—21no—
382C2×D61—21no—
383C2×D61—21no—
384C2×D61—21no—
385C2×D61—21no—
386C2×D61—44no—
387C2×D61C2×#13712yes—
388C4×C61—21no—
389C4×C61—21no—
390C4×C61—42no—
391C4×C61—42no—
392C4×C61—44no—
393C4×C61#53612yes—
394C4×C61C2×#13712yes—
395C4×C61#57512yes—
396C4×C61C2×2−1+412yes—
397Dic61—21no—
398Dic61—21no—
399Dic61—21no—
400Dic61—21no—
401Dic61—21no—
402Dic61—44no—
403Dic61—42no—
404Dic61—42no—
405Dic61C2×#13712yes—
406C2×#533—611no—
407C2×#533—611no—
408#3237—614no—
409#3236—614no—
410#3231—612no—
411#3231—612no—
412#3230—612no—
413#3229—612no—
414#3165—611no—
415#3165D6111yescharacteristic, complemented
416#3139—611no—
417#3139—611no—
418#3095—614no—
419#3078—614no—
420#2920—611no—
421C2×C61—22no—
422C2×C61C2×#53611yescharacteristic
423C2×C61C22×#13711yescharacteristic
424C2×C61C2×#57511yescharacteristic
425D61—22no—
426D61—41no—
427#533—611no—
428#533—611no—
429#533—612no—
430#533—612no—
431#533—612no—
432#533—612no—
433#533—612no—
434#533—612no—
435#533—611no—
436#533—1221no—
437#533—1221no—
438#533—1221no—
439#533—1221no—
440#533—1221no—
441#533—1221no—
442#533—1221no—
443#533—1221no—
444#533C2×D6111yescharacteristic
445C2×C4⋊Q8—611no—
446C2×C4⋊Q8—611no—
447C2×C4⋊Q8—611no—
448C2×C4⋊Q8C2×D6111yescharacteristic
449C2×#125—612no—
450C2×#125—1221no—
451C2×C22⋊Q8—612no—
452C2×C22⋊Q8—1221no—
453C2×C22⋊Q8—1221no—
454C2×C22⋊Q8—1221no—
455C2×C4×Q8—612no—
456C2×C4×Q8—1221no—
457C2×C4×Q8—1221no—
458C2×C4×Q8—1221no—
459C2×#117—612no—
460C2×#117—1221no—
461C22×C42—611no—
462#501—614no—
463#501C2×D6114yescomplemented
464#500—612no—
465#500C2×D6112yescomplemented
466#498—612no—
467#498C2×D6112yescomplemented
468#491—614no—
469#491—614no—
470#487—612no—
471#487—612no—
472#487—612no—
473#487—612no—
474#485—618no—
475#485—618no—
476#484—618no—
477#483—618no—
478#479—618no—
479#479—618no—
480#477—618no—
481#475—618no—
482#432—612no—
483#432—612no—
484#431—612no—
485#431—612no—
486#428—614no—
487#428C2×D6114yes—
488#423—612no—
489#419—614no—
490#419—614no—
491#407—612no—
492C4×M16—611no—
493C4×M16C2×D6111yescharacteristic
494C61#6086511yescharacteristic, complemented, Sylow
495C22×Q8—21no—
496C22×Q8—612no—
497C22×Q8—1221no—
498C22×Q8—1221no—
499C23×C4—611no—
500C23×C4—611no—
501C23×C4—611no—
502C2×M16—612no—
503C2×M16C22×D6112yes—
504C4⋊Q8—21no—
505C4⋊Q8—21no—
506C4⋊Q8—612no—
507C4⋊Q8—612no—
508C4⋊Q8—611no—
509C4⋊Q8—611no—
510C4⋊Q8—612no—
511C4⋊Q8—612no—
512C4⋊Q8—1221no—
513C4⋊Q8—1221no—
514C4⋊Q8—1221no—
515C4⋊Q8—1221no—
516C4⋊Q8—1221no—
517C4⋊Q8—1221no—
518C4⋊Q8C22×D6111yescharacteristic
519C4⋊Q8C22×D6111yescharacteristic
520C4⋊Q8C22×D6112yes—
521C4⋊Q8C22×D6112yes—
522#125—612no—
523#125—612no—
524#125—612no—
525#125—1222no—
526#125—1222no—
527#125—1222no—
528#125—1222no—
529#125—1222no—
530#125—1222no—
531#125C22×D6112yes—
532C22⋊Q8—21no—
533C22⋊Q8—21no—
534C22⋊Q8—614no—
535C22⋊Q8—614no—
536C22⋊Q8—1222no—
537C22⋊Q8—1222no—
538C22⋊Q8—1222no—
539C22⋊Q8—1222no—
540C22⋊Q8—1222no—
541C22⋊Q8—1222no—
542C22⋊Q8—1221no—
543C22⋊Q8—1221no—
544C22⋊Q8—1221no—
545C22⋊Q8—1221no—
546C22⋊Q8—1222no—
547C22⋊Q8—1222no—
548C22⋊Q8—1222no—
549C22⋊Q8—1222no—
550C22⋊Q8—1221no—
551C22⋊Q8—1221no—
552C4×Q8—21no—
553C4×Q8—21no—
554C4×Q8—614no—
555C4×Q8—614no—
556C4×Q8—1222no—
557C4×Q8—1222no—
558C4×Q8—1222no—
559C4×Q8—1222no—
560C4×Q8—1222no—
561C4×Q8—1221no—
562C4×Q8—1222no—
563C4×Q8—1221no—
564C4×Q8—1221no—
565C4×Q8—1222no—
566C4×Q8—1222no—
567C4×Q8—1221no—
568C4×Q8—1222no—
569C4×Q8—1222no—
570C4×Q8—1221no—
571C4×Q8—1221no—
572#117—612no—
573#117—612no—
574#117—612no—
575#117—1222no—
576#117—1222no—
577#117—1222no—
578#117—1222no—
579#117—1222no—
580#117—1222no—
581#117C22×D6112yes—
582C2×C4⋊C4—21no—
583C2×C4⋊C4—612no—
584C2×C4⋊C4—612no—
585C2×C4⋊C4—1222no—
586C2×C4⋊C4—1222no—
587C2×C4⋊C4—1221no—
588C2×C4⋊C4—1221no—
589C2×C4⋊C4—1222no—
590C2×C4⋊C4—1222no—
591C2×C4⋊C4—1221no—
592C2×C4⋊C4—1221no—
593C2×C4⋊C4C22×D6112yes—
594C2×C22⋊C4—1222no—
595C2×C22⋊C4—1222no—
596C2×C42—611no—
597C2×C42—611no—
598C2×C42—611no—
599C2×C42—611no—
600C2×C42—611no—
601C2×C42—611no—
602C2×C42—611no—
603C2×C42—611no—
604C2×C42—611no—
605C2×C42—611no—
606C2×C42—611no—
607C2×C42—1222no—
608C2×C42—1222no—
609C2×C42C22×D6111yescharacteristic
610#107—618no—
611#107C22×D6118yes—
612#106—618no—
613#106C22×D6118yes—
614C4⋊C8—614no—
615C4⋊C8—614no—
616#103—618no—
617#103—618no—
618#103—618no—
619#103—618no—
620C22⋊C8—614no—
621C22⋊C8—614no—
622#97—612no—
623#97C22×D6112yes—
624C4×C8—612no—
625C4×C8C22×D6112yes—
626C24—611no—
627C2×Q8—21no—
628C2×Q8—21no—
629C2×Q8—22no—
630C2×Q8—22no—
631C2×Q8—44no—
632C2×Q8—614no—
633C2×Q8—1222no—
634C2×Q8—1222no—
635C2×Q8—1221no—
636C2×Q8—1221no—
637C2×Q8—1222no—
638C2×Q8—1228no—
639C2×Q8—2444no—
640C2×Q8—2444no—
641C22×C4—22no—
642C22×C4—611no—
643C22×C4—611no—
644C22×C4—611no—
645C22×C4—611no—
646C22×C4—611no—
647C22×C4—611no—
648C22×C4—611no—
649C22×C4—611no—
650C22×C4—611no—
651C22×C4—611no—
652C22×C4—611no—
653C22×C4—611no—
654C22×C4—611no—
655C22×C4—611no—
656C22×C4—611no—
657C22×C4—1224no—
658C22×C4—1222no—
659C22×C4—1222no—
660C22×C4—1224no—
661C22×C4—1222no—
662C22×C4—2442no—
663C22×C4D4×D6111yescharacteristic
664C22×C4D4×D6111yescharacteristic
665C22×C4C23×D6111yescharacteristic
666M16—24no—
667M16—1224no—
668C2×C8—614no—
669C2×C8C23×D6114yes—
670C4⋊C4—22no—
671C4⋊C4—22no—
672C4⋊C4—22no—
673C4⋊C4—22no—
674C4⋊C4—21no—
675C4⋊C4—21no—
676C4⋊C4—22no—
677C4⋊C4—612no—
678C4⋊C4—612no—
679C4⋊C4—1222no—
680C4⋊C4—1222no—
681C4⋊C4—1224no—
682C4⋊C4—1224no—
683C4⋊C4—1222no—
684C4⋊C4—1222no—
685C4⋊C4—1222no—
686C4⋊C4—1222no—
687C4⋊C4—1224no—
688C4⋊C4—1224no—
689C4⋊C4—1222no—
690C4⋊C4—1222no—
691C4⋊C4—1222no—
692C4⋊C4—1222no—
693C4⋊C4—1222no—
694C4⋊C4—1222no—
695C4⋊C4—1221no—
696C4⋊C4—1221no—
697C4⋊C4—1222no—
698C4⋊C4—1222no—
699C4⋊C4C23×D6112yes—
700C4⋊C4C23×D6112yes—
701C4⋊C4C23×D6114yes—
702C22⋊C4—22no—
703C22⋊C4—1222no—
704C22⋊C4—1222no—
705C22⋊C4—1224no—
706C22⋊C4—1224no—
707C22⋊C4—1222no—
708C42—22no—
709C42—611no—
710C42—611no—
711C42—611no—
712C42—611no—
713C42—611no—
714C42—611no—
715C42—611no—
716C42—611no—
717C42—611no—
718C42—611no—
719C42—611no—
720C42—611no—
721C42—1222no—
722C42—1222no—
723C42—1224no—
724C42—1224no—
725C42—1222no—
726C42D4×D6111yescharacteristic
727C42D4×D6111yescharacteristic
728C42C23×D6111yescharacteristic
729C42C23×D6111yescharacteristic
730C23—611no—
731C23—611no—
732C23—1222no—
733C23—1222no—
734C23—2441no—
735C23C2×D4×D6111yescharacteristic
736Q8—44no—
737Q8—42no—
738Q8—44no—
739Q8—42no—
740Q8—1228no—
741Q8—2444no—
742Q8—2444no—
743Q8—2442no—
744Q8—2442no—
745Q8—2444no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—24no—
751C2×C4—44no—
752C2×C4—611no—
753C2×C4—614no—
754C2×C4—611no—
755C2×C4—611no—
756C2×C4—611no—
757C2×C4—611no—
758C2×C4—611no—
759C2×C4—1222no—
760C2×C4—1222no—
761C2×C4—1222no—
762C2×C4—1222no—
763C2×C4—1222no—
764C2×C4—1222no—
765C2×C4—1222no—
766C2×C4—1222no—
767C2×C4—1222no—
768C2×C4—1222no—
769C2×C4—1222no—
770C2×C4—1222no—
771C2×C4—1222no—
772C2×C4—1224no—
773C2×C4—2441no—
774C2×C4—2441no—
775C2×C4—2444no—
776C2×C4—2444no—
777C2×C4—2441no—
778C2×C4—2444no—
779C2×C4C2×D4×D6111yescharacteristic
780C2×C4C2×D4×D6111yescharacteristic
781C2×C4C2×D4×D6111yescharacteristic
782C2×C4C2×D4×D6111yescharacteristic
783C2×C4C2×D4×D6111yescharacteristic
784C2×C4#1451982514yes—
785C2×C4C24×D6111yescharacteristic
786C8—24no—
787C8—1224no—
788C22—21no—
789C22—21no—
790C22—612no—
791C22—1221no—
792C22—1221no—
793C22—1221no—
794C22—1221no—
795C22—1221no—
796C22—2444no—
797C22#1684033712yes—
798C22C22×D4×D6111yescharacteristic
799C4—21no—
800C4—21no—
801C4—42no—
802C4—44no—
803C4—42no—
804C4—612no—
805C4—1221no—
806C4—1221no—
807C4—1221no—
808C4—1221no—
809C4—1221no—
810C4—2442no—
811C4—2442no—
812C4—2444no—
813C4#1684033712yes—
814C4#137×D6112yes—
815C4#1684055812yes—
816C4C2×#1451982512yes—
817C2—22no—
818C2—1222no—
819C2—2441no—
820C2C2×#1684033711yescharacteristic
821C2C2×#137×D6111yescharacteristic
822C2C2×#1684055811yescharacteristic
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3165C2
socleC22×C61C23×D4
prime radicalC23×D61C2×D4
hypercenter#3165D61
hypocenterC61#60865
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3165

Complements

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

NH ≅ G/Ntype
3. #21457034C2semidirect
4. #21457026C2semidirect
5. #21456981C2semidirect
6. #21456979C2semidirect
7. #21456971C2semidirect
8. #21456964C2semidirect
9. #21456361C2semidirect
10. #21456201C2semidirect
11. #21456200C2semidirect
13. #21455623C2semidirect
15. C61×#3165C2semidirect
49. #16840168C22semidirect
50. #16840165C22semidirect
51. #16840158C22semidirect
52. #16840132C22semidirect
53. #16840131C22semidirect
54. #16840114C22semidirect
55. #16840114C22semidirect
56. #16840113C22semidirect
57. #16840113C22semidirect
62. #16840072C22semidirect
63. #16840068C22semidirect
64. #16840056C22semidirect
65. #16840046C22semidirect
78. C61×#501C22semidirect
79. C61×#500C22semidirect
80. C61×#498C22semidirect
415. #3165D61semidirect
463. #501C2×D61semidirect
465. #500C2×D61semidirect
467. #498C2×D61semidirect
494. C61#60865semidirect

Maximal subgroups

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

subgroupindex
C2×#168403172
#533×D612
#214570342
#214570262
#214569812
#214569792
#214569712
#214569642
#214563612
#214562012
#214562002
#214557692
#214556232
#214544502
C61×#31652
#6086561