Finite Group Databasebeta

← #30552273

Subgroups — #30552273

Order 15616.

2006 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459114C211yesmaximal, characteristic
2C2×C4⋊Q8×D61C211yesmaximal, characteristic, complemented
3#21457047C214yesmaximal, complemented
4#21457039C214yesmaximal, complemented
5#21456972C211yesmaximal, characteristic, complemented
6#21456970C211yesmaximal, characteristic, complemented
7#21456964C212yesmaximal, complemented
8#21456944C211yesmaximal, characteristic, complemented
9#21456936C212yesmaximal, complemented
10#21456360C212yesmaximal, complemented
11#21456209C212yesmaximal, complemented
12#21455741C214yesmaximal, complemented
13#21455631C214yesmaximal, complemented
14#21454447C211yesmaximal, characteristic, complemented
15C61×#3227C211yesmaximal, characteristic, complemented
16C22×Q8×D61—21no—
17#16840319C2211yescharacteristic
18#16840317C2211yescharacteristic
19#16840317C2211yescharacteristic
20#16840310C2211yescharacteristic
21#16840310C2211yescharacteristic
22C2×#14519777C2211yescharacteristic
23C2×#14519776—21no—
24C2×#14519776C2212yes—
25C2×#14519775—21no—
26C4⋊Q8×D61—21no—
27C4⋊Q8×D61—21no—
28C4⋊Q8×D61—21no—
29C4⋊Q8×D61—21no—
30C4⋊Q8×D61C2212yes—
31C4⋊Q8×D61C2212yes—
32C4⋊Q8×D61C2212yes—
33C4⋊Q8×D61C2212yes—
34#16840294—21no—
35#16840294C2212yes—
36#16840293—21no—
37#16840293C2212yes—
38#16840291—21no—
39#16840291—21no—
40#16840272—21no—
41#16840272C2212yes—
42#16840269—21no—
43#41×Dic61—21no—
44C4×#11758224—21no—
45C4×#11758224C2212yes—
46C2×C4⋊C4×D61—21no—
47C2×C4⋊C4×D61C2212yes—
48C2×C42×D61C2211yescharacteristic
49#16840169C2218yescomplemented
50#16840167C2212yescomplemented
51#16840165C2212yescomplemented
52#16840158C2212yescomplemented
53#16840120C2218yescomplemented
54#16840114C2212yescomplemented
55#16840113C2212yescomplemented
56#16840108C2212yescomplemented
57#16840098C2214yes—
58#16840097C2214yes—
59#16840094C2218yes—
60#16840078C2214yes—
61#16840074C2218yes—
62#16840058C2214yescomplemented
63#16840054C2214yescomplemented
64#16840052C2214yescomplemented
65#16840046C2218yescomplemented
66#16840040C2218yescomplemented
67#16839818C2212yes—
68#16839816C2212yes—
69#16839815C2211yescharacteristic
70#16839813C2212yes—
71#16839801C2218yes—
72#16839784C2212yes—
73#16839760C2218yes—
74#16839724C2212yes—
75C4×#11758189C2212yes—
76C61×#532C2211yescharacteristic
77C2×C4⋊Q8×C61C2211yescharacteristic
78C61×#498C2212yescomplemented
79C61×#486C2212yescomplemented
80C61×#481C2214yes—
81C61×#476C2214yescomplemented
82C61×#431C2211yescharacteristic
83C2×#11758224—21no—
84C2×#11758224C2312yes—
85C22×Dic122—21no—
86C22×Dic122—22no—
87C2×Q8×D61—22no—
88C2×Q8×D61—22no—
89C2×Q8×D61—22no—
90C2×Q8×D61—22no—
91C2×Q8×D61—48no—
92C22×C4×D61—22no—
93C22×C4×D61D411yescharacteristic
94C22×C4×D61D411yescharacteristic
95C22×C4×D61C2311yescharacteristic
96C2×#11758189C2314yes—
97#14519777—21no—
98#14519777—21no—
99#14519777C2311yescharacteristic
100#14519777C2312yes—
101#14519777C2312yes—
102#14519777C2311yescharacteristic
103#14519776—22no—
104#14519776—22no—
105#14519776—22no—
106#14519776—22no—
107#14519776—22no—
108#14519776—22no—
109#14519776C2314yes—
110#14519776C2314yes—
111#14519775—22no—
112#14519775—22no—
113#14519775—22no—
114#14519775—22no—
115#14519770—22no—
116#14519770—22no—
117#14519769—21no—
118#14519768—21no—
119#14519768C2312yes—
120#14519764—21no—
121#14519764C2312yes—
122#14519759—22no—
123#14519759—22no—
124#14519758—22no—
125#14519757—21no—
126#14519757C2312yes—
127#14519756—21no—
128#14519756C2312yes—
129#14519753—21no—
130#14519753—21no—
131#14519748—21no—
132#14519748—21no—
133#14519748—21no—
134#14519748C2312yes—
135#14519745—22no—
136Q8×Dic61—21no—
137Q8×Dic61—21no—
138C4×Dic122—21no—
139C4×Dic122C2312yes—
140#14519742—21no—
141#14519742C2312yes—
142D4×Dic61—22no—
143D4×Dic61—22no—
144D4×Dic61—21no—
145D4×Dic61—21no—
146D4×Dic61—21no—
147D4×Dic61C2312yes—
148C4×C22⋊D61—22no—
149C4×C22⋊D61—22no—
150#14519737—22no—
151#14519737—22no—
152#14519736—21no—
153#14519736—22no—
154#14519735—21no—
155#14519735C2312yes—
156#14519733—22no—
157#14519733—22no—
158C2×C4⋊Dic61—21no—
159C2×C4⋊Dic61C2312yes—
160C2×#11758196—22no—
161C2×#11758196—22no—
162C4⋊C4×D61—22no—
163C4⋊C4×D61—22no—
164C4⋊C4×D61—22no—
165C4⋊C4×D61—22no—
166C4⋊C4×D61—22no—
167C4⋊C4×D61—22no—
168C4⋊C4×D61C2314yes—
169C4⋊C4×D61C2314yes—
170C2×C4×Dic61—22no—
171C2×C4×Dic61D411yescharacteristic
172C2×C4×Dic61D411yescharacteristic
173C2×C4×Dic61C2311yescharacteristic
174C42×D61D411yescharacteristic
175C42×D61D411yescharacteristic
176C42×D61D411yescharacteristic
177C42×D61D411yescharacteristic
178C42×D61C2311yescharacteristic
179C42×D61C2311yescharacteristic
180C42×D61C2311yescharacteristic
181C42×D61C2311yescharacteristic
182#14519711C2318yes—
183#14519710C2318yes—
184#14519708C2318yes—
185C4⋊#92418C2312yes—
186#14519706C2314yes—
187#14519702C2318yes—
188#14519700C2318yes—
189#14519698C2318yes—
190C22⋊#92418C2312yes—
191#14519689C2314yes—
192#14519687C2314yes—
193C4×#92418C2312yes—
194C2×#41×C61—21no—
195C22×Q8×C61—21no—
196C4⋊Q8×C61—21no—
197C4⋊Q8×C61—21no—
198C4⋊Q8×C61C2312yes—
199C4⋊Q8×C61C2312yes—
200C4⋊Q8×C61C2311yescharacteristic
201#127×C61C2311yescharacteristic
202#124×C61—21no—
203#121×C61—21no—
204#121×C61C2312yes—
205C4×D4×C61—21no—
206C4×D4×C61C2312yes—
207C2×C4⋊C4×C61—21no—
208C2×C4⋊C4×C61C2312yes—
209C2×C42×C61C2311yescharacteristic
210#106×C61C2318yes—
211C4⋊C8×C61C2312yes—
212#102×C61C2318yes—
213C22⋊C8×C61C2312yes—
214C4×C8×C61C2312yes—
215C23×D61C2×D411yescharacteristic
216#41×C61—44no—
217C2×Q8×C61—22no—
218C2×Q8×C61—22no—
219C2×Q8×C61—21no—
220C2×Q8×C61—44no—
221C2×D4×C61—22no—
222C2×D4×C61—21no—
223C2×D4×C61—21no—
224C2×D4×C61C2412yes—
225C22×C4×C61—22no—
226C22×C4×C61—22no—
227C22×C4×C61C2×D411yescharacteristic
228C22×C4×C61C2×D411yescharacteristic
229C22×C4×C61C2411yescharacteristic
230C2×C22⋊D61—22no—
231C2×C22⋊D61—22no—
232C22×Dic61—22no—
233C22×Dic61—22no—
234C22×Dic61—22no—
235C22×Dic61C2×D411yescharacteristic
236C22×Dic61C2×D411yescharacteristic
237C22×Dic61C2×D411yescharacteristic
238Q8×D61—48no—
239Q8×D61—48no—
240Q8×D61—48no—
241Q8×D61—48no—
242#11758224—28no—
243#11758224—44no—
244C2×C4×D61—24no—
245C2×C4×D61—24no—
246C2×C4×D61—24no—
247C2×C4×D61—24no—
248C2×C4×D61—24no—
249C2×C4×D61—48no—
250C2×C4×D61C2×D411yescharacteristic
251C2×C4×D61C2×D411yescharacteristic
252C2×C4×D61C2×D411yescharacteristic
253C2×C4×D61C2×D411yescharacteristic
254C2×C4×D61C2×D411yescharacteristic
255C2×C4×D61C2×D411yescharacteristic
256C2×C4×D61C2×D411yescharacteristic
257C2×C4×D61C2×D411yescharacteristic
258C2×C4×D61C2×D411yescharacteristic
259C2×C4×D61C2×D411yescharacteristic
260C2×C4×D61C2411yescharacteristic
261C2×C4×D61C2411yescharacteristic
262C2×Dic122—22no—
263C2×Dic122—22no—
264C2×Dic122—21no—
265C2×Dic122—24no—
266C2×Dic122—24no—
267C2×Dic122—48no—
268C2×Dic122—44no—
269C2×Dic122C2412yes—
270C2×C8×C61C2414yes—
271C4⋊C4×C61—22no—
272C4⋊C4×C61—22no—
273C4⋊C4×C61—22no—
274C4⋊C4×C61—21no—
275C4⋊C4×C61C2414yes—
276C4⋊C4×C61C2412yes—
277C22⋊C4×C61—22no—
278C22⋊C4×C61—22no—
279C42×C61C2×D411yescharacteristic
280C42×C61C2×D411yescharacteristic
281C42×C61C2411yescharacteristic
282C42×C61C2411yescharacteristic
283C22⋊Dic61—22no—
284C22⋊Dic61—22no—
285C22⋊Dic61—22no—
286C22⋊Dic61—22no—
287C22⋊Dic61—22no—
288#11758198—22no—
289#11758198—22no—
290C4⋊Dic61—22no—
291C4⋊Dic61—22no—
292C4⋊Dic61—22no—
293C4⋊Dic61—21no—
294C4⋊Dic61—21no—
295C4⋊Dic61—21no—
296C4⋊Dic61—22no—
297C4⋊Dic61—22no—
298C4⋊Dic61C2414yes—
299C4⋊Dic61C2412yes—
300#11758196—22no—
301#11758196—22no—
302#11758196—24no—
303#11758196—24no—
304#11758196—24no—
305#11758196—24no—
306#11758196—22no—
307#11758196—22no—
308C4×Dic61—22no—
309C4×Dic61—22no—
310C4×Dic61—22no—
311C4×Dic61C2×D411yescharacteristic
312C4×Dic61C2×D411yescharacteristic
313C4×Dic61C2×D411yescharacteristic
314C4×Dic61C2×D411yescharacteristic
315C4×Dic61C2×D411yescharacteristic
316C4×Dic61C2×D411yescharacteristic
317C4×Dic61C2×D411yescharacteristic
318C4×Dic61C2×D411yescharacteristic
319C4×Dic61C2×D411yescharacteristic
320C4×Dic61C2×D411yescharacteristic
321C4×Dic61C2411yescharacteristic
322C4×Dic61C2411yescharacteristic
323C2×#92418C2414yes—
324#11758189—28no—
325C23×C61—22no—
326C23×C61C22×D411yescharacteristic
327C22×D61—22no—
328C22×D61—22no—
329C22×D61—22no—
330C22×D61C22×D411yescharacteristic
331C22×D61C22×D411yescharacteristic
332Q8×C61—44no—
333Q8×C61—44no—
334Q8×C61—42no—
335D4×C61—24no—
336D4×C61—44no—
337D4×C61—42no—
338D4×C61—42no—
339C2×C4×C61—22no—
340C2×C4×C61—22no—
341C2×C4×C61—22no—
342C2×C4×C61—24no—
343C2×C4×C61—44no—
344C2×C4×C61—44no—
345C2×C4×C61#13714yes—
346C2×C4×C61C22×D411yescharacteristic
347C2×C4×C61C22×D411yescharacteristic
348C2×C4×C61C22×D411yescharacteristic
349C2×C4×C61C22×D411yescharacteristic
350C2×C4×C61C22×D411yescharacteristic
351C2×C4×C61C2511yescharacteristic
352C22⋊D61—44no—
353C22⋊D61—44no—
354C2×Dic61—22no—
355C2×Dic61—22no—
356C2×Dic61—22no—
357C2×Dic61—22no—
358C2×Dic61—22no—
359C2×Dic61—24no—
360C2×Dic61—44no—
361C2×Dic61—44no—
362C2×Dic61—44no—
363C2×Dic61C22×D411yescharacteristic
364C2×Dic61C22×D411yescharacteristic
365C2×Dic61C22×D411yescharacteristic
366C2×Dic61C22×D411yescharacteristic
367C2×Dic61C22×D411yescharacteristic
368C2×Dic61C22×D411yescharacteristic
369C4×D61—22no—
370C4×D61—22no—
371C4×D61—22no—
372C4×D61—22no—
373C4×D61—22no—
374C4×D61—22no—
375C4×D61—22no—
376C4×D61—22no—
377C4×D61—22no—
378C4×D61—22no—
379C4×D61—48no—
380C4×D61—48no—
381C4×D61AGL(1,ℤ/8)14yes—
382C4×D612−1+414yes—
383Dic122—24no—
384Dic122—48no—
385Dic122—44no—
386Dic122—44no—
387Dic122—42no—
388Dic122—48no—
389C8×C61—24no—
390#92418—24no—
391#60860—611nomaximal, Sylow
392C22×C61—21no—
393C22×C61—21no—
394C22×C61—42no—
395C22×C61—42no—
396C22×C61—42no—
397C22×C61C2×#13712yes—
398C22×C61C23×D411yescharacteristic
399C2×D61—28no—
400C2×D61—21no—
401C2×D61—21no—
402C2×D61—21no—
403C2×D61—21no—
404C2×D61#53612yes—
405C2×D61C2×AGL(1,ℤ/8)12yes—
406C4×C61—21no—
407C4×C61—21no—
408C4×C61—44no—
409C4×C61—42no—
410C4×C61C2×AGL(1,ℤ/8)12yes—
411C4×C61C2×#13712yes—
412C4×C61C2×#13712yes—
413C4×C61C2×2−1+412yes—
414Dic61—21no—
415Dic61—21no—
416Dic61—21no—
417Dic61—21no—
418Dic61—42no—
419Dic61—44no—
420Dic61—42no—
421Dic61#53612yes—
422Dic61C2×AGL(1,ℤ/8)12yes—
423#3444—611no—
424C22×C4⋊Q8—611no—
425#3239—614no—
426#3238—614no—
427#3230—611no—
428#3230—611no—
429#3229—612no—
430#3227—611no—
431#3227D6111yescharacteristic, complemented
432#3226—612no—
433#3165—612no—
434#3141—612no—
435#3092—614no—
436#3079—614no—
437#2920—611no—
438C2×C61—22no—
439C2×C61—82no—
440C2×C61C2×#53611yescharacteristic
441C2×C61C22×AGL(1,ℤ/8)11yescharacteristic
442C2×C61C22×#13711yescharacteristic
443D61—22no—
444D61—22no—
445C23×Q8—1221no—
446#533—611no—
447#533—611no—
448#533—611no—
449#532—611no—
450#532—611no—
451#532C2×D6111yescharacteristic
452C2×C4⋊Q8—612no—
453C2×C4⋊Q8—612no—
454C2×C4⋊Q8—612no—
455C2×C4⋊Q8—612no—
456C2×C4⋊Q8—612no—
457C2×C4⋊Q8—611no—
458C2×C4⋊Q8—1221no—
459C2×C4⋊Q8—1221no—
460C2×C4⋊Q8—1221no—
461C2×C4⋊Q8—1221no—
462C2×C4⋊Q8—1221no—
463C2×C4⋊Q8—1221no—
464C2×C4⋊Q8C2×D6111yescharacteristic
465#529—612no—
466#529—612no—
467#529—1221no—
468#529—1221no—
469#529—1221no—
470#529—1221no—
471#525—612no—
472#525—1221no—
473#525—1221no—
474C4×#41—612no—
475C4×#41—1221no—
476C4×#41—1221no—
477C22×C4⋊C4—612no—
478C22×C4⋊C4—1221no—
479C22×C42—611no—
480#501—618no—
481#500—612no—
482#500—612no—
483#498—612no—
484#498C2×D6112yescomplemented
485#489—618no—
486#487—612no—
487#487—612no—
488#486—612no—
489#486C2×D6112yescomplemented
490#484—614no—
491#484—614no—
492#483—618no—
493#481—614no—
494#481C2×D6114yes—
495#480—618no—
496#477—614no—
497#477—614no—
498#476—614no—
499#476C2×D6114yescomplemented
500#475—618no—
501#474—618no—
502#432—612no—
503#432—612no—
504#431—611no—
505#431—612no—
506#431C2×D6111yescharacteristic
507#428—618no—
508#423—612no—
509#417—618no—
510#407—612no—
511C4×M16—612no—
512C61#6086011yescharacteristic, complemented, Sylow
513C2×#41—21no—
514C2×#41—612no—
515C2×#41—1221no—
516C22×Q8—21no—
517C22×Q8—1222no—
518C22×Q8—1222no—
519C22×Q8—1222no—
520C22×Q8—1222no—
521C22×Q8—1222no—
522C22×Q8—1221no—
523C22×Q8—2448no—
524C23×C4—611no—
525C23×C4—611no—
526C23×C4—611no—
527C23×C4—1222no—
528C2×M16—614no—
529C4⋊Q8—21no—
530C4⋊Q8—21no—
531C4⋊Q8—614no—
532C4⋊Q8—614no—
533C4⋊Q8—612no—
534C4⋊Q8—612no—
535C4⋊Q8—611no—
536C4⋊Q8—611no—
537C4⋊Q8—1222no—
538C4⋊Q8—1222no—
539C4⋊Q8—1222no—
540C4⋊Q8—1222no—
541C4⋊Q8—1222no—
542C4⋊Q8—1222no—
543C4⋊Q8—1222no—
544C4⋊Q8—1222no—
545C4⋊Q8—1222no—
546C4⋊Q8—1222no—
547C4⋊Q8—1221no—
548C4⋊Q8—1221no—
549C4⋊Q8C22×D6112yes—
550C4⋊Q8C22×D6112yes—
551C4⋊Q8C22×D6111yescharacteristic
552#127C22×D6111yescharacteristic
553#126—1222no—
554#126—1222no—
555#125—612no—
556#125—1221no—
557#125—1221no—
558#124—21no—
559#124—612no—
560#124—1221no—
561#123—1222no—
562#123—1222no—
563#123—1222no—
564C22⋊Q8—612no—
565C22⋊Q8—612no—
566C22⋊Q8—1221no—
567C22⋊Q8—1221no—
568C22⋊Q8—1221no—
569C22⋊Q8—1221no—
570#121—21no—
571#121—612no—
572#121—1221no—
573#121—1221no—
574#121—1221no—
575#121C22×D6112yes—
576#120—1222no—
577C4×Q8—612no—
578C4×Q8—612no—
579C4×Q8—1221no—
580C4×Q8—1221no—
581C4×Q8—1221no—
582C4×Q8—1221no—
583C4×D4—21no—
584C4×D4—612no—
585C4×D4—1221no—
586C4×D4—1221no—
587C4×D4—1221no—
588C4×D4—1222no—
589C4×D4—1222no—
590C4×D4—1222no—
591C4×D4—1222no—
592C4×D4—1222no—
593C4×D4—1222no—
594C4×D4C22×D6112yes—
595#117—612no—
596#117—1222no—
597#117—1222no—
598#117—1222no—
599#117—1221no—
600#117—1221no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—612no—
603C2×C4⋊C4—614no—
604C2×C4⋊C4—614no—
605C2×C4⋊C4—1222no—
606C2×C4⋊C4—1222no—
607C2×C4⋊C4—1222no—
608C2×C4⋊C4—1222no—
609C2×C4⋊C4—1222no—
610C2×C4⋊C4—1222no—
611C2×C4⋊C4—1222no—
612C2×C4⋊C4—1222no—
613C2×C4⋊C4—1221no—
614C2×C4⋊C4C22×D6112yes—
615C2×C42—611no—
616C2×C42—611no—
617C2×C42—611no—
618C2×C42—611no—
619C2×C42—611no—
620C2×C42—611no—
621C2×C42—611no—
622C2×C42—611no—
623C2×C42—611no—
624C2×C42—611no—
625C2×C42—611no—
626C2×C42—1222no—
627C2×C42C22×D6111yescharacteristic
628#107—618no—
629#107—618no—
630#106—618no—
631#106C22×D6118yes—
632C4⋊C8—614no—
633C4⋊C8—612no—
634C4⋊C8C22×D6112yes—
635#103—618no—
636#103—618no—
637#102—618no—
638#102C22×D6118yes—
639C22⋊C8—612no—
640C22⋊C8—614no—
641C22⋊C8C22×D6112yes—
642#97—614no—
643C4×C8—612no—
644C4×C8C22×D6112yes—
645C24—611no—
646#41—44no—
647#41—1228no—
648#41—2444no—
649C2×Q8—21no—
650C2×Q8—22no—
651C2×Q8—22no—
652C2×Q8—44no—
653C2×Q8—612no—
654C2×Q8—1224no—
655C2×Q8—1224no—
656C2×Q8—1221no—
657C2×Q8—1222no—
658C2×Q8—1222no—
659C2×Q8—2444no—
660C2×Q8—2448no—
661C2×Q8—2448no—
662C2×Q8—2448no—
663C2×Q8—2448no—
664C2×Q8—2448no—
665C2×D4—22no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—1222no—
669C2×D4—1222no—
670C2×D4C23×D6112yes—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—611no—
674C22×C4—611no—
675C22×C4—611no—
676C22×C4—611no—
677C22×C4—611no—
678C22×C4—611no—
679C22×C4—611no—
680C22×C4—611no—
681C22×C4—611no—
682C22×C4—611no—
683C22×C4—611no—
684C22×C4—611no—
685C22×C4—611no—
686C22×C4—611no—
687C22×C4—611no—
688C22×C4—1224no—
689C22×C4—1224no—
690C22×C4—1224no—
691C22×C4—1224no—
692C22×C4—1222no—
693C22×C4—1222no—
694C22×C4—1224no—
695C22×C4—1222no—
696C22×C4—2448no—
697C22×C4D4×D6111yescharacteristic
698C22×C4D4×D6111yescharacteristic
699C22×C4C23×D6111yescharacteristic
700M16—1228no—
701C2×C8—614no—
702C2×C8C23×D6114yes—
703C4⋊C4—22no—
704C4⋊C4—22no—
705C4⋊C4—22no—
706C4⋊C4—21no—
707C4⋊C4—614no—
708C4⋊C4—612no—
709C4⋊C4—1224no—
710C4⋊C4—1224no—
711C4⋊C4—1224no—
712C4⋊C4—1224no—
713C4⋊C4—1222no—
714C4⋊C4—1222no—
715C4⋊C4—1222no—
716C4⋊C4—1222no—
717C4⋊C4—1222no—
718C4⋊C4—1222no—
719C4⋊C4—1222no—
720C4⋊C4—1222no—
721C4⋊C4—1222no—
722C4⋊C4—1221no—
723C4⋊C4—1221no—
724C4⋊C4—1221no—
725C4⋊C4C23×D6114yes—
726C4⋊C4C23×D6112yes—
727C22⋊C4—22no—
728C22⋊C4—22no—
729C22⋊C4—1222no—
730C22⋊C4—1222no—
731C22⋊C4—1222no—
732C22⋊C4—1222no—
733C22⋊C4—1222no—
734C22⋊C4—1222no—
735C22⋊C4—1222no—
736C42—611no—
737C42—611no—
738C42—611no—
739C42—611no—
740C42—611no—
741C42—611no—
742C42—611no—
743C42—611no—
744C42—611no—
745C42—611no—
746C42—611no—
747C42—611no—
748C42—1222no—
749C42—1222no—
750C42—1222no—
751C42D4×D6111yescharacteristic
752C42D4×D6111yescharacteristic
753C42C23×D6111yescharacteristic
754C42C23×D6111yescharacteristic
755C23—22no—
756C23—611no—
757C23—611no—
758C23—1222no—
759C23—1222no—
760C23—1222no—
761C23C2×D4×D6111yescharacteristic
762Q8—44no—
763Q8—44no—
764Q8—42no—
765Q8—1224no—
766Q8—2444no—
767Q8—2448no—
768Q8—2448no—
769Q8—2444no—
770Q8—2442no—
771D4—24no—
772D4—44no—
773D4—42no—
774D4—42no—
775D4—2444no—
776D4—2444no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—24no—
781C2×C4—44no—
782C2×C4—44no—
783C2×C4—611no—
784C2×C4—611no—
785C2×C4—614no—
786C2×C4—614no—
787C2×C4—611no—
788C2×C4—611no—
789C2×C4—611no—
790C2×C4—611no—
791C2×C4—1222no—
792C2×C4—1222no—
793C2×C4—1222no—
794C2×C4—1222no—
795C2×C4—1222no—
796C2×C4—1222no—
797C2×C4—1222no—
798C2×C4—1222no—
799C2×C4—1222no—
800C2×C4—1222no—
801C2×C4—1222no—
802C2×C4—1222no—
803C2×C4—1222no—
804C2×C4—1222no—
805C2×C4—1222no—
806C2×C4—1224no—
807C2×C4—2448no—
808C2×C4—2448no—
809C2×C4—2444no—
810C2×C4—2444no—
811C2×C4—2444no—
812C2×C4#1451980614yes—
813C2×C4C2×D4×D6111yescharacteristic
814C2×C4C2×D4×D6111yescharacteristic
815C2×C4C2×D4×D6111yescharacteristic
816C2×C4C2×D4×D6111yescharacteristic
817C2×C4C2×D4×D6111yescharacteristic
818C2×C4C24×D6111yescharacteristic
819C8—24no—
820C8—1224no—
821C22—21no—
822C22—21no—
823C22—42no—
824C22—42no—
825C22—42no—
826C22—612no—
827C22—612no—
828C22—1228no—
829C22—1221no—
830C22—1221no—
831C22—1221no—
832C22—1221no—
833C22C2×#1451980612yes—
834C22C22×D4×D6111yescharacteristic
835C4—21no—
836C4—21no—
837C4—44no—
838C4—42no—
839C4—612no—
840C4—612no—
841C4—1221no—
842C4—1221no—
843C4—1221no—
844C4—1221no—
845C4—2444no—
846C4—2442no—
847C4—2442no—
848C4AGL(1,ℤ/8)×D6112yes—
849C4C2×#1451980612yes—
850C4C2×#1451980612yes—
851C42−1+4×D6112yes—
852C2—22no—
853C2—82no—
854C2—1222no—
855C2—1222no—
856C2#536×D6111yescharacteristic
857C2C2×AGL(1,ℤ/8)×D6111yescharacteristic
858C2C22×#1451980611yescharacteristic
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3227C2
socleC22×C61C23×D4
prime radical#21459114C2
hypercenter#3227D61
hypocenterC61#60860
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3227

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊Q8×D61C2semidirect
3. #21457047C2semidirect
4. #21457039C2semidirect
5. #21456972C2semidirect
6. #21456970C2semidirect
7. #21456964C2semidirect
8. #21456944C2semidirect
9. #21456936C2semidirect
10. #21456360C2semidirect
11. #21456209C2semidirect
12. #21455741C2semidirect
13. #21455631C2semidirect
14. #21454447C2semidirect
15. C61×#3227C2semidirect
49. #16840169C22semidirect
50. #16840167C22semidirect
51. #16840165C22semidirect
52. #16840158C22semidirect
53. #16840120C22semidirect
54. #16840114C22semidirect
55. #16840113C22semidirect
56. #16840108C22semidirect
62. #16840058C22semidirect
63. #16840054C22semidirect
64. #16840052C22semidirect
65. #16840046C22semidirect
66. #16840040C22semidirect
78. C61×#498C22semidirect
79. C61×#486C22semidirect
81. C61×#476C22semidirect
431. #3227D61semidirect
484. #498C2×D61semidirect
489. #486C2×D61semidirect
499. #476C2×D61semidirect
512. C61#60860semidirect

Maximal subgroups

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

subgroupindex
#214591142
C2×C4⋊Q8×D612
#214570472
#214570392
#214569722
#214569702
#214569642
#214569442
#214569362
#214563602
#214562092
#214557412
#214556312
#214544472
C61×#32272
#6086061