Finite Group Databasebeta

← #30552344

Subgroups — #30552344

Order 15616.

1788 conjugacy classes of subgroups.

The subgroup lattice has 982 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#533×D61C211yesmaximal, characteristic, complemented
2C2×#16840294C211yesmaximal, characteristic
3#21457058C214yesmaximal, complemented
4#21457048C212yesmaximal, complemented
5#21457039C212yesmaximal, complemented
6#21456997C212yesmaximal, complemented
7#21456996C212yesmaximal, complemented
8#21456985C214yesmaximal, complemented
9#21456369C212yesmaximal, complemented
10#21456203C212yesmaximal, complemented
11#21455769C212yesmaximal, complemented
12#21455757C212yesmaximal
13#21455626C211yesmaximal, characteristic, complemented
14#21455620C211yesmaximal, characteristic, complemented
15#21455616C211yesmaximal, characteristic, complemented
16#21454451C211yesmaximal, characteristic, complemented
17C61×#3077C211yesmaximal, characteristic, complemented
18#16840319C2211yescharacteristic
19#16840318C2212yescomplemented
20#16840317C2211yescharacteristic, complemented
21#16840317C2211yescharacteristic, complemented
22#16840316—21no—
23#16840316—21no—
24#16840315C2212yes—
25#16840314—21no—
26#16840314—21no—
27C4⋊Q8×D61C2211yescharacteristic, complemented
28C4⋊Q8×D61C2211yescharacteristic, complemented
29#16840294—21no—
30#16840294—21no—
31#16840294—21no—
32#16840294—21no—
33#16840294C2212yes—
34#16840294C2212yes—
35#16840294C2212yes—
36#16840294C2212yes—
37C2×#14519770—21no—
38C2×#14519768C2211yescharacteristic
39#125×D61C2212yescomplemented
40C2×#14519764C2211yescharacteristic
41C2×#14519759—21no—
42C2×#14519757C2211yescharacteristic
43C22⋊Q8×D61—21no—
44C22⋊Q8×D61—21no—
45C2×#14519748C2211yescharacteristic
46C2×C4×Dic122C2211yescharacteristic
47C4×Q8×D61—21no—
48C4×Q8×D61—21no—
49C2×C4×C22⋊D61—21no—
50C2×#14519736—21no—
51#117×D61C2212yes—
52C2×C42×D61C2211yescharacteristic
53#16840170C2214yescomplemented
54#16840169C2214yescomplemented
55#16840163C2214yescomplemented
56#16840162C2214yescomplemented
57#16840120C2214yescomplemented
58#16840120C2214yescomplemented
59#16840115C2214yescomplemented
60#16840115C2214yescomplemented
61#16840106C2214yescomplemented
62#16840105C2214yescomplemented
63#16840099C2214yescomplemented
64#16840094C2214yescomplemented
65#16840085C2214yes—
66#16840084C2214yes—
67#16840079C2214yes—
68#16840074C2214yes—
69#16840070C2214yescomplemented
70#16840066C2214yescomplemented
71#16840062C2214yescomplemented
72#16840058C2212yescomplemented
73#16840054C2212yescomplemented
74#16840052C2212yescomplemented
75#16840048C2212yescomplemented
76#16840044C2212yescomplemented
77#16840042C2212yescomplemented
78#16839818C2212yescomplemented
79#16839818C2212yescomplemented
80#16839814C2212yescomplemented
81#16839814C2212yescomplemented
82#16839805C2212yes—
83#16839804C2212yes—
84#16839802C2212yes—
85#16839786C2211yescharacteristic
86#16839772C2212yes—
87#16839770C2212yes—
88#16839767C2212yes—
89#16839725C2212yes—
90M16×Dic61C2212yes—
91C61×#533C2211yescharacteristic
92C2×C4×D4×C61C2211yescharacteristic
93C61×#478C2214yescomplemented
94C61×#476C2212yescomplemented
95C61×#474C2212yescomplemented
96C61×#428C2212yes—
97C61×#423C2211yescharacteristic
98C61×#418C2212yes—
99C22×Dic122C2311yescharacteristic
100C2×Q8×D61—21no—
101C2×Q8×D61—21no—
102C22×C22⋊D61—21no—
103C22×C4×D61D411yescharacteristic
104C22×C4×D61D411yescharacteristic
105C22×C4×D61C2311yescharacteristic
106C2×#11758194C2312yes—
107#14519777C2311yescharacteristic
108#14519777C2311yescharacteristic
109#14519776—21no—
110#14519776—21no—
111#14519776C2312yes—
112#14519776C2312yes—
113#14519775—21no—
114#14519775—21no—
115#14519770—22no—
116#14519770—22no—
117#14519770—22no—
118#14519770—22no—
119#14519769C2312yes—
120#14519768—21no—
121#14519768—21no—
122#14519768C2312yes—
123#14519768C2312yes—
124#14519768C2312yes—
125#14519768C2312yes—
126#14519767—22no—
127#14519767—22no—
128#14519764—21no—
129#14519764—21no—
130#14519764C2312yes—
131#14519764C2312yes—
132#14519759—22no—
133#14519759—22no—
134#14519759—22no—
135#14519759—22no—
136#14519757—21no—
137#14519757—21no—
138#14519757—21no—
139#14519757—21no—
140#14519757C2312yes—
141#14519757C2312yes—
142#14519756—21no—
143#14519756—21no—
144#14519755—22no—
145#14519755—22no—
146#14519754—22no—
147#14519754—22no—
148#14519753—21no—
149#14519753—21no—
150#14519748—21no—
151#14519748—21no—
152#14519748C2312yes—
153#14519748C2312yes—
154Q8×Dic61—21no—
155Q8×Dic61—21no—
156C4×Dic122—21no—
157C4×Dic122—21no—
158C4×Dic122—21no—
159C4×Dic122—21no—
160C4×Dic122—22no—
161C4×Dic122—22no—
162C4×Dic122C2312yes—
163C4×Dic122C2312yes—
164#14519742—21no—
165#14519742—21no—
166#14519742—22no—
167#14519742—22no—
168C4×C22⋊D61—22no—
169C4×C22⋊D61—22no—
170C4×C22⋊D61—22no—
171C4×C22⋊D61—22no—
172#14519736—22no—
173#14519736—22no—
174#14519736—22no—
175#14519736—22no—
176#14519736C2312yes—
177#14519735C2312yes—
178#14519735C2312yes—
179#14519734—22no—
180#14519733—22no—
181C2×C4⋊Dic61—21no—
182C2×C4⋊Dic61—21no—
183C2×C4⋊Dic61C2311yescharacteristic
184C2×#11758196—21no—
185C2×#11758196—21no—
186C4⋊C4×D61—22no—
187C4⋊C4×D61—22no—
188C4⋊C4×D61—21no—
189C4⋊C4×D61—21no—
190C4⋊C4×D61C2312yes—
191C4⋊C4×D61C2312yes—
192C2×C22⋊Dic61—21no—
193C2×C22⋊Dic61—21no—
194C2×C22⋊Dic61—21no—
195C2×#11758198—21no—
196C22⋊C4×D61—22no—
197C2×C4×Dic61—21no—
198C2×C4×Dic61D411yescharacteristic
199C2×C4×Dic61D411yescharacteristic
200C2×C4×Dic61C2311yescharacteristic
201C42×D61—22no—
202C42×D61D411yescharacteristic
203C42×D61D411yescharacteristic
204C42×D61D411yescharacteristic
205C42×D61D411yescharacteristic
206C42×D61C2311yescharacteristic
207C42×D61C2311yescharacteristic
208C42×D61C2311yescharacteristic
209C42×D61C2311yescharacteristic
210#14519711C2314yes—
211#14519710C2314yes—
212#14519710C2314yes—
213#14519709C2314yes—
214#14519708C2314yes—
215#14519708C2314yes—
216C4⋊#92418C2312yes—
217C4⋊#92418C2312yes—
218#14519702C2314yes—
219#14519702C2314yes—
220#14519700C2314yes—
221#14519700C2314yes—
222#14519698C2314yes—
223#14519698C2314yes—
224#14519689C2314yes—
225#14519689C2314yes—
226#14519687C2314yes—
227C8×Dic61C2314yes—
228C22×D4×C61C2311yescharacteristic
229C23×C4×C61—21no—
230C2×M16×C61C2312yes—
231C4⋊Q8×C61C2311yescharacteristic
232C4⋊Q8×C61C2311yescharacteristic
233#125×C61C2312yes—
234C22⋊Q8×C61—21no—
235C22⋊Q8×C61—21no—
236C4×Q8×C61—21no—
237C4×Q8×C61—21no—
238C4×D4×C61—21no—
239C4×D4×C61—21no—
240C4×D4×C61C2312yes—
241C4×D4×C61C2312yes—
242#117×C61C2312yes—
243C2×C4⋊C4×C61C2311yescharacteristic
244C2×C22⋊C4×C61—21no—
245C2×C42×C61C2311yescharacteristic
246#107×C61C2314yes—
247#106×C61C2314yes—
248C4⋊C8×C61C2312yes—
249C4⋊C8×C61C2312yes—
250#102×C61C2314yes—
251#102×C61C2314yes—
252C24×C61—21no—
253C23×D61C2×D411yescharacteristic
254C2×Q8×C61—21no—
255C2×Q8×C61—21no—
256C2×D4×C61—21no—
257C2×D4×C61—22no—
258C2×D4×C61—22no—
259C2×D4×C61C2412yes—
260C22×C4×C61—21no—
261C22×C4×C61—22no—
262C22×C4×C61—22no—
263C22×C4×C61—44no—
264C22×C4×C61C2×D411yescharacteristic
265C22×C4×C61C2×D411yescharacteristic
266C22×C4×C61C2411yescharacteristic
267C2×C22⋊D61—22no—
268C2×C22⋊D61—22no—
269C2×C22⋊D61—44no—
270C22×Dic61—21no—
271C22×Dic61—21no—
272C22×Dic61C2×D411yescharacteristic
273C22×Dic61C2×D411yescharacteristic
274C22×Dic61C2×D411yescharacteristic
275Q8×D61—44no—
276Q8×D61—44no—
277C2×C4×D61—22no—
278C2×C4×D61—22no—
279C2×C4×D61—22no—
280C2×C4×D61—22no—
281C2×C4×D61—42no—
282C2×C4×D61—42no—
283C2×C4×D61C2×D411yescharacteristic
284C2×C4×D61C2×D411yescharacteristic
285C2×C4×D61C2×D411yescharacteristic
286C2×C4×D61C2×D411yescharacteristic
287C2×C4×D61C2×D411yescharacteristic
288C2×C4×D61C2×D411yescharacteristic
289C2×C4×D61C2×D411yescharacteristic
290C2×C4×D61C2×D411yescharacteristic
291C2×C4×D61C2×D411yescharacteristic
292C2×C4×D61C2×D411yescharacteristic
293C2×C4×D61C2411yescharacteristic
294C2×C4×D61C2411yescharacteristic
295C2×Dic122—22no—
296C2×Dic122—22no—
297C2×Dic122—21no—
298C2×Dic122—21no—
299C2×Dic122—21no—
300C2×Dic122—22no—
301C2×Dic122—22no—
302C2×Dic122C2412yes—
303M16×C61—24no—
304C2×C8×C61C2414yes—
305C4⋊C4×C61—21no—
306C4⋊C4×C61—22no—
307C4⋊C4×C61—22no—
308C4⋊C4×C61—21no—
309C4⋊C4×C61—21no—
310C4⋊C4×C61C2412yes—
311C4⋊C4×C61C2412yes—
312C4⋊C4×C61C2412yes—
313C22⋊C4×C61—22no—
314C22⋊C4×C61—22no—
315C22⋊C4×C61—22no—
316C42×C61—22no—
317C42×C61C2×D411yescharacteristic
318C42×C61C2×D411yescharacteristic
319C42×C61C2411yescharacteristic
320C42×C61C2411yescharacteristic
321C22⋊Dic61—22no—
322C22⋊Dic61—22no—
323C22⋊Dic61—22no—
324C22⋊Dic61—22no—
325C22⋊Dic61—22no—
326C22⋊Dic61—22no—
327C22⋊Dic61—22no—
328#11758198—22no—
329#11758198—22no—
330#11758198—22no—
331#11758198—22no—
332C4⋊Dic61—21no—
333C4⋊Dic61—21no—
334C4⋊Dic61—21no—
335C4⋊Dic61—22no—
336C4⋊Dic61—22no—
337C4⋊Dic61—22no—
338C4⋊Dic61—22no—
339C4⋊Dic61—22no—
340C4⋊Dic61—22no—
341C4⋊Dic61C2412yes—
342C4⋊Dic61C2412yes—
343C4⋊Dic61C2412yes—
344#11758196—22no—
345#11758196—22no—
346#11758196—22no—
347#11758196—22no—
348#11758196—22no—
349#11758196—22no—
350#11758196—22no—
351#11758196—22no—
352#11758196—22no—
353#11758196—22no—
354#11758196—22no—
355#11758196—22no—
356C4×Dic61—22no—
357C4×Dic61—22no—
358C4×Dic61—22no—
359C4×Dic61—22no—
360C4×Dic61—22no—
361C4×Dic61C2×D411yescharacteristic
362C4×Dic61C2×D411yescharacteristic
363C4×Dic61C2×D411yescharacteristic
364C4×Dic61C2×D411yescharacteristic
365C4×Dic61C2×D411yescharacteristic
366C4×Dic61C2×D411yescharacteristic
367C4×Dic61C2×D411yescharacteristic
368C4×Dic61C2×D411yescharacteristic
369C4×Dic61C2×D411yescharacteristic
370C4×Dic61C2×D411yescharacteristic
371C4×Dic61C2411yescharacteristic
372C4×Dic61C2411yescharacteristic
373#11758194—24no—
374C2×#92418C2414yes—
375C23×C61—22no—
376C23×C61—42no—
377C23×C61—42no—
378C23×C61—42no—
379C23×C61C22×D411yescharacteristic
380C22×D61—22no—
381C22×D61—22no—
382C22×D61—41no—
383C22×D61C22×D411yescharacteristic
384C22×D61C22×D411yescharacteristic
385Q8×C61—42no—
386Q8×C61—42no—
387D4×C61—22no—
388D4×C61—22no—
389D4×C61—42no—
390C2×C4×C61—22no—
391C2×C4×C61—22no—
392C2×C4×C61—22no—
393C2×C4×C61—22no—
394C2×C4×C61—41no—
395C2×C4×C61—44no—
396C2×C4×C61—42no—
397C2×C4×C61—44no—
398C2×C4×C61C22×D411yescharacteristic
399C2×C4×C61C22×D411yescharacteristic
400C2×C4×C61C22×D411yescharacteristic
401C2×C4×C61C22×D411yescharacteristic
402C2×C4×C61C22×D411yescharacteristic
403C2×C4×C612−1+412yes—
404C2×C4×C612−1+412yes—
405C2×C4×C61C2511yescharacteristic
406C22⋊D61—44no—
407C22⋊D61—44no—
408C2×Dic61—22no—
409C2×Dic61—22no—
410C2×Dic61—22no—
411C2×Dic61—22no—
412C2×Dic61—22no—
413C2×Dic61—41no—
414C2×Dic61—41no—
415C2×Dic61—42no—
416C2×Dic61—42no—
417C2×Dic61C22×D411yescharacteristic
418C2×Dic61C22×D411yescharacteristic
419C2×Dic61C22×D411yescharacteristic
420C2×Dic61C22×D411yescharacteristic
421C2×Dic61C22×D411yescharacteristic
422C2×Dic61C22×D411yescharacteristic
423C4×D61—22no—
424C4×D61—22no—
425C4×D61—22no—
426C4×D61—22no—
427C4×D61—22no—
428C4×D61—22no—
429C4×D61—21no—
430C4×D61—21no—
431C4×D61—21no—
432C4×D61—21no—
433C4×D61—41no—
434C4×D61—41no—
435C4×D61—41no—
436C4×D61—41no—
437C4×D61—44no—
438C4×D61—44no—
439Dic122—22no—
440Dic122—22no—
441Dic122—44no—
442Dic122—44no—
443Dic122—42no—
444Dic122—42no—
445Dic122—42no—
446C8×C61—24no—
447#92418—24no—
448#60866—611nomaximal, Sylow
449C22×C61—21no—
450C22×C61—21no—
451C22×C61—42no—
452C22×C61—42no—
453C22×C61—42no—
454C22×C61—84no—
455C22×C61#53612yes—
456C22×C61C23×D411yescharacteristic
457C2×D61—21no—
458C2×D61—21no—
459C2×D61—21no—
460C2×D61—21no—
461C2×D61—21no—
462C2×D61—44no—
463C2×D61#57512yes—
464C4×C61—21no—
465C4×C61—21no—
466C4×C61—21no—
467C4×C61—42no—
468C4×C61—42no—
469C4×C61—42no—
470C4×C61#53612yes—
471C4×C61#57512yes—
472C4×C61C2×2−1+411yescharacteristic
473C4×C61C2×2−1+411yescharacteristic
474Dic61—21no—
475Dic61—21no—
476Dic61—21no—
477Dic61—21no—
478Dic61—21no—
479Dic61—21no—
480Dic61—42no—
481Dic61—42no—
482Dic61—42no—
483Dic61—42no—
484C2×#533—611no—
485C2×#529—611no—
486#3240—614no—
487#3239—612no—
488#3238—612no—
489#3233—612no—
490#3233—612no—
491#3232—614no—
492#3166—612no—
493#3140—612no—
494#3095—612no—
495#3094—612no—
496#3078—611no—
497#3078—611no—
498#3077—611no—
499#3077D6111yescharacteristic, complemented
500#2920—611no—
501C2×C61—22no—
502C2×C61—82no—
503C2×C61C2×#53611yescharacteristic
504C2×C61C2×#57511yescharacteristic
505C2×C61C2×#57511yescharacteristic
506D61—22no—
507D61—41no—
508#533—611no—
509#533—611no—
510#533—612no—
511#533—612no—
512#533—611no—
513#533—1221no—
514#533—1221no—
515#533—1221no—
516#533—1221no—
517#533C2×D6111yescharacteristic
518C2×C4⋊Q8—611no—
519C2×C4⋊Q8—611no—
520#529—612no—
521#529—612no—
522#529—612no—
523#529—612no—
524#529—1221no—
525#529—1221no—
526#529—1221no—
527#529—1221no—
528C2×#126—1221no—
529C2×#125—612no—
530C2×#125—611no—
531C2×#124—611no—
532C2×#123—1221no—
533C2×C22⋊Q8—611no—
534C2×C22⋊Q8—1221no—
535C2×C22⋊Q8—1221no—
536C2×#121—611no—
537C2×C4×Q8—611no—
538C2×C4×Q8—1221no—
539C2×C4×Q8—1221no—
540C2×C4×D4—1221no—
541C2×C4×D4C2×D6111yescharacteristic
542C2×#117—612no—
543C2×#117—1221no—
544C22×C42—611no—
545#501—614no—
546#501—614no—
547#499—614no—
548#499—614no—
549#489—614no—
550#489—614no—
551#488—614no—
552#488—614no—
553#485—614no—
554#485—614no—
555#484—614no—
556#483—614no—
557#482—614no—
558#482—614no—
559#481—614no—
560#480—614no—
561#479—614no—
562#479—614no—
563#478—614no—
564#478C2×D6114yescomplemented
565#477—612no—
566#477—612no—
567#476—612no—
568#476C2×D6112yescomplemented
569#475—612no—
570#475—612no—
571#474—612no—
572#474C2×D6112yescomplemented
573#432—612no—
574#432—612no—
575#431—612no—
576#431—612no—
577#428—612no—
578#428—612no—
579#428—612no—
580#428C2×D6112yes—
581#423—611no—
582#423C2×D6111yescharacteristic
583#419—612no—
584#419—612no—
585#418—612no—
586#418C2×D6112yes—
587#407—612no—
588C4×M16—612no—
589C61#6086611yescharacteristic, complemented, Sylow
590C22×Q8—611no—
591C22×Q8—1221no—
592C22×Q8—1221no—
593C22×D4—1221no—
594C22×D4C22×D6111yescharacteristic
595C23×C4—21no—
596C23×C4—611no—
597C23×C4—611no—
598C23×C4—611no—
599C2×M16—612no—
600C2×M16C22×D6112yes—
601C4⋊Q8—612no—
602C4⋊Q8—612no—
603C4⋊Q8—611no—
604C4⋊Q8—611no—
605C4⋊Q8—1221no—
606C4⋊Q8—1221no—
607C4⋊Q8—1221no—
608C4⋊Q8—1221no—
609C4⋊Q8C22×D6111yescharacteristic
610C4⋊Q8C22×D6111yescharacteristic
611#126—1222no—
612#126—1222no—
613#126—1222no—
614#126—1222no—
615#125—612no—
616#125—612no—
617#125—612no—
618#125—612no—
619#125—612no—
620#125—1221no—
621#125—1221no—
622#125—1222no—
623#125—1222no—
624#125C22×D6112yes—
625#124—612no—
626#124—612no—
627#124—1221no—
628#124—1221no—
629#123—1222no—
630#123—1222no—
631#123—1222no—
632#123—1222no—
633C22⋊Q8—21no—
634C22⋊Q8—21no—
635C22⋊Q8—612no—
636C22⋊Q8—612no—
637C22⋊Q8—1222no—
638C22⋊Q8—1222no—
639C22⋊Q8—1221no—
640C22⋊Q8—1221no—
641C22⋊Q8—1222no—
642C22⋊Q8—1222no—
643C22⋊Q8—1221no—
644C22⋊Q8—1221no—
645C22⋊Q8—1221no—
646C22⋊Q8—1221no—
647C22⋊Q8—1221no—
648C22⋊Q8—1221no—
649#121—612no—
650#121—612no—
651#121—1221no—
652#121—1221no—
653C4×Q8—21no—
654C4×Q8—21no—
655C4×Q8—612no—
656C4×Q8—612no—
657C4×Q8—1222no—
658C4×Q8—1222no—
659C4×Q8—1222no—
660C4×Q8—1221no—
661C4×Q8—1222no—
662C4×Q8—1221no—
663C4×Q8—1221no—
664C4×Q8—1221no—
665C4×Q8—1221no—
666C4×Q8—1221no—
667C4×Q8—1221no—
668C4×Q8—1221no—
669C4×D4—21no—
670C4×D4—21no—
671C4×D4—1222no—
672C4×D4—1222no—
673C4×D4—1222no—
674C4×D4—1222no—
675C4×D4C22×D6112yes—
676C4×D4C22×D6112yes—
677#117—612no—
678#117—612no—
679#117—612no—
680#117—1222no—
681#117—1222no—
682#117—1222no—
683#117—1222no—
684#117—1222no—
685#117—1222no—
686#117C22×D6112yes—
687C2×C4⋊C4—611no—
688C2×C4⋊C4—612no—
689C2×C4⋊C4—612no—
690C2×C4⋊C4—1222no—
691C2×C4⋊C4—1222no—
692C2×C4⋊C4—1221no—
693C2×C4⋊C4—1221no—
694C2×C4⋊C4—1221no—
695C2×C4⋊C4—1221no—
696C2×C4⋊C4—1221no—
697C2×C4⋊C4—1221no—
698C2×C4⋊C4C22×D6111yescharacteristic
699C2×C22⋊C4—21no—
700C2×C22⋊C4—1222no—
701C2×C22⋊C4—1221no—
702C2×C22⋊C4—1221no—
703C2×C22⋊C4—1221no—
704C2×C22⋊C4—1221no—
705C2×C42—611no—
706C2×C42—611no—
707C2×C42—611no—
708C2×C42—611no—
709C2×C42—611no—
710C2×C42—611no—
711C2×C42—611no—
712C2×C42—611no—
713C2×C42—611no—
714C2×C42—611no—
715C2×C42—611no—
716C2×C42—1222no—
717C2×C42—1221no—
718C2×C42C22×D6111yescharacteristic
719#107—614no—
720#107—614no—
721#107—614no—
722#107C22×D6114yes—
723#106—614no—
724#106—614no—
725#106—614no—
726#106C22×D6114yes—
727C4⋊C8—612no—
728C4⋊C8—612no—
729C4⋊C8C22×D6112yes—
730C4⋊C8C22×D6112yes—
731#103—614no—
732#103—614no—
733#103—614no—
734#103—614no—
735#102—614no—
736#102—614no—
737#102C22×D6114yes—
738#102C22×D6114yes—
739C22⋊C8—614no—
740C22⋊C8—614no—
741#97—614no—
742C4×C8—614no—
743C24—21no—
744C24—611no—
745C2×Q8—21no—
746C2×Q8—21no—
747C2×Q8—612no—
748C2×Q8—1222no—
749C2×Q8—1222no—
750C2×Q8—1221no—
751C2×Q8—1221no—
752C2×Q8—1221no—
753C2×Q8—1222no—
754C2×Q8—1222no—
755C2×Q8—2444no—
756C2×Q8—2444no—
757C2×D4—21no—
758C2×D4—22no—
759C2×D4—22no—
760C2×D4—1222no—
761C2×D4—1222no—
762C2×D4—2444no—
763C2×D4C23×D6112yes—
764C22×C4—21no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—44no—
768C22×C4—611no—
769C22×C4—611no—
770C22×C4—611no—
771C22×C4—611no—
772C22×C4—611no—
773C22×C4—611no—
774C22×C4—611no—
775C22×C4—611no—
776C22×C4—611no—
777C22×C4—611no—
778C22×C4—611no—
779C22×C4—611no—
780C22×C4—611no—
781C22×C4—611no—
782C22×C4—611no—
783C22×C4—1222no—
784C22×C4—1222no—
785C22×C4—1222no—
786C22×C4—1222no—
787C22×C4—1221no—
788C22×C4—1221no—
789C22×C4—2442no—
790C22×C4—2442no—
791C22×C4D4×D6111yescharacteristic
792C22×C4D4×D6111yescharacteristic
793C22×C4C23×D6111yescharacteristic
794M16—24no—
795M16—1224no—
796C2×C8—614no—
797C2×C8C23×D6114yes—
798C4⋊C4—22no—
799C4⋊C4—22no—
800C4⋊C4—21no—
801C4⋊C4—21no—
802C4⋊C4—21no—
803C4⋊C4—612no—
804C4⋊C4—612no—
805C4⋊C4—612no—
806C4⋊C4—1222no—
807C4⋊C4—1222no—
808C4⋊C4—1222no—
809C4⋊C4—1222no—
810C4⋊C4—1222no—
811C4⋊C4—1222no—
812C4⋊C4—1222no—
813C4⋊C4—1222no—
814C4⋊C4—1222no—
815C4⋊C4—1222no—
816C4⋊C4—1222no—
817C4⋊C4—1222no—
818C4⋊C4—1222no—
819C4⋊C4—1222no—
820C4⋊C4—1221no—
821C4⋊C4—1222no—
822C4⋊C4—1222no—
823C4⋊C4—1222no—
824C4⋊C4—1222no—
825C4⋊C4—1221no—
826C4⋊C4—1221no—
827C4⋊C4C23×D6112yes—
828C4⋊C4C23×D6112yes—
829C4⋊C4C23×D6112yes—
830C22⋊C4—22no—
831C22⋊C4—22no—
832C22⋊C4—22no—
833C22⋊C4—1222no—
834C22⋊C4—1222no—
835C22⋊C4—1222no—
836C22⋊C4—1222no—
837C22⋊C4—1222no—
838C22⋊C4—1222no—
839C22⋊C4—1222no—
840C22⋊C4—1222no—
841C22⋊C4—1222no—
842C22⋊C4—1222no—
843C22⋊C4—1222no—
844C42—22no—
845C42—611no—
846C42—611no—
847C42—611no—
848C42—611no—
849C42—611no—
850C42—611no—
851C42—611no—
852C42—611no—
853C42—611no—
854C42—611no—
855C42—611no—
856C42—611no—
857C42—1222no—
858C42—1222no—
859C42—1222no—
860C42—1222no—
861C42—1222no—
862C42D4×D6111yescharacteristic
863C42D4×D6111yescharacteristic
864C42C23×D6111yescharacteristic
865C42C23×D6111yescharacteristic
866C23—22no—
867C23—42no—
868C23—42no—
869C23—42no—
870C23—611no—
871C23—611no—
872C23—1222no—
873C23—1222no—
874C23—2441no—
875C23C2×D4×D6111yescharacteristic
876Q8—42no—
877Q8—42no—
878Q8—1222no—
879Q8—1222no—
880Q8—2442no—
881Q8—2444no—
882Q8—2444no—
883Q8—2442no—
884Q8—2442no—
885D4—22no—
886D4—22no—
887D4—42no—
888D4—2444no—
889D4—2444no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—41no—
895C2×C4—44no—
896C2×C4—42no—
897C2×C4—44no—
898C2×C4—611no—
899C2×C4—611no—
900C2×C4—611no—
901C2×C4—611no—
902C2×C4—611no—
903C2×C4—611no—
904C2×C4—1222no—
905C2×C4—1222no—
906C2×C4—1222no—
907C2×C4—1222no—
908C2×C4—1222no—
909C2×C4—1222no—
910C2×C4—1222no—
911C2×C4—1221no—
912C2×C4—1221no—
913C2×C4—1221no—
914C2×C4—1221no—
915C2×C4—1222no—
916C2×C4—1222no—
917C2×C4—1222no—
918C2×C4—1222no—
919C2×C4—2441no—
920C2×C4—2441no—
921C2×C4—2441no—
922C2×C4—2441no—
923C2×C4—2444no—
924C2×C4—2444no—
925C2×C4—2441no—
926C2×C4—2441no—
927C2×C4—2442no—
928C2×C4—2442no—
929C2×C4C2×D4×D6111yescharacteristic
930C2×C4C2×D4×D6111yescharacteristic
931C2×C4C2×D4×D6111yescharacteristic
932C2×C4C2×D4×D6111yescharacteristic
933C2×C4C2×D4×D6111yescharacteristic
934C2×C4#1451982412yes—
935C2×C4#1451982512yes—
936C2×C4C24×D6111yescharacteristic
937C8—24no—
938C8—1224no—
939C22—21no—
940C22—21no—
941C22—42no—
942C22—42no—
943C22—42no—
944C22—84no—
945C22—612no—
946C22—1221no—
947C22—1221no—
948C22—1221no—
949C22—1221no—
950C22—1221no—
951C22—2444no—
952C22#1684033512yes—
953C22C22×D4×D6111yescharacteristic
954C4—21no—
955C4—21no—
956C4—21no—
957C4—42no—
958C4—42no—
959C4—42no—
960C4—1221no—
961C4—1221no—
962C4—1221no—
963C4—1221no—
964C4—1221no—
965C4—1221no—
966C4—2442no—
967C4—2442no—
968C4—2442no—
969C4—2442no—
970C4#1684033512yes—
971C4#1684055812yes—
972C4C2×#1451982411yescharacteristic
973C4C2×#1451982511yescharacteristic
974C2—22no—
975C2—82no—
976C2—1222no—
977C2—2441no—
978C2C2×#1684033511yescharacteristic
979C2#575×D6111yescharacteristic
980C2C2×#1684055811yescharacteristic
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3077C2
socleC22×C61C23×D4
prime radicalC2×#14519748C22
hypercenter#3077D61
hypocenterC61#60866
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3077

Complements

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

NH ≅ G/Ntype
1. #533×D61C2semidirect
3. #21457058C2semidirect
4. #21457048C2semidirect
5. #21457039C2semidirect
6. #21456997C2semidirect
7. #21456996C2semidirect
8. #21456985C2semidirect
9. #21456369C2semidirect
10. #21456203C2semidirect
11. #21455769C2semidirect
13. #21455626C2semidirect
14. #21455620C2semidirect
15. #21455616C2semidirect
16. #21454451C2semidirect
17. C61×#3077C2semidirect
19. #16840318C22semidirect
20. #16840317C22semidirect
21. #16840317C22semidirect
27. C4⋊Q8×D61C22semidirect
28. C4⋊Q8×D61C22semidirect
39. #125×D61C22semidirect
53. #16840170C22semidirect
54. #16840169C22semidirect
55. #16840163C22semidirect
56. #16840162C22semidirect
57. #16840120C22semidirect
58. #16840120C22semidirect
59. #16840115C22semidirect
60. #16840115C22semidirect
61. #16840106C22semidirect
62. #16840105C22semidirect
63. #16840099C22semidirect
64. #16840094C22semidirect
69. #16840070C22semidirect
70. #16840066C22semidirect
71. #16840062C22semidirect
72. #16840058C22semidirect
73. #16840054C22semidirect
74. #16840052C22semidirect
75. #16840048C22semidirect
76. #16840044C22semidirect
77. #16840042C22semidirect
78. #16839818C22semidirect
79. #16839818C22semidirect
80. #16839814C22semidirect
81. #16839814C22semidirect
93. C61×#478C22semidirect
94. C61×#476C22semidirect
95. C61×#474C22semidirect
499. #3077D61semidirect
564. #478C2×D61semidirect
568. #476C2×D61semidirect
572. #474C2×D61semidirect
589. C61#60866semidirect

Maximal subgroups

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

subgroupindex
#533×D612
C2×#168402942
#214570582
#214570482
#214570392
#214569972
#214569962
#214569852
#214563692
#214562032
#214557692
#214557572
#214556262
#214556202
#214556162
#214544512
C61×#30772
#6086661