Finite Group Databasebeta

← #30548429

Subgroups — #30548429

Order 15616.

2138 conjugacy classes of subgroups.

The subgroup lattice has 1026 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#21455989C214yesmaximal, complemented
4#21455948C212yesmaximal, complemented
5#21455940C212yesmaximal, complemented
6#21455898C214yesmaximal, complemented
7#21455857C212yesmaximal, complemented
8#21455849C212yesmaximal, complemented
9#21455740C212yesmaximal, complemented
10#21455626C211yesmaximal, characteristic, complemented
11#21455624C211yesmaximal, characteristic, complemented
12#21455287C211yesmaximal, characteristic, complemented
13#21455051C212yesmaximal, complemented
14#21454643C212yesmaximal, complemented
15#137×Dic61C212yesmaximal, complemented
16#21454451C211yesmaximal, characteristic, complemented
17C61×#3037C211yesmaximal, characteristic, complemented
18C22×Q8×D61C2211yescharacteristic
19C2×#14519807C2212yes—
20#16840319C2211yescharacteristic
21#16840317C2211yescharacteristic
22#16840317C2211yescharacteristic
23#16840310C2211yescharacteristic
24#16840310C2211yescharacteristic
25#16840294—21no—
26#16840294—21no—
27#16840293—21no—
28#16840293—21no—
29#16840291C2212yes—
30#16840291C2212yes—
31#16840272—21no—
32#16840272—21no—
33#16840269C2212yes—
34#41×Dic61C2212yes—
35C4×#11758224—21no—
36C4×#11758224—21no—
37C2×Q8×Dic61C2211yescharacteristic
38C2×C4×Dic122—21no—
39C2×C4×Dic122C2211yescharacteristic
40C2×#14519742—21no—
41C2×#14519742C2211yescharacteristic
42C4×Q8×D61—21no—
43C4×Q8×D61—21no—
44C4×Q8×D61—21no—
45C4×Q8×D61—21no—
46C4×Q8×D61C2212yes—
47C4×Q8×D61C2212yes—
48C4×Q8×D61C2212yes—
49C4×Q8×D61C2212yes—
50C2×C4⋊C4×D61—21no—
51C2×C4⋊C4×D61C2211yescharacteristic
52C2×C42×D61—21no—
53C2×C42×D61C2211yescharacteristic
54#16840096C2214yes—
55#16840091C2214yes—
56#16840079C2214yes—
57#16840074C2214yes—
58#16840070C2214yescomplemented
59#16840069C2214yescomplemented
60#16840058C2212yescomplemented
61#16840057C2212yescomplemented
62#16840048C2212yescomplemented
63#16840047C2212yescomplemented
64#16839981C2214yescomplemented
65#16839969C2212yescomplemented
66#16839959C2212yescomplemented
67#16839916C2214yes—
68#16839916C2214yes—
69#16839899C2214yes—
70#16839899C2214yes—
71#16839869C2214yescomplemented
72#16839866C2214yescomplemented
73#16839863C2214yescomplemented
74#16839859C2214yescomplemented
75Q16×Dic61C2214yescomplemented
76#16839854C2214yescomplemented
77#16839853C2214yescomplemented
78SD16×Dic61C2214yescomplemented
79#16839818C2212yes—
80#16839818C2212yes—
81#16839814C2212yes—
82#16839814C2212yes—
83#16839804C2212yes—
84#16839802C2212yes—
85#16839786C2211yescharacteristic
86#16839772C2212yes—
87#16839771C2212yes—
88#16839763C2212yes—
89#16839725C2212yes—
90M16×Dic61C2212yes—
91C2×#137×C61C2212yes—
92C61×#532C2211yescharacteristic
93C2×C4×Q8×C61C2211yescharacteristic
94C61×#464C2214yescomplemented
95C61×#462C2212yescomplemented
96C61×#460C2212yescomplemented
97C61×#423C2211yescharacteristic
98C61×#417C2212yes—
99C2×#11758224—21no—
100C2×#11758224—21no—
101C22×Dic122—21no—
102C22×Dic122C2311yescharacteristic
103C2×Q8×D61—24no—
104C2×Q8×D61—21no—
105C2×Q8×D61—21no—
106C2×Q8×D61—24no—
107C2×Q8×D61C2312yes—
108C2×Q8×D61C2312yes—
109C22×C4×D61—21no—
110C22×C4×D61—21no—
111C22×C4×D61D411yescharacteristic
112C22×C4×D61D411yescharacteristic
113C22×C4×D61C2311yescharacteristic
114#14519807—28no—
115C2×#11758202C2314yes—
116C2×#11758200C2314yes—
117C2×#11758194C2312yes—
118#14519777C2311yescharacteristic
119#14519777C2311yescharacteristic
120#14519770—22no—
121#14519770—22no—
122#14519769C2312yes—
123#14519768—21no—
124#14519768—21no—
125#14519764—21no—
126#14519764—21no—
127#14519759—22no—
128#14519759—22no—
129#14519758—22no—
130#14519757—21no—
131#14519757—21no—
132#14519756—21no—
133#14519756—21no—
134#14519753C2312yes—
135#14519753C2312yes—
136#14519748—21no—
137#14519748—21no—
138#14519748C2312yes—
139#14519748C2312yes—
140#14519745—22no—
141Q8×Dic61—21no—
142Q8×Dic61—21no—
143Q8×Dic61C2312yes—
144Q8×Dic61C2312yes—
145Q8×Dic61C2312yes—
146Q8×Dic61C2312yes—
147C4×Dic122—21no—
148C4×Dic122—21no—
149C4×Dic122—21no—
150C4×Dic122—21no—
151C4×Dic122—22no—
152C4×Dic122—22no—
153C4×Dic122—22no—
154C4×Dic122—22no—
155C4×Dic122C2312yes—
156C4×Dic122C2312yes—
157#14519742—21no—
158#14519742—21no—
159#14519742—22no—
160#14519742—22no—
161#14519742—22no—
162#14519742—22no—
163#14519742—21no—
164#14519742—21no—
165#14519742C2312yes—
166#14519742C2312yes—
167D4×Dic61—22no—
168D4×Dic61—22no—
169D4×Dic61—21no—
170D4×Dic61—21no—
171D4×Dic61C2312yes—
172D4×Dic61C2312yes—
173C4×C22⋊D61—22no—
174C4×C22⋊D61—22no—
175#14519737—22no—
176#14519737—22no—
177#14519736—22no—
178#14519736C2312yes—
179#14519735—21no—
180#14519735—21no—
181#14519733—22no—
182#14519733—22no—
183C2×C4⋊Dic61—21no—
184C2×C4⋊Dic61C2311yescharacteristic
185C2×#11758196—21no—
186C2×#11758196—21no—
187C2×#11758196—21no—
188C4⋊C4×D61—22no—
189C4⋊C4×D61—22no—
190C4⋊C4×D61—22no—
191C4⋊C4×D61—22no—
192C4⋊C4×D61—21no—
193C4⋊C4×D61—21no—
194C4⋊C4×D61C2312yes—
195C4⋊C4×D61C2312yes—
196C2×C4×Dic61—21no—
197C2×C4×Dic61—21no—
198C2×C4×Dic61—21no—
199C2×C4×Dic61—22no—
200C2×C4×Dic61D411yescharacteristic
201C2×C4×Dic61D411yescharacteristic
202C2×C4×Dic61C2311yescharacteristic
203C42×D61—22no—
204C42×D61—22no—
205C42×D61—22no—
206C42×D61—22no—
207C42×D61D411yescharacteristic
208C42×D61D411yescharacteristic
209C42×D61D411yescharacteristic
210C42×D61D411yescharacteristic
211C42×D61C2311yescharacteristic
212C42×D61C2311yescharacteristic
213C42×D61C2311yescharacteristic
214C42×D61C2311yescharacteristic
215#14519711C2314yes—
216#14519710C2314yes—
217#14519709C2314yes—
218#14519708C2314yes—
219C4⋊#92418C2312yes—
220C4⋊#92418C2312yes—
221#14519702C2314yes—
222#14519702C2314yes—
223#14519701C2314yes—
224#14519701C2314yes—
225#14519701C2314yes—
226#14519698C2314yes—
227#14519689C2314yes—
228#14519689C2314yes—
229#14519687C2314yes—
230C8×Dic61C2314yes—
231C2×#41×C61C2312yes—
232C22×Q8×C61C2311yescharacteristic
233#137×C61—28no—
234C2×Q16×C61C2314yes—
235C2×SD16×C61C2314yes—
236C2×M16×C61C2312yes—
237C4⋊Q8×C61C2311yescharacteristic
238#127×C61C2311yescharacteristic
239#124×C61C2312yes—
240#121×C61—21no—
241#121×C61—21no—
242C4×Q8×C61—21no—
243C4×Q8×C61—21no—
244C4×Q8×C61C2312yes—
245C4×Q8×C61C2312yes—
246C4×D4×C61—21no—
247C4×D4×C61—21no—
248C2×C4⋊C4×C61—21no—
249C2×C4⋊C4×C61C2311yescharacteristic
250C2×C42×C61—21no—
251C2×C42×C61C2311yescharacteristic
252C4⋊C8×C61C2312yes—
253C4⋊C8×C61C2312yes—
254#103×C61C2314yes—
255#102×C61C2314yes—
256C23×D61C2×D411yescharacteristic
257#41×C61—24no—
258#41×C61—24no—
259C2×Q8×C61—21no—
260C2×Q8×C61—22no—
261C2×Q8×C61#4114yescomplemented
262C2×Q8×C61C2412yes—
263C2×Q8×C61C2412yes—
264C2×D4×C61—22no—
265C2×D4×C61—21no—
266C2×D4×C61—21no—
267C2×D4×C61C2412yes—
268C22×C4×C61—21no—
269C22×C4×C61—21no—
270C22×C4×C61—22no—
271C22×C4×C61C2×D411yescharacteristic
272C22×C4×C61C2×D411yescharacteristic
273C22×C4×C61C2411yescharacteristic
274C2×C22⋊D61—22no—
275C2×C22⋊D61—22no—
276C22×Dic61—21no—
277C22×Dic61—21no—
278C22×Dic61—22no—
279C22×Dic61—22no—
280C22×Dic61C2×D411yescharacteristic
281C22×Dic61C2×D411yescharacteristic
282C22×Dic61C2×D411yescharacteristic
283Q8×D61—28no—
284Q8×D61—28no—
285Q8×D61—24no—
286Q8×D61—24no—
287Q8×D61—24no—
288Q8×D61—24no—
289#11758224—44no—
290#11758224—44no—
291C2×C4×D61—28no—
292C2×C4×D61—22no—
293C2×C4×D61—22no—
294C2×C4×D61—22no—
295C2×C4×D61—22no—
296C2×C4×D61—24no—
297C2×C4×D61—22no—
298C2×C4×D61—22no—
299C2×C4×D61—42no—
300C2×C4×D61—44no—
301C2×C4×D61C2×D411yescharacteristic
302C2×C4×D61C2×D411yescharacteristic
303C2×C4×D61C2×D411yescharacteristic
304C2×C4×D61C2×D411yescharacteristic
305C2×C4×D61C2×D411yescharacteristic
306C2×C4×D61C2×D411yescharacteristic
307C2×C4×D61C2×D411yescharacteristic
308C2×C4×D61C2×D411yescharacteristic
309C2×C4×D61C2×D411yescharacteristic
310C2×C4×D61C2×D411yescharacteristic
311C2×C4×D61C2411yescharacteristic
312C2×C4×D61C2411yescharacteristic
313C2×Dic122—28no—
314C2×Dic122—21no—
315C2×Dic122—22no—
316C2×Dic122—22no—
317C2×Dic122—22no—
318C2×Dic122—21no—
319C2×Dic122—21no—
320C2×Dic122#4114yescomplemented
321C2×Dic122C2412yes—
322Q16×C61—28no—
323SD16×C61—28no—
324M16×C61—24no—
325C2×C8×C61C2414yes—
326C4⋊C4×C61—22no—
327C4⋊C4×C61—22no—
328C4⋊C4×C61—21no—
329C4⋊C4×C61—21no—
330C4⋊C4×C61—21no—
331C4⋊C4×C61C2412yes—
332C22⋊C4×C61—22no—
333C22⋊C4×C61—22no—
334C42×C61—22no—
335C42×C61—22no—
336C42×C61C2×D411yescharacteristic
337C42×C61C2×D411yescharacteristic
338C42×C61C2411yescharacteristic
339C42×C61C2411yescharacteristic
340C22⋊Dic61—22no—
341C22⋊Dic61—22no—
342C22⋊Dic61—22no—
343C22⋊Dic61—22no—
344C22⋊Dic61—22no—
345#11758202—28no—
346#11758200—28no—
347#11758198—22no—
348#11758198—22no—
349C4⋊Dic61—21no—
350C4⋊Dic61—21no—
351C4⋊Dic61—21no—
352C4⋊Dic61—22no—
353C4⋊Dic61—22no—
354C4⋊Dic61—22no—
355C4⋊Dic61—22no—
356C4⋊Dic61C2412yes—
357C4⋊Dic61C2412yes—
358C4⋊Dic61C2412yes—
359#11758196—22no—
360#11758196—22no—
361#11758196—22no—
362#11758196—22no—
363#11758196—22no—
364#11758196—22no—
365#11758196—22no—
366#11758196—22no—
367#11758196—22no—
368#11758196—22no—
369C4×Dic61—22no—
370C4×Dic61—22no—
371C4×Dic61—22no—
372C4×Dic61—22no—
373C4×Dic61—22no—
374C4×Dic61—22no—
375C4×Dic61—22no—
376C4×Dic61—22no—
377C4×Dic61—22no—
378C4×Dic61C2×D411yescharacteristic
379C4×Dic61C2×D411yescharacteristic
380C4×Dic61C2×D411yescharacteristic
381C4×Dic61C2×D411yescharacteristic
382C4×Dic61C2×D411yescharacteristic
383C4×Dic61C2×D411yescharacteristic
384C4×Dic61C2×D411yescharacteristic
385C4×Dic61C2×D411yescharacteristic
386C4×Dic61C2×D411yescharacteristic
387C4×Dic61C2×D411yescharacteristic
388C4×Dic61C2411yescharacteristic
389C4×Dic61C2411yescharacteristic
390#11758194—24no—
391C2×#92418C2414yes—
392C23×C61—22no—
393C23×C61C22×D411yescharacteristic
394C22×D61—22no—
395C22×D61—22no—
396C22×D61—22no—
397C22×D61C22×D411yescharacteristic
398C22×D61C22×D411yescharacteristic
399Q8×C61—24no—
400Q8×C61—22no—
401Q8×C61—22no—
402Q8×C61—22no—
403Q8×C61C2×#4114yes—
404D4×C61—22no—
405D4×C61—22no—
406D4×C61—42no—
407D4×C61—44no—
408D4×C61—42no—
409C2×C4×C61—24no—
410C2×C4×C61—22no—
411C2×C4×C61—22no—
412C2×C4×C61—22no—
413C2×C4×C61—22no—
414C2×C4×C61—41no—
415C2×C4×C61—42no—
416C2×C4×C61—44no—
417C2×C4×C61C22×D411yescharacteristic
418C2×C4×C61C22×D411yescharacteristic
419C2×C4×C61C22×D411yescharacteristic
420C2×C4×C61C22×D411yescharacteristic
421C2×C4×C61C22×D411yescharacteristic
422C2×C4×C61C2×#4112yes—
423C2×C4×C61C2×#4112yes—
424C2×C4×C61C2511yescharacteristic
425C22⋊D61—44no—
426C22⋊D61—44no—
427C2×Dic61—22no—
428C2×Dic61—24no—
429C2×Dic61—22no—
430C2×Dic61—22no—
431C2×Dic61—22no—
432C2×Dic61—22no—
433C2×Dic61—22no—
434C2×Dic61—41no—
435C2×Dic61—44no—
436C2×Dic61—42no—
437C2×Dic61—44no—
438C2×Dic61C22×D411yescharacteristic
439C2×Dic61C22×D411yescharacteristic
440C2×Dic61C22×D411yescharacteristic
441C2×Dic61C22×D411yescharacteristic
442C2×Dic61C22×D411yescharacteristic
443C2×Dic61C22×D411yescharacteristic
444C4×D61—28no—
445C4×D61—28no—
446C4×D61—22no—
447C4×D61—22no—
448C4×D61—22no—
449C4×D61—22no—
450C4×D61—22no—
451C4×D61—22no—
452C4×D61—21no—
453C4×D61—21no—
454C4×D61—21no—
455C4×D61—21no—
456C4×D61—22no—
457C4×D61—41no—
458C4×D61—41no—
459C4×D61—44no—
460C4×D61—44no—
461C4×D61#13714yescomplemented
462Dic122—28no—
463Dic122—28no—
464Dic122—24no—
465Dic122—22no—
466Dic122—42no—
467Dic122—42no—
468Dic122C2×#4114yes—
469C8×C61—24no—
470#92418—24no—
471#60560—611nomaximal, Sylow
472C22×C61—21no—
473C22×C61—21no—
474C22×C61—42no—
475C22×C61—42no—
476C22×C61—42no—
477C22×C61#52512yes—
478C22×C61C23×D411yescharacteristic
479C2×D61—28no—
480C2×D61—21no—
481C2×D61—21no—
482C2×D61—21no—
483C2×D61—21no—
484C2×D61C2×#13712yes—
485C2×D61#57512yes—
486C4×C61—24no—
487C4×C61—21no—
488C4×C61—21no—
489C4×C61—21no—
490C4×C61—42no—
491C4×C61—42no—
492C4×C61#52512yes—
493C4×C61C2×#13712yes—
494C4×C61C22×#4111yescharacteristic
495C4×C61C22×#4111yescharacteristic
496Dic61—21no—
497Dic61—21no—
498Dic61—24no—
499Dic61—21no—
500Dic61—21no—
501Dic61—21no—
502Dic61—42no—
503Dic61—42no—
504Dic61—42no—
505Dic61C2×#13712yes—
506#3444—611no—
507C22×C4×Q8—611no—
508#3117—614no—
509#3113—612no—
510#3112—612no—
511#3108—614no—
512#3104—612no—
513#3103—612no—
514#3092—612no—
515#3078—611no—
516#3078—611no—
517#3037—611no—
518#3037D6111yescharacteristic, complemented
519#3004—612no—
520C4×#137—612no—
521C4×#137—612no—
522#2920—611no—
523C2×C61—22no—
524C2×C61—82no—
525C2×C61C2×#52511yescharacteristic
526C2×C61C22×#13711yescharacteristic
527C2×C61C2×#57511yescharacteristic
528D61—22no—
529D61—22no—
530C23×Q8—611no—
531C2×#137—612no—
532C2×#137C2×D6112yes—
533#533—611no—
534#533—611no—
535#533—611no—
536#532—611no—
537#532—611no—
538#532C2×D6111yescharacteristic
539#529—612no—
540#529—612no—
541#529—1221no—
542#529—1221no—
543#529—1221no—
544#529—1221no—
545#525—612no—
546#525—1221no—
547#525—1221no—
548C4×#41—612no—
549C4×#41—1221no—
550C4×#41—1221no—
551C2×C4×Q8—611no—
552C2×C4×Q8—612no—
553C2×C4×Q8—612no—
554C2×C4×Q8—612no—
555C2×C4×Q8—612no—
556C2×C4×Q8—611no—
557C2×C4×Q8—611no—
558C2×C4×Q8—1221no—
559C2×C4×Q8—1221no—
560C2×C4×Q8—1221no—
561C2×C4×Q8—1221no—
562C2×C4×Q8—1221no—
563C2×C4×Q8—1221no—
564C2×C4×Q8C2×D6111yescharacteristic
565C22×C4⋊C4—611no—
566C22×C4⋊C4—1221no—
567C22×C42—611no—
568C22×C42—1221no—
569#484—614no—
570#483—614no—
571#481—614no—
572#480—614no—
573#479—614no—
574#479—614no—
575#477—612no—
576#477—612no—
577#475—612no—
578#475—612no—
579#464—614no—
580#464C2×D6114yescomplemented
581#462—612no—
582#462C2×D6112yescomplemented
583#460—612no—
584#460C2×D6112yescomplemented
585#451—614no—
586#451—614no—
587#448—614no—
588#448—614no—
589#441—614no—
590#441—614no—
591#440—614no—
592#440—614no—
593C4×Q16—614no—
594C4×Q16—614no—
595C4×SD16—614no—
596C4×SD16—614no—
597#432—612no—
598#432—612no—
599#431—612no—
600#431—612no—
601#428—612no—
602#428—612no—
603#423—611no—
604#423C2×D6111yescharacteristic
605#419—612no—
606#419—612no—
607#417—612no—
608#417C2×D6112yes—
609#407—612no—
610C4×M16—612no—
611C61#6056011yescharacteristic, complemented, Sylow
612C2×#41—1221no—
613C2×#41—1221no—
614C2×#41C22×D6112yes—
615C22×Q8—612no—
616C22×Q8—612no—
617C22×Q8—611no—
618C22×Q8—1221no—
619C22×Q8—1221no—
620C22×Q8—1221no—
621C22×Q8—1224no—
622C22×Q8—1224no—
623C22×Q8C22×D6111yescharacteristic
624C23×C4—611no—
625C23×C4—611no—
626C23×C4—611no—
627C23×C4—1221no—
628C23×C4—1221no—
629#137—28no—
630#137—1228no—
631C2×Q16—614no—
632C2×Q16C22×D6114yes—
633C2×SD16—614no—
634C2×SD16C22×D6114yes—
635C2×M16—612no—
636C2×M16C22×D6112yes—
637C4⋊Q8—611no—
638C4⋊Q8—611no—
639C4⋊Q8C22×D6111yescharacteristic
640#127C22×D6111yescharacteristic
641#126—1222no—
642#126—1222no—
643#125—612no—
644#125—1221no—
645#125—1221no—
646#124—1221no—
647#124—1221no—
648#124C22×D6112yes—
649#123—1222no—
650#123—1222no—
651#123—1222no—
652C22⋊Q8—612no—
653C22⋊Q8—612no—
654C22⋊Q8—1221no—
655C22⋊Q8—1221no—
656C22⋊Q8—1221no—
657C22⋊Q8—1221no—
658#121—21no—
659#121—21no—
660#121—612no—
661#121—612no—
662#121—1221no—
663#121—1221no—
664#120—1222no—
665C4×Q8—21no—
666C4×Q8—21no—
667C4×Q8—612no—
668C4×Q8—612no—
669C4×Q8—612no—
670C4×Q8—612no—
671C4×Q8—612no—
672C4×Q8—612no—
673C4×Q8—612no—
674C4×Q8—612no—
675C4×Q8—1222no—
676C4×Q8—1222no—
677C4×Q8—1222no—
678C4×Q8—1222no—
679C4×Q8—1221no—
680C4×Q8—1222no—
681C4×Q8—1221no—
682C4×Q8—1222no—
683C4×Q8—1222no—
684C4×Q8—1222no—
685C4×Q8—1221no—
686C4×Q8—1221no—
687C4×Q8—1221no—
688C4×Q8—1221no—
689C4×Q8—1221no—
690C4×Q8—1221no—
691C4×Q8—1221no—
692C4×Q8—1221no—
693C4×Q8C22×D6112yes—
694C4×Q8C22×D6112yes—
695C4×D4—21no—
696C4×D4—21no—
697C4×D4—612no—
698C4×D4—612no—
699C4×D4—1221no—
700C4×D4—1221no—
701C4×D4—1222no—
702C4×D4—1222no—
703C4×D4—1222no—
704C4×D4—1222no—
705C4×D4—1222no—
706C4×D4—1222no—
707#117—612no—
708#117—1222no—
709#117—1222no—
710#117—1222no—
711#117—1221no—
712#117—1221no—
713C2×C4⋊C4—21no—
714C2×C4⋊C4—611no—
715C2×C4⋊C4—612no—
716C2×C4⋊C4—612no—
717C2×C4⋊C4—1221no—
718C2×C4⋊C4—1221no—
719C2×C4⋊C4—1222no—
720C2×C4⋊C4—1222no—
721C2×C4⋊C4—1222no—
722C2×C4⋊C4—1222no—
723C2×C4⋊C4—1221no—
724C2×C4⋊C4—1221no—
725C2×C4⋊C4—1221no—
726C2×C4⋊C4—1221no—
727C2×C4⋊C4C22×D6111yescharacteristic
728C2×C42—21no—
729C2×C42—611no—
730C2×C42—611no—
731C2×C42—611no—
732C2×C42—611no—
733C2×C42—611no—
734C2×C42—611no—
735C2×C42—611no—
736C2×C42—611no—
737C2×C42—611no—
738C2×C42—611no—
739C2×C42—611no—
740C2×C42—1222no—
741C2×C42—1222no—
742C2×C42—1222no—
743C2×C42—1222no—
744C2×C42—1222no—
745C2×C42—1221no—
746C2×C42—1221no—
747C2×C42—1221no—
748C2×C42C22×D6111yescharacteristic
749#107—614no—
750#107—614no—
751#106—614no—
752#106—614no—
753C4⋊C8—612no—
754C4⋊C8—612no—
755C4⋊C8C22×D6112yes—
756C4⋊C8C22×D6112yes—
757#103—614no—
758#103—614no—
759#103—614no—
760#103—614no—
761#103—614no—
762#103C22×D6114yes—
763#102—614no—
764#102C22×D6114yes—
765C22⋊C8—614no—
766C22⋊C8—614no—
767#97—614no—
768C4×C8—614no—
769C24—611no—
770#41—24no—
771#41—24no—
772#41—2444no—
773#41—2444no—
774C2×Q8—21no—
775C2×Q8—22no—
776C2×Q8—614no—
777C2×Q8—612no—
778C2×Q8—1222no—
779C2×Q8—1222no—
780C2×Q8—1228no—
781C2×Q8—1224no—
782C2×Q8—1224no—
783C2×Q8—1228no—
784C2×Q8—1228no—
785C2×Q8—1224no—
786C2×Q8—1224no—
787C2×Q8—1221no—
788C2×Q8—1221no—
789C2×Q8—1221no—
790C2×Q8—1222no—
791C2×Q8#1175822414yescomplemented
792C2×Q8C23×D6112yes—
793C2×Q8C23×D6112yes—
794C2×D4—22no—
795C2×D4—21no—
796C2×D4—21no—
797C2×D4—1222no—
798C2×D4—1222no—
799C2×D4C23×D6112yes—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—22no—
803C22×C4—611no—
804C22×C4—611no—
805C22×C4—611no—
806C22×C4—611no—
807C22×C4—611no—
808C22×C4—611no—
809C22×C4—611no—
810C22×C4—611no—
811C22×C4—611no—
812C22×C4—611no—
813C22×C4—611no—
814C22×C4—611no—
815C22×C4—611no—
816C22×C4—611no—
817C22×C4—611no—
818C22×C4—1224no—
819C22×C4—1222no—
820C22×C4—1222no—
821C22×C4—1228no—
822C22×C4—1222no—
823C22×C4—1222no—
824C22×C4—1222no—
825C22×C4—1222no—
826C22×C4—1221no—
827C22×C4—1222no—
828C22×C4—1222no—
829C22×C4—1221no—
830C22×C4—2442no—
831C22×C4—2444no—
832C22×C4D4×D6111yescharacteristic
833C22×C4D4×D6111yescharacteristic
834C22×C4C23×D6111yescharacteristic
835Q16—28no—
836Q16—1228no—
837SD16—28no—
838SD16—1228no—
839M16—24no—
840M16—1224no—
841C2×C8—614no—
842C2×C8C23×D6114yes—
843C4⋊C4—22no—
844C4⋊C4—22no—
845C4⋊C4—21no—
846C4⋊C4—21no—
847C4⋊C4—21no—
848C4⋊C4—612no—
849C4⋊C4—612no—
850C4⋊C4—612no—
851C4⋊C4—1222no—
852C4⋊C4—1222no—
853C4⋊C4—1222no—
854C4⋊C4—1222no—
855C4⋊C4—1222no—
856C4⋊C4—1222no—
857C4⋊C4—1222no—
858C4⋊C4—1222no—
859C4⋊C4—1222no—
860C4⋊C4—1222no—
861C4⋊C4—1221no—
862C4⋊C4—1222no—
863C4⋊C4—1222no—
864C4⋊C4—1222no—
865C4⋊C4—1222no—
866C4⋊C4—1221no—
867C4⋊C4—1221no—
868C4⋊C4C23×D6112yes—
869C22⋊C4—22no—
870C22⋊C4—22no—
871C22⋊C4—1222no—
872C22⋊C4—1222no—
873C22⋊C4—1222no—
874C22⋊C4—1222no—
875C22⋊C4—1222no—
876C22⋊C4—1222no—
877C22⋊C4—1222no—
878C42—22no—
879C42—22no—
880C42—611no—
881C42—611no—
882C42—611no—
883C42—611no—
884C42—611no—
885C42—611no—
886C42—611no—
887C42—611no—
888C42—611no—
889C42—611no—
890C42—611no—
891C42—611no—
892C42—1222no—
893C42—1222no—
894C42—1222no—
895C42—1222no—
896C42—1222no—
897C42—1222no—
898C42—1222no—
899C42—1222no—
900C42—1222no—
901C42D4×D6111yescharacteristic
902C42D4×D6111yescharacteristic
903C42C23×D6111yescharacteristic
904C42C23×D6111yescharacteristic
905C23—22no—
906C23—611no—
907C23—611no—
908C23—1222no—
909C23—1222no—
910C23—1222no—
911C23C2×D4×D6111yescharacteristic
912Q8—24no—
913Q8—22no—
914Q8—22no—
915Q8—22no—
916Q8—614no—
917Q8—1228no—
918Q8—1228no—
919Q8—1224no—
920Q8—1222no—
921Q8—2442no—
922Q8—2442no—
923Q8C2×#1175822414yes—
924D4—22no—
925D4—22no—
926D4—42no—
927D4—44no—
928D4—42no—
929D4—2444no—
930D4—2444no—
931C2×C4—24no—
932C2×C4—22no—
933C2×C4—22no—
934C2×C4—22no—
935C2×C4—22no—
936C2×C4—41no—
937C2×C4—42no—
938C2×C4—44no—
939C2×C4—611no—
940C2×C4—614no—
941C2×C4—611no—
942C2×C4—611no—
943C2×C4—611no—
944C2×C4—611no—
945C2×C4—611no—
946C2×C4—1222no—
947C2×C4—1222no—
948C2×C4—1222no—
949C2×C4—1222no—
950C2×C4—1228no—
951C2×C4—1228no—
952C2×C4—1222no—
953C2×C4—1222no—
954C2×C4—1224no—
955C2×C4—1222no—
956C2×C4—1222no—
957C2×C4—1222no—
958C2×C4—1222no—
959C2×C4—1221no—
960C2×C4—1221no—
961C2×C4—1221no—
962C2×C4—1221no—
963C2×C4—1222no—
964C2×C4—1222no—
965C2×C4—1222no—
966C2×C4—2441no—
967C2×C4—2441no—
968C2×C4—2444no—
969C2×C4—2444no—
970C2×C4—2444no—
971C2×C4—2441no—
972C2×C4—2444no—
973C2×C4—2442no—
974C2×C4C2×D4×D6111yescharacteristic
975C2×C4C2×D4×D6111yescharacteristic
976C2×C4C2×D4×D6111yescharacteristic
977C2×C4C2×D4×D6111yescharacteristic
978C2×C4C2×D4×D6111yescharacteristic
979C2×C4#41×D6112yes—
980C2×C4C2×#1175822412yes—
981C2×C4C24×D6111yescharacteristic
982C8—24no—
983C8—1224no—
984C22—21no—
985C22—21no—
986C22—42no—
987C22—42no—
988C22—42no—
989C22—612no—
990C22—612no—
991C22—1228no—
992C22—1221no—
993C22—1221no—
994C22—1221no—
995C22—1221no—
996C22#1684027212yes—
997C22C22×D4×D6111yescharacteristic
998C4—21no—
999C4—21no—
1000C4—21no—
1001C4—24no—
1002C4—42no—
1003C4—42no—
1004C4—612no—
1005C4—1221no—
1006C4—1221no—
1007C4—1221no—
1008C4—1221no—
1009C4—1221no—
1010C4—1224no—
1011C4—2442no—
1012C4—2442no—
1013C4—2442no—
1014C4#1684027212yes—
1015C4#137×D6112yes—
1016C4C2×#41×D6111yescharacteristic
1017C4C22×#1175822411yescharacteristic
1018C2—22no—
1019C2—82no—
1020C2—1222no—
1021C2—1222no—
1022C2C2×#1684027211yescharacteristic
1023C2C2×#137×D6111yescharacteristic
1024C2#575×D6111yescharacteristic
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3037C2
socleC22×C61C23×D4
prime radical#21459114C2
hypercenter#3037D61
hypocenterC61#60560
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3037

Complements

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

NH ≅ G/Ntype
2. C2×C4×Q8×D61C2semidirect
3. #21455989C2semidirect
4. #21455948C2semidirect
5. #21455940C2semidirect
6. #21455898C2semidirect
7. #21455857C2semidirect
8. #21455849C2semidirect
9. #21455740C2semidirect
10. #21455626C2semidirect
11. #21455624C2semidirect
12. #21455287C2semidirect
13. #21455051C2semidirect
14. #21454643C2semidirect
15. #137×Dic61C2semidirect
16. #21454451C2semidirect
17. C61×#3037C2semidirect
58. #16840070C22semidirect
59. #16840069C22semidirect
60. #16840058C22semidirect
61. #16840057C22semidirect
62. #16840048C22semidirect
63. #16840047C22semidirect
64. #16839981C22semidirect
65. #16839969C22semidirect
66. #16839959C22semidirect
71. #16839869C22semidirect
72. #16839866C22semidirect
73. #16839863C22semidirect
74. #16839859C22semidirect
75. Q16×Dic61C22semidirect
76. #16839854C22semidirect
77. #16839853C22semidirect
78. SD16×Dic61C22semidirect
94. C61×#464C22semidirect
95. C61×#462C22semidirect
96. C61×#460C22semidirect
261. C2×Q8×C61#41semidirect
320. C2×Dic122#41semidirect
461. C4×D61#137semidirect
518. #3037D61semidirect
580. #464C2×D61semidirect
582. #462C2×D61semidirect
584. #460C2×D61semidirect
611. C61#60560semidirect
791. C2×Q8#11758224semidirect

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
#214559892
#214559482
#214559402
#214558982
#214558572
#214558492
#214557402
#214556262
#214556242
#214552872
#214550512
#214546432
#137×Dic612
#214544512
C61×#30372
#6056061