Finite Group Databasebeta

← #30546979

Subgroups — #30546979

Order 15616.

2674 conjugacy classes of subgroups.

The subgroup lattice has 934 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#137×D61C212yesmaximal, complemented
2#21459146C211yesmaximal, characteristic
3C2×#16840238C211yesmaximal, characteristic, complemented
4#21455347C214yesmaximal, complemented
5#21455344C214yesmaximal, complemented
6#21455338C214yesmaximal, complemented
7#21455335C214yesmaximal, complemented
8#21455293C211yesmaximal, characteristic, complemented
9#21455291C211yesmaximal, characteristic, complemented
10#21455290C212yesmaximal, complemented
11#21455288C212yesmaximal, complemented
12#21455287C211yesmaximal, characteristic, complemented
13#21454381C211yesmaximal, characteristic, complemented
14#21454335C212yesmaximal, complemented
15C61×#3037C211yesmaximal, characteristic, complemented
16C2×#41×D61C2212yes—
17C22×Q8×D61C2211yescharacteristic
18C2×#14519810C2212yescomplemented
19C2×#14519809C2214yes—
20C2×#14519808C2212yescomplemented
21C2×#14519807C2212yescomplemented
22C2×#14519806C2214yes—
23#137×D61—216no—
24C2×Q16×D61C2214yescomplemented
25C2×SD16×D61C2214yescomplemented
26C2×M16×D61C2212yes—
27#16840339—21no—
28#16840339—21no—
29#16840337C2212yes—
30#16840332C2212yes—
31#16840330C2212yes—
32#16840325C2212yes—
33#16840320—21no—
34#16840320—21no—
35#16840312C2211yescharacteristic
36#16840308C2212yes—
37#16840271—22no—
38#16840271—22no—
39#16840238—22no—
40#16840238—22no—
41#16840238C2214yescomplemented
42#16840238C2214yescomplemented
43C2×Q8×Dic61C2211yescharacteristic, complemented
44C2×C4×Dic122—21no—
45C2×C4×Dic122C2211yescharacteristic, complemented
46C2×#14519742—21no—
47C2×#14519742C2211yescharacteristic, complemented
48C2×#14519735—21no—
49C2×#14519735C2211yescharacteristic
50C2×#14519734—21no—
51C2×#14519734C2211yescharacteristic
52#16839987C2214yescomplemented
53#16839986C2214yescomplemented
54#16839985C2214yescomplemented
55#16839984C2214yescomplemented
56#16839983C2214yescomplemented
57#16839982C2214yescomplemented
58#16839981C2214yescomplemented
59#16839973C2212yescomplemented
60#16839972C2212yescomplemented
61#16839971C2214yescomplemented
62#16839970C2214yescomplemented
63#16839969C2212yescomplemented
64#16839963C2212yescomplemented
65#16839962C2212yescomplemented
66#16839961C2214yescomplemented
67#16839960C2214yescomplemented
68#16839959C2212yescomplemented
69#16839787C2214yescomplemented
70#16839787C2214yescomplemented
71#16839786C2211yescharacteristic, complemented
72#16839785C2212yescomplemented
73#16839769C2214yescomplemented
74#16839765C2214yescomplemented
75#16839764C2212yescomplemented
76#16839763C2212yescomplemented
77#16839761C2212yescomplemented
78#16839757C2214yes—
79#16839755C2214yes—
80C2×#137×C61C2212yescomplemented
81C61×#532C2211yescharacteristic
82C2×C4×Q8×C61C2211yescharacteristic, complemented
83C61×#464C2214yescomplemented
84C61×#462C2212yescomplemented
85C61×#460C2212yescomplemented
86C61×#423C2211yescharacteristic, complemented
87C61×#417C2212yescomplemented
88C2×#11758226C2312yes—
89C2×#11758222—22no—
90C2×#11758222C2312yes—
91C2×#11758224—22no—
92C2×#11758224C2312yes—
93#41×D61—28no—
94#41×D61—28no—
95C22×Dic122—21no—
96C22×Dic122C2311yescharacteristic
97C2×Q8×D61—22no—
98C2×Q8×D61—24no—
99C2×Q8×D61D418yescomplemented
100C2×Q8×D61C2312yes—
101C2×Q8×D61C2314yes—
102C2×D4×D61—22no—
103C2×D4×D61C2312yes—
104C22×C4×D61—21no—
105C22×C4×D61—22no—
106C22×C4×D61C2311yescharacteristic
107#14519810—28no—
108#14519809—216no—
109#14519808—28no—
110#14519807—28no—
111#14519806—216no—
112C2×Dic244C2314yes—
113C2×#11758202C2314yes—
114C2×#11758202C2314yes—
115Q16×D61—216no—
116C2×#11758190C2314yes—
117C2×#11758200C2314yes—
118C2×#11758201C2314yes—
119SD16×D61—216no—
120C2×#11758194C2312yes—
121C2×#11758189C2314yes—
122M16×D61—28no—
123C2×C8×D61C2314yes—
124#14519777C2311yescharacteristic
125#14519775C2312yes—
126#14519774C2311yescharacteristic
127#14519773C2312yes—
128#14519766C2312yes—
129#14519765C2312yes—
130#14519764C2312yes—
131#14519762—22no—
132#14519762—22no—
133#14519759—22no—
134#14519759—22no—
135#14519755—22no—
136#14519755—22no—
137#14519754—22no—
138#14519754—22no—
139#14519751—21no—
140#14519751—21no—
141#14519750—22no—
142#14519750—22no—
143#14519749—22no—
144#14519749—22no—
145#14519749—22no—
146#14519749—22no—
147#14519747—22no—
148#14519747—22no—
149#14519745—22no—
150#14519745—22no—
151Q8×Dic61—22no—
152Q8×Dic61C2314yes—
153C4×Dic122—21no—
154C4×Dic122—21no—
155C4×Dic122—24no—
156C4×Dic122—24no—
157C4×Dic122C2312yes—
158C4×Dic122C2312yes—
159#14519742—24no—
160#14519742—24no—
161#14519742—22no—
162#14519742C2314yes—
163C4×D244—21no—
164C4×D244—21no—
165C4×C22⋊D61—22no—
166C4×C22⋊D61—22no—
167#14519735—22no—
168#14519735—24no—
169#14519735—24no—
170#14519735C2314yes—
171#14519734—24no—
172#14519734—24no—
173#14519734D412yes—
174#14519734D412yes—
175#14519734C2312yes—
176#14519734C2312yes—
177C2×C4⋊Dic61—21no—
178C2×C4⋊Dic61C2311yescharacteristic
179C2×#11758196—21no—
180C2×#11758196—21no—
181C2×#11758196D411yescharacteristic
182C2×#11758196D411yescharacteristic
183C2×#11758198—21no—
184C2×#11758198D411yescharacteristic
185C2×#11758198D411yescharacteristic
186C2×C4×Dic61—21no—
187C2×C4×Dic61—21no—
188C2×C4×Dic61—21no—
189C2×C4×Dic61—21no—
190C2×C4×Dic61C2311yescharacteristic
191C4⋊#92418C2312yes—
192C4⋊#92418C2312yes—
193#14519706C2314yes—
194#14519706C2314yes—
195#14519702C2314yes—
196#14519701C2314yes—
197#14519700C2314yes—
198#14519699C2314yes—
199#14519698C2314yes—
200#14519697C2314yes—
201C2×#41×C61C2312yes—
202C22×Q8×C61C2311yescharacteristic
203#137×C61—28no—
204C2×Q16×C61C2314yes—
205C2×SD16×C61C2314yes—
206C2×M16×C61C2312yes—
207C4⋊Q8×C61C2311yescharacteristic
208#127×C61C2311yescharacteristic
209#124×C61C2312yes—
210#121×C61—21no—
211#121×C61—21no—
212C4×Q8×C61—21no—
213C4×Q8×C61—21no—
214C4×Q8×C61C2312yes—
215C4×Q8×C61C2312yes—
216C4×D4×C61—21no—
217C4×D4×C61—21no—
218C2×C4⋊C4×C61—21no—
219C2×C4⋊C4×C61C2311yescharacteristic
220C2×C42×C61—21no—
221C2×C42×C61C2311yescharacteristic
222C4⋊C8×C61C2312yes—
223C4⋊C8×C61C2312yes—
224#103×C61C2314yes—
225#102×C61C2314yes—
226C23×D61—22no—
227C23×D61C2×D411yescharacteristic
228#41×C61—24no—
229#41×C61—24no—
230C2×Q8×C61—21no—
231C2×Q8×C61—22no—
232C2×Q8×C61C2×D414yes—
233C2×Q8×C61C2412yes—
234C2×Q8×C61C2412yes—
235C2×D4×C61—22no—
236C2×D4×C61—21no—
237C2×D4×C61—21no—
238C2×D4×C61C2412yes—
239C22×C4×C61—21no—
240C22×C4×C61—21no—
241C22×C4×C61—22no—
242C22×C4×C61C2×D411yescharacteristic
243C22×C4×C61C2×D411yescharacteristic
244C22×C4×C61C2411yescharacteristic
245C2×C22⋊D61—22no—
246C2×C22⋊D61—22no—
247C2×C22⋊D61—22no—
248C2×C22⋊D61—22no—
249C2×C22⋊D61—22no—
250C22×Dic61—21no—
251C22×Dic61—21no—
252C22×Dic61—22no—
253C22×Dic61C2×D411yescharacteristic
254C22×Dic61C2×D411yescharacteristic
255C22×Dic61C2×D411yescharacteristic
256#11758226—24no—
257#11758226—24no—
258Q8×D61—216no—
259Q8×D61—28no—
260Q8×D61—24no—
261Q8×D61—24no—
262Q8×D61C2×D4116yes—
263#11758224—24no—
264#11758224—24no—
265#11758224—48no—
266D4×D61—24no—
267D4×D61—24no—
268D4×D61—48no—
269#11758222—24no—
270#11758222—24no—
271#11758222—48no—
272C2×D244—22no—
273C2×D244—21no—
274C2×D244—21no—
275C2×D244C2412yes—
276C2×C4×D61—28no—
277C2×C4×D61—24no—
278C2×C4×D61—22no—
279C2×C4×D61—22no—
280C2×C4×D61—22no—
281C2×C4×D61—48no—
282C2×C4×D61C2×D412yes—
283C2×C4×D61C2×D414yes—
284C2×C4×D61#4114yes—
285C2×C4×D61C2412yes—
286C2×Dic122—21no—
287C2×Dic122—22no—
288C2×Dic122—28no—
289C2×Dic122—24no—
290C2×Dic122—22no—
291C2×Dic122C2×D414yes—
292C2×Dic122C2412yes—
293C2×Dic122C2412yes—
294Q16×C61—28no—
295SD16×C61—28no—
296M16×C61—24no—
297C2×C8×C61C2414yes—
298C4⋊C4×C61—22no—
299C4⋊C4×C61—22no—
300C4⋊C4×C61—21no—
301C4⋊C4×C61—21no—
302C4⋊C4×C61—21no—
303C4⋊C4×C61C2412yes—
304C22⋊C4×C61—22no—
305C22⋊C4×C61—22no—
306C42×C61—22no—
307C42×C61—22no—
308C42×C61C2×D411yescharacteristic
309C42×C61C2×D411yescharacteristic
310C42×C61C2411yescharacteristic
311C42×C61C2411yescharacteristic
312C22⋊Dic61—22no—
313C22⋊Dic61—22no—
314#11758202—28no—
315#11758202—28no—
316#11758201—28no—
317#11758200—28no—
318#11758198—24no—
319#11758198—22no—
320#11758198—22no—
321#11758198—22no—
322#11758198—22no—
323#11758198C2×D412yes—
324#11758198C2×D412yes—
325#11758198C2×D412yes—
326#11758198C2×D412yes—
327C4⋊Dic61—21no—
328C4⋊Dic61—21no—
329C4⋊Dic61—21no—
330C4⋊Dic61—24no—
331C4⋊Dic61C2412yes—
332#11758196—22no—
333#11758196—22no—
334#11758196—24no—
335#11758196—22no—
336#11758196—22no—
337#11758196C2×D412yes—
338#11758196C2×D412yes—
339#11758196C2×D412yes—
340#11758196C2×D412yes—
341C4×Dic61—22no—
342C4×Dic61—22no—
343C4×Dic61—24no—
344C4×Dic61—24no—
345C4×Dic61—24no—
346C4×Dic61C2×D412yes—
347C4×Dic61C2412yes—
348#11758194—24no—
349C2×#92418C2414yes—
350Dic244—28no—
351#11758190—28no—
352#11758189—28no—
353C8×D61—28no—
354C23×C61—22no—
355C23×C61C22×D411yescharacteristic
356C22×D61—22no—
357C22×D61—41no—
358C22×D61—41no—
359C22×D61—44no—
360C22×D61—82no—
361C22×D61—82no—
362C22×D61#12114yes—
363C22×D61C22×D412yes—
364Q8×C61—24no—
365Q8×C61—22no—
366Q8×C61—22no—
367Q8×C61—22no—
368Q8×C61C22×D414yes—
369D4×C61—22no—
370D4×C61—22no—
371D4×C61—44no—
372D4×C61—81no—
373D4×C61—81no—
374C2×C4×C61—24no—
375C2×C4×C61—22no—
376C2×C4×C61—22no—
377C2×C4×C61—22no—
378C2×C4×C61—41no—
379C2×C4×C61—41no—
380C2×C4×C61—42no—
381C2×C4×C61—44no—
382C2×C4×C61C22×D411yescharacteristic
383C2×C4×C61C22×D411yescharacteristic
384C2×C4×C61C22×D411yescharacteristic
385C2×C4×C61C22×D411yescharacteristic
386C2×C4×C61C22×D411yescharacteristic
387C2×C4×C61C22×D412yes—
388C2×C4×C61C2×#4112yes—
389C2×C4×C61C2511yescharacteristic
390C22⋊D61—44no—
391C22⋊D61—44no—
392C22⋊D61—44no—
393C22⋊D61—82no—
394C22⋊D61—82no—
395C2×Dic61—24no—
396C2×Dic61—22no—
397C2×Dic61—22no—
398C2×Dic61—22no—
399C2×Dic61—41no—
400C2×Dic61—41no—
401C2×Dic61—42no—
402C2×Dic61—44no—
403C2×Dic61#12114yes—
404C2×Dic61C22×D412yes—
405C2×Dic61C22×D412yes—
406C2×Dic61C22×D412yes—
407D244—22no—
408D244—22no—
409D244—44no—
410D244—81no—
411D244—81no—
412C4×D61—216no—
413C4×D61—44no—
414C4×D61—44no—
415C4×D61—44no—
416C4×D61#12118yes—
417C4×D61C22×D414yes—
418C4×D61C2×#4114yes—
419Dic122—24no—
420Dic122—22no—
421Dic122—216no—
422Dic122—22no—
423Dic122—22no—
424Dic122—44no—
425Dic122C22×D414yes—
426C8×C61—24no—
427#92418—24no—
428#60424—611nomaximal, Sylow
429C22×C61—21no—
430C22×C61—21no—
431C22×C61—42no—
432C22×C61—42no—
433C22×C61—42no—
434C22×C61C2×#12112yes—
435C22×C61C23×D411yescharacteristic
436C2×D61—22no—
437C2×D61—22no—
438C2×D61—44no—
439C2×D61—42no—
440C2×D61—42no—
441C2×D61—42no—
442C2×D61—88no—
443C2×D61C2×#12114yes—
444C4×C61—21no—
445C4×C61—21no—
446C4×C61—21no—
447C4×C61—21no—
448C4×C61—24no—
449C4×C61—42no—
450C4×C61—42no—
451C4×C61C2×#12112yes—
452C4×C61C23×D411yescharacteristic
453C4×C61C22×#4111yescharacteristic
454Dic61—22no—
455Dic61—22no—
456Dic61—24no—
457Dic61—42no—
458Dic61—42no—
459Dic61C2×#12114yes—
460C22×#137—612no—
461#3449—611no—
462C2×#519—611no—
463#3044—614no—
464#3044—614no—
465#3043—614no—
466#3043—614no—
467#3037—611no—
468#3037—612no—
469#3037—612no—
470#3037—611no—
471#3037—611no—
472#3037D6111yescharacteristic, complemented
473#2905—611no—
474#2896—612no—
475C2×C61—22no—
476C2×C61—82no—
477C2×C61C22×#12111yescharacteristic
478C2×C61#358611yescharacteristic
479C2×C61#358611yescharacteristic
480D61—24no—
481D61—82no—
482C22×#41—612no—
483C23×Q8—611no—
484C2×#137—612no—
485C2×#137—612no—
486C2×#137—614no—
487C2×#137—614no—
488C2×#137—612no—
489C2×#137—12216no—
490C2×#137C2×D6112yescomplemented
491C22×Q16—614no—
492C22×SD16—614no—
493C22×M16—612no—
494#537—1221no—
495#537—1221no—
496#536—612no—
497#536—612no—
498#535—612no—
499#535—612no—
500#534—1221no—
501#534—1221no—
502#532—612no—
503#532—611no—
504#532C2×D6111yescharacteristic
505#525—1222no—
506#525—1222no—
507#519—614no—
508#519—614no—
509#519—1222no—
510#519—1222no—
511C2×C4×Q8—611no—
512C2×C4×Q8—611no—
513C2×C4×Q8—611no—
514C2×C4×Q8—1221no—
515C2×C4×Q8—1221no—
516C2×C4×Q8C2×D6111yescharacteristic, complemented
517C2×#117—611no—
518C2×#117—611no—
519C2×#117—1221no—
520C2×#117—1221no—
521#464—614no—
522#464—614no—
523#464—614no—
524#464—614no—
525#464—614no—
526#464—614no—
527#464—614no—
528#464C2×D6114yescomplemented
529#462—614no—
530#462—612no—
531#462—612no—
532#462—612no—
533#462—614no—
534#462C2×D6112yescomplemented
535#460—614no—
536#460—612no—
537#460—612no—
538#460—612no—
539#460—614no—
540#460C2×D6112yescomplemented
541#424—614no—
542#424—614no—
543#423—612no—
544#423—611no—
545#423C2×D6111yescharacteristic, complemented
546#419—614no—
547#418—614no—
548#417—612no—
549#417—612no—
550#417—612no—
551#417C2×D6112yescomplemented
552#416—614no—
553#416—614no—
554C61#6042411yescharacteristic, complemented, Sylow
555C2×#41—612no—
556C2×#41—612no—
557C2×#41—612no—
558C2×#41—1222no—
559C2×#41—1222no—
560C2×#41—1228no—
561C2×#41—1228no—
562C2×#41C22×D6112yes—
563C22×Q8—618no—
564C22×Q8—614no—
565C22×Q8—612no—
566C22×Q8—611no—
567C22×Q8—1221no—
568C22×Q8—1222no—
569C22×Q8—1224no—
570C22×Q8C22×D6111yescharacteristic
571C22×D4—612no—
572C22×D4—1222no—
573C23×C4—611no—
574C23×C4—1222no—
575C23×C4—1221no—
576#137—28no—
577#137—1228no—
578#137—12216no—
579#137—12216no—
580#137—1228no—
581#137—1228no—
582C2×Q16—614no—
583C2×Q16—614no—
584C2×Q16—614no—
585C2×Q16—12216no—
586C2×Q16C22×D6114yes—
587C2×SD16—614no—
588C2×SD16—614no—
589C2×SD16—614no—
590C2×SD16—12216no—
591C2×SD16C22×D6114yes—
592C2×M16—612no—
593C2×M16—614no—
594C2×M16—1228no—
595C2×M16C22×D6112yes—
596C22×C8—614no—
597C4⋊Q8—612no—
598C4⋊Q8—611no—
599C4⋊Q8C22×D6111yescharacteristic
600#127—612no—
601#127—611no—
602#127C22×D6111yescharacteristic
603#124—612no—
604#124—612no—
605#124—612no—
606#124C22×D6112yes—
607#123—1222no—
608#123—1222no—
609#123—1222no—
610#123—1222no—
611C22⋊Q8—1222no—
612C22⋊Q8—1222no—
613C22⋊Q8—1222no—
614C22⋊Q8—1222no—
615#121—21no—
616#121—21no—
617#121—1222no—
618#121—1222no—
619#121—1222no—
620#121—1222no—
621#121—1222no—
622#121—1222no—
623#121—1221no—
624#121—1221no—
625#120—1222no—
626#120—1222no—
627#120—1222no—
628#120—1222no—
629C4×Q8—21no—
630C4×Q8—21no—
631C4×Q8—614no—
632C4×Q8—614no—
633C4×Q8—612no—
634C4×Q8—612no—
635C4×Q8—1224no—
636C4×Q8—1224no—
637C4×Q8—1222no—
638C4×Q8—1222no—
639C4×Q8—1224no—
640C4×Q8—1224no—
641C4×Q8—1221no—
642C4×Q8—1221no—
643C4×Q8C22×D6112yes—
644C4×Q8C22×D6112yes—
645C4×D4—21no—
646C4×D4—21no—
647C4×D4—1222no—
648C4×D4—1222no—
649C4×D4—1221no—
650C4×D4—1221no—
651#117—612no—
652#117—612no—
653#117—612no—
654#117—612no—
655#117—614no—
656#117—1224no—
657#117—1224no—
658#117—1224no—
659#117—1224no—
660#117—1222no—
661C2×C4⋊C4—21no—
662C2×C4⋊C4—611no—
663C2×C4⋊C4—611no—
664C2×C4⋊C4—611no—
665C2×C4⋊C4—1221no—
666C2×C4⋊C4—1221no—
667C2×C4⋊C4—1221no—
668C2×C4⋊C4C22×D6111yescharacteristic
669C2×C22⋊C4—611no—
670C2×C22⋊C4—611no—
671C2×C22⋊C4—1221no—
672C2×C42—21no—
673C2×C42—611no—
674C2×C42—1221no—
675C2×C42—1221no—
676C2×C42—1221no—
677C2×C42—1221no—
678C2×C42C22×D6111yescharacteristic
679C4⋊C8—614no—
680C4⋊C8—614no—
681C4⋊C8—612no—
682C4⋊C8—612no—
683C4⋊C8C22×D6112yes—
684C4⋊C8C22×D6112yes—
685#103—614no—
686#103—614no—
687#103—614no—
688#103C22×D6114yes—
689#102—614no—
690#102—614no—
691#102—614no—
692#102C22×D6114yes—
693C24—611no—
694C24—1222no—
695#41—24no—
696#41—24no—
697#41—1224no—
698#41—1224no—
699#41—1224no—
700#41—1224no—
701#41—1224no—
702#41—1224no—
703#41—2448no—
704#41—2448no—
705C2×Q8—21no—
706C2×Q8—22no—
707C2×Q8—6116no—
708C2×Q8—614no—
709C2×Q8—612no—
710C2×Q8—612no—
711C2×Q8—1224no—
712C2×Q8—1228no—
713C2×Q8—1222no—
714C2×Q8—12216no—
715C2×Q8—1228no—
716C2×Q8—1224no—
717C2×Q8—1224no—
718C2×Q8—1221no—
719C2×Q8—1222no—
720C2×Q8D4×D6114yes—
721C2×Q8C23×D6112yes—
722C2×Q8C23×D6112yes—
723C2×D4—22no—
724C2×D4—21no—
725C2×D4—21no—
726C2×D4—612no—
727C2×D4—1222no—
728C2×D4—1224no—
729C2×D4—1224no—
730C2×D4—1222no—
731C2×D4—1222no—
732C2×D4—1222no—
733C2×D4—1222no—
734C2×D4—1222no—
735C2×D4—1221no—
736C2×D4—1221no—
737C2×D4—2448no—
738C2×D4C23×D6112yes—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—22no—
742C22×C4—611no—
743C22×C4—612no—
744C22×C4—614no—
745C22×C4—614no—
746C22×C4—612no—
747C22×C4—611no—
748C22×C4—611no—
749C22×C4—1222no—
750C22×C4—1224no—
751C22×C4—1228no—
752C22×C4—1222no—
753C22×C4—1222no—
754C22×C4—1221no—
755C22×C4—1221no—
756C22×C4—1222no—
757C22×C4—2448no—
758C22×C4D4×D6111yescharacteristic
759C22×C4D4×D6111yescharacteristic
760C22×C4C23×D6111yescharacteristic
761Q16—28no—
762Q16—1228no—
763Q16—1228no—
764Q16—1228no—
765SD16—28no—
766SD16—1228no—
767SD16—1228no—
768SD16—1228no—
769M16—24no—
770M16—1228no—
771M16—1224no—
772C2×C8—614no—
773C2×C8—1228no—
774C2×C8C23×D6114yes—
775C4⋊C4—22no—
776C4⋊C4—22no—
777C4⋊C4—21no—
778C4⋊C4—21no—
779C4⋊C4—21no—
780C4⋊C4—612no—
781C4⋊C4—612no—
782C4⋊C4—612no—
783C4⋊C4—612no—
784C4⋊C4—612no—
785C4⋊C4—1224no—
786C4⋊C4—1224no—
787C4⋊C4—1222no—
788C4⋊C4—1222no—
789C4⋊C4—1221no—
790C4⋊C4—1222no—
791C4⋊C4—1222no—
792C4⋊C4—1221no—
793C4⋊C4—1221no—
794C4⋊C4C23×D6112yes—
795C22⋊C4—22no—
796C22⋊C4—22no—
797C22⋊C4—612no—
798C22⋊C4—612no—
799C22⋊C4—612no—
800C22⋊C4—612no—
801C22⋊C4—1222no—
802C22⋊C4—1222no—
803C22⋊C4—1224no—
804C22⋊C4—1222no—
805C22⋊C4—1222no—
806C22⋊C4—1222no—
807C22⋊C4—1222no—
808C42—22no—
809C42—22no—
810C42—612no—
811C42—612no—
812C42—1224no—
813C42—1224no—
814C42—1224no—
815C42—1222no—
816C42—1222no—
817C42D4×D6111yescharacteristic
818C42D4×D6111yescharacteristic
819C42C23×D6111yescharacteristic
820C42C23×D6111yescharacteristic
821C23—22no—
822C23—612no—
823C23—614no—
824C23—1222no—
825C23—4882no—
826C23—4882no—
827C23—2441no—
828C23—2441no—
829C23—2444no—
830C23C2×D4×D6111yescharacteristic
831Q8—24no—
832Q8—22no—
833Q8—22no—
834Q8—22no—
835Q8—614no—
836Q8—12216no—
837Q8—1224no—
838Q8—1222no—
839Q8—1222no—
840Q8—1222no—
841Q8—2444no—
842Q8C2×D4×D6114yes—
843D4—22no—
844D4—22no—
845D4—44no—
846D4—81no—
847D4—81no—
848D4—1222no—
849D4—1222no—
850D4—4881no—
851D4—4881no—
852D4—4882no—
853D4—4882no—
854D4—2444no—
855D4—2444no—
856D4—2444no—
857D4—2444no—
858C2×C4—24no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—42no—
865C2×C4—44no—
866C2×C4—614no—
867C2×C4—612no—
868C2×C4—618no—
869C2×C4—614no—
870C2×C4—614no—
871C2×C4—612no—
872C2×C4—612no—
873C2×C4—12216no—
874C2×C4—1224no—
875C2×C4—1222no—
876C2×C4—1222no—
877C2×C4—1222no—
878C2×C4—2444no—
879C2×C4—2444no—
880C2×C4—2444no—
881C2×C4—2441no—
882C2×C4—2441no—
883C2×C4—2442no—
884C2×C4—2444no—
885C2×C4C2×D4×D6111yescharacteristic
886C2×C4C2×D4×D6111yescharacteristic
887C2×C4C2×D4×D6111yescharacteristic
888C2×C4C2×D4×D6111yescharacteristic
889C2×C4C2×D4×D6111yescharacteristic
890C2×C4C2×D4×D6112yes—
891C2×C4#41×D6112yes—
892C2×C4C24×D6111yescharacteristic
893C8—24no—
894C8—1224no—
895C22—21no—
896C22—21no—
897C22—42no—
898C22—42no—
899C22—42no—
900C22—614no—
901C22—1222no—
902C22—1222no—
903C22—4888no—
904C22—2444no—
905C22—2442no—
906C22—2442no—
907C22—2442no—
908C22#121×D6112yes—
909C22C22×D4×D6111yescharacteristic
910C4—24no—
911C4—21no—
912C4—21no—
913C4—21no—
914C4—21no—
915C4—42no—
916C4—42no—
917C4—614no—
918C4—1224no—
919C4—1222no—
920C4—1222no—
921C4—2442no—
922C4—2442no—
923C4#121×D6112yes—
924C4C22×D4×D6111yescharacteristic
925C4C2×#41×D6111yescharacteristic
926C2—22no—
927C2—82no—
928C2—1224no—
929C2—4882no—
930C2C2×#121×D6111yescharacteristic
931C2#2146060211yescharacteristic
932C2#2146060311yescharacteristic
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3037C2
socleC22×C61C23×D4
prime radical#21459146C2
hypercenter#3037D61
hypocenterC61#60424
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
1. C2×#137×D61C2semidirect
3. C2×#16840238C2semidirect
4. #21455347C2semidirect
5. #21455344C2semidirect
6. #21455338C2semidirect
7. #21455335C2semidirect
8. #21455293C2semidirect
9. #21455291C2semidirect
10. #21455290C2semidirect
11. #21455288C2semidirect
12. #21455287C2semidirect
13. #21454381C2semidirect
14. #21454335C2semidirect
15. C61×#3037C2semidirect
18. C2×#14519810C22semidirect
20. C2×#14519808C22semidirect
21. C2×#14519807C22semidirect
24. C2×Q16×D61C22semidirect
25. C2×SD16×D61C22semidirect
41. #16840238C22semidirect
42. #16840238C22semidirect
43. C2×Q8×Dic61C22semidirect
45. C2×C4×Dic122C22semidirect
47. C2×#14519742C22semidirect
52. #16839987C22semidirect
53. #16839986C22semidirect
54. #16839985C22semidirect
55. #16839984C22semidirect
56. #16839983C22semidirect
57. #16839982C22semidirect
58. #16839981C22semidirect
59. #16839973C22semidirect
60. #16839972C22semidirect
61. #16839971C22semidirect
62. #16839970C22semidirect
63. #16839969C22semidirect
64. #16839963C22semidirect
65. #16839962C22semidirect
66. #16839961C22semidirect
67. #16839960C22semidirect
68. #16839959C22semidirect
69. #16839787C22semidirect
70. #16839787C22semidirect
71. #16839786C22semidirect
72. #16839785C22semidirect
73. #16839769C22semidirect
74. #16839765C22semidirect
75. #16839764C22semidirect
76. #16839763C22semidirect
77. #16839761C22semidirect
80. C2×#137×C61C22semidirect
82. C2×C4×Q8×C61C22semidirect
83. C61×#464C22semidirect
84. C61×#462C22semidirect
85. C61×#460C22semidirect
86. C61×#423C22semidirect
87. C61×#417C22semidirect
99. C2×Q8×D61D4semidirect
472. #3037D61semidirect
490. C2×#137C2×D61semidirect
516. C2×C4×Q8C2×D61semidirect
528. #464C2×D61semidirect
534. #462C2×D61semidirect
540. #460C2×D61semidirect
545. #423C2×D61semidirect
551. #417C2×D61semidirect
554. C61#60424semidirect

Maximal subgroups

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

subgroupindex
C2×#137×D612
#214591462
C2×#168402382
#214553472
#214553442
#214553382
#214553352
#214552932
#214552912
#214552902
#214552882
#214552872
#214543812
#214543352
C61×#30372
#6042461