Finite Group Databasebeta

← D61×#3215 #30551263

Subgroups — D61×#3215 #30551263

Order 15616.

2242 conjugacy classes of subgroups.

The subgroup lattice has 1056 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#533×D61C211yesmaximal, characteristic, complemented
2C2×#124×D61C211yesmaximal, characteristic
3#21456824C211yesmaximal, characteristic, complemented
4#21456823C212yesmaximal, complemented
5#21456822C211yesmaximal, characteristic, complemented
6#21456821C212yesmaximal, complemented
7#21456820C214yesmaximal, complemented
8#21456819C212yesmaximal, complemented
9#21456818C211yesmaximal, characteristic, complemented
10#21456817C212yesmaximal, complemented
11#497×D61C212yesmaximal, complemented
12#489×D61C212yesmaximal, complemented
13#464×D61C214yesmaximal, complemented
14#451×D61C212yesmaximal, complemented
15#450×D61C212yesmaximal
16#432×D61C211yesmaximal, characteristic, complemented
17C61×#3215C211yesmaximal, characteristic, complemented
18C22×Q8×D61C2211yescharacteristic
19C22×D4×D61C2211yescharacteristic
20C2×Q16×D61C2214yescomplemented
21C2×SD16×D61C2214yes—
22#16840319C2211yescharacteristic, complemented
23#16840318—21no—
24#16840317C2211yescharacteristic, complemented
25#16840317C2211yescharacteristic, complemented
26#16840316—21no—
27#16840316C2212yescomplemented
28#16840315—21no—
29#16840314—21no—
30#16840314C2212yescomplemented
31C4⋊Q8×D61C2211yescharacteristic, complemented
32C4⋊Q8×D61C2211yescharacteristic, complemented
33#125×D61—21no—
34C2×#14519766C2211yescharacteristic
35C2×#14519765C2211yescharacteristic
36C2×#14519764C2211yescharacteristic
37C2×#14519763—21no—
38C2×#14519763—21no—
39#124×D61—21no—
40#124×D61—21no—
41#124×D61—21no—
42#124×D61—21no—
43#124×D61C2212yes—
44#124×D61C2212yes—
45#124×D61C2212yes—
46#124×D61C2212yes—
47C22⋊Q8×D61—21no—
48C22⋊Q8×D61C2212yes—
49C4×Q8×D61—21no—
50C4×Q8×D61C2212yescomplemented
51#117×D61—21no—
52C2×C22⋊C4×D61—21no—
53C2×C22⋊C4×D61—21no—
54C2×C42×D61C2211yescharacteristic
55#16840157C2212yescomplemented
56#16840156C2212yescomplemented
57#16840155C2214yescomplemented
58#16840154C2212yescomplemented
59#16840153C2214yescomplemented
60#16840124C2212yescomplemented
61#16840123C2214yescomplemented
62#16840122C2212yescomplemented
63#16840121C2212yescomplemented
64#16840120C2214yescomplemented
65#16839987C2214yescomplemented
66#16839986C2214yescomplemented
67#16839985C2214yescomplemented
68#16839984C2214yescomplemented
69#16839983C2214yescomplemented
70#16839982C2214yescomplemented
71#16839981C2214yescomplemented
72#16839920C2212yescomplemented
73#16839919C2214yescomplemented
74#16839918C2212yescomplemented
75#16839917C2212yescomplemented
76#16839916C2214yescomplemented
77#16839915C2212yes—
78#16839914C2214yes—
79#16839913C2212yes—
80#16839912C2212yes—
81#16839911C2214yes—
82#16839819C2211yescharacteristic, complemented
83#16839818C2212yescomplemented
84#16839817C2212yescomplemented
85#16839816C2212yescomplemented
86C4⋊C8×D61C2212yescomplemented
87#103×D61C2214yescomplemented
88#102×D61C2214yes—
89C22⋊C8×D61C2212yes—
90#97×D61C2212yescomplemented
91C61×#533C2211yescharacteristic, complemented
92C2×#124×C61C2211yescharacteristic
93C61×#497C2212yescomplemented
94C61×#489C2212yescomplemented
95C61×#464C2214yescomplemented
96C61×#451C2212yescomplemented
97C61×#450C2212yes—
98C61×#432C2211yescharacteristic, complemented
99C24×D61—21no—
100C22×Dic122—21no—
101C22×Dic122C2311yescharacteristic
102C2×Q8×D61—21no—
103C2×Q8×D61—21no—
104C2×Q8×D61—21no—
105C2×Q8×D61—44no—
106C2×Q8×D61C2312yes—
107C2×Q8×D61C2312yes—
108C2×Q8×D61C2312yes—
109C22×D244C2311yescharacteristic
110C22×C22⋊D61—21no—
111C2×D4×D61—21no—
112C2×D4×D61—21no—
113C2×D4×D61—44no—
114C2×D4×D61C2312yes—
115C2×D4×D61C2312yes—
116C22×C4×D61—21no—
117C22×C4×D61D411yescharacteristic
118C22×C4×D61D411yescharacteristic
119C22×C4×D61C2311yescharacteristic
120C2×Dic244C2314yescomplemented
121C2×#11758202C2314yescomplemented
122C2×#11758202C2314yescomplemented
123Q16×D61—48no—
124C2×#11758190C2314yes—
125C2×#11758200C2314yes—
126C2×#11758201C2314yes—
127SD16×D61—48no—
128C2×C8×D61C2314yes—
129#14519777C2311yescharacteristic, complemented
130#14519777C2311yescharacteristic, complemented
131#14519776—21no—
132#14519776—21no—
133#14519776—21no—
134#14519776C2312yescomplemented
135#14519775—21no—
136#14519775C2312yescomplemented
137#14519769—21no—
138#14519768—21no—
139#14519768—21no—
140#14519767—22no—
141#14519767—22no—
142#14519766—21no—
143#14519766—21no—
144#14519766C2312yes—
145#14519766C2312yes—
146#14519765—21no—
147#14519765—21no—
148#14519765C2312yes—
149#14519765C2312yes—
150#14519764—21no—
151#14519764—21no—
152#14519764C2312yes—
153#14519764C2312yes—
154#14519763—22no—
155#14519763—22no—
156#14519763—22no—
157#14519763—22no—
158#14519763—22no—
159#14519763—22no—
160#14519763—22no—
161#14519763—22no—
162#14519757—21no—
163#14519757C2312yes—
164#14519756—21no—
165#14519756C2312yes—
166#14519755—22no—
167#14519755—22no—
168#14519754—22no—
169#14519754—22no—
170#14519753—21no—
171#14519753C2312yes—
172Q8×Dic61—21no—
173Q8×Dic61C2312yescomplemented
174C4×Dic122—21no—
175C4×Dic122—22no—
176C4×Dic122—22no—
177C4×Dic122C2312yescomplemented
178#14519742—21no—
179#14519742—22no—
180#14519742—22no—
181#14519742C2312yescomplemented
182#14519736—21no—
183#14519735—21no—
184#14519735—21no—
185#14519734—22no—
186#14519733—22no—
187C4⋊C4×D61—21no—
188C4⋊C4×D61—21no—
189C4⋊C4×D61—21no—
190C4⋊C4×D61—22no—
191C4⋊C4×D61—22no—
192C4⋊C4×D61C2312yes—
193C2×C22⋊Dic61—21no—
194C2×C22⋊Dic61—21no—
195C2×#11758198—21no—
196C2×#11758198—21no—
197C2×#11758198—21no—
198C2×#11758198—21no—
199C22⋊C4×D61—22no—
200C22⋊C4×D61—22no—
201C22⋊C4×D61—22no—
202C22⋊C4×D61—22no—
203C22⋊C4×D61—22no—
204C22⋊C4×D61—22no—
205C22⋊C4×D61—22no—
206C22⋊C4×D61—22no—
207C22⋊C4×D61—22no—
208C2×C4×Dic61D411yescharacteristic
209C2×C4×Dic61D411yescharacteristic
210C2×C4×Dic61C2311yescharacteristic
211C42×D61—22no—
212C42×D61D411yescharacteristic
213C42×D61D411yescharacteristic
214C42×D61D411yescharacteristic
215C42×D61D411yescharacteristic
216C42×D61C2311yescharacteristic
217C42×D61C2311yescharacteristic
218C42×D61C2311yescharacteristic
219C42×D61C2311yescharacteristic
220C4⋊#92418C2312yescomplemented
221#14519706C2314yescomplemented
222#14519702C2314yescomplemented
223#14519701C2314yescomplemented
224#14519700C2314yescomplemented
225#14519699C2314yes—
226#14519698C2314yes—
227#14519697C2314yes—
228C22⋊#92418C2312yes—
229#14519689C2314yes—
230#14519688C2312yescomplemented
231#14519687C2314yescomplemented
232C22×Q8×C61C2311yescharacteristic
233C22×D4×C61C2311yescharacteristic
234C2×Q16×C61C2314yescomplemented
235C2×SD16×C61C2314yes—
236C4⋊Q8×C61C2311yescharacteristic, complemented
237C4⋊Q8×C61C2311yescharacteristic, complemented
238#125×C61—21no—
239#124×C61—21no—
240#124×C61—21no—
241#124×C61C2312yes—
242#124×C61C2312yes—
243C22⋊Q8×C61—21no—
244C22⋊Q8×C61C2312yes—
245C4×Q8×C61—21no—
246C4×Q8×C61C2312yescomplemented
247#117×C61—21no—
248C2×C22⋊C4×C61—21no—
249C2×C22⋊C4×C61—21no—
250C2×C42×C61C2311yescharacteristic
251C4⋊C8×C61C2312yescomplemented
252#103×C61C2314yescomplemented
253#102×C61C2314yes—
254C22⋊C8×C61C2312yes—
255#97×C61C2312yescomplemented
256C24×C61—21no—
257C23×D61—21no—
258C23×D61—22no—
259C23×D61—22no—
260C23×D61—44no—
261C23×D61—44no—
262C23×D61—44no—
263C23×D61C2×D411yescharacteristic
264C2×Q8×C61—21no—
265C2×Q8×C61—21no—
266C2×Q8×C61—42no—
267C2×Q8×C61C2412yes—
268C2×Q8×C61C2412yes—
269C2×D4×C61—21no—
270C2×D4×C61—42no—
271C2×D4×C61C2412yes—
272C22×C4×C61—21no—
273C22×C4×C61C2×D411yescharacteristic
274C22×C4×C61C2×D411yescharacteristic
275C22×C4×C61C2411yescharacteristic
276C2×C22⋊D61—22no—
277C2×C22⋊D61—22no—
278C2×C22⋊D61—44no—
279C22×Dic61—21no—
280C22×Dic61C2×D411yescharacteristic
281C22×Dic61C2×D411yescharacteristic
282C22×Dic61C2×D411yescharacteristic
283Q8×D61—28no—
284Q8×D61—28no—
285Q8×D61—44no—
286Q8×D61—44no—
287Q8×D61—44no—
288Q8×D61—44no—
289D4×D61—28no—
290D4×D61—44no—
291D4×D61—44no—
292D4×D61—44no—
293C2×D244—21no—
294C2×D244—42no—
295C2×D244C2412yes—
296C2×C4×D61—24no—
297C2×C4×D61—24no—
298C2×C4×D61—22no—
299C2×C4×D61—22no—
300C2×C4×D61—22no—
301C2×C4×D61—22no—
302C2×C4×D61—42no—
303C2×C4×D61—44no—
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×D61C2×D411yescharacteristic
312C2×C4×D61C2×D411yescharacteristic
313C2×C4×D61C2×D411yescharacteristic
314C2×C4×D61C2411yescharacteristic
315C2×C4×D61C2411yescharacteristic
316C2×Dic122—21no—
317C2×Dic122—21no—
318C2×Dic122—22no—
319C2×Dic122—22no—
320C2×Dic122—22no—
321C2×Dic122—22no—
322C2×Dic122—42no—
323C2×Dic122—44no—
324C2×Dic122C2412yes—
325C2×Dic122C2412yes—
326Q16×C61—44no—
327SD16×C61—44no—
328C2×C8×C61C2414yes—
329C4⋊C4×C61—21no—
330C4⋊C4×C61—21no—
331C4⋊C4×C61—21no—
332C4⋊C4×C61—22no—
333C4⋊C4×C61—22no—
334C4⋊C4×C61C2412yes—
335C22⋊C4×C61—22no—
336C22⋊C4×C61—22no—
337C22⋊C4×C61—22no—
338C22⋊C4×C61—22no—
339C22⋊C4×C61—22no—
340C42×C61—22no—
341C42×C61C2×D411yescharacteristic
342C42×C61C2×D411yescharacteristic
343C42×C61C2411yescharacteristic
344C42×C61C2411yescharacteristic
345C22⋊Dic61—22no—
346C22⋊Dic61—22no—
347C22⋊Dic61—22no—
348C22⋊Dic61—22no—
349C22⋊Dic61—22no—
350#11758202—44no—
351#11758202—44no—
352#11758201—44no—
353#11758200—44no—
354#11758198—22no—
355#11758198—22no—
356#11758198—22no—
357#11758198—22no—
358#11758198—22no—
359#11758198—22no—
360#11758198—22no—
361#11758198—22no—
362#11758198—22no—
363#11758198—22no—
364C4⋊Dic61—21no—
365C4⋊Dic61—21no—
366C4⋊Dic61—21no—
367C4⋊Dic61—22no—
368C4⋊Dic61—22no—
369C4⋊Dic61C2412yes—
370#11758196—22no—
371#11758196—22no—
372#11758196—22no—
373#11758196—22no—
374#11758196—22no—
375#11758196—22no—
376#11758196—22no—
377#11758196—22no—
378C4×Dic61—22no—
379C4×Dic61—22no—
380C4×Dic61—22no—
381C4×Dic61C2×D411yescharacteristic
382C4×Dic61C2×D411yescharacteristic
383C4×Dic61C2×D411yescharacteristic
384C4×Dic61C2×D411yescharacteristic
385C4×Dic61C2×D411yescharacteristic
386C4×Dic61C2×D411yescharacteristic
387C4×Dic61C2×D411yescharacteristic
388C4×Dic61C2×D411yescharacteristic
389C4×Dic61C2×D411yescharacteristic
390C4×Dic61C2×D411yescharacteristic
391C4×Dic61C2411yescharacteristic
392C4×Dic61C2411yescharacteristic
393C2×#92418C2414yes—
394Dic244—44no—
395#11758190—44no—
396C8×D61—28no—
397C23×C61—22no—
398C23×C61—42no—
399C23×C61—42no—
400C23×C61—42no—
401C23×C61C22×D411yescharacteristic
402C22×D61—22no—
403C22×D61—22no—
404C22×D61—22no—
405C22×D61—44no—
406C22×D61—44no—
407C22×D61—42no—
408C22×D61—42no—
409C22×D61—42no—
410C22×D61—44no—
411C22×D61—44no—
412C22×D61—44no—
413C22×D61—44no—
414C22×D61—816no—
415C22×D61#13714yes—
416C22×D61C22×D411yescharacteristic
417C22×D61C22×D411yescharacteristic
418Q8×C61—24no—
419Q8×C61—24no—
420Q8×C61—42no—
421Q8×C61—42no—
422D4×C61—24no—
423D4×C61—42no—
424C2×C4×C61—22no—
425C2×C4×C61—22no—
426C2×C4×C61—22no—
427C2×C4×C61—22no—
428C2×C4×C61—22no—
429C2×C4×C61—41no—
430C2×C4×C61—42no—
431C2×C4×C61C22×D411yescharacteristic
432C2×C4×C61C22×D411yescharacteristic
433C2×C4×C61C22×D411yescharacteristic
434C2×C4×C61C22×D411yescharacteristic
435C2×C4×C61C22×D411yescharacteristic
436C2×C4×C61C2511yescharacteristic
437C22⋊D61—44no—
438C22⋊D61—44no—
439C2×Dic61—22no—
440C2×Dic61—22no—
441C2×Dic61—22no—
442C2×Dic61—22no—
443C2×Dic61—22no—
444C2×Dic61—41no—
445C2×Dic61—42no—
446C2×Dic61C22×D411yescharacteristic
447C2×Dic61C22×D411yescharacteristic
448C2×Dic61C22×D411yescharacteristic
449C2×Dic61C22×D411yescharacteristic
450C2×Dic61C22×D411yescharacteristic
451C2×Dic61C22×D411yescharacteristic
452D244—24no—
453D244—42no—
454C4×D61—22no—
455C4×D61—22no—
456C4×D61—22no—
457C4×D61—22no—
458C4×D61—22no—
459C4×D61—22no—
460C4×D61—22no—
461C4×D61—22no—
462C4×D61—22no—
463C4×D61—41no—
464C4×D61—41no—
465C4×D61—44no—
466C4×D61—44no—
467C4×D61—44no—
468C4×D61—44no—
469C4×D61H(5,𝔽2)14yes—
470Dic122—24no—
471Dic122—24no—
472Dic122—44no—
473Dic122—44no—
474Dic122—42no—
475Dic122—42no—
476Dic122—44no—
477Dic122—44no—
478C8×C61—24no—
479#92418—24no—
480C2×#3215—611nomaximal, Sylow
481C22×C61—21no—
482C22×C61—21no—
483C22×C61—42no—
484C22×C61—42no—
485C22×C61—42no—
486C22×C61—84no—
487C22×C61C2×#13712yes—
488C22×C61C23×D411yescharacteristic
489C2×D61—21no—
490C2×D61—21no—
491C2×D61—28no—
492C2×D61—42no—
493C2×D61—42no—
494C2×D61—42no—
495C2×D61—88no—
496C2×D61—84no—
497C2×D61—88no—
498C2×D61#53512yes—
499C2×D61C2×#13712yes—
500C2×D61C2×#13712yes—
501C2×D61#57512yes—
502C4×C61—21no—
503C4×C61—21no—
504C4×C61—21no—
505C4×C61—21no—
506C4×C61—21no—
507C4×C61—42no—
508C4×C61—42no—
509C4×C61—42no—
510C4×C61C2×H(5,𝔽2)12yes—
511Dic61—21no—
512Dic61—21no—
513Dic61—21no—
514Dic61—21no—
515Dic61—21no—
516Dic61—42no—
517Dic61—42no—
518Dic61—42no—
519Dic61#53512yes—
520C2×#533—611no—
521C22×#124—611no—
522#3215—612no—
523#3215—612no—
524#3215—614no—
525#3215—612no—
526#3215—612no—
527#3215—611no—
528#3215—611no—
529#3215—611no—
530#3215D6111yescharacteristic, direct product factor
531C2×#497—612no—
532C2×#489—612no—
533C2×#464—614no—
534C2×#451—612no—
535C2×#450—612no—
536C2×#432—611no—
537C2×C61—22no—
538C2×C61—82no—
539C2×C61C2×#53511yescharacteristic
540C2×C61C22×#13711yescharacteristic
541C2×C61C2×#57511yescharacteristic
542D61—22no—
543D61—82no—
544D61#321514yesdirect product factor
545C23×Q8—611no—
546C23×D4—611no—
547C22×Q16—614no—
548C22×SD16—614no—
549#533—611no—
550#533—611no—
551#533—612no—
552#533—612no—
553#533—611no—
554#533—1221no—
555#533—1221no—
556#533—1221no—
557#533—1221no—
558#533C2×D6111yescharacteristic, complemented
559C2×C4⋊Q8—611no—
560C2×C4⋊Q8—611no—
561C2×#125—1221no—
562C2×#124—611no—
563C2×#124—611no—
564C2×#124—612no—
565C2×#124—612no—
566C2×#124—612no—
567C2×#124—612no—
568C2×#124—611no—
569C2×#124—1221no—
570C2×#124—1221no—
571C2×#124—1221no—
572C2×#124—1221no—
573C2×#124—1221no—
574C2×#124—1221no—
575C2×#124C2×D6111yescharacteristic
576C2×C22⋊Q8—612no—
577C2×C22⋊Q8—1221no—
578C2×C4×Q8—612no—
579C2×C4×Q8—1221no—
580C2×#117—1221no—
581C22×C22⋊C4—1221no—
582C22×C22⋊C4—1221no—
583C22×C42—611no—
584#497—614no—
585#497—614no—
586#497—612no—
587#497—612no—
588#497—612no—
589#497C2×D6112yescomplemented
590#489—612no—
591#489—612no—
592#489—614no—
593#489—614no—
594#489—612no—
595#489C2×D6112yescomplemented
596#464—614no—
597#464—614no—
598#464—614no—
599#464—614no—
600#464—614no—
601#464—614no—
602#464—614no—
603#464C2×D6114yescomplemented
604#451—612no—
605#451—614no—
606#451—612no—
607#451—614no—
608#451—612no—
609#451C2×D6112yescomplemented
610#450—612no—
611#450—614no—
612#450—612no—
613#450—614no—
614#450—612no—
615#450C2×D6112yes—
616#432—611no—
617#432—612no—
618#432—612no—
619#432—612no—
620#432C2×D6111yescharacteristic, complemented
621C2×C4⋊C8—612no—
622C2×#103—614no—
623C2×#102—614no—
624C2×C22⋊C8—612no—
625C2×#97—612no—
626C61C2×#321511yescharacteristic, complemented, Sylow
627C25—1221no—
628C22×Q8—612no—
629C22×Q8—612no—
630C22×Q8—612no—
631C22×Q8—611no—
632C22×Q8—1221no—
633C22×Q8—1221no—
634C22×Q8—1221no—
635C22×Q8—1221no—
636C22×Q8—2444no—
637C22×Q8C22×D6111yescharacteristic
638C22×D4—612no—
639C22×D4—612no—
640C22×D4—611no—
641C22×D4—1221no—
642C22×D4—1221no—
643C22×D4—1221no—
644C22×D4—2444no—
645C22×D4C22×D6111yescharacteristic
646C23×C4—611no—
647C23×C4—611no—
648C23×C4—611no—
649C23×C4—1221no—
650C2×Q16—614no—
651C2×Q16—614no—
652C2×Q16—614no—
653C2×Q16—2448no—
654C2×Q16C22×D6114yescomplemented
655C2×SD16—614no—
656C2×SD16—614no—
657C2×SD16—614no—
658C2×SD16—2448no—
659C2×SD16C22×D6114yes—
660C22×C8—614no—
661C4⋊Q8—612no—
662C4⋊Q8—612no—
663C4⋊Q8—611no—
664C4⋊Q8—611no—
665C4⋊Q8—1221no—
666C4⋊Q8—1221no—
667C4⋊Q8—1221no—
668C4⋊Q8—1221no—
669C4⋊Q8C22×D6111yescharacteristic, complemented
670C4⋊Q8C22×D6111yescharacteristic, complemented
671#125—21no—
672#125—1222no—
673#125—1222no—
674#125—1221no—
675#125—1221no—
676#125—1221no—
677#124—21no—
678#124—21no—
679#124—612no—
680#124—612no—
681#124—612no—
682#124—612no—
683#124—612no—
684#124—612no—
685#124—1222no—
686#124—1222no—
687#124—1222no—
688#124—1222no—
689#124—1222no—
690#124—1222no—
691#124—1222no—
692#124—1222no—
693#124—1221no—
694#124—1221no—
695#124—1221no—
696#124—1221no—
697#124—1221no—
698#124—1221no—
699#124C22×D6112yes—
700#124C22×D6112yes—
701C22⋊Q8—21no—
702C22⋊Q8—612no—
703C22⋊Q8—612no—
704C22⋊Q8—612no—
705C22⋊Q8—1222no—
706C22⋊Q8—1222no—
707C22⋊Q8—1222no—
708C22⋊Q8—1222no—
709C22⋊Q8—1221no—
710C22⋊Q8—1221no—
711C22⋊Q8—1221no—
712C22⋊Q8C22×D6112yes—
713C4×Q8—21no—
714C4×Q8—612no—
715C4×Q8—612no—
716C4×Q8—612no—
717C4×Q8—1222no—
718C4×Q8—1222no—
719C4×Q8—1222no—
720C4×Q8—1221no—
721C4×Q8—1222no—
722C4×Q8—1221no—
723C4×Q8—1221no—
724C4×Q8C22×D6112yescomplemented
725#117—21no—
726#117—1222no—
727#117—1222no—
728#117—1221no—
729#117—1221no—
730#117—1221no—
731C2×C4⋊C4—612no—
732C2×C4⋊C4—1221no—
733C2×C4⋊C4—1221no—
734C2×C4⋊C4—1222no—
735C2×C4⋊C4—1222no—
736C2×C4⋊C4—1221no—
737C2×C22⋊C4—21no—
738C2×C22⋊C4—21no—
739C2×C22⋊C4—1222no—
740C2×C22⋊C4—1222no—
741C2×C22⋊C4—1222no—
742C2×C22⋊C4—1222no—
743C2×C22⋊C4—1222no—
744C2×C22⋊C4—1222no—
745C2×C22⋊C4—1222no—
746C2×C22⋊C4—1222no—
747C2×C22⋊C4—1222no—
748C2×C22⋊C4—1221no—
749C2×C22⋊C4—1221no—
750C2×C22⋊C4—1221no—
751C2×C22⋊C4—1221no—
752C2×C22⋊C4—1221no—
753C2×C22⋊C4—1221no—
754C2×C42—611no—
755C2×C42—611no—
756C2×C42—611no—
757C2×C42—611no—
758C2×C42—611no—
759C2×C42—611no—
760C2×C42—611no—
761C2×C42—611no—
762C2×C42—611no—
763C2×C42—611no—
764C2×C42—611no—
765C2×C42—1222no—
766C2×C42C22×D6111yescharacteristic
767C4⋊C8—614no—
768C4⋊C8—612no—
769C4⋊C8C22×D6112yescomplemented
770#103—614no—
771#103—614no—
772#103—614no—
773#103C22×D6114yescomplemented
774#102—614no—
775#102—614no—
776#102—614no—
777#102C22×D6114yes—
778C22⋊C8—612no—
779C22⋊C8—614no—
780C22⋊C8C22×D6112yes—
781#97—614no—
782#97—612no—
783#97C22×D6112yescomplemented
784C24—21no—
785C24—611no—
786C24—1222no—
787C24—1222no—
788C24—1221no—
789C24—2444no—
790C24—2444no—
791C24—2444no—
792C2×Q8—21no—
793C2×Q8—21no—
794C2×Q8—42no—
795C2×Q8—612no—
796C2×Q8—612no—
797C2×Q8—1222no—
798C2×Q8—1222no—
799C2×Q8—1222no—
800C2×Q8—1222no—
801C2×Q8—1228no—
802C2×Q8—1228no—
803C2×Q8—1221no—
804C2×Q8—1221no—
805C2×Q8—2442no—
806C2×Q8—2444no—
807C2×Q8—2444no—
808C2×Q8—2444no—
809C2×Q8—2444no—
810C2×Q8—2444no—
811C2×Q8C23×D6112yes—
812C2×Q8C23×D6112yes—
813C2×D4—21no—
814C2×D4—42no—
815C2×D4—612no—
816C2×D4—1228no—
817C2×D4—1222no—
818C2×D4—1222no—
819C2×D4—1221no—
820C2×D4—2442no—
821C2×D4—2444no—
822C2×D4—2444no—
823C2×D4—2444no—
824C2×D4—2444no—
825C2×D4C23×D6112yes—
826C22×C4—21no—
827C22×C4—611no—
828C22×C4—611no—
829C22×C4—611no—
830C22×C4—611no—
831C22×C4—611no—
832C22×C4—611no—
833C22×C4—611no—
834C22×C4—611no—
835C22×C4—611no—
836C22×C4—611no—
837C22×C4—611no—
838C22×C4—611no—
839C22×C4—611no—
840C22×C4—611no—
841C22×C4—611no—
842C22×C4—1224no—
843C22×C4—1224no—
844C22×C4—1222no—
845C22×C4—1222no—
846C22×C4—1222no—
847C22×C4—1222no—
848C22×C4—1221no—
849C22×C4—2442no—
850C22×C4—2444no—
851C22×C4D4×D6111yescharacteristic
852C22×C4D4×D6111yescharacteristic
853C22×C4C23×D6111yescharacteristic
854Q16—44no—
855Q16—2444no—
856Q16—2444no—
857Q16—2444no—
858SD16—44no—
859SD16—2444no—
860SD16—2444no—
861SD16—2444no—
862C2×C8—614no—
863C2×C8—1228no—
864C2×C8C23×D6114yes—
865C4⋊C4—21no—
866C4⋊C4—21no—
867C4⋊C4—21no—
868C4⋊C4—22no—
869C4⋊C4—22no—
870C4⋊C4—612no—
871C4⋊C4—1222no—
872C4⋊C4—1222no—
873C4⋊C4—1222no—
874C4⋊C4—1222no—
875C4⋊C4—1222no—
876C4⋊C4—1222no—
877C4⋊C4—1222no—
878C4⋊C4—1222no—
879C4⋊C4—1222no—
880C4⋊C4—1222no—
881C4⋊C4—1221no—
882C4⋊C4—1221no—
883C4⋊C4—1221no—
884C4⋊C4C23×D6112yes—
885C22⋊C4—22no—
886C22⋊C4—22no—
887C22⋊C4—22no—
888C22⋊C4—22no—
889C22⋊C4—22no—
890C22⋊C4—1222no—
891C22⋊C4—1222no—
892C22⋊C4—1222no—
893C22⋊C4—1222no—
894C22⋊C4—1222no—
895C22⋊C4—1222no—
896C22⋊C4—1222no—
897C22⋊C4—1222no—
898C22⋊C4—1222no—
899C22⋊C4—1222no—
900C22⋊C4—1222no—
901C22⋊C4—1222no—
902C22⋊C4—1222no—
903C22⋊C4—1222no—
904C22⋊C4—1222no—
905C42—22no—
906C42—611no—
907C42—611no—
908C42—611no—
909C42—611no—
910C42—611no—
911C42—611no—
912C42—611no—
913C42—611no—
914C42—611no—
915C42—611no—
916C42—611no—
917C42—611no—
918C42—1222no—
919C42—1222no—
920C42—1222no—
921C42D4×D6111yescharacteristic
922C42D4×D6111yescharacteristic
923C42C23×D6111yescharacteristic
924C42C23×D6111yescharacteristic
925C23—22no—
926C23—42no—
927C23—42no—
928C23—42no—
929C23—611no—
930C23—614no—
931C23—611no—
932C23—1222no—
933C23—1222no—
934C23—1222no—
935C23—48816no—
936C23—2442no—
937C23—2442no—
938C23—2444no—
939C23—2444no—
940C23—2444no—
941C23—2444no—
942C23—2444no—
943C23—2444no—
944C23—2442no—
945C23C2×D4×D6111yescharacteristic
946Q8—24no—
947Q8—24no—
948Q8—42no—
949Q8—42no—
950Q8—1224no—
951Q8—1224no—
952Q8—2442no—
953Q8—2442no—
954Q8—2444no—
955Q8—2444no—
956Q8—2444no—
957Q8—2444no—
958D4—24no—
959D4—42no—
960D4—1224no—
961D4—2442no—
962D4—2444no—
963D4—2444no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—41no—
970C2×C4—42no—
971C2×C4—611no—
972C2×C4—614no—
973C2×C4—611no—
974C2×C4—611no—
975C2×C4—611no—
976C2×C4—611no—
977C2×C4—611no—
978C2×C4—1222no—
979C2×C4—1222no—
980C2×C4—1222no—
981C2×C4—1222no—
982C2×C4—1222no—
983C2×C4—1222no—
984C2×C4—1222no—
985C2×C4—1222no—
986C2×C4—1222no—
987C2×C4—1222no—
988C2×C4—1222no—
989C2×C4—1222no—
990C2×C4—1222no—
991C2×C4—1222no—
992C2×C4—2441no—
993C2×C4—2441no—
994C2×C4—2444no—
995C2×C4—2444no—
996C2×C4—2444no—
997C2×C4—2444no—
998C2×C4—2441no—
999C2×C4—2442no—
1000C2×C4C2×D4×D6111yescharacteristic
1001C2×C4C2×D4×D6111yescharacteristic
1002C2×C4C2×D4×D6111yescharacteristic
1003C2×C4C2×D4×D6111yescharacteristic
1004C2×C4C2×D4×D6111yescharacteristic
1005C2×C4C24×D6111yescharacteristic
1006C8—24no—
1007C8—1224no—
1008C22—21no—
1009C22—21no—
1010C22—42no—
1011C22—42no—
1012C22—42no—
1013C22—84no—
1014C22—612no—
1015C22—612no—
1016C22—612no—
1017C22—612no—
1018C22—1228no—
1019C22—1221no—
1020C22—1221no—
1021C22—4884no—
1022C22—4888no—
1023C22—4888no—
1024C22—2442no—
1025C22—2442no—
1026C22—2442no—
1027C22#137×D6112yes—
1028C22C22×D4×D6111yescharacteristic
1029C4—21no—
1030C4—21no—
1031C4—21no—
1032C4—21no—
1033C4—21no—
1034C4—42no—
1035C4—42no—
1036C4—42no—
1037C4—612no—
1038C4—1221no—
1039C4—1221no—
1040C4—1221no—
1041C4—1221no—
1042C4—1221no—
1043C4—2442no—
1044C4—2442no—
1045C4—2442no—
1046C4H(5,𝔽2)×D6112yes—
1047C2—22no—
1048C2—82no—
1049C2—614no—
1050C2—1222no—
1051C2—4882no—
1052C2#535×D6111yescharacteristic
1053C2C2×#137×D6111yescharacteristic
1054C2#575×D6111yescharacteristic
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3215C2
socleC22×C61C23×D4
prime radicalC22×D4×D61C22
hypercenter#3215D61
hypocenterC61C2×#3215
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3215

Complements

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

NH ≅ G/Ntype
1. #533×D61C2semidirect
3. #21456824C2semidirect
4. #21456823C2semidirect
5. #21456822C2semidirect
6. #21456821C2semidirect
7. #21456820C2semidirect
8. #21456819C2semidirect
9. #21456818C2semidirect
10. #21456817C2semidirect
11. #497×D61C2semidirect
12. #489×D61C2semidirect
13. #464×D61C2semidirect
14. #451×D61C2semidirect
16. #432×D61C2semidirect
17. C61×#3215C2semidirect
20. C2×Q16×D61C22semidirect
22. #16840319C22semidirect
24. #16840317C22semidirect
25. #16840317C22semidirect
27. #16840316C22semidirect
30. #16840314C22semidirect
31. C4⋊Q8×D61C22semidirect
32. C4⋊Q8×D61C22semidirect
50. C4×Q8×D61C22semidirect
55. #16840157C22semidirect
56. #16840156C22semidirect
57. #16840155C22semidirect
58. #16840154C22semidirect
59. #16840153C22semidirect
60. #16840124C22semidirect
61. #16840123C22semidirect
62. #16840122C22semidirect
63. #16840121C22semidirect
64. #16840120C22semidirect
65. #16839987C22semidirect
66. #16839986C22semidirect
67. #16839985C22semidirect
68. #16839984C22semidirect
69. #16839983C22semidirect
70. #16839982C22semidirect
71. #16839981C22semidirect
72. #16839920C22semidirect
73. #16839919C22semidirect
74. #16839918C22semidirect
75. #16839917C22semidirect
76. #16839916C22semidirect
82. #16839819C22semidirect
83. #16839818C22semidirect
84. #16839817C22semidirect
85. #16839816C22semidirect
86. C4⋊C8×D61C22semidirect
87. #103×D61C22semidirect
90. #97×D61C22semidirect
91. C61×#533C22semidirect
93. C61×#497C22semidirect
94. C61×#489C22semidirect
95. C61×#464C22semidirect
96. C61×#451C22semidirect
98. C61×#432C22semidirect
120. C2×Dic244C23semidirect
121. C2×#11758202C23semidirect
122. C2×#11758202C23semidirect
129. #14519777C23semidirect
130. #14519777C23semidirect
134. #14519776C23semidirect
136. #14519775C23semidirect
173. Q8×Dic61C23semidirect
177. C4×Dic122C23semidirect
181. #14519742C23semidirect
220. C4⋊#92418C23semidirect
221. #14519706C23semidirect
222. #14519702C23semidirect
223. #14519701C23semidirect
224. #14519700C23semidirect
230. #14519688C23semidirect
231. #14519687C23semidirect
234. C2×Q16×C61C23semidirect
236. C4⋊Q8×C61C23semidirect
237. C4⋊Q8×C61C23semidirect
246. C4×Q8×C61C23semidirect
251. C4⋊C8×C61C23semidirect
252. #103×C61C23semidirect
255. #97×C61C23semidirect
530. #3215D61direct (N × H)
544. D61#3215direct (N × H)
558. #533C2×D61semidirect
589. #497C2×D61semidirect
595. #489C2×D61semidirect
603. #464C2×D61semidirect
609. #451C2×D61semidirect
620. #432C2×D61semidirect
626. C61C2×#3215semidirect
654. C2×Q16C22×D61semidirect
669. C4⋊Q8C22×D61semidirect
670. C4⋊Q8C22×D61semidirect
724. C4×Q8C22×D61semidirect
769. C4⋊C8C22×D61semidirect
773. #103C22×D61semidirect
783. #97C22×D61semidirect

Maximal subgroups

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

subgroupindex
#533×D612
C2×#124×D612
#214568242
#214568232
#214568222
#214568212
#214568202
#214568192
#214568182
#214568172
#497×D612
#489×D612
#464×D612
#451×D612
#450×D612
#432×D612
C61×#32152
C2×#321561