Finite Group Databasebeta

← D61×#3254 #30552879

Subgroups — D61×#3254 #30552879

Order 15616.

2146 conjugacy classes of subgroups.

The subgroup lattice has 1046 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#533×D61C211yesmaximal, characteristic, complemented
2#532×D61C211yesmaximal, characteristic
3#21457208C212yesmaximal, complemented
4#21457207C211yesmaximal, characteristic, complemented
5#21457206C211yesmaximal, characteristic, complemented
6#21457205C212yesmaximal, complemented
7#21457204C212yesmaximal, complemented
8#21457203C212yesmaximal, complemented
9#21457202C211yesmaximal, characteristic, complemented
10#21457201C214yesmaximal, complemented
11#477×D61C212yesmaximal, complemented
12#474×D61C212yesmaximal, complemented
13#468×D61C214yesmaximal, complemented
14#460×D61C212yesmaximal, complemented
15#461×D61C212yesmaximal, complemented
16#423×D61C211yesmaximal, characteristic, complemented
17C61×#3254C211yesmaximal, characteristic, complemented
18C2×#41×D61—21no—
19C2×SD16×D61C2214yes—
20C2×M16×D61C2212yes—
21#16840319C2211yescharacteristic, complemented
22#16840318—21no—
23#16840317C2211yescharacteristic, complemented
24#16840317C2211yescharacteristic, complemented
25#16840316—21no—
26#16840316C2212yescomplemented
27#16840315—21no—
28#16840314—21no—
29#16840314C2212yescomplemented
30#16840313C2211yescharacteristic
31#16840312C2211yescharacteristic
32#16840311—21no—
33#16840310C2211yescharacteristic
34#16840309—21no—
35#16840309C2212yes—
36#16840308—21no—
37#16840307—21no—
38#16840307C2212yes—
39C4⋊Q8×D61C2211yescharacteristic
40C4⋊Q8×D61C2211yescharacteristic
41C4⋊Q8×D61C2211yescharacteristic
42#127×D61C2211yescharacteristic
43#125×D61—21no—
44#124×D61—21no—
45C22⋊Q8×D61—21no—
46C22⋊Q8×D61C2212yes—
47#121×D61—21no—
48#121×D61C2212yes—
49C4×Q8×D61—21no—
50C4×Q8×D61C2212yes—
51C4×D4×D61—21no—
52C4×D4×D61C2212yes—
53#117×D61—21no—
54C2×C42×D61C2211yescharacteristic
55#16840058C2212yescomplemented
56#16840057C2212yescomplemented
57#16840056C2214yescomplemented
58#16840055C2214yescomplemented
59#16840054C2212yescomplemented
60#16840043C2212yescomplemented
61#16840042C2212yescomplemented
62#16840041C2214yescomplemented
63#16840040C2214yescomplemented
64#16840039C2212yescomplemented
65#16840011C2214yescomplemented
66#16840010C2214yescomplemented
67#16840009C2214yescomplemented
68#16840008C2214yescomplemented
69#16840007C2214yescomplemented
70#16840006C2214yescomplemented
71#16840005C2214yescomplemented
72#16839968C2212yescomplemented
73#16839967C2212yescomplemented
74#16839966C2214yescomplemented
75#16839965C2214yescomplemented
76#16839964C2212yescomplemented
77#16839963C2212yescomplemented
78#16839962C2212yescomplemented
79#16839961C2214yescomplemented
80#16839960C2214yescomplemented
81#16839959C2212yescomplemented
82#107×D61C2214yes—
83#16839786C2211yescharacteristic, complemented
84#16839785C2212yescomplemented
85#16839784C2212yescomplemented
86#16839784C2212yescomplemented
87C4⋊C8×D61C2212yes—
88C4⋊C8×D61C2212yes—
89#103×D61C2214yes—
90#102×D61C2214yes—
91C61×#533C2211yescharacteristic, complemented
92C61×#532C2211yescharacteristic
93C61×#477C2212yescomplemented
94C61×#474C2212yescomplemented
95C61×#468C2214yescomplemented
96C61×#461C2212yescomplemented
97C61×#460C2212yescomplemented
98C61×#423C2211yescharacteristic, complemented
99C2×#11758226—21no—
100C2×#11758222—21no—
101C2×#11758222—22no—
102C2×#11758224—22no—
103C2×#11758224—21no—
104#41×D61—48no—
105C2×Q8×D61—21no—
106C2×Q8×D61—21no—
107C2×Q8×D61C2312yes—
108C2×D4×D61—22no—
109C2×D4×D61—21no—
110C2×D4×D61—21no—
111C2×D4×D61C2312yes—
112C22×C4×D61—22no—
113C22×C4×D61D411yescharacteristic
114C22×C4×D61D411yescharacteristic
115C22×C4×D61C2311yescharacteristic
116C2×#11758190C2314yes—
117C2×#11758200C2314yes—
118C2×#11758201C2314yes—
119SD16×D61—48no—
120C2×#11758194C2312yes—
121C2×#11758189C2314yes—
122M16×D61—44no—
123C2×C8×D61C2314yes—
124#14519777C2311yescharacteristic
125#14519777C2311yescharacteristic
126#14519777C2311yescharacteristic
127#14519776—21no—
128#14519776—21no—
129#14519776—21no—
130#14519776—21no—
131#14519776C2312yes—
132#14519776C2312yes—
133#14519775—21no—
134#14519775—21no—
135#14519775C2312yes—
136#14519774C2311yescharacteristic
137#14519773—21no—
138#14519773—21no—
139#14519773C2312yes—
140#14519769—21no—
141#14519768—21no—
142#14519768—21no—
143#14519767—22no—
144#14519767—22no—
145#14519766—21no—
146#14519765—21no—
147#14519764—21no—
148#14519763—22no—
149#14519763—22no—
150#14519757—21no—
151#14519757C2312yes—
152#14519756—21no—
153#14519756C2312yes—
154#14519755—22no—
155#14519755—22no—
156#14519754—22no—
157#14519754—22no—
158#14519753—21no—
159#14519753C2312yes—
160#14519752—21no—
161#14519752C2312yes—
162#14519751—21no—
163#14519751C2312yes—
164#14519750—22no—
165#14519750—22no—
166#14519749—22no—
167#14519749—22no—
168#14519748—21no—
169#14519748C2312yes—
170Q8×Dic61—21no—
171Q8×Dic61C2312yes—
172C4×Dic122—21no—
173C4×Dic122—22no—
174C4×Dic122—22no—
175C4×Dic122C2312yes—
176#14519742—21no—
177#14519742—22no—
178#14519742—22no—
179#14519742C2312yes—
180C4×D244—21no—
181C4×D244C2312yes—
182D4×Dic61—21no—
183D4×Dic61C2312yes—
184#14519739—21no—
185#14519739C2312yes—
186C4×C22⋊D61—22no—
187C4×C22⋊D61—22no—
188#14519737—22no—
189#14519737—22no—
190#14519736—21no—
191#14519735—21no—
192#14519735—21no—
193#14519734—22no—
194#14519733—22no—
195C4⋊C4×D61—21no—
196C4⋊C4×D61—21no—
197C4⋊C4×D61—21no—
198C4⋊C4×D61—21no—
199C4⋊C4×D61—22no—
200C4⋊C4×D61—22no—
201C4⋊C4×D61C2312yes—
202C4⋊C4×D61C2312yes—
203C22⋊C4×D61—22no—
204C22⋊C4×D61—22no—
205C22⋊C4×D61—22no—
206C2×C4×Dic61D411yescharacteristic
207C2×C4×Dic61D411yescharacteristic
208C2×C4×Dic61C2311yescharacteristic
209C42×D61—22no—
210C42×D61D411yescharacteristic
211C42×D61D411yescharacteristic
212C42×D61D411yescharacteristic
213C42×D61D411yescharacteristic
214C42×D61C2311yescharacteristic
215C42×D61C2311yescharacteristic
216C42×D61C2311yescharacteristic
217C42×D61C2311yescharacteristic
218#14519711C2314yes—
219#14519710C2314yes—
220#14519710C2314yes—
221C4⋊#92418C2312yes—
222C4⋊#92418C2312yes—
223#14519706C2314yes—
224#14519706C2314yes—
225#14519702C2314yes—
226#14519701C2314yes—
227#14519700C2314yes—
228#14519699C2314yes—
229#14519698C2314yes—
230#14519697C2314yes—
231C2×#41×C61—21no—
232C2×SD16×C61C2314yes—
233C2×M16×C61C2312yes—
234C4⋊Q8×C61C2311yescharacteristic
235C4⋊Q8×C61C2311yescharacteristic
236C4⋊Q8×C61C2311yescharacteristic
237#127×C61C2311yescharacteristic
238#125×C61—21no—
239#124×C61—21no—
240C22⋊Q8×C61—21no—
241C22⋊Q8×C61C2312yes—
242#121×C61—21no—
243#121×C61C2312yes—
244C4×Q8×C61—21no—
245C4×Q8×C61C2312yes—
246C4×D4×C61—21no—
247C4×D4×C61C2312yes—
248#117×C61—21no—
249C2×C42×C61C2311yescharacteristic
250#107×C61C2314yes—
251C4⋊C8×C61C2312yes—
252C4⋊C8×C61C2312yes—
253#103×C61C2314yes—
254#102×C61C2314yes—
255C23×D61—22no—
256C23×D61C2×D411yescharacteristic
257#41×C61—44no—
258C2×Q8×C61—21no—
259C2×Q8×C61—21no—
260C2×Q8×C61C2412yes—
261C2×D4×C61—22no—
262C2×D4×C61—21no—
263C2×D4×C61—21no—
264C2×D4×C61C2412yes—
265C22×C4×C61—22no—
266C22×C4×C61C2×D411yescharacteristic
267C22×C4×C61C2×D411yescharacteristic
268C22×C4×C61C2411yescharacteristic
269C2×C22⋊D61—22no—
270C2×C22⋊D61—22no—
271C2×C22⋊D61—22no—
272C2×C22⋊D61—22no—
273C2×C22⋊D61—22no—
274C22×Dic61—22no—
275C22×Dic61C2×D411yescharacteristic
276C22×Dic61C2×D411yescharacteristic
277C22×Dic61C2×D411yescharacteristic
278#11758226—44no—
279Q8×D61—24no—
280Q8×D61—24no—
281Q8×D61—44no—
282Q8×D61—44no—
283#11758224—44no—
284#11758224—48no—
285D4×D61—24no—
286D4×D61—24no—
287D4×D61—44no—
288D4×D61—48no—
289D4×D61—44no—
290#11758222—48no—
291#11758222—44no—
292C2×D244—22no—
293C2×D244—21no—
294C2×D244—21no—
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—22no—
303C2×C4×D61—22no—
304C2×C4×D61—22no—
305C2×C4×D61—48no—
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×D61C2×D411yescharacteristic
315C2×C4×D61C2×D411yescharacteristic
316C2×C4×D61C2411yescharacteristic
317C2×C4×D61C2411yescharacteristic
318C2×Dic122—21no—
319C2×Dic122—21no—
320C2×Dic122—22no—
321C2×Dic122—22no—
322C2×Dic122—22no—
323C2×Dic122C2412yes—
324SD16×C61—44no—
325M16×C61—42no—
326C2×C8×C61C2414yes—
327C4⋊C4×C61—21no—
328C4⋊C4×C61—21no—
329C4⋊C4×C61—21no—
330C4⋊C4×C61—21no—
331C4⋊C4×C61—22no—
332C4⋊C4×C61—22no—
333C4⋊C4×C61C2412yes—
334C4⋊C4×C61C2412yes—
335C22⋊C4×C61—22no—
336C22⋊C4×C61—22no—
337C22⋊C4×C61—22no—
338C42×C61—22no—
339C42×C61C2×D411yescharacteristic
340C42×C61C2×D411yescharacteristic
341C42×C61C2411yescharacteristic
342C42×C61C2411yescharacteristic
343C22⋊Dic61—22no—
344C22⋊Dic61—22no—
345C22⋊Dic61—22no—
346#11758201—44no—
347#11758200—44no—
348#11758198—22no—
349#11758198—22no—
350#11758198—22no—
351#11758198—22no—
352#11758198—22no—
353#11758198—22no—
354C4⋊Dic61—21no—
355C4⋊Dic61—21no—
356C4⋊Dic61—21no—
357C4⋊Dic61—21no—
358C4⋊Dic61—22no—
359C4⋊Dic61—22no—
360C4⋊Dic61C2412yes—
361C4⋊Dic61C2412yes—
362#11758196—22no—
363#11758196—22no—
364#11758196—22no—
365#11758196—22no—
366#11758196—22no—
367#11758196—22no—
368#11758196—22no—
369#11758196—22no—
370#11758196—22no—
371#11758196—22no—
372C4×Dic61—22no—
373C4×Dic61—22no—
374C4×Dic61—22no—
375C4×Dic61C2×D411yescharacteristic
376C4×Dic61C2×D411yescharacteristic
377C4×Dic61C2×D411yescharacteristic
378C4×Dic61C2×D411yescharacteristic
379C4×Dic61C2×D411yescharacteristic
380C4×Dic61C2×D411yescharacteristic
381C4×Dic61C2×D411yescharacteristic
382C4×Dic61C2×D411yescharacteristic
383C4×Dic61C2×D411yescharacteristic
384C4×Dic61C2×D411yescharacteristic
385C4×Dic61C2411yescharacteristic
386C4×Dic61C2411yescharacteristic
387#11758194—42no—
388C2×#92418C2414yes—
389#11758190—44no—
390#11758189—44no—
391C8×D61—28no—
392C23×C61—22no—
393C23×C61C22×D411yescharacteristic
394C22×D61—22no—
395C22×D61—22no—
396C22×D61—22no—
397C22×D61—22no—
398C22×D61—44no—
399C22×D61—44no—
400C22×D61—44no—
401C22×D61C22×D411yescharacteristic
402C22×D61C22×D411yescharacteristic
403Q8×C61—22no—
404Q8×C61—22no—
405Q8×C61—42no—
406Q8×C61—42no—
407D4×C61—22no—
408D4×C61—22no—
409D4×C61—42no—
410D4×C61—44no—
411D4×C61—42no—
412C2×C4×C61—22no—
413C2×C4×C61—22no—
414C2×C4×C61—21no—
415C2×C4×C61—21no—
416C2×C4×C61—22no—
417C2×C4×C61—22no—
418C2×C4×C61—22no—
419C2×C4×C61—44no—
420C2×C4×C61C22×D411yescharacteristic
421C2×C4×C61C22×D411yescharacteristic
422C2×C4×C61C22×D411yescharacteristic
423C2×C4×C61C22×D411yescharacteristic
424C2×C4×C61C22×D411yescharacteristic
425C2×C4×C61C2511yescharacteristic
426C22⋊D61—44no—
427C22⋊D61—44no—
428C22⋊D61—44no—
429C22⋊D61—44no—
430C22⋊D61—44no—
431C2×Dic61—22no—
432C2×Dic61—22no—
433C2×Dic61—22no—
434C2×Dic61—22no—
435C2×Dic61—22no—
436C2×Dic61—22no—
437C2×Dic61—44no—
438C2×Dic61C22×D411yescharacteristic
439C2×Dic61C22×D411yescharacteristic
440C2×Dic61C22×D411yescharacteristic
441C2×Dic61C22×D411yescharacteristic
442C2×Dic61C22×D411yescharacteristic
443C2×Dic61C22×D411yescharacteristic
444D244—22no—
445D244—22no—
446D244—42no—
447D244—44no—
448D244—42no—
449C4×D61—22no—
450C4×D61—22no—
451C4×D61—22no—
452C4×D61—22no—
453C4×D61—22no—
454C4×D61—21no—
455C4×D61—21no—
456C4×D61—22no—
457C4×D61—22no—
458C4×D61—22no—
459C4×D61—44no—
460C4×D61—44no—
461C4×D61—44no—
462C4×D61—44no—
463C4×D61—44no—
464C4×D61AGL(1,ℤ/8)14yes—
465C4×D61#13714yes—
466C4×D61H(5,𝔽2)12yes—
467C4×D612−1+412yes—
468Dic122—22no—
469Dic122—22no—
470Dic122—44no—
471Dic122—42no—
472Dic122—42no—
473Dic122—44no—
474Dic122—44no—
475C8×C61—24no—
476#92418—24no—
477C2×#3254—611nomaximal, Sylow
478C22×C61—21no—
479C22×C61—21no—
480C22×C61—21no—
481C22×C61—42no—
482C22×C61—42no—
483C22×C61—42no—
484C22×C61C23×D411yescharacteristic
485C2×D61—21no—
486C2×D61—21no—
487C2×D61—21no—
488C2×D61—44no—
489C2×D61—42no—
490C2×D61—42no—
491C2×D61—42no—
492C2×D61—88no—
493C2×D61#53712yes—
494C2×D61C2×AGL(1,ℤ/8)12yes—
495C2×D61C2×#13712yes—
496C4×C61—21no—
497C4×C61—21no—
498C4×C61—21no—
499C4×C61—42no—
500C4×C61—42no—
501C4×C61—42no—
502C4×C61C2×AGL(1,ℤ/8)12yes—
503C4×C61C2×#13712yes—
504C4×C61C2×H(5,𝔽2)11yescharacteristic
505C4×C61C2×2−1+411yescharacteristic
506Dic61—21no—
507Dic61—21no—
508Dic61—21no—
509Dic61—42no—
510Dic61—42no—
511Dic61—42no—
512Dic61#53712yes—
513Dic61C2×AGL(1,ℤ/8)12yes—
514Dic61C2×#13712yes—
515C2×#533—611no—
516C2×#532—611no—
517#3254—612no—
518#3254—612no—
519#3254—614no—
520#3254—612no—
521#3254—612no—
522#3254—611no—
523#3254—611no—
524#3254—611no—
525#3254D6111yescharacteristic, direct product factor
526C2×#477—612no—
527C2×#474—612no—
528C2×#468—614no—
529C2×#460—612no—
530C2×#461—612no—
531C2×#423—611no—
532C2×C61—41no—
533C2×C61—82no—
534C2×C61C2×#53711yescharacteristic
535C2×C61C22×AGL(1,ℤ/8)11yescharacteristic
536C2×C61C22×#13711yescharacteristic
537D61—41no—
538D61—82no—
539D61#325414yesdirect product factor
540C22×#41—1221no—
541C22×SD16—614no—
542C22×M16—612no—
543#533—611no—
544#533—611no—
545#533—612no—
546#533—612no—
547#533—611no—
548#533—1221no—
549#533—1221no—
550#533—1221no—
551#533—1221no—
552#533C2×D6111yescharacteristic, complemented
553#532—611no—
554#532—611no—
555#532—612no—
556#532—612no—
557#532—611no—
558#532—1221no—
559#532—1221no—
560#532—1221no—
561#532—1221no—
562#532C2×D6111yescharacteristic
563C2×C4⋊Q8—611no—
564C2×C4⋊Q8—611no—
565C2×C4⋊Q8—611no—
566C2×#127—611no—
567C2×#125—1221no—
568C2×#124—1221no—
569C2×C22⋊Q8—612no—
570C2×C22⋊Q8—1221no—
571C2×#121—612no—
572C2×#121—1221no—
573C2×C4×Q8—612no—
574C2×C4×Q8—1221no—
575C2×C4×D4—612no—
576C2×C4×D4—1221no—
577C2×#117—1221no—
578C22×C42—611no—
579#477—612no—
580#477—612no—
581#477—614no—
582#477—612no—
583#477—614no—
584#477C2×D6112yescomplemented
585#474—612no—
586#474—612no—
587#474—614no—
588#474—612no—
589#474—614no—
590#474C2×D6112yescomplemented
591#468—614no—
592#468—614no—
593#468—614no—
594#468—614no—
595#468—614no—
596#468—614no—
597#468—614no—
598#468C2×D6114yescomplemented
599#461—614no—
600#461—612no—
601#461—612no—
602#461—612no—
603#461—614no—
604#461C2×D6112yescomplemented
605#460—614no—
606#460—612no—
607#460—612no—
608#460—612no—
609#460—614no—
610#460C2×D6112yescomplemented
611C2×#107—614no—
612#423—612no—
613#423—611no—
614#423—612no—
615#423—612no—
616#423C2×D6111yescharacteristic, complemented
617C2×C4⋊C8—612no—
618C2×C4⋊C8—612no—
619C2×#103—614no—
620C2×#102—614no—
621C61C2×#325411yescharacteristic, complemented, Sylow
622C2×#41—21no—
623C2×#41—1222no—
624C2×#41—1222no—
625C2×#41—1221no—
626C2×#41—1221no—
627C2×#41—1221no—
628C2×#41—2448no—
629C22×Q8—612no—
630C22×Q8—1221no—
631C22×Q8—1221no—
632C22×D4—612no—
633C22×D4—1221no—
634C22×D4—1221no—
635C22×D4—1222no—
636C23×C4—611no—
637C23×C4—611no—
638C23×C4—611no—
639C23×C4—1222no—
640C2×SD16—614no—
641C2×SD16—614no—
642C2×SD16—614no—
643C2×SD16—2448no—
644C2×SD16C22×D6114yes—
645C2×M16—612no—
646C2×M16—614no—
647C2×M16—2444no—
648C2×M16C22×D6112yes—
649C22×C8—614no—
650C4⋊Q8—612no—
651C4⋊Q8—612no—
652C4⋊Q8—612no—
653C4⋊Q8—611no—
654C4⋊Q8—611no—
655C4⋊Q8—611no—
656C4⋊Q8—1221no—
657C4⋊Q8—1221no—
658C4⋊Q8—1221no—
659C4⋊Q8—1221no—
660C4⋊Q8—1221no—
661C4⋊Q8—1221no—
662C4⋊Q8C22×D6111yescharacteristic
663C4⋊Q8C22×D6111yescharacteristic
664C4⋊Q8C22×D6111yescharacteristic
665#127—612no—
666#127—611no—
667#127—1221no—
668#127—1221no—
669#127C22×D6111yescharacteristic
670#125—21no—
671#125—1222no—
672#125—1222no—
673#125—1221no—
674#125—1221no—
675#125—1221no—
676#124—21no—
677#124—1222no—
678#124—1222no—
679#124—1221no—
680#124—1221no—
681#124—1221no—
682C22⋊Q8—21no—
683C22⋊Q8—612no—
684C22⋊Q8—612no—
685C22⋊Q8—612no—
686C22⋊Q8—1222no—
687C22⋊Q8—1222no—
688C22⋊Q8—1222no—
689C22⋊Q8—1222no—
690C22⋊Q8—1221no—
691C22⋊Q8—1221no—
692C22⋊Q8—1221no—
693C22⋊Q8C22×D6112yes—
694#121—21no—
695#121—612no—
696#121—612no—
697#121—612no—
698#121—1222no—
699#121—1222no—
700#121—1221no—
701#121—1222no—
702#121—1221no—
703#121—1222no—
704#121—1221no—
705#121C22×D6112yes—
706C4×Q8—21no—
707C4×Q8—612no—
708C4×Q8—612no—
709C4×Q8—612no—
710C4×Q8—1222no—
711C4×Q8—1222no—
712C4×Q8—1222no—
713C4×Q8—1221no—
714C4×Q8—1222no—
715C4×Q8—1221no—
716C4×Q8—1221no—
717C4×Q8C22×D6112yes—
718C4×D4—21no—
719C4×D4—612no—
720C4×D4—612no—
721C4×D4—612no—
722C4×D4—1222no—
723C4×D4—1222no—
724C4×D4—1221no—
725C4×D4—1222no—
726C4×D4—1222no—
727C4×D4—1221no—
728C4×D4—1221no—
729C4×D4C22×D6112yes—
730#117—21no—
731#117—1222no—
732#117—1222no—
733#117—1221no—
734#117—1221no—
735#117—1221no—
736C2×C4⋊C4—612no—
737C2×C4⋊C4—612no—
738C2×C4⋊C4—1221no—
739C2×C4⋊C4—1221no—
740C2×C4⋊C4—1221no—
741C2×C4⋊C4—1222no—
742C2×C4⋊C4—1222no—
743C2×C4⋊C4—1221no—
744C2×C22⋊C4—1222no—
745C2×C22⋊C4—1222no—
746C2×C22⋊C4—1222no—
747C2×C42—611no—
748C2×C42—611no—
749C2×C42—611no—
750C2×C42—611no—
751C2×C42—611no—
752C2×C42—611no—
753C2×C42—611no—
754C2×C42—611no—
755C2×C42—611no—
756C2×C42—611no—
757C2×C42—611no—
758C2×C42—1222no—
759C2×C42C22×D6111yescharacteristic
760#107—614no—
761#107—614no—
762#107—614no—
763#107C22×D6114yes—
764C4⋊C8—614no—
765C4⋊C8—614no—
766C4⋊C8—612no—
767C4⋊C8—612no—
768C4⋊C8C22×D6112yes—
769C4⋊C8C22×D6112yes—
770#103—614no—
771#103—614no—
772#103—614no—
773#103C22×D6114yes—
774#102—614no—
775#102—614no—
776#102—614no—
777#102C22×D6114yes—
778C24—611no—
779C24—1222no—
780#41—44no—
781#41—2444no—
782#41—2448no—
783#41—2444no—
784#41—2448no—
785#41—2444no—
786C2×Q8—21no—
787C2×Q8—21no—
788C2×Q8—612no—
789C2×Q8—1222no—
790C2×Q8—1222no—
791C2×Q8—1222no—
792C2×Q8—1224no—
793C2×Q8—1224no—
794C2×Q8—1221no—
795C2×Q8—1221no—
796C2×Q8—2444no—
797C2×Q8—2444no—
798C2×Q8C23×D6112yes—
799C2×D4—22no—
800C2×D4—21no—
801C2×D4—21no—
802C2×D4—612no—
803C2×D4—1222no—
804C2×D4—1224no—
805C2×D4—1224no—
806C2×D4—1222no—
807C2×D4—1222no—
808C2×D4—1222no—
809C2×D4—1222no—
810C2×D4—1222no—
811C2×D4—1221no—
812C2×D4—1221no—
813C2×D4—2444no—
814C2×D4—2444no—
815C2×D4—2448no—
816C2×D4C23×D6112yes—
817C22×C4—22no—
818C22×C4—611no—
819C22×C4—611no—
820C22×C4—611no—
821C22×C4—611no—
822C22×C4—611no—
823C22×C4—611no—
824C22×C4—611no—
825C22×C4—611no—
826C22×C4—611no—
827C22×C4—611no—
828C22×C4—611no—
829C22×C4—611no—
830C22×C4—611no—
831C22×C4—611no—
832C22×C4—611no—
833C22×C4—1222no—
834C22×C4—1224no—
835C22×C4—1222no—
836C22×C4—1224no—
837C22×C4—1222no—
838C22×C4—1222no—
839C22×C4—1222no—
840C22×C4—1222no—
841C22×C4—1222no—
842C22×C4—1222no—
843C22×C4—2448no—
844C22×C4D4×D6111yescharacteristic
845C22×C4D4×D6111yescharacteristic
846C22×C4C23×D6111yescharacteristic
847SD16—44no—
848SD16—2444no—
849SD16—2444no—
850SD16—2444no—
851M16—42no—
852M16—2444no—
853M16—2442no—
854C2×C8—614no—
855C2×C8—1228no—
856C2×C8C23×D6114yes—
857C4⋊C4—21no—
858C4⋊C4—21no—
859C4⋊C4—21no—
860C4⋊C4—21no—
861C4⋊C4—22no—
862C4⋊C4—22no—
863C4⋊C4—612no—
864C4⋊C4—612no—
865C4⋊C4—1222no—
866C4⋊C4—1222no—
867C4⋊C4—1222no—
868C4⋊C4—1222no—
869C4⋊C4—1222no—
870C4⋊C4—1222no—
871C4⋊C4—1222no—
872C4⋊C4—1222no—
873C4⋊C4—1222no—
874C4⋊C4—1222no—
875C4⋊C4—1222no—
876C4⋊C4—1222no—
877C4⋊C4—1221no—
878C4⋊C4—1221no—
879C4⋊C4—1221no—
880C4⋊C4—1221no—
881C4⋊C4C23×D6112yes—
882C4⋊C4C23×D6112yes—
883C22⋊C4—22no—
884C22⋊C4—22no—
885C22⋊C4—22no—
886C22⋊C4—1222no—
887C22⋊C4—1222no—
888C22⋊C4—1222no—
889C22⋊C4—1222no—
890C22⋊C4—1222no—
891C22⋊C4—1222no—
892C22⋊C4—1222no—
893C22⋊C4—1222no—
894C22⋊C4—1222no—
895C42—22no—
896C42—611no—
897C42—611no—
898C42—611no—
899C42—611no—
900C42—611no—
901C42—611no—
902C42—611no—
903C42—611no—
904C42—611no—
905C42—611no—
906C42—611no—
907C42—611no—
908C42—1222no—
909C42—1222no—
910C42—1222no—
911C42D4×D6111yescharacteristic
912C42D4×D6111yescharacteristic
913C42C23×D6111yescharacteristic
914C42C23×D6111yescharacteristic
915C23—22no—
916C23—611no—
917C23—611no—
918C23—1222no—
919C23—1222no—
920C23—1222no—
921C23—1222no—
922C23—2444no—
923C23—2444no—
924C23—2444no—
925C23C2×D4×D6111yescharacteristic
926Q8—22no—
927Q8—22no—
928Q8—42no—
929Q8—42no—
930Q8—1222no—
931Q8—1222no—
932Q8—2442no—
933Q8—2444no—
934Q8—2444no—
935Q8—2444no—
936Q8—2442no—
937D4—22no—
938D4—22no—
939D4—42no—
940D4—44no—
941D4—42no—
942D4—1222no—
943D4—1222no—
944D4—2442no—
945D4—2444no—
946D4—2444no—
947D4—2444no—
948D4—2444no—
949D4—2444no—
950D4—2444no—
951D4—2442no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—21no—
955C2×C4—21no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—44no—
960C2×C4—611no—
961C2×C4—611no—
962C2×C4—611no—
963C2×C4—614no—
964C2×C4—614no—
965C2×C4—612no—
966C2×C4—612no—
967C2×C4—611no—
968C2×C4—611no—
969C2×C4—611no—
970C2×C4—1222no—
971C2×C4—1222no—
972C2×C4—1222no—
973C2×C4—1222no—
974C2×C4—1222no—
975C2×C4—1222no—
976C2×C4—1222no—
977C2×C4—1222no—
978C2×C4—1222no—
979C2×C4—1222no—
980C2×C4—1222no—
981C2×C4—1221no—
982C2×C4—1221no—
983C2×C4—1222no—
984C2×C4—1222no—
985C2×C4—1222no—
986C2×C4—2444no—
987C2×C4—2444no—
988C2×C4—2444no—
989C2×C4—2444no—
990C2×C4—2444no—
991C2×C4—2444no—
992C2×C4C2×D4×D6111yescharacteristic
993C2×C4C2×D4×D6111yescharacteristic
994C2×C4C2×D4×D6111yescharacteristic
995C2×C4C2×D4×D6111yescharacteristic
996C2×C4C2×D4×D6111yescharacteristic
997C2×C4C24×D6111yescharacteristic
998C8—24no—
999C8—1224no—
1000C22—21no—
1001C22—21no—
1002C22—21no—
1003C22—42no—
1004C22—42no—
1005C22—42no—
1006C22—612no—
1007C22—612no—
1008C22—612no—
1009C22—1221no—
1010C22—1221no—
1011C22—1221no—
1012C22—4888no—
1013C22—2444no—
1014C22—2442no—
1015C22—2442no—
1016C22—2442no—
1017C22C22×D4×D6111yescharacteristic
1018C4—21no—
1019C4—21no—
1020C4—21no—
1021C4—42no—
1022C4—42no—
1023C4—42no—
1024C4—612no—
1025C4—612no—
1026C4—612no—
1027C4—1221no—
1028C4—1221no—
1029C4—1221no—
1030C4—2442no—
1031C4—2442no—
1032C4—2442no—
1033C4AGL(1,ℤ/8)×D6112yes—
1034C4#137×D6112yes—
1035C4H(5,𝔽2)×D6111yescharacteristic
1036C42−1+4×D6111yescharacteristic
1037C2—41no—
1038C2—82no—
1039C2—614no—
1040C2—4882no—
1041C2—2441no—
1042C2#537×D6111yescharacteristic
1043C2C2×AGL(1,ℤ/8)×D6111yescharacteristic
1044C2C2×#137×D6111yescharacteristic
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3254C2
socleC22×C61C23×D4
prime radical#532×D61C2
hypercenter#3254D61
hypocenterC61C2×#3254
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3254

Complements

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

NH ≅ G/Ntype
1. #533×D61C2semidirect
3. #21457208C2semidirect
4. #21457207C2semidirect
5. #21457206C2semidirect
6. #21457205C2semidirect
7. #21457204C2semidirect
8. #21457203C2semidirect
9. #21457202C2semidirect
10. #21457201C2semidirect
11. #477×D61C2semidirect
12. #474×D61C2semidirect
13. #468×D61C2semidirect
14. #460×D61C2semidirect
15. #461×D61C2semidirect
16. #423×D61C2semidirect
17. C61×#3254C2semidirect
21. #16840319C22semidirect
23. #16840317C22semidirect
24. #16840317C22semidirect
26. #16840316C22semidirect
29. #16840314C22semidirect
55. #16840058C22semidirect
56. #16840057C22semidirect
57. #16840056C22semidirect
58. #16840055C22semidirect
59. #16840054C22semidirect
60. #16840043C22semidirect
61. #16840042C22semidirect
62. #16840041C22semidirect
63. #16840040C22semidirect
64. #16840039C22semidirect
65. #16840011C22semidirect
66. #16840010C22semidirect
67. #16840009C22semidirect
68. #16840008C22semidirect
69. #16840007C22semidirect
70. #16840006C22semidirect
71. #16840005C22semidirect
72. #16839968C22semidirect
73. #16839967C22semidirect
74. #16839966C22semidirect
75. #16839965C22semidirect
76. #16839964C22semidirect
77. #16839963C22semidirect
78. #16839962C22semidirect
79. #16839961C22semidirect
80. #16839960C22semidirect
81. #16839959C22semidirect
83. #16839786C22semidirect
84. #16839785C22semidirect
85. #16839784C22semidirect
86. #16839784C22semidirect
91. C61×#533C22semidirect
93. C61×#477C22semidirect
94. C61×#474C22semidirect
95. C61×#468C22semidirect
96. C61×#461C22semidirect
97. C61×#460C22semidirect
98. C61×#423C22semidirect
525. #3254D61direct (N × H)
539. D61#3254direct (N × H)
552. #533C2×D61semidirect
584. #477C2×D61semidirect
590. #474C2×D61semidirect
598. #468C2×D61semidirect
604. #461C2×D61semidirect
610. #460C2×D61semidirect
616. #423C2×D61semidirect
621. C61C2×#3254semidirect

Maximal subgroups

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

subgroupindex
#533×D612
#532×D612
#214572082
#214572072
#214572062
#214572052
#214572042
#214572032
#214572022
#214572012
#477×D612
#474×D612
#468×D612
#460×D612
#461×D612
#423×D612
C61×#32542
C2×#325461