Finite Group Databasebeta

← D61×#3231 #30552075

Subgroups — D61×#3231 #30552075

Order 15616.

1778 conjugacy classes of subgroups.

The subgroup lattice has 976 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#533×D61C211yesmaximal, characteristic
2#533×D61C211yesmaximal, characteristic
3#21456981C211yesmaximal, characteristic, complemented
4#21456980C211yesmaximal, characteristic, complemented
5#21456979C211yesmaximal, characteristic, complemented
6#21456978C211yesmaximal, characteristic, complemented
7#21456977C214yesmaximal, complemented
8#21456976C214yesmaximal, complemented
9#21456975C211yesmaximal, characteristic, complemented
10#21456974C211yesmaximal, characteristic, complemented
11#21456973C211yesmaximal, characteristic, complemented
12#500×D61C211yesmaximal, characteristic, complemented
13#498×D61C211yesmaximal, characteristic, complemented
14#487×D61C211yesmaximal, characteristic, complemented
15#487×D61C211yesmaximal, characteristic, complemented
16#485×D61C214yesmaximal
17#479×D61C214yesmaximal, complemented
18#431×D61C211yesmaximal, characteristic
19C61×#3231C211yesmaximal, characteristic, complemented
20#16840319C2211yescharacteristic
21#16840319C2211yescharacteristic
22#16840318—21no—
23#16840318C2212yes—
24#16840317C2211yescharacteristic
25#16840317C2211yescharacteristic
26#16840317C2211yescharacteristic
27#16840317C2211yescharacteristic
28#16840316—21no—
29#16840316—21no—
30#16840316—21no—
31#16840316C2212yes—
32#16840315—21no—
33#16840315C2212yes—
34#16840314—21no—
35#16840314—21no—
36#16840314—21no—
37#16840314C2212yes—
38C4⋊Q8×D61C2211yescharacteristic
39C4⋊Q8×D61C2211yescharacteristic
40C4⋊Q8×D61C2211yescharacteristic
41C4⋊Q8×D61C2211yescharacteristic
42#125×D61—21no—
43#125×D61C2212yes—
44C22⋊Q8×D61—21no—
45C22⋊Q8×D61—21no—
46C22⋊Q8×D61—21no—
47C22⋊Q8×D61C2212yes—
48C4×Q8×D61—21no—
49C4×Q8×D61—21no—
50C4×Q8×D61—21no—
51C4×Q8×D61C2212yes—
52#117×D61—21no—
53#117×D61C2212yes—
54C2×C42×D61C2211yescharacteristic
55#16840167C2211yescharacteristic, complemented
56#16840166C2214yescomplemented
57#16840165C2211yescharacteristic, complemented
58#16840165C2211yescharacteristic, complemented
59#16840160C2211yescharacteristic, complemented
60#16840159C2214yescomplemented
61#16840158C2211yescharacteristic, complemented
62#16840158C2211yescharacteristic, complemented
63#16840114C2211yescharacteristic, complemented
64#16840114C2211yescharacteristic, complemented
65#16840113C2211yescharacteristic, complemented
66#16840113C2211yescharacteristic, complemented
67#16840112C2211yescharacteristic, complemented
68#16840112C2211yescharacteristic, complemented
69#16840111C2214yescomplemented
70#16840111C2214yescomplemented
71#16840106C2214yes—
72#16840105C2214yes—
73#16840104C2214yes—
74#16840103C2214yes—
75#16840102C2214yes—
76#16840101C2214yes—
77#16840100C2214yes—
78#16840072C2214yescomplemented
79#16840071C2214yescomplemented
80#16840070C2214yescomplemented
81#16840069C2214yescomplemented
82#16840068C2214yescomplemented
83#16840067C2214yescomplemented
84#16840066C2214yescomplemented
85#16839815C2211yescharacteristic
86#16839814C2212yes—
87#16839813C2211yescharacteristic
88#16839813C2211yescharacteristic
89#16839812C2212yes—
90#107×D61C2214yes—
91#106×D61C2214yes—
92C4⋊C8×D61C2212yes—
93#103×D61C2214yes—
94#103×D61C2214yes—
95C22⋊C8×D61C2212yes—
96C4×C8×D61C2211yescharacteristic
97C4×C8×D61C2211yescharacteristic
98C61×#533C2211yescharacteristic
99C61×#533C2211yescharacteristic
100C61×#500C2211yescharacteristic, complemented
101C61×#498C2211yescharacteristic, complemented
102C61×#487C2211yescharacteristic, complemented
103C61×#487C2211yescharacteristic, complemented
104C61×#485C2214yes—
105C61×#479C2214yescomplemented
106C61×#431C2211yescharacteristic
107C2×Q8×D61—21no—
108C2×Q8×D61—21no—
109C2×Q8×D61—21no—
110C2×Q8×D61C2312yes—
111C22×C4×D61D411yescharacteristic
112C22×C4×D61D411yescharacteristic
113C22×C4×D61C2311yescharacteristic
114C2×C8×D61C2312yes—
115C2×C8×D61C2312yes—
116#14519777C2311yescharacteristic
117#14519777C2311yescharacteristic
118#14519777C2311yescharacteristic
119#14519777C2311yescharacteristic
120#14519776—21no—
121#14519776—21no—
122#14519776—21no—
123#14519776—21no—
124#14519776—21no—
125#14519776C2312yes—
126#14519776C2312yes—
127#14519776C2312yes—
128#14519775—21no—
129#14519775—21no—
130#14519775—21no—
131#14519775C2312yes—
132#14519769—21no—
133#14519769C2312yes—
134#14519768—21no—
135#14519768—21no—
136#14519768C2312yes—
137#14519768C2312yes—
138#14519767—22no—
139#14519767—22no—
140#14519767—22no—
141#14519767—22no—
142#14519757—21no—
143#14519757—21no—
144#14519757—21no—
145#14519757C2312yes—
146#14519756—21no—
147#14519756—21no—
148#14519756—21no—
149#14519756C2312yes—
150#14519755—22no—
151#14519755—22no—
152#14519755—22no—
153#14519755—22no—
154#14519754—22no—
155#14519754—22no—
156#14519754—22no—
157#14519754—22no—
158#14519753—21no—
159#14519753—21no—
160#14519753—21no—
161#14519753C2312yes—
162Q8×Dic61—21no—
163Q8×Dic61—21no—
164Q8×Dic61—21no—
165Q8×Dic61C2312yes—
166C4×Dic122—21no—
167C4×Dic122—21no—
168C4×Dic122—21no—
169C4×Dic122—22no—
170C4×Dic122—22no—
171C4×Dic122—22no—
172C4×Dic122—22no—
173C4×Dic122C2312yes—
174#14519742—21no—
175#14519742—21no—
176#14519742—21no—
177#14519742—22no—
178#14519742—22no—
179#14519742—22no—
180#14519742—22no—
181#14519742C2312yes—
182#14519736—21no—
183#14519736C2312yes—
184#14519735—21no—
185#14519735—21no—
186#14519735C2312yes—
187#14519735C2312yes—
188#14519734—22no—
189#14519734—22no—
190#14519733—22no—
191#14519733—22no—
192C4⋊C4×D61—21no—
193C4⋊C4×D61—21no—
194C4⋊C4×D61—22no—
195C4⋊C4×D61—22no—
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—
203C4⋊C4×D61C2312yes—
204C22⋊C4×D61—22no—
205C22⋊C4×D61—22no—
206C2×C4×Dic61D411yescharacteristic
207C2×C4×Dic61D411yescharacteristic
208C2×C4×Dic61C2311yescharacteristic
209C42×D61—22no—
210C42×D61—22no—
211C42×D61D411yescharacteristic
212C42×D61D411yescharacteristic
213C42×D61D411yescharacteristic
214C42×D61D411yescharacteristic
215C42×D61C2311yescharacteristic
216C42×D61C2311yescharacteristic
217C42×D61C2311yescharacteristic
218C42×D61C2311yescharacteristic
219#14519711C2314yes—
220#14519710C2314yes—
221#14519710C2314yes—
222#14519709C2314yes—
223#14519708C2314yes—
224#14519708C2314yes—
225C4⋊#92418C2312yes—
226#14519706C2312yes—
227#14519706C2312yes—
228#14519702C2314yes—
229#14519702C2314yes—
230#14519701C2314yes—
231#14519701C2314yes—
232#14519700C2314yes—
233#14519700C2314yes—
234C22⋊#92418C2312yes—
235#14519689C2312yes—
236#14519689C2312yes—
237C4×#92418C2311yescharacteristic
238C4×#92418C2311yescharacteristic
239C8×Dic61C2312yes—
240C8×Dic61C2312yes—
241C4⋊Q8×C61C2311yescharacteristic
242C4⋊Q8×C61C2311yescharacteristic
243C4⋊Q8×C61C2311yescharacteristic
244C4⋊Q8×C61C2311yescharacteristic
245#125×C61—21no—
246#125×C61C2312yes—
247C22⋊Q8×C61—21no—
248C22⋊Q8×C61—21no—
249C22⋊Q8×C61—21no—
250C22⋊Q8×C61C2312yes—
251C4×Q8×C61—21no—
252C4×Q8×C61—21no—
253C4×Q8×C61—21no—
254C4×Q8×C61C2312yes—
255#117×C61—21no—
256#117×C61C2312yes—
257C2×C42×C61C2311yescharacteristic
258#107×C61C2314yes—
259#106×C61C2314yes—
260C4⋊C8×C61C2312yes—
261#103×C61C2314yes—
262#103×C61C2314yes—
263C22⋊C8×C61C2312yes—
264C4×C8×C61C2311yescharacteristic
265C4×C8×C61C2311yescharacteristic
266C23×D61C2×D411yescharacteristic
267C2×Q8×C61—21no—
268C2×Q8×C61—21no—
269C2×Q8×C61—21no—
270C2×Q8×C61C2412yes—
271C22×C4×C61C2×D411yescharacteristic
272C22×C4×C61C2×D411yescharacteristic
273C22×C4×C61C2411yescharacteristic
274C22×Dic61C2×D411yescharacteristic
275C22×Dic61C2×D411yescharacteristic
276C22×Dic61C2×D411yescharacteristic
277Q8×D61—28no—
278Q8×D61—44no—
279Q8×D61—44no—
280Q8×D61—44no—
281C2×C4×D61—24no—
282C2×C4×D61—24no—
283C2×C4×D61—24no—
284C2×C4×D61—22no—
285C2×C4×D61—22no—
286C2×C4×D61—22no—
287C2×C4×D61—22no—
288C2×C4×D61C2×D411yescharacteristic
289C2×C4×D61C2×D411yescharacteristic
290C2×C4×D61C2×D411yescharacteristic
291C2×C4×D61C2×D411yescharacteristic
292C2×C4×D61C2×D411yescharacteristic
293C2×C4×D61C2×D411yescharacteristic
294C2×C4×D61C2×D411yescharacteristic
295C2×C4×D61C2×D411yescharacteristic
296C2×C4×D61C2×D411yescharacteristic
297C2×C4×D61C2×D411yescharacteristic
298C2×C4×D61C2411yescharacteristic
299C2×C4×D61C2411yescharacteristic
300C2×Dic122—21no—
301C2×Dic122—21no—
302C2×Dic122—21no—
303C2×Dic122—22no—
304C2×Dic122—22no—
305C2×Dic122—22no—
306C2×Dic122—22no—
307C2×Dic122C2412yes—
308C2×C8×C61C2412yes—
309C2×C8×C61C2412yes—
310C4⋊C4×C61—21no—
311C4⋊C4×C61—21no—
312C4⋊C4×C61—22no—
313C4⋊C4×C61—22no—
314C4⋊C4×C61—21no—
315C4⋊C4×C61—21no—
316C4⋊C4×C61—21no—
317C4⋊C4×C61—22no—
318C4⋊C4×C61—22no—
319C4⋊C4×C61C2412yes—
320C4⋊C4×C61C2412yes—
321C4⋊C4×C61C2412yes—
322C22⋊C4×C61—22no—
323C22⋊C4×C61—22no—
324C42×C61—22no—
325C42×C61—22no—
326C42×C61C2×D411yescharacteristic
327C42×C61C2×D411yescharacteristic
328C42×C61C2411yescharacteristic
329C42×C61C2411yescharacteristic
330C22⋊Dic61—22no—
331C22⋊Dic61—22no—
332#11758198—22no—
333#11758198—22no—
334#11758198—22no—
335#11758198—22no—
336C4⋊Dic61—21no—
337C4⋊Dic61—21no—
338C4⋊Dic61—21no—
339C4⋊Dic61—21no—
340C4⋊Dic61—21no—
341C4⋊Dic61—22no—
342C4⋊Dic61—22no—
343C4⋊Dic61—22no—
344C4⋊Dic61—22no—
345C4⋊Dic61C2412yes—
346C4⋊Dic61C2412yes—
347C4⋊Dic61C2412yes—
348#11758196—22no—
349#11758196—22no—
350#11758196—22no—
351#11758196—22no—
352#11758196—22no—
353#11758196—22no—
354#11758196—22no—
355#11758196—22no—
356#11758196—22no—
357#11758196—22no—
358#11758196—22no—
359#11758196—22no—
360#11758196—22no—
361#11758196—22no—
362#11758196—22no—
363#11758196—22no—
364C4×Dic61—22no—
365C4×Dic61—22no—
366C4×Dic61—22no—
367C4×Dic61—22no—
368C4×Dic61—22no—
369C4×Dic61—22no—
370C4×Dic61C2×D411yescharacteristic
371C4×Dic61C2×D411yescharacteristic
372C4×Dic61C2×D411yescharacteristic
373C4×Dic61C2×D411yescharacteristic
374C4×Dic61C2×D411yescharacteristic
375C4×Dic61C2×D411yescharacteristic
376C4×Dic61C2×D411yescharacteristic
377C4×Dic61C2×D411yescharacteristic
378C4×Dic61C2×D411yescharacteristic
379C4×Dic61C2×D411yescharacteristic
380C4×Dic61C2411yescharacteristic
381C4×Dic61C2411yescharacteristic
382C2×#92418C2412yes—
383C2×#92418C2412yes—
384C8×D61—24no—
385C8×D61—24no—
386C23×C61C22×D411yescharacteristic
387C22×D61—22no—
388C22×D61—22no—
389C22×D61—22no—
390C22×D61C22×D411yescharacteristic
391C22×D61C22×D411yescharacteristic
392Q8×C61—24no—
393Q8×C61—42no—
394Q8×C61—42no—
395Q8×C61—42no—
396C2×C4×C61—22no—
397C2×C4×C61—22no—
398C2×C4×C61—22no—
399C2×C4×C61—22no—
400C2×C4×C61—22no—
401C2×C4×C61—22no—
402C2×C4×C61—22no—
403C2×C4×C61C22×D411yescharacteristic
404C2×C4×C61C22×D411yescharacteristic
405C2×C4×C61C22×D411yescharacteristic
406C2×C4×C61C22×D411yescharacteristic
407C2×C4×C61C22×D411yescharacteristic
408C2×C4×C61C2511yescharacteristic
409C2×Dic61—22no—
410C2×Dic61—22no—
411C2×Dic61—22no—
412C2×Dic61—22no—
413C2×Dic61—22no—
414C2×Dic61—22no—
415C2×Dic61—22no—
416C2×Dic61C22×D411yescharacteristic
417C2×Dic61C22×D411yescharacteristic
418C2×Dic61C22×D411yescharacteristic
419C2×Dic61C22×D411yescharacteristic
420C2×Dic61C22×D411yescharacteristic
421C2×Dic61C22×D411yescharacteristic
422C4×D61—22no—
423C4×D61—22no—
424C4×D61—22no—
425C4×D61—22no—
426C4×D61—22no—
427C4×D61—22no—
428C4×D61—22no—
429C4×D61—22no—
430C4×D61—22no—
431C4×D61—44no—
432C4×D61—44no—
433C4×D61—44no—
434C4×D61—44no—
435C4×D61#13514yes—
436C4×D61#13714yes—
437C4×D612−1+414yes—
438Dic122—24no—
439Dic122—42no—
440Dic122—42no—
441Dic122—42no—
442Dic122—44no—
443Dic122—44no—
444Dic122—44no—
445Dic122—44no—
446C8×C61—22no—
447C8×C61—22no—
448#92418—22no—
449#92418—22no—
450C2×#3231—611nomaximal, Sylow
451C22×C61—21no—
452C22×C61—21no—
453C22×C61—21no—
454C22×C61C23×D411yescharacteristic
455C2×D61—21no—
456C2×D61—21no—
457C2×D61—21no—
458C2×D61—44no—
459C2×D61#53612yes—
460C2×D61C2×#13512yes—
461C2×D61C2×#13712yes—
462C4×C61—21no—
463C4×C61—21no—
464C4×C61—21no—
465C4×C61—42no—
466C4×C61—42no—
467C4×C61—42no—
468C4×C61—42no—
469C4×C61C2×#13512yes—
470C4×C61C2×#13712yes—
471C4×C61C2×2−1+412yes—
472Dic61—21no—
473Dic61—21no—
474Dic61—21no—
475Dic61—42no—
476Dic61—42no—
477Dic61—42no—
478Dic61—42no—
479Dic61#53612yes—
480Dic61C2×#13512yes—
481Dic61C2×#13712yes—
482C2×#533—611no—
483C2×#533—611no—
484#3231—611no—
485#3231—611no—
486#3231—611no—
487#3231—611no—
488#3231—614no—
489#3231—614no—
490#3231—611no—
491#3231—611no—
492#3231—611no—
493#3231D6111yescharacteristic, direct product factor
494C2×#500—611no—
495C2×#498—611no—
496C2×#487—611no—
497C2×#487—611no—
498C2×#485—614no—
499C2×#479—614no—
500C2×#431—611no—
501C2×C61—41no—
502C2×C61C2×#53611yescharacteristic
503C2×C61C22×#13511yescharacteristic
504C2×C61C22×#13711yescharacteristic
505D61—41no—
506D61#323114yesdirect product factor
507#533—611no—
508#533—611no—
509#533—612no—
510#533—612no—
511#533—611no—
512#533—611no—
513#533—612no—
514#533—612no—
515#533—611no—
516#533—611no—
517#533—1221no—
518#533—1221no—
519#533—1221no—
520#533—1221no—
521#533—1221no—
522#533—1221no—
523#533—1221no—
524#533—1221no—
525#533C2×D6111yescharacteristic
526#533C2×D6111yescharacteristic
527C2×C4⋊Q8—611no—
528C2×C4⋊Q8—611no—
529C2×C4⋊Q8—611no—
530C2×C4⋊Q8—611no—
531C2×#125—612no—
532C2×#125—1221no—
533C2×C22⋊Q8—612no—
534C2×C22⋊Q8—1221no—
535C2×C22⋊Q8—1221no—
536C2×C22⋊Q8—1221no—
537C2×C4×Q8—612no—
538C2×C4×Q8—1221no—
539C2×C4×Q8—1221no—
540C2×C4×Q8—1221no—
541C2×#117—612no—
542C2×#117—1221no—
543C22×C42—611no—
544#500—611no—
545#500—611no—
546#500—614no—
547#500—611no—
548#500C2×D6111yescharacteristic, complemented
549#498—611no—
550#498—611no—
551#498—614no—
552#498—611no—
553#498C2×D6111yescharacteristic, complemented
554#487—611no—
555#487—611no—
556#487—611no—
557#487—611no—
558#487—614no—
559#487—614no—
560#487—611no—
561#487—611no—
562#487C2×D6111yescharacteristic, complemented
563#487C2×D6111yescharacteristic, complemented
564#485—614no—
565#485—614no—
566#485—614no—
567#485—614no—
568#485—614no—
569#485—614no—
570#485—614no—
571#485C2×D6114yes—
572#479—614no—
573#479—614no—
574#479—614no—
575#479—614no—
576#479—614no—
577#479—614no—
578#479—614no—
579#479C2×D6114yescomplemented
580#431—611no—
581#431—612no—
582#431—612no—
583#431—611no—
584#431—611no—
585#431C2×D6111yescharacteristic
586C2×#107—614no—
587C2×#106—614no—
588C2×C4⋊C8—612no—
589C2×#103—614no—
590C2×#103—614no—
591C2×C22⋊C8—612no—
592C2×C4×C8—611no—
593C2×C4×C8—611no—
594C61C2×#323111yescharacteristic, complemented, Sylow
595C22×Q8—612no—
596C22×Q8—1221no—
597C22×Q8—1221no—
598C22×Q8—1221no—
599C23×C4—611no—
600C23×C4—611no—
601C23×C4—611no—
602C22×C8—612no—
603C22×C8—612no—
604C4⋊Q8—612no—
605C4⋊Q8—612no—
606C4⋊Q8—612no—
607C4⋊Q8—612no—
608C4⋊Q8—611no—
609C4⋊Q8—611no—
610C4⋊Q8—611no—
611C4⋊Q8—611no—
612C4⋊Q8—1221no—
613C4⋊Q8—1221no—
614C4⋊Q8—1221no—
615C4⋊Q8—1221no—
616C4⋊Q8—1221no—
617C4⋊Q8—1221no—
618C4⋊Q8—1221no—
619C4⋊Q8—1221no—
620C4⋊Q8C22×D6111yescharacteristic
621C4⋊Q8C22×D6111yescharacteristic
622C4⋊Q8C22×D6111yescharacteristic
623C4⋊Q8C22×D6111yescharacteristic
624#125—21no—
625#125—612no—
626#125—612no—
627#125—612no—
628#125—1222no—
629#125—1222no—
630#125—1222no—
631#125—1222no—
632#125—1221no—
633#125—1221no—
634#125—1221no—
635#125C22×D6112yes—
636C22⋊Q8—21no—
637C22⋊Q8—21no—
638C22⋊Q8—21no—
639C22⋊Q8—612no—
640C22⋊Q8—612no—
641C22⋊Q8—612no—
642C22⋊Q8—1222no—
643C22⋊Q8—1222no—
644C22⋊Q8—1222no—
645C22⋊Q8—1222no—
646C22⋊Q8—1222no—
647C22⋊Q8—1222no—
648C22⋊Q8—1222no—
649C22⋊Q8—1222no—
650C22⋊Q8—1221no—
651C22⋊Q8—1221no—
652C22⋊Q8—1221no—
653C22⋊Q8—1221no—
654C22⋊Q8—1221no—
655C22⋊Q8—1221no—
656C22⋊Q8—1221no—
657C22⋊Q8—1221no—
658C22⋊Q8—1221no—
659C22⋊Q8C22×D6112yes—
660C4×Q8—21no—
661C4×Q8—21no—
662C4×Q8—21no—
663C4×Q8—612no—
664C4×Q8—612no—
665C4×Q8—612no—
666C4×Q8—1222no—
667C4×Q8—1222no—
668C4×Q8—1222no—
669C4×Q8—1222no—
670C4×Q8—1222no—
671C4×Q8—1222no—
672C4×Q8—1221no—
673C4×Q8—1221no—
674C4×Q8—1222no—
675C4×Q8—1222no—
676C4×Q8—1221no—
677C4×Q8—1221no—
678C4×Q8—1221no—
679C4×Q8—1221no—
680C4×Q8—1221no—
681C4×Q8—1221no—
682C4×Q8—1221no—
683C4×Q8C22×D6112yes—
684#117—21no—
685#117—612no—
686#117—612no—
687#117—612no—
688#117—1222no—
689#117—1222no—
690#117—1222no—
691#117—1222no—
692#117—1221no—
693#117—1221no—
694#117—1221no—
695#117C22×D6112yes—
696C2×C4⋊C4—612no—
697C2×C4⋊C4—612no—
698C2×C4⋊C4—612no—
699C2×C4⋊C4—1221no—
700C2×C4⋊C4—1221no—
701C2×C4⋊C4—1222no—
702C2×C4⋊C4—1222no—
703C2×C4⋊C4—1222no—
704C2×C4⋊C4—1222no—
705C2×C4⋊C4—1221no—
706C2×C4⋊C4—1221no—
707C2×C4⋊C4—1221no—
708C2×C22⋊C4—1222no—
709C2×C22⋊C4—1222no—
710C2×C42—611no—
711C2×C42—611no—
712C2×C42—611no—
713C2×C42—611no—
714C2×C42—611no—
715C2×C42—611no—
716C2×C42—611no—
717C2×C42—611no—
718C2×C42—611no—
719C2×C42—611no—
720C2×C42—611no—
721C2×C42—1222no—
722C2×C42—1222no—
723C2×C42C22×D6111yescharacteristic
724#107—614no—
725#107—614no—
726#107—614no—
727#107C22×D6114yes—
728#106—614no—
729#106—614no—
730#106—614no—
731#106C22×D6114yes—
732C4⋊C8—612no—
733C4⋊C8—612no—
734C4⋊C8—612no—
735C4⋊C8C22×D6112yes—
736#103—614no—
737#103—614no—
738#103—614no—
739#103—614no—
740#103—614no—
741#103—614no—
742#103C22×D6114yes—
743#103C22×D6114yes—
744C22⋊C8—612no—
745C22⋊C8—612no—
746C22⋊C8—612no—
747C22⋊C8C22×D6112yes—
748C4×C8—612no—
749C4×C8—612no—
750C4×C8—611no—
751C4×C8—611no—
752C4×C8C22×D6111yescharacteristic
753C4×C8C22×D6111yescharacteristic
754C24—611no—
755C2×Q8—21no—
756C2×Q8—21no—
757C2×Q8—21no—
758C2×Q8—612no—
759C2×Q8—1222no—
760C2×Q8—1222no—
761C2×Q8—1222no—
762C2×Q8—1222no—
763C2×Q8—1228no—
764C2×Q8—1221no—
765C2×Q8—1221no—
766C2×Q8—1221no—
767C2×Q8—2444no—
768C2×Q8—2444no—
769C2×Q8—2444no—
770C2×Q8C23×D6112yes—
771C22×C4—611no—
772C22×C4—611no—
773C22×C4—611no—
774C22×C4—611no—
775C22×C4—611no—
776C22×C4—611no—
777C22×C4—611no—
778C22×C4—611no—
779C22×C4—611no—
780C22×C4—611no—
781C22×C4—611no—
782C22×C4—611no—
783C22×C4—611no—
784C22×C4—611no—
785C22×C4—611no—
786C22×C4—1224no—
787C22×C4—1224no—
788C22×C4—1224no—
789C22×C4—1222no—
790C22×C4—1222no—
791C22×C4—1222no—
792C22×C4—1222no—
793C22×C4D4×D6111yescharacteristic
794C22×C4D4×D6111yescharacteristic
795C22×C4C23×D6111yescharacteristic
796C2×C8—612no—
797C2×C8—612no—
798C2×C8—1224no—
799C2×C8—1224no—
800C2×C8C23×D6112yes—
801C2×C8C23×D6112yes—
802C4⋊C4—21no—
803C4⋊C4—21no—
804C4⋊C4—22no—
805C4⋊C4—22no—
806C4⋊C4—21no—
807C4⋊C4—21no—
808C4⋊C4—21no—
809C4⋊C4—22no—
810C4⋊C4—22no—
811C4⋊C4—612no—
812C4⋊C4—612no—
813C4⋊C4—612no—
814C4⋊C4—1222no—
815C4⋊C4—1222no—
816C4⋊C4—1222no—
817C4⋊C4—1222no—
818C4⋊C4—1222no—
819C4⋊C4—1222no—
820C4⋊C4—1222no—
821C4⋊C4—1222no—
822C4⋊C4—1222no—
823C4⋊C4—1222no—
824C4⋊C4—1222no—
825C4⋊C4—1222no—
826C4⋊C4—1222no—
827C4⋊C4—1222no—
828C4⋊C4—1222no—
829C4⋊C4—1222no—
830C4⋊C4—1222no—
831C4⋊C4—1222no—
832C4⋊C4—1222no—
833C4⋊C4—1222no—
834C4⋊C4—1221no—
835C4⋊C4—1221no—
836C4⋊C4—1221no—
837C4⋊C4—1221no—
838C4⋊C4—1221no—
839C4⋊C4C23×D6112yes—
840C4⋊C4C23×D6112yes—
841C4⋊C4C23×D6112yes—
842C22⋊C4—22no—
843C22⋊C4—22no—
844C22⋊C4—1222no—
845C22⋊C4—1222no—
846C22⋊C4—1222no—
847C22⋊C4—1222no—
848C22⋊C4—1222no—
849C22⋊C4—1222no—
850C42—22no—
851C42—22no—
852C42—611no—
853C42—611no—
854C42—611no—
855C42—611no—
856C42—611no—
857C42—611no—
858C42—611no—
859C42—611no—
860C42—611no—
861C42—611no—
862C42—611no—
863C42—611no—
864C42—1222no—
865C42—1222no—
866C42—1222no—
867C42—1222no—
868C42—1222no—
869C42—1222no—
870C42D4×D6111yescharacteristic
871C42D4×D6111yescharacteristic
872C42C23×D6111yescharacteristic
873C42C23×D6111yescharacteristic
874C23—611no—
875C23—611no—
876C23—1222no—
877C23—1222no—
878C23—1222no—
879C23C2×D4×D6111yescharacteristic
880Q8—24no—
881Q8—42no—
882Q8—42no—
883Q8—42no—
884Q8—1224no—
885Q8—2444no—
886Q8—2444no—
887Q8—2444no—
888Q8—2444no—
889Q8—2442no—
890Q8—2442no—
891Q8—2442no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—611no—
900C2×C4—611no—
901C2×C4—611no—
902C2×C4—614no—
903C2×C4—614no—
904C2×C4—614no—
905C2×C4—611no—
906C2×C4—611no—
907C2×C4—611no—
908C2×C4—1222no—
909C2×C4—1222no—
910C2×C4—1222no—
911C2×C4—1222no—
912C2×C4—1222no—
913C2×C4—1222no—
914C2×C4—1222no—
915C2×C4—1222no—
916C2×C4—1222no—
917C2×C4—1222no—
918C2×C4—1222no—
919C2×C4—1222no—
920C2×C4—1222no—
921C2×C4—1222no—
922C2×C4—1222no—
923C2×C4—1222no—
924C2×C4—2444no—
925C2×C4—2444no—
926C2×C4—2444no—
927C2×C4—2444no—
928C2×C4C2×D4×D6111yescharacteristic
929C2×C4C2×D4×D6111yescharacteristic
930C2×C4C2×D4×D6111yescharacteristic
931C2×C4C2×D4×D6111yescharacteristic
932C2×C4C2×D4×D6111yescharacteristic
933C2×C4C24×D6111yescharacteristic
934C8—22no—
935C8—22no—
936C8—1222no—
937C8—1222no—
938C22—21no—
939C22—21no—
940C22—21no—
941C22—612no—
942C22—612no—
943C22—612no—
944C22—1221no—
945C22—1221no—
946C22—1221no—
947C22—2444no—
948C22C22×D4×D6111yescharacteristic
949C4—21no—
950C4—21no—
951C4—21no—
952C4—42no—
953C4—42no—
954C4—42no—
955C4—42no—
956C4—612no—
957C4—612no—
958C4—612no—
959C4—1221no—
960C4—1221no—
961C4—1221no—
962C4—2442no—
963C4—2442no—
964C4—2442no—
965C4—2442no—
966C4#135×D6112yes—
967C4#137×D6112yes—
968C42−1+4×D6112yes—
969C2—41no—
970C2—614no—
971C2—2441no—
972C2#536×D6111yescharacteristic
973C2C2×#135×D6111yescharacteristic
974C2C2×#137×D6111yescharacteristic
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3231C2
socleC22×C61C23×D4
prime radicalC23×D61C2×D4
hypercenter#3231D61
hypocenterC61C2×#3231
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3231

Complements

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

NH ≅ G/Ntype
3. #21456981C2semidirect
4. #21456980C2semidirect
5. #21456979C2semidirect
6. #21456978C2semidirect
7. #21456977C2semidirect
8. #21456976C2semidirect
9. #21456975C2semidirect
10. #21456974C2semidirect
11. #21456973C2semidirect
12. #500×D61C2semidirect
13. #498×D61C2semidirect
14. #487×D61C2semidirect
15. #487×D61C2semidirect
17. #479×D61C2semidirect
19. C61×#3231C2semidirect
55. #16840167C22semidirect
56. #16840166C22semidirect
57. #16840165C22semidirect
58. #16840165C22semidirect
59. #16840160C22semidirect
60. #16840159C22semidirect
61. #16840158C22semidirect
62. #16840158C22semidirect
63. #16840114C22semidirect
64. #16840114C22semidirect
65. #16840113C22semidirect
66. #16840113C22semidirect
67. #16840112C22semidirect
68. #16840112C22semidirect
69. #16840111C22semidirect
70. #16840111C22semidirect
78. #16840072C22semidirect
79. #16840071C22semidirect
80. #16840070C22semidirect
81. #16840069C22semidirect
82. #16840068C22semidirect
83. #16840067C22semidirect
84. #16840066C22semidirect
100. C61×#500C22semidirect
101. C61×#498C22semidirect
102. C61×#487C22semidirect
103. C61×#487C22semidirect
105. C61×#479C22semidirect
493. #3231D61direct (N × H)
506. D61#3231direct (N × H)
548. #500C2×D61semidirect
553. #498C2×D61semidirect
562. #487C2×D61semidirect
563. #487C2×D61semidirect
579. #479C2×D61semidirect
594. C61C2×#3231semidirect

Maximal subgroups

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

subgroupindex
#533×D612
#214569812
#214569802
#214569792
#214569782
#214569772
#214569762
#214569752
#214569742
#214569732
#500×D612
#498×D612
#487×D612
#485×D612
#479×D612
#431×D612
C61×#32312
C2×#323161