Finite Group Databasebeta

← D61×#3238 #30552130

Subgroups — D61×#3238 #30552130

Order 15616.

2018 conjugacy classes of subgroups.

The subgroup lattice has 1078 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊Q8×D61C211yesmaximal, characteristic, complemented
2#529×D61C211yesmaximal, characteristic
3#21457044C212yesmaximal, complemented
4#21457043C212yesmaximal, complemented
5#21457042C211yesmaximal, characteristic, complemented
6#21457041C212yesmaximal, complemented
7#21457040C211yesmaximal, characteristic, complemented
8#21457039C212yesmaximal, complemented
9#21457038C212yesmaximal, complemented
10#21457037C211yesmaximal, characteristic, complemented
11#21457036C212yesmaximal, complemented
12#501×D61C212yesmaximal, complemented
13#489×D61C212yesmaximal, complemented
14#483×D61C212yesmaximal, complemented
15#480×D61C212yesmaximal
16#477×D61C212yesmaximal, complemented
17#476×D61C212yesmaximal, complemented
18#432×D61C211yesmaximal, characteristic, complemented
19C61×#3238C211yesmaximal, characteristic, complemented
20C22×Q8×D61—21no—
21C2×#14519777C2211yescharacteristic, complemented
22C2×#14519776—21no—
23C2×#14519776C2212yescomplemented
24C2×#14519775—21no—
25C4⋊Q8×D61—21no—
26C4⋊Q8×D61—21no—
27C4⋊Q8×D61—21no—
28C4⋊Q8×D61—21no—
29C4⋊Q8×D61C2212yes—
30C4⋊Q8×D61C2212yes—
31C4⋊Q8×D61C2212yescomplemented
32C4⋊Q8×D61C2212yescomplemented
33#16840299C2211yescharacteristic
34#16840298C2211yescharacteristic
35#16840297C2211yescharacteristic
36#16840296C2211yescharacteristic
37#16840295—21no—
38#16840294C2211yescharacteristic
39#16840293C2211yescharacteristic
40#16840292—21no—
41#16840291C2211yescharacteristic
42#16840290—21no—
43#16840289—21no—
44#126×D61—21no—
45#125×D61C2211yescharacteristic
46#124×D61C2211yescharacteristic
47#123×D61—21no—
48C22⋊Q8×D61C2211yescharacteristic
49#121×D61C2211yescharacteristic
50C4×Q8×D61C2211yescharacteristic
51C4×D4×D61—21no—
52C4×D4×D61C2211yescharacteristic
53#117×D61—21no—
54C2×C4⋊C4×D61—21no—
55C2×C4⋊C4×D61C2212yes—
56C2×C42×D61C2211yescharacteristic
57#16840172C2212yescomplemented
58#16840171C2212yescomplemented
59#16840170C2214yescomplemented
60#16840169C2214yescomplemented
61#16840168C2212yescomplemented
62#16840124C2212yescomplemented
63#16840123C2214yescomplemented
64#16840122C2212yescomplemented
65#16840121C2212yescomplemented
66#16840120C2214yescomplemented
67#16840094C2214yescomplemented
68#16840093C2212yescomplemented
69#16840092C2212yescomplemented
70#16840091C2214yescomplemented
71#16840090C2212yescomplemented
72#16840077C2214yes—
73#16840076C2212yes—
74#16840075C2212yes—
75#16840074C2214yes—
76#16840073C2212yes—
77#16840058C2212yescomplemented
78#16840057C2212yescomplemented
79#16840056C2214yescomplemented
80#16840055C2214yescomplemented
81#16840054C2212yescomplemented
82#16840053C2212yescomplemented
83#16840052C2212yescomplemented
84#16840051C2214yescomplemented
85#16840050C2214yescomplemented
86#16840049C2212yescomplemented
87#16839819C2211yescharacteristic, complemented
88#16839818C2212yescomplemented
89#16839817C2212yescomplemented
90#16839816C2212yescomplemented
91#107×D61C2214yes—
92#106×D61C2214yes—
93C4⋊C8×D61C2212yes—
94#103×D61C2214yes—
95#102×D61C2214yes—
96C22⋊C8×D61C2212yes—
97#97×D61C2212yes—
98C2×C4⋊Q8×C61C2211yescharacteristic, complemented
99C61×#529C2211yescharacteristic
100C61×#501C2212yescomplemented
101C61×#489C2212yescomplemented
102C61×#483C2212yescomplemented
103C61×#480C2212yes—
104C61×#477C2212yescomplemented
105C61×#476C2212yescomplemented
106C61×#432C2211yescharacteristic, complemented
107C22×Dic122—21no—
108C22×Dic122—22no—
109C2×Q8×D61—22no—
110C2×Q8×D61—22no—
111C2×Q8×D61—22no—
112C2×Q8×D61—22no—
113C2×Q8×D61—48no—
114C2×Q8×D61C2311yescharacteristic
115C2×D4×D61—21no—
116C2×D4×D61C2311yescharacteristic
117C22×C4×D61—22no—
118C22×C4×D61—21no—
119C22×C4×D61D411yescharacteristic
120C22×C4×D61D411yescharacteristic
121C22×C4×D61C2311yescharacteristic
122C2×C8×D61C2314yes—
123#14519777—21no—
124#14519777—21no—
125#14519777C2312yes—
126#14519777C2312yes—
127#14519776—22no—
128#14519776—22no—
129#14519776—22no—
130#14519776—22no—
131#14519776—22no—
132#14519776—22no—
133#14519776C2314yes—
134#14519776C2314yes—
135#14519775—22no—
136#14519775—22no—
137#14519775—22no—
138#14519775—22no—
139#14519772—21no—
140#14519772—21no—
141#14519772—21no—
142#14519771—21no—
143#14519770—21no—
144#14519770—21no—
145#14519770—21no—
146#14519769C2311yescharacteristic
147#14519768C2311yescharacteristic
148#14519768C2311yescharacteristic
149#14519767—21no—
150#14519767—21no—
151#14519766C2311yescharacteristic
152#14519765C2311yescharacteristic
153#14519764C2311yescharacteristic
154#14519763—21no—
155#14519763—21no—
156#14519762—21no—
157#14519762—21no—
158#14519761—21no—
159#14519760—21no—
160#14519759—21no—
161#14519759—21no—
162#14519758—21no—
163#14519757C2311yescharacteristic
164#14519756C2311yescharacteristic
165#14519755—21no—
166#14519754—21no—
167#14519753C2311yescharacteristic
168#14519752C2311yescharacteristic
169#14519751C2311yescharacteristic
170#14519750—21no—
171#14519749—21no—
172#14519748C2311yescharacteristic
173Q8×Dic61C2311yescharacteristic
174C4×Dic122—21no—
175C4×Dic122C2311yescharacteristic
176#14519742—21no—
177#14519742C2311yescharacteristic
178C4×D244—21no—
179C4×D244C2311yescharacteristic
180D4×Dic61—21no—
181D4×Dic61C2311yescharacteristic
182#14519739—21no—
183#14519739C2311yescharacteristic
184C4×C22⋊D61—21no—
185C4×C22⋊D61—21no—
186C4×C22⋊D61—21no—
187#14519737—21no—
188#14519737—21no—
189#14519737—21no—
190#14519736—21no—
191#14519735—21no—
192#14519735—21no—
193#14519734—21no—
194#14519734—21no—
195#14519733—21no—
196#14519733—21no—
197C2×C4⋊Dic61—21no—
198C2×C4⋊Dic61C2312yes—
199C2×#11758196—22no—
200C2×#11758196—22no—
201C4⋊C4×D61—22no—
202C4⋊C4×D61—22no—
203C4⋊C4×D61—22no—
204C4⋊C4×D61—22no—
205C4⋊C4×D61—22no—
206C4⋊C4×D61—22no—
207C4⋊C4×D61—21no—
208C4⋊C4×D61—21no—
209C4⋊C4×D61—21no—
210C4⋊C4×D61—21no—
211C4⋊C4×D61C2314yes—
212C4⋊C4×D61C2314yes—
213C4⋊C4×D61C2311yescharacteristic
214C4⋊C4×D61C2311yescharacteristic
215C22⋊C4×D61—21no—
216C22⋊C4×D61—21no—
217C22⋊C4×D61—21no—
218C22⋊C4×D61—21no—
219C22⋊C4×D61—21no—
220C2×C4×Dic61D411yescharacteristic
221C2×C4×Dic61D411yescharacteristic
222C2×C4×Dic61C2311yescharacteristic
223C42×D61—21no—
224C42×D61D411yescharacteristic
225C42×D61D411yescharacteristic
226C42×D61D411yescharacteristic
227C42×D61D411yescharacteristic
228C42×D61C2311yescharacteristic
229C42×D61C2311yescharacteristic
230C42×D61C2311yescharacteristic
231C42×D61C2311yescharacteristic
232#14519711C2314yes—
233#14519710C2314yes—
234#14519710C2314yes—
235#14519709C2314yes—
236#14519708C2314yes—
237#14519708C2314yes—
238C4⋊#92418C2312yes—
239#14519706C2314yes—
240#14519702C2314yes—
241#14519701C2314yes—
242#14519700C2314yes—
243#14519699C2314yes—
244#14519698C2314yes—
245#14519697C2314yes—
246C22⋊#92418C2312yes—
247#14519689C2314yes—
248#14519688C2312yes—
249#14519687C2314yes—
250C22×Q8×C61—21no—
251C4⋊Q8×C61—21no—
252C4⋊Q8×C61—21no—
253C4⋊Q8×C61C2312yes—
254C4⋊Q8×C61C2312yes—
255#126×C61—21no—
256#125×C61C2311yescharacteristic
257#124×C61C2311yescharacteristic
258#123×C61—21no—
259C22⋊Q8×C61C2311yescharacteristic
260#121×C61C2311yescharacteristic
261C4×Q8×C61C2311yescharacteristic
262C4×D4×C61—21no—
263C4×D4×C61C2311yescharacteristic
264#117×C61—21no—
265C2×C4⋊C4×C61—21no—
266C2×C4⋊C4×C61C2312yes—
267C2×C42×C61C2311yescharacteristic
268#107×C61C2314yes—
269#106×C61C2314yes—
270C4⋊C8×C61C2312yes—
271#103×C61C2314yes—
272#102×C61C2314yes—
273C22⋊C8×C61C2312yes—
274#97×C61C2312yes—
275C23×D61—21no—
276C23×D61C2×D411yescharacteristic
277C2×Q8×C61—22no—
278C2×Q8×C61—22no—
279C2×Q8×C61—44no—
280C2×Q8×C61C2411yescharacteristic
281C2×D4×C61—21no—
282C2×D4×C61C2411yescharacteristic
283C22×C4×C61—22no—
284C22×C4×C61—21no—
285C22×C4×C61C2×D411yescharacteristic
286C22×C4×C61C2×D411yescharacteristic
287C22×C4×C61C2411yescharacteristic
288C2×C22⋊D61—21no—
289C2×C22⋊D61—21no—
290C2×C22⋊D61—21no—
291C22×Dic61—22no—
292C22×Dic61—21no—
293C22×Dic61C2×D411yescharacteristic
294C22×Dic61C2×D411yescharacteristic
295C22×Dic61C2×D411yescharacteristic
296Q8×D61—24no—
297Q8×D61—48no—
298Q8×D61—48no—
299Q8×D61—48no—
300Q8×D61—48no—
301D4×D61—24no—
302D4×D61—44no—
303C2×D244—21no—
304C2×D244C2411yescharacteristic
305C2×C4×D61—24no—
306C2×C4×D61—24no—
307C2×C4×D61—24no—
308C2×C4×D61—24no—
309C2×C4×D61—24no—
310C2×C4×D61—21no—
311C2×C4×D61—21no—
312C2×C4×D61—21no—
313C2×C4×D61—21no—
314C2×C4×D61—21no—
315C2×C4×D61—48no—
316C2×C4×D61—44no—
317C2×C4×D61C2×D411yescharacteristic
318C2×C4×D61C2×D411yescharacteristic
319C2×C4×D61C2×D411yescharacteristic
320C2×C4×D61C2×D411yescharacteristic
321C2×C4×D61C2×D411yescharacteristic
322C2×C4×D61C2×D411yescharacteristic
323C2×C4×D61C2×D411yescharacteristic
324C2×C4×D61C2×D411yescharacteristic
325C2×C4×D61C2×D411yescharacteristic
326C2×C4×D61C2×D411yescharacteristic
327C2×C4×D61C2411yescharacteristic
328C2×C4×D61C2411yescharacteristic
329C2×Dic122—22no—
330C2×Dic122—22no—
331C2×Dic122—24no—
332C2×Dic122—24no—
333C2×Dic122—21no—
334C2×Dic122—48no—
335C2×Dic122—44no—
336C2×Dic122C2411yescharacteristic
337C2×C8×C61C2414yes—
338C4⋊C4×C61—22no—
339C4⋊C4×C61—22no—
340C4⋊C4×C61—22no—
341C4⋊C4×C61—21no—
342C4⋊C4×C61—21no—
343C4⋊C4×C61—21no—
344C4⋊C4×C61—21no—
345C4⋊C4×C61C2414yes—
346C4⋊C4×C61C2411yescharacteristic
347C4⋊C4×C61C2411yescharacteristic
348C22⋊C4×C61—21no—
349C22⋊C4×C61—21no—
350C22⋊C4×C61—21no—
351C22⋊C4×C61—21no—
352C22⋊C4×C61—21no—
353C42×C61—21no—
354C42×C61C2×D411yescharacteristic
355C42×C61C2×D411yescharacteristic
356C42×C61C2411yescharacteristic
357C42×C61C2411yescharacteristic
358C22⋊Dic61—21no—
359C22⋊Dic61—21no—
360C22⋊Dic61—21no—
361C22⋊Dic61—21no—
362C22⋊Dic61—21no—
363#11758198—21no—
364#11758198—21no—
365#11758198—21no—
366#11758198—21no—
367#11758198—21no—
368#11758198—21no—
369#11758198—21no—
370#11758198—21no—
371#11758198—21no—
372#11758198—21no—
373C4⋊Dic61—22no—
374C4⋊Dic61—22no—
375C4⋊Dic61—22no—
376C4⋊Dic61—21no—
377C4⋊Dic61—21no—
378C4⋊Dic61—21no—
379C4⋊Dic61—21no—
380C4⋊Dic61C2414yes—
381C4⋊Dic61C2411yescharacteristic
382C4⋊Dic61C2411yescharacteristic
383#11758196—21no—
384#11758196—21no—
385#11758196—21no—
386#11758196—21no—
387#11758196—24no—
388#11758196—24no—
389#11758196—24no—
390#11758196—24no—
391#11758196—21no—
392#11758196—21no—
393#11758196—21no—
394#11758196—21no—
395#11758196—21no—
396#11758196—21no—
397C4×Dic61—21no—
398C4×Dic61—21no—
399C4×Dic61—21no—
400C4×Dic61C2×D411yescharacteristic
401C4×Dic61C2×D411yescharacteristic
402C4×Dic61C2×D411yescharacteristic
403C4×Dic61C2×D411yescharacteristic
404C4×Dic61C2×D411yescharacteristic
405C4×Dic61C2×D411yescharacteristic
406C4×Dic61C2×D411yescharacteristic
407C4×Dic61C2×D411yescharacteristic
408C4×Dic61C2×D411yescharacteristic
409C4×Dic61C2×D411yescharacteristic
410C4×Dic61C2411yescharacteristic
411C4×Dic61C2411yescharacteristic
412C2×#92418C2414yes—
413C8×D61—28no—
414C23×C61—21no—
415C23×C61C22×D411yescharacteristic
416C22×D61—22no—
417C22×D61—22no—
418C22×D61—21no—
419C22×D61—42no—
420C22×D61—42no—
421C22×D61—42no—
422C22×D61AGL(1,ℤ/8)14yes—
423C22×D61C22×D411yescharacteristic
424C22×D61C22×D411yescharacteristic
425Q8×C61—22no—
426Q8×C61—44no—
427Q8×C61—44no—
428D4×C61—22no—
429D4×C61—42no—
430C2×C4×C61—22no—
431C2×C4×C61—22no—
432C2×C4×C61—22no—
433C2×C4×C61—21no—
434C2×C4×C61—21no—
435C2×C4×C61—24no—
436C2×C4×C61—21no—
437C2×C4×C61—44no—
438C2×C4×C61—42no—
439C2×C4×C61C22×D411yescharacteristic
440C2×C4×C61C22×D411yescharacteristic
441C2×C4×C61C22×D411yescharacteristic
442C2×C4×C61C22×D411yescharacteristic
443C2×C4×C61C22×D411yescharacteristic
444C2×C4×C61C2511yescharacteristic
445C22⋊D61—42no—
446C22⋊D61—42no—
447C22⋊D61—42no—
448C2×Dic61—22no—
449C2×Dic61—22no—
450C2×Dic61—22no—
451C2×Dic61—21no—
452C2×Dic61—21no—
453C2×Dic61—21no—
454C2×Dic61—24no—
455C2×Dic61—44no—
456C2×Dic61—42no—
457C2×Dic61C22×D411yescharacteristic
458C2×Dic61C22×D411yescharacteristic
459C2×Dic61C22×D411yescharacteristic
460C2×Dic61C22×D411yescharacteristic
461C2×Dic61C22×D411yescharacteristic
462C2×Dic61C22×D411yescharacteristic
463D244—22no—
464D244—42no—
465C4×D61—22no—
466C4×D61—22no—
467C4×D61—22no—
468C4×D61—22no—
469C4×D61—22no—
470C4×D61—22no—
471C4×D61—22no—
472C4×D61—22no—
473C4×D61—22no—
474C4×D61—22no—
475C4×D61—42no—
476C4×D61—48no—
477C4×D61—48no—
478C4×D61—42no—
479C4×D61—42no—
480C4×D61—42no—
481C4×D61—42no—
482C4×D61#13714yes—
483C4×D612−1+414yes—
484Dic122—22no—
485Dic122—48no—
486Dic122—48no—
487Dic122—44no—
488Dic122—44no—
489Dic122—42no—
490C8×C61—24no—
491#92418—24no—
492C2×#3238—611nomaximal, Sylow
493C22×C61—21no—
494C22×C61—21no—
495C22×C61—41no—
496C22×C61—41no—
497C22×C61—41no—
498C22×C61C2×AGL(1,ℤ/8)12yes—
499C22×C61C23×D411yescharacteristic
500C2×D61—21no—
501C2×D61—21no—
502C2×D61—28no—
503C2×D61—41no—
504C2×D61—41no—
505C2×D61—41no—
506C2×D61—84no—
507C2×D61#53612yes—
508C2×D61C2×AGL(1,ℤ/8)12yes—
509C2×D61C2×AGL(1,ℤ/8)12yes—
510C2×D61C2×#13712yes—
511C4×C61—21no—
512C4×C61—21no—
513C4×C61—21no—
514C4×C61—21no—
515C4×C61—41no—
516C4×C61—44no—
517C4×C61—41no—
518C4×C61—41no—
519C4×C61C2×#13712yes—
520C4×C61C2×2−1+412yes—
521Dic61—21no—
522Dic61—21no—
523Dic61—21no—
524Dic61—21no—
525Dic61—41no—
526Dic61—44no—
527Dic61—41no—
528Dic61—41no—
529Dic61#53612yes—
530Dic61C2×#13712yes—
531C22×C4⋊Q8—611no—
532C2×#529—611no—
533#3238—612no—
534#3238—612no—
535#3238—612no—
536#3238—612no—
537#3238—612no—
538#3238—612no—
539#3238—611no—
540#3238—611no—
541#3238—611no—
542#3238D6111yescharacteristic, direct product factor
543C2×#501—612no—
544C2×#489—612no—
545C2×#483—612no—
546C2×#480—612no—
547C2×#477—612no—
548C2×#476—612no—
549C2×#432—611no—
550C2×C61—22no—
551C2×C61—81no—
552C2×C61C2×#53611yescharacteristic
553C2×C61C22×AGL(1,ℤ/8)11yescharacteristic
554C2×C61C22×#13711yescharacteristic
555D61—22no—
556D61—81no—
557D61#323814yesdirect product factor
558C23×Q8—1221no—
559C2×C4⋊Q8—612no—
560C2×C4⋊Q8—612no—
561C2×C4⋊Q8—612no—
562C2×C4⋊Q8—612no—
563C2×C4⋊Q8—612no—
564C2×C4⋊Q8—611no—
565C2×C4⋊Q8—1221no—
566C2×C4⋊Q8—1221no—
567C2×C4⋊Q8—1221no—
568C2×C4⋊Q8—1221no—
569C2×C4⋊Q8—1221no—
570C2×C4⋊Q8—1221no—
571C2×C4⋊Q8C2×D6111yescharacteristic, complemented
572#529—611no—
573#529—611no—
574#529—611no—
575#529—611no—
576#529—611no—
577#529—611no—
578#529—611no—
579#529—1221no—
580#529—1221no—
581#529—1221no—
582#529—1221no—
583#529C2×D6111yescharacteristic
584C2×#126—1221no—
585C2×#125—611no—
586C2×#124—611no—
587C2×#123—1221no—
588C2×C22⋊Q8—611no—
589C2×#121—611no—
590C2×C4×Q8—611no—
591C2×C4×D4—611no—
592C2×C4×D4—1221no—
593C2×#117—1221no—
594C22×C4⋊C4—612no—
595C22×C4⋊C4—1221no—
596C22×C42—611no—
597#501—612no—
598#501—612no—
599#501—614no—
600#501—614no—
601#501—612no—
602#501C2×D6112yescomplemented
603#489—612no—
604#489—612no—
605#489—614no—
606#489—614no—
607#489—612no—
608#489C2×D6112yescomplemented
609#483—612no—
610#483—612no—
611#483—614no—
612#483—614no—
613#483—612no—
614#483C2×D6112yescomplemented
615#480—612no—
616#480—612no—
617#480—614no—
618#480—614no—
619#480—612no—
620#480C2×D6112yes—
621#477—612no—
622#477—612no—
623#477—614no—
624#477—612no—
625#477—614no—
626#477C2×D6112yescomplemented
627#476—612no—
628#476—612no—
629#476—614no—
630#476—612no—
631#476—614no—
632#476C2×D6112yescomplemented
633#432—611no—
634#432—612no—
635#432—612no—
636#432—612no—
637#432C2×D6111yescharacteristic, complemented
638C2×#107—614no—
639C2×#106—614no—
640C2×C4⋊C8—612no—
641C2×#103—614no—
642C2×#102—614no—
643C2×C22⋊C8—612no—
644C2×#97—612no—
645C61C2×#323811yescharacteristic, complemented, Sylow
646C22×Q8—21no—
647C22×Q8—611no—
648C22×Q8—1222no—
649C22×Q8—1222no—
650C22×Q8—1222no—
651C22×Q8—1222no—
652C22×Q8—1222no—
653C22×Q8—1221no—
654C22×Q8—2448no—
655C22×D4—611no—
656C22×D4—1221no—
657C23×C4—611no—
658C23×C4—611no—
659C23×C4—611no—
660C23×C4—1221no—
661C23×C4—1222no—
662C22×C8—614no—
663C4⋊Q8—21no—
664C4⋊Q8—21no—
665C4⋊Q8—614no—
666C4⋊Q8—614no—
667C4⋊Q8—612no—
668C4⋊Q8—612no—
669C4⋊Q8—1222no—
670C4⋊Q8—1222no—
671C4⋊Q8—1222no—
672C4⋊Q8—1222no—
673C4⋊Q8—1222no—
674C4⋊Q8—1222no—
675C4⋊Q8—1222no—
676C4⋊Q8—1222no—
677C4⋊Q8—1222no—
678C4⋊Q8—1222no—
679C4⋊Q8—1221no—
680C4⋊Q8—1221no—
681C4⋊Q8C22×D6112yes—
682C4⋊Q8C22×D6112yes—
683#126—21no—
684#126—1221no—
685#126—1221no—
686#126—1221no—
687#126—1221no—
688#126—1221no—
689#126—1221no—
690#126—1221no—
691#125—611no—
692#125—611no—
693#125—611no—
694#125—1221no—
695#125—1221no—
696#125C22×D6111yescharacteristic
697#124—611no—
698#124—611no—
699#124—611no—
700#124—1221no—
701#124—1221no—
702#124C22×D6111yescharacteristic
703#123—21no—
704#123—1221no—
705#123—1221no—
706#123—1221no—
707#123—1221no—
708#123—1221no—
709#123—1221no—
710#123—1221no—
711C22⋊Q8—611no—
712C22⋊Q8—611no—
713C22⋊Q8—611no—
714C22⋊Q8—1221no—
715C22⋊Q8—1221no—
716C22⋊Q8C22×D6111yescharacteristic
717#121—611no—
718#121—611no—
719#121—611no—
720#121—1221no—
721#121—1221no—
722#121C22×D6111yescharacteristic
723C4×Q8—611no—
724C4×Q8—611no—
725C4×Q8—611no—
726C4×Q8—1221no—
727C4×Q8—1221no—
728C4×Q8C22×D6111yescharacteristic
729C4×D4—21no—
730C4×D4—611no—
731C4×D4—611no—
732C4×D4—611no—
733C4×D4—1221no—
734C4×D4—1221no—
735C4×D4—1221no—
736C4×D4—1221no—
737C4×D4—1221no—
738C4×D4—1221no—
739C4×D4—1221no—
740C4×D4—1221no—
741C4×D4—1221no—
742C4×D4C22×D6111yescharacteristic
743#117—21no—
744#117—1221no—
745#117—1221no—
746#117—1221no—
747#117—1221no—
748#117—1221no—
749#117—1221no—
750#117—1221no—
751C2×C4⋊C4—21no—
752C2×C4⋊C4—612no—
753C2×C4⋊C4—614no—
754C2×C4⋊C4—614no—
755C2×C4⋊C4—611no—
756C2×C4⋊C4—611no—
757C2×C4⋊C4—1222no—
758C2×C4⋊C4—1222no—
759C2×C4⋊C4—1222no—
760C2×C4⋊C4—1222no—
761C2×C4⋊C4—1222no—
762C2×C4⋊C4—1222no—
763C2×C4⋊C4—1221no—
764C2×C4⋊C4—1221no—
765C2×C4⋊C4—1221no—
766C2×C4⋊C4—1221no—
767C2×C4⋊C4—1222no—
768C2×C4⋊C4—1222no—
769C2×C4⋊C4—1221no—
770C2×C4⋊C4C22×D6112yes—
771C2×C22⋊C4—1221no—
772C2×C22⋊C4—1221no—
773C2×C22⋊C4—1221no—
774C2×C22⋊C4—1221no—
775C2×C22⋊C4—1221no—
776C2×C42—611no—
777C2×C42—611no—
778C2×C42—611no—
779C2×C42—611no—
780C2×C42—611no—
781C2×C42—611no—
782C2×C42—611no—
783C2×C42—611no—
784C2×C42—611no—
785C2×C42—611no—
786C2×C42—611no—
787C2×C42—1221no—
788C2×C42C22×D6111yescharacteristic
789#107—614no—
790#107—614no—
791#107—614no—
792#107C22×D6114yes—
793#106—614no—
794#106—614no—
795#106—614no—
796#106C22×D6114yes—
797C4⋊C8—614no—
798C4⋊C8—612no—
799C4⋊C8C22×D6112yes—
800#103—614no—
801#103—614no—
802#103—614no—
803#103C22×D6114yes—
804#102—614no—
805#102—614no—
806#102—614no—
807#102C22×D6114yes—
808C22⋊C8—612no—
809C22⋊C8—614no—
810C22⋊C8C22×D6112yes—
811#97—614no—
812#97—612no—
813#97C22×D6112yes—
814C24—611no—
815C24—1221no—
816C2×Q8—22no—
817C2×Q8—22no—
818C2×Q8—44no—
819C2×Q8—611no—
820C2×Q8—1221no—
821C2×Q8—1224no—
822C2×Q8—1224no—
823C2×Q8—1224no—
824C2×Q8—1222no—
825C2×Q8—1222no—
826C2×Q8—2444no—
827C2×Q8—2448no—
828C2×Q8—2448no—
829C2×Q8—2448no—
830C2×Q8—2448no—
831C2×Q8—2448no—
832C2×Q8C23×D6111yescharacteristic
833C2×D4—21no—
834C2×D4—611no—
835C2×D4—1221no—
836C2×D4—1224no—
837C2×D4—1221no—
838C2×D4—1221no—
839C2×D4—1221no—
840C2×D4—2444no—
841C2×D4C23×D6111yescharacteristic
842C22×C4—22no—
843C22×C4—21no—
844C22×C4—611no—
845C22×C4—611no—
846C22×C4—611no—
847C22×C4—611no—
848C22×C4—611no—
849C22×C4—611no—
850C22×C4—611no—
851C22×C4—611no—
852C22×C4—611no—
853C22×C4—611no—
854C22×C4—611no—
855C22×C4—611no—
856C22×C4—611no—
857C22×C4—611no—
858C22×C4—611no—
859C22×C4—1224no—
860C22×C4—1224no—
861C22×C4—1221no—
862C22×C4—1224no—
863C22×C4—1221no—
864C22×C4—1221no—
865C22×C4—1221no—
866C22×C4—1224no—
867C22×C4—1224no—
868C22×C4—1221no—
869C22×C4—1222no—
870C22×C4—1221no—
871C22×C4—2444no—
872C22×C4—2448no—
873C22×C4D4×D6111yescharacteristic
874C22×C4D4×D6111yescharacteristic
875C22×C4C23×D6111yescharacteristic
876C2×C8—614no—
877C2×C8—1228no—
878C2×C8C23×D6114yes—
879C4⋊C4—22no—
880C4⋊C4—22no—
881C4⋊C4—22no—
882C4⋊C4—21no—
883C4⋊C4—21no—
884C4⋊C4—21no—
885C4⋊C4—21no—
886C4⋊C4—614no—
887C4⋊C4—611no—
888C4⋊C4—611no—
889C4⋊C4—1224no—
890C4⋊C4—1224no—
891C4⋊C4—1221no—
892C4⋊C4—1221no—
893C4⋊C4—1224no—
894C4⋊C4—1224no—
895C4⋊C4—1221no—
896C4⋊C4—1221no—
897C4⋊C4—1221no—
898C4⋊C4—1221no—
899C4⋊C4—1221no—
900C4⋊C4—1221no—
901C4⋊C4—1221no—
902C4⋊C4—1221no—
903C4⋊C4—1222no—
904C4⋊C4—1222no—
905C4⋊C4—1222no—
906C4⋊C4—1221no—
907C4⋊C4—1221no—
908C4⋊C4—1221no—
909C4⋊C4—1221no—
910C4⋊C4C23×D6114yes—
911C4⋊C4C23×D6111yescharacteristic
912C4⋊C4C23×D6111yescharacteristic
913C22⋊C4—21no—
914C22⋊C4—21no—
915C22⋊C4—21no—
916C22⋊C4—21no—
917C22⋊C4—21no—
918C22⋊C4—1221no—
919C22⋊C4—1221no—
920C22⋊C4—1221no—
921C22⋊C4—1221no—
922C22⋊C4—1221no—
923C22⋊C4—1221no—
924C22⋊C4—1221no—
925C22⋊C4—1221no—
926C22⋊C4—1221no—
927C22⋊C4—1221no—
928C22⋊C4—1221no—
929C22⋊C4—1221no—
930C22⋊C4—1221no—
931C22⋊C4—1221no—
932C22⋊C4—1221no—
933C42—21no—
934C42—611no—
935C42—611no—
936C42—611no—
937C42—611no—
938C42—611no—
939C42—611no—
940C42—611no—
941C42—611no—
942C42—611no—
943C42—611no—
944C42—611no—
945C42—611no—
946C42—1221no—
947C42—1221no—
948C42—1221no—
949C42D4×D6111yescharacteristic
950C42D4×D6111yescharacteristic
951C42C23×D6111yescharacteristic
952C42C23×D6111yescharacteristic
953C23—21no—
954C23—611no—
955C23—614no—
956C23—611no—
957C23—1222no—
958C23—1222no—
959C23—1221no—
960C23—2442no—
961C23—2442no—
962C23—2442no—
963C23C2×D4×D6111yescharacteristic
964Q8—22no—
965Q8—44no—
966Q8—44no—
967Q8—1222no—
968Q8—2444no—
969Q8—2444no—
970Q8—2442no—
971Q8—2448no—
972Q8—2448no—
973D4—22no—
974D4—42no—
975D4—1222no—
976D4—2442no—
977D4—2442no—
978D4—2442no—
979D4—2442no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—21no—
984C2×C4—21no—
985C2×C4—21no—
986C2×C4—24no—
987C2×C4—44no—
988C2×C4—42no—
989C2×C4—611no—
990C2×C4—611no—
991C2×C4—614no—
992C2×C4—614no—
993C2×C4—611no—
994C2×C4—611no—
995C2×C4—611no—
996C2×C4—611no—
997C2×C4—1222no—
998C2×C4—1222no—
999C2×C4—1222no—
1000C2×C4—1222no—
1001C2×C4—1222no—
1002C2×C4—1222no—
1003C2×C4—1222no—
1004C2×C4—1222no—
1005C2×C4—1222no—
1006C2×C4—1222no—
1007C2×C4—1222no—
1008C2×C4—1222no—
1009C2×C4—1222no—
1010C2×C4—1221no—
1011C2×C4—1221no—
1012C2×C4—1221no—
1013C2×C4—1224no—
1014C2×C4—2442no—
1015C2×C4—2442no—
1016C2×C4—2448no—
1017C2×C4—2448no—
1018C2×C4—2442no—
1019C2×C4—2442no—
1020C2×C4—2442no—
1021C2×C4—2444no—
1022C2×C4—2442no—
1023C2×C4C2×D4×D6111yescharacteristic
1024C2×C4C2×D4×D6111yescharacteristic
1025C2×C4C2×D4×D6111yescharacteristic
1026C2×C4C2×D4×D6111yescharacteristic
1027C2×C4C2×D4×D6111yescharacteristic
1028C2×C4C24×D6111yescharacteristic
1029C8—24no—
1030C8—1224no—
1031C22—21no—
1032C22—21no—
1033C22—41no—
1034C22—41no—
1035C22—41no—
1036C22—612no—
1037C22—612no—
1038C22—612no—
1039C22—612no—
1040C22—1228no—
1041C22—1221no—
1042C22—1221no—
1043C22—4884no—
1044C22—2441no—
1045C22—2441no—
1046C22—2441no—
1047C22AGL(1,ℤ/8)×D6112yes—
1048C22C22×D4×D6111yescharacteristic
1049C4—21no—
1050C4—21no—
1051C4—21no—
1052C4—21no—
1053C4—44no—
1054C4—41no—
1055C4—41no—
1056C4—41no—
1057C4—612no—
1058C4—612no—
1059C4—1221no—
1060C4—1221no—
1061C4—1221no—
1062C4—1221no—
1063C4—2444no—
1064C4—2441no—
1065C4—2441no—
1066C4—2441no—
1067C4#137×D6112yes—
1068C42−1+4×D6112yes—
1069C2—22no—
1070C2—81no—
1071C2—614no—
1072C2—1222no—
1073C2—4881no—
1074C2#536×D6111yescharacteristic
1075C2C2×AGL(1,ℤ/8)×D6111yescharacteristic
1076C2C2×#137×D6111yescharacteristic
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3238C2
socleC22×C61C23×D4
prime radical#121×D61C22
hypercenter#3238D61
hypocenterC61C2×#3238
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3238

Complements

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

NH ≅ G/Ntype
1. C2×C4⋊Q8×D61C2semidirect
3. #21457044C2semidirect
4. #21457043C2semidirect
5. #21457042C2semidirect
6. #21457041C2semidirect
7. #21457040C2semidirect
8. #21457039C2semidirect
9. #21457038C2semidirect
10. #21457037C2semidirect
11. #21457036C2semidirect
12. #501×D61C2semidirect
13. #489×D61C2semidirect
14. #483×D61C2semidirect
16. #477×D61C2semidirect
17. #476×D61C2semidirect
18. #432×D61C2semidirect
19. C61×#3238C2semidirect
21. C2×#14519777C22semidirect
23. C2×#14519776C22semidirect
31. C4⋊Q8×D61C22semidirect
32. C4⋊Q8×D61C22semidirect
57. #16840172C22semidirect
58. #16840171C22semidirect
59. #16840170C22semidirect
60. #16840169C22semidirect
61. #16840168C22semidirect
62. #16840124C22semidirect
63. #16840123C22semidirect
64. #16840122C22semidirect
65. #16840121C22semidirect
66. #16840120C22semidirect
67. #16840094C22semidirect
68. #16840093C22semidirect
69. #16840092C22semidirect
70. #16840091C22semidirect
71. #16840090C22semidirect
77. #16840058C22semidirect
78. #16840057C22semidirect
79. #16840056C22semidirect
80. #16840055C22semidirect
81. #16840054C22semidirect
82. #16840053C22semidirect
83. #16840052C22semidirect
84. #16840051C22semidirect
85. #16840050C22semidirect
86. #16840049C22semidirect
87. #16839819C22semidirect
88. #16839818C22semidirect
89. #16839817C22semidirect
90. #16839816C22semidirect
98. C2×C4⋊Q8×C61C22semidirect
100. C61×#501C22semidirect
101. C61×#489C22semidirect
102. C61×#483C22semidirect
104. C61×#477C22semidirect
105. C61×#476C22semidirect
106. C61×#432C22semidirect
542. #3238D61direct (N × H)
557. D61#3238direct (N × H)
571. C2×C4⋊Q8C2×D61semidirect
602. #501C2×D61semidirect
608. #489C2×D61semidirect
614. #483C2×D61semidirect
626. #477C2×D61semidirect
632. #476C2×D61semidirect
637. #432C2×D61semidirect
645. C61C2×#3238semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊Q8×D612
#529×D612
#214570442
#214570432
#214570422
#214570412
#214570402
#214570392
#214570382
#214570372
#214570362
#501×D612
#489×D612
#483×D612
#480×D612
#477×D612
#476×D612
#432×D612
C61×#32382
C2×#323861