Finite Group Databasebeta

← #30552277

Subgroups — #30552277

Order 15616.

2006 conjugacy classes of subgroups.

The subgroup lattice has 1100 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459112C211yesmaximal, characteristic
2C2×C4⋊Q8×D61C211yesmaximal, characteristic, complemented
3#21457053C212yesmaximal, complemented
4#21457048C212yesmaximal, complemented
5#21457044C212yesmaximal, complemented
6#21457039C212yesmaximal, complemented
7#21456969C212yesmaximal, complemented
8#21456962C212yesmaximal, complemented
9#21456946C212yesmaximal, complemented
10#21456939C212yesmaximal, complemented
11#21456363C212yesmaximal, complemented
12#21456210C212yesmaximal, complemented
13#21455745C212yesmaximal, complemented
14#21455740C212yesmaximal, complemented
15#21455635C211yesmaximal, characteristic, complemented
16#21455634C211yesmaximal, characteristic, complemented
17#21455628C211yesmaximal, characteristic, complemented
18#21454451C211yesmaximal, characteristic, complemented
19C61×#3079C211yesmaximal, characteristic, complemented
20C22×Q8×D61—21no—
21#16840316C2211yescharacteristic
22#16840316C2211yescharacteristic
23#16840315C2211yescharacteristic
24#16840309C2211yescharacteristic
25#16840309C2211yescharacteristic
26#16840308C2211yescharacteristic
27C2×#14519777C2211yescharacteristic
28C2×#14519776—21no—
29C2×#14519776C2212yes—
30C2×#14519775—21no—
31C4⋊Q8×D61—21no—
32C4⋊Q8×D61—21no—
33C4⋊Q8×D61—21no—
34C4⋊Q8×D61—21no—
35C4⋊Q8×D61C2212yes—
36C4⋊Q8×D61C2212yes—
37C4⋊Q8×D61C2212yes—
38C4⋊Q8×D61C2212yes—
39#16840299C2211yescharacteristic
40#16840299C2211yescharacteristic
41#16840294C2211yescharacteristic
42#16840294C2211yescharacteristic
43#16840292—21no—
44#16840292—21no—
45#16840290—21no—
46#16840290—21no—
47#16840274C2211yescharacteristic
48#16840271—21no—
49#16840271—21no—
50#16840269C2211yescharacteristic
51C4×#11758222—21no—
52C4×#11758222—21no—
53C4×#11758222C2211yescharacteristic
54C2×C4⋊C4×D61—21no—
55C2×C4⋊C4×D61C2212yes—
56C2×C42×D61C2211yescharacteristic
57#16840170C2214yescomplemented
58#16840169C2214yescomplemented
59#16840166C2214yescomplemented
60#16840159C2214yescomplemented
61#16840123C2214yescomplemented
62#16840120C2214yescomplemented
63#16840111C2214yescomplemented
64#16840107C2214yescomplemented
65#16840099C2214yes—
66#16840096C2214yes—
67#16840094C2214yes—
68#16840091C2214yes—
69#16840082C2214yes—
70#16840079C2214yes—
71#16840077C2214yes—
72#16840074C2214yes—
73#16840058C2212yescomplemented
74#16840057C2212yescomplemented
75#16840054C2212yescomplemented
76#16840053C2212yescomplemented
77#16840052C2212yescomplemented
78#16840049C2212yescomplemented
79#16840048C2212yescomplemented
80#16840047C2212yescomplemented
81#16840044C2212yescomplemented
82#16840043C2212yescomplemented
83#16840042C2212yescomplemented
84#16840039C2212yescomplemented
85#16839818C2212yes—
86#16839818C2212yes—
87#16839814C2212yes—
88#16839814C2212yes—
89#16839805C2212yes—
90#16839804C2212yes—
91#16839802C2212yes—
92#16839786C2211yescharacteristic
93#16839764C2212yes—
94#16839763C2212yes—
95#16839761C2212yes—
96#16839725C2212yes—
97M16×Dic61C2212yes—
98C2×C4⋊Q8×C61C2211yescharacteristic
99C4×#41×C61C2211yescharacteristic
100C61×#477C2212yescomplemented
101C61×#476C2212yescomplemented
102C61×#475C2212yescomplemented
103C61×#474C2212yescomplemented
104C61×#428C2212yes—
105C61×#423C2211yescharacteristic
106C61×#417C2212yes—
107C2×#11758222—21no—
108C2×#11758222—21no—
109C2×#11758222C2311yescharacteristic
110C22×Dic122—21no—
111C22×Dic122—22no—
112C2×Q8×D61—22no—
113C2×Q8×D61—22no—
114C2×Q8×D61—22no—
115C2×Q8×D61—22no—
116C2×Q8×D61—48no—
117C22×C4×D61—22no—
118C22×C4×D61D411yescharacteristic
119C22×C4×D61D411yescharacteristic
120C22×C4×D61C2311yescharacteristic
121C2×#11758194C2312yes—
122#14519777—21no—
123#14519777—21no—
124#14519777C2312yes—
125#14519777C2312yes—
126#14519776—22no—
127#14519776—22no—
128#14519776—22no—
129#14519776—22no—
130#14519776—22no—
131#14519776—22no—
132#14519776C2314yes—
133#14519776C2314yes—
134#14519776C2311yescharacteristic
135#14519776C2311yescharacteristic
136#14519775—22no—
137#14519775—22no—
138#14519775—22no—
139#14519775—22no—
140#14519775C2311yescharacteristic
141#14519773C2311yescharacteristic
142#14519772—21no—
143#14519772—21no—
144#14519770—21no—
145#14519770—21no—
146#14519768C2311yescharacteristic
147#14519768C2311yescharacteristic
148#14519767—21no—
149#14519767—21no—
150#14519766C2311yescharacteristic
151#14519764C2311yescharacteristic
152#14519763—21no—
153#14519763—21no—
154#14519762—21no—
155#14519762—21no—
156#14519761—21no—
157#14519759—21no—
158#14519759—21no—
159#14519758—21no—
160#14519757C2311yescharacteristic
161#14519757C2311yescharacteristic
162#14519755—21no—
163#14519755—21no—
164#14519754—21no—
165#14519754—21no—
166#14519753C2311yescharacteristic
167#14519753C2311yescharacteristic
168#14519752C2311yescharacteristic
169#14519752C2311yescharacteristic
170#14519750—21no—
171#14519750—21no—
172#14519749—21no—
173#14519749—21no—
174#14519748C2311yescharacteristic
175#14519748C2311yescharacteristic
176#14519747—21no—
177#14519745—21no—
178C4×Dic122—21no—
179C4×Dic122—21no—
180C4×Dic122—21no—
181C4×Dic122—21no—
182C4×Dic122C2311yescharacteristic
183C4×Dic122C2311yescharacteristic
184C4×D244—21no—
185C4×D244—21no—
186C4×D244—21no—
187C4×D244—21no—
188C4×D244C2311yescharacteristic
189C4×D244C2311yescharacteristic
190C4×C22⋊D61—21no—
191C4×C22⋊D61—21no—
192C4×C22⋊D61—21no—
193C4×C22⋊D61—21no—
194C4×C22⋊D61—21no—
195C4×C22⋊D61—21no—
196C4×C22⋊D61—21no—
197C4×C22⋊D61—21no—
198C4×C22⋊D61—21no—
199C4×C22⋊D61—21no—
200#14519736—21no—
201#14519736—21no—
202#14519736C2311yescharacteristic
203#14519734—21no—
204#14519734—21no—
205#14519734—21no—
206#14519734—21no—
207#14519734—21no—
208C2×C4⋊Dic61—21no—
209C2×C4⋊Dic61C2312yes—
210C2×#11758196—22no—
211C2×#11758196—22no—
212C4⋊C4×D61—22no—
213C4⋊C4×D61—22no—
214C4⋊C4×D61—22no—
215C4⋊C4×D61—22no—
216C4⋊C4×D61—22no—
217C4⋊C4×D61—22no—
218C4⋊C4×D61C2314yes—
219C4⋊C4×D61C2314yes—
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—
239C4⋊#92418C2312yes—
240#14519702C2314yes—
241#14519701C2314yes—
242#14519700C2314yes—
243#14519699C2314yes—
244#14519698C2314yes—
245#14519697C2314yes—
246#14519689C2314yes—
247#14519689C2314yes—
248#14519687C2314yes—
249C8×Dic61C2314yes—
250C2×#41×C61C2311yescharacteristic
251C22×Q8×C61—21no—
252C2×M16×C61C2312yes—
253C4⋊Q8×C61—21no—
254C4⋊Q8×C61—21no—
255C4⋊Q8×C61C2312yes—
256C4⋊Q8×C61C2312yes—
257C4×Q8×C61C2311yescharacteristic
258C4×Q8×C61C2311yescharacteristic
259C4×D4×C61—21no—
260C4×D4×C61—21no—
261C4×D4×C61C2311yescharacteristic
262C4×D4×C61C2311yescharacteristic
263#117×C61—21no—
264#117×C61C2311yescharacteristic
265C2×C4⋊C4×C61—21no—
266C2×C4⋊C4×C61C2312yes—
267C2×C42×C61—21no—
268C2×C42×C61C2311yescharacteristic
269#107×C61C2314yes—
270#106×C61C2314yes—
271C4⋊C8×C61C2312yes—
272C4⋊C8×C61C2312yes—
273#103×C61C2314yes—
274#102×C61C2314yes—
275C23×D61C2×D411yescharacteristic
276#41×C61—22no—
277#41×C61—22no—
278C2×Q8×C61—22no—
279C2×Q8×C61—22no—
280C2×Q8×C61—44no—
281C2×Q8×C61C2411yescharacteristic
282C2×D4×C61—21no—
283C2×D4×C61C2411yescharacteristic
284C22×C4×C61—22no—
285C22×C4×C61—21no—
286C22×C4×C61—21no—
287C22×C4×C61—21no—
288C22×C4×C61C2×D411yescharacteristic
289C22×C4×C61C2×D411yescharacteristic
290C22×C4×C61C2411yescharacteristic
291C2×C22⋊D61—21no—
292C2×C22⋊D61—21no—
293C2×C22⋊D61—21no—
294C2×C22⋊D61—21no—
295C2×C22⋊D61—21no—
296C22×Dic61—22no—
297C22×Dic61C2×D411yescharacteristic
298C22×Dic61C2×D411yescharacteristic
299C22×Dic61C2×D411yescharacteristic
300Q8×D61—48no—
301Q8×D61—48no—
302Q8×D61—48no—
303Q8×D61—48no—
304#11758222—22no—
305#11758222—22no—
306#11758222—44no—
307#11758222—44no—
308C2×D244—21no—
309C2×D244—21no—
310C2×D244C2411yescharacteristic
311C2×C4×D61—22no—
312C2×C4×D61—22no—
313C2×C4×D61—24no—
314C2×C4×D61—24no—
315C2×C4×D61—24no—
316C2×C4×D61—24no—
317C2×C4×D61—21no—
318C2×C4×D61—21no—
319C2×C4×D61—21no—
320C2×C4×D61—48no—
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×D61C2×D411yescharacteristic
328C2×C4×D61C2×D411yescharacteristic
329C2×C4×D61C2×D411yescharacteristic
330C2×C4×D61C2×D411yescharacteristic
331C2×C4×D61C2411yescharacteristic
332C2×C4×D61C2411yescharacteristic
333C2×Dic122—22no—
334C2×Dic122—22no—
335C2×Dic122—24no—
336C2×Dic122—24no—
337C2×Dic122—21no—
338C2×Dic122—21no—
339C2×Dic122—48no—
340C2×Dic122—44no—
341C2×Dic122C2411yescharacteristic
342M16×C61—24no—
343C2×C8×C61C2414yes—
344C4⋊C4×C61—22no—
345C4⋊C4×C61—22no—
346C4⋊C4×C61—22no—
347C4⋊C4×C61—21no—
348C4⋊C4×C61—21no—
349C4⋊C4×C61C2414yes—
350C4⋊C4×C61C2411yescharacteristic
351C4⋊C4×C61C2411yescharacteristic
352C22⋊C4×C61—21no—
353C22⋊C4×C61—21no—
354C22⋊C4×C61—21no—
355C42×C61—21no—
356C42×C61—21no—
357C42×C61—21no—
358C42×C61C2×D411yescharacteristic
359C42×C61C2×D411yescharacteristic
360C42×C61C2411yescharacteristic
361C42×C61C2411yescharacteristic
362C22⋊Dic61—21no—
363C22⋊Dic61—21no—
364C22⋊Dic61—21no—
365C22⋊Dic61—21no—
366C22⋊Dic61—21no—
367#11758198—21no—
368#11758198—21no—
369#11758198—21no—
370#11758198—21no—
371#11758198—21no—
372#11758198—21no—
373#11758198—21no—
374#11758198—21no—
375#11758198—21no—
376#11758198—21no—
377C4⋊Dic61—22no—
378C4⋊Dic61—22no—
379C4⋊Dic61—22no—
380C4⋊Dic61—21no—
381C4⋊Dic61—21no—
382C4⋊Dic61—21no—
383C4⋊Dic61—21no—
384C4⋊Dic61C2414yes—
385C4⋊Dic61C2411yescharacteristic
386C4⋊Dic61C2411yescharacteristic
387#11758196—21no—
388#11758196—21no—
389#11758196—24no—
390#11758196—24no—
391#11758196—24no—
392#11758196—24no—
393#11758196—21no—
394#11758196—21no—
395#11758196—21no—
396#11758196—21no—
397#11758196—21no—
398#11758196—21no—
399#11758196—21no—
400#11758196—21no—
401C4×Dic61—21no—
402C4×Dic61—21no—
403C4×Dic61—21no—
404C4×Dic61C2×D411yescharacteristic
405C4×Dic61C2×D411yescharacteristic
406C4×Dic61C2×D411yescharacteristic
407C4×Dic61C2×D411yescharacteristic
408C4×Dic61C2×D411yescharacteristic
409C4×Dic61C2×D411yescharacteristic
410C4×Dic61C2×D411yescharacteristic
411C4×Dic61C2×D411yescharacteristic
412C4×Dic61C2×D411yescharacteristic
413C4×Dic61C2×D411yescharacteristic
414C4×Dic61C2411yescharacteristic
415C4×Dic61C2411yescharacteristic
416#11758194—24no—
417C2×#92418C2414yes—
418C23×C61—21no—
419C23×C61C22×D411yescharacteristic
420C22×D61—22no—
421C22×D61—22no—
422C22×D61—22no—
423C22×D61—21no—
424C22×D61C22×D411yescharacteristic
425C22×D61C22×D411yescharacteristic
426Q8×C61—21no—
427Q8×C61—21no—
428Q8×C61—44no—
429Q8×C61—44no—
430D4×C61—21no—
431D4×C61—21no—
432D4×C61—42no—
433C2×C4×C61—22no—
434C2×C4×C61—22no—
435C2×C4×C61—21no—
436C2×C4×C61—24no—
437C2×C4×C61—21no—
438C2×C4×C61—21no—
439C2×C4×C61—44no—
440C2×C4×C61—42no—
441C2×C4×C61—42no—
442C2×C4×C61—42no—
443C2×C4×C61C22×D411yescharacteristic
444C2×C4×C61C22×D411yescharacteristic
445C2×C4×C61C22×D411yescharacteristic
446C2×C4×C61C22×D411yescharacteristic
447C2×C4×C61C22×D411yescharacteristic
448C2×C4×C612−1+412yes—
449C2×C4×C612−1+412yes—
450C2×C4×C61C2511yescharacteristic
451C22⋊D61—42no—
452C22⋊D61—42no—
453C22⋊D61—42no—
454C22⋊D61—42no—
455C22⋊D61—42no—
456C2×Dic61—22no—
457C2×Dic61—22no—
458C2×Dic61—22no—
459C2×Dic61—21no—
460C2×Dic61—21no—
461C2×Dic61—21no—
462C2×Dic61—24no—
463C2×Dic61—44no—
464C2×Dic61C22×D411yescharacteristic
465C2×Dic61C22×D411yescharacteristic
466C2×Dic61C22×D411yescharacteristic
467C2×Dic61C22×D411yescharacteristic
468C2×Dic61C22×D411yescharacteristic
469C2×Dic61C22×D411yescharacteristic
470D244—21no—
471D244—21no—
472D244—42no—
473D244—42no—
474C4×D61—22no—
475C4×D61—22no—
476C4×D61—22no—
477C4×D61—22no—
478C4×D61—22no—
479C4×D61—22no—
480C4×D61—21no—
481C4×D61—21no—
482C4×D61—21no—
483C4×D61—21no—
484C4×D61—22no—
485C4×D61—22no—
486C4×D61—48no—
487C4×D61—48no—
488C4×D61—42no—
489C4×D61—42no—
490C4×D61—42no—
491C4×D61AGL(1,ℤ/8)14yes—
492C4×D61#13714yes—
493Dic122—21no—
494Dic122—21no—
495Dic122—48no—
496Dic122—44no—
497Dic122—44no—
498Dic122—48no—
499Dic122—42no—
500Dic122—42no—
501C8×C61—24no—
502#92418—24no—
503#60860—611nomaximal, Sylow
504C22×C61—21no—
505C22×C61—21no—
506C22×C61—41no—
507C22×C61—41no—
508C22×C61—41no—
509C22×C61#53612yes—
510C22×C61C23×D411yescharacteristic
511C2×D61—28no—
512C2×D61—21no—
513C2×D61—21no—
514C2×D61—21no—
515C2×D61—21no—
516C2×D61—41no—
517C2×D61—41no—
518C2×D61—41no—
519C2×D61C2×AGL(1,ℤ/8)12yes—
520C2×D61C2×#13712yes—
521C4×C61—21no—
522C4×C61—21no—
523C4×C61—41no—
524C4×C61—44no—
525C4×C61—41no—
526C4×C61—41no—
527C4×C61#53612yes—
528C4×C61C2×AGL(1,ℤ/8)12yes—
529C4×C61C2×#13712yes—
530C4×C61C2×2−1+411yescharacteristic
531C4×C61C2×2−1+411yescharacteristic
532Dic61—21no—
533Dic61—21no—
534Dic61—21no—
535Dic61—21no—
536Dic61—41no—
537Dic61—44no—
538Dic61—41no—
539Dic61—41no—
540Dic61C2×AGL(1,ℤ/8)12yes—
541Dic61C2×#13712yes—
542#3444—611no—
543C22×C4⋊Q8—611no—
544#3239—612no—
545#3239—612no—
546#3238—612no—
547#3238—612no—
548#3230—612no—
549#3229—612no—
550#3227—612no—
551#3226—612no—
552#3165—612no—
553#3141—612no—
554#3092—612no—
555#3092—612no—
556#3079—611no—
557#3079—611no—
558#3079—611no—
559#3079D6111yescharacteristic, complemented
560#2920—611no—
561C2×C61—22no—
562C2×C61—81no—
563C2×C61C2×#53611yescharacteristic
564C2×C61C22×AGL(1,ℤ/8)11yescharacteristic
565C2×C61C22×#13711yescharacteristic
566D61—22no—
567D61—22no—
568D61—81no—
569C23×Q8—1221no—
570#533—611no—
571#533—611no—
572#533—611no—
573#532—611no—
574#532—611no—
575#532—611no—
576C2×C4⋊Q8—612no—
577C2×C4⋊Q8—612no—
578C2×C4⋊Q8—612no—
579C2×C4⋊Q8—612no—
580C2×C4⋊Q8—612no—
581C2×C4⋊Q8—611no—
582C2×C4⋊Q8—1221no—
583C2×C4⋊Q8—1221no—
584C2×C4⋊Q8—1221no—
585C2×C4⋊Q8—1221no—
586C2×C4⋊Q8—1221no—
587C2×C4⋊Q8—1221no—
588C2×C4⋊Q8C2×D6111yescharacteristic
589#529—611no—
590#529—611no—
591#529—611no—
592#529—611no—
593#529—1221no—
594#529—1221no—
595#529—1221no—
596#529—1221no—
597#525—611no—
598#525—611no—
599#525—1221no—
600#525—1221no—
601C4×#41—611no—
602C4×#41—1221no—
603C4×#41—1221no—
604C4×#41C2×D6111yescharacteristic
605C22×C4⋊C4—612no—
606C22×C4⋊C4—1221no—
607C22×C42—611no—
608#501—614no—
609#501—614no—
610#500—614no—
611#498—614no—
612#489—614no—
613#489—614no—
614#487—614no—
615#486—614no—
616#484—614no—
617#484—614no—
618#483—614no—
619#483—614no—
620#481—614no—
621#481—614no—
622#480—614no—
623#480—614no—
624#477—612no—
625#477—612no—
626#477—612no—
627#477C2×D6112yescomplemented
628#476—612no—
629#476—612no—
630#476—612no—
631#476C2×D6112yescomplemented
632#475—612no—
633#475—612no—
634#475—612no—
635#475C2×D6112yescomplemented
636#474—612no—
637#474—612no—
638#474—612no—
639#474C2×D6112yescomplemented
640#432—612no—
641#432—612no—
642#431—612no—
643#431—612no—
644#428—612no—
645#428—612no—
646#428—612no—
647#428C2×D6112yes—
648#423—611no—
649#423C2×D6111yescharacteristic
650#417—612no—
651#417—612no—
652#417—612no—
653#417C2×D6112yes—
654#407—612no—
655C4×M16—612no—
656C61#6086011yescharacteristic, complemented, Sylow
657C2×#41—611no—
658C2×#41—1221no—
659C2×#41—1221no—
660C2×#41C22×D6111yescharacteristic
661C22×Q8—21no—
662C22×Q8—1222no—
663C22×Q8—1222no—
664C22×Q8—1222no—
665C22×Q8—1222no—
666C22×Q8—1222no—
667C22×Q8—1221no—
668C22×Q8—2448no—
669C23×C4—611no—
670C23×C4—611no—
671C23×C4—611no—
672C23×C4—1222no—
673C2×M16—612no—
674C2×M16C22×D6112yes—
675C4⋊Q8—21no—
676C4⋊Q8—21no—
677C4⋊Q8—614no—
678C4⋊Q8—614no—
679C4⋊Q8—611no—
680C4⋊Q8—611no—
681C4⋊Q8—611no—
682C4⋊Q8—612no—
683C4⋊Q8—612no—
684C4⋊Q8—1222no—
685C4⋊Q8—1222no—
686C4⋊Q8—1222no—
687C4⋊Q8—1222no—
688C4⋊Q8—1222no—
689C4⋊Q8—1222no—
690C4⋊Q8—1222no—
691C4⋊Q8—1222no—
692C4⋊Q8—1222no—
693C4⋊Q8—1222no—
694C4⋊Q8—1221no—
695C4⋊Q8—1221no—
696C4⋊Q8C22×D6112yes—
697C4⋊Q8C22×D6112yes—
698#127—611no—
699#126—1221no—
700#126—1221no—
701#126—1221no—
702#126—1221no—
703#125—611no—
704#125—611no—
705#125—1221no—
706#125—1221no—
707#124—611no—
708#124—611no—
709#124—1221no—
710#124—1221no—
711#123—1221no—
712#123—1221no—
713#123—1221no—
714#123—1221no—
715#123—1221no—
716#123—1221no—
717C22⋊Q8—611no—
718C22⋊Q8—611no—
719C22⋊Q8—611no—
720C22⋊Q8—611no—
721C22⋊Q8—1221no—
722C22⋊Q8—1221no—
723C22⋊Q8—1221no—
724C22⋊Q8—1221no—
725#121—611no—
726#121—611no—
727#121—611no—
728#121—611no—
729#121—1221no—
730#121—1221no—
731#121—1221no—
732#121—1221no—
733#120—1221no—
734#120—1221no—
735C4×Q8—611no—
736C4×Q8—611no—
737C4×Q8—1221no—
738C4×Q8—1221no—
739C4×Q8—1221no—
740C4×Q8—1221no—
741C4×Q8C22×D6111yescharacteristic
742C4×Q8C22×D6111yescharacteristic
743C4×D4—21no—
744C4×D4—21no—
745C4×D4—611no—
746C4×D4—611no—
747C4×D4—1221no—
748C4×D4—1221no—
749C4×D4—1221no—
750C4×D4—1221no—
751C4×D4—1221no—
752C4×D4—1221no—
753C4×D4—1221no—
754C4×D4—1221no—
755C4×D4—1221no—
756C4×D4—1221no—
757C4×D4—1221no—
758C4×D4—1221no—
759C4×D4—1221no—
760C4×D4—1221no—
761C4×D4C22×D6111yescharacteristic
762C4×D4C22×D6111yescharacteristic
763#117—21no—
764#117—611no—
765#117—1221no—
766#117—1221no—
767#117—1221no—
768#117—1221no—
769#117—1221no—
770#117—1221no—
771#117—1221no—
772#117C22×D6111yescharacteristic
773C2×C4⋊C4—21no—
774C2×C4⋊C4—612no—
775C2×C4⋊C4—614no—
776C2×C4⋊C4—614no—
777C2×C4⋊C4—1222no—
778C2×C4⋊C4—1222no—
779C2×C4⋊C4—1222no—
780C2×C4⋊C4—1222no—
781C2×C4⋊C4—1222no—
782C2×C4⋊C4—1222no—
783C2×C4⋊C4—1222no—
784C2×C4⋊C4—1222no—
785C2×C4⋊C4—1221no—
786C2×C4⋊C4C22×D6112yes—
787C2×C42—21no—
788C2×C42—611no—
789C2×C42—611no—
790C2×C42—611no—
791C2×C42—611no—
792C2×C42—611no—
793C2×C42—611no—
794C2×C42—611no—
795C2×C42—611no—
796C2×C42—611no—
797C2×C42—611no—
798C2×C42—611no—
799C2×C42—1221no—
800C2×C42C22×D6111yescharacteristic
801#107—614no—
802#107—614no—
803#107—614no—
804#107C22×D6114yes—
805#106—614no—
806#106—614no—
807#106—614no—
808#106C22×D6114yes—
809C4⋊C8—612no—
810C4⋊C8—612no—
811C4⋊C8C22×D6112yes—
812C4⋊C8C22×D6112yes—
813#103—614no—
814#103—614no—
815#103—614no—
816#103C22×D6114yes—
817#102—614no—
818#102—614no—
819#102—614no—
820#102C22×D6114yes—
821C22⋊C8—614no—
822C22⋊C8—614no—
823#97—614no—
824C4×C8—614no—
825C24—611no—
826#41—22no—
827#41—22no—
828#41—1222no—
829#41—1222no—
830#41—2444no—
831#41—2444no—
832C2×Q8—22no—
833C2×Q8—22no—
834C2×Q8—44no—
835C2×Q8—611no—
836C2×Q8—1221no—
837C2×Q8—1221no—
838C2×Q8—1224no—
839C2×Q8—1224no—
840C2×Q8—1222no—
841C2×Q8—1222no—
842C2×Q8—2444no—
843C2×Q8—2448no—
844C2×Q8—2448no—
845C2×Q8—2448no—
846C2×Q8—2448no—
847C2×Q8—2448no—
848C2×Q8C23×D6111yescharacteristic
849C2×D4—21no—
850C2×D4—611no—
851C2×D4—1221no—
852C2×D4—1221no—
853C2×D4—1221no—
854C2×D4—1221no—
855C2×D4—1221no—
856C2×D4—1221no—
857C2×D4—1221no—
858C2×D4C23×D6111yescharacteristic
859C22×C4—22no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—611no—
864C22×C4—611no—
865C22×C4—611no—
866C22×C4—611no—
867C22×C4—611no—
868C22×C4—611no—
869C22×C4—611no—
870C22×C4—611no—
871C22×C4—611no—
872C22×C4—611no—
873C22×C4—611no—
874C22×C4—611no—
875C22×C4—611no—
876C22×C4—611no—
877C22×C4—611no—
878C22×C4—1224no—
879C22×C4—1224no—
880C22×C4—1224no—
881C22×C4—1224no—
882C22×C4—1222no—
883C22×C4—1222no—
884C22×C4—1222no—
885C22×C4—1221no—
886C22×C4—1221no—
887C22×C4—1221no—
888C22×C4—2448no—
889C22×C4D4×D6111yescharacteristic
890C22×C4D4×D6111yescharacteristic
891C22×C4C23×D6111yescharacteristic
892M16—24no—
893M16—1224no—
894C2×C8—614no—
895C2×C8C23×D6114yes—
896C4⋊C4—22no—
897C4⋊C4—22no—
898C4⋊C4—22no—
899C4⋊C4—21no—
900C4⋊C4—21no—
901C4⋊C4—614no—
902C4⋊C4—611no—
903C4⋊C4—611no—
904C4⋊C4—1224no—
905C4⋊C4—1224no—
906C4⋊C4—1224no—
907C4⋊C4—1224no—
908C4⋊C4—1221no—
909C4⋊C4—1221no—
910C4⋊C4—1221no—
911C4⋊C4—1221no—
912C4⋊C4—1221no—
913C4⋊C4—1221no—
914C4⋊C4—1221no—
915C4⋊C4—1221no—
916C4⋊C4—1221no—
917C4⋊C4—1221no—
918C4⋊C4—1221no—
919C4⋊C4—1221no—
920C4⋊C4—1222no—
921C4⋊C4—1222no—
922C4⋊C4—1222no—
923C4⋊C4—1221no—
924C4⋊C4—1221no—
925C4⋊C4C23×D6114yes—
926C4⋊C4C23×D6111yescharacteristic
927C4⋊C4C23×D6111yescharacteristic
928C22⋊C4—21no—
929C22⋊C4—21no—
930C22⋊C4—21no—
931C22⋊C4—1221no—
932C22⋊C4—1221no—
933C22⋊C4—1221no—
934C22⋊C4—1221no—
935C22⋊C4—1221no—
936C22⋊C4—1221no—
937C22⋊C4—1221no—
938C22⋊C4—1221no—
939C22⋊C4—1221no—
940C22⋊C4—1221no—
941C22⋊C4—1221no—
942C22⋊C4—1221no—
943C22⋊C4—1221no—
944C22⋊C4—1221no—
945C22⋊C4—1221no—
946C42—21no—
947C42—21no—
948C42—21no—
949C42—611no—
950C42—611no—
951C42—611no—
952C42—611no—
953C42—611no—
954C42—611no—
955C42—611no—
956C42—611no—
957C42—611no—
958C42—611no—
959C42—611no—
960C42—611no—
961C42—1221no—
962C42—1221no—
963C42—1221no—
964C42D4×D6111yescharacteristic
965C42D4×D6111yescharacteristic
966C42C23×D6111yescharacteristic
967C42C23×D6111yescharacteristic
968C23—21no—
969C23—611no—
970C23—611no—
971C23—1222no—
972C23—1222no—
973C23—1222no—
974C23—1221no—
975C23C2×D4×D6111yescharacteristic
976Q8—21no—
977Q8—21no—
978Q8—44no—
979Q8—44no—
980Q8—1221no—
981Q8—1221no—
982Q8—2444no—
983Q8—2448no—
984Q8—2442no—
985Q8—2442no—
986Q8—2448no—
987Q8—2444no—
988D4—21no—
989D4—21no—
990D4—42no—
991D4—1221no—
992D4—1221no—
993D4—2442no—
994D4—2442no—
995D4—2442no—
996D4—2442no—
997D4—2442no—
998D4—2442no—
999D4—2442no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—21no—
1003C2×C4—21no—
1004C2×C4—21no—
1005C2×C4—24no—
1006C2×C4—44no—
1007C2×C4—42no—
1008C2×C4—42no—
1009C2×C4—42no—
1010C2×C4—611no—
1011C2×C4—611no—
1012C2×C4—614no—
1013C2×C4—614no—
1014C2×C4—611no—
1015C2×C4—611no—
1016C2×C4—611no—
1017C2×C4—611no—
1018C2×C4—1222no—
1019C2×C4—1222no—
1020C2×C4—1222no—
1021C2×C4—1222no—
1022C2×C4—1222no—
1023C2×C4—1222no—
1024C2×C4—1222no—
1025C2×C4—1222no—
1026C2×C4—1222no—
1027C2×C4—1222no—
1028C2×C4—1222no—
1029C2×C4—1221no—
1030C2×C4—1221no—
1031C2×C4—1221no—
1032C2×C4—1221no—
1033C2×C4—1221no—
1034C2×C4—1221no—
1035C2×C4—1221no—
1036C2×C4—1224no—
1037C2×C4—2448no—
1038C2×C4—2448no—
1039C2×C4—2444no—
1040C2×C4—2442no—
1041C2×C4—2442no—
1042C2×C4—2442no—
1043C2×C4C2×D4×D6111yescharacteristic
1044C2×C4C2×D4×D6111yescharacteristic
1045C2×C4C2×D4×D6111yescharacteristic
1046C2×C4C2×D4×D6111yescharacteristic
1047C2×C4C2×D4×D6111yescharacteristic
1048C2×C4#1451982412yes—
1049C2×C4#1451982512yes—
1050C2×C4C24×D6111yescharacteristic
1051C8—24no—
1052C8—1224no—
1053C22—21no—
1054C22—21no—
1055C22—41no—
1056C22—41no—
1057C22—41no—
1058C22—612no—
1059C22—612no—
1060C22—1228no—
1061C22—1221no—
1062C22—1221no—
1063C22—1221no—
1064C22—1221no—
1065C22—2441no—
1066C22—2441no—
1067C22—2441no—
1068C22#1684033512yes—
1069C22C22×D4×D6111yescharacteristic
1070C4—21no—
1071C4—21no—
1072C4—44no—
1073C4—41no—
1074C4—41no—
1075C4—41no—
1076C4—612no—
1077C4—612no—
1078C4—1221no—
1079C4—1221no—
1080C4—1221no—
1081C4—1221no—
1082C4—2444no—
1083C4—2441no—
1084C4—2441no—
1085C4—2441no—
1086C4#1684033512yes—
1087C4AGL(1,ℤ/8)×D6112yes—
1088C4#137×D6112yes—
1089C4C2×#1451982411yescharacteristic
1090C4C2×#1451982511yescharacteristic
1091C2—22no—
1092C2—81no—
1093C2—1222no—
1094C2—1222no—
1095C2—4881no—
1096C2C2×#1684033511yescharacteristic
1097C2C2×AGL(1,ℤ/8)×D6111yescharacteristic
1098C2C2×#137×D6111yescharacteristic
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3079C2
socleC22×C61C23×D4
prime radical#21459112C2
hypercenter#3079D61
hypocenterC61#60860
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3079

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊Q8×D61C2semidirect
3. #21457053C2semidirect
4. #21457048C2semidirect
5. #21457044C2semidirect
6. #21457039C2semidirect
7. #21456969C2semidirect
8. #21456962C2semidirect
9. #21456946C2semidirect
10. #21456939C2semidirect
11. #21456363C2semidirect
12. #21456210C2semidirect
13. #21455745C2semidirect
14. #21455740C2semidirect
15. #21455635C2semidirect
16. #21455634C2semidirect
17. #21455628C2semidirect
18. #21454451C2semidirect
19. C61×#3079C2semidirect
57. #16840170C22semidirect
58. #16840169C22semidirect
59. #16840166C22semidirect
60. #16840159C22semidirect
61. #16840123C22semidirect
62. #16840120C22semidirect
63. #16840111C22semidirect
64. #16840107C22semidirect
73. #16840058C22semidirect
74. #16840057C22semidirect
75. #16840054C22semidirect
76. #16840053C22semidirect
77. #16840052C22semidirect
78. #16840049C22semidirect
79. #16840048C22semidirect
80. #16840047C22semidirect
81. #16840044C22semidirect
82. #16840043C22semidirect
83. #16840042C22semidirect
84. #16840039C22semidirect
100. C61×#477C22semidirect
101. C61×#476C22semidirect
102. C61×#475C22semidirect
103. C61×#474C22semidirect
559. #3079D61semidirect
627. #477C2×D61semidirect
631. #476C2×D61semidirect
635. #475C2×D61semidirect
639. #474C2×D61semidirect
656. C61#60860semidirect

Maximal subgroups

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

subgroupindex
#214591122
C2×C4⋊Q8×D612
#214570532
#214570482
#214570442
#214570392
#214569692
#214569622
#214569462
#214569392
#214563632
#214562102
#214557452
#214557402
#214556352
#214556342
#214556282
#214544512
C61×#30792
#6086061