Finite Group Databasebeta

← #30553043

Subgroups — #30553043

Order 15616.

1888 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×#16840317C211yesmaximal, characteristic, complemented
3#21457212C212yesmaximal, complemented
4#21457208C212yesmaximal, complemented
5#21457195C212yesmaximal, complemented
6#21457194C212yesmaximal, complemented
7#21457163C212yesmaximal, complemented
8#21457159C212yesmaximal, complemented
9#21457158C212yesmaximal, complemented
10#21457137C212yesmaximal, complemented
11#21455628C211yesmaximal, characteristic, complemented
12#21455623C212yesmaximal, complemented
13#21455452C212yesmaximal, complemented
14#21455450C212yesmaximal, complemented
15#21455307C211yesmaximal, characteristic, complemented
16#21455306C211yesmaximal, characteristic, complemented
17#21455290C212yesmaximal, complemented
18#423×D61C211yesmaximal, characteristic, complemented
19C61×#3079C211yesmaximal, characteristic, complemented
20C2×#14519810C2212yes—
21C2×#14519807C2212yes—
22C2×M16×D61C2212yes—
23#16840317—21no—
24#16840317—21no—
25#16840317—21no—
26#16840317—21no—
27#16840317C2212yes—
28#16840317C2212yes—
29#16840317C2212yes—
30#16840317C2212yes—
31#16840316C2211yescharacteristic
32#16840316C2211yescharacteristic
33#16840315C2211yescharacteristic
34#16840309C2211yescharacteristic
35#16840309C2211yescharacteristic
36#16840308C2211yescharacteristic
37C2×#14519777C2211yescharacteristic
38#16840299C2211yescharacteristic
39#16840299C2211yescharacteristic
40#16840294C2211yescharacteristic
41#16840294C2211yescharacteristic
42#16840292—21no—
43#16840292—21no—
44#16840290—21no—
45#16840290—21no—
46C2×#14519768—21no—
47#16840274C2211yescharacteristic
48#16840271—21no—
49#16840271—21no—
50#16840269C2211yescharacteristic
51C2×#14519757C2212yes—
52C2×#14519753—21no—
53C4×#11758222—21no—
54C4×#11758222—21no—
55C4×#11758222C2211yescharacteristic
56C2×Q8×Dic61—21no—
57C2×#14519742C2212yes—
58C2×#14519735—21no—
59C2×C42×D61C2211yescharacteristic
60#16840072C2214yescomplemented
61#16840068C2214yescomplemented
62#16840056C2214yescomplemented
63#16840054C2212yescomplemented
64#16840049C2212yescomplemented
65#16840046C2214yescomplemented
66#16840044C2212yescomplemented
67#16840039C2212yescomplemented
68#16840021C2214yes—
69#16840019C2214yes—
70#16840009C2214yes—
71#16840007C2214yes—
72#16840004C2214yes—
73#16840002C2214yes—
74#16839992C2214yes—
75#16839990C2214yes—
76#16839987C2214yescomplemented
77#16839983C2214yescomplemented
78#16839973C2212yescomplemented
79#16839973C2212yescomplemented
80#16839972C2212yescomplemented
81#16839972C2212yescomplemented
82#16839971C2214yescomplemented
83#16839968C2212yescomplemented
84#16839968C2212yescomplemented
85#16839967C2212yescomplemented
86#16839967C2212yescomplemented
87#16839961C2214yescomplemented
88#16839802C2212yes—
89#16839786C2211yescharacteristic
90#16839785C2212yes—
91#16839784C2212yes—
92#16839784C2212yes—
93C4⋊C8×D61C2212yes—
94C4⋊C8×D61C2212yes—
95#16839772C2212yes—
96#16839770C2212yes—
97#16839761C2212yes—
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×Dic122C2312yes—
111C22×C4×D61D411yescharacteristic
112C22×C4×D61D411yescharacteristic
113C22×C4×D61C2311yescharacteristic
114#14519810—44no—
115#14519807—44no—
116C2×Dic244C2314yes—
117C2×#11758202C2314yes—
118C2×#11758190C2314yes—
119C2×#11758200C2314yes—
120C2×#11758194C2312yes—
121C2×#11758189C2314yes—
122M16×D61—44no—
123C2×C8×D61C2314yes—
124#14519777—21no—
125#14519777—21no—
126#14519777C2312yes—
127#14519777C2312yes—
128#14519776C2311yescharacteristic
129#14519776C2311yescharacteristic
130#14519775C2311yescharacteristic
131#14519773C2311yescharacteristic
132#14519772—21no—
133#14519772—21no—
134#14519770—21no—
135#14519770—21no—
136#14519768—22no—
137#14519768—22no—
138#14519768—22no—
139#14519768—22no—
140#14519768C2311yescharacteristic
141#14519768C2311yescharacteristic
142#14519767—21no—
143#14519767—21no—
144#14519766C2311yescharacteristic
145#14519764C2311yescharacteristic
146#14519763—21no—
147#14519763—21no—
148#14519762—21no—
149#14519762—21no—
150#14519761—21no—
151#14519759—21no—
152#14519759—21no—
153#14519758—21no—
154#14519757—22no—
155#14519757—22no—
156#14519757C2314yes—
157#14519757C2311yescharacteristic
158#14519757C2314yes—
159#14519757C2311yescharacteristic
160#14519755—21no—
161#14519755—21no—
162#14519754—21no—
163#14519754—21no—
164#14519753—22no—
165#14519753—22no—
166#14519753—22no—
167#14519753—22no—
168#14519753C2311yescharacteristic
169#14519753C2311yescharacteristic
170#14519752C2311yescharacteristic
171#14519752C2311yescharacteristic
172#14519750—21no—
173#14519750—21no—
174#14519749—21no—
175#14519749—21no—
176#14519748C2311yescharacteristic
177#14519748C2311yescharacteristic
178#14519747—21no—
179#14519745—21no—
180Q8×Dic61—22no—
181Q8×Dic61—22no—
182Q8×Dic61—22no—
183Q8×Dic61—22no—
184C4×Dic122—21no—
185C4×Dic122—21no—
186C4×Dic122—21no—
187C4×Dic122—21no—
188C4×Dic122C2311yescharacteristic
189C4×Dic122C2311yescharacteristic
190#14519742—22no—
191#14519742—22no—
192#14519742C2314yes—
193#14519742C2314yes—
194C4×D244—21no—
195C4×D244—21no—
196C4×D244—21no—
197C4×D244—21no—
198C4×D244C2311yescharacteristic
199C4×D244C2311yescharacteristic
200C4×C22⋊D61—21no—
201C4×C22⋊D61—21no—
202C4×C22⋊D61—21no—
203C4×C22⋊D61—21no—
204C4×C22⋊D61—21no—
205C4×C22⋊D61—21no—
206C4×C22⋊D61—21no—
207C4×C22⋊D61—21no—
208C4×C22⋊D61—21no—
209C4×C22⋊D61—21no—
210#14519736—21no—
211#14519736—21no—
212#14519736C2311yescharacteristic
213#14519735—22no—
214#14519735—22no—
215#14519735—22no—
216#14519735—22no—
217#14519734—21no—
218#14519734—21no—
219#14519734—21no—
220#14519734—21no—
221#14519734—21no—
222C2×C4⋊Dic61—21no—
223C2×C4⋊Dic61—21no—
224C2×C4⋊Dic61—22no—
225C2×#11758196—22no—
226C2×#11758198—22no—
227C2×C4×Dic61—22no—
228C2×C4×Dic61D411yescharacteristic
229C2×C4×Dic61D411yescharacteristic
230C2×C4×Dic61C2311yescharacteristic
231C42×D61—21no—
232C42×D61D411yescharacteristic
233C42×D61D411yescharacteristic
234C42×D61D411yescharacteristic
235C42×D61D411yescharacteristic
236C42×D61C2311yescharacteristic
237C42×D61C2311yescharacteristic
238C42×D61C2311yescharacteristic
239C42×D61C2311yescharacteristic
240#14519710C2314yes—
241#14519708C2314yes—
242C4⋊#92418C2312yes—
243C4⋊#92418C2312yes—
244#14519706C2314yes—
245#14519706C2314yes—
246#14519702C2314yes—
247#14519702C2314yes—
248#14519700C2314yes—
249#14519700C2314yes—
250#14519700C2314yes—
251#14519697C2314yes—
252C2×#41×C61C2311yescharacteristic
253C22×Q8×C61—21no—
254C2×M16×C61C2312yes—
255C4⋊Q8×C61—21no—
256C4⋊Q8×C61—21no—
257C4⋊Q8×C61C2312yes—
258C4⋊Q8×C61C2312yes—
259C4×Q8×C61C2311yescharacteristic
260C4×Q8×C61C2311yescharacteristic
261C4×D4×C61—21no—
262C4×D4×C61—21no—
263C4×D4×C61C2311yescharacteristic
264C4×D4×C61C2311yescharacteristic
265#117×C61—21no—
266#117×C61C2311yescharacteristic
267C2×C4⋊C4×C61—21no—
268C2×C4⋊C4×C61C2312yes—
269C2×C42×C61—21no—
270C2×C42×C61C2311yescharacteristic
271#107×C61C2314yes—
272#106×C61C2314yes—
273C4⋊C8×C61C2312yes—
274C4⋊C8×C61C2312yes—
275#103×C61C2314yes—
276#102×C61C2314yes—
277C23×D61C2×D411yescharacteristic
278#41×C61—22no—
279#41×C61—22no—
280C2×Q8×C61—22no—
281C2×Q8×C61—22no—
282C2×Q8×C61—44no—
283C2×Q8×C61C2411yescharacteristic
284C2×D4×C61—21no—
285C2×D4×C61C2411yescharacteristic
286C22×C4×C61—22no—
287C22×C4×C61—21no—
288C22×C4×C61—21no—
289C22×C4×C61—21no—
290C22×C4×C61C2×D411yescharacteristic
291C22×C4×C61C2×D411yescharacteristic
292C22×C4×C61C2411yescharacteristic
293C2×C22⋊D61—21no—
294C2×C22⋊D61—21no—
295C2×C22⋊D61—21no—
296C2×C22⋊D61—21no—
297C2×C22⋊D61—21no—
298C22×Dic61—22no—
299C22×Dic61C2×D411yescharacteristic
300C22×Dic61C2×D411yescharacteristic
301C22×Dic61C2×D411yescharacteristic
302#11758222—22no—
303#11758222—22no—
304#11758222—44no—
305#11758222—44no—
306C2×D244—21no—
307C2×D244—21no—
308C2×D244C2411yescharacteristic
309C2×C4×D61—22no—
310C2×C4×D61—22no—
311C2×C4×D61—24no—
312C2×C4×D61—21no—
313C2×C4×D61—21no—
314C2×C4×D61—21no—
315C2×C4×D61—42no—
316C2×C4×D61C2×D411yescharacteristic
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×D61C2411yescharacteristic
327C2×C4×D61C2411yescharacteristic
328C2×Dic122—24no—
329C2×Dic122—24no—
330C2×Dic122—22no—
331C2×Dic122—21no—
332C2×Dic122—21no—
333C2×Dic122C2414yes—
334C2×Dic122C2411yescharacteristic
335M16×C61—24no—
336C2×C8×C61C2414yes—
337C4⋊C4×C61—22no—
338C4⋊C4×C61—22no—
339C4⋊C4×C61—22no—
340C4⋊C4×C61—21no—
341C4⋊C4×C61—21no—
342C4⋊C4×C61C2414yes—
343C4⋊C4×C61C2411yescharacteristic
344C4⋊C4×C61C2411yescharacteristic
345C22⋊C4×C61—21no—
346C22⋊C4×C61—21no—
347C22⋊C4×C61—21no—
348C42×C61—21no—
349C42×C61—21no—
350C42×C61—21no—
351C42×C61C2×D411yescharacteristic
352C42×C61C2×D411yescharacteristic
353C42×C61C2411yescharacteristic
354C42×C61C2411yescharacteristic
355C22⋊Dic61—21no—
356C22⋊Dic61—21no—
357C22⋊Dic61—21no—
358C22⋊Dic61—21no—
359C22⋊Dic61—21no—
360#11758202—44no—
361#11758200—44no—
362#11758198—24no—
363#11758198—24no—
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—
373#11758198—21no—
374C4⋊Dic61—22no—
375C4⋊Dic61—22no—
376C4⋊Dic61—22no—
377C4⋊Dic61—22no—
378C4⋊Dic61—24no—
379C4⋊Dic61—24no—
380C4⋊Dic61—21no—
381C4⋊Dic61—21no—
382C4⋊Dic61—21no—
383C4⋊Dic61—21no—
384C4⋊Dic61C2411yescharacteristic
385C4⋊Dic61C2411yescharacteristic
386#11758196—21no—
387#11758196—21no—
388#11758196—24no—
389#11758196—24no—
390#11758196—21no—
391#11758196—21no—
392#11758196—21no—
393#11758196—21no—
394#11758196—21no—
395#11758196—21no—
396#11758196—21no—
397#11758196—21no—
398C4×Dic61—21no—
399C4×Dic61—21no—
400C4×Dic61—21no—
401C4×Dic61—24no—
402C4×Dic61—24no—
403C4×Dic61C2×D411yescharacteristic
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×Dic61C2411yescharacteristic
414C4×Dic61C2411yescharacteristic
415#11758194—24no—
416C2×#92418C2414yes—
417Dic244—44no—
418#11758190—44no—
419#11758189—44no—
420C8×D61—44no—
421C23×C61—21no—
422C23×C61C22×D411yescharacteristic
423C22×D61—22no—
424C22×D61—22no—
425C22×D61—21no—
426C22×D61—41no—
427C22×D61C22×D411yescharacteristic
428C22×D61C22×D411yescharacteristic
429Q8×C61—21no—
430Q8×C61—21no—
431Q8×C61—44no—
432Q8×C61—44no—
433D4×C61—21no—
434D4×C61—21no—
435D4×C61—42no—
436C2×C4×C61—22no—
437C2×C4×C61—22no—
438C2×C4×C61—24no—
439C2×C4×C61—21no—
440C2×C4×C61—21no—
441C2×C4×C61—21no—
442C2×C4×C61—44no—
443C2×C4×C61—42no—
444C2×C4×C61—42no—
445C2×C4×C61—42no—
446C2×C4×C61C22×D411yescharacteristic
447C2×C4×C61C22×D411yescharacteristic
448C2×C4×C61C22×D411yescharacteristic
449C2×C4×C61C22×D411yescharacteristic
450C2×C4×C61C22×D411yescharacteristic
451C2×C4×C61H(5,𝔽2)12yes—
452C2×C4×C612−1+412yes—
453C2×C4×C61C2511yescharacteristic
454C22⋊D61—42no—
455C22⋊D61—42no—
456C22⋊D61—42no—
457C22⋊D61—42no—
458C22⋊D61—42no—
459C2×Dic61—22no—
460C2×Dic61—22no—
461C2×Dic61—21no—
462C2×Dic61—21no—
463C2×Dic61—21no—
464C2×Dic61—24no—
465C2×Dic61—41no—
466C2×Dic61—44no—
467C2×Dic61C22×D411yescharacteristic
468C2×Dic61C22×D411yescharacteristic
469C2×Dic61C22×D411yescharacteristic
470C2×Dic61C22×D411yescharacteristic
471C2×Dic61C22×D411yescharacteristic
472C2×Dic61C22×D411yescharacteristic
473D244—21no—
474D244—21no—
475D244—42no—
476D244—42no—
477C4×D61—22no—
478C4×D61—22no—
479C4×D61—22no—
480C4×D61—22no—
481C4×D61—22no—
482C4×D61—22no—
483C4×D61—21no—
484C4×D61—21no—
485C4×D61—21no—
486C4×D61—21no—
487C4×D61—22no—
488C4×D61—41no—
489C4×D61—41no—
490C4×D61—42no—
491C4×D61—42no—
492C4×D61—42no—
493C4×D61#13714yescomplemented
494Dic122—24no—
495Dic122—21no—
496Dic122—24no—
497Dic122—21no—
498Dic122—42no—
499Dic122—44no—
500Dic122—42no—
501C8×C61—24no—
502#92418—24no—
503#60918—611nomaximal, Sylow
504C22×C61—21no—
505C22×C61—21no—
506C22×C61—41no—
507C22×C61—41no—
508C22×C61—41no—
509C22×C61#53712yes—
510C22×C61C23×D411yescharacteristic
511C2×D61—21no—
512C2×D61—21no—
513C2×D61—21no—
514C2×D61—21no—
515C2×D61—21no—
516C2×D61—44no—
517C2×D61—41no—
518C2×D61—41no—
519C2×D61—41no—
520C2×D61C2×#13712yes—
521C4×C61—21no—
522C4×C61—21no—
523C4×C61—41no—
524C4×C61—41no—
525C4×C61—41no—
526C4×C61—44no—
527C4×C61#53712yes—
528C4×C61C2×#13712yes—
529C4×C61#57512yes—
530C4×C61C2×H(5,𝔽2)11yescharacteristic
531C4×C61C2×2−1+411yescharacteristic
532Dic61—21no—
533Dic61—21no—
534Dic61—21no—
535Dic61—21no—
536Dic61—21no—
537Dic61—44no—
538Dic61—41no—
539Dic61—41no—
540Dic61—41no—
541Dic61C2×#13712yes—
542#3444—611no—
543C2×#533—611no—
544#3255—612no—
545#3254—612no—
546#3252—612no—
547#3252—612no—
548#3249—612no—
549#3248—612no—
550#3248—612no—
551#3246—612no—
552#3079—611no—
553#3079D6111yescharacteristic, complemented
554#3078—612no—
555#3056—612no—
556#3056—612no—
557#3039—611no—
558#3039—611no—
559#3037—612no—
560C2×#423—611no—
561C2×C61—22no—
562C2×C61—81no—
563C2×C61C2×#53711yescharacteristic
564C2×C61C22×#13711yescharacteristic
565C2×C61C2×#57511yescharacteristic
566D61—22no—
567D61—41no—
568D61—81no—
569C2×#137—612no—
570C2×#137—612no—
571C22×M16—612no—
572#533—611no—
573#533—612no—
574#533—612no—
575#533—612no—
576#533—612no—
577#533—611no—
578#533—611no—
579#533—1221no—
580#533—1221no—
581#533—1221no—
582#533—1221no—
583#532—611no—
584#532—611no—
585#532—611no—
586C2×C4⋊Q8—611no—
587C2×C4⋊Q8C2×D6111yescharacteristic
588#529—611no—
589#529—611no—
590#529—611no—
591#529—611no—
592#529—1221no—
593#529—1221no—
594#529—1221no—
595#529—1221no—
596C2×#125—1221no—
597#525—611no—
598#525—611no—
599#525—1221no—
600#525—1221no—
601C2×C22⋊Q8—612no—
602C2×C22⋊Q8—1221no—
603C4×#41—611no—
604C4×#41—1221no—
605C4×#41—1221no—
606C4×#41C2×D6111yescharacteristic
607C2×C4×Q8—612no—
608C2×C4×Q8—1221no—
609C2×#117—1221no—
610C22×C42—611no—
611#479—614no—
612#479—614no—
613#477—612no—
614#477—614no—
615#477C2×D6112yescomplemented
616#476—612no—
617#476C2×D6112yescomplemented
618#475—612no—
619#475—614no—
620#475C2×D6112yescomplemented
621#474—612no—
622#474C2×D6112yescomplemented
623#470—614no—
624#470—614no—
625#468—614no—
626#468—614no—
627#467—614no—
628#467—614no—
629#465—614no—
630#465—614no—
631#464—614no—
632#464—614no—
633#462—612no—
634#462—612no—
635#462—612no—
636#462—612no—
637#462—614no—
638#461—612no—
639#461—612no—
640#461—612no—
641#461—612no—
642#460—614no—
643#428—612no—
644#428C2×D6112yes—
645#423—612no—
646#423—611no—
647#423—612no—
648#423—612no—
649#423C2×D6111yescharacteristic
650C2×C4⋊C8—612no—
651C2×C4⋊C8—612no—
652#419—612no—
653#419—612no—
654#417—612no—
655#417C2×D6112yes—
656C61#6091811yescharacteristic, complemented, Sylow
657C2×#41—611no—
658C2×#41—1221no—
659C2×#41—1221no—
660C2×#41C22×D6111yescharacteristic
661C22×Q8—21no—
662C22×Q8—612no—
663C23×C4—611no—
664C23×C4—611no—
665C23×C4—611no—
666#137—2444no—
667#137—2444no—
668C2×Q16—614no—
669C2×Q16—614no—
670C2×SD16—614no—
671C2×SD16—614no—
672C2×M16—612no—
673C2×M16—614no—
674C2×M16—2444no—
675C2×M16C22×D6112yes—
676C22×C8—614no—
677C4⋊Q8—21no—
678C4⋊Q8—21no—
679C4⋊Q8—611no—
680C4⋊Q8—611no—
681C4⋊Q8—611no—
682C4⋊Q8—612no—
683C4⋊Q8—612no—
684C4⋊Q8—1221no—
685C4⋊Q8—1221no—
686C4⋊Q8C22×D6112yes—
687C4⋊Q8C22×D6112yes—
688#127—611no—
689#126—1221no—
690#126—1221no—
691#126—1221no—
692#126—1221no—
693#125—611no—
694#125—611no—
695#125—1222no—
696#125—1222no—
697#125—1222no—
698#125—1222no—
699#125—1221no—
700#125—1221no—
701#124—611no—
702#124—611no—
703#124—1221no—
704#124—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—614no—
714C22⋊Q8—614no—
715C22⋊Q8—611no—
716C22⋊Q8—611no—
717C22⋊Q8—1221no—
718C22⋊Q8—1221no—
719C22⋊Q8—1222no—
720C22⋊Q8—1222no—
721C22⋊Q8—1221no—
722C22⋊Q8—1221no—
723C22⋊Q8—1222no—
724C22⋊Q8—1222no—
725C22⋊Q8—1222no—
726C22⋊Q8—1222no—
727#121—611no—
728#121—611no—
729#121—611no—
730#121—611no—
731#121—1221no—
732#121—1221no—
733#121—1221no—
734#121—1221no—
735#120—1221no—
736#120—1221no—
737C4×Q8—614no—
738C4×Q8—614no—
739C4×Q8—611no—
740C4×Q8—611no—
741C4×Q8—1221no—
742C4×Q8—1221no—
743C4×Q8—1221no—
744C4×Q8—1221no—
745C4×Q8—1222no—
746C4×Q8—1222no—
747C4×Q8—1222no—
748C4×Q8—1222no—
749C4×Q8—1222no—
750C4×Q8—1222no—
751C4×Q8C22×D6111yescharacteristic
752C4×Q8C22×D6111yescharacteristic
753C4×D4—21no—
754C4×D4—21no—
755C4×D4—611no—
756C4×D4—611no—
757C4×D4—1221no—
758C4×D4—1221no—
759C4×D4—1221no—
760C4×D4—1221no—
761C4×D4—1221no—
762C4×D4—1221no—
763C4×D4—1221no—
764C4×D4—1221no—
765C4×D4—1221no—
766C4×D4—1221no—
767C4×D4—1221no—
768C4×D4—1221no—
769C4×D4—1221no—
770C4×D4—1221no—
771C4×D4C22×D6111yescharacteristic
772C4×D4C22×D6111yescharacteristic
773#117—21no—
774#117—611no—
775#117—1221no—
776#117—1221no—
777#117—1221no—
778#117—1221no—
779#117—1221no—
780#117—1221no—
781#117—1222no—
782#117—1222no—
783#117—1222no—
784#117—1222no—
785#117—1221no—
786#117C22×D6111yescharacteristic
787C2×C4⋊C4—21no—
788C2×C4⋊C4—1222no—
789C2×C4⋊C4—1222no—
790C2×C4⋊C4—1221no—
791C2×C4⋊C4—1221no—
792C2×C4⋊C4C22×D6112yes—
793C2×C22⋊C4—1222no—
794C2×C42—21no—
795C2×C42—611no—
796C2×C42—611no—
797C2×C42—611no—
798C2×C42—611no—
799C2×C42—611no—
800C2×C42—611no—
801C2×C42—611no—
802C2×C42—611no—
803C2×C42—611no—
804C2×C42—611no—
805C2×C42—611no—
806C2×C42—1222no—
807C2×C42—1221no—
808C2×C42C22×D6111yescharacteristic
809#107—614no—
810#107C22×D6114yes—
811#106—614no—
812#106C22×D6114yes—
813C4⋊C8—614no—
814C4⋊C8—614no—
815C4⋊C8—612no—
816C4⋊C8—612no—
817C4⋊C8C22×D6112yes—
818C4⋊C8C22×D6112yes—
819#103—614no—
820#103—614no—
821#103—614no—
822#103—614no—
823#103—614no—
824#103C22×D6114yes—
825#102—614no—
826#102C22×D6114yes—
827C24—611no—
828#41—22no—
829#41—22no—
830#41—1222no—
831#41—1222no—
832#41—2444no—
833#41—2444no—
834C2×Q8—22no—
835C2×Q8—22no—
836C2×Q8—44no—
837C2×Q8—611no—
838C2×Q8—614no—
839C2×Q8—1221no—
840C2×Q8—1221no—
841C2×Q8—1222no—
842C2×Q8—1224no—
843C2×Q8—1224no—
844C2×Q8C23×D6111yescharacteristic
845C2×D4—21no—
846C2×D4—611no—
847C2×D4—1221no—
848C2×D4—1221no—
849C2×D4—1221no—
850C2×D4—1221no—
851C2×D4—1221no—
852C2×D4—1221no—
853C2×D4—1221no—
854C2×D4C23×D6111yescharacteristic
855C22×C4—22no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—611no—
860C22×C4—611no—
861C22×C4—611no—
862C22×C4—611no—
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—1224no—
875C22×C4—1222no—
876C22×C4—1222no—
877C22×C4—1222no—
878C22×C4—1221no—
879C22×C4—1221no—
880C22×C4—1221no—
881C22×C4—2442no—
882C22×C4D4×D6111yescharacteristic
883C22×C4D4×D6111yescharacteristic
884C22×C4C23×D6111yescharacteristic
885Q16—2444no—
886Q16—2444no—
887SD16—2444no—
888SD16—2444no—
889M16—24no—
890M16—1224no—
891M16—2444no—
892C2×C8—614no—
893C2×C8—2444no—
894C2×C8C23×D6114yes—
895C4⋊C4—22no—
896C4⋊C4—22no—
897C4⋊C4—22no—
898C4⋊C4—21no—
899C4⋊C4—21no—
900C4⋊C4—611no—
901C4⋊C4—611no—
902C4⋊C4—1224no—
903C4⋊C4—1224no—
904C4⋊C4—1224no—
905C4⋊C4—1224no—
906C4⋊C4—1221no—
907C4⋊C4—1221no—
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—1222no—
919C4⋊C4—1222no—
920C4⋊C4—1222no—
921C4⋊C4—1222no—
922C4⋊C4—1221no—
923C4⋊C4—1221no—
924C4⋊C4C23×D6114yes—
925C4⋊C4C23×D6111yescharacteristic
926C4⋊C4C23×D6111yescharacteristic
927C22⋊C4—21no—
928C22⋊C4—21no—
929C22⋊C4—21no—
930C22⋊C4—1221no—
931C22⋊C4—1221no—
932C22⋊C4—1221no—
933C22⋊C4—1221no—
934C22⋊C4—1224no—
935C22⋊C4—1224no—
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—
946C22⋊C4—1221no—
947C42—21no—
948C42—21no—
949C42—21no—
950C42—611no—
951C42—611no—
952C42—611no—
953C42—611no—
954C42—611no—
955C42—611no—
956C42—611no—
957C42—611no—
958C42—611no—
959C42—611no—
960C42—611no—
961C42—611no—
962C42—1224no—
963C42—1224no—
964C42—1221no—
965C42—1221no—
966C42—1221no—
967C42D4×D6111yescharacteristic
968C42D4×D6111yescharacteristic
969C42C23×D6111yescharacteristic
970C42C23×D6111yescharacteristic
971C23—21no—
972C23—611no—
973C23—611no—
974C23—1222no—
975C23—1222no—
976C23—1221no—
977C23—2441no—
978C23C2×D4×D6111yescharacteristic
979Q8—21no—
980Q8—21no—
981Q8—44no—
982Q8—44no—
983Q8—1224no—
984Q8—1221no—
985Q8—1224no—
986Q8—1221no—
987Q8—2442no—
988Q8—2442no—
989Q8—2444no—
990D4—21no—
991D4—21no—
992D4—42no—
993D4—1221no—
994D4—1221no—
995D4—2442no—
996D4—2442no—
997D4—2442no—
998D4—2442no—
999D4—2442no—
1000D4—2442no—
1001D4—2442no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—21no—
1005C2×C4—21no—
1006C2×C4—21no—
1007C2×C4—24no—
1008C2×C4—44no—
1009C2×C4—42no—
1010C2×C4—42no—
1011C2×C4—42no—
1012C2×C4—611no—
1013C2×C4—614no—
1014C2×C4—611no—
1015C2×C4—611no—
1016C2×C4—611no—
1017C2×C4—611no—
1018C2×C4—611no—
1019C2×C4—1222no—
1020C2×C4—1222no—
1021C2×C4—1222no—
1022C2×C4—1222no—
1023C2×C4—1222no—
1024C2×C4—1222no—
1025C2×C4—1222no—
1026C2×C4—1221no—
1027C2×C4—1221no—
1028C2×C4—1221no—
1029C2×C4—1221no—
1030C2×C4—1222no—
1031C2×C4—1222no—
1032C2×C4—1221no—
1033C2×C4—1221no—
1034C2×C4—1221no—
1035C2×C4—1224no—
1036C2×C4—2441no—
1037C2×C4—2441no—
1038C2×C4—2441no—
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#1451982312yes—
1049C2×C4#1451982512yes—
1050C2×C4C24×D6111yescharacteristic
1051C8—24no—
1052C8—1224no—
1053C22—21no—
1054C22—21no—
1055C22—41no—
1056C22—41no—
1057C22—41no—
1058C22—612no—
1059C22—1221no—
1060C22—1221no—
1061C22—1221no—
1062C22—1221no—
1063C22—1221no—
1064C22—2444no—
1065C22—2441no—
1066C22—2441no—
1067C22—2441no—
1068C22#1684034212yes—
1069C22C22×D4×D6111yescharacteristic
1070C4—21no—
1071C4—21no—
1072C4—41no—
1073C4—41no—
1074C4—44no—
1075C4—41no—
1076C4—612no—
1077C4—1221no—
1078C4—1221no—
1079C4—1221no—
1080C4—1221no—
1081C4—1221no—
1082C4—2441no—
1083C4—2441no—
1084C4—2441no—
1085C4—2444no—
1086C4#1684034212yes—
1087C4#137×D6112yes—
1088C4#1684055812yes—
1089C4C2×#1451982311yescharacteristic
1090C4C2×#1451982511yescharacteristic
1091C2—22no—
1092C2—81no—
1093C2—1222no—
1094C2—4881no—
1095C2—2441no—
1096C2C2×#1684034211yescharacteristic
1097C2C2×#137×D6111yescharacteristic
1098C2C2×#1684055811yescharacteristic
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3079C2
socleC22×C61C23×D4
prime radical#21459112C2
hypercenter#3079D61
hypocenterC61#60918
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×#16840317C2semidirect
3. #21457212C2semidirect
4. #21457208C2semidirect
5. #21457195C2semidirect
6. #21457194C2semidirect
7. #21457163C2semidirect
8. #21457159C2semidirect
9. #21457158C2semidirect
10. #21457137C2semidirect
11. #21455628C2semidirect
12. #21455623C2semidirect
13. #21455452C2semidirect
14. #21455450C2semidirect
15. #21455307C2semidirect
16. #21455306C2semidirect
17. #21455290C2semidirect
18. #423×D61C2semidirect
19. C61×#3079C2semidirect
60. #16840072C22semidirect
61. #16840068C22semidirect
62. #16840056C22semidirect
63. #16840054C22semidirect
64. #16840049C22semidirect
65. #16840046C22semidirect
66. #16840044C22semidirect
67. #16840039C22semidirect
76. #16839987C22semidirect
77. #16839983C22semidirect
78. #16839973C22semidirect
79. #16839973C22semidirect
80. #16839972C22semidirect
81. #16839972C22semidirect
82. #16839971C22semidirect
83. #16839968C22semidirect
84. #16839968C22semidirect
85. #16839967C22semidirect
86. #16839967C22semidirect
87. #16839961C22semidirect
100. C61×#477C22semidirect
101. C61×#476C22semidirect
102. C61×#475C22semidirect
103. C61×#474C22semidirect
493. C4×D61#137semidirect
553. #3079D61semidirect
615. #477C2×D61semidirect
617. #476C2×D61semidirect
620. #475C2×D61semidirect
622. #474C2×D61semidirect
656. C61#60918semidirect

Maximal subgroups

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

subgroupindex
#214591122
C2×#168403172
#214572122
#214572082
#214571952
#214571942
#214571632
#214571592
#214571582
#214571372
#214556282
#214556232
#214554522
#214554502
#214553072
#214553062
#214552902
#423×D612
C61×#30792
#6091861