Finite Group Databasebeta

← #29681998

Subgroups — #29681998

Order 15616.

1708 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840528C211yesmaximal, characteristic, complemented
2#21459152C211yesmaximal, characteristic
3#21454339C211yesmaximal, characteristic, complemented
4#21454336C211yesmaximal, characteristic, complemented
5C2×#16839735C211yesmaximal, characteristic, complemented
6#21446345C214yesmaximal, complemented
7#21446340C214yesmaximal, complemented
8C2×#16839518C211yesmaximal, characteristic, complemented
9C2×C61×H(3,ℤ/4)C211yesmaximal, characteristic, complemented
10C22×#11758222C2211yescharacteristic
11C22×#11758222C2211yescharacteristic
12#16840528—22no—
13#16840528—22no—
14#16840528—22no—
15#16840528C2214yes—
16C2×#14519785—22no—
17C2×#14519783—22no—
18C22×#11758194C2211yescharacteristic
19C2×M16×D61—22no—
20#16840343—22no—
21#16840338C412yescomplemented
22#16840338C2212yes—
23#16840331C412yescomplemented
24#16840331C2212yes—
25#16840324—22no—
26#16840312C414yescomplemented
27#16840274—22no—
28#16840274—22no—
29C2×#14519736C2211yescharacteristic
30#16839772C2212yescomplemented
31#16839770C2212yescomplemented
32#16839768C2212yescomplemented
33#16839766C2212yescomplemented
34#16839764—22no—
35#16839761—22no—
36#16839759—22no—
37#16839756—22no—
38#16839735—22no—
39#16839735C2214yes—
40C2×#14519691—22no—
41#16839518C2214yescomplemented
42C22×M16×C61C2211yescharacteristic
43C2×#117×C61C2211yescharacteristic
44C2×#117×C61C2211yescharacteristic
45C61×H(3,ℤ/4)C2214yescomplemented
46C2×#11758222—21no—
47C2×#11758222—21no—
48C2×#11758222—21no—
49C2×#11758222—21no—
50C2×#11758222—21no—
51C2×#11758222—21no—
52C2×#11758222—21no—
53C2×#11758222—21no—
54C2×#11758222—21no—
55C2×#11758222—21no—
56C2×#11758222—21no—
57C2×#11758222—21no—
58C2×#11758222—21no—
59C2×#11758222—21no—
60C2×#11758222—21no—
61C2×#11758222—21no—
62C2×#11758222—21no—
63C2×#11758222—21no—
64C2×#11758222C2×C412yes—
65C2×#11758222C2×C412yes—
66C2×#11758222C2×C412yes—
67C2×#11758222D412yes—
68C2×#11758222D412yes—
69C2×#11758222C2312yes—
70C22×Dic122C2×C411yescharacteristic
71C22×Dic122C2311yescharacteristic
72C22×D244C2×C411yescharacteristic
73C22×D244C2311yescharacteristic
74C22×C22⋊D61—21no—
75C22×C22⋊D61D412yes—
76C22×C4×D61—21no—
77C22×C4×D61D412yes—
78#14519785—28no—
79#14519785—28no—
80#14519783—28no—
81#14519783—28no—
82C2×#11758194—21no—
83C2×#11758194—21no—
84C2×#11758194—21no—
85C2×#11758194—21no—
86C2×#11758194D412yescomplemented
87C2×#11758194C2312yes—
88C2×#11758189—24no—
89M16×D61—28no—
90M16×D61—28no—
91C22×#92418D412yescomplemented
92C2×C8×D61—24no—
93#14519777C2×C414yescomplemented
94#14519774C2×C414yescomplemented
95#14519765C2×C414yescomplemented
96#14519765C2×C414yescomplemented
97#14519761—24no—
98#14519761—24no—
99#14519757—24no—
100#14519757—24no—
101#14519752—24no—
102#14519752—24no—
103#14519751—28no—
104#14519747—24no—
105#14519747—24no—
106C4×D244—28no—
107#14519736—21no—
108#14519736—21no—
109#14519736—21no—
110#14519736C2312yes—
111C2×C4⋊Dic61—21no—
112C2×C22⋊Dic61—21no—
113C2×C4×Dic61—21no—
114#14519702—24no—
115#14519700—24no—
116#14519699—24no—
117#14519697—24no—
118#14519691—28no—
119C23×C4×C61C2311yescharacteristic
120C2×M16×C61—21no—
121C2×M16×C61—21no—
122C2×M16×C61—21no—
123C2×M16×C61—21no—
124C2×M16×C61D412yescomplemented
125C2×M16×C61C2312yes—
126C22×C8×C61D412yescomplemented
127#117×C61—21no—
128#117×C61—21no—
129#117×C61—21no—
130#117×C61—21no—
131#117×C61—21no—
132#117×C61C2×C412yes—
133#117×C61C2312yes—
134#117×C61C2312yes—
135C2×C4⋊C4×C61—21no—
136C2×C4⋊C4×C61—21no—
137C2×C22⋊C4×C61—21no—
138C2×C22⋊C4×C61—21no—
139C2×C42×C61—21no—
140C2×C42×C61C2×C412yes—
141C24×C61C2×D411yescharacteristic
142C23×D61—21no—
143C23×D61C22⋊C412yes—
144C22×C4×C61—22no—
145C22×C4×C61—41no—
146C22×C4×C61C22×C411yescharacteristic
147C22×C4×C61C22×C411yescharacteristic
148C22×C4×C61C2×D411yescharacteristic
149C22×C4×C61C2×D411yescharacteristic
150C22×C4×C61C2×D411yescharacteristic
151C22×C4×C61C2×D411yescharacteristic
152C22×C4×C61C2×D411yescharacteristic
153C22×C4×C61C2×D411yescharacteristic
154C22×C4×C61C2×D411yescharacteristic
155C22×C4×C61#4111yescharacteristic
156C22×C4×C61#4111yescharacteristic
157C22×C4×C61#4111yescharacteristic
158C22×C4×C61#4111yescharacteristic
159C22×C4×C61C2411yescharacteristic
160C2×C22⋊D61—22no—
161C2×C22⋊D61—22no—
162C2×C22⋊D61—22no—
163C2×C22⋊D61—22no—
164C2×C22⋊D61—22no—
165C2×C22⋊D61—22no—
166C2×C22⋊D61—41no—
167C2×C22⋊D61—41no—
168C2×C22⋊D61—41no—
169C2×C22⋊D61—41no—
170C2×C22⋊D61C22⋊C414yes—
171C2×C22⋊D61C2×D414yes—
172C22×Dic61—21no—
173C22×Dic61—41no—
174C22×Dic61C22⋊C412yes—
175#11758222—22no—
176#11758222—22no—
177#11758222—22no—
178#11758222—22no—
179#11758222—22no—
180#11758222—22no—
181#11758222—22no—
182#11758222—22no—
183#11758222—22no—
184#11758222—22no—
185#11758222—22no—
186#11758222—22no—
187#11758222—22no—
188#11758222—22no—
189#11758222—22no—
190#11758222—22no—
191#11758222—22no—
192#11758222—22no—
193#11758222—22no—
194#11758222—22no—
195#11758222—22no—
196#11758222—22no—
197#11758222—22no—
198#11758222—22no—
199#11758222—41no—
200#11758222—41no—
201#11758222—41no—
202#11758222—41no—
203#11758222—41no—
204#11758222—41no—
205#11758222—41no—
206#11758222—41no—
207C2×D244—21no—
208C2×D244—21no—
209C2×D244—21no—
210C2×D244—21no—
211C2×D244—21no—
212C2×D244—21no—
213C2×D244—21no—
214C2×D244—21no—
215C2×D244—21no—
216C2×D244—28no—
217C2×D244C22⋊C412yes—
218C2×D244C22×C412yes—
219C2×D244C22×C412yes—
220C2×C4×D61—22no—
221C2×C4×D61—22no—
222C2×C4×D61—22no—
223C2×C4×D61—22no—
224C2×C4×D61—22no—
225C2×C4×D61—22no—
226C2×C4×D61—41no—
227C2×C4×D61—41no—
228C2×C4×D61—41no—
229C2×C4×D61—41no—
230C2×C4×D61C22⋊C414yes—
231C2×C4×D61C2×D414yes—
232C2×Dic122—21no—
233C2×Dic122—21no—
234C2×Dic122—21no—
235C2×Dic122—21no—
236C2×Dic122—21no—
237C2×Dic122—21no—
238C2×Dic122—21no—
239C2×Dic122—21no—
240C2×Dic122—21no—
241C2×Dic122C22⋊C412yes—
242C2×Dic122C22×C412yes—
243C2×Dic122C22×C412yes—
244M16×C61—22no—
245M16×C61—22no—
246M16×C61—22no—
247M16×C61—22no—
248C2×C8×C61—22no—
249C2×C8×C61—22no—
250C2×C8×C61C2×D414yes—
251C4⋊C4×C61—22no—
252C4⋊C4×C61—22no—
253C4⋊C4×C61—22no—
254C4⋊C4×C61—41no—
255C22⋊C4×C61—22no—
256C22⋊C4×C61—22no—
257C22⋊C4×C61—22no—
258C22⋊C4×C61—41no—
259C42×C61—22no—
260C42×C61—22no—
261C42×C61—41no—
262C42×C61C22×C414yes—
263C22⋊Dic61—22no—
264C22⋊Dic61—41no—
265#11758198—28no—
266#11758198—28no—
267C4⋊Dic61—28no—
268C4⋊Dic61—22no—
269C4⋊Dic61—41no—
270C4×Dic61—22no—
271C4×Dic61—41no—
272#11758194—22no—
273#11758194—22no—
274#11758194—22no—
275#11758194—22no—
276C2×#92418—22no—
277C2×#92418—22no—
278C2×#92418C2×D414yes—
279#11758189—216no—
280C8×D61—216no—
281C23×C61—81no—
282C23×C61C2×C22⋊C411yescharacteristic
283C23×C61C2×C22⋊C411yescharacteristic
284C23×C61#12111yescharacteristic
285C23×C61#12111yescharacteristic
286C23×C61#12111yescharacteristic
287C23×C61#12111yescharacteristic
288C23×C61C22×D411yescharacteristic
289C22×D61—22no—
290C22×D61—22no—
291C22×D61—22no—
292C22×D61—41no—
293C22×D61—41no—
294C22×D61—82no—
295C22×D61—82no—
296C22×D61C2×C22⋊C414yes—
297C2×C4×C61—24no—
298C2×C4×C61—42no—
299C2×C4×C61—82no—
300C2×C4×C61—82no—
301C2×C4×C61C2×C22⋊C411yescharacteristic
302C2×C4×C61C2×C22⋊C411yescharacteristic
303C2×C4×C61C4×D411yescharacteristic
304C2×C4×C61C4×D411yescharacteristic
305C2×C4×C61C4×D411yescharacteristic
306C2×C4×C61C4×D411yescharacteristic
307C2×C4×C61C4×D411yescharacteristic
308C2×C4×C61C4×D411yescharacteristic
309C2×C4×C61C4×D411yescharacteristic
310C2×C4×C61C4×D411yescharacteristic
311C2×C4×C61#12011yescharacteristic
312C2×C4×C61#12011yescharacteristic
313C2×C4×C61#12011yescharacteristic
314C2×C4×C61#12011yescharacteristic
315C2×C4×C61#12111yescharacteristic
316C2×C4×C61#12111yescharacteristic
317C2×C4×C61#12111yescharacteristic
318C2×C4×C61#12111yescharacteristic
319C2×C4×C61#12311yescharacteristic
320C2×C4×C61#12311yescharacteristic
321C2×C4×C61#12311yescharacteristic
322C2×C4×C61#12311yescharacteristic
323C2×C4×C61C23×C411yescharacteristic
324C2×C4×C61C22×D411yescharacteristic
325C2×C4×C61C22×D411yescharacteristic
326C2×C4×C61C22×D411yescharacteristic
327C2×C4×C61C2×#4111yescharacteristic
328C2×C4×C61C2×#4111yescharacteristic
329C22⋊D61—24no—
330C22⋊D61—24no—
331C22⋊D61—24no—
332C22⋊D61—24no—
333C22⋊D61—42no—
334C22⋊D61—42no—
335C22⋊D61—42no—
336C22⋊D61—42no—
337C2×Dic61—22no—
338C2×Dic61—22no—
339C2×Dic61—22no—
340C2×Dic61—41no—
341C2×Dic61—41no—
342C2×Dic61—42no—
343C2×Dic61—82no—
344C2×Dic61C2×C22⋊C414yes—
345D244—22no—
346D244—22no—
347D244—22no—
348D244—22no—
349D244—22no—
350D244—22no—
351D244—41no—
352D244—41no—
353D244—88no—
354C4×D61—24no—
355C4×D61—24no—
356C4×D61—24no—
357C4×D61—24no—
358C4×D61—42no—
359C4×D61—42no—
360C4×D61—42no—
361C4×D61—42no—
362Dic122—22no—
363Dic122—22no—
364Dic122—22no—
365Dic122—22no—
366Dic122—22no—
367Dic122—22no—
368Dic122—41no—
369Dic122—41no—
370C8×C61—24no—
371#92418—24no—
372#21009—611nomaximal, Sylow
373C22×C61—41no—
374C22×C61—41no—
375C22×C61—41no—
376C22×C61—41no—
377C22×C61—41no—
378C22×C61—41no—
379C22×C61—41no—
380C22×C61#38611yescharacteristic
381C22×C61#38611yescharacteristic
382C22×C61#38611yescharacteristic
383C22×C61#38611yescharacteristic
384C22×C61C22×C22⋊C411yescharacteristic
385C22×C61C2×#12111yescharacteristic
386C22×C61C2×#12111yescharacteristic
387C2×D61—24no—
388C2×D61—44no—
389C2×D61—44no—
390C2×D61—44no—
391C2×D61—42no—
392C2×D61—82no—
393C2×D61—82no—
394C2×D61—82no—
395C4×C61—44no—
396C4×C61—82no—
397C4×C61#38611yescharacteristic
398C4×C61#38611yescharacteristic
399C4×C61#38611yescharacteristic
400C4×C61#38611yescharacteristic
401C4×C61C2×C4×D411yescharacteristic
402C4×C61C2×C4×D411yescharacteristic
403C4×C61C2×#12011yescharacteristic
404C4×C61C2×#12311yescharacteristic
405Dic61—24no—
406Dic61—42no—
407Dic61—82no—
408C2×#568—611no—
409#3449—611no—
410#2896—611no—
411#2896—611no—
412C2×#410—611no—
413#1910—614no—
414#1909—614no—
415C2×H(3,ℤ/4)—611no—
416C2×H(3,ℤ/4)D6111yescharacteristic, complemented
417C2×C61—21no—
418C2×C61—21no—
419C2×C61—21no—
420C2×C61—21no—
421C2×C61—21no—
422C2×C61—21no—
423C2×C61—21no—
424C2×C61C2×#38611yescharacteristic
425D61—44no—
426D61—82no—
427C22×#41—611no—
428C22×#41—611no—
429#568—614no—
430#568—1222no—
431#568—1222no—
432#568—1222no—
433C2×#131—1222no—
434C2×#131—1222no—
435C22×M16—611no—
436C22×M16—1222no—
437C22×M16C2×D6111yescharacteristic
438#537—1222no—
439#536—612no—
440#536—612no—
441#535—612no—
442#535—612no—
443#534—1222no—
444#532—614no—
445#525—1222no—
446#525—1222no—
447C2×#117—611no—
448C2×#117C2×D6111yescharacteristic
449C2×#117C2×D6111yescharacteristic
450#419—612no—
451#419—612no—
452#418—612no—
453#418—612no—
454#417—1222no—
455#417—1222no—
456#416—1222no—
457#416—1222no—
458#410—614no—
459#410—1222no—
460C2×#99—1222no—
461H(3,ℤ/4)—614no—
462H(3,ℤ/4)C2×D6114yescomplemented
463C61#2100911yescharacteristic, complemented, Sylow
464C2×#41—612no—
465C2×#41—612no—
466C2×#41—612no—
467C2×#41—612no—
468C2×#41—612no—
469C2×#41—612no—
470C2×#41—1221no—
471C2×#41—1221no—
472C2×#41—1221no—
473C2×#41—1221no—
474C2×#41—1221no—
475C2×#41—1221no—
476C2×#41—1221no—
477C2×#41—1221no—
478C2×#41—1221no—
479C2×#41—1221no—
480C2×#41—1221no—
481C2×#41—1221no—
482C2×#41—1221no—
483C2×#41—1221no—
484C2×#41—1221no—
485C2×#41—1221no—
486C2×#41—1221no—
487C2×#41—1221no—
488C22×Q8—611no—
489C22×Q8—611no—
490C22×D4—612no—
491C22×D4—611no—
492C22×D4—611no—
493C22×D4—1221no—
494C23×C4—612no—
495C23×C4—1221no—
496C23×C4C22×D6111yescharacteristic
497#131—1228no—
498#131—1228no—
499#131—1228no—
500#131—1228no—
501C2×M16—21no—
502C2×M16—21no—
503C2×M16—21no—
504C2×M16—21no—
505C2×M16—612no—
506C2×M16—612no—
507C2×M16—1224no—
508C2×M16—1228no—
509C2×M16—1228no—
510C2×M16—1221no—
511C2×M16—1221no—
512C2×M16—1221no—
513C2×M16—1221no—
514C2×M16D24412yescomplemented
515C2×M16C22×D6112yes—
516C22×C8—612no—
517C22×C8—1224no—
518C22×C8D24412yescomplemented
519C4⋊Q8—614no—
520#127—614no—
521#124—614no—
522#124—614no—
523#123—1224no—
524#123—1224no—
525C22⋊Q8—1224no—
526C22⋊Q8—1224no—
527#121—1224no—
528#121—1224no—
529#121—1228no—
530#120—1224no—
531#120—1224no—
532C4×D4—1228no—
533#117—21no—
534#117—21no—
535#117—21no—
536#117—21no—
537#117—21no—
538#117—612no—
539#117—1221no—
540#117—1221no—
541#117—1221no—
542#117C4×D6112yes—
543#117C22×D6112yes—
544#117C22×D6112yes—
545C2×C4⋊C4—21no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—1221no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—1221no—
551C2×C42—21no—
552C2×C42—1221no—
553C2×C42C4×D6112yes—
554#103—1224no—
555#103—1224no—
556#102—1224no—
557#102—1224no—
558#99—1228no—
559C24—612no—
560C24—1221no—
561C24D4×D6111yescharacteristic
562#41—1222no—
563#41—1222no—
564#41—1222no—
565#41—1222no—
566#41—1222no—
567#41—1222no—
568#41—1222no—
569#41—1222no—
570#41—1222no—
571#41—1222no—
572#41—1222no—
573#41—1222no—
574#41—1222no—
575#41—1222no—
576#41—1222no—
577#41—1222no—
578#41—1222no—
579#41—1222no—
580#41—1222no—
581#41—1222no—
582#41—1222no—
583#41—1222no—
584#41—1222no—
585#41—1222no—
586#41—2441no—
587#41—2441no—
588#41—2441no—
589#41—2441no—
590#41—2441no—
591#41—2441no—
592#41—2441no—
593#41—2441no—
594C2×Q8—612no—
595C2×Q8—612no—
596C2×Q8—612no—
597C2×Q8—1221no—
598C2×Q8—1221no—
599C2×Q8—1221no—
600C2×Q8—1221no—
601C2×Q8—1221no—
602C2×Q8—1221no—
603C2×Q8—1221no—
604C2×Q8—1221no—
605C2×Q8—1221no—
606C2×D4—614no—
607C2×D4—614no—
608C2×D4—612no—
609C2×D4—612no—
610C2×D4—612no—
611C2×D4—1228no—
612C2×D4—1222no—
613C2×D4—1222no—
614C2×D4—1222no—
615C2×D4—1222no—
616C2×D4—1222no—
617C2×D4—1222no—
618C2×D4—1221no—
619C2×D4—1221no—
620C2×D4—1221no—
621C2×D4—1221no—
622C2×D4—1221no—
623C2×D4—1221no—
624C2×D4—1221no—
625C2×D4—1221no—
626C2×D4—1221no—
627C2×D4—2441no—
628C2×D4—2441no—
629C2×D4—2441no—
630C2×D4—2441no—
631C22×C4—22no—
632C22×C4—41no—
633C22×C4—612no—
634C22×C4—614no—
635C22×C4—614no—
636C22×C4—1222no—
637C22×C4—1222no—
638C22×C4—1222no—
639C22×C4—1222no—
640C22×C4—1221no—
641C22×C4—1222no—
642C22×C4—1222no—
643C22×C4—2441no—
644C22×C4—2441no—
645C22×C4—2441no—
646C22×C4—2441no—
647C22×C4—2441no—
648C22×C4C2×C4×D6111yescharacteristic
649C22×C4C2×C4×D6111yescharacteristic
650C22×C4C2×D24411yescharacteristic
651C22×C4C2×D24411yescharacteristic
652C22×C4#1175822211yescharacteristic
653C22×C4#1175822211yescharacteristic
654C22×C4D4×D6111yescharacteristic
655C22×C4D4×D6111yescharacteristic
656C22×C4D4×D6111yescharacteristic
657C22×C4D4×D6111yescharacteristic
658C22×C4D4×D6111yescharacteristic
659C22×C4#1175822611yescharacteristic
660C22×C4#1175822611yescharacteristic
661C22×C4C23×D6111yescharacteristic
662M16—22no—
663M16—22no—
664M16—22no—
665M16—22no—
666M16—12216no—
667M16—1222no—
668M16—1222no—
669M16—1222no—
670M16—1222no—
671C2×C8—22no—
672C2×C8—22no—
673C2×C8—614no—
674C2×C8—12216no—
675C2×C8—1222no—
676C2×C8—1222no—
677C2×C8C2×D24414yes—
678C4⋊C4—22no—
679C4⋊C4—22no—
680C4⋊C4—22no—
681C4⋊C4—41no—
682C4⋊C4—1228no—
683C4⋊C4—1222no—
684C4⋊C4—2441no—
685C22⋊C4—22no—
686C22⋊C4—22no—
687C22⋊C4—22no—
688C22⋊C4—41no—
689C22⋊C4—1228no—
690C22⋊C4—1228no—
691C22⋊C4—1222no—
692C22⋊C4—2441no—
693C42—22no—
694C42—22no—
695C42—41no—
696C42—1222no—
697C42—2441no—
698C42C2×C4×D6114yes—
699C23—81no—
700C23—614no—
701C23—1222no—
702C23—1222no—
703C23—1222no—
704C23—4882no—
705C23—4882no—
706C23—2441no—
707C23—2441no—
708C23C22⋊C4×D6111yescharacteristic
709C23C22⋊C4×D6111yescharacteristic
710C23#1451975011yescharacteristic
711C23#1451975011yescharacteristic
712C23#1451975211yescharacteristic
713C23#1451975211yescharacteristic
714C23C2×D4×D6111yescharacteristic
715Q8—1222no—
716Q8—1222no—
717Q8—1222no—
718Q8—1222no—
719Q8—1222no—
720Q8—1222no—
721Q8—2441no—
722Q8—2441no—
723D4—1224no—
724D4—1224no—
725D4—1224no—
726D4—1224no—
727D4—1222no—
728D4—1222no—
729D4—1222no—
730D4—1222no—
731D4—1222no—
732D4—1222no—
733D4—4888no—
734D4—2442no—
735D4—2442no—
736D4—2442no—
737D4—2442no—
738D4—2441no—
739D4—2441no—
740C2×C4—24no—
741C2×C4—42no—
742C2×C4—82no—
743C2×C4—82no—
744C2×C4—614no—
745C2×C4—1222no—
746C2×C4—1222no—
747C2×C4—1224no—
748C2×C4—1224no—
749C2×C4—1224no—
750C2×C4—1224no—
751C2×C4—1222no—
752C2×C4—4882no—
753C2×C4—2442no—
754C2×C4—2441no—
755C2×C4—2441no—
756C2×C4—2442no—
757C2×C4—2442no—
758C2×C4—2442no—
759C2×C4—2442no—
760C2×C4C22⋊C4×D6111yescharacteristic
761C2×C4C22⋊C4×D6111yescharacteristic
762C2×C4#1451973911yescharacteristic
763C2×C4#1451973911yescharacteristic
764C2×C4#1451973911yescharacteristic
765C2×C4#1451973911yescharacteristic
766C2×C4C4×D24411yescharacteristic
767C2×C4C4×D24411yescharacteristic
768C2×C4C4×D24411yescharacteristic
769C2×C4C4×D24411yescharacteristic
770C2×C4#1451974711yescharacteristic
771C2×C4#1451974711yescharacteristic
772C2×C4#1451974711yescharacteristic
773C2×C4#1451974711yescharacteristic
774C2×C4#1451975011yescharacteristic
775C2×C4#1451975011yescharacteristic
776C2×C4#1451975211yescharacteristic
777C2×C4#1451975211yescharacteristic
778C2×C4#1451976211yescharacteristic
779C2×C4#1451976211yescharacteristic
780C2×C4#1451976211yescharacteristic
781C2×C4#1451976211yescharacteristic
782C2×C4C22×C4×D6111yescharacteristic
783C2×C4C2×D4×D6111yescharacteristic
784C2×C4C2×D4×D6111yescharacteristic
785C2×C4C22×D24411yescharacteristic
786C2×C4C2×#1175822211yescharacteristic
787C2×C4C2×#1175822611yescharacteristic
788C8—24no—
789C8—1224no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—1224no—
798C22—4882no—
799C22—4882no—
800C22—4882no—
801C22—2444no—
802C22—2444no—
803C22—2444no—
804C22—2442no—
805C22#1683964011yescharacteristic
806C22#1683964011yescharacteristic
807C22#1683964011yescharacteristic
808C22#1683964011yescharacteristic
809C22C2×C22⋊C4×D6111yescharacteristic
810C22C2×#1451975011yescharacteristic
811C22C2×#1451975211yescharacteristic
812C4—44no—
813C4—82no—
814C4—1224no—
815C4—4882no—
816C4—2442no—
817C4#1683964011yescharacteristic
818C4#1683964011yescharacteristic
819C4#1683964011yescharacteristic
820C4#1683964011yescharacteristic
821C4C2×#1451973911yescharacteristic
822C4C2×C4×D24411yescharacteristic
823C4C2×#1451974711yescharacteristic
824C4C2×#1451976211yescharacteristic
825C2—21no—
826C2—21no—
827C2—21no—
828C2—21no—
829C2—21no—
830C2—21no—
831C2—21no—
832C2—4882no—
833C2—2444no—
834C2C2×#1683964011yescharacteristic
subgroupG/H
centerC4#16839640
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×H(3,ℤ/4)C2
socleC2×C61C2×#386
prime radical#21459152C2
cosocleC22×C4×C61C24
hypercenterC2×H(3,ℤ/4)D61
hypocenterC61#21009
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C23×C4 ◁ C2×H(3,ℤ/4)

Complements

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

NH ≅ G/Ntype
1. C2×#16840528C2semidirect
3. #21454339C2semidirect
4. #21454336C2semidirect
5. C2×#16839735C2semidirect
6. #21446345C2semidirect
7. #21446340C2semidirect
8. C2×#16839518C2semidirect
9. C2×C61×H(3,ℤ/4)C2semidirect
21. #16840338C4semidirect
23. #16840331C4semidirect
26. #16840312C4semidirect
30. #16839772C22semidirect
31. #16839770C22semidirect
32. #16839768C22semidirect
33. #16839766C22semidirect
41. #16839518C22semidirect
45. C61×H(3,ℤ/4)C22semidirect
86. C2×#11758194D4semidirect
91. C22×#92418D4semidirect
93. #14519777C2×C4semidirect
94. #14519774C2×C4semidirect
95. #14519765C2×C4semidirect
96. #14519765C2×C4semidirect
124. C2×M16×C61D4semidirect
126. C22×C8×C61D4semidirect
416. C2×H(3,ℤ/4)D61semidirect
462. H(3,ℤ/4)C2×D61semidirect
463. C61#21009semidirect
514. C2×M16D244semidirect
518. C22×C8D244semidirect

Maximal subgroups

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

subgroupindex
C2×#168405282
#214591522
#214543392
#214543362
C2×#168397352
#214463452
#214463402
C2×#168395182
C2×C61×H(3,ℤ/4)2
#2100961