Finite Group Databasebeta

← #30623921

Subgroups — #30623921

Order 15616.

1236 conjugacy classes of subgroups.

The subgroup lattice has 1060 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840749C211yesmaximal, characteristic, complemented
2C2×#16840742C211yesmaximal, characteristic, complemented
3#21462082C212yesmaximal, complemented
4#21462079C212yesmaximal, complemented
5#21462076C212yesmaximal, complemented
6#21462074C212yesmaximal, complemented
7#21462073C212yesmaximal, complemented
8#21462071C212yesmaximal, complemented
9#21459145C211yesmaximal, characteristic
10C22×#11758217—21no—
11C2×#14519856—21no—
12#16840749—21no—
13#16840749—21no—
14#16840749C2212yes—
15#16840749C2212yes—
16C2×#14519838—21no—
17C2×#14519837C2212yes—
18#16840742—21no—
19#16840742—21no—
20#16840742C2212yes—
21#16840742C2212yes—
22C2×#14519835—21no—
23C2×#14519835C2212yes—
24#16840665C2214yescomplemented
25#16840664C2214yescomplemented
26#16840663C2214yescomplemented
27#16840662C2214yescomplemented
28C22×#11758224C411yescharacteristic, complemented
29C22×#11758224C2211yescharacteristic
30#16840339—21no—
31#16840339—21no—
32#16840334—21no—
33#16840334C411yescharacteristic, complemented
34#16840334C2211yescharacteristic
35#16840327—21no—
36#16840327C411yescharacteristic, complemented
37#16840327C2211yescharacteristic
38#16840324C2211yescharacteristic
39#16840321C411yescharacteristic, complemented
40#16840321C2211yescharacteristic
41#16840307—21no—
42#16840307—21no—
43#16840270—21no—
44#16840270C411yescharacteristic, complemented
45#16840270C2211yescharacteristic
46#16840268—21no—
47#16840268C411yescharacteristic, complemented
48#16840268C2211yescharacteristic
49C2×#14519733C411yescharacteristic, complemented
50C61×#534C411yescharacteristic, complemented
51C2×#11758217—22no—
52C2×#11758217—22no—
53C2×#11758217—22no—
54C2×#11758217—41no—
55C2×#11758217—41no—
56C2×#11758217—41no—
57C22×#92420—41no—
58#14519856—22no—
59#14519856—22no—
60#14519856—41no—
61#14519856—41no—
62C2×C4⋊#6923—41no—
63C2×C22⋊#6923—22no—
64C2×C4×#6923—41no—
65#14519838—22no—
66#14519838—22no—
67#14519837—22no—
68#14519837C2314yes—
69#14519835—22no—
70#14519835—22no—
71#14519835—22no—
72#14519835C2314yes—
73C2×#11758224—21no—
74C2×#11758224—21no—
75C2×#11758224—21no—
76C2×#11758224—21no—
77C2×#11758224—41no—
78C2×#11758224—41no—
79C2×#11758224—41no—
80C2×#11758224—41no—
81C2×#11758224—41no—
82C2×#11758224—41no—
83C2×#11758224—41no—
84C2×#11758224—41no—
85C2×#11758224C2×C411yescharacteristic
86C2×#11758224C2×C411yescharacteristic
87C2×#11758224D411yescharacteristic
88C2×#11758224D411yescharacteristic
89C2×#11758224D411yescharacteristic
90C2×#11758224D411yescharacteristic
91C2×#11758224C2311yescharacteristic
92C2×#11758224C2311yescharacteristic
93C22×Dic122C2×C411yescharacteristic, complemented
94C22×Dic122D411yescharacteristic
95C22×C22⋊D61C2×C411yescharacteristic
96C22×C22⋊D61C2×C411yescharacteristic, complemented
97C22×C22⋊D61D411yescharacteristic
98C22×C22⋊D61C2311yescharacteristic
99C23×Dic61C2×C411yescharacteristic
100C23×Dic61C2×C411yescharacteristic, complemented
101C23×Dic61D411yescharacteristic
102C22×C4×D61C2×C411yescharacteristic, complemented
103C22×C4×D61D411yescharacteristic
104#14519776—21no—
105#14519776—21no—
106#14519773—21no—
107#14519773—21no—
108#14519763—21no—
109#14519763—21no—
110#14519763—21no—
111#14519763—21no—
112#14519761—21no—
113#14519761C2×C411yescharacteristic
114#14519761C2311yescharacteristic
115#14519760—21no—
116#14519760C2×C411yescharacteristic
117#14519760C2311yescharacteristic
118#14519758—21no—
119#14519758C2×C411yescharacteristic, complemented
120#14519758C2×C411yescharacteristic, complemented
121#14519755—21no—
122#14519755—21no—
123#14519755—21no—
124#14519755—21no—
125#14519754—21no—
126#14519754—21no—
127#14519754—21no—
128#14519754—21no—
129#14519751—21no—
130#14519751—21no—
131#14519750—21no—
132#14519750—21no—
133#14519750—21no—
134#14519750—21no—
135#14519749—21no—
136#14519749—21no—
137#14519749—21no—
138#14519749—21no—
139#14519749—21no—
140#14519749—21no—
141#14519749—21no—
142#14519749—21no—
143#14519747—21no—
144#14519747C2×C411yescharacteristic
145#14519747C2311yescharacteristic
146#14519746—21no—
147#14519746C2×C411yescharacteristic
148#14519746C2311yescharacteristic
149#14519745—21no—
150#14519745C2×C411yescharacteristic, complemented
151#14519745C2×C411yescharacteristic, complemented
152D4×Dic61—21no—
153D4×Dic61—21no—
154#14519739—21no—
155#14519739—21no—
156#14519737—21no—
157#14519737—21no—
158#14519737—21no—
159#14519737—21no—
160#14519733—21no—
161#14519733—21no—
162#14519733C2×C411yescharacteristic, complemented
163#14519733C2×C411yescharacteristic, complemented
164#14519733C2×C411yescharacteristic, complemented
165#14519733C2×C411yescharacteristic, complemented
166C2×#11758196—21no—
167C2×C22⋊Dic61C2×C411yescharacteristic
168C2×C4×Dic61—21no—
169C22×D4×C61C2×C411yescharacteristic
170C22×D4×C61C2×C411yescharacteristic
171#123×C61—21no—
172#123×C61C2×C411yescharacteristic, complemented
173#123×C61C2×C411yescharacteristic, complemented
174#121×C61—21no—
175#121×C61—21no—
176#120×C61—21no—
177#120×C61C2×C411yescharacteristic, complemented
178#120×C61C2×C411yescharacteristic, complemented
179C2×C22⋊C4×C61C2×C411yescharacteristic
180C24×C61C22⋊C411yescharacteristic
181C24×C61C22×C411yescharacteristic
182C24×C61C22×C411yescharacteristic
183C23×D61C22×C411yescharacteristic
184C23×D61C2×D411yescharacteristic
185C22×#6923—42no—
186C2×D4×C61—21no—
187C2×D4×C61—21no—
188C2×D4×C61—21no—
189C2×D4×C61—21no—
190C2×D4×C61—41no—
191C2×D4×C61—41no—
192C2×D4×C61—41no—
193C2×D4×C61—41no—
194C2×D4×C61C22⋊C411yescharacteristic
195C2×D4×C61C22⋊C411yescharacteristic
196C2×D4×C61C22×C411yescharacteristic
197C2×D4×C61C22×C411yescharacteristic
198C22×C4×C61—21no—
199C22×C4×C61C22⋊C411yescharacteristic
200C22×C4×C61C22×C411yescharacteristic
201C2×C22⋊D61—21no—
202C2×C22⋊D61—21no—
203C2×C22⋊D61—21no—
204C2×C22⋊D61—21no—
205C2×C22⋊D61—21no—
206C2×C22⋊D61—21no—
207C2×C22⋊D61—21no—
208C2×C22⋊D61—21no—
209C2×C22⋊D61—41no—
210C2×C22⋊D61—41no—
211C2×C22⋊D61—41no—
212C2×C22⋊D61—41no—
213C2×C22⋊D61—41no—
214C2×C22⋊D61—41no—
215C2×C22⋊D61—41no—
216C2×C22⋊D61—41no—
217C2×C22⋊D61C22⋊C411yescharacteristic
218C2×C22⋊D61C22⋊C411yescharacteristic
219C2×C22⋊D61C22×C411yescharacteristic
220C2×C22⋊D61C2×D411yescharacteristic
221C2×C22⋊D61C2×D411yescharacteristic
222C2×C22⋊D61C2×D411yescharacteristic
223C2×C22⋊D61C2×D411yescharacteristic
224C2×C22⋊D61C2411yescharacteristic
225C22×Dic61—21no—
226C22×Dic61—21no—
227C22×Dic61—21no—
228C22×Dic61—21no—
229C22×Dic61—21no—
230C22×Dic61—21no—
231C22×Dic61—21no—
232C22×Dic61—21no—
233C22×Dic61—21no—
234C22×Dic61—21no—
235C22×Dic61—21no—
236C22×Dic61—41no—
237C22×Dic61—41no—
238C22×Dic61C22⋊C411yescharacteristic
239C22×Dic61C22⋊C411yescharacteristic
240C22×Dic61C22⋊C411yescharacteristic
241C22×Dic61C22⋊C411yescharacteristic
242C22×Dic61C22⋊C411yescharacteristic
243C22×Dic61C22⋊C411yescharacteristic
244C22×Dic61C22×C411yescharacteristic
245C22×Dic61C22×C411yescharacteristic
246C22×Dic61C22×C411yescharacteristic
247C22×Dic61C2×D411yescharacteristic
248C22×Dic61C2×D411yescharacteristic
249C22×Dic61C2×D411yescharacteristic
250#11758224—41no—
251#11758224—41no—
252#11758224—41no—
253#11758224—41no—
254#11758224—41no—
255#11758224—41no—
256#11758224—41no—
257#11758224—41no—
258#11758224—41no—
259#11758224—41no—
260#11758224—41no—
261#11758224—41no—
262#11758224—41no—
263#11758224—41no—
264#11758224—41no—
265#11758224—41no—
266#11758224—42no—
267#11758224—42no—
268#11758224—42no—
269#11758224—42no—
270#11758224—42no—
271#11758224—42no—
272#11758224—41no—
273#11758224—41no—
274#11758224—41no—
275#11758224—41no—
276C2×D244—21no—
277C2×D244—21no—
278C2×C4×D61—21no—
279C2×C4×D61—21no—
280C2×C4×D61—21no—
281C2×C4×D61—21no—
282C2×C4×D61—21no—
283C2×C4×D61—21no—
284C2×C4×D61—41no—
285C2×C4×D61—41no—
286C2×C4×D61C22⋊C411yescharacteristic
287C2×C4×D61C22⋊C411yescharacteristic
288C2×C4×D61C2×D411yescharacteristic
289C2×C4×D61C2×D411yescharacteristic
290C2×Dic122—21no—
291C2×Dic122—21no—
292C2×Dic122—41no—
293C2×Dic122—41no—
294C2×Dic122—41no—
295C2×Dic122—41no—
296C2×Dic122C22⋊C411yescharacteristic
297C2×Dic122C22⋊C411yescharacteristic
298C2×Dic122C2×D411yescharacteristic
299C2×Dic122C2×D411yescharacteristic
300C22⋊#6923—24no—
301C22⋊#6923—42no—
302#11758217—24no—
303#11758217—42no—
304#11758217—42no—
305#11758217—42no—
306C2×#92420—42no—
307C2×#92420—42no—
308C2×#92420—42no—
309C4⋊#6923—42no—
310C4⋊#6923—42no—
311C4×#6923—42no—
312C4×#6923—42no—
313C4⋊C4×C61—21no—
314C4⋊C4×C61—21no—
315C22⋊C4×C61—21no—
316C22⋊C4×C61—21no—
317C22⋊C4×C61—21no—
318C22⋊C4×C61—21no—
319C22⋊C4×C61—21no—
320C22⋊C4×C61C22×C411yescharacteristic
321C22⋊C4×C61C22×C411yescharacteristic
322C22⋊Dic61—21no—
323C22⋊Dic61—21no—
324C22⋊Dic61—21no—
325C22⋊Dic61—21no—
326C22⋊Dic61—21no—
327C22⋊Dic61C22×C411yescharacteristic
328C22⋊Dic61C22×C411yescharacteristic
329#11758198—21no—
330#11758198—21no—
331#11758198—21no—
332#11758198—21no—
333#11758198—21no—
334#11758198—21no—
335#11758198—21no—
336#11758198—21no—
337C4⋊Dic61—21no—
338C4⋊Dic61—21no—
339#11758196—21no—
340#11758196—21no—
341#11758196—21no—
342#11758196—21no—
343#11758196—21no—
344#11758196—21no—
345#11758196—21no—
346#11758196—21no—
347C4×Dic61—21no—
348C4×Dic61—21no—
349C4×Dic61—21no—
350C4×Dic61—21no—
351C23×C61—21no—
352C23×C61—21no—
353C23×C61—21no—
354C23×C61—21no—
355C23×C61—21no—
356C23×C61—41no—
357C23×C61—81no—
358C23×C61—81no—
359C23×C61—81no—
360C23×C61C2×C22⋊C411yescharacteristic
361C23×C61C2×C22⋊C411yescharacteristic
362C23×C61C2×C22⋊C411yescharacteristic
363C23×C61C2×C22⋊C411yescharacteristic
364C23×C61C23×C411yescharacteristic
365C22×D61—21no—
366C22×D61—21no—
367C22×D61—21no—
368C22×D61—41no—
369C22×D61—81no—
370C22×D61—81no—
371C22×D61C2×C22⋊C411yescharacteristic
372C22×D61C22×D411yescharacteristic
373C2×#6923—44no—
374C2×#6923—84no—
375D4×C61—41no—
376D4×C61—41no—
377D4×C61—41no—
378D4×C61—41no—
379D4×C61—42no—
380D4×C61—41no—
381D4×C61—41no—
382D4×C61—81no—
383D4×C61—81no—
384C2×C4×C61—21no—
385C2×C4×C61—21no—
386C2×C4×C61—21no—
387C2×C4×C61—21no—
388C2×C4×C61—21no—
389C2×C4×C61—41no—
390C2×C4×C61—81no—
391C2×C4×C61C2×C22⋊C411yescharacteristic
392C2×C4×C61C2×C22⋊C411yescharacteristic
393C22⋊D61—41no—
394C22⋊D61—41no—
395C22⋊D61—41no—
396C22⋊D61—41no—
397C22⋊D61—41no—
398C22⋊D61—41no—
399C22⋊D61—41no—
400C22⋊D61—41no—
401C22⋊D61—42no—
402C22⋊D61—42no—
403C22⋊D61—41no—
404C22⋊D61—41no—
405C22⋊D61—41no—
406C22⋊D61—41no—
407C22⋊D61—81no—
408C22⋊D61—81no—
409C22⋊D61—81no—
410C22⋊D61—81no—
411C2×Dic61—21no—
412C2×Dic61—21no—
413C2×Dic61—21no—
414C2×Dic61—21no—
415C2×Dic61—21no—
416C2×Dic61—21no—
417C2×Dic61—21no—
418C2×Dic61—21no—
419C2×Dic61—21no—
420C2×Dic61—21no—
421C2×Dic61—21no—
422C2×Dic61—21no—
423C2×Dic61—21no—
424C2×Dic61—21no—
425C2×Dic61—21no—
426C2×Dic61—21no—
427C2×Dic61—21no—
428C2×Dic61—21no—
429C2×Dic61—21no—
430C2×Dic61—21no—
431C2×Dic61—21no—
432C2×Dic61—21no—
433C2×Dic61—21no—
434C2×Dic61—42no—
435C2×Dic61—41no—
436C2×Dic61—41no—
437C2×Dic61—41no—
438C2×Dic61—81no—
439C2×Dic61#9911yescharacteristic
440C2×Dic61#9911yescharacteristic
441C2×Dic61#9911yescharacteristic
442C2×Dic61#9911yescharacteristic
443C2×Dic61C2×C22⋊C411yescharacteristic
444C2×Dic61C2×C22⋊C411yescharacteristic
445C2×Dic61C2×C22⋊C411yescharacteristic
446C2×Dic61C2×C22⋊C411yescharacteristic
447C2×Dic61C2×C22⋊C411yescharacteristic
448C2×Dic61C22×D411yescharacteristic
449D244—81no—
450D244—81no—
451C4×D61—21no—
452C4×D61—21no—
453C4×D61—21no—
454C4×D61—21no—
455C4×D61—21no—
456C4×D61—21no—
457C4×D61—21no—
458C4×D61—21no—
459C4×D61—42no—
460C4×D61—41no—
461C4×D61—41no—
462Dic122—41no—
463Dic122—41no—
464Dic122—41no—
465Dic122—41no—
466Dic122—42no—
467Dic122—41no—
468Dic122—41no—
469#92420—44no—
470#33347—611nomaximal, Sylow
471C22×C61—21no—
472C22×C61—21no—
473C22×C61—21no—
474C22×C61—21no—
475C22×C61—41no—
476C22×C61—41no—
477C22×C61—41no—
478C22×C61—41no—
479C22×C61—41no—
480C22×C61—42no—
481C22×C61—41no—
482C22×C61—41no—
483C22×C61—41no—
484C22×C61—81no—
485C22×C61—81no—
486C22×C61—81no—
487C22×C61—82no—
488C22×C61C2×#9911yescharacteristic
489C22×C61C2×#9911yescharacteristic
490C22×C61C22×C22⋊C411yescharacteristic
491C2×D61—21no—
492C2×D61—21no—
493C2×D61—42no—
494C2×D61—41no—
495C2×D61—41no—
496C2×D61—41no—
497C2×D61—41no—
498C2×D61—41no—
499C2×D61—81no—
500C2×D61—82no—
501#6923—84no—
502C4×C61—21no—
503C4×C61—21no—
504C4×C61—41no—
505C4×C61—41no—
506C4×C61—41no—
507Dic61—21no—
508Dic61—21no—
509Dic61—21no—
510Dic61—21no—
511Dic61—41no—
512Dic61—41no—
513Dic61—41no—
514Dic61C2×#9911yescharacteristic
515Dic61C2×#9911yescharacteristic
516Dic61C2×#9911yescharacteristic
517Dic61C2×#9911yescharacteristic
518#3449—611no—
519C2×#413—611no—
520C2×#410—611no—
521#2123—612no—
522#2122—612no—
523#2121—612no—
524#2121—612no—
525#2120—612no—
526#2120—612no—
527C2×C61—21no—
528C2×C61—21no—
529C2×C61—21no—
530C2×C61—41no—
531C2×C61—41no—
532C2×C61—41no—
533C2×C61—41no—
534C2×C61—81no—
535C2×C61C22×#9911yescharacteristic
536D61—41no—
537D61—41no—
538D61—81no—
539C22×#41—611no—
540C22×#41—611no—
541C22×M16—1221no—
542#537—1221no—
543#537—1221no—
544#536—611no—
545#536—611no—
546#536—1221no—
547#535—611no—
548#535—611no—
549#535—1221no—
550#534—611no—
551#534—611no—
552#534—611no—
553#534#692311yescharacteristic, complemented
554#532—1221no—
555#532—1221no—
556#525—611no—
557#525—611no—
558#525—611no—
559#525—611no—
560#525—1221no—
561#525—1221no—
562C2×#117—611no—
563C2×#117—1221no—
564#413—612no—
565#413—612no—
566#413—1221no—
567#413—1221no—
568C2×#101—1221no—
569C2×#100—612no—
570#410—612no—
571#410—612no—
572#410—1221no—
573#410—1221no—
574C2×#99—612no—
575C2×#99—1221no—
576#352—614no—
577#352—614no—
578AΣL(1,𝔽16)—614no—
579AΣL(1,𝔽16)—614no—
580C61#3334711yescharacteristic, complemented, Sylow
581C2×#41—611no—
582C2×#41—611no—
583C2×#41—611no—
584C2×#41—611no—
585C2×#41—611no—
586C2×#41—611no—
587C2×#41—611no—
588C2×#41—611no—
589C2×#41—1221no—
590C2×#41—1221no—
591C2×#41—1221no—
592C2×#41—1221no—
593C2×#41—2441no—
594C2×#41—2441no—
595C2×#41—2441no—
596C2×#41—2441no—
597C2×#41—2441no—
598C2×#41—2441no—
599C2×#41—2441no—
600C2×#41—2441no—
601C22×Q8—611no—
602C22×Q8—611no—
603C22×D4—611no—
604C22×D4—611no—
605C22×D4—611no—
606C22×D4—611no—
607C22×D4C2×#692311yescharacteristic
608C22×D4C2×#692311yescharacteristic
609C23×C4—611no—
610C23×C4—611no—
611C23×C4—611no—
612C23×C4—611no—
613C23×C4—611no—
614C2×M16—1222no—
615C2×M16—1222no—
616C2×M16—1222no—
617C2×M16—2441no—
618C2×M16—2441no—
619C2×M16—2441no—
620C22×C8—2441no—
621C4⋊Q8—1221no—
622C4⋊Q8—1221no—
623#127—1221no—
624#127—1221no—
625#124—1221no—
626#124—1221no—
627#124—1221no—
628#124—1221no—
629#123—21no—
630#123—611no—
631#123—611no—
632#123—611no—
633#123—611no—
634#123—611no—
635#123—611no—
636#123—1221no—
637#123—1221no—
638#123—1221no—
639#123C2×#692311yescharacteristic, complemented
640#123C2×#692311yescharacteristic, complemented
641C22⋊Q8—1221no—
642C22⋊Q8—1221no—
643C22⋊Q8—1221no—
644C22⋊Q8—1221no—
645C22⋊Q8—1221no—
646C22⋊Q8—1221no—
647C22⋊Q8—1221no—
648C22⋊Q8—1221no—
649#121—21no—
650#121—21no—
651#121—1221no—
652#121—1221no—
653#121—1221no—
654#121—1221no—
655#121—1221no—
656#121—1221no—
657#121—1221no—
658#121—1221no—
659#121—1221no—
660#121—1221no—
661#121—1221no—
662#121—1221no—
663#121—1221no—
664#121—1221no—
665#120—21no—
666#120—611no—
667#120—611no—
668#120—611no—
669#120—611no—
670#120—611no—
671#120—611no—
672#120—1221no—
673#120—1221no—
674#120—1221no—
675#120C2×#692311yescharacteristic, complemented
676#120C2×#692311yescharacteristic, complemented
677C4×D4—1221no—
678C4×D4—1221no—
679C4×D4—1221no—
680C4×D4—1221no—
681C4×D4—1221no—
682C4×D4—1221no—
683C4×D4—1221no—
684C4×D4—1221no—
685#117—611no—
686#117—611no—
687#117—611no—
688#117—611no—
689#117—1221no—
690#117—1221no—
691#117—1222no—
692#117—1222no—
693#117—2441no—
694#117—2441no—
695C2×C4⋊C4—1221no—
696C2×C4⋊C4—2441no—
697C2×C22⋊C4—611no—
698C2×C22⋊C4—1222no—
699C2×C22⋊C4C2×#692311yescharacteristic
700C2×C42—1221no—
701C2×C42—2441no—
702#101—1222no—
703#101—1222no—
704#100—614no—
705#100—1222no—
706#99—614no—
707#99—1222no—
708#99—1222no—
709#99—1222no—
710C24—611no—
711C24—611no—
712C24C22⋊#692311yescharacteristic
713C24C22×#692311yescharacteristic
714C24C22×#692311yescharacteristic
715#41—2441no—
716#41—2441no—
717#41—2441no—
718#41—2441no—
719#41—2441no—
720#41—2441no—
721#41—2441no—
722#41—2441no—
723#41—2441no—
724#41—2441no—
725#41—2441no—
726#41—2441no—
727#41—2441no—
728#41—2441no—
729#41—2441no—
730#41—2441no—
731#41—2441no—
732#41—2441no—
733#41—2441no—
734#41—2441no—
735#41—2442no—
736#41—2442no—
737#41—2442no—
738#41—2442no—
739#41—2442no—
740#41—2442no—
741C2×Q8—611no—
742C2×Q8—611no—
743C2×Q8—611no—
744C2×Q8—611no—
745C2×Q8—1221no—
746C2×Q8—1221no—
747C2×Q8—2441no—
748C2×Q8—2441no—
749C2×Q8—2441no—
750C2×Q8—2441no—
751C2×D4—21no—
752C2×D4—21no—
753C2×D4—21no—
754C2×D4—21no—
755C2×D4—41no—
756C2×D4—41no—
757C2×D4—41no—
758C2×D4—41no—
759C2×D4—611no—
760C2×D4—611no—
761C2×D4—611no—
762C2×D4—611no—
763C2×D4—611no—
764C2×D4—611no—
765C2×D4—611no—
766C2×D4—611no—
767C2×D4—1221no—
768C2×D4—1221no—
769C2×D4—1221no—
770C2×D4—1221no—
771C2×D4—1221no—
772C2×D4—1221no—
773C2×D4—1221no—
774C2×D4—1221no—
775C2×D4—1221no—
776C2×D4—1221no—
777C2×D4—2441no—
778C2×D4—2441no—
779C2×D4—2441no—
780C2×D4—2441no—
781C2×D4—2441no—
782C2×D4—2441no—
783C2×D4—2441no—
784C2×D4—2441no—
785C2×D4C22⋊#692311yescharacteristic
786C2×D4C22⋊#692311yescharacteristic
787C2×D4C22×#692311yescharacteristic
788C2×D4C22×#692311yescharacteristic
789C22×C4—21no—
790C22×C4—611no—
791C22×C4—611no—
792C22×C4—611no—
793C22×C4—611no—
794C22×C4—611no—
795C22×C4—611no—
796C22×C4—611no—
797C22×C4—611no—
798C22×C4—611no—
799C22×C4—611no—
800C22×C4—611no—
801C22×C4—611no—
802C22×C4—611no—
803C22×C4—611no—
804C22×C4—611no—
805C22×C4—611no—
806C22×C4—1221no—
807C22×C4—1221no—
808C22×C4—1221no—
809C22×C4—1221no—
810C22×C4—1221no—
811C22×C4—1221no—
812C22×C4—1221no—
813C22×C4—1221no—
814C22×C4—1221no—
815C22×C4—1221no—
816C22×C4—1221no—
817C22×C4—1221no—
818C22×C4—1221no—
819C22×C4—1221no—
820C22×C4—1221no—
821C22×C4—1221no—
822C22×C4—1221no—
823C22×C4—2441no—
824C22×C4—2441no—
825C22×C4—2441no—
826C22×C4—2441no—
827C22×C4—2442no—
828C22×C4C22⋊#692311yescharacteristic
829C22×C4C22×#692311yescharacteristic
830M16—1224no—
831M16—2442no—
832M16—2442no—
833M16—2442no—
834C2×C8—2442no—
835C2×C8—2442no—
836C2×C8—2442no—
837C4⋊C4—21no—
838C4⋊C4—21no—
839C4⋊C4—1221no—
840C4⋊C4—1221no—
841C4⋊C4—1221no—
842C4⋊C4—1221no—
843C4⋊C4—1221no—
844C4⋊C4—1221no—
845C4⋊C4—1221no—
846C4⋊C4—1221no—
847C4⋊C4—1221no—
848C4⋊C4—1221no—
849C4⋊C4—2442no—
850C4⋊C4—2442no—
851C22⋊C4—21no—
852C22⋊C4—21no—
853C22⋊C4—21no—
854C22⋊C4—21no—
855C22⋊C4—21no—
856C22⋊C4—611no—
857C22⋊C4—611no—
858C22⋊C4—1221no—
859C22⋊C4—1221no—
860C22⋊C4—1221no—
861C22⋊C4—1221no—
862C22⋊C4—1221no—
863C22⋊C4—1221no—
864C22⋊C4—1221no—
865C22⋊C4—1221no—
866C22⋊C4—1221no—
867C22⋊C4—1221no—
868C22⋊C4—1221no—
869C22⋊C4—1221no—
870C22⋊C4—1221no—
871C22⋊C4—1224no—
872C22⋊C4—2442no—
873C22⋊C4C22×#692311yescharacteristic
874C22⋊C4C22×#692311yescharacteristic
875C42—1221no—
876C42—1221no—
877C42—1221no—
878C42—1221no—
879C42—2442no—
880C42—2442no—
881C23—21no—
882C23—21no—
883C23—21no—
884C23—21no—
885C23—21no—
886C23—41no—
887C23—81no—
888C23—81no—
889C23—81no—
890C23—611no—
891C23—611no—
892C23—1221no—
893C23—1221no—
894C23—1221no—
895C23—4881no—
896C23—4881no—
897C23—2441no—
898C23C2×C22⋊#692311yescharacteristic
899C23C2×C22⋊#692311yescharacteristic
900C23C2×C22⋊#692311yescharacteristic
901C23C2×C22⋊#692311yescharacteristic
902C23C23×#692311yescharacteristic
903Q8—2441no—
904Q8—2441no—
905Q8—2441no—
906Q8—2441no—
907Q8—2441no—
908Q8—2441no—
909Q8—2442no—
910D4—41no—
911D4—41no—
912D4—41no—
913D4—41no—
914D4—42no—
915D4—41no—
916D4—41no—
917D4—81no—
918D4—81no—
919D4—4881no—
920D4—4881no—
921D4—4881no—
922D4—4881no—
923D4—4881no—
924D4—4881no—
925D4—2441no—
926D4—2441no—
927D4—2441no—
928D4—2441no—
929D4—2441no—
930D4—2441no—
931D4—2441no—
932D4—2441no—
933D4—2441no—
934D4—2441no—
935D4—2442no—
936D4—2442no—
937D4—2441no—
938D4—2441no—
939C2×C4—21no—
940C2×C4—21no—
941C2×C4—21no—
942C2×C4—21no—
943C2×C4—21no—
944C2×C4—41no—
945C2×C4—81no—
946C2×C4—611no—
947C2×C4—611no—
948C2×C4—611no—
949C2×C4—611no—
950C2×C4—611no—
951C2×C4—611no—
952C2×C4—611no—
953C2×C4—611no—
954C2×C4—611no—
955C2×C4—611no—
956C2×C4—1221no—
957C2×C4—1221no—
958C2×C4—1221no—
959C2×C4—1221no—
960C2×C4—1221no—
961C2×C4—1221no—
962C2×C4—1221no—
963C2×C4—1221no—
964C2×C4—1221no—
965C2×C4—1221no—
966C2×C4—1221no—
967C2×C4—1221no—
968C2×C4—1221no—
969C2×C4—1221no—
970C2×C4—1221no—
971C2×C4—1221no—
972C2×C4—1221no—
973C2×C4—1221no—
974C2×C4—1221no—
975C2×C4—1221no—
976C2×C4—1221no—
977C2×C4—1221no—
978C2×C4—1221no—
979C2×C4—1221no—
980C2×C4—1221no—
981C2×C4—1221no—
982C2×C4—1221no—
983C2×C4—1221no—
984C2×C4—1221no—
985C2×C4—1221no—
986C2×C4—1221no—
987C2×C4—4884no—
988C2×C4—4881no—
989C2×C4—2441no—
990C2×C4—2441no—
991C2×C4—2442no—
992C2×C4—2441no—
993C2×C4—2441no—
994C2×C4—2442no—
995C2×C4—2444no—
996C2×C4—2441no—
997C2×C4C2×C22⋊#692311yescharacteristic
998C2×C4C2×C22⋊#692311yescharacteristic
999C8—2444no—
1000C22—21no—
1001C22—21no—
1002C22—21no—
1003C22—21no—
1004C22—41no—
1005C22—41no—
1006C22—41no—
1007C22—41no—
1008C22—41no—
1009C22—42no—
1010C22—41no—
1011C22—41no—
1012C22—41no—
1013C22—81no—
1014C22—81no—
1015C22—81no—
1016C22—82no—
1017C22—1221no—
1018C22—1221no—
1019C22—4881no—
1020C22—4882no—
1021C22—2441no—
1022C22—2441no—
1023C22—2441no—
1024C22—2441no—
1025C22—2442no—
1026C22—2441no—
1027C22D61⋊#9911yescharacteristic
1028C22D61⋊#9911yescharacteristic
1029C22C22×C22⋊#692311yescharacteristic
1030C4—21no—
1031C4—21no—
1032C4—41no—
1033C4—41no—
1034C4—41no—
1035C4—611no—
1036C4—611no—
1037C4—611no—
1038C4—611no—
1039C4—1221no—
1040C4—1221no—
1041C4—1221no—
1042C4—1221no—
1043C4—4884no—
1044C4—2441no—
1045C4—2441no—
1046C4—2441no—
1047C2—21no—
1048C2—21no—
1049C2—21no—
1050C2—41no—
1051C2—41no—
1052C2—41no—
1053C2—41no—
1054C2—81no—
1055C2—4881no—
1056C2—2441no—
1057C2—2441no—
1058C2C2×D61⋊#9911yescharacteristic
subgroupG/H
centerC2C2×D61⋊#99
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC61×#534C4
socleC2×C61C22×#99
prime radical#21459145C2
cosocleC2×C22⋊D61C24
hypercenter#534#6923
hypocenterC61#33347
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C23 ◁ C22×D4 ◁ #534

Complements

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

NH ≅ G/Ntype
1. C2×#16840749C2semidirect
2. C2×#16840742C2semidirect
3. #21462082C2semidirect
4. #21462079C2semidirect
5. #21462076C2semidirect
6. #21462074C2semidirect
7. #21462073C2semidirect
8. #21462071C2semidirect
24. #16840665C22semidirect
25. #16840664C22semidirect
26. #16840663C22semidirect
27. #16840662C22semidirect
28. C22×#11758224C4semidirect
33. #16840334C4semidirect
36. #16840327C4semidirect
39. #16840321C4semidirect
44. #16840270C4semidirect
47. #16840268C4semidirect
49. C2×#14519733C4semidirect
50. C61×#534C4semidirect
93. C22×Dic122C2×C4semidirect
96. C22×C22⋊D61C2×C4semidirect
100. C23×Dic61C2×C4semidirect
102. C22×C4×D61C2×C4semidirect
119. #14519758C2×C4semidirect
120. #14519758C2×C4semidirect
150. #14519745C2×C4semidirect
151. #14519745C2×C4semidirect
162. #14519733C2×C4semidirect
163. #14519733C2×C4semidirect
164. #14519733C2×C4semidirect
165. #14519733C2×C4semidirect
172. #123×C61C2×C4semidirect
173. #123×C61C2×C4semidirect
177. #120×C61C2×C4semidirect
178. #120×C61C2×C4semidirect
553. #534#6923semidirect
580. C61#33347semidirect
639. #123C2×#6923semidirect
640. #123C2×#6923semidirect
675. #120C2×#6923semidirect
676. #120C2×#6923semidirect

Maximal subgroups

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

subgroupindex
C2×#168407492
C2×#168407422
#214620822
#214620792
#214620762
#214620742
#214620732
#214620712
#214591452
#3334761