Finite Group Databasebeta

← #30623922

Subgroups — #30623922

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
1D61⋊#413C211yesmaximal, characteristic, complemented
2D61⋊#410C211yesmaximal, characteristic, complemented
3#21462082C212yesmaximal, complemented
4#21462079C212yesmaximal, complemented
5#21462077C212yesmaximal, complemented
6#21462075C212yesmaximal, complemented
7#21462072C212yesmaximal, complemented
8#21462070C212yesmaximal, complemented
9#21459149C211yesmaximal, characteristic
10C2×D61⋊M16—21no—
11C2×#14519856—21no—
12#16840749—21no—
13#16840749C2212yes—
14#16840748—21no—
15#16840748C2212yes—
16D61⋊#101—21no—
17D61⋊#100C2212yes—
18#16840743—21no—
19#16840742C2212yes—
20#16840741—21no—
21#16840741C2212yes—
22D61⋊#99—21no—
23D61⋊#99C2212yes—
24#16840665C2214yescomplemented
25#16840664C2214yescomplemented
26#16840663C2214yescomplemented
27#16840662C2214yescomplemented
28C22×#11758222C411yescharacteristic, complemented
29C2×#41×D61C2211yescharacteristic
30#16840342—21no—
31#16840341—21no—
32#16840335—21no—
33#16840334C411yescharacteristic, complemented
34#16840334C2211yescharacteristic
35#16840328—21no—
36#16840327C411yescharacteristic, complemented
37#16840327C2211yescharacteristic
38#16840323C411yescharacteristic, complemented
39#16840323C2211yescharacteristic
40#16840322C411yescharacteristic, complemented
41#16840322C2211yescharacteristic
42#16840309—21no—
43#16840309—21no—
44#16840274C2211yescharacteristic
45#16840273C2211yescharacteristic
46#16840271—21no—
47#16840271—21no—
48#16840269C411yescharacteristic, complemented
49#117×D61C411yescharacteristic, complemented
50C61×#525C411yescharacteristic, complemented
51C2×#11758213—41no—
52D61⋊M16—22no—
53D61⋊M16—22no—
54D61⋊M16—41no—
55D61⋊M16—41no—
56C2×#11758217—22no—
57C2×D61⋊C8—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#14519836—22no—
70#14519836—22no—
71#14519835—22no—
72#14519835C2314yes—
73C2×#11758226D411yescharacteristic
74C2×#11758222—21no—
75C2×#11758222—21no—
76C2×#11758222—21no—
77C2×#11758222—21no—
78C2×#11758222—41no—
79C2×#11758222—41no—
80C2×#11758222—41no—
81C2×#11758222—41no—
82C2×#11758222D411yescharacteristic
83C2×#11758222D411yescharacteristic
84C2×#11758222C2311yescharacteristic
85C2×#11758224C2×C411yescharacteristic
86C2×#11758224D411yescharacteristic
87C2×#11758224C2311yescharacteristic
88#41×D61—41no—
89#41×D61—41no—
90#41×D61—41no—
91#41×D61—41no—
92C22×Dic122C2×C411yescharacteristic, complemented
93C2×Q8×D61D411yescharacteristic
94C22×D244C2×C411yescharacteristic
95C22×C22⋊D61C2×C411yescharacteristic
96C22×C22⋊D61C2×C411yescharacteristic, complemented
97C2×D4×D61C2×C411yescharacteristic
98C2×D4×D61D411yescharacteristic
99C2×D4×D61C2311yescharacteristic
100C22×C4×D61C2×C411yescharacteristic
101C22×C4×D61C2×C411yescharacteristic, complemented
102C22×C4×D61D411yescharacteristic
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#14519762—21no—
113#14519762—21no—
114#14519761C2×C411yescharacteristic, complemented
115#14519761C2311yescharacteristic
116#14519760C2×C411yescharacteristic, complemented
117#14519760C2311yescharacteristic
118#14519759—21no—
119#14519759—21no—
120#14519758C2×C411yescharacteristic
121#14519758C2×C411yescharacteristic, complemented
122#14519757—21no—
123#14519756—21no—
124#14519755—21no—
125#14519755—21no—
126#14519754—21no—
127#14519754—21no—
128#14519753—21no—
129#14519752—21no—
130#14519752—21no—
131#14519752—21no—
132#14519751—21no—
133#14519750—21no—
134#14519750—21no—
135#14519750—21no—
136#14519750—21no—
137#14519750—21no—
138#14519750—21no—
139#14519749—21no—
140#14519749—21no—
141#14519748—21no—
142#14519748—21no—
143#14519748—21no—
144#14519747—21no—
145#14519747—21no—
146#14519747C2×C411yescharacteristic, complemented
147#14519747C2311yescharacteristic
148#14519746C2×C411yescharacteristic, complemented
149#14519746C2311yescharacteristic
150#14519745—21no—
151#14519745—21no—
152#14519745C2×C411yescharacteristic
153#14519745C2×C411yescharacteristic, complemented
154C4×D244—21no—
155C4×D244—21no—
156C4×C22⋊D61—21no—
157C4×C22⋊D61—21no—
158C4×C22⋊D61—21no—
159C4×C22⋊D61—21no—
160#14519736C2×C411yescharacteristic, complemented
161#14519735—21no—
162#14519734—21no—
163#14519733C2×C411yescharacteristic, complemented
164#14519733C2×C411yescharacteristic, complemented
165C4⋊C4×D61—21no—
166C22⋊C4×D61C2×C411yescharacteristic
167C22⋊C4×D61C2×C411yescharacteristic
168C42×D61—21no—
169C2×#41×C61C2×C411yescharacteristic
170C23×C4×C61C2×C411yescharacteristic, complemented
171#123×C61C2×C411yescharacteristic
172#123×C61C2×C411yescharacteristic, complemented
173C22⋊Q8×C61—21no—
174#121×C61—21no—
175#120×C61C2×C411yescharacteristic
176#120×C61C2×C411yescharacteristic, complemented
177C4×D4×C61—21no—
178C4×D4×C61—21no—
179#117×C61C2×C411yescharacteristic, complemented
180C24×C61C22×C411yescharacteristic
181C23×D61C22⋊C411yescharacteristic
182C23×D61C22×C411yescharacteristic
183C23×D61C22×C411yescharacteristic
184C23×D61C2×D411yescharacteristic
185C22×#6923—42no—
186#41×C61—41no—
187#41×C61—41no—
188C2×Q8×C61C22⋊C411yescharacteristic
189C2×D4×C61—21no—
190C2×D4×C61—21no—
191C2×D4×C61C22⋊C411yescharacteristic
192C2×D4×C61C22×C411yescharacteristic
193C2×D4×C61C22×C411yescharacteristic
194C22×C4×C61—21no—
195C22×C4×C61—21no—
196C22×C4×C61—41no—
197C22×C4×C61—41no—
198C22×C4×C61C22⋊C411yescharacteristic
199C22×C4×C61C22⋊C411yescharacteristic
200C22×C4×C61C22×C411yescharacteristic
201C22×C4×C61C22×C411yescharacteristic
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—21no—
210C2×C22⋊D61—41no—
211C2×C22⋊D61—41no—
212C2×C22⋊D61—41no—
213C2×C22⋊D61—41no—
214C2×C22⋊D61C22⋊C411yescharacteristic
215C2×C22⋊D61C22⋊C411yescharacteristic
216C2×C22⋊D61C22×C411yescharacteristic
217C2×C22⋊D61C2×D411yescharacteristic
218C2×C22⋊D61C2×D411yescharacteristic
219C2×C22⋊D61C2411yescharacteristic
220C22×Dic61C22⋊C411yescharacteristic
221C22×Dic61C22×C411yescharacteristic
222C22×Dic61C22×C411yescharacteristic
223C22×Dic61C2×D411yescharacteristic
224#11758226—41no—
225#11758226—41no—
226Q8×D61—41no—
227Q8×D61—41no—
228#11758224—41no—
229#11758224—41no—
230#11758224—41no—
231#11758224—41no—
232#11758224—41no—
233#11758224—41no—
234D4×D61—41no—
235D4×D61—41no—
236D4×D61—41no—
237D4×D61—41no—
238D4×D61—41no—
239D4×D61—41no—
240#11758222—41no—
241#11758222—41no—
242#11758222—41no—
243#11758222—41no—
244#11758222—41no—
245#11758222—41no—
246#11758222—42no—
247#11758222—42no—
248#11758222—42no—
249#11758222—42no—
250#11758222—42no—
251#11758222—42no—
252#11758222—41no—
253#11758222—41no—
254#11758222—41no—
255#11758222—41no—
256C2×D244—21no—
257C2×D244—21no—
258C2×D244—21no—
259C2×D244—21no—
260C2×D244—41no—
261C2×D244—41no—
262C2×D244C22⋊C411yescharacteristic
263C2×D244C2×D411yescharacteristic
264C2×D244C2×D411yescharacteristic
265C2×C4×D61—21no—
266C2×C4×D61—21no—
267C2×C4×D61—21no—
268C2×C4×D61—21no—
269C2×C4×D61—21no—
270C2×C4×D61—21no—
271C2×C4×D61—21no—
272C2×C4×D61—21no—
273C2×C4×D61—21no—
274C2×C4×D61—21no—
275C2×C4×D61—21no—
276C2×C4×D61—21no—
277C2×C4×D61—21no—
278C2×C4×D61—21no—
279C2×C4×D61—21no—
280C2×C4×D61—21no—
281C2×C4×D61—41no—
282C2×C4×D61—41no—
283C2×C4×D61C22⋊C411yescharacteristic
284C2×C4×D61C22⋊C411yescharacteristic
285C2×C4×D61C22⋊C411yescharacteristic
286C2×C4×D61C22⋊C411yescharacteristic
287C2×C4×D61C22⋊C411yescharacteristic
288C2×C4×D61C22⋊C411yescharacteristic
289C2×C4×D61C2×D411yescharacteristic
290C2×C4×D61C2×D411yescharacteristic
291C2×C4×D61C2×D411yescharacteristic
292C2×C4×D61C2×D411yescharacteristic
293C2×Dic122—21no—
294C2×Dic122—21no—
295C2×Dic122—41no—
296C2×Dic122—41no—
297C2×Dic122C22⋊C411yescharacteristic
298C2×Dic122C2×D411yescharacteristic
299C2×Dic122C2×D411yescharacteristic
300C22⋊#6923—24no—
301C22⋊#6923—42no—
302#11758217—24no—
303#11758217—42no—
304C2×#92420—42no—
305C4⋊#6923—42no—
306C4⋊#6923—42no—
307C4×#6923—42no—
308C4×#6923—42no—
309#11758213—42no—
310#11758213—42no—
311D61⋊C8—42no—
312D61⋊C8—42no—
313C4⋊C4×C61—21no—
314C4⋊C4×C61—21no—
315C4⋊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
322C42×C61—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—
337#11758198—21no—
338#11758198—21no—
339C4⋊Dic61—21no—
340C4⋊Dic61—21no—
341C4⋊Dic61—21no—
342#11758196—21no—
343#11758196—21no—
344#11758196—21no—
345#11758196—21no—
346#11758196—21no—
347#11758196—21no—
348C4×Dic61—21no—
349C4×Dic61—21no—
350C4×Dic61—21no—
351C23×C61—21no—
352C23×C61—41no—
353C23×C61—81no—
354C23×C61C2×C22⋊C411yescharacteristic
355C23×C61C2×C22⋊C411yescharacteristic
356C23×C61C23×C411yescharacteristic
357C22×D61—21no—
358C22×D61—21no—
359C22×D61—21no—
360C22×D61—21no—
361C22×D61—21no—
362C22×D61—21no—
363C22×D61—21no—
364C22×D61—41no—
365C22×D61—81no—
366C22×D61—81no—
367C22×D61—81no—
368C22×D61—81no—
369C22×D61C2×C22⋊C411yescharacteristic
370C22×D61C2×C22⋊C411yescharacteristic
371C22×D61C2×C22⋊C411yescharacteristic
372C22×D61C22×D411yescharacteristic
373C2×#6923—44no—
374C2×#6923—84no—
375Q8×C61—41no—
376D4×C61—41no—
377D4×C61—41no—
378D4×C61—41no—
379D4×C61—81no—
380D4×C61—81no—
381C2×C4×C61—21no—
382C2×C4×C61—21no—
383C2×C4×C61—21no—
384C2×C4×C61—21no—
385C2×C4×C61—21no—
386C2×C4×C61—21no—
387C2×C4×C61—21no—
388C2×C4×C61—21no—
389C2×C4×C61—21no—
390C2×C4×C61—42no—
391C2×C4×C61—41no—
392C2×C4×C61—41no—
393C2×C4×C61—41no—
394C2×C4×C61C2×C22⋊C411yescharacteristic
395C2×C4×C61C2×C22⋊C411yescharacteristic
396C2×C4×C61C2×C22⋊C411yescharacteristic
397C2×C4×C61C2×C22⋊C411yescharacteristic
398C22⋊D61—41no—
399C22⋊D61—41no—
400C22⋊D61—41no—
401C22⋊D61—41no—
402C22⋊D61—41no—
403C22⋊D61—41no—
404C22⋊D61—42no—
405C22⋊D61—42no—
406C22⋊D61—41no—
407C22⋊D61—41no—
408C22⋊D61—41no—
409C22⋊D61—41no—
410C22⋊D61—81no—
411C22⋊D61—81no—
412C22⋊D61—81no—
413C22⋊D61—81no—
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—41no—
424C2×Dic61C2×C22⋊C411yescharacteristic
425C2×Dic61C2×C22⋊C411yescharacteristic
426C2×Dic61C2×C22⋊C411yescharacteristic
427C2×Dic61C22×D411yescharacteristic
428D244—41no—
429D244—41no—
430D244—41no—
431D244—42no—
432D244—41no—
433D244—41no—
434D244—81no—
435D244—81no—
436C4×D61—21no—
437C4×D61—21no—
438C4×D61—21no—
439C4×D61—21no—
440C4×D61—21no—
441C4×D61—21no—
442C4×D61—21no—
443C4×D61—21no—
444C4×D61—21no—
445C4×D61—21no—
446C4×D61—21no—
447C4×D61—21no—
448C4×D61—21no—
449C4×D61—21no—
450C4×D61—21no—
451C4×D61—21no—
452C4×D61—21no—
453C4×D61—21no—
454C4×D61—42no—
455C4×D61—41no—
456C4×D61—41no—
457C4×D61—81no—
458C4×D61—81no—
459C4×D61#9911yescharacteristic
460C4×D61#9911yescharacteristic
461C4×D61#9911yescharacteristic
462C4×D61#9911yescharacteristic
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—41no—
475C22×C61—41no—
476C22×C61—41no—
477C22×C61—41no—
478C22×C61—41no—
479C22×C61—41no—
480C22×C61—82no—
481C22×C61C22×C22⋊C411yescharacteristic
482C2×D61—21no—
483C2×D61—21no—
484C2×D61—21no—
485C2×D61—41no—
486C2×D61—42no—
487C2×D61—42no—
488C2×D61—41no—
489C2×D61—41no—
490C2×D61—41no—
491C2×D61—41no—
492C2×D61—41no—
493C2×D61—41no—
494C2×D61—81no—
495C2×D61—81no—
496C2×D61—81no—
497C2×D61—81no—
498C2×D61—82no—
499C2×D61C2×#9911yescharacteristic
500C2×D61C2×#9911yescharacteristic
501#6923—84no—
502C4×C61—21no—
503C4×C61—21no—
504C4×C61—21no—
505C4×C61—41no—
506C4×C61—41no—
507C4×C61—41no—
508C4×C61C2×#9911yescharacteristic
509C4×C61C2×#9911yescharacteristic
510Dic61—21no—
511Dic61—21no—
512Dic61—21no—
513Dic61—41no—
514Dic61—41no—
515Dic61—41no—
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—41no—
529C2×C61—41no—
530C2×C61—41no—
531C2×C61—81no—
532C2×C61C22×#9911yescharacteristic
533D61—21no—
534D61—21no—
535D61—41no—
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—611no—
554#532—1221no—
555#532—1221no—
556#525—611no—
557#525—611no—
558#525—611no—
559#525—1221no—
560#525—1221no—
561#525#692311yescharacteristic, complemented
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—1221no—
589C2×#41—1221no—
590C2×#41—1221no—
591C2×#41—1221no—
592C2×#41—2441no—
593C2×#41—2441no—
594C2×#41—2441no—
595C2×#41—2441no—
596C2×#41—2441no—
597C2×#41—2441no—
598C2×#41—2441no—
599C2×#41—2441no—
600C2×#41C2×#692311yescharacteristic
601C22×Q8—611no—
602C22×Q8—611no—
603C22×D4—611no—
604C22×D4—611no—
605C22×D4—611no—
606C22×D4—611no—
607C22×D4—611no—
608C22×D4—611no—
609C23×C4—611no—
610C23×C4—611no—
611C23×C4—611no—
612C23×C4—611no—
613C23×C4C2×#692311yescharacteristic, complemented
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—611no—
630#123—611no—
631#123—611no—
632#123—611no—
633#123—611no—
634#123—611no—
635#123—1221no—
636#123—1221no—
637#123—1221no—
638#123—1221no—
639#123C2×#692311yescharacteristic
640#123C2×#692311yescharacteristic, complemented
641C22⋊Q8—21no—
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—1221no—
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—611no—
666#120—611no—
667#120—611no—
668#120—611no—
669#120—611no—
670#120—611no—
671#120—1221no—
672#120—1221no—
673#120—1221no—
674#120—1221no—
675#120C2×#692311yescharacteristic
676#120C2×#692311yescharacteristic, complemented
677C4×D4—21no—
678C4×D4—21no—
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—1221no—
689#117—1221no—
690#117—1222no—
691#117—1222no—
692#117—2441no—
693#117—2441no—
694#117C2×#692311yescharacteristic, complemented
695C2×C4⋊C4—1221no—
696C2×C4⋊C4—2441no—
697C2×C22⋊C4—611no—
698C2×C22⋊C4—611no—
699C2×C22⋊C4—1222no—
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—
712C24—611no—
713C24—611no—
714C24C22×#692311yescharacteristic
715#41—41no—
716#41—41no—
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—2442no—
728#41—2442no—
729#41—2442no—
730#41—2442no—
731#41—2442no—
732#41—2442no—
733#41—2441no—
734#41—2441no—
735#41—2441no—
736#41—2441no—
737#41—2441no—
738#41—2441no—
739#41—2441no—
740#41—2441no—
741C2×Q8—611no—
742C2×Q8—611no—
743C2×Q8—611no—
744C2×Q8—1221no—
745C2×Q8—1221no—
746C2×Q8—2441no—
747C2×Q8—2441no—
748C2×Q8—2441no—
749C2×Q8—2441no—
750C2×Q8C22⋊#692311yescharacteristic
751C2×D4—21no—
752C2×D4—21no—
753C2×D4—611no—
754C2×D4—611no—
755C2×D4—611no—
756C2×D4—611no—
757C2×D4—611no—
758C2×D4—611no—
759C2×D4—611no—
760C2×D4—611no—
761C2×D4—611no—
762C2×D4—1221no—
763C2×D4—1221no—
764C2×D4—1221no—
765C2×D4—1221no—
766C2×D4—1221no—
767C2×D4—1221no—
768C2×D4—1221no—
769C2×D4—1221no—
770C2×D4—1221no—
771C2×D4—1221no—
772C2×D4—1221no—
773C2×D4—1221no—
774C2×D4—2441no—
775C2×D4—2441no—
776C2×D4—2441no—
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×D4—2441no—
786C2×D4C22⋊#692311yescharacteristic
787C2×D4C22×#692311yescharacteristic
788C2×D4C22×#692311yescharacteristic
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—41no—
792C22×C4—41no—
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—611no—
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—2442no—
826C22×C4C22⋊#692311yescharacteristic
827C22×C4C22⋊#692311yescharacteristic
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—21no—
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—611no—
856C22⋊C4—611no—
857C22⋊C4—1221no—
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—21no—
876C42—1221no—
877C42—1221no—
878C42—1221no—
879C42—2442no—
880C42—2442no—
881C23—21no—
882C23—41no—
883C23—81no—
884C23—611no—
885C23—611no—
886C23—611no—
887C23—611no—
888C23—1221no—
889C23—1221no—
890C23—1221no—
891C23—1221no—
892C23—1221no—
893C23—1221no—
894C23—1221no—
895C23—4881no—
896C23—4881no—
897C23—4881no—
898C23—4881no—
899C23—2441no—
900C23C2×C22⋊#692311yescharacteristic
901C23C2×C22⋊#692311yescharacteristic
902C23C23×#692311yescharacteristic
903Q8—41no—
904Q8—2441no—
905Q8—2441no—
906Q8—2441no—
907Q8—2441no—
908Q8—2441no—
909Q8—2442no—
910D4—41no—
911D4—41no—
912D4—41no—
913D4—81no—
914D4—81no—
915D4—4881no—
916D4—4881no—
917D4—4881no—
918D4—4881no—
919D4—4881no—
920D4—4881no—
921D4—2441no—
922D4—2441no—
923D4—2441no—
924D4—2441no—
925D4—2441no—
926D4—2442no—
927D4—2441no—
928D4—2441no—
929D4—2441no—
930D4—2441no—
931D4—2441no—
932D4—2441no—
933D4—2441no—
934D4—2441no—
935D4—2442no—
936D4—2441no—
937D4—2441no—
938D4—2442no—
939C2×C4—21no—
940C2×C4—21no—
941C2×C4—21no—
942C2×C4—21no—
943C2×C4—21no—
944C2×C4—21no—
945C2×C4—21no—
946C2×C4—21no—
947C2×C4—21no—
948C2×C4—42no—
949C2×C4—41no—
950C2×C4—41no—
951C2×C4—41no—
952C2×C4—611no—
953C2×C4—611no—
954C2×C4—611no—
955C2×C4—611no—
956C2×C4—611no—
957C2×C4—611no—
958C2×C4—611no—
959C2×C4—611no—
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—4881no—
988C2×C4—4881no—
989C2×C4—4884no—
990C2×C4—2442no—
991C2×C4—2444no—
992C2×C4—2441no—
993C2×C4—2441no—
994C2×C4—2441no—
995C2×C4C2×C22⋊#692311yescharacteristic
996C2×C4C2×C22⋊#692311yescharacteristic
997C2×C4C2×C22⋊#692311yescharacteristic
998C2×C4C2×C22⋊#692311yescharacteristic
999C8—2444no—
1000C22—21no—
1001C22—21no—
1002C22—21no—
1003C22—41no—
1004C22—41no—
1005C22—41no—
1006C22—41no—
1007C22—41no—
1008C22—41no—
1009C22—82no—
1010C22—611no—
1011C22—611no—
1012C22—1221no—
1013C22—1221no—
1014C22—1221no—
1015C22—4881no—
1016C22—4881no—
1017C22—4881no—
1018C22—4881no—
1019C22—4882no—
1020C22—2441no—
1021C22—2441no—
1022C22—2441no—
1023C22—2441no—
1024C22—2441no—
1025C22—2441no—
1026C22—2442no—
1027C22—2442no—
1028C22—2441no—
1029C22C22×C22⋊#692311yescharacteristic
1030C4—21no—
1031C4—21no—
1032C4—21no—
1033C4—41no—
1034C4—41no—
1035C4—41no—
1036C4—611no—
1037C4—611no—
1038C4—1221no—
1039C4—1221no—
1040C4—1221no—
1041C4—4884no—
1042C4—2441no—
1043C4—2441no—
1044C4—2441no—
1045C4D61⋊#9911yescharacteristic
1046C4D61⋊#9911yescharacteristic
1047C2—21no—
1048C2—41no—
1049C2—41no—
1050C2—41no—
1051C2—81no—
1052C2—1221no—
1053C2—1221no—
1054C2—4881no—
1055C2—2441no—
1056C2—2441no—
1057C2—2441no—
1058C2C2×D61⋊#9911yescharacteristic
subgroupG/H
centerC4D61⋊#99
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC61×#525C4
socleC2×C61C22×#99
prime radical#21459149C2
cosocleC2×C22⋊D61C24
hypercenter#525#6923
hypocenterC61#33347
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41 ◁ #525

Complements

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

NH ≅ G/Ntype
1. D61⋊#413C2semidirect
2. D61⋊#410C2semidirect
3. #21462082C2semidirect
4. #21462079C2semidirect
5. #21462077C2semidirect
6. #21462075C2semidirect
7. #21462072C2semidirect
8. #21462070C2semidirect
24. #16840665C22semidirect
25. #16840664C22semidirect
26. #16840663C22semidirect
27. #16840662C22semidirect
28. C22×#11758222C4semidirect
33. #16840334C4semidirect
36. #16840327C4semidirect
38. #16840323C4semidirect
40. #16840322C4semidirect
48. #16840269C4semidirect
49. #117×D61C4semidirect
50. C61×#525C4semidirect
92. C22×Dic122C2×C4semidirect
96. C22×C22⋊D61C2×C4semidirect
101. C22×C4×D61C2×C4semidirect
114. #14519761C2×C4semidirect
116. #14519760C2×C4semidirect
121. #14519758C2×C4semidirect
146. #14519747C2×C4semidirect
148. #14519746C2×C4semidirect
153. #14519745C2×C4semidirect
160. #14519736C2×C4semidirect
163. #14519733C2×C4semidirect
164. #14519733C2×C4semidirect
170. C23×C4×C61C2×C4semidirect
172. #123×C61C2×C4semidirect
176. #120×C61C2×C4semidirect
179. #117×C61C2×C4semidirect
561. #525#6923semidirect
580. C61#33347semidirect
613. C23×C4C2×#6923semidirect
640. #123C2×#6923semidirect
676. #120C2×#6923semidirect
694. #117C2×#6923semidirect

Maximal subgroups

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

subgroupindex
D61⋊#4132
D61⋊#4102
#214620822
#214620792
#214620772
#214620752
#214620722
#214620702
#214591492
#3334761