Finite Group Databasebeta

← D61⋊#2123 #30623917

Subgroups — D61⋊#2123 #30623917

Order 15616.

1214 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D61⋊#413C211yesmaximal, characteristic
2D61⋊#410C211yesmaximal, characteristic
3#21462083C212yesmaximal, complemented
4#21462082C214yesmaximal, complemented
5#21462081C212yesmaximal, complemented
6D61⋊#352C214yesmaximal, complemented
7#536×D61C211yesmaximal, characteristic
8C2×D61⋊M16—21no—
9C2×#14519856—21no—
10#16840749—21no—
11#16840749C2212yes—
12#16840748—21no—
13#16840748C2212yes—
14D61⋊#101—21no—
15D61⋊#100C2212yes—
16#16840743—21no—
17#16840742C2212yes—
18#16840741—21no—
19#16840741C2212yes—
20D61⋊#99—21no—
21D61⋊#99C2212yes—
22#16840665C2218yescomplemented
23#16840664C2218yescomplemented
24C2×#41×D61C2211yescharacteristic
25C22×Q8×D61C411yescharacteristic, complemented
26#16840338C2211yescharacteristic
27#16840337—21no—
28#16840336C2211yescharacteristic
29#16840335—21no—
30#16840335—21no—
31#16840334C412yescomplemented
32#16840334C2212yes—
33#16840333C411yescharacteristic, complemented
34#16840332—21no—
35C4⋊Q8×D61—21no—
36#124×D61—21no—
37#123×D61C412yescomplemented
38#123×D61C2212yes—
39C22⋊Q8×D61—21no—
40C22⋊Q8×D61—21no—
41#117×D61C411yescharacteristic, complemented
42C61×#536C411yescharacteristic, complemented
43C2×#11758213—41no—
44D61⋊M16—22no—
45D61⋊M16—22no—
46D61⋊M16—41no—
47D61⋊M16—41no—
48C2×#11758217—22no—
49C2×D61⋊C8—41no—
50#14519856—22no—
51#14519856—22no—
52#14519856—41no—
53#14519856—41no—
54C2×C4⋊#6923—41no—
55C2×C22⋊#6923—22no—
56C2×C4×#6923—41no—
57#14519838—22no—
58#14519838—22no—
59#14519837—22no—
60#14519837C2314yes—
61#14519836—22no—
62#14519836—22no—
63#14519835—22no—
64#14519835C2314yes—
65C2×#11758226D411yescharacteristic
66C2×#11758222D411yescharacteristic
67C2×#11758222D411yescharacteristic
68C2×#11758222C2311yescharacteristic
69C2×#11758224C2×C411yescharacteristic
70C2×#11758224D411yescharacteristic
71C2×#11758224C2311yescharacteristic
72#41×D61—41no—
73#41×D61—41no—
74#41×D61—41no—
75#41×D61—41no—
76C22×Dic122C2×C411yescharacteristic, complemented
77C22×Dic122C2×C412yescomplemented
78C2×Q8×D61—21no—
79C2×Q8×D61—21no—
80C2×Q8×D61—21no—
81C2×Q8×D61—21no—
82C2×Q8×D61—41no—
83C2×Q8×D61—41no—
84C2×Q8×D61—41no—
85C2×Q8×D61—41no—
86C2×Q8×D61D411yescharacteristic
87C2×D4×D61C2×C411yescharacteristic
88C2×D4×D61D411yescharacteristic
89C2×D4×D61C2311yescharacteristic
90C22×C4×D61C2×C411yescharacteristic
91C22×C4×D61C2×C412yes—
92C22×C4×D61D411yescharacteristic
93C22×C4×D61D411yescharacteristic
94#14519777—21no—
95#14519776—22no—
96#14519776—22no—
97#14519775—21no—
98#14519775—21no—
99#14519766—21no—
100#14519765—21no—
101#14519764—21no—
102#14519763—22no—
103#14519763—22no—
104#14519762—22no—
105#14519762—22no—
106#14519761C2×C412yescomplemented
107#14519761C2312yes—
108#14519760C2×C412yescomplemented
109#14519760C2312yes—
110#14519759—22no—
111#14519759—22no—
112#14519758C2×C412yes—
113#14519758C2×C412yescomplemented
114#14519757—21no—
115#14519757—21no—
116#14519756—21no—
117#14519756—21no—
118#14519755—22no—
119#14519755—22no—
120#14519754—22no—
121#14519754—22no—
122#14519753—21no—
123#14519753—21no—
124#14519736C2×C411yescharacteristic, complemented
125#14519735—21no—
126#14519734—21no—
127#14519733C2×C412yescomplemented
128C4⋊C4×D61—21no—
129C4⋊C4×D61—22no—
130C4⋊C4×D61—22no—
131C22⋊C4×D61—22no—
132C22⋊C4×D61—22no—
133C22⋊C4×D61C2×C412yes—
134C42×D61—21no—
135C2×#41×C61C2×C411yescharacteristic
136C22×Q8×C61C2×C411yescharacteristic, complemented
137C4⋊Q8×C61—21no—
138#124×C61—21no—
139#123×C61C2×C412yes—
140#123×C61C2×C412yescomplemented
141C22⋊Q8×C61—21no—
142C22⋊Q8×C61—21no—
143#117×C61C2×C411yescharacteristic, complemented
144C23×D61C22⋊C411yescharacteristic
145C23×D61C22×C411yescharacteristic
146C23×D61C2×D411yescharacteristic
147C22×#6923—42no—
148#41×C61—41no—
149#41×C61—41no—
150C2×Q8×C61—21no—
151C2×Q8×C61—21no—
152C2×Q8×C61—41no—
153C2×Q8×C61—41no—
154C2×Q8×C61C22⋊C411yescharacteristic
155C2×D4×C61C22⋊C411yescharacteristic
156C2×D4×C61C22×C411yescharacteristic
157C2×D4×C61C22×C411yescharacteristic
158C22×C4×C61C22⋊C411yescharacteristic
159C22×C4×C61C22⋊C411yescharacteristic
160C22×C4×C61C22×C411yescharacteristic
161C22×C4×C61C22×C412yes—
162C2×C22⋊D61C22⋊C411yescharacteristic
163C2×C22⋊D61C22⋊C411yescharacteristic
164C2×C22⋊D61C22×C411yescharacteristic
165C2×C22⋊D61C2×D411yescharacteristic
166C2×C22⋊D61C2×D411yescharacteristic
167C2×C22⋊D61C2411yescharacteristic
168C22×Dic61C22⋊C411yescharacteristic
169C22×Dic61C22×C411yescharacteristic
170C22×Dic61C22×C412yes—
171C22×Dic61C2×D411yescharacteristic
172#11758226—41no—
173#11758226—41no—
174Q8×D61—41no—
175Q8×D61—41no—
176Q8×D61—42no—
177Q8×D61—42no—
178Q8×D61—42no—
179Q8×D61—42no—
180Q8×D61—42no—
181Q8×D61—42no—
182Q8×D61—41no—
183Q8×D61—41no—
184Q8×D61—41no—
185Q8×D61—41no—
186#11758224—41no—
187#11758224—41no—
188#11758224—41no—
189#11758224—41no—
190#11758224—41no—
191#11758224—41no—
192D4×D61—41no—
193D4×D61—41no—
194D4×D61—41no—
195D4×D61—41no—
196D4×D61—41no—
197D4×D61—41no—
198#11758222—41no—
199#11758222—41no—
200#11758222—41no—
201#11758222—41no—
202#11758222—41no—
203#11758222—41no—
204C2×D244C22⋊C411yescharacteristic
205C2×D244C2×D411yescharacteristic
206C2×D244C2×D411yescharacteristic
207C2×C4×D61—21no—
208C2×C4×D61—21no—
209C2×C4×D61—21no—
210C2×C4×D61—21no—
211C2×C4×D61—21no—
212C2×C4×D61—21no—
213C2×C4×D61—21no—
214C2×C4×D61—21no—
215C2×C4×D61—21no—
216C2×C4×D61—21no—
217C2×C4×D61—21no—
218C2×C4×D61—21no—
219C2×C4×D61—22no—
220C2×C4×D61—22no—
221C2×C4×D61—22no—
222C2×C4×D61—42no—
223C2×C4×D61—42no—
224C2×C4×D61C22⋊C411yescharacteristic
225C2×C4×D61C22⋊C411yescharacteristic
226C2×C4×D61C22⋊C411yescharacteristic
227C2×C4×D61C22⋊C411yescharacteristic
228C2×C4×D61C22⋊C411yescharacteristic
229C2×C4×D61C22⋊C411yescharacteristic
230C2×C4×D61C2×D411yescharacteristic
231C2×C4×D61C2×D411yescharacteristic
232C2×C4×D61C2×D411yescharacteristic
233C2×C4×D61C2×D411yescharacteristic
234C2×Dic122—21no—
235C2×Dic122—21no—
236C2×Dic122—22no—
237C2×Dic122—22no—
238C2×Dic122—42no—
239C2×Dic122—42no—
240C2×Dic122—41no—
241C2×Dic122—41no—
242C2×Dic122C22⋊C411yescharacteristic
243C2×Dic122C2×D411yescharacteristic
244C2×Dic122C2×D411yescharacteristic
245C22⋊#6923—24no—
246C22⋊#6923—42no—
247#11758217—24no—
248#11758217—42no—
249C2×#92420—42no—
250C4⋊#6923—42no—
251C4⋊#6923—42no—
252C4×#6923—42no—
253C4×#6923—42no—
254#11758213—42no—
255#11758213—42no—
256D61⋊C8—42no—
257D61⋊C8—42no—
258C4⋊C4×C61—21no—
259C4⋊C4×C61—22no—
260C4⋊C4×C61—22no—
261C22⋊C4×C61—22no—
262C22⋊C4×C61—22no—
263C22⋊C4×C61C22×C412yes—
264C42×C61—21no—
265C22⋊Dic61—22no—
266C22⋊Dic61—22no—
267C22⋊Dic61C22×C412yes—
268#11758198—22no—
269#11758198—22no—
270#11758198—22no—
271#11758198—22no—
272#11758198—22no—
273C4⋊Dic61—21no—
274C4⋊Dic61—22no—
275C4⋊Dic61—22no—
276#11758196—22no—
277#11758196—22no—
278#11758196—22no—
279#11758196—22no—
280#11758196—22no—
281C4×Dic61—21no—
282C4×Dic61—22no—
283C23×C61C2×C22⋊C411yescharacteristic
284C23×C61C2×C22⋊C411yescharacteristic
285C23×C61C23×C411yescharacteristic
286C22×D61—21no—
287C22×D61—21no—
288C22×D61—21no—
289C22×D61—21no—
290C22×D61—21no—
291C22×D61—21no—
292C22×D61—42no—
293C22×D61—42no—
294C22×D61—42no—
295C22×D61C2×C22⋊C411yescharacteristic
296C22×D61C2×C22⋊C411yescharacteristic
297C22×D61C2×C22⋊C411yescharacteristic
298C22×D61C22×D411yescharacteristic
299C2×#6923—44no—
300C2×#6923—84no—
301Q8×C61—41no—
302Q8×C61—42no—
303Q8×C61—41no—
304Q8×C61—41no—
305D4×C61—41no—
306D4×C61—41no—
307D4×C61—41no—
308C2×C4×C61—21no—
309C2×C4×C61—21no—
310C2×C4×C61—21no—
311C2×C4×C61—21no—
312C2×C4×C61—21no—
313C2×C4×C61—21no—
314C2×C4×C61—22no—
315C2×C4×C61—22no—
316C2×C4×C61—42no—
317C2×C4×C61C2×C22⋊C411yescharacteristic
318C2×C4×C61C2×C22⋊C411yescharacteristic
319C2×C4×C61C2×C22⋊C411yescharacteristic
320C2×C4×C61C2×C22⋊C411yescharacteristic
321C22⋊D61—41no—
322C22⋊D61—41no—
323C22⋊D61—41no—
324C22⋊D61—41no—
325C22⋊D61—41no—
326C22⋊D61—41no—
327C2×Dic61—21no—
328C2×Dic61—21no—
329C2×Dic61—21no—
330C2×Dic61—21no—
331C2×Dic61—21no—
332C2×Dic61—21no—
333C2×Dic61—22no—
334C2×Dic61—22no—
335C2×Dic61—42no—
336C2×Dic61C2×C22⋊C411yescharacteristic
337C2×Dic61C2×C22⋊C411yescharacteristic
338C2×Dic61C2×C22⋊C411yescharacteristic
339C2×Dic61C22×D411yescharacteristic
340D244—41no—
341D244—41no—
342D244—41no—
343C4×D61—21no—
344C4×D61—21no—
345C4×D61—21no—
346C4×D61—21no—
347C4×D61—21no—
348C4×D61—21no—
349C4×D61—21no—
350C4×D61—21no—
351C4×D61—21no—
352C4×D61—21no—
353C4×D61—21no—
354C4×D61—21no—
355C4×D61—21no—
356C4×D61—21no—
357C4×D61—21no—
358C4×D61—21no—
359C4×D61—21no—
360C4×D61—21no—
361C4×D61—44no—
362C4×D61—44no—
363C4×D61—42no—
364C4×D61—42no—
365C4×D61#9911yescharacteristic
366C4×D61#9911yescharacteristic
367C4×D61#9911yescharacteristic
368C4×D61#9911yescharacteristic
369Dic122—41no—
370Dic122—41no—
371Dic122—41no—
372Dic122—44no—
373Dic122—42no—
374Dic122—41no—
375Dic122—41no—
376Dic122—42no—
377Dic122—42no—
378#92420—44no—
379C2×#2123—611nomaximal, Sylow
380C22×C61—21no—
381C22×C61—21no—
382C22×C61—21no—
383C22×C61—41no—
384C22×C61—41no—
385C22×C61—41no—
386C22×C61C22×C22⋊C411yescharacteristic
387C2×D61—22no—
388C2×D61—21no—
389C2×D61—21no—
390C2×D61—21no—
391C2×D61—42no—
392C2×D61—42no—
393C2×D61—42no—
394C2×D61—42no—
395C2×D61—41no—
396C2×D61—41no—
397C2×D61—41no—
398C2×D61—81no—
399C2×D61—81no—
400C2×D61C2×#9911yescharacteristic
401C2×D61C2×#9911yescharacteristic
402#6923—84no—
403C4×C61—21no—
404C4×C61—21no—
405C4×C61—21no—
406C4×C61—42no—
407C4×C61—42no—
408C4×C61C2×#9911yescharacteristic
409C4×C61C2×#9911yescharacteristic
410Dic61—21no—
411Dic61—21no—
412Dic61—21no—
413Dic61—42no—
414Dic61—42no—
415Dic61C2×#9911yescharacteristic
416Dic61C2×#9911yescharacteristic
417C2×#536—611no—
418C2×#413—611no—
419C2×#410—611no—
420#2123—612no—
421#2123—614no—
422#2123—612no—
423C2×#352—614no—
424C2×C61—21no—
425C2×C61—41no—
426C2×C61—41no—
427C2×C61—41no—
428C2×C61C22×#9911yescharacteristic
429D61—21no—
430D61—41no—
431D61—41no—
432D61—41no—
433D61#212312yescomplemented
434C22×#41—611no—
435C23×Q8—611no—
436C22×M16—1221no—
437#536—611no—
438#536—611no—
439#536—612no—
440#536—612no—
441#536—611no—
442#536—1221no—
443#536—1221no—
444#536—1221no—
445#536—1221no—
446#536#692311yescharacteristic, complemented
447C2×C4⋊Q8—1221no—
448C2×#124—1221no—
449C2×#123—612no—
450C2×#123—612no—
451C2×C22⋊Q8—1221no—
452C2×C22⋊Q8—1221no—
453C2×#117—611no—
454C2×#117—1221no—
455#413—612no—
456#413—612no—
457#413—1221no—
458#413—1221no—
459C2×#101—1221no—
460C2×#100—612no—
461#410—612no—
462#410—612no—
463#410—1221no—
464#410—1221no—
465C2×#99—612no—
466C2×#99—1221no—
467#352—618no—
468#352—618no—
469C61C2×#212311yescharacteristic, complemented, Sylow
470C2×#41—611no—
471C2×#41—611no—
472C2×#41—611no—
473C2×#41—611no—
474C2×#41—611no—
475C2×#41—611no—
476C2×#41—611no—
477C2×#41—2441no—
478C2×#41—2441no—
479C2×#41—2441no—
480C2×#41—2441no—
481C2×#41C2×#692311yescharacteristic
482C22×Q8—611no—
483C22×Q8—612no—
484C22×Q8—611no—
485C22×Q8—1221no—
486C22×Q8—1221no—
487C22×Q8—1221no—
488C22×Q8—1221no—
489C22×Q8—2441no—
490C22×Q8—2441no—
491C22×Q8—2441no—
492C22×Q8—2441no—
493C22×Q8C2×#692311yescharacteristic, complemented
494C22×D4—611no—
495C22×D4—611no—
496C22×D4—611no—
497C23×C4—611no—
498C23×C4—611no—
499C23×C4—611no—
500C23×C4—612no—
501C2×M16—1222no—
502C2×M16—1222no—
503C2×M16—1222no—
504C2×M16—2441no—
505C2×M16—2441no—
506C2×M16—2441no—
507C22×C8—2441no—
508C4⋊Q8—21no—
509C4⋊Q8—1221no—
510C4⋊Q8—1222no—
511C4⋊Q8—1222no—
512C4⋊Q8—1221no—
513C4⋊Q8—1221no—
514#124—21no—
515#124—1221no—
516#124—1222no—
517#124—1222no—
518#124—1221no—
519#124—1221no—
520#123—612no—
521#123—612no—
522#123—612no—
523#123—612no—
524#123—612no—
525#123—612no—
526#123—1222no—
527#123—1222no—
528#123—1222no—
529#123—1222no—
530#123C2×#692312yes—
531#123C2×#692312yescomplemented
532C22⋊Q8—21no—
533C22⋊Q8—21no—
534C22⋊Q8—1222no—
535C22⋊Q8—1222no—
536C22⋊Q8—1222no—
537C22⋊Q8—1222no—
538C22⋊Q8—1221no—
539C22⋊Q8—1221no—
540C22⋊Q8—1221no—
541C22⋊Q8—1221no—
542C22⋊Q8—1221no—
543C22⋊Q8—1221no—
544#117—611no—
545#117—612no—
546#117—1221no—
547#117—1221no—
548#117—1222no—
549#117—1222no—
550#117—2441no—
551#117—2441no—
552#117C2×#692311yescharacteristic, complemented
553C2×C4⋊C4—1221no—
554C2×C4⋊C4—1222no—
555C2×C4⋊C4—1222no—
556C2×C4⋊C4—2441no—
557C2×C22⋊C4—612no—
558C2×C22⋊C4—1222no—
559C2×C22⋊C4—1222no—
560C2×C22⋊C4—1222no—
561C2×C42—1221no—
562C2×C42—2441no—
563#101—1222no—
564#101—1222no—
565#100—614no—
566#100—1222no—
567#99—614no—
568#99—1222no—
569#99—1222no—
570#99—1222no—
571C24—611no—
572C24—611no—
573C24—611no—
574#41—41no—
575#41—41no—
576#41—2441no—
577#41—2441no—
578#41—2441no—
579#41—2441no—
580#41—2441no—
581#41—2441no—
582#41—2441no—
583#41—2441no—
584#41—2441no—
585#41—2441no—
586#41—2441no—
587#41—2441no—
588#41—2441no—
589#41—2441no—
590C2×Q8—21no—
591C2×Q8—21no—
592C2×Q8—41no—
593C2×Q8—41no—
594C2×Q8—611no—
595C2×Q8—611no—
596C2×Q8—611no—
597C2×Q8—1222no—
598C2×Q8—1222no—
599C2×Q8—1221no—
600C2×Q8—1221no—
601C2×Q8—2441no—
602C2×Q8—2441no—
603C2×Q8—2442no—
604C2×Q8—2442no—
605C2×Q8—2441no—
606C2×Q8—2441no—
607C2×Q8—2441no—
608C2×Q8—2441no—
609C2×Q8—2441no—
610C2×Q8—2441no—
611C2×Q8—2442no—
612C2×Q8—2442no—
613C2×Q8—2442no—
614C2×Q8—2442no—
615C2×Q8—2442no—
616C2×Q8—2442no—
617C2×Q8C22⋊#692311yescharacteristic
618C2×D4—611no—
619C2×D4—611no—
620C2×D4—611no—
621C2×D4—611no—
622C2×D4—611no—
623C2×D4—611no—
624C2×D4—611no—
625C2×D4—611no—
626C2×D4—611no—
627C2×D4—2441no—
628C2×D4—2441no—
629C2×D4—2441no—
630C2×D4—2441no—
631C2×D4—2441no—
632C2×D4—2441no—
633C2×D4C22⋊#692311yescharacteristic
634C2×D4C22×#692311yescharacteristic
635C2×D4C22×#692311yescharacteristic
636C22×C4—611no—
637C22×C4—611no—
638C22×C4—611no—
639C22×C4—611no—
640C22×C4—611no—
641C22×C4—611no—
642C22×C4—611no—
643C22×C4—611no—
644C22×C4—611no—
645C22×C4—611no—
646C22×C4—611no—
647C22×C4—611no—
648C22×C4—611no—
649C22×C4—612no—
650C22×C4—1221no—
651C22×C4—1221no—
652C22×C4—1221no—
653C22×C4—1221no—
654C22×C4—1221no—
655C22×C4—1221no—
656C22×C4—1221no—
657C22×C4—1221no—
658C22×C4—1221no—
659C22×C4—1221no—
660C22×C4—1221no—
661C22×C4—1221no—
662C22×C4—1222no—
663C22×C4—1222no—
664C22×C4—1222no—
665C22×C4—2442no—
666C22×C4—2442no—
667C22×C4—2442no—
668C22×C4C22⋊#692311yescharacteristic
669C22×C4C22⋊#692311yescharacteristic
670C22×C4C22×#692311yescharacteristic
671C22×C4C22×#692312yes—
672M16—1224no—
673M16—2442no—
674M16—2442no—
675M16—2442no—
676C2×C8—2442no—
677C2×C8—2442no—
678C2×C8—2442no—
679C4⋊C4—22no—
680C4⋊C4—22no—
681C4⋊C4—21no—
682C4⋊C4—1222no—
683C4⋊C4—1222no—
684C4⋊C4—1222no—
685C4⋊C4—1222no—
686C4⋊C4—1222no—
687C4⋊C4—1222no—
688C4⋊C4—1222no—
689C4⋊C4—1221no—
690C4⋊C4—2442no—
691C4⋊C4—2442no—
692C22⋊C4—22no—
693C22⋊C4—22no—
694C22⋊C4—612no—
695C22⋊C4—1222no—
696C22⋊C4—1222no—
697C22⋊C4—1222no—
698C22⋊C4—1222no—
699C22⋊C4—1222no—
700C22⋊C4—1222no—
701C22⋊C4—1222no—
702C22⋊C4—1224no—
703C22⋊C4—2442no—
704C22⋊C4C22×#692312yes—
705C42—21no—
706C42—1222no—
707C42—1221no—
708C42—2442no—
709C42—2442no—
710C23—611no—
711C23—611no—
712C23—611no—
713C23—611no—
714C23—1221no—
715C23—1221no—
716C23—1221no—
717C23—1221no—
718C23—1221no—
719C23—1221no—
720C23—2442no—
721C23—2442no—
722C23—2442no—
723C23C2×C22⋊#692311yescharacteristic
724C23C2×C22⋊#692311yescharacteristic
725C23C23×#692311yescharacteristic
726Q8—41no—
727Q8—42no—
728Q8—41no—
729Q8—41no—
730Q8—2441no—
731Q8—2441no—
732Q8—2441no—
733Q8—2442no—
734Q8—2442no—
735Q8—2442no—
736Q8—2444no—
737Q8—2441no—
738Q8—2441no—
739D4—41no—
740D4—41no—
741D4—41no—
742D4—2441no—
743D4—2441no—
744D4—2441no—
745D4—2441no—
746D4—2441no—
747D4—2441no—
748D4—2441no—
749D4—2441no—
750D4—2441no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—42no—
760C2×C4—611no—
761C2×C4—611no—
762C2×C4—611no—
763C2×C4—611no—
764C2×C4—611no—
765C2×C4—611no—
766C2×C4—611no—
767C2×C4—611no—
768C2×C4—1221no—
769C2×C4—1221no—
770C2×C4—1221no—
771C2×C4—1221no—
772C2×C4—1221no—
773C2×C4—1221no—
774C2×C4—1221no—
775C2×C4—1221no—
776C2×C4—1221no—
777C2×C4—1221no—
778C2×C4—1221no—
779C2×C4—1221no—
780C2×C4—1221no—
781C2×C4—1221no—
782C2×C4—1221no—
783C2×C4—1221no—
784C2×C4—1221no—
785C2×C4—1221no—
786C2×C4—1221no—
787C2×C4—1221no—
788C2×C4—1221no—
789C2×C4—1221no—
790C2×C4—1221no—
791C2×C4—1221no—
792C2×C4—1222no—
793C2×C4—1222no—
794C2×C4—4884no—
795C2×C4—2442no—
796C2×C4—2442no—
797C2×C4—2444no—
798C2×C4—2444no—
799C2×C4—2444no—
800C2×C4—2442no—
801C2×C4C2×C22⋊#692311yescharacteristic
802C2×C4C2×C22⋊#692311yescharacteristic
803C2×C4C2×C22⋊#692311yescharacteristic
804C2×C4C2×C22⋊#692311yescharacteristic
805C8—2444no—
806C22—21no—
807C22—21no—
808C22—21no—
809C22—41no—
810C22—41no—
811C22—41no—
812C22—611no—
813C22—611no—
814C22—1222no—
815C22—1221no—
816C22—1221no—
817C22—1221no—
818C22—4881no—
819C22—4881no—
820C22—2441no—
821C22—2441no—
822C22—2441no—
823C22—2442no—
824C22—2442no—
825C22—2442no—
826C22—2442no—
827C22C22×C22⋊#692311yescharacteristic
828C4—21no—
829C4—21no—
830C4—21no—
831C4—42no—
832C4—42no—
833C4—611no—
834C4—611no—
835C4—1221no—
836C4—1221no—
837C4—1221no—
838C4—4884no—
839C4—2442no—
840C4—2442no—
841C4D61⋊#9911yescharacteristic
842C4D61⋊#9911yescharacteristic
843C2—21no—
844C2—41no—
845C2—41no—
846C2—41no—
847C2—612no—
848C2—1221no—
849C2—2441no—
850C2—2441no—
851C2—2441no—
852C2C2×D61⋊#9911yescharacteristic
subgroupG/H
centerC2C2×D61⋊#99
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC61×#536C4
socleC2×C61C22×#99
prime radicalC2×#41×D61C22
cosocleC2×C22⋊D61C24
hypercenter#536#6923
hypocenterC61C2×#2123
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #536

Complements

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

NH ≅ G/Ntype
3. #21462083C2semidirect
4. #21462082C2semidirect
5. #21462081C2semidirect
6. D61⋊#352C2semidirect
22. #16840665C22semidirect
23. #16840664C22semidirect
25. C22×Q8×D61C4semidirect
31. #16840334C4semidirect
33. #16840333C4semidirect
37. #123×D61C4semidirect
41. #117×D61C4semidirect
42. C61×#536C4semidirect
76. C22×Dic122C2×C4semidirect
77. C22×Dic122C2×C4semidirect
106. #14519761C2×C4semidirect
108. #14519760C2×C4semidirect
113. #14519758C2×C4semidirect
124. #14519736C2×C4semidirect
127. #14519733C2×C4semidirect
136. C22×Q8×C61C2×C4semidirect
140. #123×C61C2×C4semidirect
143. #117×C61C2×C4semidirect
433. D61#2123semidirect
446. #536#6923semidirect
469. C61C2×#2123semidirect
493. C22×Q8C2×#6923semidirect
531. #123C2×#6923semidirect
552. #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
#214620832
#214620822
#214620812
D61⋊#3522
#536×D612
C2×#212361