Finite Group Databasebeta

← D61×#2055 #29707944

Subgroups — D61×#2055 #29707944

Order 15616.

1702 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×SD16×D61C211yesmaximal, characteristic
2C2×C4⋊C8×D61C211yesmaximal, characteristic, complemented
3C2×#103×D61C211yesmaximal, characteristic, complemented
4C2×#102×D61C211yesmaximal, characteristic
5#391×D61C211yesmaximal, characteristic, complemented
6#390×D61C211yesmaximal, characteristic
7#21447138C211yesmaximal, characteristic, complemented
8#21447137C211yesmaximal, characteristic, complemented
9#21447136C211yesmaximal, characteristic, complemented
10#21447135C211yesmaximal, characteristic, complemented
11#21447134C211yesmaximal, characteristic, complemented
12#21447133C211yesmaximal, characteristic, complemented
13#21447132C211yesmaximal, characteristic, complemented
14#340×D61C211yesmaximal, characteristic, complemented
15C61×#2055C211yesmaximal, characteristic, complemented
16C22×Q8×D61C2211yescharacteristic
17C22×D4×D61C2211yescharacteristic
18C22×#11758190C2211yescharacteristic
19C22×#11758200C2211yescharacteristic
20C22×#11758201C2211yescharacteristic
21C2×SD16×D61—24no—
22C2×SD16×D61—24no—
23C2×SD16×D61—24no—
24C22×C8×D61C2211yescharacteristic
25C22×C8×D61C2211yescharacteristic
26C2×C4⋊C4×D61C2211yescharacteristic
27C2×C4⋊C4×D61C2211yescharacteristic
28C2×C22⋊C4×D61—21no—
29C2×C22⋊C4×D61—21no—
30C2×C42×D61C2211yescharacteristic
31C2×C4⋊#92418C2211yescharacteristic, complemented
32C2×#14519706C2211yescharacteristic, complemented
33C2×#14519706C2211yescharacteristic, complemented
34C4⋊C8×D61—24no—
35C2×#14519702C2211yescharacteristic, complemented
36C2×#14519701C2211yescharacteristic, complemented
37C2×#14519700C2211yescharacteristic, complemented
38#103×D61—24no—
39C2×#14519699C2211yescharacteristic
40C2×#14519698C2211yescharacteristic
41C2×#14519697C2211yescharacteristic
42#102×D61—24no—
43#16839669C2211yescharacteristic, complemented
44#16839668C2211yescharacteristic, complemented
45#16839667C2211yescharacteristic, complemented
46#16839666—21no—
47#16839666—21no—
48#16839665C2211yescharacteristic
49#16839664C2211yescharacteristic
50#16839663C2211yescharacteristic
51#16839662—21no—
52#16839662—21no—
53#95×D61—21no—
54#95×D61—21no—
55#16839525C2211yescharacteristic, complemented
56#16839524C2211yescharacteristic, complemented
57#16839524C2211yescharacteristic, complemented
58C22×SD16×C61C2211yescharacteristic
59C2×C4⋊C8×C61C2211yescharacteristic, complemented
60C2×#103×C61C2211yescharacteristic, complemented
61C2×#102×C61C2211yescharacteristic
62C61×#391C2211yescharacteristic, complemented
63C61×#390C2211yescharacteristic
64C61×#340C2211yescharacteristic, complemented
65C24×D61—21no—
66C22×Dic122—21no—
67C22×Dic122C2311yescharacteristic
68C2×Q8×D61—22no—
69C2×Q8×D61—22no—
70C2×Q8×D61—22no—
71C2×Q8×D61—22no—
72C2×Q8×D61—22no—
73C2×Q8×D61D414yes—
74C22×D244C2311yescharacteristic
75C22×C22⋊D61—21no—
76C2×D4×D61—22no—
77C2×D4×D61—22no—
78C2×D4×D61—22no—
79C2×D4×D61—22no—
80C2×D4×D61—22no—
81C2×D4×D61D414yes—
82C22×C4×D61—21no—
83C22×C4×D61—21no—
84C22×C4×D61—21no—
85C22×C4×D61D411yescharacteristic
86C22×C4×D61D411yescharacteristic
87C22×C4×D61C2311yescharacteristic
88C2×#11758190—22no—
89C2×#11758190—22no—
90C2×#11758190—22no—
91C2×#11758200—22no—
92C2×#11758200—22no—
93C2×#11758200—22no—
94C2×#11758201—22no—
95C2×#11758201—22no—
96C2×#11758201—22no—
97SD16×D61—232no—
98C22×#92418C2311yescharacteristic
99C22×#92418C2311yescharacteristic
100C2×C8×D61—22no—
101C2×C8×D61—22no—
102C2×C8×D61—22no—
103C2×C8×D61—22no—
104C2×C8×D61—22no—
105C2×C8×D61D414yes—
106C2×C4⋊Dic61C2311yescharacteristic
107C2×C4⋊Dic61C2311yescharacteristic
108C2×#11758196—21no—
109C2×#11758196—21no—
110C4⋊C4×D61—22no—
111C4⋊C4×D61—22no—
112C4⋊C4×D61—22no—
113C4⋊C4×D61—22no—
114C2×C22⋊Dic61—21no—
115C2×C22⋊Dic61—21no—
116C2×#11758198—21no—
117C2×#11758198—21no—
118C2×#11758198—21no—
119C2×#11758198—21no—
120C22⋊C4×D61—44no—
121C22⋊C4×D61—44no—
122C2×C4×Dic61D411yescharacteristic
123C2×C4×Dic61D411yescharacteristic
124C2×C4×Dic61C2311yescharacteristic
125C42×D61—22no—
126C42×D61—22no—
127C4⋊#92418—22no—
128#14519706—22no—
129#14519706—22no—
130#14519702—22no—
131#14519701—22no—
132#14519700—22no—
133#14519699—22no—
134#14519698—22no—
135#14519697—22no—
136#14519684—21no—
137#14519684—21no—
138#14519684—21no—
139#14519684—21no—
140#14519684—21no—
141#14519684—21no—
142C22×Q8×C61C2311yescharacteristic
143C22×D4×C61C2311yescharacteristic
144C2×SD16×C61—22no—
145C2×SD16×C61—22no—
146C2×SD16×C61—22no—
147C22×C8×C61C2311yescharacteristic
148C22×C8×C61C2311yescharacteristic
149C2×C4⋊C4×C61C2311yescharacteristic
150C2×C4⋊C4×C61C2311yescharacteristic
151C2×C22⋊C4×C61—21no—
152C2×C22⋊C4×C61—21no—
153C2×C42×C61C2311yescharacteristic
154C4⋊C8×C61—22no—
155#103×C61—22no—
156#102×C61—22no—
157#95×C61—21no—
158#95×C61—21no—
159C24×C61—21no—
160C23×D61—21no—
161C23×D61—24no—
162C23×D61—42no—
163C23×D61—42no—
164C23×D61—42no—
165C23×D61—42no—
166C23×D61—42no—
167C23×D61—42no—
168C23×D61C2×D411yescharacteristic
169C2×Q8×C61—21no—
170C2×Q8×C61—21no—
171C2×Q8×C61—21no—
172C2×Q8×C61—21no—
173C2×Q8×C61—21no—
174C2×Q8×C61C2×D412yes—
175C2×D4×C61—21no—
176C2×D4×C61—21no—
177C2×D4×C61—21no—
178C2×D4×C61—21no—
179C2×D4×C61—21no—
180C2×D4×C61C2×D412yes—
181C22×C4×C61—21no—
182C22×C4×C61—21no—
183C22×C4×C61—21no—
184C22×C4×C61C2×D411yescharacteristic
185C22×C4×C61C2×D411yescharacteristic
186C22×C4×C61C2411yescharacteristic
187C2×C22⋊D61—24no—
188C2×C22⋊D61—42no—
189C2×C22⋊D61—42no—
190C22×Dic61—21no—
191C22×Dic61—21no—
192C22×Dic61—21no—
193C22×Dic61C2×D411yescharacteristic
194C22×Dic61C2×D411yescharacteristic
195C22×Dic61C2×D411yescharacteristic
196Q8×D61—28no—
197Q8×D61—28no—
198Q8×D61—44no—
199Q8×D61—44no—
200D4×D61—28no—
201D4×D61—28no—
202D4×D61—44no—
203D4×D61—44no—
204C2×D244—21no—
205C2×D244—21no—
206C2×D244—21no—
207C2×D244—21no—
208C2×D244—21no—
209C2×D244C2×D412yes—
210C2×C4×D61—22no—
211C2×C4×D61—22no—
212C2×C4×D61—24no—
213C2×C4×D61—22no—
214C2×C4×D61—22no—
215C2×C4×D61—22no—
216C2×C4×D61—42no—
217C2×C4×D61—42no—
218C2×C4×D61—42no—
219C2×C4×D61—42no—
220C2×C4×D61—42no—
221C2×C4×D61—42no—
222C2×C4×D61—42no—
223C2×C4×D61—42no—
224C2×C4×D61SD1614yescomplemented
225C2×C4×D61C2×D412yes—
226C2×C4×D61C2×D412yes—
227C2×C4×D61C2×D412yes—
228C2×C4×D61#4112yes—
229C2×C4×D61#4112yes—
230C2×C4×D61#4112yes—
231C2×Dic122—21no—
232C2×Dic122—21no—
233C2×Dic122—21no—
234C2×Dic122—21no—
235C2×Dic122—21no—
236C2×Dic122—24no—
237C2×Dic122—42no—
238C2×Dic122—42no—
239C2×Dic122C2×D412yes—
240SD16×C61—28no—
241C2×C8×C61—21no—
242C2×C8×C61—21no—
243C2×C8×C61—21no—
244C2×C8×C61—21no—
245C2×C8×C61—21no—
246C2×C8×C61C2×D412yes—
247C4⋊C4×C61—21no—
248C4⋊C4×C61—21no—
249C4⋊C4×C61—21no—
250C4⋊C4×C61—21no—
251C22⋊C4×C61—42no—
252C22⋊C4×C61—42no—
253C42×C61—21no—
254C42×C61—21no—
255C22⋊Dic61—42no—
256C22⋊Dic61—42no—
257#11758201—28no—
258#11758200—28no—
259#11758198—42no—
260#11758198—42no—
261#11758198—42no—
262#11758198—42no—
263C4⋊Dic61—21no—
264C4⋊Dic61—21no—
265C4⋊Dic61—21no—
266C4⋊Dic61—21no—
267#11758196—42no—
268#11758196—42no—
269C4×Dic61—21no—
270C4×Dic61—21no—
271C4×Dic61—22no—
272C4×Dic61—22no—
273C2×#92418—21no—
274C2×#92418—21no—
275C2×#92418—21no—
276C2×#92418—21no—
277C2×#92418—21no—
278C2×#92418C2×D412yes—
279#11758190—28no—
280C8×D61—28no—
281C8×D61—44no—
282C23×C61—22no—
283C23×C61—41no—
284C23×C61—41no—
285C23×C61—41no—
286C23×C61—41no—
287C23×C61—41no—
288C23×C61—41no—
289C23×C61C22×D411yescharacteristic
290C22×D61—22no—
291C22×D61—41no—
292C22×D61—41no—
293C22×D61—41no—
294C22×D61—41no—
295C22×D61—41no—
296C22×D61—41no—
297C22×D61—48no—
298C22×D61—48no—
299C22×D61—48no—
300C22×D61—84no—
301C22×D61—84no—
302C22×D61—84no—
303C22×D61—84no—
304C22×D61#12112yes—
305C22×D61#12112yes—
306C22×D61#12112yes—
307C22×D61C2×SD1612yes—
308C22×D61#13512yes—
309C22×D61AGL(1,ℤ/8)12yes—
310C22×D61#13712yes—
311Q8×C61—22no—
312Q8×C61—22no—
313Q8×C61—41no—
314Q8×C61—41no—
315D4×C61—22no—
316D4×C61—22no—
317D4×C61—41no—
318D4×C61—41no—
319C2×C4×C61—21no—
320C2×C4×C61—21no—
321C2×C4×C61—21no—
322C2×C4×C61—22no—
323C2×C4×C61—21no—
324C2×C4×C61—21no—
325C2×C4×C61—41no—
326C2×C4×C61—41no—
327C2×C4×C61—41no—
328C2×C4×C61—41no—
329C2×C4×C61—41no—
330C2×C4×C61—41no—
331C2×C4×C61—41no—
332C2×C4×C61—41no—
333C2×C4×C61C2×SD1612yescomplemented
334C2×C4×C61C22×D411yescharacteristic
335C2×C4×C61C22×D411yescharacteristic
336C2×C4×C61C22×D411yescharacteristic
337C2×C4×C61C2×#4111yescharacteristic
338C2×C4×C61C2×#4111yescharacteristic
339C2×C4×C61C2×#4111yescharacteristic
340C22⋊D61—48no—
341C2×Dic61—21no—
342C2×Dic61—21no—
343C2×Dic61—21no—
344C2×Dic61—22no—
345C2×Dic61—21no—
346C2×Dic61—21no—
347C2×Dic61—41no—
348C2×Dic61—41no—
349C2×Dic61—41no—
350C2×Dic61—41no—
351C2×Dic61—41no—
352C2×Dic61—41no—
353C2×Dic61—41no—
354C2×Dic61—41no—
355C2×Dic61#12112yes—
356C2×Dic61#12112yes—
357C2×Dic61#12112yes—
358C2×Dic61C2×SD1612yescomplemented
359D244—22no—
360D244—22no—
361D244—41no—
362D244—41no—
363C4×D61—28no—
364C4×D61—48no—
365C4×D61—44no—
366C4×D61—84no—
367C4×D61—84no—
368C4×D61#12014yes—
369C4×D61#12314yes—
370C4×D61#12314yes—
371C4×D61#12414yes—
372Dic122—22no—
373Dic122—22no—
374Dic122—41no—
375Dic122—41no—
376Dic122—48no—
377C8×C61—22no—
378C8×C61—41no—
379#92418—22no—
380#92418—41no—
381C2×#2055—611nomaximal, Sylow
382C22×C61—42no—
383C22×C61—42no—
384C22×C61—42no—
385C22×C61—81no—
386C22×C61—81no—
387C22×C61—81no—
388C22×C61—81no—
389C22×C61C2×#12111yescharacteristic
390C22×C61C2×#12111yescharacteristic
391C22×C61C2×#12111yescharacteristic
392C22×C61C22×SD1611yescharacteristic
393C22×C61C2×#13511yescharacteristic
394C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
395C22×C61C2×#13711yescharacteristic
396C2×D61—42no—
397C2×D61—42no—
398C2×D61—42no—
399C2×D61—81no—
400C2×D61—81no—
401C2×D61—81no—
402C2×D61—81no—
403C2×D61—816no—
404C2×D61#39414yes—
405C2×D61#46014yes—
406C2×D61#46114yes—
407C2×D61#46314yes—
408C2×D61#46414yes—
409C2×D61#46514yes—
410C2×D61#46814yes—
411C4×C61—22no—
412C4×C61—42no—
413C4×C61—41no—
414C4×C61—81no—
415C4×C61—81no—
416C4×C61C2×#12011yescharacteristic
417C4×C61C2×#12311yescharacteristic
418C4×C61C2×#12311yescharacteristic
419C4×C61C2×#12411yescharacteristic
420Dic61—22no—
421Dic61—42no—
422Dic61—41no—
423Dic61—81no—
424Dic61—81no—
425Dic61#39414yes—
426C23×SD16—611no—
427C22×C4⋊C8—611no—
428C22×#103—611no—
429C22×#102—611no—
430C2×#391—611no—
431C2×#390—611no—
432#2055—611no—
433#2055—611no—
434#2055—611no—
435#2055—611no—
436#2055—611no—
437#2055—611no—
438#2055—611no—
439#2055D6111yescharacteristic, direct product factor
440C2×#340—611no—
441C2×C61—82no—
442C2×C61C2×#39411yescharacteristic
443C2×C61C2×#46111yescharacteristic
444C2×C61C2×#46311yescharacteristic
445C2×C61C2×#46011yescharacteristic
446C2×C61C2×#46411yescharacteristic
447C2×C61C2×#46511yescharacteristic
448C2×C61C2×#46811yescharacteristic
449D61—82no—
450D61#205518yesdirect product factor
451C23×Q8—611no—
452C23×D4—611no—
453C22×SD16—611no—
454C22×SD16—611no—
455C22×SD16—611no—
456C22×SD16—1224no—
457C22×SD16—1224no—
458C22×SD16—1224no—
459C22×SD16C2×D6111yescharacteristic
460C23×C8—611no—
461C23×C8—611no—
462C22×C4⋊C4—611no—
463C22×C4⋊C4—611no—
464C22×C22⋊C4—1221no—
465C22×C22⋊C4—1221no—
466C22×C42—611no—
467C2×C4⋊C8—611no—
468C2×C4⋊C8—611no—
469C2×C4⋊C8—611no—
470C2×C4⋊C8—1224no—
471C2×C4⋊C8C2×D6111yescharacteristic, complemented
472C2×#103—611no—
473C2×#103—611no—
474C2×#103—611no—
475C2×#103—1224no—
476C2×#103C2×D6111yescharacteristic, complemented
477C2×#102—611no—
478C2×#102—611no—
479C2×#102—611no—
480C2×#102—1224no—
481C2×#102C2×D6111yescharacteristic
482#391—611no—
483#391—611no—
484#391—611no—
485#391—1221no—
486#391—1221no—
487#391C2×D6111yescharacteristic, complemented
488#390—611no—
489#390—611no—
490#390—611no—
491#390—1221no—
492#390—1221no—
493#390C2×D6111yescharacteristic
494C2×#95—1221no—
495C2×#95—1221no—
496#340—611no—
497#340—611no—
498#340—611no—
499#340C2×D6111yescharacteristic, complemented
500C61C2×#205511yescharacteristic, complemented, Sylow
501C25—1221no—
502C22×Q8—614no—
503C22×Q8—611no—
504C22×Q8—1221no—
505C22×Q8—1222no—
506C22×Q8—1222no—
507C22×Q8—1222no—
508C22×Q8—1222no—
509C22×Q8—1222no—
510C22×Q8C22×D6111yescharacteristic
511C22×D4—614no—
512C22×D4—611no—
513C22×D4—1222no—
514C22×D4—1222no—
515C22×D4—1222no—
516C22×D4—1222no—
517C22×D4—1222no—
518C22×D4—1221no—
519C22×D4C22×D6111yescharacteristic
520C23×C4—611no—
521C23×C4—611no—
522C23×C4—611no—
523C23×C4—1221no—
524C23×C4—1221no—
525C23×C4—1221no—
526C2×SD16—22no—
527C2×SD16—22no—
528C2×SD16—22no—
529C2×SD16—1222no—
530C2×SD16—1222no—
531C2×SD16—1222no—
532C2×SD16—1222no—
533C2×SD16—12232no—
534C2×SD16—1222no—
535C2×SD16—1222no—
536C2×SD16—1222no—
537C2×SD16—1222no—
538C2×SD16—1222no—
539C22×C8—611no—
540C22×C8—614no—
541C22×C8—611no—
542C22×C8—1222no—
543C22×C8—1222no—
544C22×C8—1222no—
545C22×C8—1222no—
546C22×C8—1222no—
547C22×C8C22×D6111yescharacteristic
548C22×C8C22×D6111yescharacteristic
549C2×C4⋊C4—611no—
550C2×C4⋊C4—611no—
551C2×C4⋊C4—1222no—
552C2×C4⋊C4—1222no—
553C2×C4⋊C4—1222no—
554C2×C4⋊C4—1222no—
555C2×C4⋊C4—1221no—
556C2×C4⋊C4—1221no—
557C2×C4⋊C4C22×D6111yescharacteristic
558C2×C4⋊C4C22×D6111yescharacteristic
559C2×C22⋊C4—21no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4—1221no—
562C2×C22⋊C4—1221no—
563C2×C22⋊C4—1221no—
564C2×C22⋊C4—1221no—
565C2×C22⋊C4—1221no—
566C2×C22⋊C4—1221no—
567C2×C22⋊C4—2444no—
568C2×C22⋊C4—2444no—
569C2×C42—611no—
570C2×C42—611no—
571C2×C42—611no—
572C2×C42—1222no—
573C2×C42—1222no—
574C2×C42C22×D6111yescharacteristic
575C4⋊C8—22no—
576C4⋊C8—1222no—
577C4⋊C8—1222no—
578C4⋊C8—1222no—
579#103—22no—
580#103—1222no—
581#103—1222no—
582#103—1222no—
583#102—22no—
584#102—1222no—
585#102—1222no—
586#102—1222no—
587#95—21no—
588#95—21no—
589#95—1221no—
590#95—1221no—
591#95—1221no—
592#95—1221no—
593#95—1221no—
594#95—1221no—
595C24—21no—
596C24—611no—
597C24—1224no—
598C24—1221no—
599C24—2442no—
600C24—2442no—
601C24—2442no—
602C24—2442no—
603C24—2442no—
604C24—2442no—
605C2×Q8—21no—
606C2×Q8—21no—
607C2×Q8—21no—
608C2×Q8—21no—
609C2×Q8—21no—
610C2×Q8—612no—
611C2×Q8—1224no—
612C2×Q8—1228no—
613C2×Q8—1228no—
614C2×Q8—1221no—
615C2×Q8—1221no—
616C2×Q8—1221no—
617C2×Q8—1221no—
618C2×Q8—1221no—
619C2×Q8—2442no—
620C2×Q8—2442no—
621C2×Q8—2444no—
622C2×Q8—2444no—
623C2×Q8D4×D6112yes—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—612no—
630C2×D4—1228no—
631C2×D4—1228no—
632C2×D4—1224no—
633C2×D4—1221no—
634C2×D4—1221no—
635C2×D4—1221no—
636C2×D4—1221no—
637C2×D4—1221no—
638C2×D4—2444no—
639C2×D4—2444no—
640C2×D4—2442no—
641C2×D4—2442no—
642C2×D4D4×D6112yes—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—611no—
647C22×C4—612no—
648C22×C4—612no—
649C22×C4—612no—
650C22×C4—612no—
651C22×C4—612no—
652C22×C4—612no—
653C22×C4—611no—
654C22×C4—614no—
655C22×C4—611no—
656C22×C4—1222no—
657C22×C4—1222no—
658C22×C4—1222no—
659C22×C4—1222no—
660C22×C4—1222no—
661C22×C4—1224no—
662C22×C4—1221no—
663C22×C4—1221no—
664C22×C4—1221no—
665C22×C4—2442no—
666C22×C4—2442no—
667C22×C4—2442no—
668C22×C4—2442no—
669C22×C4—2442no—
670C22×C4—2442no—
671C22×C4—2442no—
672C22×C4—2442no—
673C22×C4D4×D6111yescharacteristic
674C22×C4D4×D6111yescharacteristic
675C22×C4C23×D6111yescharacteristic
676SD16—28no—
677SD16—1228no—
678SD16—1228no—
679SD16—1228no—
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—612no—
686C2×C8—1228no—
687C2×C8—1221no—
688C2×C8—1221no—
689C2×C8—1221no—
690C2×C8—1221no—
691C2×C8—1221no—
692C2×C8—2444no—
693C2×C8D4×D6112yes—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—1221no—
699C4⋊C4—1221no—
700C4⋊C4—1221no—
701C4⋊C4—1221no—
702C4⋊C4—2442no—
703C4⋊C4—2442no—
704C22⋊C4—42no—
705C22⋊C4—42no—
706C22⋊C4—2442no—
707C22⋊C4—2442no—
708C22⋊C4—2442no—
709C22⋊C4—2442no—
710C22⋊C4—2442no—
711C22⋊C4—2442no—
712C42—21no—
713C42—21no—
714C42—1222no—
715C42—1222no—
716C42—1221no—
717C42—1221no—
718C23—22no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—41no—
725C23—612no—
726C23—612no—
727C23—612no—
728C23—612no—
729C23—612no—
730C23—612no—
731C23—612no—
732C23—1222no—
733C23—4884no—
734C23—4884no—
735C23—4884no—
736C23—4884no—
737C23—2448no—
738C23—2448no—
739C23—2448no—
740C23—2441no—
741C23—2441no—
742C23—2441no—
743C23—2441no—
744C23—2441no—
745C23—2441no—
746C23C2×D4×D6111yescharacteristic
747Q8—22no—
748Q8—22no—
749Q8—41no—
750Q8—41no—
751Q8—1222no—
752Q8—1222no—
753Q8—2448no—
754Q8—2441no—
755Q8—2441no—
756D4—22no—
757D4—22no—
758D4—41no—
759D4—41no—
760D4—1222no—
761D4—1222no—
762D4—2448no—
763D4—2441no—
764D4—2441no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—22no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—612no—
780C2×C4—612no—
781C2×C4—612no—
782C2×C4—614no—
783C2×C4—614no—
784C2×C4—614no—
785C2×C4—614no—
786C2×C4—612no—
787C2×C4—1228no—
788C2×C4—1221no—
789C2×C4—1221no—
790C2×C4—1221no—
791C2×C4—1222no—
792C2×C4—1221no—
793C2×C4—1221no—
794C2×C4—4884no—
795C2×C4—4884no—
796C2×C4—2444no—
797C2×C4—2448no—
798C2×C4—2441no—
799C2×C4—2441no—
800C2×C4—2441no—
801C2×C4—2441no—
802C2×C4—2441no—
803C2×C4—2441no—
804C2×C4—2441no—
805C2×C4—2441no—
806C2×C4SD16×D6112yescomplemented
807C2×C4C2×D4×D6111yescharacteristic
808C2×C4C2×D4×D6111yescharacteristic
809C2×C4C2×D4×D6111yescharacteristic
810C2×C4#41×D6111yescharacteristic
811C2×C4#41×D6111yescharacteristic
812C2×C4#41×D6111yescharacteristic
813C8—22no—
814C8—41no—
815C8—1222no—
816C8—2441no—
817C22—42no—
818C22—42no—
819C22—42no—
820C22—81no—
821C22—81no—
822C22—81no—
823C22—81no—
824C22—614no—
825C22—614no—
826C22—614no—
827C22—614no—
828C22—614no—
829C22—614no—
830C22—614no—
831C22—48816no—
832C22—4881no—
833C22—4881no—
834C22—4881no—
835C22—4881no—
836C22—2442no—
837C22—2442no—
838C22—2442no—
839C22#121×D6111yescharacteristic
840C22#121×D6111yescharacteristic
841C22#121×D6111yescharacteristic
842C22C2×SD16×D6111yescharacteristic
843C22#135×D6111yescharacteristic
844C22AGL(1,ℤ/8)×D6111yescharacteristic
845C22#137×D6111yescharacteristic
846C4—22no—
847C4—41no—
848C4—42no—
849C4—81no—
850C4—81no—
851C4—614no—
852C4—1222no—
853C4—4881no—
854C4—4881no—
855C4—2441no—
856C4—2442no—
857C4#120×D6111yescharacteristic
858C4#123×D6111yescharacteristic
859C4#123×D6111yescharacteristic
860C4#124×D6111yescharacteristic
861C2—82no—
862C2—618no—
863C2—4882no—
864C2#394×D6111yescharacteristic
865C2#461×D6111yescharacteristic
866C2#463×D6111yescharacteristic
867C2#460×D6111yescharacteristic
868C2#464×D6111yescharacteristic
869C2#465×D6111yescharacteristic
870C2#468×D6111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2055C2
socleC23×C61C22×D4
prime radicalC22×D4×D61C22
hypercenter#2055D61
hypocenterC61C2×#2055
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2055

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C8×D61C2semidirect
3. C2×#103×D61C2semidirect
5. #391×D61C2semidirect
7. #21447138C2semidirect
8. #21447137C2semidirect
9. #21447136C2semidirect
10. #21447135C2semidirect
11. #21447134C2semidirect
12. #21447133C2semidirect
13. #21447132C2semidirect
14. #340×D61C2semidirect
15. C61×#2055C2semidirect
31. C2×C4⋊#92418C22semidirect
32. C2×#14519706C22semidirect
33. C2×#14519706C22semidirect
35. C2×#14519702C22semidirect
36. C2×#14519701C22semidirect
37. C2×#14519700C22semidirect
43. #16839669C22semidirect
44. #16839668C22semidirect
45. #16839667C22semidirect
55. #16839525C22semidirect
56. #16839524C22semidirect
57. #16839524C22semidirect
59. C2×C4⋊C8×C61C22semidirect
60. C2×#103×C61C22semidirect
62. C61×#391C22semidirect
64. C61×#340C22semidirect
224. C2×C4×D61SD16semidirect
333. C2×C4×C61C2×SD16semidirect
358. C2×Dic61C2×SD16semidirect
439. #2055D61direct (N × H)
450. D61#2055direct (N × H)
471. C2×C4⋊C8C2×D61semidirect
476. C2×#103C2×D61semidirect
487. #391C2×D61semidirect
499. #340C2×D61semidirect
500. C61C2×#2055semidirect
806. C2×C4SD16×D61semidirect

Maximal subgroups

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

subgroupindex
C22×SD16×D612
C2×C4⋊C8×D612
C2×#103×D612
C2×#102×D612
#391×D612
#390×D612
#214471382
#214471372
#214471362
#214471352
#214471342
#214471332
#214471322
#340×D612
C61×#20552
C2×#205561