Finite Group Databasebeta

← D61×#2033 #29707457

Subgroups — D61×#2033 #29707457

Order 15616.

2006 conjugacy classes of subgroups.

The subgroup lattice has 978 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#121×D61C211yesmaximal, characteristic
2C2×#107×D61C211yesmaximal, characteristic, complemented
3C2×#102×D61C211yesmaximal, characteristic, complemented
4C2×#102×D61C211yesmaximal, characteristic, complemented
5C2×C22⋊C8×D61C211yesmaximal, characteristic, complemented
6#380×D61C211yesmaximal, characteristic, complemented
7#21447004C211yesmaximal, characteristic, complemented
8#21447003C211yesmaximal, characteristic, complemented
9#21447002C211yesmaximal, characteristic, complemented
10#21447001C211yesmaximal, characteristic, complemented
11#21447000C211yesmaximal, characteristic, complemented
12#21446999C211yesmaximal, characteristic, complemented
13#21446998C211yesmaximal, characteristic, complemented
14#340×D61C211yesmaximal, characteristic, complemented
15C61×#2033C211yesmaximal, characteristic, complemented
16C22×D4×D61—21no—
17C22×D4×D61C2211yescharacteristic
18C23×C4×D61C2211yescharacteristic
19C22×C8×D61C2211yescharacteristic
20C22×C8×D61C2211yescharacteristic
21C2×#14519752C2211yescharacteristic
22C2×#14519751C2211yescharacteristic
23C2×#14519750—21no—
24C2×#14519749—21no—
25C2×#14519748C2211yescharacteristic
26#121×D61—24no—
27#121×D61—24no—
28C2×C4⋊C4×D61C2211yescharacteristic
29C2×C4⋊C4×D61C2211yescharacteristic
30C2×C4⋊C4×D61C2211yescharacteristic
31C2×C22⋊C4×D61—21no—
32C2×C22⋊C4×D61—21no—
33C2×#14519711C2211yescharacteristic, complemented
34C2×#14519710C2211yescharacteristic, complemented
35C2×#14519710C2211yescharacteristic, complemented
36#107×D61—24no—
37C2×#14519699C2211yescharacteristic, complemented
38C2×#14519699C2211yescharacteristic, complemented
39C2×#14519698C2211yescharacteristic, complemented
40C2×#14519698C2211yescharacteristic, complemented
41C2×#14519697C2211yescharacteristic, complemented
42C2×#14519697C2211yescharacteristic, complemented
43#102×D61—24no—
44#102×D61—24no—
45C2×C22⋊#92418C2211yescharacteristic, complemented
46C2×#14519689C2211yescharacteristic, complemented
47C2×#14519689C2211yescharacteristic, complemented
48C22⋊C8×D61—24no—
49#16839622C2211yescharacteristic, complemented
50#16839621—21no—
51#16839620—21no—
52#16839619C2211yescharacteristic, complemented
53#16839619C2211yescharacteristic, complemented
54#95×D61—21no—
55#16839525C2211yescharacteristic, complemented
56#16839524C2211yescharacteristic, complemented
57#16839524C2211yescharacteristic, complemented
58C2×#121×C61C2211yescharacteristic
59C2×#107×C61C2211yescharacteristic, complemented
60C2×#102×C61C2211yescharacteristic, complemented
61C2×#102×C61C2211yescharacteristic, complemented
62C2×C22⋊C8×C61C2211yescharacteristic, complemented
63C61×#380C2211yescharacteristic, complemented
64C61×#340C2211yescharacteristic, complemented
65C24×D61—21no—
66C24×D61D411yescharacteristic
67C22×D244—21no—
68C22×D244C2311yescharacteristic
69C22×C22⋊D61—21no—
70C22×C22⋊D61—21no—
71C22×C22⋊D61—21no—
72C2×D4×D61—28no—
73C2×D4×D61—22no—
74C2×D4×D61—22no—
75C2×D4×D61—22no—
76C2×D4×D61—22no—
77C2×D4×D61—22no—
78C2×D4×D61—44no—
79C2×D4×D61—44no—
80C2×D4×D61D414yes—
81C23×Dic61D411yescharacteristic
82C22×C4×D61—21no—
83C22×C4×D61—22no—
84C22×C4×D61—22no—
85C22×C4×D61—22no—
86C22×C4×D61—22no—
87C22×C4×D61—22no—
88C22×C4×D61—22no—
89C22×C4×D61—21no—
90C22×C4×D61—21no—
91C22×C4×D61D411yescharacteristic
92C22×C4×D61D411yescharacteristic
93C22×C4×D61C2311yescharacteristic
94C22×C4×D61C2311yescharacteristic
95C22×#92418C2311yescharacteristic
96C22×#92418C2311yescharacteristic
97C2×C8×D61—22no—
98C2×C8×D61—22no—
99C2×C8×D61—22no—
100C2×C8×D61—22no—
101C2×C8×D61—22no—
102C2×C8×D61D414yescomplemented
103#14519752—22no—
104#14519752—22no—
105#14519751—22no—
106#14519751—22no—
107#14519750—28no—
108#14519749—28no—
109#14519748—22no—
110#14519748—22no—
111C2×C4⋊Dic61C2311yescharacteristic
112C2×C4⋊Dic61C2311yescharacteristic
113C2×C4⋊Dic61C2311yescharacteristic
114C2×#11758196—21no—
115C2×#11758196—21no—
116C2×#11758196—21no—
117C4⋊C4×D61—22no—
118C4⋊C4×D61—22no—
119C4⋊C4×D61—22no—
120C4⋊C4×D61—22no—
121C4⋊C4×D61—22no—
122C4⋊C4×D61D414yes—
123C2×C22⋊Dic61—21no—
124C2×C22⋊Dic61—21no—
125C2×#11758198—21no—
126C2×#11758198—21no—
127C2×#11758198—21no—
128C2×#11758198—21no—
129C22⋊C4×D61—28no—
130C22⋊C4×D61—44no—
131#14519711—22no—
132#14519710—22no—
133#14519710—22no—
134#14519699—22no—
135#14519699—22no—
136#14519698—22no—
137#14519698—22no—
138#14519697—22no—
139#14519697—22no—
140C22⋊#92418—22no—
141#14519689—22no—
142#14519689—22no—
143#14519684—21no—
144#14519684—21no—
145#14519684—21no—
146C22×D4×C61—21no—
147C22×D4×C61C2311yescharacteristic
148C23×C4×C61C2311yescharacteristic
149C22×C8×C61C2311yescharacteristic
150C22×C8×C61C2311yescharacteristic
151#121×C61—22no—
152#121×C61—22no—
153C2×C4⋊C4×C61C2311yescharacteristic
154C2×C4⋊C4×C61C2311yescharacteristic
155C2×C4⋊C4×C61C2311yescharacteristic
156C2×C22⋊C4×C61—21no—
157C2×C22⋊C4×C61—21no—
158#107×C61—22no—
159#102×C61—22no—
160#102×C61—22no—
161C22⋊C8×C61—22no—
162#95×C61—21no—
163C24×C61—21no—
164C24×C61C2×D411yescharacteristic
165C23×D61—22no—
166C23×D61—22no—
167C23×D61—22no—
168C23×D61—22no—
169C23×D61—22no—
170C23×D61—22no—
171C23×D61—21no—
172C23×D61—24no—
173C23×D61—42no—
174C23×D61—42no—
175C23×D61—42no—
176C23×D61—42no—
177C23×D61—42no—
178C23×D61—42no—
179C23×D61D814yes—
180C23×D61C2×D411yescharacteristic
181C23×D61C2×D411yescharacteristic
182C2×D4×C61—24no—
183C2×D4×C61—21no—
184C2×D4×C61—21no—
185C2×D4×C61—21no—
186C2×D4×C61—21no—
187C2×D4×C61—21no—
188C2×D4×C61—42no—
189C2×D4×C61—42no—
190C2×D4×C61C2×D412yes—
191C22×C4×C61—21no—
192C22×C4×C61—21no—
193C22×C4×C61—21no—
194C22×C4×C61—21no—
195C22×C4×C61—21no—
196C22×C4×C61—21no—
197C22×C4×C61—21no—
198C22×C4×C61—21no—
199C22×C4×C61—21no—
200C22×C4×C61C2×D411yescharacteristic
201C22×C4×C61C2411yescharacteristic
202C2×C22⋊D61—24no—
203C2×C22⋊D61—24no—
204C2×C22⋊D61—24no—
205C2×C22⋊D61—42no—
206C2×C22⋊D61—42no—
207C2×C22⋊D61—42no—
208C2×C22⋊D61—42no—
209C2×C22⋊D61—42no—
210C2×C22⋊D61—42no—
211C22×Dic61—21no—
212C22×Dic61—22no—
213C22×Dic61—22no—
214C22×Dic61—22no—
215C22×Dic61—21no—
216C22×Dic61—21no—
217C22×Dic61C2×D411yescharacteristic
218C22×Dic61C2×D411yescharacteristic
219D4×D61—28no—
220D4×D61—28no—
221D4×D61—432no—
222D4×D61—44no—
223D4×D61—44no—
224C2×D244—21no—
225C2×D244—21no—
226C2×D244—21no—
227C2×D244—21no—
228C2×D244—24no—
229C2×D244—21no—
230C2×D244—42no—
231C2×D244—42no—
232C2×D244C2×D412yes—
233C2×C4×D61—22no—
234C2×C4×D61—24no—
235C2×C4×D61—22no—
236C2×C4×D61—22no—
237C2×C4×D61—21no—
238C2×C4×D61—21no—
239C2×C4×D61—21no—
240C2×C4×D61—21no—
241C2×C4×D61—21no—
242C2×C4×D61—21no—
243C2×C4×D61—22no—
244C2×C4×D61—22no—
245C2×C4×D61—22no—
246C2×C4×D61—42no—
247C2×C4×D61—42no—
248C2×C4×D61—44no—
249C2×C4×D61—44no—
250C2×C4×D61—44no—
251C2×C4×D61—44no—
252C2×C4×D61—42no—
253C2×C4×D61—42no—
254C2×C4×D61—42no—
255C2×C4×D61—42no—
256C2×C4×D61—42no—
257C2×C4×D61—42no—
258C2×C4×D61C2×D412yes—
259C2×C4×D61C2×D412yes—
260C2×C4×D61C2×D412yes—
261C2×C4×D61#4112yes—
262C2×C4×D61#4112yes—
263C2×C4×D61#4112yes—
264C2×C8×C61—21no—
265C2×C8×C61—21no—
266C2×C8×C61—21no—
267C2×C8×C61—21no—
268C2×C8×C61—21no—
269C2×C8×C61C2×D412yescomplemented
270C4⋊C4×C61—21no—
271C4⋊C4×C61—21no—
272C4⋊C4×C61—21no—
273C4⋊C4×C61—21no—
274C4⋊C4×C61—21no—
275C4⋊C4×C61C2×D412yes—
276C22⋊C4×C61—24no—
277C22⋊C4×C61—42no—
278C22⋊Dic61—24no—
279C22⋊Dic61—42no—
280#11758198—24no—
281#11758198—24no—
282#11758198—42no—
283#11758198—42no—
284C4⋊Dic61—21no—
285C4⋊Dic61—21no—
286C4⋊Dic61—21no—
287C4⋊Dic61—21no—
288C4⋊Dic61—21no—
289C4⋊Dic61C2×D412yes—
290#11758196—24no—
291#11758196—42no—
292#11758196—42no—
293C2×#92418—21no—
294C2×#92418—21no—
295C2×#92418—21no—
296C2×#92418—21no—
297C2×#92418—21no—
298C2×#92418C2×D412yescomplemented
299C8×D61—28no—
300C8×D61—44no—
301C23×C61—21no—
302C23×C61—21no—
303C23×C61—21no—
304C23×C61—21no—
305C23×C61—21no—
306C23×C61—21no—
307C23×C61—22no—
308C23×C61—41no—
309C23×C61—41no—
310C23×C61—41no—
311C23×C61—41no—
312C23×C61—41no—
313C23×C61—41no—
314C23×C61C2×D812yes—
315C23×C61C22×D411yescharacteristic
316C22×D61—21no—
317C22×D61—21no—
318C22×D61—21no—
319C22×D61—21no—
320C22×D61—21no—
321C22×D61—21no—
322C22×D61—28no—
323C22×D61—28no—
324C22×D61—28no—
325C22×D61—22no—
326C22×D61—44no—
327C22×D61—44no—
328C22×D61—44no—
329C22×D61—44no—
330C22×D61—41no—
331C22×D61—41no—
332C22×D61—41no—
333C22×D61—41no—
334C22×D61—41no—
335C22×D61—41no—
336C22×D61—48no—
337C22×D61—48no—
338C22×D61—48no—
339C22×D61—84no—
340C22×D61—84no—
341C22×D61—84no—
342C22×D61—84no—
343C22×D61#12012yes—
344C22×D61#12112yes—
345C22×D61#12312yes—
346C22×D61C2×D812yes—
347C22×D61C2×D812yes—
348C22×D61#13512yes—
349C22×D61AGL(1,ℤ/8)12yes—
350C22×D61#13712yes—
351D4×C61—22no—
352D4×C61—22no—
353D4×C61—48no—
354D4×C61—41no—
355D4×C61—41no—
356C2×C4×C61—22no—
357C2×C4×C61—21no—
358C2×C4×C61—21no—
359C2×C4×C61—21no—
360C2×C4×C61—41no—
361C2×C4×C61—41no—
362C2×C4×C61—41no—
363C2×C4×C61—41no—
364C2×C4×C61—41no—
365C2×C4×C61—41no—
366C2×C4×C61—41no—
367C2×C4×C61—41no—
368C2×C4×C61—41no—
369C2×C4×C61—41no—
370C2×C4×C61—41no—
371C2×C4×C61—41no—
372C2×C4×C61C22×D411yescharacteristic
373C2×C4×C61C22×D411yescharacteristic
374C2×C4×C61C22×D411yescharacteristic
375C2×C4×C61C2×#4111yescharacteristic
376C2×C4×C61C2×#4111yescharacteristic
377C2×C4×C61C2×#4111yescharacteristic
378C22⋊D61—48no—
379C22⋊D61—48no—
380C22⋊D61—48no—
381C2×Dic61—22no—
382C2×Dic61—21no—
383C2×Dic61—21no—
384C2×Dic61—21no—
385C2×Dic61—41no—
386C2×Dic61—41no—
387C2×Dic61—44no—
388C2×Dic61—41no—
389C2×Dic61—41no—
390C2×Dic61—41no—
391C2×Dic61—41no—
392C2×Dic61—41no—
393C2×Dic61—41no—
394C2×Dic61#12012yes—
395C2×Dic61#12112yes—
396C2×Dic61#12312yes—
397D244—22no—
398D244—22no—
399D244—48no—
400D244—41no—
401D244—41no—
402C4×D61—44no—
403C4×D61—48no—
404C4×D61—41no—
405C4×D61—41no—
406C4×D61—41no—
407C4×D61—41no—
408C4×D61—44no—
409C4×D61—84no—
410C4×D61—84no—
411C4×D61#12114yes—
412C4×D61#12114yes—
413C4×D61#12314yes—
414C4×D61#12414yes—
415C8×C61—22no—
416C8×C61—41no—
417#92418—22no—
418#92418—41no—
419C2×#2033—611nomaximal, Sylow
420C22×C61—22no—
421C22×C61—22no—
422C22×C61—22no—
423C22×C61—41no—
424C22×C61—41no—
425C22×C61—41no—
426C22×C61—41no—
427C22×C61—42no—
428C22×C61—42no—
429C22×C61—42no—
430C22×C61—81no—
431C22×C61—81no—
432C22×C61—81no—
433C22×C61—81no—
434C22×C61C2×#12011yescharacteristic
435C22×C61C2×#12111yescharacteristic
436C22×C61C2×#12311yescharacteristic
437C22×C61C22×D811yescharacteristic
438C22×C61C2×#13511yescharacteristic
439C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
440C22×C61C2×#13711yescharacteristic
441C2×D61—22no—
442C2×D61—22no—
443C2×D61—22no—
444C2×D61—41no—
445C2×D61—41no—
446C2×D61—41no—
447C2×D61—41no—
448C2×D61—416no—
449C2×D61—42no—
450C2×D61—42no—
451C2×D61—42no—
452C2×D61—81no—
453C2×D61—81no—
454C2×D61—81no—
455C2×D61—81no—
456C2×D61—816no—
457C2×D61#39414yes—
458C2×D61#44714yes—
459C2×D61#45214yes—
460C2×D61#46614yes—
461C2×D61#46814yes—
462C2×D61#48014yes—
463C2×D61#48214yes—
464C4×C61—41no—
465C4×C61—42no—
466C4×C61—81no—
467C4×C61—81no—
468C4×C61C2×#12111yescharacteristic
469C4×C61C2×#12111yescharacteristic
470C4×C61C2×#12311yescharacteristic
471C4×C61C2×#12411yescharacteristic
472Dic61—41no—
473Dic61—42no—
474Dic61—81no—
475Dic61—81no—
476Dic61#39414yes—
477C22×#121—611no—
478C22×#107—611no—
479C22×#102—611no—
480C22×#102—611no—
481C22×C22⋊C8—611no—
482C2×#380—611no—
483#2033—611no—
484#2033—611no—
485#2033—611no—
486#2033—611no—
487#2033—611no—
488#2033—611no—
489#2033—611no—
490#2033D6111yescharacteristic, direct product factor
491C2×#340—611no—
492C2×C61—42no—
493C2×C61—82no—
494C2×C61C2×#39411yescharacteristic
495C2×C61C2×#44711yescharacteristic
496C2×C61C2×#45211yescharacteristic
497C2×C61C2×#46611yescharacteristic
498C2×C61C2×#46811yescharacteristic
499C2×C61C2×#48011yescharacteristic
500C2×C61C2×#48211yescharacteristic
501D61—42no—
502D61—82no—
503D61#203318yesdirect product factor
504C23×D4—611no—
505C23×D4—1221no—
506C24×C4—611no—
507C23×C8—611no—
508C23×C8—611no—
509C2×#121—611no—
510C2×#121—611no—
511C2×#121—611no—
512C2×#121—1221no—
513C2×#121—1224no—
514C2×#121—1224no—
515C2×#121—1221no—
516C2×#121C2×D6111yescharacteristic
517C22×C4⋊C4—611no—
518C22×C4⋊C4—611no—
519C22×C4⋊C4—611no—
520C22×C22⋊C4—1221no—
521C22×C22⋊C4—1221no—
522C2×#107—611no—
523C2×#107—611no—
524C2×#107—611no—
525C2×#107—1224no—
526C2×#107C2×D6111yescharacteristic, complemented
527C2×#102—611no—
528C2×#102—611no—
529C2×#102—611no—
530C2×#102—611no—
531C2×#102—611no—
532C2×#102—611no—
533C2×#102—1224no—
534C2×#102—1224no—
535C2×#102C2×D6111yescharacteristic, complemented
536C2×#102C2×D6111yescharacteristic, complemented
537C2×C22⋊C8—611no—
538C2×C22⋊C8—611no—
539C2×C22⋊C8—611no—
540C2×C22⋊C8—1224no—
541C2×C22⋊C8C2×D6111yescharacteristic, complemented
542#380—611no—
543#380—611no—
544#380—611no—
545#380—1221no—
546#380—1221no—
547#380C2×D6111yescharacteristic, complemented
548C2×#95—1221no—
549#340—611no—
550#340—611no—
551#340—611no—
552#340C2×D6111yescharacteristic, complemented
553C61C2×#203311yescharacteristic, complemented, Sylow
554C25—611no—
555C25—1221no—
556C22×D4—21no—
557C22×D4—614no—
558C22×D4—611no—
559C22×D4—1221no—
560C22×D4—1222no—
561C22×D4—1222no—
562C22×D4—1222no—
563C22×D4—1222no—
564C22×D4—1222no—
565C22×D4—1221no—
566C22×D4—1228no—
567C22×D4—1221no—
568C22×D4—1221no—
569C22×D4—2444no—
570C22×D4—2444no—
571C22×D4C22×D6111yescharacteristic
572C23×C4—611no—
573C23×C4—611no—
574C23×C4—611no—
575C23×C4—611no—
576C23×C4—611no—
577C23×C4—1222no—
578C23×C4—1222no—
579C23×C4—1222no—
580C23×C4—1222no—
581C23×C4—1222no—
582C23×C4—1222no—
583C23×C4—1221no—
584C23×C4—1221no—
585C23×C4—1221no—
586C23×C4C22×D6111yescharacteristic
587C22×C8—611no—
588C22×C8—614no—
589C22×C8—611no—
590C22×C8—1222no—
591C22×C8—1222no—
592C22×C8—1222no—
593C22×C8—1222no—
594C22×C8—1222no—
595C22×C8C22×D6111yescharacteristic
596C22×C8C22×D6111yescharacteristic
597#121—22no—
598#121—22no—
599#121—1228no—
600#121—1222no—
601#121—1222no—
602#121—1222no—
603#121—1222no—
604#121—1228no—
605#121—1222no—
606#121—1222no—
607C2×C4⋊C4—611no—
608C2×C4⋊C4—614no—
609C2×C4⋊C4—611no—
610C2×C4⋊C4—611no—
611C2×C4⋊C4—1222no—
612C2×C4⋊C4—1222no—
613C2×C4⋊C4—1222no—
614C2×C4⋊C4—1222no—
615C2×C4⋊C4—1222no—
616C2×C4⋊C4—1221no—
617C2×C4⋊C4—1221no—
618C2×C4⋊C4—1221no—
619C2×C4⋊C4C22×D6111yescharacteristic
620C2×C4⋊C4C22×D6111yescharacteristic
621C2×C4⋊C4C22×D6111yescharacteristic
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—1228no—
625C2×C22⋊C4—1221no—
626C2×C22⋊C4—1221no—
627C2×C22⋊C4—1221no—
628C2×C22⋊C4—1221no—
629C2×C22⋊C4—1221no—
630C2×C22⋊C4—1221no—
631C2×C22⋊C4—2444no—
632#107—22no—
633#107—1222no—
634#107—1222no—
635#107—1222no—
636#102—22no—
637#102—22no—
638#102—1222no—
639#102—1222no—
640#102—1222no—
641#102—1222no—
642#102—1222no—
643#102—1222no—
644C22⋊C8—22no—
645C22⋊C8—1222no—
646C22⋊C8—1222no—
647C22⋊C8—1222no—
648#95—21no—
649#95—1221no—
650#95—1221no—
651#95—1221no—
652C24—21no—
653C24—611no—
654C24—611no—
655C24—614no—
656C24—1222no—
657C24—1222no—
658C24—1222no—
659C24—1222no—
660C24—1222no—
661C24—1222no—
662C24—1224no—
663C24—1221no—
664C24—2442no—
665C24—2442no—
666C24—2442no—
667C24—2442no—
668C24—2442no—
669C24—2442no—
670C24D4×D6111yescharacteristic
671C2×D4—24no—
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—42no—
678C2×D4—42no—
679C2×D4—612no—
680C2×D4—1224no—
681C2×D4—1228no—
682C2×D4—1228no—
683C2×D4—1224no—
684C2×D4—1224no—
685C2×D4—1224no—
686C2×D4—1221no—
687C2×D4—1221no—
688C2×D4—1221no—
689C2×D4—1221no—
690C2×D4—1221no—
691C2×D4—2442no—
692C2×D4—2442no—
693C2×D4—2444no—
694C2×D4—2444no—
695C2×D4—2442no—
696C2×D4—2442no—
697C2×D4—24432no—
698C2×D4—2442no—
699C2×D4—2442no—
700C2×D4—2442no—
701C2×D4—2442no—
702C2×D4D4×D6112yes—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—611no—
713C22×C4—612no—
714C22×C4—612no—
715C22×C4—612no—
716C22×C4—612no—
717C22×C4—612no—
718C22×C4—612no—
719C22×C4—611no—
720C22×C4—1222no—
721C22×C4—1222no—
722C22×C4—1222no—
723C22×C4—1222no—
724C22×C4—1224no—
725C22×C4—1222no—
726C22×C4—1222no—
727C22×C4—1222no—
728C22×C4—1222no—
729C22×C4—1222no—
730C22×C4—1221no—
731C22×C4—1221no—
732C22×C4—1221no—
733C22×C4—1221no—
734C22×C4—1221no—
735C22×C4—1221no—
736C22×C4—1221no—
737C22×C4—1221no—
738C22×C4—1221no—
739C22×C4—2444no—
740C22×C4—2444no—
741C22×C4—2444no—
742C22×C4—2444no—
743C22×C4—2442no—
744C22×C4—2442no—
745C22×C4—2442no—
746C22×C4—2442no—
747C22×C4—2442no—
748C22×C4—2442no—
749C22×C4—2442no—
750C22×C4—2442no—
751C22×C4D4×D6111yescharacteristic
752C22×C4C23×D6111yescharacteristic
753C2×C8—21no—
754C2×C8—21no—
755C2×C8—21no—
756C2×C8—21no—
757C2×C8—21no—
758C2×C8—612no—
759C2×C8—1228no—
760C2×C8—1221no—
761C2×C8—1221no—
762C2×C8—1221no—
763C2×C8—1221no—
764C2×C8—1221no—
765C2×C8—2444no—
766C2×C8D4×D6112yescomplemented
767C4⋊C4—21no—
768C4⋊C4—21no—
769C4⋊C4—21no—
770C4⋊C4—21no—
771C4⋊C4—21no—
772C4⋊C4—612no—
773C4⋊C4—1224no—
774C4⋊C4—1221no—
775C4⋊C4—1221no—
776C4⋊C4—1221no—
777C4⋊C4—1221no—
778C4⋊C4—1221no—
779C4⋊C4—2442no—
780C4⋊C4—2442no—
781C4⋊C4D4×D6112yes—
782C22⋊C4—24no—
783C22⋊C4—42no—
784C22⋊C4—1224no—
785C22⋊C4—1224no—
786C22⋊C4—1224no—
787C22⋊C4—2442no—
788C22⋊C4—2442no—
789C22⋊C4—2442no—
790C23—21no—
791C23—21no—
792C23—21no—
793C23—21no—
794C23—21no—
795C23—21no—
796C23—22no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—612no—
804C23—612no—
805C23—612no—
806C23—612no—
807C23—612no—
808C23—612no—
809C23—612no—
810C23—612no—
811C23—1228no—
812C23—1228no—
813C23—1228no—
814C23—1221no—
815C23—1221no—
816C23—1221no—
817C23—1221no—
818C23—1221no—
819C23—1221no—
820C23—1222no—
821C23—4884no—
822C23—4884no—
823C23—4884no—
824C23—4884no—
825C23—2448no—
826C23—2448no—
827C23—2448no—
828C23—2444no—
829C23—2444no—
830C23—2444no—
831C23—2444no—
832C23—2441no—
833C23—2441no—
834C23—2441no—
835C23—2441no—
836C23—2441no—
837C23—2441no—
838C23D8×D6112yes—
839C23C2×D4×D6111yescharacteristic
840D4—22no—
841D4—22no—
842D4—48no—
843D4—41no—
844D4—41no—
845D4—1222no—
846D4—1222no—
847D4—2448no—
848D4—2448no—
849D4—2448no—
850D4—2448no—
851D4—2441no—
852D4—2441no—
853C2×C4—21no—
854C2×C4—22no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—612no—
870C2×C4—612no—
871C2×C4—612no—
872C2×C4—614no—
873C2×C4—614no—
874C2×C4—614no—
875C2×C4—614no—
876C2×C4—1221no—
877C2×C4—1222no—
878C2×C4—1221no—
879C2×C4—1221no—
880C2×C4—4884no—
881C2×C4—4884no—
882C2×C4—2444no—
883C2×C4—2444no—
884C2×C4—2448no—
885C2×C4—2444no—
886C2×C4—2441no—
887C2×C4—2441no—
888C2×C4—2441no—
889C2×C4—2441no—
890C2×C4—2441no—
891C2×C4—2441no—
892C2×C4—2441no—
893C2×C4—2441no—
894C2×C4—2441no—
895C2×C4—2441no—
896C2×C4—2441no—
897C2×C4—2441no—
898C2×C4C2×D4×D6111yescharacteristic
899C2×C4C2×D4×D6111yescharacteristic
900C2×C4C2×D4×D6111yescharacteristic
901C2×C4#41×D6111yescharacteristic
902C2×C4#41×D6111yescharacteristic
903C2×C4#41×D6111yescharacteristic
904C8—22no—
905C8—41no—
906C8—1222no—
907C8—2441no—
908C22—22no—
909C22—22no—
910C22—22no—
911C22—41no—
912C22—41no—
913C22—41no—
914C22—41no—
915C22—42no—
916C22—42no—
917C22—42no—
918C22—81no—
919C22—81no—
920C22—81no—
921C22—81no—
922C22—614no—
923C22—614no—
924C22—614no—
925C22—614no—
926C22—614no—
927C22—614no—
928C22—614no—
929C22—1222no—
930C22—1222no—
931C22—1222no—
932C22—48816no—
933C22—4881no—
934C22—4881no—
935C22—4881no—
936C22—4881no—
937C22—24416no—
938C22—2442no—
939C22—2442no—
940C22—2442no—
941C22—2441no—
942C22—2441no—
943C22—2441no—
944C22—2441no—
945C22#120×D6111yescharacteristic
946C22#121×D6111yescharacteristic
947C22#123×D6111yescharacteristic
948C22C2×D8×D6111yescharacteristic
949C22#135×D6111yescharacteristic
950C22AGL(1,ℤ/8)×D6111yescharacteristic
951C22#137×D6111yescharacteristic
952C4—41no—
953C4—42no—
954C4—81no—
955C4—81no—
956C4—614no—
957C4—4881no—
958C4—4881no—
959C4—2441no—
960C4—2442no—
961C4#121×D6111yescharacteristic
962C4#121×D6111yescharacteristic
963C4#123×D6111yescharacteristic
964C4#124×D6111yescharacteristic
965C2—42no—
966C2—82no—
967C2—618no—
968C2—4882no—
969C2—2442no—
970C2#394×D6111yescharacteristic
971C2#447×D6111yescharacteristic
972C2#452×D6111yescharacteristic
973C2#466×D6111yescharacteristic
974C2#468×D6111yescharacteristic
975C2#480×D6111yescharacteristic
976C2#482×D6111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2033C2
socleC23×C61C22×D4
prime radicalC2×#121×D61C2
hypercenter#2033D61
hypocenterC61C2×#2033
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2033

Complements

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

NH ≅ G/Ntype
2. C2×#107×D61C2semidirect
3. C2×#102×D61C2semidirect
4. C2×#102×D61C2semidirect
5. C2×C22⋊C8×D61C2semidirect
6. #380×D61C2semidirect
7. #21447004C2semidirect
8. #21447003C2semidirect
9. #21447002C2semidirect
10. #21447001C2semidirect
11. #21447000C2semidirect
12. #21446999C2semidirect
13. #21446998C2semidirect
14. #340×D61C2semidirect
15. C61×#2033C2semidirect
33. C2×#14519711C22semidirect
34. C2×#14519710C22semidirect
35. C2×#14519710C22semidirect
37. C2×#14519699C22semidirect
38. C2×#14519699C22semidirect
39. C2×#14519698C22semidirect
40. C2×#14519698C22semidirect
41. C2×#14519697C22semidirect
42. C2×#14519697C22semidirect
45. C2×C22⋊#92418C22semidirect
46. C2×#14519689C22semidirect
47. C2×#14519689C22semidirect
49. #16839622C22semidirect
52. #16839619C22semidirect
53. #16839619C22semidirect
55. #16839525C22semidirect
56. #16839524C22semidirect
57. #16839524C22semidirect
59. C2×#107×C61C22semidirect
60. C2×#102×C61C22semidirect
61. C2×#102×C61C22semidirect
62. C2×C22⋊C8×C61C22semidirect
63. C61×#380C22semidirect
64. C61×#340C22semidirect
102. C2×C8×D61D4semidirect
269. C2×C8×C61C2×D4semidirect
298. C2×#92418C2×D4semidirect
490. #2033D61direct (N × H)
503. D61#2033direct (N × H)
526. C2×#107C2×D61semidirect
535. C2×#102C2×D61semidirect
536. C2×#102C2×D61semidirect
541. C2×C22⋊C8C2×D61semidirect
547. #380C2×D61semidirect
552. #340C2×D61semidirect
553. C61C2×#2033semidirect
766. C2×C8D4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#121×D612
C2×#107×D612
C2×#102×D612
C2×C22⋊C8×D612
#380×D612
#214470042
#214470032
#214470022
#214470012
#214470002
#214469992
#214469982
#340×D612
C61×#20332
C2×#203361