Finite Group Databasebeta

← D61×#2036 #29707481

Subgroups — D61×#2036 #29707481

Order 15616.

1662 conjugacy classes of subgroups.

The subgroup lattice has 882 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C22⋊Q8×D61C211yesmaximal, characteristic
2C2×#107×D61C211yesmaximal, characteristic, complemented
3C2×#103×D61C211yesmaximal, characteristic, complemented
4C2×#103×D61C211yesmaximal, characteristic, complemented
5C2×C22⋊C8×D61C211yesmaximal, characteristic
6#380×D61C211yesmaximal, characteristic
7#21447025C211yesmaximal, characteristic, complemented
8#21447024C211yesmaximal, characteristic, complemented
9#21447023C211yesmaximal, characteristic, complemented
10#21447022C211yesmaximal, characteristic, complemented
11#21447021C211yesmaximal, characteristic, complemented
12#21447020C211yesmaximal, characteristic, complemented
13#21447019C211yesmaximal, characteristic, complemented
14#340×D61C211yesmaximal, characteristic, complemented
15C61×#2036C211yesmaximal, characteristic, complemented
16C22×Q8×D61C2211yescharacteristic
17C23×C4×D61C2211yescharacteristic
18C22×C8×D61C2211yescharacteristic
19C22×C8×D61C2211yescharacteristic
20C2×#14519757C2211yescharacteristic
21C2×#14519756C2211yescharacteristic
22C2×#14519755—21no—
23C2×#14519754—21no—
24C2×#14519753C2211yescharacteristic
25C22⋊Q8×D61—24no—
26C22⋊Q8×D61—24no—
27C2×C4⋊C4×D61—21no—
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×#14519702C2211yescharacteristic, complemented
38C2×#14519702C2211yescharacteristic, complemented
39C2×#14519701C2211yescharacteristic, complemented
40C2×#14519701C2211yescharacteristic, complemented
41C2×#14519700C2211yescharacteristic, complemented
42C2×#14519700C2211yescharacteristic, complemented
43#103×D61—24no—
44#103×D61—24no—
45C2×C22⋊#92418C2211yescharacteristic
46C2×#14519689C2211yescharacteristic
47C2×#14519689C2211yescharacteristic
48C22⋊C8×D61—24no—
49#16839622C2211yescharacteristic
50#16839621—21no—
51#16839620—21no—
52#16839619C2211yescharacteristic
53#16839619C2211yescharacteristic
54#95×D61—21no—
55#16839525C2211yescharacteristic, complemented
56#16839524C2211yescharacteristic, complemented
57#16839524C2211yescharacteristic, complemented
58C2×C22⋊Q8×C61C2211yescharacteristic
59C2×#107×C61C2211yescharacteristic, complemented
60C2×#103×C61C2211yescharacteristic, complemented
61C2×#103×C61C2211yescharacteristic, complemented
62C2×C22⋊C8×C61C2211yescharacteristic
63C61×#380C2211yescharacteristic
64C61×#340C2211yescharacteristic, complemented
65C24×D61D411yescharacteristic
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—
74C23×Dic61D411yescharacteristic
75C22×C4×D61—21no—
76C22×C4×D61—21no—
77C22×C4×D61—22no—
78C22×C4×D61—22no—
79C22×C4×D61—22no—
80C22×C4×D61—22no—
81C22×C4×D61—22no—
82C22×C4×D61—22no—
83C22×C4×D61—21no—
84C22×C4×D61—21no—
85C22×C4×D61D411yescharacteristic
86C22×C4×D61D411yescharacteristic
87C22×C4×D61C2311yescharacteristic
88C22×C4×D61C2311yescharacteristic
89C22×#92418C2311yescharacteristic
90C22×#92418C2311yescharacteristic
91C2×C8×D61—22no—
92C2×C8×D61—22no—
93C2×C8×D61—22no—
94C2×C8×D61—22no—
95C2×C8×D61—22no—
96C2×C8×D61D414yes—
97#14519757—22no—
98#14519757—22no—
99#14519756—22no—
100#14519756—22no—
101#14519755—28no—
102#14519754—28no—
103#14519753—22no—
104#14519753—22no—
105C2×C4⋊Dic61—21no—
106C2×C4⋊Dic61C2311yescharacteristic
107C2×C4⋊Dic61C2311yescharacteristic
108C2×C4⋊Dic61C2311yescharacteristic
109C2×#11758196—21no—
110C2×#11758196—21no—
111C2×#11758196—21no—
112C2×#11758196—21no—
113C2×#11758196—21no—
114C4⋊C4×D61—28no—
115C4⋊C4×D61—22no—
116C4⋊C4×D61—22no—
117C4⋊C4×D61—22no—
118C4⋊C4×D61—22no—
119C4⋊C4×D61—22no—
120C4⋊C4×D61D414yes—
121C2×C22⋊Dic61—21no—
122C2×C22⋊Dic61—21no—
123C2×#11758198—21no—
124C2×#11758198—21no—
125C2×#11758198—21no—
126C2×#11758198—21no—
127C22⋊C4×D61—28no—
128C22⋊C4×D61—44no—
129#14519711—22no—
130#14519710—22no—
131#14519710—22no—
132#14519702—22no—
133#14519702—22no—
134#14519701—22no—
135#14519701—22no—
136#14519700—22no—
137#14519700—22no—
138C22⋊#92418—22no—
139#14519689—22no—
140#14519689—22no—
141#14519684—21no—
142#14519684—21no—
143#14519684—21no—
144C22×Q8×C61C2311yescharacteristic
145C23×C4×C61C2311yescharacteristic
146C22×C8×C61C2311yescharacteristic
147C22×C8×C61C2311yescharacteristic
148C22⋊Q8×C61—22no—
149C22⋊Q8×C61—22no—
150C2×C4⋊C4×C61—21no—
151C2×C4⋊C4×C61C2311yescharacteristic
152C2×C4⋊C4×C61C2311yescharacteristic
153C2×C4⋊C4×C61C2311yescharacteristic
154C2×C22⋊C4×C61—21no—
155C2×C22⋊C4×C61—21no—
156#107×C61—22no—
157#103×C61—22no—
158#103×C61—22no—
159C22⋊C8×C61—22no—
160#95×C61—21no—
161C24×C61C2×D411yescharacteristic
162C23×D61—22no—
163C23×D61—22no—
164C23×D61—22no—
165C23×D61—22no—
166C23×D61—22no—
167C23×D61—22no—
168C23×D61Q1614yes—
169C23×D61C2×D411yescharacteristic
170C23×D61C2×D411yescharacteristic
171C2×Q8×C61—21no—
172C2×Q8×C61—21no—
173C2×Q8×C61—21no—
174C2×Q8×C61—21no—
175C2×Q8×C61—21no—
176C2×Q8×C61C2×D412yes—
177C22×C4×C61—21no—
178C22×C4×C61—21no—
179C22×C4×C61—21no—
180C22×C4×C61—21no—
181C22×C4×C61—21no—
182C22×C4×C61—21no—
183C22×C4×C61—21no—
184C22×C4×C61—21no—
185C22×C4×C61—21no—
186C22×C4×C61—21no—
187C22×C4×C61C2×D411yescharacteristic
188C22×C4×C61C2411yescharacteristic
189C22×Dic61—21no—
190C22×Dic61—21no—
191C22×Dic61—22no—
192C22×Dic61—22no—
193C22×Dic61—22no—
194C22×Dic61—21no—
195C22×Dic61—21no—
196C22×Dic61C2×D411yescharacteristic
197C22×Dic61C2×D411yescharacteristic
198Q8×D61—28no—
199Q8×D61—28no—
200Q8×D61—44no—
201Q8×D61—44no—
202C2×C4×D61—22no—
203C2×C4×D61—24no—
204C2×C4×D61—24no—
205C2×C4×D61—22no—
206C2×C4×D61—22no—
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—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—44no—
221C2×C4×D61—44no—
222C2×C4×D61—44no—
223C2×C4×D61—44no—
224C2×C4×D61—42no—
225C2×C4×D61—42no—
226C2×C4×D61—42no—
227C2×C4×D61—42no—
228C2×C4×D61—42no—
229C2×C4×D61—42no—
230C2×C4×D61C2×D412yes—
231C2×C4×D61C2×D412yes—
232C2×C4×D61C2×D412yes—
233C2×C4×D61#4112yes—
234C2×C4×D61#4112yes—
235C2×C4×D61#4112yes—
236C2×Dic122—21no—
237C2×Dic122—21no—
238C2×Dic122—21no—
239C2×Dic122—21no—
240C2×Dic122—21no—
241C2×Dic122—24no—
242C2×Dic122—42no—
243C2×Dic122—42no—
244C2×Dic122C2×D412yes—
245C2×C8×C61—21no—
246C2×C8×C61—21no—
247C2×C8×C61—21no—
248C2×C8×C61—21no—
249C2×C8×C61—21no—
250C2×C8×C61C2×D412yes—
251C4⋊C4×C61—24no—
252C4⋊C4×C61—21no—
253C4⋊C4×C61—21no—
254C4⋊C4×C61—21no—
255C4⋊C4×C61—21no—
256C4⋊C4×C61—21no—
257C4⋊C4×C61C2×D412yes—
258C22⋊C4×C61—24no—
259C22⋊C4×C61—42no—
260C22⋊Dic61—24no—
261C22⋊Dic61—42no—
262#11758198—24no—
263#11758198—24no—
264#11758198—42no—
265#11758198—42no—
266C4⋊Dic61—24no—
267C4⋊Dic61—21no—
268C4⋊Dic61—21no—
269C4⋊Dic61—21no—
270C4⋊Dic61—21no—
271C4⋊Dic61—21no—
272C4⋊Dic61C2×D412yes—
273#11758196—24no—
274#11758196—24no—
275#11758196—24no—
276#11758196—42no—
277#11758196—42no—
278C2×#92418—21no—
279C2×#92418—21no—
280C2×#92418—21no—
281C2×#92418—21no—
282C2×#92418—21no—
283C2×#92418C2×D412yes—
284C8×D61—28no—
285C8×D61—44no—
286C23×C61—21no—
287C23×C61—21no—
288C23×C61—21no—
289C23×C61—21no—
290C23×C61—21no—
291C23×C61—21no—
292C23×C61C2×Q1612yes—
293C23×C61C22×D411yescharacteristic
294C22×D61—21no—
295C22×D61—21no—
296C22×D61—21no—
297C22×D61—21no—
298C22×D61—21no—
299C22×D61—21no—
300C22×D61—28no—
301C22×D61—28no—
302C22×D61—28no—
303C22×D61—44no—
304C22×D61—44no—
305C22×D61—44no—
306C22×D61—44no—
307C22×D61#12012yes—
308C22×D61#12112yes—
309C22×D61#12312yes—
310C22×D61C2×Q1612yes—
311C22×D61C2×Q1612yes—
312C22×D61#13512yes—
313C22×D61AGL(1,ℤ/8)12yes—
314C22×D61#13712yes—
315Q8×C61—22no—
316Q8×C61—22no—
317Q8×C61—41no—
318Q8×C61—41no—
319C2×C4×C61—21no—
320C2×C4×C61—22no—
321C2×C4×C61—22no—
322C2×C4×C61—21no—
323C2×C4×C61—21no—
324C2×C4×C61—41no—
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×C61—41no—
334C2×C4×C61—41no—
335C2×C4×C61—41no—
336C2×C4×C61—41no—
337C2×C4×C61—41no—
338C2×C4×C61C22×D411yescharacteristic
339C2×C4×C61C22×D411yescharacteristic
340C2×C4×C61C22×D411yescharacteristic
341C2×C4×C61C2×#4111yescharacteristic
342C2×C4×C61C2×#4111yescharacteristic
343C2×C4×C61C2×#4111yescharacteristic
344C2×Dic61—22no—
345C2×Dic61—21no—
346C2×Dic61—22no—
347C2×Dic61—21no—
348C2×Dic61—21no—
349C2×Dic61—41no—
350C2×Dic61—41no—
351C2×Dic61—41no—
352C2×Dic61—41no—
353C2×Dic61—44no—
354C2×Dic61—41no—
355C2×Dic61—41no—
356C2×Dic61—41no—
357C2×Dic61—41no—
358C2×Dic61—41no—
359C2×Dic61—41no—
360C2×Dic61#12012yes—
361C2×Dic61#12112yes—
362C2×Dic61#12312yes—
363C4×D61—44no—
364C4×D61—48no—
365C4×D61—48no—
366C4×D61—41no—
367C4×D61—41no—
368C4×D61—41no—
369C4×D61—41no—
370C4×D61—44no—
371C4×D61—84no—
372C4×D61—84no—
373C4×D61#12114yes—
374C4×D61#12114yes—
375C4×D61#12314yes—
376C4×D61#12414yes—
377Dic122—22no—
378Dic122—22no—
379Dic122—41no—
380Dic122—41no—
381Dic122—48no—
382C8×C61—22no—
383C8×C61—41no—
384#92418—22no—
385#92418—41no—
386C2×#2036—611nomaximal, Sylow
387C22×C61—22no—
388C22×C61—22no—
389C22×C61—22no—
390C22×C61—41no—
391C22×C61—41no—
392C22×C61—41no—
393C22×C61—41no—
394C22×C61C2×#12011yescharacteristic
395C22×C61C2×#12111yescharacteristic
396C22×C61C2×#12311yescharacteristic
397C22×C61C22×Q1611yescharacteristic
398C22×C61C2×#13511yescharacteristic
399C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
400C22×C61C2×#13711yescharacteristic
401C2×D61—22no—
402C2×D61—22no—
403C2×D61—22no—
404C2×D61—41no—
405C2×D61—41no—
406C2×D61—41no—
407C2×D61—41no—
408C2×D61—416no—
409C2×D61#39414yes—
410C2×D61#44914yes—
411C2×D61#45114yes—
412C2×D61#46714yes—
413C2×D61#46814yes—
414C2×D61#48414yes—
415C2×D61#48514yes—
416C4×C61—42no—
417C4×C61—41no—
418C4×C61—42no—
419C4×C61—81no—
420C4×C61—81no—
421C4×C61C2×#12111yescharacteristic
422C4×C61C2×#12111yescharacteristic
423C4×C61C2×#12311yescharacteristic
424C4×C61C2×#12411yescharacteristic
425Dic61—42no—
426Dic61—41no—
427Dic61—42no—
428Dic61—81no—
429Dic61—81no—
430Dic61#39414yes—
431C22×C22⋊Q8—611no—
432C22×#107—611no—
433C22×#103—611no—
434C22×#103—611no—
435C22×C22⋊C8—611no—
436C2×#380—611no—
437#2036—611no—
438#2036—611no—
439#2036—611no—
440#2036—611no—
441#2036—611no—
442#2036—611no—
443#2036—611no—
444#2036D6111yescharacteristic, direct product factor
445C2×#340—611no—
446C2×C61—42no—
447C2×C61C2×#39411yescharacteristic
448C2×C61C2×#45111yescharacteristic
449C2×C61C2×#44911yescharacteristic
450C2×C61C2×#46711yescharacteristic
451C2×C61C2×#46811yescharacteristic
452C2×C61C2×#48511yescharacteristic
453C2×C61C2×#48411yescharacteristic
454D61—42no—
455D61#203618yesdirect product factor
456C23×Q8—611no—
457C24×C4—611no—
458C23×C8—611no—
459C23×C8—611no—
460C2×C22⋊Q8—611no—
461C2×C22⋊Q8—611no—
462C2×C22⋊Q8—611no—
463C2×C22⋊Q8—1221no—
464C2×C22⋊Q8—1221no—
465C2×C22⋊Q8—1224no—
466C2×C22⋊Q8—1224no—
467C2×C22⋊Q8C2×D6111yescharacteristic
468C22×C4⋊C4—611no—
469C22×C4⋊C4—611no—
470C22×C4⋊C4—611no—
471C22×C4⋊C4—1221no—
472C22×C22⋊C4—1221no—
473C22×C22⋊C4—1221no—
474C2×#107—611no—
475C2×#107—611no—
476C2×#107—611no—
477C2×#107—1224no—
478C2×#107C2×D6111yescharacteristic, complemented
479C2×#103—611no—
480C2×#103—611no—
481C2×#103—611no—
482C2×#103—611no—
483C2×#103—611no—
484C2×#103—611no—
485C2×#103—1224no—
486C2×#103—1224no—
487C2×#103C2×D6111yescharacteristic, complemented
488C2×#103C2×D6111yescharacteristic, complemented
489C2×C22⋊C8—611no—
490C2×C22⋊C8—611no—
491C2×C22⋊C8—611no—
492C2×C22⋊C8—1224no—
493C2×C22⋊C8C2×D6111yescharacteristic
494#380—611no—
495#380—611no—
496#380—611no—
497#380—1221no—
498#380—1221no—
499#380C2×D6111yescharacteristic
500C2×#95—1221no—
501#340—611no—
502#340—611no—
503#340—611no—
504#340C2×D6111yescharacteristic, complemented
505C61C2×#203611yescharacteristic, complemented, Sylow
506C25—611no—
507C22×Q8—614no—
508C22×Q8—611no—
509C22×Q8—1221no—
510C22×Q8—1222no—
511C22×Q8—1222no—
512C22×Q8—1222no—
513C22×Q8—1222no—
514C22×Q8—1222no—
515C22×Q8C22×D6111yescharacteristic
516C23×C4—611no—
517C23×C4—611no—
518C23×C4—611no—
519C23×C4—611no—
520C23×C4—611no—
521C23×C4—1222no—
522C23×C4—1222no—
523C23×C4—1222no—
524C23×C4—1222no—
525C23×C4—1222no—
526C23×C4—1222no—
527C23×C4—1221no—
528C23×C4—1221no—
529C23×C4—1221no—
530C23×C4—1221no—
531C23×C4C22×D6111yescharacteristic
532C22×C8—611no—
533C22×C8—614no—
534C22×C8—611no—
535C22×C8—1222no—
536C22×C8—1222no—
537C22×C8—1222no—
538C22×C8—1222no—
539C22×C8—1222no—
540C22×C8C22×D6111yescharacteristic
541C22×C8C22×D6111yescharacteristic
542C22⋊Q8—22no—
543C22⋊Q8—22no—
544C22⋊Q8—1228no—
545C22⋊Q8—1222no—
546C22⋊Q8—1228no—
547C22⋊Q8—1222no—
548C22⋊Q8—1222no—
549C22⋊Q8—1222no—
550C22⋊Q8—1222no—
551C22⋊Q8—1222no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—611no—
554C2×C4⋊C4—614no—
555C2×C4⋊C4—611no—
556C2×C4⋊C4—611no—
557C2×C4⋊C4—1222no—
558C2×C4⋊C4—1228no—
559C2×C4⋊C4—1222no—
560C2×C4⋊C4—1222no—
561C2×C4⋊C4—1222no—
562C2×C4⋊C4—1222no—
563C2×C4⋊C4—1221no—
564C2×C4⋊C4—1221no—
565C2×C4⋊C4—1221no—
566C2×C4⋊C4—1221no—
567C2×C4⋊C4—1221no—
568C2×C4⋊C4—1221no—
569C2×C4⋊C4C22×D6111yescharacteristic
570C2×C4⋊C4C22×D6111yescharacteristic
571C2×C4⋊C4C22×D6111yescharacteristic
572C2×C22⋊C4—21no—
573C2×C22⋊C4—21no—
574C2×C22⋊C4—1228no—
575C2×C22⋊C4—1221no—
576C2×C22⋊C4—1221no—
577C2×C22⋊C4—1221no—
578C2×C22⋊C4—1221no—
579C2×C22⋊C4—1221no—
580C2×C22⋊C4—1221no—
581C2×C22⋊C4—2444no—
582#107—22no—
583#107—1222no—
584#107—1222no—
585#107—1222no—
586#103—22no—
587#103—22no—
588#103—1222no—
589#103—1222no—
590#103—1222no—
591#103—1222no—
592#103—1222no—
593#103—1222no—
594C22⋊C8—22no—
595C22⋊C8—1222no—
596C22⋊C8—1222no—
597C22⋊C8—1222no—
598#95—21no—
599#95—1221no—
600#95—1221no—
601#95—1221no—
602C24—611no—
603C24—611no—
604C24—614no—
605C24—1222no—
606C24—1222no—
607C24—1222no—
608C24—1222no—
609C24—1222no—
610C24—1222no—
611C24D4×D6111yescharacteristic
612C2×Q8—21no—
613C2×Q8—21no—
614C2×Q8—21no—
615C2×Q8—21no—
616C2×Q8—21no—
617C2×Q8—612no—
618C2×Q8—1224no—
619C2×Q8—1228no—
620C2×Q8—1228no—
621C2×Q8—1221no—
622C2×Q8—1221no—
623C2×Q8—1221no—
624C2×Q8—1221no—
625C2×Q8—1221no—
626C2×Q8—2442no—
627C2×Q8—2442no—
628C2×Q8—2444no—
629C2×Q8—2444no—
630C2×Q8D4×D6112yes—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—611no—
642C22×C4—612no—
643C22×C4—612no—
644C22×C4—612no—
645C22×C4—612no—
646C22×C4—612no—
647C22×C4—612no—
648C22×C4—611no—
649C22×C4—1222no—
650C22×C4—1222no—
651C22×C4—1222no—
652C22×C4—1224no—
653C22×C4—1224no—
654C22×C4—1222no—
655C22×C4—1222no—
656C22×C4—1222no—
657C22×C4—1222no—
658C22×C4—1222no—
659C22×C4—1222no—
660C22×C4—1221no—
661C22×C4—1221no—
662C22×C4—1221no—
663C22×C4—1221no—
664C22×C4—1221no—
665C22×C4—1221no—
666C22×C4—1221no—
667C22×C4—1221no—
668C22×C4—1221no—
669C22×C4—1221no—
670C22×C4—2444no—
671C22×C4—2444no—
672C22×C4—2444no—
673C22×C4—2444no—
674C22×C4—2442no—
675C22×C4—2442no—
676C22×C4—2442no—
677C22×C4—2442no—
678C22×C4—2442no—
679C22×C4—2442no—
680C22×C4—2442no—
681C22×C4—2442no—
682C22×C4—2442no—
683C22×C4—2442no—
684C22×C4D4×D6111yescharacteristic
685C22×C4C23×D6111yescharacteristic
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—612no—
692C2×C8—1228no—
693C2×C8—1221no—
694C2×C8—1221no—
695C2×C8—1221no—
696C2×C8—1221no—
697C2×C8—1221no—
698C2×C8—2444no—
699C2×C8D4×D6112yes—
700C4⋊C4—24no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—21no—
706C4⋊C4—612no—
707C4⋊C4—1224no—
708C4⋊C4—1224no—
709C4⋊C4—1224no—
710C4⋊C4—1224no—
711C4⋊C4—1221no—
712C4⋊C4—1221no—
713C4⋊C4—1221no—
714C4⋊C4—1221no—
715C4⋊C4—1221no—
716C4⋊C4—2442no—
717C4⋊C4—2442no—
718C4⋊C4D4×D6112yes—
719C22⋊C4—24no—
720C22⋊C4—42no—
721C22⋊C4—1224no—
722C22⋊C4—1224no—
723C22⋊C4—1224no—
724C22⋊C4—2442no—
725C22⋊C4—2442no—
726C22⋊C4—2442no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—612no—
734C23—612no—
735C23—612no—
736C23—612no—
737C23—612no—
738C23—612no—
739C23—612no—
740C23—612no—
741C23—1228no—
742C23—1228no—
743C23—1228no—
744C23—1221no—
745C23—1221no—
746C23—1221no—
747C23—1221no—
748C23—1221no—
749C23—1221no—
750C23—2444no—
751C23—2444no—
752C23—2444no—
753C23—2444no—
754C23Q16×D6112yes—
755C23C2×D4×D6111yescharacteristic
756Q8—22no—
757Q8—22no—
758Q8—41no—
759Q8—41no—
760Q8—1222no—
761Q8—1222no—
762Q8—2448no—
763Q8—2441no—
764Q8—2441no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—41no—
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—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—612no—
785C2×C4—612no—
786C2×C4—612no—
787C2×C4—614no—
788C2×C4—614no—
789C2×C4—614no—
790C2×C4—614no—
791C2×C4—1222no—
792C2×C4—1222no—
793C2×C4—1221no—
794C2×C4—1221no—
795C2×C4—1221no—
796C2×C4—4884no—
797C2×C4—4884no—
798C2×C4—2444no—
799C2×C4—2444no—
800C2×C4—2448no—
801C2×C4—2448no—
802C2×C4—2444no—
803C2×C4—2441no—
804C2×C4—2441no—
805C2×C4—2441no—
806C2×C4—2441no—
807C2×C4—2441no—
808C2×C4—2441no—
809C2×C4—2441no—
810C2×C4—2441no—
811C2×C4—2441no—
812C2×C4—2441no—
813C2×C4—2441no—
814C2×C4—2441no—
815C2×C4—2441no—
816C2×C4—2441no—
817C2×C4C2×D4×D6111yescharacteristic
818C2×C4C2×D4×D6111yescharacteristic
819C2×C4C2×D4×D6111yescharacteristic
820C2×C4#41×D6111yescharacteristic
821C2×C4#41×D6111yescharacteristic
822C2×C4#41×D6111yescharacteristic
823C8—22no—
824C8—41no—
825C8—1222no—
826C8—2441no—
827C22—22no—
828C22—22no—
829C22—22no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—614no—
835C22—614no—
836C22—614no—
837C22—614no—
838C22—614no—
839C22—614no—
840C22—614no—
841C22—1222no—
842C22—1222no—
843C22—1222no—
844C22—24416no—
845C22—2441no—
846C22—2441no—
847C22—2441no—
848C22—2441no—
849C22#120×D6111yescharacteristic
850C22#121×D6111yescharacteristic
851C22#123×D6111yescharacteristic
852C22C2×Q16×D6111yescharacteristic
853C22#135×D6111yescharacteristic
854C22AGL(1,ℤ/8)×D6111yescharacteristic
855C22#137×D6111yescharacteristic
856C4—41no—
857C4—42no—
858C4—42no—
859C4—81no—
860C4—81no—
861C4—614no—
862C4—4881no—
863C4—4881no—
864C4—2441no—
865C4—2442no—
866C4—2442no—
867C4#121×D6111yescharacteristic
868C4#121×D6111yescharacteristic
869C4#123×D6111yescharacteristic
870C4#124×D6111yescharacteristic
871C2—42no—
872C2—618no—
873C2—2442no—
874C2#394×D6111yescharacteristic
875C2#451×D6111yescharacteristic
876C2#449×D6111yescharacteristic
877C2#467×D6111yescharacteristic
878C2#468×D6111yescharacteristic
879C2#485×D6111yescharacteristic
880C2#484×D6111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2036C2
socleC23×C61C22×D4
prime radicalC24×D61D4
hypercenter#2036D61
hypocenterC61C2×#2036
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2036

Complements

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

NH ≅ G/Ntype
2. C2×#107×D61C2semidirect
3. C2×#103×D61C2semidirect
4. C2×#103×D61C2semidirect
7. #21447025C2semidirect
8. #21447024C2semidirect
9. #21447023C2semidirect
10. #21447022C2semidirect
11. #21447021C2semidirect
12. #21447020C2semidirect
13. #21447019C2semidirect
14. #340×D61C2semidirect
15. C61×#2036C2semidirect
33. C2×#14519711C22semidirect
34. C2×#14519710C22semidirect
35. C2×#14519710C22semidirect
37. C2×#14519702C22semidirect
38. C2×#14519702C22semidirect
39. C2×#14519701C22semidirect
40. C2×#14519701C22semidirect
41. C2×#14519700C22semidirect
42. C2×#14519700C22semidirect
55. #16839525C22semidirect
56. #16839524C22semidirect
57. #16839524C22semidirect
59. C2×#107×C61C22semidirect
60. C2×#103×C61C22semidirect
61. C2×#103×C61C22semidirect
64. C61×#340C22semidirect
444. #2036D61direct (N × H)
455. D61#2036direct (N × H)
478. C2×#107C2×D61semidirect
487. C2×#103C2×D61semidirect
488. C2×#103C2×D61semidirect
504. #340C2×D61semidirect
505. C61C2×#2036semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊Q8×D612
C2×#107×D612
C2×#103×D612
C2×C22⋊C8×D612
#380×D612
#214470252
#214470242
#214470232
#214470222
#214470212
#214470202
#214470192
#340×D612
C61×#20362
C2×#203661