Finite Group Databasebeta

← #29713096

Subgroups — #29713096

Order 15616.

1768 conjugacy classes of subgroups.

The subgroup lattice has 942 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840083C211yesmaximal, characteristic, complemented
2C2×#16839767C211yesmaximal, characteristic, complemented
3#21450116C211yesmaximal, characteristic, complemented
4#21447050C211yesmaximal, characteristic, complemented
5#21447050C211yesmaximal, characteristic, complemented
6#21447005C211yesmaximal, characteristic, complemented
7#21446998C211yesmaximal, characteristic, complemented
8#21446258C211yesmaximal, characteristic, complemented
9#21446117C211yesmaximal, characteristic, complemented
10#21446080C211yesmaximal, characteristic, complemented
11#21446066C211yesmaximal, characteristic, complemented
12#21445750C211yesmaximal, characteristic, complemented
13#21445750C211yesmaximal, characteristic, complemented
14#21445750C211yesmaximal, characteristic, complemented
15C2×D42×C61C211yesmaximal, characteristic
16C22×#11758194C2211yescharacteristic, complemented
17C2×#14519736C2211yescharacteristic, complemented
18#16840083—24no—
19C2×#14519710C2211yescharacteristic, complemented
20C2×#14519708C2211yescharacteristic, complemented
21#16839767—24no—
22C2×#14519698C2211yescharacteristic
23C2×#14519698C2211yescharacteristic
24C2×#14519698C2211yescharacteristic
25C2×#14519698C2211yescharacteristic
26C2×#14519698C2211yescharacteristic, complemented
27C2×#14519698C2211yescharacteristic, complemented
28C2×#14519698C2211yescharacteristic, complemented
29C2×#14519698C2211yescharacteristic, complemented
30C2×#14519698C2211yescharacteristic, complemented
31C2×#14519698C2211yescharacteristic, complemented
32C2×#14519698C2211yescharacteristic, complemented
33C2×#14519698C2211yescharacteristic, complemented
34C2×C22⋊#92418C2211yescharacteristic, complemented
35C2×C22⋊#92418C2211yescharacteristic, complemented
36C2×C22⋊#92418C2211yescharacteristic, complemented
37#16839690—21no—
38#16839676—21no—
39#16839660C2211yescharacteristic, complemented
40#16839660C2211yescharacteristic, complemented
41#16839650—21no—
42#16839643—21no—
43#16839622C2211yescharacteristic, complemented
44#16839622C2211yescharacteristic, complemented
45#16839622C2211yescharacteristic, complemented
46#16839524C2211yescharacteristic, complemented
47#16839524C2211yescharacteristic, complemented
48#16839517C2211yescharacteristic, complemented
49#16839517C2211yescharacteristic, complemented
50C23×D4×C61—21no—
51C23×D4×C61C2211yescharacteristic
52C23×D4×C61C2211yescharacteristic
53D42×C61—24no—
54D42×C61—24no—
55C2×#127×C61C2211yescharacteristic
56C2×#121×C61—21no—
57C2×#121×C61C2211yescharacteristic
58C2×#121×C61C2211yescharacteristic
59C2×#120×C61—21no—
60C2×#120×C61—21no—
61C2×C4×D4×C61C2211yescharacteristic
62C2×C4×D4×C61C2211yescharacteristic
63C2×#11758194—22no—
64C2×#11758194—41no—
65C2×#11758194—41no—
66C22×#92418C2311yescharacteristic
67C22×#92418C2311yescharacteristic
68C22×#92418C2311yescharacteristic
69C22×#92418C2311yescharacteristic
70#14519736—22no—
71#14519736—22no—
72C2×C4⋊Dic61C2311yescharacteristic
73C2×C4⋊Dic61C2311yescharacteristic
74C2×C4⋊Dic61C2311yescharacteristic
75C2×C4⋊Dic61C2311yescharacteristic
76C2×#11758196—21no—
77C2×#11758196—21no—
78C2×C22⋊Dic61—21no—
79C2×C22⋊Dic61—21no—
80C2×C22⋊Dic61—21no—
81C2×C22⋊Dic61—21no—
82C2×C4×Dic61—21no—
83#14519710—22no—
84#14519708—22no—
85#14519698—22no—
86#14519698—22no—
87#14519698—22no—
88#14519698—22no—
89#14519698—22no—
90#14519698—22no—
91#14519698—22no—
92#14519698—22no—
93#14519698—41no—
94#14519698—41no—
95#14519698—41no—
96#14519698—41no—
97C22⋊#92418—22no—
98C22⋊#92418—41no—
99C22⋊#92418—41no—
100#14519684—21no—
101#14519684—21no—
102#14519684—21no—
103#14519684—21no—
104#14519684—21no—
105C25×C61—21no—
106C25×C61—21no—
107C22×D4×C61—22no—
108C22×D4×C61—22no—
109C22×D4×C61—28no—
110C22×D4×C61—21no—
111C22×D4×C61—21no—
112C22×D4×C61—22no—
113C22×D4×C61—22no—
114C22×D4×C61—22no—
115C22×D4×C61—22no—
116C22×D4×C61—21no—
117C22×D4×C61—22no—
118C22×D4×C61—21no—
119C22×D4×C61—21no—
120C22×D4×C61—21no—
121C22×D4×C61—41no—
122C22×D4×C61—41no—
123C22×D4×C61—41no—
124C22×D4×C61—41no—
125C22×D4×C61—44no—
126C22×D4×C61—44no—
127C22×D4×C61D411yescharacteristic
128C22×D4×C61D414yes—
129C22×D4×C61C2311yescharacteristic
130C22×D4×C61C2311yescharacteristic
131C22×D4×C61C2311yescharacteristic
132C23×C4×C61—21no—
133C23×C4×C61C2311yescharacteristic
134C23×C4×C61C2311yescharacteristic
135#127×C61—22no—
136#127×C61—22no—
137#121×C61—28no—
138#121×C61—22no—
139#121×C61—22no—
140#121×C61—22no—
141#121×C61D414yes—
142#120×C61—28no—
143#120×C61—28no—
144C4×D4×C61—22no—
145C4×D4×C61—22no—
146C4×D4×C61—22no—
147C4×D4×C61—22no—
148C2×C4⋊C4×C61D411yescharacteristic
149C2×C4⋊C4×C61C2311yescharacteristic
150C2×C22⋊C4×C61—21no—
151C2×C22⋊C4×C61—21no—
152C2×C22⋊C4×C61—21no—
153C2×C22⋊C4×C61D411yescharacteristic
154C2×C22⋊C4×C61D411yescharacteristic
155C2×C42×C61C2311yescharacteristic
156C24×C61—21no—
157C24×C61—24no—
158C24×C61—21no—
159C24×C61—21no—
160C24×C61—24no—
161C24×C61—42no—
162C24×C61—42no—
163C24×C61—42no—
164C24×C61—42no—
165C24×C61—42no—
166C24×C61—42no—
167C24×C61—42no—
168C24×C61—42no—
169C24×C61—81no—
170C24×C61—81no—
171C24×C61—81no—
172C24×C61—81no—
173C24×C61C2×D411yescharacteristic
174C24×C61C2×D411yescharacteristic
175C2×D4×C61—22no—
176C2×D4×C61—22no—
177C2×D4×C61—28no—
178C2×D4×C61—24no—
179C2×D4×C61—24no—
180C2×D4×C61—24no—
181C2×D4×C61—24no—
182C2×D4×C61—24no—
183C2×D4×C61—24no—
184C2×D4×C61—22no—
185C2×D4×C61—21no—
186C2×D4×C61—21no—
187C2×D4×C61—21no—
188C2×D4×C61—21no—
189C2×D4×C61—21no—
190C2×D4×C61—21no—
191C2×D4×C61—21no—
192C2×D4×C61—21no—
193C2×D4×C61—21no—
194C2×D4×C61—21no—
195C2×D4×C61—21no—
196C2×D4×C61—21no—
197C2×D4×C61—21no—
198C2×D4×C61—44no—
199C2×D4×C61—44no—
200C2×D4×C61—44no—
201C2×D4×C61—42no—
202C2×D4×C61—42no—
203C2×D4×C61—42no—
204C2×D4×C61—42no—
205C2×D4×C61—42no—
206C2×D4×C61—44no—
207C2×D4×C61—44no—
208C2×D4×C61—432no—
209C2×D4×C61—44no—
210C2×D4×C61—42no—
211C2×D4×C61—42no—
212C2×D4×C61—42no—
213C2×D4×C61—42no—
214C2×D4×C61—44no—
215C2×D4×C61—42no—
216C2×D4×C61—81no—
217C2×D4×C61—81no—
218C2×D4×C61C2×D412yes—
219C2×D4×C61C2×D412yes—
220C2×D4×C61C2×D412yes—
221C2×D4×C61#4112yes—
222C2×D4×C61#4112yes—
223C22×C4×C61—21no—
224C22×C4×C61—21no—
225C22×C4×C61—21no—
226C22×C4×C61—21no—
227C22×C4×C61—24no—
228C22×C4×C61—21no—
229C22×C4×C61—21no—
230C22×C4×C61—21no—
231C22×C4×C61—21no—
232C22×C4×C61—21no—
233C22×C4×C61—21no—
234C22×C4×C61—21no—
235C22×C4×C61—42no—
236C22×C4×C61—42no—
237C22×C4×C61C2×D411yescharacteristic
238C22×C4×C61C2×D411yescharacteristic
239C22×C4×C61C2×D411yescharacteristic
240C22×C4×C61C2×D412yes—
241C22×C4×C61C2×D412yes—
242C22×C4×C61C2×D411yescharacteristic
243C22×C4×C61C2411yescharacteristic
244C22×Dic61—21no—
245C22×Dic61—21no—
246C22×Dic61—21no—
247C22×Dic61—21no—
248C4⋊C4×C61—22no—
249C4⋊C4×C61—21no—
250C4⋊C4×C61C2×D412yes—
251C22⋊C4×C61—24no—
252C22⋊C4×C61—24no—
253C22⋊C4×C61—22no—
254C22⋊C4×C61—24no—
255C22⋊C4×C61—22no—
256C42×C61—21no—
257C42×C61—21no—
258C22⋊Dic61—42no—
259C22⋊Dic61—42no—
260C22⋊Dic61—81no—
261C22⋊Dic61—81no—
262C4⋊Dic61—21no—
263C4⋊Dic61—21no—
264C4⋊Dic61—21no—
265C4⋊Dic61—21no—
266C4⋊Dic61—21no—
267C4⋊Dic61—21no—
268C4⋊Dic61—21no—
269C4⋊Dic61—21no—
270#11758196—42no—
271#11758196—81no—
272C4×Dic61—42no—
273#11758194—44no—
274C2×#92418—21no—
275C2×#92418—21no—
276C2×#92418—21no—
277C2×#92418—21no—
278C2×#92418—21no—
279C2×#92418—21no—
280C2×#92418—21no—
281C2×#92418—21no—
282C2×#92418—21no—
283C2×#92418—21no—
284C2×#92418—21no—
285C2×#92418—21no—
286C23×C61—21no—
287C23×C61—22no—
288C23×C61—21no—
289C23×C61—21no—
290C23×C61—21no—
291C23×C61—21no—
292C23×C61—22no—
293C23×C61—22no—
294C23×C61—21no—
295C23×C61—21no—
296C23×C61—21no—
297C23×C61—21no—
298C23×C61—21no—
299C23×C61—21no—
300C23×C61—21no—
301C23×C61—22no—
302C23×C61—22no—
303C23×C61—48no—
304C23×C61—48no—
305C23×C61—48no—
306C23×C61—48no—
307C23×C61—41no—
308C23×C61—41no—
309C23×C61—41no—
310C23×C61—41no—
311C23×C61—41no—
312C23×C61—41no—
313C23×C61—41no—
314C23×C61—41no—
315C23×C61—41no—
316C23×C61—41no—
317C23×C61—41no—
318C23×C61—41no—
319C23×C61—41no—
320C23×C61—41no—
321C23×C61—41no—
322C23×C61—41no—
323C23×C61—84no—
324C23×C61—84no—
325C23×C61—84no—
326C23×C61—84no—
327C23×C61—84no—
328C23×C61—84no—
329C23×C61—84no—
330C23×C61—84no—
331C23×C61—84no—
332C23×C61—84no—
333C23×C61#12012yes—
334C23×C61AGL(1,ℤ/8)12yes—
335C23×C61C22×D411yescharacteristic
336D4×C61—28no—
337D4×C61—22no—
338D4×C61—22no—
339D4×C61—22no—
340D4×C61—22no—
341D4×C61—22no—
342D4×C61—22no—
343D4×C61—22no—
344D4×C61—48no—
345D4×C61—48no—
346D4×C61—48no—
347D4×C61—48no—
348D4×C61—48no—
349D4×C61—41no—
350D4×C61—41no—
351D4×C61—41no—
352D4×C61—41no—
353D4×C61—84no—
354D4×C61#12314yes—
355C2×C4×C61—21no—
356C2×C4×C61—21no—
357C2×C4×C61—21no—
358C2×C4×C61—21no—
359C2×C4×C61—22no—
360C2×C4×C61—22no—
361C2×C4×C61—22no—
362C2×C4×C61—22no—
363C2×C4×C61—21no—
364C2×C4×C61—21no—
365C2×C4×C61—22no—
366C2×C4×C61—21no—
367C2×C4×C61—21no—
368C2×C4×C61—21no—
369C2×C4×C61—21no—
370C2×C4×C61—48no—
371C2×C4×C61—41no—
372C2×C4×C61—41no—
373C2×C4×C61—41no—
374C2×C4×C61—41no—
375C2×C4×C61—41no—
376C2×C4×C61—41no—
377C2×C4×C61#12012yes—
378C2×C4×C61AGL(1,ℤ/8)12yes—
379C2×C4×C61C22×D411yescharacteristic
380C2×C4×C61C22×D411yescharacteristic
381C2×C4×C61C2×#4111yescharacteristic
382C2×C4×C61C2×#4111yescharacteristic
383C2×C4×C61H(5,𝔽2)11yescharacteristic
384C2×C4×C61H(5,𝔽2)11yescharacteristic
385C2×Dic61—41no—
386C2×Dic61—41no—
387C2×Dic61—41no—
388C2×Dic61—41no—
389C2×Dic61—41no—
390C2×Dic61—41no—
391C2×Dic61—41no—
392C2×Dic61—41no—
393C2×Dic61—41no—
394C2×Dic61—41no—
395C2×Dic61—41no—
396C2×Dic61—41no—
397#92418—41no—
398#92418—41no—
399#92418—41no—
400#92418—41no—
401#24044—611nomaximal, Sylow
402C22×C61—22no—
403C22×C61—24no—
404C22×C61—22no—
405C22×C61—22no—
406C22×C61—22no—
407C22×C61—22no—
408C22×C61—22no—
409C22×C61—41no—
410C22×C61—42no—
411C22×C61—41no—
412C22×C61—42no—
413C22×C61—41no—
414C22×C61—42no—
415C22×C61—41no—
416C22×C61—42no—
417C22×C61—41no—
418C22×C61—41no—
419C22×C61—42no—
420C22×C61—41no—
421C22×C61—41no—
422C22×C61—42no—
423C22×C61—42no—
424C22×C61—42no—
425C22×C61—42no—
426C22×C61—42no—
427C22×C61—42no—
428C22×C61—42no—
429C22×C61—816no—
430C22×C61—816no—
431C22×C61—81no—
432C22×C61—81no—
433C22×C61—81no—
434C22×C61—81no—
435C22×C61—81no—
436C22×C61—81no—
437C22×C61—81no—
438C22×C61—81no—
439C22×C61C2×#12011yescharacteristic
440C22×C61#54611yescharacteristic
441C22×C61#54611yescharacteristic
442C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
443C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
444C22×C61#57611yescharacteristic
445C22×C61#57711yescharacteristic
446C4×C61—22no—
447C4×C61—22no—
448C4×C61—41no—
449C4×C61—42no—
450C4×C61—41no—
451C4×C61C2×#12311yescharacteristic
452C4×C61#53411yescharacteristic
453C4×C61#54611yescharacteristic
454C4×C61#54611yescharacteristic
455Dic61—81no—
456Dic61—81no—
457Dic61—81no—
458Dic61—81no—
459C2×D42D6111yescharacteristic
460C2×#482—611no—
461C2×#418—611no—
462#2485—611no—
463#2041—611no—
464#2041—611no—
465#2034—611no—
466#2033—611no—
467#1895—611no—
468#1870—611no—
469#1864—611no—
470#1862—611no—
471#1786—611no—
472#1786—611no—
473#1786—611no—
474C2×C61—42no—
475C2×C61—42no—
476C2×C61—44no—
477C2×C61—82no—
478C2×C61—82no—
479C2×C61#240511yescharacteristic
480C2×C61#300311yescharacteristic
481C2×C61#301211yescharacteristic
482C2×C61#331011yescharacteristic
483C2×C61#331811yescharacteristic
484C2×C61#332411yescharacteristic
485C2×C61#332511yescharacteristic
486C23×D4—21no—
487C23×D4C2×D6111yescharacteristic
488C23×D4C2×D6111yescharacteristic
489C22×M16—611no—
490D42—24no—
491D42—24no—
492C2×#127C2×D6111yescharacteristic
493C2×#121—21no—
494C2×#121C2×D6111yescharacteristic
495C2×#121C2×D6111yescharacteristic
496C2×#120—21no—
497C2×#120—21no—
498C2×C4×D4C2×D6111yescharacteristic
499C2×C4×D4C2×D6111yescharacteristic
500C2×#117—611no—
501#482—1224no—
502C2×#107—611no—
503C2×#106—611no—
504#418—1224no—
505C2×#102—611no—
506C2×#102—611no—
507C2×#102—611no—
508C2×#102—611no—
509C2×#102—611no—
510C2×#102—611no—
511C2×#102—611no—
512C2×#102—611no—
513C2×#102—611no—
514C2×#102—611no—
515C2×#102—611no—
516C2×#102—611no—
517C2×C22⋊C8—611no—
518C2×C22⋊C8—611no—
519C2×C22⋊C8—611no—
520#397—1221no—
521#394—1221no—
522#389—611no—
523#389—611no—
524#388—1221no—
525#387—1221no—
526#380—611no—
527#380—611no—
528#380—611no—
529#340—611no—
530#340—611no—
531#336—611no—
532#336—611no—
533C61#2404411yescharacteristic, complemented, Sylow
534C25—21no—
535C25—21no—
536C22×D4—22no—
537C22×D4—22no—
538C22×D4—28no—
539C22×D4—21no—
540C22×D4—21no—
541C22×D4—22no—
542C22×D4—22no—
543C22×D4—22no—
544C22×D4—22no—
545C22×D4—21no—
546C22×D4—21no—
547C22×D4—21no—
548C22×D4—22no—
549C22×D4—21no—
550C22×D4—41no—
551C22×D4—41no—
552C22×D4—41no—
553C22×D4—41no—
554C22×D4—44no—
555C22×D4—44no—
556C22×D4C22⋊D6111yescharacteristic
557C22×D4C22⋊D6114yes—
558C22×D4C22×D6111yescharacteristic
559C22×D4C22×D6111yescharacteristic
560C22×D4C22×D6111yescharacteristic
561C23×C4—21no—
562C23×C4C22×D6111yescharacteristic
563C23×C4C22×D6111yescharacteristic
564C2×M16—1222no—
565C2×M16—2441no—
566C2×M16—2441no—
567C22×C8—611no—
568C22×C8—611no—
569C22×C8—611no—
570C22×C8—611no—
571#127—22no—
572#127—22no—
573#121—28no—
574#121—22no—
575#121—22no—
576#121—22no—
577#121C22⋊D6114yes—
578#120—28no—
579#120—28no—
580C4×D4—22no—
581C4×D4—22no—
582C4×D4—22no—
583C4×D4—22no—
584#117—1222no—
585#117—1222no—
586C2×C4⋊C4—611no—
587C2×C4⋊C4—611no—
588C2×C4⋊C4—611no—
589C2×C4⋊C4—611no—
590C2×C4⋊C4—1221no—
591C2×C4⋊C4—1221no—
592C2×C4⋊C4C22⋊D6111yescharacteristic
593C2×C4⋊C4C22×D6111yescharacteristic
594C2×C22⋊C4—21no—
595C2×C22⋊C4—21no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—1221no—
598C2×C22⋊C4—1221no—
599C2×C22⋊C4—1221no—
600C2×C22⋊C4—1221no—
601C2×C22⋊C4C22⋊D6111yescharacteristic
602C2×C22⋊C4C22⋊D6111yescharacteristic
603C2×C42—1221no—
604C2×C42C22×D6111yescharacteristic
605#107—1222no—
606#106—1222no—
607#102—1222no—
608#102—1222no—
609#102—1222no—
610#102—1222no—
611#102—1222no—
612#102—1222no—
613#102—1222no—
614#102—1222no—
615#102—2441no—
616#102—2441no—
617#102—2441no—
618#102—2441no—
619C22⋊C8—1222no—
620C22⋊C8—2441no—
621C22⋊C8—2441no—
622#95—1221no—
623#95—1221no—
624#95—1221no—
625#95—1221no—
626#95—1221no—
627C24—21no—
628C24—24no—
629C24—21no—
630C24—21no—
631C24—24no—
632C24—42no—
633C24—42no—
634C24—42no—
635C24—42no—
636C24—42no—
637C24—42no—
638C24—42no—
639C24—42no—
640C24—81no—
641C24—81no—
642C24—81no—
643C24—81no—
644C24C2×C22⋊D6111yescharacteristic
645C24C2×C22⋊D6111yescharacteristic
646C2×D4—22no—
647C2×D4—22no—
648C2×D4—28no—
649C2×D4—24no—
650C2×D4—24no—
651C2×D4—24no—
652C2×D4—24no—
653C2×D4—24no—
654C2×D4—21no—
655C2×D4—21no—
656C2×D4—21no—
657C2×D4—21no—
658C2×D4—21no—
659C2×D4—21no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—24no—
668C2×D4—22no—
669C2×D4—44no—
670C2×D4—44no—
671C2×D4—44no—
672C2×D4—42no—
673C2×D4—42no—
674C2×D4—42no—
675C2×D4—42no—
676C2×D4—42no—
677C2×D4—44no—
678C2×D4—44no—
679C2×D4—432no—
680C2×D4—44no—
681C2×D4—42no—
682C2×D4—42no—
683C2×D4—42no—
684C2×D4—42no—
685C2×D4—44no—
686C2×D4—42no—
687C2×D4—81no—
688C2×D4—81no—
689C2×D4#1175822412yes—
690C2×D4#1175822412yes—
691C2×D4C2×C22⋊D6112yes—
692C2×D4C2×C22⋊D6112yes—
693C2×D4C2×C22⋊D6112yes—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—24no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—42no—
707C22×C4—42no—
708C22×C4—1221no—
709C22×C4—1221no—
710C22×C4—1221no—
711C22×C4—1221no—
712C22×C4C2×C22⋊D6111yescharacteristic
713C22×C4C2×C22⋊D6111yescharacteristic
714C22×C4C2×C22⋊D6112yes—
715C22×C4C2×C22⋊D6112yes—
716C22×C4C2×C22⋊D6111yescharacteristic
717C22×C4C2×C22⋊D6111yescharacteristic
718C22×C4C23×D6111yescharacteristic
719M16—2444no—
720C2×C8—1221no—
721C2×C8—1221no—
722C2×C8—1221no—
723C2×C8—1221no—
724C2×C8—1221no—
725C2×C8—1221no—
726C2×C8—1221no—
727C2×C8—1221no—
728C2×C8—1221no—
729C2×C8—1221no—
730C2×C8—1221no—
731C2×C8—1221no—
732C4⋊C4—21no—
733C4⋊C4—22no—
734C4⋊C4—1221no—
735C4⋊C4—1221no—
736C4⋊C4—1221no—
737C4⋊C4—1221no—
738C4⋊C4—1221no—
739C4⋊C4—1221no—
740C4⋊C4—1221no—
741C4⋊C4—1221no—
742C4⋊C4—4881no—
743C4⋊C4—2442no—
744C4⋊C4C2×C22⋊D6112yes—
745C22⋊C4—24no—
746C22⋊C4—24no—
747C22⋊C4—22no—
748C22⋊C4—24no—
749C22⋊C4—22no—
750C22⋊C4—4881no—
751C22⋊C4—4881no—
752C22⋊C4—2442no—
753C22⋊C4—2442no—
754C42—21no—
755C42—21no—
756C42—2442no—
757C23—21no—
758C23—22no—
759C23—21no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—21no—
764C23—21no—
765C23—21no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—21no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—48no—
775C23—48no—
776C23—48no—
777C23—48no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—84no—
795C23—84no—
796C23—84no—
797C23—84no—
798C23—84no—
799C23—84no—
800C23—84no—
801C23—84no—
802C23—84no—
803C23—84no—
804C23#1451974612yes—
805C23#1451980312yes—
806C23C22×C22⋊D6111yescharacteristic
807D4—28no—
808D4—22no—
809D4—22no—
810D4—22no—
811D4—22no—
812D4—22no—
813D4—22no—
814D4—22no—
815D4—48no—
816D4—48no—
817D4—48no—
818D4—48no—
819D4—48no—
820D4—41no—
821D4—41no—
822D4—41no—
823D4—41no—
824D4—84no—
825D4#1451975814yes—
826C2×C4—21no—
827C2×C4—21no—
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—22no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—48no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—2441no—
849C2×C4—2441no—
850C2×C4—2441no—
851C2×C4—2441no—
852C2×C4—2441no—
853C2×C4—2441no—
854C2×C4—2441no—
855C2×C4—2441no—
856C2×C4—2441no—
857C2×C4—2441no—
858C2×C4—2441no—
859C2×C4—2441no—
860C2×C4#1451974612yes—
861C2×C4#1451980312yes—
862C2×C4C22×C22⋊D6111yescharacteristic
863C2×C4C22×C22⋊D6111yescharacteristic
864C2×C4C2×#1175822411yescharacteristic
865C2×C4C2×#1175822411yescharacteristic
866C2×C4#1451982211yescharacteristic
867C2×C4#1451982211yescharacteristic
868C8—2441no—
869C8—2441no—
870C8—2441no—
871C8—2441no—
872C22—22no—
873C22—22no—
874C22—22no—
875C22—22no—
876C22—24no—
877C22—22no—
878C22—22no—
879C22—41no—
880C22—42no—
881C22—41no—
882C22—42no—
883C22—41no—
884C22—41no—
885C22—42no—
886C22—41no—
887C22—41no—
888C22—42no—
889C22—41no—
890C22—42no—
891C22—41no—
892C22—42no—
893C22—42no—
894C22—42no—
895C22—42no—
896C22—42no—
897C22—42no—
898C22—42no—
899C22—816no—
900C22—816no—
901C22—81no—
902C22—81no—
903C22—81no—
904C22—81no—
905C22—81no—
906C22—81no—
907C22—81no—
908C22—81no—
909C22C2×#1451974611yescharacteristic
910C22#1684040611yescharacteristic
911C22#1684040611yescharacteristic
912C22C2×#1451980311yescharacteristic
913C22C2×#1451980311yescharacteristic
914C22#1684056511yescharacteristic
915C22#1684057311yescharacteristic
916C4—22no—
917C4—22no—
918C4—41no—
919C4—41no—
920C4—42no—
921C4—4881no—
922C4—4881no—
923C4—4881no—
924C4—4881no—
925C4C2×#1451975811yescharacteristic
926C4#1684032111yescharacteristic
927C4#1684040611yescharacteristic
928C4#1684040611yescharacteristic
929C2—42no—
930C2—42no—
931C2—44no—
932C2—82no—
933C2—82no—
934C2#2144914211yescharacteristic
935C2#2145504611yescharacteristic
936C2#2145512311yescharacteristic
937C2#2145784011yescharacteristic
938C2#2145796011yescharacteristic
939C2#2145805011yescharacteristic
940C2#2145806111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
Fitting, prime radicalC2×D42×C61C2
socleC23×C61C22×D4
hypercenterC2×D42D61
hypocenterC61#24044
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×D42

Complements

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

NH ≅ G/Ntype
1. C2×#16840083C2semidirect
2. C2×#16839767C2semidirect
3. #21450116C2semidirect
4. #21447050C2semidirect
5. #21447050C2semidirect
6. #21447005C2semidirect
7. #21446998C2semidirect
8. #21446258C2semidirect
9. #21446117C2semidirect
10. #21446080C2semidirect
11. #21446066C2semidirect
12. #21445750C2semidirect
13. #21445750C2semidirect
14. #21445750C2semidirect
16. C22×#11758194C22semidirect
17. C2×#14519736C22semidirect
19. C2×#14519710C22semidirect
20. C2×#14519708C22semidirect
26. C2×#14519698C22semidirect
27. C2×#14519698C22semidirect
28. C2×#14519698C22semidirect
29. C2×#14519698C22semidirect
30. C2×#14519698C22semidirect
31. C2×#14519698C22semidirect
32. C2×#14519698C22semidirect
33. C2×#14519698C22semidirect
34. C2×C22⋊#92418C22semidirect
35. C2×C22⋊#92418C22semidirect
36. C2×C22⋊#92418C22semidirect
39. #16839660C22semidirect
40. #16839660C22semidirect
43. #16839622C22semidirect
44. #16839622C22semidirect
45. #16839622C22semidirect
46. #16839524C22semidirect
47. #16839524C22semidirect
48. #16839517C22semidirect
49. #16839517C22semidirect
533. C61#24044semidirect

Maximal subgroups

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

subgroupindex
C2×#168400832
C2×#168397672
#214501162
#214470502
#214470052
#214469982
#214462582
#214461172
#214460802
#214460662
#214457502
C2×D42×C612
#2404461