Finite Group Databasebeta

← #29713044

Subgroups — #29713044

Order 15616.

1322 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840100C211yesmaximal, characteristic, complemented
2C2×#16839758C211yesmaximal, characteristic, complemented
3#21450116C211yesmaximal, characteristic, complemented
4#21447055C211yesmaximal, characteristic, complemented
5#21447055C211yesmaximal, characteristic, complemented
6#21447005C211yesmaximal, characteristic, complemented
7#21446998C211yesmaximal, characteristic, complemented
8#21446243C211yesmaximal, characteristic, complemented
9#21446112C211yesmaximal, characteristic, complemented
10#21446087C211yesmaximal, characteristic, complemented
11#21446073C211yesmaximal, characteristic, complemented
12#21445759C211yesmaximal, characteristic, complemented
13#21445754C211yesmaximal, characteristic, complemented
14#21445754C211yesmaximal, characteristic, complemented
15C2×C61×#548C211yesmaximal, characteristic
16C23×#92418C2211yescharacteristic
17C2×#14519736C2211yescharacteristic
18#16840100—24no—
19C2×#14519710C2211yescharacteristic
20C2×#14519708C2211yescharacteristic
21#16839758—24no—
22C2×#14519701C2211yescharacteristic
23C2×#14519701C2211yescharacteristic
24C2×#14519701C2211yescharacteristic
25C2×#14519701C2211yescharacteristic
26C2×#14519701C2211yescharacteristic
27C2×#14519701C2211yescharacteristic
28C2×#14519701C2211yescharacteristic
29C2×#14519701C2211yescharacteristic
30C2×#14519698C2211yescharacteristic
31C2×#14519698C2211yescharacteristic
32C2×#14519698C2211yescharacteristic
33C2×#14519698C2211yescharacteristic
34C2×C22⋊#92418C2211yescharacteristic
35C2×C22⋊#92418C2211yescharacteristic
36C2×C22⋊#92418C2211yescharacteristic
37#16839690—21no—
38#16839676—21no—
39#16839660C2211yescharacteristic
40#16839660C2211yescharacteristic
41#16839650—21no—
42#16839643—21no—
43#16839622C2211yescharacteristic
44#16839622C2211yescharacteristic
45#16839622C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839517C2211yescharacteristic
49#16839517C2211yescharacteristic
50C22×#41×C61C2211yescharacteristic
51C23×Q8×C61C2211yescharacteristic
52C61×#548—24no—
53C61×#548—24no—
54C2×#124×C61—21no—
55C2×#124×C61C2211yescharacteristic
56C2×C22⋊Q8×C61—21no—
57C2×C22⋊Q8×C61C2211yescharacteristic
58C2×#121×C61—21no—
59C2×#121×C61C2211yescharacteristic
60C2×C4×Q8×C61C2211yescharacteristic
61C2×C4×D4×C61—21no—
62C2×C4×D4×C61C2211yescharacteristic
63C22×#92418—22no—
64C22×#92418—41no—
65C22×#92418—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#14519701—22no—
86#14519701—22no—
87#14519701—22no—
88#14519701—22no—
89#14519701—22no—
90#14519701—22no—
91#14519701—41no—
92#14519701—41no—
93#14519698—22no—
94#14519698—22no—
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—
105C2×#41×C61—22no—
106C2×#41×C61—22no—
107C2×#41×C61—22no—
108C2×#41×C61—41no—
109C2×#41×C61—41no—
110C2×#41×C61D414yes—
111C22×Q8×C61—22no—
112C22×Q8×C61—22no—
113C22×Q8×C61—21no—
114C22×Q8×C61—22no—
115C22×Q8×C61—22no—
116C22×Q8×C61—41no—
117C22×Q8×C61—41no—
118C22×Q8×C61C2311yescharacteristic
119C22×Q8×C61C2311yescharacteristic
120C22×D4×C61—21no—
121C22×D4×C61—21no—
122C22×D4×C61D411yescharacteristic
123C22×D4×C61C2311yescharacteristic
124C23×C4×C61—21no—
125C23×C4×C61—21no—
126C23×C4×C61C2311yescharacteristic
127C23×C4×C61C2311yescharacteristic
128#124×C61—28no—
129#124×C61—22no—
130#124×C61—22no—
131C22⋊Q8×C61—28no—
132C22⋊Q8×C61—22no—
133C22⋊Q8×C61D414yes—
134#121×C61—28no—
135#121×C61—22no—
136#121×C61—22no—
137C4×Q8×C61—22no—
138C4×Q8×C61—22no—
139C4×D4×C61—28no—
140C4×D4×C61—22no—
141C4×D4×C61—22no—
142C2×C4⋊C4×C61—21no—
143C2×C4⋊C4×C61—21no—
144C2×C4⋊C4×C61D411yescharacteristic
145C2×C4⋊C4×C61C2311yescharacteristic
146C2×C22⋊C4×C61—21no—
147C2×C22⋊C4×C61—21no—
148C2×C22⋊C4×C61—21no—
149C2×C22⋊C4×C61—21no—
150C2×C22⋊C4×C61D411yescharacteristic
151C2×C22⋊C4×C61D411yescharacteristic
152C2×C42×C61—21no—
153C2×C42×C61C2311yescharacteristic
154C24×C61—21no—
155C24×C61C2×D411yescharacteristic
156C24×C61C2×D411yescharacteristic
157#41×C61—28no—
158#41×C61—44no—
159#41×C61—44no—
160#41×C61—44no—
161C2×Q8×C61—24no—
162C2×Q8×C61—21no—
163C2×Q8×C61—21no—
164C2×Q8×C61—21no—
165C2×Q8×C61—21no—
166C2×Q8×C61—21no—
167C2×Q8×C61—21no—
168C2×Q8×C61—21no—
169C2×Q8×C61—21no—
170C2×Q8×C61—42no—
171C2×Q8×C61—42no—
172C2×Q8×C61—44no—
173C2×Q8×C61—44no—
174C2×Q8×C61—44no—
175C2×Q8×C61—44no—
176C2×Q8×C61C2×D412yes—
177C2×Q8×C61C2×D412yes—
178C2×Q8×C61#4112yes—
179C2×Q8×C61#4112yes—
180C2×D4×C61—24no—
181C2×D4×C61—22no—
182C2×D4×C61—24no—
183C2×D4×C61—22no—
184C2×D4×C61—21no—
185C2×D4×C61—21no—
186C2×D4×C61—21no—
187C2×D4×C61—21no—
188C2×D4×C61—21no—
189C2×D4×C61—41no—
190C2×D4×C61—42no—
191C2×D4×C61—42no—
192C2×D4×C61—42no—
193C2×D4×C61—42no—
194C2×D4×C61C2×D412yes—
195C22×C4×C61—21no—
196C22×C4×C61—21no—
197C22×C4×C61—21no—
198C22×C4×C61—21no—
199C22×C4×C61—21no—
200C22×C4×C61—24no—
201C22×C4×C61—21no—
202C22×C4×C61—21no—
203C22×C4×C61—24no—
204C22×C4×C61—21no—
205C22×C4×C61—21no—
206C22×C4×C61—21no—
207C22×C4×C61—21no—
208C22×C4×C61—21no—
209C22×C4×C61—21no—
210C22×C4×C61—42no—
211C22×C4×C61—42no—
212C22×C4×C61—42no—
213C22×C4×C61—42no—
214C22×C4×C61C2×D411yescharacteristic
215C22×C4×C61C2×D411yescharacteristic
216C22×C4×C61C2×D411yescharacteristic
217C22×C4×C61C2×D411yescharacteristic
218C22×C4×C61C2×D412yes—
219C22×C4×C61C2×D412yes—
220C22×C4×C61C2411yescharacteristic
221C22×Dic61—21no—
222C22×Dic61—21no—
223C22×Dic61—21no—
224C22×Dic61—21no—
225C4⋊C4×C61—24no—
226C4⋊C4×C61—24no—
227C4⋊C4×C61—22no—
228C4⋊C4×C61—21no—
229C4⋊C4×C61C2×D412yes—
230C22⋊C4×C61—24no—
231C22⋊C4×C61—24no—
232C22⋊C4×C61—24no—
233C22⋊C4×C61—24no—
234C22⋊C4×C61—22no—
235C22⋊C4×C61—22no—
236C42×C61—24no—
237C42×C61—21no—
238C42×C61—21no—
239C22⋊Dic61—42no—
240C22⋊Dic61—42no—
241C22⋊Dic61—81no—
242C22⋊Dic61—81no—
243C4⋊Dic61—21no—
244C4⋊Dic61—21no—
245C4⋊Dic61—21no—
246C4⋊Dic61—21no—
247C4⋊Dic61—21no—
248C4⋊Dic61—21no—
249C4⋊Dic61—21no—
250C4⋊Dic61—21no—
251#11758196—42no—
252#11758196—81no—
253C4×Dic61—42no—
254C2×#92418—21no—
255C2×#92418—21no—
256C2×#92418—21no—
257C2×#92418—21no—
258C2×#92418—21no—
259C2×#92418—21no—
260C2×#92418—21no—
261C2×#92418—21no—
262C2×#92418—21no—
263C2×#92418—21no—
264C2×#92418—21no—
265C2×#92418—21no—
266C2×#92418—44no—
267C23×C61—21no—
268C23×C61—21no—
269C23×C61—21no—
270C23×C61—21no—
271C23×C61—21no—
272C23×C61—21no—
273C23×C61—21no—
274C23×C61—21no—
275C23×C61—21no—
276C23×C61—21no—
277C23×C61—21no—
278C23×C61—21no—
279C23×C61—22no—
280C23×C61—41no—
281C23×C61—41no—
282C23×C61—41no—
283C23×C61—41no—
284C23×C61—41no—
285C23×C61—41no—
286C23×C61#12012yes—
287C23×C61#13512yes—
288C23×C61C22×D411yescharacteristic
289Q8×C61—22no—
290Q8×C61—22no—
291Q8×C61—22no—
292Q8×C61—22no—
293Q8×C61—22no—
294Q8×C61—48no—
295Q8×C61—41no—
296Q8×C61—41no—
297Q8×C61#12314yes—
298D4×C61—22no—
299D4×C61—22no—
300D4×C61—48no—
301D4×C61—44no—
302D4×C61—48no—
303D4×C61—41no—
304D4×C61—41no—
305C2×C4×C61—22no—
306C2×C4×C61—21no—
307C2×C4×C61—21no—
308C2×C4×C61—22no—
309C2×C4×C61—22no—
310C2×C4×C61—22no—
311C2×C4×C61—22no—
312C2×C4×C61—22no—
313C2×C4×C61—22no—
314C2×C4×C61—21no—
315C2×C4×C61—21no—
316C2×C4×C61—22no—
317C2×C4×C61—22no—
318C2×C4×C61—21no—
319C2×C4×C61—21no—
320C2×C4×C61—21no—
321C2×C4×C61—21no—
322C2×C4×C61—21no—
323C2×C4×C61—21no—
324C2×C4×C61—21no—
325C2×C4×C61—48no—
326C2×C4×C61—48no—
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#12012yes—
336C2×C4×C61C22×D411yescharacteristic
337C2×C4×C61C22×D411yescharacteristic
338C2×C4×C61C2×#4111yescharacteristic
339C2×C4×C61C2×#4111yescharacteristic
340C2×C4×C61H(5,𝔽2)11yescharacteristic
341C2×C4×C61H(5,𝔽2)11yescharacteristic
342C2×Dic61—41no—
343C2×Dic61—41no—
344C2×Dic61—41no—
345C2×Dic61—41no—
346C2×Dic61—41no—
347C2×Dic61—41no—
348C2×Dic61—41no—
349C2×Dic61—41no—
350C2×Dic61—41no—
351C2×Dic61—41no—
352C2×Dic61—41no—
353C2×Dic61—41no—
354#92418—41no—
355#92418—41no—
356#92418—41no—
357#92418—41no—
358#24040—611nomaximal, Sylow
359C22×C61—22no—
360C22×C61—22no—
361C22×C61—22no—
362C22×C61—22no—
363C22×C61—22no—
364C22×C61—22no—
365C22×C61—41no—
366C22×C61—41no—
367C22×C61—41no—
368C22×C61—41no—
369C22×C61—41no—
370C22×C61—41no—
371C22×C61—41no—
372C22×C61—41no—
373C22×C61—42no—
374C22×C61—42no—
375C22×C61—42no—
376C22×C61—81no—
377C22×C61—81no—
378C22×C61—81no—
379C22×C61—81no—
380C22×C61C2×#12011yescharacteristic
381C22×C61#54611yescharacteristic
382C22×C61#54611yescharacteristic
383C22×C61C2×#13511yescharacteristic
384C22×C61#57511yescharacteristic
385C22×C61#57711yescharacteristic
386C22×C61#57811yescharacteristic
387C4×C61—22no—
388C4×C61—24no—
389C4×C61—41no—
390C4×C61—42no—
391C4×C61—41no—
392C4×C61—42no—
393C4×C61—41no—
394C4×C61C2×#12311yescharacteristic
395C4×C61#53411yescharacteristic
396C4×C61#54611yescharacteristic
397C4×C61#54611yescharacteristic
398Dic61—81no—
399Dic61—81no—
400Dic61—81no—
401Dic61—81no—
402C2×#548D6111yescharacteristic
403C2×#485—611no—
404C2×#416—611no—
405#2485—611no—
406#2042—611no—
407#2042—611no—
408#2034—611no—
409#2033—611no—
410#1892—611no—
411#1869—611no—
412#1865—611no—
413#1863—611no—
414#1788—611no—
415#1787—611no—
416#1787—611no—
417C2×C61—42no—
418C2×C61—42no—
419C2×C61—82no—
420C2×C61#240511yescharacteristic
421C2×C61#300211yescharacteristic
422C2×C61#301311yescharacteristic
423C2×C61#330011yescharacteristic
424C2×C61#330111yescharacteristic
425C2×C61#331311yescharacteristic
426C2×C61#332111yescharacteristic
427C22×#41C2×D6111yescharacteristic
428C23×Q8C2×D6111yescharacteristic
429C23×C8—611no—
430#548—24no—
431#548—24no—
432C2×#124—21no—
433C2×#124C2×D6111yescharacteristic
434C2×C22⋊Q8—21no—
435C2×C22⋊Q8C2×D6111yescharacteristic
436C2×#121—21no—
437C2×#121C2×D6111yescharacteristic
438C2×C4×Q8C2×D6111yescharacteristic
439C2×C4×D4—21no—
440C2×C4×D4C2×D6111yescharacteristic
441C2×#117—611no—
442#485—1224no—
443C2×#107—611no—
444C2×#106—611no—
445#416—1224no—
446C2×#103—611no—
447C2×#103—611no—
448C2×#103—611no—
449C2×#103—611no—
450C2×#103—611no—
451C2×#103—611no—
452C2×#103—611no—
453C2×#103—611no—
454C2×#102—611no—
455C2×#102—611no—
456C2×#102—611no—
457C2×#102—611no—
458C2×C22⋊C8—611no—
459C2×C22⋊C8—611no—
460C2×C22⋊C8—611no—
461#397—1221no—
462#394—1221no—
463#389—611no—
464#389—611no—
465#388—1221no—
466#387—1221no—
467#380—611no—
468#380—611no—
469#380—611no—
470#340—611no—
471#340—611no—
472#336—611no—
473#336—611no—
474C61#2404011yescharacteristic, complemented, Sylow
475C2×#41—22no—
476C2×#41—22no—
477C2×#41—22no—
478C2×#41—41no—
479C2×#41—41no—
480C2×#41C22⋊D6114yes—
481C22×Q8—22no—
482C22×Q8—22no—
483C22×Q8—21no—
484C22×Q8—22no—
485C22×Q8—22no—
486C22×Q8—41no—
487C22×Q8—41no—
488C22×Q8C22×D6111yescharacteristic
489C22×Q8C22×D6111yescharacteristic
490C22×D4—21no—
491C22×D4—21no—
492C22×D4C22⋊D6111yescharacteristic
493C22×D4C22×D6111yescharacteristic
494C23×C4—21no—
495C23×C4—21no—
496C23×C4C22×D6111yescharacteristic
497C23×C4C22×D6111yescharacteristic
498C22×C8—611no—
499C22×C8—611no—
500C22×C8—611no—
501C22×C8—611no—
502C22×C8—1222no—
503C22×C8—2441no—
504C22×C8—2441no—
505#124—28no—
506#124—22no—
507#124—22no—
508C22⋊Q8—28no—
509C22⋊Q8—22no—
510C22⋊Q8C22⋊D6114yes—
511#121—28no—
512#121—22no—
513#121—22no—
514C4×Q8—22no—
515C4×Q8—22no—
516C4×D4—28no—
517C4×D4—22no—
518C4×D4—22no—
519#117—1222no—
520#117—1222no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—21no—
523C2×C4⋊C4—611no—
524C2×C4⋊C4—611no—
525C2×C4⋊C4—611no—
526C2×C4⋊C4—611no—
527C2×C4⋊C4—1221no—
528C2×C4⋊C4—1221no—
529C2×C4⋊C4C22⋊D6111yescharacteristic
530C2×C4⋊C4C22×D6111yescharacteristic
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—1221no—
536C2×C22⋊C4—1221no—
537C2×C22⋊C4—1221no—
538C2×C22⋊C4—1221no—
539C2×C22⋊C4C22⋊D6111yescharacteristic
540C2×C22⋊C4C22⋊D6111yescharacteristic
541C2×C42—21no—
542C2×C42—1221no—
543C2×C42C22×D6111yescharacteristic
544#107—1222no—
545#106—1222no—
546#103—1222no—
547#103—1222no—
548#103—1222no—
549#103—1222no—
550#103—1222no—
551#103—1222no—
552#103—2441no—
553#103—2441no—
554#102—1222no—
555#102—1222no—
556#102—2441no—
557#102—2441no—
558C22⋊C8—1222no—
559C22⋊C8—2441no—
560C22⋊C8—2441no—
561#95—1221no—
562#95—1221no—
563#95—1221no—
564#95—1221no—
565#95—1221no—
566C24—21no—
567C24C2×C22⋊D6111yescharacteristic
568C24C2×C22⋊D6111yescharacteristic
569#41—28no—
570#41—44no—
571#41—44no—
572#41—44no—
573C2×Q8—24no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8—21no—
580C2×Q8—21no—
581C2×Q8—21no—
582C2×Q8—42no—
583C2×Q8—42no—
584C2×Q8—44no—
585C2×Q8—44no—
586C2×Q8—44no—
587C2×Q8—44no—
588C2×Q8#1175822412yes—
589C2×Q8#1175822412yes—
590C2×Q8C2×C22⋊D6112yes—
591C2×Q8C2×C22⋊D6112yes—
592C2×D4—24no—
593C2×D4—22no—
594C2×D4—24no—
595C2×D4—22no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—41no—
602C2×D4—42no—
603C2×D4—42no—
604C2×D4—42no—
605C2×D4—42no—
606C2×D4C2×C22⋊D6112yes—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—24no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—24no—
622C22×C4—42no—
623C22×C4—42no—
624C22×C4—42no—
625C22×C4—42no—
626C22×C4—1221no—
627C22×C4—1221no—
628C22×C4—1221no—
629C22×C4—1221no—
630C22×C4C2×C22⋊D6111yescharacteristic
631C22×C4C2×C22⋊D6111yescharacteristic
632C22×C4C2×C22⋊D6111yescharacteristic
633C22×C4C2×C22⋊D6112yes—
634C22×C4C2×C22⋊D6112yes—
635C22×C4C2×C22⋊D6111yescharacteristic
636C22×C4C23×D6111yescharacteristic
637C2×C8—1221no—
638C2×C8—1221no—
639C2×C8—1221no—
640C2×C8—1221no—
641C2×C8—1221no—
642C2×C8—1221no—
643C2×C8—1221no—
644C2×C8—1221no—
645C2×C8—1221no—
646C2×C8—1221no—
647C2×C8—1221no—
648C2×C8—1221no—
649C2×C8—2444no—
650C4⋊C4—24no—
651C4⋊C4—21no—
652C4⋊C4—24no—
653C4⋊C4—22no—
654C4⋊C4—1221no—
655C4⋊C4—1221no—
656C4⋊C4—1221no—
657C4⋊C4—1221no—
658C4⋊C4—1221no—
659C4⋊C4—1221no—
660C4⋊C4—1221no—
661C4⋊C4—1221no—
662C4⋊C4—4881no—
663C4⋊C4—2442no—
664C4⋊C4C2×C22⋊D6112yes—
665C22⋊C4—24no—
666C22⋊C4—24no—
667C22⋊C4—24no—
668C22⋊C4—24no—
669C22⋊C4—22no—
670C22⋊C4—22no—
671C22⋊C4—4881no—
672C22⋊C4—4881no—
673C22⋊C4—2442no—
674C22⋊C4—2442no—
675C42—24no—
676C42—21no—
677C42—21no—
678C42—2442no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—22no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23#1451974612yes—
699C23#1451979712yes—
700C23C22×C22⋊D6111yescharacteristic
701Q8—22no—
702Q8—22no—
703Q8—22no—
704Q8—22no—
705Q8—22no—
706Q8—48no—
707Q8—41no—
708Q8—41no—
709Q8#1451975814yes—
710D4—22no—
711D4—22no—
712D4—48no—
713D4—44no—
714D4—48no—
715D4—41no—
716D4—41no—
717C2×C4—22no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—48no—
738C2×C4—48no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—2441no—
748C2×C4—2441no—
749C2×C4—2441no—
750C2×C4—2441no—
751C2×C4—2441no—
752C2×C4—2441no—
753C2×C4—2441no—
754C2×C4—2441no—
755C2×C4—2441no—
756C2×C4—2441no—
757C2×C4—2441no—
758C2×C4—2441no—
759C2×C4#1451974612yes—
760C2×C4C22×C22⋊D6111yescharacteristic
761C2×C4C22×C22⋊D6111yescharacteristic
762C2×C4C2×#1175822411yescharacteristic
763C2×C4C2×#1175822411yescharacteristic
764C2×C4#1451982211yescharacteristic
765C2×C4#1451982211yescharacteristic
766C8—2441no—
767C8—2441no—
768C8—2441no—
769C8—2441no—
770C22—22no—
771C22—22no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—81no—
788C22—81no—
789C22—81no—
790C22—81no—
791C22C2×#1451974611yescharacteristic
792C22#1684040611yescharacteristic
793C22#1684040611yescharacteristic
794C22C2×#1451979711yescharacteristic
795C22#1684056011yescharacteristic
796C22#1684057011yescharacteristic
797C22#1684057711yescharacteristic
798C4—22no—
799C4—24no—
800C4—41no—
801C4—41no—
802C4—42no—
803C4—41no—
804C4—42no—
805C4—4881no—
806C4—4881no—
807C4—4881no—
808C4—4881no—
809C4C2×#1451975811yescharacteristic
810C4#1684032111yescharacteristic
811C4#1684040611yescharacteristic
812C4#1684040611yescharacteristic
813C2—42no—
814C2—42no—
815C2—82no—
816C2#2144914211yescharacteristic
817C2#2145503711yescharacteristic
818C2#2145513411yescharacteristic
819C2#2145770611yescharacteristic
820C2#2145772111yescharacteristic
821C2#2145788511yescharacteristic
822C2#2145800511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
Fitting, prime radicalC2×C61×#548C2
socleC23×C61C22×D4
hypercenterC2×#548D61
hypocenterC61#24040
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C2×#16840100C2semidirect
2. C2×#16839758C2semidirect
3. #21450116C2semidirect
4. #21447055C2semidirect
5. #21447055C2semidirect
6. #21447005C2semidirect
7. #21446998C2semidirect
8. #21446243C2semidirect
9. #21446112C2semidirect
10. #21446087C2semidirect
11. #21446073C2semidirect
12. #21445759C2semidirect
13. #21445754C2semidirect
14. #21445754C2semidirect
474. C61#24040semidirect

Maximal subgroups

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

subgroupindex
C2×#168401002
C2×#168397582
#214501162
#214470552
#214470052
#214469982
#214462432
#214461122
#214460872
#214460732
#214457592
#214457542
C2×C61×#5482
#2404061