Finite Group Databasebeta

← #29717634

Subgroups — #29717634

Order 15616.

1632 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839996C211yesmaximal, characteristic, complemented
2C2×#16839907C211yesmaximal, characteristic, complemented
3C2×#16839896C211yesmaximal, characteristic, complemented
4C2×#16839758C211yesmaximal, characteristic, complemented
5#21449237C211yesmaximal, characteristic, complemented
6#21447055C211yesmaximal, characteristic, complemented
7#21447019C211yesmaximal, characteristic, complemented
8#21446896C211yesmaximal, characteristic, complemented
9#21446820C211yesmaximal, characteristic, complemented
10#21446167C211yesmaximal, characteristic, complemented
11#21446142C211yesmaximal, characteristic, complemented
12#21446112C211yesmaximal, characteristic, complemented
13#21446066C211yesmaximal, characteristic, complemented
14#21445750C211yesmaximal, characteristic, complemented
15C2×C61×#546C211yesmaximal, characteristic, complemented
16C22×#11758201C2211yescharacteristic, complemented
17C22×#11758199C2211yescharacteristic
18C22×#11758199C2211yescharacteristic
19C23×#92418C2211yescharacteristic, complemented
20C2×#14519751C2211yescharacteristic
21C2×#14519751C2211yescharacteristic, complemented
22C2×#14519736C2211yescharacteristic, complemented
23#16839996—24no—
24#16839907—24no—
25#16839896—24no—
26C2×#14519710C2211yescharacteristic, complemented
27#16839758—24no—
28C2×#14519701C2211yescharacteristic, complemented
29C2×#14519701C2211yescharacteristic, complemented
30C2×#14519701C2211yescharacteristic, complemented
31C2×#14519698C2211yescharacteristic
32C2×#14519698C2211yescharacteristic
33C2×#14519698C2211yescharacteristic
34C2×#14519698C2211yescharacteristic
35C2×#14519698C2211yescharacteristic
36C2×#14519698C2211yescharacteristic
37C2×#14519697C2211yescharacteristic, complemented
38C2×C22⋊#92418C2211yescharacteristic
39C2×C22⋊#92418C2211yescharacteristic
40C2×C22⋊#92418C2211yescharacteristic, complemented
41#16839677—21no—
42#16839670—21no—
43#16839664C2211yescharacteristic, complemented
44#16839662—21no—
45#16839660C2211yescharacteristic, complemented
46#16839652—21no—
47#16839622C2211yescharacteristic
48#16839524C2211yescharacteristic, complemented
49#16839524C2211yescharacteristic, complemented
50#16839517C2211yescharacteristic, complemented
51#16839517C2211yescharacteristic, complemented
52C22×#41×C61C2211yescharacteristic
53C23×D4×C61C2211yescharacteristic
54C61×#546—24no—
55C61×#546—24no—
56C2×#124×C61C2211yescharacteristic
57C2×#123×C61—21no—
58C2×C22⋊Q8×C61C2211yescharacteristic
59C2×#121×C61—21no—
60C2×#121×C61C2211yescharacteristic
61C2×#120×C61—21no—
62C2×C4×D4×C61C2211yescharacteristic
63C2×C4×D4×C61C2211yescharacteristic
64C22×C22⋊C4×C61—21no—
65C22×D244C2311yescharacteristic
66C22×C22⋊D61—21no—
67C22×C22⋊D61—21no—
68C2×#11758201—22no—
69C2×#11758201—41no—
70C2×#11758201—41no—
71C2×#11758199—22no—
72C2×#11758199—22no—
73C2×#11758199—22no—
74C2×#11758199—22no—
75C2×#11758199—22no—
76C2×#11758199—41no—
77C22×#92418—22no—
78C22×#92418—22no—
79C22×#92418—41no—
80C22×#92418C2311yescharacteristic
81C22×#92418C2311yescharacteristic
82C22×#92418C2311yescharacteristic
83C22×#92418C2311yescharacteristic
84#14519751—22no—
85#14519751—22no—
86#14519751—22no—
87#14519751—41no—
88#14519736—22no—
89#14519736—41no—
90C2×C4⋊Dic61C2311yescharacteristic
91C2×C4⋊Dic61C2311yescharacteristic
92C2×C4⋊Dic61C2311yescharacteristic
93C2×#11758196—21no—
94C2×C22⋊Dic61—21no—
95C2×C22⋊Dic61—21no—
96C2×#11758198—21no—
97C2×#11758198—21no—
98C2×#11758198—21no—
99C2×#11758198—21no—
100C2×C4×Dic61—21no—
101#14519710—22no—
102#14519701—22no—
103#14519701—22no—
104#14519701—22no—
105#14519698—22no—
106#14519698—22no—
107#14519698—22no—
108#14519698—22no—
109#14519698—41no—
110#14519698D414yescomplemented
111#14519697—22no—
112C22⋊#92418—22no—
113C22⋊#92418—22no—
114C22⋊#92418—41no—
115#14519684—21no—
116#14519684—21no—
117C25×C61—21no—
118C2×#41×C61—22no—
119C2×#41×C61—22no—
120C2×#41×C61—22no—
121C2×#41×C61—41no—
122C2×#41×C61—41no—
123C2×#41×C61D414yescomplemented
124C22×Q8×C61C2311yescharacteristic
125C22×D4×C61—21no—
126C22×D4×C61—21no—
127C22×D4×C61—22no—
128C22×D4×C61—22no—
129C22×D4×C61—22no—
130C22×D4×C61—22no—
131C22×D4×C61—21no—
132C22×D4×C61—41no—
133C22×D4×C61—41no—
134C22×D4×C61D411yescharacteristic
135C22×D4×C61C2311yescharacteristic
136C22×D4×C61C2311yescharacteristic
137C23×C4×C61—21no—
138C23×C4×C61—21no—
139C23×C4×C61C2311yescharacteristic
140C23×C4×C61C2311yescharacteristic
141#124×C61—22no—
142#124×C61—22no—
143#123×C61—28no—
144C22⋊Q8×C61—22no—
145C22⋊Q8×C61—22no—
146#121×C61—28no—
147#121×C61—22no—
148#121×C61D414yescomplemented
149#120×C61—28no—
150C4×D4×C61—22no—
151C4×D4×C61—22no—
152C4×D4×C61—22no—
153C4×D4×C61—22no—
154C2×C4⋊C4×C61—21no—
155C2×C4⋊C4×C61D411yescharacteristic
156C2×C4⋊C4×C61C2311yescharacteristic
157C2×C22⋊C4×C61—28no—
158C2×C22⋊C4×C61—21no—
159C2×C22⋊C4×C61—21no—
160C2×C22⋊C4×C61—21no—
161C2×C22⋊C4×C61—21no—
162C2×C22⋊C4×C61—21no—
163C2×C22⋊C4×C61D411yescharacteristic
164C2×C22⋊C4×C61D411yescharacteristic
165C2×C42×C61C2311yescharacteristic
166C24×C61—21no—
167C24×C61—24no—
168C24×C61—21no—
169C24×C61—42no—
170C24×C61—42no—
171C24×C61—42no—
172C24×C61—42no—
173C24×C61—81no—
174C24×C61—81no—
175C24×C61C2×D411yescharacteristic
176C24×C61C2×D411yescharacteristic
177C23×D61—21no—
178#41×C61—28no—
179#41×C61—44no—
180#41×C61—44no—
181#41×C61—44no—
182C2×Q8×C61—21no—
183C2×Q8×C61—21no—
184C2×Q8×C61—21no—
185C2×Q8×C61—21no—
186C2×Q8×C61—21no—
187C2×Q8×C61C2×D412yes—
188C2×D4×C61—24no—
189C2×D4×C61—22no—
190C2×D4×C61—24no—
191C2×D4×C61—22no—
192C2×D4×C61—24no—
193C2×D4×C61—21no—
194C2×D4×C61—21no—
195C2×D4×C61—21no—
196C2×D4×C61—21no—
197C2×D4×C61—21no—
198C2×D4×C61—21no—
199C2×D4×C61—21no—
200C2×D4×C61—21no—
201C2×D4×C61—41no—
202C2×D4×C61—42no—
203C2×D4×C61—42no—
204C2×D4×C61—44no—
205C2×D4×C61—44no—
206C2×D4×C61—44no—
207C2×D4×C61—42no—
208C2×D4×C61—42no—
209C2×D4×C61—44no—
210C2×D4×C61—81no—
211C2×D4×C61—81no—
212C2×D4×C61C2×D412yes—
213C2×D4×C61C2×D412yes—
214C2×D4×C61C2×D412yes—
215C2×D4×C61#4112yes—
216C22×C4×C61—21no—
217C22×C4×C61—21no—
218C22×C4×C61—21no—
219C22×C4×C61—21no—
220C22×C4×C61—21no—
221C22×C4×C61—21no—
222C22×C4×C61—24no—
223C22×C4×C61—24no—
224C22×C4×C61—21no—
225C22×C4×C61—21no—
226C22×C4×C61—21no—
227C22×C4×C61—21no—
228C22×C4×C61—21no—
229C22×C4×C61—21no—
230C22×C4×C61—42no—
231C22×C4×C61—42no—
232C22×C4×C61—81no—
233C22×C4×C61—81no—
234C22×C4×C61C2×D411yescharacteristic
235C22×C4×C61C2×D411yescharacteristic
236C22×C4×C61C2×D411yescharacteristic
237C22×C4×C61C2×D411yescharacteristic
238C22×C4×C61C2×D412yes—
239C22×C4×C61C2×D412yes—
240C22×C4×C61C2411yescharacteristic
241C2×C22⋊D61—42no—
242C2×C22⋊D61—42no—
243C2×C22⋊D61—42no—
244C2×C22⋊D61—81no—
245C2×C22⋊D61—81no—
246C2×C22⋊D61—81no—
247C22×Dic61—21no—
248C22×Dic61—21no—
249C22×Dic61—21no—
250C2×D244—21no—
251C2×D244—21no—
252C2×D244—21no—
253C2×D244—21no—
254C2×D244—21no—
255C2×D244—21no—
256C4⋊C4×C61—24no—
257C4⋊C4×C61—22no—
258C4⋊C4×C61—21no—
259C4⋊C4×C61C2×D412yes—
260C22⋊C4×C61—24no—
261C22⋊C4×C61—24no—
262C22⋊C4×C61—24no—
263C22⋊C4×C61—24no—
264C22⋊C4×C61—22no—
265C22⋊C4×C61—22no—
266C22⋊C4×C61—24no—
267C42×C61—21no—
268C42×C61—21no—
269C22⋊Dic61—42no—
270C22⋊Dic61—81no—
271#11758201—44no—
272#11758199—44no—
273#11758199—44no—
274#11758198—42no—
275#11758198—42no—
276#11758198—42no—
277#11758198—81no—
278C4⋊Dic61—21no—
279C4⋊Dic61—21no—
280C4⋊Dic61—21no—
281C4⋊Dic61—21no—
282C4⋊Dic61—21no—
283C4⋊Dic61C2×D412yes—
284#11758196—81no—
285C4×Dic61—42no—
286C2×#92418—21no—
287C2×#92418—21no—
288C2×#92418—21no—
289C2×#92418—21no—
290C2×#92418—21no—
291C2×#92418—21no—
292C2×#92418—21no—
293C2×#92418—21no—
294C2×#92418—21no—
295C2×#92418—21no—
296C2×#92418—21no—
297C2×#92418—44no—
298C2×#92418C2×D412yes—
299C23×C61—21no—
300C23×C61—22no—
301C23×C61—21no—
302C23×C61—21no—
303C23×C61—22no—
304C23×C61—21no—
305C23×C61—21no—
306C23×C61—22no—
307C23×C61—21no—
308C23×C61—21no—
309C23×C61—21no—
310C23×C61—21no—
311C23×C61—21no—
312C23×C61—21no—
313C23×C61—21no—
314C23×C61—22no—
315C23×C61—48no—
316C23×C61—48no—
317C23×C61—41no—
318C23×C61—41no—
319C23×C61—41no—
320C23×C61—41no—
321C23×C61—41no—
322C23×C61—41no—
323C23×C61—41no—
324C23×C61—41no—
325C23×C61—41no—
326C23×C61—41no—
327C23×C61—84no—
328C23×C61—84no—
329C23×C61—84no—
330C23×C61—84no—
331C23×C61—84no—
332C23×C61#12012yes—
333C23×C61#13512yes—
334C23×C61C22×D411yescharacteristic
335C22×D61—41no—
336C22×D61—41no—
337C22×D61—41no—
338C22×D61—41no—
339C22×D61—41no—
340C22×D61—41no—
341C22×D61—41no—
342Q8×C61—22no—
343Q8×C61—22no—
344Q8×C61—41no—
345Q8×C61—41no—
346D4×C61—22no—
347D4×C61—22no—
348D4×C61—22no—
349D4×C61—22no—
350D4×C61—22no—
351D4×C61—44no—
352D4×C61—48no—
353D4×C61—48no—
354D4×C61—41no—
355D4×C61—41no—
356D4×C61—84no—
357D4×C61#12114yes—
358C2×C4×C61—21no—
359C2×C4×C61—21no—
360C2×C4×C61—22no—
361C2×C4×C61—22no—
362C2×C4×C61—22no—
363C2×C4×C61—22no—
364C2×C4×C61—21no—
365C2×C4×C61—21no—
366C2×C4×C61—22no—
367C2×C4×C61—22no—
368C2×C4×C61—21no—
369C2×C4×C61—21no—
370C2×C4×C61—21no—
371C2×C4×C61—21no—
372C2×C4×C61—21no—
373C2×C4×C61—21no—
374C2×C4×C61—21no—
375C2×C4×C61—48no—
376C2×C4×C61—41no—
377C2×C4×C61—41no—
378C2×C4×C61—41no—
379C2×C4×C61—41no—
380C2×C4×C61—41no—
381C2×C4×C61—41no—
382C2×C4×C61—41no—
383C2×C4×C61—41no—
384C2×C4×C61—84no—
385C2×C4×C61#12012yes—
386C2×C4×C61C22×D411yescharacteristic
387C2×C4×C61C22×D411yescharacteristic
388C2×C4×C61C22×D411yescharacteristic
389C2×C4×C61C2×#4111yescharacteristic
390C2×C4×C61H(5,𝔽2)11yescharacteristic
391C2×C4×C61H(5,𝔽2)11yescharacteristic
392C22⋊D61—84no—
393C22⋊D61—84no—
394C2×Dic61—22no—
395C2×Dic61—41no—
396C2×Dic61—41no—
397C2×Dic61—41no—
398C2×Dic61—41no—
399C2×Dic61—41no—
400C2×Dic61—41no—
401C2×Dic61—41no—
402C2×Dic61—41no—
403D244—41no—
404D244—41no—
405D244—41no—
406D244—41no—
407#92418—22no—
408#92418—41no—
409#92418—41no—
410#92418—41no—
411#24428—611nomaximal, Sylow
412C22×C61—22no—
413C22×C61—24no—
414C22×C61—22no—
415C22×C61—22no—
416C22×C61—22no—
417C22×C61—22no—
418C22×C61—22no—
419C22×C61—41no—
420C22×C61—42no—
421C22×C61—42no—
422C22×C61—41no—
423C22×C61—41no—
424C22×C61—41no—
425C22×C61—42no—
426C22×C61—41no—
427C22×C61—42no—
428C22×C61—41no—
429C22×C61—42no—
430C22×C61—41no—
431C22×C61—41no—
432C22×C61—42no—
433C22×C61—42no—
434C22×C61—42no—
435C22×C61—42no—
436C22×C61—816no—
437C22×C61—81no—
438C22×C61—81no—
439C22×C61—81no—
440C22×C61—81no—
441C22×C61C2×#12011yescharacteristic
442C22×C61D4211yescharacteristic
443C22×C61#54611yescharacteristic
444C22×C61C2×#13511yescharacteristic
445C22×C61#57511yescharacteristic
446C22×C61#57611yescharacteristic
447C22×C61#57611yescharacteristic
448C2×D61—81no—
449C2×D61—81no—
450C2×D61—81no—
451C2×D61—81no—
452C2×D61—81no—
453C2×D61—81no—
454C2×D61—81no—
455C4×C61—22no—
456C4×C61—41no—
457C4×C61—42no—
458C4×C61—41no—
459C4×C61—41no—
460C4×C61—42no—
461C4×C61C2×#12111yescharacteristic
462C4×C61#53411yescharacteristic
463C4×C61D4211yescharacteristic
464C4×C61#54611yescharacteristic
465Dic61—42no—
466Dic61—81no—
467Dic61—81no—
468C2×#546D6111yescharacteristic, complemented
469C2×#466—611no—
470C2×#449—611no—
471C2×#447—611no—
472C2×#416—611no—
473#2414—611no—
474#2042—611no—
475#2036—611no—
476#2012—611no—
477#2000—611no—
478#1879—611no—
479#1875—611no—
480#1869—611no—
481#1862—611no—
482#1786—611no—
483C2×C61—42no—
484C2×C61—42no—
485C2×C61—44no—
486C2×C61—82no—
487C2×C61#241011yescharacteristic
488C2×C61#300211yescharacteristic
489C2×C61#300811yescharacteristic
490C2×C61#326811yescharacteristic
491C2×C61#328011yescharacteristic
492C2×C61#329711yescharacteristic
493C2×C61#331911yescharacteristic
494D61—161no—
495C22×#41C2×D6111yescharacteristic
496C23×D4C2×D6111yescharacteristic
497C22×SD16—611no—
498C22×D8—611no—
499C22×D8—611no—
500C23×C8—611no—
501#546—24no—
502#546—24no—
503C2×#124C2×D6111yescharacteristic
504C2×#123—21no—
505C2×C22⋊Q8C2×D6111yescharacteristic
506C2×#121—21no—
507C2×#121—611no—
508C2×#121—611no—
509C2×#121C2×D6111yescharacteristic
510C2×#120—21no—
511C2×C4×D4C2×D6111yescharacteristic
512C2×C4×D4C2×D6111yescharacteristic
513C2×#117—611no—
514C22×C22⋊C4—21no—
515#466—1224no—
516#449—1224no—
517#447—1224no—
518C2×#107—611no—
519#416—1224no—
520C2×#103—611no—
521C2×#103—611no—
522C2×#103—611no—
523C2×#102—611no—
524C2×#102—611no—
525C2×#102—611no—
526C2×#102—611no—
527C2×#102—611no—
528C2×#102—611no—
529C2×#102—611no—
530C2×C22⋊C8—611no—
531C2×C22⋊C8—611no—
532C2×C22⋊C8—611no—
533#394—1221no—
534#392—1221no—
535#390—611no—
536#390—1221no—
537#389—611no—
538#388—1221no—
539#380—611no—
540#340—611no—
541#340—611no—
542#336—611no—
543#336—611no—
544C61#2442811yescharacteristic, complemented, Sylow
545C25—21no—
546C2×#41—22no—
547C2×#41—22no—
548C2×#41—22no—
549C2×#41—41no—
550C2×#41—41no—
551C2×#41C22⋊D6114yescomplemented
552C22×Q8C22×D6111yescharacteristic
553C22×D4—21no—
554C22×D4—21no—
555C22×D4—22no—
556C22×D4—22no—
557C22×D4—22no—
558C22×D4—22no—
559C22×D4—21no—
560C22×D4—41no—
561C22×D4—41no—
562C22×D4—611no—
563C22×D4—1221no—
564C22×D4—1221no—
565C22×D4C22⋊D6111yescharacteristic
566C22×D4C22×D6111yescharacteristic
567C22×D4C22×D6111yescharacteristic
568C23×C4—21no—
569C23×C4—21no—
570C23×C4C22×D6111yescharacteristic
571C23×C4C22×D6111yescharacteristic
572C2×SD16—1222no—
573C2×SD16—2441no—
574C2×SD16—2441no—
575C2×D8—1222no—
576C2×D8—1222no—
577C2×D8—1222no—
578C2×D8—1222no—
579C2×D8—1222no—
580C2×D8—2441no—
581C22×C8—611no—
582C22×C8—611no—
583C22×C8—611no—
584C22×C8—611no—
585C22×C8—1222no—
586C22×C8—1222no—
587C22×C8—2441no—
588#124—22no—
589#124—22no—
590#123—28no—
591C22⋊Q8—22no—
592C22⋊Q8—22no—
593#121—28no—
594#121—22no—
595#121—1222no—
596#121—1222no—
597#121—1222no—
598#121—2441no—
599#121C22⋊D6114yescomplemented
600#120—28no—
601C4×D4—22no—
602C4×D4—22no—
603C4×D4—22no—
604C4×D4—22no—
605#117—1222no—
606#117—2441no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—611no—
609C2×C4⋊C4—611no—
610C2×C4⋊C4—611no—
611C2×C4⋊C4—1221no—
612C2×C4⋊C4C22⋊D6111yescharacteristic
613C2×C4⋊C4C22×D6111yescharacteristic
614C2×C22⋊C4—28no—
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—1221no—
621C2×C22⋊C4—1221no—
622C2×C22⋊C4—1221no—
623C2×C22⋊C4—1221no—
624C2×C22⋊C4—1221no—
625C2×C22⋊C4—1221no—
626C2×C22⋊C4C22⋊D6111yescharacteristic
627C2×C22⋊C4C22⋊D6111yescharacteristic
628C2×C42—1221no—
629C2×C42C22×D6111yescharacteristic
630#107—1222no—
631#103—1222no—
632#103—1222no—
633#103—1222no—
634#102—614no—
635#102—1222no—
636#102—1222no—
637#102—1222no—
638#102—1222no—
639#102—1222no—
640#102—2441no—
641C22⋊C8—1222no—
642C22⋊C8—1222no—
643C22⋊C8—2441no—
644#95—1221no—
645#95—1221no—
646C24—21no—
647C24—24no—
648C24—21no—
649C24—42no—
650C24—42no—
651C24—42no—
652C24—42no—
653C24—81no—
654C24—81no—
655C24—1221no—
656C24C2×C22⋊D6111yescharacteristic
657C24C2×C22⋊D6111yescharacteristic
658#41—28no—
659#41—44no—
660#41—44no—
661#41—44no—
662C2×Q8—21no—
663C2×Q8—21no—
664C2×Q8—21no—
665C2×Q8—21no—
666C2×Q8—21no—
667C2×Q8C2×C22⋊D6112yes—
668C2×D4—24no—
669C2×D4—22no—
670C2×D4—24no—
671C2×D4—22no—
672C2×D4—24no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—41no—
682C2×D4—42no—
683C2×D4—42no—
684C2×D4—44no—
685C2×D4—44no—
686C2×D4—44no—
687C2×D4—42no—
688C2×D4—42no—
689C2×D4—44no—
690C2×D4—81no—
691C2×D4—81no—
692C2×D4—1221no—
693C2×D4—1221no—
694C2×D4—1221no—
695C2×D4—1221no—
696C2×D4—1221no—
697C2×D4—1221no—
698C2×D4—4881no—
699C2×D4—4881no—
700C2×D4—4881no—
701C2×D4—2442no—
702C2×D4—2442no—
703C2×D4—2442no—
704C2×D4D4×D6112yes—
705C2×D4#1175822412yes—
706C2×D4C2×C22⋊D6112yes—
707C2×D4C2×C22⋊D6112yes—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—24no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—24no—
722C22×C4—42no—
723C22×C4—42no—
724C22×C4—81no—
725C22×C4—81no—
726C22×C4—1221no—
727C22×C4—1221no—
728C22×C4—1221no—
729C22×C4C2×C22⋊D6111yescharacteristic
730C22×C4C2×C22⋊D6111yescharacteristic
731C22×C4C2×C22⋊D6111yescharacteristic
732C22×C4C2×C22⋊D6112yes—
733C22×C4C2×C22⋊D6112yes—
734C22×C4C2×C22⋊D6111yescharacteristic
735C22×C4C23×D6111yescharacteristic
736SD16—2444no—
737D8—2444no—
738D8—2444no—
739C2×C8—612no—
740C2×C8—1221no—
741C2×C8—1221no—
742C2×C8—1221no—
743C2×C8—1221no—
744C2×C8—1221no—
745C2×C8—1221no—
746C2×C8—1221no—
747C2×C8—1221no—
748C2×C8—1221no—
749C2×C8—1221no—
750C2×C8—1221no—
751C2×C8—2444no—
752C4⋊C4—24no—
753C4⋊C4—21no—
754C4⋊C4—22no—
755C4⋊C4—612no—
756C4⋊C4—1221no—
757C4⋊C4—1221no—
758C4⋊C4—1221no—
759C4⋊C4—1221no—
760C4⋊C4—1221no—
761C4⋊C4—4881no—
762C4⋊C4C2×C22⋊D6112yes—
763C22⋊C4—24no—
764C22⋊C4—24no—
765C22⋊C4—24no—
766C22⋊C4—24no—
767C22⋊C4—22no—
768C22⋊C4—22no—
769C22⋊C4—24no—
770C22⋊C4—4881no—
771C22⋊C4—4881no—
772C22⋊C4—2442no—
773C22⋊C4—2442no—
774C22⋊C4—2442no—
775C22⋊C4—2442no—
776C42—21no—
777C42—21no—
778C42—2442no—
779C23—21no—
780C23—22no—
781C23—21no—
782C23—21no—
783C23—21no—
784C23—21no—
785C23—21no—
786C23—21no—
787C23—21no—
788C23—21no—
789C23—21no—
790C23—22no—
791C23—21no—
792C23—21no—
793C23—22no—
794C23—22no—
795C23—48no—
796C23—48no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—84no—
808C23—84no—
809C23—84no—
810C23—84no—
811C23—84no—
812C23—2441no—
813C23—2441no—
814C23—2441no—
815C23—2441no—
816C23—2441no—
817C23—2441no—
818C23—2441no—
819C23#1451974612yes—
820C23#1451979712yes—
821C23C22×C22⋊D6111yescharacteristic
822Q8—22no—
823Q8—22no—
824Q8—41no—
825Q8—41no—
826D4—22no—
827D4—22no—
828D4—22no—
829D4—22no—
830D4—22no—
831D4—44no—
832D4—48no—
833D4—48no—
834D4—41no—
835D4—41no—
836D4—84no—
837D4—4884no—
838D4—4884no—
839D4—2441no—
840D4—2441no—
841D4—2441no—
842D4—2441no—
843D4#1451974914yes—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—48no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—84no—
871C2×C4—1222no—
872C2×C4—2441no—
873C2×C4—2441no—
874C2×C4—2441no—
875C2×C4—2441no—
876C2×C4—2441no—
877C2×C4—2441no—
878C2×C4—2441no—
879C2×C4—2441no—
880C2×C4#1451974612yes—
881C2×C4C2×D4×D6111yescharacteristic
882C2×C4C22×C22⋊D6111yescharacteristic
883C2×C4C22×C22⋊D6111yescharacteristic
884C2×C4C2×#1175822411yescharacteristic
885C2×C4#1451982211yescharacteristic
886C2×C4#1451982211yescharacteristic
887C8—1222no—
888C8—2441no—
889C8—2441no—
890C8—2441no—
891C22—22no—
892C22—22no—
893C22—22no—
894C22—22no—
895C22—22no—
896C22—24no—
897C22—22no—
898C22—41no—
899C22—42no—
900C22—41no—
901C22—41no—
902C22—42no—
903C22—41no—
904C22—42no—
905C22—42no—
906C22—41no—
907C22—41no—
908C22—42no—
909C22—41no—
910C22—42no—
911C22—41no—
912C22—42no—
913C22—42no—
914C22—42no—
915C22—816no—
916C22—81no—
917C22—81no—
918C22—81no—
919C22—81no—
920C22—4881no—
921C22—4881no—
922C22—4881no—
923C22—4881no—
924C22—4881no—
925C22—4881no—
926C22—4881no—
927C22C2×#1451974611yescharacteristic
928C22D4×C22⋊D6111yescharacteristic
929C22#1684040611yescharacteristic
930C22C2×#1451979711yescharacteristic
931C22#1684056011yescharacteristic
932C22#1684056511yescharacteristic
933C22#1684056511yescharacteristic
934C4—22no—
935C4—41no—
936C4—41no—
937C4—42no—
938C4—41no—
939C4—42no—
940C4—4881no—
941C4—4881no—
942C4—2442no—
943C4C2×#1451974911yescharacteristic
944C4#1684032111yescharacteristic
945C4D4×C22⋊D6111yescharacteristic
946C4#1684040611yescharacteristic
947C2—42no—
948C2—42no—
949C2—44no—
950C2—82no—
951C2—9761no—
952C2#2144919311yescharacteristic
953C2#2145503711yescharacteristic
954C2#2145508711yescharacteristic
955C2#2145735511yescharacteristic
956C2#2145750011yescharacteristic
957C2#2145766911yescharacteristic
958C2#2145797511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#546C2
socleC23×C61C22×D4
hypercenterC2×#546D61
hypocenterC61#24428
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#546

Complements

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

NH ≅ G/Ntype
1. C2×#16839996C2semidirect
2. C2×#16839907C2semidirect
3. C2×#16839896C2semidirect
4. C2×#16839758C2semidirect
5. #21449237C2semidirect
6. #21447055C2semidirect
7. #21447019C2semidirect
8. #21446896C2semidirect
9. #21446820C2semidirect
10. #21446167C2semidirect
11. #21446142C2semidirect
12. #21446112C2semidirect
13. #21446066C2semidirect
14. #21445750C2semidirect
15. C2×C61×#546C2semidirect
16. C22×#11758201C22semidirect
19. C23×#92418C22semidirect
21. C2×#14519751C22semidirect
22. C2×#14519736C22semidirect
26. C2×#14519710C22semidirect
28. C2×#14519701C22semidirect
29. C2×#14519701C22semidirect
30. C2×#14519701C22semidirect
37. C2×#14519697C22semidirect
40. C2×C22⋊#92418C22semidirect
43. #16839664C22semidirect
45. #16839660C22semidirect
48. #16839524C22semidirect
49. #16839524C22semidirect
50. #16839517C22semidirect
51. #16839517C22semidirect
110. #14519698D4semidirect
123. C2×#41×C61D4semidirect
148. #121×C61D4semidirect
468. C2×#546D61semidirect
544. C61#24428semidirect
551. C2×#41C22⋊D61semidirect
599. #121C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168399962
C2×#168399072
C2×#168398962
C2×#168397582
#214492372
#214470552
#214470192
#214468962
#214468202
#214461672
#214461422
#214461122
#214460662
#214457502
C2×C61×#5462
#2442861