Finite Group Databasebeta

← #29711033

Subgroups — #29711033

Order 15616.

1934 conjugacy classes of subgroups.

The subgroup lattice has 1020 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519797C211yesmaximal, characteristic, complemented
2C2×#16839905C211yesmaximal, characteristic, complemented
3C2×#16839913C211yesmaximal, characteristic, complemented
4C2×#16839896C211yesmaximal, characteristic, complemented
5#21449164C211yesmaximal, characteristic, complemented
6#21446913C211yesmaximal, characteristic, complemented
7#21446896C211yesmaximal, characteristic, complemented
8#21446827C211yesmaximal, characteristic, complemented
9#21446820C211yesmaximal, characteristic, complemented
10#21446248C211yesmaximal, characteristic, complemented
11#21446167C211yesmaximal, characteristic, complemented
12#21446153C211yesmaximal, characteristic, complemented
13#21446112C211yesmaximal, characteristic, complemented
14#21445759C211yesmaximal, characteristic, complemented
15C2×C61×#546C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic, complemented
17C2×#14519797—24no—
18C2×#14519797—24no—
19C2×#14519797—24no—
20C22×#11758202C2211yescharacteristic, complemented
21C22×#11758200C2211yescharacteristic
22C22×#11758200C2211yescharacteristic
23C22×#11758201C2211yescharacteristic, complemented
24C22×#11758199C2211yescharacteristic
25C22×#11758199C2211yescharacteristic
26C23×#92418C2211yescharacteristic, complemented
27C2×#14519756C2211yescharacteristic
28C2×#14519751C2211yescharacteristic
29#16839913—24no—
30#16839905—24no—
31#16839896—24no—
32C2×#14519701C2211yescharacteristic, complemented
33C2×#14519701C2211yescharacteristic, complemented
34C2×#14519700C2211yescharacteristic, complemented
35C2×#14519698C2211yescharacteristic
36C2×#14519698C2211yescharacteristic
37C2×#14519698C2211yescharacteristic
38C2×#14519698C2211yescharacteristic
39C2×#14519697C2211yescharacteristic, complemented
40C2×C22⋊#92418C2211yescharacteristic
41C2×C22⋊#92418C2211yescharacteristic
42C2×C22⋊#92418C2211yescharacteristic, complemented
43#16839677—21no—
44#16839670—21no—
45#16839668C2211yescharacteristic, complemented
46#16839664C2211yescharacteristic, complemented
47#16839638—21no—
48#16839633—21no—
49#16839622C2211yescharacteristic, complemented
50#16839524C2211yescharacteristic, complemented
51#16839524C2211yescharacteristic, complemented
52#16839517C2211yescharacteristic, complemented
53#16839517C2211yescharacteristic, complemented
54C22×#41×C61C2211yescharacteristic
55C23×D4×C61C2211yescharacteristic
56C61×#546—24no—
57C61×#546—24no—
58C2×#124×C61C2211yescharacteristic
59C2×#123×C61—21no—
60C2×C22⋊Q8×C61C2211yescharacteristic
61C2×#121×C61—21no—
62C2×#121×C61C2211yescharacteristic
63C2×#120×C61—21no—
64C2×C4×D4×C61C2211yescharacteristic
65C2×C4×D4×C61C2211yescharacteristic
66C22×C22⋊C4×C61—21no—
67C2×#11758222—22no—
68C2×#11758222—22no—
69C2×#11758222—22no—
70C2×#11758222—22no—
71C2×#11758222—41no—
72C2×#11758222—41no—
73C22×Dic122C2311yescharacteristic
74C22×D244C2311yescharacteristic
75C22×C22⋊D61—21no—
76C22×C22⋊D61—21no—
77C22×C4×D61—21no—
78#14519797—232no—
79C2×#11758202—22no—
80C2×#11758202—22no—
81C2×#11758202—22no—
82C2×#11758200—22no—
83C2×#11758200—22no—
84C2×#11758200—22no—
85C2×#11758200—22no—
86C2×#11758200—41no—
87C2×#11758200D414yescomplemented
88C2×#11758201—22no—
89C2×#11758201—22no—
90C2×#11758201—22no—
91C2×#11758199—22no—
92C2×#11758199—22no—
93C2×#11758199—22no—
94C2×#11758199—22no—
95C2×#11758199—41no—
96C2×#11758199D414yescomplemented
97C22×#92418—22no—
98C22×#92418—22no—
99C22×#92418—22no—
100C22×#92418C2311yescharacteristic
101C22×#92418C2311yescharacteristic
102C22×#92418C2311yescharacteristic
103C22×#92418C2311yescharacteristic
104#14519756—22no—
105#14519756—41no—
106#14519751—22no—
107#14519751—41no—
108C2×C4⋊Dic61C2311yescharacteristic
109C2×C4⋊Dic61C2311yescharacteristic
110C2×#11758196—21no—
111C2×C22⋊Dic61—21no—
112C2×C22⋊Dic61—21no—
113C2×#11758198—21no—
114C2×#11758198—21no—
115C2×#11758198—21no—
116#14519701—41no—
117#14519701—41no—
118#14519700—22no—
119#14519698—22no—
120#14519698—22no—
121#14519698—22no—
122#14519698—22no—
123#14519697—22no—
124C22⋊#92418—22no—
125C22⋊#92418—22no—
126C22⋊#92418—22no—
127#14519684—21no—
128#14519684—21no—
129#14519684—21no—
130C25×C61—21no—
131C2×#41×C61—22no—
132C2×#41×C61—22no—
133C2×#41×C61—22no—
134C2×#41×C61—41no—
135C2×#41×C61—41no—
136C2×#41×C61D414yescomplemented
137C22×Q8×C61C2311yescharacteristic
138C22×D4×C61—21no—
139C22×D4×C61—21no—
140C22×D4×C61—22no—
141C22×D4×C61—22no—
142C22×D4×C61—22no—
143C22×D4×C61—22no—
144C22×D4×C61—21no—
145C22×D4×C61—41no—
146C22×D4×C61—41no—
147C22×D4×C61D411yescharacteristic
148C22×D4×C61C2311yescharacteristic
149C22×D4×C61C2311yescharacteristic
150C23×C4×C61—21no—
151C23×C4×C61—21no—
152C23×C4×C61C2311yescharacteristic
153C23×C4×C61C2311yescharacteristic
154#124×C61—22no—
155#124×C61—22no—
156#123×C61—28no—
157C22⋊Q8×C61—22no—
158C22⋊Q8×C61—22no—
159#121×C61—28no—
160#121×C61—22no—
161#121×C61D414yescomplemented
162#120×C61—28no—
163C4×D4×C61—22no—
164C4×D4×C61—22no—
165C4×D4×C61—22no—
166C4×D4×C61—22no—
167C2×C4⋊C4×C61—21no—
168C2×C4⋊C4×C61D411yescharacteristic
169C2×C4⋊C4×C61C2311yescharacteristic
170C2×C22⋊C4×C61—28no—
171C2×C22⋊C4×C61—21no—
172C2×C22⋊C4×C61—21no—
173C2×C22⋊C4×C61—21no—
174C2×C22⋊C4×C61—21no—
175C2×C22⋊C4×C61—21no—
176C2×C22⋊C4×C61D411yescharacteristic
177C2×C22⋊C4×C61D411yescharacteristic
178C2×C42×C61C2311yescharacteristic
179C24×C61—21no—
180C24×C61—24no—
181C24×C61—21no—
182C24×C61—42no—
183C24×C61—42no—
184C24×C61—42no—
185C24×C61—42no—
186C24×C61—81no—
187C24×C61—81no—
188C24×C61C2×D411yescharacteristic
189C24×C61C2×D411yescharacteristic
190C23×D61—21no—
191#41×C61—28no—
192#41×C61—44no—
193#41×C61—44no—
194#41×C61—44no—
195C2×Q8×C61—21no—
196C2×Q8×C61—21no—
197C2×Q8×C61—21no—
198C2×Q8×C61—21no—
199C2×Q8×C61—21no—
200C2×Q8×C61C2×D412yes—
201C2×D4×C61—24no—
202C2×D4×C61—22no—
203C2×D4×C61—24no—
204C2×D4×C61—22no—
205C2×D4×C61—24no—
206C2×D4×C61—21no—
207C2×D4×C61—21no—
208C2×D4×C61—21no—
209C2×D4×C61—21no—
210C2×D4×C61—21no—
211C2×D4×C61—21no—
212C2×D4×C61—21no—
213C2×D4×C61—21no—
214C2×D4×C61—41no—
215C2×D4×C61—42no—
216C2×D4×C61—42no—
217C2×D4×C61—44no—
218C2×D4×C61—44no—
219C2×D4×C61—44no—
220C2×D4×C61—42no—
221C2×D4×C61—42no—
222C2×D4×C61—44no—
223C2×D4×C61—81no—
224C2×D4×C61—81no—
225C2×D4×C61C2×D412yes—
226C2×D4×C61C2×D412yes—
227C2×D4×C61C2×D412yes—
228C2×D4×C61C2×D412yes—
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—24no—
236C22×C4×C61—24no—
237C22×C4×C61—21no—
238C22×C4×C61—21no—
239C22×C4×C61—21no—
240C22×C4×C61—21no—
241C22×C4×C61—21no—
242C22×C4×C61—21no—
243C22×C4×C61—42no—
244C22×C4×C61—42no—
245C22×C4×C61—81no—
246C22×C4×C61—81no—
247C22×C4×C61C2×D411yescharacteristic
248C22×C4×C61C2×D411yescharacteristic
249C22×C4×C61C2×D411yescharacteristic
250C22×C4×C61C2×D411yescharacteristic
251C22×C4×C61C2×D412yes—
252C22×C4×C61C2×D412yes—
253C22×C4×C61C2411yescharacteristic
254C2×C22⋊D61—42no—
255C2×C22⋊D61—42no—
256C2×C22⋊D61—42no—
257C2×C22⋊D61—42no—
258C2×C22⋊D61—42no—
259C2×C22⋊D61—81no—
260C22×Dic61—21no—
261C22×Dic61—21no—
262C22×Dic61—21no—
263#11758222—28no—
264#11758222—44no—
265#11758222—44no—
266#11758222—44no—
267C2×D244—21no—
268C2×D244—21no—
269C2×D244—21no—
270C2×D244—21no—
271C2×D244—21no—
272C2×D244C2×D412yes—
273C2×C4×D61—42no—
274C2×C4×D61—42no—
275C2×C4×D61—42no—
276C2×Dic122—21no—
277C2×Dic122—21no—
278C2×Dic122—21no—
279C2×Dic122—21no—
280C2×Dic122—21no—
281C2×Dic122C2×D412yes—
282C4⋊C4×C61—24no—
283C4⋊C4×C61—22no—
284C4⋊C4×C61—21no—
285C4⋊C4×C61C2×D412yes—
286C22⋊C4×C61—24no—
287C22⋊C4×C61—24no—
288C22⋊C4×C61—24no—
289C22⋊C4×C61—24no—
290C22⋊C4×C61—22no—
291C22⋊C4×C61—22no—
292C22⋊C4×C61—24no—
293C42×C61—21no—
294C42×C61—21no—
295C22⋊Dic61—42no—
296C22⋊Dic61—81no—
297#11758202—28no—
298#11758201—28no—
299#11758200—28no—
300#11758200—44no—
301#11758199—28no—
302#11758199—44no—
303#11758198—42no—
304#11758198—42no—
305#11758198—81no—
306C4⋊Dic61—21no—
307C4⋊Dic61—21no—
308C4⋊Dic61—21no—
309C4⋊Dic61—21no—
310#11758196—42no—
311C2×#92418—28no—
312C2×#92418—21no—
313C2×#92418—21no—
314C2×#92418—21no—
315C2×#92418—21no—
316C2×#92418—21no—
317C2×#92418—21no—
318C2×#92418—21no—
319C2×#92418—21no—
320C2×#92418—21no—
321C2×#92418—21no—
322C2×#92418C2×D412yes—
323C2×#92418C2×D412yes—
324C23×C61—21no—
325C23×C61—22no—
326C23×C61—21no—
327C23×C61—21no—
328C23×C61—21no—
329C23×C61—21no—
330C23×C61—22no—
331C23×C61—22no—
332C23×C61—21no—
333C23×C61—21no—
334C23×C61—21no—
335C23×C61—21no—
336C23×C61—21no—
337C23×C61—21no—
338C23×C61—21no—
339C23×C61—22no—
340C23×C61—48no—
341C23×C61—48no—
342C23×C61—41no—
343C23×C61—41no—
344C23×C61—41no—
345C23×C61—41no—
346C23×C61—41no—
347C23×C61—41no—
348C23×C61—41no—
349C23×C61—41no—
350C23×C61—41no—
351C23×C61—41no—
352C23×C61—84no—
353C23×C61—84no—
354C23×C61—84no—
355C23×C61—84no—
356C23×C61—84no—
357C23×C61#12012yes—
358C23×C61#13512yescomplemented
359C23×C61C22×D411yescharacteristic
360C22×D61—22no—
361C22×D61—41no—
362C22×D61—41no—
363C22×D61—41no—
364C22×D61—41no—
365C22×D61—41no—
366C22×D61—41no—
367Q8×C61—22no—
368Q8×C61—22no—
369Q8×C61—41no—
370Q8×C61—41no—
371D4×C61—22no—
372D4×C61—22no—
373D4×C61—22no—
374D4×C61—22no—
375D4×C61—22no—
376D4×C61—44no—
377D4×C61—48no—
378D4×C61—48no—
379D4×C61—41no—
380D4×C61—41no—
381D4×C61—84no—
382D4×C61#12014yes—
383C2×C4×C61—21no—
384C2×C4×C61—21no—
385C2×C4×C61—22no—
386C2×C4×C61—22no—
387C2×C4×C61—22no—
388C2×C4×C61—22no—
389C2×C4×C61—21no—
390C2×C4×C61—21no—
391C2×C4×C61—22no—
392C2×C4×C61—22no—
393C2×C4×C61—21no—
394C2×C4×C61—21no—
395C2×C4×C61—21no—
396C2×C4×C61—21no—
397C2×C4×C61—21no—
398C2×C4×C61—21no—
399C2×C4×C61—21no—
400C2×C4×C61—48no—
401C2×C4×C61—41no—
402C2×C4×C61—41no—
403C2×C4×C61—41no—
404C2×C4×C61—41no—
405C2×C4×C61—41no—
406C2×C4×C61—41no—
407C2×C4×C61—41no—
408C2×C4×C61—41no—
409C2×C4×C61—84no—
410C2×C4×C61#12012yes—
411C2×C4×C61C22×D411yescharacteristic
412C2×C4×C61C22×D411yescharacteristic
413C2×C4×C61C22×D411yescharacteristic
414C2×C4×C61C22×D411yescharacteristic
415C2×C4×C61H(5,𝔽2)11yescharacteristic
416C2×C4×C61H(5,𝔽2)11yescharacteristic
417C22⋊D61—48no—
418C22⋊D61—84no—
419C2×Dic61—22no—
420C2×Dic61—41no—
421C2×Dic61—41no—
422C2×Dic61—41no—
423C2×Dic61—41no—
424C2×Dic61—41no—
425C2×Dic61—41no—
426C2×Dic61—41no—
427C2×Dic61—41no—
428D244—22no—
429D244—22no—
430D244—41no—
431D244—41no—
432C4×D61—48no—
433Dic122—22no—
434Dic122—22no—
435Dic122—41no—
436Dic122—41no—
437#92418—22no—
438#92418—22no—
439#92418—41no—
440#92418—41no—
441#23850—611nomaximal, Sylow
442C22×C61—22no—
443C22×C61—24no—
444C22×C61—22no—
445C22×C61—22no—
446C22×C61—22no—
447C22×C61—22no—
448C22×C61—22no—
449C22×C61—41no—
450C22×C61—42no—
451C22×C61—41no—
452C22×C61—41no—
453C22×C61—42no—
454C22×C61—42no—
455C22×C61—41no—
456C22×C61—41no—
457C22×C61—41no—
458C22×C61—42no—
459C22×C61—41no—
460C22×C61—42no—
461C22×C61—41no—
462C22×C61—42no—
463C22×C61—42no—
464C22×C61—42no—
465C22×C61—42no—
466C22×C61—816no—
467C22×C61—81no—
468C22×C61—81no—
469C22×C61—81no—
470C22×C61—81no—
471C22×C61C2×#12011yescharacteristic
472C22×C61D4211yescharacteristic
473C22×C61D4211yescharacteristic
474C22×C61C2×#13511yescharacteristic
475C22×C61#57511yescharacteristic
476C22×C61#57611yescharacteristic
477C22×C61#57711yescharacteristic
478C2×D61—42no—
479C2×D61—42no—
480C2×D61—42no—
481C2×D61—81no—
482C2×D61—81no—
483C2×D61—81no—
484C2×D61—81no—
485C4×C61—22no—
486C4×C61—41no—
487C4×C61—42no—
488C4×C61—41no—
489C4×C61—41no—
490C4×C61—42no—
491C4×C61C2×#12011yescharacteristic
492C4×C61#53411yescharacteristic
493C4×C61D4211yescharacteristic
494C4×C61D4211yescharacteristic
495Dic61—42no—
496Dic61—81no—
497Dic61—81no—
498C22×#135—611no—
499C2×#546D6111yescharacteristic, complemented
500C2×#449—611no—
501C2×#450—611no—
502C2×#447—611no—
503#2407—611no—
504#2015—611no—
505#2012—611no—
506#2001—611no—
507#2000—611no—
508#1893—611no—
509#1879—611no—
510#1877—611no—
511#1869—611no—
512#1788—611no—
513C2×C61—42no—
514C2×C61—42no—
515C2×C61—44no—
516C2×C61—82no—
517C2×C61#240311yescharacteristic
518C2×C61#300211yescharacteristic
519C2×C61#301211yescharacteristic
520C2×C61#326711yescharacteristic
521C2×C61#326811yescharacteristic
522C2×C61#328011yescharacteristic
523C2×C61#328211yescharacteristic
524D61—82no—
525C22×#41—611no—
526C22×#41C2×D6111yescharacteristic
527C23×D4C2×D6111yescharacteristic
528C2×#135—1224no—
529C2×#135—1224no—
530C2×#135—1224no—
531C22×Q16—611no—
532C22×SD16—611no—
533C22×SD16—611no—
534C22×SD16—611no—
535C22×D8—611no—
536C22×D8—611no—
537C23×C8—611no—
538#546—24no—
539#546—24no—
540C2×#124C2×D6111yescharacteristic
541C2×#123—21no—
542C2×C22⋊Q8—611no—
543C2×C22⋊Q8C2×D6111yescharacteristic
544C2×#121—21no—
545C2×#121—611no—
546C2×#121C2×D6111yescharacteristic
547C2×#120—21no—
548C2×C4×D4C2×D6111yescharacteristic
549C2×C4×D4C2×D6111yescharacteristic
550C22×C22⋊C4—21no—
551#450—1224no—
552#449—1224no—
553#447—1224no—
554C2×#103—611no—
555C2×#103—611no—
556C2×#103—611no—
557C2×#102—611no—
558C2×#102—611no—
559C2×#102—611no—
560C2×#102—611no—
561C2×#102—611no—
562C2×C22⋊C8—611no—
563C2×C22⋊C8—611no—
564C2×C22⋊C8—611no—
565#394—1221no—
566#392—1221no—
567#391—611no—
568#390—611no—
569#386—1221no—
570#385—1221no—
571#380—611no—
572#340—611no—
573#340—611no—
574#336—611no—
575#336—611no—
576C61#2385011yescharacteristic, complemented, Sylow
577C25—21no—
578C2×#41—22no—
579C2×#41—22no—
580C2×#41—22no—
581C2×#41—41no—
582C2×#41—41no—
583C2×#41—1222no—
584C2×#41—1222no—
585C2×#41—1222no—
586C2×#41—1222no—
587C2×#41—2441no—
588C2×#41—2441no—
589C2×#41C22⋊D6114yescomplemented
590C22×Q8—611no—
591C22×Q8C22×D6111yescharacteristic
592C22×D4—21no—
593C22×D4—21no—
594C22×D4—22no—
595C22×D4—22no—
596C22×D4—22no—
597C22×D4—22no—
598C22×D4—21no—
599C22×D4—41no—
600C22×D4—41no—
601C22×D4—611no—
602C22×D4—1221no—
603C22×D4—1221no—
604C22×D4C22⋊D6111yescharacteristic
605C22×D4C22×D6111yescharacteristic
606C22×D4C22×D6111yescharacteristic
607C23×C4—21no—
608C23×C4—21no—
609C23×C4—1221no—
610C23×C4C22×D6111yescharacteristic
611C23×C4C22×D6111yescharacteristic
612#135—12232no—
613C2×Q16—1222no—
614C2×Q16—1222no—
615C2×Q16—1222no—
616C2×SD16—614no—
617C2×SD16—1222no—
618C2×SD16—1222no—
619C2×SD16—1222no—
620C2×SD16—1222no—
621C2×SD16—1222no—
622C2×SD16—1222no—
623C2×SD16—1222no—
624C2×SD16—2441no—
625C2×D8—614no—
626C2×D8—1222no—
627C2×D8—1222no—
628C2×D8—1222no—
629C2×D8—1222no—
630C2×D8—2441no—
631C22×C8—611no—
632C22×C8—611no—
633C22×C8—611no—
634C22×C8—611no—
635C22×C8—1222no—
636C22×C8—1222no—
637C22×C8—1222no—
638#124—22no—
639#124—22no—
640#123—28no—
641C22⋊Q8—22no—
642C22⋊Q8—22no—
643C22⋊Q8—1222no—
644C22⋊Q8—2441no—
645#121—28no—
646#121—22no—
647#121—1222no—
648#121—2441no—
649#121C22⋊D6114yescomplemented
650#120—28no—
651C4×D4—22no—
652C4×D4—22no—
653C4×D4—22no—
654C4×D4—22no—
655C2×C4⋊C4—21no—
656C2×C4⋊C4—611no—
657C2×C4⋊C4—611no—
658C2×C4⋊C4—1221no—
659C2×C4⋊C4C22⋊D6111yescharacteristic
660C2×C4⋊C4C22×D6111yescharacteristic
661C2×C22⋊C4—28no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—1221no—
668C2×C22⋊C4—1221no—
669C2×C22⋊C4—1221no—
670C2×C22⋊C4—1221no—
671C2×C22⋊C4—1221no—
672C2×C22⋊C4C22⋊D6111yescharacteristic
673C2×C22⋊C4C22⋊D6111yescharacteristic
674C2×C42C22×D6111yescharacteristic
675#103—1222no—
676#103—2441no—
677#103—2441no—
678#102—1222no—
679#102—1222no—
680#102—1222no—
681#102—1222no—
682#102—1222no—
683C22⋊C8—1222no—
684C22⋊C8—1222no—
685C22⋊C8—1222no—
686#95—1221no—
687#95—1221no—
688#95—1221no—
689C24—21no—
690C24—24no—
691C24—21no—
692C24—42no—
693C24—42no—
694C24—42no—
695C24—42no—
696C24—81no—
697C24—81no—
698C24—1221no—
699C24C2×C22⋊D6111yescharacteristic
700C24C2×C22⋊D6111yescharacteristic
701#41—28no—
702#41—44no—
703#41—44no—
704#41—44no—
705#41—1228no—
706#41—2444no—
707#41—2444no—
708#41—2444no—
709C2×Q8—21no—
710C2×Q8—21no—
711C2×Q8—21no—
712C2×Q8—21no—
713C2×Q8—21no—
714C2×Q8—612no—
715C2×Q8—1221no—
716C2×Q8—1221no—
717C2×Q8—1221no—
718C2×Q8—1221no—
719C2×Q8—1221no—
720C2×Q8C2×C22⋊D6112yes—
721C2×D4—24no—
722C2×D4—22no—
723C2×D4—24no—
724C2×D4—22no—
725C2×D4—24no—
726C2×D4—21no—
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—21no—
733C2×D4—21no—
734C2×D4—41no—
735C2×D4—42no—
736C2×D4—42no—
737C2×D4—44no—
738C2×D4—44no—
739C2×D4—44no—
740C2×D4—42no—
741C2×D4—42no—
742C2×D4—44no—
743C2×D4—81no—
744C2×D4—81no—
745C2×D4—612no—
746C2×D4—1221no—
747C2×D4—1221no—
748C2×D4—1221no—
749C2×D4—1221no—
750C2×D4—1221no—
751C2×D4—4881no—
752C2×D4—2442no—
753C2×D4—2442no—
754C2×D4—2442no—
755C2×D4—2442no—
756C2×D4—2442no—
757C2×D4D4×D6112yes—
758C2×D4D4×D6112yes—
759C2×D4C2×C22⋊D6112yes—
760C2×D4C2×C22⋊D6112yes—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—24no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—24no—
775C22×C4—42no—
776C22×C4—42no—
777C22×C4—81no—
778C22×C4—81no—
779C22×C4—1221no—
780C22×C4—1221no—
781C22×C4—1221no—
782C22×C4—2442no—
783C22×C4—2442no—
784C22×C4—2442no—
785C22×C4C2×C22⋊D6111yescharacteristic
786C22×C4C2×C22⋊D6111yescharacteristic
787C22×C4C2×C22⋊D6111yescharacteristic
788C22×C4C2×C22⋊D6112yes—
789C22×C4C2×C22⋊D6112yes—
790C22×C4C2×C22⋊D6111yescharacteristic
791C22×C4C23×D6111yescharacteristic
792Q16—1228no—
793SD16—1228no—
794SD16—1228no—
795SD16—2444no—
796D8—1228no—
797D8—2444no—
798C2×C8—612no—
799C2×C8—612no—
800C2×C8—1228no—
801C2×C8—1221no—
802C2×C8—1221no—
803C2×C8—1221no—
804C2×C8—1221no—
805C2×C8—1221no—
806C2×C8—1221no—
807C2×C8—1221no—
808C2×C8—1221no—
809C2×C8—1221no—
810C2×C8—1221no—
811C4⋊C4—24no—
812C4⋊C4—21no—
813C4⋊C4—22no—
814C4⋊C4—1221no—
815C4⋊C4—1221no—
816C4⋊C4—1221no—
817C4⋊C4—1221no—
818C4⋊C4—2442no—
819C4⋊C4C2×C22⋊D6112yes—
820C22⋊C4—24no—
821C22⋊C4—24no—
822C22⋊C4—24no—
823C22⋊C4—24no—
824C22⋊C4—22no—
825C22⋊C4—22no—
826C22⋊C4—24no—
827C22⋊C4—4881no—
828C22⋊C4—4881no—
829C22⋊C4—2442no—
830C22⋊C4—2442no—
831C22⋊C4—2442no—
832C42—21no—
833C42—21no—
834C23—21no—
835C23—22no—
836C23—21no—
837C23—21no—
838C23—21no—
839C23—21no—
840C23—21no—
841C23—21no—
842C23—21no—
843C23—21no—
844C23—21no—
845C23—21no—
846C23—21no—
847C23—22no—
848C23—22no—
849C23—22no—
850C23—48no—
851C23—48no—
852C23—41no—
853C23—41no—
854C23—41no—
855C23—41no—
856C23—41no—
857C23—41no—
858C23—41no—
859C23—41no—
860C23—41no—
861C23—41no—
862C23—84no—
863C23—84no—
864C23—84no—
865C23—84no—
866C23—84no—
867C23—1222no—
868C23—2441no—
869C23—2441no—
870C23—2441no—
871C23—2441no—
872C23—2441no—
873C23—2441no—
874C23#1451974612yes—
875C23#1451979712yescomplemented
876C23C22×C22⋊D6111yescharacteristic
877Q8—22no—
878Q8—22no—
879Q8—41no—
880Q8—41no—
881Q8—1222no—
882Q8—1222no—
883Q8—2441no—
884Q8—2441no—
885D4—22no—
886D4—22no—
887D4—22no—
888D4—22no—
889D4—22no—
890D4—44no—
891D4—48no—
892D4—48no—
893D4—41no—
894D4—41no—
895D4—84no—
896D4—1222no—
897D4—1222no—
898D4—4884no—
899D4—2448no—
900D4—2441no—
901D4—2441no—
902D4#1451974514yes—
903C2×C4—21no—
904C2×C4—21no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—21no—
914C2×C4—21no—
915C2×C4—21no—
916C2×C4—21no—
917C2×C4—21no—
918C2×C4—21no—
919C2×C4—21no—
920C2×C4—48no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—84no—
930C2×C4—1222no—
931C2×C4—2448no—
932C2×C4—2441no—
933C2×C4—2441no—
934C2×C4—2441no—
935C2×C4—2441no—
936C2×C4—2441no—
937C2×C4—2441no—
938C2×C4—2441no—
939C2×C4—2441no—
940C2×C4#1451974612yes—
941C2×C4C2×D4×D6111yescharacteristic
942C2×C4C2×D4×D6111yescharacteristic
943C2×C4C22×C22⋊D6111yescharacteristic
944C2×C4C22×C22⋊D6111yescharacteristic
945C2×C4#1451982211yescharacteristic
946C2×C4#1451982211yescharacteristic
947C8—1222no—
948C8—1222no—
949C8—2441no—
950C8—2441no—
951C22—22no—
952C22—22no—
953C22—22no—
954C22—22no—
955C22—24no—
956C22—22no—
957C22—22no—
958C22—42no—
959C22—41no—
960C22—41no—
961C22—42no—
962C22—41no—
963C22—42no—
964C22—41no—
965C22—41no—
966C22—41no—
967C22—42no—
968C22—42no—
969C22—41no—
970C22—41no—
971C22—42no—
972C22—42no—
973C22—42no—
974C22—42no—
975C22—816no—
976C22—81no—
977C22—81no—
978C22—81no—
979C22—81no—
980C22—4881no—
981C22—4881no—
982C22—4881no—
983C22—4881no—
984C22—2442no—
985C22—2442no—
986C22—2442no—
987C22C2×#1451974611yescharacteristic
988C22D4×C22⋊D6111yescharacteristic
989C22D4×C22⋊D6111yescharacteristic
990C22C2×#1451979711yescharacteristic
991C22#1684056011yescharacteristic
992C22#1684056511yescharacteristic
993C22#1684057311yescharacteristic
994C4—22no—
995C4—41no—
996C4—42no—
997C4—41no—
998C4—42no—
999C4—41no—
1000C4—4881no—
1001C4—4881no—
1002C4—2442no—
1003C4C2×#1451974511yescharacteristic
1004C4#1684032111yescharacteristic
1005C4D4×C22⋊D6111yescharacteristic
1006C4D4×C22⋊D6111yescharacteristic
1007C2—42no—
1008C2—42no—
1009C2—44no—
1010C2—82no—
1011C2—4882no—
1012C2#2144912911yescharacteristic
1013C2#2145503711yescharacteristic
1014C2#2145512311yescharacteristic
1015C2#2145734011yescharacteristic
1016C2#2145735511yescharacteristic
1017C2#2145750011yescharacteristic
1018C2#2145752211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#546C2
socleC23×C61C22×D4
hypercenterC2×#546D61
hypocenterC61#23850
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. C22×#14519797C2semidirect
2. C2×#16839905C2semidirect
3. C2×#16839913C2semidirect
4. C2×#16839896C2semidirect
5. #21449164C2semidirect
6. #21446913C2semidirect
7. #21446896C2semidirect
8. #21446827C2semidirect
9. #21446820C2semidirect
10. #21446248C2semidirect
11. #21446167C2semidirect
12. #21446153C2semidirect
13. #21446112C2semidirect
14. #21445759C2semidirect
15. C2×C61×#546C2semidirect
16. C22×#11758222C22semidirect
20. C22×#11758202C22semidirect
23. C22×#11758201C22semidirect
26. C23×#92418C22semidirect
32. C2×#14519701C22semidirect
33. C2×#14519701C22semidirect
34. C2×#14519700C22semidirect
39. C2×#14519697C22semidirect
42. C2×C22⋊#92418C22semidirect
45. #16839668C22semidirect
46. #16839664C22semidirect
49. #16839622C22semidirect
50. #16839524C22semidirect
51. #16839524C22semidirect
52. #16839517C22semidirect
53. #16839517C22semidirect
87. C2×#11758200D4semidirect
96. C2×#11758199D4semidirect
136. C2×#41×C61D4semidirect
161. #121×C61D4semidirect
358. C23×C61#135semidirect
499. C2×#546D61semidirect
576. C61#23850semidirect
589. C2×#41C22⋊D61semidirect
649. #121C22⋊D61semidirect
875. C23#14519797semidirect

Maximal subgroups

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

subgroupindex
C22×#145197972
C2×#168399052
C2×#168399132
C2×#168398962
#214491642
#214469132
#214468962
#214468272
#214468202
#214462482
#214461672
#214461532
#214461122
#214457592
C2×C61×#5462
#2385061