Finite Group Databasebeta

← #29713017

Subgroups — #29713017

Order 15616.

1462 conjugacy classes of subgroups.

The subgroup lattice has 874 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840408C211yesmaximal, characteristic
2C2×#16840086C211yesmaximal, characteristic, complemented
3C2×#16839756C211yesmaximal, characteristic, complemented
4#21447060C211yesmaximal, characteristic, complemented
5#21447060C211yesmaximal, characteristic, complemented
6#21447022C211yesmaximal, characteristic, complemented
7#21447015C211yesmaximal, characteristic, complemented
8#21446245C211yesmaximal, characteristic, complemented
9#21446112C211yesmaximal, characteristic, complemented
10#21446079C211yesmaximal, characteristic, complemented
11#21446065C211yesmaximal, characteristic, complemented
12#21445757C211yesmaximal, characteristic, complemented
13#21445749C211yesmaximal, characteristic, complemented
14#21445749C211yesmaximal, characteristic, complemented
15C61×#2485C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C23×D244C2211yescharacteristic
18C23×#92418C2211yescharacteristic, complemented
19#16840408—24no—
20#16840408—24no—
21C2×#14519765C2211yescharacteristic
22C2×#14519762—21no—
23C2×#14519756C2211yescharacteristic
24C2×#14519751C2211yescharacteristic
25C2×#14519750—21no—
26C2×#14519745—21no—
27C2×C4×D244C2211yescharacteristic
28C2×C22⋊C4×D61—21no—
29#16840086—24no—
30C2×#14519710C2211yescharacteristic, complemented
31C2×#14519708C2211yescharacteristic, complemented
32#16839756—24no—
33C2×#14519700C2211yescharacteristic, complemented
34C2×#14519700C2211yescharacteristic, complemented
35C2×#14519700C2211yescharacteristic, complemented
36C2×#14519700C2211yescharacteristic, complemented
37C2×#14519697C2211yescharacteristic
38C2×#14519697C2211yescharacteristic
39C2×#14519697C2211yescharacteristic
40C2×#14519697C2211yescharacteristic
41C2×#14519697C2211yescharacteristic
42C2×#14519697C2211yescharacteristic
43C2×#14519697C2211yescharacteristic
44C2×#14519697C2211yescharacteristic
45C2×C22⋊#92418C2211yescharacteristic
46C2×C22⋊#92418C2211yescharacteristic
47C2×C22⋊#92418C2211yescharacteristic, complemented
48#16839524C2211yescharacteristic, complemented
49#16839524C2211yescharacteristic, complemented
50#16839517C2211yescharacteristic, complemented
51#16839517C2211yescharacteristic, complemented
52C2×C4×D4×C61C2211yescharacteristic
53C2×#117×C61C2211yescharacteristic, complemented
54C61×#397—21no—
55C61×#394—21no—
56C61×#389C2211yescharacteristic, complemented
57C61×#389C2211yescharacteristic, complemented
58C61×#388—21no—
59C61×#387—21no—
60C61×#380C2211yescharacteristic
61C61×#380C2211yescharacteristic
62C61×#380C2211yescharacteristic, complemented
63C24×D61—21no—
64C2×#11758222—22no—
65C2×#11758222—22no—
66C2×#11758222—22no—
67C2×#11758222—41no—
68C2×#11758222—41no—
69C2×#11758222D414yes—
70C22×Dic122C2311yescharacteristic
71C22×D244—21no—
72C22×D244—22no—
73C22×D244—22no—
74C22×D244—22no—
75C22×D244—22no—
76C22×D244—41no—
77C22×D244—41no—
78C22×D244C2311yescharacteristic
79C22×D244C2311yescharacteristic
80C22×C22⋊D61—21no—
81C22×C22⋊D61—21no—
82C22×C4×D61—21no—
83C22×C4×D61—21no—
84C22×#92418—22no—
85C22×#92418—41no—
86C22×#92418—41no—
87C22×#92418C2311yescharacteristic
88C22×#92418C2311yescharacteristic
89C22×#92418C2311yescharacteristic
90C22×#92418C2311yescharacteristic
91#14519765—22no—
92#14519765—22no—
93#14519762—28no—
94#14519756—22no—
95#14519756—22no—
96#14519751—22no—
97#14519751D414yes—
98#14519750—28no—
99#14519745—28no—
100C4×D244—22no—
101C4×D244—22no—
102C2×C4⋊Dic61C2311yescharacteristic
103C2×#11758196—21no—
104C2×C22⋊Dic61—21no—
105C2×#11758198—21no—
106C2×#11758198—21no—
107C2×#11758198—21no—
108C2×#11758198—21no—
109C22⋊C4×D61—28no—
110#14519710—22no—
111#14519708—22no—
112#14519700—22no—
113#14519700—22no—
114#14519700—41no—
115#14519700—41no—
116#14519697—22no—
117#14519697—22no—
118#14519697—22no—
119#14519697—22no—
120#14519697—22no—
121#14519697—22no—
122#14519697—41no—
123#14519697—41no—
124C22⋊#92418—22no—
125C22⋊#92418—41no—
126C22⋊#92418—41no—
127C22×D4×C61D411yescharacteristic
128C23×C4×C61C2311yescharacteristic
129C23×C4×C61C2311yescharacteristic
130C4×D4×C61—22no—
131C4×D4×C61—22no—
132#117×C61—22no—
133#117×C61—22no—
134C2×C4⋊C4×C61—21no—
135C2×C4⋊C4×C61—21no—
136C2×C4⋊C4×C61D411yescharacteristic
137C2×C4⋊C4×C61C2311yescharacteristic
138C2×C4⋊C4×C61C2311yescharacteristic
139C2×C4⋊C4×C61C2311yescharacteristic
140C2×C4⋊C4×C61C2311yescharacteristic
141C2×C22⋊C4×C61—21no—
142C2×C22⋊C4×C61—21no—
143C2×C22⋊C4×C61—21no—
144C2×C22⋊C4×C61—21no—
145C2×C22⋊C4×C61D411yescharacteristic
146C2×C22⋊C4×C61D411yescharacteristic
147C2×C42×C61—21no—
148C2×C42×C61C2311yescharacteristic
149#95×C61—21no—
150#95×C61—21no—
151#95×C61—21no—
152#95×C61—21no—
153#95×C61—21no—
154C24×C61C2×D411yescharacteristic
155C24×C61C2×D411yescharacteristic
156C23×D61—21no—
157C23×D61—21no—
158C23×D61—24no—
159C23×D61—42no—
160C23×D61—42no—
161C23×D61—42no—
162C23×D61—42no—
163C23×D61—81no—
164C23×D61—81no—
165C2×D4×C61—22no—
166C2×D4×C61—22no—
167C2×D4×C61—41no—
168C22×C4×C61—21no—
169C22×C4×C61—21no—
170C22×C4×C61—21no—
171C22×C4×C61—21no—
172C22×C4×C61—21no—
173C22×C4×C61—21no—
174C22×C4×C61—21no—
175C22×C4×C61—21no—
176C22×C4×C61—21no—
177C22×C4×C61—21no—
178C22×C4×C61—21no—
179C22×C4×C61—21no—
180C22×C4×C61—21no—
181C22×C4×C61—21no—
182C22×C4×C61C2×D411yescharacteristic
183C22×C4×C61C2×D411yescharacteristic
184C22×C4×C61C2×D411yescharacteristic
185C22×C4×C61C2×D411yescharacteristic
186C22×C4×C61C2×D412yes—
187C22×C4×C61C2×D412yes—
188C22×C4×C61C2411yescharacteristic
189C2×C22⋊D61—24no—
190C2×C22⋊D61—24no—
191C2×C22⋊D61—42no—
192C2×C22⋊D61—42no—
193C2×C22⋊D61—81no—
194C2×C22⋊D61—81no—
195C22×Dic61—21no—
196C22×Dic61—21no—
197#11758222—28no—
198#11758222—44no—
199#11758222—44no—
200#11758222—44no—
201C2×D244—21no—
202C2×D244—21no—
203C2×D244—21no—
204C2×D244—21no—
205C2×D244—21no—
206C2×D244—21no—
207C2×D244—21no—
208C2×D244—24no—
209C2×D244—21no—
210C2×D244—44no—
211C2×D244—44no—
212C2×D244—44no—
213C2×D244—42no—
214C2×D244—42no—
215C2×D244—44no—
216C2×D244C2×D412yes—
217C2×D244C2×D412yes—
218C2×D244#4112yes—
219C2×D244#4112yes—
220C2×C4×D61—24no—
221C2×C4×D61—24no—
222C2×C4×D61—42no—
223C2×C4×D61—42no—
224C2×C4×D61—81no—
225C2×C4×D61—81no—
226C2×Dic122—21no—
227C2×Dic122—21no—
228C2×Dic122—21no—
229C2×Dic122—21no—
230C2×Dic122—21no—
231C2×Dic122C2×D412yes—
232C4⋊C4×C61—22no—
233C4⋊C4×C61—21no—
234C4⋊C4×C61—21no—
235C4⋊C4×C61—21no—
236C4⋊C4×C61—21no—
237C4⋊C4×C61—21no—
238C4⋊C4×C61—21no—
239C4⋊C4×C61—21no—
240C4⋊C4×C61—21no—
241C4⋊C4×C61—42no—
242C4⋊C4×C61—81no—
243C22⋊C4×C61—22no—
244C22⋊C4×C61—22no—
245C22⋊C4×C61—42no—
246C22⋊C4×C61—42no—
247C22⋊C4×C61—81no—
248C22⋊C4×C61—81no—
249C42×C61—21no—
250C42×C61—21no—
251C42×C61—42no—
252C22⋊Dic61—24no—
253#11758198—24no—
254#11758198—24no—
255#11758198—24no—
256#11758198—24no—
257C4⋊Dic61—21no—
258C4⋊Dic61C2×D412yes—
259#11758196—24no—
260C2×#92418—21no—
261C2×#92418—21no—
262C2×#92418—21no—
263C2×#92418—21no—
264C2×#92418—21no—
265C2×#92418—21no—
266C2×#92418—21no—
267C2×#92418—21no—
268C2×#92418—21no—
269C2×#92418—21no—
270C2×#92418—21no—
271C2×#92418—21no—
272C2×#92418—44no—
273C23×C61—21no—
274C23×C61—21no—
275C23×C61—21no—
276C23×C61—21no—
277C23×C61—21no—
278C23×C61—21no—
279C23×C61—21no—
280C23×C61—21no—
281C23×C61—21no—
282C23×C61—21no—
283C23×C61—21no—
284C23×C61—21no—
285C23×C61#12012yes—
286C23×C61#13512yes—
287C23×C61C22×D411yescharacteristic
288C22×D61—22no—
289C22×D61—22no—
290C22×D61—22no—
291C22×D61—22no—
292C22×D61—48no—
293C22×D61—41no—
294C22×D61—41no—
295C22×D61—41no—
296C22×D61—41no—
297C22×D61—48no—
298C22×D61—41no—
299C22×D61—41no—
300C22×D61—41no—
301C22×D61—41no—
302C22×D61—41no—
303C22×D61—41no—
304C22×D61—84no—
305C22×D61—84no—
306C22×D61—84no—
307C22×D61—84no—
308C22×D61—84no—
309D4×C61—44no—
310C2×C4×C61—21no—
311C2×C4×C61—21no—
312C2×C4×C61—22no—
313C2×C4×C61—22no—
314C2×C4×C61—22no—
315C2×C4×C61—22no—
316C2×C4×C61—21no—
317C2×C4×C61—21no—
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—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×C61—41no—
339C2×C4×C61—41no—
340C2×C4×C61—41no—
341C2×C4×C61#12012yes—
342C2×C4×C61C22×D411yescharacteristic
343C2×C4×C61C22×D411yescharacteristic
344C2×C4×C61C2×#4111yescharacteristic
345C2×C4×C61C2×#4111yescharacteristic
346C2×C4×C61H(5,𝔽2)11yescharacteristic
347C2×C4×C61H(5,𝔽2)11yescharacteristic
348C22⋊D61—48no—
349C22⋊D61—84no—
350C2×Dic61—22no—
351C2×Dic61—22no—
352C2×Dic61—41no—
353C2×Dic61—41no—
354C2×Dic61—41no—
355C2×Dic61—41no—
356D244—22no—
357D244—22no—
358D244—22no—
359D244—22no—
360D244—22no—
361D244—48no—
362D244—41no—
363D244—41no—
364D244#12314yes—
365C4×D61—48no—
366C4×D61—84no—
367Dic122—22no—
368Dic122—22no—
369Dic122—41no—
370Dic122—41no—
371#92418—41no—
372#92418—41no—
373#92418—41no—
374#92418—41no—
375#24037—611nomaximal, Sylow
376C22×C61—22no—
377C22×C61—22no—
378C22×C61—22no—
379C22×C61—22no—
380C22×C61—22no—
381C22×C61—22no—
382C22×C61—41no—
383C22×C61—41no—
384C22×C61—41no—
385C22×C61—41no—
386C22×C61—41no—
387C22×C61—41no—
388C22×C61—41no—
389C22×C61—41no—
390C22×C61C2×#12011yescharacteristic
391C22×C61#54611yescharacteristic
392C22×C61#54611yescharacteristic
393C22×C61C2×#13511yescharacteristic
394C22×C61#57511yescharacteristic
395C22×C61#57611yescharacteristic
396C22×C61#57711yescharacteristic
397C2×D61—24no—
398C2×D61—42no—
399C2×D61—42no—
400C2×D61—42no—
401C2×D61—42no—
402C2×D61—42no—
403C2×D61—42no—
404C2×D61—42no—
405C2×D61—42no—
406C2×D61—42no—
407C2×D61—816no—
408C2×D61—81no—
409C2×D61—81no—
410C2×D61—81no—
411C2×D61—81no—
412C4×C61—22no—
413C4×C61—41no—
414C4×C61—41no—
415C4×C61—41no—
416C4×C61—81no—
417C4×C61—81no—
418C4×C61—81no—
419C4×C61—81no—
420C4×C61C2×#12311yescharacteristic
421C4×C61#53411yescharacteristic
422C4×C61#54611yescharacteristic
423C4×C61#54611yescharacteristic
424Dic61—42no—
425Dic61—42no—
426C2×#546—611no—
427C2×#482—611no—
428C2×#416—611no—
429#2485D6111yescharacteristic, complemented
430#2042—611no—
431#2042—611no—
432#2036—611no—
433#2035—611no—
434#1893—611no—
435#1869—611no—
436#1864—611no—
437#1862—611no—
438#1788—611no—
439#1786—611no—
440#1786—611no—
441C2×C61—42no—
442C2×C61—42no—
443C2×C61#240511yescharacteristic
444C2×C61#300211yescharacteristic
445C2×C61#301211yescharacteristic
446C2×C61#329611yescharacteristic
447C2×C61#329711yescharacteristic
448C2×C61#331111yescharacteristic
449C2×C61#331911yescharacteristic
450D61—44no—
451D61—82no—
452C22×#41—611no—
453C23×D4—611no—
454C23×C8—611no—
455#546—1224no—
456#546—1224no—
457C2×#124—611no—
458C2×#123—1221no—
459C2×C22⋊Q8—611no—
460C2×#121—611no—
461C2×#121—1221no—
462C2×#120—1221no—
463C2×C4×D4—611no—
464C2×C4×D4C2×D6111yescharacteristic
465C2×#117C2×D6111yescharacteristic, complemented
466C22×C22⋊C4—1221no—
467#482—1224no—
468C2×#107—611no—
469C2×#106—611no—
470#416—1224no—
471C2×#103—611no—
472C2×#103—611no—
473C2×#103—611no—
474C2×#103—611no—
475C2×#102—611no—
476C2×#102—611no—
477C2×#102—611no—
478C2×#102—611no—
479C2×#102—611no—
480C2×#102—611no—
481C2×#102—611no—
482C2×#102—611no—
483C2×C22⋊C8—611no—
484C2×C22⋊C8—611no—
485C2×C22⋊C8—611no—
486#397—21no—
487#394—21no—
488#389C2×D6111yescharacteristic, complemented
489#389C2×D6111yescharacteristic, complemented
490#388—21no—
491#387—21no—
492#380C2×D6111yescharacteristic
493#380C2×D6111yescharacteristic
494#380C2×D6111yescharacteristic, complemented
495#340—611no—
496#340—611no—
497#336—611no—
498#336—611no—
499C61#2403711yescharacteristic, complemented, Sylow
500C25—1221no—
501C2×#41—614no—
502C2×#41—1222no—
503C2×#41—1222no—
504C2×#41—1222no—
505C2×#41—2441no—
506C2×#41—2441no—
507C22×Q8—611no—
508C22×D4—611no—
509C22×D4—611no—
510C22×D4—1222no—
511C22×D4—1222no—
512C22×D4—1222no—
513C22×D4—1222no—
514C22×D4—1221no—
515C22×D4—1221no—
516C22×D4—1221no—
517C22×D4—2441no—
518C22×D4—2441no—
519C22×D4C22⋊D6111yescharacteristic
520C23×C4—1221no—
521C23×C4—1221no—
522C23×C4C22×D6111yescharacteristic
523C23×C4C22×D6111yescharacteristic
524C22×C8—611no—
525C22×C8—611no—
526C22×C8—611no—
527C22×C8—611no—
528C22×C8—1222no—
529C22×C8—2441no—
530C22×C8—2441no—
531#124—1222no—
532#124—1222no—
533#123—1228no—
534C22⋊Q8—1222no—
535C22⋊Q8—1222no—
536#121—614no—
537#121—1228no—
538#121—1222no—
539#120—1228no—
540C4×D4—22no—
541C4×D4—22no—
542C4×D4—1222no—
543C4×D4—1222no—
544#117—22no—
545#117—22no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—21no—
548C2×C4⋊C4—611no—
549C2×C4⋊C4—1221no—
550C2×C4⋊C4C22⋊D6111yescharacteristic
551C2×C4⋊C4C22×D6111yescharacteristic
552C2×C4⋊C4C22×D6111yescharacteristic
553C2×C4⋊C4C22×D6111yescharacteristic
554C2×C4⋊C4C22×D6111yescharacteristic
555C2×C22⋊C4—21no—
556C2×C22⋊C4—21no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—1228no—
560C2×C22⋊C4—1221no—
561C2×C22⋊C4—1221no—
562C2×C22⋊C4—1221no—
563C2×C22⋊C4—1221no—
564C2×C22⋊C4—1221no—
565C2×C22⋊C4C22⋊D6111yescharacteristic
566C2×C22⋊C4C22⋊D6111yescharacteristic
567C2×C42—21no—
568C2×C42C22×D6111yescharacteristic
569#107—1222no—
570#106—1222no—
571#103—1222no—
572#103—1222no—
573#103—2441no—
574#103—2441no—
575#102—1222no—
576#102—1222no—
577#102—1222no—
578#102—1222no—
579#102—1222no—
580#102—1222no—
581#102—2441no—
582#102—2441no—
583C22⋊C8—1222no—
584C22⋊C8—2441no—
585C22⋊C8—2441no—
586#95—21no—
587#95—21no—
588#95—21no—
589#95—21no—
590#95—21no—
591C24—1224no—
592C24—1221no—
593C24—1221no—
594C24—4881no—
595C24—4881no—
596C24—2442no—
597C24—2442no—
598C24—2442no—
599C24—2442no—
600C24C2×C22⋊D6111yescharacteristic
601C24C2×C22⋊D6111yescharacteristic
602#41—1228no—
603#41—2444no—
604#41—2444no—
605#41—2444no—
606C2×Q8—612no—
607C2×Q8—1221no—
608C2×Q8—1221no—
609C2×Q8—1221no—
610C2×Q8—1221no—
611C2×Q8—1221no—
612C2×D4—22no—
613C2×D4—22no—
614C2×D4—41no—
615C2×D4—612no—
616C2×D4—612no—
617C2×D4—612no—
618C2×D4—612no—
619C2×D4—1224no—
620C2×D4—1224no—
621C2×D4—1224no—
622C2×D4—1221no—
623C2×D4—1221no—
624C2×D4—1221no—
625C2×D4—1221no—
626C2×D4—1221no—
627C2×D4—1221no—
628C2×D4—1221no—
629C2×D4—1221no—
630C2×D4—4881no—
631C2×D4—4881no—
632C2×D4—2442no—
633C2×D4—2442no—
634C2×D4—2444no—
635C2×D4—2444no—
636C2×D4—2444no—
637C2×D4—2444no—
638C2×D4—2442no—
639C2×D4—2442no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—1224no—
655C22×C4—1221no—
656C22×C4—1221no—
657C22×C4—1224no—
658C22×C4—4881no—
659C22×C4—4881no—
660C22×C4—2442no—
661C22×C4—2442no—
662C22×C4D4×D6112yes—
663C22×C4D4×D6112yes—
664C22×C4C2×C22⋊D6111yescharacteristic
665C22×C4C2×C22⋊D6111yescharacteristic
666C22×C4C2×C22⋊D6111yescharacteristic
667C22×C4C2×C22⋊D6111yescharacteristic
668C22×C4C23×D6111yescharacteristic
669C2×C8—1221no—
670C2×C8—1221no—
671C2×C8—1221no—
672C2×C8—1221no—
673C2×C8—1221no—
674C2×C8—1221no—
675C2×C8—1221no—
676C2×C8—1221no—
677C2×C8—1221no—
678C2×C8—1221no—
679C2×C8—1221no—
680C2×C8—1221no—
681C2×C8—2444no—
682C4⋊C4—22no—
683C4⋊C4—21no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—42no—
692C4⋊C4—81no—
693C4⋊C4—612no—
694C4⋊C4—1224no—
695C4⋊C4—1221no—
696C22⋊C4—22no—
697C22⋊C4—22no—
698C22⋊C4—42no—
699C22⋊C4—42no—
700C22⋊C4—81no—
701C22⋊C4—81no—
702C22⋊C4—1224no—
703C22⋊C4—1224no—
704C22⋊C4—1224no—
705C22⋊C4—1224no—
706C22⋊C4—1224no—
707C42—21no—
708C42—21no—
709C42—42no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—1222no—
723C23—1222no—
724C23—1222no—
725C23—1222no—
726C23—4884no—
727C23—4884no—
728C23—4884no—
729C23—4884no—
730C23—4884no—
731C23—2448no—
732C23—2448no—
733C23—2441no—
734C23—2441no—
735C23—2441no—
736C23—2441no—
737C23—2441no—
738C23—2441no—
739C23—2441no—
740C23—2441no—
741C23—2441no—
742C23—2441no—
743C23#1451974512yes—
744C23#1451979712yes—
745C23C22×C22⋊D6111yescharacteristic
746Q8—1222no—
747Q8—1222no—
748Q8—2441no—
749Q8—2441no—
750D4—44no—
751D4—614no—
752D4—1222no—
753D4—1222no—
754D4—1222no—
755D4—1222no—
756D4—1222no—
757D4—4884no—
758D4—2448no—
759D4—2448no—
760D4—2441no—
761D4—2441no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—1222no—
794C2×C4—1222no—
795C2×C4—4884no—
796C2×C4—2448no—
797C2×C4—2441no—
798C2×C4—2441no—
799C2×C4—2441no—
800C2×C4—2441no—
801C2×C4#1451974512yes—
802C2×C4C2×D4×D6111yescharacteristic
803C2×C4C2×D4×D6111yescharacteristic
804C2×C4#41×D6111yescharacteristic
805C2×C4#41×D6111yescharacteristic
806C2×C4#1451982311yescharacteristic
807C2×C4#1451982311yescharacteristic
808C8—2441no—
809C8—2441no—
810C8—2441no—
811C8—2441no—
812C22—22no—
813C22—22no—
814C22—22no—
815C22—22no—
816C22—22no—
817C22—22no—
818C22—41no—
819C22—41no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—1224no—
827C22—48816no—
828C22—4881no—
829C22—4881no—
830C22—4881no—
831C22—4881no—
832C22—2442no—
833C22—2442no—
834C22—2442no—
835C22—2442no—
836C22—2442no—
837C22—2442no—
838C22—2442no—
839C22—2442no—
840C22—2442no—
841C22C2×#1451974511yescharacteristic
842C22#1684040011yescharacteristic
843C22#1684040011yescharacteristic
844C22C2×#1451979711yescharacteristic
845C22#1684056011yescharacteristic
846C22#1684056511yescharacteristic
847C22#1684057011yescharacteristic
848C4—22no—
849C4—41no—
850C4—41no—
851C4—41no—
852C4—81no—
853C4—81no—
854C4—81no—
855C4—81no—
856C4—2442no—
857C4—2442no—
858C4#123×D6111yescharacteristic
859C4#1684032311yescharacteristic
860C4#1684040411yescharacteristic
861C4#1684040411yescharacteristic
862C2—42no—
863C2—42no—
864C2—4882no—
865C2—2444no—
866C2#2144914311yescharacteristic
867C2#2145503511yescharacteristic
868C2#2145512011yescharacteristic
869C2#2145764811yescharacteristic
870C2#2145766311yescharacteristic
871C2#2145784911yescharacteristic
872C2#2145796911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2485C2
socleC23×C61C22×D4
prime radicalC2×#16840408C2
hypercenter#2485D61
hypocenterC61#24037
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2485

Complements

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

NH ≅ G/Ntype
2. C2×#16840086C2semidirect
3. C2×#16839756C2semidirect
4. #21447060C2semidirect
5. #21447060C2semidirect
6. #21447022C2semidirect
7. #21447015C2semidirect
8. #21446245C2semidirect
9. #21446112C2semidirect
10. #21446079C2semidirect
11. #21446065C2semidirect
12. #21445757C2semidirect
13. #21445749C2semidirect
14. #21445749C2semidirect
15. C61×#2485C2semidirect
18. C23×#92418C22semidirect
30. C2×#14519710C22semidirect
31. C2×#14519708C22semidirect
33. C2×#14519700C22semidirect
34. C2×#14519700C22semidirect
35. C2×#14519700C22semidirect
36. C2×#14519700C22semidirect
47. C2×C22⋊#92418C22semidirect
48. #16839524C22semidirect
49. #16839524C22semidirect
50. #16839517C22semidirect
51. #16839517C22semidirect
53. C2×#117×C61C22semidirect
56. C61×#389C22semidirect
57. C61×#389C22semidirect
62. C61×#380C22semidirect
429. #2485D61semidirect
465. C2×#117C2×D61semidirect
488. #389C2×D61semidirect
489. #389C2×D61semidirect
494. #380C2×D61semidirect
499. C61#24037semidirect

Maximal subgroups

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

subgroupindex
C2×#168404082
C2×#168400862
C2×#168397562
#214470602
#214470222
#214470152
#214462452
#214461122
#214460792
#214460652
#214457572
#214457492
C61×#24852
#2403761