Finite Group Databasebeta

← #29722417

Subgroups — #29722417

Order 15616.

1026 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840006C211yesmaximal, characteristic, complemented
2C2×#16840006C211yesmaximal, characteristic, complemented
3C2×#16839840C211yesmaximal, characteristic, complemented
4C2×#16839802C211yesmaximal, characteristic, complemented
5#21449248C211yesmaximal, characteristic, complemented
6#21447207C211yesmaximal, characteristic, complemented
7#21447197C211yesmaximal, characteristic, complemented
8#21447022C211yesmaximal, characteristic, complemented
9#21447005C211yesmaximal, characteristic, complemented
10#21446672C211yesmaximal, characteristic, complemented
11#21446549C211yesmaximal, characteristic, complemented
12#21446142C211yesmaximal, characteristic, complemented
13#21446126C211yesmaximal, characteristic, complemented
14#21445850C211yesmaximal, characteristic, complemented
15C61×#2416C211yesmaximal, characteristic
16C22×#11758200C2211yescharacteristic
17C22×#11758194C2211yescharacteristic
18C22×#11758194C2211yescharacteristic
19C2×#14519756C2211yescharacteristic
20C2×#14519756C2211yescharacteristic
21C2×#14519736C2211yescharacteristic
22#16840006—24no—
23#16840006—24no—
24#16839840—24no—
25#16839802—24no—
26C2×#14519710C2211yescharacteristic
27C2×#14519710C2211yescharacteristic
28C2×#14519710C2211yescharacteristic
29C2×#14519708C2211yescharacteristic
30C2×#14519708C2211yescharacteristic
31C2×C4⋊#92418C2211yescharacteristic
32C2×#14519700C2211yescharacteristic
33C2×#14519700C2211yescharacteristic
34C2×#14519700C2211yescharacteristic
35C2×#14519698C2211yescharacteristic
36C2×#14519698C2211yescharacteristic
37C2×#14519698C2211yescharacteristic
38C2×C22⋊#92418C2211yescharacteristic
39C2×C22⋊#92418C2211yescharacteristic
40C2×C4×#92418C2211yescharacteristic
41#16839690—21no—
42#16839676—21no—
43#16839668C2211yescharacteristic
44#16839660C2211yescharacteristic
45#16839657—21no—
46#16839656—21no—
47#16839622C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52C2×#121×C61—21no—
53C2×#121×C61C2211yescharacteristic
54C2×#121×C61C2211yescharacteristic
55C2×C4×D4×C61C2211yescharacteristic
56C22×C4⋊C4×C61C2211yescharacteristic
57C61×#396—21no—
58C61×#394—21no—
59C61×#390C2211yescharacteristic
60C61×#389C2211yescharacteristic
61C61×#386—21no—
62C61×#380C2211yescharacteristic
63C22×Dic122C2311yescharacteristic
64C2×#11758200—22no—
65C2×#11758200—22no—
66C2×#11758200—22no—
67C2×#11758194—22no—
68C2×#11758194—22no—
69C2×#11758194—22no—
70C2×#11758194—22no—
71C2×#11758194—22no—
72C2×#11758194D414yescomplemented
73C22×#92418C2311yescharacteristic
74C22×#92418C2311yescharacteristic
75C22×#92418C2311yescharacteristic
76C22×#92418C2311yescharacteristic
77#14519756—22no—
78#14519756—22no—
79#14519756—22no—
80#14519756—41no—
81#14519736—22no—
82#14519736—41no—
83C2×C4⋊Dic61C2311yescharacteristic
84C2×C4⋊Dic61C2311yescharacteristic
85C2×C4⋊Dic61C2311yescharacteristic
86C2×#11758196—21no—
87C2×#11758196—21no—
88C2×#11758196—21no—
89C2×C22⋊Dic61—21no—
90C2×C22⋊Dic61—21no—
91C2×C22⋊Dic61—21no—
92C2×C22⋊Dic61—21no—
93C2×C4×Dic61—21no—
94#14519710—22no—
95#14519710—22no—
96#14519710D414yescomplemented
97#14519708—22no—
98#14519708—22no—
99C4⋊#92418—22no—
100#14519700—22no—
101#14519700—22no—
102#14519700—41no—
103#14519698—22no—
104#14519698—22no—
105#14519698—41no—
106C22⋊#92418—22no—
107C22⋊#92418—22no—
108C4×#92418—22no—
109#14519684—21no—
110#14519684—21no—
111#14519684—21no—
112#14519684—21no—
113C22×D4×C61—21no—
114C22×D4×C61—21no—
115C22×D4×C61D411yescharacteristic
116C22×D4×C61C2311yescharacteristic
117C23×C4×C61—21no—
118C23×C4×C61C2311yescharacteristic
119C23×C4×C61C2311yescharacteristic
120#121×C61—22no—
121#121×C61—22no—
122#121×C61—22no—
123#121×C61—41no—
124#121×C61—44no—
125C4×D4×C61—22no—
126C4×D4×C61—22no—
127C2×C4⋊C4×C61—22no—
128C2×C4⋊C4×C61—21no—
129C2×C4⋊C4×C61—21no—
130C2×C4⋊C4×C61—41no—
131C2×C4⋊C4×C61D411yescharacteristic
132C2×C4⋊C4×C61C2311yescharacteristic
133C2×C4⋊C4×C61C2311yescharacteristic
134C2×C4⋊C4×C61C2311yescharacteristic
135C2×C22⋊C4×C61—21no—
136C2×C22⋊C4×C61—21no—
137C2×C22⋊C4×C61—21no—
138C2×C22⋊C4×C61—21no—
139C2×C22⋊C4×C61—21no—
140C2×C22⋊C4×C61D411yescharacteristic
141C2×C22⋊C4×C61D411yescharacteristic
142C2×C42×C61C2311yescharacteristic
143#95×C61—21no—
144#95×C61—21no—
145C24×C61—21no—
146C24×C61C2×D411yescharacteristic
147C24×C61C2×D411yescharacteristic
148C2×D4×C61—22no—
149C2×D4×C61—22no—
150C2×D4×C61—21no—
151C2×D4×C61—21no—
152C2×D4×C61—21no—
153C2×D4×C61—21no—
154C2×D4×C61—21no—
155C2×D4×C61—21no—
156C2×D4×C61—41no—
157C2×D4×C61—42no—
158C2×D4×C61—42no—
159C2×D4×C61—42no—
160C2×D4×C61—42no—
161C2×D4×C61—42no—
162C2×D4×C61—81no—
163C22×C4×C61—21no—
164C22×C4×C61—21no—
165C22×C4×C61—21no—
166C22×C4×C61—21no—
167C22×C4×C61—21no—
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—42no—
177C22×C4×C61—42no—
178C22×C4×C61—81no—
179C22×C4×C61C2×D411yescharacteristic
180C22×C4×C61C2×D411yescharacteristic
181C22×C4×C61C2×D411yescharacteristic
182C22×C4×C61C2×D412yes—
183C22×C4×C61C2×D411yescharacteristic
184C22×C4×C61#4112yes—
185C22×C4×C61C2411yescharacteristic
186C22×Dic61—21no—
187C22×Dic61—21no—
188C22×Dic61—21no—
189C22×Dic61—21no—
190C2×Dic122—21no—
191C2×Dic122—21no—
192C2×Dic122—21no—
193C2×Dic122—21no—
194C2×Dic122—21no—
195C2×Dic122—21no—
196C4⋊C4×C61—22no—
197C4⋊C4×C61—21no—
198C4⋊C4×C61—21no—
199C4⋊C4×C61—21no—
200C4⋊C4×C61—21no—
201C4⋊C4×C61—21no—
202C4⋊C4×C61—42no—
203C4⋊C4×C61—42no—
204C4⋊C4×C61C2×D412yes—
205C22⋊C4×C61—22no—
206C22⋊C4×C61—22no—
207C22⋊C4×C61—42no—
208C22⋊C4×C61—42no—
209C22⋊C4×C61—42no—
210C22⋊C4×C61—42no—
211C22⋊C4×C61—81no—
212C42×C61—21no—
213C42×C61—21no—
214C22⋊Dic61—42no—
215C22⋊Dic61—42no—
216C22⋊Dic61—42no—
217C22⋊Dic61—42no—
218#11758200—44no—
219C4⋊Dic61—21no—
220C4⋊Dic61—21no—
221C4⋊Dic61—21no—
222C4⋊Dic61—21no—
223C4⋊Dic61—21no—
224C4⋊Dic61C2×D412yes—
225#11758196—42no—
226#11758196—42no—
227#11758196—42no—
228C4×Dic61—42no—
229#11758194—28no—
230#11758194—44no—
231C2×#92418—21no—
232C2×#92418—21no—
233C2×#92418—21no—
234C2×#92418—21no—
235C2×#92418—21no—
236C2×#92418—21no—
237C2×#92418—21no—
238C2×#92418—21no—
239C2×#92418C2×D412yes—
240C2×#92418C2×D412yes—
241C2×#92418C2×D412yes—
242C2×#92418#4112yes—
243C23×C61—21no—
244C23×C61—21no—
245C23×C61—21no—
246C23×C61—21no—
247C23×C61—21no—
248C23×C61—21no—
249C23×C61—21no—
250C23×C61—21no—
251C23×C61—21no—
252C23×C61—21no—
253C23×C61—21no—
254C23×C61—21no—
255C23×C61—21no—
256C23×C61—41no—
257C23×C61—41no—
258C23×C61—41no—
259C23×C61—41no—
260C23×C61—41no—
261C23×C61—41no—
262C23×C61—41no—
263C23×C61#12112yes—
264C23×C61C22×D411yescharacteristic
265D4×C61—44no—
266D4×C61—41no—
267D4×C61—41no—
268D4×C61—41no—
269D4×C61—41no—
270D4×C61—84no—
271D4×C61—84no—
272C2×C4×C61—21no—
273C2×C4×C61—21no—
274C2×C4×C61—21no—
275C2×C4×C61—21no—
276C2×C4×C61—22no—
277C2×C4×C61—22no—
278C2×C4×C61—22no—
279C2×C4×C61—22no—
280C2×C4×C61—21no—
281C2×C4×C61—21no—
282C2×C4×C61—21no—
283C2×C4×C61—22no—
284C2×C4×C61—21no—
285C2×C4×C61—21no—
286C2×C4×C61—21no—
287C2×C4×C61—41no—
288C2×C4×C61—41no—
289C2×C4×C61—41no—
290C2×C4×C61—41no—
291C2×C4×C61—41no—
292C2×C4×C61—41no—
293C2×C4×C61—41no—
294C2×C4×C61—41no—
295C2×C4×C61—41no—
296C2×C4×C61—41no—
297C2×C4×C61—41no—
298C2×C4×C61—41no—
299C2×C4×C61—84no—
300C2×C4×C61#12112yes—
301C2×C4×C61AGL(1,ℤ/8)12yes—
302C2×C4×C61C22×D411yescharacteristic
303C2×C4×C61C22×D411yescharacteristic
304C2×C4×C61C2×#4111yescharacteristic
305C2×C4×C61C2×#4111yescharacteristic
306C2×C4×C61H(5,𝔽2)11yescharacteristic
307C2×C4×C612−1+411yescharacteristic
308C2×Dic61—22no—
309C2×Dic61—41no—
310C2×Dic61—41no—
311C2×Dic61—41no—
312C2×Dic61—41no—
313C2×Dic61—41no—
314C2×Dic61—41no—
315C2×Dic61—41no—
316C2×Dic61—41no—
317C2×Dic61—41no—
318C2×Dic61—41no—
319C2×Dic61—41no—
320Dic122—41no—
321Dic122—41no—
322Dic122—41no—
323Dic122—41no—
324#92418—22no—
325#92418—41no—
326#92418—41no—
327#92418#12114yescomplemented
328#24794—611nomaximal, Sylow
329C22×C61—22no—
330C22×C61—22no—
331C22×C61—22no—
332C22×C61—41no—
333C22×C61—41no—
334C22×C61—41no—
335C22×C61—41no—
336C22×C61—41no—
337C22×C61—41no—
338C22×C61—41no—
339C22×C61—41no—
340C22×C61—41no—
341C22×C61—41no—
342C22×C61—41no—
343C22×C61—81no—
344C22×C61—81no—
345C22×C61—81no—
346C22×C61—81no—
347C22×C61—81no—
348C22×C61—81no—
349C22×C61—81no—
350C22×C61C2×#12111yescharacteristic
351C22×C61D4211yescharacteristic
352C22×C61#54711yescharacteristic
353C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
354C22×C61#57511yescharacteristic
355C22×C61#57711yescharacteristic
356C22×C61#57811yescharacteristic
357C4×C61—22no—
358C4×C61—22no—
359C4×C61—41no—
360C4×C61—42no—
361C4×C61—41no—
362C4×C61—81no—
363C4×C61—81no—
364C4×C61C2×#12111yescharacteristic
365C4×C61#53711yescharacteristic
366C4×C61#54811yescharacteristic
367C4×C61#55311yescharacteristic
368Dic61—42no—
369Dic61—81no—
370Dic61—81no—
371Dic61—81no—
372C2×#468—611no—
373C2×#468—611no—
374C2×#436—611no—
375C2×#428—611no—
376#2416D6111yescharacteristic
377#2415—611no—
378#2067—611no—
379#2066—611no—
380#2036—611no—
381#2034—611no—
382#1968—611no—
383#1942—611no—
384#1875—611no—
385#1872—611no—
386#1809—611no—
387C2×C61—42no—
388C2×C61—81no—
389C2×C61—161no—
390C2×C61#241611yescharacteristic
391C2×C61#305511yescharacteristic
392C2×C61#306311yescharacteristic
393C2×C61#327211yescharacteristic
394C2×C61#327711yescharacteristic
395C2×C61#335111yescharacteristic
396C2×C61#335311yescharacteristic
397C22×SD16—611no—
398C22×M16—611no—
399C22×M16—611no—
400C2×C22⋊Q8—611no—
401C2×C22⋊Q8—611no—
402C2×#121—21no—
403C2×#121C2×D6111yescharacteristic
404C2×#121C2×D6111yescharacteristic
405C2×C4×D4C2×D6111yescharacteristic
406C2×#117—611no—
407C22×C4⋊C4C2×D6111yescharacteristic
408#468—1224no—
409#468—1224no—
410#436—1224no—
411#428—1224no—
412C2×#107—611no—
413C2×#107—611no—
414C2×#107—611no—
415C2×#106—611no—
416C2×#106—611no—
417C2×C4⋊C8—611no—
418C2×#103—611no—
419C2×#103—611no—
420C2×#103—611no—
421C2×#102—611no—
422C2×#102—611no—
423C2×#102—611no—
424C2×C22⋊C8—611no—
425C2×C22⋊C8—611no—
426C2×C4×C8—611no—
427#397—1221no—
428#396—21no—
429#394—21no—
430#394—1221no—
431#391—611no—
432#390C2×D6111yescharacteristic
433#389—611no—
434#389—1221no—
435#389C2×D6111yescharacteristic
436#388—1221no—
437#386—21no—
438#380—611no—
439#380C2×D6111yescharacteristic
440#340—611no—
441#340—611no—
442#340—611no—
443#340—611no—
444C61#2479411yescharacteristic, complemented, Sylow
445C22×Q8—611no—
446C22×D4—21no—
447C22×D4—21no—
448C22×D4C22⋊D6111yescharacteristic
449C22×D4C22×D6111yescharacteristic
450C23×C4—21no—
451C23×C4C22×D6111yescharacteristic
452C23×C4C22×D6111yescharacteristic
453C2×SD16—1222no—
454C2×SD16—1222no—
455C2×SD16—1222no—
456C2×M16—614no—
457C2×M16—1222no—
458C2×M16—1222no—
459C2×M16—1222no—
460C2×M16—1222no—
461C2×M16—1222no—
462C22×C8—611no—
463C22×C8—611no—
464C22×C8—611no—
465C22×C8—611no—
466C22⋊Q8—1222no—
467C22⋊Q8—1222no—
468C22⋊Q8—1222no—
469C22⋊Q8—2441no—
470#121—22no—
471#121—22no—
472#121—22no—
473#121—41no—
474#121—44no—
475C4×D4—22no—
476C4×D4—22no—
477#117—1222no—
478#117—2441no—
479C2×C4⋊C4—22no—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—21no—
482C2×C4⋊C4—41no—
483C2×C4⋊C4—611no—
484C2×C4⋊C4—611no—
485C2×C4⋊C4—611no—
486C2×C4⋊C4—1221no—
487C2×C4⋊C4—1221no—
488C2×C4⋊C4—1221no—
489C2×C4⋊C4C22⋊D6111yescharacteristic
490C2×C4⋊C4C22×D6111yescharacteristic
491C2×C4⋊C4C22×D6111yescharacteristic
492C2×C4⋊C4C22×D6111yescharacteristic
493C2×C22⋊C4—21no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—21no—
497C2×C22⋊C4—21no—
498C2×C22⋊C4—1221no—
499C2×C22⋊C4—1221no—
500C2×C22⋊C4—1221no—
501C2×C22⋊C4—1221no—
502C2×C22⋊C4C22⋊D6111yescharacteristic
503C2×C22⋊C4C22⋊D6111yescharacteristic
504C2×C42—1221no—
505C2×C42C22×D6111yescharacteristic
506#107—614no—
507#107—1222no—
508#107—1222no—
509#106—1222no—
510#106—1222no—
511C4⋊C8—1222no—
512#103—1222no—
513#103—1222no—
514#103—2441no—
515#102—1222no—
516#102—1222no—
517#102—2441no—
518C22⋊C8—1222no—
519C22⋊C8—1222no—
520C4×C8—1222no—
521#95—21no—
522#95—21no—
523#95—1221no—
524#95—1221no—
525#95—1221no—
526#95—1221no—
527C24—21no—
528C24C2×C22⋊D6111yescharacteristic
529C24C2×C22⋊D6111yescharacteristic
530C2×Q8—1221no—
531C2×Q8—1221no—
532C2×Q8—1221no—
533C2×Q8—1221no—
534C2×Q8—1221no—
535C2×Q8—1221no—
536C2×D4—22no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—22no—
544C2×D4—41no—
545C2×D4—42no—
546C2×D4—42no—
547C2×D4—42no—
548C2×D4—42no—
549C2×D4—42no—
550C2×D4—81no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—42no—
565C22×C4—42no—
566C22×C4—81no—
567C22×C4—1221no—
568C22×C4—1221no—
569C22×C4—1221no—
570C22×C4—1221no—
571C22×C4D4×D6112yes—
572C22×C4#1175822412yes—
573C22×C4C2×C22⋊D6111yescharacteristic
574C22×C4C2×C22⋊D6111yescharacteristic
575C22×C4C2×C22⋊D6111yescharacteristic
576C22×C4C2×C22⋊D6111yescharacteristic
577C22×C4C23×D6111yescharacteristic
578SD16—2444no—
579M16—1228no—
580M16—2444no—
581C2×C8—612no—
582C2×C8—612no—
583C2×C8—612no—
584C2×C8—612no—
585C2×C8—1221no—
586C2×C8—1221no—
587C2×C8—1221no—
588C2×C8—1221no—
589C2×C8—1221no—
590C2×C8—1221no—
591C2×C8—1221no—
592C2×C8—1221no—
593C4⋊C4—21no—
594C4⋊C4—22no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—42no—
600C4⋊C4—42no—
601C4⋊C4—612no—
602C4⋊C4—1221no—
603C4⋊C4—1221no—
604C4⋊C4—1221no—
605C4⋊C4—1221no—
606C4⋊C4—1221no—
607C4⋊C4—2442no—
608C4⋊C4—2442no—
609C4⋊C4—2442no—
610C4⋊C4D4×D6112yes—
611C22⋊C4—22no—
612C22⋊C4—22no—
613C22⋊C4—42no—
614C22⋊C4—42no—
615C22⋊C4—42no—
616C22⋊C4—42no—
617C22⋊C4—81no—
618C22⋊C4—2442no—
619C22⋊C4—2442no—
620C22⋊C4—2442no—
621C22⋊C4—2442no—
622C42—21no—
623C42—21no—
624C42—2442no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23#1451974912yes—
646C23C22×C22⋊D6111yescharacteristic
647Q8—2441no—
648Q8—2441no—
649Q8—2441no—
650Q8—2441no—
651D4—44no—
652D4—41no—
653D4—41no—
654D4—41no—
655D4—41no—
656D4—84no—
657D4—84no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—22no—
672C2×C4—21no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—84no—
686C2×C4—1222no—
687C2×C4—2441no—
688C2×C4—2441no—
689C2×C4—2441no—
690C2×C4—2441no—
691C2×C4—2441no—
692C2×C4—2441no—
693C2×C4—2441no—
694C2×C4—2441no—
695C2×C4—2441no—
696C2×C4—2441no—
697C2×C4—2441no—
698C2×C4#1451974912yes—
699C2×C4#1451980312yes—
700C2×C4C2×D4×D6111yescharacteristic
701C2×C4C2×D4×D6111yescharacteristic
702C2×C4#41×D6111yescharacteristic
703C2×C4C2×#1175822411yescharacteristic
704C2×C4#1451982211yescharacteristic
705C2×C4#1451982411yescharacteristic
706C8—614no—
707C8—1222no—
708C8—2441no—
709C8—2441no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—81no—
725C22—81no—
726C22—81no—
727C22—81no—
728C22—81no—
729C22—81no—
730C22—81no—
731C22C2×#1451974911yescharacteristic
732C22D4×C22⋊D6111yescharacteristic
733C22#1684041111yescharacteristic
734C22C2×#1451980311yescharacteristic
735C22#1684056011yescharacteristic
736C22#1684057311yescharacteristic
737C22#1684057711yescharacteristic
738C4—22no—
739C4—22no—
740C4—42no—
741C4—41no—
742C4—41no—
743C4—81no—
744C4—81no—
745C4—4881no—
746C4—4881no—
747C4—4881no—
748C4—2442no—
749C4#121×D6111yescharacteristic
750C4#1684033911yescharacteristic
751C4#1684041811yescharacteristic
752C4#1684045511yescharacteristic
753C2—42no—
754C2—81no—
755C2—161no—
756C2#2144925611yescharacteristic
757C2#2145543411yescharacteristic
758C2#2145551211yescharacteristic
759C2#2145741511yescharacteristic
760C2#2145747211yescharacteristic
761C2#2145837311yescharacteristic
762C2#2145840311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
Fitting, prime radicalC61×#2416C2
socleC23×C61C22×D4
hypercenter#2416D61
hypocenterC61#24794
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2416

Complements

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

NH ≅ G/Ntype
1. C2×#16840006C2semidirect
2. C2×#16840006C2semidirect
3. C2×#16839840C2semidirect
4. C2×#16839802C2semidirect
5. #21449248C2semidirect
6. #21447207C2semidirect
7. #21447197C2semidirect
8. #21447022C2semidirect
9. #21447005C2semidirect
10. #21446672C2semidirect
11. #21446549C2semidirect
12. #21446142C2semidirect
13. #21446126C2semidirect
14. #21445850C2semidirect
72. C2×#11758194D4semidirect
96. #14519710D4semidirect
327. #92418#121semidirect
444. C61#24794semidirect

Maximal subgroups

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

subgroupindex
C2×#168400062
C2×#168398402
C2×#168398022
#214492482
#214472072
#214471972
#214470222
#214470052
#214466722
#214465492
#214461422
#214461262
#214458502
C61×#24162
#2479461