Finite Group Databasebeta

← #29722312

Subgroups — #29722312

Order 15616.

1054 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840006C211yesmaximal, characteristic, complemented
2C2×#16839989C211yesmaximal, characteristic, complemented
3C2×#16839834C211yesmaximal, characteristic, complemented
4C22×#14519710C211yesmaximal, characteristic, complemented
5#21449270C211yesmaximal, characteristic, complemented
6#21447211C211yesmaximal, characteristic, complemented
7#21447207C211yesmaximal, characteristic, complemented
8#21447022C211yesmaximal, characteristic, complemented
9#21446998C211yesmaximal, characteristic, complemented
10#21446699C211yesmaximal, characteristic, complemented
11#21446554C211yesmaximal, characteristic, complemented
12#21446137C211yesmaximal, characteristic, complemented
13#21446126C211yesmaximal, characteristic, complemented
14#21445850C211yesmaximal, characteristic, complemented
15C61×#2416C211yesmaximal, characteristic
16C22×#11758200C2211yescharacteristic
17C22×#11758194C2211yescharacteristic
18C23×#92418C2211yescharacteristic
19C2×#14519756C2211yescharacteristic
20C2×#14519756C2211yescharacteristic
21C22×C4⋊Dic61C2211yescharacteristic
22#16840006—24no—
23#16839989—24no—
24#16839834—24no—
25C2×#14519710—24no—
26C2×#14519710C2211yescharacteristic
27C2×#14519710C2211yescharacteristic
28C2×#14519710C2211yescharacteristic
29C2×#14519710C2211yescharacteristic
30C2×#14519708C2211yescharacteristic
31C2×C4⋊#92418C2211yescharacteristic
32C2×#14519700C2211yescharacteristic
33C2×#14519700C2211yescharacteristic
34C2×#14519700C2211yescharacteristic
35C2×#14519698C2211yescharacteristic
36C2×#14519698C2211yescharacteristic
37C2×#14519698C2211yescharacteristic
38C2×C22⋊#92418C2211yescharacteristic
39C2×C22⋊#92418C2211yescharacteristic
40C2×#14519688C2211yescharacteristic
41#16839695—21no—
42#16839685—21no—
43#16839668C2211yescharacteristic
44#16839660C2211yescharacteristic
45#16839642—21no—
46#16839622C2211yescharacteristic
47#16839620—21no—
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
64C23×Dic61—21no—
65C2×#11758200—22no—
66C2×#11758200—22no—
67C2×#11758200—22no—
68C2×#11758194—22no—
69C2×#11758194—22no—
70C2×#11758194—22no—
71C22×#92418—22no—
72C22×#92418—22no—
73C22×#92418D414yescomplemented
74C22×#92418C2311yescharacteristic
75C22×#92418C2311yescharacteristic
76C22×#92418C2311yescharacteristic
77C22×#92418C2311yescharacteristic
78#14519756—22no—
79#14519756—22no—
80#14519756—22no—
81#14519756—41no—
82C2×C4⋊Dic61—22no—
83C2×C4⋊Dic61—21no—
84C2×C4⋊Dic61—41no—
85C2×C4⋊Dic61C2311yescharacteristic
86C2×C4⋊Dic61C2311yescharacteristic
87C2×C4⋊Dic61C2311yescharacteristic
88C2×#11758196—21no—
89C2×#11758196—21no—
90C2×#11758196—21no—
91C2×C22⋊Dic61—21no—
92C2×C22⋊Dic61—21no—
93C2×C22⋊Dic61—21no—
94#14519710—22no—
95#14519710—22no—
96#14519710—22no—
97#14519710D414yescomplemented
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—
108#14519688—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—22no—
151C2×D4×C61—21no—
152C2×D4×C61—21no—
153C2×D4×C61—21no—
154C2×D4×C61—21no—
155C2×D4×C61—21no—
156C2×D4×C61—21no—
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×D411yescharacteristic
183C22×C4×C61C2×D412yes—
184C22×C4×C61#4112yes—
185C22×C4×C61C2411yescharacteristic
186C22×Dic61—21no—
187C22×Dic61—21no—
188C22×Dic61—21no—
189C22×Dic61—21no—
190C22×Dic61—42no—
191C22×Dic61—42no—
192C22×Dic61—81no—
193C2×Dic122—21no—
194C2×Dic122—21no—
195C2×Dic122—21no—
196C2×Dic122—21no—
197C2×Dic122—21no—
198C2×Dic122—21no—
199C4⋊C4×C61—22no—
200C4⋊C4×C61—21no—
201C4⋊C4×C61—21no—
202C4⋊C4×C61—21no—
203C4⋊C4×C61—21no—
204C4⋊C4×C61—21no—
205C4⋊C4×C61—42no—
206C4⋊C4×C61—42no—
207C4⋊C4×C61C2×D412yes—
208C22⋊C4×C61—22no—
209C22⋊C4×C61—22no—
210C22⋊C4×C61—42no—
211C22⋊C4×C61—42no—
212C22⋊C4×C61—42no—
213C22⋊C4×C61—42no—
214C22⋊C4×C61—81no—
215C42×C61—21no—
216C42×C61—21no—
217C22⋊Dic61—42no—
218C22⋊Dic61—42no—
219C22⋊Dic61—81no—
220#11758200—44no—
221C4⋊Dic61—21no—
222C4⋊Dic61—21no—
223C4⋊Dic61—21no—
224C4⋊Dic61—21no—
225C4⋊Dic61—21no—
226C4⋊Dic61—42no—
227C4⋊Dic61C2×D412yes—
228#11758196—42no—
229#11758196—42no—
230#11758196—81no—
231#11758194—44no—
232C2×#92418—21no—
233C2×#92418—21no—
234C2×#92418—28no—
235C2×#92418—21no—
236C2×#92418—21no—
237C2×#92418—21no—
238C2×#92418—21no—
239C2×#92418—21no—
240C2×#92418—21no—
241C2×#92418C2×D412yes—
242C2×#92418C2×D412yes—
243C2×#92418C2×D412yes—
244C2×#92418#4112yes—
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×C61AGL(1,ℤ/8)12yes—
265C23×C61#13712yes—
266C23×C61C22×D411yescharacteristic
267D4×C61—44no—
268D4×C61—41no—
269D4×C61—41no—
270D4×C61—41no—
271D4×C61—41no—
272D4×C61—84no—
273D4×C61—84no—
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—21no—
284C2×C4×C61—22no—
285C2×C4×C61—21no—
286C2×C4×C61—21no—
287C2×C4×C61—21no—
288C2×C4×C61—21no—
289C2×C4×C61—21no—
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—41no—
300C2×C4×C61—41no—
301C2×C4×C61—41no—
302C2×C4×C61—84no—
303C2×C4×C61#12112yes—
304C2×C4×C61C22×D411yescharacteristic
305C2×C4×C61C22×D411yescharacteristic
306C2×C4×C61C2×#4111yescharacteristic
307C2×C4×C61C2×#4111yescharacteristic
308C2×C4×C61H(5,𝔽2)11yescharacteristic
309C2×C4×C612−1+411yescharacteristic
310C2×Dic61—22no—
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—
320C2×Dic61—41no—
321C2×Dic61—41no—
322C2×Dic61—84no—
323Dic122—41no—
324Dic122—41no—
325Dic122—41no—
326Dic122—41no—
327#92418—22no—
328#92418—41no—
329#92418—41no—
330#92418#12114yescomplemented
331#24787—611nomaximal, Sylow
332C22×C61—22no—
333C22×C61—22no—
334C22×C61—22no—
335C22×C61—22no—
336C22×C61—22no—
337C22×C61—22no—
338C22×C61—41no—
339C22×C61—41no—
340C22×C61—41no—
341C22×C61—41no—
342C22×C61—41no—
343C22×C61—41no—
344C22×C61—41no—
345C22×C61—81no—
346C22×C61—81no—
347C22×C61—81no—
348C22×C61—81no—
349C22×C61—81no—
350C22×C61—81no—
351C22×C61—81no—
352C22×C61#46814yescomplemented
353C22×C61C2×#12111yescharacteristic
354C22×C61D4211yescharacteristic
355C22×C61#54711yescharacteristic
356C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
357C22×C61C2×#13711yescharacteristic
358C22×C61#57611yescharacteristic
359C22×C61#57811yescharacteristic
360C4×C61—22no—
361C4×C61—41no—
362C4×C61—42no—
363C4×C61—41no—
364C4×C61—41no—
365C4×C61—81no—
366C4×C61—81no—
367C4×C61C2×#12111yescharacteristic
368C4×C61#53711yescharacteristic
369C4×C61#54811yescharacteristic
370C4×C61#55311yescharacteristic
371Dic61—42no—
372Dic61—81no—
373Dic61—81no—
374Dic61—81no—
375C2×#468—611no—
376C2×#465—611no—
377C2×#435—611no—
378C22×#107—611no—
379#2417—611no—
380#2416D6111yescharacteristic
381#2068—611no—
382#2067—611no—
383#2036—611no—
384#2033—611no—
385#1973—611no—
386#1943—611no—
387#1874—611no—
388#1872—611no—
389#1809—611no—
390C2×C61—24no—
391C2×C61—81no—
392C2×C61—161no—
393C2×C61#241611yescharacteristic
394C2×C61C2×#46811yescharacteristic
395C2×C61#306111yescharacteristic
396C2×C61#326411yescharacteristic
397C2×C61#327011yescharacteristic
398C2×C61#334311yescharacteristic
399C2×C61#334611yescharacteristic
400C22×SD16—611no—
401C22×M16—611no—
402C23×C8—611no—
403C2×C22⋊Q8—611no—
404C2×C22⋊Q8—611no—
405C2×#121—21no—
406C2×#121C2×D6111yescharacteristic
407C2×#121C2×D6111yescharacteristic
408C2×C4×D4C2×D6111yescharacteristic
409C22×C4⋊C4—611no—
410C22×C4⋊C4C2×D6111yescharacteristic
411#468—1224no—
412#465—1224no—
413#435—1224no—
414C2×#107—611no—
415C2×#107—611no—
416C2×#107—611no—
417C2×#107—611no—
418C2×#107—1224no—
419C2×#106—611no—
420C2×C4⋊C8—611no—
421C2×#103—611no—
422C2×#103—611no—
423C2×#103—611no—
424C2×#102—611no—
425C2×#102—611no—
426C2×#102—611no—
427C2×C22⋊C8—611no—
428C2×C22⋊C8—611no—
429C2×#97—611no—
430#398—1221no—
431#396—21no—
432#396—1221no—
433#394—21no—
434#391—611no—
435#390C2×D6111yescharacteristic
436#389—611no—
437#389C2×D6111yescharacteristic
438#386—21no—
439#386—1221no—
440#380—611no—
441#380—1221no—
442#380C2×D6111yescharacteristic
443#340—611no—
444#340—611no—
445#340—611no—
446#340—611no—
447C61#2478711yescharacteristic, complemented, Sylow
448C22×Q8—611no—
449C22×D4—21no—
450C22×D4—21no—
451C22×D4C22⋊D6111yescharacteristic
452C22×D4C22×D6111yescharacteristic
453C23×C4—21no—
454C23×C4—1221no—
455C23×C4C22×D6111yescharacteristic
456C23×C4C22×D6111yescharacteristic
457C2×SD16—1222no—
458C2×SD16—1222no—
459C2×SD16—1222no—
460C2×M16—1222no—
461C2×M16—1222no—
462C2×M16—1222no—
463C22×C8—611no—
464C22×C8—614no—
465C22×C8—611no—
466C22×C8—611no—
467C22×C8—611no—
468C22×C8—1222no—
469C22×C8—1222no—
470C22⋊Q8—1222no—
471C22⋊Q8—1222no—
472C22⋊Q8—1222no—
473C22⋊Q8—2441no—
474#121—22no—
475#121—22no—
476#121—22no—
477#121—41no—
478#121—44no—
479C4×D4—22no—
480C4×D4—22no—
481C2×C4⋊C4—22no—
482C2×C4⋊C4—21no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—41no—
485C2×C4⋊C4—611no—
486C2×C4⋊C4—611no—
487C2×C4⋊C4—611no—
488C2×C4⋊C4—1222no—
489C2×C4⋊C4—1221no—
490C2×C4⋊C4—1221no—
491C2×C4⋊C4—1221no—
492C2×C4⋊C4—1221no—
493C2×C4⋊C4—2441no—
494C2×C4⋊C4C22⋊D6111yescharacteristic
495C2×C4⋊C4C22×D6111yescharacteristic
496C2×C4⋊C4C22×D6111yescharacteristic
497C2×C4⋊C4C22×D6111yescharacteristic
498C2×C22⋊C4—21no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—1221no—
504C2×C22⋊C4—1221no—
505C2×C22⋊C4—1221no—
506C2×C22⋊C4C22⋊D6111yescharacteristic
507C2×C22⋊C4C22⋊D6111yescharacteristic
508C2×C42C22×D6111yescharacteristic
509#107—614no—
510#107—1222no—
511#107—1222no—
512#107—1222no—
513#106—1222no—
514C4⋊C8—1222no—
515#103—1222no—
516#103—1222no—
517#103—2441no—
518#102—1222no—
519#102—1222no—
520#102—2441no—
521C22⋊C8—1222no—
522C22⋊C8—1222no—
523#97—1222no—
524#95—21no—
525#95—21no—
526#95—1221no—
527#95—1221no—
528#95—1221no—
529#95—1221no—
530C24—21no—
531C24C2×C22⋊D6111yescharacteristic
532C24C2×C22⋊D6111yescharacteristic
533C2×Q8—1221no—
534C2×Q8—1221no—
535C2×Q8—1221no—
536C2×Q8—1221no—
537C2×Q8—1221no—
538C2×Q8—1221no—
539C2×D4—22no—
540C2×D4—22no—
541C2×D4—22no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—42no—
549C2×D4—42no—
550C2×D4—42no—
551C2×D4—42no—
552C2×D4—42no—
553C2×D4—81no—
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—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—42no—
568C22×C4—42no—
569C22×C4—81no—
570C22×C4—1221no—
571C22×C4—1221no—
572C22×C4—1221no—
573C22×C4—1221no—
574C22×C4—4881no—
575C22×C4—2442no—
576C22×C4—2442no—
577C22×C4D4×D6112yes—
578C22×C4#1175822412yes—
579C22×C4C2×C22⋊D6111yescharacteristic
580C22×C4C2×C22⋊D6111yescharacteristic
581C22×C4C2×C22⋊D6111yescharacteristic
582C22×C4C2×C22⋊D6111yescharacteristic
583C22×C4C23×D6111yescharacteristic
584SD16—2444no—
585M16—2444no—
586C2×C8—612no—
587C2×C8—612no—
588C2×C8—612no—
589C2×C8—612no—
590C2×C8—1228no—
591C2×C8—1221no—
592C2×C8—1221no—
593C2×C8—1221no—
594C2×C8—1221no—
595C2×C8—1221no—
596C2×C8—1221no—
597C2×C8—1221no—
598C2×C8—1221no—
599C4⋊C4—21no—
600C4⋊C4—22no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—42no—
606C4⋊C4—42no—
607C4⋊C4—612no—
608C4⋊C4—1221no—
609C4⋊C4—1221no—
610C4⋊C4—1221no—
611C4⋊C4—1221no—
612C4⋊C4—1221no—
613C4⋊C4—4881no—
614C4⋊C4—2442no—
615C4⋊C4—2442no—
616C4⋊C4—2442no—
617C4⋊C4D4×D6112yes—
618C22⋊C4—22no—
619C22⋊C4—22no—
620C22⋊C4—42no—
621C22⋊C4—42no—
622C22⋊C4—42no—
623C22⋊C4—42no—
624C22⋊C4—81no—
625C22⋊C4—4881no—
626C22⋊C4—2442no—
627C22⋊C4—2442no—
628C42—21no—
629C42—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23#1451974912yes—
649C23#1451980312yes—
650C23#1451980712yes—
651C23C22×C22⋊D6111yescharacteristic
652Q8—2441no—
653Q8—2441no—
654Q8—2441no—
655Q8—2441no—
656D4—44no—
657D4—41no—
658D4—41no—
659D4—41no—
660D4—41no—
661D4—84no—
662D4—84no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—22no—
678C2×C4—21no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—84no—
692C2×C4—1222no—
693C2×C4—4884no—
694C2×C4—2441no—
695C2×C4—2441no—
696C2×C4—2441no—
697C2×C4—2441no—
698C2×C4—2441no—
699C2×C4—2441no—
700C2×C4—2441no—
701C2×C4—2441no—
702C2×C4—2441no—
703C2×C4—2441no—
704C2×C4—2441no—
705C2×C4#1451974912yes—
706C2×C4C2×D4×D6111yescharacteristic
707C2×C4C2×D4×D6111yescharacteristic
708C2×C4#41×D6111yescharacteristic
709C2×C4C2×#1175822411yescharacteristic
710C2×C4#1451982211yescharacteristic
711C2×C4#1451982411yescharacteristic
712C8—614no—
713C8—1222no—
714C8—2441no—
715C8—2441no—
716C22—22no—
717C22—22no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—81no—
730C22—81no—
731C22—81no—
732C22—81no—
733C22—81no—
734C22—81no—
735C22—81no—
736C22#1684000614yescomplemented
737C22C2×#1451974911yescharacteristic
738C22D4×C22⋊D6111yescharacteristic
739C22#1684041111yescharacteristic
740C22C2×#1451980311yescharacteristic
741C22C2×#1451980711yescharacteristic
742C22#1684056511yescharacteristic
743C22#1684057711yescharacteristic
744C4—22no—
745C4—41no—
746C4—41no—
747C4—41no—
748C4—42no—
749C4—81no—
750C4—81no—
751C4—4881no—
752C4—4881no—
753C4—4881no—
754C4—2442no—
755C4#121×D6111yescharacteristic
756C4#1684033911yescharacteristic
757C4#1684041811yescharacteristic
758C4#1684045511yescharacteristic
759C2—24no—
760C2—81no—
761C2—161no—
762C2#2144925611yescharacteristic
763C2C2×#1684000611yescharacteristic
764C2#2145548611yescharacteristic
765C2#2145729511yescharacteristic
766C2#2145738511yescharacteristic
767C2#2145825311yescharacteristic
768C2#2145830411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
Fitting, prime radicalC61×#2416C2
socleC23×C61C22×D4
hypercenter#2416D61
hypocenterC61#24787
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×#16839989C2semidirect
3. C2×#16839834C2semidirect
4. C22×#14519710C2semidirect
5. #21449270C2semidirect
6. #21447211C2semidirect
7. #21447207C2semidirect
8. #21447022C2semidirect
9. #21446998C2semidirect
10. #21446699C2semidirect
11. #21446554C2semidirect
12. #21446137C2semidirect
13. #21446126C2semidirect
14. #21445850C2semidirect
73. C22×#92418D4semidirect
97. #14519710D4semidirect
330. #92418#121semidirect
352. C22×C61#468semidirect
447. C61#24787semidirect
736. C22#16840006semidirect

Maximal subgroups

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

subgroupindex
C2×#168400062
C2×#168399892
C2×#168398342
C22×#145197102
#214492702
#214472112
#214472072
#214470222
#214469982
#214466992
#214465542
#214461372
#214461262
#214458502
C61×#24162
#2478761