Finite Group Databasebeta

← #25129288

Subgroups — #25129288

Order 11008.

1448 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583410C211yesmaximal, characteristic
2C2×#14583241C211yesmaximal, characteristic, complemented
3C2×#14583224C211yesmaximal, characteristic, complemented
4#19136978C211yesmaximal, characteristic, complemented
5#19135799C211yesmaximal, characteristic, complemented
6#19135792C211yesmaximal, characteristic, complemented
7#19135785C211yesmaximal, characteristic, complemented
8#19135778C211yesmaximal, characteristic, complemented
9#19134915C211yesmaximal, characteristic, complemented
10#19134905C211yesmaximal, characteristic, complemented
11#19134796C211yesmaximal, characteristic, complemented
12#19134796C211yesmaximal, characteristic, complemented
13#19134536C211yesmaximal, characteristic, complemented
14#19134536C211yesmaximal, characteristic, complemented
15C43×#1779C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17#14583410—24no—
18#14583410—24no—
19C2×#13063308—21no—
20C2×#13063304C2211yescharacteristic
21C2×#13063304C2211yescharacteristic
22C2×#13063299C2211yescharacteristic
23C2×#13063299C2211yescharacteristic
24C2×#13063294—21no—
25C2×C4×C22⋊D43—21no—
26C2×C4×C22⋊D43—21no—
27C2×#13063284C2211yescharacteristic
28C2×#13063284C2211yescharacteristic
29C2×#13063284C2211yescharacteristic
30#14583241—24no—
31#14583224—24no—
32C2×#13063259C2211yescharacteristic, complemented
33C2×#13063259C2211yescharacteristic, complemented
34C2×#13063257C2211yescharacteristic, complemented
35C2×#13063257C2211yescharacteristic, complemented
36C2×#13063250C2211yescharacteristic, complemented
37C2×#13063250C2211yescharacteristic, complemented
38C2×#13063250C2211yescharacteristic, complemented
39C2×#13063250C2211yescharacteristic, complemented
40C2×#13063247C2211yescharacteristic, complemented
41C2×#13063247C2211yescharacteristic, complemented
42C2×#13063247C2211yescharacteristic, complemented
43C2×#13063247C2211yescharacteristic, complemented
44#14582762—21no—
45#14582759C2211yescharacteristic
46#14582759C2211yescharacteristic
47#14582759C2211yescharacteristic
48#14582759C2211yescharacteristic
49#14582755—21no—
50C4×C22⋊Dic43—21no—
51C4×C22⋊Dic43—21no—
52#14582662C2211yescharacteristic, complemented
53#14582662C2211yescharacteristic, complemented
54#14582662C2211yescharacteristic, complemented
55#14582662C2211yescharacteristic, complemented
56C24×C4×C43C2211yescharacteristic
57C2×C22⋊C8×C43C2211yescharacteristic
58C2×C22⋊C8×C43C2211yescharacteristic
59C2×C22⋊C8×C43C2211yescharacteristic
60C2×C22⋊C8×C43C2211yescharacteristic
61C2×C22⋊C8×C43C2211yescharacteristic
62C2×C22⋊C8×C43C2211yescharacteristic
63C2×#10621898—22no—
64C2×#10621898—22no—
65C2×#10621898—22no—
66C2×#10621898—22no—
67C2×#10621898—41no—
68C2×#10621898—41no—
69C22×Dic86C2311yescharacteristic
70C22×D172C2311yescharacteristic
71C22×C22⋊D43—21no—
72C22×C22⋊D43—21no—
73C22×C22⋊D43—21no—
74C22×C4×D43—21no—
75#13063308—28no—
76#13063304—22no—
77#13063304—22no—
78#13063304—22no—
79#13063304D414yes—
80#13063299—22no—
81#13063299—22no—
82#13063299—22no—
83#13063299D414yes—
84#13063294—28no—
85C4×C22⋊D43—28no—
86C4×C22⋊D43—28no—
87#13063284—22no—
88#13063284—22no—
89#13063284—22no—
90#13063284—22no—
91#13063284—41no—
92#13063284—41no—
93C2×C4⋊Dic43C2311yescharacteristic
94C2×C4⋊Dic43C2311yescharacteristic
95C2×C4⋊Dic43C2311yescharacteristic
96C2×C4⋊Dic43C2311yescharacteristic
97C2×C4⋊Dic43C2311yescharacteristic
98C2×C4⋊Dic43C2311yescharacteristic
99C2×Dic43⋊C4—21no—
100C2×Dic43⋊C4—21no—
101C2×C22⋊Dic43—21no—
102C2×C22⋊Dic43—21no—
103C2×C22⋊Dic43—21no—
104C2×C22⋊Dic43—21no—
105C2×C22⋊Dic43—21no—
106C2×C22⋊Dic43—21no—
107C2×C22⋊Dic43—21no—
108C2×C22⋊Dic43—21no—
109C2×C22⋊Dic43—21no—
110C2×(C2×D43)⋊C4—21no—
111C2×(C2×D43)⋊C4—21no—
112C2×C4×Dic43—21no—
113C2×C4×Dic43—21no—
114C2×C4×Dic43—21no—
115#13063259—22no—
116#13063259—22no—
117#13063257—22no—
118#13063257—22no—
119#13063250—22no—
120#13063250—22no—
121#13063250—41no—
122#13063250—41no—
123#13063247—22no—
124#13063247—22no—
125#13063247—41no—
126#13063247—41no—
127C43⋊#95—21no—
128C43⋊#95—21no—
129C43⋊#95—21no—
130C43⋊#95—21no—
131C25×C43D411yescharacteristic
132C23×C4×C43—22no—
133C23×C4×C43—22no—
134C23×C4×C43—22no—
135C23×C4×C43—22no—
136C23×C4×C43—41no—
137C23×C4×C43—41no—
138C23×C4×C43D411yescharacteristic
139C23×C4×C43D411yescharacteristic
140C23×C4×C43D411yescharacteristic
141C23×C4×C43C2311yescharacteristic
142C23×C4×C43C2311yescharacteristic
143C23×C4×C43C2311yescharacteristic
144C22×C8×C43C2311yescharacteristic
145C22×C8×C43C2311yescharacteristic
146C22×C8×C43C2311yescharacteristic
147C22×C8×C43C2311yescharacteristic
148C22⋊C8×C43—22no—
149C22⋊C8×C43—22no—
150C22⋊C8×C43—22no—
151C22⋊C8×C43—22no—
152C22⋊C8×C43—41no—
153C22⋊C8×C43—41no—
154C24×C43—22no—
155C24×C43—22no—
156C24×C43—22no—
157C24×C43—41no—
158C24×C43—41no—
159C24×C43—41no—
160C24×C43—41no—
161C24×C43C2×D411yescharacteristic
162C24×C43C2×D411yescharacteristic
163C24×C43C2×D411yescharacteristic
164C23×D43—21no—
165C22×C4×C43—21no—
166C22×C4×C43—21no—
167C22×C4×C43—21no—
168C22×C4×C43—21no—
169C22×C4×C43—21no—
170C22×C4×C43—21no—
171C22×C4×C43—21no—
172C22×C4×C43—21no—
173C22×C4×C43—22no—
174C22×C4×C43—22no—
175C22×C4×C43—22no—
176C22×C4×C43—22no—
177C22×C4×C43—21no—
178C22×C4×C43—21no—
179C22×C4×C43—21no—
180C22×C4×C43—21no—
181C22×C4×C43—21no—
182C22×C4×C43—21no—
183C22×C4×C43—22no—
184C22×C4×C43—22no—
185C22×C4×C43—41no—
186C22×C4×C43—41no—
187C22×C4×C43—41no—
188C22×C4×C43—44no—
189C22×C4×C43—44no—
190C22×C4×C43—44no—
191C22×C4×C43—44no—
192C22×C4×C43C2×D412yes—
193C22×C4×C43C2×D412yes—
194C22×C4×C43C2×D411yescharacteristic
195C22×C4×C43C2×D411yescharacteristic
196C22×C4×C43C2×D411yescharacteristic
197C22×C4×C43#4112yes—
198C22×C4×C43#4112yes—
199C22×C4×C43C2411yescharacteristic
200C2×C22⋊D43—24no—
201C2×C22⋊D43—24no—
202C2×C22⋊D43—24no—
203C2×C22⋊D43—42no—
204C2×C22⋊D43—42no—
205C2×C22⋊D43—42no—
206C2×C22⋊D43—42no—
207C2×C22⋊D43—42no—
208C2×C22⋊D43—42no—
209C22×Dic43—21no—
210C22×Dic43—21no—
211C22×Dic43—21no—
212C22×Dic43—21no—
213C22×Dic43—21no—
214C22×Dic43—21no—
215C22×Dic43—21no—
216#10621898—44no—
217#10621898—44no—
218#10621898—44no—
219#10621898—44no—
220C2×D172—21no—
221C2×D172—21no—
222C2×D172—21no—
223C2×D172—21no—
224C2×D172—21no—
225C2×D172C2×D412yes—
226C2×C4×D43—24no—
227C2×C4×D43—42no—
228C2×C4×D43—42no—
229C2×Dic86—21no—
230C2×Dic86—21no—
231C2×Dic86—21no—
232C2×Dic86—21no—
233C2×Dic86—21no—
234C2×Dic86C2×D412yes—
235C2×C8×C43—21no—
236C2×C8×C43—21no—
237C2×C8×C43—21no—
238C2×C8×C43—21no—
239C2×C8×C43—21no—
240C2×C8×C43—21no—
241C2×C8×C43—21no—
242C2×C8×C43—21no—
243C2×C8×C43—21no—
244C2×C8×C43—21no—
245C2×C8×C43—21no—
246C2×C8×C43—21no—
247C22⋊Dic43—24no—
248C22⋊Dic43—24no—
249C22⋊Dic43—24no—
250C22⋊Dic43—42no—
251C22⋊Dic43—42no—
252C22⋊Dic43—42no—
253C22⋊Dic43—42no—
254C22⋊Dic43—42no—
255C22⋊Dic43—42no—
256(C2×D43)⋊C4—24no—
257(C2×D43)⋊C4—24no—
258C4⋊Dic43—21no—
259C4⋊Dic43—21no—
260C4⋊Dic43—21no—
261C4⋊Dic43—21no—
262C4⋊Dic43—21no—
263C4⋊Dic43—21no—
264C4⋊Dic43—21no—
265C4⋊Dic43—21no—
266C4⋊Dic43—21no—
267C4⋊Dic43—21no—
268C4⋊Dic43C2×D412yes—
269C4⋊Dic43C2×D412yes—
270Dic43⋊C4—24no—
271Dic43⋊C4—24no—
272C4×Dic43—24no—
273C4×Dic43—42no—
274C4×Dic43—42no—
275C23×C43—21no—
276C23×C43—21no—
277C23×C43—21no—
278C23×C43—21no—
279C23×C43—21no—
280C23×C43—21no—
281C23×C43—21no—
282C23×C43—21no—
283C23×C43—21no—
284C23×C43—21no—
285C23×C43—21no—
286C23×C43—21no—
287C23×C43—21no—
288C23×C43—21no—
289C23×C43—21no—
290C23×C43—21no—
291C23×C43—21no—
292C23×C43—21no—
293C23×C43—44no—
294C23×C43—44no—
295C23×C43—44no—
296C23×C43—44no—
297C23×C43—44no—
298C23×C43—44no—
299C23×C43—44no—
300C23×C43#12012yes—
301C23×C43#12312yes—
302C23×C43#13512yes—
303C23×C43C22×D411yescharacteristic
304C22×D43—22no—
305C22×D43—41no—
306C22×D43—41no—
307C22×D43—41no—
308C22×D43—41no—
309C22×D43—41no—
310C22×D43—41no—
311C2×C4×C43—21no—
312C2×C4×C43—21no—
313C2×C4×C43—21no—
314C2×C4×C43—21no—
315C2×C4×C43—22no—
316C2×C4×C43—22no—
317C2×C4×C43—22no—
318C2×C4×C43—22no—
319C2×C4×C43—22no—
320C2×C4×C43—22no—
321C2×C4×C43—22no—
322C2×C4×C43—22no—
323C2×C4×C43—21no—
324C2×C4×C43—21no—
325C2×C4×C43—21no—
326C2×C4×C43—44no—
327C2×C4×C43—44no—
328C2×C4×C43—44no—
329C2×C4×C43—41no—
330C2×C4×C43—41no—
331C2×C4×C43—41no—
332C2×C4×C43—41no—
333C2×C4×C43#12012yes—
334C2×C4×C43#12312yes—
335C2×C4×C43C22×D411yescharacteristic
336C2×C4×C43C22×D411yescharacteristic
337C2×C4×C43C2×#4111yescharacteristic
338C2×C4×C43C2×#4111yescharacteristic
339C2×C4×C43H(5,𝔽2)11yescharacteristic
340C2×C4×C43H(5,𝔽2)11yescharacteristic
341C22⋊D43—48no—
342C22⋊D43—48no—
343C22⋊D43—48no—
344C2×Dic43—22no—
345C2×Dic43—22no—
346C2×Dic43—22no—
347C2×Dic43—41no—
348C2×Dic43—41no—
349C2×Dic43—41no—
350C2×Dic43—41no—
351C2×Dic43—41no—
352C2×Dic43—41no—
353C2×Dic43—41no—
354C2×Dic43—41no—
355C2×Dic43—41no—
356C2×Dic43—41no—
357C2×Dic43—41no—
358C2×Dic43—41no—
359C2×Dic43—41no—
360C2×Dic43—41no—
361C2×Dic43—41no—
362C2×Dic43—41no—
363C2×Dic43—41no—
364C2×Dic43—41no—
365D172—22no—
366D172—22no—
367D172—41no—
368D172—41no—
369C4×D43—48no—
370Dic86—22no—
371Dic86—22no—
372Dic86—41no—
373Dic86—41no—
374C8×C43—41no—
375C8×C43—41no—
376C8×C43—41no—
377C8×C43—41no—
378#24008—431nomaximal, Sylow
379C22×C43—22no—
380C22×C43—22no—
381C22×C43—22no—
382C22×C43—22no—
383C22×C43—22no—
384C22×C43—22no—
385C22×C43—22no—
386C22×C43—22no—
387C22×C43—22no—
388C22×C43—416no—
389C22×C43—41no—
390C22×C43—41no—
391C22×C43—41no—
392C22×C43—41no—
393C22×C43—41no—
394C22×C43—41no—
395C22×C43—41no—
396C22×C43—41no—
397C22×C43—41no—
398C22×C43—41no—
399C22×C43—41no—
400C22×C43—41no—
401C22×C43C2×#12011yescharacteristic
402C22×C43C2×#12311yescharacteristic
403C22×C43#53411yescharacteristic
404C22×C43C2×#13511yescharacteristic
405C22×C43#57511yescharacteristic
406C22×C43#57511yescharacteristic
407C22×C43#57511yescharacteristic
408C2×D43—42no—
409C2×D43—42no—
410C2×D43—42no—
411C2×D43—81no—
412C2×D43—81no—
413C2×D43—81no—
414C2×D43—81no—
415C4×C43—22no—
416C4×C43—22no—
417C4×C43—41no—
418C4×C43#54611yescharacteristic
419C4×C43#54611yescharacteristic
420C4×C43#54611yescharacteristic
421C4×C43#54611yescharacteristic
422Dic43—42no—
423Dic43—42no—
424Dic43—42no—
425Dic43—81no—
426Dic43—81no—
427Dic43—81no—
428Dic43—81no—
429C2×#525—431no—
430C2×#485—431no—
431C2×#482—431no—
432#2280—431no—
433#2036—431no—
434#2035—431no—
435#2034—431no—
436#2033—431no—
437#1875—431no—
438#1873—431no—
439#1854—431no—
440#1854—431no—
441#1788—431no—
442#1788—431no—
443#1779D4311yescharacteristic, complemented
444C2×C43—42no—
445C2×C43—42no—
446C2×C43—42no—
447C2×C43#240511yescharacteristic
448C2×C43#300211yescharacteristic
449C2×C43#300511yescharacteristic
450C2×C43#309111yescharacteristic
451C2×C43#309311yescharacteristic
452C2×C43#319111yescharacteristic
453C2×C43#319711yescharacteristic
454D43—82no—
455C22×#41—431no—
456C24×C4C2×D4311yescharacteristic
457#525—864no—
458#525—864no—
459C2×#123—861no—
460C2×C22⋊Q8—431no—
461C2×C22⋊Q8—431no—
462C2×#121—431no—
463C2×#121—431no—
464C2×#120—861no—
465C2×C4×D4—861no—
466C2×C4×D4—861no—
467C2×#117—431no—
468C2×#117—431no—
469C2×#117—431no—
470#485—864no—
471#482—864no—
472C2×#107—431no—
473C2×#107—431no—
474C2×#106—431no—
475C2×#106—431no—
476C2×#103—431no—
477C2×#103—431no—
478C2×#103—431no—
479C2×#103—431no—
480C2×#102—431no—
481C2×#102—431no—
482C2×#102—431no—
483C2×#102—431no—
484C2×C22⋊C8C2×D4311yescharacteristic
485C2×C22⋊C8C2×D4311yescharacteristic
486C2×C22⋊C8C2×D4311yescharacteristic
487C2×C22⋊C8C2×D4311yescharacteristic
488C2×C22⋊C8C2×D4311yescharacteristic
489C2×C22⋊C8C2×D4311yescharacteristic
490#381—861no—
491#380—431no—
492#380—431no—
493#380—431no—
494#380—431no—
495#379—861no—
496C4×C22⋊C4—861no—
497C4×C22⋊C4—861no—
498#340—431no—
499#340—431no—
500#340—431no—
501#340—431no—
502C43#2400811yescharacteristic, complemented, Sylow
503C25D17211yescharacteristic
504C2×#41—862no—
505C2×#41—862no—
506C2×#41—862no—
507C2×#41—862no—
508C2×#41—1721no—
509C2×#41—1721no—
510C22×Q8—431no—
511C22×D4—431no—
512C22×D4—861no—
513C22×D4—861no—
514C22×D4—861no—
515C23×C4—22no—
516C23×C4—22no—
517C23×C4—22no—
518C23×C4—22no—
519C23×C4—41no—
520C23×C4—41no—
521C23×C4—861no—
522C23×C4D17211yescharacteristic
523C23×C4D17211yescharacteristic
524C23×C4D17211yescharacteristic
525C23×C4C22×D4311yescharacteristic
526C23×C4C22×D4311yescharacteristic
527C23×C4C22×D4311yescharacteristic
528C22×C8C22×D4311yescharacteristic
529C22×C8C22×D4311yescharacteristic
530C22×C8C22×D4311yescharacteristic
531C22×C8C22×D4311yescharacteristic
532#123—868no—
533C22⋊Q8—434no—
534C22⋊Q8—862no—
535C22⋊Q8—862no—
536C22⋊Q8—862no—
537#121—434no—
538#121—862no—
539#121—862no—
540#121—862no—
541#120—868no—
542C4×D4—868no—
543C4×D4—868no—
544#117—862no—
545#117—862no—
546#117—862no—
547#117—862no—
548#117—1721no—
549#117—1721no—
550C2×C4⋊C4—431no—
551C2×C4⋊C4—431no—
552C2×C4⋊C4—431no—
553C2×C4⋊C4—431no—
554C2×C4⋊C4—431no—
555C2×C4⋊C4—431no—
556C2×C4⋊C4—861no—
557C2×C4⋊C4—861no—
558C2×C22⋊C4—861no—
559C2×C22⋊C4—861no—
560C2×C22⋊C4—861no—
561C2×C22⋊C4—861no—
562C2×C22⋊C4—861no—
563C2×C22⋊C4—861no—
564C2×C22⋊C4—861no—
565C2×C22⋊C4—861no—
566C2×C22⋊C4—861no—
567C2×C22⋊C4—861no—
568C2×C22⋊C4—861no—
569C2×C42—861no—
570C2×C42—861no—
571C2×C42—861no—
572#107—862no—
573#107—862no—
574#106—862no—
575#106—862no—
576#103—862no—
577#103—862no—
578#103—1721no—
579#103—1721no—
580#102—862no—
581#102—862no—
582#102—1721no—
583#102—1721no—
584C22⋊C8—22no—
585C22⋊C8—22no—
586C22⋊C8—22no—
587C22⋊C8—22no—
588C22⋊C8—41no—
589C22⋊C8—41no—
590#95—861no—
591#95—861no—
592#95—861no—
593#95—861no—
594C24—22no—
595C24—22no—
596C24—22no—
597C24—41no—
598C24—41no—
599C24—41no—
600C24—41no—
601C24—861no—
602C24C2×D17211yescharacteristic
603C24C2×D17211yescharacteristic
604C24C2×D17211yescharacteristic
605#41—1724no—
606#41—1724no—
607#41—1724no—
608#41—1724no—
609C2×Q8—432no—
610C2×Q8—861no—
611C2×Q8—861no—
612C2×Q8—861no—
613C2×Q8—861no—
614C2×Q8—861no—
615C2×D4—432no—
616C2×D4—864no—
617C2×D4—864no—
618C2×D4—864no—
619C2×D4—861no—
620C2×D4—861no—
621C2×D4—861no—
622C2×D4—861no—
623C2×D4—861no—
624C2×D4—1722no—
625C2×D4—1722no—
626C2×D4—1722no—
627C2×D4—1722no—
628C2×D4—1722no—
629C2×D4—1722no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—41no—
651C22×C4—41no—
652C22×C4—41no—
653C22×C4—44no—
654C22×C4—44no—
655C22×C4—44no—
656C22×C4—44no—
657C22×C4—864no—
658C22×C4—861no—
659C22×C4—861no—
660C22×C4—861no—
661C22×C4—861no—
662C22×C4—861no—
663C22×C4—861no—
664C22×C4—861no—
665C22×C4—1722no—
666C22×C4—1722no—
667C22×C4C2×D17211yescharacteristic
668C22×C4C2×D17211yescharacteristic
669C22×C4C2×D17211yescharacteristic
670C22×C4D4×D4312yes—
671C22×C4D4×D4312yes—
672C22×C4#1062190012yes—
673C22×C4#1062190012yes—
674C22×C4C23×D4311yescharacteristic
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C4⋊C4—432no—
688C4⋊C4—432no—
689C4⋊C4—864no—
690C4⋊C4—864no—
691C4⋊C4—861no—
692C4⋊C4—861no—
693C4⋊C4—861no—
694C4⋊C4—861no—
695C4⋊C4—861no—
696C4⋊C4—861no—
697C4⋊C4—861no—
698C4⋊C4—861no—
699C4⋊C4—861no—
700C4⋊C4—861no—
701C22⋊C4—864no—
702C22⋊C4—864no—
703C22⋊C4—864no—
704C22⋊C4—864no—
705C22⋊C4—864no—
706C22⋊C4—1722no—
707C22⋊C4—1722no—
708C22⋊C4—1722no—
709C22⋊C4—1722no—
710C22⋊C4—1722no—
711C22⋊C4—1722no—
712C42—864no—
713C42—1722no—
714C42—1722no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—44no—
734C23—44no—
735C23—44no—
736C23—44no—
737C23—44no—
738C23—44no—
739C23—44no—
740C23—862no—
741C23—1721no—
742C23—1721no—
743C23—1721no—
744C23—1721no—
745C23—1721no—
746C23—1721no—
747C23#1306329512yes—
748C23#1306330912yes—
749C23#1306334712yes—
750C23C22×D17211yescharacteristic
751Q8—862no—
752Q8—862no—
753Q8—1721no—
754Q8—1721no—
755D4—862no—
756D4—862no—
757D4—1728no—
758D4—1728no—
759D4—1728no—
760D4—1721no—
761D4—1721no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—44no—
778C2×C4—44no—
779C2×C4—44no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—862no—
785C2×C4—862no—
786C2×C4—862no—
787C2×C4—1728no—
788C2×C4—1721no—
789C2×C4—1721no—
790C2×C4—1721no—
791C2×C4—1721no—
792C2×C4—1721no—
793C2×C4—1721no—
794C2×C4—1721no—
795C2×C4—1721no—
796C2×C4—1721no—
797C2×C4—1721no—
798C2×C4—1721no—
799C2×C4—1721no—
800C2×C4—1721no—
801C2×C4—1721no—
802C2×C4—1721no—
803C2×C4—1721no—
804C2×C4—1721no—
805C2×C4—1721no—
806C2×C4#1306329512yes—
807C2×C4#1306330912yes—
808C2×C4C2×D4×D4311yescharacteristic
809C2×C4C2×D4×D4311yescharacteristic
810C2×C4C2×#1062190011yescharacteristic
811C2×C4C2×#1062190011yescharacteristic
812C2×C4#1306337011yescharacteristic
813C2×C4#1306337011yescharacteristic
814C8—41no—
815C8—41no—
816C8—41no—
817C8—41no—
818C22—22no—
819C22—22no—
820C22—22no—
821C22—22no—
822C22—22no—
823C22—22no—
824C22—22no—
825C22—22no—
826C22—22no—
827C22—416no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—41no—
836C22—41no—
837C22—41no—
838C22—41no—
839C22—41no—
840C22—3441no—
841C22—3441no—
842C22—3441no—
843C22—3441no—
844C22—1722no—
845C22—1722no—
846C22—1722no—
847C22C2×#1306329511yescharacteristic
848C22C2×#1306330911yescharacteristic
849C22#1458346111yescharacteristic
850C22C2×#1306334711yescharacteristic
851C22#1458369911yescharacteristic
852C22#1458369911yescharacteristic
853C22#1458369911yescharacteristic
854C4—22no—
855C4—22no—
856C4—41no—
857C4—3441no—
858C4—3441no—
859C4—3441no—
860C4—3441no—
861C4—1722no—
862C4—1722no—
863C4—1722no—
864C4#1458353611yescharacteristic
865C4#1458353611yescharacteristic
866C4#1458353611yescharacteristic
867C4#1458353611yescharacteristic
868C2—42no—
869C2—42no—
870C2—42no—
871C2—3442no—
872C2#1913792311yescharacteristic
873C2#1914381711yescharacteristic
874C2#1914384011yescharacteristic
875C2#1914451011yescharacteristic
876C2#1914452811yescharacteristic
877C2#1914538811yescharacteristic
878C2#1914543711yescharacteristic
subgroupG/H
centerC23C22×D172
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1779C2
socleC23×C43C22×D4
prime radicalC2×#14583410C2
hypercenter#1779D43
hypocenterC43#24008
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C24×C4 ◁ #1779

Complements

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

NH ≅ G/Ntype
2. C2×#14583241C2semidirect
3. C2×#14583224C2semidirect
4. #19136978C2semidirect
5. #19135799C2semidirect
6. #19135792C2semidirect
7. #19135785C2semidirect
8. #19135778C2semidirect
9. #19134915C2semidirect
10. #19134905C2semidirect
11. #19134796C2semidirect
12. #19134796C2semidirect
13. #19134536C2semidirect
14. #19134536C2semidirect
15. C43×#1779C2semidirect
32. C2×#13063259C22semidirect
33. C2×#13063259C22semidirect
34. C2×#13063257C22semidirect
35. C2×#13063257C22semidirect
36. C2×#13063250C22semidirect
37. C2×#13063250C22semidirect
38. C2×#13063250C22semidirect
39. C2×#13063250C22semidirect
40. C2×#13063247C22semidirect
41. C2×#13063247C22semidirect
42. C2×#13063247C22semidirect
43. C2×#13063247C22semidirect
52. #14582662C22semidirect
53. #14582662C22semidirect
54. #14582662C22semidirect
55. #14582662C22semidirect
443. #1779D43semidirect
502. C43#24008semidirect

Maximal subgroups

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

subgroupindex
C2×#145834102
C2×#145832412
C2×#145832242
#191369782
#191357992
#191357922
#191357852
#191357782
#191349152
#191349052
#191347962
#191345362
C43×#17792
#2400843