Finite Group Databasebeta

← #25129283

Subgroups — #25129283

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×#14583406C211yesmaximal, characteristic
2C2×#14583238C211yesmaximal, characteristic, complemented
3C2×#14583221C211yesmaximal, characteristic, complemented
4#19136977C211yesmaximal, characteristic, complemented
5#19135797C211yesmaximal, characteristic, complemented
6#19135789C211yesmaximal, characteristic, complemented
7#19135783C211yesmaximal, characteristic, complemented
8#19135775C211yesmaximal, characteristic, complemented
9#19134914C211yesmaximal, characteristic, complemented
10#19134904C211yesmaximal, characteristic, complemented
11#19134796C211yesmaximal, characteristic, complemented
12#19134792C211yesmaximal, characteristic, complemented
13#19134535C211yesmaximal, characteristic, complemented
14#19134504C211yesmaximal, characteristic, complemented
15C43×#1788C211yesmaximal, characteristic, complemented
16C23×C4×D43C2211yescharacteristic
17#14583406—24no—
18#14583406—24no—
19C2×#13063306—21no—
20C2×#13063301C2211yescharacteristic
21C2×#13063301C2211yescharacteristic
22C2×#13063296C2211yescharacteristic
23C2×#13063296C2211yescharacteristic
24C2×#13063293—21no—
25C2×C4×C22⋊D43—21no—
26C2×C4×C22⋊D43—21no—
27C2×#13063284C2211yescharacteristic
28C2×#13063283C2211yescharacteristic
29C2×#13063283C2211yescharacteristic
30#14583238—24no—
31#14583221—24no—
32C2×#13063259C2211yescharacteristic, complemented
33C2×#13063258C2211yescharacteristic, complemented
34C2×#13063257C2211yescharacteristic, complemented
35C2×#13063256C2211yescharacteristic, complemented
36C2×#13063249C2211yescharacteristic, complemented
37C2×#13063249C2211yescharacteristic, complemented
38C2×#13063246C2211yescharacteristic, complemented
39C2×#13063246C2211yescharacteristic, complemented
40C2×C22⋊(C43⋊C8)C2211yescharacteristic
41C2×(C2×D43)⋊C8C2211yescharacteristic
42C2×(C2×D43)⋊C8C2211yescharacteristic
43C2×(C2×D43)⋊C8C2211yescharacteristic
44C2×(C2×D43)⋊C8C2211yescharacteristic
45#14582761—21no—
46#14582759C2211yescharacteristic
47#14582756C2211yescharacteristic
48#14582756C2211yescharacteristic
49#14582754—21no—
50C22⋊C4×Dic43—21no—
51#14582746—21no—
52#14582662C2211yescharacteristic, complemented
53#14582662C2211yescharacteristic, complemented
54#14582661C2211yescharacteristic, complemented
55#14582661C2211yescharacteristic, complemented
56C22×#41×C43C2211yescharacteristic
57C2×#103×C43C2211yescharacteristic, complemented
58C2×#103×C43C2211yescharacteristic, complemented
59C2×#102×C43C2211yescharacteristic, complemented
60C2×#102×C43C2211yescharacteristic, complemented
61C2×C22⋊C8×C43C2211yescharacteristic
62C43×#380C2211yescharacteristic
63C24×D43D411yescharacteristic
64C22×C22⋊D43—21no—
65C22×C22⋊D43—21no—
66C23×Dic43D411yescharacteristic
67C22×C4×D43—22no—
68C22×C4×D43—22no—
69C22×C4×D43—22no—
70C22×C4×D43—22no—
71C22×C4×D43—41no—
72C22×C4×D43—41no—
73C22×C4×D43D411yescharacteristic
74C22×C4×D43D411yescharacteristic
75C22×C4×D43C2311yescharacteristic
76C22×C4×D43C2311yescharacteristic
77C22×C43⋊C8C2311yescharacteristic
78C22×C43⋊C8C2311yescharacteristic
79#13063306—28no—
80#13063301—22no—
81#13063301—22no—
82#13063301—22no—
83#13063301D414yes—
84#13063296—22no—
85#13063296—22no—
86#13063296—22no—
87#13063296D414yes—
88#13063293—28no—
89C4×C22⋊D43—28no—
90C4×C22⋊D43—28no—
91#13063284—22no—
92#13063284—22no—
93#13063283—22no—
94#13063283—22no—
95#13063283—41no—
96#13063283—41no—
97C2×C4⋊Dic43C2311yescharacteristic
98C2×C4⋊Dic43C2311yescharacteristic
99C2×C4⋊Dic43C2311yescharacteristic
100C2×C4⋊Dic43C2311yescharacteristic
101C2×Dic43⋊C4—21no—
102C2×Dic43⋊C4—21no—
103C2×C22⋊Dic43—21no—
104C2×C22⋊Dic43—21no—
105C2×C22⋊Dic43—21no—
106C2×C22⋊Dic43—21no—
107C2×(C2×D43)⋊C4—21no—
108C2×(C2×D43)⋊C4—21no—
109C2×(C2×D43)⋊C4—21no—
110C2×(C2×D43)⋊C4—21no—
111C2×(C2×D43)⋊C4—21no—
112C2×(C2×D43)⋊C4—21no—
113C2×C4×Dic43—21no—
114C2×C4×Dic43—21no—
115C2×C4×Dic43—21no—
116#13063259—22no—
117#13063258—22no—
118#13063257—22no—
119#13063256—22no—
120#13063249—22no—
121#13063249—41no—
122#13063246—22no—
123#13063246—41no—
124C22⋊(C43⋊C8)—22no—
125(C2×D43)⋊C8—22no—
126(C2×D43)⋊C8—22no—
127(C2×D43)⋊C8—41no—
128(C2×D43)⋊C8—41no—
129C43⋊#95—21no—
130C43⋊#95—21no—
131C43⋊#95—21no—
132C2×#41×C43—22no—
133C2×#41×C43—22no—
134C2×#41×C43—22no—
135C2×#41×C43—22no—
136C2×#41×C43—41no—
137C2×#41×C43—41no—
138C22×Q8×C43C2311yescharacteristic
139C22×D4×C43—21no—
140C22×D4×C43C2311yescharacteristic
141C23×C4×C43—21no—
142C23×C4×C43C2311yescharacteristic
143C22×C8×C43C2311yescharacteristic
144C22×C8×C43C2311yescharacteristic
145C2×C4⋊C4×C43C2311yescharacteristic
146C2×C4⋊C4×C43C2311yescharacteristic
147C2×C22⋊C4×C43—21no—
148#103×C43—22no—
149#103×C43—41no—
150#102×C43—22no—
151#102×C43—41no—
152C22⋊C8×C43—22no—
153#95×C43—21no—
154C24×C43—21no—
155C24×C43C2×D411yescharacteristic
156C23×D43—22no—
157C23×D43—22no—
158C23×D43—22no—
159C23×D43—41no—
160C23×D43—41no—
161C23×D43—41no—
162C23×D43—41no—
163C23×D43C2×D411yescharacteristic
164C23×D43C2×D411yescharacteristic
165#41×C43—44no—
166#41×C43—44no—
167#41×C43—44no—
168#41×C43—44no—
169C2×Q8×C43—21no—
170C2×Q8×C43—21no—
171C2×Q8×C43—21no—
172C2×Q8×C43—21no—
173C2×Q8×C43—21no—
174C2×Q8×C43C2×D412yes—
175C2×D4×C43—24no—
176C2×D4×C43—21no—
177C2×D4×C43—21no—
178C2×D4×C43—21no—
179C2×D4×C43—21no—
180C2×D4×C43—21no—
181C2×D4×C43—42no—
182C2×D4×C43—42no—
183C2×D4×C43C2×D412yes—
184C22×C4×C43—21no—
185C22×C4×C43—21no—
186C22×C4×C43—21no—
187C22×C4×C43—21no—
188C22×C4×C43—24no—
189C22×C4×C43—21no—
190C22×C4×C43—21no—
191C22×C4×C43—21no—
192C22×C4×C43—42no—
193C22×C4×C43—42no—
194C22×C4×C43C2×D411yescharacteristic
195C22×C4×C43#4112yes—
196C22×C4×C43#4112yes—
197C22×C4×C43C2411yescharacteristic
198C2×C22⋊D43—24no—
199C2×C22⋊D43—24no—
200C2×C22⋊D43—42no—
201C2×C22⋊D43—42no—
202C2×C22⋊D43—42no—
203C2×C22⋊D43—42no—
204C22×Dic43—22no—
205C22×Dic43—22no—
206C22×Dic43—21no—
207C22×Dic43—21no—
208C22×Dic43—21no—
209C22×Dic43—21no—
210C22×Dic43—41no—
211C22×Dic43C2×D411yescharacteristic
212C22×Dic43C2×D411yescharacteristic
213C2×C4×D43—21no—
214C2×C4×D43—21no—
215C2×C4×D43—21no—
216C2×C4×D43—21no—
217C2×C4×D43—22no—
218C2×C4×D43—22no—
219C2×C4×D43—21no—
220C2×C4×D43—21no—
221C2×C4×D43—21no—
222C2×C4×D43—21no—
223C2×C4×D43—21no—
224C2×C4×D43—21no—
225C2×C4×D43—22no—
226C2×C4×D43—22no—
227C2×C4×D43—41no—
228C2×C4×D43—41no—
229C2×C4×D43—44no—
230C2×C4×D43—44no—
231C2×C4×D43—44no—
232C2×C4×D43—44no—
233C2×C4×D43C2×D412yes—
234C2×C4×D43C2×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—
241C4⋊C4×C43—21no—
242C4⋊C4×C43—21no—
243C4⋊C4×C43—21no—
244C4⋊C4×C43—21no—
245C22⋊C4×C43—42no—
246C22⋊Dic43—24no—
247C22⋊Dic43—24no—
248C22⋊Dic43—24no—
249C22⋊Dic43—42no—
250(C2×D43)⋊C4—24no—
251(C2×D43)⋊C4—24no—
252(C2×D43)⋊C4—42no—
253(C2×D43)⋊C4—42no—
254(C2×D43)⋊C4—42no—
255(C2×D43)⋊C4—42no—
256C4⋊Dic43—21no—
257C4⋊Dic43—21no—
258C4⋊Dic43—21no—
259C4⋊Dic43—21no—
260C4⋊Dic43—21no—
261C4⋊Dic43—21no—
262C4⋊Dic43C2×D412yes—
263C4⋊Dic43C2×D412yes—
264Dic43⋊C4—24no—
265Dic43⋊C4—24no—
266C4×Dic43—24no—
267C4×Dic43—42no—
268C4×Dic43—42no—
269C2×C43⋊C8—21no—
270C2×C43⋊C8—21no—
271C2×C43⋊C8—21no—
272C2×C43⋊C8—21no—
273C2×C43⋊C8—21no—
274C2×C43⋊C8—21no—
275C23×C43—21no—
276C23×C43—21no—
277C23×C43—21no—
278C23×C43—21no—
279C23×C43—21no—
280C23×C43—21no—
281C23×C43—22no—
282C23×C43—41no—
283C23×C43—41no—
284C23×C43—41no—
285C23×C43—41no—
286C23×C43—41no—
287C23×C43—41no—
288C23×C43#12312yes—
289C23×C43C22×D411yescharacteristic
290C22×D43—21no—
291C22×D43—21no—
292C22×D43—21no—
293C22×D43—21no—
294C22×D43—21no—
295C22×D43—21no—
296C22×D43—21no—
297C22×D43—21no—
298C22×D43—21no—
299C22×D43—21no—
300C22×D43—21no—
301C22×D43—21no—
302C22×D43—44no—
303C22×D43—44no—
304C22×D43—44no—
305C22×D43—44no—
306C22×D43—44no—
307C22×D43—44no—
308C22×D43—44no—
309C22×D43#12012yes—
310C22×D43#13512yes—
311Q8×C43—22no—
312Q8×C43—22no—
313Q8×C43—41no—
314Q8×C43—41no—
315D4×C43—22no—
316D4×C43—22no—
317D4×C43—48no—
318D4×C43—41no—
319D4×C43—41no—
320C2×C4×C43—21no—
321C2×C4×C43—21no—
322C2×C4×C43—22no—
323C2×C4×C43—22no—
324C2×C4×C43—22no—
325C2×C4×C43—22no—
326C2×C4×C43—22no—
327C2×C4×C43—48no—
328C2×C4×C43—41no—
329C2×C4×C43—41no—
330C2×C4×C43—41no—
331C2×C4×C43—41no—
332C2×C4×C43—41no—
333C2×C4×C43—41no—
334C2×C4×C43—41no—
335C2×C4×C43—41no—
336C2×C4×C43#12312yes—
337C2×C4×C43C22×D411yescharacteristic
338C2×C4×C43C22×D411yescharacteristic
339C2×C4×C43C2×#4111yescharacteristic
340C2×C4×C43C2×#4111yescharacteristic
341C2×C4×C43H(5,𝔽2)11yescharacteristic
342C2×C4×C43H(5,𝔽2)11yescharacteristic
343C22⋊D43—48no—
344C22⋊D43—48no—
345C2×Dic43—21no—
346C2×Dic43—21no—
347C2×Dic43—22no—
348C2×Dic43—22no—
349C2×Dic43—21no—
350C2×Dic43—21no—
351C2×Dic43—21no—
352C2×Dic43—44no—
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#12012yes—
364C4×D43—22no—
365C4×D43—22no—
366C4×D43—22no—
367C4×D43—22no—
368C4×D43—44no—
369C4×D43—44no—
370C4×D43—41no—
371C4×D43—41no—
372C4×D43—41no—
373C4×D43—41no—
374C8×C43—41no—
375C8×C43—41no—
376C43⋊C8—41no—
377C43⋊C8—41no—
378#24008—431nomaximal, Sylow
379C22×C43—22no—
380C22×C43—22no—
381C22×C43—22no—
382C22×C43—41no—
383C22×C43—41no—
384C22×C43—41no—
385C22×C43—41no—
386C22×C43—42no—
387C22×C43—42no—
388C22×C43—42no—
389C22×C43—81no—
390C22×C43—81no—
391C22×C43—81no—
392C22×C43—81no—
393C22×C43C2×#12011yescharacteristic
394C22×C43C2×#12311yescharacteristic
395C22×C43#53411yescharacteristic
396C22×C43C2×#13511yescharacteristic
397C22×C43#57511yescharacteristic
398C22×C43#57511yescharacteristic
399C22×C43#57511yescharacteristic
400C2×D43—22no—
401C2×D43—22no—
402C2×D43—22no—
403C2×D43—22no—
404C2×D43—22no—
405C2×D43—22no—
406C2×D43—416no—
407C2×D43—41no—
408C2×D43—41no—
409C2×D43—41no—
410C2×D43—41no—
411C2×D43—41no—
412C2×D43—41no—
413C2×D43—41no—
414C2×D43—41no—
415C4×C43—22no—
416C4×C43—42no—
417C4×C43—81no—
418C4×C43—81no—
419C4×C43#54611yescharacteristic
420C4×C43#54611yescharacteristic
421C4×C43#54611yescharacteristic
422C4×C43#54611yescharacteristic
423Dic43—22no—
424Dic43—41no—
425Dic43—42no—
426Dic43—42no—
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#1788D4311yescharacteristic, complemented
443#1779—431no—
444C2×C43—42no—
445C2×C43—82no—
446C2×C43#240511yescharacteristic
447C2×C43#300211yescharacteristic
448C2×C43#300511yescharacteristic
449C2×C43#309111yescharacteristic
450C2×C43#309311yescharacteristic
451C2×C43#319111yescharacteristic
452C2×C43#319711yescharacteristic
453D43—42no—
454D43—42no—
455C22×#41C2×D4311yescharacteristic
456C24×C4—431no—
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×#103C2×D4311yescharacteristic, complemented
479C2×#103C2×D4311yescharacteristic, complemented
480C2×#102—431no—
481C2×#102—431no—
482C2×#102C2×D4311yescharacteristic, complemented
483C2×#102C2×D4311yescharacteristic, complemented
484C2×C22⋊C8—431no—
485C2×C22⋊C8—431no—
486C2×C22⋊C8—431no—
487C2×C22⋊C8—431no—
488C2×C22⋊C8—431no—
489C2×C22⋊C8C2×D4311yescharacteristic
490#381—861no—
491#380—431no—
492#380—431no—
493#380—431no—
494#380C2×D4311yescharacteristic
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
503C25—431no—
504C2×#41—22no—
505C2×#41—22no—
506C2×#41—22no—
507C2×#41—22no—
508C2×#41—41no—
509C2×#41—41no—
510C22×Q8C22×D4311yescharacteristic
511C22×D4—21no—
512C22×D4—861no—
513C22×D4—861no—
514C22×D4C22×D4311yescharacteristic
515C23×C4—21no—
516C23×C4—431no—
517C23×C4—431no—
518C23×C4—431no—
519C23×C4—431no—
520C23×C4—431no—
521C23×C4—862no—
522C23×C4—862no—
523C23×C4—862no—
524C23×C4—862no—
525C23×C4—1721no—
526C23×C4—1721no—
527C23×C4C22×D4311yescharacteristic
528C22×C8—431no—
529C22×C8—431no—
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—861no—
555C2×C4⋊C4—861no—
556C2×C4⋊C4C22×D4311yescharacteristic
557C2×C4⋊C4C22×D4311yescharacteristic
558C2×C22⋊C4—21no—
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—22no—
577#103—41no—
578#103—862no—
579#103—1721no—
580#102—22no—
581#102—41no—
582#102—862no—
583#102—1721no—
584C22⋊C8—22no—
585C22⋊C8—862no—
586C22⋊C8—862no—
587C22⋊C8—862no—
588C22⋊C8—1721no—
589C22⋊C8—1721no—
590#95—21no—
591#95—861no—
592#95—861no—
593#95—861no—
594C24—21no—
595C24—431no—
596C24—431no—
597C24—862no—
598C24—862no—
599C24—862no—
600C24—1721no—
601C24—1721no—
602C24—1721no—
603C24—1721no—
604C24D4×D4311yescharacteristic
605#41—44no—
606#41—44no—
607#41—44no—
608#41—44no—
609C2×Q8—21no—
610C2×Q8—21no—
611C2×Q8—21no—
612C2×Q8—21no—
613C2×Q8—21no—
614C2×Q8D4×D4312yes—
615C2×D4—24no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—42no—
622C2×D4—42no—
623C2×D4—864no—
624C2×D4—864no—
625C2×D4—1722no—
626C2×D4—1722no—
627C2×D4—1722no—
628C2×D4—1722no—
629C2×D4D4×D4312yes—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—24no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—42no—
639C22×C4—42no—
640C22×C4—431no—
641C22×C4—432no—
642C22×C4—432no—
643C22×C4—431no—
644C22×C4—862no—
645C22×C4—862no—
646C22×C4—862no—
647C22×C4—861no—
648C22×C4—861no—
649C22×C4—861no—
650C22×C4—861no—
651C22×C4—862no—
652C22×C4—861no—
653C22×C4—861no—
654C22×C4—862no—
655C22×C4—862no—
656C22×C4—861no—
657C22×C4—861no—
658C22×C4—861no—
659C22×C4—861no—
660C22×C4—861no—
661C22×C4—861no—
662C22×C4—861no—
663C22×C4—861no—
664C22×C4—1721no—
665C22×C4—1721no—
666C22×C4—1724no—
667C22×C4—1724no—
668C22×C4—1724no—
669C22×C4—1724no—
670C22×C4—1721no—
671C22×C4#1062189812yes—
672C22×C4D4×D4311yescharacteristic
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—861no—
682C2×C8—861no—
683C2×C8—861no—
684C2×C8—861no—
685C2×C8—861no—
686C2×C8—861no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—432no—
692C4⋊C4—432no—
693C4⋊C4—864no—
694C4⋊C4—864no—
695C4⋊C4—861no—
696C4⋊C4—861no—
697C4⋊C4—861no—
698C4⋊C4—861no—
699C4⋊C4—861no—
700C4⋊C4—861no—
701C22⋊C4—42no—
702C22⋊C4—864no—
703C22⋊C4—864no—
704C22⋊C4—864no—
705C22⋊C4—864no—
706C22⋊C4—864no—
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—22no—
722C23—41no—
723C23—41no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—41no—
728C23—432no—
729C23—432no—
730C23—861no—
731C23—861no—
732C23—861no—
733C23—861no—
734C23—861no—
735C23—861no—
736C23—861no—
737C23—861no—
738C23—861no—
739C23—861no—
740C23—861no—
741C23—861no—
742C23—1724no—
743C23—1724no—
744C23—1724no—
745C23—1724no—
746C23—1724no—
747C23—1724no—
748C23—1724no—
749C23#1306330712yes—
750C23C2×D4×D4311yescharacteristic
751Q8—22no—
752Q8—22no—
753Q8—41no—
754Q8—41no—
755D4—22no—
756D4—22no—
757D4—48no—
758D4—41no—
759D4—41no—
760D4—1728no—
761D4—1728no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—48no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—432no—
779C2×C4—861no—
780C2×C4—861no—
781C2×C4—862no—
782C2×C4—862no—
783C2×C4—862no—
784C2×C4—862no—
785C2×C4—862no—
786C2×C4—862no—
787C2×C4—861no—
788C2×C4—861no—
789C2×C4—861no—
790C2×C4—1724no—
791C2×C4—1724no—
792C2×C4—1724no—
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—1721no—
807C2×C4#1306330712yes—
808C2×C4C2×D4×D4311yescharacteristic
809C2×C4C2×D4×D4311yescharacteristic
810C2×C4C2×#1062190011yescharacteristic
811C2×C4C2×#1062189811yescharacteristic
812C2×C4#1306337011yescharacteristic
813C2×C4#1306337011yescharacteristic
814C8—41no—
815C8—41no—
816C8—1721no—
817C8—1721no—
818C22—22no—
819C22—22no—
820C22—22no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—42no—
826C22—42no—
827C22—42no—
828C22—81no—
829C22—81no—
830C22—81no—
831C22—81no—
832C22—862no—
833C22—862no—
834C22—862no—
835C22—862no—
836C22—862no—
837C22—862no—
838C22—17216no—
839C22—1721no—
840C22—1721no—
841C22—1721no—
842C22—1721no—
843C22—1721no—
844C22—1721no—
845C22—1721no—
846C22—1721no—
847C22#120×D4311yescharacteristic
848C22C2×#1306330711yescharacteristic
849C22#1458345911yescharacteristic
850C22#135×D4311yescharacteristic
851C22#1458369511yescharacteristic
852C22#1458369611yescharacteristic
853C22#1458369811yescharacteristic
854C4—22no—
855C4—42no—
856C4—81no—
857C4—81no—
858C4—862no—
859C4—3441no—
860C4—3441no—
861C4—1721no—
862C4—1722no—
863C4—1722no—
864C4#1458353611yescharacteristic
865C4#1458353611yescharacteristic
866C4#1458353911yescharacteristic
867C4#1458353911yescharacteristic
868C2—42no—
869C2—82no—
870C2—1722no—
871C2—1722no—
872C2#1913792011yescharacteristic
873C2#1914381011yescharacteristic
874C2#1914383811yescharacteristic
875C2#1914450611yescharacteristic
876C2#1914452511yescharacteristic
877C2#1914538711yescharacteristic
878C2#1914543411yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1788C2
socleC23×C43C22×D4
prime radicalC2×#14583406C2
hypercenter#1788D43
hypocenterC43#24008
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1788

Complements

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

NH ≅ G/Ntype
2. C2×#14583238C2semidirect
3. C2×#14583221C2semidirect
4. #19136977C2semidirect
5. #19135797C2semidirect
6. #19135789C2semidirect
7. #19135783C2semidirect
8. #19135775C2semidirect
9. #19134914C2semidirect
10. #19134904C2semidirect
11. #19134796C2semidirect
12. #19134792C2semidirect
13. #19134535C2semidirect
14. #19134504C2semidirect
15. C43×#1788C2semidirect
32. C2×#13063259C22semidirect
33. C2×#13063258C22semidirect
34. C2×#13063257C22semidirect
35. C2×#13063256C22semidirect
36. C2×#13063249C22semidirect
37. C2×#13063249C22semidirect
38. C2×#13063246C22semidirect
39. C2×#13063246C22semidirect
52. #14582662C22semidirect
53. #14582662C22semidirect
54. #14582661C22semidirect
55. #14582661C22semidirect
57. C2×#103×C43C22semidirect
58. C2×#103×C43C22semidirect
59. C2×#102×C43C22semidirect
60. C2×#102×C43C22semidirect
442. #1788D43semidirect
478. C2×#103C2×D43semidirect
479. C2×#103C2×D43semidirect
482. C2×#102C2×D43semidirect
483. C2×#102C2×D43semidirect
502. C43#24008semidirect

Maximal subgroups

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

subgroupindex
C2×#145834062
C2×#145832382
C2×#145832212
#191369772
#191357972
#191357892
#191357832
#191357752
#191349142
#191349042
#191347962
#191347922
#191345352
#191345042
C43×#17882
#2400843