Finite Group Databasebeta

← #25129286

Subgroups — #25129286

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×#14583240C211yesmaximal, characteristic, complemented
3C2×#14583223C211yesmaximal, characteristic, complemented
4#19135798C211yesmaximal, characteristic, complemented
5#19135791C211yesmaximal, characteristic, complemented
6#19135784C211yesmaximal, characteristic, complemented
7#19135777C211yesmaximal, characteristic, complemented
8#19134917C211yesmaximal, characteristic, complemented
9#19134907C211yesmaximal, characteristic, complemented
10#19134792C211yesmaximal, characteristic, complemented
11#19134792C211yesmaximal, characteristic, complemented
12#19134533C211yesmaximal, characteristic, complemented
13#19134533C211yesmaximal, characteristic, complemented
14#19134505C211yesmaximal, characteristic, complemented
15C43×#2280C211yesmaximal, 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
28#14583240—24no—
29#14583223—24no—
30C2×#13063258C2211yescharacteristic, complemented
31C2×#13063258C2211yescharacteristic, complemented
32C2×#13063256C2211yescharacteristic, complemented
33C2×#13063256C2211yescharacteristic, complemented
34C2×#13063248C2211yescharacteristic, complemented
35C2×#13063248C2211yescharacteristic, complemented
36C2×#13063248C2211yescharacteristic, complemented
37C2×#13063248C2211yescharacteristic, complemented
38C2×#13063245C2211yescharacteristic, complemented
39C2×#13063245C2211yescharacteristic, complemented
40C2×#13063245C2211yescharacteristic, complemented
41C2×#13063245C2211yescharacteristic, complemented
42C2×C22⋊(C43⋊C8)C2211yescharacteristic
43C2×C22⋊(C43⋊C8)C2211yescharacteristic
44C2×C22⋊(C43⋊C8)C2211yescharacteristic
45C2×C22⋊(C43⋊C8)C2211yescharacteristic
46C2×C22⋊(C43⋊C8)C2211yescharacteristic
47C2×C22⋊(C43⋊C8)C2211yescharacteristic
48#14582661C2211yescharacteristic, complemented
49#14582661C2211yescharacteristic, complemented
50#14582661C2211yescharacteristic, complemented
51#14582661C2211yescharacteristic, complemented
52C24×C4×C43C2211yescharacteristic
53C2×#117×C43C2211yescharacteristic
54C2×#117×C43C2211yescharacteristic
55C43×#381—21no—
56C43×#380C2211yescharacteristic
57C43×#380C2211yescharacteristic
58C43×#380C2211yescharacteristic
59C43×#380C2211yescharacteristic
60C43×#379—21no—
61C4×C22⋊C4×C43—21no—
62C4×C22⋊C4×C43—21no—
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—
75C22×C43⋊C8C2311yescharacteristic
76C22×C43⋊C8C2311yescharacteristic
77C22×C43⋊C8C2311yescharacteristic
78C22×C43⋊C8C2311yescharacteristic
79#13063308—28no—
80#13063304—22no—
81#13063304—22no—
82#13063304—22no—
83#13063304D414yes—
84#13063299—22no—
85#13063299—22no—
86#13063299—22no—
87#13063299D414yes—
88#13063294—28no—
89C4×C22⋊D43—28no—
90C4×C22⋊D43—28no—
91#13063284—22no—
92#13063284—22no—
93C2×C4⋊Dic43C2311yescharacteristic
94C2×C4⋊Dic43C2311yescharacteristic
95C2×Dic43⋊C4—21no—
96C2×Dic43⋊C4—21no—
97C2×C22⋊Dic43—21no—
98C2×C22⋊Dic43—21no—
99C2×C22⋊Dic43—21no—
100C2×(C2×D43)⋊C4—21no—
101C2×(C2×D43)⋊C4—21no—
102C2×C4×Dic43—21no—
103#13063258—22no—
104#13063258—22no—
105#13063256—22no—
106#13063256—22no—
107#13063248—22no—
108#13063248—22no—
109#13063248—41no—
110#13063248—41no—
111#13063245—22no—
112#13063245—22no—
113#13063245—41no—
114#13063245—41no—
115C22⋊(C43⋊C8)—22no—
116C22⋊(C43⋊C8)—22no—
117C22⋊(C43⋊C8)—22no—
118C22⋊(C43⋊C8)—22no—
119C22⋊(C43⋊C8)—41no—
120C22⋊(C43⋊C8)—41no—
121C25×C43D411yescharacteristic
122C23×C4×C43—22no—
123C23×C4×C43—22no—
124C23×C4×C43—22no—
125C23×C4×C43—22no—
126C23×C4×C43—41no—
127C23×C4×C43—41no—
128C23×C4×C43D411yescharacteristic
129C23×C4×C43D411yescharacteristic
130C23×C4×C43D411yescharacteristic
131C23×C4×C43C2311yescharacteristic
132C23×C4×C43C2311yescharacteristic
133C23×C4×C43C2311yescharacteristic
134#117×C43—22no—
135#117×C43—22no—
136#117×C43—41no—
137#117×C43—41no—
138C2×C4⋊C4×C43C2311yescharacteristic
139C2×C4⋊C4×C43C2311yescharacteristic
140C2×C4⋊C4×C43C2311yescharacteristic
141C2×C4⋊C4×C43C2311yescharacteristic
142C2×C22⋊C4×C43—21no—
143C2×C22⋊C4×C43—21no—
144C2×C22⋊C4×C43—21no—
145C2×C22⋊C4×C43—21no—
146C2×C22⋊C4×C43—21no—
147C2×C22⋊C4×C43—21no—
148C2×C42×C43—21no—
149C2×C42×C43—21no—
150#95×C43—21no—
151#95×C43—21no—
152#95×C43—21no—
153#95×C43—21no—
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—21no—
186C22×C4×C43—21no—
187C22×C4×C43—21no—
188C22×C4×C43—21no—
189C22×C4×C43—41no—
190C22×C4×C43—41no—
191C22×C4×C43—41no—
192C22×C4×C43—44no—
193C22×C4×C43—44no—
194C22×C4×C43—44no—
195C22×C4×C43—44no—
196C22×C4×C43C2×D412yes—
197C22×C4×C43C2×D412yes—
198C22×C4×C43C2×D411yescharacteristic
199C22×C4×C43C2×D411yescharacteristic
200C22×C4×C43C2×D411yescharacteristic
201C22×C4×C43#4112yes—
202C22×C4×C43#4112yes—
203C22×C4×C43C2411yescharacteristic
204C2×C22⋊D43—24no—
205C2×C22⋊D43—24no—
206C2×C22⋊D43—24no—
207C2×C22⋊D43—42no—
208C2×C22⋊D43—42no—
209C2×C22⋊D43—42no—
210C2×C22⋊D43—42no—
211C2×C22⋊D43—42no—
212C2×C22⋊D43—42no—
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—
235C4⋊C4×C43—21no—
236C4⋊C4×C43—21no—
237C4⋊C4×C43—21no—
238C4⋊C4×C43—21no—
239C4⋊C4×C43—21no—
240C4⋊C4×C43—21no—
241C4⋊C4×C43—21no—
242C4⋊C4×C43—21no—
243C22⋊C4×C43—42no—
244C22⋊C4×C43—42no—
245C22⋊C4×C43—42no—
246C22⋊C4×C43—42no—
247C22⋊C4×C43—42no—
248C22⋊C4×C43—42no—
249C42×C43—42no—
250C42×C43—42no—
251C22⋊Dic43—24no—
252C22⋊Dic43—24no—
253C22⋊Dic43—24no—
254(C2×D43)⋊C4—24no—
255(C2×D43)⋊C4—24no—
256C4⋊Dic43—21no—
257C4⋊Dic43—21no—
258C4⋊Dic43C2×D412yes—
259C4⋊Dic43C2×D412yes—
260Dic43⋊C4—24no—
261Dic43⋊C4—24no—
262C4×Dic43—24no—
263C2×C43⋊C8—21no—
264C2×C43⋊C8—21no—
265C2×C43⋊C8—21no—
266C2×C43⋊C8—21no—
267C2×C43⋊C8—21no—
268C2×C43⋊C8—21no—
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—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—41no—
334C2×C4×C43—41no—
335C2×C4×C43—41no—
336C2×C4×C43—41no—
337C2×C4×C43—41no—
338C2×C4×C43—41no—
339C2×C4×C43—41no—
340C2×C4×C43—41no—
341C2×C4×C43—41no—
342C2×C4×C43—41no—
343C2×C4×C43—41no—
344C2×C4×C43—41no—
345C2×C4×C43#12012yes—
346C2×C4×C43#12312yes—
347C2×C4×C43C22×D411yescharacteristic
348C2×C4×C43C22×D411yescharacteristic
349C2×C4×C43C2×#4111yescharacteristic
350C2×C4×C43C2×#4111yescharacteristic
351C2×C4×C43H(5,𝔽2)11yescharacteristic
352C2×C4×C43H(5,𝔽2)11yescharacteristic
353C22⋊D43—48no—
354C22⋊D43—48no—
355C22⋊D43—48no—
356C2×Dic43—22no—
357C2×Dic43—22no—
358C2×Dic43—22no—
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—
374C43⋊C8—41no—
375C43⋊C8—41no—
376C43⋊C8—41no—
377C43⋊C8—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—81no—
419C4×C43—81no—
420C4×C43—81no—
421C4×C43—81no—
422C4×C43#54611yescharacteristic
423C4×C43#54611yescharacteristic
424C4×C43#54611yescharacteristic
425C4×C43#54611yescharacteristic
426Dic43—42no—
427Dic43—42no—
428Dic43—42no—
429C2×#525—431no—
430C2×#485—431no—
431C2×#482—431no—
432#2280D4311yescharacteristic, complemented
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#1779—431no—
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×#117C2×D4311yescharacteristic
469C2×#117C2×D4311yescharacteristic
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⋊C8—431no—
485C2×C22⋊C8—431no—
486C2×C22⋊C8—431no—
487C2×C22⋊C8—431no—
488C2×C22⋊C8—431no—
489C2×C22⋊C8—431no—
490#381—21no—
491#380C2×D4311yescharacteristic
492#380C2×D4311yescharacteristic
493#380C2×D4311yescharacteristic
494#380C2×D4311yescharacteristic
495#379—21no—
496C4×C22⋊C4—21no—
497C4×C22⋊C4—21no—
498#340—431no—
499#340—431no—
500#340—431no—
501#340—431no—
502C43#2400811yescharacteristic, complemented, Sylow
503C25C22⋊D4311yescharacteristic
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×C4C22⋊D4311yescharacteristic
523C23×C4C22⋊D4311yescharacteristic
524C23×C4C22⋊D4311yescharacteristic
525C23×C4C22×D4311yescharacteristic
526C23×C4C22×D4311yescharacteristic
527C23×C4C22×D4311yescharacteristic
528C22×C8—431no—
529C22×C8—431no—
530C22×C8—431no—
531C22×C8—431no—
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—22no—
545#117—22no—
546#117—41no—
547#117—41no—
548#117—862no—
549#117—862no—
550C2×C4⋊C4—431no—
551C2×C4⋊C4—431no—
552C2×C4⋊C4—861no—
553C2×C4⋊C4—861no—
554C2×C4⋊C4C22×D4311yescharacteristic
555C2×C4⋊C4C22×D4311yescharacteristic
556C2×C4⋊C4C22×D4311yescharacteristic
557C2×C4⋊C4C22×D4311yescharacteristic
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—21no—
564C2×C22⋊C4—861no—
565C2×C22⋊C4—861no—
566C2×C22⋊C4—861no—
567C2×C22⋊C4—861no—
568C2×C22⋊C4—861no—
569C2×C42—21no—
570C2×C42—21no—
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—862no—
585C22⋊C8—862no—
586C22⋊C8—862no—
587C22⋊C8—862no—
588C22⋊C8—1721no—
589C22⋊C8—1721no—
590#95—21no—
591#95—21no—
592#95—21no—
593#95—21no—
594C24—22no—
595C24—22no—
596C24—22no—
597C24—41no—
598C24—41no—
599C24—41no—
600C24—41no—
601C24—861no—
602C24C2×C22⋊D4311yescharacteristic
603C24C2×C22⋊D4311yescharacteristic
604C24C2×C22⋊D4311yescharacteristic
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—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—41no—
655C22×C4—41no—
656C22×C4—41no—
657C22×C4—44no—
658C22×C4—44no—
659C22×C4—44no—
660C22×C4—44no—
661C22×C4—864no—
662C22×C4—861no—
663C22×C4—861no—
664C22×C4—861no—
665C22×C4—1722no—
666C22×C4—1722no—
667C22×C4#1062189812yes—
668C22×C4#1062189812yes—
669C22×C4D4×D4312yes—
670C22×C4D4×D4312yes—
671C22×C4C2×C22⋊D4311yescharacteristic
672C22×C4C2×C22⋊D4311yescharacteristic
673C22×C4C2×C22⋊D4311yescharacteristic
674C22×C4C23×D4311yescharacteristic
675C2×C8—861no—
676C2×C8—861no—
677C2×C8—861no—
678C2×C8—861no—
679C2×C8—861no—
680C2×C8—861no—
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—21no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—432no—
696C4⋊C4—432no—
697C4⋊C4—864no—
698C4⋊C4—864no—
699C4⋊C4—861no—
700C4⋊C4—861no—
701C22⋊C4—42no—
702C22⋊C4—42no—
703C22⋊C4—42no—
704C22⋊C4—42no—
705C22⋊C4—42no—
706C22⋊C4—42no—
707C22⋊C4—864no—
708C22⋊C4—864no—
709C22⋊C4—864no—
710C22⋊C4—864no—
711C22⋊C4—864no—
712C42—42no—
713C42—42no—
714C42—864no—
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#1306329312yes—
748C23#1306330812yes—
749C23#1306334512yes—
750C23C22×C22⋊D4311yescharacteristic
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—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—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—862no—
797C2×C4—862no—
798C2×C4—862no—
799C2×C4—1728no—
800C2×C4—1721no—
801C2×C4—1721no—
802C2×C4—1721no—
803C2×C4—1721no—
804C2×C4—1721no—
805C2×C4—1721no—
806C2×C4#1306329312yes—
807C2×C4#1306330812yes—
808C2×C4C2×D4×D4311yescharacteristic
809C2×C4C2×D4×D4311yescharacteristic
810C2×C4C2×#1062189811yescharacteristic
811C2×C4C2×#1062189811yescharacteristic
812C2×C4#1306337011yescharacteristic
813C2×C4#1306337011yescharacteristic
814C8—1721no—
815C8—1721no—
816C8—1721no—
817C8—1721no—
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×#1306329311yescharacteristic
848C22C2×#1306330811yescharacteristic
849C22#1458345811yescharacteristic
850C22C2×#1306334511yescharacteristic
851C22#1458369711yescharacteristic
852C22#1458369711yescharacteristic
853C22#1458369711yescharacteristic
854C4—22no—
855C4—22no—
856C4—41no—
857C4—81no—
858C4—81no—
859C4—81no—
860C4—81no—
861C4—1722no—
862C4—1722no—
863C4—1722no—
864C4#1458353911yescharacteristic
865C4#1458353911yescharacteristic
866C4#1458353911yescharacteristic
867C4#1458353911yescharacteristic
868C2—42no—
869C2—42no—
870C2—42no—
871C2—3442no—
872C2#1913792211yescharacteristic
873C2#1914381111yescharacteristic
874C2#1914383511yescharacteristic
875C2#1914450811yescharacteristic
876C2#1914452611yescharacteristic
877C2#1914538311yescharacteristic
878C2#1914543211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2280C2
socleC23×C43C22×D4
prime radicalC2×#14583410C2
hypercenter#2280D43
hypocenterC43#24008
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C24×C4 ◁ #2280

Complements

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

NH ≅ G/Ntype
2. C2×#14583240C2semidirect
3. C2×#14583223C2semidirect
4. #19135798C2semidirect
5. #19135791C2semidirect
6. #19135784C2semidirect
7. #19135777C2semidirect
8. #19134917C2semidirect
9. #19134907C2semidirect
10. #19134792C2semidirect
11. #19134792C2semidirect
12. #19134533C2semidirect
13. #19134533C2semidirect
14. #19134505C2semidirect
15. C43×#2280C2semidirect
30. C2×#13063258C22semidirect
31. C2×#13063258C22semidirect
32. C2×#13063256C22semidirect
33. C2×#13063256C22semidirect
34. C2×#13063248C22semidirect
35. C2×#13063248C22semidirect
36. C2×#13063248C22semidirect
37. C2×#13063248C22semidirect
38. C2×#13063245C22semidirect
39. C2×#13063245C22semidirect
40. C2×#13063245C22semidirect
41. C2×#13063245C22semidirect
48. #14582661C22semidirect
49. #14582661C22semidirect
50. #14582661C22semidirect
51. #14582661C22semidirect
432. #2280D43semidirect
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×#145832402
C2×#145832232
#191357982
#191357912
#191357842
#191357772
#191349172
#191349072
#191347922
#191345332
#191345052
C43×#22802
#2400843