Finite Group Databasebeta

← #25139016

Subgroups — #25139016

Order 11008.

1006 conjugacy classes of subgroups.

The subgroup lattice has 762 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583147C211yesmaximal, characteristic, complemented
2C2×#14583147C211yesmaximal, characteristic, complemented
3C2×#14582977C211yesmaximal, characteristic, complemented
4C2×#14582939C211yesmaximal, characteristic, complemented
5#19138013C211yesmaximal, characteristic
6#19135990C211yesmaximal, characteristic, complemented
7#19135966C211yesmaximal, characteristic, complemented
8#19135788C211yesmaximal, characteristic, complemented
9#19135777C211yesmaximal, characteristic, complemented
10#19135452C211yesmaximal, characteristic, complemented
11#19135325C211yesmaximal, characteristic, complemented
12#19134912C211yesmaximal, characteristic, complemented
13#19134908C211yesmaximal, characteristic, complemented
14#19134626C211yesmaximal, characteristic, complemented
15C43×#2417C211yesmaximal, characteristic, complemented
16C22×#10621884C2211yescharacteristic
17C22×#10621877C2211yescharacteristic
18C22×#10621877C2211yescharacteristic
19C2×#13063299C2211yescharacteristic
20C2×#13063299C2211yescharacteristic
21C2×#13063284C2211yescharacteristic
22#14583147—24no—
23#14583147—24no—
24#14582977—24no—
25#14582939—24no—
26C2×#13063258C2211yescharacteristic
27C2×#13063258C2211yescharacteristic
28C2×#13063258C2211yescharacteristic
29C2×#13063256C2211yescharacteristic
30C2×#13063256C2211yescharacteristic
31C2×C4⋊(C43⋊C8)C2211yescharacteristic
32C2×#13063249C2211yescharacteristic
33C2×#13063249C2211yescharacteristic
34C2×#13063249C2211yescharacteristic
35C2×#13063245C2211yescharacteristic
36C2×#13063245C2211yescharacteristic
37C2×#13063245C2211yescharacteristic
38C2×C22⋊(C43⋊C8)C2211yescharacteristic
39C2×C22⋊(C43⋊C8)C2211yescharacteristic
40C2×C4×C43⋊C8C2211yescharacteristic
41#14582814—21no—
42#14582807—21no—
43#14582801C2211yescharacteristic
44#14582799—21no—
45#14582797C2211yescharacteristic
46#14582789—21no—
47#14582759C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52C2×C22⋊Q8×C43C2211yescharacteristic
53C2×C22⋊Q8×C43C2211yescharacteristic
54C2×C4×D4×C43C2211yescharacteristic
55C22×C4⋊C4×C43C2211yescharacteristic
56C43×#398—21no—
57C43×#396—21no—
58C43×#391C2211yescharacteristic
59C43×#389C2211yescharacteristic
60C43×#386—21no—
61C43×#380—21no—
62C43×#380C2211yescharacteristic
63C22×D172C2311yescharacteristic
64C22×C22⋊D43—21no—
65C22×C22⋊D43—21no—
66C2×#10621884—22no—
67C2×#10621884—22no—
68C2×#10621884—22no—
69C2×#10621877—22no—
70C2×#10621877—22no—
71C2×#10621877—22no—
72C2×#10621877—22no—
73C2×#10621877—22no—
74C2×#10621877D414yescomplemented
75C22×C43⋊C8C2311yescharacteristic
76C22×C43⋊C8C2311yescharacteristic
77C22×C43⋊C8C2311yescharacteristic
78C22×C43⋊C8C2311yescharacteristic
79#13063299—22no—
80#13063299—22no—
81#13063299—22no—
82#13063299—41no—
83#13063284—22no—
84#13063284—41no—
85C2×C4⋊Dic43C2311yescharacteristic
86C2×C4⋊Dic43C2311yescharacteristic
87C2×C4⋊Dic43C2311yescharacteristic
88C2×Dic43⋊C4—21no—
89C2×C22⋊Dic43—21no—
90C2×C22⋊Dic43—21no—
91C2×(C2×D43)⋊C4—21no—
92C2×(C2×D43)⋊C4—21no—
93C2×(C2×D43)⋊C4—21no—
94C2×(C2×D43)⋊C4—21no—
95C2×C4×Dic43—21no—
96#13063258—22no—
97#13063258—22no—
98#13063258D414yescomplemented
99#13063256—22no—
100#13063256—22no—
101C4⋊(C43⋊C8)—22no—
102#13063249—22no—
103#13063249—22no—
104#13063249—41no—
105#13063245—22no—
106#13063245—22no—
107#13063245—41no—
108C22⋊(C43⋊C8)—22no—
109C22⋊(C43⋊C8)—22no—
110C4×C43⋊C8—22no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C22×Q8×C43C2311yescharacteristic
114C22×D4×C43D411yescharacteristic
115C23×C4×C43—21no—
116C23×C4×C43C2311yescharacteristic
117C23×C4×C43C2311yescharacteristic
118C22⋊Q8×C43—22no—
119C22⋊Q8×C43—22no—
120C22⋊Q8×C43—22no—
121C22⋊Q8×C43—41no—
122C4×D4×C43—22no—
123C4×D4×C43—22no—
124C2×C4⋊C4×C43—22no—
125C2×C4⋊C4×C43—21no—
126C2×C4⋊C4×C43—21no—
127C2×C4⋊C4×C43—21no—
128C2×C4⋊C4×C43—21no—
129C2×C4⋊C4×C43—41no—
130C2×C4⋊C4×C43D411yescharacteristic
131C2×C4⋊C4×C43C2311yescharacteristic
132C2×C4⋊C4×C43C2311yescharacteristic
133C2×C4⋊C4×C43C2311yescharacteristic
134C2×C22⋊C4×C43—21no—
135C2×C22⋊C4×C43—21no—
136C2×C22⋊C4×C43—21no—
137C2×C22⋊C4×C43D411yescharacteristic
138C2×C22⋊C4×C43D411yescharacteristic
139C2×C42×C43C2311yescharacteristic
140#95×C43—21no—
141#95×C43—21no—
142#95×C43—21no—
143#95×C43—21no—
144C24×C43C2×D411yescharacteristic
145C24×C43C2×D411yescharacteristic
146C23×D43—21no—
147C2×Q8×C43—21no—
148C2×Q8×C43—21no—
149C2×Q8×C43—21no—
150C2×Q8×C43—21no—
151C2×Q8×C43—21no—
152C2×Q8×C43—21no—
153C2×D4×C43—22no—
154C2×D4×C43—22no—
155C2×D4×C43—41no—
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43—21no—
159C22×C4×C43—21no—
160C22×C4×C43—21no—
161C22×C4×C43—21no—
162C22×C4×C43—21no—
163C22×C4×C43—21no—
164C22×C4×C43—21no—
165C22×C4×C43—21no—
166C22×C4×C43—21no—
167C22×C4×C43—21no—
168C22×C4×C43—21no—
169C22×C4×C43—21no—
170C22×C4×C43—42no—
171C22×C4×C43—42no—
172C22×C4×C43—81no—
173C22×C4×C43C2×D412yes—
174C22×C4×C43C2×D411yescharacteristic
175C22×C4×C43C2×D411yescharacteristic
176C22×C4×C43C2×D411yescharacteristic
177C22×C4×C43C2×D411yescharacteristic
178C22×C4×C43#4112yes—
179C22×C4×C43C2411yescharacteristic
180C2×C22⋊D43—42no—
181C2×C22⋊D43—42no—
182C2×C22⋊D43—42no—
183C2×C22⋊D43—81no—
184C2×C22⋊D43—81no—
185C2×C22⋊D43—81no—
186C22×Dic43—21no—
187C22×Dic43—21no—
188C22×Dic43—21no—
189C2×D172—21no—
190C2×D172—21no—
191C2×D172—21no—
192C2×D172—21no—
193C2×D172—21no—
194C2×D172—21no—
195C4⋊C4×C43—22no—
196C4⋊C4×C43—21no—
197C4⋊C4×C43—21no—
198C4⋊C4×C43—21no—
199C4⋊C4×C43—21no—
200C4⋊C4×C43—21no—
201C4⋊C4×C43—42no—
202C4⋊C4×C43—42no—
203C4⋊C4×C43—42no—
204C4⋊C4×C43—81no—
205C4⋊C4×C43C2×D412yes—
206C22⋊C4×C43—22no—
207C22⋊C4×C43—22no—
208C22⋊C4×C43—42no—
209C22⋊C4×C43—42no—
210C22⋊C4×C43—81no—
211C42×C43—21no—
212C42×C43—21no—
213C22⋊Dic43—42no—
214C22⋊Dic43—81no—
215#10621884—44no—
216(C2×D43)⋊C4—42no—
217(C2×D43)⋊C4—42no—
218(C2×D43)⋊C4—42no—
219(C2×D43)⋊C4—81no—
220C4⋊Dic43—21no—
221C4⋊Dic43—21no—
222C4⋊Dic43—21no—
223C4⋊Dic43—21no—
224C4⋊Dic43—21no—
225C4⋊Dic43C2×D412yes—
226Dic43⋊C4—81no—
227C4×Dic43—42no—
228#10621877—28no—
229#10621877—44no—
230C2×C43⋊C8—21no—
231C2×C43⋊C8—21no—
232C2×C43⋊C8—21no—
233C2×C43⋊C8—21no—
234C2×C43⋊C8—21no—
235C2×C43⋊C8—21no—
236C2×C43⋊C8—21no—
237C2×C43⋊C8—21no—
238C2×C43⋊C8C2×D412yes—
239C2×C43⋊C8C2×D412yes—
240C2×C43⋊C8C2×D412yes—
241C2×C43⋊C8#4112yes—
242C23×C43—21no—
243C23×C43—21no—
244C23×C43—21no—
245C23×C43—21no—
246C23×C43—21no—
247C23×C43—21no—
248C23×C43—21no—
249C23×C43—21no—
250C23×C43—21no—
251C23×C43—21no—
252C23×C43—21no—
253C23×C43—21no—
254C23×C43—21no—
255C23×C43#12112yes—
256C23×C43C22×D411yescharacteristic
257C22×D43—41no—
258C22×D43—41no—
259C22×D43—41no—
260C22×D43—41no—
261C22×D43—41no—
262C22×D43—41no—
263C22×D43—41no—
264Q8×C43—41no—
265Q8×C43—41no—
266Q8×C43—41no—
267Q8×C43—41no—
268D4×C43—44no—
269C2×C4×C43—21no—
270C2×C4×C43—21no—
271C2×C4×C43—21no—
272C2×C4×C43—21no—
273C2×C4×C43—22no—
274C2×C4×C43—22no—
275C2×C4×C43—22no—
276C2×C4×C43—22no—
277C2×C4×C43—21no—
278C2×C4×C43—21no—
279C2×C4×C43—21no—
280C2×C4×C43—22no—
281C2×C4×C43—21no—
282C2×C4×C43—21no—
283C2×C4×C43—21no—
284C2×C4×C43—41no—
285C2×C4×C43—41no—
286C2×C4×C43—41no—
287C2×C4×C43—41no—
288C2×C4×C43—41no—
289C2×C4×C43—41no—
290C2×C4×C43—41no—
291C2×C4×C43—41no—
292C2×C4×C43—41no—
293C2×C4×C43—41no—
294C2×C4×C43—41no—
295C2×C4×C43—41no—
296C2×C4×C43—41no—
297C2×C4×C43—41no—
298C2×C4×C43—41no—
299C2×C4×C43—84no—
300C2×C4×C43#12112yes—
301C2×C4×C43#13712yes—
302C2×C4×C43C22×D411yescharacteristic
303C2×C4×C43C22×D411yescharacteristic
304C2×C4×C43C2×#4111yescharacteristic
305C2×C4×C43C2×#4111yescharacteristic
306C2×C4×C43H(5,𝔽2)11yescharacteristic
307C2×C4×C432−1+411yescharacteristic
308C22⋊D43—84no—
309C22⋊D43—84no—
310C2×Dic43—22no—
311C2×Dic43—41no—
312C2×Dic43—41no—
313C2×Dic43—41no—
314C2×Dic43—41no—
315C2×Dic43—41no—
316C2×Dic43—41no—
317C2×Dic43—41no—
318C2×Dic43—41no—
319D172—41no—
320D172—41no—
321D172—41no—
322D172—41no—
323C43⋊C8—22no—
324C43⋊C8—41no—
325C43⋊C8—41no—
326C43⋊C8#12114yes—
327#24795—431nomaximal, Sylow
328C22×C43—22no—
329C22×C43—22no—
330C22×C43—22no—
331C22×C43—41no—
332C22×C43—41no—
333C22×C43—41no—
334C22×C43—41no—
335C22×C43—41no—
336C22×C43—41no—
337C22×C43—41no—
338C22×C43—41no—
339C22×C43—41no—
340C22×C43—41no—
341C22×C43—41no—
342C22×C43C2×#12111yescharacteristic
343C22×C43D4211yescharacteristic
344C22×C43#54711yescharacteristic
345C22×C43C2×#13711yescharacteristic
346C22×C43#57511yescharacteristic
347C22×C43#57611yescharacteristic
348C22×C43#57711yescharacteristic
349C2×D43—81no—
350C2×D43—81no—
351C2×D43—81no—
352C2×D43—81no—
353C2×D43—81no—
354C2×D43—81no—
355C2×D43—81no—
356C4×C43—22no—
357C4×C43—22no—
358C4×C43—41no—
359C4×C43—42no—
360C4×C43—41no—
361C4×C43—81no—
362C4×C43—81no—
363C4×C43—81no—
364C4×C43C2×#12111yescharacteristic
365C4×C43#53711yescharacteristic
366C4×C43#54811yescharacteristic
367C4×C43#55311yescharacteristic
368Dic43—42no—
369Dic43—81no—
370Dic43—81no—
371C2×#468—431no—
372C2×#468—431no—
373C2×#436—431no—
374C2×#428—431no—
375#2417D4311yescharacteristic, complemented
376#2414—431no—
377#2068—431no—
378#2065—431no—
379#2035—431no—
380#2033—431no—
381#1968—431no—
382#1942—431no—
383#1874—431no—
384#1873—431no—
385#1809—431no—
386C2×C43—42no—
387C2×C43—81no—
388C2×C43#241611yescharacteristic
389C2×C43#305611yescharacteristic
390C2×C43#306211yescharacteristic
391C2×C43#327311yescharacteristic
392C2×C43#327811yescharacteristic
393C2×C43#335111yescharacteristic
394C2×C43#335711yescharacteristic
395D43—161no—
396C22×SD16—431no—
397C22×M16—431no—
398C22×M16—431no—
399C2×C22⋊Q8C2×D4311yescharacteristic
400C2×C22⋊Q8C2×D4311yescharacteristic
401C2×#121—431no—
402C2×#121—431no—
403C2×C4×D4C2×D4311yescharacteristic
404C2×#117—431no—
405C22×C4⋊C4C2×D4311yescharacteristic
406#468—864no—
407#468—864no—
408#436—864no—
409#428—864no—
410C2×#107—431no—
411C2×#107—431no—
412C2×#107—431no—
413C2×#106—431no—
414C2×#106—431no—
415C2×C4⋊C8—431no—
416C2×#103—431no—
417C2×#103—431no—
418C2×#103—431no—
419C2×#102—431no—
420C2×#102—431no—
421C2×#102—431no—
422C2×C22⋊C8—431no—
423C2×C22⋊C8—431no—
424C2×C4×C8—431no—
425#398—21no—
426#396—21no—
427#394—861no—
428#392—861no—
429#391C2×D4311yescharacteristic
430#390—431no—
431#390—861no—
432#389—431no—
433#389C2×D4311yescharacteristic
434#388—861no—
435#386—21no—
436#380—21no—
437#380—431no—
438#380C2×D4311yescharacteristic
439#340—431no—
440#340—431no—
441#340—431no—
442#340—431no—
443C43#2479511yescharacteristic, complemented, Sylow
444C22×Q8C22×D4311yescharacteristic
445C22×D4—431no—
446C22×D4—861no—
447C22×D4—861no—
448C22×D4C22⋊D4311yescharacteristic
449C23×C4—21no—
450C23×C4C22×D4311yescharacteristic
451C23×C4C22×D4311yescharacteristic
452C2×SD16—862no—
453C2×SD16—862no—
454C2×SD16—862no—
455C2×M16—434no—
456C2×M16—862no—
457C2×M16—862no—
458C2×M16—862no—
459C2×M16—862no—
460C2×M16—862no—
461C22×C8—431no—
462C22×C8—431no—
463C22×C8—431no—
464C22×C8—431no—
465C22⋊Q8—22no—
466C22⋊Q8—22no—
467C22⋊Q8—22no—
468C22⋊Q8—41no—
469#121—862no—
470#121—862no—
471#121—862no—
472#121—1721no—
473C4×D4—22no—
474C4×D4—22no—
475#117—862no—
476#117—1721no—
477C2×C4⋊C4—22no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—21no—
482C2×C4⋊C4—41no—
483C2×C4⋊C4—431no—
484C2×C4⋊C4—431no—
485C2×C4⋊C4—431no—
486C2×C4⋊C4—861no—
487C2×C4⋊C4C22⋊D4311yescharacteristic
488C2×C4⋊C4C22×D4311yescharacteristic
489C2×C4⋊C4C22×D4311yescharacteristic
490C2×C4⋊C4C22×D4311yescharacteristic
491C2×C22⋊C4—21no—
492C2×C22⋊C4—21no—
493C2×C22⋊C4—21no—
494C2×C22⋊C4—861no—
495C2×C22⋊C4—861no—
496C2×C22⋊C4—861no—
497C2×C22⋊C4—861no—
498C2×C22⋊C4—861no—
499C2×C22⋊C4—861no—
500C2×C22⋊C4C22⋊D4311yescharacteristic
501C2×C22⋊C4C22⋊D4311yescharacteristic
502C2×C42—861no—
503C2×C42C22×D4311yescharacteristic
504#107—434no—
505#107—862no—
506#107—862no—
507#106—862no—
508#106—862no—
509C4⋊C8—862no—
510#103—862no—
511#103—862no—
512#103—1721no—
513#102—862no—
514#102—862no—
515#102—1721no—
516C22⋊C8—862no—
517C22⋊C8—862no—
518C4×C8—862no—
519#95—21no—
520#95—21no—
521#95—21no—
522#95—21no—
523#95—861no—
524#95—861no—
525C24—861no—
526C24C2×C22⋊D4311yescharacteristic
527C24C2×C22⋊D4311yescharacteristic
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8—21no—
534C2×D4—22no—
535C2×D4—22no—
536C2×D4—41no—
537C2×D4—861no—
538C2×D4—861no—
539C2×D4—861no—
540C2×D4—861no—
541C2×D4—861no—
542C2×D4—861no—
543C2×D4—3441no—
544C2×D4—3441no—
545C2×D4—3441no—
546C2×D4—1722no—
547C2×D4—1722no—
548C2×D4—1722no—
549C22×C4—21no—
550C22×C4—21no—
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—42no—
564C22×C4—42no—
565C22×C4—81no—
566C22×C4—861no—
567C22×C4—861no—
568C22×C4—861no—
569C22×C4D4×D4312yes—
570C22×C4#1062190012yes—
571C22×C4C2×C22⋊D4311yescharacteristic
572C22×C4C2×C22⋊D4311yescharacteristic
573C22×C4C2×C22⋊D4311yescharacteristic
574C22×C4C2×C22⋊D4311yescharacteristic
575C22×C4C23×D4311yescharacteristic
576SD16—1724no—
577M16—868no—
578M16—1724no—
579C2×C8—432no—
580C2×C8—432no—
581C2×C8—432no—
582C2×C8—432no—
583C2×C8—861no—
584C2×C8—861no—
585C2×C8—861no—
586C2×C8—861no—
587C2×C8—861no—
588C2×C8—861no—
589C2×C8—861no—
590C2×C8—861no—
591C4⋊C4—22no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—42no—
598C4⋊C4—42no—
599C4⋊C4—42no—
600C4⋊C4—81no—
601C4⋊C4—432no—
602C4⋊C4—861no—
603C4⋊C4—861no—
604C4⋊C4—861no—
605C4⋊C4—861no—
606C4⋊C4—861no—
607C4⋊C4—3441no—
608C4⋊C4D4×D4312yes—
609C22⋊C4—22no—
610C22⋊C4—22no—
611C22⋊C4—42no—
612C22⋊C4—42no—
613C22⋊C4—81no—
614C22⋊C4—3441no—
615C22⋊C4—3441no—
616C22⋊C4—1722no—
617C22⋊C4—1722no—
618C22⋊C4—1722no—
619C22⋊C4—1722no—
620C42—21no—
621C42—21no—
622C42—1722no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—1721no—
637C23—1721no—
638C23—1721no—
639C23—1721no—
640C23—1721no—
641C23—1721no—
642C23—1721no—
643C23#1306329712yes—
644C23C22×C22⋊D4311yescharacteristic
645Q8—41no—
646Q8—41no—
647Q8—41no—
648Q8—41no—
649D4—44no—
650D4—3444no—
651D4—3444no—
652D4—1721no—
653D4—1721no—
654D4—1721no—
655D4—1721no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—22no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—41no—
672C2×C4—41no—
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—41no—
686C2×C4—84no—
687C2×C4—862no—
688C2×C4—1721no—
689C2×C4—1721no—
690C2×C4—1721no—
691C2×C4—1721no—
692C2×C4—1721no—
693C2×C4—1721no—
694C2×C4—1721no—
695C2×C4—1721no—
696C2×C4#1306329712yes—
697C2×C4#1306335612yes—
698C2×C4C2×D4×D4311yescharacteristic
699C2×C4C2×D4×D4311yescharacteristic
700C2×C4#41×D4311yescharacteristic
701C2×C4C2×#1062190011yescharacteristic
702C2×C4#1306337011yescharacteristic
703C2×C4#1306337211yescharacteristic
704C8—434no—
705C8—862no—
706C8—1721no—
707C8—1721no—
708C22—22no—
709C22—22no—
710C22—22no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—3441no—
723C22—3441no—
724C22—3441no—
725C22—3441no—
726C22—3441no—
727C22—3441no—
728C22—3441no—
729C22C2×#1306329711yescharacteristic
730C22D4×C22⋊D4311yescharacteristic
731C22#1458354811yescharacteristic
732C22C2×#1306335611yescharacteristic
733C22#1458369711yescharacteristic
734C22#1458370211yescharacteristic
735C22#1458370711yescharacteristic
736C4—22no—
737C4—22no—
738C4—41no—
739C4—42no—
740C4—41no—
741C4—81no—
742C4—81no—
743C4—81no—
744C4—3441no—
745C4—3441no—
746C4—1722no—
747C4#121×D4311yescharacteristic
748C4#1458347611yescharacteristic
749C4#1458355511yescharacteristic
750C4#1458359211yescharacteristic
751C2—42no—
752C2—81no—
753C2—6881no—
754C2#1913803211yescharacteristic
755C2#1914422111yescharacteristic
756C2#1914427711yescharacteristic
757C2#1914620211yescharacteristic
758C2#1914625711yescharacteristic
759C2#1914715511yescharacteristic
760C2#1914722111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2417C2
socleC23×C43C22×D4
prime radical#19138013C2
hypercenter#2417D43
hypocenterC43#24795
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2417

Complements

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

NH ≅ G/Ntype
1. C2×#14583147C2semidirect
2. C2×#14583147C2semidirect
3. C2×#14582977C2semidirect
4. C2×#14582939C2semidirect
6. #19135990C2semidirect
7. #19135966C2semidirect
8. #19135788C2semidirect
9. #19135777C2semidirect
10. #19135452C2semidirect
11. #19135325C2semidirect
12. #19134912C2semidirect
13. #19134908C2semidirect
14. #19134626C2semidirect
15. C43×#2417C2semidirect
74. C2×#10621877D4semidirect
98. #13063258D4semidirect
375. #2417D43semidirect
443. C43#24795semidirect

Maximal subgroups

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

subgroupindex
C2×#145831472
C2×#145829772
C2×#145829392
#191380132
#191359902
#191359662
#191357882
#191357772
#191354522
#191353252
#191349122
#191349082
#191346262
C43×#24172
#2479543