Finite Group Databasebeta

← #25003249

Subgroups — #25003249

Order 11008.

1350 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583473C211yesmaximal, characteristic
2C22×#13063251C211yesmaximal, characteristic
3C2×#14582901C211yesmaximal, characteristic
4C2×#14582806C211yesmaximal, characteristic, complemented
5#19134315C211yesmaximal, characteristic, complemented
6C2×#14582660C211yesmaximal, characteristic, complemented
7C22×#101×C43C211yesmaximal, characteristic, complemented
8C22×#10621898C2211yescharacteristic
9#14583473—22no—
10#14583473—22no—
11#14583473—22no—
12#14583473C414yescomplemented
13C2×#13063323—21no—
14C2×#13063314—21no—
15C2×#13063308—22no—
16C2×#13063301—22no—
17C2×#13063284C2211yescharacteristic
18C22×C4⋊Dic43C2211yescharacteristic
19C22×C4×Dic43C2211yescharacteristic
20C2×#13063251—22no—
21C2×#13063251—22no—
22C2×#13063251—22no—
23#14582901—22no—
24#14582901—22no—
25C2×#13063250—21no—
26C2×#13063247—21no—
27#14582806—22no—
28#14582806—22no—
29C2×C43⋊#95—22no—
30#14582662—22no—
31#14582660—22no—
32C23×Q8×C43C2211yescharacteristic
33C22×M16×C43C2211yescharacteristic
34C22×M16×C43C2211yescharacteristic
35C2×#101×C43—22no—
36C2×#101×C43—22no—
37C2×#101×C43—22no—
38C2×#10621898—21no—
39C2×#10621898—21no—
40C2×#10621898—21no—
41C2×#10621898—21no—
42C2×#10621898—21no—
43C2×#10621898—21no—
44C2×#10621898—21no—
45C2×#10621898—21no—
46C2×#10621898—21no—
47C2×#10621898—21no—
48C2×#10621898C2×C412yes—
49C2×#10621898D412yes—
50C22×Dic86D411yescharacteristic
51C22×D172D411yescharacteristic
52C22×C22⋊D43—21no—
53C23×Dic43—21no—
54C23×Dic43—21no—
55C22×C4×D43—21no—
56#13063323—24no—
57#13063323—24no—
58#13063314—24no—
59#13063314—24no—
60#13063308—28no—
61#13063308—28no—
62#13063301—28no—
63#13063301—28no—
64#13063284—21no—
65#13063284—21no—
66#13063284C2×C412yes—
67#13063284D412yes—
68C2×C4⋊Dic43—21no—
69C2×C4⋊Dic43—21no—
70C2×C4⋊Dic43—21no—
71C2×C4⋊Dic43—21no—
72C2×C4⋊Dic43—21no—
73C2×C4⋊Dic43D412yes—
74C2×C4⋊Dic43D412yes—
75C2×Dic43⋊C4—24no—
76C2×C22⋊Dic43—21no—
77C2×(C2×D43)⋊C4—24no—
78C2×C4×Dic43—21no—
79C2×C4×Dic43—21no—
80C2×C4×Dic43—21no—
81C2×C4×Dic43—21no—
82C2×C4×Dic43—21no—
83C2×C4×Dic43—21no—
84C2×C4×Dic43D412yes—
85#13063251—28no—
86#13063250—24no—
87#13063247—24no—
88C43⋊#95—28no—
89C22×Q8×C43—21no—
90C22×Q8×C43—21no—
91C22×Q8×C43—21no—
92C22×Q8×C43—21no—
93C22×Q8×C43—21no—
94C22×Q8×C43—21no—
95C22×Q8×C43—21no—
96C22×Q8×C43—21no—
97C22×Q8×C43—21no—
98C22×Q8×C43—21no—
99C22×Q8×C43—21no—
100C22×Q8×C43—21no—
101C22×Q8×C43C2×C412yes—
102C22×Q8×C43D412yes—
103C23×C4×C43D412yes—
104C23×C4×C43C2311yescharacteristic
105C2×M16×C43—21no—
106C2×M16×C43—21no—
107C2×M16×C43—21no—
108C2×M16×C43—21no—
109C2×M16×C43—21no—
110C2×M16×C43—21no—
111C2×M16×C43—21no—
112C2×M16×C43—21no—
113C2×M16×C43—21no—
114C2×M16×C43—21no—
115C2×M16×C43D412yes—
116C2×M16×C43D412yes—
117C22×C8×C43—21no—
118C22×C8×C43—21no—
119#101×C43—28no—
120C24×C43C2×D411yescharacteristic
121C23×D43—21no—
122C2×Q8×C43—22no—
123C2×Q8×C43—22no—
124C2×Q8×C43—22no—
125C2×Q8×C43—22no—
126C2×Q8×C43—22no—
127C2×Q8×C43—22no—
128C2×Q8×C43—22no—
129C2×Q8×C43—22no—
130C2×Q8×C43—22no—
131C2×Q8×C43—22no—
132C2×Q8×C43—22no—
133C2×Q8×C43—22no—
134C2×Q8×C43—41no—
135C2×Q8×C43—41no—
136C2×Q8×C43—41no—
137C2×Q8×C43—41no—
138C2×Q8×C43—41no—
139C2×Q8×C43—41no—
140C2×Q8×C43—41no—
141C2×Q8×C43—41no—
142C2×Q8×C43—41no—
143C2×Q8×C43—41no—
144C2×Q8×C43—41no—
145C2×Q8×C43—41no—
146C2×Q8×C43—41no—
147C2×Q8×C43—41no—
148C2×Q8×C43—41no—
149C2×Q8×C43—41no—
150C22×C4×C43—22no—
151C22×C4×C43—22no—
152C22×C4×C43—22no—
153C22×C4×C43—22no—
154C22×C4×C43—22no—
155C22×C4×C43—22no—
156C22×C4×C43C22⋊C414yes—
157C22×C4×C43C22×C411yescharacteristic
158C22×C4×C43C2×D411yescharacteristic
159C22×C4×C43C2×D411yescharacteristic
160C22×C4×C43C2×D411yescharacteristic
161C22×C4×C43C2×D411yescharacteristic
162C22×C4×C43C2×D411yescharacteristic
163C22×C4×C43C2×D411yescharacteristic
164C22×C4×C43C2×D411yescharacteristic
165C22×C4×C43C2×D411yescharacteristic
166C22×C4×C43C2×D411yescharacteristic
167C22×C4×C43#4111yescharacteristic
168C22×C4×C43#4111yescharacteristic
169C22×C4×C43#4111yescharacteristic
170C22×C4×C43#4111yescharacteristic
171C2×C22⋊D43—22no—
172C2×C22⋊D43—22no—
173C2×C22⋊D43—41no—
174C2×C22⋊D43—41no—
175C2×C22⋊D43—41no—
176C2×C22⋊D43—41no—
177C22×Dic43—24no—
178C22×Dic43—22no—
179C22×Dic43—22no—
180C22×Dic43—21no—
181C22×Dic43—22no—
182C22×Dic43—42no—
183C22×Dic43—44no—
184C22×Dic43—41no—
185C22×Dic43—41no—
186C22×Dic43—41no—
187C22×Dic43—41no—
188#10621898—22no—
189#10621898—22no—
190#10621898—22no—
191#10621898—22no—
192#10621898—22no—
193#10621898—22no—
194#10621898—22no—
195#10621898—22no—
196#10621898—41no—
197#10621898—41no—
198#10621898—41no—
199#10621898—41no—
200#10621898—41no—
201#10621898—41no—
202#10621898—41no—
203#10621898—41no—
204C2×D172—21no—
205C2×D172—21no—
206C2×D172—21no—
207C2×D172—21no—
208C2×D172—21no—
209C2×D172C22⋊C412yes—
210C2×C4×D43—22no—
211C2×C4×D43—22no—
212C2×C4×D43—41no—
213C2×C4×D43—41no—
214C2×C4×D43—41no—
215C2×C4×D43—41no—
216C2×Dic86—21no—
217C2×Dic86—21no—
218C2×Dic86—21no—
219C2×Dic86—21no—
220C2×Dic86—21no—
221C2×Dic86C22⋊C412yes—
222M16×C43—22no—
223M16×C43—22no—
224M16×C43—22no—
225M16×C43—22no—
226M16×C43—41no—
227M16×C43—41no—
228M16×C43—41no—
229M16×C43—41no—
230C2×C8×C43—22no—
231C2×C8×C43—22no—
232C2×C8×C43—41no—
233C2×C8×C43—41no—
234C2×C8×C43—41no—
235C2×C8×C43—41no—
236C22⋊Dic43—22no—
237C22⋊Dic43—22no—
238(C2×D43)⋊C4—216no—
239C4⋊Dic43—22no—
240C4⋊Dic43—22no—
241C4⋊Dic43—22no—
242C4⋊Dic43—41no—
243C4⋊Dic43—41no—
244C4⋊Dic43C22⋊C414yes—
245Dic43⋊C4—216no—
246C4×Dic43—22no—
247C4×Dic43—22no—
248C4×Dic43—22no—
249C4×Dic43—22no—
250C4×Dic43—41no—
251C4×Dic43—41no—
252C23×C43—22no—
253C23×C43—22no—
254C23×C43C2×C22⋊C411yescharacteristic
255C23×C43#12011yescharacteristic
256C23×C43#12011yescharacteristic
257C23×C43#12011yescharacteristic
258C23×C43#12111yescharacteristic
259C23×C43#12111yescharacteristic
260C23×C43#12311yescharacteristic
261C22×D43—22no—
262C22×D43—41no—
263C22×D43—41no—
264C22×D43—42no—
265C22×D43—42no—
266Q8×C43—42no—
267Q8×C43—42no—
268Q8×C43—42no—
269Q8×C43—42no—
270Q8×C43—42no—
271Q8×C43—42no—
272Q8×C43—42no—
273Q8×C43—42no—
274C2×C4×C43—24no—
275C2×C4×C43—24no—
276C2×C4×C43—24no—
277C2×C4×C43—42no—
278C2×C4×C43—42no—
279C2×C4×C43—42no—
280C2×C4×C43—42no—
281C2×C4×C43C2×C22⋊C411yescharacteristic
282C2×C4×C43C2×C22⋊C411yescharacteristic
283C2×C4×C43C4×D411yescharacteristic
284C2×C4×C43C4×D411yescharacteristic
285C2×C4×C43C4×D411yescharacteristic
286C2×C4×C43C4×D411yescharacteristic
287C2×C4×C43#12011yescharacteristic
288C2×C4×C43#12011yescharacteristic
289C2×C4×C43#12011yescharacteristic
290C2×C4×C43#12011yescharacteristic
291C2×C4×C43#12011yescharacteristic
292C2×C4×C43#12111yescharacteristic
293C2×C4×C43#12111yescharacteristic
294C2×C4×C43#12111yescharacteristic
295C2×C4×C43#12111yescharacteristic
296C2×C4×C43#12111yescharacteristic
297C2×C4×C43#12111yescharacteristic
298C2×C4×C43#12111yescharacteristic
299C2×C4×C43#12111yescharacteristic
300C2×C4×C43#12111yescharacteristic
301C2×C4×C43#12111yescharacteristic
302C2×C4×C43#12311yescharacteristic
303C2×C4×C43#12311yescharacteristic
304C2×C4×C43#12311yescharacteristic
305C2×C4×C43#12411yescharacteristic
306C2×C4×C43#12411yescharacteristic
307C2×C4×C43#12711yescharacteristic
308C2×C4×C43#12711yescharacteristic
309C22⋊D43—42no—
310C22⋊D43—42no—
311C22⋊D43—42no—
312C22⋊D43—42no—
313C2×Dic43—24no—
314C2×Dic43—24no—
315C2×Dic43—22no—
316C2×Dic43—44no—
317C2×Dic43—42no—
318C2×Dic43—44no—
319C2×Dic43—42no—
320C2×Dic43—41no—
321C2×Dic43—41no—
322C2×Dic43—42no—
323C2×Dic43—42no—
324C2×Dic43—44no—
325C2×Dic43—42no—
326C2×Dic43—82no—
327C2×Dic43—82no—
328D172—22no—
329D172—22no—
330D172—41no—
331D172—41no—
332C4×D43—42no—
333C4×D43—42no—
334C4×D43—42no—
335C4×D43—42no—
336Dic86—22no—
337Dic86—22no—
338Dic86—41no—
339Dic86—41no—
340C8×C43—42no—
341C8×C43—42no—
342#10998—431nomaximal, Sylow
343C22×C43—22no—
344C22×C43—22no—
345C22×C43—21no—
346C22×C43—21no—
347C22×C43—21no—
348C22×C43—21no—
349C22×C43—22no—
350C22×C43—22no—
351C22×C43#37911yescharacteristic
352C22×C43#38611yescharacteristic
353C22×C43#38611yescharacteristic
354C22×C43#39211yescharacteristic
355C22×C43#39211yescharacteristic
356C22×C43#39411yescharacteristic
357C22×C43#39411yescharacteristic
358C22×C43#45412yes—
359C22×C43#45612yes—
360C2×D43—44no—
361C2×D43—42no—
362C2×D43—81no—
363C2×D43—81no—
364C2×D43—82no—
365C4×C43—44no—
366C4×C43#38611yescharacteristic
367C4×C43#38611yescharacteristic
368C4×C43#39011yescharacteristic
369C4×C43#39011yescharacteristic
370C4×C43#39211yescharacteristic
371C4×C43#39211yescharacteristic
372C4×C43#39411yescharacteristic
373C4×C43#39411yescharacteristic
374Dic43—44no—
375Dic43—44no—
376Dic43—42no—
377Dic43—82no—
378C2×#536—431no—
379C22×#104—431no—
380C2×#417—431no—
381C22×#101D4311yescharacteristic, complemented
382C2×#391—431no—
383#1736—431no—
384C2×#339—431no—
385C2×C43—21no—
386C2×C43—21no—
387C2×C43—21no—
388C2×C43—21no—
389C2×C43#143811yescharacteristic
390C2×C43#179312yes—
391C2×C43#200311yescharacteristic
392C2×C43#200511yescharacteristic
393C2×C43#203812yes—
394D43—82no—
395C22×#41—431no—
396C23×Q8C2×D4311yescharacteristic
397C22×M16C2×D4311yescharacteristic
398C22×M16C2×D4311yescharacteristic
399#536—434no—
400#536—862no—
401#536—862no—
402#536—862no—
403C2×C4⋊Q8—861no—
404C2×#124—861no—
405C2×#123—862no—
406C2×C22⋊Q8—862no—
407C2×#117—431no—
408C22×C4⋊C4—431no—
409C22×C42—431no—
410C2×#104—862no—
411C2×#104—862no—
412C2×#104—862no—
413#417—862no—
414#417—862no—
415C2×#103—861no—
416C2×#102—861no—
417C2×#101—22no—
418C2×#101—22no—
419C2×#101—22no—
420#391—862no—
421#391—862no—
422C2×#95—862no—
423#340—862no—
424#339—862no—
425C43#1099811yescharacteristic, complemented, Sylow
426C2×#41—432no—
427C2×#41—432no—
428C2×#41—861no—
429C2×#41—861no—
430C2×#41—861no—
431C2×#41—861no—
432C2×#41—861no—
433C2×#41—861no—
434C2×#41—861no—
435C2×#41—861no—
436C2×#41—861no—
437C2×#41—861no—
438C22×Q8—21no—
439C22×Q8—21no—
440C22×Q8—21no—
441C22×Q8—21no—
442C22×Q8—21no—
443C22×Q8—21no—
444C22×Q8—21no—
445C22×Q8—21no—
446C22×Q8—21no—
447C22×Q8—21no—
448C22×Q8—21no—
449C22×Q8—21no—
450C22×Q8—431no—
451C22×Q8C4×D4312yes—
452C22×Q8C22⋊D4312yes—
453C22×D4—431no—
454C22×D4—861no—
455C23×C4—861no—
456C23×C4—861no—
457C23×C4—861no—
458C23×C4D17212yes—
459C23×C4C22×D4311yescharacteristic
460C2×M16—21no—
461C2×M16—21no—
462C2×M16—21no—
463C2×M16—21no—
464C2×M16—21no—
465C2×M16—21no—
466C2×M16—21no—
467C2×M16—21no—
468C2×M16—21no—
469C2×M16—21no—
470C2×M16C22⋊D4312yes—
471C2×M16C22⋊D4312yes—
472C22×C8—21no—
473C22×C8—21no—
474C4⋊Q8—864no—
475C4⋊Q8—864no—
476#124—864no—
477#124—864no—
478#123—868no—
479#123—868no—
480C22⋊Q8—868no—
481C22⋊Q8—868no—
482#117—432no—
483#117—432no—
484#117—861no—
485#117—861no—
486C2×C4⋊C4—432no—
487C2×C4⋊C4—432no—
488C2×C4⋊C4—864no—
489C2×C4⋊C4—861no—
490C2×C4⋊C4—861no—
491C2×C4⋊C4—861no—
492C2×C4⋊C4—861no—
493C2×C4⋊C4—861no—
494C2×C22⋊C4—864no—
495C2×C22⋊C4—861no—
496C2×C42—432no—
497C2×C42—861no—
498C2×C42—861no—
499C2×C42—861no—
500C2×C42—861no—
501C2×C42—861no—
502C2×C42—861no—
503#104—868no—
504#103—864no—
505#102—864no—
506#101—28no—
507#95—868no—
508C24—861no—
509C24C2×D17211yescharacteristic
510#41—862no—
511#41—862no—
512#41—862no—
513#41—862no—
514#41—862no—
515#41—862no—
516#41—862no—
517#41—862no—
518#41—1721no—
519#41—1721no—
520#41—1721no—
521#41—1721no—
522#41—1721no—
523#41—1721no—
524#41—1721no—
525#41—1721no—
526C2×Q8—22no—
527C2×Q8—22no—
528C2×Q8—22no—
529C2×Q8—22no—
530C2×Q8—22no—
531C2×Q8—22no—
532C2×Q8—22no—
533C2×Q8—22no—
534C2×Q8—22no—
535C2×Q8—22no—
536C2×Q8—22no—
537C2×Q8—22no—
538C2×Q8—41no—
539C2×Q8—41no—
540C2×Q8—41no—
541C2×Q8—41no—
542C2×Q8—41no—
543C2×Q8—41no—
544C2×Q8—41no—
545C2×Q8—41no—
546C2×Q8—41no—
547C2×Q8—41no—
548C2×Q8—41no—
549C2×Q8—41no—
550C2×Q8—41no—
551C2×Q8—41no—
552C2×Q8—41no—
553C2×Q8—41no—
554C2×Q8—432no—
555C2×Q8—861no—
556C2×Q8—861no—
557C2×Q8—861no—
558C2×Q8—861no—
559C2×Q8—861no—
560C2×D4—432no—
561C2×D4—862no—
562C2×D4—862no—
563C2×D4—861no—
564C2×D4—861no—
565C2×D4—861no—
566C2×D4—861no—
567C2×D4—861no—
568C2×D4—1721no—
569C2×D4—1721no—
570C2×D4—1721no—
571C2×D4—1721no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—864no—
579C22×C4—862no—
580C22×C4—862no—
581C22×C4—861no—
582C22×C4—862no—
583C22×C4—862no—
584C22×C4—862no—
585C22×C4—1724no—
586C22×C4—1721no—
587C22×C4—1721no—
588C22×C4—1722no—
589C22×C4—1721no—
590C22×C4—1721no—
591C22×C4—1721no—
592C22×C4—1721no—
593C22×C4—1721no—
594C22×C4—1721no—
595C22×C4(C2×D43)⋊C414yes—
596C22×C4C2×C4×D4311yescharacteristic
597C22×C4#1062189811yescharacteristic
598C22×C4#1062189811yescharacteristic
599C22×C4D4×D4311yescharacteristic
600C22×C4D4×D4311yescharacteristic
601C22×C4D4×D4311yescharacteristic
602C22×C4D4×D4311yescharacteristic
603C22×C4D4×D4311yescharacteristic
604C22×C4D4×D4311yescharacteristic
605C22×C4#1062190011yescharacteristic
606C22×C4#1062190011yescharacteristic
607C22×C4C2×C22⋊D4311yescharacteristic
608C22×C4C2×C22⋊D4311yescharacteristic
609C22×C4C2×C22⋊D4311yescharacteristic
610M16—22no—
611M16—22no—
612M16—22no—
613M16—22no—
614M16—41no—
615M16—41no—
616M16—41no—
617M16—41no—
618C2×C8—22no—
619C2×C8—22no—
620C2×C8—41no—
621C2×C8—41no—
622C2×C8—41no—
623C2×C8—41no—
624C4⋊C4—434no—
625C4⋊C4—8616no—
626C4⋊C4—862no—
627C4⋊C4—862no—
628C4⋊C4—862no—
629C4⋊C4—1721no—
630C4⋊C4—1721no—
631C22⋊C4—8616no—
632C22⋊C4—862no—
633C22⋊C4—862no—
634C42—862no—
635C42—862no—
636C42—862no—
637C42—862no—
638C42—1721no—
639C42—1721no—
640C23—22no—
641C23—22no—
642C23—862no—
643C23—1721no—
644C23—1721no—
645C23—1722no—
646C23—1722no—
647C23C2×(C2×D43)⋊C411yescharacteristic
648C23#1306329511yescharacteristic
649C23#1306329511yescharacteristic
650C23#1306329511yescharacteristic
651C23#1306329911yescharacteristic
652C23#1306329911yescharacteristic
653C23#1306330911yescharacteristic
654Q8—42no—
655Q8—42no—
656Q8—42no—
657Q8—42no—
658Q8—42no—
659Q8—42no—
660Q8—42no—
661Q8—42no—
662Q8—862no—
663Q8—862no—
664Q8—1721no—
665Q8—1721no—
666D4—862no—
667D4—862no—
668D4—1722no—
669D4—1722no—
670D4—1722no—
671D4—1722no—
672D4—1721no—
673D4—1721no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—24no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—864no—
682C2×C4—864no—
683C2×C4—862no—
684C2×C4—3442no—
685C2×C4—3442no—
686C2×C4—1724no—
687C2×C4—1722no—
688C2×C4—1724no—
689C2×C4—1724no—
690C2×C4—1722no—
691C2×C4—1722no—
692C2×C4—1721no—
693C2×C4—1721no—
694C2×C4—1722no—
695C2×C4—1722no—
696C2×C4—1722no—
697C2×C4—1722no—
698C2×C4—1722no—
699C2×C4—1722no—
700C2×C4C22⋊C4×D4311yescharacteristic
701C2×C4C22⋊C4×D4311yescharacteristic
702C2×C4(C22⋊D43)⋊C411yescharacteristic
703C2×C4(C22⋊D43)⋊C411yescharacteristic
704C2×C4C4×C22⋊D4311yescharacteristic
705C2×C4C4×C22⋊D4311yescharacteristic
706C2×C4#1306329311yescharacteristic
707C2×C4#1306329311yescharacteristic
708C2×C4#1306329311yescharacteristic
709C2×C4#1306329311yescharacteristic
710C2×C4#1306329411yescharacteristic
711C2×C4#1306329611yescharacteristic
712C2×C4#1306329611yescharacteristic
713C2×C4#1306329711yescharacteristic
714C2×C4#1306329711yescharacteristic
715C2×C4#1306329711yescharacteristic
716C2×C4#1306329711yescharacteristic
717C2×C4#1306329811yescharacteristic
718C2×C4#1306329811yescharacteristic
719C2×C4#1306329811yescharacteristic
720C2×C4#1306329811yescharacteristic
721C2×C4#1306330711yescharacteristic
722C2×C4#1306330711yescharacteristic
723C2×C4#1306330811yescharacteristic
724C2×C4#1306331111yescharacteristic
725C2×C4#1306331111yescharacteristic
726C2×C4#1306332111yescharacteristic
727C2×C4#1306332111yescharacteristic
728C8—42no—
729C8—42no—
730C22—22no—
731C22—22no—
732C22—22no—
733C22—22no—
734C22—21no—
735C22—21no—
736C22—21no—
737C22—21no—
738C22—3442no—
739C22—3441no—
740C22—3441no—
741C22—1724no—
742C22—1722no—
743C22#1458275411yescharacteristic
744C22#1458277611yescharacteristic
745C22#1458277811yescharacteristic
746C22#1458280811yescharacteristic
747C22#1458280811yescharacteristic
748C22#1458281511yescharacteristic
749C22#1458281511yescharacteristic
750C22#1458307412yes—
751C22#1458308412yes—
752C4—44no—
753C4—3442no—
754C4—1724no—
755C4—1724no—
756C4—1722no—
757C4#1458277511yescharacteristic
758C4#1458277511yescharacteristic
759C4#1458279911yescharacteristic
760C4#1458279911yescharacteristic
761C4#1458280711yescharacteristic
762C4#1458280711yescharacteristic
763C4#1458281411yescharacteristic
764C4#1458281411yescharacteristic
765C2—21no—
766C2—21no—
767C2—21no—
768C2—21no—
769C2—3442no—
770C2#1913283411yescharacteristic
771C2#1913455612yes—
772C2#1913561911yescharacteristic
773C2#1913563311yescharacteristic
774C2#1913581312yes—
subgroupG/H
centerC23#13063295
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC22×#101×C43C2
socleC23×C43#120
prime radicalC22×#10621898C22
cosocleC23×C4×C43C23
hypercenterC22×#101D43
hypocenterC43#10998
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#101

Complements

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

NH ≅ G/Ntype
4. C2×#14582806C2semidirect
5. #19134315C2semidirect
6. C2×#14582660C2semidirect
7. C22×#101×C43C2semidirect
12. #14583473C4semidirect
381. C22×#101D43semidirect
425. C43#10998semidirect

Maximal subgroups

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

subgroupindex
C2×#145834732
C22×#130632512
C2×#145829012
C2×#145828062
#191343152
C2×#145826602
C22×#101×C432
#1099843