Finite Group Databasebeta

← #25003250

Subgroups — #25003250

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×#14583475C211yesmaximal, characteristic
2C22×#13063253C211yesmaximal, characteristic
3C2×#14582901C211yesmaximal, characteristic
4C22×#13063243C211yesmaximal, characteristic, complemented
5C2×#14582805C211yesmaximal, characteristic, complemented
6#19134316C211yesmaximal, characteristic, complemented
7C2×C43×#339C211yesmaximal, characteristic, complemented
8C22×#10621898C2211yescharacteristic
9C23×Dic86C2211yescharacteristic
10C22×#10621877C2211yescharacteristic
11#14583475—22no—
12#14583475—22no—
13#14583475—22no—
14#14583475C414yescomplemented
15C2×#13063325—21no—
16C2×#13063313—21no—
17C2×#13063309—22no—
18C2×#13063305—22no—
19C22×C4⋊Dic43C2211yescharacteristic
20C2×#13063253—22no—
21C2×#13063253—22no—
22C2×#13063253—22no—
23#14582901—22no—
24#14582901—22no—
25C2×#13063250—21no—
26C2×#13063247—21no—
27C2×#13063243—22no—
28C2×#13063243—22no—
29C2×#13063243—22no—
30#14582805—22no—
31#14582805—22no—
32C2×C43⋊#95—22no—
33#14582661—22no—
34C22×M16×C43C2211yescharacteristic
35C2×#117×C43C2211yescharacteristic
36C22×C42×C43C2211yescharacteristic
37C43×#339—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×Dic86—21no—
51C22×Dic86—21no—
52C22×Dic86—21no—
53C22×Dic86—21no—
54C22×Dic86—21no—
55C22×Dic86—21no—
56C22×Dic86—21no—
57C22×Dic86—21no—
58C22×Dic86—21no—
59C22×Dic86—21no—
60C22×Dic86—21no—
61C22×Dic86—21no—
62C22×Dic86C2×C412yes—
63C22×Dic86D412yes—
64C22×Dic86D411yescharacteristic
65C22×D172D411yescharacteristic
66C22×C22⋊D43—21no—
67C23×Dic43—21no—
68C23×Dic43D412yes—
69C22×C4×D43—21no—
70C2×#10621877—21no—
71C2×#10621877—21no—
72C2×#10621877—21no—
73C2×#10621877—21no—
74C2×#10621877—21no—
75C2×#10621877D412yes—
76C22×C43⋊C8—21no—
77#13063325—24no—
78#13063325—24no—
79#13063313—24no—
80#13063313—24no—
81#13063309—28no—
82#13063309—28no—
83#13063305—28no—
84#13063305—28no—
85C2×C4⋊Dic43—24no—
86C2×C4⋊Dic43—21no—
87C2×C4⋊Dic43—21no—
88C2×C4⋊Dic43—21no—
89C2×C4⋊Dic43—21no—
90C2×C4⋊Dic43—21no—
91C2×C4⋊Dic43D412yes—
92C2×(C2×D43)⋊C4—24no—
93#13063253—28no—
94#13063250—24no—
95#13063247—24no—
96#13063243—28no—
97C43⋊#95—28no—
98C23×C4×C43—21no—
99C23×C4×C43C2311yescharacteristic
100C2×M16×C43—21no—
101C2×M16×C43—21no—
102C2×M16×C43—21no—
103C2×M16×C43—21no—
104C2×M16×C43—21no—
105C2×M16×C43D412yes—
106C22×C8×C43—21no—
107#117×C43—21no—
108#117×C43—21no—
109#117×C43C2×C412yes—
110#117×C43D412yes—
111C2×C4⋊C4×C43D412yes—
112C2×C22⋊C4×C43—21no—
113C2×C42×C43—21no—
114C2×C42×C43—21no—
115C2×C42×C43—21no—
116C2×C42×C43—21no—
117C2×C42×C43—21no—
118C2×C42×C43—21no—
119C2×C42×C43D412yes—
120C24×C43C2×D411yescharacteristic
121C23×D43—21no—
122C22×C4×C43—24no—
123C22×C4×C43—22no—
124C22×C4×C43—22no—
125C22×C4×C43—42no—
126C22×C4×C43—41no—
127C22×C4×C43—41no—
128C22×C4×C43C22×C411yescharacteristic
129C22×C4×C43C2×D411yescharacteristic
130C22×C4×C43C2×D411yescharacteristic
131C22×C4×C43C2×D411yescharacteristic
132C22×C4×C43C2×D411yescharacteristic
133C22×C4×C43C2×D411yescharacteristic
134C22×C4×C43C2×D411yescharacteristic
135C22×C4×C43C2×D411yescharacteristic
136C22×C4×C43C2×D411yescharacteristic
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43#4111yescharacteristic
139C22×C4×C43#4111yescharacteristic
140C22×C4×C43#4111yescharacteristic
141C22×C4×C43#4111yescharacteristic
142C2×C22⋊D43—22no—
143C2×C22⋊D43—22no—
144C2×C22⋊D43—41no—
145C2×C22⋊D43—41no—
146C2×C22⋊D43—41no—
147C2×C22⋊D43—41no—
148C22×Dic43—22no—
149C22×Dic43—22no—
150C22×Dic43—21no—
151C22×Dic43—22no—
152C22×Dic43—22no—
153C22×Dic43—22no—
154C22×Dic43—22no—
155C22×Dic43—22no—
156C22×Dic43—44no—
157C22×Dic43—41no—
158C22×Dic43—41no—
159C22×Dic43C22⋊C414yes—
160#10621898—22no—
161#10621898—22no—
162#10621898—22no—
163#10621898—22no—
164#10621898—22no—
165#10621898—22no—
166#10621898—22no—
167#10621898—22no—
168#10621898—41no—
169#10621898—41no—
170#10621898—41no—
171#10621898—41no—
172#10621898—41no—
173#10621898—41no—
174#10621898—41no—
175#10621898—41no—
176C2×D172—21no—
177C2×D172—21no—
178C2×D172—21no—
179C2×D172—21no—
180C2×D172—21no—
181C2×D172C22⋊C412yes—
182C2×C4×D43—22no—
183C2×C4×D43—22no—
184C2×C4×D43—41no—
185C2×C4×D43—41no—
186C2×C4×D43—41no—
187C2×C4×D43—41no—
188C2×Dic86—21no—
189C2×Dic86—21no—
190C2×Dic86—21no—
191C2×Dic86—21no—
192C2×Dic86—22no—
193C2×Dic86—22no—
194C2×Dic86—22no—
195C2×Dic86—22no—
196C2×Dic86—22no—
197C2×Dic86—22no—
198C2×Dic86—22no—
199C2×Dic86—22no—
200C2×Dic86—22no—
201C2×Dic86—21no—
202C2×Dic86—22no—
203C2×Dic86—22no—
204C2×Dic86—22no—
205C2×Dic86—41no—
206C2×Dic86—41no—
207C2×Dic86—41no—
208C2×Dic86—41no—
209C2×Dic86—41no—
210C2×Dic86—41no—
211C2×Dic86—41no—
212C2×Dic86—41no—
213C2×Dic86—41no—
214C2×Dic86—41no—
215C2×Dic86—41no—
216C2×Dic86—41no—
217C2×Dic86—41no—
218C2×Dic86—41no—
219C2×Dic86—41no—
220C2×Dic86—41no—
221C2×Dic86C22⋊C412yes—
222M16×C43—22no—
223M16×C43—22no—
224M16×C43—41no—
225M16×C43—41no—
226C2×C8×C43—22no—
227C2×C8×C43—41no—
228C2×C8×C43—41no—
229C4⋊C4×C43—22no—
230C4⋊C4×C43C22⋊C414yes—
231C22⋊C4×C43—22no—
232C22⋊C4×C43—22no—
233C42×C43—22no—
234C42×C43—22no—
235C42×C43—22no—
236C42×C43—22no—
237C42×C43—41no—
238C42×C43—41no—
239(C2×D43)⋊C4—216no—
240C4⋊Dic43—216no—
241C4⋊Dic43—22no—
242C4⋊Dic43—22no—
243C4⋊Dic43—41no—
244C4⋊Dic43—41no—
245#10621877—22no—
246#10621877—22no—
247#10621877—41no—
248#10621877—41no—
249C2×C43⋊C8—22no—
250C2×C43⋊C8—41no—
251C2×C43⋊C8—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—
266C2×C4×C43—24no—
267C2×C4×C43—24no—
268C2×C4×C43—44no—
269C2×C4×C43—42no—
270C2×C4×C43—44no—
271C2×C4×C43—42no—
272C2×C4×C43—42no—
273C2×C4×C43—42no—
274C2×C4×C43C2×C22⋊C411yescharacteristic
275C2×C4×C43C2×C22⋊C411yescharacteristic
276C2×C4×C43C4×D411yescharacteristic
277C2×C4×C43C4×D411yescharacteristic
278C2×C4×C43C4×D411yescharacteristic
279C2×C4×C43C4×D411yescharacteristic
280C2×C4×C43#12011yescharacteristic
281C2×C4×C43#12011yescharacteristic
282C2×C4×C43#12011yescharacteristic
283C2×C4×C43#12011yescharacteristic
284C2×C4×C43#12011yescharacteristic
285C2×C4×C43#12111yescharacteristic
286C2×C4×C43#12111yescharacteristic
287C2×C4×C43#12111yescharacteristic
288C2×C4×C43#12111yescharacteristic
289C2×C4×C43#12111yescharacteristic
290C2×C4×C43#12111yescharacteristic
291C2×C4×C43#12111yescharacteristic
292C2×C4×C43#12111yescharacteristic
293C2×C4×C43#12111yescharacteristic
294C2×C4×C43#12111yescharacteristic
295C2×C4×C43#12311yescharacteristic
296C2×C4×C43#12311yescharacteristic
297C2×C4×C43#12311yescharacteristic
298C2×C4×C43#12411yescharacteristic
299C2×C4×C43#12411yescharacteristic
300C2×C4×C43#12711yescharacteristic
301C2×C4×C43#12711yescharacteristic
302C22⋊D43—42no—
303C22⋊D43—42no—
304C22⋊D43—42no—
305C22⋊D43—42no—
306C2×Dic43—22no—
307C2×Dic43—24no—
308C2×Dic43—24no—
309C2×Dic43—24no—
310C2×Dic43—41no—
311C2×Dic43—42no—
312C2×Dic43—42no—
313C2×Dic43—41no—
314C2×Dic43—42no—
315C2×Dic43—42no—
316C2×Dic43—44no—
317C2×Dic43—42no—
318C2×Dic43—82no—
319C2×Dic43—82no—
320D172—22no—
321D172—22no—
322D172—41no—
323D172—41no—
324C4×D43—42no—
325C4×D43—42no—
326C4×D43—42no—
327C4×D43—42no—
328Dic86—22no—
329Dic86—22no—
330Dic86—42no—
331Dic86—42no—
332Dic86—42no—
333Dic86—42no—
334Dic86—42no—
335Dic86—42no—
336Dic86—41no—
337Dic86—42no—
338Dic86—42no—
339Dic86—41no—
340C8×C43—42no—
341C43⋊C8—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—44no—
367C4×C43#38611yescharacteristic
368C4×C43#38611yescharacteristic
369C4×C43#39011yescharacteristic
370C4×C43#39011yescharacteristic
371C4×C43#39211yescharacteristic
372C4×C43#39211yescharacteristic
373C4×C43#39411yescharacteristic
374C4×C43#39411yescharacteristic
375Dic43—42no—
376Dic43—44no—
377Dic43—82no—
378C2×#536—431no—
379C22×#104—431no—
380C2×#417—431no—
381C22×#101—431no—
382C2×#391—431no—
383#1736—431no—
384C2×#339D4311yescharacteristic, complemented
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×Q8—431no—
397C22×M16—431no—
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×#117C2×D4311yescharacteristic
408C22×C4⋊C4—431no—
409C22×C42C2×D4311yescharacteristic
410C2×#104—862no—
411C2×#104—862no—
412C2×#104—862no—
413#417—862no—
414#417—862no—
415C2×#103—861no—
416C2×#102—861no—
417C2×#101—862no—
418C2×#101—862no—
419C2×#101—862no—
420#391—862no—
421#391—862no—
422C2×#95—862no—
423#340—862no—
424#339—22no—
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—432no—
439C22×Q8—432no—
440C22×Q8—431no—
441C22×Q8—861no—
442C22×Q8—861no—
443C22×Q8—861no—
444C22×Q8—861no—
445C22×Q8—861no—
446C22×Q8—861no—
447C22×Q8—861no—
448C22×Q8—861no—
449C22×Q8—861no—
450C22×Q8—861no—
451C22×Q8—861no—
452C22×Q8—861no—
453C22×D4—431no—
454C22×D4—861no—
455C23×C4—21no—
456C23×C4—432no—
457C23×C4—861no—
458C23×C4—861no—
459C23×C4C22×D4311yescharacteristic
460C2×M16—21no—
461C2×M16—21no—
462C2×M16—21no—
463C2×M16—21no—
464C2×M16—21no—
465C2×M16—432no—
466C2×M16—861no—
467C2×M16—861no—
468C2×M16—861no—
469C2×M16—861no—
470C2×M16—861no—
471C2×M16D17212yes—
472C22×C8—21no—
473C22×C8—861no—
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—21no—
483#117—21no—
484#117C4×D4312yes—
485#117C22⋊D4312yes—
486C2×C4⋊C4—432no—
487C2×C4⋊C4—864no—
488C2×C4⋊C4—861no—
489C2×C4⋊C4—861no—
490C2×C4⋊C4—861no—
491C2×C4⋊C4—861no—
492C2×C4⋊C4—861no—
493C2×C4⋊C4D17212yes—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—864no—
496C2×C42—21no—
497C2×C42—21no—
498C2×C42—21no—
499C2×C42—21no—
500C2×C42—21no—
501C2×C42—21no—
502C2×C42D17212yes—
503#104—868no—
504#103—864no—
505#102—864no—
506#101—868no—
507#95—868no—
508C24—861no—
509C24D4×D4311yescharacteristic
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—432no—
527C2×Q8—862no—
528C2×Q8—862no—
529C2×Q8—862no—
530C2×Q8—862no—
531C2×Q8—862no—
532C2×Q8—862no—
533C2×Q8—862no—
534C2×Q8—861no—
535C2×Q8—862no—
536C2×Q8—862no—
537C2×Q8—862no—
538C2×Q8—862no—
539C2×Q8—862no—
540C2×Q8—861no—
541C2×Q8—861no—
542C2×Q8—861no—
543C2×Q8—861no—
544C2×Q8—1721no—
545C2×Q8—1721no—
546C2×Q8—1721no—
547C2×Q8—1721no—
548C2×Q8—1721no—
549C2×Q8—1721no—
550C2×Q8—1721no—
551C2×Q8—1721no—
552C2×Q8—1721no—
553C2×Q8—1721no—
554C2×Q8—1721no—
555C2×Q8—1721no—
556C2×Q8—1721no—
557C2×Q8—1721no—
558C2×Q8—1721no—
559C2×Q8—1721no—
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—24no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—42no—
576C22×C4—41no—
577C22×C4—41no—
578C22×C4—434no—
579C22×C4—862no—
580C22×C4—862no—
581C22×C4—862no—
582C22×C4—861no—
583C22×C4—862no—
584C22×C4—862no—
585C22×C4—862no—
586C22×C4—862no—
587C22×C4—862no—
588C22×C4—862no—
589C22×C4—1724no—
590C22×C4—1721no—
591C22×C4—1721no—
592C22×C4—1721no—
593C22×C4—1721no—
594C22×C4—1721no—
595C22×C4—1721no—
596C22×C4C2×C4×D4311yescharacteristic
597C22×C4C2×D17211yescharacteristic
598C22×C4C2×D17211yescharacteristic
599C22×C4C2×D17211yescharacteristic
600C22×C4#1062189811yescharacteristic
601C22×C4#1062189811yescharacteristic
602C22×C4D4×D4311yescharacteristic
603C22×C4D4×D4311yescharacteristic
604C22×C4D4×D4311yescharacteristic
605C22×C4D4×D4311yescharacteristic
606C22×C4D4×D4311yescharacteristic
607C22×C4#1062190211yescharacteristic
608C22×C4#1062190211yescharacteristic
609C22×C4C2×C22⋊D4311yescharacteristic
610M16—22no—
611M16—22no—
612M16—41no—
613M16—41no—
614M16—862no—
615M16—862no—
616M16—1721no—
617M16—1721no—
618C2×C8—22no—
619C2×C8—41no—
620C2×C8—41no—
621C2×C8—862no—
622C2×C8—1721no—
623C2×C8—1721no—
624C4⋊C4—22no—
625C4⋊C4—8616no—
626C4⋊C4—862no—
627C4⋊C4—862no—
628C4⋊C4—1721no—
629C4⋊C4—1721no—
630C4⋊C4(C2×D43)⋊C414yes—
631C22⋊C4—22no—
632C22⋊C4—22no—
633C22⋊C4—8616no—
634C42—22no—
635C42—22no—
636C42—22no—
637C42—22no—
638C42—41no—
639C42—41no—
640C23—22no—
641C23—22no—
642C23—862no—
643C23—1721no—
644C23—1721no—
645C23—1722no—
646C23—1722no—
647C23C22⋊C4×D4311yescharacteristic
648C23#1306329311yescharacteristic
649C23#1306329511yescharacteristic
650C23#1306329511yescharacteristic
651C23#1306329811yescharacteristic
652C23#1306330011yescharacteristic
653C23#1306331011yescharacteristic
654Q8—862no—
655Q8—862no—
656Q8—1722no—
657Q8—1722no—
658Q8—1722no—
659Q8—1721no—
660Q8—1722no—
661Q8—1722no—
662Q8—1721no—
663Q8—1722no—
664Q8—1722no—
665Q8—1722no—
666D4—862no—
667D4—862no—
668D4—1722no—
669D4—1722no—
670D4—1722no—
671D4—1722no—
672D4—1721no—
673D4—1721no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—44no—
677C2×C4—44no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—864no—
683C2×C4—862no—
684C2×C4—864no—
685C2×C4—864no—
686C2×C4—3442no—
687C2×C4—3442no—
688C2×C4—1724no—
689C2×C4—1722no—
690C2×C4—1722no—
691C2×C4—1722no—
692C2×C4—1721no—
693C2×C4—1722no—
694C2×C4—1722no—
695C2×C4—1721no—
696C2×C4—1722no—
697C2×C4—1722no—
698C2×C4—1722no—
699C2×C4—1722no—
700C2×C4C22⋊C4×D4311yescharacteristic
701C2×C4C2×(C2×D43)⋊C411yescharacteristic
702C2×C4#1306328711yescharacteristic
703C2×C4#1306328711yescharacteristic
704C2×C4C4×D17211yescharacteristic
705C2×C4C4×D17211yescharacteristic
706C2×C4#1306329311yescharacteristic
707C2×C4#1306329511yescharacteristic
708C2×C4#1306329511yescharacteristic
709C2×C4#1306329511yescharacteristic
710C2×C4#1306329511yescharacteristic
711C2×C4#1306329811yescharacteristic
712C2×C4#1306329811yescharacteristic
713C2×C4#1306329811yescharacteristic
714C2×C4#1306329911yescharacteristic
715C2×C4#1306329911yescharacteristic
716C2×C4#1306330011yescharacteristic
717C2×C4#1306330011yescharacteristic
718C2×C4#1306330011yescharacteristic
719C2×C4#1306330011yescharacteristic
720C2×C4#1306330011yescharacteristic
721C2×C4#1306331011yescharacteristic
722C2×C4#1306331011yescharacteristic
723C2×C4#1306331011yescharacteristic
724C2×C4#1306331311yescharacteristic
725C2×C4#1306331411yescharacteristic
726C2×C4#1306332111yescharacteristic
727C2×C4#1306332211yescharacteristic
728C8—42no—
729C8—1722no—
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#1458277711yescharacteristic
745C22#1458277711yescharacteristic
746C22#1458280811yescharacteristic
747C22#1458280911yescharacteristic
748C22#1458281611yescharacteristic
749C22#1458281711yescharacteristic
750C22#1458307312yes—
751C22#1458308312yes—
752C4—44no—
753C4—44no—
754C4—3442no—
755C4—1724no—
756C4—1722no—
757C4#1458277711yescharacteristic
758C4#1458277711yescharacteristic
759C4#1458280011yescharacteristic
760C4#1458280111yescharacteristic
761C4#1458280811yescharacteristic
762C4#1458280911yescharacteristic
763C4#1458281611yescharacteristic
764C4#1458281711yescharacteristic
765C2—21no—
766C2—21no—
767C2—21no—
768C2—21no—
769C2—3442no—
770C2#1913283511yescharacteristic
771C2#1913455512yes—
772C2#1913562011yescharacteristic
773C2#1913563411yescharacteristic
774C2#1913581512yes—
subgroupG/H
centerC23#13063295
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC2×C43×#339C2
socleC23×C43#120
prime radicalC22×#10621898C22
cosocleC23×C4×C43C23
hypercenterC2×#339D43
hypocenterC43#10998
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#339

Complements

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

NH ≅ G/Ntype
4. C22×#13063243C2semidirect
5. C2×#14582805C2semidirect
6. #19134316C2semidirect
7. C2×C43×#339C2semidirect
14. #14583475C4semidirect
384. C2×#339D43semidirect
425. C43#10998semidirect

Maximal subgroups

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

subgroupindex
C2×#145834752
C22×#130632532
C2×#145829012
C22×#130632432
C2×#145828052
#191343162
C2×C43×#3392
#1099843