Finite Group Databasebeta

← #25003380

Subgroups — #25003380

Order 11008.

1406 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063350C211yesmaximal, characteristic
2C2×#14582900C211yesmaximal, characteristic, complemented
3C22×#13063247C211yesmaximal, characteristic, complemented
4C22×#13063241C211yesmaximal, characteristic, complemented
5C2×#14582667C211yesmaximal, characteristic, complemented
6C2×#14582664C211yesmaximal, characteristic, complemented
7C2×C43×#408C211yesmaximal, characteristic, complemented
8C23×D172C2211yescharacteristic
9C2×#13063350—22no—
10C2×#13063350—22no—
11C2×#13063350—22no—
12C2×#13063350—22no—
13C2×#13063350—22no—
14C2×#13063350C414yescomplemented
15C22×#10621884—21no—
16C22×#10621882—21no—
17C22×#10621877C2211yescharacteristic
18C22×#10621877C2211yescharacteristic
19C22×C4⋊Dic43C2211yescharacteristic
20#14582900—22no—
21#14582900—22no—
22C2×#13063249—21no—
23C2×#13063247—22no—
24C2×#13063247—22no—
25C2×#13063247—22no—
26C2×#13063246—21no—
27C2×#13063241—22no—
28C2×#13063241—22no—
29C2×#13063241—22no—
30#14582667—22no—
31#14582664—22no—
32C22×#41×C43C2211yescharacteristic
33C22×M16×C43C2211yescharacteristic
34C23×C8×C43C2211yescharacteristic
35C43×#408—22no—
36C43×#408—22no—
37C2×C22⋊C8×C43—22no—
38C24×D43—21no—
39C22×D172—21no—
40C22×D172—21no—
41C22×D172—21no—
42C22×D172—21no—
43C22×D172—21no—
44C22×D172—21no—
45C22×D172—21no—
46C22×D172—21no—
47C22×D172—21no—
48C22×D172—21no—
49C22×D172—21no—
50C22×D172C2×C412yes—
51C22×D172D412yes—
52C22×D172D412yes—
53C23×Dic43—21no—
54#13063350—28no—
55#13063350—28no—
56#13063350—28no—
57#13063350—28no—
58C2×#10621884—24no—
59C2×#10621884—24no—
60C2×#10621884—24no—
61C2×#10621882—24no—
62C2×#10621882—24no—
63C2×#10621882—24no—
64C2×#10621877—21no—
65C2×#10621877—21no—
66C2×#10621877—21no—
67C2×#10621877—21no—
68C2×#10621877—21no—
69C2×#10621877—21no—
70C2×#10621877—21no—
71C2×#10621877—21no—
72C2×#10621877C2×C412yes—
73C2×#10621877D412yes—
74C2×#10621877D412yes—
75C2×#10621877D412yes—
76C22×C43⋊C8—21no—
77C22×C43⋊C8—21no—
78C2×C4⋊Dic43—21no—
79C2×C4⋊Dic43—21no—
80C2×C4⋊Dic43—21no—
81C2×C4⋊Dic43—21no—
82C2×C4⋊Dic43—21no—
83C2×C4⋊Dic43D412yes—
84#13063249—24no—
85#13063247—28no—
86#13063246—24no—
87#13063241—28no—
88C2×#41×C43—21no—
89C2×#41×C43—21no—
90C2×#41×C43—21no—
91C2×#41×C43—21no—
92C2×#41×C43—21no—
93C2×#41×C43—21no—
94C2×#41×C43—21no—
95C2×#41×C43—21no—
96C2×#41×C43—21no—
97C2×#41×C43—21no—
98C2×#41×C43C2×C412yes—
99C2×#41×C43D412yes—
100C22×Q8×C43D411yescharacteristic
101C22×D4×C43—21no—
102C22×D4×C43D411yescharacteristic
103C23×C4×C43—21no—
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×C43D412yes—
111C22×C8×C43—21no—
112C22×C8×C43—21no—
113C22×C8×C43—21no—
114C22×C8×C43—21no—
115C22×C8×C43—21no—
116C22×C8×C43—21no—
117C22×C8×C43—21no—
118C22×C8×C43D412yes—
119C22⋊C8×C43—28no—
120C24×C43—21no—
121C24×C43#4111yescharacteristic
122C23×D43—22no—
123C23×D43—22no—
124C23×D43—22no—
125C23×D43—41no—
126C23×D43—41no—
127C23×D43—41no—
128C23×D43—41no—
129C23×D43—82no—
130C23×D43—82no—
131#41×C43—22no—
132#41×C43—22no—
133#41×C43—22no—
134#41×C43—22no—
135#41×C43—22no—
136#41×C43—22no—
137#41×C43—22no—
138#41×C43—22no—
139#41×C43—41no—
140#41×C43—41no—
141#41×C43—41no—
142#41×C43—41no—
143#41×C43—41no—
144#41×C43—41no—
145#41×C43—41no—
146#41×C43—41no—
147C2×Q8×C43—21no—
148C2×Q8×C43—21no—
149C2×Q8×C43—21no—
150C2×Q8×C43—21no—
151C2×Q8×C43—21no—
152C2×Q8×C43C22⋊C412yes—
153C2×D4×C43—21no—
154C2×D4×C43—22no—
155C2×D4×C43—22no—
156C2×D4×C43—21no—
157C2×D4×C43—21no—
158C2×D4×C43—21no—
159C2×D4×C43—21no—
160C2×D4×C43—41no—
161C2×D4×C43—41no—
162C2×D4×C43—41no—
163C2×D4×C43—41no—
164C2×D4×C43C22⋊C412yes—
165C22×C4×C43—22no—
166C22×C4×C43—22no—
167C22×C4×C43—21no—
168C22×C4×C43—41no—
169C22×C4×C43—41no—
170C22×C4×C43—41no—
171C22×C4×C43—41no—
172C22×C4×C43C22×C411yescharacteristic
173C22×C4×C43C2×D411yescharacteristic
174C22×C4×C43C2×D411yescharacteristic
175C22×C4×C43C2×D411yescharacteristic
176C22×C4×C43C2×D411yescharacteristic
177C22×C4×C43C2×D411yescharacteristic
178C22×C4×C43C2×D411yescharacteristic
179C22×C4×C43C2×D411yescharacteristic
180C22×C4×C43C2×D411yescharacteristic
181C22×C4×C43C2×D411yescharacteristic
182C22×C4×C43C2×D411yescharacteristic
183C22×C4×C43#4111yescharacteristic
184C22×C4×C43#4111yescharacteristic
185C22×C4×C43#4111yescharacteristic
186C22×Dic43—22no—
187C22×Dic43—41no—
188C22×Dic43—41no—
189C22×Dic43—82no—
190C2×D172—22no—
191C2×D172—22no—
192C2×D172—22no—
193C2×D172—22no—
194C2×D172—22no—
195C2×D172—22no—
196C2×D172—22no—
197C2×D172—22no—
198C2×D172—22no—
199C2×D172—22no—
200C2×D172—22no—
201C2×D172—22no—
202C2×D172—22no—
203C2×D172—22no—
204C2×D172—22no—
205C2×D172—41no—
206C2×D172—41no—
207C2×D172—41no—
208C2×D172—41no—
209C2×D172—41no—
210C2×D172—41no—
211C2×D172—41no—
212C2×D172—41no—
213C2×D172—41no—
214C2×D172—41no—
215C2×D172—41no—
216C2×D172—41no—
217C2×D172C22⋊C414yes—
218M16×C43—22no—
219M16×C43—22no—
220M16×C43—41no—
221M16×C43—41no—
222C2×C8×C43—22no—
223C2×C8×C43—22no—
224C2×C8×C43—22no—
225C2×C8×C43—22no—
226C2×C8×C43—41no—
227C2×C8×C43—41no—
228C2×C8×C43—41no—
229C2×C8×C43—41no—
230C2×C8×C43—41no—
231C2×C8×C43—41no—
232#10621884—216no—
233#10621882—216no—
234C4⋊Dic43—22no—
235C4⋊Dic43—22no—
236C4⋊Dic43—41no—
237C4⋊Dic43—41no—
238#10621877—22no—
239#10621877—22no—
240#10621877—22no—
241#10621877—22no—
242#10621877—22no—
243#10621877—41no—
244#10621877—41no—
245#10621877C22⋊C414yes—
246C2×C43⋊C8—22no—
247C2×C43⋊C8—22no—
248C2×C43⋊C8—22no—
249C2×C43⋊C8—22no—
250C2×C43⋊C8—41no—
251C2×C43⋊C8—41no—
252C23×C43—22no—
253C23×C43—22no—
254C23×C43—22no—
255C23×C43—41no—
256C23×C43—41no—
257C23×C43—42no—
258C23×C43—42no—
259C23×C43C4×D411yescharacteristic
260C23×C43#12111yescharacteristic
261C23×C43#12111yescharacteristic
262C23×C43#12111yescharacteristic
263C23×C43#12311yescharacteristic
264C23×C43#12311yescharacteristic
265C23×C43#12411yescharacteristic
266C22×D43—24no—
267C22×D43—42no—
268C22×D43—42no—
269C22×D43—42no—
270C22×D43—42no—
271C22×D43—42no—
272C22×D43—42no—
273C22×D43—84no—
274C22×D43—84no—
275C22×D43—82no—
276C22×D43—82no—
277C22×D43—82no—
278C22×D43—82no—
279C22×D43—84no—
280C22×D43—84no—
281C22×D43—82no—
282C22×D43—82no—
283Q8×C43—22no—
284Q8×C43—22no—
285Q8×C43—41no—
286Q8×C43—41no—
287D4×C43—22no—
288D4×C43—22no—
289D4×C43—42no—
290D4×C43—42no—
291D4×C43—42no—
292D4×C43—42no—
293D4×C43—41no—
294D4×C43—41no—
295C2×C4×C43—22no—
296C2×C4×C43—41no—
297C2×C4×C43—41no—
298C2×C4×C43—42no—
299C2×C4×C43—42no—
300C2×C4×C43—42no—
301C2×C4×C43—42no—
302C2×C4×C43C2×C22⋊C411yescharacteristic
303C2×C4×C43C2×C22⋊C411yescharacteristic
304C2×C4×C43C2×C22⋊C411yescharacteristic
305C2×C4×C43C4×D411yescharacteristic
306C2×C4×C43C4×D411yescharacteristic
307C2×C4×C43C4×D411yescharacteristic
308C2×C4×C43#12011yescharacteristic
309C2×C4×C43#12011yescharacteristic
310C2×C4×C43#12011yescharacteristic
311C2×C4×C43#12011yescharacteristic
312C2×C4×C43#12011yescharacteristic
313C2×C4×C43#12011yescharacteristic
314C2×C4×C43#12011yescharacteristic
315C2×C4×C43#12011yescharacteristic
316C2×C4×C43#12111yescharacteristic
317C2×C4×C43#12111yescharacteristic
318C2×C4×C43#12111yescharacteristic
319C2×C4×C43#12111yescharacteristic
320C2×C4×C43#12111yescharacteristic
321C2×C4×C43#12111yescharacteristic
322C2×C4×C43#12111yescharacteristic
323C2×C4×C43#12111yescharacteristic
324C2×C4×C43#12111yescharacteristic
325C2×C4×C43#12311yescharacteristic
326C2×C4×C43#12311yescharacteristic
327C2×C4×C43#12411yescharacteristic
328C2×C4×C43#12711yescharacteristic
329C2×C4×C43#12711yescharacteristic
330C2×Dic43—42no—
331C2×Dic43—82no—
332C2×Dic43—82no—
333C2×Dic43—82no—
334D172—24no—
335D172—24no—
336D172—42no—
337D172—42no—
338D172—42no—
339D172—42no—
340D172—42no—
341D172—42no—
342C8×C43—42no—
343C8×C43—42no—
344C43⋊C8—24no—
345C43⋊C8—42no—
346#11020—431nomaximal, Sylow
347C22×C43—22no—
348C22×C43—22no—
349C22×C43—22no—
350C22×C43—22no—
351C22×C43—21no—
352C22×C43—21no—
353C22×C43—21no—
354C22×C43—21no—
355C22×C43—44no—
356C22×C43—42no—
357C22×C43—82no—
358C22×C43—81no—
359C22×C43—81no—
360C22×C43#38611yescharacteristic
361C22×C43#38611yescharacteristic
362C22×C43#39011yescharacteristic
363C22×C43#39211yescharacteristic
364C22×C43#39411yescharacteristic
365C22×C43#39411yescharacteristic
366C22×C43#39411yescharacteristic
367C22×C43#47112yes—
368C22×C43#47212yes—
369C2×D43—44no—
370C2×D43—84no—
371C2×D43—84no—
372C2×D43—84no—
373C2×D43—84no—
374C2×D43—84no—
375C2×D43—82no—
376C2×D43—82no—
377C2×D43—84no—
378C4×C43—42no—
379C4×C43#37911yescharacteristic
380C4×C43#38611yescharacteristic
381C4×C43#38611yescharacteristic
382C4×C43#39011yescharacteristic
383C4×C43#39211yescharacteristic
384C4×C43#39211yescharacteristic
385C4×C43#39211yescharacteristic
386C4×C43#39411yescharacteristic
387Dic43—82no—
388C22×AGL(1,ℤ/8)—431no—
389C2×#417—431no—
390C22×#102—431no—
391C22×#100—431no—
392C2×#408D4311yescharacteristic, complemented
393C2×#343—431no—
394C2×#341—431no—
395C2×C43—21no—
396C2×C43—21no—
397C2×C43—21no—
398C2×C43—21no—
399C2×C43—82no—
400C2×C43#143811yescharacteristic
401C2×C43#190712yes—
402C2×C43#201811yescharacteristic
403C2×C43#201911yescharacteristic
404C2×C43#205112yes—
405D43—84no—
406C22×#41C2×D4311yescharacteristic
407C23×D4—431no—
408C2×AGL(1,ℤ/8)—434no—
409C2×AGL(1,ℤ/8)—862no—
410C2×AGL(1,ℤ/8)—862no—
411C2×AGL(1,ℤ/8)—862no—
412C2×AGL(1,ℤ/8)—862no—
413C2×AGL(1,ℤ/8)—862no—
414C22×SD16—861no—
415C22×D8—861no—
416C22×M16—431no—
417C22×M16—431no—
418C22×M16C2×D4311yescharacteristic
419C23×C8C2×D4311yescharacteristic
420C22×C4⋊C4—431no—
421#417—862no—
422#417—862no—
423C2×#103—861no—
424C2×#102—862no—
425C2×#102—862no—
426C2×#102—861no—
427C2×#102—862no—
428C2×#100—862no—
429C2×#100—862no—
430C2×#100—862no—
431#408—22no—
432#408—22no—
433C2×C22⋊C8—22no—
434#343—862no—
435#341—862no—
436C43#1102011yescharacteristic, complemented, Sylow
437C25—861no—
438C2×#41—21no—
439C2×#41—21no—
440C2×#41—21no—
441C2×#41—21no—
442C2×#41—21no—
443C2×#41—21no—
444C2×#41—21no—
445C2×#41—21no—
446C2×#41—21no—
447C2×#41—21no—
448C2×#41C4×D4312yes—
449C2×#41C22⋊D4312yes—
450C22×Q8D17211yescharacteristic
451C22×D4—21no—
452C22×D4—432no—
453C22×D4—432no—
454C22×D4—432no—
455C22×D4—861no—
456C22×D4—861no—
457C22×D4—861no—
458C22×D4—861no—
459C22×D4—861no—
460C22×D4—861no—
461C22×D4—861no—
462C22×D4—861no—
463C22×D4—861no—
464C22×D4—861no—
465C22×D4—861no—
466C22×D4D17211yescharacteristic
467C23×C4—21no—
468C23×C4—861no—
469C23×C4C22×D4311yescharacteristic
470AGL(1,ℤ/8)—868no—
471AGL(1,ℤ/8)—868no—
472AGL(1,ℤ/8)—868no—
473AGL(1,ℤ/8)—868no—
474C2×SD16—864no—
475C2×SD16—864no—
476C2×SD16—864no—
477C2×D8—864no—
478C2×D8—864no—
479C2×D8—864no—
480C2×M16—21no—
481C2×M16—21no—
482C2×M16—21no—
483C2×M16—21no—
484C2×M16—21no—
485C2×M16—432no—
486C2×M16—432no—
487C2×M16—432no—
488C2×M16—432no—
489C2×M16—861no—
490C2×M16—861no—
491C2×M16—861no—
492C2×M16—861no—
493C2×M16—861no—
494C2×M16—861no—
495C2×M16—861no—
496C2×M16—861no—
497C2×M16C22⋊D4312yes—
498C22×C8—21no—
499C22×C8—21no—
500C22×C8—21no—
501C22×C8—21no—
502C22×C8—21no—
503C22×C8—21no—
504C22×C8—21no—
505C22×C8—861no—
506C22×C8—861no—
507C22×C8C22⋊D4312yes—
508C2×C4⋊C4—432no—
509C2×C4⋊C4—861no—
510C2×C4⋊C4—861no—
511C2×C4⋊C4—861no—
512C2×C4⋊C4—861no—
513C2×C4⋊C4—861no—
514#103—864no—
515#102—868no—
516#102—864no—
517#100—868no—
518C22⋊C8—28no—
519C24—21no—
520C24—862no—
521C24—862no—
522C24—862no—
523C24—3442no—
524C24—3442no—
525C24—1721no—
526C24—1721no—
527C24—1721no—
528C24—1721no—
529C24#1062189811yescharacteristic
530#41—22no—
531#41—22no—
532#41—22no—
533#41—22no—
534#41—22no—
535#41—22no—
536#41—22no—
537#41—22no—
538#41—41no—
539#41—41no—
540#41—41no—
541#41—41no—
542#41—41no—
543#41—41no—
544#41—41no—
545#41—41no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8(C2×D43)⋊C412yes—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—41no—
560C2×D4—41no—
561C2×D4—41no—
562C2×D4—41no—
563C2×D4—434no—
564C2×D4—862no—
565C2×D4—862no—
566C2×D4—862no—
567C2×D4—862no—
568C2×D4—862no—
569C2×D4—862no—
570C2×D4—862no—
571C2×D4—862no—
572C2×D4—862no—
573C2×D4—862no—
574C2×D4—862no—
575C2×D4—862no—
576C2×D4—862no—
577C2×D4—862no—
578C2×D4—862no—
579C2×D4—1721no—
580C2×D4—1721no—
581C2×D4—1721no—
582C2×D4—1721no—
583C2×D4—1721no—
584C2×D4—1721no—
585C2×D4—1721no—
586C2×D4—1721no—
587C2×D4—1721no—
588C2×D4—1721no—
589C2×D4—1721no—
590C2×D4—1721no—
591C2×D4(C2×D43)⋊C412yes—
592C22×C4—21no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—41no—
596C22×C4—41no—
597C22×C4—41no—
598C22×C4—41no—
599C22×C4—862no—
600C22×C4—3442no—
601C22×C4—1721no—
602C22×C4—1721no—
603C22×C4C2×C4×D4311yescharacteristic
604C22×C4C2×D17211yescharacteristic
605C22×C4#1062189811yescharacteristic
606C22×C4D4×D4311yescharacteristic
607C22×C4D4×D4311yescharacteristic
608C22×C4D4×D4311yescharacteristic
609C22×C4D4×D4311yescharacteristic
610C22×C4D4×D4311yescharacteristic
611C22×C4D4×D4311yescharacteristic
612C22×C4#1062190011yescharacteristic
613C22×C4#1062190011yescharacteristic
614C22×C4C2×C22⋊D4311yescharacteristic
615C22×C4C2×C22⋊D4311yescharacteristic
616C22×C4C2×C22⋊D4311yescharacteristic
617SD16—8616no—
618D8—8616no—
619M16—22no—
620M16—22no—
621M16—41no—
622M16—41no—
623M16—434no—
624M16—862no—
625M16—862no—
626M16—862no—
627M16—862no—
628M16—862no—
629M16—1721no—
630M16—1721no—
631C2×C8—22no—
632C2×C8—22no—
633C2×C8—22no—
634C2×C8—22no—
635C2×C8—41no—
636C2×C8—41no—
637C2×C8—41no—
638C2×C8—41no—
639C2×C8—41no—
640C2×C8—41no—
641C2×C8—862no—
642C2×C8—862no—
643C2×C8—862no—
644C2×C8—862no—
645C2×C8—1721no—
646C2×C8—1721no—
647C4⋊C4—862no—
648C4⋊C4—862no—
649C4⋊C4—1721no—
650C4⋊C4—1721no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—41no—
655C23—41no—
656C23—42no—
657C23—42no—
658C23—864no—
659C23—3444no—
660C23—3444no—
661C23—3442no—
662C23—3442no—
663C23—3444no—
664C23—3444no—
665C23—3442no—
666C23—3442no—
667C23—3442no—
668C23—3442no—
669C23—1722no—
670C23—1722no—
671C23—1722no—
672C23—1722no—
673C23—1722no—
674C23—1722no—
675C23C4×C22⋊D4311yescharacteristic
676C23#1306329811yescharacteristic
677C23#1306329811yescharacteristic
678C23#1306329911yescharacteristic
679C23#1306330711yescharacteristic
680C23#1306330811yescharacteristic
681C23#1306331111yescharacteristic
682Q8—22no—
683Q8—22no—
684Q8—41no—
685Q8—41no—
686D4—22no—
687D4—22no—
688D4—42no—
689D4—42no—
690D4—42no—
691D4—42no—
692D4—41no—
693D4—41no—
694D4—864no—
695D4—864no—
696D4—1722no—
697D4—1722no—
698D4—1722no—
699D4—1722no—
700D4—1722no—
701D4—1722no—
702C2×C4—22no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—3442no—
710C2×C4—3442no—
711C2×C4—3442no—
712C2×C4—1722no—
713C2×C4C22⋊C4×D4311yescharacteristic
714C2×C4C22⋊C4×D4311yescharacteristic
715C2×C4C2×(C2×D43)⋊C411yescharacteristic
716C2×C4(C22⋊D43)⋊C411yescharacteristic
717C2×C4(C22⋊D43)⋊C411yescharacteristic
718C2×C4C4×C22⋊D4311yescharacteristic
719C2×C4#1306329311yescharacteristic
720C2×C4#1306329311yescharacteristic
721C2×C4#1306329311yescharacteristic
722C2×C4#1306329311yescharacteristic
723C2×C4#1306329411yescharacteristic
724C2×C4#1306329511yescharacteristic
725C2×C4#1306329511yescharacteristic
726C2×C4#1306329511yescharacteristic
727C2×C4#1306329611yescharacteristic
728C2×C4#1306329611yescharacteristic
729C2×C4#1306329711yescharacteristic
730C2×C4#1306329711yescharacteristic
731C2×C4#1306329711yescharacteristic
732C2×C4#1306329711yescharacteristic
733C2×C4#1306329811yescharacteristic
734C2×C4#1306329811yescharacteristic
735C2×C4#1306329911yescharacteristic
736C2×C4#1306330711yescharacteristic
737C2×C4#1306330911yescharacteristic
738C2×C4#1306331111yescharacteristic
739C2×C4#1306332111yescharacteristic
740C2×C4#1306332111yescharacteristic
741C8—42no—
742C8—42no—
743C8—864no—
744C8—1722no—
745C22—22no—
746C22—22no—
747C22—22no—
748C22—22no—
749C22—21no—
750C22—21no—
751C22—21no—
752C22—21no—
753C22—44no—
754C22—42no—
755C22—82no—
756C22—81no—
757C22—81no—
758C22—3444no—
759C22—3444no—
760C22—3444no—
761C22—3444no—
762C22—3444no—
763C22—3444no—
764C22—3442no—
765C22—3442no—
766C22—1724no—
767C22#1458277511yescharacteristic
768C22#1458277811yescharacteristic
769C22#1458279911yescharacteristic
770C22#1458280811yescharacteristic
771C22#1458281411yescharacteristic
772C22#1458281411yescharacteristic
773C22#1458281511yescharacteristic
774C22#1458316212yes—
775C22#1458316912yes—
776C4—42no—
777C4—3442no—
778C4#1458275411yescharacteristic
779C4#1458277511yescharacteristic
780C4#1458277611yescharacteristic
781C4#1458279911yescharacteristic
782C4#1458280711yescharacteristic
783C4#1458280711yescharacteristic
784C4#1458280811yescharacteristic
785C4#1458281511yescharacteristic
786C2—21no—
787C2—21no—
788C2—21no—
789C2—21no—
790C2—82no—
791C2—3444no—
792C2#1913283411yescharacteristic
793C2#1913510312yes—
794C2#1913570411yescharacteristic
795C2#1913571011yescharacteristic
796C2#1913588612yes—
subgroupG/H
centerC23#13063299
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC2×C43×#408C2
socleC23×C43#121
prime radicalC22×#13063350C2
cosocleC23×C4×C43C23
hypercenterC2×#408D43
hypocenterC43#11020
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#408

Complements

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

NH ≅ G/Ntype
2. C2×#14582900C2semidirect
3. C22×#13063247C2semidirect
4. C22×#13063241C2semidirect
5. C2×#14582667C2semidirect
6. C2×#14582664C2semidirect
7. C2×C43×#408C2semidirect
14. C2×#13063350C4semidirect
392. C2×#408D43semidirect
436. C43#11020semidirect

Maximal subgroups

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

subgroupindex
C22×#130633502
C2×#145829002
C22×#130632472
C22×#130632412
C2×#145826672
C2×#145826642
C2×C43×#4082
#1102043