Finite Group Databasebeta

← #25003261

Subgroups — #25003261

Order 11008.

1292 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582916C211yesmaximal, characteristic, complemented
2#19143114C211yesmaximal, characteristic, complemented
3C2×#14582883C211yesmaximal, characteristic, complemented
4C2×#14582873C211yesmaximal, characteristic, complemented
5#19134305C211yesmaximal, characteristic, complemented
6C2×#14582655C211yesmaximal, characteristic, complemented
7C43×#3449C211yesmaximal, characteristic
8C22×#10621877C2211yescharacteristic
9C22×#10621877C2211yescharacteristic
10C2×#13063284C2211yescharacteristic
11C2×#13063284C2211yescharacteristic
12#14582916—22no—
13#14582916—22no—
14C2×#13063252—22no—
15#14582908—21no—
16#14582904—21no—
17#14582900—22no—
18#14582895—22no—
19#14582883—22no—
20#14582883—22no—
21C2×#13063244—21no—
22C2×#13063242—21no—
23#14582873—22no—
24#14582873—22no—
25C2×#13063240—22no—
26#14582659—22no—
27#14582655—22no—
28C22×#41×C43C2211yescharacteristic
29C22×#41×C43C2211yescharacteristic
30C43×#537—22no—
31C43×#536—21no—
32C43×#536—21no—
33C43×#535—21no—
34C43×#535—21no—
35C43×#534—22no—
36C43×#532—22no—
37C43×#525—22no—
38C43×#525C414yescomplemented
39C2×#117×C43C2211yescharacteristic
40C2×#10621877—21no—
41C2×#10621877—21no—
42C2×#10621877—21no—
43C2×#10621877—21no—
44C2×#10621877—21no—
45C2×#10621877—21no—
46C2×#10621877—21no—
47C2×#10621877—21no—
48C2×#10621877—21no—
49C2×#10621877—21no—
50C2×#10621877D412yescomplemented
51C2×#10621877D412yescomplemented
52C22×C43⋊C8—21no—
53C22×C43⋊C8—21no—
54#13063284—21no—
55#13063284—21no—
56#13063284—21no—
57#13063284—21no—
58#13063284—21no—
59#13063284—21no—
60#13063284D412yescomplemented
61#13063284D412yescomplemented
62C2×C4⋊Dic43—21no—
63C2×C4⋊Dic43—21no—
64C2×C22⋊Dic43—21no—
65C2×C22⋊Dic43—21no—
66C2×C4×Dic43—21no—
67C2×C4×Dic43—21no—
68#13063252—28no—
69#13063249—24no—
70#13063246—24no—
71#13063244—24no—
72#13063242—24no—
73#13063240—28no—
74C2×#41×C43—21no—
75C2×#41×C43—21no—
76C2×#41×C43—21no—
77C2×#41×C43—21no—
78C2×#41×C43—21no—
79C2×#41×C43—21no—
80C2×#41×C43—21no—
81C2×#41×C43—21no—
82C2×#41×C43—21no—
83C2×#41×C43—21no—
84C2×#41×C43—21no—
85C2×#41×C43—21no—
86C2×#41×C43—21no—
87C2×#41×C43—21no—
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×C43C2×C412yes—
97C2×#41×C43D412yes—
98C22×Q8×C43D411yescharacteristic
99C22×Q8×C43D411yescharacteristic
100C22×D4×C43—21no—
101C22×D4×C43D412yes—
102C22×D4×C43D411yescharacteristic
103C22×D4×C43D411yescharacteristic
104C23×C4×C43—21no—
105C23×C4×C43C2×C412yes—
106C23×C4×C43C2311yescharacteristic
107C4⋊Q8×C43—22no—
108#127×C43—22no—
109#124×C43—22no—
110#124×C43—22no—
111#123×C43—24no—
112#123×C43—24no—
113C22⋊Q8×C43—24no—
114C22⋊Q8×C43—24no—
115#121×C43—24no—
116#121×C43—28no—
117#121×C43—24no—
118#120×C43—24no—
119#120×C43—24no—
120C4×D4×C43—28no—
121#117×C43—21no—
122#117×C43—21no—
123#117×C43C2×C412yes—
124#117×C43D412yes—
125C2×C4⋊C4×C43—21no—
126C2×C22⋊C4×C43—21no—
127C2×C42×C43D412yes—
128C24×C43—21no—
129C24×C43C22⋊C412yes—
130C24×C43C2×D411yescharacteristic
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—
147#41×C43—41no—
148#41×C43—41no—
149#41×C43—41no—
150#41×C43—41no—
151#41×C43—41no—
152#41×C43—41no—
153#41×C43—41no—
154#41×C43—41no—
155#41×C43—41no—
156#41×C43—41no—
157#41×C43—41no—
158#41×C43—41no—
159#41×C43—41no—
160#41×C43—41no—
161#41×C43—41no—
162#41×C43—41no—
163C2×Q8×C43—21no—
164C2×Q8×C43—21no—
165C2×Q8×C43—21no—
166C2×Q8×C43—21no—
167C2×Q8×C43—21no—
168C2×Q8×C43—21no—
169C2×Q8×C43—21no—
170C2×Q8×C43—21no—
171C2×Q8×C43—21no—
172C2×Q8×C43—21no—
173C2×Q8×C43—21no—
174C2×Q8×C43C22⋊C412yes—
175C2×D4×C43—28no—
176C2×D4×C43—21no—
177C2×D4×C43—21no—
178C2×D4×C43—21no—
179C2×D4×C43—21no—
180C2×D4×C43—21no—
181C2×D4×C43—21no—
182C2×D4×C43—21no—
183C2×D4×C43—22no—
184C2×D4×C43—22no—
185C2×D4×C43—22no—
186C2×D4×C43—22no—
187C2×D4×C43—22no—
188C2×D4×C43—22no—
189C2×D4×C43—22no—
190C2×D4×C43—22no—
191C2×D4×C43—21no—
192C2×D4×C43—21no—
193C2×D4×C43—21no—
194C2×D4×C43—21no—
195C2×D4×C43—41no—
196C2×D4×C43—41no—
197C2×D4×C43—41no—
198C2×D4×C43—41no—
199C2×D4×C43C22⋊C412yes—
200C22×C4×C43—22no—
201C22×C4×C43—22no—
202C22×C4×C43—22no—
203C22×C4×C43—22no—
204C22×C4×C43—22no—
205C22×C4×C43—22no—
206C22×C4×C43—22no—
207C22×C4×C43—22no—
208C22×C4×C43—21no—
209C22×C4×C43—22no—
210C22×C4×C43—41no—
211C22×C4×C43—41no—
212C22×C4×C43—41no—
213C22×C4×C43—41no—
214C22×C4×C43C22⋊C412yes—
215C22×C4×C43C22×C411yescharacteristic
216C22×C4×C43C2×D411yescharacteristic
217C22×C4×C43C2×D411yescharacteristic
218C22×C4×C43C2×D411yescharacteristic
219C22×C4×C43C2×D411yescharacteristic
220C22×C4×C43C2×D411yescharacteristic
221C22×C4×C43C2×D411yescharacteristic
222C22×C4×C43C2×D411yescharacteristic
223C22×C4×C43C2×D411yescharacteristic
224C22×C4×C43C2×D411yescharacteristic
225C22×C4×C43#4111yescharacteristic
226C22×C4×C43#4111yescharacteristic
227C22×C4×C43#4111yescharacteristic
228C22×C4×C43#4111yescharacteristic
229C22×Dic43—41no—
230C22×Dic43—41no—
231C4⋊C4×C43—28no—
232C4⋊C4×C43—22no—
233C4⋊C4×C43—22no—
234C22⋊C4×C43—28no—
235C22⋊C4×C43—28no—
236C22⋊C4×C43—22no—
237C22⋊C4×C43—22no—
238C42×C43—22no—
239C42×C43C22⋊C414yes—
240C22⋊Dic43—22no—
241C22⋊Dic43—22no—
242C22⋊Dic43—41no—
243C22⋊Dic43—41no—
244C4⋊Dic43—22no—
245C4⋊Dic43—22no—
246C4⋊Dic43—41no—
247C4⋊Dic43—41no—
248C4×Dic43—22no—
249C4×Dic43—22no—
250C4×Dic43—41no—
251C4×Dic43—41no—
252#10621877—22no—
253#10621877—22no—
254#10621877—22no—
255#10621877—22no—
256#10621877—41no—
257#10621877—41no—
258#10621877—41no—
259#10621877—41no—
260C2×C43⋊C8—22no—
261C2×C43⋊C8—22no—
262C2×C43⋊C8—41no—
263C2×C43⋊C8—41no—
264C2×C43⋊C8—41no—
265C2×C43⋊C8—41no—
266C23×C43—22no—
267C23×C43—22no—
268C23×C43—22no—
269C23×C43—22no—
270C23×C43—41no—
271C23×C43—41no—
272C23×C43—81no—
273C23×C43—82no—
274C23×C43—82no—
275C23×C43C2×C22⋊C411yescharacteristic
276C23×C43#12011yescharacteristic
277C23×C43#12011yescharacteristic
278C23×C43#12011yescharacteristic
279C23×C43#12111yescharacteristic
280C23×C43#12111yescharacteristic
281C23×C43#12311yescharacteristic
282Q8×C43—22no—
283Q8×C43—22no—
284Q8×C43—41no—
285Q8×C43—41no—
286Q8×C43—41no—
287Q8×C43—41no—
288Q8×C43—41no—
289Q8×C43—41no—
290D4×C43—22no—
291D4×C43—22no—
292D4×C43—42no—
293D4×C43—42no—
294D4×C43—42no—
295D4×C43—42no—
296D4×C43—42no—
297D4×C43—42no—
298D4×C43—42no—
299D4×C43—42no—
300D4×C43—41no—
301D4×C43—41no—
302D4×C43—41no—
303D4×C43—41no—
304D4×C43—41no—
305D4×C43—41no—
306D4×C43—88no—
307C2×C4×C43—24no—
308C2×C4×C43—22no—
309C2×C4×C43—22no—
310C2×C4×C43—22no—
311C2×C4×C43—22no—
312C2×C4×C43—41no—
313C2×C4×C43—41no—
314C2×C4×C43—42no—
315C2×C4×C43—42no—
316C2×C4×C43—42no—
317C2×C4×C43—42no—
318C2×C4×C43—42no—
319C2×C4×C43—42no—
320C2×C4×C43—42no—
321C2×C4×C43—42no—
322C2×C4×C43—82no—
323C2×C4×C43C2×C22⋊C411yescharacteristic
324C2×C4×C43C2×C22⋊C411yescharacteristic
325C2×C4×C43C4×D411yescharacteristic
326C2×C4×C43C4×D411yescharacteristic
327C2×C4×C43C4×D411yescharacteristic
328C2×C4×C43C4×D411yescharacteristic
329C2×C4×C43#12011yescharacteristic
330C2×C4×C43#12011yescharacteristic
331C2×C4×C43#12011yescharacteristic
332C2×C4×C43#12011yescharacteristic
333C2×C4×C43#12011yescharacteristic
334C2×C4×C43#12111yescharacteristic
335C2×C4×C43#12111yescharacteristic
336C2×C4×C43#12111yescharacteristic
337C2×C4×C43#12111yescharacteristic
338C2×C4×C43#12111yescharacteristic
339C2×C4×C43#12111yescharacteristic
340C2×C4×C43#12111yescharacteristic
341C2×C4×C43#12111yescharacteristic
342C2×C4×C43#12111yescharacteristic
343C2×C4×C43#12111yescharacteristic
344C2×C4×C43#12311yescharacteristic
345C2×C4×C43#12311yescharacteristic
346C2×C4×C43#12311yescharacteristic
347C2×C4×C43#12411yescharacteristic
348C2×C4×C43#12411yescharacteristic
349C2×C4×C43#12711yescharacteristic
350C2×C4×C43#12711yescharacteristic
351C2×Dic43—42no—
352C2×Dic43—42no—
353C2×Dic43—82no—
354C2×Dic43—82no—
355C43⋊C8—42no—
356C43⋊C8—42no—
357#11000—431nomaximal, Sylow
358C22×C43—41no—
359C22×C43—41no—
360C22×C43—41no—
361C22×C43—41no—
362C22×C43—41no—
363C22×C43—41no—
364C22×C43—41no—
365C22×C43—44no—
366C22×C43—44no—
367C22×C43—42no—
368C22×C43—42no—
369C22×C43—82no—
370C22×C43—82no—
371C22×C43—82no—
372C22×C43—82no—
373C22×C43#37911yescharacteristic
374C22×C43#38611yescharacteristic
375C22×C43#38611yescharacteristic
376C22×C43#39211yescharacteristic
377C22×C43#39211yescharacteristic
378C22×C43#39411yescharacteristic
379C22×C43#39411yescharacteristic
380C4×C43—44no—
381C4×C43—42no—
382C4×C43—42no—
383C4×C43#38611yescharacteristic
384C4×C43#38611yescharacteristic
385C4×C43#39011yescharacteristic
386C4×C43#39011yescharacteristic
387C4×C43#39211yescharacteristic
388C4×C43#39211yescharacteristic
389C4×C43#39411yescharacteristic
390C4×C43#39411yescharacteristic
391Dic43—82no—
392Dic43—82no—
393#3449D4311yescharacteristic
394C2×#421—431no—
395#2896—431no—
396C2×#413—431no—
397C2×#410—431no—
398#1733—431no—
399C2×H(3,ℤ/4)—431no—
400C2×C43—21no—
401C2×C43—21no—
402C2×C43—21no—
403C2×C43—21no—
404C2×C43—21no—
405C2×C43—21no—
406C2×C43—21no—
407C2×C43—82no—
408C2×C43—82no—
409C2×C43#143811yescharacteristic
410C22×#41C2×D4311yescharacteristic
411C22×#41C2×D4311yescharacteristic
412C22×M16—431no—
413C22×M16—431no—
414#537—22no—
415#536—21no—
416#536—21no—
417#535—21no—
418#535—21no—
419#534—22no—
420#532—22no—
421#525—22no—
422#525Dic4314yescomplemented
423C2×#117—431no—
424C2×#117—431no—
425C2×#117C2×D4311yescharacteristic
426#421—862no—
427#421—862no—
428C2×#104—862no—
429#419—861no—
430#418—861no—
431#417—862no—
432#416—862no—
433#413—862no—
434#413—862no—
435C2×#101—861no—
436C2×#100—861no—
437#410—862no—
438#410—862no—
439C2×#99—862no—
440#339—862no—
441H(3,ℤ/4)—862no—
442C43#1100011yescharacteristic, complemented, Sylow
443C2×#41—21no—
444C2×#41—21no—
445C2×#41—21no—
446C2×#41—21no—
447C2×#41—21no—
448C2×#41—21no—
449C2×#41—21no—
450C2×#41—21no—
451C2×#41—21no—
452C2×#41—21no—
453C2×#41—21no—
454C2×#41—21no—
455C2×#41—21no—
456C2×#41—21no—
457C2×#41—21no—
458C2×#41—21no—
459C2×#41—21no—
460C2×#41—21no—
461C2×#41—21no—
462C2×#41—21no—
463C2×#41—21no—
464C2×#41—21no—
465C2×#41C2×Dic4312yes—
466C2×#41C22⋊D4312yes—
467C22×Q8C22⋊D4311yescharacteristic
468C22×Q8C22⋊D4311yescharacteristic
469C22×D4—21no—
470C22×D4C22⋊D4312yes—
471C22×D4C22⋊D4311yescharacteristic
472C22×D4C22⋊D4311yescharacteristic
473C23×C4—21no—
474C23×C4C2×Dic4312yes—
475C23×C4C22×D4311yescharacteristic
476C2×M16—432no—
477C2×M16—432no—
478C2×M16—861no—
479C2×M16—861no—
480C2×M16—861no—
481C2×M16—861no—
482C2×M16—861no—
483C2×M16—861no—
484C2×M16—861no—
485C2×M16—861no—
486C2×M16—861no—
487C2×M16—861no—
488C22×C8—861no—
489C22×C8—861no—
490C4⋊Q8—22no—
491#127—22no—
492#124—22no—
493#124—22no—
494#123—24no—
495#123—24no—
496C22⋊Q8—24no—
497C22⋊Q8—24no—
498#121—24no—
499#121—28no—
500#121—24no—
501#120—24no—
502#120—24no—
503C4×D4—28no—
504#117—21no—
505#117—21no—
506#117—432no—
507#117—432no—
508#117—861no—
509#117—861no—
510#117—861no—
511#117—861no—
512#117—861no—
513#117—861no—
514#117C2×Dic4312yes—
515#117C22⋊D4312yes—
516C2×C4⋊C4—21no—
517C2×C4⋊C4—861no—
518C2×C4⋊C4—861no—
519C2×C22⋊C4—21no—
520C2×C22⋊C4—861no—
521C2×C22⋊C4—861no—
522C2×C42—861no—
523C2×C42—861no—
524C2×C42C22⋊D4312yes—
525#104—868no—
526#103—864no—
527#102—864no—
528#101—864no—
529#100—864no—
530#99—868no—
531C24—21no—
532C24C22⋊Dic4312yes—
533C24C2×C22⋊D4311yescharacteristic
534#41—22no—
535#41—22no—
536#41—22no—
537#41—22no—
538#41—22no—
539#41—22no—
540#41—22no—
541#41—22no—
542#41—41no—
543#41—41no—
544#41—41no—
545#41—41no—
546#41—41no—
547#41—41no—
548#41—41no—
549#41—41no—
550#41—41no—
551#41—41no—
552#41—41no—
553#41—41no—
554#41—41no—
555#41—41no—
556#41—41no—
557#41—41no—
558#41—41no—
559#41—41no—
560#41—41no—
561#41—41no—
562#41—41no—
563#41—41no—
564#41—41no—
565#41—41no—
566C2×Q8—21no—
567C2×Q8—21no—
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8—21no—
572C2×Q8—21no—
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8C22⋊Dic4312yes—
578C2×D4—22no—
579C2×D4—22no—
580C2×D4—22no—
581C2×D4—22no—
582C2×D4—22no—
583C2×D4—22no—
584C2×D4—22no—
585C2×D4—22no—
586C2×D4—28no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—41no—
599C2×D4—41no—
600C2×D4—41no—
601C2×D4—41no—
602C2×D4C22⋊Dic4312yes—
603C22×C4—21no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—41no—
614C22×C4—41no—
615C22×C4—41no—
616C22×C4—41no—
617C22×C4—1721no—
618C22×C4—1721no—
619C22×C4C22⋊Dic4312yes—
620C22×C4D4×D4311yescharacteristic
621C22×C4D4×D4311yescharacteristic
622C22×C4D4×D4311yescharacteristic
623C22×C4D4×D4311yescharacteristic
624C22×C4#1062190011yescharacteristic
625C22×C4#1062190011yescharacteristic
626C22×C4#1062190011yescharacteristic
627C22×C4#1062190011yescharacteristic
628C22×C4C22×Dic4311yescharacteristic
629C22×C4C2×C22⋊D4311yescharacteristic
630C22×C4C2×C22⋊D4311yescharacteristic
631C22×C4C2×C22⋊D4311yescharacteristic
632C22×C4C2×C22⋊D4311yescharacteristic
633C22×C4C2×C22⋊D4311yescharacteristic
634M16—862no—
635M16—862no—
636M16—862no—
637M16—862no—
638M16—1721no—
639M16—1721no—
640M16—1721no—
641M16—1721no—
642C2×C8—862no—
643C2×C8—862no—
644C2×C8—1721no—
645C2×C8—1721no—
646C2×C8—1721no—
647C2×C8—1721no—
648C4⋊C4—28no—
649C4⋊C4—22no—
650C4⋊C4—22no—
651C4⋊C4—862no—
652C4⋊C4—862no—
653C4⋊C4—1721no—
654C4⋊C4—1721no—
655C22⋊C4—28no—
656C22⋊C4—28no—
657C22⋊C4—22no—
658C22⋊C4—22no—
659C22⋊C4—862no—
660C22⋊C4—862no—
661C22⋊C4—1721no—
662C22⋊C4—1721no—
663C42—22no—
664C42—862no—
665C42—862no—
666C42—1721no—
667C42—1721no—
668C42C22⋊Dic4314yes—
669C23—22no—
670C23—22no—
671C23—22no—
672C23—22no—
673C23—41no—
674C23—41no—
675C23—81no—
676C23—82no—
677C23—82no—
678C23C2×C22⋊Dic4311yescharacteristic
679C23#1306329311yescharacteristic
680C23#1306329411yescharacteristic
681C23#1306329411yescharacteristic
682C23#1306329711yescharacteristic
683C23#1306329711yescharacteristic
684C23#1306330611yescharacteristic
685Q8—22no—
686Q8—22no—
687Q8—41no—
688Q8—41no—
689Q8—41no—
690Q8—41no—
691Q8—41no—
692Q8—41no—
693D4—22no—
694D4—22no—
695D4—42no—
696D4—42no—
697D4—42no—
698D4—42no—
699D4—42no—
700D4—42no—
701D4—42no—
702D4—42no—
703D4—41no—
704D4—41no—
705D4—41no—
706D4—41no—
707D4—41no—
708D4—41no—
709D4—88no—
710C2×C4—24no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—82no—
726C2×C4—3442no—
727C2×C4—3442no—
728C2×C4—1722no—
729C2×C4—1722no—
730C2×C4C2×C22⋊Dic4311yescharacteristic
731C2×C4C2×C22⋊Dic4311yescharacteristic
732C2×C4D4×Dic4311yescharacteristic
733C2×C4D4×Dic4311yescharacteristic
734C2×C4D4×Dic4311yescharacteristic
735C2×C4D4×Dic4311yescharacteristic
736C2×C4#1306329311yescharacteristic
737C2×C4#1306329311yescharacteristic
738C2×C4#1306329311yescharacteristic
739C2×C4#1306329411yescharacteristic
740C2×C4#1306329411yescharacteristic
741C2×C4#1306329611yescharacteristic
742C2×C4#1306329611yescharacteristic
743C2×C4#1306329611yescharacteristic
744C2×C4#1306329611yescharacteristic
745C2×C4#1306329711yescharacteristic
746C2×C4#1306329711yescharacteristic
747C2×C4#1306329711yescharacteristic
748C2×C4#1306329711yescharacteristic
749C2×C4#1306329711yescharacteristic
750C2×C4#1306329711yescharacteristic
751C2×C4#1306330611yescharacteristic
752C2×C4#1306330611yescharacteristic
753C2×C4#1306330611yescharacteristic
754C2×C4#1306331211yescharacteristic
755C2×C4#1306331211yescharacteristic
756C2×C4#1306332111yescharacteristic
757C2×C4#1306332111yescharacteristic
758C8—1722no—
759C8—1722no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—41no—
765C22—41no—
766C22—41no—
767C22—44no—
768C22—44no—
769C22—42no—
770C22—42no—
771C22—82no—
772C22—82no—
773C22—82no—
774C22—82no—
775C22#1458275511yescharacteristic
776C22#1458277911yescharacteristic
777C22#1458277911yescharacteristic
778C22#1458280711yescharacteristic
779C22#1458280711yescharacteristic
780C22#1458281311yescharacteristic
781C22#1458281311yescharacteristic
782C4—44no—
783C4—42no—
784C4—42no—
785C4—3442no—
786C4—3442no—
787C4#1458277911yescharacteristic
788C4#1458277911yescharacteristic
789C4#1458280211yescharacteristic
790C4#1458280211yescharacteristic
791C4#1458280711yescharacteristic
792C4#1458280711yescharacteristic
793C4#1458281311yescharacteristic
794C4#1458281311yescharacteristic
795C2—21no—
796C2—21no—
797C2—21no—
798C2—21no—
799C2—21no—
800C2—21no—
801C2—21no—
802C2—82no—
803C2—82no—
804C2#1913283611yescharacteristic
subgroupG/H
centerC4#14582802
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
Fitting, prime radicalC43×#3449C2
socleC2×C43#1438
cosocleC23×C4×C43C23
hypercenter#3449D43
hypocenterC43#11000
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C23×C4 ◁ #3449

Complements

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

NH ≅ G/Ntype
1. C2×#14582916C2semidirect
2. #19143114C2semidirect
3. C2×#14582883C2semidirect
4. C2×#14582873C2semidirect
5. #19134305C2semidirect
6. C2×#14582655C2semidirect
38. C43×#525C4semidirect
50. C2×#10621877D4semidirect
51. C2×#10621877D4semidirect
60. #13063284D4semidirect
61. #13063284D4semidirect
422. #525Dic43semidirect
442. C43#11000semidirect

Maximal subgroups

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

subgroupindex
C2×#145829162
#191431142
C2×#145828832
C2×#145828732
#191343052
C2×#145826552
C43×#34492
#1100043