Finite Group Databasebeta

← #25003390

Subgroups — #25003390

Order 11008.

1278 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063356C211yesmaximal, characteristic
2C2×#14582898C211yesmaximal, characteristic
3C22×#13063244C211yesmaximal, characteristic, complemented
4C2×#14582865C211yesmaximal, characteristic
5C2×#14582668C211yesmaximal, characteristic, complemented
6C2×#14582664C211yesmaximal, characteristic, complemented
7C22×#103×C43C211yesmaximal, characteristic, complemented
8C22×#10621898C2211yescharacteristic
9C2×#13063356—22no—
10C2×#13063356—22no—
11C2×#13063356—22no—
12C2×#13063356—22no—
13C2×#13063356—22no—
14C2×#13063356C414yescomplemented
15C22×#10621885—21no—
16C22×#10621884—21no—
17C22×#10621877C2211yescharacteristic
18C22×#10621877C2211yescharacteristic
19C22×#10621877C2211yescharacteristic
20#14582898—22no—
21#14582898—22no—
22C2×#13063248—21no—
23C2×#13063245—21no—
24C2×#13063244—22no—
25C2×#13063244—22no—
26C2×#13063244—22no—
27#14582865—22no—
28#14582865—22no—
29C2×(C2×D43)⋊C8—22no—
30#14582668—22no—
31#14582664—22no—
32C23×Q8×C43C2211yescharacteristic
33C23×C8×C43C2211yescharacteristic
34C22×C4⋊C4×C43C2211yescharacteristic
35C2×#103×C43—22no—
36C2×#103×C43—22no—
37C2×#103×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—
53C22×C4×D43—21no—
54#13063356—28no—
55#13063356—28no—
56#13063356—28no—
57#13063356—28no—
58C2×#10621885—24no—
59C2×#10621885—24no—
60C2×#10621885—24no—
61C2×#10621884—24no—
62C2×#10621884—24no—
63C2×#10621884—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×#10621877—21no—
73C2×#10621877—21no—
74C2×#10621877—21no—
75C2×#10621877—21no—
76C2×#10621877—21no—
77C2×#10621877C2×C412yes—
78C2×#10621877D412yes—
79C2×#10621877D412yes—
80C2×#10621877D412yes—
81C2×#10621877D412yes—
82C22×C43⋊C8—21no—
83C22×C43⋊C8—21no—
84C22×C43⋊C8—21no—
85#13063248—24no—
86#13063245—24no—
87#13063244—28no—
88(C2×D43)⋊C8—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×C43C2×C412yes—
101C22×Q8×C43D412yes—
102C22×Q8×C43D412yes—
103C23×C4×C43—21no—
104C23×C4×C43—21no—
105C23×C4×C43C2311yescharacteristic
106C22×C8×C43—21no—
107C22×C8×C43—21no—
108C22×C8×C43—21no—
109C22×C8×C43—21no—
110C22×C8×C43—21no—
111C22×C8×C43—21no—
112C22×C8×C43D412yes—
113C2×C4⋊C4×C43—21no—
114C2×C4⋊C4×C43—21no—
115C2×C4⋊C4×C43—21no—
116C2×C4⋊C4×C43—21no—
117C2×C4⋊C4×C43—21no—
118C2×C4⋊C4×C43D412yes—
119#103×C43—28no—
120C24×C43#4111yescharacteristic
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—22no—
135C2×Q8×C43—22no—
136C2×Q8×C43—22no—
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×C43C22⋊C414yes—
150C22×C4×C43—22no—
151C22×C4×C43—22no—
152C22×C4×C43—22no—
153C22×C4×C43—22no—
154C22×C4×C43—41no—
155C22×C4×C43—41no—
156C22×C4×C43—41no—
157C22×C4×C43—41no—
158C22×C4×C43—41no—
159C22×C4×C43—41no—
160C22×C4×C43—82no—
161C22×C4×C43C22×C411yescharacteristic
162C22×C4×C43C2×D411yescharacteristic
163C22×C4×C43C2×D411yescharacteristic
164C22×C4×C43C2×D411yescharacteristic
165C22×C4×C43C2×D411yescharacteristic
166C22×C4×C43C2×D411yescharacteristic
167C22×C4×C43C2×D411yescharacteristic
168C22×C4×C43C2×D411yescharacteristic
169C22×C4×C43C2×D411yescharacteristic
170C22×C4×C43C2×D411yescharacteristic
171C22×C4×C43C2×D411yescharacteristic
172C22×C4×C43#4111yescharacteristic
173C22×C4×C43#4111yescharacteristic
174C22×C4×C43#4111yescharacteristic
175C2×C22⋊D43—22no—
176C2×C22⋊D43—22no—
177C2×C22⋊D43—41no—
178C2×C22⋊D43—41no—
179C2×C22⋊D43—41no—
180C2×C22⋊D43—41no—
181C22×Dic43—21no—
182#10621898—22no—
183#10621898—22no—
184#10621898—22no—
185#10621898—22no—
186#10621898—22no—
187#10621898—22no—
188#10621898—22no—
189#10621898—22no—
190#10621898—41no—
191#10621898—41no—
192#10621898—41no—
193#10621898—41no—
194#10621898—41no—
195#10621898—41no—
196#10621898—41no—
197#10621898—41no—
198C2×D172—21no—
199C2×D172—21no—
200C2×D172—21no—
201C2×D172—21no—
202C2×D172—21no—
203C2×D172C22⋊C412yes—
204C2×C4×D43—22no—
205C2×C4×D43—22no—
206C2×C4×D43—41no—
207C2×C4×D43—41no—
208C2×C4×D43—41no—
209C2×C4×D43—41no—
210C2×Dic86—21no—
211C2×Dic86—21no—
212C2×Dic86—21no—
213C2×Dic86—21no—
214C2×Dic86—21no—
215C2×Dic86C22⋊C412yes—
216C2×C8×C43—22no—
217C2×C8×C43—22no—
218C2×C8×C43—22no—
219C2×C8×C43—41no—
220C2×C8×C43—41no—
221C2×C8×C43—41no—
222C2×C8×C43—41no—
223C4⋊C4×C43—22no—
224C4⋊C4×C43—22no—
225C4⋊C4×C43—41no—
226C4⋊C4×C43—41no—
227#10621885—216no—
228#10621884—216no—
229#10621877—22no—
230#10621877—22no—
231#10621877—22no—
232#10621877—22no—
233#10621877—22no—
234#10621877—22no—
235#10621877—22no—
236#10621877—41no—
237#10621877—41no—
238#10621877—41no—
239#10621877—41no—
240#10621877C22⋊C414yes—
241C2×C43⋊C8—22no—
242C2×C43⋊C8—22no—
243C2×C43⋊C8—22no—
244C2×C43⋊C8—22no—
245C2×C43⋊C8—22no—
246C2×C43⋊C8—41no—
247C2×C43⋊C8—41no—
248C2×C43⋊C8—41no—
249C2×C43⋊C8—41no—
250C23×C43—22no—
251C23×C43—22no—
252C23×C43C4×D411yescharacteristic
253C23×C43#12111yescharacteristic
254C23×C43#12111yescharacteristic
255C23×C43#12111yescharacteristic
256C23×C43#12311yescharacteristic
257C23×C43#12311yescharacteristic
258C23×C43#12411yescharacteristic
259C22×D43—22no—
260C22×D43—41no—
261C22×D43—41no—
262C22×D43—42no—
263C22×D43—42no—
264Q8×C43—24no—
265Q8×C43—24no—
266Q8×C43—42no—
267Q8×C43—42no—
268Q8×C43—42no—
269Q8×C43—42no—
270Q8×C43—42no—
271Q8×C43—42no—
272C2×C4×C43—24no—
273C2×C4×C43—42no—
274C2×C4×C43—42no—
275C2×C4×C43—42no—
276C2×C4×C43—42no—
277C2×C4×C43—42no—
278C2×C4×C43—42no—
279C2×C4×C43—42no—
280C2×C4×C43—82no—
281C2×C4×C43—82no—
282C2×C4×C43—82no—
283C2×C4×C43C2×C22⋊C411yescharacteristic
284C2×C4×C43C2×C22⋊C411yescharacteristic
285C2×C4×C43C2×C22⋊C411yescharacteristic
286C2×C4×C43C4×D411yescharacteristic
287C2×C4×C43C4×D411yescharacteristic
288C2×C4×C43C4×D411yescharacteristic
289C2×C4×C43#12011yescharacteristic
290C2×C4×C43#12011yescharacteristic
291C2×C4×C43#12011yescharacteristic
292C2×C4×C43#12011yescharacteristic
293C2×C4×C43#12011yescharacteristic
294C2×C4×C43#12011yescharacteristic
295C2×C4×C43#12011yescharacteristic
296C2×C4×C43#12011yescharacteristic
297C2×C4×C43#12111yescharacteristic
298C2×C4×C43#12111yescharacteristic
299C2×C4×C43#12111yescharacteristic
300C2×C4×C43#12111yescharacteristic
301C2×C4×C43#12111yescharacteristic
302C2×C4×C43#12111yescharacteristic
303C2×C4×C43#12111yescharacteristic
304C2×C4×C43#12111yescharacteristic
305C2×C4×C43#12111yescharacteristic
306C2×C4×C43#12311yescharacteristic
307C2×C4×C43#12311yescharacteristic
308C2×C4×C43#12411yescharacteristic
309C2×C4×C43#12711yescharacteristic
310C2×C4×C43#12711yescharacteristic
311C22⋊D43—42no—
312C22⋊D43—42no—
313C22⋊D43—42no—
314C22⋊D43—42no—
315C2×Dic43—22no—
316C2×Dic43—41no—
317C2×Dic43—41no—
318D172—22no—
319D172—22no—
320D172—41no—
321D172—41no—
322C4×D43—42no—
323C4×D43—42no—
324C4×D43—42no—
325C4×D43—42no—
326Dic86—22no—
327Dic86—22no—
328Dic86—41no—
329Dic86—41no—
330C8×C43—42no—
331C43⋊C8—24no—
332C43⋊C8—42no—
333C43⋊C8—42no—
334#11021—431nomaximal, Sylow
335C22×C43—22no—
336C22×C43—22no—
337C22×C43—22no—
338C22×C43—22no—
339C22×C43—21no—
340C22×C43—21no—
341C22×C43—21no—
342C22×C43—21no—
343C22×C43#38611yescharacteristic
344C22×C43#38611yescharacteristic
345C22×C43#39011yescharacteristic
346C22×C43#39211yescharacteristic
347C22×C43#39411yescharacteristic
348C22×C43#39411yescharacteristic
349C22×C43#39411yescharacteristic
350C22×C43#47112yes—
351C22×C43#47312yes—
352C2×D43—44no—
353C2×D43—42no—
354C2×D43—82no—
355C2×D43—81no—
356C2×D43—81no—
357C4×C43—44no—
358C4×C43—82no—
359C4×C43#37911yescharacteristic
360C4×C43#38611yescharacteristic
361C4×C43#38611yescharacteristic
362C4×C43#39011yescharacteristic
363C4×C43#39211yescharacteristic
364C4×C43#39211yescharacteristic
365C4×C43#39211yescharacteristic
366C4×C43#39411yescharacteristic
367Dic43—42no—
368C22×#137—431no—
369C2×#417—431no—
370C22×#103D4311yescharacteristic, complemented
371C22×#101—431no—
372C2×#408—431no—
373C2×#343—431no—
374C2×#341—431no—
375C2×C43—21no—
376C2×C43—21no—
377C2×C43—21no—
378C2×C43—21no—
379C2×C43#143811yescharacteristic
380C2×C43#190812yes—
381C2×C43#201911yescharacteristic
382C2×C43#202011yescharacteristic
383C2×C43#205212yes—
384D43—82no—
385C22×#41—431no—
386C23×Q8C2×D4311yescharacteristic
387C2×#137—434no—
388C2×#137—862no—
389C2×#137—862no—
390C2×#137—862no—
391C2×#137—862no—
392C2×#137—862no—
393C22×Q16—861no—
394C22×SD16—861no—
395C22×M16—431no—
396C22×M16—431no—
397C22×M16—431no—
398C23×C8C2×D4311yescharacteristic
399C22×C4⋊C4C2×D4311yescharacteristic
400#417—862no—
401#417—862no—
402C2×#103—22no—
403C2×#103—22no—
404C2×#103—22no—
405C2×#103—861no—
406C2×#102—861no—
407C2×#101—862no—
408C2×#101—862no—
409C2×#101—862no—
410#408—862no—
411#408—862no—
412C2×C22⋊C8—862no—
413#343—862no—
414#341—862no—
415C43#1102111yescharacteristic, complemented, Sylow
416C2×#41—432no—
417C2×#41—432no—
418C2×#41—861no—
419C2×#41—861no—
420C2×#41—861no—
421C2×#41—861no—
422C2×#41—861no—
423C2×#41—861no—
424C2×#41—861no—
425C2×#41—861no—
426C2×#41—861no—
427C2×#41—861no—
428C22×Q8—21no—
429C22×Q8—21no—
430C22×Q8—21no—
431C22×Q8—21no—
432C22×Q8—21no—
433C22×Q8—21no—
434C22×Q8—21no—
435C22×Q8—21no—
436C22×Q8—21no—
437C22×Q8—21no—
438C22×Q8—21no—
439C22×Q8—431no—
440C22×Q8C4×D4312yes—
441C22×Q8D17212yes—
442C22×Q8C22⋊D4312yes—
443C22×D4—431no—
444C22×D4—861no—
445C23×C4—21no—
446C23×C4—21no—
447C23×C4—861no—
448C23×C4C22×D4311yescharacteristic
449#137—868no—
450#137—868no—
451#137—868no—
452#137—868no—
453C2×Q16—864no—
454C2×Q16—864no—
455C2×Q16—864no—
456C2×SD16—864no—
457C2×SD16—864no—
458C2×SD16—864no—
459C2×M16—432no—
460C2×M16—432no—
461C2×M16—432no—
462C2×M16—432no—
463C2×M16—432no—
464C2×M16—861no—
465C2×M16—861no—
466C2×M16—861no—
467C2×M16—861no—
468C2×M16—861no—
469C2×M16—861no—
470C2×M16—861no—
471C2×M16—861no—
472C2×M16—861no—
473C2×M16—861no—
474C2×M16—861no—
475C2×M16—861no—
476C2×M16—861no—
477C22×C8—21no—
478C22×C8—21no—
479C22×C8—21no—
480C22×C8—21no—
481C22×C8—21no—
482C22×C8—21no—
483C22×C8—861no—
484C22×C8—861no—
485C22×C8—861no—
486C22×C8C22⋊D4312yes—
487C2×C4⋊C4—21no—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4C22⋊D4312yes—
493#103—28no—
494#103—864no—
495#102—864no—
496#101—868no—
497C22⋊C8—868no—
498C24—861no—
499C24#1062190011yescharacteristic
500#41—862no—
501#41—862no—
502#41—862no—
503#41—862no—
504#41—862no—
505#41—862no—
506#41—862no—
507#41—862no—
508#41—1721no—
509#41—1721no—
510#41—1721no—
511#41—1721no—
512#41—1721no—
513#41—1721no—
514#41—1721no—
515#41—1721no—
516C2×Q8—22no—
517C2×Q8—22no—
518C2×Q8—22no—
519C2×Q8—22no—
520C2×Q8—22no—
521C2×Q8—22no—
522C2×Q8—22no—
523C2×Q8—22no—
524C2×Q8—22no—
525C2×Q8—22no—
526C2×Q8—22no—
527C2×Q8—22no—
528C2×Q8—22no—
529C2×Q8—22no—
530C2×Q8—22no—
531C2×Q8—41no—
532C2×Q8—41no—
533C2×Q8—41no—
534C2×Q8—41no—
535C2×Q8—41no—
536C2×Q8—41no—
537C2×Q8—41no—
538C2×Q8—41no—
539C2×Q8—41no—
540C2×Q8—41no—
541C2×Q8—41no—
542C2×Q8—41no—
543C2×Q8—432no—
544C2×Q8—861no—
545C2×Q8—861no—
546C2×Q8—861no—
547C2×Q8—861no—
548C2×Q8—861no—
549C2×Q8(C2×D43)⋊C414yes—
550C2×D4—432no—
551C2×D4—862no—
552C2×D4—862no—
553C2×D4—861no—
554C2×D4—861no—
555C2×D4—861no—
556C2×D4—861no—
557C2×D4—861no—
558C2×D4—1721no—
559C2×D4—1721no—
560C2×D4—1721no—
561C2×D4—1721no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—41no—
567C22×C4—41no—
568C22×C4—41no—
569C22×C4—41no—
570C22×C4—41no—
571C22×C4—41no—
572C22×C4—82no—
573C22×C4—861no—
574C22×C4—862no—
575C22×C4—862no—
576C22×C4—1721no—
577C22×C4—1721no—
578C22×C4—1721no—
579C22×C4—1721no—
580C22×C4C2×C4×D4311yescharacteristic
581C22×C4C2×D17211yescharacteristic
582C22×C4#1062189811yescharacteristic
583C22×C4#1062189811yescharacteristic
584C22×C4D4×D4311yescharacteristic
585C22×C4D4×D4311yescharacteristic
586C22×C4D4×D4311yescharacteristic
587C22×C4D4×D4311yescharacteristic
588C22×C4D4×D4311yescharacteristic
589C22×C4D4×D4311yescharacteristic
590C22×C4#1062190011yescharacteristic
591C22×C4C2×C22⋊D4311yescharacteristic
592C22×C4C2×C22⋊D4311yescharacteristic
593C22×C4C2×C22⋊D4311yescharacteristic
594Q16—8616no—
595SD16—8616no—
596M16—434no—
597M16—862no—
598M16—862no—
599M16—862no—
600M16—862no—
601M16—862no—
602M16—862no—
603M16—862no—
604M16—1721no—
605M16—1721no—
606M16—1721no—
607M16—1721no—
608C2×C8—22no—
609C2×C8—22no—
610C2×C8—22no—
611C2×C8—41no—
612C2×C8—41no—
613C2×C8—41no—
614C2×C8—41no—
615C2×C8—862no—
616C2×C8—862no—
617C2×C8—862no—
618C2×C8—862no—
619C2×C8—862no—
620C2×C8—1721no—
621C2×C8—1721no—
622C2×C8—1721no—
623C2×C8—1721no—
624C4⋊C4—22no—
625C4⋊C4—22no—
626C4⋊C4—41no—
627C4⋊C4—41no—
628C23—22no—
629C23—22no—
630C23—862no—
631C23—1721no—
632C23—1721no—
633C23—1722no—
634C23—1722no—
635C23(C22⋊D43)⋊C411yescharacteristic
636C23#1306329611yescharacteristic
637C23#1306329711yescharacteristic
638C23#1306329711yescharacteristic
639C23#1306330711yescharacteristic
640C23#1306330911yescharacteristic
641C23#1306331111yescharacteristic
642Q8—24no—
643Q8—24no—
644Q8—42no—
645Q8—42no—
646Q8—42no—
647Q8—42no—
648Q8—42no—
649Q8—42no—
650Q8—862no—
651Q8—862no—
652Q8—1721no—
653Q8—1721no—
654D4—862no—
655D4—862no—
656D4—1722no—
657D4—1722no—
658D4—1722no—
659D4—1722no—
660D4—1721no—
661D4—1721no—
662C2×C4—24no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—82no—
671C2×C4—82no—
672C2×C4—82no—
673C2×C4—862no—
674C2×C4—1721no—
675C2×C4—1721no—
676C2×C4—1722no—
677C2×C4—1722no—
678C2×C4—1722no—
679C2×C4—1722no—
680C2×C4C22⋊C4×D4311yescharacteristic
681C2×C4C22⋊C4×D4311yescharacteristic
682C2×C4C2×(C2×D43)⋊C411yescharacteristic
683C2×C4(C22⋊D43)⋊C411yescharacteristic
684C2×C4C4×C22⋊D4311yescharacteristic
685C2×C4C4×C22⋊D4311yescharacteristic
686C2×C4#1306329311yescharacteristic
687C2×C4#1306329311yescharacteristic
688C2×C4#1306329311yescharacteristic
689C2×C4#1306329311yescharacteristic
690C2×C4#1306329411yescharacteristic
691C2×C4#1306329511yescharacteristic
692C2×C4#1306329511yescharacteristic
693C2×C4#1306329511yescharacteristic
694C2×C4#1306329611yescharacteristic
695C2×C4#1306329711yescharacteristic
696C2×C4#1306329711yescharacteristic
697C2×C4#1306329811yescharacteristic
698C2×C4#1306329811yescharacteristic
699C2×C4#1306329811yescharacteristic
700C2×C4#1306329811yescharacteristic
701C2×C4#1306329911yescharacteristic
702C2×C4#1306329911yescharacteristic
703C2×C4#1306330711yescharacteristic
704C2×C4#1306330811yescharacteristic
705C2×C4#1306331111yescharacteristic
706C2×C4#1306332111yescharacteristic
707C2×C4#1306332111yescharacteristic
708C8—42no—
709C8—864no—
710C8—1722no—
711C8—1722no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—22no—
716C22—21no—
717C22—21no—
718C22—21no—
719C22—21no—
720C22—3442no—
721C22—3441no—
722C22—3441no—
723C22—1724no—
724C22—1722no—
725C22#1458277511yescharacteristic
726C22#1458277611yescharacteristic
727C22#1458279911yescharacteristic
728C22#1458280711yescharacteristic
729C22#1458281411yescharacteristic
730C22#1458281511yescharacteristic
731C22#1458281511yescharacteristic
732C22#1458315912yes—
733C22#1458317112yes—
734C4—44no—
735C4—82no—
736C4—1722no—
737C4#1458275411yescharacteristic
738C4#1458277511yescharacteristic
739C4#1458277811yescharacteristic
740C4#1458279911yescharacteristic
741C4#1458280711yescharacteristic
742C4#1458280811yescharacteristic
743C4#1458280811yescharacteristic
744C4#1458281411yescharacteristic
745C2—21no—
746C2—21no—
747C2—21no—
748C2—21no—
749C2—3442no—
750C2#1913283411yescharacteristic
751C2#1913511312yes—
752C2#1913570711yescharacteristic
753C2#1913571411yescharacteristic
754C2#1913589512yes—
subgroupG/H
centerC23#13063296
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC22×#103×C43C2
socleC23×C43#121
prime radicalC22×#10621898C22
cosocleC23×C4×C43C23
hypercenterC22×#103D43
hypocenterC43#11021
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#103

Complements

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

NH ≅ G/Ntype
3. C22×#13063244C2semidirect
5. C2×#14582668C2semidirect
6. C2×#14582664C2semidirect
7. C22×#103×C43C2semidirect
14. C2×#13063356C4semidirect
370. C22×#103D43semidirect
415. C43#11021semidirect

Maximal subgroups

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

subgroupindex
C22×#130633562
C2×#145828982
C22×#130632442
C2×#145828652
C2×#145826682
C2×#145826642
C22×#103×C432
#1102143