Finite Group Databasebeta

← #25003225

Subgroups — #25003225

Order 11008.

1494 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583410C211yesmaximal, characteristic
2C2×#14582915C211yesmaximal, characteristic, complemented
3#19143115C211yesmaximal, characteristic, complemented
4#19136978C211yesmaximal, characteristic, complemented
5#19134306C211yesmaximal, characteristic, complemented
6C2×#14582656C211yesmaximal, characteristic, complemented
7C2×C43×#407C211yesmaximal, characteristic, complemented
8C22×#10621898C2211yescharacteristic
9#14583410—22no—
10#14583410—22no—
11#14583410—22no—
12#14583410C414yescomplemented
13C2×#13063308—21no—
14C2×#13063304—21no—
15C2×#13063299—21no—
16C2×#13063294—21no—
17C2×C4×C22⋊D43—22no—
18C2×#13063284C2211yescharacteristic
19C2×#13063284C2211yescharacteristic
20C2×#13063284C2211yescharacteristic
21#14582915—22no—
22#14582915—22no—
23C2×#13063251—22no—
24#14582909—21no—
25#14582905—21no—
26#14582901—22no—
27#14582896—22no—
28#14582762—21no—
29#14582759—22no—
30#14582755—21no—
31C4×C22⋊Dic43—22no—
32#14582660—22no—
33#14582656—22no—
34C24×C4×C43C2211yescharacteristic
35C22×M16×C43C2211yescharacteristic
36C22×M16×C43C2211yescharacteristic
37C43×#407—22no—
38C43×#407—22no—
39C2×C22⋊C8×C43—22no—
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×#10621898—21no—
49C2×#10621898—21no—
50C2×#10621898C2×C412yes—
51C2×#10621898D412yes—
52C22×Dic86D411yescharacteristic
53C22×D172D411yescharacteristic
54C22×C22⋊D43—22no—
55C22×C22⋊D43—21no—
56C22×C4×D43—21no—
57#13063308—24no—
58#13063308—24no—
59#13063304—24no—
60#13063304—24no—
61#13063299—24no—
62#13063299—24no—
63#13063294—24no—
64#13063294—24no—
65C4×C22⋊D43—28no—
66C4×C22⋊D43—28no—
67#13063284—21no—
68#13063284—21no—
69#13063284—21no—
70#13063284—21no—
71#13063284—21no—
72#13063284—21no—
73#13063284—21no—
74#13063284—21no—
75#13063284—21no—
76#13063284—21no—
77#13063284C2×C412yes—
78#13063284D412yes—
79C2×C4⋊Dic43—21no—
80C2×C4⋊Dic43—21no—
81C2×C4⋊Dic43D412yescomplemented
82C2×Dic43⋊C4—22no—
83C2×C22⋊Dic43—22no—
84C2×C22⋊Dic43—21no—
85C2×C22⋊Dic43—24no—
86C2×C22⋊Dic43—21no—
87C2×C22⋊Dic43—21no—
88C2×(C2×D43)⋊C4—22no—
89C2×C4×Dic43—21no—
90C2×C4×Dic43D412yes—
91C2×C4×Dic43D412yescomplemented
92#13063251—28no—
93#13063250—24no—
94#13063247—24no—
95C43⋊#95—24no—
96C25×C43D411yescharacteristic
97C23×C4×C43—21no—
98C23×C4×C43—21no—
99C23×C4×C43—21no—
100C23×C4×C43—21no—
101C23×C4×C43—21no—
102C23×C4×C43—21no—
103C23×C4×C43—21no—
104C23×C4×C43—21no—
105C23×C4×C43—21no—
106C23×C4×C43—21no—
107C23×C4×C43—21no—
108C23×C4×C43—21no—
109C23×C4×C43C2×C412yes—
110C23×C4×C43D411yescharacteristic
111C23×C4×C43D412yes—
112C23×C4×C43C2311yescharacteristic
113C2×M16×C43—21no—
114C2×M16×C43—21no—
115C2×M16×C43—21no—
116C2×M16×C43—21no—
117C2×M16×C43—21no—
118C2×M16×C43—21no—
119C2×M16×C43—21no—
120C2×M16×C43—21no—
121C2×M16×C43—21no—
122C2×M16×C43—21no—
123C2×M16×C43—21no—
124C2×M16×C43D412yescomplemented
125C22×C8×C43—21no—
126C22×C8×C43D412yescomplemented
127C22⋊C8×C43—28no—
128C24×C43—21no—
129C24×C43—21no—
130C24×C43—21no—
131C24×C43—21no—
132C24×C43—21no—
133C24×C43—21no—
134C24×C43—44no—
135C24×C43C22⋊C412yes—
136C24×C43C2×D411yescharacteristic
137C23×D43—21no—
138C22×C4×C43—22no—
139C22×C4×C43—22no—
140C22×C4×C43—22no—
141C22×C4×C43—22no—
142C22×C4×C43—22no—
143C22×C4×C43—22no—
144C22×C4×C43—22no—
145C22×C4×C43—22no—
146C22×C4×C43—22no—
147C22×C4×C43—22no—
148C22×C4×C43—22no—
149C22×C4×C43—22no—
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43—21no—
154C22×C4×C43—21no—
155C22×C4×C43—21no—
156C22×C4×C43—41no—
157C22×C4×C43—41no—
158C22×C4×C43—41no—
159C22×C4×C43—41no—
160C22×C4×C43—41no—
161C22×C4×C43—41no—
162C22×C4×C43—41no—
163C22×C4×C43—41no—
164C22×C4×C43—41no—
165C22×C4×C43—41no—
166C22×C4×C43—41no—
167C22×C4×C43—41no—
168C22×C4×C43—41no—
169C22×C4×C43—41no—
170C22×C4×C43—41no—
171C22×C4×C43—41no—
172C22×C4×C43C22⋊C412yes—
173C22×C4×C43C22×C411yescharacteristic
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×C4×C43#4111yescharacteristic
187C2×C22⋊D43—28no—
188C2×C22⋊D43—22no—
189C2×C22⋊D43—22no—
190C2×C22⋊D43—48no—
191C2×C22⋊D43—41no—
192C2×C22⋊D43—41no—
193C2×C22⋊D43—41no—
194C2×C22⋊D43—41no—
195C22×Dic43—22no—
196C22×Dic43—21no—
197C22×Dic43—22no—
198C22×Dic43—22no—
199#10621898—22no—
200#10621898—22no—
201#10621898—22no—
202#10621898—22no—
203#10621898—22no—
204#10621898—22no—
205#10621898—22no—
206#10621898—22no—
207#10621898—41no—
208#10621898—41no—
209#10621898—41no—
210#10621898—41no—
211#10621898—41no—
212#10621898—41no—
213#10621898—41no—
214#10621898—41no—
215C2×D172—21no—
216C2×D172—21no—
217C2×D172—21no—
218C2×D172—21no—
219C2×D172—21no—
220C2×D172C22⋊C412yescomplemented
221C2×C4×D43—22no—
222C2×C4×D43—22no—
223C2×C4×D43—41no—
224C2×C4×D43—41no—
225C2×C4×D43—41no—
226C2×C4×D43—41no—
227C2×Dic86—21no—
228C2×Dic86—21no—
229C2×Dic86—21no—
230C2×Dic86—21no—
231C2×Dic86—21no—
232C2×Dic86C22⋊C412yescomplemented
233M16×C43—22no—
234M16×C43—22no—
235M16×C43—41no—
236M16×C43—41no—
237M16×C43—41no—
238M16×C43—41no—
239M16×C43—41no—
240M16×C43—41no—
241C2×C8×C43—22no—
242C2×C8×C43—22no—
243C2×C8×C43—22no—
244C2×C8×C43—22no—
245C2×C8×C43—41no—
246C2×C8×C43—41no—
247C22⋊Dic43—28no—
248C22⋊Dic43—22no—
249C22⋊Dic43—22no—
250C22⋊Dic43—48no—
251C22⋊Dic43—41no—
252C22⋊Dic43—41no—
253C22⋊Dic43—41no—
254C22⋊Dic43—41no—
255(C2×D43)⋊C4—28no—
256C4⋊Dic43—22no—
257C4⋊Dic43—22no—
258C4⋊Dic43—22no—
259C4⋊Dic43—22no—
260C4⋊Dic43—41no—
261C4⋊Dic43—41no—
262Dic43⋊C4—28no—
263C4×Dic43—22no—
264C4×Dic43—22no—
265C4×Dic43—22no—
266C4×Dic43—41no—
267C4×Dic43—41no—
268C4×Dic43C22⋊C414yescomplemented
269C23×C43—24no—
270C23×C43—24no—
271C23×C43—24no—
272C23×C43—22no—
273C23×C43—22no—
274C23×C43—22no—
275C23×C43—44no—
276C23×C43—42no—
277C23×C43—42no—
278C23×C43—42no—
279C23×C43—42no—
280C23×C43—44no—
281C23×C43—44no—
282C23×C43—44no—
283C23×C43—41no—
284C23×C43—41no—
285C23×C43—41no—
286C23×C43—41no—
287C23×C43C2×C22⋊C411yescharacteristic
288C23×C43#12011yescharacteristic
289C23×C43#12011yescharacteristic
290C23×C43#12011yescharacteristic
291C23×C43#12111yescharacteristic
292C23×C43#12111yescharacteristic
293C23×C43#12311yescharacteristic
294C22×D43—22no—
295C22×D43—44no—
296C22×D43—41no—
297C22×D43—41no—
298C2×C4×C43—22no—
299C2×C4×C43—22no—
300C2×C4×C43—22no—
301C2×C4×C43—41no—
302C2×C4×C43—41no—
303C2×C4×C43—41no—
304C2×C4×C43—41no—
305C2×C4×C43—42no—
306C2×C4×C43—42no—
307C2×C4×C43—42no—
308C2×C4×C43—42no—
309C2×C4×C43—42no—
310C2×C4×C43—42no—
311C2×C4×C43—42no—
312C2×C4×C43—42no—
313C2×C4×C43C2×C22⋊C411yescharacteristic
314C2×C4×C43C2×C22⋊C411yescharacteristic
315C2×C4×C43C4×D411yescharacteristic
316C2×C4×C43C4×D411yescharacteristic
317C2×C4×C43C4×D411yescharacteristic
318C2×C4×C43C4×D411yescharacteristic
319C2×C4×C43#12011yescharacteristic
320C2×C4×C43#12011yescharacteristic
321C2×C4×C43#12011yescharacteristic
322C2×C4×C43#12011yescharacteristic
323C2×C4×C43#12011yescharacteristic
324C2×C4×C43#12111yescharacteristic
325C2×C4×C43#12111yescharacteristic
326C2×C4×C43#12111yescharacteristic
327C2×C4×C43#12111yescharacteristic
328C2×C4×C43#12111yescharacteristic
329C2×C4×C43#12111yescharacteristic
330C2×C4×C43#12111yescharacteristic
331C2×C4×C43#12111yescharacteristic
332C2×C4×C43#12111yescharacteristic
333C2×C4×C43#12111yescharacteristic
334C2×C4×C43#12311yescharacteristic
335C2×C4×C43#12311yescharacteristic
336C2×C4×C43#12311yescharacteristic
337C2×C4×C43#12411yescharacteristic
338C2×C4×C43#12411yescharacteristic
339C2×C4×C43#12711yescharacteristic
340C2×C4×C43#12711yescharacteristic
341C22⋊D43—416no—
342C22⋊D43—42no—
343C22⋊D43—42no—
344C22⋊D43—42no—
345C22⋊D43—42no—
346C2×Dic43—24no—
347C2×Dic43—22no—
348C2×Dic43—44no—
349C2×Dic43—41no—
350C2×Dic43—41no—
351C2×Dic43—44no—
352C2×Dic43—44no—
353C2×Dic43—42no—
354C2×Dic43—42no—
355D172—22no—
356D172—22no—
357D172—41no—
358D172—41no—
359C4×D43—42no—
360C4×D43—42no—
361C4×D43—42no—
362C4×D43—42no—
363Dic86—22no—
364Dic86—22no—
365Dic86—41no—
366Dic86—41no—
367C8×C43—42no—
368C8×C43—42no—
369#10994—431nomaximal, Sylow
370C22×C43—22no—
371C22×C43—22no—
372C22×C43—22no—
373C22×C43—24no—
374C22×C43—24no—
375C22×C43—24no—
376C22×C43—41no—
377C22×C43—41no—
378C22×C43—41no—
379C22×C43—41no—
380C22×C43—42no—
381C22×C43—44no—
382C22×C43—44no—
383C22×C43—42no—
384C22×C43—42no—
385C22×C43—44no—
386C22×C43—42no—
387C22×C43—44no—
388C22×C43#37911yescharacteristic
389C22×C43#38611yescharacteristic
390C22×C43#38611yescharacteristic
391C22×C43#39211yescharacteristic
392C22×C43#39211yescharacteristic
393C22×C43#39411yescharacteristic
394C22×C43#39411yescharacteristic
395C2×D43—44no—
396C2×D43—42no—
397C2×D43—82no—
398C2×D43—82no—
399C4×C43—42no—
400C4×C43#38611yescharacteristic
401C4×C43#38611yescharacteristic
402C4×C43#39011yescharacteristic
403C4×C43#39011yescharacteristic
404C4×C43#39211yescharacteristic
405C4×C43#39211yescharacteristic
406C4×C43#39411yescharacteristic
407C4×C43#39411yescharacteristic
408Dic43—44no—
409Dic43—42no—
410Dic43—82no—
411Dic43—82no—
412C2×#525—431no—
413C2×#421—431no—
414#2896—431no—
415C2×#407D4311yescharacteristic, complemented
416#2280—431no—
417#1733—431no—
418C2×H(3,ℤ/4)—431no—
419C2×C43—21no—
420C2×C43—21no—
421C2×C43—21no—
422C2×C43—21no—
423C2×C43—21no—
424C2×C43—21no—
425C2×C43—44no—
426C2×C43#143811yescharacteristic
427C2×C43#201012yes—
428D43—82no—
429C22×#41—431no—
430C24×C4C2×D4311yescharacteristic
431C22×M16C2×D4311yescharacteristic
432C22×M16C2×D4311yescharacteristic
433#525—434no—
434#525—862no—
435#525—862no—
436#525—862no—
437C2×#123—861no—
438C2×C22⋊Q8—861no—
439C2×#121—861no—
440C2×#120—861no—
441C2×C4×D4—862no—
442C2×#117—431no—
443C2×#117—431no—
444C2×#117—431no—
445#421—862no—
446#421—862no—
447C2×#104—862no—
448#419—861no—
449#418—861no—
450#417—862no—
451#416—862no—
452#407—22no—
453#407—22no—
454C2×C22⋊C8—22no—
455#381—861no—
456#380—862no—
457#379—861no—
458C4×C22⋊C4—862no—
459#339—862no—
460H(3,ℤ/4)—862no—
461C43#1099411yescharacteristic, complemented, Sylow
462C25D17211yescharacteristic
463C2×#41—432no—
464C2×#41—432no—
465C2×#41—861no—
466C2×#41—861no—
467C2×#41—861no—
468C2×#41—861no—
469C2×#41—861no—
470C2×#41—861no—
471C2×#41—861no—
472C2×#41—861no—
473C2×#41—861no—
474C2×#41—861no—
475C22×Q8—431no—
476C22×D4—431no—
477C22×D4—862no—
478C22×D4—861no—
479C23×C4—21no—
480C23×C4—21no—
481C23×C4—21no—
482C23×C4—21no—
483C23×C4—21no—
484C23×C4—21no—
485C23×C4—21no—
486C23×C4—21no—
487C23×C4—21no—
488C23×C4—21no—
489C23×C4—21no—
490C23×C4—21no—
491C23×C4—861no—
492C23×C4C4×D4312yes—
493C23×C4D17211yescharacteristic
494C23×C4C22⋊D4312yes—
495C23×C4C22×D4311yescharacteristic
496C2×M16—21no—
497C2×M16—21no—
498C2×M16—21no—
499C2×M16—21no—
500C2×M16—21no—
501C2×M16—21no—
502C2×M16—21no—
503C2×M16—21no—
504C2×M16—21no—
505C2×M16—21no—
506C2×M16—21no—
507C2×M16C22⋊D4312yescomplemented
508C22×C8—21no—
509C22×C8C22⋊D4312yescomplemented
510#123—864no—
511#123—864no—
512C22⋊Q8—864no—
513C22⋊Q8—864no—
514#121—864no—
515#121—864no—
516#120—864no—
517#120—864no—
518C4×D4—868no—
519C4×D4—868no—
520#117—432no—
521#117—432no—
522#117—861no—
523#117—861no—
524#117—861no—
525#117—861no—
526#117—861no—
527#117—861no—
528#117—861no—
529#117—861no—
530#117—861no—
531#117—861no—
532C2×C4⋊C4—432no—
533C2×C4⋊C4—862no—
534C2×C4⋊C4—861no—
535C2×C4⋊C4—861no—
536C2×C22⋊C4—862no—
537C2×C22⋊C4—862no—
538C2×C22⋊C4—861no—
539C2×C22⋊C4—864no—
540C2×C22⋊C4—861no—
541C2×C22⋊C4—861no—
542C2×C42—432no—
543C2×C42—432no—
544C2×C42—861no—
545#104—868no—
546#103—864no—
547#102—864no—
548C22⋊C8—28no—
549#95—864no—
550C24—21no—
551C24—21no—
552C24—21no—
553C24—21no—
554C24—21no—
555C24—21no—
556C24—44no—
557C24—861no—
558C24(C2×D43)⋊C412yes—
559C24C2×D17211yescharacteristic
560#41—862no—
561#41—862no—
562#41—862no—
563#41—862no—
564#41—862no—
565#41—862no—
566#41—862no—
567#41—862no—
568#41—1721no—
569#41—1721no—
570#41—1721no—
571#41—1721no—
572#41—1721no—
573#41—1721no—
574#41—1721no—
575#41—1721no—
576C2×Q8—432no—
577C2×Q8—861no—
578C2×Q8—861no—
579C2×Q8—861no—
580C2×Q8—861no—
581C2×Q8—861no—
582C2×D4—432no—
583C2×D4—868no—
584C2×D4—862no—
585C2×D4—862no—
586C2×D4—861no—
587C2×D4—861no—
588C2×D4—861no—
589C2×D4—861no—
590C2×D4—861no—
591C2×D4—1728no—
592C2×D4—1721no—
593C2×D4—1721no—
594C2×D4—1721no—
595C2×D4—1721no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—22no—
603C22×C4—22no—
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—22no—
614C22×C4—41no—
615C22×C4—41no—
616C22×C4—41no—
617C22×C4—41no—
618C22×C4—41no—
619C22×C4—41no—
620C22×C4—41no—
621C22×C4—41no—
622C22×C4—41no—
623C22×C4—41no—
624C22×C4—41no—
625C22×C4—41no—
626C22×C4—41no—
627C22×C4—41no—
628C22×C4—41no—
629C22×C4—41no—
630C22×C4—862no—
631C22×C4—861no—
632C22×C4—862no—
633C22×C4—862no—
634C22×C4—862no—
635C22×C4—862no—
636C22×C4—1721no—
637C22×C4—1721no—
638C22×C4—1721no—
639C22×C4—1721no—
640C22×C4(C2×D43)⋊C412yes—
641C22×C4C2×C4×D4311yescharacteristic
642C22×C4#1062189811yescharacteristic
643C22×C4#1062189811yescharacteristic
644C22×C4D4×D4311yescharacteristic
645C22×C4D4×D4311yescharacteristic
646C22×C4D4×D4311yescharacteristic
647C22×C4D4×D4311yescharacteristic
648C22×C4D4×D4311yescharacteristic
649C22×C4D4×D4311yescharacteristic
650C22×C4#1062190011yescharacteristic
651C22×C4#1062190011yescharacteristic
652C22×C4C2×C22⋊D4311yescharacteristic
653C22×C4C2×C22⋊D4311yescharacteristic
654C22×C4C2×C22⋊D4311yescharacteristic
655M16—22no—
656M16—22no—
657M16—41no—
658M16—41no—
659M16—41no—
660M16—41no—
661M16—41no—
662M16—41no—
663C2×C8—22no—
664C2×C8—22no—
665C2×C8—22no—
666C2×C8—22no—
667C2×C8—41no—
668C2×C8—41no—
669C4⋊C4—868no—
670C4⋊C4—862no—
671C4⋊C4—862no—
672C4⋊C4—862no—
673C4⋊C4—862no—
674C4⋊C4—1721no—
675C4⋊C4—1721no—
676C22⋊C4—868no—
677C22⋊C4—868no—
678C22⋊C4—862no—
679C22⋊C4—862no—
680C22⋊C4—1728no—
681C22⋊C4—1721no—
682C22⋊C4—1721no—
683C22⋊C4—1721no—
684C22⋊C4—1721no—
685C42—434no—
686C42—862no—
687C42—862no—
688C42—862no—
689C42—1721no—
690C42—1721no—
691C23—24no—
692C23—24no—
693C23—24no—
694C23—22no—
695C23—22no—
696C23—22no—
697C23—44no—
698C23—42no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—44no—
703C23—44no—
704C23—44no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—862no—
710C23—1724no—
711C23—1721no—
712C23—1721no—
713C23C2×(C2×D43)⋊C411yescharacteristic
714C23#1306329511yescharacteristic
715C23#1306329511yescharacteristic
716C23#1306329511yescharacteristic
717C23#1306329911yescharacteristic
718C23#1306329911yescharacteristic
719C23#1306330911yescharacteristic
720Q8—862no—
721Q8—862no—
722Q8—1721no—
723Q8—1721no—
724D4—862no—
725D4—862no—
726D4—17216no—
727D4—1722no—
728D4—1722no—
729D4—1722no—
730D4—1722no—
731D4—1721no—
732D4—1721no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—864no—
749C2×C4—862no—
750C2×C4—1724no—
751C2×C4—1724no—
752C2×C4—1722no—
753C2×C4—1722no—
754C2×C4—1724no—
755C2×C4—1721no—
756C2×C4—1721no—
757C2×C4—1722no—
758C2×C4—1722no—
759C2×C4—1722no—
760C2×C4—1722no—
761C2×C4C22⋊C4×D4311yescharacteristic
762C2×C4C22⋊C4×D4311yescharacteristic
763C2×C4(C22⋊D43)⋊C411yescharacteristic
764C2×C4(C22⋊D43)⋊C411yescharacteristic
765C2×C4C4×C22⋊D4311yescharacteristic
766C2×C4C4×C22⋊D4311yescharacteristic
767C2×C4#1306329311yescharacteristic
768C2×C4#1306329311yescharacteristic
769C2×C4#1306329311yescharacteristic
770C2×C4#1306329311yescharacteristic
771C2×C4#1306329411yescharacteristic
772C2×C4#1306329611yescharacteristic
773C2×C4#1306329611yescharacteristic
774C2×C4#1306329711yescharacteristic
775C2×C4#1306329711yescharacteristic
776C2×C4#1306329711yescharacteristic
777C2×C4#1306329711yescharacteristic
778C2×C4#1306329811yescharacteristic
779C2×C4#1306329811yescharacteristic
780C2×C4#1306329811yescharacteristic
781C2×C4#1306329811yescharacteristic
782C2×C4#1306330711yescharacteristic
783C2×C4#1306330711yescharacteristic
784C2×C4#1306330811yescharacteristic
785C2×C4#1306331111yescharacteristic
786C2×C4#1306331111yescharacteristic
787C2×C4#1306332111yescharacteristic
788C2×C4#1306332111yescharacteristic
789C8—42no—
790C8—42no—
791C22—22no—
792C22—22no—
793C22—22no—
794C22—24no—
795C22—24no—
796C22—24no—
797C22—41no—
798C22—41no—
799C22—41no—
800C22—41no—
801C22—44no—
802C22—42no—
803C22—42no—
804C22—42no—
805C22—44no—
806C22—44no—
807C22—42no—
808C22—44no—
809C22—3442no—
810C22—3442no—
811C22—1724no—
812C22—1722no—
813C22#1458275411yescharacteristic
814C22#1458277611yescharacteristic
815C22#1458277811yescharacteristic
816C22#1458280811yescharacteristic
817C22#1458280811yescharacteristic
818C22#1458281511yescharacteristic
819C22#1458281511yescharacteristic
820C4—42no—
821C4—3442no—
822C4—3442no—
823C4—1724no—
824C4—1722no—
825C4#1458277511yescharacteristic
826C4#1458277511yescharacteristic
827C4#1458279911yescharacteristic
828C4#1458279911yescharacteristic
829C4#1458280711yescharacteristic
830C4#1458280711yescharacteristic
831C4#1458281411yescharacteristic
832C4#1458281411yescharacteristic
833C2—21no—
834C2—21no—
835C2—21no—
836C2—21no—
837C2—21no—
838C2—21no—
839C2—44no—
840C2—3442no—
841C2#1913283411yescharacteristic
842C2#1913566212yes—
subgroupG/H
centerC2×C4#13063321
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC2×C43×#407C2
socleC22×C43#392
prime radicalC2×#14583410C2
cosocleC23×C4×C43C23
hypercenterC2×#407D43
hypocenterC43#10994
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#407

Complements

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

NH ≅ G/Ntype
2. C2×#14582915C2semidirect
3. #19143115C2semidirect
4. #19136978C2semidirect
5. #19134306C2semidirect
6. C2×#14582656C2semidirect
7. C2×C43×#407C2semidirect
12. #14583410C4semidirect
81. C2×C4⋊Dic43D4semidirect
91. C2×C4×Dic43D4semidirect
124. C2×M16×C43D4semidirect
126. C22×C8×C43D4semidirect
220. C2×D172C22⋊C4semidirect
232. C2×Dic86C22⋊C4semidirect
268. C4×Dic43C22⋊C4semidirect
415. C2×#407D43semidirect
461. C43#10994semidirect
507. C2×M16C22⋊D43semidirect
509. C22×C8C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145834102
C2×#145829152
#191431152
#191369782
#191343062
C2×#145826562
C2×C43×#4072
#1099443