Finite Group Databasebeta

← #25003232

Subgroups — #25003232

Order 11008.

1306 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
1#19147924C211yesmaximal, characteristic
2C2×#14582881C211yesmaximal, characteristic, complemented
3C2×#14582867C211yesmaximal, characteristic, complemented
4C2×#14582866C211yesmaximal, characteristic, complemented
5#19134333C211yesmaximal, characteristic, complemented
6#19134293C211yesmaximal, characteristic, complemented
7C2×C43×#413C211yesmaximal, characteristic, complemented
8C22×#10621898C2211yescharacteristic
9C22×#10621877C2211yescharacteristic
10C23×C43⋊C8C2211yescharacteristic
11#14583477—22no—
12#14583473—21no—
13#14583470—21no—
14#14583466—21no—
15#14583463—21no—
16#14583458C414yes—
17#14583445—22no—
18#14583410—22no—
19#14583406—22no—
20C2×#13063284C2211yescharacteristic
21#14582881—22no—
22#14582881—22no—
23C2×#13063243—21no—
24C2×#13063241—21no—
25#14582867—22no—
26#14582867—22no—
27#14582866—22no—
28#14582866—22no—
29C2×C22⋊(C43⋊C8)—22no—
30C2×(C2×D43)⋊C8—22no—
31#14582667—22no—
32#14582653—22no—
33C22×#41×C43C2211yescharacteristic
34C22×M16×C43C2211yescharacteristic
35C22×M16×C43C2211yescharacteristic
36C43×#413—22no—
37C43×#413—22no—
38C2×#101×C43—21no—
39C2×#100×C43—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×#10621898—21no—
49C2×#10621898—21no—
50C2×#10621898—21no—
51C2×#10621898—21no—
52C22×Dic86D411yescharacteristic
53C22×D172D411yescharacteristic
54C22×C22⋊D43C2×C412yes—
55C22×C4×D43D412yes—
56C2×#10621877—21no—
57C2×#10621877—21no—
58C2×#10621877—21no—
59C2×#10621877—21no—
60C2×#10621877—21no—
61C2×#10621877D412yescomplemented
62C22×C43⋊C8—21no—
63C22×C43⋊C8—21no—
64C22×C43⋊C8—21no—
65C22×C43⋊C8—21no—
66C22×C43⋊C8—21no—
67C22×C43⋊C8—21no—
68C22×C43⋊C8—21no—
69C22×C43⋊C8D412yescomplemented
70#13063323—22no—
71#13063321—22no—
72#13063314—22no—
73#13063312—22no—
74#13063308—24no—
75#13063306—24no—
76#13063304—24no—
77#13063301—24no—
78#13063299—24no—
79#13063297—28no—
80#13063296—24no—
81#13063294—24no—
82#13063293—24no—
83C4×C22⋊D43—28no—
84#13063284—21no—
85#13063284—21no—
86#13063284—21no—
87#13063284—21no—
88C2×C4⋊Dic43D412yes—
89C2×C22⋊Dic43C2×C412yes—
90C2×C4×Dic43D412yes—
91#13063243—24no—
92#13063241—24no—
93C22⋊(C43⋊C8)—28no—
94(C2×D43)⋊C8—28no—
95C2×#41×C43—21no—
96C2×#41×C43—21no—
97C2×#41×C43—21no—
98C2×#41×C43—21no—
99C2×#41×C43—21no—
100C2×#41×C43—21no—
101C2×#41×C43—21no—
102C2×#41×C43—21no—
103C2×#41×C43—21no—
104C2×#41×C43—21no—
105C2×#41×C43—21no—
106C2×#41×C43—21no—
107C22×Q8×C43D411yescharacteristic
108C22×D4×C43C2×C412yes—
109C22×D4×C43D411yescharacteristic
110C23×C4×C43D412yes—
111C23×C4×C43C2311yescharacteristic
112C2×M16×C43—21no—
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×C43D412yescomplemented
123C2×M16×C43D412yescomplemented
124C22×C8×C43—21no—
125C22×C8×C43—21no—
126#101×C43—24no—
127#100×C43—24no—
128C24×C43C22⋊C412yes—
129C24×C43C22×C411yescharacteristic
130C23×D43C22⋊C412yes—
131#41×C43—41no—
132#41×C43—41no—
133#41×C43—41no—
134#41×C43—41no—
135#41×C43—41no—
136#41×C43—41no—
137#41×C43—41no—
138#41×C43—41no—
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×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43—21no—
157C2×D4×C43—21no—
158C2×D4×C43—21no—
159C2×D4×C43—22no—
160C2×D4×C43—22no—
161C2×D4×C43—22no—
162C2×D4×C43—22no—
163C2×D4×C43—22no—
164C2×D4×C43—22no—
165C22×C4×C43—22no—
166C22×C4×C43—22no—
167C22×C4×C43—22no—
168C22×C4×C43—22no—
169C22×C4×C43—22no—
170C22×C4×C43—22no—
171C22×C4×C43C22⋊C412yes—
172C22×C4×C43C2×D411yescharacteristic
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×C43#4111yescharacteristic
183C22×C4×C43#4111yescharacteristic
184C22×C4×C43#4111yescharacteristic
185C22×C4×C43#4111yescharacteristic
186C2×C22⋊D43—28no—
187C2×C22⋊D43—22no—
188C2×C22⋊D43—22no—
189C2×C22⋊D43—22no—
190C2×C22⋊D43—22no—
191C2×C22⋊D43—22no—
192C2×C22⋊D43—22no—
193C22×Dic43C22⋊C412yes—
194C22×Dic43C22⋊C414yes—
195#10621898—41no—
196#10621898—41no—
197#10621898—41no—
198#10621898—41no—
199#10621898—41no—
200#10621898—41no—
201#10621898—41no—
202#10621898—41no—
203#10621898—41no—
204#10621898—41no—
205#10621898—41no—
206#10621898—41no—
207#10621898—41no—
208#10621898—41no—
209#10621898—41no—
210#10621898—41no—
211C2×D172—21no—
212C2×D172—21no—
213C2×D172—21no—
214C2×D172—21no—
215C2×D172—21no—
216C2×D172—21no—
217C2×C4×D43—22no—
218C2×C4×D43—22no—
219C2×C4×D43—22no—
220C2×C4×D43—22no—
221C2×C4×D43—22no—
222C2×C4×D43—22no—
223C2×Dic86—21no—
224C2×Dic86—21no—
225C2×Dic86—21no—
226C2×Dic86—21no—
227C2×Dic86—21no—
228C2×Dic86—21no—
229M16×C43—22no—
230M16×C43—22no—
231M16×C43—22no—
232M16×C43—22no—
233M16×C43—41no—
234M16×C43—41no—
235M16×C43—41no—
236M16×C43—41no—
237C2×C8×C43—22no—
238C2×C8×C43—22no—
239C2×C8×C43—41no—
240C2×C8×C43—41no—
241C2×C8×C43—41no—
242C2×C8×C43—41no—
243C22⋊Dic43—28no—
244C22⋊Dic43—22no—
245C22⋊Dic43—22no—
246(C2×D43)⋊C4—28no—
247C4⋊Dic43—22no—
248C4⋊Dic43—22no—
249Dic43⋊C4—28no—
250C4×Dic43—22no—
251C4×Dic43—22no—
252#10621877—22no—
253#10621877—22no—
254#10621877—41no—
255#10621877—41no—
256C2×C43⋊C8—22no—
257C2×C43⋊C8—22no—
258C2×C43⋊C8—22no—
259C2×C43⋊C8—22no—
260C2×C43⋊C8—41no—
261C2×C43⋊C8—41no—
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—42no—
270C23×C43—44no—
271C23×C43C2×C22⋊C411yescharacteristic
272C23×C43C2×C22⋊C411yescharacteristic
273C23×C43C2×C22⋊C411yescharacteristic
274C23×C43C4×D411yescharacteristic
275C23×C43C4×D411yescharacteristic
276C23×C43C4×D411yescharacteristic
277C23×C43C4×D411yescharacteristic
278C22×D43—22no—
279C22×D43—22no—
280C22×D43—22no—
281C22×D43—44no—
282Q8×C43—41no—
283Q8×C43—41no—
284Q8×C43—41no—
285Q8×C43—41no—
286D4×C43—42no—
287D4×C43—42no—
288D4×C43—42no—
289D4×C43—42no—
290D4×C43—41no—
291D4×C43—41no—
292D4×C43—41no—
293D4×C43—41no—
294C2×C4×C43—22no—
295C2×C4×C43—22no—
296C2×C4×C43—22no—
297C2×C4×C43—42no—
298C2×C4×C43—42no—
299C2×C4×C43—42no—
300C2×C4×C43—42no—
301C2×C4×C43#12011yescharacteristic
302C2×C4×C43#12011yescharacteristic
303C2×C4×C43#12011yescharacteristic
304C2×C4×C43#12011yescharacteristic
305C2×C4×C43#12011yescharacteristic
306C2×C4×C43#12011yescharacteristic
307C2×C4×C43#12011yescharacteristic
308C2×C4×C43#12011yescharacteristic
309C2×C4×C43#12111yescharacteristic
310C2×C4×C43#12111yescharacteristic
311C2×C4×C43#12111yescharacteristic
312C2×C4×C43#12111yescharacteristic
313C2×C4×C43#12111yescharacteristic
314C2×C4×C43#12111yescharacteristic
315C2×C4×C43#12111yescharacteristic
316C2×C4×C43#12111yescharacteristic
317C2×C4×C43#12111yescharacteristic
318C2×C4×C43#12111yescharacteristic
319C2×C4×C43#12111yescharacteristic
320C2×C4×C43#12111yescharacteristic
321C2×C4×C43#12311yescharacteristic
322C2×C4×C43#12311yescharacteristic
323C2×C4×C43#12311yescharacteristic
324C2×C4×C43#12311yescharacteristic
325C2×C4×C43#12411yescharacteristic
326C2×C4×C43#12411yescharacteristic
327C2×C4×C43#12711yescharacteristic
328C2×C4×C43#12711yescharacteristic
329C22⋊D43—42no—
330C22⋊D43—42no—
331C22⋊D43—42no—
332C22⋊D43—42no—
333C22⋊D43—88no—
334C2×Dic43—24no—
335C2×Dic43—22no—
336C2×Dic43—22no—
337C2×Dic43—22no—
338C2×Dic43—44no—
339D172—41no—
340D172—41no—
341D172—41no—
342D172—41no—
343C4×D43—42no—
344C4×D43—42no—
345C4×D43—42no—
346C4×D43—42no—
347Dic86—41no—
348Dic86—41no—
349Dic86—41no—
350Dic86—41no—
351C8×C43—42no—
352C8×C43—42no—
353C43⋊C8—42no—
354C43⋊C8—42no—
355#10996—431nomaximal, Sylow
356C22×C43—22no—
357C22×C43—22no—
358C22×C43—22no—
359C22×C43—41no—
360C22×C43—41no—
361C22×C43—41no—
362C22×C43—41no—
363C22×C43—44no—
364C22×C43—42no—
365C22×C43—44no—
366C22×C43—82no—
367C22×C43#37911yescharacteristic
368C22×C43#38611yescharacteristic
369C22×C43#38611yescharacteristic
370C22×C43#38611yescharacteristic
371C22×C43#38611yescharacteristic
372C22×C43#39011yescharacteristic
373C22×C43#39011yescharacteristic
374C2×D43—44no—
375C2×D43—42no—
376C2×D43—44no—
377C2×D43—82no—
378C4×C43—42no—
379C4×C43#39211yescharacteristic
380C4×C43#39211yescharacteristic
381C4×C43#39211yescharacteristic
382C4×C43#39211yescharacteristic
383C4×C43#39411yescharacteristic
384C4×C43#39411yescharacteristic
385C4×C43#39411yescharacteristic
386C4×C43#39411yescharacteristic
387Dic43—42no—
388Dic43—44no—
389#3449—431no—
390C2×#413—431no—
391C2×#413D4311yescharacteristic, complemented
392C2×#408—431no—
393C2×#408—431no—
394#1742—431no—
395#1729—431no—
396C2×C43—21no—
397C2×C43—21no—
398C2×C43—21no—
399C2×C43—21no—
400C2×C43—21no—
401C2×C43—21no—
402C2×C43—82no—
403C2×C43#143811yescharacteristic
404C2×C43#179112yes—
405D43—82no—
406C22×#41—431no—
407C22×#41C2×D4311yescharacteristic
408C22×M16—431no—
409C22×M16C2×D4311yescharacteristic
410C22×M16C2×D4311yescharacteristic
411C23×C8—431no—
412#537—862no—
413#536—861no—
414#536—861no—
415#535—861no—
416#535—861no—
417#534—434no—
418#532—862no—
419#525—862no—
420#525—862no—
421C2×#117—431no—
422#413—22no—
423#413—22no—
424#413—862no—
425#413—862no—
426C2×#101—21no—
427C2×#101—861no—
428C2×#100—21no—
429C2×#100—861no—
430#408—862no—
431#408—862no—
432#408—862no—
433#408—862no—
434C2×C22⋊C8—862no—
435C2×C22⋊C8—862no—
436#343—862no—
437#336—862no—
438C43#1099611yescharacteristic, complemented, Sylow
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×#41—21no—
449C2×#41—21no—
450C2×#41—21no—
451C2×#41—861no—
452C2×#41—861no—
453C2×#41—861no—
454C2×#41—861no—
455C2×#41—861no—
456C2×#41—861no—
457C2×#41—861no—
458C2×#41—861no—
459C2×#41—861no—
460C2×#41—861no—
461C2×#41—861no—
462C2×#41—861no—
463C22×Q8—431no—
464C22×Q8C22⋊D4311yescharacteristic
465C22×D4—432no—
466C22×D4—431no—
467C22×D4C4×D4312yes—
468C22×D4C22⋊D4311yescharacteristic
469C23×C4—432no—
470C23×C4D17212yes—
471C23×C4C22×D4311yescharacteristic
472C2×M16—21no—
473C2×M16—21no—
474C2×M16—21no—
475C2×M16—21no—
476C2×M16—21no—
477C2×M16—21no—
478C2×M16—21no—
479C2×M16—21no—
480C2×M16—21no—
481C2×M16—21no—
482C2×M16—432no—
483C2×M16—861no—
484C2×M16—861no—
485C2×M16—861no—
486C2×M16—861no—
487C2×M16—861no—
488C2×M16C22⋊D4312yescomplemented
489C2×M16C22⋊D4312yescomplemented
490C22×C8—21no—
491C22×C8—21no—
492C22×C8—432no—
493C22×C8—861no—
494C22×C8—861no—
495C22×C8—861no—
496C22×C8—861no—
497C22×C8—861no—
498C22×C8—861no—
499C22×C8—861no—
500C4⋊Q8—862no—
501#127—862no—
502#124—862no—
503#124—862no—
504#123—864no—
505#123—864no—
506C22⋊Q8—864no—
507C22⋊Q8—864no—
508#121—864no—
509#121—868no—
510#121—864no—
511#120—864no—
512#120—864no—
513C4×D4—868no—
514#117—861no—
515#117—861no—
516#117—861no—
517#117—861no—
518C2×C4⋊C4—432no—
519C2×C22⋊C4—432no—
520C2×C42—432no—
521#101—24no—
522#101—864no—
523#100—24no—
524#100—864no—
525C22⋊C8—868no—
526C22⋊C8—868no—
527C24—432no—
528C24(C2×D43)⋊C412yes—
529C24C2×C4×D4311yescharacteristic
530#41—41no—
531#41—41no—
532#41—41no—
533#41—41no—
534#41—41no—
535#41—41no—
536#41—41no—
537#41—41no—
538#41—41no—
539#41—41no—
540#41—41no—
541#41—41no—
542#41—41no—
543#41—41no—
544#41—41no—
545#41—41no—
546#41—1721no—
547#41—1721no—
548#41—1721no—
549#41—1721no—
550#41—1721no—
551#41—1721no—
552#41—1721no—
553#41—1721no—
554#41—1721no—
555#41—1721no—
556#41—1721no—
557#41—1721no—
558#41—1721no—
559#41—1721no—
560#41—1721no—
561#41—1721no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—21no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8—21no—
568C2×Q8—861no—
569C2×Q8—861no—
570C2×Q8—861no—
571C2×Q8—861no—
572C2×Q8—861no—
573C2×Q8—861no—
574C2×D4—22no—
575C2×D4—22no—
576C2×D4—22no—
577C2×D4—22no—
578C2×D4—22no—
579C2×D4—22no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—868no—
587C2×D4—862no—
588C2×D4—862no—
589C2×D4—862no—
590C2×D4—862no—
591C2×D4—862no—
592C2×D4—862no—
593C2×D4—861no—
594C2×D4—861no—
595C2×D4—861no—
596C2×D4—861no—
597C2×D4—861no—
598C2×D4—861no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—432no—
606C22×C4—434no—
607C22×C4—862no—
608C22×C4—862no—
609C22×C4—862no—
610C22×C4—862no—
611C22×C4—862no—
612C22×C4—862no—
613C22×C4(C2×D43)⋊C412yes—
614C22×C4C2×D17211yescharacteristic
615C22×C4#1062189811yescharacteristic
616C22×C4#1062189811yescharacteristic
617C22×C4D4×D4311yescharacteristic
618C22×C4D4×D4311yescharacteristic
619C22×C4D4×D4311yescharacteristic
620C22×C4D4×D4311yescharacteristic
621C22×C4D4×D4311yescharacteristic
622C22×C4D4×D4311yescharacteristic
623C22×C4#1062190011yescharacteristic
624C22×C4#1062190011yescharacteristic
625C22×C4C2×C22⋊D4311yescharacteristic
626C22×C4C2×C22⋊D4311yescharacteristic
627C22×C4C2×C22⋊D4311yescharacteristic
628M16—22no—
629M16—22no—
630M16—22no—
631M16—22no—
632M16—41no—
633M16—41no—
634M16—41no—
635M16—41no—
636M16—862no—
637M16—862no—
638M16—1721no—
639M16—1721no—
640C2×C8—22no—
641C2×C8—22no—
642C2×C8—41no—
643C2×C8—41no—
644C2×C8—41no—
645C2×C8—41no—
646C2×C8—862no—
647C2×C8—862no—
648C2×C8—862no—
649C2×C8—862no—
650C2×C8—1721no—
651C2×C8—1721no—
652C2×C8—1721no—
653C2×C8—1721no—
654C2×C8—1721no—
655C2×C8—1721no—
656C4⋊C4—868no—
657C4⋊C4—862no—
658C4⋊C4—862no—
659C22⋊C4—868no—
660C22⋊C4—868no—
661C22⋊C4—862no—
662C22⋊C4—862no—
663C42—862no—
664C42—862no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—42no—
669C23—44no—
670C23—862no—
671C23—862no—
672C23—862no—
673C23—1724no—
674C23C22⋊C4×D4311yescharacteristic
675C23C22⋊C4×D4311yescharacteristic
676C23C2×(C2×D43)⋊C411yescharacteristic
677C23(C22⋊D43)⋊C411yescharacteristic
678C23(C22⋊D43)⋊C411yescharacteristic
679C23C4×C22⋊D4311yescharacteristic
680C23C4×C22⋊D4311yescharacteristic
681Q8—41no—
682Q8—41no—
683Q8—41no—
684Q8—41no—
685Q8—1721no—
686Q8—1721no—
687Q8—1721no—
688Q8—1721no—
689D4—42no—
690D4—42no—
691D4—42no—
692D4—42no—
693D4—41no—
694D4—41no—
695D4—41no—
696D4—41no—
697D4—3448no—
698D4—1722no—
699D4—1722no—
700D4—1722no—
701D4—1722no—
702D4—1721no—
703D4—1721no—
704D4—1721no—
705D4—1721no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—864no—
714C2×C4—862no—
715C2×C4—862no—
716C2×C4—862no—
717C2×C4—1722no—
718C2×C4—1722no—
719C2×C4—1722no—
720C2×C4—1722no—
721C2×C4—1724no—
722C2×C4#1306329311yescharacteristic
723C2×C4#1306329311yescharacteristic
724C2×C4#1306329311yescharacteristic
725C2×C4#1306329311yescharacteristic
726C2×C4#1306329411yescharacteristic
727C2×C4#1306329511yescharacteristic
728C2×C4#1306329511yescharacteristic
729C2×C4#1306329511yescharacteristic
730C2×C4#1306329611yescharacteristic
731C2×C4#1306329611yescharacteristic
732C2×C4#1306329711yescharacteristic
733C2×C4#1306329711yescharacteristic
734C2×C4#1306329711yescharacteristic
735C2×C4#1306329711yescharacteristic
736C2×C4#1306329811yescharacteristic
737C2×C4#1306329811yescharacteristic
738C2×C4#1306329811yescharacteristic
739C2×C4#1306329811yescharacteristic
740C2×C4#1306329911yescharacteristic
741C2×C4#1306329911yescharacteristic
742C2×C4#1306330711yescharacteristic
743C2×C4#1306330711yescharacteristic
744C2×C4#1306330811yescharacteristic
745C2×C4#1306330911yescharacteristic
746C2×C4#1306331111yescharacteristic
747C2×C4#1306331111yescharacteristic
748C2×C4#1306332111yescharacteristic
749C2×C4#1306332111yescharacteristic
750C8—42no—
751C8—42no—
752C8—1722no—
753C8—1722no—
754C22—22no—
755C22—22no—
756C22—22no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—44no—
762C22—44no—
763C22—42no—
764C22—82no—
765C22—3442no—
766C22—1724no—
767C22—1724no—
768C22—1722no—
769C22#1458275411yescharacteristic
770C22#1458277511yescharacteristic
771C22#1458277511yescharacteristic
772C22#1458277611yescharacteristic
773C22#1458277811yescharacteristic
774C22#1458279911yescharacteristic
775C22#1458279911yescharacteristic
776C4—42no—
777C4—1724no—
778C4—1722no—
779C4#1458280711yescharacteristic
780C4#1458280711yescharacteristic
781C4#1458280811yescharacteristic
782C4#1458280811yescharacteristic
783C4#1458281411yescharacteristic
784C4#1458281411yescharacteristic
785C4#1458281511yescharacteristic
786C4#1458281511yescharacteristic
787C2—21no—
788C2—21no—
789C2—21no—
790C2—21no—
791C2—21no—
792C2—21no—
793C2—82no—
794C2—3442no—
795C2#1913283411yescharacteristic
796C2#1913454412yes—
subgroupG/H
centerC2×C4#13063295
commutatorC24×C43C22×C4
FrattiniC23×C4C22×D43
FittingC2×C43×#413C2
socleC22×C43#379
prime radical#19147924C2
cosocleC23×C4×C43C23
hypercenterC2×#413D43
hypocenterC43#10996
LCSG ▷ C24×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#413

Complements

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

NH ≅ G/Ntype
2. C2×#14582881C2semidirect
3. C2×#14582867C2semidirect
4. C2×#14582866C2semidirect
5. #19134333C2semidirect
6. #19134293C2semidirect
7. C2×C43×#413C2semidirect
61. C2×#10621877D4semidirect
69. C22×C43⋊C8D4semidirect
122. C2×M16×C43D4semidirect
123. C2×M16×C43D4semidirect
391. C2×#413D43semidirect
438. C43#10996semidirect
488. C2×M16C22⋊D43semidirect
489. C2×M16C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
#191479242
C2×#145828812
C2×#145828672
C2×#145828662
#191343332
#191342932
C2×C43×#4132
#1099643