Finite Group Databasebeta

← #25003255

Subgroups — #25003255

Order 11008.

1310 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147924C211yesmaximal, characteristic
2C2×#14582916C211yesmaximal, characteristic, complemented
3C2×#14582872C211yesmaximal, characteristic, complemented
4C2×#14582865C211yesmaximal, characteristic, complemented
5#19134312C211yesmaximal, characteristic, complemented
6#19134305C211yesmaximal, characteristic, complemented
7C2×C43×#416C211yesmaximal, characteristic, complemented
8C22×#10621898C2211yescharacteristic
9C22×#10621877C2211yescharacteristic
10#14583477—22no—
11#14583473—21no—
12#14583470C412yescomplemented
13#14583466—21no—
14#14583463C412yescomplemented
15#14583458—22no—
16#14583445—22no—
17#14583410—22no—
18#14583406—22no—
19C2×#13063284C2211yescharacteristic
20C2×#13063284C2211yescharacteristic
21#14582916—22no—
22#14582916—22no—
23C2×#13063252—22no—
24#14582872—22no—
25#14582872—22no—
26C2×#13063239—22no—
27#14582865—22no—
28#14582865—22no—
29C2×(C2×D43)⋊C8—22no—
30#14582662—22no—
31#14582659—22no—
32C22×#41×C43C2211yescharacteristic
33C23×C8×C43C2211yescharacteristic
34C2×#117×C43C2211yescharacteristic
35C43×#416—22no—
36C43×#416—22no—
37C2×#103×C43—21no—
38C2×#102×C43—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×#10621898—21no—
49C2×#10621898—21no—
50C2×#10621898—21no—
51C22×Dic86C2×C411yescharacteristic
52C22×D172C2×C411yescharacteristic
53C22×C22⋊D43D412yes—
54C22×C4×D43D412yes—
55C2×#10621877—21no—
56C2×#10621877—21no—
57C2×#10621877—21no—
58C2×#10621877—21no—
59C2×#10621877—21no—
60C2×#10621877D412yescomplemented
61C22×C43⋊C8—21no—
62#13063323—22no—
63#13063321—22no—
64#13063314—22no—
65#13063312—22no—
66#13063308—24no—
67#13063306—24no—
68#13063304—24no—
69#13063301—24no—
70#13063299—24no—
71#13063297—28no—
72#13063296—24no—
73#13063294—24no—
74#13063293—24no—
75C4×C22⋊D43—28no—
76#13063284—21no—
77#13063284—21no—
78#13063284—21no—
79#13063284—21no—
80#13063284—21no—
81#13063284C2×C412yes—
82#13063284D412yes—
83#13063284D412yescomplemented
84C2×C4⋊Dic43—21no—
85C2×C4⋊Dic43D412yes—
86C2×C22⋊Dic43—21no—
87C2×C22⋊Dic43—21no—
88C2×C4×Dic43—21no—
89C2×C4×Dic43—21no—
90#13063252—28no—
91#13063239—28no—
92(C2×D43)⋊C8—28no—
93C2×#41×C43—21no—
94C2×#41×C43—21no—
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×C43C2×C412yes—
104C2×#41×C43D412yes—
105C22×Q8×C43D411yescharacteristic
106C22×D4×C43—21no—
107C22×D4×C43D411yescharacteristic
108C23×C4×C43—21no—
109C23×C4×C43C2311yescharacteristic
110C22×C8×C43—21no—
111C22×C8×C43—21no—
112C22×C8×C43—21no—
113C22×C8×C43—21no—
114C22×C8×C43—21no—
115C22×C8×C43—21no—
116C22×C8×C43D412yescomplemented
117#117×C43—21no—
118#117×C43—21no—
119#117×C43—21no—
120#117×C43D412yescomplemented
121C2×C4⋊C4×C43—21no—
122C2×C22⋊C4×C43—21no—
123C2×C42×C43—21no—
124#103×C43—24no—
125#102×C43—24no—
126C24×C43—21no—
127C24×C43C2×D411yescharacteristic
128C23×D43C22⋊C412yes—
129#41×C43—22no—
130#41×C43—22no—
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—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—
145C2×Q8×C43—21no—
146C2×Q8×C43—21no—
147C2×Q8×C43—21no—
148C2×Q8×C43—21no—
149C2×Q8×C43—21no—
150C2×Q8×C43C22⋊C412yes—
151C2×D4×C43—21no—
152C2×D4×C43—22no—
153C2×D4×C43—22no—
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43—21no—
157C2×D4×C43—21no—
158C2×D4×C43—41no—
159C2×D4×C43—41no—
160C2×D4×C43—41no—
161C2×D4×C43—41no—
162C2×D4×C43C22⋊C412yes—
163C22×C4×C43—22no—
164C22×C4×C43—22no—
165C22×C4×C43—21no—
166C22×C4×C43—41no—
167C22×C4×C43—41no—
168C22×C4×C43—41no—
169C22×C4×C43—41no—
170C22×C4×C43—41no—
171C22×C4×C43C22×C411yescharacteristic
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×C43#4111yescharacteristic
182C22×C4×C43#4111yescharacteristic
183C22×C4×C43#4111yescharacteristic
184C22×C4×C43#4111yescharacteristic
185C2×C22⋊D43—28no—
186C2×C22⋊D43—22no—
187C2×C22⋊D43—22no—
188C2×C22⋊D43—22no—
189C2×C22⋊D43—22no—
190C2×C22⋊D43—22no—
191C2×C22⋊D43—22no—
192C22×Dic43—22no—
193C22×Dic43—41no—
194C22×Dic43C22⋊C412yes—
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—
229C2×C8×C43—22no—
230C2×C8×C43—22no—
231C2×C8×C43—22no—
232C2×C8×C43—41no—
233C2×C8×C43—41no—
234C2×C8×C43—41no—
235C2×C8×C43—41no—
236C4⋊C4×C43—22no—
237C4⋊C4×C43—41no—
238C22⋊C4×C43—22no—
239C22⋊C4×C43—41no—
240C42×C43—22no—
241C42×C43—41no—
242C22⋊Dic43—28no—
243C22⋊Dic43—22no—
244C22⋊Dic43—22no—
245C22⋊Dic43—22no—
246C22⋊Dic43—41no—
247(C2×D43)⋊C4—28no—
248C4⋊Dic43—22no—
249C4⋊Dic43—22no—
250C4⋊Dic43—41no—
251C4⋊Dic43C22⋊C414yes—
252Dic43⋊C4—28no—
253C4×Dic43—22no—
254C4×Dic43—22no—
255C4×Dic43—22no—
256C4×Dic43—41no—
257#10621877—22no—
258#10621877—22no—
259#10621877—41no—
260#10621877—41no—
261C2×C43⋊C8—22no—
262C2×C43⋊C8—41no—
263C2×C43⋊C8—41no—
264C23×C43—22no—
265C23×C43—42no—
266C23×C43—41no—
267C23×C43—41no—
268C23×C43—82no—
269C23×C43C2×C22⋊C411yescharacteristic
270C23×C43#12011yescharacteristic
271C23×C43#12011yescharacteristic
272C23×C43#12011yescharacteristic
273C23×C43#12111yescharacteristic
274C23×C43#12111yescharacteristic
275C23×C43#12311yescharacteristic
276C22×D43—22no—
277C22×D43—22no—
278C22×D43—22no—
279C22×D43—44no—
280Q8×C43—22no—
281Q8×C43—22no—
282Q8×C43—41no—
283Q8×C43—41no—
284D4×C43—22no—
285D4×C43—22no—
286D4×C43—42no—
287D4×C43—42no—
288D4×C43—42no—
289D4×C43—42no—
290D4×C43—41no—
291D4×C43—41no—
292C2×C4×C43—22no—
293C2×C4×C43—41no—
294C2×C4×C43—41no—
295C2×C4×C43—42no—
296C2×C4×C43—42no—
297C2×C4×C43—42no—
298C2×C4×C43—42no—
299C2×C4×C43—42no—
300C2×C4×C43—82no—
301C2×C4×C43C2×C22⋊C411yescharacteristic
302C2×C4×C43C2×C22⋊C411yescharacteristic
303C2×C4×C43C4×D411yescharacteristic
304C2×C4×C43C4×D411yescharacteristic
305C2×C4×C43C4×D411yescharacteristic
306C2×C4×C43C4×D411yescharacteristic
307C2×C4×C43#12011yescharacteristic
308C2×C4×C43#12011yescharacteristic
309C2×C4×C43#12011yescharacteristic
310C2×C4×C43#12011yescharacteristic
311C2×C4×C43#12011yescharacteristic
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#12111yescharacteristic
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—42no—
339C2×Dic43—82no—
340C2×Dic43—82no—
341D172—41no—
342D172—41no—
343D172—41no—
344D172—41no—
345C4×D43—42no—
346C4×D43—42no—
347C4×D43—42no—
348C4×D43—42no—
349Dic86—41no—
350Dic86—41no—
351Dic86—41no—
352Dic86—41no—
353C8×C43—42no—
354C43⋊C8—42no—
355#10999—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—82no—
366C22×C43—82no—
367C22×C43#37911yescharacteristic
368C22×C43#38611yescharacteristic
369C22×C43#38611yescharacteristic
370C22×C43#39211yescharacteristic
371C22×C43#39211yescharacteristic
372C22×C43#39411yescharacteristic
373C22×C43#39411yescharacteristic
374C2×D43—44no—
375C2×D43—44no—
376C2×D43—42no—
377C2×D43—82no—
378C4×C43—42no—
379C4×C43—82no—
380C4×C43#38611yescharacteristic
381C4×C43#38611yescharacteristic
382C4×C43#39011yescharacteristic
383C4×C43#39011yescharacteristic
384C4×C43#39211yescharacteristic
385C4×C43#39211yescharacteristic
386C4×C43#39411yescharacteristic
387C4×C43#39411yescharacteristic
388Dic43—44no—
389Dic43—42no—
390Dic43—82no—
391#3449—431no—
392C2×#421—431no—
393C2×#416D4311yescharacteristic, complemented
394C2×#410—431no—
395C2×#408—431no—
396#1735—431no—
397#1733—431no—
398C2×C43—21no—
399C2×C43—21no—
400C2×C43—21no—
401C2×C43—21no—
402C2×C43—21no—
403C2×C43—21no—
404C2×C43—82no—
405C2×C43#143811yescharacteristic
406C2×C43#179412yes—
407D43—82no—
408C22×#41—431no—
409C22×#41C2×D4311yescharacteristic
410C22×M16—431no—
411C23×C8C2×D4311yescharacteristic
412#537—862no—
413#536—432no—
414#536—861no—
415#535—432no—
416#535—861no—
417#534—862no—
418#532—862no—
419#525—862no—
420#525—862no—
421C2×#117—431no—
422C2×#117—431no—
423C2×#117C2×D4311yescharacteristic
424#421—862no—
425#421—862no—
426C2×#104—862no—
427#416—22no—
428#416—22no—
429C2×#103—21no—
430C2×#102—21no—
431#410—862no—
432#410—862no—
433C2×#99—862no—
434#408—862no—
435#408—862no—
436C2×C22⋊C8—862no—
437#340—862no—
438#339—862no—
439C43#1099911yescharacteristic, complemented, Sylow
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—861no—
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×#41C4×D4312yes—
463C2×#41D17212yes—
464C22×Q8—431no—
465C22×Q8C22⋊D4311yescharacteristic
466C22×D4—21no—
467C22×D4—432no—
468C22×D4—431no—
469C22×D4C22⋊D4311yescharacteristic
470C23×C4—21no—
471C23×C4—432no—
472C23×C4C22×D4311yescharacteristic
473C2×M16—432no—
474C2×M16—861no—
475C2×M16—861no—
476C2×M16—861no—
477C2×M16—861no—
478C2×M16—861no—
479C22×C8—21no—
480C22×C8—21no—
481C22×C8—21no—
482C22×C8—21no—
483C22×C8—21no—
484C22×C8—21no—
485C22×C8—861no—
486C22×C8C22⋊D4312yescomplemented
487C4⋊Q8—862no—
488#127—862no—
489#124—862no—
490#124—862no—
491#123—864no—
492#123—864no—
493C22⋊Q8—864no—
494C22⋊Q8—864no—
495#121—864no—
496#121—864no—
497#121—868no—
498#120—864no—
499#120—864no—
500C4×D4—868no—
501#117—21no—
502#117—21no—
503#117—21no—
504#117—432no—
505#117—432no—
506#117—432no—
507#117—861no—
508#117—861no—
509#117—861no—
510#117—861no—
511#117—861no—
512#117C22⋊D4312yescomplemented
513C2×C4⋊C4—21no—
514C2×C4⋊C4—432no—
515C2×C4⋊C4—861no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—861no—
518C2×C22⋊C4—861no—
519C2×C42—21no—
520C2×C42—861no—
521C2×C42—861no—
522#104—868no—
523#103—24no—
524#102—24no—
525#99—868no—
526C22⋊C8—868no—
527C24—21no—
528C24—432no—
529C24D4×D4311yescharacteristic
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—
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—861no—
568C2×Q8—861no—
569C2×Q8—861no—
570C2×Q8—861no—
571C2×Q8—861no—
572C2×Q8—861no—
573C2×Q8(C2×D43)⋊C412yes—
574C2×D4—22no—
575C2×D4—22no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—41no—
582C2×D4—41no—
583C2×D4—41no—
584C2×D4—41no—
585C2×D4—868no—
586C2×D4—862no—
587C2×D4—862no—
588C2×D4—862no—
589C2×D4—862no—
590C2×D4—862no—
591C2×D4—862no—
592C2×D4—861no—
593C2×D4—861no—
594C2×D4—861no—
595C2×D4—861no—
596C2×D4—861no—
597C2×D4—861no—
598C2×D4(C2×D43)⋊C412yes—
599C22×C4—21no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—41no—
603C22×C4—41no—
604C22×C4—41no—
605C22×C4—41no—
606C22×C4—41no—
607C22×C4—432no—
608C22×C4—862no—
609C22×C4—862no—
610C22×C4—862no—
611C22×C4—862no—
612C22×C4—862no—
613C22×C4—862no—
614C22×C4—862no—
615C22×C4—1721no—
616C22×C4C2×C4×D4311yescharacteristic
617C22×C4C2×D17211yescharacteristic
618C22×C4#1062189811yescharacteristic
619C22×C4#1062189811yescharacteristic
620C22×C4D4×D4311yescharacteristic
621C22×C4D4×D4311yescharacteristic
622C22×C4D4×D4311yescharacteristic
623C22×C4D4×D4311yescharacteristic
624C22×C4D4×D4311yescharacteristic
625C22×C4#1062190011yescharacteristic
626C22×C4#1062190011yescharacteristic
627C22×C4C2×C22⋊D4311yescharacteristic
628C22×C4C2×C22⋊D4311yescharacteristic
629C22×C4C2×C22⋊D4311yescharacteristic
630M16—862no—
631M16—862no—
632M16—1721no—
633M16—1721no—
634C2×C8—22no—
635C2×C8—22no—
636C2×C8—22no—
637C2×C8—41no—
638C2×C8—41no—
639C2×C8—41no—
640C2×C8—41no—
641C2×C8—862no—
642C2×C8—1721no—
643C2×C8—1721no—
644C4⋊C4—22no—
645C4⋊C4—41no—
646C4⋊C4—434no—
647C4⋊C4—868no—
648C4⋊C4—862no—
649C4⋊C4—862no—
650C4⋊C4—1721no—
651C22⋊C4—22no—
652C22⋊C4—41no—
653C22⋊C4—868no—
654C22⋊C4—868no—
655C22⋊C4—862no—
656C22⋊C4—862no—
657C22⋊C4—862no—
658C22⋊C4—1721no—
659C42—22no—
660C42—41no—
661C42—862no—
662C42—862no—
663C42—862no—
664C42—1721no—
665C23—22no—
666C23—42no—
667C23—41no—
668C23—41no—
669C23—82no—
670C23—862no—
671C23—862no—
672C23—862no—
673C23—1724no—
674C23C22⋊C4×D4311yescharacteristic
675C23#1306329311yescharacteristic
676C23#1306329311yescharacteristic
677C23#1306329511yescharacteristic
678C23#1306329611yescharacteristic
679C23#1306329811yescharacteristic
680C23#1306330711yescharacteristic
681Q8—22no—
682Q8—22no—
683Q8—41no—
684Q8—41no—
685Q8—1721no—
686Q8—1721no—
687Q8—1721no—
688Q8—1721no—
689D4—22no—
690D4—22no—
691D4—42no—
692D4—42no—
693D4—42no—
694D4—42no—
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—41no—
708C2×C4—41no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—82no—
715C2×C4—864no—
716C2×C4—862no—
717C2×C4—862no—
718C2×C4—862no—
719C2×C4—3442no—
720C2×C4—3442no—
721C2×C4—1722no—
722C2×C4—1722no—
723C2×C4—1722no—
724C2×C4—1722no—
725C2×C4—1722no—
726C2×C4C22⋊C4×D4311yescharacteristic
727C2×C4C2×(C2×D43)⋊C411yescharacteristic
728C2×C4(C22⋊D43)⋊C411yescharacteristic
729C2×C4(C22⋊D43)⋊C411yescharacteristic
730C2×C4C4×C22⋊D4311yescharacteristic
731C2×C4C4×C22⋊D4311yescharacteristic
732C2×C4#1306329311yescharacteristic
733C2×C4#1306329311yescharacteristic
734C2×C4#1306329411yescharacteristic
735C2×C4#1306329511yescharacteristic
736C2×C4#1306329511yescharacteristic
737C2×C4#1306329611yescharacteristic
738C2×C4#1306329711yescharacteristic
739C2×C4#1306329711yescharacteristic
740C2×C4#1306329711yescharacteristic
741C2×C4#1306329711yescharacteristic
742C2×C4#1306329811yescharacteristic
743C2×C4#1306329811yescharacteristic
744C2×C4#1306329811yescharacteristic
745C2×C4#1306329911yescharacteristic
746C2×C4#1306329911yescharacteristic
747C2×C4#1306330711yescharacteristic
748C2×C4#1306330811yescharacteristic
749C2×C4#1306330911yescharacteristic
750C2×C4#1306331111yescharacteristic
751C2×C4#1306331111yescharacteristic
752C2×C4#1306332111yescharacteristic
753C2×C4#1306332111yescharacteristic
754C8—42no—
755C8—1722no—
756C22—22no—
757C22—22no—
758C22—22no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—44no—
764C22—42no—
765C22—82no—
766C22—82no—
767C22—3442no—
768C22—1724no—
769C22—1724no—
770C22—1722no—
771C22#1458275411yescharacteristic
772C22#1458277511yescharacteristic
773C22#1458277511yescharacteristic
774C22#1458280711yescharacteristic
775C22#1458280811yescharacteristic
776C22#1458281411yescharacteristic
777C22#1458281511yescharacteristic
778C4—42no—
779C4—82no—
780C4—3442no—
781C4—1724no—
782C4—1722no—
783C4#1458277611yescharacteristic
784C4#1458277811yescharacteristic
785C4#1458279911yescharacteristic
786C4#1458279911yescharacteristic
787C4#1458280711yescharacteristic
788C4#1458280811yescharacteristic
789C4#1458281411yescharacteristic
790C4#1458281511yescharacteristic
791C2—21no—
792C2—21no—
793C2—21no—
794C2—21no—
795C2—21no—
796C2—21no—
797C2—82no—
798C2—3442no—
799C2#1913283411yescharacteristic
800C2#1913456012yes—
subgroupG/H
centerC2×C4#13063295
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC2×C43×#416C2
socleC22×C43#379
prime radical#19147924C2
cosocleC23×C4×C43C23
hypercenterC2×#416D43
hypocenterC43#10999
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#416

Complements

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

NH ≅ G/Ntype
2. C2×#14582916C2semidirect
3. C2×#14582872C2semidirect
4. C2×#14582865C2semidirect
5. #19134312C2semidirect
6. #19134305C2semidirect
7. C2×C43×#416C2semidirect
12. #14583470C4semidirect
14. #14583463C4semidirect
60. C2×#10621877D4semidirect
83. #13063284D4semidirect
116. C22×C8×C43D4semidirect
120. #117×C43D4semidirect
393. C2×#416D43semidirect
439. C43#10999semidirect
486. C22×C8C22⋊D43semidirect
512. #117C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
#191479242
C2×#145829162
C2×#145828722
C2×#145828652
#191343122
#191343052
C2×C43×#4162
#1099943