Finite Group Databasebeta

← #25003415

Subgroups — #25003415

Order 11008.

1278 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063345C211yesmaximal, characteristic
2C2×#14582917C211yesmaximal, characteristic, complemented
3C2×#14582916C211yesmaximal, characteristic, complemented
4C2×#14582872C211yesmaximal, characteristic, complemented
5#19134311C211yesmaximal, characteristic, complemented
6#19134292C211yesmaximal, characteristic, complemented
7C2×C43×#410C211yesmaximal, characteristic, complemented
8C22×#10621898C2211yescharacteristic
9C2×#13063345—22no—
10C2×#13063345—22no—
11C2×#13063345—22no—
12C2×#13063345—22no—
13C2×#13063345—22no—
14C2×#13063345—22no—
15C22×#10621885C411yescharacteristic, complemented
16C22×#10621883C411yescharacteristic, complemented
17C22×#10621884C411yescharacteristic, complemented
18C22×#10621882C411yescharacteristic, complemented
19C22×#10621877C2211yescharacteristic
20C23×C43⋊C8C2211yescharacteristic
21C2×#13063284C2211yescharacteristic
22#14582917—22no—
23#14582917—22no—
24#14582916—22no—
25#14582916—22no—
26C2×#13063253—22no—
27C2×#13063252—22no—
28#14582872—22no—
29#14582872—22no—
30C2×#13063239—22no—
31#14582661—22no—
32#14582654—22no—
33C22×#41×C43C2211yescharacteristic
34C2×#117×C43C2211yescharacteristic
35C2×#117×C43C2211yescharacteristic
36C43×#410—22no—
37C43×#410—22no—
38C2×#99×C43—22no—
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×#10621898D412yes—
50C2×#10621898D412yes—
51C22×Dic86C2×C411yescharacteristic
52C22×D172C2×C411yescharacteristic
53C22×C22⋊D43—21no—
54C22×C4×D43—21no—
55#13063345—28no—
56#13063345—28no—
57#13063345—28no—
58#13063345—28no—
59C2×#10621885—22no—
60C2×#10621885—22no—
61C2×#10621885—22no—
62C2×#10621883—22no—
63C2×#10621883—22no—
64C2×#10621883—22no—
65C2×#10621884—22no—
66C2×#10621884—22no—
67C2×#10621884—22no—
68C2×#10621882—22no—
69C2×#10621882—22no—
70C2×#10621882—22no—
71C2×#10621877—21no—
72C2×#10621877—21no—
73C2×#10621877—21no—
74C2×#10621877—21no—
75C2×#10621877—21no—
76C2×#10621877D412yes—
77C22×C43⋊C8—21no—
78C22×C43⋊C8—21no—
79C22×C43⋊C8—21no—
80C22×C43⋊C8—21no—
81C22×C43⋊C8—21no—
82C22×C43⋊C8C2×C411yescharacteristic
83C22×C43⋊C8C2×C411yescharacteristic
84C22×C43⋊C8D412yes—
85C22×C43⋊C8D412yes—
86#13063284—21no—
87#13063284—21no—
88#13063284—21no—
89#13063284D412yes—
90C2×C4⋊Dic43—21no—
91C2×C22⋊Dic43—21no—
92C2×C4×Dic43—21no—
93#13063253—28no—
94#13063252—28no—
95#13063239—28no—
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×C43D412yes—
107C2×#41×C43D412yes—
108C22×Q8×C43C2×C411yescharacteristic
109C22×D4×C43—21no—
110C22×D4×C43C2×C411yescharacteristic
111C23×C4×C43—21no—
112C23×C4×C43C2311yescharacteristic
113#117×C43—21no—
114#117×C43—21no—
115#117×C43—21no—
116#117×C43—21no—
117#117×C43—21no—
118#117×C43—21no—
119#117×C43—21no—
120#117×C43D412yes—
121C2×C4⋊C4×C43—21no—
122C2×C4⋊C4×C43—21no—
123C2×C22⋊C4×C43—21no—
124C2×C22⋊C4×C43D412yes—
125C2×C42×C43—21no—
126C2×C42×C43—21no—
127#99×C43—28no—
128C24×C43—21no—
129C24×C43C2×D411yescharacteristic
130C23×D43—21no—
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—
147C2×Q8×C43—21no—
148C2×Q8×C43—21no—
149C2×Q8×C43—21no—
150C2×Q8×C43—21no—
151C2×Q8×C43—21no—
152C2×Q8×C43C22⋊C412yes—
153C2×D4×C43—21no—
154C2×D4×C43—22no—
155C2×D4×C43—22no—
156C2×D4×C43—21no—
157C2×D4×C43—21no—
158C2×D4×C43—21no—
159C2×D4×C43—21no—
160C2×D4×C43—41no—
161C2×D4×C43—41no—
162C2×D4×C43—41no—
163C2×D4×C43—41no—
164C2×D4×C43C22⋊C412yes—
165C22×C4×C43—22no—
166C22×C4×C43—22no—
167C22×C4×C43—21no—
168C22×C4×C43—22no—
169C22×C4×C43—41no—
170C22×C4×C43—41no—
171C22×C4×C43—41no—
172C22×C4×C43—41no—
173C22×C4×C43—41no—
174C22×C4×C43C22×C411yescharacteristic
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×C43C2×D411yescharacteristic
184C22×C4×C43#4111yescharacteristic
185C22×C4×C43#4111yescharacteristic
186C22×C4×C43#4111yescharacteristic
187C22×C4×C43#4111yescharacteristic
188C2×C22⋊D43—22no—
189C2×C22⋊D43—22no—
190C2×C22⋊D43—41no—
191C2×C22⋊D43—41no—
192C2×C22⋊D43—41no—
193C2×C22⋊D43—41no—
194C22×Dic43—21no—
195C22×Dic43—41no—
196#10621898—22no—
197#10621898—22no—
198#10621898—22no—
199#10621898—22no—
200#10621898—22no—
201#10621898—22no—
202#10621898—22no—
203#10621898—22no—
204#10621898—41no—
205#10621898—41no—
206#10621898—41no—
207#10621898—41no—
208#10621898—41no—
209#10621898—41no—
210#10621898—41no—
211#10621898—41no—
212C2×D172—21no—
213C2×D172—21no—
214C2×D172—21no—
215C2×D172—21no—
216C2×D172—21no—
217C2×D172C22⋊C412yes—
218C2×C4×D43—22no—
219C2×C4×D43—22no—
220C2×C4×D43—41no—
221C2×C4×D43—41no—
222C2×C4×D43—41no—
223C2×C4×D43—41no—
224C2×Dic86—21no—
225C2×Dic86—21no—
226C2×Dic86—21no—
227C2×Dic86—21no—
228C2×Dic86—21no—
229C2×Dic86C22⋊C412yes—
230C4⋊C4×C43—22no—
231C4⋊C4×C43—41no—
232C4⋊C4×C43—41no—
233C4⋊C4×C43—41no—
234C22⋊C4×C43—22no—
235C22⋊C4×C43—22no—
236C22⋊C4×C43—22no—
237C22⋊C4×C43—41no—
238C42×C43—22no—
239C42×C43—41no—
240C42×C43—41no—
241C42×C43—41no—
242C22⋊Dic43—22no—
243C22⋊Dic43—41no—
244#10621885—28no—
245#10621884—28no—
246#10621883—28no—
247#10621882—28no—
248C4⋊Dic43—22no—
249C4⋊Dic43—41no—
250C4×Dic43—22no—
251C4×Dic43—41no—
252#10621877—22no—
253#10621877—22no—
254#10621877—41no—
255#10621877—41no—
256C2×C43⋊C8—21no—
257C2×C43⋊C8—21no—
258C2×C43⋊C8—21no—
259C2×C43⋊C8—21no—
260C2×C43⋊C8—22no—
261C2×C43⋊C8—22no—
262C2×C43⋊C8—22no—
263C2×C43⋊C8—22no—
264C2×C43⋊C8—22no—
265C2×C43⋊C8—41no—
266C2×C43⋊C8—41no—
267C2×C43⋊C8C22⋊C412yes—
268C2×C43⋊C8C22⋊C412yes—
269C23×C43—22no—
270C23×C43—42no—
271C23×C43—41no—
272C23×C43—41no—
273C23×C43—82no—
274C23×C43C4×D411yescharacteristic
275C23×C43#12011yescharacteristic
276C23×C43#12011yescharacteristic
277C23×C43#12111yescharacteristic
278C23×C43#12111yescharacteristic
279C23×C43#12111yescharacteristic
280C23×C43#12711yescharacteristic
281C22×D43—22no—
282C22×D43—41no—
283C22×D43—41no—
284C22×D43—82no—
285Q8×C43—22no—
286Q8×C43—22no—
287Q8×C43—41no—
288Q8×C43—41no—
289D4×C43—22no—
290D4×C43—22no—
291D4×C43—42no—
292D4×C43—42no—
293D4×C43—42no—
294D4×C43—42no—
295D4×C43—41no—
296D4×C43—41no—
297C2×C4×C43—22no—
298C2×C4×C43—41no—
299C2×C4×C43—41no—
300C2×C4×C43—42no—
301C2×C4×C43—42no—
302C2×C4×C43—42no—
303C2×C4×C43—42no—
304C2×C4×C43—44no—
305C2×C4×C43—42no—
306C2×C4×C43—42no—
307C2×C4×C43—82no—
308C2×C4×C43C2×C22⋊C411yescharacteristic
309C2×C4×C43C2×C22⋊C411yescharacteristic
310C2×C4×C43C2×C22⋊C411yescharacteristic
311C2×C4×C43C4×D411yescharacteristic
312C2×C4×C43C4×D411yescharacteristic
313C2×C4×C43C4×D411yescharacteristic
314C2×C4×C43#12011yescharacteristic
315C2×C4×C43#12011yescharacteristic
316C2×C4×C43#12011yescharacteristic
317C2×C4×C43#12011yescharacteristic
318C2×C4×C43#12011yescharacteristic
319C2×C4×C43#12011yescharacteristic
320C2×C4×C43#12111yescharacteristic
321C2×C4×C43#12111yescharacteristic
322C2×C4×C43#12111yescharacteristic
323C2×C4×C43#12111yescharacteristic
324C2×C4×C43#12111yescharacteristic
325C2×C4×C43#12111yescharacteristic
326C2×C4×C43#12111yescharacteristic
327C2×C4×C43#12111yescharacteristic
328C2×C4×C43#12111yescharacteristic
329C2×C4×C43#12311yescharacteristic
330C2×C4×C43#12311yescharacteristic
331C2×C4×C43#12311yescharacteristic
332C2×C4×C43#12311yescharacteristic
333C2×C4×C43#12411yescharacteristic
334C2×C4×C43#12411yescharacteristic
335C2×C4×C43#12711yescharacteristic
336C22⋊D43—42no—
337C22⋊D43—42no—
338C22⋊D43—42no—
339C22⋊D43—42no—
340C2×Dic43—22no—
341C2×Dic43—41no—
342C2×Dic43—41no—
343C2×Dic43—42no—
344C2×Dic43—82no—
345D172—22no—
346D172—22no—
347D172—41no—
348D172—41no—
349C4×D43—42no—
350C4×D43—42no—
351C4×D43—42no—
352C4×D43—42no—
353Dic86—22no—
354Dic86—22no—
355Dic86—41no—
356Dic86—41no—
357C43⋊C8—22no—
358C43⋊C8—22no—
359C43⋊C8—42no—
360#11026—431nomaximal, Sylow
361C22×C43—22no—
362C22×C43—22no—
363C22×C43—22no—
364C22×C43—41no—
365C22×C43—41no—
366C22×C43—41no—
367C22×C43—41no—
368C22×C43—42no—
369C22×C43—82no—
370C22×C43—82no—
371C22×C43—82no—
372C22×C43#38611yescharacteristic
373C22×C43#38611yescharacteristic
374C22×C43#39011yescharacteristic
375C22×C43#39211yescharacteristic
376C22×C43#39211yescharacteristic
377C22×C43#39211yescharacteristic
378C22×C43#39411yescharacteristic
379C2×D43—42no—
380C2×D43—82no—
381C2×D43—82no—
382C2×D43—82no—
383C4×C43—42no—
384C4×C43—82no—
385C4×C43—82no—
386C4×C43#37911yescharacteristic
387C4×C43#38611yescharacteristic
388C4×C43#38611yescharacteristic
389C4×C43#39011yescharacteristic
390C4×C43#39211yescharacteristic
391C4×C43#39411yescharacteristic
392C4×C43#39411yescharacteristic
393C4×C43#39411yescharacteristic
394Dic43—42no—
395Dic43—82no—
396C22×#135—431no—
397C2×#421—431no—
398C2×#421—431no—
399C2×#410—431no—
400C2×#410D4311yescharacteristic, complemented
401#1735—431no—
402#1729—431no—
403C2×C43—21no—
404C2×C43—21no—
405C2×C43—21no—
406C2×C43—21no—
407C2×C43—21no—
408C2×C43—21no—
409C2×C43—82no—
410C2×C43#143811yescharacteristic
411C2×C43#197612yes—
412D43—82no—
413C22×#41—431no—
414C22×#41C2×D4311yescharacteristic
415C2×#135—862no—
416C2×#135—862no—
417C2×#135—862no—
418C2×#135—862no—
419C2×#135—862no—
420C2×#135—862no—
421C22×Q16—431no—
422C22×SD16—431no—
423C22×SD16—431no—
424C22×D8—431no—
425C22×M16—431no—
426C23×C8—431no—
427C2×#117—431no—
428C2×#117C2×D4311yescharacteristic
429C2×#117C2×D4311yescharacteristic
430#421—862no—
431#421—862no—
432#421—862no—
433#421—862no—
434C2×#104—862no—
435C2×#104—862no—
436#410—22no—
437#410—22no—
438#410—862no—
439#410—862no—
440C2×#99—22no—
441C2×#99—862no—
442#340—862no—
443#336—862no—
444C43#1102611yescharacteristic, complemented, Sylow
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—432no—
456C2×#41—432no—
457C2×#41—861no—
458C2×#41—861no—
459C2×#41—861no—
460C2×#41—861no—
461C2×#41—861no—
462C2×#41—861no—
463C2×#41—861no—
464C2×#41—861no—
465C2×#41—861no—
466C2×#41—861no—
467C2×#41D17212yes—
468C2×#41C22⋊D4312yes—
469C22×Q8—431no—
470C22×Q8C4×D4311yescharacteristic
471C22×D4—21no—
472C22×D4—431no—
473C22×D4—861no—
474C22×D4C4×D4311yescharacteristic
475C23×C4—21no—
476C23×C4—861no—
477C23×C4C22×D4311yescharacteristic
478#135—868no—
479#135—868no—
480#135—868no—
481#135—868no—
482C2×Q16—862no—
483C2×Q16—862no—
484C2×Q16—862no—
485C2×SD16—862no—
486C2×SD16—862no—
487C2×SD16—862no—
488C2×SD16—862no—
489C2×SD16—862no—
490C2×SD16—862no—
491C2×D8—862no—
492C2×D8—862no—
493C2×D8—862no—
494C2×M16—432no—
495C2×M16—861no—
496C2×M16—861no—
497C2×M16—861no—
498C2×M16—861no—
499C2×M16—861no—
500C22×C8—431no—
501C22×C8—431no—
502C22×C8—432no—
503C22×C8—432no—
504C22×C8—861no—
505C22×C8—861no—
506C22×C8—861no—
507C22×C8—861no—
508C22×C8—861no—
509#117—21no—
510#117—21no—
511#117—21no—
512#117—21no—
513#117—21no—
514#117—21no—
515#117—21no—
516#117—432no—
517#117—861no—
518#117—861no—
519#117—861no—
520#117C22⋊D4312yes—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—21no—
523C2×C4⋊C4—861no—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—861no—
526C2×C22⋊C4C22⋊D4312yes—
527C2×C42—21no—
528C2×C42—21no—
529C2×C42—861no—
530#104—868no—
531#104—868no—
532#99—28no—
533#99—868no—
534C24—21no—
535C24—861no—
536C24C2×C22⋊D4311yescharacteristic
537#41—22no—
538#41—22no—
539#41—22no—
540#41—22no—
541#41—22no—
542#41—22no—
543#41—22no—
544#41—22no—
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—862no—
554#41—862no—
555#41—862no—
556#41—862no—
557#41—862no—
558#41—862no—
559#41—862no—
560#41—862no—
561#41—1721no—
562#41—1721no—
563#41—1721no—
564#41—1721no—
565#41—1721no—
566#41—1721no—
567#41—1721no—
568#41—1721no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8—21no—
572C2×Q8—21no—
573C2×Q8—21no—
574C2×Q8—432no—
575C2×Q8—861no—
576C2×Q8—861no—
577C2×Q8—861no—
578C2×Q8—861no—
579C2×Q8—861no—
580C2×Q8(C2×D43)⋊C412yes—
581C2×D4—22no—
582C2×D4—22no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—41no—
589C2×D4—41no—
590C2×D4—41no—
591C2×D4—41no—
592C2×D4—432no—
593C2×D4—862no—
594C2×D4—862no—
595C2×D4—861no—
596C2×D4—861no—
597C2×D4—861no—
598C2×D4—861no—
599C2×D4—861no—
600C2×D4—1721no—
601C2×D4—1721no—
602C2×D4—1721no—
603C2×D4—1721no—
604C2×D4(C2×D43)⋊C412yes—
605C22×C4—21no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—41no—
610C22×C4—41no—
611C22×C4—41no—
612C22×C4—41no—
613C22×C4—41no—
614C22×C4—861no—
615C22×C4—862no—
616C22×C4—862no—
617C22×C4—1721no—
618C22×C4—1721no—
619C22×C4—1721no—
620C22×C4—1721no—
621C22×C4—1721no—
622C22×C4C2×C4×D4311yescharacteristic
623C22×C4C2×D17211yescharacteristic
624C22×C4#1062189811yescharacteristic
625C22×C4#1062189811yescharacteristic
626C22×C4D4×D4311yescharacteristic
627C22×C4D4×D4311yescharacteristic
628C22×C4D4×D4311yescharacteristic
629C22×C4D4×D4311yescharacteristic
630C22×C4D4×D4311yescharacteristic
631C22×C4D4×D4311yescharacteristic
632C22×C4#1062190011yescharacteristic
633C22×C4#1062190011yescharacteristic
634C22×C4C2×C22⋊D4311yescharacteristic
635C22×C4C2×C22⋊D4311yescharacteristic
636Q16—868no—
637SD16—868no—
638SD16—868no—
639D8—868no—
640M16—862no—
641M16—862no—
642M16—1721no—
643M16—1721no—
644C2×C8—432no—
645C2×C8—432no—
646C2×C8—861no—
647C2×C8—861no—
648C2×C8—861no—
649C2×C8—861no—
650C2×C8—862no—
651C2×C8—862no—
652C2×C8—862no—
653C2×C8—862no—
654C2×C8—862no—
655C2×C8—1721no—
656C2×C8—1721no—
657C4⋊C4—22no—
658C4⋊C4—41no—
659C4⋊C4—41no—
660C4⋊C4—41no—
661C4⋊C4—862no—
662C4⋊C4—1721no—
663C22⋊C4—22no—
664C22⋊C4—22no—
665C22⋊C4—22no—
666C22⋊C4—41no—
667C22⋊C4—862no—
668C22⋊C4—1721no—
669C42—22no—
670C42—41no—
671C42—41no—
672C42—41no—
673C42—862no—
674C42—1721no—
675C23—22no—
676C23—42no—
677C23—41no—
678C23—41no—
679C23—82no—
680C23—862no—
681C23—3442no—
682C23—1721no—
683C23—1721no—
684C23C4×C22⋊D4311yescharacteristic
685C23#1306329311yescharacteristic
686C23#1306329411yescharacteristic
687C23#1306329611yescharacteristic
688C23#1306329711yescharacteristic
689C23#1306329911yescharacteristic
690C23#1306332111yescharacteristic
691Q8—22no—
692Q8—22no—
693Q8—41no—
694Q8—41no—
695Q8—862no—
696Q8—862no—
697Q8—1721no—
698Q8—1721no—
699D4—22no—
700D4—22no—
701D4—42no—
702D4—42no—
703D4—42no—
704D4—42no—
705D4—41no—
706D4—41no—
707D4—862no—
708D4—862no—
709D4—1722no—
710D4—1722no—
711D4—1722no—
712D4—1722no—
713D4—1721no—
714D4—1721no—
715C2×C4—22no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—44no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—82no—
726C2×C4—862no—
727C2×C4—3442no—
728C2×C4—1722no—
729C2×C4—1721no—
730C2×C4—1721no—
731C2×C4—1722no—
732C2×C4—1722no—
733C2×C4—1722no—
734C2×C4—1722no—
735C2×C4C22⋊C4×D4311yescharacteristic
736C2×C4C22⋊C4×D4311yescharacteristic
737C2×C4C2×(C2×D43)⋊C411yescharacteristic
738C2×C4(C22⋊D43)⋊C411yescharacteristic
739C2×C4(C22⋊D43)⋊C411yescharacteristic
740C2×C4C4×C22⋊D4311yescharacteristic
741C2×C4#1306329311yescharacteristic
742C2×C4#1306329311yescharacteristic
743C2×C4#1306329311yescharacteristic
744C2×C4#1306329511yescharacteristic
745C2×C4#1306329511yescharacteristic
746C2×C4#1306329511yescharacteristic
747C2×C4#1306329611yescharacteristic
748C2×C4#1306329711yescharacteristic
749C2×C4#1306329711yescharacteristic
750C2×C4#1306329711yescharacteristic
751C2×C4#1306329811yescharacteristic
752C2×C4#1306329811yescharacteristic
753C2×C4#1306329811yescharacteristic
754C2×C4#1306329811yescharacteristic
755C2×C4#1306329911yescharacteristic
756C2×C4#1306330711yescharacteristic
757C2×C4#1306330711yescharacteristic
758C2×C4#1306330811yescharacteristic
759C2×C4#1306330911yescharacteristic
760C2×C4#1306331111yescharacteristic
761C2×C4#1306331111yescharacteristic
762C2×C4#1306332111yescharacteristic
763C8—862no—
764C8—862no—
765C8—1722no—
766C22—22no—
767C22—22no—
768C22—22no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—42no—
774C22—82no—
775C22—82no—
776C22—82no—
777C22—3442no—
778C22—3442no—
779C22—3442no—
780C22—1722no—
781C22#1458277511yescharacteristic
782C22#1458277811yescharacteristic
783C22#1458279911yescharacteristic
784C22#1458280711yescharacteristic
785C22#1458280711yescharacteristic
786C22#1458280811yescharacteristic
787C22#1458281511yescharacteristic
788C4—42no—
789C4—82no—
790C4—82no—
791C4—3442no—
792C4—1722no—
793C4#1458275411yescharacteristic
794C4#1458277511yescharacteristic
795C4#1458277611yescharacteristic
796C4#1458279911yescharacteristic
797C4#1458280811yescharacteristic
798C4#1458281411yescharacteristic
799C4#1458281411yescharacteristic
800C4#1458281511yescharacteristic
801C2—21no—
802C2—21no—
803C2—21no—
804C2—21no—
805C2—21no—
806C2—21no—
807C2—82no—
808C2—3442no—
809C2#1913283411yescharacteristic
810C2#1913549012yes—
subgroupG/H
centerC2×C4#13063298
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC2×C43×#410C2
socleC22×C43#390
prime radicalC22×#13063345C2
cosocleC23×C4×C43C23
hypercenterC2×#410D43
hypocenterC43#11026
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#410

Complements

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

NH ≅ G/Ntype
2. C2×#14582917C2semidirect
3. C2×#14582916C2semidirect
4. C2×#14582872C2semidirect
5. #19134311C2semidirect
6. #19134292C2semidirect
7. C2×C43×#410C2semidirect
15. C22×#10621885C4semidirect
16. C22×#10621883C4semidirect
17. C22×#10621884C4semidirect
18. C22×#10621882C4semidirect
400. C2×#410D43semidirect
444. C43#11026semidirect

Maximal subgroups

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

subgroupindex
C22×#130633452
C2×#145829172
C2×#145829162
C2×#145828722
#191343112
#191342922
C2×C43×#4102
#1102643