Finite Group Databasebeta

← #25098251

Subgroups — #25098251

Order 11008.

1700 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583665C211yesmaximal, characteristic, complemented
2#19147924C211yesmaximal, characteristic
3C2×#14582881C211yesmaximal, characteristic, complemented
4#19143040C211yesmaximal, characteristic, complemented
5#19135010C218yesmaximal, complemented
6C2×#14582671C211yesmaximal, characteristic, complemented
7C2×#14582670C211yesmaximal, characteristic, complemented
8C43×#2879C211yesmaximal, characteristic, complemented
9C22×#10621898C2211yescharacteristic
10#14583665—22no—
11#14583665—22no—
12#14583665—22no—
13#14583665C2214yes—
14C2×#13063333—22no—
15C2×#13063331—22no—
16C22×#10621877C2211yescharacteristic
17C22×#10621877C2211yescharacteristic
18C2×M16×D43—22no—
19#14583477—22no—
20#14583473C412yes—
21#14583470—21no—
22#14583466C412yes—
23#14583463—21no—
24#14583458C414yes—
25#14583445—22no—
26#14583410C2214yes—
27#14583406—22no—
28C2×#13063284C2211yescharacteristic
29#14582881—22no—
30#14582881C2214yes—
31C2×#13063243—21no—
32C2×#13063241—21no—
33#14582866—22no—
34#14582866—22no—
35#14582863C2214yescomplemented
36#14582671C2214yescomplemented
37#14582670C2214yescomplemented
38C22×#41×C43C2211yescharacteristic
39C22×M16×C43C2211yescharacteristic
40C22×M16×C43C2211yescharacteristic
41C43×#408—22no—
42C43×#408—22no—
43C43×#407C2214yescomplemented
44C2×#10621898—21no—
45C2×#10621898—21no—
46C2×#10621898—21no—
47C2×#10621898—21no—
48C2×#10621898—21no—
49C2×#10621898—21no—
50C2×#10621898—21no—
51C2×#10621898—21no—
52C2×#10621898C2×C412yes—
53C2×#10621898D412yes—
54C2×#10621898D412yes—
55C2×#10621898C2312yes—
56C22×Dic86D411yescharacteristic
57C22×D172D411yescharacteristic
58C22×C22⋊D43C2×C412yes—
59C22×C4×D43D412yes—
60#13063333—28no—
61#13063333—28no—
62#13063331—28no—
63#13063331—28no—
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×#10621877D412yescomplemented
74C2×#10621877C2312yes—
75C2×#10621877C2312yes—
76C2×#10621872—24no—
77M16×D43—28no—
78M16×D43—28no—
79C22×C43⋊C8—21no—
80C22×C43⋊C8D412yescomplemented
81C2×C8×D43—24no—
82#13063323—22no—
83#13063321—22no—
84#13063314—22no—
85#13063312—22no—
86#13063308C2×C418yes—
87#13063306—24no—
88#13063304—24no—
89#13063301—24no—
90#13063299—24no—
91#13063297—28no—
92#13063296—24no—
93#13063294C2×C418yes—
94#13063293—24no—
95C4×C22⋊D43—28no—
96#13063284—21no—
97#13063284—21no—
98#13063284C2×C412yes—
99#13063284C2312yes—
100C2×C4⋊Dic43—21no—
101C2×C22⋊Dic43C2×C412yes—
102C2×C4×Dic43—21no—
103#13063243—24no—
104#13063241—24no—
105C22⋊(C43⋊C8)—28no—
106C2×#41×C43—21no—
107C2×#41×C43—21no—
108C2×#41×C43—21no—
109C2×#41×C43—21no—
110C2×#41×C43—21no—
111C2×#41×C43—21no—
112C2×#41×C43—21no—
113C2×#41×C43—21no—
114C2×#41×C43—21no—
115C2×#41×C43—21no—
116C2×#41×C43—21no—
117C2×#41×C43—21no—
118C22×Q8×C43C2×C411yescharacteristic
119C22×D4×C43C2×C412yes—
120C22×D4×C43C2×C411yescharacteristic
121C23×C4×C43C2312yes—
122C23×C4×C43C2311yescharacteristic
123C2×M16×C43—21no—
124C2×M16×C43—21no—
125C2×M16×C43—21no—
126C2×M16×C43—21no—
127C2×M16×C43—21no—
128C2×M16×C43—21no—
129C2×M16×C43—21no—
130C2×M16×C43—21no—
131C2×M16×C43—21no—
132C2×M16×C43D412yescomplemented
133C2×M16×C43C2312yes—
134C2×M16×C43C2312yes—
135C22×C8×C43—21no—
136C22×C8×C43D412yescomplemented
137C22⋊C8×C43—28no—
138C24×C43C22×C412yes—
139C24×C43C22×C411yescharacteristic
140C23×D43C22⋊C412yes—
141#41×C43—41no—
142#41×C43—41no—
143#41×C43—41no—
144#41×C43—41no—
145#41×C43—41no—
146#41×C43—41no—
147#41×C43—41no—
148#41×C43—41no—
149#41×C43—41no—
150#41×C43—41no—
151#41×C43—41no—
152#41×C43—41no—
153#41×C43—41no—
154#41×C43—41no—
155#41×C43—41no—
156#41×C43—41no—
157C2×Q8×C43—21no—
158C2×Q8×C43—21no—
159C2×Q8×C43—21no—
160C2×Q8×C43—21no—
161C2×Q8×C43—21no—
162C2×Q8×C43—21no—
163C2×D4×C43—21no—
164C2×D4×C43—21no—
165C2×D4×C43—21no—
166C2×D4×C43—21no—
167C2×D4×C43—21no—
168C2×D4×C43—21no—
169C2×D4×C43—22no—
170C2×D4×C43—22no—
171C2×D4×C43—22no—
172C2×D4×C43—22no—
173C2×D4×C43—22no—
174C2×D4×C43—22no—
175C22×C4×C43—22no—
176C22×C4×C43—22no—
177C22×C4×C43—22no—
178C22×C4×C43—22no—
179C22×C4×C43—22no—
180C22×C4×C43—22no—
181C22×C4×C43C22×C412yes—
182C22×C4×C43C22×C411yescharacteristic
183C22×C4×C43C2×D411yescharacteristic
184C22×C4×C43C2×D411yescharacteristic
185C22×C4×C43C2×D411yescharacteristic
186C22×C4×C43C2×D411yescharacteristic
187C22×C4×C43C2×D411yescharacteristic
188C22×C4×C43C2×D411yescharacteristic
189C22×C4×C43C2×D411yescharacteristic
190C22×C4×C43C2×D411yescharacteristic
191C22×C4×C43#4111yescharacteristic
192C22×C4×C43#4111yescharacteristic
193C22×C4×C43#4111yescharacteristic
194C22×C4×C43#4111yescharacteristic
195C22×C4×C43C2411yescharacteristic
196C2×C22⋊D43—22no—
197C2×C22⋊D43—22no—
198C2×C22⋊D43—22no—
199C2×C22⋊D43—22no—
200C2×C22⋊D43—28no—
201C2×C22⋊D43C22⋊C414yes—
202C2×C22⋊D43C22×C414yes—
203C22×Dic43—22no—
204C22×Dic43C22⋊C412yes—
205#10621898—22no—
206#10621898—22no—
207#10621898—22no—
208#10621898—22no—
209#10621898—22no—
210#10621898—22no—
211#10621898—22no—
212#10621898—22no—
213#10621898—22no—
214#10621898—22no—
215#10621898—22no—
216#10621898—22no—
217#10621898—22no—
218#10621898—22no—
219#10621898—22no—
220#10621898—22no—
221C2×D172—21no—
222C2×D172—21no—
223C2×D172—21no—
224C2×D172—21no—
225C2×D172C22⋊C412yes—
226C2×D172C2×D412yes—
227C2×C4×D43—22no—
228C2×C4×D43—22no—
229C2×C4×D43—22no—
230C2×C4×D43—22no—
231C2×C4×D43C22⋊C414yes—
232C2×C4×D43C2×D414yes—
233C2×Dic86—21no—
234C2×Dic86—21no—
235C2×Dic86—21no—
236C2×Dic86—21no—
237C2×Dic86C22⋊C412yes—
238C2×Dic86C2×D412yes—
239M16×C43—22no—
240M16×C43—22no—
241M16×C43—22no—
242M16×C43—22no—
243M16×C43—22no—
244M16×C43—22no—
245M16×C43—41no—
246M16×C43—41no—
247C2×C8×C43—22no—
248C2×C8×C43—22no—
249C2×C8×C43—22no—
250C2×C8×C43—41no—
251C2×C8×C43—41no—
252C2×C8×C43C2×D414yes—
253C22⋊Dic43—28no—
254C22⋊Dic43—22no—
255C22⋊Dic43C22×C414yes—
256(C2×D43)⋊C4—28no—
257C4⋊Dic43—22no—
258C4⋊Dic43—22no—
259Dic43⋊C4—28no—
260C4×Dic43—22no—
261C4×Dic43—22no—
262#10621877—22no—
263#10621877—22no—
264#10621877—22no—
265#10621877—22no—
266#10621877—22no—
267#10621877—22no—
268#10621877—41no—
269#10621877—41no—
270C2×C43⋊C8—22no—
271C2×C43⋊C8—22no—
272C2×C43⋊C8—22no—
273C2×C43⋊C8—41no—
274C2×C43⋊C8—41no—
275C2×C43⋊C8C2×D414yes—
276#10621872—216no—
277C8×D43—216no—
278C23×C43—22no—
279C23×C43—22no—
280C23×C43—22no—
281C23×C43—81no—
282C23×C43—82no—
283C23×C43C2×C22⋊C411yescharacteristic
284C23×C43C2×C22⋊C411yescharacteristic
285C23×C43C4×D411yescharacteristic
286C23×C43C4×D411yescharacteristic
287C23×C43C4×D411yescharacteristic
288C23×C43C4×D411yescharacteristic
289C23×C43C23×C411yescharacteristic
290C22×D43—22no—
291C22×D43—22no—
292C22×D43—82no—
293C22×D43C2×C22⋊C414yes—
294Q8×C43—41no—
295Q8×C43—41no—
296Q8×C43—41no—
297Q8×C43—41no—
298D4×C43—42no—
299D4×C43—42no—
300D4×C43—42no—
301D4×C43—42no—
302D4×C43—41no—
303D4×C43—41no—
304D4×C43—41no—
305D4×C43—41no—
306C2×C4×C43—22no—
307C2×C4×C43—22no—
308C2×C4×C43—22no—
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#12111yescharacteristic
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#12311yescharacteristic
332C2×C4×C43#12311yescharacteristic
333C2×C4×C43#12311yescharacteristic
334C2×C4×C43#12311yescharacteristic
335C2×C4×C43C22×D411yescharacteristic
336C2×C4×C43C22×D411yescharacteristic
337C2×C4×C43C22×D411yescharacteristic
338C2×C4×C43C22×D411yescharacteristic
339C2×C4×C43C2×#4111yescharacteristic
340C2×C4×C43C2×#4111yescharacteristic
341C22⋊D43—24no—
342C22⋊D43—24no—
343C22⋊D43—24no—
344C22⋊D43—24no—
345C22⋊D43—88no—
346C2×Dic43—22no—
347C2×Dic43—22no—
348C2×Dic43—24no—
349C2×Dic43—82no—
350C2×Dic43C2×C22⋊C414yes—
351D172—22no—
352D172—22no—
353D172—22no—
354D172—22no—
355C4×D43—24no—
356C4×D43—24no—
357C4×D43—24no—
358C4×D43—24no—
359Dic86—22no—
360Dic86—22no—
361Dic86—22no—
362Dic86—22no—
363C8×C43—24no—
364C8×C43—42no—
365C43⋊C8—24no—
366C43⋊C8—42no—
367#20964—431nomaximal, Sylow
368C22×C43—41no—
369C22×C43—41no—
370C22×C43—41no—
371C22×C43—41no—
372C22×C43—41no—
373C22×C43—41no—
374C22×C43—41no—
375C22×C43—44no—
376C22×C43—44no—
377C22×C43—44no—
378C22×C43—42no—
379C22×C43#38611yescharacteristic
380C22×C43#38611yescharacteristic
381C22×C43#38611yescharacteristic
382C22×C43#38611yescharacteristic
383C22×C43C22×C22⋊C411yescharacteristic
384C22×C43C2×C4×D411yescharacteristic
385C22×C43C2×C4×D411yescharacteristic
386C2×D43—24no—
387C2×D43—44no—
388C2×D43—44no—
389C2×D43—82no—
390C4×C43—42no—
391C4×C43#38611yescharacteristic
392C4×C43#38611yescharacteristic
393C4×C43#38611yescharacteristic
394C4×C43#38611yescharacteristic
395C4×C43C2×#12011yescharacteristic
396C4×C43C2×#12111yescharacteristic
397C4×C43C2×#12111yescharacteristic
398C4×C43C2×#12311yescharacteristic
399Dic43—24no—
400Dic43—44no—
401C2×#568—431no—
402#3449—431no—
403C2×#413—431no—
404#2879—431no—
405#2879D4311yescharacteristic, complemented
406#1891—438no—
407C2×#344—431no—
408C2×#344—431no—
409C2×C43—21no—
410C2×C43—21no—
411C2×C43—21no—
412C2×C43—21no—
413C2×C43—21no—
414C2×C43—21no—
415C2×C43—21no—
416C2×C43—82no—
417C2×C43C2×#38611yescharacteristic
418D43—44no—
419C22×#41—431no—
420C22×#41C2×D4311yescharacteristic
421#568—434no—
422#568—862no—
423#568—862no—
424#568—862no—
425C2×#131—862no—
426C2×#131—862no—
427C22×M16—431no—
428C22×M16—431no—
429C22×M16—862no—
430C22×M16C2×D4311yescharacteristic
431C22×M16C2×D4311yescharacteristic
432#537—862no—
433#536—432no—
434#536—861no—
435#535—432no—
436#535—861no—
437#534—434no—
438#532—862no—
439#525—434no—
440#525—862no—
441C2×#117—431no—
442#413—434no—
443#413—862no—
444C2×#101—861no—
445C2×#100—861no—
446#408—22no—
447#408—22no—
448#408—862no—
449#408—862no—
450#407—434no—
451#407C2×D4314yescomplemented
452#344—434no—
453#344—434no—
454C43#2096411yescharacteristic, complemented, Sylow
455C2×#41—21no—
456C2×#41—21no—
457C2×#41—21no—
458C2×#41—21no—
459C2×#41—21no—
460C2×#41—21no—
461C2×#41—21no—
462C2×#41—21no—
463C2×#41—21no—
464C2×#41—21no—
465C2×#41—21no—
466C2×#41—21no—
467C2×#41—432no—
468C2×#41—432no—
469C2×#41—432no—
470C2×#41—432no—
471C2×#41—861no—
472C2×#41—861no—
473C2×#41—861no—
474C2×#41—861no—
475C2×#41—861no—
476C2×#41—861no—
477C2×#41—861no—
478C2×#41—861no—
479C22×Q8—431no—
480C22×Q8C4×D4311yescharacteristic
481C22×D4—432no—
482C22×D4—431no—
483C22×D4C4×D4312yes—
484C22×D4C4×D4311yescharacteristic
485C23×C4—432no—
486C23×C4C22×D4312yes—
487C23×C4C22×D4311yescharacteristic
488#131—868no—
489#131—868no—
490#131—868no—
491#131—868no—
492C2×M16—21no—
493C2×M16—21no—
494C2×M16—21no—
495C2×M16—21no—
496C2×M16—21no—
497C2×M16—21no—
498C2×M16—21no—
499C2×M16—21no—
500C2×M16—21no—
501C2×M16—432no—
502C2×M16—432no—
503C2×M16—432no—
504C2×M16—864no—
505C2×M16—868no—
506C2×M16—868no—
507C2×M16—861no—
508C2×M16—861no—
509C2×M16—861no—
510C2×M16—861no—
511C2×M16—861no—
512C2×M16—861no—
513C2×M16—861no—
514C2×M16—861no—
515C2×M16—861no—
516C2×M16C22⋊D4312yescomplemented
517C2×M16C22×D4312yes—
518C2×M16C22×D4312yes—
519C22×C8—21no—
520C22×C8—432no—
521C22×C8—864no—
522C22×C8—861no—
523C22×C8C22⋊D4312yescomplemented
524C4⋊Q8—862no—
525#127—862no—
526#124—862no—
527#124—862no—
528#123—438no—
529#123—864no—
530C22⋊Q8—864no—
531C22⋊Q8—864no—
532#121—864no—
533#121—864no—
534#121—868no—
535#120—438no—
536#120—864no—
537C4×D4—868no—
538#117—432no—
539#117—432no—
540#117—861no—
541#117—861no—
542C2×C4⋊C4—861no—
543C2×C22⋊C4—432no—
544C2×C42—861no—
545#101—864no—
546#100—864no—
547C22⋊C8—28no—
548C22⋊C8—868no—
549C24—432no—
550C24C2×C4×D4312yes—
551C24C2×C4×D4311yescharacteristic
552#41—41no—
553#41—41no—
554#41—41no—
555#41—41no—
556#41—41no—
557#41—41no—
558#41—41no—
559#41—41no—
560#41—41no—
561#41—41no—
562#41—41no—
563#41—41no—
564#41—41no—
565#41—41no—
566#41—41no—
567#41—41no—
568#41—862no—
569#41—862no—
570#41—862no—
571#41—862no—
572#41—862no—
573#41—862no—
574#41—862no—
575#41—862no—
576#41—862no—
577#41—862no—
578#41—862no—
579#41—862no—
580#41—862no—
581#41—862no—
582#41—862no—
583#41—862no—
584C2×Q8—21no—
585C2×Q8—21no—
586C2×Q8—21no—
587C2×Q8—21no—
588C2×Q8—21no—
589C2×Q8—21no—
590C2×Q8—432no—
591C2×Q8—432no—
592C2×Q8—861no—
593C2×Q8—861no—
594C2×Q8—861no—
595C2×Q8—861no—
596C2×D4—22no—
597C2×D4—22no—
598C2×D4—22no—
599C2×D4—22no—
600C2×D4—22no—
601C2×D4—22no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—434no—
609C2×D4—434no—
610C2×D4—432no—
611C2×D4—432no—
612C2×D4—862no—
613C2×D4—862no—
614C2×D4—862no—
615C2×D4—862no—
616C2×D4—868no—
617C2×D4—861no—
618C2×D4—861no—
619C2×D4—861no—
620C2×D4—861no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—432no—
628C22×C4—434no—
629C22×C4—434no—
630C22×C4—862no—
631C22×C4—862no—
632C22×C4—862no—
633C22×C4—862no—
634C22×C4—862no—
635C22×C4C2×C4×D4312yes—
636C22×C4C2×C4×D4311yescharacteristic
637C22×C4#1062189811yescharacteristic
638C22×C4#1062189811yescharacteristic
639C22×C4D4×D4311yescharacteristic
640C22×C4D4×D4311yescharacteristic
641C22×C4D4×D4311yescharacteristic
642C22×C4D4×D4311yescharacteristic
643C22×C4D4×D4311yescharacteristic
644C22×C4D4×D4311yescharacteristic
645C22×C4#1062190011yescharacteristic
646C22×C4#1062190011yescharacteristic
647C22×C4C2×C22⋊D4311yescharacteristic
648C22×C4C2×C22⋊D4311yescharacteristic
649C22×C4C23×D4311yescharacteristic
650M16—22no—
651M16—22no—
652M16—22no—
653M16—22no—
654M16—22no—
655M16—22no—
656M16—41no—
657M16—41no—
658M16—8616no—
659M16—862no—
660M16—862no—
661M16—862no—
662M16—862no—
663M16—862no—
664M16—862no—
665M16—1721no—
666M16—1721no—
667C2×C8—22no—
668C2×C8—22no—
669C2×C8—22no—
670C2×C8—41no—
671C2×C8—41no—
672C2×C8—434no—
673C2×C8—8616no—
674C2×C8—862no—
675C2×C8—862no—
676C2×C8—862no—
677C2×C8—1721no—
678C2×C8—1721no—
679C2×C8C2×C22⋊D4314yes—
680C4⋊C4—868no—
681C4⋊C4—862no—
682C4⋊C4—862no—
683C22⋊C4—434no—
684C22⋊C4—868no—
685C22⋊C4—868no—
686C22⋊C4—862no—
687C42—862no—
688C42—862no—
689C23—22no—
690C23—22no—
691C23—22no—
692C23—81no—
693C23—82no—
694C23—434no—
695C23—862no—
696C23—862no—
697C23—3442no—
698C23C22⋊C4×D4311yescharacteristic
699C23C22⋊C4×D4311yescharacteristic
700C23(C22⋊D43)⋊C411yescharacteristic
701C23(C22⋊D43)⋊C411yescharacteristic
702C23C4×C22⋊D4311yescharacteristic
703C23C4×C22⋊D4311yescharacteristic
704C23C22×C4×D4311yescharacteristic
705Q8—41no—
706Q8—41no—
707Q8—41no—
708Q8—41no—
709Q8—862no—
710Q8—862no—
711Q8—862no—
712Q8—862no—
713D4—42no—
714D4—42no—
715D4—42no—
716D4—42no—
717D4—41no—
718D4—41no—
719D4—41no—
720D4—41no—
721D4—864no—
722D4—864no—
723D4—864no—
724D4—864no—
725D4—862no—
726D4—862no—
727D4—862no—
728D4—862no—
729D4—3448no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—434no—
738C2×C4—862no—
739C2×C4—862no—
740C2×C4—864no—
741C2×C4—864no—
742C2×C4—864no—
743C2×C4—864no—
744C2×C4—864no—
745C2×C4—3442no—
746C2×C4C22⋊C4×D4311yescharacteristic
747C2×C4C22⋊C4×D4311yescharacteristic
748C2×C4(C22⋊D43)⋊C411yescharacteristic
749C2×C4(C22⋊D43)⋊C411yescharacteristic
750C2×C4C4×C22⋊D4311yescharacteristic
751C2×C4C4×C22⋊D4311yescharacteristic
752C2×C4#1306329311yescharacteristic
753C2×C4#1306329311yescharacteristic
754C2×C4#1306329311yescharacteristic
755C2×C4#1306329311yescharacteristic
756C2×C4#1306329611yescharacteristic
757C2×C4#1306329611yescharacteristic
758C2×C4#1306329611yescharacteristic
759C2×C4#1306329611yescharacteristic
760C2×C4#1306329811yescharacteristic
761C2×C4#1306329811yescharacteristic
762C2×C4#1306329811yescharacteristic
763C2×C4#1306329811yescharacteristic
764C2×C4#1306330711yescharacteristic
765C2×C4#1306330711yescharacteristic
766C2×C4#1306330711yescharacteristic
767C2×C4#1306330711yescharacteristic
768C2×C4C2×D4×D4311yescharacteristic
769C2×C4C2×D4×D4311yescharacteristic
770C2×C4C2×D4×D4311yescharacteristic
771C2×C4C22×C22⋊D4311yescharacteristic
772C2×C4C2×#1062190011yescharacteristic
773C2×C4C2×#1062189811yescharacteristic
774C8—24no—
775C8—42no—
776C8—864no—
777C8—1722no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—44no—
786C22—44no—
787C22—44no—
788C22—42no—
789C22—864no—
790C22—3442no—
791C22—1724no—
792C22—1724no—
793C22#1458277511yescharacteristic
794C22#1458277511yescharacteristic
795C22#1458277511yescharacteristic
796C22#1458277511yescharacteristic
797C22C2×C22⋊C4×D4311yescharacteristic
798C22C2×(C22⋊D43)⋊C411yescharacteristic
799C22C2×C4×C22⋊D4311yescharacteristic
800C4—42no—
801C4—864no—
802C4—1724no—
803C4#1458277511yescharacteristic
804C4#1458277511yescharacteristic
805C4#1458277511yescharacteristic
806C4#1458277511yescharacteristic
807C4C2×#1306329311yescharacteristic
808C4C2×#1306329611yescharacteristic
809C4C2×#1306329811yescharacteristic
810C4C2×#1306330711yescharacteristic
811C2—21no—
812C2—21no—
813C2—21no—
814C2—21no—
815C2—21no—
816C2—21no—
817C2—21no—
818C2—82no—
819C2—1724no—
820C2C2×#1458277511yescharacteristic
subgroupG/H
centerC4C2×#13063293
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#2879C2
socleC2×C43C2×#386
prime radical#19147924C2
cosocleC22×C4×C43C24
hypercenter#2879D43
hypocenterC43#20964
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C23×C4 ◁ #2879

Complements

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

NH ≅ G/Ntype
1. C2×#14583665C2semidirect
3. C2×#14582881C2semidirect
4. #19143040C2semidirect
5. #19135010C2semidirect
6. C2×#14582671C2semidirect
7. C2×#14582670C2semidirect
8. C43×#2879C2semidirect
35. #14582863C22semidirect
36. #14582671C22semidirect
37. #14582670C22semidirect
43. C43×#407C22semidirect
73. C2×#10621877D4semidirect
80. C22×C43⋊C8D4semidirect
132. C2×M16×C43D4semidirect
136. C22×C8×C43D4semidirect
405. #2879D43semidirect
451. #407C2×D43semidirect
454. C43#20964semidirect
516. C2×M16C22⋊D43semidirect
523. C22×C8C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145836652
#191479242
C2×#145828812
#191430402
#191350102
C2×#145826712
C2×#145826702
C43×#28792
#2096443