Finite Group Databasebeta

← #25098253

Subgroups — #25098253

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#19147928C211yesmaximal, characteristic
3C2×#14582881C211yesmaximal, characteristic, complemented
4#19143039C211yesmaximal, characteristic, complemented
5#19143039C211yesmaximal, characteristic, complemented
6#19135012C218yesmaximal, complemented
7C2×#14582669C211yesmaximal, characteristic, complemented
8C2×C43×#344C211yesmaximal, characteristic, complemented
9C22×#10621898C2211yescharacteristic
10C22×#10621898C2211yescharacteristic
11#14583665—22no—
12#14583665—22no—
13#14583665—22no—
14#14583665C2214yes—
15C2×#13063333—22no—
16C2×#13063331—22no—
17C22×#10621877C2211yescharacteristic
18C22×#10621877C2211yescharacteristic
19C2×M16×D43—22no—
20#14583480—22no—
21#14583475—21no—
22#14583475C412yes—
23#14583468—21no—
24#14583468C412yes—
25#14583461C414yes—
26#14583449—22no—
27#14583411—22no—
28#14583411C2214yes—
29#14582881—22no—
30#14582881C2214yes—
31C2×#13063243—21no—
32C2×#13063241—21no—
33#14582867—22no—
34#14582867—22no—
35#14582865—22no—
36#14582865—22no—
37#14582862C2214yescomplemented
38#14582862C2214yescomplemented
39#14582669C2214yescomplemented
40C22×M16×C43C2211yescharacteristic
41C22×M16×C43C2211yescharacteristic
42C2×#117×C43C2211yescharacteristic
43C43×#344C2214yescomplemented
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×#10621898—21no—
53C2×#10621898—21no—
54C2×#10621898—21no—
55C2×#10621898—21no—
56C2×#10621898—21no—
57C2×#10621898—21no—
58C2×#10621898—21no—
59C2×#10621898—21no—
60C2×#10621898—21no—
61C2×#10621898—21no—
62C2×#10621898—21no—
63C2×#10621898—21no—
64C2×#10621898C2×C412yes—
65C2×#10621898D412yes—
66C2×#10621898D412yes—
67C2×#10621898C2312yes—
68C22×Dic86C2×C411yescharacteristic
69C22×Dic86D411yescharacteristic
70C22×D172C2×C411yescharacteristic
71C22×D172D411yescharacteristic
72C22×C22⋊D43C2×C412yes—
73C22×C22⋊D43C2×C412yes—
74C22×C4×D43D412yes—
75C22×C4×D43C2312yes—
76#13063333—28no—
77#13063333—28no—
78#13063331—28no—
79#13063331—28no—
80C2×#10621877—21no—
81C2×#10621877—21no—
82C2×#10621877—21no—
83C2×#10621877—21no—
84C2×#10621877—21no—
85C2×#10621877—21no—
86C2×#10621877—21no—
87C2×#10621877—21no—
88C2×#10621877—21no—
89C2×#10621877D412yescomplemented
90C2×#10621877C2312yes—
91C2×#10621877C2312yes—
92C2×#10621872—24no—
93M16×D43—28no—
94M16×D43—28no—
95C22×C43⋊C8—21no—
96C22×C43⋊C8D412yescomplemented
97C2×C8×D43—24no—
98#13063325—22no—
99#13063322—22no—
100#13063313—22no—
101#13063313—22no—
102#13063309—24no—
103#13063309C2×C418yes—
104#13063305—24no—
105#13063305—24no—
106#13063300—24no—
107#13063300—24no—
108#13063299—28no—
109#13063295—24no—
110#13063295C2×C418yes—
111C4×D172—28no—
112#13063243—24no—
113#13063241—24no—
114(C2×D43)⋊C8—28no—
115(C2×D43)⋊C8—28no—
116C23×C4×C43C2311yescharacteristic
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×C43—21no—
125C2×M16×C43—21no—
126C2×M16×C43D412yescomplemented
127C2×M16×C43C2312yes—
128C2×M16×C43C2312yes—
129C22×C8×C43—21no—
130C22×C8×C43D412yescomplemented
131#117×C43—21no—
132#117×C43—21no—
133#117×C43C2×C412yes—
134#117×C43C2312yes—
135C2×C4⋊C4×C43—21no—
136C2×C22⋊C4×C43C2×C412yes—
137C2×C42×C43—21no—
138C24×C43C22×C411yescharacteristic
139C23×D43C22⋊C412yes—
140C23×D43C22×C412yes—
141C22×C4×C43—22no—
142C22×C4×C43C22×C411yescharacteristic
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43C2×D411yescharacteristic
147C22×C4×C43C2×D411yescharacteristic
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43#4111yescharacteristic
152C22×C4×C43#4111yescharacteristic
153C22×C4×C43#4111yescharacteristic
154C22×C4×C43#4111yescharacteristic
155C22×C4×C43C2411yescharacteristic
156C2×C22⋊D43—22no—
157C2×C22⋊D43—22no—
158C2×C22⋊D43—22no—
159C2×C22⋊D43—22no—
160C2×C22⋊D43—22no—
161C2×C22⋊D43—22no—
162C2×C22⋊D43—22no—
163C2×C22⋊D43—22no—
164C2×C22⋊D43—22no—
165C2×C22⋊D43—22no—
166C2×C22⋊D43C22⋊C414yes—
167C2×C22⋊D43C22×C414yes—
168C22×Dic43C22⋊C412yes—
169C22×Dic43C22×C412yes—
170#10621898—22no—
171#10621898—22no—
172#10621898—22no—
173#10621898—22no—
174#10621898—22no—
175#10621898—22no—
176#10621898—22no—
177#10621898—22no—
178#10621898—22no—
179#10621898—22no—
180#10621898—22no—
181#10621898—22no—
182#10621898—22no—
183#10621898—22no—
184#10621898—22no—
185#10621898—22no—
186#10621898—41no—
187#10621898—41no—
188#10621898—41no—
189#10621898—41no—
190#10621898—41no—
191#10621898—41no—
192#10621898—41no—
193#10621898—41no—
194#10621898—41no—
195#10621898—41no—
196#10621898—41no—
197#10621898—41no—
198#10621898—41no—
199#10621898—41no—
200#10621898—41no—
201#10621898—41no—
202C2×D172—21no—
203C2×D172—21no—
204C2×D172—21no—
205C2×D172—21no—
206C2×D172—21no—
207C2×D172—21no—
208C2×D172—21no—
209C2×D172—21no—
210C2×D172—21no—
211C2×D172—21no—
212C2×D172—28no—
213C2×D172C22⋊C412yes—
214C2×D172C2×D412yes—
215C2×C4×D43—22no—
216C2×C4×D43—22no—
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×C4×D43—22no—
224C2×C4×D43—22no—
225C2×C4×D43C22⋊C414yes—
226C2×C4×D43C2×D414yes—
227C2×Dic86—21no—
228C2×Dic86—21no—
229C2×Dic86—21no—
230C2×Dic86—21no—
231C2×Dic86—21no—
232C2×Dic86—21no—
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—
253C4⋊C4×C43—22no—
254C4⋊C4×C43—22no—
255C22⋊C4×C43—22no—
256C22⋊C4×C43C22×C414yes—
257C42×C43—22no—
258C42×C43—22no—
259(C2×D43)⋊C4—28no—
260(C2×D43)⋊C4—28no—
261C4⋊Dic43—28no—
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—81no—
279C23×C43C2×C22⋊C411yescharacteristic
280C23×C43C2×C22⋊C411yescharacteristic
281C23×C43C4×D411yescharacteristic
282C23×C43C4×D411yescharacteristic
283C23×C43C4×D411yescharacteristic
284C23×C43C4×D411yescharacteristic
285C23×C43C23×C411yescharacteristic
286C22×D43—22no—
287C22×D43—22no—
288C22×D43—22no—
289C22×D43—22no—
290C22×D43—22no—
291C22×D43—82no—
292C22×D43—82no—
293C22×D43C2×C22⋊C414yes—
294C2×C4×C43—24no—
295C2×C4×C43—82no—
296C2×C4×C43C2×C22⋊C411yescharacteristic
297C2×C4×C43C2×C22⋊C411yescharacteristic
298C2×C4×C43C4×D411yescharacteristic
299C2×C4×C43C4×D411yescharacteristic
300C2×C4×C43C4×D411yescharacteristic
301C2×C4×C43C4×D411yescharacteristic
302C2×C4×C43#12011yescharacteristic
303C2×C4×C43#12011yescharacteristic
304C2×C4×C43#12011yescharacteristic
305C2×C4×C43#12011yescharacteristic
306C2×C4×C43#12111yescharacteristic
307C2×C4×C43#12111yescharacteristic
308C2×C4×C43#12111yescharacteristic
309C2×C4×C43#12111yescharacteristic
310C2×C4×C43#12111yescharacteristic
311C2×C4×C43#12111yescharacteristic
312C2×C4×C43#12111yescharacteristic
313C2×C4×C43#12111yescharacteristic
314C2×C4×C43#12311yescharacteristic
315C2×C4×C43#12311yescharacteristic
316C2×C4×C43#12311yescharacteristic
317C2×C4×C43#12311yescharacteristic
318C2×C4×C43C22×D411yescharacteristic
319C2×C4×C43C22×D411yescharacteristic
320C2×C4×C43C22×D411yescharacteristic
321C2×C4×C43C22×D411yescharacteristic
322C2×C4×C43C2×#4111yescharacteristic
323C2×C4×C43C2×#4111yescharacteristic
324C22⋊D43—24no—
325C22⋊D43—24no—
326C22⋊D43—24no—
327C22⋊D43—24no—
328C22⋊D43—42no—
329C22⋊D43—42no—
330C22⋊D43—42no—
331C22⋊D43—42no—
332C2×Dic43—22no—
333C2×Dic43—22no—
334C2×Dic43—22no—
335C2×Dic43—22no—
336C2×Dic43—22no—
337C2×Dic43C2×C22⋊C414yes—
338D172—22no—
339D172—22no—
340D172—22no—
341D172—22no—
342D172—41no—
343D172—41no—
344D172—41no—
345D172—41no—
346D172—88no—
347C4×D43—24no—
348C4×D43—24no—
349C4×D43—24no—
350C4×D43—24no—
351C4×D43—42no—
352C4×D43—42no—
353C4×D43—42no—
354C4×D43—42no—
355Dic86—22no—
356Dic86—22no—
357Dic86—22no—
358Dic86—22no—
359Dic86—41no—
360Dic86—41no—
361Dic86—41no—
362Dic86—41no—
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#38611yescharacteristic
376C22×C43#38611yescharacteristic
377C22×C43#38611yescharacteristic
378C22×C43#38611yescharacteristic
379C22×C43C22×C22⋊C411yescharacteristic
380C22×C43C2×C4×D411yescharacteristic
381C22×C43C2×C4×D411yescharacteristic
382C2×D43—24no—
383C2×D43—44no—
384C2×D43—44no—
385C2×D43—44no—
386C2×D43—44no—
387C2×D43—44no—
388C2×D43—42no—
389C2×D43—82no—
390C4×C43—44no—
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—42no—
401C2×#568—431no—
402#3449—431no—
403C2×#413—431no—
404#2879—431no—
405#2879—431no—
406#1891—438no—
407C2×#344—431no—
408C2×#344D4311yescharacteristic, complemented
409C2×C43—21no—
410C2×C43—21no—
411C2×C43—21no—
412C2×C43—21no—
413C2×C43—21no—
414C2×C43—21no—
415C2×C43—21no—
416C2×C43C2×#38611yescharacteristic
417D43—44no—
418D43—82no—
419C22×#41—431no—
420C22×#41—431no—
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×#117C2×D4311yescharacteristic
442#413—434no—
443#413—862no—
444C2×#101—861no—
445C2×#100—861no—
446#408—862no—
447#408—862no—
448#408—862no—
449#408—862no—
450#407—434no—
451#407—434no—
452#344—434no—
453#344C2×D4314yescomplemented
454C43#2096411yescharacteristic, complemented, Sylow
455C2×#41—432no—
456C2×#41—432no—
457C2×#41—432no—
458C2×#41—432no—
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×#41—861no—
468C2×#41—861no—
469C2×#41—861no—
470C2×#41—861no—
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×Q8—431no—
481C22×D4—432no—
482C22×D4—432no—
483C22×D4—431no—
484C22×D4—431no—
485C23×C4—432no—
486C23×C4—432no—
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×M16D17212yescomplemented
517C2×M16C22×D4312yes—
518C2×M16C22×D4312yes—
519C22×C8—21no—
520C22×C8—432no—
521C22×C8—864no—
522C22×C8—861no—
523C22×C8D17212yescomplemented
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—21no—
539#117—21no—
540#117C4×D4312yes—
541#117C22×D4312yes—
542C2×C4⋊C4—21no—
543C2×C22⋊C4C4×D4312yes—
544C2×C42—21no—
545#101—864no—
546#100—864no—
547C22⋊C8—868no—
548C22⋊C8—868no—
549C24—432no—
550C24—432no—
551C24C2×C4×D4311yescharacteristic
552#41—862no—
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—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—
576#41—1721no—
577#41—1721no—
578#41—1721no—
579#41—1721no—
580#41—1721no—
581#41—1721no—
582#41—1721no—
583#41—1721no—
584C2×Q8—432no—
585C2×Q8—432no—
586C2×Q8—861no—
587C2×Q8—861no—
588C2×Q8—861no—
589C2×Q8—861no—
590C2×Q8—861no—
591C2×Q8—861no—
592C2×Q8—861no—
593C2×Q8—861no—
594C2×Q8—861no—
595C2×Q8—861no—
596C2×D4—434no—
597C2×D4—434no—
598C2×D4—432no—
599C2×D4—432no—
600C2×D4—868no—
601C2×D4—862no—
602C2×D4—862no—
603C2×D4—862no—
604C2×D4—862no—
605C2×D4—862no—
606C2×D4—862no—
607C2×D4—862no—
608C2×D4—862no—
609C2×D4—862no—
610C2×D4—862no—
611C2×D4—861no—
612C2×D4—861no—
613C2×D4—861no—
614C2×D4—861no—
615C2×D4—861no—
616C2×D4—861no—
617C2×D4—861no—
618C2×D4—861no—
619C2×D4—861no—
620C2×D4—861no—
621C22×C4—22no—
622C22×C4—432no—
623C22×C4—434no—
624C22×C4—434no—
625C22×C4—432no—
626C22×C4—862no—
627C22×C4—862no—
628C22×C4—862no—
629C22×C4—862no—
630C22×C4—862no—
631C22×C4—862no—
632C22×C4—862no—
633C22×C4—862no—
634C22×C4—862no—
635C22×C4—862no—
636C22×C4C2×C4×D4311yescharacteristic
637C22×C4C2×D17211yescharacteristic
638C22×C4C2×D17211yescharacteristic
639C22×C4#1062189811yescharacteristic
640C22×C4#1062189811yescharacteristic
641C22×C4D4×D4311yescharacteristic
642C22×C4D4×D4311yescharacteristic
643C22×C4D4×D4311yescharacteristic
644C22×C4D4×D4311yescharacteristic
645C22×C4D4×D4311yescharacteristic
646C22×C4D4×D4311yescharacteristic
647C22×C4#1062190211yescharacteristic
648C22×C4#1062190211yescharacteristic
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×D17214yes—
680C4⋊C4—22no—
681C4⋊C4—22no—
682C4⋊C4—868no—
683C22⋊C4—22no—
684C22⋊C4—868no—
685C22⋊C4—868no—
686C22⋊C4C2×C4×D4314yes—
687C42—22no—
688C42—22no—
689C23—81no—
690C23—434no—
691C23—862no—
692C23—862no—
693C23—862no—
694C23—862no—
695C23—862no—
696C23—3442no—
697C23—3442no—
698C23C22⋊C4×D4311yescharacteristic
699C23C22⋊C4×D4311yescharacteristic
700C23#1306328711yescharacteristic
701C23#1306328711yescharacteristic
702C23C4×D17211yescharacteristic
703C23C4×D17211yescharacteristic
704C23C22×C4×D4311yescharacteristic
705Q8—862no—
706Q8—862no—
707Q8—862no—
708Q8—862no—
709Q8—1721no—
710Q8—1721no—
711Q8—1721no—
712Q8—1721no—
713D4—864no—
714D4—864no—
715D4—864no—
716D4—864no—
717D4—862no—
718D4—862no—
719D4—862no—
720D4—862no—
721D4—3448no—
722D4—1722no—
723D4—1722no—
724D4—1722no—
725D4—1722no—
726D4—1721no—
727D4—1721no—
728D4—1721no—
729D4—1721no—
730C2×C4—24no—
731C2×C4—82no—
732C2×C4—434no—
733C2×C4—862no—
734C2×C4—862no—
735C2×C4—864no—
736C2×C4—864no—
737C2×C4—864no—
738C2×C4—864no—
739C2×C4—862no—
740C2×C4—862no—
741C2×C4—862no—
742C2×C4—1722no—
743C2×C4—1722no—
744C2×C4—1722no—
745C2×C4—1722no—
746C2×C4C22⋊C4×D4311yescharacteristic
747C2×C4C22⋊C4×D4311yescharacteristic
748C2×C4#1306328711yescharacteristic
749C2×C4#1306328711yescharacteristic
750C2×C4C4×D17211yescharacteristic
751C2×C4C4×D17211yescharacteristic
752C2×C4#1306329511yescharacteristic
753C2×C4#1306329511yescharacteristic
754C2×C4#1306329511yescharacteristic
755C2×C4#1306329511yescharacteristic
756C2×C4#1306329811yescharacteristic
757C2×C4#1306329811yescharacteristic
758C2×C4#1306329811yescharacteristic
759C2×C4#1306329811yescharacteristic
760C2×C4#1306330011yescharacteristic
761C2×C4#1306330011yescharacteristic
762C2×C4#1306330011yescharacteristic
763C2×C4#1306330011yescharacteristic
764C2×C4#1306331011yescharacteristic
765C2×C4#1306331011yescharacteristic
766C2×C4#1306331011yescharacteristic
767C2×C4#1306331011yescharacteristic
768C2×C4C2×D4×D4311yescharacteristic
769C2×C4C2×D4×D4311yescharacteristic
770C2×C4C2×D4×D4311yescharacteristic
771C2×C4C22×D17211yescharacteristic
772C2×C4C2×#1062189811yescharacteristic
773C2×C4C2×#1062190211yescharacteristic
774C8—24no—
775C8—42no—
776C8—864no—
777C8—1722no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—864no—
786C22—3442no—
787C22—1724no—
788C22—1724no—
789C22—1724no—
790C22—1724no—
791C22—1724no—
792C22—1722no—
793C22#1458277711yescharacteristic
794C22#1458277711yescharacteristic
795C22#1458277711yescharacteristic
796C22#1458277711yescharacteristic
797C22C2×C22⋊C4×D4311yescharacteristic
798C22C2×#1306328711yescharacteristic
799C22C2×C4×D17211yescharacteristic
800C4—44no—
801C4—864no—
802C4—1722no—
803C4#1458277711yescharacteristic
804C4#1458277711yescharacteristic
805C4#1458277711yescharacteristic
806C4#1458277711yescharacteristic
807C4C2×#1306329511yescharacteristic
808C4C2×#1306329811yescharacteristic
809C4C2×#1306330011yescharacteristic
810C4C2×#1306331011yescharacteristic
811C2—21no—
812C2—21no—
813C2—21no—
814C2—21no—
815C2—21no—
816C2—21no—
817C2—21no—
818C2—3442no—
819C2—1724no—
820C2C2×#1458277711yescharacteristic
subgroupG/H
centerC4C2×#13063295
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#344C2
socleC2×C43C2×#386
prime radical#19147928C2
cosocleC22×C4×C43C24
hypercenterC2×#344D43
hypocenterC43#20964
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C23×C4 ◁ C2×#344

Complements

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

NH ≅ G/Ntype
1. C2×#14583665C2semidirect
3. C2×#14582881C2semidirect
4. #19143039C2semidirect
5. #19143039C2semidirect
6. #19135012C2semidirect
7. C2×#14582669C2semidirect
8. C2×C43×#344C2semidirect
37. #14582862C22semidirect
38. #14582862C22semidirect
39. #14582669C22semidirect
43. C43×#344C22semidirect
89. C2×#10621877D4semidirect
96. C22×C43⋊C8D4semidirect
126. C2×M16×C43D4semidirect
130. C22×C8×C43D4semidirect
408. C2×#344D43semidirect
453. #344C2×D43semidirect
454. C43#20964semidirect
516. C2×M16D172semidirect
523. C22×C8D172semidirect

Maximal subgroups

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

subgroupindex
C2×#145836652
#191479282
C2×#145828812
#191430392
#191350122
C2×#145826692
C2×C43×#3442
#2096443