Finite Group Databasebeta

← #25960176

Subgroups — #25960176

Order 11008.

4902 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583734C211yesmaximal, characteristic
2C2×#14583664C211yesmaximal, characteristic, complemented
3#520×D43C211yesmaximal, characteristic, complemented
4#19143129C211yesmaximal, characteristic, complemented
5#19143126C213yesmaximal, complemented
6#19143125C211yesmaximal, characteristic, complemented
7#19143124C213yesmaximal, complemented
8#19143121C211yesmaximal, characteristic, complemented
9#19143120C213yesmaximal, complemented
10#19143116C213yesmaximal, complemented
11#19143110C213yesmaximal, complemented
12#19143109C213yesmaximal, complemented
13C2×#14582897C213yesmaximal, complemented
14#417×D43C213yesmaximal, complemented
15C43×#2897C211yesmaximal, characteristic, complemented
16#14583734—28no—
17#14583734C4116yescomplemented
18C2×#13063372—21no—
19C2×#13063372C2211yescharacteristic
20C2×#13063372C2213yes—
21C2×#13063370—23no—
22C2×#13063370C2213yes—
23C22×#10621900—23no—
24C22×#10621900C2213yes—
25C2×#41×D43—21no—
26C2×#41×D43C2213yes—
27C2×#41×D43C2211yescharacteristic
28#14583664—28no—
29C2×#13063333C2213yescomplemented
30C2×#13063332C2211yescharacteristic, complemented
31C2×#13063331C2213yescomplemented
32C22×#10621872C2213yescomplemented
33C2×M16×D43C2213yescomplemented
34#14583382C2211yescharacteristic, complemented
35#14583381—21no—
36#14583380C2213yescomplemented
37#14583379C2213yescomplemented
38#14583378—23no—
39C4×Q8×D43—21no—
40C4×D4×D43—23no—
41#117×D43C2213yescomplemented
42C2×C4⋊C4×D43C2213yescomplemented
43#14582909C2213yescomplemented
44#14582907C2213yescomplemented
45#14582906C2213yescomplemented
46#14582906C2213yescomplemented
47#14582904C2213yescomplemented
48#14582902C2213yescomplemented
49#14582902C2213yescomplemented
50#14582901C2213yescomplemented
51#14582900C2213yescomplemented
52#14582899C2213yescomplemented
53#14582899C2211yescharacteristic, complemented
54#14582898C2213yescomplemented
55#14582897C2216yescomplemented
56#14582897C2213yescomplemented
57#14582897C2216yescomplemented
58#14582897C2216yescomplemented
59#14582897C2213yescomplemented
60#14582896C2213yescomplemented
61#14582895C2213yescomplemented
62#14582893C2213yescomplemented
63#14582892C2216yescomplemented
64#14582892C2216yescomplemented
65C2×#13063250C2213yescomplemented
66C2×#13063248C2213yescomplemented
67#103×D43C2216yescomplemented
68C2×#13063246C2213yescomplemented
69#102×D43C2216yescomplemented
70C2×H(5,𝔽2)×C43C2211yescharacteristic
71C2×#131×C43C2211yescharacteristic, complemented
72C43×#520C2211yescharacteristic, complemented
73C43×#418C2213yescomplemented
74C43×#417C2213yescomplemented
75C43×#416C2213yescomplemented
76C2×#102×C43C2213yescomplemented
77#13063372—24no—
78#13063372—216no—
79#13063372—212no—
80#13063372C2×C4124yescomplemented
81#13063372C2×C418yescomplemented
82#13063370—248no—
83#13063370—212no—
84#13063370C2×C4124yescomplemented
85C2×#10621902D411yescharacteristic
86C2×#10621902C2311yescharacteristic
87C2×#10621898—23no—
88C2×#10621898—23no—
89C2×#10621898C2313yes—
90C2×#10621898C2313yes—
91C2×#10621900—23no—
92C2×#10621900—26no—
93C2×#10621900—23no—
94C2×#10621900—248no—
95C2×#10621900—23no—
96C2×#10621900—23no—
97C2×#10621900—212no—
98C2×#10621900—23no—
99C2×#10621900C2×C4124yescomplemented
100C2×#10621900D413yes—
101C2×#10621900C2313yes—
102C2×#10621900C2316yes—
103#41×D43—216no—
104#41×D43—212no—
105#41×D43C2×C418yes—
106#41×D43C2×C4124yescomplemented
107#41×D43D418yes—
108C22×Dic86—23no—
109C22×Dic86C2313yes—
110C2×Q8×D43—21no—
111C2×Q8×D43D411yescharacteristic
112C2×Q8×D43C2313yes—
113C22×C22⋊D43—23no—
114C22×C22⋊D43—26no—
115C2×D4×D43—23no—
116C2×D4×D43—23no—
117C2×D4×D43D413yes—
118C2×D4×D43C2313yes—
119C23×Dic43—23no—
120C22×C4×D43—23no—
121C22×C4×D43—23no—
122C22×C4×D43C2313yes—
123#13063333—212no—
124#13063332—24no—
125#13063331—212no—
126C2×#10621877C2313yes—
127C2×#10621872—212no—
128C2×#10621872C2313yes—
129C2×#10621872C2311yescharacteristic
130C2×#10621872C2313yes—
131C2×#10621872C2313yes—
132M16×D43—212no—
133C22×C43⋊C8C2313yes—
134C2×C8×D43C2316yes—
135Q8×Dic43—21no—
136C4×Dic86—23no—
137#13063290—23no—
138C4×D172—23no—
139D4×Dic43—23no—
140#13063287—23no—
141C4×C22⋊D43—26no—
142(C22⋊D43)⋊C4—26no—
143#13063284C2313yes—
144#13063283C2313yes—
145#13063283C2313yes—
146#13063282—23no—
147#13063281—23no—
148C2×C4⋊Dic43C2313yes—
149C2×Dic43⋊C4—23no—
150C4⋊C4×D43—23no—
151C4⋊C4×D43—23no—
152C4⋊C4×D43C2313yes—
153C4⋊C4×D43C2316yes—
154C4⋊C4×D43C2311yescharacteristic
155C22⋊C4×D43—23no—
156C42×D43—23no—
157#13063250C2316yes—
158#13063250C2313yes—
159#13063250C2313yes—
160#13063249C2313yes—
161#13063249C2311yescharacteristic
162#13063248C2316yes—
163#13063248C2313yes—
164#13063248C2313yes—
165#13063247C2313yes—
166#13063247C2311yescharacteristic
167#13063246C2316yes—
168#13063246C2313yes—
169#13063246C2313yes—
170#13063245C2313yes—
171#13063245C2311yescharacteristic
172H(5,𝔽2)×C43—24no—
173H(5,𝔽2)×C43C2×C418yescomplemented
174C2×#41×C43—21no—
175C2×#41×C43C2313yes—
176C2×#41×C43C2311yescharacteristic
177C22×D4×C43—23no—
178C22×D4×C43C2313yes—
179#131×C43—24no—
180C2×M16×C43C2313yes—
181C22×C8×C43C2313yes—
182C4×Q8×C43—21no—
183C4×D4×C43—23no—
184#117×C43C2313yes—
185C2×C4⋊C4×C43C2313yes—
186#103×C43C2313yes—
187#103×C43C2311yescharacteristic
188#102×C43C2316yes—
189#102×C43C2313yes—
190#102×C43C2313yes—
191C24×C43—23no—
192C23×D43—23no—
193C23×D43C2×D413yes—
194#41×C43—28no—
195#41×C43—26no—
196#41×C43C22×C414yes—
197#41×C43C22×C4112yescomplemented
198#41×C43C2×D414yes—
199C2×Q8×C43C2×D411yescharacteristic
200C2×Q8×C43C2411yescharacteristic
201C2×D4×C43—224no—
202C2×D4×C43—23no—
203C2×D4×C43—26no—
204C2×D4×C43—23no—
205C2×D4×C43C22×C4112yescomplemented
206C2×D4×C43C2×D413yes—
207C2×D4×C43C2413yes—
208C22×C4×C43—23no—
209C22×C4×C43—23no—
210C22×C4×C43C2413yes—
211C2×C22⋊D43—248no—
212C2×C22⋊D43—23no—
213C2×C22⋊D43—23no—
214C2×C22⋊D43—224no—
215C2×C22⋊D43—26no—
216C2×C22⋊D43—23no—
217C2×C22⋊D43C2×D416yes—
218C22×Dic43—224no—
219C22×Dic43—23no—
220C22×Dic43—26no—
221C22×Dic43—23no—
222C22×Dic43—23no—
223C22×Dic43C2×D413yes—
224#10621902—22no—
225#10621902C22⋊C418yes—
226#10621902C22×C414yes—
227Q8×D43—28no—
228Q8×D43—26no—
229Q8×D43C22⋊C418yes—
230Q8×D43C22×C4112yescomplemented
231#10621900—224no—
232#10621900—248no—
233#10621900—224no—
234#10621900—224no—
235#10621900—224no—
236#10621900—26no—
237#10621900—212no—
238#10621900—224no—
239#10621900C22⋊C4124yes—
240#10621900C22×C4112yes—
241#10621900C22×C4124yescomplemented
242D4×D43—224no—
243D4×D43—26no—
244D4×D43—224no—
245D4×D43C22⋊C4124yes—
246D4×D43C22×C4112yescomplemented
247#10621898—26no—
248#10621898—224no—
249#10621898—224no—
250#10621898C22×C4112yes—
251#10621898C22×C4112yescomplemented
252#10621898C2×D4112yes—
253C2×D172—21no—
254C2×D172C2×D413yes—
255C2×D172C2411yescharacteristic
256C2×C4×D43—23no—
257C2×C4×D43—21no—
258C2×C4×D43—224no—
259C2×C4×D43—23no—
260C2×C4×D43—21no—
261C2×C4×D43—23no—
262C2×C4×D43—26no—
263C2×C4×D43—86no—
264C2×C4×D43C22×C4112yes—
265C2×C4×D43C2×D4112yes—
266C2×C4×D43C2×D413yes—
267C2×C4×D43C2×D413yes—
268C2×C4×D43C2411yescharacteristic
269C2×C4×D43C2413yes—
270C2×Dic86—23no—
271C2×Dic86—26no—
272C2×Dic86—23no—
273C2×Dic86—224no—
274C2×Dic86C22×C4112yescomplemented
275C2×Dic86C2×D413yes—
276C2×Dic86C2413yes—
277M16×C43—26no—
278C2×C8×C43—26no—
279C2×C8×C43C2411yescharacteristic
280C2×C8×C43C2413yes—
281C4⋊C4×C43—23no—
282C4⋊C4×C43C2413yes—
283C4⋊C4×C43C2411yescharacteristic
284C22⋊C4×C43—23no—
285C42×C43—23no—
286C22⋊Dic43—23no—
287(C2×D43)⋊C4—23no—
288(C2×D43)⋊C4—23no—
289C4⋊Dic43—23no—
290C4⋊Dic43C2413yes—
291C4⋊Dic43C2411yescharacteristic
292Dic43⋊C4—23no—
293Dic43⋊C4—26no—
294Dic43⋊C4—21no—
295C4×Dic43—23no—
296C4×Dic43—23no—
297C4×Dic43—23no—
298#10621877—26no—
299C2×C43⋊C8—26no—
300C2×C43⋊C8C2413yes—
301C2×C43⋊C8C2411yescharacteristic
302#10621872—26no—
303#10621872—22no—
304#10621872—26no—
305#10621872—26no—
306C8×D43—212no—
307C23×C43—23no—
308C23×C43—212no—
309C23×C43—83no—
310C23×C43—83no—
311C23×C43C22×D413yes—
312C22×D43—21no—
313C22×D43—212no—
314C22×D43—43no—
315C22×D43—43no—
316C22×D43—83no—
317C22×D43—83no—
318C22×D43C2×C22⋊C4112yes—
319C22×D43C22×D413yes—
320C22×D43C22×D411yescharacteristic
321Q8×C43—21no—
322Q8×C43C2×C22⋊C414yes—
323Q8×C43C23×C412yes—
324D4×C43—212no—
325D4×C43—212no—
326D4×C43—23no—
327D4×C43C2×C22⋊C4112yes—
328D4×C43C23×C416yes—
329C2×C4×C43—21no—
330C2×C4×C43—212no—
331C2×C4×C43—21no—
332C2×C4×C43—23no—
333C2×C4×C43—83no—
334C2×C4×C43C23×C416yes—
335C2×C4×C43C22×D413yes—
336C2×C4×C43C22×D416yes—
337C2×C4×C43C2511yescharacteristic
338C22⋊D43—212no—
339C22⋊D43—212no—
340C22⋊D43—224no—
341C22⋊D43—212no—
342C22⋊D43C2×C22⋊C4124yes—
343C2×Dic43—212no—
344C2×Dic43—23no—
345C2×Dic43—224no—
346C2×Dic43—212no—
347C2×Dic43—21no—
348C2×Dic43—23no—
349C2×Dic43—83no—
350C2×Dic43C2×C22⋊C4112yes—
351C2×Dic43C22×D413yes—
352C2×Dic43C22×D411yescharacteristic
353D172—24no—
354D172—21no—
355D172C2×C22⋊C4112yes—
356D172C23×C412yes—
357C4×D43—212no—
358C4×D43—212no—
359C4×D43—24no—
360C4×D43—42no—
361C4×D43—46no—
362C4×D43—86no—
363C4×D43C2×C22⋊C4112yes—
364C4×D43C2×C22⋊C4112yes—
365C4×D43C23×C412yes—
366C4×D43C23×C416yes—
367C4×D43C22×D416yes—
368C4×D43C22×D412yes—
369Dic86—212no—
370Dic86—23no—
371Dic86—212no—
372Dic86C2×C22⋊C4112yes—
373Dic86C23×C416yes—
374C8×C43—23no—
375C8×C43—21no—
376C43⋊C8—23no—
377C43⋊C8—21no—
378#60089—431nomaximal, Sylow
379C22×C43—23no—
380C22×C43—23no—
381C22×C43—26no—
382C22×C43—43no—
383C22×C43—43no—
384C22×C43—812no—
385C22×C43C22×C22⋊C416yes—
386C22×C43C23×D411yescharacteristic
387C2×D43—21no—
388C2×D43—23no—
389C2×D43—21no—
390C2×D43—23no—
391C2×D43—22no—
392C2×D43—412no—
393C2×D43—41no—
394C2×D43—41no—
395C2×D43—812no—
396C2×D43C22×C22⋊C416yes—
397C2×D43C22×C22⋊C412yes—
398C4×C43—22no—
399C4×C43—43no—
400C4×C43—41no—
401C4×C43C22×C22⋊C416yes—
402C4×C43C24×C411yescharacteristic
403C4×C43C23×D411yescharacteristic
404Dic43—26no—
405Dic43—43no—
406Dic43—41no—
407Dic43C22×C22⋊C416yes—
408Dic43C22×C22⋊C412yes—
409C2×#585—431no—
410C2×#568—431no—
411C2×#520—431no—
412#2898—433no—
413#2898—433no—
414#2898—431no—
415#2898—431no—
416#2897—433no—
417#2897—433no—
418#2897—431no—
419#2897D4311yescharacteristic, complemented
420#2896—433no—
421#2896—433no—
422C2×#417—433no—
423C2×#417—433no—
424C2×C43—26no—
425C2×C43—46no—
426C2×C43C23×C22⋊C411yescharacteristic
427C2×C43#358511yescharacteristic
428C2×C43#358611yescharacteristic
429D43—22no—
430D43—26no—
431D43—42no—
432#585—4316no—
433#585—868no—
434C2×2−1+4—433no—
435C2×2−1+4—431no—
436C2×2−1+4—861no—
437C2×H(5,𝔽2)—433no—
438C2×H(5,𝔽2)—863no—
439C2×H(5,𝔽2)C2×D4311yescharacteristic
440C22×#41—431no—
441C22×#41—433no—
442C22×#41—433no—
443C22×#41—863no—
444C22×#41—861no—
445#568—868no—
446C2×#131—431no—
447C2×#131—433no—
448C2×#131—433no—
449C2×#131C2×D4311yescharacteristic, complemented
450C22×M16—433no—
451C22×M16—433no—
452#520—431no—
453#520—433no—
454#520—433no—
455#520—863no—
456#520—861no—
457#520C2×D4311yescharacteristic, complemented
458C2×C4×Q8—861no—
459C2×C4×D4—863no—
460C2×#117—433no—
461C22×C4⋊C4—433no—
462#419—433no—
463#419—433no—
464#419—433no—
465#419—433no—
466#418—433no—
467#418—433no—
468#418—433no—
469#418C2×D4313yescomplemented
470#417—433no—
471#417—433no—
472#417—433no—
473#417—433no—
474#417—431no—
475#417—436no—
476#417—433no—
477#417—436no—
478#417—436no—
479#417—433no—
480#417C2×D4313yescomplemented
481#416—433no—
482#416—433no—
483#416—433no—
484#416—436no—
485#416—436no—
486#416C2×D4313yescomplemented
487C2×#103—433no—
488C2×#103—433no—
489C2×#103—436no—
490C2×#102—433no—
491C2×#102—436no—
492C2×#102C2×D4313yescomplemented
493C43#6008911yescharacteristic, complemented, Sylow
4942−1+4—438no—
4952−1+4—4324no—
4962−1+4—8616no—
4972−1+4—8612no—
4982−1+4—864no—
499H(5,𝔽2)—24no—
500H(5,𝔽2)—4324no—
501H(5,𝔽2)—8648no—
502H(5,𝔽2)—8612no—
503H(5,𝔽2)C4×D4318yescomplemented
504C2×#41—21no—
505C2×#41—438no—
506C2×#41—438no—
507C2×#41—431no—
508C2×#41—433no—
509C2×#41—433no—
510C2×#41—4324no—
511C2×#41—431no—
512C2×#41—4324no—
513C2×#41—433no—
514C2×#41—436no—
515C2×#41—433no—
516C2×#41—863no—
517C2×#41—863no—
518C2×#41—863no—
519C2×#41—863no—
520C2×#41—863no—
521C2×#41—8612no—
522C2×#41—8612no—
523C2×#41—866no—
524C2×#41—863no—
525C2×#41—8648no—
526C2×#41—8616no—
527C2×#41—863no—
528C2×#41C22×D4313yes—
529C2×#41C22×D4311yescharacteristic
530C22×Q8—431no—
531C22×Q8—433no—
532C22×Q8—433no—
533C22×Q8—863no—
534C22×Q8—861no—
535C22×D4—23no—
536C22×D4—433no—
537C22×D4—433no—
538C22×D4—863no—
539C22×D4—863no—
540C22×D4—866no—
541C22×D4—863no—
542C22×D4C22×D4313yes—
543C23×C4—433no—
544C23×C4—863no—
545C23×C4—863no—
546C23×C4—863no—
547#131—24no—
548#131—8612no—
549#131—8612no—
550#131—864no—
551C2×M16—433no—
552C2×M16—433no—
553C2×M16—431no—
554C2×M16—433no—
555C2×M16—433no—
556C2×M16—8612no—
557C2×M16—8612no—
558C2×M16C22×D4313yes—
559C22×C8—433no—
560C22×C8—436no—
561C22×C8C22×D4313yes—
562C4×Q8—21no—
563C4×Q8—863no—
564C4×Q8—863no—
565C4×Q8—861no—
566C4×D4—23no—
567C4×D4—863no—
568C4×D4—866no—
569C4×D4—863no—
570C4×D4—866no—
571C4×D4—863no—
572#117—433no—
573#117—433no—
574#117—433no—
575#117—863no—
576#117—863no—
577#117C22×D4313yes—
578C2×C4⋊C4—433no—
579C2×C4⋊C4—433no—
580C2×C4⋊C4—436no—
581C2×C4⋊C4—431no—
582C2×C4⋊C4—863no—
583C2×C4⋊C4—863no—
584C2×C4⋊C4—863no—
585C2×C4⋊C4C22×D4313yes—
586C2×C22⋊C4—863no—
587C2×C42—863no—
588#103—433no—
589#103—431no—
590#103—436no—
591#103—433no—
592#103—433no—
593#103—436no—
594#103—433no—
595#103—433no—
596#103C22×D4313yes—
597#103C22×D4311yescharacteristic
598#102—436no—
599#102—433no—
600#102—433no—
601#102—433no—
602#102—431no—
603#102—433no—
604#102—431no—
605#102C22×D4316yes—
606#102C22×D4313yes—
607#102C22×D4313yes—
608C24—23no—
609C24—433no—
610C24—863no—
611#41—28no—
612#41—26no—
613#41—438no—
614#41—4324no—
615#41—4312no—
616#41—4312no—
617#41—434no—
618#41—4312no—
619#41—4324no—
620#41—4312no—
621#41—8624no—
622#41—8624no—
623#41—8624no—
624#41—8624no—
625#41—866no—
626#41—8624no—
627#41—8612no—
628#41—862no—
629#41—8648no—
630#41—8624no—
631#41—8624no—
632#41—866no—
633#41C2×C4×D4314yes—
634#41C2×C4×D43112yescomplemented
635#41D4×D4314yes—
636C2×Q8—438no—
637C2×Q8—433no—
638C2×Q8—4312no—
639C2×Q8—4312no—
640C2×Q8—433no—
641C2×Q8—863no—
642C2×Q8—8624no—
643C2×Q8—866no—
644C2×Q8—868no—
645C2×Q8—863no—
646C2×Q8—866no—
647C2×Q8D4×D4311yescharacteristic
648C2×Q8C23×D4311yescharacteristic
649C2×D4—23no—
650C2×D4—224no—
651C2×D4—23no—
652C2×D4—26no—
653C2×D4—436no—
654C2×D4—4324no—
655C2×D4—4312no—
656C2×D4—433no—
657C2×D4—431no—
658C2×D4—861no—
659C2×D4—866no—
660C2×D4—863no—
661C2×D4—8624no—
662C2×D4—8624no—
663C2×D4—8648no—
664C2×D4—866no—
665C2×D4—863no—
666C2×D4—8624no—
667C2×D4—863no—
668C2×D4C2×C4×D43112yescomplemented
669C2×D4D4×D4313yes—
670C2×D4C23×D4313yes—
671C22×C4—23no—
672C22×C4—23no—
673C22×C4—433no—
674C22×C4—4312no—
675C22×C4—433no—
676C22×C4—433no—
677C22×C4—4312no—
678C22×C4—431no—
679C22×C4—433no—
680C22×C4—861no—
681C22×C4—8624no—
682C22×C4—863no—
683C22×C4—866no—
684C22×C4—861no—
685C22×C4—863no—
686C22×C4—863no—
687C22×C4—866no—
688C22×C4—8624no—
689C22×C4—863no—
690C22×C4—863no—
691C22×C4—863no—
692C22×C4—3446no—
693C22×C4C23×D4313yes—
694M16—26no—
695M16—862no—
696M16—866no—
697M16—866no—
698M16—866no—
699M16—866no—
700C2×C8—26no—
701C2×C8—431no—
702C2×C8—433no—
703C2×C8—8612no—
704C2×C8—866no—
705C2×C8C23×D4313yes—
706C2×C8C23×D4311yescharacteristic
707C4⋊C4—23no—
708C4⋊C4—433no—
709C4⋊C4—431no—
710C4⋊C4—863no—
711C4⋊C4—866no—
712C4⋊C4—861no—
713C4⋊C4—863no—
714C4⋊C4C23×D4313yes—
715C4⋊C4C23×D4311yescharacteristic
716C22⋊C4—23no—
717C22⋊C4—863no—
718C22⋊C4—863no—
719C22⋊C4—863no—
720C42—23no—
721C42—863no—
722C42—863no—
723C42—863no—
724C23—23no—
725C23—212no—
726C23—83no—
727C23—83no—
728C23—433no—
729C23—431no—
730C23—4312no—
731C23—8612no—
732C23—861no—
733C23—3443no—
734C23—3443no—
735C23—1723no—
736C23—1723no—
737C23C2×D4×D4313yes—
738Q8—21no—
739Q8—4312no—
740Q8—436no—
741Q8—8612no—
742Q8—8612no—
743Q8—863no—
744Q8C22⋊C4×D4314yes—
745Q8C22×C4×D4312yes—
746D4—212no—
747D4—212no—
748D4—23no—
749D4—4324no—
750D4—4312no—
751D4—432no—
752D4—864no—
753D4—8612no—
754D4—8612no—
755D4—8624no—
756D4—8612no—
757D4—861no—
758D4C22⋊C4×D43112yes—
759D4C22×C4×D4316yes—
760C2×C4—21no—
761C2×C4—212no—
762C2×C4—21no—
763C2×C4—23no—
764C2×C4—83no—
765C2×C4—4312no—
766C2×C4—433no—
767C2×C4—431no—
768C2×C4—4312no—
769C2×C4—4312no—
770C2×C4—432no—
771C2×C4—436no—
772C2×C4—436no—
773C2×C4—432no—
774C2×C4—864no—
775C2×C4—8612no—
776C2×C4—8612no—
777C2×C4—8624no—
778C2×C4—8612no—
779C2×C4—863no—
780C2×C4—8612no—
781C2×C4—861no—
782C2×C4—863no—
783C2×C4—3446no—
784C2×C4—3443no—
785C2×C4—1726no—
786C2×C4—1722no—
787C2×C4C22×C4×D4316yes—
788C2×C4C2×D4×D4313yes—
789C2×C4C2×D4×D4316yes—
790C2×C4C24×D4311yescharacteristic
791C8—21no—
792C8—23no—
793C8—863no—
794C8—861no—
795C22—23no—
796C22—23no—
797C22—26no—
798C22—43no—
799C22—43no—
800C22—812no—
801C22—432no—
802C22—436no—
803C22—863no—
804C22—861no—
805C22—861no—
806C22—863no—
807C22—862no—
808C22—34412no—
809C22—17212no—
810C22—1721no—
811C22—1721no—
812C22C2×C22⋊C4×D4316yes—
813C22C22×D4×D4311yescharacteristic
814C4—22no—
815C4—43no—
816C4—41no—
817C4—432no—
818C4—436no—
819C4—866no—
820C4—1723no—
821C4—1721no—
822C4C2×C22⋊C4×D4316yes—
823C4C23×C4×D4311yescharacteristic
824C4C22×D4×D4311yescharacteristic
825C2—26no—
826C2—46no—
827C2—866no—
828C2—862no—
829C2—1722no—
830C2C22×C22⋊C4×D4311yescharacteristic
831C2#1914937011yescharacteristic
832C2#1914937711yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutatorC4×C43C24×C4
FrattiniC2×C4C24×D43
FittingC43×#2897C2
socleC22×C43C23×D4
prime radicalC2×#14583734C2
cosocleC2×C4×C43C25
hypercenter#2897D43
hypocenterC43#60089
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×#41 ◁ #2897

Complements

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

NH ≅ G/Ntype
2. C2×#14583664C2semidirect
3. #520×D43C2semidirect
4. #19143129C2semidirect
5. #19143126C2semidirect
6. #19143125C2semidirect
7. #19143124C2semidirect
8. #19143121C2semidirect
9. #19143120C2semidirect
10. #19143116C2semidirect
11. #19143110C2semidirect
12. #19143109C2semidirect
13. C2×#14582897C2semidirect
14. #417×D43C2semidirect
15. C43×#2897C2semidirect
17. #14583734C4semidirect
29. C2×#13063333C22semidirect
30. C2×#13063332C22semidirect
31. C2×#13063331C22semidirect
32. C22×#10621872C22semidirect
33. C2×M16×D43C22semidirect
34. #14583382C22semidirect
36. #14583380C22semidirect
37. #14583379C22semidirect
41. #117×D43C22semidirect
42. C2×C4⋊C4×D43C22semidirect
43. #14582909C22semidirect
44. #14582907C22semidirect
45. #14582906C22semidirect
46. #14582906C22semidirect
47. #14582904C22semidirect
48. #14582902C22semidirect
49. #14582902C22semidirect
50. #14582901C22semidirect
51. #14582900C22semidirect
52. #14582899C22semidirect
53. #14582899C22semidirect
54. #14582898C22semidirect
55. #14582897C22semidirect
56. #14582897C22semidirect
57. #14582897C22semidirect
58. #14582897C22semidirect
59. #14582897C22semidirect
60. #14582896C22semidirect
61. #14582895C22semidirect
62. #14582893C22semidirect
63. #14582892C22semidirect
64. #14582892C22semidirect
65. C2×#13063250C22semidirect
66. C2×#13063248C22semidirect
67. #103×D43C22semidirect
68. C2×#13063246C22semidirect
69. #102×D43C22semidirect
71. C2×#131×C43C22semidirect
72. C43×#520C22semidirect
73. C43×#418C22semidirect
74. C43×#417C22semidirect
75. C43×#416C22semidirect
76. C2×#102×C43C22semidirect
80. #13063372C2×C4semidirect
81. #13063372C2×C4semidirect
84. #13063370C2×C4semidirect
99. C2×#10621900C2×C4semidirect
106. #41×D43C2×C4semidirect
173. H(5,𝔽2)×C43C2×C4semidirect
197. #41×C43C22×C4semidirect
205. C2×D4×C43C22×C4semidirect
230. Q8×D43C22×C4semidirect
241. #10621900C22×C4semidirect
246. D4×D43C22×C4semidirect
251. #10621898C22×C4semidirect
274. C2×Dic86C22×C4semidirect
419. #2897D43semidirect
449. C2×#131C2×D43semidirect
457. #520C2×D43semidirect
469. #418C2×D43semidirect
480. #417C2×D43semidirect
486. #416C2×D43semidirect
492. C2×#102C2×D43semidirect
493. C43#60089semidirect
503. H(5,𝔽2)C4×D43semidirect
634. #41C2×C4×D43semidirect
668. C2×D4C2×C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145837342
C2×#145836642
#520×D432
#191431292
#191431262
#191431252
#191431242
#191431212
#191431202
#191431162
#191431102
#191431092
C2×#145828972
#417×D432
C43×#28972
#6008943