Finite Group Databasebeta

← #25960157

Subgroups — #25960157

Order 11008.

4874 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583734C211yesmaximal, characteristic
2C2×#131×D43C211yesmaximal, characteristic, complemented
3#19147795C211yesmaximal, 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#19143111C213yesmaximal, complemented
12#19143109C213yesmaximal, complemented
13C2×#14582892C213yesmaximal, complemented
14#416×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
28C2×#13063333C2213yescomplemented
29C2×#13063332C2211yescharacteristic, complemented
30C2×#13063331C2213yescomplemented
31#131×D43—28no—
32C2×M16×D43C2213yescomplemented
33C22×C8×D43C2213yescomplemented
34#14583382C2211yescharacteristic, complemented
35#14583380C2213yescomplemented
36#14583379C2213yescomplemented
37#14583375—21no—
38#14583371—23no—
39C4×#10621902—21no—
40C4×#10621900—23no—
41C2×#13063283C2213yescomplemented
42#117×D43C2213yescomplemented
43#14582909C2213yescomplemented
44#14582907C2213yescomplemented
45#14582906C2216yescomplemented
46#14582904C2213yescomplemented
47#14582902C2216yescomplemented
48#14582901C2213yescomplemented
49#14582900C2213yescomplemented
50#14582898C2213yescomplemented
51#14582897C2216yescomplemented
52#14582897C2216yescomplemented
53#14582896C2213yescomplemented
54#14582895C2213yescomplemented
55#14582894C2211yescharacteristic, complemented
56#14582894C2213yescomplemented
57#14582893C2213yescomplemented
58#14582892C2213yescomplemented
59#14582892C2213yescomplemented
60#14582892C2216yescomplemented
61#14582892C2216yescomplemented
62#14582892C2216yescomplemented
63C2×#13063250C2213yescomplemented
64C2×#13063248C2213yescomplemented
65#103×D43C2213yescomplemented
66#103×D43C2213yescomplemented
67C2×#13063246C2213yescomplemented
68#102×D43C2213yescomplemented
69#102×D43C2213yescomplemented
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×D43C2313yes—
122#13063333—212no—
123#13063332—24no—
124#13063331—212no—
125C2×#10621877C2313yes—
126C2×#10621872C2316yes—
127M16×D43—212no—
128C22×C43⋊C8C2313yes—
129C2×C8×D43—212no—
130C2×C8×D43C2313yes—
131C2×C8×D43C2313yes—
132C2×C8×D43C2311yescharacteristic
133C2×C8×D43C2313yes—
134Q8×Dic43—21no—
135C4×Dic86—23no—
136#13063290—23no—
137C4×D172—23no—
138D4×Dic43—23no—
139#13063287—23no—
140C4×C22⋊D43—26no—
141(C22⋊D43)⋊C4—26no—
142#13063284C2313yes—
143#13063283—23no—
144#13063283—23no—
145#13063283C2311yescharacteristic
146#13063283C2313yes—
147#13063283C2316yes—
148#13063282—23no—
149#13063281—23no—
150C2×C4⋊Dic43C2313yes—
151C4⋊C4×D43C2313yes—
152C4⋊C4×D43C2313yes—
153C2×(C2×D43)⋊C4—23no—
154C22⋊C4×D43—23no—
155C2×C4×Dic43—23no—
156C42×D43—23no—
157#13063250C2313yes—
158#13063250C2313yes—
159#13063250C2316yes—
160#13063249C2311yescharacteristic
161#13063249C2313yes—
162#13063248C2313yes—
163#13063248C2313yes—
164#13063248C2316yes—
165#13063247C2311yescharacteristic
166#13063247C2313yes—
167#13063246C2313yes—
168#13063246C2313yes—
169#13063246C2316yes—
170#13063245C2311yescharacteristic
171#13063245C2313yes—
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×C43C2311yescharacteristic
187#103×C43C2313yes—
188#102×C43C2313yes—
189#102×C43C2313yes—
190#102×C43C2316yes—
191C24×C43—23no—
192C23×D43—23no—
193C23×D43C2×D413yes—
194#41×C43—28no—
195#41×C43—26no—
196#41×C43C22×C4112yes—
197#41×C43C22×C414yes—
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×C4112yes—
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—23no—
216C2×C22⋊D43—26no—
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×C4112yes—
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×C4124yes—
242D4×D43—224no—
243D4×D43—26no—
244D4×D43—224no—
245D4×D43C22⋊C4124yes—
246D4×D43C22×C4112yes—
247#10621898—26no—
248#10621898—224no—
249#10621898—224no—
250#10621898C22×C4112yes—
251#10621898C22×C4112yes—
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—23no—
261C2×C4×D43—23no—
262C2×C4×D43C22×C4112yes—
263C2×C4×D43C2×D4112yes—
264C2×C4×D43C2×D413yes—
265C2×C4×D43C2×D413yes—
266C2×C4×D43C2413yes—
267C2×C4×D43C2411yescharacteristic
268C2×Dic86—23no—
269C2×Dic86—26no—
270C2×Dic86—23no—
271C2×Dic86—224no—
272C2×Dic86C22×C4112yes—
273C2×Dic86C2×D413yes—
274C2×Dic86C2413yes—
275M16×C43—26no—
276C2×C8×C43—26no—
277C2×C8×C43C2411yescharacteristic
278C2×C8×C43C2413yes—
279C4⋊C4×C43—23no—
280C4⋊C4×C43C2413yes—
281C4⋊C4×C43C2411yescharacteristic
282C22⋊C4×C43—23no—
283C42×C43—23no—
284C22⋊Dic43—23no—
285(C2×D43)⋊C4—21no—
286(C2×D43)⋊C4—23no—
287(C2×D43)⋊C4—26no—
288C4⋊Dic43—23no—
289C4⋊Dic43C2411yescharacteristic
290C4⋊Dic43C2413yes—
291Dic43⋊C4—23no—
292Dic43⋊C4—23no—
293C4×Dic43—23no—
294C4×Dic43—21no—
295C4×Dic43—23no—
296C4×Dic43—26no—
297#10621877—26no—
298C2×C43⋊C8—26no—
299C2×C43⋊C8C2411yescharacteristic
300C2×C43⋊C8C2413yes—
301#10621872—212no—
302C8×D43—22no—
303C8×D43—26no—
304C8×D43—26no—
305C8×D43—26no—
306C23×C43—23no—
307C23×C43—212no—
308C23×C43—83no—
309C23×C43—83no—
310C23×C43C22×D413yes—
311C22×D43—21no—
312C22×D43—212no—
313C22×D43—43no—
314C22×D43—43no—
315C22×D43—83no—
316C22×D43—83no—
317C22×D43C2×C22⋊C4112yes—
318C22×D43C22×D411yescharacteristic
319C22×D43C22×D413yes—
320Q8×C43—21no—
321Q8×C43C2×C22⋊C414yes—
322Q8×C43C23×C412yes—
323D4×C43—212no—
324D4×C43—212no—
325D4×C43—23no—
326D4×C43C2×C22⋊C4112yes—
327D4×C43C23×C416yes—
328C2×C4×C43—21no—
329C2×C4×C43—212no—
330C2×C4×C43—23no—
331C2×C4×C43—21no—
332C2×C4×C43—83no—
333C2×C4×C43C23×C416yes—
334C2×C4×C43C22×D413yes—
335C2×C4×C43C22×D416yes—
336C2×C4×C43C2511yescharacteristic
337C22⋊D43—212no—
338C22⋊D43—224no—
339C22⋊D43—212no—
340C22⋊D43—212no—
341C22⋊D43C2×C22⋊C4124yes—
342C2×Dic43—212no—
343C2×Dic43—23no—
344C2×Dic43—224no—
345C2×Dic43—212no—
346C2×Dic43—21no—
347C2×Dic43—23no—
348C2×Dic43—83no—
349C2×Dic43C2×C22⋊C4112yes—
350C2×Dic43C22×D411yescharacteristic
351C2×Dic43C22×D413yes—
352D172—24no—
353D172—21no—
354D172C2×C22⋊C4112yes—
355D172C23×C412yes—
356C4×D43—212no—
357C4×D43—212no—
358C4×D43—24no—
359C4×D43—83no—
360C4×D43—83no—
361C4×D43C2×C22⋊C4112yes—
362C4×D43C2×C22⋊C4112yes—
363C4×D43C23×C412yes—
364C4×D43C23×C416yes—
365C4×D43C22×D412yes—
366C4×D43C22×D416yes—
367Dic86—212no—
368Dic86—23no—
369Dic86—212no—
370Dic86C2×C22⋊C4112yes—
371Dic86C23×C416yes—
372C8×C43—21no—
373C8×C43—23no—
374C43⋊C8—21no—
375C43⋊C8—23no—
376#60086—431nomaximal, Sylow
377C22×C43—23no—
378C22×C43—23no—
379C22×C43—26no—
380C22×C43—43no—
381C22×C43—43no—
382C22×C43—812no—
383C22×C43C22×C22⋊C416yes—
384C22×C43C23×D411yescharacteristic
385C2×D43—21no—
386C2×D43—21no—
387C2×D43—23no—
388C2×D43—23no—
389C2×D43—22no—
390C2×D43—412no—
391C2×D43—41no—
392C2×D43—41no—
393C2×D43—812no—
394C2×D43C22×C22⋊C416yes—
395C2×D43C22×C22⋊C412yes—
396C4×C43—22no—
397C4×C43—41no—
398C4×C43—43no—
399C4×C43C22×C22⋊C416yes—
400C4×C43C24×C411yescharacteristic
401C4×C43C23×D411yescharacteristic
402Dic43—26no—
403Dic43—41no—
404Dic43—43no—
405Dic43C22×C22⋊C416yes—
406Dic43C22×C22⋊C412yes—
407C2×#585—431no—
408C22×#131—431no—
409#3428—431no—
410#2898—433no—
411#2898—433no—
412#2898—431no—
413#2898—431no—
414#2897—433no—
415#2897—433no—
416#2897—431no—
417#2897D4311yescharacteristic, complemented
418#2896—433no—
419#2896—433no—
420C2×#416—433no—
421C2×#416—433no—
422C2×C43—26no—
423C2×C43—46no—
424C2×C43C23×C22⋊C411yescharacteristic
425C2×C43#358411yescharacteristic
426C2×C43#358411yescharacteristic
427D43—22no—
428D43—26no—
429D43—42no—
430#585—4316no—
431#585—868no—
432C2×2−1+4—433no—
433C2×2−1+4—431no—
434C2×2−1+4—861no—
435C2×H(5,𝔽2)—433no—
436C2×H(5,𝔽2)—863no—
437C2×H(5,𝔽2)C2×D4311yescharacteristic
438C22×#41—431no—
439C22×#41—433no—
440C22×#41—433no—
441C22×#41—863no—
442C22×#41—861no—
443C2×#131—431no—
444C2×#131—433no—
445C2×#131—433no—
446C2×#131—868no—
447C2×#131C2×D4311yescharacteristic, complemented
448C22×M16—433no—
449C23×C8—433no—
450#520—431no—
451#520—433no—
452#520—433no—
453#520C2×D4311yescharacteristic, complemented
454#519—861no—
455#518—863no—
456C4×#41—863no—
457C4×#41—861no—
458C2×#117—433no—
459C2×#117—433no—
460#419—433no—
461#419—433no—
462#419—436no—
463#418—433no—
464#418—436no—
465#418C2×D4313yescomplemented
466#417—433no—
467#417—433no—
468#417—433no—
469#417—436no—
470#417—436no—
471#417C2×D4313yescomplemented
472#416—433no—
473#416—433no—
474#416—433no—
475#416—431no—
476#416—433no—
477#416—433no—
478#416—433no—
479#416—436no—
480#416—436no—
481#416—436no—
482#416C2×D4313yescomplemented
483C2×#103—433no—
484C2×#103—433no—
485C2×#103—433no—
486C2×#103—433no—
487C2×#102—433no—
488C2×#102—433no—
489C2×#102—433no—
490C2×#102C2×D4313yescomplemented
491C43#6008611yescharacteristic, complemented, Sylow
4922−1+4—4324no—
4932−1+4—438no—
4942−1+4—8616no—
4952−1+4—8612no—
4962−1+4—864no—
497H(5,𝔽2)—24no—
498H(5,𝔽2)—4324no—
499H(5,𝔽2)—8648no—
500H(5,𝔽2)—8612no—
501H(5,𝔽2)C4×D4318yescomplemented
502C2×#41—21no—
503C2×#41—438no—
504C2×#41—438no—
505C2×#41—431no—
506C2×#41—433no—
507C2×#41—433no—
508C2×#41—4324no—
509C2×#41—431no—
510C2×#41—4324no—
511C2×#41—433no—
512C2×#41—436no—
513C2×#41—433no—
514C2×#41—863no—
515C2×#41—863no—
516C2×#41—863no—
517C2×#41—863no—
518C2×#41—863no—
519C2×#41—8612no—
520C2×#41—8612no—
521C2×#41—866no—
522C2×#41—863no—
523C2×#41—8648no—
524C2×#41—8616no—
525C2×#41—863no—
526C2×#41C22×D4313yes—
527C2×#41C22×D4311yescharacteristic
528C22×Q8—431no—
529C22×Q8—433no—
530C22×Q8—433no—
531C22×Q8—863no—
532C22×Q8—861no—
533C22×D4—23no—
534C22×D4—433no—
535C22×D4—433no—
536C22×D4—863no—
537C22×D4—863no—
538C22×D4—866no—
539C22×D4—863no—
540C22×D4C22×D4313yes—
541C23×C4—433no—
542C23×C4—863no—
543C23×C4—863no—
544#131—24no—
545#131—8612no—
546#131—8612no—
547#131—864no—
548C2×M16—433no—
549C2×M16—436no—
550C2×M16—8612no—
551C2×M16C22×D4313yes—
552C22×C8—433no—
553C22×C8—431no—
554C22×C8—433no—
555C22×C8—433no—
556C22×C8—433no—
557C22×C8—8612no—
558C22×C8C22×D4313yes—
559C4×Q8—21no—
560C4×Q8—863no—
561C4×Q8—863no—
562C4×Q8—861no—
563C4×D4—23no—
564C4×D4—863no—
565C4×D4—866no—
566C4×D4—863no—
567C4×D4—866no—
568C4×D4—863no—
569#117—433no—
570#117—431no—
571#117—433no—
572#117—436no—
573#117—863no—
574#117—863no—
575#117—863no—
576#117—863no—
577#117C22×D4313yes—
578C2×C4⋊C4—433no—
579C2×C4⋊C4—433no—
580C2×C4⋊C4—433no—
581C2×C4⋊C4C22×D4313yes—
582C2×C22⋊C4—863no—
583C2×C22⋊C4—863no—
584C2×C42—863no—
585C2×C42—863no—
586#103—431no—
587#103—433no—
588#103—433no—
589#103—433no—
590#103—436no—
591#103—433no—
592#103—433no—
593#103—436no—
594#103C22×D4311yescharacteristic
595#103C22×D4313yes—
596#102—433no—
597#102—433no—
598#102—436no—
599#102—431no—
600#102—433no—
601#102—431no—
602#102—433no—
603#102C22×D4313yes—
604#102C22×D4313yes—
605#102C22×D4316yes—
606C24—23no—
607C24—433no—
608C24—863no—
609#41—28no—
610#41—26no—
611#41—438no—
612#41—4324no—
613#41—4312no—
614#41—4312no—
615#41—434no—
616#41—4312no—
617#41—4324no—
618#41—4312no—
619#41—8624no—
620#41—8624no—
621#41—8624no—
622#41—8624no—
623#41—866no—
624#41—8624no—
625#41—8612no—
626#41—862no—
627#41—8648no—
628#41—8624no—
629#41—8624no—
630#41—866no—
631#41C2×C4×D43112yes—
632#41C2×C4×D4314yes—
633#41D4×D4314yes—
634C2×Q8—438no—
635C2×Q8—433no—
636C2×Q8—4312no—
637C2×Q8—4312no—
638C2×Q8—433no—
639C2×Q8—863no—
640C2×Q8—8624no—
641C2×Q8—866no—
642C2×Q8—868no—
643C2×Q8—863no—
644C2×Q8—866no—
645C2×Q8D4×D4311yescharacteristic
646C2×Q8C23×D4311yescharacteristic
647C2×D4—23no—
648C2×D4—224no—
649C2×D4—23no—
650C2×D4—26no—
651C2×D4—436no—
652C2×D4—4324no—
653C2×D4—4312no—
654C2×D4—433no—
655C2×D4—431no—
656C2×D4—861no—
657C2×D4—866no—
658C2×D4—863no—
659C2×D4—8624no—
660C2×D4—8624no—
661C2×D4—8648no—
662C2×D4—863no—
663C2×D4—866no—
664C2×D4—8624no—
665C2×D4—863no—
666C2×D4C2×C4×D43112yes—
667C2×D4D4×D4313yes—
668C2×D4C23×D4313yes—
669C22×C4—23no—
670C22×C4—23no—
671C22×C4—433no—
672C22×C4—4312no—
673C22×C4—433no—
674C22×C4—433no—
675C22×C4—4312no—
676C22×C4—433no—
677C22×C4—431no—
678C22×C4—861no—
679C22×C4—8624no—
680C22×C4—863no—
681C22×C4—863no—
682C22×C4—863no—
683C22×C4—863no—
684C22×C4—866no—
685C22×C4—8624no—
686C22×C4—863no—
687C22×C4—863no—
688C22×C4—863no—
689C22×C4C23×D4313yes—
690M16—26no—
691M16—8612no—
692M16—866no—
693C2×C8—26no—
694C2×C8—431no—
695C2×C8—433no—
696C2×C8—862no—
697C2×C8—866no—
698C2×C8—866no—
699C2×C8—866no—
700C2×C8—866no—
701C2×C8C23×D4311yescharacteristic
702C2×C8C23×D4313yes—
703C4⋊C4—23no—
704C4⋊C4—433no—
705C4⋊C4—431no—
706C4⋊C4—863no—
707C4⋊C4—863no—
708C4⋊C4—863no—
709C4⋊C4C23×D4311yescharacteristic
710C4⋊C4C23×D4313yes—
711C22⋊C4—23no—
712C22⋊C4—861no—
713C22⋊C4—863no—
714C22⋊C4—866no—
715C22⋊C4—863no—
716C42—23no—
717C42—861no—
718C42—863no—
719C42—866no—
720C42—863no—
721C23—23no—
722C23—212no—
723C23—83no—
724C23—83no—
725C23—431no—
726C23—433no—
727C23—4312no—
728C23—8612no—
729C23—861no—
730C23—3443no—
731C23—3443no—
732C23—1723no—
733C23—1723no—
734C23C2×D4×D4313yes—
735Q8—21no—
736Q8—4312no—
737Q8—436no—
738Q8—8612no—
739Q8—8612no—
740Q8—863no—
741Q8C22⋊C4×D4314yes—
742Q8C22×C4×D4312yes—
743D4—212no—
744D4—212no—
745D4—23no—
746D4—4324no—
747D4—4312no—
748D4—432no—
749D4—864no—
750D4—8612no—
751D4—8612no—
752D4—8624no—
753D4—8612no—
754D4—861no—
755D4C22⋊C4×D43112yes—
756D4C22×C4×D4316yes—
757C2×C4—21no—
758C2×C4—212no—
759C2×C4—21no—
760C2×C4—23no—
761C2×C4—83no—
762C2×C4—4312no—
763C2×C4—431no—
764C2×C4—433no—
765C2×C4—4312no—
766C2×C4—4312no—
767C2×C4—432no—
768C2×C4—436no—
769C2×C4—432no—
770C2×C4—436no—
771C2×C4—864no—
772C2×C4—8612no—
773C2×C4—8612no—
774C2×C4—8624no—
775C2×C4—8612no—
776C2×C4—863no—
777C2×C4—8612no—
778C2×C4—861no—
779C2×C4—863no—
780C2×C4—3443no—
781C2×C4—3443no—
782C2×C4—3443no—
783C2×C4C22×C4×D4316yes—
784C2×C4C2×D4×D4313yes—
785C2×C4C2×D4×D4316yes—
786C2×C4C24×D4311yescharacteristic
787C8—21no—
788C8—23no—
789C8—861no—
790C8—863no—
791C22—23no—
792C22—23no—
793C22—26no—
794C22—43no—
795C22—43no—
796C22—812no—
797C22—432no—
798C22—436no—
799C22—863no—
800C22—861no—
801C22—863no—
802C22—861no—
803C22—862no—
804C22—34412no—
805C22—17212no—
806C22—1721no—
807C22—1721no—
808C22C2×C22⋊C4×D4316yes—
809C22C22×D4×D4311yescharacteristic
810C4—22no—
811C4—43no—
812C4—41no—
813C4—432no—
814C4—436no—
815C4—866no—
816C4—1721no—
817C4—1723no—
818C4C2×C22⋊C4×D4316yes—
819C4C23×C4×D4311yescharacteristic
820C4C22×D4×D4311yescharacteristic
821C2—26no—
822C2—46no—
823C2—866no—
824C2—862no—
825C2—1722no—
826C2C22×C22⋊C4×D4311yescharacteristic
827C2#1914936311yescharacteristic
828C2#1914936711yescharacteristic
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#60086
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×#131×D43C2semidirect
3. #19147795C2semidirect
4. #19143129C2semidirect
5. #19143126C2semidirect
6. #19143125C2semidirect
7. #19143124C2semidirect
8. #19143121C2semidirect
9. #19143120C2semidirect
10. #19143116C2semidirect
11. #19143111C2semidirect
12. #19143109C2semidirect
13. C2×#14582892C2semidirect
14. #416×D43C2semidirect
15. C43×#2897C2semidirect
17. #14583734C4semidirect
28. C2×#13063333C22semidirect
29. C2×#13063332C22semidirect
30. C2×#13063331C22semidirect
32. C2×M16×D43C22semidirect
33. C22×C8×D43C22semidirect
34. #14583382C22semidirect
35. #14583380C22semidirect
36. #14583379C22semidirect
41. C2×#13063283C22semidirect
42. #117×D43C22semidirect
43. #14582909C22semidirect
44. #14582907C22semidirect
45. #14582906C22semidirect
46. #14582904C22semidirect
47. #14582902C22semidirect
48. #14582901C22semidirect
49. #14582900C22semidirect
50. #14582898C22semidirect
51. #14582897C22semidirect
52. #14582897C22semidirect
53. #14582896C22semidirect
54. #14582895C22semidirect
55. #14582894C22semidirect
56. #14582894C22semidirect
57. #14582893C22semidirect
58. #14582892C22semidirect
59. #14582892C22semidirect
60. #14582892C22semidirect
61. #14582892C22semidirect
62. #14582892C22semidirect
63. C2×#13063250C22semidirect
64. C2×#13063248C22semidirect
65. #103×D43C22semidirect
66. #103×D43C22semidirect
67. C2×#13063246C22semidirect
68. #102×D43C22semidirect
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
417. #2897D43semidirect
447. C2×#131C2×D43semidirect
453. #520C2×D43semidirect
465. #418C2×D43semidirect
471. #417C2×D43semidirect
482. #416C2×D43semidirect
490. C2×#102C2×D43semidirect
491. C43#60086semidirect
501. H(5,𝔽2)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×#131×D432
#191477952
#191431292
#191431262
#191431252
#191431242
#191431212
#191431202
#191431162
#191431112
#191431092
C2×#145828922
#416×D432
C43×#28972
#6008643