Finite Group Databasebeta

← #25960170

Subgroups — #25960170

Order 11008.

4810 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×2−1+4×D43C211yesmaximal, characteristic
2C2×#14583664C211yesmaximal, characteristic, complemented
3#19147795C211yesmaximal, characteristic, complemented
4#19143129C211yesmaximal, characteristic, complemented
5#19143128C211yesmaximal, characteristic, complemented
6#19143127C213yesmaximal, complemented
7#19143126C213yesmaximal, complemented
8#19143125C211yesmaximal, characteristic, complemented
9#19143124C213yesmaximal, complemented
10#19143123C213yesmaximal, complemented
11#19143111C213yesmaximal, complemented
12#19143110C213yesmaximal, complemented
13C2×#14582906C213yesmaximal, complemented
14#419×D43C213yesmaximal, complemented
15C43×#2898C211yesmaximal, characteristic, complemented
16C2×#13063373—21no—
17C2×#13063373C2213yes—
18C2×#13063372—23no—
19C2×#13063372C2211yescharacteristic
20C2×#13063372C2213yes—
212−1+4×D43—28no—
222−1+4×D43C4116yescomplemented
23C2×#41×D43—23no—
24C2×#41×D43C2213yes—
25C2×#41×D43C2211yescharacteristic
26C22×Q8×D43—21no—
27C22×Q8×D43C2213yes—
28#14583664—28no—
29C2×#13063333C2213yescomplemented
30C2×#13063332C2211yescharacteristic, complemented
31C2×#13063331C2213yescomplemented
32C22×#10621872C2213yes—
33C2×M16×D43C2213yes—
34#14583382C2211yescharacteristic, complemented
35#14583380C2213yescomplemented
36#14583379C2213yescomplemented
37#14583375—21no—
38#14583371—23no—
39C4×#10621902—21no—
40C4×#10621900—23no—
41C2×#13063283C2213yes—
42#117×D43C2213yes—
43#14582909C2213yescomplemented
44#14582908C2213yescomplemented
45#14582907C2213yescomplemented
46#14582906C2213yes—
47#14582906C2216yes—
48#14582906C2213yes—
49#14582906C2216yescomplemented
50#14582906C2216yescomplemented
51#14582902C2211yescharacteristic
52#14582902C2213yes—
53#14582901C2213yescomplemented
54#14582900C2213yescomplemented
55#14582899C2213yescomplemented
56#14582899C2213yescomplemented
57#14582898C2213yescomplemented
58#14582897C2213yescomplemented
59#14582897C2213yescomplemented
60#14582896C2213yescomplemented
61#14582895C2213yescomplemented
62#14582894C2216yescomplemented
63#14582893C2213yescomplemented
64#14582892C2216yescomplemented
65C2×#13063250C2213yescomplemented
66C2×#13063249C2213yescomplemented
67C2×#13063248C2213yescomplemented
68#103×D43C2216yescomplemented
69#103×D43C2216yescomplemented
70C2×2−1+4×C43C2211yescharacteristic
71C2×#131×C43C2211yescharacteristic, complemented
72C43×#520C2211yescharacteristic, complemented
73C43×#419C2213yescomplemented
74C43×#417C2213yescomplemented
75C43×#416C2213yescomplemented
76C2×#103×C43C2213yescomplemented
77#13063373—216no—
78#13063373—212no—
79#13063373C2×C4124yescomplemented
80#13063372—24no—
81#13063372—248no—
82#13063372—212no—
83#13063372C2×C4124yescomplemented
84#13063372C2×C418yescomplemented
85C2×#10621902—23no—
86C2×#10621902D411yescharacteristic
87C2×#10621902C2313yes—
88C2×#10621898—26no—
89C2×#10621898—23no—
90C2×#10621898—23no—
91C2×#10621898C2313yes—
92C2×#10621898C2313yes—
93C2×#10621900—23no—
94C2×#10621900—26no—
95C2×#10621900—23no—
96C2×#10621900D413yes—
97C2×#10621900C2313yes—
98#41×D43—248no—
99#41×D43—212no—
100#41×D43C2×C418yes—
101#41×D43C2×C4124yescomplemented
102#41×D43D418yes—
103C22×Dic86—23no—
104C22×Dic86—23no—
105C22×Dic86C2313yes—
106C2×Q8×D43—21no—
107C2×Q8×D43—216no—
108C2×Q8×D43—23no—
109C2×Q8×D43—212no—
110C2×Q8×D43—23no—
111C2×Q8×D43—23no—
112C2×Q8×D43C2×C4124yescomplemented
113C2×Q8×D43D411yescharacteristic
114C2×Q8×D43C2316yes—
115C2×Q8×D43C2313yes—
116C2×D4×D43—23no—
117C2×D4×D43D413yes—
118C2×D4×D43C2311yescharacteristic
119C22×C4×D43—23no—
120C22×C4×D43—23no—
121C22×C4×D43C2313yes—
122#13063333—212no—
123#13063332—24no—
124#13063331—212no—
125C2×#10621877C2313yes—
126C2×#10621872—212no—
127C2×#10621872C2313yes—
128C2×#10621872C2311yescharacteristic
129C2×#10621872C2313yes—
130C2×#10621872C2313yes—
131M16×D43—212no—
132C22×C43⋊C8C2313yes—
133C2×C8×D43C2316yes—
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#13063250C2316yes—
159#13063250C2313yes—
160#13063249C2313yes—
161#13063249C2316yes—
162#13063249C2313yes—
163#13063248C2313yes—
164#13063248C2316yes—
165#13063248C2313yes—
166#13063247C2313yes—
167#13063247C2311yescharacteristic
168#13063246C2313yes—
169#13063246C2311yescharacteristic
170#13063245C2311yescharacteristic
171#13063245C2313yes—
1722−1+4×C43—24no—
1732−1+4×C43C2×C418yescomplemented
174C2×#41×C43—23no—
175C2×#41×C43C2313yes—
176C2×#41×C43C2311yescharacteristic
177C22×Q8×C43—21no—
178C22×Q8×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×C43C2316yes—
188#103×C43C2313yes—
189#102×C43C2313yes—
190#102×C43C2311yescharacteristic
191C23×D43—21no—
192C23×D43C2×D413yes—
193#41×C43—224no—
194#41×C43—26no—
195#41×C43C22×C4112yes—
196#41×C43C22×C414yes—
197#41×C43C2×D414yes—
198C2×Q8×C43—28no—
199C2×Q8×C43—23no—
200C2×Q8×C43—26no—
201C2×Q8×C43C22×C4112yes—
202C2×Q8×C43C2×D411yescharacteristic
203C2×Q8×C43C2413yes—
204C2×D4×C43—23no—
205C2×D4×C43C2×D413yes—
206C2×D4×C43C2411yescharacteristic
207C22×C4×C43—23no—
208C22×C4×C43—23no—
209C22×C4×C43—23no—
210C22×C4×C43C2413yes—
211C2×C22⋊D43—21no—
212C2×C22⋊D43—23no—
213C2×C22⋊D43—23no—
214C2×C22⋊D43C2×D416yes—
215C22×Dic43—23no—
216C22×Dic43—23no—
217C22×Dic43—23no—
218C22×Dic43C2×D413yes—
219#10621902—224no—
220#10621902—26no—
221#10621902C22⋊C418yes—
222#10621902C22×C4112yes—
223Q8×D43—28no—
224Q8×D43—224no—
225Q8×D43—224no—
226Q8×D43—26no—
227Q8×D43—212no—
228Q8×D43—224no—
229Q8×D43C22⋊C418yes—
230Q8×D43C22×C4112yes—
231Q8×D43C22×C4124yes—
232#10621900—224no—
233#10621900—248no—
234#10621900—224no—
235#10621900—26no—
236#10621900C22⋊C4124yes—
237#10621900C22×C4112yes—
238D4×D43—22no—
239D4×D43—224no—
240D4×D43C22⋊C4124yes—
241D4×D43C22×C414yes—
242#10621898—26no—
243#10621898—248no—
244#10621898—224no—
245#10621898—224no—
246#10621898C22×C4112yes—
247#10621898C22×C4112yes—
248#10621898C2×D4112yes—
249C2×D172—23no—
250C2×D172C2×D413yes—
251C2×D172C2411yescharacteristic
252C2×C4×D43—23no—
253C2×C4×D43—23no—
254C2×C4×D43—224no—
255C2×C4×D43—224no—
256C2×C4×D43—23no—
257C2×C4×D43—26no—
258C2×C4×D43—23no—
259C2×C4×D43—23no—
260C2×C4×D43C22×C4112yes—
261C2×C4×D43C2×D4112yes—
262C2×C4×D43C2×D413yes—
263C2×C4×D43C2×D413yes—
264C2×C4×D43C2413yes—
265C2×C4×D43C2411yescharacteristic
266C2×Dic86—23no—
267C2×Dic86—26no—
268C2×Dic86—224no—
269C2×Dic86—23no—
270C2×Dic86—26no—
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⋊C8C2413yes—
300C2×C43⋊C8C2411yescharacteristic
301#10621872—26no—
302#10621872—22no—
303#10621872—26no—
304#10621872—26no—
305C8×D43—212no—
306C23×C43—21no—
307C23×C43C22×D413yes—
308C22×D43—21no—
309C22×D43—24no—
310C22×D43—43no—
311C22×D43—43no—
312C22×D43—42no—
313C22×D43—42no—
314C22×D43C2×C22⋊C4112yes—
315C22×D43C22×D411yescharacteristic
316C22×D43C22×D413yes—
317Q8×C43—212no—
318Q8×C43—23no—
319Q8×C43C2×C22⋊C414yes—
320Q8×C43C23×C416yes—
321D4×C43—212no—
322D4×C43—21no—
323D4×C43C2×C22⋊C4112yes—
324D4×C43C23×C412yes—
325C2×C4×C43—212no—
326C2×C4×C43—23no—
327C2×C4×C43—212no—
328C2×C4×C43—23no—
329C2×C4×C43—21no—
330C2×C4×C43—83no—
331C2×C4×C43C23×C416yes—
332C2×C4×C43C22×D413yes—
333C2×C4×C43C22×D416yes—
334C2×C4×C43C2511yescharacteristic
335C22⋊D43—212no—
336C22⋊D43—212no—
337C22⋊D43—24no—
338C22⋊D43C2×C22⋊C4124yes—
339C2×Dic43—212no—
340C2×Dic43—23no—
341C2×Dic43—212no—
342C2×Dic43—21no—
343C2×Dic43—23no—
344C2×Dic43—83no—
345C2×Dic43C2×C22⋊C4112yes—
346C2×Dic43C22×D411yescharacteristic
347C2×Dic43C22×D413yes—
348D172—212no—
349D172—21no—
350D172C2×C22⋊C4112yes—
351D172C23×C412yes—
352C4×D43—212no—
353C4×D43—224no—
354C4×D43—212no—
355C4×D43—212no—
356C4×D43—83no—
357C4×D43—83no—
358C4×D43C2×C22⋊C4112yes—
359C4×D43C2×C22⋊C4112yes—
360C4×D43C23×C412yes—
361C4×D43C23×C416yes—
362C4×D43C22×D416yes—
363C4×D43C22×D412yes—
364Dic86—212no—
365Dic86—23no—
366Dic86—212no—
367Dic86—224no—
368Dic86C2×C22⋊C4112yes—
369Dic86C23×C416yes—
370C8×C43—23no—
371C8×C43—21no—
372C43⋊C8—23no—
373C43⋊C8—21no—
374#60088—431nomaximal, Sylow
375C22×C43—23no—
376C22×C43—23no—
377C22×C43—22no—
378C22×C43—41no—
379C22×C43—41no—
380C22×C43C22×C22⋊C416yes—
381C22×C43C23×D411yescharacteristic
382C2×D43—21no—
383C2×D43—21no—
384C2×D43—23no—
385C2×D43—23no—
386C2×D43—22no—
387C2×D43—412no—
388C2×D43—48no—
389C2×D43—41no—
390C2×D43—41no—
391C2×D43C22×C22⋊C412yes—
392C2×D43C22×C22⋊C416yes—
393C4×C43—26no—
394C4×C43—41no—
395C4×C43—43no—
396C4×C43C22×C22⋊C416yes—
397C4×C43C24×C411yescharacteristic
398C4×C43C23×D411yescharacteristic
399Dic43—26no—
400Dic43—41no—
401Dic43—43no—
402Dic43C22×C22⋊C412yes—
403Dic43C22×C22⋊C416yes—
404C22×2−1+4—431no—
405C2×#568—431no—
406#3428—431no—
407#2898—433no—
408#2898—433no—
409#2898—433no—
410#2898—433no—
411#2898—431no—
412#2898—431no—
413#2898—431no—
414#2898D4311yescharacteristic, complemented
415#2896—433no—
416#2896—433no—
417C2×#419—433no—
418C2×#419—433no—
419C2×C43—26no—
420C2×C43—42no—
421C2×C43C23×C22⋊C411yescharacteristic
422C2×C43#358611yescharacteristic
423C2×C43#358611yescharacteristic
424D43—22no—
425D43—26no—
426D43—42no—
427C2×2−1+4—4316no—
428C2×2−1+4—433no—
429C2×2−1+4—431no—
430C2×2−1+4—433no—
431C2×2−1+4—861no—
432C2×2−1+4—863no—
433C2×2−1+4—868no—
434C2×2−1+4C2×D4311yescharacteristic
435C22×#41—431no—
436C22×#41—433no—
437C22×#41—863no—
438C23×Q8—433no—
439C23×Q8—861no—
440#568—868no—
441C2×#131—431no—
442C2×#131—433no—
443C2×#131—433no—
444C2×#131C2×D4311yescharacteristic, complemented
445C22×M16—433no—
446C22×M16—433no—
447#520—431no—
448#520—433no—
449#520—433no—
450#520C2×D4311yescharacteristic, complemented
451#519—861no—
452#518—863no—
453C4×#41—863no—
454C4×#41—861no—
455C2×#117—433no—
456C2×#117—433no—
457#419—433no—
458#419—433no—
459#419—433no—
460#419—433no—
461#419—436no—
462#419—433no—
463#419—436no—
464#419—436no—
465#419C2×D4313yescomplemented
466#418—433no—
467#418—431no—
468#417—433no—
469#417—433no—
470#417—433no—
471#417—433no—
472#417—433no—
473#417—433no—
474#417—433no—
475#417C2×D4313yescomplemented
476#416—433no—
477#416—433no—
478#416—433no—
479#416—436no—
480#416—436no—
481#416C2×D4313yescomplemented
482C2×#103—433no—
483C2×#103—433no—
484C2×#103—433no—
485C2×#103—436no—
486C2×#103—436no—
487C2×#103C2×D4313yescomplemented
488C43#6008811yescharacteristic, complemented, Sylow
4892−1+4—24no—
4902−1+4—4324no—
4912−1+4—438no—
4922−1+4—4324no—
4932−1+4—8616no—
4942−1+4—8612no—
4952−1+4—8648no—
4962−1+4—8612no—
4972−1+4—864no—
4982−1+4C4×D4318yescomplemented
499C2×#41—23no—
500C2×#41—438no—
501C2×#41—438no—
502C2×#41—431no—
503C2×#41—433no—
504C2×#41—433no—
505C2×#41—4324no—
506C2×#41—433no—
507C2×#41—433no—
508C2×#41—433no—
509C2×#41—863no—
510C2×#41—866no—
511C2×#41—863no—
512C2×#41—863no—
513C2×#41—8612no—
514C2×#41—866no—
515C2×#41—863no—
516C2×#41—8648no—
517C2×#41—863no—
518C2×#41C22×D4313yes—
519C2×#41C22×D4311yescharacteristic
520C22×Q8—21no—
521C22×Q8—431no—
522C22×Q8—4324no—
523C22×Q8—433no—
524C22×Q8—436no—
525C22×Q8—433no—
526C22×Q8—863no—
527C22×Q8—863no—
528C22×Q8—863no—
529C22×Q8—863no—
530C22×Q8—8612no—
531C22×Q8—8616no—
532C22×Q8—863no—
533C22×Q8—861no—
534C22×Q8C22×D4313yes—
535C22×D4—433no—
536C22×D4—431no—
537C22×D4—863no—
538C23×C4—433no—
539C23×C4—863no—
540C23×C4—863no—
541#131—24no—
542#131—8612no—
543#131—8612no—
544#131—864no—
545C2×M16—433no—
546C2×M16—433no—
547C2×M16—431no—
548C2×M16—433no—
549C2×M16—433no—
550C2×M16—8612no—
551C2×M16—8612no—
552C2×M16C22×D4313yes—
553C22×C8—433no—
554C22×C8—436no—
555C22×C8C22×D4313yes—
556C4×Q8—21no—
557C4×Q8—863no—
558C4×Q8—863no—
559C4×Q8—861no—
560C4×D4—23no—
561C4×D4—863no—
562C4×D4—866no—
563C4×D4—863no—
564C4×D4—866no—
565C4×D4—863no—
566#117—433no—
567#117—431no—
568#117—433no—
569#117—436no—
570#117—863no—
571#117—863no—
572#117—863no—
573#117—863no—
574#117C22×D4313yes—
575C2×C4⋊C4—433no—
576C2×C4⋊C4—433no—
577C2×C4⋊C4—433no—
578C2×C4⋊C4C22×D4313yes—
579C2×C22⋊C4—863no—
580C2×C22⋊C4—863no—
581C2×C42—863no—
582C2×C42—863no—
583#103—433no—
584#103—436no—
585#103—433no—
586#103—433no—
587#103—436no—
588#103—433no—
589#103—433no—
590#103—436no—
591#103—433no—
592#103C22×D4313yes—
593#103C22×D4316yes—
594#103C22×D4313yes—
595#102—433no—
596#102—431no—
597#102—433no—
598#102—431no—
599#102—431no—
600#102—433no—
601#102C22×D4313yes—
602#102C22×D4311yescharacteristic
603C24—433no—
604C24—861no—
605#41—224no—
606#41—26no—
607#41—438no—
608#41—4324no—
609#41—4312no—
610#41—4312no—
611#41—4312no—
612#41—4312no—
613#41—4312no—
614#41—8624no—
615#41—8648no—
616#41—8624no—
617#41—8624no—
618#41—866no—
619#41—866no—
620#41—8648no—
621#41—8624no—
622#41—8624no—
623#41—866no—
624#41C2×C4×D43112yes—
625#41C2×C4×D4314yes—
626#41D4×D4314yes—
627C2×Q8—28no—
628C2×Q8—23no—
629C2×Q8—26no—
630C2×Q8—438no—
631C2×Q8—433no—
632C2×Q8—4312no—
633C2×Q8—4324no—
634C2×Q8—4312no—
635C2×Q8—433no—
636C2×Q8—863no—
637C2×Q8—866no—
638C2×Q8—8624no—
639C2×Q8—8624no—
640C2×Q8—8624no—
641C2×Q8—866no—
642C2×Q8—8624no—
643C2×Q8—8612no—
644C2×Q8—8624no—
645C2×Q8—868no—
646C2×Q8—863no—
647C2×Q8—866no—
648C2×Q8C2×C4×D43112yes—
649C2×Q8D4×D4311yescharacteristic
650C2×Q8C23×D4313yes—
651C2×D4—23no—
652C2×D4—436no—
653C2×D4—4324no—
654C2×D4—434no—
655C2×D4—433no—
656C2×D4—431no—
657C2×D4—863no—
658C2×D4—862no—
659C2×D4—861no—
660C2×D4—8624no—
661C2×D4—863no—
662C2×D4—863no—
663C2×D4D4×D4313yes—
664C2×D4C23×D4311yescharacteristic
665C22×C4—23no—
666C22×C4—23no—
667C22×C4—23no—
668C22×C4—433no—
669C22×C4—4312no—
670C22×C4—433no—
671C22×C4—433no—
672C22×C4—4312no—
673C22×C4—433no—
674C22×C4—431no—
675C22×C4—863no—
676C22×C4—8624no—
677C22×C4—863no—
678C22×C4—8624no—
679C22×C4—866no—
680C22×C4—863no—
681C22×C4—863no—
682C22×C4—863no—
683C22×C4—863no—
684C22×C4—863no—
685C22×C4—863no—
686C22×C4C23×D4313yes—
687M16—26no—
688M16—862no—
689M16—866no—
690M16—866no—
691M16—866no—
692M16—866no—
693C2×C8—26no—
694C2×C8—431no—
695C2×C8—433no—
696C2×C8—8612no—
697C2×C8—866no—
698C2×C8C23×D4313yes—
699C2×C8C23×D4311yescharacteristic
700C4⋊C4—23no—
701C4⋊C4—433no—
702C4⋊C4—431no—
703C4⋊C4—863no—
704C4⋊C4—863no—
705C4⋊C4—863no—
706C4⋊C4C23×D4311yescharacteristic
707C4⋊C4C23×D4313yes—
708C22⋊C4—23no—
709C22⋊C4—861no—
710C22⋊C4—863no—
711C22⋊C4—866no—
712C22⋊C4—863no—
713C42—23no—
714C42—861no—
715C42—863no—
716C42—866no—
717C42—863no—
718C23—21no—
719C23—431no—
720C23—433no—
721C23—4312no—
722C23—864no—
723C23—861no—
724C23—1723no—
725C23—1723no—
726C23—1722no—
727C23—1722no—
728C23C2×D4×D4313yes—
729Q8—212no—
730Q8—23no—
731Q8—4312no—
732Q8—436no—
733Q8—8612no—
734Q8—8624no—
735Q8—8612no—
736Q8—863no—
737Q8C22⋊C4×D4314yes—
738Q8C22×C4×D4316yes—
739D4—212no—
740D4—21no—
741D4—4324no—
742D4—4312no—
743D4—432no—
744D4—8612no—
745D4—864no—
746D4—8612no—
747D4—8612no—
748D4—861no—
749D4C22⋊C4×D43112yes—
750D4C22×C4×D4312yes—
751C2×C4—212no—
752C2×C4—23no—
753C2×C4—212no—
754C2×C4—21no—
755C2×C4—23no—
756C2×C4—83no—
757C2×C4—4312no—
758C2×C4—431no—
759C2×C4—433no—
760C2×C4—4312no—
761C2×C4—4312no—
762C2×C4—432no—
763C2×C4—436no—
764C2×C4—436no—
765C2×C4—432no—
766C2×C4—8612no—
767C2×C4—8612no—
768C2×C4—8624no—
769C2×C4—8612no—
770C2×C4—8612no—
771C2×C4—863no—
772C2×C4—8612no—
773C2×C4—861no—
774C2×C4—863no—
775C2×C4—3443no—
776C2×C4—3443no—
777C2×C4—3443no—
778C2×C4C22×C4×D4316yes—
779C2×C4C2×D4×D4313yes—
780C2×C4C2×D4×D4316yes—
781C2×C4C24×D4311yescharacteristic
782C8—21no—
783C8—23no—
784C8—863no—
785C8—861no—
786C22—23no—
787C22—23no—
788C22—22no—
789C22—41no—
790C22—41no—
791C22—432no—
792C22—436no—
793C22—863no—
794C22—861no—
795C22—863no—
796C22—861no—
797C22—862no—
798C22—17212no—
799C22—1728no—
800C22—1721no—
801C22—1721no—
802C22C2×C22⋊C4×D4316yes—
803C22C22×D4×D4311yescharacteristic
804C4—26no—
805C4—43no—
806C4—41no—
807C4—432no—
808C4—436no—
809C4—866no—
810C4—1721no—
811C4—1723no—
812C4C2×C22⋊C4×D4316yes—
813C4C23×C4×D4311yescharacteristic
814C4C22×D4×D4311yescharacteristic
815C2—26no—
816C2—42no—
817C2—862no—
818C2—866no—
819C2—1722no—
820C2C22×C22⋊C4×D4311yescharacteristic
821C2#1914937711yescharacteristic
822C2#1914938011yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutatorC4×C43C24×C4
FrattiniC2×C4C24×D43
FittingC43×#2898C2
socleC22×C43C23×D4
prime radicalC2×2−1+4×D43C2
cosocleC2×C4×C43C25
hypercenter#2898D43
hypocenterC43#60088
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×#41 ◁ #2898

Complements

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

NH ≅ G/Ntype
2. C2×#14583664C2semidirect
3. #19147795C2semidirect
4. #19143129C2semidirect
5. #19143128C2semidirect
6. #19143127C2semidirect
7. #19143126C2semidirect
8. #19143125C2semidirect
9. #19143124C2semidirect
10. #19143123C2semidirect
11. #19143111C2semidirect
12. #19143110C2semidirect
13. C2×#14582906C2semidirect
14. #419×D43C2semidirect
15. C43×#2898C2semidirect
22. 2−1+4×D43C4semidirect
29. C2×#13063333C22semidirect
30. C2×#13063332C22semidirect
31. C2×#13063331C22semidirect
34. #14583382C22semidirect
35. #14583380C22semidirect
36. #14583379C22semidirect
43. #14582909C22semidirect
44. #14582908C22semidirect
45. #14582907C22semidirect
49. #14582906C22semidirect
50. #14582906C22semidirect
53. #14582901C22semidirect
54. #14582900C22semidirect
55. #14582899C22semidirect
56. #14582899C22semidirect
57. #14582898C22semidirect
58. #14582897C22semidirect
59. #14582897C22semidirect
60. #14582896C22semidirect
61. #14582895C22semidirect
62. #14582894C22semidirect
63. #14582893C22semidirect
64. #14582892C22semidirect
65. C2×#13063250C22semidirect
66. C2×#13063249C22semidirect
67. C2×#13063248C22semidirect
68. #103×D43C22semidirect
69. #103×D43C22semidirect
71. C2×#131×C43C22semidirect
72. C43×#520C22semidirect
73. C43×#419C22semidirect
74. C43×#417C22semidirect
75. C43×#416C22semidirect
76. C2×#103×C43C22semidirect
79. #13063373C2×C4semidirect
83. #13063372C2×C4semidirect
84. #13063372C2×C4semidirect
101. #41×D43C2×C4semidirect
112. C2×Q8×D43C2×C4semidirect
173. 2−1+4×C43C2×C4semidirect
414. #2898D43semidirect
444. C2×#131C2×D43semidirect
450. #520C2×D43semidirect
465. #419C2×D43semidirect
475. #417C2×D43semidirect
481. #416C2×D43semidirect
487. C2×#103C2×D43semidirect
488. C43#60088semidirect
498. 2−1+4C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×2−1+4×D432
C2×#145836642
#191477952
#191431292
#191431282
#191431272
#191431262
#191431252
#191431242
#191431232
#191431112
#191431102
C2×#145829062
#419×D432
C43×#28982
#6008843