Finite Group Databasebeta

← #25964292

Subgroups — #25964292

Order 11008.

2006 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148411C211yesmaximal, characteristic, complemented
2C4×#13063373C211yesmaximal, characteristic
3#19144451C212yesmaximal, complemented
4#19144443C214yesmaximal, complemented
5#19144433C212yesmaximal, complemented
6#19144432C214yesmaximal, complemented
7#19144409C212yesmaximal, complemented
8#19144404C211yesmaximal, characteristic, complemented
9#19144401C212yesmaximal, complemented
10#19144400C211yesmaximal, characteristic, complemented
11#19144386C212yesmaximal, complemented
12#19144385C211yesmaximal, characteristic, complemented
13#477×D43C212yesmaximal, complemented
14#19143191C212yesmaximal, complemented
15#19143160C211yesmaximal, characteristic, complemented
16#19143123C212yesmaximal
17C2×C43×#477C211yesmaximal, characteristic, complemented
18C2×#13063373C2211yescharacteristic
19C2×#13063331C2212yes—
20#14583629—21no—
21#14583624—21no—
22#14583610—21no—
23#14583604—22no—
24#14583564—21no—
25Q8×C22⋊D43—22no—
26#14583530C2212yes—
27#14583526C2214yes—
28#14583456C2211yescharacteristic
29#14583454C2212yes—
30C4⋊Q8×D43C2212yes—
31#14583381—21no—
32#14583381C2212yes—
33#14583380—22no—
34#14583380C2211yescharacteristic
35#14583380C2211yescharacteristic
36#14583380C2212yes—
37#14583377C2211yescharacteristic
38#14583375—21no—
39#14583375C2212yes—
40C4×#10621902—21no—
41C4×#10621902C2212yes—
42C4×#10621898—22no—
43C4×#10621898C2211yescharacteristic
44C4×#10621898C2211yescharacteristic
45C4×Q8×D43—21no—
46C4×Q8×D43C2212yes—
47#14583208C2214yes—
48#14583207C2212yes—
49#14583206C2214yes—
50#14583205C2214yes—
51#14583204C2214yes—
52#14583202C2214yes—
53#14583200C2212yes—
54#14583195C2211yescharacteristic
55#14583194C2212yes—
56#14583193C2214yes—
57#14583192C2214yes—
58#14583191C2212yes—
59#14583190C2211yescharacteristic
60#14583186C2212yes—
61#14583185C2211yescharacteristic
62#14583184C2212yes—
63#14583182C2214yes—
64#14583181C2212yes—
65#14583180C2211yescharacteristic
66#14583178C2214yes—
67#14583176C2212yes—
68#14582940C2214yes—
69#14582940C2214yes—
70#14582939C2212yes—
71#14582939C2212yes—
72#14582937C2212yes—
73#14582936C2214yes—
74#107×D43C2214yes—
75#14582925C2212yes—
76#14582924C2214yes—
77#14582923C2211yescharacteristic
78#14582921C2212yes—
79C4⋊C8×D43C2212yes—
80#14582908C2212yes—
81#14582906C2214yes—
82#14582899C2214yes—
83#14582898C2212yes—
84#14582896C2212yes—
85#14582894C2214yes—
86#103×D43C2214yes—
87C2×C4⋊Q8×C43C2211yescharacteristic
88C2×C4×Q8×C43C2211yescharacteristic
89C43×#477C2212yes—
90C43×#477C2212yes—
91C43×#477C2214yes—
92C2×#107×C43C2212yes—
93C2×C4⋊C8×C43C2211yescharacteristic
94C2×#103×C43C2212yes—
95#13063373—24no—
96#13063373Q818yescomplemented
97C2×#10621902—21no—
98C2×#10621902C2312yes—
99C2×#10621898—22no—
100C2×#10621898C2311yescharacteristic
101C2×#10621898C2311yescharacteristic
102C2×Q8×D43—22no—
103C2×Q8×D43—21no—
104C2×Q8×D43C2312yes—
105#13063331—28no—
106C2×#10621877C2312yes—
107C2×#10621872C2314yes—
108C2×C8×D43C2314yes—
109#13063325C2311yescharacteristic
110#13063325C2311yescharacteristic
111#13063324—22no—
112#13063324—22no—
113#13063324C2314yes—
114#13063323—24no—
115#13063323—22no—
116#13063317C2312yes—
117#13063316—22no—
118#13063316C2314yes—
119#13063315—24no—
120#13063305—22no—
121#13063304—21no—
122#13063304—21no—
123#13063304—24no—
124#13063303—24no—
125#13063301—22no—
126#13063301—24no—
127Q8×Dic43—21no—
128Q8×Dic43—21no—
129Q8×Dic43—22no—
130Q8×Dic43C2312yes—
131Q8×Dic43C2312yes—
132C4×Dic86—21no—
133C4×Dic86—21no—
134C4×Dic86—22no—
135C4×Dic86—22no—
136C4×Dic86D411yescharacteristic
137C4×Dic86D411yescharacteristic
138C4×Dic86C2311yescharacteristic
139C4×Dic86C2311yescharacteristic
140#13063290—21no—
141#13063290—22no—
142#13063290—22no—
143#13063290—22no—
144#13063290—22no—
145#13063290C2312yes—
146C4×D172—22no—
147C4×D172—22no—
148C4×D172D411yescharacteristic
149C4×D172D411yescharacteristic
150C4×D172C2311yescharacteristic
151C4×D172C2311yescharacteristic
152#13063287—22no—
153#13063287—21no—
154#13063287—22no—
155#13063287—22no—
156#13063287C2312yes—
157C4×C22⋊D43—21no—
158C4×C22⋊D43—21no—
159C4×C22⋊D43—24no—
160C4×C22⋊D43—22no—
161C4×C22⋊D43—22no—
162C4×C22⋊D43D412yes—
163C4×C22⋊D43D412yes—
164#13063284—22no—
165#13063284C2311yescharacteristic
166#13063284C2312yes—
167#13063284C2311yescharacteristic
168#13063283—22no—
169#13063283—21no—
170#13063283—22no—
171#13063283C2312yes—
172#13063283C2314yes—
173#13063282—21no—
174#13063282—22no—
175#13063282—22no—
176#13063282C2312yes—
177C4⋊C4×D43—22no—
178C4⋊C4×D43—22no—
179C4⋊C4×D43—21no—
180C4⋊C4×D43—22no—
181C4⋊C4×D43C2312yes—
182C4⋊C4×D43C2314yes—
183C42×D43—22no—
184C42×D43—21no—
185C42×D43—22no—
186C42×D43C2312yes—
187#13063259C2312yes—
188#13063259C2312yes—
189#13063258C2314yes—
190#13063258C2314yes—
191#13063257C2312yes—
192#13063257C2312yes—
193#13063256C2314yes—
194#13063256C2314yes—
195C4⋊(C43⋊C8)C2312yes—
196C4⋊(C43⋊C8)C2312yes—
197Dic43⋊C8C2314yes—
198Dic43⋊C8C2314yes—
199#13063250C2312yes—
200#13063250C2312yes—
201#13063249C2314yes—
202#13063249C2314yes—
203#13063248C2314yes—
204#13063247C2312yes—
205#13063247C2312yes—
206#13063245C2314yes—
207C22×Q8×C43—21no—
208C22×Q8×C43C2311yescharacteristic
209C22×C8×C43C2312yes—
210C4⋊Q8×C43—21no—
211C4⋊Q8×C43—21no—
212C4⋊Q8×C43C2312yes—
213C4⋊Q8×C43C2312yes—
214C4×Q8×C43—21no—
215C4×Q8×C43—21no—
216C4×Q8×C43C2312yes—
217C4×Q8×C43C2312yes—
218C2×C4⋊C4×C43—21no—
219C2×C4⋊C4×C43—21no—
220C2×C4⋊C4×C43C2311yescharacteristic
221C2×C4⋊C4×C43C2312yes—
222C2×C42×C43—21no—
223C2×C42×C43C2311yescharacteristic
224#107×C43C2314yes—
225#107×C43C2314yes—
226C4⋊C8×C43C2311yescharacteristic
227C4⋊C8×C43C2311yescharacteristic
228C4⋊C8×C43C2312yes—
229#103×C43C2314yes—
230#103×C43C2314yes—
231C2×Q8×C43—21no—
232C2×Q8×C43—22no—
233C2×Q8×C43—22no—
234C2×Q8×C43—22no—
235C2×Q8×C43—82no—
236C2×Q8×C43C2×Q814yescomplemented
237C2×Q8×C43C2412yes—
238C22×C4×C43—21no—
239C22×C4×C43—21no—
240C22×C4×C43—22no—
241C22×C4×C43C2×D411yescharacteristic
242C22×C4×C43C2×D411yescharacteristic
243C22×C4×C43C2411yescharacteristic
244C2×C22⋊D43—21no—
245C2×C22⋊D43C2×D412yes—
246#10621902—28no—
247#10621902—24no—
248#10621902C2×Q818yescomplemented
249Q8×D43—24no—
250Q8×D43—28no—
251Q8×D43—84no—
252Q8×D43C2×Q818yescomplemented
253#10621898—22no—
254#10621898—216no—
255#10621898C2×Q814yes—
256#10621898C2×Q814yescomplemented
257#10621898#4114yes—
258C2×D172—22no—
259C2×D172C2×D411yescharacteristic
260C2×D172C2411yescharacteristic
261C2×C4×D43—21no—
262C2×C4×D43—22no—
263C2×C4×D43—21no—
264C2×C4×D43—21no—
265C2×C4×D43—22no—
266C2×C4×D43—22no—
267C2×C4×D43—22no—
268C2×C4×D43—24no—
269C2×C4×D43C2×D412yes—
270C2×C4×D43C2×D412yes—
271C2×C4×D43C2412yes—
272C2×Dic86—22no—
273C2×Dic86—21no—
274C2×Dic86—21no—
275C2×Dic86—24no—
276C2×Dic86C2×D411yescharacteristic
277C2×Dic86C2411yescharacteristic
278C2×C8×C43—24no—
279C2×C8×C43C2412yes—
280C2×C8×C43C2412yes—
281C4⋊C4×C43—22no—
282C4⋊C4×C43—22no—
283C4⋊C4×C43—22no—
284C4⋊C4×C43—22no—
285C4⋊C4×C43—21no—
286C4⋊C4×C43—22no—
287C4⋊C4×C43C2414yes—
288C4⋊C4×C43C2412yes—
289C42×C43—22no—
290C42×C43—22no—
291C42×C43C2×D411yescharacteristic
292C42×C43C2×D411yescharacteristic
293C42×C43C2411yescharacteristic
294C42×C43C2411yescharacteristic
295C22⋊Dic43—21no—
296C22⋊Dic43—22no—
297C22⋊Dic43C2×D412yes—
298(C2×D43)⋊C4—21no—
299(C2×D43)⋊C4—21no—
300(C2×D43)⋊C4—22no—
301(C2×D43)⋊C4—22no—
302(C2×D43)⋊C4—24no—
303(C2×D43)⋊C4C2×D412yes—
304(C2×D43)⋊C4C2×D412yes—
305C4⋊Dic43—21no—
306C4⋊Dic43—21no—
307C4⋊Dic43—22no—
308C4⋊Dic43—22no—
309C4⋊Dic43—24no—
310C4⋊Dic43C2×D411yescharacteristic
311C4⋊Dic43C2×D411yescharacteristic
312C4⋊Dic43C2412yes—
313C4⋊Dic43C2412yes—
314C4⋊Dic43C2411yescharacteristic
315C4⋊Dic43C2411yescharacteristic
316Dic43⋊C4—21no—
317Dic43⋊C4—21no—
318Dic43⋊C4—22no—
319Dic43⋊C4—22no—
320Dic43⋊C4—22no—
321Dic43⋊C4—22no—
322Dic43⋊C4—24no—
323Dic43⋊C4—24no—
324Dic43⋊C4—24no—
325Dic43⋊C4C2×D412yes—
326Dic43⋊C4C2×D412yes—
327C4×Dic43—21no—
328C4×Dic43—21no—
329C4×Dic43—21no—
330C4×Dic43—22no—
331C4×Dic43—22no—
332C4×Dic43—22no—
333C4×Dic43—22no—
334C4×Dic43—22no—
335C4×Dic43—24no—
336C4×Dic43C2×D412yes—
337C4×Dic43C2×D412yes—
338C4×Dic43C2412yes—
339#10621877—24no—
340C2×C43⋊C8C2414yes—
341#10621872—28no—
342C8×D43—28no—
343C23×C43C22×D411yescharacteristic
344C22×D43—21no—
345C22×D43C22×D412yes—
346Q8×C43—24no—
347Q8×C43—22no—
348Q8×C43—44no—
349Q8×C43—82no—
350Q8×C43C22×Q814yes—
351C2×C4×C43—24no—
352C2×C4×C43—22no—
353C2×C4×C43—22no—
354C2×C4×C43—22no—
355C2×C4×C43—24no—
356C2×C4×C43—41no—
357C2×C4×C43—81no—
358C2×C4×C43—82no—
359C2×C4×C43C22×D411yescharacteristic
360C2×C4×C43C22×D411yescharacteristic
361C2×C4×C43C22×D411yescharacteristic
362C2×C4×C43C22×D411yescharacteristic
363C2×C4×C43C22×D411yescharacteristic
364C2×C4×C43C22×Q812yes—
365C2×C4×C43C2×#4112yes—
366C2×C4×C43C2511yescharacteristic
367C22⋊D43—24no—
368C22⋊D43C22⋊Q818yes—
369C2×Dic43—21no—
370C2×Dic43—21no—
371C2×Dic43—21no—
372C2×Dic43—22no—
373C2×Dic43—22no—
374C2×Dic43C22×D412yes—
375C2×Dic43C22×D412yes—
376C2×Dic43C22×D412yes—
377D172—28no—
378D172—21no—
379D172C22⋊Q814yes—
380D172C22×Q812yes—
381C4×D43—28no—
382C4×D43—24no—
383C4×D43—24no—
384C4×D43—28no—
385C4×D43—42no—
386C4×D43—42no—
387C4×D43—82no—
388C4×D43—81no—
389C4×D43—82no—
390C4×D43—84no—
391C4×D43C22×Q814yes—
392C4×D43C2×#4114yes—
393Dic86—21no—
394Dic86—28no—
395Dic86—42no—
396Dic86—42no—
397Dic86—84no—
398Dic86C22⋊Q814yes—
399Dic86C22×Q812yes—
400C8×C43—22no—
401C8×C43—22no—
402C43⋊C8—24no—
403#60498—431nomaximal, Sylow
404C22×C43—21no—
405C22×C43—21no—
406C22×C43C2×C22⋊Q812yes—
407C22×C43C23×D411yescharacteristic
408C2×D43—22no—
409C2×D43—22no—
410C2×D43—22no—
411C2×D43—41no—
412C2×D43—41no—
413C2×D43C2×C22⋊Q814yes—
414C4×C43—21no—
415C4×C43—21no—
416C4×C43—24no—
417C4×C43—21no—
418C4×C43—44no—
419C4×C43—42no—
420C4×C43C2×C22⋊Q812yes—
421C4×C43#57812yes—
422C4×C43C23×Q811yescharacteristic
423C4×C43C22×#4111yescharacteristic
424Dic43—22no—
425Dic43—22no—
426Dic43—22no—
427Dic43—42no—
428Dic43—41no—
429Dic43—42no—
430Dic43—41no—
431Dic43C2×C22⋊Q814yes—
432#3503—431no—
433C4×2−1+4—431no—
434#3083—434no—
435#3083—432no—
436#3082—434no—
437#3082—432no—
438#3079—432no—
439#3079—431no—
440#3078—432no—
441#3078—431no—
442#3076—432no—
443#3076—431no—
444C2×#477—432no—
445C2×#477D4311yescharacteristic, complemented
446#2913—432no—
447#2906—431no—
448#2898—432no—
449C2×C43—22no—
450C2×C43C22×C22⋊Q811yescharacteristic
451C2×C43C2×#57811yescharacteristic
452C2×C43#358511yescharacteristic
453D43—24no—
454D43—42no—
455C2×2−1+4—431no—
456C2×#131—432no—
457Q82—861no—
458#557—861no—
459#554—862no—
460#554—861no—
461D4×Q8—861no—
462D4×Q8—862no—
463#544—434no—
464#544—432no—
465#533—432no—
466#533—431no—
467C2×C4⋊Q8—432no—
468C2×C4⋊Q8C2×D4311yescharacteristic
469#520—432no—
470#520—431no—
471#520—432no—
472#520—431no—
473#520—862no—
474#520—861no—
475#519—431no—
476#519—432no—
477#519—861no—
478C4×#41—431no—
479C4×#41—432no—
480C4×#41—431no—
481C4×#41—862no—
482C4×#41—861no—
483C2×C4×Q8—432no—
484C2×C4×Q8—861no—
485C2×C4×Q8C2×D4311yescharacteristic
486#479—434no—
487#479—434no—
488#479—432no—
489#479—434no—
490#479—434no—
491#478—434no—
492#478—432no—
493#477—432no—
494#477—432no—
495#477—434no—
496#477—431no—
497#477—434no—
498#477C2×D4312yes—
499#477C2×D4312yes—
500#477C2×D4314yes—
501#476—432no—
502#476—431no—
503#475—432no—
504#475—432no—
505#475—431no—
506#475—434no—
507#474—432no—
508#474—434no—
509#474—431no—
510#428—432no—
511#428—432no—
512#428—434no—
513#428—434no—
514#427—432no—
515#427—434no—
516C2×#107—434no—
517C2×#107C2×D4312yes—
518#424—432no—
519#424—434no—
520#423—431no—
521#423—432no—
522C2×C4⋊C8—432no—
523C2×C4⋊C8C2×D4311yescharacteristic
524#419—432no—
525#419—434no—
526#417—432no—
527#417—434no—
528#416—432no—
529#416—434no—
530C2×#103—434no—
531C2×#103C2×D4312yes—
532C43#6049811yescharacteristic, complemented, Sylow
5332−1+4—438no—
5342−1+4—864no—
535C2×#41—431no—
536C2×#41—432no—
537C2×#41—431no—
538C2×#41—862no—
539C2×#41—861no—
540C22×Q8—21no—
541C22×Q8—432no—
542C22×Q8—862no—
543C22×Q8—861no—
544C22×Q8C22×D4311yescharacteristic
545#131—868no—
546C2×M16—432no—
547C2×M16—434no—
548C22×C8—434no—
549C22×C8C22×D4312yes—
550C4⋊Q8—21no—
551C4⋊Q8—21no—
552C4⋊Q8—434no—
553C4⋊Q8—431no—
554C4⋊Q8—431no—
555C4⋊Q8—862no—
556C4⋊Q8—862no—
557C4⋊Q8—862no—
558C4⋊Q8—864no—
559C4⋊Q8C22×D4312yes—
560C4⋊Q8C22×D4312yes—
561#125—434no—
562#125—432no—
563#125—864no—
564#125—862no—
565C22⋊Q8—864no—
566C22⋊Q8—864no—
567C22⋊Q8—864no—
568C22⋊Q8—862no—
569C22⋊Q8—862no—
570C22⋊Q8—861no—
571C22⋊Q8—861no—
572C4×Q8—21no—
573C4×Q8—21no—
574C4×Q8—431no—
575C4×Q8—431no—
576C4×Q8—432no—
577C4×Q8—432no—
578C4×Q8—432no—
579C4×Q8—431no—
580C4×Q8—431no—
581C4×Q8—862no—
582C4×Q8—862no—
583C4×Q8—862no—
584C4×Q8—862no—
585C4×Q8—862no—
586C4×Q8—862no—
587C4×Q8—861no—
588C4×Q8—862no—
589C4×Q8—861no—
590C4×Q8—861no—
591C4×Q8—861no—
592C4×Q8—861no—
593C4×Q8C22×D4312yes—
594C4×Q8C22×D4312yes—
595C4×D4—432no—
596C4×D4—432no—
597C4×D4—432no—
598C4×D4—431no—
599C4×D4—431no—
600C4×D4—431no—
601C4×D4—431no—
602C4×D4—862no—
603C4×D4—862no—
604C4×D4—862no—
605C4×D4—862no—
606C4×D4—862no—
607C4×D4—861no—
608C4×D4—862no—
609C4×D4—862no—
610C4×D4—864no—
611C4×D4—861no—
612C4×D4—861no—
613#117—431no—
614#117—432no—
615#117—431no—
616#117—432no—
617#117—432no—
618#117—434no—
619#117—862no—
620#117—862no—
621#117—862no—
622#117—862no—
623#117—862no—
624#117—861no—
625#117—861no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—432no—
629C2×C4⋊C4—434no—
630C2×C4⋊C4—862no—
631C2×C4⋊C4—861no—
632C2×C4⋊C4—862no—
633C2×C4⋊C4—862no—
634C2×C4⋊C4C22×D4311yescharacteristic
635C2×C4⋊C4C22×D4312yes—
636C2×C42—21no—
637C2×C42—432no—
638C2×C42—862no—
639C2×C42—862no—
640C2×C42—861no—
641C2×C42C22×D4311yescharacteristic
642#107—432no—
643#107—432no—
644#107—434no—
645#107—434no—
646#107C22×D4314yes—
647#107C22×D4314yes—
648#106—432no—
649#106—432no—
650#106—434no—
651#106—434no—
652C4⋊C8—434no—
653C4⋊C8—434no—
654C4⋊C8—432no—
655C4⋊C8—432no—
656C4⋊C8C22×D4311yescharacteristic
657C4⋊C8C22×D4311yescharacteristic
658C4⋊C8C22×D4312yes—
659#103—434no—
660#103—434no—
661#103—432no—
662#103—432no—
663#103—434no—
664#103C22×D4314yes—
665#103C22×D4314yes—
666#102—432no—
667#102—432no—
668#102—434no—
669#41—434no—
670#41—434no—
671#41—438no—
672#41—434no—
673#41—8616no—
674#41—864no—
675#41—868no—
676#41—862no—
677C2×Q8—21no—
678C2×Q8—22no—
679C2×Q8—22no—
680C2×Q8—22no—
681C2×Q8—82no—
682C2×Q8—431no—
683C2×Q8—438no—
684C2×Q8—431no—
685C2×Q8—862no—
686C2×Q8—864no—
687C2×Q8—864no—
688C2×Q8—868no—
689C2×Q8—861no—
690C2×Q8—861no—
691C2×Q8—3444no—
692C2×Q8Q8×D4314yescomplemented
693C2×Q8C23×D4312yes—
694C2×D4—432no—
695C2×D4—431no—
696C2×D4—431no—
697C2×D4—862no—
698C2×D4—861no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—22no—
702C22×C4—432no—
703C22×C4—432no—
704C22×C4—432no—
705C22×C4—862no—
706C22×C4—862no—
707C22×C4—862no—
708C22×C4—862no—
709C22×C4—864no—
710C22×C4—861no—
711C22×C4—861no—
712C22×C4—861no—
713C22×C4D4×D4311yescharacteristic
714C22×C4D4×D4311yescharacteristic
715C22×C4C23×D4311yescharacteristic
716M16—868no—
717M16—864no—
718C2×C8—24no—
719C2×C8—434no—
720C2×C8—868no—
721C2×C8C23×D4312yes—
722C2×C8C23×D4312yes—
723C4⋊C4—22no—
724C4⋊C4—22no—
725C4⋊C4—22no—
726C4⋊C4—22no—
727C4⋊C4—21no—
728C4⋊C4—22no—
729C4⋊C4—432no—
730C4⋊C4—431no—
731C4⋊C4—432no—
732C4⋊C4—431no—
733C4⋊C4—432no—
734C4⋊C4—432no—
735C4⋊C4—431no—
736C4⋊C4—431no—
737C4⋊C4—862no—
738C4⋊C4—864no—
739C4⋊C4—862no—
740C4⋊C4—862no—
741C4⋊C4—864no—
742C4⋊C4—862no—
743C4⋊C4—864no—
744C4⋊C4—864no—
745C4⋊C4—861no—
746C4⋊C4—861no—
747C4⋊C4—861no—
748C4⋊C4—861no—
749C4⋊C4—862no—
750C4⋊C4—862no—
751C4⋊C4C23×D4314yes—
752C4⋊C4C23×D4312yes—
753C22⋊C4—432no—
754C22⋊C4—432no—
755C22⋊C4—432no—
756C22⋊C4—862no—
757C22⋊C4—862no—
758C22⋊C4—864no—
759C22⋊C4—861no—
760C22⋊C4—862no—
761C22⋊C4—861no—
762C22⋊C4—861no—
763C42—22no—
764C42—22no—
765C42—432no—
766C42—432no—
767C42—432no—
768C42—862no—
769C42—862no—
770C42—862no—
771C42—862no—
772C42—864no—
773C42—861no—
774C42—861no—
775C42—861no—
776C42—862no—
777C42D4×D4311yescharacteristic
778C42D4×D4311yescharacteristic
779C42C23×D4311yescharacteristic
780C42C23×D4311yescharacteristic
781C23—432no—
782C23—861no—
783C23C2×D4×D4311yescharacteristic
784Q8—24no—
785Q8—22no—
786Q8—44no—
787Q8—82no—
788Q8—434no—
789Q8—432no—
790Q8—868no—
791Q8—861no—
792Q8—3444no—
793Q8—1722no—
794Q8—1722no—
795Q8C2×Q8×D4314yes—
796D4—438no—
797D4—434no—
798D4—432no—
799D4—868no—
800D4—864no—
801D4—861no—
802C2×C4—24no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—24no—
807C2×C4—41no—
808C2×C4—82no—
809C2×C4—81no—
810C2×C4—432no—
811C2×C4—434no—
812C2×C4—434no—
813C2×C4—432no—
814C2×C4—432no—
815C2×C4—868no—
816C2×C4—868no—
817C2×C4—861no—
818C2×C4—864no—
819C2×C4—864no—
820C2×C4—861no—
821C2×C4—861no—
822C2×C4—862no—
823C2×C4—862no—
824C2×C4—3441no—
825C2×C4—3442no—
826C2×C4—3444no—
827C2×C4—3442no—
828C2×C4—1722no—
829C2×C4—1722no—
830C2×C4C2×D4×D4311yescharacteristic
831C2×C4C2×D4×D4311yescharacteristic
832C2×C4C2×D4×D4311yescharacteristic
833C2×C4C2×D4×D4311yescharacteristic
834C2×C4C2×D4×D4311yescharacteristic
835C2×C4C2×Q8×D4312yes—
836C2×C4#41×D4312yes—
837C2×C4C24×D4311yescharacteristic
838C8—22no—
839C8—22no—
840C8—864no—
841C22—21no—
842C22—21no—
843C22—434no—
844C22—862no—
845C22—862no—
846C22—862no—
847C22—1721no—
848C22—1721no—
849C22C22⋊Q8×D4312yes—
850C22C22×D4×D4311yescharacteristic
851C4—24no—
852C4—21no—
853C4—21no—
854C4—21no—
855C4—42no—
856C4—44no—
857C4—434no—
858C4—862no—
859C4—862no—
860C4—862no—
861C4—1721no—
862C4—1722no—
863C4—1721no—
864C4—1722no—
865C4C22⋊Q8×D4312yes—
866C4#1458371212yes—
867C4C22×Q8×D4311yescharacteristic
868C4C2×#41×D4311yescharacteristic
869C2—22no—
870C2—864no—
871C2—1722no—
872C2C2×C22⋊Q8×D4311yescharacteristic
873C2C2×#1458371211yescharacteristic
874C2#1914937111yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#477C2
socleC22×C43C23×D4
prime radicalC2×#13063373C22
hypercenterC2×#477D43
hypocenterC43#60498
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#477

Complements

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

NH ≅ G/Ntype
1. #19148411C2semidirect
3. #19144451C2semidirect
4. #19144443C2semidirect
5. #19144433C2semidirect
6. #19144432C2semidirect
7. #19144409C2semidirect
8. #19144404C2semidirect
9. #19144401C2semidirect
10. #19144400C2semidirect
11. #19144386C2semidirect
12. #19144385C2semidirect
13. #477×D43C2semidirect
14. #19143191C2semidirect
15. #19143160C2semidirect
17. C2×C43×#477C2semidirect
96. #13063373Q8semidirect
236. C2×Q8×C43C2×Q8semidirect
248. #10621902C2×Q8semidirect
252. Q8×D43C2×Q8semidirect
256. #10621898C2×Q8semidirect
445. C2×#477D43semidirect
532. C43#60498semidirect
692. C2×Q8Q8×D43semidirect

Maximal subgroups

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

subgroupindex
#191484112
C4×#130633732
#191444512
#191444432
#191444332
#191444322
#191444092
#191444042
#191444012
#191444002
#191443862
#191443852
#477×D432
#191431912
#191431602
#191431232
C2×C43×#4772
#6049843