Finite Group Databasebeta

← #25964296

Subgroups — #25964296

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#19148407C211yesmaximal, characteristic, complemented
2C4×#13063373C211yesmaximal, characteristic
3#19144449C214yesmaximal, complemented
4#19144445C212yesmaximal, complemented
5#19144439C212yesmaximal, complemented
6#19144434C214yesmaximal, complemented
7#19144411C211yesmaximal, characteristic, complemented
8#19144409C212yesmaximal, complemented
9#19144395C212yesmaximal, complemented
10#19144378C212yesmaximal, complemented
11#19144377C211yesmaximal, characteristic, complemented
12C2×#14583194C211yesmaximal, characteristic, complemented
13#477×D43C212yesmaximal, complemented
14#19143194C212yesmaximal, complemented
15#19143164C211yesmaximal, characteristic, complemented
16#19143127C212yesmaximal
17C43×#3078C211yesmaximal, characteristic, complemented
18C2×#13063373C2211yescharacteristic
19C2×#13063333C2212yes—
20Q8×Dic86—21no—
21#14583627—21no—
22#14583609—21no—
23#14583607—22no—
24Q8×D172—21no—
25#14583562—22no—
26#14583529C2214yes—
27#14583527C2212yes—
28#14583454C2212yes—
29C2×#13063325C2211yescharacteristic
30C4⋊Q8×D43C2212yes—
31#14583381—21no—
32#14583381C2212yes—
33#14583380—22no—
34#14583380C2211yescharacteristic
35#14583380C2211yescharacteristic
36#14583379C2212yes—
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#14583209C2214yes—
48#14583208C2214yes—
49#14583204C2214yes—
50#14583203C2212yes—
51#14583198C2214yes—
52#14583196C2212yes—
53#14583195C2212yes—
54#14583194C2214yes—
55#14583194C2212yes—
56#14583194C2212yes—
57#14583193C2214yes—
58#14583192C2214yes—
59#14583191C2211yescharacteristic
60#14583190C2212yes—
61#14583186C2211yescharacteristic
62#14583185C2212yes—
63#14583182C2214yes—
64#14583181C2211yescharacteristic
65#14583180C2212yes—
66#14583178C2214yes—
67#14583176C2211yescharacteristic
68#14582941C2212yes—
69#14582940C2214yes—
70#14582938C2214yes—
71#14582935C2212yes—
72#14582934C2214yes—
73C2×#13063258C2212yes—
74#107×D43C2214yes—
75#14582927C2212yes—
76#14582924C2214yes—
77#14582921C2212yes—
78C2×C4⋊(C43⋊C8)C2211yescharacteristic
79C4⋊C8×D43C2212yes—
80#14582906C2214yes—
81#14582901C2212yes—
82#14582899C2214yes—
83#14582894C2214yes—
84#14582893C2212yes—
85C2×#13063249C2212yes—
86#103×D43C2214yes—
87C43×#533C2211yescharacteristic
88C2×C4×Q8×C43C2211yescharacteristic
89C43×#479C2214yes—
90C43×#477C2212yes—
91C43×#475C2212yes—
92C43×#428C2212yes—
93C43×#423C2211yescharacteristic
94C43×#419C2212yes—
95#13063373—24no—
96#13063373Q818yescomplemented
97C2×#10621902—21no—
98C2×#10621902C2312yes—
99C2×#10621898—22no—
100C2×#10621898C2311yescharacteristic
101C2×#10621898C2311yescharacteristic
102C22×Dic86—21no—
103C2×Q8×D43—22no—
104C2×Q8×D43—21no—
105C2×Q8×D43C2312yes—
106#13063333—28no—
107C2×#10621872C2314yes—
108C22×C43⋊C8C2312yes—
109C2×C8×D43C2314yes—
110#13063325—21no—
111#13063325—21no—
112#13063325—22no—
113#13063325C2312yes—
114#13063325C2312yes—
115#13063324—24no—
116#13063324—22no—
117#13063324C2314yes—
118#13063323—22no—
119#13063317—22no—
120#13063316C2314yes—
121#13063315—24no—
122#13063305—22no—
123#13063305—24no—
124#13063303—24no—
125#13063302—24no—
126#13063301—22no—
127Q8×Dic43—21no—
128Q8×Dic43—21no—
129Q8×Dic43—22no—
130Q8×Dic43C2312yes—
131Q8×Dic43C2312yes—
132C4×Dic86—22no—
133C4×Dic86—22no—
134C4×Dic86—22no—
135C4×Dic86D411yescharacteristic
136C4×Dic86D411yescharacteristic
137C4×Dic86C2311yescharacteristic
138C4×Dic86C2311yescharacteristic
139#13063290—21no—
140#13063290—22no—
141#13063290—22no—
142#13063290—22no—
143#13063290C2312yes—
144C4×D172—22no—
145C4×D172—22no—
146C4×D172—22no—
147C4×D172D411yescharacteristic
148C4×D172D411yescharacteristic
149C4×D172C2311yescharacteristic
150C4×D172C2311yescharacteristic
151#13063287—21no—
152#13063287—22no—
153#13063287—22no—
154#13063287C2312yes—
155C4×C22⋊D43—21no—
156C4×C22⋊D43—21no—
157C4×C22⋊D43—22no—
158C4×C22⋊D43—22no—
159C4×C22⋊D43D412yes—
160C4×C22⋊D43D412yes—
161(C22⋊D43)⋊C4—24no—
162#13063284—22no—
163#13063284C2311yescharacteristic
164#13063284C2311yescharacteristic
165#13063283—22no—
166#13063283—21no—
167#13063283—22no—
168#13063283C2312yes—
169#13063283C2314yes—
170#13063282—21no—
171#13063282—22no—
172#13063282—22no—
173#13063282C2312yes—
174C2×C4⋊Dic43—21no—
175C2×C4⋊Dic43C2312yes—
176C4⋊C4×D43—22no—
177C4⋊C4×D43—22no—
178C4⋊C4×D43—21no—
179C4⋊C4×D43—22no—
180C4⋊C4×D43C2312yes—
181C4⋊C4×D43C2314yes—
182C42×D43—22no—
183C42×D43—21no—
184C42×D43—22no—
185C42×D43C2312yes—
186#13063259C2314yes—
187#13063258C2312yes—
188#13063258C2314yes—
189#13063258C2312yes—
190#13063258C2314yes—
191#13063257C2314yes—
192#13063256C2312yes—
193#13063256C2312yes—
194C4⋊(C43⋊C8)C2311yescharacteristic
195C4⋊(C43⋊C8)C2311yescharacteristic
196C4⋊(C43⋊C8)C2312yes—
197Dic43⋊C8C2314yes—
198Dic43⋊C8C2314yes—
199#13063250C2314yes—
200#13063249C2314yes—
201#13063249C2314yes—
202#13063248C2312yes—
203#13063248C2312yes—
204#13063247C2314yes—
205#13063245C2312yes—
206#13063245C2312yes—
207C22×Q8×C43C2311yescharacteristic
208C2×M16×C43C2312yes—
209C4⋊Q8×C43C2311yescharacteristic
210C4⋊Q8×C43C2311yescharacteristic
211#125×C43C2312yes—
212C22⋊Q8×C43—21no—
213C22⋊Q8×C43—21no—
214C4×Q8×C43—21no—
215C4×Q8×C43—21no—
216C4×Q8×C43—21no—
217C4×Q8×C43—21no—
218C4×Q8×C43C2312yes—
219C4×Q8×C43C2312yes—
220#117×C43C2312yes—
221C2×C4⋊C4×C43—21no—
222C2×C4⋊C4×C43C2311yescharacteristic
223C2×C42×C43—21no—
224C2×C42×C43C2311yescharacteristic
225#107×C43C2314yes—
226#106×C43C2314yes—
227C4⋊C8×C43C2312yes—
228C4⋊C8×C43C2312yes—
229#103×C43C2314yes—
230#103×C43C2314yes—
231C2×Q8×C43—21no—
232C2×Q8×C43—21no—
233C2×Q8×C43—21no—
234C2×Q8×C43—22no—
235C2×Q8×C43C2×Q814yescomplemented
236C2×Q8×C43C2412yes—
237C22×C4×C43—21no—
238C22×C4×C43—21no—
239C22×C4×C43C2×D411yescharacteristic
240C22×C4×C43C2×D411yescharacteristic
241C22×C4×C43C2411yescharacteristic
242C2×C22⋊D43—21no—
243C2×C22⋊D43C2×D412yes—
244C22×Dic43—22no—
245#10621902—28no—
246#10621902—24no—
247#10621902C2×Q818yescomplemented
248Q8×D43—24no—
249Q8×D43—28no—
250Q8×D43—84no—
251Q8×D43C2×Q818yescomplemented
252#10621898—22no—
253#10621898—216no—
254#10621898C2×Q814yes—
255#10621898C2×Q814yescomplemented
256#10621898#4114yes—
257C2×D172—22no—
258C2×D172C2×D411yescharacteristic
259C2×D172C2411yescharacteristic
260C2×C4×D43—21no—
261C2×C4×D43—22no—
262C2×C4×D43—21no—
263C2×C4×D43—21no—
264C2×C4×D43—22no—
265C2×C4×D43—22no—
266C2×C4×D43—22no—
267C2×C4×D43—24no—
268C2×C4×D43C2×D412yes—
269C2×C4×D43C2×D412yes—
270C2×C4×D43C2412yes—
271C2×Dic86—22no—
272C2×Dic86—22no—
273C2×Dic86—22no—
274C2×Dic86—24no—
275C2×Dic86—82no—
276C2×Dic86C2×D411yescharacteristic
277C2×Dic86C2411yescharacteristic
278M16×C43—24no—
279C2×C8×C43C2414yes—
280C4⋊C4×C43—22no—
281C4⋊C4×C43—22no—
282C4⋊C4×C43—21no—
283C4⋊C4×C43—22no—
284C4⋊C4×C43—22no—
285C4⋊C4×C43—21no—
286C4⋊C4×C43—21no—
287C4⋊C4×C43C2412yes—
288C4⋊C4×C43C2412yes—
289C4⋊C4×C43C2412yes—
290C22⋊C4×C43—22no—
291C42×C43—22no—
292C42×C43—22no—
293C42×C43—22no—
294C42×C43C2×D411yescharacteristic
295C42×C43C2×D411yescharacteristic
296C42×C43C2411yescharacteristic
297C42×C43C2411yescharacteristic
298C22⋊Dic43—21no—
299C22⋊Dic43C2×D412yes—
300(C2×D43)⋊C4—21no—
301(C2×D43)⋊C4—21no—
302(C2×D43)⋊C4—22no—
303(C2×D43)⋊C4—22no—
304(C2×D43)⋊C4—24no—
305(C2×D43)⋊C4C2×D412yes—
306(C2×D43)⋊C4C2×D412yes—
307C4⋊Dic43—22no—
308C4⋊Dic43—22no—
309C4⋊Dic43—22no—
310C4⋊Dic43—22no—
311C4⋊Dic43—22no—
312C4⋊Dic43—24no—
313C4⋊Dic43C2×D411yescharacteristic
314C4⋊Dic43C2×D411yescharacteristic
315C4⋊Dic43C2414yes—
316C4⋊Dic43C2411yescharacteristic
317C4⋊Dic43C2411yescharacteristic
318Dic43⋊C4—21no—
319Dic43⋊C4—21no—
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—24no—
335C4×Dic43C2×D412yes—
336C4×Dic43C2×D412yes—
337C4×Dic43C2412yes—
338C2×C43⋊C8—24no—
339C2×C43⋊C8C2412yes—
340C2×C43⋊C8C2412yes—
341#10621872—28no—
342C8×D43—28no—
343C23×C43C22×D411yescharacteristic
344C22×D43—21no—
345C22×D43C22×D412yes—
346Q8×C43—24no—
347Q8×C43—22no—
348Q8×C43—42no—
349Q8×C43—42no—
350Q8×C43C22×Q814yes—
351C2×C4×C43—24no—
352C2×C4×C43—22no—
353C2×C4×C43—22no—
354C2×C4×C43—22no—
355C2×C4×C43—22no—
356C2×C4×C43—22no—
357C2×C4×C43—41no—
358C2×C4×C43—81no—
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—24no—
373C2×Dic43—82no—
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—44no—
396Dic86—84no—
397Dic86—82no—
398Dic86C22⋊Q814yes—
399Dic86C22×Q812yes—
400C8×C43—24no—
401C43⋊C8—22no—
402C43⋊C8—22no—
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—42no—
419C4×C43—42no—
420C4×C43—42no—
421C4×C43C2×C22⋊Q812yes—
422C4×C43#57812yes—
423C4×C43C23×Q811yescharacteristic
424C4×C43C22×#4111yescharacteristic
425Dic43—22no—
426Dic43—22no—
427Dic43—22no—
428Dic43—44no—
429Dic43—41no—
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#3078D4311yescharacteristic, complemented
442#3076—432no—
443#3076—431no—
444C2×#477—432no—
445C2×#477—431no—
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—861no—
460#554—862no—
461D4×Q8—861no—
462D4×Q8—862no—
463#544—434no—
464#544—432no—
465#533—432no—
466#533C2×D4311yescharacteristic
467C2×C4⋊Q8—432no—
468C2×C4⋊Q8—431no—
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—432no—
487#479—434no—
488#479—434no—
489#479—434no—
490#479C2×D4314yes—
491#478—432no—
492#478—434no—
493#477—431no—
494#477—432no—
495#477—432no—
496#477—434no—
497#477—434no—
498#477—432no—
499#477—434no—
500#477C2×D4312yes—
501#476—431no—
502#476—432no—
503#475—431no—
504#475—432no—
505#475—434no—
506#475C2×D4312yes—
507#474—431no—
508#474—434no—
509#474—432no—
510#428—432no—
511#428—434no—
512#428—434no—
513#428C2×D4312yes—
514#427—432no—
515#427—434no—
516C2×#107—432no—
517C2×#107—434no—
518#424—432no—
519#424—434no—
520#423—432no—
521#423C2×D4311yescharacteristic
522C2×C4⋊C8—431no—
523C2×C4⋊C8—432no—
524#419—434no—
525#419C2×D4312yes—
526#417—432no—
527#417—434no—
528#416—432no—
529#416—434no—
530C2×#103—432no—
531C2×#103—434no—
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—432no—
541C22×Q8—862no—
542C22×Q8—861no—
543C22×Q8—861no—
544C22×Q8C22×D4311yescharacteristic
545#131—868no—
546C2×M16—434no—
547C2×M16C22×D4312yes—
548C22×C8—432no—
549C22×C8—434no—
550C4⋊Q8—434no—
551C4⋊Q8—432no—
552C4⋊Q8—432no—
553C4⋊Q8—862no—
554C4⋊Q8—862no—
555C4⋊Q8—862no—
556C4⋊Q8—864no—
557C4⋊Q8—861no—
558C4⋊Q8—861no—
559C4⋊Q8C22×D4311yescharacteristic
560C4⋊Q8C22×D4311yescharacteristic
561#125—434no—
562#125—862no—
563#125—864no—
564#125C22×D4312yes—
565C22⋊Q8—21no—
566C22⋊Q8—21no—
567C22⋊Q8—864no—
568C22⋊Q8—864no—
569C22⋊Q8—864no—
570C22⋊Q8—862no—
571C22⋊Q8—862no—
572C4×Q8—21no—
573C4×Q8—21no—
574C4×Q8—21no—
575C4×Q8—21no—
576C4×Q8—431no—
577C4×Q8—431no—
578C4×Q8—432no—
579C4×Q8—432no—
580C4×Q8—432no—
581C4×Q8—431no—
582C4×Q8—431no—
583C4×Q8—862no—
584C4×Q8—862no—
585C4×Q8—862no—
586C4×Q8—862no—
587C4×Q8—862no—
588C4×Q8—862no—
589C4×Q8—862no—
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—864no—
606C4×D4—862no—
607C4×D4—862no—
608C4×D4—862no—
609C4×D4—861no—
610C4×D4—862no—
611C4×D4—861no—
612C4×D4—861no—
613#117—431no—
614#117—432no—
615#117—431no—
616#117—432no—
617#117—434no—
618#117—862no—
619#117—862no—
620#117—862no—
621#117—862no—
622#117—862no—
623#117—861no—
624#117—861no—
625#117C22×D4312yes—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—432no—
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⋊C4—861no—
635C2×C4⋊C4C22×D4311yescharacteristic
636C2×C42—21no—
637C2×C42—432no—
638C2×C42—862no—
639C2×C42—862no—
640C2×C42—861no—
641C2×C42C22×D4311yescharacteristic
642#107—434no—
643#107—434no—
644#107—432no—
645#107—434no—
646#107—432no—
647#107C22×D4314yes—
648#106—434no—
649#106—432no—
650#106—432no—
651#106C22×D4314yes—
652C4⋊C8—434no—
653C4⋊C8—434no—
654C4⋊C8—431no—
655C4⋊C8—431no—
656C4⋊C8—432no—
657C4⋊C8C22×D4312yes—
658C4⋊C8C22×D4312yes—
659#103—434no—
660#103—434no—
661#103—434no—
662#103—432no—
663#103—432no—
664#103C22×D4314yes—
665#103C22×D4314yes—
666#102—434no—
667#102—432no—
668#102—432no—
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—21no—
679C2×Q8—21no—
680C2×Q8—22no—
681C2×Q8—431no—
682C2×Q8—438no—
683C2×Q8—431no—
684C2×Q8—862no—
685C2×Q8—864no—
686C2×Q8—864no—
687C2×Q8—868no—
688C2×Q8—862no—
689C2×Q8—862no—
690C2×Q8—3442no—
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—432no—
702C22×C4—432no—
703C22×C4—432no—
704C22×C4—862no—
705C22×C4—862no—
706C22×C4—862no—
707C22×C4—862no—
708C22×C4—864no—
709C22×C4—861no—
710C22×C4—862no—
711C22×C4—861no—
712C22×C4—861no—
713C22×C4D4×D4311yescharacteristic
714C22×C4D4×D4311yescharacteristic
715C22×C4C23×D4311yescharacteristic
716M16—24no—
717M16—868no—
718C2×C8—432no—
719C2×C8—432no—
720C2×C8—868no—
721C2×C8—864no—
722C2×C8C23×D4314yes—
723C4⋊C4—22no—
724C4⋊C4—22no—
725C4⋊C4—21no—
726C4⋊C4—21no—
727C4⋊C4—21no—
728C4⋊C4—22no—
729C4⋊C4—22no—
730C4⋊C4—432no—
731C4⋊C4—431no—
732C4⋊C4—432no—
733C4⋊C4—431no—
734C4⋊C4—434no—
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—862no—
746C4⋊C4—861no—
747C4⋊C4—862no—
748C4⋊C4—862no—
749C4⋊C4—861no—
750C4⋊C4C23×D4312yes—
751C4⋊C4C23×D4312yes—
752C4⋊C4C23×D4312yes—
753C22⋊C4—22no—
754C22⋊C4—432no—
755C22⋊C4—432no—
756C22⋊C4—432no—
757C22⋊C4—862no—
758C22⋊C4—862no—
759C22⋊C4—864no—
760C22⋊C4—861no—
761C22⋊C4—861no—
762C22⋊C4—861no—
763C42—22no—
764C42—22no—
765C42—22no—
766C42—432no—
767C42—432no—
768C42—432no—
769C42—862no—
770C42—862no—
771C42—862no—
772C42—862no—
773C42—864no—
774C42—861no—
775C42—861no—
776C42—861no—
777C42D4×D4311yescharacteristic
778C42D4×D4311yescharacteristic
779C42C23×D4311yescharacteristic
780C42C23×D4311yescharacteristic
781C23—432no—
782C23—861no—
783C23C2×D4×D4311yescharacteristic
784Q8—24no—
785Q8—22no—
786Q8—42no—
787Q8—42no—
788Q8—434no—
789Q8—432no—
790Q8—868no—
791Q8—861no—
792Q8—3442no—
793Q8—3444no—
794Q8—1724no—
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—22no—
807C2×C4—22no—
808C2×C4—41no—
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—864no—
823C2×C4—3441no—
824C2×C4—3442no—
825C2×C4—3444no—
826C2×C4—3442no—
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—24no—
839C8—862no—
840C8—862no—
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—42no—
857C4—42no—
858C4—434no—
859C4—862no—
860C4—862no—
861C4—862no—
862C4—1721no—
863C4—1721no—
864C4—1724no—
865C4C22⋊Q8×D4312yes—
866C4#1458371512yes—
867C4C22×Q8×D4311yescharacteristic
868C4C2×#41×D4311yescharacteristic
869C2—22no—
870C2—864no—
871C2—1722no—
872C2C2×C22⋊Q8×D4311yescharacteristic
873C2C2×#1458371511yescharacteristic
874C2#1914937211yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3078C2
socleC22×C43C23×D4
prime radicalC2×#13063373C22
hypercenter#3078D43
hypocenterC43#60498
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3078

Complements

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

NH ≅ G/Ntype
1. #19148407C2semidirect
3. #19144449C2semidirect
4. #19144445C2semidirect
5. #19144439C2semidirect
6. #19144434C2semidirect
7. #19144411C2semidirect
8. #19144409C2semidirect
9. #19144395C2semidirect
10. #19144378C2semidirect
11. #19144377C2semidirect
12. C2×#14583194C2semidirect
13. #477×D43C2semidirect
14. #19143194C2semidirect
15. #19143164C2semidirect
17. C43×#3078C2semidirect
96. #13063373Q8semidirect
235. C2×Q8×C43C2×Q8semidirect
247. #10621902C2×Q8semidirect
251. Q8×D43C2×Q8semidirect
255. #10621898C2×Q8semidirect
441. #3078D43semidirect
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
#191484072
C4×#130633732
#191444492
#191444452
#191444392
#191444342
#191444112
#191444092
#191443952
#191443782
#191443772
C2×#145831942
#477×D432
#191431942
#191431642
#191431272
C43×#30782
#6049843