Finite Group Databasebeta

← #25964293

Subgroups — #25964293

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×#13063372C211yesmaximal, characteristic
3#19144447C214yesmaximal, complemented
4#19144444C212yesmaximal, complemented
5#19144440C212yesmaximal, complemented
6#19144436C214yesmaximal, complemented
7#19144410C211yesmaximal, characteristic, complemented
8#19144407C212yesmaximal, complemented
9#19144396C211yesmaximal, characteristic, complemented
10#19144395C212yesmaximal, complemented
11#19144376C212yesmaximal, complemented
12C2×#14583195C211yesmaximal, characteristic, complemented
13#477×D43C212yesmaximal, complemented
14#19143192C212yesmaximal, complemented
15#19143160C211yesmaximal, characteristic, complemented
16#19143124C212yesmaximal
17C43×#3076C211yesmaximal, characteristic, complemented
18C2×#13063372C2211yescharacteristic
19C2×#13063331C2212yes—
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#14583382C2211yescharacteristic
32#14583379—21no—
33#14583379C2211yescharacteristic
34#14583379C2212yes—
35#14583378—22no—
36#14583378C2212yes—
37#14583376—21no—
38#14583376C2211yescharacteristic
39#14583375C2212yes—
40C4×#10621898—21no—
41C4×#10621898C2211yescharacteristic
42C4×#10621900—22no—
43C4×#10621900C2212yes—
44C2×C4×Dic86—21no—
45C2×C4×Dic86C2211yescharacteristic
46C4×Q8×D43C2212yes—
47#14583209C2214yes—
48#14583208C2214yes—
49#14583205C2214yes—
50#14583203C2214yes—
51#14583197C2214yes—
52#14583195C2212yes—
53#14583195C2212yes—
54#14583195C2214yes—
55#14583194C2212yes—
56#14583193C2214yes—
57#14583192C2214yes—
58#14583191C2212yes—
59#14583189C2212yes—
60#14583184C2212yes—
61#14583183C2214yes—
62#14583181C2212yes—
63#14583179C2212yes—
64#14583177C2214yes—
65#14582942C2212yes—
66#14582942C2212yes—
67#14582938C2214yes—
68#14582938C2214yes—
69#14582936C2214yes—
70C2×#13063259C2212yes—
71#107×D43C2214yes—
72#14582925C2212yes—
73#14582924C2214yes—
74#14582923C2211yescharacteristic
75#14582921C2212yes—
76C4⋊C8×D43C2212yes—
77#14582907C2212yes—
78#14582906C2214yes—
79#14582900C2212yes—
80#14582897C2214yes—
81#14582892C2214yes—
82C2×#13063250C2212yes—
83#103×D43C2214yes—
84C43×#533C2211yescharacteristic
85C4×#41×C43C2211yescharacteristic
86C43×#479C2212yes—
87C43×#478C2212yes—
88C43×#477C2211yescharacteristic
89C43×#476C2211yescharacteristic
90C43×#475C2211yescharacteristic
91C43×#474C2211yescharacteristic
92C43×#427C2212yes—
93C2×C4⋊C8×C43C2211yescharacteristic
94C43×#416C2212yes—
95#13063372—24no—
96#13063372Q818yescomplemented
97C2×#10621898—21no—
98C2×#10621898C2311yescharacteristic
99C2×#10621900—22no—
100C2×#10621900C2312yes—
101C22×Dic86—21no—
102C22×Dic86—21no—
103C22×Dic86C2311yescharacteristic
104C2×Q8×D43—22no—
105C2×Q8×D43C2312yes—
106#13063331—28no—
107C2×#10621877C2312yes—
108C2×#10621872C2314yes—
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—22no—
128Q8×Dic43C2312yes—
129C4×Dic86—21no—
130C4×Dic86—22no—
131C4×Dic86—21no—
132C4×Dic86—21no—
133C4×Dic86—21no—
134C4×Dic86—21no—
135C4×Dic86—22no—
136C4×Dic86—22no—
137C4×Dic86D411yescharacteristic
138C4×Dic86D411yescharacteristic
139C4×Dic86C2312yes—
140C4×Dic86C2312yes—
141#13063290—22no—
142#13063290—22no—
143#13063290—22no—
144#13063290C2312yes—
145#13063290C2312yes—
146C4×D172—22no—
147C4×D172—21no—
148C4×D172D411yescharacteristic
149C4×D172D411yescharacteristic
150D4×Dic43—22no—
151D4×Dic43C2312yes—
152C4×C22⋊D43—22no—
153C4×C22⋊D43—22no—
154C4×C22⋊D43D412yes—
155C4×C22⋊D43D412yes—
156(C22⋊D43)⋊C4—24no—
157(C22⋊D43)⋊C4—22no—
158(C22⋊D43)⋊C4—22no—
159(C22⋊D43)⋊C4—22no—
160#13063284—21no—
161#13063284C2311yescharacteristic
162#13063283—22no—
163#13063283C2312yes—
164#13063283C2314yes—
165#13063282—22no—
166#13063282C2312yes—
167#13063281—22no—
168#13063281—22no—
169#13063281—22no—
170C2×C4⋊Dic43—21no—
171C2×C4⋊Dic43—21no—
172C2×C4⋊Dic43C2311yescharacteristic
173C2×C4⋊Dic43C2312yes—
174C2×Dic43⋊C4—21no—
175C2×Dic43⋊C4—22no—
176C4⋊C4×D43—22no—
177C4⋊C4×D43—22no—
178C4⋊C4×D43C2312yes—
179C4⋊C4×D43C2314yes—
180C2×C4×Dic43—21no—
181C2×C4×Dic43—22no—
182C42×D43—22no—
183C42×D43C2312yes—
184#13063259C2314yes—
185#13063259C2314yes—
186#13063258C2314yes—
187#13063258C2314yes—
188#13063256C2314yes—
189#13063256C2314yes—
190C4⋊(C43⋊C8)C2312yes—
191C4⋊(C43⋊C8)C2312yes—
192Dic43⋊C8C2314yes—
193Dic43⋊C8C2314yes—
194#13063250C2314yes—
195#13063250C2314yes—
196#13063249C2314yes—
197#13063248C2314yes—
198#13063248C2314yes—
199#13063246C2314yes—
200C2×#41×C43C2311yescharacteristic
201C22×C8×C43C2312yes—
202C4⋊Q8×C43C2311yescharacteristic
203C4⋊Q8×C43C2311yescharacteristic
204#125×C43C2312yes—
205C22⋊Q8×C43—21no—
206C22⋊Q8×C43—21no—
207C4×Q8×C43—21no—
208C4×Q8×C43—21no—
209C4×Q8×C43C2311yescharacteristic
210C4×Q8×C43C2311yescharacteristic
211C4×D4×C43—21no—
212C4×D4×C43—21no—
213C4×D4×C43C2311yescharacteristic
214C4×D4×C43C2311yescharacteristic
215#117×C43—21no—
216#117×C43C2311yescharacteristic
217#117×C43C2312yes—
218C2×C42×C43—21no—
219C2×C42×C43C2311yescharacteristic
220#107×C43C2312yes—
221#107×C43C2312yes—
222#106×C43C2312yes—
223#106×C43C2312yes—
224C4⋊C8×C43C2311yescharacteristic
225C4⋊C8×C43C2311yescharacteristic
226C4⋊C8×C43C2312yes—
227#103×C43C2312yes—
228#103×C43C2312yes—
229#102×C43C2312yes—
230#102×C43C2312yes—
231#41×C43—22no—
232#41×C43C2×Q814yescomplemented
233C2×Q8×C43—21no—
234C2×Q8×C43—21no—
235C2×Q8×C43C2411yescharacteristic
236C2×D4×C43—21no—
237C2×D4×C43C2411yescharacteristic
238C22×C4×C43—21no—
239C22×C4×C43—21no—
240C22×C4×C43—21no—
241C22×C4×C43C2×D411yescharacteristic
242C22×C4×C43C2×D411yescharacteristic
243C22×C4×C43C2411yescharacteristic
244C2×C22⋊D43—22no—
245C2×C22⋊D43C2×D412yes—
246C22×Dic43—22no—
247C22×Dic43—22no—
248C22×Dic43—21no—
249C22×Dic43—21no—
250C22×Dic43—22no—
251Q8×D43—24no—
252Q8×D43—84no—
253Q8×D43C2×Q818yescomplemented
254#10621900—216no—
255#10621900—24no—
256#10621900C2×Q818yescomplemented
257#10621898—28no—
258#10621898C2×Q814yes—
259#10621898#4114yes—
260C2×D172C2×D411yescharacteristic
261C2×C4×D43—22no—
262C2×C4×D43—22no—
263C2×C4×D43—24no—
264C2×C4×D43C2×D412yes—
265C2×C4×D43C2×D412yes—
266C2×C4×D43C2412yes—
267C2×Dic86—21no—
268C2×Dic86—22no—
269C2×Dic86—22no—
270C2×Dic86—28no—
271C2×Dic86—22no—
272C2×Dic86—22no—
273C2×Dic86—24no—
274C2×Dic86—82no—
275C2×Dic86C2×D411yescharacteristic
276C2×Dic86C2×Q814yescomplemented
277C2×Dic86C2412yes—
278C2×C8×C43—24no—
279C2×C8×C43C2412yes—
280C2×C8×C43C2412yes—
281C4⋊C4×C43—21no—
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×C43C2411yescharacteristic
290C4⋊C4×C43C2411yescharacteristic
291C22⋊C4×C43—21no—
292C22⋊C4×C43—21no—
293C22⋊C4×C43—21no—
294C22⋊C4×C43—22no—
295C42×C43—21no—
296C42×C43—21no—
297C42×C43—21no—
298C42×C43—22no—
299C42×C43C2×D411yescharacteristic
300C42×C43C2×D411yescharacteristic
301C42×C43C2411yescharacteristic
302C42×C43C2411yescharacteristic
303C22⋊Dic43—22no—
304C22⋊Dic43C2×D412yes—
305(C2×D43)⋊C4—22no—
306(C2×D43)⋊C4—24no—
307(C2×D43)⋊C4C2×D412yes—
308(C2×D43)⋊C4C2×D412yes—
309C4⋊Dic43—22no—
310C4⋊Dic43—21no—
311C4⋊Dic43—22no—
312C4⋊Dic43—22no—
313C4⋊Dic43—22no—
314C4⋊Dic43—24no—
315C4⋊Dic43C2×D411yescharacteristic
316C4⋊Dic43C2×D411yescharacteristic
317C4⋊Dic43C2414yes—
318C4⋊Dic43C2412yes—
319Dic43⋊C4—22no—
320Dic43⋊C4—22no—
321Dic43⋊C4—22no—
322Dic43⋊C4—24no—
323Dic43⋊C4—22no—
324Dic43⋊C4—24no—
325Dic43⋊C4—22no—
326Dic43⋊C4—24no—
327Dic43⋊C4C2×D412yes—
328Dic43⋊C4C2×D412yes—
329C4×Dic43—22no—
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×C43—21no—
344C23×C43C22×D411yescharacteristic
345C22×D43C22×D412yes—
346Q8×C43—21no—
347Q8×C43—42no—
348Q8×C43—42no—
349Q8×C43C22×Q812yes—
350D4×C43—24no—
351D4×C43—21no—
352D4×C43C22×Q812yes—
353C2×C4×C43—21no—
354C2×C4×C43—24no—
355C2×C4×C43—22no—
356C2×C4×C43—21no—
357C2×C4×C43—21no—
358C2×C4×C43—22no—
359C2×C4×C43—22no—
360C2×C4×C43—41no—
361C2×C4×C43—42no—
362C2×C4×C43—81no—
363C2×C4×C43C22×D411yescharacteristic
364C2×C4×C43C22×D411yescharacteristic
365C2×C4×C43C22×D411yescharacteristic
366C2×C4×C43C22×D411yescharacteristic
367C2×C4×C43C22×D411yescharacteristic
368C2×C4×C43C22×Q812yes—
369C2×C4×C43C2×#4112yes—
370C2×C4×C43C2511yescharacteristic
371C22⋊D43—28no—
372C22⋊D43C22⋊Q818yes—
373C2×Dic43—24no—
374C2×Dic43—22no—
375C2×Dic43—28no—
376C2×Dic43—22no—
377C2×Dic43—24no—
378C2×Dic43—82no—
379C2×Dic43—82no—
380C2×Dic43—81no—
381C2×Dic43C22×D412yes—
382C2×Dic43C22×D412yes—
383C2×Dic43C22×D412yes—
384D172C22⋊Q814yes—
385C4×D43—28no—
386C4×D43—24no—
387C4×D43—42no—
388C4×D43—82no—
389C4×D43—84no—
390C4×D43C22×Q814yes—
391C4×D43C2×#4114yes—
392Dic86—24no—
393Dic86—22no—
394Dic86—28no—
395Dic86—44no—
396Dic86—84no—
397Dic86—82no—
398Dic86C22⋊Q814yes—
399Dic86C22×Q814yes—
400C8×C43—22no—
401C8×C43—22no—
402C43⋊C8—24no—
403#60498—431nomaximal, Sylow
404C22×C43—21no—
405C22×C43—21no—
406C22×C43—22no—
407C22×C43—41no—
408C22×C43—41no—
409C22×C43C2×C22⋊Q812yes—
410C22×C43C23×D411yescharacteristic
411C2×D43—22no—
412C2×D43—22no—
413C2×D43C2×C22⋊Q814yes—
414C4×C43—21no—
415C4×C43—21no—
416C4×C43—22no—
417C4×C43—21no—
418C4×C43—42no—
419C4×C43—41no—
420C4×C43—41no—
421C4×C43—42no—
422C4×C43C2×C22⋊Q812yes—
423C4×C43#57812yes—
424C4×C43C23×Q811yescharacteristic
425C4×C43C22×#4111yescharacteristic
426Dic43—22no—
427Dic43—24no—
428Dic43—22no—
429Dic43—44no—
430Dic43—42no—
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#3076D4311yescharacteristic, complemented
444C2×#477—432no—
445C2×#477—431no—
446#2913—432no—
447#2906—431no—
448#2898—432no—
449C2×C43—22no—
450C2×C43—42no—
451C2×C43C22×C22⋊Q811yescharacteristic
452C2×C43C2×#57811yescharacteristic
453C2×C43#358511yescharacteristic
454D43—24no—
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—431no—
472#520—432no—
473#520—861no—
474#520—862no—
475#519—432no—
476#519—431no—
477#519—861no—
478C4×#41—431no—
479C4×#41—432no—
480C4×#41—861no—
481C4×#41—862no—
482C4×#41C2×D4311yescharacteristic
483C2×C4×Q8—432no—
484C2×C4×Q8—431no—
485C2×C4×Q8—861no—
486#479—434no—
487#479—434no—
488#479—434no—
489#479—434no—
490#479C2×D4312yes—
491#478—434no—
492#478C2×D4312yes—
493#477—432no—
494#477—432no—
495#477—434no—
496#477—432no—
497#477—432no—
498#477—434no—
499#477—434no—
500#477C2×D4311yescharacteristic
501#476—432no—
502#476C2×D4311yescharacteristic
503#475—432no—
504#475—432no—
505#475—434no—
506#475C2×D4311yescharacteristic
507#474—432no—
508#474—434no—
509#474C2×D4311yescharacteristic
510#428—432no—
511#428—432no—
512#428—434no—
513#428—434no—
514#427—434no—
515#427C2×D4312yes—
516C2×#107—432no—
517C2×#107—434no—
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—434no—
529#416C2×D4312yes—
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—861no—
538C2×#41—862no—
539C2×#41C22×D4311yescharacteristic
540C22×Q8—432no—
541C22×Q8—431no—
542C22×Q8—861no—
543C22×Q8—862no—
544C22×Q8—861no—
545#131—868no—
546C2×M16—432no—
547C2×M16—434no—
548C22×C8—434no—
549C22×C8C22×D4312yes—
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—431no—
575C4×Q8—431no—
576C4×Q8—432no—
577C4×Q8—432no—
578C4×Q8—432no—
579C4×Q8—432no—
580C4×Q8—432no—
581C4×Q8—862no—
582C4×Q8—861no—
583C4×Q8—862no—
584C4×Q8—861no—
585C4×Q8—861no—
586C4×Q8—862no—
587C4×Q8—862no—
588C4×Q8—862no—
589C4×Q8—862no—
590C4×Q8—862no—
591C4×Q8—861no—
592C4×Q8—861no—
593C4×Q8C22×D4311yescharacteristic
594C4×Q8C22×D4311yescharacteristic
595C4×D4—21no—
596C4×D4—21no—
597C4×D4—432no—
598C4×D4—432no—
599C4×D4—432no—
600C4×D4—431no—
601C4×D4—431no—
602C4×D4—861no—
603C4×D4—862no—
604C4×D4—862no—
605C4×D4—862no—
606C4×D4—862no—
607C4×D4—864no—
608C4×D4—862no—
609C4×D4—862no—
610C4×D4—862no—
611C4×D4C22×D4311yescharacteristic
612C4×D4C22×D4311yescharacteristic
613#117—21no—
614#117—431no—
615#117—432no—
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#117C22×D4311yescharacteristic
625#117C22×D4312yes—
626C2×C4⋊C4—431no—
627C2×C4⋊C4—432no—
628C2×C4⋊C4—432no—
629C2×C4⋊C4—434no—
630C2×C4⋊C4—862no—
631C2×C4⋊C4—862no—
632C2×C4⋊C4—862no—
633C2×C4⋊C4—861no—
634C2×C4⋊C4—861no—
635C2×C4⋊C4—861no—
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—434no—
645#107—434no—
646#107C22×D4312yes—
647#107C22×D4312yes—
648#106—434no—
649#106—434no—
650#106C22×D4312yes—
651#106C22×D4312yes—
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—434no—
662#103—434no—
663#103—434no—
664#103C22×D4312yes—
665#103C22×D4312yes—
666#102—434no—
667#102C22×D4312yes—
668#102C22×D4312yes—
669#41—22no—
670#41—434no—
671#41—434no—
672#41—438no—
673#41—868no—
674#41—864no—
675#41—8616no—
676#41Q8×D4314yescomplemented
677C2×Q8—21no—
678C2×Q8—21no—
679C2×Q8—431no—
680C2×Q8—438no—
681C2×Q8—434no—
682C2×Q8—432no—
683C2×Q8—862no—
684C2×Q8—864no—
685C2×Q8—868no—
686C2×Q8—864no—
687C2×Q8—861no—
688C2×Q8—862no—
689C2×Q8—862no—
690C2×Q8—862no—
691C2×Q8—3442no—
692C2×Q8—3444no—
693C2×Q8C23×D4311yescharacteristic
694C2×D4—21no—
695C2×D4—432no—
696C2×D4—431no—
697C2×D4—862no—
698C2×D4C23×D4311yescharacteristic
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—432no—
703C22×C4—432no—
704C22×C4—432no—
705C22×C4—862no—
706C22×C4—862no—
707C22×C4—864no—
708C22×C4—862no—
709C22×C4—862no—
710C22×C4—861no—
711C22×C4—861no—
712C22×C4—862no—
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—21no—
724C4⋊C4—21no—
725C4⋊C4—21no—
726C4⋊C4—21no—
727C4⋊C4—22no—
728C4⋊C4—22no—
729C4⋊C4—432no—
730C4⋊C4—431no—
731C4⋊C4—432no—
732C4⋊C4—431no—
733C4⋊C4—434no—
734C4⋊C4—432no—
735C4⋊C4—862no—
736C4⋊C4—864no—
737C4⋊C4—862no—
738C4⋊C4—862no—
739C4⋊C4—864no—
740C4⋊C4—862no—
741C4⋊C4—864no—
742C4⋊C4—864no—
743C4⋊C4—861no—
744C4⋊C4—862no—
745C4⋊C4—862no—
746C4⋊C4—862no—
747C4⋊C4—862no—
748C4⋊C4—862no—
749C4⋊C4C23×D4312yes—
750C4⋊C4C23×D4312yes—
751C4⋊C4C23×D4311yescharacteristic
752C4⋊C4C23×D4311yescharacteristic
753C22⋊C4—21no—
754C22⋊C4—22no—
755C22⋊C4—21no—
756C22⋊C4—21no—
757C22⋊C4—432no—
758C22⋊C4—432no—
759C22⋊C4—432no—
760C22⋊C4—862no—
761C22⋊C4—864no—
762C22⋊C4—862no—
763C42—21no—
764C42—21no—
765C42—21no—
766C42—22no—
767C42—432no—
768C42—432no—
769C42—432no—
770C42—862no—
771C42—862no—
772C42—862no—
773C42—862no—
774C42—864no—
775C42—862no—
776C42—862no—
777C42D4×D4311yescharacteristic
778C42D4×D4311yescharacteristic
779C42C23×D4311yescharacteristic
780C42C23×D4311yescharacteristic
781C23—21no—
782C23—432no—
783C23C2×D4×D4311yescharacteristic
784Q8—21no—
785Q8—42no—
786Q8—42no—
787Q8—434no—
788Q8—434no—
789Q8—868no—
790Q8—864no—
791Q8—862no—
792Q8—3442no—
793Q8—3444no—
794Q8—1724no—
795Q8C2×Q8×D4312yes—
796D4—24no—
797D4—21no—
798D4—438no—
799D4—434no—
800D4—868no—
801D4C2×Q8×D4312yes—
802C2×C4—21no—
803C2×C4—24no—
804C2×C4—22no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—41no—
810C2×C4—42no—
811C2×C4—81no—
812C2×C4—432no—
813C2×C4—434no—
814C2×C4—434no—
815C2×C4—432no—
816C2×C4—432no—
817C2×C4—868no—
818C2×C4—868no—
819C2×C4—864no—
820C2×C4—862no—
821C2×C4—864no—
822C2×C4—862no—
823C2×C4—864no—
824C2×C4—3444no—
825C2×C4—3442no—
826C2×C4—3442no—
827C2×C4—3442no—
828C2×C4—3441no—
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—22no—
844C22—41no—
845C22—41no—
846C22—434no—
847C22—862no—
848C22—862no—
849C22C22⋊Q8×D4312yes—
850C22C22×D4×D4311yescharacteristic
851C4—22no—
852C4—21no—
853C4—21no—
854C4—21no—
855C4—41no—
856C4—42no—
857C4—41no—
858C4—42no—
859C4—434no—
860C4—864no—
861C4—862no—
862C4—862no—
863C4—1722no—
864C4—1724no—
865C4C22⋊Q8×D4312yes—
866C4#1458371312yes—
867C4C22×Q8×D4311yescharacteristic
868C4C2×#41×D4311yescharacteristic
869C2—22no—
870C2—42no—
871C2—864no—
872C2C2×C22⋊Q8×D4311yescharacteristic
873C2C2×#1458371311yescharacteristic
874C2#1914937211yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3076C2
socleC22×C43C23×D4
prime radicalC2×#13063372C22
hypercenter#3076D43
hypocenterC43#60498
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3076

Complements

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

NH ≅ G/Ntype
1. #19148407C2semidirect
3. #19144447C2semidirect
4. #19144444C2semidirect
5. #19144440C2semidirect
6. #19144436C2semidirect
7. #19144410C2semidirect
8. #19144407C2semidirect
9. #19144396C2semidirect
10. #19144395C2semidirect
11. #19144376C2semidirect
12. C2×#14583195C2semidirect
13. #477×D43C2semidirect
14. #19143192C2semidirect
15. #19143160C2semidirect
17. C43×#3076C2semidirect
96. #13063372Q8semidirect
232. #41×C43C2×Q8semidirect
253. Q8×D43C2×Q8semidirect
256. #10621900C2×Q8semidirect
276. C2×Dic86C2×Q8semidirect
443. #3076D43semidirect
532. C43#60498semidirect
676. #41Q8×D43semidirect

Maximal subgroups

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

subgroupindex
#191484072
C4×#130633722
#191444472
#191444442
#191444402
#191444362
#191444102
#191444072
#191443962
#191443952
#191443762
C2×#145831952
#477×D432
#191431922
#191431602
#191431242
C43×#30762
#6049843