Finite Group Databasebeta

← #25981323

Subgroups — #25981323

Order 11008.

2090 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148391C211yesmaximal, characteristic
2C2×#14583562C211yesmaximal, characteristic
3#19146469C214yesmaximal, complemented
4#19146466C214yesmaximal, complemented
5#19146344C214yesmaximal, complemented
6#19146340C214yesmaximal, complemented
7#19145541C212yesmaximal, complemented
8#19145369C212yesmaximal, complemented
9#19145367C211yesmaximal, characteristic, complemented
10#19144631C212yesmaximal, complemented
11C2×#14583057C211yesmaximal, characteristic, complemented
12C2×#14583054C211yesmaximal, characteristic, complemented
13#451×D43C212yesmaximal, complemented
14#19143617C211yesmaximal, characteristic
15C43×#3189C211yesmaximal, characteristic, complemented
16C23×Dic86C2211yescharacteristic
17C22×Q8×D43C2211yescharacteristic
18C22×Dic172C2212yescomplemented
19C22×#10621885C2212yescomplemented
20C2×Q16×D43C2214yescomplemented
21#14583607C2212yes—
22#14583604—22no—
23#14583604C2212yes—
24#14583603—22no—
25Q8×C22⋊D43C2212yes—
26#14583562—22no—
27#14583562—22no—
28#14583562C2214yes—
29#14583562C2214yes—
30#14583562C2212yes—
31#14583528—21no—
32#14583525—21no—
33#14583524—21no—
34#14583451C2212yes—
35C2×#13063324—21no—
36C2×#13063323C2211yescharacteristic
37C2×#13063305C2211yescharacteristic
38C2×#13063304C2211yescharacteristic
39C2×#13063303—21no—
40C2×#13063302—21no—
41C22⋊Q8×D43C2212yes—
42#14583372—21no—
43C2×#13063290C2211yescharacteristic
44C2×C4×C22⋊D43C2211yescharacteristic
45C2×(C22⋊D43)⋊C4—21no—
46#14583277C2214yescomplemented
47#14583248C2214yescomplemented
48#14583236C2214yescomplemented
49#14583234C2212yes—
50#14583232C2212yescomplemented
51#14583193C2214yescomplemented
52#14583141C2214yescomplemented
53#14583139C2214yescomplemented
54#14583138C2214yescomplemented
55#14583108C2214yescomplemented
56#14583108C2214yescomplemented
57#14583107C2214yescomplemented
58#14583057C2212yes—
59#14583057C2212yes—
60#14583057C2214yescomplemented
61#14583056C2214yescomplemented
62#14583056C2214yescomplemented
63#14583055C2212yes—
64#14583054C2212yes—
65#14583054C2212yes—
66#14583054C2212yescomplemented
67#14583054C2214yescomplemented
68#14583053C2214yescomplemented
69#14582993C2214yescomplemented
70#14582991C2214yescomplemented
71C8×C22⋊D43C2214yes—
72(C22⋊D43)⋊C8C2214yes—
73#14582949C2212yes—
74C2×#13063250C2212yescomplemented
75C2×#13063248C2212yescomplemented
76#103×D43C2214yescomplemented
77C2×C22⋊(C43⋊C8)C2211yescharacteristic
78C22⋊C8×D43C2212yes—
79C2×C22⋊Q8×C43C2211yescharacteristic
80C2×C22⋊Q8×C43C2211yescharacteristic
81C43×#484C2212yes—
82C43×#484C2212yescomplemented
83C43×#467C2214yescomplemented
84C43×#451C2212yes—
85C43×#451C2212yescomplemented
86C2×C22⋊C8×C43C2211yescharacteristic
87C22×Dic86—21no—
88C22×Dic86—21no—
89C22×Dic86—21no—
90C22×Dic86—21no—
91C22×Dic86—44no—
92C22×Dic86C2311yescharacteristic
93C22×Dic86C2312yes—
94C22×Dic86C2312yes—
95C22×Dic86C2311yescharacteristic
96C22×Dic86C2311yescharacteristic
97C2×Q8×D43—22no—
98C2×Q8×D43—44no—
99C2×Q8×D43C2314yes—
100C2×Q8×D43C2312yes—
101C22×C22⋊D43D411yescharacteristic
102C23×Dic43—21no—
103C22×C4×D43—21no—
104C22×C4×D43C2311yescharacteristic
105C2×Dic172—44no—
106C2×Dic172C2314yes—
107C2×Dic172C2314yes—
108C2×#10621885—44no—
109C2×#10621885C2314yes—
110C2×#10621885C2314yes—
111C2×#10621885C2314yes—
112Q16×D43—48no—
113C22×C43⋊C8C2312yes—
114C2×C8×D43C2314yes—
115#13063324—24no—
116#13063324—24no—
117#13063324—22no—
118#13063324C2312yes—
119#13063323—22no—
120#13063323—22no—
121#13063323C2314yes—
122#13063323C2312yes—
123#13063315—22no—
124#13063315—22no—
125#13063315—22no—
126#13063305—22no—
127#13063305—22no—
128#13063305C2314yes—
129#13063305C2312yes—
130#13063304—21no—
131#13063304—21no—
132#13063304—22no—
133#13063304—22no—
134#13063304C2312yes—
135#13063304C2312yes—
136#13063303—22no—
137#13063303—24no—
138#13063303—24no—
139#13063303—22no—
140#13063303—22no—
141#13063302—22no—
142#13063302—22no—
143#13063302—24no—
144#13063302—24no—
145#13063302—22no—
146#13063302—22no—
147#13063301—22no—
148#13063301C2312yes—
149Q8×Dic43C2312yes—
150#13063290—22no—
151#13063290—22no—
152#13063290C2314yes—
153#13063290C2312yes—
154C4×C22⋊D43—22no—
155C4×C22⋊D43—22no—
156C4×C22⋊D43D412yes—
157C4×C22⋊D43D412yes—
158C4×C22⋊D43C2312yes—
159C4×C22⋊D43C2312yes—
160(C22⋊D43)⋊C4—24no—
161(C22⋊D43)⋊C4—24no—
162(C22⋊D43)⋊C4—22no—
163(C22⋊D43)⋊C4—22no—
164#13063281—22no—
165C2×C4⋊Dic43—21no—
166C2×C4⋊Dic43C2311yescharacteristic
167C2×Dic43⋊C4—21no—
168C2×Dic43⋊C4—21no—
169C2×Dic43⋊C4—21no—
170C2×Dic43⋊C4—21no—
171C2×Dic43⋊C4D411yescharacteristic
172C4⋊C4×D43—22no—
173C4⋊C4×D43C2312yes—
174C2×C22⋊Dic43—21no—
175C2×C22⋊Dic43D411yescharacteristic
176C2×(C2×D43)⋊C4—21no—
177C2×(C2×D43)⋊C4D411yescharacteristic
178C22⋊C4×D43—22no—
179C2×C4×Dic43—21no—
180C2×C4×Dic43C2311yescharacteristic
181#13063258C2314yes—
182Dic43⋊C8C2314yes—
183#13063250C2314yes—
184#13063250C2314yes—
185#13063249C2314yes—
186#13063248C2314yes—
187#13063248C2314yes—
188#13063248C2314yes—
189C22⋊(C43⋊C8)C2312yes—
190C22⋊(C43⋊C8)C2312yes—
191(C2×D43)⋊C8C2314yes—
192C8×Dic43C2314yes—
193C22×Q8×C43C2311yescharacteristic
194C22×Q8×C43C2311yescharacteristic
195C23×C4×C43C2311yescharacteristic
196C2×Q16×C43C2314yes—
197C22×C8×C43C2312yes—
198C22⋊Q8×C43—21no—
199C22⋊Q8×C43—21no—
200C22⋊Q8×C43—21no—
201C22⋊Q8×C43—21no—
202C22⋊Q8×C43C2312yes—
203C22⋊Q8×C43C2312yes—
204C22⋊Q8×C43C2312yes—
205C22⋊Q8×C43C2312yes—
206C2×C4⋊C4×C43—21no—
207C2×C4⋊C4×C43—21no—
208C2×C4⋊C4×C43C2311yescharacteristic
209C2×C4⋊C4×C43C2311yescharacteristic
210C2×C22⋊C4×C43—21no—
211C2×C22⋊C4×C43—21no—
212#107×C43C2314yes—
213#103×C43C2314yes—
214#103×C43C2314yes—
215C22⋊C8×C43C2312yes—
216C22⋊C8×C43C2312yes—
217C24×C43C2×D411yescharacteristic
218C23×D43C2×D411yescharacteristic
219C2×Q8×C43—21no—
220C2×Q8×C43—21no—
221C2×Q8×C43—42no—
222C2×Q8×C43—42no—
223C2×Q8×C43C2412yes—
224C2×Q8×C43C2412yes—
225C22×C4×C43—21no—
226C22×C4×C43—21no—
227C22×C4×C43—21no—
228C22×C4×C43—21no—
229C22×C4×C43—42no—
230C22×C4×C43C2×D411yescharacteristic
231C22×C4×C43C2×D411yescharacteristic
232C22×C4×C43C2×D411yescharacteristic
233C22×C4×C43C2411yescharacteristic
234C22×C4×C43C2411yescharacteristic
235C22×C4×C43C2411yescharacteristic
236C2×C22⋊D43Q1618yescomplemented
237C2×C22⋊D43C2×D412yes—
238C2×C22⋊D43C2×D412yes—
239C22×Dic43—21no—
240C22×Dic43—21no—
241C22×Dic43—22no—
242C22×Dic43—22no—
243C22×Dic43—21no—
244C22×Dic43—21no—
245C22×Dic43—44no—
246C22×Dic43C2×D411yescharacteristic
247C22×Dic43C2×D411yescharacteristic
248C22×Dic43C2×D411yescharacteristic
249Q8×D43—28no—
250Q8×D43—44no—
251Q8×D43—48no—
252Q8×D43—44no—
253C2×C4×D43—24no—
254C2×C4×D43—22no—
255C2×C4×D43—22no—
256C2×C4×D43—42no—
257C2×C4×D43—44no—
258C2×C4×D43C2×D412yes—
259C2×C4×D43C2412yes—
260C2×Dic86—21no—
261C2×Dic86—24no—
262C2×Dic86—24no—
263C2×Dic86—24no—
264C2×Dic86—22no—
265C2×Dic86—22no—
266C2×Dic86—21no—
267C2×Dic86—24no—
268C2×Dic86—21no—
269C2×Dic86—22no—
270C2×Dic86—22no—
271C2×Dic86—42no—
272C2×Dic86—42no—
273C2×Dic86—42no—
274C2×Dic86—42no—
275C2×Dic86—44no—
276C2×Dic86—44no—
277C2×Dic86—44no—
278C2×Dic86—44no—
279C2×Dic86C2412yes—
280C2×Dic86C2412yes—
281C2×Dic86C2412yes—
282Q16×C43—44no—
283C2×C8×C43—42no—
284C2×C8×C43C2414yes—
285C4⋊C4×C43—22no—
286C4⋊C4×C43—22no—
287C4⋊C4×C43—22no—
288C4⋊C4×C43—22no—
289C4⋊C4×C43—21no—
290C4⋊C4×C43—21no—
291C4⋊C4×C43C2412yes—
292C4⋊C4×C43C2412yes—
293C22⋊C4×C43—22no—
294C22⋊C4×C43—22no—
295C22⋊C4×C43—22no—
296C22⋊C4×C43—22no—
297C22⋊Dic43—22no—
298C22⋊Dic43—22no—
299C22⋊Dic43C2×D412yes—
300C22⋊Dic43C2×D412yes—
301#10621885—28no—
302#10621885—44no—
303#10621885—44no—
304(C2×D43)⋊C4—22no—
305(C2×D43)⋊C4—22no—
306(C2×D43)⋊C4—24no—
307(C2×D43)⋊C4C2×D412yes—
308(C2×D43)⋊C4C2×D412yes—
309C4⋊Dic43—21no—
310C4⋊Dic43—22no—
311C4⋊Dic43—24no—
312C4⋊Dic43—22no—
313C4⋊Dic43C2412yes—
314Dic43⋊C4—22no—
315Dic43⋊C4—22no—
316Dic43⋊C4—22no—
317Dic43⋊C4—22no—
318Dic43⋊C4—24no—
319Dic43⋊C4—24no—
320Dic43⋊C4—24no—
321Dic43⋊C4—22no—
322Dic43⋊C4—22no—
323Dic43⋊C4—22no—
324Dic43⋊C4—22no—
325Dic43⋊C4C2×D412yes—
326Dic43⋊C4C2×D412yes—
327C4×Dic43—24no—
328C4×Dic43—22no—
329C4×Dic43—22no—
330C4×Dic43C2×D412yes—
331C4×Dic43C2412yes—
332C2×C43⋊C8—42no—
333C2×C43⋊C8C2414yes—
334Dic172—28no—
335Dic172—44no—
336C8×D43—44no—
337C23×C43—41no—
338C23×C43—41no—
339C23×C43C2×Q1614yescomplemented
340C23×C43C22×D411yescharacteristic
341C23×C43C22×D411yescharacteristic
342C23×C43C22×D411yescharacteristic
343C22×D43—41no—
344C22×D43—41no—
345C22×D43C2×Q1614yescomplemented
346C22×D43C22×D412yes—
347Q8×C43—24no—
348Q8×C43—24no—
349Q8×C43—42no—
350Q8×C43—81no—
351C2×C4×C43—22no—
352C2×C4×C43—22no—
353C2×C4×C43—22no—
354C2×C4×C43—22no—
355C2×C4×C43—22no—
356C2×C4×C43—22no—
357C2×C4×C43—22no—
358C2×C4×C43—41no—
359C2×C4×C43—41no—
360C2×C4×C43—41no—
361C2×C4×C43—42no—
362C2×C4×C43—42no—
363C2×C4×C43—81no—
364C2×C4×C43—81no—
365C2×C4×C43C22×D411yescharacteristic
366C2×C4×C43C22×D411yescharacteristic
367C2×C4×C43C22×D411yescharacteristic
368C2×C4×C43C2511yescharacteristic
369C22⋊D43C2×Q1618yescomplemented
370C22⋊D43C2×Q1618yescomplemented
371C2×Dic43—24no—
372C2×Dic43—22no—
373C2×Dic43—22no—
374C2×Dic43—22no—
375C2×Dic43—22no—
376C2×Dic43—41no—
377C2×Dic43—41no—
378C2×Dic43—44no—
379C2×Dic43—44no—
380C2×Dic43—42no—
381C2×Dic43—81no—
382C2×Dic43—81no—
383C2×Dic43C2×Q1614yescomplemented
384C2×Dic43C22×D412yes—
385C2×Dic43C22×D412yes—
386C2×Dic43C22×D412yes—
387C4×D43—24no—
388C4×D43—42no—
389C4×D43—48no—
390C4×D43—82no—
391C4×D43—82no—
392Dic86—24no—
393Dic86—22no—
394Dic86—24no—
395Dic86—22no—
396Dic86—22no—
397Dic86—48no—
398Dic86—44no—
399Dic86—44no—
400Dic86—42no—
401Dic86—82no—
402Dic86—82no—
403Dic86—81no—
404Dic86H(5,𝔽2)14yes—
405C8×C43—24no—
406C43⋊C8—24no—
407#61563—431nomaximal, Sylow
408C22×C43—21no—
409C22×C43—21no—
410C22×C43—21no—
411C22×C43—21no—
412C22×C43—21no—
413C22×C43—21no—
414C22×C43—44no—
415C22×C43C22×Q1612yes—
416C22×C43C22×Q1612yes—
417C22×C43C22×Q1612yes—
418C22×C43C23×D411yescharacteristic
419C2×D43—22no—
420C2×D43—22no—
421C2×D43—44no—
422C2×D43C22×Q1614yes—
423C4×C43—21no—
424C4×C43—21no—
425C4×C43—21no—
426C4×C43—42no—
427C4×C43—42no—
428C4×C43—42no—
429C4×C43—42no—
430C4×C43C2×H(5,𝔽2)12yes—
431Dic43—22no—
432Dic43—24no—
433Dic43—22no—
434Dic43—42no—
435Dic43—42no—
436Dic43—42no—
437Dic43C22×Q1614yes—
438#3501—431no—
439C2×D4×Q8—431no—
440#3299—434no—
441#3299—434no—
442D4×Q16—434no—
443D4×Q16—434no—
444#3209—432no—
445#3189—432no—
446#3189—431no—
447#3189D4311yescharacteristic, complemented
448#3104—432no—
449C2×#451—432no—
450C2×#451—431no—
451C2×#451—431no—
452#2972—431no—
453C2×C43—22no—
454C2×C43—22no—
455C2×C43—22no—
456C2×C43#348411yescharacteristic
457C2×C43C23×Q1611yescharacteristic
458C2×C43#358611yescharacteristic
459D43—24no—
460C23×Q8—431no—
461C23×Q8—431no—
462C22×Q16—432no—
463C22×Q16—434no—
464C22×Q16—432no—
465#554—432no—
466#554—432no—
467#554—862no—
468#554—862no—
469D4×Q8—432no—
470D4×Q8—434no—
471D4×Q8—434no—
472D4×Q8—432no—
473D4×Q8—862no—
474D4×Q8—862no—
475#544—861no—
476#543—861no—
477#543—861no—
478#533—432no—
479C2×C4⋊Q8—431no—
480C2×C4⋊Q8—861no—
481C2×C22⋊Q8—431no—
482C2×C22⋊Q8—432no—
483C2×C22⋊Q8—431no—
484C2×C22⋊Q8—861no—
485C2×C22⋊Q8—861no—
486C2×C22⋊Q8C2×D4311yescharacteristic
487C2×C22⋊Q8C2×D4311yescharacteristic
488#518—861no—
489C2×C4×Q8—431no—
490C2×C4×D4—431no—
491C2×C4×D4—861no—
492#494—434no—
493#487—434no—
494#484—432no—
495#484—432no—
496#484—434no—
497#484C2×D4312yes—
498#484C2×D4312yescomplemented
499#477—434no—
500#467—434no—
501#467—434no—
502#467—434no—
503#467C2×D4314yescomplemented
504#462—434no—
505#462—434no—
506#462—434no—
507#451—432no—
508#451—434no—
509#451—432no—
510#451—432no—
511#451—432no—
512#451—434no—
513#451—434no—
514#451—434no—
515#451—432no—
516#451—432no—
517#451—434no—
518#451C2×D4312yes—
519#451C2×D4312yescomplemented
520C4×Q16—434no—
521C4×Q16—434no—
522C8×D4—434no—
523C8×D4—434no—
524#431—432no—
525C2×#103—432no—
526C2×#103—432no—
527C2×#103—434no—
528C2×C22⋊C8—431no—
529C2×C22⋊C8—432no—
530C2×C22⋊C8C2×D4311yescharacteristic
531C43#6156311yescharacteristic, complemented, Sylow
532C22×Q8—434no—
533C22×Q8—432no—
534C22×Q8—431no—
535C22×Q8—432no—
536C22×Q8—432no—
537C22×Q8—431no—
538C22×Q8—431no—
539C22×Q8—861no—
540C22×Q8—862no—
541C22×Q8—861no—
542C22×Q8—861no—
543C22×Q8—861no—
544C22×Q8—1724no—
545C22×Q8—1724no—
546C22×Q8C22×D4311yescharacteristic
547C22×Q8C22×D4311yescharacteristic
548C22×D4—431no—
549C23×C4—431no—
550C23×C4—861no—
551C23×C4—861no—
552C23×C4C22×D4311yescharacteristic
553C2×Q16—434no—
554C2×Q16—434no—
555C2×Q16—434no—
556C2×Q16—434no—
557C2×Q16—434no—
558C2×Q16—1724no—
559C2×Q16—1728no—
560C2×Q16—1724no—
561C2×Q16C22×D4314yes—
562C22×C8—432no—
563C22×C8—434no—
564C22×C8C22×D4312yes—
565C4⋊Q8—432no—
566C4⋊Q8—434no—
567C4⋊Q8—432no—
568C4⋊Q8—862no—
569C4⋊Q8—864no—
570C4⋊Q8—864no—
571C4⋊Q8—862no—
572C4⋊Q8—862no—
573#125—862no—
574#125—862no—
575#125—862no—
576C22⋊Q8—21no—
577C22⋊Q8—21no—
578C22⋊Q8—21no—
579C22⋊Q8—21no—
580C22⋊Q8—432no—
581C22⋊Q8—432no—
582C22⋊Q8—432no—
583C22⋊Q8—434no—
584C22⋊Q8—432no—
585C22⋊Q8—864no—
586C22⋊Q8—864no—
587C22⋊Q8—862no—
588C22⋊Q8—862no—
589C22⋊Q8—862no—
590C22⋊Q8—862no—
591C22⋊Q8—864no—
592C22⋊Q8—864no—
593C22⋊Q8—862no—
594C22⋊Q8—862no—
595C22⋊Q8—862no—
596C22⋊Q8—862no—
597C22⋊Q8—862no—
598C22⋊Q8—862no—
599C22⋊Q8—862no—
600C22⋊Q8—862no—
601C22⋊Q8—861no—
602C22⋊Q8—861no—
603C22⋊Q8C22×D4312yes—
604C22⋊Q8C22×D4312yes—
605C22⋊Q8C22×D4312yes—
606C22⋊Q8C22×D4312yes—
607C4×Q8—432no—
608C4×Q8—434no—
609C4×Q8—432no—
610C4×Q8—862no—
611C4×Q8—862no—
612C4×D4—432no—
613C4×D4—432no—
614C4×D4—432no—
615C4×D4—432no—
616C4×D4—864no—
617C4×D4—864no—
618C4×D4—862no—
619C4×D4—862no—
620C4×D4—862no—
621C4×D4—862no—
622#117—862no—
623C2×C4⋊C4—21no—
624C2×C4⋊C4—21no—
625C2×C4⋊C4—431no—
626C2×C4⋊C4—431no—
627C2×C4⋊C4—432no—
628C2×C4⋊C4—862no—
629C2×C4⋊C4—861no—
630C2×C4⋊C4—861no—
631C2×C4⋊C4—861no—
632C2×C4⋊C4—861no—
633C2×C4⋊C4—861no—
634C2×C4⋊C4C22×D4311yescharacteristic
635C2×C4⋊C4C22×D4311yescharacteristic
636C2×C22⋊C4—21no—
637C2×C22⋊C4—21no—
638C2×C22⋊C4—431no—
639C2×C22⋊C4—431no—
640C2×C22⋊C4—862no—
641C2×C22⋊C4—861no—
642C2×C22⋊C4—861no—
643C2×C42—431no—
644C2×C42—861no—
645#107—434no—
646#107C22×D4314yes—
647C4⋊C8—434no—
648#103—434no—
649#103—434no—
650#103—434no—
651#103—434no—
652#103—434no—
653#103—434no—
654#103C22×D4314yes—
655#103C22×D4314yes—
656C22⋊C8—432no—
657C22⋊C8—432no—
658C22⋊C8—434no—
659C22⋊C8C22×D4312yes—
660C22⋊C8C22×D4312yes—
661C4×C8—434no—
662C24—431no—
663C24D4×D4311yescharacteristic
664C2×Q8—21no—
665C2×Q8—21no—
666C2×Q8—42no—
667C2×Q8—42no—
668C2×Q8—432no—
669C2×Q8—432no—
670C2×Q8—432no—
671C2×Q8—862no—
672C2×Q8—862no—
673C2×Q8—864no—
674C2×Q8—864no—
675C2×Q8—864no—
676C2×Q8—864no—
677C2×Q8—861no—
678C2×Q8—861no—
679C2×Q8—862no—
680C2×Q8—862no—
681C2×Q8—861no—
682C2×Q8—868no—
683C2×Q8—1722no—
684C2×Q8—1722no—
685C2×Q8—1722no—
686C2×Q8—1722no—
687C2×Q8—1724no—
688C2×Q8—1724no—
689C2×Q8—1724no—
690C2×Q8—1724no—
691C2×Q8—1724no—
692C2×Q8—1724no—
693C2×Q8—1728no—
694C2×Q8C23×D4312yes—
695C2×Q8C23×D4312yes—
696C2×D4—438no—
697C2×D4—432no—
698C2×D4—432no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—42no—
704C22×C4—431no—
705C22×C4—431no—
706C22×C4—431no—
707C22×C4—432no—
708C22×C4—432no—
709C22×C4—862no—
710C22×C4—862no—
711C22×C4—864no—
712C22×C4—861no—
713C22×C4—861no—
714C22×C4—861no—
715C22×C4—861no—
716C22×C4—862no—
717C22×C4—862no—
718C22×C4—1722no—
719C22×C4—1724no—
720C22×C4—1724no—
721C22×C4D4×D4311yescharacteristic
722C22×C4D4×D4311yescharacteristic
723C22×C4D4×D4311yescharacteristic
724C22×C4C23×D4311yescharacteristic
725C22×C4C23×D4311yescharacteristic
726C22×C4C23×D4311yescharacteristic
727Q16—44no—
728Q16—868no—
729Q16—868no—
730Q16—1724no—
731Q16—1724no—
732Q16—1724no—
733C2×C8—42no—
734C2×C8—434no—
735C2×C8—1724no—
736C2×C8—1722no—
737C2×C8C23×D4314yes—
738C4⋊C4—22no—
739C4⋊C4—22no—
740C4⋊C4—22no—
741C4⋊C4—22no—
742C4⋊C4—21no—
743C4⋊C4—21no—
744C4⋊C4—432no—
745C4⋊C4—432no—
746C4⋊C4—432no—
747C4⋊C4—862no—
748C4⋊C4—864no—
749C4⋊C4—864no—
750C4⋊C4—862no—
751C4⋊C4—862no—
752C4⋊C4—864no—
753C4⋊C4—864no—
754C4⋊C4—862no—
755C4⋊C4—862no—
756C4⋊C4—862no—
757C4⋊C4—862no—
758C4⋊C4—862no—
759C4⋊C4—861no—
760C4⋊C4—862no—
761C4⋊C4—862no—
762C4⋊C4C23×D4312yes—
763C4⋊C4C23×D4312yes—
764C22⋊C4—22no—
765C22⋊C4—22no—
766C22⋊C4—22no—
767C22⋊C4—22no—
768C22⋊C4—432no—
769C22⋊C4—432no—
770C22⋊C4—432no—
771C22⋊C4—432no—
772C22⋊C4—864no—
773C22⋊C4—862no—
774C22⋊C4—862no—
775C22⋊C4—862no—
776C22⋊C4—862no—
777C42—432no—
778C42—432no—
779C42—864no—
780C42—862no—
781C42—862no—
782C23—41no—
783C23—41no—
784C23—432no—
785C23—434no—
786C23—1721no—
787C23—1721no—
788C23Q16×D4314yescomplemented
789C23C2×D4×D4311yescharacteristic
790C23C2×D4×D4311yescharacteristic
791C23C2×D4×D4311yescharacteristic
792Q8—24no—
793Q8—24no—
794Q8—42no—
795Q8—81no—
796Q8—434no—
797Q8—864no—
798Q8—862no—
799Q8—864no—
800Q8—862no—
801Q8—862no—
802Q8—3441no—
803Q8—3442no—
804Q8—3442no—
805Q8—1724no—
806Q8—1724no—
807Q8—1722no—
808Q8—1728no—
809D4—438no—
810D4—438no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—81no—
824C2×C4—81no—
825C2×C4—434no—
826C2×C4—432no—
827C2×C4—432no—
828C2×C4—432no—
829C2×C4—864no—
830C2×C4—862no—
831C2×C4—864no—
832C2×C4—862no—
833C2×C4—862no—
834C2×C4—862no—
835C2×C4—3442no—
836C2×C4—3442no—
837C2×C4—3441no—
838C2×C4—3441no—
839C2×C4—1722no—
840C2×C4—1728no—
841C2×C4—1721no—
842C2×C4—1721no—
843C2×C4—1724no—
844C2×C4—1724no—
845C2×C4—1722no—
846C2×C4C2×D4×D4311yescharacteristic
847C2×C4C2×D4×D4311yescharacteristic
848C2×C4C2×D4×D4311yescharacteristic
849C2×C4C24×D4311yescharacteristic
850C8—24no—
851C8—864no—
852C22—21no—
853C22—21no—
854C22—21no—
855C22—21no—
856C22—21no—
857C22—21no—
858C22—44no—
859C22—434no—
860C22—862no—
861C22—862no—
862C22—1724no—
863C22C2×Q16×D4312yes—
864C22C2×Q16×D4312yes—
865C22C2×Q16×D4312yes—
866C22C22×D4×D4311yescharacteristic
867C4—21no—
868C4—21no—
869C4—21no—
870C4—42no—
871C4—42no—
872C4—42no—
873C4—42no—
874C4—434no—
875C4—862no—
876C4—862no—
877C4—864no—
878C4—1722no—
879C4—1722no—
880C4—1722no—
881C4H(5,𝔽2)×D4312yes—
882C2—22no—
883C2—22no—
884C2—22no—
885C2—864no—
886C2#1914822711yescharacteristic
887C2C22×Q16×D4311yescharacteristic
888C2#1914937911yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3189C2
socleC22×C43C23×D4
prime radicalC22×C22⋊D43D4
hypercenter#3189D43
hypocenterC43#61563
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3189

Complements

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

NH ≅ G/Ntype
3. #19146469C2semidirect
4. #19146466C2semidirect
5. #19146344C2semidirect
6. #19146340C2semidirect
7. #19145541C2semidirect
8. #19145369C2semidirect
9. #19145367C2semidirect
10. #19144631C2semidirect
11. C2×#14583057C2semidirect
12. C2×#14583054C2semidirect
13. #451×D43C2semidirect
15. C43×#3189C2semidirect
18. C22×Dic172C22semidirect
19. C22×#10621885C22semidirect
20. C2×Q16×D43C22semidirect
46. #14583277C22semidirect
47. #14583248C22semidirect
48. #14583236C22semidirect
50. #14583232C22semidirect
51. #14583193C22semidirect
52. #14583141C22semidirect
53. #14583139C22semidirect
54. #14583138C22semidirect
55. #14583108C22semidirect
56. #14583108C22semidirect
57. #14583107C22semidirect
60. #14583057C22semidirect
61. #14583056C22semidirect
62. #14583056C22semidirect
66. #14583054C22semidirect
67. #14583054C22semidirect
68. #14583053C22semidirect
69. #14582993C22semidirect
70. #14582991C22semidirect
74. C2×#13063250C22semidirect
75. C2×#13063248C22semidirect
76. #103×D43C22semidirect
82. C43×#484C22semidirect
83. C43×#467C22semidirect
85. C43×#451C22semidirect
236. C2×C22⋊D43Q16semidirect
339. C23×C43C2×Q16semidirect
345. C22×D43C2×Q16semidirect
369. C22⋊D43C2×Q16semidirect
370. C22⋊D43C2×Q16semidirect
383. C2×Dic43C2×Q16semidirect
447. #3189D43semidirect
498. #484C2×D43semidirect
503. #467C2×D43semidirect
519. #451C2×D43semidirect
531. C43#61563semidirect
788. C23Q16×D43semidirect

Maximal subgroups

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

subgroupindex
#191483912
C2×#145835622
#191464692
#191464662
#191463442
#191463402
#191455412
#191453692
#191453672
#191446312
C2×#145830572
C2×#145830542
#451×D432
#191436172
C43×#31892
#6156343