Finite Group Databasebeta

← #25981320

Subgroups — #25981320

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×Q8×C22⋊D43C211yesmaximal, characteristic
3#19146467C214yesmaximal, complemented
4#19146464C214yesmaximal, complemented
5Q16×C22⋊D43C214yesmaximal, complemented
6#19146340C214yesmaximal, complemented
7#19145541C212yesmaximal, complemented
8#19145370C211yesmaximal, characteristic, complemented
9#19145368C212yesmaximal, complemented
10#19145367C211yesmaximal, characteristic, complemented
11#19144629C212yesmaximal, complemented
12C2×#14583055C211yesmaximal, characteristic, complemented
13#451×D43C212yesmaximal, complemented
14#19143617C211yesmaximal, characteristic
15C2×C43×#451C211yesmaximal, characteristic, complemented
16C22×Q8×D43C2211yescharacteristic
17C22×#10621885C2212yescomplemented
18C2×Q16×D43C2214yescomplemented
19#14583607C2212yes—
20#14583604—22no—
21#14583604C2212yes—
22#14583603—22no—
23Q8×C22⋊D43—22no—
24Q8×C22⋊D43—22no—
25Q8×C22⋊D43C2214yes—
26Q8×C22⋊D43C2214yes—
27Q8×C22⋊D43C2212yes—
28#14583562C2212yes—
29#14583528—21no—
30#14583525—21no—
31#14583524—21no—
32#14583451C2212yes—
33C2×#13063323—21no—
34C2×#13063323C2211yescharacteristic
35C2×#13063304—21no—
36C2×#13063304C2211yescharacteristic
37C2×#13063304C2211yescharacteristic
38C2×#13063301—21no—
39C2×#13063301C2211yescharacteristic
40C22⋊Q8×D43C2212yes—
41#14583372—21no—
42C2×Q8×Dic43C2211yescharacteristic
43C2×C4×C22⋊D43—21no—
44C2×C4×C22⋊D43C2211yescharacteristic
45#14583277C2214yescomplemented
46#14583248C2214yescomplemented
47#14583235C2212yes—
48#14583235C2212yescomplemented
49#14583234C2212yescomplemented
50#14583233C2214yescomplemented
51#14583232C2212yes—
52#14583192C2214yescomplemented
53#14583140C2214yescomplemented
54#14583139C2214yescomplemented
55#14583138C2214yescomplemented
56#14583137C2214yescomplemented
57#14583108C2214yescomplemented
58#14583107C2214yescomplemented
59#14583107C2214yescomplemented
60#14583057C2212yes—
61#14583057C2212yescomplemented
62#14583056C2214yescomplemented
63#14583055C2212yes—
64#14583055C2212yes—
65#14583055C2212yescomplemented
66#14583055C2214yescomplemented
67#14583054C2212yes—
68#14583053C2214yescomplemented
69#14583053C2214yescomplemented
70Q16×Dic43C2214yescomplemented
71#14582991C2214yescomplemented
72C8×C22⋊D43C2214yes—
73(C22⋊D43)⋊C8C2214yes—
74#14582949C2212yes—
75C2×#13063249C2212yescomplemented
76#103×D43C2214yescomplemented
77C2×C22⋊(C43⋊C8)C2211yescharacteristic
78C22⋊C8×D43C2212yes—
79C23×Q8×C43C2211yescharacteristic
80C22×Q16×C43C2212yescomplemented
81C2×C22⋊Q8×C43C2211yescharacteristic
82C43×#451C2212yes—
83C43×#451C2212yes—
84C43×#451C2214yescomplemented
85C2×#103×C43C2212yescomplemented
86C2×C22⋊C8×C43C2211yescharacteristic
87C22×Dic86—21no—
88C22×Dic86C2311yescharacteristic
89C22×Dic86C2311yescharacteristic
90C2×Q8×D43—22no—
91C2×Q8×D43—44no—
92C2×Q8×D43C2314yes—
93C2×Q8×D43C2312yes—
94C22×C22⋊D43D411yescharacteristic
95C22×C4×D43—21no—
96C22×C4×D43C2311yescharacteristic
97C2×Dic172C2314yes—
98C2×#10621885—44no—
99C2×#10621885C2314yes—
100C2×#10621885C2314yes—
101C2×#10621885C2314yes—
102Q16×D43—48no—
103C22×C43⋊C8C2312yes—
104C2×C8×D43C2314yes—
105#13063324—22no—
106#13063324C2312yes—
107#13063323—24no—
108#13063323—24no—
109#13063323—22no—
110#13063323—22no—
111#13063323C2312yes—
112#13063323C2314yes—
113#13063315—22no—
114#13063315—22no—
115#13063315—22no—
116#13063305—22no—
117#13063305C2312yes—
118#13063304—21no—
119#13063304—21no—
120#13063304—21no—
121#13063304—21no—
122#13063304—24no—
123#13063304—24no—
124#13063304—22no—
125#13063304—22no—
126#13063304C2312yes—
127#13063304C2312yes—
128#13063304C2312yes—
129#13063304C2312yes—
130#13063303—22no—
131#13063303—22no—
132#13063303—22no—
133#13063302—22no—
134#13063302—22no—
135#13063302—22no—
136#13063302—22no—
137#13063301—22no—
138#13063301—24no—
139#13063301—24no—
140#13063301—22no—
141#13063301C2314yes—
142#13063301C2312yes—
143Q8×Dic43—22no—
144Q8×Dic43C2314yes—
145Q8×Dic43C2312yes—
146#13063290—22no—
147#13063290C2312yes—
148C4×C22⋊D43—24no—
149C4×C22⋊D43—24no—
150C4×C22⋊D43—22no—
151C4×C22⋊D43—22no—
152C4×C22⋊D43D412yes—
153C4×C22⋊D43D412yes—
154C4×C22⋊D43C2312yes—
155C4×C22⋊D43C2312yes—
156(C22⋊D43)⋊C4—22no—
157(C22⋊D43)⋊C4—22no—
158#13063281—22no—
159C2×C4⋊Dic43—21no—
160C2×C4⋊Dic43C2311yescharacteristic
161C2×C4⋊Dic43C2311yescharacteristic
162C2×Dic43⋊C4—21no—
163C2×Dic43⋊C4—21no—
164C2×Dic43⋊C4—21no—
165C2×Dic43⋊C4—21no—
166C2×Dic43⋊C4—21no—
167C2×Dic43⋊C4D411yescharacteristic
168C4⋊C4×D43—22no—
169C4⋊C4×D43C2312yes—
170C2×C22⋊Dic43—21no—
171C2×C22⋊Dic43—21no—
172C2×C22⋊Dic43D411yescharacteristic
173C2×(C2×D43)⋊C4—21no—
174C2×(C2×D43)⋊C4D411yescharacteristic
175C22⋊C4×D43—22no—
176C2×C4×Dic43—21no—
177C2×C4×Dic43C2311yescharacteristic
178#13063259C2314yes—
179#13063258C2314yes—
180Dic43⋊C8C2314yes—
181#13063250C2314yes—
182#13063250C2314yes—
183#13063249C2314yes—
184#13063249C2314yes—
185#13063249C2314yes—
186#13063248C2314yes—
187C22⋊(C43⋊C8)C2312yes—
188C22⋊(C43⋊C8)C2312yes—
189(C2×D43)⋊C8C2314yes—
190C8×Dic43C2314yes—
191C22×Q8×C43—21no—
192C22×Q8×C43—21no—
193C22×Q8×C43—21no—
194C22×Q8×C43—44no—
195C22×Q8×C43C2311yescharacteristic
196C22×Q8×C43C2312yes—
197C22×Q8×C43C2312yes—
198C22×Q8×C43C2311yescharacteristic
199C22×Q8×C43C2311yescharacteristic
200C23×C4×C43—21no—
201C23×C4×C43C2311yescharacteristic
202C2×Q16×C43—44no—
203C2×Q16×C43C2314yes—
204C2×Q16×C43C2314yes—
205C22×C8×C43C2312yes—
206C22⋊Q8×C43—21no—
207C22⋊Q8×C43—21no—
208C22⋊Q8×C43C2312yes—
209C22⋊Q8×C43C2312yes—
210C2×C4⋊C4×C43—21no—
211C2×C4⋊C4×C43C2311yescharacteristic
212C2×C22⋊C4×C43—21no—
213#103×C43C2314yes—
214#103×C43C2314yes—
215C22⋊C8×C43C2312yes—
216C22⋊C8×C43C2312yes—
217C24×C43C2×D411yescharacteristic
218C23×D43C2×D411yescharacteristic
219C2×Q8×C43—24no—
220C2×Q8×C43—21no—
221C2×Q8×C43—22no—
222C2×Q8×C43—22no—
223C2×Q8×C43—21no—
224C2×Q8×C43—21no—
225C2×Q8×C43—24no—
226C2×Q8×C43—24no—
227C2×Q8×C43—42no—
228C2×Q8×C43—42no—
229C2×Q8×C43—42no—
230C2×Q8×C43—44no—
231C2×Q8×C43—42no—
232C2×Q8×C43—44no—
233C2×Q8×C43—44no—
234C2×Q8×C43C2412yes—
235C2×Q8×C43C2412yes—
236C2×Q8×C43C2412yes—
237C22×C4×C43—21no—
238C22×C4×C43—21no—
239C22×C4×C43—22no—
240C22×C4×C43—22no—
241C22×C4×C43—21no—
242C22×C4×C43—21no—
243C22×C4×C43—42no—
244C22×C4×C43—44no—
245C22×C4×C43C2×D411yescharacteristic
246C22×C4×C43C2×D411yescharacteristic
247C22×C4×C43C2×D411yescharacteristic
248C22×C4×C43C2411yescharacteristic
249C22×C4×C43C2411yescharacteristic
250C22×C4×C43C2411yescharacteristic
251C2×C22⋊D43Q1618yescomplemented
252C2×C22⋊D43C2×D412yes—
253C2×C22⋊D43C2×D412yes—
254C22×Dic43—21no—
255C22×Dic43—21no—
256C22×Dic43—21no—
257C22×Dic43—21no—
258C22×Dic43C2×D411yescharacteristic
259C22×Dic43C2×D411yescharacteristic
260C22×Dic43C2×D411yescharacteristic
261Q8×D43—28no—
262Q8×D43—44no—
263Q8×D43—44no—
264Q8×D43—48no—
265C2×C4×D43—24no—
266C2×C4×D43—22no—
267C2×C4×D43—22no—
268C2×C4×D43—42no—
269C2×C4×D43—44no—
270C2×C4×D43C2×D412yes—
271C2×C4×D43C2412yes—
272C2×Dic86—21no—
273C2×Dic86—24no—
274C2×Dic86—21no—
275C2×Dic86—22no—
276C2×Dic86—22no—
277C2×Dic86—42no—
278C2×Dic86—42no—
279C2×Dic86—44no—
280C2×Dic86C2412yes—
281C2×Dic86C2412yes—
282Q16×C43—28no—
283Q16×C43—44no—
284C2×C8×C43—42no—
285C2×C8×C43C2414yes—
286C4⋊C4×C43—22no—
287C4⋊C4×C43—22no—
288C4⋊C4×C43—21no—
289C4⋊C4×C43C2412yes—
290C22⋊C4×C43—22no—
291C22⋊C4×C43—22no—
292C22⋊Dic43—22no—
293C22⋊Dic43—22no—
294C22⋊Dic43—22no—
295C22⋊Dic43—22no—
296C22⋊Dic43C2×D412yes—
297C22⋊Dic43C2×D412yes—
298#10621885—28no—
299#10621885—44no—
300#10621885—44no—
301(C2×D43)⋊C4—22no—
302(C2×D43)⋊C4—22no—
303(C2×D43)⋊C4—24no—
304(C2×D43)⋊C4C2×D412yes—
305(C2×D43)⋊C4C2×D412yes—
306C4⋊Dic43—21no—
307C4⋊Dic43—21no—
308C4⋊Dic43—22no—
309C4⋊Dic43—24no—
310C4⋊Dic43—22no—
311C4⋊Dic43C2412yes—
312C4⋊Dic43C2412yes—
313Dic43⋊C4—22no—
314Dic43⋊C4—22no—
315Dic43⋊C4—22no—
316Dic43⋊C4—22no—
317Dic43⋊C4—22no—
318Dic43⋊C4—22no—
319Dic43⋊C4—24no—
320Dic43⋊C4—24no—
321Dic43⋊C4—24no—
322Dic43⋊C4—22no—
323Dic43⋊C4—22no—
324Dic43⋊C4—22no—
325Dic43⋊C4—22no—
326Dic43⋊C4C2×D412yes—
327Dic43⋊C4C2×D412yes—
328C4×Dic43—24no—
329C4×Dic43—22no—
330C4×Dic43—22no—
331C4×Dic43C2×D412yes—
332C4×Dic43C2412yes—
333C2×C43⋊C8—42no—
334C2×C43⋊C8C2414yes—
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—22no—
349Q8×C43—22no—
350Q8×C43—24no—
351Q8×C43—22no—
352Q8×C43—44no—
353Q8×C43—44no—
354Q8×C43—42no—
355Q8×C43—81no—
356Q8×C43H(5,𝔽2)14yes—
357C2×C4×C43—24no—
358C2×C4×C43—22no—
359C2×C4×C43—22no—
360C2×C4×C43—22no—
361C2×C4×C43—22no—
362C2×C4×C43—22no—
363C2×C4×C43—22no—
364C2×C4×C43—22no—
365C2×C4×C43—41no—
366C2×C4×C43—41no—
367C2×C4×C43—41no—
368C2×C4×C43—44no—
369C2×C4×C43—44no—
370C2×C4×C43—42no—
371C2×C4×C43—81no—
372C2×C4×C43—81no—
373C2×C4×C43C22×D411yescharacteristic
374C2×C4×C43C22×D411yescharacteristic
375C2×C4×C43C22×D411yescharacteristic
376C2×C4×C43C2511yescharacteristic
377C22⋊D43C2×Q1618yescomplemented
378C22⋊D43C2×Q1618yescomplemented
379C2×Dic43—22no—
380C2×Dic43—22no—
381C2×Dic43—22no—
382C2×Dic43—22no—
383C2×Dic43—41no—
384C2×Dic43—41no—
385C2×Dic43—42no—
386C2×Dic43—42no—
387C2×Dic43—81no—
388C2×Dic43—81no—
389C2×Dic43C2×Q1614yescomplemented
390C2×Dic43C22×D412yes—
391C2×Dic43C22×D412yes—
392C2×Dic43C22×D412yes—
393C4×D43—24no—
394C4×D43—42no—
395C4×D43—48no—
396C4×D43—82no—
397C4×D43—82no—
398Dic86—24no—
399Dic86—24no—
400Dic86—48no—
401Dic86—42no—
402Dic86—82no—
403Dic86—82no—
404Dic86—81no—
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—24no—
424C4×C43—21no—
425C4×C43—21no—
426C4×C43—21no—
427C4×C43—42no—
428C4×C43—42no—
429C4×C43—42no—
430C4×C43C2×H(5,𝔽2)12yes—
431Dic43—22no—
432Dic43—22no—
433Dic43—42no—
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#3189—431no—
448#3104—432no—
449C2×#451—432no—
450C2×#451—431no—
451C2×#451D4311yescharacteristic, complemented
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×Q8C2×D4311yescharacteristic
462C22×Q16—432no—
463C22×Q16—434no—
464C22×Q16C2×D4312yescomplemented
465#554—432no—
466#554—432no—
467#554—862no—
468#554—862no—
469D4×Q8—434no—
470D4×Q8—434no—
471D4×Q8—432no—
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—431no—
483C2×C22⋊Q8—431no—
484C2×C22⋊Q8—432no—
485C2×C22⋊Q8—861no—
486C2×C22⋊Q8—861no—
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#484—432no—
498#484—432no—
499#477—434no—
500#467—434no—
501#467—434no—
502#467—434no—
503#467—434no—
504#462—434no—
505#462—434no—
506#462—434no—
507#451—432no—
508#451—432no—
509#451—432no—
510#451—434no—
511#451—434no—
512#451—434no—
513#451—432no—
514#451—434no—
515#451—432no—
516#451—432no—
517#451C2×D4312yes—
518#451C2×D4312yes—
519#451C2×D4314yescomplemented
520C4×Q16—434no—
521C4×Q16—434no—
522C8×D4—434no—
523C8×D4—434no—
524#431—432no—
525C2×#103—432no—
526C2×#103—434no—
527C2×#103C2×D4312yescomplemented
528C2×C22⋊C8—431no—
529C2×C22⋊C8—432no—
530C2×C22⋊C8C2×D4311yescharacteristic
531C43#6156311yescharacteristic, complemented, Sylow
532C22×Q8—21no—
533C22×Q8—21no—
534C22×Q8—21no—
535C22×Q8—44no—
536C22×Q8—434no—
537C22×Q8—432no—
538C22×Q8—431no—
539C22×Q8—431no—
540C22×Q8—861no—
541C22×Q8—862no—
542C22×Q8—1724no—
543C22×Q8C22×D4311yescharacteristic
544C22×Q8C22×D4312yes—
545C22×Q8C22×D4312yes—
546C22×Q8C22×D4311yescharacteristic
547C22×Q8C22×D4311yescharacteristic
548C22×D4—431no—
549C23×C4—21no—
550C23×C4—431no—
551C23×C4—861no—
552C23×C4C22×D4311yescharacteristic
553C2×Q16—44no—
554C2×Q16—434no—
555C2×Q16—434no—
556C2×Q16—434no—
557C2×Q16—434no—
558C2×Q16—1728no—
559C2×Q16—1724no—
560C2×Q16C22×D4314yes—
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—862no—
570C4⋊Q8—864no—
571C4⋊Q8—864no—
572C4⋊Q8—862no—
573#125—862no—
574#125—862no—
575#125—862no—
576C22⋊Q8—21no—
577C22⋊Q8—21no—
578C22⋊Q8—434no—
579C22⋊Q8—432no—
580C22⋊Q8—432no—
581C22⋊Q8—432no—
582C22⋊Q8—432no—
583C22⋊Q8—432no—
584C22⋊Q8—432no—
585C22⋊Q8—862no—
586C22⋊Q8—862no—
587C22⋊Q8—862no—
588C22⋊Q8—862no—
589C22⋊Q8—862no—
590C22⋊Q8—862no—
591C22⋊Q8—862no—
592C22⋊Q8—864no—
593C22⋊Q8—864no—
594C22⋊Q8—862no—
595C22⋊Q8—862no—
596C22⋊Q8—864no—
597C22⋊Q8—864no—
598C22⋊Q8—862no—
599C22⋊Q8—862no—
600C22⋊Q8—862no—
601C22⋊Q8—861no—
602C22⋊Q8—861no—
603C22⋊Q8—861no—
604C22⋊Q8—861no—
605C22⋊Q8C22×D4312yes—
606C22⋊Q8C22×D4312yes—
607C4×Q8—434no—
608C4×Q8—432no—
609C4×Q8—432no—
610C4×Q8—862no—
611C4×Q8—862no—
612C4×D4—432no—
613C4×D4—432no—
614C4×D4—432no—
615C4×D4—432no—
616C4×D4—862no—
617C4×D4—862no—
618C4×D4—864no—
619C4×D4—864no—
620C4×D4—862no—
621C4×D4—862no—
622#117—862no—
623C2×C4⋊C4—21no—
624C2×C4⋊C4—431no—
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⋊C4—861no—
635C2×C4⋊C4C22×D4311yescharacteristic
636C2×C22⋊C4—21no—
637C2×C22⋊C4—431no—
638C2×C22⋊C4—431no—
639C2×C22⋊C4—862no—
640C2×C22⋊C4—861no—
641C2×C22⋊C4—861no—
642C2×C22⋊C4—861no—
643C2×C42—431no—
644C2×C42—861no—
645#107—434no—
646#107—434no—
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—24no—
665C2×Q8—21no—
666C2×Q8—22no—
667C2×Q8—22no—
668C2×Q8—21no—
669C2×Q8—21no—
670C2×Q8—24no—
671C2×Q8—24no—
672C2×Q8—42no—
673C2×Q8—42no—
674C2×Q8—42no—
675C2×Q8—44no—
676C2×Q8—42no—
677C2×Q8—44no—
678C2×Q8—44no—
679C2×Q8—432no—
680C2×Q8—432no—
681C2×Q8—862no—
682C2×Q8—862no—
683C2×Q8—864no—
684C2×Q8—861no—
685C2×Q8—861no—
686C2×Q8—868no—
687C2×Q8—1722no—
688C2×Q8—1722no—
689C2×Q8—1724no—
690C2×Q8—1724no—
691C2×Q8—1724no—
692C2×Q8—1728no—
693C2×Q8C23×D4312yes—
694C2×Q8C23×D4312yes—
695C2×Q8C23×D4312yes—
696C2×D4—438no—
697C2×D4—432no—
698C2×D4—432no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—22no—
702C22×C4—22no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—42no—
706C22×C4—44no—
707C22×C4—431no—
708C22×C4—431no—
709C22×C4—431no—
710C22×C4—432no—
711C22×C4—432no—
712C22×C4—862no—
713C22×C4—862no—
714C22×C4—864no—
715C22×C4—861no—
716C22×C4—861no—
717C22×C4—861no—
718C22×C4—861no—
719C22×C4—1722no—
720C22×C4—1724no—
721C22×C4D4×D4311yescharacteristic
722C22×C4D4×D4311yescharacteristic
723C22×C4D4×D4311yescharacteristic
724C22×C4C23×D4311yescharacteristic
725C22×C4C23×D4311yescharacteristic
726C22×C4C23×D4311yescharacteristic
727Q16—28no—
728Q16—44no—
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—21no—
741C4⋊C4—432no—
742C4⋊C4—432no—
743C4⋊C4—432no—
744C4⋊C4—432no—
745C4⋊C4—862no—
746C4⋊C4—864no—
747C4⋊C4—864no—
748C4⋊C4—862no—
749C4⋊C4—862no—
750C4⋊C4—864no—
751C4⋊C4—864no—
752C4⋊C4—862no—
753C4⋊C4—862no—
754C4⋊C4—862no—
755C4⋊C4—862no—
756C4⋊C4—862no—
757C4⋊C4—861no—
758C4⋊C4—861no—
759C4⋊C4—862no—
760C4⋊C4—862no—
761C4⋊C4—862no—
762C4⋊C4—862no—
763C4⋊C4C23×D4312yes—
764C22⋊C4—22no—
765C22⋊C4—22no—
766C22⋊C4—432no—
767C22⋊C4—432no—
768C22⋊C4—432no—
769C22⋊C4—432no—
770C22⋊C4—862no—
771C22⋊C4—862no—
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—22no—
794Q8—24no—
795Q8—22no—
796Q8—22no—
797Q8—44no—
798Q8—44no—
799Q8—42no—
800Q8—81no—
801Q8—864no—
802Q8—864no—
803Q8—3441no—
804Q8—3442no—
805Q8—3442no—
806Q8—1728no—
807Q8—1722no—
808Q8#1306337014yes—
809D4—438no—
810D4—438no—
811C2×C4—24no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—44no—
823C2×C4—44no—
824C2×C4—42no—
825C2×C4—81no—
826C2×C4—81no—
827C2×C4—434no—
828C2×C4—432no—
829C2×C4—432no—
830C2×C4—432no—
831C2×C4—864no—
832C2×C4—862no—
833C2×C4—862no—
834C2×C4—862no—
835C2×C4—862no—
836C2×C4—3442no—
837C2×C4—3442no—
838C2×C4—3441no—
839C2×C4—3441no—
840C2×C4—1722no—
841C2×C4—1728no—
842C2×C4—1721no—
843C2×C4—1721no—
844C2×C4—1722no—
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—24no—
868C4—21no—
869C4—21no—
870C4—21no—
871C4—42no—
872C4—42no—
873C4—42no—
874C4—434no—
875C4—862no—
876C4—862no—
877C4—1722no—
878C4—1722no—
879C4—1722no—
880C4—1722no—
881C4C2×#1306337012yes—
882C2—22no—
883C2—22no—
884C2—22no—
885C2—864no—
886C2#1914822411yescharacteristic
887C2C22×Q16×D4311yescharacteristic
888C2#1914937811yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#451C2
socleC22×C43C23×D4
prime radicalC22×C22⋊D43D4
hypercenterC2×#451D43
hypocenterC43#61563
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#451

Complements

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

NH ≅ G/Ntype
3. #19146467C2semidirect
4. #19146464C2semidirect
5. Q16×C22⋊D43C2semidirect
6. #19146340C2semidirect
7. #19145541C2semidirect
8. #19145370C2semidirect
9. #19145368C2semidirect
10. #19145367C2semidirect
11. #19144629C2semidirect
12. C2×#14583055C2semidirect
13. #451×D43C2semidirect
15. C2×C43×#451C2semidirect
17. C22×#10621885C22semidirect
18. C2×Q16×D43C22semidirect
45. #14583277C22semidirect
46. #14583248C22semidirect
48. #14583235C22semidirect
49. #14583234C22semidirect
50. #14583233C22semidirect
52. #14583192C22semidirect
53. #14583140C22semidirect
54. #14583139C22semidirect
55. #14583138C22semidirect
56. #14583137C22semidirect
57. #14583108C22semidirect
58. #14583107C22semidirect
59. #14583107C22semidirect
61. #14583057C22semidirect
62. #14583056C22semidirect
65. #14583055C22semidirect
66. #14583055C22semidirect
68. #14583053C22semidirect
69. #14583053C22semidirect
70. Q16×Dic43C22semidirect
71. #14582991C22semidirect
75. C2×#13063249C22semidirect
76. #103×D43C22semidirect
80. C22×Q16×C43C22semidirect
84. C43×#451C22semidirect
85. C2×#103×C43C22semidirect
251. C2×C22⋊D43Q16semidirect
339. C23×C43C2×Q16semidirect
345. C22×D43C2×Q16semidirect
377. C22⋊D43C2×Q16semidirect
378. C22⋊D43C2×Q16semidirect
389. C2×Dic43C2×Q16semidirect
451. C2×#451D43semidirect
464. C22×Q16C2×D43semidirect
519. #451C2×D43semidirect
527. C2×#103C2×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×Q8×C22⋊D432
#191464672
#191464642
Q16×C22⋊D432
#191463402
#191455412
#191453702
#191453682
#191453672
#191446292
C2×#145830552
#451×D432
#191436172
C2×C43×#4512
#6156343