Finite Group Databasebeta

← #25968916

Subgroups — #25968916

Order 11008.

1756 conjugacy classes of subgroups.

The subgroup lattice has 938 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583455C211yesmaximal, characteristic
2#533×D43C211yesmaximal, characteristic
3#19145810C212yesmaximal, complemented
4#19145804C212yesmaximal, complemented
5#19145803C211yesmaximal, characteristic, complemented
6#19145801C211yesmaximal, characteristic, complemented
7#19145797C211yesmaximal, characteristic, complemented
8#19145753C214yesmaximal, complemented
9#19145744C212yesmaximal, complemented
10#19145737C212yesmaximal, complemented
11#19145140C212yesmaximal, complemented
12#19144974C212yesmaximal, complemented
13#19144540C212yesmaximal
14#19144538C212yesmaximal
15#19144398C214yesmaximal, complemented
16#19143225C211yesmaximal, characteristic
17C43×#3236C211yesmaximal, characteristic, complemented
18#14583456C2211yescharacteristic
19#14583455—21no—
20#14583455—21no—
21#14583455—21no—
22#14583455—21no—
23#14583455—21no—
24#14583455C2212yes—
25#14583455C2212yes—
26#14583455C2212yes—
27#14583455C2212yes—
28#14583454C2211yescharacteristic
29#14583454C2211yescharacteristic
30#14583453—21no—
31#14583453C2212yes—
32#14583452—21no—
33#14583451—21no—
34#14583451C2212yes—
35C2×#13063324C2211yescharacteristic
36C2×#13063324C2211yescharacteristic
37C4⋊Q8×D43C2211yescharacteristic
38C4⋊Q8×D43C2211yescharacteristic
39C2×#13063317C2211yescharacteristic
40#125×D43—21no—
41C2×#13063303—21no—
42C2×#13063303—21no—
43C22⋊Q8×D43—21no—
44C22⋊Q8×D43C2212yes—
45C2×#13063290—21no—
46C2×#13063290—21no—
47C4×Q8×D43—21no—
48C4×Q8×D43C2212yes—
49C2×#13063283C2211yescharacteristic
50C2×#13063283C2211yescharacteristic
51#117×D43—21no—
52C2×C42×D43C2211yescharacteristic
53#14583309C2212yescomplemented
54#14583308C2212yescomplemented
55#14583305C2212yescomplemented
56#14583303C2214yescomplemented
57#14583296C2214yescomplemented
58#14583269C2212yescomplemented
59#14583268C2212yescomplemented
60#14583267C2212yescomplemented
61#14583248C2214yescomplemented
62#14583248C2214yescomplemented
63#14583243C2214yes—
64#14583242C2214yes—
65#14583239C2214yes—
66#14583238C2214yes—
67#14583235C2212yes—
68#14583234C2212yes—
69#14583232C2212yes—
70#14583230C2212yes—
71#14583229C2212yes—
72#14583227C2212yes—
73#14583207C2214yescomplemented
74#14583206C2214yescomplemented
75#14583203C2214yescomplemented
76#14583193C2214yescomplemented
77#14583192C2214yescomplemented
78#14583183C2214yescomplemented
79#14583182C2214yescomplemented
80#14582956C2211yescharacteristic
81#14582954C2212yes—
82#14582951C2212yes—
83#14582949C2212yes—
84#14582940C2214yes—
85#14582938C2214yes—
86#14582921C2212yes—
87#14582906C2214yes—
88#14582906C2214yes—
89#14582861C2212yes—
90#14582851C2212yes—
91C43×#533C2211yescharacteristic
92C2×#125×C43C2211yescharacteristic
93C43×#501C2212yescomplemented
94C43×#491C2212yescomplemented
95C43×#484C2212yes—
96C43×#483C2212yes—
97C43×#479C2214yescomplemented
98C43×#432C2211yescharacteristic
99C22×Dic86—21no—
100C22×Dic86—21no—
101C2×Q8×D43—21no—
102C2×Q8×D43C2312yes—
103C22×C4×D43D411yescharacteristic
104C22×C4×D43D411yescharacteristic
105C22×C4×D43C2311yescharacteristic
106C2×#10621872C2314yes—
107#13063325C2311yescharacteristic
108#13063325C2311yescharacteristic
109#13063324—21no—
110#13063324—21no—
111#13063324—21no—
112#13063324—21no—
113#13063324—21no—
114#13063324—21no—
115#13063324—21no—
116#13063324C2312yes—
117#13063324C2312yes—
118#13063324C2312yes—
119#13063324C2312yes—
120#13063324C2312yes—
121#13063323—21no—
122#13063323C2312yes—
123#13063317—21no—
124#13063317—21no—
125#13063317—21no—
126#13063317C2312yes—
127#13063317C2312yes—
128#13063316—21no—
129#13063316—21no—
130#13063315—22no—
131#13063315—22no—
132#13063305—21no—
133#13063305C2312yes—
134#13063304—21no—
135#13063304C2312yes—
136#13063303—22no—
137#13063303—22no—
138#13063303—22no—
139#13063303—22no—
140#13063303—22no—
141#13063303—22no—
142#13063303—22no—
143#13063303—22no—
144#13063303—22no—
145#13063303—22no—
146#13063302—22no—
147#13063302—22no—
148#13063301—21no—
149#13063301C2312yes—
150Q8×Dic43—21no—
151Q8×Dic43C2312yes—
152C4×Dic86—21no—
153C4×Dic86—22no—
154C4×Dic86—22no—
155C4×Dic86C2312yes—
156#13063290—21no—
157#13063290—22no—
158#13063290—22no—
159#13063290—22no—
160#13063290—22no—
161#13063290—22no—
162#13063290—22no—
163#13063290—22no—
164#13063290—22no—
165#13063290—22no—
166#13063290—22no—
167#13063290C2312yes—
168#13063284—21no—
169#13063283—21no—
170#13063283—21no—
171#13063283—21no—
172#13063283—21no—
173#13063283—21no—
174#13063283—21no—
175#13063283C2312yes—
176#13063283C2312yes—
177#13063283C2312yes—
178#13063283C2312yes—
179#13063282—22no—
180#13063281—22no—
181C2×C4⋊Dic43C2311yescharacteristic
182C2×C4⋊Dic43C2311yescharacteristic
183C2×Dic43⋊C4—21no—
184C2×Dic43⋊C4—21no—
185C2×Dic43⋊C4—21no—
186C2×Dic43⋊C4—21no—
187C4⋊C4×D43—21no—
188C4⋊C4×D43—21no—
189C4⋊C4×D43—21no—
190C4⋊C4×D43—22no—
191C4⋊C4×D43—22no—
192C4⋊C4×D43C2312yes—
193C2×(C2×D43)⋊C4—21no—
194C2×(C2×D43)⋊C4—21no—
195C22⋊C4×D43—22no—
196C2×C4×Dic43—21no—
197C2×C4×Dic43—21no—
198C2×C4×Dic43D411yescharacteristic
199C2×C4×Dic43D411yescharacteristic
200C2×C4×Dic43C2311yescharacteristic
201C42×D43—22no—
202C42×D43D411yescharacteristic
203C42×D43D411yescharacteristic
204C42×D43D411yescharacteristic
205C42×D43D411yescharacteristic
206C42×D43C2311yescharacteristic
207C42×D43C2311yescharacteristic
208C42×D43C2311yescharacteristic
209C42×D43C2311yescharacteristic
210#13063259C2314yes—
211#13063258C2314yes—
212#13063258C2314yes—
213#13063257C2314yes—
214#13063256C2314yes—
215#13063256C2314yes—
216C4⋊(C43⋊C8)C2312yes—
217Dic43⋊C8C2314yes—
218#13063250C2314yes—
219#13063250C2314yes—
220#13063249C2314yes—
221#13063249C2314yes—
222#13063248C2314yes—
223#13063248C2314yes—
224C22⋊(C43⋊C8)C2312yes—
225(C2×D43)⋊C8C2314yes—
226#13063236C2312yes—
227C8×Dic43C2314yes—
228C4⋊Q8×C43C2311yescharacteristic
229C4⋊Q8×C43C2311yescharacteristic
230#125×C43—21no—
231#125×C43—21no—
232#125×C43—21no—
233#125×C43C2312yes—
234#125×C43C2312yes—
235C22⋊Q8×C43—21no—
236C22⋊Q8×C43C2312yes—
237C4×Q8×C43—21no—
238C4×Q8×C43C2312yes—
239#117×C43—21no—
240C2×C4⋊C4×C43—21no—
241C2×C4⋊C4×C43—21no—
242C2×C4⋊C4×C43C2311yescharacteristic
243C2×C4⋊C4×C43C2311yescharacteristic
244C2×C42×C43C2311yescharacteristic
245#107×C43C2314yes—
246#106×C43C2314yes—
247C4⋊C8×C43C2312yes—
248#103×C43C2314yes—
249#103×C43C2314yes—
250C22⋊C8×C43C2312yes—
251#97×C43C2312yes—
252C23×D43C2×D411yescharacteristic
253C2×Q8×C43—21no—
254C2×Q8×C43C2412yes—
255C22×C4×C43—21no—
256C22×C4×C43—21no—
257C22×C4×C43C2×D411yescharacteristic
258C22×C4×C43C2×D411yescharacteristic
259C22×C4×C43C2411yescharacteristic
260C22×Dic43—21no—
261C22×Dic43—21no—
262C22×Dic43C2×D411yescharacteristic
263C22×Dic43C2×D411yescharacteristic
264C22×Dic43C2×D411yescharacteristic
265Q8×D43—28no—
266Q8×D43—44no—
267C2×C4×D43—24no—
268C2×C4×D43—24no—
269C2×C4×D43—22no—
270C2×C4×D43—22no—
271C2×C4×D43—42no—
272C2×C4×D43C2×D411yescharacteristic
273C2×C4×D43C2×D411yescharacteristic
274C2×C4×D43C2×D411yescharacteristic
275C2×C4×D43C2×D411yescharacteristic
276C2×C4×D43C2×D411yescharacteristic
277C2×C4×D43C2×D411yescharacteristic
278C2×C4×D43C2×D411yescharacteristic
279C2×C4×D43C2×D411yescharacteristic
280C2×C4×D43C2×D411yescharacteristic
281C2×C4×D43C2×D411yescharacteristic
282C2×C4×D43C2411yescharacteristic
283C2×C4×D43C2411yescharacteristic
284C2×Dic86—21no—
285C2×Dic86—22no—
286C2×Dic86—22no—
287C2×Dic86—22no—
288C2×Dic86—22no—
289C2×Dic86—22no—
290C2×Dic86—22no—
291C2×Dic86—44no—
292C2×Dic86—44no—
293C2×Dic86C2412yes—
294C2×C8×C43C2414yes—
295C4⋊C4×C43—22no—
296C4⋊C4×C43—22no—
297C4⋊C4×C43—22no—
298C4⋊C4×C43—22no—
299C4⋊C4×C43—21no—
300C4⋊C4×C43—21no—
301C4⋊C4×C43—21no—
302C4⋊C4×C43—21no—
303C4⋊C4×C43—21no—
304C4⋊C4×C43—22no—
305C4⋊C4×C43—22no—
306C4⋊C4×C43C2412yes—
307C4⋊C4×C43C2412yes—
308C4⋊C4×C43C2412yes—
309C22⋊C4×C43—22no—
310C42×C43—22no—
311C42×C43C2×D411yescharacteristic
312C42×C43C2×D411yescharacteristic
313C42×C43C2411yescharacteristic
314C42×C43C2411yescharacteristic
315C22⋊Dic43—22no—
316(C2×D43)⋊C4—22no—
317(C2×D43)⋊C4—22no—
318(C2×D43)⋊C4—22no—
319(C2×D43)⋊C4—22no—
320(C2×D43)⋊C4—22no—
321(C2×D43)⋊C4—22no—
322C4⋊Dic43—21no—
323C4⋊Dic43—21no—
324C4⋊Dic43—21no—
325C4⋊Dic43—21no—
326C4⋊Dic43—21no—
327C4⋊Dic43—22no—
328C4⋊Dic43—22no—
329C4⋊Dic43C2412yes—
330C4⋊Dic43C2412yes—
331C4⋊Dic43C2412yes—
332Dic43⋊C4—22no—
333Dic43⋊C4—22no—
334Dic43⋊C4—22no—
335Dic43⋊C4—22no—
336Dic43⋊C4—22no—
337Dic43⋊C4—22no—
338Dic43⋊C4—22no—
339Dic43⋊C4—22no—
340Dic43⋊C4—22no—
341Dic43⋊C4—22no—
342Dic43⋊C4—22no—
343Dic43⋊C4—22no—
344Dic43⋊C4—22no—
345Dic43⋊C4—22no—
346Dic43⋊C4—22no—
347Dic43⋊C4—22no—
348C4×Dic43—22no—
349C4×Dic43—22no—
350C4×Dic43—22no—
351C4×Dic43—22no—
352C4×Dic43—22no—
353C4×Dic43—22no—
354C4×Dic43—22no—
355C4×Dic43C2×D411yescharacteristic
356C4×Dic43C2×D411yescharacteristic
357C4×Dic43C2×D411yescharacteristic
358C4×Dic43C2×D411yescharacteristic
359C4×Dic43C2×D411yescharacteristic
360C4×Dic43C2×D411yescharacteristic
361C4×Dic43C2×D411yescharacteristic
362C4×Dic43C2×D411yescharacteristic
363C4×Dic43C2×D411yescharacteristic
364C4×Dic43C2×D411yescharacteristic
365C4×Dic43C2411yescharacteristic
366C4×Dic43C2411yescharacteristic
367C2×C43⋊C8C2414yes—
368#10621872—28no—
369C23×C43C22×D411yescharacteristic
370C22×D43—22no—
371C22×D43—22no—
372C22×D43—41no—
373C22×D43C22×D411yescharacteristic
374C22×D43C22×D411yescharacteristic
375Q8×C43—24no—
376Q8×C43—42no—
377C2×C4×C43—22no—
378C2×C4×C43—22no—
379C2×C4×C43—22no—
380C2×C4×C43—22no—
381C2×C4×C43—22no—
382C2×C4×C43—22no—
383C2×C4×C43—41no—
384C2×C4×C43—42no—
385C2×C4×C43—42no—
386C2×C4×C43C22×D411yescharacteristic
387C2×C4×C43C22×D411yescharacteristic
388C2×C4×C43C22×D411yescharacteristic
389C2×C4×C43C22×D411yescharacteristic
390C2×C4×C43C22×D411yescharacteristic
391C2×C4×C43C2511yescharacteristic
392C2×Dic43—22no—
393C2×Dic43—22no—
394C2×Dic43—22no—
395C2×Dic43—22no—
396C2×Dic43—22no—
397C2×Dic43—22no—
398C2×Dic43—42no—
399C2×Dic43—42no—
400C2×Dic43#13714yes—
401C2×Dic43C22×D411yescharacteristic
402C2×Dic43C22×D411yescharacteristic
403C2×Dic43C22×D411yescharacteristic
404C2×Dic43C22×D411yescharacteristic
405C2×Dic43C22×D411yescharacteristic
406C2×Dic43C22×D411yescharacteristic
407C4×D43—22no—
408C4×D43—22no—
409C4×D43—22no—
410C4×D43—22no—
411C4×D43—22no—
412C4×D43—22no—
413C4×D43—22no—
414C4×D43—22no—
415C4×D43—22no—
416C4×D43—41no—
417C4×D43—41no—
418C4×D43—44no—
419C4×D43—44no—
420C4×D432−1+414yes—
421Dic86—24no—
422Dic86—44no—
423Dic86—42no—
424Dic86—44no—
425Dic86—44no—
426Dic86—44no—
427Dic86—44no—
428Dic86—44no—
429C8×C43—24no—
430C43⋊C8—24no—
431#60865—431nomaximal, Sylow
432C22×C43—21no—
433C22×C43—21no—
434C22×C43C2×#13712yes—
435C22×C43C23×D411yescharacteristic
436C2×D43—21no—
437C2×D43—21no—
438C2×D43—21no—
439C2×D43—21no—
440C2×D43—21no—
441C2×D43—44no—
442C2×D43#53612yes—
443C4×C43—21no—
444C4×C43—21no—
445C4×C43—21no—
446C4×C43—21no—
447C4×C43—21no—
448C4×C43—42no—
449C4×C43—42no—
450C4×C43—42no—
451C4×C43—42no—
452C4×C43C2×2−1+412yes—
453Dic43—21no—
454Dic43—21no—
455Dic43—42no—
456Dic43—42no—
457Dic43—42no—
458Dic43—42no—
459Dic43#53612yes—
460Dic43C2×#13712yes—
461Dic43C2×#13712yes—
462Dic43#57512yes—
463C2×#533—431no—
464C2×#533—431no—
465#3237—432no—
466#3237—432no—
467#3236—431no—
468#3236—431no—
469#3236—431no—
470#3236D4311yescharacteristic, complemented
471#3231—434no—
472#3230—432no—
473#3229—432no—
474#3165—432no—
475#3139—432no—
476#3095—432no—
477#3095—432no—
478#3078—434no—
479#2920—431no—
480C2×C43—22no—
481C2×C43C2×#53611yescharacteristic
482C2×C43C22×#13711yescharacteristic
483C2×C43C2×#57511yescharacteristic
484D43—22no—
485D43—41no—
486#533—432no—
487#533—432no—
488#533—432no—
489#533—432no—
490#533—431no—
491#533—431no—
492#533—432no—
493#533—432no—
494#533—431no—
495#533—861no—
496#533—861no—
497#533—861no—
498#533—861no—
499#533—861no—
500#533—861no—
501#533—861no—
502#533—861no—
503#533C2×D4311yescharacteristic
504C2×C4⋊Q8—431no—
505C2×C4⋊Q8—431no—
506C2×C4⋊Q8—431no—
507C2×C4⋊Q8—431no—
508C2×#125—431no—
509C2×#125—861no—
510C2×#125C2×D4311yescharacteristic
511C2×C22⋊Q8—432no—
512C2×C22⋊Q8—861no—
513C2×C22⋊Q8—861no—
514C2×C22⋊Q8—861no—
515C2×C4×Q8—432no—
516C2×C4×Q8—861no—
517C2×C4×Q8—861no—
518C2×C4×Q8—861no—
519C2×#117—431no—
520C2×#117—431no—
521C2×#117—861no—
522C22×C42—431no—
523#501—432no—
524#501—432no—
525#501—432no—
526#501C2×D4312yescomplemented
527#500—434no—
528#498—434no—
529#491—432no—
530#491—432no—
531#491—432no—
532#491C2×D4312yescomplemented
533#487—434no—
534#487—434no—
535#485—434no—
536#485—434no—
537#485—434no—
538#485—434no—
539#484—432no—
540#484—432no—
541#484—432no—
542#484C2×D4312yes—
543#483—432no—
544#483—432no—
545#483—432no—
546#483C2×D4312yes—
547#479—434no—
548#479—434no—
549#479—434no—
550#479C2×D4314yescomplemented
551#477—434no—
552#477—434no—
553#475—434no—
554#475—434no—
555#432—431no—
556#432—432no—
557#432C2×D4311yescharacteristic
558#431—432no—
559#431—432no—
560#428—434no—
561#428—434no—
562#423—432no—
563#419—434no—
564#419—434no—
565#407—432no—
566C4×M16—432no—
567C43#6086511yescharacteristic, complemented, Sylow
568C22×Q8—432no—
569C22×Q8—861no—
570C22×Q8—861no—
571C22×Q8—861no—
572C23×C4—431no—
573C23×C4—431no—
574C23×C4—431no—
575C2×M16—434no—
576C4⋊Q8—432no—
577C4⋊Q8—432no—
578C4⋊Q8—432no—
579C4⋊Q8—432no—
580C4⋊Q8—432no—
581C4⋊Q8—432no—
582C4⋊Q8—431no—
583C4⋊Q8—431no—
584C4⋊Q8—861no—
585C4⋊Q8—861no—
586C4⋊Q8—861no—
587C4⋊Q8—861no—
588C4⋊Q8—861no—
589C4⋊Q8—861no—
590C4⋊Q8—861no—
591C4⋊Q8—861no—
592C4⋊Q8C22×D4311yescharacteristic
593C4⋊Q8C22×D4311yescharacteristic
594#125—21no—
595#125—21no—
596#125—21no—
597#125—432no—
598#125—432no—
599#125—862no—
600#125—862no—
601#125—861no—
602#125—861no—
603#125—861no—
604#125—861no—
605#125—861no—
606#125C22×D4312yes—
607#125C22×D4312yes—
608C22⋊Q8—21no—
609C22⋊Q8—432no—
610C22⋊Q8—432no—
611C22⋊Q8—432no—
612C22⋊Q8—862no—
613C22⋊Q8—862no—
614C22⋊Q8—862no—
615C22⋊Q8—862no—
616C22⋊Q8—862no—
617C22⋊Q8—862no—
618C22⋊Q8—862no—
619C22⋊Q8—862no—
620C22⋊Q8—862no—
621C22⋊Q8—862no—
622C22⋊Q8—862no—
623C22⋊Q8—862no—
624C22⋊Q8—861no—
625C22⋊Q8—861no—
626C22⋊Q8—861no—
627C22⋊Q8C22×D4312yes—
628C4×Q8—21no—
629C4×Q8—432no—
630C4×Q8—432no—
631C4×Q8—432no—
632C4×Q8—862no—
633C4×Q8—862no—
634C4×Q8—862no—
635C4×Q8—862no—
636C4×Q8—862no—
637C4×Q8—862no—
638C4×Q8—862no—
639C4×Q8—861no—
640C4×Q8—862no—
641C4×Q8—862no—
642C4×Q8—862no—
643C4×Q8—862no—
644C4×Q8—862no—
645C4×Q8—861no—
646C4×Q8—861no—
647C4×Q8C22×D4312yes—
648#117—21no—
649#117—432no—
650#117—432no—
651#117—432no—
652#117—432no—
653#117—862no—
654#117—862no—
655#117—861no—
656#117—861no—
657#117—861no—
658#117—861no—
659#117—861no—
660#117—861no—
661#117—861no—
662C2×C4⋊C4—21no—
663C2×C4⋊C4—21no—
664C2×C4⋊C4—431no—
665C2×C4⋊C4—431no—
666C2×C4⋊C4—432no—
667C2×C4⋊C4—861no—
668C2×C4⋊C4—861no—
669C2×C4⋊C4—862no—
670C2×C4⋊C4—862no—
671C2×C4⋊C4—861no—
672C2×C4⋊C4—861no—
673C2×C4⋊C4—861no—
674C2×C4⋊C4—861no—
675C2×C4⋊C4—861no—
676C2×C4⋊C4C22×D4311yescharacteristic
677C2×C4⋊C4C22×D4311yescharacteristic
678C2×C22⋊C4—862no—
679C2×C22⋊C4—861no—
680C2×C22⋊C4—861no—
681C2×C42—431no—
682C2×C42—431no—
683C2×C42—431no—
684C2×C42—431no—
685C2×C42—431no—
686C2×C42—431no—
687C2×C42—431no—
688C2×C42—431no—
689C2×C42—431no—
690C2×C42—431no—
691C2×C42—431no—
692C2×C42—862no—
693C2×C42—861no—
694C2×C42—861no—
695C2×C42C22×D4311yescharacteristic
696#107—434no—
697#107—434no—
698#107—434no—
699#107C22×D4314yes—
700#106—434no—
701#106—434no—
702#106—434no—
703#106C22×D4314yes—
704C4⋊C8—434no—
705C4⋊C8—432no—
706C4⋊C8C22×D4312yes—
707#103—434no—
708#103—434no—
709#103—434no—
710#103—434no—
711#103—434no—
712#103—434no—
713#103C22×D4314yes—
714#103C22×D4314yes—
715C22⋊C8—432no—
716C22⋊C8—434no—
717C22⋊C8C22×D4312yes—
718#97—432no—
719#97C22×D4312yes—
720C4×C8—434no—
721C24—431no—
722C2×Q8—21no—
723C2×Q8—432no—
724C2×Q8—862no—
725C2×Q8—862no—
726C2×Q8—862no—
727C2×Q8—862no—
728C2×Q8—862no—
729C2×Q8—862no—
730C2×Q8—868no—
731C2×Q8—861no—
732C2×Q8—1724no—
733C2×Q8—1724no—
734C2×Q8—1724no—
735C2×Q8C23×D4312yes—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—431no—
739C22×C4—431no—
740C22×C4—431no—
741C22×C4—431no—
742C22×C4—431no—
743C22×C4—431no—
744C22×C4—431no—
745C22×C4—431no—
746C22×C4—431no—
747C22×C4—431no—
748C22×C4—431no—
749C22×C4—431no—
750C22×C4—431no—
751C22×C4—431no—
752C22×C4—431no—
753C22×C4—864no—
754C22×C4—864no—
755C22×C4—862no—
756C22×C4—862no—
757C22×C4—861no—
758C22×C4—861no—
759C22×C4—1722no—
760C22×C4D4×D4311yescharacteristic
761C22×C4D4×D4311yescharacteristic
762C22×C4C23×D4311yescharacteristic
763M16—868no—
764C2×C8—434no—
765C2×C8C23×D4314yes—
766C4⋊C4—22no—
767C4⋊C4—22no—
768C4⋊C4—22no—
769C4⋊C4—22no—
770C4⋊C4—21no—
771C4⋊C4—21no—
772C4⋊C4—21no—
773C4⋊C4—22no—
774C4⋊C4—22no—
775C4⋊C4—21no—
776C4⋊C4—21no—
777C4⋊C4—432no—
778C4⋊C4—432no—
779C4⋊C4—432no—
780C4⋊C4—862no—
781C4⋊C4—862no—
782C4⋊C4—862no—
783C4⋊C4—862no—
784C4⋊C4—862no—
785C4⋊C4—862no—
786C4⋊C4—862no—
787C4⋊C4—862no—
788C4⋊C4—862no—
789C4⋊C4—862no—
790C4⋊C4—862no—
791C4⋊C4—862no—
792C4⋊C4—861no—
793C4⋊C4—861no—
794C4⋊C4—861no—
795C4⋊C4—861no—
796C4⋊C4—862no—
797C4⋊C4—862no—
798C4⋊C4—862no—
799C4⋊C4—862no—
800C4⋊C4—862no—
801C4⋊C4—862no—
802C4⋊C4—861no—
803C4⋊C4C23×D4312yes—
804C4⋊C4C23×D4312yes—
805C4⋊C4C23×D4312yes—
806C22⋊C4—22no—
807C22⋊C4—862no—
808C22⋊C4—862no—
809C22⋊C4—862no—
810C22⋊C4—862no—
811C22⋊C4—862no—
812C22⋊C4—862no—
813C22⋊C4—862no—
814C42—22no—
815C42—431no—
816C42—431no—
817C42—431no—
818C42—431no—
819C42—431no—
820C42—431no—
821C42—431no—
822C42—431no—
823C42—431no—
824C42—431no—
825C42—431no—
826C42—431no—
827C42—862no—
828C42—862no—
829C42—862no—
830C42—862no—
831C42—862no—
832C42—862no—
833C42—862no—
834C42D4×D4311yescharacteristic
835C42D4×D4311yescharacteristic
836C42C23×D4311yescharacteristic
837C42C23×D4311yescharacteristic
838C23—431no—
839C23—431no—
840C23—862no—
841C23—862no—
842C23—1721no—
843C23C2×D4×D4311yescharacteristic
844Q8—24no—
845Q8—42no—
846Q8—864no—
847Q8—1722no—
848Q8—1724no—
849Q8—1724no—
850Q8—1724no—
851Q8—1724no—
852Q8—1724no—
853Q8—1724no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—41no—
861C2×C4—42no—
862C2×C4—42no—
863C2×C4—434no—
864C2×C4—431no—
865C2×C4—431no—
866C2×C4—431no—
867C2×C4—431no—
868C2×C4—434no—
869C2×C4—431no—
870C2×C4—431no—
871C2×C4—862no—
872C2×C4—862no—
873C2×C4—862no—
874C2×C4—862no—
875C2×C4—862no—
876C2×C4—862no—
877C2×C4—862no—
878C2×C4—862no—
879C2×C4—862no—
880C2×C4—862no—
881C2×C4—862no—
882C2×C4—862no—
883C2×C4—862no—
884C2×C4—862no—
885C2×C4—862no—
886C2×C4—1721no—
887C2×C4—1721no—
888C2×C4—1724no—
889C2×C4—1724no—
890C2×C4—1722no—
891C2×C4—1722no—
892C2×C4C2×D4×D4311yescharacteristic
893C2×C4C2×D4×D4311yescharacteristic
894C2×C4C2×D4×D4311yescharacteristic
895C2×C4C2×D4×D4311yescharacteristic
896C2×C4C2×D4×D4311yescharacteristic
897C2×C4C24×D4311yescharacteristic
898C8—24no—
899C8—864no—
900C22—21no—
901C22—21no—
902C22—432no—
903C22—861no—
904C22—861no—
905C22—861no—
906C22—861no—
907C22—861no—
908C22—1724no—
909C22#137×D4312yes—
910C22C22×D4×D4311yescharacteristic
911C4—21no—
912C4—21no—
913C4—21no—
914C4—21no—
915C4—21no—
916C4—42no—
917C4—42no—
918C4—42no—
919C4—42no—
920C4—432no—
921C4—432no—
922C4—432no—
923C4—432no—
924C4—861no—
925C4—861no—
926C4—1722no—
927C4—1722no—
928C4—1722no—
929C4—1722no—
930C42−1+4×D4312yes—
931C2—22no—
932C2—862no—
933C2—1721no—
934C2#536×D4311yescharacteristic
935C2C2×#137×D4311yescharacteristic
936C2#575×D4311yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3236C2
socleC22×C43C23×D4
prime radicalC23×D43C2×D4
hypercenter#3236D43
hypocenterC43#60865
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3236

Complements

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

NH ≅ G/Ntype
3. #19145810C2semidirect
4. #19145804C2semidirect
5. #19145803C2semidirect
6. #19145801C2semidirect
7. #19145797C2semidirect
8. #19145753C2semidirect
9. #19145744C2semidirect
10. #19145737C2semidirect
11. #19145140C2semidirect
12. #19144974C2semidirect
15. #19144398C2semidirect
17. C43×#3236C2semidirect
53. #14583309C22semidirect
54. #14583308C22semidirect
55. #14583305C22semidirect
56. #14583303C22semidirect
57. #14583296C22semidirect
58. #14583269C22semidirect
59. #14583268C22semidirect
60. #14583267C22semidirect
61. #14583248C22semidirect
62. #14583248C22semidirect
73. #14583207C22semidirect
74. #14583206C22semidirect
75. #14583203C22semidirect
76. #14583193C22semidirect
77. #14583192C22semidirect
78. #14583183C22semidirect
79. #14583182C22semidirect
93. C43×#501C22semidirect
94. C43×#491C22semidirect
97. C43×#479C22semidirect
470. #3236D43semidirect
526. #501C2×D43semidirect
532. #491C2×D43semidirect
550. #479C2×D43semidirect
567. C43#60865semidirect

Maximal subgroups

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

subgroupindex
C2×#145834552
#533×D432
#191458102
#191458042
#191458032
#191458012
#191457972
#191457532
#191457442
#191457372
#191451402
#191449742
#191445402
#191445382
#191443982
#191432252
C43×#32362
#6086543