Finite Group Databasebeta

← #25965018

Subgroups — #25965018

Order 11008.

2138 conjugacy classes of subgroups.

The subgroup lattice has 1026 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147892C211yesmaximal, characteristic
2C2×C4×Q8×D43C211yesmaximal, characteristic, complemented
3#19144771C214yesmaximal, complemented
4#19144727C212yesmaximal, complemented
5#19144719C212yesmaximal, complemented
6#19144680C214yesmaximal, complemented
7#19144636C212yesmaximal, complemented
8#19144628C212yesmaximal, complemented
9#19144521C212yesmaximal, complemented
10#19144396C211yesmaximal, characteristic, complemented
11#19144069C211yesmaximal, characteristic, complemented
12#19144067C211yesmaximal, characteristic, complemented
13#19143831C212yesmaximal, complemented
14#19143413C212yesmaximal, complemented
15#19143410C212yesmaximal, complemented
16#19143227C211yesmaximal, characteristic, complemented
17C43×#3078C211yesmaximal, characteristic, complemented
18C22×Q8×D43C2211yescharacteristic
19C2×#13063358C2212yes—
20C2×#13063356C2212yes—
21#14583454C2211yescharacteristic
22#14583454C2211yescharacteristic
23#14583450C2211yescharacteristic
24#14583450C2211yescharacteristic
25#14583449C2211yescharacteristic
26#14583436—21no—
27#14583436—21no—
28#14583435—21no—
29#14583435—21no—
30#14583434C2212yes—
31#14583434C2212yes—
32#14583412—21no—
33#14583412—21no—
34#14583411C2212yes—
35C4×#10621902—21no—
36C4×#10621902—21no—
37#14583367C2212yes—
38C2×Q8×Dic43C2211yescharacteristic
39C2×C4×Dic86—21no—
40C2×C4×Dic86C2211yescharacteristic
41C2×#13063290—21no—
42C2×#13063290C2211yescharacteristic
43C4×Q8×D43—21no—
44C4×Q8×D43—21no—
45C4×Q8×D43—21no—
46C4×Q8×D43—21no—
47C4×Q8×D43C2212yes—
48C4×Q8×D43C2212yes—
49C4×Q8×D43C2212yes—
50C4×Q8×D43C2212yes—
51C2×C4⋊C4×D43—21no—
52C2×C4⋊C4×D43C2211yescharacteristic
53C2×C42×D43—21no—
54C2×C42×D43C2211yescharacteristic
55#14583236C2214yes—
56#14583231C2214yes—
57#14583219C2214yes—
58#14583214C2214yes—
59#14583203C2214yescomplemented
60#14583191C2212yescomplemented
61#14583181C2212yescomplemented
62#14583122C2214yescomplemented
63#14583121C2214yescomplemented
64#14583110C2212yescomplemented
65#14583109C2212yescomplemented
66#14583100C2212yescomplemented
67#14583099C2212yescomplemented
68#14583056C2214yes—
69#14583056C2214yes—
70#14583039C2214yes—
71#14583039C2214yes—
72#14583005C2214yescomplemented
73#14583003C2214yescomplemented
74#14583002C2214yescomplemented
75#14582998C2214yescomplemented
76#14582993C2214yescomplemented
77#14582991C2214yescomplemented
78#14582986C2214yescomplemented
79#14582984C2214yescomplemented
80#14582955C2212yes—
81#14582955C2212yes—
82#14582951C2212yes—
83#14582951C2212yes—
84#14582942C2212yes—
85#14582923C2211yescharacteristic
86#14582907C2212yes—
87#14582901C2212yes—
88#14582898C2212yes—
89#14582862C2212yes—
90M16×Dic43C2212yes—
91C43×#533C2211yescharacteristic
92C2×C4×Q8×C43C2211yescharacteristic
93C43×#479C2214yescomplemented
94C43×#477C2212yescomplemented
95C43×#475C2212yescomplemented
96C43×#428C2212yes—
97C43×#423C2211yescharacteristic
98C43×#419C2212yes—
99C2×#10621902—21no—
100C2×#10621902—21no—
101C2×#10621898C2312yes—
102C22×Dic86—21no—
103C22×Dic86C2311yescharacteristic
104C2×Q8×D43—24no—
105C2×Q8×D43—21no—
106C2×Q8×D43—21no—
107C2×Q8×D43—24no—
108C2×Q8×D43C2312yes—
109C2×Q8×D43C2312yes—
110C22×C4×D43—21no—
111C22×C4×D43—21no—
112C22×C4×D43D411yescharacteristic
113C22×C4×D43D411yescharacteristic
114C22×C4×D43C2311yescharacteristic
115#13063358—28no—
116#13063356—28no—
117C2×Dic172C2314yes—
118C2×#10621885C2314yes—
119C2×#10621873C2314yes—
120C2×#10621884C2314yes—
121C2×#10621877C2312yes—
122#13063325C2311yescharacteristic
123#13063322C2311yescharacteristic
124#13063320—22no—
125#13063320—22no—
126#13063316—21no—
127#13063316—21no—
128#13063314—21no—
129#13063314—21no—
130#13063313C2312yes—
131#13063310—22no—
132#13063310—22no—
133#13063309—22no—
134#13063305C2312yes—
135#13063305C2312yes—
136#13063301—21no—
137#13063301—21no—
138#13063300—21no—
139#13063300—21no—
140#13063300C2312yes—
141#13063300C2312yes—
142#13063299—21no—
143#13063299—21no—
144#13063295—22no—
145Q8×Dic43—21no—
146Q8×Dic43—21no—
147Q8×Dic43—21no—
148Q8×Dic43—21no—
149Q8×Dic43C2312yes—
150Q8×Dic43C2312yes—
151C4×Dic86—21no—
152C4×Dic86—21no—
153C4×Dic86—22no—
154C4×Dic86—22no—
155C4×Dic86—22no—
156C4×Dic86—22no—
157C4×Dic86C2312yes—
158C4×Dic86C2312yes—
159#13063290—21no—
160#13063290—21no—
161#13063290—22no—
162#13063290—22no—
163#13063290—22no—
164#13063290—22no—
165#13063290C2312yes—
166#13063290C2312yes—
167#13063290C2312yes—
168#13063290C2312yes—
169C4×D172—22no—
170C4×D172—22no—
171C4×D172—21no—
172C4×D172—21no—
173#13063287—22no—
174#13063287—22no—
175#13063287—21no—
176#13063287—21no—
177#13063287C2312yes—
178#13063287C2312yes—
179(C22⋊D43)⋊C4—22no—
180(C22⋊D43)⋊C4—22no—
181#13063283—21no—
182#13063283—21no—
183#13063283—22no—
184#13063283—22no—
185#13063282—22no—
186C2×C4⋊Dic43—21no—
187C2×C4⋊Dic43C2311yescharacteristic
188C2×Dic43⋊C4—21no—
189C2×Dic43⋊C4—21no—
190C2×Dic43⋊C4—21no—
191C4⋊C4×D43—22no—
192C4⋊C4×D43—22no—
193C4⋊C4×D43—22no—
194C4⋊C4×D43—22no—
195C4⋊C4×D43—21no—
196C4⋊C4×D43—21no—
197C4⋊C4×D43C2312yes—
198C4⋊C4×D43C2312yes—
199C2×C4×Dic43—21no—
200C2×C4×Dic43—21no—
201C2×C4×Dic43—21no—
202C2×C4×Dic43D411yescharacteristic
203C2×C4×Dic43D411yescharacteristic
204C2×C4×Dic43C2311yescharacteristic
205C42×D43—22no—
206C42×D43—22no—
207C42×D43—22no—
208C42×D43—22no—
209C42×D43—22no—
210C42×D43D411yescharacteristic
211C42×D43D411yescharacteristic
212C42×D43D411yescharacteristic
213C42×D43D411yescharacteristic
214C42×D43C2311yescharacteristic
215C42×D43C2311yescharacteristic
216C42×D43C2311yescharacteristic
217C42×D43C2311yescharacteristic
218#13063258C2314yes—
219#13063256C2314yes—
220C4⋊(C43⋊C8)C2312yes—
221C4⋊(C43⋊C8)C2312yes—
222#13063250C2314yes—
223#13063248C2314yes—
224#13063248C2314yes—
225#13063248C2314yes—
226#13063247C2314yes—
227#13063245C2314yes—
228(C2×D43)⋊C8C2314yes—
229(C2×D43)⋊C8C2314yes—
230#13063235C2314yes—
231C8×Dic43C2314yes—
232C22×Q8×C43C2311yescharacteristic
233C2×M16×C43C2312yes—
234C4⋊Q8×C43C2311yescharacteristic
235C4⋊Q8×C43C2311yescharacteristic
236#125×C43C2312yes—
237C22⋊Q8×C43—21no—
238C22⋊Q8×C43—21no—
239C4×Q8×C43—21no—
240C4×Q8×C43—21no—
241C4×Q8×C43—21no—
242C4×Q8×C43—21no—
243C4×Q8×C43C2312yes—
244C4×Q8×C43C2312yes—
245#117×C43C2312yes—
246C2×C4⋊C4×C43—21no—
247C2×C4⋊C4×C43C2311yescharacteristic
248C2×C42×C43—21no—
249C2×C42×C43C2311yescharacteristic
250#107×C43C2314yes—
251#106×C43C2314yes—
252C4⋊C8×C43C2312yes—
253C4⋊C8×C43C2312yes—
254#103×C43C2314yes—
255#103×C43C2314yes—
256C23×D43C2×D411yescharacteristic
257C2×Q8×C43—21no—
258C2×Q8×C43—21no—
259C2×Q8×C43—21no—
260C2×Q8×C43—22no—
261C2×Q8×C43#4114yescomplemented
262C2×Q8×C43C2412yes—
263C22×C4×C43—21no—
264C22×C4×C43—21no—
265C22×C4×C43C2×D411yescharacteristic
266C22×C4×C43C2×D411yescharacteristic
267C22×C4×C43C2411yescharacteristic
268C2×C22⋊D43—22no—
269C22×Dic43—21no—
270C22×Dic43—21no—
271C22×Dic43C2×D411yescharacteristic
272C22×Dic43C2×D411yescharacteristic
273C22×Dic43C2×D411yescharacteristic
274#10621902—44no—
275#10621902—44no—
276Q8×D43—28no—
277Q8×D43—28no—
278Q8×D43—24no—
279Q8×D43—24no—
280Q8×D43—24no—
281Q8×D43—24no—
282#10621898—24no—
283#10621898—24no—
284C2×D172—21no—
285C2×D172—21no—
286C2×D172—22no—
287C2×D172—22no—
288C2×D172C2412yes—
289C2×C4×D43—28no—
290C2×C4×D43—22no—
291C2×C4×D43—22no—
292C2×C4×D43—24no—
293C2×C4×D43—22no—
294C2×C4×D43—22no—
295C2×C4×D43—22no—
296C2×C4×D43—22no—
297C2×C4×D43—22no—
298C2×C4×D43—22no—
299C2×C4×D43—22no—
300C2×C4×D43—42no—
301C2×C4×D43—44no—
302C2×C4×D43C2×D411yescharacteristic
303C2×C4×D43C2×D411yescharacteristic
304C2×C4×D43C2×D411yescharacteristic
305C2×C4×D43C2×D411yescharacteristic
306C2×C4×D43C2×D411yescharacteristic
307C2×C4×D43C2×D411yescharacteristic
308C2×C4×D43C2×D411yescharacteristic
309C2×C4×D43C2×D411yescharacteristic
310C2×C4×D43C2×D411yescharacteristic
311C2×C4×D43C2×D411yescharacteristic
312C2×C4×D43C2411yescharacteristic
313C2×C4×D43C2411yescharacteristic
314C2×Dic86—28no—
315C2×Dic86—21no—
316C2×Dic86—22no—
317C2×Dic86—22no—
318C2×Dic86—22no—
319C2×Dic86#4114yescomplemented
320C2×Dic86C2412yes—
321C2×Dic86C2412yes—
322M16×C43—24no—
323C2×C8×C43C2414yes—
324C4⋊C4×C43—22no—
325C4⋊C4×C43—22no—
326C4⋊C4×C43—21no—
327C4⋊C4×C43—22no—
328C4⋊C4×C43—22no—
329C4⋊C4×C43—21no—
330C4⋊C4×C43—21no—
331C4⋊C4×C43C2412yes—
332C4⋊C4×C43C2412yes—
333C4⋊C4×C43C2412yes—
334C22⋊C4×C43—22no—
335C42×C43—22no—
336C42×C43—22no—
337C42×C43—22no—
338C42×C43C2×D411yescharacteristic
339C42×C43C2×D411yescharacteristic
340C42×C43C2411yescharacteristic
341C42×C43C2411yescharacteristic
342#10621885—28no—
343#10621884—28no—
344(C2×D43)⋊C4—22no—
345(C2×D43)⋊C4—22no—
346(C2×D43)⋊C4—22no—
347(C2×D43)⋊C4—22no—
348(C2×D43)⋊C4—22no—
349(C2×D43)⋊C4—22no—
350(C2×D43)⋊C4—22no—
351(C2×D43)⋊C4—22no—
352C4⋊Dic43—21no—
353C4⋊Dic43—21no—
354C4⋊Dic43—21no—
355C4⋊Dic43—22no—
356C4⋊Dic43—22no—
357C4⋊Dic43—22no—
358C4⋊Dic43—22no—
359C4⋊Dic43C2412yes—
360Dic43⋊C4—22no—
361Dic43⋊C4—22no—
362Dic43⋊C4—22no—
363Dic43⋊C4—22no—
364Dic43⋊C4—22no—
365Dic43⋊C4—22no—
366Dic43⋊C4—22no—
367Dic43⋊C4—22no—
368C4×Dic43—22no—
369C4×Dic43—22no—
370C4×Dic43—22no—
371C4×Dic43—22no—
372C4×Dic43—22no—
373C4×Dic43—22no—
374C4×Dic43—22no—
375C4×Dic43—22no—
376C4×Dic43C2×D411yescharacteristic
377C4×Dic43C2×D411yescharacteristic
378C4×Dic43C2×D411yescharacteristic
379C4×Dic43C2×D411yescharacteristic
380C4×Dic43C2×D411yescharacteristic
381C4×Dic43C2×D411yescharacteristic
382C4×Dic43C2×D411yescharacteristic
383C4×Dic43C2×D411yescharacteristic
384C4×Dic43C2×D411yescharacteristic
385C4×Dic43C2×D411yescharacteristic
386C4×Dic43C2411yescharacteristic
387C4×Dic43C2411yescharacteristic
388#10621877—24no—
389C2×C43⋊C8C2414yes—
390Dic172—28no—
391#10621873—28no—
392C23×C43C22×D411yescharacteristic
393C22×D43—22no—
394C22×D43—22no—
395C22×D43—22no—
396C22×D43—22no—
397C22×D43C22×D411yescharacteristic
398C22×D43C22×D411yescharacteristic
399Q8×C43—24no—
400Q8×C43—22no—
401Q8×C43—42no—
402Q8×C43—42no—
403Q8×C43C2×#4114yes—
404C2×C4×C43—24no—
405C2×C4×C43—22no—
406C2×C4×C43—22no—
407C2×C4×C43—22no—
408C2×C4×C43—22no—
409C2×C4×C43—22no—
410C2×C4×C43—41no—
411C2×C4×C43—42no—
412C2×C4×C43C22×D411yescharacteristic
413C2×C4×C43C22×D411yescharacteristic
414C2×C4×C43C22×D411yescharacteristic
415C2×C4×C43C22×D411yescharacteristic
416C2×C4×C43C22×D411yescharacteristic
417C2×C4×C43C2×#4112yes—
418C2×C4×C43C2×#4112yes—
419C2×C4×C43C2511yescharacteristic
420C22⋊D43—44no—
421C2×Dic43—22no—
422C2×Dic43—24no—
423C2×Dic43—22no—
424C2×Dic43—22no—
425C2×Dic43—22no—
426C2×Dic43—22no—
427C2×Dic43—41no—
428C2×Dic43—42no—
429C2×Dic43C22×D411yescharacteristic
430C2×Dic43C22×D411yescharacteristic
431C2×Dic43C22×D411yescharacteristic
432C2×Dic43C22×D411yescharacteristic
433C2×Dic43C22×D411yescharacteristic
434C2×Dic43C22×D411yescharacteristic
435D172—22no—
436D172—22no—
437D172—42no—
438D172—44no—
439D172—44no—
440D172—42no—
441C4×D43—28no—
442C4×D43—28no—
443C4×D43—22no—
444C4×D43—22no—
445C4×D43—22no—
446C4×D43—22no—
447C4×D43—22no—
448C4×D43—22no—
449C4×D43—21no—
450C4×D43—21no—
451C4×D43—21no—
452C4×D43—21no—
453C4×D43—22no—
454C4×D43—41no—
455C4×D43—41no—
456C4×D43—44no—
457C4×D43—44no—
458C4×D43—44no—
459C4×D43—44no—
460C4×D43—44no—
461C4×D43#13714yescomplemented
462Dic86—28no—
463Dic86—28no—
464Dic86—24no—
465Dic86—22no—
466Dic86—22no—
467Dic86—22no—
468Dic86C2×#4114yes—
469C8×C43—24no—
470C43⋊C8—24no—
471#60560—431nomaximal, Sylow
472C22×C43—21no—
473C22×C43—21no—
474C22×C43#52512yes—
475C22×C43C23×D411yescharacteristic
476C2×D43—28no—
477C2×D43—21no—
478C2×D43—21no—
479C2×D43—21no—
480C2×D43—21no—
481C2×D43—42no—
482C2×D43—42no—
483C2×D43—42no—
484C2×D43C2×#13712yes—
485C2×D43#57512yes—
486C4×C43—24no—
487C4×C43—21no—
488C4×C43—21no—
489C4×C43—21no—
490C4×C43—42no—
491C4×C43—42no—
492C4×C43—42no—
493C4×C43#52512yes—
494C4×C43C2×#13712yes—
495C4×C43C22×#4111yescharacteristic
496C4×C43C22×#4111yescharacteristic
497Dic43—21no—
498Dic43—21no—
499Dic43—24no—
500Dic43—21no—
501Dic43—21no—
502Dic43—21no—
503Dic43—42no—
504Dic43—42no—
505Dic43C2×#13712yes—
506#3444—431no—
507C22×C4×Q8—431no—
508#3117—434no—
509#3113—432no—
510#3112—432no—
511#3108—434no—
512#3104—432no—
513#3103—432no—
514#3092—432no—
515#3078—431no—
516#3078D4311yescharacteristic, complemented
517#3037—431no—
518#3037—431no—
519#3004—432no—
520C4×#137—432no—
521C4×#137—432no—
522#2920—431no—
523C2×C43—22no—
524C2×C43C2×#52511yescharacteristic
525C2×C43C22×#13711yescharacteristic
526C2×C43C2×#57511yescharacteristic
527D43—22no—
528D43—22no—
529D43—82no—
530C23×Q8—431no—
531C2×#137—432no—
532C2×#137—432no—
533#533—431no—
534#533—431no—
535#533C2×D4311yescharacteristic
536#532—431no—
537#532—431no—
538#532—431no—
539#529—432no—
540#529—432no—
541#529—861no—
542#529—861no—
543#529—861no—
544#529—861no—
545#525—432no—
546#525—861no—
547#525—861no—
548C4×#41—432no—
549C4×#41—861no—
550C4×#41—861no—
551C2×C4×Q8—431no—
552C2×C4×Q8—432no—
553C2×C4×Q8—432no—
554C2×C4×Q8—432no—
555C2×C4×Q8—432no—
556C2×C4×Q8—431no—
557C2×C4×Q8—431no—
558C2×C4×Q8—861no—
559C2×C4×Q8—861no—
560C2×C4×Q8—861no—
561C2×C4×Q8—861no—
562C2×C4×Q8—861no—
563C2×C4×Q8—861no—
564C2×C4×Q8C2×D4311yescharacteristic
565C22×C4⋊C4—431no—
566C22×C4⋊C4—861no—
567C22×C42—431no—
568C22×C42—861no—
569#484—434no—
570#483—434no—
571#481—434no—
572#480—434no—
573#479—434no—
574#479C2×D4314yescomplemented
575#477—432no—
576#477C2×D4312yescomplemented
577#475—432no—
578#475C2×D4312yescomplemented
579#464—434no—
580#464—434no—
581#462—432no—
582#462—432no—
583#460—432no—
584#460—432no—
585#451—434no—
586#451—434no—
587#448—434no—
588#448—434no—
589#441—434no—
590#441—434no—
591#440—434no—
592#440—434no—
593C4×Q16—434no—
594C4×Q16—434no—
595C4×SD16—434no—
596C4×SD16—434no—
597#432—432no—
598#432—432no—
599#431—432no—
600#431—432no—
601#428—432no—
602#428C2×D4312yes—
603#423—431no—
604#423C2×D4311yescharacteristic
605#419—432no—
606#419C2×D4312yes—
607#417—432no—
608#417—432no—
609#407—432no—
610C4×M16—432no—
611C43#6056011yescharacteristic, complemented, Sylow
612C2×#41—432no—
613C2×#41—861no—
614C2×#41—861no—
615C22×Q8—432no—
616C22×Q8—432no—
617C22×Q8—431no—
618C22×Q8—861no—
619C22×Q8—861no—
620C22×Q8—861no—
621C22×Q8—864no—
622C22×Q8—864no—
623C22×Q8C22×D4311yescharacteristic
624C23×C4—431no—
625C23×C4—431no—
626C23×C4—431no—
627C23×C4—861no—
628C23×C4—861no—
629#137—868no—
630#137—868no—
631C2×Q16—434no—
632C2×Q16—434no—
633C2×SD16—434no—
634C2×SD16—434no—
635C2×M16—432no—
636C2×M16C22×D4312yes—
637C4⋊Q8—431no—
638C4⋊Q8C22×D4311yescharacteristic
639C4⋊Q8C22×D4311yescharacteristic
640#127—431no—
641#126—862no—
642#126—862no—
643#125—861no—
644#125—861no—
645#125C22×D4312yes—
646#124—432no—
647#124—861no—
648#124—861no—
649#123—862no—
650#123—862no—
651#123—862no—
652C22⋊Q8—21no—
653C22⋊Q8—21no—
654C22⋊Q8—432no—
655C22⋊Q8—432no—
656C22⋊Q8—861no—
657C22⋊Q8—861no—
658#121—432no—
659#121—432no—
660#121—861no—
661#121—861no—
662#121—861no—
663#121—861no—
664#120—862no—
665C4×Q8—21no—
666C4×Q8—21no—
667C4×Q8—21no—
668C4×Q8—21no—
669C4×Q8—432no—
670C4×Q8—432no—
671C4×Q8—432no—
672C4×Q8—432no—
673C4×Q8—432no—
674C4×Q8—432no—
675C4×Q8—432no—
676C4×Q8—432no—
677C4×Q8—862no—
678C4×Q8—862no—
679C4×Q8—862no—
680C4×Q8—862no—
681C4×Q8—861no—
682C4×Q8—862no—
683C4×Q8—861no—
684C4×Q8—862no—
685C4×Q8—862no—
686C4×Q8—862no—
687C4×Q8—861no—
688C4×Q8—861no—
689C4×Q8—861no—
690C4×Q8—861no—
691C4×Q8—861no—
692C4×Q8—861no—
693C4×Q8C22×D4312yes—
694C4×Q8C22×D4312yes—
695C4×D4—432no—
696C4×D4—432no—
697C4×D4—862no—
698C4×D4—862no—
699C4×D4—861no—
700C4×D4—861no—
701C4×D4—862no—
702C4×D4—862no—
703C4×D4—862no—
704C4×D4—862no—
705C4×D4—861no—
706C4×D4—861no—
707#117—862no—
708#117—862no—
709#117—862no—
710#117—861no—
711#117—861no—
712#117C22×D4312yes—
713C2×C4⋊C4—21no—
714C2×C4⋊C4—431no—
715C2×C4⋊C4—432no—
716C2×C4⋊C4—432no—
717C2×C4⋊C4—861no—
718C2×C4⋊C4—861no—
719C2×C4⋊C4—862no—
720C2×C4⋊C4—862no—
721C2×C4⋊C4—862no—
722C2×C4⋊C4—862no—
723C2×C4⋊C4—861no—
724C2×C4⋊C4—861no—
725C2×C4⋊C4—861no—
726C2×C4⋊C4—861no—
727C2×C4⋊C4C22×D4311yescharacteristic
728C2×C42—21no—
729C2×C42—431no—
730C2×C42—431no—
731C2×C42—431no—
732C2×C42—431no—
733C2×C42—431no—
734C2×C42—431no—
735C2×C42—431no—
736C2×C42—431no—
737C2×C42—431no—
738C2×C42—431no—
739C2×C42—431no—
740C2×C42—862no—
741C2×C42—862no—
742C2×C42—862no—
743C2×C42—862no—
744C2×C42—862no—
745C2×C42—861no—
746C2×C42—861no—
747C2×C42—861no—
748C2×C42C22×D4311yescharacteristic
749#107—434no—
750#107C22×D4314yes—
751#106—434no—
752#106C22×D4314yes—
753C4⋊C8—432no—
754C4⋊C8—432no—
755C4⋊C8C22×D4312yes—
756C4⋊C8C22×D4312yes—
757#103—434no—
758#103—434no—
759#103—434no—
760#103—434no—
761#103C22×D4314yes—
762#103C22×D4314yes—
763#102—434no—
764#102—434no—
765C22⋊C8—434no—
766C22⋊C8—434no—
767#97—434no—
768C4×C8—434no—
769C24—431no—
770#41—864no—
771#41—864no—
772#41—1724no—
773#41—1724no—
774C2×Q8—21no—
775C2×Q8—21no—
776C2×Q8—21no—
777C2×Q8—22no—
778C2×Q8—434no—
779C2×Q8—432no—
780C2×Q8—432no—
781C2×Q8—862no—
782C2×Q8—862no—
783C2×Q8—868no—
784C2×Q8—864no—
785C2×Q8—864no—
786C2×Q8—868no—
787C2×Q8—868no—
788C2×Q8—864no—
789C2×Q8—864no—
790C2×Q8—861no—
791C2×Q8—862no—
792C2×Q8#1062190214yescomplemented
793C2×Q8C23×D4312yes—
794C2×D4—432no—
795C2×D4—862no—
796C2×D4—862no—
797C2×D4—862no—
798C2×D4—861no—
799C2×D4—861no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—431no—
803C22×C4—431no—
804C22×C4—431no—
805C22×C4—431no—
806C22×C4—431no—
807C22×C4—431no—
808C22×C4—431no—
809C22×C4—431no—
810C22×C4—431no—
811C22×C4—431no—
812C22×C4—431no—
813C22×C4—431no—
814C22×C4—431no—
815C22×C4—431no—
816C22×C4—431no—
817C22×C4—864no—
818C22×C4—862no—
819C22×C4—862no—
820C22×C4—862no—
821C22×C4—862no—
822C22×C4—868no—
823C22×C4—862no—
824C22×C4—862no—
825C22×C4—861no—
826C22×C4—862no—
827C22×C4—862no—
828C22×C4—861no—
829C22×C4—862no—
830C22×C4—1722no—
831C22×C4—1724no—
832C22×C4D4×D4311yescharacteristic
833C22×C4D4×D4311yescharacteristic
834C22×C4C23×D4311yescharacteristic
835Q16—868no—
836Q16—868no—
837SD16—868no—
838SD16—868no—
839M16—24no—
840M16—864no—
841C2×C8—434no—
842C2×C8C23×D4314yes—
843C4⋊C4—22no—
844C4⋊C4—22no—
845C4⋊C4—21no—
846C4⋊C4—21no—
847C4⋊C4—21no—
848C4⋊C4—22no—
849C4⋊C4—22no—
850C4⋊C4—432no—
851C4⋊C4—862no—
852C4⋊C4—862no—
853C4⋊C4—862no—
854C4⋊C4—862no—
855C4⋊C4—862no—
856C4⋊C4—862no—
857C4⋊C4—862no—
858C4⋊C4—862no—
859C4⋊C4—862no—
860C4⋊C4—862no—
861C4⋊C4—861no—
862C4⋊C4—862no—
863C4⋊C4—862no—
864C4⋊C4—861no—
865C4⋊C4—861no—
866C4⋊C4C23×D4312yes—
867C4⋊C4C23×D4312yes—
868C4⋊C4C23×D4312yes—
869C22⋊C4—22no—
870C22⋊C4—862no—
871C22⋊C4—862no—
872C22⋊C4—862no—
873C22⋊C4—862no—
874C22⋊C4—862no—
875C22⋊C4—862no—
876C22⋊C4—862no—
877C22⋊C4—862no—
878C42—22no—
879C42—22no—
880C42—22no—
881C42—431no—
882C42—431no—
883C42—431no—
884C42—431no—
885C42—431no—
886C42—431no—
887C42—431no—
888C42—431no—
889C42—431no—
890C42—431no—
891C42—431no—
892C42—431no—
893C42—862no—
894C42—862no—
895C42—862no—
896C42—862no—
897C42—862no—
898C42—862no—
899C42—862no—
900C42—862no—
901C42D4×D4311yescharacteristic
902C42D4×D4311yescharacteristic
903C42C23×D4311yescharacteristic
904C42C23×D4311yescharacteristic
905C23—431no—
906C23—431no—
907C23—862no—
908C23—862no—
909C23—862no—
910C23—862no—
911C23C2×D4×D4311yescharacteristic
912Q8—24no—
913Q8—22no—
914Q8—42no—
915Q8—42no—
916Q8—434no—
917Q8—868no—
918Q8—868no—
919Q8—864no—
920Q8—862no—
921Q8—862no—
922Q8—862no—
923Q8C2×#1062190214yes—
924D4—862no—
925D4—862no—
926D4—1722no—
927D4—1724no—
928D4—1724no—
929D4—1724no—
930D4—1722no—
931C2×C4—24no—
932C2×C4—22no—
933C2×C4—22no—
934C2×C4—22no—
935C2×C4—22no—
936C2×C4—22no—
937C2×C4—41no—
938C2×C4—42no—
939C2×C4—431no—
940C2×C4—434no—
941C2×C4—431no—
942C2×C4—431no—
943C2×C4—431no—
944C2×C4—431no—
945C2×C4—431no—
946C2×C4—862no—
947C2×C4—862no—
948C2×C4—862no—
949C2×C4—862no—
950C2×C4—868no—
951C2×C4—868no—
952C2×C4—862no—
953C2×C4—862no—
954C2×C4—864no—
955C2×C4—862no—
956C2×C4—862no—
957C2×C4—862no—
958C2×C4—862no—
959C2×C4—861no—
960C2×C4—861no—
961C2×C4—861no—
962C2×C4—861no—
963C2×C4—862no—
964C2×C4—862no—
965C2×C4—1721no—
966C2×C4—1721no—
967C2×C4—1724no—
968C2×C4—1724no—
969C2×C4—1724no—
970C2×C4—1724no—
971C2×C4—1721no—
972C2×C4—1722no—
973C2×C4—1724no—
974C2×C4C2×D4×D4311yescharacteristic
975C2×C4C2×D4×D4311yescharacteristic
976C2×C4C2×D4×D4311yescharacteristic
977C2×C4C2×D4×D4311yescharacteristic
978C2×C4C2×D4×D4311yescharacteristic
979C2×C4#41×D4312yes—
980C2×C4C2×#1062190212yes—
981C2×C4C24×D4311yescharacteristic
982C8—24no—
983C8—864no—
984C22—21no—
985C22—21no—
986C22—432no—
987C22—432no—
988C22—868no—
989C22—861no—
990C22—861no—
991C22—861no—
992C22—861no—
993C22—1722no—
994C22—1722no—
995C22—1722no—
996C22#1458341212yes—
997C22C22×D4×D4311yescharacteristic
998C4—21no—
999C4—21no—
1000C4—21no—
1001C4—24no—
1002C4—42no—
1003C4—42no—
1004C4—42no—
1005C4—432no—
1006C4—861no—
1007C4—861no—
1008C4—861no—
1009C4—861no—
1010C4—861no—
1011C4—864no—
1012C4—1722no—
1013C4—1722no—
1014C4#1458341212yes—
1015C4#137×D4312yes—
1016C4C2×#41×D4311yescharacteristic
1017C4C22×#1062190211yescharacteristic
1018C2—22no—
1019C2—862no—
1020C2—862no—
1021C2—3442no—
1022C2C2×#1458341211yescharacteristic
1023C2C2×#137×D4311yescharacteristic
1024C2#575×D4311yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3078C2
socleC22×C43C23×D4
prime radical#19147892C2
hypercenter#3078D43
hypocenterC43#60560
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
2. C2×C4×Q8×D43C2semidirect
3. #19144771C2semidirect
4. #19144727C2semidirect
5. #19144719C2semidirect
6. #19144680C2semidirect
7. #19144636C2semidirect
8. #19144628C2semidirect
9. #19144521C2semidirect
10. #19144396C2semidirect
11. #19144069C2semidirect
12. #19144067C2semidirect
13. #19143831C2semidirect
14. #19143413C2semidirect
15. #19143410C2semidirect
16. #19143227C2semidirect
17. C43×#3078C2semidirect
59. #14583203C22semidirect
60. #14583191C22semidirect
61. #14583181C22semidirect
62. #14583122C22semidirect
63. #14583121C22semidirect
64. #14583110C22semidirect
65. #14583109C22semidirect
66. #14583100C22semidirect
67. #14583099C22semidirect
72. #14583005C22semidirect
73. #14583003C22semidirect
74. #14583002C22semidirect
75. #14582998C22semidirect
76. #14582993C22semidirect
77. #14582991C22semidirect
78. #14582986C22semidirect
79. #14582984C22semidirect
93. C43×#479C22semidirect
94. C43×#477C22semidirect
95. C43×#475C22semidirect
261. C2×Q8×C43#41semidirect
319. C2×Dic86#41semidirect
461. C4×D43#137semidirect
516. #3078D43semidirect
574. #479C2×D43semidirect
576. #477C2×D43semidirect
578. #475C2×D43semidirect
611. C43#60560semidirect
792. C2×Q8#10621902semidirect

Maximal subgroups

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

subgroupindex
#191478922
C2×C4×Q8×D432
#191447712
#191447272
#191447192
#191446802
#191446362
#191446282
#191445212
#191443962
#191440692
#191440672
#191438312
#191434132
#191434102
#191432272
C43×#30782
#6056043