Finite Group Databasebeta

← #25965131

Subgroups — #25965131

Order 11008.

2010 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583509C211yesmaximal, characteristic, complemented
2#19147796C211yesmaximal, characteristic
3#19144891C214yesmaximal, complemented
4#19144843C214yesmaximal, complemented
5#19144812C214yesmaximal, complemented
6#19144804C214yesmaximal, complemented
7#19144543C211yesmaximal, characteristic, complemented
8#19144416C212yesmaximal, complemented
9#19144081C212yesmaximal, complemented
10#19143857C211yesmaximal, characteristic
11#19143853C211yesmaximal, characteristic
12#19143413C212yesmaximal, complemented
13#19143410C212yesmaximal, complemented
14#19143230C211yesmaximal, characteristic, complemented
15C43×#3095C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C2×#13063358C2212yes—
18C2×#13063356C2212yes—
19#14583509—22no—
20#14583509—22no—
21#14583509C2214yes—
22#14583509C2214yescomplemented
23C2×#13063323C2211yescharacteristic, complemented
24C2×#13063318—21no—
25C2×#13063318—21no—
26C2×#13063316—21no—
27C2×#13063316C2211yescharacteristic, complemented
28C2×#13063315—21no—
29C2×#13063304C2211yescharacteristic
30#14583380C2212yes—
31#14583380C2212yes—
32#14583379—21no—
33#14583379—21no—
34#14583376C2212yes—
35#14583373C2212yes—
36#14583372—21no—
37#14583372—21no—
38C4×#10621898—22no—
39#14583367C2212yes—
40#14583367C2212yes—
41C2×Q8×Dic43C2211yescharacteristic, complemented
42C2×#13063290C2211yescharacteristic, complemented
43C2×#13063284C2211yescharacteristic
44#117×D43—22no—
45#14583240C2214yes—
46#14583234C2212yescomplemented
47#14583229C2212yescomplemented
48#14583209C2214yescomplemented
49#14583205C2214yescomplemented
50#14583202C2214yescomplemented
51#14583198C2214yescomplemented
52#14583108C2214yescomplemented
53#14583108C2214yescomplemented
54#14583103C2214yescomplemented
55#14583103C2214yescomplemented
56#14583063C2214yes—
57#14583059C2214yes—
58#14583057C2212yes—
59#14583054C2212yes—
60#14583052C2212yes—
61#14583049C2212yes—
62#14583005C2214yescomplemented
63#14583003C2214yescomplemented
64#14583002C2214yescomplemented
65#14582998C2214yescomplemented
66#14582993C2214yescomplemented
67#14582991C2214yescomplemented
68#14582986C2214yescomplemented
69#14582984C2214yescomplemented
70#14582957C2214yes—
71#14582957C2214yescomplemented
72#14582942C2212yescomplemented
73#14582922C2212yescomplemented
74#14582907C2212yescomplemented
75#14582901C2212yes—
76#14582898C2212yes—
77#14582863C2211yescharacteristic
78M16×Dic43C2212yescomplemented
79C2×C22⋊Q8×C43C2211yescharacteristic
80C2×#117×C43C2211yescharacteristic
81C43×#485C2214yes—
82C43×#484C2212yescomplemented
83C43×#483C2212yescomplemented
84C43×#428C2212yescomplemented
85C43×#419C2212yescomplemented
86C43×#407C2211yescharacteristic
87C2×#10621898—21no—
88C2×#10621898—21no—
89C2×#10621898—28no—
90C2×#10621898C2312yes—
91C2×#10621898C2312yes—
92C22×Dic86C2311yescharacteristic
93C22×Dic86C2311yescharacteristic
94C22×D172C2311yescharacteristic
95C22×C22⋊D43—21no—
96C22×C4×D43—21no—
97#13063358—28no—
98#13063356—28no—
99C2×Dic172C2314yes—
100C2×#10621885C2314yes—
101C2×#10621873C2314yes—
102C2×#10621884C2314yes—
103C2×#10621877C2312yes—
104#13063323—22no—
105#13063323C2314yes—
106#13063318—24no—
107#13063318—24no—
108#13063318—24no—
109#13063318—24no—
110#13063316—24no—
111#13063316—24no—
112#13063316—22no—
113#13063316C2314yes—
114#13063315—24no—
115#13063315—24no—
116#13063304—21no—
117#13063304—21no—
118#13063304C2312yes—
119#13063304C2312yes—
120Q8×Dic43—22no—
121Q8×Dic43C2314yes—
122C4×Dic86—22no—
123C4×Dic86—22no—
124#13063290—22no—
125#13063290C2314yes—
126#13063290C2312yes—
127#13063290C2312yes—
128#13063290C2312yes—
129#13063290C2312yes—
130C4×D172—22no—
131C4×D172—22no—
132#13063287C2312yes—
133#13063287C2312yes—
134#13063287C2312yes—
135#13063287C2312yes—
136C4×C22⋊D43—22no—
137C4×C22⋊D43—22no—
138C4×C22⋊D43—22no—
139C4×C22⋊D43—22no—
140(C22⋊D43)⋊C4—22no—
141(C22⋊D43)⋊C4—22no—
142(C22⋊D43)⋊C4—22no—
143(C22⋊D43)⋊C4—22no—
144#13063284D412yes—
145#13063284D412yes—
146#13063284C2312yes—
147#13063284C2312yes—
148#13063283—22no—
149#13063283—22no—
150#13063282—22no—
151#13063282—22no—
152#13063281—22no—
153#13063281—22no—
154C2×C4⋊Dic43—21no—
155C2×C4⋊Dic43—21no—
156C2×C4⋊Dic43D411yescharacteristic
157C2×C4⋊Dic43D411yescharacteristic
158C2×C4⋊Dic43C2311yescharacteristic
159C2×Dic43⋊C4—21no—
160C2×Dic43⋊C4—21no—
161C2×Dic43⋊C4—21no—
162C2×Dic43⋊C4—21no—
163C2×Dic43⋊C4—21no—
164C4⋊C4×D43—22no—
165C4⋊C4×D43—22no—
166C2×C22⋊Dic43—21no—
167C2×C22⋊Dic43D411yescharacteristic
168C2×C22⋊Dic43D411yescharacteristic
169C22⋊C4×D43—22no—
170C22⋊C4×D43—22no—
171C2×C4×Dic43—21no—
172C2×C4×Dic43—21no—
173C2×C4×Dic43C2311yescharacteristic
174C2×C4×Dic43C2311yescharacteristic
175C42×D43—22no—
176C42×D43—22no—
177#13063258C2314yes—
178#13063256C2314yes—
179Dic43⋊C8C2314yes—
180Dic43⋊C8C2314yes—
181#13063250C2314yes—
182#13063248C2314yes—
183#13063248C2314yes—
184#13063248C2314yes—
185#13063247C2314yes—
186#13063245C2314yes—
187C22⋊(C43⋊C8)C2312yes—
188C22⋊(C43⋊C8)C2312yes—
189#13063235C2314yes—
190C8×Dic43C2314yes—
191C22×Q8×C43C2311yescharacteristic
192C23×C4×C43C2311yescharacteristic
193C2×M16×C43C2312yes—
194C22⋊Q8×C43—21no—
195C22⋊Q8×C43—21no—
196C22⋊Q8×C43C2312yes—
197C22⋊Q8×C43C2312yes—
198#117×C43—21no—
199#117×C43—21no—
200#117×C43C2312yes—
201#117×C43C2312yes—
202C2×C4⋊C4×C43—21no—
203C2×C4⋊C4×C43C2311yescharacteristic
204C2×C4⋊C4×C43C2311yescharacteristic
205C2×C4⋊C4×C43C2311yescharacteristic
206C2×C22⋊C4×C43—21no—
207C2×C22⋊C4×C43—21no—
208C2×C42×C43—21no—
209#107×C43C2314yes—
210#106×C43C2314yes—
211#103×C43C2314yes—
212#103×C43C2314yes—
213C22⋊C8×C43C2312yes—
214C22⋊C8×C43C2312yes—
215C24×C43C2×D411yescharacteristic
216C23×D43—21no—
217C2×Q8×C43—21no—
218C2×Q8×C43—24no—
219C2×Q8×C43C2412yes—
220C22×C4×C43—24no—
221C22×C4×C43—21no—
222C22×C4×C43—21no—
223C22×C4×C43—21no—
224C22×C4×C43—21no—
225C22×C4×C43C2×D411yescharacteristic
226C22×C4×C43C2×D411yescharacteristic
227C22×C4×C43C2×D411yescharacteristic
228C22×C4×C43C2411yescharacteristic
229C22×C4×C43C2411yescharacteristic
230C22×C4×C43C2411yescharacteristic
231C2×C22⋊D43—28no—
232C2×C22⋊D43—22no—
233C2×C22⋊D43—22no—
234C22×Dic43—21no—
235C22×Dic43—21no—
236C22×Dic43—21no—
237C22×Dic43C2×D411yescharacteristic
238C22×Dic43C2×D411yescharacteristic
239C22×Dic43C2×D411yescharacteristic
240C22×Dic43C2×D411yescharacteristic
241#10621898—28no—
242#10621898—28no—
243#10621898—24no—
244#10621898—24no—
245#10621898—24no—
246#10621898#4118yes—
247C2×D172—21no—
248C2×D172—24no—
249C2×D172C2412yes—
250C2×C4×D43—28no—
251C2×C4×D43—22no—
252C2×C4×D43—22no—
253C2×C4×D43—22no—
254C2×C4×D43—22no—
255C2×C4×D43—22no—
256C2×C4×D43—22no—
257C2×Dic86—21no—
258C2×Dic86—24no—
259C2×Dic86—24no—
260C2×Dic86—21no—
261C2×Dic86C2412yes—
262C2×Dic86C2412yes—
263M16×C43—24no—
264C2×C8×C43C2414yes—
265C4⋊C4×C43—22no—
266C4⋊C4×C43—22no—
267C4⋊C4×C43—21no—
268C4⋊C4×C43—21no—
269C4⋊C4×C43—21no—
270C4⋊C4×C43C2412yes—
271C4⋊C4×C43C2412yes—
272C4⋊C4×C43C2412yes—
273C22⋊C4×C43—22no—
274C22⋊C4×C43—22no—
275C22⋊C4×C43—22no—
276C22⋊C4×C43—22no—
277C42×C43—22no—
278C42×C43—22no—
279C22⋊Dic43—22no—
280C22⋊Dic43—22no—
281C22⋊Dic43C2×D412yes—
282C22⋊Dic43C2×D412yes—
283C22⋊Dic43C2×D412yes—
284C22⋊Dic43C2×D412yes—
285#10621885—28no—
286#10621884—28no—
287(C2×D43)⋊C4—22no—
288(C2×D43)⋊C4—22no—
289(C2×D43)⋊C4—22no—
290(C2×D43)⋊C4—22no—
291C4⋊Dic43—21no—
292C4⋊Dic43—24no—
293C4⋊Dic43—24no—
294C4⋊Dic43C2×D412yes—
295C4⋊Dic43C2×D412yes—
296C4⋊Dic43C2×D412yes—
297C4⋊Dic43C2×D412yes—
298C4⋊Dic43C2412yes—
299Dic43⋊C4—22no—
300Dic43⋊C4—22no—
301Dic43⋊C4—22no—
302Dic43⋊C4—22no—
303Dic43⋊C4—22no—
304Dic43⋊C4—22no—
305Dic43⋊C4—24no—
306Dic43⋊C4—24no—
307Dic43⋊C4—24no—
308Dic43⋊C4—24no—
309C4×Dic43—22no—
310C4×Dic43—22no—
311C4×Dic43—22no—
312C4×Dic43—22no—
313C4×Dic43—24no—
314C4×Dic43—24no—
315C4×Dic43C2×D412yes—
316C4×Dic43C2×D412yes—
317C4×Dic43C2412yes—
318C4×Dic43C2412yes—
319#10621877—24no—
320C2×C43⋊C8C2414yes—
321Dic172—28no—
322#10621873—28no—
323C23×C43—22no—
324C23×C43—41no—
325C23×C43—41no—
326C23×C43C22×D411yescharacteristic
327C23×C43C22×D411yescharacteristic
328C23×C43C22×D411yescharacteristic
329C22×D43—22no—
330C22×D43—24no—
331C22×D43—81no—
332C22×D43—81no—
333Q8×C43—24no—
334Q8×C43—42no—
335C2×C4×C43—22no—
336C2×C4×C43—22no—
337C2×C4×C43—22no—
338C2×C4×C43—22no—
339C2×C4×C43—22no—
340C2×C4×C43—22no—
341C2×C4×C43—22no—
342C2×C4×C43—22no—
343C2×C4×C43—22no—
344C2×C4×C43—42no—
345C2×C4×C43—42no—
346C2×C4×C43—81no—
347C2×C4×C43—81no—
348C2×C4×C43C22×D411yescharacteristic
349C2×C4×C43C22×D411yescharacteristic
350C2×C4×C43C22×D411yescharacteristic
351C2×C4×C43C2×#4114yes—
352C2×C4×C43C2511yescharacteristic
353C22⋊D43—28no—
354C22⋊D43—28no—
355C2×Dic43—24no—
356C2×Dic43—22no—
357C2×Dic43—22no—
358C2×Dic43—22no—
359C2×Dic43—41no—
360C2×Dic43—41no—
361C2×Dic43—41no—
362C2×Dic43—41no—
363C2×Dic43—42no—
364C2×Dic43—42no—
365C2×Dic43C22×D412yes—
366C2×Dic43C22×D412yes—
367C2×Dic43C22×D412yes—
368C2×Dic43C22×D412yes—
369D172—24no—
370D172—22no—
371D172C2×#4114yes—
372C4×D43—28no—
373C4×D43—28no—
374C4×D43—82no—
375C4×D43—82no—
376C4×D43—82no—
377C4×D43—82no—
378Dic86—24no—
379Dic86—22no—
380Dic86—24no—
381Dic86—42no—
382Dic86C2×#4114yes—
383C8×C43—24no—
384C43⋊C8—24no—
385#60569—431nomaximal, Sylow
386C22×C43—21no—
387C22×C43—21no—
388C22×C43—21no—
389C22×C43—21no—
390C22×C43—21no—
391C22×C43—21no—
392C22×C43—21no—
393C22×C43—21no—
394C22×C43—82no—
395C22×C43#52512yes—
396C22×C43C23×D411yescharacteristic
397C2×D43—24no—
398C2×D43—42no—
399C2×D43—42no—
400C2×D43—84no—
401C4×C43—21no—
402C4×C43—21no—
403C4×C43—42no—
404C4×C43—42no—
405C4×C43—42no—
406C4×C43—42no—
407C4×C43#52512yes—
408C4×C43C22×#4112yes—
409Dic43—22no—
410Dic43—22no—
411Dic43—22no—
412Dic43—22no—
413Dic43—24no—
414Dic43—42no—
415Dic43—42no—
416C2×#541—431no—
417#3428—431no—
418#3127—434no—
419#3123—434no—
420#3120—434no—
421#3120—434no—
422#3095—431no—
423#3095D4311yescharacteristic, complemented
424#3080—432no—
425#3039—432no—
426#3007—431no—
427#3007—431no—
428C4×#137—432no—
429C4×#137—432no—
430#2921—431no—
431C2×C43—22no—
432C2×C43—41no—
433C2×C43—41no—
434C2×C43C2×#52511yescharacteristic
435C2×C43#358611yescharacteristic
436C2×C43#358611yescharacteristic
437D43—44no—
438C22×#41—431no—
439C2×#137—432no—
440C2×#137—432no—
441#541—434no—
442#541—434no—
443#541—862no—
444#541—862no—
445C2×C4⋊Q8—431no—
446C2×#126—861no—
447C2×#126—861no—
448C2×#125—431no—
449C2×#125—861no—
450C2×#125—861no—
451C2×C22⋊Q8—431no—
452C2×C22⋊Q8C2×D4311yescharacteristic
453#520—432no—
454#520—432no—
455#520—861no—
456#520—861no—
457#519—432no—
458#518—432no—
459#518—861no—
460#518—861no—
461C4×#41—432no—
462C4×#41—432no—
463C4×#41—862no—
464C2×C4×Q8—431no—
465C2×C4×Q8—431no—
466C2×#117—431no—
467C2×#117—862no—
468C2×#117C2×D4311yescharacteristic
469#485—434no—
470#485C2×D4314yes—
471#484—432no—
472#484C2×D4312yescomplemented
473#483—432no—
474#483C2×D4312yescomplemented
475#479—434no—
476#479—434no—
477#478—434no—
478#478—434no—
479#462—434no—
480#462—434no—
481#461—434no—
482#461—434no—
483#452—434no—
484#452—434no—
485#451—432no—
486#451—432no—
487#450—432no—
488#450—432no—
489#441—434no—
490#441—434no—
491#440—434no—
492#440—434no—
493C4×Q16—434no—
494C4×Q16—434no—
495C4×SD16—434no—
496C4×SD16—434no—
497#433—434no—
498#433—434no—
499#428—432no—
500#428C2×D4312yescomplemented
501#423—432no—
502#419—432no—
503#419C2×D4312yescomplemented
504#417—432no—
505#417—432no—
506#407—431no—
507#407C2×D4311yescharacteristic
508C4×M16—432no—
509C43#6056911yescharacteristic, complemented, Sylow
510C2×#41—432no—
511C2×#41—432no—
512C2×#41—868no—
513C2×#41—861no—
514C2×#41—861no—
515C22×Q8—431no—
516C22×Q8—431no—
517C22×Q8C22×D4311yescharacteristic
518C22×D4—431no—
519C22×D4—861no—
520C23×C4—861no—
521C23×C4C22×D4311yescharacteristic
522#137—868no—
523#137—868no—
524C2×Q16—434no—
525C2×Q16—434no—
526C2×SD16—434no—
527C2×SD16—434no—
528C2×M16—432no—
529C2×M16C22×D4312yes—
530C4⋊Q8—434no—
531C4⋊Q8—862no—
532#126—864no—
533#126—864no—
534#126—864no—
535#126—864no—
536#125—434no—
537#125—862no—
538#125—864no—
539#125—864no—
540#125—864no—
541#125—864no—
542C22⋊Q8—21no—
543C22⋊Q8—21no—
544C22⋊Q8—432no—
545C22⋊Q8—432no—
546C22⋊Q8—861no—
547C22⋊Q8—861no—
548C22⋊Q8C22×D4312yes—
549C22⋊Q8C22×D4312yes—
550C4×Q8—434no—
551C4×Q8—434no—
552C4×Q8—432no—
553C4×Q8—432no—
554C4×Q8—432no—
555C4×Q8—432no—
556C4×Q8—862no—
557C4×Q8—862no—
558C4×Q8—862no—
559C4×Q8—862no—
560C4×D4—432no—
561C4×D4—432no—
562C4×D4—432no—
563C4×D4—432no—
564C4×D4—862no—
565C4×D4—862no—
566C4×D4—862no—
567C4×D4—862no—
568C4×D4—862no—
569C4×D4—862no—
570C4×D4—862no—
571C4×D4—862no—
572C4×D4—862no—
573C4×D4—862no—
574#117—21no—
575#117—21no—
576#117—432no—
577#117—432no—
578#117—432no—
579#117—432no—
580#117—862no—
581#117—862no—
582#117—862no—
583#117—862no—
584#117—862no—
585#117—862no—
586#117C22×D4312yes—
587#117C22×D4312yes—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—431no—
590C2×C4⋊C4—431no—
591C2×C4⋊C4—431no—
592C2×C4⋊C4—862no—
593C2×C4⋊C4—862no—
594C2×C4⋊C4—861no—
595C2×C4⋊C4—861no—
596C2×C4⋊C4—861no—
597C2×C4⋊C4—861no—
598C2×C4⋊C4—861no—
599C2×C4⋊C4—861no—
600C2×C4⋊C4—861no—
601C2×C4⋊C4C22×D4311yescharacteristic
602C2×C4⋊C4C22×D4311yescharacteristic
603C2×C4⋊C4C22×D4311yescharacteristic
604C2×C22⋊C4—21no—
605C2×C22⋊C4—21no—
606C2×C22⋊C4—431no—
607C2×C22⋊C4—431no—
608C2×C22⋊C4—862no—
609C2×C22⋊C4—862no—
610C2×C22⋊C4—861no—
611C2×C42—21no—
612C2×C42—431no—
613C2×C42—431no—
614C2×C42—862no—
615C2×C42—862no—
616C2×C42—861no—
617C2×C42—861no—
618#107—434no—
619#107C22×D4314yes—
620#106—434no—
621#106C22×D4314yes—
622C4⋊C8—434no—
623C4⋊C8—434no—
624#103—434no—
625#103—434no—
626#103—434no—
627#103—434no—
628#103C22×D4314yes—
629#103C22×D4314yes—
630#102—434no—
631#102—434no—
632C22⋊C8—432no—
633C22⋊C8—432no—
634C22⋊C8C22×D4312yes—
635C22⋊C8C22×D4312yes—
636#97—434no—
637C4×C8—434no—
638C24—861no—
639C24D4×D4311yescharacteristic
640#41—438no—
641#41—864no—
642#41—864no—
643#41—868no—
644#41—868no—
645#41—864no—
646C2×Q8—21no—
647C2×Q8—24no—
648C2×Q8—432no—
649C2×Q8—432no—
650C2×Q8—864no—
651C2×Q8—861no—
652C2×Q8—861no—
653C2×Q8—864no—
654C2×Q8C23×D4312yes—
655C2×D4—432no—
656C2×D4—864no—
657C2×D4—868no—
658C2×D4—862no—
659C2×D4—862no—
660C2×D4—861no—
661C22×C4—24no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—431no—
667C22×C4—431no—
668C22×C4—431no—
669C22×C4—431no—
670C22×C4—862no—
671C22×C4—862no—
672C22×C4—862no—
673C22×C4—862no—
674C22×C4—868no—
675C22×C4—861no—
676C22×C4—862no—
677C22×C4—862no—
678C22×C4—861no—
679C22×C4—861no—
680C22×C4D4×D4311yescharacteristic
681C22×C4D4×D4311yescharacteristic
682C22×C4D4×D4311yescharacteristic
683C22×C4C23×D4311yescharacteristic
684C22×C4C23×D4311yescharacteristic
685C22×C4C23×D4311yescharacteristic
686Q16—868no—
687Q16—868no—
688SD16—868no—
689SD16—868no—
690M16—24no—
691M16—864no—
692C2×C8—434no—
693C2×C8C23×D4314yes—
694C4⋊C4—22no—
695C4⋊C4—22no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—432no—
700C4⋊C4—432no—
701C4⋊C4—432no—
702C4⋊C4—432no—
703C4⋊C4—432no—
704C4⋊C4—862no—
705C4⋊C4—862no—
706C4⋊C4—862no—
707C4⋊C4—862no—
708C4⋊C4—864no—
709C4⋊C4—864no—
710C4⋊C4—864no—
711C4⋊C4—864no—
712C4⋊C4—864no—
713C4⋊C4—864no—
714C4⋊C4—861no—
715C4⋊C4—862no—
716C4⋊C4—862no—
717C4⋊C4C23×D4312yes—
718C4⋊C4C23×D4312yes—
719C4⋊C4C23×D4312yes—
720C22⋊C4—22no—
721C22⋊C4—22no—
722C22⋊C4—22no—
723C22⋊C4—22no—
724C22⋊C4—432no—
725C22⋊C4—432no—
726C22⋊C4—432no—
727C22⋊C4—432no—
728C22⋊C4—862no—
729C22⋊C4—862no—
730C22⋊C4—862no—
731C22⋊C4—862no—
732C22⋊C4—862no—
733C22⋊C4—862no—
734C42—22no—
735C42—22no—
736C42—432no—
737C42—432no—
738C42—432no—
739C42—432no—
740C42—862no—
741C42—862no—
742C42—862no—
743C42—862no—
744C42—864no—
745C42—864no—
746C23—22no—
747C23—41no—
748C23—41no—
749C23—864no—
750C23—862no—
751C23—3441no—
752C23—3441no—
753C23C2×D4×D4311yescharacteristic
754C23C2×D4×D4311yescharacteristic
755C23C2×D4×D4311yescharacteristic
756Q8—24no—
757Q8—42no—
758Q8—434no—
759Q8—864no—
760Q8—862no—
761Q8—864no—
762Q8—1722no—
763D4—434no—
764D4—864no—
765D4—868no—
766D4—868no—
767D4—862no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—81no—
780C2×C4—81no—
781C2×C4—432no—
782C2×C4—432no—
783C2×C4—432no—
784C2×C4—432no—
785C2×C4—868no—
786C2×C4—864no—
787C2×C4—862no—
788C2×C4—868no—
789C2×C4—862no—
790C2×C4—862no—
791C2×C4—3442no—
792C2×C4—3442no—
793C2×C4—3442no—
794C2×C4—3442no—
795C2×C4—1721no—
796C2×C4—1721no—
797C2×C4—1721no—
798C2×C4—1721no—
799C2×C4—1722no—
800C2×C4—1722no—
801C2×C4C2×D4×D4311yescharacteristic
802C2×C4C2×D4×D4311yescharacteristic
803C2×C4C2×D4×D4311yescharacteristic
804C2×C4#41×D4314yes—
805C2×C4C24×D4311yescharacteristic
806C8—24no—
807C8—864no—
808C22—21no—
809C22—21no—
810C22—21no—
811C22—21no—
812C22—21no—
813C22—21no—
814C22—21no—
815C22—21no—
816C22—82no—
817C22—864no—
818C22—3444no—
819C22—1722no—
820C22—1722no—
821C22#1458340712yes—
822C22C22×D4×D4311yescharacteristic
823C4—21no—
824C4—21no—
825C4—42no—
826C4—42no—
827C4—42no—
828C4—42no—
829C4—864no—
830C4—862no—
831C4—862no—
832C4—862no—
833C4—862no—
834C4—1722no—
835C4—1722no—
836C4#1458340712yes—
837C4C2×#41×D4312yes—
838C2—22no—
839C2—41no—
840C2—41no—
841C2—1724no—
842C2C2×#1458340711yescharacteristic
843C2#1914937811yescharacteristic
844C2#1914937911yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3095C2
socleC22×C43C23×D4
prime radicalC22×#10621898C22
hypercenter#3095D43
hypocenterC43#60569
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3095

Complements

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

NH ≅ G/Ntype
1. C2×#14583509C2semidirect
3. #19144891C2semidirect
4. #19144843C2semidirect
5. #19144812C2semidirect
6. #19144804C2semidirect
7. #19144543C2semidirect
8. #19144416C2semidirect
9. #19144081C2semidirect
12. #19143413C2semidirect
13. #19143410C2semidirect
14. #19143230C2semidirect
15. C43×#3095C2semidirect
22. #14583509C22semidirect
23. C2×#13063323C22semidirect
27. C2×#13063316C22semidirect
41. C2×Q8×Dic43C22semidirect
42. C2×#13063290C22semidirect
46. #14583234C22semidirect
47. #14583229C22semidirect
48. #14583209C22semidirect
49. #14583205C22semidirect
50. #14583202C22semidirect
51. #14583198C22semidirect
52. #14583108C22semidirect
53. #14583108C22semidirect
54. #14583103C22semidirect
55. #14583103C22semidirect
62. #14583005C22semidirect
63. #14583003C22semidirect
64. #14583002C22semidirect
65. #14582998C22semidirect
66. #14582993C22semidirect
67. #14582991C22semidirect
68. #14582986C22semidirect
69. #14582984C22semidirect
71. #14582957C22semidirect
72. #14582942C22semidirect
73. #14582922C22semidirect
74. #14582907C22semidirect
78. M16×Dic43C22semidirect
82. C43×#484C22semidirect
83. C43×#483C22semidirect
84. C43×#428C22semidirect
85. C43×#419C22semidirect
423. #3095D43semidirect
472. #484C2×D43semidirect
474. #483C2×D43semidirect
500. #428C2×D43semidirect
503. #419C2×D43semidirect
509. C43#60569semidirect

Maximal subgroups

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

subgroupindex
C2×#145835092
#191477962
#191448912
#191448432
#191448122
#191448042
#191445432
#191444162
#191440812
#191438572
#191438532
#191434132
#191434102
#191432302
C43×#30952
#6056943