Finite Group Databasebeta

← #25965089

Subgroups — #25965089

Order 11008.

2078 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147987C211yesmaximal, characteristic, complemented
2C2×#14583378C211yesmaximal, characteristic, complemented
3#19144877C214yesmaximal, complemented
4#19144862C214yesmaximal, complemented
5#19144814C214yesmaximal, complemented
6#19144799C214yesmaximal, complemented
7#19144521C212yesmaximal, complemented
8#19144396C211yesmaximal, characteristic, complemented
9#19144069C211yesmaximal, characteristic, complemented
10#19144059C211yesmaximal, characteristic, complemented
11#19143839C212yesmaximal, complemented
12#19143413C212yesmaximal, complemented
13#19143399C212yesmaximal, complemented
14#19143232C211yesmaximal, characteristic, complemented
15C43×#3077C211yesmaximal, characteristic, complemented
16C22×#10621900C2211yescharacteristic
17C2×#13063358C2212yes—
18C2×#13063351C2212yes—
19#14583523C2212yescomplemented
20#14583523C2212yescomplemented
21#14583512C2212yescomplemented
22#14583505C2212yescomplemented
23#14583498—21no—
24#14583498—21no—
25#14583489—21no—
26#14583489—21no—
27#14583449C2211yescharacteristic
28#14583436—22no—
29#14583436—22no—
30#14583411C2212yes—
31#14583378—22no—
32#14583378—22no—
33#14583378C2214yes—
34#14583378C2214yes—
35#14583367C2212yes—
36C2×C4×Dic86C2211yescharacteristic
37C2×#13063290C2211yescharacteristic
38C2×D4×Dic43C2211yescharacteristic
39C2×C4×C22⋊D43—21no—
40C2×(C22⋊D43)⋊C4—21no—
41C2×#13063282C2211yescharacteristic
42C2×#13063281—21no—
43C22×Dic43⋊C4—21no—
44C2×C4⋊C4×D43C2211yescharacteristic
45#14583236C2214yescomplemented
46#14583231C2214yescomplemented
47#14583219C2214yescomplemented
48#14583214C2214yescomplemented
49#14583203C2214yescomplemented
50#14583191C2212yescomplemented
51#14583181C2212yescomplemented
52#14583122C2214yescomplemented
53#14583114C2214yescomplemented
54#14583110C2212yescomplemented
55#14583104C2212yescomplemented
56#14583100C2212yescomplemented
57#14583094C2212yescomplemented
58#14583062C2214yes—
59#14583062C2214yes—
60#14583045C2214yes—
61#14583045C2214yes—
62#14583008C2214yescomplemented
63#14583005C2214yescomplemented
64#14582998C2214yescomplemented
65#14582996C2214yescomplemented
66#14582993C2214yescomplemented
67#14582990C2214yescomplemented
68#14582986C2214yescomplemented
69#14582979C2214yescomplemented
70#14582959C2214yescomplemented
71#14582959C2214yescomplemented
72#14582942C2212yes—
73#14582923C2211yescharacteristic
74#14582907C2212yes—
75#14582901C2212yes—
76#14582898C2212yes—
77#14582862C2212yes—
78M16×Dic43C2212yes—
79C43×#533C2211yescharacteristic
80C2×C4×D4×C43C2211yescharacteristic
81C43×#478C2214yescomplemented
82C43×#476C2212yescomplemented
83C43×#474C2212yescomplemented
84C43×#428C2212yes—
85C43×#423C2211yescharacteristic
86C43×#418C2212yes—
87C2×#10621898C2312yes—
88C2×#10621900—24no—
89C2×#10621900—22no—
90C2×#10621900—24no—
91C2×#10621900C2314yes—
92C22×Dic86C2311yescharacteristic
93C22×C22⋊D43—21no—
94C23×Dic43—21no—
95C23×Dic43—21no—
96C22×C4×D43—21no—
97C22×C4×D43C2311yescharacteristic
98#13063358—28no—
99#13063351—28no—
100C2×Dic172C2314yes—
101C2×#10621873C2314yes—
102C2×#10621883C2314yes—
103C2×#10621882C2314yes—
104C2×#10621877C2312yes—
105#13063325C2311yescharacteristic
106#13063322C2311yescharacteristic
107#13063320—22no—
108#13063320—22no—
109#13063320—22no—
110#13063320—22no—
111#13063316—22no—
112#13063316—22no—
113#13063314—22no—
114#13063314—22no—
115#13063313C2312yes—
116#13063310—22no—
117#13063310—22no—
118#13063310—22no—
119#13063310—22no—
120#13063309—22no—
121#13063305C2312yes—
122#13063305C2312yes—
123#13063301—22no—
124#13063301—22no—
125#13063300—22no—
126#13063300—22no—
127#13063300C2312yes—
128#13063300C2312yes—
129#13063299—21no—
130#13063299—21no—
131#13063295—22no—
132C4×Dic86—21no—
133C4×Dic86—21no—
134C4×Dic86C2312yes—
135C4×Dic86C2312yes—
136#13063290—22no—
137#13063290C2314yes—
138#13063290C2312yes—
139#13063290C2312yes—
140C4×D172—22no—
141C4×D172—22no—
142C4×D172—21no—
143C4×D172—21no—
144D4×Dic43—22no—
145D4×Dic43C2314yes—
146#13063287C2312yes—
147#13063287C2312yes—
148C4×C22⋊D43—24no—
149C4×C22⋊D43—24no—
150(C22⋊D43)⋊C4—22no—
151(C22⋊D43)⋊C4—22no—
152(C22⋊D43)⋊C4—24no—
153(C22⋊D43)⋊C4—24no—
154#13063282—22no—
155#13063282D412yes—
156#13063282D412yes—
157#13063282C2312yes—
158#13063282C2312yes—
159#13063281—24no—
160#13063281—24no—
161C2×C4⋊Dic43C2311yescharacteristic
162C2×Dic43⋊C4—21no—
163C2×Dic43⋊C4—21no—
164C2×Dic43⋊C4—21no—
165C2×Dic43⋊C4—24no—
166C2×Dic43⋊C4—24no—
167C2×Dic43⋊C4D411yescharacteristic
168C2×Dic43⋊C4D411yescharacteristic
169C4⋊C4×D43—22no—
170C4⋊C4×D43C2314yes—
171C2×C22⋊Dic43—21no—
172C2×(C2×D43)⋊C4D411yescharacteristic
173C2×(C2×D43)⋊C4D411yescharacteristic
174C2×C4×Dic43—21no—
175C2×C4×Dic43—21no—
176C2×C4×Dic43C2311yescharacteristic
177C42×D43—22no—
178#13063258C2314yes—
179#13063256C2314yes—
180C4⋊(C43⋊C8)C2312yes—
181C4⋊(C43⋊C8)C2312yes—
182#13063250C2314yes—
183#13063248C2314yes—
184#13063248C2314yes—
185#13063248C2314yes—
186#13063247C2314yes—
187#13063245C2314yes—
188(C2×D43)⋊C8C2314yes—
189(C2×D43)⋊C8C2314yes—
190#13063235C2314yes—
191C8×Dic43C2314yes—
192C22×D4×C43C2311yescharacteristic
193C23×C4×C43—21no—
194C2×M16×C43C2312yes—
195C4⋊Q8×C43C2311yescharacteristic
196C4⋊Q8×C43C2311yescharacteristic
197#125×C43C2312yes—
198C22⋊Q8×C43—21no—
199C22⋊Q8×C43—21no—
200C4×Q8×C43—21no—
201C4×Q8×C43—21no—
202C4×D4×C43—21no—
203C4×D4×C43—21no—
204C4×D4×C43C2312yes—
205C4×D4×C43C2312yes—
206#117×C43C2312yes—
207C2×C4⋊C4×C43C2311yescharacteristic
208C2×C22⋊C4×C43—21no—
209C2×C42×C43C2311yescharacteristic
210#107×C43C2314yes—
211#106×C43C2314yes—
212C4⋊C8×C43C2312yes—
213C4⋊C8×C43C2312yes—
214#102×C43C2314yes—
215#102×C43C2314yes—
216C24×C43—21no—
217C23×D43C2×D411yescharacteristic
218C2×Q8×C43—21no—
219C2×Q8×C43—21no—
220C2×D4×C43—21no—
221C2×D4×C43—22no—
222C2×D4×C43#4114yes—
223C2×D4×C43C2412yes—
224C22×C4×C43—22no—
225C22×C4×C43—22no—
226C22×C4×C43—21no—
227C22×C4×C43—82no—
228C22×C4×C43C2×D411yescharacteristic
229C22×C4×C43C2×D411yescharacteristic
230C22×C4×C43C2411yescharacteristic
231C2×C22⋊D43—28no—
232C2×C22⋊D43—22no—
233C2×C22⋊D43—24no—
234C22×Dic43—28no—
235C22×Dic43—24no—
236C22×Dic43—24no—
237C22×Dic43—21no—
238C22×Dic43—21no—
239C22×Dic43—82no—
240C22×Dic43C2×D411yescharacteristic
241C22×Dic43C2×D411yescharacteristic
242C22×Dic43C2×D411yescharacteristic
243#10621900—216no—
244#10621900—28no—
245#10621900—28no—
246#10621898—24no—
247#10621898—24no—
248C2×D172—21no—
249C2×D172—21no—
250C2×D172—22no—
251C2×D172—22no—
252C2×D172C2412yes—
253C2×C4×D43—22no—
254C2×C4×D43—22no—
255C2×C4×D43—22no—
256C2×C4×D43—22no—
257C2×C4×D43—22no—
258C2×C4×D43—24no—
259C2×C4×D43—82no—
260C2×C4×D43C2×D412yes—
261C2×C4×D43C2412yes—
262C2×Dic86—21no—
263C2×Dic86—22no—
264C2×Dic86#4114yes—
265C2×Dic86C2412yes—
266C2×Dic86C2412yes—
267M16×C43—24no—
268C2×C8×C43C2414yes—
269C4⋊C4×C43—21no—
270C4⋊C4×C43—22no—
271C4⋊C4×C43—22no—
272C4⋊C4×C43—21no—
273C4⋊C4×C43—21no—
274C4⋊C4×C43C2412yes—
275C4⋊C4×C43C2412yes—
276C4⋊C4×C43C2412yes—
277C22⋊C4×C43—22no—
278C22⋊C4×C43—22no—
279C22⋊C4×C43—22no—
280C42×C43—22no—
281C42×C43C2×D411yescharacteristic
282C42×C43C2×D411yescharacteristic
283C42×C43C2411yescharacteristic
284C42×C43C2411yescharacteristic
285C22⋊Dic43—24no—
286#10621883—28no—
287#10621882—28no—
288(C2×D43)⋊C4—22no—
289(C2×D43)⋊C4—22no—
290(C2×D43)⋊C4—22no—
291(C2×D43)⋊C4—22no—
292(C2×D43)⋊C4—22no—
293(C2×D43)⋊C4—22no—
294(C2×D43)⋊C4—22no—
295(C2×D43)⋊C4—22no—
296(C2×D43)⋊C4C2×D412yes—
297(C2×D43)⋊C4C2×D412yes—
298(C2×D43)⋊C4C2×D412yes—
299(C2×D43)⋊C4C2×D412yes—
300C4⋊Dic43—21no—
301C4⋊Dic43—21no—
302C4⋊Dic43—21no—
303C4⋊Dic43—22no—
304C4⋊Dic43—22no—
305C4⋊Dic43C2412yes—
306Dic43⋊C4—22no—
307Dic43⋊C4—22no—
308Dic43⋊C4—24no—
309Dic43⋊C4—24no—
310Dic43⋊C4—22no—
311Dic43⋊C4—22no—
312Dic43⋊C4C2×D412yes—
313Dic43⋊C4C2×D412yes—
314Dic43⋊C4C2×D412yes—
315Dic43⋊C4C2×D412yes—
316C4×Dic43—22no—
317C4×Dic43—22no—
318C4×Dic43—22no—
319C4×Dic43—22no—
320C4×Dic43—24no—
321C4×Dic43C2×D412yes—
322C4×Dic43C2412yes—
323#10621877—24no—
324C2×C43⋊C8C2414yes—
325Dic172—28no—
326#10621873—28no—
327C23×C43—24no—
328C23×C43—22no—
329C23×C43—42no—
330C23×C43—42no—
331C23×C43C22×D411yescharacteristic
332C22×D43—22no—
333C22×D43—22no—
334C22×D43—41no—
335C22×D43—41no—
336C22×D43C22×D412yes—
337Q8×C43—81no—
338Q8×C43—81no—
339D4×C43—24no—
340D4×C43—22no—
341D4×C43C2×#4114yes—
342C2×C4×C43—22no—
343C2×C4×C43—22no—
344C2×C4×C43—22no—
345C2×C4×C43—41no—
346C2×C4×C43—41no—
347C2×C4×C43—42no—
348C2×C4×C43—82no—
349C2×C4×C43—82no—
350C2×C4×C43C22×D411yescharacteristic
351C2×C4×C43C22×D411yescharacteristic
352C2×C4×C43C22×D411yescharacteristic
353C2×C4×C43C22×D411yescharacteristic
354C2×C4×C43C22×D411yescharacteristic
355C2×C4×C43C2×#4112yes—
356C2×C4×C43C2×#4112yes—
357C2×C4×C43C2511yescharacteristic
358C22⋊D43—216no—
359C22⋊D43—44no—
360C2×Dic43—216no—
361C2×Dic43—24no—
362C2×Dic43—22no—
363C2×Dic43—22no—
364C2×Dic43—22no—
365C2×Dic43—22no—
366C2×Dic43—41no—
367C2×Dic43—41no—
368C2×Dic43—42no—
369C2×Dic43—84no—
370C2×Dic43C22×D412yes—
371C2×Dic43C22×D412yes—
372C2×Dic43C22×D412yes—
373D172—22no—
374D172—22no—
375D172—81no—
376D172—81no—
377D172—82no—
378D172—82no—
379C4×D43—24no—
380C4×D43—22no—
381C4×D43—22no—
382C4×D43—44no—
383C4×D43—82no—
384C4×D43—82no—
385C4×D43—84no—
386Dic86—24no—
387Dic86—22no—
388Dic86—22no—
389Dic86—22no—
390Dic86C2×#4114yes—
391C8×C43—24no—
392C43⋊C8—24no—
393#60565—431nomaximal, Sylow
394C22×C43—21no—
395C22×C43—21no—
396C22×C43—24no—
397C22×C43—48no—
398C22×C43—42no—
399C22×C43—42no—
400C22×C43#52512yes—
401C22×C43C23×D411yescharacteristic
402C2×D43—22no—
403C2×D43—22no—
404C2×D43—22no—
405C2×D43—44no—
406C2×D43—42no—
407C2×D43—42no—
408C2×D43—42no—
409C4×C43—21no—
410C4×C43—21no—
411C4×C43—21no—
412C4×C43—21no—
413C4×C43—42no—
414C4×C43—42no—
415C4×C43—42no—
416C4×C43#52512yes—
417C4×C43C22×#4111yescharacteristic
418C4×C43C22×#4111yescharacteristic
419Dic43—22no—
420Dic43—22no—
421Dic43—24no—
422Dic43—22no—
423Dic43—42no—
424Dic43—42no—
425#3455—431no—
426C2×#520—431no—
427#3125—434no—
428#3124—434no—
429#3120—434no—
430#3119—434no—
431#3092—432no—
432#3078—431no—
433#3077D4311yescharacteristic, complemented
434#3037—431no—
435#3036—431no—
436#3005—432no—
437C4×#137—432no—
438C4×AGL(1,ℤ/8)—432no—
439#2921—431no—
440C2×C43—22no—
441C2×C43—44no—
442C2×C43C2×#52511yescharacteristic
443C2×C43#358511yescharacteristic
444C2×C43#358611yescharacteristic
445D43—42no—
446D43—82no—
447C22×#41—431no—
448C2×#137—432no—
449C2×AGL(1,ℤ/8)—432no—
450#542—432no—
451#542—432no—
452#541—432no—
453#540—432no—
454#539—861no—
455#539—861no—
456#538—861no—
457#538—861no—
458#533C2×D4311yescharacteristic
459#532—431no—
460#529—862no—
461#529—862no—
462#525—432no—
463#520—434no—
464#520—434no—
465#520—862no—
466#520—862no—
467C4×#41—432no—
468C2×C4×Q8—431no—
469C2×C4×Q8—431no—
470C2×C4×D4—431no—
471C2×C4×D4—861no—
472C2×C4×D4—861no—
473C2×C4×D4C2×D4311yescharacteristic
474C2×#117—431no—
475C2×#117—861no—
476C22×C4⋊C4—431no—
477C22×C4⋊C4—861no—
478#484—434no—
479#483—434no—
480#481—434no—
481#480—434no—
482#479—434no—
483#478C2×D4314yescomplemented
484#477—432no—
485#476C2×D4312yescomplemented
486#475—432no—
487#474C2×D4312yescomplemented
488#464—434no—
489#463—434no—
490#462—432no—
491#461—432no—
492#460—432no—
493#459—432no—
494#452—434no—
495#452—434no—
496#449—434no—
497#449—434no—
498#442—434no—
499#441—434no—
500#440—434no—
501#440—434no—
502C4×Q16—434no—
503C4×SD16—434no—
504C4×SD16—434no—
505C4×D8—434no—
506#433—434no—
507#433—434no—
508#428—432no—
509#428C2×D4312yes—
510#423—431no—
511#423C2×D4311yescharacteristic
512#419—432no—
513#418C2×D4312yes—
514#417—432no—
515#417—432no—
516#407—432no—
517C4×M16—432no—
518C43#6056511yescharacteristic, complemented, Sylow
519C2×#41—434no—
520C2×#41—432no—
521C2×#41—862no—
522C2×#41—864no—
523C2×#41—864no—
524C22×Q8—431no—
525C22×D4—861no—
526C22×D4C22×D4311yescharacteristic
527C23×C4—21no—
528C23×C4—431no—
529C23×C4—861no—
530C23×C4—861no—
531C23×C4—861no—
532#137—868no—
533AGL(1,ℤ/8)—868no—
534C2×Q16—434no—
535C2×SD16—434no—
536C2×SD16—434no—
537C2×D8—434no—
538C2×M16—432no—
539C2×M16C22×D4312yes—
540C4⋊Q8—431no—
541C4⋊Q8C22×D4311yescharacteristic
542C4⋊Q8C22×D4311yescharacteristic
543#127—431no—
544#126—862no—
545#126—862no—
546#126—862no—
547#126—862no—
548#125—862no—
549#125—862no—
550#125C22×D4312yes—
551#124—432no—
552#124—862no—
553#124—862no—
554#123—862no—
555#123—862no—
556#123—862no—
557#123—862no—
558#123—862no—
559C22⋊Q8—21no—
560C22⋊Q8—21no—
561C22⋊Q8—432no—
562C22⋊Q8—432no—
563C22⋊Q8—862no—
564C22⋊Q8—862no—
565#121—432no—
566#121—432no—
567#121—862no—
568#121—862no—
569#121—861no—
570#121—861no—
571#120—862no—
572C4×Q8—21no—
573C4×Q8—21no—
574C4×Q8—434no—
575C4×Q8—432no—
576C4×Q8—432no—
577C4×Q8—432no—
578C4×Q8—432no—
579C4×Q8—862no—
580C4×Q8—861no—
581C4×Q8—861no—
582C4×D4—21no—
583C4×D4—21no—
584C4×D4—434no—
585C4×D4—432no—
586C4×D4—432no—
587C4×D4—862no—
588C4×D4—862no—
589C4×D4—862no—
590C4×D4—864no—
591C4×D4—864no—
592C4×D4—862no—
593C4×D4—862no—
594C4×D4—864no—
595C4×D4—864no—
596C4×D4—861no—
597C4×D4—861no—
598C4×D4C22×D4312yes—
599C4×D4C22×D4312yes—
600#117—432no—
601#117—432no—
602#117—432no—
603#117—432no—
604#117—862no—
605#117—864no—
606#117—864no—
607#117C22×D4312yes—
608C2×C4⋊C4—431no—
609C2×C4⋊C4—431no—
610C2×C4⋊C4—431no—
611C2×C4⋊C4—434no—
612C2×C4⋊C4—862no—
613C2×C4⋊C4—864no—
614C2×C4⋊C4—864no—
615C2×C4⋊C4—861no—
616C2×C4⋊C4—861no—
617C2×C4⋊C4—861no—
618C2×C4⋊C4C22×D4311yescharacteristic
619C2×C22⋊C4—21no—
620C2×C22⋊C4—431no—
621C2×C22⋊C4—431no—
622C2×C22⋊C4—861no—
623C2×C42—431no—
624C2×C42—862no—
625C2×C42—861no—
626C2×C42—861no—
627C2×C42C22×D4311yescharacteristic
628#107—434no—
629#107C22×D4314yes—
630#106—434no—
631#106C22×D4314yes—
632C4⋊C8—432no—
633C4⋊C8—432no—
634C4⋊C8C22×D4312yes—
635C4⋊C8C22×D4312yes—
636#103—434no—
637#103—434no—
638#103—434no—
639#103—434no—
640#102—434no—
641#102—434no—
642#102C22×D4314yes—
643#102C22×D4314yes—
644C22⋊C8—434no—
645C22⋊C8—434no—
646#97—434no—
647C4×C8—434no—
648C24—21no—
649C24—431no—
650#41—868no—
651#41—8616no—
652#41—868no—
653#41—864no—
654#41—864no—
655C2×Q8—21no—
656C2×Q8—21no—
657C2×Q8—434no—
658C2×Q8—432no—
659C2×Q8—432no—
660C2×Q8—861no—
661C2×Q8—862no—
662C2×D4—21no—
663C2×D4—22no—
664C2×D4—432no—
665C2×D4—862no—
666C2×D4—862no—
667C2×D4—864no—
668C2×D4—868no—
669C2×D4—862no—
670C2×D4—861no—
671C2×D4—861no—
672C2×D4#1062190214yes—
673C2×D4C23×D4312yes—
674C22×C4—21no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—82no—
678C22×C4—431no—
679C22×C4—431no—
680C22×C4—431no—
681C22×C4—432no—
682C22×C4—432no—
683C22×C4—862no—
684C22×C4—862no—
685C22×C4—864no—
686C22×C4—864no—
687C22×C4—864no—
688C22×C4—868no—
689C22×C4—861no—
690C22×C4—862no—
691C22×C4—862no—
692C22×C4—861no—
693C22×C4—862no—
694C22×C4—3442no—
695C22×C4—3442no—
696C22×C4D4×D4311yescharacteristic
697C22×C4D4×D4311yescharacteristic
698C22×C4C23×D4311yescharacteristic
699Q16—868no—
700SD16—868no—
701SD16—868no—
702D8—868no—
703M16—24no—
704M16—864no—
705C2×C8—434no—
706C2×C8C23×D4314yes—
707C4⋊C4—21no—
708C4⋊C4—22no—
709C4⋊C4—22no—
710C4⋊C4—21no—
711C4⋊C4—21no—
712C4⋊C4—432no—
713C4⋊C4—432no—
714C4⋊C4—432no—
715C4⋊C4—432no—
716C4⋊C4—432no—
717C4⋊C4—864no—
718C4⋊C4—864no—
719C4⋊C4—862no—
720C4⋊C4—862no—
721C4⋊C4—862no—
722C4⋊C4—862no—
723C4⋊C4—861no—
724C4⋊C4—862no—
725C4⋊C4—862no—
726C4⋊C4—861no—
727C4⋊C4—861no—
728C4⋊C4C23×D4312yes—
729C4⋊C4C23×D4312yes—
730C4⋊C4C23×D4312yes—
731C22⋊C4—22no—
732C22⋊C4—22no—
733C22⋊C4—22no—
734C22⋊C4—432no—
735C22⋊C4—432no—
736C22⋊C4—432no—
737C22⋊C4—432no—
738C22⋊C4—862no—
739C22⋊C4—862no—
740C22⋊C4—862no—
741C22⋊C4—862no—
742C22⋊C4—862no—
743C22⋊C4—862no—
744C22⋊C4—864no—
745C22⋊C4—862no—
746C22⋊C4—862no—
747C42—22no—
748C42—432no—
749C42—432no—
750C42—864no—
751C42—862no—
752C42—862no—
753C42—862no—
754C42—862no—
755C42D4×D4311yescharacteristic
756C42D4×D4311yescharacteristic
757C42C23×D4311yescharacteristic
758C42C23×D4311yescharacteristic
759C23—24no—
760C23—22no—
761C23—42no—
762C23—42no—
763C23—432no—
764C23—862no—
765C23—862no—
766C23—1721no—
767C23—1721no—
768C23C2×D4×D4311yescharacteristic
769Q8—81no—
770Q8—81no—
771Q8—434no—
772Q8—864no—
773Q8—862no—
774Q8—862no—
775Q8—862no—
776D4—24no—
777D4—22no—
778D4—8616no—
779D4—862no—
780D4—862no—
781D4—3441no—
782D4—3441no—
783D4—3442no—
784D4—3442no—
785D4—1724no—
786D4C2×#1062190214yes—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—42no—
793C2×C4—82no—
794C2×C4—82no—
795C2×C4—432no—
796C2×C4—432no—
797C2×C4—432no—
798C2×C4—8616no—
799C2×C4—862no—
800C2×C4—864no—
801C2×C4—862no—
802C2×C4—864no—
803C2×C4—862no—
804C2×C4—862no—
805C2×C4—862no—
806C2×C4—862no—
807C2×C4—3442no—
808C2×C4—3442no—
809C2×C4—3444no—
810C2×C4—3444no—
811C2×C4—1721no—
812C2×C4—1721no—
813C2×C4—1722no—
814C2×C4—1724no—
815C2×C4C2×D4×D4311yescharacteristic
816C2×C4C2×D4×D4311yescharacteristic
817C2×C4C2×D4×D4311yescharacteristic
818C2×C4C2×D4×D4311yescharacteristic
819C2×C4C2×D4×D4311yescharacteristic
820C2×C4#41×D4312yes—
821C2×C4C2×#1062190212yes—
822C2×C4C24×D4311yescharacteristic
823C8—24no—
824C8—864no—
825C22—21no—
826C22—21no—
827C22—24no—
828C22—48no—
829C22—42no—
830C22—42no—
831C22—862no—
832C22—862no—
833C22—862no—
834C22—1724no—
835C22—1722no—
836C22—1722no—
837C22—1722no—
838C22#1458341212yes—
839C22C22×D4×D4311yescharacteristic
840C4—21no—
841C4—21no—
842C4—21no—
843C4—21no—
844C4—42no—
845C4—42no—
846C4—42no—
847C4—862no—
848C4—862no—
849C4—864no—
850C4—862no—
851C4—1722no—
852C4—1722no—
853C4#1458341212yes—
854C4C2×#41×D4311yescharacteristic
855C4C22×#1062190211yescharacteristic
856C2—22no—
857C2—44no—
858C2—3442no—
859C2—1722no—
860C2C2×#1458341211yescharacteristic
861C2#1914937111yescharacteristic
862C2#1914937911yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3077C2
socleC22×C43C23×D4
hypercenter#3077D43
hypocenterC43#60565
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3077

Complements

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

NH ≅ G/Ntype
1. #19147987C2semidirect
2. C2×#14583378C2semidirect
3. #19144877C2semidirect
4. #19144862C2semidirect
5. #19144814C2semidirect
6. #19144799C2semidirect
7. #19144521C2semidirect
8. #19144396C2semidirect
9. #19144069C2semidirect
10. #19144059C2semidirect
11. #19143839C2semidirect
12. #19143413C2semidirect
13. #19143399C2semidirect
14. #19143232C2semidirect
15. C43×#3077C2semidirect
19. #14583523C22semidirect
20. #14583523C22semidirect
21. #14583512C22semidirect
22. #14583505C22semidirect
45. #14583236C22semidirect
46. #14583231C22semidirect
47. #14583219C22semidirect
48. #14583214C22semidirect
49. #14583203C22semidirect
50. #14583191C22semidirect
51. #14583181C22semidirect
52. #14583122C22semidirect
53. #14583114C22semidirect
54. #14583110C22semidirect
55. #14583104C22semidirect
56. #14583100C22semidirect
57. #14583094C22semidirect
62. #14583008C22semidirect
63. #14583005C22semidirect
64. #14582998C22semidirect
65. #14582996C22semidirect
66. #14582993C22semidirect
67. #14582990C22semidirect
68. #14582986C22semidirect
69. #14582979C22semidirect
70. #14582959C22semidirect
71. #14582959C22semidirect
81. C43×#478C22semidirect
82. C43×#476C22semidirect
83. C43×#474C22semidirect
433. #3077D43semidirect
483. #478C2×D43semidirect
485. #476C2×D43semidirect
487. #474C2×D43semidirect
518. C43#60565semidirect

Maximal subgroups

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

subgroupindex
#191479872
C2×#145833782
#191448772
#191448622
#191448142
#191447992
#191445212
#191443962
#191440692
#191440592
#191438392
#191434132
#191433992
#191432322
C43×#30772
#6056543