Finite Group Databasebeta

← #25965097

Subgroups — #25965097

Order 11008.

2002 conjugacy classes of subgroups.

The subgroup lattice has 838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147984C211yesmaximal, characteristic
2C2×#14583375C211yesmaximal, characteristic, complemented
3#19144893C214yesmaximal, complemented
4#19144884C214yesmaximal, complemented
5#19144823C214yesmaximal, complemented
6#19144821C214yesmaximal, complemented
7#19144525C212yesmaximal, complemented
8#19144402C211yesmaximal, characteristic, complemented
9#19144400C211yesmaximal, characteristic, complemented
10#19144063C211yesmaximal, characteristic, complemented
11#19143827C212yesmaximal, complemented
12#19143419C212yesmaximal, complemented
13#137×Dic43C212yesmaximal, complemented
14#19143232C211yesmaximal, characteristic, complemented
15C43×#3037C211yesmaximal, characteristic, complemented
16C22×Q8×D43C2211yescharacteristic
17C2×#13063355C2212yes—
18#14583518C2212yes—
19#14583518C2212yes—
20#14583510C2212yes—
21#14583503C2212yes—
22#14583494—21no—
23#14583494—21no—
24#14583486—21no—
25#14583486—21no—
26#14583456C2211yescharacteristic
27#14583429—22no—
28#14583429—22no—
29#14583406C2212yes—
30#14583375—22no—
31#14583375—22no—
32#14583375C2214yes—
33#14583375C2214yes—
34#41×Dic43C2212yes—
35C2×Q8×Dic43C2211yescharacteristic
36C2×C4×Dic86—21no—
37C2×C4×Dic86C2211yescharacteristic
38C2×#13063290—21no—
39C2×#13063290C2211yescharacteristic
40C2×#13063283—21no—
41C2×#13063283C2211yescharacteristic
42C2×#13063282—21no—
43C2×#13063282C2211yescharacteristic
44#14583239C2214yes—
45#14583238C2214yes—
46#14583222C2214yes—
47#14583221C2214yes—
48#14583207C2214yescomplemented
49#14583206C2214yescomplemented
50#14583195C2212yescomplemented
51#14583194C2212yescomplemented
52#14583185C2212yescomplemented
53#14583184C2212yescomplemented
54#14583118C2214yescomplemented
55#14583106C2212yescomplemented
56#14583096C2212yescomplemented
57#14583053C2214yes—
58#14583053C2214yes—
59#14583036C2214yes—
60#14583036C2214yes—
61#14583006C2214yescomplemented
62#14583003C2214yescomplemented
63#14583000C2214yescomplemented
64#14582996C2214yescomplemented
65Q16×Dic43C2214yescomplemented
66#14582991C2214yescomplemented
67#14582990C2214yescomplemented
68SD16×Dic43C2214yescomplemented
69#14582959C2214yes—
70#14582959C2214yes—
71#14582941C2212yes—
72#14582939C2212yes—
73#14582923C2211yescharacteristic
74#14582909C2212yes—
75#14582908C2212yes—
76#14582900C2212yes—
77#14582862C2212yes—
78M16×Dic43C2212yes—
79C2×#137×C43C2212yes—
80C43×#532C2211yescharacteristic
81C2×C4×Q8×C43C2211yescharacteristic
82C43×#464C2214yescomplemented
83C43×#462C2212yescomplemented
84C43×#460C2212yescomplemented
85C43×#423C2211yescharacteristic
86C43×#417C2212yes—
87C22×Dic86—21no—
88C22×Dic86C2311yescharacteristic
89C2×Q8×D43—24no—
90C2×Q8×D43—22no—
91C2×Q8×D43—24no—
92C2×Q8×D43C2314yes—
93C22×C4×D43—21no—
94C22×C4×D43C2311yescharacteristic
95#13063355—28no—
96C2×#10621885C2314yes—
97C2×#10621883C2314yes—
98C2×#10621877C2312yes—
99#13063325C2311yescharacteristic
100#13063325C2311yescharacteristic
101#13063320—22no—
102#13063320—22no—
103#13063318—22no—
104#13063318—22no—
105#13063317C2312yes—
106#13063315—22no—
107#13063315—22no—
108#13063311—22no—
109#13063311—22no—
110#13063309—22no—
111#13063309—22no—
112#13063306—22no—
113#13063306—22no—
114#13063306—22no—
115#13063304—21no—
116#13063304—21no—
117#13063302—22no—
118#13063302—22no—
119#13063301C2312yes—
120#13063301C2312yes—
121#13063297—22no—
122#13063297—22no—
123#13063296C2312yes—
124#13063296C2312yes—
125#13063293—22no—
126Q8×Dic43—22no—
127Q8×Dic43C2314yes—
128Q8×Dic43C2312yes—
129Q8×Dic43C2312yes—
130C4×Dic86—21no—
131C4×Dic86—21no—
132C4×Dic86—21no—
133C4×Dic86—21no—
134C4×Dic86—24no—
135C4×Dic86—24no—
136C4×Dic86C2312yes—
137C4×Dic86C2312yes—
138#13063290—24no—
139#13063290—24no—
140#13063290—22no—
141#13063290C2314yes—
142D4×Dic43—22no—
143D4×Dic43—22no—
144D4×Dic43C2312yes—
145D4×Dic43C2312yes—
146C4×C22⋊D43—22no—
147C4×C22⋊D43—22no—
148#13063284—22no—
149#13063284C2312yes—
150#13063283—22no—
151#13063283—24no—
152#13063283—24no—
153#13063283C2314yes—
154#13063282—24no—
155#13063282—24no—
156#13063282D412yes—
157#13063282D412yes—
158#13063282C2312yes—
159#13063282C2312yes—
160C2×C4⋊Dic43—21no—
161C2×C4⋊Dic43C2311yescharacteristic
162C2×Dic43⋊C4—21no—
163C2×Dic43⋊C4—21no—
164C2×Dic43⋊C4D411yescharacteristic
165C2×Dic43⋊C4D411yescharacteristic
166C2×(C2×D43)⋊C4—21no—
167C2×(C2×D43)⋊C4D411yescharacteristic
168C2×(C2×D43)⋊C4D411yescharacteristic
169C2×C4×Dic43—21no—
170C2×C4×Dic43—21no—
171C2×C4×Dic43—21no—
172C2×C4×Dic43—21no—
173C2×C4×Dic43—22no—
174C2×C4×Dic43C2311yescharacteristic
175#13063259C2314yes—
176#13063258C2314yes—
177#13063257C2314yes—
178#13063256C2314yes—
179C4⋊(C43⋊C8)C2312yes—
180C4⋊(C43⋊C8)C2312yes—
181#13063250C2314yes—
182#13063250C2314yes—
183#13063249C2314yes—
184#13063249C2314yes—
185#13063249C2314yes—
186#13063246C2314yes—
187(C2×D43)⋊C8C2314yes—
188(C2×D43)⋊C8C2314yes—
189#13063235C2314yes—
190C8×Dic43C2314yes—
191C2×#41×C43C2312yes—
192C22×Q8×C43C2311yescharacteristic
193#137×C43—28no—
194C2×Q16×C43C2314yes—
195C2×SD16×C43C2314yes—
196C2×M16×C43C2312yes—
197C4⋊Q8×C43C2311yescharacteristic
198#127×C43C2311yescharacteristic
199#124×C43C2312yes—
200#121×C43—21no—
201#121×C43—21no—
202C4×Q8×C43—21no—
203C4×Q8×C43—21no—
204C4×Q8×C43C2312yes—
205C4×Q8×C43C2312yes—
206C4×D4×C43—21no—
207C4×D4×C43—21no—
208C2×C4⋊C4×C43—21no—
209C2×C4⋊C4×C43C2311yescharacteristic
210C2×C42×C43—21no—
211C2×C42×C43C2311yescharacteristic
212C4⋊C8×C43C2312yes—
213C4⋊C8×C43C2312yes—
214#103×C43C2314yes—
215#102×C43C2314yes—
216C23×D43C2×D411yescharacteristic
217#41×C43—24no—
218#41×C43—24no—
219C2×Q8×C43—21no—
220C2×Q8×C43—22no—
221C2×Q8×C43#4114yes—
222C2×Q8×C43C2412yes—
223C2×Q8×C43C2412yes—
224C2×D4×C43—21no—
225C2×D4×C43—21no—
226C2×D4×C43—22no—
227C2×D4×C43C2412yes—
228C22×C4×C43—22no—
229C22×C4×C43—21no—
230C22×C4×C43—21no—
231C22×C4×C43C2×D411yescharacteristic
232C22×C4×C43C2×D411yescharacteristic
233C22×C4×C43C2411yescharacteristic
234C2×C22⋊D43—22no—
235C2×C22⋊D43—22no—
236C22×Dic43—22no—
237C22×Dic43—22no—
238C22×Dic43—21no—
239C22×Dic43—21no—
240C22×Dic43C2×D411yescharacteristic
241C22×Dic43C2×D411yescharacteristic
242C22×Dic43C2×D411yescharacteristic
243Q8×D43—216no—
244Q8×D43—28no—
245Q8×D43—28no—
246C2×C4×D43—28no—
247C2×C4×D43—22no—
248C2×C4×D43—22no—
249C2×C4×D43—24no—
250C2×C4×D43C2×D412yes—
251C2×C4×D43C2412yes—
252C2×Dic86—28no—
253C2×Dic86—21no—
254C2×Dic86—22no—
255C2×Dic86—24no—
256C2×Dic86—21no—
257C2×Dic86—21no—
258C2×Dic86#4114yes—
259C2×Dic86C2412yes—
260Q16×C43—28no—
261SD16×C43—28no—
262M16×C43—24no—
263C2×C8×C43C2414yes—
264C4⋊C4×C43—22no—
265C4⋊C4×C43—22no—
266C4⋊C4×C43—21no—
267C4⋊C4×C43—21no—
268C4⋊C4×C43—21no—
269C4⋊C4×C43C2412yes—
270C22⋊C4×C43—22no—
271C22⋊C4×C43—22no—
272C42×C43—22no—
273C42×C43—22no—
274C42×C43C2×D411yescharacteristic
275C42×C43C2×D411yescharacteristic
276C42×C43C2411yescharacteristic
277C42×C43C2411yescharacteristic
278C22⋊Dic43—22no—
279C22⋊Dic43—22no—
280C22⋊Dic43—22no—
281C22⋊Dic43—22no—
282C22⋊Dic43—22no—
283#10621885—28no—
284#10621883—28no—
285(C2×D43)⋊C4—24no—
286(C2×D43)⋊C4—22no—
287(C2×D43)⋊C4—22no—
288(C2×D43)⋊C4C2×D412yes—
289(C2×D43)⋊C4C2×D412yes—
290(C2×D43)⋊C4C2×D412yes—
291(C2×D43)⋊C4C2×D412yes—
292C4⋊Dic43—21no—
293C4⋊Dic43—21no—
294C4⋊Dic43—21no—
295C4⋊Dic43—24no—
296C4⋊Dic43—22no—
297C4⋊Dic43—22no—
298C4⋊Dic43C2412yes—
299C4⋊Dic43C2412yes—
300C4⋊Dic43C2412yes—
301Dic43⋊C4—22no—
302Dic43⋊C4—22no—
303Dic43⋊C4—22no—
304Dic43⋊C4—22no—
305Dic43⋊C4—24no—
306Dic43⋊C4—22no—
307Dic43⋊C4—22no—
308Dic43⋊C4C2×D412yes—
309Dic43⋊C4C2×D412yes—
310Dic43⋊C4C2×D412yes—
311Dic43⋊C4C2×D412yes—
312C4×Dic43—22no—
313C4×Dic43—22no—
314C4×Dic43—22no—
315C4×Dic43—24no—
316C4×Dic43—24no—
317C4×Dic43—24no—
318C4×Dic43—22no—
319C4×Dic43—22no—
320C4×Dic43C2×D412yes—
321C4×Dic43C2412yes—
322#10621877—24no—
323C2×C43⋊C8C2414yes—
324C23×C43—22no—
325C23×C43C22×D411yescharacteristic
326C22×D43—22no—
327C22×D43—41no—
328C22×D43—41no—
329C22×D43C22×D412yes—
330Q8×C43—24no—
331Q8×C43—22no—
332Q8×C43—22no—
333Q8×C43—22no—
334Q8×C43C2×#4114yes—
335D4×C43—22no—
336D4×C43—22no—
337D4×C43—44no—
338D4×C43—81no—
339D4×C43—81no—
340C2×C4×C43—24no—
341C2×C4×C43—22no—
342C2×C4×C43—22no—
343C2×C4×C43—22no—
344C2×C4×C43—41no—
345C2×C4×C43—41no—
346C2×C4×C43—42no—
347C2×C4×C43—44no—
348C2×C4×C43C22×D411yescharacteristic
349C2×C4×C43C22×D411yescharacteristic
350C2×C4×C43C22×D411yescharacteristic
351C2×C4×C43C22×D411yescharacteristic
352C2×C4×C43C22×D411yescharacteristic
353C2×C4×C43C2×#4112yes—
354C2×C4×C43C2×#4112yes—
355C2×C4×C43C2511yescharacteristic
356C22⋊D43—82no—
357C22⋊D43—82no—
358C2×Dic43—22no—
359C2×Dic43—24no—
360C2×Dic43—22no—
361C2×Dic43—22no—
362C2×Dic43—22no—
363C2×Dic43—22no—
364C2×Dic43—41no—
365C2×Dic43—41no—
366C2×Dic43—42no—
367C2×Dic43—82no—
368C2×Dic43—82no—
369C2×Dic43C22×D412yes—
370C2×Dic43C22×D412yes—
371C2×Dic43C22×D412yes—
372C4×D43—216no—
373C4×D43—24no—
374C4×D43—22no—
375C4×D43—22no—
376Dic86—216no—
377Dic86—24no—
378Dic86—22no—
379Dic86—81no—
380Dic86—81no—
381Dic86C2×#4114yes—
382C8×C43—24no—
383C43⋊C8—24no—
384#60566—431nomaximal, Sylow
385C22×C43—21no—
386C22×C43—21no—
387C22×C43—42no—
388C22×C43—42no—
389C22×C43—42no—
390C22×C43#52512yes—
391C22×C43C23×D411yescharacteristic
392C2×D43—22no—
393C2×D43—22no—
394C2×D43—22no—
395C2×D43—44no—
396C4×C43—21no—
397C4×C43—21no—
398C4×C43—21no—
399C4×C43—21no—
400C4×C43—24no—
401C4×C43—42no—
402C4×C43—42no—
403C4×C43#52512yes—
404C4×C43C22×#4111yescharacteristic
405C4×C43C22×#4111yescharacteristic
406Dic43—22no—
407Dic43—22no—
408Dic43—22no—
409Dic43—24no—
410Dic43—42no—
411Dic43—42no—
412Dic43—42no—
413#3455—431no—
414C2×#519—431no—
415#3127—434no—
416#3126—434no—
417#3121—434no—
418#3121—434no—
419#3093—432no—
420#3078—431no—
421#3078—431no—
422#3037—431no—
423#3037D4311yescharacteristic, complemented
424#3004—432no—
425C4×#137—432no—
426C4×#137—432no—
427#2921—431no—
428C2×C43—22no—
429C2×C43—82no—
430C2×C43C2×#52511yescharacteristic
431C2×C43#358611yescharacteristic
432C2×C43#358611yescharacteristic
433D43—42no—
434C23×Q8—431no—
435C2×#137—432no—
436C2×#137C2×D4312yes—
437#542—432no—
438#542—432no—
439#541—432no—
440#540—432no—
441#539—861no—
442#539—861no—
443#538—861no—
444#538—861no—
445#533—431no—
446#532C2×D4311yescharacteristic
447#529—862no—
448#529—862no—
449#525—432no—
450#519—434no—
451#519—434no—
452#519—862no—
453#519—862no—
454C4×#41—432no—
455C2×C4×Q8—431no—
456C2×C4×Q8—431no—
457C2×C4×Q8—431no—
458C2×C4×Q8—861no—
459C2×C4×Q8—861no—
460C2×C4×Q8C2×D4311yescharacteristic
461C2×#117—431no—
462C2×#117—431no—
463C2×#117—861no—
464C2×#117—861no—
465#485—434no—
466#485—434no—
467#482—434no—
468#482—434no—
469#479—434no—
470#479—434no—
471#477—432no—
472#477—432no—
473#475—432no—
474#475—432no—
475#464—434no—
476#464C2×D4314yescomplemented
477#462—432no—
478#462C2×D4312yescomplemented
479#460—432no—
480#460C2×D4312yescomplemented
481#451—434no—
482#451—434no—
483#448—434no—
484#448—434no—
485#441—434no—
486#441—434no—
487#440—434no—
488#440—434no—
489C4×Q16—434no—
490C4×Q16—434no—
491C4×SD16—434no—
492C4×SD16—434no—
493#433—434no—
494#433—434no—
495#428—432no—
496#428—432no—
497#423—431no—
498#423C2×D4311yescharacteristic
499#419—432no—
500#419—432no—
501#417—432no—
502#417C2×D4312yes—
503#407—432no—
504C4×M16—432no—
505C43#6056611yescharacteristic, complemented, Sylow
506C2×#41C22×D4312yes—
507C22×Q8—434no—
508C22×Q8—431no—
509C22×Q8—861no—
510C22×Q8—862no—
511C22×Q8—864no—
512C22×Q8—864no—
513C22×Q8C22×D4311yescharacteristic
514C23×C4—431no—
515C23×C4—861no—
516#137—28no—
517#137—868no—
518C2×Q16—434no—
519C2×Q16C22×D4314yes—
520C2×SD16—434no—
521C2×SD16C22×D4314yes—
522C2×M16—432no—
523C2×M16C22×D4312yes—
524C4⋊Q8—431no—
525C4⋊Q8—431no—
526C4⋊Q8C22×D4311yescharacteristic
527#127C22×D4311yescharacteristic
528#126—862no—
529#126—862no—
530#126—862no—
531#126—862no—
532#125—432no—
533#125—862no—
534#125—862no—
535#124—862no—
536#124—862no—
537#124C22×D4312yes—
538#123—862no—
539#123—862no—
540#123—862no—
541#123—862no—
542#123—862no—
543C22⋊Q8—432no—
544C22⋊Q8—432no—
545C22⋊Q8—862no—
546C22⋊Q8—862no—
547C22⋊Q8—861no—
548C22⋊Q8—861no—
549#121—21no—
550#121—21no—
551#121—432no—
552#121—432no—
553#121—862no—
554#121—862no—
555#120—862no—
556C4×Q8—21no—
557C4×Q8—21no—
558C4×Q8—434no—
559C4×Q8—432no—
560C4×Q8—432no—
561C4×Q8—434no—
562C4×Q8—432no—
563C4×Q8—432no—
564C4×Q8—864no—
565C4×Q8—864no—
566C4×Q8—862no—
567C4×Q8—862no—
568C4×Q8—864no—
569C4×Q8—864no—
570C4×Q8—861no—
571C4×Q8—861no—
572C4×Q8—861no—
573C4×Q8—861no—
574C4×Q8C22×D4312yes—
575C4×Q8C22×D4312yes—
576C4×D4—21no—
577C4×D4—21no—
578C4×D4—432no—
579C4×D4—432no—
580C4×D4—862no—
581C4×D4—862no—
582C4×D4—862no—
583C4×D4—862no—
584#117—432no—
585#117—432no—
586#117—432no—
587#117—432no—
588#117—432no—
589#117—434no—
590#117—864no—
591#117—864no—
592#117—862no—
593#117—864no—
594#117—864no—
595#117—862no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—431no—
598C2×C4⋊C4—431no—
599C2×C4⋊C4—431no—
600C2×C4⋊C4—861no—
601C2×C4⋊C4—861no—
602C2×C4⋊C4—861no—
603C2×C4⋊C4C22×D4311yescharacteristic
604C2×C22⋊C4—431no—
605C2×C22⋊C4—431no—
606C2×C22⋊C4—861no—
607C2×C42—21no—
608C2×C42—431no—
609C2×C42—862no—
610C2×C42—861no—
611C2×C42—861no—
612C2×C42—861no—
613C2×C42—861no—
614C2×C42C22×D4311yescharacteristic
615#107—434no—
616#107—434no—
617#106—434no—
618#106—434no—
619C4⋊C8—432no—
620C4⋊C8—432no—
621C4⋊C8C22×D4312yes—
622C4⋊C8C22×D4312yes—
623#103—434no—
624#103—434no—
625#103—434no—
626#103—434no—
627#103—434no—
628#103C22×D4314yes—
629#102—434no—
630#102C22×D4314yes—
631C22⋊C8—434no—
632C22⋊C8—434no—
633#97—434no—
634C4×C8—434no—
635C24—431no—
636#41—24no—
637#41—24no—
638C2×Q8—21no—
639C2×Q8—22no—
640C2×Q8—434no—
641C2×Q8—432no—
642C2×Q8—864no—
643C2×Q8—868no—
644C2×Q8—868no—
645C2×Q8—8616no—
646C2×Q8—868no—
647C2×Q8—861no—
648C2×Q8—861no—
649C2×Q8—861no—
650C2×Q8—862no—
651C2×Q8#1062190014yes—
652C2×Q8C23×D4312yes—
653C2×Q8C23×D4312yes—
654C2×D4—22no—
655C2×D4—21no—
656C2×D4—21no—
657C2×D4—862no—
658C2×D4—862no—
659C2×D4C23×D4312yes—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—22no—
663C22×C4—431no—
664C22×C4—431no—
665C22×C4—431no—
666C22×C4—432no—
667C22×C4—432no—
668C22×C4—864no—
669C22×C4—868no—
670C22×C4—862no—
671C22×C4—862no—
672C22×C4—861no—
673C22×C4—862no—
674C22×C4—862no—
675C22×C4—861no—
676C22×C4D4×D4311yescharacteristic
677C22×C4D4×D4311yescharacteristic
678C22×C4C23×D4311yescharacteristic
679Q16—28no—
680Q16—868no—
681SD16—28no—
682SD16—868no—
683M16—24no—
684M16—864no—
685C2×C8—434no—
686C2×C8C23×D4314yes—
687C4⋊C4—22no—
688C4⋊C4—22no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—432no—
693C4⋊C4—432no—
694C4⋊C4—432no—
695C4⋊C4—432no—
696C4⋊C4—432no—
697C4⋊C4—432no—
698C4⋊C4—432no—
699C4⋊C4—864no—
700C4⋊C4—864no—
701C4⋊C4—862no—
702C4⋊C4—862no—
703C4⋊C4—862no—
704C4⋊C4—862no—
705C4⋊C4—861no—
706C4⋊C4—862no—
707C4⋊C4—862no—
708C4⋊C4—862no—
709C4⋊C4—862no—
710C4⋊C4—861no—
711C4⋊C4—861no—
712C4⋊C4C23×D4312yes—
713C22⋊C4—22no—
714C22⋊C4—22no—
715C22⋊C4—432no—
716C22⋊C4—432no—
717C22⋊C4—432no—
718C22⋊C4—432no—
719C22⋊C4—864no—
720C22⋊C4—862no—
721C22⋊C4—862no—
722C22⋊C4—862no—
723C22⋊C4—862no—
724C22⋊C4—862no—
725C22⋊C4—862no—
726C22⋊C4—862no—
727C42—22no—
728C42—22no—
729C42—432no—
730C42—432no—
731C42—864no—
732C42—864no—
733C42—864no—
734C42—862no—
735C42—862no—
736C42—862no—
737C42—862no—
738C42—862no—
739C42D4×D4311yescharacteristic
740C42D4×D4311yescharacteristic
741C42C23×D4311yescharacteristic
742C42C23×D4311yescharacteristic
743C23—22no—
744C23—432no—
745C23—862no—
746C23—1721no—
747C23—1721no—
748C23C2×D4×D4311yescharacteristic
749Q8—24no—
750Q8—22no—
751Q8—22no—
752Q8—22no—
753Q8—434no—
754Q8—8616no—
755Q8—864no—
756Q8—862no—
757Q8—3441no—
758Q8—3441no—
759Q8C2×#1062190014yes—
760D4—22no—
761D4—22no—
762D4—44no—
763D4—81no—
764D4—81no—
765D4—3442no—
766D4—3442no—
767C2×C4—24no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—42no—
774C2×C4—44no—
775C2×C4—432no—
776C2×C4—432no—
777C2×C4—432no—
778C2×C4—8616no—
779C2×C4—862no—
780C2×C4—864no—
781C2×C4—862no—
782C2×C4—864no—
783C2×C4—862no—
784C2×C4—862no—
785C2×C4—862no—
786C2×C4—862no—
787C2×C4—862no—
788C2×C4—3442no—
789C2×C4—3442no—
790C2×C4—1721no—
791C2×C4—1721no—
792C2×C4—1722no—
793C2×C4C2×D4×D4311yescharacteristic
794C2×C4C2×D4×D4311yescharacteristic
795C2×C4C2×D4×D4311yescharacteristic
796C2×C4C2×D4×D4311yescharacteristic
797C2×C4C2×D4×D4311yescharacteristic
798C2×C4#41×D4312yes—
799C2×C4C2×#1062190012yes—
800C2×C4C24×D4311yescharacteristic
801C8—24no—
802C8—864no—
803C22—21no—
804C22—21no—
805C22—42no—
806C22—42no—
807C22—42no—
808C22—862no—
809C22—862no—
810C22—862no—
811C22—1724no—
812C22#1458340912yes—
813C22C22×D4×D4311yescharacteristic
814C4—24no—
815C4—21no—
816C4—21no—
817C4—21no—
818C4—21no—
819C4—42no—
820C4—42no—
821C4—862no—
822C4—864no—
823C4—862no—
824C4—862no—
825C4—1722no—
826C4—1722no—
827C4—1722no—
828C4#1458340912yes—
829C4C2×#41×D4311yescharacteristic
830C4C22×#1062190011yescharacteristic
831C2—22no—
832C2—82no—
833C2—1722no—
834C2C2×#1458340911yescharacteristic
835C2#1914937811yescharacteristic
836C2#1914937911yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3037C2
socleC22×C43C23×D4
prime radical#19147984C2
hypercenter#3037D43
hypocenterC43#60566
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3037

Complements

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

NH ≅ G/Ntype
2. C2×#14583375C2semidirect
3. #19144893C2semidirect
4. #19144884C2semidirect
5. #19144823C2semidirect
6. #19144821C2semidirect
7. #19144525C2semidirect
8. #19144402C2semidirect
9. #19144400C2semidirect
10. #19144063C2semidirect
11. #19143827C2semidirect
12. #19143419C2semidirect
13. #137×Dic43C2semidirect
14. #19143232C2semidirect
15. C43×#3037C2semidirect
48. #14583207C22semidirect
49. #14583206C22semidirect
50. #14583195C22semidirect
51. #14583194C22semidirect
52. #14583185C22semidirect
53. #14583184C22semidirect
54. #14583118C22semidirect
55. #14583106C22semidirect
56. #14583096C22semidirect
61. #14583006C22semidirect
62. #14583003C22semidirect
63. #14583000C22semidirect
64. #14582996C22semidirect
65. Q16×Dic43C22semidirect
66. #14582991C22semidirect
67. #14582990C22semidirect
68. SD16×Dic43C22semidirect
82. C43×#464C22semidirect
83. C43×#462C22semidirect
84. C43×#460C22semidirect
423. #3037D43semidirect
476. #464C2×D43semidirect
478. #462C2×D43semidirect
480. #460C2×D43semidirect
505. C43#60566semidirect

Maximal subgroups

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

subgroupindex
#191479842
C2×#145833752
#191448932
#191448842
#191448232
#191448212
#191445252
#191444022
#191444002
#191440632
#191438272
#191434192
#137×Dic432
#191432322
C43×#30372
#6056643