Finite Group Databasebeta

← #25968695

Subgroups — #25968695

Order 11008.

1800 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#19147892C211yesmaximal, characteristic
2C2×#14583454C211yesmaximal, characteristic, complemented
3#19145779C214yesmaximal, complemented
4#19145768C214yesmaximal, complemented
5#19145751C212yesmaximal, complemented
6#19145736C211yesmaximal, characteristic, complemented
7#19145734C212yesmaximal, complemented
8#19145723C211yesmaximal, characteristic, complemented
9#19145718C211yesmaximal, characteristic, complemented
10#19145106C212yesmaximal, complemented
11#19144919C212yesmaximal, complemented
12#19144511C214yesmaximal, complemented
13#19144386C214yesmaximal, complemented
14#431×D43C211yesmaximal, characteristic, complemented
15C43×#3230C211yesmaximal, characteristic, complemented
16#14583454—21no—
17#14583454—21no—
18#14583454—21no—
19#14583454—21no—
20#14583454C2211yescharacteristic
21#14583454C2212yes—
22#14583454C2212yes—
23#14583454C2212yes—
24#14583454C2212yes—
25#14583454C2211yescharacteristic
26#14583450C2211yescharacteristic
27#14583450C2211yescharacteristic
28#14583449C2211yescharacteristic
29C2×#13063325C2211yescharacteristic
30#14583436—21no—
31#14583436C2212yes—
32#14583435—21no—
33#14583435C2212yes—
34#14583434—21no—
35#14583434—21no—
36C2×#13063316C2212yes—
37#14583412—21no—
38#14583412C2212yes—
39#14583411—21no—
40C2×#13063305—21no—
41C2×#13063301—21no—
42C4×#10621902—21no—
43C4×#10621902C2212yes—
44#14583367—21no—
45C2×Q8×Dic43—21no—
46C2×#13063290—21no—
47C2×#13063283C2212yes—
48C2×C42×D43C2211yescharacteristic
49#14583304C2212yescomplemented
50#14583300C2218yescomplemented
51#14583295C2212yescomplemented
52#14583295C2212yescomplemented
53#14583255C2218yescomplemented
54#14583249C2212yescomplemented
55#14583247C2212yescomplemented
56#14583246C2212yescomplemented
57#14583239C2218yes—
58#14583227C2214yes—
59#14583226C2218yes—
60#14583217C2214yes—
61#14583213C2214yes—
62#14583208C2218yescomplemented
63#14583202C2218yescomplemented
64#14583186C2214yescomplemented
65#14583184C2214yescomplemented
66#14583180C2214yescomplemented
67#14582952C2211yescharacteristic
68#14582951C2212yes—
69#14582950C2212yes—
70#14582949C2212yes—
71#14582936C2218yes—
72C4⋊C8×D43C2212yes—
73#14582894C2218yes—
74C22⋊C8×D43C2212yes—
75C4×C8×D43C2212yes—
76C43×#533C2211yescharacteristic
77C2×C4⋊Q8×C43C2211yescharacteristic
78C43×#500C2212yescomplemented
79C43×#487C2212yescomplemented
80C43×#484C2214yes—
81C43×#477C2214yescomplemented
82C43×#431C2211yescharacteristic
83C2×#10621902—21no—
84C2×#10621902C2312yes—
85C2×#10621898—21no—
86C22×Dic86—21no—
87C22×C4×D43D411yescharacteristic
88C22×C4×D43D411yescharacteristic
89C22×C4×D43C2311yescharacteristic
90C2×C8×D43C2314yes—
91#13063325—21no—
92#13063325—21no—
93#13063325C2311yescharacteristic
94#13063325C2312yes—
95#13063325C2312yes—
96#13063322C2311yescharacteristic
97#13063320—22no—
98#13063320—22no—
99#13063316—22no—
100#13063316—22no—
101#13063316—21no—
102#13063316C2312yes—
103#13063316C2314yes—
104#13063316C2314yes—
105#13063314—21no—
106#13063314C2312yes—
107#13063313—21no—
108#13063310—22no—
109#13063310—22no—
110#13063309—22no—
111#13063305—22no—
112#13063305—22no—
113#13063305—22no—
114#13063305—22no—
115#13063305—21no—
116#13063305—21no—
117#13063301—22no—
118#13063301—22no—
119#13063301—22no—
120#13063301—22no—
121#13063301—21no—
122#13063301C2312yes—
123#13063300—21no—
124#13063300—21no—
125#13063300—21no—
126#13063300C2312yes—
127#13063299—21no—
128#13063299C2312yes—
129#13063295—22no—
130Q8×Dic43—22no—
131Q8×Dic43—22no—
132Q8×Dic43—22no—
133Q8×Dic43—22no—
134Q8×Dic43—21no—
135Q8×Dic43C2312yes—
136#13063290—22no—
137#13063290—22no—
138#13063290—22no—
139#13063290—22no—
140#13063290—21no—
141#13063290—21no—
142C4×D172—22no—
143C4×D172—22no—
144C4×D172—21no—
145C4×D172C2312yes—
146#13063287—22no—
147#13063287—22no—
148#13063287—21no—
149#13063287—21no—
150#13063287—21no—
151#13063287C2312yes—
152(C22⋊D43)⋊C4—22no—
153(C22⋊D43)⋊C4—22no—
154#13063283—22no—
155#13063283—22no—
156#13063283—21no—
157#13063283—22no—
158#13063283—22no—
159#13063283C2314yes—
160#13063283C2314yes—
161#13063283C2312yes—
162#13063282—22no—
163C2×C4⋊Dic43—21no—
164C2×C4⋊Dic43—22no—
165C2×C4⋊Dic43C2312yes—
166C2×Dic43⋊C4—22no—
167C2×(C2×D43)⋊C4—22no—
168C2×C4×Dic43—22no—
169C2×C4×Dic43D411yescharacteristic
170C2×C4×Dic43D411yescharacteristic
171C2×C4×Dic43C2311yescharacteristic
172C42×D43—22no—
173C42×D43D411yescharacteristic
174C42×D43D411yescharacteristic
175C42×D43D411yescharacteristic
176C42×D43D411yescharacteristic
177C42×D43C2311yescharacteristic
178C42×D43C2311yescharacteristic
179C42×D43C2311yescharacteristic
180C42×D43C2311yescharacteristic
181#13063259C2318yes—
182#13063256C2318yes—
183#13063256C2318yes—
184C4⋊(C43⋊C8)C2312yes—
185Dic43⋊C8C2314yes—
186#13063249C2318yes—
187#13063247C2318yes—
188#13063245C2318yes—
189C22⋊(C43⋊C8)C2312yes—
190(C2×D43)⋊C8C2314yes—
191C4×C43⋊C8C2312yes—
192C8×Dic43C2314yes—
193C22×Q8×C43—21no—
194C4⋊Q8×C43—21no—
195C4⋊Q8×C43—21no—
196C4⋊Q8×C43C2311yescharacteristic
197C4⋊Q8×C43C2311yescharacteristic
198C4⋊Q8×C43C2312yes—
199C4⋊Q8×C43C2312yes—
200#125×C43—21no—
201C22⋊Q8×C43—21no—
202C22⋊Q8×C43C2312yes—
203C4×Q8×C43—21no—
204C4×Q8×C43C2312yes—
205#117×C43—21no—
206C2×C4⋊C4×C43—21no—
207C2×C4⋊C4×C43C2312yes—
208C2×C42×C43C2311yescharacteristic
209#107×C43C2318yes—
210C4⋊C8×C43C2312yes—
211#103×C43C2318yes—
212C22⋊C8×C43C2312yes—
213C4×C8×C43C2312yes—
214C23×D43C2×D411yescharacteristic
215C2×Q8×C43—21no—
216C2×Q8×C43—22no—
217C2×Q8×C43—22no—
218C2×Q8×C43—44no—
219C2×Q8×C43C2412yes—
220C22×C4×C43—22no—
221C22×C4×C43C2×D411yescharacteristic
222C22×C4×C43C2×D411yescharacteristic
223C22×C4×C43C2411yescharacteristic
224C2×C22⋊D43—22no—
225C22×Dic43—22no—
226C22×Dic43C2×D411yescharacteristic
227C22×Dic43C2×D411yescharacteristic
228C22×Dic43C2×D411yescharacteristic
229#10621902—28no—
230#10621902—44no—
231#10621898—44no—
232C2×D172—21no—
233C2×D172—21no—
234C2×D172—22no—
235C2×D172—22no—
236C2×D172C2412yes—
237C2×C4×D43—24no—
238C2×C4×D43—24no—
239C2×C4×D43—22no—
240C2×C4×D43—22no—
241C2×C4×D43—22no—
242C2×C4×D43—42no—
243C2×C4×D43C2×D411yescharacteristic
244C2×C4×D43C2×D411yescharacteristic
245C2×C4×D43C2×D411yescharacteristic
246C2×C4×D43C2×D411yescharacteristic
247C2×C4×D43C2×D411yescharacteristic
248C2×C4×D43C2×D411yescharacteristic
249C2×C4×D43C2×D411yescharacteristic
250C2×C4×D43C2×D411yescharacteristic
251C2×C4×D43C2×D411yescharacteristic
252C2×C4×D43C2×D411yescharacteristic
253C2×C4×D43C2411yescharacteristic
254C2×C4×D43C2411yescharacteristic
255C2×Dic86—21no—
256C2×Dic86—22no—
257C2×Dic86—22no—
258C2×Dic86—44no—
259C2×C8×C43C2414yes—
260C4⋊C4×C43—22no—
261C4⋊C4×C43—22no—
262C4⋊C4×C43—22no—
263C4⋊C4×C43—21no—
264C4⋊C4×C43—21no—
265C4⋊C4×C43—21no—
266C4⋊C4×C43—22no—
267C4⋊C4×C43—22no—
268C4⋊C4×C43C2414yes—
269C4⋊C4×C43C2412yes—
270C22⋊C4×C43—22no—
271C42×C43—22no—
272C42×C43C2×D411yescharacteristic
273C42×C43C2×D411yescharacteristic
274C42×C43C2411yescharacteristic
275C42×C43C2411yescharacteristic
276(C2×D43)⋊C4—22no—
277(C2×D43)⋊C4—22no—
278(C2×D43)⋊C4—22no—
279(C2×D43)⋊C4—22no—
280(C2×D43)⋊C4—22no—
281(C2×D43)⋊C4—22no—
282(C2×D43)⋊C4—24no—
283(C2×D43)⋊C4—24no—
284(C2×D43)⋊C4—22no—
285(C2×D43)⋊C4—22no—
286C4⋊Dic43—22no—
287C4⋊Dic43—22no—
288C4⋊Dic43—22no—
289C4⋊Dic43—21no—
290C4⋊Dic43—24no—
291C4⋊Dic43—24no—
292C4⋊Dic43—22no—
293C4⋊Dic43—22no—
294C4⋊Dic43C2414yes—
295C4⋊Dic43C2412yes—
296Dic43⋊C4—24no—
297Dic43⋊C4—24no—
298Dic43⋊C4—22no—
299Dic43⋊C4—22no—
300C4×Dic43—22no—
301C4×Dic43—22no—
302C4×Dic43—24no—
303C4×Dic43—24no—
304C4×Dic43C2×D411yescharacteristic
305C4×Dic43C2×D411yescharacteristic
306C4×Dic43C2×D411yescharacteristic
307C4×Dic43C2×D411yescharacteristic
308C4×Dic43C2×D411yescharacteristic
309C4×Dic43C2×D411yescharacteristic
310C4×Dic43C2×D411yescharacteristic
311C4×Dic43C2×D411yescharacteristic
312C4×Dic43C2×D411yescharacteristic
313C4×Dic43C2×D411yescharacteristic
314C4×Dic43C2411yescharacteristic
315C4×Dic43C2411yescharacteristic
316C2×C43⋊C8C2414yes—
317C8×D43—28no—
318C23×C43C22×D411yescharacteristic
319C22×D43—22no—
320C22×D43—22no—
321C22×D43—22no—
322C22×D43—41no—
323C22×D43C22×D411yescharacteristic
324C22×D43C22×D411yescharacteristic
325Q8×C43—24no—
326Q8×C43—44no—
327Q8×C43—42no—
328Q8×C43—44no—
329C2×C4×C43—22no—
330C2×C4×C43—22no—
331C2×C4×C43—24no—
332C2×C4×C43—22no—
333C2×C4×C43—22no—
334C2×C4×C43—44no—
335C2×C4×C43#13514yes—
336C2×C4×C43C22×D411yescharacteristic
337C2×C4×C43C22×D411yescharacteristic
338C2×C4×C43C22×D411yescharacteristic
339C2×C4×C43C22×D411yescharacteristic
340C2×C4×C43C22×D411yescharacteristic
341C2×C4×C43C2511yescharacteristic
342C22⋊D43—44no—
343C2×Dic43—22no—
344C2×Dic43—22no—
345C2×Dic43—24no—
346C2×Dic43—22no—
347C2×Dic43—41no—
348C2×Dic43—44no—
349C2×Dic43C22×D411yescharacteristic
350C2×Dic43C22×D411yescharacteristic
351C2×Dic43C22×D411yescharacteristic
352C2×Dic43C22×D411yescharacteristic
353C2×Dic43C22×D411yescharacteristic
354C2×Dic43C22×D411yescharacteristic
355D172—24no—
356D172—44no—
357D172—44no—
358D172—42no—
359D172—42no—
360C4×D43—22no—
361C4×D43—22no—
362C4×D43—22no—
363C4×D43—22no—
364C4×D43—22no—
365C4×D43—22no—
366C4×D43—22no—
367C4×D43—22no—
368C4×D43—22no—
369C4×D43—41no—
370C4×D43—41no—
371C4×D43—44no—
372C4×D43—44no—
373C4×D43—44no—
374C4×D432−1+414yes—
375Dic86—44no—
376Dic86—44no—
377Dic86—42no—
378C8×C43—24no—
379C43⋊C8—24no—
380#60846—431nomaximal, Sylow
381C22×C43—21no—
382C22×C43—21no—
383C22×C43C2×#13512yes—
384C22×C43C23×D411yescharacteristic
385C2×D43—21no—
386C2×D43—21no—
387C2×D43—21no—
388C2×D43—21no—
389C2×D43—21no—
390C2×D43—44no—
391C2×D43—42no—
392C2×D43—42no—
393C2×D43—42no—
394C2×D43#53612yes—
395C4×C43—21no—
396C4×C43—21no—
397C4×C43—42no—
398C4×C43—42no—
399C4×C43—44no—
400C4×C43C2×#13512yes—
401C4×C43C2×#13512yes—
402C4×C43#57512yes—
403C4×C43C2×2−1+412yes—
404Dic43—21no—
405Dic43—21no—
406Dic43—21no—
407Dic43—21no—
408Dic43—21no—
409Dic43—44no—
410Dic43—42no—
411Dic43#53612yes—
412#3444—431no—
413C2×#533—431no—
414#3233—434no—
415#3232—434no—
416#3231—432no—
417#3230D4311yescharacteristic, complemented
418#3229—431no—
419#3228—432no—
420#3227—431no—
421#3226—431no—
422#3160—432no—
423#3131—432no—
424#3091—434no—
425#3076—434no—
426C2×#431—431no—
427C2×C43—22no—
428C2×C43C2×#53611yescharacteristic
429C2×C43C22×#13511yescharacteristic
430C2×C43C2×#57511yescharacteristic
431D43—22no—
432D43—41no—
433D43—82no—
434#533—432no—
435#533—432no—
436#533—431no—
437#533—432no—
438#533—432no—
439#533—431no—
440#533—861no—
441#533—861no—
442#533—861no—
443#533—861no—
444#533C2×D4311yescharacteristic
445#532—431no—
446#532—431no—
447#532—431no—
448C2×C4⋊Q8—431no—
449C2×C4⋊Q8C2×D4311yescharacteristic
450#529—432no—
451#529—432no—
452#529—861no—
453#529—861no—
454#529—861no—
455#529—861no—
456C2×#125—432no—
457#525—432no—
458#525—861no—
459#525—861no—
460C2×C22⋊Q8—861no—
461C2×C22⋊Q8—861no—
462C4×#41—432no—
463C4×#41—861no—
464C4×#41—861no—
465C2×C4×Q8—861no—
466C2×C4×Q8—861no—
467C2×#117—432no—
468C22×C42—431no—
469#500—432no—
470#500C2×D4312yescomplemented
471#499—438no—
472#498—432no—
473#498—432no—
474#488—438no—
475#487—432no—
476#487C2×D4312yescomplemented
477#486—432no—
478#486—432no—
479#485—438no—
480#484C2×D4314yes—
481#483—434no—
482#482—438no—
483#481—434no—
484#480—434no—
485#479—438no—
486#478—438no—
487#477C2×D4314yescomplemented
488#476—434no—
489#475—434no—
490#474—434no—
491#431—431no—
492#431—432no—
493#431—432no—
494#431—432no—
495#431C2×D4311yescharacteristic
496#427—438no—
497C2×C4⋊C8—432no—
498#416—438no—
499C2×C22⋊C8—432no—
500C2×C4×C8—432no—
501C43#6084611yescharacteristic, complemented, Sylow
502C2×#41—432no—
503C2×#41—861no—
504C2×#41—861no—
505C22×Q8—21no—
506C22×Q8—861no—
507C23×C4—431no—
508C23×C4—431no—
509C23×C4—431no—
510C22×C8—434no—
511C4⋊Q8—21no—
512C4⋊Q8—21no—
513C4⋊Q8—432no—
514C4⋊Q8—432no—
515C4⋊Q8—431no—
516C4⋊Q8—861no—
517C4⋊Q8—861no—
518C4⋊Q8C22×D4311yescharacteristic
519C4⋊Q8C22×D4312yes—
520C4⋊Q8C22×D4312yes—
521C4⋊Q8C22×D4311yescharacteristic
522#127—431no—
523#126—862no—
524#126—862no—
525#125—21no—
526#125—434no—
527#125—434no—
528#125—432no—
529#125—862no—
530#125—862no—
531#125—861no—
532#124—432no—
533#124—861no—
534#124—861no—
535#123—862no—
536#123—862no—
537#123—862no—
538C22⋊Q8—21no—
539C22⋊Q8—432no—
540C22⋊Q8—862no—
541C22⋊Q8—862no—
542C22⋊Q8—862no—
543C22⋊Q8—862no—
544C22⋊Q8—861no—
545C22⋊Q8—861no—
546C22⋊Q8—862no—
547C22⋊Q8—862no—
548C22⋊Q8—862no—
549C22⋊Q8—862no—
550C22⋊Q8—861no—
551C22⋊Q8C22×D4312yes—
552#121—432no—
553#121—432no—
554#121—861no—
555#121—861no—
556#121—861no—
557#121—861no—
558#120—862no—
559C4×Q8—21no—
560C4×Q8—432no—
561C4×Q8—862no—
562C4×Q8—862no—
563C4×Q8—862no—
564C4×Q8—862no—
565C4×Q8—861no—
566C4×Q8—861no—
567C4×Q8—862no—
568C4×Q8—862no—
569C4×Q8—862no—
570C4×Q8—862no—
571C4×Q8—861no—
572C4×Q8C22×D4312yes—
573C4×D4—432no—
574C4×D4—432no—
575C4×D4—862no—
576C4×D4—862no—
577C4×D4—861no—
578C4×D4—861no—
579C4×D4—861no—
580C4×D4—862no—
581C4×D4—862no—
582C4×D4—862no—
583C4×D4—862no—
584C4×D4—861no—
585#117—21no—
586#117—434no—
587#117—434no—
588#117—432no—
589#117—862no—
590#117—862no—
591#117—862no—
592#117—862no—
593#117—862no—
594#117—861no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—432no—
597C2×C4⋊C4—862no—
598C2×C4⋊C4—862no—
599C2×C4⋊C4—861no—
600C2×C4⋊C4C22×D4312yes—
601C2×C22⋊C4—862no—
602C2×C42—431no—
603C2×C42—431no—
604C2×C42—431no—
605C2×C42—431no—
606C2×C42—431no—
607C2×C42—431no—
608C2×C42—431no—
609C2×C42—431no—
610C2×C42—431no—
611C2×C42—431no—
612C2×C42—431no—
613C2×C42—862no—
614C2×C42—862no—
615C2×C42C22×D4311yescharacteristic
616#107—438no—
617#107C22×D4318yes—
618#106—438no—
619#106—438no—
620C4⋊C8—434no—
621C4⋊C8—432no—
622C4⋊C8C22×D4312yes—
623#103—438no—
624#103C22×D4318yes—
625#102—438no—
626#102—438no—
627C22⋊C8—432no—
628C22⋊C8—434no—
629C22⋊C8C22×D4312yes—
630C4×C8—434no—
631C4×C8—432no—
632C4×C8C22×D4312yes—
633C24—431no—
634#41—868no—
635#41—1724no—
636#41—1724no—
637C2×Q8—21no—
638C2×Q8—22no—
639C2×Q8—22no—
640C2×Q8—44no—
641C2×Q8—861no—
642C2×Q8—862no—
643C2×Q8—862no—
644C2×Q8—1724no—
645C2×Q8C23×D4312yes—
646C2×D4—432no—
647C2×D4—862no—
648C2×D4—862no—
649C2×D4—862no—
650C2×D4—861no—
651C2×D4—861no—
652C22×C4—22no—
653C22×C4—431no—
654C22×C4—431no—
655C22×C4—431no—
656C22×C4—431no—
657C22×C4—431no—
658C22×C4—431no—
659C22×C4—431no—
660C22×C4—431no—
661C22×C4—431no—
662C22×C4—431no—
663C22×C4—431no—
664C22×C4—431no—
665C22×C4—431no—
666C22×C4—431no—
667C22×C4—431no—
668C22×C4—864no—
669C22×C4—862no—
670C22×C4—862no—
671C22×C4—864no—
672C22×C4—862no—
673C22×C4—862no—
674C22×C4—1722no—
675C22×C4D4×D4311yescharacteristic
676C22×C4D4×D4311yescharacteristic
677C22×C4C23×D4311yescharacteristic
678C2×C8—434no—
679C2×C8—868no—
680C2×C8C23×D4314yes—
681C4⋊C4—22no—
682C4⋊C4—22no—
683C4⋊C4—22no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—22no—
688C4⋊C4—22no—
689C4⋊C4—434no—
690C4⋊C4—432no—
691C4⋊C4—864no—
692C4⋊C4—864no—
693C4⋊C4—864no—
694C4⋊C4—864no—
695C4⋊C4—862no—
696C4⋊C4—862no—
697C4⋊C4—862no—
698C4⋊C4—862no—
699C4⋊C4—862no—
700C4⋊C4—862no—
701C4⋊C4—862no—
702C4⋊C4—861no—
703C4⋊C4C23×D4314yes—
704C4⋊C4C23×D4312yes—
705C22⋊C4—22no—
706C22⋊C4—862no—
707C22⋊C4—862no—
708C22⋊C4—862no—
709C22⋊C4—862no—
710C22⋊C4—864no—
711C22⋊C4—864no—
712C22⋊C4—862no—
713C22⋊C4—862no—
714C22⋊C4—862no—
715C22⋊C4—862no—
716C42—22no—
717C42—431no—
718C42—431no—
719C42—431no—
720C42—431no—
721C42—431no—
722C42—431no—
723C42—431no—
724C42—431no—
725C42—431no—
726C42—431no—
727C42—431no—
728C42—431no—
729C42—862no—
730C42—864no—
731C42—864no—
732C42—862no—
733C42D4×D4311yescharacteristic
734C42D4×D4311yescharacteristic
735C42C23×D4311yescharacteristic
736C42C23×D4311yescharacteristic
737C23—431no—
738C23—431no—
739C23—862no—
740C23—862no—
741C23—862no—
742C23—1721no—
743C23C2×D4×D4311yescharacteristic
744Q8—24no—
745Q8—44no—
746Q8—44no—
747Q8—42no—
748Q8—1724no—
749Q8—1724no—
750Q8—1722no—
751D4—864no—
752D4—1724no—
753D4—1724no—
754D4—1724no—
755D4—1722no—
756D4—1722no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—24no—
762C2×C4—44no—
763C2×C4—431no—
764C2×C4—434no—
765C2×C4—431no—
766C2×C4—431no—
767C2×C4—431no—
768C2×C4—431no—
769C2×C4—431no—
770C2×C4—862no—
771C2×C4—862no—
772C2×C4—862no—
773C2×C4—862no—
774C2×C4—862no—
775C2×C4—862no—
776C2×C4—862no—
777C2×C4—862no—
778C2×C4—862no—
779C2×C4—862no—
780C2×C4—862no—
781C2×C4—862no—
782C2×C4—864no—
783C2×C4—1721no—
784C2×C4—1721no—
785C2×C4—1724no—
786C2×C4—1724no—
787C2×C4—1721no—
788C2×C4—1724no—
789C2×C4—1724no—
790C2×C4#1306334814yes—
791C2×C4C2×D4×D4311yescharacteristic
792C2×C4C2×D4×D4311yescharacteristic
793C2×C4C2×D4×D4311yescharacteristic
794C2×C4C2×D4×D4311yescharacteristic
795C2×C4C2×D4×D4311yescharacteristic
796C2×C4C24×D4311yescharacteristic
797C8—24no—
798C8—864no—
799C22—21no—
800C22—21no—
801C22—432no—
802C22—861no—
803C22—861no—
804C22—861no—
805C22—861no—
806C22—861no—
807C22—1724no—
808C22—1722no—
809C22—1722no—
810C22—1722no—
811C22C2×#1306334812yes—
812C22C22×D4×D4311yescharacteristic
813C4—21no—
814C4—21no—
815C4—44no—
816C4—42no—
817C4—42no—
818C4—432no—
819C4—861no—
820C4—861no—
821C4—861no—
822C4—861no—
823C4—861no—
824C4—1722no—
825C4—1724no—
826C4C2×#1306334812yes—
827C4C2×#1306334812yes—
828C4#1458369512yes—
829C42−1+4×D4312yes—
830C2—22no—
831C2—862no—
832C2—3442no—
833C2—1721no—
834C2#536×D4311yescharacteristic
835C2C22×#1306334811yescharacteristic
836C2C2×#1458369511yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3230C2
socleC22×C43C23×D4
prime radical#19147892C2
hypercenter#3230D43
hypocenterC43#60846
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3230

Complements

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

NH ≅ G/Ntype
2. C2×#14583454C2semidirect
3. #19145779C2semidirect
4. #19145768C2semidirect
5. #19145751C2semidirect
6. #19145736C2semidirect
7. #19145734C2semidirect
8. #19145723C2semidirect
9. #19145718C2semidirect
10. #19145106C2semidirect
11. #19144919C2semidirect
12. #19144511C2semidirect
13. #19144386C2semidirect
14. #431×D43C2semidirect
15. C43×#3230C2semidirect
49. #14583304C22semidirect
50. #14583300C22semidirect
51. #14583295C22semidirect
52. #14583295C22semidirect
53. #14583255C22semidirect
54. #14583249C22semidirect
55. #14583247C22semidirect
56. #14583246C22semidirect
62. #14583208C22semidirect
63. #14583202C22semidirect
64. #14583186C22semidirect
65. #14583184C22semidirect
66. #14583180C22semidirect
78. C43×#500C22semidirect
79. C43×#487C22semidirect
81. C43×#477C22semidirect
417. #3230D43semidirect
470. #500C2×D43semidirect
476. #487C2×D43semidirect
487. #477C2×D43semidirect
501. C43#60846semidirect

Maximal subgroups

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

subgroupindex
#191478922
C2×#145834542
#191457792
#191457682
#191457512
#191457362
#191457342
#191457232
#191457182
#191451062
#191449192
#191445112
#191443862
#431×D432
C43×#32302
#6084643