Finite Group Databasebeta

← #25966715

Subgroups — #25966715

Order 11008.

1976 conjugacy classes of subgroups.

The subgroup lattice has 1012 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147892C211yesmaximal, characteristic
2#533×D43C211yesmaximal, characteristic, complemented
3#19145339C211yesmaximal, characteristic, complemented
4#19145338C211yesmaximal, characteristic, complemented
5#19145316C211yesmaximal, characteristic, complemented
6#19145315C211yesmaximal, characteristic, complemented
7#19145299C214yesmaximal, complemented
8#19145199C214yesmaximal, complemented
9#19145177C211yesmaximal, characteristic, complemented
10#19145155C211yesmaximal, characteristic, complemented
11#19145154C211yesmaximal, characteristic, complemented
12#19145138C211yesmaximal, characteristic, complemented
13#19145053C211yesmaximal, characteristic, complemented
14#19144990C211yesmaximal, characteristic, complemented
15#19144972C211yesmaximal, characteristic, complemented
16#19144222C214yesmaximal, complemented
17C4×#13063357C214yesmaximal, complemented
18C2×C4×#10621872C211yesmaximal, characteristic, complemented
19C43×#3170C211yesmaximal, characteristic, complemented
20C2×#13063357C2214yes—
21C22×#10621872C2212yes—
22#14583456C2211yescharacteristic
23#14583455—21no—
24#14583454C2211yescharacteristic
25#14583454C2211yescharacteristic
26#14583454C2211yescharacteristic
27#14583454C2211yescharacteristic
28#14583453—21no—
29#14583453C2212yes—
30#14583452—21no—
31#14583451—21no—
32#14583451C2212yes—
33#14583450C2211yescharacteristic
34#14583450C2211yescharacteristic
35#14583449C2211yescharacteristic
36C4⋊Q8×D43C2211yescharacteristic
37C4⋊Q8×D43C2211yescharacteristic
38#14583436—21no—
39#14583436C2212yes—
40#14583435—21no—
41#14583435C2212yes—
42#14583434—21no—
43#14583434—21no—
44#125×D43—21no—
45#14583412—21no—
46#14583412C2212yes—
47#14583411—21no—
48C22⋊Q8×D43—21no—
49C22⋊Q8×D43C2212yes—
50C4×#10621902—21no—
51C4×#10621902C2212yes—
52#14583367—21no—
53C4×Q8×D43—21no—
54C4×Q8×D43C2212yes—
55#117×D43—21no—
56C2×C42×D43C2211yescharacteristic
57#14583307C2214yescomplemented
58#14583302C2211yescharacteristic, complemented
59#14583297C2211yescharacteristic, complemented
60#14583295C2211yescharacteristic, complemented
61#14583292C2214yescomplemented
62#14583278C2211yescharacteristic, complemented
63#14583273C2211yescharacteristic, complemented
64#14583272C2211yescharacteristic, complemented
65#14583266C2214yescomplemented
66#14583260C2214yescomplemented
67#14583251C2211yescharacteristic, complemented
68#14583250C2211yescharacteristic, complemented
69#14583249C2211yescharacteristic, complemented
70#14583249C2211yescharacteristic, complemented
71#14583247C2211yescharacteristic, complemented
72#14583246C2211yescharacteristic, complemented
73#14583156C2214yes—
74#14583154C2214yes—
75#14583148C2214yes—
76#14583146C2214yes—
77#14583138C2214yes—
78#14583130C2214yes—
79#14583128C2214yes—
80#14583006C2214yescomplemented
81#14583003C2214yescomplemented
82#14583002C2214yescomplemented
83#14582998C2214yescomplemented
84C4×#10621885C2214yescomplemented
85C4×#10621873C2214yescomplemented
86C4×#10621884C2214yescomplemented
87#14582940C2214yes—
88#14582906C2214yes—
89#14582899C2214yes—
90C4×#10621872C2211yescharacteristic
91C4×#10621872C2211yescharacteristic
92C4×#10621872C2211yescharacteristic
93C4×#10621872C2211yescharacteristic
94C4×#10621872C2212yes—
95C4×#10621872C2212yes—
96C2×#13063235C2212yes—
97C2×C4×C43⋊C8C2211yescharacteristic
98C43×#533C2211yescharacteristic
99C43×#533C2211yescharacteristic
100C43×#500C2211yescharacteristic, complemented
101C43×#494C2211yescharacteristic, complemented
102C43×#487C2211yescharacteristic, complemented
103C43×#487C2211yescharacteristic, complemented
104C43×#467C2214yes—
105C4×Q16×C43C2214yescomplemented
106C2×C4×C8×C43C2211yescharacteristic
107C2×#10621902—21no—
108C2×#10621902C2312yes—
109C2×#10621898—21no—
110C2×Q8×D43—21no—
111C2×Q8×D43C2312yes—
112C22×C4×D43D411yescharacteristic
113C22×C4×D43D411yescharacteristic
114C22×C4×D43C2311yescharacteristic
115#13063357—216no—
116C2×#10621885C2314yes—
117C2×#10621873C2314yes—
118C2×#10621884C2314yes—
119C2×#10621872—28no—
120C2×#10621872C2312yes—
121C2×#10621872C2312yes—
122C2×#10621872C2312yes—
123C2×#10621872C2312yes—
124C22×C43⋊C8C2312yes—
125#13063325C2311yescharacteristic
126#13063325C2311yescharacteristic
127#13063325C2311yescharacteristic
128#13063324—21no—
129#13063324—21no—
130#13063324—21no—
131#13063324C2312yes—
132#13063323—21no—
133#13063323C2312yes—
134#13063322C2311yescharacteristic
135#13063320—22no—
136#13063320—22no—
137#13063317—21no—
138#13063316—21no—
139#13063316—21no—
140#13063316—21no—
141#13063316C2312yes—
142#13063315—22no—
143#13063315—22no—
144#13063314—21no—
145#13063314C2312yes—
146#13063313—21no—
147#13063310—22no—
148#13063310—22no—
149#13063309—22no—
150#13063305—21no—
151#13063305—21no—
152#13063305—21no—
153#13063305C2312yes—
154#13063304—21no—
155#13063304C2312yes—
156#13063303—22no—
157#13063303—22no—
158#13063302—22no—
159#13063302—22no—
160#13063301—21no—
161#13063301—21no—
162#13063301C2312yes—
163#13063301C2312yes—
164#13063300—21no—
165#13063300—21no—
166#13063300—21no—
167#13063300C2312yes—
168#13063299—21no—
169#13063299C2312yes—
170#13063295—22no—
171Q8×Dic43—21no—
172Q8×Dic43—21no—
173Q8×Dic43C2312yes—
174Q8×Dic43C2312yes—
175C4×Dic86—21no—
176C4×Dic86—22no—
177C4×Dic86—22no—
178C4×Dic86C2312yes—
179#13063290—21no—
180#13063290—22no—
181#13063290—22no—
182#13063290—21no—
183#13063290—21no—
184#13063290C2312yes—
185C4×D172—22no—
186C4×D172—22no—
187C4×D172—21no—
188C4×D172C2312yes—
189#13063287—22no—
190#13063287—22no—
191#13063287—21no—
192#13063287—21no—
193#13063287—21no—
194#13063287C2312yes—
195(C22⋊D43)⋊C4—22no—
196(C22⋊D43)⋊C4—22no—
197#13063284—21no—
198#13063283—21no—
199#13063283—21no—
200#13063283—21no—
201#13063283—22no—
202#13063283—22no—
203#13063283C2312yes—
204#13063282—22no—
205#13063282—22no—
206#13063281—22no—
207C4⋊C4×D43—21no—
208C4⋊C4×D43—21no—
209C4⋊C4×D43—21no—
210C4⋊C4×D43—22no—
211C4⋊C4×D43—22no—
212C4⋊C4×D43C2312yes—
213C22⋊C4×D43—22no—
214C2×C4×Dic43D411yescharacteristic
215C2×C4×Dic43D411yescharacteristic
216C2×C4×Dic43C2311yescharacteristic
217C42×D43—22no—
218C42×D43—22no—
219C42×D43D411yescharacteristic
220C42×D43D411yescharacteristic
221C42×D43D411yescharacteristic
222C42×D43D411yescharacteristic
223C42×D43C2311yescharacteristic
224C42×D43C2311yescharacteristic
225C42×D43C2311yescharacteristic
226C42×D43C2311yescharacteristic
227#13063258C2314yes—
228#13063257C2314yes—
229#13063256C2314yes—
230#13063250C2314yes—
231#13063249C2314yes—
232#13063249C2314yes—
233#13063248C2314yes—
234#13063247C2314yes—
235#13063245C2314yes—
236#13063235C2312yes—
237#13063235C2312yes—
238#13063235C2312yes—
239#13063235C2312yes—
240C4×C43⋊C8C2311yescharacteristic
241C4×C43⋊C8C2312yes—
242C4×C43⋊C8C2311yescharacteristic
243C2×Q16×C43C2314yes—
244C22×C8×C43C2312yes—
245C4⋊Q8×C43C2311yescharacteristic
246C4⋊Q8×C43C2311yescharacteristic
247C4⋊Q8×C43C2311yescharacteristic
248C4⋊Q8×C43C2311yescharacteristic
249#125×C43—21no—
250#125×C43—21no—
251C22⋊Q8×C43—21no—
252C22⋊Q8×C43—21no—
253C22⋊Q8×C43C2312yes—
254C22⋊Q8×C43C2312yes—
255C4×Q8×C43—21no—
256C4×Q8×C43—21no—
257C4×Q8×C43C2312yes—
258C4×Q8×C43C2312yes—
259#117×C43—21no—
260#117×C43—21no—
261C2×C42×C43C2311yescharacteristic
262#107×C43C2314yes—
263#103×C43C2314yes—
264#103×C43C2314yes—
265C4×C8×C43C2311yescharacteristic
266C4×C8×C43C2312yes—
267C4×C8×C43C2311yescharacteristic
268C23×D43C2×D411yescharacteristic
269C2×Q8×C43—21no—
270C2×Q8×C43—21no—
271C2×Q8×C43C2412yes—
272C2×Q8×C43C2412yes—
273C22×C4×C43C2×D411yescharacteristic
274C22×C4×C43C2×D411yescharacteristic
275C22×C4×C43C2411yescharacteristic
276C2×C22⋊D43—22no—
277C22×Dic43C2×D411yescharacteristic
278C22×Dic43C2×D411yescharacteristic
279C22×Dic43C2×D411yescharacteristic
280#10621902—28no—
281#10621902—44no—
282Q8×D43—28no—
283Q8×D43—44no—
284#10621898—44no—
285C2×D172—21no—
286C2×D172—21no—
287C2×D172—22no—
288C2×D172—22no—
289C2×D172C2412yes—
290C2×C4×D43—24no—
291C2×C4×D43—24no—
292C2×C4×D43—22no—
293C2×C4×D43—22no—
294C2×C4×D43—22no—
295C2×C4×D43—22no—
296C2×C4×D43—22no—
297C2×C4×D43—42no—
298C2×C4×D43C2×D411yescharacteristic
299C2×C4×D43C2×D411yescharacteristic
300C2×C4×D43C2×D411yescharacteristic
301C2×C4×D43C2×D411yescharacteristic
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×D43C2411yescharacteristic
309C2×C4×D43C2411yescharacteristic
310C2×Dic86—21no—
311C2×Dic86—21no—
312C2×Dic86—22no—
313C2×Dic86—22no—
314C2×Dic86C2412yes—
315Q16×C43—28no—
316C2×C8×C43—24no—
317C2×C8×C43C2412yes—
318C2×C8×C43C2412yes—
319C4⋊C4×C43—21no—
320C4⋊C4×C43—21no—
321C4⋊C4×C43—21no—
322C4⋊C4×C43—21no—
323C4⋊C4×C43—21no—
324C4⋊C4×C43—21no—
325C4⋊C4×C43—22no—
326C4⋊C4×C43—22no—
327C4⋊C4×C43—22no—
328C4⋊C4×C43—22no—
329C4⋊C4×C43C2412yes—
330C4⋊C4×C43C2412yes—
331C22⋊C4×C43—22no—
332C22⋊C4×C43—22no—
333C42×C43—22no—
334C42×C43—22no—
335C42×C43C2×D411yescharacteristic
336C42×C43C2×D411yescharacteristic
337C42×C43C2411yescharacteristic
338C42×C43C2411yescharacteristic
339C22⋊Dic43—22no—
340#10621885—28no—
341#10621884—28no—
342(C2×D43)⋊C4—22no—
343(C2×D43)⋊C4—22no—
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—21no—
356C4⋊Dic43—22no—
357C4⋊Dic43—22no—
358C4⋊Dic43—22no—
359C4⋊Dic43—22no—
360C4⋊Dic43C2412yes—
361C4⋊Dic43C2412yes—
362Dic43⋊C4—22no—
363Dic43⋊C4—22no—
364Dic43⋊C4—22no—
365Dic43⋊C4—22no—
366Dic43⋊C4—22no—
367Dic43⋊C4—22no—
368Dic43⋊C4—22no—
369Dic43⋊C4—22no—
370Dic43⋊C4—22no—
371Dic43⋊C4—22no—
372C4×Dic43—22no—
373C4×Dic43—22no—
374C4×Dic43—22no—
375C4×Dic43—22no—
376C4×Dic43—22no—
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×Dic43C2×D411yescharacteristic
387C4×Dic43C2411yescharacteristic
388C4×Dic43C2411yescharacteristic
389C2×C43⋊C8—24no—
390C2×C43⋊C8C2412yes—
391C2×C43⋊C8C2412yes—
392#10621873—28no—
393#10621872—24no—
394#10621872—24no—
395#10621872—24no—
396#10621872#4118yescomplemented
397C23×C43C22×D411yescharacteristic
398C22×D43—22no—
399C22×D43—22no—
400C22×D43—22no—
401C22×D43—41no—
402C22×D43C22×D411yescharacteristic
403C22×D43C22×D411yescharacteristic
404Q8×C43—24no—
405Q8×C43—24no—
406Q8×C43—42no—
407Q8×C43—42no—
408C2×C4×C43—22no—
409C2×C4×C43—22no—
410C2×C4×C43—22no—
411C2×C4×C43—22no—
412C2×C4×C43—22no—
413C2×C4×C43—22no—
414C2×C4×C43#13714yescomplemented
415C2×C4×C43C22×D411yescharacteristic
416C2×C4×C43C22×D411yescharacteristic
417C2×C4×C43C22×D411yescharacteristic
418C2×C4×C43C22×D411yescharacteristic
419C2×C4×C43C22×D411yescharacteristic
420C2×C4×C43C2511yescharacteristic
421C22⋊D43—44no—
422C2×Dic43—22no—
423C2×Dic43—22no—
424C2×Dic43—22no—
425C2×Dic43—22no—
426C2×Dic43—22no—
427C2×Dic43—41no—
428C2×Dic43C22×D411yescharacteristic
429C2×Dic43C22×D411yescharacteristic
430C2×Dic43C22×D411yescharacteristic
431C2×Dic43C22×D411yescharacteristic
432C2×Dic43C22×D411yescharacteristic
433C2×Dic43C22×D411yescharacteristic
434D172—24no—
435D172—44no—
436D172—44no—
437D172—42no—
438D172—42no—
439C4×D43—22no—
440C4×D43—22no—
441C4×D43—22no—
442C4×D43—22no—
443C4×D43—22no—
444C4×D43—22no—
445C4×D43—22no—
446C4×D43—22no—
447C4×D43—22no—
448C4×D43—41no—
449C4×D43—41no—
450C4×D43—44no—
451C4×D43—44no—
452C4×D43—44no—
453C4×D43—44no—
454C4×D43—44no—
455C4×D43C2×#4114yes—
456Dic86—24no—
457Dic86—44no—
458Dic86—42no—
459Dic86—42no—
460Dic86—44no—
461C8×C43—22no—
462C8×C43C2×#4114yes—
463C43⋊C8—22no—
464C43⋊C8C2×#4114yes—
465#60701—431nomaximal, Sylow
466C22×C43—21no—
467C22×C43—21no—
468C22×C43C2×#13712yes—
469C22×C43C23×D411yescharacteristic
470C2×D43—21no—
471C2×D43—21no—
472C2×D43—21no—
473C2×D43—21no—
474C2×D43—21no—
475C2×D43—44no—
476C2×D43—42no—
477C2×D43—42no—
478C2×D43—42no—
479C2×D43#53212yes—
480C4×C43—21no—
481C4×C43—21no—
482C4×C43—42no—
483C4×C43—42no—
484C4×C43—42no—
485C4×C43—42no—
486C4×C43C2×#13712yes—
487C4×C43C2×#13712yes—
488C4×C43#57512yes—
489C4×C43C22×#4112yes—
490Dic43—21no—
491Dic43—21no—
492Dic43—21no—
493Dic43—21no—
494Dic43—21no—
495Dic43—42no—
496Dic43—42no—
497Dic43—42no—
498Dic43#53212yes—
499#3444—431no—
500C2×#533—431no—
501#3185—431no—
502#3185—431no—
503#3182—431no—
504#3182—431no—
505#3181—434no—
506#3172—434no—
507#3170—431no—
508#3170D4311yescharacteristic, complemented
509#3167—431no—
510#3167—431no—
511#3165—431no—
512#3152—431no—
513#3141—431no—
514#3139—431no—
515#3056—434no—
516C4×#137—434no—
517C2×C4×M16—431no—
518C2×C43—22no—
519C2×C43C2×#53211yescharacteristic
520C2×C43C22×#13711yescharacteristic
521C2×C43C2×#57511yescharacteristic
522D43—22no—
523D43—41no—
524D43—82no—
525C2×#137—434no—
526C22×M16—432no—
527#533—431no—
528#533—431no—
529#533—431no—
530#533—431no—
531#533—432no—
532#533—432no—
533#533—431no—
534#533—861no—
535#533—861no—
536#533—861no—
537#533—861no—
538#533C2×D4311yescharacteristic
539#533C2×D4311yescharacteristic
540#532—431no—
541#532—431no—
542#532—431no—
543C2×C4⋊Q8—431no—
544C2×C4⋊Q8—431no—
545#529—432no—
546#529—432no—
547#529—861no—
548#529—861no—
549#529—861no—
550#529—861no—
551C2×#125—861no—
552#525—432no—
553#525—861no—
554#525—861no—
555C2×C22⋊Q8—432no—
556C2×C22⋊Q8—861no—
557C4×#41—432no—
558C4×#41—861no—
559C4×#41—861no—
560C2×C4×Q8—432no—
561C2×C4×Q8—861no—
562C2×#117—861no—
563C22×C42—431no—
564#501—434no—
565#500—431no—
566#500C2×D4311yescharacteristic, complemented
567#498—431no—
568#498—431no—
569#497—434no—
570#494—431no—
571#494C2×D4311yescharacteristic, complemented
572#492—431no—
573#492—431no—
574#491—434no—
575#489—434no—
576#487—431no—
577#487—431no—
578#487—431no—
579#487—431no—
580#487C2×D4311yescharacteristic, complemented
581#487C2×D4311yescharacteristic, complemented
582#486—431no—
583#486—431no—
584#470—434no—
585#470—434no—
586#468—434no—
587#468—434no—
588#467—434no—
589#467C2×D4314yes—
590#465—434no—
591#465—434no—
592#441—434no—
593#441—434no—
594#440—434no—
595#440—434no—
596C4×Q16—434no—
597C4×Q16C2×D4314yescomplemented
598C4×SD16—434no—
599C4×SD16—434no—
600#428—434no—
601#419—434no—
602#417—434no—
603C4×M16—431no—
604C4×M16—431no—
605C4×M16—432no—
606C4×M16—431no—
607C4×M16—431no—
608C4×M16—432no—
609C2×#97—432no—
610C2×C4×C8—431no—
611C2×C4×C8C2×D4311yescharacteristic
612C43#6070111yescharacteristic, complemented, Sylow
613C2×#41—432no—
614C2×#41—861no—
615C2×#41—861no—
616C22×Q8—432no—
617C22×Q8—861no—
618C23×C4—431no—
619C23×C4—431no—
620C23×C4—431no—
621#137—8616no—
622C2×Q16—434no—
623C2×Q16C22×D4314yes—
624C2×SD16—434no—
625C2×SD16—434no—
626C2×M16—432no—
627C2×M16—432no—
628C2×M16—432no—
629C2×M16—432no—
630C2×M16—868no—
631C22×C8—432no—
632C22×C8C22×D4312yes—
633C4⋊Q8—432no—
634C4⋊Q8—432no—
635C4⋊Q8—431no—
636C4⋊Q8—431no—
637C4⋊Q8—431no—
638C4⋊Q8—861no—
639C4⋊Q8—861no—
640C4⋊Q8—861no—
641C4⋊Q8—861no—
642C4⋊Q8C22×D4311yescharacteristic
643C4⋊Q8C22×D4311yescharacteristic
644C4⋊Q8C22×D4311yescharacteristic
645C4⋊Q8C22×D4311yescharacteristic
646#127—431no—
647#126—862no—
648#126—862no—
649#125—21no—
650#125—21no—
651#125—432no—
652#125—862no—
653#125—862no—
654#125—861no—
655#125—861no—
656#125—861no—
657#125—861no—
658#124—432no—
659#124—861no—
660#124—861no—
661#123—862no—
662#123—862no—
663#123—862no—
664C22⋊Q8—21no—
665C22⋊Q8—21no—
666C22⋊Q8—432no—
667C22⋊Q8—432no—
668C22⋊Q8—432no—
669C22⋊Q8—432no—
670C22⋊Q8—862no—
671C22⋊Q8—862no—
672C22⋊Q8—862no—
673C22⋊Q8—862no—
674C22⋊Q8—861no—
675C22⋊Q8—861no—
676C22⋊Q8—861no—
677C22⋊Q8—861no—
678C22⋊Q8—861no—
679C22⋊Q8—861no—
680C22⋊Q8C22×D4312yes—
681C22⋊Q8C22×D4312yes—
682#121—432no—
683#121—432no—
684#121—861no—
685#121—861no—
686#121—861no—
687#121—861no—
688#120—862no—
689C4×Q8—21no—
690C4×Q8—21no—
691C4×Q8—432no—
692C4×Q8—432no—
693C4×Q8—432no—
694C4×Q8—432no—
695C4×Q8—862no—
696C4×Q8—862no—
697C4×Q8—862no—
698C4×Q8—861no—
699C4×Q8—862no—
700C4×Q8—861no—
701C4×Q8—861no—
702C4×Q8—861no—
703C4×Q8—861no—
704C4×Q8—861no—
705C4×Q8C22×D4312yes—
706C4×Q8C22×D4312yes—
707C4×D4—432no—
708C4×D4—432no—
709C4×D4—862no—
710C4×D4—862no—
711C4×D4—861no—
712C4×D4—861no—
713C4×D4—861no—
714C4×D4—862no—
715C4×D4—862no—
716C4×D4—862no—
717C4×D4—862no—
718C4×D4—861no—
719#117—21no—
720#117—21no—
721#117—432no—
722#117—862no—
723#117—862no—
724#117—862no—
725#117—862no—
726#117—862no—
727#117—861no—
728#117—861no—
729#117—861no—
730#117—861no—
731C2×C4⋊C4—432no—
732C2×C4⋊C4—861no—
733C2×C4⋊C4—861no—
734C2×C4⋊C4—862no—
735C2×C4⋊C4—862no—
736C2×C4⋊C4—861no—
737C2×C22⋊C4—862no—
738C2×C42—431no—
739C2×C42—431no—
740C2×C42—431no—
741C2×C42—431no—
742C2×C42—431no—
743C2×C42—431no—
744C2×C42—431no—
745C2×C42—431no—
746C2×C42—431no—
747C2×C42—431no—
748C2×C42—431no—
749C2×C42—862no—
750C2×C42—862no—
751C2×C42C22×D4311yescharacteristic
752#107—434no—
753#107C22×D4314yes—
754#106—434no—
755#106—434no—
756#103—434no—
757#103—434no—
758#103—434no—
759#103—434no—
760#103C22×D4314yes—
761#103C22×D4314yes—
762#102—434no—
763#102—434no—
764#97—432no—
765#97—432no—
766#97—432no—
767#97—432no—
768C4×C8—432no—
769C4×C8—431no—
770C4×C8—431no—
771C4×C8C22×D4312yes—
772C4×C8C22×D4311yescharacteristic
773C4×C8C22×D4311yescharacteristic
774C24—431no—
775#41—868no—
776#41—1724no—
777#41—1724no—
778C2×Q8—21no—
779C2×Q8—21no—
780C2×Q8—432no—
781C2×Q8—862no—
782C2×Q8—862no—
783C2×Q8—868no—
784C2×Q8—861no—
785C2×Q8—861no—
786C2×Q8—1724no—
787C2×Q8C23×D4312yes—
788C2×Q8C23×D4312yes—
789C2×D4—432no—
790C2×D4—862no—
791C2×D4—862no—
792C2×D4—862no—
793C2×D4—861no—
794C2×D4—861no—
795C22×C4—431no—
796C22×C4—431no—
797C22×C4—431no—
798C22×C4—431no—
799C22×C4—431no—
800C22×C4—431no—
801C22×C4—431no—
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—864no—
811C22×C4—862no—
812C22×C4—862no—
813C22×C4—862no—
814C22×C4—862no—
815C22×C4—864no—
816C22×C4—862no—
817C22×C4—1722no—
818C22×C4D4×D4311yescharacteristic
819C22×C4D4×D4311yescharacteristic
820C22×C4C23×D4311yescharacteristic
821Q16—28no—
822Q16—868no—
823SD16—868no—
824SD16—868no—
825M16—438no—
826M16—864no—
827M16—864no—
828M16—864no—
829C2×C8—24no—
830C2×C8—432no—
831C2×C8—432no—
832C2×C8—864no—
833C2×C8C23×D4312yes—
834C2×C8C23×D4312yes—
835C4⋊C4—21no—
836C4⋊C4—21no—
837C4⋊C4—21no—
838C4⋊C4—22no—
839C4⋊C4—22no—
840C4⋊C4—21no—
841C4⋊C4—21no—
842C4⋊C4—21no—
843C4⋊C4—22no—
844C4⋊C4—22no—
845C4⋊C4—432no—
846C4⋊C4—432no—
847C4⋊C4—862no—
848C4⋊C4—862no—
849C4⋊C4—862no—
850C4⋊C4—862no—
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—861no—
860C4⋊C4—861no—
861C4⋊C4—862no—
862C4⋊C4—862no—
863C4⋊C4—861no—
864C4⋊C4—861no—
865C4⋊C4C23×D4312yes—
866C4⋊C4C23×D4312yes—
867C22⋊C4—22no—
868C22⋊C4—22no—
869C22⋊C4—862no—
870C22⋊C4—862no—
871C22⋊C4—862no—
872C22⋊C4—862no—
873C22⋊C4—862no—
874C22⋊C4—862no—
875C22⋊C4—862no—
876C22⋊C4—862no—
877C22⋊C4—862no—
878C22⋊C4—862no—
879C22⋊C4—862no—
880C42—22no—
881C42—22no—
882C42—431no—
883C42—431no—
884C42—431no—
885C42—431no—
886C42—431no—
887C42—431no—
888C42—431no—
889C42—431no—
890C42—431no—
891C42—431no—
892C42—431no—
893C42—431no—
894C42—862no—
895C42—862no—
896C42—862no—
897C42—862no—
898C42—862no—
899C42D4×D4311yescharacteristic
900C42D4×D4311yescharacteristic
901C42C23×D4311yescharacteristic
902C42C23×D4311yescharacteristic
903C23—431no—
904C23—431no—
905C23—862no—
906C23—862no—
907C23—862no—
908C23—1721no—
909C23C2×D4×D4311yescharacteristic
910Q8—24no—
911Q8—24no—
912Q8—42no—
913Q8—42no—
914Q8—864no—
915Q8—1724no—
916Q8—1724no—
917Q8—1722no—
918Q8—1722no—
919D4—864no—
920D4—1724no—
921D4—1724no—
922D4—1724no—
923D4—1722no—
924D4—1722no—
925C2×C4—22no—
926C2×C4—22no—
927C2×C4—22no—
928C2×C4—22no—
929C2×C4—22no—
930C2×C4—22no—
931C2×C4—431no—
932C2×C4—434no—
933C2×C4—431no—
934C2×C4—431no—
935C2×C4—431no—
936C2×C4—431no—
937C2×C4—431no—
938C2×C4—862no—
939C2×C4—862no—
940C2×C4—862no—
941C2×C4—862no—
942C2×C4—862no—
943C2×C4—862no—
944C2×C4—862no—
945C2×C4—862no—
946C2×C4—862no—
947C2×C4—862no—
948C2×C4—862no—
949C2×C4—862no—
950C2×C4—862no—
951C2×C4—862no—
952C2×C4—1721no—
953C2×C4—1721no—
954C2×C4—1724no—
955C2×C4—1724no—
956C2×C4—1724no—
957C2×C4—1724no—
958C2×C4—1721no—
959C2×C4—1724no—
960C2×C4#1306335714yescomplemented
961C2×C4C2×D4×D4311yescharacteristic
962C2×C4C2×D4×D4311yescharacteristic
963C2×C4C2×D4×D4311yescharacteristic
964C2×C4C2×D4×D4311yescharacteristic
965C2×C4C2×D4×D4311yescharacteristic
966C2×C4C24×D4311yescharacteristic
967C8—22no—
968C8—434no—
969C8—862no—
970C8#41×D4314yes—
971C22—21no—
972C22—21no—
973C22—432no—
974C22—861no—
975C22—861no—
976C22—861no—
977C22—861no—
978C22—861no—
979C22—1724no—
980C22—1722no—
981C22—1722no—
982C22—1722no—
983C22C2×#1306335712yes—
984C22C22×D4×D4311yescharacteristic
985C4—21no—
986C4—21no—
987C4—42no—
988C4—42no—
989C4—42no—
990C4—42no—
991C4—432no—
992C4—861no—
993C4—861no—
994C4—861no—
995C4—861no—
996C4—861no—
997C4—1722no—
998C4—1722no—
999C4—1722no—
1000C4C2×#1306335712yes—
1001C4C2×#1306335712yes—
1002C4#1458369612yes—
1003C4C2×#41×D4312yes—
1004C2—22no—
1005C2—862no—
1006C2—3442no—
1007C2—1721no—
1008C2#532×D4311yescharacteristic
1009C2C22×#1306335711yescharacteristic
1010C2C2×#1458369611yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3170C2
socleC22×C43C23×D4
prime radical#19147892C2
hypercenter#3170D43
hypocenterC43#60701
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3170

Complements

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

NH ≅ G/Ntype
2. #533×D43C2semidirect
3. #19145339C2semidirect
4. #19145338C2semidirect
5. #19145316C2semidirect
6. #19145315C2semidirect
7. #19145299C2semidirect
8. #19145199C2semidirect
9. #19145177C2semidirect
10. #19145155C2semidirect
11. #19145154C2semidirect
12. #19145138C2semidirect
13. #19145053C2semidirect
14. #19144990C2semidirect
15. #19144972C2semidirect
16. #19144222C2semidirect
17. C4×#13063357C2semidirect
18. C2×C4×#10621872C2semidirect
19. C43×#3170C2semidirect
57. #14583307C22semidirect
58. #14583302C22semidirect
59. #14583297C22semidirect
60. #14583295C22semidirect
61. #14583292C22semidirect
62. #14583278C22semidirect
63. #14583273C22semidirect
64. #14583272C22semidirect
65. #14583266C22semidirect
66. #14583260C22semidirect
67. #14583251C22semidirect
68. #14583250C22semidirect
69. #14583249C22semidirect
70. #14583249C22semidirect
71. #14583247C22semidirect
72. #14583246C22semidirect
80. #14583006C22semidirect
81. #14583003C22semidirect
82. #14583002C22semidirect
83. #14582998C22semidirect
84. C4×#10621885C22semidirect
85. C4×#10621873C22semidirect
86. C4×#10621884C22semidirect
100. C43×#500C22semidirect
101. C43×#494C22semidirect
102. C43×#487C22semidirect
103. C43×#487C22semidirect
105. C4×Q16×C43C22semidirect
396. #10621872#41semidirect
414. C2×C4×C43#137semidirect
508. #3170D43semidirect
566. #500C2×D43semidirect
571. #494C2×D43semidirect
580. #487C2×D43semidirect
581. #487C2×D43semidirect
597. C4×Q16C2×D43semidirect
612. C43#60701semidirect
960. C2×C4#13063357semidirect

Maximal subgroups

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

subgroupindex
#191478922
#533×D432
#191453392
#191453382
#191453162
#191453152
#191452992
#191451992
#191451772
#191451552
#191451542
#191451382
#191450532
#191449902
#191449722
#191442222
C4×#130633572
C2×C4×#106218722
C43×#31702
#6070143