Finite Group Databasebeta

← #25968917

Subgroups — #25968917

Order 11008.

1756 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583453C211yesmaximal, characteristic
2#533×D43C211yesmaximal, characteristic
3#19145808C212yesmaximal, complemented
4#19145807C212yesmaximal, complemented
5#19145799C214yesmaximal, complemented
6#19145753C214yesmaximal, complemented
7#19145745C212yesmaximal, complemented
8#19145738C212yesmaximal, complemented
9#19145139C212yesmaximal, complemented
10#19144973C212yesmaximal, complemented
11#19144545C212yesmaximal
12#19144541C212yesmaximal
13#19144402C211yesmaximal, characteristic, complemented
14#19144400C211yesmaximal, characteristic, complemented
15#19144396C211yesmaximal, characteristic, complemented
16#19143227C211yesmaximal, characteristic
17C43×#3078C211yesmaximal, characteristic, complemented
18#14583456C2211yescharacteristic
19#14583455C2212yes—
20#14583454C2211yescharacteristic
21#14583454C2211yescharacteristic
22#14583453—21no—
23#14583453—21no—
24#14583453—21no—
25#14583453—21no—
26#14583453—21no—
27#14583453—21no—
28#14583453C2212yes—
29#14583453C2212yes—
30#14583453C2212yes—
31#14583453C2212yes—
32#14583452C2212yes—
33#14583451—21no—
34#14583451—21no—
35C2×#13063324C2211yescharacteristic
36C2×#13063323C2211yescharacteristic
37C4⋊Q8×D43C2211yescharacteristic
38C4⋊Q8×D43C2211yescharacteristic
39C2×#13063315—21no—
40#125×D43C2212yes—
41C2×#13063305C2211yescharacteristic
42C2×#13063303—21no—
43C2×#13063301C2211yescharacteristic
44C22⋊Q8×D43—21no—
45C22⋊Q8×D43—21no—
46C2×C4×Dic86—21no—
47C2×C4×Dic86C2211yescharacteristic
48C4×Q8×D43—21no—
49C4×Q8×D43—21no—
50C2×#13063282—21no—
51#117×D43C2212yes—
52C2×C42×D43C2211yescharacteristic
53#14583307C2214yescomplemented
54#14583306C2214yescomplemented
55#14583303C2214yescomplemented
56#14583296C2214yescomplemented
57#14583266C2214yescomplemented
58#14583266C2214yescomplemented
59#14583248C2214yescomplemented
60#14583248C2214yescomplemented
61#14583243C2214yes—
62#14583242C2214yes—
63#14583239C2214yes—
64#14583238C2214yes—
65#14583236C2214yes—
66#14583233C2214yes—
67#14583231C2214yes—
68#14583228C2214yes—
69#14583207C2214yescomplemented
70#14583206C2214yescomplemented
71#14583203C2214yescomplemented
72#14583195C2212yescomplemented
73#14583194C2212yescomplemented
74#14583191C2212yescomplemented
75#14583185C2212yescomplemented
76#14583184C2212yescomplemented
77#14583181C2212yescomplemented
78#14582955C2212yes—
79#14582955C2212yes—
80#14582951C2212yes—
81#14582951C2212yes—
82#14582942C2212yes—
83#14582941C2212yes—
84#14582939C2212yes—
85#14582923C2211yescharacteristic
86#14582909C2212yes—
87#14582908C2212yes—
88#14582907C2212yes—
89#14582862C2212yes—
90M16×Dic43C2212yes—
91C43×#533C2211yescharacteristic
92C2×C4×Q8×C43C2211yescharacteristic
93C43×#479C2214yescomplemented
94C43×#477C2212yescomplemented
95C43×#475C2212yescomplemented
96C43×#428C2212yes—
97C43×#423C2211yescharacteristic
98C43×#419C2212yes—
99C22×Dic86—21no—
100C22×Dic86C2311yescharacteristic
101C2×Q8×D43—21no—
102C2×Q8×D43—21no—
103C22×C4×D43D411yescharacteristic
104C22×C4×D43D411yescharacteristic
105C22×C4×D43C2311yescharacteristic
106C2×#10621877C2312yes—
107#13063325C2311yescharacteristic
108#13063325C2311yescharacteristic
109#13063324—21no—
110#13063324—21no—
111#13063324—21no—
112#13063324—21no—
113#13063324C2312yes—
114#13063324C2312yes—
115#13063324C2312yes—
116#13063324C2312yes—
117#13063323—21no—
118#13063323—21no—
119#13063323—21no—
120#13063323—21no—
121#13063323C2312yes—
122#13063323C2312yes—
123#13063317C2312yes—
124#13063316C2312yes—
125#13063316C2312yes—
126#13063315—22no—
127#13063315—22no—
128#13063315—22no—
129#13063315—22no—
130#13063315—22no—
131#13063315—22no—
132#13063305—21no—
133#13063305—21no—
134#13063305—21no—
135#13063305—21no—
136#13063305C2312yes—
137#13063305C2312yes—
138#13063304—21no—
139#13063304—21no—
140#13063303—22no—
141#13063303—22no—
142#13063303—22no—
143#13063303—22no—
144#13063303—22no—
145#13063303—22no—
146#13063302—22no—
147#13063302—22no—
148#13063301—21no—
149#13063301—21no—
150#13063301—21no—
151#13063301—21no—
152#13063301C2312yes—
153#13063301C2312yes—
154Q8×Dic43—21no—
155Q8×Dic43—21no—
156C4×Dic86—21no—
157C4×Dic86—21no—
158C4×Dic86—21no—
159C4×Dic86—21no—
160C4×Dic86—22no—
161C4×Dic86—22no—
162C4×Dic86—22no—
163C4×Dic86—22no—
164C4×Dic86—22no—
165C4×Dic86—22no—
166C4×Dic86C2312yes—
167C4×Dic86C2312yes—
168#13063290—21no—
169#13063290—21no—
170#13063290—22no—
171#13063290—22no—
172#13063284C2312yes—
173#13063283C2312yes—
174#13063283C2312yes—
175#13063282—22no—
176#13063282—22no—
177#13063282—22no—
178#13063282—22no—
179#13063282—22no—
180#13063281—22no—
181C2×C4⋊Dic43—21no—
182C2×C4⋊Dic43C2311yescharacteristic
183C2×Dic43⋊C4—21no—
184C2×Dic43⋊C4—21no—
185C2×Dic43⋊C4—21no—
186C2×Dic43⋊C4—21no—
187C2×Dic43⋊C4—21no—
188C4⋊C4×D43—22no—
189C4⋊C4×D43—22no—
190C4⋊C4×D43—21no—
191C4⋊C4×D43—21no—
192C4⋊C4×D43C2312yes—
193C4⋊C4×D43C2312yes—
194C2×(C2×D43)⋊C4—21no—
195C2×(C2×D43)⋊C4—21no—
196C22⋊C4×D43—22no—
197C2×C4×Dic43—21no—
198C2×C4×Dic43D411yescharacteristic
199C2×C4×Dic43D411yescharacteristic
200C2×C4×Dic43C2311yescharacteristic
201C42×D43—22no—
202C42×D43D411yescharacteristic
203C42×D43D411yescharacteristic
204C42×D43D411yescharacteristic
205C42×D43D411yescharacteristic
206C42×D43C2311yescharacteristic
207C42×D43C2311yescharacteristic
208C42×D43C2311yescharacteristic
209C42×D43C2311yescharacteristic
210#13063259C2314yes—
211#13063258C2314yes—
212#13063258C2314yes—
213#13063257C2314yes—
214#13063256C2314yes—
215#13063256C2314yes—
216C4⋊(C43⋊C8)C2312yes—
217C4⋊(C43⋊C8)C2312yes—
218#13063250C2314yes—
219#13063250C2314yes—
220#13063249C2314yes—
221#13063249C2314yes—
222#13063248C2314yes—
223#13063248C2314yes—
224(C2×D43)⋊C8C2314yes—
225(C2×D43)⋊C8C2314yes—
226#13063235C2314yes—
227C8×Dic43C2314yes—
228C22×Q8×C43C2311yescharacteristic
229C2×M16×C43C2312yes—
230C4⋊Q8×C43C2311yescharacteristic
231C4⋊Q8×C43C2311yescharacteristic
232#125×C43C2312yes—
233C22⋊Q8×C43—21no—
234C22⋊Q8×C43—21no—
235C4×Q8×C43—21no—
236C4×Q8×C43—21no—
237C4×Q8×C43—21no—
238C4×Q8×C43—21no—
239C4×Q8×C43C2312yes—
240C4×Q8×C43C2312yes—
241#117×C43C2312yes—
242C2×C4⋊C4×C43—21no—
243C2×C4⋊C4×C43C2311yescharacteristic
244C2×C42×C43—21no—
245C2×C42×C43C2311yescharacteristic
246#107×C43C2314yes—
247#106×C43C2314yes—
248C4⋊C8×C43C2312yes—
249C4⋊C8×C43C2312yes—
250#103×C43C2314yes—
251#103×C43C2314yes—
252C23×D43C2×D411yescharacteristic
253C2×Q8×C43—21no—
254C2×Q8×C43—21no—
255C2×Q8×C43—21no—
256C2×Q8×C43—22no—
257C2×Q8×C43—22no—
258C2×Q8×C43C2412yes—
259C22×C4×C43—21no—
260C22×C4×C43—21no—
261C22×C4×C43C2×D411yescharacteristic
262C22×C4×C43C2×D411yescharacteristic
263C22×C4×C43C2411yescharacteristic
264C22×Dic43—21no—
265C22×Dic43—21no—
266C22×Dic43C2×D411yescharacteristic
267C22×Dic43C2×D411yescharacteristic
268C22×Dic43C2×D411yescharacteristic
269Q8×D43—44no—
270Q8×D43—44no—
271C2×C4×D43—22no—
272C2×C4×D43—22no—
273C2×C4×D43—24no—
274C2×C4×D43—22no—
275C2×C4×D43—22no—
276C2×C4×D43—42no—
277C2×C4×D43C2×D411yescharacteristic
278C2×C4×D43C2×D411yescharacteristic
279C2×C4×D43C2×D411yescharacteristic
280C2×C4×D43C2×D411yescharacteristic
281C2×C4×D43C2×D411yescharacteristic
282C2×C4×D43C2×D411yescharacteristic
283C2×C4×D43C2×D411yescharacteristic
284C2×C4×D43C2×D411yescharacteristic
285C2×C4×D43C2×D411yescharacteristic
286C2×C4×D43C2×D411yescharacteristic
287C2×C4×D43C2411yescharacteristic
288C2×C4×D43C2411yescharacteristic
289C2×Dic86—22no—
290C2×Dic86—22no—
291C2×Dic86—21no—
292C2×Dic86—21no—
293C2×Dic86—21no—
294C2×Dic86—22no—
295C2×Dic86—22no—
296C2×Dic86—22no—
297C2×Dic86—22no—
298C2×Dic86—44no—
299C2×Dic86C2412yes—
300M16×C43—24no—
301C2×C8×C43C2414yes—
302C4⋊C4×C43—22no—
303C4⋊C4×C43—22no—
304C4⋊C4×C43—21no—
305C4⋊C4×C43—22no—
306C4⋊C4×C43—22no—
307C4⋊C4×C43—21no—
308C4⋊C4×C43—21no—
309C4⋊C4×C43C2412yes—
310C4⋊C4×C43C2412yes—
311C4⋊C4×C43C2412yes—
312C22⋊C4×C43—22no—
313C42×C43—22no—
314C42×C43—22no—
315C42×C43—22no—
316C42×C43C2×D411yescharacteristic
317C42×C43C2×D411yescharacteristic
318C42×C43C2411yescharacteristic
319C42×C43C2411yescharacteristic
320C22⋊Dic43—22no—
321(C2×D43)⋊C4—22no—
322(C2×D43)⋊C4—22no—
323(C2×D43)⋊C4—22no—
324(C2×D43)⋊C4—22no—
325(C2×D43)⋊C4—22no—
326(C2×D43)⋊C4—22no—
327C4⋊Dic43—21no—
328C4⋊Dic43—21no—
329C4⋊Dic43—21no—
330C4⋊Dic43—22no—
331C4⋊Dic43—22no—
332C4⋊Dic43—22no—
333C4⋊Dic43—22no—
334C4⋊Dic43C2412yes—
335C4⋊Dic43C2412yes—
336C4⋊Dic43C2412yes—
337Dic43⋊C4—22no—
338Dic43⋊C4—22no—
339Dic43⋊C4—22no—
340Dic43⋊C4—22no—
341Dic43⋊C4—22no—
342Dic43⋊C4—22no—
343Dic43⋊C4—22no—
344Dic43⋊C4—22no—
345Dic43⋊C4—22no—
346Dic43⋊C4—22no—
347Dic43⋊C4—22no—
348Dic43⋊C4—22no—
349Dic43⋊C4—22no—
350Dic43⋊C4—22no—
351Dic43⋊C4—22no—
352Dic43⋊C4—22no—
353Dic43⋊C4—22no—
354Dic43⋊C4—22no—
355C4×Dic43—22no—
356C4×Dic43—22no—
357C4×Dic43—22no—
358C4×Dic43—22no—
359C4×Dic43—22no—
360C4×Dic43C2×D411yescharacteristic
361C4×Dic43C2×D411yescharacteristic
362C4×Dic43C2×D411yescharacteristic
363C4×Dic43C2×D411yescharacteristic
364C4×Dic43C2×D411yescharacteristic
365C4×Dic43C2×D411yescharacteristic
366C4×Dic43C2×D411yescharacteristic
367C4×Dic43C2×D411yescharacteristic
368C4×Dic43C2×D411yescharacteristic
369C4×Dic43C2×D411yescharacteristic
370C4×Dic43C2411yescharacteristic
371C4×Dic43C2411yescharacteristic
372#10621877—24no—
373C2×C43⋊C8C2414yes—
374C23×C43C22×D411yescharacteristic
375C22×D43—22no—
376C22×D43—22no—
377C22×D43—41no—
378C22×D43C22×D411yescharacteristic
379C22×D43C22×D411yescharacteristic
380Q8×C43—22no—
381Q8×C43—22no—
382Q8×C43—42no—
383Q8×C43—42no—
384Q8×C43—42no—
385C2×C4×C43—22no—
386C2×C4×C43—22no—
387C2×C4×C43—22no—
388C2×C4×C43—22no—
389C2×C4×C43—22no—
390C2×C4×C43—41no—
391C2×C4×C43—42no—
392C2×C4×C43—42no—
393C2×C4×C43C22×D411yescharacteristic
394C2×C4×C43C22×D411yescharacteristic
395C2×C4×C43C22×D411yescharacteristic
396C2×C4×C43C22×D411yescharacteristic
397C2×C4×C43C22×D411yescharacteristic
398C2×C4×C432−1+412yes—
399C2×C4×C432−1+412yes—
400C2×C4×C43C2511yescharacteristic
401C2×Dic43—22no—
402C2×Dic43—22no—
403C2×Dic43—22no—
404C2×Dic43—22no—
405C2×Dic43—22no—
406C2×Dic43—22no—
407C2×Dic43—22no—
408C2×Dic43—42no—
409C2×Dic43—42no—
410C2×Dic43C22×D411yescharacteristic
411C2×Dic43C22×D411yescharacteristic
412C2×Dic43C22×D411yescharacteristic
413C2×Dic43C22×D411yescharacteristic
414C2×Dic43C22×D411yescharacteristic
415C2×Dic43C22×D411yescharacteristic
416C4×D43—22no—
417C4×D43—22no—
418C4×D43—22no—
419C4×D43—22no—
420C4×D43—21no—
421C4×D43—21no—
422C4×D43—21no—
423C4×D43—21no—
424C4×D43—22no—
425C4×D43—22no—
426C4×D43—22no—
427C4×D43—41no—
428C4×D43—41no—
429C4×D43—44no—
430C4×D43—44no—
431C4×D43#13714yes—
432Dic86—22no—
433Dic86—22no—
434Dic86—44no—
435Dic86—42no—
436Dic86—42no—
437Dic86—42no—
438Dic86—44no—
439Dic86—44no—
440Dic86—44no—
441C8×C43—24no—
442C43⋊C8—24no—
443#60865—431nomaximal, Sylow
444C22×C43—21no—
445C22×C43—21no—
446C22×C43#53612yes—
447C22×C43C23×D411yescharacteristic
448C2×D43—21no—
449C2×D43—21no—
450C2×D43—21no—
451C2×D43—21no—
452C2×D43—21no—
453C2×D43—44no—
454C2×D43C2×#13712yes—
455C4×C43—21no—
456C4×C43—21no—
457C4×C43—21no—
458C4×C43—42no—
459C4×C43—42no—
460C4×C43—42no—
461C4×C43—42no—
462C4×C43#53612yes—
463C4×C43C2×#13712yes—
464C4×C43C2×2−1+411yescharacteristic
465C4×C43C2×2−1+411yescharacteristic
466Dic43—21no—
467Dic43—21no—
468Dic43—21no—
469Dic43—21no—
470Dic43—42no—
471Dic43—42no—
472Dic43—42no—
473Dic43—42no—
474Dic43C2×#13712yes—
475Dic43#57512yes—
476C2×#533—431no—
477C2×#533—431no—
478#3237—432no—
479#3237—432no—
480#3236—434no—
481#3231—434no—
482#3230—432no—
483#3229—432no—
484#3165—432no—
485#3139—432no—
486#3095—432no—
487#3095—432no—
488#3078—431no—
489#3078—431no—
490#3078—431no—
491#3078D4311yescharacteristic, complemented
492#2920—431no—
493C2×C43—22no—
494C2×C43C2×#53611yescharacteristic
495C2×C43C22×#13711yescharacteristic
496C2×C43C2×#57511yescharacteristic
497D43—22no—
498D43—41no—
499#533—431no—
500#533—431no—
501#533—432no—
502#533—432no—
503#533—432no—
504#533—432no—
505#533—432no—
506#533—432no—
507#533—431no—
508#533—861no—
509#533—861no—
510#533—861no—
511#533—861no—
512#533—861no—
513#533—861no—
514#533—861no—
515#533—861no—
516#533C2×D4311yescharacteristic
517C2×C4⋊Q8—431no—
518C2×C4⋊Q8—431no—
519C2×C4⋊Q8—431no—
520C2×C4⋊Q8—431no—
521C2×#125—432no—
522C2×#125—861no—
523C2×C22⋊Q8—431no—
524C2×C22⋊Q8—431no—
525C2×C22⋊Q8—861no—
526C2×C22⋊Q8—861no—
527C2×C22⋊Q8—861no—
528C2×C4×Q8—431no—
529C2×C4×Q8—861no—
530C2×C4×Q8—861no—
531C2×C4×Q8—861no—
532C2×C4×Q8C2×D4311yescharacteristic
533C2×#117—432no—
534C2×#117—861no—
535C22×C42—431no—
536#501—434no—
537#501—434no—
538#500—434no—
539#498—434no—
540#491—434no—
541#491—434no—
542#487—434no—
543#487—434no—
544#485—434no—
545#485—434no—
546#485—434no—
547#485—434no—
548#484—434no—
549#484—434no—
550#483—434no—
551#483—434no—
552#479—434no—
553#479—434no—
554#479—434no—
555#479C2×D4314yescomplemented
556#477—432no—
557#477—432no—
558#477—432no—
559#477C2×D4312yescomplemented
560#475—432no—
561#475—432no—
562#475—432no—
563#475C2×D4312yescomplemented
564#432—432no—
565#432—432no—
566#431—432no—
567#431—432no—
568#428—432no—
569#428—432no—
570#428—432no—
571#428C2×D4312yes—
572#423—431no—
573#423C2×D4311yescharacteristic
574#419—432no—
575#419—432no—
576#419—432no—
577#419C2×D4312yes—
578#407—432no—
579C4×M16—432no—
580C43#6086511yescharacteristic, complemented, Sylow
581C22×Q8—431no—
582C22×Q8—861no—
583C22×Q8—861no—
584C22×Q8—861no—
585C22×Q8C22×D4311yescharacteristic
586C23×C4—431no—
587C23×C4—431no—
588C23×C4—431no—
589C2×M16—432no—
590C2×M16C22×D4312yes—
591C4⋊Q8—432no—
592C4⋊Q8—432no—
593C4⋊Q8—432no—
594C4⋊Q8—432no—
595C4⋊Q8—432no—
596C4⋊Q8—432no—
597C4⋊Q8—431no—
598C4⋊Q8—431no—
599C4⋊Q8—861no—
600C4⋊Q8—861no—
601C4⋊Q8—861no—
602C4⋊Q8—861no—
603C4⋊Q8—861no—
604C4⋊Q8—861no—
605C4⋊Q8—861no—
606C4⋊Q8—861no—
607C4⋊Q8C22×D4311yescharacteristic
608C4⋊Q8C22×D4311yescharacteristic
609#125—432no—
610#125—432no—
611#125—432no—
612#125—862no—
613#125—862no—
614#125—862no—
615#125—862no—
616#125—862no—
617#125—862no—
618#125C22×D4312yes—
619C22⋊Q8—21no—
620C22⋊Q8—21no—
621C22⋊Q8—432no—
622C22⋊Q8—432no—
623C22⋊Q8—432no—
624C22⋊Q8—432no—
625C22⋊Q8—862no—
626C22⋊Q8—862no—
627C22⋊Q8—861no—
628C22⋊Q8—861no—
629C22⋊Q8—862no—
630C22⋊Q8—862no—
631C22⋊Q8—862no—
632C22⋊Q8—862no—
633C22⋊Q8—862no—
634C22⋊Q8—862no—
635C22⋊Q8—861no—
636C22⋊Q8—861no—
637C22⋊Q8—861no—
638C22⋊Q8—861no—
639C22⋊Q8—861no—
640C22⋊Q8—861no—
641C22⋊Q8—861no—
642C22⋊Q8—861no—
643C4×Q8—21no—
644C4×Q8—21no—
645C4×Q8—21no—
646C4×Q8—21no—
647C4×Q8—432no—
648C4×Q8—432no—
649C4×Q8—862no—
650C4×Q8—862no—
651C4×Q8—862no—
652C4×Q8—862no—
653C4×Q8—862no—
654C4×Q8—862no—
655C4×Q8—862no—
656C4×Q8—861no—
657C4×Q8—862no—
658C4×Q8—861no—
659C4×Q8—861no—
660C4×Q8—861no—
661C4×Q8—861no—
662C4×Q8—861no—
663C4×Q8—861no—
664C4×Q8—861no—
665C4×Q8C22×D4312yes—
666C4×Q8C22×D4312yes—
667#117—432no—
668#117—432no—
669#117—432no—
670#117—862no—
671#117—862no—
672#117—862no—
673#117—862no—
674#117—862no—
675#117—862no—
676#117C22×D4312yes—
677C2×C4⋊C4—21no—
678C2×C4⋊C4—431no—
679C2×C4⋊C4—432no—
680C2×C4⋊C4—432no—
681C2×C4⋊C4—862no—
682C2×C4⋊C4—862no—
683C2×C4⋊C4—861no—
684C2×C4⋊C4—861no—
685C2×C4⋊C4—861no—
686C2×C4⋊C4—861no—
687C2×C4⋊C4—861no—
688C2×C4⋊C4—861no—
689C2×C4⋊C4—861no—
690C2×C4⋊C4—861no—
691C2×C4⋊C4C22×D4311yescharacteristic
692C2×C22⋊C4—862no—
693C2×C22⋊C4—861no—
694C2×C22⋊C4—861no—
695C2×C42—21no—
696C2×C42—431no—
697C2×C42—431no—
698C2×C42—431no—
699C2×C42—431no—
700C2×C42—431no—
701C2×C42—431no—
702C2×C42—431no—
703C2×C42—431no—
704C2×C42—431no—
705C2×C42—431no—
706C2×C42—431no—
707C2×C42—862no—
708C2×C42—861no—
709C2×C42C22×D4311yescharacteristic
710#107—434no—
711#107—434no—
712#107—434no—
713#107C22×D4314yes—
714#106—434no—
715#106—434no—
716#106—434no—
717#106C22×D4314yes—
718C4⋊C8—432no—
719C4⋊C8—432no—
720C4⋊C8C22×D4312yes—
721C4⋊C8C22×D4312yes—
722#103—434no—
723#103—434no—
724#103—434no—
725#103—434no—
726#103—434no—
727#103—434no—
728#103C22×D4314yes—
729#103C22×D4314yes—
730C22⋊C8—434no—
731C22⋊C8—434no—
732#97—434no—
733C4×C8—434no—
734C24—431no—
735C2×Q8—21no—
736C2×Q8—21no—
737C2×Q8—21no—
738C2×Q8—22no—
739C2×Q8—22no—
740C2×Q8—432no—
741C2×Q8—862no—
742C2×Q8—862no—
743C2×Q8—862no—
744C2×Q8—862no—
745C2×Q8—861no—
746C2×Q8—861no—
747C2×Q8—861no—
748C2×Q8—862no—
749C2×Q8—862no—
750C2×Q8—1724no—
751C2×Q8—1724no—
752C2×Q8—1724no—
753C2×Q8C23×D4312yes—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—431no—
757C22×C4—431no—
758C22×C4—431no—
759C22×C4—431no—
760C22×C4—431no—
761C22×C4—431no—
762C22×C4—431no—
763C22×C4—431no—
764C22×C4—431no—
765C22×C4—431no—
766C22×C4—431no—
767C22×C4—431no—
768C22×C4—431no—
769C22×C4—431no—
770C22×C4—431no—
771C22×C4—864no—
772C22×C4—862no—
773C22×C4—862no—
774C22×C4—862no—
775C22×C4—862no—
776C22×C4—861no—
777C22×C4—861no—
778C22×C4—1722no—
779C22×C4D4×D4311yescharacteristic
780C22×C4D4×D4311yescharacteristic
781C22×C4C23×D4311yescharacteristic
782M16—24no—
783M16—864no—
784C2×C8—434no—
785C2×C8C23×D4314yes—
786C4⋊C4—22no—
787C4⋊C4—22no—
788C4⋊C4—22no—
789C4⋊C4—22no—
790C4⋊C4—21no—
791C4⋊C4—21no—
792C4⋊C4—21no—
793C4⋊C4—432no—
794C4⋊C4—432no—
795C4⋊C4—432no—
796C4⋊C4—862no—
797C4⋊C4—862no—
798C4⋊C4—862no—
799C4⋊C4—862no—
800C4⋊C4—862no—
801C4⋊C4—862no—
802C4⋊C4—862no—
803C4⋊C4—862no—
804C4⋊C4—862no—
805C4⋊C4—862no—
806C4⋊C4—862no—
807C4⋊C4—862no—
808C4⋊C4—862no—
809C4⋊C4—862no—
810C4⋊C4—862no—
811C4⋊C4—862no—
812C4⋊C4—862no—
813C4⋊C4—862no—
814C4⋊C4—861no—
815C4⋊C4—862no—
816C4⋊C4—862no—
817C4⋊C4—862no—
818C4⋊C4—862no—
819C4⋊C4—861no—
820C4⋊C4—861no—
821C4⋊C4C23×D4312yes—
822C4⋊C4C23×D4312yes—
823C4⋊C4C23×D4312yes—
824C22⋊C4—22no—
825C22⋊C4—862no—
826C22⋊C4—862no—
827C22⋊C4—862no—
828C22⋊C4—862no—
829C22⋊C4—862no—
830C22⋊C4—862no—
831C22⋊C4—862no—
832C42—22no—
833C42—22no—
834C42—22no—
835C42—431no—
836C42—431no—
837C42—431no—
838C42—431no—
839C42—431no—
840C42—431no—
841C42—431no—
842C42—431no—
843C42—431no—
844C42—431no—
845C42—431no—
846C42—431no—
847C42—862no—
848C42—862no—
849C42—862no—
850C42—862no—
851C42—862no—
852C42D4×D4311yescharacteristic
853C42D4×D4311yescharacteristic
854C42C23×D4311yescharacteristic
855C42C23×D4311yescharacteristic
856C23—431no—
857C23—431no—
858C23—862no—
859C23—862no—
860C23—1721no—
861C23C2×D4×D4311yescharacteristic
862Q8—22no—
863Q8—22no—
864Q8—42no—
865Q8—42no—
866Q8—42no—
867Q8—862no—
868Q8—862no—
869Q8—1722no—
870Q8—1724no—
871Q8—1724no—
872Q8—1724no—
873Q8—1724no—
874Q8—1722no—
875Q8—1722no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—41no—
882C2×C4—42no—
883C2×C4—42no—
884C2×C4—431no—
885C2×C4—431no—
886C2×C4—434no—
887C2×C4—431no—
888C2×C4—431no—
889C2×C4—431no—
890C2×C4—431no—
891C2×C4—862no—
892C2×C4—862no—
893C2×C4—862no—
894C2×C4—862no—
895C2×C4—862no—
896C2×C4—862no—
897C2×C4—862no—
898C2×C4—862no—
899C2×C4—862no—
900C2×C4—862no—
901C2×C4—861no—
902C2×C4—861no—
903C2×C4—861no—
904C2×C4—861no—
905C2×C4—862no—
906C2×C4—862no—
907C2×C4—862no—
908C2×C4—862no—
909C2×C4—1721no—
910C2×C4—1721no—
911C2×C4—1724no—
912C2×C4—1724no—
913C2×C4—1722no—
914C2×C4—1722no—
915C2×C4C2×D4×D4311yescharacteristic
916C2×C4C2×D4×D4311yescharacteristic
917C2×C4C2×D4×D4311yescharacteristic
918C2×C4C2×D4×D4311yescharacteristic
919C2×C4C2×D4×D4311yescharacteristic
920C2×C4#1306337212yes—
921C2×C4#1306337312yes—
922C2×C4C24×D4311yescharacteristic
923C8—24no—
924C8—864no—
925C22—21no—
926C22—21no—
927C22—432no—
928C22—861no—
929C22—861no—
930C22—861no—
931C22—861no—
932C22—861no—
933C22—1724no—
934C22#1458347212yes—
935C22C22×D4×D4311yescharacteristic
936C4—21no—
937C4—21no—
938C4—21no—
939C4—42no—
940C4—42no—
941C4—42no—
942C4—42no—
943C4—432no—
944C4—432no—
945C4—861no—
946C4—861no—
947C4—861no—
948C4—861no—
949C4—1722no—
950C4—1722no—
951C4—1722no—
952C4—1722no—
953C4#1458347212yes—
954C4#137×D4312yes—
955C4C2×#1306337211yescharacteristic
956C4C2×#1306337311yescharacteristic
957C2—22no—
958C2—862no—
959C2—1721no—
960C2C2×#1458347211yescharacteristic
961C2C2×#137×D4311yescharacteristic
962C2#575×D4311yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3078C2
socleC22×C43C23×D4
prime radicalC23×D43C2×D4
hypercenter#3078D43
hypocenterC43#60865
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3078

Complements

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

NH ≅ G/Ntype
3. #19145808C2semidirect
4. #19145807C2semidirect
5. #19145799C2semidirect
6. #19145753C2semidirect
7. #19145745C2semidirect
8. #19145738C2semidirect
9. #19145139C2semidirect
10. #19144973C2semidirect
13. #19144402C2semidirect
14. #19144400C2semidirect
15. #19144396C2semidirect
17. C43×#3078C2semidirect
53. #14583307C22semidirect
54. #14583306C22semidirect
55. #14583303C22semidirect
56. #14583296C22semidirect
57. #14583266C22semidirect
58. #14583266C22semidirect
59. #14583248C22semidirect
60. #14583248C22semidirect
69. #14583207C22semidirect
70. #14583206C22semidirect
71. #14583203C22semidirect
72. #14583195C22semidirect
73. #14583194C22semidirect
74. #14583191C22semidirect
75. #14583185C22semidirect
76. #14583184C22semidirect
77. #14583181C22semidirect
93. C43×#479C22semidirect
94. C43×#477C22semidirect
95. C43×#475C22semidirect
491. #3078D43semidirect
555. #479C2×D43semidirect
559. #477C2×D43semidirect
563. #475C2×D43semidirect
580. C43#60865semidirect

Maximal subgroups

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

subgroupindex
C2×#145834532
#533×D432
#191458082
#191458072
#191457992
#191457532
#191457452
#191457382
#191451392
#191449732
#191445452
#191445412
#191444022
#191444002
#191443962
#191432272
C43×#30782
#6086543