Finite Group Databasebeta

← #25968903

Subgroups — #25968903

Order 11008.

2036 conjugacy classes of subgroups.

The subgroup lattice has 1016 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583452C211yesmaximal, characteristic, complemented
2C2×#14583444C211yesmaximal, characteristic
3#19145790C214yesmaximal, complemented
4#19145784C212yesmaximal, complemented
5#19145782C212yesmaximal, complemented
6#19145729C214yesmaximal, complemented
7#19145721C212yesmaximal, complemented
8#19145714C212yesmaximal, complemented
9#19145139C212yesmaximal, complemented
10#19144967C212yesmaximal, complemented
11#19144536C211yesmaximal, characteristic, complemented
12#19144535C211yesmaximal, characteristic, complemented
13#19144531C211yesmaximal, characteristic, complemented
14#19144391C212yesmaximal, complemented
15#19144389C212yesmaximal, complemented
16#19143224C211yesmaximal, characteristic, complemented
17C43×#3094C211yesmaximal, characteristic, complemented
18C22×#10621900—21no—
19#14583452—21no—
20#14583452—21no—
21#14583452—21no—
22#14583452—21no—
23#14583452C2212yes—
24#14583452C2212yes—
25#14583452C2212yescomplemented
26#14583452C2212yescomplemented
27#14583444—21no—
28#14583444—21no—
29#14583444—21no—
30#14583444—21no—
31#14583444C2212yes—
32#14583444C2212yes—
33#14583444C2212yes—
34#14583444C2212yes—
35C2×#13063324C2211yescharacteristic
36C2×#13063324C2211yescharacteristic, complemented
37C2×#13063324C2211yescharacteristic, complemented
38C2×#13063321C2211yescharacteristic
39C2×#13063316C2211yescharacteristic, complemented
40C2×#13063316C2211yescharacteristic, complemented
41C2×#13063311—21no—
42C2×#13063302—21no—
43C2×#13063302—21no—
44C2×#13063299C2211yescharacteristic
45C2×#13063297—21no—
46C2×C4×Dic86—21no—
47C2×C4×Dic86—21no—
48C2×D4×Dic43C2211yescharacteristic
49C2×#13063287C2211yescharacteristic
50C2×(C22⋊D43)⋊C4—21no—
51C2×#13063284C2211yescharacteristic
52C22×C4×Dic43C2211yescharacteristic
53#14583307C2214yescomplemented
54#14583306C2214yescomplemented
55#14583303C2214yescomplemented
56#14583296C2214yescomplemented
57#14583262C2214yescomplemented
58#14583262C2214yescomplemented
59#14583244C2214yescomplemented
60#14583244C2214yescomplemented
61#14583224C2214yescomplemented
62#14583223C2214yescomplemented
63#14583220C2214yescomplemented
64#14583218C2212yescomplemented
65#14583217C2212yescomplemented
66#14583215C2212yescomplemented
67#14583213C2212yescomplemented
68#14583212C2212yescomplemented
69#14583210C2212yescomplemented
70#14583202C2214yescomplemented
71#14583201C2214yescomplemented
72#14583198C2214yescomplemented
73#14583197C2214yescomplemented
74#14583188C2214yescomplemented
75#14583187C2214yescomplemented
76#14583178C2214yescomplemented
77#14583177C2214yescomplemented
78#14582953C2212yescomplemented
79#14582953C2212yescomplemented
80#14582949C2212yescomplemented
81#14582949C2212yescomplemented
82#14582942C2212yes—
83#14582941C2212yes—
84#14582939C2212yes—
85#14582922C2212yes—
86#14582905C2212yes—
87#14582904C2212yes—
88#14582903C2212yes—
89#14582863C2211yescharacteristic
90M16×Dic43C2212yes—
91C2×#121×C43C2211yescharacteristic
92C2×#117×C43C2211yescharacteristic
93C43×#482C2214yescomplemented
94C43×#481C2212yescomplemented
95C43×#480C2212yescomplemented
96C43×#428C2212yes—
97C43×#418C2212yes—
98C43×#407C2211yescharacteristic
99C2×#10621900—22no—
100C2×#10621900—22no—
101C2×#10621900—22no—
102C2×#10621900—22no—
103C2×#10621900—48no—
104C22×Dic86—21no—
105C22×Dic86—21no—
106C22×Dic86—21no—
107C22×D172C2311yescharacteristic
108C22×C22⋊D43—21no—
109C22×C22⋊D43—21no—
110C22×C22⋊D43—21no—
111C23×Dic43—21no—
112C23×Dic43D411yescharacteristic
113C23×Dic43D411yescharacteristic
114C22×C4×D43—21no—
115C2×#10621877C2312yes—
116#13063324—21no—
117#13063324—21no—
118#13063324—21no—
119#13063324—21no—
120#13063324—21no—
121#13063324—21no—
122#13063324C2312yes—
123#13063324C2312yes—
124#13063324C2312yes—
125#13063324C2312yes—
126#13063324C2312yes—
127#13063324C2312yes—
128#13063321—21no—
129#13063321—21no—
130#13063321C2312yes—
131#13063321C2312yes—
132#13063316—21no—
133#13063316—21no—
134#13063316—21no—
135#13063316—21no—
136#13063316C2312yes—
137#13063316C2312yes—
138#13063316C2312yes—
139#13063316C2312yes—
140#13063311—22no—
141#13063311—22no—
142#13063311—22no—
143#13063311—22no—
144#13063302—22no—
145#13063302—22no—
146#13063302—22no—
147#13063302—22no—
148#13063302—22no—
149#13063302—22no—
150#13063302—22no—
151#13063302—22no—
152#13063299—21no—
153#13063299—21no—
154#13063299C2312yes—
155#13063299C2312yes—
156#13063297—22no—
157#13063297—22no—
158#13063297—22no—
159#13063297—22no—
160C4×Dic86—22no—
161C4×Dic86—22no—
162C4×Dic86—22no—
163C4×Dic86—22no—
164C4×Dic86—22no—
165C4×Dic86—22no—
166C4×Dic86—22no—
167C4×Dic86—22no—
168D4×Dic43—21no—
169D4×Dic43—21no—
170D4×Dic43C2312yes—
171D4×Dic43C2312yes—
172#13063287—21no—
173#13063287—21no—
174#13063287C2312yes—
175#13063287C2312yes—
176(C22⋊D43)⋊C4—22no—
177(C22⋊D43)⋊C4—22no—
178(C22⋊D43)⋊C4—22no—
179(C22⋊D43)⋊C4—22no—
180#13063284—21no—
181#13063284—21no—
182#13063284C2312yes—
183#13063284C2312yes—
184C2×C4⋊Dic43—21no—
185C2×C4⋊Dic43—21no—
186C2×C4⋊Dic43C2311yescharacteristic
187C2×C4⋊Dic43C2311yescharacteristic
188C2×C4⋊Dic43C2311yescharacteristic
189C2×Dic43⋊C4—21no—
190C2×Dic43⋊C4—21no—
191C2×Dic43⋊C4—21no—
192C2×Dic43⋊C4—21no—
193C2×Dic43⋊C4—21no—
194C2×C22⋊Dic43—21no—
195C2×C22⋊Dic43—21no—
196C2×(C2×D43)⋊C4—21no—
197C2×(C2×D43)⋊C4—21no—
198C2×C4×Dic43—21no—
199C2×C4×Dic43D411yescharacteristic
200C2×C4×Dic43D411yescharacteristic
201C2×C4×Dic43D411yescharacteristic
202C2×C4×Dic43D411yescharacteristic
203C2×C4×Dic43D411yescharacteristic
204C2×C4×Dic43D411yescharacteristic
205C2×C4×Dic43C2311yescharacteristic
206C2×C4×Dic43C2311yescharacteristic
207C2×C4×Dic43C2311yescharacteristic
208C2×C4×Dic43C2311yescharacteristic
209C2×C4×Dic43C2311yescharacteristic
210C2×C4×Dic43C2311yescharacteristic
211#13063259C2314yes—
212#13063258C2314yes—
213#13063258C2314yes—
214#13063257C2314yes—
215#13063256C2314yes—
216#13063256C2314yes—
217Dic43⋊C8C2314yes—
218Dic43⋊C8C2314yes—
219#13063247C2314yes—
220#13063247C2314yes—
221#13063246C2314yes—
222#13063246C2314yes—
223#13063245C2314yes—
224#13063245C2314yes—
225C22⋊(C43⋊C8)C2312yes—
226C22⋊(C43⋊C8)C2312yes—
227#13063235C2314yes—
228C8×Dic43C2314yes—
229C22×D4×C43—21no—
230C22×D4×C43C2311yescharacteristic
231C23×C4×C43C2311yescharacteristic
232C2×M16×C43C2312yes—
233#121×C43—21no—
234#121×C43—21no—
235#121×C43C2312yes—
236#121×C43C2312yes—
237#117×C43—21no—
238#117×C43—21no—
239#117×C43C2312yes—
240#117×C43C2312yes—
241C2×C4⋊C4×C43C2311yescharacteristic
242C2×C4⋊C4×C43C2311yescharacteristic
243C2×C4⋊C4×C43C2311yescharacteristic
244C2×C22⋊C4×C43—21no—
245C2×C22⋊C4×C43—21no—
246C2×C42×C43—21no—
247#107×C43C2314yes—
248#106×C43C2314yes—
249#102×C43C2314yes—
250#102×C43C2314yes—
251C22⋊C8×C43C2312yes—
252C22⋊C8×C43C2312yes—
253C24×C43—21no—
254C24×C43C2×D411yescharacteristic
255C23×D43—21no—
256C2×D4×C43—21no—
257C2×D4×C43—22no—
258C2×D4×C43—22no—
259C2×D4×C43—24no—
260C2×D4×C43—44no—
261C2×D4×C43C2412yes—
262C22×C4×C43—24no—
263C22×C4×C43—21no—
264C22×C4×C43—21no—
265C22×C4×C43—21no—
266C22×C4×C43C2×D411yescharacteristic
267C22×C4×C43C2×D411yescharacteristic
268C22×C4×C43C2×D411yescharacteristic
269C22×C4×C43C2411yescharacteristic
270C22×C4×C43C2411yescharacteristic
271C22×C4×C43C2411yescharacteristic
272C2×C22⋊D43—22no—
273C2×C22⋊D43—22no—
274C2×C22⋊D43—22no—
275C2×C22⋊D43—22no—
276C2×C22⋊D43—22no—
277C2×C22⋊D43—22no—
278C2×C22⋊D43—44no—
279C2×C22⋊D43—44no—
280C2×C22⋊D43—44no—
281C22×Dic43—24no—
282C22×Dic43—22no—
283C22×Dic43—22no—
284C22×Dic43—21no—
285C22×Dic43—21no—
286C22×Dic43—21no—
287C22×Dic43—42no—
288C22×Dic43—44no—
289C22×Dic43C2×D411yescharacteristic
290C22×Dic43C2×D411yescharacteristic
291C22×Dic43C2×D411yescharacteristic
292C22×Dic43C2×D411yescharacteristic
293C22×Dic43C2×D411yescharacteristic
294C22×Dic43C2×D411yescharacteristic
295C22×Dic43C2×D411yescharacteristic
296C22×Dic43C2×D411yescharacteristic
297C22×Dic43C2×D411yescharacteristic
298C22×Dic43C2×D411yescharacteristic
299C22×Dic43C2×D411yescharacteristic
300C22×Dic43C2×D411yescharacteristic
301#10621900—48no—
302#10621900—48no—
303#10621900—48no—
304#10621900—48no—
305C2×D172—21no—
306C2×D172—24no—
307C2×D172C2412yes—
308C2×C4×D43—22no—
309C2×C4×D43—22no—
310C2×C4×D43—44no—
311C2×Dic86—22no—
312C2×Dic86—22no—
313C2×Dic86—22no—
314C2×Dic86—22no—
315C2×Dic86—22no—
316C2×Dic86—22no—
317C2×Dic86—44no—
318C2×Dic86—44no—
319C2×Dic86—44no—
320M16×C43—24no—
321C2×C8×C43C2414yes—
322C4⋊C4×C43—21no—
323C4⋊C4×C43—21no—
324C4⋊C4×C43—21no—
325C4⋊C4×C43C2412yes—
326C4⋊C4×C43C2412yes—
327C4⋊C4×C43C2412yes—
328C22⋊C4×C43—22no—
329C22⋊C4×C43—22no—
330C22⋊C4×C43—22no—
331C22⋊C4×C43—22no—
332C42×C43—22no—
333C42×C43—22no—
334C22⋊Dic43—22no—
335C22⋊Dic43—22no—
336C22⋊Dic43—22no—
337C22⋊Dic43—22no—
338(C2×D43)⋊C4—22no—
339(C2×D43)⋊C4—22no—
340(C2×D43)⋊C4—22no—
341(C2×D43)⋊C4—22no—
342C4⋊Dic43—21no—
343C4⋊Dic43—21no—
344C4⋊Dic43—21no—
345C4⋊Dic43—22no—
346C4⋊Dic43—22no—
347C4⋊Dic43—22no—
348C4⋊Dic43—22no—
349C4⋊Dic43C2412yes—
350C4⋊Dic43C2412yes—
351C4⋊Dic43C2412yes—
352Dic43⋊C4—22no—
353Dic43⋊C4—22no—
354Dic43⋊C4—22no—
355Dic43⋊C4—22no—
356Dic43⋊C4—22no—
357Dic43⋊C4—22no—
358Dic43⋊C4—22no—
359Dic43⋊C4—22no—
360Dic43⋊C4—22no—
361Dic43⋊C4—22no—
362C4×Dic43—22no—
363C4×Dic43—22no—
364C4×Dic43C2×D411yescharacteristic
365C4×Dic43C2×D411yescharacteristic
366C4×Dic43C2×D411yescharacteristic
367C4×Dic43C2×D411yescharacteristic
368C4×Dic43C2×D411yescharacteristic
369C4×Dic43C2×D411yescharacteristic
370C4×Dic43C2×D411yescharacteristic
371C4×Dic43C2×D411yescharacteristic
372C4×Dic43C2×D411yescharacteristic
373C4×Dic43C2×D411yescharacteristic
374C4×Dic43C2×D411yescharacteristic
375C4×Dic43C2×D411yescharacteristic
376C4×Dic43C2411yescharacteristic
377C4×Dic43C2411yescharacteristic
378C4×Dic43C2411yescharacteristic
379C4×Dic43C2411yescharacteristic
380#10621877—24no—
381C2×C43⋊C8C2414yes—
382C23×C43—22no—
383C23×C43—22no—
384C23×C43—22no—
385C23×C43—41no—
386C23×C43—42no—
387C23×C43—42no—
388C23×C43—42no—
389C23×C43C22×D411yescharacteristic
390C23×C43C22×D411yescharacteristic
391C23×C43C22×D411yescharacteristic
392C22×D43—22no—
393C22×D43—42no—
394C22×D43—42no—
395C22×D43—42no—
396D4×C43—24no—
397D4×C43—44no—
398D4×C43—44no—
399D4×C43—42no—
400C2×C4×C43—22no—
401C2×C4×C43—22no—
402C2×C4×C43—22no—
403C2×C4×C43—22no—
404C2×C4×C43—22no—
405C2×C4×C43—22no—
406C2×C4×C43—22no—
407C2×C4×C43—22no—
408C2×C4×C43—42no—
409C2×C4×C43—42no—
410C2×C4×C43—42no—
411C2×C4×C43C22×D411yescharacteristic
412C2×C4×C43C22×D411yescharacteristic
413C2×C4×C43C22×D411yescharacteristic
414C2×C4×C432−1+414yes—
415C2×C4×C43C2511yescharacteristic
416C22⋊D43—44no—
417C22⋊D43—44no—
418C22⋊D43—44no—
419C22⋊D43—44no—
420C22⋊D43—44no—
421C22⋊D43—44no—
422C2×Dic43—22no—
423C2×Dic43—22no—
424C2×Dic43—22no—
425C2×Dic43—22no—
426C2×Dic43—22no—
427C2×Dic43—22no—
428C2×Dic43—22no—
429C2×Dic43—22no—
430C2×Dic43—22no—
431C2×Dic43—22no—
432C2×Dic43—22no—
433C2×Dic43—41no—
434C2×Dic43—41no—
435C2×Dic43—41no—
436C2×Dic43—44no—
437C2×Dic43—42no—
438C2×Dic43—42no—
439C2×Dic43—42no—
440C2×Dic43—44no—
441C2×Dic43AGL(1,ℤ/8)14yes—
442C2×Dic43C22×D411yescharacteristic
443C2×Dic43C22×D411yescharacteristic
444C2×Dic43C22×D411yescharacteristic
445C2×Dic43C22×D411yescharacteristic
446C2×Dic43C22×D411yescharacteristic
447C2×Dic43C22×D411yescharacteristic
448C2×Dic43C22×D411yescharacteristic
449C2×Dic43C22×D411yescharacteristic
450D172—24no—
451D172—42no—
452C4×D43—44no—
453C4×D43—44no—
454Dic86—44no—
455Dic86—44no—
456Dic86—44no—
457Dic86—44no—
458Dic86—44no—
459Dic86—44no—
460C8×C43—24no—
461C43⋊C8—24no—
462#60864—431nomaximal, Sylow
463C22×C43—21no—
464C22×C43—21no—
465C22×C43—21no—
466C22×C43—21no—
467C22×C43—21no—
468C22×C43—21no—
469C22×C43—21no—
470C22×C43—44no—
471C22×C43—42no—
472C22×C43—42no—
473C22×C43—42no—
474C22×C43—84no—
475C22×C43#53612yes—
476C22×C43C2×AGL(1,ℤ/8)12yes—
477C22×C43C23×D411yescharacteristic
478C2×D43—42no—
479C2×D43—42no—
480C2×D43—42no—
481C2×D43—84no—
482C4×C43—21no—
483C4×C43—21no—
484C4×C43—42no—
485C4×C43—42no—
486C4×C43—42no—
487C4×C43#53612yes—
488C4×C43C2×2−1+412yes—
489Dic43—21no—
490Dic43—21no—
491Dic43—21no—
492Dic43—21no—
493Dic43—21no—
494Dic43—42no—
495Dic43—42no—
496Dic43—42no—
497Dic43C2×AGL(1,ℤ/8)12yes—
498Dic43C2×AGL(1,ℤ/8)12yes—
499Dic43#57512yes—
500C2×#533—431no—
501C2×#532—431no—
502#3235—434no—
503#3234—432no—
504#3234—432no—
505#3228—434no—
506#3227—432no—
507#3226—432no—
508#3165—432no—
509#3138—432no—
510#3094—431no—
511#3094—431no—
512#3094—431no—
513#3094D4311yescharacteristic, complemented
514#3077—432no—
515#3077—432no—
516#2920—431no—
517C2×C43—22no—
518C2×C43—22no—
519C2×C43—41no—
520C2×C43—82no—
521C2×C43C2×#53611yescharacteristic
522C2×C43C22×AGL(1,ℤ/8)11yescharacteristic
523C2×C43C2×#57511yescharacteristic
524D43—82no—
525C22×#41—861no—
526#533—432no—
527#533—432no—
528#533—432no—
529#533—432no—
530#533—861no—
531#533—861no—
532#533—861no—
533#533—861no—
534#532—432no—
535#532—432no—
536#532—432no—
537#532—432no—
538#532—861no—
539#532—861no—
540#532—861no—
541#532—861no—
542C2×C4⋊Q8—431no—
543C2×C4⋊Q8—431no—
544C2×C4⋊Q8—431no—
545C2×#127—431no—
546C2×#125—431no—
547C2×#125—431no—
548C2×#124—861no—
549C2×C22⋊Q8—861no—
550C2×C22⋊Q8—861no—
551C2×#121—431no—
552C2×#121—861no—
553C2×#121C2×D4311yescharacteristic
554C2×C4×Q8—861no—
555C2×C4×Q8—861no—
556C2×C4×D4—431no—
557C2×C4×D4—431no—
558C2×C4×D4—861no—
559C2×#117—431no—
560C2×#117C2×D4311yescharacteristic
561C22×C42—431no—
562#501—434no—
563#501—434no—
564#500—434no—
565#498—434no—
566#490—434no—
567#490—434no—
568#486—434no—
569#486—434no—
570#482—434no—
571#482—434no—
572#482—434no—
573#482C2×D4314yescomplemented
574#481—432no—
575#481—432no—
576#481—432no—
577#481C2×D4312yescomplemented
578#480—432no—
579#480—432no—
580#480—432no—
581#480C2×D4312yescomplemented
582#478—434no—
583#478—434no—
584#478—434no—
585#478—434no—
586#476—434no—
587#476—434no—
588#474—434no—
589#474—434no—
590#432—432no—
591#432—432no—
592#431—432no—
593#431—432no—
594#428—432no—
595#428—432no—
596#428—432no—
597#428C2×D4312yes—
598#423—432no—
599#418—432no—
600#418—432no—
601#418—432no—
602#418C2×D4312yes—
603#407—431no—
604#407C2×D4311yescharacteristic
605C4×M16—432no—
606C43#6086411yescharacteristic, complemented, Sylow
607C2×#41—862no—
608C2×#41—862no—
609C2×#41—862no—
610C2×#41—862no—
611C2×#41—1728no—
612C22×Q8—861no—
613C22×Q8—861no—
614C22×Q8—861no—
615C22×D4—21no—
616C22×D4—431no—
617C22×D4—861no—
618C22×D4—861no—
619C22×D4—861no—
620C22×D4C22×D4311yescharacteristic
621C23×C4—431no—
622C23×C4—431no—
623C23×C4—861no—
624C23×C4—861no—
625C23×C4C22×D4311yescharacteristic
626C2×M16—432no—
627C2×M16C22×D4312yes—
628C4⋊Q8—432no—
629C4⋊Q8—432no—
630C4⋊Q8—432no—
631C4⋊Q8—432no—
632C4⋊Q8—432no—
633C4⋊Q8—432no—
634C4⋊Q8—861no—
635C4⋊Q8—861no—
636C4⋊Q8—861no—
637C4⋊Q8—861no—
638C4⋊Q8—861no—
639C4⋊Q8—861no—
640#127—432no—
641#127—432no—
642#127—861no—
643#127—861no—
644#125—432no—
645#125—432no—
646#125—432no—
647#125—432no—
648#125—861no—
649#125—861no—
650#125—861no—
651#125—861no—
652#124—862no—
653#124—862no—
654#124—862no—
655#124—862no—
656C22⋊Q8—862no—
657C22⋊Q8—862no—
658C22⋊Q8—862no—
659C22⋊Q8—862no—
660C22⋊Q8—862no—
661C22⋊Q8—862no—
662C22⋊Q8—862no—
663C22⋊Q8—862no—
664#121—21no—
665#121—21no—
666#121—432no—
667#121—432no—
668#121—862no—
669#121—862no—
670#121—862no—
671#121—862no—
672#121—861no—
673#121—861no—
674#121C22×D4312yes—
675#121C22×D4312yes—
676C4×Q8—862no—
677C4×Q8—862no—
678C4×Q8—862no—
679C4×Q8—862no—
680C4×Q8—862no—
681C4×Q8—862no—
682C4×Q8—862no—
683C4×Q8—862no—
684C4×D4—432no—
685C4×D4—432no—
686C4×D4—432no—
687C4×D4—432no—
688C4×D4—862no—
689C4×D4—862no—
690C4×D4—862no—
691C4×D4—862no—
692C4×D4—861no—
693C4×D4—861no—
694C4×D4—861no—
695C4×D4—861no—
696#117—21no—
697#117—21no—
698#117—432no—
699#117—432no—
700#117—861no—
701#117—861no—
702#117C22×D4312yes—
703#117C22×D4312yes—
704C2×C4⋊C4—431no—
705C2×C4⋊C4—431no—
706C2×C4⋊C4—431no—
707C2×C4⋊C4—861no—
708C2×C4⋊C4—861no—
709C2×C4⋊C4—861no—
710C2×C4⋊C4—861no—
711C2×C4⋊C4—861no—
712C2×C4⋊C4—861no—
713C2×C4⋊C4—861no—
714C2×C4⋊C4C22×D4311yescharacteristic
715C2×C4⋊C4C22×D4311yescharacteristic
716C2×C4⋊C4C22×D4311yescharacteristic
717C2×C22⋊C4—21no—
718C2×C22⋊C4—21no—
719C2×C22⋊C4—861no—
720C2×C22⋊C4—861no—
721C2×C22⋊C4—861no—
722C2×C22⋊C4—861no—
723C2×C42—21no—
724C2×C42—431no—
725C2×C42—431no—
726C2×C42—431no—
727C2×C42—431no—
728C2×C42—431no—
729C2×C42—431no—
730C2×C42—431no—
731C2×C42—431no—
732C2×C42—431no—
733C2×C42—431no—
734C2×C42—431no—
735C2×C42—431no—
736C2×C42—861no—
737#107—434no—
738#107—434no—
739#107—434no—
740#107C22×D4314yes—
741#106—434no—
742#106—434no—
743#106—434no—
744#106C22×D4314yes—
745C4⋊C8—434no—
746C4⋊C8—434no—
747#102—434no—
748#102—434no—
749#102—434no—
750#102—434no—
751#102—434no—
752#102—434no—
753#102C22×D4314yes—
754#102C22×D4314yes—
755C22⋊C8—432no—
756C22⋊C8—432no—
757C22⋊C8C22×D4312yes—
758C22⋊C8C22×D4312yes—
759#97—434no—
760C4×C8—434no—
761C24—21no—
762C24—861no—
763C24D4×D4311yescharacteristic
764#41—1728no—
765#41—1728no—
766#41—1728no—
767#41—1728no—
768C2×Q8—862no—
769C2×Q8—862no—
770C2×Q8—862no—
771C2×Q8—862no—
772C2×Q8—862no—
773C2×Q8—862no—
774C2×Q8—1724no—
775C2×Q8—1724no—
776C2×Q8—1724no—
777C2×D4—22no—
778C2×D4—22no—
779C2×D4—21no—
780C2×D4—24no—
781C2×D4—44no—
782C2×D4—432no—
783C2×D4—862no—
784C2×D4—862no—
785C2×D4—862no—
786C2×D4—862no—
787C2×D4—862no—
788C2×D4—862no—
789C2×D4—861no—
790C2×D4—864no—
791C2×D4—1724no—
792C2×D4—1724no—
793C2×D4—1724no—
794C2×D4C23×D4312yes—
795C22×C4—24no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
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—431no—
811C22×C4—862no—
812C22×C4—862no—
813C22×C4—864no—
814C22×C4—862no—
815C22×C4—862no—
816C22×C4—861no—
817C22×C4—861no—
818C22×C4—861no—
819C22×C4—1724no—
820C22×C4—1722no—
821C22×C4—1724no—
822C22×C4D4×D4311yescharacteristic
823C22×C4D4×D4311yescharacteristic
824C22×C4D4×D4311yescharacteristic
825C22×C4C23×D4311yescharacteristic
826C22×C4C23×D4311yescharacteristic
827C22×C4C23×D4311yescharacteristic
828M16—24no—
829M16—864no—
830C2×C8—434no—
831C2×C8C23×D4314yes—
832C4⋊C4—21no—
833C4⋊C4—21no—
834C4⋊C4—21no—
835C4⋊C4—432no—
836C4⋊C4—432no—
837C4⋊C4—432no—
838C4⋊C4—862no—
839C4⋊C4—862no—
840C4⋊C4—862no—
841C4⋊C4—862no—
842C4⋊C4—862no—
843C4⋊C4—862no—
844C4⋊C4—862no—
845C4⋊C4—862no—
846C4⋊C4—862no—
847C4⋊C4—862no—
848C4⋊C4—862no—
849C4⋊C4—862no—
850C4⋊C4—862no—
851C4⋊C4—862no—
852C4⋊C4—861no—
853C4⋊C4—861no—
854C4⋊C4—861no—
855C4⋊C4C23×D4312yes—
856C4⋊C4C23×D4312yes—
857C4⋊C4C23×D4312yes—
858C22⋊C4—22no—
859C22⋊C4—22no—
860C22⋊C4—22no—
861C22⋊C4—22no—
862C22⋊C4—862no—
863C22⋊C4—862no—
864C22⋊C4—862no—
865C22⋊C4—862no—
866C22⋊C4—862no—
867C22⋊C4—862no—
868C22⋊C4—862no—
869C22⋊C4—862no—
870C42—22no—
871C42—22no—
872C42—431no—
873C42—431no—
874C42—431no—
875C42—431no—
876C42—431no—
877C42—431no—
878C42—431no—
879C42—431no—
880C42—431no—
881C42—431no—
882C42—431no—
883C42—431no—
884C42—431no—
885C42—431no—
886C42—431no—
887C42—431no—
888C42—862no—
889C42—862no—
890C23—22no—
891C23—22no—
892C23—22no—
893C23—41no—
894C23—42no—
895C23—42no—
896C23—42no—
897C23—862no—
898C23—1722no—
899C23—1722no—
900C23—1722no—
901C23C2×D4×D4311yescharacteristic
902C23C2×D4×D4311yescharacteristic
903C23C2×D4×D4311yescharacteristic
904Q8—1724no—
905Q8—1724no—
906Q8—1724no—
907Q8—1724no—
908Q8—1724no—
909Q8—1724no—
910D4—24no—
911D4—44no—
912D4—44no—
913D4—42no—
914D4—864no—
915D4—1724no—
916D4—1724no—
917D4—1724no—
918D4—1724no—
919D4—1724no—
920D4—1724no—
921D4—1722no—
922C2×C4—22no—
923C2×C4—22no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—22no—
927C2×C4—22no—
928C2×C4—22no—
929C2×C4—22no—
930C2×C4—42no—
931C2×C4—42no—
932C2×C4—42no—
933C2×C4—434no—
934C2×C4—431no—
935C2×C4—431no—
936C2×C4—431no—
937C2×C4—431no—
938C2×C4—431no—
939C2×C4—431no—
940C2×C4—431no—
941C2×C4—431no—
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—862no—
953C2×C4—1724no—
954C2×C4—1724no—
955C2×C4—1724no—
956C2×C4—1721no—
957C2×C4—1721no—
958C2×C4—1721no—
959C2×C4—1724no—
960C2×C4—1722no—
961C2×C4—1722no—
962C2×C4—1722no—
963C2×C4C2×D4×D4311yescharacteristic
964C2×C4C2×D4×D4311yescharacteristic
965C2×C4C2×D4×D4311yescharacteristic
966C2×C4#1306337214yes—
967C2×C4C24×D4311yescharacteristic
968C8—24no—
969C8—864no—
970C22—21no—
971C22—21no—
972C22—21no—
973C22—21no—
974C22—21no—
975C22—21no—
976C22—21no—
977C22—44no—
978C22—42no—
979C22—42no—
980C22—42no—
981C22—84no—
982C22—3444no—
983C22—1722no—
984C22—1722no—
985C22—1722no—
986C22#1458347112yes—
987C22AGL(1,ℤ/8)×D4312yes—
988C22C22×D4×D4311yescharacteristic
989C4—21no—
990C4—21no—
991C4—42no—
992C4—42no—
993C4—42no—
994C4—432no—
995C4—432no—
996C4—432no—
997C4—861no—
998C4—861no—
999C4—861no—
1000C4—861no—
1001C4—861no—
1002C4—1722no—
1003C4—1722no—
1004C4—1722no—
1005C4#1458347112yes—
1006C4C2×#1306337212yes—
1007C2—22no—
1008C2—22no—
1009C2—41no—
1010C2—82no—
1011C2—3442no—
1012C2C2×#1458347111yescharacteristic
1013C2C2×AGL(1,ℤ/8)×D4311yescharacteristic
1014C2#575×D4311yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3094C2
socleC22×C43C23×D4
prime radicalC2×#14583444C2
hypercenter#3094D43
hypocenterC43#60864
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3094

Complements

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

NH ≅ G/Ntype
1. C2×#14583452C2semidirect
3. #19145790C2semidirect
4. #19145784C2semidirect
5. #19145782C2semidirect
6. #19145729C2semidirect
7. #19145721C2semidirect
8. #19145714C2semidirect
9. #19145139C2semidirect
10. #19144967C2semidirect
11. #19144536C2semidirect
12. #19144535C2semidirect
13. #19144531C2semidirect
14. #19144391C2semidirect
15. #19144389C2semidirect
16. #19143224C2semidirect
17. C43×#3094C2semidirect
25. #14583452C22semidirect
26. #14583452C22semidirect
36. C2×#13063324C22semidirect
37. C2×#13063324C22semidirect
39. C2×#13063316C22semidirect
40. C2×#13063316C22semidirect
53. #14583307C22semidirect
54. #14583306C22semidirect
55. #14583303C22semidirect
56. #14583296C22semidirect
57. #14583262C22semidirect
58. #14583262C22semidirect
59. #14583244C22semidirect
60. #14583244C22semidirect
61. #14583224C22semidirect
62. #14583223C22semidirect
63. #14583220C22semidirect
64. #14583218C22semidirect
65. #14583217C22semidirect
66. #14583215C22semidirect
67. #14583213C22semidirect
68. #14583212C22semidirect
69. #14583210C22semidirect
70. #14583202C22semidirect
71. #14583201C22semidirect
72. #14583198C22semidirect
73. #14583197C22semidirect
74. #14583188C22semidirect
75. #14583187C22semidirect
76. #14583178C22semidirect
77. #14583177C22semidirect
78. #14582953C22semidirect
79. #14582953C22semidirect
80. #14582949C22semidirect
81. #14582949C22semidirect
93. C43×#482C22semidirect
94. C43×#481C22semidirect
95. C43×#480C22semidirect
513. #3094D43semidirect
573. #482C2×D43semidirect
577. #481C2×D43semidirect
581. #480C2×D43semidirect
606. C43#60864semidirect

Maximal subgroups

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

subgroupindex
C2×#145834522
C2×#145834442
#191457902
#191457842
#191457822
#191457292
#191457212
#191457142
#191451392
#191449672
#191445362
#191445352
#191445312
#191443912
#191443892
#191432242
C43×#30942
#6086443