Finite Group Databasebeta

← #25968693

Subgroups — #25968693

Order 11008.

1800 conjugacy classes of subgroups.

The subgroup lattice has 992 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#19145777C214yesmaximal, complemented
4#19145767C214yesmaximal, complemented
5#19145750C211yesmaximal, characteristic, complemented
6#19145742C211yesmaximal, characteristic, complemented
7#19145735C211yesmaximal, characteristic, complemented
8#19145733C211yesmaximal, characteristic, complemented
9#19145731C211yesmaximal, characteristic, complemented
10#19145724C211yesmaximal, characteristic, complemented
11#19145717C211yesmaximal, characteristic, complemented
12#19145106C211yesmaximal, characteristic, complemented
13#19145104C211yesmaximal, characteristic, complemented
14#19144919C211yesmaximal, characteristic, complemented
15#19144919C211yesmaximal, characteristic, complemented
16#19144513C214yesmaximal, complemented
17#19144382C214yesmaximal, complemented
18#431×D43C211yesmaximal, characteristic, complemented
19C43×#3231C211yesmaximal, characteristic, complemented
20#14583456C2211yescharacteristic
21#14583455C2212yes—
22#14583454C2211yescharacteristic
23#14583454C2211yescharacteristic
24#14583454C2211yescharacteristic
25#14583454C2211yescharacteristic
26#14583453—21no—
27#14583453—21no—
28#14583452C2212yes—
29#14583451—21no—
30#14583451—21no—
31#14583450C2211yescharacteristic
32#14583450C2211yescharacteristic
33#14583449C2211yescharacteristic
34C4⋊Q8×D43C2211yescharacteristic
35C4⋊Q8×D43C2211yescharacteristic
36#14583436—21no—
37#14583436C2212yes—
38#14583435—21no—
39#14583435C2212yes—
40#14583434—21no—
41#14583434—21no—
42#125×D43C2212yes—
43#14583412—21no—
44#14583412C2212yes—
45#14583411—21no—
46C22⋊Q8×D43—21no—
47C22⋊Q8×D43—21no—
48C4×#10621902—21no—
49C4×#10621902C2212yes—
50#14583367—21no—
51C4×Q8×D43—21no—
52C4×Q8×D43—21no—
53#117×D43C2212yes—
54C2×C42×D43C2211yescharacteristic
55#14583304C2211yescharacteristic, complemented
56#14583302C2211yescharacteristic, complemented
57#14583302C2211yescharacteristic, complemented
58#14583300C2214yescomplemented
59#14583299C2214yescomplemented
60#14583297C2211yescharacteristic, complemented
61#14583295C2211yescharacteristic, complemented
62#14583295C2211yescharacteristic, complemented
63#14583255C2214yescomplemented
64#14583255C2214yescomplemented
65#14583249C2211yescharacteristic, complemented
66#14583249C2211yescharacteristic, complemented
67#14583247C2211yescharacteristic, complemented
68#14583247C2211yescharacteristic, complemented
69#14583246C2211yescharacteristic, complemented
70#14583246C2211yescharacteristic, complemented
71#14583237C2214yes—
72#14583233C2214yes—
73#14583228C2214yes—
74#14583224C2214yes—
75#14583223C2214yes—
76#14583219C2214yes—
77#14583214C2214yes—
78#14583206C2214yescomplemented
79#14583200C2214yescomplemented
80#14583196C2214yescomplemented
81#14583192C2214yescomplemented
82#14583188C2214yescomplemented
83#14583182C2214yescomplemented
84#14583178C2214yescomplemented
85#14582952C2211yescharacteristic
86#14582951C2212yes—
87#14582950C2211yescharacteristic
88#14582950C2211yescharacteristic
89#14582949C2212yes—
90#14582936C2214yes—
91#14582934C2214yes—
92C4⋊C8×D43C2212yes—
93#14582894C2214yes—
94#14582894C2214yes—
95C22⋊C8×D43C2212yes—
96C4×C8×D43C2211yescharacteristic
97C4×C8×D43C2211yescharacteristic
98C43×#533C2211yescharacteristic
99C43×#533C2211yescharacteristic
100C43×#500C2211yescharacteristic, complemented
101C43×#498C2211yescharacteristic, complemented
102C43×#487C2211yescharacteristic, complemented
103C43×#487C2211yescharacteristic, complemented
104C43×#485C2214yes—
105C43×#479C2214yescomplemented
106C43×#431C2211yescharacteristic
107C2×#10621902—21no—
108C2×#10621902C2312yes—
109C2×#10621898—21no—
110C2×Q8×D43—21no—
111C2×Q8×D43—21no—
112C22×C4×D43D411yescharacteristic
113C22×C4×D43D411yescharacteristic
114C22×C4×D43C2311yescharacteristic
115C2×C8×D43C2312yes—
116C2×C8×D43C2312yes—
117#13063325C2311yescharacteristic
118#13063325C2311yescharacteristic
119#13063325C2311yescharacteristic
120#13063324—21no—
121#13063324—21no—
122#13063324C2312yes—
123#13063324C2312yes—
124#13063323—21no—
125#13063323—21no—
126#13063322C2311yescharacteristic
127#13063320—22no—
128#13063320—22no—
129#13063317C2312yes—
130#13063316—21no—
131#13063316C2312yes—
132#13063316C2312yes—
133#13063316C2312yes—
134#13063315—22no—
135#13063315—22no—
136#13063314—21no—
137#13063314C2312yes—
138#13063313—21no—
139#13063310—22no—
140#13063310—22no—
141#13063309—22no—
142#13063305—21no—
143#13063305—21no—
144#13063305—21no—
145#13063305—21no—
146#13063304—21no—
147#13063304—21no—
148#13063303—22no—
149#13063303—22no—
150#13063302—22no—
151#13063302—22no—
152#13063301—21no—
153#13063301—21no—
154#13063301—21no—
155#13063301C2312yes—
156#13063300—21no—
157#13063300—21no—
158#13063300—21no—
159#13063300C2312yes—
160#13063299—21no—
161#13063299C2312yes—
162#13063295—22no—
163Q8×Dic43—21no—
164Q8×Dic43—21no—
165Q8×Dic43—21no—
166Q8×Dic43C2312yes—
167C4×Dic86—21no—
168C4×Dic86—21no—
169C4×Dic86—22no—
170C4×Dic86—22no—
171#13063290—21no—
172#13063290—21no—
173#13063290—22no—
174#13063290—22no—
175#13063290—21no—
176#13063290—21no—
177C4×D172—22no—
178C4×D172—22no—
179C4×D172—21no—
180C4×D172C2312yes—
181#13063287—22no—
182#13063287—22no—
183#13063287—21no—
184#13063287—21no—
185#13063287—21no—
186#13063287C2312yes—
187(C22⋊D43)⋊C4—22no—
188(C22⋊D43)⋊C4—22no—
189#13063284C2312yes—
190#13063283—21no—
191#13063283—22no—
192#13063283—22no—
193#13063283C2312yes—
194#13063283C2312yes—
195#13063283C2312yes—
196#13063282—22no—
197#13063282—22no—
198#13063281—22no—
199C4⋊C4×D43—22no—
200C4⋊C4×D43—22no—
201C4⋊C4×D43—21no—
202C4⋊C4×D43—21no—
203C4⋊C4×D43C2312yes—
204C4⋊C4×D43C2312yes—
205C22⋊C4×D43—22no—
206C2×C4×Dic43D411yescharacteristic
207C2×C4×Dic43D411yescharacteristic
208C2×C4×Dic43C2311yescharacteristic
209C42×D43—22no—
210C42×D43—22no—
211C42×D43D411yescharacteristic
212C42×D43D411yescharacteristic
213C42×D43D411yescharacteristic
214C42×D43D411yescharacteristic
215C42×D43C2311yescharacteristic
216C42×D43C2311yescharacteristic
217C42×D43C2311yescharacteristic
218C42×D43C2311yescharacteristic
219#13063259C2314yes—
220#13063258C2314yes—
221#13063258C2314yes—
222#13063257C2314yes—
223#13063256C2314yes—
224#13063256C2314yes—
225C4⋊(C43⋊C8)C2312yes—
226Dic43⋊C8C2312yes—
227Dic43⋊C8C2312yes—
228#13063249C2314yes—
229#13063249C2314yes—
230#13063247C2314yes—
231#13063247C2314yes—
232#13063245C2314yes—
233#13063245C2314yes—
234C22⋊(C43⋊C8)C2312yes—
235(C2×D43)⋊C8C2312yes—
236(C2×D43)⋊C8C2312yes—
237C4×C43⋊C8C2311yescharacteristic
238C4×C43⋊C8C2311yescharacteristic
239C8×Dic43C2312yes—
240C8×Dic43C2312yes—
241C4⋊Q8×C43C2311yescharacteristic
242C4⋊Q8×C43C2311yescharacteristic
243C4⋊Q8×C43C2311yescharacteristic
244C4⋊Q8×C43C2311yescharacteristic
245#125×C43—21no—
246#125×C43C2312yes—
247C22⋊Q8×C43—21no—
248C22⋊Q8×C43—21no—
249C22⋊Q8×C43—21no—
250C22⋊Q8×C43C2312yes—
251C4×Q8×C43—21no—
252C4×Q8×C43—21no—
253C4×Q8×C43—21no—
254C4×Q8×C43C2312yes—
255#117×C43—21no—
256#117×C43C2312yes—
257C2×C42×C43C2311yescharacteristic
258#107×C43C2314yes—
259#106×C43C2314yes—
260C4⋊C8×C43C2312yes—
261#103×C43C2314yes—
262#103×C43C2314yes—
263C22⋊C8×C43C2312yes—
264C4×C8×C43C2311yescharacteristic
265C4×C8×C43C2311yescharacteristic
266C23×D43C2×D411yescharacteristic
267C2×Q8×C43—21no—
268C2×Q8×C43—21no—
269C2×Q8×C43—21no—
270C2×Q8×C43C2412yes—
271C22×C4×C43C2×D411yescharacteristic
272C22×C4×C43C2×D411yescharacteristic
273C22×C4×C43C2411yescharacteristic
274C2×C22⋊D43—22no—
275C22×Dic43C2×D411yescharacteristic
276C22×Dic43C2×D411yescharacteristic
277C22×Dic43C2×D411yescharacteristic
278#10621902—28no—
279#10621902—44no—
280Q8×D43—44no—
281Q8×D43—44no—
282#10621898—44no—
283C2×D172—21no—
284C2×D172—21no—
285C2×D172—22no—
286C2×D172—22no—
287C2×D172C2412yes—
288C2×C4×D43—24no—
289C2×C4×D43—24no—
290C2×C4×D43—22no—
291C2×C4×D43—22no—
292C2×C4×D43—22no—
293C2×C4×D43—22no—
294C2×C4×D43—22no—
295C2×C4×D43—42no—
296C2×C4×D43C2×D411yescharacteristic
297C2×C4×D43C2×D411yescharacteristic
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×D43C2411yescharacteristic
307C2×C4×D43C2411yescharacteristic
308C2×Dic86—21no—
309C2×Dic86—21no—
310C2×Dic86—21no—
311C2×Dic86—22no—
312C2×Dic86—22no—
313C2×C8×C43C2412yes—
314C2×C8×C43C2412yes—
315C4⋊C4×C43—21no—
316C4⋊C4×C43—21no—
317C4⋊C4×C43—22no—
318C4⋊C4×C43—22no—
319C4⋊C4×C43—21no—
320C4⋊C4×C43—21no—
321C4⋊C4×C43—21no—
322C4⋊C4×C43—22no—
323C4⋊C4×C43—22no—
324C4⋊C4×C43C2412yes—
325C4⋊C4×C43C2412yes—
326C4⋊C4×C43C2412yes—
327C22⋊C4×C43—22no—
328C22⋊C4×C43—22no—
329C42×C43—22no—
330C42×C43—22no—
331C42×C43C2×D411yescharacteristic
332C42×C43C2×D411yescharacteristic
333C42×C43C2411yescharacteristic
334C42×C43C2411yescharacteristic
335C22⋊Dic43—22no—
336(C2×D43)⋊C4—22no—
337(C2×D43)⋊C4—22no—
338(C2×D43)⋊C4—22no—
339(C2×D43)⋊C4—22no—
340(C2×D43)⋊C4—22no—
341(C2×D43)⋊C4—22no—
342(C2×D43)⋊C4—22no—
343(C2×D43)⋊C4—22no—
344(C2×D43)⋊C4—22no—
345(C2×D43)⋊C4—22no—
346C4⋊Dic43—21no—
347C4⋊Dic43—21no—
348C4⋊Dic43—21no—
349C4⋊Dic43—22no—
350C4⋊Dic43—22no—
351C4⋊Dic43—22no—
352C4⋊Dic43—22no—
353C4⋊Dic43C2412yes—
354C4⋊Dic43C2412yes—
355C4⋊Dic43C2412yes—
356Dic43⋊C4—22no—
357Dic43⋊C4—22no—
358Dic43⋊C4—22no—
359Dic43⋊C4—22no—
360Dic43⋊C4—22no—
361Dic43⋊C4—22no—
362Dic43⋊C4—22no—
363Dic43⋊C4—22no—
364Dic43⋊C4—22no—
365Dic43⋊C4—22no—
366C4×Dic43—22no—
367C4×Dic43—22no—
368C4×Dic43—22no—
369C4×Dic43—22no—
370C4×Dic43—22no—
371C4×Dic43C2×D411yescharacteristic
372C4×Dic43C2×D411yescharacteristic
373C4×Dic43C2×D411yescharacteristic
374C4×Dic43C2×D411yescharacteristic
375C4×Dic43C2×D411yescharacteristic
376C4×Dic43C2×D411yescharacteristic
377C4×Dic43C2×D411yescharacteristic
378C4×Dic43C2×D411yescharacteristic
379C4×Dic43C2×D411yescharacteristic
380C4×Dic43C2×D411yescharacteristic
381C4×Dic43C2411yescharacteristic
382C4×Dic43C2411yescharacteristic
383C2×C43⋊C8C2412yes—
384C2×C43⋊C8C2412yes—
385C8×D43—24no—
386C8×D43—24no—
387C23×C43C22×D411yescharacteristic
388C22×D43—22no—
389C22×D43—22no—
390C22×D43—22no—
391C22×D43—41no—
392C22×D43C22×D411yescharacteristic
393C22×D43C22×D411yescharacteristic
394Q8×C43—24no—
395Q8×C43—42no—
396Q8×C43—42no—
397Q8×C43—42no—
398C2×C4×C43—22no—
399C2×C4×C43—22no—
400C2×C4×C43—22no—
401C2×C4×C43—22no—
402C2×C4×C43—22no—
403C2×C4×C43—22no—
404C2×C4×C43—22no—
405C2×C4×C43C22×D411yescharacteristic
406C2×C4×C43C22×D411yescharacteristic
407C2×C4×C43C22×D411yescharacteristic
408C2×C4×C43C22×D411yescharacteristic
409C2×C4×C43C22×D411yescharacteristic
410C2×C4×C43C2511yescharacteristic
411C22⋊D43—44no—
412C2×Dic43—22no—
413C2×Dic43—22no—
414C2×Dic43—22no—
415C2×Dic43—22no—
416C2×Dic43—22no—
417C2×Dic43—41no—
418C2×Dic43C22×D411yescharacteristic
419C2×Dic43C22×D411yescharacteristic
420C2×Dic43C22×D411yescharacteristic
421C2×Dic43C22×D411yescharacteristic
422C2×Dic43C22×D411yescharacteristic
423C2×Dic43C22×D411yescharacteristic
424D172—24no—
425D172—44no—
426D172—44no—
427D172—42no—
428D172—42no—
429C4×D43—22no—
430C4×D43—22no—
431C4×D43—22no—
432C4×D43—22no—
433C4×D43—22no—
434C4×D43—22no—
435C4×D43—22no—
436C4×D43—22no—
437C4×D43—41no—
438C4×D43—41no—
439C4×D43—44no—
440C4×D43—44no—
441C4×D43—44no—
442C4×D43—44no—
443C4×D43—44no—
444C4×D43#13514yes—
445C4×D432−1+414yes—
446Dic86—44no—
447Dic86—42no—
448Dic86—42no—
449Dic86—42no—
450Dic86—44no—
451C8×C43—22no—
452C8×C43—22no—
453C43⋊C8—22no—
454C43⋊C8—22no—
455#60846—431nomaximal, Sylow
456C22×C43—21no—
457C22×C43—21no—
458C22×C43—21no—
459C22×C43C23×D411yescharacteristic
460C2×D43—21no—
461C2×D43—21no—
462C2×D43—21no—
463C2×D43—21no—
464C2×D43—44no—
465C2×D43—42no—
466C2×D43—42no—
467C2×D43—42no—
468C2×D43#53612yes—
469C2×D43C2×#13512yes—
470C4×C43—21no—
471C4×C43—21no—
472C4×C43—21no—
473C4×C43—42no—
474C4×C43—42no—
475C4×C43—42no—
476C4×C43—42no—
477C4×C43C2×#13512yes—
478C4×C43#57512yes—
479C4×C43C2×2−1+412yes—
480Dic43—21no—
481Dic43—21no—
482Dic43—21no—
483Dic43—21no—
484Dic43—42no—
485Dic43—42no—
486Dic43—42no—
487Dic43#53612yes—
488Dic43C2×#13512yes—
489#3444—431no—
490C2×#533—431no—
491#3233—434no—
492#3232—434no—
493#3231—431no—
494#3231D4311yescharacteristic, complemented
495#3230—431no—
496#3229—431no—
497#3228—431no—
498#3228—431no—
499#3227—431no—
500#3226—431no—
501#3160—431no—
502#3160—431no—
503#3131—431no—
504#3131—431no—
505#3091—434no—
506#3076—434no—
507C2×#431—431no—
508C2×C43—41no—
509C2×C43C2×#53611yescharacteristic
510C2×C43C22×#13511yescharacteristic
511C2×C43C2×#57511yescharacteristic
512D43—22no—
513D43—22no—
514D43—82no—
515#533—431no—
516#533—431no—
517#533—431no—
518#533—432no—
519#533—432no—
520#533—431no—
521#533—431no—
522#533—861no—
523#533—861no—
524#533—861no—
525#533—861no—
526#533C2×D4311yescharacteristic
527#533C2×D4311yescharacteristic
528#532—431no—
529#532—431no—
530#532—431no—
531C2×C4⋊Q8—431no—
532C2×C4⋊Q8—431no—
533#529—432no—
534#529—432no—
535#529—861no—
536#529—861no—
537#529—861no—
538#529—861no—
539C2×#125—432no—
540#525—432no—
541#525—861no—
542#525—861no—
543C2×C22⋊Q8—861no—
544C2×C22⋊Q8—861no—
545C4×#41—432no—
546C4×#41—861no—
547C4×#41—861no—
548C2×C4×Q8—861no—
549C2×C4×Q8—861no—
550C2×#117—432no—
551C22×C42—431no—
552#500—431no—
553#500—431no—
554#500—431no—
555#500C2×D4311yescharacteristic, complemented
556#499—434no—
557#499—434no—
558#498—431no—
559#498—431no—
560#498—431no—
561#498C2×D4311yescharacteristic, complemented
562#488—434no—
563#488—434no—
564#487—431no—
565#487—431no—
566#487C2×D4311yescharacteristic, complemented
567#487C2×D4311yescharacteristic, complemented
568#486—431no—
569#486—431no—
570#486—431no—
571#486—431no—
572#485—434no—
573#485C2×D4314yes—
574#484—434no—
575#483—434no—
576#482—434no—
577#482—434no—
578#481—434no—
579#480—434no—
580#479—434no—
581#479C2×D4314yescomplemented
582#478—434no—
583#478—434no—
584#477—434no—
585#476—434no—
586#475—434no—
587#474—434no—
588#431—431no—
589#431—432no—
590#431—432no—
591#431—431no—
592#431—431no—
593#431C2×D4311yescharacteristic
594#427—434no—
595#427—434no—
596C2×C4⋊C8—432no—
597#416—434no—
598#416—434no—
599C2×C22⋊C8—432no—
600C2×C4×C8—431no—
601C2×C4×C8—431no—
602C43#6084611yescharacteristic, complemented, Sylow
603C2×#41—432no—
604C2×#41—861no—
605C2×#41—861no—
606C22×Q8—861no—
607C22×Q8—861no—
608C23×C4—431no—
609C23×C4—431no—
610C23×C4—431no—
611C22×C8—432no—
612C22×C8—432no—
613C4⋊Q8—432no—
614C4⋊Q8—432no—
615C4⋊Q8—431no—
616C4⋊Q8—431no—
617C4⋊Q8—431no—
618C4⋊Q8—861no—
619C4⋊Q8—861no—
620C4⋊Q8—861no—
621C4⋊Q8—861no—
622C4⋊Q8C22×D4311yescharacteristic
623C4⋊Q8C22×D4311yescharacteristic
624C4⋊Q8C22×D4311yescharacteristic
625C4⋊Q8C22×D4311yescharacteristic
626#127—431no—
627#126—862no—
628#126—862no—
629#125—21no—
630#125—432no—
631#125—432no—
632#125—432no—
633#125—432no—
634#125—862no—
635#125—862no—
636#125—861no—
637#125C22×D4312yes—
638#124—432no—
639#124—861no—
640#124—861no—
641#123—862no—
642#123—862no—
643#123—862no—
644C22⋊Q8—21no—
645C22⋊Q8—21no—
646C22⋊Q8—21no—
647C22⋊Q8—432no—
648C22⋊Q8—862no—
649C22⋊Q8—862no—
650C22⋊Q8—862no—
651C22⋊Q8—862no—
652C22⋊Q8—861no—
653C22⋊Q8—861no—
654C22⋊Q8—861no—
655C22⋊Q8—861no—
656C22⋊Q8—861no—
657C22⋊Q8—861no—
658C22⋊Q8—861no—
659C22⋊Q8—861no—
660C22⋊Q8—861no—
661C22⋊Q8C22×D4312yes—
662#121—432no—
663#121—432no—
664#121—861no—
665#121—861no—
666#121—861no—
667#121—861no—
668#120—862no—
669C4×Q8—21no—
670C4×Q8—21no—
671C4×Q8—21no—
672C4×Q8—432no—
673C4×Q8—862no—
674C4×Q8—862no—
675C4×Q8—862no—
676C4×Q8—862no—
677C4×Q8—861no—
678C4×Q8—861no—
679C4×Q8—861no—
680C4×Q8—861no—
681C4×Q8—861no—
682C4×Q8—861no—
683C4×Q8—861no—
684C4×Q8—861no—
685C4×Q8—861no—
686C4×Q8C22×D4312yes—
687C4×D4—432no—
688C4×D4—432no—
689C4×D4—862no—
690C4×D4—862no—
691C4×D4—861no—
692C4×D4—861no—
693C4×D4—861no—
694C4×D4—862no—
695C4×D4—862no—
696C4×D4—862no—
697C4×D4—862no—
698C4×D4—861no—
699#117—21no—
700#117—432no—
701#117—432no—
702#117—432no—
703#117—432no—
704#117—862no—
705#117—862no—
706#117—862no—
707#117—862no—
708#117—862no—
709#117—861no—
710#117C22×D4312yes—
711C2×C4⋊C4—432no—
712C2×C4⋊C4—432no—
713C2×C4⋊C4—862no—
714C2×C4⋊C4—862no—
715C2×C4⋊C4—861no—
716C2×C4⋊C4—861no—
717C2×C22⋊C4—862no—
718C2×C42—431no—
719C2×C42—431no—
720C2×C42—431no—
721C2×C42—431no—
722C2×C42—431no—
723C2×C42—431no—
724C2×C42—431no—
725C2×C42—431no—
726C2×C42—431no—
727C2×C42—431no—
728C2×C42—431no—
729C2×C42—862no—
730C2×C42—862no—
731C2×C42C22×D4311yescharacteristic
732#107—434no—
733#107—434no—
734#107—434no—
735#107C22×D4314yes—
736#106—434no—
737#106—434no—
738#106—434no—
739#106C22×D4314yes—
740C4⋊C8—432no—
741C4⋊C8—432no—
742C4⋊C8—432no—
743C4⋊C8C22×D4312yes—
744#103—434no—
745#103—434no—
746#103C22×D4314yes—
747#103C22×D4314yes—
748#102—434no—
749#102—434no—
750#102—434no—
751#102—434no—
752C22⋊C8—432no—
753C22⋊C8—432no—
754C22⋊C8—432no—
755C22⋊C8C22×D4312yes—
756C4×C8—432no—
757C4×C8—432no—
758C4×C8—431no—
759C4×C8—431no—
760C4×C8C22×D4311yescharacteristic
761C4×C8C22×D4311yescharacteristic
762C24—431no—
763#41—868no—
764#41—1724no—
765#41—1724no—
766C2×Q8—21no—
767C2×Q8—21no—
768C2×Q8—21no—
769C2×Q8—862no—
770C2×Q8—862no—
771C2×Q8—861no—
772C2×Q8—861no—
773C2×Q8—861no—
774C2×Q8—1724no—
775C2×Q8—1724no—
776C2×Q8C23×D4312yes—
777C2×D4—432no—
778C2×D4—862no—
779C2×D4—862no—
780C2×D4—862no—
781C2×D4—861no—
782C2×D4—861no—
783C22×C4—431no—
784C22×C4—431no—
785C22×C4—431no—
786C22×C4—431no—
787C22×C4—431no—
788C22×C4—431no—
789C22×C4—431no—
790C22×C4—431no—
791C22×C4—431no—
792C22×C4—431no—
793C22×C4—431no—
794C22×C4—431no—
795C22×C4—431no—
796C22×C4—431no—
797C22×C4—431no—
798C22×C4—864no—
799C22×C4—864no—
800C22×C4—862no—
801C22×C4—862no—
802C22×C4—862no—
803C22×C4—862no—
804C22×C4—862no—
805C22×C4—1722no—
806C22×C4D4×D4311yescharacteristic
807C22×C4D4×D4311yescharacteristic
808C22×C4C23×D4311yescharacteristic
809C2×C8—432no—
810C2×C8—432no—
811C2×C8—864no—
812C2×C8—864no—
813C2×C8C23×D4312yes—
814C2×C8C23×D4312yes—
815C4⋊C4—22no—
816C4⋊C4—22no—
817C4⋊C4—21no—
818C4⋊C4—21no—
819C4⋊C4—21no—
820C4⋊C4—21no—
821C4⋊C4—21no—
822C4⋊C4—22no—
823C4⋊C4—22no—
824C4⋊C4—432no—
825C4⋊C4—432no—
826C4⋊C4—432no—
827C4⋊C4—862no—
828C4⋊C4—862no—
829C4⋊C4—862no—
830C4⋊C4—862no—
831C4⋊C4—862no—
832C4⋊C4—862no—
833C4⋊C4—862no—
834C4⋊C4—862no—
835C4⋊C4—862no—
836C4⋊C4—862no—
837C4⋊C4—862no—
838C4⋊C4—862no—
839C4⋊C4—862no—
840C4⋊C4—862no—
841C4⋊C4—861no—
842C4⋊C4—861no—
843C4⋊C4—861no—
844C4⋊C4C23×D4312yes—
845C4⋊C4C23×D4312yes—
846C4⋊C4C23×D4312yes—
847C22⋊C4—22no—
848C22⋊C4—22no—
849C22⋊C4—862no—
850C22⋊C4—862no—
851C22⋊C4—862no—
852C22⋊C4—862no—
853C22⋊C4—862no—
854C22⋊C4—862no—
855C22⋊C4—862no—
856C22⋊C4—862no—
857C22⋊C4—862no—
858C22⋊C4—862no—
859C22⋊C4—862no—
860C42—22no—
861C42—22no—
862C42—431no—
863C42—431no—
864C42—431no—
865C42—431no—
866C42—431no—
867C42—431no—
868C42—431no—
869C42—431no—
870C42—431no—
871C42—431no—
872C42—431no—
873C42—431no—
874C42—862no—
875C42—862no—
876C42—862no—
877C42—862no—
878C42—862no—
879C42D4×D4311yescharacteristic
880C42D4×D4311yescharacteristic
881C42C23×D4311yescharacteristic
882C42C23×D4311yescharacteristic
883C23—431no—
884C23—431no—
885C23—862no—
886C23—862no—
887C23—862no—
888C23—1721no—
889C23C2×D4×D4311yescharacteristic
890Q8—24no—
891Q8—42no—
892Q8—42no—
893Q8—42no—
894Q8—1724no—
895Q8—1724no—
896Q8—1722no—
897Q8—1722no—
898Q8—1722no—
899D4—864no—
900D4—1724no—
901D4—1724no—
902D4—1724no—
903D4—1722no—
904D4—1722no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—431no—
913C2×C4—431no—
914C2×C4—434no—
915C2×C4—434no—
916C2×C4—431no—
917C2×C4—431no—
918C2×C4—431no—
919C2×C4—431no—
920C2×C4—862no—
921C2×C4—862no—
922C2×C4—862no—
923C2×C4—862no—
924C2×C4—862no—
925C2×C4—862no—
926C2×C4—862no—
927C2×C4—862no—
928C2×C4—862no—
929C2×C4—862no—
930C2×C4—862no—
931C2×C4—862no—
932C2×C4—862no—
933C2×C4—1721no—
934C2×C4—1721no—
935C2×C4—1724no—
936C2×C4—1724no—
937C2×C4—1724no—
938C2×C4—1724no—
939C2×C4—1724no—
940C2×C4—1721no—
941C2×C4C2×D4×D4311yescharacteristic
942C2×C4C2×D4×D4311yescharacteristic
943C2×C4C2×D4×D4311yescharacteristic
944C2×C4C2×D4×D4311yescharacteristic
945C2×C4C2×D4×D4311yescharacteristic
946C2×C4C24×D4311yescharacteristic
947C8—22no—
948C8—22no—
949C8—862no—
950C8—862no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—432no—
955C22—432no—
956C22—861no—
957C22—861no—
958C22—861no—
959C22—861no—
960C22—1724no—
961C22—1722no—
962C22—1722no—
963C22—1722no—
964C22C22×D4×D4311yescharacteristic
965C4—21no—
966C4—21no—
967C4—21no—
968C4—42no—
969C4—42no—
970C4—42no—
971C4—42no—
972C4—432no—
973C4—432no—
974C4—861no—
975C4—861no—
976C4—861no—
977C4—861no—
978C4—1722no—
979C4—1722no—
980C4—1722no—
981C4#135×D4312yes—
982C4#1458369812yes—
983C42−1+4×D4312yes—
984C2—41no—
985C2—862no—
986C2—862no—
987C2—3442no—
988C2#536×D4311yescharacteristic
989C2C2×#135×D4311yescharacteristic
990C2C2×#1458369811yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3231C2
socleC22×C43C23×D4
prime radical#19147892C2
hypercenter#3231D43
hypocenterC43#60846
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3231

Complements

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

NH ≅ G/Ntype
2. #533×D43C2semidirect
3. #19145777C2semidirect
4. #19145767C2semidirect
5. #19145750C2semidirect
6. #19145742C2semidirect
7. #19145735C2semidirect
8. #19145733C2semidirect
9. #19145731C2semidirect
10. #19145724C2semidirect
11. #19145717C2semidirect
12. #19145106C2semidirect
13. #19145104C2semidirect
14. #19144919C2semidirect
15. #19144919C2semidirect
16. #19144513C2semidirect
17. #19144382C2semidirect
18. #431×D43C2semidirect
19. C43×#3231C2semidirect
55. #14583304C22semidirect
56. #14583302C22semidirect
57. #14583302C22semidirect
58. #14583300C22semidirect
59. #14583299C22semidirect
60. #14583297C22semidirect
61. #14583295C22semidirect
62. #14583295C22semidirect
63. #14583255C22semidirect
64. #14583255C22semidirect
65. #14583249C22semidirect
66. #14583249C22semidirect
67. #14583247C22semidirect
68. #14583247C22semidirect
69. #14583246C22semidirect
70. #14583246C22semidirect
78. #14583206C22semidirect
79. #14583200C22semidirect
80. #14583196C22semidirect
81. #14583192C22semidirect
82. #14583188C22semidirect
83. #14583182C22semidirect
84. #14583178C22semidirect
100. C43×#500C22semidirect
101. C43×#498C22semidirect
102. C43×#487C22semidirect
103. C43×#487C22semidirect
105. C43×#479C22semidirect
494. #3231D43semidirect
555. #500C2×D43semidirect
561. #498C2×D43semidirect
566. #487C2×D43semidirect
567. #487C2×D43semidirect
581. #479C2×D43semidirect
602. C43#60846semidirect

Maximal subgroups

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

subgroupindex
#191478922
#533×D432
#191457772
#191457672
#191457502
#191457422
#191457352
#191457332
#191457312
#191457242
#191457172
#191451062
#191451042
#191449192
#191445132
#191443822
#431×D432
C43×#32312
#6084643