Finite Group Databasebeta

← #25096726

Subgroups — #25096726

Order 11008.

1336 conjugacy classes of subgroups.

The subgroup lattice has 962 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#41×D43C211yesmaximal, characteristic
2#19143227C211yesmaximal, characteristic, complemented
3#19136991C211yesmaximal, characteristic, complemented
4#19134693C212yesmaximal, complemented
5#19134616C211yesmaximal, characteristic, complemented
6#19134615C211yesmaximal, characteristic, complemented
7#19134612C211yesmaximal, characteristic, complemented
8#19134537C212yesmaximal
9#19134407C212yesmaximal, complemented
10#19134404C212yesmaximal, complemented
11C43×#1806C211yesmaximal, characteristic, complemented
12C2×#41×D43C2211yescharacteristic
13#41×Dic43C2211yescharacteristic
14C4×#10621902C411yescharacteristic, complemented
15C4×#10621902C411yescharacteristic, complemented
16C4×#10621898—21no—
17C4×#10621898C2211yescharacteristic
18#14583367—21no—
19#14583367C2211yescharacteristic
20C4×#10621900—21no—
21C4×#10621900—21no—
22C4×#10621900C411yescharacteristic, complemented
23C4×#10621900C411yescharacteristic, complemented
24C4×Q8×D43C411yescharacteristic, complemented
25C4×Q8×D43C411yescharacteristic, complemented
26C4×D4×D43—21no—
27C4×D4×D43—21no—
28C4×D4×D43C411yescharacteristic, complemented
29C4×D4×D43C411yescharacteristic, complemented
30#117×D43—21no—
31#117×D43C2211yescharacteristic
32C2×C42×D43—21no—
33C2×C42×D43C2211yescharacteristic
34#14582955—21no—
35#14582955—21no—
36#14582951—21no—
37#14582951—21no—
38#14582923C2211yescharacteristic, complemented
39C2×#13063253C2212yes—
40C2×#13063252C2212yes—
41C2×#13063251C2212yes—
42#14582862C2212yes—
43M16×Dic43C2212yescomplemented
44#14582766—21no—
45#14582764—21no—
46#14582761—21no—
47#14582756—21no—
48C4×C4⋊Dic43C2211yescharacteristic, complemented
49C4×(C2×D43)⋊C4C2212yes—
50#14582745C2212yescomplemented
51#14582660C2212yescomplemented
52#14582659C2212yescomplemented
53#14582658C2212yescomplemented
54C4×#41×C43C2211yescharacteristic
55C43×#423C2211yescharacteristic, complemented
56C2×#104×C43C2212yes—
57C4×C4⋊C4×C43C2211yescharacteristic, complemented
58C43×#339C2212yescomplemented
59C2×#10621902C2×C411yescharacteristic
60C2×#10621898—21no—
61C2×#10621898C2311yescharacteristic
62C2×#10621900—21no—
63C2×#10621900C2×C411yescharacteristic
64#41×D43—22no—
65#41×D43—22no—
66#41×D43—22no—
67#41×D43—22no—
68C2×Q8×D43C2×C411yescharacteristic
69C2×D4×D43—21no—
70C2×D4×D43C2×C411yescharacteristic
71C22×C4×D43—21no—
72C22×C4×D43—21no—
73C22×C4×D43—21no—
74C22×C4×D43D411yescharacteristic
75C22×C4×D43D411yescharacteristic
76C22×C4×D43C2311yescharacteristic
77C2×#10621877C2312yes—
78Q8×Dic43C2×C411yescharacteristic
79Q8×Dic43C2×C411yescharacteristic
80C4×Dic86—21no—
81C4×Dic86—21no—
82C4×Dic86C2×C411yescharacteristic
83C4×Dic86C2×C411yescharacteristic
84#13063290—21no—
85#13063290—21no—
86#13063290C2×C411yescharacteristic
87#13063290C2×C411yescharacteristic
88C4×D172—21no—
89C4×D172—21no—
90C4×D172C2×C411yescharacteristic
91C4×D172C2×C411yescharacteristic
92D4×Dic43—21no—
93D4×Dic43—21no—
94D4×Dic43C2×C411yescharacteristic
95D4×Dic43C2×C411yescharacteristic
96#13063287—21no—
97#13063287—21no—
98#13063287C2×C411yescharacteristic
99#13063287C2×C411yescharacteristic
100C4×C22⋊D43—21no—
101C4×C22⋊D43—21no—
102C4×C22⋊D43—21no—
103C4×C22⋊D43—21no—
104C4×C22⋊D43—21no—
105C4×C22⋊D43—21no—
106(C22⋊D43)⋊C4—21no—
107(C22⋊D43)⋊C4—21no—
108(C22⋊D43)⋊C4—21no—
109(C22⋊D43)⋊C4—21no—
110(C22⋊D43)⋊C4—21no—
111(C22⋊D43)⋊C4—21no—
112#13063284—21no—
113#13063284C2311yescharacteristic
114#13063283—21no—
115#13063283—21no—
116#13063283C2×C411yescharacteristic
117#13063283C2×C411yescharacteristic
118#13063282—21no—
119#13063282—21no—
120#13063282—21no—
121#13063281—21no—
122#13063281—21no—
123#13063281—21no—
124C2×C4⋊Dic43—21no—
125C4⋊C4×D43—21no—
126C4⋊C4×D43—21no—
127C4⋊C4×D43C2×C411yescharacteristic
128C4⋊C4×D43C2×C411yescharacteristic
129C2×(C2×D43)⋊C4—22no—
130C22⋊C4×D43—21no—
131C22⋊C4×D43—21no—
132C22⋊C4×D43—21no—
133C2×C4×Dic43—21no—
134C2×C4×Dic43—21no—
135C2×C4×Dic43—21no—
136C2×C4×Dic43D411yescharacteristic
137C2×C4×Dic43D411yescharacteristic
138C2×C4×Dic43C2312yes—
139C2×C4×Dic43C2311yescharacteristic
140C42×D43—21no—
141C42×D43—21no—
142C42×D43—21no—
143C42×D43—21no—
144C42×D43—21no—
145C42×D43—21no—
146C42×D43—21no—
147C42×D43C2×C411yescharacteristic
148C42×D43C2×C411yescharacteristic
149C42×D43C2×C411yescharacteristic
150C42×D43C2×C411yescharacteristic
151C42×D43D411yescharacteristic
152C42×D43D411yescharacteristic
153C42×D43D411yescharacteristic
154C42×D43D411yescharacteristic
155C4⋊(C43⋊C8)—21no—
156C4⋊(C43⋊C8)—21no—
157#13063253—24no—
158#13063252—24no—
159#13063251—24no—
160(C2×D43)⋊C8—22no—
161(C2×D43)⋊C8—22no—
162#13063235—22no—
163C8×Dic43—22no—
164C43⋊#95—21no—
165C43⋊#95—22no—
166C43⋊#95—22no—
167C43⋊#95—22no—
168C2×#41×C43C2311yescharacteristic
169C2×M16×C43C2312yes—
170C4×Q8×C43C2×C411yescharacteristic
171C4×Q8×C43C2×C411yescharacteristic
172C4×D4×C43—21no—
173C4×D4×C43—21no—
174C4×D4×C43C2×C411yescharacteristic
175C4×D4×C43C2×C411yescharacteristic
176#117×C43—21no—
177#117×C43C2311yescharacteristic
178C2×C4⋊C4×C43—21no—
179C2×C42×C43—21no—
180C2×C42×C43C2312yes—
181C2×C42×C43C2311yescharacteristic
182C4⋊C8×C43—21no—
183C4⋊C8×C43—21no—
184#104×C43—24no—
185#95×C43—21no—
186C23×D43—21no—
187C23×D43C2×D411yescharacteristic
188#41×C43—21no—
189#41×C43—21no—
190#41×C43#4112yes—
191#41×C43#4112yes—
192C2×Q8×C43C22×C411yescharacteristic
193C2×D4×C43—21no—
194C2×D4×C43C22×C411yescharacteristic
195C22×C4×C43—21no—
196C22×C4×C43—21no—
197C22×C4×C43—21no—
198C22×C4×C43—22no—
199C22×C4×C43C2×D411yescharacteristic
200C22×C4×C43C2×D411yescharacteristic
201C22×C4×C43C2411yescharacteristic
202C2×C22⋊D43—21no—
203C2×C22⋊D43—21no—
204C2×C22⋊D43—21no—
205C22×Dic43—21no—
206C22×Dic43—21no—
207C22×Dic43—21no—
208C22×Dic43—22no—
209C22×Dic43C2×D411yescharacteristic
210C22×Dic43C2×D411yescharacteristic
211C22×Dic43C2×D411yescharacteristic
212#10621902—22no—
213#10621902—22no—
214Q8×D43—22no—
215Q8×D43—22no—
216#10621900—24no—
217#10621900—24no—
218#10621900—22no—
219#10621900—22no—
220D4×D43—24no—
221D4×D43—24no—
222D4×D43—22no—
223D4×D43—22no—
224#10621898—24no—
225#10621898—24no—
226#10621898—21no—
227#10621898—21no—
228#10621898#4112yes—
229#10621898#4112yes—
230C2×D172—21no—
231C2×D172C22×C411yescharacteristic
232C2×C4×D43—24no—
233C2×C4×D43—24no—
234C2×C4×D43—21no—
235C2×C4×D43—21no—
236C2×C4×D43—21no—
237C2×C4×D43—21no—
238C2×C4×D43—21no—
239C2×C4×D43—21no—
240C2×C4×D43—21no—
241C2×C4×D43—21no—
242C2×C4×D43—21no—
243C2×C4×D43—21no—
244C2×C4×D43—21no—
245C2×C4×D43—21no—
246C2×C4×D43—21no—
247C2×C4×D43—42no—
248C2×C4×D43—42no—
249C2×C4×D43—44no—
250C2×C4×D43—44no—
251C2×C4×D43C22⋊C411yescharacteristic
252C2×C4×D43C22⋊C411yescharacteristic
253C2×C4×D43C22⋊C411yescharacteristic
254C2×C4×D43C22⋊C411yescharacteristic
255C2×C4×D43C22⋊C411yescharacteristic
256C2×C4×D43C22⋊C411yescharacteristic
257C2×C4×D43C22⋊C411yescharacteristic
258C2×C4×D43C22⋊C411yescharacteristic
259C2×C4×D43C22×C411yescharacteristic
260C2×C4×D43C22×C411yescharacteristic
261C2×C4×D43C2×D411yescharacteristic
262C2×C4×D43C2×D411yescharacteristic
263C2×Dic86—21no—
264C2×Dic86C22×C411yescharacteristic
265M16×C43—22no—
266M16×C43—22no—
267C2×C8×C43—22no—
268C4⋊C4×C43—21no—
269C4⋊C4×C43—21no—
270C4⋊C4×C43—42no—
271C4⋊C4×C43C22×C411yescharacteristic
272C4⋊C4×C43C22×C411yescharacteristic
273C22⋊C4×C43—21no—
274C22⋊C4×C43—21no—
275C22⋊C4×C43—21no—
276C42×C43—21no—
277C42×C43—21no—
278C42×C43—21no—
279C42×C43—22no—
280C42×C43—22no—
281C42×C43C22×C411yescharacteristic
282C42×C43C22×C411yescharacteristic
283C42×C43C2×D411yescharacteristic
284C42×C43C2×D411yescharacteristic
285C22⋊Dic43—21no—
286C22⋊Dic43—21no—
287C22⋊Dic43—21no—
288(C2×D43)⋊C4—21no—
289(C2×D43)⋊C4—21no—
290(C2×D43)⋊C4—21no—
291(C2×D43)⋊C4—21no—
292(C2×D43)⋊C4—21no—
293(C2×D43)⋊C4—21no—
294(C2×D43)⋊C4—44no—
295C4⋊Dic43—21no—
296C4⋊Dic43—21no—
297C4⋊Dic43—42no—
298C4⋊Dic43C22×C411yescharacteristic
299C4⋊Dic43C22×C411yescharacteristic
300Dic43⋊C4—21no—
301Dic43⋊C4—21no—
302Dic43⋊C4—21no—
303Dic43⋊C4—21no—
304Dic43⋊C4—21no—
305Dic43⋊C4—21no—
306C4×Dic43—21no—
307C4×Dic43—21no—
308C4×Dic43—21no—
309C4×Dic43—21no—
310C4×Dic43—21no—
311C4×Dic43—21no—
312C4×Dic43—21no—
313C4×Dic43—21no—
314C4×Dic43—21no—
315C4×Dic43—22no—
316C4×Dic43—22no—
317C4×Dic43C22⋊C411yescharacteristic
318C4×Dic43C22⋊C411yescharacteristic
319C4×Dic43C22⋊C411yescharacteristic
320C4×Dic43C22⋊C411yescharacteristic
321C4×Dic43C22⋊C411yescharacteristic
322C4×Dic43C22⋊C411yescharacteristic
323C4×Dic43C22⋊C411yescharacteristic
324C4×Dic43C22⋊C411yescharacteristic
325C4×Dic43C22×C411yescharacteristic
326C4×Dic43C22×C411yescharacteristic
327C4×Dic43C2×D411yescharacteristic
328C4×Dic43C2×D411yescharacteristic
329#10621877—22no—
330#10621877—22no—
331C2×C43⋊C8—22no—
332C23×C43—21no—
333C23×C43C22×D411yescharacteristic
334C22×D43—24no—
335C22×D43—21no—
336C22×D43—21no—
337C22×D43—21no—
338C22×D43—22no—
339C22×D43—41no—
340C22×D43—42no—
341C22×D43—42no—
342C22×D43C2×C22⋊C411yescharacteristic
343C22×D43C2×C22⋊C411yescharacteristic
344Q8×C43—21no—
345Q8×C43#11712yes—
346D4×C43—22no—
347D4×C43—22no—
348D4×C43—21no—
349D4×C43#11712yes—
350C2×C4×C43—21no—
351C2×C4×C43—22no—
352C2×C4×C43—22no—
353C2×C4×C43—22no—
354C2×C4×C43—21no—
355C2×C4×C43—21no—
356C2×C4×C43—41no—
357C2×C4×C43—42no—
358C2×C4×C43—42no—
359C2×C4×C43—42no—
360C2×C4×C43—42no—
361C2×C4×C43—42no—
362C2×C4×C43C2×C22⋊C411yescharacteristic
363C2×C4×C43C2×C22⋊C411yescharacteristic
364C2×C4×C43C2×C22⋊C411yescharacteristic
365C2×C4×C43C2×C22⋊C411yescharacteristic
366C2×C4×C43C23×C411yescharacteristic
367C2×C4×C43C22×D411yescharacteristic
368C2×C4×C43C2×#4111yescharacteristic
369C2×C4×C43C2×#4111yescharacteristic
370C2×C4×C43C2×#4111yescharacteristic
371C2×C4×C43C2×#4111yescharacteristic
372C22⋊D43—24no—
373C22⋊D43—24no—
374C22⋊D43—22no—
375C22⋊D43—22no—
376C2×Dic43—24no—
377C2×Dic43—21no—
378C2×Dic43—21no—
379C2×Dic43—21no—
380C2×Dic43—21no—
381C2×Dic43—21no—
382C2×Dic43—41no—
383C2×Dic43—41no—
384C2×Dic43—42no—
385C2×Dic43—42no—
386C2×Dic43—42no—
387C2×Dic43—42no—
388C2×Dic43—42no—
389C2×Dic43C2×C22⋊C411yescharacteristic
390C2×Dic43C2×C22⋊C411yescharacteristic
391C2×Dic43C2×C22⋊C411yescharacteristic
392C2×Dic43C2×C22⋊C411yescharacteristic
393C2×Dic43C2×C22⋊C411yescharacteristic
394C2×Dic43C2×C22⋊C411yescharacteristic
395D172—24no—
396D172—21no—
397D172#11712yes—
398C4×D43—24no—
399C4×D43—24no—
400C4×D43—22no—
401C4×D43—22no—
402C4×D43—21no—
403C4×D43—21no—
404C4×D43—21no—
405C4×D43—21no—
406C4×D43—21no—
407C4×D43—21no—
408C4×D43—22no—
409C4×D43—22no—
410C4×D43—21no—
411C4×D43—21no—
412C4×D43—22no—
413C4×D43—22no—
414C4×D43—41no—
415C4×D43—41no—
416C4×D43—41no—
417C4×D43—41no—
418C4×D43—42no—
419C4×D43—42no—
420C4×D43—42no—
421C4×D43—42no—
422C4×D43—42no—
423C4×D43—42no—
424Dic86—24no—
425Dic86—21no—
426Dic86#11712yes—
427C8×C43—42no—
428C43⋊C8—42no—
429#20748—431nomaximal, Sylow
430C22×C43—21no—
431C22×C43—21no—
432C22×C43—22no—
433C22×C43—41no—
434C22×C43—41no—
435C22×C43C22×C22⋊C411yescharacteristic
436C22×C43#52511yescharacteristic
437C22×C43#52511yescharacteristic
438C2×D43—21no—
439C2×D43—21no—
440C2×D43—21no—
441C2×D43—21no—
442C2×D43—22no—
443C2×D43—21no—
444C2×D43—42no—
445C2×D43—42no—
446C2×D43—48no—
447C2×D43—41no—
448C2×D43—41no—
449C2×D43#42112yes—
450C4×C43—21no—
451C4×C43—21no—
452C4×C43—21no—
453C4×C43—22no—
454C4×C43—41no—
455C4×C43—41no—
456C4×C43—82no—
457C4×C43#42112yes—
458C4×C43C2×#11711yescharacteristic
459C4×C43C2×#11711yescharacteristic
460C4×C43#52511yescharacteristic
461C4×C43#52511yescharacteristic
462Dic43—21no—
463Dic43—21no—
464Dic43—21no—
465Dic43—21no—
466Dic43—21no—
467Dic43—22no—
468Dic43—21no—
469Dic43—41no—
470Dic43—41no—
471Dic43—82no—
472C2×C4×#41—431no—
473#2920—431no—
474#2283—431no—
475#1826—432no—
476#1806—431no—
477#1806—431no—
478#1806—431no—
479#1806D4311yescharacteristic, complemented
480#1789—432no—
481#1759—432no—
482#1759—432no—
483C2×C43—21no—
484C2×C43—21no—
485C2×C43—42no—
486C2×C43#228011yescharacteristic
487C2×C43C2×#42111yescharacteristic
488C2×C43C2×#42111yescharacteristic
489D43—22no—
490D43—41no—
491D43—42no—
492C22×#41—431no—
493C4×#41—431no—
494C4×#41—431no—
495C4×#41—431no—
496C4×#41—431no—
497C4×#41—431no—
498C4×#41—431no—
499C4×#41—431no—
500C4×#41—861no—
501C4×#41—861no—
502C4×#41—861no—
503C4×#41—861no—
504C4×#41C2×D4311yescharacteristic
505C2×C4×Q8—431no—
506C2×C4×Q8—431no—
507C2×C4×D4—431no—
508C2×C4×D4—431no—
509C2×C4×D4—861no—
510C2×C4×D4—861no—
511C2×#117—431no—
512C2×#117—861no—
513C22×C42—431no—
514C22×C42—861no—
515#432—861no—
516#432—861no—
517#431—861no—
518#431—861no—
519#423—431no—
520#423C2×D4311yescharacteristic, complemented
521C2×#104—432no—
522C2×#104—432no—
523C2×#104—432no—
524C2×#104C2×D4312yes—
525#407—432no—
526C4×M16—432no—
527#383—861no—
528#382—861no—
529#381—861no—
530#380—861no—
531C4×C4⋊C4—431no—
532C4×C4⋊C4C2×D4311yescharacteristic, complemented
533C4×C22⋊C4—432no—
534#376—432no—
535#339—432no—
536#339—432no—
537#339—432no—
538#339C2×D4312yescomplemented
539C43#2074811yescharacteristic, complemented, Sylow
540C2×#41—431no—
541C2×#41—431no—
542C2×#41—431no—
543C2×#41—861no—
544C2×#41—861no—
545C2×#41—862no—
546C2×#41—862no—
547C2×#41—862no—
548C2×#41—862no—
549C2×#41C22×D4311yescharacteristic
550C22×Q8—431no—
551C22×D4—431no—
552C22×D4—861no—
553C23×C4—431no—
554C23×C4—431no—
555C23×C4—431no—
556C23×C4—861no—
557C23×C4—861no—
558C23×C4—861no—
559C2×M16—432no—
560C2×M16C22×D4312yes—
561C4×Q8—431no—
562C4×Q8—431no—
563C4×Q8—431no—
564C4×Q8—431no—
565C4×Q8—431no—
566C4×Q8—431no—
567C4×Q8—861no—
568C4×Q8—861no—
569C4×Q8—861no—
570C4×Q8—861no—
571C4×Q8C4×D4311yescharacteristic
572C4×Q8C4×D4311yescharacteristic
573C4×D4—21no—
574C4×D4—21no—
575C4×D4—431no—
576C4×D4—431no—
577C4×D4—431no—
578C4×D4—431no—
579C4×D4—431no—
580C4×D4—431no—
581C4×D4—861no—
582C4×D4—861no—
583C4×D4—861no—
584C4×D4—861no—
585C4×D4—861no—
586C4×D4—861no—
587C4×D4—861no—
588C4×D4—861no—
589C4×D4—861no—
590C4×D4—861no—
591C4×D4—861no—
592C4×D4—861no—
593C4×D4—861no—
594C4×D4—861no—
595C4×D4—861no—
596C4×D4—861no—
597C4×D4—861no—
598C4×D4—861no—
599C4×D4C4×D4311yescharacteristic
600C4×D4C4×D4311yescharacteristic
601#117—21no—
602#117—431no—
603#117—431no—
604#117—431no—
605#117—861no—
606#117—861no—
607#117—861no—
608#117—861no—
609#117—861no—
610#117—861no—
611#117—861no—
612#117—861no—
613#117—861no—
614#117C22×D4311yescharacteristic
615C2×C4⋊C4—21no—
616C2×C4⋊C4—431no—
617C2×C4⋊C4—431no—
618C2×C4⋊C4—861no—
619C2×C4⋊C4—861no—
620C2×C4⋊C4—861no—
621C2×C22⋊C4—861no—
622C2×C22⋊C4—861no—
623C2×C22⋊C4—861no—
624C2×C22⋊C4—862no—
625C2×C42—21no—
626C2×C42—431no—
627C2×C42—431no—
628C2×C42—431no—
629C2×C42—431no—
630C2×C42—431no—
631C2×C42—431no—
632C2×C42—431no—
633C2×C42—431no—
634C2×C42—431no—
635C2×C42—431no—
636C2×C42—431no—
637C2×C42—432no—
638C2×C42—861no—
639C2×C42—861no—
640C2×C42—861no—
641C2×C42—861no—
642C2×C42—861no—
643C2×C42—861no—
644C2×C42—861no—
645C2×C42—861no—
646C2×C42—861no—
647C2×C42—861no—
648C2×C42C22×D4312yes—
649C2×C42C22×D4311yescharacteristic
650C4⋊C8—21no—
651C4⋊C8—21no—
652C4⋊C8—861no—
653C4⋊C8—861no—
654#104—24no—
655#104—864no—
656#104—864no—
657#104—864no—
658C22⋊C8—862no—
659C22⋊C8—862no—
660#97—862no—
661C4×C8—862no—
662#95—21no—
663#95—862no—
664#95—862no—
665#95—862no—
666#95—861no—
667C24—431no—
668C24—861no—
669#41—21no—
670#41—21no—
671#41—432no—
672#41—432no—
673#41—864no—
674#41—864no—
675#41—862no—
676#41—864no—
677#41—864no—
678#41—862no—
679#41—862no—
680#41—862no—
681#41—861no—
682#41—861no—
683#41#1062190012yes—
684#41#1062190212yes—
685C2×Q8—431no—
686C2×Q8—861no—
687C2×Q8—862no—
688C2×Q8—862no—
689C2×Q8C2×C4×D4311yescharacteristic
690C2×D4—21no—
691C2×D4—431no—
692C2×D4—861no—
693C2×D4—861no—
694C2×D4—862no—
695C2×D4—864no—
696C2×D4—864no—
697C2×D4—861no—
698C2×D4—861no—
699C2×D4—862no—
700C2×D4C2×C4×D4311yescharacteristic
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—22no—
705C22×C4—431no—
706C22×C4—431no—
707C22×C4—431no—
708C22×C4—431no—
709C22×C4—431no—
710C22×C4—431no—
711C22×C4—431no—
712C22×C4—431no—
713C22×C4—431no—
714C22×C4—431no—
715C22×C4—431no—
716C22×C4—431no—
717C22×C4—431no—
718C22×C4—431no—
719C22×C4—431no—
720C22×C4—861no—
721C22×C4—861no—
722C22×C4—861no—
723C22×C4—861no—
724C22×C4—864no—
725C22×C4—864no—
726C22×C4—861no—
727C22×C4—861no—
728C22×C4—861no—
729C22×C4—861no—
730C22×C4—861no—
731C22×C4—861no—
732C22×C4—861no—
733C22×C4—861no—
734C22×C4—861no—
735C22×C4—861no—
736C22×C4—861no—
737C22×C4—861no—
738C22×C4—862no—
739C22×C4—1722no—
740C22×C4—1722no—
741C22×C4—1724no—
742C22×C4—1724no—
743C22×C4D4×D4311yescharacteristic
744C22×C4D4×D4311yescharacteristic
745C22×C4C23×D4311yescharacteristic
746M16—22no—
747M16—22no—
748M16—862no—
749M16—862no—
750C2×C8—22no—
751C2×C8—862no—
752C4⋊C4—21no—
753C4⋊C4—21no—
754C4⋊C4—42no—
755C4⋊C4—431no—
756C4⋊C4—431no—
757C4⋊C4—861no—
758C4⋊C4—861no—
759C4⋊C4—861no—
760C4⋊C4—861no—
761C4⋊C4—861no—
762C4⋊C4—861no—
763C4⋊C4—861no—
764C4⋊C4—861no—
765C4⋊C4—1722no—
766C4⋊C4C2×C4×D4311yescharacteristic
767C4⋊C4C2×C4×D4311yescharacteristic
768C22⋊C4—21no—
769C22⋊C4—21no—
770C22⋊C4—21no—
771C22⋊C4—861no—
772C22⋊C4—861no—
773C22⋊C4—861no—
774C22⋊C4—861no—
775C22⋊C4—861no—
776C22⋊C4—861no—
777C22⋊C4—861no—
778C22⋊C4—861no—
779C22⋊C4—861no—
780C22⋊C4—1724no—
781C42—21no—
782C42—21no—
783C42—21no—
784C42—22no—
785C42—22no—
786C42—431no—
787C42—431no—
788C42—431no—
789C42—431no—
790C42—431no—
791C42—431no—
792C42—431no—
793C42—431no—
794C42—431no—
795C42—431no—
796C42—431no—
797C42—431no—
798C42—861no—
799C42—861no—
800C42—861no—
801C42—861no—
802C42—861no—
803C42—861no—
804C42—861no—
805C42—861no—
806C42—861no—
807C42—862no—
808C42—862no—
809C42C2×C4×D4311yescharacteristic
810C42C2×C4×D4311yescharacteristic
811C42D4×D4311yescharacteristic
812C42D4×D4311yescharacteristic
813C23—21no—
814C23—431no—
815C23—431no—
816C23—862no—
817C23—864no—
818C23—861no—
819C23—861no—
820C23—861no—
821C23—1721no—
822C23—1722no—
823C23—1722no—
824C23C2×D4×D4311yescharacteristic
825Q8—21no—
826Q8—432no—
827Q8—864no—
828Q8—861no—
829Q8#1306328312yes—
830D4—22no—
831D4—22no—
832D4—21no—
833D4—432no—
834D4—864no—
835D4—864no—
836D4—864no—
837D4—862no—
838D4—862no—
839D4—861no—
840D4#1306328312yes—
841C2×C4—21no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—41no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—431no—
854C2×C4—431no—
855C2×C4—431no—
856C2×C4—431no—
857C2×C4—431no—
858C2×C4—431no—
859C2×C4—862no—
860C2×C4—862no—
861C2×C4—864no—
862C2×C4—864no—
863C2×C4—864no—
864C2×C4—861no—
865C2×C4—861no—
866C2×C4—861no—
867C2×C4—861no—
868C2×C4—861no—
869C2×C4—861no—
870C2×C4—861no—
871C2×C4—861no—
872C2×C4—861no—
873C2×C4—862no—
874C2×C4—861no—
875C2×C4—861no—
876C2×C4—862no—
877C2×C4—862no—
878C2×C4—862no—
879C2×C4—861no—
880C2×C4—861no—
881C2×C4—1721no—
882C2×C4—1721no—
883C2×C4—1721no—
884C2×C4—1721no—
885C2×C4—1722no—
886C2×C4—1722no—
887C2×C4—1722no—
888C2×C4—1722no—
889C2×C4—1722no—
890C2×C4—1721no—
891C2×C4—1721no—
892C2×C4—1722no—
893C2×C4—1722no—
894C2×C4—1722no—
895C2×C4—1722no—
896C2×C4—1722no—
897C2×C4—1722no—
898C2×C4C22⋊C4×D4311yescharacteristic
899C2×C4C22⋊C4×D4311yescharacteristic
900C2×C4C22⋊C4×D4311yescharacteristic
901C2×C4C22⋊C4×D4311yescharacteristic
902C2×C4C22×C4×D4311yescharacteristic
903C2×C4C2×D4×D4311yescharacteristic
904C2×C4#41×D4311yescharacteristic
905C2×C4#41×D4311yescharacteristic
906C2×C4C2×#1062190011yescharacteristic
907C2×C4C2×#1062190211yescharacteristic
908C8—42no—
909C8—1722no—
910C22—21no—
911C22—21no—
912C22—22no—
913C22—41no—
914C22—41no—
915C22—432no—
916C22—861no—
917C22—861no—
918C22—862no—
919C22—861no—
920C22—861no—
921C22—861no—
922C22—1722no—
923C22—1722no—
924C22—1728no—
925C22—1721no—
926C22—1721no—
927C22C2×C22⋊C4×D4311yescharacteristic
928C22#1458340911yescharacteristic
929C22#1458341211yescharacteristic
930C4—22no—
931C4—21no—
932C4—21no—
933C4—21no—
934C4—41no—
935C4—41no—
936C4—82no—
937C4—861no—
938C4—861no—
939C4—862no—
940C4—861no—
941C4—861no—
942C4—861no—
943C4—861no—
944C4—3442no—
945C4—1721no—
946C4—1721no—
947C4#1458291412yes—
948C4#117×D4311yescharacteristic
949C4C2×#1306328311yescharacteristic
950C4#1458340911yescharacteristic
951C4#1458341211yescharacteristic
952C2—21no—
953C2—21no—
954C2—42no—
955C2—862no—
956C2—1721no—
957C2—1722no—
958C2#1913697711yescharacteristic
959C2#421×D4311yescharacteristic
960C2C2×#1458291411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1806C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#41×D43C22
cosocleC22×C4×C43C24
hypercenter#1806D43
hypocenterC43#20748
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1806

Complements

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

NH ≅ G/Ntype
2. #19143227C2semidirect
3. #19136991C2semidirect
4. #19134693C2semidirect
5. #19134616C2semidirect
6. #19134615C2semidirect
7. #19134612C2semidirect
9. #19134407C2semidirect
10. #19134404C2semidirect
11. C43×#1806C2semidirect
14. C4×#10621902C4semidirect
15. C4×#10621902C4semidirect
22. C4×#10621900C4semidirect
23. C4×#10621900C4semidirect
24. C4×Q8×D43C4semidirect
25. C4×Q8×D43C4semidirect
28. C4×D4×D43C4semidirect
29. C4×D4×D43C4semidirect
38. #14582923C22semidirect
43. M16×Dic43C22semidirect
48. C4×C4⋊Dic43C22semidirect
50. #14582745C22semidirect
51. #14582660C22semidirect
52. #14582659C22semidirect
53. #14582658C22semidirect
55. C43×#423C22semidirect
57. C4×C4⋊C4×C43C22semidirect
58. C43×#339C22semidirect
479. #1806D43semidirect
520. #423C2×D43semidirect
532. C4×C4⋊C4C2×D43semidirect
538. #339C2×D43semidirect
539. C43#20748semidirect

Maximal subgroups

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

subgroupindex
C4×#41×D432
#191432272
#191369912
#191346932
#191346162
#191346152
#191346122
#191345372
#191344072
#191344042
C43×#18062
#2074843