Finite Group Databasebeta

← #25096719

Subgroups — #25096719

Order 11008.

1428 conjugacy classes of subgroups.

The subgroup lattice has 968 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#41×D43C211yesmaximal, characteristic
2#19143227C211yesmaximal, characteristic, complemented
3C4×#13063283C211yesmaximal, characteristic, complemented
4#19134693C212yesmaximal, complemented
5#19134616C211yesmaximal, characteristic, complemented
6#19134615C211yesmaximal, characteristic, complemented
7#19134612C211yesmaximal, characteristic, complemented
8#19134537C212yesmaximal
9#104×Dic43C212yesmaximal, complemented
10#19134399C212yesmaximal, 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
30C2×#13063283—21no—
31#117×D43—21no—
32#117×D43C2211yescharacteristic
33C2×C42×D43—21no—
34C2×C42×D43C2211yescharacteristic
35#14582955—21no—
36#14582955—21no—
37#14582951—21no—
38#14582951—21no—
39#14582923C2211yescharacteristic, complemented
40C2×#13063253C2212yes—
41C2×#13063252C2212yes—
42C2×#13063251C2212yes—
43#14582862C2212yes—
44M16×Dic43C2212yescomplemented
45C4⋊C4×Dic43—21no—
46C4×C4⋊Dic43C2211yescharacteristic, complemented
47C4×(C2×D43)⋊C4C2212yes—
48#14582746—21no—
49#14582744—21no—
50C42×Dic43C2212yescomplemented
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—28no—
115#13063283—21no—
116#13063283—21no—
117#13063283C2×C411yescharacteristic
118#13063283C2×C411yescharacteristic
119#13063282—21no—
120#13063282—21no—
121#13063282—21no—
122#13063281—21no—
123#13063281—21no—
124#13063281—21no—
125C2×C4⋊Dic43—21no—
126C4⋊C4×D43—21no—
127C4⋊C4×D43—21no—
128C4⋊C4×D43C2×C411yescharacteristic
129C4⋊C4×D43C2×C411yescharacteristic
130C2×(C2×D43)⋊C4—22no—
131C22⋊C4×D43—21no—
132C22⋊C4×D43—21no—
133C22⋊C4×D43—21no—
134C2×C4×Dic43—22no—
135C2×C4×Dic43—21no—
136C2×C4×Dic43—21no—
137C2×C4×Dic43—21no—
138C2×C4×Dic43—22no—
139C2×C4×Dic43D411yescharacteristic
140C2×C4×Dic43D411yescharacteristic
141C2×C4×Dic43C2312yes—
142C2×C4×Dic43C2311yescharacteristic
143C42×D43—21no—
144C42×D43—21no—
145C42×D43—21no—
146C42×D43—21no—
147C42×D43—21no—
148C42×D43—21no—
149C42×D43—21no—
150C42×D43C2×C411yescharacteristic
151C42×D43C2×C411yescharacteristic
152C42×D43C2×C411yescharacteristic
153C42×D43C2×C411yescharacteristic
154C42×D43D411yescharacteristic
155C42×D43D411yescharacteristic
156C42×D43D411yescharacteristic
157C42×D43D411yescharacteristic
158C4⋊(C43⋊C8)—21no—
159C4⋊(C43⋊C8)—21no—
160#13063253—24no—
161#13063252—24no—
162#13063251—24no—
163(C2×D43)⋊C8—22no—
164(C2×D43)⋊C8—22no—
165#13063235—22no—
166C8×Dic43—22no—
167C43⋊#95—21no—
168C43⋊#95—22no—
169C2×#41×C43C2311yescharacteristic
170C2×M16×C43C2312yes—
171C4×Q8×C43C2×C411yescharacteristic
172C4×Q8×C43C2×C411yescharacteristic
173C4×D4×C43—21no—
174C4×D4×C43—21no—
175C4×D4×C43C2×C411yescharacteristic
176C4×D4×C43C2×C411yescharacteristic
177#117×C43—21no—
178#117×C43C2311yescharacteristic
179C2×C4⋊C4×C43—21no—
180C2×C42×C43—21no—
181C2×C42×C43C2312yes—
182C2×C42×C43C2311yescharacteristic
183C4⋊C8×C43—21no—
184C4⋊C8×C43—21no—
185#104×C43—24no—
186#95×C43—21no—
187C23×D43—21no—
188C23×D43C2×D411yescharacteristic
189#41×C43—21no—
190#41×C43—21no—
191#41×C43#4112yes—
192#41×C43#4112yes—
193C2×Q8×C43C22×C411yescharacteristic
194C2×D4×C43—21no—
195C2×D4×C43C22×C411yescharacteristic
196C22×C4×C43—21no—
197C22×C4×C43—21no—
198C22×C4×C43—21no—
199C22×C4×C43—22no—
200C22×C4×C43C2×D411yescharacteristic
201C22×C4×C43C2×D411yescharacteristic
202C22×C4×C43C2411yescharacteristic
203C2×C22⋊D43—21no—
204C2×C22⋊D43—21no—
205C2×C22⋊D43—21no—
206C22×Dic43—21no—
207C22×Dic43—21no—
208C22×Dic43—21no—
209C22×Dic43—22no—
210C22×Dic43C2×D411yescharacteristic
211C22×Dic43C2×D411yescharacteristic
212C22×Dic43C2×D411yescharacteristic
213#10621902—22no—
214#10621902—22no—
215Q8×D43—22no—
216Q8×D43—22no—
217#10621900—24no—
218#10621900—24no—
219#10621900—22no—
220#10621900—22no—
221D4×D43—24no—
222D4×D43—24no—
223D4×D43—22no—
224D4×D43—22no—
225#10621898—24no—
226#10621898—24no—
227#10621898—21no—
228#10621898—21no—
229#10621898#4112yes—
230#10621898#4112yes—
231C2×D172—21no—
232C2×D172C22×C411yescharacteristic
233C2×C4×D43—24no—
234C2×C4×D43—24no—
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—24no—
242C2×C4×D43—21no—
243C2×C4×D43—21no—
244C2×C4×D43—21no—
245C2×C4×D43—21no—
246C2×C4×D43—21no—
247C2×C4×D43—21no—
248C2×C4×D43—21no—
249C2×C4×D43—42no—
250C2×C4×D43—44no—
251C2×C4×D43—44no—
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×D43C22×C411yescharacteristic
262C2×C4×D43C2×D411yescharacteristic
263C2×C4×D43C2×D411yescharacteristic
264C2×Dic86—21no—
265C2×Dic86C22×C411yescharacteristic
266M16×C43—22no—
267M16×C43—22no—
268C2×C8×C43—22no—
269C4⋊C4×C43—24no—
270C4⋊C4×C43—21no—
271C4⋊C4×C43—21no—
272C4⋊C4×C43C22×C411yescharacteristic
273C4⋊C4×C43C22×C411yescharacteristic
274C22⋊C4×C43—21no—
275C22⋊C4×C43—21no—
276C22⋊C4×C43—21no—
277C42×C43—21no—
278C42×C43—21no—
279C42×C43—21no—
280C42×C43—22no—
281C42×C43—22no—
282C42×C43C22×C411yescharacteristic
283C42×C43C22×C411yescharacteristic
284C42×C43C2×D411yescharacteristic
285C42×C43C2×D411yescharacteristic
286C22⋊Dic43—21no—
287C22⋊Dic43—21no—
288C22⋊Dic43—21no—
289(C2×D43)⋊C4—28no—
290(C2×D43)⋊C4—21no—
291(C2×D43)⋊C4—21no—
292(C2×D43)⋊C4—21no—
293(C2×D43)⋊C4—21no—
294(C2×D43)⋊C4—21no—
295(C2×D43)⋊C4—21no—
296C4⋊Dic43—24no—
297C4⋊Dic43—21no—
298C4⋊Dic43—21no—
299C4⋊Dic43C22×C411yescharacteristic
300C4⋊Dic43C22×C411yescharacteristic
301Dic43⋊C4—21no—
302Dic43⋊C4—21no—
303Dic43⋊C4—21no—
304Dic43⋊C4—21no—
305Dic43⋊C4—21no—
306Dic43⋊C4—21no—
307C4×Dic43—28no—
308C4×Dic43—21no—
309C4×Dic43—21no—
310C4×Dic43—21no—
311C4×Dic43—21no—
312C4×Dic43—21no—
313C4×Dic43—21no—
314C4×Dic43—21no—
315C4×Dic43—21no—
316C4×Dic43—21no—
317C4×Dic43—22no—
318C4×Dic43—22no—
319C4×Dic43—44no—
320C4×Dic43C22⋊C411yescharacteristic
321C4×Dic43C22⋊C411yescharacteristic
322C4×Dic43C22⋊C411yescharacteristic
323C4×Dic43C22⋊C411yescharacteristic
324C4×Dic43C22⋊C411yescharacteristic
325C4×Dic43C22⋊C411yescharacteristic
326C4×Dic43C22⋊C411yescharacteristic
327C4×Dic43C22⋊C411yescharacteristic
328C4×Dic43C22×C411yescharacteristic
329C4×Dic43C22×C411yescharacteristic
330C4×Dic43C2×D411yescharacteristic
331C4×Dic43C2×D411yescharacteristic
332#10621877—22no—
333#10621877—22no—
334C2×C43⋊C8—22no—
335C23×C43—21no—
336C23×C43C22×D411yescharacteristic
337C22×D43—24no—
338C22×D43—21no—
339C22×D43—21no—
340C22×D43—21no—
341C22×D43—22no—
342C22×D43—41no—
343C22×D43—42no—
344C22×D43—42no—
345C22×D43C2×C22⋊C411yescharacteristic
346C22×D43C2×C22⋊C411yescharacteristic
347Q8×C43—21no—
348Q8×C43#11712yescomplemented
349D4×C43—22no—
350D4×C43—22no—
351D4×C43—21no—
352D4×C43#11712yescomplemented
353C2×C4×C43—21no—
354C2×C4×C43—22no—
355C2×C4×C43—22no—
356C2×C4×C43—22no—
357C2×C4×C43—24no—
358C2×C4×C43—21no—
359C2×C4×C43—21no—
360C2×C4×C43—41no—
361C2×C4×C43—42no—
362C2×C4×C43—42no—
363C2×C4×C43—42no—
364C2×C4×C43—42no—
365C2×C4×C43C2×C22⋊C411yescharacteristic
366C2×C4×C43C2×C22⋊C411yescharacteristic
367C2×C4×C43C2×C22⋊C411yescharacteristic
368C2×C4×C43C2×C22⋊C411yescharacteristic
369C2×C4×C43C23×C411yescharacteristic
370C2×C4×C43C22×D411yescharacteristic
371C2×C4×C43C2×#4111yescharacteristic
372C2×C4×C43C2×#4111yescharacteristic
373C2×C4×C43C2×#4111yescharacteristic
374C2×C4×C43C2×#4111yescharacteristic
375C22⋊D43—24no—
376C22⋊D43—24no—
377C22⋊D43—22no—
378C22⋊D43—22no—
379C2×Dic43—24no—
380C2×Dic43—21no—
381C2×Dic43—21no—
382C2×Dic43—21no—
383C2×Dic43—22no—
384C2×Dic43—22no—
385C2×Dic43—24no—
386C2×Dic43—21no—
387C2×Dic43—21no—
388C2×Dic43—42no—
389C2×Dic43—42no—
390C2×Dic43—42no—
391C2×Dic43—42no—
392C2×Dic43C2×C22⋊C411yescharacteristic
393C2×Dic43C2×C22⋊C411yescharacteristic
394C2×Dic43C2×C22⋊C411yescharacteristic
395C2×Dic43C2×C22⋊C411yescharacteristic
396C2×Dic43C2×C22⋊C411yescharacteristic
397C2×Dic43C2×C22⋊C411yescharacteristic
398D172—24no—
399D172—21no—
400D172#11712yescomplemented
401C4×D43—24no—
402C4×D43—24no—
403C4×D43—22no—
404C4×D43—21no—
405C4×D43—21no—
406C4×D43—21no—
407C4×D43—21no—
408C4×D43—21no—
409C4×D43—21no—
410C4×D43—22no—
411C4×D43—22no—
412C4×D43—21no—
413C4×D43—21no—
414C4×D43—22no—
415C4×D43—22no—
416C4×D43—22no—
417C4×D43—22no—
418C4×D43—41no—
419C4×D43—41no—
420C4×D43—42no—
421C4×D43—42no—
422C4×D43—42no—
423C4×D43—42no—
424C4×D43—42no—
425C4×D43—42no—
426C4×D43#10414yescomplemented
427Dic86—24no—
428Dic86—21no—
429Dic86#11712yescomplemented
430C8×C43—42no—
431C43⋊C8—42no—
432#20747—431nomaximal, Sylow
433C22×C43—21no—
434C22×C43—21no—
435C22×C43—22no—
436C22×C43—41no—
437C22×C43—41no—
438C22×C43C22×C22⋊C411yescharacteristic
439C22×C43#52511yescharacteristic
440C22×C43#52511yescharacteristic
441C2×D43—21no—
442C2×D43—21no—
443C2×D43—21no—
444C2×D43—21no—
445C2×D43—22no—
446C2×D43—21no—
447C2×D43—42no—
448C2×D43—42no—
449C2×D43—48no—
450C2×D43—41no—
451C2×D43—41no—
452C2×D43C2×#10412yes—
453C4×C43—21no—
454C4×C43—21no—
455C4×C43—21no—
456C4×C43—22no—
457C4×C43—44no—
458C4×C43—41no—
459C4×C43—41no—
460C4×C43C2×#10412yes—
461C4×C43C2×#11711yescharacteristic
462C4×C43C2×#11711yescharacteristic
463C4×C43#52511yescharacteristic
464C4×C43#52511yescharacteristic
465Dic43—21no—
466Dic43—21no—
467Dic43—21no—
468Dic43—22no—
469Dic43—21no—
470Dic43—44no—
471Dic43—41no—
472Dic43—41no—
473Dic43C2×#10412yes—
474Dic43#42112yes—
475C2×C4×#41—431no—
476#2920—431no—
477C4×#117—431no—
478#1826—432no—
479#1806—431no—
480#1806—431no—
481#1806—431no—
482#1806D4311yescharacteristic, complemented
483#1789—432no—
484C4×#104—432no—
485C4×#104—432no—
486C2×C43—21no—
487C2×C43—21no—
488C2×C43—42no—
489C2×C43#228011yescharacteristic
490C2×C43C22×#10411yescharacteristic
491C2×C43C2×#42111yescharacteristic
492D43—22no—
493D43—41no—
494D43—42no—
495C22×#41—431no—
496C4×#41—431no—
497C4×#41—431no—
498C4×#41—431no—
499C4×#41—431no—
500C4×#41—431no—
501C4×#41—431no—
502C4×#41—431no—
503C4×#41—861no—
504C4×#41—861no—
505C4×#41—861no—
506C4×#41—861no—
507C4×#41C2×D4311yescharacteristic
508C2×C4×Q8—431no—
509C2×C4×Q8—431no—
510C2×C4×D4—431no—
511C2×C4×D4—431no—
512C2×C4×D4—861no—
513C2×C4×D4—861no—
514C2×#117—431no—
515C2×#117—861no—
516C2×#117—861no—
517C22×C42—431no—
518C22×C42—861no—
519#432—861no—
520#432—861no—
521#431—861no—
522#431—861no—
523#423—431no—
524#423C2×D4311yescharacteristic, complemented
525C2×#104—432no—
526C2×#104—432no—
527C2×#104—432no—
528C2×#104C2×D4312yes—
529#407—432no—
530C4×M16—432no—
531C4×C4⋊C4—431no—
532C4×C4⋊C4—861no—
533C4×C4⋊C4C2×D4311yescharacteristic, complemented
534C4×C22⋊C4—432no—
535C4×C22⋊C4—861no—
536#376—861no—
537C43—432no—
538#339—432no—
539#339—432no—
540#339—432no—
541#339C2×D4312yescomplemented
542C43#2074711yescharacteristic, complemented, Sylow
543C2×#41—431no—
544C2×#41—431no—
545C2×#41—431no—
546C2×#41—861no—
547C2×#41—861no—
548C2×#41—862no—
549C2×#41—862no—
550C2×#41—862no—
551C2×#41—862no—
552C2×#41C22×D4311yescharacteristic
553C22×Q8—431no—
554C22×D4—431no—
555C22×D4—861no—
556C23×C4—431no—
557C23×C4—431no—
558C23×C4—431no—
559C23×C4—861no—
560C23×C4—861no—
561C23×C4—861no—
562C2×M16—432no—
563C2×M16C22×D4312yes—
564C4×Q8—431no—
565C4×Q8—431no—
566C4×Q8—431no—
567C4×Q8—431no—
568C4×Q8—431no—
569C4×Q8—431no—
570C4×Q8—861no—
571C4×Q8—861no—
572C4×Q8—861no—
573C4×Q8—861no—
574C4×Q8C4×D4311yescharacteristic
575C4×Q8C4×D4311yescharacteristic
576C4×D4—21no—
577C4×D4—21no—
578C4×D4—431no—
579C4×D4—431no—
580C4×D4—431no—
581C4×D4—431no—
582C4×D4—431no—
583C4×D4—431no—
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×D4—861no—
600C4×D4—861no—
601C4×D4—861no—
602C4×D4C4×D4311yescharacteristic
603C4×D4C4×D4311yescharacteristic
604#117—21no—
605#117—431no—
606#117—431no—
607#117—431no—
608#117—861no—
609#117—861no—
610#117—861no—
611#117—861no—
612#117—861no—
613#117—861no—
614#117—861no—
615#117—861no—
616#117—868no—
617#117—861no—
618#117C22×D4311yescharacteristic
619C2×C4⋊C4—21no—
620C2×C4⋊C4—431no—
621C2×C4⋊C4—431no—
622C2×C4⋊C4—861no—
623C2×C4⋊C4—861no—
624C2×C4⋊C4—861no—
625C2×C22⋊C4—861no—
626C2×C22⋊C4—861no—
627C2×C22⋊C4—861no—
628C2×C22⋊C4—862no—
629C2×C42—21no—
630C2×C42—431no—
631C2×C42—431no—
632C2×C42—431no—
633C2×C42—431no—
634C2×C42—431no—
635C2×C42—431no—
636C2×C42—431no—
637C2×C42—431no—
638C2×C42—431no—
639C2×C42—431no—
640C2×C42—431no—
641C2×C42—432no—
642C2×C42—861no—
643C2×C42—861no—
644C2×C42—861no—
645C2×C42—861no—
646C2×C42—861no—
647C2×C42—861no—
648C2×C42—861no—
649C2×C42—861no—
650C2×C42—861no—
651C2×C42—862no—
652C2×C42—861no—
653C2×C42—862no—
654C2×C42C22×D4312yes—
655C2×C42C22×D4311yescharacteristic
656C4⋊C8—21no—
657C4⋊C8—21no—
658C4⋊C8—861no—
659C4⋊C8—861no—
660#104—24no—
661#104—864no—
662#104—864no—
663#104—864no—
664C22⋊C8—862no—
665C22⋊C8—862no—
666#97—862no—
667C4×C8—862no—
668#95—21no—
669#95—862no—
670#95—861no—
671C24—431no—
672C24—861no—
673#41—21no—
674#41—21no—
675#41—432no—
676#41—432no—
677#41—864no—
678#41—864no—
679#41—862no—
680#41—864no—
681#41—864no—
682#41—862no—
683#41—862no—
684#41—862no—
685#41—861no—
686#41—861no—
687#41#1062190012yes—
688#41#1062190212yes—
689C2×Q8—431no—
690C2×Q8—861no—
691C2×Q8—862no—
692C2×Q8—862no—
693C2×Q8C2×C4×D4311yescharacteristic
694C2×D4—21no—
695C2×D4—431no—
696C2×D4—861no—
697C2×D4—861no—
698C2×D4—862no—
699C2×D4—864no—
700C2×D4—864no—
701C2×D4—861no—
702C2×D4—861no—
703C2×D4—862no—
704C2×D4C2×C4×D4311yescharacteristic
705C22×C4—21no—
706C22×C4—22no—
707C22×C4—21no—
708C22×C4—21no—
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—431no—
721C22×C4—431no—
722C22×C4—431no—
723C22×C4—431no—
724C22×C4—861no—
725C22×C4—864no—
726C22×C4—861no—
727C22×C4—861no—
728C22×C4—861no—
729C22×C4—864no—
730C22×C4—864no—
731C22×C4—861no—
732C22×C4—861no—
733C22×C4—861no—
734C22×C4—861no—
735C22×C4—861no—
736C22×C4—861no—
737C22×C4—861no—
738C22×C4—861no—
739C22×C4—861no—
740C22×C4—861no—
741C22×C4—862no—
742C22×C4—861no—
743C22×C4—861no—
744C22×C4—1724no—
745C22×C4—1722no—
746C22×C4—1724no—
747C22×C4D4×D4311yescharacteristic
748C22×C4D4×D4311yescharacteristic
749C22×C4C23×D4311yescharacteristic
750M16—22no—
751M16—22no—
752M16—862no—
753M16—862no—
754C2×C8—22no—
755C2×C8—862no—
756C4⋊C4—24no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—431no—
760C4⋊C4—431no—
761C4⋊C4—861no—
762C4⋊C4—861no—
763C4⋊C4—861no—
764C4⋊C4—861no—
765C4⋊C4—861no—
766C4⋊C4—861no—
767C4⋊C4—864no—
768C4⋊C4—861no—
769C4⋊C4—861no—
770C4⋊C4C2×C4×D4311yescharacteristic
771C4⋊C4C2×C4×D4311yescharacteristic
772C22⋊C4—21no—
773C22⋊C4—21no—
774C22⋊C4—21no—
775C22⋊C4—861no—
776C22⋊C4—861no—
777C22⋊C4—861no—
778C22⋊C4—861no—
779C22⋊C4—868no—
780C22⋊C4—861no—
781C22⋊C4—861no—
782C22⋊C4—861no—
783C22⋊C4—861no—
784C22⋊C4—861no—
785C42—21no—
786C42—21no—
787C42—21no—
788C42—22no—
789C42—22no—
790C42—431no—
791C42—431no—
792C42—431no—
793C42—431no—
794C42—431no—
795C42—431no—
796C42—431no—
797C42—431no—
798C42—431no—
799C42—431no—
800C42—431no—
801C42—431no—
802C42—861no—
803C42—861no—
804C42—861no—
805C42—861no—
806C42—861no—
807C42—861no—
808C42—868no—
809C42—861no—
810C42—861no—
811C42—861no—
812C42—862no—
813C42—862no—
814C42—1724no—
815C42C2×C4×D4311yescharacteristic
816C42C2×C4×D4311yescharacteristic
817C42D4×D4311yescharacteristic
818C42D4×D4311yescharacteristic
819C23—21no—
820C23—431no—
821C23—431no—
822C23—862no—
823C23—864no—
824C23—861no—
825C23—861no—
826C23—861no—
827C23—1721no—
828C23—1722no—
829C23—1722no—
830C23C2×D4×D4311yescharacteristic
831Q8—21no—
832Q8—432no—
833Q8—864no—
834Q8—861no—
835Q8#1306328312yescomplemented
836D4—22no—
837D4—22no—
838D4—21no—
839D4—432no—
840D4—864no—
841D4—864no—
842D4—864no—
843D4—862no—
844D4—862no—
845D4—861no—
846D4#1306328312yescomplemented
847C2×C4—21no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—24no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—41no—
855C2×C4—42no—
856C2×C4—42no—
857C2×C4—42no—
858C2×C4—42no—
859C2×C4—431no—
860C2×C4—431no—
861C2×C4—434no—
862C2×C4—431no—
863C2×C4—431no—
864C2×C4—431no—
865C2×C4—431no—
866C2×C4—862no—
867C2×C4—862no—
868C2×C4—862no—
869C2×C4—862no—
870C2×C4—864no—
871C2×C4—864no—
872C2×C4—862no—
873C2×C4—862no—
874C2×C4—864no—
875C2×C4—861no—
876C2×C4—861no—
877C2×C4—861no—
878C2×C4—861no—
879C2×C4—861no—
880C2×C4—861no—
881C2×C4—861no—
882C2×C4—861no—
883C2×C4—861no—
884C2×C4—862no—
885C2×C4—861no—
886C2×C4—861no—
887C2×C4—862no—
888C2×C4—862no—
889C2×C4—864no—
890C2×C4—861no—
891C2×C4—861no—
892C2×C4—1721no—
893C2×C4—1721no—
894C2×C4—1722no—
895C2×C4—1722no—
896C2×C4—1722no—
897C2×C4—1722no—
898C2×C4—1722no—
899C2×C4—1722no—
900C2×C4—1722no—
901C2×C4—1722no—
902C2×C4—1722no—
903C2×C4—1722no—
904C2×C4C22⋊C4×D4311yescharacteristic
905C2×C4C22⋊C4×D4311yescharacteristic
906C2×C4C22⋊C4×D4311yescharacteristic
907C2×C4C22⋊C4×D4311yescharacteristic
908C2×C4C22×C4×D4311yescharacteristic
909C2×C4C2×D4×D4311yescharacteristic
910C2×C4#41×D4311yescharacteristic
911C2×C4#41×D4311yescharacteristic
912C2×C4C2×#1062190011yescharacteristic
913C2×C4C2×#1062190211yescharacteristic
914C8—42no—
915C8—1722no—
916C22—21no—
917C22—21no—
918C22—22no—
919C22—41no—
920C22—41no—
921C22—432no—
922C22—861no—
923C22—861no—
924C22—862no—
925C22—861no—
926C22—861no—
927C22—861no—
928C22—1722no—
929C22—1722no—
930C22—1728no—
931C22—1721no—
932C22—1721no—
933C22C2×C22⋊C4×D4311yescharacteristic
934C22#1458340911yescharacteristic
935C22#1458341211yescharacteristic
936C4—22no—
937C4—21no—
938C4—21no—
939C4—21no—
940C4—44no—
941C4—41no—
942C4—41no—
943C4—432no—
944C4—432no—
945C4—861no—
946C4—861no—
947C4—862no—
948C4—861no—
949C4—861no—
950C4—1724no—
951C4—1721no—
952C4—1721no—
953C4#104×D4312yes—
954C4#117×D4311yescharacteristic
955C4C2×#1306328311yescharacteristic
956C4#1458340911yescharacteristic
957C4#1458341211yescharacteristic
958C2—21no—
959C2—21no—
960C2—42no—
961C2—862no—
962C2—1721no—
963C2—1722no—
964C2#1913697711yescharacteristic
965C2C2×#104×D4311yescharacteristic
966C2#421×D4311yescharacteristic
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#20747
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. C4×#13063283C2semidirect
4. #19134693C2semidirect
5. #19134616C2semidirect
6. #19134615C2semidirect
7. #19134612C2semidirect
9. #104×Dic43C2semidirect
10. #19134399C2semidirect
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
39. #14582923C22semidirect
44. M16×Dic43C22semidirect
46. C4×C4⋊Dic43C22semidirect
50. C42×Dic43C22semidirect
51. #14582660C22semidirect
52. #14582659C22semidirect
53. #14582658C22semidirect
55. C43×#423C22semidirect
57. C4×C4⋊C4×C43C22semidirect
58. C43×#339C22semidirect
348. Q8×C43#117semidirect
352. D4×C43#117semidirect
400. D172#117semidirect
426. C4×D43#104semidirect
429. Dic86#117semidirect
482. #1806D43semidirect
524. #423C2×D43semidirect
533. C4×C4⋊C4C2×D43semidirect
541. #339C2×D43semidirect
542. C43#20747semidirect
835. Q8#13063283semidirect
846. D4#13063283semidirect

Maximal subgroups

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

subgroupindex
C4×#41×D432
#191432272
C4×#130632832
#191346932
#191346162
#191346152
#191346122
#191345372
#104×Dic432
#191343992
C43×#18062
#2074743