Finite Group Databasebeta

← D43×#2431 #25264926

Subgroups — D43×#2431 #25264926

Order 11008.

6278 conjugacy classes of subgroups.

The subgroup lattice has 1188 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#41×D43C211yesmaximal, characteristic, complemented
2C2×#127×D43C211yesmaximal, characteristic, complemented
3C2×#124×D43C211yesmaximal, characteristic, complemented
4C2×#121×D43C211yesmaximal, characteristic, complemented
5#19138217C211yesmaximal, characteristic, complemented
6#19138216C211yesmaximal, characteristic, complemented
7#19138215C211yesmaximal, characteristic, complemented
8#19138214C211yesmaximal, characteristic, complemented
9#19138213C211yesmaximal, characteristic, complemented
10#19138212C214yesmaximal, complemented
11#19138211C211yesmaximal, characteristic, complemented
12#19138210C211yesmaximal, characteristic, complemented
13#19138209C214yesmaximal, complemented
14#392×D43C214yesmaximal, complemented
15#391×D43C211yesmaximal, characteristic, complemented
16#390×D43C211yesmaximal, characteristic, complemented
17#386×D43C214yesmaximal, complemented
18C4×C22⋊C4×D43C211yesmaximal, characteristic, complemented
19C43×#2431C211yesmaximal, characteristic, complemented
20C22×#10621902C2211yescharacteristic, complemented
21C22×#10621898C2212yescomplemented
22C22×#10621898C2211yescharacteristic, complemented
23C22×#10621900C2212yescomplemented
24C22×#10621900C2211yescharacteristic, complemented
25C2×#41×D43—28no—
26C2×#41×D43—28no—
27C2×#41×D43—28no—
28C22×Q8×D43C2211yescharacteristic
29C22×D4×D43C2211yescharacteristic
30C22×D4×D43C2212yes—
31C22×D4×D43C2214yes—
32C22×D4×D43C2211yescharacteristic
33C22×D4×D43C2212yes—
34C23×C4×D43C2212yes—
35C23×C4×D43C2211yescharacteristic
36C2×#13063322C2211yescharacteristic, complemented
37C2×#13063321C2214yescomplemented
38C2×#13063321C2211yescharacteristic, complemented
39C2×#13063321C2211yescharacteristic, complemented
40#127×D43—28no—
41C2×#13063314C2211yescharacteristic, complemented
42C2×#13063313C2211yescharacteristic, complemented
43C2×#13063312C2211yescharacteristic, complemented
44C2×#13063311C2214yescomplemented
45#124×D43—28no—
46C2×#13063300C2211yescharacteristic, complemented
47C2×#13063299C2211yescharacteristic, complemented
48C2×#13063298C2212yescomplemented
49C2×#13063297C2212yescomplemented
50C2×#13063296C2211yescharacteristic, complemented
51#121×D43—28no—
52C2×C4⋊C4×D43C2211yescharacteristic
53C2×C22⋊C4×D43C2212yes—
54C2×C22⋊C4×D43C2214yes—
55C2×C22⋊C4×D43C2212yes—
56C2×C22⋊C4×D43C2214yes—
57C2×C42×D43C2211yescharacteristic
58C2×C42×D43C2211yescharacteristic
59#14582809C2214yescomplemented
60#14582808C2214yescomplemented
61#14582808C2214yescomplemented
62#14582808C2214yescomplemented
63#14582807C2214yescomplemented
64#14582807C2214yescomplemented
65#14582807C2214yescomplemented
66#14582806C2211yescharacteristic, complemented
67#14582805C2211yescharacteristic, complemented
68#14582804C2211yescharacteristic, complemented
69#14582803C2214yescomplemented
70#14582802C2211yescharacteristic, complemented
71#14582801C2211yescharacteristic, complemented
72#14582800C2211yescharacteristic, complemented
73#14582799C2214yescomplemented
74#14582779C2214yescomplemented
75#14582778C2214yescomplemented
76#14582777C2214yescomplemented
77#14582777C2214yescomplemented
78#14582776C2214yescomplemented
79#14582775C2214yescomplemented
80#14582775C2214yescomplemented
81C22⋊C4×Dic43C2212yescomplemented
82C4×(C2×D43)⋊C4C2211yescharacteristic, complemented
83C4×(C2×D43)⋊C4C2211yescharacteristic, complemented
84C4×C22⋊Dic43C2211yescharacteristic, complemented
85#14582746C2212yescomplemented
86#95×D43C2214yes—
87#95×D43C2212yes—
88C22×#41×C43C2211yescharacteristic, complemented
89C2×#127×C43C2211yescharacteristic, complemented
90C2×#124×C43C2211yescharacteristic, complemented
91C2×#121×C43C2211yescharacteristic, complemented
92C43×#392C2214yescomplemented
93C43×#391C2211yescharacteristic, complemented
94C43×#390C2211yescharacteristic, complemented
95C43×#386C2214yescomplemented
96C4×C22⋊C4×C43C2211yescharacteristic, complemented
97C24×D43C2312yes—
98C24×D43C2311yescharacteristic
99C24×D43C2312yes—
100C2×#10621902—24no—
101C2×#10621902—24no—
102C2×#10621902—24no—
103C2×#10621898—24no—
104C2×#10621898—28no—
105C2×#10621898—24no—
106C2×#10621898—28no—
107C2×#10621898—28no—
108C2×#10621898—24no—
109C2×#10621900—24no—
110C2×#10621900—28no—
111C2×#10621900—28no—
112C2×#10621900—24no—
113C2×#10621900—28no—
114C2×#10621900—24no—
115#41×D43—2128no—
116C22×Dic86C2312yes—
117C22×Dic86C2311yescharacteristic
118C2×Q8×D43—24no—
119C2×Q8×D43—24no—
120C2×Q8×D43D418yescomplemented
121C22×D172C2312yes—
122C22×D172C2311yescharacteristic
123C22×D172C2314yes—
124C22×D172C2311yescharacteristic
125C22×D172C2312yes—
126C22×C22⋊D43C2312yes—
127C22×C22⋊D43C2312yes—
128C22×C22⋊D43C2312yes—
129C22×C22⋊D43C2314yes—
130C22×C22⋊D43C2314yes—
131C22×C22⋊D43C2312yes—
132C22×C22⋊D43C2312yes—
133C22×C22⋊D43C2312yes—
134C2×D4×D43—28no—
135C2×D4×D43—28no—
136C2×D4×D43—28no—
137C2×D4×D43—216no—
138C2×D4×D43—28no—
139C2×D4×D43—24no—
140C2×D4×D43—24no—
141C2×D4×D43—24no—
142C2×D4×D43—24no—
143C2×D4×D43—24no—
144C2×D4×D43—216no—
145C2×D4×D43—48no—
146C2×D4×D43—48no—
147C2×D4×D43D418yescomplemented
148C23×Dic43C2312yes—
149C23×Dic43C2311yescharacteristic
150C22×C4×D43—28no—
151C22×C4×D43—28no—
152C22×C4×D43—28no—
153C22×C4×D43—24no—
154C22×C4×D43—24no—
155C22×C4×D43D418yescomplemented
156C22×C4×D43C2312yes—
157C22×C4×D43C2312yes—
158C22×C4×D43C2312yes—
159C22×C4×D43C2312yes—
160C22×C4×D43C2311yescharacteristic
161C22×C4×D43C2312yes—
162C22×C4×D43C2311yescharacteristic
163C22×C4×D43C2311yescharacteristic
164C22×C4×D43C2312yes—
165C22×C4×D43C2311yescharacteristic
166#13063322—24no—
167#13063321—24no—
168#13063321—216no—
169#13063321—24no—
170#13063314—24no—
171#13063313—24no—
172#13063312—24no—
173#13063311—216no—
174#13063300—24no—
175#13063299—24no—
176#13063298—28no—
177#13063297—28no—
178#13063296—24no—
179C2×C4⋊Dic43C2311yescharacteristic
180C2×Dic43⋊C4C2312yes—
181C4⋊C4×D43—24no—
182C2×C22⋊Dic43C2312yes—
183C2×C22⋊Dic43C2314yes—
184C2×C22⋊Dic43C2312yes—
185C2×C22⋊Dic43C2314yes—
186C2×(C2×D43)⋊C4C2312yes—
187C2×(C2×D43)⋊C4C2314yes—
188C2×(C2×D43)⋊C4C2312yes—
189C2×(C2×D43)⋊C4C2314yes—
190C2×(C2×D43)⋊C4C2312yes—
191C2×(C2×D43)⋊C4C2312yes—
192C2×(C2×D43)⋊C4C2314yes—
193C2×(C2×D43)⋊C4C2314yes—
194C22⋊C4×D43—28no—
195C22⋊C4×D43—216no—
196C22⋊C4×D43—28no—
197C22⋊C4×D43—48no—
198C2×C4×Dic43C2312yes—
199C2×C4×Dic43C2311yescharacteristic
200C2×C4×Dic43C2312yes—
201C2×C4×Dic43C2311yescharacteristic
202C42×D43—24no—
203C42×D43—24no—
204C43⋊#95C2314yes—
205C43⋊#95C2314yes—
206C43⋊#95C2314yes—
207C43⋊#95C2312yes—
208C43⋊#95C2312yes—
209C43⋊#95C2312yes—
210C2×#41×C43—24no—
211C2×#41×C43—24no—
212C2×#41×C43—24no—
213C22×Q8×C43C2311yescharacteristic
214C22×D4×C43C2312yes—
215C22×D4×C43C2311yescharacteristic
216C22×D4×C43C2314yes—
217C22×D4×C43C2311yescharacteristic
218C22×D4×C43C2312yes—
219C23×C4×C43C2312yes—
220C23×C4×C43C2311yescharacteristic
221#127×C43—24no—
222#124×C43—24no—
223#121×C43—24no—
224C2×C4⋊C4×C43C2311yescharacteristic
225C2×C22⋊C4×C43C2312yes—
226C2×C22⋊C4×C43C2314yes—
227C2×C22⋊C4×C43C2312yes—
228C2×C22⋊C4×C43C2314yes—
229C2×C42×C43C2311yescharacteristic
230C2×C42×C43C2311yescharacteristic
231#95×C43C2314yes—
232#95×C43C2312yes—
233C24×C43C2412yes—
234C24×C43C2411yescharacteristic
235C24×C43C2412yes—
236C23×D43—24no—
237C23×D43—22no—
238C23×D43—24no—
239C23×D43—22no—
240C23×D43—24no—
241C23×D43—28no—
242C23×D43—28no—
243C23×D43—24no—
244C23×D43—24no—
245C23×D43—24no—
246C23×D43—24no—
247C23×D43—28no—
248C23×D43—28no—
249C23×D43C2×D418yes—
250C23×D43C2×D414yes—
251C23×D43C2412yes—
252C23×D43C2411yescharacteristic
253C23×D43C2412yes—
254C23×D43C2411yescharacteristic
255#41×C43—232no—
256C2×Q8×C43—22no—
257C2×Q8×C43—22no—
258C2×Q8×C43C2×D414yescomplemented
259C2×D4×C43—24no—
260C2×D4×C43—22no—
261C2×D4×C43—22no—
262C2×D4×C43—22no—
263C2×D4×C43—22no—
264C2×D4×C43—22no—
265C2×D4×C43—28no—
266C2×D4×C43—24no—
267C2×D4×C43—24no—
268C2×D4×C43—24no—
269C2×D4×C43—28no—
270C2×D4×C43—44no—
271C2×D4×C43—44no—
272C2×D4×C43C2×D414yescomplemented
273C22×C4×C43—24no—
274C22×C4×C43—24no—
275C22×C4×C43—22no—
276C22×C4×C43—22no—
277C22×C4×C43—24no—
278C22×C4×C43C2×D414yescomplemented
279C22×C4×C43C2412yes—
280C22×C4×C43C2412yes—
281C22×C4×C43C2411yescharacteristic
282C22×C4×C43C2412yes—
283C22×C4×C43C2412yes—
284C22×C4×C43C2411yescharacteristic
285C2×C22⋊D43—24no—
286C2×C22⋊D43—24no—
287C2×C22⋊D43—24no—
288C2×C22⋊D43—24no—
289C2×C22⋊D43—24no—
290C2×C22⋊D43—24no—
291C2×C22⋊D43—24no—
292C2×C22⋊D43—28no—
293C2×C22⋊D43—28no—
294C2×C22⋊D43—24no—
295C2×C22⋊D43—24no—
296C2×C22⋊D43—24no—
297C2×C22⋊D43—28no—
298C2×C22⋊D43—24no—
299C2×C22⋊D43—24no—
300C2×C22⋊D43—24no—
301C2×C22⋊D43—28no—
302C2×C22⋊D43—44no—
303C2×C22⋊D43—44no—
304C2×C22⋊D43—44no—
305C2×C22⋊D43—44no—
306C2×C22⋊D43C2×D418yescomplemented
307C22×Dic43—24no—
308C22×Dic43—24no—
309C22×Dic43—22no—
310C22×Dic43—22no—
311C22×Dic43—24no—
312C22×Dic43C2×D414yescomplemented
313C22×Dic43C2412yes—
314C22×Dic43C2412yes—
315C22×Dic43C2411yescharacteristic
316C22×Dic43C2412yes—
317C22×Dic43C2412yes—
318C22×Dic43C2411yescharacteristic
319#10621902—232no—
320Q8×D43—232no—
321#10621900—232no—
322#10621900—264no—
323D4×D43—264no—
324D4×D43—232no—
325D4×D43—464no—
326D4×D43—432no—
327D4×D43—416no—
328#10621898—232no—
329#10621898—264no—
330C2×D172—24no—
331C2×D172—22no—
332C2×D172—22no—
333C2×D172—22no—
334C2×D172—22no—
335C2×D172—22no—
336C2×D172—28no—
337C2×D172—24no—
338C2×D172—24no—
339C2×D172—24no—
340C2×D172—28no—
341C2×D172—44no—
342C2×D172—44no—
343C2×D172C2×D414yescomplemented
344C2×C4×D43—264no—
345C2×C4×D43—24no—
346C2×C4×D43—22no—
347C2×C4×D43—22no—
348C2×C4×D43—24no—
349C2×C4×D43—24no—
350C2×C4×D43—24no—
351C2×C4×D43—22no—
352C2×C4×D43—22no—
353C2×C4×D43—232no—
354C2×C4×D43—24no—
355C2×C4×D43—22no—
356C2×C4×D43—22no—
357C2×C4×D43—24no—
358C2×C4×D43—24no—
359C2×C4×D43—24no—
360C2×C4×D43—24no—
361C2×C4×D43—24no—
362C2×C4×D43—24no—
363C2×C4×D43—24no—
364C2×C4×D43—24no—
365C2×C4×D43—24no—
366C2×C4×D43—28no—
367C2×C4×D43C2×D414yes—
368C2×C4×D43C2×D418yes—
369C2×C4×D43C2×D414yes—
370C2×C4×D43C2×D414yes—
371C2×C4×D43C2×D414yes—
372C2×C4×D43C2×D414yescomplemented
373C2×C4×D43C2×D414yescomplemented
374C2×C4×D43#4118yescomplemented
375C2×Dic86—22no—
376C2×Dic86—22no—
377C2×Dic86—24no—
378C2×Dic86—24no—
379C2×Dic86C2×D418yescomplemented
380C2×Dic86C2×D414yescomplemented
381C4⋊C4×C43—22no—
382C22⋊C4×C43—24no—
383C22⋊C4×C43—28no—
384C22⋊C4×C43—24no—
385C22⋊C4×C43—44no—
386C42×C43—22no—
387C42×C43—22no—
388C22⋊Dic43—24no—
389C22⋊Dic43—28no—
390C22⋊Dic43—24no—
391C22⋊Dic43—44no—
392(C2×D43)⋊C4—24no—
393(C2×D43)⋊C4—28no—
394(C2×D43)⋊C4—24no—
395(C2×D43)⋊C4—24no—
396(C2×D43)⋊C4—28no—
397(C2×D43)⋊C4—24no—
398(C2×D43)⋊C4—44no—
399(C2×D43)⋊C4—44no—
400C4⋊Dic43—22no—
401Dic43⋊C4—24no—
402C4×Dic43—22no—
403C4×Dic43—22no—
404C4×Dic43—24no—
405C4×Dic43—24no—
406C23×C43—22no—
407C23×C43—21no—
408C23×C43—22no—
409C23×C43—21no—
410C23×C43—22no—
411C23×C43—24no—
412C23×C43—24no—
413C23×C43—22no—
414C23×C43—22no—
415C23×C43—22no—
416C23×C43—22no—
417C23×C43—24no—
418C23×C43—24no—
419C23×C43C22×D414yes—
420C23×C43C22×D412yes—
421C23×C43C2511yescharacteristic
422C22×D43—22no—
423C22×D43—21no—
424C22×D43—22no—
425C22×D43—21no—
426C22×D43—22no—
427C22×D43—24no—
428C22×D43—24no—
429C22×D43—22no—
430C22×D43—216no—
431C22×D43—28no—
432C22×D43—28no—
433C22×D43—28no—
434C22×D43—232no—
435C22×D43—22no—
436C22×D43—22no—
437C22×D43—22no—
438C22×D43—24no—
439C22×D43—24no—
440C22×D43—48no—
441C22×D43—48no—
442C22×D43—48no—
443C22×D43—48no—
444C22×D43—416no—
445C22×D43—48no—
446C22×D43—48no—
447C22×D43—48no—
448C22×D43—416no—
449C22×D43—416no—
450C22×D43C22×D414yes—
451C22×D43C22×D412yes—
452C22×D43C22×D412yes—
453C22×D43C22×D412yes—
454C22×D43C22×D412yes—
455C22×D43C2×#4114yes—
456C22×D43H(5,𝔽2)14yes—
457Q8×C43—28no—
458D4×C43—216no—
459D4×C43—28no—
460D4×C43—416no—
461D4×C43—48no—
462D4×C43—44no—
463C2×C4×C43—216no—
464C2×C4×C43—22no—
465C2×C4×C43—22no—
466C2×C4×C43—22no—
467C2×C4×C43—21no—
468C2×C4×C43—21no—
469C2×C4×C43—22no—
470C2×C4×C43—28no—
471C2×C4×C43—22no—
472C2×C4×C43—22no—
473C2×C4×C43—22no—
474C2×C4×C43—22no—
475C2×C4×C43—24no—
476C2×C4×C43C22×D414yes—
477C2×C4×C43C22×D412yes—
478C2×C4×C43C22×D412yes—
479C2×C4×C43C22×D412yes—
480C2×C4×C43C22×D412yes—
481C2×C4×C43C2×#4114yescomplemented
482C22⋊D43—216no—
483C22⋊D43—216no—
484C22⋊D43—216no—
485C22⋊D43—416no—
486C22⋊D43—416no—
487C22⋊D43—48no—
488C22⋊D43—48no—
489C22⋊D43—48no—
490C2×Dic43—216no—
491C2×Dic43—22no—
492C2×Dic43—22no—
493C2×Dic43—22no—
494C2×Dic43—21no—
495C2×Dic43—21no—
496C2×Dic43—22no—
497C2×Dic43—28no—
498C2×Dic43—22no—
499C2×Dic43—22no—
500C2×Dic43—22no—
501C2×Dic43—22no—
502C2×Dic43—24no—
503C2×Dic43C22×D414yes—
504C2×Dic43C22×D412yes—
505C2×Dic43C22×D412yes—
506C2×Dic43C22×D412yes—
507C2×Dic43C22×D412yes—
508C2×Dic43C2×#4114yescomplemented
509D172—216no—
510D172—28no—
511D172—416no—
512D172—48no—
513D172—44no—
514C4×D43—216no—
515C4×D43—216no—
516C4×D43—28no—
517C4×D43—216no—
518C4×D43—216no—
519C4×D43—28no—
520C4×D43—28no—
521C4×D43—48no—
522C4×D43—48no—
523C4×D43#120116yes—
524Dic86—28no—
525Dic86—216no—
526C2×#2431—431nomaximal, Sylow
527C22×C43—24no—
528C22×C43—22no—
529C22×C43—22no—
530C22×C43—22no—
531C22×C43—28no—
532C22×C43—42no—
533C22×C43—42no—
534C22×C43—42no—
535C22×C43—42no—
536C22×C43—44no—
537C22×C43—42no—
538C22×C43—42no—
539C22×C43—42no—
540C22×C43—44no—
541C22×C43—44no—
542C22×C43C23×D411yescharacteristic
543C22×C43C23×D411yescharacteristic
544C22×C43C23×D411yescharacteristic
545C22×C43C22×#4112yes—
546C22×C43C2×H(5,𝔽2)12yes—
547C2×D43—24no—
548C2×D43—22no—
549C2×D43—22no—
550C2×D43—22no—
551C2×D43—28no—
552C2×D43—42no—
553C2×D43—42no—
554C2×D43—42no—
555C2×D43—42no—
556C2×D43—44no—
557C2×D43—416no—
558C2×D43—432no—
559C2×D43—42no—
560C2×D43—42no—
561C2×D43—42no—
562C2×D43—44no—
563C2×D43—44no—
564C2×D43—816no—
565C2×D43C2×#12014yes—
566C2×D43#53214yes—
567C2×D43#53514yes—
568C2×D43#54618yes—
569C2×D43#55018yes—
570C4×C43—24no—
571C4×C43—22no—
572C4×C43—24no—
573C4×C43—42no—
574C4×C43—42no—
575C4×C43C2×#12014yes—
576Dic43—24no—
577Dic43—22no—
578Dic43—24no—
579Dic43—42no—
580Dic43—42no—
581Dic43C2×#12014yes—
582C23×#41—431no—
583C22×#127—431no—
584C22×#124—431no—
585C22×#121—431no—
586#2431—434no—
587#2431—431no—
588#2431—431no—
589#2431—434no—
590#2431—431no—
591#2431—431no—
592#2431—431no—
593#2431—431no—
594#2431—431no—
595#2431D4311yescharacteristic, direct product factor
596C2×#392—434no—
597C2×#391—431no—
598C2×#390—431no—
599C2×#386—434no—
600C2×C4×C22⋊C4—431no—
601C2×C43—42no—
602C2×C43—44no—
603C2×C43—82no—
604C2×C43C22×#12011yescharacteristic
605C2×C43C2×#53211yescharacteristic
606C2×C43C2×#53511yescharacteristic
607C2×C43C2×#54612yes—
608C2×C43C2×#55012yes—
609D43—42no—
610D43—44no—
611D43—82no—
612D43#243118yesdirect product factor
613C22×#41—431no—
614C22×#41—432no—
615C22×#41—431no—
616C22×#41—432no—
617C22×#41—431no—
618C22×#41—868no—
619C22×#41—868no—
620C22×#41—868no—
621C22×#41C2×D4311yescharacteristic, complemented
622C23×Q8—431no—
623C23×D4—431no—
624C23×D4—432no—
625C23×D4—431no—
626C23×D4—434no—
627C23×D4—432no—
628C24×C4—431no—
629C24×C4—432no—
630C2×#127—434no—
631C2×#127—431no—
632C2×#127—431no—
633C2×#127—431no—
634C2×#127—868no—
635C2×#127C2×D4311yescharacteristic, complemented
636C2×#124—431no—
637C2×#124—431no—
638C2×#124—434no—
639C2×#124—431no—
640C2×#124—868no—
641C2×#124C2×D4311yescharacteristic, complemented
642C2×#121—431no—
643C2×#121—432no—
644C2×#121—431no—
645C2×#121—431no—
646C2×#121—432no—
647C2×#121—868no—
648C2×#121C2×D4311yescharacteristic, complemented
649C22×C4⋊C4—431no—
650C22×C22⋊C4—432no—
651C22×C22⋊C4—434no—
652C22×C22⋊C4—432no—
653C22×C22⋊C4—434no—
654C22×C42—431no—
655C22×C42—431no—
656#392—434no—
657#392—434no—
658#392—434no—
659#392—434no—
660#392—434no—
661#392—434no—
662#392—434no—
663#392C2×D4314yescomplemented
664#391—431no—
665#391—431no—
666#391—431no—
667#391—434no—
668#391C2×D4311yescharacteristic, complemented
669#390—431no—
670#390—431no—
671#390—434no—
672#390—431no—
673#390C2×D4311yescharacteristic, complemented
674#386—434no—
675#386—434no—
676#386—434no—
677#386—434no—
678#386—434no—
679#386—434no—
680#386—434no—
681#386C2×D4314yescomplemented
682C4×C22⋊C4—431no—
683C4×C22⋊C4—432no—
684C4×C22⋊C4—431no—
685C4×C22⋊C4—431no—
686C4×C22⋊C4—432no—
687C4×C22⋊C4C2×D4311yescharacteristic, complemented
688C2×#95—434no—
689C2×#95—432no—
690C43C2×#243111yescharacteristic, complemented, Sylow
691C25—431no—
692C25—432no—
693C25—432no—
694C2×#41—24no—
695C2×#41—24no—
696C2×#41—24no—
697C2×#41—868no—
698C2×#41—868no—
699C2×#41—864no—
700C2×#41—868no—
701C2×#41—864no—
702C2×#41—868no—
703C2×#41—864no—
704C2×#41—864no—
705C2×#41—868no—
706C2×#41—868no—
707C2×#41—864no—
708C2×#41—864no—
709C2×#41—86128no—
710C2×#41—864no—
711C2×#41—864no—
712C2×#41—864no—
713C22×Q8—438no—
714C22×Q8—432no—
715C22×Q8—431no—
716C22×Q8—864no—
717C22×Q8—864no—
718C22×Q8C22×D4311yescharacteristic
719C22×D4—432no—
720C22×D4—438no—
721C22×D4—432no—
722C22×D4—432no—
723C22×D4—432no—
724C22×D4—434no—
725C22×D4—434no—
726C22×D4—432no—
727C22×D4—432no—
728C22×D4—431no—
729C22×D4—431no—
730C22×D4—432no—
731C22×D4—434no—
732C22×D4—432no—
733C22×D4—864no—
734C22×D4—864no—
735C22×D4—868no—
736C22×D4—864no—
737C22×D4—864no—
738C22×D4—864no—
739C22×D4—8616no—
740C22×D4—868no—
741C22×D4—868no—
742C22×D4—868no—
743C22×D4—8616no—
744C22×D4—1728no—
745C22×D4—1728no—
746C22×D4C22×D4311yescharacteristic
747C22×D4C22×D4312yes—
748C22×D4C22×D4314yes—
749C22×D4C22×D4311yescharacteristic
750C22×D4C22×D4312yes—
751C23×C4—431no—
752C23×C4—431no—
753C23×C4—438no—
754C23×C4—431no—
755C23×C4—432no—
756C23×C4—432no—
757C23×C4—431no—
758C23×C4—431no—
759C23×C4—432no—
760C23×C4—432no—
761C23×C4—432no—
762C23×C4—432no—
763C23×C4—432no—
764C23×C4—864no—
765C23×C4—864no—
766C23×C4—868no—
767C23×C4—868no—
768C23×C4—868no—
769C23×C4C22×D4312yes—
770C23×C4C22×D4311yescharacteristic
771#127—24no—
772#127—864no—
773#127—8616no—
774#127—864no—
775#127—864no—
776#124—24no—
777#124—864no—
778#124—8616no—
779#124—864no—
780#124—864no—
781#121—24no—
782#121—868no—
783#121—864no—
784#121—864no—
785#121—868no—
786#121—864no—
787C2×C4⋊C4—432no—
788C2×C4⋊C4—431no—
789C2×C4⋊C4—864no—
790C2×C4⋊C4C22×D4311yescharacteristic
791C2×C22⋊C4—432no—
792C2×C22⋊C4—434no—
793C2×C22⋊C4—432no—
794C2×C22⋊C4—432no—
795C2×C22⋊C4—432no—
796C2×C22⋊C4—434no—
797C2×C22⋊C4—434no—
798C2×C22⋊C4—432no—
799C2×C22⋊C4—432no—
800C2×C22⋊C4—434no—
801C2×C22⋊C4—434no—
802C2×C22⋊C4—434no—
803C2×C22⋊C4—868no—
804C2×C22⋊C4—8616no—
805C2×C22⋊C4—868no—
806C2×C22⋊C4—1728no—
807C2×C22⋊C4C22×D4312yes—
808C2×C22⋊C4C22×D4314yes—
809C2×C22⋊C4C22×D4312yes—
810C2×C22⋊C4C22×D4314yes—
811C2×C42—432no—
812C2×C42—431no—
813C2×C42—432no—
814C2×C42—431no—
815C2×C42—864no—
816C2×C42—864no—
817C2×C42C22×D4311yescharacteristic
818C2×C42C22×D4311yescharacteristic
819#95—432no—
820#95—432no—
821#95—432no—
822#95—434no—
823#95—434no—
824#95—434no—
825#95C22×D4312yes—
826#95C22×D4314yes—
827C24—431no—
828C24—434no—
829C24—438no—
830C24—431no—
831C24—432no—
832C24—432no—
833C24—864no—
834C24—868no—
835C24—862no—
836C24—864no—
837C24—864no—
838C24—862no—
839C24—868no—
840C24—864no—
841C24—864no—
842C24—864no—
843C24—864no—
844C24—868no—
845C24—868no—
846C24C23×D4312yes—
847C24C23×D4311yescharacteristic
848C24C23×D4312yes—
849#41—232no—
850#41—8664no—
851#41—8632no—
852#41—8664no—
853#41—8632no—
854#41—8632no—
855C2×Q8—22no—
856C2×Q8—22no—
857C2×Q8—438no—
858C2×Q8—434no—
859C2×Q8—864no—
860C2×Q8—864no—
861C2×Q8—8632no—
862C2×Q8—862no—
863C2×Q8—862no—
864C2×Q8D4×D4314yescomplemented
865C2×D4—24no—
866C2×D4—24no—
867C2×D4—24no—
868C2×D4—28no—
869C2×D4—24no—
870C2×D4—22no—
871C2×D4—22no—
872C2×D4—22no—
873C2×D4—22no—
874C2×D4—22no—
875C2×D4—28no—
876C2×D4—44no—
877C2×D4—44no—
878C2×D4—438no—
879C2×D4—434no—
880C2×D4—864no—
881C2×D4—864no—
882C2×D4—864no—
883C2×D4—868no—
884C2×D4—8632no—
885C2×D4—864no—
886C2×D4—864no—
887C2×D4—864no—
888C2×D4—864no—
889C2×D4—864no—
890C2×D4—864no—
891C2×D4—864no—
892C2×D4—868no—
893C2×D4—868no—
894C2×D4—8664no—
895C2×D4—864no—
896C2×D4—864no—
897C2×D4—864no—
898C2×D4—864no—
899C2×D4—864no—
900C2×D4—868no—
901C2×D4—864no—
902C2×D4—868no—
903C2×D4—864no—
904C2×D4—862no—
905C2×D4—862no—
906C2×D4—862no—
907C2×D4—862no—
908C2×D4—862no—
909C2×D4—868no—
910C2×D4—1724no—
911C2×D4—1724no—
912C2×D4—17216no—
913C2×D4—17264no—
914C2×D4—1724no—
915C2×D4—1724no—
916C2×D4—1724no—
917C2×D4—1724no—
918C2×D4—17232no—
919C2×D4D4×D4314yescomplemented
920C22×C4—24no—
921C22×C4—24no—
922C22×C4—24no—
923C22×C4—22no—
924C22×C4—22no—
925C22×C4—431no—
926C22×C4—434no—
927C22×C4—434no—
928C22×C4—434no—
929C22×C4—434no—
930C22×C4—432no—
931C22×C4—431no—
932C22×C4—432no—
933C22×C4—434no—
934C22×C4—438no—
935C22×C4—434no—
936C22×C4—434no—
937C22×C4—438no—
938C22×C4—432no—
939C22×C4—432no—
940C22×C4—862no—
941C22×C4—862no—
942C22×C4—864no—
943C22×C4—864no—
944C22×C4—8632no—
945C22×C4—864no—
946C22×C4—862no—
947C22×C4—862no—
948C22×C4—864no—
949C22×C4—864no—
950C22×C4—864no—
951C22×C4—864no—
952C22×C4—864no—
953C22×C4—8664no—
954C22×C4—864no—
955C22×C4—864no—
956C22×C4—864no—
957C22×C4—864no—
958C22×C4—868no—
959C22×C4—862no—
960C22×C4—862no—
961C22×C4—864no—
962C22×C4—864no—
963C22×C4—864no—
964C22×C4—864no—
965C22×C4—864no—
966C22×C4—862no—
967C22×C4—862no—
968C22×C4D4×D4314yescomplemented
969C22×C4C23×D4312yes—
970C22×C4C23×D4312yes—
971C22×C4C23×D4311yescharacteristic
972C22×C4C23×D4312yes—
973C22×C4C23×D4312yes—
974C22×C4C23×D4311yescharacteristic
975C4⋊C4—22no—
976C4⋊C4—864no—
977C4⋊C4—862no—
978C22⋊C4—24no—
979C22⋊C4—28no—
980C22⋊C4—24no—
981C22⋊C4—44no—
982C22⋊C4—864no—
983C22⋊C4—868no—
984C22⋊C4—864no—
985C22⋊C4—864no—
986C22⋊C4—868no—
987C22⋊C4—864no—
988C22⋊C4—864no—
989C22⋊C4—868no—
990C22⋊C4—864no—
991C22⋊C4—1724no—
992C22⋊C4—1724no—
993C22⋊C4—1724no—
994C42—22no—
995C42—22no—
996C42—864no—
997C42—864no—
998C42—862no—
999C42—862no—
1000C23—21no—
1001C23—22no—
1002C23—21no—
1003C23—22no—
1004C23—22no—
1005C23—24no—
1006C23—24no—
1007C23—22no—
1008C23—22no—
1009C23—22no—
1010C23—22no—
1011C23—24no—
1012C23—24no—
1013C23—432no—
1014C23—432no—
1015C23—432no—
1016C23—434no—
1017C23—434no—
1018C23—432no—
1019C23—434no—
1020C23—868no—
1021C23—8616no—
1022C23—868no—
1023C23—8632no—
1024C23—868no—
1025C23—861no—
1026C23—861no—
1027C23—862no—
1028C23—862no—
1029C23—862no—
1030C23—864no—
1031C23—864no—
1032C23—862no—
1033C23—862no—
1034C23—862no—
1035C23—862no—
1036C23—864no—
1037C23—864no—
1038C23—17216no—
1039C23—1728no—
1040C23—1728no—
1041C23—17216no—
1042C23—1728no—
1043C23—1728no—
1044C23—1728no—
1045C23—17216no—
1046C23—1728no—
1047C23—1728no—
1048C23C2×D4×D4314yes—
1049C23C2×D4×D4312yes—
1050C23C24×D4311yescharacteristic
1051Q8—28no—
1052Q8—8616no—
1053Q8—868no—
1054D4—216no—
1055D4—28no—
1056D4—416no—
1057D4—48no—
1058D4—44no—
1059D4—8616no—
1060D4—8616no—
1061D4—8616no—
1062D4—8616no—
1063D4—868no—
1064D4—17216no—
1065D4—1728no—
1066D4—1728no—
1067D4—17216no—
1068D4—17216no—
1069D4—1728no—
1070D4—1728no—
1071D4—1724no—
1072C2×C4—216no—
1073C2×C4—22no—
1074C2×C4—21no—
1075C2×C4—21no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—28no—
1080C2×C4—22no—
1081C2×C4—22no—
1082C2×C4—22no—
1083C2×C4—22no—
1084C2×C4—24no—
1085C2×C4—432no—
1086C2×C4—432no—
1087C2×C4—432no—
1088C2×C4—4316no—
1089C2×C4—432no—
1090C2×C4—434no—
1091C2×C4—434no—
1092C2×C4—868no—
1093C2×C4—868no—
1094C2×C4—8616no—
1095C2×C4—8616no—
1096C2×C4—8616no—
1097C2×C4—8616no—
1098C2×C4—868no—
1099C2×C4—8616no—
1100C2×C4—862no—
1101C2×C4—861no—
1102C2×C4—861no—
1103C2×C4—862no—
1104C2×C4—862no—
1105C2×C4—862no—
1106C2×C4—868no—
1107C2×C4—862no—
1108C2×C4—862no—
1109C2×C4—862no—
1110C2×C4—862no—
1111C2×C4—864no—
1112C2×C4—1728no—
1113C2×C4—1728no—
1114C2×C4C2×D4×D4312yes—
1115C2×C4C2×D4×D4314yes—
1116C2×C4C2×D4×D4312yes—
1117C2×C4C2×D4×D4312yes—
1118C2×C4C2×D4×D4312yes—
1119C2×C4#41×D4314yescomplemented
1120C22—28no—
1121C22—24no—
1122C22—22no—
1123C22—22no—
1124C22—22no—
1125C22—42no—
1126C22—42no—
1127C22—44no—
1128C22—42no—
1129C22—42no—
1130C22—44no—
1131C22—42no—
1132C22—44no—
1133C22—42no—
1134C22—42no—
1135C22—438no—
1136C22—434no—
1137C22—438no—
1138C22—434no—
1139C22—434no—
1140C22—868no—
1141C22—862no—
1142C22—864no—
1143C22—862no—
1144C22—862no—
1145C22—34416no—
1146C22—17216no—
1147C22—17232no—
1148C22—1724no—
1149C22—1722no—
1150C22—1724no—
1151C22—1722no—
1152C22—1722no—
1153C22—1722no—
1154C22—1722no—
1155C22—1724no—
1156C22—1722no—
1157C22—1722no—
1158C22C22×D4×D4311yescharacteristic
1159C22C22×D4×D4311yescharacteristic
1160C22C22×D4×D4311yescharacteristic
1161C22C2×#41×D4312yes—
1162C22H(5,𝔽2)×D4312yes—
1163C4—24no—
1164C4—22no—
1165C4—24no—
1166C4—42no—
1167C4—42no—
1168C4—434no—
1169C4—864no—
1170C4—862no—
1171C4—864no—
1172C4—1722no—
1173C4—1722no—
1174C4#120×D4314yes—
1175C2—44no—
1176C2—42no—
1177C2—82no—
1178C2—438no—
1179C2—3442no—
1180C2—1724no—
1181C2—1722no—
1182C2C2×#120×D4311yescharacteristic
1183C2#532×D4311yescharacteristic
1184C2#535×D4311yescharacteristic
1185C2#546×D4312yes—
1186C2#550×D4312yes—
subgroupG/H
center, FrattiniC23C24×D43
commutator, socle, cosocleC23×C43C25
FittingC43×#2431C2
hypercenter#2431D43
hypocenterC43C2×#2431
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #2431

Complements

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

NH ≅ G/Ntype
1. C22×#41×D43C2semidirect
2. C2×#127×D43C2semidirect
3. C2×#124×D43C2semidirect
4. C2×#121×D43C2semidirect
5. #19138217C2semidirect
6. #19138216C2semidirect
7. #19138215C2semidirect
8. #19138214C2semidirect
9. #19138213C2semidirect
10. #19138212C2semidirect
11. #19138211C2semidirect
12. #19138210C2semidirect
13. #19138209C2semidirect
14. #392×D43C2semidirect
15. #391×D43C2semidirect
16. #390×D43C2semidirect
17. #386×D43C2semidirect
18. C4×C22⋊C4×D43C2semidirect
19. C43×#2431C2semidirect
20. C22×#10621902C22semidirect
21. C22×#10621898C22semidirect
22. C22×#10621898C22semidirect
23. C22×#10621900C22semidirect
24. C22×#10621900C22semidirect
36. C2×#13063322C22semidirect
37. C2×#13063321C22semidirect
38. C2×#13063321C22semidirect
39. C2×#13063321C22semidirect
41. C2×#13063314C22semidirect
42. C2×#13063313C22semidirect
43. C2×#13063312C22semidirect
44. C2×#13063311C22semidirect
46. C2×#13063300C22semidirect
47. C2×#13063299C22semidirect
48. C2×#13063298C22semidirect
49. C2×#13063297C22semidirect
50. C2×#13063296C22semidirect
59. #14582809C22semidirect
60. #14582808C22semidirect
61. #14582808C22semidirect
62. #14582808C22semidirect
63. #14582807C22semidirect
64. #14582807C22semidirect
65. #14582807C22semidirect
66. #14582806C22semidirect
67. #14582805C22semidirect
68. #14582804C22semidirect
69. #14582803C22semidirect
70. #14582802C22semidirect
71. #14582801C22semidirect
72. #14582800C22semidirect
73. #14582799C22semidirect
74. #14582779C22semidirect
75. #14582778C22semidirect
76. #14582777C22semidirect
77. #14582777C22semidirect
78. #14582776C22semidirect
79. #14582775C22semidirect
80. #14582775C22semidirect
81. C22⋊C4×Dic43C22semidirect
82. C4×(C2×D43)⋊C4C22semidirect
83. C4×(C2×D43)⋊C4C22semidirect
84. C4×C22⋊Dic43C22semidirect
85. #14582746C22semidirect
88. C22×#41×C43C22semidirect
89. C2×#127×C43C22semidirect
90. C2×#124×C43C22semidirect
91. C2×#121×C43C22semidirect
92. C43×#392C22semidirect
93. C43×#391C22semidirect
94. C43×#390C22semidirect
95. C43×#386C22semidirect
96. C4×C22⋊C4×C43C22semidirect
120. C2×Q8×D43D4semidirect
147. C2×D4×D43D4semidirect
155. C22×C4×D43D4semidirect
258. C2×Q8×C43C2×D4semidirect
272. C2×D4×C43C2×D4semidirect
278. C22×C4×C43C2×D4semidirect
306. C2×C22⋊D43C2×D4semidirect
312. C22×Dic43C2×D4semidirect
343. C2×D172C2×D4semidirect
372. C2×C4×D43C2×D4semidirect
373. C2×C4×D43C2×D4semidirect
374. C2×C4×D43#41semidirect
379. C2×Dic86C2×D4semidirect
380. C2×Dic86C2×D4semidirect
481. C2×C4×C43C2×#41semidirect
508. C2×Dic43C2×#41semidirect
595. #2431D43direct (N × H)
612. D43#2431direct (N × H)
621. C22×#41C2×D43semidirect
635. C2×#127C2×D43semidirect
641. C2×#124C2×D43semidirect
648. C2×#121C2×D43semidirect
663. #392C2×D43semidirect
668. #391C2×D43semidirect
673. #390C2×D43semidirect
681. #386C2×D43semidirect
687. C4×C22⋊C4C2×D43semidirect
690. C43C2×#2431semidirect
864. C2×Q8D4×D43semidirect
919. C2×D4D4×D43semidirect
968. C22×C4D4×D43semidirect
1119. C2×C4#41×D43semidirect

Maximal subgroups

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

subgroupindex
C22×#41×D432
C2×#127×D432
C2×#124×D432
C2×#121×D432
#191382172
#191382162
#191382152
#191382142
#191382132
#191382122
#191382112
#191382102
#191382092
#392×D432
#391×D432
#390×D432
#386×D432
C4×C22⋊C4×D432
C43×#24312
C2×#243143