Finite Group Databasebeta

← #25133849

Subgroups — #25133849

Order 11008.

1508 conjugacy classes of subgroups.

The subgroup lattice has 954 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583150C211yesmaximal, characteristic, complemented
2C2×#14583130C211yesmaximal, characteristic, complemented
3C2×#14583044C211yesmaximal, characteristic, complemented
4C2×#14582866C211yesmaximal, characteristic, complemented
5#19140319C211yesmaximal, characteristic, complemented
6#19135788C211yesmaximal, characteristic, complemented
7#19135781C211yesmaximal, characteristic, complemented
8#19135596C211yesmaximal, characteristic, complemented
9#19135591C211yesmaximal, characteristic, complemented
10#19135029C211yesmaximal, characteristic, complemented
11#19135024C211yesmaximal, characteristic, complemented
12#19134912C211yesmaximal, characteristic, complemented
13#19134788C211yesmaximal, characteristic, complemented
14#19134535C211yesmaximal, characteristic, complemented
15C2×C43×#537C211yesmaximal, characteristic, complemented
16C22×#10621884C2211yescharacteristic
17C22×#10621882C2211yescharacteristic
18C22×#10621877C2211yescharacteristic
19C23×C43⋊C8C2211yescharacteristic
20C2×#13063299C2211yescharacteristic
21C2×#13063299C2211yescharacteristic
22C2×#13063299C2211yescharacteristic
23#14583150—24no—
24#14583130—24no—
25#14583044—24no—
26C2×#13063256C2211yescharacteristic
27C2×#13063256C2211yescharacteristic
28C2×#13063249C2211yescharacteristic
29C2×#13063249C2211yescharacteristic
30C2×#13063249C2211yescharacteristic
31C2×#13063246C2211yescharacteristic
32C2×#13063246C2211yescharacteristic
33C2×#13063246C2211yescharacteristic
34C2×#13063245C2211yescharacteristic
35C2×#13063245C2211yescharacteristic
36#14582866—24no—
37C2×C22⋊(C43⋊C8)C2211yescharacteristic
38C2×C22⋊(C43⋊C8)C2211yescharacteristic
39C2×C22⋊(C43⋊C8)C2211yescharacteristic
40C2×C22⋊(C43⋊C8)C2211yescharacteristic
41#14582810—21no—
42#14582807—21no—
43#14582807—21no—
44#14582807—21no—
45#14582759C2211yescharacteristic
46#14582759C2211yescharacteristic
47#14582759C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52C22×#41×C43C2211yescharacteristic
53C22×#41×C43C2211yescharacteristic
54C43×#537—24no—
55C43×#537—24no—
56C2×C22⋊Q8×C43—21no—
57C2×C22⋊Q8×C43C2211yescharacteristic
58C2×C22⋊Q8×C43C2211yescharacteristic
59C2×#121×C43—21no—
60C2×#121×C43—21no—
61C2×#121×C43—21no—
62C2×#121×C43C2211yescharacteristic
63C2×#121×C43C2211yescharacteristic
64C22×C4⋊C4×C43C2211yescharacteristic
65C22×D172C2311yescharacteristic
66C22×C22⋊D43—21no—
67C22×C22⋊D43—21no—
68C22×C22⋊D43—21no—
69C2×#10621884—22no—
70C2×#10621884—22no—
71C2×#10621884—41no—
72C2×#10621882—22no—
73C2×#10621882—22no—
74C2×#10621882—41no—
75C2×#10621877—22no—
76C2×#10621877—22no—
77C2×#10621877—41no—
78C22×C43⋊C8—22no—
79C22×C43⋊C8—22no—
80C22×C43⋊C8—41no—
81C22×C43⋊C8C2311yescharacteristic
82C22×C43⋊C8C2311yescharacteristic
83C22×C43⋊C8C2311yescharacteristic
84C22×C43⋊C8C2311yescharacteristic
85#13063299—22no—
86#13063299—22no—
87#13063299—22no—
88#13063299—22no—
89#13063299—41no—
90#13063299—41no—
91C2×C4⋊Dic43C2311yescharacteristic
92C2×C4⋊Dic43C2311yescharacteristic
93C2×C4⋊Dic43C2311yescharacteristic
94C2×C22⋊Dic43—21no—
95C2×C22⋊Dic43—21no—
96C2×C22⋊Dic43—21no—
97C2×(C2×D43)⋊C4—21no—
98C2×(C2×D43)⋊C4—21no—
99C2×(C2×D43)⋊C4—21no—
100#13063256—22no—
101#13063256—22no—
102#13063249—22no—
103#13063249—22no—
104#13063249—41no—
105#13063246—22no—
106#13063246—22no—
107#13063246—41no—
108#13063245—22no—
109#13063245—22no—
110C22⋊(C43⋊C8)—22no—
111C22⋊(C43⋊C8)—22no—
112C22⋊(C43⋊C8)—22no—
113C22⋊(C43⋊C8)D414yescomplemented
114C43⋊#95—21no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C2×#41×C43—22no—
118C2×#41×C43—22no—
119C2×#41×C43—22no—
120C2×#41×C43—22no—
121C2×#41×C43—22no—
122C2×#41×C43—22no—
123C2×#41×C43—22no—
124C2×#41×C43—22no—
125C2×#41×C43—41no—
126C2×#41×C43—41no—
127C2×#41×C43—41no—
128C2×#41×C43—41no—
129C22×Q8×C43D411yescharacteristic
130C22×Q8×C43C2311yescharacteristic
131C22×D4×C43—21no—
132C22×D4×C43—21no—
133C22×D4×C43—21no—
134C22×D4×C43D411yescharacteristic
135C22×D4×C43D411yescharacteristic
136C22×D4×C43D411yescharacteristic
137C22×D4×C43C2311yescharacteristic
138C23×C4×C43—21no—
139C23×C4×C43—21no—
140C23×C4×C43C2311yescharacteristic
141C23×C4×C43C2311yescharacteristic
142C23×C4×C43C2311yescharacteristic
143C22⋊Q8×C43—28no—
144C22⋊Q8×C43—22no—
145C22⋊Q8×C43—22no—
146C22⋊Q8×C43—22no—
147C22⋊Q8×C43D414yescomplemented
148#121×C43—28no—
149#121×C43—28no—
150#121×C43—28no—
151#121×C43—22no—
152#121×C43—22no—
153#121×C43—22no—
154#121×C43D414yescomplemented
155C2×C4⋊C4×C43—21no—
156C2×C4⋊C4×C43—21no—
157C2×C4⋊C4×C43—21no—
158C2×C4⋊C4×C43—22no—
159C2×C4⋊C4×C43—22no—
160C2×C4⋊C4×C43C2311yescharacteristic
161C2×C4⋊C4×C43C2311yescharacteristic
162C2×C22⋊C4×C43—21no—
163C2×C22⋊C4×C43—21no—
164C2×C22⋊C4×C43—21no—
165C2×C22⋊C4×C43—21no—
166C24×C43—21no—
167C24×C43C2×D411yescharacteristic
168C24×C43C2×D411yescharacteristic
169C24×C43C2×D411yescharacteristic
170C23×D43—21no—
171#41×C43—44no—
172#41×C43—44no—
173#41×C43—44no—
174#41×C43—44no—
175#41×C43—44no—
176#41×C43—44no—
177#41×C43—44no—
178#41×C43—44no—
179C2×Q8×C43—22no—
180C2×Q8×C43—22no—
181C2×Q8×C43—21no—
182C2×Q8×C43—21no—
183C2×Q8×C43—21no—
184C2×Q8×C43—21no—
185C2×Q8×C43—21no—
186C2×Q8×C43—41no—
187C2×Q8×C43C2×D412yes—
188C2×D4×C43—24no—
189C2×D4×C43—24no—
190C2×D4×C43—22no—
191C2×D4×C43—22no—
192C2×D4×C43—21no—
193C2×D4×C43—22no—
194C2×D4×C43—22no—
195C2×D4×C43—24no—
196C2×D4×C43—22no—
197C2×D4×C43—22no—
198C2×D4×C43—21no—
199C2×D4×C43—21no—
200C2×D4×C43—21no—
201C2×D4×C43—21no—
202C2×D4×C43—41no—
203C2×D4×C43—41no—
204C2×D4×C43—41no—
205C2×D4×C43—42no—
206C2×D4×C43—42no—
207C2×D4×C43—81no—
208C2×D4×C43—81no—
209C2×D4×C43—81no—
210C2×D4×C43—81no—
211C2×D4×C43C2×D412yes—
212C22×C4×C43—21no—
213C22×C4×C43—21no—
214C22×C4×C43—21no—
215C22×C4×C43—21no—
216C22×C4×C43—21no—
217C22×C4×C43—21no—
218C22×C4×C43—21no—
219C22×C4×C43—21no—
220C22×C4×C43—24no—
221C22×C4×C43—24no—
222C22×C4×C43—21no—
223C22×C4×C43—21no—
224C22×C4×C43—21no—
225C22×C4×C43—21no—
226C22×C4×C43—21no—
227C22×C4×C43—21no—
228C22×C4×C43—21no—
229C22×C4×C43—21no—
230C22×C4×C43—21no—
231C22×C4×C43—42no—
232C22×C4×C43—42no—
233C22×C4×C43—81no—
234C22×C4×C43—81no—
235C22×C4×C43C2×D412yes—
236C22×C4×C43C2×D412yes—
237C22×C4×C43C2×D412yes—
238C22×C4×C43C2×D411yescharacteristic
239C22×C4×C43C2×D411yescharacteristic
240C22×C4×C43C2×D411yescharacteristic
241C22×C4×C43#4112yes—
242C22×C4×C43C2411yescharacteristic
243C2×C22⋊D43—42no—
244C2×C22⋊D43—42no—
245C2×C22⋊D43—42no—
246C2×C22⋊D43—81no—
247C2×C22⋊D43—81no—
248C2×C22⋊D43—81no—
249C2×C22⋊D43—81no—
250C2×C22⋊D43—81no—
251C2×C22⋊D43—81no—
252C22×Dic43—21no—
253C22×Dic43—21no—
254C22×Dic43—21no—
255C2×D172—21no—
256C2×D172—21no—
257C2×D172—21no—
258C2×D172—21no—
259C2×D172—21no—
260C2×D172—21no—
261C4⋊C4×C43—24no—
262C4⋊C4×C43—24no—
263C4⋊C4×C43—24no—
264C4⋊C4×C43—21no—
265C4⋊C4×C43—21no—
266C4⋊C4×C43C2×D412yes—
267C4⋊C4×C43C2×D412yes—
268C22⋊C4×C43—24no—
269C22⋊C4×C43—24no—
270C22⋊C4×C43—24no—
271C22⋊C4×C43—24no—
272C22⋊Dic43—81no—
273C22⋊Dic43—81no—
274C22⋊Dic43—81no—
275#10621884—44no—
276#10621882—44no—
277(C2×D43)⋊C4—42no—
278(C2×D43)⋊C4—42no—
279(C2×D43)⋊C4—42no—
280C4⋊Dic43—21no—
281C4⋊Dic43—21no—
282C4⋊Dic43—21no—
283C4⋊Dic43—21no—
284C4⋊Dic43—21no—
285C4⋊Dic43—21no—
286#10621877—44no—
287C2×C43⋊C8—21no—
288C2×C43⋊C8—21no—
289C2×C43⋊C8—21no—
290C2×C43⋊C8—21no—
291C2×C43⋊C8—21no—
292C2×C43⋊C8—21no—
293C2×C43⋊C8—21no—
294C2×C43⋊C8—21no—
295C2×C43⋊C8—21no—
296C2×C43⋊C8—21no—
297C2×C43⋊C8—44no—
298C2×C43⋊C8C2×D412yes—
299C2×C43⋊C8C2×D412yes—
300C23×C43—21no—
301C23×C43—21no—
302C23×C43—21no—
303C23×C43—21no—
304C23×C43—21no—
305C23×C43—21no—
306C23×C43—21no—
307C23×C43—21no—
308C23×C43—21no—
309C23×C43—21no—
310C23×C43—21no—
311C23×C43—21no—
312C23×C43—21no—
313C23×C43—22no—
314C23×C43—21no—
315C23×C43—21no—
316C23×C43—21no—
317C23×C43—21no—
318C23×C43—21no—
319C23×C43—21no—
320C23×C43—41no—
321C23×C43—41no—
322C23×C43—41no—
323C23×C43—41no—
324C23×C43—41no—
325C23×C43—41no—
326C23×C43#12012yes—
327C23×C43#12112yes—
328C23×C43C22×D411yescharacteristic
329C22×D43—41no—
330C22×D43—41no—
331C22×D43—41no—
332C22×D43—41no—
333C22×D43—41no—
334C22×D43—41no—
335C22×D43—41no—
336Q8×C43—22no—
337Q8×C43—22no—
338Q8×C43—44no—
339Q8×C43—41no—
340Q8×C43—41no—
341D4×C43—22no—
342D4×C43—22no—
343D4×C43—44no—
344D4×C43—44no—
345D4×C43—44no—
346D4×C43—48no—
347D4×C43—41no—
348D4×C43—41no—
349D4×C43—84no—
350D4×C43—84no—
351C2×C4×C43—21no—
352C2×C4×C43—21no—
353C2×C4×C43—21no—
354C2×C4×C43—21no—
355C2×C4×C43—22no—
356C2×C4×C43—22no—
357C2×C4×C43—22no—
358C2×C4×C43—22no—
359C2×C4×C43—22no—
360C2×C4×C43—22no—
361C2×C4×C43—22no—
362C2×C4×C43—22no—
363C2×C4×C43—22no—
364C2×C4×C43—22no—
365C2×C4×C43—22no—
366C2×C4×C43—21no—
367C2×C4×C43—21no—
368C2×C4×C43—21no—
369C2×C4×C43—48no—
370C2×C4×C43—41no—
371C2×C4×C43—41no—
372C2×C4×C43—41no—
373C2×C4×C43—41no—
374C2×C4×C43—41no—
375C2×C4×C43—41no—
376C2×C4×C43—41no—
377C2×C4×C43—41no—
378C2×C4×C43—41no—
379C2×C4×C43—41no—
380C2×C4×C43—84no—
381C2×C4×C43#12012yes—
382C2×C4×C43#12112yes—
383C2×C4×C43C22×D411yescharacteristic
384C2×C4×C43C22×D411yescharacteristic
385C2×C4×C43C22×D411yescharacteristic
386C2×C4×C43C2×#4111yescharacteristic
387C2×C4×C43H(5,𝔽2)11yescharacteristic
388C2×C4×C43H(5,𝔽2)11yescharacteristic
389C22⋊D43—84no—
390C22⋊D43—84no—
391C22⋊D43—84no—
392C2×Dic43—41no—
393C2×Dic43—41no—
394C2×Dic43—41no—
395C2×Dic43—41no—
396C2×Dic43—41no—
397C2×Dic43—41no—
398C2×Dic43—41no—
399C2×Dic43—41no—
400C2×Dic43—41no—
401D172—41no—
402D172—41no—
403D172—41no—
404D172—41no—
405C43⋊C8—22no—
406C43⋊C8—22no—
407C43⋊C8—41no—
408C43⋊C8—41no—
409#24397—431nomaximal, Sylow
410C22×C43—22no—
411C22×C43—22no—
412C22×C43—22no—
413C22×C43—22no—
414C22×C43—22no—
415C22×C43—22no—
416C22×C43—41no—
417C22×C43—41no—
418C22×C43—41no—
419C22×C43—41no—
420C22×C43—41no—
421C22×C43—41no—
422C22×C43—41no—
423C22×C43—41no—
424C22×C43—41no—
425C22×C43—42no—
426C22×C43—41no—
427C22×C43—41no—
428C22×C43—41no—
429C22×C43—42no—
430C22×C43—41no—
431C22×C43—42no—
432C22×C43—41no—
433C22×C43—41no—
434C22×C43—81no—
435C22×C43—81no—
436C22×C43—81no—
437C22×C43—81no—
438C22×C43C2×#12011yescharacteristic
439C22×C43C2×#12111yescharacteristic
440C22×C43#53411yescharacteristic
441C22×C43#57611yescharacteristic
442C22×C43#57711yescharacteristic
443C22×C43#57711yescharacteristic
444C22×C43#57711yescharacteristic
445C2×D43—81no—
446C2×D43—81no—
447C2×D43—81no—
448C2×D43—81no—
449C2×D43—81no—
450C2×D43—81no—
451C2×D43—81no—
452C4×C43—22no—
453C4×C43—22no—
454C4×C43—41no—
455C4×C43—42no—
456C4×C43—42no—
457C4×C43—42no—
458C4×C43D4211yescharacteristic
459C4×C43D4211yescharacteristic
460C4×C43#54611yescharacteristic
461C4×C43#54611yescharacteristic
462Dic43—81no—
463Dic43—81no—
464Dic43—81no—
465C2×#537D4311yescharacteristic, complemented
466C2×#469—431no—
467C2×#465—431no—
468C2×#449—431no—
469C2×#408—431no—
470#2615—431no—
471#2035—431no—
472#2034—431no—
473#2000—431no—
474#1999—431no—
475#1894—431no—
476#1893—431no—
477#1874—431no—
478#1853—431no—
479#1788—431no—
480C2×C43—42no—
481C2×C43—42no—
482C2×C43—81no—
483C2×C43—82no—
484C2×C43#241011yescharacteristic
485C2×C43#301011yescharacteristic
486C2×C43#301211yescharacteristic
487C2×C43#306011yescharacteristic
488C2×C43#306211yescharacteristic
489C2×C43#319811yescharacteristic
490C2×C43#320411yescharacteristic
491D43—161no—
492C22×#41C2×D4311yescharacteristic
493C22×#41C2×D4311yescharacteristic
494C22×SD16—431no—
495C22×D8—431no—
496C22×M16—431no—
497C23×C8—431no—
498#537—24no—
499#537—24no—
500C2×C22⋊Q8—21no—
501C2×C22⋊Q8C2×D4311yescharacteristic
502C2×C22⋊Q8C2×D4311yescharacteristic
503C2×#121—21no—
504C2×#121—21no—
505C2×#121—21no—
506C2×#121—431no—
507C2×#121—431no—
508C2×#121—431no—
509C2×#121C2×D4311yescharacteristic
510C2×#121C2×D4311yescharacteristic
511C22×C4⋊C4C2×D4311yescharacteristic
512#469—864no—
513#465—864no—
514#449—864no—
515C2×#106—431no—
516C2×#106—431no—
517C2×#103—431no—
518C2×#103—431no—
519C2×#103—431no—
520C2×#102—431no—
521C2×#102—431no—
522C2×#102—431no—
523C2×#102—431no—
524C2×#102—431no—
525#408—864no—
526C2×C22⋊C8—431no—
527C2×C22⋊C8—431no—
528C2×C22⋊C8—431no—
529C2×C22⋊C8—431no—
530#393—861no—
531#392—861no—
532#392—861no—
533#392—861no—
534#380—431no—
535#380—431no—
536#380—431no—
537#340—431no—
538#340—431no—
539#340—431no—
540#340—431no—
541C43#2439711yescharacteristic, complemented, Sylow
542C2×#41—22no—
543C2×#41—22no—
544C2×#41—22no—
545C2×#41—22no—
546C2×#41—22no—
547C2×#41—22no—
548C2×#41—22no—
549C2×#41—22no—
550C2×#41—41no—
551C2×#41—41no—
552C2×#41—41no—
553C2×#41—41no—
554C22×Q8C22⋊D4311yescharacteristic
555C22×Q8C22×D4311yescharacteristic
556C22×D4—21no—
557C22×D4—21no—
558C22×D4—21no—
559C22×D4—431no—
560C22×D4—861no—
561C22×D4—861no—
562C22×D4—861no—
563C22×D4C22⋊D4311yescharacteristic
564C22×D4C22⋊D4311yescharacteristic
565C22×D4C22⋊D4311yescharacteristic
566C22×D4C22×D4311yescharacteristic
567C23×C4—21no—
568C23×C4—21no—
569C23×C4C22×D4311yescharacteristic
570C23×C4C22×D4311yescharacteristic
571C23×C4C22×D4311yescharacteristic
572C2×SD16—862no—
573C2×SD16—862no—
574C2×SD16—1721no—
575C2×D8—862no—
576C2×D8—862no—
577C2×D8—1721no—
578C2×M16—862no—
579C2×M16—862no—
580C2×M16—1721no—
581C22×C8—431no—
582C22×C8—431no—
583C22×C8—431no—
584C22×C8—431no—
585C22×C8—862no—
586C22×C8—862no—
587C22×C8—1721no—
588C22⋊Q8—28no—
589C22⋊Q8—22no—
590C22⋊Q8—22no—
591C22⋊Q8—22no—
592C22⋊Q8C22⋊D4314yescomplemented
593#121—28no—
594#121—28no—
595#121—28no—
596#121—22no—
597#121—22no—
598#121—22no—
599#121—862no—
600#121—862no—
601#121—862no—
602#121—862no—
603#121—1721no—
604#121—1721no—
605#121C22⋊D4314yescomplemented
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—22no—
610C2×C4⋊C4—22no—
611C2×C4⋊C4—431no—
612C2×C4⋊C4—431no—
613C2×C4⋊C4—431no—
614C2×C4⋊C4C22×D4311yescharacteristic
615C2×C4⋊C4C22×D4311yescharacteristic
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—861no—
621C2×C22⋊C4—861no—
622C2×C22⋊C4—861no—
623C2×C22⋊C4—861no—
624C2×C22⋊C4—861no—
625C2×C22⋊C4—861no—
626#106—862no—
627#106—862no—
628#103—862no—
629#103—862no—
630#103—1721no—
631#102—862no—
632#102—862no—
633#102—862no—
634#102—862no—
635#102—1721no—
636C22⋊C8—434no—
637C22⋊C8—862no—
638C22⋊C8—862no—
639C22⋊C8—862no—
640#95—861no—
641#95—861no—
642#95—861no—
643C24—21no—
644C24—861no—
645C24C2×C22⋊D4311yescharacteristic
646C24C2×C22⋊D4311yescharacteristic
647C24C2×C22⋊D4311yescharacteristic
648#41—44no—
649#41—44no—
650#41—44no—
651#41—44no—
652#41—44no—
653#41—44no—
654#41—44no—
655#41—44no—
656C2×Q8—22no—
657C2×Q8—22no—
658C2×Q8—21no—
659C2×Q8—21no—
660C2×Q8—21no—
661C2×Q8—21no—
662C2×Q8—21no—
663C2×Q8—41no—
664C2×Q8C2×C22⋊D4312yes—
665C2×D4—24no—
666C2×D4—22no—
667C2×D4—22no—
668C2×D4—22no—
669C2×D4—22no—
670C2×D4—24no—
671C2×D4—24no—
672C2×D4—22no—
673C2×D4—22no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—41no—
680C2×D4—41no—
681C2×D4—41no—
682C2×D4—42no—
683C2×D4—42no—
684C2×D4—81no—
685C2×D4—81no—
686C2×D4—81no—
687C2×D4—81no—
688C2×D4—861no—
689C2×D4—861no—
690C2×D4—861no—
691C2×D4—861no—
692C2×D4—861no—
693C2×D4—861no—
694C2×D4—3441no—
695C2×D4—3441no—
696C2×D4—3441no—
697C2×D4—3441no—
698C2×D4—3441no—
699C2×D4—3441no—
700C2×D4—1722no—
701C2×D4—1722no—
702C2×D4—1722no—
703C2×D4C2×C22⋊D4312yes—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—24no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—24no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—42no—
724C22×C4—42no—
725C22×C4—81no—
726C22×C4—81no—
727C22×C4—861no—
728C22×C4—861no—
729C22×C4—861no—
730C22×C4D4×D4312yes—
731C22×C4#1062190012yes—
732C22×C4C2×C22⋊D4311yescharacteristic
733C22×C4C2×C22⋊D4311yescharacteristic
734C22×C4C2×C22⋊D4312yes—
735C22×C4C2×C22⋊D4312yes—
736C22×C4C2×C22⋊D4311yescharacteristic
737C22×C4C23×D4311yescharacteristic
738SD16—1724no—
739D8—1724no—
740M16—1724no—
741C2×C8—432no—
742C2×C8—432no—
743C2×C8—861no—
744C2×C8—861no—
745C2×C8—861no—
746C2×C8—861no—
747C2×C8—861no—
748C2×C8—861no—
749C2×C8—861no—
750C2×C8—861no—
751C2×C8—861no—
752C2×C8—861no—
753C2×C8—1724no—
754C4⋊C4—24no—
755C4⋊C4—24no—
756C4⋊C4—24no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—861no—
760C4⋊C4—861no—
761C4⋊C4—861no—
762C4⋊C4—861no—
763C4⋊C4—861no—
764C4⋊C4—861no—
765C4⋊C4C2×C22⋊D4312yes—
766C4⋊C4C2×C22⋊D4312yes—
767C22⋊C4—24no—
768C22⋊C4—24no—
769C22⋊C4—24no—
770C22⋊C4—24no—
771C22⋊C4—3441no—
772C22⋊C4—3441no—
773C22⋊C4—3441no—
774C22⋊C4—1722no—
775C22⋊C4—1722no—
776C22⋊C4—1722no—
777C23—21no—
778C23—21no—
779C23—21no—
780C23—21no—
781C23—21no—
782C23—21no—
783C23—21no—
784C23—21no—
785C23—21no—
786C23—21no—
787C23—21no—
788C23—21no—
789C23—21no—
790C23—22no—
791C23—21no—
792C23—21no—
793C23—21no—
794C23—21no—
795C23—21no—
796C23—21no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—1721no—
804C23—1721no—
805C23—1721no—
806C23—1721no—
807C23—1721no—
808C23—1721no—
809C23—1721no—
810C23#1306329412yes—
811C23#1306329712yes—
812C23C22×C22⋊D4311yescharacteristic
813Q8—22no—
814Q8—22no—
815Q8—44no—
816Q8—41no—
817Q8—41no—
818D4—22no—
819D4—22no—
820D4—44no—
821D4—44no—
822D4—44no—
823D4—48no—
824D4—41no—
825D4—41no—
826D4—84no—
827D4—84no—
828D4—3444no—
829D4—3444no—
830D4—3444no—
831D4—1721no—
832D4—1721no—
833D4—1721no—
834D4—1721no—
835C2×C4—21no—
836C2×C4—21no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—48no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—84no—
865C2×C4—1721no—
866C2×C4—1721no—
867C2×C4—1721no—
868C2×C4—1721no—
869C2×C4—1721no—
870C2×C4—1721no—
871C2×C4—1721no—
872C2×C4—1721no—
873C2×C4—1721no—
874C2×C4#1306329412yes—
875C2×C4#1306329712yes—
876C2×C4C2×D4×D4311yescharacteristic
877C2×C4C22×C22⋊D4311yescharacteristic
878C2×C4C22×C22⋊D4311yescharacteristic
879C2×C4C2×#1062190011yescharacteristic
880C2×C4#1306337011yescharacteristic
881C2×C4#1306337011yescharacteristic
882C8—862no—
883C8—862no—
884C8—1721no—
885C8—1721no—
886C22—22no—
887C22—22no—
888C22—22no—
889C22—22no—
890C22—22no—
891C22—22no—
892C22—41no—
893C22—41no—
894C22—41no—
895C22—41no—
896C22—41no—
897C22—41no—
898C22—41no—
899C22—41no—
900C22—41no—
901C22—41no—
902C22—41no—
903C22—42no—
904C22—41no—
905C22—41no—
906C22—42no—
907C22—41no—
908C22—42no—
909C22—41no—
910C22—81no—
911C22—81no—
912C22—81no—
913C22—81no—
914C22—3441no—
915C22—3441no—
916C22—3441no—
917C22—3441no—
918C22—3441no—
919C22—3441no—
920C22—3441no—
921C22C2×#1306329411yescharacteristic
922C22C2×#1306329711yescharacteristic
923C22#1458345811yescharacteristic
924C22#1458370211yescharacteristic
925C22#1458370711yescharacteristic
926C22#1458370711yescharacteristic
927C22#1458371011yescharacteristic
928C4—22no—
929C4—22no—
930C4—41no—
931C4—42no—
932C4—42no—
933C4—42no—
934C4—3441no—
935C4—3441no—
936C4—3441no—
937C4D4×C22⋊D4311yescharacteristic
938C4D4×C22⋊D4311yescharacteristic
939C4#1458354311yescharacteristic
940C4#1458354311yescharacteristic
941C2—42no—
942C2—42no—
943C2—81no—
944C2—82no—
945C2—6881no—
946C2#1913796911yescharacteristic
947C2#1914388111yescharacteristic
948C2#1914389911yescharacteristic
949C2#1914425411yescharacteristic
950C2#1914427711yescharacteristic
951C2#1914544111yescharacteristic
952C2#1914550111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#537C2
socleC23×C43C22×D4
hypercenterC2×#537D43
hypocenterC43#24397
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×#41 ◁ C2×#537

Complements

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

NH ≅ G/Ntype
1. C2×#14583150C2semidirect
2. C2×#14583130C2semidirect
3. C2×#14583044C2semidirect
4. C2×#14582866C2semidirect
5. #19140319C2semidirect
6. #19135788C2semidirect
7. #19135781C2semidirect
8. #19135596C2semidirect
9. #19135591C2semidirect
10. #19135029C2semidirect
11. #19135024C2semidirect
12. #19134912C2semidirect
13. #19134788C2semidirect
14. #19134535C2semidirect
15. C2×C43×#537C2semidirect
113. C22⋊(C43⋊C8)D4semidirect
147. C22⋊Q8×C43D4semidirect
154. #121×C43D4semidirect
465. C2×#537D43semidirect
541. C43#24397semidirect
592. C22⋊Q8C22⋊D43semidirect
605. #121C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145831502
C2×#145831302
C2×#145830442
C2×#145828662
#191403192
#191357882
#191357812
#191355962
#191355912
#191350292
#191350242
#191349122
#191347882
#191345352
C2×C43×#5372
#2439743