Finite Group Databasebeta

← #25133834

Subgroups — #25133834

Order 11008.

1444 conjugacy classes of subgroups.

The subgroup lattice has 914 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583147C211yesmaximal, characteristic, complemented
2C2×#14583130C211yesmaximal, characteristic, complemented
3C2×#14583038C211yesmaximal, characteristic, complemented
4C2×#14582866C211yesmaximal, characteristic, complemented
5#19140319C211yesmaximal, characteristic
6#19135795C211yesmaximal, characteristic, complemented
7#19135788C211yesmaximal, characteristic, complemented
8#19135596C211yesmaximal, characteristic, complemented
9#19135596C211yesmaximal, characteristic, complemented
10#19135029C211yesmaximal, characteristic, complemented
11#19135019C211yesmaximal, characteristic, complemented
12#19134917C211yesmaximal, characteristic, complemented
13#19134794C211yesmaximal, characteristic, complemented
14#19134530C211yesmaximal, characteristic, complemented
15C2×C43×#536C211yesmaximal, characteristic, complemented
16C22×#10621884C2211yescharacteristic
17C22×#10621884C2211yescharacteristic
18C22×#10621877C2211yescharacteristic
19C23×C43⋊C8C2211yescharacteristic
20C2×#13063299C2211yescharacteristic
21C2×#13063299C2211yescharacteristic
22C2×#13063299C2211yescharacteristic
23#14583147—24no—
24#14583130—24no—
25#14583038—24no—
26C2×#13063258C2211yescharacteristic
27C2×#13063256C2211yescharacteristic
28C2×#13063249C2211yescharacteristic
29C2×#13063249C2211yescharacteristic
30C2×#13063249C2211yescharacteristic
31C2×#13063249C2211yescharacteristic
32C2×#13063249C2211yescharacteristic
33C2×#13063249C2211yescharacteristic
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
53C23×Q8×C43C2211yescharacteristic
54C43×#536—24no—
55C43×#536—24no—
56C2×C4⋊Q8×C43—21no—
57C2×#124×C43—21no—
58C2×#123×C43—21no—
59C2×#123×C43—21no—
60C2×C22⋊Q8×C43C2211yescharacteristic
61C2×C22⋊Q8×C43C2211yescharacteristic
62C2×C22⋊Q8×C43C2211yescharacteristic
63C2×C22⋊Q8×C43C2211yescharacteristic
64C2×#117×C43C2211yescharacteristic
65C22×D172C2311yescharacteristic
66C22×C22⋊D43—21no—
67C22×C22⋊D43—21no—
68C22×C22⋊D43—21no—
69C2×#10621884—22no—
70C2×#10621884—22no—
71C2×#10621884—22no—
72C2×#10621884—22no—
73C2×#10621884—41no—
74C2×#10621884—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#13063258—22no—
101#13063256—22no—
102#13063249—22no—
103#13063249—22no—
104#13063249—22no—
105#13063249—22no—
106#13063249—41no—
107#13063249—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—41no—
122C2×#41×C43—41no—
123C22×Q8×C43—22no—
124C22×Q8×C43—22no—
125C22×Q8×C43—21no—
126C22×Q8×C43—22no—
127C22×Q8×C43—22no—
128C22×Q8×C43—41no—
129C22×Q8×C43—41no—
130C22×Q8×C43D411yescharacteristic
131C22×Q8×C43C2311yescharacteristic
132C22×Q8×C43C2311yescharacteristic
133C22×D4×C43D411yescharacteristic
134C22×D4×C43D411yescharacteristic
135C22×D4×C43D411yescharacteristic
136C23×C4×C43—21no—
137C23×C4×C43C2311yescharacteristic
138C23×C4×C43C2311yescharacteristic
139C23×C4×C43C2311yescharacteristic
140C4⋊Q8×C43—28no—
141#124×C43—28no—
142#123×C43—28no—
143#123×C43—28no—
144C22⋊Q8×C43—22no—
145C22⋊Q8×C43—22no—
146C22⋊Q8×C43—22no—
147C22⋊Q8×C43—22no—
148C22⋊Q8×C43—22no—
149C22⋊Q8×C43—22no—
150C22⋊Q8×C43D414yescomplemented
151C22⋊Q8×C43D414yescomplemented
152#117×C43—22no—
153#117×C43—22no—
154C2×C4⋊C4×C43—21no—
155C2×C4⋊C4×C43—21no—
156C2×C4⋊C4×C43—21no—
157C2×C4⋊C4×C43—21no—
158C2×C4⋊C4×C43C2311yescharacteristic
159C2×C4⋊C4×C43C2311yescharacteristic
160C2×C22⋊C4×C43—21no—
161C2×C22⋊C4×C43—21no—
162C2×C22⋊C4×C43—21no—
163C2×C22⋊C4×C43—21no—
164C2×C22⋊C4×C43—21no—
165C2×C42×C43—21no—
166C24×C43C2×D411yescharacteristic
167C24×C43C2×D411yescharacteristic
168C24×C43C2×D411yescharacteristic
169C23×D43—21no—
170#41×C43—44no—
171#41×C43—44no—
172#41×C43—44no—
173#41×C43—44no—
174C2×Q8×C43—24no—
175C2×Q8×C43—22no—
176C2×Q8×C43—22no—
177C2×Q8×C43—21no—
178C2×Q8×C43—21no—
179C2×Q8×C43—21no—
180C2×Q8×C43—21no—
181C2×Q8×C43—21no—
182C2×Q8×C43—21no—
183C2×Q8×C43—21no—
184C2×Q8×C43—21no—
185C2×Q8×C43—21no—
186C2×Q8×C43—21no—
187C2×Q8×C43—41no—
188C2×Q8×C43—44no—
189C2×Q8×C43—44no—
190C2×Q8×C43—44no—
191C2×Q8×C43—44no—
192C2×Q8×C43—42no—
193C2×Q8×C43—42no—
194C2×Q8×C43C2×D412yes—
195C2×Q8×C43C2×D412yes—
196C2×D4×C43—22no—
197C2×D4×C43—22no—
198C2×D4×C43—22no—
199C2×D4×C43—22no—
200C2×D4×C43—22no—
201C2×D4×C43—22no—
202C2×D4×C43—41no—
203C2×D4×C43—41no—
204C2×D4×C43—41no—
205C22×C4×C43—21no—
206C22×C4×C43—21no—
207C22×C4×C43—21no—
208C22×C4×C43—21no—
209C22×C4×C43—21no—
210C22×C4×C43—21no—
211C22×C4×C43—21no—
212C22×C4×C43—21no—
213C22×C4×C43—24no—
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—21no—
221C22×C4×C43—21no—
222C22×C4×C43—21no—
223C22×C4×C43—21no—
224C22×C4×C43—42no—
225C22×C4×C43—42no—
226C22×C4×C43C2×D412yes—
227C22×C4×C43C2×D412yes—
228C22×C4×C43C2×D412yes—
229C22×C4×C43C2×D411yescharacteristic
230C22×C4×C43C2×D411yescharacteristic
231C22×C4×C43C2×D411yescharacteristic
232C22×C4×C43#4112yes—
233C22×C4×C43C2411yescharacteristic
234C2×C22⋊D43—42no—
235C2×C22⋊D43—42no—
236C2×C22⋊D43—42no—
237C2×C22⋊D43—81no—
238C2×C22⋊D43—81no—
239C2×C22⋊D43—81no—
240C2×C22⋊D43—81no—
241C2×C22⋊D43—81no—
242C2×C22⋊D43—81no—
243C22×Dic43—21no—
244C22×Dic43—21no—
245C22×Dic43—21no—
246C2×D172—21no—
247C2×D172—21no—
248C2×D172—21no—
249C2×D172—21no—
250C2×D172—21no—
251C2×D172—21no—
252C4⋊C4×C43—24no—
253C4⋊C4×C43—24no—
254C4⋊C4×C43—24no—
255C4⋊C4×C43—24no—
256C4⋊C4×C43—21no—
257C4⋊C4×C43—21no—
258C4⋊C4×C43C2×D412yes—
259C4⋊C4×C43C2×D412yes—
260C22⋊C4×C43—24no—
261C22⋊C4×C43—24no—
262C22⋊C4×C43—24no—
263C22⋊C4×C43—24no—
264C22⋊C4×C43—24no—
265C42×C43—24no—
266C22⋊Dic43—81no—
267C22⋊Dic43—81no—
268C22⋊Dic43—81no—
269#10621884—44no—
270#10621884—44no—
271(C2×D43)⋊C4—42no—
272(C2×D43)⋊C4—42no—
273(C2×D43)⋊C4—42no—
274C4⋊Dic43—21no—
275C4⋊Dic43—21no—
276C4⋊Dic43—21no—
277C4⋊Dic43—21no—
278C4⋊Dic43—21no—
279C4⋊Dic43—21no—
280#10621877—44no—
281C2×C43⋊C8—21no—
282C2×C43⋊C8—21no—
283C2×C43⋊C8—21no—
284C2×C43⋊C8—21no—
285C2×C43⋊C8—21no—
286C2×C43⋊C8—21no—
287C2×C43⋊C8—21no—
288C2×C43⋊C8—21no—
289C2×C43⋊C8—21no—
290C2×C43⋊C8—21no—
291C2×C43⋊C8—44no—
292C2×C43⋊C8C2×D412yes—
293C2×C43⋊C8C2×D412yes—
294C23×C43—21no—
295C23×C43—21no—
296C23×C43—21no—
297C23×C43—21no—
298C23×C43—21no—
299C23×C43—21no—
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#12012yes—
314C23×C43#12112yes—
315C23×C43C22×D411yescharacteristic
316C22×D43—41no—
317C22×D43—41no—
318C22×D43—41no—
319C22×D43—41no—
320C22×D43—41no—
321C22×D43—41no—
322C22×D43—41no—
323Q8×C43—22no—
324Q8×C43—22no—
325Q8×C43—22no—
326Q8×C43—22no—
327Q8×C43—44no—
328Q8×C43—48no—
329Q8×C43—41no—
330Q8×C43—41no—
331Q8×C43—41no—
332Q8×C43—41no—
333D4×C43—44no—
334D4×C43—44no—
335D4×C43—44no—
336C2×C4×C43—21no—
337C2×C4×C43—21no—
338C2×C4×C43—21no—
339C2×C4×C43—21no—
340C2×C4×C43—22no—
341C2×C4×C43—22no—
342C2×C4×C43—22no—
343C2×C4×C43—22no—
344C2×C4×C43—22no—
345C2×C4×C43—22no—
346C2×C4×C43—22no—
347C2×C4×C43—22no—
348C2×C4×C43—22no—
349C2×C4×C43—22no—
350C2×C4×C43—22no—
351C2×C4×C43—22no—
352C2×C4×C43—21no—
353C2×C4×C43—21no—
354C2×C4×C43—21no—
355C2×C4×C43—48no—
356C2×C4×C43—41no—
357C2×C4×C43—41no—
358C2×C4×C43—41no—
359C2×C4×C43—41no—
360C2×C4×C43—41no—
361C2×C4×C43—41no—
362C2×C4×C43—41no—
363C2×C4×C43—41no—
364C2×C4×C43—41no—
365C2×C4×C43—41no—
366C2×C4×C43—41no—
367C2×C4×C43—41no—
368C2×C4×C43#12012yes—
369C2×C4×C43#12112yes—
370C2×C4×C43C22×D411yescharacteristic
371C2×C4×C43C22×D411yescharacteristic
372C2×C4×C43C22×D411yescharacteristic
373C2×C4×C43C2×#4111yescharacteristic
374C2×C4×C43H(5,𝔽2)11yescharacteristic
375C2×C4×C43H(5,𝔽2)11yescharacteristic
376C22⋊D43—84no—
377C22⋊D43—84no—
378C22⋊D43—84no—
379C2×Dic43—41no—
380C2×Dic43—41no—
381C2×Dic43—41no—
382C2×Dic43—41no—
383C2×Dic43—41no—
384C2×Dic43—41no—
385C2×Dic43—41no—
386C2×Dic43—41no—
387C2×Dic43—41no—
388D172—41no—
389D172—41no—
390D172—41no—
391D172—41no—
392C43⋊C8—22no—
393C43⋊C8—22no—
394C43⋊C8—41no—
395C43⋊C8—41no—
396#24396—431nomaximal, Sylow
397C22×C43—22no—
398C22×C43—22no—
399C22×C43—22no—
400C22×C43—22no—
401C22×C43—22no—
402C22×C43—22no—
403C22×C43—41no—
404C22×C43—41no—
405C22×C43—41no—
406C22×C43—41no—
407C22×C43—41no—
408C22×C43—41no—
409C22×C43—41no—
410C22×C43—41no—
411C22×C43—41no—
412C22×C43—41no—
413C22×C43—41no—
414C22×C43—41no—
415C22×C43—41no—
416C22×C43—41no—
417C22×C43—41no—
418C22×C43C2×#12011yescharacteristic
419C22×C43C2×#12111yescharacteristic
420C22×C43#53411yescharacteristic
421C22×C43#57711yescharacteristic
422C22×C43#57711yescharacteristic
423C22×C43#57711yescharacteristic
424C22×C43#57811yescharacteristic
425C2×D43—81no—
426C2×D43—81no—
427C2×D43—81no—
428C2×D43—81no—
429C2×D43—81no—
430C2×D43—81no—
431C2×D43—81no—
432C4×C43—22no—
433C4×C43—22no—
434C4×C43—41no—
435C4×C43—42no—
436C4×C43—42no—
437C4×C43—42no—
438C4×C43—42no—
439C4×C43D4211yescharacteristic
440C4×C43D4211yescharacteristic
441C4×C43#54611yescharacteristic
442C4×C43#54611yescharacteristic
443Dic43—81no—
444Dic43—81no—
445Dic43—81no—
446C2×#536D4311yescharacteristic, complemented
447C2×#468—431no—
448C2×#465—431no—
449C2×#448—431no—
450C2×#408—431no—
451#2615—431no—
452#2036—431no—
453#2035—431no—
454#2000—431no—
455#2000—431no—
456#1894—431no—
457#1892—431no—
458#1875—431no—
459#1854—431no—
460#1787—431no—
461C2×C43—42no—
462C2×C43—42no—
463C2×C43—81no—
464C2×C43#241011yescharacteristic
465C2×C43#301011yescharacteristic
466C2×C43#301311yescharacteristic
467C2×C43#305711yescharacteristic
468C2×C43#306311yescharacteristic
469C2×C43#320011yescharacteristic
470C2×C43#320111yescharacteristic
471D43—161no—
472C22×#41C2×D4311yescharacteristic
473C23×Q8C2×D4311yescharacteristic
474C22×SD16—431no—
475C22×SD16—431no—
476C22×M16—431no—
477C23×C8—431no—
478#536—24no—
479#536—24no—
480C2×C4⋊Q8—21no—
481C2×#124—21no—
482C2×#123—21no—
483C2×#123—21no—
484C2×C22⋊Q8C2×D4311yescharacteristic
485C2×C22⋊Q8C2×D4311yescharacteristic
486C2×C22⋊Q8C2×D4311yescharacteristic
487C2×C22⋊Q8C2×D4311yescharacteristic
488C2×#121—431no—
489C2×#121—431no—
490C2×#121—431no—
491C2×#117C2×D4311yescharacteristic
492#468—864no—
493#465—864no—
494#448—864no—
495C2×#107—431no—
496C2×#106—431no—
497C2×#103—431no—
498C2×#103—431no—
499C2×#103—431no—
500C2×#103—431no—
501C2×#103—431no—
502C2×#103—431no—
503C2×#102—431no—
504C2×#102—431no—
505#408—864no—
506C2×C22⋊C8—431no—
507C2×C22⋊C8—431no—
508C2×C22⋊C8—431no—
509C2×C22⋊C8—431no—
510#393—861no—
511#392—861no—
512#392—861no—
513#392—861no—
514#380—431no—
515#380—431no—
516#380—431no—
517#340—431no—
518#340—431no—
519#340—431no—
520#340—431no—
521C43#2439611yescharacteristic, complemented, Sylow
522C2×#41—22no—
523C2×#41—22no—
524C2×#41—22no—
525C2×#41—22no—
526C2×#41—41no—
527C2×#41—41no—
528C22×Q8—22no—
529C22×Q8—22no—
530C22×Q8—21no—
531C22×Q8—22no—
532C22×Q8—22no—
533C22×Q8—41no—
534C22×Q8—41no—
535C22×Q8C22⋊D4311yescharacteristic
536C22×Q8C22×D4311yescharacteristic
537C22×Q8C22×D4311yescharacteristic
538C22×D4—431no—
539C22×D4—861no—
540C22×D4—861no—
541C22×D4—861no—
542C22×D4C22⋊D4311yescharacteristic
543C22×D4C22⋊D4311yescharacteristic
544C22×D4C22⋊D4311yescharacteristic
545C23×C4—21no—
546C23×C4C22×D4311yescharacteristic
547C23×C4C22×D4311yescharacteristic
548C23×C4C22×D4311yescharacteristic
549C2×SD16—862no—
550C2×SD16—862no—
551C2×SD16—862no—
552C2×SD16—862no—
553C2×SD16—1721no—
554C2×SD16—1721no—
555C2×M16—862no—
556C2×M16—862no—
557C2×M16—1721no—
558C22×C8—431no—
559C22×C8—431no—
560C22×C8—431no—
561C22×C8—431no—
562C22×C8—862no—
563C22×C8—862no—
564C22×C8—1721no—
565C4⋊Q8—28no—
566#124—28no—
567#123—28no—
568#123—28no—
569C22⋊Q8—22no—
570C22⋊Q8—22no—
571C22⋊Q8—22no—
572C22⋊Q8—22no—
573C22⋊Q8—22no—
574C22⋊Q8—22no—
575C22⋊Q8C22⋊D4314yescomplemented
576C22⋊Q8C22⋊D4314yescomplemented
577#121—862no—
578#121—862no—
579#121—862no—
580#121—862no—
581#121—1721no—
582#121—1721no—
583#117—22no—
584#117—22no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—431no—
590C2×C4⋊C4—431no—
591C2×C4⋊C4—431no—
592C2×C4⋊C4C22×D4311yescharacteristic
593C2×C4⋊C4C22×D4311yescharacteristic
594C2×C22⋊C4—21no—
595C2×C22⋊C4—21no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—861no—
600C2×C22⋊C4—861no—
601C2×C22⋊C4—861no—
602C2×C22⋊C4—861no—
603C2×C22⋊C4—861no—
604C2×C22⋊C4—861no—
605C2×C42—21no—
606#107—862no—
607#106—862no—
608#103—862no—
609#103—862no—
610#103—862no—
611#103—862no—
612#103—1721no—
613#103—1721no—
614#102—862no—
615#102—862no—
616C22⋊C8—434no—
617C22⋊C8—862no—
618C22⋊C8—862no—
619C22⋊C8—862no—
620#95—861no—
621#95—861no—
622#95—861no—
623C24—861no—
624C24C2×C22⋊D4311yescharacteristic
625C24C2×C22⋊D4311yescharacteristic
626C24C2×C22⋊D4311yescharacteristic
627#41—44no—
628#41—44no—
629#41—44no—
630#41—44no—
631C2×Q8—24no—
632C2×Q8—22no—
633C2×Q8—22no—
634C2×Q8—21no—
635C2×Q8—21no—
636C2×Q8—21no—
637C2×Q8—21no—
638C2×Q8—21no—
639C2×Q8—21no—
640C2×Q8—21no—
641C2×Q8—21no—
642C2×Q8—21no—
643C2×Q8—21no—
644C2×Q8—41no—
645C2×Q8—44no—
646C2×Q8—44no—
647C2×Q8—44no—
648C2×Q8—44no—
649C2×Q8—42no—
650C2×Q8—42no—
651C2×Q8C2×C22⋊D4312yes—
652C2×Q8C2×C22⋊D4312yes—
653C2×D4—22no—
654C2×D4—22no—
655C2×D4—22no—
656C2×D4—22no—
657C2×D4—22no—
658C2×D4—22no—
659C2×D4—41no—
660C2×D4—41no—
661C2×D4—41no—
662C2×D4—861no—
663C2×D4—861no—
664C2×D4—861no—
665C2×D4—861no—
666C2×D4—861no—
667C2×D4—861no—
668C2×D4—3441no—
669C2×D4—3441no—
670C2×D4—3441no—
671C2×D4—3441no—
672C2×D4—3441no—
673C2×D4—3441no—
674C2×D4—1722no—
675C2×D4—1722no—
676C2×D4—1722no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—24no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—42no—
697C22×C4—42no—
698C22×C4—861no—
699C22×C4—861no—
700C22×C4—861no—
701C22×C4D4×D4312yes—
702C22×C4#1062190012yes—
703C22×C4C2×C22⋊D4311yescharacteristic
704C22×C4C2×C22⋊D4311yescharacteristic
705C22×C4C2×C22⋊D4312yes—
706C22×C4C2×C22⋊D4312yes—
707C22×C4C2×C22⋊D4311yescharacteristic
708C22×C4C23×D4311yescharacteristic
709SD16—1724no—
710SD16—1724no—
711M16—1724no—
712C2×C8—432no—
713C2×C8—432no—
714C2×C8—861no—
715C2×C8—861no—
716C2×C8—861no—
717C2×C8—861no—
718C2×C8—861no—
719C2×C8—861no—
720C2×C8—861no—
721C2×C8—861no—
722C2×C8—861no—
723C2×C8—861no—
724C2×C8—1724no—
725C4⋊C4—24no—
726C4⋊C4—24no—
727C4⋊C4—24no—
728C4⋊C4—24no—
729C4⋊C4—21no—
730C4⋊C4—21no—
731C4⋊C4—861no—
732C4⋊C4—861no—
733C4⋊C4—861no—
734C4⋊C4—861no—
735C4⋊C4—861no—
736C4⋊C4—861no—
737C4⋊C4C2×C22⋊D4312yes—
738C4⋊C4C2×C22⋊D4312yes—
739C22⋊C4—24no—
740C22⋊C4—24no—
741C22⋊C4—24no—
742C22⋊C4—24no—
743C22⋊C4—24no—
744C22⋊C4—3441no—
745C22⋊C4—3441no—
746C22⋊C4—3441no—
747C22⋊C4—1722no—
748C22⋊C4—1722no—
749C22⋊C4—1722no—
750C42—24no—
751C23—21no—
752C23—21no—
753C23—21no—
754C23—21no—
755C23—21no—
756C23—21no—
757C23—21no—
758C23—21no—
759C23—21no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—21no—
764C23—21no—
765C23—21no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—21no—
770C23—1721no—
771C23—1721no—
772C23—1721no—
773C23—1721no—
774C23—1721no—
775C23—1721no—
776C23—1721no—
777C23#1306329412yes—
778C23#1306329712yes—
779C23C22×C22⋊D4311yescharacteristic
780Q8—22no—
781Q8—22no—
782Q8—22no—
783Q8—22no—
784Q8—44no—
785Q8—48no—
786Q8—41no—
787Q8—41no—
788Q8—41no—
789Q8—41no—
790D4—44no—
791D4—44no—
792D4—44no—
793D4—3444no—
794D4—3444no—
795D4—3444no—
796D4—1721no—
797D4—1721no—
798D4—1721no—
799D4—1721no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—48no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—1721no—
833C2×C4—1721no—
834C2×C4—1721no—
835C2×C4—1721no—
836C2×C4—1721no—
837C2×C4—1721no—
838C2×C4—1721no—
839C2×C4—1721no—
840C2×C4—1721no—
841C2×C4#1306329412yes—
842C2×C4#1306329712yes—
843C2×C4C2×D4×D4311yescharacteristic
844C2×C4C22×C22⋊D4311yescharacteristic
845C2×C4C22×C22⋊D4311yescharacteristic
846C2×C4C2×#1062190011yescharacteristic
847C2×C4#1306337011yescharacteristic
848C2×C4#1306337011yescharacteristic
849C8—862no—
850C8—862no—
851C8—1721no—
852C8—1721no—
853C22—22no—
854C22—22no—
855C22—22no—
856C22—22no—
857C22—22no—
858C22—22no—
859C22—41no—
860C22—41no—
861C22—41no—
862C22—41no—
863C22—41no—
864C22—41no—
865C22—41no—
866C22—41no—
867C22—41no—
868C22—41no—
869C22—41no—
870C22—41no—
871C22—41no—
872C22—41no—
873C22—41no—
874C22—3441no—
875C22—3441no—
876C22—3441no—
877C22—3441no—
878C22—3441no—
879C22—3441no—
880C22—3441no—
881C22C2×#1306329411yescharacteristic
882C22C2×#1306329711yescharacteristic
883C22#1458345811yescharacteristic
884C22#1458370711yescharacteristic
885C22#1458370711yescharacteristic
886C22#1458370711yescharacteristic
887C22#1458371411yescharacteristic
888C4—22no—
889C4—22no—
890C4—41no—
891C4—42no—
892C4—42no—
893C4—42no—
894C4—42no—
895C4—3441no—
896C4—3441no—
897C4—3441no—
898C4D4×C22⋊D4311yescharacteristic
899C4D4×C22⋊D4311yescharacteristic
900C4#1458354311yescharacteristic
901C4#1458354311yescharacteristic
902C2—42no—
903C2—42no—
904C2—81no—
905C2—6881no—
906C2#1913796911yescharacteristic
907C2#1914388111yescharacteristic
908C2#1914391011yescharacteristic
909C2#1914423611yescharacteristic
910C2#1914428211yescharacteristic
911C2#1914546211yescharacteristic
912C2#1914547711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#536C2
socleC23×C43C22×D4
prime radical#19140319C2
hypercenterC2×#536D43
hypocenterC43#24396
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×#41 ◁ C2×#536

Complements

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

NH ≅ G/Ntype
1. C2×#14583147C2semidirect
2. C2×#14583130C2semidirect
3. C2×#14583038C2semidirect
4. C2×#14582866C2semidirect
6. #19135795C2semidirect
7. #19135788C2semidirect
8. #19135596C2semidirect
9. #19135596C2semidirect
10. #19135029C2semidirect
11. #19135019C2semidirect
12. #19134917C2semidirect
13. #19134794C2semidirect
14. #19134530C2semidirect
15. C2×C43×#536C2semidirect
113. C22⋊(C43⋊C8)D4semidirect
150. C22⋊Q8×C43D4semidirect
151. C22⋊Q8×C43D4semidirect
446. C2×#536D43semidirect
521. C43#24396semidirect
575. C22⋊Q8C22⋊D43semidirect
576. C22⋊Q8C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145831472
C2×#145831302
C2×#145830382
C2×#145828662
#191403192
#191357952
#191357882
#191355962
#191350292
#191350192
#191349172
#191347942
#191345302
C2×C43×#5362
#2439643