Finite Group Databasebeta

← #25147577

Subgroups — #25147577

Order 11008.

1034 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583155C211yesmaximal, characteristic, complemented
2C2×#14583126C211yesmaximal, characteristic, complemented
3C2×#14583118C211yesmaximal, characteristic, complemented
4C2×#14582971C211yesmaximal, characteristic, complemented
5#19139517C211yesmaximal, characteristic, complemented
6#19135788C211yesmaximal, characteristic, complemented
7#19135781C211yesmaximal, characteristic, complemented
8#19135603C211yesmaximal, characteristic, complemented
9#19135598C211yesmaximal, characteristic, complemented
10#19135412C211yesmaximal, characteristic, complemented
11#19135358C211yesmaximal, characteristic, complemented
12#19135034C211yesmaximal, characteristic, complemented
13#19135019C211yesmaximal, characteristic, complemented
14#19134428C211yesmaximal, characteristic, complemented
15C43×#2540C211yesmaximal, characteristic
16C22×#10621885C2211yescharacteristic
17C22×#10621883C2211yescharacteristic
18C22×#10621877C2211yescharacteristic
19C23×C43⋊C8C2211yescharacteristic
20C2×#13063304C2211yescharacteristic
21C2×#13063304C2211yescharacteristic
22C2×C4×Dic86C2211yescharacteristic
23#14583155—24no—
24#14583126—24no—
25#14583118—24no—
26#14582971—24no—
27C2×#13063256C2211yescharacteristic
28C2×#13063256C2211yescharacteristic
29C2×C4⋊(C43⋊C8)C2211yescharacteristic
30C2×#13063249C2211yescharacteristic
31C2×#13063249C2211yescharacteristic
32C2×#13063249C2211yescharacteristic
33C2×#13063248C2211yescharacteristic
34C2×#13063248C2211yescharacteristic
35C2×#13063246C2211yescharacteristic
36C2×#13063246C2211yescharacteristic
37C2×#13063246C2211yescharacteristic
38C2×C22⋊(C43⋊C8)C2211yescharacteristic
39C2×C22⋊(C43⋊C8)C2211yescharacteristic
40C2×#13063236C2211yescharacteristic
41#14582822—21no—
42#14582822—21no—
43#14582802—21no—
44#14582795—21no—
45#14582769C2211yescharacteristic
46#14582759C2211yescharacteristic
47#14582759C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52C2×#124×C43C2211yescharacteristic
53C2×C22⋊Q8×C43C2211yescharacteristic
54C2×C22⋊Q8×C43C2211yescharacteristic
55C2×#121×C43C2211yescharacteristic
56C2×#121×C43C2211yescharacteristic
57C2×C4×D4×C43C2211yescharacteristic
58C43×#399—21no—
59C43×#392—21no—
60C43×#390—21no—
61C43×#390—21no—
62C4×C4⋊C4×C43C2211yescharacteristic
63C22×Dic86C2311yescharacteristic
64C2×#10621885—22no—
65C2×#10621885—22no—
66C2×#10621885—41no—
67C2×#10621883—22no—
68C2×#10621883—22no—
69C2×#10621883—41no—
70C2×#10621877—22no—
71C2×#10621877—22no—
72C2×#10621877—41no—
73C22×C43⋊C8—22no—
74C22×C43⋊C8—22no—
75C22×C43⋊C8—41no—
76C22×C43⋊C8C2311yescharacteristic
77C22×C43⋊C8C2311yescharacteristic
78C22×C43⋊C8C2311yescharacteristic
79C22×C43⋊C8C2311yescharacteristic
80#13063304—22no—
81#13063304—22no—
82#13063304—41no—
83#13063304—41no—
84C4×Dic86—22no—
85C4×Dic86—22no—
86C2×C4⋊Dic43—21no—
87C2×C4⋊Dic43—21no—
88C2×C4⋊Dic43C2311yescharacteristic
89C2×C4⋊Dic43C2311yescharacteristic
90C2×C4⋊Dic43C2311yescharacteristic
91C2×Dic43⋊C4—21no—
92C2×Dic43⋊C4—21no—
93C2×Dic43⋊C4—21no—
94C2×C22⋊Dic43—21no—
95C2×C22⋊Dic43—21no—
96C2×C22⋊Dic43—21no—
97C2×C22⋊Dic43—21no—
98C2×C4×Dic43—21no—
99#13063256—22no—
100#13063256—22no—
101C4⋊(C43⋊C8)D414yescomplemented
102#13063249—22no—
103#13063249—22no—
104#13063249—41no—
105#13063248—22no—
106#13063248D414yescomplemented
107#13063246—22no—
108#13063246—22no—
109#13063246—41no—
110C22⋊(C43⋊C8)—22no—
111C22⋊(C43⋊C8)—22no—
112#13063236—22no—
113C43⋊#95—21no—
114C43⋊#95—21no—
115C22×Q8×C43C2311yescharacteristic
116C22×D4×C43—21no—
117C22×D4×C43—21no—
118C22×D4×C43D411yescharacteristic
119C22×D4×C43C2311yescharacteristic
120C23×C4×C43C2311yescharacteristic
121C23×C4×C43C2311yescharacteristic
122#124×C43—22no—
123#124×C43—22no—
124C22⋊Q8×C43—22no—
125C22⋊Q8×C43—22no—
126C22⋊Q8×C43—41no—
127C22⋊Q8×C43—41no—
128#121×C43—22no—
129#121×C43—22no—
130#121×C43—41no—
131#121×C43—41no—
132C4×D4×C43—22no—
133C4×D4×C43—22no—
134C2×C4⋊C4×C43—21no—
135C2×C4⋊C4×C43—21no—
136C2×C4⋊C4×C43D411yescharacteristic
137C2×C4⋊C4×C43C2311yescharacteristic
138C2×C4⋊C4×C43C2311yescharacteristic
139C2×C22⋊C4×C43—21no—
140C2×C22⋊C4×C43—21no—
141C2×C22⋊C4×C43—21no—
142C2×C22⋊C4×C43—21no—
143C2×C22⋊C4×C43—21no—
144C2×C22⋊C4×C43—21no—
145C2×C22⋊C4×C43D411yescharacteristic
146C2×C22⋊C4×C43D411yescharacteristic
147C2×C42×C43—21no—
148C2×C42×C43C2311yescharacteristic
149#95×C43—21no—
150C24×C43—21no—
151C24×C43C2×D411yescharacteristic
152C24×C43C2×D411yescharacteristic
153C2×Q8×C43—21no—
154C2×Q8×C43—21no—
155C2×Q8×C43—21no—
156C2×Q8×C43—21no—
157C2×Q8×C43—21no—
158C2×Q8×C43—21no—
159C2×D4×C43—22no—
160C2×D4×C43—22no—
161C2×D4×C43—21no—
162C2×D4×C43—21no—
163C2×D4×C43—21no—
164C2×D4×C43—21no—
165C2×D4×C43—21no—
166C2×D4×C43—21no—
167C2×D4×C43—41no—
168C2×D4×C43—42no—
169C2×D4×C43—42no—
170C2×D4×C43—42no—
171C2×D4×C43—42no—
172C2×D4×C43—81no—
173C2×D4×C43—81no—
174C22×C4×C43—21no—
175C22×C4×C43—21no—
176C22×C4×C43—21no—
177C22×C4×C43—21no—
178C22×C4×C43—21no—
179C22×C4×C43—21no—
180C22×C4×C43—21no—
181C22×C4×C43—21no—
182C22×C4×C43—21no—
183C22×C4×C43—21no—
184C22×C4×C43—21no—
185C22×C4×C43—21no—
186C22×C4×C43—21no—
187C22×C4×C43—21no—
188C22×C4×C43—21no—
189C22×C4×C43C2×D411yescharacteristic
190C22×C4×C43C2×D411yescharacteristic
191C22×C4×C43C2×D411yescharacteristic
192C22×C4×C43C2×D411yescharacteristic
193C22×C4×C43C2411yescharacteristic
194C22×Dic43—21no—
195C22×Dic43—21no—
196C22×Dic43—21no—
197C22×Dic43—21no—
198C2×Dic86—21no—
199C2×Dic86—21no—
200C2×Dic86—21no—
201C2×Dic86—21no—
202C2×Dic86—21no—
203C2×Dic86C2×D412yes—
204C4⋊C4×C43—22no—
205C4⋊C4×C43—21no—
206C4⋊C4×C43—21no—
207C4⋊C4×C43—42no—
208C4⋊C4×C43—42no—
209C4⋊C4×C43C2×D412yes—
210C4⋊C4×C43#4112yes—
211C22⋊C4×C43—22no—
212C22⋊C4×C43—22no—
213C22⋊C4×C43—42no—
214C22⋊C4×C43—42no—
215C22⋊C4×C43—42no—
216C22⋊C4×C43—42no—
217C22⋊C4×C43—42no—
218C22⋊C4×C43—42no—
219C42×C43—81no—
220C42×C43C2×D412yes—
221C42×C43#4112yes—
222C22⋊Dic43—42no—
223C22⋊Dic43—42no—
224C22⋊Dic43—81no—
225C22⋊Dic43—81no—
226#10621885—44no—
227#10621883—44no—
228C4⋊Dic43—21no—
229C4⋊Dic43—21no—
230C4⋊Dic43—21no—
231C4⋊Dic43—21no—
232C4⋊Dic43—21no—
233C4⋊Dic43—21no—
234C4⋊Dic43—42no—
235C4⋊Dic43—81no—
236Dic43⋊C4—42no—
237Dic43⋊C4—42no—
238Dic43⋊C4—42no—
239C4×Dic43—42no—
240#10621877—44no—
241C2×C43⋊C8—21no—
242C2×C43⋊C8—21no—
243C2×C43⋊C8—21no—
244C2×C43⋊C8—21no—
245C2×C43⋊C8—21no—
246C2×C43⋊C8—21no—
247C2×C43⋊C8—21no—
248C2×C43⋊C8—21no—
249C2×C43⋊C8—21no—
250C2×C43⋊C8—44no—
251C2×C43⋊C8C2×D412yes—
252C2×C43⋊C8C2×D412yes—
253C2×C43⋊C8C2×D412yes—
254C23×C43—21no—
255C23×C43—21no—
256C23×C43—21no—
257C23×C43—21no—
258C23×C43—21no—
259C23×C43—21no—
260C23×C43—21no—
261C23×C43—21no—
262C23×C43—21no—
263C23×C43—21no—
264C23×C43—21no—
265C23×C43—21no—
266C23×C43—21no—
267C23×C43—41no—
268C23×C43—41no—
269C23×C43—41no—
270C23×C43—41no—
271C23×C43—41no—
272C23×C43—41no—
273C23×C43—41no—
274C23×C43#13712yes—
275C23×C43C22×D411yescharacteristic
276Q8×C43—41no—
277Q8×C43—41no—
278Q8×C43—41no—
279Q8×C43—41no—
280D4×C43—44no—
281D4×C43—41no—
282D4×C43—41no—
283D4×C43—41no—
284D4×C43—41no—
285D4×C43—84no—
286D4×C43—84no—
287C2×C4×C43—21no—
288C2×C4×C43—21no—
289C2×C4×C43—21no—
290C2×C4×C43—21no—
291C2×C4×C43—21no—
292C2×C4×C43—21no—
293C2×C4×C43—21no—
294C2×C4×C43—21no—
295C2×C4×C43—22no—
296C2×C4×C43—22no—
297C2×C4×C43—21no—
298C2×C4×C43—21no—
299C2×C4×C43—41no—
300C2×C4×C43—41no—
301C2×C4×C43—41no—
302C2×C4×C43—41no—
303C2×C4×C43—41no—
304C2×C4×C43—41no—
305C2×C4×C43—41no—
306C2×C4×C43—41no—
307C2×C4×C43—41no—
308C2×C4×C43—41no—
309C2×C4×C43—41no—
310C2×C4×C43—41no—
311C2×C4×C43—41no—
312C2×C4×C43—41no—
313C2×C4×C43—41no—
314C2×C4×C43#12112yes—
315C2×C4×C43#12112yes—
316C2×C4×C43C22×D411yescharacteristic
317C2×C4×C43C22×D411yescharacteristic
318C2×C4×C43C2×#4111yescharacteristic
319C2×C4×C43C2×#4111yescharacteristic
320C2×C4×C43H(5,𝔽2)11yescharacteristic
321C2×C4×C43H(5,𝔽2)11yescharacteristic
322C2×Dic43—22no—
323C2×Dic43—41no—
324C2×Dic43—41no—
325C2×Dic43—41no—
326C2×Dic43—41no—
327C2×Dic43—41no—
328C2×Dic43—41no—
329C2×Dic43—41no—
330C2×Dic43—41no—
331C2×Dic43—41no—
332C2×Dic43—41no—
333C2×Dic43—41no—
334Dic86—22no—
335Dic86—22no—
336Dic86—41no—
337Dic86—41no—
338C43⋊C8—22no—
339C43⋊C8—22no—
340C43⋊C8—22no—
341C43⋊C8—41no—
342#25403—431nomaximal, Sylow
343C22×C43—22no—
344C22×C43—22no—
345C22×C43—22no—
346C22×C43—41no—
347C22×C43—41no—
348C22×C43—41no—
349C22×C43—41no—
350C22×C43—41no—
351C22×C43—41no—
352C22×C43—41no—
353C22×C43—41no—
354C22×C43—41no—
355C22×C43—41no—
356C22×C43—41no—
357C22×C43—81no—
358C22×C43—81no—
359C22×C43—81no—
360C22×C43—81no—
361C22×C43—81no—
362C22×C43—81no—
363C22×C43—81no—
364C22×C43C2×#12111yescharacteristic
365C22×C43D4211yescharacteristic
366C22×C43#54611yescharacteristic
367C22×C43C2×#13711yescharacteristic
368C22×C43#57511yescharacteristic
369C22×C43#57711yescharacteristic
370C22×C43#57711yescharacteristic
371C4×C43—22no—
372C4×C43—22no—
373C4×C43—41no—
374C4×C43—41no—
375C4×C43—42no—
376C4×C43—42no—
377C4×C43—81no—
378C4×C43#53211yescharacteristic
379C4×C43#54011yescharacteristic
380C4×C43D4211yescharacteristic
381C4×C43#55011yescharacteristic
382Dic43—42no—
383Dic43—81no—
384Dic43—81no—
385Dic43—81no—
386C2×#470—431no—
387C2×#465—431no—
388C2×#464—431no—
389C2×#435—431no—
390#2540D4311yescharacteristic
391#2538—431no—
392#2035—431no—
393#2034—431no—
394#2001—431no—
395#2000—431no—
396#1959—431no—
397#1948—431no—
398#1895—431no—
399#1892—431no—
400#1763—431no—
401C2×C43—42no—
402C2×C43—81no—
403C2×C43—161no—
404C2×C43#242811yescharacteristic
405C2×C43#305611yescharacteristic
406C2×C43#306011yescharacteristic
407C2×C43#326611yescharacteristic
408C2×C43#327111yescharacteristic
409C2×C43#331111yescharacteristic
410C2×C43#331611yescharacteristic
411C22×Q16—431no—
412C22×SD16—431no—
413C22×M16—431no—
414C23×C8—431no—
415C2×#124C2×D4311yescharacteristic
416C2×C22⋊Q8—431no—
417C2×C22⋊Q8—431no—
418C2×C22⋊Q8C2×D4311yescharacteristic
419C2×C22⋊Q8C2×D4311yescharacteristic
420C2×#121C2×D4311yescharacteristic
421C2×#121C2×D4311yescharacteristic
422C2×C4×Q8—431no—
423C2×C4×D4C2×D4311yescharacteristic
424#470—864no—
425#465—864no—
426#464—864no—
427#435—864no—
428C2×#106—431no—
429C2×#106—431no—
430C2×C4⋊C8—431no—
431C2×#103—431no—
432C2×#103—431no—
433C2×#103—431no—
434C2×#103—431no—
435C2×#103—431no—
436C2×#102—431no—
437C2×#102—431no—
438C2×#102—431no—
439C2×C22⋊C8—431no—
440C2×C22⋊C8—431no—
441C2×#97—431no—
442#399—21no—
443#396—861no—
444#396—861no—
445#392—21no—
446#390—21no—
447#390—21no—
448#390—861no—
449#389—861no—
450#384—431no—
451#380—431no—
452#380—431no—
453C4×C4⋊C4C2×D4311yescharacteristic
454#340—431no—
455#340—431no—
456#340—431no—
457#340—431no—
458C43#2540311yescharacteristic, complemented, Sylow
459C22×Q8—431no—
460C22×Q8C22×D4311yescharacteristic
461C22×D4—21no—
462C22×D4—21no—
463C22×D4C22⋊D4311yescharacteristic
464C22×D4C22×D4311yescharacteristic
465C23×C4C22×D4311yescharacteristic
466C23×C4C22×D4311yescharacteristic
467C2×Q16—862no—
468C2×Q16—862no—
469C2×Q16—1721no—
470C2×SD16—862no—
471C2×SD16—862no—
472C2×SD16—1721no—
473C2×M16—862no—
474C2×M16—862no—
475C2×M16—1721no—
476C22×C8—431no—
477C22×C8—431no—
478C22×C8—431no—
479C22×C8—431no—
480C22×C8—862no—
481C22×C8—862no—
482C22×C8—1721no—
483#124—22no—
484#124—22no—
485C22⋊Q8—22no—
486C22⋊Q8—22no—
487C22⋊Q8—41no—
488C22⋊Q8—41no—
489C22⋊Q8—862no—
490C22⋊Q8—862no—
491C22⋊Q8—1721no—
492C22⋊Q8—1721no—
493#121—22no—
494#121—22no—
495#121—41no—
496#121—41no—
497C4×Q8—862no—
498C4×Q8—862no—
499C4×D4—22no—
500C4×D4—22no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—431no—
504C2×C4⋊C4—431no—
505C2×C4⋊C4—431no—
506C2×C4⋊C4—861no—
507C2×C4⋊C4—861no—
508C2×C4⋊C4—861no—
509C2×C4⋊C4—861no—
510C2×C4⋊C4—861no—
511C2×C4⋊C4C22⋊D4311yescharacteristic
512C2×C4⋊C4C22×D4311yescharacteristic
513C2×C4⋊C4C22×D4311yescharacteristic
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4—21no—
520C2×C22⋊C4—861no—
521C2×C22⋊C4—861no—
522C2×C22⋊C4—861no—
523C2×C22⋊C4—861no—
524C2×C22⋊C4C22⋊D4311yescharacteristic
525C2×C22⋊C4C22⋊D4311yescharacteristic
526C2×C42—21no—
527C2×C42—861no—
528C2×C42C22×D4311yescharacteristic
529#106—862no—
530#106—862no—
531C4⋊C8—434no—
532#103—434no—
533#103—862no—
534#103—862no—
535#103—862no—
536#103—1721no—
537#102—862no—
538#102—862no—
539#102—1721no—
540C22⋊C8—862no—
541C22⋊C8—862no—
542#97—862no—
543#95—21no—
544#95—861no—
545#95—861no—
546C24—21no—
547C24C2×C22⋊D4311yescharacteristic
548C24C2×C22⋊D4311yescharacteristic
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8—21no—
555C2×Q8—432no—
556C2×Q8—861no—
557C2×Q8—861no—
558C2×Q8—861no—
559C2×Q8—861no—
560C2×Q8—861no—
561C2×D4—22no—
562C2×D4—22no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—41no—
570C2×D4—42no—
571C2×D4—42no—
572C2×D4—42no—
573C2×D4—42no—
574C2×D4—81no—
575C2×D4—81no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—861no—
592C22×C4—861no—
593C22×C4—861no—
594C22×C4—861no—
595C22×C4C2×C22⋊D4311yescharacteristic
596C22×C4C2×C22⋊D4311yescharacteristic
597C22×C4C2×C22⋊D4311yescharacteristic
598C22×C4C2×C22⋊D4311yescharacteristic
599C22×C4C23×D4311yescharacteristic
600Q16—1724no—
601SD16—1724no—
602M16—1724no—
603C2×C8—432no—
604C2×C8—432no—
605C2×C8—432no—
606C2×C8—861no—
607C2×C8—861no—
608C2×C8—861no—
609C2×C8—861no—
610C2×C8—861no—
611C2×C8—861no—
612C2×C8—861no—
613C2×C8—861no—
614C2×C8—861no—
615C2×C8—1724no—
616C4⋊C4—22no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—42no—
620C4⋊C4—42no—
621C4⋊C4—861no—
622C4⋊C4—861no—
623C4⋊C4—861no—
624C4⋊C4—861no—
625C4⋊C4—861no—
626C4⋊C4—861no—
627C4⋊C4—3441no—
628C4⋊C4—1722no—
629C4⋊C4—1722no—
630C4⋊C4—1722no—
631C4⋊C4—1722no—
632C4⋊C4D4×D4312yes—
633C4⋊C4#1062190012yes—
634C22⋊C4—22no—
635C22⋊C4—22no—
636C22⋊C4—42no—
637C22⋊C4—42no—
638C22⋊C4—42no—
639C22⋊C4—42no—
640C22⋊C4—42no—
641C22⋊C4—42no—
642C22⋊C4—3441no—
643C22⋊C4—3441no—
644C22⋊C4—1722no—
645C22⋊C4—1722no—
646C42—81no—
647C42—1722no—
648C42D4×D4312yes—
649C42#1062190012yes—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23#1306335512yes—
671C23C22×C22⋊D4311yescharacteristic
672Q8—41no—
673Q8—41no—
674Q8—41no—
675Q8—41no—
676Q8—862no—
677Q8—862no—
678Q8—1721no—
679Q8—1721no—
680D4—44no—
681D4—41no—
682D4—41no—
683D4—41no—
684D4—41no—
685D4—84no—
686D4—84no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—22no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—22no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—862no—
715C2×C4—1721no—
716C2×C4—1721no—
717C2×C4—1721no—
718C2×C4—1721no—
719C2×C4—1721no—
720C2×C4—1721no—
721C2×C4—1721no—
722C2×C4—1721no—
723C2×C4—1721no—
724C2×C4—1721no—
725C2×C4—1721no—
726C2×C4#1306329712yes—
727C2×C4#1306329712yes—
728C2×C4C2×D4×D4311yescharacteristic
729C2×C4C2×D4×D4311yescharacteristic
730C2×C4C2×#1062190011yescharacteristic
731C2×C4C2×#1062190011yescharacteristic
732C2×C4#1306337011yescharacteristic
733C2×C4#1306337011yescharacteristic
734C8—862no—
735C8—862no—
736C8—862no—
737C8—1721no—
738C22—22no—
739C22—22no—
740C22—22no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—81no—
753C22—81no—
754C22—81no—
755C22—81no—
756C22—81no—
757C22—81no—
758C22—81no—
759C22C2×#1306329711yescharacteristic
760C22D4×C22⋊D4311yescharacteristic
761C22#1458354311yescharacteristic
762C22C2×#1306335511yescharacteristic
763C22#1458369711yescharacteristic
764C22#1458370711yescharacteristic
765C22#1458371011yescharacteristic
766C4—22no—
767C4—22no—
768C4—42no—
769C4—42no—
770C4—41no—
771C4—41no—
772C4—81no—
773C4—3441no—
774C4—3441no—
775C4—3441no—
776C4—1722no—
777C4#1458344711yescharacteristic
778C4#1458350311yescharacteristic
779C4#1458353411yescharacteristic
780C4#1458356911yescharacteristic
781C2—42no—
782C2—81no—
783C2—161no—
784C2#1913818611yescharacteristic
785C2#1914422711yescharacteristic
786C2#1914425411yescharacteristic
787C2#1914610111yescharacteristic
788C2#1914618111yescharacteristic
789C2#1914663111yescharacteristic
790C2#1914670611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
Fitting, prime radicalC43×#2540C2
socleC23×C43C22×D4
hypercenter#2540D43
hypocenterC43#25403
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2540

Complements

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

NH ≅ G/Ntype
1. C2×#14583155C2semidirect
2. C2×#14583126C2semidirect
3. C2×#14583118C2semidirect
4. C2×#14582971C2semidirect
5. #19139517C2semidirect
6. #19135788C2semidirect
7. #19135781C2semidirect
8. #19135603C2semidirect
9. #19135598C2semidirect
10. #19135412C2semidirect
11. #19135358C2semidirect
12. #19135034C2semidirect
13. #19135019C2semidirect
14. #19134428C2semidirect
101. C4⋊(C43⋊C8)D4semidirect
106. #13063248D4semidirect
458. C43#25403semidirect

Maximal subgroups

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

subgroupindex
C2×#145831552
C2×#145831262
C2×#145831182
C2×#145829712
#191395172
#191357882
#191357812
#191356032
#191355982
#191354122
#191353582
#191350342
#191350192
#191344282
C43×#25402
#2540343