Finite Group Databasebeta

← #25129244

Subgroups — #25129244

Order 11008.

1520 conjugacy classes of subgroups.

The subgroup lattice has 894 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583406C211yesmaximal, characteristic
2C2×#14583228C211yesmaximal, characteristic, complemented
3C2×#14583211C211yesmaximal, characteristic, complemented
4#380×D43C211yesmaximal, characteristic, complemented
5#19135797C211yesmaximal, characteristic, complemented
6#19135796C211yesmaximal, characteristic, complemented
7#19135783C211yesmaximal, characteristic, complemented
8#19135782C211yesmaximal, characteristic, complemented
9#19134909C211yesmaximal, characteristic, complemented
10#19134899C211yesmaximal, characteristic, complemented
11#19134796C211yesmaximal, characteristic, complemented
12#19134792C211yesmaximal, characteristic, complemented
13#19134535C211yesmaximal, characteristic, complemented
14#19134504C211yesmaximal, characteristic, complemented
15C43×#1788C211yesmaximal, characteristic, complemented
16C23×C4×D43C2211yescharacteristic
17#14583406—24no—
18#14583406—24no—
19C2×#13063306—21no—
20C2×#13063301C2211yescharacteristic
21C2×#13063301C2211yescharacteristic
22C2×#13063296C2211yescharacteristic
23C2×#13063296C2211yescharacteristic
24C2×#13063293—21no—
25C2×C4×C22⋊D43—21no—
26C2×C4×C22⋊D43—21no—
27C2×#13063284C2211yescharacteristic
28C2×C4⋊C4×D43C2211yescharacteristic
29C2×C4⋊C4×D43C2211yescharacteristic
30C2×C22⋊C4×D43—21no—
31#14583228—24no—
32#14583211—24no—
33C2×#13063259C2211yescharacteristic, complemented
34C2×#13063258C2211yescharacteristic, complemented
35C2×#13063257C2211yescharacteristic, complemented
36C2×#13063256C2211yescharacteristic, complemented
37C2×#13063249C2211yescharacteristic, complemented
38C2×#13063249C2211yescharacteristic, complemented
39C2×#13063246C2211yescharacteristic, complemented
40C2×#13063246C2211yescharacteristic, complemented
41C2×C22⋊(C43⋊C8)C2211yescharacteristic
42C2×(C2×D43)⋊C8C2211yescharacteristic
43C2×(C2×D43)⋊C8C2211yescharacteristic
44C2×(C2×D43)⋊C8C2211yescharacteristic
45C2×(C2×D43)⋊C8C2211yescharacteristic
46#14582759C2211yescharacteristic
47#14582758—21no—
48#14582757—21no—
49#14582756C2211yescharacteristic
50#14582756C2211yescharacteristic
51#95×D43—21no—
52#14582662C2211yescharacteristic, complemented
53#14582662C2211yescharacteristic, complemented
54#14582661C2211yescharacteristic, complemented
55#14582661C2211yescharacteristic, complemented
56C22×#41×C43C2211yescharacteristic
57C2×#103×C43C2211yescharacteristic, complemented
58C2×#103×C43C2211yescharacteristic, complemented
59C2×#102×C43C2211yescharacteristic, complemented
60C2×#102×C43C2211yescharacteristic, complemented
61C2×C22⋊C8×C43C2211yescharacteristic
62C43×#380C2211yescharacteristic
63C24×D43D411yescharacteristic
64C22×C22⋊D43—21no—
65C22×C22⋊D43—21no—
66C23×Dic43D411yescharacteristic
67C22×C4×D43—22no—
68C22×C4×D43—22no—
69C22×C4×D43—22no—
70C22×C4×D43—22no—
71C22×C4×D43—21no—
72C22×C4×D43—21no—
73C22×C4×D43—41no—
74C22×C4×D43—41no—
75C22×C4×D43D411yescharacteristic
76C22×C4×D43D411yescharacteristic
77C22×C4×D43C2311yescharacteristic
78C22×C4×D43C2311yescharacteristic
79C22×C43⋊C8C2311yescharacteristic
80C22×C43⋊C8C2311yescharacteristic
81#13063306—28no—
82#13063301—22no—
83#13063301—22no—
84#13063301—22no—
85#13063301D414yes—
86#13063296—22no—
87#13063296—22no—
88#13063296—22no—
89#13063296D414yes—
90#13063293—28no—
91C4×C22⋊D43—28no—
92C4×C22⋊D43—28no—
93#13063284—22no—
94#13063284—22no—
95C2×C4⋊Dic43C2311yescharacteristic
96C2×C4⋊Dic43C2311yescharacteristic
97C2×C4⋊Dic43C2311yescharacteristic
98C2×C4⋊Dic43C2311yescharacteristic
99C2×Dic43⋊C4—21no—
100C2×Dic43⋊C4—21no—
101C2×Dic43⋊C4—21no—
102C2×Dic43⋊C4—21no—
103C4⋊C4×D43—22no—
104C4⋊C4×D43—22no—
105C4⋊C4×D43—41no—
106C4⋊C4×D43—41no—
107C2×C22⋊Dic43—21no—
108C2×C22⋊Dic43—21no—
109C2×C22⋊Dic43—21no—
110C2×C22⋊Dic43—21no—
111C2×(C2×D43)⋊C4—21no—
112C2×(C2×D43)⋊C4—21no—
113C2×(C2×D43)⋊C4—21no—
114C2×(C2×D43)⋊C4—21no—
115C22⋊C4×D43—44no—
116C2×C4×Dic43—21no—
117#13063259—22no—
118#13063258—22no—
119#13063257—22no—
120#13063256—22no—
121#13063249—22no—
122#13063249—41no—
123#13063246—22no—
124#13063246—41no—
125C22⋊(C43⋊C8)—22no—
126(C2×D43)⋊C8—22no—
127(C2×D43)⋊C8—22no—
128(C2×D43)⋊C8—41no—
129(C2×D43)⋊C8—41no—
130C43⋊#95—21no—
131C43⋊#95—21no—
132C43⋊#95—21no—
133C2×#41×C43—22no—
134C2×#41×C43—22no—
135C2×#41×C43—22no—
136C2×#41×C43—22no—
137C2×#41×C43—41no—
138C2×#41×C43—41no—
139C22×Q8×C43C2311yescharacteristic
140C22×D4×C43—21no—
141C22×D4×C43C2311yescharacteristic
142C23×C4×C43—21no—
143C23×C4×C43C2311yescharacteristic
144C22×C8×C43C2311yescharacteristic
145C22×C8×C43C2311yescharacteristic
146C2×C4⋊C4×C43C2311yescharacteristic
147C2×C4⋊C4×C43C2311yescharacteristic
148C2×C22⋊C4×C43—21no—
149#103×C43—22no—
150#103×C43—41no—
151#102×C43—22no—
152#102×C43—41no—
153C22⋊C8×C43—22no—
154#95×C43—21no—
155C24×C43—21no—
156C24×C43C2×D411yescharacteristic
157C23×D43—22no—
158C23×D43—22no—
159C23×D43—22no—
160C23×D43—22no—
161C23×D43—22no—
162C23×D43—41no—
163C23×D43—41no—
164C23×D43C2×D411yescharacteristic
165C23×D43C2×D411yescharacteristic
166#41×C43—44no—
167#41×C43—44no—
168#41×C43—44no—
169#41×C43—44no—
170C2×Q8×C43—21no—
171C2×Q8×C43—21no—
172C2×Q8×C43—21no—
173C2×Q8×C43—21no—
174C2×Q8×C43—21no—
175C2×Q8×C43C2×D412yes—
176C2×D4×C43—24no—
177C2×D4×C43—21no—
178C2×D4×C43—21no—
179C2×D4×C43—21no—
180C2×D4×C43—21no—
181C2×D4×C43—21no—
182C2×D4×C43—42no—
183C2×D4×C43—42no—
184C2×D4×C43C2×D412yes—
185C22×C4×C43—21no—
186C22×C4×C43—21no—
187C22×C4×C43—21no—
188C22×C4×C43—21no—
189C22×C4×C43—24no—
190C22×C4×C43—21no—
191C22×C4×C43—21no—
192C22×C4×C43—21no—
193C22×C4×C43—42no—
194C22×C4×C43—42no—
195C22×C4×C43C2×D411yescharacteristic
196C22×C4×C43#4112yes—
197C22×C4×C43#4112yes—
198C22×C4×C43C2411yescharacteristic
199C2×C22⋊D43—24no—
200C2×C22⋊D43—24no—
201C2×C22⋊D43—42no—
202C2×C22⋊D43—42no—
203C2×C22⋊D43—42no—
204C2×C22⋊D43—42no—
205C22×Dic43—22no—
206C22×Dic43—22no—
207C22×Dic43—21no—
208C22×Dic43—21no—
209C22×Dic43—21no—
210C22×Dic43—21no—
211C22×Dic43—41no—
212C22×Dic43C2×D411yescharacteristic
213C22×Dic43C2×D411yescharacteristic
214C2×C4×D43—21no—
215C2×C4×D43—21no—
216C2×C4×D43—21no—
217C2×C4×D43—21no—
218C2×C4×D43—22no—
219C2×C4×D43—22no—
220C2×C4×D43—21no—
221C2×C4×D43—21no—
222C2×C4×D43—21no—
223C2×C4×D43—21no—
224C2×C4×D43—21no—
225C2×C4×D43—21no—
226C2×C4×D43—22no—
227C2×C4×D43—22no—
228C2×C4×D43—41no—
229C2×C4×D43—41no—
230C2×C4×D43—42no—
231C2×C4×D43—42no—
232C2×C4×D43—44no—
233C2×C4×D43—44no—
234C2×C4×D43—44no—
235C2×C4×D43—44no—
236C2×C4×D43—42no—
237C2×C4×D43—42no—
238C2×C4×D43—42no—
239C2×C4×D43—42no—
240C2×C4×D43C2×D412yes—
241C2×C4×D43C2×D412yes—
242C2×C8×C43—21no—
243C2×C8×C43—21no—
244C2×C8×C43—21no—
245C2×C8×C43—21no—
246C2×C8×C43—21no—
247C2×C8×C43—21no—
248C4⋊C4×C43—21no—
249C4⋊C4×C43—21no—
250C4⋊C4×C43—21no—
251C4⋊C4×C43—21no—
252C22⋊C4×C43—42no—
253C22⋊Dic43—24no—
254C22⋊Dic43—24no—
255C22⋊Dic43—24no—
256C22⋊Dic43—42no—
257(C2×D43)⋊C4—24no—
258(C2×D43)⋊C4—24no—
259(C2×D43)⋊C4—42no—
260(C2×D43)⋊C4—42no—
261C4⋊Dic43—21no—
262C4⋊Dic43—21no—
263C4⋊Dic43—21no—
264C4⋊Dic43—21no—
265C4⋊Dic43—21no—
266C4⋊Dic43—21no—
267C4⋊Dic43C2×D412yes—
268C4⋊Dic43C2×D412yes—
269Dic43⋊C4—24no—
270Dic43⋊C4—24no—
271Dic43⋊C4—42no—
272Dic43⋊C4—42no—
273C4×Dic43—24no—
274C2×C43⋊C8—21no—
275C2×C43⋊C8—21no—
276C2×C43⋊C8—21no—
277C2×C43⋊C8—21no—
278C2×C43⋊C8—21no—
279C2×C43⋊C8—21no—
280C23×C43—21no—
281C23×C43—21no—
282C23×C43—21no—
283C23×C43—21no—
284C23×C43—21no—
285C23×C43—21no—
286C23×C43—22no—
287C23×C43—41no—
288C23×C43—41no—
289C23×C43—41no—
290C23×C43—41no—
291C23×C43—41no—
292C23×C43—41no—
293C23×C43#12312yes—
294C23×C43C22×D411yescharacteristic
295C22×D43—21no—
296C22×D43—21no—
297C22×D43—21no—
298C22×D43—21no—
299C22×D43—28no—
300C22×D43—21no—
301C22×D43—21no—
302C22×D43—21no—
303C22×D43—21no—
304C22×D43—21no—
305C22×D43—21no—
306C22×D43—44no—
307C22×D43—44no—
308C22×D43—44no—
309C22×D43—44no—
310C22×D43—44no—
311C22×D43—44no—
312C22×D43#12012yes—
313C22×D43#13512yes—
314C22×D43AGL(1,ℤ/8)12yes—
315C22×D43#13712yes—
316Q8×C43—22no—
317Q8×C43—22no—
318Q8×C43—41no—
319Q8×C43—41no—
320D4×C43—22no—
321D4×C43—22no—
322D4×C43—48no—
323D4×C43—41no—
324D4×C43—41no—
325C2×C4×C43—21no—
326C2×C4×C43—21no—
327C2×C4×C43—22no—
328C2×C4×C43—22no—
329C2×C4×C43—22no—
330C2×C4×C43—22no—
331C2×C4×C43—22no—
332C2×C4×C43—48no—
333C2×C4×C43—41no—
334C2×C4×C43—41no—
335C2×C4×C43—41no—
336C2×C4×C43—41no—
337C2×C4×C43—41no—
338C2×C4×C43—41no—
339C2×C4×C43—41no—
340C2×C4×C43—41no—
341C2×C4×C43#12312yes—
342C2×C4×C43C22×D411yescharacteristic
343C2×C4×C43C22×D411yescharacteristic
344C2×C4×C43C2×#4111yescharacteristic
345C2×C4×C43C2×#4111yescharacteristic
346C2×C4×C43H(5,𝔽2)11yescharacteristic
347C2×C4×C43H(5,𝔽2)11yescharacteristic
348C22⋊D43—48no—
349C22⋊D43—48no—
350C2×Dic43—21no—
351C2×Dic43—21no—
352C2×Dic43—22no—
353C2×Dic43—22no—
354C2×Dic43—21no—
355C2×Dic43—21no—
356C2×Dic43—21no—
357C2×Dic43—44no—
358C2×Dic43—41no—
359C2×Dic43—41no—
360C2×Dic43—41no—
361C2×Dic43—41no—
362C2×Dic43—41no—
363C2×Dic43—41no—
364C2×Dic43—41no—
365C2×Dic43—41no—
366C2×Dic43—41no—
367C2×Dic43—41no—
368C2×Dic43#12012yes—
369C4×D43—22no—
370C4×D43—22no—
371C4×D43—22no—
372C4×D43—22no—
373C4×D43—44no—
374C4×D43—44no—
375C4×D43—41no—
376C4×D43—41no—
377C4×D43—41no—
378C4×D43—41no—
379C4×D43—84no—
380C4×D43—84no—
381C8×C43—41no—
382C8×C43—41no—
383C43⋊C8—41no—
384C43⋊C8—41no—
385#24004—431nomaximal, Sylow
386C22×C43—22no—
387C22×C43—22no—
388C22×C43—22no—
389C22×C43—41no—
390C22×C43—41no—
391C22×C43—41no—
392C22×C43—41no—
393C22×C43—42no—
394C22×C43—42no—
395C22×C43—42no—
396C22×C43—81no—
397C22×C43—81no—
398C22×C43—81no—
399C22×C43—81no—
400C22×C43C2×#12011yescharacteristic
401C22×C43C2×#12311yescharacteristic
402C22×C43#53411yescharacteristic
403C22×C43C2×#13511yescharacteristic
404C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
405C22×C43C2×#13711yescharacteristic
406C22×C43#57511yescharacteristic
407C2×D43—22no—
408C2×D43—22no—
409C2×D43—22no—
410C2×D43—22no—
411C2×D43—22no—
412C2×D43—22no—
413C2×D43—22no—
414C2×D43—22no—
415C2×D43—22no—
416C2×D43—416no—
417C2×D43—41no—
418C2×D43—41no—
419C2×D43—41no—
420C2×D43—41no—
421C2×D43#44914yes—
422C4×C43—22no—
423C4×C43—42no—
424C4×C43—81no—
425C4×C43—81no—
426C4×C43#54611yescharacteristic
427C4×C43#54611yescharacteristic
428C4×C43#54611yescharacteristic
429C4×C43#54611yescharacteristic
430Dic43—22no—
431Dic43—41no—
432Dic43—42no—
433Dic43—42no—
434Dic43—81no—
435Dic43—81no—
436C2×#525—431no—
437C2×#483—431no—
438C2×#480—431no—
439C2×#380—431no—
440#2036—431no—
441#2036—431no—
442#2034—431no—
443#2034—431no—
444#1874—431no—
445#1872—431no—
446#1854—431no—
447#1854—431no—
448#1788—431no—
449#1788D4311yescharacteristic, complemented
450#1779—431no—
451C2×C43—42no—
452C2×C43—82no—
453C2×C43#240511yescharacteristic
454C2×C43C2×#44911yescharacteristic
455C2×C43#300711yescharacteristic
456C2×C43#309111yescharacteristic
457C2×C43#309211yescharacteristic
458C2×C43#319011yescharacteristic
459C2×C43#319411yescharacteristic
460D43—24no—
461D43—42no—
462C22×#41C2×D4311yescharacteristic
463C24×C4—431no—
464#525—864no—
465#525—864no—
466C2×#123—861no—
467C2×C22⋊Q8—431no—
468C2×C22⋊Q8—431no—
469C2×#121—431no—
470C2×#121—431no—
471C2×#120—861no—
472C2×C4×D4—861no—
473C2×C4×D4—861no—
474C2×#117—431no—
475C22×C4⋊C4—431no—
476C22×C4⋊C4—431no—
477C22×C22⋊C4—861no—
478#483—864no—
479#480—864no—
480C2×#107—431no—
481C2×#107—431no—
482C2×#106—431no—
483C2×#106—431no—
484C2×#103—431no—
485C2×#103—431no—
486C2×#103C2×D4311yescharacteristic, complemented
487C2×#103C2×D4311yescharacteristic, complemented
488C2×#102—431no—
489C2×#102—431no—
490C2×#102C2×D4311yescharacteristic, complemented
491C2×#102C2×D4311yescharacteristic, complemented
492C2×C22⋊C8—431no—
493C2×C22⋊C8—431no—
494C2×C22⋊C8—431no—
495C2×C22⋊C8—431no—
496C2×C22⋊C8—431no—
497C2×C22⋊C8C2×D4311yescharacteristic
498#380—431no—
499#380—431no—
500#380—431no—
501#380—861no—
502#380—861no—
503#380C2×D4311yescharacteristic
504C2×#95—861no—
505#340—431no—
506#340—431no—
507#340—431no—
508#340—431no—
509C43#2400411yescharacteristic, complemented, Sylow
510C25—431no—
511C2×#41—22no—
512C2×#41—22no—
513C2×#41—22no—
514C2×#41—22no—
515C2×#41—41no—
516C2×#41—41no—
517C22×Q8C22×D4311yescharacteristic
518C22×D4—21no—
519C22×D4—861no—
520C22×D4—861no—
521C22×D4C22×D4311yescharacteristic
522C23×C4—21no—
523C23×C4—431no—
524C23×C4—431no—
525C23×C4—431no—
526C23×C4—431no—
527C23×C4—431no—
528C23×C4—862no—
529C23×C4—862no—
530C23×C4—861no—
531C23×C4—861no—
532C23×C4—862no—
533C23×C4—862no—
534C23×C4—1721no—
535C23×C4—1721no—
536C23×C4C22×D4311yescharacteristic
537C22×C8—431no—
538C22×C8—431no—
539C22×C8C22×D4311yescharacteristic
540C22×C8C22×D4311yescharacteristic
541#123—868no—
542C22⋊Q8—434no—
543C22⋊Q8—862no—
544C22⋊Q8—862no—
545C22⋊Q8—862no—
546#121—434no—
547#121—862no—
548#121—862no—
549#121—862no—
550#120—868no—
551C4×D4—868no—
552C4×D4—868no—
553#117—862no—
554#117—862no—
555C2×C4⋊C4—431no—
556C2×C4⋊C4—431no—
557C2×C4⋊C4—431no—
558C2×C4⋊C4—431no—
559C2×C4⋊C4—862no—
560C2×C4⋊C4—862no—
561C2×C4⋊C4—861no—
562C2×C4⋊C4—861no—
563C2×C4⋊C4—861no—
564C2×C4⋊C4—861no—
565C2×C4⋊C4—1721no—
566C2×C4⋊C4—1721no—
567C2×C4⋊C4C22×D4311yescharacteristic
568C2×C4⋊C4C22×D4311yescharacteristic
569C2×C22⋊C4—21no—
570C2×C22⋊C4—861no—
571C2×C22⋊C4—861no—
572C2×C22⋊C4—861no—
573C2×C22⋊C4—861no—
574C2×C22⋊C4—861no—
575C2×C22⋊C4—861no—
576C2×C22⋊C4—861no—
577C2×C22⋊C4—861no—
578C2×C22⋊C4—1724no—
579C2×C42—861no—
580#107—862no—
581#107—862no—
582#106—862no—
583#106—862no—
584#103—22no—
585#103—41no—
586#103—862no—
587#103—1721no—
588#102—22no—
589#102—41no—
590#102—862no—
591#102—1721no—
592C22⋊C8—22no—
593C22⋊C8—862no—
594C22⋊C8—862no—
595C22⋊C8—862no—
596C22⋊C8—1721no—
597C22⋊C8—1721no—
598#95—21no—
599#95—861no—
600#95—861no—
601#95—861no—
602C24—21no—
603C24—431no—
604C24—431no—
605C24—862no—
606C24—862no—
607C24—862no—
608C24—862no—
609C24—862no—
610C24—1721no—
611C24—1721no—
612C24D4×D4311yescharacteristic
613#41—44no—
614#41—44no—
615#41—44no—
616#41—44no—
617C2×Q8—21no—
618C2×Q8—21no—
619C2×Q8—21no—
620C2×Q8—21no—
621C2×Q8—21no—
622C2×Q8D4×D4312yes—
623C2×D4—24no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—42no—
630C2×D4—42no—
631C2×D4—864no—
632C2×D4—864no—
633C2×D4—1722no—
634C2×D4—1722no—
635C2×D4—1722no—
636C2×D4—1722no—
637C2×D4D4×D4312yes—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—24no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—42no—
647C22×C4—42no—
648C22×C4—431no—
649C22×C4—432no—
650C22×C4—432no—
651C22×C4—431no—
652C22×C4—862no—
653C22×C4—862no—
654C22×C4—862no—
655C22×C4—861no—
656C22×C4—861no—
657C22×C4—861no—
658C22×C4—861no—
659C22×C4—862no—
660C22×C4—861no—
661C22×C4—861no—
662C22×C4—862no—
663C22×C4—862no—
664C22×C4—861no—
665C22×C4—861no—
666C22×C4—861no—
667C22×C4—861no—
668C22×C4—861no—
669C22×C4—861no—
670C22×C4—861no—
671C22×C4—861no—
672C22×C4—1721no—
673C22×C4—1721no—
674C22×C4—1724no—
675C22×C4—1724no—
676C22×C4—1724no—
677C22×C4—1724no—
678C22×C4—1722no—
679C22×C4—1722no—
680C22×C4—1722no—
681C22×C4—1722no—
682C22×C4—1722no—
683C22×C4—1722no—
684C22×C4—1721no—
685C22×C4#1062189812yes—
686C22×C4D4×D4311yescharacteristic
687C22×C4#1062190012yes—
688C22×C4C23×D4311yescharacteristic
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—21no—
694C2×C8—21no—
695C2×C8—861no—
696C2×C8—861no—
697C2×C8—861no—
698C2×C8—861no—
699C2×C8—861no—
700C2×C8—861no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—432no—
706C4⋊C4—432no—
707C4⋊C4—864no—
708C4⋊C4—864no—
709C4⋊C4—861no—
710C4⋊C4—861no—
711C4⋊C4—861no—
712C4⋊C4—861no—
713C4⋊C4—861no—
714C4⋊C4—861no—
715C4⋊C4—1722no—
716C4⋊C4—1722no—
717C22⋊C4—42no—
718C22⋊C4—864no—
719C22⋊C4—864no—
720C22⋊C4—864no—
721C22⋊C4—864no—
722C22⋊C4—864no—
723C22⋊C4—1722no—
724C22⋊C4—1722no—
725C22⋊C4—1722no—
726C42—864no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—22no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—432no—
741C23—432no—
742C23—432no—
743C23—432no—
744C23—868no—
745C23—861no—
746C23—861no—
747C23—861no—
748C23—861no—
749C23—861no—
750C23—861no—
751C23—861no—
752C23—861no—
753C23—861no—
754C23—861no—
755C23—1724no—
756C23—1724no—
757C23—1724no—
758C23—1724no—
759C23—1724no—
760C23—1724no—
761C23#1306330712yes—
762C23C2×D4×D4311yescharacteristic
763Q8—22no—
764Q8—22no—
765Q8—41no—
766Q8—41no—
767D4—22no—
768D4—22no—
769D4—48no—
770D4—41no—
771D4—41no—
772D4—1728no—
773D4—1728no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—48no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—432no—
791C2×C4—861no—
792C2×C4—861no—
793C2×C4—862no—
794C2×C4—862no—
795C2×C4—862no—
796C2×C4—862no—
797C2×C4—862no—
798C2×C4—862no—
799C2×C4—861no—
800C2×C4—861no—
801C2×C4—861no—
802C2×C4—3444no—
803C2×C4—3444no—
804C2×C4—1724no—
805C2×C4—1724no—
806C2×C4—1724no—
807C2×C4—1721no—
808C2×C4—1721no—
809C2×C4—1721no—
810C2×C4—1721no—
811C2×C4—1721no—
812C2×C4—1721no—
813C2×C4—1721no—
814C2×C4—1721no—
815C2×C4—1721no—
816C2×C4—1721no—
817C2×C4—1721no—
818C2×C4—1721no—
819C2×C4—1721no—
820C2×C4—1721no—
821C2×C4#1306330712yes—
822C2×C4C2×D4×D4311yescharacteristic
823C2×C4C2×D4×D4311yescharacteristic
824C2×C4C2×#1062190011yescharacteristic
825C2×C4C2×#1062189811yescharacteristic
826C2×C4#1306337011yescharacteristic
827C2×C4#1306337011yescharacteristic
828C8—41no—
829C8—41no—
830C8—1721no—
831C8—1721no—
832C22—22no—
833C22—22no—
834C22—22no—
835C22—41no—
836C22—41no—
837C22—41no—
838C22—41no—
839C22—42no—
840C22—42no—
841C22—42no—
842C22—81no—
843C22—81no—
844C22—81no—
845C22—81no—
846C22—434no—
847C22—862no—
848C22—862no—
849C22—862no—
850C22—862no—
851C22—862no—
852C22—862no—
853C22—862no—
854C22—862no—
855C22—862no—
856C22—17216no—
857C22—1721no—
858C22—1721no—
859C22—1721no—
860C22—1721no—
861C22#120×D4311yescharacteristic
862C22C2×#1306330711yescharacteristic
863C22#1458345911yescharacteristic
864C22#135×D4311yescharacteristic
865C22AGL(1,ℤ/8)×D4311yescharacteristic
866C22#137×D4311yescharacteristic
867C22#1458369611yescharacteristic
868C4—22no—
869C4—42no—
870C4—81no—
871C4—81no—
872C4—862no—
873C4—3441no—
874C4—3441no—
875C4—1722no—
876C4—1721no—
877C4—1722no—
878C4#1458353611yescharacteristic
879C4#1458353611yescharacteristic
880C4#1458353911yescharacteristic
881C4#1458353911yescharacteristic
882C2—42no—
883C2—82no—
884C2—864no—
885C2—1722no—
886C2#1913792011yescharacteristic
887C2#449×D4311yescharacteristic
888C2#1914385211yescharacteristic
889C2#1914450611yescharacteristic
890C2#1914451611yescharacteristic
891C2#1914537411yescharacteristic
892C2#1914540711yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1788C2
socleC23×C43C22×D4
prime radicalC2×#14583406C2
hypercenter#1788D43
hypocenterC43#24004
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1788

Complements

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

NH ≅ G/Ntype
2. C2×#14583228C2semidirect
3. C2×#14583211C2semidirect
4. #380×D43C2semidirect
5. #19135797C2semidirect
6. #19135796C2semidirect
7. #19135783C2semidirect
8. #19135782C2semidirect
9. #19134909C2semidirect
10. #19134899C2semidirect
11. #19134796C2semidirect
12. #19134792C2semidirect
13. #19134535C2semidirect
14. #19134504C2semidirect
15. C43×#1788C2semidirect
33. C2×#13063259C22semidirect
34. C2×#13063258C22semidirect
35. C2×#13063257C22semidirect
36. C2×#13063256C22semidirect
37. C2×#13063249C22semidirect
38. C2×#13063249C22semidirect
39. C2×#13063246C22semidirect
40. C2×#13063246C22semidirect
52. #14582662C22semidirect
53. #14582662C22semidirect
54. #14582661C22semidirect
55. #14582661C22semidirect
57. C2×#103×C43C22semidirect
58. C2×#103×C43C22semidirect
59. C2×#102×C43C22semidirect
60. C2×#102×C43C22semidirect
449. #1788D43semidirect
486. C2×#103C2×D43semidirect
487. C2×#103C2×D43semidirect
490. C2×#102C2×D43semidirect
491. C2×#102C2×D43semidirect
509. C43#24004semidirect

Maximal subgroups

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

subgroupindex
C2×#145834062
C2×#145832282
C2×#145832112
#380×D432
#191357972
#191357962
#191357832
#191357822
#191349092
#191348992
#191347962
#191347922
#191345352
#191345042
C43×#17882
#2400443