Finite Group Databasebeta

← #25112245

Subgroups — #25112245

Order 11008.

1530 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583548C211yesmaximal, characteristic
2C2×#14582975C211yesmaximal, characteristic, complemented
3C2×#14582897C211yesmaximal, characteristic, complemented
4C4⋊C4×C22⋊D43C211yesmaximal, characteristic, complemented
5#19135516C211yesmaximal, characteristic, complemented
6#19135395C211yesmaximal, characteristic, complemented
7#19135028C211yesmaximal, characteristic, complemented
8#19135025C211yesmaximal, characteristic, complemented
9#19134902C211yesmaximal, characteristic, complemented
10#19134899C211yesmaximal, characteristic, complemented
11#19134593C211yesmaximal, characteristic, complemented
12#19134535C211yesmaximal, characteristic, complemented
13#19134532C211yesmaximal, characteristic, complemented
14#102×Dic43C211yesmaximal, characteristic, complemented
15C2×C43×#417C211yesmaximal, characteristic, complemented
16C22×#10621900C2211yescharacteristic
17C22×#10621872C2211yescharacteristic
18#14583548—24no—
19#14583548C418yescomplemented
20C2×#13063323C2211yescharacteristic
21C2×#13063308—21no—
22C2×#13063306—21no—
23C2×#13063304C2211yescharacteristic
24C2×#13063301C2211yescharacteristic
25C2×#13063297—21no—
26C2×D4×Dic43C2211yescharacteristic
27C2×C4×C22⋊D43—21no—
28C2×C4×C22⋊D43C2211yescharacteristic
29C22×Dic43⋊C4—21no—
30C2×C4⋊C4×D43C2211yescharacteristic
31#14582975—24no—
32C2×Dic43⋊C8C2211yescharacteristic
33#14582897—24no—
34C2×#13063250C2211yescharacteristic
35C2×#13063250C2211yescharacteristic
36C2×#13063249C2211yescharacteristic
37C2×#13063249C2211yescharacteristic
38C2×#13063248C2211yescharacteristic
39C2×#13063248C2211yescharacteristic
40C2×#13063246C2211yescharacteristic
41C2×#13063246C2211yescharacteristic
42C2×C22⋊(C43⋊C8)C2211yescharacteristic
43C2×(C2×D43)⋊C8C2211yescharacteristic
44C2×C8×Dic43C2211yescharacteristic
45#14582794—21no—
46#14582772—21no—
47#14582770—21no—
48#14582768C2211yescharacteristic
49#14582759C2211yescharacteristic
50#14582756C2211yescharacteristic
51C4⋊C4×Dic43C2211yescharacteristic
52#14582662C2211yescharacteristic
53#14582662C2211yescharacteristic
54#14582661C2211yescharacteristic
55#14582661C2211yescharacteristic
56C22×#41×C43C2211yescharacteristic
57C22×M16×C43C2211yescharacteristic
58C22×C4⋊C4×C43C2211yescharacteristic
59C43×#417—24no—
60C2×#103×C43C2211yescharacteristic
61C2×#103×C43C2211yescharacteristic
62C2×#102×C43C2211yescharacteristic
63C2×#102×C43C2211yescharacteristic
64C2×#10621900—22no—
65C2×#10621900—22no—
66C2×#10621900—22no—
67C2×#10621900—41no—
68C2×#10621900—41no—
69C2×#10621900C2×C414yescomplemented
70C22×Dic86C2311yescharacteristic
71C22×C22⋊D43—21no—
72C22×C22⋊D43D411yescharacteristic
73C23×Dic43—21no—
74C23×Dic43—21no—
75C22×C4×D43—21no—
76C22×C4×D43C2311yescharacteristic
77C2×#10621872—22no—
78C2×#10621872—22no—
79C2×#10621872—41no—
80C22×C43⋊C8C2311yescharacteristic
81C22×C43⋊C8C2311yescharacteristic
82#13063323—22no—
83#13063323C2×C414yescomplemented
84#13063308—28no—
85#13063306—28no—
86#13063304—22no—
87#13063304C2×C414yescomplemented
88#13063301—22no—
89#13063301C2×C414yescomplemented
90#13063297—28no—
91D4×Dic43—22no—
92D4×Dic43C2×C414yescomplemented
93C4×C22⋊D43—44no—
94C4×C22⋊D43C2×C414yes—
95C4×C22⋊D43D414yes—
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—
103C2×Dic43⋊C4—28no—
104C2×Dic43⋊C4—21no—
105C2×Dic43⋊C4—21no—
106C2×Dic43⋊C4—21no—
107C2×Dic43⋊C4D411yescharacteristic
108C4⋊C4×D43—22no—
109C4⋊C4×D43—41no—
110C2×C22⋊Dic43—21no—
111C2×C22⋊Dic43—21no—
112C2×C22⋊Dic43—21no—
113C2×C22⋊Dic43D411yescharacteristic
114C2×(C2×D43)⋊C4—21no—
115C2×(C2×D43)⋊C4—21no—
116C2×(C2×D43)⋊C4D411yescharacteristic
117C2×C4×Dic43—21no—
118C2×C4×Dic43C2311yescharacteristic
119Dic43⋊C8—22no—
120#13063250—22no—
121#13063250—41no—
122#13063249—41no—
123#13063249—41no—
124#13063248—22no—
125#13063248—41no—
126#13063246—22no—
127#13063246—22no—
128C22⋊(C43⋊C8)—22no—
129(C2×D43)⋊C8—22no—
130C8×Dic43—22no—
131C43⋊#95—21no—
132C43⋊#95—21no—
133C43⋊#95—21no—
134C2×#41×C43—22no—
135C2×#41×C43—22no—
136C2×#41×C43—22no—
137C2×#41×C43—41no—
138C2×#41×C43—41no—
139C2×#41×C43C2×C414yescomplemented
140C22×Q8×C43C2311yescharacteristic
141C22×D4×C43—21no—
142C22×D4×C43C2311yescharacteristic
143C23×C4×C43—21no—
144C23×C4×C43—21no—
145C23×C4×C43C2311yescharacteristic
146C2×M16×C43—22no—
147C2×M16×C43—22no—
148C2×M16×C43—41no—
149C22×C8×C43C2311yescharacteristic
150C22×C8×C43C2311yescharacteristic
151C2×C4⋊C4×C43—22no—
152C2×C4⋊C4×C43—21no—
153C2×C4⋊C4×C43—41no—
154C2×C4⋊C4×C43C2311yescharacteristic
155C2×C4⋊C4×C43C2311yescharacteristic
156#103×C43—22no—
157#103×C43—22no—
158#102×C43—22no—
159#102×C43D414yescomplemented
160C24×C43—21no—
161C24×C43C2×D411yescharacteristic
162C23×D43C2×D411yescharacteristic
163#41×C43—28no—
164#41×C43—44no—
165#41×C43—44no—
166#41×C43—44no—
167C2×Q8×C43—21no—
168C2×Q8×C43—21no—
169C2×Q8×C43—21no—
170C2×Q8×C43—21no—
171C2×Q8×C43—21no—
172C2×Q8×C43C22×C412yes—
173C2×D4×C43—21no—
174C2×D4×C43—21no—
175C2×D4×C43—21no—
176C2×D4×C43—24no—
177C2×D4×C43—42no—
178C2×D4×C43—42no—
179C2×D4×C43C22×C412yes—
180C2×D4×C43C2×D412yes—
181C2×D4×C43#4112yes—
182C22×C4×C43—21no—
183C22×C4×C43—21no—
184C22×C4×C43—21no—
185C22×C4×C43—21no—
186C22×C4×C43—24no—
187C22×C4×C43—21no—
188C22×C4×C43—21no—
189C22×C4×C43—21no—
190C22×C4×C43—42no—
191C22×C4×C43—42no—
192C22×C4×C43—42no—
193C22×C4×C43—42no—
194C22×C4×C43—81no—
195C22×C4×C43C22×C412yes—
196C22×C4×C43C2×D412yes—
197C22×C4×C43C2×D411yescharacteristic
198C22×C4×C43C2411yescharacteristic
199C2×C22⋊D43—22no—
200C2×C22⋊D43—22no—
201C2×C22⋊D43—24no—
202C2×C22⋊D43—42no—
203C2×C22⋊D43—42no—
204C2×C22⋊D43C22⋊C414yes—
205C22×Dic43—24no—
206C22×Dic43—24no—
207C22×Dic43—21no—
208C22×Dic43—21no—
209C22×Dic43—21no—
210C22×Dic43—21no—
211C22×Dic43—42no—
212C22×Dic43—42no—
213C22×Dic43—42no—
214C22×Dic43—42no—
215C22×Dic43C2×D411yescharacteristic
216C22×Dic43C2×D411yescharacteristic
217C22×Dic43C2×D411yescharacteristic
218#10621900—28no—
219#10621900—44no—
220#10621900—44no—
221#10621900—44no—
222C2×C4×D43—21no—
223C2×C4×D43—21no—
224C2×C4×D43—21no—
225C2×C4×D43—21no—
226C2×C4×D43—42no—
227C2×C4×D43—42no—
228C2×C4×D43—81no—
229C2×C4×D43C22×C412yes—
230C2×C4×D43C2×D412yes—
231C2×Dic86—21no—
232C2×Dic86—21no—
233C2×Dic86—21no—
234C2×Dic86—21no—
235C2×Dic86—21no—
236C2×Dic86C22×C412yes—
237M16×C43—44no—
238C2×C8×C43—21no—
239C2×C8×C43—21no—
240C2×C8×C43—21no—
241C2×C8×C43—21no—
242C2×C8×C43—21no—
243C2×C8×C43C2×D412yes—
244C4⋊C4×C43—21no—
245C4⋊C4×C43—21no—
246C4⋊C4×C43—21no—
247C4⋊C4×C43—42no—
248C4⋊C4×C43C2×D412yes—
249C22⋊Dic43—24no—
250C22⋊Dic43—24no—
251C22⋊Dic43—42no—
252C22⋊Dic43C22⋊C414yes—
253(C2×D43)⋊C4—24no—
254(C2×D43)⋊C4—42no—
255(C2×D43)⋊C4C22⋊C414yes—
256C4⋊Dic43—21no—
257C4⋊Dic43—21no—
258C4⋊Dic43—21no—
259C4⋊Dic43—21no—
260C4⋊Dic43—21no—
261C4⋊Dic43C22×C412yes—
262Dic43⋊C4—24no—
263Dic43⋊C4—24no—
264Dic43⋊C4—24no—
265Dic43⋊C4—24no—
266Dic43⋊C4—42no—
267Dic43⋊C4—42no—
268Dic43⋊C4—81no—
269Dic43⋊C4C22⋊C414yes—
270C4×Dic43—42no—
271C4×Dic43C22×C412yes—
272C4×Dic43C2×D412yes—
273C2×C43⋊C8—21no—
274C2×C43⋊C8—21no—
275C2×C43⋊C8—21no—
276C2×C43⋊C8—21no—
277C2×C43⋊C8—21no—
278C2×C43⋊C8—21no—
279#10621872—44no—
280C23×C43—22no—
281C23×C43—22no—
282C23×C43—21no—
283C23×C43—22no—
284C23×C43—21no—
285C23×C43—21no—
286C23×C43—21no—
287C23×C43—21no—
288C23×C43—21no—
289C23×C43—41no—
290C23×C43—41no—
291C23×C43—41no—
292C23×C43—41no—
293C23×C43C2×C22⋊C412yes—
294C23×C43C22×D411yescharacteristic
295C22×D43—21no—
296C22×D43—21no—
297C22×D43—21no—
298C22×D43—21no—
299C22×D43—21no—
300C22×D43—21no—
301C22×D43C2×C22⋊C412yes—
302Q8×C43—22no—
303Q8×C43—22no—
304Q8×C43—41no—
305Q8×C43—41no—
306D4×C43—22no—
307D4×C43—22no—
308D4×C43—22no—
309D4×C43—48no—
310D4×C43C4×D414yescomplemented
311C2×C4×C43—21no—
312C2×C4×C43—21no—
313C2×C4×C43—22no—
314C2×C4×C43—22no—
315C2×C4×C43—22no—
316C2×C4×C43—22no—
317C2×C4×C43—22no—
318C2×C4×C43—22no—
319C2×C4×C43—48no—
320C2×C4×C43—41no—
321C2×C4×C43—41no—
322C2×C4×C43—41no—
323C2×C4×C43—41no—
324C2×C4×C43—41no—
325C2×C4×C43—41no—
326C2×C4×C43—41no—
327C2×C4×C43—84no—
328C2×C4×C43C2×C22⋊C412yes—
329C2×C4×C43C23×C411yescharacteristic
330C2×C4×C43C22×D411yescharacteristic
331C2×C4×C43C22×D411yescharacteristic
332C2×C4×C43C2×#4111yescharacteristic
333C2×C4×C43H(5,𝔽2)11yescharacteristic
334C2×C4×C43H(5,𝔽2)11yescharacteristic
335C22⋊D43—28no—
336C22⋊D43—48no—
337C2×Dic43—21no—
338C2×Dic43—21no—
339C2×Dic43—21no—
340C2×Dic43—21no—
341C2×Dic43—22no—
342C2×Dic43—22no—
343C2×Dic43—48no—
344C2×Dic43—41no—
345C2×Dic43—41no—
346C2×Dic43—41no—
347C2×Dic43—41no—
348C2×Dic43—48no—
349C2×Dic43—41no—
350C2×Dic43—41no—
351C2×Dic43—41no—
352C2×Dic43—41no—
353C2×Dic43—41no—
354C2×Dic43—41no—
355C2×Dic43C2×C22⋊C412yes—
356C2×Dic43C2×C22⋊C412yes—
357C2×Dic43C2×C22⋊C412yes—
358C2×Dic43AGL(1,ℤ/8)12yes—
359C2×Dic43#13712yes—
360C4×D43—22no—
361C4×D43—22no—
362C4×D43—22no—
363C4×D43—22no—
364C4×D43—84no—
365Dic86—22no—
366Dic86—22no—
367Dic86—41no—
368Dic86—41no—
369C8×C43—22no—
370C8×C43—41no—
371C43⋊C8—41no—
372C43⋊C8—41no—
373#22431—431nomaximal, Sylow
374C22×C43—24no—
375C22×C43—22no—
376C22×C43—22no—
377C22×C43—22no—
378C22×C43—41no—
379C22×C43—42no—
380C22×C43—41no—
381C22×C43—42no—
382C22×C43—42no—
383C22×C43—42no—
384C22×C43—41no—
385C22×C43—42no—
386C22×C43—41no—
387C22×C43—42no—
388C22×C43C22×C22⋊C411yescharacteristic
389C22×C43D4211yescharacteristic
390C22×C43#54611yescharacteristic
391C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
392C22×C43C2×#13711yescharacteristic
393C22×C43#57711yescharacteristic
394C22×C43#57811yescharacteristic
395C2×D43—22no—
396C2×D43—22no—
397C2×D43—22no—
398C2×D43—41no—
399C2×D43—41no—
400C2×D43—41no—
401C2×D43—41no—
402C4×C43—22no—
403C4×C43—42no—
404C4×C43—42no—
405C4×C43—81no—
406C4×C43C2×C4×D411yescharacteristic
407C4×C43#51811yescharacteristic
408C4×C43D4211yescharacteristic
409C4×C43#54611yescharacteristic
410Dic43—22no—
411Dic43—22no—
412Dic43—42no—
413Dic43—42no—
414Dic43—81no—
415Dic43—81no—
416Dic43#41714yescomplemented
417C2×#547—431no—
418C2×#436—431no—
419C2×#417—431no—
420C2×#417D4311yescharacteristic, complemented
421D4×C4⋊C4—431no—
422#1981—431no—
423#1956—431no—
424#1894—431no—
425#1894—431no—
426#1872—431no—
427#1872—431no—
428#1802—431no—
429#1788—431no—
430#1788—431no—
431C4×#102—431no—
432C2×C43—42no—
433C2×C43—44no—
434C2×C43D4×C22⋊C411yescharacteristic
435C2×C43C2×#41711yescharacteristic
436C2×C43#289811yescharacteristic
437C2×C43#327211yescharacteristic
438C2×C43#327611yescharacteristic
439C2×C43#333011yescharacteristic
440C2×C43#333111yescharacteristic
441D43—42no—
442C22×#41—431no—
443C22×#41C2×D4311yescharacteristic
444C22×M16—431no—
445C22×M16C2×D4311yescharacteristic
446#547—438no—
447#547—864no—
448C2×C4⋊Q8—431no—
449C2×#123—861no—
450C2×#123—861no—
451C2×C22⋊Q8—431no—
452C2×C22⋊Q8—431no—
453C2×#121—861no—
454C2×C4×D4—431no—
455C2×C4×D4—431no—
456C2×C4×D4—861no—
457C22×C4⋊C4—431no—
458C22×C4⋊C4—861no—
459C22×C4⋊C4C2×D4311yescharacteristic
460#436—864no—
461C2×C4⋊C8—431no—
462#417—24no—
463#417—864no—
464C2×#103—431no—
465C2×#103—431no—
466C2×#103—431no—
467C2×#103—431no—
468C2×#103—431no—
469C2×#103—431no—
470C2×#103C2×D4311yescharacteristic
471C2×#103C2×D4311yescharacteristic
472C2×#102—431no—
473C2×#102—431no—
474C2×#102C2×D4311yescharacteristic
475C2×#102C2×D4311yescharacteristic
476C2×C22⋊C8—431no—
477C2×C22⋊C8—431no—
478C2×C4×C8—431no—
479#389—861no—
480#385—861no—
481#385—861no—
482#384—431no—
483#380—431no—
484#380—431no—
485C4×C4⋊C4—431no—
486#340—431no—
487#340—431no—
488#340—431no—
489#340—431no—
490C43#2243111yescharacteristic, complemented, Sylow
491C2×#41—22no—
492C2×#41—22no—
493C2×#41—22no—
494C2×#41—41no—
495C2×#41—41no—
496C2×#41—434no—
497C2×#41—862no—
498C2×#41—862no—
499C2×#41—862no—
500C2×#41—1721no—
501C2×#41—1721no—
502C2×#41C4×D4314yescomplemented
503C22×Q8—431no—
504C22×Q8C22×D4311yescharacteristic
505C22×D4—21no—
506C22×D4—431no—
507C22×D4—861no—
508C22×D4C22×D4311yescharacteristic
509C23×C4—21no—
510C23×C4—21no—
511C23×C4—431no—
512C23×C4—861no—
513C23×C4—861no—
514C23×C4—861no—
515C23×C4C22×D4311yescharacteristic
516C2×M16—22no—
517C2×M16—22no—
518C2×M16—41no—
519C2×M16—862no—
520C2×M16—862no—
521C2×M16—1721no—
522C22×C8—431no—
523C22×C8—431no—
524C22×C8C22×D4311yescharacteristic
525C22×C8C22×D4311yescharacteristic
526C4⋊Q8—434no—
527C4⋊Q8—862no—
528#123—868no—
529#123—868no—
530C22⋊Q8—434no—
531C22⋊Q8—434no—
532C22⋊Q8—862no—
533C22⋊Q8—862no—
534#121—868no—
535C4×D4—434no—
536C4×D4—434no—
537C4×D4—434no—
538C4×D4—862no—
539C4×D4—1724no—
540C2×C4⋊C4—22no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4—41no—
543C2×C4⋊C4—431no—
544C2×C4⋊C4—431no—
545C2×C4⋊C4—431no—
546C2×C4⋊C4—431no—
547C2×C4⋊C4—868no—
548C2×C4⋊C4—861no—
549C2×C4⋊C4—861no—
550C2×C4⋊C4—861no—
551C2×C4⋊C4—861no—
552C2×C4⋊C4—862no—
553C2×C4⋊C4—861no—
554C2×C4⋊C4—861no—
555C2×C4⋊C4—861no—
556C2×C4⋊C4—1721no—
557C2×C4⋊C4C22×D4311yescharacteristic
558C2×C4⋊C4C22×D4311yescharacteristic
559C2×C22⋊C4—431no—
560C2×C22⋊C4—431no—
561C2×C22⋊C4—861no—
562C2×C22⋊C4—861no—
563C2×C22⋊C4—861no—
564C2×C22⋊C4—861no—
565C2×C22⋊C4—861no—
566C2×C42—431no—
567C2×C42—861no—
568C4⋊C8—862no—
569#103—22no—
570#103—22no—
571#103—862no—
572#103—862no—
573#103—1721no—
574#103—1721no—
575#103—1721no—
576#103—1721no—
577#102—22no—
578#102—862no—
579#102—862no—
580#102C22⋊D4314yescomplemented
581C22⋊C8—862no—
582C22⋊C8—862no—
583C4×C8—862no—
584#95—861no—
585#95—861no—
586#95—861no—
587C24—21no—
588C24—431no—
589C24D4×D4311yescharacteristic
590#41—28no—
591#41—44no—
592#41—44no—
593#41—44no—
594#41—868no—
595#41—1724no—
596#41—1724no—
597#41—1724no—
598C2×Q8—21no—
599C2×Q8—21no—
600C2×Q8—21no—
601C2×Q8—21no—
602C2×Q8—21no—
603C2×Q8—432no—
604C2×Q8—861no—
605C2×Q8—861no—
606C2×Q8—861no—
607C2×Q8—861no—
608C2×Q8—861no—
609C2×Q8C2×C4×D4312yes—
610C2×D4—24no—
611C2×D4—21no—
612C2×D4—21no—
613C2×D4—21no—
614C2×D4—42no—
615C2×D4—42no—
616C2×D4—434no—
617C2×D4—862no—
618C2×D4—862no—
619C2×D4—864no—
620C2×D4—1722no—
621C2×D4—1722no—
622C2×D4C2×C4×D4312yes—
623C2×D4#1062189812yes—
624C2×D4C2×C22⋊D4312yes—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—24no—
632C22×C4—21no—
633C22×C4—42no—
634C22×C4—42no—
635C22×C4—42no—
636C22×C4—42no—
637C22×C4—81no—
638C22×C4—431no—
639C22×C4—431no—
640C22×C4—431no—
641C22×C4—432no—
642C22×C4—432no—
643C22×C4—864no—
644C22×C4—864no—
645C22×C4—861no—
646C22×C4—861no—
647C22×C4—861no—
648C22×C4—861no—
649C22×C4—861no—
650C22×C4—861no—
651C22×C4—861no—
652C22×C4—861no—
653C22×C4—3441no—
654C22×C4—1722no—
655C22×C4—1722no—
656C22×C4—1722no—
657C22×C4—1722no—
658C22×C4—1722no—
659C22×C4—1722no—
660C22×C4C2×C4×D4312yes—
661C22×C4D4×D4311yescharacteristic
662C22×C4D4×D4312yes—
663C22×C4C23×D4311yescharacteristic
664M16—44no—
665M16—1724no—
666C2×C8—21no—
667C2×C8—21no—
668C2×C8—21no—
669C2×C8—21no—
670C2×C8—21no—
671C2×C8—861no—
672C2×C8—861no—
673C2×C8—861no—
674C2×C8—861no—
675C2×C8—861no—
676C2×C8—861no—
677C2×C8C2×C22⋊D4312yes—
678C4⋊C4—21no—
679C4⋊C4—21no—
680C4⋊C4—21no—
681C4⋊C4—42no—
682C4⋊C4—434no—
683C4⋊C4—432no—
684C4⋊C4—864no—
685C4⋊C4—864no—
686C4⋊C4—864no—
687C4⋊C4—864no—
688C4⋊C4—861no—
689C4⋊C4—861no—
690C4⋊C4—861no—
691C4⋊C4—861no—
692C4⋊C4—861no—
693C4⋊C4—3441no—
694C4⋊C4—1722no—
695C4⋊C4—1722no—
696C4⋊C4C2×C22⋊D4312yes—
697C22⋊C4—434no—
698C22⋊C4—434no—
699C22⋊C4—864no—
700C22⋊C4—864no—
701C22⋊C4—864no—
702C22⋊C4—1722no—
703C22⋊C4—1722no—
704C42—432no—
705C42—432no—
706C42—1722no—
707C23—22no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23—22no—
714C23—21no—
715C23—22no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—432no—
721C23—861no—
722C23—861no—
723C23—861no—
724C23—861no—
725C23—861no—
726C23—861no—
727C23C22⋊C4×D4312yes—
728C23C2×D4×D4311yescharacteristic
729Q8—22no—
730Q8—22no—
731Q8—41no—
732Q8—41no—
733Q8—862no—
734Q8—862no—
735Q8—1721no—
736Q8—1721no—
737D4—22no—
738D4—22no—
739D4—22no—
740D4—48no—
741D4—868no—
742D4—1728no—
743D4C4×C22⋊D4314yescomplemented
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—48no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—84no—
761C2×C4—432no—
762C2×C4—432no—
763C2×C4—432no—
764C2×C4—432no—
765C2×C4—432no—
766C2×C4—861no—
767C2×C4—861no—
768C2×C4—861no—
769C2×C4—861no—
770C2×C4—862no—
771C2×C4—862no—
772C2×C4—862no—
773C2×C4—862no—
774C2×C4—862no—
775C2×C4—862no—
776C2×C4—3444no—
777C2×C4—1728no—
778C2×C4—1728no—
779C2×C4—1721no—
780C2×C4—1721no—
781C2×C4—1721no—
782C2×C4—1721no—
783C2×C4—1721no—
784C2×C4—1721no—
785C2×C4—1721no—
786C2×C4—1721no—
787C2×C4—1721no—
788C2×C4—1721no—
789C2×C4C22⋊C4×D4312yes—
790C2×C4C22×C4×D4311yescharacteristic
791C2×C4C2×D4×D4311yescharacteristic
792C2×C4C22×C22⋊D4311yescharacteristic
793C2×C4C2×#1062189811yescharacteristic
794C2×C4#1306337011yescharacteristic
795C2×C4#1306337011yescharacteristic
796C8—22no—
797C8—41no—
798C8—1721no—
799C8—1721no—
800C22—22no—
801C22—24no—
802C22—22no—
803C22—22no—
804C22—41no—
805C22—42no—
806C22—41no—
807C22—42no—
808C22—42no—
809C22—41no—
810C22—42no—
811C22—42no—
812C22—41no—
813C22—42no—
814C22—862no—
815C22—862no—
816C22—862no—
817C22—1721no—
818C22—1721no—
819C22—1721no—
820C22—1721no—
821C22C2×C22⋊C4×D4311yescharacteristic
822C22D4×C22⋊D4311yescharacteristic
823C22#1458353911yescharacteristic
824C22AGL(1,ℤ/8)×D4311yescharacteristic
825C22#137×D4311yescharacteristic
826C22#1458370911yescharacteristic
827C22#1458371511yescharacteristic
828C4—22no—
829C4—42no—
830C4—42no—
831C4—81no—
832C4—434no—
833C4—862no—
834C4—862no—
835C4—3441no—
836C4—3441no—
837C4—1722no—
838C4—1722no—
839C4C2×C4×C22⋊D4311yescharacteristic
840C4#1458337211yescharacteristic
841C4D4×C22⋊D4311yescharacteristic
842C4#1458353911yescharacteristic
843C2—42no—
844C2—44no—
845C2—1722no—
846C2C22⋊C4×C22⋊D4311yescharacteristic
847C2#417×D4311yescharacteristic
848C2#1914312611yescharacteristic
849C2#1914618911yescharacteristic
850C2#1914623511yescharacteristic
851C2#1914689611yescharacteristic
852C2#1914690711yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#417C2
socleC23×C43C22×D4
prime radicalC2×#14583548C2
cosocleC22×C4×C43C24
hypercenterC2×#417D43
hypocenterC43#22431
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#417

Complements

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

NH ≅ G/Ntype
2. C2×#14582975C2semidirect
3. C2×#14582897C2semidirect
4. C4⋊C4×C22⋊D43C2semidirect
5. #19135516C2semidirect
6. #19135395C2semidirect
7. #19135028C2semidirect
8. #19135025C2semidirect
9. #19134902C2semidirect
10. #19134899C2semidirect
11. #19134593C2semidirect
12. #19134535C2semidirect
13. #19134532C2semidirect
14. #102×Dic43C2semidirect
15. C2×C43×#417C2semidirect
19. #14583548C4semidirect
69. C2×#10621900C2×C4semidirect
83. #13063323C2×C4semidirect
87. #13063304C2×C4semidirect
89. #13063301C2×C4semidirect
92. D4×Dic43C2×C4semidirect
139. C2×#41×C43C2×C4semidirect
159. #102×C43D4semidirect
310. D4×C43C4×D4semidirect
416. Dic43#417semidirect
420. C2×#417D43semidirect
490. C43#22431semidirect
502. C2×#41C4×D43semidirect
580. #102C22⋊D43semidirect
743. D4C4×C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145835482
C2×#145829752
C2×#145828972
C4⋊C4×C22⋊D432
#191355162
#191353952
#191350282
#191350252
#191349022
#191348992
#191345932
#191345352
#191345322
#102×Dic432
C2×C43×#4172
#2243143