Finite Group Databasebeta

← #25112108

Subgroups — #25112108

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×#14583556C211yesmaximal, characteristic
2C2×#14582968C211yesmaximal, characteristic, complemented
3C2×#103×D43C211yesmaximal, characteristic, complemented
4C4⋊C4×C22⋊D43C211yesmaximal, characteristic, complemented
5#19135526C211yesmaximal, characteristic, complemented
6#19135410C211yesmaximal, characteristic, complemented
7#19135028C211yesmaximal, characteristic, complemented
8#19135020C211yesmaximal, characteristic, complemented
9#19134909C211yesmaximal, characteristic, complemented
10#19134902C211yesmaximal, characteristic, complemented
11#19134598C211yesmaximal, characteristic, complemented
12#19134535C211yesmaximal, characteristic, complemented
13#19134528C211yesmaximal, characteristic, complemented
14#19134427C211yesmaximal, characteristic, complemented
15C2×C43×#417C211yesmaximal, characteristic, complemented
16C22×Q8×D43C2211yescharacteristic
17C22×C8×D43C2211yescharacteristic
18#14583556—24no—
19#14583556C418yescomplemented
20C2×#13063312—21no—
21C2×#13063312C2211yescharacteristic
22C2×#13063304—21no—
23C2×#13063304C2211yescharacteristic
24C2×#13063296—21no—
25C2×#13063296C2211yescharacteristic
26C2×Q8×Dic43C2211yescharacteristic
27C2×C4×C22⋊D43—21no—
28C2×C4×C22⋊D43—21no—
29C2×C4×C22⋊D43C2211yescharacteristic
30C2×C4⋊C4×D43C2211yescharacteristic
31#14582968—24no—
32C2×Dic43⋊C8C2211yescharacteristic
33C2×#13063250C2211yescharacteristic
34C2×#13063250C2211yescharacteristic
35C2×#13063249C2211yescharacteristic
36C2×#13063249C2211yescharacteristic
37C2×#13063248C2211yescharacteristic
38C2×#13063248C2211yescharacteristic
39#103×D43—24no—
40C2×#13063246C2211yescharacteristic
41C2×#13063246C2211yescharacteristic
42C2×C22⋊(C43⋊C8)C2211yescharacteristic
43C2×(C2×D43)⋊C8C2211yescharacteristic
44C2×#13063235C2211yescharacteristic
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
64C22×Dic86—21no—
65C22×Dic86C2311yescharacteristic
66C2×Q8×D43—22no—
67C2×Q8×D43—22no—
68C2×Q8×D43—22no—
69C2×Q8×D43—41no—
70C2×Q8×D43—41no—
71C2×Q8×D43C2×C414yescomplemented
72C22×C22⋊D43—21no—
73C22×C22⋊D43D411yescharacteristic
74C22×C4×D43—21no—
75C22×C4×D43—21no—
76C22×C4×D43C2311yescharacteristic
77C22×C43⋊C8C2311yescharacteristic
78C22×C43⋊C8C2311yescharacteristic
79C2×C8×D43—22no—
80C2×C8×D43—22no—
81C2×C8×D43—41no—
82#13063312—28no—
83#13063312—22no—
84#13063312C2×C414yescomplemented
85#13063304—22no—
86#13063304—28no—
87#13063304C2×C414yescomplemented
88#13063296—28no—
89#13063296—22no—
90#13063296C2×C414yescomplemented
91Q8×Dic43—22no—
92Q8×Dic43C2×C414yescomplemented
93C4×C22⋊D43—28no—
94C4×C22⋊D43—44no—
95C4×C22⋊D43C2×C414yes—
96C4×C22⋊D43D414yes—
97C2×C4⋊Dic43—21no—
98C2×C4⋊Dic43C2311yescharacteristic
99C2×C4⋊Dic43C2311yescharacteristic
100C2×C4⋊Dic43C2311yescharacteristic
101C2×Dic43⋊C4—21no—
102C2×Dic43⋊C4—21no—
103C2×Dic43⋊C4—21no—
104C2×Dic43⋊C4—21no—
105C2×Dic43⋊C4D411yescharacteristic
106C4⋊C4×D43—22no—
107C4⋊C4×D43—41no—
108C2×C22⋊Dic43—21no—
109C2×C22⋊Dic43—21no—
110C2×C22⋊Dic43—21no—
111C2×C22⋊Dic43—21no—
112C2×C22⋊Dic43—21no—
113C2×C22⋊Dic43D411yescharacteristic
114C2×(C2×D43)⋊C4—21no—
115C2×(C2×D43)⋊C4D411yescharacteristic
116C2×C4×Dic43—21no—
117C2×C4×Dic43—21no—
118C2×C4×Dic43C2311yescharacteristic
119Dic43⋊C8—22no—
120#13063250—22no—
121#13063250—41no—
122#13063249—22no—
123#13063249—22no—
124#13063248—22no—
125#13063248—41no—
126#13063246—41no—
127#13063246—41no—
128C22⋊(C43⋊C8)—22no—
129(C2×D43)⋊C8—22no—
130#13063235—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×C43D414yescomplemented
158#102×C43—22no—
159#102×C43—22no—
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×C43C22×C412yes—
171C2×Q8×C43C2×D412yes—
172C2×Q8×C43#4112yes—
173C2×D4×C43—21no—
174C2×D4×C43—24no—
175C2×D4×C43—21no—
176C2×D4×C43—21no—
177C2×D4×C43—21no—
178C2×D4×C43—21no—
179C2×D4×C43—42no—
180C2×D4×C43—42no—
181C2×D4×C43C22×C412yes—
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—24no—
200C2×C22⋊D43—22no—
201C2×C22⋊D43—22no—
202C2×C22⋊D43—42no—
203C2×C22⋊D43—42no—
204C2×C22⋊D43C22⋊C414yes—
205C22×Dic43—21no—
206C22×Dic43—21no—
207C22×Dic43—21no—
208C22×Dic43—21no—
209C22×Dic43C2×D411yescharacteristic
210C22×Dic43C2×D411yescharacteristic
211C22×Dic43C2×D411yescharacteristic
212Q8×D43—28no—
213Q8×D43—44no—
214Q8×D43—44no—
215Q8×D43—44no—
216C2×C4×D43—21no—
217C2×C4×D43—21no—
218C2×C4×D43—21no—
219C2×C4×D43—21no—
220C2×C4×D43—24no—
221C2×C4×D43—42no—
222C2×C4×D43—42no—
223C2×C4×D43—42no—
224C2×C4×D43—42no—
225C2×C4×D43—81no—
226C2×C4×D43C22×C412yes—
227C2×C4×D43C2×D412yes—
228C2×Dic86—21no—
229C2×Dic86—21no—
230C2×Dic86—21no—
231C2×Dic86—21no—
232C2×Dic86—21no—
233C2×Dic86—24no—
234C2×Dic86—42no—
235C2×Dic86—42no—
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—24no—
252C22⋊Dic43—24no—
253C22⋊Dic43—42no—
254C22⋊Dic43C22⋊C414yes—
255(C2×D43)⋊C4—42no—
256(C2×D43)⋊C4C22⋊C414yes—
257C4⋊Dic43—21no—
258C4⋊Dic43—24no—
259C4⋊Dic43—21no—
260C4⋊Dic43—21no—
261C4⋊Dic43—21no—
262C4⋊Dic43—21no—
263C4⋊Dic43C22×C412yes—
264Dic43⋊C4—24no—
265Dic43⋊C4—42no—
266Dic43⋊C4—42no—
267Dic43⋊C4—81no—
268Dic43⋊C4C22⋊C414yes—
269C4×Dic43—24no—
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—
279C8×D43—44no—
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×C43C2×C22⋊C412yes—
294C23×C43C22×D411yescharacteristic
295C22×D43—21no—
296C22×D43—21no—
297C22×D43—21no—
298C22×D43—21no—
299C22×D43C2×C22⋊C412yes—
300C22×D43AGL(1,ℤ/8)12yes—
301C22×D43#13712yes—
302Q8×C43—22no—
303Q8×C43—22no—
304Q8×C43—22no—
305Q8×C43C4×D414yescomplemented
306D4×C43—22no—
307D4×C43—22no—
308D4×C43—48no—
309D4×C43—41no—
310D4×C43—41no—
311C2×C4×C43—22no—
312C2×C4×C43—21no—
313C2×C4×C43—22no—
314C2×C4×C43—22no—
315C2×C4×C43—21no—
316C2×C4×C43—22no—
317C2×C4×C43—22no—
318C2×C4×C43—22no—
319C2×C4×C43—22no—
320C2×C4×C43—22no—
321C2×C4×C43—48no—
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—21no—
342C2×Dic43—21no—
343C2×Dic43—22no—
344C2×Dic43—22no—
345C2×Dic43—41no—
346C2×Dic43—41no—
347C2×Dic43—41no—
348C2×Dic43—41no—
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—
358C4×D43—22no—
359C4×D43—22no—
360C4×D43—22no—
361C4×D43—22no—
362C4×D43—48no—
363C4×D43—84no—
364Dic86—22no—
365Dic86—22no—
366Dic86—48no—
367Dic86—41no—
368Dic86—41no—
369C8×C43—22no—
370C8×C43—41no—
371C43⋊C8—41no—
372C43⋊C8—41no—
373#22421—431nomaximal, Sylow
374C22×C43—22no—
375C22×C43—22no—
376C22×C43—22no—
377C22×C43—41no—
378C22×C43—41no—
379C22×C43—41no—
380C22×C43—41no—
381C22×C43—42no—
382C22×C43—42no—
383C22×C43—42no—
384C22×C43—81no—
385C22×C43—81no—
386C22×C43—81no—
387C22×C43—81no—
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—22no—
399C2×D43—22no—
400C2×D43—22no—
401C2×D43#41714yescomplemented
402C4×C43—24no—
403C4×C43—22no—
404C4×C43—42no—
405C4×C43—81no—
406C4×C43C2×C4×D411yescharacteristic
407C4×C43#51811yescharacteristic
408C4×C43D4211yescharacteristic
409C4×C43#54611yescharacteristic
410Dic43—22no—
411Dic43—22no—
412Dic43—22no—
413Dic43—42no—
414Dic43—42no—
415Dic43—81no—
416Dic43—81no—
417C2×#548—431no—
418C2×#435—431no—
419C2×#417D4311yescharacteristic, complemented
420C22×#103—431no—
421D4×C4⋊C4—431no—
422#1983—431no—
423#1959—431no—
424#1894—431no—
425#1893—431no—
426#1874—431no—
427#1872—431no—
428#1803—431no—
429#1788—431no—
430#1787—431no—
431#1763—431no—
432C2×C43—42no—
433C2×C43—82no—
434C2×C43D4×C22⋊C411yescharacteristic
435C2×C43C2×#41711yescharacteristic
436C2×C43#289811yescharacteristic
437C2×C43#326511yescharacteristic
438C2×C43#327011yescharacteristic
439C2×C43#330811yescharacteristic
440C2×C43#331611yescharacteristic
441D43—24no—
442C22×#41C2×D4311yescharacteristic
443C23×Q8—431no—
444C22×M16C2×D4311yescharacteristic
445C23×C8—431no—
446#548—438no—
447#548—864no—
448C2×#124—431no—
449C2×#124—861no—
450C2×C22⋊Q8—431no—
451C2×C22⋊Q8—861no—
452C2×#121—431no—
453C2×#121—861no—
454C2×C4×Q8—431no—
455C2×C4×D4—431no—
456C2×C4×D4—861no—
457C2×C4×D4—861no—
458C22×C4⋊C4—431no—
459C22×C4⋊C4C2×D4311yescharacteristic
460#435—864no—
461C2×C4⋊C8—431no—
462#417—24no—
463C2×#103—431no—
464C2×#103—431no—
465C2×#103—431no—
466C2×#103—431no—
467C2×#103—431no—
468C2×#103—431no—
469C2×#103—864no—
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×#97—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#2242111yescharacteristic, complemented, Sylow
491C2×#41—22no—
492C2×#41—22no—
493C2×#41—22no—
494C2×#41—41no—
495C2×#41—41no—
496C2×#41C4×D4314yescomplemented
497C22×Q8—434no—
498C22×Q8—431no—
499C22×Q8—861no—
500C22×Q8—862no—
501C22×Q8—862no—
502C22×Q8—862no—
503C22×Q8—1721no—
504C22×Q8—1721no—
505C22×Q8C22×D4311yescharacteristic
506C22×D4—21no—
507C22×D4—431no—
508C22×D4—861no—
509C22×D4C22×D4311yescharacteristic
510C23×C4—21no—
511C23×C4—21no—
512C23×C4—431no—
513C23×C4—861no—
514C23×C4—861no—
515C23×C4C22×D4311yescharacteristic
516C2×M16—22no—
517C2×M16—22no—
518C2×M16—41no—
519C22×C8—431no—
520C22×C8—431no—
521C22×C8—862no—
522C22×C8—862no—
523C22×C8—1721no—
524C22×C8C22×D4311yescharacteristic
525C22×C8C22×D4311yescharacteristic
526#124—434no—
527#124—862no—
528#124—868no—
529C22⋊Q8—434no—
530C22⋊Q8—868no—
531C22⋊Q8—862no—
532#121—434no—
533#121—862no—
534#121—868no—
535C4×Q8—434no—
536C4×Q8—862no—
537C4×D4—434no—
538C4×D4—434no—
539C4×D4—868no—
540C4×D4—1724no—
541C2×C4⋊C4—22no—
542C2×C4⋊C4—21no—
543C2×C4⋊C4—41no—
544C2×C4⋊C4—431no—
545C2×C4⋊C4—431no—
546C2×C4⋊C4—431no—
547C2×C4⋊C4—431no—
548C2×C4⋊C4—861no—
549C2×C4⋊C4—861no—
550C2×C4⋊C4—862no—
551C2×C4⋊C4—861no—
552C2×C4⋊C4—861no—
553C2×C4⋊C4—861no—
554C2×C4⋊C4—1721no—
555C2×C4⋊C4C22×D4311yescharacteristic
556C2×C4⋊C4C22×D4311yescharacteristic
557C2×C22⋊C4—431no—
558C2×C22⋊C4—431no—
559C2×C22⋊C4—861no—
560C2×C22⋊C4—861no—
561C2×C22⋊C4—861no—
562C2×C22⋊C4—861no—
563C2×C22⋊C4—861no—
564C2×C22⋊C4—861no—
565C2×C42—431no—
566C2×C42—861no—
567C2×C42—861no—
568C4⋊C8—862no—
569#103—22no—
570#103—862no—
571#103—862no—
572#103—862no—
573#103—862no—
574#103—1721no—
575#103—1721no—
576#103C22⋊D4314yescomplemented
577#102—22no—
578#102—22no—
579#102—1721no—
580#102—1721no—
581C22⋊C8—862no—
582C22⋊C8—862no—
583#97—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—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8—21no—
597C2×Q8—432no—
598C2×Q8—864no—
599C2×Q8—861no—
600C2×Q8—868no—
601C2×Q8—861no—
602C2×Q8—861no—
603C2×Q8—861no—
604C2×Q8—861no—
605C2×Q8—1722no—
606C2×Q8—1722no—
607C2×Q8—1724no—
608C2×Q8—1724no—
609C2×Q8—1724no—
610C2×Q8C2×C4×D4312yes—
611C2×Q8#1062189812yes—
612C2×Q8C2×C22⋊D4312yes—
613C2×D4—24no—
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—42no—
620C2×D4—42no—
621C2×D4—434no—
622C2×D4—862no—
623C2×D4—862no—
624C2×D4—864no—
625C2×D4—1722no—
626C2×D4—1722no—
627C2×D4C2×C4×D4312yes—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—24no—
635C22×C4—21no—
636C22×C4—42no—
637C22×C4—42no—
638C22×C4—42no—
639C22×C4—42no—
640C22×C4—81no—
641C22×C4—431no—
642C22×C4—431no—
643C22×C4—431no—
644C22×C4—432no—
645C22×C4—432no—
646C22×C4—864no—
647C22×C4—861no—
648C22×C4—861no—
649C22×C4—861no—
650C22×C4—861no—
651C22×C4—861no—
652C22×C4—861no—
653C22×C4—861no—
654C22×C4—861no—
655C22×C4—3441no—
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—
665C2×C8—21no—
666C2×C8—21no—
667C2×C8—21no—
668C2×C8—21no—
669C2×C8—21no—
670C2×C8—861no—
671C2×C8—861no—
672C2×C8—861no—
673C2×C8—861no—
674C2×C8—861no—
675C2×C8—861no—
676C2×C8—1724no—
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—861no—
687C4⋊C4—861no—
688C4⋊C4—861no—
689C4⋊C4—861no—
690C4⋊C4—861no—
691C4⋊C4—3441no—
692C4⋊C4—1722no—
693C4⋊C4—1722no—
694C4⋊C4C2×C22⋊D4312yes—
695C22⋊C4—434no—
696C22⋊C4—434no—
697C22⋊C4—864no—
698C22⋊C4—864no—
699C22⋊C4—864no—
700C22⋊C4—864no—
701C22⋊C4—1722no—
702C22⋊C4—1722no—
703C42—432no—
704C42—432no—
705C42—864no—
706C42—1722no—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23—22no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—432no—
721C23—432no—
722C23—432no—
723C23—861no—
724C23—861no—
725C23—861no—
726C23—861no—
727C23C22⋊C4×D4312yes—
728C23C2×D4×D4311yescharacteristic
729Q8—22no—
730Q8—22no—
731Q8—22no—
732Q8—862no—
733Q8—862no—
734Q8—1728no—
735Q8—1721no—
736Q8—1721no—
737Q8C4×C22⋊D4314yescomplemented
738D4—22no—
739D4—22no—
740D4—48no—
741D4—41no—
742D4—41no—
743D4—868no—
744D4—1728no—
745C2×C4—22no—
746C2×C4—21no—
747C2×C4—22no—
748C2×C4—21no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—48no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—84no—
762C2×C4—432no—
763C2×C4—432no—
764C2×C4—432no—
765C2×C4—861no—
766C2×C4—861no—
767C2×C4—861no—
768C2×C4—861no—
769C2×C4—861no—
770C2×C4—861no—
771C2×C4—862no—
772C2×C4—862no—
773C2×C4—862no—
774C2×C4—862no—
775C2×C4—862no—
776C2×C4—862no—
777C2×C4—3444no—
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—22no—
802C22—22no—
803C22—41no—
804C22—41no—
805C22—41no—
806C22—41no—
807C22—42no—
808C22—42no—
809C22—42no—
810C22—81no—
811C22—81no—
812C22—81no—
813C22—81no—
814C22—434no—
815C22—862no—
816C22—862no—
817C22—862no—
818C22—862no—
819C22—862no—
820C22—862no—
821C22C2×C22⋊C4×D4311yescharacteristic
822C22D4×C22⋊D4311yescharacteristic
823C22#1458353911yescharacteristic
824C22AGL(1,ℤ/8)×D4311yescharacteristic
825C22#137×D4311yescharacteristic
826C22#1458370911yescharacteristic
827C22#1458371511yescharacteristic
828C4—22no—
829C4—24no—
830C4—42no—
831C4—81no—
832C4—862no—
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—82no—
845C2—864no—
846C2C22⋊C4×C22⋊D4311yescharacteristic
847C2#417×D4311yescharacteristic
848C2#1914312611yescharacteristic
849C2#1914608411yescharacteristic
850C2#1914615911yescharacteristic
851C2#1914658711yescharacteristic
852C2#1914670711yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#417C2
socleC23×C43C22×D4
prime radicalC2×#14583556C2
cosocleC22×C4×C43C24
hypercenterC2×#417D43
hypocenterC43#22421
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×#14582968C2semidirect
3. C2×#103×D43C2semidirect
4. C4⋊C4×C22⋊D43C2semidirect
5. #19135526C2semidirect
6. #19135410C2semidirect
7. #19135028C2semidirect
8. #19135020C2semidirect
9. #19134909C2semidirect
10. #19134902C2semidirect
11. #19134598C2semidirect
12. #19134535C2semidirect
13. #19134528C2semidirect
14. #19134427C2semidirect
15. C2×C43×#417C2semidirect
19. #14583556C4semidirect
71. C2×Q8×D43C2×C4semidirect
84. #13063312C2×C4semidirect
87. #13063304C2×C4semidirect
90. #13063296C2×C4semidirect
92. Q8×Dic43C2×C4semidirect
139. C2×#41×C43C2×C4semidirect
157. #103×C43D4semidirect
305. Q8×C43C4×D4semidirect
401. C2×D43#417semidirect
419. C2×#417D43semidirect
490. C43#22421semidirect
496. C2×#41C4×D43semidirect
576. #103C22⋊D43semidirect
737. Q8C4×C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145835562
C2×#145829682
C2×#103×D432
C4⋊C4×C22⋊D432
#191355262
#191354102
#191350282
#191350202
#191349092
#191349022
#191345982
#191345352
#191345282
#191344272
C2×C43×#4172
#2242143