Finite Group Databasebeta

← #25112112

Subgroups — #25112112

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×#14583561C211yesmaximal, characteristic
2C2×#14582972C211yesmaximal, characteristic, complemented
3C2×#14582899C211yesmaximal, characteristic, complemented
4C2×#103×D43C211yesmaximal, characteristic, complemented
5C4⋊C4×D172C211yesmaximal, characteristic, complemented
6#19135527C211yesmaximal, characteristic, complemented
7#19135411C211yesmaximal, characteristic, complemented
8#19135027C211yesmaximal, characteristic, complemented
9#19135022C211yesmaximal, characteristic, complemented
10#19134911C211yesmaximal, characteristic, complemented
11#19134901C211yesmaximal, characteristic, complemented
12#19134600C211yesmaximal, characteristic, complemented
13#19134534C211yesmaximal, characteristic, complemented
14#19134528C211yesmaximal, characteristic, complemented
15C43×#1763C211yesmaximal, characteristic, complemented
16C22×#10621902C2211yescharacteristic
17C22×Q8×D43C2211yescharacteristic
18C22×#10621872C2211yescharacteristic
19C22×C8×D43C2211yescharacteristic
20#14583561—24no—
21#14583561C418yescomplemented
22C2×#13063313—21no—
23C2×#13063313C2211yescharacteristic
24C2×#13063305—21no—
25C2×#13063305C2211yescharacteristic
26C2×#13063300—21no—
27C2×#13063300C2211yescharacteristic
28C2×C4×D172—21no—
29C2×C4×D172—21no—
30C2×C4×D172C2211yescharacteristic
31C2×C4⋊C4×D43C2211yescharacteristic
32C2×C4⋊C4×D43C2211yescharacteristic
33#14582972—24no—
34C2×C4⋊(C43⋊C8)C2211yescharacteristic
35#14582899—24no—
36C2×#13063250C2211yescharacteristic
37C2×#13063250C2211yescharacteristic
38C2×#13063249C2211yescharacteristic
39C2×#13063249C2211yescharacteristic
40C2×#13063248C2211yescharacteristic
41C2×#13063248C2211yescharacteristic
42#103×D43—24no—
43C2×#13063247C2211yescharacteristic
44C2×#13063247C2211yescharacteristic
45C2×#13063245C2211yescharacteristic
46C2×#13063245C2211yescharacteristic
47C2×(C2×D43)⋊C8C2211yescharacteristic
48C2×(C2×D43)⋊C8C2211yescharacteristic
49#14582797—21no—
50#14582773—21no—
51#14582773—21no—
52#14582769C2211yescharacteristic
53#14582756C2211yescharacteristic
54#14582756C2211yescharacteristic
55#14582661C2211yescharacteristic
56#14582661C2211yescharacteristic
57C2×C4×Q8×C43C2211yescharacteristic
58C2×#103×C43C2211yescharacteristic
59C2×#103×C43C2211yescharacteristic
60C2×#97×C43C2211yescharacteristic
61C4×C4⋊C4×C43C2211yescharacteristic
62C43×#340C2211yescharacteristic
63C43×#340C2211yescharacteristic
64C2×#10621902—22no—
65C2×#10621902—22no—
66C2×#10621902—22no—
67C2×#10621902—41no—
68C2×#10621902—41no—
69C2×#10621902C2×C414yescomplemented
70C22×Dic86—21no—
71C22×Dic86C2311yescharacteristic
72C2×Q8×D43—22no—
73C2×Q8×D43—22no—
74C2×Q8×D43—22no—
75C2×Q8×D43—41no—
76C2×Q8×D43—41no—
77C2×Q8×D43C2×C414yescomplemented
78C22×D172—21no—
79C22×D172—21no—
80C22×D172D411yescharacteristic
81C22×D172C2311yescharacteristic
82C22×C4×D43—21no—
83C22×C4×D43—21no—
84C22×C4×D43—21no—
85C22×C4×D43—21no—
86C22×C4×D43C2311yescharacteristic
87C22×C4×D43C2311yescharacteristic
88C2×#10621872—22no—
89C2×#10621872—22no—
90C2×#10621872—41no—
91C22×C43⋊C8C2311yescharacteristic
92C22×C43⋊C8C2311yescharacteristic
93C2×C8×D43—22no—
94C2×C8×D43—22no—
95C2×C8×D43—41no—
96#13063313—22no—
97#13063313—28no—
98#13063313C2×C414yescomplemented
99#13063305—22no—
100#13063305—28no—
101#13063305C2×C414yescomplemented
102#13063300—28no—
103#13063300—22no—
104#13063300C2×C414yescomplemented
105C4×D172—28no—
106C4×D172—44no—
107C4×D172C2×C414yes—
108C4×D172D414yes—
109C2×C4⋊Dic43—21no—
110C2×C4⋊Dic43—21no—
111C2×C4⋊Dic43—21no—
112C2×C4⋊Dic43D411yescharacteristic
113C2×C4⋊Dic43C2311yescharacteristic
114C2×C4⋊Dic43C2311yescharacteristic
115C2×Dic43⋊C4—21no—
116C2×Dic43⋊C4—21no—
117C4⋊C4×D43—22no—
118C4⋊C4×D43—22no—
119C4⋊C4×D43—41no—
120C4⋊C4×D43—41no—
121C2×(C2×D43)⋊C4—21no—
122C2×(C2×D43)⋊C4—21no—
123C2×(C2×D43)⋊C4—21no—
124C2×(C2×D43)⋊C4—21no—
125C2×(C2×D43)⋊C4—21no—
126C2×(C2×D43)⋊C4—21no—
127C2×(C2×D43)⋊C4D411yescharacteristic
128C2×(C2×D43)⋊C4D411yescharacteristic
129C4⋊(C43⋊C8)—22no—
130#13063250—22no—
131#13063250—41no—
132#13063249—22no—
133#13063249—22no—
134#13063248—22no—
135#13063248—41no—
136#13063247—22no—
137#13063247—41no—
138#13063245—22no—
139#13063245—41no—
140(C2×D43)⋊C8—22no—
141(C2×D43)⋊C8—22no—
142C43⋊#95—21no—
143C43⋊#95—21no—
144C22×Q8×C43C2311yescharacteristic
145C22×C8×C43C2311yescharacteristic
146C22×C8×C43C2311yescharacteristic
147C4×Q8×C43—22no—
148C4×Q8×C43C2×C414yescomplemented
149C2×C4⋊C4×C43—21no—
150C2×C4⋊C4×C43C2311yescharacteristic
151C2×C4⋊C4×C43C2311yescharacteristic
152C2×C4⋊C4×C43C2311yescharacteristic
153C2×C42×C43—21no—
154C2×C42×C43—21no—
155C2×C42×C43C2311yescharacteristic
156#103×C43—22no—
157#103×C43D414yescomplemented
158#97×C43—22no—
159#95×C43—21no—
160C23×D43—21no—
161C23×D43C2×D411yescharacteristic
162C23×D43C2×D411yescharacteristic
163C2×Q8×C43—21no—
164C2×Q8×C43—21no—
165C2×Q8×C43—21no—
166C2×Q8×C43C22×C412yes—
167C2×Q8×C43C2×D412yes—
168C2×Q8×C43#4112yes—
169C22×C4×C43—21no—
170C22×C4×C43—21no—
171C22×C4×C43—21no—
172C22×C4×C43—21no—
173C22×C4×C43C2×D411yescharacteristic
174C22×C4×C43C2×D411yescharacteristic
175C22×C4×C43C2411yescharacteristic
176C22×Dic43—21no—
177C22×Dic43—21no—
178C22×Dic43—21no—
179C22×Dic43C2×D411yescharacteristic
180C22×Dic43C2×D411yescharacteristic
181#10621902—28no—
182#10621902—44no—
183#10621902—44no—
184#10621902—44no—
185Q8×D43—28no—
186Q8×D43—44no—
187Q8×D43—44no—
188Q8×D43—44no—
189C2×D172—21no—
190C2×D172—24no—
191C2×D172—24no—
192C2×D172—22no—
193C2×D172—22no—
194C2×D172—21no—
195C2×D172—21no—
196C2×D172—21no—
197C2×D172—21no—
198C2×D172—42no—
199C2×D172—42no—
200C2×D172—42no—
201C2×D172—42no—
202C2×D172C22⋊C414yes—
203C2×D172C22×C412yes—
204C2×C4×D43—21no—
205C2×C4×D43—21no—
206C2×C4×D43—21no—
207C2×C4×D43—21no—
208C2×C4×D43—21no—
209C2×C4×D43—21no—
210C2×C4×D43—21no—
211C2×C4×D43—21no—
212C2×C4×D43—24no—
213C2×C4×D43—24no—
214C2×C4×D43—42no—
215C2×C4×D43—42no—
216C2×C4×D43—42no—
217C2×C4×D43—42no—
218C2×C4×D43—42no—
219C2×C4×D43—42no—
220C2×C4×D43—42no—
221C2×C4×D43—42no—
222C2×C4×D43—81no—
223C2×C4×D43—81no—
224C2×C4×D43C22×C412yes—
225C2×C4×D43C22×C412yes—
226C2×C4×D43C2×D412yes—
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—
237C2×C8×C43—21no—
238C2×C8×C43—21no—
239C2×C8×C43—21no—
240C2×C8×C43—21no—
241C2×C8×C43—21no—
242C2×C8×C43C2×D412yes—
243C4⋊C4×C43—24no—
244C4⋊C4×C43—21no—
245C4⋊C4×C43—21no—
246C4⋊C4×C43—21no—
247C4⋊C4×C43—21no—
248C4⋊C4×C43C22×C412yes—
249C4⋊C4×C43C2×D412yes—
250C42×C43—24no—
251C42×C43—42no—
252C42×C43C22×C412yes—
253C42×C43C2×D412yes—
254(C2×D43)⋊C4—24no—
255(C2×D43)⋊C4—24no—
256(C2×D43)⋊C4—24no—
257(C2×D43)⋊C4—24no—
258(C2×D43)⋊C4—42no—
259(C2×D43)⋊C4—42no—
260(C2×D43)⋊C4C22⋊C414yes—
261(C2×D43)⋊C4C22⋊C414yes—
262C4⋊Dic43—24no—
263C4⋊Dic43—21no—
264C4⋊Dic43—21no—
265C4⋊Dic43—21no—
266C4⋊Dic43—21no—
267C4⋊Dic43—42no—
268C4⋊Dic43—81no—
269C4⋊Dic43C22⋊C414yes—
270Dic43⋊C4—42no—
271Dic43⋊C4—42no—
272C2×C43⋊C8—21no—
273C2×C43⋊C8—21no—
274C2×C43⋊C8—21no—
275C2×C43⋊C8—21no—
276C2×C43⋊C8—21no—
277C2×C43⋊C8—21no—
278#10621872—44no—
279C8×D43—44no—
280C23×C43C22×D411yescharacteristic
281C22×D43—21no—
282C22×D43—21no—
283C22×D43—21no—
284C22×D43—21no—
285C22×D43—21no—
286C22×D43—21no—
287C22×D43—21no—
288C22×D43—21no—
289C22×D43—21no—
290C22×D43—21no—
291C22×D43—22no—
292C22×D43—41no—
293C22×D43—41no—
294C22×D43—41no—
295C22×D43—41no—
296C22×D43—41no—
297C22×D43—41no—
298C22×D43C2×C22⋊C412yes—
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
306C2×C4×C43—22no—
307C2×C4×C43—22no—
308C2×C4×C43—22no—
309C2×C4×C43—21no—
310C2×C4×C43—21no—
311C2×C4×C43—21no—
312C2×C4×C43—21no—
313C2×C4×C43—22no—
314C2×C4×C43—22no—
315C2×C4×C43—41no—
316C2×C4×C43—41no—
317C2×C4×C43—41no—
318C2×C4×C43—41no—
319C2×C4×C43—41no—
320C2×C4×C43—41no—
321C2×C4×C43—41no—
322C2×C4×C43C2×C22⋊C412yes—
323C2×C4×C43C2×C22⋊C412yes—
324C2×C4×C43C23×C411yescharacteristic
325C2×C4×C43C22×D411yescharacteristic
326C2×C4×C43C22×D411yescharacteristic
327C2×C4×C43C2×#4111yescharacteristic
328C2×C4×C43H(5,𝔽2)11yescharacteristic
329C2×C4×C43H(5,𝔽2)11yescharacteristic
330C2×Dic43—21no—
331C2×Dic43—21no—
332C2×Dic43—21no—
333C2×Dic43—21no—
334C2×Dic43—22no—
335C2×Dic43—41no—
336C2×Dic43—41no—
337C2×Dic43—41no—
338C2×Dic43—41no—
339C2×Dic43—41no—
340C2×Dic43—41no—
341C2×Dic43—41no—
342C2×Dic43—41no—
343C2×Dic43C2×C22⋊C412yes—
344C2×Dic43C2×C22⋊C412yes—
345D172—28no—
346D172—22no—
347D172—22no—
348D172—48no—
349D172—48no—
350D172—41no—
351D172—41no—
352C4×D43—22no—
353C4×D43—22no—
354C4×D43—22no—
355C4×D43—22no—
356C4×D43—22no—
357C4×D43—22no—
358C4×D43—22no—
359C4×D43—22no—
360C4×D43—48no—
361C4×D43—48no—
362C4×D43—84no—
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×C43C22×C22⋊C411yescharacteristic
375C22×C43D4211yescharacteristic
376C22×C43#54611yescharacteristic
377C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
378C22×C43C2×#13711yescharacteristic
379C22×C43#57711yescharacteristic
380C22×C43#57811yescharacteristic
381C2×D43—22no—
382C2×D43—22no—
383C2×D43—22no—
384C2×D43—22no—
385C2×D43—22no—
386C2×D43—22no—
387C2×D43—22no—
388C2×D43—22no—
389C2×D43—22no—
390C2×D43—41no—
391C2×D43—41no—
392C2×D43—41no—
393C2×D43—41no—
394C2×D43—42no—
395C2×D43—42no—
396C2×D43—42no—
397C2×D43—81no—
398C2×D43—81no—
399C2×D43—81no—
400C2×D43—81no—
401C2×D43#41714yescomplemented
402C4×C43—24no—
403C4×C43—22no—
404C4×C43—22no—
405C4×C43—42no—
406C4×C43—42no—
407C4×C43—81no—
408C4×C43C2×C4×D411yescharacteristic
409C4×C43#51811yescharacteristic
410C4×C43D4211yescharacteristic
411C4×C43#54611yescharacteristic
412Dic43—22no—
413Dic43—22no—
414Dic43—42no—
415Dic43—81no—
416Dic43—81no—
417C2×#548—431no—
418C2×#435—431no—
419C2×#417—431no—
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#1763D4311yescharacteristic, complemented
432C2×C43D4×C22⋊C411yescharacteristic
433C2×C43C2×#41711yescharacteristic
434C2×C43#289811yescharacteristic
435C2×C43#326511yescharacteristic
436C2×C43#327011yescharacteristic
437C2×C43#330811yescharacteristic
438C2×C43#331611yescharacteristic
439D43—24no—
440D43—42no—
441D43—82no—
442C22×#41—431no—
443C23×Q8—431no—
444C22×M16—431no—
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×Q8C2×D4311yescharacteristic
455C2×C4×D4—431no—
456C2×C4×D4—861no—
457C2×C4×D4—861no—
458C22×C4⋊C4—431no—
459C22×C4⋊C4—431no—
460#435—864no—
461C2×C4⋊C8—431no—
462#417—864no—
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×#102—431no—
475C2×#102—431no—
476C2×C22⋊C8—431no—
477C2×C22⋊C8—431no—
478C2×#97C2×D4311yescharacteristic
479#389—861no—
480#385—861no—
481#385—861no—
482#384—431no—
483#380—431no—
484#380—431no—
485C4×C4⋊C4C2×D4311yescharacteristic
486#340—431no—
487#340—431no—
488#340C2×D4311yescharacteristic
489#340C2×D4311yescharacteristic
490C43#2242111yescharacteristic, complemented, Sylow
491C2×#41—434no—
492C2×#41—862no—
493C2×#41—862no—
494C2×#41—862no—
495C2×#41—1721no—
496C2×#41—1721no—
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—431no—
507C22×D4—431no—
508C22×D4—861no—
509C22×D4—861no—
510C23×C4—431no—
511C23×C4—431no—
512C23×C4—861no—
513C23×C4—861no—
514C23×C4—861no—
515C23×C4—861no—
516C2×M16—862no—
517C2×M16—862no—
518C2×M16—1721no—
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—868no—
528#124—862no—
529C22⋊Q8—434no—
530C22⋊Q8—868no—
531C22⋊Q8—862no—
532#121—434no—
533#121—862no—
534#121—868no—
535C4×Q8—22no—
536C4×Q8C4×D4314yescomplemented
537C4×D4—434no—
538C4×D4—434no—
539C4×D4—868no—
540C4×D4—1724no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4—431no—
543C2×C4⋊C4—431no—
544C2×C4⋊C4—431no—
545C2×C4⋊C4—861no—
546C2×C4⋊C4—862no—
547C2×C4⋊C4—862no—
548C2×C4⋊C4—861no—
549C2×C4⋊C4—861no—
550C2×C4⋊C4—861no—
551C2×C4⋊C4—861no—
552C2×C4⋊C4—1721no—
553C2×C4⋊C4—1721no—
554C2×C4⋊C4C22×D4311yescharacteristic
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—21no—
566C2×C42—21no—
567C2×C42C22×D4311yescharacteristic
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#103D17214yescomplemented
577#102—862no—
578#102—862no—
579#102—1721no—
580#102—1721no—
581C22⋊C8—862no—
582C22⋊C8—862no—
583#97—22no—
584#95—21no—
585#95—861no—
586#95—861no—
587C24—431no—
588C24—431no—
589C24—861no—
590#41—868no—
591#41—1724no—
592#41—1724no—
593#41—1724no—
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×Q8C2×D17212yes—
612C2×Q8#1062189812yes—
613C2×D4—434no—
614C2×D4—432no—
615C2×D4—862no—
616C2×D4—862no—
617C2×D4—864no—
618C2×D4—864no—
619C2×D4—861no—
620C2×D4—861no—
621C2×D4—861no—
622C2×D4—861no—
623C2×D4—861no—
624C2×D4—1722no—
625C2×D4—1722no—
626C2×D4—1722no—
627C2×D4—1722no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—431no—
633C22×C4—431no—
634C22×C4—432no—
635C22×C4—432no—
636C22×C4—432no—
637C22×C4—432no—
638C22×C4—864no—
639C22×C4—864no—
640C22×C4—861no—
641C22×C4—861no—
642C22×C4—861no—
643C22×C4—861no—
644C22×C4—861no—
645C22×C4—861no—
646C22×C4—861no—
647C22×C4—861no—
648C22×C4—861no—
649C22×C4—861no—
650C22×C4—861no—
651C22×C4—3441no—
652C22×C4—3441no—
653C22×C4—1722no—
654C22×C4—1722no—
655C22×C4—1722no—
656C22×C4—1722no—
657C22×C4—1722no—
658C22×C4—1722no—
659C22×C4—1722no—
660C22×C4—1722no—
661C22×C4D4×D4311yescharacteristic
662C22×C4D4×D4311yescharacteristic
663C22×C4C23×D4311yescharacteristic
664M16—1724no—
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×D17212yes—
678C4⋊C4—24no—
679C4⋊C4—21no—
680C4⋊C4—21no—
681C4⋊C4—21no—
682C4⋊C4—21no—
683C4⋊C4—434no—
684C4⋊C4—864no—
685C4⋊C4—861no—
686C4⋊C4—861no—
687C4⋊C4—861no—
688C4⋊C4—861no—
689C4⋊C4—3441no—
690C4⋊C4—1722no—
691C4⋊C4—1722no—
692C4⋊C4—1722no—
693C4⋊C4C2×C4×D4312yes—
694C4⋊C4C2×D17212yes—
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—24no—
704C42—42no—
705C42C2×C4×D4312yes—
706C42D4×D4312yes—
707C23—432no—
708C23—432no—
709C23—432no—
710C23—432no—
711C23—861no—
712C23—861no—
713C23—861no—
714C23—861no—
715C23—861no—
716C23—861no—
717C23—861no—
718C23—861no—
719C23—861no—
720C23—861no—
721C23—862no—
722C23—1721no—
723C23—1721no—
724C23—1721no—
725C23—1721no—
726C23—1721no—
727C23—1721no—
728C23C2×D4×D4311yescharacteristic
729Q8—22no—
730Q8—22no—
731Q8—22no—
732Q8—862no—
733Q8—862no—
734Q8—1728no—
735Q8—1721no—
736Q8—1721no—
737Q8C4×D17214yescomplemented
738D4—868no—
739D4—862no—
740D4—862no—
741D4—1728no—
742D4—1728no—
743D4—1721no—
744D4—1721no—
745C2×C4—22no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—432no—
762C2×C4—432no—
763C2×C4—861no—
764C2×C4—861no—
765C2×C4—861no—
766C2×C4—861no—
767C2×C4—862no—
768C2×C4—862no—
769C2×C4—862no—
770C2×C4—862no—
771C2×C4—862no—
772C2×C4—862no—
773C2×C4—862no—
774C2×C4—862no—
775C2×C4—862no—
776C2×C4—3444no—
777C2×C4—3444no—
778C2×C4—1728no—
779C2×C4—1728no—
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×C4C22⋊C4×D4312yes—
789C2×C4C22⋊C4×D4312yes—
790C2×C4C22×C4×D4311yescharacteristic
791C2×C4C2×D4×D4311yescharacteristic
792C2×C4C22×D17211yescharacteristic
793C2×C4C2×#1062189811yescharacteristic
794C2×C4#1306337111yescharacteristic
795C2×C4#1306337111yescharacteristic
796C8—22no—
797C8—41no—
798C8—1721no—
799C8—1721no—
800C22—434no—
801C22—862no—
802C22—862no—
803C22—862no—
804C22—862no—
805C22—862no—
806C22—862no—
807C22—862no—
808C22—862no—
809C22—862no—
810C22—3441no—
811C22—3441no—
812C22—3441no—
813C22—3441no—
814C22—1722no—
815C22—1722no—
816C22—1722no—
817C22—1721no—
818C22—1721no—
819C22—1721no—
820C22—1721no—
821C22C2×C22⋊C4×D4311yescharacteristic
822C22D4×D17211yescharacteristic
823C22#1458354511yescharacteristic
824C22AGL(1,ℤ/8)×D4311yescharacteristic
825C22#137×D4311yescharacteristic
826C22#1458370811yescharacteristic
827C22#1458371511yescharacteristic
828C4—24no—
829C4—22no—
830C4—22no—
831C4—42no—
832C4—42no—
833C4—81no—
834C4—862no—
835C4—862no—
836C4—3441no—
837C4—3441no—
838C4—1722no—
839C4C2×C4×D17211yescharacteristic
840C4#1458337311yescharacteristic
841C4D4×D17211yescharacteristic
842C4#1458354511yescharacteristic
843C2—864no—
844C2—3442no—
845C2—1722no—
846C2C22⋊C4×D17211yescharacteristic
847C2#417×D4311yescharacteristic
848C2#1914312711yescharacteristic
849C2#1914609211yescharacteristic
850C2#1914616711yescharacteristic
851C2#1914659111yescharacteristic
852C2#1914671111yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1763C2
socleC23×C43C22×D4
prime radicalC2×#14583561C2
cosocleC22×C4×C43C24
hypercenter#1763D43
hypocenterC43#22421
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1763

Complements

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

NH ≅ G/Ntype
2. C2×#14582972C2semidirect
3. C2×#14582899C2semidirect
4. C2×#103×D43C2semidirect
5. C4⋊C4×D172C2semidirect
6. #19135527C2semidirect
7. #19135411C2semidirect
8. #19135027C2semidirect
9. #19135022C2semidirect
10. #19134911C2semidirect
11. #19134901C2semidirect
12. #19134600C2semidirect
13. #19134534C2semidirect
14. #19134528C2semidirect
15. C43×#1763C2semidirect
21. #14583561C4semidirect
69. C2×#10621902C2×C4semidirect
77. C2×Q8×D43C2×C4semidirect
98. #13063313C2×C4semidirect
101. #13063305C2×C4semidirect
104. #13063300C2×C4semidirect
148. C4×Q8×C43C2×C4semidirect
157. #103×C43D4semidirect
305. Q8×C43C4×D4semidirect
401. C2×D43#417semidirect
431. #1763D43semidirect
490. C43#22421semidirect
536. C4×Q8C4×D43semidirect
576. #103D172semidirect
737. Q8C4×D172semidirect

Maximal subgroups

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

subgroupindex
C2×#145835612
C2×#145829722
C2×#145828992
C2×#103×D432
C4⋊C4×D1722
#191355272
#191354112
#191350272
#191350222
#191349112
#191349012
#191346002
#191345342
#191345282
C43×#17632
#2242143