Finite Group Databasebeta

← #25102310

Subgroups — #25102310

Order 11008.

1616 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583371C211yesmaximal, characteristic, complemented
2C2×#14583031C211yesmaximal, characteristic
3C2×#14583009C211yesmaximal, characteristic, complemented
4#19137282C211yesmaximal, characteristic, complemented
5#19134945C211yesmaximal, characteristic, complemented
6#19134940C211yesmaximal, characteristic, complemented
7#19134914C211yesmaximal, characteristic, complemented
8#19134854C211yesmaximal, characteristic, complemented
9#19134839C211yesmaximal, characteristic, complemented
10#19134791C211yesmaximal, characteristic, complemented
11#19134524C211yesmaximal, characteristic, complemented
12#19134420C211yesmaximal, characteristic, complemented
13C4×#13063247C211yesmaximal, characteristic, complemented
14#19134362C211yesmaximal, characteristic, complemented
15C2×C4×D8×C43C211yesmaximal, characteristic, complemented
16C22×D4×D43C2211yescharacteristic
17C22×#10621882C2211yescharacteristic
18C2×#13063296C2211yescharacteristic
19#14583371—24no—
20#14583371—24no—
21C2×C4×D172C2211yescharacteristic
22C2×D4×Dic43C2211yescharacteristic
23C2×#13063287C2211yescharacteristic
24C2×C4×C22⋊D43—21no—
25C2×(C22⋊D43)⋊C4—21no—
26C2×#13063283C2211yescharacteristic
27C2×#13063282C2211yescharacteristic
28C22×(C2×D43)⋊C4—21no—
29C2×C22⋊C4×D43—21no—
30#14583031C418yescomplemented
31#14583009—24no—
32C2×#13063256C2211yescharacteristic, complemented
33C2×#13063247C2211yescharacteristic
34C2×#13063247C2211yescharacteristic
35C2×#13063246C2211yescharacteristic
36C2×#13063246C2211yescharacteristic
37C2×#13063246C2211yescharacteristic, complemented
38C2×#13063245C2211yescharacteristic
39C2×(C2×D43)⋊C8C2211yescharacteristic
40C2×(C2×D43)⋊C8C2211yescharacteristic
41C2×#13063236C2211yescharacteristic, complemented
42#14582802C2211yescharacteristic, complemented
43#14582799—21no—
44#14582795C2211yescharacteristic, complemented
45#14582793—21no—
46#14582778—21no—
47#14582772—21no—
48#14582756C2211yescharacteristic
49C4×C4⋊Dic43C2211yescharacteristic, complemented
50#14582662C2211yescharacteristic, complemented
51#14582662C2211yescharacteristic, complemented
52#14582661C2211yescharacteristic, complemented
53#14582661C2211yescharacteristic, complemented
54#14582653C2211yescharacteristic, complemented
55#14582653C2211yescharacteristic, complemented
56C22×D8×C43C2211yescharacteristic
57C2×C4×D4×C43C2211yescharacteristic
58C2×C4×D4×C43C2211yescharacteristic, complemented
59C4×D8×C43—24no—
60C2×#107×C43C2211yescharacteristic, complemented
61C2×#102×C43C2211yescharacteristic
62C2×#102×C43C2211yescharacteristic, complemented
63C2×C4×C8×C43C2211yescharacteristic, complemented
64C24×D43—21no—
65C22×D172C2311yescharacteristic
66C22×C22⋊D43—21no—
67C22×C22⋊D43—21no—
68C2×D4×D43—22no—
69C2×D4×D43—22no—
70C2×D4×D43—22no—
71C2×D4×D43—22no—
72C2×D4×D43—22no—
73C2×D4×D43C2×C414yescomplemented
74C23×Dic43—21no—
75C22×C4×D43—21no—
76C22×C4×D43—21no—
77C22×C4×D43C2311yescharacteristic
78C2×#10621882—22no—
79C2×#10621882—22no—
80C2×#10621882C2×C414yescomplemented
81C22×C43⋊C8C2311yescharacteristic
82C22×C43⋊C8C2311yescharacteristic
83#13063296—22no—
84#13063296C2×C414yescomplemented
85C4×D172—22no—
86C4×D172D414yescomplemented
87D4×Dic43—22no—
88D4×Dic43—22no—
89#13063287—22no—
90#13063287—22no—
91C4×C22⋊D43—28no—
92(C22⋊D43)⋊C4—28no—
93#13063283—22no—
94#13063283—22no—
95#13063282—22no—
96#13063282—22no—
97C2×C4⋊Dic43C2311yescharacteristic
98C2×C4⋊Dic43C2311yescharacteristic
99C2×C4⋊Dic43C2311yescharacteristic
100C2×Dic43⋊C4—21no—
101C2×Dic43⋊C4D411yescharacteristic
102C2×Dic43⋊C4D411yescharacteristic
103C2×C22⋊Dic43—21no—
104C2×C22⋊Dic43—21no—
105C2×C22⋊Dic43—21no—
106C2×C22⋊Dic43—21no—
107C2×(C2×D43)⋊C4—28no—
108C2×(C2×D43)⋊C4—21no—
109C2×(C2×D43)⋊C4—21no—
110C2×(C2×D43)⋊C4—21no—
111C2×(C2×D43)⋊C4—21no—
112C2×(C2×D43)⋊C4D411yescharacteristic
113C2×(C2×D43)⋊C4D411yescharacteristic
114C22⋊C4×D43—28no—
115C2×C4×Dic43—21no—
116C2×C4×Dic43—21no—
117C2×C4×Dic43C2311yescharacteristic
118#13063256—22no—
119#13063247—22no—
120#13063247C2×C414yescomplemented
121#13063246—22no—
122#13063246—22no—
123#13063246C2×C414yescomplemented
124#13063245—22no—
125(C2×D43)⋊C8—22no—
126(C2×D43)⋊C8C2×C414yescomplemented
127#13063236—22no—
128C43⋊#95—21no—
129C43⋊#95—21no—
130C43⋊#95—21no—
131C22×D4×C43C2311yescharacteristic
132C22×D4×C43C2311yescharacteristic
133C23×C4×C43—21no—
134C23×C4×C43—21no—
135C2×D8×C43—22no—
136C2×D8×C43—22no—
137C2×D8×C43C2×C414yescomplemented
138C22×C8×C43C2311yescharacteristic
139C22×C8×C43C2311yescharacteristic
140C4×D4×C43—22no—
141C4×D4×C43—22no—
142C4×D4×C43—22no—
143C4×D4×C43D414yescomplemented
144C2×C4⋊C4×C43C2311yescharacteristic
145C2×C4⋊C4×C43C2311yescharacteristic
146C2×C22⋊C4×C43—21no—
147C2×C22⋊C4×C43—21no—
148C2×C42×C43C2311yescharacteristic
149#107×C43—22no—
150#102×C43—22no—
151#102×C43—22no—
152C4×C8×C43—22no—
153C24×C43—21no—
154C24×C43—21no—
155C23×D43—21no—
156C23×D43—24no—
157C23×D43—24no—
158C23×D43—24no—
159C23×D43—81no—
160C23×D43—81no—
161C23×D43—81no—
162C23×D43—81no—
163C23×D43C2×D411yescharacteristic
164C2×D4×C43—21no—
165C2×D4×C43—21no—
166C2×D4×C43—21no—
167C2×D4×C43—21no—
168C2×D4×C43—21no—
169C2×D4×C43—21no—
170C2×D4×C43—21no—
171C2×D4×C43—21no—
172C2×D4×C43C22×C412yes—
173C2×D4×C43C22×C412yes—
174C2×D4×C43C2×D412yes—
175C2×D4×C43#4112yes—
176C22×C4×C43—24no—
177C22×C4×C43—21no—
178C22×C4×C43—21no—
179C22×C4×C43—42no—
180C22×C4×C43—81no—
181C22×C4×C43—81no—
182C22×C4×C43—81no—
183C22×C4×C43—81no—
184C22×C4×C43C2×D411yescharacteristic
185C22×C4×C43C2×D411yescharacteristic
186C22×C4×C43C2411yescharacteristic
187C2×C22⋊D43—24no—
188C2×C22⋊D43—24no—
189C2×C22⋊D43—24no—
190C2×C22⋊D43—24no—
191C2×C22⋊D43—81no—
192C2×C22⋊D43—81no—
193C22×Dic43—24no—
194C22×Dic43—21no—
195C22×Dic43—21no—
196C22×Dic43—21no—
197C22×Dic43—81no—
198C22×Dic43—81no—
199C22×Dic43C2×D411yescharacteristic
200C22×Dic43C2×D411yescharacteristic
201C22×Dic43C2×D411yescharacteristic
202D4×D43—28no—
203D4×D43—28no—
204D4×D43—28no—
205D4×D43—28no—
206C2×D172—21no—
207C2×D172—21no—
208C2×D172—21no—
209C2×D172C22×C412yes—
210C2×D172C2×D412yes—
211C2×D172#4112yes—
212C2×C4×D43—21no—
213C2×C4×D43—21no—
214C2×C4×D43—21no—
215C2×C4×D43—21no—
216C2×C4×D43—24no—
217C2×C4×D43—24no—
218C2×C4×D43—81no—
219C2×C4×D43—81no—
220C2×C4×D43—81no—
221C2×C4×D43—81no—
222C2×C4×D43C22×C412yes—
223C2×C4×D43#4112yes—
224D8×C43—28no—
225C2×C8×C43—21no—
226C2×C8×C43—21no—
227C2×C8×C43—21no—
228C2×C8×C43—21no—
229C2×C8×C43—21no—
230C2×C8×C43C22×C412yes—
231C4⋊C4×C43—21no—
232C4⋊C4×C43—21no—
233C4⋊C4×C43—21no—
234C4⋊C4×C43C2×D412yes—
235C22⋊C4×C43—24no—
236C22⋊C4×C43—42no—
237C42×C43C2×D412yes—
238C42×C43C2×D412yes—
239C22⋊Dic43—24no—
240C22⋊Dic43—24no—
241C22⋊Dic43—81no—
242C22⋊Dic43—81no—
243#10621882—28no—
244(C2×D43)⋊C4—24no—
245(C2×D43)⋊C4—24no—
246(C2×D43)⋊C4—22no—
247(C2×D43)⋊C4—22no—
248(C2×D43)⋊C4—24no—
249(C2×D43)⋊C4—81no—
250C4⋊Dic43—21no—
251C4⋊Dic43—21no—
252C4⋊Dic43—21no—
253C4⋊Dic43—21no—
254C4⋊Dic43C22×C412yes—
255C4⋊Dic43C2×D412yes—
256Dic43⋊C4—22no—
257Dic43⋊C4—22no—
258Dic43⋊C4—81no—
259C4×Dic43—24no—
260C4×Dic43—21no—
261C4×Dic43—21no—
262C4×Dic43—81no—
263C2×C43⋊C8—21no—
264C2×C43⋊C8—21no—
265C2×C43⋊C8—21no—
266C2×C43⋊C8—21no—
267C2×C43⋊C8—21no—
268C2×C43⋊C8C22×C412yes—
269C23×C43—22no—
270C23×C43—22no—
271C23×C43—22no—
272C23×C43—22no—
273C23×C43—41no—
274C23×C43—41no—
275C23×C43—41no—
276C23×C43—41no—
277C23×C43—41no—
278C23×C43—41no—
279C23×C43—41no—
280C23×C43—41no—
281C23×C43—41no—
282C23×C43—41no—
283C23×C43C22×D411yescharacteristic
284C22×D43—22no—
285C22×D43—21no—
286C22×D43—22no—
287C22×D43—21no—
288C22×D43—22no—
289C22×D43—21no—
290C22×D43—21no—
291C22×D43—21no—
292C22×D43—21no—
293C22×D43—216no—
294C22×D43—41no—
295C22×D43—41no—
296C22×D43—41no—
297C22×D43—41no—
298C22×D43—84no—
299C22×D43—84no—
300C22×D43—84no—
301C22×D43—84no—
302C22×D43—84no—
303C22×D43—84no—
304C22×D43C4×D412yes—
305D4×C43—22no—
306D4×C43—22no—
307D4×C43—22no—
308D4×C43—22no—
309D4×C43—22no—
310D4×C43—41no—
311D4×C43—41no—
312D4×C43C4×D414yes—
313C2×C4×C43—21no—
314C2×C4×C43—21no—
315C2×C4×C43—21no—
316C2×C4×C43—21no—
317C2×C4×C43—22no—
318C2×C4×C43—41no—
319C2×C4×C43—41no—
320C2×C4×C43—41no—
321C2×C4×C43—41no—
322C2×C4×C43—41no—
323C2×C4×C43—84no—
324C2×C4×C43—84no—
325C2×C4×C43#12012yes—
326C2×C4×C43#12012yes—
327C2×C4×C43C23×C411yescharacteristic
328C2×C4×C43C22×D411yescharacteristic
329C2×C4×C43C22×D411yescharacteristic
330C2×C4×C43C2×#4111yescharacteristic
331C2×C4×C43C2×#4111yescharacteristic
332C2×C4×C43C2×#4111yescharacteristic
333C22⋊D43—216no—
334C22⋊D43—84no—
335C2×Dic43—21no—
336C2×Dic43—21no—
337C2×Dic43—22no—
338C2×Dic43—21no—
339C2×Dic43—21no—
340C2×Dic43—22no—
341C2×Dic43—21no—
342C2×Dic43—21no—
343C2×Dic43—21no—
344C2×Dic43—21no—
345C2×Dic43—41no—
346C2×Dic43—41no—
347C2×Dic43—41no—
348C2×Dic43—41no—
349C2×Dic43—41no—
350C2×Dic43—41no—
351C2×Dic43—41no—
352C2×Dic43—84no—
353C2×Dic43C4×D412yes—
354D172—22no—
355D172—22no—
356D172—22no—
357D172C4×D414yes—
358C4×D43—22no—
359C4×D43—22no—
360C4×D43—22no—
361C4×D43—22no—
362C4×D43—84no—
363C4×D43—84no—
364C8×C43—22no—
365C8×C43—41no—
366C43⋊C8—22no—
367C43⋊C8—41no—
368#21458—431nomaximal, Sylow
369C22×C43—24no—
370C22×C43—42no—
371C22×C43—42no—
372C22×C43—42no—
373C22×C43—42no—
374C22×C43—42no—
375C22×C43—42no—
376C22×C43—42no—
377C22×C43—42no—
378C22×C43—42no—
379C22×C43—81no—
380C22×C43—81no—
381C22×C43—81no—
382C22×C43—81no—
383C22×C43C2×C4×D411yescharacteristic
384C22×C43C2×#12011yescharacteristic
385C22×C43#52511yescharacteristic
386C22×C43#57611yescharacteristic
387C22×C43#57611yescharacteristic
388C22×C43#57611yescharacteristic
389C22×C43#57711yescharacteristic
390C2×D43—22no—
391C2×D43—22no—
392C2×D43—22no—
393C2×D43—24no—
394C2×D43—41no—
395C2×D43—42no—
396C2×D43—41no—
397C2×D43—42no—
398C2×D43—42no—
399C2×D43—42no—
400C2×D43—41no—
401C2×D43—42no—
402C2×D43—41no—
403C2×D43—42no—
404C2×D43—816no—
405C4×C43—22no—
406C4×C43—22no—
407C4×C43—42no—
408C4×C43—81no—
409C4×C43C2×C4×D411yescharacteristic
410C4×C43C2×C4×D411yescharacteristic
411C4×C43#52511yescharacteristic
412C4×C43#52511yescharacteristic
413Dic43—22no—
414Dic43—42no—
415Dic43—41no—
416Dic43—42no—
417Dic43—41no—
418Dic43—81no—
419C2×#518—431no—
420C2×#447—431no—
421C2×#442—431no—
422C2×C4×D8D4311yescharacteristic, complemented
423#2324—431no—
424#1879—431no—
425#1879—431no—
426#1875—431no—
427#1864—431no—
428#1862—431no—
429#1854—431no—
430#1786—431no—
431#1762—431no—
432C4×#102—431no—
433#1750—431no—
434C2×C43—44no—
435C2×C43—82no—
436C2×C43C4×#12011yescharacteristic
437C2×C43#294611yescharacteristic
438C2×C43#294811yescharacteristic
439C2×C43#300811yescharacteristic
440C2×C43#301211yescharacteristic
441C2×C43#311811yescharacteristic
442C2×C43#312211yescharacteristic
443D43—42no—
444D43—44no—
445C23×D4—431no—
446C22×D8—431no—
447C22×D8C2×D4311yescharacteristic
448C2×#121—431no—
449#518—864no—
450#518—864no—
451C2×C4×D4—431no—
452C2×C4×D4—431no—
453C2×C4×D4—431no—
454C2×C4×D4—861no—
455C2×C4×D4—861no—
456C2×C4×D4C2×D4311yescharacteristic
457C2×C4×D4C2×D4311yescharacteristic, complemented
458C2×#117—431no—
459C2×#117—431no—
460C22×C22⋊C4—861no—
461C22×C22⋊C4—861no—
462#447—438no—
463#442—864no—
464C4×D8—24no—
465C2×#107C2×D4311yescharacteristic, complemented
466C2×#106—431no—
467C2×#102—431no—
468C2×#102—431no—
469C2×#102—431no—
470C2×#102—431no—
471C2×#102—431no—
472C2×#102—431no—
473C2×#102C2×D4311yescharacteristic
474C2×#102C2×D4311yescharacteristic, complemented
475C2×C22⋊C8—431no—
476C2×C22⋊C8—431no—
477C2×#97—431no—
478C2×C4×C8C2×D4311yescharacteristic, complemented
479#390—431no—
480#390—861no—
481#389—431no—
482#388—861no—
483#386—861no—
484#385—861no—
485#380—431no—
486C4×C4⋊C4—431no—
487#340—431no—
488#340—431no—
489#340—431no—
490#340—431no—
491#336—431no—
492#336—431no—
493C43#2145811yescharacteristic, complemented, Sylow
494C25—861no—
495C22×D4—434no—
496C22×D4—431no—
497C22×D4—862no—
498C22×D4—861no—
499C22×D4—862no—
500C22×D4—862no—
501C22×D4—862no—
502C22×D4—862no—
503C22×D4—861no—
504C22×D4C22×D4311yescharacteristic
505C22×D4C22×D4311yescharacteristic
506C23×C4—21no—
507C23×C4—21no—
508C23×C4—431no—
509C23×C4—861no—
510C23×C4—861no—
511C23×C4—861no—
512C2×D8—22no—
513C2×D8—22no—
514C2×D8—434no—
515C2×D8—862no—
516C2×D8—862no—
517C2×D8C4×D4314yescomplemented
518C22×C8—431no—
519C22×C8—431no—
520C22×C8C22×D4311yescharacteristic
521C22×C8C22×D4311yescharacteristic
522#121—434no—
523#121—862no—
524C4×D4—22no—
525C4×D4—22no—
526C4×D4—22no—
527C4×D4—434no—
528C4×D4—868no—
529C4×D4—862no—
530C4×D4—862no—
531C4×D4—868no—
532C4×D4—862no—
533C4×D4—862no—
534C4×D4—862no—
535C4×D4C22⋊D4314yescomplemented
536#117—862no—
537#117—862no—
538#117—862no—
539#117—862no—
540C2×C4⋊C4—431no—
541C2×C4⋊C4—431no—
542C2×C4⋊C4—431no—
543C2×C4⋊C4—431no—
544C2×C4⋊C4—431no—
545C2×C4⋊C4—861no—
546C2×C4⋊C4C22×D4311yescharacteristic
547C2×C4⋊C4C22×D4311yescharacteristic
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—431no—
551C2×C22⋊C4—431no—
552C2×C22⋊C4—868no—
553C2×C22⋊C4—861no—
554C2×C22⋊C4—861no—
555C2×C22⋊C4—868no—
556C2×C22⋊C4—861no—
557C2×C22⋊C4—861no—
558C2×C22⋊C4—861no—
559C2×C22⋊C4—861no—
560C2×C22⋊C4—861no—
561C2×C22⋊C4—861no—
562C2×C42—431no—
563C2×C42—861no—
564C2×C42—861no—
565C2×C42C22×D4311yescharacteristic
566#107—22no—
567#106—862no—
568#102—22no—
569#102—22no—
570#102—434no—
571#102—434no—
572#102—862no—
573#102—862no—
574#102—862no—
575#102—862no—
576C22⋊C8—434no—
577C22⋊C8—862no—
578#97—862no—
579C4×C8—22no—
580#95—861no—
581#95—861no—
582#95—861no—
583C24—21no—
584C24—21no—
585C24—431no—
586C24—864no—
587C24—864no—
588C24—864no—
589C24—861no—
590C24—3441no—
591C24—3441no—
592C24—3441no—
593C24—3441no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—432no—
603C2×D4—432no—
604C2×D4—432no—
605C2×D4—864no—
606C2×D4—868no—
607C2×D4—868no—
608C2×D4—868no—
609C2×D4—864no—
610C2×D4—864no—
611C2×D4—868no—
612C2×D4—864no—
613C2×D4—861no—
614C2×D4—861no—
615C2×D4—861no—
616C2×D4—3441no—
617C2×D4—3441no—
618C2×D4C2×C4×D4312yes—
619C2×D4C2×C4×D4312yes—
620C2×D4#1062189812yes—
621C2×D4C2×C22⋊D4312yes—
622C22×C4—21no—
623C22×C4—24no—
624C22×C4—21no—
625C22×C4—42no—
626C22×C4—81no—
627C22×C4—81no—
628C22×C4—81no—
629C22×C4—81no—
630C22×C4—431no—
631C22×C4—432no—
632C22×C4—432no—
633C22×C4—431no—
634C22×C4—431no—
635C22×C4—864no—
636C22×C4—861no—
637C22×C4—861no—
638C22×C4—861no—
639C22×C4—861no—
640C22×C4—864no—
641C22×C4—861no—
642C22×C4—861no—
643C22×C4—864no—
644C22×C4—861no—
645C22×C4—3441no—
646C22×C4—3441no—
647C22×C4—3441no—
648C22×C4—3441no—
649C22×C4—3441no—
650C22×C4—3441no—
651C22×C4D4×D4311yescharacteristic
652C22×C4D4×D4311yescharacteristic
653C22×C4C23×D4311yescharacteristic
654D8—28no—
655D8—868no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—432no—
662C2×C8—861no—
663C2×C8—861no—
664C2×C8—861no—
665C2×C8—861no—
666C2×C8—861no—
667C2×C8C2×C4×D4312yes—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—432no—
672C4⋊C4—432no—
673C4⋊C4—862no—
674C4⋊C4—862no—
675C4⋊C4—861no—
676C4⋊C4—861no—
677C4⋊C4—861no—
678C4⋊C4—861no—
679C4⋊C4—3441no—
680C4⋊C4C2×C22⋊D4312yes—
681C22⋊C4—24no—
682C22⋊C4—42no—
683C22⋊C4—864no—
684C22⋊C4—864no—
685C22⋊C4—864no—
686C22⋊C4—864no—
687C22⋊C4—862no—
688C22⋊C4—862no—
689C22⋊C4—864no—
690C22⋊C4—3441no—
691C22⋊C4—3441no—
692C22⋊C4—3441no—
693C42—864no—
694C42—861no—
695C42—861no—
696C42—3441no—
697C42D4×D4312yes—
698C42C2×C22⋊D4312yes—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—432no—
714C23—8616no—
715C23—862no—
716C23—861no—
717C23—862no—
718C23—861no—
719C23—862no—
720C23—861no—
721C23—861no—
722C23—861no—
723C23—861no—
724C23—3444no—
725C23—3444no—
726C23—3444no—
727C23—3444no—
728C23—3444no—
729C23—3444no—
730C23—1721no—
731C23—1721no—
732C23—1721no—
733C23—1721no—
734C23C2×D4×D4311yescharacteristic
735D4—22no—
736D4—22no—
737D4—22no—
738D4—22no—
739D4—22no—
740D4—41no—
741D4—41no—
742D4—434no—
743D4—8616no—
744D4—862no—
745D4—862no—
746D4—862no—
747D4—3444no—
748D4C4×C22⋊D4314yes—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—22no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—84no—
760C2×C4—84no—
761C2×C4—432no—
762C2×C4—861no—
763C2×C4—861no—
764C2×C4—862no—
765C2×C4—862no—
766C2×C4—862no—
767C2×C4—862no—
768C2×C4—862no—
769C2×C4—862no—
770C2×C4—861no—
771C2×C4—861no—
772C2×C4—861no—
773C2×C4—861no—
774C2×C4—861no—
775C2×C4—861no—
776C2×C4—3444no—
777C2×C4—3444no—
778C2×C4—3444no—
779C2×C4—1721no—
780C2×C4—1721no—
781C2×C4—1721no—
782C2×C4—1721no—
783C2×C4—1721no—
784C2×C4—1721no—
785C2×C4—1721no—
786C2×C4#1306329312yes—
787C2×C4#1306329312yes—
788C2×C4C22×C4×D4311yescharacteristic
789C2×C4C2×D4×D4311yescharacteristic
790C2×C4C22×C22⋊D4311yescharacteristic
791C2×C4#41×D4311yescharacteristic
792C2×C4#41×D4311yescharacteristic
793C2×C4C2×#1062189811yescharacteristic
794C8—22no—
795C8—41no—
796C8—862no—
797C8—1721no—
798C22—24no—
799C22—42no—
800C22—42no—
801C22—42no—
802C22—42no—
803C22—42no—
804C22—42no—
805C22—42no—
806C22—42no—
807C22—42no—
808C22—81no—
809C22—81no—
810C22—81no—
811C22—81no—
812C22—862no—
813C22—862no—
814C22—864no—
815C22—862no—
816C22—34416no—
817C22—1722no—
818C22—1721no—
819C22—1722no—
820C22—1721no—
821C22—1722no—
822C22—1722no—
823C22—1721no—
824C22—1722no—
825C22—1721no—
826C22—1722no—
827C22C4×D4×D4311yescharacteristic
828C22C2×#1306329311yescharacteristic
829C22#1458340811yescharacteristic
830C22#1458370011yescharacteristic
831C22#1458370011yescharacteristic
832C22#1458370111yescharacteristic
833C22#1458370611yescharacteristic
834C4—22no—
835C4—22no—
836C4—42no—
837C4—81no—
838C4—862no—
839C4—3441no—
840C4—1722no—
841C4—1721no—
842C4—1721no—
843C4—1722no—
844C4C4×D4×D4311yescharacteristic
845C4C2×C4×C22⋊D4311yescharacteristic
846C4#1458340611yescharacteristic
847C4#1458340811yescharacteristic
848C2—44no—
849C2—82no—
850C2—1722no—
851C2—1724no—
852C2C4×#1306329311yescharacteristic
853C2#1914342011yescharacteristic
854C2#1914344211yescharacteristic
855C2#1914385911yescharacteristic
856C2#1914389511yescharacteristic
857C2#1914477511yescharacteristic
858C2#1914483511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C4×D8×C43C2
socleC23×C43C22×D4
prime radicalC2×#14583031C2
cosocleC22×C4×C43C24
hypercenterC2×C4×D8D43
hypocenterC43#21458
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×D8

Complements

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

NH ≅ G/Ntype
1. C2×#14583371C2semidirect
3. C2×#14583009C2semidirect
4. #19137282C2semidirect
5. #19134945C2semidirect
6. #19134940C2semidirect
7. #19134914C2semidirect
8. #19134854C2semidirect
9. #19134839C2semidirect
10. #19134791C2semidirect
11. #19134524C2semidirect
12. #19134420C2semidirect
13. C4×#13063247C2semidirect
14. #19134362C2semidirect
15. C2×C4×D8×C43C2semidirect
30. #14583031C4semidirect
32. C2×#13063256C22semidirect
37. C2×#13063246C22semidirect
41. C2×#13063236C22semidirect
42. #14582802C22semidirect
44. #14582795C22semidirect
49. C4×C4⋊Dic43C22semidirect
50. #14582662C22semidirect
51. #14582662C22semidirect
52. #14582661C22semidirect
53. #14582661C22semidirect
54. #14582653C22semidirect
55. #14582653C22semidirect
58. C2×C4×D4×C43C22semidirect
60. C2×#107×C43C22semidirect
62. C2×#102×C43C22semidirect
63. C2×C4×C8×C43C22semidirect
73. C2×D4×D43C2×C4semidirect
80. C2×#10621882C2×C4semidirect
84. #13063296C2×C4semidirect
86. C4×D172D4semidirect
120. #13063247C2×C4semidirect
123. #13063246C2×C4semidirect
126. (C2×D43)⋊C8C2×C4semidirect
137. C2×D8×C43C2×C4semidirect
143. C4×D4×C43D4semidirect
422. C2×C4×D8D43semidirect
457. C2×C4×D4C2×D43semidirect
465. C2×#107C2×D43semidirect
474. C2×#102C2×D43semidirect
478. C2×C4×C8C2×D43semidirect
493. C43#21458semidirect
517. C2×D8C4×D43semidirect
535. C4×D4C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145833712
C2×#145830312
C2×#145830092
#191372822
#191349452
#191349402
#191349142
#191348542
#191348392
#191347912
#191345242
#191344202
C4×#130632472
#191343622
C2×C4×D8×C432
#2145843