Finite Group Databasebeta

← #25102322

Subgroups — #25102322

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×#14583034C211yesmaximal, characteristic
3C2×#14583009C211yesmaximal, characteristic, complemented
4C2×C4×D344C211yesmaximal, characteristic, complemented
5#19137289C211yesmaximal, characteristic, complemented
6#19134944C211yesmaximal, characteristic, complemented
7#19134941C211yesmaximal, characteristic, complemented
8#19134916C211yesmaximal, characteristic, complemented
9#19134857C211yesmaximal, characteristic, complemented
10#19134844C211yesmaximal, characteristic, complemented
11#19134797C211yesmaximal, characteristic, complemented
12#19134524C211yesmaximal, characteristic, complemented
13#19134423C211yesmaximal, characteristic, complemented
14#19134362C211yesmaximal, characteristic, complemented
15C4×#102×C43C211yesmaximal, characteristic, complemented
16C22×D4×D43C2211yescharacteristic
17C22×D344C2211yescharacteristic
18C22×#10621882C2211yescharacteristic
19C2×#13063300C2211yescharacteristic
20#14583371—24no—
21#14583371—24no—
22C2×C4×D172C2211yescharacteristic
23C2×C4×D172C2211yescharacteristic, complemented
24C2×D4×Dic43C2211yescharacteristic
25C2×#13063287C2211yescharacteristic
26C2×C4×C22⋊D43—21no—
27C2×(C22⋊D43)⋊C4—21no—
28C2×#13063283C2211yescharacteristic
29C2×#13063282C2211yescharacteristic
30C22×(C2×D43)⋊C4—21no—
31C2×C22⋊C4×D43—21no—
32#14583034C418yescomplemented
33#14583009—24no—
34C4×D344—24no—
35C2×#13063259C2211yescharacteristic, complemented
36C2×#13063256C2211yescharacteristic, complemented
37C2×#13063247C2211yescharacteristic
38C2×#13063247C2211yescharacteristic, complemented
39C2×#13063246C2211yescharacteristic
40C2×#13063245C2211yescharacteristic
41C2×#13063245C2211yescharacteristic
42C2×#13063245C2211yescharacteristic, complemented
43C2×(C2×D43)⋊C8C2211yescharacteristic
44C2×(C2×D43)⋊C8C2211yescharacteristic
45C2×#13063236C2211yescharacteristic, complemented
46#14582801—21no—
47#14582800C2211yescharacteristic, complemented
48#14582798C2211yescharacteristic, complemented
49#14582790—21no—
50#14582777—21no—
51#14582773—21no—
52#14582756C2211yescharacteristic
53#14582661C2211yescharacteristic, complemented
54#14582661C2211yescharacteristic, complemented
55#14582653C2211yescharacteristic, complemented
56#14582653C2211yescharacteristic, complemented
57C2×C4×D4×C43C2211yescharacteristic
58C2×#102×C43C2211yescharacteristic
59C2×#102×C43C2211yescharacteristic
60C2×C4×C8×C43C2211yescharacteristic, complemented
61C4×C4⋊C4×C43C2211yescharacteristic, complemented
62C43×#340C2211yescharacteristic, complemented
63C43×#340C2211yescharacteristic, complemented
64C24×D43—21no—
65C22×D172—21no—
66C22×D172C2311yescharacteristic
67C22×D172C2311yescharacteristic
68C22×C22⋊D43—21no—
69C2×D4×D43—22no—
70C2×D4×D43—22no—
71C2×D4×D43—22no—
72C2×D4×D43—22no—
73C2×D4×D43—22no—
74C2×D4×D43C2×C414yescomplemented
75C23×Dic43—21no—
76C22×C4×D43—21no—
77C22×C4×D43—21no—
78C22×C4×D43—21no—
79C22×C4×D43C2311yescharacteristic
80C2×D344—22no—
81C2×D344—22no—
82C2×D344C2×C414yescomplemented
83C2×#10621882—22no—
84C2×#10621882—22no—
85C2×#10621882C2×C414yescomplemented
86C22×C43⋊C8C2311yescharacteristic
87C22×C43⋊C8C2311yescharacteristic
88#13063300—22no—
89#13063300C2×C414yescomplemented
90C4×D172—22no—
91C4×D172—22no—
92C4×D172—22no—
93C4×D172D414yescomplemented
94D4×Dic43—22no—
95D4×Dic43—22no—
96#13063287—22no—
97#13063287—22no—
98C4×C22⋊D43—28no—
99(C22⋊D43)⋊C4—28no—
100#13063283—22no—
101#13063283—22no—
102#13063282—22no—
103#13063282—22no—
104C2×C4⋊Dic43—21no—
105C2×C4⋊Dic43C2311yescharacteristic
106C2×C4⋊Dic43C2311yescharacteristic
107C2×Dic43⋊C4D411yescharacteristic
108C2×Dic43⋊C4D411yescharacteristic
109C2×C22⋊Dic43—21no—
110C2×(C2×D43)⋊C4—28no—
111C2×(C2×D43)⋊C4—21no—
112C2×(C2×D43)⋊C4—21no—
113C2×(C2×D43)⋊C4—21no—
114C2×(C2×D43)⋊C4—21no—
115C2×(C2×D43)⋊C4—21no—
116C2×(C2×D43)⋊C4—21no—
117C2×(C2×D43)⋊C4—21no—
118C2×(C2×D43)⋊C4—21no—
119C2×(C2×D43)⋊C4D411yescharacteristic
120C2×(C2×D43)⋊C4D411yescharacteristic
121C22⋊C4×D43—28no—
122C2×C4×Dic43—21no—
123C2×C4×Dic43C2311yescharacteristic
124#13063259—22no—
125#13063256—22no—
126#13063247—22no—
127#13063247—22no—
128#13063246—22no—
129#13063245—22no—
130#13063245—22no—
131#13063245C2×C414yescomplemented
132(C2×D43)⋊C8—22no—
133(C2×D43)⋊C8C2×C414yescomplemented
134#13063236—22no—
135C43⋊#95—21no—
136C43⋊#95—21no—
137C22×D4×C43C2311yescharacteristic
138C23×C4×C43—21no—
139C22×C8×C43C2311yescharacteristic
140C22×C8×C43C2311yescharacteristic
141C4×D4×C43—22no—
142C4×D4×C43D414yescomplemented
143C2×C4⋊C4×C43C2311yescharacteristic
144C2×C4⋊C4×C43C2311yescharacteristic
145C2×C4⋊C4×C43C2311yescharacteristic
146C2×C22⋊C4×C43—21no—
147C2×C42×C43—21no—
148C2×C42×C43C2311yescharacteristic
149#102×C43—22no—
150#102×C43C2×C414yescomplemented
151C4×C8×C43—22no—
152#95×C43—21no—
153C24×C43—21no—
154C23×D43—21no—
155C23×D43—24no—
156C23×D43—24no—
157C23×D43—24no—
158C23×D43—21no—
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×C43C22×C412yes—
168C2×D4×C43C2×D412yes—
169C2×D4×C43#4112yes—
170C22×C4×C43—24no—
171C22×C4×C43—21no—
172C22×C4×C43—21no—
173C22×C4×C43—21no—
174C22×C4×C43—81no—
175C22×C4×C43—81no—
176C22×C4×C43C2×D411yescharacteristic
177C22×C4×C43C2×D411yescharacteristic
178C22×C4×C43C2411yescharacteristic
179C2×C22⋊D43—24no—
180C2×C22⋊D43—24no—
181C2×C22⋊D43—24no—
182C22×Dic43—24no—
183C22×Dic43—21no—
184C22×Dic43—21no—
185C22×Dic43—81no—
186C22×Dic43—81no—
187C22×Dic43C2×D411yescharacteristic
188C22×Dic43C2×D411yescharacteristic
189C22×Dic43C2×D411yescharacteristic
190D4×D43—28no—
191D4×D43—28no—
192D4×D43—28no—
193D4×D43—28no—
194C2×D172—21no—
195C2×D172—21no—
196C2×D172—21no—
197C2×D172—21no—
198C2×D172—24no—
199C2×D172—21no—
200C2×D172—21no—
201C2×D172—21no—
202C2×D172—21no—
203C2×D172—81no—
204C2×D172—81no—
205C2×D172C22×C412yes—
206C2×D172C22×C412yes—
207C2×D172C2×D412yes—
208C2×D172#4112yes—
209C2×C4×D43—21no—
210C2×C4×D43—21no—
211C2×C4×D43—21no—
212C2×C4×D43—21no—
213C2×C4×D43—24no—
214C2×C4×D43—24no—
215C2×C4×D43—42no—
216C2×C4×D43—81no—
217C2×C4×D43—81no—
218C2×C4×D43—81no—
219C2×C4×D43—81no—
220C2×C4×D43—81no—
221C2×C4×D43—81no—
222C2×C4×D43C22×C412yes—
223C2×C4×D43#4112yes—
224C2×C8×C43—21no—
225C2×C8×C43—21no—
226C2×C8×C43—21no—
227C2×C8×C43—21no—
228C2×C8×C43—21no—
229C2×C8×C43C22×C412yes—
230C4⋊C4×C43—21no—
231C4⋊C4×C43—21no—
232C4⋊C4×C43—21no—
233C4⋊C4×C43—21no—
234C4⋊C4×C43C22×C412yes—
235C4⋊C4×C43C2×D412yes—
236C22⋊C4×C43—24no—
237C42×C43—81no—
238C42×C43C2×D412yes—
239C42×C43C2×D412yes—
240C22⋊Dic43—24no—
241#10621882—28no—
242(C2×D43)⋊C4—24no—
243(C2×D43)⋊C4—24no—
244(C2×D43)⋊C4—22no—
245(C2×D43)⋊C4—22no—
246(C2×D43)⋊C4—24no—
247(C2×D43)⋊C4—24no—
248(C2×D43)⋊C4—42no—
249(C2×D43)⋊C4—81no—
250(C2×D43)⋊C4—81no—
251(C2×D43)⋊C4—81no—
252C4⋊Dic43—21no—
253C4⋊Dic43—21no—
254C4⋊Dic43—21no—
255C4⋊Dic43—81no—
256C4⋊Dic43C2×D412yes—
257Dic43⋊C4—22no—
258Dic43⋊C4—22no—
259C4×Dic43—24no—
260C4×Dic43—21no—
261C4×Dic43—21no—
262C2×C43⋊C8—21no—
263C2×C43⋊C8—21no—
264C2×C43⋊C8—21no—
265C2×C43⋊C8—21no—
266C2×C43⋊C8—21no—
267C2×C43⋊C8C22×C412yes—
268D344—28no—
269C23×C43—22no—
270C23×C43—22no—
271C23×C43—22no—
272C23×C43—41no—
273C23×C43—41no—
274C23×C43—41no—
275C23×C43—41no—
276C23×C43C22×D411yescharacteristic
277C22×D43—22no—
278C22×D43—21no—
279C22×D43—22no—
280C22×D43—21no—
281C22×D43—22no—
282C22×D43—21no—
283C22×D43—21no—
284C22×D43—21no—
285C22×D43—21no—
286C22×D43—216no—
287C22×D43—22no—
288C22×D43—41no—
289C22×D43—41no—
290C22×D43—41no—
291C22×D43—41no—
292C22×D43—41no—
293C22×D43—41no—
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×C43C4×D414yes—
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×C43—84no—
323C2×C4×C43#12012yes—
324C2×C4×C43#12012yes—
325C2×C4×C43C23×C411yescharacteristic
326C2×C4×C43C22×D411yescharacteristic
327C2×C4×C43C22×D411yescharacteristic
328C2×C4×C43C2×#4111yescharacteristic
329C2×C4×C43C2×#4111yescharacteristic
330C2×C4×C43C2×#4111yescharacteristic
331C22⋊D43—216no—
332C2×Dic43—21no—
333C2×Dic43—21no—
334C2×Dic43—21no—
335C2×Dic43—21no—
336C2×Dic43—22no—
337C2×Dic43—21no—
338C2×Dic43—21no—
339C2×Dic43—21no—
340C2×Dic43—21no—
341C2×Dic43—41no—
342C2×Dic43—41no—
343C2×Dic43—41no—
344C2×Dic43—41no—
345C2×Dic43—41no—
346C2×Dic43—84no—
347C2×Dic43C4×D412yes—
348D172—22no—
349D172—22no—
350D172—22no—
351D172—22no—
352D172—22no—
353D172—41no—
354D172—41no—
355D172—84no—
356D172C4×D414yes—
357C4×D43—22no—
358C4×D43—22no—
359C4×D43—22no—
360C4×D43—22no—
361C4×D43—84no—
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×C43C2×C4×D411yescharacteristic
377C22×C43C2×#12011yescharacteristic
378C22×C43#52511yescharacteristic
379C22×C43#57611yescharacteristic
380C22×C43#57611yescharacteristic
381C22×C43#57611yescharacteristic
382C22×C43#57711yescharacteristic
383C2×D43—22no—
384C2×D43—22no—
385C2×D43—22no—
386C2×D43—24no—
387C2×D43—41no—
388C2×D43—42no—
389C2×D43—41no—
390C2×D43—42no—
391C2×D43—42no—
392C2×D43—42no—
393C2×D43—41no—
394C2×D43—42no—
395C2×D43—41no—
396C2×D43—42no—
397C2×D43—42no—
398C2×D43—42no—
399C2×D43—42no—
400C2×D43—816no—
401C2×D43—81no—
402C2×D43—81no—
403C2×D43—81no—
404C2×D43—81no—
405C4×C43—22no—
406C4×C43—22no—
407C4×C43—42no—
408C4×C43—42no—
409C4×C43—81no—
410C4×C43C2×C4×D411yescharacteristic
411C4×C43C2×C4×D411yescharacteristic
412C4×C43#52511yescharacteristic
413C4×C43#52511yescharacteristic
414Dic43—22no—
415Dic43—42no—
416Dic43—41no—
417Dic43—41no—
418Dic43—81no—
419C2×#518—431no—
420C2×#447—431no—
421C2×#442—431no—
422C2×C4×D8—431no—
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×#102D4311yescharacteristic, complemented
433#1750—431no—
434C2×C43—44no—
435C2×C43C4×#12011yescharacteristic
436C2×C43#294611yescharacteristic
437C2×C43#294811yescharacteristic
438C2×C43#300811yescharacteristic
439C2×C43#301211yescharacteristic
440C2×C43#311811yescharacteristic
441C2×C43#312211yescharacteristic
442D43—42no—
443D43—44no—
444D43—82no—
445C23×D4—431no—
446C22×D8—431no—
447C22×D8—431no—
448C2×#121—431no—
449#518—864no—
450#518—864no—
451C2×C4×D4—431no—
452C2×C4×D4—431no—
453C2×C4×D4—431no—
454C2×C4×D4—431no—
455C2×C4×D4—861no—
456C2×C4×D4—861no—
457C2×C4×D4C2×D4311yescharacteristic
458C2×#117—431no—
459C2×#117—431no—
460C22×C22⋊C4—861no—
461C22×C22⋊C4—861no—
462#447—438no—
463#442—864no—
464C4×D8—864no—
465C2×#107—431no—
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
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⋊C4C2×D4311yescharacteristic, complemented
487#340—431no—
488#340—431no—
489#340C2×D4311yescharacteristic, complemented
490#340C2×D4311yescharacteristic, complemented
491#336—431no—
492#336—431no—
493C43#2145811yescharacteristic, complemented, Sylow
494C25—861no—
495C22×D4—434no—
496C22×D4—431no—
497C22×D4—431no—
498C22×D4—861no—
499C22×D4—862no—
500C22×D4—861no—
501C22×D4—862no—
502C22×D4—862no—
503C22×D4—862no—
504C22×D4—862no—
505C22×D4C22×D4311yescharacteristic
506C23×C4—21no—
507C23×C4—431no—
508C23×C4—861no—
509C23×C4—861no—
510C23×C4—861no—
511C23×C4—861no—
512C2×D8—434no—
513C2×D8—434no—
514C2×D8—862no—
515C2×D8—862no—
516C2×D8—862no—
517C2×D8—862no—
518C22×C8—431no—
519C22×C8—431no—
520C22×C8C22×D4311yescharacteristic
521C22×C8C22×D4311yescharacteristic
522#121—434no—
523#121—862no—
524C4×D4—22no—
525C4×D4—434no—
526C4×D4—868no—
527C4×D4—862no—
528C4×D4—862no—
529C4×D4—868no—
530C4×D4—862no—
531C4×D4—862no—
532C4×D4—862no—
533C4×D4—862no—
534C4×D4—862no—
535C4×D4D17214yescomplemented
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—861no—
545C2×C4⋊C4C22×D4311yescharacteristic
546C2×C4⋊C4C22×D4311yescharacteristic
547C2×C4⋊C4C22×D4311yescharacteristic
548C2×C22⋊C4—21no—
549C2×C22⋊C4—431no—
550C2×C22⋊C4—431no—
551C2×C22⋊C4—868no—
552C2×C22⋊C4—861no—
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—21no—
563C2×C42—431no—
564C2×C42—861no—
565C2×C42C22×D4311yescharacteristic
566#107—862no—
567#106—862no—
568#102—22no—
569#102—434no—
570#102—862no—
571#102—862no—
572#102—862no—
573#102—862no—
574#102—862no—
575#102C4×D4314yescomplemented
576C22⋊C8—434no—
577C22⋊C8—862no—
578#97—862no—
579C4×C8—22no—
580#95—21no—
581#95—861no—
582#95—861no—
583C24—21no—
584C24—431no—
585C24—864no—
586C24—864no—
587C24—864no—
588C24—861no—
589C24—861no—
590C24—3441no—
591C24—3441no—
592C24—3441no—
593C24—3441no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—432no—
598C2×D4—432no—
599C2×D4—432no—
600C2×D4—432no—
601C2×D4—864no—
602C2×D4—864no—
603C2×D4—868no—
604C2×D4—868no—
605C2×D4—868no—
606C2×D4—864no—
607C2×D4—864no—
608C2×D4—868no—
609C2×D4—861no—
610C2×D4—861no—
611C2×D4—861no—
612C2×D4—861no—
613C2×D4—861no—
614C2×D4—861no—
615C2×D4—861no—
616C2×D4—861no—
617C2×D4—3441no—
618C2×D4—3441no—
619C2×D4C2×C4×D4312yes—
620C2×D4C2×D17212yes—
621C2×D4#1062189812yes—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—24no—
625C22×C4—21no—
626C22×C4—81no—
627C22×C4—81no—
628C22×C4—431no—
629C22×C4—432no—
630C22×C4—432no—
631C22×C4—431no—
632C22×C4—431no—
633C22×C4—864no—
634C22×C4—861no—
635C22×C4—861no—
636C22×C4—861no—
637C22×C4—861no—
638C22×C4—864no—
639C22×C4—861no—
640C22×C4—864no—
641C22×C4—861no—
642C22×C4—3441no—
643C22×C4—3441no—
644C22×C4—3441no—
645C22×C4—3441no—
646C22×C4—3441no—
647C22×C4—3441no—
648C22×C4—3441no—
649C22×C4—3441no—
650C22×C4—1722no—
651C22×C4D4×D4311yescharacteristic
652C22×C4D4×D4311yescharacteristic
653C22×C4C23×D4311yescharacteristic
654D8—868no—
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—21no—
672C4⋊C4—432no—
673C4⋊C4—862no—
674C4⋊C4—862no—
675C4⋊C4—861no—
676C4⋊C4—861no—
677C4⋊C4—861no—
678C4⋊C4—3441no—
679C4⋊C4C2×C4×D4312yes—
680C4⋊C4C2×D17212yes—
681C22⋊C4—24no—
682C22⋊C4—864no—
683C22⋊C4—864no—
684C22⋊C4—864no—
685C22⋊C4—864no—
686C22⋊C4—862no—
687C22⋊C4—862no—
688C22⋊C4—864no—
689C22⋊C4—3441no—
690C22⋊C4—3441no—
691C22⋊C4—3441no—
692C22⋊C4—1722no—
693C42—81no—
694C42—864no—
695C42—861no—
696C42—861no—
697C42C2×D17212yes—
698C42D4×D4312yes—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—432no—
707C23—8616no—
708C23—862no—
709C23—861no—
710C23—862no—
711C23—861no—
712C23—862no—
713C23—861no—
714C23—861no—
715C23—861no—
716C23—861no—
717C23—862no—
718C23—3444no—
719C23—3444no—
720C23—3444no—
721C23—3444no—
722C23—3444no—
723C23—3444no—
724C23—1721no—
725C23—1721no—
726C23—1721no—
727C23—1721no—
728C23—1721no—
729C23—1721no—
730C23—1721no—
731C23—1721no—
732C23—1721no—
733C23—1721no—
734C23C2×D4×D4311yescharacteristic
735D4—22no—
736D4—22no—
737D4—22no—
738D4—434no—
739D4—8616no—
740D4—862no—
741D4—862no—
742D4—862no—
743D4—862no—
744D4—862no—
745D4—3444no—
746D4—1721no—
747D4—1721no—
748D4C4×D17214yes—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—84no—
763C2×C4—432no—
764C2×C4—861no—
765C2×C4—861no—
766C2×C4—862no—
767C2×C4—862no—
768C2×C4—862no—
769C2×C4—862no—
770C2×C4—862no—
771C2×C4—861no—
772C2×C4—861no—
773C2×C4—861no—
774C2×C4—861no—
775C2×C4—861no—
776C2×C4—861no—
777C2×C4—3444no—
778C2×C4—3444no—
779C2×C4—3444no—
780C2×C4—3444no—
781C2×C4—1721no—
782C2×C4—1721no—
783C2×C4—1721no—
784C2×C4—1721no—
785C2×C4—1721no—
786C2×C4#1306329512yes—
787C2×C4#1306329512yes—
788C2×C4C22×C4×D4311yescharacteristic
789C2×C4C2×D4×D4311yescharacteristic
790C2×C4C22×D17211yescharacteristic
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—862no—
806C22—862no—
807C22—864no—
808C22—862no—
809C22—34416no—
810C22—3441no—
811C22—3441no—
812C22—3441no—
813C22—3441no—
814C22—1722no—
815C22—1722no—
816C22—1722no—
817C22—1722no—
818C22—1721no—
819C22—1722no—
820C22—1721no—
821C22—1722no—
822C22—1722no—
823C22—1721no—
824C22—1722no—
825C22—1721no—
826C22—1722no—
827C22C4×D4×D4311yescharacteristic
828C22C2×#1306329511yescharacteristic
829C22#1458340811yescharacteristic
830C22#1458370011yescharacteristic
831C22#1458370111yescharacteristic
832C22#1458370111yescharacteristic
833C22#1458370511yescharacteristic
834C4—22no—
835C4—22no—
836C4—42no—
837C4—42no—
838C4—81no—
839C4—862no—
840C4—3441no—
841C4—1721no—
842C4—1722no—
843C4—1721no—
844C4C4×D4×D4311yescharacteristic
845C4C2×C4×D17211yescharacteristic
846C4#1458340811yescharacteristic
847C4#1458341111yescharacteristic
848C2—44no—
849C2—3442no—
850C2—1722no—
851C2—1724no—
852C2C4×#1306329511yescharacteristic
853C2#1914342211yescharacteristic
854C2#1914344211yescharacteristic
855C2#1914386611yescharacteristic
856C2#1914390411yescharacteristic
857C2#1914478511yescharacteristic
858C2#1914483511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC4×#102×C43C2
socleC23×C43C22×D4
prime radicalC2×#14583034C2
cosocleC22×C4×C43C24
hypercenterC4×#102D43
hypocenterC43#21458
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×#102

Complements

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

NH ≅ G/Ntype
1. C2×#14583371C2semidirect
3. C2×#14583009C2semidirect
4. C2×C4×D344C2semidirect
5. #19137289C2semidirect
6. #19134944C2semidirect
7. #19134941C2semidirect
8. #19134916C2semidirect
9. #19134857C2semidirect
10. #19134844C2semidirect
11. #19134797C2semidirect
12. #19134524C2semidirect
13. #19134423C2semidirect
14. #19134362C2semidirect
15. C4×#102×C43C2semidirect
23. C2×C4×D172C22semidirect
32. #14583034C4semidirect
35. C2×#13063259C22semidirect
36. C2×#13063256C22semidirect
38. C2×#13063247C22semidirect
42. C2×#13063245C22semidirect
45. C2×#13063236C22semidirect
47. #14582800C22semidirect
48. #14582798C22semidirect
53. #14582661C22semidirect
54. #14582661C22semidirect
55. #14582653C22semidirect
56. #14582653C22semidirect
60. C2×C4×C8×C43C22semidirect
61. C4×C4⋊C4×C43C22semidirect
62. C43×#340C22semidirect
63. C43×#340C22semidirect
74. C2×D4×D43C2×C4semidirect
82. C2×D344C2×C4semidirect
85. C2×#10621882C2×C4semidirect
89. #13063300C2×C4semidirect
93. C4×D172D4semidirect
131. #13063245C2×C4semidirect
133. (C2×D43)⋊C8C2×C4semidirect
142. C4×D4×C43D4semidirect
150. #102×C43C2×C4semidirect
432. C4×#102D43semidirect
478. C2×C4×C8C2×D43semidirect
486. C4×C4⋊C4C2×D43semidirect
489. #340C2×D43semidirect
490. #340C2×D43semidirect
493. C43#21458semidirect
535. C4×D4D172semidirect
575. #102C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145833712
C2×#145830342
C2×#145830092
C2×C4×D3442
#191372892
#191349442
#191349412
#191349162
#191348572
#191348442
#191347972
#191345242
#191344232
#191343622
C4×#102×C432
#2145843