Finite Group Databasebeta

← #25102309

Subgroups — #25102309

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×#14583374C211yesmaximal, characteristic, complemented
2C2×#14583033C211yesmaximal, characteristic
3C2×#14583008C211yesmaximal, characteristic, complemented
4C2×#14582979C211yesmaximal, characteristic, complemented
5#19137284C211yesmaximal, characteristic, complemented
6#19134941C211yesmaximal, characteristic, complemented
7#19134941C211yesmaximal, characteristic, complemented
8#19134915C211yesmaximal, characteristic, complemented
9#19134854C211yesmaximal, characteristic, complemented
10#19134840C211yesmaximal, characteristic, complemented
11#19134792C211yesmaximal, characteristic, complemented
12#19134422C211yesmaximal, characteristic, complemented
13#102×Dic43C211yesmaximal, characteristic, complemented
14#19134363C211yesmaximal, characteristic, complemented
15C43×#1786C211yesmaximal, characteristic, complemented
16C22×#10621882C2211yescharacteristic
17C22×#10621882C2211yescharacteristic
18C2×#13063299C2211yescharacteristic
19#14583374—24no—
20#14583374—24no—
21C2×D4×Dic43—21no—
22C2×D4×Dic43—21no—
23C2×D4×Dic43C2211yescharacteristic
24C2×D4×Dic43C2211yescharacteristic
25C2×D4×Dic43C2211yescharacteristic
26C2×D4×Dic43C2211yescharacteristic
27C2×#13063287C2211yescharacteristic, complemented
28C2×#13063284C2211yescharacteristic
29C2×#13063284C2211yescharacteristic
30C22×C22⋊Dic43—21no—
31C22×C22⋊Dic43—21no—
32#14583033C418yescomplemented
33#14583008—24no—
34#14582979—24no—
35C2×#13063258C2211yescharacteristic, complemented
36C2×#13063256C2211yescharacteristic, complemented
37C2×#13063247C2211yescharacteristic, complemented
38C2×#13063247C2211yescharacteristic, complemented
39C2×#13063246C2211yescharacteristic
40C2×#13063246C2211yescharacteristic
41C2×C22⋊(C43⋊C8)C2211yescharacteristic
42C2×#13063235C2211yescharacteristic, complemented
43C2×C8×Dic43C2211yescharacteristic, complemented
44#14582800C2211yescharacteristic, complemented
45#14582799—21no—
46#14582795C2211yescharacteristic, complemented
47#14582791—21no—
48#14582775—21no—
49#14582773—21no—
50C4⋊C4×Dic43C2211yescharacteristic, complemented
51#14582662C2211yescharacteristic, complemented
52#14582662C2211yescharacteristic, complemented
53#14582661C2211yescharacteristic, complemented
54#14582661C2211yescharacteristic, complemented
55#14582653C2211yescharacteristic, complemented
56#14582653C2211yescharacteristic, complemented
57C23×D4×C43C2211yescharacteristic
58C2×#102×C43C2211yescharacteristic
59C2×#102×C43C2211yescharacteristic
60C2×#102×C43C2211yescharacteristic
61C2×#102×C43C2211yescharacteristic
62C2×C22⋊C8×C43C2211yescharacteristic
63C43×#380C2211yescharacteristic
64C22×D172C2311yescharacteristic
65C22×C22⋊D43—21no—
66C23×Dic43—21no—
67C23×Dic43—21no—
68C23×Dic43—21no—
69C23×Dic43—21no—
70C22×C4×D43—21no—
71C2×#10621882—22no—
72C2×#10621882—22no—
73C2×#10621882—22no—
74C2×#10621882—22no—
75C2×#10621882C2×C414yescomplemented
76C2×#10621882C2×C414yescomplemented
77C22×C43⋊C8C2311yescharacteristic
78C22×C43⋊C8C2311yescharacteristic
79#13063299—22no—
80#13063299C2×C414yescomplemented
81D4×Dic43—28no—
82D4×Dic43—28no—
83D4×Dic43—22no—
84D4×Dic43—22no—
85D4×Dic43—22no—
86D4×Dic43—22no—
87D4×Dic43—22no—
88D4×Dic43—22no—
89D4×Dic43D414yescomplemented
90D4×Dic43D414yescomplemented
91#13063287—22no—
92#13063287—22no—
93#13063284—22no—
94#13063284—22no—
95#13063284—22no—
96#13063284—22no—
97C2×C4⋊Dic43D411yescharacteristic
98C2×C4⋊Dic43D411yescharacteristic
99C2×C4⋊Dic43C2311yescharacteristic
100C2×C4⋊Dic43C2311yescharacteristic
101C2×C4⋊Dic43C2311yescharacteristic
102C2×Dic43⋊C4—21no—
103C2×C22⋊Dic43—28no—
104C2×C22⋊Dic43—28no—
105C2×C22⋊Dic43—21no—
106C2×C22⋊Dic43—21no—
107C2×C22⋊Dic43—21no—
108C2×C22⋊Dic43—21no—
109C2×C22⋊Dic43—21no—
110C2×C22⋊Dic43D411yescharacteristic
111C2×C22⋊Dic43D411yescharacteristic
112C2×(C2×D43)⋊C4—21no—
113C2×(C2×D43)⋊C4—21no—
114C2×(C2×D43)⋊C4—21no—
115C2×(C2×D43)⋊C4—21no—
116C2×C4×Dic43—21no—
117C2×C4×Dic43—21no—
118C2×C4×Dic43C2311yescharacteristic
119C2×C4×Dic43C2311yescharacteristic
120#13063258—22no—
121#13063256—22no—
122#13063247—22no—
123#13063247—22no—
124#13063246C2×C414yescomplemented
125#13063246C2×C414yescomplemented
126C22⋊(C43⋊C8)C2×C414yescomplemented
127#13063235—22no—
128C8×Dic43—22no—
129C43⋊#95—21no—
130C43⋊#95—21no—
131C25×C43—21no—
132C22×D4×C43—22no—
133C22×D4×C43—22no—
134C22×D4×C43—22no—
135C22×D4×C43—22no—
136C22×D4×C43—21no—
137C22×D4×C43—22no—
138C22×D4×C43C2×C414yescomplemented
139C22×D4×C43C2311yescharacteristic
140C22×D4×C43C2311yescharacteristic
141C23×C4×C43C2311yescharacteristic
142C22×C8×C43C2311yescharacteristic
143C22×C8×C43C2311yescharacteristic
144C2×C4⋊C4×C43C2311yescharacteristic
145C2×C4⋊C4×C43C2311yescharacteristic
146C2×C22⋊C4×C43—21no—
147#102×C43—22no—
148#102×C43—22no—
149#102×C43—22no—
150#102×C43—22no—
151C22⋊C8×C43—22no—
152#95×C43—21no—
153C24×C43—24no—
154C24×C43—24no—
155C24×C43—21no—
156C24×C43—21no—
157C24×C43—24no—
158C24×C43—81no—
159C24×C43—81no—
160C24×C43—81no—
161C24×C43—81no—
162C24×C43C2×D411yescharacteristic
163C23×D43—21no—
164C2×D4×C43—28no—
165C2×D4×C43—28no—
166C2×D4×C43—24no—
167C2×D4×C43—24no—
168C2×D4×C43—28no—
169C2×D4×C43—28no—
170C2×D4×C43—24no—
171C2×D4×C43—21no—
172C2×D4×C43—21no—
173C2×D4×C43—21no—
174C2×D4×C43—21no—
175C2×D4×C43—21no—
176C2×D4×C43—21no—
177C2×D4×C43C22×C412yes—
178C2×D4×C43C22×C412yes—
179C2×D4×C43C2×D412yes—
180C2×D4×C43C2×D412yes—
181C2×D4×C43#4112yes—
182C2×D4×C43#4112yes—
183C22×C4×C43—21no—
184C22×C4×C43—21no—
185C22×C4×C43—21no—
186C22×C4×C43—21no—
187C22×C4×C43—21no—
188C22×C4×C43—21no—
189C22×C4×C43C22×C412yes—
190C22×C4×C43C2×D411yescharacteristic
191C22×C4×C43#4112yes—
192C22×C4×C43C2411yescharacteristic
193C2×C22⋊D43—24no—
194C2×C22⋊D43—81no—
195C2×C22⋊D43—81no—
196C22×Dic43—24no—
197C22×Dic43—24no—
198C22×Dic43—24no—
199C22×Dic43—24no—
200C22×Dic43—21no—
201C22×Dic43—21no—
202C22×Dic43—21no—
203C22×Dic43—81no—
204C22×Dic43—81no—
205C22×Dic43—81no—
206C22×Dic43—81no—
207C22×Dic43—81no—
208C22×Dic43—81no—
209C22×Dic43—81no—
210C22×Dic43—81no—
211C22×Dic43C2×D411yescharacteristic
212C22×Dic43C2×D411yescharacteristic
213C22×Dic43C2×D411yescharacteristic
214C22×Dic43C2×D411yescharacteristic
215C2×D172—21no—
216C2×D172—21no—
217C2×D172—21no—
218C2×D172—21no—
219C2×D172—21no—
220C2×D172C22×C412yes—
221C2×C4×D43—42no—
222C2×C4×D43—81no—
223C2×C4×D43—81no—
224C2×C8×C43—21no—
225C2×C8×C43—21no—
226C2×C8×C43—21no—
227C2×C8×C43—21no—
228C2×C8×C43—21no—
229C2×C8×C43—21no—
230C4⋊C4×C43—21no—
231C4⋊C4×C43—21no—
232C4⋊C4×C43—21no—
233C4⋊C4×C43—21no—
234C22⋊C4×C43—81no—
235C22⋊Dic43—24no—
236C22⋊Dic43—24no—
237C22⋊Dic43—24no—
238C22⋊Dic43—22no—
239C22⋊Dic43—22no—
240C22⋊Dic43—24no—
241C22⋊Dic43—24no—
242#10621882—28no—
243#10621882—28no—
244(C2×D43)⋊C4—24no—
245(C2×D43)⋊C4—42no—
246(C2×D43)⋊C4—81no—
247(C2×D43)⋊C4—81no—
248C4⋊Dic43—21no—
249C4⋊Dic43—21no—
250C4⋊Dic43—21no—
251C4⋊Dic43—22no—
252C4⋊Dic43—22no—
253C4⋊Dic43C22×C412yes—
254C4⋊Dic43C2×D412yes—
255C4⋊Dic43C2×D412yes—
256Dic43⋊C4—81no—
257C4×Dic43—24no—
258C4×Dic43—21no—
259C4×Dic43—21no—
260C4×Dic43—81no—
261C4×Dic43C2×D412yes—
262C4×Dic43C2×D412yes—
263C2×C43⋊C8—21no—
264C2×C43⋊C8—21no—
265C2×C43⋊C8—21no—
266C2×C43⋊C8—21no—
267C2×C43⋊C8C22×C412yes—
268C2×C43⋊C8C22×C412yes—
269C23×C43—216no—
270C23×C43—22no—
271C23×C43—22no—
272C23×C43—21no—
273C23×C43—22no—
274C23×C43—22no—
275C23×C43—21no—
276C23×C43—22no—
277C23×C43—22no—
278C23×C43—21no—
279C23×C43—21no—
280C23×C43—21no—
281C23×C43—21no—
282C23×C43—41no—
283C23×C43—41no—
284C23×C43—41no—
285C23×C43—41no—
286C23×C43—41no—
287C23×C43—41no—
288C23×C43—41no—
289C23×C43—41no—
290C23×C43—84no—
291C23×C43—84no—
292C23×C43—84no—
293C23×C43—84no—
294C23×C43—84no—
295C23×C43—84no—
296C23×C43C4×D412yes—
297C23×C43C22×D411yescharacteristic
298C22×D43—22no—
299C22×D43—41no—
300C22×D43—41no—
301C22×D43—41no—
302C22×D43—41no—
303C22×D43—41no—
304C22×D43—41no—
305D4×C43—216no—
306D4×C43—22no—
307D4×C43—22no—
308D4×C43—22no—
309D4×C43—22no—
310D4×C43—22no—
311D4×C43—22no—
312D4×C43C4×D414yes—
313D4×C43C4×D414yes—
314C2×C4×C43—21no—
315C2×C4×C43—21no—
316C2×C4×C43—22no—
317C2×C4×C43—22no—
318C2×C4×C43—22no—
319C2×C4×C43—22no—
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×C43C4×D412yes—
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—84no—
334C2×Dic43—21no—
335C2×Dic43—21no—
336C2×Dic43—21no—
337C2×Dic43—21no—
338C2×Dic43—22no—
339C2×Dic43—21no—
340C2×Dic43—21no—
341C2×Dic43—22no—
342C2×Dic43—22no—
343C2×Dic43—21no—
344C2×Dic43—21no—
345C2×Dic43—21no—
346C2×Dic43—21no—
347C2×Dic43—41no—
348C2×Dic43—41no—
349C2×Dic43—41no—
350C2×Dic43—41no—
351C2×Dic43—41no—
352C2×Dic43—41no—
353C2×Dic43—84no—
354C2×Dic43—84no—
355C2×Dic43—84no—
356C2×Dic43—84no—
357C2×Dic43#12012yes—
358C2×Dic43#12012yes—
359D172—22no—
360D172—22no—
361D172—41no—
362D172—41no—
363C4×D43—84no—
364C8×C43—41no—
365C8×C43—41no—
366C43⋊C8—22no—
367C43⋊C8—22no—
368#21458—431nomaximal, Sylow
369C22×C43—22no—
370C22×C43—22no—
371C22×C43—22no—
372C22×C43—24no—
373C22×C43—24no—
374C22×C43—41no—
375C22×C43—42no—
376C22×C43—42no—
377C22×C43—41no—
378C22×C43—42no—
379C22×C43—42no—
380C22×C43—42no—
381C22×C43—42no—
382C22×C43—42no—
383C22×C43—42no—
384C22×C43—41no—
385C22×C43—42no—
386C22×C43—42no—
387C22×C43—41no—
388C22×C43—42no—
389C22×C43—42no—
390C22×C43—816no—
391C22×C43C2×C4×D411yescharacteristic
392C22×C43C2×#12011yescharacteristic
393C22×C43#52511yescharacteristic
394C22×C43#57611yescharacteristic
395C22×C43#57611yescharacteristic
396C22×C43#57611yescharacteristic
397C22×C43#57711yescharacteristic
398C2×D43—42no—
399C2×D43—42no—
400C2×D43—42no—
401C2×D43—81no—
402C2×D43—81no—
403C2×D43—81no—
404C2×D43—81no—
405C4×C43—22no—
406C4×C43—81no—
407C4×C43—81no—
408C4×C43C2×C4×D411yescharacteristic
409C4×C43C2×C4×D411yescharacteristic
410C4×C43#52511yescharacteristic
411C4×C43#52511yescharacteristic
412Dic43—22no—
413Dic43—22no—
414Dic43—42no—
415Dic43—41no—
416Dic43—42no—
417Dic43—41no—
418Dic43—42no—
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#1786D4311yescharacteristic, complemented
431#1762—431no—
432C4×#102—431no—
433#1750—431no—
434C2×C43—42no—
435C2×C43—44no—
436C2×C43—44no—
437C2×C43C4×#12011yescharacteristic
438C2×C43#294611yescharacteristic
439C2×C43#294811yescharacteristic
440C2×C43#300811yescharacteristic
441C2×C43#301211yescharacteristic
442C2×C43#311811yescharacteristic
443C2×C43#312211yescharacteristic
444D43—82no—
445C23×D4C2×D4311yescharacteristic
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—431no—
456C2×C4×D4—861no—
457C2×C4×D4—861no—
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×#102C2×D4311yescharacteristic
472C2×#102C2×D4311yescharacteristic
473C2×#102C2×D4311yescharacteristic
474C2×#102C2×D4311yescharacteristic
475C2×C22⋊C8—431no—
476C2×C22⋊C8C2×D4311yescharacteristic
477C2×#97—431no—
478C2×C4×C8—431no—
479#390—431no—
480#390—861no—
481#389—431no—
482#388—861no—
483#386—861no—
484#385—861no—
485#380C2×D4311yescharacteristic
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—21no—
495C22×D4—22no—
496C22×D4—22no—
497C22×D4—22no—
498C22×D4—22no—
499C22×D4—21no—
500C22×D4—22no—
501C22×D4—431no—
502C22×D4—861no—
503C22×D4C4×D4314yescomplemented
504C22×D4C22×D4311yescharacteristic
505C22×D4C22×D4311yescharacteristic
506C23×C4—861no—
507C23×C4—861no—
508C23×C4—861no—
509C23×C4—861no—
510C23×C4—861no—
511C23×C4C22×D4311yescharacteristic
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—434no—
525C4×D4—434no—
526C4×D4—862no—
527C4×D4—862no—
528C4×D4—862no—
529C4×D4—862no—
530C4×D4—862no—
531C4×D4—862no—
532C4×D4—868no—
533C4×D4—868no—
534C4×D4—862no—
535C4×D4—862no—
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—431no—
550C2×C22⋊C4—431no—
551C2×C22⋊C4—861no—
552C2×C22⋊C4—861no—
553C2×C22⋊C4—861no—
554C2×C22⋊C4—861no—
555C2×C22⋊C4—868no—
556C2×C22⋊C4—868no—
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—431no—
564C2×C42—861no—
565C2×C42—861no—
566#107—862no—
567#106—862no—
568#102—22no—
569#102—22no—
570#102—22no—
571#102—22no—
572#102—434no—
573#102—434no—
574#102—862no—
575#102—862no—
576C22⋊C8—22no—
577C22⋊C8—434no—
578#97—862no—
579C4×C8—862no—
580#95—21no—
581#95—861no—
582#95—861no—
583C24—24no—
584C24—24no—
585C24—21no—
586C24—21no—
587C24—24no—
588C24—81no—
589C24—81no—
590C24—81no—
591C24—81no—
592C24—861no—
593C24D4×D4311yescharacteristic
594C2×D4—24no—
595C2×D4—24no—
596C2×D4—28no—
597C2×D4—28no—
598C2×D4—28no—
599C2×D4—28no—
600C2×D4—24no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—432no—
608C2×D4—864no—
609C2×D4—861no—
610C2×D4—861no—
611C2×D4—861no—
612C2×D4—861no—
613C2×D4—861no—
614C2×D4—3441no—
615C2×D4—3441no—
616C2×D4C2×C4×D4312yes—
617C2×D4C2×C4×D4312yes—
618C2×D4D4×D4312yes—
619C2×D4D4×D4312yes—
620C2×D4#1062190012yes—
621C2×D4#1062190012yes—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—431no—
629C22×C4—431no—
630C22×C4—431no—
631C22×C4—431no—
632C22×C4—864no—
633C22×C4—864no—
634C22×C4—864no—
635C22×C4—864no—
636C22×C4—861no—
637C22×C4—861no—
638C22×C4—861no—
639C22×C4—3441no—
640C22×C4—3441no—
641C22×C4—3441no—
642C22×C4—3441no—
643C22×C4—3441no—
644C22×C4—3441no—
645C22×C4—3441no—
646C22×C4—3441no—
647C22×C4—3441no—
648C22×C4—3441no—
649C22×C4—1722no—
650C22×C4C2×C4×D4312yes—
651C22×C4D4×D4311yescharacteristic
652C22×C4#1062190012yes—
653C22×C4C23×D4311yescharacteristic
654D8—868no—
655D8—868no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—21no—
662C2×C8—432no—
663C2×C8—432no—
664C2×C8—861no—
665C2×C8—861no—
666C2×C8—861no—
667C2×C8—861no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—432no—
673C4⋊C4—432no—
674C4⋊C4—432no—
675C4⋊C4—862no—
676C4⋊C4—862no—
677C4⋊C4—861no—
678C4⋊C4—861no—
679C4⋊C4—861no—
680C4⋊C4—3441no—
681C22⋊C4—81no—
682C22⋊C4—862no—
683C22⋊C4—862no—
684C22⋊C4—864no—
685C22⋊C4—864no—
686C22⋊C4—864no—
687C22⋊C4—864no—
688C22⋊C4—864no—
689C22⋊C4—864no—
690C22⋊C4—3441no—
691C22⋊C4—3441no—
692C22⋊C4—1722no—
693C42—432no—
694C42—432no—
695C42—864no—
696C42—861no—
697C42—861no—
698C42—3441no—
699C23—216no—
700C23—22no—
701C23—22no—
702C23—21no—
703C23—22no—
704C23—22no—
705C23—21no—
706C23—22no—
707C23—22no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—84no—
721C23—84no—
722C23—84no—
723C23—84no—
724C23—84no—
725C23—84no—
726C23—862no—
727C23—1721no—
728C23—1721no—
729C23—1721no—
730C23—1721no—
731C23—1721no—
732C23—1721no—
733C23(C22⋊D43)⋊C412yes—
734C23C2×D4×D4311yescharacteristic
735D4—216no—
736D4—22no—
737D4—22no—
738D4—22no—
739D4—22no—
740D4—22no—
741D4—22no—
742D4—862no—
743D4—862no—
744D4—3444no—
745D4—1721no—
746D4—1721no—
747D4(C22⋊D43)⋊C414yes—
748D4(C22⋊D43)⋊C414yes—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—22no—
752C2×C4—22no—
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—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—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—3444no—
780C2×C4—3444no—
781C2×C4—1721no—
782C2×C4—1721no—
783C2×C4—1721no—
784C2×C4—1721no—
785C2×C4—1721no—
786C2×C4—1721no—
787C2×C4(C22⋊D43)⋊C412yes—
788C2×C4C22×C4×D4311yescharacteristic
789C2×C4C2×D4×D4311yescharacteristic
790C2×C4C2×D4×D4311yescharacteristic
791C2×C4C2×#1062190011yescharacteristic
792C2×C4C2×#1062190011yescharacteristic
793C2×C4C2×#1062190011yescharacteristic
794C8—41no—
795C8—41no—
796C8—862no—
797C8—862no—
798C22—22no—
799C22—22no—
800C22—24no—
801C22—24no—
802C22—22no—
803C22—42no—
804C22—42no—
805C22—41no—
806C22—42no—
807C22—42no—
808C22—41no—
809C22—42no—
810C22—42no—
811C22—42no—
812C22—42no—
813C22—41no—
814C22—42no—
815C22—42no—
816C22—41no—
817C22—42no—
818C22—42no—
819C22—816no—
820C22—3441no—
821C22—3441no—
822C22—3441no—
823C22—3441no—
824C22—1722no—
825C22—1722no—
826C22—1722no—
827C22C2×(C22⋊D43)⋊C411yescharacteristic
828C22#120×D4311yescharacteristic
829C22#1458340511yescharacteristic
830C22#1458370011yescharacteristic
831C22#1458370311yescharacteristic
832C22#1458370311yescharacteristic
833C22#1458370511yescharacteristic
834C4—22no—
835C4—81no—
836C4—81no—
837C4—862no—
838C4—862no—
839C4—1722no—
840C4—1721no—
841C4—1722no—
842C4—1721no—
843C4—1722no—
844C4C2×(C22⋊D43)⋊C411yescharacteristic
845C4C2×(C22⋊D43)⋊C411yescharacteristic
846C4#1458340511yescharacteristic
847C4#1458340511yescharacteristic
848C2—42no—
849C2—44no—
850C2—44no—
851C2—3442no—
852C2#1913709411yescharacteristic
853C2#1914342111yescharacteristic
854C2#1914344311yescharacteristic
855C2#1914385811yescharacteristic
856C2#1914390011yescharacteristic
857C2#1914478011yescharacteristic
858C2#1914483211yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1786C2
socleC23×C43C22×D4
prime radicalC2×#14583033C2
cosocleC22×C4×C43C24
hypercenter#1786D43
hypocenterC43#21458
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1786

Complements

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

NH ≅ G/Ntype
1. C2×#14583374C2semidirect
3. C2×#14583008C2semidirect
4. C2×#14582979C2semidirect
5. #19137284C2semidirect
6. #19134941C2semidirect
7. #19134941C2semidirect
8. #19134915C2semidirect
9. #19134854C2semidirect
10. #19134840C2semidirect
11. #19134792C2semidirect
12. #19134422C2semidirect
13. #102×Dic43C2semidirect
14. #19134363C2semidirect
15. C43×#1786C2semidirect
27. C2×#13063287C22semidirect
32. #14583033C4semidirect
35. C2×#13063258C22semidirect
36. C2×#13063256C22semidirect
37. C2×#13063247C22semidirect
38. C2×#13063247C22semidirect
42. C2×#13063235C22semidirect
43. C2×C8×Dic43C22semidirect
44. #14582800C22semidirect
46. #14582795C22semidirect
50. C4⋊C4×Dic43C22semidirect
51. #14582662C22semidirect
52. #14582662C22semidirect
53. #14582661C22semidirect
54. #14582661C22semidirect
55. #14582653C22semidirect
56. #14582653C22semidirect
75. C2×#10621882C2×C4semidirect
76. C2×#10621882C2×C4semidirect
80. #13063299C2×C4semidirect
89. D4×Dic43D4semidirect
90. D4×Dic43D4semidirect
124. #13063246C2×C4semidirect
125. #13063246C2×C4semidirect
126. C22⋊(C43⋊C8)C2×C4semidirect
138. C22×D4×C43C2×C4semidirect
430. #1786D43semidirect
493. C43#21458semidirect
503. C22×D4C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145833742
C2×#145830332
C2×#145830082
C2×#145829792
#191372842
#191349412
#191349152
#191348542
#191348402
#191347922
#191344222
#102×Dic432
#191343632
C43×#17862
#2145843