Finite Group Databasebeta

← #25119004

Subgroups — #25119004

Order 11008.

1122 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583011C211yesmaximal, characteristic, complemented
2C2×D8×Dic43C211yesmaximal, characteristic, complemented
3#19137660C211yesmaximal, characteristic, complemented
4#19137505C211yesmaximal, characteristic, complemented
5#19135420C211yesmaximal, characteristic, complemented
6#19135365C211yesmaximal, characteristic, complemented
7#19135294C211yesmaximal, characteristic, complemented
8#19135280C211yesmaximal, characteristic, complemented
9#19134945C211yesmaximal, characteristic, complemented
10#19134945C211yesmaximal, characteristic, complemented
11#19134858C211yesmaximal, characteristic, complemented
12#19134844C211yesmaximal, characteristic, complemented
13#19134472C211yesmaximal, characteristic, complemented
14#19134420C211yesmaximal, characteristic, complemented
15C2×C43×#459C211yesmaximal, characteristic
16C2×D4×Dic43—21no—
17C2×D4×Dic43C2211yescharacteristic
18C2×D4×Dic43C2211yescharacteristic
19C2×D4×Dic43C2211yescharacteristic
20C2×D4×Dic43C2211yescharacteristic
21#14583011—24no—
22D8×Dic43—24no—
23C2×#13063259C2211yescharacteristic
24C2×#13063257C2211yescharacteristic
25C2×#13063246C2211yescharacteristic
26C2×#13063246C2211yescharacteristic
27C2×#13063246C2211yescharacteristic
28C2×#13063246C2211yescharacteristic
29C2×#13063246C2211yescharacteristic
30C2×#13063246C2211yescharacteristic
31C2×#13063236C2211yescharacteristic
32C2×#13063235C2211yescharacteristic
33C2×C8×Dic43C2211yescharacteristic
34#14582802—21no—
35#14582802C2211yescharacteristic
36#14582802C2211yescharacteristic
37#14582798C2211yescharacteristic
38#14582798C2211yescharacteristic
39#14582779—21no—
40#14582779—21no—
41#14582774—21no—
42#14582774—21no—
43#14582765C2211yescharacteristic
44#14582759—21no—
45C4×C4⋊Dic43C2211yescharacteristic
46C4×C4⋊Dic43C2211yescharacteristic
47C2×C43⋊#95—21no—
48#14582662C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582653C2211yescharacteristic
53#14582653C2211yescharacteristic
54C22×D8×C43C2211yescharacteristic
55C22×D8×C43C2211yescharacteristic
56C2×#127×C43C2211yescharacteristic
57C2×C4×D4×C43C2211yescharacteristic
58C43×#459C418yescomplemented
59C2×C4⋊C8×C43C2211yescharacteristic
60C2×#102×C43C2211yescharacteristic
61C2×#102×C43C2211yescharacteristic
62C23×Dic43—21no—
63C23×Dic43—21no—
64C23×Dic43—21no—
65C23×Dic43—21no—
66C22×C43⋊C8C2311yescharacteristic
67C22×C43⋊C8C2311yescharacteristic
68D4×Dic43—22no—
69D4×Dic43—22no—
70D4×Dic43—22no—
71D4×Dic43—22no—
72D4×Dic43—41no—
73D4×Dic43—41no—
74D4×Dic43—41no—
75D4×Dic43—41no—
76D4×Dic43—44no—
77C2×C4⋊Dic43—21no—
78C2×C4⋊Dic43—21no—
79C2×C4⋊Dic43D411yescharacteristic
80C2×C4⋊Dic43D411yescharacteristic
81C2×C4⋊Dic43C2311yescharacteristic
82C2×C4⋊Dic43C2311yescharacteristic
83C2×C4⋊Dic43C2311yescharacteristic
84C2×C4⋊Dic43C2311yescharacteristic
85C2×C22⋊Dic43—21no—
86C2×C22⋊Dic43—21no—
87C2×C22⋊Dic43—21no—
88C2×C22⋊Dic43—21no—
89C2×C22⋊Dic43—21no—
90C2×C22⋊Dic43—21no—
91C2×C22⋊Dic43—21no—
92C2×C22⋊Dic43—21no—
93C2×C4×Dic43—21no—
94C2×C4×Dic43C2311yescharacteristic
95C2×C4×Dic43C2311yescharacteristic
96#13063259—22no—
97#13063257—22no—
98#13063246—22no—
99#13063246—22no—
100#13063246—22no—
101#13063246—41no—
102#13063246—41no—
103#13063246D414yescomplemented
104#13063236—22no—
105#13063235—22no—
106C8×Dic43—22no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C43⋊#95D411yescharacteristic
113C43⋊#95D411yescharacteristic
114C22×D4×C43—21no—
115C22×D4×C43—21no—
116C22×D4×C43C2311yescharacteristic
117C22×D4×C43C2311yescharacteristic
118C22×D4×C43C2311yescharacteristic
119C23×C4×C43—21no—
120C2×D8×C43—22no—
121C2×D8×C43—22no—
122C2×D8×C43—22no—
123C2×D8×C43—22no—
124C2×D8×C43C2×C414yescomplemented
125C2×D8×C43C2×C414yescomplemented
126C22×C8×C43C2311yescharacteristic
127C22×C8×C43C2311yescharacteristic
128#127×C43—22no—
129#127×C43C2×C414yescomplemented
130C4×D4×C43—22no—
131C4×D4×C43C2×C414yescomplemented
132C2×C4⋊C4×C43C2311yescharacteristic
133C2×C22⋊C4×C43—21no—
134C2×C42×C43C2311yescharacteristic
135C4⋊C8×C43C2×C414yescomplemented
136#102×C43C2×C414yescomplemented
137#102×C43C2×C414yescomplemented
138C24×C43—21no—
139C24×C43—21no—
140C24×C43—21no—
141C2×D4×C43—24no—
142C2×D4×C43—24no—
143C2×D4×C43—21no—
144C2×D4×C43—21no—
145C2×D4×C43—21no—
146C2×D4×C43—21no—
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43—42no—
157C2×D4×C43—42no—
158C2×D4×C43—81no—
159C2×D4×C43—81no—
160C2×D4×C43C22×C412yes—
161C2×D4×C43C22×C412yes—
162C2×D4×C43C22×C412yes—
163C2×D4×C43C2×D412yes—
164C2×D4×C43#4112yes—
165C22×C4×C43—24no—
166C22×C4×C43—21no—
167C22×C4×C43—81no—
168C22×C4×C43—81no—
169C22×C4×C43C2×D411yescharacteristic
170C22×C4×C43C2×D411yescharacteristic
171C22×C4×C43C2411yescharacteristic
172C22×Dic43—21no—
173C22×Dic43—21no—
174C22×Dic43—21no—
175C22×Dic43—21no—
176C22×Dic43—42no—
177C22×Dic43—42no—
178C22×Dic43—42no—
179C22×Dic43—42no—
180C22×Dic43—42no—
181C22×Dic43—42no—
182C22×Dic43—42no—
183C22×Dic43—42no—
184C22×Dic43—81no—
185C22×Dic43—81no—
186C22×Dic43—81no—
187C22×Dic43—81no—
188C22×Dic43C2×D411yescharacteristic
189C22×Dic43C2×D411yescharacteristic
190C22×Dic43C2×D411yescharacteristic
191C22×Dic43C2×D411yescharacteristic
192D8×C43—28no—
193D8×C43—28no—
194C2×C8×C43—21no—
195C2×C8×C43—21no—
196C2×C8×C43—21no—
197C2×C8×C43—21no—
198C2×C8×C43C22×C412yes—
199C2×C8×C43C22×C412yes—
200C4⋊C4×C43—21no—
201C4⋊C4×C43C22×C412yes—
202C22⋊C4×C43—24no—
203C42×C43C22×C412yes—
204C42×C43#4112yes—
205C22⋊Dic43—42no—
206C22⋊Dic43—42no—
207C22⋊Dic43—42no—
208C22⋊Dic43—42no—
209C22⋊Dic43—42no—
210C22⋊Dic43—42no—
211C22⋊Dic43—81no—
212C22⋊Dic43—81no—
213C4⋊Dic43—21no—
214C4⋊Dic43—22no—
215C4⋊Dic43—21no—
216C4⋊Dic43—21no—
217C4⋊Dic43—21no—
218C4⋊Dic43—21no—
219C4⋊Dic43—21no—
220C4⋊Dic43—21no—
221C4⋊Dic43—41no—
222C4⋊Dic43—81no—
223C4⋊Dic43—81no—
224C4⋊Dic43C2×D412yes—
225C4×Dic43—21no—
226C4×Dic43—21no—
227C4×Dic43—21no—
228C4×Dic43—21no—
229C4×Dic43—42no—
230C2×C43⋊C8—21no—
231C2×C43⋊C8—21no—
232C2×C43⋊C8—21no—
233C2×C43⋊C8—21no—
234C2×C43⋊C8—21no—
235C2×C43⋊C8C2×D412yes—
236C23×C43—22no—
237C23×C43—22no—
238C23×C43—22no—
239C23×C43—22no—
240C23×C43—22no—
241C23×C43—41no—
242C23×C43—41no—
243C23×C43—41no—
244C23×C43—41no—
245C23×C43—41no—
246C23×C43—41no—
247C23×C43—41no—
248C23×C43—41no—
249C23×C43—41no—
250C23×C43—41no—
251C23×C43—41no—
252C23×C43—41no—
253C23×C43—41no—
254C23×C43—41no—
255C23×C43—41no—
256C23×C43—41no—
257C23×C43C22×D411yescharacteristic
258D4×C43—22no—
259D4×C43—22no—
260D4×C43—22no—
261D4×C43—22no—
262D4×C43—22no—
263D4×C43—22no—
264D4×C43—22no—
265D4×C43—48no—
266D4×C43—41no—
267D4×C43—41no—
268D4×C43—41no—
269D4×C43—41no—
270D4×C43—84no—
271D4×C43C4×D414yescomplemented
272C2×C4×C43—21no—
273C2×C4×C43—21no—
274C2×C4×C43—21no—
275C2×C4×C43—21no—
276C2×C4×C43—22no—
277C2×C4×C43—41no—
278C2×C4×C43—41no—
279C2×C4×C43—84no—
280C2×C4×C43C4×D412yes—
281C2×C4×C43C4×D412yes—
282C2×C4×C43C23×C411yescharacteristic
283C2×C4×C43C22×D411yescharacteristic
284C2×C4×C43C2×#4111yescharacteristic
285C2×C4×C43C2×#4111yescharacteristic
286C2×C4×C43H(5,𝔽2)11yescharacteristic
287C2×C4×C432−1+411yescharacteristic
288C2×Dic43—21no—
289C2×Dic43—21no—
290C2×Dic43—21no—
291C2×Dic43—21no—
292C2×Dic43—21no—
293C2×Dic43—22no—
294C2×Dic43—21no—
295C2×Dic43—21no—
296C2×Dic43—21no—
297C2×Dic43—21no—
298C2×Dic43—21no—
299C2×Dic43—21no—
300C2×Dic43—41no—
301C2×Dic43—41no—
302C2×Dic43—41no—
303C2×Dic43—41no—
304C2×Dic43—41no—
305C2×Dic43—41no—
306C2×Dic43—41no—
307C2×Dic43—41no—
308C2×Dic43—41no—
309C2×Dic43—41no—
310C2×Dic43—41no—
311C2×Dic43—84no—
312C2×Dic43—84no—
313C2×Dic43—84no—
314C2×Dic43—84no—
315C2×Dic43AGL(1,ℤ/8)12yes—
316C8×C43—22no—
317C8×C43—22no—
318C43⋊C8—22no—
319C43⋊C8—41no—
320#23008—431nomaximal, Sylow
321C22×C43—24no—
322C22×C43—42no—
323C22×C43—42no—
324C22×C43—42no—
325C22×C43—42no—
326C22×C43—42no—
327C22×C43—42no—
328C22×C43—42no—
329C22×C43—42no—
330C22×C43—42no—
331C22×C43—42no—
332C22×C43—42no—
333C22×C43—42no—
334C22×C43—81no—
335C22×C43—81no—
336C22×C43—81no—
337C22×C43—81no—
338C22×C43—81no—
339C22×C43—81no—
340C22×C43—81no—
341C22×C43—81no—
342C22×C43C2×C4×D411yescharacteristic
343C22×C43D4211yescharacteristic
344C22×C43#54811yescharacteristic
345C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
346C22×C43#57511yescharacteristic
347C22×C43#57611yescharacteristic
348C22×C43#57611yescharacteristic
349C4×C43—22no—
350C4×C43—22no—
351C4×C43—42no—
352C4×C43C2×C4×D411yescharacteristic
353C4×C43#52011yescharacteristic
354C4×C43#54711yescharacteristic
355C4×C43#55311yescharacteristic
356Dic43—22no—
357Dic43—41no—
358Dic43—42no—
359Dic43—41no—
360Dic43—41no—
361Dic43—81no—
362Dic43—81no—
363Dic43—81no—
364C2×#459D4311yescharacteristic
365C2×#442—431no—
366C2×C4×D8—431no—
367#2366—431no—
368#2349—431no—
369#1961—431no—
370#1949—431no—
371#1936—431no—
372#1934—431no—
373#1879—431no—
374#1879—431no—
375#1864—431no—
376#1862—431no—
377#1771—431no—
378#1762—431no—
379C2×C43—44no—
380C2×C43—82no—
381C2×C43—82no—
382C2×C43#236111yescharacteristic
383C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
384C2×C43#294811yescharacteristic
385C2×C43#326411yescharacteristic
386C2×C43#326811yescharacteristic
387C2×C43#336611yescharacteristic
388C2×C43#337011yescharacteristic
389C22×D8C2×D4311yescharacteristic
390C22×D8C2×D4311yescharacteristic
391C2×#127C2×D4311yescharacteristic
392C2×C4×D4—431no—
393C2×C4×D4—431no—
394C2×C4×D4—431no—
395C2×C4×D4—431no—
396C2×C4×D4—861no—
397C2×C4×D4C2×D4311yescharacteristic
398#459Dic4318yescomplemented
399#442—864no—
400C4×D8—864no—
401C2×#107—431no—
402C2×#106—431no—
403C2×C4⋊C8C2×D4311yescharacteristic
404C2×#102—431no—
405C2×#102—431no—
406C2×#102—431no—
407C2×#102—431no—
408C2×#102—431no—
409C2×#102—431no—
410C2×#102C2×D4311yescharacteristic
411C2×#102C2×D4311yescharacteristic
412C2×#97—431no—
413C2×#97—431no—
414C2×C4×C8—431no—
415#390—431no—
416#390—431no—
417#390—861no—
418#389—431no—
419#389—431no—
420#386—861no—
421#386—861no—
422#385—861no—
423#385—861no—
424#382—431no—
425#380—861no—
426C4×C4⋊C4—431no—
427C4×C4⋊C4—431no—
428C2×#95—861no—
429#340—431no—
430#340—431no—
431#340—431no—
432#340—431no—
433#336—431no—
434#336—431no—
435C43#2300811yescharacteristic, complemented, Sylow
436C22×D4—21no—
437C22×D4—21no—
438C22×D4C22×D4311yescharacteristic
439C22×D4C22×D4311yescharacteristic
440C22×D4C22×D4311yescharacteristic
441C23×C4—21no—
442C23×C4—861no—
443C23×C4—861no—
444C23×C4—861no—
445C23×C4—861no—
446C2×D8—22no—
447C2×D8—22no—
448C2×D8—22no—
449C2×D8—22no—
450C2×D8C2×Dic4314yescomplemented
451C2×D8C2×Dic4314yescomplemented
452C22×C8—431no—
453C22×C8—431no—
454C22×C8C22×D4311yescharacteristic
455C22×C8C22×D4311yescharacteristic
456#127—22no—
457#127C2×Dic4314yescomplemented
458C4×D4—22no—
459C4×D4—862no—
460C4×D4—862no—
461C4×D4—862no—
462C4×D4—862no—
463C4×D4—1721no—
464C4×D4—1721no—
465C4×D4—1721no—
466C4×D4—1721no—
467C4×D4—1724no—
468C4×D4C2×Dic4314yescomplemented
469C2×C4⋊C4—431no—
470C2×C4⋊C4—431no—
471C2×C4⋊C4—431no—
472C2×C4⋊C4—431no—
473C2×C4⋊C4—431no—
474C2×C4⋊C4—431no—
475C2×C4⋊C4—861no—
476C2×C4⋊C4—861no—
477C2×C4⋊C4C22×D4311yescharacteristic
478C2×C22⋊C4—21no—
479C2×C22⋊C4—861no—
480C2×C22⋊C4—861no—
481C2×C22⋊C4—861no—
482C2×C22⋊C4—861no—
483C2×C22⋊C4—861no—
484C2×C22⋊C4—861no—
485C2×C22⋊C4—861no—
486C2×C22⋊C4—861no—
487C2×C42—431no—
488C2×C42—431no—
489C2×C42—861no—
490C2×C42C22×D4311yescharacteristic
491#107—862no—
492#106—862no—
493C4⋊C8C2×Dic4314yescomplemented
494#102—434no—
495#102—862no—
496#102—862no—
497#102—862no—
498#102—1721no—
499#102—1721no—
500#102C2×Dic4314yescomplemented
501#102C2×Dic4314yescomplemented
502#97—862no—
503#97—862no—
504C4×C8—862no—
505#95—431no—
506#95—431no—
507#95—861no—
508#95—861no—
509#95—861no—
510#95—861no—
511#95—861no—
512C24—21no—
513C24—21no—
514C24—21no—
515C2×D4—24no—
516C2×D4—24no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—21no—
527C2×D4—21no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—42no—
531C2×D4—42no—
532C2×D4—81no—
533C2×D4—81no—
534C2×D4D4×D4312yes—
535C2×D4#1062190012yes—
536C2×D4C22×Dic4312yes—
537C2×D4C22×Dic4312yes—
538C2×D4C22×Dic4312yes—
539C22×C4—21no—
540C22×C4—24no—
541C22×C4—81no—
542C22×C4—81no—
543C22×C4—431no—
544C22×C4—431no—
545C22×C4—431no—
546C22×C4—431no—
547C22×C4—861no—
548C22×C4—861no—
549C22×C4—861no—
550C22×C4—861no—
551C22×C4—3441no—
552C22×C4—3441no—
553C22×C4—3441no—
554C22×C4—3441no—
555C22×C4—1722no—
556C22×C4—1722no—
557C22×C4—1722no—
558C22×C4—1722no—
559C22×C4—1722no—
560C22×C4—1722no—
561C22×C4—1722no—
562C22×C4—1722no—
563C22×C4D4×D4311yescharacteristic
564C22×C4D4×D4311yescharacteristic
565C22×C4C23×D4311yescharacteristic
566D8—28no—
567D8—28no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—432no—
573C2×C8—861no—
574C2×C8—861no—
575C2×C8—861no—
576C2×C8—861no—
577C2×C8—861no—
578C2×C8C22×Dic4312yes—
579C2×C8C22×Dic4312yes—
580C4⋊C4—21no—
581C4⋊C4—432no—
582C4⋊C4—862no—
583C4⋊C4—861no—
584C4⋊C4—861no—
585C4⋊C4—861no—
586C4⋊C4—861no—
587C4⋊C4—861no—
588C4⋊C4—861no—
589C4⋊C4—861no—
590C4⋊C4—3441no—
591C4⋊C4—3441no—
592C4⋊C4—1721no—
593C4⋊C4C22×Dic4312yes—
594C22⋊C4—24no—
595C22⋊C4—3441no—
596C22⋊C4—3441no—
597C22⋊C4—1722no—
598C22⋊C4—1722no—
599C22⋊C4—1722no—
600C22⋊C4—1722no—
601C22⋊C4—1722no—
602C22⋊C4—1722no—
603C42—861no—
604C42—861no—
605C42—861no—
606C42—861no—
607C42—1722no—
608C42#1062190012yes—
609C42C22×Dic4312yes—
610C23—22no—
611C23—22no—
612C23—22no—
613C23—22no—
614C23—22no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23C2×D4×D4311yescharacteristic
632D4—22no—
633D4—22no—
634D4—22no—
635D4—22no—
636D4—22no—
637D4—22no—
638D4—22no—
639D4—48no—
640D4—41no—
641D4—41no—
642D4—41no—
643D4—41no—
644D4—84no—
645D4D4×Dic4314yescomplemented
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—22no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—84no—
654C2×C4—432no—
655C2×C4—861no—
656C2×C4—861no—
657C2×C4—861no—
658C2×C4—861no—
659C2×C4—861no—
660C2×C4—861no—
661C2×C4—861no—
662C2×C4—861no—
663C2×C4—861no—
664C2×C4—861no—
665C2×C4—861no—
666C2×C4—862no—
667C2×C4—3444no—
668C2×C4—3444no—
669C2×C4—3444no—
670C2×C4—3444no—
671C2×C4—1721no—
672C2×C4—1721no—
673C2×C4—1721no—
674C2×C4—1721no—
675C2×C4—1721no—
676C2×C4—1721no—
677C2×C4—1721no—
678C2×C4—1721no—
679C2×C4—1721no—
680C2×C4—1721no—
681C2×C4—1721no—
682C2×C4D4×Dic4312yes—
683C2×C4D4×Dic4312yes—
684C2×C4C23×Dic4311yescharacteristic
685C2×C4C2×D4×D4311yescharacteristic
686C2×C4C2×#1062190011yescharacteristic
687C2×C4C2×#1062190011yescharacteristic
688C2×C4#1306337111yescharacteristic
689C2×C4#1306337211yescharacteristic
690C8—22no—
691C8—22no—
692C8—862no—
693C8—1721no—
694C22—24no—
695C22—42no—
696C22—42no—
697C22—42no—
698C22—42no—
699C22—42no—
700C22—42no—
701C22—42no—
702C22—42no—
703C22—42no—
704C22—42no—
705C22—42no—
706C22—42no—
707C22—81no—
708C22—81no—
709C22—81no—
710C22—81no—
711C22—81no—
712C22—81no—
713C22—81no—
714C22—81no—
715C22C2×D4×Dic4311yescharacteristic
716C22#1458353311yescharacteristic
717C22#1458355511yescharacteristic
718C22AGL(1,ℤ/8)×D4311yescharacteristic
719C22#1458369511yescharacteristic
720C22#1458370011yescharacteristic
721C22#1458370011yescharacteristic
722C4—22no—
723C4—22no—
724C4—42no—
725C4—862no—
726C4—3441no—
727C4—3441no—
728C4—3441no—
729C4—1721no—
730C4—1722no—
731C4—1721no—
732C4—1721no—
733C4C2×D4×Dic4311yescharacteristic
734C4#1458338211yescharacteristic
735C4#1458354911yescharacteristic
736C4#1458360111yescharacteristic
737C2—44no—
738C2—82no—
739C2—82no—
740C2#1913761511yescharacteristic
741C2AGL(1,ℤ/8)×Dic4311yescharacteristic
742C2#1914344711yescharacteristic
743C2#1914607011yescharacteristic
744C2#1914614111yescharacteristic
745C2#1914729711yescharacteristic
746C2#1914734111yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
Fitting, prime radicalC2×C43×#459C2
socleC23×C43C22×D4
cosocleC22×C4×C43C24
hypercenterC2×#459D43
hypocenterC43#23008
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#459

Complements

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

NH ≅ G/Ntype
1. C2×#14583011C2semidirect
2. C2×D8×Dic43C2semidirect
3. #19137660C2semidirect
4. #19137505C2semidirect
5. #19135420C2semidirect
6. #19135365C2semidirect
7. #19135294C2semidirect
8. #19135280C2semidirect
9. #19134945C2semidirect
10. #19134945C2semidirect
11. #19134858C2semidirect
12. #19134844C2semidirect
13. #19134472C2semidirect
14. #19134420C2semidirect
58. C43×#459C4semidirect
103. #13063246D4semidirect
124. C2×D8×C43C2×C4semidirect
125. C2×D8×C43C2×C4semidirect
129. #127×C43C2×C4semidirect
131. C4×D4×C43C2×C4semidirect
135. C4⋊C8×C43C2×C4semidirect
136. #102×C43C2×C4semidirect
137. #102×C43C2×C4semidirect
271. D4×C43C4×D4semidirect
398. #459Dic43semidirect
435. C43#23008semidirect
450. C2×D8C2×Dic43semidirect
451. C2×D8C2×Dic43semidirect
457. #127C2×Dic43semidirect
468. C4×D4C2×Dic43semidirect
493. C4⋊C8C2×Dic43semidirect
500. #102C2×Dic43semidirect
501. #102C2×Dic43semidirect
645. D4D4×Dic43semidirect

Maximal subgroups

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

subgroupindex
C2×#145830112
C2×D8×Dic432
#191376602
#191375052
#191354202
#191353652
#191352942
#191352802
#191349452
#191348582
#191348442
#191344722
#191344202
C2×C43×#4592
#2300843