Finite Group Databasebeta

← #25004854

Subgroups — #25004854

Order 11008.

886 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582768C211yesmaximal, characteristic
2C2×#14582662C211yesmaximal, characteristic
3C2×#14582661C211yesmaximal, characteristic
4C2×#14582661C211yesmaximal, characteristic
5C2×#14582653C211yesmaximal, characteristic
6#19132824C211yesmaximal, characteristic
7C2×C43×#340C211yesmaximal, characteristic
8C23×C43⋊C8C2211yescharacteristic
9C22×C4⋊Dic43C2211yescharacteristic
10C22×C4⋊Dic43C2211yescharacteristic
11C22×Dic43⋊C4—21no—
12C22×Dic43⋊C4—21no—
13C22×C4×Dic43C2211yescharacteristic
14#14582768—22no—
15#14582768—22no—
16C2×C43⋊#95—21no—
17C2×C43⋊#95—21no—
18#14582662—22no—
19#14582661—22no—
20#14582661—22no—
21#14582653C414yescomplemented
22C23×C8×C43C2211yescharacteristic
23C22×C4⋊C4×C43C2211yescharacteristic
24C22×C4⋊C4×C43C2211yescharacteristic
25C43×#340—22no—
26C23×Dic43—21no—
27C23×Dic43—21no—
28C23×Dic43D411yescharacteristic
29C23×Dic43D411yescharacteristic
30C22×C43⋊C8—21no—
31C22×C43⋊C8—21no—
32C22×C43⋊C8—21no—
33C22×C43⋊C8—21no—
34C22×C43⋊C8—21no—
35C22×C43⋊C8—21no—
36C22×C43⋊C8C2×C412yes—
37C2×C4⋊Dic43—21no—
38C2×C4⋊Dic43—21no—
39C2×C4⋊Dic43—21no—
40C2×C4⋊Dic43—21no—
41C2×C4⋊Dic43—21no—
42C2×C4⋊Dic43—21no—
43C2×C4⋊Dic43—21no—
44C2×C4⋊Dic43—21no—
45C2×C4⋊Dic43—21no—
46C2×C4⋊Dic43—21no—
47C2×C4⋊Dic43D412yes—
48C2×C4⋊Dic43Q812yes—
49C2×Dic43⋊C4—24no—
50C2×Dic43⋊C4—24no—
51C2×Dic43⋊C4—42no—
52C2×Dic43⋊C4—42no—
53C2×Dic43⋊C4—42no—
54C2×Dic43⋊C4—42no—
55C2×C4×Dic43—21no—
56C2×C4×Dic43—21no—
57C2×C4×Dic43—21no—
58C2×C4×Dic43—21no—
59C2×C4×Dic43C2×C412yes—
60C2×C4×Dic43Q812yes—
61C43⋊#95—42no—
62C43⋊#95—42no—
63C23×C4×C43—21no—
64C23×C4×C43—21no—
65C23×C4×C43C2311yescharacteristic
66C22×C8×C43—21no—
67C22×C8×C43—21no—
68C22×C8×C43—21no—
69C22×C8×C43—21no—
70C22×C8×C43—21no—
71C22×C8×C43—21no—
72C22×C8×C43C2×C412yes—
73C2×C4⋊C4×C43—21no—
74C2×C4⋊C4×C43—21no—
75C2×C4⋊C4×C43—21no—
76C2×C4⋊C4×C43—21no—
77C2×C4⋊C4×C43—21no—
78C2×C4⋊C4×C43—21no—
79C2×C4⋊C4×C43—21no—
80C2×C4⋊C4×C43—21no—
81C2×C4⋊C4×C43—21no—
82C2×C4⋊C4×C43—21no—
83C2×C4⋊C4×C43D412yes—
84C2×C4⋊C4×C43D412yes—
85C24×C43C2×D411yescharacteristic
86C22×C4×C43—22no—
87C22×C4×C43—22no—
88C22×C4×C43—41no—
89C22×C4×C43—41no—
90C22×C4×C43—41no—
91C22×C4×C43—41no—
92C22×C4×C43—41no—
93C22×C4×C43—41no—
94C22×C4×C43—41no—
95C22×C4×C43—41no—
96C22×C4×C43—41no—
97C22×C4×C43—41no—
98C22×C4×C43—41no—
99C22×C4×C43—41no—
100C22×C4×C43C22×C411yescharacteristic
101C22×C4×C43C2×D411yescharacteristic
102C22×C4×C43C2×D411yescharacteristic
103C22×C4×C43C2×D411yescharacteristic
104C22×C4×C43C2×Q811yescharacteristic
105C22×C4×C43C2×Q811yescharacteristic
106C22×C4×C43#4111yescharacteristic
107C22×C4×C43#4111yescharacteristic
108C22×C4×C43#4111yescharacteristic
109C22×C4×C43#4111yescharacteristic
110C22×C4×C43#4111yescharacteristic
111C22×C4×C43#4111yescharacteristic
112C22×C4×C43#4111yescharacteristic
113C22×C4×C43#4111yescharacteristic
114C22×Dic43—21no—
115C22×Dic43—21no—
116C22×Dic43—22no—
117C22×Dic43—22no—
118C22×Dic43—21no—
119C22×Dic43—21no—
120C22×Dic43—21no—
121C22×Dic43—21no—
122C22×Dic43—21no—
123C22×Dic43—21no—
124C22×Dic43—41no—
125C22×Dic43—41no—
126C22×Dic43—41no—
127C22×Dic43—41no—
128C22×Dic43—41no—
129C22×Dic43—41no—
130C22×Dic43—41no—
131C22×Dic43—41no—
132C22×Dic43—41no—
133C22×Dic43—41no—
134C22×Dic43—41no—
135C22×Dic43—41no—
136C22×Dic43C4⋊C412yes—
137C22×Dic43C4⋊C412yes—
138C22×Dic43D812yes—
139C22×Dic43SD1612yes—
140C22×Dic43SD1612yes—
141C22×Dic43Q1612yes—
142C2×C8×C43—22no—
143C2×C8×C43—22no—
144C2×C8×C43—22no—
145C2×C8×C43—41no—
146C2×C8×C43—41no—
147C2×C8×C43—41no—
148C2×C8×C43—41no—
149C4⋊C4×C43—22no—
150C4⋊C4×C43—22no—
151C4⋊C4×C43—22no—
152C4⋊C4×C43—22no—
153C4⋊C4×C43—41no—
154C4⋊C4×C43—41no—
155C4⋊C4×C43—41no—
156C4⋊C4×C43—41no—
157C4⋊Dic43—22no—
158C4⋊Dic43—22no—
159C4⋊Dic43—22no—
160C4⋊Dic43—22no—
161C4⋊Dic43—41no—
162C4⋊Dic43—41no—
163C4⋊Dic43—41no—
164C4⋊Dic43—41no—
165Dic43⋊C4—48no—
166Dic43⋊C4—48no—
167C4×Dic43—22no—
168C4×Dic43—22no—
169C4×Dic43—22no—
170C4×Dic43—22no—
171C2×C43⋊C8—22no—
172C2×C43⋊C8—22no—
173C2×C43⋊C8—22no—
174C2×C43⋊C8—41no—
175C2×C43⋊C8—41no—
176C2×C43⋊C8—41no—
177C2×C43⋊C8—41no—
178C23×C43C2×C4⋊C411yescharacteristic
179C23×C43#12011yescharacteristic
180C23×C43#12111yescharacteristic
181C23×C43C22⋊Q811yescharacteristic
182C23×C43#12311yescharacteristic
183C23×C43#12411yescharacteristic
184C23×C43#12411yescharacteristic
185C23×C43C2×D811yescharacteristic
186C23×C43C2×SD1611yescharacteristic
187C23×C43C2×SD1611yescharacteristic
188C23×C43C2×Q1611yescharacteristic
189C23×C43AGL(1,ℤ/8)11yescharacteristic
190C23×C43AGL(1,ℤ/8)11yescharacteristic
191C23×C43#13711yescharacteristic
192C23×C43#13711yescharacteristic
193C2×C4×C43—42no—
194C2×C4×C43—42no—
195C2×C4×C43—42no—
196C2×C4×C43—42no—
197C2×C4×C43—42no—
198C2×C4×C43—42no—
199C2×C4×C43—81no—
200C2×C4×C43—81no—
201C2×C4×C43—81no—
202C2×C4×C43—81no—
203C2×C4×C43—81no—
204C2×C4×C43—81no—
205C2×C4×C43—81no—
206C2×C4×C43—81no—
207C2×C4×C43#11711yescharacteristic
208C2×C4×C43#11711yescharacteristic
209C2×C4×C43C4×D411yescharacteristic
210C2×C4×C43C4×D411yescharacteristic
211C2×C4×C43C4×D411yescharacteristic
212C2×C4×C43C4×Q811yescharacteristic
213C2×C4×C43#12111yescharacteristic
214C2×C4×C43#12111yescharacteristic
215C2×C4×C43C22⋊Q811yescharacteristic
216C2×C4×C43C22⋊Q811yescharacteristic
217C2×C4×C43C22⋊Q811yescharacteristic
218C2×C4×C43C22⋊Q811yescharacteristic
219C2×C4×C43#12311yescharacteristic
220C2×C4×C43#12311yescharacteristic
221C2×C4×C43#12311yescharacteristic
222C2×C4×C43#12311yescharacteristic
223C2×C4×C43#12411yescharacteristic
224C2×C4×C43#12411yescharacteristic
225C2×C4×C43#12511yescharacteristic
226C2×C4×C43#12511yescharacteristic
227C2×C4×C43#12511yescharacteristic
228C2×C4×C43#12511yescharacteristic
229C2×C4×C43#12511yescharacteristic
230C2×C4×C43#12611yescharacteristic
231C2×C4×C43#12611yescharacteristic
232C2×C4×C43#12611yescharacteristic
233C2×C4×C43#12611yescharacteristic
234C2×C4×C43C4⋊Q811yescharacteristic
235C2×Dic43—22no—
236C2×Dic43—22no—
237C2×Dic43—22no—
238C2×Dic43—22no—
239C2×Dic43—22no—
240C2×Dic43—22no—
241C2×Dic43—22no—
242C2×Dic43—22no—
243C2×Dic43—22no—
244C2×Dic43—22no—
245C2×Dic43—22no—
246C2×Dic43—22no—
247C2×Dic43—42no—
248C2×Dic43—42no—
249C2×Dic43—42no—
250C2×Dic43—42no—
251C2×Dic43—42no—
252C2×Dic43—42no—
253C2×Dic43—81no—
254C2×Dic43—81no—
255C2×Dic43—81no—
256C2×Dic43—81no—
257C2×Dic43—81no—
258C2×Dic43—81no—
259C2×Dic43—81no—
260C2×Dic43—81no—
261C2×Dic43#10614yes—
262C2×Dic43#10714yes—
263C8×C43—42no—
264C43⋊C8—42no—
265#11267—431nomaximal, Sylow
266C22×C43#38211yescharacteristic
267C22×C43#38511yescharacteristic
268C22×C43#38911yescharacteristic
269C22×C43#39311yescharacteristic
270C22×C43#39411yescharacteristic
271C22×C43#39711yescharacteristic
272C22×C43#40011yescharacteristic
273C22×C43C2×#10611yescharacteristic
274C22×C43C2×#10711yescharacteristic
275C22×C43#42811yescharacteristic
276C22×C43#42811yescharacteristic
277C22×C43#44711yescharacteristic
278C22×C43#44811yescharacteristic
279C22×C43#45011yescharacteristic
280C22×C43#45111yescharacteristic
281C22×C43#45911yescharacteristic
282C22×C43#46011yescharacteristic
283C22×C43#46111yescharacteristic
284C22×C43#46211yescharacteristic
285C22×C43#47411yescharacteristic
286C22×C43#47511yescharacteristic
287C22×C43#47611yescharacteristic
288C22×C43#47711yescharacteristic
289C22×C43#48011yescharacteristic
290C22×C43#48111yescharacteristic
291C22×C43#48311yescharacteristic
292C22×C43#48411yescharacteristic
293C22×C43#48611yescharacteristic
294C22×C43#48611yescharacteristic
295C22×C43#48711yescharacteristic
296C22×C43#48711yescharacteristic
297C22×C43#48911yescharacteristic
298C22×C43#48911yescharacteristic
299C22×C43#49011yescharacteristic
300C22×C43#49111yescharacteristic
301C4×C43—82no—
302C4×C43—82no—
303C4×C43#38711yescharacteristic
304C4×C43#38711yescharacteristic
305C4×C43#38811yescharacteristic
306C4×C43#38811yescharacteristic
307C4×C43#39811yescharacteristic
308C4×C43#39811yescharacteristic
309C4×C43#40011yescharacteristic
310C4×C43#40011yescharacteristic
311Dic43—24no—
312Dic43—24no—
313Dic43—82no—
314Dic43—82no—
315C2×#384—431no—
316C2×#340—431no—
317C2×#340—431no—
318C2×#340—431no—
319C2×#340D4311yescharacteristic
320C2×#336—431no—
321C4⋊#95—431no—
322C2×C43#144211yescharacteristic
323C2×C43#183411yescharacteristic
324C2×C43#183611yescharacteristic
325C2×C43#185211yescharacteristic
326C2×C43#185311yescharacteristic
327C2×C43#194711yescharacteristic
328C2×C43#194811yescharacteristic
329C2×C43#202311yescharacteristic
330C2×C43#202411yescharacteristic
331C2×C43#204111yescharacteristic
332C2×C43#204311yescharacteristic
333C2×C43#207111yescharacteristic
334C2×C43#207211yescharacteristic
335C2×C43#209911yescharacteristic
336C2×C43#210011yescharacteristic
337C23×C8—431no—
338C23×C8C2×D4311yescharacteristic
339C22×C4⋊C4—431no—
340C22×C4⋊C4—431no—
341C22×C4⋊C4—861no—
342C22×C4⋊C4—861no—
343C22×C4⋊C4C2×D4311yescharacteristic
344C22×C4⋊C4C2×D4311yescharacteristic
345C22×C42—431no—
346#384—862no—
347#384—862no—
348C2×#95—861no—
349C2×#95—861no—
350#340—22no—
351#340—862no—
352#340—862no—
353#340—862no—
354#336—434no—
355C43#1126711yescharacteristic, complemented, Sylow
356C23×C4—21no—
357C23×C4—21no—
358C23×C4—431no—
359C23×C4—431no—
360C23×C4—861no—
361C23×C4—861no—
362C23×C4C22×D4311yescharacteristic
363C22×C8—21no—
364C22×C8—21no—
365C22×C8—21no—
366C22×C8—21no—
367C22×C8—21no—
368C22×C8—21no—
369C22×C8—432no—
370C22×C8—861no—
371C22×C8—861no—
372C22×C8—861no—
373C22×C8—861no—
374C22×C8—861no—
375C22×C8—861no—
376C22×C8C4×D4312yes—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—432no—
388C2×C4⋊C4—432no—
389C2×C4⋊C4—861no—
390C2×C4⋊C4—861no—
391C2×C4⋊C4—861no—
392C2×C4⋊C4—861no—
393C2×C4⋊C4—861no—
394C2×C4⋊C4—861no—
395C2×C4⋊C4—861no—
396C2×C4⋊C4—861no—
397C2×C4⋊C4—864no—
398C2×C4⋊C4—864no—
399C2×C4⋊C4—861no—
400C2×C4⋊C4—861no—
401C2×C4⋊C4—1722no—
402C2×C4⋊C4—1722no—
403C2×C4⋊C4—1722no—
404C2×C4⋊C4—1722no—
405C2×C4⋊C4D17212yes—
406C2×C4⋊C4C22⋊D4312yes—
407C2×C42—432no—
408C2×C42—432no—
409C2×C42—861no—
410C2×C42—861no—
411C2×C42—861no—
412C2×C42—861no—
413#95—1722no—
414#95—1722no—
415C24D4×D4311yescharacteristic
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—41no—
419C22×C4—41no—
420C22×C4—41no—
421C22×C4—41no—
422C22×C4—41no—
423C22×C4—41no—
424C22×C4—41no—
425C22×C4—41no—
426C22×C4—41no—
427C22×C4—41no—
428C22×C4—41no—
429C22×C4—41no—
430C22×C4—432no—
431C22×C4—432no—
432C22×C4—432no—
433C22×C4—432no—
434C22×C4—432no—
435C22×C4—432no—
436C22×C4—861no—
437C22×C4—861no—
438C22×C4—861no—
439C22×C4—861no—
440C22×C4—861no—
441C22×C4—861no—
442C22×C4—861no—
443C22×C4—861no—
444C22×C4—862no—
445C22×C4—862no—
446C22×C4—1721no—
447C22×C4—1721no—
448C22×C4—1721no—
449C22×C4—1721no—
450C22×C4—1721no—
451C22×C4—1721no—
452C22×C4—1721no—
453C22×C4—1721no—
454C22×C4—1721no—
455C22×C4—1721no—
456C22×C4—1721no—
457C22×C4—1721no—
458C22×C4C2×C4×D4311yescharacteristic
459C22×C4C2×D17211yescharacteristic
460C22×C4#1062189811yescharacteristic
461C22×C4#1062189811yescharacteristic
462C22×C4#1062189811yescharacteristic
463C22×C4#1062189811yescharacteristic
464C22×C4D4×D4311yescharacteristic
465C22×C4#1062190011yescharacteristic
466C22×C4#1062190011yescharacteristic
467C22×C4#1062190011yescharacteristic
468C22×C4#1062190011yescharacteristic
469C22×C4Q8×D4311yescharacteristic
470C22×C4Q8×D4311yescharacteristic
471C22×C4C2×C22⋊D4311yescharacteristic
472C2×C8—22no—
473C2×C8—22no—
474C2×C8—22no—
475C2×C8—41no—
476C2×C8—41no—
477C2×C8—41no—
478C2×C8—41no—
479C2×C8—862no—
480C2×C8—862no—
481C2×C8—862no—
482C2×C8—1721no—
483C2×C8—1721no—
484C2×C8—1721no—
485C2×C8—1721no—
486C4⋊C4—22no—
487C4⋊C4—22no—
488C4⋊C4—22no—
489C4⋊C4—22no—
490C4⋊C4—41no—
491C4⋊C4—41no—
492C4⋊C4—41no—
493C4⋊C4—41no—
494C4⋊C4—862no—
495C4⋊C4—862no—
496C4⋊C4—862no—
497C4⋊C4—862no—
498C4⋊C4—1728no—
499C4⋊C4—1728no—
500C4⋊C4—1721no—
501C4⋊C4—1721no—
502C4⋊C4—1721no—
503C4⋊C4—1721no—
504C42—862no—
505C42—862no—
506C42—862no—
507C42—862no—
508C23C4⋊C4×D4311yescharacteristic
509C23#1306329511yescharacteristic
510C23#1306329711yescharacteristic
511C23#1306330311yescharacteristic
512C23#1306330711yescharacteristic
513C23#1306331111yescharacteristic
514C23#1306331111yescharacteristic
515C23D8×D4311yescharacteristic
516C23SD16×D4311yescharacteristic
517C23SD16×D4311yescharacteristic
518C23Q16×D4311yescharacteristic
519C23#1306334911yescharacteristic
520C23#1306335211yescharacteristic
521C23#1306335411yescharacteristic
522C23#1306335711yescharacteristic
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—81no—
530C2×C4—81no—
531C2×C4—81no—
532C2×C4—81no—
533C2×C4—81no—
534C2×C4—81no—
535C2×C4—81no—
536C2×C4—81no—
537C2×C4—434no—
538C2×C4—434no—
539C2×C4—862no—
540C2×C4—862no—
541C2×C4—862no—
542C2×C4—862no—
543C2×C4—862no—
544C2×C4—862no—
545C2×C4—862no—
546C2×C4—862no—
547C2×C4—862no—
548C2×C4—862no—
549C2×C4—862no—
550C2×C4—862no—
551C2×C4—3441no—
552C2×C4—3441no—
553C2×C4—3441no—
554C2×C4—3441no—
555C2×C4—3441no—
556C2×C4—3441no—
557C2×C4—3441no—
558C2×C4—3441no—
559C2×C4—1722no—
560C2×C4—1722no—
561C2×C4—1722no—
562C2×C4—1722no—
563C2×C4—1722no—
564C2×C4—1722no—
565C2×C4#1306328111yescharacteristic
566C2×C4#1306328211yescharacteristic
567C2×C4(C22⋊D43)⋊C411yescharacteristic
568C2×C4C4×C22⋊D4311yescharacteristic
569C2×C4C4×D17211yescharacteristic
570C2×C4#1306329011yescharacteristic
571C2×C4#1306329611yescharacteristic
572C2×C4#1306329911yescharacteristic
573C2×C4#1306330311yescharacteristic
574C2×C4#1306330311yescharacteristic
575C2×C4#1306330511yescharacteristic
576C2×C4#1306330511yescharacteristic
577C2×C4#1306330611yescharacteristic
578C2×C4#1306330711yescharacteristic
579C2×C4#1306330811yescharacteristic
580C2×C4#1306330911yescharacteristic
581C2×C4#1306331111yescharacteristic
582C2×C4#1306331311yescharacteristic
583C2×C4#1306331511yescharacteristic
584C2×C4#1306331511yescharacteristic
585C2×C4#1306331511yescharacteristic
586C2×C4#1306331511yescharacteristic
587C2×C4#1306331511yescharacteristic
588C2×C4#1306331811yescharacteristic
589C2×C4#1306331811yescharacteristic
590C2×C4#1306331811yescharacteristic
591C2×C4#1306331911yescharacteristic
592C2×C4#1306332311yescharacteristic
593C8—42no—
594C8—1722no—
595C22#1458276311yescharacteristic
596C22#1458277311yescharacteristic
597C22#1458279411yescharacteristic
598C22#1458281211yescharacteristic
599C22#1458281511yescharacteristic
600C22#1458282711yescharacteristic
601C22#1458284011yescharacteristic
602C22#106×D4311yescharacteristic
603C22#107×D4311yescharacteristic
604C22#1458293811yescharacteristic
605C22#1458294011yescharacteristic
606C22#1458303411yescharacteristic
607C22#1458303911yescharacteristic
608C22#1458305111yescharacteristic
609C22#1458305611yescharacteristic
610C22#1458309211yescharacteristic
611C22#1458309711yescharacteristic
612C22#1458310211yescharacteristic
613C22#1458310711yescharacteristic
614C22#1458317811yescharacteristic
615C22#1458318311yescharacteristic
616C22#1458318811yescharacteristic
617C22#1458319311yescharacteristic
618C22#1458321111yescharacteristic
619C22#1458321611yescharacteristic
620C22#1458322811yescharacteristic
621C22#1458323311yescharacteristic
622C22#1458324411yescharacteristic
623C22#1458324411yescharacteristic
624C22#1458324811yescharacteristic
625C22#1458324811yescharacteristic
626C22#1458325711yescharacteristic
627C22#1458326011yescharacteristic
628C22#1458326211yescharacteristic
629C22#1458326611yescharacteristic
630C4—82no—
631C4—82no—
632C4—864no—
633C4—864no—
634C4—3442no—
635C4—3442no—
636C4#1458278111yescharacteristic
637C4#1458278411yescharacteristic
638C4#1458278711yescharacteristic
639C4#1458279011yescharacteristic
640C4#1458282911yescharacteristic
641C4#1458283011yescharacteristic
642C4#1458283911yescharacteristic
643C4#1458284011yescharacteristic
644C2#1913285011yescharacteristic
645C2#1913472111yescharacteristic
646C2#1913472711yescharacteristic
647C2#1913478411yescharacteristic
648C2#1913478911yescharacteristic
649C2#1913535011yescharacteristic
650C2#1913535511yescharacteristic
651C2#1913573011yescharacteristic
652C2#1913573511yescharacteristic
653C2#1913582811yescharacteristic
654C2#1913584011yescharacteristic
655C2#1913600111yescharacteristic
656C2#1913600611yescharacteristic
657C2#1913615511yescharacteristic
658C2#1913616011yescharacteristic
subgroupG/H
centerC24D4×D43
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC2×C43×#340C2
socle, prime radicalC24×C43C2×D4
cosocleC23×C4×C43C23
hypercenterC2×#340D43
hypocenterC43#11267
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C24 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
21. #14582653C4semidirect
355. C43#11267semidirect

Maximal subgroups

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

subgroupindex
C2×#145827682
C2×#145826622
C2×#145826612
C2×#145826532
#191328242
C2×C43×#3402
#1126743