Finite Group Databasebeta

← #25004505

Subgroups — #25004505

Order 11008.

958 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582795C211yesmaximal, characteristic
2C2×#14582768C211yesmaximal, characteristic
3C2×#14582662C211yesmaximal, characteristic
4C2×#14582661C211yesmaximal, characteristic
5C2×#14582661C211yesmaximal, characteristic
6C2×#14582653C211yesmaximal, characteristic
7C2×C43×#340C211yesmaximal, characteristic
8C23×C43⋊C8C2211yescharacteristic
9C22×C4⋊Dic43C2211yescharacteristic
10C22×C4⋊Dic43C2211yescharacteristic
11C22×Dic43⋊C4—21no—
12C22×Dic43⋊C4—21no—
13C22×Dic43⋊C4—21no—
14C22×C4×Dic43C2211yescharacteristic
15#14582795—22no—
16#14582795C414yescomplemented
17#14582768—22no—
18#14582768—22no—
19C2×C43⋊#95—21no—
20#14582662—22no—
21#14582661—22no—
22#14582661—22no—
23#14582653—22no—
24C23×C8×C43C2211yescharacteristic
25C22×C4⋊C4×C43C2211yescharacteristic
26C22×C4⋊C4×C43C2211yescharacteristic
27C43×#340—22no—
28C23×Dic43—21no—
29C23×Dic43—21no—
30C23×Dic43D411yescharacteristic
31C23×Dic43D411yescharacteristic
32C22×C43⋊C8—21no—
33C22×C43⋊C8—21no—
34C22×C43⋊C8—21no—
35C22×C43⋊C8—21no—
36C22×C43⋊C8—21no—
37C22×C43⋊C8—21no—
38C22×C43⋊C8Q812yes—
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⋊Dic43C2×C412yes—
48C2×C4⋊Dic43D412yes—
49C2×C4⋊Dic43D412yes—
50C2×C4⋊Dic43Q812yes—
51C2×Dic43⋊C4—24no—
52C2×Dic43⋊C4—24no—
53C2×Dic43⋊C4—24no—
54C2×Dic43⋊C4—42no—
55C2×Dic43⋊C4—42no—
56C2×Dic43⋊C4—42no—
57C2×Dic43⋊C4—42no—
58C2×Dic43⋊C4—42no—
59C2×Dic43⋊C4—42no—
60C2×C4×Dic43—21no—
61C2×C4×Dic43—21no—
62C2×C4×Dic43—21no—
63C2×C4×Dic43—21no—
64C2×C4×Dic43C2×C412yes—
65C2×C4×Dic43D412yes—
66C43⋊#95—24no—
67C23×C4×C43—21no—
68C23×C4×C43—21no—
69C23×C4×C43C2311yescharacteristic
70C22×C8×C43—21no—
71C22×C8×C43—21no—
72C22×C8×C43—21no—
73C22×C8×C43—21no—
74C22×C8×C43—21no—
75C22×C8×C43—21no—
76C22×C8×C43Q812yes—
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×C43—21no—
84C2×C4⋊C4×C43—21no—
85C2×C4⋊C4×C43—21no—
86C2×C4⋊C4×C43—21no—
87C2×C4⋊C4×C43C2×C412yes—
88C2×C4⋊C4×C43D412yes—
89C24×C43C2×D411yescharacteristic
90C22×C4×C43—22no—
91C22×C4×C43—22no—
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×C43—41no—
101C22×C4×C43—41no—
102C22×C4×C43—41no—
103C22×C4×C43—41no—
104C22×C4×C43C22×C411yescharacteristic
105C22×C4×C43C2×D411yescharacteristic
106C22×C4×C43C2×D411yescharacteristic
107C22×C4×C43C2×D411yescharacteristic
108C22×C4×C43C2×D411yescharacteristic
109C22×C4×C43C2×Q811yescharacteristic
110C22×C4×C43C2×Q811yescharacteristic
111C22×C4×C43C2×Q811yescharacteristic
112C22×C4×C43#4111yescharacteristic
113C22×C4×C43#4111yescharacteristic
114C22×C4×C43#4111yescharacteristic
115C22×C4×C43#4111yescharacteristic
116C22×C4×C43#4111yescharacteristic
117C22×C4×C43#4111yescharacteristic
118C22×Dic43—22no—
119C22×Dic43—21no—
120C22×Dic43—21no—
121C22×Dic43—22no—
122C22×Dic43—22no—
123C22×Dic43—22no—
124C22×Dic43—21no—
125C22×Dic43—21no—
126C22×Dic43—21no—
127C22×Dic43—21no—
128C22×Dic43—21no—
129C22×Dic43—21no—
130C22×Dic43—41no—
131C22×Dic43—41no—
132C22×Dic43—41no—
133C22×Dic43—41no—
134C22×Dic43—41no—
135C22×Dic43—41no—
136C22×Dic43—41no—
137C22×Dic43—41no—
138C22×Dic43—41no—
139C22×Dic43—41no—
140C22×Dic43C22⋊C412yes—
141C22×Dic43C22⋊C412yes—
142C22×Dic43D812yes—
143C22×Dic43SD1612yes—
144C22×Dic43SD1612yes—
145C22×Dic43Q1612yes—
146C2×C8×C43—22no—
147C2×C8×C43—22no—
148C2×C8×C43—22no—
149C2×C8×C43—41no—
150C2×C8×C43—41no—
151C2×C8×C43—41no—
152C2×C8×C43—41no—
153C4⋊C4×C43—22no—
154C4⋊C4×C43—22no—
155C4⋊C4×C43—22no—
156C4⋊C4×C43—22no—
157C4⋊C4×C43—41no—
158C4⋊C4×C43—41no—
159C4⋊C4×C43—41no—
160C4⋊C4×C43—41no—
161C4⋊Dic43—22no—
162C4⋊Dic43—22no—
163C4⋊Dic43—22no—
164C4⋊Dic43—22no—
165C4⋊Dic43—22no—
166C4⋊Dic43—41no—
167C4⋊Dic43—41no—
168C4⋊Dic43C4⋊C414yescomplemented
169Dic43⋊C4—48no—
170Dic43⋊C4—48no—
171Dic43⋊C4—48no—
172C4×Dic43—22no—
173C4×Dic43—22no—
174C4×Dic43—22no—
175C4×Dic43—22no—
176C2×C43⋊C8—22no—
177C2×C43⋊C8—22no—
178C2×C43⋊C8—22no—
179C2×C43⋊C8—41no—
180C2×C43⋊C8—41no—
181C2×C43⋊C8—41no—
182C2×C43⋊C8—41no—
183C23×C43C2×C22⋊C411yescharacteristic
184C23×C43#12011yescharacteristic
185C23×C43#12111yescharacteristic
186C23×C43C22⋊Q811yescharacteristic
187C23×C43#12311yescharacteristic
188C23×C43#12411yescharacteristic
189C23×C43C4⋊Q811yescharacteristic
190C23×C43C2×D811yescharacteristic
191C23×C43C2×SD1611yescharacteristic
192C23×C43C2×SD1611yescharacteristic
193C23×C43C2×Q1611yescharacteristic
194C23×C43AGL(1,ℤ/8)11yescharacteristic
195C23×C43AGL(1,ℤ/8)11yescharacteristic
196C23×C43#13711yescharacteristic
197C23×C43#13711yescharacteristic
198C2×C4×C43—42no—
199C2×C4×C43—42no—
200C2×C4×C43—42no—
201C2×C4×C43—42no—
202C2×C4×C43—42no—
203C2×C4×C43—42no—
204C2×C4×C43—81no—
205C2×C4×C43—81no—
206C2×C4×C43—81no—
207C2×C4×C43—81no—
208C2×C4×C43—81no—
209C2×C4×C43—81no—
210C2×C4×C43—81no—
211C2×C4×C43—81no—
212C2×C4×C43C2×C4⋊C411yescharacteristic
213C2×C4×C43#11711yescharacteristic
214C2×C4×C43C4×D411yescharacteristic
215C2×C4×C43C4×D411yescharacteristic
216C2×C4×C43C4×Q811yescharacteristic
217C2×C4×C43C4×Q811yescharacteristic
218C2×C4×C43#12111yescharacteristic
219C2×C4×C43#12111yescharacteristic
220C2×C4×C43#12111yescharacteristic
221C2×C4×C43#12111yescharacteristic
222C2×C4×C43#12111yescharacteristic
223C2×C4×C43C22⋊Q811yescharacteristic
224C2×C4×C43C22⋊Q811yescharacteristic
225C2×C4×C43C22⋊Q811yescharacteristic
226C2×C4×C43C22⋊Q811yescharacteristic
227C2×C4×C43C22⋊Q811yescharacteristic
228C2×C4×C43C22⋊Q811yescharacteristic
229C2×C4×C43C22⋊Q811yescharacteristic
230C2×C4×C43#12311yescharacteristic
231C2×C4×C43#12311yescharacteristic
232C2×C4×C43#12511yescharacteristic
233C2×C4×C43#12511yescharacteristic
234C2×C4×C43#12511yescharacteristic
235C2×C4×C43#12511yescharacteristic
236C2×C4×C43#12611yescharacteristic
237C2×C4×C43#12611yescharacteristic
238C2×C4×C43C4⋊Q811yescharacteristic
239C2×C4×C43C4⋊Q811yescharacteristic
240C2×Dic43—22no—
241C2×Dic43—22no—
242C2×Dic43—22no—
243C2×Dic43—22no—
244C2×Dic43—22no—
245C2×Dic43—22no—
246C2×Dic43—22no—
247C2×Dic43—22no—
248C2×Dic43—22no—
249C2×Dic43—22no—
250C2×Dic43—22no—
251C2×Dic43—22no—
252C2×Dic43—24no—
253C2×Dic43—42no—
254C2×Dic43—42no—
255C2×Dic43—42no—
256C2×Dic43—42no—
257C2×Dic43—42no—
258C2×Dic43—42no—
259C2×Dic43—42no—
260C2×Dic43—42no—
261C2×Dic43—42no—
262C2×Dic43—81no—
263C2×Dic43—81no—
264C2×Dic43—81no—
265C2×Dic43—81no—
266C2×Dic43#10214yes—
267C2×Dic43#10314yes—
268C8×C43—42no—
269C43⋊C8—42no—
270#11207—431nomaximal, Sylow
271C22×C43#38011yescharacteristic
272C22×C43#38611yescharacteristic
273C22×C43#39111yescharacteristic
274C22×C43#39411yescharacteristic
275C22×C43#39511yescharacteristic
276C22×C43#39811yescharacteristic
277C22×C43#40011yescharacteristic
278C22×C43C2×#10211yescharacteristic
279C22×C43C2×#10311yescharacteristic
280C22×C43#41711yescharacteristic
281C22×C43#41711yescharacteristic
282C22×C43#44711yescharacteristic
283C22×C43#44811yescharacteristic
284C22×C43#45011yescharacteristic
285C22×C43#45111yescharacteristic
286C22×C43#45911yescharacteristic
287C22×C43#46011yescharacteristic
288C22×C43#46111yescharacteristic
289C22×C43#46211yescharacteristic
290C22×C43#47411yescharacteristic
291C22×C43#47511yescharacteristic
292C22×C43#47611yescharacteristic
293C22×C43#47711yescharacteristic
294C22×C43#48011yescharacteristic
295C22×C43#48111yescharacteristic
296C22×C43#48311yescharacteristic
297C22×C43#48411yescharacteristic
298C22×C43#48611yescharacteristic
299C22×C43#48711yescharacteristic
300C22×C43#49011yescharacteristic
301C22×C43#49111yescharacteristic
302C22×C43#49811yescharacteristic
303C22×C43#50011yescharacteristic
304C22×C43#50111yescharacteristic
305C22×C43#50111yescharacteristic
306C4×C43—82no—
307C4×C43—82no—
308C4×C43#38711yescharacteristic
309C4×C43#38711yescharacteristic
310C4×C43#38911yescharacteristic
311C4×C43#38911yescharacteristic
312C4×C43#39611yescharacteristic
313C4×C43#39611yescharacteristic
314C4×C43#39811yescharacteristic
315C4×C43#39811yescharacteristic
316Dic43—24no—
317Dic43—24no—
318Dic43—44no—
319Dic43—82no—
320C2×#389—431no—
321C2×#384—431no—
322C2×#340—431no—
323C2×#340—431no—
324C2×#340—431no—
325C2×#340D4311yescharacteristic
326C2×#336—431no—
327C2×C43#144111yescharacteristic
328C2×C43#180211yescharacteristic
329C2×C43#180311yescharacteristic
330C2×C43#187211yescharacteristic
331C2×C43#187411yescharacteristic
332C2×C43#199011yescharacteristic
333C2×C43#199211yescharacteristic
334C2×C43#204111yescharacteristic
335C2×C43#204311yescharacteristic
336C2×C43#205711yescharacteristic
337C2×C43#205811yescharacteristic
338C2×C43#208311yescharacteristic
339C2×C43#208411yescharacteristic
340C2×C43#209911yescharacteristic
341C2×C43#210011yescharacteristic
342C23×C8—431no—
343C23×C8C2×D4311yescharacteristic
344C22×C4⋊C4—431no—
345C22×C4⋊C4—431no—
346C22×C4⋊C4—861no—
347C22×C4⋊C4—861no—
348C22×C4⋊C4—861no—
349C22×C4⋊C4C2×D4311yescharacteristic
350C22×C4⋊C4C2×D4311yescharacteristic
351C22×C42—431no—
352#389—434no—
353#389—862no—
354#384—862no—
355#384—862no—
356C2×#95—861no—
357#340—22no—
358#340—862no—
359#340—862no—
360#340—862no—
361#336—862no—
362C43#1120711yescharacteristic, complemented, Sylow
363C23×C4—21no—
364C23×C4—21no—
365C23×C4—431no—
366C23×C4—431no—
367C23×C4—861no—
368C23×C4—861no—
369C23×C4C22×D4311yescharacteristic
370C22×C8—21no—
371C22×C8—21no—
372C22×C8—21no—
373C22×C8—21no—
374C22×C8—21no—
375C22×C8—21no—
376C22×C8—432no—
377C22×C8—861no—
378C22×C8—861no—
379C22×C8—861no—
380C22×C8—861no—
381C22×C8—861no—
382C22×C8—861no—
383C22×C8Dic8612yes—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—432no—
395C2×C4⋊C4—432no—
396C2×C4⋊C4—432no—
397C2×C4⋊C4—432no—
398C2×C4⋊C4—861no—
399C2×C4⋊C4—861no—
400C2×C4⋊C4—861no—
401C2×C4⋊C4—861no—
402C2×C4⋊C4—861no—
403C2×C4⋊C4—861no—
404C2×C4⋊C4—861no—
405C2×C4⋊C4—864no—
406C2×C4⋊C4—864no—
407C2×C4⋊C4—864no—
408C2×C4⋊C4—861no—
409C2×C4⋊C4—1722no—
410C2×C4⋊C4—1722no—
411C2×C4⋊C4—1722no—
412C2×C4⋊C4—1722no—
413C2×C4⋊C4—1722no—
414C2×C4⋊C4—1722no—
415C2×C4⋊C4C4×D4312yes—
416C2×C4⋊C4C22⋊D4312yes—
417C2×C42—432no—
418C2×C42—432no—
419C2×C42—861no—
420C2×C42—861no—
421C2×C42—861no—
422C2×C42—861no—
423#95—864no—
424C24D4×D4311yescharacteristic
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—41no—
428C22×C4—41no—
429C22×C4—41no—
430C22×C4—41no—
431C22×C4—41no—
432C22×C4—41no—
433C22×C4—41no—
434C22×C4—41no—
435C22×C4—41no—
436C22×C4—41no—
437C22×C4—41no—
438C22×C4—41no—
439C22×C4—432no—
440C22×C4—432no—
441C22×C4—432no—
442C22×C4—432no—
443C22×C4—432no—
444C22×C4—432no—
445C22×C4—861no—
446C22×C4—861no—
447C22×C4—861no—
448C22×C4—861no—
449C22×C4—861no—
450C22×C4—861no—
451C22×C4—861no—
452C22×C4—861no—
453C22×C4—862no—
454C22×C4—862no—
455C22×C4—862no—
456C22×C4—862no—
457C22×C4—1721no—
458C22×C4—1721no—
459C22×C4—1721no—
460C22×C4—1721no—
461C22×C4—1721no—
462C22×C4—1721no—
463C22×C4—1721no—
464C22×C4—1721no—
465C22×C4—1721no—
466C22×C4—1721no—
467C22×C4C2×Dic8611yescharacteristic
468C22×C4C2×C4×D4311yescharacteristic
469C22×C4#1062189811yescharacteristic
470C22×C4#1062189811yescharacteristic
471C22×C4#1062189811yescharacteristic
472C22×C4#1062189811yescharacteristic
473C22×C4D4×D4311yescharacteristic
474C22×C4D4×D4311yescharacteristic
475C22×C4D4×D4311yescharacteristic
476C22×C4#1062190011yescharacteristic
477C22×C4#1062190011yescharacteristic
478C22×C4Q8×D4311yescharacteristic
479C22×C4Q8×D4311yescharacteristic
480C22×C4C2×C22⋊D4311yescharacteristic
481C2×C8—22no—
482C2×C8—22no—
483C2×C8—22no—
484C2×C8—41no—
485C2×C8—41no—
486C2×C8—41no—
487C2×C8—41no—
488C2×C8—862no—
489C2×C8—862no—
490C2×C8—862no—
491C2×C8—1721no—
492C2×C8—1721no—
493C2×C8—1721no—
494C2×C8—1721no—
495C4⋊C4—22no—
496C4⋊C4—22no—
497C4⋊C4—22no—
498C4⋊C4—22no—
499C4⋊C4—41no—
500C4⋊C4—41no—
501C4⋊C4—41no—
502C4⋊C4—41no—
503C4⋊C4—434no—
504C4⋊C4—862no—
505C4⋊C4—862no—
506C4⋊C4—862no—
507C4⋊C4—862no—
508C4⋊C4—862no—
509C4⋊C4—1728no—
510C4⋊C4—1728no—
511C4⋊C4—1728no—
512C4⋊C4—1721no—
513C4⋊C4—1721no—
514C42—862no—
515C42—862no—
516C42—862no—
517C42—862no—
518C23C22⋊C4×D4311yescharacteristic
519C23#1306329311yescharacteristic
520C23#1306329811yescharacteristic
521C23#1306330311yescharacteristic
522C23#1306330711yescharacteristic
523C23#1306331111yescharacteristic
524C23#1306332411yescharacteristic
525C23D8×D4311yescharacteristic
526C23SD16×D4311yescharacteristic
527C23SD16×D4311yescharacteristic
528C23Q16×D4311yescharacteristic
529C23#1306334911yescharacteristic
530C23#1306335211yescharacteristic
531C23#1306335411yescharacteristic
532C23#1306335711yescharacteristic
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—81no—
540C2×C4—81no—
541C2×C4—81no—
542C2×C4—81no—
543C2×C4—81no—
544C2×C4—81no—
545C2×C4—81no—
546C2×C4—81no—
547C2×C4—434no—
548C2×C4—434no—
549C2×C4—862no—
550C2×C4—862no—
551C2×C4—862no—
552C2×C4—862no—
553C2×C4—862no—
554C2×C4—862no—
555C2×C4—862no—
556C2×C4—862no—
557C2×C4—862no—
558C2×C4—862no—
559C2×C4—862no—
560C2×C4—862no—
561C2×C4—864no—
562C2×C4—3441no—
563C2×C4—3441no—
564C2×C4—3441no—
565C2×C4—3441no—
566C2×C4—1722no—
567C2×C4—1722no—
568C2×C4—1722no—
569C2×C4—1722no—
570C2×C4—1722no—
571C2×C4—1722no—
572C2×C4—1722no—
573C2×C4—1722no—
574C2×C4—1722no—
575C2×C4C4⋊C4×D4311yescharacteristic
576C2×C4#1306328211yescharacteristic
577C2×C4(C22⋊D43)⋊C411yescharacteristic
578C2×C4C4×C22⋊D4311yescharacteristic
579C2×C4#1306329011yescharacteristic
580C2×C4C4×Dic8611yescharacteristic
581C2×C4#1306329611yescharacteristic
582C2×C4#1306329711yescharacteristic
583C2×C4#1306329811yescharacteristic
584C2×C4#1306329811yescharacteristic
585C2×C4#1306329811yescharacteristic
586C2×C4#1306330211yescharacteristic
587C2×C4#1306330211yescharacteristic
588C2×C4#1306330311yescharacteristic
589C2×C4#1306330311yescharacteristic
590C2×C4#1306330311yescharacteristic
591C2×C4#1306330311yescharacteristic
592C2×C4#1306330411yescharacteristic
593C2×C4#1306330711yescharacteristic
594C2×C4#1306330811yescharacteristic
595C2×C4#1306331511yescharacteristic
596C2×C4#1306331511yescharacteristic
597C2×C4#1306331511yescharacteristic
598C2×C4#1306331711yescharacteristic
599C2×C4#1306331811yescharacteristic
600C2×C4#1306331911yescharacteristic
601C2×C4#1306332311yescharacteristic
602C2×C4#1306332411yescharacteristic
603C8—42no—
604C8—1722no—
605C22#1458275811yescharacteristic
606C22#1458277511yescharacteristic
607C22#1458280311yescharacteristic
608C22#1458281411yescharacteristic
609C22#1458281911yescharacteristic
610C22#1458283311yescharacteristic
611C22#1458284011yescharacteristic
612C22#102×D4311yescharacteristic
613C22#103×D4311yescharacteristic
614C22#1458289711yescharacteristic
615C22#1458289911yescharacteristic
616C22#1458303111yescharacteristic
617C22#1458303611yescharacteristic
618C22#1458304811yescharacteristic
619C22#1458305311yescharacteristic
620C22#1458309311yescharacteristic
621C22#1458309811yescharacteristic
622C22#1458310311yescharacteristic
623C22#1458310811yescharacteristic
624C22#1458317811yescharacteristic
625C22#1458318311yescharacteristic
626C22#1458318811yescharacteristic
627C22#1458319311yescharacteristic
628C22#1458321111yescharacteristic
629C22#1458321611yescharacteristic
630C22#1458322811yescharacteristic
631C22#1458323311yescharacteristic
632C22#1458324411yescharacteristic
633C22#1458324811yescharacteristic
634C22#1458326211yescharacteristic
635C22#1458326611yescharacteristic
636C22#1458329611yescharacteristic
637C22#1458330311yescharacteristic
638C22#1458330611yescharacteristic
639C22#1458330711yescharacteristic
640C4—82no—
641C4—82no—
642C4—864no—
643C4—864no—
644C4—3442no—
645C4—1724no—
646C4#1458278111yescharacteristic
647C4#1458278311yescharacteristic
648C4#1458279411yescharacteristic
649C4#1458279611yescharacteristic
650C4#1458282211yescharacteristic
651C4#1458282311yescharacteristic
652C4#1458283011yescharacteristic
653C4#1458283311yescharacteristic
654C2#1913284611yescharacteristic
655C2#1913459411yescharacteristic
656C2#1913459911yescharacteristic
657C2#1913489911yescharacteristic
658C2#1913490911yescharacteristic
659C2#1913555411yescharacteristic
660C2#1913556211yescharacteristic
661C2#1913582711yescharacteristic
662C2#1913583911yescharacteristic
663C2#1913592111yescharacteristic
664C2#1913592611yescharacteristic
665C2#1913607011yescharacteristic
666C2#1913607511yescharacteristic
667C2#1913615511yescharacteristic
668C2#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#11207
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
16. #14582795C4semidirect
168. C4⋊Dic43C4⋊C4semidirect
362. C43#11207semidirect

Maximal subgroups

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

subgroupindex
C2×#145827952
C2×#145827682
C2×#145826622
C2×#145826612
C2×#145826532
C2×C43×#3402
#1120743