Finite Group Databasebeta

← #25005226

Subgroups — #25005226

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
1C22×#13063256C211yesmaximal, characteristic
2C2×#14582798C211yesmaximal, characteristic
3C2×#14582795C211yesmaximal, characteristic
4C2×#14582662C211yesmaximal, characteristic
5C2×#14582661C211yesmaximal, characteristic
6C2×#14582653C211yesmaximal, characteristic
7C2×C43×#340C211yesmaximal, characteristic
8C23×C43⋊C8C2211yescharacteristic
9C22×C4⋊Dic43—21no—
10C22×C4⋊Dic43C2211yescharacteristic
11C22×C4⋊Dic43C2211yescharacteristic
12C22×Dic43⋊C4—21no—
13C22×C4×Dic43C2211yescharacteristic
14C2×#13063256—22no—
15C2×#13063256—22no—
16C2×#13063256—22no—
17#14582798—22no—
18#14582798—22no—
19#14582795—22no—
20#14582795—22no—
21C2×C43⋊#95—21no—
22C2×C43⋊#95—21no—
23#14582662—22no—
24#14582661C414yescomplemented
25#14582653—22no—
26C23×C8×C43C2211yescharacteristic
27C22×C4⋊C4×C43C2211yescharacteristic
28C22×C4⋊C4×C43C2211yescharacteristic
29C43×#340—22no—
30C23×Dic43—21no—
31C23×Dic43—21no—
32C23×Dic43D411yescharacteristic
33C23×Dic43D411yescharacteristic
34C22×C43⋊C8—21no—
35C22×C43⋊C8—21no—
36C22×C43⋊C8—21no—
37C22×C43⋊C8—21no—
38C22×C43⋊C8C2×C412yes—
39C22×C43⋊C8D412yes—
40C22×C43⋊C8Q812yes—
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⋊Dic43—21no—
48C2×C4⋊Dic43—24no—
49C2×C4⋊Dic43—21no—
50C2×C4⋊Dic43—42no—
51C2×C4⋊Dic43—42no—
52C2×C4⋊Dic43C2×C412yes—
53C2×C4⋊Dic43D412yes—
54C2×C4⋊Dic43D412yes—
55C2×C4⋊Dic43Q812yes—
56C2×Dic43⋊C4—24no—
57C2×Dic43⋊C4—42no—
58C2×Dic43⋊C4—42no—
59C2×C4×Dic43—21no—
60C2×C4×Dic43—21no—
61C2×C4×Dic43—21no—
62C2×C4×Dic43—21no—
63C2×C4×Dic43—21no—
64C2×C4×Dic43—21no—
65#13063256—28no—
66C43⋊#95—24no—
67C43⋊#95—24no—
68C23×C4×C43—21no—
69C23×C4×C43—21no—
70C23×C4×C43C2311yescharacteristic
71C22×C8×C43—21no—
72C22×C8×C43—21no—
73C22×C8×C43—21no—
74C22×C8×C43—21no—
75C22×C8×C43—21no—
76C22×C8×C43—21no—
77C22×C8×C43Q812yes—
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×C43C2×C412yes—
87C2×C4⋊C4×C43D412yes—
88C2×C4⋊C4×C43D412yes—
89C2×C4⋊C4×C43Q812yes—
90C24×C43C2×D411yescharacteristic
91C22×C4×C43—22no—
92C22×C4×C43—22no—
93C22×C4×C43—22no—
94C22×C4×C43—22no—
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×C43—41no—
105C22×C4×C43C22×C411yescharacteristic
106C22×C4×C43C2×D411yescharacteristic
107C22×C4×C43C2×D411yescharacteristic
108C22×C4×C43C2×D411yescharacteristic
109C22×C4×C43C2×D411yescharacteristic
110C22×C4×C43C2×D411yescharacteristic
111C22×C4×C43C2×Q811yescharacteristic
112C22×C4×C43C2×Q811yescharacteristic
113C22×C4×C43C2×Q811yescharacteristic
114C22×C4×C43C2×Q811yescharacteristic
115C22×C4×C43#4111yescharacteristic
116C22×C4×C43#4111yescharacteristic
117C22×C4×C43#4111yescharacteristic
118C22×C4×C43#4111yescharacteristic
119C22×Dic43—22no—
120C22×Dic43—21no—
121C22×Dic43—21no—
122C22×Dic43—22no—
123C22×Dic43—21no—
124C22×Dic43—21no—
125C22×Dic43—22no—
126C22×Dic43—21no—
127C22×Dic43—21no—
128C22×Dic43—22no—
129C22×Dic43—21no—
130C22×Dic43—21no—
131C22×Dic43—21no—
132C22×Dic43—21no—
133C22×Dic43—21no—
134C22×Dic43—21no—
135C22×Dic43—41no—
136C22×Dic43—41no—
137C22×Dic43—41no—
138C22×Dic43—41no—
139C22×Dic43—41no—
140C22×Dic43—41no—
141C22×Dic43—41no—
142C22×Dic43—41no—
143C22×Dic43—41no—
144C22×Dic43—41no—
145C22×Dic43SD1612yes—
146C22×Dic43SD1612yes—
147C2×C8×C43—22no—
148C2×C8×C43—22no—
149C2×C8×C43—22no—
150C2×C8×C43—41no—
151C2×C8×C43—41no—
152C2×C8×C43—41no—
153C2×C8×C43—41no—
154C4⋊C4×C43—22no—
155C4⋊C4×C43—22no—
156C4⋊C4×C43—22no—
157C4⋊C4×C43—22no—
158C4⋊C4×C43—22no—
159C4⋊C4×C43—41no—
160C4⋊C4×C43—41no—
161C4⋊C4×C43C4⋊C414yescomplemented
162C4⋊Dic43—22no—
163C4⋊Dic43—22no—
164C4⋊Dic43—22no—
165C4⋊Dic43—22no—
166C4⋊Dic43—22no—
167C4⋊Dic43—48no—
168C4⋊Dic43—41no—
169C4⋊Dic43—41no—
170C4⋊Dic43C4⋊C414yescomplemented
171Dic43⋊C4—48no—
172C4×Dic43—41no—
173C4×Dic43—41no—
174C4×Dic43—41no—
175C4×Dic43—41no—
176C2×C43⋊C8—22no—
177C2×C43⋊C8—22no—
178C2×C43⋊C8—22no—
179C2×C43⋊C8—22no—
180C2×C43⋊C8—22no—
181C2×C43⋊C8—22no—
182C2×C43⋊C8C4⋊C414yescomplemented
183C23×C43C4×D411yescharacteristic
184C23×C43#12011yescharacteristic
185C23×C43#12011yescharacteristic
186C23×C43#12111yescharacteristic
187C23×C43C22⋊Q811yescharacteristic
188C23×C43C22⋊Q811yescharacteristic
189C23×C43C4⋊Q811yescharacteristic
190C23×C43C2×SD1611yescharacteristic
191C23×C43C2×SD1611yescharacteristic
192C23×C43#13511yescharacteristic
193C23×C43#13511yescharacteristic
194C23×C43AGL(1,ℤ/8)11yescharacteristic
195C23×C43AGL(1,ℤ/8)11yescharacteristic
196C23×C43#13711yescharacteristic
197C23×C43#13711yescharacteristic
198C2×C4×C43—24no—
199C2×C4×C43—42no—
200C2×C4×C43—42no—
201C2×C4×C43—42no—
202C2×C4×C43—42no—
203C2×C4×C43—42no—
204C2×C4×C43—42no—
205C2×C4×C43—42no—
206C2×C4×C43—42no—
207C2×C4×C43—42no—
208C2×C4×C43—81no—
209C2×C4×C43—81no—
210C2×C4×C43—81no—
211C2×C4×C43—81no—
212C2×C4×C43C2×C4⋊C411yescharacteristic
213C2×C4×C43C2×C4⋊C411yescharacteristic
214C2×C4×C43C2×C4⋊C411yescharacteristic
215C2×C4×C43C4×D411yescharacteristic
216C2×C4×C43C4×D411yescharacteristic
217C2×C4×C43C4×Q811yescharacteristic
218C2×C4×C43#12011yescharacteristic
219C2×C4×C43#12111yescharacteristic
220C2×C4×C43#12111yescharacteristic
221C2×C4×C43C22⋊Q811yescharacteristic
222C2×C4×C43C22⋊Q811yescharacteristic
223C2×C4×C43C22⋊Q811yescharacteristic
224C2×C4×C43C22⋊Q811yescharacteristic
225C2×C4×C43C22⋊Q811yescharacteristic
226C2×C4×C43C22⋊Q811yescharacteristic
227C2×C4×C43C22⋊Q811yescharacteristic
228C2×C4×C43#12311yescharacteristic
229C2×C4×C43#12311yescharacteristic
230C2×C4×C43#12311yescharacteristic
231C2×C4×C43#12511yescharacteristic
232C2×C4×C43#12511yescharacteristic
233C2×C4×C43#12511yescharacteristic
234C2×C4×C43#12711yescharacteristic
235C2×C4×C43C4⋊Q811yescharacteristic
236C2×C4×C43C4⋊Q811yescharacteristic
237C2×C4×C43C4⋊Q811yescharacteristic
238C2×C4×C43C4⋊Q811yescharacteristic
239C2×C4×C43C4⋊Q811yescharacteristic
240C2×Dic43—24no—
241C2×Dic43—22no—
242C2×Dic43—22no—
243C2×Dic43—22no—
244C2×Dic43—22no—
245C2×Dic43—22no—
246C2×Dic43—22no—
247C2×Dic43—41no—
248C2×Dic43—41no—
249C2×Dic43—42no—
250C2×Dic43—42no—
251C2×Dic43—41no—
252C2×Dic43—41no—
253C2×Dic43—42no—
254C2×Dic43—42no—
255C2×Dic43—41no—
256C2×Dic43—41no—
257C2×Dic43—41no—
258C2×Dic43—41no—
259C2×Dic43—42no—
260C2×Dic43—42no—
261C2×Dic43—42no—
262C2×Dic43—42no—
263C2×Dic43—42no—
264C2×Dic43—81no—
265C2×Dic43—81no—
266C2×Dic43—81no—
267C2×Dic43—81no—
268C8×C43—42no—
269C43⋊C8—24no—
270#11327—431nomaximal, Sylow
271C22×C43#38511yescharacteristic
272C22×C43#38511yescharacteristic
273C22×C43#38911yescharacteristic
274C22×C43#39211yescharacteristic
275C22×C43#39511yescharacteristic
276C22×C43#39511yescharacteristic
277C22×C43#39811yescharacteristic
278C22×C43C4×SD1611yescharacteristic
279C22×C43C4×SD1611yescharacteristic
280C22×C43#44111yescharacteristic
281C22×C43#44211yescharacteristic
282C22×C43#44811yescharacteristic
283C22×C43#44811yescharacteristic
284C22×C43#44911yescharacteristic
285C22×C43#44911yescharacteristic
286C22×C43#45011yescharacteristic
287C22×C43#45011yescharacteristic
288C22×C43#45211yescharacteristic
289C22×C43#45211yescharacteristic
290C22×C43#46511yescharacteristic
291C22×C43#46511yescharacteristic
292C22×C43#46811yescharacteristic
293C22×C43#46811yescharacteristic
294C22×C43#47511yescharacteristic
295C22×C43#47511yescharacteristic
296C22×C43#47611yescharacteristic
297C22×C43#47611yescharacteristic
298C22×C43#47811yescharacteristic
299C22×C43#47811yescharacteristic
300C22×C43#47911yescharacteristic
301C22×C43#47911yescharacteristic
302C22×C43#49811yescharacteristic
303C22×C43#49911yescharacteristic
304C22×C43#50111yescharacteristic
305C22×C43#50111yescharacteristic
306C4×C43—44no—
307C4×C43—82no—
308C4×C43#38411yescharacteristic
309C4×C43#38511yescharacteristic
310C4×C43#38911yescharacteristic
311C4×C43#38911yescharacteristic
312C4×C43#39511yescharacteristic
313C4×C43#39811yescharacteristic
314C4×C43#39811yescharacteristic
315C4×C43#39911yescharacteristic
316Dic43—44no—
317Dic43—42no—
318Dic43—42no—
319Dic43—82no—
320C22×#106—431no—
321C2×#389—431no—
322C2×#389—431no—
323C2×#340—431no—
324C2×#340—431no—
325C2×#340D4311yescharacteristic
326C2×#336—431no—
327C2×C43#144411yescharacteristic
328C2×C43#186411yescharacteristic
329C2×C43#186411yescharacteristic
330C2×C43#186511yescharacteristic
331C2×C43#186511yescharacteristic
332C2×C43#194111yescharacteristic
333C2×C43#194311yescharacteristic
334C2×C43#200011yescharacteristic
335C2×C43#200011yescharacteristic
336C2×C43#205811yescharacteristic
337C2×C43#205811yescharacteristic
338C2×C43#205911yescharacteristic
339C2×C43#205911yescharacteristic
340C2×C43#208811yescharacteristic
341C2×C43#208811yescharacteristic
342C23×C8—431no—
343C23×C8C2×D4311yescharacteristic
344C22×C4⋊C4—431no—
345C22×C4⋊C4—431no—
346C22×C4⋊C4—861no—
347C22×C4⋊C4—861no—
348C22×C4⋊C4C2×D4311yescharacteristic
349C22×C4⋊C4C2×D4311yescharacteristic
350C22×C42—431no—
351C2×#106—862no—
352C2×#106—862no—
353C2×#106—862no—
354#389—862no—
355#389—862no—
356#389—862no—
357#389—862no—
358C2×#95—861no—
359C2×#95—861no—
360#340—22no—
361#340—434no—
362#340—862no—
363#336—862no—
364C43#1132711yescharacteristic, complemented, Sylow
365C23×C4—21no—
366C23×C4—21no—
367C23×C4—431no—
368C23×C4—431no—
369C23×C4—861no—
370C23×C4—861no—
371C23×C4C22×D4311yescharacteristic
372C22×C8—21no—
373C22×C8—21no—
374C22×C8—21no—
375C22×C8—21no—
376C22×C8—21no—
377C22×C8—21no—
378C22×C8—432no—
379C22×C8—432no—
380C22×C8—432no—
381C22×C8—861no—
382C22×C8—861no—
383C22×C8—861no—
384C22×C8—861no—
385C22×C8Dic8612yes—
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—861no—
408C2×C4⋊C4—1722no—
409C2×C4⋊C4—1722no—
410C2×C4⋊C4—1722no—
411C2×C4⋊C4—1722no—
412C2×C4⋊C4Dic8612yes—
413C2×C4⋊C4C4×D4312yes—
414C2×C4⋊C4D17212yes—
415C2×C4⋊C4C22⋊D4312yes—
416C2×C42—861no—
417C2×C42—861no—
418C2×C42—861no—
419C2×C42—861no—
420C2×C42—861no—
421C2×C42—861no—
422#106—868no—
423#95—864no—
424#95—864no—
425C24D4×D4311yescharacteristic
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
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—41no—
440C22×C4—432no—
441C22×C4—432no—
442C22×C4—862no—
443C22×C4—861no—
444C22×C4—861no—
445C22×C4—861no—
446C22×C4—862no—
447C22×C4—861no—
448C22×C4—861no—
449C22×C4—861no—
450C22×C4—862no—
451C22×C4—861no—
452C22×C4—861no—
453C22×C4—861no—
454C22×C4—861no—
455C22×C4—861no—
456C22×C4—861no—
457C22×C4—862no—
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×C4—1721no—
468C22×C4C2×Dic8611yescharacteristic
469C22×C4C2×Dic8611yescharacteristic
470C22×C4C2×C4×D4311yescharacteristic
471C22×C4C2×D17211yescharacteristic
472C22×C4#1062189811yescharacteristic
473C22×C4#1062189811yescharacteristic
474C22×C4D4×D4311yescharacteristic
475C22×C4D4×D4311yescharacteristic
476C22×C4D4×D4311yescharacteristic
477C22×C4#1062190011yescharacteristic
478C22×C4#1062190011yescharacteristic
479C22×C4Q8×D4311yescharacteristic
480C22×C4Q8×D4311yescharacteristic
481C22×C4C2×C22⋊D4311yescharacteristic
482C2×C8—22no—
483C2×C8—22no—
484C2×C8—22no—
485C2×C8—41no—
486C2×C8—41no—
487C2×C8—41no—
488C2×C8—41no—
489C2×C8—434no—
490C2×C8—862no—
491C2×C8—862no—
492C2×C8—862no—
493C2×C8—862no—
494C2×C8—862no—
495C2×C8—862no—
496C4⋊C4—22no—
497C4⋊C4—22no—
498C4⋊C4—22no—
499C4⋊C4—22no—
500C4⋊C4—22no—
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—1721no—
512C4⋊C4—1721no—
513C4⋊C4Dic43⋊C414yescomplemented
514C42—1721no—
515C42—1721no—
516C42—1721no—
517C42—1721no—
518C23(C22⋊D43)⋊C411yescharacteristic
519C23#1306329311yescharacteristic
520C23#1306329511yescharacteristic
521C23#1306329811yescharacteristic
522C23#1306330211yescharacteristic
523C23#1306330311yescharacteristic
524C23#1306332411yescharacteristic
525C23SD16×D4311yescharacteristic
526C23SD16×D4311yescharacteristic
527C23#1306334411yescharacteristic
528C23#1306334811yescharacteristic
529C23#1306334911yescharacteristic
530C23#1306335211yescharacteristic
531C23#1306335411yescharacteristic
532C23#1306335711yescharacteristic
533C2×C4—24no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—81no—
544C2×C4—81no—
545C2×C4—81no—
546C2×C4—81no—
547C2×C4—862no—
548C2×C4—862no—
549C2×C4—862no—
550C2×C4—862no—
551C2×C4—864no—
552C2×C4—862no—
553C2×C4—862no—
554C2×C4—3441no—
555C2×C4—3441no—
556C2×C4—3441no—
557C2×C4—3441no—
558C2×C4—1722no—
559C2×C4—1722no—
560C2×C4—1722no—
561C2×C4—1721no—
562C2×C4—1721no—
563C2×C4—1722no—
564C2×C4—1722no—
565C2×C4—1721no—
566C2×C4—1721no—
567C2×C4—1721no—
568C2×C4—1721no—
569C2×C4—1721no—
570C2×C4—1721no—
571C2×C4—1722no—
572C2×C4—1722no—
573C2×C4—1722no—
574C2×C4—1722no—
575C2×C4C4⋊C4×D4311yescharacteristic
576C2×C4C4⋊C4×D4311yescharacteristic
577C2×C4C2×Dic43⋊C411yescharacteristic
578C2×C4(C22⋊D43)⋊C411yescharacteristic
579C2×C4C4×D17211yescharacteristic
580C2×C4C4×Dic8611yescharacteristic
581C2×C4#1306329511yescharacteristic
582C2×C4#1306329811yescharacteristic
583C2×C4#1306329911yescharacteristic
584C2×C4#1306330211yescharacteristic
585C2×C4#1306330211yescharacteristic
586C2×C4#1306330211yescharacteristic
587C2×C4#1306330311yescharacteristic
588C2×C4#1306330411yescharacteristic
589C2×C4#1306330511yescharacteristic
590C2×C4#1306330511yescharacteristic
591C2×C4#1306330611yescharacteristic
592C2×C4#1306330711yescharacteristic
593C2×C4#1306330711yescharacteristic
594C2×C4#1306331511yescharacteristic
595C2×C4#1306331511yescharacteristic
596C2×C4#1306331711yescharacteristic
597C2×C4#1306332111yescharacteristic
598C2×C4#1306332311yescharacteristic
599C2×C4#1306332411yescharacteristic
600C2×C4#1306332411yescharacteristic
601C2×C4#1306332411yescharacteristic
602C2×C4#1306332511yescharacteristic
603C8—42no—
604C8—864no—
605C22#1458277111yescharacteristic
606C22#1458277311yescharacteristic
607C22#1458279611yescharacteristic
608C22#1458280811yescharacteristic
609C22#1458281911yescharacteristic
610C22#1458282011yescharacteristic
611C22#1458283311yescharacteristic
612C22#1458298411yescharacteristic
613C22#1458299011yescharacteristic
614C22#1458300311yescharacteristic
615C22#1458300811yescharacteristic
616C22#1458303611yescharacteristic
617C22#1458303911yescharacteristic
618C22#1458304111yescharacteristic
619C22#1458304711yescharacteristic
620C22#1458304811yescharacteristic
621C22#1458305111yescharacteristic
622C22#1458306011yescharacteristic
623C22#1458306211yescharacteristic
624C22#1458312711yescharacteristic
625C22#1458313111yescharacteristic
626C22#1458314411yescharacteristic
627C22#1458314811yescharacteristic
628C22#1458318211yescharacteristic
629C22#1458318311yescharacteristic
630C22#1458318711yescharacteristic
631C22#1458318811yescharacteristic
632C22#1458319711yescharacteristic
633C22#1458320211yescharacteristic
634C22#1458320511yescharacteristic
635C22#1458320811yescharacteristic
636C22#1458329611yescharacteristic
637C22#1458330011yescharacteristic
638C22#1458330611yescharacteristic
639C22#1458330711yescharacteristic
640C4—44no—
641C4—82no—
642C4—3442no—
643C4—1722no—
644C4—1722no—
645C4—1724no—
646C4#1458276811yescharacteristic
647C4#1458277311yescharacteristic
648C4#1458279611yescharacteristic
649C4#1458279711yescharacteristic
650C4#1458282011yescharacteristic
651C4#1458282911yescharacteristic
652C4#1458283311yescharacteristic
653C4#1458283511yescharacteristic
654C2#1913285911yescharacteristic
655C2#1913485411yescharacteristic
656C2#1913485711yescharacteristic
657C2#1913486111yescharacteristic
658C2#1913486411yescharacteristic
659C2#1913532211yescharacteristic
660C2#1913533211yescharacteristic
661C2#1913559711yescharacteristic
662C2#1913559911yescharacteristic
663C2#1913592611yescharacteristic
664C2#1913592711yescharacteristic
665C2#1913593111yescharacteristic
666C2#1913593611yescharacteristic
667C2#1913609811yescharacteristic
668C2#1913609911yescharacteristic
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#11327
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
24. #14582661C4semidirect
161. C4⋊C4×C43C4⋊C4semidirect
170. C4⋊Dic43C4⋊C4semidirect
182. C2×C43⋊C8C4⋊C4semidirect
364. C43#11327semidirect
513. C4⋊C4Dic43⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×#130632562
C2×#145827982
C2×#145827952
C2×#145826622
C2×#145826612
C2×#145826532
C2×C43×#3402
#1132743