Finite Group Databasebeta

← #25119187

Subgroups — #25119187

Order 11008.

1066 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583126C211yesmaximal, characteristic
2C2×C4×#10621883C211yesmaximal, characteristic, complemented
3C22×#13063256C211yesmaximal, characteristic, complemented
4#19137598C211yesmaximal, characteristic, complemented
5#19135448C211yesmaximal, characteristic, complemented
6#19135320C211yesmaximal, characteristic, complemented
7#19135229C211yesmaximal, characteristic, complemented
8#19135219C211yesmaximal, characteristic, complemented
9#19134913C211yesmaximal, characteristic
10#19134902C211yesmaximal, characteristic, complemented
11#19134862C211yesmaximal, characteristic, complemented
12#19134856C211yesmaximal, characteristic, complemented
13C4×#13063256C211yesmaximal, characteristic, complemented
14C22⋊C4×C43⋊C8C211yesmaximal, characteristic, complemented
15C43×#2361C211yesmaximal, characteristic
16C22×#10621883C2211yescharacteristic
17C23×C43⋊C8C2211yescharacteristic
18C2×#13063304C2211yescharacteristic
19C2×C4×Dic86C2211yescharacteristic
20C22×C4⋊Dic43C2211yescharacteristic
21#14583126C418yescomplemented
22C4×#10621883—24no—
23C2×#13063256—24no—
24C2×#13063256C2211yescharacteristic
25C2×#13063256C2211yescharacteristic
26C2×#13063256C2211yescharacteristic
27C2×#13063256C2211yescharacteristic
28C2×#13063256C2211yescharacteristic
29C2×#13063248C2211yescharacteristic
30C2×#13063248C2211yescharacteristic
31C2×#13063248C2211yescharacteristic
32C2×#13063246C2211yescharacteristic
33C2×#13063246C2211yescharacteristic
34C2×#13063246C2211yescharacteristic
35C2×C22⋊(C43⋊C8)C2211yescharacteristic
36C2×C4×C43⋊C8C2211yescharacteristic
37C2×C4×C43⋊C8C2211yescharacteristic
38#14582805C2211yescharacteristic
39#14582797C2211yescharacteristic
40#14582796—21no—
41#14582786—21no—
42#14582771—21no—
43C4×C4⋊Dic43C2211yescharacteristic
44C22⋊C4×Dic43—21no—
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582654C2211yescharacteristic
50#14582654C2211yescharacteristic
51C2×#121×C43C2211yescharacteristic
52C2×C4×D4×C43—21no—
53C2×C4×D4×C43C2211yescharacteristic
54C22×C4⋊C4×C43C2211yescharacteristic
55C43×#390C2211yescharacteristic
56C43×#389C2211yescharacteristic
57C43×#388—21no—
58C43×#386—21no—
59C43×#385—21no—
60C4×C4⋊C4×C43C2211yescharacteristic
61C4×C22⋊C4×C43C2211yescharacteristic
62C22×Dic86C2311yescharacteristic
63C23×Dic43—21no—
64C2×#10621883—22no—
65C2×#10621883—22no—
66C2×#10621883C2×C414yescomplemented
67C22×C43⋊C8—22no—
68C22×C43⋊C8—22no—
69C22×C43⋊C8C2×C414yescomplemented
70C22×C43⋊C8C2311yescharacteristic
71C22×C43⋊C8C2311yescharacteristic
72C22×C43⋊C8C2311yescharacteristic
73C22×C43⋊C8C2311yescharacteristic
74#13063304—22no—
75#13063304C2×C414yescomplemented
76C4×Dic86—22no—
77C4×Dic86—41no—
78C2×C4⋊Dic43—22no—
79C2×C4⋊Dic43—21no—
80C2×C4⋊Dic43—41no—
81C2×C4⋊Dic43C2311yescharacteristic
82C2×C4⋊Dic43C2311yescharacteristic
83C2×C4⋊Dic43C2311yescharacteristic
84C2×Dic43⋊C4—21no—
85C2×Dic43⋊C4—21no—
86C2×Dic43⋊C4—21no—
87C2×C22⋊Dic43—21no—
88C2×C4×Dic43—21no—
89C2×C4×Dic43—21no—
90#13063256—22no—
91#13063256—22no—
92#13063256—22no—
93#13063256C2×C414yescomplemented
94#13063256D414yescomplemented
95#13063248—22no—
96#13063248—41no—
97#13063248C2×C414yescomplemented
98#13063246—22no—
99#13063246—41no—
100#13063246C2×C414yescomplemented
101C22⋊(C43⋊C8)—22no—
102C4×C43⋊C8—22no—
103C4×C43⋊C8—22no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C22×D4×C43—21no—
109C22×D4×C43C2311yescharacteristic
110C23×C4×C43—21no—
111C23×C4×C43—21no—
112C23×C4×C43C2311yescharacteristic
113#121×C43—22no—
114#121×C43C2×C414yes—
115C4×D4×C43—22no—
116C4×D4×C43—41no—
117C4×D4×C43—44no—
118C2×C4⋊C4×C43—22no—
119C2×C4⋊C4×C43—21no—
120C2×C4⋊C4×C43—21no—
121C2×C4⋊C4×C43—41no—
122C2×C4⋊C4×C43C2311yescharacteristic
123C2×C4⋊C4×C43C2311yescharacteristic
124C2×C4⋊C4×C43C2311yescharacteristic
125C2×C22⋊C4×C43—21no—
126C2×C22⋊C4×C43—21no—
127C2×C22⋊C4×C43—21no—
128C2×C22⋊C4×C43—21no—
129C2×C22⋊C4×C43D411yescharacteristic
130C2×C22⋊C4×C43D411yescharacteristic
131C2×C42×C43—21no—
132C2×C42×C43C2311yescharacteristic
133C2×C42×C43C2311yescharacteristic
134#95×C43—21no—
135#95×C43—21no—
136#95×C43D411yescharacteristic
137#95×C43D411yescharacteristic
138C24×C43—21no—
139C24×C43C2×D411yescharacteristic
140C2×D4×C43—21no—
141C2×D4×C43—24no—
142C2×D4×C43—21no—
143C2×D4×C43—21no—
144C2×D4×C43—21no—
145C2×D4×C43—21no—
146C2×D4×C43—42no—
147C2×D4×C43—42no—
148C2×D4×C43C22×C412yes—
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43—21no—
154C22×C4×C43—21no—
155C22×C4×C43—21no—
156C22×C4×C43—42no—
157C22×C4×C43—42no—
158C22×C4×C43—42no—
159C22×C4×C43—42no—
160C22×C4×C43—81no—
161C22×C4×C43—81no—
162C22×C4×C43C22×C412yes—
163C22×C4×C43C2×D411yescharacteristic
164C22×C4×C43C2×D411yescharacteristic
165C22×C4×C43C2×D411yescharacteristic
166C22×C4×C43C2×D411yescharacteristic
167C22×C4×C43C2×D411yescharacteristic
168C22×C4×C43#4112yes—
169C22×C4×C43C2411yescharacteristic
170C22×Dic43—21no—
171C22×Dic43—21no—
172C22×Dic43—21no—
173C22×Dic43—21no—
174C22×Dic43—42no—
175C22×Dic43—42no—
176C22×Dic43—81no—
177C2×Dic86—21no—
178C2×Dic86—21no—
179C2×Dic86—21no—
180C2×Dic86—21no—
181C2×Dic86—21no—
182C2×Dic86C22×C412yes—
183C4⋊C4×C43—21no—
184C4⋊C4×C43—21no—
185C4⋊C4×C43—21no—
186C4⋊C4×C43—21no—
187C4⋊C4×C43—42no—
188C4⋊C4×C43—42no—
189C4⋊C4×C43C22×C412yes—
190C4⋊C4×C43C2×D412yes—
191C22⋊C4×C43—24no—
192C22⋊C4×C43—22no—
193C22⋊C4×C43—42no—
194C22⋊C4×C43—42no—
195C22⋊C4×C43—81no—
196C22⋊C4×C43SD1614yescomplemented
197C42×C43—21no—
198C42×C43—21no—
199C42×C43—21no—
200C42×C43—21no—
201C42×C43—42no—
202C22⋊Dic43—24no—
203#10621883—28no—
204C4⋊Dic43—21no—
205C4⋊Dic43—21no—
206C4⋊Dic43—21no—
207C4⋊Dic43—21no—
208C4⋊Dic43—42no—
209C4⋊Dic43C22×C412yes—
210C4⋊Dic43C2×D412yes—
211Dic43⋊C4—24no—
212Dic43⋊C4—42no—
213Dic43⋊C4—81no—
214C4×Dic43—42no—
215C4×Dic43—81no—
216C2×C43⋊C8—21no—
217C2×C43⋊C8—21no—
218C2×C43⋊C8—28no—
219C2×C43⋊C8—21no—
220C2×C43⋊C8—21no—
221C2×C43⋊C8—21no—
222C2×C43⋊C8—21no—
223C2×C43⋊C8—21no—
224C2×C43⋊C8—21no—
225C2×C43⋊C8C22×C412yes—
226C2×C43⋊C8C22×C412yes—
227C2×C43⋊C8C2×D412yes—
228C2×C43⋊C8#4112yes—
229C23×C43—21no—
230C23×C43—21no—
231C23×C43—21no—
232C23×C43—21no—
233C23×C43—22no—
234C23×C43—41no—
235C23×C43—41no—
236C23×C43—41no—
237C23×C43—41no—
238C23×C43—41no—
239C23×C43—41no—
240C23×C43C4×D412yes—
241C23×C43C2×SD1612yes—
242C23×C43#13512yes—
243C23×C43C22×D411yescharacteristic
244D4×C43—22no—
245D4×C43—22no—
246D4×C43—48no—
247D4×C43—41no—
248D4×C43—41no—
249C2×C4×C43—21no—
250C2×C4×C43—21no—
251C2×C4×C43—21no—
252C2×C4×C43—21no—
253C2×C4×C43—21no—
254C2×C4×C43—21no—
255C2×C4×C43—22no—
256C2×C4×C43—22no—
257C2×C4×C43—22no—
258C2×C4×C43—22no—
259C2×C4×C43—22no—
260C2×C4×C43—21no—
261C2×C4×C43—22no—
262C2×C4×C43—21no—
263C2×C4×C43—21no—
264C2×C4×C43—21no—
265C2×C4×C43—21no—
266C2×C4×C43—21no—
267C2×C4×C43—41no—
268C2×C4×C43—41no—
269C2×C4×C43—41no—
270C2×C4×C43—41no—
271C2×C4×C43—41no—
272C2×C4×C43—41no—
273C2×C4×C43—41no—
274C2×C4×C43—84no—
275C2×C4×C43—84no—
276C2×C4×C43C4×D412yes—
277C2×C4×C43C2×SD1612yes—
278C2×C4×C43C2×SD1612yes—
279C2×C4×C43C23×C411yescharacteristic
280C2×C4×C43C22×D411yescharacteristic
281C2×C4×C43C2×#4111yescharacteristic
282C2×C4×C43C2×#4111yescharacteristic
283C2×C4×C43H(5,𝔽2)11yescharacteristic
284C2×C4×C432−1+411yescharacteristic
285C2×Dic43—22no—
286C2×Dic43—22no—
287C2×Dic43—22no—
288C2×Dic43—41no—
289C2×Dic43—41no—
290C2×Dic43—41no—
291C2×Dic43—41no—
292C2×Dic43—41no—
293C2×Dic43—41no—
294C2×Dic43—41no—
295C2×Dic43—41no—
296C2×Dic43—41no—
297C2×Dic43—84no—
298Dic86—22no—
299Dic86—22no—
300Dic86—41no—
301Dic86—41no—
302C43⋊C8—22no—
303C43⋊C8—41no—
304C43⋊C8—41no—
305C43⋊C8C4×D414yescomplemented
306#23022—431nomaximal, Sylow
307C22×C43—22no—
308C22×C43—22no—
309C22×C43—22no—
310C22×C43—22no—
311C22×C43—22no—
312C22×C43—22no—
313C22×C43—42no—
314C22×C43—42no—
315C22×C43—42no—
316C22×C43—81no—
317C22×C43—81no—
318C22×C43—81no—
319C22×C43—81no—
320C22×C43C4×SD1614yescomplemented
321C22×C43C2×C4×D411yescharacteristic
322C22×C43D4211yescharacteristic
323C22×C43#54711yescharacteristic
324C22×C43C22×SD1611yescharacteristic
325C22×C43C2×#13511yescharacteristic
326C22×C43#57711yescharacteristic
327C22×C43#57711yescharacteristic
328C4×C43—22no—
329C4×C43—22no—
330C4×C43—22no—
331C4×C43—41no—
332C4×C43—42no—
333C4×C43—42no—
334C4×C43—41no—
335C4×C43—81no—
336C4×C43C2×C4×D411yescharacteristic
337C4×C43#52011yescharacteristic
338C4×C43#54811yescharacteristic
339C4×C43#55311yescharacteristic
340Dic43—42no—
341Dic43—42no—
342Dic43—42no—
343Dic43—81no—
344C2×#465—431no—
345C2×C4×SD16—431no—
346C22×#106—431no—
347#2361D4311yescharacteristic
348#2360—431no—
349#1968—431no—
350#1941—431no—
351#1927—431no—
352#1926—431no—
353#1874—431no—
354#1872—431no—
355#1865—431no—
356#1864—431no—
357C4×#106—431no—
358C8×C22⋊C4—431no—
359C2×C43—24no—
360C2×C43—82no—
361C2×C43#236111yescharacteristic
362C2×C43C2×C4×SD1611yescharacteristic
363C2×C43#295211yescharacteristic
364C2×C43D4×SD1611yescharacteristic
365C2×C43#328211yescharacteristic
366C2×C43#333511yescharacteristic
367C2×C43#333711yescharacteristic
368C22×SD16—431no—
369C23×C8—431no—
370C2×C22⋊Q8—431no—
371C2×#121C2×D4311yescharacteristic
372C2×C4×Q8—431no—
373C2×C4×D4—21no—
374C2×C4×D4C2×D4311yescharacteristic
375C22×C4⋊C4—431no—
376C22×C4⋊C4C2×D4311yescharacteristic
377#465—438no—
378C4×SD16—864no—
379C2×#106—431no—
380C2×#106—431no—
381C2×#106—431no—
382C2×#106—431no—
383C2×#106—431no—
384C2×#106—864no—
385C2×#103—431no—
386C2×#103—431no—
387C2×#103—431no—
388C2×#102—431no—
389C2×#102—431no—
390C2×#102—431no—
391C2×C22⋊C8—431no—
392C2×C4×C8—431no—
393C2×C4×C8—431no—
394#391—431no—
395#390C2×D4311yescharacteristic
396#389—431no—
397#389—861no—
398#389C2×D4311yescharacteristic
399#388—21no—
400#387—861no—
401#386—21no—
402#385—21no—
403#385—861no—
404C4×C4⋊C4—431no—
405C4×C4⋊C4C2×D4311yescharacteristic
406C4×C22⋊C4—861no—
407C4×C22⋊C4C2×D4311yescharacteristic
408#340—431no—
409#340—431no—
410#340—431no—
411#340—431no—
412#336—431no—
413#336—431no—
414C43#2302211yescharacteristic, complemented, Sylow
415C22×Q8—431no—
416C22×D4—21no—
417C22×D4C22×D4311yescharacteristic
418C23×C4—21no—
419C23×C4—21no—
420C23×C4—861no—
421C23×C4C22×D4311yescharacteristic
422C2×SD16—434no—
423C2×SD16—862no—
424C2×SD16—862no—
425C22×C8—431no—
426C22×C8—434no—
427C22×C8—431no—
428C22×C8—431no—
429C22×C8—431no—
430C22×C8—862no—
431C22×C8—862no—
432C22⋊Q8—434no—
433C22⋊Q8—862no—
434#121—22no—
435#121C4×D4314yes—
436C4×Q8—862no—
437C4×Q8—1721no—
438C4×D4—22no—
439C4×D4—41no—
440C4×D4—44no—
441C2×C4⋊C4—22no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4—21no—
444C2×C4⋊C4—41no—
445C2×C4⋊C4—431no—
446C2×C4⋊C4—431no—
447C2×C4⋊C4—431no—
448C2×C4⋊C4—862no—
449C2×C4⋊C4—861no—
450C2×C4⋊C4—861no—
451C2×C4⋊C4—861no—
452C2×C4⋊C4—861no—
453C2×C4⋊C4—1721no—
454C2×C4⋊C4C22×D4311yescharacteristic
455C2×C4⋊C4C22×D4311yescharacteristic
456C2×C4⋊C4C22×D4311yescharacteristic
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4—21no—
461C2×C22⋊C4—861no—
462C2×C22⋊C4C22⋊D4311yescharacteristic
463C2×C22⋊C4C22⋊D4311yescharacteristic
464C2×C42—21no—
465C2×C42—861no—
466C2×C42—861no—
467C2×C42C22×D4311yescharacteristic
468C2×C42C22×D4311yescharacteristic
469#106—434no—
470#106—434no—
471#106—862no—
472#106—862no—
473#106—862no—
474#103—434no—
475#103—862no—
476#103—1721no—
477#102—434no—
478#102—862no—
479#102—1721no—
480C22⋊C8—862no—
481C4×C8—862no—
482C4×C8—862no—
483#95—21no—
484#95—21no—
485#95—861no—
486#95—861no—
487#95—861no—
488#95—861no—
489#95C22⋊D4311yescharacteristic
490#95C22⋊D4311yescharacteristic
491C24—21no—
492C24C2×C22⋊D4311yescharacteristic
493C2×Q8—432no—
494C2×Q8—861no—
495C2×Q8—861no—
496C2×Q8—861no—
497C2×Q8—861no—
498C2×Q8—861no—
499C2×D4—24no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—42no—
506C2×D4—42no—
507C2×D4C2×C4×D4312yes—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—42no—
516C22×C4—42no—
517C22×C4—42no—
518C22×C4—42no—
519C22×C4—81no—
520C22×C4—81no—
521C22×C4—861no—
522C22×C4—861no—
523C22×C4—861no—
524C22×C4—861no—
525C22×C4—3441no—
526C22×C4—1722no—
527C22×C4—1722no—
528C22×C4C2×C4×D4312yes—
529C22×C4#1062189812yes—
530C22×C4C2×C22⋊D4311yescharacteristic
531C22×C4C2×C22⋊D4311yescharacteristic
532C22×C4C2×C22⋊D4311yescharacteristic
533C22×C4C2×C22⋊D4311yescharacteristic
534C22×C4C2×C22⋊D4311yescharacteristic
535C22×C4C23×D4311yescharacteristic
536SD16—868no—
537C2×C8—432no—
538C2×C8—432no—
539C2×C8—432no—
540C2×C8—432no—
541C2×C8—868no—
542C2×C8—861no—
543C2×C8—861no—
544C2×C8—861no—
545C2×C8—861no—
546C2×C8—861no—
547C2×C8—861no—
548C2×C8—861no—
549C2×C8—861no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—42no—
555C4⋊C4—42no—
556C4⋊C4—432no—
557C4⋊C4—432no—
558C4⋊C4—864no—
559C4⋊C4—861no—
560C4⋊C4—861no—
561C4⋊C4—861no—
562C4⋊C4—861no—
563C4⋊C4—3441no—
564C4⋊C4—1722no—
565C4⋊C4—1722no—
566C4⋊C4C2×C4×D4312yes—
567C4⋊C4D4×D4312yes—
568C22⋊C4—22no—
569C22⋊C4—24no—
570C22⋊C4—42no—
571C22⋊C4—42no—
572C22⋊C4—81no—
573C22⋊C4—864no—
574C22⋊C4#1062188314yescomplemented
575C42—21no—
576C42—21no—
577C42—21no—
578C42—21no—
579C42—42no—
580C42—3441no—
581C42—1722no—
582C23—21no—
583C23—21no—
584C23—21no—
585C23—21no—
586C23—22no—
587C23—41no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23C4×C22⋊D4312yes—
594C23C2×#1062188312yes—
595C23#1306334512yes—
596C23C22×C22⋊D4311yescharacteristic
597Q8—862no—
598Q8—862no—
599Q8—1721no—
600Q8—1721no—
601D4—22no—
602D4—22no—
603D4—48no—
604D4—41no—
605D4—41no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—22no—
623C2×C4—21no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—84no—
632C2×C4—84no—
633C2×C4—862no—
634C2×C4—862no—
635C2×C4—862no—
636C2×C4—3444no—
637C2×C4—1721no—
638C2×C4—1721no—
639C2×C4—1721no—
640C2×C4—1721no—
641C2×C4—1721no—
642C2×C4—1721no—
643C2×C4—1721no—
644C2×C4—1721no—
645C2×C4—1721no—
646C2×C4C4×C22⋊D4312yes—
647C2×C4C2×#1062188312yes—
648C2×C4C2×#1062188312yes—
649C2×C4C22×C4×D4311yescharacteristic
650C2×C4C2×D4×D4311yescharacteristic
651C2×C4#41×D4311yescharacteristic
652C2×C4C2×#1062189811yescharacteristic
653C2×C4#1306337011yescharacteristic
654C2×C4#1306337211yescharacteristic
655C8—434no—
656C8—862no—
657C8—1721no—
658C8—1721no—
659C22—22no—
660C22—22no—
661C22—22no—
662C22—22no—
663C22—22no—
664C22—22no—
665C22—42no—
666C22—42no—
667C22—42no—
668C22—81no—
669C22—81no—
670C22—81no—
671C22—81no—
672C22C4×#1062188314yescomplemented
673C22C2×C4×C22⋊D4311yescharacteristic
674C22D4×C22⋊D4311yescharacteristic
675C22#1458354811yescharacteristic
676C22C22×#1062188311yescharacteristic
677C22C2×#1306334511yescharacteristic
678C22#1458370711yescharacteristic
679C22#1458371011yescharacteristic
680C4—22no—
681C4—22no—
682C4—22no—
683C4—42no—
684C4—41no—
685C4—42no—
686C4—41no—
687C4—81no—
688C4—3441no—
689C4—1722no—
690C4—1722no—
691C4—1722no—
692C4C4×D4×D4311yescharacteristic
693C4#1458337811yescharacteristic
694C4#1458355811yescharacteristic
695C4#1458359811yescharacteristic
696C2—24no—
697C2—82no—
698C2#1913761211yescharacteristic
699C2C2×C4×#1062188311yescharacteristic
700C2#1914347611yescharacteristic
701C2D4×#1062188311yescharacteristic
702C2#1914630311yescharacteristic
703C2#1914695211yescharacteristic
704C2#1914696811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#2361C2
socleC23×C43C22×D4
prime radicalC2×#121×C43C22
cosocleC22×C4×C43C24
hypercenter#2361D43
hypocenterC43#23022
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2361

Complements

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

NH ≅ G/Ntype
2. C2×C4×#10621883C2semidirect
3. C22×#13063256C2semidirect
4. #19137598C2semidirect
5. #19135448C2semidirect
6. #19135320C2semidirect
7. #19135229C2semidirect
8. #19135219C2semidirect
10. #19134902C2semidirect
11. #19134862C2semidirect
12. #19134856C2semidirect
13. C4×#13063256C2semidirect
14. C22⋊C4×C43⋊C8C2semidirect
21. #14583126C4semidirect
66. C2×#10621883C2×C4semidirect
69. C22×C43⋊C8C2×C4semidirect
75. #13063304C2×C4semidirect
93. #13063256C2×C4semidirect
94. #13063256D4semidirect
97. #13063248C2×C4semidirect
100. #13063246C2×C4semidirect
196. C22⋊C4×C43SD16semidirect
305. C43⋊C8C4×D4semidirect
320. C22×C43C4×SD16semidirect
414. C43#23022semidirect
574. C22⋊C4#10621883semidirect
672. C22C4×#10621883semidirect

Maximal subgroups

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

subgroupindex
C2×#145831262
C2×C4×#106218832
C22×#130632562
#191375982
#191354482
#191353202
#191352292
#191352192
#191349132
#191349022
#191348622
#191348562
C4×#130632562
C22⋊C4×C43⋊C82
C43×#23612
#2302243