Finite Group Databasebeta

← #25132771

Subgroups — #25132771

Order 11008.

1068 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×#14583196C211yesmaximal, characteristic, complemented
2C2×#14583186C211yesmaximal, characteristic, complemented
3#19137288C211yesmaximal, characteristic
4#19135930C211yesmaximal, characteristic, complemented
5#19135925C211yesmaximal, characteristic, complemented
6#19135738C211yesmaximal, characteristic, complemented
7#19135728C211yesmaximal, characteristic, complemented
8#19135553C211yesmaximal, characteristic, complemented
9#19135548C211yesmaximal, characteristic, complemented
10#19134917C211yesmaximal, characteristic
11#19134912C211yesmaximal, characteristic
12#19134794C211yesmaximal, characteristic, complemented
13#19134788C211yesmaximal, characteristic, complemented
14#19134579C211yesmaximal, characteristic, complemented
15C2×C43×#544C211yesmaximal, characteristic, complemented
16C2×#13063299C2211yescharacteristic
17C2×C4×D172C2211yescharacteristic
18#14583196—24no—
19#14583186—24no—
20C2×#13063258C2211yescharacteristic
21C2×#13063256C2211yescharacteristic
22C2×#13063256C2211yescharacteristic
23C2×#13063256C2211yescharacteristic
24C2×C4⋊(C43⋊C8)C2211yescharacteristic
25C2×C4⋊(C43⋊C8)C2211yescharacteristic
26C2×#13063245C2211yescharacteristic
27C2×#13063245C2211yescharacteristic
28C2×#13063245C2211yescharacteristic
29C2×#13063245C2211yescharacteristic
30C2×C22⋊(C43⋊C8)C2211yescharacteristic
31C2×C22⋊(C43⋊C8)C2211yescharacteristic
32#14582801C2211yescharacteristic
33#14582799—21no—
34#14582797C2211yescharacteristic
35#14582789—21no—
36#14582775—21no—
37#14582770—21no—
38#14582759C2211yescharacteristic
39C4×C4⋊Dic43C2211yescharacteristic
40#14582661C2211yescharacteristic
41#14582661C2211yescharacteristic
42#14582661C2211yescharacteristic
43#14582661C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582654C2211yescharacteristic
49#14582654C2211yescharacteristic
50C43×#544—24no—
51C43×#544—24no—
52C2×C4⋊Q8×C43—21no—
53C2×C4⋊Q8×C43C2211yescharacteristic
54C2×C4⋊Q8×C43C2211yescharacteristic
55C2×#125×C43—21no—
56C2×#125×C43C2211yescharacteristic
57C2×#125×C43C2211yescharacteristic
58C2×C22⋊Q8×C43—21no—
59C2×C22⋊Q8×C43—21no—
60C2×#117×C43C2211yescharacteristic
61C2×#117×C43C2211yescharacteristic
62C22×C4⋊C4×C43C2211yescharacteristic
63C22×D172C2311yescharacteristic
64C22×C22⋊D43—21no—
65C22×C4×D43—21no—
66C22×C43⋊C8C2311yescharacteristic
67C22×C43⋊C8C2311yescharacteristic
68C22×C43⋊C8C2311yescharacteristic
69C22×C43⋊C8C2311yescharacteristic
70#13063299—22no—
71#13063299Q814yescomplemented
72C4×D172—22no—
73C4×D172—22no—
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
77C2×Dic43⋊C4—21no—
78C2×C22⋊Dic43—21no—
79C2×(C2×D43)⋊C4—21no—
80C2×(C2×D43)⋊C4—21no—
81C2×(C2×D43)⋊C4—21no—
82C2×(C2×D43)⋊C4—21no—
83C2×C4×Dic43—21no—
84#13063258—22no—
85#13063256—22no—
86#13063256—22no—
87#13063256—22no—
88C4⋊(C43⋊C8)—22no—
89C4⋊(C43⋊C8)—22no—
90#13063245—22no—
91#13063245—22no—
92#13063245—22no—
93#13063245—22no—
94C22⋊(C43⋊C8)—22no—
95C22⋊(C43⋊C8)—22no—
96C43⋊#95—21no—
97C43⋊#95—21no—
98C43⋊#95—21no—
99C22×Q8×C43—21no—
100C22×Q8×C43—21no—
101C23×C4×C43—21no—
102C23×C4×C43C2311yescharacteristic
103C4⋊Q8×C43—28no—
104C4⋊Q8×C43—22no—
105C4⋊Q8×C43—22no—
106C4⋊Q8×C43—22no—
107C4⋊Q8×C43D414yescomplemented
108#125×C43—28no—
109#125×C43—22no—
110#125×C43—22no—
111#125×C43—22no—
112#125×C43D414yescomplemented
113C22⋊Q8×C43—28no—
114C22⋊Q8×C43—28no—
115#117×C43—22no—
116#117×C43—22no—
117#117×C43—22no—
118#117×C43—22no—
119C2×C4⋊C4×C43—21no—
120C2×C4⋊C4×C43—21no—
121C2×C4⋊C4×C43—21no—
122C2×C4⋊C4×C43—21no—
123C2×C4⋊C4×C43—21no—
124C2×C4⋊C4×C43—21no—
125C2×C4⋊C4×C43—21no—
126C2×C4⋊C4×C43—22no—
127C2×C4⋊C4×C43—22no—
128C2×C4⋊C4×C43D411yescharacteristic
129C2×C4⋊C4×C43D411yescharacteristic
130C2×C4⋊C4×C43C2311yescharacteristic
131C2×C4⋊C4×C43C2311yescharacteristic
132C2×C4⋊C4×C43C2311yescharacteristic
133C2×C4⋊C4×C43C2311yescharacteristic
134C2×C22⋊C4×C43—21no—
135C2×C22⋊C4×C43D411yescharacteristic
136C2×C22⋊C4×C43D411yescharacteristic
137C2×C42×C43—21no—
138C2×C42×C43C2311yescharacteristic
139C2×C42×C43C2311yescharacteristic
140C24×C43C2×D411yescharacteristic
141C23×D43—21no—
142C2×Q8×C43—24no—
143C2×Q8×C43—24no—
144C2×Q8×C43—81no—
145C2×Q8×C43—81no—
146C2×Q8×C43—81no—
147C2×Q8×C43—81no—
148C22×C4×C43—21no—
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43—24no—
153C22×C4×C43—21no—
154C22×C4×C43—21no—
155C22×C4×C43—21no—
156C22×C4×C43—21no—
157C22×C4×C43—81no—
158C22×C4×C43—81no—
159C22×C4×C43C2×D411yescharacteristic
160C22×C4×C43C2×D411yescharacteristic
161C22×C4×C43C2×D411yescharacteristic
162C22×C4×C43C2×D411yescharacteristic
163C22×C4×C43C2×D411yescharacteristic
164C22×C4×C43C2×Q812yes—
165C22×C4×C43#4112yes—
166C22×C4×C43C2411yescharacteristic
167C2×C22⋊D43—24no—
168C2×C22⋊D43—81no—
169C2×C22⋊D43—81no—
170C22×Dic43—21no—
171C22×Dic43—21no—
172C22×Dic43—21no—
173C2×D172—21no—
174C2×D172—21no—
175C2×D172—21no—
176C2×D172—21no—
177C2×D172—21no—
178C2×D172C2×Q812yes—
179C2×C4×D43—42no—
180C2×C4×D43—81no—
181C2×C4×D43—81no—
182C4⋊C4×C43—24no—
183C4⋊C4×C43—24no—
184C4⋊C4×C43—24no—
185C4⋊C4×C43—24no—
186C4⋊C4×C43—24no—
187C4⋊C4×C43—24no—
188C4⋊C4×C43—24no—
189C4⋊C4×C43—22no—
190C4⋊C4×C43—22no—
191C4⋊C4×C43—21no—
192C4⋊C4×C43—21no—
193C4⋊C4×C43—21no—
194C4⋊C4×C43—21no—
195C4⋊C4×C43C2×D412yes—
196C4⋊C4×C43C2×D412yes—
197C4⋊C4×C43C2×D412yes—
198C4⋊C4×C43C2×D412yes—
199C22⋊C4×C43—24no—
200C22⋊C4×C43—22no—
201C22⋊C4×C43—22no—
202C42×C43—24no—
203C42×C43—21no—
204C42×C43—21no—
205C42×C43C2×D412yes—
206C42×C43C2×D412yes—
207C22⋊Dic43—81no—
208(C2×D43)⋊C4—24no—
209(C2×D43)⋊C4—42no—
210(C2×D43)⋊C4—81no—
211(C2×D43)⋊C4—81no—
212C4⋊Dic43—21no—
213C4⋊Dic43—21no—
214C4⋊Dic43—21no—
215C4⋊Dic43—21no—
216C4⋊Dic43—21no—
217C4⋊Dic43C2×Q812yes—
218Dic43⋊C4—81no—
219C4×Dic43—81no—
220C2×C43⋊C8—21no—
221C2×C43⋊C8—21no—
222C2×C43⋊C8—21no—
223C2×C43⋊C8—21no—
224C2×C43⋊C8—21no—
225C2×C43⋊C8—21no—
226C2×C43⋊C8—21no—
227C2×C43⋊C8—21no—
228C2×C43⋊C8—21no—
229C2×C43⋊C8—21no—
230C2×C43⋊C8—21no—
231C2×C43⋊C8—21no—
232C23×C43—21no—
233C23×C43—21no—
234C23×C43—21no—
235C23×C43—21no—
236C23×C43—21no—
237C23×C43—21no—
238C23×C43C22⋊Q812yes—
239C23×C43C22×D411yescharacteristic
240C22×D43—22no—
241C22×D43—41no—
242C22×D43—41no—
243C22×D43—41no—
244C22×D43—41no—
245C22×D43—41no—
246C22×D43—41no—
247Q8×C43—84no—
248Q8×C43—84no—
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—21no—
260C2×C4×C43—22no—
261C2×C4×C43—21no—
262C2×C4×C43—22no—
263C2×C4×C43—22no—
264C2×C4×C43—22no—
265C2×C4×C43—21no—
266C2×C4×C43—21no—
267C2×C4×C43—21no—
268C2×C4×C43—21no—
269C2×C4×C43—41no—
270C2×C4×C43—41no—
271C2×C4×C43—41no—
272C2×C4×C43—41no—
273C2×C4×C43—41no—
274C2×C4×C43—41no—
275C2×C4×C43—41no—
276C2×C4×C43—41no—
277C2×C4×C43—84no—
278C2×C4×C43#12012yes—
279C2×C4×C43#12012yes—
280C2×C4×C43C22⋊Q812yes—
281C2×C4×C43C22×D411yescharacteristic
282C2×C4×C43C22×D411yescharacteristic
283C2×C4×C43C22×Q811yescharacteristic
284C2×C4×C43C2×#4111yescharacteristic
285C2×C4×C432−1+411yescharacteristic
286C2×C4×C432−1+411yescharacteristic
287C22⋊D43—84no—
288C2×Dic43—22no—
289C2×Dic43—41no—
290C2×Dic43—41no—
291C2×Dic43—41no—
292C2×Dic43—41no—
293C2×Dic43—41no—
294C2×Dic43—41no—
295C2×Dic43—41no—
296C2×Dic43—41no—
297D172—22no—
298D172—22no—
299D172—41no—
300D172—41no—
301C4×D43—84no—
302C43⋊C8—41no—
303C43⋊C8—41no—
304C43⋊C8—41no—
305C43⋊C8—41no—
306#24309—431nomaximal, Sylow
307C22×C43—22no—
308C22×C43—22no—
309C22×C43—22no—
310C22×C43—41no—
311C22×C43—41no—
312C22×C43—41no—
313C22×C43—41no—
314C22×C43C2×#12011yescharacteristic
315C22×C43C2×C22⋊Q811yescharacteristic
316C22×C43#53611yescharacteristic
317C22×C43#57611yescharacteristic
318C22×C43#57711yescharacteristic
319C22×C43#57711yescharacteristic
320C22×C43#57711yescharacteristic
321C2×D43—42no—
322C2×D43—42no—
323C2×D43—42no—
324C2×D43—81no—
325C2×D43—81no—
326C2×D43—81no—
327C2×D43—81no—
328C4×C43—22no—
329C4×C43—22no—
330C4×C43—22no—
331C4×C43—41no—
332C4×C43—42no—
333C4×C43—41no—
334C4×C43—42no—
335C4×C43—42no—
336C4×C43—42no—
337C4×C43#54811yescharacteristic
338C4×C43#54811yescharacteristic
339C4×C43D4×Q811yescharacteristic
340C4×C43D4×Q811yescharacteristic
341Dic43—42no—
342Dic43—81no—
343Dic43—81no—
344C2×#544D4311yescharacteristic, complemented
345C2×#478—431no—
346C2×#476—431no—
347#2324—431no—
348#2059—431no—
349#2058—431no—
350#2025—431no—
351#2023—431no—
352#1989—431no—
353#1988—431no—
354#1875—431no—
355#1874—431no—
356#1854—431no—
357#1853—431no—
358#1798—431no—
359C2×C43—42no—
360C2×C43#240911yescharacteristic
361C2×C43#301011yescharacteristic
362C2×C43#301211yescharacteristic
363C2×C43#308111yescharacteristic
364C2×C43#308411yescharacteristic
365C2×C43#324111yescharacteristic
366C2×C43#324411yescharacteristic
367D43—82no—
368#544—24no—
369#544—24no—
370C2×C4⋊Q8—21no—
371C2×C4⋊Q8C2×D4311yescharacteristic
372C2×C4⋊Q8C2×D4311yescharacteristic
373C2×#125—21no—
374C2×#125C2×D4311yescharacteristic
375C2×#125C2×D4311yescharacteristic
376C2×C22⋊Q8—21no—
377C2×C22⋊Q8—21no—
378C2×#121—431no—
379C2×C4×D4—431no—
380C2×#117C2×D4311yescharacteristic
381C2×#117C2×D4311yescharacteristic
382C22×C4⋊C4C2×D4311yescharacteristic
383#478—864no—
384#476—864no—
385C2×#107—431no—
386C2×#106—431no—
387C2×#106—431no—
388C2×#106—431no—
389C2×C4⋊C8—431no—
390C2×C4⋊C8—431no—
391C2×#102—431no—
392C2×#102—431no—
393C2×#102—431no—
394C2×#102—431no—
395C2×C22⋊C8—431no—
396C2×C22⋊C8—431no—
397#390—431no—
398#390—861no—
399#389—431no—
400#388—861no—
401#386—861no—
402#385—861no—
403#380—431no—
404C4×C4⋊C4—431no—
405#340—431no—
406#340—431no—
407#340—431no—
408#340—431no—
409#340—431no—
410#340—431no—
411#340—431no—
412#340—431no—
413#336—431no—
414#336—431no—
415C43#2430911yescharacteristic, complemented, Sylow
416C22×Q8—21no—
417C22×Q8—21no—
418C22×D4—431no—
419C22×D4—861no—
420C23×C4—21no—
421C23×C4—861no—
422C23×C4C22×D4311yescharacteristic
423C22×C8—431no—
424C22×C8—431no—
425C22×C8—431no—
426C22×C8—431no—
427C4⋊Q8—28no—
428C4⋊Q8—22no—
429C4⋊Q8—22no—
430C4⋊Q8—22no—
431C4⋊Q8C22⋊D4314yescomplemented
432#125—28no—
433#125—22no—
434#125—22no—
435#125—22no—
436#125C22⋊D4314yescomplemented
437C22⋊Q8—28no—
438C22⋊Q8—28no—
439#121—434no—
440#121—862no—
441C4×D4—862no—
442C4×D4—862no—
443#117—22no—
444#117—22no—
445#117—22no—
446#117—22no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4—21no—
449C2×C4⋊C4—21no—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—21no—
454C2×C4⋊C4—22no—
455C2×C4⋊C4—22no—
456C2×C4⋊C4—431no—
457C2×C4⋊C4—431no—
458C2×C4⋊C4—431no—
459C2×C4⋊C4—861no—
460C2×C4⋊C4C22⋊D4311yescharacteristic
461C2×C4⋊C4C22⋊D4311yescharacteristic
462C2×C4⋊C4C22×D4311yescharacteristic
463C2×C4⋊C4C22×D4311yescharacteristic
464C2×C4⋊C4C22×D4311yescharacteristic
465C2×C4⋊C4C22×D4311yescharacteristic
466C2×C22⋊C4—21no—
467C2×C22⋊C4—861no—
468C2×C22⋊C4—861no—
469C2×C22⋊C4—861no—
470C2×C22⋊C4—861no—
471C2×C22⋊C4—861no—
472C2×C22⋊C4C22⋊D4311yescharacteristic
473C2×C22⋊C4C22⋊D4311yescharacteristic
474C2×C42—21no—
475C2×C42—861no—
476C2×C42C22×D4311yescharacteristic
477C2×C42C22×D4311yescharacteristic
478#107—862no—
479#106—862no—
480#106—862no—
481#106—862no—
482C4⋊C8—862no—
483C4⋊C8—862no—
484#102—862no—
485#102—862no—
486#102—862no—
487#102—862no—
488C22⋊C8—862no—
489C22⋊C8—862no—
490#95—861no—
491#95—861no—
492#95—861no—
493C24—861no—
494C24C2×C22⋊D4311yescharacteristic
495C2×Q8—24no—
496C2×Q8—24no—
497C2×Q8—81no—
498C2×Q8—81no—
499C2×Q8—81no—
500C2×Q8—81no—
501C2×D4—432no—
502C2×D4—864no—
503C2×D4—861no—
504C2×D4—861no—
505C2×D4—861no—
506C2×D4—861no—
507C2×D4—861no—
508C2×D4—3441no—
509C2×D4—3441no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—24no—
519C22×C4—81no—
520C22×C4—81no—
521C22×C4—861no—
522C22×C4—861no—
523C22×C4—861no—
524C22×C4—3441no—
525C22×C4—3441no—
526C22×C4—1722no—
527C22×C4Q8×D4312yes—
528C22×C4#1062190212yes—
529C22×C4C2×C22⋊D4311yescharacteristic
530C22×C4C2×C22⋊D4311yescharacteristic
531C22×C4C2×C22⋊D4311yescharacteristic
532C22×C4C2×C22⋊D4311yescharacteristic
533C22×C4C2×C22⋊D4311yescharacteristic
534C22×C4C23×D4311yescharacteristic
535C2×C8—861no—
536C2×C8—861no—
537C2×C8—861no—
538C2×C8—861no—
539C2×C8—861no—
540C2×C8—861no—
541C2×C8—861no—
542C2×C8—861no—
543C2×C8—861no—
544C2×C8—861no—
545C2×C8—861no—
546C2×C8—861no—
547C4⋊C4—24no—
548C4⋊C4—24no—
549C4⋊C4—24no—
550C4⋊C4—24no—
551C4⋊C4—24no—
552C4⋊C4—24no—
553C4⋊C4—24no—
554C4⋊C4—22no—
555C4⋊C4—22no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—432no—
561C4⋊C4—861no—
562C4⋊C4—861no—
563C4⋊C4—861no—
564C4⋊C4—861no—
565C4⋊C4—861no—
566C4⋊C4—3441no—
567C4⋊C4C2×C22⋊D4312yes—
568C4⋊C4C2×C22⋊D4312yes—
569C4⋊C4C2×C22⋊D4312yes—
570C4⋊C4C2×C22⋊D4312yes—
571C22⋊C4—24no—
572C22⋊C4—22no—
573C22⋊C4—22no—
574C22⋊C4—864no—
575C22⋊C4—3441no—
576C22⋊C4—3441no—
577C22⋊C4—3441no—
578C22⋊C4—1722no—
579C42—24no—
580C42—21no—
581C42—21no—
582C42—3441no—
583C42C2×C22⋊D4312yes—
584C42C2×C22⋊D4312yes—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—21no—
591C23—862no—
592C23—1721no—
593C23—1721no—
594C23—1721no—
595C23—1721no—
596C23—1721no—
597C23—1721no—
598C23#1306330112yes—
599C23C22×C22⋊D4311yescharacteristic
600Q8—84no—
601Q8—84no—
602D4—862no—
603D4—862no—
604D4—3444no—
605D4—1721no—
606D4—1721no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—21no—
618C2×C4—22no—
619C2×C4—21no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—84no—
636C2×C4—862no—
637C2×C4—3444no—
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×C4#1306329412yes—
647C2×C4#1306329412yes—
648C2×C4#1306330112yes—
649C2×C4C22×C22⋊D4311yescharacteristic
650C2×C4C22×C22⋊D4311yescharacteristic
651C2×C4C2×Q8×D4311yescharacteristic
652C2×C4C2×#1062190211yescharacteristic
653C2×C4#1306337311yescharacteristic
654C2×C4#1306337311yescharacteristic
655C8—1721no—
656C8—1721no—
657C8—1721no—
658C8—1721no—
659C22—22no—
660C22—22no—
661C22—22no—
662C22—41no—
663C22—41no—
664C22—41no—
665C22—41no—
666C22—3441no—
667C22—3441no—
668C22—3441no—
669C22—3441no—
670C22—1722no—
671C22—1722no—
672C22—1722no—
673C22C2×#1306329411yescharacteristic
674C22C2×#1306330111yescharacteristic
675C22#1458347311yescharacteristic
676C22#1458370211yescharacteristic
677C22#1458370711yescharacteristic
678C22#1458370711yescharacteristic
679C22#1458371011yescharacteristic
680C4—22no—
681C4—22no—
682C4—22no—
683C4—41no—
684C4—42no—
685C4—41no—
686C4—42no—
687C4—42no—
688C4—42no—
689C4—3441no—
690C4—3441no—
691C4—1722no—
692C4#1458356011yescharacteristic
693C4#1458356011yescharacteristic
694C4Q8×C22⋊D4311yescharacteristic
695C4Q8×C22⋊D4311yescharacteristic
696C2—42no—
697C2—3442no—
698C2#1913795411yescharacteristic
699C2#1914388111yescharacteristic
700C2#1914389911yescharacteristic
701C2#1914442011yescharacteristic
702C2#1914445311yescharacteristic
703C2#1914584811yescharacteristic
704C2#1914589311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#544C2
socleC23×C43C22×D4
prime radicalC2×#13063299C22
hypercenterC2×#544D43
hypocenterC43#24309
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#544

Complements

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

NH ≅ G/Ntype
1. C2×#14583196C2semidirect
2. C2×#14583186C2semidirect
4. #19135930C2semidirect
5. #19135925C2semidirect
6. #19135738C2semidirect
7. #19135728C2semidirect
8. #19135553C2semidirect
9. #19135548C2semidirect
12. #19134794C2semidirect
13. #19134788C2semidirect
14. #19134579C2semidirect
15. C2×C43×#544C2semidirect
71. #13063299Q8semidirect
107. C4⋊Q8×C43D4semidirect
112. #125×C43D4semidirect
344. C2×#544D43semidirect
415. C43#24309semidirect
431. C4⋊Q8C22⋊D43semidirect
436. #125C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145831962
C2×#145831862
#191372882
#191359302
#191359252
#191357382
#191357282
#191355532
#191355482
#191349172
#191349122
#191347942
#191347882
#191345792
C2×C43×#5442
#2430943