Finite Group Databasebeta

← #25131741

Subgroups — #25131741

Order 11008.

1420 conjugacy classes of subgroups.

The subgroup lattice has 874 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583111C211yesmaximal, characteristic, complemented
2C2×#14583101C211yesmaximal, characteristic, complemented
3C2×#14583044C211yesmaximal, characteristic
4C2×#14583038C211yesmaximal, characteristic, complemented
5#19137288C211yesmaximal, characteristic, complemented
6#19135838C211yesmaximal, characteristic, complemented
7#19135831C211yesmaximal, characteristic, complemented
8#19135678C211yesmaximal, characteristic, complemented
9#19135672C211yesmaximal, characteristic, complemented
10#19135528C211yesmaximal, characteristic, complemented
11#19135519C211yesmaximal, characteristic, complemented
12#19134579C211yesmaximal, characteristic, complemented
13#19134535C211yesmaximal, characteristic, complemented
14#19134530C211yesmaximal, characteristic, complemented
15C2×C43×#536C211yesmaximal, characteristic, complemented
16C22×#10621884C2211yescharacteristic
17C22×#10621884C2211yescharacteristic
18C22×#10621884C2211yescharacteristic
19C22×#10621882C2211yescharacteristic
20C2×#13063299C2211yescharacteristic
21C2×C4×D172C2211yescharacteristic
22#14583111—24no—
23#14583101—24no—
24#14583044—24no—
25#14583038—24no—
26C2×C4⋊(C43⋊C8)C2211yescharacteristic
27C2×C4⋊(C43⋊C8)C2211yescharacteristic
28C2×#13063249C2211yescharacteristic
29C2×#13063249C2211yescharacteristic
30C2×#13063249C2211yescharacteristic
31C2×#13063249C2211yescharacteristic
32C2×#13063249C2211yescharacteristic
33C2×#13063249C2211yescharacteristic
34C2×#13063249C2211yescharacteristic
35C2×#13063249C2211yescharacteristic
36C2×#13063249C2211yescharacteristic
37C2×#13063246C2211yescharacteristic
38C2×#13063246C2211yescharacteristic
39C2×#13063246C2211yescharacteristic
40C2×C22⋊(C43⋊C8)C2211yescharacteristic
41C2×C22⋊(C43⋊C8)C2211yescharacteristic
42#14582801C2211yescharacteristic
43#14582799—21no—
44#14582797C2211yescharacteristic
45#14582789—21no—
46#14582775—21no—
47#14582770—21no—
48#14582759C2211yescharacteristic
49C4×C4⋊Dic43C2211yescharacteristic
50#14582654C2211yescharacteristic
51#14582654C2211yescharacteristic
52C22×#41×C43C2211yescharacteristic
53C23×Q8×C43C2211yescharacteristic
54C43×#536—24no—
55C43×#536—24no—
56C2×C4⋊Q8×C43C2211yescharacteristic
57C2×C4⋊Q8×C43C2211yescharacteristic
58C2×#124×C43C2211yescharacteristic
59C2×#124×C43C2211yescharacteristic
60C2×#123×C43—21no—
61C2×#123×C43—21no—
62C2×C22⋊Q8×C43—21no—
63C2×C22⋊Q8×C43—21no—
64C2×#117×C43C2211yescharacteristic
65C22×D172C2311yescharacteristic
66C22×C22⋊D43—21no—
67C22×C4×D43—21no—
68C2×#10621884—22no—
69C2×#10621884—22no—
70C2×#10621884—22no—
71C2×#10621884—22no—
72C2×#10621884—22no—
73C2×#10621884—22no—
74C2×#10621884—41no—
75C2×#10621884—41no—
76C2×#10621884—41no—
77C2×#10621882—22no—
78C2×#10621882—22no—
79C2×#10621882—41no—
80C22×C43⋊C8C2311yescharacteristic
81C22×C43⋊C8C2311yescharacteristic
82C22×C43⋊C8C2311yescharacteristic
83C22×C43⋊C8C2311yescharacteristic
84#13063299—22no—
85#13063299D414yes—
86C4×D172—22no—
87C4×D172—22no—
88C2×C4⋊Dic43C2311yescharacteristic
89C2×C4⋊Dic43C2311yescharacteristic
90C2×C4⋊Dic43C2311yescharacteristic
91C2×Dic43⋊C4—21no—
92C2×C22⋊Dic43—21no—
93C2×(C2×D43)⋊C4—21no—
94C2×(C2×D43)⋊C4—21no—
95C2×(C2×D43)⋊C4—21no—
96C2×(C2×D43)⋊C4—21no—
97C2×C4×Dic43—21no—
98C4⋊(C43⋊C8)—22no—
99C4⋊(C43⋊C8)—22no—
100#13063249—22no—
101#13063249—22no—
102#13063249—22no—
103#13063249—22no—
104#13063249—22no—
105#13063249—22no—
106#13063249—41no—
107#13063249—41no—
108#13063249—41no—
109#13063246—22no—
110#13063246—22no—
111#13063246—41no—
112C22⋊(C43⋊C8)—22no—
113C22⋊(C43⋊C8)—22no—
114C43⋊#95—21no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C2×#41×C43—22no—
118C2×#41×C43—22no—
119C2×#41×C43—22no—
120C2×#41×C43—22no—
121C2×#41×C43—41no—
122C2×#41×C43—41no—
123C22×Q8×C43—22no—
124C22×Q8×C43—22no—
125C22×Q8×C43—21no—
126C22×Q8×C43—22no—
127C22×Q8×C43—22no—
128C22×Q8×C43—41no—
129C22×Q8×C43—41no—
130C22×Q8×C43C2311yescharacteristic
131C22×Q8×C43C2311yescharacteristic
132C22×Q8×C43C2311yescharacteristic
133C22×D4×C43—21no—
134C22×D4×C43C2311yescharacteristic
135C23×C4×C43—21no—
136C23×C4×C43—21no—
137C23×C4×C43C2311yescharacteristic
138C4⋊Q8×C43—22no—
139C4⋊Q8×C43—22no—
140C4⋊Q8×C43—22no—
141C4⋊Q8×C43D414yescomplemented
142#124×C43—22no—
143#124×C43—22no—
144#124×C43—22no—
145#124×C43D414yescomplemented
146#123×C43—28no—
147#123×C43—28no—
148C22⋊Q8×C43—28no—
149C22⋊Q8×C43—28no—
150#117×C43—22no—
151#117×C43—22no—
152C2×C4⋊C4×C43—21no—
153C2×C4⋊C4×C43—21no—
154C2×C4⋊C4×C43—21no—
155C2×C4⋊C4×C43—21no—
156C2×C4⋊C4×C43D411yescharacteristic
157C2×C4⋊C4×C43D411yescharacteristic
158C2×C22⋊C4×C43—21no—
159C2×C22⋊C4×C43—21no—
160C2×C22⋊C4×C43—21no—
161C2×C22⋊C4×C43—21no—
162C2×C22⋊C4×C43D411yescharacteristic
163C2×C22⋊C4×C43D411yescharacteristic
164C2×C42×C43C2311yescharacteristic
165C2×C42×C43C2311yescharacteristic
166C24×C43—21no—
167C24×C43C2×D411yescharacteristic
168C23×D43—21no—
169#41×C43—44no—
170#41×C43—44no—
171#41×C43—44no—
172#41×C43—44no—
173C2×Q8×C43—24no—
174C2×Q8×C43—21no—
175C2×Q8×C43—21no—
176C2×Q8×C43—21no—
177C2×Q8×C43—21no—
178C2×Q8×C43—21no—
179C2×Q8×C43—21no—
180C2×Q8×C43—21no—
181C2×Q8×C43—21no—
182C2×Q8×C43—21no—
183C2×Q8×C43—21no—
184C2×Q8×C43—21no—
185C2×Q8×C43—21no—
186C2×Q8×C43—21no—
187C2×Q8×C43—21no—
188C2×Q8×C43—21no—
189C2×Q8×C43—44no—
190C2×Q8×C43—44no—
191C2×Q8×C43—44no—
192C2×Q8×C43—44no—
193C2×Q8×C43—42no—
194C2×Q8×C43—42no—
195C2×Q8×C43C2×D412yes—
196C2×Q8×C43C2×D412yes—
197C2×Q8×C43C2×D412yes—
198C2×D4×C43—24no—
199C2×D4×C43—21no—
200C2×D4×C43—21no—
201C2×D4×C43—21no—
202C2×D4×C43—21no—
203C2×D4×C43—21no—
204C2×D4×C43—42no—
205C2×D4×C43—42no—
206C2×D4×C43C2×D412yes—
207C22×C4×C43—21no—
208C22×C4×C43—21no—
209C22×C4×C43—21no—
210C22×C4×C43—21no—
211C22×C4×C43—24no—
212C22×C4×C43—24no—
213C22×C4×C43—21no—
214C22×C4×C43—21no—
215C22×C4×C43—21no—
216C22×C4×C43—42no—
217C22×C4×C43—42no—
218C22×C4×C43—42no—
219C22×C4×C43—42no—
220C22×C4×C43C2×D412yes—
221C22×C4×C43C2×D411yescharacteristic
222C22×C4×C43C2×D411yescharacteristic
223C22×C4×C43C2×D411yescharacteristic
224C22×C4×C43C2×D411yescharacteristic
225C22×C4×C43C2×D411yescharacteristic
226C22×C4×C43#4112yes—
227C22×C4×C43C2411yescharacteristic
228C2×C22⋊D43—24no—
229C2×C22⋊D43—81no—
230C2×C22⋊D43—81no—
231C22×Dic43—21no—
232C22×Dic43—21no—
233C22×Dic43—21no—
234C2×D172—21no—
235C2×D172—21no—
236C2×D172—21no—
237C2×D172—21no—
238C2×D172—21no—
239C2×D172C2×D412yes—
240C2×C4×D43—42no—
241C2×C4×D43—81no—
242C2×C4×D43—81no—
243C4⋊C4×C43—24no—
244C4⋊C4×C43—24no—
245C4⋊C4×C43—24no—
246C4⋊C4×C43—24no—
247C4⋊C4×C43—22no—
248C4⋊C4×C43—22no—
249C22⋊C4×C43—24no—
250C22⋊C4×C43—24no—
251C22⋊C4×C43—24no—
252C22⋊C4×C43—24no—
253C22⋊C4×C43—22no—
254C22⋊C4×C43—22no—
255C42×C43—21no—
256C42×C43—21no—
257C42×C43C2×D412yes—
258C42×C43C2×D412yes—
259C22⋊Dic43—81no—
260#10621884—44no—
261#10621884—44no—
262#10621884—44no—
263#10621882—44no—
264(C2×D43)⋊C4—24no—
265(C2×D43)⋊C4—42no—
266(C2×D43)⋊C4—81no—
267(C2×D43)⋊C4—81no—
268C4⋊Dic43—21no—
269C4⋊Dic43—21no—
270C4⋊Dic43—21no—
271C4⋊Dic43—21no—
272C4⋊Dic43—21no—
273C4⋊Dic43C2×D412yes—
274Dic43⋊C4—81no—
275C4×Dic43—81no—
276C2×C43⋊C8—21no—
277C2×C43⋊C8—21no—
278C2×C43⋊C8—21no—
279C2×C43⋊C8—21no—
280C2×C43⋊C8—21no—
281C2×C43⋊C8—21no—
282C2×C43⋊C8—21no—
283C2×C43⋊C8—21no—
284C2×C43⋊C8—21no—
285C2×C43⋊C8—21no—
286C2×C43⋊C8—21no—
287C2×C43⋊C8—21no—
288C23×C43—21no—
289C23×C43—21no—
290C23×C43—21no—
291C23×C43—21no—
292C23×C43—21no—
293C23×C43—21no—
294C23×C43—22no—
295C23×C43—41no—
296C23×C43—41no—
297C23×C43—41no—
298C23×C43—41no—
299C23×C43—41no—
300C23×C43—41no—
301C23×C43#12112yes—
302C23×C43C22×D411yescharacteristic
303C22×D43—22no—
304C22×D43—41no—
305C22×D43—41no—
306C22×D43—41no—
307C22×D43—41no—
308C22×D43—41no—
309C22×D43—41no—
310Q8×C43—22no—
311Q8×C43—22no—
312Q8×C43—22no—
313Q8×C43—22no—
314Q8×C43—22no—
315Q8×C43—22no—
316Q8×C43—48no—
317Q8×C43—41no—
318Q8×C43—41no—
319Q8×C43—41no—
320Q8×C43—41no—
321Q8×C43—41no—
322Q8×C43—41no—
323D4×C43—22no—
324D4×C43—22no—
325D4×C43—48no—
326D4×C43—41no—
327D4×C43—41no—
328C2×C4×C43—21no—
329C2×C4×C43—21no—
330C2×C4×C43—21no—
331C2×C4×C43—21no—
332C2×C4×C43—21no—
333C2×C4×C43—21no—
334C2×C4×C43—22no—
335C2×C4×C43—22no—
336C2×C4×C43—22no—
337C2×C4×C43—22no—
338C2×C4×C43—21no—
339C2×C4×C43—21no—
340C2×C4×C43—22no—
341C2×C4×C43—22no—
342C2×C4×C43—22no—
343C2×C4×C43—21no—
344C2×C4×C43—21no—
345C2×C4×C43—21no—
346C2×C4×C43—21no—
347C2×C4×C43—48no—
348C2×C4×C43—48no—
349C2×C4×C43—41no—
350C2×C4×C43—41no—
351C2×C4×C43—41no—
352C2×C4×C43—41no—
353C2×C4×C43—41no—
354C2×C4×C43—41no—
355C2×C4×C43#12012yes—
356C2×C4×C43#12012yes—
357C2×C4×C43#12112yes—
358C2×C4×C43C22×D411yescharacteristic
359C2×C4×C43C22×D411yescharacteristic
360C2×C4×C43C22×D411yescharacteristic
361C2×C4×C43C2×#4111yescharacteristic
362C2×C4×C43H(5,𝔽2)11yescharacteristic
363C2×C4×C43H(5,𝔽2)11yescharacteristic
364C22⋊D43—84no—
365C2×Dic43—22no—
366C2×Dic43—41no—
367C2×Dic43—41no—
368C2×Dic43—41no—
369C2×Dic43—41no—
370C2×Dic43—41no—
371C2×Dic43—41no—
372C2×Dic43—41no—
373C2×Dic43—41no—
374D172—22no—
375D172—22no—
376D172—41no—
377D172—41no—
378C4×D43—84no—
379C43⋊C8—41no—
380C43⋊C8—41no—
381C43⋊C8—41no—
382C43⋊C8—41no—
383#24219—431nomaximal, Sylow
384C22×C43—22no—
385C22×C43—22no—
386C22×C43—22no—
387C22×C43—41no—
388C22×C43—41no—
389C22×C43—41no—
390C22×C43—41no—
391C22×C43—42no—
392C22×C43—42no—
393C22×C43—42no—
394C22×C43—81no—
395C22×C43—81no—
396C22×C43—81no—
397C22×C43—81no—
398C22×C43C2×#12011yescharacteristic
399C22×C43C2×#12111yescharacteristic
400C22×C43#53511yescharacteristic
401C22×C43#57711yescharacteristic
402C22×C43#57711yescharacteristic
403C22×C43#57711yescharacteristic
404C22×C43#57811yescharacteristic
405C2×D43—42no—
406C2×D43—42no—
407C2×D43—42no—
408C2×D43—81no—
409C2×D43—81no—
410C2×D43—81no—
411C2×D43—81no—
412C4×C43—22no—
413C4×C43—22no—
414C4×C43—22no—
415C4×C43—42no—
416C4×C43—42no—
417C4×C43—42no—
418C4×C43—41no—
419C4×C43—41no—
420C4×C43D4211yescharacteristic
421C4×C43D4211yescharacteristic
422C4×C43#54611yescharacteristic
423C4×C43#54611yescharacteristic
424Dic43—42no—
425Dic43—81no—
426Dic43—81no—
427C2×#536D4311yescharacteristic, complemented
428C2×#463—431no—
429C2×#461—431no—
430C2×#449—431no—
431C2×#448—431no—
432#2324—431no—
433#2043—431no—
434#2042—431no—
435#2013—431no—
436#2012—431no—
437#1983—431no—
438#1981—431no—
439#1798—431no—
440#1788—431no—
441#1787—431no—
442C2×C43—42no—
443C2×C43—82no—
444C2×C43#240811yescharacteristic
445C2×C43#301011yescharacteristic
446C2×C43#301311yescharacteristic
447C2×C43#304211yescharacteristic
448C2×C43#304611yescharacteristic
449C2×C43#322111yescharacteristic
450C2×C43#322511yescharacteristic
451D43—82no—
452C22×#41C2×D4311yescharacteristic
453C23×Q8C2×D4311yescharacteristic
454C22×SD16—431no—
455C22×SD16—431no—
456C22×SD16—431no—
457C22×D8—431no—
458#536—24no—
459#536—24no—
460C2×C4⋊Q8C2×D4311yescharacteristic
461C2×C4⋊Q8C2×D4311yescharacteristic
462C2×#124C2×D4311yescharacteristic
463C2×#124C2×D4311yescharacteristic
464C2×#123—21no—
465C2×#123—21no—
466C2×C22⋊Q8—21no—
467C2×C22⋊Q8—21no—
468C2×#121—431no—
469C2×C4×D4—431no—
470C2×#117C2×D4311yescharacteristic
471#463—864no—
472#461—864no—
473#449—864no—
474#448—864no—
475C2×C4⋊C8—431no—
476C2×C4⋊C8—431no—
477C2×#103—431no—
478C2×#103—431no—
479C2×#103—431no—
480C2×#103—431no—
481C2×#103—431no—
482C2×#103—431no—
483C2×#103—431no—
484C2×#103—431no—
485C2×#103—431no—
486C2×#102—431no—
487C2×#102—431no—
488C2×#102—431no—
489C2×C22⋊C8—431no—
490C2×C22⋊C8—431no—
491#390—431no—
492#390—861no—
493#389—431no—
494#388—861no—
495#386—861no—
496#385—861no—
497#380—431no—
498C4×C4⋊C4—431no—
499#336—431no—
500#336—431no—
501C43#2421911yescharacteristic, complemented, Sylow
502C2×#41—22no—
503C2×#41—22no—
504C2×#41—22no—
505C2×#41—22no—
506C2×#41—41no—
507C2×#41—41no—
508C22×Q8—22no—
509C22×Q8—22no—
510C22×Q8—21no—
511C22×Q8—22no—
512C22×Q8—22no—
513C22×Q8—41no—
514C22×Q8—41no—
515C22×Q8C22×D4311yescharacteristic
516C22×Q8C22×D4311yescharacteristic
517C22×Q8C22×D4311yescharacteristic
518C22×D4—21no—
519C22×D4—431no—
520C22×D4—861no—
521C22×D4C22×D4311yescharacteristic
522C23×C4—21no—
523C23×C4—21no—
524C23×C4—861no—
525C23×C4C22×D4311yescharacteristic
526C2×SD16—862no—
527C2×SD16—862no—
528C2×SD16—862no—
529C2×SD16—862no—
530C2×SD16—862no—
531C2×SD16—862no—
532C2×SD16—1721no—
533C2×SD16—1721no—
534C2×SD16—1721no—
535C2×D8—862no—
536C2×D8—862no—
537C2×D8—1721no—
538C22×C8—431no—
539C22×C8—431no—
540C22×C8—431no—
541C22×C8—431no—
542C4⋊Q8—22no—
543C4⋊Q8—22no—
544C4⋊Q8—22no—
545C4⋊Q8C22⋊D4314yescomplemented
546#124—22no—
547#124—22no—
548#124—22no—
549#124C22⋊D4314yescomplemented
550#123—28no—
551#123—28no—
552C22⋊Q8—28no—
553C22⋊Q8—28no—
554#121—434no—
555#121—862no—
556C4×D4—862no—
557C4×D4—862no—
558#117—22no—
559#117—22no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—21no—
563C2×C4⋊C4—21no—
564C2×C4⋊C4—431no—
565C2×C4⋊C4—431no—
566C2×C4⋊C4—431no—
567C2×C4⋊C4—861no—
568C2×C4⋊C4C22⋊D4311yescharacteristic
569C2×C4⋊C4C22⋊D4311yescharacteristic
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—21no—
574C2×C22⋊C4—861no—
575C2×C22⋊C4—861no—
576C2×C22⋊C4—861no—
577C2×C22⋊C4—861no—
578C2×C22⋊C4—861no—
579C2×C22⋊C4C22⋊D4311yescharacteristic
580C2×C22⋊C4C22⋊D4311yescharacteristic
581C2×C42—861no—
582C2×C42C22×D4311yescharacteristic
583C2×C42C22×D4311yescharacteristic
584C4⋊C8—862no—
585C4⋊C8—862no—
586#103—862no—
587#103—862no—
588#103—862no—
589#103—862no—
590#103—862no—
591#103—862no—
592#103—1721no—
593#103—1721no—
594#103—1721no—
595#102—862no—
596#102—862no—
597#102—1721no—
598C22⋊C8—862no—
599C22⋊C8—862no—
600#95—861no—
601#95—861no—
602#95—861no—
603C24—21no—
604C24—861no—
605C24C2×C22⋊D4311yescharacteristic
606#41—44no—
607#41—44no—
608#41—44no—
609#41—44no—
610C2×Q8—24no—
611C2×Q8—21no—
612C2×Q8—21no—
613C2×Q8—21no—
614C2×Q8—21no—
615C2×Q8—21no—
616C2×Q8—21no—
617C2×Q8—21no—
618C2×Q8—21no—
619C2×Q8—21no—
620C2×Q8—21no—
621C2×Q8—21no—
622C2×Q8—21no—
623C2×Q8—21no—
624C2×Q8—21no—
625C2×Q8—21no—
626C2×Q8—44no—
627C2×Q8—44no—
628C2×Q8—44no—
629C2×Q8—44no—
630C2×Q8—42no—
631C2×Q8—42no—
632C2×Q8C2×C22⋊D4312yes—
633C2×Q8C2×C22⋊D4312yes—
634C2×Q8C2×C22⋊D4312yes—
635C2×D4—24no—
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—42no—
642C2×D4—42no—
643C2×D4—432no—
644C2×D4—864no—
645C2×D4—861no—
646C2×D4—861no—
647C2×D4—861no—
648C2×D4—861no—
649C2×D4—861no—
650C2×D4—3441no—
651C2×D4—3441no—
652C2×D4C2×C22⋊D4312yes—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—24no—
658C22×C4—24no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—42no—
663C22×C4—42no—
664C22×C4—42no—
665C22×C4—42no—
666C22×C4—861no—
667C22×C4—861no—
668C22×C4—861no—
669C22×C4—3441no—
670C22×C4—3441no—
671C22×C4—1722no—
672C22×C4D4×D4312yes—
673C22×C4#1062190012yes—
674C22×C4C2×C22⋊D4311yescharacteristic
675C22×C4C2×C22⋊D4311yescharacteristic
676C22×C4C2×C22⋊D4311yescharacteristic
677C22×C4C2×C22⋊D4311yescharacteristic
678C22×C4C2×C22⋊D4311yescharacteristic
679C22×C4C23×D4311yescharacteristic
680SD16—1724no—
681SD16—1724no—
682SD16—1724no—
683D8—1724no—
684C2×C8—861no—
685C2×C8—861no—
686C2×C8—861no—
687C2×C8—861no—
688C2×C8—861no—
689C2×C8—861no—
690C2×C8—861no—
691C2×C8—861no—
692C2×C8—861no—
693C2×C8—861no—
694C2×C8—861no—
695C2×C8—861no—
696C4⋊C4—24no—
697C4⋊C4—24no—
698C4⋊C4—24no—
699C4⋊C4—24no—
700C4⋊C4—22no—
701C4⋊C4—22no—
702C4⋊C4—432no—
703C4⋊C4—861no—
704C4⋊C4—861no—
705C4⋊C4—861no—
706C4⋊C4—861no—
707C4⋊C4—861no—
708C4⋊C4—3441no—
709C22⋊C4—24no—
710C22⋊C4—24no—
711C22⋊C4—24no—
712C22⋊C4—24no—
713C22⋊C4—22no—
714C22⋊C4—22no—
715C22⋊C4—864no—
716C22⋊C4—3441no—
717C22⋊C4—3441no—
718C22⋊C4—3441no—
719C22⋊C4—1722no—
720C42—21no—
721C42—21no—
722C42—3441no—
723C42C2×C22⋊D4312yes—
724C42C2×C22⋊D4312yes—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—22no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—862no—
739C23—1721no—
740C23—1721no—
741C23—1721no—
742C23—1721no—
743C23—1721no—
744C23—1721no—
745C23#1306329612yes—
746C23C22×C22⋊D4311yescharacteristic
747Q8—22no—
748Q8—22no—
749Q8—22no—
750Q8—22no—
751Q8—22no—
752Q8—22no—
753Q8—48no—
754Q8—41no—
755Q8—41no—
756Q8—41no—
757Q8—41no—
758Q8—41no—
759Q8—41no—
760D4—22no—
761D4—22no—
762D4—48no—
763D4—41no—
764D4—41no—
765D4—862no—
766D4—862no—
767D4—3444no—
768D4—1721no—
769D4—1721no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—48no—
790C2×C4—48no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—862no—
798C2×C4—3444no—
799C2×C4—1721no—
800C2×C4—1721no—
801C2×C4—1721no—
802C2×C4—1721no—
803C2×C4—1721no—
804C2×C4—1721no—
805C2×C4—1721no—
806C2×C4—1721no—
807C2×C4#1306329412yes—
808C2×C4#1306329412yes—
809C2×C4#1306329612yes—
810C2×C4C2×D4×D4311yescharacteristic
811C2×C4C22×C22⋊D4311yescharacteristic
812C2×C4C22×C22⋊D4311yescharacteristic
813C2×C4C2×#1062190011yescharacteristic
814C2×C4#1306337011yescharacteristic
815C2×C4#1306337011yescharacteristic
816C8—1721no—
817C8—1721no—
818C8—1721no—
819C8—1721no—
820C22—22no—
821C22—22no—
822C22—22no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—42no—
828C22—42no—
829C22—42no—
830C22—81no—
831C22—81no—
832C22—81no—
833C22—81no—
834C22—3441no—
835C22—3441no—
836C22—3441no—
837C22—3441no—
838C22—1722no—
839C22—1722no—
840C22—1722no—
841C22C2×#1306329411yescharacteristic
842C22C2×#1306329611yescharacteristic
843C22#1458346611yescharacteristic
844C22#1458370711yescharacteristic
845C22#1458370711yescharacteristic
846C22#1458370711yescharacteristic
847C22#1458371411yescharacteristic
848C4—22no—
849C4—22no—
850C4—22no—
851C4—42no—
852C4—42no—
853C4—42no—
854C4—41no—
855C4—41no—
856C4—3441no—
857C4—3441no—
858C4—1722no—
859C4D4×C22⋊D4311yescharacteristic
860C4D4×C22⋊D4311yescharacteristic
861C4#1458354311yescharacteristic
862C4#1458354311yescharacteristic
863C2—42no—
864C2—82no—
865C2—3442no—
866C2#1913794511yescharacteristic
867C2#1914388111yescharacteristic
868C2#1914391011yescharacteristic
869C2#1914410311yescharacteristic
870C2#1914414111yescharacteristic
871C2#1914565611yescharacteristic
872C2#1914570411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#536C2
socleC23×C43C22×D4
prime radicalC2×#14583044C2
hypercenterC2×#536D43
hypocenterC43#24219
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#536

Complements

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

NH ≅ G/Ntype
1. C2×#14583111C2semidirect
2. C2×#14583101C2semidirect
4. C2×#14583038C2semidirect
5. #19137288C2semidirect
6. #19135838C2semidirect
7. #19135831C2semidirect
8. #19135678C2semidirect
9. #19135672C2semidirect
10. #19135528C2semidirect
11. #19135519C2semidirect
12. #19134579C2semidirect
13. #19134535C2semidirect
14. #19134530C2semidirect
15. C2×C43×#536C2semidirect
141. C4⋊Q8×C43D4semidirect
145. #124×C43D4semidirect
427. C2×#536D43semidirect
501. C43#24219semidirect
545. C4⋊Q8C22⋊D43semidirect
549. #124C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145831112
C2×#145831012
C2×#145830442
C2×#145830382
#191372882
#191358382
#191358312
#191356782
#191356722
#191355282
#191355192
#191345792
#191345352
#191345302
C2×C43×#5362
#2421943