Finite Group Databasebeta

← #25098397

Subgroups — #25098397

Order 11008.

2102 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583461C211yesmaximal, characteristic
2C2×#14583372C211yesmaximal, characteristic, complemented
3C22×#13063239C211yesmaximal, characteristic, complemented
4C22×#13063239C211yesmaximal, characteristic, complemented
5#19137170C211yesmaximal, characteristic, complemented
6#19135052C214yesmaximal, complemented
7#19135047C214yesmaximal, complemented
8C2×#14582666C211yesmaximal, characteristic, complemented
9C2×C43×#342C211yesmaximal, characteristic, complemented
10C23×C22⋊D43C2211yescharacteristic
11C23×C22⋊D43C2211yescharacteristic
12#14583461—22no—
13#14583461—22no—
14#14583461—22no—
15#14583461—22no—
16C2×#13063309C412yescomplemented
17C2×#13063309C2212yes—
18C2×#13063299C414yescomplemented
19C2×#13063295C412yescomplemented
20C2×#13063295C2212yes—
21#14583372—24no—
22#14583372—24no—
23C2×C4×C22⋊D43—22no—
24C2×(C22⋊D43)⋊C4—22no—
25C2×#13063281C2212yescomplemented
26C22×C22⋊Dic43C2211yescharacteristic
27C22×C22⋊Dic43C2211yescharacteristic
28C2×C22⋊C4×D43C2212yescomplemented
29C2×#13063239—24no—
30C2×#13063239—24no—
31C2×#13063239C2214yes—
32C2×#13063239C2214yes—
33#14582778—22no—
34#14582776—22no—
35#14582760C2212yescomplemented
36#14582754C2212yescomplemented
37#14582666C2214yescomplemented
38C22×C22⋊C4×C43C2211yescharacteristic
39C22×C22⋊C4×C43C2211yescharacteristic
40C22×C22⋊C4×C43C2211yescharacteristic
41C43×#342C2214yescomplemented
42C24×D43C2×C411yescharacteristic, complemented
43C24×D43C2311yescharacteristic
44C22×D172C2×C414yescomplemented
45C22×C22⋊D43—22no—
46C22×C22⋊D43—22no—
47C22×C22⋊D43—22no—
48C22×C22⋊D43—22no—
49C22×C22⋊D43—22no—
50C22×C22⋊D43—22no—
51C22×C22⋊D43—21no—
52C22×C22⋊D43—21no—
53C22×C22⋊D43—21no—
54C22×C22⋊D43—21no—
55C22×C22⋊D43—22no—
56C22×C22⋊D43—22no—
57C22×C22⋊D43C2×C412yes—
58C22×C22⋊D43C2×C412yes—
59C22×C22⋊D43C2×C412yescomplemented
60C22×C22⋊D43D412yes—
61C22×C22⋊D43D412yes—
62C22×C22⋊D43D412yes—
63C22×C22⋊D43D412yes—
64C22×C22⋊D43C2312yes—
65C23×Dic43—21no—
66C23×Dic43—21no—
67C23×Dic43C2×C411yescharacteristic, complemented
68C23×Dic43C2311yescharacteristic
69C22×C4×D43—22no—
70#13063309—24no—
71#13063309—24no—
72#13063309—24no—
73#13063309—24no—
74#13063299—28no—
75#13063299—28no—
76#13063295—24no—
77#13063295—24no—
78#13063295—24no—
79#13063295—24no—
80C4×C22⋊D43—216no—
81(C22⋊D43)⋊C4—216no—
82#13063281—24no—
83#13063281—24no—
84C2×C4⋊Dic43C2×C414yescomplemented
85C2×Dic43⋊C4—22no—
86C2×C22⋊Dic43—21no—
87C2×C22⋊Dic43—22no—
88C2×C22⋊Dic43—22no—
89C2×C22⋊Dic43—22no—
90C2×C22⋊Dic43—21no—
91C2×C22⋊Dic43D414yescomplemented
92C2×C22⋊Dic43C2312yes—
93C2×C22⋊Dic43C2312yes—
94C2×(C2×D43)⋊C4—22no—
95C2×(C2×D43)⋊C4—24no—
96C2×(C2×D43)⋊C4C2×C414yescomplemented
97C2×(C2×D43)⋊C4C2×C414yescomplemented
98C22⋊C4×D43—24no—
99C22⋊C4×D43—24no—
100C2×C4×Dic43—22no—
101#13063239—28no—
102#13063239—28no—
103C43⋊#95—24no—
104C25×C43C2311yescharacteristic
105C23×C4×C43—21no—
106C23×C4×C43—21no—
107C23×C4×C43C2×C412yescomplemented
108C2×C22⋊C4×C43—21no—
109C2×C22⋊C4×C43—22no—
110C2×C22⋊C4×C43—21no—
111C2×C22⋊C4×C43—21no—
112C2×C22⋊C4×C43—21no—
113C2×C22⋊C4×C43—21no—
114C2×C22⋊C4×C43—22no—
115C2×C22⋊C4×C43—22no—
116C2×C22⋊C4×C43—21no—
117C2×C22⋊C4×C43C2×C412yescomplemented
118C2×C22⋊C4×C43D414yescomplemented
119C2×C22⋊C4×C43C2312yes—
120C2×C22⋊C4×C43C2312yes—
121C2×C22⋊C4×C43C2312yes—
122C24×C43—82no—
123C24×C43C22×C411yescharacteristic
124C24×C43C22×C411yescharacteristic
125C24×C43C2×D411yescharacteristic
126C24×C43C2×D411yescharacteristic
127C24×C43C2×D411yescharacteristic
128C24×C43C2×D411yescharacteristic
129C24×C43C2×D412yes—
130C24×C43C2×D412yes—
131C24×C43#4112yes—
132C24×C43#4112yes—
133C24×C43C2411yescharacteristic
134C23×D43—21no—
135C23×D43—21no—
136C23×D43—21no—
137C23×D43—21no—
138C23×D43—21no—
139C23×D43—21no—
140C23×D43—22no—
141C23×D43—22no—
142C23×D43—82no—
143C23×D43—82no—
144C23×D43C22×C412yes—
145C23×D43C22×C412yes—
146C23×D43C2×D412yes—
147C23×D43C2×D412yes—
148C22×C4×C43—22no—
149C22×C4×C43—22no—
150C22×C4×C43—24no—
151C22×C4×C43—22no—
152C22×C4×C43—22no—
153C22×C4×C43—42no—
154C22×C4×C43—82no—
155C22×C4×C43—82no—
156C22×C4×C43—82no—
157C22×C4×C43C22×C414yes—
158C2×C22⋊D43—22no—
159C2×C22⋊D43—22no—
160C2×C22⋊D43—24no—
161C2×C22⋊D43—24no—
162C2×C22⋊D43—24no—
163C2×C22⋊D43—24no—
164C2×C22⋊D43—24no—
165C2×C22⋊D43—24no—
166C2×C22⋊D43—24no—
167C2×C22⋊D43—24no—
168C2×C22⋊D43—24no—
169C2×C22⋊D43—24no—
170C2×C22⋊D43—24no—
171C2×C22⋊D43—24no—
172C2×C22⋊D43—24no—
173C2×C22⋊D43—24no—
174C2×C22⋊D43—22no—
175C2×C22⋊D43—22no—
176C2×C22⋊D43—22no—
177C2×C22⋊D43—22no—
178C2×C22⋊D43—22no—
179C2×C22⋊D43—22no—
180C2×C22⋊D43—42no—
181C2×C22⋊D43—42no—
182C2×C22⋊D43—42no—
183C2×C22⋊D43—42no—
184C2×C22⋊D43—42no—
185C2×C22⋊D43—42no—
186C2×C22⋊D43—42no—
187C2×C22⋊D43—42no—
188C2×C22⋊D43C22⋊C414yes—
189C2×C22⋊D43C22⋊C414yes—
190C2×C22⋊D43C22⋊C414yes—
191C2×C22⋊D43C22⋊C414yes—
192C22×Dic43—21no—
193C22×Dic43—21no—
194C22×Dic43—22no—
195C22×Dic43—22no—
196C22×Dic43—24no—
197C22×Dic43—21no—
198C22×Dic43—21no—
199C22×Dic43—22no—
200C22×Dic43—22no—
201C22×Dic43—21no—
202C22×Dic43—21no—
203C22×Dic43—42no—
204C22×Dic43—82no—
205C22×Dic43—82no—
206C22×Dic43C22×C412yes—
207C22×Dic43C22×C412yes—
208C22×Dic43C2×D412yes—
209C22×Dic43C2×D412yes—
210C2×D172—28no—
211C2×D172—84no—
212C2×C4×D43—28no—
213C2×C4×D43—84no—
214C22⋊C4×C43—22no—
215C22⋊C4×C43—22no—
216C22⋊C4×C43—24no—
217C22⋊C4×C43—22no—
218C22⋊C4×C43—22no—
219C22⋊C4×C43—22no—
220C22⋊C4×C43—22no—
221C22⋊C4×C43—22no—
222C22⋊C4×C43—42no—
223C22⋊C4×C43C2×D414yes—
224C22⋊Dic43—24no—
225C22⋊Dic43—22no—
226C22⋊Dic43—22no—
227C22⋊Dic43—22no—
228C22⋊Dic43—42no—
229C22⋊Dic43C2×D414yes—
230(C2×D43)⋊C4—28no—
231(C2×D43)⋊C4—28no—
232(C2×D43)⋊C4—28no—
233(C2×D43)⋊C4—84no—
234C4⋊Dic43—28no—
235Dic43⋊C4—28no—
236C4×Dic43—28no—
237C23×C43—42no—
238C23×C43—42no—
239C23×C43—42no—
240C23×C43—42no—
241C23×C43—42no—
242C23×C43—42no—
243C23×C43—42no—
244C23×C43—82no—
245C23×C43—82no—
246C23×C43—82no—
247C23×C43—82no—
248C23×C43C2×C22⋊C411yescharacteristic
249C23×C43C2×C22⋊C411yescharacteristic
250C23×C43C2×C22⋊C411yescharacteristic
251C23×C43C2×C22⋊C411yescharacteristic
252C23×C43C4×D412yes—
253C23×C43C4×D412yes—
254C23×C43C4×D412yes—
255C23×C43C4×D412yes—
256C23×C43#12012yes—
257C23×C43#12012yes—
258C23×C43#12112yes—
259C23×C43#12112yes—
260C23×C43#12112yes—
261C23×C43#12112yes—
262C23×C43#12312yes—
263C23×C43#12312yes—
264C23×C43C23×C411yescharacteristic
265C23×C43C22×D411yescharacteristic
266C23×C43C22×D411yescharacteristic
267C23×C43C22×D411yescharacteristic
268C23×C43C22×D411yescharacteristic
269C23×C43C2×#4111yescharacteristic
270C23×C43C2×#4111yescharacteristic
271C22×D43—22no—
272C22×D43—22no—
273C22×D43—22no—
274C22×D43—22no—
275C22×D43—22no—
276C22×D43—22no—
277C22×D43—22no—
278C22×D43—22no—
279C22×D43—22no—
280C22×D43—44no—
281C22×D43—44no—
282C22×D43—44no—
283C22×D43—42no—
284C22×D43—42no—
285C22×D43—44no—
286C22×D43—82no—
287C22×D43—82no—
288C22×D43—82no—
289C22×D43—82no—
290C22×D43—82no—
291C22×D43—82no—
292C22×D43—84no—
293C22×D43—84no—
294C22×D43C2×C22⋊C414yes—
295C2×C4×C43—24no—
296C2×C4×C43—24no—
297C2×C4×C43—44no—
298C2×C4×C43—44no—
299C2×C4×C43—44no—
300C2×C4×C43—42no—
301C2×C4×C43—82no—
302C2×C4×C43—82no—
303C2×C4×C43—84no—
304C2×C4×C43—84no—
305C22⋊D43—28no—
306C22⋊D43—28no—
307C22⋊D43—28no—
308C22⋊D43—28no—
309C22⋊D43—42no—
310C22⋊D43—42no—
311C22⋊D43—42no—
312C22⋊D43—42no—
313C22⋊D43—44no—
314C22⋊D43—44no—
315C2×Dic43—22no—
316C2×Dic43—22no—
317C2×Dic43—22no—
318C2×Dic43—22no—
319C2×Dic43—22no—
320C2×Dic43—22no—
321C2×Dic43—22no—
322C2×Dic43—22no—
323C2×Dic43—22no—
324C2×Dic43—24no—
325C2×Dic43—44no—
326C2×Dic43—42no—
327C2×Dic43—42no—
328C2×Dic43—44no—
329C2×Dic43—42no—
330C2×Dic43—84no—
331C2×Dic43—84no—
332C2×Dic43C2×C22⋊C414yes—
333D172—88no—
334C4×D43—88no—
335#20984—431nomaximal, Sylow
336C22×C43—22no—
337C22×C43—22no—
338C22×C43—22no—
339C22×C43—22no—
340C22×C43—22no—
341C22×C43—22no—
342C22×C43—22no—
343C22×C43—42no—
344C22×C43—42no—
345C22×C43—41no—
346C22×C43—41no—
347C22×C43—41no—
348C22×C43—41no—
349C22×C43—42no—
350C22×C43—42no—
351C22×C43—42no—
352C22×C43—42no—
353C22×C43—42no—
354C22×C43—42no—
355C22×C43—42no—
356C22×C43—42no—
357C22×C43—42no—
358C22×C43—42no—
359C22×C43#38612yes—
360C22×C43#38612yes—
361C22×C43#38612yes—
362C22×C43#38612yes—
363C22×C43C22×C22⋊C411yescharacteristic
364C22×C43C2×C4×D411yescharacteristic
365C22×C43C2×C4×D411yescharacteristic
366C22×C43C2×#12011yescharacteristic
367C22×C43C2×#12111yescharacteristic
368C22×C43C2×#12111yescharacteristic
369C22×C43C2×#12311yescharacteristic
370C2×D43—28no—
371C2×D43—24no—
372C2×D43—44no—
373C2×D43—44no—
374C2×D43—44no—
375C2×D43—42no—
376C2×D43—82no—
377C2×D43—82no—
378C2×D43—82no—
379C2×D43—82no—
380C2×D43—84no—
381C2×D43—84no—
382C2×D43—82no—
383C2×D43—82no—
384C4×C43—44no—
385C4×C43—44no—
386C4×C43—82no—
387Dic43—24no—
388Dic43—44no—
389Dic43—42no—
390Dic43—82no—
391C2×#534—431no—
392C2×#518—431no—
393C22×#99—431no—
394C22×#99—431no—
395#2308—431no—
396#1899—434no—
397#1898—434no—
398C2×#342—431no—
399C2×#342D4311yescharacteristic, complemented
400C2×C43—21no—
401C2×C43—21no—
402C2×C43—21no—
403C2×C43—21no—
404C2×C43—21no—
405C2×C43—21no—
406C2×C43—22no—
407C2×C43—22no—
408C2×C43—22no—
409C2×C43—22no—
410C2×C43C2×#38611yescharacteristic
411C2×C43#288312yes—
412D43—44no—
413D43—82no—
414C23×D4—431no—
415C23×D4—431no—
416#534—862no—
417#534—862no—
418#534—862no—
419#534—862no—
420C2×#123—432no—
421C2×#123—432no—
422C2×#121—434no—
423C2×#120—432no—
424C2×#120—432no—
425#518—864no—
426#518—864no—
427C2×C4×D4—862no—
428C2×C4×D4—862no—
429C2×#117—432no—
430C22×C22⋊C4—431no—
431C22×C22⋊C4—431no—
432C22×C22⋊C4—432no—
433C22×C22⋊C4C2×D4311yescharacteristic
434C22×C22⋊C4C2×D4311yescharacteristic
435C22×C22⋊C4C2×D4311yescharacteristic
436C2×#99—434no—
437C2×#99—434no—
438C2×#99—864no—
439C2×#99—864no—
440#386—862no—
441#386—862no—
442#381—432no—
443#379—432no—
444#342—434no—
445#342C2×D4314yescomplemented
446C43#2098411yescharacteristic, complemented, Sylow
447C25—431no—
448C25—431no—
449C25C22×D4311yescharacteristic
450C22×D4—432no—
451C22×D4—432no—
452C22×D4—432no—
453C22×D4—432no—
454C22×D4—432no—
455C22×D4—432no—
456C22×D4—432no—
457C22×D4—432no—
458C22×D4—434no—
459C22×D4—862no—
460C22×D4—862no—
461C22×D4—862no—
462C22×D4—862no—
463C22×D4—862no—
464C22×D4—862no—
465C22×D4—861no—
466C22×D4—861no—
467C22×D4—861no—
468C22×D4—861no—
469C22×D4—862no—
470C22×D4—862no—
471C23×C4—21no—
472C23×C4—21no—
473C23×C4—431no—
474C23×C4—431no—
475C23×C4—862no—
476C23×C4—861no—
477C23×C4—861no—
478C23×C4C4×D4312yescomplemented
479#123—864no—
480#123—864no—
481#123—864no—
482#123—864no—
483#121—868no—
484#121—868no—
485#120—864no—
486#120—864no—
487#120—864no—
488#120—864no—
489C4×D4—8616no—
490C4×D4—8616no—
491#117—864no—
492#117—864no—
493C2×C4⋊C4—434no—
494C2×C4⋊C4—862no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—22no—
497C2×C22⋊C4—21no—
498C2×C22⋊C4—21no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—22no—
502C2×C22⋊C4—22no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—434no—
505C2×C22⋊C4—432no—
506C2×C22⋊C4—434no—
507C2×C22⋊C4—434no—
508C2×C22⋊C4—432no—
509C2×C22⋊C4—864no—
510C2×C22⋊C4—862no—
511C2×C22⋊C4—862no—
512C2×C22⋊C4—861no—
513C2×C22⋊C4—864no—
514C2×C22⋊C4—862no—
515C2×C22⋊C4—862no—
516C2×C22⋊C4—864no—
517C2×C22⋊C4—861no—
518C2×C22⋊C4C4×D4312yescomplemented
519C2×C22⋊C4D17214yescomplemented
520C2×C22⋊C4C22×D4312yes—
521C2×C22⋊C4C22×D4312yes—
522C2×C22⋊C4C22×D4312yes—
523C2×C42—862no—
524#99—868no—
525#99—868no—
526#95—864no—
527C24—82no—
528C24—432no—
529C24—432no—
530C24—432no—
531C24—432no—
532C24—861no—
533C24—861no—
534C24—861no—
535C24—861no—
536C24—861no—
537C24—861no—
538C24—862no—
539C24—862no—
540C24—3442no—
541C24—3442no—
542C24C2×C4×D4311yescharacteristic
543C24C2×C4×D4311yescharacteristic
544C24C2×D17212yes—
545C24#1062189812yes—
546C24D4×D4311yescharacteristic
547C24D4×D4311yescharacteristic
548C24D4×D4311yescharacteristic
549C24D4×D4311yescharacteristic
550C24D4×D4312yes—
551C24#1062190212yes—
552C24C23×D4311yescharacteristic
553C2×D4—434no—
554C2×D4—434no—
555C2×D4—434no—
556C2×D4—434no—
557C2×D4—868no—
558C2×D4—864no—
559C2×D4—864no—
560C2×D4—864no—
561C2×D4—864no—
562C2×D4—864no—
563C2×D4—864no—
564C2×D4—864no—
565C2×D4—864no—
566C2×D4—864no—
567C2×D4—864no—
568C2×D4—864no—
569C2×D4—864no—
570C2×D4—862no—
571C2×D4—862no—
572C2×D4—864no—
573C2×D4—864no—
574C2×D4—862no—
575C2×D4—862no—
576C2×D4—862no—
577C2×D4—862no—
578C2×D4—862no—
579C2×D4—862no—
580C2×D4—3444no—
581C2×D4—1722no—
582C2×D4—1722no—
583C2×D4—1722no—
584C2×D4—1722no—
585C2×D4—1722no—
586C2×D4—1722no—
587C2×D4—1722no—
588C2×D4—1722no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—24no—
593C22×C4—22no—
594C22×C4—42no—
595C22×C4—82no—
596C22×C4—82no—
597C22×C4—82no—
598C22×C4—432no—
599C22×C4—432no—
600C22×C4—432no—
601C22×C4—432no—
602C22×C4—868no—
603C22×C4—861no—
604C22×C4—861no—
605C22×C4—861no—
606C22×C4—861no—
607C22×C4—864no—
608C22×C4—861no—
609C22×C4—861no—
610C22×C4—862no—
611C22×C4—862no—
612C22×C4—862no—
613C22×C4—862no—
614C22×C4—3444no—
615C22×C4—3442no—
616C22×C4—3442no—
617C22×C4—1722no—
618C22×C4C2×C4×D4314yes—
619C4⋊C4—868no—
620C4⋊C4—868no—
621C22⋊C4—22no—
622C22⋊C4—22no—
623C22⋊C4—24no—
624C22⋊C4—22no—
625C22⋊C4—22no—
626C22⋊C4—22no—
627C22⋊C4—22no—
628C22⋊C4—22no—
629C22⋊C4—42no—
630C22⋊C4—434no—
631C22⋊C4—868no—
632C22⋊C4—868no—
633C22⋊C4—868no—
634C22⋊C4—864no—
635C22⋊C4—862no—
636C22⋊C4—862no—
637C22⋊C4—862no—
638C22⋊C4—3444no—
639C22⋊C4—1722no—
640C22⋊C4C2×D17214yes—
641C42—868no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—82no—
650C23—82no—
651C23—82no—
652C23—82no—
653C23—434no—
654C23—862no—
655C23—862no—
656C23—862no—
657C23—862no—
658C23—862no—
659C23—862no—
660C23—862no—
661C23—862no—
662C23—862no—
663C23—3442no—
664C23—3442no—
665C23—3444no—
666C23—3444no—
667C23—3442no—
668C23—3442no—
669C23—3442no—
670C23—3442no—
671C23—1724no—
672C23—1724no—
673C23—1724no—
674C23—1724no—
675C23—1722no—
676C23—1722no—
677C23C22⋊C4×D4311yescharacteristic
678C23C22⋊C4×D4311yescharacteristic
679C23C22⋊C4×D4311yescharacteristic
680C23C22⋊C4×D4311yescharacteristic
681C23#1306328712yes—
682C23#1306328712yes—
683C23C4×D17212yes—
684C23C4×D17212yes—
685C23#1306329512yes—
686C23#1306329512yes—
687C23#1306329812yes—
688C23#1306329812yes—
689C23#1306330012yes—
690C23#1306330012yes—
691C23#1306331012yes—
692C23#1306331012yes—
693C23C22×C4×D4311yescharacteristic
694C23C2×D4×D4311yescharacteristic
695C23C2×D4×D4311yescharacteristic
696C23C2×D4×D4311yescharacteristic
697C23C22×D17211yescharacteristic
698C23C2×#1062189811yescharacteristic
699C23C2×#1062190211yescharacteristic
700D4—868no—
701D4—868no—
702D4—868no—
703D4—868no—
704D4—3448no—
705D4—1722no—
706D4—1722no—
707D4—1722no—
708D4—1722no—
709D4—1724no—
710D4—1724no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—44no—
714C2×C4—44no—
715C2×C4—44no—
716C2×C4—42no—
717C2×C4—82no—
718C2×C4—82no—
719C2×C4—84no—
720C2×C4—84no—
721C2×C4—434no—
722C2×C4—862no—
723C2×C4—862no—
724C2×C4—862no—
725C2×C4—862no—
726C2×C4—862no—
727C2×C4—862no—
728C2×C4—862no—
729C2×C4—862no—
730C2×C4—862no—
731C2×C4—864no—
732C2×C4—3448no—
733C2×C4—3444no—
734C2×C4—3444no—
735C2×C4—1724no—
736C2×C4—1722no—
737C2×C4—1724no—
738C2×C4—1722no—
739C2×C4—1722no—
740C22—22no—
741C22—22no—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—22no—
746C22—22no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22—42no—
761C22—42no—
762C22—42no—
763C22—868no—
764C22—864no—
765C22—3442no—
766C22—3442no—
767C22—3444no—
768C22—3444no—
769C22—3442no—
770C22—3442no—
771C22—3442no—
772C22—3442no—
773C22—1724no—
774C22—1724no—
775C22—1724no—
776C22—1722no—
777C22#1458277712yes—
778C22#1458277712yes—
779C22#1458277712yes—
780C22#1458277712yes—
781C22C2×C22⋊C4×D4311yescharacteristic
782C22C2×#1306328711yescharacteristic
783C22C2×C4×D17211yescharacteristic
784C22C2×#1306329511yescharacteristic
785C22C2×#1306329811yescharacteristic
786C22C2×#1306330011yescharacteristic
787C22C2×#1306331011yescharacteristic
788C4—44no—
789C4—44no—
790C4—82no—
791C4—864no—
792C4—3442no—
793C4—1724no—
794C4—1722no—
795C2—21no—
796C2—21no—
797C2—21no—
798C2—21no—
799C2—21no—
800C2—22no—
801C2—22no—
802C2—21no—
803C2—22no—
804C2—22no—
805C2—3442no—
806C2—1724no—
807C2C2×#1458277711yescharacteristic
808C2#1914305312yes—
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC24C23×D43
FittingC2×C43×#342C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#14583461C2
cosocleC24×C43C24
hypercenterC2×#342D43
hypocenterC43#20984
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C25 ◁ C2×#342

Complements

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

NH ≅ G/Ntype
2. C2×#14583372C2semidirect
3. C22×#13063239C2semidirect
4. C22×#13063239C2semidirect
5. #19137170C2semidirect
6. #19135052C2semidirect
7. #19135047C2semidirect
8. C2×#14582666C2semidirect
9. C2×C43×#342C2semidirect
16. C2×#13063309C4semidirect
18. C2×#13063299C4semidirect
19. C2×#13063295C4semidirect
25. C2×#13063281C22semidirect
28. C2×C22⋊C4×D43C22semidirect
35. #14582760C22semidirect
36. #14582754C22semidirect
37. #14582666C22semidirect
41. C43×#342C22semidirect
42. C24×D43C2×C4semidirect
44. C22×D172C2×C4semidirect
59. C22×C22⋊D43C2×C4semidirect
67. C23×Dic43C2×C4semidirect
84. C2×C4⋊Dic43C2×C4semidirect
91. C2×C22⋊Dic43D4semidirect
96. C2×(C2×D43)⋊C4C2×C4semidirect
97. C2×(C2×D43)⋊C4C2×C4semidirect
107. C23×C4×C43C2×C4semidirect
117. C2×C22⋊C4×C43C2×C4semidirect
118. C2×C22⋊C4×C43D4semidirect
399. C2×#342D43semidirect
445. #342C2×D43semidirect
446. C43#20984semidirect
478. C23×C4C4×D43semidirect
518. C2×C22⋊C4C4×D43semidirect
519. C2×C22⋊C4D172semidirect

Maximal subgroups

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

subgroupindex
C2×#145834612
C2×#145833722
C22×#130632392
#191371702
#191350522
#191350472
C2×#145826662
C2×C43×#3422
#2098443