Finite Group Databasebeta

← #25102321

Subgroups — #25102321

Order 11008.

1616 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583373C211yesmaximal, characteristic, complemented
2C2×#14583032C211yesmaximal, characteristic
3C2×#14583008C211yesmaximal, characteristic, complemented
4C2×#14582979C211yesmaximal, characteristic, complemented
5#19137290C211yesmaximal, characteristic, complemented
6#19134940C211yesmaximal, characteristic, complemented
7#19134940C211yesmaximal, characteristic, complemented
8#19134857C211yesmaximal, characteristic, complemented
9#19134843C211yesmaximal, characteristic, complemented
10#19134794C211yesmaximal, characteristic, complemented
11#19134527C211yesmaximal, characteristic, complemented
12#19134419C211yesmaximal, characteristic, complemented
13#19134409C211yesmaximal, characteristic, complemented
14#19134363C211yesmaximal, characteristic, complemented
15C43×#1875C211yesmaximal, characteristic, complemented
16C23×D172C2211yescharacteristic
17C22×#10621882C2211yescharacteristic
18C22×#10621882C2211yescharacteristic
19#14583373—24no—
20#14583373—24no—
21C2×C4×D172—21no—
22C2×C4×D172—21no—
23C2×D4×Dic43C2211yescharacteristic, complemented
24C2×#13063287C2211yescharacteristic
25C2×#13063287C2211yescharacteristic
26C2×#13063287C2211yescharacteristic
27C2×#13063287C2211yescharacteristic
28C2×#13063284C2211yescharacteristic
29C2×C22⋊C4×D43—21no—
30C2×C22⋊C4×D43—21no—
31#14583032C418yescomplemented
32#14583008—24no—
33#14582979—24no—
34C2×#13063258C2211yescharacteristic, complemented
35C2×#13063256C2211yescharacteristic, complemented
36C2×#13063247C2211yescharacteristic
37C2×#13063247C2211yescharacteristic
38C2×#13063247C2211yescharacteristic
39C2×#13063247C2211yescharacteristic
40C2×#13063245C2211yescharacteristic
41C2×#13063245C2211yescharacteristic
42C2×C22⋊(C43⋊C8)C2211yescharacteristic
43C2×#13063235C2211yescharacteristic, complemented
44C2×C8×Dic43C2211yescharacteristic, complemented
45#14582802—21no—
46#14582802C2211yescharacteristic, complemented
47#14582798C2211yescharacteristic, complemented
48#14582792—21no—
49#14582779—21no—
50#14582774—21no—
51#14582759C2211yescharacteristic
52C4⋊C4×Dic43C2211yescharacteristic, complemented
53#14582661C2211yescharacteristic, complemented
54#14582661C2211yescharacteristic, complemented
55#14582653C2211yescharacteristic, complemented
56#14582653C2211yescharacteristic, complemented
57C2×#121×C43C2211yescharacteristic
58C2×#117×C43C2211yescharacteristic
59C2×#102×C43C2211yescharacteristic, complemented
60C2×#102×C43C2211yescharacteristic, complemented
61C2×C22⋊C8×C43C2211yescharacteristic
62C43×#340C2211yescharacteristic, complemented
63C43×#340C2211yescharacteristic, complemented
64C24×D43—21no—
65C22×D172—21no—
66C22×D172—22no—
67C22×D172—22no—
68C22×D172—22no—
69C22×D172—22no—
70C22×D172—22no—
71C22×D172C2×C414yescomplemented
72C22×D172C2311yescharacteristic
73C22×D172C2311yescharacteristic
74C23×Dic43—21no—
75C22×C4×D43—21no—
76C22×C4×D43—21no—
77C22×C4×D43—21no—
78C22×C4×D43—21no—
79C2×#10621882—22no—
80C2×#10621882—22no—
81C2×#10621882—22no—
82C2×#10621882—22no—
83C2×#10621882C2×C414yescomplemented
84C2×#10621882C2×C414yescomplemented
85C22×C43⋊C8C2311yescharacteristic
86C22×C43⋊C8C2311yescharacteristic
87C4×D172—28no—
88C4×D172—28no—
89D4×Dic43—22no—
90D4×Dic43—22no—
91#13063287—22no—
92#13063287—22no—
93#13063287—22no—
94#13063287—22no—
95#13063287—22no—
96#13063287—22no—
97#13063287D414yescomplemented
98#13063287D414yescomplemented
99#13063284—22no—
100#13063284—22no—
101C2×C4⋊Dic43—21no—
102C2×C4⋊Dic43D411yescharacteristic
103C2×C4⋊Dic43D411yescharacteristic
104C2×C4⋊Dic43C2311yescharacteristic
105C2×C4⋊Dic43C2311yescharacteristic
106C2×C22⋊Dic43—21no—
107C2×C22⋊Dic43—21no—
108C2×C22⋊Dic43—21no—
109C2×C22⋊Dic43—21no—
110C2×C22⋊Dic43D411yescharacteristic
111C2×C22⋊Dic43D411yescharacteristic
112C2×(C2×D43)⋊C4—21no—
113C2×(C2×D43)⋊C4—21no—
114C2×(C2×D43)⋊C4—21no—
115C2×(C2×D43)⋊C4—21no—
116C22⋊C4×D43—28no—
117C22⋊C4×D43—28no—
118C2×C4×Dic43—21no—
119C2×C4×Dic43C2311yescharacteristic
120C2×C4×Dic43C2311yescharacteristic
121#13063258—22no—
122#13063256—22no—
123#13063247—22no—
124#13063247—22no—
125#13063247—22no—
126#13063247—22no—
127#13063245C2×C414yescomplemented
128#13063245C2×C414yescomplemented
129C22⋊(C43⋊C8)C2×C414yescomplemented
130#13063235—22no—
131C8×Dic43—22no—
132C43⋊#95—21no—
133C43⋊#95—21no—
134C43⋊#95—21no—
135C22×D4×C43—21no—
136C22×D4×C43C2311yescharacteristic
137C23×C4×C43C2311yescharacteristic
138C22×C8×C43C2311yescharacteristic
139C22×C8×C43C2311yescharacteristic
140#121×C43—22no—
141#121×C43C2×C414yescomplemented
142#117×C43—22no—
143#117×C43—22no—
144C2×C4⋊C4×C43C2311yescharacteristic
145C2×C4⋊C4×C43C2311yescharacteristic
146C2×C4⋊C4×C43C2311yescharacteristic
147C2×C22⋊C4×C43—21no—
148C2×C22⋊C4×C43—21no—
149C2×C42×C43—21no—
150#102×C43—22no—
151#102×C43—22no—
152C22⋊C8×C43—22no—
153C24×C43—21no—
154C24×C43C2×D411yescharacteristic
155C23×D43—21no—
156C23×D43—21no—
157C23×D43—24no—
158C23×D43—24no—
159C23×D43—24no—
160C23×D43—81no—
161C23×D43—81no—
162C23×D43—81no—
163C23×D43—81no—
164C2×D4×C43—21no—
165C2×D4×C43—24no—
166C2×D4×C43—21no—
167C2×D4×C43—21no—
168C2×D4×C43—21no—
169C2×D4×C43—21no—
170C2×D4×C43—81no—
171C2×D4×C43—81no—
172C2×D4×C43C22×C412yes—
173C22×C4×C43—21no—
174C22×C4×C43—21no—
175C22×C4×C43—21no—
176C22×C4×C43—21no—
177C22×C4×C43—21no—
178C22×C4×C43—21no—
179C22×C4×C43—21no—
180C22×C4×C43C22×C412yes—
181C22×C4×C43C2×D411yescharacteristic
182C22×C4×C43#4112yes—
183C22×C4×C43C2411yescharacteristic
184C22×Dic43—21no—
185C22×Dic43—21no—
186C22×Dic43—42no—
187C22×Dic43—81no—
188C22×Dic43—81no—
189C22×Dic43C2×D411yescharacteristic
190C22×Dic43C2×D411yescharacteristic
191C22×Dic43C2×D411yescharacteristic
192C22×Dic43C2×D411yescharacteristic
193C2×D172—24no—
194C2×D172—24no—
195C2×D172—28no—
196C2×D172—28no—
197C2×D172—24no—
198C2×D172—21no—
199C2×D172—21no—
200C2×D172—21no—
201C2×D172—21no—
202C2×D172—21no—
203C2×D172—21no—
204C2×D172—28no—
205C2×D172—28no—
206C2×D172C22×C412yes—
207C2×D172C22×C412yes—
208C2×D172C2×D412yes—
209C2×D172C2×D412yes—
210C2×D172#4112yes—
211C2×D172#4112yes—
212C2×C4×D43—24no—
213C2×C4×D43—24no—
214C2×C4×D43—24no—
215C2×C4×D43—24no—
216C2×C4×D43—81no—
217C2×C4×D43—81no—
218C2×C4×D43—81no—
219C2×C4×D43—81no—
220C2×C4×D43—81no—
221C2×C4×D43—81no—
222C2×C4×D43—81no—
223C2×C4×D43—81no—
224C2×C8×C43—21no—
225C2×C8×C43—21no—
226C2×C8×C43—21no—
227C2×C8×C43—21no—
228C2×C8×C43—21no—
229C2×C8×C43—21no—
230C4⋊C4×C43—21no—
231C4⋊C4×C43—21no—
232C4⋊C4×C43—21no—
233C4⋊C4×C43C22×C412yes—
234C4⋊C4×C43C2×D412yes—
235C4⋊C4×C43C2×D412yes—
236C22⋊C4×C43—24no—
237C22⋊C4×C43—24no—
238C42×C43—24no—
239C22⋊Dic43—22no—
240C22⋊Dic43—22no—
241C22⋊Dic43—42no—
242C22⋊Dic43—81no—
243C22⋊Dic43—81no—
244C22⋊Dic43—81no—
245#10621882—28no—
246#10621882—28no—
247(C2×D43)⋊C4—24no—
248(C2×D43)⋊C4—24no—
249(C2×D43)⋊C4—24no—
250(C2×D43)⋊C4—24no—
251C4⋊Dic43—22no—
252C4⋊Dic43—22no—
253C4⋊Dic43—21no—
254C4⋊Dic43—21no—
255C4⋊Dic43—21no—
256C4⋊Dic43—21no—
257C4⋊Dic43—81no—
258C4×Dic43—21no—
259C4×Dic43—21no—
260C4×Dic43—81no—
261C4×Dic43C2×D412yes—
262C4×Dic43C2×D412yes—
263C2×C43⋊C8—21no—
264C2×C43⋊C8—21no—
265C2×C43⋊C8—21no—
266C2×C43⋊C8—21no—
267C2×C43⋊C8C22×C412yes—
268C2×C43⋊C8C22×C412yes—
269C23×C43—21no—
270C23×C43—21no—
271C23×C43—21no—
272C23×C43—21no—
273C23×C43—21no—
274C23×C43—21no—
275C23×C43—22no—
276C23×C43—41no—
277C23×C43—41no—
278C23×C43—41no—
279C23×C43—41no—
280C23×C43—41no—
281C23×C43—41no—
282C23×C43C4×D412yes—
283C23×C43C22×D411yescharacteristic
284C22×D43—22no—
285C22×D43—22no—
286C22×D43—22no—
287C22×D43—22no—
288C22×D43—22no—
289C22×D43—22no—
290C22×D43—216no—
291C22×D43—41no—
292C22×D43—41no—
293C22×D43—41no—
294C22×D43—41no—
295C22×D43—41no—
296C22×D43—41no—
297C22×D43—41no—
298C22×D43—41no—
299C22×D43—84no—
300C22×D43—84no—
301C22×D43—84no—
302C22×D43—84no—
303C22×D43—84no—
304C22×D43—84no—
305D4×C43—22no—
306D4×C43—22no—
307D4×C43—41no—
308D4×C43—41no—
309D4×C43—84no—
310C2×C4×C43—21no—
311C2×C4×C43—21no—
312C2×C4×C43—22no—
313C2×C4×C43—22no—
314C2×C4×C43—22no—
315C2×C4×C43—22no—
316C2×C4×C43—22no—
317C2×C4×C43—22no—
318C2×C4×C43—22no—
319C2×C4×C43—41no—
320C2×C4×C43—41no—
321C2×C4×C43—41no—
322C2×C4×C43—41no—
323C2×C4×C43—41no—
324C2×C4×C43—41no—
325C2×C4×C43C4×D412yes—
326C2×C4×C43C23×C411yescharacteristic
327C2×C4×C43C22×D411yescharacteristic
328C2×C4×C43C22×D411yescharacteristic
329C2×C4×C43C2×#4111yescharacteristic
330C2×C4×C43C2×#4111yescharacteristic
331C2×C4×C43C2×#4111yescharacteristic
332C2×Dic43—21no—
333C2×Dic43—21no—
334C2×Dic43—21no—
335C2×Dic43—21no—
336C2×Dic43—21no—
337C2×Dic43—21no—
338C2×Dic43—21no—
339C2×Dic43—21no—
340C2×Dic43—21no—
341C2×Dic43—21no—
342C2×Dic43—41no—
343C2×Dic43—41no—
344C2×Dic43—41no—
345C2×Dic43—41no—
346C2×Dic43—41no—
347C2×Dic43—41no—
348C2×Dic43—84no—
349C2×Dic43#12012yes—
350C2×Dic43#12012yes—
351D172—216no—
352D172—22no—
353D172—22no—
354D172—22no—
355D172—22no—
356D172—22no—
357D172—22no—
358D172C4×D414yes—
359D172C4×D414yes—
360C4×D43—84no—
361C4×D43—84no—
362C4×D43—84no—
363C4×D43—84no—
364C8×C43—41no—
365C8×C43—41no—
366C43⋊C8—22no—
367C43⋊C8—22no—
368#21458—431nomaximal, Sylow
369C22×C43—22no—
370C22×C43—22no—
371C22×C43—22no—
372C22×C43—41no—
373C22×C43—41no—
374C22×C43—41no—
375C22×C43—41no—
376C22×C43—42no—
377C22×C43—42no—
378C22×C43—42no—
379C22×C43—81no—
380C22×C43—81no—
381C22×C43—81no—
382C22×C43—81no—
383C22×C43C2×C4×D411yescharacteristic
384C22×C43C2×#12011yescharacteristic
385C22×C43#52511yescharacteristic
386C22×C43#57611yescharacteristic
387C22×C43#57611yescharacteristic
388C22×C43#57611yescharacteristic
389C22×C43#57711yescharacteristic
390C2×D43—24no—
391C2×D43—24no—
392C2×D43—42no—
393C2×D43—42no—
394C2×D43—42no—
395C2×D43—42no—
396C2×D43—42no—
397C2×D43—42no—
398C2×D43—42no—
399C2×D43—42no—
400C2×D43—42no—
401C2×D43—42no—
402C2×D43—42no—
403C2×D43—42no—
404C2×D43—816no—
405C4×C43—22no—
406C4×C43—42no—
407C4×C43—42no—
408C4×C43—42no—
409C4×C43C2×C4×D411yescharacteristic
410C4×C43C2×C4×D411yescharacteristic
411C4×C43#52511yescharacteristic
412C4×C43#52511yescharacteristic
413Dic43—22no—
414Dic43—22no—
415Dic43—41no—
416Dic43—41no—
417Dic43—81no—
418Dic43—81no—
419C2×#518—431no—
420C2×#447—431no—
421C2×#442—431no—
422C2×C4×D8—431no—
423#2324—431no—
424#1879—431no—
425#1879—431no—
426#1875D4311yescharacteristic, complemented
427#1864—431no—
428#1862—431no—
429#1854—431no—
430#1786—431no—
431#1762—431no—
432C4×#102—431no—
433#1750—431no—
434C2×C43—42no—
435C2×C43—82no—
436C2×C43C4×#12011yescharacteristic
437C2×C43#294611yescharacteristic
438C2×C43#294811yescharacteristic
439C2×C43#300811yescharacteristic
440C2×C43#301211yescharacteristic
441C2×C43#311811yescharacteristic
442C2×C43#312211yescharacteristic
443D43—44no—
444D43—44no—
445C23×D4—431no—
446C22×D8—431no—
447C22×D8—431no—
448C2×#121C2×D4311yescharacteristic
449#518—864no—
450#518—864no—
451C2×C4×D4—431no—
452C2×C4×D4—431no—
453C2×C4×D4—431no—
454C2×C4×D4—431no—
455C2×C4×D4—431no—
456C2×C4×D4—861no—
457C2×C4×D4—861no—
458C2×#117—431no—
459C2×#117C2×D4311yescharacteristic
460C22×C22⋊C4—861no—
461C22×C22⋊C4—861no—
462#447—438no—
463#442—864no—
464C4×D8—864no—
465C2×#107—431no—
466C2×#106—431no—
467C2×#102—431no—
468C2×#102—431no—
469C2×#102—431no—
470C2×#102—431no—
471C2×#102—431no—
472C2×#102—431no—
473C2×#102C2×D4311yescharacteristic, complemented
474C2×#102C2×D4311yescharacteristic, complemented
475C2×C22⋊C8—431no—
476C2×C22⋊C8C2×D4311yescharacteristic
477C2×#97—431no—
478C2×C4×C8—431no—
479#390—431no—
480#390—861no—
481#389—431no—
482#388—861no—
483#386—861no—
484#385—861no—
485#380—431no—
486C4×C4⋊C4—431no—
487#340—431no—
488#340—431no—
489#340C2×D4311yescharacteristic, complemented
490#340C2×D4311yescharacteristic, complemented
491#336—431no—
492#336—431no—
493C43#2145811yescharacteristic, complemented, Sylow
494C25—861no—
495C22×D4—21no—
496C22×D4—434no—
497C22×D4—431no—
498C22×D4—431no—
499C22×D4—862no—
500C22×D4—862no—
501C22×D4—862no—
502C22×D4—862no—
503C22×D4—861no—
504C22×D4—862no—
505C22×D4C22×D4311yescharacteristic
506C23×C4—861no—
507C23×C4—861no—
508C23×C4—861no—
509C23×C4—861no—
510C23×C4—861no—
511C23×C4C22×D4311yescharacteristic
512C2×D8—434no—
513C2×D8—434no—
514C2×D8—862no—
515C2×D8—862no—
516C2×D8—862no—
517C2×D8—862no—
518C22×C8—431no—
519C22×C8—431no—
520C22×C8C22×D4311yescharacteristic
521C22×C8C22×D4311yescharacteristic
522#121—22no—
523#121C4×D4314yescomplemented
524C4×D4—434no—
525C4×D4—434no—
526C4×D4—868no—
527C4×D4—868no—
528C4×D4—862no—
529C4×D4—862no—
530C4×D4—862no—
531C4×D4—862no—
532C4×D4—862no—
533C4×D4—862no—
534C4×D4—862no—
535C4×D4—862no—
536#117—22no—
537#117—22no—
538#117—862no—
539#117—862no—
540C2×C4⋊C4—431no—
541C2×C4⋊C4—431no—
542C2×C4⋊C4—431no—
543C2×C4⋊C4—431no—
544C2×C4⋊C4—861no—
545C2×C4⋊C4C22×D4311yescharacteristic
546C2×C4⋊C4C22×D4311yescharacteristic
547C2×C4⋊C4C22×D4311yescharacteristic
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—431no—
551C2×C22⋊C4—431no—
552C2×C22⋊C4—868no—
553C2×C22⋊C4—868no—
554C2×C22⋊C4—861no—
555C2×C22⋊C4—861no—
556C2×C22⋊C4—861no—
557C2×C22⋊C4—861no—
558C2×C22⋊C4—861no—
559C2×C22⋊C4—861no—
560C2×C22⋊C4—861no—
561C2×C22⋊C4—861no—
562C2×C42—21no—
563C2×C42—431no—
564C2×C42—431no—
565C2×C42—861no—
566#107—862no—
567#106—862no—
568#102—22no—
569#102—22no—
570#102—434no—
571#102—434no—
572#102—862no—
573#102—862no—
574#102—862no—
575#102—862no—
576C22⋊C8—22no—
577C22⋊C8—434no—
578#97—862no—
579C4×C8—862no—
580#95—861no—
581#95—861no—
582#95—861no—
583C24—21no—
584C24—864no—
585C24—864no—
586C24—864no—
587C24—861no—
588C24—861no—
589C24—3441no—
590C24—3441no—
591C24—3441no—
592C24—3441no—
593C24D4×D4311yescharacteristic
594C2×D4—24no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—81no—
601C2×D4—81no—
602C2×D4—432no—
603C2×D4—432no—
604C2×D4—432no—
605C2×D4—432no—
606C2×D4—432no—
607C2×D4—432no—
608C2×D4—868no—
609C2×D4—868no—
610C2×D4—864no—
611C2×D4—864no—
612C2×D4—868no—
613C2×D4—868no—
614C2×D4—864no—
615C2×D4—861no—
616C2×D4—861no—
617C2×D4—861no—
618C2×D4—861no—
619C2×D4—861no—
620C2×D4—861no—
621C2×D4C2×C4×D4312yes—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—431no—
630C22×C4—431no—
631C22×C4—431no—
632C22×C4—431no—
633C22×C4—864no—
634C22×C4—864no—
635C22×C4—864no—
636C22×C4—864no—
637C22×C4—861no—
638C22×C4—861no—
639C22×C4—3441no—
640C22×C4—3441no—
641C22×C4—3441no—
642C22×C4—3441no—
643C22×C4—3441no—
644C22×C4—3441no—
645C22×C4—3441no—
646C22×C4—3441no—
647C22×C4—3441no—
648C22×C4—3441no—
649C22×C4—1722no—
650C22×C4C2×C4×D4312yes—
651C22×C4D4×D4311yescharacteristic
652C22×C4#1062190012yes—
653C22×C4C23×D4311yescharacteristic
654D8—868no—
655D8—868no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—21no—
662C2×C8—432no—
663C2×C8—432no—
664C2×C8—861no—
665C2×C8—861no—
666C2×C8—861no—
667C2×C8—861no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—862no—
672C4⋊C4—862no—
673C4⋊C4—861no—
674C4⋊C4—861no—
675C4⋊C4—861no—
676C4⋊C4—861no—
677C4⋊C4—3441no—
678C4⋊C4C2×C4×D4312yes—
679C4⋊C4D4×D4312yes—
680C4⋊C4D4×D4312yes—
681C22⋊C4—24no—
682C22⋊C4—24no—
683C22⋊C4—864no—
684C22⋊C4—864no—
685C22⋊C4—864no—
686C22⋊C4—864no—
687C22⋊C4—862no—
688C22⋊C4—862no—
689C22⋊C4—3441no—
690C22⋊C4—3441no—
691C22⋊C4—3441no—
692C22⋊C4—1722no—
693C42—24no—
694C42—432no—
695C42—432no—
696C42—861no—
697C42—861no—
698C42—3441no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—22no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—8616no—
713C23—862no—
714C23—862no—
715C23—862no—
716C23—862no—
717C23—862no—
718C23—862no—
719C23—3444no—
720C23—3444no—
721C23—3444no—
722C23—3444no—
723C23—3444no—
724C23—3444no—
725C23—1721no—
726C23—1721no—
727C23—1721no—
728C23—1721no—
729C23—1721no—
730C23—1721no—
731C23—1721no—
732C23—1721no—
733C23(C22⋊D43)⋊C412yes—
734C23C2×D4×D4311yescharacteristic
735D4—22no—
736D4—22no—
737D4—41no—
738D4—41no—
739D4—84no—
740D4—434no—
741D4—434no—
742D4—8616no—
743D4—862no—
744D4—862no—
745D4—862no—
746D4—862no—
747D4—862no—
748D4—862no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—432no—
765C2×C4—432no—
766C2×C4—861no—
767C2×C4—861no—
768C2×C4—861no—
769C2×C4—861no—
770C2×C4—861no—
771C2×C4—861no—
772C2×C4—861no—
773C2×C4—861no—
774C2×C4—861no—
775C2×C4—861no—
776C2×C4—3444no—
777C2×C4—3444no—
778C2×C4—3444no—
779C2×C4—3444no—
780C2×C4—3444no—
781C2×C4—1721no—
782C2×C4—1721no—
783C2×C4—1721no—
784C2×C4—1721no—
785C2×C4—1721no—
786C2×C4—1721no—
787C2×C4(C22⋊D43)⋊C412yes—
788C2×C4C22×C4×D4311yescharacteristic
789C2×C4C2×D4×D4311yescharacteristic
790C2×C4C2×D4×D4311yescharacteristic
791C2×C4#41×D4311yescharacteristic
792C2×C4#41×D4311yescharacteristic
793C2×C4C2×#1062190011yescharacteristic
794C8—41no—
795C8—41no—
796C8—862no—
797C8—862no—
798C22—22no—
799C22—22no—
800C22—22no—
801C22—41no—
802C22—41no—
803C22—41no—
804C22—41no—
805C22—42no—
806C22—42no—
807C22—42no—
808C22—81no—
809C22—81no—
810C22—81no—
811C22—81no—
812C22—864no—
813C22—864no—
814C22—34416no—
815C22—1722no—
816C22—1722no—
817C22—1722no—
818C22—1722no—
819C22—1722no—
820C22—1722no—
821C22—1722no—
822C22—1722no—
823C22—1722no—
824C22—1722no—
825C22—1722no—
826C22—1722no—
827C22C2×(C22⋊D43)⋊C411yescharacteristic
828C22#120×D4311yescharacteristic
829C22#1458340711yescharacteristic
830C22#1458370111yescharacteristic
831C22#1458370311yescharacteristic
832C22#1458370311yescharacteristic
833C22#1458370611yescharacteristic
834C4—22no—
835C4—42no—
836C4—42no—
837C4—42no—
838C4—862no—
839C4—862no—
840C4—3441no—
841C4—3441no—
842C4—1721no—
843C4—1721no—
844C4C4×D4×D4311yescharacteristic
845C4C4×D4×D4311yescharacteristic
846C4#1458340911yescharacteristic
847C4#1458340911yescharacteristic
848C2—42no—
849C2—82no—
850C2—1724no—
851C2—1724no—
852C2#1913710011yescharacteristic
853C2#1914343011yescharacteristic
854C2#1914344311yescharacteristic
855C2#1914386011yescharacteristic
856C2#1914389711yescharacteristic
857C2#1914477411yescharacteristic
858C2#1914483411yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1875C2
socleC23×C43C22×D4
prime radicalC2×#14583032C2
cosocleC22×C4×C43C24
hypercenter#1875D43
hypocenterC43#21458
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1875

Complements

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

NH ≅ G/Ntype
1. C2×#14583373C2semidirect
3. C2×#14583008C2semidirect
4. C2×#14582979C2semidirect
5. #19137290C2semidirect
6. #19134940C2semidirect
7. #19134940C2semidirect
8. #19134857C2semidirect
9. #19134843C2semidirect
10. #19134794C2semidirect
11. #19134527C2semidirect
12. #19134419C2semidirect
13. #19134409C2semidirect
14. #19134363C2semidirect
15. C43×#1875C2semidirect
23. C2×D4×Dic43C22semidirect
31. #14583032C4semidirect
34. C2×#13063258C22semidirect
35. C2×#13063256C22semidirect
43. C2×#13063235C22semidirect
44. C2×C8×Dic43C22semidirect
46. #14582802C22semidirect
47. #14582798C22semidirect
52. C4⋊C4×Dic43C22semidirect
53. #14582661C22semidirect
54. #14582661C22semidirect
55. #14582653C22semidirect
56. #14582653C22semidirect
59. C2×#102×C43C22semidirect
60. C2×#102×C43C22semidirect
62. C43×#340C22semidirect
63. C43×#340C22semidirect
71. C22×D172C2×C4semidirect
83. C2×#10621882C2×C4semidirect
84. C2×#10621882C2×C4semidirect
97. #13063287D4semidirect
98. #13063287D4semidirect
127. #13063245C2×C4semidirect
128. #13063245C2×C4semidirect
129. C22⋊(C43⋊C8)C2×C4semidirect
141. #121×C43C2×C4semidirect
426. #1875D43semidirect
473. C2×#102C2×D43semidirect
474. C2×#102C2×D43semidirect
489. #340C2×D43semidirect
490. #340C2×D43semidirect
493. C43#21458semidirect
523. #121C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145833732
C2×#145830322
C2×#145830082
C2×#145829792
#191372902
#191349402
#191348572
#191348432
#191347942
#191345272
#191344192
#191344092
#191343632
C43×#18752
#2145843