Finite Group Databasebeta

← #25112059

Subgroups — #25112059

Order 11008.

1542 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583568C211yesmaximal, characteristic
2C2×(C22⋊D43)⋊C8C211yesmaximal, characteristic, complemented
3C2×#14582895C211yesmaximal, characteristic, complemented
4C2×#14582894C211yesmaximal, characteristic, complemented
5#19137539C211yesmaximal, characteristic, complemented
6#19135520C211yesmaximal, characteristic, complemented
7#19135399C211yesmaximal, characteristic, complemented
8#19135021C211yesmaximal, characteristic, complemented
9#19135020C211yesmaximal, characteristic, complemented
10#19134915C211yesmaximal, characteristic, complemented
11#19134914C211yesmaximal, characteristic, complemented
12#19134598C211yesmaximal, characteristic, complemented
13#19134534C211yesmaximal, characteristic, complemented
14#103×Dic43C211yesmaximal, characteristic, complemented
15C43×#1788C211yesmaximal, characteristic, complemented
16C22×#10621902C2211yescharacteristic
17C23×C43⋊C8C2211yescharacteristic
18C22×C8×D43C2211yescharacteristic
19#14583568—24no—
20#14583568C418yescomplemented
21C2×#13063321—21no—
22C2×#13063321C2211yescharacteristic
23C2×#13063299—21no—
24C2×#13063299C2211yescharacteristic
25C2×#13063296—21no—
26C2×#13063296C2211yescharacteristic
27C2×Q8×Dic43C2211yescharacteristic
28C2×C4×C22⋊D43—21no—
29C2×C4×C22⋊D43C2211yescharacteristic
30C2×#13063284C2211yescharacteristic
31C2×#13063283C2211yescharacteristic
32(C22⋊D43)⋊C8—24no—
33C2×Dic43⋊C8C2211yescharacteristic
34#14582895—24no—
35#14582894—24no—
36C2×#13063249C2211yescharacteristic
37C2×#13063249C2211yescharacteristic
38C2×#13063247C2211yescharacteristic
39C2×#13063247C2211yescharacteristic
40C2×#13063246C2211yescharacteristic
41C2×#13063246C2211yescharacteristic
42C2×#13063245C2211yescharacteristic
43C2×#13063245C2211yescharacteristic
44C2×(C2×D43)⋊C8C2211yescharacteristic
45C2×C8×Dic43C2211yescharacteristic
46#14582799—21no—
47#14582793—21no—
48#14582788—21no—
49#14582768C2211yescharacteristic
50#14582756C2211yescharacteristic
51C4⋊C4×Dic43C2211yescharacteristic
52#14582750—21no—
53#14582662C2211yescharacteristic
54#14582662C2211yescharacteristic
55#14582661C2211yescharacteristic
56#14582661C2211yescharacteristic
57C22×#41×C43C2211yescharacteristic
58C2×#103×C43C2211yescharacteristic
59C2×#103×C43C2211yescharacteristic
60C2×#102×C43C2211yescharacteristic
61C2×#102×C43C2211yescharacteristic
62C2×C22⋊C8×C43C2211yescharacteristic
63C43×#380C2211yescharacteristic
64C2×#10621902—22no—
65C2×#10621902—22no—
66C2×#10621902—22no—
67C2×#10621902—41no—
68C2×#10621902—41no—
69C2×#10621902C2×C414yes—
70C22×D172—21no—
71C22×D172C2311yescharacteristic
72C22×C22⋊D43—21no—
73C22×C22⋊D43—21no—
74C22×C22⋊D43—21no—
75C22×C22⋊D43—21no—
76C22×C22⋊D43D411yescharacteristic
77C22×C4×D43—21no—
78C22×C4×D43C2311yescharacteristic
79C22×C43⋊C8—22no—
80C22×C43⋊C8—22no—
81C22×C43⋊C8—41no—
82C22×C43⋊C8C2311yescharacteristic
83C22×C43⋊C8C2311yescharacteristic
84C2×C8×D43—22no—
85C2×C8×D43—22no—
86C2×C8×D43—41no—
87#13063321—28no—
88#13063321—22no—
89#13063321C2×C414yes—
90#13063299—22no—
91#13063299—28no—
92#13063299C2×C414yes—
93#13063296—22no—
94#13063296—28no—
95#13063296C2×C414yes—
96Q8×Dic43—22no—
97Q8×Dic43C2×C414yes—
98C4×C22⋊D43—28no—
99C4×C22⋊D43C2×C414yes—
100C4×C22⋊D43D414yes—
101#13063284—22no—
102#13063284—41no—
103#13063283—22no—
104#13063283—41no—
105C2×C4⋊Dic43—21no—
106C2×C4⋊Dic43C2311yescharacteristic
107C2×C4⋊Dic43C2311yescharacteristic
108C2×C4⋊Dic43C2311yescharacteristic
109C2×Dic43⋊C4—21no—
110C2×Dic43⋊C4—21no—
111C2×Dic43⋊C4D411yescharacteristic
112C2×C22⋊Dic43—21no—
113C2×C22⋊Dic43—21no—
114C2×C22⋊Dic43D411yescharacteristic
115C2×(C2×D43)⋊C4—21no—
116C2×(C2×D43)⋊C4—21no—
117C2×(C2×D43)⋊C4—21no—
118C2×(C2×D43)⋊C4D411yescharacteristic
119C2×C4×Dic43—21no—
120C2×C4×Dic43—21no—
121C2×C4×Dic43—21no—
122C2×C4×Dic43—21no—
123C2×C4×Dic43C2311yescharacteristic
124Dic43⋊C8—22no—
125#13063249—22no—
126#13063249D414yescomplemented
127#13063247—22no—
128#13063247—41no—
129#13063246—22no—
130#13063246—22no—
131#13063245—22no—
132#13063245—41no—
133(C2×D43)⋊C8—22no—
134C8×Dic43—22no—
135C43⋊#95—21no—
136C43⋊#95—21no—
137C2×#41×C43—22no—
138C2×#41×C43—22no—
139C2×#41×C43—22no—
140C2×#41×C43—41no—
141C2×#41×C43—41no—
142C2×#41×C43C2×C414yes—
143C22×Q8×C43C2311yescharacteristic
144C22×D4×C43—21no—
145C22×D4×C43C2311yescharacteristic
146C23×C4×C43—21no—
147C23×C4×C43C2311yescharacteristic
148C22×C8×C43C2311yescharacteristic
149C22×C8×C43C2311yescharacteristic
150C2×C4⋊C4×C43C2311yescharacteristic
151C2×C4⋊C4×C43C2311yescharacteristic
152C2×C22⋊C4×C43—21no—
153#103×C43—22no—
154#103×C43—22no—
155#102×C43—41no—
156#102×C43—41no—
157C22⋊C8×C43—22no—
158#95×C43—21no—
159C24×C43—21no—
160C24×C43C2×D411yescharacteristic
161C23×D43—21no—
162C23×D43C2×D411yescharacteristic
163#41×C43—28no—
164#41×C43—44no—
165#41×C43—44no—
166#41×C43—44no—
167C2×Q8×C43—21no—
168C2×Q8×C43—21no—
169C2×Q8×C43—21no—
170C2×Q8×C43C22×C412yes—
171C2×Q8×C43C2×D412yes—
172C2×Q8×C43#4112yes—
173C2×D4×C43—21no—
174C2×D4×C43—24no—
175C2×D4×C43—21no—
176C2×D4×C43—21no—
177C2×D4×C43—21no—
178C2×D4×C43—21no—
179C2×D4×C43—42no—
180C2×D4×C43—42no—
181C2×D4×C43C22×C412yes—
182C22×C4×C43—21no—
183C22×C4×C43—21no—
184C22×C4×C43—21no—
185C22×C4×C43—21no—
186C22×C4×C43—24no—
187C22×C4×C43—21no—
188C22×C4×C43—21no—
189C22×C4×C43—21no—
190C22×C4×C43—42no—
191C22×C4×C43—42no—
192C22×C4×C43C22×C412yes—
193C22×C4×C43C2×D412yes—
194C22×C4×C43C2×D411yescharacteristic
195C22×C4×C43C2411yescharacteristic
196C2×C22⋊D43—24no—
197C2×C22⋊D43—24no—
198C2×C22⋊D43—22no—
199C2×C22⋊D43—22no—
200C2×C22⋊D43—24no—
201C2×C22⋊D43—24no—
202C2×C22⋊D43—42no—
203C2×C22⋊D43—42no—
204C2×C22⋊D43—81no—
205C2×C22⋊D43—81no—
206C2×C22⋊D43—81no—
207C2×C22⋊D43—81no—
208C2×C22⋊D43—81no—
209C2×C22⋊D43—81no—
210C2×C22⋊D43C22⋊C414yes—
211C22×Dic43—21no—
212C22×Dic43—21no—
213C22×Dic43—21no—
214C22×Dic43C2×D411yescharacteristic
215C22×Dic43C2×D411yescharacteristic
216C22×Dic43C2×D411yescharacteristic
217#10621902—28no—
218#10621902—44no—
219#10621902—44no—
220#10621902—44no—
221C2×D172—21no—
222C2×D172—24no—
223C2×D172—21no—
224C2×D172—21no—
225C2×D172—21no—
226C2×D172—21no—
227C2×D172—42no—
228C2×D172—42no—
229C2×D172C22×C412yes—
230C2×C4×D43—21no—
231C2×C4×D43—21no—
232C2×C4×D43—21no—
233C2×C4×D43—21no—
234C2×C4×D43—24no—
235C2×C4×D43—42no—
236C2×C4×D43—42no—
237C2×C4×D43C22×C412yes—
238C2×C4×D43C2×D412yes—
239C2×C8×C43—21no—
240C2×C8×C43—21no—
241C2×C8×C43—21no—
242C2×C8×C43—21no—
243C2×C8×C43—21no—
244C2×C8×C43—21no—
245C4⋊C4×C43—21no—
246C4⋊C4×C43—21no—
247C4⋊C4×C43—21no—
248C4⋊C4×C43—21no—
249C22⋊C4×C43—81no—
250C22⋊Dic43—24no—
251C22⋊Dic43—42no—
252C22⋊Dic43C22⋊C414yes—
253(C2×D43)⋊C4—24no—
254(C2×D43)⋊C4—42no—
255(C2×D43)⋊C4—81no—
256(C2×D43)⋊C4C22⋊C414yes—
257C4⋊Dic43—21no—
258C4⋊Dic43—21no—
259C4⋊Dic43—24no—
260C4⋊Dic43—21no—
261C4⋊Dic43—21no—
262C4⋊Dic43C22×C412yes—
263C4⋊Dic43C2×D412yes—
264Dic43⋊C4—42no—
265Dic43⋊C4—81no—
266Dic43⋊C4C22⋊C414yes—
267C4×Dic43—24no—
268C4×Dic43—42no—
269C4×Dic43—42no—
270C4×Dic43—42no—
271C4×Dic43C22×C412yes—
272C4×Dic43C2×D412yes—
273C2×C43⋊C8—21no—
274C2×C43⋊C8—21no—
275C2×C43⋊C8—21no—
276C2×C43⋊C8—21no—
277C2×C43⋊C8—21no—
278C2×C43⋊C8—44no—
279C2×C43⋊C8C2×D412yes—
280C8×D43—44no—
281C23×C43—21no—
282C23×C43—21no—
283C23×C43—21no—
284C23×C43—21no—
285C23×C43—21no—
286C23×C43—21no—
287C23×C43—22no—
288C23×C43—41no—
289C23×C43—41no—
290C23×C43—41no—
291C23×C43—41no—
292C23×C43—41no—
293C23×C43—41no—
294C23×C43C2×C22⋊C412yes—
295C23×C43C22×D411yescharacteristic
296C22×D43—21no—
297C22×D43—21no—
298C22×D43—21no—
299C22×D43—21no—
300C22×D43—21no—
301C22×D43—21no—
302C22×D43—22no—
303C22×D43—41no—
304C22×D43—41no—
305C22×D43—41no—
306C22×D43—41no—
307C22×D43—41no—
308C22×D43—41no—
309C22×D43C2×C22⋊C412yes—
310Q8×C43—22no—
311Q8×C43—22no—
312Q8×C43—22no—
313Q8×C43C4×D414yes—
314D4×C43—22no—
315D4×C43—22no—
316D4×C43—48no—
317D4×C43—41no—
318D4×C43—41no—
319C2×C4×C43—22no—
320C2×C4×C43—21no—
321C2×C4×C43—22no—
322C2×C4×C43—22no—
323C2×C4×C43—21no—
324C2×C4×C43—22no—
325C2×C4×C43—22no—
326C2×C4×C43—22no—
327C2×C4×C43—22no—
328C2×C4×C43—48no—
329C2×C4×C43—41no—
330C2×C4×C43—41no—
331C2×C4×C43—41no—
332C2×C4×C43—41no—
333C2×C4×C43—41no—
334C2×C4×C43—41no—
335C2×C4×C43C2×C22⋊C412yes—
336C2×C4×C43C23×C411yescharacteristic
337C2×C4×C43C22×D411yescharacteristic
338C2×C4×C43C22×D411yescharacteristic
339C2×C4×C43C2×#4111yescharacteristic
340C2×C4×C43H(5,𝔽2)11yescharacteristic
341C2×C4×C43H(5,𝔽2)11yescharacteristic
342C22⋊D43—28no—
343C22⋊D43—48no—
344C22⋊D43—84no—
345C22⋊D43—84no—
346C22⋊D43—84no—
347C2×Dic43—21no—
348C2×Dic43—21no—
349C2×Dic43—21no—
350C2×Dic43—21no—
351C2×Dic43—22no—
352C2×Dic43—22no—
353C2×Dic43—41no—
354C2×Dic43—41no—
355C2×Dic43—41no—
356C2×Dic43—41no—
357C2×Dic43—41no—
358C2×Dic43—41no—
359C2×Dic43—41no—
360C2×Dic43C2×C22⋊C412yes—
361C2×Dic43C2×C22⋊C412yes—
362C2×Dic43C2×C22⋊C412yes—
363C2×Dic43#13512yes—
364C2×Dic43#13512yes—
365D172—22no—
366D172—22no—
367D172—48no—
368D172—41no—
369D172—41no—
370C4×D43—22no—
371C4×D43—22no—
372C4×D43—22no—
373C4×D43—22no—
374C4×D43—48no—
375C8×C43—41no—
376C8×C43—41no—
377C43⋊C8—22no—
378C43⋊C8—41no—
379#22418—431nomaximal, Sylow
380C22×C43—22no—
381C22×C43—22no—
382C22×C43—22no—
383C22×C43—41no—
384C22×C43—41no—
385C22×C43—41no—
386C22×C43—41no—
387C22×C43—42no—
388C22×C43—42no—
389C22×C43—42no—
390C22×C43—81no—
391C22×C43—81no—
392C22×C43—81no—
393C22×C43—81no—
394C22×C43C22×C22⋊C411yescharacteristic
395C22×C43D4211yescharacteristic
396C22×C43#54611yescharacteristic
397C22×C43C2×#13511yescharacteristic
398C22×C43C2×#13511yescharacteristic
399C22×C43#57611yescharacteristic
400C22×C43#57711yescharacteristic
401C2×D43—22no—
402C2×D43—22no—
403C2×D43—22no—
404C2×D43—41no—
405C2×D43—41no—
406C2×D43—41no—
407C2×D43—41no—
408C2×D43—42no—
409C2×D43—42no—
410C2×D43—42no—
411C2×D43—81no—
412C2×D43—81no—
413C2×D43—81no—
414C2×D43—81no—
415C4×C43—24no—
416C4×C43—22no—
417C4×C43—81no—
418C4×C43—81no—
419C4×C43C2×C4×D411yescharacteristic
420C4×C43#51811yescharacteristic
421C4×C43D4211yescharacteristic
422C4×C43#54611yescharacteristic
423Dic43—22no—
424Dic43—22no—
425Dic43—42no—
426Dic43—42no—
427Dic43—81no—
428Dic43#41614yescomplemented
429C2×#550—431no—
430C2×C8×D4—431no—
431C2×#416—431no—
432C2×#416—431no—
433#2354—431no—
434#1982—431no—
435#1957—431no—
436#1893—431no—
437#1893—431no—
438#1875—431no—
439#1875—431no—
440#1803—431no—
441#1788—431no—
442#1788D4311yescharacteristic, complemented
443C4×#103—431no—
444C2×C43—42no—
445C2×C43—82no—
446C2×C43D4×C22⋊C411yescharacteristic
447C2×C43C2×#41611yescharacteristic
448C2×C43#289711yescharacteristic
449C2×C43#328411yescharacteristic
450C2×C43#328711yescharacteristic
451C2×C43#330411yescharacteristic
452C2×C43#330511yescharacteristic
453D43—42no—
454D43—82no—
455C22×#41—431no—
456C22×#41C2×D4311yescharacteristic
457C23×C8—431no—
458C23×C8—431no—
459#550—438no—
460#550—864no—
461C2×#127—431no—
462C2×#127—861no—
463C2×#121—431no—
464C2×#121—431no—
465C2×#121—861no—
466C2×#121—861no—
467C2×C4×Q8—431no—
468C2×C4×D4—431no—
469C2×C4×D4—861no—
470C2×#117—431no—
471C2×#117—431no—
472C8×D4—864no—
473C2×C4⋊C8—431no—
474#416—864no—
475#416—864no—
476C2×#103—431no—
477C2×#103—431no—
478C2×#103C2×D4311yescharacteristic
479C2×#103C2×D4311yescharacteristic
480C2×#102—431no—
481C2×#102—431no—
482C2×#102—431no—
483C2×#102—431no—
484C2×#102—431no—
485C2×#102—431no—
486C2×#102C2×D4311yescharacteristic
487C2×#102C2×D4311yescharacteristic
488C2×C22⋊C8—431no—
489C2×C22⋊C8C2×D4311yescharacteristic
490C2×C4×C8—431no—
491#390—861no—
492#388—861no—
493#388—861no—
494#384—431no—
495#380—431no—
496#380C2×D4311yescharacteristic
497C4×C4⋊C4—431no—
498C4×C4⋊C4—861no—
499#340—431no—
500#340—431no—
501#340—431no—
502#340—431no—
503C43#2241811yescharacteristic, complemented, Sylow
504C2×#41—22no—
505C2×#41—22no—
506C2×#41—22no—
507C2×#41—41no—
508C2×#41—41no—
509C2×#41—434no—
510C2×#41—862no—
511C2×#41—862no—
512C2×#41—862no—
513C2×#41—1721no—
514C2×#41—1721no—
515C2×#41C4×D4314yes—
516C22×Q8C22×D4311yescharacteristic
517C22×D4—21no—
518C22×D4—431no—
519C22×D4—431no—
520C22×D4—861no—
521C22×D4—861no—
522C22×D4—861no—
523C22×D4—861no—
524C22×D4—861no—
525C22×D4C22×D4311yescharacteristic
526C23×C4—21no—
527C23×C4—431no—
528C23×C4—861no—
529C23×C4C22×D4311yescharacteristic
530C22×C8—431no—
531C22×C8—431no—
532C22×C8—862no—
533C22×C8—862no—
534C22×C8—862no—
535C22×C8—862no—
536C22×C8—1721no—
537C22×C8—1721no—
538C22×C8C22×D4311yescharacteristic
539C22×C8C22×D4311yescharacteristic
540#127—434no—
541#127—862no—
542#127—868no—
543#121—434no—
544#121—434no—
545#121—868no—
546#121—868no—
547#121—862no—
548#121—862no—
549C4×Q8—434no—
550C4×Q8—862no—
551C4×D4—434no—
552C4×D4—434no—
553C4×D4—868no—
554#117—862no—
555#117—862no—
556#117—1721no—
557#117—1721no—
558C2×C4⋊C4—431no—
559C2×C4⋊C4—431no—
560C2×C4⋊C4—431no—
561C2×C4⋊C4—431no—
562C2×C4⋊C4—861no—
563C2×C4⋊C4—861no—
564C2×C4⋊C4—861no—
565C2×C4⋊C4C22×D4311yescharacteristic
566C2×C4⋊C4C22×D4311yescharacteristic
567C2×C22⋊C4—21no—
568C2×C22⋊C4—431no—
569C2×C22⋊C4—431no—
570C2×C22⋊C4—861no—
571C2×C22⋊C4—861no—
572C2×C22⋊C4—861no—
573C2×C22⋊C4—861no—
574C2×C22⋊C4—861no—
575C2×C42—431no—
576C2×C42—861no—
577C2×C42—861no—
578C2×C42—861no—
579C2×C42—861no—
580C4⋊C8—862no—
581#103—22no—
582#103—22no—
583#103—434no—
584#103—862no—
585#102—41no—
586#102—41no—
587#102—862no—
588#102—862no—
589#102—862no—
590#102—862no—
591#102—1721no—
592#102—1721no—
593C22⋊C8—22no—
594C22⋊C8—862no—
595C4×C8—862no—
596#95—21no—
597#95—861no—
598#95—861no—
599C24—21no—
600C24—431no—
601C24—861no—
602C24D4×D4311yescharacteristic
603#41—28no—
604#41—44no—
605#41—44no—
606#41—44no—
607#41—868no—
608#41—1724no—
609#41—1724no—
610#41—1724no—
611C2×Q8—21no—
612C2×Q8—21no—
613C2×Q8—21no—
614C2×Q8C2×C4×D4312yes—
615C2×Q8D4×D4312yes—
616C2×Q8#1062190012yes—
617C2×D4—24no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—42no—
624C2×D4—42no—
625C2×D4—434no—
626C2×D4—432no—
627C2×D4—864no—
628C2×D4—862no—
629C2×D4—862no—
630C2×D4—864no—
631C2×D4—864no—
632C2×D4—864no—
633C2×D4—864no—
634C2×D4—861no—
635C2×D4—861no—
636C2×D4—861no—
637C2×D4—861no—
638C2×D4—861no—
639C2×D4—3441no—
640C2×D4—3441no—
641C2×D4—3441no—
642C2×D4—3441no—
643C2×D4—3441no—
644C2×D4—3441no—
645C2×D4—1722no—
646C2×D4—1722no—
647C2×D4—1722no—
648C2×D4—1722no—
649C2×D4C2×C4×D4312yes—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—24no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—42no—
659C22×C4—42no—
660C22×C4—431no—
661C22×C4—431no—
662C22×C4—431no—
663C22×C4—432no—
664C22×C4—432no—
665C22×C4—864no—
666C22×C4—861no—
667C22×C4—861no—
668C22×C4—861no—
669C22×C4—861no—
670C22×C4—861no—
671C22×C4—861no—
672C22×C4—861no—
673C22×C4—1722no—
674C22×C4—1722no—
675C22×C4C2×C4×D4312yes—
676C22×C4D4×D4311yescharacteristic
677C22×C4D4×D4312yes—
678C22×C4C23×D4311yescharacteristic
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—432no—
686C2×C8—861no—
687C2×C8—861no—
688C2×C8—861no—
689C2×C8—861no—
690C2×C8—861no—
691C2×C8—1724no—
692C2×C8—1724no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—434no—
698C4⋊C4—432no—
699C4⋊C4—432no—
700C4⋊C4—864no—
701C4⋊C4—861no—
702C4⋊C4—861no—
703C4⋊C4—861no—
704C4⋊C4—861no—
705C4⋊C4—3441no—
706C4⋊C4—1722no—
707C22⋊C4—81no—
708C22⋊C4—434no—
709C22⋊C4—434no—
710C22⋊C4—864no—
711C22⋊C4—864no—
712C22⋊C4—3441no—
713C22⋊C4—1722no—
714C22⋊C4—1722no—
715C42—432no—
716C42—432no—
717C42—864no—
718C42—1722no—
719C42—1722no—
720C42—1722no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—22no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—432no—
735C23—861no—
736C23—861no—
737C23—861no—
738C23—861no—
739C23—861no—
740C23—861no—
741C23—862no—
742C23—1721no—
743C23—1721no—
744C23—1721no—
745C23—1721no—
746C23—1721no—
747C23—1721no—
748C23C22⋊C4×D4312yes—
749C23C2×D4×D4311yescharacteristic
750Q8—22no—
751Q8—22no—
752Q8—22no—
753Q8(C22⋊D43)⋊C414yes—
754D4—22no—
755D4—22no—
756D4—48no—
757D4—41no—
758D4—41no—
759D4—868no—
760D4—862no—
761D4—862no—
762D4—3444no—
763D4—3444no—
764D4—3444no—
765D4—1728no—
766D4—1728no—
767D4—1721no—
768D4—1721no—
769C2×C4—22no—
770C2×C4—21no—
771C2×C4—22no—
772C2×C4—21no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—48no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—432no—
786C2×C4—432no—
787C2×C4—432no—
788C2×C4—432no—
789C2×C4—432no—
790C2×C4—861no—
791C2×C4—861no—
792C2×C4—861no—
793C2×C4—861no—
794C2×C4—862no—
795C2×C4—862no—
796C2×C4—862no—
797C2×C4—862no—
798C2×C4—862no—
799C2×C4—862no—
800C2×C4—1728no—
801C2×C4—1721no—
802C2×C4—1721no—
803C2×C4—1721no—
804C2×C4—1721no—
805C2×C4—1721no—
806C2×C4—1721no—
807C2×C4—1721no—
808C2×C4C22⋊C4×D4312yes—
809C2×C4C22×C4×D4311yescharacteristic
810C2×C4C2×D4×D4311yescharacteristic
811C2×C4C2×D4×D4311yescharacteristic
812C2×C4C2×#1062190011yescharacteristic
813C2×C4#1306337011yescharacteristic
814C2×C4#1306337011yescharacteristic
815C8—41no—
816C8—41no—
817C8—862no—
818C8—1721no—
819C22—22no—
820C22—22no—
821C22—22no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—42no—
827C22—42no—
828C22—42no—
829C22—81no—
830C22—81no—
831C22—81no—
832C22—81no—
833C22—862no—
834C22—862no—
835C22—862no—
836C22—3441no—
837C22—3441no—
838C22—3441no—
839C22—3441no—
840C22—1722no—
841C22—1722no—
842C22—1722no—
843C22—1721no—
844C22—1721no—
845C22—1721no—
846C22—1721no—
847C22C2×C22⋊C4×D4311yescharacteristic
848C22#1458353111yescharacteristic
849C22#1458353611yescharacteristic
850C22#135×D4311yescharacteristic
851C22#135×D4311yescharacteristic
852C22#1458370311yescharacteristic
853C22#1458370811yescharacteristic
854C4—22no—
855C4—24no—
856C4—81no—
857C4—81no—
858C4—434no—
859C4—862no—
860C4—862no—
861C4—3441no—
862C4—1722no—
863C4—1722no—
864C4C2×(C22⋊D43)⋊C411yescharacteristic
865C4#1458337211yescharacteristic
866C4#1458353111yescharacteristic
867C4#1458353611yescharacteristic
868C2—42no—
869C2—82no—
870C2—3442no—
871C2—1722no—
872C2#1913741111yescharacteristic
873C2#416×D4311yescharacteristic
874C2#1914311911yescharacteristic
875C2#1914631811yescharacteristic
876C2#1914634811yescharacteristic
877C2#1914652711yescharacteristic
878C2#1914653811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1788C2
socleC23×C43C22×D4
prime radicalC2×#14583568C2
cosocleC22×C4×C43C24
hypercenter#1788D43
hypocenterC43#22418
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1788

Complements

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

NH ≅ G/Ntype
2. C2×(C22⋊D43)⋊C8C2semidirect
3. C2×#14582895C2semidirect
4. C2×#14582894C2semidirect
5. #19137539C2semidirect
6. #19135520C2semidirect
7. #19135399C2semidirect
8. #19135021C2semidirect
9. #19135020C2semidirect
10. #19134915C2semidirect
11. #19134914C2semidirect
12. #19134598C2semidirect
13. #19134534C2semidirect
14. #103×Dic43C2semidirect
15. C43×#1788C2semidirect
20. #14583568C4semidirect
126. #13063249D4semidirect
428. Dic43#416semidirect
442. #1788D43semidirect
503. C43#22418semidirect

Maximal subgroups

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

subgroupindex
C2×#145835682
C2×(C22⋊D43)⋊C82
C2×#145828952
C2×#145828942
#191375392
#191355202
#191353992
#191350212
#191350202
#191349152
#191349142
#191345982
#191345342
#103×Dic432
C43×#17882
#2241843