Finite Group Databasebeta

← #25134218

Subgroups — #25134218

Order 11008.

1632 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583133C211yesmaximal, characteristic, complemented
2C2×#14583044C211yesmaximal, characteristic, complemented
3C2×#14583033C211yesmaximal, characteristic, complemented
4C2×#14582895C211yesmaximal, characteristic, complemented
5#19138013C211yesmaximal, characteristic, complemented
6#19135831C211yesmaximal, characteristic, complemented
7#19135795C211yesmaximal, characteristic, complemented
8#19135672C211yesmaximal, characteristic, complemented
9#19135596C211yesmaximal, characteristic, complemented
10#19134943C211yesmaximal, characteristic, complemented
11#19134918C211yesmaximal, characteristic, complemented
12#19134888C211yesmaximal, characteristic, complemented
13#19134842C211yesmaximal, characteristic, complemented
14#19134526C211yesmaximal, characteristic, complemented
15C2×C43×#546C211yesmaximal, characteristic, complemented
16C22×#10621884C2211yescharacteristic, complemented
17C22×#10621882C2211yescharacteristic
18C22×#10621882C2211yescharacteristic
19C23×C43⋊C8C2211yescharacteristic, complemented
20C2×#13063299C2211yescharacteristic
21C2×#13063299C2211yescharacteristic, complemented
22C2×#13063284C2211yescharacteristic, complemented
23#14583133—24no—
24#14583044—24no—
25#14583033—24no—
26C2×#13063258C2211yescharacteristic, complemented
27#14582895—24no—
28C2×#13063249C2211yescharacteristic, complemented
29C2×#13063249C2211yescharacteristic, complemented
30C2×#13063249C2211yescharacteristic, complemented
31C2×#13063246C2211yescharacteristic
32C2×#13063246C2211yescharacteristic
33C2×#13063246C2211yescharacteristic
34C2×#13063246C2211yescharacteristic
35C2×#13063246C2211yescharacteristic
36C2×#13063246C2211yescharacteristic
37C2×#13063245C2211yescharacteristic, complemented
38C2×C22⋊(C43⋊C8)C2211yescharacteristic
39C2×C22⋊(C43⋊C8)C2211yescharacteristic
40C2×C22⋊(C43⋊C8)C2211yescharacteristic, complemented
41#14582814—21no—
42#14582807—21no—
43#14582801C2211yescharacteristic, complemented
44#14582799—21no—
45#14582797C2211yescharacteristic, complemented
46#14582789—21no—
47#14582759C2211yescharacteristic
48#14582661C2211yescharacteristic, complemented
49#14582661C2211yescharacteristic, complemented
50#14582654C2211yescharacteristic, complemented
51#14582654C2211yescharacteristic, complemented
52C22×#41×C43C2211yescharacteristic
53C23×D4×C43C2211yescharacteristic
54C43×#546—24no—
55C43×#546—24no—
56C2×#124×C43C2211yescharacteristic
57C2×#123×C43—21no—
58C2×C22⋊Q8×C43C2211yescharacteristic
59C2×#121×C43—21no—
60C2×#121×C43C2211yescharacteristic
61C2×#120×C43—21no—
62C2×C4×D4×C43C2211yescharacteristic
63C2×C4×D4×C43C2211yescharacteristic
64C22×C22⋊C4×C43—21no—
65C22×D172C2311yescharacteristic
66C22×C22⋊D43—21no—
67C22×C22⋊D43—21no—
68C2×#10621884—22no—
69C2×#10621884—41no—
70C2×#10621884—41no—
71C2×#10621882—22no—
72C2×#10621882—22no—
73C2×#10621882—22no—
74C2×#10621882—22no—
75C2×#10621882—22no—
76C2×#10621882—41no—
77C22×C43⋊C8—22no—
78C22×C43⋊C8—22no—
79C22×C43⋊C8—41no—
80C22×C43⋊C8C2311yescharacteristic
81C22×C43⋊C8C2311yescharacteristic
82C22×C43⋊C8C2311yescharacteristic
83C22×C43⋊C8C2311yescharacteristic
84#13063299—22no—
85#13063299—22no—
86#13063299—22no—
87#13063299—41no—
88#13063284—22no—
89#13063284—41no—
90C2×C4⋊Dic43C2311yescharacteristic
91C2×C4⋊Dic43C2311yescharacteristic
92C2×C4⋊Dic43C2311yescharacteristic
93C2×Dic43⋊C4—21no—
94C2×C22⋊Dic43—21no—
95C2×C22⋊Dic43—21no—
96C2×(C2×D43)⋊C4—21no—
97C2×(C2×D43)⋊C4—21no—
98C2×(C2×D43)⋊C4—21no—
99C2×(C2×D43)⋊C4—21no—
100C2×C4×Dic43—21no—
101#13063258—22no—
102#13063249—22no—
103#13063249—22no—
104#13063249—22no—
105#13063246—22no—
106#13063246—22no—
107#13063246—22no—
108#13063246—22no—
109#13063246—41no—
110#13063246D414yescomplemented
111#13063245—22no—
112C22⋊(C43⋊C8)—22no—
113C22⋊(C43⋊C8)—22no—
114C22⋊(C43⋊C8)—41no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C25×C43—21no—
118C2×#41×C43—22no—
119C2×#41×C43—22no—
120C2×#41×C43—22no—
121C2×#41×C43—41no—
122C2×#41×C43—41no—
123C2×#41×C43D414yescomplemented
124C22×Q8×C43C2311yescharacteristic
125C22×D4×C43—21no—
126C22×D4×C43—21no—
127C22×D4×C43—22no—
128C22×D4×C43—22no—
129C22×D4×C43—22no—
130C22×D4×C43—22no—
131C22×D4×C43—21no—
132C22×D4×C43—41no—
133C22×D4×C43—41no—
134C22×D4×C43D411yescharacteristic
135C22×D4×C43C2311yescharacteristic
136C22×D4×C43C2311yescharacteristic
137C23×C4×C43—21no—
138C23×C4×C43—21no—
139C23×C4×C43C2311yescharacteristic
140C23×C4×C43C2311yescharacteristic
141#124×C43—22no—
142#124×C43—22no—
143#123×C43—28no—
144C22⋊Q8×C43—22no—
145C22⋊Q8×C43—22no—
146#121×C43—28no—
147#121×C43—22no—
148#121×C43D414yescomplemented
149#120×C43—28no—
150C4×D4×C43—22no—
151C4×D4×C43—22no—
152C4×D4×C43—22no—
153C4×D4×C43—22no—
154C2×C4⋊C4×C43—21no—
155C2×C4⋊C4×C43D411yescharacteristic
156C2×C4⋊C4×C43C2311yescharacteristic
157C2×C22⋊C4×C43—28no—
158C2×C22⋊C4×C43—21no—
159C2×C22⋊C4×C43—21no—
160C2×C22⋊C4×C43—21no—
161C2×C22⋊C4×C43—21no—
162C2×C22⋊C4×C43—21no—
163C2×C22⋊C4×C43D411yescharacteristic
164C2×C22⋊C4×C43D411yescharacteristic
165C2×C42×C43C2311yescharacteristic
166C24×C43—21no—
167C24×C43—24no—
168C24×C43—21no—
169C24×C43—42no—
170C24×C43—42no—
171C24×C43—42no—
172C24×C43—42no—
173C24×C43—81no—
174C24×C43—81no—
175C24×C43C2×D411yescharacteristic
176C24×C43C2×D411yescharacteristic
177C23×D43—21no—
178#41×C43—28no—
179#41×C43—44no—
180#41×C43—44no—
181#41×C43—44no—
182C2×Q8×C43—21no—
183C2×Q8×C43—21no—
184C2×Q8×C43—21no—
185C2×Q8×C43—21no—
186C2×Q8×C43—21no—
187C2×Q8×C43C2×D412yes—
188C2×D4×C43—24no—
189C2×D4×C43—21no—
190C2×D4×C43—21no—
191C2×D4×C43—21no—
192C2×D4×C43—21no—
193C2×D4×C43—22no—
194C2×D4×C43—24no—
195C2×D4×C43—24no—
196C2×D4×C43—22no—
197C2×D4×C43—21no—
198C2×D4×C43—21no—
199C2×D4×C43—21no—
200C2×D4×C43—21no—
201C2×D4×C43—41no—
202C2×D4×C43—42no—
203C2×D4×C43—42no—
204C2×D4×C43—42no—
205C2×D4×C43—42no—
206C2×D4×C43—44no—
207C2×D4×C43—44no—
208C2×D4×C43—44no—
209C2×D4×C43—44no—
210C2×D4×C43—81no—
211C2×D4×C43—81no—
212C2×D4×C43C2×D412yes—
213C2×D4×C43C2×D412yes—
214C2×D4×C43C2×D412yes—
215C2×D4×C43#4112yes—
216C22×C4×C43—21no—
217C22×C4×C43—21no—
218C22×C4×C43—21no—
219C22×C4×C43—21no—
220C22×C4×C43—24no—
221C22×C4×C43—24no—
222C22×C4×C43—21no—
223C22×C4×C43—21no—
224C22×C4×C43—21no—
225C22×C4×C43—21no—
226C22×C4×C43—21no—
227C22×C4×C43—21no—
228C22×C4×C43—21no—
229C22×C4×C43—21no—
230C22×C4×C43—42no—
231C22×C4×C43—42no—
232C22×C4×C43—81no—
233C22×C4×C43—81no—
234C22×C4×C43C2×D412yes—
235C22×C4×C43C2×D412yes—
236C22×C4×C43C2×D411yescharacteristic
237C22×C4×C43C2×D411yescharacteristic
238C22×C4×C43C2×D411yescharacteristic
239C22×C4×C43C2×D411yescharacteristic
240C22×C4×C43C2411yescharacteristic
241C2×C22⋊D43—42no—
242C2×C22⋊D43—42no—
243C2×C22⋊D43—42no—
244C2×C22⋊D43—81no—
245C2×C22⋊D43—81no—
246C2×C22⋊D43—81no—
247C22×Dic43—21no—
248C22×Dic43—21no—
249C22×Dic43—21no—
250C2×D172—21no—
251C2×D172—21no—
252C2×D172—21no—
253C2×D172—21no—
254C2×D172—21no—
255C2×D172—21no—
256C4⋊C4×C43—24no—
257C4⋊C4×C43—22no—
258C4⋊C4×C43—21no—
259C4⋊C4×C43C2×D412yes—
260C22⋊C4×C43—24no—
261C22⋊C4×C43—24no—
262C22⋊C4×C43—24no—
263C22⋊C4×C43—24no—
264C22⋊C4×C43—22no—
265C22⋊C4×C43—24no—
266C22⋊C4×C43—22no—
267C42×C43—21no—
268C42×C43—21no—
269C22⋊Dic43—42no—
270C22⋊Dic43—81no—
271#10621884—44no—
272#10621882—44no—
273#10621882—44no—
274(C2×D43)⋊C4—42no—
275(C2×D43)⋊C4—42no—
276(C2×D43)⋊C4—42no—
277(C2×D43)⋊C4—81no—
278C4⋊Dic43—21no—
279C4⋊Dic43—21no—
280C4⋊Dic43—21no—
281C4⋊Dic43—21no—
282C4⋊Dic43—21no—
283C4⋊Dic43C2×D412yes—
284Dic43⋊C4—81no—
285C4×Dic43—42no—
286C2×C43⋊C8—21no—
287C2×C43⋊C8—21no—
288C2×C43⋊C8—21no—
289C2×C43⋊C8—21no—
290C2×C43⋊C8—21no—
291C2×C43⋊C8—21no—
292C2×C43⋊C8—21no—
293C2×C43⋊C8—21no—
294C2×C43⋊C8—21no—
295C2×C43⋊C8—21no—
296C2×C43⋊C8—21no—
297C2×C43⋊C8—44no—
298C2×C43⋊C8C2×D412yes—
299C23×C43—21no—
300C23×C43—22no—
301C23×C43—21no—
302C23×C43—21no—
303C23×C43—22no—
304C23×C43—21no—
305C23×C43—21no—
306C23×C43—22no—
307C23×C43—21no—
308C23×C43—21no—
309C23×C43—21no—
310C23×C43—21no—
311C23×C43—21no—
312C23×C43—21no—
313C23×C43—21no—
314C23×C43—22no—
315C23×C43—48no—
316C23×C43—48no—
317C23×C43—41no—
318C23×C43—41no—
319C23×C43—41no—
320C23×C43—41no—
321C23×C43—41no—
322C23×C43—41no—
323C23×C43—41no—
324C23×C43—41no—
325C23×C43—41no—
326C23×C43—41no—
327C23×C43—84no—
328C23×C43—84no—
329C23×C43—84no—
330C23×C43—84no—
331C23×C43—84no—
332C23×C43#12012yes—
333C23×C43#13512yes—
334C23×C43C22×D411yescharacteristic
335C22×D43—41no—
336C22×D43—41no—
337C22×D43—41no—
338C22×D43—41no—
339C22×D43—41no—
340C22×D43—41no—
341C22×D43—41no—
342Q8×C43—22no—
343Q8×C43—22no—
344Q8×C43—41no—
345Q8×C43—41no—
346D4×C43—22no—
347D4×C43—22no—
348D4×C43—22no—
349D4×C43—22no—
350D4×C43—22no—
351D4×C43—44no—
352D4×C43—48no—
353D4×C43—48no—
354D4×C43—41no—
355D4×C43—41no—
356D4×C43—84no—
357D4×C43#12114yes—
358C2×C4×C43—21no—
359C2×C4×C43—21no—
360C2×C4×C43—22no—
361C2×C4×C43—22no—
362C2×C4×C43—22no—
363C2×C4×C43—22no—
364C2×C4×C43—21no—
365C2×C4×C43—21no—
366C2×C4×C43—22no—
367C2×C4×C43—22no—
368C2×C4×C43—21no—
369C2×C4×C43—21no—
370C2×C4×C43—21no—
371C2×C4×C43—21no—
372C2×C4×C43—21no—
373C2×C4×C43—21no—
374C2×C4×C43—21no—
375C2×C4×C43—48no—
376C2×C4×C43—41no—
377C2×C4×C43—41no—
378C2×C4×C43—41no—
379C2×C4×C43—41no—
380C2×C4×C43—41no—
381C2×C4×C43—41no—
382C2×C4×C43—41no—
383C2×C4×C43—41no—
384C2×C4×C43—84no—
385C2×C4×C43#12012yes—
386C2×C4×C43C22×D411yescharacteristic
387C2×C4×C43C22×D411yescharacteristic
388C2×C4×C43C22×D411yescharacteristic
389C2×C4×C43C2×#4111yescharacteristic
390C2×C4×C43H(5,𝔽2)11yescharacteristic
391C2×C4×C43H(5,𝔽2)11yescharacteristic
392C22⋊D43—84no—
393C22⋊D43—84no—
394C2×Dic43—22no—
395C2×Dic43—41no—
396C2×Dic43—41no—
397C2×Dic43—41no—
398C2×Dic43—41no—
399C2×Dic43—41no—
400C2×Dic43—41no—
401C2×Dic43—41no—
402C2×Dic43—41no—
403D172—41no—
404D172—41no—
405D172—41no—
406D172—41no—
407C43⋊C8—22no—
408C43⋊C8—41no—
409C43⋊C8—41no—
410C43⋊C8—41no—
411#24428—431nomaximal, Sylow
412C22×C43—24no—
413C22×C43—22no—
414C22×C43—22no—
415C22×C43—22no—
416C22×C43—22no—
417C22×C43—22no—
418C22×C43—22no—
419C22×C43—41no—
420C22×C43—42no—
421C22×C43—41no—
422C22×C43—42no—
423C22×C43—41no—
424C22×C43—41no—
425C22×C43—42no—
426C22×C43—41no—
427C22×C43—42no—
428C22×C43—41no—
429C22×C43—42no—
430C22×C43—41no—
431C22×C43—41no—
432C22×C43—42no—
433C22×C43—42no—
434C22×C43—42no—
435C22×C43—42no—
436C22×C43—816no—
437C22×C43—81no—
438C22×C43—81no—
439C22×C43—81no—
440C22×C43—81no—
441C22×C43C2×#12011yescharacteristic
442C22×C43D4211yescharacteristic
443C22×C43#54611yescharacteristic
444C22×C43C2×#13511yescharacteristic
445C22×C43#57511yescharacteristic
446C22×C43#57611yescharacteristic
447C22×C43#57611yescharacteristic
448C2×D43—81no—
449C2×D43—81no—
450C2×D43—81no—
451C2×D43—81no—
452C2×D43—81no—
453C2×D43—81no—
454C2×D43—81no—
455C4×C43—22no—
456C4×C43—41no—
457C4×C43—42no—
458C4×C43—41no—
459C4×C43—41no—
460C4×C43—42no—
461C4×C43C2×#12111yescharacteristic
462C4×C43#53411yescharacteristic
463C4×C43D4211yescharacteristic
464C4×C43#54611yescharacteristic
465Dic43—42no—
466Dic43—81no—
467Dic43—81no—
468C2×#546D4311yescharacteristic, complemented
469C2×#466—431no—
470C2×#449—431no—
471C2×#447—431no—
472C2×#416—431no—
473#2414—431no—
474#2042—431no—
475#2036—431no—
476#2012—431no—
477#2000—431no—
478#1879—431no—
479#1875—431no—
480#1869—431no—
481#1862—431no—
482#1786—431no—
483C2×C43—42no—
484C2×C43—42no—
485C2×C43—44no—
486C2×C43—82no—
487C2×C43#241011yescharacteristic
488C2×C43#300211yescharacteristic
489C2×C43#300811yescharacteristic
490C2×C43#326811yescharacteristic
491C2×C43#328011yescharacteristic
492C2×C43#329711yescharacteristic
493C2×C43#331911yescharacteristic
494D43—161no—
495C22×#41C2×D4311yescharacteristic
496C23×D4C2×D4311yescharacteristic
497C22×SD16—431no—
498C22×D8—431no—
499C22×D8—431no—
500C23×C8—431no—
501#546—24no—
502#546—24no—
503C2×#124C2×D4311yescharacteristic
504C2×#123—21no—
505C2×C22⋊Q8C2×D4311yescharacteristic
506C2×#121—21no—
507C2×#121—431no—
508C2×#121—431no—
509C2×#121C2×D4311yescharacteristic
510C2×#120—21no—
511C2×C4×D4C2×D4311yescharacteristic
512C2×C4×D4C2×D4311yescharacteristic
513C2×#117—431no—
514C22×C22⋊C4—21no—
515#466—864no—
516#449—864no—
517#447—864no—
518C2×#107—431no—
519#416—864no—
520C2×#103—431no—
521C2×#103—431no—
522C2×#103—431no—
523C2×#102—431no—
524C2×#102—431no—
525C2×#102—431no—
526C2×#102—431no—
527C2×#102—431no—
528C2×#102—431no—
529C2×#102—431no—
530C2×C22⋊C8—431no—
531C2×C22⋊C8—431no—
532C2×C22⋊C8—431no—
533#394—861no—
534#392—861no—
535#390—431no—
536#390—861no—
537#389—431no—
538#388—861no—
539#380—431no—
540#340—431no—
541#340—431no—
542#336—431no—
543#336—431no—
544C43#2442811yescharacteristic, complemented, Sylow
545C25—21no—
546C2×#41—22no—
547C2×#41—22no—
548C2×#41—22no—
549C2×#41—41no—
550C2×#41—41no—
551C2×#41C22⋊D4314yescomplemented
552C22×Q8C22×D4311yescharacteristic
553C22×D4—21no—
554C22×D4—21no—
555C22×D4—22no—
556C22×D4—22no—
557C22×D4—22no—
558C22×D4—22no—
559C22×D4—21no—
560C22×D4—41no—
561C22×D4—41no—
562C22×D4—431no—
563C22×D4—861no—
564C22×D4—861no—
565C22×D4C22⋊D4311yescharacteristic
566C22×D4C22×D4311yescharacteristic
567C22×D4C22×D4311yescharacteristic
568C23×C4—21no—
569C23×C4—21no—
570C23×C4C22×D4311yescharacteristic
571C23×C4C22×D4311yescharacteristic
572C2×SD16—862no—
573C2×SD16—1721no—
574C2×SD16—1721no—
575C2×D8—862no—
576C2×D8—862no—
577C2×D8—862no—
578C2×D8—862no—
579C2×D8—862no—
580C2×D8—1721no—
581C22×C8—431no—
582C22×C8—431no—
583C22×C8—431no—
584C22×C8—431no—
585C22×C8—862no—
586C22×C8—862no—
587C22×C8—1721no—
588#124—22no—
589#124—22no—
590#123—28no—
591C22⋊Q8—22no—
592C22⋊Q8—22no—
593#121—28no—
594#121—22no—
595#121—862no—
596#121—862no—
597#121—862no—
598#121—1721no—
599#121C22⋊D4314yescomplemented
600#120—28no—
601C4×D4—22no—
602C4×D4—22no—
603C4×D4—22no—
604C4×D4—22no—
605#117—862no—
606#117—1721no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—431no—
609C2×C4⋊C4—431no—
610C2×C4⋊C4—431no—
611C2×C4⋊C4—861no—
612C2×C4⋊C4C22⋊D4311yescharacteristic
613C2×C4⋊C4C22×D4311yescharacteristic
614C2×C22⋊C4—28no—
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—861no—
621C2×C22⋊C4—861no—
622C2×C22⋊C4—861no—
623C2×C22⋊C4—861no—
624C2×C22⋊C4—861no—
625C2×C22⋊C4—861no—
626C2×C22⋊C4C22⋊D4311yescharacteristic
627C2×C22⋊C4C22⋊D4311yescharacteristic
628C2×C42—861no—
629C2×C42C22×D4311yescharacteristic
630#107—862no—
631#103—862no—
632#103—862no—
633#103—862no—
634#102—434no—
635#102—862no—
636#102—862no—
637#102—862no—
638#102—862no—
639#102—862no—
640#102—1721no—
641C22⋊C8—862no—
642C22⋊C8—862no—
643C22⋊C8—1721no—
644#95—861no—
645#95—861no—
646C24—21no—
647C24—24no—
648C24—21no—
649C24—42no—
650C24—42no—
651C24—42no—
652C24—42no—
653C24—81no—
654C24—81no—
655C24—861no—
656C24C2×C22⋊D4311yescharacteristic
657C24C2×C22⋊D4311yescharacteristic
658#41—28no—
659#41—44no—
660#41—44no—
661#41—44no—
662C2×Q8—21no—
663C2×Q8—21no—
664C2×Q8—21no—
665C2×Q8—21no—
666C2×Q8—21no—
667C2×Q8C2×C22⋊D4312yes—
668C2×D4—24no—
669C2×D4—22no—
670C2×D4—24no—
671C2×D4—22no—
672C2×D4—24no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—41no—
682C2×D4—42no—
683C2×D4—42no—
684C2×D4—44no—
685C2×D4—44no—
686C2×D4—44no—
687C2×D4—42no—
688C2×D4—42no—
689C2×D4—44no—
690C2×D4—81no—
691C2×D4—81no—
692C2×D4—861no—
693C2×D4—861no—
694C2×D4—861no—
695C2×D4—861no—
696C2×D4—861no—
697C2×D4—861no—
698C2×D4—3441no—
699C2×D4—3441no—
700C2×D4—3441no—
701C2×D4—1722no—
702C2×D4—1722no—
703C2×D4—1722no—
704C2×D4D4×D4312yes—
705C2×D4#1062190012yes—
706C2×D4C2×C22⋊D4312yes—
707C2×D4C2×C22⋊D4312yes—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—24no—
715C22×C4—24no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—42no—
723C22×C4—42no—
724C22×C4—81no—
725C22×C4—81no—
726C22×C4—861no—
727C22×C4—861no—
728C22×C4—861no—
729C22×C4C2×C22⋊D4311yescharacteristic
730C22×C4C2×C22⋊D4311yescharacteristic
731C22×C4C2×C22⋊D4311yescharacteristic
732C22×C4C2×C22⋊D4311yescharacteristic
733C22×C4C2×C22⋊D4312yes—
734C22×C4C2×C22⋊D4312yes—
735C22×C4C23×D4311yescharacteristic
736SD16—1724no—
737D8—1724no—
738D8—1724no—
739C2×C8—432no—
740C2×C8—861no—
741C2×C8—861no—
742C2×C8—861no—
743C2×C8—861no—
744C2×C8—861no—
745C2×C8—861no—
746C2×C8—861no—
747C2×C8—861no—
748C2×C8—861no—
749C2×C8—861no—
750C2×C8—861no—
751C2×C8—1724no—
752C4⋊C4—24no—
753C4⋊C4—22no—
754C4⋊C4—21no—
755C4⋊C4—432no—
756C4⋊C4—861no—
757C4⋊C4—861no—
758C4⋊C4—861no—
759C4⋊C4—861no—
760C4⋊C4—861no—
761C4⋊C4—3441no—
762C4⋊C4C2×C22⋊D4312yes—
763C22⋊C4—24no—
764C22⋊C4—24no—
765C22⋊C4—24no—
766C22⋊C4—24no—
767C22⋊C4—22no—
768C22⋊C4—22no—
769C22⋊C4—24no—
770C22⋊C4—3441no—
771C22⋊C4—3441no—
772C22⋊C4—1722no—
773C22⋊C4—1722no—
774C22⋊C4—1722no—
775C22⋊C4—1722no—
776C42—21no—
777C42—21no—
778C42—1722no—
779C23—21no—
780C23—22no—
781C23—21no—
782C23—21no—
783C23—21no—
784C23—21no—
785C23—21no—
786C23—21no—
787C23—21no—
788C23—21no—
789C23—21no—
790C23—22no—
791C23—21no—
792C23—21no—
793C23—22no—
794C23—22no—
795C23—48no—
796C23—48no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—84no—
808C23—84no—
809C23—84no—
810C23—84no—
811C23—84no—
812C23—1721no—
813C23—1721no—
814C23—1721no—
815C23—1721no—
816C23—1721no—
817C23—1721no—
818C23—1721no—
819C23#1306329412yes—
820C23#1306334512yes—
821C23C22×C22⋊D4311yescharacteristic
822Q8—22no—
823Q8—22no—
824Q8—41no—
825Q8—41no—
826D4—22no—
827D4—22no—
828D4—22no—
829D4—22no—
830D4—22no—
831D4—44no—
832D4—48no—
833D4—48no—
834D4—41no—
835D4—41no—
836D4—84no—
837D4—3444no—
838D4—3444no—
839D4—1721no—
840D4—1721no—
841D4—1721no—
842D4—1721no—
843D4#1306329714yes—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—48no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—84no—
871C2×C4—862no—
872C2×C4—1721no—
873C2×C4—1721no—
874C2×C4—1721no—
875C2×C4—1721no—
876C2×C4—1721no—
877C2×C4—1721no—
878C2×C4—1721no—
879C2×C4—1721no—
880C2×C4#1306329412yes—
881C2×C4C2×D4×D4311yescharacteristic
882C2×C4C22×C22⋊D4311yescharacteristic
883C2×C4C22×C22⋊D4311yescharacteristic
884C2×C4C2×#1062190011yescharacteristic
885C2×C4#1306337011yescharacteristic
886C2×C4#1306337011yescharacteristic
887C8—862no—
888C8—1721no—
889C8—1721no—
890C8—1721no—
891C22—22no—
892C22—22no—
893C22—22no—
894C22—22no—
895C22—24no—
896C22—22no—
897C22—22no—
898C22—41no—
899C22—42no—
900C22—42no—
901C22—41no—
902C22—41no—
903C22—42no—
904C22—41no—
905C22—42no—
906C22—41no—
907C22—41no—
908C22—42no—
909C22—41no—
910C22—41no—
911C22—42no—
912C22—42no—
913C22—42no—
914C22—42no—
915C22—816no—
916C22—81no—
917C22—81no—
918C22—81no—
919C22—81no—
920C22—3441no—
921C22—3441no—
922C22—3441no—
923C22—3441no—
924C22—3441no—
925C22—3441no—
926C22—3441no—
927C22C2×#1306329411yescharacteristic
928C22D4×C22⋊D4311yescharacteristic
929C22#1458354311yescharacteristic
930C22C2×#1306334511yescharacteristic
931C22#1458369711yescharacteristic
932C22#1458370211yescharacteristic
933C22#1458370211yescharacteristic
934C4—22no—
935C4—41no—
936C4—41no—
937C4—42no—
938C4—41no—
939C4—42no—
940C4—3441no—
941C4—3441no—
942C4—1722no—
943C4C2×#1306329711yescharacteristic
944C4#1458345811yescharacteristic
945C4D4×C22⋊D4311yescharacteristic
946C4#1458354311yescharacteristic
947C2—42no—
948C2—42no—
949C2—44no—
950C2—82no—
951C2—6881no—
952C2#1913796911yescharacteristic
953C2#1914381311yescharacteristic
954C2#1914386311yescharacteristic
955C2#1914613111yescharacteristic
956C2#1914627611yescharacteristic
957C2#1914644511yescharacteristic
958C2#1914675111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#546C2
socleC23×C43C22×D4
hypercenterC2×#546D43
hypocenterC43#24428
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#546

Complements

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

NH ≅ G/Ntype
1. C2×#14583133C2semidirect
2. C2×#14583044C2semidirect
3. C2×#14583033C2semidirect
4. C2×#14582895C2semidirect
5. #19138013C2semidirect
6. #19135831C2semidirect
7. #19135795C2semidirect
8. #19135672C2semidirect
9. #19135596C2semidirect
10. #19134943C2semidirect
11. #19134918C2semidirect
12. #19134888C2semidirect
13. #19134842C2semidirect
14. #19134526C2semidirect
15. C2×C43×#546C2semidirect
16. C22×#10621884C22semidirect
19. C23×C43⋊C8C22semidirect
21. C2×#13063299C22semidirect
22. C2×#13063284C22semidirect
26. C2×#13063258C22semidirect
28. C2×#13063249C22semidirect
29. C2×#13063249C22semidirect
30. C2×#13063249C22semidirect
37. C2×#13063245C22semidirect
40. C2×C22⋊(C43⋊C8)C22semidirect
43. #14582801C22semidirect
45. #14582797C22semidirect
48. #14582661C22semidirect
49. #14582661C22semidirect
50. #14582654C22semidirect
51. #14582654C22semidirect
110. #13063246D4semidirect
123. C2×#41×C43D4semidirect
148. #121×C43D4semidirect
468. C2×#546D43semidirect
544. C43#24428semidirect
551. C2×#41C22⋊D43semidirect
599. #121C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145831332
C2×#145830442
C2×#145830332
C2×#145828952
#191380132
#191358312
#191357952
#191356722
#191355962
#191349432
#191349182
#191348882
#191348422
#191345262
C2×C43×#5462
#2442843