Finite Group Databasebeta

← #25102191

Subgroups — #25102191

Order 11008.

1532 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×Q8×D43C211yesmaximal, characteristic, complemented
2C2×#14583036C211yesmaximal, characteristic
3C2×#14582990C211yesmaximal, characteristic, complemented
4C2×SD16×Dic43C211yesmaximal, characteristic, complemented
5#19137111C211yesmaximal, characteristic
6#19134953C211yesmaximal, characteristic, complemented
7#19134909C211yesmaximal, characteristic
8#19134866C211yesmaximal, characteristic, complemented
9#19134863C211yesmaximal, characteristic, complemented
10#19134789C211yesmaximal, characteristic, complemented
11#19134528C211yesmaximal, characteristic, complemented
12#103×Dic43C211yesmaximal, characteristic, complemented
13#19134414C211yesmaximal, characteristic, complemented
14#19134352C211yesmaximal, characteristic, complemented
15C43×#1880C211yesmaximal, characteristic, complemented
16C22×Q8×D43C2211yescharacteristic
17C22×#10621883C2211yescharacteristic
18C2×#13063296C2211yescharacteristic
19C2×Q8×Dic43C2211yescharacteristic
20C2×C4×Dic86—21no—
21C2×C4×Dic86C2211yescharacteristic
22C2×#13063290—21no—
23C2×#13063290C2211yescharacteristic
24C4×Q8×D43—24no—
25C4×Q8×D43—24no—
26C2×D4×Dic43C2211yescharacteristic
27C2×(C22⋊D43)⋊C4—21no—
28C2×C4⋊C4×D43—21no—
29C2×C4⋊C4×D43C2211yescharacteristic
30C2×C42×D43—21no—
31C2×C42×D43C2211yescharacteristic
32#14583036C418yescomplemented
33#14582990—24no—
34SD16×Dic43—24no—
35C2×#13063257C2211yescharacteristic
36C2×#13063256C2211yescharacteristic
37C2×#13063250C2211yescharacteristic
38C2×#13063250C2211yescharacteristic
39C2×#13063249C2211yescharacteristic
40C2×#13063249C2211yescharacteristic
41C2×#13063248C2211yescharacteristic
42C2×#13063246C2211yescharacteristic
43C2×(C2×D43)⋊C8C2211yescharacteristic
44C2×(C2×D43)⋊C8C2211yescharacteristic
45C2×C8×Dic43C2211yescharacteristic
46C2×C8×Dic43C2211yescharacteristic
47#14582797C2211yescharacteristic
48#14582793—21no—
49#14582775—21no—
50#14582756C2211yescharacteristic
51C4⋊C4×Dic43C2211yescharacteristic
52C22⋊C4×Dic43—21no—
53#14582662C2211yescharacteristic
54#14582661C2211yescharacteristic
55#14582661C2211yescharacteristic
56#14582654C2211yescharacteristic
57C22×SD16×C43C2211yescharacteristic
58C2×C4×Q8×C43C2211yescharacteristic
59C2×#103×C43C2211yescharacteristic
60C2×#102×C43C2211yescharacteristic
61C43×#390C2211yescharacteristic
62C43×#340C2211yescharacteristic
63C43×#336C2211yescharacteristic
64C22×Dic86—21no—
65C22×Dic86C2311yescharacteristic
66C2×Q8×D43—22no—
67C2×Q8×D43—22no—
68C2×Q8×D43—22no—
69C2×Q8×D43—22no—
70C2×Q8×D43—22no—
71C2×Q8×D43C2×C414yescomplemented
72C22×C22⋊D43—21no—
73C23×Dic43—21no—
74C22×C4×D43—21no—
75C22×C4×D43—21no—
76C22×C4×D43D411yescharacteristic
77C22×C4×D43D411yescharacteristic
78C22×C4×D43C2311yescharacteristic
79C2×#10621883—22no—
80C2×#10621883—22no—
81C2×#10621883C2×C414yescomplemented
82C22×C43⋊C8C2311yescharacteristic
83C22×C43⋊C8C2311yescharacteristic
84#13063296—22no—
85#13063296C2×C414yes—
86Q8×Dic43—22no—
87Q8×Dic43D414yescomplemented
88C4×Dic86—28no—
89C4×Dic86—22no—
90C4×Dic86—22no—
91#13063290—28no—
92#13063290—22no—
93#13063290D414yescomplemented
94D4×Dic43—22no—
95D4×Dic43—22no—
96(C22⋊D43)⋊C4—44no—
97C2×C4⋊Dic43—21no—
98C2×C4⋊Dic43C2311yescharacteristic
99C2×C4⋊Dic43C2311yescharacteristic
100C2×C4⋊Dic43C2311yescharacteristic
101C2×Dic43⋊C4—21no—
102C2×Dic43⋊C4—21no—
103C2×Dic43⋊C4—21no—
104C2×Dic43⋊C4—21no—
105C4⋊C4×D43—28no—
106C4⋊C4×D43—22no—
107C4⋊C4×D43—22no—
108C2×C22⋊Dic43—21no—
109C2×C22⋊Dic43—21no—
110C2×(C2×D43)⋊C4—21no—
111C2×C4×Dic43—21no—
112C2×C4×Dic43—21no—
113C2×C4×Dic43—21no—
114C2×C4×Dic43—21no—
115C2×C4×Dic43D411yescharacteristic
116C2×C4×Dic43D411yescharacteristic
117C2×C4×Dic43C2311yescharacteristic
118C42×D43—28no—
119C42×D43—22no—
120C42×D43—22no—
121#13063257—22no—
122#13063256—22no—
123#13063250—22no—
124#13063250C2×C414yescomplemented
125#13063249—22no—
126#13063249C2×C414yescomplemented
127#13063248—22no—
128#13063246—22no—
129(C2×D43)⋊C8—22no—
130(C2×D43)⋊C8C2×C414yescomplemented
131C8×Dic43—22no—
132C8×Dic43—22no—
133C43⋊#95—21no—
134C43⋊#95—21no—
135C43⋊#95—21no—
136C22×Q8×C43C2311yescharacteristic
137C22×D4×C43C2311yescharacteristic
138C2×SD16×C43—22no—
139C2×SD16×C43—22no—
140C2×SD16×C43C2×C414yescomplemented
141C22×C8×C43C2311yescharacteristic
142C22×C8×C43C2311yescharacteristic
143C4×Q8×C43—22no—
144C4×Q8×C43—22no—
145C2×C4⋊C4×C43—21no—
146C2×C4⋊C4×C43C2311yescharacteristic
147C2×C4⋊C4×C43C2311yescharacteristic
148C2×C22⋊C4×C43—21no—
149C2×C22⋊C4×C43—21no—
150C2×C42×C43—21no—
151C2×C42×C43C2311yescharacteristic
152#103×C43—22no—
153#102×C43—22no—
154C24×C43—21no—
155C23×D43C2×D411yescharacteristic
156C2×Q8×C43—21no—
157C2×Q8×C43—21no—
158C2×Q8×C43—21no—
159C2×Q8×C43C22×C412yes—
160C2×Q8×C43C2×D412yes—
161C2×Q8×C43#4112yes—
162C2×D4×C43—21no—
163C2×D4×C43—21no—
164C2×D4×C43—21no—
165C2×D4×C43—21no—
166C2×D4×C43—21no—
167C2×D4×C43C22×C412yes—
168C22×C4×C43—21no—
169C22×C4×C43—21no—
170C22×C4×C43—21no—
171C22×C4×C43C2×D411yescharacteristic
172C22×C4×C43C2×D411yescharacteristic
173C22×C4×C43C2411yescharacteristic
174C2×C22⋊D43—24no—
175C2×C22⋊D43—42no—
176C2×C22⋊D43—42no—
177C22×Dic43—21no—
178C22×Dic43—21no—
179C22×Dic43—21no—
180C22×Dic43—21no—
181C22×Dic43—42no—
182C22×Dic43—42no—
183C22×Dic43—42no—
184C22×Dic43C2×D411yescharacteristic
185C22×Dic43C2×D411yescharacteristic
186C22×Dic43C2×D411yescharacteristic
187Q8×D43—28no—
188Q8×D43—28no—
189Q8×D43—28no—
190Q8×D43—28no—
191C2×C4×D43—24no—
192C2×C4×D43—24no—
193C2×C4×D43—21no—
194C2×C4×D43—21no—
195C2×C4×D43—21no—
196C2×C4×D43—21no—
197C2×C4×D43—22no—
198C2×C4×D43—22no—
199C2×C4×D43—24no—
200C2×C4×D43—22no—
201C2×C4×D43—24no—
202C2×C4×D43—22no—
203C2×C4×D43—41no—
204C2×C4×D43—42no—
205C2×C4×D43—42no—
206C2×C4×D43SD1614yescomplemented
207C2×C4×D43C22×C412yes—
208C2×C4×D43#4112yes—
209C2×Dic86—24no—
210C2×Dic86—24no—
211C2×Dic86—21no—
212C2×Dic86—21no—
213C2×Dic86—21no—
214C2×Dic86—24no—
215C2×Dic86C22×C412yes—
216C2×Dic86C2×D412yes—
217C2×Dic86#4112yes—
218SD16×C43—28no—
219C2×C8×C43—21no—
220C2×C8×C43—21no—
221C2×C8×C43—21no—
222C2×C8×C43—21no—
223C2×C8×C43—21no—
224C2×C8×C43C22×C412yes—
225C4⋊C4×C43—24no—
226C4⋊C4×C43—21no—
227C4⋊C4×C43—21no—
228C4⋊C4×C43—21no—
229C4⋊C4×C43C2×D412yes—
230C22⋊C4×C43—42no—
231C22⋊C4×C43—42no—
232C42×C43—24no—
233C42×C43—21no—
234C42×C43—21no—
235C22⋊Dic43—24no—
236C22⋊Dic43—42no—
237#10621883—28no—
238(C2×D43)⋊C4—42no—
239C4⋊Dic43—21no—
240C4⋊Dic43—21no—
241C4⋊Dic43—24no—
242C4⋊Dic43—21no—
243C4⋊Dic43—21no—
244C4⋊Dic43C22×C412yes—
245C4⋊Dic43C2×D412yes—
246Dic43⋊C4—24no—
247Dic43⋊C4—24no—
248Dic43⋊C4—24no—
249Dic43⋊C4—42no—
250C4×Dic43—24no—
251C4×Dic43—24no—
252C4×Dic43—24no—
253C4×Dic43—22no—
254C4×Dic43—22no—
255C4×Dic43—42no—
256C4×Dic43C2×D412yes—
257C4×Dic43C2×D412yes—
258C2×C43⋊C8—21no—
259C2×C43⋊C8—21no—
260C2×C43⋊C8—21no—
261C2×C43⋊C8—21no—
262C2×C43⋊C8—21no—
263C2×C43⋊C8C22×C412yes—
264C23×C43—22no—
265C23×C43—41no—
266C23×C43—41no—
267C23×C43—41no—
268C23×C43—41no—
269C23×C43—41no—
270C23×C43—41no—
271C23×C43C22×D411yescharacteristic
272C22×D43—21no—
273C22×D43—21no—
274C22×D43—21no—
275C22×D43—21no—
276C22×D43C4×D412yes—
277C22×D43C2×SD1612yes—
278C22×D43#13512yes—
279Q8×C43—22no—
280Q8×C43—22no—
281Q8×C43—22no—
282Q8×C43C4×D414yescomplemented
283D4×C43—22no—
284D4×C43—22no—
285D4×C43—41no—
286D4×C43—41no—
287C2×C4×C43—22no—
288C2×C4×C43—21no—
289C2×C4×C43—22no—
290C2×C4×C43—22no—
291C2×C4×C43—21no—
292C2×C4×C43—21no—
293C2×C4×C43—22no—
294C2×C4×C43—21no—
295C2×C4×C43—21no—
296C2×C4×C43—41no—
297C2×C4×C43—41no—
298C2×C4×C43—41no—
299C2×C4×C43—41no—
300C2×C4×C43—41no—
301C2×C4×C43C2×SD1612yes—
302C2×C4×C43C23×C411yescharacteristic
303C2×C4×C43C22×D411yescharacteristic
304C2×C4×C43C22×D411yescharacteristic
305C2×C4×C43C2×#4111yescharacteristic
306C2×C4×C43C2×#4111yescharacteristic
307C2×C4×C43C2×#4111yescharacteristic
308C22⋊D43—48no—
309C2×Dic43—22no—
310C2×Dic43—21no—
311C2×Dic43—22no—
312C2×Dic43—21no—
313C2×Dic43—22no—
314C2×Dic43—21no—
315C2×Dic43—21no—
316C2×Dic43—22no—
317C2×Dic43—22no—
318C2×Dic43—41no—
319C2×Dic43—41no—
320C2×Dic43—41no—
321C2×Dic43—41no—
322C2×Dic43—41no—
323C2×Dic43—41no—
324C2×Dic43—41no—
325C2×Dic43—84no—
326C2×Dic43C4×D412yes—
327C2×Dic43#12012yes—
328C2×Dic43#12012yes—
329C2×Dic43C2×SD1612yes—
330C2×Dic43#13712yes—
331C4×D43—216no—
332C4×D43—22no—
333C4×D43—22no—
334C4×D43—22no—
335C4×D43—22no—
336C4×D43—28no—
337C4×D43—44no—
338C4×D43—48no—
339Dic86—216no—
340Dic86—22no—
341Dic86—22no—
342Dic86—22no—
343Dic86C4×D414yescomplemented
344C8×C43—22no—
345C8×C43—41no—
346C43⋊C8—22no—
347C43⋊C8—41no—
348C4×#448—431nomaximal, Sylow
349C22×C43—42no—
350C22×C43—42no—
351C22×C43—42no—
352C22×C43—81no—
353C22×C43—81no—
354C22×C43—81no—
355C22×C43—81no—
356C22×C43C2×C4×D411yescharacteristic
357C22×C43C2×#12011yescharacteristic
358C22×C43#52511yescharacteristic
359C22×C43C22×SD1611yescharacteristic
360C22×C43C2×#13511yescharacteristic
361C22×C43C2×#13711yescharacteristic
362C22×C43#57511yescharacteristic
363C2×D43—22no—
364C2×D43—22no—
365C2×D43—22no—
366C2×D43—22no—
367C2×D43—22no—
368C2×D43—22no—
369C2×D43C4×SD1614yescomplemented
370C4×C43—22no—
371C4×C43—24no—
372C4×C43—41no—
373C4×C43—42no—
374C4×C43—81no—
375C4×C43C2×C4×D411yescharacteristic
376C4×C43C2×C4×D411yescharacteristic
377C4×C43#52511yescharacteristic
378C4×C43#52511yescharacteristic
379Dic43—22no—
380Dic43—22no—
381Dic43—24no—
382Dic43—42no—
383Dic43—42no—
384Dic43—81no—
385Dic43#44814yescomplemented
386C22×C4×Q8—431no—
387C2×#448—431no—
388C2×C4×SD16—431no—
389C2×C4×SD16—431no—
390C4×#121—431no—
391#1880—431no—
392#1880D4311yescharacteristic, complemented
393#1874—431no—
394#1865—431no—
395#1865—431no—
396#1853—431no—
397#1787—431no—
398C4×#103—431no—
399C4×#103—431no—
400C4×C22⋊C8—431no—
401C2×C43—82no—
402C2×C43C4×#12011yescharacteristic
403C2×C43C2×C4×SD1611yescharacteristic
404C2×C43C4×#13711yescharacteristic
405C2×C43C2×#44811yescharacteristic
406C2×C43#300211yescharacteristic
407C2×C43#310311yescharacteristic
408C2×C43#310811yescharacteristic
409D43—24no—
410C23×Q8—431no—
411C22×SD16—431no—
412C22×SD16C2×D4311yescharacteristic
413C2×#121—431no—
414C2×C4×Q8—431no—
415C2×C4×Q8—431no—
416C2×C4×Q8—431no—
417C2×C4×Q8—861no—
418C2×C4×Q8—861no—
419C2×C4×Q8—864no—
420C2×C4×Q8—864no—
421C2×C4×Q8C2×D4311yescharacteristic
422C2×C4×D4—431no—
423C2×C4×D4—861no—
424C22×C4⋊C4—431no—
425C22×C4⋊C4—861no—
426C22×C42—431no—
427C22×C42—861no—
428#448—438no—
429C4×SD16—864no—
430C4×SD16—864no—
431C2×#106—431no—
432C2×#106—431no—
433C2×#103—431no—
434C2×#103—431no—
435C2×#103—431no—
436C2×#103—431no—
437C2×#103—431no—
438C2×#103C2×D4311yescharacteristic
439C2×#102—431no—
440C2×#102C2×D4311yescharacteristic
441C2×C22⋊C8—431no—
442C2×C22⋊C8—431no—
443C2×C4×C8—431no—
444C2×C4×C8—431no—
445#390C2×D4311yescharacteristic
446#389—431no—
447#388—861no—
448#386—861no—
449#380—431no—
450C4×C4⋊C4—431no—
451C4×C22⋊C4—861no—
452#340—431no—
453#340—431no—
454#340—431no—
455#340C2×D4311yescharacteristic
456#336—431no—
457#336C2×D4311yescharacteristic
458C43C4×#44811yescharacteristic, complemented, Sylow
459C22×Q8—434no—
460C22×Q8—431no—
461C22×Q8—861no—
462C22×Q8—862no—
463C22×Q8—862no—
464C22×Q8—862no—
465C22×Q8—862no—
466C22×Q8—862no—
467C22×Q8C22×D4311yescharacteristic
468C22×D4—861no—
469C22×D4C22×D4311yescharacteristic
470C23×C4—431no—
471C23×C4—431no—
472C23×C4—431no—
473C23×C4—861no—
474C23×C4—861no—
475C23×C4—861no—
476C2×SD16—22no—
477C2×SD16—22no—
478C2×SD16—434no—
479C2×SD16—862no—
480C2×SD16—862no—
481C2×SD16C4×D4314yescomplemented
482C22×C8—431no—
483C22×C8—431no—
484C22×C8C22×D4311yescharacteristic
485C22×C8C22×D4311yescharacteristic
486#121—434no—
487#121—862no—
488C4×Q8—22no—
489C4×Q8—22no—
490C4×Q8—434no—
491C4×Q8—434no—
492C4×Q8—862no—
493C4×Q8—862no—
494C4×Q8—868no—
495C4×Q8—862no—
496C4×Q8—862no—
497C4×Q8—868no—
498C4×D4—862no—
499C4×D4—862no—
500C4×D4—1724no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—431no—
503C2×C4⋊C4—431no—
504C2×C4⋊C4—431no—
505C2×C4⋊C4—862no—
506C2×C4⋊C4—868no—
507C2×C4⋊C4—861no—
508C2×C4⋊C4—861no—
509C2×C4⋊C4—861no—
510C2×C4⋊C4—861no—
511C2×C4⋊C4—862no—
512C2×C4⋊C4—861no—
513C2×C4⋊C4C22×D4311yescharacteristic
514C2×C4⋊C4C22×D4311yescharacteristic
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—861no—
518C2×C22⋊C4—861no—
519C2×C22⋊C4—861no—
520C2×C42—21no—
521C2×C42—431no—
522C2×C42—431no—
523C2×C42—431no—
524C2×C42—862no—
525C2×C42—862no—
526C2×C42—868no—
527C2×C42—861no—
528C2×C42—861no—
529C2×C42—861no—
530C2×C42—861no—
531C2×C42C22×D4311yescharacteristic
532#106—862no—
533#106—862no—
534#103—22no—
535#103—434no—
536#103—434no—
537#103—862no—
538#103—862no—
539#103—862no—
540#102—22no—
541#102—862no—
542C22⋊C8—434no—
543C22⋊C8—862no—
544C4×C8—862no—
545C4×C8—862no—
546#95—861no—
547#95—861no—
548#95—861no—
549C24—21no—
550C24—431no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8—432no—
555C2×Q8—432no—
556C2×Q8—432no—
557C2×Q8—864no—
558C2×Q8—864no—
559C2×Q8—864no—
560C2×Q8—868no—
561C2×Q8—868no—
562C2×Q8—868no—
563C2×Q8—868no—
564C2×Q8—861no—
565C2×Q8—861no—
566C2×Q8—861no—
567C2×Q8C2×C4×D4312yes—
568C2×Q8D4×D4312yes—
569C2×Q8#1062190012yes—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—864no—
576C2×D4—1722no—
577C2×D4—1722no—
578C2×D4C2×C4×D4312yes—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—431no—
583C22×C4—431no—
584C22×C4—431no—
585C22×C4—434no—
586C22×C4—432no—
587C22×C4—432no—
588C22×C4—862no—
589C22×C4—862no—
590C22×C4—862no—
591C22×C4—864no—
592C22×C4—864no—
593C22×C4—864no—
594C22×C4—862no—
595C22×C4—864no—
596C22×C4—861no—
597C22×C4—861no—
598C22×C4—861no—
599C22×C4—861no—
600C22×C4—861no—
601C22×C4—861no—
602C22×C4—861no—
603C22×C4—861no—
604C22×C4—1721no—
605C22×C4—1722no—
606C22×C4—1722no—
607C22×C4—1722no—
608C22×C4—1722no—
609C22×C4—1722no—
610C22×C4D4×D4311yescharacteristic
611C22×C4D4×D4311yescharacteristic
612C22×C4C23×D4311yescharacteristic
613SD16—28no—
614SD16—868no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—432no—
621C2×C8—861no—
622C2×C8—861no—
623C2×C8—861no—
624C2×C8—861no—
625C2×C8—861no—
626C2×C8C2×C4×D4312yes—
627C4⋊C4—24no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—432no—
632C4⋊C4—432no—
633C4⋊C4—864no—
634C4⋊C4—864no—
635C4⋊C4—864no—
636C4⋊C4—864no—
637C4⋊C4—861no—
638C4⋊C4—861no—
639C4⋊C4—861no—
640C4⋊C4—861no—
641C4⋊C4—1722no—
642C4⋊C4D4×D4312yes—
643C22⋊C4—42no—
644C22⋊C4—42no—
645C22⋊C4—864no—
646C22⋊C4—1722no—
647C22⋊C4—1722no—
648C42—24no—
649C42—21no—
650C42—21no—
651C42—432no—
652C42—432no—
653C42—862no—
654C42—862no—
655C42—864no—
656C42—864no—
657C42—864no—
658C42—1722no—
659C23—22no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—432no—
667C23—432no—
668C23—432no—
669C23—861no—
670C23—861no—
671C23—861no—
672C23—861no—
673C23C2×D4×D4311yescharacteristic
674Q8—22no—
675Q8—22no—
676Q8—22no—
677Q8—434no—
678Q8—8616no—
679Q8—862no—
680Q8—862no—
681Q8—862no—
682Q8(C22⋊D43)⋊C414yescomplemented
683D4—22no—
684D4—22no—
685D4—41no—
686D4—41no—
687D4—1728no—
688C2×C4—22no—
689C2×C4—21no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—22no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—432no—
703C2×C4—432no—
704C2×C4—432no—
705C2×C4—432no—
706C2×C4—432no—
707C2×C4—868no—
708C2×C4—8616no—
709C2×C4—862no—
710C2×C4—861no—
711C2×C4—862no—
712C2×C4—861no—
713C2×C4—862no—
714C2×C4—861no—
715C2×C4—861no—
716C2×C4—862no—
717C2×C4—862no—
718C2×C4—862no—
719C2×C4—862no—
720C2×C4—862no—
721C2×C4—862no—
722C2×C4—3444no—
723C2×C4—1724no—
724C2×C4—1728no—
725C2×C4—1721no—
726C2×C4—1721no—
727C2×C4—1721no—
728C2×C4—1721no—
729C2×C4—1721no—
730C2×C4—1721no—
731C2×C4—1721no—
732C2×C4SD16×D4312yes—
733C2×C4C22×C4×D4311yescharacteristic
734C2×C4C2×D4×D4311yescharacteristic
735C2×C4C2×D4×D4311yescharacteristic
736C2×C4#41×D4311yescharacteristic
737C2×C4#41×D4311yescharacteristic
738C2×C4C2×#1062190011yescharacteristic
739C8—22no—
740C8—41no—
741C8—862no—
742C8—1721no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—81no—
747C22—81no—
748C22—81no—
749C22—81no—
750C22—434no—
751C22—862no—
752C22—862no—
753C22—862no—
754C22—862no—
755C22—862no—
756C22—862no—
757C22C4×D4×D4311yescharacteristic
758C22#120×D4311yescharacteristic
759C22#1458340911yescharacteristic
760C22C2×SD16×D4311yescharacteristic
761C22#135×D4311yescharacteristic
762C22#137×D4311yescharacteristic
763C22#1458369511yescharacteristic
764C4—24no—
765C4—22no—
766C4—41no—
767C4—42no—
768C4—81no—
769C4—434no—
770C4—862no—
771C4—864no—
772C4—862no—
773C4—3441no—
774C4—1722no—
775C4—1722no—
776C4C4×D4×D4311yescharacteristic
777C4C2×(C22⋊D43)⋊C411yescharacteristic
778C4#1458340711yescharacteristic
779C4#1458340911yescharacteristic
780C2—82no—
781C2—864no—
782C2#1913710011yescharacteristic
783C2C4×SD16×D4311yescharacteristic
784C2#1914341711yescharacteristic
785C2#448×D4311yescharacteristic
786C2#1914381011yescharacteristic
787C2#1914462511yescharacteristic
788C2#1914467411yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1880C2
socleC23×C43C22×D4
prime radicalC2×#13063296C22
cosocleC22×C4×C43C24
hypercenter#1880D43
hypocenterC43C4×#448
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1880

Complements

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

NH ≅ G/Ntype
1. C2×C4×Q8×D43C2semidirect
3. C2×#14582990C2semidirect
4. C2×SD16×Dic43C2semidirect
6. #19134953C2semidirect
8. #19134866C2semidirect
9. #19134863C2semidirect
10. #19134789C2semidirect
11. #19134528C2semidirect
12. #103×Dic43C2semidirect
13. #19134414C2semidirect
14. #19134352C2semidirect
15. C43×#1880C2semidirect
32. #14583036C4semidirect
71. C2×Q8×D43C2×C4semidirect
81. C2×#10621883C2×C4semidirect
87. Q8×Dic43D4semidirect
93. #13063290D4semidirect
124. #13063250C2×C4semidirect
126. #13063249C2×C4semidirect
130. (C2×D43)⋊C8C2×C4semidirect
140. C2×SD16×C43C2×C4semidirect
206. C2×C4×D43SD16semidirect
282. Q8×C43C4×D4semidirect
343. Dic86C4×D4semidirect
369. C2×D43C4×SD16semidirect
385. Dic43#448semidirect
392. #1880D43semidirect
458. C43C4×#448semidirect
481. C2×SD16C4×D43semidirect
682. Q8(C22⋊D43)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×C4×Q8×D432
C2×#145830362
C2×#145829902
C2×SD16×Dic432
#191371112
#191349532
#191349092
#191348662
#191348632
#191347892
#191345282
#103×Dic432
#191344142
#191343522
C43×#18802
C4×#44843