Finite Group Databasebeta

← #25116858

Subgroups — #25116858

Order 11008.

1302 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583000C211yesmaximal, characteristic, complemented
2C22×#13063246C211yesmaximal, characteristic
3#19137604C211yesmaximal, characteristic, complemented
4D4×C22⋊Dic43C211yesmaximal, characteristic
5#19135478C211yesmaximal, characteristic, complemented
6#19135294C211yesmaximal, characteristic, complemented
7#19135217C211yesmaximal, characteristic, complemented
8#19135019C211yesmaximal, characteristic, complemented
9#19134952C211yesmaximal, characteristic, complemented
10#19134931C211yesmaximal, characteristic, complemented
11#19134844C211yesmaximal, characteristic, complemented
12#19134785C211yesmaximal, characteristic, complemented
13#19134422C211yesmaximal, characteristic, complemented
14#19134374C211yesmaximal, characteristic, complemented
15C2×C43×#450C211yesmaximal, characteristic
16C23×C43⋊C8C2211yescharacteristic
17C2×Q8×Dic43C2211yescharacteristic, complemented
18C2×D4×Dic43C2211yescharacteristic
19C2×D4×Dic43C2211yescharacteristic
20C22×C4⋊Dic43C2211yescharacteristic
21C22×C22⋊Dic43—21no—
22#14583000—24no—
23C2×#13063259C2211yescharacteristic, complemented
24C2×#13063259C2211yescharacteristic, complemented
25C2×#13063249C2211yescharacteristic, complemented
26C2×#13063249C2211yescharacteristic, complemented
27C2×#13063246—24no—
28C2×#13063246C2211yescharacteristic
29C2×#13063246C2211yescharacteristic
30C2×#13063246C2211yescharacteristic
31C2×#13063246C2211yescharacteristic
32C2×#13063235C2211yescharacteristic, complemented
33C2×#13063235C2211yescharacteristic, complemented
34#14582806C2211yescharacteristic, complemented
35#14582802C2211yescharacteristic
36#14582802C2211yescharacteristic
37#14582798—21no—
38#14582798C2211yescharacteristic, complemented
39#14582785—21no—
40#14582779—21no—
41#14582779—21no—
42#14582774—21no—
43#14582759C2211yescharacteristic
44#14582755—21no—
45C4⋊C4×Dic43C2211yescharacteristic, complemented
46C22⋊C4×Dic43—21no—
47C4×C22⋊Dic43C2211yescharacteristic
48#14582662C2211yescharacteristic, complemented
49#14582662C2211yescharacteristic, complemented
50#14582661C2211yescharacteristic, complemented
51#14582661C2211yescharacteristic, complemented
52#14582653C2211yescharacteristic, complemented
53#14582653C2211yescharacteristic, complemented
54C23×D4×C43C2211yescharacteristic
55C22×SD16×C43C2211yescharacteristic
56C22×SD16×C43C2211yescharacteristic
57C2×C22⋊Q8×C43C2211yescharacteristic
58C43×#450C418yescomplemented
59C2×#102×C43C2211yescharacteristic
60C2×#102×C43C2211yescharacteristic
61C2×C22⋊C8×C43C2211yescharacteristic
62C23×Dic43—21no—
63C23×Dic43—21no—
64C23×Dic43—21no—
65C22×C43⋊C8—22no—
66C22×C43⋊C8—22no—
67C22×C43⋊C8—41no—
68C22×C43⋊C8C2311yescharacteristic
69C22×C43⋊C8C2311yescharacteristic
70Q8×Dic43—22no—
71Q8×Dic43—41no—
72D4×Dic43—22no—
73D4×Dic43—22no—
74D4×Dic43—41no—
75D4×Dic43—41no—
76C2×C4⋊Dic43—22no—
77C2×C4⋊Dic43—21no—
78C2×C4⋊Dic43—21no—
79C2×C4⋊Dic43—21no—
80C2×C4⋊Dic43—41no—
81C2×C4⋊Dic43C2311yescharacteristic
82C2×C4⋊Dic43C2311yescharacteristic
83C2×C4⋊Dic43C2311yescharacteristic
84C2×C4⋊Dic43C2311yescharacteristic
85C2×C22⋊Dic43—21no—
86C2×C22⋊Dic43—21no—
87C2×C22⋊Dic43—21no—
88C2×C22⋊Dic43—21no—
89C2×C22⋊Dic43—21no—
90C2×C22⋊Dic43—21no—
91C2×C22⋊Dic43—21no—
92C2×C22⋊Dic43—44no—
93C2×C22⋊Dic43D411yescharacteristic
94C2×C22⋊Dic43D411yescharacteristic
95C2×C4×Dic43—21no—
96C2×C4×Dic43—21no—
97C2×C4×Dic43C2311yescharacteristic
98C2×C4×Dic43C2311yescharacteristic
99#13063259—22no—
100#13063259—41no—
101#13063249—22no—
102#13063249—41no—
103#13063246—22no—
104#13063246—22no—
105#13063246—22no—
106#13063246D414yes—
107#13063235—22no—
108#13063235—41no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C43⋊#95—21no—
114C43⋊#95D411yescharacteristic
115C43⋊#95D411yescharacteristic
116C25×C43—21no—
117C22×Q8×C43C2311yescharacteristic
118C22×D4×C43—22no—
119C22×D4×C43—22no—
120C22×D4×C43—21no—
121C22×D4×C43—22no—
122C22×D4×C43—41no—
123C22×D4×C43—41no—
124C22×D4×C43C2×C414yes—
125C22×D4×C43C2311yescharacteristic
126C22×D4×C43C2311yescharacteristic
127C23×C4×C43C2311yescharacteristic
128C2×SD16×C43—22no—
129C2×SD16×C43—22no—
130C2×SD16×C43—41no—
131C2×SD16×C43—41no—
132C2×SD16×C43C2×C414yescomplemented
133C2×SD16×C43C2×C414yescomplemented
134C22×C8×C43C2311yescharacteristic
135C22×C8×C43C2311yescharacteristic
136C22⋊Q8×C43—22no—
137C22⋊Q8×C43C2×C414yescomplemented
138C2×C4⋊C4×C43—21no—
139C2×C4⋊C4×C43C2311yescharacteristic
140C2×C22⋊C4×C43—21no—
141#102×C43C2×C414yescomplemented
142#102×C43C2×C414yescomplemented
143C22⋊C8×C43C2×C414yescomplemented
144C24×C43—21no—
145C24×C43—21no—
146C24×C43—24no—
147C24×C43—42no—
148C24×C43—42no—
149C24×C43—42no—
150C24×C43—42no—
151C24×C43—81no—
152C24×C43—81no—
153C24×C43C2×D411yescharacteristic
154C2×Q8×C43—21no—
155C2×Q8×C43—21no—
156C2×Q8×C43—21no—
157C2×Q8×C43—21no—
158C2×Q8×C43—21no—
159C2×Q8×C43C22×C412yes—
160C2×D4×C43—24no—
161C2×D4×C43—21no—
162C2×D4×C43—21no—
163C2×D4×C43—21no—
164C2×D4×C43—21no—
165C2×D4×C43—28no—
166C2×D4×C43—21no—
167C2×D4×C43—21no—
168C2×D4×C43—21no—
169C2×D4×C43—21no—
170C2×D4×C43—42no—
171C2×D4×C43—42no—
172C2×D4×C43—44no—
173C2×D4×C43—44no—
174C2×D4×C43—44no—
175C2×D4×C43C22×C412yes—
176C2×D4×C43C22×C412yes—
177C2×D4×C43C2×D412yes—
178C2×D4×C43#4112yes—
179C22×C4×C43—21no—
180C22×C4×C43—21no—
181C22×C4×C43—21no—
182C22×C4×C43—21no—
183C22×C4×C43—21no—
184C22×C4×C43—21no—
185C22×C4×C43C22×C412yes—
186C22×C4×C43C2×D411yescharacteristic
187C22×C4×C43#4112yes—
188C22×C4×C43C2411yescharacteristic
189C22×Dic43—21no—
190C22×Dic43—21no—
191C22×Dic43—21no—
192C22×Dic43—21no—
193C22×Dic43—42no—
194C22×Dic43—42no—
195C22×Dic43—42no—
196C22×Dic43—42no—
197C22×Dic43—42no—
198C22×Dic43—42no—
199C22×Dic43—81no—
200C22×Dic43—81no—
201C22×Dic43—81no—
202C22×Dic43C2×D411yescharacteristic
203C22×Dic43C2×D411yescharacteristic
204C22×Dic43C2×D411yescharacteristic
205C22×Dic43C2×D411yescharacteristic
206SD16×C43—28no—
207SD16×C43—44no—
208C2×C8×C43—21no—
209C2×C8×C43—21no—
210C2×C8×C43—21no—
211C2×C8×C43—21no—
212C2×C8×C43C22×C412yes—
213C2×C8×C43C22×C412yes—
214C4⋊C4×C43—24no—
215C4⋊C4×C43—21no—
216C4⋊C4×C43C22×C412yes—
217C22⋊C4×C43—24no—
218C22⋊Dic43—22no—
219C22⋊Dic43—22no—
220C22⋊Dic43—42no—
221C22⋊Dic43—42no—
222C22⋊Dic43—42no—
223C22⋊Dic43—42no—
224C22⋊Dic43—42no—
225C22⋊Dic43—81no—
226C22⋊Dic43—81no—
227C4⋊Dic43—21no—
228C4⋊Dic43—21no—
229C4⋊Dic43—21no—
230C4⋊Dic43—21no—
231C4⋊Dic43—21no—
232C4⋊Dic43—21no—
233C4⋊Dic43—21no—
234C4⋊Dic43—42no—
235C4⋊Dic43—42no—
236C4⋊Dic43—81no—
237C4⋊Dic43C2×D412yes—
238C4×Dic43—21no—
239C4×Dic43—21no—
240C4×Dic43—21no—
241C4×Dic43—21no—
242C4×Dic43—42no—
243C4×Dic43—81no—
244C2×C43⋊C8—21no—
245C2×C43⋊C8—21no—
246C2×C43⋊C8—21no—
247C2×C43⋊C8—21no—
248C2×C43⋊C8—21no—
249C2×C43⋊C8—44no—
250C2×C43⋊C8C2×D412yes—
251C23×C43—21no—
252C23×C43—21no—
253C23×C43—21no—
254C23×C43—21no—
255C23×C43—22no—
256C23×C43—22no—
257C23×C43—22no—
258C23×C43—22no—
259C23×C43—48no—
260C23×C43—41no—
261C23×C43—41no—
262C23×C43—41no—
263C23×C43—41no—
264C23×C43—41no—
265C23×C43—41no—
266C23×C43—41no—
267C23×C43—41no—
268C23×C43—41no—
269C23×C43—41no—
270C23×C43—48no—
271C23×C43—84no—
272C23×C43—84no—
273C23×C43—84no—
274C23×C43—84no—
275C23×C43—84no—
276C23×C43C4×D412yes—
277C23×C43AGL(1,ℤ/8)12yes—
278C23×C43#13712yes—
279C23×C43C22×D411yescharacteristic
280Q8×C43—22no—
281Q8×C43—22no—
282Q8×C43—41no—
283Q8×C43—41no—
284D4×C43—22no—
285D4×C43—22no—
286D4×C43—22no—
287D4×C43—22no—
288D4×C43—22no—
289D4×C43—48no—
290D4×C43—41no—
291D4×C43—41no—
292D4×C43C4×D414yes—
293C2×C4×C43—21no—
294C2×C4×C43—21no—
295C2×C4×C43—22no—
296C2×C4×C43—22no—
297C2×C4×C43—22no—
298C2×C4×C43—22no—
299C2×C4×C43—22no—
300C2×C4×C43—22no—
301C2×C4×C43—41no—
302C2×C4×C43—41no—
303C2×C4×C43—41no—
304C2×C4×C43—41no—
305C2×C4×C43C4×D412yes—
306C2×C4×C43C23×C411yescharacteristic
307C2×C4×C43C22×D411yescharacteristic
308C2×C4×C43C2×#4111yescharacteristic
309C2×C4×C43C2×#4111yescharacteristic
310C2×C4×C43H(5,𝔽2)11yescharacteristic
311C2×C4×C43H(5,𝔽2)11yescharacteristic
312C2×Dic43—21no—
313C2×Dic43—21no—
314C2×Dic43—22no—
315C2×Dic43—21no—
316C2×Dic43—21no—
317C2×Dic43—21no—
318C2×Dic43—21no—
319C2×Dic43—21no—
320C2×Dic43—21no—
321C2×Dic43—21no—
322C2×Dic43—21no—
323C2×Dic43—21no—
324C2×Dic43—21no—
325C2×Dic43—41no—
326C2×Dic43—41no—
327C2×Dic43—41no—
328C2×Dic43—41no—
329C2×Dic43—41no—
330C2×Dic43—41no—
331C2×Dic43—41no—
332C2×Dic43—41no—
333C2×Dic43—41no—
334C2×Dic43—41no—
335C2×Dic43—41no—
336C2×Dic43—84no—
337C2×Dic43—84no—
338C2×Dic43—84no—
339C8×C43—22no—
340C8×C43—22no—
341C43⋊C8—22no—
342C43⋊C8—41no—
343#22854—431nomaximal, Sylow
344C22×C43—22no—
345C22×C43—22no—
346C22×C43—22no—
347C22×C43—22no—
348C22×C43—22no—
349C22×C43—22no—
350C22×C43—24no—
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—42no—
360C22×C43—816no—
361C22×C43—81no—
362C22×C43—81no—
363C22×C43—81no—
364C22×C43—81no—
365C22×C43#44014yescomplemented
366C22×C43C2×C4×D411yescharacteristic
367C22×C43D4211yescharacteristic
368C22×C43#54611yescharacteristic
369C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
370C22×C43C2×#13711yescharacteristic
371C22×C43#57611yescharacteristic
372C22×C43#57711yescharacteristic
373C4×C43—22no—
374C4×C43—42no—
375C4×C43—42no—
376C4×C43C2×C4×D411yescharacteristic
377C4×C43#51811yescharacteristic
378C4×C43#54611yescharacteristic
379C4×C43#55111yescharacteristic
380Dic43—41no—
381Dic43—42no—
382Dic43—41no—
383Dic43—41no—
384Dic43—41no—
385Dic43—81no—
386Dic43—81no—
387Dic43—81no—
388C2×#450D4311yescharacteristic
389C2×#440—431no—
390C22×#102—431no—
391#2360—431no—
392D4×C22⋊C4—431no—
393#1973—431no—
394#1936—431no—
395#1925—431no—
396#1892—431no—
397#1880—431no—
398#1877—431no—
399#1862—431no—
400#1852—431no—
401#1762—431no—
402#1752—431no—
403C2×C43—24no—
404C2×C43—44no—
405C2×C43—82no—
406C2×C43#235811yescharacteristic
407C2×C43C2×#44011yescharacteristic
408C2×C43#294611yescharacteristic
409C2×C43#326411yescharacteristic
410C2×C43#326611yescharacteristic
411C2×C43#331011yescharacteristic
412C2×C43#331411yescharacteristic
413C23×D4C2×D4311yescharacteristic
414C22×SD16C2×D4311yescharacteristic
415C22×SD16C2×D4311yescharacteristic
416C23×C8—431no—
417C2×C22⋊Q8C2×D4311yescharacteristic
418C2×C4×Q8—431no—
419C2×C4×D4—431no—
420C2×C4×D4—431no—
421C22×C4⋊C4—431no—
422C22×C22⋊C4—861no—
423#450Dic4318yescomplemented
424#440—864no—
425C2×#107—431no—
426C2×#107—431no—
427C2×#103—431no—
428C2×#103—431no—
429C2×#102—431no—
430C2×#102—431no—
431C2×#102—431no—
432C2×#102—431no—
433C2×#102—864no—
434C2×#102C2×D4311yescharacteristic
435C2×#102C2×D4311yescharacteristic
436C2×C22⋊C8C2×D4311yescharacteristic
437C2×#97—431no—
438C2×#97—431no—
439#391—431no—
440#390—431no—
441#390—431no—
442#389—431no—
443#389—861no—
444#387—861no—
445#386—861no—
446#386—861no—
447#385—861no—
448#380—431no—
449#379—861no—
450C4×C4⋊C4—431no—
451C4×C22⋊C4—431no—
452C4×C22⋊C4—861no—
453#340—431no—
454#340—431no—
455#340—431no—
456#340—431no—
457#336—431no—
458#336—431no—
459C43#2285411yescharacteristic, complemented, Sylow
460C25—21no—
461C22×Q8C22×D4311yescharacteristic
462C22×D4—22no—
463C22×D4—22no—
464C22×D4—21no—
465C22×D4—22no—
466C22×D4—41no—
467C22×D4—41no—
468C22×D4C2×Dic4314yes—
469C22×D4C22×D4311yescharacteristic
470C22×D4C22×D4311yescharacteristic
471C23×C4—861no—
472C23×C4—861no—
473C23×C4—861no—
474C23×C4C22×D4311yescharacteristic
475C2×SD16—22no—
476C2×SD16—22no—
477C2×SD16—41no—
478C2×SD16—41no—
479C2×SD16C2×Dic4314yescomplemented
480C2×SD16C2×Dic4314yescomplemented
481C22×C8—431no—
482C22×C8—431no—
483C22×C8—862no—
484C22×C8—862no—
485C22×C8—1721no—
486C22×C8C22×D4311yescharacteristic
487C22×C8C22×D4311yescharacteristic
488C22⋊Q8—22no—
489C22⋊Q8C2×Dic4314yescomplemented
490C4×Q8—862no—
491C4×Q8—1721no—
492C4×D4—862no—
493C4×D4—862no—
494C4×D4—1721no—
495C4×D4—1721no—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—431no—
498C2×C4⋊C4—431no—
499C2×C4⋊C4—431no—
500C2×C4⋊C4—431no—
501C2×C4⋊C4—862no—
502C2×C4⋊C4—861no—
503C2×C4⋊C4—861no—
504C2×C4⋊C4—861no—
505C2×C4⋊C4—1721no—
506C2×C4⋊C4C22×D4311yescharacteristic
507C2×C22⋊C4—21no—
508C2×C22⋊C4—431no—
509C2×C22⋊C4—431no—
510C2×C22⋊C4—861no—
511C2×C22⋊C4—861no—
512C2×C22⋊C4—861no—
513C2×C22⋊C4—861no—
514C2×C22⋊C4—861no—
515C2×C22⋊C4—861no—
516C2×C22⋊C4—861no—
517C2×C22⋊C4—1724no—
518C2×C42—431no—
519C2×C42—431no—
520C2×C42—861no—
521C2×C42—861no—
522#107—862no—
523#107—1721no—
524#103—862no—
525#103—1721no—
526#102—434no—
527#102—862no—
528#102—862no—
529#102—862no—
530#102C2×Dic4314yescomplemented
531#102C2×Dic4314yescomplemented
532C22⋊C8C2×Dic4314yescomplemented
533#97—862no—
534#97—1721no—
535#95—431no—
536#95—431no—
537#95—861no—
538#95—861no—
539#95—861no—
540#95—861no—
541#95—861no—
542C24—21no—
543C24—21no—
544C24—24no—
545C24—42no—
546C24—42no—
547C24—42no—
548C24—42no—
549C24—81no—
550C24—81no—
551C24D4×D4311yescharacteristic
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8—21no—
555C2×Q8—21no—
556C2×Q8—21no—
557C2×Q8C22×Dic4312yes—
558C2×D4—28no—
559C2×D4—24no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—44no—
569C2×D4—44no—
570C2×D4—44no—
571C2×D4—42no—
572C2×D4—42no—
573C2×D4D4×D4312yes—
574C2×D4#1062190012yes—
575C2×D4C22×Dic4312yes—
576C2×D4C22×Dic4312yes—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—431no—
584C22×C4—431no—
585C22×C4—431no—
586C22×C4—431no—
587C22×C4—861no—
588C22×C4—861no—
589C22×C4—861no—
590C22×C4—861no—
591C22×C4—3441no—
592C22×C4—3441no—
593C22×C4—3441no—
594C22×C4—1722no—
595C22×C4—1722no—
596C22×C4—1722no—
597C22×C4—1722no—
598C22×C4—1722no—
599C22×C4—1722no—
600C22×C4D4×D4311yescharacteristic
601C22×C4#1062190012yes—
602C22×C4C22×Dic4312yes—
603C22×C4C23×D4311yescharacteristic
604SD16—28no—
605SD16—44no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—432no—
611C2×C8—861no—
612C2×C8—861no—
613C2×C8—861no—
614C2×C8—861no—
615C2×C8—861no—
616C2×C8—1724no—
617C2×C8C22×Dic4312yes—
618C2×C8C22×Dic4312yes—
619C4⋊C4—24no—
620C4⋊C4—21no—
621C4⋊C4—432no—
622C4⋊C4—861no—
623C4⋊C4—861no—
624C4⋊C4—861no—
625C4⋊C4—861no—
626C4⋊C4—861no—
627C4⋊C4—861no—
628C4⋊C4—861no—
629C4⋊C4—3441no—
630C4⋊C4—1722no—
631C4⋊C4—1722no—
632C4⋊C4C22×Dic4312yes—
633C22⋊C4—24no—
634C22⋊C4—862no—
635C22⋊C4—862no—
636C22⋊C4—3441no—
637C22⋊C4—3441no—
638C22⋊C4—1722no—
639C22⋊C4—1722no—
640C22⋊C4—1722no—
641C22⋊C4—1722no—
642C22⋊C4—1722no—
643C42—861no—
644C42—861no—
645C42—861no—
646C42—861no—
647C42—3441no—
648C42—1722no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—48no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—48no—
667C23—41no—
668C23—41no—
669C23—84no—
670C23—84no—
671C23—84no—
672C23—84no—
673C23—84no—
674C23D4×Dic4312yes—
675C23#1306335212yes—
676C23#1306335412yes—
677C23C2×D4×D4311yescharacteristic
678Q8—22no—
679Q8—22no—
680Q8—41no—
681Q8—41no—
682D4—22no—
683D4—22no—
684D4—22no—
685D4—22no—
686D4—22no—
687D4—48no—
688D4—41no—
689D4—41no—
690D4D4×Dic4314yes—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—861no—
704C2×C4—861no—
705C2×C4—861no—
706C2×C4—861no—
707C2×C4—861no—
708C2×C4—861no—
709C2×C4—861no—
710C2×C4—861no—
711C2×C4—861no—
712C2×C4—861no—
713C2×C4—862no—
714C2×C4—861no—
715C2×C4—861no—
716C2×C4—3444no—
717C2×C4—3444no—
718C2×C4—3444no—
719C2×C4—1721no—
720C2×C4—1721no—
721C2×C4—1721no—
722C2×C4—1721no—
723C2×C4—1721no—
724C2×C4—1721no—
725C2×C4—1721no—
726C2×C4—1721no—
727C2×C4—1721no—
728C2×C4—1721no—
729C2×C4—1721no—
730C2×C4D4×Dic4312yes—
731C2×C4C23×Dic4311yescharacteristic
732C2×C4C2×D4×D4311yescharacteristic
733C2×C4C2×#1062190011yescharacteristic
734C2×C4C2×#1062190011yescharacteristic
735C2×C4#1306337011yescharacteristic
736C2×C4#1306337011yescharacteristic
737C8—22no—
738C8—22no—
739C8—862no—
740C8—1721no—
741C22—22no—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—22no—
746C22—22no—
747C22—24no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—816no—
758C22—81no—
759C22—81no—
760C22—81no—
761C22—81no—
762C22#1458300014yescomplemented
763C22C2×D4×Dic4311yescharacteristic
764C22#1458353111yescharacteristic
765C22#1458353611yescharacteristic
766C22C2×#1306335211yescharacteristic
767C22C2×#1306335411yescharacteristic
768C22#1458370311yescharacteristic
769C22#1458370911yescharacteristic
770C4—22no—
771C4—42no—
772C4—42no—
773C4—3441no—
774C4—3441no—
775C4—3441no—
776C4—1721no—
777C4—1722no—
778C4—1721no—
779C4—1721no—
780C4—1721no—
781C4C2×D4×Dic4311yescharacteristic
782C4#1458337411yescharacteristic
783C4#1458353611yescharacteristic
784C4#1458358011yescharacteristic
785C2—24no—
786C2—44no—
787C2—82no—
788C2#1913757911yescharacteristic
789C2C2×#1458300011yescharacteristic
790C2#1914342811yescharacteristic
791C2#1914607911yescharacteristic
792C2#1914610911yescharacteristic
793C2#1914662011yescharacteristic
794C2#1914668011yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#450C2
socleC23×C43C22×D4
prime radicalC23×D4×C43C22
cosocleC22×C4×C43C24
hypercenterC2×#450D43
hypocenterC43#22854
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#450

Complements

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

NH ≅ G/Ntype
1. C2×#14583000C2semidirect
3. #19137604C2semidirect
5. #19135478C2semidirect
6. #19135294C2semidirect
7. #19135217C2semidirect
8. #19135019C2semidirect
9. #19134952C2semidirect
10. #19134931C2semidirect
11. #19134844C2semidirect
12. #19134785C2semidirect
13. #19134422C2semidirect
14. #19134374C2semidirect
17. C2×Q8×Dic43C22semidirect
23. C2×#13063259C22semidirect
24. C2×#13063259C22semidirect
25. C2×#13063249C22semidirect
26. C2×#13063249C22semidirect
32. C2×#13063235C22semidirect
33. C2×#13063235C22semidirect
34. #14582806C22semidirect
38. #14582798C22semidirect
45. C4⋊C4×Dic43C22semidirect
48. #14582662C22semidirect
49. #14582662C22semidirect
50. #14582661C22semidirect
51. #14582661C22semidirect
52. #14582653C22semidirect
53. #14582653C22semidirect
58. C43×#450C4semidirect
132. C2×SD16×C43C2×C4semidirect
133. C2×SD16×C43C2×C4semidirect
137. C22⋊Q8×C43C2×C4semidirect
141. #102×C43C2×C4semidirect
142. #102×C43C2×C4semidirect
143. C22⋊C8×C43C2×C4semidirect
365. C22×C43#440semidirect
423. #450Dic43semidirect
459. C43#22854semidirect
479. C2×SD16C2×Dic43semidirect
480. C2×SD16C2×Dic43semidirect
489. C22⋊Q8C2×Dic43semidirect
530. #102C2×Dic43semidirect
531. #102C2×Dic43semidirect
532. C22⋊C8C2×Dic43semidirect
762. C22#14583000semidirect

Maximal subgroups

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

subgroupindex
C2×#145830002
C22×#130632462
#191376042
D4×C22⋊Dic432
#191354782
#191352942
#191352172
#191350192
#191349522
#191349312
#191348442
#191347852
#191344222
#191343742
C2×C43×#4502
#2285443