Finite Group Databasebeta

← #25123927

Subgroups — #25123927

Order 11008.

1362 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×#14583529C211yesmaximal, characteristic, complemented
2C2×#14582902C211yesmaximal, characteristic
3C2×#102×D43C211yesmaximal, characteristic
4#19137174C211yesmaximal, characteristic
5#19135740C211yesmaximal, characteristic, complemented
6#19135739C211yesmaximal, characteristic, complemented
7#19135738C211yesmaximal, characteristic, complemented
8#19135732C211yesmaximal, characteristic, complemented
9#19135731C211yesmaximal, characteristic, complemented
10#19135730C211yesmaximal, characteristic, complemented
11#19135729C211yesmaximal, characteristic, complemented
12#19134313C211yesmaximal, characteristic, complemented
13#19134310C211yesmaximal, characteristic, complemented
14#19134290C211yesmaximal, characteristic, complemented
15C43×#2025C211yesmaximal, characteristic, complemented
16C22×D4×D43C2211yescharacteristic
17C22×#10621872C2211yescharacteristic
18C22×C8×D43C2211yescharacteristic
19#14583529—24no—
20#14583529—24no—
21C2×#13063325C2211yescharacteristic, complemented
22C2×#13063324—21no—
23C2×#13063324C2211yescharacteristic, complemented
24C2×#13063316C2211yescharacteristic, complemented
25C2×#13063315—21no—
26C2×#13063305—21no—
27C2×#13063303—21no—
28C2×#13063283C2211yescharacteristic
29C2×#13063283C2211yescharacteristic
30C2×#13063282C2211yescharacteristic
31C2×C4⋊C4×D43C2211yescharacteristic
32#14582902—24no—
33C2×#13063247C2211yescharacteristic
34C2×#13063247C2211yescharacteristic
35C2×#13063246C2211yescharacteristic
36C2×#13063246C2211yescharacteristic
37C2×#13063245C2211yescharacteristic
38C2×#13063245C2211yescharacteristic
39#102×D43—24no—
40#14582802C2211yescharacteristic
41#14582801C2211yescharacteristic
42#14582800C2211yescharacteristic
43#14582799—21no—
44#14582799—21no—
45#14582754—21no—
46#14582754—21no—
47#14582662C2211yescharacteristic, complemented
48#14582662C2211yescharacteristic, complemented
49#14582661C2211yescharacteristic, complemented
50#14582661C2211yescharacteristic, complemented
51#14582661C2211yescharacteristic, complemented
52#14582661C2211yescharacteristic, complemented
53#14582654C2211yescharacteristic, complemented
54#14582653C2211yescharacteristic, complemented
55#14582653C2211yescharacteristic, complemented
56C2×#125×C43C2211yescharacteristic, complemented
57C2×#102×C43C2211yescharacteristic
58C2×#102×C43C2211yescharacteristic
59C43×#390C2211yescharacteristic
60C43×#340C2211yescharacteristic, complemented
61C43×#340C2211yescharacteristic, complemented
62C43×#336C2211yescharacteristic, complemented
63C24×D43—21no—
64C22×Dic86—21no—
65C22×Dic86—21no—
66C22×D172C2311yescharacteristic
67C22×C22⋊D43—21no—
68C2×D4×D43—22no—
69C2×D4×D43—22no—
70C2×D4×D43—22no—
71C2×D4×D43—22no—
72C2×D4×D43—22no—
73C2×D4×D43Q814yescomplemented
74C22×C4×D43—21no—
75C22×C4×D43C2311yescharacteristic
76C2×#10621872—22no—
77C2×#10621872—22no—
78C2×#10621872—22no—
79C22×C43⋊C8C2311yescharacteristic
80C22×C43⋊C8C2311yescharacteristic
81C2×C8×D43—22no—
82C2×C8×D43—22no—
83C2×C8×D43—22no—
84#13063325—22no—
85#13063325—22no—
86#13063324—28no—
87#13063324—22no—
88#13063324—22no—
89#13063316—22no—
90#13063316—22no—
91#13063315—28no—
92#13063305—28no—
93#13063303—28no—
94#13063283—22no—
95#13063283—22no—
96#13063283—22no—
97#13063283D414yes—
98#13063282—22no—
99#13063282—22no—
100C2×C4⋊Dic43—21no—
101C2×C4⋊Dic43—21no—
102C2×C4⋊Dic43C2311yescharacteristic
103C2×C4⋊Dic43C2311yescharacteristic
104C2×C4⋊Dic43C2311yescharacteristic
105C2×Dic43⋊C4—21no—
106C2×Dic43⋊C4—21no—
107C2×Dic43⋊C4—21no—
108C2×Dic43⋊C4D411yescharacteristic
109C2×Dic43⋊C4D411yescharacteristic
110C4⋊C4×D43—22no—
111C4⋊C4×D43D414yes—
112C2×C22⋊Dic43—21no—
113C2×C22⋊Dic43—21no—
114C2×(C2×D43)⋊C4—21no—
115C2×(C2×D43)⋊C4—21no—
116C2×(C2×D43)⋊C4—21no—
117C2×(C2×D43)⋊C4—21no—
118C2×(C2×D43)⋊C4—21no—
119C2×(C2×D43)⋊C4—21no—
120C2×(C2×D43)⋊C4D411yescharacteristic
121C2×(C2×D43)⋊C4D411yescharacteristic
122C2×C4×Dic43—21no—
123C2×C4×Dic43—21no—
124C2×C4×Dic43C2311yescharacteristic
125#13063247—22no—
126#13063247—22no—
127#13063246—22no—
128#13063246—22no—
129#13063245—22no—
130#13063245—22no—
131C22×D4×C43C2311yescharacteristic
132C22×C8×C43C2311yescharacteristic
133C22×C8×C43C2311yescharacteristic
134#125×C43—22no—
135#125×C43—22no—
136C2×C4⋊C4×C43—21no—
137C2×C4⋊C4×C43—21no—
138C2×C4⋊C4×C43C2311yescharacteristic
139C2×C4⋊C4×C43C2311yescharacteristic
140C2×C4⋊C4×C43C2311yescharacteristic
141C2×C22⋊C4×C43—21no—
142C2×C22⋊C4×C43—21no—
143C2×C42×C43C2311yescharacteristic
144#102×C43—22no—
145#102×C43—22no—
146C24×C43—21no—
147C23×D43—21no—
148C23×D43—24no—
149C23×D43—42no—
150C23×D43—42no—
151C23×D43—81no—
152C23×D43—81no—
153C23×D43—81no—
154C23×D43—81no—
155C23×D43C2×D411yescharacteristic
156C2×D4×C43—21no—
157C2×D4×C43—21no—
158C2×D4×C43—21no—
159C2×D4×C43—21no—
160C2×D4×C43—21no—
161C2×D4×C43C2×Q812yes—
162C22×C4×C43—21no—
163C22×C4×C43—21no—
164C22×C4×C43—21no—
165C22×C4×C43C2×D411yescharacteristic
166C22×C4×C43C2×D411yescharacteristic
167C22×C4×C43C2411yescharacteristic
168C2×C22⋊D43—24no—
169C2×C22⋊D43—42no—
170C2×C22⋊D43—42no—
171C22×Dic43—21no—
172C22×Dic43—21no—
173C22×Dic43—21no—
174C22×Dic43C2×D411yescharacteristic
175C22×Dic43C2×D411yescharacteristic
176C22×Dic43C2×D411yescharacteristic
177D4×D43—28no—
178D4×D43—28no—
179D4×D43—44no—
180D4×D43—44no—
181C2×D172—21no—
182C2×D172—21no—
183C2×D172—21no—
184C2×D172—21no—
185C2×D172—21no—
186C2×D172C2×Q812yes—
187C2×C4×D43—24no—
188C2×C4×D43—81no—
189C2×C4×D43—81no—
190C2×C4×D43C2×D412yes—
191C2×C4×D43C2×D412yes—
192C2×C4×D43C2×Q812yes—
193C2×C4×D43#4112yes—
194C2×C4×D43#4112yes—
195C2×C4×D43#4112yes—
196C2×Dic86—24no—
197C2×Dic86—24no—
198C2×Dic86—81no—
199C2×Dic86—81no—
200C2×Dic86—81no—
201C2×Dic86—81no—
202C2×C8×C43—21no—
203C2×C8×C43—21no—
204C2×C8×C43—21no—
205C2×C8×C43—21no—
206C2×C8×C43—21no—
207C2×C8×C43—21no—
208C4⋊C4×C43—24no—
209C4⋊C4×C43—24no—
210C4⋊C4×C43—21no—
211C4⋊C4×C43—21no—
212C4⋊C4×C43—21no—
213C4⋊C4×C43—21no—
214C4⋊C4×C43C2×D412yes—
215C4⋊C4×C43C2×D412yes—
216C22⋊C4×C43—81no—
217C22⋊C4×C43—81no—
218C42×C43—21no—
219C42×C43—21no—
220C22⋊Dic43—81no—
221C22⋊Dic43—81no—
222(C2×D43)⋊C4—24no—
223(C2×D43)⋊C4—22no—
224(C2×D43)⋊C4—22no—
225(C2×D43)⋊C4—42no—
226(C2×D43)⋊C4—81no—
227(C2×D43)⋊C4—81no—
228(C2×D43)⋊C4—81no—
229(C2×D43)⋊C4—81no—
230C4⋊Dic43—24no—
231C4⋊Dic43—24no—
232C4⋊Dic43—21no—
233C4⋊Dic43—21no—
234C4⋊Dic43—21no—
235C4⋊Dic43—21no—
236C4⋊Dic43C2×D412yes—
237C4⋊Dic43C2×D412yes—
238Dic43⋊C4—24no—
239Dic43⋊C4—24no—
240Dic43⋊C4—24no—
241Dic43⋊C4—22no—
242Dic43⋊C4—22no—
243C4×Dic43—21no—
244C4×Dic43—21no—
245C4×Dic43—24no—
246C4×Dic43—42no—
247C2×C43⋊C8—21no—
248C2×C43⋊C8—21no—
249C2×C43⋊C8—21no—
250C2×C43⋊C8—21no—
251C2×C43⋊C8—21no—
252C2×C43⋊C8—21no—
253#10621872—44no—
254C8×D43—44no—
255C23×C43—22no—
256C23×C43—41no—
257C23×C43—41no—
258C23×C43—41no—
259C23×C43—41no—
260C23×C43—41no—
261C23×C43—41no—
262C23×C43C22×D411yescharacteristic
263C22×D43—21no—
264C22×D43—21no—
265C22×D43—21no—
266C22×D43—21no—
267C22×D43—22no—
268C22×D43—41no—
269C22×D43—41no—
270C22×D43—41no—
271C22×D43—41no—
272C22×D43—41no—
273C22×D43—41no—
274C22×D43—48no—
275C22×D43—84no—
276C22×D43—84no—
277C22×D43—84no—
278C22×D43—84no—
279C22×D43—84no—
280C22×D43—84no—
281C22×D43#12012yes—
282C22×D43C22⋊Q812yes—
283C22×D43#12412yes—
284D4×C43—22no—
285D4×C43—22no—
286D4×C43—41no—
287D4×C43—41no—
288C2×C4×C43—22no—
289C2×C4×C43—22no—
290C2×C4×C43—21no—
291C2×C4×C43—21no—
292C2×C4×C43—21no—
293C2×C4×C43—21no—
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×C43—41no—
302C2×C4×C43—41no—
303C2×C4×C43C22×D411yescharacteristic
304C2×C4×C43C22×D411yescharacteristic
305C2×C4×C43C22×Q811yescharacteristic
306C2×C4×C43C2×#4111yescharacteristic
307C2×C4×C43C2×#4111yescharacteristic
308C2×C4×C43C2×#4111yescharacteristic
309C22⋊D43—48no—
310C2×Dic43—21no—
311C2×Dic43—21no—
312C2×Dic43—22no—
313C2×Dic43—22no—
314C2×Dic43—21no—
315C2×Dic43—21no—
316C2×Dic43—21no—
317C2×Dic43—21no—
318C2×Dic43—41no—
319C2×Dic43—41no—
320C2×Dic43—41no—
321C2×Dic43—41no—
322C2×Dic43—41no—
323C2×Dic43—41no—
324C2×Dic43—41no—
325C2×Dic43#12012yes—
326C2×Dic43C22⋊Q812yes—
327C2×Dic43#12412yes—
328D172—22no—
329D172—22no—
330D172—41no—
331D172—41no—
332C4×D43—84no—
333C4×D43C22⋊Q814yes—
334C4×D43C22⋊Q814yes—
335C4×D43#12414yes—
336C4×D43#12414yes—
337Dic86—84no—
338Dic86—84no—
339C8×C43—41no—
340C8×C43—41no—
341C43⋊C8—41no—
342C43⋊C8—41no—
343#23456—431nomaximal, Sylow
344C22×C43—42no—
345C22×C43—42no—
346C22×C43—42no—
347C22×C43—81no—
348C22×C43—81no—
349C22×C43—81no—
350C22×C43—81no—
351C22×C43C2×#12011yescharacteristic
352C22×C43C2×C22⋊Q811yescharacteristic
353C22×C43C2×#12411yescharacteristic
354C22×C43#57611yescharacteristic
355C22×C43#57611yescharacteristic
356C22×C43#57711yescharacteristic
357C22×C43#57711yescharacteristic
358C2×D43—22no—
359C2×D43—22no—
360C2×D43—22no—
361C2×D43—22no—
362C2×D43—22no—
363C2×D43—22no—
364C2×D43—42no—
365C2×D43—42no—
366C2×D43—42no—
367C2×D43—816no—
368C2×D43—81no—
369C2×D43—81no—
370C2×D43—81no—
371C2×D43—81no—
372C2×D43#39314yes—
373C4×C43—41no—
374C4×C43—42no—
375C4×C43—41no—
376C4×C43—42no—
377C4×C43—81no—
378C4×C43C2×C22⋊Q811yescharacteristic
379C4×C43C2×C22⋊Q811yescharacteristic
380C4×C43C2×#12411yescharacteristic
381C4×C43C2×#12411yescharacteristic
382Dic43—41no—
383Dic43—42no—
384Dic43—42no—
385Dic43—41no—
386Dic43—81no—
387Dic43#39314yes—
388C2×#544—431no—
389C2×#418—431no—
390C22×#102—431no—
391#2309—431no—
392#2025—431no—
393#2025—431no—
394#2025—431no—
395#2025D4311yescharacteristic, complemented
396#2023—431no—
397#2023—431no—
398#2023—431no—
399#2023—431no—
400#1736—431no—
401#1735—431no—
402#1729—431no—
403C2×C43—82no—
404C2×C43C2×#39311yescharacteristic
405C2×C43#300811yescharacteristic
406C2×C43#301011yescharacteristic
407C2×C43#308111yescharacteristic
408C2×C43#308111yescharacteristic
409C2×C43#313611yescharacteristic
410C2×C43#313611yescharacteristic
411D43—24no—
412D43—82no—
413C23×D4—431no—
414C22×M16—431no—
415C23×C8—431no—
416#544—864no—
417#544—864no—
418C2×C4⋊Q8—431no—
419C2×C4⋊Q8—431no—
420C2×C4⋊Q8—861no—
421C2×#125—431no—
422C2×#125—861no—
423C2×#125C2×D4311yescharacteristic, complemented
424C2×C22⋊Q8—861no—
425C2×C22⋊Q8—861no—
426C2×#117—431no—
427C2×#117—431no—
428C2×#117—431no—
429C22×C4⋊C4—431no—
430#418—864no—
431C2×#102—431no—
432C2×#102—431no—
433C2×#102—431no—
434C2×#102—431no—
435C2×#102—431no—
436C2×#102—431no—
437C2×#102—864no—
438C2×#102C2×D4311yescharacteristic
439C2×#102C2×D4311yescharacteristic
440#390—431no—
441#390—431no—
442#390—431no—
443#390—861no—
444#390—861no—
445#390C2×D4311yescharacteristic
446#379—861no—
447#379—861no—
448#340—431no—
449#340—431no—
450#340—431no—
451#340—431no—
452#340—431no—
453#340—431no—
454#340C2×D4311yescharacteristic, complemented
455#340C2×D4311yescharacteristic, complemented
456#336—431no—
457#336—431no—
458#336—431no—
459#336C2×D4311yescharacteristic, complemented
460C43#2345611yescharacteristic, complemented, Sylow
461C25—861no—
462C22×Q8—861no—
463C22×Q8—861no—
464C22×D4—434no—
465C22×D4—431no—
466C22×D4—862no—
467C22×D4—862no—
468C22×D4—862no—
469C22×D4—862no—
470C22×D4—862no—
471C22×D4—861no—
472C22×D4C22×D4311yescharacteristic
473C23×C4—431no—
474C23×C4—861no—
475C2×M16—862no—
476C2×M16—862no—
477C2×M16—862no—
478C22×C8—431no—
479C22×C8—431no—
480C22×C8—862no—
481C22×C8—862no—
482C22×C8—862no—
483C22×C8C22×D4311yescharacteristic
484C22×C8C22×D4311yescharacteristic
485C4⋊Q8—862no—
486C4⋊Q8—862no—
487C4⋊Q8—862no—
488C4⋊Q8—868no—
489C4⋊Q8—862no—
490#125—22no—
491#125—22no—
492#125—862no—
493#125—868no—
494#125—862no—
495C22⋊Q8—868no—
496C22⋊Q8—868no—
497#117—434no—
498#117—862no—
499#117—862no—
500#117—862no—
501#117—862no—
502#117—862no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—431no—
506C2×C4⋊C4—431no—
507C2×C4⋊C4—434no—
508C2×C4⋊C4—431no—
509C2×C4⋊C4—431no—
510C2×C4⋊C4—431no—
511C2×C4⋊C4—862no—
512C2×C4⋊C4—861no—
513C2×C4⋊C4—861no—
514C2×C4⋊C4—861no—
515C2×C4⋊C4—861no—
516C2×C4⋊C4—861no—
517C2×C4⋊C4C22×D4311yescharacteristic
518C2×C4⋊C4C22×D4311yescharacteristic
519C2×C4⋊C4C22×D4311yescharacteristic
520C2×C22⋊C4—21no—
521C2×C22⋊C4—21no—
522C2×C22⋊C4—431no—
523C2×C22⋊C4—431no—
524C2×C22⋊C4—861no—
525C2×C22⋊C4—861no—
526C2×C22⋊C4—861no—
527C2×C22⋊C4—861no—
528C2×C22⋊C4—861no—
529C2×C22⋊C4—861no—
530C2×C22⋊C4—861no—
531C2×C22⋊C4—861no—
532C2×C42—431no—
533C2×C42—861no—
534C2×C42—861no—
535C2×C42C22×D4311yescharacteristic
536#102—22no—
537#102—22no—
538#102—862no—
539#102—862no—
540#102—862no—
541#102—862no—
542#102—862no—
543#102—862no—
544C24—21no—
545C24—431no—
546C24—864no—
547C24—861no—
548C24—3441no—
549C24—3441no—
550C24—3441no—
551C24—3441no—
552C24—1722no—
553C24—1722no—
554C2×Q8—864no—
555C2×Q8—864no—
556C2×Q8—3441no—
557C2×Q8—3441no—
558C2×Q8—3441no—
559C2×Q8—3441no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—432no—
566C2×D4—868no—
567C2×D4—868no—
568C2×D4—864no—
569C2×D4—861no—
570C2×D4—861no—
571C2×D4—861no—
572C2×D4—861no—
573C2×D4—861no—
574C2×D4—1724no—
575C2×D4—1724no—
576C2×D4—1722no—
577C2×D4—1722no—
578C2×D4Q8×D4312yes—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—431no—
583C22×C4—432no—
584C22×C4—432no—
585C22×C4—432no—
586C22×C4—432no—
587C22×C4—432no—
588C22×C4—432no—
589C22×C4—431no—
590C22×C4—431no—
591C22×C4—864no—
592C22×C4—861no—
593C22×C4—861no—
594C22×C4—861no—
595C22×C4—3441no—
596C22×C4—3441no—
597C22×C4D4×D4311yescharacteristic
598C22×C4D4×D4311yescharacteristic
599C22×C4C23×D4311yescharacteristic
600M16—1724no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—861no—
608C2×C8—861no—
609C2×C8—861no—
610C2×C8—861no—
611C2×C8—861no—
612C2×C8—861no—
613C2×C8—1724no—
614C4⋊C4—24no—
615C4⋊C4—24no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—432no—
621C4⋊C4—432no—
622C4⋊C4—864no—
623C4⋊C4—862no—
624C4⋊C4—862no—
625C4⋊C4—864no—
626C4⋊C4—864no—
627C4⋊C4—864no—
628C4⋊C4—864no—
629C4⋊C4—861no—
630C4⋊C4—861no—
631C4⋊C4—861no—
632C4⋊C4—861no—
633C4⋊C4D4×D4312yes—
634C4⋊C4D4×D4312yes—
635C22⋊C4—81no—
636C22⋊C4—81no—
637C22⋊C4—862no—
638C22⋊C4—862no—
639C22⋊C4—864no—
640C22⋊C4—3441no—
641C22⋊C4—3441no—
642C22⋊C4—3441no—
643C22⋊C4—3441no—
644C22⋊C4—3441no—
645C22⋊C4—3441no—
646C22⋊C4—1722no—
647C42—21no—
648C42—21no—
649C42—864no—
650C42—861no—
651C42—861no—
652C42—1722no—
653C23—22no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—432no—
661C23—432no—
662C23—432no—
663C23—861no—
664C23—861no—
665C23—861no—
666C23—861no—
667C23—862no—
668C23—3444no—
669C23—3444no—
670C23—3444no—
671C23—3444no—
672C23—3444no—
673C23—3444no—
674C23—1728no—
675C23—1721no—
676C23—1721no—
677C23—1721no—
678C23—1721no—
679C23—1721no—
680C23—1721no—
681C23C2×D4×D4311yescharacteristic
682Q8—3444no—
683Q8—3444no—
684D4—22no—
685D4—22no—
686D4—41no—
687D4—41no—
688D4—862no—
689D4—862no—
690D4—1728no—
691D4—1721no—
692D4—1721no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—432no—
709C2×C4—432no—
710C2×C4—432no—
711C2×C4—434no—
712C2×C4—434no—
713C2×C4—434no—
714C2×C4—434no—
715C2×C4—862no—
716C2×C4—861no—
717C2×C4—861no—
718C2×C4—862no—
719C2×C4—861no—
720C2×C4—861no—
721C2×C4—861no—
722C2×C4—861no—
723C2×C4—3444no—
724C2×C4—1721no—
725C2×C4—1721no—
726C2×C4—1721no—
727C2×C4—1721no—
728C2×C4—1721no—
729C2×C4—1721no—
730C2×C4—1721no—
731C2×C4C2×D4×D4311yescharacteristic
732C2×C4C2×D4×D4311yescharacteristic
733C2×C4C2×Q8×D4311yescharacteristic
734C2×C4#41×D4311yescharacteristic
735C2×C4#41×D4311yescharacteristic
736C2×C4#41×D4311yescharacteristic
737C8—41no—
738C8—41no—
739C8—1721no—
740C8—1721no—
741C22—42no—
742C22—42no—
743C22—42no—
744C22—81no—
745C22—81no—
746C22—81no—
747C22—81no—
748C22—434no—
749C22—862no—
750C22—862no—
751C22—862no—
752C22—862no—
753C22—862no—
754C22—862no—
755C22—34416no—
756C22—3441no—
757C22—3441no—
758C22—3441no—
759C22—3441no—
760C22—1722no—
761C22—1722no—
762C22—1722no—
763C22#120×D4311yescharacteristic
764C22C22⋊Q8×D4311yescharacteristic
765C22#124×D4311yescharacteristic
766C22#1458370111yescharacteristic
767C22#1458370311yescharacteristic
768C22#1458370611yescharacteristic
769C22#1458370911yescharacteristic
770C4—41no—
771C4—42no—
772C4—41no—
773C4—42no—
774C4—81no—
775C4—434no—
776C4—3441no—
777C4—1721no—
778C4—1722no—
779C4—1722no—
780C4—1721no—
781C4C22⋊Q8×D4311yescharacteristic
782C4C22⋊Q8×D4311yescharacteristic
783C4#124×D4311yescharacteristic
784C4#124×D4311yescharacteristic
785C2—82no—
786C2—864no—
787C2—3442no—
788C2#393×D4311yescharacteristic
789C2#1914386011yescharacteristic
790C2#1914387811yescharacteristic
791C2#1914442311yescharacteristic
792C2#1914442511yescharacteristic
793C2#1914494811yescharacteristic
794C2#1914495011yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2025C2
socleC23×C43C22×D4
prime radicalC22×D4×D43C22
hypercenter#2025D43
hypocenterC43#23456
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2025

Complements

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

NH ≅ G/Ntype
1. C2×#14583529C2semidirect
5. #19135740C2semidirect
6. #19135739C2semidirect
7. #19135738C2semidirect
8. #19135732C2semidirect
9. #19135731C2semidirect
10. #19135730C2semidirect
11. #19135729C2semidirect
12. #19134313C2semidirect
13. #19134310C2semidirect
14. #19134290C2semidirect
15. C43×#2025C2semidirect
21. C2×#13063325C22semidirect
23. C2×#13063324C22semidirect
24. C2×#13063316C22semidirect
47. #14582662C22semidirect
48. #14582662C22semidirect
49. #14582661C22semidirect
50. #14582661C22semidirect
51. #14582661C22semidirect
52. #14582661C22semidirect
53. #14582654C22semidirect
54. #14582653C22semidirect
55. #14582653C22semidirect
56. C2×#125×C43C22semidirect
60. C43×#340C22semidirect
61. C43×#340C22semidirect
62. C43×#336C22semidirect
73. C2×D4×D43Q8semidirect
395. #2025D43semidirect
423. C2×#125C2×D43semidirect
454. #340C2×D43semidirect
455. #340C2×D43semidirect
459. #336C2×D43semidirect
460. C43#23456semidirect

Maximal subgroups

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

subgroupindex
C2×#145835292
C2×#145829022
C2×#102×D432
#191371742
#191357402
#191357392
#191357382
#191357322
#191357312
#191357302
#191357292
#191343132
#191343102
#191342902
C43×#20252
#2345643