Finite Group Databasebeta

← #25144042

Subgroups — #25144042

Order 11008.

1186 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583096C211yesmaximal, characteristic, complemented
2C2×#14583037C211yesmaximal, characteristic, complemented
3C2×#14583037C211yesmaximal, characteristic, complemented
4C2×C4×#10621883C211yesmaximal, characteristic, complemented
5C22⋊C4×Dic86C211yesmaximal, characteristic, complemented
6#19135973C211yesmaximal, characteristic, complemented
7#19135781C211yesmaximal, characteristic, complemented
8#19135781C211yesmaximal, characteristic, complemented
9#19135683C211yesmaximal, characteristic, complemented
10#19135448C211yesmaximal, characteristic, complemented
11#19135203C211yesmaximal, characteristic, complemented
12#19134953C211yesmaximal, characteristic, complemented
13#19134929C211yesmaximal, characteristic, complemented
14#19134862C211yesmaximal, characteristic, complemented
15C43×#2428C211yesmaximal, characteristic
16C23×Dic86C2211yescharacteristic
17C22×#10621883C2211yescharacteristic
18C22×#10621883C2211yescharacteristic
19C22×#10621883C2211yescharacteristic
20C22×#10621883C2211yescharacteristic
21C2×C4×Dic86C2211yescharacteristic
22C2×C4×Dic86C2211yescharacteristic
23#14583096—24no—
24#14583037—24no—
25#14583037—24no—
26C4×#10621883—24no—
27C2×#13063256C2211yescharacteristic
28C2×#13063256C2211yescharacteristic
29C2×C4⋊(C43⋊C8)C2211yescharacteristic
30C2×#13063248C2211yescharacteristic
31C2×#13063248C2211yescharacteristic
32C2×#13063248C2211yescharacteristic
33C2×#13063248C2211yescharacteristic
34C2×#13063246C2211yescharacteristic
35C2×#13063246C2211yescharacteristic
36C2×#13063246C2211yescharacteristic
37C2×#13063246C2211yescharacteristic
38C2×C22⋊(C43⋊C8)C2211yescharacteristic
39C2×C22⋊(C43⋊C8)C2211yescharacteristic
40C2×C4×C43⋊C8C2211yescharacteristic
41#14582805C2211yescharacteristic
42#14582805C2211yescharacteristic
43#14582803—21no—
44#14582803—21no—
45#14582759C2211yescharacteristic
46#14582757—21no—
47C22⋊C4×Dic43—21no—
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582654C2211yescharacteristic
51#14582654C2211yescharacteristic
52C2×#127×C43C2211yescharacteristic
53C2×#121×C43—21no—
54C2×#121×C43C2211yescharacteristic
55C2×#121×C43C2211yescharacteristic
56C2×C4×D4×C43C2211yescharacteristic
57C43×#394—21no—
58C43×#392—21no—
59C43×#390C2211yescharacteristic
60C43×#389C2211yescharacteristic
61C43×#386—21no—
62C4×C22⋊C4×C43C2211yescharacteristic
63C22×Dic86—21no—
64C22×Dic86—22no—
65C22×Dic86—22no—
66C22×Dic86—22no—
67C22×Dic86—22no—
68C22×Dic86—41no—
69C22×Dic86—41no—
70C22×Dic86C2311yescharacteristic
71C22×Dic86C2311yescharacteristic
72C23×Dic43—21no—
73C2×#10621883—22no—
74C2×#10621883—22no—
75C2×#10621883—22no—
76C2×#10621883—22no—
77C2×#10621883—22no—
78C2×#10621883—22no—
79C2×#10621883—22no—
80C2×#10621883—22no—
81C2×#10621883—22no—
82C2×#10621883—41no—
83C2×#10621883—41no—
84C2×#10621883D414yescomplemented
85C22×C43⋊C8C2311yescharacteristic
86C22×C43⋊C8C2311yescharacteristic
87C22×C43⋊C8C2311yescharacteristic
88C22×C43⋊C8C2311yescharacteristic
89C4×Dic86—22no—
90C4×Dic86—22no—
91C4×Dic86—41no—
92C4×Dic86—41no—
93C2×C4⋊Dic43C2311yescharacteristic
94C2×C4⋊Dic43C2311yescharacteristic
95C2×Dic43⋊C4—21no—
96C2×Dic43⋊C4—21no—
97C2×C22⋊Dic43—21no—
98C2×C4×Dic43—21no—
99C2×C4×Dic43—21no—
100#13063256—22no—
101#13063256—41no—
102C4⋊(C43⋊C8)—22no—
103#13063248—22no—
104#13063248—22no—
105#13063248—22no—
106#13063248D414yescomplemented
107#13063246—22no—
108#13063246—22no—
109#13063246—22no—
110#13063246—41no—
111C22⋊(C43⋊C8)—22no—
112C22⋊(C43⋊C8)—22no—
113C4×C43⋊C8—22no—
114C43⋊#95—21no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C43⋊#95—21no—
118C43⋊#95—21no—
119C22×D4×C43—21no—
120C22×D4×C43—21no—
121C22×D4×C43—21no—
122C22×D4×C43—21no—
123C22×D4×C43C2311yescharacteristic
124C22×D4×C43C2311yescharacteristic
125C23×C4×C43—21no—
126C23×C4×C43C2311yescharacteristic
127#127×C43—22no—
128#127×C43—41no—
129#121×C43—22no—
130#121×C43—22no—
131#121×C43—41no—
132#121×C43—41no—
133#121×C43—44no—
134C4×D4×C43—22no—
135C4×D4×C43—41no—
136C2×C4⋊C4×C43—21no—
137C2×C4⋊C4×C43C2311yescharacteristic
138C2×C4⋊C4×C43C2311yescharacteristic
139C2×C22⋊C4×C43—21no—
140C2×C22⋊C4×C43—21no—
141C2×C22⋊C4×C43—21no—
142C2×C22⋊C4×C43—21no—
143C2×C22⋊C4×C43—21no—
144C2×C22⋊C4×C43D411yescharacteristic
145C2×C22⋊C4×C43D411yescharacteristic
146C2×C42×C43C2311yescharacteristic
147C2×C42×C43C2311yescharacteristic
148#95×C43—21no—
149#95×C43D411yescharacteristic
150#95×C43D411yescharacteristic
151C24×C43—21no—
152C24×C43—21no—
153C24×C43C2×D411yescharacteristic
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43—21no—
157C2×D4×C43—21no—
158C2×D4×C43—21no—
159C2×D4×C43—21no—
160C2×D4×C43—21no—
161C2×D4×C43—21no—
162C2×D4×C43—21no—
163C2×D4×C43—21no—
164C2×D4×C43—21no—
165C2×D4×C43—42no—
166C2×D4×C43—42no—
167C2×D4×C43—42no—
168C2×D4×C43—42no—
169C2×D4×C43—42no—
170C2×D4×C43—42no—
171C2×D4×C43—42no—
172C2×D4×C43—42no—
173C2×D4×C43—81no—
174C2×D4×C43—81no—
175C2×D4×C43—81no—
176C2×D4×C43—81no—
177C2×D4×C43C2×D412yes—
178C22×C4×C43—21no—
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×C43—21no—
186C22×C4×C43—42no—
187C22×C4×C43—42no—
188C22×C4×C43—81no—
189C22×C4×C43C2×D411yescharacteristic
190C22×C4×C43C2×D411yescharacteristic
191C22×C4×C43C2×D411yescharacteristic
192C22×C4×C43C2×D411yescharacteristic
193C22×C4×C43C2×D411yescharacteristic
194C22×C4×C43C2411yescharacteristic
195C22×Dic43—24no—
196C22×Dic43—21no—
197C22×Dic43—21no—
198C22×Dic43—21no—
199C22×Dic43—21no—
200C22×Dic43—42no—
201C22×Dic43—42no—
202C2×Dic86—21no—
203C2×Dic86—21no—
204C2×Dic86—21no—
205C2×Dic86—21no—
206C2×Dic86—21no—
207C2×Dic86—21no—
208C2×Dic86—21no—
209C2×Dic86—24no—
210C2×Dic86—21no—
211C2×Dic86—44no—
212C2×Dic86—44no—
213C2×Dic86—44no—
214C2×Dic86—42no—
215C2×Dic86—42no—
216C2×Dic86—44no—
217C2×Dic86C2×D412yes—
218C2×Dic86C2×D412yes—
219C2×Dic86#4112yes—
220C2×Dic86#4112yes—
221C4⋊C4×C43—21no—
222C4⋊C4×C43—21no—
223C4⋊C4×C43—21no—
224C4⋊C4×C43—42no—
225C4⋊C4×C43C2×D412yes—
226C22⋊C4×C43—41no—
227C22⋊C4×C43—42no—
228C22⋊C4×C43—42no—
229C22⋊C4×C43—42no—
230C22⋊C4×C43—42no—
231C22⋊C4×C43—81no—
232C22⋊C4×C43SD1614yescomplemented
233C42×C43—21no—
234C42×C43—21no—
235C42×C43—21no—
236C42×C43—21no—
237C22⋊Dic43—42no—
238#10621883—28no—
239#10621883—44no—
240#10621883—44no—
241#10621883—44no—
242C4⋊Dic43—21no—
243C4⋊Dic43—21no—
244C4⋊Dic43—21no—
245C4⋊Dic43—21no—
246Dic43⋊C4—42no—
247Dic43⋊C4—42no—
248C4×Dic43—42no—
249C4×Dic43—42no—
250C2×C43⋊C8—21no—
251C2×C43⋊C8—21no—
252C2×C43⋊C8—21no—
253C2×C43⋊C8—21no—
254C2×C43⋊C8—21no—
255C2×C43⋊C8—21no—
256C2×C43⋊C8—21no—
257C2×C43⋊C8—21no—
258C2×C43⋊C8—21no—
259C2×C43⋊C8—21no—
260C2×C43⋊C8C2×D412yes—
261C2×C43⋊C8C2×D412yes—
262C23×C43—21no—
263C23×C43—21no—
264C23×C43—21no—
265C23×C43—21no—
266C23×C43—21no—
267C23×C43—21no—
268C23×C43—22no—
269C23×C43—41no—
270C23×C43—41no—
271C23×C43—41no—
272C23×C43—41no—
273C23×C43—41no—
274C23×C43—41no—
275C23×C43—41no—
276C23×C43—41no—
277C23×C43—41no—
278C23×C43—41no—
279C23×C43—41no—
280C23×C43—41no—
281C23×C43—41no—
282C23×C43C2×SD1612yes—
283C23×C43C22×D411yescharacteristic
284D4×C43—22no—
285D4×C43—22no—
286D4×C43—41no—
287D4×C43—41no—
288D4×C43—41no—
289D4×C43—41no—
290D4×C43—41no—
291D4×C43—41no—
292D4×C43—84no—
293D4×C43—84no—
294D4×C43—84no—
295D4×C43—84no—
296C2×C4×C43—21no—
297C2×C4×C43—21no—
298C2×C4×C43—21no—
299C2×C4×C43—21no—
300C2×C4×C43—21no—
301C2×C4×C43—21no—
302C2×C4×C43—21no—
303C2×C4×C43—22no—
304C2×C4×C43—21no—
305C2×C4×C43—21no—
306C2×C4×C43—21no—
307C2×C4×C43—21no—
308C2×C4×C43—21no—
309C2×C4×C43—21no—
310C2×C4×C43—41no—
311C2×C4×C43—41no—
312C2×C4×C43—41no—
313C2×C4×C43—41no—
314C2×C4×C43—41no—
315C2×C4×C43—41no—
316C2×C4×C43—41no—
317C2×C4×C43—41no—
318C2×C4×C43—41no—
319C2×C4×C43—84no—
320C2×C4×C43C2×SD1612yes—
321C2×C4×C43C2×SD1612yes—
322C2×C4×C43C22×D411yescharacteristic
323C2×C4×C43C22×D411yescharacteristic
324C2×C4×C43C2×#4111yescharacteristic
325C2×C4×C43C2×#4111yescharacteristic
326C2×C4×C43H(5,𝔽2)11yescharacteristic
327C2×C4×C43H(5,𝔽2)11yescharacteristic
328C2×Dic43—22no—
329C2×Dic43—22no—
330C2×Dic43—22no—
331C2×Dic43—22no—
332C2×Dic43—48no—
333C2×Dic43—41no—
334C2×Dic43—41no—
335C2×Dic43—41no—
336C2×Dic43—41no—
337C2×Dic43—41no—
338C2×Dic43—41no—
339C2×Dic43—41no—
340C2×Dic43—41no—
341Dic86—22no—
342Dic86—22no—
343Dic86—22no—
344Dic86—22no—
345Dic86—22no—
346Dic86—48no—
347Dic86—41no—
348Dic86—41no—
349Dic86#12114yescomplemented
350C43⋊C8—22no—
351C43⋊C8—22no—
352C43⋊C8—41no—
353C43⋊C8—41no—
354#25153—431nomaximal, Sylow
355C22×C43—22no—
356C22×C43—22no—
357C22×C43—22no—
358C22×C43—41no—
359C22×C43—41no—
360C22×C43—41no—
361C22×C43—41no—
362C22×C43—42no—
363C22×C43—42no—
364C22×C43—42no—
365C22×C43—81no—
366C22×C43—81no—
367C22×C43—81no—
368C22×C43—81no—
369C22×C43—81no—
370C22×C43—81no—
371C22×C43—81no—
372C22×C43—81no—
373C22×C43—81no—
374C22×C43—81no—
375C22×C43—81no—
376C22×C43#52511yescharacteristic
377C22×C43D4211yescharacteristic
378C22×C43D4211yescharacteristic
379C22×C43C22×SD1611yescharacteristic
380C22×C43#57511yescharacteristic
381C22×C43#57711yescharacteristic
382C22×C43#57711yescharacteristic
383C4×C43—22no—
384C4×C43—22no—
385C4×C43—41no—
386C4×C43—41no—
387C4×C43—41no—
388C4×C43—42no—
389C4×C43—81no—
390C4×C43C2×#12111yescharacteristic
391C4×C43#53811yescharacteristic
392C4×C43#54611yescharacteristic
393C4×C43#54611yescharacteristic
394Dic43—24no—
395Dic43—42no—
396Dic43—81no—
397Dic43—81no—
398C2×#460—431no—
399C2×#448—431no—
400C2×#448—431no—
401C2×C4×SD16—431no—
402#2428D4311yescharacteristic
403Q8×C22⋊C4—431no—
404#2066—431no—
405#2034—431no—
406#2034—431no—
407#2014—431no—
408#1968—431no—
409#1923—431no—
410#1880—431no—
411#1877—431no—
412#1865—431no—
413C2×C43—42no—
414C2×C43—82no—
415C2×C43—161no—
416C2×C43#242411yescharacteristic
417C2×C43#310311yescharacteristic
418C2×C43#312611yescharacteristic
419C2×C43#327111yescharacteristic
420C2×C43#327511yescharacteristic
421C2×C43D4×SD1611yescharacteristic
422C2×C43D4×SD1611yescharacteristic
423C23×Q8—431no—
424C22×SD16—431no—
425C22×SD16—431no—
426C22×SD16—431no—
427C22×SD16—431no—
428C2×#127C2×D4311yescharacteristic
429C2×#121—21no—
430C2×#121C2×D4311yescharacteristic
431C2×#121C2×D4311yescharacteristic
432C2×C4×Q8—431no—
433C2×C4×Q8—431no—
434C2×C4×D4C2×D4311yescharacteristic
435#460—864no—
436#448—864no—
437#448—864no—
438C4×SD16—864no—
439C2×#106—431no—
440C2×#106—431no—
441C2×C4⋊C8—431no—
442C2×#103—431no—
443C2×#103—431no—
444C2×#103—431no—
445C2×#103—431no—
446C2×#102—431no—
447C2×#102—431no—
448C2×#102—431no—
449C2×#102—431no—
450C2×C22⋊C8—431no—
451C2×C22⋊C8—431no—
452C2×C4×C8—431no—
453#394—21no—
454#392—21no—
455#391—431no—
456#391—431no—
457#391—861no—
458#391—861no—
459#390C2×D4311yescharacteristic
460#389C2×D4311yescharacteristic
461#386—21no—
462#380—431no—
463#380—861no—
464C4×C22⋊C4—861no—
465C4×C22⋊C4C2×D4311yescharacteristic
466#340—431no—
467#340—431no—
468#336—431no—
469#336—431no—
470C43#2515311yescharacteristic, complemented, Sylow
471C22×Q8—431no—
472C22×Q8—431no—
473C22×Q8—862no—
474C22×Q8—862no—
475C22×Q8—862no—
476C22×Q8—862no—
477C22×Q8—861no—
478C22×Q8—1721no—
479C22×Q8—1721no—
480C22×D4—21no—
481C22×D4—21no—
482C22×D4—21no—
483C22×D4—21no—
484C22×D4C22×D4311yescharacteristic
485C22×D4C22×D4311yescharacteristic
486C23×C4—21no—
487C23×C4—861no—
488C23×C4C22×D4311yescharacteristic
489C2×SD16—434no—
490C2×SD16—862no—
491C2×SD16—862no—
492C2×SD16—862no—
493C2×SD16—862no—
494C2×SD16—862no—
495C2×SD16—862no—
496C2×SD16—862no—
497C2×SD16—862no—
498C2×SD16—862no—
499C2×SD16—1721no—
500C2×SD16—1721no—
501C22×C8—431no—
502C22×C8—431no—
503C22×C8—431no—
504C22×C8—431no—
505#127—22no—
506#127—41no—
507#121—22no—
508#121—22no—
509#121—41no—
510#121—41no—
511#121—44no—
512C4×Q8—862no—
513C4×Q8—862no—
514C4×Q8—1721no—
515C4×Q8—1721no—
516C4×D4—22no—
517C4×D4—41no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—431no—
520C2×C4⋊C4—431no—
521C2×C4⋊C4—861no—
522C2×C4⋊C4—861no—
523C2×C4⋊C4C22×D4311yescharacteristic
524C2×C4⋊C4C22×D4311yescharacteristic
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—861no—
531C2×C22⋊C4C22⋊D4311yescharacteristic
532C2×C22⋊C4C22⋊D4311yescharacteristic
533C2×C42—861no—
534C2×C42—861no—
535C2×C42C22×D4311yescharacteristic
536C2×C42C22×D4311yescharacteristic
537#106—862no—
538#106—1721no—
539C4⋊C8—862no—
540#103—434no—
541#103—862no—
542#103—862no—
543#103—862no—
544#102—862no—
545#102—862no—
546#102—862no—
547#102—1721no—
548C22⋊C8—862no—
549C22⋊C8—862no—
550C4×C8—862no—
551#95—21no—
552#95—861no—
553#95—861no—
554#95—861no—
555#95—861no—
556#95—861no—
557#95C22⋊D4311yescharacteristic
558#95C22⋊D4311yescharacteristic
559C24—21no—
560C24—21no—
561C24C2×C22⋊D4311yescharacteristic
562C2×Q8—432no—
563C2×Q8—432no—
564C2×Q8—432no—
565C2×Q8—432no—
566C2×Q8—864no—
567C2×Q8—861no—
568C2×Q8—861no—
569C2×Q8—861no—
570C2×Q8—861no—
571C2×Q8—861no—
572C2×Q8—861no—
573C2×Q8—861no—
574C2×Q8—861no—
575C2×Q8—1722no—
576C2×Q8—1722no—
577C2×Q8—1724no—
578C2×Q8—1724no—
579C2×Q8—1724no—
580C2×Q8—1724no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—42no—
593C2×D4—42no—
594C2×D4—42no—
595C2×D4—42no—
596C2×D4—42no—
597C2×D4—42no—
598C2×D4—42no—
599C2×D4—42no—
600C2×D4—81no—
601C2×D4—81no—
602C2×D4—81no—
603C2×D4—81no—
604C2×D4D4×D4312yes—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—42no—
614C22×C4—42no—
615C22×C4—81no—
616C22×C4—861no—
617C22×C4—864no—
618C22×C4—861no—
619C22×C4—861no—
620C22×C4—861no—
621C22×C4—1722no—
622C22×C4—1722no—
623C22×C4C2×C22⋊D4311yescharacteristic
624C22×C4C2×C22⋊D4311yescharacteristic
625C22×C4C2×C22⋊D4311yescharacteristic
626C22×C4C2×C22⋊D4311yescharacteristic
627C22×C4C2×C22⋊D4311yescharacteristic
628C22×C4C23×D4311yescharacteristic
629SD16—868no—
630SD16—1724no—
631SD16—1724no—
632SD16—1724no—
633C2×C8—432no—
634C2×C8—432no—
635C2×C8—861no—
636C2×C8—861no—
637C2×C8—861no—
638C2×C8—861no—
639C2×C8—861no—
640C2×C8—861no—
641C2×C8—861no—
642C2×C8—861no—
643C2×C8—861no—
644C2×C8—861no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—42no—
649C4⋊C4—861no—
650C4⋊C4—861no—
651C4⋊C4—861no—
652C4⋊C4—861no—
653C4⋊C4—1722no—
654C4⋊C4—1722no—
655C4⋊C4D4×D4312yes—
656C22⋊C4—41no—
657C22⋊C4—42no—
658C22⋊C4—42no—
659C22⋊C4—42no—
660C22⋊C4—42no—
661C22⋊C4—81no—
662C22⋊C4—1722no—
663C22⋊C4#1062188314yescomplemented
664C42—21no—
665C42—21no—
666C42—21no—
667C42—21no—
668C42—1722no—
669C42—1722no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—22no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23C2×#1062188312yes—
691C23C22×C22⋊D4311yescharacteristic
692Q8—434no—
693Q8—862no—
694Q8—862no—
695Q8—862no—
696Q8—862no—
697Q8—862no—
698Q8—1728no—
699Q8—1721no—
700Q8—1721no—
701D4—22no—
702D4—22no—
703D4—41no—
704D4—41no—
705D4—41no—
706D4—41no—
707D4—41no—
708D4—41no—
709D4—84no—
710D4—84no—
711D4—84no—
712D4—84no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—22no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—84no—
737C2×C4—862no—
738C2×C4—862no—
739C2×C4—862no—
740C2×C4—862no—
741C2×C4—1728no—
742C2×C4—1721no—
743C2×C4—1721no—
744C2×C4—1721no—
745C2×C4—1721no—
746C2×C4—1721no—
747C2×C4—1721no—
748C2×C4—1721no—
749C2×C4—1721no—
750C2×C4C2×#1062188312yes—
751C2×C4C2×#1062188312yes—
752C2×C4C2×D4×D4311yescharacteristic
753C2×C4C2×D4×D4311yescharacteristic
754C2×C4#41×D4311yescharacteristic
755C2×C4#41×D4311yescharacteristic
756C2×C4#1306337011yescharacteristic
757C2×C4#1306337011yescharacteristic
758C8—862no—
759C8—862no—
760C8—1721no—
761C8—1721no—
762C22—22no—
763C22—22no—
764C22—22no—
765C22—41no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—42no—
770C22—42no—
771C22—42no—
772C22—81no—
773C22—81no—
774C22—81no—
775C22—81no—
776C22—81no—
777C22—81no—
778C22—81no—
779C22—81no—
780C22—81no—
781C22—81no—
782C22—81no—
783C22#1458340611yescharacteristic
784C22D4×C22⋊D4311yescharacteristic
785C22D4×C22⋊D4311yescharacteristic
786C22C22×#1062188311yescharacteristic
787C22#1458369711yescharacteristic
788C22#1458371011yescharacteristic
789C22#1458371011yescharacteristic
790C4—22no—
791C4—22no—
792C4—42no—
793C4—41no—
794C4—41no—
795C4—41no—
796C4—81no—
797C4—864no—
798C4—3441no—
799C4—3441no—
800C4—1722no—
801C4#121×D4311yescharacteristic
802C4#1458348111yescharacteristic
803C4#1458353811yescharacteristic
804C4#1458354611yescharacteristic
805C2—42no—
806C2—82no—
807C2—161no—
808C2#1913812811yescharacteristic
809C2#1914462211yescharacteristic
810C2#1914488111yescharacteristic
811C2#1914617611yescharacteristic
812C2#1914622211yescharacteristic
813C2D4×#1062188311yescharacteristic
814C2D4×#1062188311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
Fitting, prime radicalC43×#2428C2
socleC23×C43C22×D4
hypercenter#2428D43
hypocenterC43#25153
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2428

Complements

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

NH ≅ G/Ntype
1. C2×#14583096C2semidirect
2. C2×#14583037C2semidirect
3. C2×#14583037C2semidirect
4. C2×C4×#10621883C2semidirect
5. C22⋊C4×Dic86C2semidirect
6. #19135973C2semidirect
7. #19135781C2semidirect
8. #19135781C2semidirect
9. #19135683C2semidirect
10. #19135448C2semidirect
11. #19135203C2semidirect
12. #19134953C2semidirect
13. #19134929C2semidirect
14. #19134862C2semidirect
84. C2×#10621883D4semidirect
106. #13063248D4semidirect
232. C22⋊C4×C43SD16semidirect
349. Dic86#121semidirect
470. C43#25153semidirect
663. C22⋊C4#10621883semidirect

Maximal subgroups

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

subgroupindex
C2×#145830962
C2×#145830372
C2×C4×#106218832
C22⋊C4×Dic862
#191359732
#191357812
#191356832
#191354482
#191352032
#191349532
#191349292
#191348622
C43×#24282
#2515343