Finite Group Databasebeta

← #25098341

Subgroups — #25098341

Order 11008.

1818 conjugacy classes of subgroups.

The subgroup lattice has 906 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063331C211yesmaximal, characteristic, complemented
2C2×#14583478C211yesmaximal, characteristic
3C2×#14582897C211yesmaximal, characteristic, complemented
4C2×#14582892C211yesmaximal, characteristic, complemented
5#19137184C211yesmaximal, characteristic, complemented
6#19135034C211yesmaximal, characteristic, complemented
7#19135030C211yesmaximal, characteristic, complemented
8#19135027C211yesmaximal, characteristic, complemented
9#19135026C211yesmaximal, characteristic, complemented
10#19135020C211yesmaximal, characteristic, complemented
11#19135018C211yesmaximal, characteristic, complemented
12#19135017C211yesmaximal, characteristic, complemented
13#19134313C211yesmaximal, characteristic, complemented
14#340×D43C211yesmaximal, characteristic, complemented
15C43×#1893C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C22×#10621900C2211yescharacteristic
18C2×#13063331—24no—
19C2×#13063331—24no—
20C2×#13063331—24no—
21C22×#10621877C2211yescharacteristic
22C22×#10621872C2211yescharacteristic
23C22×#10621872C2211yescharacteristic
24C22×C8×D43C2211yescharacteristic
25C22×C8×D43C2211yescharacteristic
26#14583478—24no—
27#14583478C418yescomplemented
28C2×#13063305C2211yescharacteristic
29C2×#13063304C2211yescharacteristic
30C2×#13063302—21no—
31C2×#13063298—21no—
32C2×#13063297—21no—
33C2×#13063296—21no—
34C2×#13063296C2211yescharacteristic
35C2×#13063283C2211yescharacteristic
36C2×C4⋊C4×D43C2211yescharacteristic
37C2×C4⋊C4×D43C2211yescharacteristic
38#14582897—24no—
39#14582892—24no—
40C2×#13063250C2211yescharacteristic
41C2×#13063250C2211yescharacteristic
42C2×#13063248C2211yescharacteristic
43C2×#13063248C2211yescharacteristic
44C2×#13063246C2211yescharacteristic
45C2×#13063246C2211yescharacteristic
46#14582803—21no—
47#14582799—21no—
48#14582777—21no—
49#14582775—21no—
50#14582759C2211yescharacteristic
51#14582756C2211yescharacteristic
52#14582756C2211yescharacteristic
53#14582662C2211yescharacteristic
54#14582662C2211yescharacteristic
55#14582661C2211yescharacteristic
56#14582661C2211yescharacteristic
57#14582661C2211yescharacteristic
58#14582661C2211yescharacteristic
59C23×C8×C43C2211yescharacteristic
60C2×#121×C43C2211yescharacteristic
61C2×#102×C43C2211yescharacteristic
62C2×#102×C43C2211yescharacteristic
63C43×#380C2211yescharacteristic
64C43×#340C2211yescharacteristic
65C43×#340C2211yescharacteristic
66C2×#10621898—22no—
67C2×#10621898—22no—
68C2×#10621898—22no—
69C2×#10621898—22no—
70C2×#10621898C2×C414yes—
71C2×#10621898D414yes—
72C2×#10621900—22no—
73C2×#10621900—22no—
74C2×#10621900—22no—
75C2×#10621900—22no—
76C2×#10621900—22no—
77C2×#10621900C2×C414yes—
78C22×Dic86D411yescharacteristic
79C22×Dic86C2311yescharacteristic
80C22×D172D411yescharacteristic
81C22×C22⋊D43—21no—
82C22×C22⋊D43—21no—
83C22×C22⋊D43D411yescharacteristic
84C22×C22⋊D43D411yescharacteristic
85C23×Dic43—21no—
86C22×C4×D43—21no—
87C22×C4×D43—21no—
88C22×C4×D43C2311yescharacteristic
89C22×C4×D43C2311yescharacteristic
90#13063331—232no—
91C2×#10621877—22no—
92C2×#10621877—22no—
93C2×#10621877—22no—
94C2×#10621872—22no—
95C2×#10621872—22no—
96C2×#10621872—22no—
97C2×#10621872—22no—
98C2×#10621872—22no—
99C2×#10621872D414yescomplemented
100C22×C43⋊C8C2311yescharacteristic
101C22×C43⋊C8C2311yescharacteristic
102C2×C8×D43—22no—
103C2×C8×D43—22no—
104C2×C8×D43—22no—
105C2×C8×D43—22no—
106C2×C8×D43—22no—
107C2×C8×D43D414yescomplemented
108#13063305—22no—
109#13063305C2×C414yescomplemented
110#13063304—22no—
111#13063304C2×C414yescomplemented
112#13063302—28no—
113#13063298—28no—
114#13063297—28no—
115#13063296—28no—
116#13063296—22no—
117#13063296C2×C414yescomplemented
118#13063283—22no—
119#13063283—22no—
120C2×C4⋊Dic43—21no—
121C2×C4⋊Dic43C2311yescharacteristic
122C2×C4⋊Dic43C2311yescharacteristic
123C2×C4⋊Dic43C2311yescharacteristic
124C2×Dic43⋊C4—21no—
125C2×Dic43⋊C4—21no—
126C2×Dic43⋊C4—21no—
127C4⋊C4×D43—22no—
128C4⋊C4×D43—22no—
129C4⋊C4×D43—22no—
130C4⋊C4×D43C2×C414yes—
131C2×C22⋊Dic43—21no—
132C2×C22⋊Dic43—21no—
133C2×C22⋊Dic43—21no—
134C2×(C2×D43)⋊C4—21no—
135C2×(C2×D43)⋊C4—21no—
136C2×(C2×D43)⋊C4—21no—
137C2×(C2×D43)⋊C4—21no—
138C2×C4×Dic43—21no—
139#13063250—22no—
140#13063250—22no—
141#13063248—22no—
142#13063248—22no—
143#13063246—22no—
144#13063246—22no—
145C43⋊#95—21no—
146C43⋊#95—21no—
147C43⋊#95—21no—
148C22×D4×C43—21no—
149C22×D4×C43C2311yescharacteristic
150C23×C4×C43C2311yescharacteristic
151C22×C8×C43—22no—
152C22×C8×C43—22no—
153C22×C8×C43—22no—
154C22×C8×C43C2311yescharacteristic
155C22×C8×C43C2311yescharacteristic
156#121×C43—22no—
157#121×C43C2×C414yescomplemented
158C2×C4⋊C4×C43C2311yescharacteristic
159C2×C4⋊C4×C43C2311yescharacteristic
160C2×C4⋊C4×C43C2311yescharacteristic
161C2×C22⋊C4×C43—21no—
162C2×C22⋊C4×C43—21no—
163#102×C43—22no—
164#102×C43—22no—
165#95×C43—21no—
166C24×C43—21no—
167C24×C43C2×D411yescharacteristic
168C23×D43C2×D411yescharacteristic
169C23×D43C2×D411yescharacteristic
170C2×D4×C43—21no—
171C2×D4×C43—24no—
172C2×D4×C43—21no—
173C2×D4×C43—21no—
174C2×D4×C43—21no—
175C2×D4×C43—21no—
176C2×D4×C43—81no—
177C2×D4×C43—81no—
178C2×D4×C43C22×C412yes—
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×C43C22×C412yes—
187C22×C4×C43C2×D412yes—
188C22×C4×C43C2×D411yescharacteristic
189C22×C4×C43C2411yescharacteristic
190C2×C22⋊D43—22no—
191C2×C22⋊D43—22no—
192C2×C22⋊D43—24no—
193C2×C22⋊D43—24no—
194C2×C22⋊D43—22no—
195C2×C22⋊D43—22no—
196C2×C22⋊D43—42no—
197C2×C22⋊D43—42no—
198C2×C22⋊D43—81no—
199C2×C22⋊D43—81no—
200C2×C22⋊D43C22⋊C414yes—
201C2×C22⋊D43C22⋊C414yes—
202C22×Dic43—24no—
203C22×Dic43—21no—
204C22×Dic43—21no—
205C22×Dic43—21no—
206C22×Dic43—21no—
207C22×Dic43—42no—
208C22×Dic43—42no—
209C22×Dic43C2×D411yescharacteristic
210C22×Dic43C2×D411yescharacteristic
211#10621900—28no—
212#10621900—28no—
213#10621900—44no—
214#10621900—44no—
215#10621898—28no—
216#10621898—28no—
217#10621898—28no—
218#10621898—28no—
219C2×D172—22no—
220C2×D172—22no—
221C2×D172C22⋊C414yes—
222C2×C4×D43—21no—
223C2×C4×D43—21no—
224C2×C4×D43—21no—
225C2×C4×D43—21no—
226C2×C4×D43—24no—
227C2×C4×D43—42no—
228C2×C4×D43—81no—
229C2×C4×D43—81no—
230C2×C4×D43—81no—
231C2×C4×D43—81no—
232C2×C4×D43C22×C412yes—
233C2×C4×D43C22×C412yes—
234C2×C4×D43C2×D412yes—
235C2×C4×D43C2×D412yes—
236C2×C4×D43C2×D412yes—
237C2×C4×D43C2×D412yes—
238C2×C4×D43#4112yes—
239C2×C4×D43#4112yes—
240C2×Dic86—22no—
241C2×Dic86—22no—
242C2×Dic86—21no—
243C2×Dic86—21no—
244C2×Dic86—21no—
245C2×Dic86—21no—
246C2×Dic86—21no—
247C2×Dic86C22⋊C414yes—
248C2×Dic86C22×C412yes—
249C2×C8×C43—28no—
250C2×C8×C43—21no—
251C2×C8×C43—21no—
252C2×C8×C43—21no—
253C2×C8×C43—21no—
254C2×C8×C43C2×D412yes—
255C2×C8×C43C2×D412yes—
256C4⋊C4×C43—21no—
257C4⋊C4×C43—21no—
258C4⋊C4×C43—21no—
259C4⋊C4×C43—21no—
260C4⋊C4×C43—21no—
261C4⋊C4×C43C22×C412yes—
262C22⋊C4×C43—24no—
263C22⋊C4×C43—81no—
264C22⋊Dic43—24no—
265C22⋊Dic43—24no—
266C22⋊Dic43—81no—
267(C2×D43)⋊C4—24no—
268(C2×D43)⋊C4—42no—
269(C2×D43)⋊C4—81no—
270(C2×D43)⋊C4—81no—
271C4⋊Dic43—21no—
272C4⋊Dic43—24no—
273C4⋊Dic43—21no—
274C4⋊Dic43—21no—
275C4⋊Dic43—21no—
276C4⋊Dic43—21no—
277C4⋊Dic43C22×C412yes—
278Dic43⋊C4—24no—
279Dic43⋊C4—24no—
280Dic43⋊C4—42no—
281C4×Dic43—42no—
282#10621877—28no—
283C2×C43⋊C8—21no—
284C2×C43⋊C8—21no—
285C2×C43⋊C8—21no—
286C2×C43⋊C8—21no—
287C2×C43⋊C8C2×D412yes—
288C2×C43⋊C8C2×D412yes—
289#10621872—28no—
290#10621872—28no—
291C8×D43—28no—
292C8×D43—28no—
293C23×C43—21no—
294C23×C43—21no—
295C23×C43—21no—
296C23×C43—21no—
297C23×C43—21no—
298C23×C43—21no—
299C23×C43—22no—
300C23×C43—41no—
301C23×C43—41no—
302C23×C43—41no—
303C23×C43—41no—
304C23×C43—41no—
305C23×C43—41no—
306C23×C43C2×C22⋊C412yes—
307C23×C43C22×D411yescharacteristic
308C22×D43—21no—
309C22×D43—21no—
310C22×D43—21no—
311C22×D43—21no—
312C22×D43—21no—
313C22×D43—21no—
314C22×D43—21no—
315C22×D43—21no—
316C22×D43—21no—
317C22×D43—21no—
318C22×D43C2×C22⋊C412yes—
319C22×D43C2×C22⋊C412yes—
320C22×D43#12112yes—
321C22×D43#12112yes—
322D4×C43—22no—
323D4×C43—22no—
324D4×C43—41no—
325D4×C43—41no—
326D4×C43—84no—
327C2×C4×C43—21no—
328C2×C4×C43—21no—
329C2×C4×C43—22no—
330C2×C4×C43—22no—
331C2×C4×C43—22no—
332C2×C4×C43—22no—
333C2×C4×C43—22no—
334C2×C4×C43—41no—
335C2×C4×C43—41no—
336C2×C4×C43—41no—
337C2×C4×C43—41no—
338C2×C4×C43—41no—
339C2×C4×C43—41no—
340C2×C4×C43—41no—
341C2×C4×C43—41no—
342C2×C4×C43C2×C22⋊C412yes—
343C2×C4×C43C23×C411yescharacteristic
344C2×C4×C43C22×D411yescharacteristic
345C2×C4×C43C22×D411yescharacteristic
346C2×C4×C43C22×D411yescharacteristic
347C2×C4×C43C2×#4111yescharacteristic
348C2×C4×C43C2×#4111yescharacteristic
349C22⋊D43—28no—
350C22⋊D43—28no—
351C22⋊D43—48no—
352C22⋊D43—84no—
353C2×Dic43—21no—
354C2×Dic43—21no—
355C2×Dic43—22no—
356C2×Dic43—22no—
357C2×Dic43—41no—
358C2×Dic43—41no—
359C2×Dic43—41no—
360C2×Dic43—41no—
361C2×Dic43—48no—
362C2×Dic43—41no—
363C2×Dic43—41no—
364C2×Dic43—41no—
365C2×Dic43—41no—
366C2×Dic43—41no—
367C2×Dic43—41no—
368C2×Dic43C2×C22⋊C412yes—
369C2×Dic43C2×C22⋊C412yes—
370C2×Dic43#12112yes—
371C2×Dic43#12112yes—
372D172—28no—
373C4×D43—22no—
374C4×D43—22no—
375C4×D43—22no—
376C4×D43—22no—
377C4×D43—84no—
378C4×D43—84no—
379C4×D43C4×D414yes—
380C4×D43C4×D414yes—
381C4×D43#12014yes—
382C4×D43#12314yes—
383Dic86—28no—
384Dic86—22no—
385Dic86—22no—
386Dic86—41no—
387Dic86—41no—
388C8×C43—22no—
389C8×C43—22no—
390C43⋊C8—22no—
391C43⋊C8—22no—
392#20976—431nomaximal, Sylow
393C22×C43—22no—
394C22×C43—22no—
395C22×C43—22no—
396C22×C43—41no—
397C22×C43—41no—
398C22×C43—41no—
399C22×C43—41no—
400C22×C43—42no—
401C22×C43—42no—
402C22×C43—42no—
403C22×C43—81no—
404C22×C43—81no—
405C22×C43—81no—
406C22×C43—81no—
407C22×C43C22×C22⋊C411yescharacteristic
408C22×C43C2×#12111yescharacteristic
409C22×C43C2×#12111yescharacteristic
410C22×C43#57611yescharacteristic
411C22×C43#57711yescharacteristic
412C22×C43#57711yescharacteristic
413C22×C43#57811yescharacteristic
414C2×D43—22no—
415C2×D43—22no—
416C2×D43—22no—
417C2×D43—22no—
418C2×D43—22no—
419C2×D43—22no—
420C2×D43—22no—
421C2×D43—22no—
422C2×D43—22no—
423C2×D43—41no—
424C2×D43—41no—
425C2×D43—41no—
426C2×D43—41no—
427C2×D43#38614yes—
428C4×C43—22no—
429C4×C43—42no—
430C4×C43—81no—
431C4×C43—81no—
432C4×C43C2×C4×D411yescharacteristic
433C4×C43C2×C4×D411yescharacteristic
434C4×C43C2×#12011yescharacteristic
435C4×C43C2×#12311yescharacteristic
436Dic43—22no—
437Dic43—42no—
438Dic43—42no—
439Dic43—81no—
440Dic43—81no—
441Dic43#38614yes—
442C22×#131—431no—
443C2×#537—431no—
444C2×#417—431no—
445C2×#416—431no—
446#2311—431no—
447#1895—431no—
448#1895—431no—
449#1894—431no—
450#1894—431no—
451#1893—431no—
452#1893D4311yescharacteristic, complemented
453#1892—431no—
454#1892—431no—
455#1736—431no—
456C2×#340—431no—
457C2×C43—42no—
458C2×C43—82no—
459C2×C43C2×#38611yescharacteristic
460C2×C43#289711yescharacteristic
461C2×C43#289811yescharacteristic
462C2×C43#306011yescharacteristic
463C2×C43#306111yescharacteristic
464C2×C43#306211yescharacteristic
465C2×C43#306311yescharacteristic
466D43—24no—
467D43—42no—
468C22×#41—431no—
469C22×#41—431no—
470C2×#131—864no—
471C2×#131—864no—
472C2×#131—864no—
473C22×M16—431no—
474C22×M16—431no—
475C22×M16—431no—
476C23×C8—431no—
477C23×C8—431no—
478C23×C8C2×D4311yescharacteristic
479#537—438no—
480#537—864no—
481C2×C22⋊Q8—431no—
482C2×C22⋊Q8—431no—
483C2×C22⋊Q8—861no—
484C2×#121—431no—
485C2×#121—861no—
486C2×#121—861no—
487C2×#121—861no—
488C2×#121C2×D4311yescharacteristic
489C2×#117—431no—
490C22×C4⋊C4—431no—
491C22×C4⋊C4—431no—
492#417—864no—
493#416—864no—
494C2×#103—431no—
495C2×#103—431no—
496C2×#103—431no—
497C2×#103—431no—
498C2×#102—431no—
499C2×#102—431no—
500C2×#102C2×D4311yescharacteristic
501C2×#102C2×D4311yescharacteristic
502#391—861no—
503#390—861no—
504#386—861no—
505#386—861no—
506#380—431no—
507#380—431no—
508#380—431no—
509#380C2×D4311yescharacteristic
510#340—431no—
511#340—431no—
512#340—431no—
513#340—431no—
514#340—431no—
515#340—431no—
516#340C2×D4311yescharacteristic
517#340C2×D4311yescharacteristic
518C43#2097611yescharacteristic, complemented, Sylow
519C2×#41—434no—
520C2×#41—434no—
521C2×#41—434no—
522C2×#41—862no—
523C2×#41—862no—
524C2×#41—862no—
525C2×#41—862no—
526C2×#41—862no—
527C2×#41—862no—
528C2×#41—862no—
529C2×#41—862no—
530C2×#41—862no—
531C22×Q8—431no—
532C22×Q8—431no—
533C22×D4—21no—
534C22×D4—431no—
535C22×D4—431no—
536C22×D4—431no—
537C22×D4—861no—
538C22×D4—861no—
539C22×D4C22×D4311yescharacteristic
540C23×C4—431no—
541C23×C4—431no—
542C23×C4—861no—
543C23×C4—861no—
544C23×C4—861no—
545C23×C4C22×D4311yescharacteristic
546#131—8632no—
547C2×M16—434no—
548C2×M16—862no—
549C2×M16—862no—
550C2×M16—862no—
551C2×M16—862no—
552C2×M16—862no—
553C2×M16—862no—
554C2×M16—862no—
555C2×M16—862no—
556C22×C8—22no—
557C22×C8—22no—
558C22×C8—22no—
559C22×C8—431no—
560C22×C8—431no—
561C22×C8—434no—
562C22×C8—862no—
563C22×C8—862no—
564C22×C8—862no—
565C22×C8—862no—
566C22×C8—862no—
567C22×C8C22×D4311yescharacteristic
568C22×C8C22×D4311yescharacteristic
569C22⋊Q8—434no—
570C22⋊Q8—434no—
571C22⋊Q8—868no—
572C22⋊Q8—862no—
573C22⋊Q8—862no—
574#121—22no—
575#121—434no—
576#121—868no—
577#121—862no—
578#121—868no—
579#121—868no—
580#121C4×D4314yescomplemented
581#117—862no—
582#117—862no—
583C2×C4⋊C4—431no—
584C2×C4⋊C4—434no—
585C2×C4⋊C4—431no—
586C2×C4⋊C4—431no—
587C2×C4⋊C4—862no—
588C2×C4⋊C4—862no—
589C2×C4⋊C4—862no—
590C2×C4⋊C4—861no—
591C2×C4⋊C4—861no—
592C2×C4⋊C4—861no—
593C2×C4⋊C4—861no—
594C2×C4⋊C4C22×D4311yescharacteristic
595C2×C4⋊C4C22×D4311yescharacteristic
596C2×C4⋊C4C22×D4311yescharacteristic
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—861no—
600C2×C22⋊C4—861no—
601C2×C22⋊C4—861no—
602C2×C22⋊C4—861no—
603C2×C22⋊C4—861no—
604C2×C22⋊C4—861no—
605C2×C22⋊C4—861no—
606C2×C42—861no—
607#103—862no—
608#103—862no—
609#103—862no—
610#103—862no—
611#102—22no—
612#102—22no—
613#102—862no—
614#102—862no—
615#95—21no—
616#95—861no—
617#95—861no—
618#95—861no—
619C24—21no—
620C24—431no—
621C24—431no—
622C24D4×D4311yescharacteristic
623#41—868no—
624#41—868no—
625#41—868no—
626#41—868no—
627#41—868no—
628#41—868no—
629#41—1724no—
630#41—1724no—
631C2×Q8—434no—
632C2×Q8—432no—
633C2×Q8—862no—
634C2×Q8—862no—
635C2×Q8—861no—
636C2×Q8—861no—
637C2×Q8—861no—
638C2×Q8—861no—
639C2×Q8—861no—
640C2×D4—24no—
641C2×D4—21no—
642C2×D4—21no—
643C2×D4—21no—
644C2×D4—21no—
645C2×D4—21no—
646C2×D4—81no—
647C2×D4—81no—
648C2×D4—434no—
649C2×D4—434no—
650C2×D4—434no—
651C2×D4—862no—
652C2×D4—862no—
653C2×D4—862no—
654C2×D4—862no—
655C2×D4—862no—
656C2×D4—862no—
657C2×D4—864no—
658C2×D4—864no—
659C2×D4—3441no—
660C2×D4—3441no—
661C2×D4—1722no—
662C2×D4—1722no—
663C2×D4C2×C4×D4312yes—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—431no—
672C22×C4—432no—
673C22×C4—432no—
674C22×C4—432no—
675C22×C4—432no—
676C22×C4—432no—
677C22×C4—432no—
678C22×C4—431no—
679C22×C4—432no—
680C22×C4—432no—
681C22×C4—864no—
682C22×C4—864no—
683C22×C4—861no—
684C22×C4—861no—
685C22×C4—861no—
686C22×C4—861no—
687C22×C4—861no—
688C22×C4—861no—
689C22×C4—861no—
690C22×C4—861no—
691C22×C4—3441no—
692C22×C4—3441no—
693C22×C4—3441no—
694C22×C4—3441no—
695C22×C4—1722no—
696C22×C4—1722no—
697C22×C4—1722no—
698C22×C4C2×C4×D4312yes—
699C22×C4D4×D4311yescharacteristic
700C22×C4D4×D4312yes—
701C22×C4C23×D4311yescharacteristic
702M16—868no—
703M16—868no—
704M16—868no—
705C2×C8—28no—
706C2×C8—21no—
707C2×C8—21no—
708C2×C8—21no—
709C2×C8—21no—
710C2×C8—432no—
711C2×C8—432no—
712C2×C8—868no—
713C2×C8—868no—
714C2×C8—861no—
715C2×C8—861no—
716C2×C8—861no—
717C2×C8—861no—
718C2×C8D4×D4312yes—
719C2×C8D4×D4312yes—
720C4⋊C4—21no—
721C4⋊C4—21no—
722C4⋊C4—21no—
723C4⋊C4—21no—
724C4⋊C4—21no—
725C4⋊C4—432no—
726C4⋊C4—864no—
727C4⋊C4—864no—
728C4⋊C4—864no—
729C4⋊C4—861no—
730C4⋊C4—861no—
731C4⋊C4—861no—
732C4⋊C4—861no—
733C4⋊C4—861no—
734C4⋊C4—1722no—
735C4⋊C4C2×C4×D4312yes—
736C22⋊C4—24no—
737C22⋊C4—81no—
738C22⋊C4—864no—
739C22⋊C4—864no—
740C22⋊C4—864no—
741C22⋊C4—3441no—
742C22⋊C4—3441no—
743C22⋊C4—3441no—
744C22⋊C4—1722no—
745C42—1722no—
746C23—21no—
747C23—21no—
748C23—21no—
749C23—21no—
750C23—21no—
751C23—21no—
752C23—22no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—41no—
758C23—41no—
759C23—432no—
760C23—432no—
761C23—432no—
762C23—432no—
763C23—861no—
764C23—861no—
765C23—861no—
766C23—861no—
767C23—861no—
768C23—861no—
769C23—861no—
770C23—861no—
771C23—861no—
772C23—861no—
773C23C22⋊C4×D4312yes—
774C23C2×D4×D4311yescharacteristic
775Q8—868no—
776Q8—862no—
777Q8—862no—
778Q8—1721no—
779Q8—1721no—
780D4—22no—
781D4—22no—
782D4—41no—
783D4—41no—
784D4—84no—
785D4—868no—
786D4—868no—
787D4—868no—
788D4—3444no—
789D4—1728no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—432no—
806C2×C4—432no—
807C2×C4—432no—
808C2×C4—434no—
809C2×C4—434no—
810C2×C4—434no—
811C2×C4—434no—
812C2×C4—432no—
813C2×C4—861no—
814C2×C4—861no—
815C2×C4—862no—
816C2×C4—862no—
817C2×C4—862no—
818C2×C4—862no—
819C2×C4—862no—
820C2×C4—862no—
821C2×C4—3444no—
822C2×C4—3444no—
823C2×C4—1728no—
824C2×C4—1721no—
825C2×C4—1721no—
826C2×C4—1721no—
827C2×C4—1721no—
828C2×C4—1721no—
829C2×C4—1721no—
830C2×C4—1721no—
831C2×C4—1721no—
832C2×C4—1721no—
833C2×C4—1721no—
834C2×C4C22⋊C4×D4312yes—
835C2×C4C22×C4×D4311yescharacteristic
836C2×C4C2×D4×D4311yescharacteristic
837C2×C4C2×D4×D4311yescharacteristic
838C2×C4C2×D4×D4311yescharacteristic
839C2×C4#41×D4311yescharacteristic
840C2×C4#41×D4311yescharacteristic
841C8—22no—
842C8—22no—
843C8—862no—
844C8—862no—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—41no—
849C22—41no—
850C22—41no—
851C22—41no—
852C22—42no—
853C22—42no—
854C22—42no—
855C22—81no—
856C22—81no—
857C22—81no—
858C22—81no—
859C22—434no—
860C22—862no—
861C22—862no—
862C22—862no—
863C22—862no—
864C22—862no—
865C22—862no—
866C22—862no—
867C22—862no—
868C22—862no—
869C22—1721no—
870C22—1721no—
871C22—1721no—
872C22—1721no—
873C22C2×C22⋊C4×D4311yescharacteristic
874C22#121×D4311yescharacteristic
875C22#121×D4311yescharacteristic
876C22#1458370011yescharacteristic
877C22#1458370511yescharacteristic
878C22#1458370611yescharacteristic
879C22#1458371311yescharacteristic
880C4—22no—
881C4—42no—
882C4—81no—
883C4—81no—
884C4—434no—
885C4—862no—
886C4—3441no—
887C4—3441no—
888C4—1722no—
889C4—1722no—
890C4C4×D4×D4311yescharacteristic
891C4C4×D4×D4311yescharacteristic
892C4#120×D4311yescharacteristic
893C4#123×D4311yescharacteristic
894C2—42no—
895C2—82no—
896C2—864no—
897C2—1722no—
898C2#386×D4311yescharacteristic
899C2#1914311611yescharacteristic
900C2#1914312411yescharacteristic
901C2#1914425211yescharacteristic
902C2#1914426011yescharacteristic
903C2#1914427411yescharacteristic
904C2#1914427911yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1893C2
socleC23×C43C22×D4
prime radicalC2×#14583478C2
cosocleC22×C4×C43C24
hypercenter#1893D43
hypocenterC43#20976
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1893

Complements

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

NH ≅ G/Ntype
1. C22×#13063331C2semidirect
3. C2×#14582897C2semidirect
4. C2×#14582892C2semidirect
5. #19137184C2semidirect
6. #19135034C2semidirect
7. #19135030C2semidirect
8. #19135027C2semidirect
9. #19135026C2semidirect
10. #19135020C2semidirect
11. #19135018C2semidirect
12. #19135017C2semidirect
13. #19134313C2semidirect
14. #340×D43C2semidirect
15. C43×#1893C2semidirect
27. #14583478C4semidirect
99. C2×#10621872D4semidirect
107. C2×C8×D43D4semidirect
109. #13063305C2×C4semidirect
111. #13063304C2×C4semidirect
117. #13063296C2×C4semidirect
157. #121×C43C2×C4semidirect
452. #1893D43semidirect
518. C43#20976semidirect
580. #121C4×D43semidirect

Maximal subgroups

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

subgroupindex
C22×#130633312
C2×#145834782
C2×#145828972
C2×#145828922
#191371842
#191350342
#191350302
#191350272
#191350262
#191350202
#191350182
#191350172
#191343132
#340×D432
C43×#18932
#2097643