Finite Group Databasebeta

← #25098344

Subgroups — #25098344

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×#13063333C211yesmaximal, characteristic, complemented
2C2×#14583479C211yesmaximal, characteristic
3C2×#14582899C211yesmaximal, characteristic, complemented
4C2×#14582894C211yesmaximal, characteristic, complemented
5#19137184C211yesmaximal, characteristic, complemented
6#19135033C211yesmaximal, characteristic, complemented
7#19135032C211yesmaximal, characteristic, complemented
8#19135025C211yesmaximal, characteristic, complemented
9#19135022C211yesmaximal, characteristic, complemented
10#19135021C211yesmaximal, characteristic, complemented
11#19135019C211yesmaximal, characteristic, complemented
12#19135015C211yesmaximal, characteristic, complemented
13#19134313C211yesmaximal, characteristic, complemented
14#340×D43C211yesmaximal, characteristic, complemented
15C43×#1894C211yesmaximal, characteristic, complemented
16C22×#10621902C2211yescharacteristic
17C22×#10621898C2211yescharacteristic
18C2×#13063333—24no—
19C2×#13063333—24no—
20C2×#13063333—24no—
21C22×#10621872C2211yescharacteristic
22C22×#10621872C2211yescharacteristic
23C23×C43⋊C8C2211yescharacteristic
24C22×C8×D43C2211yescharacteristic
25C22×C8×D43C2211yescharacteristic
26#14583479—24no—
27#14583479C418yescomplemented
28C2×#13063303—21no—
29C2×#13063301C2211yescharacteristic
30C2×#13063300—21no—
31C2×#13063300C2211yescharacteristic
32C2×#13063299C2211yescharacteristic
33C2×#13063298—21no—
34C2×#13063298—21no—
35C2×#13063283C2211yescharacteristic
36C2×C4⋊C4×D43C2211yescharacteristic
37C2×C4⋊C4×D43C2211yescharacteristic
38#14582899—24no—
39#14582894—24no—
40C2×#13063249C2211yescharacteristic
41C2×#13063249C2211yescharacteristic
42C2×#13063247C2211yescharacteristic
43C2×#13063247C2211yescharacteristic
44C2×#13063245C2211yescharacteristic
45C2×#13063245C2211yescharacteristic
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
59C22×M16×C43C2211yescharacteristic
60C2×C22⋊Q8×C43C2211yescharacteristic
61C2×#103×C43C2211yescharacteristic
62C2×#103×C43C2211yescharacteristic
63C43×#380C2211yescharacteristic
64C43×#340C2211yescharacteristic
65C43×#340C2211yescharacteristic
66C2×#10621902—22no—
67C2×#10621902—22no—
68C2×#10621902—22no—
69C2×#10621902—22no—
70C2×#10621902—22no—
71C2×#10621902C2×C414yes—
72C2×#10621898—22no—
73C2×#10621898—22no—
74C2×#10621898—22no—
75C2×#10621898—22no—
76C2×#10621898C2×C414yes—
77C2×#10621898D414yes—
78C22×Dic86D411yescharacteristic
79C22×D172—21no—
80C22×D172—21no—
81C22×D172D411yescharacteristic
82C22×D172C2311yescharacteristic
83C22×C22⋊D43—21no—
84C22×C22⋊D43D411yescharacteristic
85C22×C22⋊D43D411yescharacteristic
86C22×C4×D43—21no—
87C22×C4×D43—21no—
88C22×C4×D43—21no—
89C22×C4×D43C2311yescharacteristic
90C22×C4×D43C2311yescharacteristic
91#13063333—232no—
92C2×#10621872—22no—
93C2×#10621872—22no—
94C2×#10621872—22no—
95C2×#10621872—22no—
96C2×#10621872—22no—
97C2×#10621872D414yescomplemented
98C22×C43⋊C8—22no—
99C22×C43⋊C8—22no—
100C22×C43⋊C8—22no—
101C22×C43⋊C8C2311yescharacteristic
102C22×C43⋊C8C2311yescharacteristic
103C2×C8×D43—22no—
104C2×C8×D43—22no—
105C2×C8×D43—22no—
106C2×C8×D43—22no—
107C2×C8×D43—22no—
108C2×C8×D43D414yescomplemented
109#13063303—28no—
110#13063301—22no—
111#13063301C2×C414yescomplemented
112#13063300—28no—
113#13063300—22no—
114#13063300C2×C414yescomplemented
115#13063299—22no—
116#13063299C2×C414yescomplemented
117#13063298—28no—
118#13063298—28no—
119#13063283—22no—
120#13063283—22no—
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×(C2×D43)⋊C4—21no—
133C2×(C2×D43)⋊C4—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#13063249—22no—
140#13063249—22no—
141#13063247—22no—
142#13063247—22no—
143#13063245—22no—
144#13063245—22no—
145C43⋊#95—21no—
146C43⋊#95—21no—
147C43⋊#95—21no—
148C22×Q8×C43C2311yescharacteristic
149C23×C4×C43C2311yescharacteristic
150C2×M16×C43—22no—
151C2×M16×C43—22no—
152C2×M16×C43—22no—
153C22×C8×C43C2311yescharacteristic
154C22×C8×C43C2311yescharacteristic
155C22⋊Q8×C43—22no—
156C22⋊Q8×C43C2×C414yescomplemented
157C2×C4⋊C4×C43—21no—
158C2×C4⋊C4×C43C2311yescharacteristic
159C2×C4⋊C4×C43C2311yescharacteristic
160C2×C4⋊C4×C43C2311yescharacteristic
161C2×C22⋊C4×C43—21no—
162C2×C22⋊C4×C43—21no—
163#103×C43—22no—
164#103×C43—22no—
165#95×C43—21no—
166C24×C43C2×D411yescharacteristic
167C23×D43—21no—
168C23×D43C2×D411yescharacteristic
169C23×D43C2×D411yescharacteristic
170C2×Q8×C43—21no—
171C2×Q8×C43—21no—
172C2×Q8×C43—21no—
173C2×Q8×C43—21no—
174C2×Q8×C43—21no—
175C2×Q8×C43C22×C412yes—
176C22×C4×C43—21no—
177C22×C4×C43—21no—
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×C43C22×C412yes—
185C22×C4×C43C2×D412yes—
186C22×C4×C43C2×D411yescharacteristic
187C22×C4×C43C2411yescharacteristic
188C2×C22⋊D43—22no—
189C2×C22⋊D43—22no—
190C2×C22⋊D43—24no—
191C2×C22⋊D43—22no—
192C2×C22⋊D43—22no—
193C2×C22⋊D43—81no—
194C2×C22⋊D43—81no—
195C2×C22⋊D43C22⋊C414yes—
196C2×C22⋊D43C22⋊C414yes—
197C22×Dic43—21no—
198C22×Dic43—21no—
199C22×Dic43—21no—
200C22×Dic43C2×D411yescharacteristic
201C22×Dic43C2×D411yescharacteristic
202#10621902—28no—
203#10621902—28no—
204#10621902—44no—
205#10621902—44no—
206#10621898—28no—
207#10621898—28no—
208#10621898—28no—
209#10621898—28no—
210C2×D172—21no—
211C2×D172—24no—
212C2×D172—24no—
213C2×D172—22no—
214C2×D172—22no—
215C2×D172—21no—
216C2×D172—21no—
217C2×D172—21no—
218C2×D172—21no—
219C2×D172—42no—
220C2×D172—42no—
221C2×D172—81no—
222C2×D172—81no—
223C2×D172C22⋊C414yes—
224C2×D172C22×C412yes—
225C2×C4×D43—21no—
226C2×C4×D43—21no—
227C2×C4×D43—21no—
228C2×C4×D43—21no—
229C2×C4×D43—24no—
230C2×C4×D43—24no—
231C2×C4×D43—42no—
232C2×C4×D43—42no—
233C2×C4×D43—42no—
234C2×C4×D43—81no—
235C2×C4×D43—81no—
236C2×C4×D43—81no—
237C2×C4×D43—81no—
238C2×C4×D43C22×C412yes—
239C2×C4×D43C22×C412yes—
240C2×C4×D43C2×D412yes—
241C2×C4×D43C2×D412yes—
242C2×C4×D43C2×D412yes—
243C2×C4×D43C2×D412yes—
244C2×C4×D43#4112yes—
245C2×C4×D43#4112yes—
246C2×Dic86—22no—
247C2×Dic86—22no—
248C2×Dic86C22⋊C414yes—
249M16×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—24no—
257C4⋊C4×C43—21no—
258C4⋊C4×C43—21no—
259C4⋊C4×C43—21no—
260C4⋊C4×C43—21no—
261C4⋊C4×C43—21no—
262C4⋊C4×C43C22×C412yes—
263C22⋊C4×C43—24no—
264C22⋊C4×C43—81no—
265C22⋊Dic43—81no—
266(C2×D43)⋊C4—24no—
267(C2×D43)⋊C4—24no—
268(C2×D43)⋊C4—24no—
269(C2×D43)⋊C4—42no—
270(C2×D43)⋊C4—81no—
271(C2×D43)⋊C4—81no—
272C4⋊Dic43—21no—
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—
282C2×C43⋊C8—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×C43C2×C22⋊C412yes—
300C23×C43C22×D411yescharacteristic
301C22×D43—21no—
302C22×D43—21no—
303C22×D43—21no—
304C22×D43—21no—
305C22×D43—21no—
306C22×D43—21no—
307C22×D43—21no—
308C22×D43—21no—
309C22×D43—21no—
310C22×D43—21no—
311C22×D43—22no—
312C22×D43—41no—
313C22×D43—41no—
314C22×D43—41no—
315C22×D43—41no—
316C22×D43—41no—
317C22×D43—41no—
318C22×D43C2×C22⋊C412yes—
319C22×D43C2×C22⋊C412yes—
320C22×D43#12112yes—
321C22×D43#12112yes—
322Q8×C43—22no—
323Q8×C43—22no—
324Q8×C43—41no—
325Q8×C43—41no—
326C2×C4×C43—21no—
327C2×C4×C43—21no—
328C2×C4×C43—22no—
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×C43—41no—
343C2×C4×C43—41no—
344C2×C4×C43C2×C22⋊C412yes—
345C2×C4×C43C23×C411yescharacteristic
346C2×C4×C43C22×D411yescharacteristic
347C2×C4×C43C22×D411yescharacteristic
348C2×C4×C43C22×D411yescharacteristic
349C2×C4×C43C2×#4111yescharacteristic
350C2×C4×C43C2×#4111yescharacteristic
351C22⋊D43—28no—
352C22⋊D43—28no—
353C22⋊D43—84no—
354C2×Dic43—21no—
355C2×Dic43—21no—
356C2×Dic43—22no—
357C2×Dic43—41no—
358C2×Dic43—41no—
359C2×Dic43—41no—
360C2×Dic43—41no—
361C2×Dic43—41no—
362C2×Dic43—41no—
363C2×Dic43—41no—
364C2×Dic43—41no—
365C2×Dic43C2×C22⋊C412yes—
366C2×Dic43C2×C22⋊C412yes—
367C2×Dic43#12112yes—
368C2×Dic43#12112yes—
369D172—28no—
370D172—22no—
371D172—22no—
372D172—48no—
373D172—41no—
374D172—41no—
375D172—84no—
376C4×D43—22no—
377C4×D43—22no—
378C4×D43—22no—
379C4×D43—22no—
380C4×D43—48no—
381C4×D43—84no—
382C4×D43—84no—
383C4×D43C4×D414yes—
384C4×D43C4×D414yes—
385C4×D43#12014yes—
386C4×D43#12314yes—
387Dic86—28no—
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×C43C22×C22⋊C411yescharacteristic
401C22×C43C2×#12111yescharacteristic
402C22×C43C2×#12111yescharacteristic
403C22×C43#57611yescharacteristic
404C22×C43#57711yescharacteristic
405C22×C43#57711yescharacteristic
406C22×C43#57811yescharacteristic
407C2×D43—22no—
408C2×D43—22no—
409C2×D43—22no—
410C2×D43—22no—
411C2×D43—22no—
412C2×D43—22no—
413C2×D43—22no—
414C2×D43—22no—
415C2×D43—22no—
416C2×D43—41no—
417C2×D43—41no—
418C2×D43—41no—
419C2×D43—41no—
420C2×D43—42no—
421C2×D43—42no—
422C2×D43—42no—
423C2×D43—81no—
424C2×D43—81no—
425C2×D43—81no—
426C2×D43—81no—
427C2×D43#38614yes—
428C4×C43—22no—
429C4×C43—42no—
430C4×C43—42no—
431C4×C43—81no—
432C4×C43—81no—
433C4×C43C2×C4×D411yescharacteristic
434C4×C43C2×C4×D411yescharacteristic
435C4×C43C2×#12011yescharacteristic
436C4×C43C2×#12311yescharacteristic
437Dic43—22no—
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#1894D4311yescharacteristic, complemented
451#1893—431no—
452#1893—431no—
453#1892—431no—
454#1892—431no—
455#1736—431no—
456C2×#340—431no—
457C2×C43—42no—
458C2×C43C2×#38611yescharacteristic
459C2×C43#289711yescharacteristic
460C2×C43#289811yescharacteristic
461C2×C43#306011yescharacteristic
462C2×C43#306111yescharacteristic
463C2×C43#306211yescharacteristic
464C2×C43#306311yescharacteristic
465D43—24no—
466D43—42no—
467D43—82no—
468C22×#41—431no—
469C22×#41—431no—
470C2×#131—864no—
471C2×#131—864no—
472C2×#131—864no—
473C22×M16—431no—
474C22×M16—431no—
475C22×M16C2×D4311yescharacteristic
476C23×C8—431no—
477C23×C8—431no—
478C23×C8—431no—
479#537—438no—
480#537—864no—
481C2×C22⋊Q8—431no—
482C2×C22⋊Q8—861no—
483C2×C22⋊Q8C2×D4311yescharacteristic
484C2×#121—431no—
485C2×#121—431no—
486C2×#121—861no—
487C2×#121—861no—
488C2×#121—861no—
489C2×#117—431no—
490C22×C4⋊C4—431no—
491C22×C4⋊C4—431no—
492#417—864no—
493#416—864no—
494C2×#103—431no—
495C2×#103—431no—
496C2×#103C2×D4311yescharacteristic
497C2×#103C2×D4311yescharacteristic
498C2×#102—431no—
499C2×#102—431no—
500C2×#102—431no—
501C2×#102—431no—
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×Q8C22×D4311yescharacteristic
533C22×D4—431no—
534C22×D4—431no—
535C22×D4—431no—
536C22×D4—431no—
537C22×D4—861no—
538C22×D4—861no—
539C22×D4—861no—
540C23×C4—431no—
541C23×C4—431no—
542C23×C4—861no—
543C23×C4—861no—
544C23×C4—861no—
545C23×C4C22×D4311yescharacteristic
546#131—8632no—
547C2×M16—22no—
548C2×M16—22no—
549C2×M16—22no—
550C2×M16—434no—
551C2×M16—862no—
552C2×M16—862no—
553C2×M16—862no—
554C2×M16—862no—
555C2×M16—862no—
556C22×C8—431no—
557C22×C8—431no—
558C22×C8—434no—
559C22×C8—862no—
560C22×C8—862no—
561C22×C8—862no—
562C22×C8—862no—
563C22×C8—862no—
564C22×C8—862no—
565C22×C8—862no—
566C22×C8—862no—
567C22×C8C22×D4311yescharacteristic
568C22×C8C22×D4311yescharacteristic
569C22⋊Q8—22no—
570C22⋊Q8—434no—
571C22⋊Q8—868no—
572C22⋊Q8—862no—
573C22⋊Q8C4×D4314yescomplemented
574#121—434no—
575#121—434no—
576#121—868no—
577#121—868no—
578#121—862no—
579#121—868no—
580#121—862no—
581#117—862no—
582#117—862no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—431no—
585C2×C4⋊C4—434no—
586C2×C4⋊C4—431no—
587C2×C4⋊C4—431no—
588C2×C4⋊C4—862no—
589C2×C4⋊C4—862no—
590C2×C4⋊C4—862no—
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—22no—
608#103—22no—
609#103—862no—
610#103—862no—
611#102—862no—
612#102—862no—
613#102—862no—
614#102—862no—
615#95—21no—
616#95—861no—
617#95—861no—
618#95—861no—
619C24—431no—
620C24—431no—
621C24—861no—
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—21no—
632C2×Q8—21no—
633C2×Q8—21no—
634C2×Q8—21no—
635C2×Q8—21no—
636C2×Q8—434no—
637C2×Q8—862no—
638C2×Q8—862no—
639C2×Q8C2×C4×D4312yes—
640C2×D4—434no—
641C2×D4—434no—
642C2×D4—434no—
643C2×D4—432no—
644C2×D4—862no—
645C2×D4—862no—
646C2×D4—864no—
647C2×D4—864no—
648C2×D4—862no—
649C2×D4—862no—
650C2×D4—862no—
651C2×D4—862no—
652C2×D4—864no—
653C2×D4—861no—
654C2×D4—861no—
655C2×D4—861no—
656C2×D4—861no—
657C2×D4—861no—
658C2×D4—3441no—
659C2×D4—3441no—
660C2×D4—3441no—
661C2×D4—3441no—
662C2×D4—1722no—
663C2×D4—1722no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—431no—
673C22×C4—432no—
674C22×C4—432no—
675C22×C4—432no—
676C22×C4—432no—
677C22×C4—432no—
678C22×C4—432no—
679C22×C4—431no—
680C22×C4—432no—
681C22×C4—432no—
682C22×C4—864no—
683C22×C4—864no—
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—28no—
703M16—868no—
704M16—868no—
705C2×C8—21no—
706C2×C8—21no—
707C2×C8—21no—
708C2×C8—21no—
709C2×C8—432no—
710C2×C8—432no—
711C2×C8—868no—
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—24no—
721C4⋊C4—21no—
722C4⋊C4—21no—
723C4⋊C4—21no—
724C4⋊C4—21no—
725C4⋊C4—21no—
726C4⋊C4—432no—
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—432no—
753C23—432no—
754C23—432no—
755C23—432no—
756C23—861no—
757C23—861no—
758C23—861no—
759C23—861no—
760C23—861no—
761C23—861no—
762C23—861no—
763C23—861no—
764C23—861no—
765C23—861no—
766C23—862no—
767C23—1721no—
768C23—1721no—
769C23—1721no—
770C23—1721no—
771C23—1721no—
772C23—1721no—
773C23C22⋊C4×D4312yes—
774C23C2×D4×D4311yescharacteristic
775Q8—22no—
776Q8—22no—
777Q8—41no—
778Q8—41no—
779Q8—868no—
780D4—868no—
781D4—868no—
782D4—868no—
783D4—862no—
784D4—862no—
785D4—3444no—
786D4—3444no—
787D4—1728no—
788D4—1721no—
789D4—1721no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—432no—
809C2×C4—432no—
810C2×C4—432no—
811C2×C4—434no—
812C2×C4—434no—
813C2×C4—434no—
814C2×C4—434no—
815C2×C4—432no—
816C2×C4—861no—
817C2×C4—861no—
818C2×C4—862no—
819C2×C4—862no—
820C2×C4—862no—
821C2×C4—862no—
822C2×C4—862no—
823C2×C4—3444no—
824C2×C4—3444no—
825C2×C4—1728no—
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—434no—
853C22—862no—
854C22—862no—
855C22—862no—
856C22—862no—
857C22—862no—
858C22—862no—
859C22—862no—
860C22—862no—
861C22—862no—
862C22—3441no—
863C22—3441no—
864C22—3441no—
865C22—3441no—
866C22—1722no—
867C22—1722no—
868C22—1722no—
869C22—1721no—
870C22—1721no—
871C22—1721no—
872C22—1721no—
873C22C2×C22⋊C4×D4311yescharacteristic
874C22#121×D4311yescharacteristic
875C22#121×D4311yescharacteristic
876C22#1458370311yescharacteristic
877C22#1458370811yescharacteristic
878C22#1458370811yescharacteristic
879C22#1458371511yescharacteristic
880C4—22no—
881C4—42no—
882C4—42no—
883C4—81no—
884C4—81no—
885C4—434no—
886C4—862no—
887C4—3441no—
888C4—3441no—
889C4—1722no—
890C4C4×D4×D4311yescharacteristic
891C4C4×D4×D4311yescharacteristic
892C4#120×D4311yescharacteristic
893C4#123×D4311yescharacteristic
894C2—42no—
895C2—864no—
896C2—3442no—
897C2—1722no—
898C2#386×D4311yescharacteristic
899C2#1914311911yescharacteristic
900C2#1914312711yescharacteristic
901C2#1914425911yescharacteristic
902C2#1914426311yescharacteristic
903C2#1914427011yescharacteristic
904C2#1914428311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1894C2
socleC23×C43C22×D4
prime radicalC2×#14583479C2
cosocleC22×C4×C43C24
hypercenter#1894D43
hypocenterC43#20976
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1894

Complements

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

NH ≅ G/Ntype
1. C22×#13063333C2semidirect
3. C2×#14582899C2semidirect
4. C2×#14582894C2semidirect
5. #19137184C2semidirect
6. #19135033C2semidirect
7. #19135032C2semidirect
8. #19135025C2semidirect
9. #19135022C2semidirect
10. #19135021C2semidirect
11. #19135019C2semidirect
12. #19135015C2semidirect
13. #19134313C2semidirect
14. #340×D43C2semidirect
15. C43×#1894C2semidirect
27. #14583479C4semidirect
97. C2×#10621872D4semidirect
108. C2×C8×D43D4semidirect
111. #13063301C2×C4semidirect
114. #13063300C2×C4semidirect
116. #13063299C2×C4semidirect
156. C22⋊Q8×C43C2×C4semidirect
450. #1894D43semidirect
518. C43#20976semidirect
573. C22⋊Q8C4×D43semidirect

Maximal subgroups

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

subgroupindex
C22×#130633332
C2×#145834792
C2×#145828992
C2×#145828942
#191371842
#191350332
#191350322
#191350252
#191350222
#191350212
#191350192
#191350152
#191343132
#340×D432
C43×#18942
#2097643