Finite Group Databasebeta

← #25098060

Subgroups — #25098060

Order 11008.

1814 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063344C211yesmaximal, characteristic
2C2×#14583378C211yesmaximal, characteristic, complemented
3C2×#14582897C211yesmaximal, characteristic, complemented
4C2×#14582897C211yesmaximal, characteristic, complemented
5#19137185C211yesmaximal, characteristic, complemented
6#19134953C211yesmaximal, characteristic, complemented
7#19134947C211yesmaximal, characteristic, complemented
8#19134945C211yesmaximal, characteristic, complemented
9#19134937C211yesmaximal, characteristic, complemented
10#19134935C211yesmaximal, characteristic, complemented
11#19134929C211yesmaximal, characteristic, complemented
12#19134927C211yesmaximal, characteristic, complemented
13#340×D43C211yesmaximal, characteristic, complemented
14#19134290C211yesmaximal, characteristic, complemented
15C43×#1879C211yesmaximal, characteristic, complemented
16C22×#10621900C2211yescharacteristic
17C22×#10621900C2211yescharacteristic
18C2×#13063344—24no—
19C2×#13063344—24no—
20C2×#13063344C418yescomplemented
21C22×Dic172C2211yescharacteristic
22C22×#10621883C2211yescharacteristic
23C22×#10621883C2211yescharacteristic
24C22×#10621872C2211yescharacteristic
25C22×C8×D43C2211yescharacteristic
26#14583378—24no—
27#14583378—24no—
28C2×C4×Dic86C2211yescharacteristic
29C2×#13063290C2211yescharacteristic
30C2×D4×Dic43C2211yescharacteristic
31C2×C4×C22⋊D43—21no—
32C2×(C22⋊D43)⋊C4—21no—
33C2×#13063282C2211yescharacteristic
34C2×#13063281—21no—
35C22×Dic43⋊C4—21no—
36C2×C4⋊C4×D43C2211yescharacteristic
37C2×C4⋊C4×D43C2211yescharacteristic
38#14582897—24no—
39#14582897—24no—
40C2×#13063250C2211yescharacteristic
41C2×#13063250C2211yescharacteristic
42C2×#13063248C2211yescharacteristic
43C2×#13063248C2211yescharacteristic
44C2×#13063246C2211yescharacteristic
45C2×#13063246C2211yescharacteristic
46#14582805C2211yescharacteristic
47#14582804C2211yescharacteristic
48#14582802C2211yescharacteristic
49#14582775—21no—
50#14582775—21no—
51#14582757—21no—
52#14582757—21no—
53#14582662C2211yescharacteristic
54#14582661C2211yescharacteristic
55#14582661C2211yescharacteristic
56#14582654C2211yescharacteristic
57#14582653C2211yescharacteristic
58#14582653C2211yescharacteristic
59C22×D8×C43C2211yescharacteristic
60C2×C4×D4×C43C2211yescharacteristic
61C2×#102×C43C2211yescharacteristic
62C2×#102×C43C2211yescharacteristic
63C43×#390C2211yescharacteristic
64C43×#340C2211yescharacteristic
65C43×#336C2211yescharacteristic
66C2×#10621900—22no—
67C2×#10621900—22no—
68C2×#10621900—22no—
69C2×#10621900—22no—
70C2×#10621900—22no—
71C2×#10621900—22no—
72C2×#10621900—22no—
73C2×#10621900—22no—
74C2×#10621900C2×C414yes—
75C2×#10621900C2×C414yescomplemented
76C2×#10621900D414yes—
77C2×#10621900D414yes—
78C22×Dic86C2311yescharacteristic
79C22×Dic86C2311yescharacteristic
80C22×C22⋊D43—21no—
81C22×C22⋊D43—21no—
82C23×Dic43—21no—
83C23×Dic43—21no—
84C23×Dic43—21no—
85C22×C4×D43—21no—
86C22×C4×D43—21no—
87C22×C4×D43C2311yescharacteristic
88#13063344—232no—
89C2×Dic172—22no—
90C2×Dic172—22no—
91C2×Dic172C2×C414yescomplemented
92C2×#10621883—22no—
93C2×#10621883—22no—
94C2×#10621883—22no—
95C2×#10621883—22no—
96C2×#10621883C2×C414yescomplemented
97C2×#10621883C2×C414yescomplemented
98C2×#10621872—22no—
99C2×#10621872—22no—
100C2×#10621872—22no—
101C22×C43⋊C8C2311yescharacteristic
102C22×C43⋊C8C2311yescharacteristic
103C2×C8×D43—22no—
104C2×C8×D43—22no—
105C2×C8×D43C2×C414yescomplemented
106C4×Dic86—22no—
107C4×Dic86—22no—
108#13063290—22no—
109#13063290—22no—
110D4×Dic43—22no—
111D4×Dic43—22no—
112C4×C22⋊D43—28no—
113(C22⋊D43)⋊C4—28no—
114#13063282—22no—
115#13063282—22no—
116#13063281—28no—
117C2×C4⋊Dic43C2311yescharacteristic
118C2×C4⋊Dic43C2311yescharacteristic
119C2×Dic43⋊C4—28no—
120C2×Dic43⋊C4—21no—
121C2×Dic43⋊C4—21no—
122C2×Dic43⋊C4—21no—
123C2×Dic43⋊C4—21no—
124C2×Dic43⋊C4D411yescharacteristic
125C2×Dic43⋊C4D411yescharacteristic
126C4⋊C4×D43—22no—
127C4⋊C4×D43—22no—
128C4⋊C4×D43—22no—
129C4⋊C4×D43D414yes—
130C2×C22⋊Dic43—21no—
131C2×C22⋊Dic43—21no—
132C2×C22⋊Dic43—21no—
133C2×(C2×D43)⋊C4D411yescharacteristic
134C2×(C2×D43)⋊C4D411yescharacteristic
135C2×C4×Dic43—21no—
136C2×C4×Dic43—21no—
137C2×C4×Dic43C2311yescharacteristic
138#13063250—22no—
139#13063250—22no—
140#13063248—22no—
141#13063248—22no—
142#13063246—22no—
143#13063246—22no—
144C43⋊#95—21no—
145C43⋊#95—21no—
146C43⋊#95—21no—
147C43⋊#95—21no—
148C22×D4×C43C2311yescharacteristic
149C22×D4×C43C2311yescharacteristic
150C23×C4×C43—21no—
151C2×D8×C43—22no—
152C2×D8×C43—22no—
153C2×D8×C43C2×C414yescomplemented
154C22×C8×C43C2311yescharacteristic
155C22×C8×C43C2311yescharacteristic
156C4×D4×C43—22no—
157C4×D4×C43—22no—
158C2×C4⋊C4×C43C2311yescharacteristic
159C2×C4⋊C4×C43C2311yescharacteristic
160C2×C22⋊C4×C43—21no—
161C2×C22⋊C4×C43—21no—
162C2×C22⋊C4×C43—21no—
163C2×C42×C43C2311yescharacteristic
164#102×C43—22no—
165#102×C43—22no—
166C24×C43—21no—
167C24×C43—21no—
168C23×D43C2×D411yescharacteristic
169C2×D4×C43—21no—
170C2×D4×C43—21no—
171C2×D4×C43—21no—
172C2×D4×C43—21no—
173C2×D4×C43—21no—
174C2×D4×C43—21no—
175C2×D4×C43—21no—
176C2×D4×C43—21no—
177C2×D4×C43C22×C412yes—
178C2×D4×C43C22×C412yes—
179C2×D4×C43C2×D412yes—
180C2×D4×C43C2×D412yes—
181C22×C4×C43—24no—
182C22×C4×C43—21no—
183C22×C4×C43—21no—
184C22×C4×C43—81no—
185C22×C4×C43—81no—
186C22×C4×C43C2×D411yescharacteristic
187C22×C4×C43C2×D411yescharacteristic
188C22×C4×C43C2411yescharacteristic
189C2×C22⋊D43—24no—
190C2×C22⋊D43—24no—
191C2×C22⋊D43—24no—
192C2×C22⋊D43—24no—
193C2×C22⋊D43—42no—
194C2×C22⋊D43—42no—
195C22×Dic43—24no—
196C22×Dic43—24no—
197C22×Dic43—24no—
198C22×Dic43—24no—
199C22×Dic43—24no—
200C22×Dic43—21no—
201C22×Dic43—21no—
202C22×Dic43—21no—
203C22×Dic43—21no—
204C22×Dic43—42no—
205C22×Dic43—42no—
206C22×Dic43—81no—
207C22×Dic43—81no—
208C22×Dic43C2×D411yescharacteristic
209C22×Dic43C2×D411yescharacteristic
210C22×Dic43C2×D411yescharacteristic
211#10621900—28no—
212#10621900—28no—
213#10621900—28no—
214#10621900—28no—
215#10621900—28no—
216#10621900—44no—
217#10621900—44no—
218#10621900C22⋊C4116yescomplemented
219C2×C4×D43—24no—
220C2×C4×D43—42no—
221C2×C4×D43—81no—
222C2×C4×D43—81no—
223C2×C4×D43—81no—
224C2×C4×D43—81no—
225C2×C4×D43C22×C412yes—
226C2×C4×D43C2×D412yes—
227C2×C4×D43C2×D412yes—
228C2×C4×D43C2×D412yes—
229C2×C4×D43#4112yes—
230C2×C4×D43#4112yes—
231C2×Dic86—21no—
232C2×Dic86—21no—
233C2×Dic86—21no—
234C2×Dic86—21no—
235C2×Dic86—21no—
236C2×Dic86—21no—
237C2×Dic86—21no—
238C2×Dic86—21no—
239C2×Dic86C22×C412yes—
240C2×Dic86C22×C412yes—
241C2×Dic86C2×D412yes—
242C2×Dic86C2×D412yes—
243D8×C43—28no—
244C2×C8×C43—21no—
245C2×C8×C43—21no—
246C2×C8×C43—21no—
247C2×C8×C43—21no—
248C2×C8×C43—21no—
249C2×C8×C43C22×C412yes—
250C4⋊C4×C43—21no—
251C4⋊C4×C43—21no—
252C4⋊C4×C43—21no—
253C4⋊C4×C43C2×D412yes—
254C22⋊C4×C43—24no—
255C22⋊C4×C43—81no—
256C22⋊C4×C43—81no—
257C42×C43—21no—
258C42×C43—21no—
259C22⋊Dic43—24no—
260C22⋊Dic43—81no—
261C22⋊Dic43—81no—
262#10621883—28no—
263#10621883—28no—
264(C2×D43)⋊C4—22no—
265(C2×D43)⋊C4—22no—
266C4⋊Dic43—21no—
267C4⋊Dic43—21no—
268C4⋊Dic43—21no—
269C4⋊Dic43C2×D412yes—
270Dic43⋊C4—24no—
271Dic43⋊C4—24no—
272Dic43⋊C4—24no—
273Dic43⋊C4—22no—
274Dic43⋊C4—22no—
275Dic43⋊C4—42no—
276C4×Dic43—24no—
277C4×Dic43—24no—
278C4×Dic43—21no—
279C4×Dic43—21no—
280C2×C43⋊C8—21no—
281C2×C43⋊C8—21no—
282C2×C43⋊C8—21no—
283C2×C43⋊C8—21no—
284C2×C43⋊C8—21no—
285C2×C43⋊C8C22×C412yes—
286Dic172—28no—
287#10621872—44no—
288C8×D43—28no—
289C23×C43—22no—
290C23×C43—22no—
291C23×C43—22no—
292C23×C43—22no—
293C23×C43—41no—
294C23×C43—41no—
295C23×C43—41no—
296C23×C43—41no—
297C23×C43—41no—
298C23×C43—41no—
299C23×C43—41no—
300C23×C43—41no—
301C23×C43—41no—
302C23×C43—41no—
303C23×C43C22×D411yescharacteristic
304C22×D43—21no—
305C22×D43—21no—
306C22×D43—21no—
307C22×D43—21no—
308C22×D43C4×D412yes—
309C22×D43#12012yes—
310C22×D43#12112yes—
311D4×C43—22no—
312D4×C43—22no—
313D4×C43—22no—
314D4×C43—22no—
315D4×C43—22no—
316D4×C43—41no—
317D4×C43—41no—
318D4×C43C2×C22⋊C414yes—
319C2×C4×C43—21no—
320C2×C4×C43—22no—
321C2×C4×C43—21no—
322C2×C4×C43—21no—
323C2×C4×C43—21no—
324C2×C4×C43—21no—
325C2×C4×C43—21no—
326C2×C4×C43—41no—
327C2×C4×C43—41no—
328C2×C4×C43—41no—
329C2×C4×C43—41no—
330C2×C4×C43—41no—
331C2×C4×C43—84no—
332C2×C4×C43C23×C411yescharacteristic
333C2×C4×C43C22×D411yescharacteristic
334C2×C4×C43C22×D411yescharacteristic
335C2×C4×C43C22×D411yescharacteristic
336C2×C4×C43C2×#4111yescharacteristic
337C2×C4×C43C2×#4111yescharacteristic
338C22⋊D43—216no—
339C22⋊D43—48no—
340C2×Dic43—22no—
341C2×Dic43—22no—
342C2×Dic43—22no—
343C2×Dic43—216no—
344C2×Dic43—22no—
345C2×Dic43—21no—
346C2×Dic43—21no—
347C2×Dic43—22no—
348C2×Dic43—21no—
349C2×Dic43—21no—
350C2×Dic43—21no—
351C2×Dic43—21no—
352C2×Dic43—41no—
353C2×Dic43—41no—
354C2×Dic43—41no—
355C2×Dic43—41no—
356C2×Dic43—48no—
357C2×Dic43—41no—
358C2×Dic43—41no—
359C2×Dic43—41no—
360C2×Dic43—84no—
361C2×Dic43C4×D412yes—
362C2×Dic43#12012yes—
363C2×Dic43#12112yes—
364C4×D43—84no—
365C4×D43—84no—
366C4×D43C2×C22⋊C414yes—
367C4×D43C4×D414yes—
368C4×D43#12114yes—
369C4×D43#12314yes—
370Dic86—22no—
371Dic86—22no—
372Dic86—22no—
373Dic86—22no—
374Dic86—22no—
375Dic86—41no—
376Dic86—41no—
377Dic86C2×C22⋊C414yes—
378C8×C43—22no—
379C8×C43—41no—
380C43⋊C8—22no—
381C43⋊C8—41no—
382#20937—431nomaximal, Sylow
383C22×C43—24no—
384C22×C43—42no—
385C22×C43—42no—
386C22×C43—42no—
387C22×C43—42no—
388C22×C43—42no—
389C22×C43—42no—
390C22×C43—42no—
391C22×C43—42no—
392C22×C43—42no—
393C22×C43—81no—
394C22×C43—81no—
395C22×C43—81no—
396C22×C43—81no—
397C22×C43C2×C4×D411yescharacteristic
398C22×C43C2×#12011yescharacteristic
399C22×C43C2×#12111yescharacteristic
400C22×C43#57611yescharacteristic
401C22×C43#57711yescharacteristic
402C22×C43#57711yescharacteristic
403C22×C43#57811yescharacteristic
404C2×D43—22no—
405C2×D43—22no—
406C2×D43—22no—
407C2×D43—22no—
408C2×D43—22no—
409C2×D43—22no—
410C2×D43#38614yes—
411C4×C43—42no—
412C4×C43—41no—
413C4×C43—41no—
414C4×C43—81no—
415C4×C43C22×C22⋊C411yescharacteristic
416C4×C43C2×C4×D411yescharacteristic
417C4×C43C2×#12111yescharacteristic
418C4×C43C2×#12311yescharacteristic
419Dic43—24no—
420Dic43—42no—
421Dic43—41no—
422Dic43—41no—
423Dic43—42no—
424Dic43—81no—
425Dic43#38614yes—
426C22×#135—431no—
427C2×#520—431no—
428C2×#417—431no—
429C2×#417—431no—
430#2311—431no—
431#1880—431no—
432#1880—431no—
433#1879—431no—
434#1879D4311yescharacteristic, complemented
435#1878—431no—
436#1878—431no—
437#1877—431no—
438#1877—431no—
439C2×#340—431no—
440#1729—431no—
441C2×C43—44no—
442C2×C43—82no—
443C2×C43C2×#38611yescharacteristic
444C2×C43#295111yescharacteristic
445C2×C43#295211yescharacteristic
446C2×C43#301211yescharacteristic
447C2×C43#301311yescharacteristic
448C2×C43#304511yescharacteristic
449C2×C43#304611yescharacteristic
450D43—24no—
451C22×#41—431no—
452C22×#41—431no—
453C2×#135—438no—
454C2×#135—864no—
455C2×#135—864no—
456C22×Q16—431no—
457C22×SD16—431no—
458C22×SD16—431no—
459C22×D8C2×D4311yescharacteristic
460C22×M16—431no—
461C23×C8—431no—
462#520—864no—
463#520—864no—
464C2×C4×Q8—431no—
465C2×C4×Q8—431no—
466C2×C4×D4—431no—
467C2×C4×D4—861no—
468C2×C4×D4—861no—
469C2×C4×D4C2×D4311yescharacteristic
470C2×#117—431no—
471C2×#117—861no—
472C22×C4⋊C4—431no—
473C22×C4⋊C4—431no—
474C22×C4⋊C4—861no—
475#417—864no—
476#417—864no—
477C2×#103—431no—
478C2×#103—431no—
479C2×#103—431no—
480C2×#103—431no—
481C2×#102—431no—
482C2×#102—431no—
483C2×#102C2×D4311yescharacteristic
484C2×#102C2×D4311yescharacteristic
485#391—431no—
486#391—431no—
487#390—431no—
488#390C2×D4311yescharacteristic
489#386—861no—
490#386—861no—
491#380—861no—
492#380—861no—
493#340—431no—
494#340—431no—
495#340—431no—
496#340C2×D4311yescharacteristic
497#336—431no—
498#336—431no—
499#336—431no—
500#336C2×D4311yescharacteristic
501C43#2093711yescharacteristic, complemented, Sylow
502C2×#41—434no—
503C2×#41—434no—
504C2×#41—434no—
505C2×#41—434no—
506C2×#41—862no—
507C2×#41—862no—
508C2×#41—862no—
509C2×#41—862no—
510C2×#41—862no—
511C2×#41—862no—
512C2×#41—862no—
513C2×#41—862no—
514C22×Q8—431no—
515C22×Q8—431no—
516C22×D4—861no—
517C22×D4—861no—
518C22×D4C22×D4311yescharacteristic
519C22×D4C22×D4311yescharacteristic
520C23×C4—21no—
521C23×C4—431no—
522C23×C4—861no—
523C23×C4—861no—
524C23×C4—861no—
525C23×C4—861no—
526C23×C4—861no—
527#135—8632no—
528C2×Q16—434no—
529C2×Q16—862no—
530C2×Q16—862no—
531C2×SD16—434no—
532C2×SD16—434no—
533C2×SD16—862no—
534C2×SD16—862no—
535C2×SD16—862no—
536C2×SD16—862no—
537C2×D8—22no—
538C2×D8—22no—
539C2×D8C4×D4314yescomplemented
540C2×M16—862no—
541C2×M16—862no—
542C2×M16—862no—
543C22×C8—431no—
544C22×C8—434no—
545C22×C8—431no—
546C22×C8—862no—
547C22×C8—862no—
548C22×C8C22×D4311yescharacteristic
549C22×C8C22×D4311yescharacteristic
550C4×Q8—862no—
551C4×Q8—862no—
552C4×Q8—862no—
553C4×Q8—862no—
554C4×D4—22no—
555C4×D4—22no—
556C4×D4—868no—
557C4×D4—862no—
558C4×D4—868no—
559C4×D4—862no—
560#117—862no—
561#117—862no—
562#117—868no—
563C2×C4⋊C4—431no—
564C2×C4⋊C4—434no—
565C2×C4⋊C4—431no—
566C2×C4⋊C4—431no—
567C2×C4⋊C4—431no—
568C2×C4⋊C4—862no—
569C2×C4⋊C4—862no—
570C2×C4⋊C4—862no—
571C2×C4⋊C4—861no—
572C2×C4⋊C4—861no—
573C2×C4⋊C4—868no—
574C2×C4⋊C4—861no—
575C2×C4⋊C4—861no—
576C2×C4⋊C4C22×D4311yescharacteristic
577C2×C4⋊C4C22×D4311yescharacteristic
578C2×C22⋊C4—21no—
579C2×C22⋊C4—21no—
580C2×C22⋊C4—21no—
581C2×C22⋊C4—431no—
582C2×C22⋊C4—431no—
583C2×C22⋊C4—861no—
584C2×C22⋊C4—861no—
585C2×C22⋊C4—861no—
586C2×C42—431no—
587C2×C42—861no—
588C2×C42—861no—
589C2×C42C22×D4311yescharacteristic
590#103—862no—
591#103—862no—
592#103—862no—
593#103—862no—
594#102—22no—
595#102—22no—
596#102—862no—
597#102—862no—
598#95—861no—
599#95—861no—
600#95—861no—
601#95—861no—
602C24—21no—
603C24—21no—
604C24—431no—
605#41—4316no—
606#41—868no—
607#41—868no—
608#41—868no—
609#41—868no—
610#41—868no—
611#41—1724no—
612#41—1724no—
613C2×Q8—432no—
614C2×Q8—432no—
615C2×Q8—432no—
616C2×Q8—432no—
617C2×Q8—861no—
618C2×Q8—861no—
619C2×Q8—861no—
620C2×Q8—861no—
621C2×Q8—861no—
622C2×Q8—861no—
623C2×Q8—861no—
624C2×Q8—861no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—864no—
634C2×D4—864no—
635C2×D4—864no—
636C2×D4—864no—
637C2×D4—1722no—
638C2×D4—1722no—
639C2×D4C2×C4×D4312yes—
640C2×D4C2×C4×D4312yes—
641C2×D4D4×D4312yes—
642C2×D4D4×D4312yes—
643C22×C4—21no—
644C22×C4—24no—
645C22×C4—21no—
646C22×C4—81no—
647C22×C4—81no—
648C22×C4—431no—
649C22×C4—432no—
650C22×C4—432no—
651C22×C4—432no—
652C22×C4—432no—
653C22×C4—432no—
654C22×C4—432no—
655C22×C4—431no—
656C22×C4—431no—
657C22×C4—864no—
658C22×C4—864no—
659C22×C4—864no—
660C22×C4—864no—
661C22×C4—864no—
662C22×C4—861no—
663C22×C4—864no—
664C22×C4—861no—
665C22×C4—861no—
666C22×C4—861no—
667C22×C4—3441no—
668C22×C4—3441no—
669C22×C4—3441no—
670C22×C4—3441no—
671C22×C4—3441no—
672C22×C4—3441no—
673C22×C4—1722no—
674C22×C4—1722no—
675C22×C4—1722no—
676C22×C4D4×D4311yescharacteristic
677C22×C4D4×D4311yescharacteristic
678C22×C4C23×D4311yescharacteristic
679Q16—868no—
680SD16—868no—
681SD16—868no—
682D8—28no—
683M16—1724no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—432no—
690C2×C8—868no—
691C2×C8—861no—
692C2×C8—861no—
693C2×C8—861no—
694C2×C8—861no—
695C2×C8—861no—
696C2×C8C2×C4×D4312yes—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—432no—
701C4⋊C4—862no—
702C4⋊C4—864no—
703C4⋊C4—862no—
704C4⋊C4—864no—
705C4⋊C4—864no—
706C4⋊C4—861no—
707C4⋊C4—861no—
708C4⋊C4—861no—
709C4⋊C4—1722no—
710C4⋊C4D4×D4312yes—
711C22⋊C4—24no—
712C22⋊C4—81no—
713C22⋊C4—81no—
714C22⋊C4—862no—
715C22⋊C4—862no—
716C22⋊C4—864no—
717C22⋊C4—3441no—
718C22⋊C4—3441no—
719C42—21no—
720C42—21no—
721C42—864no—
722C42—864no—
723C42—861no—
724C42—861no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—432no—
740C23—432no—
741C23—432no—
742C23—861no—
743C23—861no—
744C23—861no—
745C23—861no—
746C23C2×D4×D4311yescharacteristic
747Q8—434no—
748Q8—862no—
749Q8—862no—
750Q8—862no—
751Q8—862no—
752Q8—862no—
753Q8—1721no—
754Q8—1721no—
755D4—22no—
756D4—22no—
757D4—22no—
758D4—22no—
759D4—22no—
760D4—41no—
761D4—41no—
762D4—8616no—
763D4—1728no—
764D4C22⋊C4×D4314yes—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—22no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—84no—
778C2×C4—432no—
779C2×C4—432no—
780C2×C4—432no—
781C2×C4—434no—
782C2×C4—434no—
783C2×C4—434no—
784C2×C4—434no—
785C2×C4—8616no—
786C2×C4—862no—
787C2×C4—862no—
788C2×C4—862no—
789C2×C4—862no—
790C2×C4—861no—
791C2×C4—862no—
792C2×C4—861no—
793C2×C4—861no—
794C2×C4—861no—
795C2×C4—861no—
796C2×C4—861no—
797C2×C4—3444no—
798C2×C4—3444no—
799C2×C4—3444no—
800C2×C4—1728no—
801C2×C4—1721no—
802C2×C4—1721no—
803C2×C4—1721no—
804C2×C4—1721no—
805C2×C4—1721no—
806C2×C4—1721no—
807C2×C4—1721no—
808C2×C4C22×C4×D4311yescharacteristic
809C2×C4C2×D4×D4311yescharacteristic
810C2×C4C2×D4×D4311yescharacteristic
811C2×C4C2×D4×D4311yescharacteristic
812C2×C4#41×D4311yescharacteristic
813C2×C4#41×D4311yescharacteristic
814C8—22no—
815C8—41no—
816C8—862no—
817C8—1721no—
818C22—24no—
819C22—42no—
820C22—42no—
821C22—42no—
822C22—42no—
823C22—42no—
824C22—42no—
825C22—42no—
826C22—42no—
827C22—42no—
828C22—81no—
829C22—81no—
830C22—81no—
831C22—81no—
832C22—434no—
833C22—862no—
834C22—862no—
835C22—862no—
836C22—862no—
837C22—862no—
838C22—862no—
839C22C4×D4×D4311yescharacteristic
840C22#120×D4311yescharacteristic
841C22#121×D4311yescharacteristic
842C22#1458370011yescharacteristic
843C22#1458370911yescharacteristic
844C22#1458370911yescharacteristic
845C22#1458371311yescharacteristic
846C4—41no—
847C4—42no—
848C4—41no—
849C4—81no—
850C4—434no—
851C4—864no—
852C4—3441no—
853C4—1721no—
854C4—1722no—
855C4—1721no—
856C4—1722no—
857C4C2×C22⋊C4×D4311yescharacteristic
858C4C4×D4×D4311yescharacteristic
859C4#121×D4311yescharacteristic
860C4#123×D4311yescharacteristic
861C2—44no—
862C2—82no—
863C2—864no—
864C2#386×D4311yescharacteristic
865C2#1914346511yescharacteristic
866C2#1914347711yescharacteristic
867C2#1914389411yescharacteristic
868C2#1914390811yescharacteristic
869C2#1914412911yescharacteristic
870C2#1914414611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1879C2
socleC23×C43C22×D4
prime radicalC22×#13063344C2
cosocleC22×C4×C43C24
hypercenter#1879D43
hypocenterC43#20937
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1879

Complements

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

NH ≅ G/Ntype
2. C2×#14583378C2semidirect
3. C2×#14582897C2semidirect
4. C2×#14582897C2semidirect
5. #19137185C2semidirect
6. #19134953C2semidirect
7. #19134947C2semidirect
8. #19134945C2semidirect
9. #19134937C2semidirect
10. #19134935C2semidirect
11. #19134929C2semidirect
12. #19134927C2semidirect
13. #340×D43C2semidirect
14. #19134290C2semidirect
15. C43×#1879C2semidirect
20. C2×#13063344C4semidirect
75. C2×#10621900C2×C4semidirect
91. C2×Dic172C2×C4semidirect
96. C2×#10621883C2×C4semidirect
97. C2×#10621883C2×C4semidirect
105. C2×C8×D43C2×C4semidirect
153. C2×D8×C43C2×C4semidirect
218. #10621900C22⋊C4semidirect
434. #1879D43semidirect
501. C43#20937semidirect
539. C2×D8C4×D43semidirect

Maximal subgroups

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

subgroupindex
C22×#130633442
C2×#145833782
C2×#145828972
#191371852
#191349532
#191349472
#191349452
#191349372
#191349352
#191349292
#191349272
#340×D432
#191342902
C43×#18792
#2093743