Finite Group Databasebeta

← #25102426

Subgroups — #25102426

Order 11008.

1420 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583380C211yesmaximal, characteristic
2C2×#14583059C211yesmaximal, characteristic
3C2×#14583002C211yesmaximal, characteristic, complemented
4C2×#14582991C211yesmaximal, characteristic, complemented
5#19137279C211yesmaximal, characteristic, complemented
6#19134933C211yesmaximal, characteristic, complemented
7#19134926C211yesmaximal, characteristic, complemented
8#19134850C211yesmaximal, characteristic, complemented
9#19134843C211yesmaximal, characteristic, complemented
10#19134783C211yesmaximal, characteristic, complemented
11#19134536C211yesmaximal, characteristic
12#19134424C211yesmaximal, characteristic, complemented
13#19134409C211yesmaximal, characteristic, complemented
14#19134363C211yesmaximal, characteristic, complemented
15C43×#1872C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C22×#10621885C2211yescharacteristic
18C22×#10621884C2211yescharacteristic
19#14583380—24no—
20#14583380—24no—
21C2×Q8×Dic43C2211yescharacteristic
22C2×#13063290C2211yescharacteristic
23C2×#13063290C2211yescharacteristic
24C2×#13063287C2211yescharacteristic
25C2×#13063287C2211yescharacteristic
26C2×C4×C22⋊D43—21no—
27C2×C4×C22⋊D43—21no—
28C2×#13063284C2211yescharacteristic
29C2×#13063283—21no—
30C2×C4⋊C4×D43—21no—
31#14583059C418yescomplemented
32#14583002—24no—
33#14582991—24no—
34C2×#13063258C2211yescharacteristic
35C2×#13063258C2211yescharacteristic
36C2×#13063250C2211yescharacteristic
37C2×#13063250C2211yescharacteristic
38C2×#13063248C2211yescharacteristic
39C2×#13063247C2211yescharacteristic
40C2×#13063247C2211yescharacteristic
41C2×#13063245C2211yescharacteristic
42C2×C22⋊(C43⋊C8)C2211yescharacteristic
43C2×#13063235C2211yescharacteristic
44C2×C8×Dic43C2211yescharacteristic
45#14582806C2211yescharacteristic
46#14582798—21no—
47#14582798C2211yescharacteristic
48#14582792—21no—
49#14582792—21no—
50#14582785—21no—
51#14582759C2211yescharacteristic
52C4⋊C4×Dic43C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582661C2211yescharacteristic
55#14582653C2211yescharacteristic
56#14582653C2211yescharacteristic
57C2×C22⋊Q8×C43C2211yescharacteristic
58C22×C4⋊C4×C43C2211yescharacteristic
59C2×#103×C43C2211yescharacteristic
60C2×#103×C43C2211yescharacteristic
61C2×C22⋊C8×C43C2211yescharacteristic
62C43×#340C2211yescharacteristic
63C43×#340C2211yescharacteristic
64C2×#10621898—22no—
65C2×#10621898—22no—
66C2×#10621898—22no—
67C2×#10621898—22no—
68C2×#10621898—22no—
69C2×#10621898C2×C414yes—
70C22×Dic86C2311yescharacteristic
71C22×D172C2311yescharacteristic
72C22×C22⋊D43—21no—
73C22×C4×D43—21no—
74C22×C4×D43—21no—
75C22×C4×D43—21no—
76C2×#10621885—22no—
77C2×#10621885—22no—
78C2×#10621885C2×C414yescomplemented
79C2×#10621884—22no—
80C2×#10621884—22no—
81C2×#10621884C2×C414yescomplemented
82C22×C43⋊C8C2311yescharacteristic
83C22×C43⋊C8C2311yescharacteristic
84Q8×Dic43—22no—
85Q8×Dic43—22no—
86#13063290—22no—
87#13063290—22no—
88#13063290—22no—
89#13063290D414yes—
90#13063287—22no—
91#13063287—22no—
92#13063287—22no—
93#13063287D414yes—
94C4×C22⋊D43—28no—
95C4×C22⋊D43—28no—
96#13063284—22no—
97#13063284—22no—
98#13063283—28no—
99C2×C4⋊Dic43—21no—
100C2×C4⋊Dic43—21no—
101C2×C4⋊Dic43D411yescharacteristic
102C2×C4⋊Dic43D411yescharacteristic
103C2×C4⋊Dic43C2311yescharacteristic
104C2×C4⋊Dic43C2311yescharacteristic
105C2×Dic43⋊C4—21no—
106C2×Dic43⋊C4—21no—
107C4⋊C4×D43—28no—
108C2×C22⋊Dic43—21no—
109C2×C22⋊Dic43D411yescharacteristic
110C2×C22⋊Dic43D411yescharacteristic
111C2×(C2×D43)⋊C4—21no—
112C2×(C2×D43)⋊C4—21no—
113C2×C4×Dic43—21no—
114C2×C4×Dic43—21no—
115C2×C4×Dic43—21no—
116C2×C4×Dic43—21no—
117C2×C4×Dic43C2311yescharacteristic
118C2×C4×Dic43C2311yescharacteristic
119#13063258—22no—
120#13063258—22no—
121#13063250—22no—
122#13063250—22no—
123#13063248C2×C414yescomplemented
124#13063247—22no—
125#13063247—22no—
126#13063245C2×C414yescomplemented
127C22⋊(C43⋊C8)C2×C414yescomplemented
128#13063235—22no—
129C8×Dic43—22no—
130C43⋊#95—21no—
131C43⋊#95—21no—
132C43⋊#95—21no—
133C43⋊#95—21no—
134C43⋊#95—21no—
135C22×Q8×C43C2311yescharacteristic
136C23×C4×C43—21no—
137C23×C4×C43C2311yescharacteristic
138C22×C8×C43C2311yescharacteristic
139C22×C8×C43C2311yescharacteristic
140C22⋊Q8×C43—22no—
141C22⋊Q8×C43C2×C414yescomplemented
142C2×C4⋊C4×C43—21no—
143C2×C4⋊C4×C43—21no—
144C2×C4⋊C4×C43—22no—
145C2×C4⋊C4×C43—22no—
146C2×C4⋊C4×C43C2311yescharacteristic
147C2×C4⋊C4×C43C2311yescharacteristic
148C2×C4⋊C4×C43C2311yescharacteristic
149C2×C22⋊C4×C43—21no—
150#103×C43—22no—
151#103×C43—22no—
152C22⋊C8×C43—22no—
153C24×C43C2×D411yescharacteristic
154C23×D43—21no—
155C2×Q8×C43—21no—
156C2×Q8×C43—21no—
157C2×Q8×C43—21no—
158C2×Q8×C43—21no—
159C2×Q8×C43—21no—
160C2×Q8×C43C22×C412yes—
161C22×C4×C43—21no—
162C22×C4×C43—21no—
163C22×C4×C43—21no—
164C22×C4×C43—21no—
165C22×C4×C43—24no—
166C22×C4×C43—21no—
167C22×C4×C43—21no—
168C22×C4×C43—21no—
169C22×C4×C43—21no—
170C22×C4×C43—81no—
171C22×C4×C43—81no—
172C22×C4×C43C22×C412yes—
173C22×C4×C43C2×D411yescharacteristic
174C22×C4×C43#4112yes—
175C22×C4×C43C2411yescharacteristic
176C2×C22⋊D43—24no—
177C2×C22⋊D43—24no—
178C2×C22⋊D43—24no—
179C22×Dic43—21no—
180C22×Dic43—21no—
181C22×Dic43—21no—
182C22×Dic43C2×D411yescharacteristic
183C22×Dic43C2×D411yescharacteristic
184C22×Dic43C2×D411yescharacteristic
185C22×Dic43C2×D411yescharacteristic
186#10621898—28no—
187#10621898—28no—
188#10621898—28no—
189#10621898—28no—
190C2×D172—21no—
191C2×D172—21no—
192C2×D172—21no—
193C2×D172C22×C412yes—
194C2×D172C2×D412yes—
195C2×D172#4112yes—
196C2×C4×D43—24no—
197C2×C4×D43—24no—
198C2×C4×D43—24no—
199C2×C4×D43—24no—
200C2×C4×D43—24no—
201C2×C4×D43—81no—
202C2×C4×D43—81no—
203C2×C4×D43—81no—
204C2×C4×D43—81no—
205C2×Dic86—21no—
206C2×Dic86—21no—
207C2×Dic86—21no—
208C2×Dic86C22×C412yes—
209C2×Dic86C2×D412yes—
210C2×Dic86#4112yes—
211C2×C8×C43—21no—
212C2×C8×C43—21no—
213C2×C8×C43—21no—
214C2×C8×C43—21no—
215C2×C8×C43—21no—
216C2×C8×C43—21no—
217C4⋊C4×C43—24no—
218C4⋊C4×C43—24no—
219C4⋊C4×C43—21no—
220C4⋊C4×C43—21no—
221C4⋊C4×C43—21no—
222C4⋊C4×C43C22×C412yes—
223C4⋊C4×C43C2×D412yes—
224C4⋊C4×C43C2×D412yes—
225C22⋊C4×C43—24no—
226C22⋊Dic43—22no—
227C22⋊Dic43—22no—
228C22⋊Dic43—81no—
229#10621885—28no—
230#10621884—28no—
231(C2×D43)⋊C4—24no—
232(C2×D43)⋊C4—24no—
233C4⋊Dic43—22no—
234C4⋊Dic43—22no—
235C4⋊Dic43—21no—
236C4⋊Dic43—21no—
237C4⋊Dic43—21no—
238C4⋊Dic43—21no—
239C4⋊Dic43—42no—
240C4⋊Dic43—81no—
241Dic43⋊C4—24no—
242Dic43⋊C4—24no—
243C4×Dic43—24no—
244C4×Dic43—21no—
245C4×Dic43—21no—
246C4×Dic43—24no—
247C4×Dic43—42no—
248C4×Dic43—81no—
249C4×Dic43C2×D412yes—
250C4×Dic43C2×D412yes—
251C2×C43⋊C8—21no—
252C2×C43⋊C8—21no—
253C2×C43⋊C8—21no—
254C2×C43⋊C8—21no—
255C2×C43⋊C8C22×C412yes—
256C2×C43⋊C8C22×C412yes—
257C23×C43—21no—
258C23×C43—21no—
259C23×C43—21no—
260C23×C43—21no—
261C23×C43—21no—
262C23×C43—21no—
263C23×C43C4×D412yes—
264C23×C43C22×D411yescharacteristic
265C22×D43—22no—
266C22×D43—22no—
267C22×D43—22no—
268C22×D43—41no—
269C22×D43—41no—
270C22×D43—41no—
271C22×D43—41no—
272Q8×C43—22no—
273Q8×C43—22no—
274Q8×C43—41no—
275Q8×C43—41no—
276C2×C4×C43—21no—
277C2×C4×C43—21no—
278C2×C4×C43—22no—
279C2×C4×C43—22no—
280C2×C4×C43—22no—
281C2×C4×C43—22no—
282C2×C4×C43—22no—
283C2×C4×C43—22no—
284C2×C4×C43—22no—
285C2×C4×C43—22no—
286C2×C4×C43—41no—
287C2×C4×C43—41no—
288C2×C4×C43—41no—
289C2×C4×C43—41no—
290C2×C4×C43—41no—
291C2×C4×C43—41no—
292C2×C4×C43—41no—
293C2×C4×C43—41no—
294C2×C4×C43—84no—
295C2×C4×C43C4×D412yes—
296C2×C4×C43C23×C411yescharacteristic
297C2×C4×C43C22×D411yescharacteristic
298C2×C4×C43C22×D411yescharacteristic
299C2×C4×C43C2×#4111yescharacteristic
300C2×C4×C43C2×#4111yescharacteristic
301C2×C4×C43C2×#4111yescharacteristic
302C22⋊D43—216no—
303C2×Dic43—22no—
304C2×Dic43—22no—
305C2×Dic43—22no—
306C2×Dic43—21no—
307C2×Dic43—21no—
308C2×Dic43—21no—
309C2×Dic43—21no—
310C2×Dic43—21no—
311C2×Dic43—21no—
312C2×Dic43—21no—
313C2×Dic43—21no—
314C2×Dic43—21no—
315C2×Dic43—21no—
316C2×Dic43—41no—
317C2×Dic43—41no—
318C2×Dic43—41no—
319C2×Dic43—41no—
320C2×Dic43—41no—
321C2×Dic43—41no—
322C2×Dic43#12012yes—
323C2×Dic43#12012yes—
324D172—22no—
325D172—22no—
326D172—22no—
327D172C4×D414yes—
328C4×D43—216no—
329C4×D43—84no—
330C4×D43—84no—
331Dic86—22no—
332Dic86—22no—
333Dic86—22no—
334Dic86C4×D414yes—
335C8×C43—41no—
336C8×C43—41no—
337C43⋊C8—22no—
338C43⋊C8—22no—
339#21465—431nomaximal, Sylow
340C22×C43—22no—
341C22×C43—22no—
342C22×C43—22no—
343C22×C43—41no—
344C22×C43—41no—
345C22×C43—41no—
346C22×C43—41no—
347C22×C43C2×C4×D411yescharacteristic
348C22×C43C2×#12011yescharacteristic
349C22×C43#52511yescharacteristic
350C22×C43#57611yescharacteristic
351C22×C43#57711yescharacteristic
352C22×C43#57811yescharacteristic
353C22×C43#57811yescharacteristic
354C2×D43—24no—
355C2×D43—42no—
356C2×D43—42no—
357C2×D43—42no—
358C2×D43—42no—
359C2×D43—42no—
360C2×D43—42no—
361C4×C43—22no—
362C4×C43—42no—
363C4×C43—42no—
364C4×C43—42no—
365C4×C43—42no—
366C4×C43C2×C4×D411yescharacteristic
367C4×C43C2×C4×D411yescharacteristic
368C4×C43#52511yescharacteristic
369C4×C43#52511yescharacteristic
370Dic43—22no—
371Dic43—22no—
372Dic43—24no—
373Dic43—41no—
374Dic43—41no—
375Dic43—81no—
376Dic43—81no—
377C2×#520—431no—
378C2×#452—431no—
379C2×#440—431no—
380C2×C4×Q16—431no—
381#2323—431no—
382#1878—431no—
383#1877—431no—
384#1872D4311yescharacteristic, complemented
385#1863—431no—
386#1862—431no—
387#1852—431no—
388#1788—431no—
389#1763—431no—
390C4×#102—431no—
391#1750—431no—
392C2×C43—42no—
393C2×C43C4×#12011yescharacteristic
394C2×C43#294711yescharacteristic
395C2×C43#295111yescharacteristic
396C2×C43#301111yescharacteristic
397C2×C43#301211yescharacteristic
398C2×C43#312011yescharacteristic
399C2×C43#312411yescharacteristic
400D43—44no—
401C22×#41—431no—
402C22×Q16—431no—
403C22×SD16—431no—
404C2×C22⋊Q8C2×D4311yescharacteristic
405#520—864no—
406#520—864no—
407C2×C4×Q8—431no—
408C2×C4×Q8—431no—
409C2×C4×Q8—431no—
410C2×C4×D4—431no—
411C2×C4×D4—431no—
412C2×C4×D4—861no—
413C2×C4×D4—861no—
414C2×#117—431no—
415C2×#117—861no—
416C22×C4⋊C4—861no—
417C22×C4⋊C4C2×D4311yescharacteristic
418#452—438no—
419#440—864no—
420C4×Q16—864no—
421C2×#107—431no—
422C2×#107—431no—
423C2×#103—431no—
424C2×#103—431no—
425C2×#103—431no—
426C2×#103C2×D4311yescharacteristic
427C2×#103C2×D4311yescharacteristic
428C2×#102—431no—
429C2×#102—431no—
430C2×#102—431no—
431C2×C22⋊C8—431no—
432C2×C22⋊C8C2×D4311yescharacteristic
433C2×#97—431no—
434C2×C4×C8—431no—
435#391—431no—
436#389—431no—
437#389—861no—
438#388—861no—
439#388—861no—
440#387—861no—
441#380—431no—
442C4×C4⋊C4—431no—
443#340—431no—
444#340—431no—
445#340C2×D4311yescharacteristic
446#340C2×D4311yescharacteristic
447#336—431no—
448#336—431no—
449C43#2146511yescharacteristic, complemented, Sylow
450C2×#41—434no—
451C2×#41—862no—
452C2×#41—862no—
453C2×#41—862no—
454C2×#41—862no—
455C2×#41—862no—
456C22×Q8—431no—
457C22×Q8C22×D4311yescharacteristic
458C22×D4—431no—
459C22×D4—861no—
460C23×C4—21no—
461C23×C4—861no—
462C23×C4—861no—
463C23×C4—861no—
464C23×C4C22×D4311yescharacteristic
465C2×Q16—434no—
466C2×Q16—862no—
467C2×Q16—862no—
468C2×SD16—434no—
469C2×SD16—862no—
470C2×SD16—862no—
471C22×C8—431no—
472C22×C8—431no—
473C22×C8C22×D4311yescharacteristic
474C22×C8C22×D4311yescharacteristic
475C22⋊Q8—22no—
476C22⋊Q8C4×D4314yescomplemented
477C4×Q8—434no—
478C4×Q8—862no—
479C4×Q8—862no—
480C4×Q8—862no—
481C4×Q8—862no—
482C4×Q8—862no—
483C4×D4—434no—
484C4×D4—862no—
485C4×D4—862no—
486C4×D4—868no—
487C4×D4—868no—
488C4×D4—862no—
489#117—862no—
490#117—862no—
491#117—868no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—22no—
495C2×C4⋊C4—22no—
496C2×C4⋊C4—431no—
497C2×C4⋊C4—431no—
498C2×C4⋊C4—431no—
499C2×C4⋊C4—431no—
500C2×C4⋊C4—868no—
501C2×C4⋊C4—861no—
502C2×C4⋊C4—861no—
503C2×C4⋊C4—861no—
504C2×C4⋊C4—861no—
505C2×C4⋊C4C22×D4311yescharacteristic
506C2×C4⋊C4C22×D4311yescharacteristic
507C2×C4⋊C4C22×D4311yescharacteristic
508C2×C22⋊C4—21no—
509C2×C22⋊C4—431no—
510C2×C22⋊C4—431no—
511C2×C22⋊C4—861no—
512C2×C22⋊C4—861no—
513C2×C22⋊C4—861no—
514C2×C42—431no—
515C2×C42—431no—
516C2×C42—861no—
517C2×C42—861no—
518C2×C42—861no—
519C2×C42—861no—
520#107—862no—
521#107—862no—
522#103—22no—
523#103—22no—
524#103—434no—
525#103—862no—
526#103—862no—
527#102—434no—
528#102—862no—
529#102—862no—
530C22⋊C8—22no—
531C22⋊C8—434no—
532#97—862no—
533C4×C8—862no—
534#95—861no—
535#95—861no—
536#95—861no—
537#95—861no—
538#95—861no—
539C24—861no—
540C24D4×D4311yescharacteristic
541#41—868no—
542#41—868no—
543#41—868no—
544#41—868no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—432no—
551C2×Q8—432no—
552C2×Q8—432no—
553C2×Q8—861no—
554C2×Q8—861no—
555C2×Q8—861no—
556C2×Q8C2×C4×D4312yes—
557C2×D4—432no—
558C2×D4—432no—
559C2×D4—432no—
560C2×D4—864no—
561C2×D4—864no—
562C2×D4—864no—
563C2×D4—861no—
564C2×D4—861no—
565C2×D4—861no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—24no—
575C22×C4—81no—
576C22×C4—81no—
577C22×C4—431no—
578C22×C4—431no—
579C22×C4—431no—
580C22×C4—431no—
581C22×C4—864no—
582C22×C4—864no—
583C22×C4—864no—
584C22×C4—864no—
585C22×C4—861no—
586C22×C4—864no—
587C22×C4—861no—
588C22×C4—861no—
589C22×C4—3441no—
590C22×C4—3441no—
591C22×C4—3441no—
592C22×C4—3441no—
593C22×C4C2×C4×D4312yes—
594C22×C4D4×D4311yescharacteristic
595C22×C4#1062190012yes—
596C22×C4C23×D4311yescharacteristic
597Q16—868no—
598SD16—868no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—432no—
606C2×C8—432no—
607C2×C8—861no—
608C2×C8—861no—
609C2×C8—861no—
610C2×C8—861no—
611C4⋊C4—24no—
612C4⋊C4—24no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—862no—
617C4⋊C4—862no—
618C4⋊C4—864no—
619C4⋊C4—864no—
620C4⋊C4—861no—
621C4⋊C4—861no—
622C4⋊C4—861no—
623C4⋊C4—861no—
624C4⋊C4—3441no—
625C4⋊C4—1722no—
626C4⋊C4C2×C4×D4312yes—
627C4⋊C4D4×D4312yes—
628C4⋊C4D4×D4312yes—
629C22⋊C4—24no—
630C22⋊C4—864no—
631C22⋊C4—864no—
632C22⋊C4—862no—
633C22⋊C4—862no—
634C22⋊C4—3441no—
635C42—432no—
636C42—432no—
637C42—864no—
638C42—864no—
639C42—861no—
640C42—861no—
641C42—3441no—
642C42—1722no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—862no—
650C23—862no—
651C23—862no—
652C23—1721no—
653C23—1721no—
654C23—1721no—
655C23—1721no—
656C23(C22⋊D43)⋊C412yes—
657C23C2×D4×D4311yescharacteristic
658Q8—22no—
659Q8—22no—
660Q8—41no—
661Q8—41no—
662Q8—434no—
663Q8—862no—
664Q8—862no—
665Q8—862no—
666D4—434no—
667D4—8616no—
668D4—862no—
669D4—862no—
670D4—862no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—84no—
690C2×C4—432no—
691C2×C4—432no—
692C2×C4—8616no—
693C2×C4—862no—
694C2×C4—862no—
695C2×C4—862no—
696C2×C4—861no—
697C2×C4—861no—
698C2×C4—861no—
699C2×C4—861no—
700C2×C4—861no—
701C2×C4—861no—
702C2×C4—861no—
703C2×C4—861no—
704C2×C4—861no—
705C2×C4—861no—
706C2×C4—3444no—
707C2×C4—3444no—
708C2×C4—1721no—
709C2×C4—1721no—
710C2×C4—1721no—
711C2×C4—1721no—
712C2×C4—1721no—
713C2×C4—1721no—
714C2×C4(C22⋊D43)⋊C412yes—
715C2×C4C22×C4×D4311yescharacteristic
716C2×C4C2×D4×D4311yescharacteristic
717C2×C4C2×D4×D4311yescharacteristic
718C2×C4#41×D4311yescharacteristic
719C2×C4#41×D4311yescharacteristic
720C2×C4C2×#1062190011yescharacteristic
721C8—41no—
722C8—41no—
723C8—862no—
724C8—862no—
725C22—22no—
726C22—22no—
727C22—22no—
728C22—41no—
729C22—41no—
730C22—41no—
731C22—41no—
732C22—864no—
733C22—1722no—
734C22—1722no—
735C22—1722no—
736C22—1722no—
737C22—1722no—
738C22—1722no—
739C22C2×(C22⋊D43)⋊C411yescharacteristic
740C22#120×D4311yescharacteristic
741C22#1458340711yescharacteristic
742C22#1458370311yescharacteristic
743C22#1458370511yescharacteristic
744C22#1458371211yescharacteristic
745C22#1458371511yescharacteristic
746C4—22no—
747C4—42no—
748C4—42no—
749C4—42no—
750C4—42no—
751C4—864no—
752C4—862no—
753C4—862no—
754C4—3441no—
755C4—3441no—
756C4—1721no—
757C4—1721no—
758C4C4×D4×D4311yescharacteristic
759C4C4×D4×D4311yescharacteristic
760C4#1458340911yescharacteristic
761C4#1458340911yescharacteristic
762C2—42no—
763C2—1724no—
764C2#1913710011yescharacteristic
765C2#1914343211yescharacteristic
766C2#1914346611yescharacteristic
767C2#1914388511yescharacteristic
768C2#1914390011yescharacteristic
769C2#1914481211yescharacteristic
770C2#1914486011yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1872C2
socleC23×C43C22×D4
prime radicalC22×#10621898C22
cosocleC22×C4×C43C24
hypercenter#1872D43
hypocenterC43#21465
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1872

Complements

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

NH ≅ G/Ntype
3. C2×#14583002C2semidirect
4. C2×#14582991C2semidirect
5. #19137279C2semidirect
6. #19134933C2semidirect
7. #19134926C2semidirect
8. #19134850C2semidirect
9. #19134843C2semidirect
10. #19134783C2semidirect
12. #19134424C2semidirect
13. #19134409C2semidirect
14. #19134363C2semidirect
15. C43×#1872C2semidirect
31. #14583059C4semidirect
78. C2×#10621885C2×C4semidirect
81. C2×#10621884C2×C4semidirect
123. #13063248C2×C4semidirect
126. #13063245C2×C4semidirect
127. C22⋊(C43⋊C8)C2×C4semidirect
141. C22⋊Q8×C43C2×C4semidirect
384. #1872D43semidirect
449. C43#21465semidirect
476. C22⋊Q8C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145833802
C2×#145830592
C2×#145830022
C2×#145829912
#191372792
#191349332
#191349262
#191348502
#191348432
#191347832
#191345362
#191344242
#191344092
#191343632
C43×#18722
#2146543