Finite Group Databasebeta

← #25102294

Subgroups — #25102294

Order 11008.

1468 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×Dic43C211yesmaximal, characteristic
2C2×#14583061C211yesmaximal, characteristic
3C2×#14583003C211yesmaximal, characteristic, complemented
4C2×#14582996C211yesmaximal, characteristic, complemented
5#19137123C211yesmaximal, characteristic, complemented
6#19134934C211yesmaximal, characteristic, complemented
7#19134927C211yesmaximal, characteristic, complemented
8#19134905C211yesmaximal, characteristic, complemented
9#19134854C211yesmaximal, characteristic, complemented
10#19134847C211yesmaximal, characteristic, complemented
11#19134792C211yesmaximal, characteristic, complemented
12#19134427C211yesmaximal, characteristic, complemented
13#19134422C211yesmaximal, characteristic, complemented
14#19134359C211yesmaximal, characteristic, complemented
15C43×#1788C211yesmaximal, characteristic
16C22×#10621885C2211yescharacteristic
17C22×#10621883C2211yescharacteristic
18C2×#13063304C2211yescharacteristic
19#41×Dic43—24no—
20#41×Dic43—24no—
21C2×Q8×Dic43C2211yescharacteristic
22C2×Q8×Dic43C2211yescharacteristic
23C2×#13063290C2211yescharacteristic
24C2×D4×Dic43—21no—
25C2×D4×Dic43—21no—
26C2×D4×Dic43C2211yescharacteristic
27C2×D4×Dic43C2211yescharacteristic
28C2×#13063284—21no—
29C2×#13063284C2211yescharacteristic
30C22×C4×Dic43—21no—
31C22×C4×Dic43C2211yescharacteristic
32#14583061C418yescomplemented
33#14583003—24no—
34#14582996—24no—
35C2×#13063258C2211yescharacteristic
36C2×#13063256C2211yescharacteristic
37C2×#13063250C2211yescharacteristic
38C2×#13063250C2211yescharacteristic
39C2×#13063249C2211yescharacteristic
40C2×#13063246C2211yescharacteristic
41C2×C22⋊(C43⋊C8)C2211yescharacteristic
42C2×#13063235C2211yescharacteristic
43C2×#13063235C2211yescharacteristic
44#14582804C2211yescharacteristic
45#14582795C2211yescharacteristic
46#14582781—21no—
47#14582771—21no—
48C4⋊C4×Dic43C2211yescharacteristic
49#14582750—21no—
50C22⋊C4×Dic43—21no—
51#14582662C2211yescharacteristic
52#14582662C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582661C2211yescharacteristic
55#14582653C2211yescharacteristic
56#14582653C2211yescharacteristic
57C22×#41×C43C2211yescharacteristic
58C2×#103×C43C2211yescharacteristic
59C2×#103×C43C2211yescharacteristic
60C2×#102×C43C2211yescharacteristic
61C2×#102×C43C2211yescharacteristic
62C2×C22⋊C8×C43C2211yescharacteristic
63C43×#380C2211yescharacteristic
64C22×Dic86C2311yescharacteristic
65C23×Dic43—21no—
66C23×Dic43—21no—
67C23×Dic43D411yescharacteristic
68C23×Dic43D411yescharacteristic
69C2×#10621885—22no—
70C2×#10621885—22no—
71C2×#10621885C2×C414yescomplemented
72C2×#10621883—22no—
73C2×#10621883—22no—
74C2×#10621883C2×C414yescomplemented
75C22×C43⋊C8C2311yescharacteristic
76C22×C43⋊C8C2311yescharacteristic
77#13063304—22no—
78#13063304C2×C414yescomplemented
79Q8×Dic43—22no—
80Q8×Dic43—22no—
81Q8×Dic43—22no—
82Q8×Dic43D414yes—
83#13063290—22no—
84#13063290—22no—
85D4×Dic43—28no—
86D4×Dic43—28no—
87D4×Dic43—22no—
88D4×Dic43—22no—
89D4×Dic43—22no—
90D4×Dic43D414yes—
91#13063284—28no—
92#13063284—22no—
93#13063284—22no—
94C2×C4⋊Dic43—21no—
95C2×C4⋊Dic43—21no—
96C2×C4⋊Dic43C2311yescharacteristic
97C2×C4⋊Dic43C2311yescharacteristic
98C2×C4⋊Dic43C2311yescharacteristic
99C2×Dic43⋊C4—21no—
100C2×Dic43⋊C4—21no—
101C2×Dic43⋊C4—21no—
102C2×C22⋊Dic43—21no—
103C2×C22⋊Dic43—21no—
104C2×C22⋊Dic43—21no—
105C2×C22⋊Dic43—21no—
106C2×C4×Dic43—28no—
107C2×C4×Dic43—21no—
108C2×C4×Dic43—21no—
109C2×C4×Dic43—21no—
110C2×C4×Dic43—22no—
111C2×C4×Dic43—22no—
112C2×C4×Dic43—21no—
113C2×C4×Dic43—21no—
114C2×C4×Dic43D411yescharacteristic
115C2×C4×Dic43D411yescharacteristic
116C2×C4×Dic43C2311yescharacteristic
117C2×C4×Dic43C2311yescharacteristic
118#13063258—22no—
119#13063256—22no—
120#13063250—22no—
121#13063250—22no—
122#13063249C2×C414yescomplemented
123#13063246C2×C414yescomplemented
124C22⋊(C43⋊C8)C2×C414yescomplemented
125#13063235—22no—
126#13063235—22no—
127C43⋊#95—21no—
128C43⋊#95—21no—
129C43⋊#95—21no—
130C43⋊#95—21no—
131C2×#41×C43—22no—
132C2×#41×C43—22no—
133C2×#41×C43—22no—
134C2×#41×C43—22no—
135C2×#41×C43—22no—
136C2×#41×C43C2×C414yes—
137C22×Q8×C43C2311yescharacteristic
138C22×D4×C43—21no—
139C22×D4×C43C2311yescharacteristic
140C23×C4×C43—21no—
141C23×C4×C43C2311yescharacteristic
142C22×C8×C43C2311yescharacteristic
143C22×C8×C43C2311yescharacteristic
144C2×C4⋊C4×C43C2311yescharacteristic
145C2×C4⋊C4×C43C2311yescharacteristic
146C2×C22⋊C4×C43—21no—
147#103×C43—22no—
148#103×C43—22no—
149#102×C43—22no—
150#102×C43—22no—
151C22⋊C8×C43—22no—
152#95×C43—21no—
153C24×C43—21no—
154C24×C43C2×D411yescharacteristic
155#41×C43—28no—
156#41×C43—28no—
157#41×C43—28no—
158#41×C43—28no—
159C2×Q8×C43—21no—
160C2×Q8×C43—21no—
161C2×Q8×C43—21no—
162C2×Q8×C43C22×C412yes—
163C2×Q8×C43C2×D412yes—
164C2×Q8×C43#4112yes—
165C2×D4×C43—24no—
166C2×D4×C43—24no—
167C2×D4×C43—21no—
168C2×D4×C43—21no—
169C2×D4×C43—21no—
170C2×D4×C43—24no—
171C2×D4×C43C22×C412yes—
172C2×D4×C43C2×D412yes—
173C2×D4×C43#4112yes—
174C22×C4×C43—24no—
175C22×C4×C43—24no—
176C22×C4×C43—24no—
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×D411yescharacteristic
186C22×C4×C43#4112yes—
187C22×C4×C43C2411yescharacteristic
188C22×Dic43—24no—
189C22×Dic43—22no—
190C22×Dic43—22no—
191C22×Dic43—24no—
192C22×Dic43—22no—
193C22×Dic43—21no—
194C22×Dic43—21no—
195C22×Dic43—21no—
196C22×Dic43—21no—
197C22×Dic43—41no—
198C22×Dic43—41no—
199C22×Dic43—41no—
200C22×Dic43—42no—
201C22×Dic43—42no—
202C22×Dic43—42no—
203C22×Dic43—42no—
204C22×Dic43C2×D411yescharacteristic
205C22×Dic43C2×D411yescharacteristic
206C22×Dic43C2×D411yescharacteristic
207C22×Dic43C2×D411yescharacteristic
208C2×Dic86—21no—
209C2×Dic86—21no—
210C2×Dic86—21no—
211C2×Dic86—21no—
212C2×Dic86—21no—
213C2×Dic86C22×C412yes—
214C2×C8×C43—21no—
215C2×C8×C43—21no—
216C2×C8×C43—21no—
217C2×C8×C43—21no—
218C2×C8×C43—21no—
219C2×C8×C43—21no—
220C4⋊C4×C43—21no—
221C4⋊C4×C43—21no—
222C4⋊C4×C43—21no—
223C4⋊C4×C43—21no—
224C22⋊C4×C43—42no—
225C22⋊Dic43—24no—
226C22⋊Dic43—24no—
227C22⋊Dic43—24no—
228C22⋊Dic43—24no—
229#10621885—28no—
230#10621883—28no—
231C4⋊Dic43—24no—
232C4⋊Dic43—21no—
233C4⋊Dic43—21no—
234C4⋊Dic43—21no—
235C4⋊Dic43—24no—
236C4⋊Dic43C22×C412yes—
237C4⋊Dic43C2×D412yes—
238C4⋊Dic43C2×D412yes—
239Dic43⋊C4—24no—
240Dic43⋊C4—42no—
241Dic43⋊C4—42no—
242C4×Dic43—24no—
243C4×Dic43—24no—
244C4×Dic43—21no—
245C4×Dic43—21no—
246C4×Dic43—22no—
247C4×Dic43—24no—
248C4×Dic43—22no—
249C4×Dic43—42no—
250C4×Dic43—42no—
251C4×Dic43C2×D412yes—
252C4×Dic43C2×D412yes—
253C2×C43⋊C8—21no—
254C2×C43⋊C8—21no—
255C2×C43⋊C8—21no—
256C2×C43⋊C8—21no—
257C2×C43⋊C8C22×C412yes—
258C2×C43⋊C8C22×C412yes—
259C23×C43—22no—
260C23×C43—21no—
261C23×C43—22no—
262C23×C43—21no—
263C23×C43—22no—
264C23×C43—21no—
265C23×C43—21no—
266C23×C43—21no—
267C23×C43—21no—
268C23×C43—41no—
269C23×C43—41no—
270C23×C43—41no—
271C23×C43—41no—
272C23×C43C4×D412yes—
273C23×C43C22×D411yescharacteristic
274Q8×C43—22no—
275Q8×C43—22no—
276Q8×C43—22no—
277Q8×C43C4×D414yes—
278D4×C43—216no—
279D4×C43—22no—
280D4×C43—22no—
281D4×C43—22no—
282D4×C43C4×D414yes—
283C2×C4×C43—216no—
284C2×C4×C43—22no—
285C2×C4×C43—21no—
286C2×C4×C43—22no—
287C2×C4×C43—21no—
288C2×C4×C43—22no—
289C2×C4×C43—22no—
290C2×C4×C43—22no—
291C2×C4×C43—22no—
292C2×C4×C43—22no—
293C2×C4×C43—41no—
294C2×C4×C43—41no—
295C2×C4×C43—41no—
296C2×C4×C43—41no—
297C2×C4×C43—41no—
298C2×C4×C43—41no—
299C2×C4×C43C4×D412yes—
300C2×C4×C43C23×C411yescharacteristic
301C2×C4×C43C22×D411yescharacteristic
302C2×C4×C43C22×D411yescharacteristic
303C2×C4×C43C2×#4111yescharacteristic
304C2×C4×C43C2×#4111yescharacteristic
305C2×C4×C43C2×#4111yescharacteristic
306C2×Dic43—21no—
307C2×Dic43—21no—
308C2×Dic43—21no—
309C2×Dic43—21no—
310C2×Dic43—21no—
311C2×Dic43—21no—
312C2×Dic43—22no—
313C2×Dic43—22no—
314C2×Dic43—21no—
315C2×Dic43—22no—
316C2×Dic43—22no—
317C2×Dic43—21no—
318C2×Dic43—21no—
319C2×Dic43—44no—
320C2×Dic43—44no—
321C2×Dic43—48no—
322C2×Dic43—48no—
323C2×Dic43—41no—
324C2×Dic43—41no—
325C2×Dic43—41no—
326C2×Dic43—41no—
327C2×Dic43—41no—
328C2×Dic43—41no—
329C2×Dic43—41no—
330C2×Dic43—41no—
331C2×Dic43#12012yes—
332C2×Dic43#12012yes—
333C2×Dic43#13712yes—
334Dic86—22no—
335Dic86—22no—
336Dic86—41no—
337Dic86—41no—
338C8×C43—41no—
339C8×C43—41no—
340C43⋊C8—22no—
341C43⋊C8—22no—
342#21457—431nomaximal, Sylow
343C22×C43—22no—
344C22×C43—22no—
345C22×C43—24no—
346C22×C43—22no—
347C22×C43—41no—
348C22×C43—42no—
349C22×C43—41no—
350C22×C43—42no—
351C22×C43—42no—
352C22×C43—42no—
353C22×C43—41no—
354C22×C43—42no—
355C22×C43—41no—
356C22×C43—42no—
357C22×C43C2×C4×D411yescharacteristic
358C22×C43C2×#12011yescharacteristic
359C22×C43#52511yescharacteristic
360C22×C43C2×#13711yescharacteristic
361C22×C43#57511yescharacteristic
362C22×C43#57511yescharacteristic
363C22×C43#57511yescharacteristic
364C4×C43—22no—
365C4×C43—24no—
366C4×C43—81no—
367C4×C43—81no—
368C4×C43C2×C4×D411yescharacteristic
369C4×C43C2×C4×D411yescharacteristic
370C4×C43#52511yescharacteristic
371C4×C43#52511yescharacteristic
372Dic43—22no—
373Dic43—22no—
374Dic43—22no—
375Dic43—42no—
376Dic43—41no—
377Dic43—42no—
378Dic43—42no—
379Dic43—42no—
380C2×C4×#41—431no—
381C2×#452—431no—
382C2×#441—431no—
383C2×#440—431no—
384C4×C22⋊Q8—431no—
385#1878—431no—
386#1877—431no—
387#1873—431no—
388#1864—431no—
389#1863—431no—
390#1854—431no—
391#1788D4311yescharacteristic
392#1763—431no—
393#1762—431no—
394#1749—431no—
395C2×C43—42no—
396C2×C43—44no—
397C2×C43C4×#12011yescharacteristic
398C2×C43#294311yescharacteristic
399C2×C43C4×#13711yescharacteristic
400C2×C43#300511yescharacteristic
401C2×C43#300711yescharacteristic
402C2×C43#311111yescharacteristic
403C2×C43#311611yescharacteristic
404C22×#41C2×D4311yescharacteristic
405C22×Q16—431no—
406C22×SD16—431no—
407C2×C22⋊Q8—431no—
408C4×#41—864no—
409C4×#41—864no—
410C2×C4×Q8—431no—
411C2×C4×Q8—431no—
412C2×C4×Q8—431no—
413C2×C4×D4—431no—
414C2×C4×D4—431no—
415C2×C4×D4—861no—
416C2×C4×D4—861no—
417C2×#117—431no—
418C2×#117—861no—
419C22×C42—431no—
420C22×C42—861no—
421#452—438no—
422#441—864no—
423#440—864no—
424C2×#107—431no—
425C2×#106—431no—
426C2×#103—431no—
427C2×#103—431no—
428C2×#103—431no—
429C2×#103C2×D4311yescharacteristic
430C2×#103C2×D4311yescharacteristic
431C2×#102—431no—
432C2×#102C2×D4311yescharacteristic
433C2×#102C2×D4311yescharacteristic
434C2×C22⋊C8—431no—
435C2×C22⋊C8C2×D4311yescharacteristic
436C2×#97—431no—
437C2×#97—431no—
438#391—431no—
439#389—431no—
440#387—861no—
441#385—861no—
442#380C2×D4311yescharacteristic
443C4×C4⋊C4—431no—
444C4×C4⋊C4—861no—
445C4×C22⋊C4—861no—
446#340—431no—
447#340—431no—
448#340—431no—
449#340—431no—
450#336—431no—
451#336—431no—
452C43#2145711yescharacteristic, complemented, Sylow
453C2×#41—22no—
454C2×#41—22no—
455C2×#41—22no—
456C2×#41—22no—
457C2×#41—22no—
458C2×#41C4×D4314yes—
459C22×Q8—431no—
460C22×Q8C22×D4311yescharacteristic
461C22×D4—21no—
462C22×D4C22×D4311yescharacteristic
463C23×C4—21no—
464C23×C4—431no—
465C23×C4—431no—
466C23×C4—861no—
467C23×C4—861no—
468C23×C4C22×D4311yescharacteristic
469C2×Q16—434no—
470C2×Q16—862no—
471C2×Q16—862no—
472C2×SD16—434no—
473C2×SD16—862no—
474C2×SD16—862no—
475C22×C8—431no—
476C22×C8—431no—
477C22×C8C22×D4311yescharacteristic
478C22×C8C22×D4311yescharacteristic
479C22⋊Q8—434no—
480C22⋊Q8—862no—
481C4×Q8—434no—
482C4×Q8—862no—
483C4×Q8—862no—
484C4×Q8—862no—
485C4×Q8—862no—
486C4×Q8—862no—
487C4×D4—434no—
488C4×D4—862no—
489C4×D4—862no—
490C4×D4—868no—
491C4×D4—868no—
492C4×D4—862no—
493#117—862no—
494#117—862no—
495#117—868no—
496C2×C4⋊C4—431no—
497C2×C4⋊C4—431no—
498C2×C4⋊C4—431no—
499C2×C4⋊C4—861no—
500C2×C4⋊C4—861no—
501C2×C4⋊C4—861no—
502C2×C4⋊C4—861no—
503C2×C4⋊C4—861no—
504C2×C4⋊C4C22×D4311yescharacteristic
505C2×C4⋊C4C22×D4311yescharacteristic
506C2×C22⋊C4—21no—
507C2×C22⋊C4—861no—
508C2×C22⋊C4—861no—
509C2×C22⋊C4—861no—
510C2×C22⋊C4—861no—
511C2×C42—431no—
512C2×C42—431no—
513C2×C42—431no—
514C2×C42—431no—
515C2×C42—862no—
516C2×C42—862no—
517C2×C42—861no—
518C2×C42—861no—
519C2×C42—868no—
520C2×C42—861no—
521C2×C42—861no—
522C2×C42—861no—
523#107—862no—
524#106—862no—
525#103—22no—
526#103—22no—
527#103—434no—
528#103—862no—
529#103—862no—
530#102—22no—
531#102—22no—
532#102—434no—
533C22⋊C8—22no—
534C22⋊C8—434no—
535#97—862no—
536#97—862no—
537#95—21no—
538#95—861no—
539#95—861no—
540#95—861no—
541#95—861no—
542C24—21no—
543C24D4×D4311yescharacteristic
544#41—28no—
545#41—28no—
546#41—28no—
547#41—28no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—432no—
552C2×Q8—861no—
553C2×Q8—861no—
554C2×Q8—861no—
555C2×Q8—861no—
556C2×Q8—861no—
557C2×Q8C2×C4×D4312yes—
558C2×Q8D4×D4312yes—
559C2×Q8#1062190012yes—
560C2×D4—24no—
561C2×D4—24no—
562C2×D4—24no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4C2×C4×D4312yes—
567C2×D4D4×D4312yes—
568C2×D4#1062190012yes—
569C22×C4—24no—
570C22×C4—24no—
571C22×C4—21no—
572C22×C4—24no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—431no—
580C22×C4—431no—
581C22×C4—431no—
582C22×C4—431no—
583C22×C4—864no—
584C22×C4—862no—
585C22×C4—862no—
586C22×C4—862no—
587C22×C4—864no—
588C22×C4—861no—
589C22×C4—861no—
590C22×C4—861no—
591C22×C4—861no—
592C22×C4—1722no—
593C22×C4—1721no—
594C22×C4—1721no—
595C22×C4—1721no—
596C22×C4—1722no—
597C22×C4—1722no—
598C22×C4—1722no—
599C22×C4C2×C4×D4312yes—
600C22×C4D4×D4311yescharacteristic
601C22×C4#1062190012yes—
602C22×C4C23×D4311yescharacteristic
603Q16—868no—
604SD16—868no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—432no—
612C2×C8—432no—
613C2×C8—861no—
614C2×C8—861no—
615C2×C8—861no—
616C2×C8—861no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—432no—
622C4⋊C4—432no—
623C4⋊C4—432no—
624C4⋊C4—864no—
625C4⋊C4—864no—
626C4⋊C4—864no—
627C4⋊C4—861no—
628C4⋊C4—861no—
629C4⋊C4—861no—
630C4⋊C4—1722no—
631C4⋊C4—1722no—
632C22⋊C4—42no—
633C22⋊C4—864no—
634C22⋊C4—864no—
635C22⋊C4—864no—
636C22⋊C4—864no—
637C42—432no—
638C42—432no—
639C42—862no—
640C42—862no—
641C42—864no—
642C42—864no—
643C42—864no—
644C42—861no—
645C42—861no—
646C42—1722no—
647C42—1722no—
648C23—22no—
649C23—21no—
650C23—22no—
651C23—21no—
652C23—22no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23(C22⋊D43)⋊C412yes—
662C23C2×D4×D4311yescharacteristic
663Q8—22no—
664Q8—22no—
665Q8—22no—
666Q8—862no—
667Q8—862no—
668Q8—1721no—
669Q8—1721no—
670Q8(C22⋊D43)⋊C414yes—
671D4—216no—
672D4—22no—
673D4—22no—
674D4—22no—
675D4(C22⋊D43)⋊C414yes—
676C2×C4—216no—
677C2×C4—22no—
678C2×C4—21no—
679C2×C4—22no—
680C2×C4—21no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—432no—
693C2×C4—432no—
694C2×C4—432no—
695C2×C4—861no—
696C2×C4—861no—
697C2×C4—861no—
698C2×C4—861no—
699C2×C4—861no—
700C2×C4—861no—
701C2×C4—862no—
702C2×C4—862no—
703C2×C4—862no—
704C2×C4—862no—
705C2×C4—861no—
706C2×C4—861no—
707C2×C4—861no—
708C2×C4—1724no—
709C2×C4—1724no—
710C2×C4—1728no—
711C2×C4—1728no—
712C2×C4—1721no—
713C2×C4—1721no—
714C2×C4—1721no—
715C2×C4—1721no—
716C2×C4—1721no—
717C2×C4—1721no—
718C2×C4—1721no—
719C2×C4—1721no—
720C2×C4(C22⋊D43)⋊C412yes—
721C2×C4C22×C4×D4311yescharacteristic
722C2×C4C2×D4×D4311yescharacteristic
723C2×C4C2×D4×D4311yescharacteristic
724C2×C4C2×#1062190011yescharacteristic
725C2×C4C2×#1062190011yescharacteristic
726C2×C4C2×#1062190011yescharacteristic
727C8—41no—
728C8—41no—
729C8—862no—
730C8—862no—
731C22—22no—
732C22—24no—
733C22—22no—
734C22—22no—
735C22—41no—
736C22—42no—
737C22—41no—
738C22—42no—
739C22—41no—
740C22—42no—
741C22—42no—
742C22—41no—
743C22—42no—
744C22—42no—
745C22C2×(C22⋊D43)⋊C411yescharacteristic
746C22#120×D4311yescharacteristic
747C22#1458340511yescharacteristic
748C22#137×D4311yescharacteristic
749C22#1458369511yescharacteristic
750C22#1458369611yescharacteristic
751C22#1458369611yescharacteristic
752C4—22no—
753C4—24no—
754C4—81no—
755C4—81no—
756C4—862no—
757C4—862no—
758C4—862no—
759C4—1722no—
760C4—1721no—
761C4—1722no—
762C4—1722no—
763C4—1722no—
764C4C2×(C22⋊D43)⋊C411yescharacteristic
765C4C2×(C22⋊D43)⋊C411yescharacteristic
766C4#1458340511yescharacteristic
767C4#1458340511yescharacteristic
768C2—42no—
769C2—44no—
770C2#1913709411yescharacteristic
771C2#1914339111yescharacteristic
772C2#1914341911yescharacteristic
773C2#1914383311yescharacteristic
774C2#1914385211yescharacteristic
775C2#1914469711yescharacteristic
776C2#1914475011yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1788C2
socleC23×C43C22×D4
prime radicalC22×#41×C43C22
cosocleC22×C4×C43C24
hypercenter#1788D43
hypocenterC43#21457
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1788

Complements

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

NH ≅ G/Ntype
3. C2×#14583003C2semidirect
4. C2×#14582996C2semidirect
5. #19137123C2semidirect
6. #19134934C2semidirect
7. #19134927C2semidirect
8. #19134905C2semidirect
9. #19134854C2semidirect
10. #19134847C2semidirect
11. #19134792C2semidirect
12. #19134427C2semidirect
13. #19134422C2semidirect
14. #19134359C2semidirect
32. #14583061C4semidirect
71. C2×#10621885C2×C4semidirect
74. C2×#10621883C2×C4semidirect
78. #13063304C2×C4semidirect
122. #13063249C2×C4semidirect
123. #13063246C2×C4semidirect
124. C22⋊(C43⋊C8)C2×C4semidirect
452. C43#21457semidirect

Maximal subgroups

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

subgroupindex
C2×#41×Dic432
C2×#145830612
C2×#145830032
C2×#145829962
#191371232
#191349342
#191349272
#191349052
#191348542
#191348472
#191347922
#191344272
#191344222
#191343592
C43×#17882
#2145743