Finite Group Databasebeta

← #25112950

Subgroups — #25112950

Order 11008.

1390 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583554C211yesmaximal, characteristic
2C2×#14582972C211yesmaximal, characteristic, complemented
3#19137527C211yesmaximal, characteristic, complemented
4#19135568C211yesmaximal, characteristic, complemented
5#19135543C211yesmaximal, characteristic, complemented
6#19135030C211yesmaximal, characteristic, complemented
7#19135020C211yesmaximal, characteristic, complemented
8#19134914C211yesmaximal, characteristic, complemented
9#19134909C211yesmaximal, characteristic, complemented
10#19134684C211yesmaximal, characteristic, complemented
11#19134680C211yesmaximal, characteristic, complemented
12#19134605C211yesmaximal, characteristic, complemented
13#19134313C211yesmaximal, characteristic, complemented
14#340×D43C211yesmaximal, characteristic, complemented
15C43×#1762C211yesmaximal, characteristic, complemented
16C22×#10621898—21no—
17C22×#10621872C2211yescharacteristic
18C22×C8×D43C2211yescharacteristic
19#14583554—24no—
20#14583554C418yescomplemented
21C2×#13063325C2211yescharacteristic
22C2×#13063307—21no—
23C2×#13063307—21no—
24C2×#13063304—21no—
25C2×#13063296C2211yescharacteristic
26C2×#13063296C2211yescharacteristic
27C2×C4×D172C2211yescharacteristic
28C2×#13063283C2211yescharacteristic
29C2×C4⋊C4×D43C2211yescharacteristic
30C2×C4⋊C4×D43C2211yescharacteristic
31C2×C4⋊C4×D43C2211yescharacteristic
32#14582972—24no—
33C2×C4⋊(C43⋊C8)C2211yescharacteristic
34C2×#13063246C2211yescharacteristic
35C2×#13063246C2211yescharacteristic
36C2×(C2×D43)⋊C8C2211yescharacteristic
37C2×(C2×D43)⋊C8C2211yescharacteristic
38#14582790—21no—
39#14582784—21no—
40#14582777—21no—
41#14582765C2211yescharacteristic
42#14582756C2211yescharacteristic
43#14582756C2211yescharacteristic
44C4×(C2×D43)⋊C4—21no—
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582661C2211yescharacteristic
55C2×C4×D4×C43C2211yescharacteristic
56C2×#102×C43C2211yescharacteristic
57C2×#102×C43C2211yescharacteristic
58C2×#97×C43C2211yescharacteristic
59C4×C4⋊C4×C43C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C43×#340C2211yescharacteristic
62C2×#10621898—28no—
63C2×#10621898—44no—
64C2×#10621898—44no—
65C22×Dic86—21no—
66C22×D172D411yescharacteristic
67C22×C22⋊D43—21no—
68C22×C22⋊D43—21no—
69C22×C4×D43—21no—
70C22×C4×D43—21no—
71C22×C4×D43—21no—
72C22×C4×D43C2311yescharacteristic
73C22×C4×D43C2311yescharacteristic
74C2×#10621872—22no—
75C2×#10621872—22no—
76C2×#10621872—41no—
77C22×C43⋊C8C2311yescharacteristic
78C22×C43⋊C8C2311yescharacteristic
79C2×C8×D43—22no—
80C2×C8×D43—22no—
81C2×C8×D43—41no—
82#13063325—22no—
83#13063325C2×C414yescomplemented
84#13063307—28no—
85#13063307—28no—
86#13063304—28no—
87#13063296—22no—
88#13063296—22no—
89#13063296C2×C414yes—
90#13063296C2×C414yescomplemented
91C4×D172C2×C414yes—
92C4×D172D414yes—
93#13063283—22no—
94#13063283—41no—
95C2×C4⋊Dic43—21no—
96C2×C4⋊Dic43D411yescharacteristic
97C2×C4⋊Dic43C2311yescharacteristic
98C2×C4⋊Dic43C2311yescharacteristic
99C2×C4⋊Dic43C2311yescharacteristic
100C2×C4⋊Dic43C2311yescharacteristic
101C2×Dic43⋊C4—21no—
102C2×Dic43⋊C4—21no—
103C2×Dic43⋊C4—21no—
104C4⋊C4×D43—22no—
105C4⋊C4×D43—22no—
106C4⋊C4×D43—22no—
107C4⋊C4×D43—41no—
108C4⋊C4×D43C2×C414yes—
109C4⋊C4×D43C2×C414yescomplemented
110C2×C22⋊Dic43—21no—
111C2×C22⋊Dic43—21no—
112C2×(C2×D43)⋊C4—21no—
113C2×(C2×D43)⋊C4—21no—
114C2×(C2×D43)⋊C4—21no—
115C2×(C2×D43)⋊C4D411yescharacteristic
116C2×(C2×D43)⋊C4D411yescharacteristic
117C2×C4×Dic43—21no—
118C4⋊(C43⋊C8)—22no—
119#13063246—41no—
120#13063246—41no—
121(C2×D43)⋊C8—22no—
122(C2×D43)⋊C8—22no—
123C43⋊#95—21no—
124C43⋊#95—21no—
125C43⋊#95—21no—
126C43⋊#95—21no—
127C22×D4×C43C2311yescharacteristic
128C23×C4×C43—21no—
129C22×C8×C43C2311yescharacteristic
130C22×C8×C43C2311yescharacteristic
131C4×D4×C43—22no—
132C4×D4×C43C2×C414yescomplemented
133C2×C4⋊C4×C43C2311yescharacteristic
134C2×C4⋊C4×C43C2311yescharacteristic
135C2×C4⋊C4×C43C2311yescharacteristic
136C2×C22⋊C4×C43—21no—
137C2×C42×C43—21no—
138C2×C42×C43C2311yescharacteristic
139#102×C43—22no—
140#102×C43—22no—
141#97×C43—22no—
142#95×C43—21no—
143C24×C43—21no—
144C23×D43C2×D411yescharacteristic
145C23×D43C2×D411yescharacteristic
146C2×D4×C43—21no—
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43C22×C412yes—
152C22×C4×C43—24no—
153C22×C4×C43—21no—
154C22×C4×C43—21no—
155C22×C4×C43—21no—
156C22×C4×C43—42no—
157C22×C4×C43—42no—
158C22×C4×C43C2×D411yescharacteristic
159C22×C4×C43C2×D411yescharacteristic
160C22×C4×C43C2411yescharacteristic
161C2×C22⋊D43—24no—
162C2×C22⋊D43—24no—
163C2×C22⋊D43—42no—
164C2×C22⋊D43—42no—
165C2×C22⋊D43—42no—
166C2×C22⋊D43—42no—
167C22×Dic43—21no—
168C22×Dic43—21no—
169C22×Dic43—21no—
170C22×Dic43—21no—
171C22×Dic43C2×D411yescharacteristic
172C22×Dic43C2×D411yescharacteristic
173#10621898—432no—
174C2×D172—22no—
175C2×D172—22no—
176C2×D172C22⋊C414yes—
177C2×C4×D43—21no—
178C2×C4×D43—21no—
179C2×C4×D43—21no—
180C2×C4×D43—21no—
181C2×C4×D43—21no—
182C2×C4×D43—21no—
183C2×C4×D43—21no—
184C2×C4×D43—21no—
185C2×C4×D43—24no—
186C2×C4×D43—24no—
187C2×C4×D43—42no—
188C2×C4×D43—42no—
189C2×C4×D43—42no—
190C2×C4×D43—42no—
191C2×C4×D43—42no—
192C2×C4×D43—42no—
193C2×C4×D43—81no—
194C2×C4×D43C22×C412yes—
195C2×C4×D43C22×C412yes—
196C2×C4×D43C2×D412yes—
197C2×C4×D43C2×D412yes—
198C2×Dic86—24no—
199C2×Dic86—42no—
200C2×Dic86—42no—
201C2×C8×C43—21no—
202C2×C8×C43—21no—
203C2×C8×C43—21no—
204C2×C8×C43—21no—
205C2×C8×C43—21no—
206C2×C8×C43#4112yescomplemented
207C4⋊C4×C43—21no—
208C4⋊C4×C43—21no—
209C4⋊C4×C43—21no—
210C4⋊C4×C43—21no—
211C4⋊C4×C43C22×C412yes—
212C4⋊C4×C43#4112yescomplemented
213C22⋊C4×C43—24no—
214C42×C43—81no—
215C42×C43C22×C412yes—
216C42×C43C2×D412yes—
217C22⋊Dic43—24no—
218C22⋊Dic43—24no—
219(C2×D43)⋊C4—42no—
220(C2×D43)⋊C4—42no—
221(C2×D43)⋊C4—81no—
222(C2×D43)⋊C4C22⋊C414yes—
223(C2×D43)⋊C4C22⋊C414yes—
224C4⋊Dic43—24no—
225C4⋊Dic43—21no—
226C4⋊Dic43—21no—
227C4⋊Dic43—21no—
228C4⋊Dic43—21no—
229C4⋊Dic43—21no—
230C4⋊Dic43—21no—
231C4⋊Dic43C22⋊C414yes—
232C4⋊Dic43C22×C412yes—
233C4⋊Dic43C22×C412yes—
234Dic43⋊C4—24no—
235Dic43⋊C4—24no—
236Dic43⋊C4—42no—
237C4×Dic43—42no—
238C2×C43⋊C8—21no—
239C2×C43⋊C8—21no—
240C2×C43⋊C8—21no—
241C2×C43⋊C8—21no—
242C2×C43⋊C8—21no—
243C2×C43⋊C8—21no—
244#10621872—44no—
245C8×D43—44no—
246C23×C43—22no—
247C23×C43—41no—
248C23×C43—41no—
249C23×C43—41no—
250C23×C43—41no—
251C23×C43—41no—
252C23×C43—41no—
253C23×C43C22×D411yescharacteristic
254C22×D43—21no—
255C22×D43—21no—
256C22×D43—21no—
257C22×D43—21no—
258C22×D43—21no—
259C22×D43—21no—
260C22×D43—21no—
261C22×D43—21no—
262C22×D43—21no—
263C22×D43—21no—
264C22×D43C2×C22⋊C412yes—
265C22×D43C2×C22⋊C412yes—
266C22×D43AGL(1,ℤ/8)12yes—
267C22×D43AGL(1,ℤ/8)12yes—
268D4×C43—22no—
269D4×C43—22no—
270D4×C43—41no—
271D4×C43—41no—
272C2×C4×C43—21no—
273C2×C4×C43—21no—
274C2×C4×C43—21no—
275C2×C4×C43—21no—
276C2×C4×C43—22no—
277C2×C4×C43—22no—
278C2×C4×C43—48no—
279C2×C4×C43—41no—
280C2×C4×C43—41no—
281C2×C4×C43—41no—
282C2×C4×C43—41no—
283C2×C4×C43—41no—
284C2×C4×C43—41no—
285C2×C4×C43—41no—
286C2×C4×C43C2×C22⋊C412yes—
287C2×C4×C43C2×C22⋊C412yes—
288C2×C4×C43C23×C411yescharacteristic
289C2×C4×C43C22×D411yescharacteristic
290C2×C4×C43C2×#4111yescharacteristic
291C2×C4×C43C2×#4111yescharacteristic
292C2×C4×C43H(5,𝔽2)11yescharacteristic
293C2×C4×C432−1+411yescharacteristic
294C22⋊D43—48no—
295C22⋊D43—48no—
296C2×Dic43—21no—
297C2×Dic43—21no—
298C2×Dic43—21no—
299C2×Dic43—21no—
300C2×Dic43—22no—
301C2×Dic43—22no—
302C2×Dic43—41no—
303C2×Dic43—41no—
304C2×Dic43—41no—
305C2×Dic43—41no—
306C2×Dic43—41no—
307C2×Dic43—41no—
308C2×Dic43—41no—
309C2×Dic43—41no—
310C2×Dic43—41no—
311C2×Dic43—41no—
312C2×Dic43C2×C22⋊C412yes—
313C2×Dic43C2×C22⋊C412yes—
314D172—28no—
315C4×D43—22no—
316C4×D43—22no—
317C4×D43—22no—
318C4×D43—22no—
319C4×D43—22no—
320C4×D43—22no—
321C4×D43—22no—
322C4×D43—22no—
323C4×D43—48no—
324C4×D43—48no—
325C4×D43—84no—
326Dic86—48no—
327C8×C43—22no—
328C8×C43—41no—
329C43⋊C8—41no—
330C43⋊C8—41no—
331#22495—431nomaximal, Sylow
332C22×C43—42no—
333C22×C43—42no—
334C22×C43—42no—
335C22×C43—81no—
336C22×C43—81no—
337C22×C43—81no—
338C22×C43—81no—
339C22×C43C22×C22⋊C411yescharacteristic
340C22×C43#54611yescharacteristic
341C22×C43#54711yescharacteristic
342C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
343C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
344C22×C43#57711yescharacteristic
345C22×C43#57811yescharacteristic
346C2×D43—22no—
347C2×D43—22no—
348C2×D43—22no—
349C2×D43—22no—
350C2×D43—22no—
351C2×D43—22no—
352C2×D43—22no—
353C2×D43—22no—
354C2×D43—22no—
355C2×D43—41no—
356C2×D43—41no—
357C2×D43—41no—
358C2×D43—41no—
359C2×D43#41814yes—
360C4×C43—22no—
361C4×C43—22no—
362C4×C43—42no—
363C4×C43—42no—
364C4×C43—81no—
365C4×C43C4×#4111yescharacteristic
366C4×C43#52011yescharacteristic
367C4×C43#54611yescharacteristic
368C4×C43#54711yescharacteristic
369Dic43—22no—
370Dic43—22no—
371Dic43—42no—
372Dic43—42no—
373Dic43—81no—
374Dic43—81no—
375C2×#547—431no—
376C2×#435—431no—
377#2352—431no—
378#1993—431no—
379#1987—431no—
380#1895—431no—
381#1893—431no—
382#1875—431no—
383#1874—431no—
384#1824—431no—
385#1823—431no—
386#1804—431no—
387#1762D4311yescharacteristic, complemented
388#1736—431no—
389C2×#340—431no—
390C2×C43—82no—
391C2×C43#233911yescharacteristic
392C2×C43C2×#41811yescharacteristic
393C2×C43#289811yescharacteristic
394C2×C43#330611yescharacteristic
395C2×C43#330811yescharacteristic
396C2×C43#334311yescharacteristic
397C2×C43#334511yescharacteristic
398D43—24no—
399D43—42no—
400C22×#41—861no—
401C22×M16—431no—
402C23×C8—431no—
403#547—438no—
404#547—864no—
405C2×C4⋊Q8—431no—
406C2×#123—861no—
407C2×#123—861no—
408C2×C22⋊Q8—861no—
409C2×#121—431no—
410C2×#121—431no—
411C2×C4×D4—431no—
412C2×C4×D4C2×D4311yescharacteristic
413C2×#117—431no—
414C22×C4⋊C4—431no—
415C22×C4⋊C4—431no—
416C22×C4⋊C4—431no—
417#435—864no—
418C2×C4⋊C8—431no—
419C2×#102—431no—
420C2×#102—431no—
421C2×#102C2×D4311yescharacteristic
422C2×#102C2×D4311yescharacteristic
423C2×C22⋊C8—431no—
424C2×C22⋊C8—431no—
425C2×#97C2×D4311yescharacteristic
426#388—861no—
427#387—861no—
428#386—861no—
429#382—431no—
430#380—431no—
431#380—431no—
432C4×C4⋊C4C2×D4311yescharacteristic
433C4×C22⋊C4—861no—
434#340—431no—
435#340—431no—
436#340—431no—
437#340—431no—
438#340—431no—
439#340—431no—
440#340—431no—
441#340—431no—
442#340—431no—
443#340—431no—
444#340C2×D4311yescharacteristic
445#340C2×D4311yescharacteristic
446C43#2249511yescharacteristic, complemented, Sylow
447C2×#41—868no—
448C2×#41—1724no—
449C2×#41—1724no—
450C22×Q8—861no—
451C22×D4—431no—
452C22×D4—861no—
453C22×D4—861no—
454C22×D4C22×D4311yescharacteristic
455C23×C4—21no—
456C23×C4—431no—
457C23×C4—431no—
458C23×C4—861no—
459C23×C4—861no—
460C23×C4—861no—
461C2×M16—862no—
462C2×M16—862no—
463C2×M16—1721no—
464C22×C8—431no—
465C22×C8—431no—
466C22×C8—862no—
467C22×C8—862no—
468C22×C8—1721no—
469C22×C8C22×D4311yescharacteristic
470C22×C8C22×D4311yescharacteristic
471C4⋊Q8—434no—
472C4⋊Q8—862no—
473#123—868no—
474#123—868no—
475C22⋊Q8—868no—
476#121—434no—
477#121—434no—
478#121—862no—
479#121—862no—
480C4×D4—22no—
481C4×D4—434no—
482C4×D4—434no—
483C4×D4C4×D4314yescomplemented
484#117—862no—
485#117—1721no—
486C2×C4⋊C4—431no—
487C2×C4⋊C4—431no—
488C2×C4⋊C4—431no—
489C2×C4⋊C4—434no—
490C2×C4⋊C4—434no—
491C2×C4⋊C4—431no—
492C2×C4⋊C4—431no—
493C2×C4⋊C4—862no—
494C2×C4⋊C4—862no—
495C2×C4⋊C4—861no—
496C2×C4⋊C4—861no—
497C2×C4⋊C4—861no—
498C2×C4⋊C4—862no—
499C2×C4⋊C4—861no—
500C2×C4⋊C4—1721no—
501C2×C4⋊C4C22×D4311yescharacteristic
502C2×C4⋊C4C22×D4311yescharacteristic
503C2×C4⋊C4C22×D4311yescharacteristic
504C2×C22⋊C4—21no—
505C2×C22⋊C4—431no—
506C2×C22⋊C4—431no—
507C2×C22⋊C4—861no—
508C2×C22⋊C4—861no—
509C2×C22⋊C4—861no—
510C2×C22⋊C4—861no—
511C2×C22⋊C4—861no—
512C2×C42—21no—
513C2×C42—861no—
514C2×C42C22×D4311yescharacteristic
515C4⋊C8—862no—
516#102—22no—
517#102—22no—
518#102—1721no—
519#102—1721no—
520C22⋊C8—862no—
521C22⋊C8—862no—
522#97—22no—
523#95—21no—
524#95—861no—
525#95—861no—
526#95—861no—
527#95—861no—
528C24—21no—
529C24—431no—
530C24—431no—
531#41—17232no—
532C2×Q8—864no—
533C2×Q8—1722no—
534C2×Q8—1722no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—434no—
541C2×D4—862no—
542C2×D4—862no—
543C2×D4—864no—
544C2×D4—864no—
545C2×D4—1722no—
546C2×D4—1722no—
547C2×D4—1722no—
548C2×D4—1722no—
549C2×D4C2×C4×D4312yes—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—24no—
553C22×C4—21no—
554C22×C4—42no—
555C22×C4—42no—
556C22×C4—431no—
557C22×C4—431no—
558C22×C4—432no—
559C22×C4—432no—
560C22×C4—432no—
561C22×C4—432no—
562C22×C4—864no—
563C22×C4—864no—
564C22×C4—861no—
565C22×C4—861no—
566C22×C4—861no—
567C22×C4—861no—
568C22×C4—861no—
569C22×C4—861no—
570C22×C4—861no—
571C22×C4—861no—
572C22×C4—861no—
573C22×C4—861no—
574C22×C4—861no—
575C22×C4—861no—
576C22×C4—3441no—
577C22×C4—1722no—
578C22×C4—1722no—
579C22×C4—1722no—
580C22×C4—1722no—
581C22×C4—1722no—
582C22×C4—1722no—
583C22×C4D4×D4311yescharacteristic
584C22×C4D4×D4311yescharacteristic
585C22×C4C23×D4311yescharacteristic
586M16—1724no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—861no—
593C2×C8—861no—
594C2×C8—861no—
595C2×C8—861no—
596C2×C8—861no—
597C2×C8—861no—
598C2×C8—1724no—
599C2×C8#1062189812yescomplemented
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—434no—
605C4⋊C4—432no—
606C4⋊C4—432no—
607C4⋊C4—864no—
608C4⋊C4—864no—
609C4⋊C4—864no—
610C4⋊C4—861no—
611C4⋊C4—861no—
612C4⋊C4—861no—
613C4⋊C4—861no—
614C4⋊C4—861no—
615C4⋊C4—861no—
616C4⋊C4—1722no—
617C4⋊C4C2×C4×D4312yes—
618C4⋊C4#1062189812yescomplemented
619C22⋊C4—24no—
620C22⋊C4—434no—
621C22⋊C4—434no—
622C22⋊C4—864no—
623C22⋊C4—864no—
624C22⋊C4—3441no—
625C22⋊C4—1722no—
626C22⋊C4—1722no—
627C42—81no—
628C42—1722no—
629C42C2×C4×D4312yes—
630C42D4×D4312yes—
631C23—22no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—432no—
639C23—432no—
640C23—432no—
641C23—432no—
642C23—861no—
643C23—861no—
644C23—861no—
645C23—861no—
646C23—861no—
647C23—861no—
648C23—861no—
649C23—861no—
650C23—861no—
651C23—861no—
652C23C2×D4×D4311yescharacteristic
653Q8—1728no—
654D4—22no—
655D4—22no—
656D4—41no—
657D4—41no—
658D4—868no—
659D4—1728no—
660D4—1728no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—48no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—432no—
676C2×C4—432no—
677C2×C4—861no—
678C2×C4—861no—
679C2×C4—861no—
680C2×C4—861no—
681C2×C4—862no—
682C2×C4—862no—
683C2×C4—862no—
684C2×C4—862no—
685C2×C4—862no—
686C2×C4—862no—
687C2×C4—862no—
688C2×C4—862no—
689C2×C4—862no—
690C2×C4—862no—
691C2×C4—3444no—
692C2×C4—1728no—
693C2×C4—1728no—
694C2×C4—1721no—
695C2×C4—1721no—
696C2×C4—1721no—
697C2×C4—1721no—
698C2×C4—1721no—
699C2×C4—1721no—
700C2×C4—1721no—
701C2×C4—1721no—
702C2×C4—1721no—
703C2×C4—1721no—
704C2×C4C22⋊C4×D4312yes—
705C2×C4C22⋊C4×D4312yes—
706C2×C4C22×C4×D4311yescharacteristic
707C2×C4C2×D4×D4311yescharacteristic
708C2×C4C2×#1062189811yescharacteristic
709C2×C4C2×#1062189811yescharacteristic
710C2×C4#1306337111yescharacteristic
711C2×C4#1306337211yescharacteristic
712C8—22no—
713C8—41no—
714C8—1721no—
715C8—1721no—
716C22—42no—
717C22—42no—
718C22—42no—
719C22—81no—
720C22—81no—
721C22—81no—
722C22—81no—
723C22—434no—
724C22—862no—
725C22—862no—
726C22—862no—
727C22—862no—
728C22—862no—
729C22—862no—
730C22—862no—
731C22—862no—
732C22—862no—
733C22—1721no—
734C22—1721no—
735C22—1721no—
736C22—1721no—
737C22C2×C22⋊C4×D4311yescharacteristic
738C22#1458354511yescharacteristic
739C22#1458355411yescharacteristic
740C22AGL(1,ℤ/8)×D4311yescharacteristic
741C22AGL(1,ℤ/8)×D4311yescharacteristic
742C22#1458370911yescharacteristic
743C22#1458371511yescharacteristic
744C4—22no—
745C4—22no—
746C4—42no—
747C4—42no—
748C4—81no—
749C4—862no—
750C4—862no—
751C4—3441no—
752C4—3441no—
753C4—1722no—
754C4—1722no—
755C4C4×#1062189811yescharacteristic
756C4#1458337911yescharacteristic
757C4#1458354511yescharacteristic
758C4#1458355411yescharacteristic
759C2—82no—
760C2—864no—
761C2—1722no—
762C2#1913742611yescharacteristic
763C2#418×D4311yescharacteristic
764C2#1914312611yescharacteristic
765C2#1914656111yescharacteristic
766C2#1914659111yescharacteristic
767C2#1914704011yescharacteristic
768C2#1914707011yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1762C2
socleC23×C43C22×D4
prime radicalC2×#14583554C2
cosocleC22×C4×C43C24
hypercenter#1762D43
hypocenterC43#22495
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1762

Complements

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

NH ≅ G/Ntype
2. C2×#14582972C2semidirect
3. #19137527C2semidirect
4. #19135568C2semidirect
5. #19135543C2semidirect
6. #19135030C2semidirect
7. #19135020C2semidirect
8. #19134914C2semidirect
9. #19134909C2semidirect
10. #19134684C2semidirect
11. #19134680C2semidirect
12. #19134605C2semidirect
13. #19134313C2semidirect
14. #340×D43C2semidirect
15. C43×#1762C2semidirect
20. #14583554C4semidirect
83. #13063325C2×C4semidirect
90. #13063296C2×C4semidirect
109. C4⋊C4×D43C2×C4semidirect
132. C4×D4×C43C2×C4semidirect
206. C2×C8×C43#41semidirect
212. C4⋊C4×C43#41semidirect
387. #1762D43semidirect
446. C43#22495semidirect
483. C4×D4C4×D43semidirect
599. C2×C8#10621898semidirect
618. C4⋊C4#10621898semidirect

Maximal subgroups

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

subgroupindex
C2×#145835542
C2×#145829722
#191375272
#191355682
#191355432
#191350302
#191350202
#191349142
#191349092
#191346842
#191346802
#191346052
#191343132
#340×D432
C43×#17622
#2249543