Finite Group Databasebeta

← #25153651

Subgroups — #25153651

Order 11008.

1206 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×#14583176C211yesmaximal, characteristic, complemented
2C22×#13063245C211yesmaximal, characteristic
3C22⋊C4×D172C211yesmaximal, characteristic
4#19136124C211yesmaximal, characteristic, complemented
5#19135980C211yesmaximal, characteristic, complemented
6#19135980C211yesmaximal, characteristic, complemented
7#19135728C211yesmaximal, characteristic, complemented
8#19134841C211yesmaximal, characteristic, complemented
9#19134841C211yesmaximal, characteristic, complemented
10#19134783C211yesmaximal, characteristic, complemented
11#19134775C211yesmaximal, characteristic, complemented
12#19134622C211yesmaximal, characteristic, complemented
13#19134592C211yesmaximal, characteristic, complemented
14#19134525C211yesmaximal, characteristic
15C43×#2440C211yesmaximal, characteristic, complemented
16C23×D172C2211yescharacteristic
17C23×C43⋊C8C2211yescharacteristic
18C2×C4×D172C2211yescharacteristic
19C2×C4×D172C2211yescharacteristic
20C2×C22⋊C4×D43—21no—
21#14583176—24no—
22C2×#13063258C2211yescharacteristic, complemented
23C2×#13063258C2211yescharacteristic, complemented
24C2×#13063258C2211yescharacteristic, complemented
25C2×#13063258C2211yescharacteristic, complemented
26C2×C4⋊(C43⋊C8)C2211yescharacteristic, complemented
27C2×C4⋊(C43⋊C8)C2211yescharacteristic, complemented
28C2×#13063245—24no—
29C2×#13063245C2211yescharacteristic
30C2×#13063245C2211yescharacteristic
31C2×#13063245C2211yescharacteristic
32C2×#13063245C2211yescharacteristic
33C2×#13063245C2211yescharacteristic
34C2×#13063245C2211yescharacteristic
35C2×#13063245C2211yescharacteristic
36C2×#13063245C2211yescharacteristic
37C2×C22⋊(C43⋊C8)C2211yescharacteristic
38#14582801C2211yescharacteristic
39#14582801C2211yescharacteristic
40#14582777—21no—
41#14582777—21no—
42#14582759C2211yescharacteristic
43#14582754—21no—
44#14582661C2211yescharacteristic, complemented
45#14582661C2211yescharacteristic, complemented
46#14582661C2211yescharacteristic, complemented
47#14582661C2211yescharacteristic, complemented
48#14582654C2211yescharacteristic, complemented
49#14582654C2211yescharacteristic, complemented
50C2×C4⋊Q8×C43C2211yescharacteristic, complemented
51C2×C22⋊Q8×C43—21no—
52C22×C4⋊C4×C43C2211yescharacteristic
53C43×#398—21no—
54C43×#395—21no—
55C43×#389C2211yescharacteristic, complemented
56C43×#389C2211yescharacteristic, complemented
57C43×#385—21no—
58C43×#384C2211yescharacteristic, complemented
59C43×#380C2211yescharacteristic
60C4×C22⋊C4×C43C2211yescharacteristic
61C24×D43—21no—
62C22×D172—22no—
63C22×D172—22no—
64C22×D172—21no—
65C22×D172—22no—
66C22×D172—41no—
67C22×D172—41no—
68C22×D172Q814yescomplemented
69C22×D172C2311yescharacteristic
70C22×D172C2311yescharacteristic
71C22×C4×D43—21no—
72C22×C4×D43—21no—
73C22×C43⋊C8—22no—
74C22×C43⋊C8—22no—
75C22×C43⋊C8—41no—
76C22×C43⋊C8C2311yescharacteristic
77C22×C43⋊C8C2311yescharacteristic
78C22×C43⋊C8C2311yescharacteristic
79C22×C43⋊C8C2311yescharacteristic
80C4×D172—22no—
81C4×D172—22no—
82C4×D172—41no—
83C4×D172—41no—
84C2×C4⋊Dic43C2311yescharacteristic
85C2×C4⋊Dic43C2311yescharacteristic
86C2×C22⋊Dic43—21no—
87C2×(C2×D43)⋊C4—21no—
88C2×(C2×D43)⋊C4—21no—
89C2×(C2×D43)⋊C4—21no—
90C2×(C2×D43)⋊C4—21no—
91C2×(C2×D43)⋊C4—21no—
92C2×(C2×D43)⋊C4—21no—
93C22⋊C4×D43—44no—
94#13063258—22no—
95#13063258—22no—
96#13063258—41no—
97#13063258—41no—
98C4⋊(C43⋊C8)—22no—
99C4⋊(C43⋊C8)—41no—
100#13063245—22no—
101#13063245—22no—
102#13063245—22no—
103#13063245—22no—
104#13063245—22no—
105#13063245—41no—
106#13063245—41no—
107#13063245D414yes—
108C22⋊(C43⋊C8)—22no—
109C43⋊#95—21no—
110C22×Q8×C43—21no—
111C23×C4×C43—21no—
112C23×C4×C43C2311yescharacteristic
113C4⋊Q8×C43—22no—
114C4⋊Q8×C43—41no—
115C22⋊Q8×C43—44no—
116C2×C4⋊C4×C43—22no—
117C2×C4⋊C4×C43—21no—
118C2×C4⋊C4×C43—21no—
119C2×C4⋊C4×C43—21no—
120C2×C4⋊C4×C43—21no—
121C2×C4⋊C4×C43—21no—
122C2×C4⋊C4×C43—21no—
123C2×C4⋊C4×C43—41no—
124C2×C4⋊C4×C43C2311yescharacteristic
125C2×C4⋊C4×C43C2311yescharacteristic
126C2×C4⋊C4×C43C2311yescharacteristic
127C2×C4⋊C4×C43C2311yescharacteristic
128C2×C22⋊C4×C43—21no—
129C2×C22⋊C4×C43D411yescharacteristic
130C2×C22⋊C4×C43D411yescharacteristic
131C2×C42×C43C2311yescharacteristic
132C2×C42×C43C2311yescharacteristic
133#95×C43—21no—
134#95×C43—21no—
135#95×C43—21no—
136#95×C43D411yescharacteristic
137#95×C43D411yescharacteristic
138C24×C43C2×D411yescharacteristic
139C23×D43—21no—
140C23×D43—21no—
141C23×D43—24no—
142C23×D43—42no—
143C23×D43—42no—
144C23×D43—42no—
145C23×D43—42no—
146C23×D43—81no—
147C23×D43—81no—
148C2×Q8×C43—42no—
149C2×Q8×C43—42no—
150C2×Q8×C43—81no—
151C22×C4×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43—21no—
154C22×C4×C43—21no—
155C22×C4×C43—21no—
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43—21no—
159C22×C4×C43—42no—
160C22×C4×C43—42no—
161C22×C4×C43—81no—
162C22×C4×C43C2×D411yescharacteristic
163C22×C4×C43C2×D411yescharacteristic
164C22×C4×C43C2×D411yescharacteristic
165C22×C4×C43C2×D411yescharacteristic
166C22×C4×C43C2×D411yescharacteristic
167C22×C4×C43C2×Q812yes—
168C22×C4×C43#4112yes—
169C22×C4×C43C2411yescharacteristic
170C22×Dic43—21no—
171C22×Dic43—21no—
172C2×D172—21no—
173C2×D172—21no—
174C2×D172—21no—
175C2×D172—24no—
176C2×D172—21no—
177C2×D172—21no—
178C2×D172—21no—
179C2×D172—21no—
180C2×D172—21no—
181C2×D172—28no—
182C2×D172—42no—
183C2×D172—42no—
184C2×D172—44no—
185C2×D172—44no—
186C2×D172—44no—
187C2×D172C2×D412yes—
188C2×D172C2×Q812yes—
189C2×D172C2×Q812yes—
190C2×D172#4112yes—
191C2×C4×D43—42no—
192C2×C4×D43—42no—
193C2×C4×D43—42no—
194C2×C4×D43—42no—
195C2×C4×D43—81no—
196C2×C4×D43—81no—
197C4⋊C4×C43—21no—
198C4⋊C4×C43—21no—
199C4⋊C4×C43—21no—
200C4⋊C4×C43—21no—
201C4⋊C4×C43—21no—
202C4⋊C4×C43—21no—
203C4⋊C4×C43—21no—
204C4⋊C4×C43—42no—
205C4⋊C4×C43—42no—
206C4⋊C4×C43—42no—
207C4⋊C4×C43—42no—
208C4⋊C4×C43—42no—
209C4⋊C4×C43—81no—
210C4⋊C4×C43C2×D412yes—
211C22⋊C4×C43—22no—
212C22⋊C4×C43—42no—
213C22⋊C4×C43D814yes—
214C42×C43—21no—
215C42×C43—21no—
216C42×C43—21no—
217C42×C43—21no—
218C22⋊Dic43—42no—
219(C2×D43)⋊C4—42no—
220(C2×D43)⋊C4—42no—
221(C2×D43)⋊C4—42no—
222(C2×D43)⋊C4—42no—
223(C2×D43)⋊C4—81no—
224(C2×D43)⋊C4—81no—
225C4⋊Dic43—21no—
226C4⋊Dic43—21no—
227C4⋊Dic43—21no—
228C4⋊Dic43—21no—
229C2×C43⋊C8—21no—
230C2×C43⋊C8—21no—
231C2×C43⋊C8—21no—
232C2×C43⋊C8—21no—
233C2×C43⋊C8—21no—
234C2×C43⋊C8—21no—
235C2×C43⋊C8—21no—
236C2×C43⋊C8—21no—
237C2×C43⋊C8—21no—
238C2×C43⋊C8—21no—
239C2×C43⋊C8—21no—
240C2×C43⋊C8—44no—
241C2×C43⋊C8C2×D412yes—
242C23×C43—21no—
243C23×C43—21no—
244C23×C43—21no—
245C23×C43—21no—
246C23×C43C22⋊Q812yes—
247C23×C43C2×D812yes—
248C23×C43#13712yes—
249C23×C43C22×D411yescharacteristic
250C22×D43—22no—
251C22×D43—22no—
252C22×D43—22no—
253C22×D43—22no—
254C22×D43—48no—
255C22×D43—41no—
256C22×D43—41no—
257C22×D43—41no—
258C22×D43—41no—
259C22×D43—41no—
260C22×D43—41no—
261C22×D43—41no—
262C22×D43—41no—
263C22×D43—41no—
264C22×D43—41no—
265C22×D43—48no—
266C22×D43—84no—
267C22×D43—84no—
268C22×D43—84no—
269C22×D43—84no—
270C22×D43—84no—
271Q8×C43—84no—
272C2×C4×C43—21no—
273C2×C4×C43—21no—
274C2×C4×C43—21no—
275C2×C4×C43—21no—
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—21no—
283C2×C4×C43—22no—
284C2×C4×C43—21no—
285C2×C4×C43—21no—
286C2×C4×C43—21no—
287C2×C4×C43—21no—
288C2×C4×C43—21no—
289C2×C4×C43—41no—
290C2×C4×C43—41no—
291C2×C4×C43—41no—
292C2×C4×C43—41no—
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×C43—41no—
300C2×C4×C43—84no—
301C2×C4×C43C22⋊Q812yes—
302C2×C4×C43C2×D812yes—
303C2×C4×C43C2×D812yes—
304C2×C4×C43C22×D411yescharacteristic
305C2×C4×C43C22×Q811yescharacteristic
306C2×C4×C43C2×#4111yescharacteristic
307C2×C4×C43C2×#4111yescharacteristic
308C2×C4×C43H(5,𝔽2)11yescharacteristic
309C2×C4×C43H(5,𝔽2)11yescharacteristic
310C2×Dic43—41no—
311C2×Dic43—41no—
312C2×Dic43—41no—
313C2×Dic43—41no—
314C2×Dic43—41no—
315C2×Dic43—41no—
316D172—22no—
317D172—22no—
318D172—22no—
319D172—22no—
320D172—22no—
321D172—48no—
322D172—41no—
323D172—41no—
324D172C22⋊Q814yescomplemented
325C4×D43—84no—
326C4×D43—84no—
327C43⋊C8—22no—
328C43⋊C8—41no—
329C43⋊C8—41no—
330C43⋊C8—41no—
331#25950—431nomaximal, Sylow
332C22×C43—22no—
333C22×C43—22no—
334C22×C43—22no—
335C22×C43—22no—
336C22×C43—22no—
337C22×C43—22no—
338C22×C43#47414yescomplemented
339C22×C43C2×C22⋊Q811yescharacteristic
340C22×C43D4211yescharacteristic
341C22×C43#54611yescharacteristic
342C22×C43C22×D811yescharacteristic
343C22×C43C2×#13711yescharacteristic
344C22×C43#57611yescharacteristic
345C22×C43#57711yescharacteristic
346C2×D43—24no—
347C2×D43—42no—
348C2×D43—42no—
349C2×D43—42no—
350C2×D43—42no—
351C2×D43—42no—
352C2×D43—42no—
353C2×D43—42no—
354C2×D43—42no—
355C2×D43—42no—
356C2×D43—816no—
357C2×D43—81no—
358C2×D43—81no—
359C2×D43—81no—
360C2×D43—81no—
361C4×C43—22no—
362C4×C43—22no—
363C4×C43—22no—
364C4×C43—41no—
365C4×C43—42no—
366C4×C43—41no—
367C4×C43—81no—
368C4×C43—81no—
369C4×C43—81no—
370C4×C43C2×C22⋊Q811yescharacteristic
371C4×C43#54311yescharacteristic
372C4×C43#54611yescharacteristic
373C4×C43#55111yescharacteristic
374Dic43—81no—
375Dic43—81no—
376C2×#474—431no—
377C22×#102—431no—
378#2440D4311yescharacteristic, complemented
379D4×C22⋊C4—431no—
380#2093—431no—
381#2067—431no—
382#2067—431no—
383#2023—431no—
384#1862—431no—
385#1862—431no—
386#1852—431no—
387#1850—431no—
388#1808—431no—
389#1802—431no—
390#1786—431no—
391C2×C43—24no—
392C2×C43#243711yescharacteristic
393C2×C43C2×#47411yescharacteristic
394C2×C43#308111yescharacteristic
395C2×C43#326611yescharacteristic
396C2×C43D4×D811yescharacteristic
397C2×C43#329411yescharacteristic
398C2×C43#331411yescharacteristic
399D43—44no—
400D43—82no—
401C23×D4—431no—
402C23×C8—431no—
403C2×C4⋊Q8C2×D4311yescharacteristic, complemented
404C2×C22⋊Q8—21no—
405C2×C4×D4—431no—
406C2×C4×D4—431no—
407C22×C4⋊C4C2×D4311yescharacteristic
408C22×C22⋊C4—861no—
409#474—864no—
410C2×#107—431no—
411C2×#107—431no—
412C2×#107—431no—
413C2×#107—431no—
414C2×C4⋊C8—431no—
415C2×C4⋊C8—431no—
416C2×#102—431no—
417C2×#102—431no—
418C2×#102—431no—
419C2×#102—431no—
420C2×#102—431no—
421C2×#102—431no—
422C2×#102—431no—
423C2×#102—431no—
424C2×#102—864no—
425C2×C22⋊C8—431no—
426#398—21no—
427#395—21no—
428#390—431no—
429#390—431no—
430#389C2×D4311yescharacteristic, complemented
431#389C2×D4311yescharacteristic, complemented
432#386—861no—
433#386—861no—
434#385—21no—
435#384C2×D4311yescharacteristic, complemented
436#380—431no—
437#380C2×D4311yescharacteristic
438#379—861no—
439C4×C22⋊C4C2×D4311yescharacteristic
440#340—431no—
441#340—431no—
442#340—431no—
443#340—431no—
444#336—431no—
445#336—431no—
446C43#2595011yescharacteristic, complemented, Sylow
447C25—861no—
448C22×Q8—21no—
449C22×D4—434no—
450C22×D4—431no—
451C22×D4—431no—
452C22×D4—862no—
453C22×D4—862no—
454C22×D4—862no—
455C22×D4—861no—
456C22×D4—1721no—
457C22×D4—1721no—
458C23×C4—21no—
459C23×C4—861no—
460C23×C4—861no—
461C23×C4C22×D4311yescharacteristic
462C22×C8—431no—
463C22×C8—431no—
464C22×C8—431no—
465C22×C8—431no—
466C22×C8—862no—
467C22×C8—862no—
468C22×C8—1721no—
469C4⋊Q8—22no—
470C4⋊Q8—41no—
471C22⋊Q8—44no—
472C4×D4—862no—
473C4×D4—862no—
474C4×D4—1721no—
475C4×D4—1721no—
476C2×C4⋊C4—22no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—21no—
482C2×C4⋊C4—21no—
483C2×C4⋊C4—41no—
484C2×C4⋊C4—431no—
485C2×C4⋊C4—431no—
486C2×C4⋊C4C22×D4311yescharacteristic
487C2×C4⋊C4C22×D4311yescharacteristic
488C2×C4⋊C4C22×D4311yescharacteristic
489C2×C4⋊C4C22×D4311yescharacteristic
490C2×C22⋊C4—21no—
491C2×C22⋊C4—861no—
492C2×C22⋊C4—861no—
493C2×C22⋊C4—861no—
494C2×C22⋊C4—861no—
495C2×C22⋊C4—861no—
496C2×C22⋊C4—861no—
497C2×C22⋊C4—861no—
498C2×C22⋊C4—1724no—
499C2×C22⋊C4C22⋊D4311yescharacteristic
500C2×C22⋊C4C22⋊D4311yescharacteristic
501C2×C42C22×D4311yescharacteristic
502C2×C42C22×D4311yescharacteristic
503#107—862no—
504#107—862no—
505#107—1721no—
506#107—1721no—
507C4⋊C8—862no—
508C4⋊C8—1721no—
509#102—434no—
510#102—862no—
511#102—862no—
512#102—862no—
513#102—862no—
514#102—862no—
515#102—1721no—
516#102—1721no—
517C22⋊C8—862no—
518#95—21no—
519#95—21no—
520#95—21no—
521#95—861no—
522#95C22⋊D4311yescharacteristic
523#95C22⋊D4311yescharacteristic
524C24—861no—
525C24—864no—
526C24—861no—
527C24—3441no—
528C24—3441no—
529C24—1722no—
530C24—1722no—
531C24—1722no—
532C24—1722no—
533C24C2×C22⋊D4311yescharacteristic
534C2×Q8—42no—
535C2×Q8—42no—
536C2×Q8—81no—
537C2×D4—432no—
538C2×D4—432no—
539C2×D4—432no—
540C2×D4—432no—
541C2×D4—868no—
542C2×D4—864no—
543C2×D4—861no—
544C2×D4—861no—
545C2×D4—861no—
546C2×D4—861no—
547C2×D4—861no—
548C2×D4—861no—
549C2×D4—861no—
550C2×D4—861no—
551C2×D4—1724no—
552C2×D4—1724no—
553C2×D4—1724no—
554C2×D4—1722no—
555C2×D4—1722no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—42no—
565C22×C4—42no—
566C22×C4—81no—
567C22×C4—861no—
568C22×C4—861no—
569C22×C4—3441no—
570C22×C4—3441no—
571C22×C4—1722no—
572C22×C4—1722no—
573C22×C4—1722no—
574C22×C4—1722no—
575C22×C4Q8×D4312yes—
576C22×C4#1062190212yes—
577C22×C4C2×C22⋊D4311yescharacteristic
578C22×C4C2×C22⋊D4311yescharacteristic
579C22×C4C2×C22⋊D4311yescharacteristic
580C22×C4C2×C22⋊D4311yescharacteristic
581C22×C4C2×C22⋊D4311yescharacteristic
582C22×C4C23×D4311yescharacteristic
583C2×C8—432no—
584C2×C8—861no—
585C2×C8—861no—
586C2×C8—861no—
587C2×C8—861no—
588C2×C8—861no—
589C2×C8—861no—
590C2×C8—861no—
591C2×C8—861no—
592C2×C8—861no—
593C2×C8—861no—
594C2×C8—861no—
595C2×C8—1724no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—42no—
604C4⋊C4—42no—
605C4⋊C4—42no—
606C4⋊C4—42no—
607C4⋊C4—42no—
608C4⋊C4—81no—
609C4⋊C4—861no—
610C4⋊C4—861no—
611C4⋊C4—861no—
612C4⋊C4—861no—
613C4⋊C4D4×D4312yes—
614C22⋊C4—22no—
615C22⋊C4—42no—
616C22⋊C4—3441no—
617C22⋊C4—3441no—
618C22⋊C4—1722no—
619C22⋊C4—1722no—
620C22⋊C4—1722no—
621C22⋊C4—1722no—
622C22⋊C4—1722no—
623C22⋊C4#1062188214yes—
624C42—21no—
625C42—21no—
626C42—21no—
627C42—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—862no—
633C23—862no—
634C23—862no—
635C23—862no—
636C23—3444no—
637C23—3444no—
638C23—3444no—
639C23—3444no—
640C23—3444no—
641C23—1728no—
642C23—1721no—
643C23—1728no—
644C23—1721no—
645C23—1721no—
646C23—1721no—
647C23—1721no—
648C23—1721no—
649C23—1721no—
650C23—1721no—
651C23—1721no—
652C23—1721no—
653C23#1306330112yes—
654C23C2×#1062188212yes—
655C23#1306335612yes—
656C23C22×C22⋊D4311yescharacteristic
657Q8—84no—
658D4—434no—
659D4—862no—
660D4—862no—
661D4—862no—
662D4—862no—
663D4—862no—
664D4—1728no—
665D4—1721no—
666D4—1721no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—22no—
683C2×C4—21no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—84no—
696C2×C4—3444no—
697C2×C4—3444no—
698C2×C4—1721no—
699C2×C4—1721no—
700C2×C4—1721no—
701C2×C4—1721no—
702C2×C4—1721no—
703C2×C4—1721no—
704C2×C4#1306330112yes—
705C2×C4C2×#1062188212yes—
706C2×C4C2×#1062188212yes—
707C2×C4C2×D4×D4311yescharacteristic
708C2×C4C2×Q8×D4311yescharacteristic
709C2×C4#41×D4311yescharacteristic
710C2×C4C2×#1062190211yescharacteristic
711C2×C4#1306337011yescharacteristic
712C2×C4#1306337111yescharacteristic
713C8—862no—
714C8—1721no—
715C8—1721no—
716C8—1721no—
717C22—22no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—864no—
724C22—34416no—
725C22—3441no—
726C22—3441no—
727C22—3441no—
728C22—3441no—
729C22—1722no—
730C22—1722no—
731C22—1722no—
732C22—1722no—
733C22—1722no—
734C22—1722no—
735C22—1722no—
736C22—1722no—
737C22—1722no—
738C22#1458317614yescomplemented
739C22C2×#1306330111yescharacteristic
740C22D4×C22⋊D4311yescharacteristic
741C22#1458353711yescharacteristic
742C22C22×#1062188211yescharacteristic
743C22C2×#1306335611yescharacteristic
744C22#1458370211yescharacteristic
745C22#1458370711yescharacteristic
746C4—22no—
747C4—22no—
748C4—22no—
749C4—42no—
750C4—41no—
751C4—41no—
752C4—81no—
753C4—81no—
754C4—81no—
755C4—3441no—
756C4—3441no—
757C4C22⋊Q8×D4311yescharacteristic
758C4#1458352411yescharacteristic
759C4#1458354011yescharacteristic
760C4#1458357611yescharacteristic
761C2—24no—
762C2—3442no—
763C2—1724no—
764C2#1913825811yescharacteristic
765C2C2×#1458317611yescharacteristic
766C2#1914442011yescharacteristic
767C2#1914610611yescharacteristic
768C2D4×#1062188211yescharacteristic
769C2#1914640211yescharacteristic
770C2#1914667011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2440C2
socleC23×C43C22×D4
prime radicalC23×D172C22
hypercenter#2440D43
hypocenterC43#25950
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2440

Complements

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

NH ≅ G/Ntype
1. C2×#14583176C2semidirect
4. #19136124C2semidirect
5. #19135980C2semidirect
6. #19135980C2semidirect
7. #19135728C2semidirect
8. #19134841C2semidirect
9. #19134841C2semidirect
10. #19134783C2semidirect
11. #19134775C2semidirect
12. #19134622C2semidirect
13. #19134592C2semidirect
15. C43×#2440C2semidirect
22. C2×#13063258C22semidirect
23. C2×#13063258C22semidirect
24. C2×#13063258C22semidirect
25. C2×#13063258C22semidirect
26. C2×C4⋊(C43⋊C8)C22semidirect
27. C2×C4⋊(C43⋊C8)C22semidirect
44. #14582661C22semidirect
45. #14582661C22semidirect
46. #14582661C22semidirect
47. #14582661C22semidirect
48. #14582654C22semidirect
49. #14582654C22semidirect
50. C2×C4⋊Q8×C43C22semidirect
55. C43×#389C22semidirect
56. C43×#389C22semidirect
58. C43×#384C22semidirect
68. C22×D172Q8semidirect
324. D172C22⋊Q8semidirect
338. C22×C43#474semidirect
378. #2440D43semidirect
403. C2×C4⋊Q8C2×D43semidirect
430. #389C2×D43semidirect
431. #389C2×D43semidirect
435. #384C2×D43semidirect
446. C43#25950semidirect
738. C22#14583176semidirect

Maximal subgroups

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

subgroupindex
C2×#145831762
C22×#130632452
C22⋊C4×D1722
#191361242
#191359802
#191357282
#191348412
#191347832
#191347752
#191346222
#191345922
#191345252
C43×#24402
#2595043