Finite Group Databasebeta

← #25144012

Subgroups — #25144012

Order 11008.

1078 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583106C211yesmaximal, characteristic, complemented
2C2×#14583059C211yesmaximal, characteristic
3C2×#14583059C211yesmaximal, characteristic
4C2×C4×#10621885C211yesmaximal, characteristic, complemented
5#19137435C211yesmaximal, characteristic
6#19135980C211yesmaximal, characteristic, complemented
7#19135795C211yesmaximal, characteristic, complemented
8#19135788C211yesmaximal, characteristic, complemented
9#19135678C211yesmaximal, characteristic, complemented
10#19135452C211yesmaximal, characteristic, complemented
11#19135203C211yesmaximal, characteristic, complemented
12#19134950C211yesmaximal, characteristic, complemented
13#19134939C211yesmaximal, characteristic, complemented
14#19134862C211yesmaximal, characteristic, complemented
15C43×#2429C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C22×#10621885C2211yescharacteristic
18C22×#10621885C2211yescharacteristic
19C22×#10621884C2211yescharacteristic
20C22×#10621884C2211yescharacteristic
21C2×C4×Dic86C2211yescharacteristic
22C2×C4×Dic86C2211yescharacteristic
23#14583106—24no—
24#14583059—24no—
25#14583059—24no—
26C4×#10621885—24no—
27C2×#13063258C2211yescharacteristic
28C2×#13063256C2211yescharacteristic
29C2×C4⋊(C43⋊C8)C2211yescharacteristic
30C2×#13063249C2211yescharacteristic
31C2×#13063249C2211yescharacteristic
32C2×#13063249C2211yescharacteristic
33C2×#13063249C2211yescharacteristic
34C2×#13063248C2211yescharacteristic
35C2×#13063248C2211yescharacteristic
36C2×#13063245C2211yescharacteristic
37C2×#13063245C2211yescharacteristic
38C2×C22⋊(C43⋊C8)C2211yescharacteristic
39C2×C22⋊(C43⋊C8)C2211yescharacteristic
40C2×C4×C43⋊C8C2211yescharacteristic
41#14582801C2211yescharacteristic
42#14582801C2211yescharacteristic
43#14582799—21no—
44#14582799—21no—
45#14582759C2211yescharacteristic
46#14582758—21no—
47#14582746—21no—
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582654C2211yescharacteristic
51#14582654C2211yescharacteristic
52C2×C4⋊Q8×C43C2211yescharacteristic
53C2×C22⋊Q8×C43C2211yescharacteristic
54C2×C22⋊Q8×C43C2211yescharacteristic
55C2×C4×Q8×C43C2211yescharacteristic
56C43×#398—21no—
57C43×#396—21no—
58C43×#391C2211yescharacteristic
59C43×#389—21no—
60C43×#389C2211yescharacteristic
61C43×#388—21no—
62C4×C22⋊C4×C43C2211yescharacteristic
63C2×#10621898—22no—
64C2×#10621898—22no—
65C2×#10621898—22no—
66C2×#10621898—22no—
67C2×#10621898—41no—
68C2×#10621898—41no—
69C22×Dic86C2311yescharacteristic
70C22×D172C2311yescharacteristic
71C22×C22⋊D43—21no—
72C22×C4×D43—21no—
73C2×#10621885—22no—
74C2×#10621885—22no—
75C2×#10621885—22no—
76C2×#10621885—22no—
77C2×#10621885—22no—
78C2×#10621885D414yes—
79C2×#10621884—22no—
80C2×#10621884—22no—
81C2×#10621884—22no—
82C2×#10621884—22no—
83C2×#10621884—41no—
84C2×#10621884—41no—
85C22×C43⋊C8C2311yescharacteristic
86C22×C43⋊C8C2311yescharacteristic
87C22×C43⋊C8C2311yescharacteristic
88C22×C43⋊C8C2311yescharacteristic
89C4×Dic86—22no—
90C4×Dic86—22no—
91C4×Dic86—41no—
92C4×Dic86—41no—
93C2×C4⋊Dic43C2311yescharacteristic
94C2×C4⋊Dic43C2311yescharacteristic
95C2×Dic43⋊C4—21no—
96C2×Dic43⋊C4—21no—
97C2×C22⋊Dic43—21no—
98C2×(C2×D43)⋊C4—21no—
99C2×(C2×D43)⋊C4—21no—
100C2×(C2×D43)⋊C4—21no—
101C2×(C2×D43)⋊C4—21no—
102C2×C4×Dic43—21no—
103C2×C4×Dic43—21no—
104#13063258—22no—
105#13063256—41no—
106C4⋊(C43⋊C8)—22no—
107#13063249—22no—
108#13063249—22no—
109#13063249—22no—
110#13063249—41no—
111#13063248—22no—
112#13063248D414yes—
113#13063245—22no—
114#13063245—22no—
115C22⋊(C43⋊C8)—22no—
116C22⋊(C43⋊C8)—22no—
117C4×C43⋊C8—22no—
118C43⋊#95—21no—
119C22×Q8×C43C2311yescharacteristic
120C22×Q8×C43C2311yescharacteristic
121C23×C4×C43C2311yescharacteristic
122C4⋊Q8×C43—22no—
123C4⋊Q8×C43—41no—
124C22⋊Q8×C43—22no—
125C22⋊Q8×C43—22no—
126C22⋊Q8×C43—41no—
127C22⋊Q8×C43—41no—
128C4×Q8×C43—22no—
129C4×Q8×C43—41no—
130C2×C4⋊C4×C43—21no—
131C2×C4⋊C4×C43—21no—
132C2×C4⋊C4×C43—21no—
133C2×C4⋊C4×C43—21no—
134C2×C4⋊C4×C43—21no—
135C2×C4⋊C4×C43—21no—
136C2×C4⋊C4×C43C2311yescharacteristic
137C2×C4⋊C4×C43C2311yescharacteristic
138C2×C22⋊C4×C43—21no—
139C2×C22⋊C4×C43—21no—
140C2×C22⋊C4×C43D411yescharacteristic
141C2×C22⋊C4×C43D411yescharacteristic
142C2×C42×C43—21no—
143C2×C42×C43C2311yescharacteristic
144C2×C42×C43C2311yescharacteristic
145#95×C43—21no—
146#95×C43—21no—
147#95×C43—21no—
148#95×C43D411yescharacteristic
149#95×C43D411yescharacteristic
150C24×C43C2×D411yescharacteristic
151C23×D43—21no—
152C2×Q8×C43—21no—
153C2×Q8×C43—21no—
154C2×Q8×C43—21no—
155C2×Q8×C43—21no—
156C2×Q8×C43—21no—
157C2×Q8×C43—21no—
158C2×Q8×C43—21no—
159C2×Q8×C43—21no—
160C2×Q8×C43—21no—
161C2×Q8×C43—21no—
162C2×Q8×C43—21no—
163C2×Q8×C43C2×D412yes—
164C22×C4×C43—21no—
165C22×C4×C43—21no—
166C22×C4×C43—21no—
167C22×C4×C43—21no—
168C22×C4×C43—21no—
169C22×C4×C43—21no—
170C22×C4×C43—21no—
171C22×C4×C43—21no—
172C22×C4×C43—21no—
173C22×C4×C43—21no—
174C22×C4×C43C2×D411yescharacteristic
175C22×C4×C43C2×D411yescharacteristic
176C22×C4×C43C2×D411yescharacteristic
177C22×C4×C43C2×D411yescharacteristic
178C22×C4×C43C2×D411yescharacteristic
179C22×C4×C43C2411yescharacteristic
180C2×C22⋊D43—24no—
181C2×C22⋊D43—42no—
182C2×C22⋊D43—42no—
183C22×Dic43—21no—
184C22×Dic43—21no—
185C22×Dic43—21no—
186#10621898—44no—
187#10621898—44no—
188#10621898—44no—
189#10621898—44no—
190C2×D172—21no—
191C2×D172—21no—
192C2×D172—21no—
193C2×D172—21no—
194C2×D172—21no—
195C2×D172#4112yes—
196C2×C4×D43—24no—
197C2×C4×D43—42no—
198C2×C4×D43—42no—
199C2×Dic86—21no—
200C2×Dic86—21no—
201C2×Dic86—21no—
202C2×Dic86C2×D412yes—
203C2×Dic86C2×D412yes—
204C2×Dic86#4112yes—
205C4⋊C4×C43—21no—
206C4⋊C4×C43—21no—
207C4⋊C4×C43—21no—
208C4⋊C4×C43—42no—
209C4⋊C4×C43—42no—
210C4⋊C4×C43—42no—
211C4⋊C4×C43—42no—
212C4⋊C4×C43—42no—
213C4⋊C4×C43—42no—
214C4⋊C4×C43C2×D412yes—
215C22⋊C4×C43—22no—
216C22⋊C4×C43—22no—
217C22⋊C4×C43—42no—
218C22⋊C4×C43—42no—
219C42×C43—21no—
220C42×C43—21no—
221C42×C43—21no—
222C42×C43—21no—
223C42×C43—42no—
224C22⋊Dic43—81no—
225#10621885—28no—
226#10621885—44no—
227#10621884—44no—
228#10621884—44no—
229(C2×D43)⋊C4—42no—
230(C2×D43)⋊C4—42no—
231(C2×D43)⋊C4—81no—
232(C2×D43)⋊C4—81no—
233C4⋊Dic43—21no—
234C4⋊Dic43—21no—
235C4⋊Dic43—21no—
236C4⋊Dic43—21no—
237Dic43⋊C4—42no—
238Dic43⋊C4—42no—
239C4×Dic43—42no—
240C4×Dic43—42no—
241C2×C43⋊C8—21no—
242C2×C43⋊C8—21no—
243C2×C43⋊C8—21no—
244C2×C43⋊C8—21no—
245C2×C43⋊C8—21no—
246C2×C43⋊C8—21no—
247C2×C43⋊C8—21no—
248C2×C43⋊C8—21no—
249C2×C43⋊C8—21no—
250C2×C43⋊C8—21no—
251C2×C43⋊C8C2×D412yes—
252C2×C43⋊C8C2×D412yes—
253C23×C43—21no—
254C23×C43—21no—
255C23×C43—21no—
256C23×C43—21no—
257C23×C43—21no—
258C23×C43—21no—
259C23×C43—21no—
260C23×C43C22×D411yescharacteristic
261C22×D43—22no—
262C22×D43—41no—
263C22×D43—41no—
264C22×D43—41no—
265C22×D43—41no—
266C22×D43—41no—
267C22×D43—41no—
268Q8×C43—22no—
269Q8×C43—22no—
270Q8×C43—41no—
271Q8×C43—41no—
272Q8×C43—41no—
273Q8×C43—41no—
274Q8×C43—41no—
275Q8×C43—41no—
276C2×C4×C43—21no—
277C2×C4×C43—21no—
278C2×C4×C43—21no—
279C2×C4×C43—21no—
280C2×C4×C43—21no—
281C2×C4×C43—21no—
282C2×C4×C43—21no—
283C2×C4×C43—22no—
284C2×C4×C43—22no—
285C2×C4×C43—21no—
286C2×C4×C43—21no—
287C2×C4×C43—21no—
288C2×C4×C43—21no—
289C2×C4×C43—21no—
290C2×C4×C43—21no—
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—41no—
301C2×C4×C43—41no—
302C2×C4×C43—41no—
303C2×C4×C43—41no—
304C2×C4×C43—41no—
305C2×C4×C43#13512yes—
306C2×C4×C43#13712yes—
307C2×C4×C43C22×D411yescharacteristic
308C2×C4×C43C22×D411yescharacteristic
309C2×C4×C43C2×#4111yescharacteristic
310C2×C4×C43C2×#4111yescharacteristic
311C2×C4×C43H(5,𝔽2)11yescharacteristic
312C2×C4×C43H(5,𝔽2)11yescharacteristic
313C22⋊D43—48no—
314C2×Dic43—22no—
315C2×Dic43—22no—
316C2×Dic43—22no—
317C2×Dic43—41no—
318C2×Dic43—41no—
319C2×Dic43—41no—
320C2×Dic43—41no—
321C2×Dic43—41no—
322C2×Dic43—41no—
323D172—22no—
324D172—22no—
325D172—41no—
326D172—41no—
327C4×D43—48no—
328Dic86—22no—
329Dic86—22no—
330Dic86—22no—
331Dic86#12114yes—
332C43⋊C8—22no—
333C43⋊C8—22no—
334C43⋊C8—41no—
335C43⋊C8—41no—
336#25151—431nomaximal, Sylow
337C22×C43—41no—
338C22×C43—41no—
339C22×C43—41no—
340C22×C43—41no—
341C22×C43—41no—
342C22×C43—41no—
343C22×C43—41no—
344C22×C43#52511yescharacteristic
345C22×C43D4211yescharacteristic
346C22×C43D4211yescharacteristic
347C22×C43C2×#13511yescharacteristic
348C22×C43C2×#13711yescharacteristic
349C22×C43#57711yescharacteristic
350C22×C43#57811yescharacteristic
351C2×D43—42no—
352C2×D43—42no—
353C2×D43—42no—
354C2×D43—81no—
355C2×D43—81no—
356C2×D43—81no—
357C2×D43—81no—
358C4×C43—22no—
359C4×C43—22no—
360C4×C43—41no—
361C4×C43—42no—
362C4×C43—41no—
363C4×C43—41no—
364C4×C43—42no—
365C4×C43—81no—
366C4×C43—81no—
367C4×C43C2×#12111yescharacteristic
368C4×C43#53811yescharacteristic
369C4×C43#54611yescharacteristic
370C4×C43#54611yescharacteristic
371Dic43—24no—
372Dic43—81no—
373Dic43—81no—
374C2×#462—431no—
375C2×#452—431no—
376C2×#452—431no—
377C2×C4×Q16—431no—
378#2429D4311yescharacteristic, complemented
379#2341—431no—
380#2067—431no—
381#2036—431no—
382#2035—431no—
383#2013—431no—
384#1968—431no—
385#1923—431no—
386#1880—431no—
387#1878—431no—
388#1865—431no—
389C2×C43—81no—
390C2×C43#242411yescharacteristic
391C2×C43#310711yescharacteristic
392C2×C43#312011yescharacteristic
393C2×C43#327011yescharacteristic
394C2×C43#327811yescharacteristic
395C2×C43#328411yescharacteristic
396C2×C43#328511yescharacteristic
397D43—82no—
398C22×#41—431no—
399C22×Q16—431no—
400C22×Q16—431no—
401C22×SD16—431no—
402C22×SD16—431no—
403C2×C4⋊Q8C2×D4311yescharacteristic
404C2×C22⋊Q8C2×D4311yescharacteristic
405C2×C22⋊Q8C2×D4311yescharacteristic
406C2×C4×Q8—431no—
407C2×C4×Q8—431no—
408C2×C4×Q8C2×D4311yescharacteristic
409#462—864no—
410#452—864no—
411#452—864no—
412C4×Q16—864no—
413C2×#107—431no—
414C2×#106—431no—
415C2×C4⋊C8—431no—
416C2×#103—431no—
417C2×#103—431no—
418C2×#103—431no—
419C2×#103—431no—
420C2×#103—431no—
421C2×#103—431no—
422C2×#102—431no—
423C2×#102—431no—
424C2×C22⋊C8—431no—
425C2×C22⋊C8—431no—
426C2×C4×C8—431no—
427#398—21no—
428#396—21no—
429#391C2×D4311yescharacteristic
430#390—431no—
431#390—431no—
432#390—861no—
433#390—861no—
434#389—21no—
435#389C2×D4311yescharacteristic
436#388—21no—
437#380—431no—
438#380—861no—
439C4×C22⋊C4—861no—
440C4×C22⋊C4C2×D4311yescharacteristic
441#340—431no—
442#340—431no—
443#336—431no—
444#336—431no—
445C43#2515111yescharacteristic, complemented, Sylow
446C2×#41—862no—
447C2×#41—862no—
448C2×#41—862no—
449C2×#41—862no—
450C2×#41—1721no—
451C2×#41—1721no—
452C22×Q8—431no—
453C22×Q8C22×D4311yescharacteristic
454C22×Q8C22×D4311yescharacteristic
455C22×D4—431no—
456C22×D4—861no—
457C23×C4—861no—
458C23×C4C22×D4311yescharacteristic
459C2×Q16—434no—
460C2×Q16—862no—
461C2×Q16—862no—
462C2×Q16—862no—
463C2×Q16—862no—
464C2×Q16—862no—
465C2×SD16—862no—
466C2×SD16—862no—
467C2×SD16—862no—
468C2×SD16—862no—
469C2×SD16—1721no—
470C2×SD16—1721no—
471C22×C8—431no—
472C22×C8—431no—
473C22×C8—431no—
474C22×C8—431no—
475C4⋊Q8—22no—
476C4⋊Q8—41no—
477C22⋊Q8—22no—
478C22⋊Q8—22no—
479C22⋊Q8—41no—
480C22⋊Q8—41no—
481C4×Q8—22no—
482C4×Q8—41no—
483C4×Q8—862no—
484C4×Q8—862no—
485C4×Q8—1721no—
486C4×Q8—1721no—
487C2×C4⋊C4—21no—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—431no—
494C2×C4⋊C4—431no—
495C2×C4⋊C4—861no—
496C2×C4⋊C4—861no—
497C2×C4⋊C4C22×D4311yescharacteristic
498C2×C4⋊C4C22×D4311yescharacteristic
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—861no—
502C2×C22⋊C4—861no—
503C2×C22⋊C4—861no—
504C2×C22⋊C4—861no—
505C2×C22⋊C4—861no—
506C2×C22⋊C4C22⋊D4311yescharacteristic
507C2×C22⋊C4C22⋊D4311yescharacteristic
508C2×C42—21no—
509C2×C42—861no—
510C2×C42—861no—
511C2×C42C22×D4311yescharacteristic
512C2×C42C22×D4311yescharacteristic
513#107—862no—
514#106—1721no—
515C4⋊C8—862no—
516#103—434no—
517#103—862no—
518#103—862no—
519#103—862no—
520#103—862no—
521#103—1721no—
522#102—862no—
523#102—862no—
524C22⋊C8—862no—
525C22⋊C8—862no—
526C4×C8—862no—
527#95—21no—
528#95—21no—
529#95—21no—
530#95—861no—
531#95C22⋊D4311yescharacteristic
532#95C22⋊D4311yescharacteristic
533C24—861no—
534C24C2×C22⋊D4311yescharacteristic
535#41—1724no—
536#41—1724no—
537#41—1724no—
538#41—1724no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8—21no—
544C2×Q8—21no—
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×Q8D4×D4312yes—
557C2×D4—432no—
558C2×D4—864no—
559C2×D4—861no—
560C2×D4—861no—
561C2×D4—861no—
562C2×D4—861no—
563C2×D4—861no—
564C2×D4—1722no—
565C2×D4—1722no—
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—21no—
575C22×C4—21no—
576C22×C4—864no—
577C22×C4—861no—
578C22×C4—861no—
579C22×C4—861no—
580C22×C4—1722no—
581C22×C4—1722no—
582C22×C4C2×C22⋊D4311yescharacteristic
583C22×C4C2×C22⋊D4311yescharacteristic
584C22×C4C2×C22⋊D4311yescharacteristic
585C22×C4C2×C22⋊D4311yescharacteristic
586C22×C4C2×C22⋊D4311yescharacteristic
587C22×C4C23×D4311yescharacteristic
588Q16—868no—
589Q16—1724no—
590SD16—1724no—
591SD16—1724no—
592C2×C8—432no—
593C2×C8—432no—
594C2×C8—861no—
595C2×C8—861no—
596C2×C8—861no—
597C2×C8—861no—
598C2×C8—861no—
599C2×C8—861no—
600C2×C8—861no—
601C2×C8—861no—
602C2×C8—861no—
603C2×C8—861no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—42no—
608C4⋊C4—42no—
609C4⋊C4—42no—
610C4⋊C4—42no—
611C4⋊C4—42no—
612C4⋊C4—42no—
613C4⋊C4—861no—
614C4⋊C4—861no—
615C4⋊C4—861no—
616C4⋊C4—861no—
617C4⋊C4—1722no—
618C4⋊C4—1722no—
619C4⋊C4D4×D4312yes—
620C22⋊C4—22no—
621C22⋊C4—22no—
622C22⋊C4—42no—
623C22⋊C4—42no—
624C22⋊C4—3441no—
625C22⋊C4—3441no—
626C22⋊C4—3441no—
627C22⋊C4—1722no—
628C22⋊C4—1722no—
629C42—21no—
630C42—21no—
631C42—21no—
632C42—21no—
633C42—42no—
634C42—1722no—
635C42—1722no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—862no—
644C23—1721no—
645C23—1721no—
646C23—1721no—
647C23—1721no—
648C23—1721no—
649C23—1721no—
650C23C22×C22⋊D4311yescharacteristic
651Q8—22no—
652Q8—22no—
653Q8—41no—
654Q8—41no—
655Q8—41no—
656Q8—41no—
657Q8—41no—
658Q8—41no—
659Q8—434no—
660Q8—862no—
661Q8—862no—
662Q8—862no—
663D4—862no—
664D4—862no—
665D4—1728no—
666D4—1721no—
667D4—1721no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—41no—
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—41no—
696C2×C4—41no—
697C2×C4—862no—
698C2×C4—862no—
699C2×C4—862no—
700C2×C4—1728no—
701C2×C4—1721no—
702C2×C4—1721no—
703C2×C4—1721no—
704C2×C4—1721no—
705C2×C4—1721no—
706C2×C4—1721no—
707C2×C4#1306334512yes—
708C2×C4#1306335612yes—
709C2×C4C2×D4×D4311yescharacteristic
710C2×C4C2×D4×D4311yescharacteristic
711C2×C4#41×D4311yescharacteristic
712C2×C4#41×D4311yescharacteristic
713C2×C4#1306337011yescharacteristic
714C2×C4#1306337011yescharacteristic
715C8—862no—
716C8—862no—
717C8—1721no—
718C8—1721no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—3441no—
727C22—3441no—
728C22—3441no—
729C22—3441no—
730C22—1722no—
731C22—1722no—
732C22—1722no—
733C22#1458340611yescharacteristic
734C22D4×C22⋊D4311yescharacteristic
735C22D4×C22⋊D4311yescharacteristic
736C22C2×#1306334511yescharacteristic
737C22C2×#1306335611yescharacteristic
738C22#1458370711yescharacteristic
739C22#1458371411yescharacteristic
740C4—22no—
741C4—22no—
742C4—41no—
743C4—41no—
744C4—42no—
745C4—41no—
746C4—42no—
747C4—81no—
748C4—81no—
749C4—864no—
750C4—3441no—
751C4—3441no—
752C4#121×D4311yescharacteristic
753C4#1458348111yescharacteristic
754C4#1458353811yescharacteristic
755C4#1458354611yescharacteristic
756C2—81no—
757C2—3442no—
758C2#1913812811yescharacteristic
759C2#1914466011yescharacteristic
760C2#1914480311yescharacteristic
761C2#1914616611yescharacteristic
762C2#1914625711yescharacteristic
763C2#1914632111yescharacteristic
764C2#1914633211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2429C2
socleC23×C43C22×D4
prime radicalC22×#10621898C22
hypercenter#2429D43
hypocenterC43#25151
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2429

Complements

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

NH ≅ G/Ntype
1. C2×#14583106C2semidirect
4. C2×C4×#10621885C2semidirect
6. #19135980C2semidirect
7. #19135795C2semidirect
8. #19135788C2semidirect
9. #19135678C2semidirect
10. #19135452C2semidirect
11. #19135203C2semidirect
12. #19134950C2semidirect
13. #19134939C2semidirect
14. #19134862C2semidirect
15. C43×#2429C2semidirect
378. #2429D43semidirect
445. C43#25151semidirect

Maximal subgroups

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

subgroupindex
C2×#145831062
C2×#145830592
C2×C4×#106218852
#191374352
#191359802
#191357952
#191357882
#191356782
#191354522
#191352032
#191349502
#191349392
#191348622
C43×#24292
#2515143