Finite Group Databasebeta

← #25140168

Subgroups — #25140168

Order 11008.

1168 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583210C211yesmaximal, characteristic, complemented
2C2×#14582904C211yesmaximal, characteristic, complemented
3#19137524C211yesmaximal, characteristic, complemented
4#19136116C211yesmaximal, characteristic, complemented
5#19136008C211yesmaximal, characteristic, complemented
6#19135781C211yesmaximal, characteristic, complemented
7#19135781C211yesmaximal, characteristic, complemented
8#19135219C211yesmaximal, characteristic, complemented
9#19135212C211yesmaximal, characteristic, complemented
10#19134913C211yesmaximal, characteristic, complemented
11#19134893C211yesmaximal, characteristic, complemented
12#19134792C211yesmaximal, characteristic, complemented
13#19134626C211yesmaximal, characteristic, complemented
14#19134526C211yesmaximal, characteristic, complemented
15C43×#2408C211yesmaximal, characteristic
16C22×#10621877C2211yescharacteristic
17C2×#13063284C2211yescharacteristic
18C22×C4⋊Dic43C2211yescharacteristic, complemented
19#14583210—24no—
20C2×#13063258C2211yescharacteristic, complemented
21C2×#13063258C2211yescharacteristic, complemented
22C2×#13063256C2211yescharacteristic, complemented
23C2×#13063256C2211yescharacteristic, complemented
24#14582904—24no—
25C2×#13063246C2211yescharacteristic
26C2×#13063246C2211yescharacteristic
27C2×#13063246C2211yescharacteristic
28C2×#13063246C2211yescharacteristic
29C2×#13063246C2211yescharacteristic
30C2×#13063246C2211yescharacteristic
31C2×#13063246C2211yescharacteristic
32C2×#13063246C2211yescharacteristic
33C2×C22⋊(C43⋊C8)C2211yescharacteristic
34C2×C22⋊(C43⋊C8)C2211yescharacteristic, complemented
35C2×C22⋊(C43⋊C8)C2211yescharacteristic, complemented
36#14582792—21no—
37#14582785—21no—
38#14582779—21no—
39#14582765C2211yescharacteristic, complemented
40#14582759C2211yescharacteristic
41#14582759C2211yescharacteristic, complemented
42C4×C4⋊Dic43C2211yescharacteristic, complemented
43C22⋊C4×Dic43—21no—
44#14582661C2211yescharacteristic, complemented
45#14582661C2211yescharacteristic, complemented
46#14582661C2211yescharacteristic, complemented
47#14582661C2211yescharacteristic, complemented
48#14582654C2211yescharacteristic, complemented
49#14582654C2211yescharacteristic, complemented
50C23×D4×C43C2211yescharacteristic
51C2×#121×C43C2211yescharacteristic
52C2×#121×C43C2211yescharacteristic
53C2×#120×C43—21no—
54C2×C4×D4×C43C2211yescharacteristic
55C43×#394—21no—
56C43×#392—21no—
57C43×#390C2211yescharacteristic
58C43×#390C2211yescharacteristic
59C43×#380C2211yescharacteristic
60C43×#379—21no—
61C23×Dic43—21no—
62C2×#10621877—22no—
63C2×#10621877—22no—
64C2×#10621877—41no—
65C22×C43⋊C8C2311yescharacteristic
66C22×C43⋊C8C2311yescharacteristic
67C22×C43⋊C8C2311yescharacteristic
68C22×C43⋊C8C2311yescharacteristic
69#13063284—22no—
70#13063284—41no—
71C2×C4⋊Dic43—22no—
72C2×C4⋊Dic43—21no—
73C2×C4⋊Dic43—41no—
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
77C2×C4⋊Dic43C2311yescharacteristic
78C2×C22⋊Dic43—21no—
79C2×C22⋊Dic43—21no—
80C2×C22⋊Dic43—21no—
81C2×C4×Dic43—21no—
82C2×C4×Dic43—21no—
83#13063258—22no—
84#13063258—22no—
85#13063256—41no—
86#13063256—41no—
87#13063246—22no—
88#13063246—22no—
89#13063246—22no—
90#13063246—22no—
91#13063246—22no—
92#13063246—41no—
93#13063246—41no—
94#13063246D414yescomplemented
95C22⋊(C43⋊C8)—22no—
96C22⋊(C43⋊C8)—22no—
97C22⋊(C43⋊C8)—41no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C25×C43—21no—
104C22×D4×C43—22no—
105C22×D4×C43—22no—
106C22×D4×C43—21no—
107C22×D4×C43—21no—
108C22×D4×C43—21no—
109C22×D4×C43—22no—
110C22×D4×C43—22no—
111C22×D4×C43—41no—
112C22×D4×C43—41no—
113C22×D4×C43D411yescharacteristic
114C22×D4×C43C2311yescharacteristic
115C22×D4×C43C2311yescharacteristic
116C23×C4×C43C2311yescharacteristic
117C23×C4×C43C2311yescharacteristic
118#121×C43—22no—
119#121×C43—22no—
120#121×C43—41no—
121#121×C43—41no—
122#120×C43—44no—
123C4×D4×C43—22no—
124C4×D4×C43—22no—
125C2×C4⋊C4×C43D411yescharacteristic
126C2×C4⋊C4×C43C2311yescharacteristic
127C2×C4⋊C4×C43C2311yescharacteristic
128C2×C22⋊C4×C43—21no—
129C2×C22⋊C4×C43—21no—
130C2×C22⋊C4×C43—21no—
131C2×C22⋊C4×C43—21no—
132C2×C22⋊C4×C43—21no—
133C2×C22⋊C4×C43—21no—
134C2×C22⋊C4×C43—21no—
135C2×C22⋊C4×C43D411yescharacteristic
136C2×C22⋊C4×C43D411yescharacteristic
137C2×C42×C43C2311yescharacteristic
138#95×C43—21no—
139C24×C43—21no—
140C24×C43—21no—
141C24×C43—42no—
142C24×C43—42no—
143C24×C43—42no—
144C24×C43—42no—
145C24×C43—42no—
146C24×C43—81no—
147C24×C43—81no—
148C24×C43C2×D411yescharacteristic
149C24×C43C2×D411yescharacteristic
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—22no—
153C2×D4×C43—22no—
154C2×D4×C43—28no—
155C2×D4×C43—21no—
156C2×D4×C43—21no—
157C2×D4×C43—21no—
158C2×D4×C43—21no—
159C2×D4×C43—21no—
160C2×D4×C43—21no—
161C2×D4×C43—21no—
162C2×D4×C43—21no—
163C2×D4×C43—41no—
164C2×D4×C43—42no—
165C2×D4×C43—42no—
166C2×D4×C43—42no—
167C2×D4×C43—42no—
168C2×D4×C43—44no—
169C2×D4×C43—44no—
170C2×D4×C43—44no—
171C2×D4×C43—42no—
172C2×D4×C43—42no—
173C2×D4×C43—42no—
174C2×D4×C43—81no—
175C2×D4×C43—81no—
176C2×D4×C43C2×D412yes—
177C2×D4×C43#4112yes—
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×C43—21no—
185C22×C4×C43—21no—
186C22×C4×C43—21no—
187C22×C4×C43—21no—
188C22×C4×C43—21no—
189C22×C4×C43—21no—
190C22×C4×C43C2×D411yescharacteristic
191C22×C4×C43C2×D411yescharacteristic
192C22×C4×C43C2×D411yescharacteristic
193C22×C4×C43C2×D411yescharacteristic
194C22×C4×C43#4112yes—
195C22×C4×C43#4112yes—
196C22×C4×C43C2411yescharacteristic
197C22×Dic43—21no—
198C22×Dic43—21no—
199C22×Dic43—21no—
200C22×Dic43—21no—
201C22×Dic43—42no—
202C22×Dic43—42no—
203C22×Dic43—81no—
204C4⋊C4×C43—22no—
205C4⋊C4×C43—21no—
206C4⋊C4×C43—21no—
207C4⋊C4×C43—21no—
208C4⋊C4×C43—21no—
209C22⋊C4×C43—22no—
210C22⋊C4×C43—22no—
211C22⋊C4×C43—42no—
212C22⋊C4×C43—42no—
213C22⋊C4×C43—42no—
214C22⋊C4×C43—42no—
215C22⋊C4×C43—42no—
216C22⋊C4×C43—81no—
217C22⋊C4×C43—81no—
218C42×C43—21no—
219C42×C43—21no—
220C22⋊Dic43—42no—
221C22⋊Dic43—42no—
222C22⋊Dic43—81no—
223C4⋊Dic43—21no—
224C4⋊Dic43—21no—
225C4⋊Dic43—21no—
226C4⋊Dic43—21no—
227C4⋊Dic43—21no—
228C4⋊Dic43—21no—
229C4⋊Dic43—21no—
230C4⋊Dic43—42no—
231C4⋊Dic43C2×D412yes—
232C4×Dic43—42no—
233C4×Dic43—81no—
234#10621877—44no—
235C2×C43⋊C8—21no—
236C2×C43⋊C8—21no—
237C2×C43⋊C8—21no—
238C2×C43⋊C8—21no—
239C2×C43⋊C8—21no—
240C2×C43⋊C8—21no—
241C2×C43⋊C8—21no—
242C2×C43⋊C8—21no—
243C2×C43⋊C8—21no—
244C2×C43⋊C8—21no—
245C2×C43⋊C8—21no—
246C2×C43⋊C8C2×D412yes—
247C23×C43—21no—
248C23×C43—21no—
249C23×C43—21no—
250C23×C43—21no—
251C23×C43—21no—
252C23×C43—21no—
253C23×C43—21no—
254C23×C43—21no—
255C23×C43—21no—
256C23×C43—21no—
257C23×C43—21no—
258C23×C43—21no—
259C23×C43—22no—
260C23×C43—22no—
261C23×C43—48no—
262C23×C43—41no—
263C23×C43—41no—
264C23×C43—41no—
265C23×C43—41no—
266C23×C43—41no—
267C23×C43—41no—
268C23×C43—41no—
269C23×C43—41no—
270C23×C43—41no—
271C23×C43—41no—
272C23×C43—41no—
273C23×C43—41no—
274C23×C43—84no—
275C23×C43—84no—
276C23×C43—84no—
277C23×C43—84no—
278C23×C43—84no—
279C23×C43—84no—
280C23×C43#12312yes—
281C23×C43AGL(1,ℤ/8)12yes—
282C23×C43C22×D411yescharacteristic
283D4×C43—22no—
284D4×C43—22no—
285D4×C43—22no—
286D4×C43—22no—
287D4×C43—48no—
288D4×C43—44no—
289D4×C43—41no—
290D4×C43—41no—
291D4×C43—41no—
292D4×C43—41no—
293D4×C43—84no—
294D4×C43—84no—
295C2×C4×C43—21no—
296C2×C4×C43—21no—
297C2×C4×C43—22no—
298C2×C4×C43—22no—
299C2×C4×C43—22no—
300C2×C4×C43—22no—
301C2×C4×C43—21no—
302C2×C4×C43—21no—
303C2×C4×C43—21no—
304C2×C4×C43—21no—
305C2×C4×C43—21no—
306C2×C4×C43—21no—
307C2×C4×C43—21no—
308C2×C4×C43—21no—
309C2×C4×C43—21no—
310C2×C4×C43—41no—
311C2×C4×C43—41no—
312C2×C4×C43—41no—
313C2×C4×C43—41no—
314C2×C4×C43—41no—
315C2×C4×C43—41no—
316C2×C4×C43—41no—
317C2×C4×C43—41no—
318C2×C4×C43—41no—
319C2×C4×C43—41no—
320C2×C4×C43#12312yes—
321C2×C4×C43C22×D411yescharacteristic
322C2×C4×C43C2×#4111yescharacteristic
323C2×C4×C43C2×#4111yescharacteristic
324C2×C4×C43C2×#4111yescharacteristic
325C2×C4×C43H(5,𝔽2)11yescharacteristic
326C2×C4×C43H(5,𝔽2)11yescharacteristic
327C2×Dic43—22no—
328C2×Dic43—41no—
329C2×Dic43—41no—
330C2×Dic43—41no—
331C2×Dic43—41no—
332C2×Dic43—41no—
333C2×Dic43—41no—
334C2×Dic43—41no—
335C2×Dic43—41no—
336C2×Dic43—41no—
337C2×Dic43—41no—
338C2×Dic43—41no—
339C2×Dic43—84no—
340C43⋊C8—22no—
341C43⋊C8—41no—
342C43⋊C8—41no—
343C43⋊C8—41no—
344#24882—431nomaximal, Sylow
345C22×C43—22no—
346C22×C43—22no—
347C22×C43—22no—
348C22×C43—22no—
349C22×C43—22no—
350C22×C43—22no—
351C22×C43—41no—
352C22×C43—41no—
353C22×C43—41no—
354C22×C43—41no—
355C22×C43—41no—
356C22×C43—41no—
357C22×C43—41no—
358C22×C43—41no—
359C22×C43—42no—
360C22×C43—42no—
361C22×C43—42no—
362C22×C43—42no—
363C22×C43—42no—
364C22×C43—42no—
365C22×C43—816no—
366C22×C43—81no—
367C22×C43—81no—
368C22×C43—81no—
369C22×C43—81no—
370C22×C43—81no—
371C22×C43—81no—
372C22×C43—81no—
373C22×C43—81no—
374C22×C43C2×#12311yescharacteristic
375C22×C43D4211yescharacteristic
376C22×C43#54611yescharacteristic
377C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
378C22×C43#57511yescharacteristic
379C22×C43#57611yescharacteristic
380C22×C43#57711yescharacteristic
381C4×C43—22no—
382C4×C43—41no—
383C4×C43—41no—
384C4×C43—41no—
385C4×C43—81no—
386C4×C43—81no—
387C4×C43#52511yescharacteristic
388C4×C43#53811yescharacteristic
389C4×C43#54611yescharacteristic
390C4×C43#55111yescharacteristic
391Dic43—42no—
392Dic43—81no—
393Dic43—81no—
394Dic43—81no—
395C2×#480—431no—
396C2×#418—431no—
397#2408D4311yescharacteristic
398#2352—431no—
399#2092—431no—
400#2073—431no—
401#2034—431no—
402#2034—431no—
403#1926—431no—
404#1925—431no—
405#1874—431no—
406#1870—431no—
407#1854—431no—
408#1809—431no—
409#1786—431no—
410C2×C43—42no—
411C2×C43—42no—
412C2×C43—82no—
413C2×C43—82no—
414C2×C43#241811yescharacteristic
415C2×C43#309411yescharacteristic
416C2×C43#309611yescharacteristic
417C2×C43#326411yescharacteristic
418C2×C43#327511yescharacteristic
419C2×C43#331011yescharacteristic
420C2×C43#332211yescharacteristic
421C23×D4C2×D4311yescharacteristic
422C22×M16—431no—
423C2×#121C2×D4311yescharacteristic
424C2×#121C2×D4311yescharacteristic
425C2×#120—21no—
426C2×C4×D4C2×D4311yescharacteristic
427C2×#117—431no—
428C22×C4⋊C4—431no—
429#480—864no—
430C2×#107—431no—
431C2×#107—431no—
432C2×#106—431no—
433C2×#106—431no—
434#418—864no—
435C2×#102—431no—
436C2×#102—431no—
437C2×#102—431no—
438C2×#102—431no—
439C2×#102—431no—
440C2×#102—431no—
441C2×#102—431no—
442C2×#102—431no—
443C2×C22⋊C8—431no—
444C2×C22⋊C8—431no—
445C2×C22⋊C8—431no—
446#394—21no—
447#392—21no—
448#390C2×D4311yescharacteristic
449#390C2×D4311yescharacteristic
450#388—861no—
451#387—861no—
452#386—861no—
453#382—431no—
454#380—431no—
455#380—431no—
456#380C2×D4311yescharacteristic
457#379—21no—
458C4×C4⋊C4—431no—
459C4×C22⋊C4—861no—
460#340—431no—
461#340—431no—
462#340—431no—
463#340—431no—
464#336—431no—
465#336—431no—
466C43#2488211yescharacteristic, complemented, Sylow
467C25—21no—
468C22×D4—22no—
469C22×D4—22no—
470C22×D4—21no—
471C22×D4—21no—
472C22×D4—22no—
473C22×D4—22no—
474C22×D4—21no—
475C22×D4—41no—
476C22×D4—41no—
477C22×D4C22⋊D4311yescharacteristic
478C22×D4C22×D4311yescharacteristic
479C22×D4C22×D4311yescharacteristic
480C23×C4—861no—
481C23×C4C22×D4311yescharacteristic
482C23×C4C22×D4311yescharacteristic
483C2×M16—862no—
484C2×M16—862no—
485C2×M16—1721no—
486C22×C8—431no—
487C22×C8—431no—
488C22×C8—431no—
489C22×C8—431no—
490#121—22no—
491#121—22no—
492#121—41no—
493#121—41no—
494#120—44no—
495C4×D4—22no—
496C4×D4—22no—
497#117—862no—
498#117—1721no—
499C2×C4⋊C4—431no—
500C2×C4⋊C4—431no—
501C2×C4⋊C4—431no—
502C2×C4⋊C4—431no—
503C2×C4⋊C4—862no—
504C2×C4⋊C4—861no—
505C2×C4⋊C4—1721no—
506C2×C4⋊C4C22⋊D4311yescharacteristic
507C2×C4⋊C4C22×D4311yescharacteristic
508C2×C4⋊C4C22×D4311yescharacteristic
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—861no—
517C2×C22⋊C4—861no—
518C2×C22⋊C4—861no—
519C2×C22⋊C4C22⋊D4311yescharacteristic
520C2×C22⋊C4C22⋊D4311yescharacteristic
521C2×C42—861no—
522C2×C42—861no—
523C2×C42C22×D4311yescharacteristic
524#107—862no—
525#107—862no—
526#106—1721no—
527#106—1721no—
528#102—434no—
529#102—862no—
530#102—862no—
531#102—862no—
532#102—862no—
533#102—862no—
534#102—1721no—
535#102—1721no—
536C22⋊C8—862no—
537C22⋊C8—862no—
538C22⋊C8—1721no—
539#95—21no—
540#95—861no—
541#95—861no—
542#95—861no—
543#95—861no—
544#95—861no—
545C24—21no—
546C24—21no—
547C24—42no—
548C24—42no—
549C24—42no—
550C24—42no—
551C24—42no—
552C24—81no—
553C24—81no—
554C24C2×C22⋊D4311yescharacteristic
555C24C2×C22⋊D4311yescharacteristic
556C2×D4—28no—
557C2×D4—22no—
558C2×D4—22no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—44no—
570C2×D4—44no—
571C2×D4—41no—
572C2×D4—42no—
573C2×D4—42no—
574C2×D4—44no—
575C2×D4—42no—
576C2×D4—42no—
577C2×D4—42no—
578C2×D4—42no—
579C2×D4—42no—
580C2×D4—81no—
581C2×D4—81no—
582C2×D4D4×D4312yes—
583C2×D4#1062190012yes—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—861no—
597C22×C4—861no—
598C22×C4—861no—
599C22×C4—861no—
600C22×C4—3441no—
601C22×C4—1722no—
602C22×C4—1722no—
603C22×C4#1062190012yes—
604C22×C4#1062190012yes—
605C22×C4C2×C22⋊D4311yescharacteristic
606C22×C4C2×C22⋊D4311yescharacteristic
607C22×C4C2×C22⋊D4311yescharacteristic
608C22×C4C2×C22⋊D4311yescharacteristic
609C22×C4C23×D4311yescharacteristic
610M16—1724no—
611C2×C8—432no—
612C2×C8—861no—
613C2×C8—861no—
614C2×C8—861no—
615C2×C8—861no—
616C2×C8—861no—
617C2×C8—861no—
618C2×C8—861no—
619C2×C8—861no—
620C2×C8—861no—
621C2×C8—861no—
622C2×C8—861no—
623C4⋊C4—22no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—432no—
629C4⋊C4—861no—
630C4⋊C4—861no—
631C4⋊C4—861no—
632C4⋊C4—861no—
633C4⋊C4—861no—
634C4⋊C4—861no—
635C4⋊C4—861no—
636C4⋊C4—1722no—
637C22⋊C4—22no—
638C22⋊C4—22no—
639C22⋊C4—42no—
640C22⋊C4—42no—
641C22⋊C4—42no—
642C22⋊C4—42no—
643C22⋊C4—42no—
644C22⋊C4—81no—
645C22⋊C4—81no—
646C22⋊C4—3441no—
647C22⋊C4—1722no—
648C22⋊C4—1722no—
649C42—21no—
650C42—21no—
651C42—3441no—
652C42—1722no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—22no—
666C23—22no—
667C23—48no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—84no—
681C23—84no—
682C23—84no—
683C23—84no—
684C23—84no—
685C23—84no—
686C23#1306330612yes—
687C23#1306335112yes—
688C23C22×C22⋊D4311yescharacteristic
689D4—22no—
690D4—22no—
691D4—22no—
692D4—22no—
693D4—48no—
694D4—44no—
695D4—41no—
696D4—41no—
697D4—41no—
698D4—41no—
699D4—84no—
700D4—84no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—862no—
727C2×C4—3444no—
728C2×C4—1721no—
729C2×C4—1721no—
730C2×C4—1721no—
731C2×C4—1721no—
732C2×C4—1721no—
733C2×C4—1721no—
734C2×C4—1721no—
735C2×C4—1721no—
736C2×C4—1721no—
737C2×C4—1721no—
738C2×C4—1721no—
739C2×C4#1306330612yes—
740C2×C4C2×D4×D4311yescharacteristic
741C2×C4C2×#1062190011yescharacteristic
742C2×C4C2×#1062190011yescharacteristic
743C2×C4C2×#1062190011yescharacteristic
744C2×C4#1306337011yescharacteristic
745C2×C4#1306337011yescharacteristic
746C8—862no—
747C8—1721no—
748C8—1721no—
749C8—1721no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—42no—
765C22—42no—
766C22—42no—
767C22—42no—
768C22—42no—
769C22—42no—
770C22—816no—
771C22—81no—
772C22—81no—
773C22—81no—
774C22—81no—
775C22—81no—
776C22—81no—
777C22—81no—
778C22—81no—
779C22C2×#1306330611yescharacteristic
780C22D4×C22⋊D4311yescharacteristic
781C22#1458354311yescharacteristic
782C22C2×#1306335111yescharacteristic
783C22#1458369711yescharacteristic
784C22#1458370211yescharacteristic
785C22#1458371011yescharacteristic
786C4—22no—
787C4—41no—
788C4—41no—
789C4—41no—
790C4—81no—
791C4—81no—
792C4—3441no—
793C4—3441no—
794C4—3441no—
795C4—1722no—
796C4#1458340511yescharacteristic
797C4#1458348411yescharacteristic
798C4#1458353611yescharacteristic
799C4#1458358011yescharacteristic
800C2—42no—
801C2—42no—
802C2—82no—
803C2—82no—
804C2#1913805311yescharacteristic
805C2#1914453111yescharacteristic
806C2#1914454711yescharacteristic
807C2#1914607111yescharacteristic
808C2#1914622211yescharacteristic
809C2#1914661611yescharacteristic
810C2#1914679611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
Fitting, prime radicalC43×#2408C2
socleC23×C43C22×D4
hypercenter#2408D43
hypocenterC43#24882
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2408

Complements

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

NH ≅ G/Ntype
1. C2×#14583210C2semidirect
2. C2×#14582904C2semidirect
3. #19137524C2semidirect
4. #19136116C2semidirect
5. #19136008C2semidirect
6. #19135781C2semidirect
7. #19135781C2semidirect
8. #19135219C2semidirect
9. #19135212C2semidirect
10. #19134913C2semidirect
11. #19134893C2semidirect
12. #19134792C2semidirect
13. #19134626C2semidirect
14. #19134526C2semidirect
18. C22×C4⋊Dic43C22semidirect
20. C2×#13063258C22semidirect
21. C2×#13063258C22semidirect
22. C2×#13063256C22semidirect
23. C2×#13063256C22semidirect
34. C2×C22⋊(C43⋊C8)C22semidirect
35. C2×C22⋊(C43⋊C8)C22semidirect
39. #14582765C22semidirect
41. #14582759C22semidirect
42. C4×C4⋊Dic43C22semidirect
44. #14582661C22semidirect
45. #14582661C22semidirect
46. #14582661C22semidirect
47. #14582661C22semidirect
48. #14582654C22semidirect
49. #14582654C22semidirect
94. #13063246D4semidirect
466. C43#24882semidirect

Maximal subgroups

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

subgroupindex
C2×#145832102
C2×#145829042
#191375242
#191361162
#191360082
#191357812
#191352192
#191352122
#191349132
#191348932
#191347922
#191346262
#191345262
C43×#24082
#2488243