Finite Group Databasebeta

← #25103238

Subgroups — #25103238

Order 11008.

1170 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583150C211yesmaximal, characteristic
2C2×#14582979C211yesmaximal, characteristic, complemented
3C2×M16×Dic43C211yesmaximal, characteristic, complemented
4#121×Dic43C211yesmaximal, characteristic, complemented
5#19137101C211yesmaximal, characteristic, complemented
6#19135468C211yesmaximal, characteristic, complemented
7#19135337C211yesmaximal, characteristic, complemented
8#19135293C211yesmaximal, characteristic, complemented
9#19135289C211yesmaximal, characteristic, complemented
10#19135033C211yesmaximal, characteristic, complemented
11#19134626C211yesmaximal, characteristic, complemented
12#19134483C211yesmaximal, characteristic, complemented
13#102×Dic43C211yesmaximal, characteristic, complemented
14#19134409C211yesmaximal, characteristic, complemented
15C43×#1895C211yesmaximal, characteristic, complemented
16C22×#10621882C2211yescharacteristic
17C22×#10621877C2211yescharacteristic
18C2×#13063299C2211yescharacteristic
19C2×D4×Dic43—21no—
20C2×D4×Dic43C2211yescharacteristic
21C2×#13063287C2211yescharacteristic
22C2×(C22⋊D43)⋊C4—21no—
23C22×C4×Dic43C2211yescharacteristic
24#14583150C418yescomplemented
25#14582979—24no—
26C2×#13063258C2211yescharacteristic
27C2×#13063256C2211yescharacteristic
28C2×#13063256C2211yescharacteristic
29C2×#13063247C2211yescharacteristic
30C2×#13063247C2211yescharacteristic
31C2×#13063246C2211yescharacteristic
32C2×#13063245C2211yescharacteristic
33M16×Dic43—24no—
34C2×#13063235C2211yescharacteristic
35C2×#13063235C2211yescharacteristic
36C2×C8×Dic43C2211yescharacteristic
37C2×C8×Dic43C2211yescharacteristic
38#14582802C2211yescharacteristic
39#14582800C2211yescharacteristic
40#14582798C2211yescharacteristic
41#14582795C2211yescharacteristic
42#14582792—21no—
43#14582788—21no—
44#14582779—21no—
45#14582776—21no—
46#14582759C2211yescharacteristic
47C4⋊C4×Dic43C2211yescharacteristic
48C4⋊C4×Dic43C2211yescharacteristic
49C22⋊C4×Dic43—21no—
50#14582746—21no—
51#14582662C2211yescharacteristic
52#14582662C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582661C2211yescharacteristic
55C22×M16×C43C2211yescharacteristic
56C2×#121×C43C2211yescharacteristic
57C2×#102×C43C2211yescharacteristic
58C2×#102×C43C2211yescharacteristic
59C43×#380C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C43×#340C2211yescharacteristic
62C22×D172C2311yescharacteristic
63C22×C22⋊D43—21no—
64C23×Dic43—21no—
65C23×Dic43D411yescharacteristic
66C23×Dic43D411yescharacteristic
67C22×C4×D43—21no—
68C2×#10621882—22no—
69C2×#10621882—22no—
70C2×#10621882C2×C414yescomplemented
71C2×#10621877—22no—
72C2×#10621877—22no—
73C2×#10621877C2×C414yescomplemented
74C22×C43⋊C8C2311yescharacteristic
75C22×C43⋊C8C2311yescharacteristic
76#13063299—22no—
77#13063299C2×C414yescomplemented
78D4×Dic43—22no—
79D4×Dic43—22no—
80D4×Dic43—44no—
81#13063287—22no—
82#13063287—22no—
83(C22⋊D43)⋊C4—44no—
84C2×C4⋊Dic43—21no—
85C2×C4⋊Dic43C2311yescharacteristic
86C2×C4⋊Dic43C2311yescharacteristic
87C2×C4⋊Dic43C2311yescharacteristic
88C2×Dic43⋊C4—21no—
89C2×C22⋊Dic43—21no—
90C2×C22⋊Dic43—21no—
91C2×C22⋊Dic43—21no—
92C2×C22⋊Dic43—21no—
93C2×(C2×D43)⋊C4—21no—
94C2×(C2×D43)⋊C4—21no—
95C2×(C2×D43)⋊C4—21no—
96C2×(C2×D43)⋊C4—21no—
97C2×C4×Dic43—22no—
98C2×C4×Dic43—22no—
99C2×C4×Dic43—21no—
100C2×C4×Dic43—21no—
101C2×C4×Dic43D411yescharacteristic
102C2×C4×Dic43D411yescharacteristic
103C2×C4×Dic43C2311yescharacteristic
104C2×C4×Dic43C2311yescharacteristic
105#13063258—22no—
106#13063256—22no—
107#13063256C2×C414yescomplemented
108#13063247—22no—
109#13063247—22no—
110#13063246C2×C414yescomplemented
111#13063245C2×C414yescomplemented
112#13063235—22no—
113#13063235—22no—
114C8×Dic43—22no—
115C8×Dic43D414yescomplemented
116C43⋊#95—21no—
117C43⋊#95—21no—
118C43⋊#95—21no—
119C43⋊#95—21no—
120C43⋊#95—21no—
121C22×D4×C43—21no—
122C22×D4×C43C2311yescharacteristic
123C23×C4×C43C2311yescharacteristic
124C2×M16×C43—22no—
125C2×M16×C43—22no—
126C2×M16×C43—22no—
127C22×C8×C43C2311yescharacteristic
128C22×C8×C43C2311yescharacteristic
129#121×C43—22no—
130#121×C43C2×C414yescomplemented
131C2×C4⋊C4×C43C2311yescharacteristic
132C2×C4⋊C4×C43C2311yescharacteristic
133C2×C4⋊C4×C43C2311yescharacteristic
134C2×C22⋊C4×C43—21no—
135C2×C22⋊C4×C43—21no—
136#102×C43—22no—
137#102×C43—22no—
138#95×C43—21no—
139C24×C43—21no—
140C24×C43C2×D411yescharacteristic
141C23×D43—21no—
142C2×D4×C43—21no—
143C2×D4×C43—24no—
144C2×D4×C43—21no—
145C2×D4×C43—21no—
146C2×D4×C43—21no—
147C2×D4×C43—21no—
148C2×D4×C43—42no—
149C2×D4×C43—42no—
150C2×D4×C43C22×C412yes—
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×C43C22×C412yes—
159C22×C4×C43C2×D411yescharacteristic
160C22×C4×C43#4112yes—
161C22×C4×C43C2411yescharacteristic
162C2×C22⋊D43—24no—
163C2×C22⋊D43—42no—
164C2×C22⋊D43—42no—
165C22×Dic43—22no—
166C22×Dic43—22no—
167C22×Dic43—22no—
168C22×Dic43—22no—
169C22×Dic43—21no—
170C22×Dic43—21no—
171C22×Dic43—21no—
172C22×Dic43—41no—
173C22×Dic43—41no—
174C22×Dic43—42no—
175C22×Dic43—42no—
176C22×Dic43—42no—
177C22×Dic43C2×D411yescharacteristic
178C22×Dic43C2×D411yescharacteristic
179C22×Dic43C2×D411yescharacteristic
180C22×Dic43C2×D411yescharacteristic
181C2×D172—21no—
182C2×D172—21no—
183C2×D172—21no—
184C2×D172—21no—
185C2×D172—21no—
186C2×D172C22×C412yes—
187C2×C4×D43—42no—
188C2×C4×D43—42no—
189C2×C4×D43—42no—
190M16×C43—28no—
191C2×C8×C43—21no—
192C2×C8×C43—21no—
193C2×C8×C43—21no—
194C2×C8×C43—21no—
195C2×C8×C43C2×D412yes—
196C2×C8×C43#4112yes—
197C4⋊C4×C43—21no—
198C4⋊C4×C43—21no—
199C4⋊C4×C43—21no—
200C4⋊C4×C43—21no—
201C4⋊C4×C43—21no—
202C4⋊C4×C43C22×C412yes—
203C22⋊C4×C43—24no—
204C22⋊C4×C43—42no—
205C22⋊Dic43—42no—
206C22⋊Dic43—42no—
207C22⋊Dic43—42no—
208C22⋊Dic43—42no—
209#10621882—28no—
210(C2×D43)⋊C4—24no—
211(C2×D43)⋊C4—42no—
212(C2×D43)⋊C4—42no—
213(C2×D43)⋊C4—42no—
214C4⋊Dic43—21no—
215C4⋊Dic43—21no—
216C4⋊Dic43—21no—
217C4⋊Dic43—21no—
218C4⋊Dic43—21no—
219C4⋊Dic43—42no—
220C4⋊Dic43C22×C412yes—
221Dic43⋊C4—42no—
222C4×Dic43—21no—
223C4×Dic43—21no—
224C4×Dic43—22no—
225C4×Dic43—22no—
226C4×Dic43—42no—
227C4×Dic43—42no—
228C4×Dic43C2×D412yes—
229C4×Dic43#4112yes—
230#10621877—28no—
231C2×C43⋊C8—21no—
232C2×C43⋊C8—21no—
233C2×C43⋊C8C22×C412yes—
234C2×C43⋊C8C22×C412yes—
235C2×C43⋊C8C2×D412yes—
236C2×C43⋊C8#4112yes—
237C23×C43—21no—
238C23×C43—21no—
239C23×C43—21no—
240C23×C43—21no—
241C23×C43—21no—
242C23×C43—21no—
243C23×C43—22no—
244C23×C43—41no—
245C23×C43—41no—
246C23×C43—41no—
247C23×C43—41no—
248C23×C43—41no—
249C23×C43—41no—
250C23×C43C4×D412yes—
251C23×C43C22×D411yescharacteristic
252C22×D43—22no—
253C22×D43—41no—
254C22×D43—41no—
255C22×D43—41no—
256C22×D43—41no—
257C22×D43—41no—
258C22×D43—41no—
259D4×C43—22no—
260D4×C43—22no—
261D4×C43—48no—
262D4×C43—41no—
263D4×C43—41no—
264C2×C4×C43—21no—
265C2×C4×C43—21no—
266C2×C4×C43—22no—
267C2×C4×C43—22no—
268C2×C4×C43—22no—
269C2×C4×C43—22no—
270C2×C4×C43—22no—
271C2×C4×C43—41no—
272C2×C4×C43—41no—
273C2×C4×C43—41no—
274C2×C4×C43—41no—
275C2×C4×C43—41no—
276C2×C4×C43—41no—
277C2×C4×C43—41no—
278C2×C4×C43—41no—
279C2×C4×C43C4×D412yes—
280C2×C4×C43C23×C411yescharacteristic
281C2×C4×C43C22×D411yescharacteristic
282C2×C4×C43C2×#4111yescharacteristic
283C2×C4×C43C2×#4111yescharacteristic
284C2×C4×C43C2×#4111yescharacteristic
285C2×C4×C43C2×#4111yescharacteristic
286C22⋊D43—48no—
287C2×Dic43—21no—
288C2×Dic43—21no—
289C2×Dic43—22no—
290C2×Dic43—21no—
291C2×Dic43—21no—
292C2×Dic43—21no—
293C2×Dic43—21no—
294C2×Dic43—21no—
295C2×Dic43—21no—
296C2×Dic43—44no—
297C2×Dic43—41no—
298C2×Dic43—41no—
299C2×Dic43—44no—
300C2×Dic43—41no—
301C2×Dic43—41no—
302C2×Dic43—41no—
303C2×Dic43—41no—
304C2×Dic43—41no—
305C2×Dic43—41no—
306C2×Dic43—84no—
307C2×Dic43#12112yes—
308C2×Dic43#12112yes—
309C2×Dic43AGL(1,ℤ/8)12yes—
310C2×Dic43AGL(1,ℤ/8)12yes—
311D172—22no—
312D172—22no—
313D172—41no—
314D172—41no—
315C4×D43—84no—
316C8×C43—22no—
317C8×C43—22no—
318C43⋊C8—22no—
319C43⋊C8C4×D414yescomplemented
320C4×#469—431nomaximal, Sylow
321C22×C43—22no—
322C22×C43—22no—
323C22×C43—22no—
324C22×C43—41no—
325C22×C43—41no—
326C22×C43—41no—
327C22×C43—41no—
328C22×C43—42no—
329C22×C43—42no—
330C22×C43—42no—
331C22×C43—81no—
332C22×C43—81no—
333C22×C43—81no—
334C22×C43—81no—
335C22×C43C2×C4×D411yescharacteristic
336C22×C43C2×#12111yescharacteristic
337C22×C43#53211yescharacteristic
338C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
339C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
340C22×C43#57511yescharacteristic
341C22×C43#57511yescharacteristic
342C2×D43—42no—
343C2×D43—42no—
344C2×D43—42no—
345C2×D43—81no—
346C2×D43—81no—
347C2×D43—81no—
348C2×D43—81no—
349C4×C43—22no—
350C4×C43—42no—
351C4×C43—81no—
352C4×C43—81no—
353C4×C43C2×C4×D411yescharacteristic
354C4×C43C4×#4111yescharacteristic
355C4×C43#52511yescharacteristic
356C4×C43#52911yescharacteristic
357Dic43—22no—
358Dic43—42no—
359Dic43—41no—
360Dic43—41no—
361Dic43—81no—
362Dic43—81no—
363Dic43#46914yescomplemented
364C2×#469—431no—
365C2×C4×D8—431no—
366C2×C4×M16—431no—
367C4×#121—431no—
368C4×#121—431no—
369#1972—431no—
370#1944—431no—
371#1936—431no—
372#1936—431no—
373#1895—431no—
374#1895D4311yescharacteristic, complemented
375#1809—431no—
376C4×#106—431no—
377C4×#102—431no—
378C4×#102—431no—
379C2×C43—42no—
380C2×C43—82no—
381C2×C43C4×#12111yescharacteristic
382C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
383C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
384C2×C43C2×#46911yescharacteristic
385C2×C43#305411yescharacteristic
386C2×C43#317111yescharacteristic
387C2×C43#317111yescharacteristic
388D43—82no—
389C22×D8—431no—
390C22×M16—431no—
391C22×M16C2×D4311yescharacteristic
392C2×#121—431no—
393C2×#121C2×D4311yescharacteristic
394C2×C4×D4—431no—
395C2×C4×D4—431no—
396C2×C4×D4—861no—
397C2×C4×D4—861no—
398C22×C42—431no—
399#469—438no—
400C4×D8—864no—
401C2×#107—431no—
402C2×#106—431no—
403C2×#106—431no—
404C2×#102—431no—
405C2×#102—431no—
406C2×#102—431no—
407C2×#102—431no—
408C2×#102C2×D4311yescharacteristic
409C2×#102C2×D4311yescharacteristic
410C4×M16—864no—
411C2×#97—431no—
412C2×#97—431no—
413C2×C4×C8—431no—
414C2×C4×C8—431no—
415#390—431no—
416#390—431no—
417#389—431no—
418#389—431no—
419#388—861no—
420#388—861no—
421#386—861no—
422#386—861no—
423#380—431no—
424#380C2×D4311yescharacteristic
425C4×C4⋊C4—431no—
426C4×C4⋊C4—431no—
427C4×C22⋊C4—861no—
428C4×C22⋊C4—861no—
429#340—431no—
430#340—431no—
431#340—431no—
432#340—431no—
433#340C2×D4311yescharacteristic
434#340C2×D4311yescharacteristic
435C43C4×#46911yescharacteristic, complemented, Sylow
436C22×D4—21no—
437C22×D4—431no—
438C22×D4—861no—
439C22×D4C22×D4311yescharacteristic
440C23×C4—431no—
441C23×C4—431no—
442C23×C4—861no—
443C23×C4—861no—
444C23×C4C22×D4311yescharacteristic
445C2×D8—434no—
446C2×D8—862no—
447C2×D8—862no—
448C2×M16—22no—
449C2×M16—22no—
450C2×M16—22no—
451C2×M16—434no—
452C2×M16—862no—
453C2×M16—862no—
454C22×C8—431no—
455C22×C8—431no—
456C22×C8C22×D4311yescharacteristic
457C22×C8C22×D4311yescharacteristic
458#121—22no—
459#121—434no—
460#121—862no—
461#121C4×D4314yescomplemented
462C4×D4—862no—
463C4×D4—862no—
464C4×D4—862no—
465C4×D4—862no—
466C4×D4—1724no—
467C4×D4—1724no—
468C2×C4⋊C4—431no—
469C2×C4⋊C4—431no—
470C2×C4⋊C4—431no—
471C2×C4⋊C4—861no—
472C2×C4⋊C4—861no—
473C2×C4⋊C4C22×D4311yescharacteristic
474C2×C4⋊C4C22×D4311yescharacteristic
475C2×C4⋊C4C22×D4311yescharacteristic
476C2×C22⋊C4—21no—
477C2×C22⋊C4—21no—
478C2×C22⋊C4—861no—
479C2×C22⋊C4—861no—
480C2×C22⋊C4—861no—
481C2×C22⋊C4—861no—
482C2×C22⋊C4—861no—
483C2×C22⋊C4—861no—
484C2×C22⋊C4—861no—
485C2×C22⋊C4—861no—
486C2×C42—431no—
487C2×C42—431no—
488C2×C42—431no—
489C2×C42—431no—
490C2×C42—862no—
491C2×C42—862no—
492C2×C42—861no—
493C2×C42—861no—
494#107—862no—
495#106—434no—
496#106—862no—
497#102—22no—
498#102—22no—
499#102—434no—
500#102—434no—
501#102—862no—
502#102—862no—
503#97—862no—
504#97—862no—
505C4×C8—434no—
506C4×C8—862no—
507#95—21no—
508#95—861no—
509#95—861no—
510#95—861no—
511#95—861no—
512#95—861no—
513C24—21no—
514C24—861no—
515C24D4×D4311yescharacteristic
516C2×D4—24no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—42no—
523C2×D4—42no—
524C2×D4—432no—
525C2×D4—864no—
526C2×D4—861no—
527C2×D4—861no—
528C2×D4—861no—
529C2×D4—861no—
530C2×D4—861no—
531C2×D4—1722no—
532C2×D4—1722no—
533C2×D4C2×C4×D4312yes—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—431no—
542C22×C4—431no—
543C22×C4—431no—
544C22×C4—431no—
545C22×C4—862no—
546C22×C4—862no—
547C22×C4—862no—
548C22×C4—862no—
549C22×C4—861no—
550C22×C4—861no—
551C22×C4—861no—
552C22×C4—1722no—
553C22×C4—1722no—
554C22×C4—1722no—
555C22×C4—1722no—
556C22×C4—1722no—
557C22×C4—1722no—
558C22×C4—1721no—
559C22×C4—1721no—
560C22×C4C2×C4×D4312yes—
561C22×C4D4×D4311yescharacteristic
562C22×C4#1062190012yes—
563C22×C4C23×D4311yescharacteristic
564D8—868no—
565M16—28no—
566M16—868no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—432no—
572C2×C8—432no—
573C2×C8—432no—
574C2×C8—432no—
575C2×C8—861no—
576C2×C8—861no—
577C2×C8D4×D4312yes—
578C2×C8#1062190012yes—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—432no—
585C4⋊C4—861no—
586C4⋊C4—861no—
587C4⋊C4—861no—
588C4⋊C4—861no—
589C4⋊C4—861no—
590C4⋊C4—1722no—
591C4⋊C4—1722no—
592C4⋊C4C2×C4×D4312yes—
593C22⋊C4—24no—
594C22⋊C4—42no—
595C22⋊C4—864no—
596C22⋊C4—1722no—
597C22⋊C4—1722no—
598C22⋊C4—1722no—
599C22⋊C4—1722no—
600C22⋊C4—1722no—
601C22⋊C4—1722no—
602C22⋊C4—1722no—
603C42—432no—
604C42—432no—
605C42—862no—
606C42—862no—
607C42—861no—
608C42—861no—
609C42—1722no—
610C42—1722no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—22no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—862no—
625C23—1721no—
626C23—1721no—
627C23—1721no—
628C23—1721no—
629C23—1721no—
630C23—1721no—
631C23(C22⋊D43)⋊C412yes—
632C23C2×D4×D4311yescharacteristic
633D4—22no—
634D4—22no—
635D4—48no—
636D4—41no—
637D4—41no—
638D4—862no—
639D4—862no—
640D4—1728no—
641D4—1721no—
642D4—1721no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—432no—
659C2×C4—432no—
660C2×C4—432no—
661C2×C4—432no—
662C2×C4—861no—
663C2×C4—861no—
664C2×C4—862no—
665C2×C4—861no—
666C2×C4—861no—
667C2×C4—861no—
668C2×C4—861no—
669C2×C4—861no—
670C2×C4—861no—
671C2×C4—3444no—
672C2×C4—3444no—
673C2×C4—1724no—
674C2×C4—1724no—
675C2×C4—1721no—
676C2×C4—1721no—
677C2×C4—1721no—
678C2×C4—1721no—
679C2×C4—1721no—
680C2×C4—1721no—
681C2×C4—1721no—
682C2×C4—1721no—
683C2×C4(C22⋊D43)⋊C412yes—
684C2×C4C22×C4×D4311yescharacteristic
685C2×C4C2×D4×D4311yescharacteristic
686C2×C4#41×D4311yescharacteristic
687C2×C4#41×D4311yescharacteristic
688C2×C4C2×#1062190011yescharacteristic
689C2×C4C2×#1062190011yescharacteristic
690C8—22no—
691C8—22no—
692C8—434no—
693C8—862no—
694C22—22no—
695C22—22no—
696C22—22no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—41no—
701C22—42no—
702C22—42no—
703C22—42no—
704C22—81no—
705C22—81no—
706C22—81no—
707C22—81no—
708C22—3441no—
709C22—3441no—
710C22—3441no—
711C22—3441no—
712C22—1722no—
713C22—1722no—
714C22—1722no—
715C22C2×(C22⋊D43)⋊C411yescharacteristic
716C22#121×D4311yescharacteristic
717C22#1458344411yescharacteristic
718C22AGL(1,ℤ/8)×D4311yescharacteristic
719C22AGL(1,ℤ/8)×D4311yescharacteristic
720C22#1458369511yescharacteristic
721C22#1458369811yescharacteristic
722C4—22no—
723C4—42no—
724C4—81no—
725C4—81no—
726C4—434no—
727C4—862no—
728C4—3441no—
729C4—3441no—
730C4—1721no—
731C4—1722no—
732C4—1721no—
733C4C4×D4×D4311yescharacteristic
734C4C4×#1062190011yescharacteristic
735C4#1458340511yescharacteristic
736C4#1458342611yescharacteristic
737C2—42no—
738C2—82no—
739C2—3442no—
740C2#1913710511yescharacteristic
741C2#1914339911yescharacteristic
742C2#1914340811yescharacteristic
743C2#469×D4311yescharacteristic
744C2#1914419911yescharacteristic
745C2#1914518311yescharacteristic
746C2#1914518511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1895C2
socleC23×C43C22×D4
prime radicalC2×#14583150C2
cosocleC22×C4×C43C24
hypercenter#1895D43
hypocenterC43C4×#469
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1895

Complements

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

NH ≅ G/Ntype
2. C2×#14582979C2semidirect
3. C2×M16×Dic43C2semidirect
4. #121×Dic43C2semidirect
5. #19137101C2semidirect
6. #19135468C2semidirect
7. #19135337C2semidirect
8. #19135293C2semidirect
9. #19135289C2semidirect
10. #19135033C2semidirect
11. #19134626C2semidirect
12. #19134483C2semidirect
13. #102×Dic43C2semidirect
14. #19134409C2semidirect
15. C43×#1895C2semidirect
24. #14583150C4semidirect
70. C2×#10621882C2×C4semidirect
73. C2×#10621877C2×C4semidirect
77. #13063299C2×C4semidirect
107. #13063256C2×C4semidirect
110. #13063246C2×C4semidirect
111. #13063245C2×C4semidirect
115. C8×Dic43D4semidirect
130. #121×C43C2×C4semidirect
319. C43⋊C8C4×D4semidirect
363. Dic43#469semidirect
374. #1895D43semidirect
435. C43C4×#469semidirect
461. #121C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145831502
C2×#145829792
C2×M16×Dic432
#121×Dic432
#191371012
#191354682
#191353372
#191352932
#191352892
#191350332
#191346262
#191344832
#102×Dic432
#191344092
C43×#18952
C4×#46943