Finite Group Databasebeta

← #25113692

Subgroups — #25113692

Order 11008.

1178 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#102×D43C211yesmaximal, characteristic
2#19137471C211yesmaximal, characteristic, complemented
3D4×(C2×D43)⋊C4C211yesmaximal, characteristic
4#19135293C211yesmaximal, characteristic, complemented
5#19135291C211yesmaximal, characteristic, complemented
6#19135216C211yesmaximal, characteristic, complemented
7#19135214C211yesmaximal, characteristic, complemented
8#19134844C211yesmaximal, characteristic, complemented
9#19134684C211yesmaximal, characteristic, complemented
10#19134621C211yesmaximal, characteristic, complemented
11#19134524C211yesmaximal, characteristic
12#19134422C211yesmaximal, characteristic, complemented
13#19134420C211yesmaximal, characteristic, complemented
14#19134370C211yesmaximal, characteristic, complemented
15C43×#1862C211yesmaximal, characteristic, complemented
16C22×D4×D43C2211yescharacteristic
17C22×C8×D43C2211yescharacteristic
18C2×D4×Dic43C2211yescharacteristic
19C2×C4⋊C4×D43C2211yescharacteristic
20C22×(C2×D43)⋊C4—21no—
21C2×#13063259C2211yescharacteristic, complemented
22C2×#13063247C2211yescharacteristic
23C2×#13063247C2211yescharacteristic
24C2×#13063246C2211yescharacteristic
25C2×#13063246C2211yescharacteristic
26C2×#13063245C2211yescharacteristic
27C2×#13063245C2211yescharacteristic
28#102×D43C418yescomplemented
29C2×(C2×D43)⋊C8C2211yescharacteristic
30C2×#13063236C2211yescharacteristic, complemented
31C2×#13063235C2211yescharacteristic, complemented
32#14582801C2211yescharacteristic
33#14582800C2211yescharacteristic
34#14582798C2211yescharacteristic, complemented
35#14582786—21no—
36#14582780—21no—
37#14582778—21no—
38#14582776—21no—
39#14582756—21no—
40#14582756C2211yescharacteristic
41#14582756C2211yescharacteristic
42#14582754—21no—
43C4⋊C4×Dic43C2211yescharacteristic, complemented
44C4×C4⋊Dic43C2211yescharacteristic, complemented
45C4×(C2×D43)⋊C4C2211yescharacteristic
46#14582746—21no—
47#14582662C2211yescharacteristic, complemented
48#14582661C2211yescharacteristic, complemented
49#14582661C2211yescharacteristic, complemented
50#14582661C2211yescharacteristic, complemented
51#14582661C2211yescharacteristic, complemented
52#14582653C2211yescharacteristic, complemented
53C2×C4×D4×C43C2211yescharacteristic
54C2×#107×C43C2211yescharacteristic, complemented
55C2×#102×C43C2211yescharacteristic
56C2×#102×C43C2211yescharacteristic
57C43×#389C2211yescharacteristic, complemented
58C43×#340C2211yescharacteristic, complemented
59C43×#336C2211yescharacteristic, complemented
60C24×D43—21no—
61C22×D172C2311yescharacteristic
62C22×C22⋊D43—21no—
63C2×D4×D43—22no—
64C2×D4×D43—22no—
65C2×D4×D43—22no—
66C2×D4×D43—41no—
67C2×D4×D43—41no—
68C2×D4×D43C2×C414yes—
69C23×Dic43—21no—
70C22×C4×D43—21no—
71C22×C4×D43C2311yescharacteristic
72C22×C43⋊C8C2311yescharacteristic
73C22×C43⋊C8C2311yescharacteristic
74C2×C8×D43—41no—
75C2×C8×D43—41no—
76C2×C8×D43C2×C414yescomplemented
77D4×Dic43—22no—
78D4×Dic43—41no—
79C2×C4⋊Dic43—21no—
80C2×C4⋊Dic43C2311yescharacteristic
81C2×C4⋊Dic43C2311yescharacteristic
82C2×C4⋊Dic43C2311yescharacteristic
83C2×Dic43⋊C4—21no—
84C4⋊C4×D43—22no—
85C4⋊C4×D43C2×C414yescomplemented
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—
93C2×(C2×D43)⋊C4—44no—
94C2×(C2×D43)⋊C4D411yescharacteristic
95C2×(C2×D43)⋊C4D411yescharacteristic
96C2×C4×Dic43—21no—
97C2×C4×Dic43—21no—
98C2×C4×Dic43C2311yescharacteristic
99#13063259—41no—
100#13063247—41no—
101#13063247C2×C414yescomplemented
102#13063246—22no—
103#13063246C2×C414yes—
104#13063245—41no—
105#13063245C2×C414yescomplemented
106(C2×D43)⋊C8—22no—
107#13063236—41no—
108#13063235—41no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C43⋊#95—21no—
114C43⋊#95D411yescharacteristic
115C43⋊#95D411yescharacteristic
116C22×D4×C43C2311yescharacteristic
117C23×C4×C43—21no—
118C22×C8×C43C2311yescharacteristic
119C22×C8×C43C2311yescharacteristic
120C4×D4×C43—22no—
121C4×D4×C43—41no—
122C2×C4⋊C4×C43—21no—
123C2×C4⋊C4×C43C2311yescharacteristic
124C2×C4⋊C4×C43C2311yescharacteristic
125C2×C4⋊C4×C43C2311yescharacteristic
126C2×C22⋊C4×C43—21no—
127C2×C42×C43C2311yescharacteristic
128#107×C43—41no—
129#102×C43—22no—
130#102×C43C2×C414yes—
131#95×C43—21no—
132C24×C43—21no—
133C23×D43—21no—
134C23×D43—24no—
135C23×D43—42no—
136C23×D43—42no—
137C23×D43—42no—
138C23×D43—42no—
139C23×D43—81no—
140C23×D43—81no—
141C23×D43C2×D411yescharacteristic
142C2×D4×C43—21no—
143C2×D4×C43—21no—
144C2×D4×C43—21no—
145C2×D4×C43C22×C412yes—
146C2×D4×C43#4112yes—
147C2×D4×C43#4112yes—
148C22×C4×C43—21no—
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43—42no—
152C22×C4×C43—42no—
153C22×C4×C43—81no—
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43C2×D411yescharacteristic
156C22×C4×C43C2411yescharacteristic
157C2×C22⋊D43—24no—
158C2×C22⋊D43—42no—
159C2×C22⋊D43—42no—
160C22×Dic43—21no—
161C22×Dic43—21no—
162C22×Dic43—21no—
163C22×Dic43—42no—
164C22×Dic43—42no—
165C22×Dic43—81no—
166C22×Dic43C2×D411yescharacteristic
167C22×Dic43C2×D411yescharacteristic
168C22×Dic43C2×D411yescharacteristic
169D4×D43—28no—
170D4×D43—44no—
171D4×D43—44no—
172D4×D43—44no—
173C2×D172—21no—
174C2×D172—21no—
175C2×D172—21no—
176C2×D172—21no—
177C2×D172—21no—
178C2×D172C22×C412yes—
179C2×C4×D43—21no—
180C2×C4×D43—21no—
181C2×C4×D43—21no—
182C2×C4×D43—21no—
183C2×C4×D43—24no—
184C2×C4×D43—81no—
185C2×C4×D43—81no—
186C2×C4×D43C22×C412yes—
187C2×C4×D43#4112yes—
188C2×C8×C43—21no—
189C2×C8×C43—21no—
190C2×C8×C43—21no—
191C2×C8×C43—21no—
192C2×C8×C43—21no—
193C2×C8×C43C22×C412yes—
194C4⋊C4×C43—21no—
195C4⋊C4×C43—21no—
196C4⋊C4×C43—21no—
197C4⋊C4×C43—21no—
198C4⋊C4×C43—21no—
199C4⋊C4×C43—81no—
200C4⋊C4×C43C22×C412yes—
201C22⋊C4×C43—42no—
202C42×C43—21no—
203C42×C43—21no—
204C22⋊Dic43—42no—
205(C2×D43)⋊C4—22no—
206(C2×D43)⋊C4—22no—
207(C2×D43)⋊C4—42no—
208(C2×D43)⋊C4—42no—
209(C2×D43)⋊C4—42no—
210(C2×D43)⋊C4—42no—
211(C2×D43)⋊C4—81no—
212(C2×D43)⋊C4—81no—
213C4⋊Dic43—21no—
214C4⋊Dic43—21no—
215C4⋊Dic43—21no—
216C4⋊Dic43—21no—
217C4⋊Dic43—21no—
218C4⋊Dic43—81no—
219C4⋊Dic43C22×C412yes—
220Dic43⋊C4—24no—
221C4×Dic43—21no—
222C4×Dic43—21no—
223C4×Dic43—81no—
224C4×Dic43—81no—
225C2×C43⋊C8—21no—
226C2×C43⋊C8—21no—
227C2×C43⋊C8—21no—
228C2×C43⋊C8—21no—
229C2×C43⋊C8—21no—
230C2×C43⋊C8C22×C412yes—
231C8×D43—44no—
232C23×C43—22no—
233C23×C43—22no—
234C23×C43—22no—
235C23×C43—41no—
236C23×C43—41no—
237C23×C43—41no—
238C23×C43—41no—
239C23×C43C22×D411yescharacteristic
240C22×D43—21no—
241C22×D43—21no—
242C22×D43—21no—
243C22×D43—21no—
244C22×D43—22no—
245C22×D43—48no—
246C22×D43—41no—
247C22×D43—41no—
248C22×D43—41no—
249C22×D43—41no—
250C22×D43—41no—
251C22×D43—41no—
252C22×D43—48no—
253C22×D43—84no—
254C22×D43—84no—
255C22×D43—84no—
256C22×D43—84no—
257C22×D43—84no—
258C22×D43C4×D412yes—
259C22×D43AGL(1,ℤ/8)12yes—
260C22×D43#13712yes—
261D4×C43—22no—
262D4×C43—22no—
263D4×C43—22no—
264D4×C43#11714yes—
265C2×C4×C43—22no—
266C2×C4×C43—21no—
267C2×C4×C43—21no—
268C2×C4×C43—21no—
269C2×C4×C43—21no—
270C2×C4×C43—21no—
271C2×C4×C43—21no—
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×C43—41no—
280C2×C4×C43—84no—
281C2×C4×C43C23×C411yescharacteristic
282C2×C4×C43C2×#4111yescharacteristic
283C2×C4×C43C2×#4111yescharacteristic
284C2×C4×C43C2×#4111yescharacteristic
285C2×C4×C43H(5,𝔽2)11yescharacteristic
286C2×C4×C43H(5,𝔽2)11yescharacteristic
287C22⋊D43—48no—
288C2×Dic43—21no—
289C2×Dic43—21no—
290C2×Dic43—22no—
291C2×Dic43—21no—
292C2×Dic43—21no—
293C2×Dic43—21no—
294C2×Dic43—21no—
295C2×Dic43—21no—
296C2×Dic43—21no—
297C2×Dic43—41no—
298C2×Dic43—41no—
299C2×Dic43—41no—
300C2×Dic43—41no—
301C2×Dic43—41no—
302C2×Dic43—41no—
303C2×Dic43—41no—
304C2×Dic43—41no—
305C2×Dic43—84no—
306C2×Dic43C4×D412yes—
307D172—22no—
308D172—22no—
309D172—41no—
310D172—41no—
311C4×D43—22no—
312C4×D43—22no—
313C4×D43—22no—
314C4×D43—22no—
315C4×D43—84no—
316C8×C43—22no—
317C8×C43—41no—
318C43⋊C8—22no—
319C43⋊C8—41no—
320#22566—431nomaximal, Sylow
321C22×C43—24no—
322C22×C43—42no—
323C22×C43—42no—
324C22×C43—42no—
325C22×C43—42no—
326C22×C43—42no—
327C22×C43—42no—
328C22×C43C2×C4×D411yescharacteristic
329C22×C43#54611yescharacteristic
330C22×C43#54611yescharacteristic
331C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
332C22×C43C2×#13711yescharacteristic
333C22×C43#57611yescharacteristic
334C22×C43#57611yescharacteristic
335C2×D43—22no—
336C2×D43—22no—
337C2×D43—22no—
338C2×D43—22no—
339C2×D43—22no—
340C2×D43—22no—
341C2×D43—42no—
342C2×D43—42no—
343C2×D43—42no—
344C2×D43—816no—
345C2×D43—81no—
346C2×D43—81no—
347C2×D43—81no—
348C2×D43—81no—
349C2×D43#44014yes—
350C4×C43—42no—
351C4×C43—41no—
352C4×C43—41no—
353C4×C43—81no—
354C4×C43—81no—
355C4×C43C2×#11711yescharacteristic
356C4×C43#51811yescharacteristic
357C4×C43#55111yescharacteristic
358C4×C43#55111yescharacteristic
359Dic43—22no—
360Dic43—42no—
361Dic43—41no—
362Dic43—41no—
363Dic43—81no—
364Dic43—81no—
365C22×#102—431no—
366#2345—431no—
367D4×C22⋊C4—431no—
368#1936—431no—
369#1936—431no—
370#1925—431no—
371#1925—431no—
372#1862—431no—
373#1862D4311yescharacteristic, complemented
374#1824—431no—
375#1808—431no—
376#1786—431no—
377#1762—431no—
378#1762—431no—
379#1752—431no—
380C2×C43—44no—
381C2×C43#234211yescharacteristic
382C2×C43C2×#44011yescharacteristic
383C2×C43#294811yescharacteristic
384C2×C43#331411yescharacteristic
385C2×C43#331411yescharacteristic
386C2×C43#331811yescharacteristic
387C2×C43#331811yescharacteristic
388D43—24no—
389D43—82no—
390C23×D4—431no—
391C23×C8—431no—
392C2×C4×D4—431no—
393C2×C4×D4C2×D4311yescharacteristic
394C22×C4⋊C4—431no—
395C22×C22⋊C4—861no—
396C2×#107—431no—
397C2×#107C2×D4311yescharacteristic, complemented
398C2×#102—431no—
399C2×#102—431no—
400C2×#102—431no—
401C2×#102—438no—
402C2×#102—431no—
403C2×#102—431no—
404C2×#102—431no—
405C2×#102C2×D4311yescharacteristic
406C2×#102C2×D4311yescharacteristic
407C2×C22⋊C8—431no—
408C2×#97—431no—
409C2×#97—431no—
410#390—431no—
411#390—431no—
412#389—431no—
413#389C2×D4311yescharacteristic, complemented
414#387—861no—
415#387—861no—
416#386—861no—
417#386—861no—
418#380—431no—
419#380—431no—
420#380—861no—
421#379—861no—
422C4×C4⋊C4—431no—
423C4×C4⋊C4—431no—
424C4×C22⋊C4—431no—
425C4×C22⋊C4—861no—
426#340—431no—
427#340—431no—
428#340—431no—
429#340—431no—
430#340—431no—
431#340C2×D4311yescharacteristic, complemented
432#336—431no—
433#336C2×D4311yescharacteristic, complemented
434C43#2256611yescharacteristic, complemented, Sylow
435C25—861no—
436C22×D4—434no—
437C22×D4—431no—
438C22×D4—862no—
439C22×D4—861no—
440C22×D4—862no—
441C22×D4—862no—
442C22×D4—1721no—
443C22×D4—1721no—
444C22×D4C22×D4311yescharacteristic
445C23×C4—21no—
446C23×C4—431no—
447C23×C4—861no—
448C23×C4—861no—
449C22×C8—431no—
450C22×C8—434no—
451C22×C8—431no—
452C22×C8—1721no—
453C22×C8—1721no—
454C22×C8C22×D4311yescharacteristic
455C22×C8C22×D4311yescharacteristic
456C4×D4—22no—
457C4×D4—41no—
458C4×D4—862no—
459C4×D4—1721no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4—431no—
462C2×C4⋊C4—434no—
463C2×C4⋊C4—431no—
464C2×C4⋊C4—431no—
465C2×C4⋊C4—862no—
466C2×C4⋊C4—861no—
467C2×C4⋊C4—861no—
468C2×C4⋊C4C22×D4311yescharacteristic
469C2×C4⋊C4C22×D4311yescharacteristic
470C2×C4⋊C4C22×D4311yescharacteristic
471C2×C22⋊C4—21no—
472C2×C22⋊C4—431no—
473C2×C22⋊C4—431no—
474C2×C22⋊C4—861no—
475C2×C22⋊C4—861no—
476C2×C22⋊C4—861no—
477C2×C22⋊C4—861no—
478C2×C22⋊C4—861no—
479C2×C22⋊C4—861no—
480C2×C22⋊C4—861no—
481C2×C22⋊C4—1724no—
482C2×C42—431no—
483C2×C42—861no—
484C2×C42—861no—
485C2×C42C22×D4311yescharacteristic
486#107—41no—
487#107—1721no—
488#102—22no—
489#102—434no—
490#102—434no—
491#102—434no—
492#102—862no—
493#102—1721no—
494#102—1721no—
495#102C4×D4314yes—
496C22⋊C8—862no—
497#97—1721no—
498#97—1721no—
499#95—21no—
500#95—431no—
501#95—431no—
502#95—861no—
503#95—861no—
504#95—861no—
505#95—861no—
506#95—861no—
507C24—21no—
508C24—431no—
509C24—864no—
510C24—861no—
511C24—3441no—
512C24—3441no—
513C24—1722no—
514C24—1722no—
515C24—1722no—
516C24—1722no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—432no—
521C2×D4—864no—
522C2×D4—868no—
523C2×D4—861no—
524C2×D4—861no—
525C2×D4—861no—
526C2×D4—861no—
527C2×D4—861no—
528C2×D4—1724no—
529C2×D4—1724no—
530C2×D4—1724no—
531C2×D4—1722no—
532C2×D4—1722no—
533C2×D4C2×C4×D4312yes—
534C2×D4#1062190012yes—
535C2×D4#1062190212yes—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—42no—
540C22×C4—42no—
541C22×C4—81no—
542C22×C4—431no—
543C22×C4—432no—
544C22×C4—432no—
545C22×C4—431no—
546C22×C4—431no—
547C22×C4—864no—
548C22×C4—861no—
549C22×C4—861no—
550C22×C4—861no—
551C22×C4—861no—
552C22×C4—861no—
553C22×C4—861no—
554C22×C4—861no—
555C22×C4—3441no—
556C22×C4—3441no—
557C22×C4—3441no—
558C22×C4—1722no—
559C22×C4—1722no—
560C22×C4D4×D4311yescharacteristic
561C22×C4D4×D4311yescharacteristic
562C22×C4C23×D4311yescharacteristic
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—432no—
569C2×C8—861no—
570C2×C8—861no—
571C2×C8—861no—
572C2×C8—861no—
573C2×C8—861no—
574C2×C8—1724no—
575C2×C8C2×C4×D4312yes—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—81no—
582C4⋊C4—432no—
583C4⋊C4—864no—
584C4⋊C4—861no—
585C4⋊C4—861no—
586C4⋊C4—861no—
587C4⋊C4—861no—
588C4⋊C4—861no—
589C4⋊C4—3441no—
590C4⋊C4C2×C4×D4312yes—
591C22⋊C4—42no—
592C22⋊C4—862no—
593C22⋊C4—862no—
594C22⋊C4—3441no—
595C22⋊C4—3441no—
596C22⋊C4—1722no—
597C22⋊C4—1722no—
598C22⋊C4—1722no—
599C22⋊C4—1722no—
600C22⋊C4—1722no—
601C42—21no—
602C42—21no—
603C42—861no—
604C42—861no—
605C42—3441no—
606C42—3441no—
607C23—22no—
608C23—22no—
609C23—22no—
610C23—41no—
611C23—41no—
612C23—41no—
613C23—41no—
614C23—432no—
615C23—432no—
616C23—432no—
617C23—861no—
618C23—861no—
619C23—861no—
620C23—861no—
621C23—862no—
622C23—3444no—
623C23—3444no—
624C23—3444no—
625C23—3444no—
626C23—3444no—
627C23—1728no—
628C23—1728no—
629C23—1721no—
630C23—1721no—
631C23—1721no—
632C23—1721no—
633C23—1721no—
634C23—1721no—
635C23C2×D4×D4311yescharacteristic
636D4—22no—
637D4—22no—
638D4—22no—
639D4—862no—
640D4—862no—
641D4—1728no—
642D4—1721no—
643D4—1721no—
644D4#1306328314yes—
645C2×C4—22no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—84no—
661C2×C4—432no—
662C2×C4—861no—
663C2×C4—861no—
664C2×C4—862no—
665C2×C4—862no—
666C2×C4—862no—
667C2×C4—862no—
668C2×C4—862no—
669C2×C4—861no—
670C2×C4—861no—
671C2×C4—861no—
672C2×C4—861no—
673C2×C4—861no—
674C2×C4—861no—
675C2×C4—3444no—
676C2×C4—3444no—
677C2×C4—1721no—
678C2×C4—1721no—
679C2×C4—1721no—
680C2×C4—1721no—
681C2×C4—1721no—
682C2×C4—1721no—
683C2×C4—1721no—
684C2×C4—1721no—
685C2×C4C22×C4×D4311yescharacteristic
686C2×C4#41×D4311yescharacteristic
687C2×C4C2×#1062190011yescharacteristic
688C2×C4C2×#1062190211yescharacteristic
689C2×C4#1306337011yescharacteristic
690C2×C4#1306337111yescharacteristic
691C8—22no—
692C8—41no—
693C8—862no—
694C8—1721no—
695C22—24no—
696C22—42no—
697C22—42no—
698C22—42no—
699C22—42no—
700C22—42no—
701C22—42no—
702C22—434no—
703C22—862no—
704C22—862no—
705C22—862no—
706C22—862no—
707C22—862no—
708C22—862no—
709C22—34416no—
710C22—3441no—
711C22—3441no—
712C22—3441no—
713C22—3441no—
714C22—1722no—
715C22—1722no—
716C22—1722no—
717C22C4×D4×D4311yescharacteristic
718C22#1458353611yescharacteristic
719C22#1458354011yescharacteristic
720C22AGL(1,ℤ/8)×D4311yescharacteristic
721C22#137×D4311yescharacteristic
722C22#1458370011yescharacteristic
723C22#1458370111yescharacteristic
724C4—42no—
725C4—41no—
726C4—41no—
727C4—81no—
728C4—81no—
729C4—862no—
730C4—3441no—
731C4—3441no—
732C4—1722no—
733C4—1721no—
734C4—1721no—
735C4C2×#1306328311yescharacteristic
736C4#1458337111yescharacteristic
737C4#1458357211yescharacteristic
738C4#1458357611yescharacteristic
739C2—44no—
740C2—864no—
741C2—3442no—
742C2#1913744211yescharacteristic
743C2#440×D4311yescharacteristic
744C2#1914344211yescharacteristic
745C2#1914666911yescharacteristic
746C2#1914667311yescharacteristic
747C2#1914672911yescharacteristic
748C2#1914673311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1862C2
socleC23×C43C22×D4
prime radicalC22×D4×D43C22
cosocleC22×C4×C43C24
hypercenter#1862D43
hypocenterC43#22566
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1862

Complements

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

NH ≅ G/Ntype
2. #19137471C2semidirect
4. #19135293C2semidirect
5. #19135291C2semidirect
6. #19135216C2semidirect
7. #19135214C2semidirect
8. #19134844C2semidirect
9. #19134684C2semidirect
10. #19134621C2semidirect
12. #19134422C2semidirect
13. #19134420C2semidirect
14. #19134370C2semidirect
15. C43×#1862C2semidirect
21. C2×#13063259C22semidirect
28. #102×D43C4semidirect
30. C2×#13063236C22semidirect
31. C2×#13063235C22semidirect
34. #14582798C22semidirect
43. C4⋊C4×Dic43C22semidirect
44. C4×C4⋊Dic43C22semidirect
47. #14582662C22semidirect
48. #14582661C22semidirect
49. #14582661C22semidirect
50. #14582661C22semidirect
51. #14582661C22semidirect
52. #14582653C22semidirect
54. C2×#107×C43C22semidirect
57. C43×#389C22semidirect
58. C43×#340C22semidirect
59. C43×#336C22semidirect
76. C2×C8×D43C2×C4semidirect
85. C4⋊C4×D43C2×C4semidirect
101. #13063247C2×C4semidirect
105. #13063245C2×C4semidirect
373. #1862D43semidirect
397. C2×#107C2×D43semidirect
413. #389C2×D43semidirect
431. #340C2×D43semidirect
433. #336C2×D43semidirect
434. C43#22566semidirect

Maximal subgroups

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

subgroupindex
C2×#102×D432
#191374712
D4×(C2×D43)⋊C42
#191352932
#191352912
#191352162
#191352142
#191348442
#191346842
#191346212
#191345242
#191344222
#191344202
#191343702
C43×#18622
#2256643