Finite Group Databasebeta

← #25113857

Subgroups — #25113857

Order 11008.

1150 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582903C211yesmaximal, characteristic
2C22⋊C4×D172C211yesmaximal, characteristic
3#19135291C211yesmaximal, characteristic, complemented
4#19135277C211yesmaximal, characteristic, complemented
5#19135222C211yesmaximal, characteristic, complemented
6#19135215C211yesmaximal, characteristic, complemented
7#19134855C211yesmaximal, characteristic, complemented
8#19134841C211yesmaximal, characteristic, complemented
9#19134690C211yesmaximal, characteristic, complemented
10#19134626C211yesmaximal, characteristic, complemented
11#19134525C211yesmaximal, characteristic
12#19134423C211yesmaximal, characteristic, complemented
13C4×#13063245C211yesmaximal, characteristic, complemented
14#19134379C211yesmaximal, characteristic, complemented
15C43×#2347C211yesmaximal, characteristic, complemented
16C23×D172C2211yescharacteristic
17C22×#10621877C2211yescharacteristic
18C2×C4×D172C2211yescharacteristic
19C2×C4×D172C2211yescharacteristic
20C2×C22⋊C4×D43—21no—
21C2×#13063258C2211yescharacteristic, complemented
22C2×#13063256C2211yescharacteristic, complemented
23#14582903C418yescomplemented
24C2×#13063245C2211yescharacteristic
25C2×#13063245C2211yescharacteristic
26C2×#13063245C2211yescharacteristic
27C2×#13063245C2211yescharacteristic
28C2×#13063245C2211yescharacteristic
29C2×#13063245C2211yescharacteristic
30C2×#13063245C2211yescharacteristic
31C2×#13063245C2211yescharacteristic
32C2×C22⋊(C43⋊C8)C2211yescharacteristic
33C2×#13063236C2211yescharacteristic, complemented
34C2×C4×C43⋊C8C2211yescharacteristic, complemented
35#14582801C2211yescharacteristic
36#14582801C2211yescharacteristic
37#14582777—21no—
38#14582777—21no—
39#14582759C2211yescharacteristic
40#14582754—21no—
41#14582661C2211yescharacteristic, complemented
42#14582661C2211yescharacteristic, complemented
43#14582661C2211yescharacteristic, complemented
44#14582661C2211yescharacteristic, complemented
45#14582661C2211yescharacteristic, complemented
46#14582661C2211yescharacteristic, complemented
47#14582654C2211yescharacteristic, complemented
48#14582654C2211yescharacteristic, complemented
49C2×#117×C43C2211yescharacteristic
50C43×#389C2211yescharacteristic, complemented
51C43×#389C2211yescharacteristic, complemented
52C43×#388—21no—
53C43×#388—21no—
54C43×#383—21no—
55C43×#380C2211yescharacteristic
56C4×C4⋊C4×C43—21no—
57C4×C4⋊C4×C43C2211yescharacteristic, complemented
58C4×C4⋊C4×C43C2211yescharacteristic, complemented
59C4×C22⋊C4×C43C2211yescharacteristic
60C24×D43—21no—
61C22×D172—22no—
62C22×D172—22no—
63C22×D172—21no—
64C22×D172—22no—
65C22×D172—41no—
66C22×D172—41no—
67C22×D172C2×C414yes—
68C22×D172C2311yescharacteristic
69C22×D172C2311yescharacteristic
70C22×C4×D43—21no—
71C22×C4×D43—21no—
72C2×#10621877—41no—
73C2×#10621877—41no—
74C2×#10621877C2×C414yescomplemented
75C22×C43⋊C8C2311yescharacteristic
76C22×C43⋊C8C2311yescharacteristic
77C22×C43⋊C8C2311yescharacteristic
78C22×C43⋊C8C2311yescharacteristic
79C4×D172—22no—
80C4×D172—22no—
81C4×D172—41no—
82C4×D172—41no—
83C2×C4⋊Dic43C2311yescharacteristic
84C2×C4⋊Dic43C2311yescharacteristic
85C2×C22⋊Dic43—21no—
86C2×(C2×D43)⋊C4—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—
92C22⋊C4×D43—44no—
93#13063258—41no—
94#13063256—41no—
95#13063245—22no—
96#13063245—22no—
97#13063245—41no—
98#13063245—41no—
99#13063245C2×C414yes—
100#13063245C2×C414yes—
101#13063245C2×C414yescomplemented
102#13063245C2×C414yescomplemented
103C22⋊(C43⋊C8)—22no—
104#13063236—41no—
105C4×C43⋊C8—41no—
106C43⋊#95—21no—
107C23×C4×C43C2311yescharacteristic
108#117×C43—22no—
109#117×C43C2×C414yescomplemented
110C2×C4⋊C4×C43—21no—
111C2×C4⋊C4×C43—21no—
112C2×C4⋊C4×C43C2311yescharacteristic
113C2×C4⋊C4×C43C2311yescharacteristic
114C2×C4⋊C4×C43C2311yescharacteristic
115C2×C4⋊C4×C43C2311yescharacteristic
116C2×C22⋊C4×C43—21no—
117C2×C22⋊C4×C43—21no—
118C2×C22⋊C4×C43D411yescharacteristic
119C2×C22⋊C4×C43D411yescharacteristic
120C2×C42×C43—21no—
121C2×C42×C43—21no—
122C2×C42×C43—21no—
123C2×C42×C43C2311yescharacteristic
124C2×C42×C43C2311yescharacteristic
125#95×C43—21no—
126#95×C43—21no—
127#95×C43—21no—
128#95×C43—21no—
129#95×C43—21no—
130#95×C43D411yescharacteristic
131#95×C43D411yescharacteristic
132C24×C43C2×D411yescharacteristic
133C23×D43—21no—
134C23×D43—21no—
135C23×D43—24no—
136C23×D43—42no—
137C23×D43—42no—
138C23×D43—42no—
139C23×D43—42no—
140C23×D43—81no—
141C23×D43—81no—
142C22×C4×C43—21no—
143C22×C4×C43—21no—
144C22×C4×C43—21no—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43—21no—
148C22×C4×C43—21no—
149C22×C4×C43—21no—
150C22×C4×C43C22×C412yes—
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43C2×D411yescharacteristic
156C22×C4×C43#4112yes—
157C22×C4×C43C2411yescharacteristic
158C22×Dic43—21no—
159C22×Dic43—21no—
160C2×D172—21no—
161C2×D172—21no—
162C2×D172—21no—
163C2×D172—24no—
164C2×D172—21no—
165C2×D172—21no—
166C2×D172—21no—
167C2×D172—21no—
168C2×D172—21no—
169C2×D172—28no—
170C2×D172—42no—
171C2×D172—42no—
172C2×D172—44no—
173C2×D172—44no—
174C2×D172—44no—
175C2×D172C22×C412yes—
176C2×D172C22×C412yes—
177C2×D172#4112yes—
178C2×D172#4112yes—
179C2×C4×D43—42no—
180C2×C4×D43—42no—
181C2×C4×D43—42no—
182C2×C4×D43—42no—
183C2×C4×D43—81no—
184C2×C4×D43—81no—
185C4⋊C4×C43—21no—
186C4⋊C4×C43—21no—
187C4⋊C4×C43—21no—
188C4⋊C4×C43—21no—
189C4⋊C4×C43—21no—
190C4⋊C4×C43—21no—
191C4⋊C4×C43—42no—
192C4⋊C4×C43—42no—
193C4⋊C4×C43C22×C412yes—
194C4⋊C4×C43C22×C412yes—
195C22⋊C4×C43—22no—
196C22⋊C4×C43—24no—
197C22⋊C4×C43—41no—
198C22⋊C4×C43—81no—
199C42×C43—24no—
200C42×C43—21no—
201C42×C43—21no—
202C42×C43—21no—
203C42×C43—21no—
204C42×C43—81no—
205C42×C43—81no—
206C22⋊Dic43—42no—
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—
217#10621877—44no—
218C2×C43⋊C8—21no—
219C2×C43⋊C8—21no—
220C2×C43⋊C8—21no—
221C2×C43⋊C8—21no—
222C2×C43⋊C8—21no—
223C2×C43⋊C8—21no—
224C2×C43⋊C8—21no—
225C2×C43⋊C8—21no—
226C2×C43⋊C8—21no—
227C2×C43⋊C8—21no—
228C2×C43⋊C8C22×C412yes—
229C2×C43⋊C8C22×C412yes—
230C23×C43—21no—
231C23×C43—21no—
232C23×C43—21no—
233C23×C43—21no—
234C23×C43—21no—
235C23×C43—21no—
236C23×C43C4×D412yes—
237C23×C43C22×D411yescharacteristic
238C22×D43—22no—
239C22×D43—22no—
240C22×D43—22no—
241C22×D43—22no—
242C22×D43—48no—
243C22×D43—41no—
244C22×D43—41no—
245C22×D43—41no—
246C22×D43—41no—
247C22×D43—48no—
248C22×D43—41no—
249C22×D43—41no—
250C22×D43—41no—
251C22×D43—41no—
252C22×D43—41no—
253C22×D43—41no—
254C22×D43—84no—
255C22×D43—84no—
256C22×D43—84no—
257C22×D43—84no—
258C22×D43—84no—
259C2×C4×C43—21no—
260C2×C4×C43—21no—
261C2×C4×C43—21no—
262C2×C4×C43—21no—
263C2×C4×C43—22no—
264C2×C4×C43—22no—
265C2×C4×C43—22no—
266C2×C4×C43—22no—
267C2×C4×C43—22no—
268C2×C4×C43—22no—
269C2×C4×C43—21no—
270C2×C4×C43—21no—
271C2×C4×C43—21no—
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—41no—
279C2×C4×C43—41no—
280C2×C4×C43—41no—
281C2×C4×C43—41no—
282C2×C4×C43—41no—
283C2×C4×C43—41no—
284C2×C4×C43—41no—
285C2×C4×C43—41no—
286C2×C4×C43—41no—
287C2×C4×C43—41no—
288C2×C4×C43C4×D412yes—
289C2×C4×C43AGL(1,ℤ/8)12yes—
290C2×C4×C43C23×C411yescharacteristic
291C2×C4×C43C2×#4111yescharacteristic
292C2×C4×C43C2×#4111yescharacteristic
293C2×C4×C43C2×#4111yescharacteristic
294C2×C4×C43H(5,𝔽2)11yescharacteristic
295C2×C4×C43H(5,𝔽2)11yescharacteristic
296C2×Dic43—41no—
297C2×Dic43—41no—
298C2×Dic43—41no—
299C2×Dic43—41no—
300C2×Dic43—41no—
301C2×Dic43—41no—
302D172—22no—
303D172—22no—
304D172—22no—
305D172—22no—
306D172—22no—
307D172—48no—
308D172—41no—
309D172—41no—
310D172#11714yes—
311C4×D43—84no—
312C4×D43—84no—
313C43⋊C8—22no—
314C43⋊C8—22no—
315C43⋊C8—41no—
316C43⋊C8—41no—
317#22580—431nomaximal, Sylow
318C22×C43—22no—
319C22×C43—22no—
320C22×C43—22no—
321C22×C43—41no—
322C22×C43—41no—
323C22×C43—41no—
324C22×C43—41no—
325C22×C43C2×C4×D411yescharacteristic
326C22×C43#54611yescharacteristic
327C22×C43#54611yescharacteristic
328C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
329C22×C43#57511yescharacteristic
330C22×C43#57611yescharacteristic
331C22×C43#57711yescharacteristic
332C2×D43—24no—
333C2×D43—42no—
334C2×D43—42no—
335C2×D43—42no—
336C2×D43—42no—
337C2×D43—42no—
338C2×D43—42no—
339C2×D43—42no—
340C2×D43—42no—
341C2×D43—42no—
342C2×D43—816no—
343C2×D43—81no—
344C2×D43—81no—
345C2×D43—81no—
346C2×D43—81no—
347C4×C43—22no—
348C4×C43—22no—
349C4×C43—42no—
350C4×C43—42no—
351C4×C43—41no—
352C4×C43—41no—
353C4×C43—41no—
354C4×C43—81no—
355C4×C43—81no—
356C4×C43C2×#11711yescharacteristic
357C4×C43#51811yescharacteristic
358C4×C43#55111yescharacteristic
359C4×C43#55111yescharacteristic
360Dic43—81no—
361Dic43—81no—
362C2×#418—431no—
363#2347D4311yescharacteristic, complemented
364D4×C22⋊C4—431no—
365#1936—431no—
366#1934—431no—
367#1926—431no—
368#1925—431no—
369#1864—431no—
370#1862—431no—
371#1825—431no—
372#1809—431no—
373#1786—431no—
374#1762—431no—
375C4×#102—431no—
376#1753—431no—
377C2×C43—42no—
378C2×C43#234211yescharacteristic
379C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
380C2×C43#294611yescharacteristic
381C2×C43#331111yescharacteristic
382C2×C43#331811yescharacteristic
383C2×C43#332211yescharacteristic
384C2×C43#332411yescharacteristic
385D43—44no—
386D43—82no—
387C23×D4—431no—
388C22×M16—431no—
389C2×C4×D4—431no—
390C2×C4×D4—431no—
391C2×#117C2×D4311yescharacteristic
392C22×C22⋊C4—861no—
393C2×#107—431no—
394C2×#106—431no—
395#418—438no—
396C2×#102—431no—
397C2×#102—431no—
398C2×#102—431no—
399C2×#102—431no—
400C2×#102—431no—
401C2×#102—431no—
402C2×#102—431no—
403C2×#102—431no—
404C2×C22⋊C8—431no—
405C2×#97—431no—
406C2×C4×C8—431no—
407#390—431no—
408#390—431no—
409#389C2×D4311yescharacteristic, complemented
410#389C2×D4311yescharacteristic, complemented
411#388—21no—
412#388—21no—
413#386—861no—
414#386—861no—
415#383—21no—
416#380—431no—
417#380C2×D4311yescharacteristic
418#379—861no—
419C4×C4⋊C4—21no—
420C4×C4⋊C4C2×D4311yescharacteristic, complemented
421C4×C4⋊C4C2×D4311yescharacteristic, complemented
422C4×C22⋊C4C2×D4311yescharacteristic
423#340—431no—
424#340—431no—
425#340—431no—
426#340—431no—
427#340—431no—
428#340—431no—
429#336—431no—
430#336—431no—
431C43#2258011yescharacteristic, complemented, Sylow
432C25—861no—
433C22×D4—434no—
434C22×D4—431no—
435C22×D4—431no—
436C22×D4—862no—
437C22×D4—862no—
438C22×D4—862no—
439C22×D4—861no—
440C22×D4—1721no—
441C22×D4—1721no—
442C23×C4—861no—
443C23×C4—861no—
444C23×C4C22×D4311yescharacteristic
445C2×M16—434no—
446C2×M16—1721no—
447C2×M16—1721no—
448C22×C8—431no—
449C22×C8—431no—
450C22×C8—431no—
451C22×C8—431no—
452C4×D4—862no—
453C4×D4—862no—
454C4×D4—1721no—
455C4×D4—1721no—
456#117—22no—
457#117C4×D4314yescomplemented
458C2×C4⋊C4—21no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4—431no—
461C2×C4⋊C4—431no—
462C2×C4⋊C4C22×D4311yescharacteristic
463C2×C4⋊C4C22×D4311yescharacteristic
464C2×C4⋊C4C22×D4311yescharacteristic
465C2×C4⋊C4C22×D4311yescharacteristic
466C2×C22⋊C4—21no—
467C2×C22⋊C4—21no—
468C2×C22⋊C4—861no—
469C2×C22⋊C4—861no—
470C2×C22⋊C4—861no—
471C2×C22⋊C4—861no—
472C2×C22⋊C4—861no—
473C2×C22⋊C4—861no—
474C2×C22⋊C4—861no—
475C2×C22⋊C4—1724no—
476C2×C22⋊C4C22⋊D4311yescharacteristic
477C2×C22⋊C4C22⋊D4311yescharacteristic
478C2×C42—21no—
479C2×C42—21no—
480C2×C42—21no—
481C2×C42C22×D4311yescharacteristic
482C2×C42C22×D4311yescharacteristic
483#107—1721no—
484#106—1721no—
485#102—434no—
486#102—434no—
487#102—434no—
488#102—434no—
489#102—862no—
490#102—862no—
491#102—1721no—
492#102—1721no—
493C22⋊C8—862no—
494#97—1721no—
495C4×C8—1721no—
496#95—21no—
497#95—21no—
498#95—21no—
499#95—21no—
500#95—21no—
501#95—861no—
502#95C22⋊D4311yescharacteristic
503#95C22⋊D4311yescharacteristic
504C24—861no—
505C24—864no—
506C24—861no—
507C24—3441no—
508C24—3441no—
509C24—1722no—
510C24—1722no—
511C24—1722no—
512C24—1722no—
513C24C2×C22⋊D4311yescharacteristic
514C2×D4—432no—
515C2×D4—432no—
516C2×D4—432no—
517C2×D4—432no—
518C2×D4—868no—
519C2×D4—864no—
520C2×D4—861no—
521C2×D4—861no—
522C2×D4—861no—
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—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—861no—
542C22×C4—861no—
543C22×C4—3441no—
544C22×C4—3441no—
545C22×C4—1722no—
546C22×C4—1722no—
547C22×C4—1722no—
548C22×C4—1722no—
549C22×C4C2×C4×D4312yes—
550C22×C4#1062189812yes—
551C22×C4C2×C22⋊D4311yescharacteristic
552C22×C4C2×C22⋊D4311yescharacteristic
553C22×C4C2×C22⋊D4311yescharacteristic
554C22×C4C2×C22⋊D4311yescharacteristic
555C22×C4C2×C22⋊D4311yescharacteristic
556C22×C4C23×D4311yescharacteristic
557M16—1724no—
558C2×C8—432no—
559C2×C8—432no—
560C2×C8—861no—
561C2×C8—861no—
562C2×C8—861no—
563C2×C8—861no—
564C2×C8—861no—
565C2×C8—861no—
566C2×C8—861no—
567C2×C8—861no—
568C2×C8—861no—
569C2×C8—861no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—42no—
577C4⋊C4—42no—
578C4⋊C4—861no—
579C4⋊C4—861no—
580C4⋊C4—861no—
581C4⋊C4—861no—
582C4⋊C4C2×C4×D4312yes—
583C4⋊C4C2×C4×D4312yes—
584C22⋊C4—24no—
585C22⋊C4—22no—
586C22⋊C4—41no—
587C22⋊C4—81no—
588C22⋊C4—3441no—
589C22⋊C4—3441no—
590C22⋊C4—1722no—
591C22⋊C4—1722no—
592C22⋊C4—1722no—
593C22⋊C4—1722no—
594C22⋊C4—1722no—
595C42—24no—
596C42—21no—
597C42—21no—
598C42—21no—
599C42—21no—
600C42—81no—
601C42—81no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—862no—
609C23—862no—
610C23—862no—
611C23—862no—
612C23—3444no—
613C23—3444no—
614C23—3444no—
615C23—3444no—
616C23—3444no—
617C23—1728no—
618C23—1728no—
619C23—1721no—
620C23—1721no—
621C23—1721no—
622C23—1721no—
623C23—1721no—
624C23—1721no—
625C23—1721no—
626C23—1721no—
627C23—1721no—
628C23—1721no—
629C23C4×C22⋊D4312yes—
630C23C22×C22⋊D4311yescharacteristic
631D4—434no—
632D4—862no—
633D4—862no—
634D4—862no—
635D4—862no—
636D4—862no—
637D4—1728no—
638D4—1721no—
639D4—1721no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—3444no—
670C2×C4—3444no—
671C2×C4—1721no—
672C2×C4—1721no—
673C2×C4—1721no—
674C2×C4—1721no—
675C2×C4—1721no—
676C2×C4—1721no—
677C2×C4C4×C22⋊D4312yes—
678C2×C4#1306335012yes—
679C2×C4C22×C4×D4311yescharacteristic
680C2×C4#41×D4311yescharacteristic
681C2×C4#41×D4311yescharacteristic
682C2×C4C2×#1062189811yescharacteristic
683C2×C4#1306337111yescharacteristic
684C2×C4#1306337111yescharacteristic
685C8—862no—
686C8—862no—
687C8—1721no—
688C8—1721no—
689C22—22no—
690C22—22no—
691C22—22no—
692C22—41no—
693C22—41no—
694C22—41no—
695C22—41no—
696C22—864no—
697C22—34416no—
698C22—3441no—
699C22—3441no—
700C22—3441no—
701C22—3441no—
702C22—1722no—
703C22—1722no—
704C22—1722no—
705C22—1722no—
706C22—1722no—
707C22—1722no—
708C22—1722no—
709C22—1722no—
710C22—1722no—
711C22C2×C4×C22⋊D4311yescharacteristic
712C22#1458353711yescharacteristic
713C22#1458353711yescharacteristic
714C22C2×#1306335011yescharacteristic
715C22#1458369711yescharacteristic
716C22#1458370211yescharacteristic
717C22#1458370711yescharacteristic
718C4—22no—
719C4—22no—
720C4—41no—
721C4—41no—
722C4—41no—
723C4—42no—
724C4—42no—
725C4—81no—
726C4—81no—
727C4—3441no—
728C4—3441no—
729C4#117×D4311yescharacteristic
730C4#1458337311yescharacteristic
731C4#1458357311yescharacteristic
732C4#1458357311yescharacteristic
733C2—42no—
734C2—3442no—
735C2—1724no—
736C2#1913744511yescharacteristic
737C2C4×#1306335011yescharacteristic
738C2#1914342311yescharacteristic
739C2#1914662511yescharacteristic
740C2#1914673011yescharacteristic
741C2#1914679011yescharacteristic
742C2#1914682011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#2347C2
socleC23×C43C22×D4
prime radicalC23×D172C22
cosocleC22×C4×C43C24
hypercenter#2347D43
hypocenterC43#22580
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2347

Complements

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

NH ≅ G/Ntype
3. #19135291C2semidirect
4. #19135277C2semidirect
5. #19135222C2semidirect
6. #19135215C2semidirect
7. #19134855C2semidirect
8. #19134841C2semidirect
9. #19134690C2semidirect
10. #19134626C2semidirect
12. #19134423C2semidirect
13. C4×#13063245C2semidirect
14. #19134379C2semidirect
15. C43×#2347C2semidirect
21. C2×#13063258C22semidirect
22. C2×#13063256C22semidirect
23. #14582903C4semidirect
33. C2×#13063236C22semidirect
34. C2×C4×C43⋊C8C22semidirect
41. #14582661C22semidirect
42. #14582661C22semidirect
43. #14582661C22semidirect
44. #14582661C22semidirect
45. #14582661C22semidirect
46. #14582661C22semidirect
47. #14582654C22semidirect
48. #14582654C22semidirect
50. C43×#389C22semidirect
51. C43×#389C22semidirect
57. C4×C4⋊C4×C43C22semidirect
58. C4×C4⋊C4×C43C22semidirect
74. C2×#10621877C2×C4semidirect
101. #13063245C2×C4semidirect
102. #13063245C2×C4semidirect
109. #117×C43C2×C4semidirect
363. #2347D43semidirect
409. #389C2×D43semidirect
410. #389C2×D43semidirect
420. C4×C4⋊C4C2×D43semidirect
421. C4×C4⋊C4C2×D43semidirect
431. C43#22580semidirect
457. #117C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145829032
C22⋊C4×D1722
#191352912
#191352772
#191352222
#191352152
#191348552
#191348412
#191346902
#191346262
#191345252
#191344232
C4×#130632452
#191343792
C43×#23472
#2258043