Finite Group Databasebeta

← #25113852

Subgroups — #25113852

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×#14582904C211yesmaximal, characteristic
2#19137486C211yesmaximal, characteristic, complemented
3#19135295C211yesmaximal, characteristic, complemented
4#19135281C211yesmaximal, characteristic, complemented
5#19135219C211yesmaximal, characteristic, complemented
6#19135212C211yesmaximal, characteristic, complemented
7#19134856C211yesmaximal, characteristic, complemented
8#19134842C211yesmaximal, characteristic, complemented
9#19134687C211yesmaximal, characteristic, complemented
10#19134626C211yesmaximal, characteristic, complemented
11#19134526C211yesmaximal, characteristic
12#19134420C211yesmaximal, characteristic, complemented
13C4×#13063246C211yesmaximal, characteristic, complemented
14#19134379C211yesmaximal, characteristic, complemented
15D4×C22⋊C4×C43C211yesmaximal, characteristic
16C22×#10621877C2211yescharacteristic
17C2×#13063284C2211yescharacteristic
18C2×#13063258C2211yescharacteristic, complemented
19C2×#13063256C2211yescharacteristic, complemented
20#14582904C418yescomplemented
21C2×#13063246C2211yescharacteristic
22C2×#13063246C2211yescharacteristic
23C2×#13063246C2211yescharacteristic
24C2×#13063246C2211yescharacteristic
25C2×#13063246C2211yescharacteristic
26C2×#13063246C2211yescharacteristic
27C2×#13063246C2211yescharacteristic
28C2×#13063246C2211yescharacteristic
29C2×C22⋊(C43⋊C8)C2211yescharacteristic
30C2×#13063236C2211yescharacteristic, complemented
31C2×C4×C43⋊C8C2211yescharacteristic, complemented
32#14582797C2211yescharacteristic, complemented
33#14582797C2211yescharacteristic, complemented
34#14582793—21no—
35#14582793—21no—
36#14582766—21no—
37#14582759C2211yescharacteristic
38C4×C4⋊Dic43C2211yescharacteristic, complemented
39C4×C4⋊Dic43C2211yescharacteristic, complemented
40#14582750—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
49C23×D4×C43C2211yescharacteristic
50C2×C4×D4×C43C2211yescharacteristic
51C2×C4×D4×C43C2211yescharacteristic
52C22×C22⋊C4×C43—21no—
53C43×#390C2211yescharacteristic
54C43×#390C2211yescharacteristic
55C43×#386—21no—
56C43×#386—21no—
57C43×#380C2211yescharacteristic
58C43×#379—21no—
59C4×C22⋊C4×C43C2211yescharacteristic
60C2×#10621877—41no—
61C2×#10621877—41no—
62C2×#10621877C2×C414yescomplemented
63C22×C43⋊C8C2311yescharacteristic
64C22×C43⋊C8C2311yescharacteristic
65C22×C43⋊C8C2311yescharacteristic
66C22×C43⋊C8C2311yescharacteristic
67#13063284—22no—
68#13063284C2×C414yescomplemented
69C2×C4⋊Dic43C2311yescharacteristic
70C2×C4⋊Dic43C2311yescharacteristic
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
73C2×Dic43⋊C4—21no—
74C2×Dic43⋊C4—21no—
75C2×C22⋊Dic43—21no—
76C2×C22⋊Dic43—21no—
77C2×C4×Dic43—21no—
78C2×C4×Dic43—21no—
79C2×C4×Dic43—21no—
80#13063258—41no—
81#13063256—41no—
82#13063246—22no—
83#13063246—22no—
84#13063246—41no—
85#13063246—41no—
86#13063246C2×C414yes—
87#13063246C2×C414yes—
88#13063246C2×C414yescomplemented
89#13063246C2×C414yescomplemented
90C22⋊(C43⋊C8)—22no—
91#13063236—41no—
92C4×C43⋊C8—41no—
93C43⋊#95—21no—
94C43⋊#95—21no—
95C43⋊#95—21no—
96C43⋊#95—21no—
97C43⋊#95—21no—
98C25×C43—21no—
99C22×D4×C43—22no—
100C22×D4×C43—22no—
101C22×D4×C43—21no—
102C22×D4×C43—22no—
103C22×D4×C43—41no—
104C22×D4×C43—41no—
105C22×D4×C43C2×C414yes—
106C22×D4×C43C2311yescharacteristic
107C22×D4×C43C2311yescharacteristic
108C23×C4×C43—21no—
109C23×C4×C43—21no—
110C23×C4×C43C2311yescharacteristic
111C4×D4×C43—22no—
112C4×D4×C43—22no—
113C4×D4×C43—41no—
114C4×D4×C43—41no—
115C2×C4⋊C4×C43C2311yescharacteristic
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C22⋊C4×C43—21no—
118C2×C22⋊C4×C43—21no—
119C2×C22⋊C4×C43—21no—
120C2×C22⋊C4×C43—21no—
121C2×C22⋊C4×C43—21no—
122C2×C22⋊C4×C43—21no—
123C2×C22⋊C4×C43—21no—
124C2×C22⋊C4×C43—44no—
125C2×C22⋊C4×C43D411yescharacteristic
126C2×C22⋊C4×C43D411yescharacteristic
127C2×C42×C43C2311yescharacteristic
128C2×C42×C43C2311yescharacteristic
129#95×C43—21no—
130#95×C43D411yescharacteristic
131#95×C43D411yescharacteristic
132C24×C43—21no—
133C24×C43—21no—
134C24×C43—24no—
135C24×C43—42no—
136C24×C43—42no—
137C24×C43—42no—
138C24×C43—42no—
139C24×C43—81no—
140C24×C43—81no—
141C24×C43C2×D411yescharacteristic
142C2×D4×C43—24no—
143C2×D4×C43—21no—
144C2×D4×C43—21no—
145C2×D4×C43—21no—
146C2×D4×C43—21no—
147C2×D4×C43—28no—
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—42no—
153C2×D4×C43—42no—
154C2×D4×C43—44no—
155C2×D4×C43—44no—
156C2×D4×C43—44no—
157C2×D4×C43C22×C412yes—
158C2×D4×C43C22×C412yes—
159C2×D4×C43#4112yes—
160C2×D4×C43#4112yes—
161C22×C4×C43—21no—
162C22×C4×C43—21no—
163C22×C4×C43—21no—
164C22×C4×C43—21no—
165C22×C4×C43—21no—
166C22×C4×C43—21no—
167C22×C4×C43—42no—
168C22×C4×C43—42no—
169C22×C4×C43—42no—
170C22×C4×C43—42no—
171C22×C4×C43—81no—
172C22×C4×C43—81no—
173C22×C4×C43C22×C412yes—
174C22×C4×C43C2×D411yescharacteristic
175C22×C4×C43C2×D411yescharacteristic
176C22×C4×C43C2×D411yescharacteristic
177C22×C4×C43C2×D411yescharacteristic
178C22×C4×C43C2×D411yescharacteristic
179C22×C4×C43#4112yes—
180C22×C4×C43C2411yescharacteristic
181C22×Dic43—21no—
182C22×Dic43—21no—
183C22×Dic43—21no—
184C22×Dic43—21no—
185C4⋊C4×C43—21no—
186C4⋊C4×C43—21no—
187C4⋊C4×C43—21no—
188C4⋊C4×C43—21no—
189C22⋊C4×C43—22no—
190C22⋊C4×C43—41no—
191C22⋊C4×C43—42no—
192C22⋊C4×C43—42no—
193C22⋊C4×C43—42no—
194C22⋊C4×C43—42no—
195C22⋊C4×C43—42no—
196C22⋊C4×C43—81no—
197C22⋊C4×C43—81no—
198C42×C43—21no—
199C42×C43—21no—
200C42×C43—21no—
201C42×C43—21no—
202C22⋊Dic43—24no—
203C22⋊Dic43—81no—
204C4⋊Dic43—21no—
205C4⋊Dic43—21no—
206C4⋊Dic43—21no—
207C4⋊Dic43—21no—
208C4⋊Dic43—21no—
209C4⋊Dic43—21no—
210C4⋊Dic43C22×C412yes—
211C4⋊Dic43C22×C412yes—
212Dic43⋊C4—42no—
213Dic43⋊C4—42no—
214C4×Dic43—24no—
215C4×Dic43—81no—
216C4×Dic43—81no—
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—22no—
231C23×C43—22no—
232C23×C43—22no—
233C23×C43—21no—
234C23×C43—21no—
235C23×C43—21no—
236C23×C43—21no—
237C23×C43—21no—
238C23×C43—21no—
239C23×C43—22no—
240C23×C43—48no—
241C23×C43—48no—
242C23×C43—41no—
243C23×C43—41no—
244C23×C43—41no—
245C23×C43—41no—
246C23×C43—41no—
247C23×C43—41no—
248C23×C43—41no—
249C23×C43—41no—
250C23×C43—41no—
251C23×C43—41no—
252C23×C43—84no—
253C23×C43—84no—
254C23×C43—84no—
255C23×C43—84no—
256C23×C43—84no—
257C23×C43C4×D412yes—
258C23×C43C22×D411yescharacteristic
259D4×C43—22no—
260D4×C43—22no—
261D4×C43—22no—
262D4×C43—22no—
263D4×C43—22no—
264D4×C43—48no—
265D4×C43—41no—
266D4×C43—41no—
267D4×C43#11714yes—
268C2×C4×C43—21no—
269C2×C4×C43—21no—
270C2×C4×C43—21no—
271C2×C4×C43—21no—
272C2×C4×C43—22no—
273C2×C4×C43—22no—
274C2×C4×C43—22no—
275C2×C4×C43—22no—
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—21no—
284C2×C4×C43—21no—
285C2×C4×C43—41no—
286C2×C4×C43—41no—
287C2×C4×C43—41no—
288C2×C4×C43—41no—
289C2×C4×C43—41no—
290C2×C4×C43—41no—
291C2×C4×C43—84no—
292C2×C4×C43—84no—
293C2×C4×C43C4×D412yes—
294C2×C4×C43AGL(1,ℤ/8)12yes—
295C2×C4×C43C23×C411yescharacteristic
296C2×C4×C43C2×#4111yescharacteristic
297C2×C4×C43C2×#4111yescharacteristic
298C2×C4×C43C2×#4111yescharacteristic
299C2×C4×C43H(5,𝔽2)11yescharacteristic
300C2×C4×C43H(5,𝔽2)11yescharacteristic
301C2×Dic43—22no—
302C2×Dic43—22no—
303C2×Dic43—41no—
304C2×Dic43—41no—
305C2×Dic43—41no—
306C2×Dic43—41no—
307C2×Dic43—41no—
308C2×Dic43—41no—
309C2×Dic43—41no—
310C2×Dic43—41no—
311C2×Dic43—41no—
312C2×Dic43—41no—
313C43⋊C8—22no—
314C43⋊C8—22no—
315C43⋊C8—41no—
316C43⋊C8—41no—
317#22580—431nomaximal, Sylow
318C22×C43—24no—
319C22×C43—22no—
320C22×C43—22no—
321C22×C43—22no—
322C22×C43—42no—
323C22×C43—42no—
324C22×C43—41no—
325C22×C43—42no—
326C22×C43—41no—
327C22×C43—42no—
328C22×C43—41no—
329C22×C43—42no—
330C22×C43—41no—
331C22×C43—42no—
332C22×C43—42no—
333C22×C43—42no—
334C22×C43—42no—
335C22×C43—816no—
336C22×C43—81no—
337C22×C43—81no—
338C22×C43—81no—
339C22×C43—81no—
340C22×C43C2×C4×D411yescharacteristic
341C22×C43#54611yescharacteristic
342C22×C43#54611yescharacteristic
343C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
344C22×C43#57511yescharacteristic
345C22×C43#57611yescharacteristic
346C22×C43#57711yescharacteristic
347C4×C43—22no—
348C4×C43—22no—
349C4×C43—41no—
350C4×C43—41no—
351C4×C43—41no—
352C4×C43—81no—
353C4×C43—81no—
354C4×C43C2×#11711yescharacteristic
355C4×C43#51811yescharacteristic
356C4×C43#55111yescharacteristic
357C4×C43#55111yescharacteristic
358Dic43—42no—
359Dic43—42no—
360Dic43—81no—
361Dic43—81no—
362C2×#418—431no—
363#2347—431no—
364D4×C22⋊C4D4311yescharacteristic
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—44no—
379C2×C43—82no—
380C2×C43#234211yescharacteristic
381C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
382C2×C43#294611yescharacteristic
383C2×C43#331111yescharacteristic
384C2×C43#331811yescharacteristic
385C2×C43#332211yescharacteristic
386C2×C43#332411yescharacteristic
387C23×D4C2×D4311yescharacteristic
388C22×M16—431no—
389C2×C4×D4C2×D4311yescharacteristic
390C2×C4×D4C2×D4311yescharacteristic
391C2×#117—431no—
392C22×C22⋊C4—21no—
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#390C2×D4311yescharacteristic
408#390C2×D4311yescharacteristic
409#389—431no—
410#389—431no—
411#388—861no—
412#388—861no—
413#386—21no—
414#386—21no—
415#383—861no—
416#380—431no—
417#380C2×D4311yescharacteristic
418#379—21no—
419C4×C4⋊C4—431no—
420C4×C4⋊C4—431no—
421C4×C4⋊C4—861no—
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—21no—
433C22×D4—22no—
434C22×D4—22no—
435C22×D4—22no—
436C22×D4—21no—
437C22×D4—41no—
438C22×D4—41no—
439C22×D4C4×D4314yes—
440C22×D4C22×D4311yescharacteristic
441C22×D4C22×D4311yescharacteristic
442C23×C4—21no—
443C23×C4—21no—
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—22no—
453C4×D4—22no—
454C4×D4—41no—
455C4×D4—41no—
456#117—434no—
457#117—862no—
458C2×C4⋊C4—431no—
459C2×C4⋊C4—431no—
460C2×C4⋊C4—431no—
461C2×C4⋊C4—431no—
462C2×C4⋊C4—861no—
463C2×C4⋊C4—861no—
464C2×C4⋊C4C22×D4311yescharacteristic
465C2×C4⋊C4C22×D4311yescharacteristic
466C2×C22⋊C4—21no—
467C2×C22⋊C4—21no—
468C2×C22⋊C4—21no—
469C2×C22⋊C4—21no—
470C2×C22⋊C4—21no—
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4—44no—
474C2×C22⋊C4—861no—
475C2×C22⋊C4—861no—
476C2×C22⋊C4C22⋊D4311yescharacteristic
477C2×C22⋊C4C22⋊D4311yescharacteristic
478C2×C42—861no—
479C2×C42—861no—
480C2×C42—861no—
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—861no—
498#95—861no—
499#95—861no—
500#95—861no—
501#95—861no—
502#95C22⋊D4311yescharacteristic
503#95C22⋊D4311yescharacteristic
504C24—21no—
505C24—21no—
506C24—24no—
507C24—42no—
508C24—42no—
509C24—42no—
510C24—42no—
511C24—81no—
512C24—81no—
513C24C2×C22⋊D4311yescharacteristic
514C2×D4—28no—
515C2×D4—24no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—44no—
525C2×D4—44no—
526C2×D4—44no—
527C2×D4—42no—
528C2×D4—42no—
529C2×D4C2×C4×D4312yes—
530C2×D4C2×C4×D4312yes—
531C2×D4#1062190012yes—
532C2×D4#1062190012yes—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—42no—
540C22×C4—42no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4—81no—
544C22×C4—81no—
545C22×C4—861no—
546C22×C4—861no—
547C22×C4—861no—
548C22×C4—861no—
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—432no—
575C4⋊C4—432no—
576C4⋊C4—861no—
577C4⋊C4—861no—
578C4⋊C4—861no—
579C4⋊C4—861no—
580C4⋊C4—861no—
581C4⋊C4—861no—
582C4⋊C4—1722no—
583C4⋊C4—1722no—
584C22⋊C4—22no—
585C22⋊C4—41no—
586C22⋊C4—42no—
587C22⋊C4—42no—
588C22⋊C4—42no—
589C22⋊C4—42no—
590C22⋊C4—42no—
591C22⋊C4—81no—
592C22⋊C4—81no—
593C22⋊C4—864no—
594C22⋊C4—3441no—
595C42—21no—
596C42—21no—
597C42—21no—
598C42—21no—
599C42—864no—
600C42—3441no—
601C42—3441no—
602C23—22no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—22no—
608C23—22no—
609C23—21no—
610C23—21no—
611C23—22no—
612C23—48no—
613C23—48no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—84no—
625C23—84no—
626C23—84no—
627C23—84no—
628C23—84no—
629C23C4×C22⋊D4312yes—
630C23C22×C22⋊D4311yescharacteristic
631D4—22no—
632D4—22no—
633D4—22no—
634D4—22no—
635D4—22no—
636D4—48no—
637D4—41no—
638D4—41no—
639D4#1306328114yes—
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—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—84no—
664C2×C4—84no—
665C2×C4—862no—
666C2×C4—862no—
667C2×C4—1721no—
668C2×C4—1721no—
669C2×C4—1721no—
670C2×C4—1721no—
671C2×C4—1721no—
672C2×C4—1721no—
673C2×C4—1721no—
674C2×C4—1721no—
675C2×C4—1721no—
676C2×C4—1721no—
677C2×C4C4×C22⋊D4312yes—
678C2×C4#1306335112yes—
679C2×C4C22×C4×D4311yescharacteristic
680C2×C4C2×#1062190011yescharacteristic
681C2×C4C2×#1062190011yescharacteristic
682C2×C4C2×#1062189811yescharacteristic
683C2×C4#1306337011yescharacteristic
684C2×C4#1306337011yescharacteristic
685C8—862no—
686C8—862no—
687C8—1721no—
688C8—1721no—
689C22—22no—
690C22—22no—
691C22—24no—
692C22—22no—
693C22—42no—
694C22—41no—
695C22—42no—
696C22—42no—
697C22—41no—
698C22—41no—
699C22—42no—
700C22—42no—
701C22—42no—
702C22—41no—
703C22—42no—
704C22—42no—
705C22—42no—
706C22—816no—
707C22—81no—
708C22—81no—
709C22—81no—
710C22—81no—
711C22C2×C4×C22⋊D4311yescharacteristic
712C22#1458354311yescharacteristic
713C22#1458354311yescharacteristic
714C22C2×#1306335111yescharacteristic
715C22#1458369711yescharacteristic
716C22#1458370211yescharacteristic
717C22#1458371011yescharacteristic
718C4—22no—
719C4—22no—
720C4—41no—
721C4—41no—
722C4—41no—
723C4—81no—
724C4—81no—
725C4—3441no—
726C4—3441no—
727C4—1722no—
728C4—1722no—
729C4C2×#1306328111yescharacteristic
730C4#1458337211yescharacteristic
731C4#1458357511yescharacteristic
732C4#1458357511yescharacteristic
733C2—42no—
734C2—44no—
735C2—82no—
736C2#1913744011yescharacteristic
737C2C4×#1306335111yescharacteristic
738C2#1914342711yescharacteristic
739C2#1914663111yescharacteristic
740C2#1914673611yescharacteristic
741C2#1914679611yescharacteristic
742C2#1914682611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingD4×C22⋊C4×C43C2
socleC23×C43C22×D4
prime radicalC23×D4×C43C22
cosocleC22×C4×C43C24
hypercenterD4×C22⋊C4D43
hypocenterC43#22580
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ D4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #19137486C2semidirect
3. #19135295C2semidirect
4. #19135281C2semidirect
5. #19135219C2semidirect
6. #19135212C2semidirect
7. #19134856C2semidirect
8. #19134842C2semidirect
9. #19134687C2semidirect
10. #19134626C2semidirect
12. #19134420C2semidirect
13. C4×#13063246C2semidirect
14. #19134379C2semidirect
18. C2×#13063258C22semidirect
19. C2×#13063256C22semidirect
20. #14582904C4semidirect
30. C2×#13063236C22semidirect
31. C2×C4×C43⋊C8C22semidirect
32. #14582797C22semidirect
33. #14582797C22semidirect
38. C4×C4⋊Dic43C22semidirect
39. C4×C4⋊Dic43C22semidirect
41. #14582661C22semidirect
42. #14582661C22semidirect
43. #14582661C22semidirect
44. #14582661C22semidirect
45. #14582661C22semidirect
46. #14582661C22semidirect
47. #14582654C22semidirect
48. #14582654C22semidirect
62. C2×#10621877C2×C4semidirect
68. #13063284C2×C4semidirect
88. #13063246C2×C4semidirect
89. #13063246C2×C4semidirect
431. C43#22580semidirect

Maximal subgroups

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

subgroupindex
C2×#145829042
#191374862
#191352952
#191352812
#191352192
#191352122
#191348562
#191348422
#191346872
#191346262
#191345262
#191344202
C4×#130632462
#191343792
D4×C22⋊C4×C432
#2258043