Finite Group Databasebeta

← #25116880

Subgroups — #25116880

Order 11008.

1118 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583061C211yesmaximal, characteristic
2C2×#14582999C211yesmaximal, characteristic, complemented
3C2×#14582895C211yesmaximal, characteristic
4#19137620C211yesmaximal, characteristic, complemented
5#19135465C211yesmaximal, characteristic, complemented
6#19135288C211yesmaximal, characteristic, complemented
7#19135233C211yesmaximal, characteristic, complemented
8#19135016C211yesmaximal, characteristic, complemented
9#19134939C211yesmaximal, characteristic, complemented
10#19134929C211yesmaximal, characteristic, complemented
11#19134856C211yesmaximal, characteristic, complemented
12#19134792C211yesmaximal, characteristic, complemented
13#19134420C211yesmaximal, characteristic, complemented
14#19134373C211yesmaximal, characteristic, complemented
15C43×#2339C211yesmaximal, characteristic
16C22×#10621885C2211yescharacteristic
17C22×#10621883C2211yescharacteristic
18C23×C43⋊C8C2211yescharacteristic
19C2×#13063304C2211yescharacteristic
20C2×C4×Dic86C2211yescharacteristic
21C2×#13063284C2211yescharacteristic
22#14583061C418yescomplemented
23#14582999—24no—
24C2×#13063258C2211yescharacteristic
25C2×#13063256C2211yescharacteristic
26#14582895—24no—
27C2×#13063249C2211yescharacteristic
28C2×#13063249C2211yescharacteristic
29C2×#13063249C2211yescharacteristic
30C2×#13063248C2211yescharacteristic
31C2×#13063248C2211yescharacteristic
32C2×#13063246C2211yescharacteristic
33C2×#13063246C2211yescharacteristic
34C2×#13063246C2211yescharacteristic
35C2×C22⋊(C43⋊C8)C2211yescharacteristic
36C2×#13063236C2211yescharacteristic
37C2×#13063236C2211yescharacteristic
38#14582805C2211yescharacteristic
39#14582797C2211yescharacteristic
40#14582793—21no—
41#14582787—21no—
42#14582781—21no—
43C4×C4⋊Dic43C2211yescharacteristic
44#14582750—21no—
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582654C2211yescharacteristic
50#14582654C2211yescharacteristic
51C22×#41×C43C2211yescharacteristic
52C2×C4×D4×C43C2211yescharacteristic
53C2×C4×D4×C43C2211yescharacteristic
54C43×#391C2211yescharacteristic
55C43×#391C2211yescharacteristic
56C43×#386—21no—
57C43×#386—21no—
58C43×#381—21no—
59C43×#380C2211yescharacteristic
60C4×C22⋊C4×C43C2211yescharacteristic
61C2×#95×C43—21no—
62C22×Dic86C2311yescharacteristic
63C2×#10621885—41no—
64C2×#10621885—41no—
65C2×#10621885C2×C414yescomplemented
66C2×#10621883—22no—
67C2×#10621883—22no—
68C2×#10621883C2×C414yes—
69C22×C43⋊C8—22no—
70C22×C43⋊C8—22no—
71C22×C43⋊C8—41no—
72C22×C43⋊C8C2311yescharacteristic
73C22×C43⋊C8C2311yescharacteristic
74C22×C43⋊C8C2311yescharacteristic
75C22×C43⋊C8C2311yescharacteristic
76#13063304—22no—
77#13063304C2×C414yescomplemented
78C4×Dic86—22no—
79C4×Dic86—41no—
80#13063284—22no—
81#13063284—41no—
82C2×C4⋊Dic43C2311yescharacteristic
83C2×C4⋊Dic43C2311yescharacteristic
84C2×C4⋊Dic43C2311yescharacteristic
85C2×Dic43⋊C4—21no—
86C2×Dic43⋊C4—21no—
87C2×Dic43⋊C4—21no—
88C2×C22⋊Dic43—21no—
89C2×C22⋊Dic43—21no—
90C2×C4×Dic43—21no—
91C2×C4×Dic43—21no—
92C2×C4×Dic43—21no—
93#13063258—22no—
94#13063256—41no—
95#13063249—22no—
96#13063249—22no—
97#13063249C2×C414yescomplemented
98#13063248—22no—
99#13063248—41no—
100#13063246—22no—
101#13063246C2×C414yes—
102#13063246D414yes—
103C22⋊(C43⋊C8)C2×C414yescomplemented
104#13063236—22no—
105#13063236—41no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C2×#41×C43—22no—
111C2×#41×C43—22no—
112C2×#41×C43—22no—
113C2×#41×C43—41no—
114C2×#41×C43—41no—
115C2×#41×C43C2×C414yes—
116C22×Q8×C43C2311yescharacteristic
117C22×D4×C43—21no—
118C22×D4×C43C2311yescharacteristic
119C23×C4×C43—21no—
120C23×C4×C43—21no—
121C23×C4×C43—21no—
122C23×C4×C43C2311yescharacteristic
123C4×D4×C43—22no—
124C4×D4×C43—22no—
125C4×D4×C43—41no—
126C4×D4×C43—41no—
127C2×C4⋊C4×C43C2311yescharacteristic
128C2×C4⋊C4×C43C2311yescharacteristic
129C2×C22⋊C4×C43—21no—
130C2×C22⋊C4×C43—21no—
131C2×C22⋊C4×C43—21no—
132C2×C22⋊C4×C43D411yescharacteristic
133C2×C22⋊C4×C43D411yescharacteristic
134C2×C42×C43C2311yescharacteristic
135C2×C42×C43C2311yescharacteristic
136#95×C43—21no—
137#95×C43—21no—
138#95×C43—21no—
139#95×C43—21no—
140#95×C43—21no—
141#95×C43D411yescharacteristic
142#95×C43D411yescharacteristic
143C24×C43—21no—
144C24×C43C2×D411yescharacteristic
145#41×C43—28no—
146#41×C43—44no—
147#41×C43—44no—
148#41×C43—44no—
149C2×Q8×C43—21no—
150C2×Q8×C43—21no—
151C2×Q8×C43—21no—
152C2×Q8×C43—21no—
153C2×Q8×C43—21no—
154C2×Q8×C43C22×C412yes—
155C2×D4×C43—21no—
156C2×D4×C43—21no—
157C2×D4×C43—21no—
158C2×D4×C43—24no—
159C2×D4×C43—42no—
160C2×D4×C43—42no—
161C2×D4×C43C22×C412yes—
162C2×D4×C43C2×D412yes—
163C2×D4×C43#4112yes—
164C22×C4×C43—21no—
165C22×C4×C43—21no—
166C22×C4×C43—21no—
167C22×C4×C43—21no—
168C22×C4×C43—24no—
169C22×C4×C43—21no—
170C22×C4×C43—21no—
171C22×C4×C43—21no—
172C22×C4×C43—42no—
173C22×C4×C43—42no—
174C22×C4×C43—42no—
175C22×C4×C43—42no—
176C22×C4×C43—42no—
177C22×C4×C43—42no—
178C22×C4×C43—81no—
179C22×C4×C43—81no—
180C22×C4×C43C22×C412yes—
181C22×C4×C43C2×D411yescharacteristic
182C22×C4×C43C2×D411yescharacteristic
183C22×C4×C43C2×D411yescharacteristic
184C22×C4×C43C2×D411yescharacteristic
185C22×C4×C43C2×D411yescharacteristic
186C22×C4×C43#4112yes—
187C22×C4×C43C2411yescharacteristic
188C22×Dic43—21no—
189C22×Dic43—21no—
190C22×Dic43—21no—
191C22×Dic43—21no—
192C2×Dic86—21no—
193C2×Dic86—21no—
194C2×Dic86—21no—
195C2×Dic86—21no—
196C2×Dic86—21no—
197C2×Dic86C22×C412yes—
198C4⋊C4×C43—21no—
199C4⋊C4×C43—21no—
200C4⋊C4×C43—21no—
201C4⋊C4×C43—21no—
202C22⋊C4×C43—41no—
203C22⋊C4×C43—41no—
204C22⋊C4×C43—42no—
205C22⋊C4×C43—42no—
206C22⋊C4×C43—81no—
207C42×C43—21no—
208C42×C43—21no—
209C42×C43—21no—
210C42×C43—21no—
211C22⋊Dic43—24no—
212C22⋊Dic43—42no—
213#10621885—44no—
214#10621883—28no—
215C4⋊Dic43—21no—
216C4⋊Dic43—21no—
217C4⋊Dic43—21no—
218C4⋊Dic43—21no—
219C4⋊Dic43C22×C412yes—
220C4⋊Dic43C2×D412yes—
221Dic43⋊C4—24no—
222Dic43⋊C4—42no—
223Dic43⋊C4—42no—
224C4×Dic43—42no—
225C4×Dic43—42no—
226C4×Dic43—42no—
227C2×C43⋊C8—21no—
228C2×C43⋊C8—21no—
229C2×C43⋊C8—21no—
230C2×C43⋊C8—21no—
231C2×C43⋊C8—21no—
232C2×C43⋊C8—21no—
233C2×C43⋊C8—21no—
234C2×C43⋊C8—21no—
235C2×C43⋊C8—21no—
236C2×C43⋊C8—44no—
237C2×C43⋊C8C22×C412yes—
238C2×C43⋊C8C22×C412yes—
239C2×C43⋊C8C2×D412yes—
240C23×C43—22no—
241C23×C43—21no—
242C23×C43—22no—
243C23×C43—22no—
244C23×C43—21no—
245C23×C43—21no—
246C23×C43—21no—
247C23×C43—21no—
248C23×C43—21no—
249C23×C43—41no—
250C23×C43—41no—
251C23×C43—41no—
252C23×C43—41no—
253C23×C43C4×D412yes—
254C23×C43C22×D411yescharacteristic
255Q8×C43—22no—
256Q8×C43—22no—
257Q8×C43—41no—
258Q8×C43—41no—
259D4×C43—22no—
260D4×C43—22no—
261D4×C43—22no—
262D4×C43—48no—
263D4×C43C4×D414yes—
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—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—21no—
279C2×C4×C43—21no—
280C2×C4×C43—21no—
281C2×C4×C43—21no—
282C2×C4×C43—21no—
283C2×C4×C43—48no—
284C2×C4×C43—41no—
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—41no—
292C2×C4×C43—84no—
293C2×C4×C43—84no—
294C2×C4×C43C4×D412yes—
295C2×C4×C43C23×C411yescharacteristic
296C2×C4×C43C22×D411yescharacteristic
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—22no—
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—
313Dic86—22no—
314Dic86—22no—
315Dic86—41no—
316Dic86—41no—
317C43⋊C8—22no—
318C43⋊C8—22no—
319C43⋊C8—22no—
320C43⋊C8—41no—
321#22856—431nomaximal, Sylow
322C22×C43—24no—
323C22×C43—22no—
324C22×C43—22no—
325C22×C43—22no—
326C22×C43—42no—
327C22×C43—42no—
328C22×C43—41no—
329C22×C43—42no—
330C22×C43—41no—
331C22×C43—42no—
332C22×C43—41no—
333C22×C43—42no—
334C22×C43—41no—
335C22×C43—42no—
336C22×C43C2×C4×D411yescharacteristic
337C22×C43D4211yescharacteristic
338C22×C43#54611yescharacteristic
339C22×C43#57511yescharacteristic
340C22×C43#57511yescharacteristic
341C22×C43#57711yescharacteristic
342C22×C43#57811yescharacteristic
343C4×C43—22no—
344C4×C43—42no—
345C4×C43—41no—
346C4×C43—41no—
347C4×C43—41no—
348C4×C43—41no—
349C4×C43—81no—
350C4×C43—81no—
351C4×C43C2×C4×D411yescharacteristic
352C4×C43#51811yescharacteristic
353C4×C43#54611yescharacteristic
354C4×C43#55111yescharacteristic
355Dic43—42no—
356Dic43—42no—
357Dic43—42no—
358Dic43—81no—
359C2×#452—431no—
360C2×#440—431no—
361C2×#416—431no—
362#2362—431no—
363#2339D4311yescharacteristic
364#1971—431no—
365#1935—431no—
366#1928—431no—
367#1892—431no—
368#1878—431no—
369#1877—431no—
370#1864—431no—
371#1854—431no—
372#1762—431no—
373#1752—431no—
374C2×C43—42no—
375C2×C43—44no—
376C2×C43#235811yescharacteristic
377C2×C43#294311yescharacteristic
378C2×C43#294711yescharacteristic
379C2×C43#326711yescharacteristic
380C2×C43#326911yescharacteristic
381C2×C43#331111yescharacteristic
382C2×C43#331511yescharacteristic
383C22×#41C2×D4311yescharacteristic
384C22×Q16—431no—
385C22×SD16—431no—
386C23×C8—431no—
387C2×C22⋊Q8—431no—
388C2×C4×Q8—431no—
389C2×C4×D4C2×D4311yescharacteristic
390C2×C4×D4C2×D4311yescharacteristic
391C2×#117—431no—
392#452—438no—
393#440—864no—
394C2×#107—431no—
395C2×#106—431no—
396#416—864no—
397C2×#103—431no—
398C2×#103—431no—
399C2×#103—431no—
400C2×#103—431no—
401C2×#103—431no—
402C2×#102—431no—
403C2×#102—431no—
404C2×#102—431no—
405C2×C22⋊C8—431no—
406C2×#97—431no—
407C2×#97—431no—
408#391—431no—
409#391C2×D4311yescharacteristic
410#391C2×D4311yescharacteristic
411#389—431no—
412#388—861no—
413#388—861no—
414#387—861no—
415#386—21no—
416#386—21no—
417#381—21no—
418#380C2×D4311yescharacteristic
419C4×C4⋊C4—431no—
420C4×C4⋊C4—861no—
421C4×C22⋊C4C2×D4311yescharacteristic
422C2×#95—21no—
423#340—431no—
424#340—431no—
425#340—431no—
426#340—431no—
427#336—431no—
428#336—431no—
429C43#2285611yescharacteristic, complemented, Sylow
430C2×#41—22no—
431C2×#41—22no—
432C2×#41—22no—
433C2×#41—41no—
434C2×#41—41no—
435C2×#41C4×D4314yes—
436C22×Q8—431no—
437C22×Q8C22×D4311yescharacteristic
438C22×D4—21no—
439C22×D4C22×D4311yescharacteristic
440C23×C4—21no—
441C23×C4—21no—
442C23×C4—21no—
443C23×C4C22×D4311yescharacteristic
444C2×Q16—434no—
445C2×Q16—1721no—
446C2×Q16—1721no—
447C2×SD16—434no—
448C2×SD16—862no—
449C2×SD16—862no—
450C22×C8—431no—
451C22×C8—431no—
452C22×C8—431no—
453C22×C8—431no—
454C22×C8—862no—
455C22×C8—862no—
456C22×C8—1721no—
457C22⋊Q8—434no—
458C22⋊Q8—862no—
459C4×Q8—862no—
460C4×Q8—1721no—
461C4×D4—22no—
462C4×D4—22no—
463C4×D4—41no—
464C4×D4—41no—
465#117—862no—
466#117—1721no—
467C2×C4⋊C4—431no—
468C2×C4⋊C4—431no—
469C2×C4⋊C4—431no—
470C2×C4⋊C4—861no—
471C2×C4⋊C4—861no—
472C2×C4⋊C4—861no—
473C2×C4⋊C4C22×D4311yescharacteristic
474C2×C4⋊C4C22×D4311yescharacteristic
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—21no—
478C2×C22⋊C4—861no—
479C2×C22⋊C4—861no—
480C2×C22⋊C4C22⋊D4311yescharacteristic
481C2×C22⋊C4C22⋊D4311yescharacteristic
482C2×C42—861no—
483C2×C42—861no—
484C2×C42—861no—
485C2×C42C22×D4311yescharacteristic
486C2×C42C22×D4311yescharacteristic
487#107—862no—
488#106—1721no—
489#103—434no—
490#103—862no—
491#103—862no—
492#103—862no—
493#103—1721no—
494#102—434no—
495#102—434no—
496#102—862no—
497C22⋊C8—434no—
498#97—862no—
499#97—1721no—
500#95—21no—
501#95—21no—
502#95—21no—
503#95—21no—
504#95—21no—
505#95—861no—
506#95—861no—
507#95—861no—
508#95—861no—
509#95C22⋊D4311yescharacteristic
510#95C22⋊D4311yescharacteristic
511C24—21no—
512C24C2×C22⋊D4311yescharacteristic
513#41—28no—
514#41—44no—
515#41—44no—
516#41—44no—
517C2×Q8—21no—
518C2×Q8—21no—
519C2×Q8—21no—
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—432no—
523C2×Q8—861no—
524C2×Q8—861no—
525C2×Q8—861no—
526C2×Q8—861no—
527C2×Q8—861no—
528C2×Q8C2×C4×D4312yes—
529C2×D4—24no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—42no—
534C2×D4—42no—
535C2×D4C2×C4×D4312yes—
536C2×D4D4×D4312yes—
537C2×D4#1062190012yes—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—24no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—42no—
547C22×C4—42no—
548C22×C4—42no—
549C22×C4—42no—
550C22×C4—42no—
551C22×C4—42no—
552C22×C4—81no—
553C22×C4—81no—
554C22×C4—861no—
555C22×C4—861no—
556C22×C4—861no—
557C22×C4—861no—
558C22×C4C2×C4×D4312yes—
559C22×C4#1062189812yes—
560C22×C4C2×C22⋊D4311yescharacteristic
561C22×C4C2×C22⋊D4311yescharacteristic
562C22×C4C2×C22⋊D4311yescharacteristic
563C22×C4C2×C22⋊D4311yescharacteristic
564C22×C4C2×C22⋊D4311yescharacteristic
565C22×C4C23×D4311yescharacteristic
566Q16—1724no—
567SD16—868no—
568C2×C8—432no—
569C2×C8—432no—
570C2×C8—432no—
571C2×C8—861no—
572C2×C8—861no—
573C2×C8—861no—
574C2×C8—861no—
575C2×C8—861no—
576C2×C8—861no—
577C2×C8—861no—
578C2×C8—861no—
579C2×C8—861no—
580C2×C8—1724no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—432no—
586C4⋊C4—432no—
587C4⋊C4—864no—
588C4⋊C4—861no—
589C4⋊C4—861no—
590C4⋊C4—861no—
591C4⋊C4—861no—
592C4⋊C4—1722no—
593C4⋊C4—1722no—
594C22⋊C4—41no—
595C22⋊C4—41no—
596C22⋊C4—42no—
597C22⋊C4—42no—
598C22⋊C4—81no—
599C22⋊C4—864no—
600C22⋊C4—1722no—
601C42—21no—
602C42—21no—
603C42—21no—
604C42—21no—
605C42—1722no—
606C42—1722no—
607C42—1722no—
608C23—22no—
609C23—21no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—22no—
614C23—21no—
615C23—22no—
616C23—21no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23C4×C22⋊D4312yes—
622C23C22×C22⋊D4311yescharacteristic
623Q8—22no—
624Q8—22no—
625Q8—41no—
626Q8—41no—
627Q8—862no—
628Q8—862no—
629Q8—1721no—
630Q8—1721no—
631D4—22no—
632D4—22no—
633D4—22no—
634D4—48no—
635D4(C22⋊D43)⋊C414yes—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—48no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—84no—
665C2×C4—84no—
666C2×C4—862no—
667C2×C4—862no—
668C2×C4—862no—
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×C4—1721no—
678C2×C4C4×C22⋊D4312yes—
679C2×C4C22×C4×D4311yescharacteristic
680C2×C4C2×D4×D4311yescharacteristic
681C2×C4C2×#1062190011yescharacteristic
682C2×C4C2×#1062189811yescharacteristic
683C2×C4#1306337011yescharacteristic
684C2×C4#1306337011yescharacteristic
685C8—862no—
686C8—862no—
687C8—862no—
688C8—1721no—
689C22—22no—
690C22—22no—
691C22—24no—
692C22—22no—
693C22—42no—
694C22—42no—
695C22—41no—
696C22—42no—
697C22—41no—
698C22—41no—
699C22—42no—
700C22—41no—
701C22—42no—
702C22—42no—
703C22C2×C4×C22⋊D4311yescharacteristic
704C22D4×C22⋊D4311yescharacteristic
705C22#1458354311yescharacteristic
706C22#1458369711yescharacteristic
707C22#1458369711yescharacteristic
708C22#1458371011yescharacteristic
709C22#1458371411yescharacteristic
710C4—22no—
711C4—42no—
712C4—41no—
713C4—41no—
714C4—41no—
715C4—41no—
716C4—81no—
717C4—81no—
718C4—3441no—
719C4—1722no—
720C4—1722no—
721C4—1722no—
722C4C2×(C22⋊D43)⋊C411yescharacteristic
723C4#1458337211yescharacteristic
724C4#1458353911yescharacteristic
725C4#1458357511yescharacteristic
726C2—42no—
727C2—44no—
728C2#1913757411yescharacteristic
729C2#1914339311yescharacteristic
730C2#1914343411yescharacteristic
731C2#1914611611yescharacteristic
732C2#1914614611yescharacteristic
733C2#1914663111yescharacteristic
734C2#1914669111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#2339C2
socleC23×C43C22×D4
prime radicalC22×#41×C43C22
cosocleC22×C4×C43C24
hypercenter#2339D43
hypocenterC43#22856
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2339

Complements

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

NH ≅ G/Ntype
2. C2×#14582999C2semidirect
4. #19137620C2semidirect
5. #19135465C2semidirect
6. #19135288C2semidirect
7. #19135233C2semidirect
8. #19135016C2semidirect
9. #19134939C2semidirect
10. #19134929C2semidirect
11. #19134856C2semidirect
12. #19134792C2semidirect
13. #19134420C2semidirect
14. #19134373C2semidirect
22. #14583061C4semidirect
65. C2×#10621885C2×C4semidirect
77. #13063304C2×C4semidirect
97. #13063249C2×C4semidirect
103. C22⋊(C43⋊C8)C2×C4semidirect
429. C43#22856semidirect

Maximal subgroups

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

subgroupindex
C2×#145830612
C2×#145829992
C2×#145828952
#191376202
#191354652
#191352882
#191352332
#191350162
#191349392
#191349292
#191348562
#191347922
#191344202
#191343732
C43×#23392
#2285643