Finite Group Databasebeta

← #25125441

Subgroups — #25125441

Order 11008.

1126 conjugacy classes of subgroups.

The subgroup lattice has 746 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582934C211yesmaximal, characteristic, complemented
2C2×C22⋊C8×D43C211yesmaximal, characteristic
3#19136977C211yesmaximal, characteristic
4#19136977C211yesmaximal, characteristic
5#19136030C211yesmaximal, characteristic, complemented
6#19136029C211yesmaximal, characteristic, complemented
7#19136028C211yesmaximal, characteristic, complemented
8#19136027C211yesmaximal, characteristic, complemented
9#19136026C211yesmaximal, characteristic, complemented
10#19136022C211yesmaximal, characteristic, complemented
11#19136021C211yesmaximal, characteristic, complemented
12#19134310C211yesmaximal, characteristic, complemented
13#19134310C211yesmaximal, characteristic, complemented
14#19134310C211yesmaximal, characteristic, complemented
15C43×#2077C211yesmaximal, characteristic, complemented
16C23×C4×D43C2211yescharacteristic
17C22×C8×D43C2211yescharacteristic
18C22×C8×D43C2211yescharacteristic
19C2×#13063283C2211yescharacteristic
20C2×#13063283C2211yescharacteristic
21C2×#13063283C2211yescharacteristic
22C2×#13063283C2211yescharacteristic
23#14582934—24no—
24C2×#13063258C2211yescharacteristic, complemented
25C2×#13063258C2211yescharacteristic, complemented
26C2×#13063257C2211yescharacteristic, complemented
27C2×C22⋊(C43⋊C8)C2211yescharacteristic
28C2×(C2×D43)⋊C8C2211yescharacteristic
29C2×(C2×D43)⋊C8C2211yescharacteristic
30C22⋊C8×D43—24no—
31#14582761—21no—
32#14582761—21no—
33#14582759C2211yescharacteristic
34#14582759C2211yescharacteristic
35#14582756C2211yescharacteristic
36#14582756C2211yescharacteristic
37#14582756C2211yescharacteristic
38#14582756C2211yescharacteristic
39#14582754—21no—
40#14582754—21no—
41C22⋊C4×Dic43—21no—
42C22⋊C4×Dic43—21no—
43#14582746—21no—
44#14582746—21no—
45#14582662C2211yescharacteristic, complemented
46#14582662C2211yescharacteristic, complemented
47#14582662C2211yescharacteristic, complemented
48#14582661C2211yescharacteristic, complemented
49#14582661C2211yescharacteristic, complemented
50#14582661C2211yescharacteristic, complemented
51#14582661C2211yescharacteristic, complemented
52#14582661C2211yescharacteristic, complemented
53#14582661C2211yescharacteristic, complemented
54C2×#106×C43C2211yescharacteristic, complemented
55C2×C22⋊C8×C43C2211yescharacteristic
56C43×#380C2211yescharacteristic
57C43×#380C2211yescharacteristic
58C43×#340C2211yescharacteristic, complemented
59C43×#340C2211yescharacteristic, complemented
60C43×#340C2211yescharacteristic, complemented
61C24×D43D411yescharacteristic
62C23×Dic43D411yescharacteristic
63C22×C4×D43—22no—
64C22×C4×D43—22no—
65C22×C4×D43—22no—
66C22×C4×D43—22no—
67C22×C4×D43—22no—
68C22×C4×D43—22no—
69C22×C4×D43D411yescharacteristic
70C22×C4×D43D411yescharacteristic
71C22×C4×D43C2311yescharacteristic
72C22×C4×D43C2311yescharacteristic
73C22×C43⋊C8C2311yescharacteristic
74C22×C43⋊C8C2311yescharacteristic
75C2×C8×D43—22no—
76C2×C8×D43—22no—
77C2×C8×D43—22no—
78C2×C8×D43—22no—
79C2×C8×D43—22no—
80C2×C8×D43D414yes—
81#13063283—22no—
82#13063283—22no—
83#13063283—22no—
84#13063283—22no—
85#13063283—22no—
86#13063283—22no—
87#13063283—22no—
88#13063283—22no—
89C2×C4⋊Dic43C2311yescharacteristic
90C2×C4⋊Dic43C2311yescharacteristic
91C2×C4⋊Dic43C2311yescharacteristic
92C2×C4⋊Dic43C2311yescharacteristic
93C2×C22⋊Dic43—21no—
94C2×C22⋊Dic43—21no—
95C2×(C2×D43)⋊C4—21no—
96C2×(C2×D43)⋊C4—21no—
97C2×(C2×D43)⋊C4—21no—
98C2×(C2×D43)⋊C4—21no—
99C2×(C2×D43)⋊C4—21no—
100C2×(C2×D43)⋊C4—21no—
101C2×(C2×D43)⋊C4—21no—
102C2×(C2×D43)⋊C4—21no—
103C2×C4×Dic43—21no—
104C2×C4×Dic43—21no—
105C2×C4×Dic43—21no—
106C2×C4×Dic43—21no—
107#13063258—22no—
108#13063258—22no—
109#13063257—22no—
110C22⋊(C43⋊C8)—22no—
111(C2×D43)⋊C8—22no—
112(C2×D43)⋊C8—22no—
113C43⋊#95—21no—
114C43⋊#95—21no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C43⋊#95—21no—
118C43⋊#95—21no—
119C23×C4×C43C2311yescharacteristic
120C22×C8×C43C2311yescharacteristic
121C22×C8×C43C2311yescharacteristic
122C2×C4⋊C4×C43C2311yescharacteristic
123C2×C4⋊C4×C43C2311yescharacteristic
124C2×C4⋊C4×C43C2311yescharacteristic
125C2×C4⋊C4×C43C2311yescharacteristic
126C2×C22⋊C4×C43—21no—
127C2×C22⋊C4×C43—21no—
128#106×C43—22no—
129C22⋊C8×C43—22no—
130#95×C43—21no—
131#95×C43—21no—
132C24×C43C2×D411yescharacteristic
133C23×D43—22no—
134C23×D43—22no—
135C23×D43—22no—
136C23×D43—22no—
137C23×D43—22no—
138C23×D43—41no—
139C23×D43—41no—
140C23×D43C2×D411yescharacteristic
141C23×D43C2×D411yescharacteristic
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×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2411yescharacteristic
154C22×Dic43—22no—
155C22×Dic43—22no—
156C22×Dic43—22no—
157C22×Dic43—21no—
158C22×Dic43—21no—
159C22×Dic43—21no—
160C22×Dic43—21no—
161C22×Dic43C2×D411yescharacteristic
162C22×Dic43C2×D411yescharacteristic
163C2×C4×D43—21no—
164C2×C4×D43—21no—
165C2×C4×D43—21no—
166C2×C4×D43—21no—
167C2×C4×D43—21no—
168C2×C4×D43—21no—
169C2×C4×D43—22no—
170C2×C4×D43—22no—
171C2×C4×D43—22no—
172C2×C4×D43—22no—
173C2×C4×D43—22no—
174C2×C4×D43—22no—
175C2×C4×D43—44no—
176C2×C4×D43—44no—
177C2×C4×D43—44no—
178C2×C4×D43—44no—
179C2×C4×D43C2×D412yes—
180C2×C4×D43#4112yes—
181C2×C4×D43#4112yes—
182C2×C4×D43#4112yes—
183C2×C4×D43#4112yes—
184C2×C4×D43#4112yes—
185C2×C8×C43—21no—
186C2×C8×C43—21no—
187C2×C8×C43—21no—
188C2×C8×C43—21no—
189C2×C8×C43—21no—
190C2×C8×C43C2×D412yes—
191C4⋊C4×C43—21no—
192C4⋊C4×C43—21no—
193C4⋊C4×C43—21no—
194C4⋊C4×C43—21no—
195C4⋊C4×C43—21no—
196C4⋊C4×C43—21no—
197C4⋊C4×C43—21no—
198C4⋊C4×C43—21no—
199C22⋊C4×C43—42no—
200C22⋊C4×C43—42no—
201C22⋊Dic43—42no—
202C22⋊Dic43—42no—
203(C2×D43)⋊C4—42no—
204(C2×D43)⋊C4—42no—
205(C2×D43)⋊C4—42no—
206(C2×D43)⋊C4—42no—
207(C2×D43)⋊C4—42no—
208(C2×D43)⋊C4—42no—
209(C2×D43)⋊C4—42no—
210(C2×D43)⋊C4—42no—
211C4⋊Dic43—21no—
212C4⋊Dic43—21no—
213C4⋊Dic43—21no—
214C4⋊Dic43—21no—
215C4⋊Dic43—21no—
216C4⋊Dic43—21no—
217C4⋊Dic43—21no—
218C4⋊Dic43—21no—
219C4×Dic43—42no—
220C4×Dic43—42no—
221C4×Dic43—42no—
222C4×Dic43—42no—
223C2×C43⋊C8—21no—
224C2×C43⋊C8—21no—
225C2×C43⋊C8—21no—
226C2×C43⋊C8—21no—
227C2×C43⋊C8—21no—
228C2×C43⋊C8C2×D412yes—
229C8×D43—28no—
230C8×D43—44no—
231C23×C43—21no—
232C23×C43—21no—
233C23×C43—21no—
234C23×C43—21no—
235C23×C43—21no—
236C23×C43—21no—
237C23×C43#13512yes—
238C23×C43C22×D411yescharacteristic
239C22×D43—21no—
240C22×D43—21no—
241C22×D43—21no—
242C22×D43—21no—
243C22×D43—28no—
244C22×D43—21no—
245C22×D43—21no—
246C22×D43—21no—
247C22×D43—21no—
248C22×D43—21no—
249C22×D43—21no—
250C22×D43—44no—
251C22×D43—44no—
252C22×D43—44no—
253C22×D43—44no—
254C22×D43—44no—
255C22×D43—44no—
256C22×D43#12112yes—
257C22×D43#12312yes—
258C22×D43#12312yes—
259C22×D43#13512yes—
260C2×C4×C43—21no—
261C2×C4×C43—21no—
262C2×C4×C43—21no—
263C2×C4×C43—41no—
264C2×C4×C43—41no—
265C2×C4×C43—41no—
266C2×C4×C43—41no—
267C2×C4×C43—41no—
268C2×C4×C43—41no—
269C2×C4×C43—41no—
270C2×C4×C43—41no—
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×C43C22×D411yescharacteristic
280C2×C4×C43C2×#4111yescharacteristic
281C2×C4×C43C2×#4111yescharacteristic
282C2×C4×C43C2×#4111yescharacteristic
283C2×C4×C43C2×#4111yescharacteristic
284C2×C4×C43C2×#4111yescharacteristic
285C2×Dic43—21no—
286C2×Dic43—21no—
287C2×Dic43—21no—
288C2×Dic43—44no—
289C2×Dic43—41no—
290C2×Dic43—41no—
291C2×Dic43—41no—
292C2×Dic43—41no—
293C2×Dic43—41no—
294C2×Dic43—41no—
295C2×Dic43—41no—
296C2×Dic43—41no—
297C2×Dic43—41no—
298C2×Dic43—41no—
299C2×Dic43—41no—
300C2×Dic43—41no—
301C2×Dic43#12112yes—
302C2×Dic43#12312yes—
303C2×Dic43#12312yes—
304C4×D43—44no—
305C4×D43—41no—
306C4×D43—41no—
307C4×D43—41no—
308C4×D43—41no—
309C4×D43—44no—
310C4×D43#12314yes—
311C4×D43#12414yes—
312C4×D43#12614yes—
313C4×D43#12614yes—
314C8×C43—22no—
315C8×C43—41no—
316C43⋊C8—22no—
317C43⋊C8—41no—
318#23638—431nomaximal, Sylow
319C22×C43—22no—
320C22×C43—22no—
321C22×C43—22no—
322C22×C43—41no—
323C22×C43—41no—
324C22×C43—41no—
325C22×C43—41no—
326C22×C43C2×#12111yescharacteristic
327C22×C43C2×#12311yescharacteristic
328C22×C43C2×#12311yescharacteristic
329C22×C43C2×#13511yescharacteristic
330C22×C43C2×#13511yescharacteristic
331C22×C43#57511yescharacteristic
332C22×C43#57511yescharacteristic
333C2×D43—22no—
334C2×D43—22no—
335C2×D43—22no—
336C2×D43—22no—
337C2×D43—22no—
338C2×D43—22no—
339C2×D43—22no—
340C2×D43—22no—
341C2×D43—22no—
342C2×D43—416no—
343C2×D43—41no—
344C2×D43—41no—
345C2×D43—41no—
346C2×D43—41no—
347C2×D43#39714yes—
348C4×C43—41no—
349C4×C43—81no—
350C4×C43—81no—
351C4×C43—81no—
352C4×C43—81no—
353C4×C43C2×#12311yescharacteristic
354C4×C43C2×#12411yescharacteristic
355C4×C43C2×#12611yescharacteristic
356C4×C43C2×#12611yescharacteristic
357Dic43—41no—
358Dic43—81no—
359Dic43—81no—
360Dic43—81no—
361Dic43—81no—
362Dic43#39714yes—
363C2×#427—431no—
364C22×C22⋊C8—431no—
365#2280—431no—
366#2280—431no—
367#2077—431no—
368#2077—431no—
369#2077—431no—
370#2077D4311yescharacteristic, complemented
371#2076—431no—
372#2076—431no—
373#2075—431no—
374#2075—431no—
375#1735—431no—
376#1735—431no—
377#1735—431no—
378C2×C43—42no—
379C2×C43C2×#39711yescharacteristic
380C2×C43#305011yescharacteristic
381C2×C43#305411yescharacteristic
382C2×C43#309111yescharacteristic
383C2×C43#309111yescharacteristic
384C2×C43#309111yescharacteristic
385C2×C43#309111yescharacteristic
386D43—24no—
387D43—42no—
388C24×C4—431no—
389C23×C8—431no—
390C23×C8—431no—
391C2×#117—431no—
392C2×#117—431no—
393C2×#117—431no—
394C2×#117—431no—
395#427—864no—
396C2×#107—431no—
397C2×#107—431no—
398C2×#106—431no—
399C2×#106C2×D4311yescharacteristic, complemented
400C2×C22⋊C8—431no—
401C2×C22⋊C8—431no—
402C2×C22⋊C8—431no—
403C2×C22⋊C8—864no—
404C2×C22⋊C8C2×D4311yescharacteristic
405#381—861no—
406#381—861no—
407#380—431no—
408#380—431no—
409#380—431no—
410#380—431no—
411#380—431no—
412#380—431no—
413#380C2×D4311yescharacteristic
414#380C2×D4311yescharacteristic
415#379—861no—
416#379—861no—
417C4×C22⋊C4—861no—
418C4×C22⋊C4—861no—
419C4×C22⋊C4—861no—
420C4×C22⋊C4—861no—
421#340—431no—
422#340—431no—
423#340—431no—
424#340—431no—
425#340—431no—
426#340—431no—
427#340—431no—
428#340—431no—
429#340—431no—
430#340C2×D4311yescharacteristic, complemented
431#340C2×D4311yescharacteristic, complemented
432#340C2×D4311yescharacteristic, complemented
433C43#2363811yescharacteristic, complemented, Sylow
434C25—431no—
435C23×C4—431no—
436C23×C4—431no—
437C23×C4—431no—
438C23×C4—431no—
439C23×C4—431no—
440C23×C4—862no—
441C23×C4—862no—
442C23×C4—862no—
443C23×C4—862no—
444C23×C4—862no—
445C23×C4—862no—
446C23×C4C22×D4311yescharacteristic
447C22×C8—431no—
448C22×C8—434no—
449C22×C8—431no—
450C22×C8—862no—
451C22×C8—862no—
452C22×C8—862no—
453C22×C8—862no—
454C22×C8—862no—
455C22×C8C22×D4311yescharacteristic
456C22×C8C22×D4311yescharacteristic
457#117—862no—
458#117—862no—
459#117—862no—
460#117—862no—
461#117—862no—
462#117—862no—
463#117—862no—
464#117—862no—
465C2×C4⋊C4—431no—
466C2×C4⋊C4—431no—
467C2×C4⋊C4—431no—
468C2×C4⋊C4—431no—
469C2×C4⋊C4C22×D4311yescharacteristic
470C2×C4⋊C4C22×D4311yescharacteristic
471C2×C4⋊C4C22×D4311yescharacteristic
472C2×C4⋊C4C22×D4311yescharacteristic
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
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—861no—
482C2×C22⋊C4—861no—
483C2×C22⋊C4—861no—
484C2×C22⋊C4—861no—
485C2×C42—861no—
486C2×C42—861no—
487C2×C42—861no—
488C2×C42—861no—
489#107—862no—
490#107—862no—
491#106—22no—
492#106—862no—
493C22⋊C8—22no—
494C22⋊C8—862no—
495C22⋊C8—862no—
496C22⋊C8—862no—
497#95—21no—
498#95—21no—
499#95—861no—
500#95—861no—
501#95—861no—
502#95—861no—
503#95—861no—
504#95—861no—
505C24—431no—
506C24—431no—
507C24—862no—
508C24—862no—
509C24—862no—
510C24—862no—
511C24—862no—
512C24—1721no—
513C24—1721no—
514C24D4×D4311yescharacteristic
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—431no—
526C22×C4—432no—
527C22×C4—432no—
528C22×C4—432no—
529C22×C4—432no—
530C22×C4—432no—
531C22×C4—432no—
532C22×C4—431no—
533C22×C4—862no—
534C22×C4—862no—
535C22×C4—862no—
536C22×C4—862no—
537C22×C4—862no—
538C22×C4—862no—
539C22×C4—862no—
540C22×C4—862no—
541C22×C4—862no—
542C22×C4—861no—
543C22×C4—861no—
544C22×C4—861no—
545C22×C4—861no—
546C22×C4—861no—
547C22×C4—861no—
548C22×C4—861no—
549C22×C4—861no—
550C22×C4—861no—
551C22×C4—861no—
552C22×C4—1724no—
553C22×C4—1724no—
554C22×C4—1724no—
555C22×C4—1724no—
556C22×C4D4×D4311yescharacteristic
557C22×C4C23×D4311yescharacteristic
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—432no—
564C2×C8—868no—
565C2×C8—861no—
566C2×C8—861no—
567C2×C8—861no—
568C2×C8—861no—
569C2×C8—861no—
570C2×C8—1724no—
571C2×C8D4×D4312yes—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—861no—
581C4⋊C4—861no—
582C4⋊C4—861no—
583C4⋊C4—861no—
584C4⋊C4—861no—
585C4⋊C4—861no—
586C4⋊C4—861no—
587C4⋊C4—861no—
588C22⋊C4—42no—
589C22⋊C4—42no—
590C22⋊C4—1722no—
591C22⋊C4—1722no—
592C22⋊C4—1722no—
593C22⋊C4—1722no—
594C22⋊C4—1722no—
595C22⋊C4—1722no—
596C22⋊C4—1722no—
597C22⋊C4—1722no—
598C22⋊C4—1722no—
599C22⋊C4—1722no—
600C42—1722no—
601C42—1722no—
602C42—1722no—
603C42—1722no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23—432no—
611C23—432no—
612C23—432no—
613C23—432no—
614C23—868no—
615C23—861no—
616C23—861no—
617C23—861no—
618C23—861no—
619C23—861no—
620C23—861no—
621C23—861no—
622C23—861no—
623C23—861no—
624C23—861no—
625C23—1724no—
626C23—1724no—
627C23—1724no—
628C23—1724no—
629C23—1724no—
630C23—1724no—
631C23#1306334612yes—
632C23C2×D4×D4311yescharacteristic
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—432no—
653C2×C4—432no—
654C2×C4—432no—
655C2×C4—434no—
656C2×C4—434no—
657C2×C4—434no—
658C2×C4—434no—
659C2×C4—861no—
660C2×C4—861no—
661C2×C4—861no—
662C2×C4—1724no—
663C2×C4—1724no—
664C2×C4—1724no—
665C2×C4—1721no—
666C2×C4—1721no—
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×C4—1721no—
678C2×C4—1721no—
679C2×C4—1721no—
680C2×C4—1721no—
681C2×C4C2×D4×D4311yescharacteristic
682C2×C4#41×D4311yescharacteristic
683C2×C4#41×D4311yescharacteristic
684C2×C4#41×D4311yescharacteristic
685C2×C4#41×D4311yescharacteristic
686C2×C4#41×D4311yescharacteristic
687C8—22no—
688C8—41no—
689C8—862no—
690C8—1721no—
691C22—22no—
692C22—22no—
693C22—22no—
694C22—41no—
695C22—41no—
696C22—41no—
697C22—41no—
698C22—434no—
699C22—862no—
700C22—862no—
701C22—862no—
702C22—862no—
703C22—862no—
704C22—862no—
705C22—862no—
706C22—862no—
707C22—862no—
708C22—17216no—
709C22—1721no—
710C22—1721no—
711C22—1721no—
712C22—1721no—
713C22#121×D4311yescharacteristic
714C22#123×D4311yescharacteristic
715C22#123×D4311yescharacteristic
716C22#135×D4311yescharacteristic
717C22C2×#1306334611yescharacteristic
718C22#1458369511yescharacteristic
719C22#1458369811yescharacteristic
720C4—41no—
721C4—81no—
722C4—81no—
723C4—81no—
724C4—81no—
725C4—434no—
726C4—3441no—
727C4—3441no—
728C4—3441no—
729C4—3441no—
730C4—1721no—
731C4#123×D4311yescharacteristic
732C4#124×D4311yescharacteristic
733C4#126×D4311yescharacteristic
734C4#126×D4311yescharacteristic
735C2—42no—
736C2—864no—
737C2—1722no—
738C2#397×D4311yescharacteristic
739C2#1914417111yescharacteristic
740C2#1914419911yescharacteristic
741C2#1914450511yescharacteristic
742C2#1914450711yescharacteristic
743C2#1914450911yescharacteristic
744C2#1914451311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2077C2
socleC23×C43C22×D4
prime radicalC24×D43D4
hypercenter#2077D43
hypocenterC43#23638
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2077

Complements

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

NH ≅ G/Ntype
1. C2×#14582934C2semidirect
5. #19136030C2semidirect
6. #19136029C2semidirect
7. #19136028C2semidirect
8. #19136027C2semidirect
9. #19136026C2semidirect
10. #19136022C2semidirect
11. #19136021C2semidirect
12. #19134310C2semidirect
13. #19134310C2semidirect
14. #19134310C2semidirect
15. C43×#2077C2semidirect
24. C2×#13063258C22semidirect
25. C2×#13063258C22semidirect
26. C2×#13063257C22semidirect
45. #14582662C22semidirect
46. #14582662C22semidirect
47. #14582662C22semidirect
48. #14582661C22semidirect
49. #14582661C22semidirect
50. #14582661C22semidirect
51. #14582661C22semidirect
52. #14582661C22semidirect
53. #14582661C22semidirect
54. C2×#106×C43C22semidirect
58. C43×#340C22semidirect
59. C43×#340C22semidirect
60. C43×#340C22semidirect
370. #2077D43semidirect
399. C2×#106C2×D43semidirect
430. #340C2×D43semidirect
431. #340C2×D43semidirect
432. #340C2×D43semidirect
433. C43#23638semidirect

Maximal subgroups

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

subgroupindex
C2×#145829342
C2×C22⋊C8×D432
#191369772
#191360302
#191360292
#191360282
#191360272
#191360262
#191360222
#191360212
#191343102
C43×#20772
#2363843