Finite Group Databasebeta

← #25119121

Subgroups — #25119121

Order 11008.

864 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144044C211yesmaximal, characteristic
2C2×#14583019C211yesmaximal, characteristic, complemented
3C2×#14583014C211yesmaximal, characteristic, complemented
4#19143160C211yesmaximal, characteristic, complemented
5#19135428C211yesmaximal, characteristic, complemented
6#19135370C211yesmaximal, characteristic, complemented
7#19135309C211yesmaximal, characteristic, complemented
8#19135302C211yesmaximal, characteristic, complemented
9#19134925C211yesmaximal, characteristic, complemented
10#19134925C211yesmaximal, characteristic, complemented
11#19134870C211yesmaximal, characteristic, complemented
12#19134870C211yesmaximal, characteristic, complemented
13#19134454C211yesmaximal, characteristic, complemented
14#19134408C211yesmaximal, characteristic, complemented
15C43×#2935C211yesmaximal, characteristic, complemented
16C2×#13063345C2211yescharacteristic
17C2×#13063345C2211yescharacteristic
18C2×#13063331C2211yescharacteristic
19C2×#13063331C2211yescharacteristic
20C4×#10621898C2211yescharacteristic
21#14583118C411yescharacteristic, complemented
22#14583118C411yescharacteristic, complemented
23#14583111C411yescharacteristic, complemented
24#14583111C411yescharacteristic, complemented
25#14583106C411yescharacteristic, complemented
26#14583101C411yescharacteristic, complemented
27#14583096C411yescharacteristic, complemented
28#14583091C411yescharacteristic, complemented
29#14583019—24no—
30#14583014—24no—
31C2×#13063260C2211yescharacteristic
32C2×#13063260C2211yescharacteristic
33#14582925C2211yescharacteristic
34#14582925C2211yescharacteristic
35#14582924—21no—
36#14582924—21no—
37#14582923C2211yescharacteristic
38#14582921—21no—
39C2×C4⋊(C43⋊C8)C2211yescharacteristic
40C4⋊C8×D43—21no—
41C2×#13063252C2211yescharacteristic
42C2×#13063252C2211yescharacteristic
43C2×#13063252C2211yescharacteristic
44C2×#13063252C2211yescharacteristic
45C2×#13063251C2211yescharacteristic
46C2×#13063251C2211yescharacteristic
47#14582895C2211yescharacteristic
48#14582895C2211yescharacteristic
49C2×#13063235C2211yescharacteristic
50C2×C8×Dic43C2211yescharacteristic
51#14582745C2211yescharacteristic
52#14582663C2211yescharacteristic
53#14582663C2211yescharacteristic
54#14582660C2211yescharacteristic
55#14582660C2211yescharacteristic
56#14582653C2211yescharacteristic
57#14582653C2211yescharacteristic
58C2×#131×C43C2211yescharacteristic
59C2×#131×C43C2211yescharacteristic
60C43×#532C2211yescharacteristic
61C43×#436—21no—
62C43×#435—21no—
63C43×#435—21no—
64C8×D4×C43—21no—
65C2×C4⋊C8×C43C2211yescharacteristic
66C43×#408C2211yescharacteristic
67C43×#408C2211yescharacteristic
68C4×M16×C43C2211yescharacteristic
69C2×#10621898C2311yescharacteristic
70#13063345—22no—
71#13063345—22no—
72#13063345—22no—
73#13063345—22no—
74C2×#10621885C2×C411yescharacteristic
75C2×#10621885C2×C411yescharacteristic
76C2×#10621883C2×C411yescharacteristic
77C2×#10621883C2×C411yescharacteristic
78C2×#10621884C2×C411yescharacteristic
79C2×#10621884C2×C411yescharacteristic
80C2×#10621882C2×C411yescharacteristic
81C2×#10621882C2×C411yescharacteristic
82#13063331—22no—
83#13063331—22no—
84#13063331—41no—
85#13063331—41no—
86C2×#10621877C2311yescharacteristic
87C2×#10621877C2311yescharacteristic
88C2×#10621872—21no—
89C2×#10621872—21no—
90C22×C43⋊C8C2311yescharacteristic
91C22×C43⋊C8C2311yescharacteristic
92C2×C8×D43—21no—
93C2×C8×D43—21no—
94C4×Dic86C2×C411yescharacteristic
95C4×Dic86C2×C411yescharacteristic
96C4×D172C2×C411yescharacteristic
97C4×D172C2×C411yescharacteristic
98C4×C22⋊D43—21no—
99C4×C22⋊D43—21no—
100#13063284C2311yescharacteristic
101#13063282—21no—
102C2×C4×Dic43C2311yescharacteristic
103C2×C4×Dic43C2311yescharacteristic
104C42×D43—21no—
105#13063260—22no—
106#13063260—22no—
107C4⋊(C43⋊C8)—21no—
108C4⋊(C43⋊C8)—21no—
109C4⋊(C43⋊C8)C2×C411yescharacteristic
110C4⋊(C43⋊C8)C2×C411yescharacteristic
111C4⋊(C43⋊C8)C2×C411yescharacteristic
112C4⋊(C43⋊C8)C2×C411yescharacteristic
113Dic43⋊C8—21no—
114Dic43⋊C8—21no—
115Dic43⋊C8—21no—
116Dic43⋊C8—21no—
117#13063252—22no—
118#13063252—22no—
119#13063252—41no—
120#13063252—41no—
121#13063251—22no—
122#13063251D414yescomplemented
123#13063249C2×C411yescharacteristic
124#13063249C2×C411yescharacteristic
125#13063249C2×C411yescharacteristic
126#13063249C2×C411yescharacteristic
127#13063246C2×C411yescharacteristic
128#13063246C2×C411yescharacteristic
129#13063246C2×C411yescharacteristic
130#13063246C2×C411yescharacteristic
131#13063235—22no—
132C8×Dic43—22no—
133C43⋊#95—21no—
134C43⋊#95—21no—
135C2×#41×C43C2311yescharacteristic
136C2×#41×C43C2311yescharacteristic
137#131×C43—22no—
138#131×C43—22no—
139#131×C43—41no—
140#131×C43—41no—
141C2×M16×C43—21no—
142C2×M16×C43—21no—
143C2×M16×C43C2311yescharacteristic
144C2×M16×C43C2311yescharacteristic
145C22×C8×C43—21no—
146C22×C8×C43—21no—
147C22×C8×C43C2311yescharacteristic
148C22×C8×C43C2311yescharacteristic
149C4⋊Q8×C43C2×C411yescharacteristic
150#127×C43C2×C411yescharacteristic
151#124×C43C2×C411yescharacteristic
152#124×C43C2×C411yescharacteristic
153#121×C43—21no—
154#121×C43—21no—
155C4×D4×C43—21no—
156C4×D4×C43—21no—
157C2×C42×C43C2311yescharacteristic
158C4⋊C8×C43D411yescharacteristic
159C4⋊C8×C43D411yescharacteristic
160C4⋊C8×C43D411yescharacteristic
161C4⋊C8×C43D411yescharacteristic
162C22⋊C8×C43—21no—
163C22⋊C8×C43—21no—
164C22⋊C8×C43—21no—
165C22⋊C8×C43—21no—
166#97×C43—21no—
167C4×C8×C43—21no—
168#41×C43—21no—
169#41×C43—21no—
170#41×C43—21no—
171#41×C43—21no—
172#41×C43—21no—
173#41×C43—21no—
174#41×C43—21no—
175#41×C43—21no—
176C2×Q8×C43C22×C411yescharacteristic
177C2×Q8×C43C22×C411yescharacteristic
178C2×D4×C43—21no—
179C2×D4×C43—21no—
180C2×D4×C43—21no—
181C2×D4×C43—21no—
182C2×D4×C43C22×C411yescharacteristic
183C2×D4×C43C22×C411yescharacteristic
184C22×C4×C43—21no—
185C22×C4×C43—21no—
186C22×C4×C43#4111yescharacteristic
187C22×C4×C43#4111yescharacteristic
188C22×C4×C43C2411yescharacteristic
189C2×C22⋊D43—21no—
190C22×Dic43—21no—
191C22×Dic43—21no—
192#10621898—21no—
193#10621898—21no—
194#10621898C2×D412yes—
195#10621898#4112yes—
196C2×D172C22×C411yescharacteristic
197C2×C4×D43—21no—
198C2×C4×D43—21no—
199C2×C4×D43—21no—
200C2×Dic86C22×C411yescharacteristic
201M16×C43—21no—
202M16×C43—21no—
203M16×C43—21no—
204M16×C43—42no—
205M16×C43—42no—
206M16×C43C2×D412yes—
207C2×C8×C43—21no—
208C2×C8×C43—21no—
209C2×C8×C43—21no—
210C2×C8×C43—21no—
211C2×C8×C43—21no—
212C2×C8×C43—21no—
213C2×C8×C43—42no—
214C2×C8×C43—42no—
215C2×C8×C43C2×D411yescharacteristic
216C2×C8×C43C2×D411yescharacteristic
217C2×C8×C43C2×D411yescharacteristic
218C2×C8×C43C2×D411yescharacteristic
219C4⋊C4×C43—21no—
220C4⋊C4×C43—21no—
221C22⋊C4×C43—21no—
222C22⋊C4×C43—21no—
223C22⋊C4×C43—21no—
224C22⋊C4×C43—21no—
225C42×C43C22×C411yescharacteristic
226C42×C43C22×C411yescharacteristic
227C42×C43C2×D411yescharacteristic
228C42×C43C2×D411yescharacteristic
229C22⋊Dic43—21no—
230#10621885—22no—
231#10621885—22no—
232#10621884—22no—
233#10621884—22no—
234#10621883—22no—
235#10621883—22no—
236#10621882—22no—
237#10621882—22no—
238(C2×D43)⋊C4—21no—
239(C2×D43)⋊C4—21no—
240C4⋊Dic43C22×C411yescharacteristic
241C4⋊Dic43C22×C411yescharacteristic
242Dic43⋊C4—21no—
243Dic43⋊C4—21no—
244C4×Dic43—21no—
245C4×Dic43—21no—
246C4×Dic43—21no—
247C4×Dic43—21no—
248C4×Dic43—21no—
249C4×Dic43—21no—
250C4×Dic43C2×D412yes—
251#10621877—21no—
252#10621877—21no—
253#10621877—21no—
254#10621877—21no—
255C2×C43⋊C8—21no—
256C2×C43⋊C8—21no—
257C2×C43⋊C8—21no—
258C2×C43⋊C8—21no—
259C2×C43⋊C8—21no—
260C2×C43⋊C8—21no—
261C2×C43⋊C8C22×C411yescharacteristic
262C2×C43⋊C8C22×C411yescharacteristic
263C2×C43⋊C8C22×C411yescharacteristic
264C2×C43⋊C8C22×C411yescharacteristic
265#10621872—42no—
266#10621872—42no—
267C8×D43—42no—
268C8×D43—42no—
269C23×C43—21no—
270C23×C43—21no—
271C23×C43C2×#4111yescharacteristic
272C22×D43—21no—
273Q8×C43—21no—
274Q8×C43—21no—
275Q8×C43—21no—
276Q8×C43—21no—
277D4×C43—21no—
278D4×C43—21no—
279D4×C43—21no—
280D4×C43—21no—
281D4×C43—42no—
282D4×C43—41no—
283D4×C43—41no—
284D4×C43—41no—
285D4×C43—41no—
286D4×C43—81no—
287C2×C4×C43—21no—
288C2×C4×C43—21no—
289C2×C4×C43—41no—
290C2×C4×C43—41no—
291C2×C4×C43—41no—
292C2×C4×C43—41no—
293C2×C4×C43—41no—
294C2×C4×C43—41no—
295C2×C4×C43C4×D411yescharacteristic
296C2×C4×C43C4×D411yescharacteristic
297C2×C4×C43C4×D411yescharacteristic
298C2×C4×C43C4×D411yescharacteristic
299C2×C4×C43C23×C411yescharacteristic
300C2×C4×C43C22×D411yescharacteristic
301C2×C4×C43C22×D411yescharacteristic
302C2×C4×C43C2×#4111yescharacteristic
303C2×C4×C43H(5,𝔽2)11yescharacteristic
304C2×C4×C432−1+411yescharacteristic
305C22⋊D43—22no—
306C22⋊D43—22no—
307C2×Dic43—21no—
308C2×Dic43—21no—
309C2×Dic43—21no—
310C2×Dic43—22no—
311C2×Dic43—41no—
312C2×Dic43—41no—
313C2×Dic43—41no—
314C2×Dic43—41no—
315C2×Dic43—41no—
316D172—21no—
317D172C4×D412yes—
318C4×D43—22no—
319C4×D43—22no—
320C4×D43—42no—
321C4×D43—81no—
322Dic86—21no—
323Dic86C4×D412yes—
324C8×C43—21no—
325C8×C43—21no—
326C8×C43—21no—
327C8×C43—21no—
328C8×C43—22no—
329C8×C43—41no—
330C43⋊C8—21no—
331C43⋊C8—21no—
332C43⋊C8—21no—
333C43⋊C8—21no—
334C43⋊C8—41no—
335C43⋊C8—41no—
336#23017—431nomaximal, Sylow
337C22×C43—21no—
338C22×C43—21no—
339C22×C43—41no—
340C22×C43—41no—
341C22×C43—41no—
342C22×C43—41no—
343C22×C43—41no—
344C22×C43—41no—
345C22×C43C2×C4×D411yescharacteristic
346C22×C43#54711yescharacteristic
347C22×C43#55311yescharacteristic
348C2×D43—22no—
349C2×D43—41no—
350C2×D43—41no—
351C4×C43—21no—
352C4×C43—21no—
353C4×C43—21no—
354C4×C43—21no—
355C4×C43—41no—
356C4×C43—41no—
357C4×C43C2×C4×D411yescharacteristic
358C4×C43#52011yescharacteristic
359C4×C43D4211yescharacteristic
360C4×C43#54811yescharacteristic
361Dic43—22no—
362Dic43—42no—
363Dic43—41no—
364Dic43—41no—
365Dic43—81no—
366#3035—431no—
367C2×#444—431no—
368C2×#443—431no—
369#2935D4311yescharacteristic, complemented
370#2906—431no—
371#1963—431no—
372#1950—431no—
373#1938—431no—
374#1937—431no—
375#1876—431no—
376#1876—431no—
377#1866—431no—
378#1866—431no—
379#1768—431no—
380#1759—431no—
381C2×C43—21no—
382C2×C43—21no—
383C2×C43—81no—
384C2×C43—81no—
385C2×C43#236111yescharacteristic
386C2×C43#295511yescharacteristic
387C2×C43#295711yescharacteristic
388D43—42no—
389C2×#135—431no—
390C2×#135—431no—
391C2×#131—431no—
392C2×#131—431no—
393C2×#131C2×D4311yescharacteristic
394C2×#131C2×D4311yescharacteristic
395#532C2×D4311yescharacteristic
396C4×#41—431no—
397#464—431no—
398#464—431no—
399#463—431no—
400#463—431no—
401#462—431no—
402#461—431no—
403#460—431no—
404#459—431no—
405#444—864no—
406#443—864no—
407#436—21no—
408#435—21no—
409#435—21no—
410C8×D4—21no—
411C2×#108—431no—
412C2×#108—431no—
413#424—431no—
414#424—431no—
415#424—861no—
416#424—861no—
417#423—431no—
418#423—861no—
419C2×C4⋊C8—431no—
420C2×C4⋊C8—861no—
421C2×C4⋊C8C2×D4311yescharacteristic
422C2×#104—431no—
423C2×#104—431no—
424C2×#104—431no—
425C2×#104—431no—
426C2×#104—431no—
427C2×#104—431no—
428#416—431no—
429#416—431no—
430#408C2×D4311yescharacteristic
431#408C2×D4311yescharacteristic
432C4×M16C2×D4311yescharacteristic
433C2×#97—431no—
434C2×C4×C8—431no—
435#376—431no—
436#341—431no—
437#341—431no—
438#339—431no—
439#339—431no—
440#336—431no—
441#336—431no—
442C43#2301711yescharacteristic, complemented, Sylow
443C2×#41—431no—
444C2×#41C22×D4311yescharacteristic
445C2×#41C22×D4311yescharacteristic
446#135—862no—
447#135—862no—
448#135—862no—
449#135—862no—
450C2×Q16—431no—
451C2×Q16—431no—
452C2×SD16—431no—
453C2×SD16—431no—
454C2×SD16—431no—
455C2×SD16—431no—
456C2×D8—431no—
457C2×D8—431no—
458#131—22no—
459#131—22no—
460#131—41no—
461#131—41no—
462#131—862no—
463#131—862no—
464#131—1721no—
465#131—1721no—
466C2×M16—21no—
467C2×M16—21no—
468C2×M16—431no—
469C2×M16—431no—
470C2×M16—861no—
471C2×M16—861no—
472C2×M16C22×D4311yescharacteristic
473C2×M16C22×D4311yescharacteristic
474C22×C8—21no—
475C22×C8—21no—
476C22×C8—431no—
477C22×C8—431no—
478C22×C8—861no—
479C22×C8—861no—
480C22×C8C22×D4311yescharacteristic
481C22×C8C22×D4311yescharacteristic
482C4⋊Q8C4×D4311yescharacteristic
483#127C4×D4311yescharacteristic
484#124C4×D4311yescharacteristic
485#124C4×D4311yescharacteristic
486#121—21no—
487#121—21no—
488C4×Q8—431no—
489C4×Q8—431no—
490C4×D4—21no—
491C4×D4—21no—
492C4×D4—431no—
493C4×D4—431no—
494C4×D4—861no—
495C4×D4—861no—
496#117—431no—
497#117—861no—
498C2×C42—431no—
499C2×C42—431no—
500C2×C42—861no—
501C2×C42C22×D4311yescharacteristic
502#108—862no—
503#108—862no—
504C4⋊C8—431no—
505C4⋊C8—431no—
506C4⋊C8—431no—
507C4⋊C8—431no—
508C4⋊C8—861no—
509C4⋊C8—861no—
510C4⋊C8—861no—
511C4⋊C8—861no—
512C4⋊C8—861no—
513C4⋊C8—861no—
514C4⋊C8C22⋊D4311yescharacteristic
515C4⋊C8C22⋊D4311yescharacteristic
516C4⋊C8C22⋊D4311yescharacteristic
517C4⋊C8C22⋊D4311yescharacteristic
518#104—434no—
519#104—862no—
520#104—862no—
521#104—862no—
522#104—1721no—
523#104—1721no—
524#103—431no—
525#103—431no—
526#103—431no—
527#103—431no—
528#102—431no—
529#102—431no—
530#102—431no—
531#102—431no—
532C22⋊C8—21no—
533C22⋊C8—21no—
534C22⋊C8—21no—
535C22⋊C8—21no—
536#97—21no—
537#97—862no—
538C4×C8—21no—
539C4×C8—862no—
540#95—861no—
541#95—861no—
542#41—21no—
543#41—21no—
544#41—21no—
545#41—21no—
546#41—21no—
547#41—21no—
548#41—21no—
549#41—21no—
550#41—432no—
551#41—432no—
552#41—861no—
553#41—861no—
554C2×Q8—431no—
555C2×Q8C2×C4×D4311yescharacteristic
556C2×Q8C2×C4×D4311yescharacteristic
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—431no—
562C2×D4—861no—
563C2×D4C2×C4×D4311yescharacteristic
564C2×D4C2×C4×D4311yescharacteristic
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—861no—
568C22×C4—861no—
569C22×C4—861no—
570C22×C4—861no—
571C22×C4—861no—
572C22×C4#1062189811yescharacteristic
573C22×C4#1062189811yescharacteristic
574C22×C4C23×D4311yescharacteristic
575Q16—862no—
576Q16—862no—
577SD16—862no—
578SD16—862no—
579SD16—862no—
580SD16—862no—
581D8—862no—
582D8—862no—
583M16—21no—
584M16—21no—
585M16—21no—
586M16—42no—
587M16—42no—
588M16—861no—
589M16—861no—
590M16—861no—
591M16—861no—
592M16—1722no—
593M16—1722no—
594M16D4×D4312yes—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—42no—
602C2×C8—42no—
603C2×C8—431no—
604C2×C8—431no—
605C2×C8—431no—
606C2×C8—431no—
607C2×C8—861no—
608C2×C8—861no—
609C2×C8—861no—
610C2×C8—861no—
611C2×C8—861no—
612C2×C8—861no—
613C2×C8—1722no—
614C2×C8—1722no—
615C2×C8C2×C22⋊D4311yescharacteristic
616C2×C8C2×C22⋊D4311yescharacteristic
617C2×C8C2×C22⋊D4311yescharacteristic
618C2×C8C2×C22⋊D4311yescharacteristic
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—431no—
622C4⋊C4—431no—
623C4⋊C4—861no—
624C4⋊C4—861no—
625C22⋊C4—21no—
626C22⋊C4—21no—
627C22⋊C4—21no—
628C22⋊C4—21no—
629C22⋊C4—861no—
630C22⋊C4—861no—
631C22⋊C4—861no—
632C42—432no—
633C42—861no—
634C42—861no—
635C42—861no—
636C42—861no—
637C42—861no—
638C42—861no—
639C42C2×C4×D4311yescharacteristic
640C42C2×C4×D4311yescharacteristic
641C42C2×C22⋊D4311yescharacteristic
642C42C2×C22⋊D4311yescharacteristic
643C23—21no—
644C23—21no—
645C23—861no—
646C23C2×#1062189811yescharacteristic
647Q8—21no—
648Q8—21no—
649Q8—21no—
650Q8—21no—
651Q8—432no—
652Q8—861no—
653D4—21no—
654D4—21no—
655D4—21no—
656D4—21no—
657D4—42no—
658D4—41no—
659D4—41no—
660D4—41no—
661D4—41no—
662D4—81no—
663D4—432no—
664D4—862no—
665D4—862no—
666D4—861no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—861no—
676C2×C4—862no—
677C2×C4—862no—
678C2×C4—862no—
679C2×C4—861no—
680C2×C4—861no—
681C2×C4—3441no—
682C2×C4—1722no—
683C2×C4—1721no—
684C2×C4—1721no—
685C2×C4—1721no—
686C2×C4—1721no—
687C2×C4—1721no—
688C2×C4C4×C22⋊D4311yescharacteristic
689C2×C4C4×C22⋊D4311yescharacteristic
690C2×C4C4×C22⋊D4311yescharacteristic
691C2×C4C4×C22⋊D4311yescharacteristic
692C2×C4C22×C4×D4311yescharacteristic
693C2×C4C2×D4×D4311yescharacteristic
694C2×C4C22×C22⋊D4311yescharacteristic
695C2×C4#41×D4311yescharacteristic
696C2×C4#1306337011yescharacteristic
697C2×C4#1306337211yescharacteristic
698C8—21no—
699C8—21no—
700C8—21no—
701C8—21no—
702C8—22no—
703C8—41no—
704C8—861no—
705C8—861no—
706C8—861no—
707C8—861no—
708C8—1721no—
709C8—1721no—
710C22—21no—
711C22—21no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—862no—
719C22—1721no—
720C22—1721no—
721C22C2×C4×C22⋊D4311yescharacteristic
722C22#1458355411yescharacteristic
723C22#1458359911yescharacteristic
724C4—21no—
725C4—21no—
726C4—21no—
727C4—21no—
728C4—41no—
729C4—41no—
730C4—862no—
731C4—3441no—
732C4—1722no—
733C4—1721no—
734C4—1721no—
735C4C4×D4×D4311yescharacteristic
736C4#1458337811yescharacteristic
737C4D4×C22⋊D4311yescharacteristic
738C4#1458355611yescharacteristic
739C2—21no—
740C2—21no—
741C2—81no—
742C2—81no—
743C2—1722no—
744C2#1913760711yescharacteristic
745C2#1914349611yescharacteristic
746C2#1914351011yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#2935C2
socleC22×C43C2×C4×D4
prime radical#19144044C2
cosocleC22×C4×C43C24
hypercenter#2935D43
hypocenterC43#23017
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C4⋊C8 ◁ #2935

Complements

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

NH ≅ G/Ntype
2. C2×#14583019C2semidirect
3. C2×#14583014C2semidirect
4. #19143160C2semidirect
5. #19135428C2semidirect
6. #19135370C2semidirect
7. #19135309C2semidirect
8. #19135302C2semidirect
9. #19134925C2semidirect
10. #19134925C2semidirect
11. #19134870C2semidirect
12. #19134870C2semidirect
13. #19134454C2semidirect
14. #19134408C2semidirect
15. C43×#2935C2semidirect
21. #14583118C4semidirect
22. #14583118C4semidirect
23. #14583111C4semidirect
24. #14583111C4semidirect
25. #14583106C4semidirect
26. #14583101C4semidirect
27. #14583096C4semidirect
28. #14583091C4semidirect
122. #13063251D4semidirect
369. #2935D43semidirect
442. C43#23017semidirect

Maximal subgroups

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

subgroupindex
#191440442
C2×#145830192
C2×#145830142
#191431602
#191354282
#191353702
#191353092
#191353022
#191349252
#191348702
#191344542
#191344082
C43×#29352
#2301743