Finite Group Databasebeta

← #25135436

Subgroups — #25135436

Order 11008.

1056 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583052C211yesmaximal, characteristic
2#19140392C211yesmaximal, characteristic, complemented
3#19137175C211yesmaximal, characteristic
4#19135982C211yesmaximal, characteristic, complemented
5#19135968C211yesmaximal, characteristic, complemented
6#19135913C211yesmaximal, characteristic, complemented
7#19135913C211yesmaximal, characteristic, complemented
8#19135476C211yesmaximal, characteristic, complemented
9#19135449C211yesmaximal, characteristic, complemented
10#19135292C211yesmaximal, characteristic, complemented
11#19135278C211yesmaximal, characteristic, complemented
12#19134905C211yesmaximal, characteristic, complemented
13#19134796C211yesmaximal, characteristic, complemented
14#19134527C211yesmaximal, characteristic
15C2×C43×#433C211yesmaximal, characteristic, complemented
16C23×D172C2211yescharacteristic
17C22×#10621873C2211yescharacteristic
18C22×#10621873C2211yescharacteristic
19C2×#13063304C2211yescharacteristic
20C2×#13063284C2211yescharacteristic
21#14583052—24no—
22C2×#13063259C2211yescharacteristic, complemented
23C2×#13063257C2211yescharacteristic, complemented
24C2×#13063250C2211yescharacteristic, complemented
25C2×#13063250C2211yescharacteristic, complemented
26C2×#13063247C2211yescharacteristic
27C2×#13063247C2211yescharacteristic
28C2×#13063247C2211yescharacteristic
29C2×#13063247C2211yescharacteristic
30C2×#13063247C2211yescharacteristic
31C2×#13063247C2211yescharacteristic
32#14582837—21no—
33#14582830—21no—
34#14582827—21no—
35#14582827—21no—
36#14582805C2211yescharacteristic, complemented
37#14582805C2211yescharacteristic, complemented
38#14582801C2211yescharacteristic
39#14582801C2211yescharacteristic
40#14582801C2211yescharacteristic
41#14582801C2211yescharacteristic
42#14582800—21no—
43#14582800—21no—
44#14582797C2211yescharacteristic, complemented
45#14582797C2211yescharacteristic, complemented
46#14582759C2211yescharacteristic
47#14582754—21no—
48#14582754—21no—
49#14582662C2211yescharacteristic, complemented
50#14582662C2211yescharacteristic, complemented
51#14582662C2211yescharacteristic, complemented
52#14582662C2211yescharacteristic, complemented
53C2×#117×C43C2211yescharacteristic
54C43×#433—24no—
55C2×C4⋊C8×C43C2211yescharacteristic, complemented
56C2×C4⋊C8×C43C2211yescharacteristic, complemented
57C2×C22⋊C8×C43C2211yescharacteristic
58C2×C22⋊C8×C43C2211yescharacteristic
59C2×#97×C43C2211yescharacteristic, complemented
60C2×C4×C8×C43C2211yescharacteristic, complemented
61C24×D43—21no—
62C22×Dic86C2311yescharacteristic
63C22×D172—21no—
64C22×D172—22no—
65C22×D172—22no—
66C22×D172—22no—
67C22×D172—22no—
68C22×D172—41no—
69C22×D172—41no—
70C22×D172C2311yescharacteristic
71C22×D172C2311yescharacteristic
72C2×#10621873—22no—
73C2×#10621873—22no—
74C2×#10621873—22no—
75C2×#10621873—22no—
76C2×#10621873—41no—
77C2×#10621873—41no—
78#13063304—22no—
79#13063304—22no—
80#13063284—41no—
81#13063284—41no—
82C2×C4⋊Dic43C2311yescharacteristic
83C2×C4⋊Dic43C2311yescharacteristic
84C2×C4⋊Dic43C2311yescharacteristic
85C2×C4⋊Dic43C2311yescharacteristic
86C2×C4⋊Dic43C2311yescharacteristic
87C2×Dic43⋊C4—21no—
88C2×Dic43⋊C4—21no—
89C2×Dic43⋊C4—21no—
90C2×C22⋊Dic43—21no—
91C2×C22⋊Dic43—21no—
92C2×C22⋊Dic43—21no—
93C2×(C2×D43)⋊C4—21no—
94C2×(C2×D43)⋊C4—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×C4×Dic43—21no—
102#13063259—41no—
103#13063257—41no—
104#13063250—41no—
105#13063250—41no—
106#13063247—22no—
107#13063247—22no—
108#13063247—22no—
109#13063247—22no—
110#13063247—41no—
111#13063247—41no—
112C43⋊#95—21no—
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
122C22×C8×C43C2311yescharacteristic
123C22×C8×C43C2311yescharacteristic
124#117×C43—22no—
125#117×C43—22no—
126C2×C4⋊C4×C43D411yescharacteristic
127C2×C4⋊C4×C43D411yescharacteristic
128C2×C22⋊C4×C43D411yescharacteristic
129C2×C22⋊C4×C43D411yescharacteristic
130C2×C42×C43C2311yescharacteristic
131C2×C42×C43C2311yescharacteristic
132C4⋊C8×C43—22no—
133C4⋊C8×C43—22no—
134C22⋊C8×C43—22no—
135C22⋊C8×C43D414yes—
136#97×C43—22no—
137C4×C8×C43—22no—
138C24×C43C2×D411yescharacteristic
139C23×D43—21no—
140C23×D43—21no—
141C23×D43—24no—
142C23×D43—42no—
143C23×D43—42no—
144C23×D43—81no—
145C23×D43—81no—
146C23×D43—81no—
147C23×D43—81no—
148C22×C4×C43—21no—
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43C2×D412yes—
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43C2×D411yescharacteristic
156C22×C4×C43C2×D411yescharacteristic
157C22×C4×C43C2×D411yescharacteristic
158C22×C4×C43#4112yes—
159C22×C4×C43C2411yescharacteristic
160C22×Dic43—21no—
161C22×Dic43—21no—
162C22×Dic43—21no—
163C22×Dic43—21no—
164C22×Dic43—21no—
165C22×Dic43—21no—
166C2×D172—24no—
167C2×D172—21no—
168C2×D172—21no—
169C2×D172—21no—
170C2×D172—21no—
171C2×D172—21no—
172C2×D172—21no—
173C2×D172—21no—
174C2×D172—21no—
175C2×D172—21no—
176C2×D172—21no—
177C2×D172—44no—
178C2×D172—44no—
179C2×D172—44no—
180C2×D172—44no—
181C2×D172—42no—
182C2×D172—42no—
183C2×D172#4112yes—
184C2×D172#4112yes—
185C2×Dic86—21no—
186C2×Dic86—21no—
187C2×Dic86—21no—
188C2×Dic86—21no—
189C2×Dic86—21no—
190C2×Dic86—21no—
191C2×C8×C43—21no—
192C2×C8×C43—21no—
193C2×C8×C43—21no—
194C2×C8×C43—21no—
195C2×C8×C43—21no—
196C2×C8×C43—21no—
197C2×C8×C43—21no—
198C2×C8×C43—21no—
199C2×C8×C43—21no—
200C2×C8×C43—21no—
201C2×C8×C43C2×D412yes—
202C2×C8×C43C2×D412yes—
203C4⋊C4×C43—22no—
204C4⋊C4×C43—22no—
205C22⋊C4×C43—22no—
206C22⋊C4×C43—22no—
207C42×C43—21no—
208C42×C43—21no—
209C42×C43—21no—
210C42×C43—21no—
211C22⋊Dic43—42no—
212C22⋊Dic43—42no—
213C22⋊Dic43—81no—
214(C2×D43)⋊C4—81no—
215(C2×D43)⋊C4—81no—
216(C2×D43)⋊C4—81no—
217(C2×D43)⋊C4—81no—
218(C2×D43)⋊C4—81no—
219(C2×D43)⋊C4—81no—
220(C2×D43)⋊C4—81no—
221(C2×D43)⋊C4—81no—
222C4⋊Dic43—21no—
223C4⋊Dic43—21no—
224C4⋊Dic43—21no—
225C4⋊Dic43—21no—
226C4⋊Dic43—21no—
227C4⋊Dic43—21no—
228C4⋊Dic43—21no—
229C4⋊Dic43—21no—
230C4⋊Dic43—21no—
231C4⋊Dic43—21no—
232Dic43⋊C4—42no—
233Dic43⋊C4—81no—
234Dic43⋊C4—81no—
235C4×Dic43—42no—
236#10621873—44no—
237#10621873—44no—
238C23×C43—21no—
239C23×C43—21no—
240C23×C43—21no—
241C23×C43—21no—
242C23×C43—21no—
243C23×C43—21no—
244C23×C43#12112yes—
245C23×C43C22×D411yescharacteristic
246C22×D43—22no—
247C22×D43—22no—
248C22×D43—48no—
249C22×D43—41no—
250C22×D43—41no—
251C22×D43—41no—
252C22×D43—41no—
253C22×D43—41no—
254C22×D43—41no—
255C22×D43—41no—
256C22×D43—41no—
257C22×D43—41no—
258C22×D43—41no—
259C22×D43—41no—
260C22×D43—41no—
261C22×D43—84no—
262C22×D43—84no—
263C22×D43—84no—
264C22×D43—84no—
265C22×D43—84no—
266C22×D43—84no—
267C2×C4×C43—21no—
268C2×C4×C43—21no—
269C2×C4×C43—22no—
270C2×C4×C43—22no—
271C2×C4×C43—22no—
272C2×C4×C43—22no—
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—21no—
284C2×C4×C43—21no—
285C2×C4×C43#12112yes—
286C2×C4×C43C22×D411yescharacteristic
287C2×C4×C43C2×#4111yescharacteristic
288C2×C4×C43C2×#4111yescharacteristic
289C2×C4×C43C2×#4111yescharacteristic
290C2×C4×C43H(5,𝔽2)11yescharacteristic
291C2×C4×C43H(5,𝔽2)11yescharacteristic
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—41no—
302C2×Dic43—41no—
303C2×Dic43—41no—
304C2×Dic43—41no—
305C2×Dic43—41no—
306C2×Dic43—41no—
307C2×Dic43—41no—
308C2×Dic43—41no—
309C2×Dic43—41no—
310D172—22no—
311D172—22no—
312D172—22no—
313D172—22no—
314D172—48no—
315D172—41no—
316D172—41no—
317D172—41no—
318D172—41no—
319Dic86—41no—
320Dic86—41no—
321Dic86—41no—
322Dic86—41no—
323C8×C43—22no—
324C8×C43—22no—
325C8×C43—41no—
326C8×C43—41no—
327#24516—431nomaximal, Sylow
328C22×C43—22no—
329C22×C43—22no—
330C22×C43—22no—
331C22×C43—41no—
332C22×C43—41no—
333C22×C43—41no—
334C22×C43—41no—
335C22×C43C2×#12111yescharacteristic
336C22×C43#52511yescharacteristic
337C22×C43#53511yescharacteristic
338C22×C43#57611yescharacteristic
339C22×C43#57711yescharacteristic
340C22×C43#57711yescharacteristic
341C22×C43#57711yescharacteristic
342C2×D43—42no—
343C2×D43—42no—
344C2×D43—42no—
345C2×D43—42no—
346C2×D43—42no—
347C2×D43—42no—
348C2×D43—816no—
349C2×D43—81no—
350C2×D43—81no—
351C2×D43—81no—
352C2×D43—81no—
353C2×D43—81no—
354C2×D43—81no—
355C2×D43—81no—
356C2×D43—81no—
357C4×C43—22no—
358C4×C43—41no—
359C4×C43—41no—
360C4×C43—41no—
361C4×C43—41no—
362C4×C43#54611yescharacteristic
363C4×C43#54611yescharacteristic
364C4×C43#55111yescharacteristic
365C4×C43#55111yescharacteristic
366Dic43—81no—
367Dic43—81no—
368Dic43—81no—
369Dic43—81no—
370Dic43—81no—
371Dic43—81no—
372C2×#450—431no—
373C2×#433D4311yescharacteristic, complemented
374#2625—431no—
375#2309—431no—
376#2067—431no—
377#2065—431no—
378#2055—431no—
379#2055—431no—
380#1973—431no—
381#1968—431no—
382#1936—431no—
383#1934—431no—
384#1873—431no—
385#1854—431no—
386#1786—431no—
387C2×C43—42no—
388C2×C43#241111yescharacteristic
389C2×C43#305711yescharacteristic
390C2×C43#306211yescharacteristic
391C2×C43#311811yescharacteristic
392C2×C43#312311yescharacteristic
393C2×C43#322211yescharacteristic
394C2×C43#322411yescharacteristic
395D43—82no—
396D43—82no—
397C23×D4—431no—
398C22×SD16—431no—
399C22×SD16—431no—
400C2×C22⋊Q8—431no—
401C2×#117—431no—
402C2×#117C2×D4311yescharacteristic
403#450—864no—
404#433—24no—
405C2×#107—431no—
406C2×#106—431no—
407C2×C4⋊C8C2×D4311yescharacteristic, complemented
408C2×C4⋊C8C2×D4311yescharacteristic, complemented
409C2×#103—431no—
410C2×#103—431no—
411C2×#102—431no—
412C2×#102—431no—
413C2×#102—431no—
414C2×#102—431no—
415C2×#102—431no—
416C2×#102—431no—
417C2×C22⋊C8C2×D4311yescharacteristic
418C2×C22⋊C8C2×D4311yescharacteristic
419C2×#97C2×D4311yescharacteristic, complemented
420C2×C4×C8C2×D4311yescharacteristic, complemented
421#400—861no—
422#398—861no—
423#397—861no—
424#397—861no—
425#391—431no—
426#391—431no—
427#390—431no—
428#390—431no—
429#390—431no—
430#390—431no—
431#390—861no—
432#390—861no—
433#389—431no—
434#389—431no—
435#380—431no—
436#379—861no—
437#379—861no—
438#340—431no—
439#340—431no—
440#340—431no—
441#340—431no—
442C43#2451611yescharacteristic, complemented, Sylow
443C25—861no—
444C22×Q8—431no—
445C22×D4—431no—
446C22×D4—431no—
447C22×D4—862no—
448C22×D4—862no—
449C22×D4—861no—
450C22×D4—862no—
451C22×D4—862no—
452C22×D4—1721no—
453C22×D4—1721no—
454C23×C4C22×D4311yescharacteristic
455C2×SD16—862no—
456C2×SD16—862no—
457C2×SD16—862no—
458C2×SD16—862no—
459C2×SD16—1721no—
460C2×SD16—1721no—
461C22×C8C22×D4311yescharacteristic
462C22×C8C22×D4311yescharacteristic
463C22×C8C22×D4311yescharacteristic
464C22×C8C22×D4311yescharacteristic
465C22⋊Q8—862no—
466C22⋊Q8—862no—
467#117—22no—
468#117—22no—
469#117—1721no—
470#117—1721no—
471C2×C4⋊C4—431no—
472C2×C4⋊C4—431no—
473C2×C4⋊C4—431no—
474C2×C4⋊C4—431no—
475C2×C4⋊C4—431no—
476C2×C4⋊C4—861no—
477C2×C4⋊C4—861no—
478C2×C4⋊C4—861no—
479C2×C4⋊C4D17211yescharacteristic
480C2×C4⋊C4D17211yescharacteristic
481C2×C22⋊C4—861no—
482C2×C22⋊C4—861no—
483C2×C22⋊C4—861no—
484C2×C22⋊C4—861no—
485C2×C22⋊C4—861no—
486C2×C22⋊C4—861no—
487C2×C22⋊C4—861no—
488C2×C22⋊C4—861no—
489C2×C22⋊C4—861no—
490C2×C22⋊C4—861no—
491C2×C22⋊C4—861no—
492C2×C22⋊C4D17211yescharacteristic
493C2×C22⋊C4D17211yescharacteristic
494C2×C42—861no—
495C2×C42C22×D4311yescharacteristic
496C2×C42C22×D4311yescharacteristic
497#107—1721no—
498#106—1721no—
499C4⋊C8—22no—
500C4⋊C8—22no—
501#103—1721no—
502#103—1721no—
503#102—862no—
504#102—862no—
505#102—862no—
506#102—862no—
507#102—1721no—
508#102—1721no—
509C22⋊C8—22no—
510C22⋊C8C22⋊D4314yes—
511#97—22no—
512C4×C8—22no—
513#95—861no—
514#95—861no—
515#95—861no—
516#95—861no—
517#95—861no—
518#95—861no—
519#95—861no—
520C24—864no—
521C24—861no—
522C24—861no—
523C24—3441no—
524C24—3441no—
525C24—3441no—
526C24—3441no—
527C24—1722no—
528C24—1722no—
529C24C2×D17211yescharacteristic
530C2×Q8—861no—
531C2×Q8—861no—
532C2×Q8—861no—
533C2×Q8—861no—
534C2×Q8—861no—
535C2×Q8—861no—
536C2×D4—432no—
537C2×D4—432no—
538C2×D4—864no—
539C2×D4—861no—
540C2×D4—861no—
541C2×D4—861no—
542C2×D4—861no—
543C2×D4—861no—
544C2×D4—861no—
545C2×D4—861no—
546C2×D4—861no—
547C2×D4—861no—
548C2×D4—861no—
549C2×D4—1724no—
550C2×D4—1724no—
551C2×D4—1724no—
552C2×D4—1724no—
553C2×D4—1722no—
554C2×D4—1722no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—861no—
560C22×C4—861no—
561C22×C4—861no—
562C22×C4—861no—
563C22×C4—861no—
564C22×C4—861no—
565C22×C4C2×D17211yescharacteristic
566C22×C4C2×D17211yescharacteristic
567C22×C4C2×D17211yescharacteristic
568C22×C4C2×D17211yescharacteristic
569C22×C4C2×D17211yescharacteristic
570C22×C4#1062189812yes—
571C22×C4C2×C22⋊D4312yes—
572C22×C4C23×D4311yescharacteristic
573SD16—1724no—
574SD16—1724no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8C2×C22⋊D4312yes—
586C2×C8C2×C22⋊D4312yes—
587C4⋊C4—22no—
588C4⋊C4—22no—
589C4⋊C4—861no—
590C4⋊C4—861no—
591C4⋊C4—861no—
592C4⋊C4—861no—
593C4⋊C4—861no—
594C4⋊C4—861no—
595C4⋊C4—861no—
596C4⋊C4—861no—
597C4⋊C4—861no—
598C4⋊C4—861no—
599C4⋊C4—3441no—
600C4⋊C4—3441no—
601C4⋊C4—1722no—
602C22⋊C4—22no—
603C22⋊C4—22no—
604C22⋊C4—3441no—
605C22⋊C4—3441no—
606C22⋊C4—3441no—
607C22⋊C4—3441no—
608C22⋊C4—3441no—
609C22⋊C4—3441no—
610C22⋊C4—3441no—
611C22⋊C4—3441no—
612C22⋊C4—3441no—
613C22⋊C4—1722no—
614C22⋊C4—1722no—
615C42—21no—
616C42—21no—
617C42—21no—
618C42—21no—
619C42—1722no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—862no—
627C23—862no—
628C23—3444no—
629C23—3444no—
630C23—3444no—
631C23—3444no—
632C23—3444no—
633C23—3444no—
634C23—1728no—
635C23—1721no—
636C23—1721no—
637C23—1721no—
638C23—1721no—
639C23—1721no—
640C23—1721no—
641C23—1721no—
642C23—1721no—
643C23—1721no—
644C23—1721no—
645C23—1721no—
646C23—1721no—
647C23#1306329912yes—
648C23C22×D17211yescharacteristic
649Q8—1721no—
650Q8—1721no—
651Q8—1721no—
652Q8—1721no—
653D4—862no—
654D4—862no—
655D4—862no—
656D4—862no—
657D4—1728no—
658D4—1721no—
659D4—1721no—
660D4—1721no—
661D4—1721no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—1721no—
681C2×C4—1721no—
682C2×C4—1721no—
683C2×C4—1721no—
684C2×C4—1721no—
685C2×C4—1721no—
686C2×C4—1721no—
687C2×C4—1721no—
688C2×C4—1721no—
689C2×C4—1721no—
690C2×C4—1721no—
691C2×C4—1721no—
692C2×C4—1721no—
693C2×C4—1721no—
694C2×C4—1721no—
695C2×C4—1721no—
696C2×C4—1721no—
697C2×C4—1721no—
698C2×C4#1306329912yes—
699C2×C4C22×C22⋊D4311yescharacteristic
700C2×C4#41×D4311yescharacteristic
701C2×C4#41×D4311yescharacteristic
702C2×C4C2×#1062189811yescharacteristic
703C2×C4#1306337111yescharacteristic
704C2×C4#1306337111yescharacteristic
705C8—22no—
706C8—22no—
707C8—41no—
708C8—41no—
709C22—22no—
710C22—22no—
711C22—22no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—34416no—
717C22—3441no—
718C22—3441no—
719C22—3441no—
720C22—3441no—
721C22—3441no—
722C22—3441no—
723C22—3441no—
724C22—3441no—
725C22—1722no—
726C22—1722no—
727C22—1722no—
728C22—1722no—
729C22—1722no—
730C22—1722no—
731C22C2×#1306329911yescharacteristic
732C22#1458341111yescharacteristic
733C22#1458346811yescharacteristic
734C22#1458370411yescharacteristic
735C22#1458371111yescharacteristic
736C22#1458371111yescharacteristic
737C22#1458371111yescharacteristic
738C4—22no—
739C4—41no—
740C4—41no—
741C4—41no—
742C4—41no—
743C4—3441no—
744C4—3441no—
745C4—3441no—
746C4—3441no—
747C4—3441no—
748C4—3441no—
749C4#1458353711yescharacteristic
750C4#1458353711yescharacteristic
751C4#1458357311yescharacteristic
752C4#1458357311yescharacteristic
753C2—42no—
754C2—3442no—
755C2—3442no—
756C2#1913797411yescharacteristic
757C2#1914423411yescharacteristic
758C2#1914427511yescharacteristic
759C2#1914478111yescharacteristic
760C2#1914484811yescharacteristic
761C2#1914566911yescharacteristic
762C2#1914569111yescharacteristic
subgroupG/H
centerC23C22×D172
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#433C2
socleC23×C43C22×D4
prime radicalC23×D172C22
hypercenterC2×#433D43
hypocenterC43#24516
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#433

Complements

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

NH ≅ G/Ntype
2. #19140392C2semidirect
4. #19135982C2semidirect
5. #19135968C2semidirect
6. #19135913C2semidirect
7. #19135913C2semidirect
8. #19135476C2semidirect
9. #19135449C2semidirect
10. #19135292C2semidirect
11. #19135278C2semidirect
12. #19134905C2semidirect
13. #19134796C2semidirect
15. C2×C43×#433C2semidirect
22. C2×#13063259C22semidirect
23. C2×#13063257C22semidirect
24. C2×#13063250C22semidirect
25. C2×#13063250C22semidirect
36. #14582805C22semidirect
37. #14582805C22semidirect
44. #14582797C22semidirect
45. #14582797C22semidirect
49. #14582662C22semidirect
50. #14582662C22semidirect
51. #14582662C22semidirect
52. #14582662C22semidirect
55. C2×C4⋊C8×C43C22semidirect
56. C2×C4⋊C8×C43C22semidirect
59. C2×#97×C43C22semidirect
60. C2×C4×C8×C43C22semidirect
373. C2×#433D43semidirect
407. C2×C4⋊C8C2×D43semidirect
408. C2×C4⋊C8C2×D43semidirect
419. C2×#97C2×D43semidirect
420. C2×C4×C8C2×D43semidirect
442. C43#24516semidirect

Maximal subgroups

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

subgroupindex
C2×#145830522
#191403922
#191371752
#191359822
#191359682
#191359132
#191354762
#191354492
#191352922
#191352782
#191349052
#191347962
#191345272
C2×C43×#4332
#2451643