Finite Group Databasebeta

← #25149713

Subgroups — #25149713

Order 11008.

1124 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583606C211yesmaximal, characteristic
2C2×#14583230C211yesmaximal, characteristic, complemented
3C2×#14583157C211yesmaximal, characteristic, complemented
4#19138024C211yesmaximal, characteristic
5#19135929C211yesmaximal, characteristic, complemented
6#19135792C211yesmaximal, characteristic, complemented
7#19135737C211yesmaximal, characteristic, complemented
8#19135605C211yesmaximal, characteristic, complemented
9#19134935C211yesmaximal, characteristic, complemented
10#19134905C211yesmaximal, characteristic, complemented
11#19134900C211yesmaximal, characteristic, complemented
12#19134866C211yesmaximal, characteristic, complemented
13#19134790C211yesmaximal, characteristic, complemented
14#19134315C211yesmaximal, characteristic, complemented
15C43×#1870C211yesmaximal, characteristic
16C22×Dic172C2211yescharacteristic
17#14583606—24no—
18#14583606—24no—
19C2×#13063325C2211yescharacteristic
20C2×#13063316—21no—
21C2×#13063304C2211yescharacteristic
22C2×#13063304C2211yescharacteristic
23C2×#13063304C2211yescharacteristic
24C2×#13063304C2211yescharacteristic
25C2×#13063302—21no—
26C2×#13063302—21no—
27C2×C4×Dic86C2211yescharacteristic
28C2×D4×Dic43—21no—
29C2×#13063284C2211yescharacteristic
30C22×C4⋊Dic43C2211yescharacteristic
31C22×C4⋊Dic43C2211yescharacteristic
32#14583230—24no—
33#14583157—24no—
34C2×#13063257C2211yescharacteristic
35C2×#13063257C2211yescharacteristic
36C2×#13063257C2211yescharacteristic
37C2×#13063250C2211yescharacteristic
38C2×#13063250C2211yescharacteristic
39C2×#13063250C2211yescharacteristic
40C2×#13063250C2211yescharacteristic
41C2×#13063250C2211yescharacteristic
42C2×#13063250C2211yescharacteristic
43#14582827—21no—
44#14582813—21no—
45#14582805C2211yescharacteristic
46#14582797C2211yescharacteristic
47#14582794—21no—
48#14582793—21no—
49#14582759C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582662C2211yescharacteristic
52#14582662C2211yescharacteristic
53#14582662C2211yescharacteristic
54#14582662C2211yescharacteristic
55#14582662C2211yescharacteristic
56C22×M16×C43C2211yescharacteristic
57C2×C4×D4×C43C2211yescharacteristic
58C2×C22⋊C8×C43C2211yescharacteristic
59C2×C22⋊C8×C43C2211yescharacteristic
60C2×C22⋊C8×C43C2211yescharacteristic
61C43×#336C2211yescharacteristic
62C43×#336C2211yescharacteristic
63C22×Dic86—21no—
64C22×Dic86C2311yescharacteristic
65C22×Dic86C2311yescharacteristic
66C23×Dic43—21no—
67C23×Dic43—21no—
68C2×Dic172—22no—
69C2×Dic172—22no—
70C2×Dic172—41no—
71#13063325—22no—
72#13063325—22no—
73#13063316—28no—
74#13063304—22no—
75#13063304—22no—
76#13063304—22no—
77#13063304—22no—
78#13063304—22no—
79#13063304—22no—
80#13063304—41no—
81#13063304D414yes—
82#13063302—28no—
83#13063302—28no—
84C4×Dic86—22no—
85C4×Dic86—22no—
86D4×Dic43—28no—
87#13063284—22no—
88#13063284—41no—
89C2×C4⋊Dic43—22no—
90C2×C4⋊Dic43—21no—
91C2×C4⋊Dic43—21no—
92C2×C4⋊Dic43—21no—
93C2×C4⋊Dic43—22no—
94C2×C4⋊Dic43—22no—
95C2×C4⋊Dic43D414yes—
96C2×C4⋊Dic43C2311yescharacteristic
97C2×C4⋊Dic43C2311yescharacteristic
98C2×C4⋊Dic43C2311yescharacteristic
99C2×C4⋊Dic43C2311yescharacteristic
100C2×C4⋊Dic43C2311yescharacteristic
101C2×C4⋊Dic43C2311yescharacteristic
102C2×Dic43⋊C4—21no—
103C2×Dic43⋊C4—21no—
104C2×Dic43⋊C4—21no—
105C2×Dic43⋊C4—21no—
106C2×Dic43⋊C4—21no—
107C2×Dic43⋊C4—21no—
108C2×C22⋊Dic43—21no—
109C2×C22⋊Dic43—21no—
110C2×C22⋊Dic43—21no—
111C2×C22⋊Dic43—21no—
112C2×C22⋊Dic43—21no—
113C2×C22⋊Dic43—21no—
114C2×C4×Dic43—21no—
115C2×C4×Dic43—21no—
116#13063257—22no—
117#13063257—22no—
118#13063257—22no—
119#13063250—22no—
120#13063250—22no—
121#13063250—22no—
122#13063250—22no—
123#13063250—22no—
124#13063250—41no—
125C43⋊#95—21no—
126C43⋊#95—21no—
127C43⋊#95—21no—
128C43⋊#95—21no—
129C22×D4×C43D411yescharacteristic
130C23×C4×C43C2311yescharacteristic
131C23×C4×C43C2311yescharacteristic
132C2×M16×C43—22no—
133C2×M16×C43—22no—
134C2×M16×C43—41no—
135C22×C8×C43C2311yescharacteristic
136C22×C8×C43C2311yescharacteristic
137C22×C8×C43C2311yescharacteristic
138C22×C8×C43C2311yescharacteristic
139C4×D4×C43—22no—
140C4×D4×C43—22no—
141C2×C4⋊C4×C43D411yescharacteristic
142C2×C22⋊C4×C43D411yescharacteristic
143C2×C22⋊C4×C43D411yescharacteristic
144C2×C42×C43C2311yescharacteristic
145C22⋊C8×C43—22no—
146C22⋊C8×C43—22no—
147C22⋊C8×C43—41no—
148C24×C43C2×D411yescharacteristic
149C24×C43C2×D411yescharacteristic
150C2×D4×C43—22no—
151C2×D4×C43—22no—
152C2×D4×C43—22no—
153C22×C4×C43—21no—
154C22×C4×C43—21no—
155C22×C4×C43—21no—
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43—21no—
159C22×C4×C43—21no—
160C22×C4×C43—21no—
161C22×C4×C43—21no—
162C22×C4×C43—21no—
163C22×C4×C43C2×D412yes—
164C22×C4×C43C2×D412yes—
165C22×C4×C43C2×D411yescharacteristic
166C22×C4×C43C2×D411yescharacteristic
167C22×C4×C43C2×D411yescharacteristic
168C22×C4×C43C2×D411yescharacteristic
169C22×C4×C43C2411yescharacteristic
170C22×Dic43—24no—
171C22×Dic43—24no—
172C22×Dic43—21no—
173C22×Dic43—21no—
174C22×Dic43—21no—
175C22×Dic43—21no—
176C22×Dic43—21no—
177C22×Dic43—21no—
178C22×Dic43—21no—
179C22×Dic43—21no—
180C22×Dic43—81no—
181C22×Dic43—81no—
182C22×Dic43—81no—
183C22×Dic43—81no—
184C2×Dic86—21no—
185C2×Dic86—21no—
186C2×Dic86—21no—
187C2×Dic86—21no—
188C2×Dic86—21no—
189C2×Dic86—21no—
190C2×Dic86—21no—
191C2×Dic86—21no—
192C2×Dic86—21no—
193C2×Dic86—21no—
194C2×Dic86—21no—
195C2×Dic86—24no—
196C2×Dic86—81no—
197C2×Dic86—81no—
198C2×Dic86C2×D412yes—
199M16×C43—44no—
200C2×C8×C43—21no—
201C2×C8×C43—21no—
202C2×C8×C43—21no—
203C2×C8×C43—21no—
204C2×C8×C43—21no—
205C2×C8×C43—21no—
206C2×C8×C43—21no—
207C2×C8×C43—21no—
208C2×C8×C43—21no—
209C2×C8×C43—21no—
210C2×C8×C43—21no—
211C2×C8×C43#4112yes—
212C4⋊C4×C43—22no—
213C22⋊C4×C43—22no—
214C22⋊C4×C43—22no—
215C42×C43—21no—
216C42×C43—21no—
217C22⋊Dic43—24no—
218C22⋊Dic43—24no—
219C22⋊Dic43—42no—
220C22⋊Dic43—42no—
221C22⋊Dic43—42no—
222C22⋊Dic43—42no—
223C4⋊Dic43—24no—
224C4⋊Dic43—24no—
225C4⋊Dic43—24no—
226C4⋊Dic43—21no—
227C4⋊Dic43—21no—
228C4⋊Dic43—21no—
229C4⋊Dic43—21no—
230C4⋊Dic43—21no—
231C4⋊Dic43—21no—
232C4⋊Dic43—21no—
233C4⋊Dic43—21no—
234C4⋊Dic43C2×D412yes—
235C4⋊Dic43C2×D412yes—
236C4⋊Dic43C2×D412yes—
237C4⋊Dic43#4112yes—
238Dic43⋊C4—24no—
239Dic43⋊C4—24no—
240Dic43⋊C4—24no—
241Dic43⋊C4—42no—
242Dic43⋊C4—42no—
243Dic43⋊C4—42no—
244C4×Dic43—24no—
245C4×Dic43—42no—
246Dic172—44no—
247C23×C43—21no—
248C23×C43—21no—
249C23×C43—21no—
250C23×C43—21no—
251C23×C43—21no—
252C23×C43—21no—
253C23×C43—21no—
254C23×C43—21no—
255C23×C43—21no—
256C23×C43—21no—
257C23×C43—21no—
258C23×C43—21no—
259C23×C43#12012yes—
260C23×C43#13712yes—
261C23×C43C22×D411yescharacteristic
262D4×C43—28no—
263C2×C4×C43—21no—
264C2×C4×C43—21no—
265C2×C4×C43—21no—
266C2×C4×C43—21no—
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—41no—
278C2×C4×C43—41no—
279C2×C4×C43—41no—
280C2×C4×C43—41no—
281C2×C4×C43#12012yes—
282C2×C4×C43#13712yes—
283C2×C4×C43C22×D411yescharacteristic
284C2×C4×C43C22×D411yescharacteristic
285C2×C4×C43C2×#4111yescharacteristic
286C2×C4×C43C2×#4111yescharacteristic
287C2×C4×C43H(5,𝔽2)11yescharacteristic
288C2×C4×C432−1+411yescharacteristic
289C2×Dic43—22no—
290C2×Dic43—22no—
291C2×Dic43—22no—
292C2×Dic43—22no—
293C2×Dic43—22no—
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—
310C2×Dic43—41no—
311C2×Dic43—41no—
312C2×Dic43—41no—
313C2×Dic43—84no—
314C2×Dic43—84no—
315Dic86—22no—
316Dic86—22no—
317Dic86—41no—
318Dic86—41no—
319Dic86—41no—
320Dic86—41no—
321Dic86—41no—
322Dic86—41no—
323Dic86—84no—
324C8×C43—22no—
325C8×C43—41no—
326C8×C43—41no—
327C8×C43—41no—
328#25561—431nomaximal, Sylow
329C22×C43—22no—
330C22×C43—22no—
331C22×C43—22no—
332C22×C43—22no—
333C22×C43—22no—
334C22×C43—22no—
335C22×C43—41no—
336C22×C43—41no—
337C22×C43—41no—
338C22×C43—41no—
339C22×C43—41no—
340C22×C43—41no—
341C22×C43—41no—
342C22×C43—41no—
343C22×C43C2×#12011yescharacteristic
344C22×C43#54611yescharacteristic
345C22×C43#54711yescharacteristic
346C22×C43C2×#13711yescharacteristic
347C22×C43C2×#13711yescharacteristic
348C22×C43#57711yescharacteristic
349C22×C43#57711yescharacteristic
350C4×C43—22no—
351C4×C43—22no—
352C4×C43—41no—
353C4×C43—41no—
354C4×C43#53211yescharacteristic
355C4×C43#53711yescharacteristic
356C4×C43#54611yescharacteristic
357C4×C43#54711yescharacteristic
358Dic43—42no—
359Dic43—42no—
360Dic43—42no—
361Dic43—42no—
362Dic43—42no—
363Dic43—81no—
364Dic43—81no—
365Dic43—81no—
366C2×#554—431no—
367C2×#483—431no—
368C2×#470—431no—
369#2415—431no—
370#2058—431no—
371#2035—431no—
372#2024—431no—
373#2001—431no—
374#1878—431no—
375#1873—431no—
376#1872—431no—
377#1870D4311yescharacteristic
378#1865—431no—
379#1853—431no—
380#1736—431no—
381C2×C43—42no—
382C2×C43—42no—
383C2×C43#243011yescharacteristic
384C2×C43#300411yescharacteristic
385C2×C43#300911yescharacteristic
386C2×C43#331611yescharacteristic
387C2×C43#333111yescharacteristic
388C2×C43#334411yescharacteristic
389C2×C43#335611yescharacteristic
390C22×Q16—431no—
391C22×M16C2×D4311yescharacteristic
392#554—864no—
393#554—864no—
394C2×C4⋊Q8—431no—
395C2×#125—861no—
396C2×C22⋊Q8—431no—
397C2×C22⋊Q8—431no—
398C2×C22⋊Q8—431no—
399C2×C22⋊Q8—431no—
400C2×C22⋊Q8—861no—
401C2×C22⋊Q8—861no—
402C2×C4×Q8—431no—
403C2×C4×D4—861no—
404C2×C4×D4C2×D4311yescharacteristic
405C2×#117—431no—
406C22×C4⋊C4—431no—
407C22×C4⋊C4—431no—
408#483—864no—
409#470—864no—
410C2×#106—431no—
411C2×#106—431no—
412C2×#106—431no—
413C2×#103—431no—
414C2×#103—431no—
415C2×#103—431no—
416C2×#103—431no—
417C2×#103—431no—
418C2×#103—431no—
419C2×C22⋊C8C2×D4311yescharacteristic
420C2×C22⋊C8C2×D4311yescharacteristic
421C2×C22⋊C8C2×D4311yescharacteristic
422#397—861no—
423#394—861no—
424#391—431no—
425#389—431no—
426#389—861no—
427#388—861no—
428#380—431no—
429#340—431no—
430#340—431no—
431#340—431no—
432#340—431no—
433#340—431no—
434#340—431no—
435#336C2×D4311yescharacteristic
436#336C2×D4311yescharacteristic
437C43#2556111yescharacteristic, complemented, Sylow
438C22×Q8—431no—
439C22×Q8—431no—
440C22×Q8—861no—
441C22×D4D17211yescharacteristic
442C23×C4—861no—
443C23×C4—861no—
444C23×C4C22×D4311yescharacteristic
445C23×C4C22×D4311yescharacteristic
446C2×Q16—862no—
447C2×Q16—862no—
448C2×Q16—1721no—
449C2×M16—22no—
450C2×M16—22no—
451C2×M16—41no—
452C22×C8C22×D4311yescharacteristic
453C22×C8C22×D4311yescharacteristic
454C22×C8C22×D4311yescharacteristic
455C22×C8C22×D4311yescharacteristic
456C4⋊Q8—862no—
457C4⋊Q8—862no—
458#125—868no—
459C22⋊Q8—434no—
460C22⋊Q8—868no—
461C22⋊Q8—868no—
462C22⋊Q8—862no—
463C22⋊Q8—862no—
464C22⋊Q8—862no—
465C22⋊Q8—862no—
466C22⋊Q8—862no—
467C22⋊Q8—862no—
468C22⋊Q8—1721no—
469C4×Q8—862no—
470C4×Q8—862no—
471C4×D4—22no—
472C4×D4—22no—
473C4×D4—868no—
474#117—862no—
475#117—1721no—
476C2×C4⋊C4—434no—
477C2×C4⋊C4—431no—
478C2×C4⋊C4—431no—
479C2×C4⋊C4—431no—
480C2×C4⋊C4—431no—
481C2×C4⋊C4—431no—
482C2×C4⋊C4—431no—
483C2×C4⋊C4—862no—
484C2×C4⋊C4—862no—
485C2×C4⋊C4—861no—
486C2×C4⋊C4—861no—
487C2×C4⋊C4—861no—
488C2×C4⋊C4—861no—
489C2×C4⋊C4—861no—
490C2×C4⋊C4—861no—
491C2×C4⋊C4—862no—
492C2×C4⋊C4—861no—
493C2×C4⋊C4—861no—
494C2×C4⋊C4—861no—
495C2×C4⋊C4D17211yescharacteristic
496C2×C22⋊C4—861no—
497C2×C22⋊C4—861no—
498C2×C22⋊C4—861no—
499C2×C22⋊C4—861no—
500C2×C22⋊C4—861no—
501C2×C22⋊C4—861no—
502C2×C22⋊C4D17211yescharacteristic
503C2×C22⋊C4D17211yescharacteristic
504C2×C42—861no—
505C2×C42—861no—
506C2×C42C22×D4311yescharacteristic
507#106—862no—
508#106—862no—
509#106—862no—
510#103—862no—
511#103—862no—
512#103—862no—
513#103—862no—
514#103—862no—
515#103—1721no—
516C22⋊C8—22no—
517C22⋊C8—22no—
518C22⋊C8—41no—
519#95—861no—
520#95—861no—
521#95—861no—
522#95—861no—
523C24C2×D17211yescharacteristic
524C24C2×D17211yescharacteristic
525C2×Q8—432no—
526C2×Q8—864no—
527C2×Q8—861no—
528C2×Q8—861no—
529C2×Q8—861no—
530C2×Q8—861no—
531C2×Q8—861no—
532C2×Q8—861no—
533C2×Q8—861no—
534C2×Q8—861no—
535C2×Q8—861no—
536C2×Q8—861no—
537C2×Q8—861no—
538C2×Q8—3441no—
539C2×Q8—3441no—
540C2×D4—22no—
541C2×D4—22no—
542C2×D4—22no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—864no—
554C22×C4—864no—
555C22×C4—861no—
556C22×C4—861no—
557C22×C4—861no—
558C22×C4—861no—
559C22×C4—861no—
560C22×C4—861no—
561C22×C4—861no—
562C22×C4—861no—
563C22×C4—3441no—
564C22×C4—3441no—
565C22×C4—3441no—
566C22×C4—3441no—
567C22×C4C2×D17211yescharacteristic
568C22×C4C2×D17211yescharacteristic
569C22×C4C2×D17211yescharacteristic
570C22×C4C2×D17211yescharacteristic
571C22×C4D4×D4312yes—
572C22×C4D4×D4312yes—
573C22×C4C23×D4311yescharacteristic
574Q16—1724no—
575M16—44no—
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×C8—21no—
586C2×C8—21no—
587C2×C8#1062190012yes—
588C4⋊C4—22no—
589C4⋊C4—432no—
590C4⋊C4—432no—
591C4⋊C4—432no—
592C4⋊C4—432no—
593C4⋊C4—864no—
594C4⋊C4—864no—
595C4⋊C4—864no—
596C4⋊C4—864no—
597C4⋊C4—864no—
598C4⋊C4—864no—
599C4⋊C4—861no—
600C4⋊C4—861no—
601C4⋊C4—861no—
602C4⋊C4—861no—
603C4⋊C4—861no—
604C4⋊C4—861no—
605C4⋊C4—861no—
606C4⋊C4—861no—
607C4⋊C4—1722no—
608C4⋊C4—1722no—
609C4⋊C4—1722no—
610C22⋊C4—22no—
611C22⋊C4—22no—
612C22⋊C4—864no—
613C22⋊C4—864no—
614C22⋊C4—1722no—
615C22⋊C4—1722no—
616C22⋊C4—1722no—
617C22⋊C4—1722no—
618C42—21no—
619C42—21no—
620C42—864no—
621C42—1722no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23#1306329512yes—
635C23#1306335812yes—
636C23C22×D17211yescharacteristic
637Q8—862no—
638Q8—862no—
639Q8—3444no—
640Q8—1721no—
641Q8—1721no—
642Q8—1721no—
643Q8—1721no—
644Q8—1721no—
645Q8—1721no—
646D4—28no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—862no—
666C2×C4—862no—
667C2×C4—862no—
668C2×C4—862no—
669C2×C4—862no—
670C2×C4—3444no—
671C2×C4—3444no—
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×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#1306329512yes—
692C2×C4#1306335812yes—
693C2×C4C2×D4×D4311yescharacteristic
694C2×C4C2×D4×D4311yescharacteristic
695C2×C4#41×D4311yescharacteristic
696C2×C4C2×#1062190011yescharacteristic
697C2×C4#1306337011yescharacteristic
698C2×C4#1306337211yescharacteristic
699C8—22no—
700C8—41no—
701C8—41no—
702C8—41no—
703C22—22no—
704C22—22no—
705C22—22no—
706C22—22no—
707C22—22no—
708C22—22no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22C2×#1306329511yescharacteristic
718C22#1458354411yescharacteristic
719C22#1458355311yescharacteristic
720C22C2×#1306335811yescharacteristic
721C22C2×#1306335811yescharacteristic
722C22#1458371111yescharacteristic
723C22#1458371111yescharacteristic
724C4—22no—
725C4—22no—
726C4—41no—
727C4—41no—
728C4—3441no—
729C4—3441no—
730C4—3441no—
731C4—1722no—
732C4—1722no—
733C4—1722no—
734C4—1722no—
735C4—1722no—
736C4#1458344411yescharacteristic
737C4#1458347611yescharacteristic
738C4#1458353611yescharacteristic
739C4#1458354711yescharacteristic
740C2—42no—
741C2—42no—
742C2#1913820311yescharacteristic
743C2#1914383211yescharacteristic
744C2#1914387411yescharacteristic
745C2#1914670811yescharacteristic
746C2#1914691211yescharacteristic
747C2#1914705211yescharacteristic
748C2#1914721111yescharacteristic
subgroupG/H
centerC23C22×D172
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1870C2
socleC23×C43C22×D4
prime radicalC22×D4×C43D4
hypercenter#1870D43
hypocenterC43#25561
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #1870

Complements

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

NH ≅ G/Ntype
2. C2×#14583230C2semidirect
3. C2×#14583157C2semidirect
5. #19135929C2semidirect
6. #19135792C2semidirect
7. #19135737C2semidirect
8. #19135605C2semidirect
9. #19134935C2semidirect
10. #19134905C2semidirect
11. #19134900C2semidirect
12. #19134866C2semidirect
13. #19134790C2semidirect
14. #19134315C2semidirect
437. C43#25561semidirect

Maximal subgroups

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

subgroupindex
C2×#145836062
C2×#145832302
C2×#145831572
#191380242
#191359292
#191357922
#191357372
#191356052
#191349352
#191349052
#191349002
#191348662
#191347902
#191343152
C43×#18702
#2556143