Finite Group Databasebeta

← #25154049

Subgroups — #25154049

Order 11008.

1136 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583200C211yesmaximal, characteristic, complemented
2C2×#14582905C211yesmaximal, characteristic
3#19138308C211yesmaximal, characteristic, complemented
4C22⋊C4×D172C211yesmaximal, characteristic
5#19136127C211yesmaximal, characteristic, complemented
6#19135982C211yesmaximal, characteristic, complemented
7#19135982C211yesmaximal, characteristic, complemented
8#19135742C211yesmaximal, characteristic, complemented
9#19134859C211yesmaximal, characteristic, complemented
10#19134845C211yesmaximal, characteristic, complemented
11#19134796C211yesmaximal, characteristic, complemented
12#19134628C211yesmaximal, characteristic, complemented
13#19134596C211yesmaximal, characteristic, complemented
14#19134527C211yesmaximal, characteristic
15C43×#1851C211yesmaximal, characteristic, complemented
16C23×D172C2211yescharacteristic
17C2×#13063317C2211yescharacteristic, complemented
18C2×C4×D172C2211yescharacteristic
19C2×C4×D172C2211yescharacteristic
20C2×#13063284C2211yescharacteristic
21C2×C22⋊C4×D43—21no—
22#14583200—24no—
23C2×#13063259C2211yescharacteristic, complemented
24C2×#13063259C2211yescharacteristic, complemented
25C2×#13063257C2211yescharacteristic, complemented
26C2×#13063257C2211yescharacteristic, complemented
27#14582905—24no—
28C2×#13063247C2211yescharacteristic
29C2×#13063247C2211yescharacteristic
30C2×#13063247C2211yescharacteristic
31C2×#13063247C2211yescharacteristic
32C2×#13063247C2211yescharacteristic
33C2×#13063247C2211yescharacteristic
34C2×#13063247C2211yescharacteristic
35C2×#13063247C2211yescharacteristic
36#14582835—21no—
37#14582822—21no—
38#14582801C2211yescharacteristic
39#14582801C2211yescharacteristic
40#14582797C2211yescharacteristic, complemented
41#14582797C2211yescharacteristic, complemented
42#14582796—21no—
43#14582782—21no—
44#14582777—21no—
45#14582777—21no—
46#14582769C2211yescharacteristic, complemented
47#14582759C2211yescharacteristic
48#14582759C2211yescharacteristic
49#14582754—21no—
50#14582662C2211yescharacteristic, complemented
51#14582662C2211yescharacteristic, complemented
52#14582662C2211yescharacteristic, complemented
53#14582662C2211yescharacteristic, complemented
54C22×M16×C43C2211yescharacteristic
55C2×C4⋊C8×C43C2211yescharacteristic, complemented
56C2×C4⋊C8×C43C2211yescharacteristic, complemented
57C2×C22⋊C8×C43C2211yescharacteristic
58C4×C22⋊C4×C43C2211yescharacteristic
59C43×#336C2211yescharacteristic, complemented
60C43×#336C2211yescharacteristic, complemented
61C24×D43—21no—
62C22×D172—22no—
63C22×D172—22no—
64C22×D172—21no—
65C22×D172—22no—
66C22×D172—41no—
67C22×D172—41no—
68C22×D172Q814yes—
69C22×D172C2311yescharacteristic
70C22×D172C2311yescharacteristic
71C22×C4×D43—21no—
72C22×C4×D43—21no—
73#13063317—22no—
74#13063317—41no—
75C4×D172—22no—
76C4×D172—22no—
77C4×D172—41no—
78C4×D172—41no—
79#13063284—22no—
80#13063284—41no—
81C2×C4⋊Dic43—21no—
82C2×C4⋊Dic43—21no—
83C2×C4⋊Dic43C2311yescharacteristic
84C2×C4⋊Dic43C2311yescharacteristic
85C2×C4⋊Dic43C2311yescharacteristic
86C2×C4⋊Dic43C2311yescharacteristic
87C2×C4⋊Dic43C2311yescharacteristic
88C2×C4⋊Dic43C2311yescharacteristic
89C2×Dic43⋊C4—21no—
90C2×Dic43⋊C4—21no—
91C2×Dic43⋊C4—21no—
92C2×Dic43⋊C4—21no—
93C2×C22⋊Dic43—21no—
94C2×C22⋊Dic43—21no—
95C2×C22⋊Dic43—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—
102C22⋊C4×D43—44no—
103C2×C4×Dic43—21no—
104#13063259—22no—
105#13063259—41no—
106#13063257—22no—
107#13063257—41no—
108#13063247—22no—
109#13063247—22no—
110#13063247—22no—
111#13063247—22no—
112#13063247—22no—
113#13063247—41no—
114#13063247—41no—
115#13063247D414yes—
116C43⋊#95—21no—
117C43⋊#95—21no—
118C43⋊#95—21no—
119C43⋊#95—21no—
120C23×C4×C43C2311yescharacteristic
121C2×M16×C43—22no—
122C2×M16×C43—22no—
123C2×M16×C43—41no—
124C22×C8×C43C2311yescharacteristic
125C22×C8×C43C2311yescharacteristic
126C22×C8×C43C2311yescharacteristic
127C22×C8×C43C2311yescharacteristic
128C2×C22⋊C4×C43D411yescharacteristic
129C2×C22⋊C4×C43D411yescharacteristic
130C2×C42×C43C2311yescharacteristic
131C2×C42×C43C2311yescharacteristic
132C4⋊C8×C43—22no—
133C4⋊C8×C43—41no—
134C22⋊C8×C43—22no—
135#95×C43D411yescharacteristic
136#95×C43D411yescharacteristic
137C24×C43C2×D411yescharacteristic
138C23×D43—21no—
139C23×D43—21no—
140C23×D43—24no—
141C23×D43—42no—
142C23×D43—42no—
143C23×D43—42no—
144C23×D43—42no—
145C23×D43—81no—
146C23×D43—81no—
147C22×C4×C43—21no—
148C22×C4×C43—21no—
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43C2×D411yescharacteristic
156C22×C4×C43C2×Q812yes—
157C22×C4×C43#4112yes—
158C22×C4×C43C2411yescharacteristic
159C22×Dic43—21no—
160C22×Dic43—21no—
161C22×Dic43—21no—
162C22×Dic43—21no—
163C22×Dic43—21no—
164C22×Dic43—21no—
165C2×D172—21no—
166C2×D172—21no—
167C2×D172—21no—
168C2×D172—24no—
169C2×D172—21no—
170C2×D172—21no—
171C2×D172—21no—
172C2×D172—21no—
173C2×D172—21no—
174C2×D172—28no—
175C2×D172—42no—
176C2×D172—42no—
177C2×D172—44no—
178C2×D172—44no—
179C2×D172—44no—
180C2×D172C2×D412yes—
181C2×D172C2×Q812yes—
182C2×D172C2×Q812yes—
183C2×D172#4112yes—
184C2×C4×D43—42no—
185C2×C4×D43—42no—
186C2×C4×D43—42no—
187C2×C4×D43—42no—
188C2×C4×D43—81no—
189C2×C4×D43—81no—
190M16×C43—44no—
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×C43—21no—
202C2×C8×C43C2×D412yes—
203C22⋊C4×C43—22no—
204C22⋊C4×C43—41no—
205C42×C43—21no—
206C42×C43—21no—
207C42×C43—21no—
208C42×C43—21no—
209C22⋊Dic43—42no—
210C22⋊Dic43—42no—
211C22⋊Dic43—81no—
212(C2×D43)⋊C4—42no—
213(C2×D43)⋊C4—42no—
214(C2×D43)⋊C4—42no—
215(C2×D43)⋊C4—42no—
216(C2×D43)⋊C4—81no—
217(C2×D43)⋊C4—81no—
218C4⋊Dic43—21no—
219C4⋊Dic43—21no—
220C4⋊Dic43—21no—
221C4⋊Dic43—21no—
222C4⋊Dic43—21no—
223C4⋊Dic43—21no—
224C4⋊Dic43—21no—
225C4⋊Dic43—21no—
226C4⋊Dic43—21no—
227C4⋊Dic43—21no—
228C4⋊Dic43—21no—
229C4⋊Dic43—42no—
230C4⋊Dic43—81no—
231C4⋊Dic43C2×D412yes—
232Dic43⋊C4—42no—
233Dic43⋊C4—42no—
234Dic43⋊C4—42no—
235Dic43⋊C4—81no—
236C4×Dic43—42no—
237C23×C43—21no—
238C23×C43—21no—
239C23×C43—21no—
240C23×C43—21no—
241C23×C43—21no—
242C23×C43—21no—
243C23×C43C22⋊Q812yes—
244C23×C43C22×D411yescharacteristic
245C22×D43—22no—
246C22×D43—22no—
247C22×D43—22no—
248C22×D43—22no—
249C22×D43—48no—
250C22×D43—41no—
251C22×D43—41no—
252C22×D43—41no—
253C22×D43—41no—
254C22×D43—48no—
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—
266C2×C4×C43—21no—
267C2×C4×C43—21no—
268C2×C4×C43—21no—
269C2×C4×C43—21no—
270C2×C4×C43—22no—
271C2×C4×C43—22no—
272C2×C4×C43—22no—
273C2×C4×C43—22no—
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×C43C22⋊Q812yes—
284C2×C4×C43AGL(1,ℤ/8)12yes—
285C2×C4×C43C22×D411yescharacteristic
286C2×C4×C43C22×Q811yescharacteristic
287C2×C4×C43C2×#4111yescharacteristic
288C2×C4×C43C2×#4111yescharacteristic
289C2×C4×C43H(5,𝔽2)11yescharacteristic
290C2×C4×C43H(5,𝔽2)11yescharacteristic
291C2×Dic43—22no—
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—
309D172—22no—
310D172—22no—
311D172—22no—
312D172—22no—
313D172—22no—
314D172—48no—
315D172—41no—
316D172—41no—
317D172C22⋊Q814yes—
318C4×D43—84no—
319C4×D43—84no—
320C8×C43—22no—
321C8×C43—41no—
322C8×C43—41no—
323C8×C43—41no—
324#25976—431nomaximal, Sylow
325C22×C43—22no—
326C22×C43—22no—
327C22×C43—22no—
328C22×C43—41no—
329C22×C43—41no—
330C22×C43—41no—
331C22×C43—41no—
332C22×C43C2×C22⋊Q811yescharacteristic
333C22×C43D4211yescharacteristic
334C22×C43#54611yescharacteristic
335C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
336C22×C43#57511yescharacteristic
337C22×C43#57611yescharacteristic
338C22×C43#57711yescharacteristic
339C2×D43—24no—
340C2×D43—42no—
341C2×D43—42no—
342C2×D43—42no—
343C2×D43—42no—
344C2×D43—42no—
345C2×D43—42no—
346C2×D43—42no—
347C2×D43—42no—
348C2×D43—42no—
349C2×D43—816no—
350C2×D43—81no—
351C2×D43—81no—
352C2×D43—81no—
353C2×D43—81no—
354C4×C43—22no—
355C4×C43—22no—
356C4×C43—41no—
357C4×C43—41no—
358C4×C43—41no—
359C4×C43C2×C22⋊Q811yescharacteristic
360C4×C43#54311yescharacteristic
361C4×C43#54611yescharacteristic
362C4×C43#55111yescharacteristic
363Dic43—42no—
364Dic43—81no—
365Dic43—81no—
366Dic43—81no—
367Dic43—81no—
368Dic43—81no—
369C2×#478—431no—
370C2×#418—431no—
371#2441—431no—
372D4×C22⋊C4—431no—
373#2094—431no—
374#2067—431no—
375#2067—431no—
376#2025—431no—
377#1864—431no—
378#1862—431no—
379#1854—431no—
380#1851D4311yescharacteristic, complemented
381#1809—431no—
382#1802—431no—
383#1786—431no—
384C2×C43—42no—
385C2×C43#243711yescharacteristic
386C2×C43#307711yescharacteristic
387C2×C43#308111yescharacteristic
388C2×C43#326811yescharacteristic
389C2×C43#327211yescharacteristic
390C2×C43#331811yescharacteristic
391C2×C43#332311yescharacteristic
392D43—44no—
393D43—82no—
394C23×D4—431no—
395C22×M16C2×D4311yescharacteristic
396C2×#125—431no—
397C2×C4×D4—431no—
398C2×C4×D4—431no—
399C2×#117—431no—
400C22×C22⋊C4—861no—
401#478—864no—
402C2×#107—431no—
403C2×#107—431no—
404C2×#106—431no—
405C2×#106—431no—
406C2×C4⋊C8C2×D4311yescharacteristic, complemented
407C2×C4⋊C8C2×D4311yescharacteristic, complemented
408#418—864no—
409C2×#102—431no—
410C2×#102—431no—
411C2×#102—431no—
412C2×#102—431no—
413C2×#102—431no—
414C2×#102—431no—
415C2×#102—431no—
416C2×#102—431no—
417C2×C22⋊C8C2×D4311yescharacteristic
418#399—861no—
419#396—861no—
420#390—431no—
421#390—431no—
422#389—431no—
423#389—431no—
424#389—861no—
425#387—861no—
426#386—861no—
427#386—861no—
428#384—431no—
429#380—431no—
430#380—431no—
431#379—861no—
432C4×C22⋊C4C2×D4311yescharacteristic
433#340—431no—
434#340—431no—
435#340—431no—
436#340—431no—
437#336C2×D4311yescharacteristic, complemented
438#336C2×D4311yescharacteristic, complemented
439C43#2597611yescharacteristic, complemented, Sylow
440C25—861no—
441C22×D4—434no—
442C22×D4—431no—
443C22×D4—431no—
444C22×D4—862no—
445C22×D4—862no—
446C22×D4—861no—
447C22×D4—862no—
448C22×D4—1721no—
449C22×D4—1721no—
450C23×C4—861no—
451C23×C4—861no—
452C23×C4C22×D4311yescharacteristic
453C2×M16—22no—
454C2×M16—22no—
455C2×M16—41no—
456C22×C8C22×D4311yescharacteristic
457C22×C8C22×D4311yescharacteristic
458C22×C8C22×D4311yescharacteristic
459C22×C8C22×D4311yescharacteristic
460#125—862no—
461#125—1721no—
462C4×D4—862no—
463C4×D4—862no—
464C4×D4—1721no—
465C4×D4—1721no—
466#117—862no—
467#117—1721no—
468C2×C4⋊C4—431no—
469C2×C4⋊C4—431no—
470C2×C4⋊C4—431no—
471C2×C4⋊C4—431no—
472C2×C4⋊C4—431no—
473C2×C4⋊C4—431no—
474C2×C4⋊C4—861no—
475C2×C4⋊C4—861no—
476C2×C4⋊C4—861no—
477C2×C4⋊C4—861no—
478C2×C4⋊C4—861no—
479C2×C4⋊C4—861no—
480C2×C22⋊C4—861no—
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—1724no—
490C2×C22⋊C4D17211yescharacteristic
491C2×C22⋊C4D17211yescharacteristic
492C2×C42—861no—
493C2×C42C22×D4311yescharacteristic
494C2×C42C22×D4311yescharacteristic
495#107—862no—
496#107—1721no—
497#106—862no—
498#106—1721no—
499C4⋊C8—22no—
500C4⋊C8—41no—
501#102—434no—
502#102—862no—
503#102—862no—
504#102—862no—
505#102—862no—
506#102—862no—
507#102—1721no—
508#102—1721no—
509C22⋊C8—22no—
510#95—861no—
511#95—861no—
512#95—861no—
513#95—861no—
514#95D17211yescharacteristic
515#95D17211yescharacteristic
516C24—861no—
517C24—864no—
518C24—861no—
519C24—3441no—
520C24—3441no—
521C24—1722no—
522C24—1722no—
523C24—1722no—
524C24—1722no—
525C24C2×D17211yescharacteristic
526C2×D4—432no—
527C2×D4—432no—
528C2×D4—432no—
529C2×D4—432no—
530C2×D4—868no—
531C2×D4—864no—
532C2×D4—861no—
533C2×D4—861no—
534C2×D4—861no—
535C2×D4—861no—
536C2×D4—861no—
537C2×D4—861no—
538C2×D4—861no—
539C2×D4—861no—
540C2×D4—1724no—
541C2×D4—1724no—
542C2×D4—1724no—
543C2×D4—1722no—
544C2×D4—1722no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—861no—
550C22×C4—861no—
551C22×C4—861no—
552C22×C4—861no—
553C22×C4—861no—
554C22×C4—861no—
555C22×C4—3441no—
556C22×C4—3441no—
557C22×C4—1722no—
558C22×C4—1722no—
559C22×C4—1722no—
560C22×C4—1722no—
561C22×C4C2×D17211yescharacteristic
562C22×C4C2×D17211yescharacteristic
563C22×C4C2×D17211yescharacteristic
564C22×C4C2×D17211yescharacteristic
565C22×C4C2×D17211yescharacteristic
566C22×C4#1062190012yes—
567C22×C4Q8×D4312yes—
568C22×C4C23×D4311yescharacteristic
569M16—44no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8D4×D4312yes—
582C4⋊C4—432no—
583C4⋊C4—861no—
584C4⋊C4—861no—
585C4⋊C4—861no—
586C4⋊C4—861no—
587C4⋊C4—861no—
588C4⋊C4—861no—
589C4⋊C4—861no—
590C4⋊C4—861no—
591C4⋊C4—861no—
592C4⋊C4—861no—
593C4⋊C4—861no—
594C4⋊C4—3441no—
595C4⋊C4—3441no—
596C4⋊C4—1722no—
597C4⋊C4—1722no—
598C4⋊C4—1722no—
599C4⋊C4—1722no—
600C22⋊C4—22no—
601C22⋊C4—41no—
602C22⋊C4—3441no—
603C22⋊C4—3441no—
604C22⋊C4—3441no—
605C22⋊C4—1722no—
606C22⋊C4—1722no—
607C22⋊C4—1722no—
608C22⋊C4—1722no—
609C22⋊C4—1722no—
610C22⋊C4—1722no—
611C42—21no—
612C42—21no—
613C42—21no—
614C42—21no—
615C42—1722no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—862no—
623C23—862no—
624C23—862no—
625C23—862no—
626C23—3444no—
627C23—3444no—
628C23—3444no—
629C23—3444no—
630C23—3444no—
631C23—1728no—
632C23—1728no—
633C23—1721no—
634C23—1721no—
635C23—1721no—
636C23—1721no—
637C23—1721no—
638C23—1721no—
639C23—1721no—
640C23—1721no—
641C23—1721no—
642C23—1721no—
643C23#1306330512yes—
644C23C22×D17211yescharacteristic
645D4—434no—
646D4—862no—
647D4—862no—
648D4—862no—
649D4—862no—
650D4—862no—
651D4—1728no—
652D4—1721no—
653D4—1721no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—862no—
672C2×C4—3444no—
673C2×C4—3444no—
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#1306330512yes—
692C2×C4#1306335312yes—
693C2×C4C2×D4×D4311yescharacteristic
694C2×C4C2×Q8×D4311yescharacteristic
695C2×C4#41×D4311yescharacteristic
696C2×C4C2×#1062190011yescharacteristic
697C2×C4#1306337011yescharacteristic
698C2×C4#1306337111yescharacteristic
699C8—22no—
700C8—41no—
701C8—41no—
702C8—41no—
703C22—22no—
704C22—22no—
705C22—22no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—864no—
711C22—34416no—
712C22—3441no—
713C22—3441no—
714C22—3441no—
715C22—3441no—
716C22—1722no—
717C22—1722no—
718C22—1722no—
719C22—1722no—
720C22—1722no—
721C22—1722no—
722C22—1722no—
723C22—1722no—
724C22—1722no—
725C22C2×#1306330511yescharacteristic
726C22D4×D17211yescharacteristic
727C22#1458354411yescharacteristic
728C22C2×#1306335311yescharacteristic
729C22#1458369911yescharacteristic
730C22#1458370411yescharacteristic
731C22#1458371111yescharacteristic
732C4—22no—
733C4—22no—
734C4—41no—
735C4—41no—
736C4—41no—
737C4—3441no—
738C4—3441no—
739C4—3441no—
740C4—3441no—
741C4—3441no—
742C4—1722no—
743C4C22⋊Q8×D4311yescharacteristic
744C4#1458352411yescharacteristic
745C4#1458353611yescharacteristic
746C4#1458357211yescharacteristic
747C2—42no—
748C2—3442no—
749C2—1724no—
750C2#1913825911yescharacteristic
751C2#1914439411yescharacteristic
752C2#1914442711yescharacteristic
753C2#1914614011yescharacteristic
754C2#1914619711yescharacteristic
755C2#1914673811yescharacteristic
756C2#1914681311yescharacteristic
subgroupG/H
centerC23C22×D172
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1851C2
socleC23×C43C22×D4
prime radicalC23×D172C22
hypercenter#1851D43
hypocenterC43#25976
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #1851

Complements

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

NH ≅ G/Ntype
1. C2×#14583200C2semidirect
3. #19138308C2semidirect
5. #19136127C2semidirect
6. #19135982C2semidirect
7. #19135982C2semidirect
8. #19135742C2semidirect
9. #19134859C2semidirect
10. #19134845C2semidirect
11. #19134796C2semidirect
12. #19134628C2semidirect
13. #19134596C2semidirect
15. C43×#1851C2semidirect
17. C2×#13063317C22semidirect
23. C2×#13063259C22semidirect
24. C2×#13063259C22semidirect
25. C2×#13063257C22semidirect
26. C2×#13063257C22semidirect
40. #14582797C22semidirect
41. #14582797C22semidirect
46. #14582769C22semidirect
50. #14582662C22semidirect
51. #14582662C22semidirect
52. #14582662C22semidirect
53. #14582662C22semidirect
55. C2×C4⋊C8×C43C22semidirect
56. C2×C4⋊C8×C43C22semidirect
59. C43×#336C22semidirect
60. C43×#336C22semidirect
380. #1851D43semidirect
406. C2×C4⋊C8C2×D43semidirect
407. C2×C4⋊C8C2×D43semidirect
437. #336C2×D43semidirect
438. #336C2×D43semidirect
439. C43#25976semidirect

Maximal subgroups

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

subgroupindex
C2×#145832002
C2×#145829052
#191383082
C22⋊C4×D1722
#191361272
#191359822
#191357422
#191348592
#191348452
#191347962
#191346282
#191345962
#191345272
C43×#18512
#2597643