Finite Group Databasebeta

← #25153659

Subgroups — #25153659

Order 11008.

1206 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583180C211yesmaximal, characteristic, complemented
2C22×#13063247C211yesmaximal, characteristic
3#19138297C211yesmaximal, characteristic, complemented
4C22⋊C4×D172C211yesmaximal, characteristic
5#19136122C211yesmaximal, characteristic, complemented
6#19135982C211yesmaximal, characteristic, complemented
7#19135982C211yesmaximal, characteristic, complemented
8#19135732C211yesmaximal, characteristic, complemented
9#19134845C211yesmaximal, characteristic, complemented
10#19134845C211yesmaximal, characteristic, complemented
11#19134785C211yesmaximal, characteristic, complemented
12#19134624C211yesmaximal, characteristic, complemented
13#19134596C211yesmaximal, characteristic, complemented
14#19134527C211yesmaximal, characteristic
15C43×#1850C211yesmaximal, characteristic, complemented
16C23×D172C2211yescharacteristic
17C2×#13063325C2211yescharacteristic, complemented
18C2×#13063302—21no—
19C2×C4×D172C2211yescharacteristic
20C2×C4×D172C2211yescharacteristic
21C22×C4⋊Dic43C2211yescharacteristic
22C2×C22⋊C4×D43—21no—
23#14583180—24no—
24C2×#13063259C2211yescharacteristic, complemented
25C2×#13063259C2211yescharacteristic, complemented
26C2×#13063259C2211yescharacteristic, complemented
27C2×#13063259C2211yescharacteristic, complemented
28C2×#13063247—24no—
29C2×#13063247C2211yescharacteristic
30C2×#13063247C2211yescharacteristic
31C2×#13063247C2211yescharacteristic
32C2×#13063247C2211yescharacteristic
33C2×#13063247C2211yescharacteristic
34C2×#13063247C2211yescharacteristic
35C2×#13063247C2211yescharacteristic
36C2×#13063247C2211yescharacteristic
37#14582831—21no—
38#14582820—21no—
39#14582801C2211yescharacteristic
40#14582801C2211yescharacteristic
41#14582797C2211yescharacteristic, complemented
42#14582797C2211yescharacteristic, complemented
43#14582777—21no—
44#14582777—21no—
45#14582774—21no—
46#14582769C2211yescharacteristic, complemented
47#14582759C2211yescharacteristic
48#14582759C2211yescharacteristic
49#14582754—21no—
50#14582662C2211yescharacteristic, complemented
51#14582662C2211yescharacteristic, complemented
52#14582662C2211yescharacteristic, complemented
53#14582662C2211yescharacteristic, complemented
54C23×C8×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×Dic86—21no—
63C22×D172—22no—
64C22×D172—22no—
65C22×D172—21no—
66C22×D172—22no—
67C22×D172—41no—
68C22×D172—41no—
69C22×D172Q814yescomplemented
70C22×D172C2311yescharacteristic
71C22×D172C2311yescharacteristic
72C23×Dic43—21no—
73C22×C4×D43—21no—
74C22×C4×D43—21no—
75#13063325—22no—
76#13063325—41no—
77#13063302—44no—
78C4×D172—22no—
79C4×D172—22no—
80C4×D172—41no—
81C4×D172—41no—
82C2×C4⋊Dic43—22no—
83C2×C4⋊Dic43—21no—
84C2×C4⋊Dic43—21no—
85C2×C4⋊Dic43—21no—
86C2×C4⋊Dic43—21no—
87C2×C4⋊Dic43—41no—
88C2×C4⋊Dic43C2311yescharacteristic
89C2×C4⋊Dic43C2311yescharacteristic
90C2×C4⋊Dic43C2311yescharacteristic
91C2×C4⋊Dic43C2311yescharacteristic
92C2×C4⋊Dic43C2311yescharacteristic
93C2×C4⋊Dic43C2311yescharacteristic
94C2×Dic43⋊C4—21no—
95C2×Dic43⋊C4—21no—
96C2×C22⋊Dic43—21no—
97C2×C22⋊Dic43—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×(C2×D43)⋊C4—21no—
104C22⋊C4×D43—44no—
105#13063259—22no—
106#13063259—22no—
107#13063259—41no—
108#13063259—41no—
109#13063247—22no—
110#13063247—22no—
111#13063247—22no—
112#13063247—22no—
113#13063247—22no—
114#13063247—41no—
115#13063247—41no—
116#13063247D414yes—
117C43⋊#95—21no—
118C43⋊#95—21no—
119C43⋊#95—21no—
120C43⋊#95—21no—
121C23×C4×C43C2311yescharacteristic
122C22×C8×C43—22no—
123C22×C8×C43—22no—
124C22×C8×C43—41no—
125C22×C8×C43C2311yescharacteristic
126C22×C8×C43C2311yescharacteristic
127C22×C8×C43C2311yescharacteristic
128C22×C8×C43C2311yescharacteristic
129C2×C22⋊C4×C43D411yescharacteristic
130C2×C22⋊C4×C43D411yescharacteristic
131C2×C42×C43C2311yescharacteristic
132C2×C42×C43C2311yescharacteristic
133C4⋊C8×C43—22no—
134C4⋊C8×C43—41no—
135C22⋊C8×C43—22no—
136#95×C43D411yescharacteristic
137#95×C43D411yescharacteristic
138C24×C43C2×D411yescharacteristic
139C23×D43—21no—
140C23×D43—21no—
141C23×D43—24no—
142C23×D43—42no—
143C23×D43—42no—
144C23×D43—42no—
145C23×D43—42no—
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×D411yescharacteristic
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43C2×D411yescharacteristic
156C22×C4×C43C2×D411yescharacteristic
157C22×C4×C43C2×Q812yes—
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—
166C22×Dic43—42no—
167C22×Dic43—42no—
168C22×Dic43—81no—
169C2×D172—21no—
170C2×D172—21no—
171C2×D172—21no—
172C2×D172—24no—
173C2×D172—21no—
174C2×D172—21no—
175C2×D172—21no—
176C2×D172—21no—
177C2×D172—21no—
178C2×D172—28no—
179C2×D172—42no—
180C2×D172—42no—
181C2×D172—44no—
182C2×D172—44no—
183C2×D172—44no—
184C2×D172C2×D412yes—
185C2×D172C2×Q812yes—
186C2×D172C2×Q812yes—
187C2×D172#4112yes—
188C2×C4×D43—42no—
189C2×C4×D43—42no—
190C2×C4×D43—42no—
191C2×C4×D43—42no—
192C2×C4×D43—81no—
193C2×C4×D43—81no—
194C2×Dic86—42no—
195C2×Dic86—42no—
196C2×Dic86—81no—
197C2×C8×C43—21no—
198C2×C8×C43—21no—
199C2×C8×C43—21no—
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—44no—
209C2×C8×C43C2×D412yes—
210C22⋊C4×C43—22no—
211C22⋊C4×C43D814yes—
212C42×C43—21no—
213C42×C43—21no—
214C42×C43—21no—
215C42×C43—21no—
216C22⋊Dic43—42no—
217C22⋊Dic43—42no—
218(C2×D43)⋊C4—42no—
219(C2×D43)⋊C4—42no—
220(C2×D43)⋊C4—42no—
221(C2×D43)⋊C4—42no—
222(C2×D43)⋊C4—81no—
223(C2×D43)⋊C4—81no—
224C4⋊Dic43—21no—
225C4⋊Dic43—21no—
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⋊Dic43—21no—
235C4⋊Dic43—42no—
236C4⋊Dic43—42no—
237C4⋊Dic43—42no—
238C4⋊Dic43—81no—
239C4⋊Dic43C2×D412yes—
240Dic43⋊C4—42no—
241Dic43⋊C4—42no—
242C23×C43—21no—
243C23×C43—21no—
244C23×C43—21no—
245C23×C43—21no—
246C23×C43C22⋊Q812yes—
247C23×C43C2×D812yes—
248C23×C43#13712yes—
249C23×C43C22×D411yescharacteristic
250C22×D43—22no—
251C22×D43—22no—
252C22×D43—22no—
253C22×D43—22no—
254C22×D43—48no—
255C22×D43—41no—
256C22×D43—41no—
257C22×D43—41no—
258C22×D43—41no—
259C22×D43—41no—
260C22×D43—41no—
261C22×D43—41no—
262C22×D43—41no—
263C22×D43—41no—
264C22×D43—41no—
265C22×D43—48no—
266C22×D43—84no—
267C22×D43—84no—
268C22×D43—84no—
269C22×D43—84no—
270C22×D43—84no—
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—22no—
278C2×C4×C43—22no—
279C2×C4×C43—22no—
280C2×C4×C43—22no—
281C2×C4×C43—21no—
282C2×C4×C43—21no—
283C2×C4×C43—21no—
284C2×C4×C43—21no—
285C2×C4×C43—21no—
286C2×C4×C43—21no—
287C2×C4×C43C22⋊Q812yes—
288C2×C4×C43C2×D812yes—
289C2×C4×C43C2×D812yes—
290C2×C4×C43C22×D411yescharacteristic
291C2×C4×C43C22×Q811yescharacteristic
292C2×C4×C43C2×#4111yescharacteristic
293C2×C4×C43C2×#4111yescharacteristic
294C2×C4×C43H(5,𝔽2)11yescharacteristic
295C2×C4×C43H(5,𝔽2)11yescharacteristic
296C2×Dic43—22no—
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—41no—
314C2×Dic43—84no—
315D172—22no—
316D172—22no—
317D172—22no—
318D172—22no—
319D172—22no—
320D172—48no—
321D172—41no—
322D172—41no—
323D172C22⋊Q814yescomplemented
324C4×D43—84no—
325C4×D43—84no—
326Dic86—84no—
327C8×C43—22no—
328C8×C43—41no—
329C8×C43—41no—
330C8×C43—41no—
331#25950—431nomaximal, Sylow
332C22×C43—22no—
333C22×C43—22no—
334C22×C43—22no—
335C22×C43—22no—
336C22×C43—22no—
337C22×C43—22no—
338C22×C43#47414yescomplemented
339C22×C43C2×C22⋊Q811yescharacteristic
340C22×C43D4211yescharacteristic
341C22×C43#54611yescharacteristic
342C22×C43C22×D811yescharacteristic
343C22×C43C2×#13711yescharacteristic
344C22×C43#57611yescharacteristic
345C22×C43#57711yescharacteristic
346C2×D43—24no—
347C2×D43—42no—
348C2×D43—42no—
349C2×D43—42no—
350C2×D43—42no—
351C2×D43—42no—
352C2×D43—42no—
353C2×D43—42no—
354C2×D43—42no—
355C2×D43—42no—
356C2×D43—816no—
357C2×D43—81no—
358C2×D43—81no—
359C2×D43—81no—
360C2×D43—81no—
361C4×C43—22no—
362C4×C43—22no—
363C4×C43—22no—
364C4×C43—41no—
365C4×C43—41no—
366C4×C43C2×C22⋊Q811yescharacteristic
367C4×C43#54311yescharacteristic
368C4×C43#54611yescharacteristic
369C4×C43#55111yescharacteristic
370Dic43—42no—
371Dic43—81no—
372Dic43—81no—
373Dic43—81no—
374Dic43—81no—
375Dic43—81no—
376C2×#474—431no—
377C22×#102—431no—
378#2440—431no—
379D4×C22⋊C4—431no—
380#2093—431no—
381#2067—431no—
382#2067—431no—
383#2023—431no—
384#1862—431no—
385#1862—431no—
386#1852—431no—
387#1850D4311yescharacteristic, complemented
388#1808—431no—
389#1802—431no—
390#1786—431no—
391C2×C43—24no—
392C2×C43#243711yescharacteristic
393C2×C43C2×#47411yescharacteristic
394C2×C43#308111yescharacteristic
395C2×C43#326611yescharacteristic
396C2×C43D4×D811yescharacteristic
397C2×C43#329411yescharacteristic
398C2×C43#331411yescharacteristic
399D43—44no—
400D43—82no—
401C23×D4—431no—
402C23×C8C2×D4311yescharacteristic
403C2×C4⋊Q8—431no—
404C2×C22⋊Q8—861no—
405C2×C4×D4—431no—
406C2×C4×D4—431no—
407C22×C4⋊C4—431no—
408C22×C22⋊C4—861no—
409#474—864no—
410C2×#107—431no—
411C2×#107—431no—
412C2×#107—431no—
413C2×#107—431no—
414C2×C4⋊C8C2×D4311yescharacteristic, complemented
415C2×C4⋊C8C2×D4311yescharacteristic, complemented
416C2×#102—431no—
417C2×#102—431no—
418C2×#102—431no—
419C2×#102—431no—
420C2×#102—431no—
421C2×#102—431no—
422C2×#102—431no—
423C2×#102—431no—
424C2×#102—864no—
425C2×C22⋊C8C2×D4311yescharacteristic
426#398—861no—
427#395—861no—
428#390—431no—
429#390—431no—
430#389—431no—
431#389—431no—
432#386—861no—
433#386—861no—
434#385—861no—
435#384—431no—
436#380—431no—
437#380—431no—
438#379—861no—
439C4×C22⋊C4C2×D4311yescharacteristic
440#340—431no—
441#340—431no—
442#340—431no—
443#340—431no—
444#336C2×D4311yescharacteristic, complemented
445#336C2×D4311yescharacteristic, complemented
446C43#2595011yescharacteristic, complemented, Sylow
447C25—861no—
448C22×Q8—861no—
449C22×D4—434no—
450C22×D4—431no—
451C22×D4—431no—
452C22×D4—862no—
453C22×D4—862no—
454C22×D4—861no—
455C22×D4—862no—
456C22×D4—1721no—
457C22×D4—1721no—
458C23×C4—861no—
459C23×C4—861no—
460C23×C4—861no—
461C23×C4C22×D4311yescharacteristic
462C22×C8—22no—
463C22×C8—22no—
464C22×C8—41no—
465C22×C8C22×D4311yescharacteristic
466C22×C8C22×D4311yescharacteristic
467C22×C8C22×D4311yescharacteristic
468C22×C8C22×D4311yescharacteristic
469C4⋊Q8—862no—
470C4⋊Q8—1721no—
471C22⋊Q8—1724no—
472C4×D4—862no—
473C4×D4—862no—
474C4×D4—1721no—
475C4×D4—1721no—
476C2×C4⋊C4—431no—
477C2×C4⋊C4—431no—
478C2×C4⋊C4—431no—
479C2×C4⋊C4—431no—
480C2×C4⋊C4—431no—
481C2×C4⋊C4—431no—
482C2×C4⋊C4—862no—
483C2×C4⋊C4—861no—
484C2×C4⋊C4—861no—
485C2×C4⋊C4—861no—
486C2×C4⋊C4—861no—
487C2×C4⋊C4—861no—
488C2×C4⋊C4—861no—
489C2×C4⋊C4—1721no—
490C2×C22⋊C4—861no—
491C2×C22⋊C4—861no—
492C2×C22⋊C4—861no—
493C2×C22⋊C4—861no—
494C2×C22⋊C4—861no—
495C2×C22⋊C4—861no—
496C2×C22⋊C4—861no—
497C2×C22⋊C4—861no—
498C2×C22⋊C4—1724no—
499C2×C22⋊C4D17211yescharacteristic
500C2×C22⋊C4D17211yescharacteristic
501C2×C42C22×D4311yescharacteristic
502C2×C42C22×D4311yescharacteristic
503#107—862no—
504#107—862no—
505#107—1721no—
506#107—1721no—
507C4⋊C8—22no—
508C4⋊C8—41no—
509#102—434no—
510#102—862no—
511#102—862no—
512#102—862no—
513#102—862no—
514#102—862no—
515#102—1721no—
516#102—1721no—
517C22⋊C8—22no—
518#95—861no—
519#95—861no—
520#95—861no—
521#95—861no—
522#95D17211yescharacteristic
523#95D17211yescharacteristic
524C24—861no—
525C24—864no—
526C24—861no—
527C24—3441no—
528C24—3441no—
529C24—1722no—
530C24—1722no—
531C24—1722no—
532C24—1722no—
533C24C2×D17211yescharacteristic
534C2×Q8—3441no—
535C2×Q8—1722no—
536C2×Q8—1722no—
537C2×D4—432no—
538C2×D4—432no—
539C2×D4—432no—
540C2×D4—432no—
541C2×D4—868no—
542C2×D4—864no—
543C2×D4—861no—
544C2×D4—861no—
545C2×D4—861no—
546C2×D4—861no—
547C2×D4—861no—
548C2×D4—861no—
549C2×D4—861no—
550C2×D4—861no—
551C2×D4—1724no—
552C2×D4—1724no—
553C2×D4—1724no—
554C2×D4—1722no—
555C2×D4—1722no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—861no—
561C22×C4—861no—
562C22×C4—861no—
563C22×C4—861no—
564C22×C4—861no—
565C22×C4—861no—
566C22×C4—3441no—
567C22×C4—3441no—
568C22×C4—3441no—
569C22×C4—1722no—
570C22×C4—1722no—
571C22×C4—1722no—
572C22×C4—1722no—
573C22×C4—1722no—
574C22×C4—1722no—
575C22×C4C2×D17211yescharacteristic
576C22×C4C2×D17211yescharacteristic
577C22×C4C2×D17211yescharacteristic
578C22×C4C2×D17211yescharacteristic
579C22×C4C2×D17211yescharacteristic
580C22×C4#1062190012yes—
581C22×C4Q8×D4312yes—
582C22×C4C23×D4311yescharacteristic
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—44no—
595C2×C8D4×D4312yes—
596C4⋊C4—432no—
597C4⋊C4—861no—
598C4⋊C4—861no—
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—861no—
608C4⋊C4—3441no—
609C4⋊C4—1722no—
610C4⋊C4—1722no—
611C4⋊C4—1722no—
612C4⋊C4—1722no—
613C4⋊C4—1722no—
614C22⋊C4—22no—
615C22⋊C4—3441no—
616C22⋊C4—3441no—
617C22⋊C4—1722no—
618C22⋊C4—1722no—
619C22⋊C4—1722no—
620C22⋊C4—1722no—
621C22⋊C4—1722no—
622C22⋊C4—1722no—
623C22⋊C4D34414yes—
624C42—21no—
625C42—21no—
626C42—21no—
627C42—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—862no—
633C23—862no—
634C23—862no—
635C23—862no—
636C23—3444no—
637C23—3444no—
638C23—3444no—
639C23—3444no—
640C23—3444no—
641C23—1728no—
642C23—1721no—
643C23—1728no—
644C23—1721no—
645C23—1721no—
646C23—1721no—
647C23—1721no—
648C23—1721no—
649C23—1721no—
650C23—1721no—
651C23—1721no—
652C23—1721no—
653C23#1306330512yes—
654C23C2×D34412yes—
655C23#1306335812yes—
656C23C22×D17211yescharacteristic
657Q8—3444no—
658D4—434no—
659D4—862no—
660D4—862no—
661D4—862no—
662D4—862no—
663D4—862no—
664D4—1728no—
665D4—1721no—
666D4—1721no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—862no—
684C2×C4—3444no—
685C2×C4—3444no—
686C2×C4—3444no—
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—1721no—
699C2×C4—1721no—
700C2×C4—1721no—
701C2×C4—1721no—
702C2×C4—1721no—
703C2×C4—1721no—
704C2×C4#1306330512yes—
705C2×C4C2×D34412yes—
706C2×C4C2×D34412yes—
707C2×C4C2×D4×D4311yescharacteristic
708C2×C4C2×Q8×D4311yescharacteristic
709C2×C4#41×D4311yescharacteristic
710C2×C4C2×#1062190011yescharacteristic
711C2×C4#1306337011yescharacteristic
712C2×C4#1306337111yescharacteristic
713C8—22no—
714C8—41no—
715C8—41no—
716C8—41no—
717C22—22no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—864no—
724C22—34416no—
725C22—3441no—
726C22—3441no—
727C22—3441no—
728C22—3441no—
729C22—1722no—
730C22—1722no—
731C22—1722no—
732C22—1722no—
733C22—1722no—
734C22—1722no—
735C22—1722no—
736C22—1722no—
737C22—1722no—
738C22#1458318014yescomplemented
739C22C2×#1306330511yescharacteristic
740C22D4×D17211yescharacteristic
741C22#1458354411yescharacteristic
742C22C22×D34411yescharacteristic
743C22C2×#1306335811yescharacteristic
744C22#1458370411yescharacteristic
745C22#1458371111yescharacteristic
746C4—22no—
747C4—22no—
748C4—22no—
749C4—41no—
750C4—41no—
751C4—3441no—
752C4—3441no—
753C4—3441no—
754C4—3441no—
755C4—3441no—
756C4—1722no—
757C4C22⋊Q8×D4311yescharacteristic
758C4#1458352411yescharacteristic
759C4#1458353611yescharacteristic
760C4#1458357211yescharacteristic
761C2—24no—
762C2—3442no—
763C2—1724no—
764C2#1913825911yescharacteristic
765C2C2×#1458318011yescharacteristic
766C2#1914442711yescharacteristic
767C2#1914611011yescharacteristic
768C2D4×D34411yescharacteristic
769C2#1914640911yescharacteristic
770C2#1914667811yescharacteristic
subgroupG/H
centerC23C22×D172
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1850C2
socleC23×C43C22×D4
prime radicalC23×D172C22
hypercenter#1850D43
hypocenterC43#25950
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #1850

Complements

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

NH ≅ G/Ntype
1. C2×#14583180C2semidirect
3. #19138297C2semidirect
5. #19136122C2semidirect
6. #19135982C2semidirect
7. #19135982C2semidirect
8. #19135732C2semidirect
9. #19134845C2semidirect
10. #19134845C2semidirect
11. #19134785C2semidirect
12. #19134624C2semidirect
13. #19134596C2semidirect
15. C43×#1850C2semidirect
17. C2×#13063325C22semidirect
24. C2×#13063259C22semidirect
25. C2×#13063259C22semidirect
26. C2×#13063259C22semidirect
27. C2×#13063259C22semidirect
41. #14582797C22semidirect
42. #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
69. C22×D172Q8semidirect
323. D172C22⋊Q8semidirect
338. C22×C43#474semidirect
387. #1850D43semidirect
414. C2×C4⋊C8C2×D43semidirect
415. C2×C4⋊C8C2×D43semidirect
444. #336C2×D43semidirect
445. #336C2×D43semidirect
446. C43#25950semidirect
738. C22#14583180semidirect

Maximal subgroups

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

subgroupindex
C2×#145831802
C22×#130632472
#191382972
C22⋊C4×D1722
#191361222
#191359822
#191357322
#191348452
#191347852
#191346242
#191345962
#191345272
C43×#18502
#2595043