Finite Group Databasebeta

← #25139019

Subgroups — #25139019

Order 11008.

1006 conjugacy classes of subgroups.

The subgroup lattice has 762 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583145C211yesmaximal, characteristic, complemented
2C2×#14583145C211yesmaximal, characteristic, complemented
3C2×#14582941C211yesmaximal, characteristic, complemented
4#19138046C211yesmaximal, characteristic, complemented
5#19138013C211yesmaximal, characteristic
6#19135989C211yesmaximal, characteristic, complemented
7#19135968C211yesmaximal, characteristic, complemented
8#19135792C211yesmaximal, characteristic, complemented
9#19135778C211yesmaximal, characteristic, complemented
10#19135449C211yesmaximal, characteristic, complemented
11#19135328C211yesmaximal, characteristic, complemented
12#19134910C211yesmaximal, characteristic, complemented
13#19134905C211yesmaximal, characteristic, complemented
14#19134628C211yesmaximal, characteristic, complemented
15C2×C43×#436C211yesmaximal, characteristic, complemented
16C22×#10621873C2211yescharacteristic
17C2×#13063304C2211yescharacteristic
18C2×#13063304C2211yescharacteristic
19C2×#13063299C2211yescharacteristic
20C2×#13063299C2211yescharacteristic
21C2×#13063284C2211yescharacteristic
22C22×C4⋊Dic43C2211yescharacteristic
23#14583145—24no—
24#14583145—24no—
25#14582941—24no—
26C2×#13063259C2211yescharacteristic
27C2×#13063259C2211yescharacteristic
28C2×#13063259C2211yescharacteristic
29C2×#13063257C2211yescharacteristic
30C2×#13063257C2211yescharacteristic
31C2×#13063250C2211yescharacteristic
32C2×#13063250C2211yescharacteristic
33C2×#13063250C2211yescharacteristic
34C2×#13063247C2211yescharacteristic
35C2×#13063247C2211yescharacteristic
36C2×#13063247C2211yescharacteristic
37#14582832—21no—
38#14582822—21no—
39#14582814—21no—
40#14582807—21no—
41#14582805C2211yescharacteristic
42#14582801C2211yescharacteristic
43#14582799—21no—
44#14582797C2211yescharacteristic
45#14582797C2211yescharacteristic
46#14582789—21no—
47#14582779—21no—
48#14582759C2211yescharacteristic
49#14582759C2211yescharacteristic
50#14582757—21no—
51#14582662C2211yescharacteristic
52#14582662C2211yescharacteristic
53#14582662C2211yescharacteristic
54#14582662C2211yescharacteristic
55C22×M16×C43C2211yescharacteristic
56C22×M16×C43C2211yescharacteristic
57C2×C4×D4×C43C2211yescharacteristic
58C43×#436—24no—
59C2×C4⋊C8×C43C2211yescharacteristic
60C2×C22⋊C8×C43C2211yescharacteristic
61C2×C22⋊C8×C43C2211yescharacteristic
62C2×C4×C8×C43C2211yescharacteristic
63C22×Dic86C2311yescharacteristic
64C22×D172C2311yescharacteristic
65C22×C22⋊D43—21no—
66C22×C22⋊D43—21no—
67C23×Dic43—21no—
68C2×#10621873—22no—
69C2×#10621873—22no—
70C2×#10621873—22no—
71#13063304—22no—
72#13063304—22no—
73#13063304—22no—
74#13063304—41no—
75#13063299—22no—
76#13063299—22no—
77#13063299—22no—
78#13063299—41no—
79#13063284—22no—
80#13063284—41no—
81C2×C4⋊Dic43—22no—
82C2×C4⋊Dic43—21no—
83C2×C4⋊Dic43—41no—
84C2×C4⋊Dic43C2311yescharacteristic
85C2×C4⋊Dic43C2311yescharacteristic
86C2×C4⋊Dic43C2311yescharacteristic
87C2×C4⋊Dic43C2311yescharacteristic
88C2×C4⋊Dic43C2311yescharacteristic
89C2×C4⋊Dic43C2311yescharacteristic
90C2×Dic43⋊C4—21no—
91C2×Dic43⋊C4—21no—
92C2×Dic43⋊C4—21no—
93C2×Dic43⋊C4—21no—
94C2×C22⋊Dic43—21no—
95C2×C22⋊Dic43—21no—
96C2×C22⋊Dic43—21no—
97C2×C22⋊Dic43—21no—
98C2×C22⋊Dic43—21no—
99C2×(C2×D43)⋊C4—21no—
100C2×(C2×D43)⋊C4—21no—
101C2×(C2×D43)⋊C4—21no—
102C2×(C2×D43)⋊C4—21no—
103C2×C4×Dic43—21no—
104#13063259—22no—
105#13063259—22no—
106#13063259D414yescomplemented
107#13063257—22no—
108#13063257—22no—
109#13063250—22no—
110#13063250—22no—
111#13063250—41no—
112#13063247—22no—
113#13063247—22no—
114#13063247—41no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C43⋊#95—21no—
118C43⋊#95—21no—
119C43⋊#95—21no—
120C43⋊#95—21no—
121C22×D4×C43D411yescharacteristic
122C23×C4×C43C2311yescharacteristic
123C23×C4×C43C2311yescharacteristic
124C2×M16×C43—22no—
125C2×M16×C43—22no—
126C2×M16×C43—22no—
127C2×M16×C43—22no—
128C2×M16×C43—22no—
129C2×M16×C43D414yescomplemented
130C22×C8×C43C2311yescharacteristic
131C22×C8×C43C2311yescharacteristic
132C22×C8×C43C2311yescharacteristic
133C22×C8×C43C2311yescharacteristic
134C4×D4×C43—22no—
135C4×D4×C43—22no—
136C2×C4⋊C4×C43D411yescharacteristic
137C2×C22⋊C4×C43D411yescharacteristic
138C2×C22⋊C4×C43D411yescharacteristic
139C2×C42×C43C2311yescharacteristic
140C4⋊C8×C43—22no—
141C22⋊C8×C43—22no—
142C22⋊C8×C43—22no—
143C4×C8×C43—22no—
144C24×C43C2×D411yescharacteristic
145C24×C43C2×D411yescharacteristic
146C23×D43—21no—
147C2×D4×C43—22no—
148C2×D4×C43—22no—
149C2×D4×C43—41no—
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43—21no—
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×C43C2×D412yes—
161C22×C4×C43C2×D411yescharacteristic
162C22×C4×C43C2×D411yescharacteristic
163C22×C4×C43C2×D411yescharacteristic
164C22×C4×C43C2×D411yescharacteristic
165C22×C4×C43#4112yes—
166C22×C4×C43C2411yescharacteristic
167C2×C22⋊D43—42no—
168C2×C22⋊D43—42no—
169C2×C22⋊D43—42no—
170C2×C22⋊D43—81no—
171C2×C22⋊D43—81no—
172C2×C22⋊D43—81no—
173C22×Dic43—21no—
174C22×Dic43—21no—
175C22×Dic43—21no—
176C22×Dic43—21no—
177C22×Dic43—21no—
178C22×Dic43—21no—
179C22×Dic43—21no—
180C22×Dic43—42no—
181C22×Dic43—42no—
182C22×Dic43—81no—
183C2×D172—21no—
184C2×D172—21no—
185C2×D172—21no—
186C2×D172—21no—
187C2×D172—21no—
188C2×D172—21no—
189C2×Dic86—21no—
190C2×Dic86—21no—
191C2×Dic86—21no—
192C2×Dic86—21no—
193C2×Dic86—21no—
194C2×Dic86—21no—
195M16×C43—28no—
196M16×C43—44no—
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×C43C2×D412yes—
206C2×C8×C43C2×D412yes—
207C2×C8×C43C2×D412yes—
208C2×C8×C43#4112yes—
209C4⋊C4×C43—22no—
210C22⋊C4×C43—22no—
211C22⋊C4×C43—22no—
212C42×C43—21no—
213C42×C43—21no—
214C22⋊Dic43—42no—
215C22⋊Dic43—42no—
216C22⋊Dic43—42no—
217C22⋊Dic43—81no—
218C22⋊Dic43—81no—
219(C2×D43)⋊C4—42no—
220(C2×D43)⋊C4—42no—
221(C2×D43)⋊C4—42no—
222(C2×D43)⋊C4—81no—
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—
232C4⋊Dic43—21no—
233C4⋊Dic43—42no—
234C4⋊Dic43C2×D412yes—
235C4⋊Dic43C2×D412yes—
236Dic43⋊C4—42no—
237Dic43⋊C4—42no—
238Dic43⋊C4—81no—
239Dic43⋊C4—81no—
240C4×Dic43—42no—
241#10621873—44no—
242C23×C43—21no—
243C23×C43—21no—
244C23×C43—21no—
245C23×C43—21no—
246C23×C43—21no—
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#12112yes—
256C23×C43C22×D411yescharacteristic
257C22×D43—41no—
258C22×D43—41no—
259C22×D43—41no—
260C22×D43—41no—
261C22×D43—41no—
262C22×D43—41no—
263C22×D43—41no—
264D4×C43—44no—
265C2×C4×C43—21no—
266C2×C4×C43—21no—
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—41no—
280C2×C4×C43—41no—
281C2×C4×C43—41no—
282C2×C4×C43—41no—
283C2×C4×C43#12112yes—
284C2×C4×C43#13712yes—
285C2×C4×C43C22×D411yescharacteristic
286C2×C4×C43C22×D411yescharacteristic
287C2×C4×C43C2×#4111yescharacteristic
288C2×C4×C43C2×#4111yescharacteristic
289C2×C4×C43H(5,𝔽2)11yescharacteristic
290C2×C4×C432−1+411yescharacteristic
291C22⋊D43—84no—
292C22⋊D43—84no—
293C2×Dic43—22no—
294C2×Dic43—22no—
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—41no—
314C2×Dic43—84no—
315D172—41no—
316D172—41no—
317D172—41no—
318D172—41no—
319Dic86—41no—
320Dic86—41no—
321Dic86—41no—
322Dic86—41no—
323C8×C43—22no—
324C8×C43—41no—
325C8×C43—41no—
326C8×C43#12114yes—
327#24795—431nomaximal, Sylow
328C22×C43—22no—
329C22×C43—22no—
330C22×C43—22no—
331C22×C43—41no—
332C22×C43—41no—
333C22×C43—41no—
334C22×C43—41no—
335C22×C43—41no—
336C22×C43—41no—
337C22×C43—41no—
338C22×C43—41no—
339C22×C43—41no—
340C22×C43—41no—
341C22×C43—41no—
342C22×C43C2×#12111yescharacteristic
343C22×C43D4211yescharacteristic
344C22×C43#54711yescharacteristic
345C22×C43C2×#13711yescharacteristic
346C22×C43#57511yescharacteristic
347C22×C43#57611yescharacteristic
348C22×C43#57711yescharacteristic
349C2×D43—81no—
350C2×D43—81no—
351C2×D43—81no—
352C2×D43—81no—
353C2×D43—81no—
354C2×D43—81no—
355C2×D43—81no—
356C4×C43—22no—
357C4×C43—22no—
358C4×C43—41no—
359C4×C43—41no—
360C4×C43C2×#12111yescharacteristic
361C4×C43#53711yescharacteristic
362C4×C43#54811yescharacteristic
363C4×C43#55311yescharacteristic
364Dic43—42no—
365Dic43—42no—
366Dic43—81no—
367Dic43—81no—
368Dic43—81no—
369Dic43—81no—
370Dic43—81no—
371C2×#468—431no—
372C2×#468—431no—
373C2×#436D4311yescharacteristic, complemented
374C2×#428—431no—
375#2417—431no—
376#2414—431no—
377#2068—431no—
378#2065—431no—
379#2035—431no—
380#2033—431no—
381#1968—431no—
382#1942—431no—
383#1874—431no—
384#1873—431no—
385#1809—431no—
386C2×C43—42no—
387C2×C43—81no—
388C2×C43#241611yescharacteristic
389C2×C43#305611yescharacteristic
390C2×C43#306211yescharacteristic
391C2×C43#327311yescharacteristic
392C2×C43#327811yescharacteristic
393C2×C43#335111yescharacteristic
394C2×C43#335711yescharacteristic
395D43—161no—
396C22×SD16—431no—
397C22×M16C2×D4311yescharacteristic
398C22×M16C2×D4311yescharacteristic
399C2×C22⋊Q8—431no—
400C2×C22⋊Q8—431no—
401C2×#121—431no—
402C2×#121—431no—
403C2×C4×D4C2×D4311yescharacteristic
404C2×#117—431no—
405C22×C4⋊C4—431no—
406#468—864no—
407#468—864no—
408#436—24no—
409#428—864no—
410C2×#107—431no—
411C2×#107—431no—
412C2×#107—431no—
413C2×#106—431no—
414C2×#106—431no—
415C2×C4⋊C8C2×D4311yescharacteristic
416C2×#103—431no—
417C2×#103—431no—
418C2×#103—431no—
419C2×#102—431no—
420C2×#102—431no—
421C2×#102—431no—
422C2×C22⋊C8C2×D4311yescharacteristic
423C2×C22⋊C8C2×D4311yescharacteristic
424C2×C4×C8C2×D4311yescharacteristic
425#398—861no—
426#396—861no—
427#394—861no—
428#392—861no—
429#391—431no—
430#390—431no—
431#390—861no—
432#389—431no—
433#389—431no—
434#388—861no—
435#386—861no—
436#380—431no—
437#380—431no—
438#380—861no—
439#340—431no—
440#340—431no—
441#340—431no—
442#340—431no—
443C43#2479511yescharacteristic, complemented, Sylow
444C22×Q8—431no—
445C22×D4—431no—
446C22×D4—861no—
447C22×D4—861no—
448C22×D4D17211yescharacteristic
449C23×C4—861no—
450C23×C4C22×D4311yescharacteristic
451C23×C4C22×D4311yescharacteristic
452C2×SD16—862no—
453C2×SD16—862no—
454C2×SD16—862no—
455C2×M16—22no—
456C2×M16—22no—
457C2×M16—22no—
458C2×M16—22no—
459C2×M16—22no—
460C2×M16C22⋊D4314yescomplemented
461C22×C8C22×D4311yescharacteristic
462C22×C8C22×D4311yescharacteristic
463C22×C8C22×D4311yescharacteristic
464C22×C8C22×D4311yescharacteristic
465C22⋊Q8—862no—
466C22⋊Q8—862no—
467C22⋊Q8—862no—
468C22⋊Q8—1721no—
469#121—862no—
470#121—862no—
471#121—862no—
472#121—1721no—
473C4×D4—22no—
474C4×D4—22no—
475#117—862no—
476#117—1721no—
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—861no—
485C2×C4⋊C4—861no—
486C2×C4⋊C4—861no—
487C2×C4⋊C4—861no—
488C2×C4⋊C4—861no—
489C2×C4⋊C4—1721no—
490C2×C4⋊C4D17211yescharacteristic
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—861no—
499C2×C22⋊C4—861no—
500C2×C22⋊C4D17211yescharacteristic
501C2×C22⋊C4D17211yescharacteristic
502C2×C42—861no—
503C2×C42C22×D4311yescharacteristic
504#107—434no—
505#107—862no—
506#107—862no—
507#106—862no—
508#106—862no—
509C4⋊C8—22no—
510#103—862no—
511#103—862no—
512#103—1721no—
513#102—862no—
514#102—862no—
515#102—1721no—
516C22⋊C8—22no—
517C22⋊C8—22no—
518C4×C8—22no—
519#95—861no—
520#95—861no—
521#95—861no—
522#95—861no—
523#95—861no—
524#95—861no—
525C24—861no—
526C24C2×D17211yescharacteristic
527C24C2×D17211yescharacteristic
528C2×Q8—861no—
529C2×Q8—861no—
530C2×Q8—861no—
531C2×Q8—861no—
532C2×Q8—861no—
533C2×Q8—861no—
534C2×D4—22no—
535C2×D4—22no—
536C2×D4—41no—
537C2×D4—861no—
538C2×D4—861no—
539C2×D4—861no—
540C2×D4—861no—
541C2×D4—861no—
542C2×D4—861no—
543C2×D4—3441no—
544C2×D4—3441no—
545C2×D4—3441no—
546C2×D4—1722no—
547C2×D4—1722no—
548C2×D4—1722no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
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×C4—861no—
566C22×C4—3441no—
567C22×C4—1722no—
568C22×C4—1722no—
569C22×C4C2×D17211yescharacteristic
570C22×C4C2×D17211yescharacteristic
571C22×C4C2×D17211yescharacteristic
572C22×C4C2×D17211yescharacteristic
573C22×C4#1062189812yes—
574C22×C4C2×C22⋊D4312yes—
575C22×C4C23×D4311yescharacteristic
576SD16—1724no—
577M16—28no—
578M16—44no—
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×C8D4×D4312yes—
588C2×C8#1062190012yes—
589C2×C8C2×C22⋊D4312yes—
590C2×C8C2×C22⋊D4312yes—
591C4⋊C4—22no—
592C4⋊C4—432no—
593C4⋊C4—432no—
594C4⋊C4—861no—
595C4⋊C4—861no—
596C4⋊C4—861no—
597C4⋊C4—861no—
598C4⋊C4—861no—
599C4⋊C4—861no—
600C4⋊C4—861no—
601C4⋊C4—861no—
602C4⋊C4—861no—
603C4⋊C4—861no—
604C4⋊C4—3441no—
605C4⋊C4—3441no—
606C4⋊C4—1722no—
607C4⋊C4—1722no—
608C4⋊C4—1722no—
609C22⋊C4—22no—
610C22⋊C4—22no—
611C22⋊C4—3441no—
612C22⋊C4—3441no—
613C22⋊C4—3441no—
614C22⋊C4—1722no—
615C22⋊C4—1722no—
616C22⋊C4—1722no—
617C22⋊C4—1722no—
618C22⋊C4—1722no—
619C22⋊C4—1722no—
620C42—21no—
621C42—21no—
622C42—1722no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—1721no—
637C23—1721no—
638C23—1721no—
639C23—1721no—
640C23—1721no—
641C23—1721no—
642C23—1721no—
643C23#1306329912yes—
644C23C22×D17211yescharacteristic
645Q8—1721no—
646Q8—1721no—
647Q8—1721no—
648Q8—1721no—
649D4—44no—
650D4—3444no—
651D4—3444no—
652D4—1721no—
653D4—1721no—
654D4—1721no—
655D4—1721no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—862no—
675C2×C4—862no—
676C2×C4—3444no—
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—1721no—
692C2×C4—1721no—
693C2×C4—1721no—
694C2×C4—1721no—
695C2×C4—1721no—
696C2×C4#1306329912yes—
697C2×C4#1306335812yes—
698C2×C4C2×D4×D4311yescharacteristic
699C2×C4C22×C22⋊D4311yescharacteristic
700C2×C4C2×#1062190011yescharacteristic
701C2×C4C2×#1062189811yescharacteristic
702C2×C4#1306337111yescharacteristic
703C2×C4#1306337211yescharacteristic
704C8—22no—
705C8—41no—
706C8—41no—
707C8#1306329714yes—
708C22—22no—
709C22—22no—
710C22—22no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—3441no—
723C22—3441no—
724C22—3441no—
725C22—3441no—
726C22—3441no—
727C22—3441no—
728C22—3441no—
729C22C2×#1306329911yescharacteristic
730C22D4×D17211yescharacteristic
731C22#1458355311yescharacteristic
732C22C2×#1306335811yescharacteristic
733C22#1458369911yescharacteristic
734C22#1458370411yescharacteristic
735C22#1458371111yescharacteristic
736C4—22no—
737C4—22no—
738C4—41no—
739C4—41no—
740C4—3441no—
741C4—3441no—
742C4—3441no—
743C4—3441no—
744C4—3441no—
745C4—1722no—
746C4—1722no—
747C4C2×#1306329711yescharacteristic
748C4#1458347711yescharacteristic
749C4#1458355811yescharacteristic
750C4#1458359511yescharacteristic
751C2—42no—
752C2—81no—
753C2—6881no—
754C2#1913803511yescharacteristic
755C2#1914422511yescharacteristic
756C2#1914427511yescharacteristic
757C2#1914620711yescharacteristic
758C2#1914626311yescharacteristic
759C2#1914715711yescharacteristic
760C2#1914722211yescharacteristic
subgroupG/H
centerC23C22×D172
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#436C2
socleC23×C43C22×D4
prime radical#19138013C2
hypercenterC2×#436D43
hypocenterC43#24795
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#436

Complements

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

NH ≅ G/Ntype
1. C2×#14583145C2semidirect
2. C2×#14583145C2semidirect
3. C2×#14582941C2semidirect
4. #19138046C2semidirect
6. #19135989C2semidirect
7. #19135968C2semidirect
8. #19135792C2semidirect
9. #19135778C2semidirect
10. #19135449C2semidirect
11. #19135328C2semidirect
12. #19134910C2semidirect
13. #19134905C2semidirect
14. #19134628C2semidirect
15. C2×C43×#436C2semidirect
106. #13063259D4semidirect
129. C2×M16×C43D4semidirect
373. C2×#436D43semidirect
443. C43#24795semidirect
460. C2×M16C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145831452
C2×#145829412
#191380462
#191380132
#191359892
#191359682
#191357922
#191357782
#191354492
#191353282
#191349102
#191349052
#191346282
C2×C43×#4362
#2479543