Finite Group Databasebeta

← #25129634

Subgroups — #25129634

Order 11008.

1322 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583556C211yesmaximal, characteristic
2C2×#14583240C211yesmaximal, characteristic, complemented
3#19138886C211yesmaximal, characteristic, complemented
4#19135834C211yesmaximal, characteristic, complemented
5#19135834C211yesmaximal, characteristic, complemented
6#19135782C211yesmaximal, characteristic, complemented
7#19135775C211yesmaximal, characteristic, complemented
8#19135018C211yesmaximal, characteristic, complemented
9#19134887C211yesmaximal, characteristic, complemented
10#19134861C211yesmaximal, characteristic, complemented
11#19134847C211yesmaximal, characteristic, complemented
12#19134535C211yesmaximal, characteristic, complemented
13#19134528C211yesmaximal, characteristic, complemented
14#19134528C211yesmaximal, characteristic, complemented
15C2×C43×#416C211yesmaximal, characteristic, complemented
16C22×Q8×D43C2211yescharacteristic
17#14583556—24no—
18#14583556—24no—
19C2×#13063312—21no—
20C2×#13063312C2211yescharacteristic
21C2×#13063304—21no—
22C2×#13063304C2211yescharacteristic
23C2×#13063296—21no—
24C2×#13063296C2211yescharacteristic
25C2×Q8×Dic43C2211yescharacteristic
26C2×C4×C22⋊D43—21no—
27C2×C4×C22⋊D43C2211yescharacteristic
28#14583240—24no—
29C2×#13063258C2211yescharacteristic
30C2×#13063256C2211yescharacteristic
31C2×#13063250C2211yescharacteristic
32C2×#13063250C2211yescharacteristic
33C2×#13063249C2211yescharacteristic
34C2×#13063249C2211yescharacteristic
35C2×#13063248C2211yescharacteristic
36C2×#13063248C2211yescharacteristic
37C2×#13063246C2211yescharacteristic
38C2×#13063246C2211yescharacteristic
39C2×C22⋊(C43⋊C8)C2211yescharacteristic
40C2×(C2×D43)⋊C8C2211yescharacteristic
41C2×(C2×D43)⋊C8C2211yescharacteristic
42#14582827—21no—
43#14582814—21no—
44#14582795C2211yescharacteristic
45#14582795C2211yescharacteristic
46#14582790—21no—
47#14582783—21no—
48#14582759C2211yescharacteristic
49#14582756C2211yescharacteristic
50#14582756C2211yescharacteristic
51#14582662C2211yescharacteristic
52#14582662C2211yescharacteristic
53#14582653C2211yescharacteristic
54#14582653C2211yescharacteristic
55C22×#41×C43C2211yescharacteristic
56C23×C8×C43C2211yescharacteristic
57C2×#117×C43C2211yescharacteristic
58C43×#416—24no—
59C2×#103×C43C2211yescharacteristic
60C2×#103×C43C2211yescharacteristic
61C2×#102×C43C2211yescharacteristic
62C2×#102×C43C2211yescharacteristic
63C22×Dic86—21no—
64C22×Dic86C2311yescharacteristic
65C2×Q8×D43—22no—
66C2×Q8×D43—22no—
67C2×Q8×D43—22no—
68C2×Q8×D43—22no—
69C2×Q8×D43—41no—
70C2×Q8×D43—41no—
71C22×C22⋊D43—21no—
72C22×C22⋊D43D411yescharacteristic
73C22×C4×D43—21no—
74C22×C4×D43C2311yescharacteristic
75C22×C43⋊C8C2311yescharacteristic
76C22×C43⋊C8C2311yescharacteristic
77#13063312—28no—
78#13063312—22no—
79#13063312—22no—
80#13063304—28no—
81#13063304—22no—
82#13063304D414yes—
83#13063296—28no—
84#13063296—22no—
85#13063296—22no—
86Q8×Dic43—22no—
87Q8×Dic43—22no—
88C4×C22⋊D43—28no—
89C4×C22⋊D43—22no—
90C4×C22⋊D43—22no—
91C2×C4⋊Dic43—21no—
92C2×C4⋊Dic43C2311yescharacteristic
93C2×C4⋊Dic43C2311yescharacteristic
94C2×C4⋊Dic43C2311yescharacteristic
95C2×Dic43⋊C4—21no—
96C2×Dic43⋊C4—21no—
97C2×Dic43⋊C4—21no—
98C2×Dic43⋊C4D411yescharacteristic
99C2×C22⋊Dic43—21no—
100C2×C22⋊Dic43—21no—
101C2×C22⋊Dic43—21no—
102C2×C22⋊Dic43—21no—
103C2×C22⋊Dic43—21no—
104C2×C22⋊Dic43D411yescharacteristic
105C2×(C2×D43)⋊C4—21no—
106C2×(C2×D43)⋊C4—21no—
107C2×(C2×D43)⋊C4D411yescharacteristic
108C2×C4×Dic43—21no—
109C2×C4×Dic43C2311yescharacteristic
110#13063258—22no—
111#13063256—22no—
112#13063250—41no—
113#13063250—41no—
114#13063249—22no—
115#13063249—22no—
116#13063248—22no—
117#13063248—22no—
118#13063246—41no—
119#13063246—41no—
120C22⋊(C43⋊C8)—22no—
121(C2×D43)⋊C8—41no—
122(C2×D43)⋊C8—41no—
123C43⋊#95—21no—
124C43⋊#95—21no—
125C43⋊#95—21no—
126C43⋊#95—21no—
127C43⋊#95—21no—
128C2×#41×C43—22no—
129C2×#41×C43—22no—
130C2×#41×C43—22no—
131C2×#41×C43—41no—
132C2×#41×C43—41no—
133C2×#41×C43D414yes—
134C22×Q8×C43C2311yescharacteristic
135C22×D4×C43—21no—
136C22×D4×C43C2311yescharacteristic
137C23×C4×C43—21no—
138C23×C4×C43C2311yescharacteristic
139C22×C8×C43—22no—
140C22×C8×C43—41no—
141C22×C8×C43—41no—
142C22×C8×C43C2311yescharacteristic
143C22×C8×C43C2311yescharacteristic
144#117×C43—22no—
145#117×C43—22no—
146C2×C4⋊C4×C43C2311yescharacteristic
147C2×C4⋊C4×C43C2311yescharacteristic
148C2×C22⋊C4×C43—21no—
149C2×C42×C43—21no—
150#103×C43—22no—
151#103×C43—22no—
152#102×C43—22no—
153#102×C43—22no—
154C24×C43—21no—
155C24×C43C2×D411yescharacteristic
156C23×D43C2×D411yescharacteristic
157#41×C43—28no—
158#41×C43—44no—
159#41×C43—44no—
160#41×C43—44no—
161C2×Q8×C43—21no—
162C2×Q8×C43—21no—
163C2×Q8×C43—21no—
164C2×Q8×C43C2×D412yes—
165C2×Q8×C43#4112yes—
166C2×Q8×C43#4112yes—
167C2×D4×C43—21no—
168C2×D4×C43—24no—
169C2×D4×C43—21no—
170C2×D4×C43—21no—
171C2×D4×C43—21no—
172C2×D4×C43—21no—
173C2×D4×C43—42no—
174C2×D4×C43—42no—
175C2×D4×C43C2×D412yes—
176C22×C4×C43—21no—
177C22×C4×C43—21no—
178C22×C4×C43—21no—
179C22×C4×C43—21no—
180C22×C4×C43—24no—
181C22×C4×C43—21no—
182C22×C4×C43—21no—
183C22×C4×C43—21no—
184C22×C4×C43—42no—
185C22×C4×C43—42no—
186C22×C4×C43C2×D412yes—
187C22×C4×C43C2×D412yes—
188C22×C4×C43C2×D411yescharacteristic
189C22×C4×C43C2411yescharacteristic
190C2×C22⋊D43—24no—
191C2×C22⋊D43—22no—
192C2×C22⋊D43—22no—
193C2×C22⋊D43—41no—
194C2×C22⋊D43—42no—
195C2×C22⋊D43—42no—
196C22×Dic43—21no—
197C22×Dic43—21no—
198C22×Dic43—21no—
199C22×Dic43—21no—
200C22×Dic43C2×D411yescharacteristic
201C22×Dic43C2×D411yescharacteristic
202C22×Dic43C2×D411yescharacteristic
203Q8×D43—44no—
204Q8×D43—44no—
205Q8×D43—44no—
206Q8×D43—44no—
207C2×C4×D43—24no—
208C2×C4×D43—21no—
209C2×C4×D43—21no—
210C2×C4×D43—21no—
211C2×C4×D43—21no—
212C2×C4×D43—21no—
213C2×C4×D43—21no—
214C2×C4×D43—42no—
215C2×C4×D43—42no—
216C2×Dic86—21no—
217C2×Dic86—21no—
218C2×Dic86—21no—
219C2×Dic86—21no—
220C2×Dic86—24no—
221C2×Dic86—21no—
222C2×Dic86—42no—
223C2×Dic86—42no—
224C2×Dic86C2×D412yes—
225C2×C8×C43—21no—
226C2×C8×C43—21no—
227C2×C8×C43—21no—
228C2×C8×C43—21no—
229C2×C8×C43—21no—
230C2×C8×C43—21no—
231C2×C8×C43—44no—
232C4⋊C4×C43—21no—
233C4⋊C4×C43—21no—
234C4⋊C4×C43—21no—
235C4⋊C4×C43—21no—
236C22⋊C4×C43—42no—
237C42×C43—42no—
238C22⋊Dic43—24no—
239C22⋊Dic43—24no—
240C22⋊Dic43—24no—
241C22⋊Dic43—24no—
242C22⋊Dic43—22no—
243C22⋊Dic43—81no—
244(C2×D43)⋊C4—22no—
245(C2×D43)⋊C4—42no—
246(C2×D43)⋊C4—81no—
247C4⋊Dic43—24no—
248C4⋊Dic43—21no—
249C4⋊Dic43—21no—
250C4⋊Dic43—21no—
251C4⋊Dic43—21no—
252C4⋊Dic43—21no—
253C4⋊Dic43C2×D412yes—
254Dic43⋊C4—24no—
255Dic43⋊C4—22no—
256Dic43⋊C4—42no—
257Dic43⋊C4—81no—
258C4×Dic43—24no—
259C4×Dic43—21no—
260C4×Dic43—21no—
261C2×C43⋊C8—21no—
262C2×C43⋊C8—21no—
263C2×C43⋊C8—21no—
264C2×C43⋊C8—21no—
265C2×C43⋊C8—21no—
266C2×C43⋊C8—21no—
267C23×C43—21no—
268C23×C43—21no—
269C23×C43—21no—
270C23×C43—21no—
271C23×C43—21no—
272C23×C43—21no—
273C23×C43—22no—
274C23×C43—41no—
275C23×C43—41no—
276C23×C43—41no—
277C23×C43—41no—
278C23×C43—41no—
279C23×C43—41no—
280C23×C43#12012yes—
281C23×C43C22×D411yescharacteristic
282C22×D43—21no—
283C22×D43—21no—
284C22×D43—21no—
285C22×D43—21no—
286C22×D43—21no—
287C22×D43—21no—
288C22×D43#13512yes—
289Q8×C43—22no—
290Q8×C43—22no—
291Q8×C43—22no—
292Q8×C43#12314yes—
293D4×C43—22no—
294D4×C43—22no—
295D4×C43—48no—
296D4×C43—41no—
297D4×C43—41no—
298C2×C4×C43—22no—
299C2×C4×C43—22no—
300C2×C4×C43—22no—
301C2×C4×C43—21no—
302C2×C4×C43—21no—
303C2×C4×C43—22no—
304C2×C4×C43—22no—
305C2×C4×C43—22no—
306C2×C4×C43—22no—
307C2×C4×C43—48no—
308C2×C4×C43—41no—
309C2×C4×C43—41no—
310C2×C4×C43—41no—
311C2×C4×C43—41no—
312C2×C4×C43—41no—
313C2×C4×C43—41no—
314C2×C4×C43#12012yes—
315C2×C4×C43C22×D411yescharacteristic
316C2×C4×C43C22×D411yescharacteristic
317C2×C4×C43C2×#4111yescharacteristic
318C2×C4×C43C2×#4111yescharacteristic
319C2×C4×C43H(5,𝔽2)11yescharacteristic
320C2×C4×C43H(5,𝔽2)11yescharacteristic
321C22⋊D43—44no—
322C22⋊D43—48no—
323C2×Dic43—21no—
324C2×Dic43—21no—
325C2×Dic43—22no—
326C2×Dic43—21no—
327C2×Dic43—22no—
328C2×Dic43—21no—
329C2×Dic43—21no—
330C2×Dic43—21no—
331C2×Dic43—21no—
332C2×Dic43—21no—
333C2×Dic43—21no—
334C2×Dic43—41no—
335C2×Dic43—41no—
336C2×Dic43—41no—
337C2×Dic43—41no—
338C2×Dic43—41no—
339C2×Dic43—41no—
340C2×Dic43—41no—
341C2×Dic43—41no—
342C2×Dic43—41no—
343C2×Dic43—41no—
344C4×D43—48no—
345C4×D43—41no—
346C4×D43—41no—
347C4×D43—41no—
348C4×D43—41no—
349Dic86—22no—
350Dic86—22no—
351Dic86—48no—
352Dic86—41no—
353Dic86—41no—
354C8×C43—41no—
355C8×C43—41no—
356C43⋊C8—41no—
357C43⋊C8—41no—
358#24040—431nomaximal, Sylow
359C22×C43—22no—
360C22×C43—22no—
361C22×C43—22no—
362C22×C43—41no—
363C22×C43—41no—
364C22×C43—41no—
365C22×C43—41no—
366C22×C43—42no—
367C22×C43—42no—
368C22×C43—42no—
369C22×C43—81no—
370C22×C43—81no—
371C22×C43—81no—
372C22×C43—81no—
373C22×C43C2×#12011yescharacteristic
374C22×C43#54611yescharacteristic
375C22×C43#54611yescharacteristic
376C22×C43C2×#13511yescharacteristic
377C22×C43#57511yescharacteristic
378C22×C43#57711yescharacteristic
379C22×C43#57811yescharacteristic
380C2×D43—22no—
381C2×D43—22no—
382C2×D43—22no—
383C2×D43—41no—
384C2×D43—41no—
385C2×D43—41no—
386C2×D43—41no—
387C4×C43—24no—
388C4×C43—22no—
389C4×C43—81no—
390C4×C43—81no—
391C4×C43C2×#12311yescharacteristic
392C4×C43#53411yescharacteristic
393C4×C43#54611yescharacteristic
394C4×C43#54611yescharacteristic
395Dic43—42no—
396Dic43—41no—
397Dic43—41no—
398Dic43—42no—
399Dic43—41no—
400Dic43—81no—
401Dic43—81no—
402C2×#548—431no—
403C2×#485—431no—
404C2×#416D4311yescharacteristic, complemented
405#2485—431no—
406#2042—431no—
407#2042—431no—
408#2034—431no—
409#2033—431no—
410#1892—431no—
411#1869—431no—
412#1865—431no—
413#1863—431no—
414#1788—431no—
415#1787—431no—
416#1787—431no—
417C2×C43—42no—
418C2×C43—82no—
419C2×C43#240511yescharacteristic
420C2×C43#300211yescharacteristic
421C2×C43#301311yescharacteristic
422C2×C43#330011yescharacteristic
423C2×C43#330111yescharacteristic
424C2×C43#331311yescharacteristic
425C2×C43#332111yescharacteristic
426D43—42no—
427C22×#41C2×D4311yescharacteristic
428C23×Q8—431no—
429C23×C8C2×D4311yescharacteristic
430#548—864no—
431#548—864no—
432C2×#124—431no—
433C2×#124—861no—
434C2×C22⋊Q8—431no—
435C2×C22⋊Q8—861no—
436C2×#121—431no—
437C2×#121—861no—
438C2×C4×Q8—431no—
439C2×C4×D4—431no—
440C2×C4×D4—861no—
441C2×#117C2×D4311yescharacteristic
442#485—864no—
443C2×#107—431no—
444C2×#106—431no—
445#416—24no—
446C2×#103—431no—
447C2×#103—431no—
448C2×#103—431no—
449C2×#103—431no—
450C2×#103—431no—
451C2×#103—431no—
452C2×#103C2×D4311yescharacteristic
453C2×#103C2×D4311yescharacteristic
454C2×#102—431no—
455C2×#102—431no—
456C2×#102C2×D4311yescharacteristic
457C2×#102C2×D4311yescharacteristic
458C2×C22⋊C8—431no—
459C2×C22⋊C8—431no—
460C2×C22⋊C8—431no—
461#397—861no—
462#394—861no—
463#389—431no—
464#389—431no—
465#388—861no—
466#387—861no—
467#380—431no—
468#380—431no—
469#380—431no—
470#340—431no—
471#340—431no—
472#336—431no—
473#336—431no—
474C43#2404011yescharacteristic, complemented, Sylow
475C2×#41—22no—
476C2×#41—22no—
477C2×#41—22no—
478C2×#41—41no—
479C2×#41—41no—
480C2×#41C22⋊D4314yes—
481C22×Q8—431no—
482C22×Q8—861no—
483C22×Q8—862no—
484C22×Q8—862no—
485C22×Q8—862no—
486C22×Q8—862no—
487C22×Q8—1721no—
488C22×Q8—1721no—
489C22×Q8C22×D4311yescharacteristic
490C22×D4—21no—
491C22×D4—431no—
492C22×D4—861no—
493C22×D4C22×D4311yescharacteristic
494C23×C4—21no—
495C23×C4—431no—
496C23×C4—861no—
497C23×C4C22×D4311yescharacteristic
498C22×C8—22no—
499C22×C8—41no—
500C22×C8—41no—
501C22×C8—431no—
502C22×C8—431no—
503C22×C8C22×D4311yescharacteristic
504C22×C8C22×D4311yescharacteristic
505#124—862no—
506#124—868no—
507#124—862no—
508C22⋊Q8—434no—
509C22⋊Q8—868no—
510C22⋊Q8—862no—
511#121—862no—
512#121—868no—
513#121—862no—
514C4×Q8—862no—
515C4×Q8—862no—
516C4×D4—868no—
517C4×D4—862no—
518C4×D4—862no—
519#117—22no—
520#117—22no—
521C2×C4⋊C4—431no—
522C2×C4⋊C4—431no—
523C2×C4⋊C4—431no—
524C2×C4⋊C4—431no—
525C2×C4⋊C4—861no—
526C2×C4⋊C4—861no—
527C2×C4⋊C4—861no—
528C2×C4⋊C4—861no—
529C2×C4⋊C4C22×D4311yescharacteristic
530C2×C4⋊C4C22×D4311yescharacteristic
531C2×C22⋊C4—21no—
532C2×C22⋊C4—431no—
533C2×C22⋊C4—431no—
534C2×C22⋊C4—861no—
535C2×C22⋊C4—861no—
536C2×C22⋊C4—861no—
537C2×C22⋊C4—861no—
538C2×C22⋊C4—861no—
539C2×C22⋊C4—861no—
540C2×C22⋊C4—861no—
541C2×C42—21no—
542C2×C42—431no—
543C2×C42—861no—
544#107—862no—
545#106—862no—
546#103—22no—
547#103—22no—
548#103—862no—
549#103—862no—
550#103—862no—
551#103—862no—
552#103—1721no—
553#103—1721no—
554#102—22no—
555#102—22no—
556#102—1721no—
557#102—1721no—
558C22⋊C8—862no—
559C22⋊C8—1721no—
560C22⋊C8—1721no—
561#95—861no—
562#95—861no—
563#95—861no—
564#95—861no—
565#95—861no—
566C24—21no—
567C24—431no—
568C24D4×D4311yescharacteristic
569#41—28no—
570#41—44no—
571#41—44no—
572#41—44no—
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—432no—
577C2×Q8—864no—
578C2×Q8—861no—
579C2×Q8—861no—
580C2×Q8—861no—
581C2×Q8—861no—
582C2×Q8—861no—
583C2×Q8—1722no—
584C2×Q8—1722no—
585C2×Q8—1724no—
586C2×Q8—1724no—
587C2×Q8—1724no—
588C2×Q8—1724no—
589C2×Q8#1062189812yes—
590C2×Q8#1062189812yes—
591C2×Q8C2×C22⋊D4312yes—
592C2×D4—24no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—42no—
599C2×D4—42no—
600C2×D4—862no—
601C2×D4—864no—
602C2×D4—862no—
603C2×D4—1721no—
604C2×D4—1722no—
605C2×D4—1722no—
606C2×D4C2×C22⋊D4312yes—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—24no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—42no—
616C22×C4—42no—
617C22×C4—431no—
618C22×C4—431no—
619C22×C4—431no—
620C22×C4—864no—
621C22×C4—861no—
622C22×C4—861no—
623C22×C4—861no—
624C22×C4—861no—
625C22×C4—861no—
626C22×C4—861no—
627C22×C4—861no—
628C22×C4—861no—
629C22×C4—861no—
630C22×C4—861no—
631C22×C4—1722no—
632C22×C4—1722no—
633C22×C4D4×D4311yescharacteristic
634C22×C4D4×D4312yes—
635C22×C4C2×C22⋊D4312yes—
636C22×C4C23×D4311yescharacteristic
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—44no—
644C2×C8—861no—
645C2×C8—861no—
646C2×C8—861no—
647C2×C8—861no—
648C2×C8—861no—
649C2×C8—861no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—432no—
655C4⋊C4—864no—
656C4⋊C4—862no—
657C4⋊C4—864no—
658C4⋊C4—861no—
659C4⋊C4—861no—
660C4⋊C4—861no—
661C4⋊C4—861no—
662C4⋊C4—861no—
663C4⋊C4—3441no—
664C4⋊C4—1722no—
665C22⋊C4—42no—
666C22⋊C4—864no—
667C22⋊C4—864no—
668C22⋊C4—864no—
669C22⋊C4—862no—
670C22⋊C4—864no—
671C22⋊C4—862no—
672C22⋊C4—3441no—
673C22⋊C4—3441no—
674C22⋊C4—1722no—
675C42—42no—
676C42—864no—
677C42—861no—
678C42—861no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—22no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—432no—
693C23—861no—
694C23—861no—
695C23—861no—
696C23—861no—
697C23—861no—
698C23—861no—
699C23#1306329312yes—
700C23C2×D4×D4311yescharacteristic
701Q8—22no—
702Q8—22no—
703Q8—22no—
704Q8—862no—
705Q8—862no—
706Q8—1728no—
707Q8—1721no—
708Q8—1721no—
709Q8#1306330814yes—
710D4—22no—
711D4—22no—
712D4—48no—
713D4—41no—
714D4—41no—
715D4—1724no—
716D4—1728no—
717C2×C4—22no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—48no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—861no—
734C2×C4—862no—
735C2×C4—861no—
736C2×C4—861no—
737C2×C4—862no—
738C2×C4—861no—
739C2×C4—861no—
740C2×C4—861no—
741C2×C4—861no—
742C2×C4—861no—
743C2×C4—861no—
744C2×C4—1728no—
745C2×C4—1721no—
746C2×C4—1721no—
747C2×C4—1721no—
748C2×C4—1721no—
749C2×C4—1721no—
750C2×C4—1721no—
751C2×C4—1721no—
752C2×C4—1721no—
753C2×C4—1721no—
754C2×C4—1721no—
755C2×C4—1721no—
756C2×C4—1721no—
757C2×C4—1721no—
758C2×C4—1721no—
759C2×C4#1306329312yes—
760C2×C4C2×D4×D4311yescharacteristic
761C2×C4C22×C22⋊D4311yescharacteristic
762C2×C4C2×#1062189811yescharacteristic
763C2×C4C2×#1062189811yescharacteristic
764C2×C4#1306337011yescharacteristic
765C2×C4#1306337011yescharacteristic
766C8—41no—
767C8—41no—
768C8—1721no—
769C8—1721no—
770C22—22no—
771C22—22no—
772C22—22no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22—81no—
781C22—81no—
782C22—81no—
783C22—81no—
784C22—862no—
785C22—862no—
786C22—862no—
787C22—1721no—
788C22—1721no—
789C22—1721no—
790C22—1721no—
791C22C2×#1306329311yescharacteristic
792C22#1458353911yescharacteristic
793C22#1458353911yescharacteristic
794C22#135×D4311yescharacteristic
795C22#1458369611yescharacteristic
796C22#1458370611yescharacteristic
797C22#1458371311yescharacteristic
798C4—22no—
799C4—24no—
800C4—81no—
801C4—81no—
802C4—3441no—
803C4—3441no—
804C4—1721no—
805C4—1722no—
806C4—1721no—
807C4—1722no—
808C4—1721no—
809C4C2×#1306330811yescharacteristic
810C4#1458345811yescharacteristic
811C4#1458353911yescharacteristic
812C4#1458353911yescharacteristic
813C2—42no—
814C2—82no—
815C2—1722no—
816C2#1913792211yescharacteristic
817C2#1914380911yescharacteristic
818C2#1914390611yescharacteristic
819C2#1914648311yescharacteristic
820C2#1914649811yescharacteristic
821C2#1914665711yescharacteristic
822C2#1914677711yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#416C2
socleC23×C43C22×D4
prime radicalC2×#14583556C2
hypercenterC2×#416D43
hypocenterC43#24040
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#416

Complements

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

NH ≅ G/Ntype
2. C2×#14583240C2semidirect
3. #19138886C2semidirect
4. #19135834C2semidirect
5. #19135834C2semidirect
6. #19135782C2semidirect
7. #19135775C2semidirect
8. #19135018C2semidirect
9. #19134887C2semidirect
10. #19134861C2semidirect
11. #19134847C2semidirect
12. #19134535C2semidirect
13. #19134528C2semidirect
14. #19134528C2semidirect
15. C2×C43×#416C2semidirect
404. C2×#416D43semidirect
474. C43#24040semidirect

Maximal subgroups

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

subgroupindex
C2×#145835562
C2×#145832402
#191388862
#191358342
#191357822
#191357752
#191350182
#191348872
#191348612
#191348472
#191345352
#191345282
C2×C43×#4162
#2404043