Finite Group Databasebeta

← #25124104

Subgroups — #25124104

Order 11008.

1650 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583406C211yesmaximal, characteristic
2C2×#14582939C211yesmaximal, characteristic, complemented
3C2×#14582900C211yesmaximal, characteristic, complemented
4C2×#14582862C211yesmaximal, characteristic, complemented
5C2×#14582756C211yesmaximal, characteristic, complemented
6#19135796C212yesmaximal, complemented
7#19135789C212yesmaximal, complemented
8#19135782C212yesmaximal, complemented
9#19135775C212yesmaximal, complemented
10#19134315C211yesmaximal, characteristic, complemented
11C2×C43×#417C211yesmaximal, characteristic, complemented
12C23×C4×D43C2211yescharacteristic
13C22×#10621877C2211yescharacteristic
14#14583406—24no—
15#14583406—24no—
16C2×#13063306—21no—
17C2×#13063301C2211yescharacteristic
18C2×#13063301C2211yescharacteristic
19C2×#13063296C2211yescharacteristic
20C2×#13063296C2211yescharacteristic
21C2×#13063293—21no—
22C2×C4×C22⋊D43—21no—
23C2×C4×C22⋊D43—21no—
24C2×#13063284C2211yescharacteristic
25C22×C4⋊Dic43C2211yescharacteristic
26C22×(C2×D43)⋊C4—21no—
27#14582939—24no—
28C2×#13063258C2212yescomplemented
29C2×#13063256C2212yescomplemented
30#14582900—24no—
31C2×#13063249C2212yescomplemented
32C2×#13063246C2212yescomplemented
33#14582862—24no—
34C2×(C2×D43)⋊C8C2212yes—
35C2×(C2×D43)⋊C8C2212yes—
36#14582756—21no—
37#14582756—21no—
38#14582756C2212yes—
39#14582756C2212yes—
40C2×C43⋊#95—21no—
41#14582662C2212yescomplemented
42#14582662C2212yescomplemented
43C22×#41×C43C2211yescharacteristic
44C22×M16×C43C2211yescharacteristic
45C22×C4⋊C4×C43C2211yescharacteristic
46C43×#417—24no—
47C2×#103×C43C2212yescomplemented
48C2×#102×C43C2212yescomplemented
49C24×D43D411yescharacteristic
50C22×C22⋊D43—21no—
51C22×C22⋊D43—21no—
52C23×Dic43—21no—
53C23×Dic43D411yescharacteristic
54C22×C4×D43—22no—
55C22×C4×D43—22no—
56C22×C4×D43—22no—
57C22×C4×D43—22no—
58C22×C4×D43—22no—
59C22×C4×D43—22no—
60C22×C4×D43D411yescharacteristic
61C22×C4×D43D411yescharacteristic
62C22×C4×D43C2311yescharacteristic
63C22×C4×D43C2311yescharacteristic
64C2×#10621877—22no—
65C2×#10621877—22no—
66C2×#10621877D414yescomplemented
67C22×C43⋊C8C2312yes—
68#13063306—28no—
69#13063301—22no—
70#13063301—22no—
71#13063301—22no—
72#13063301—22no—
73#13063296—22no—
74#13063296—22no—
75#13063296—22no—
76#13063296—22no—
77#13063293—28no—
78C4×C22⋊D43—28no—
79C4×C22⋊D43—28no—
80#13063284—22no—
81#13063284D414yes—
82C2×C4⋊Dic43—22no—
83C2×C4⋊Dic43—22no—
84C2×C4⋊Dic43—21no—
85C2×C4⋊Dic43C2312yes—
86C2×C4⋊Dic43C2311yescharacteristic
87C2×C4⋊Dic43C2311yescharacteristic
88C2×Dic43⋊C4—21no—
89C2×Dic43⋊C4—21no—
90C2×C22⋊Dic43—21no—
91C2×C22⋊Dic43—21no—
92C2×C22⋊Dic43—21no—
93C2×(C2×D43)⋊C4—21no—
94C2×(C2×D43)⋊C4—21no—
95C2×(C2×D43)⋊C4—22no—
96C2×(C2×D43)⋊C4—22no—
97C2×(C2×D43)⋊C4—44no—
98C2×C4×Dic43—21no—
99#13063258—24no—
100#13063256—24no—
101#13063249—24no—
102#13063246—24no—
103(C2×D43)⋊C8—24no—
104(C2×D43)⋊C8—24no—
105C43⋊#95—22no—
106C43⋊#95—22no—
107C2×#41×C43—22no—
108C2×#41×C43—22no—
109C2×#41×C43—22no—
110C2×#41×C43—22no—
111C2×#41×C43—22no—
112C2×#41×C43D414yes—
113C22×Q8×C43C2311yescharacteristic
114C22×D4×C43—21no—
115C22×D4×C43C2311yescharacteristic
116C23×C4×C43—21no—
117C23×C4×C43—21no—
118C23×C4×C43C2311yescharacteristic
119C2×M16×C43—22no—
120C2×M16×C43—22no—
121C2×M16×C43—22no—
122C22×C8×C43C2312yes—
123C2×C4⋊C4×C43—22no—
124C2×C4⋊C4×C43—22no—
125C2×C4⋊C4×C43—21no—
126C2×C4⋊C4×C43C2312yes—
127#103×C43—24no—
128#102×C43—24no—
129C24×C43—21no—
130C24×C43C2×D411yescharacteristic
131C23×D43—22no—
132C23×D43—22no—
133C23×D43—22no—
134C23×D43—22no—
135C23×D43—22no—
136C23×D43—41no—
137C23×D43—41no—
138C23×D43C2×D411yescharacteristic
139C23×D43C2×D411yescharacteristic
140#41×C43—28no—
141#41×C43—28no—
142#41×C43—44no—
143#41×C43—44no—
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43—21no—
147C2×Q8×C43—21no—
148C2×Q8×C43—21no—
149C2×Q8×C43C2×D412yes—
150C2×D4×C43—21no—
151C2×D4×C43—24no—
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43—42no—
157C2×D4×C43—42no—
158C2×D4×C43C2×D412yes—
159C22×C4×C43—24no—
160C22×C4×C43—21no—
161C22×C4×C43—22no—
162C22×C4×C43—42no—
163C22×C4×C43—42no—
164C22×C4×C43—42no—
165C22×C4×C43—42no—
166C22×C4×C43—42no—
167C22×C4×C43C2×D412yes—
168C22×C4×C43C2×D412yes—
169C22×C4×C43C2×D412yes—
170C22×C4×C43C2×D411yescharacteristic
171C22×C4×C43#4112yes—
172C22×C4×C43#4112yes—
173C22×C4×C43#4112yes—
174C22×C4×C43C2411yescharacteristic
175C2×C22⋊D43—24no—
176C2×C22⋊D43—24no—
177C2×C22⋊D43—42no—
178C2×C22⋊D43—42no—
179C2×C22⋊D43—42no—
180C2×C22⋊D43—42no—
181C22×Dic43—22no—
182C22×Dic43—22no—
183C22×Dic43—22no—
184C22×Dic43—21no—
185C22×Dic43—21no—
186C22×Dic43—22no—
187C22×Dic43—42no—
188C22×Dic43—42no—
189C22×Dic43—42no—
190C22×Dic43C2×D411yescharacteristic
191C22×Dic43C2×D411yescharacteristic
192C2×C4×D43—22no—
193C2×C4×D43—22no—
194C2×C4×D43—22no—
195C2×C4×D43—22no—
196C2×C4×D43—22no—
197C2×C4×D43—22no—
198C2×C4×D43—21no—
199C2×C4×D43—21no—
200C2×C4×D43—21no—
201C2×C4×D43—21no—
202C2×C4×D43—21no—
203C2×C4×D43—21no—
204C2×C4×D43—21no—
205C2×C4×D43—21no—
206C2×C4×D43—21no—
207C2×C4×D43—21no—
208C2×C4×D43—21no—
209C2×C4×D43—21no—
210C2×C4×D43—44no—
211C2×C4×D43—44no—
212C2×C4×D43—44no—
213C2×C4×D43—44no—
214M16×C43—44no—
215C2×C8×C43—22no—
216C2×C8×C43—22no—
217C2×C8×C43—22no—
218C4⋊C4×C43—22no—
219C4⋊C4×C43—22no—
220C4⋊C4×C43—42no—
221C22⋊Dic43—24no—
222C22⋊Dic43—24no—
223C22⋊Dic43—24no—
224(C2×D43)⋊C4—24no—
225(C2×D43)⋊C4—24no—
226(C2×D43)⋊C4—44no—
227(C2×D43)⋊C4—44no—
228C4⋊Dic43—21no—
229C4⋊Dic43—21no—
230C4⋊Dic43—22no—
231C4⋊Dic43—22no—
232C4⋊Dic43—42no—
233C4⋊Dic43C2×D412yes—
234C4⋊Dic43C2×D412yes—
235Dic43⋊C4—24no—
236Dic43⋊C4—24no—
237C4×Dic43—24no—
238#10621877—28no—
239C2×C43⋊C8—22no—
240C2×C43⋊C8—22no—
241C2×C43⋊C8C2×D414yes—
242C23×C43—21no—
243C23×C43—21no—
244C23×C43—21no—
245C23×C43—21no—
246C23×C43—22no—
247C23×C43—41no—
248C23×C43—41no—
249C23×C43—41no—
250C23×C43—41no—
251C23×C43—41no—
252C23×C43—41no—
253C23×C43#12012yes—
254C23×C43#12112yes—
255C23×C43#12312yes—
256C23×C43C22×D411yescharacteristic
257C22×D43—28no—
258C22×D43—21no—
259C22×D43—21no—
260C22×D43—21no—
261C22×D43—21no—
262C22×D43—21no—
263C22×D43—21no—
264C22×D43—21no—
265C22×D43—21no—
266C22×D43—21no—
267C22×D43—21no—
268C22×D43—21no—
269C22×D43—21no—
270C22×D43—44no—
271C22×D43—44no—
272C22×D43—44no—
273C22×D43—44no—
274C22×D43—44no—
275C22×D43—44no—
276C22×D43AGL(1,ℤ/8)12yes—
277C22×D43#13712yes—
278Q8×C43—22no—
279Q8×C43—22no—
280Q8×C43—41no—
281Q8×C43—41no—
282D4×C43—22no—
283D4×C43—22no—
284D4×C43—48no—
285D4×C43—41no—
286D4×C43—41no—
287C2×C4×C43—22no—
288C2×C4×C43—41no—
289C2×C4×C43—41no—
290C2×C4×C43—48no—
291C2×C4×C43—42no—
292C2×C4×C43—42no—
293C2×C4×C43—42no—
294C2×C4×C43—84no—
295C2×C4×C43#12012yes—
296C2×C4×C43#12114yes—
297C2×C4×C43#12114yes—
298C2×C4×C43#12112yes—
299C2×C4×C43#12312yes—
300C2×C4×C43#12314yes—
301C2×C4×C43#12414yes—
302C2×C4×C43C22×D411yescharacteristic
303C2×C4×C43C22×D411yescharacteristic
304C2×C4×C43C22×D411yescharacteristic
305C2×C4×C43C2×#4111yescharacteristic
306C2×C4×C43C2×#4111yescharacteristic
307C2×C4×C43C2×#4111yescharacteristic
308C22⋊D43—48no—
309C22⋊D43—48no—
310C2×Dic43—22no—
311C2×Dic43—22no—
312C2×Dic43—21no—
313C2×Dic43—21no—
314C2×Dic43—21no—
315C2×Dic43—21no—
316C2×Dic43—21no—
317C2×Dic43—21no—
318C2×Dic43—41no—
319C2×Dic43—41no—
320C2×Dic43—41no—
321C2×Dic43—41no—
322C2×Dic43—44no—
323C2×Dic43—42no—
324C2×Dic43—42no—
325C2×Dic43—42no—
326C2×Dic43—84no—
327C4×D43—41no—
328C4×D43—41no—
329C4×D43—41no—
330C4×D43—41no—
331C4×D43—41no—
332C4×D43—41no—
333C4×D43—41no—
334C4×D43—41no—
335C4×D43—44no—
336C4×D43—44no—
337C8×C43—42no—
338C43⋊C8—24no—
339#23482—431nomaximal, Sylow
340C22×C43—22no—
341C22×C43—22no—
342C22×C43—22no—
343C22×C43—22no—
344C22×C43—22no—
345C22×C43—22no—
346C22×C43—42no—
347C22×C43—42no—
348C22×C43—42no—
349C22×C43—81no—
350C22×C43—81no—
351C22×C43—81no—
352C22×C43—81no—
353C22×C43#39414yes—
354C22×C43C2×#12011yescharacteristic
355C22×C43C2×#12111yescharacteristic
356C22×C43C2×#12311yescharacteristic
357C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
358C22×C43C2×#13711yescharacteristic
359C22×C43#57511yescharacteristic
360C22×C43#57511yescharacteristic
361C2×D43—22no—
362C2×D43—22no—
363C2×D43—22no—
364C2×D43—22no—
365C2×D43—22no—
366C2×D43—22no—
367C2×D43—416no—
368C2×D43—41no—
369C2×D43—41no—
370C2×D43—41no—
371C2×D43—41no—
372C2×D43—41no—
373C2×D43—41no—
374C2×D43—41no—
375C2×D43—41no—
376C4×C43—42no—
377C4×C43—82no—
378C4×C43#39414yes—
379C4×C43C2×#12111yescharacteristic
380C4×C43C2×#12111yescharacteristic
381C4×C43C2×#12311yescharacteristic
382C4×C43C2×#12411yescharacteristic
383Dic43—41no—
384Dic43—41no—
385Dic43—42no—
386Dic43—42no—
387Dic43—82no—
388C2×#525—431no—
389C2×#428—431no—
390C2×#417—431no—
391C2×#417D4311yescharacteristic, complemented
392C2×#407—431no—
393C2×#380—431no—
394#2036—432no—
395#2035—432no—
396#2034—432no—
397#2033—432no—
398#1736—431no—
399C2×C43—24no—
400C2×C43—82no—
401C2×C43C2×#39411yescharacteristic
402C2×C43#300611yescharacteristic
403C2×C43#300711yescharacteristic
404C2×C43#305511yescharacteristic
405C2×C43#305611yescharacteristic
406C2×C43#309211yescharacteristic
407C2×C43#309311yescharacteristic
408D43—42no—
409D43—42no—
410C22×#41C2×D4311yescharacteristic
411C24×C4—431no—
412C22×M16—431no—
413C22×M16C2×D4311yescharacteristic
414#525—864no—
415#525—864no—
416C2×#123—861no—
417C2×C22⋊Q8—431no—
418C2×C22⋊Q8—431no—
419C2×#121—431no—
420C2×#121—431no—
421C2×#120—861no—
422C2×C4×D4—861no—
423C2×C4×D4—861no—
424C2×#117—431no—
425C22×C4⋊C4—431no—
426C22×C4⋊C4C2×D4311yescharacteristic
427C22×C22⋊C4—861no—
428#428—864no—
429C2×#107—432no—
430C2×#106—432no—
431#417—24no—
432#417—864no—
433C2×#103—432no—
434C2×#103C2×D4312yescomplemented
435C2×#102—432no—
436C2×#102C2×D4312yescomplemented
437#407—864no—
438C2×C22⋊C8—432no—
439C2×C22⋊C8—432no—
440#380—432no—
441#380—432no—
442#380—861no—
443#380—861no—
444C2×#95—861no—
445#340—432no—
446#340—432no—
447C43#2348211yescharacteristic, complemented, Sylow
448C25—431no—
449C2×#41—22no—
450C2×#41—22no—
451C2×#41—22no—
452C2×#41—22no—
453C2×#41—22no—
454C2×#41C22⋊D4314yes—
455C22×Q8C22×D4311yescharacteristic
456C22×D4—21no—
457C22×D4—861no—
458C22×D4—861no—
459C22×D4C22×D4311yescharacteristic
460C23×C4—21no—
461C23×C4—21no—
462C23×C4—431no—
463C23×C4—431no—
464C23×C4—431no—
465C23×C4—431no—
466C23×C4—431no—
467C23×C4—862no—
468C23×C4—862no—
469C23×C4—862no—
470C23×C4—862no—
471C23×C4—862no—
472C23×C4—862no—
473C23×C4—861no—
474C23×C4C22×D4311yescharacteristic
475C2×M16—22no—
476C2×M16—22no—
477C2×M16—22no—
478C2×M16—434no—
479C2×M16—862no—
480C2×M16—862no—
481C22×C8—432no—
482C22×C8C22×D4312yes—
483#123—868no—
484C22⋊Q8—862no—
485C22⋊Q8—862no—
486C22⋊Q8—862no—
487C22⋊Q8—862no—
488#121—862no—
489#121—862no—
490#121—862no—
491#121—862no—
492#120—868no—
493C4×D4—868no—
494C4×D4—868no—
495#117—434no—
496#117—862no—
497C2×C4⋊C4—22no—
498C2×C4⋊C4—22no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—431no—
501C2×C4⋊C4—431no—
502C2×C4⋊C4—432no—
503C2×C4⋊C4—861no—
504C2×C4⋊C4—861no—
505C2×C4⋊C4—862no—
506C2×C4⋊C4—862no—
507C2×C4⋊C4—861no—
508C2×C4⋊C4C22×D4312yes—
509C2×C22⋊C4—861no—
510C2×C22⋊C4—861no—
511C2×C22⋊C4—861no—
512C2×C22⋊C4—861no—
513C2×C22⋊C4—861no—
514C2×C22⋊C4—862no—
515C2×C22⋊C4—862no—
516C2×C22⋊C4—1724no—
517C2×C42—861no—
518#107—864no—
519#106—864no—
520#103—24no—
521#103—864no—
522#102—24no—
523#102—864no—
524C22⋊C8—864no—
525C22⋊C8—864no—
526#95—862no—
527#95—862no—
528C24—21no—
529C24—431no—
530C24—431no—
531C24—862no—
532C24—862no—
533C24—862no—
534C24—862no—
535C24—862no—
536C24—1721no—
537C24—1721no—
538C24D4×D4311yescharacteristic
539#41—28no—
540#41—28no—
541#41—44no—
542#41—44no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8C2×C22⋊D4312yes—
549C2×D4—24no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—42no—
556C2×D4—42no—
557C2×D4—864no—
558C2×D4—864no—
559C2×D4—1722no—
560C2×D4—1722no—
561C2×D4—1722no—
562C2×D4—1722no—
563C2×D4C2×C22⋊D4312yes—
564C22×C4—21no—
565C22×C4—24no—
566C22×C4—22no—
567C22×C4—42no—
568C22×C4—42no—
569C22×C4—42no—
570C22×C4—42no—
571C22×C4—42no—
572C22×C4—431no—
573C22×C4—431no—
574C22×C4—862no—
575C22×C4—862no—
576C22×C4—862no—
577C22×C4—861no—
578C22×C4—861no—
579C22×C4—862no—
580C22×C4—862no—
581C22×C4—862no—
582C22×C4—862no—
583C22×C4—862no—
584C22×C4—862no—
585C22×C4—861no—
586C22×C4—861no—
587C22×C4—861no—
588C22×C4—861no—
589C22×C4—861no—
590C22×C4—861no—
591C22×C4—861no—
592C22×C4—861no—
593C22×C4—861no—
594C22×C4—861no—
595C22×C4—861no—
596C22×C4—861no—
597C22×C4—862no—
598C22×C4—1722no—
599C22×C4—1722no—
600C22×C4—1722no—
601C22×C4—1724no—
602C22×C4—1724no—
603C22×C4—1724no—
604C22×C4—1724no—
605C22×C4#1062189812yes—
606C22×C4#1062189812yes—
607C22×C4D4×D4311yescharacteristic
608C22×C4D4×D4312yes—
609C22×C4D4×D4312yes—
610C22×C4#1062190012yes—
611C22×C4C2×C22⋊D4312yes—
612C22×C4C23×D4311yescharacteristic
613M16—44no—
614M16—868no—
615C2×C8—22no—
616C2×C8—22no—
617C2×C8—22no—
618C2×C8—434no—
619C2×C8—862no—
620C2×C8—862no—
621C4⋊C4—22no—
622C4⋊C4—22no—
623C4⋊C4—42no—
624C4⋊C4—432no—
625C4⋊C4—432no—
626C4⋊C4—864no—
627C4⋊C4—864no—
628C4⋊C4—861no—
629C4⋊C4—861no—
630C4⋊C4—862no—
631C4⋊C4—862no—
632C4⋊C4—1722no—
633C22⋊C4—864no—
634C22⋊C4—864no—
635C22⋊C4—864no—
636C22⋊C4—864no—
637C22⋊C4—864no—
638C22⋊C4—1724no—
639C22⋊C4—1724no—
640C42—864no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—22no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—432no—
653C23—432no—
654C23—868no—
655C23—861no—
656C23—861no—
657C23—861no—
658C23—861no—
659C23—861no—
660C23—861no—
661C23—861no—
662C23—861no—
663C23—861no—
664C23—861no—
665C23—861no—
666C23—861no—
667C23—1724no—
668C23—1724no—
669C23—1724no—
670C23—1724no—
671C23—1724no—
672C23—1724no—
673C23#1306329312yes—
674C23#1306329812yes—
675C23#1306330712yes—
676C23C2×D4×D4311yescharacteristic
677Q8—22no—
678Q8—22no—
679Q8—41no—
680Q8—41no—
681D4—22no—
682D4—22no—
683D4—48no—
684D4—41no—
685D4—41no—
686D4—1728no—
687D4—1728no—
688C2×C4—22no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—48no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—84no—
696C2×C4—862no—
697C2×C4—862no—
698C2×C4—861no—
699C2×C4—861no—
700C2×C4—861no—
701C2×C4—861no—
702C2×C4—861no—
703C2×C4—861no—
704C2×C4—3444no—
705C2×C4—1722no—
706C2×C4—1722no—
707C2×C4—1722no—
708C2×C4—1724no—
709C2×C4—1721no—
710C2×C4—1721no—
711C2×C4—1721no—
712C2×C4—1721no—
713C2×C4—1724no—
714C2×C4—1724no—
715C2×C4—1721no—
716C2×C4—1721no—
717C2×C4—1721no—
718C2×C4—1721no—
719C2×C4—1721no—
720C2×C4—1721no—
721C2×C4—1721no—
722C2×C4—1721no—
723C2×C4#1306329312yes—
724C2×C4#1306329714yes—
725C2×C4#1306329812yes—
726C2×C4#1306329814yes—
727C2×C4#1306330712yes—
728C2×C4#1306330814yes—
729C2×C4#1306331114yes—
730C2×C4C2×D4×D4311yescharacteristic
731C2×C4C2×D4×D4311yescharacteristic
732C2×C4C22×C22⋊D4311yescharacteristic
733C2×C4C2×#1062190011yescharacteristic
734C2×C4C2×#1062189811yescharacteristic
735C2×C4C2×#1062189811yescharacteristic
736C8—42no—
737C8—864no—
738C22—22no—
739C22—22no—
740C22—22no—
741C22—22no—
742C22—22no—
743C22—22no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—81no—
748C22—81no—
749C22—81no—
750C22—81no—
751C22—862no—
752C22—862no—
753C22—862no—
754C22—862no—
755C22—862no—
756C22—862no—
757C22—17216no—
758C22—1721no—
759C22—1721no—
760C22—1721no—
761C22—1721no—
762C22—1721no—
763C22—1721no—
764C22—1721no—
765C22—1721no—
766C22#1458281414yes—
767C22C2×#1306329311yescharacteristic
768C22C2×#1306329811yescharacteristic
769C22C2×#1306330711yescharacteristic
770C22AGL(1,ℤ/8)×D4311yescharacteristic
771C22#137×D4311yescharacteristic
772C22#1458369511yescharacteristic
773C22#1458369811yescharacteristic
774C4—42no—
775C4—82no—
776C4—3442no—
777C4—1721no—
778C4—1721no—
779C4—1722no—
780C4—1722no—
781C4#1458281414yes—
782C4C2×#1306329711yescharacteristic
783C4C2×#1306329811yescharacteristic
784C4C2×#1306330811yescharacteristic
785C4C2×#1306331111yescharacteristic
786C2—24no—
787C2—82no—
788C2—1722no—
789C2—1722no—
790C2C2×#1458281411yescharacteristic
791C2#1914384311yescharacteristic
792C2#1914385111yescharacteristic
793C2#1914421711yescharacteristic
794C2#1914422811yescharacteristic
795C2#1914451611yescharacteristic
796C2#1914452511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#417C2
socleC23×C43C22×D4
prime radicalC2×#14583406C2
hypercenterC2×#417D43
hypocenterC43#23482
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#417

Complements

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

NH ≅ G/Ntype
2. C2×#14582939C2semidirect
3. C2×#14582900C2semidirect
4. C2×#14582862C2semidirect
5. C2×#14582756C2semidirect
6. #19135796C2semidirect
7. #19135789C2semidirect
8. #19135782C2semidirect
9. #19135775C2semidirect
10. #19134315C2semidirect
11. C2×C43×#417C2semidirect
28. C2×#13063258C22semidirect
29. C2×#13063256C22semidirect
31. C2×#13063249C22semidirect
32. C2×#13063246C22semidirect
41. #14582662C22semidirect
42. #14582662C22semidirect
47. C2×#103×C43C22semidirect
48. C2×#102×C43C22semidirect
66. C2×#10621877D4semidirect
391. C2×#417D43semidirect
434. C2×#103C2×D43semidirect
436. C2×#102C2×D43semidirect
447. C43#23482semidirect

Maximal subgroups

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

subgroupindex
C2×#145834062
C2×#145829392
C2×#145829002
C2×#145828622
C2×#145827562
#191357962
#191357892
#191357822
#191357752
#191343152
C2×C43×#4172
#2348243