Finite Group Databasebeta

← #25117306

Subgroups — #25117306

Order 11008.

1274 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583051C211yesmaximal, characteristic
2C2×#14582990C211yesmaximal, characteristic, complemented
3C2×#14582902C211yesmaximal, characteristic
4#19137624C211yesmaximal, characteristic, complemented
5D4×(C2×D43)⋊C4C211yesmaximal, characteristic
6#19135476C211yesmaximal, characteristic, complemented
7#19135279C211yesmaximal, characteristic, complemented
8#19135222C211yesmaximal, characteristic, complemented
9#19135027C211yesmaximal, characteristic, complemented
10#19134951C211yesmaximal, characteristic, complemented
11#19134929C211yesmaximal, characteristic, complemented
12#19134844C211yesmaximal, characteristic, complemented
13#19134797C211yesmaximal, characteristic, complemented
14#19134380C211yesmaximal, characteristic, complemented
15C43×#1762C211yesmaximal, characteristic, complemented
16C22×D4×D43C2211yescharacteristic
17C22×#10621873C2211yescharacteristic
18C22×#10621883C2211yescharacteristic
19C22×#10621872C2211yescharacteristic
20C2×#13063305C2211yescharacteristic
21C2×#13063290C2211yescharacteristic, complemented
22C2×D4×Dic43C2211yescharacteristic
23C2×#13063283C2211yescharacteristic
24C22×(C2×D43)⋊C4—21no—
25#14583051C418yescomplemented
26#14582990—24no—
27C2×#13063259C2211yescharacteristic, complemented
28C2×#13063256C2211yescharacteristic, complemented
29#14582902—24no—
30C2×#13063250C2211yescharacteristic, complemented
31C2×#13063248C2211yescharacteristic, complemented
32C2×#13063247C2211yescharacteristic
33C2×#13063246C2211yescharacteristic
34C2×#13063245C2211yescharacteristic
35C2×#13063245C2211yescharacteristic
36C2×(C2×D43)⋊C8C2211yescharacteristic
37C2×C8×Dic43C2211yescharacteristic, complemented
38#14582805C2211yescharacteristic, complemented
39#14582801C2211yescharacteristic
40#14582800C2211yescharacteristic
41#14582798C2211yescharacteristic, complemented
42#14582791—21no—
43#14582790—21no—
44#14582784—21no—
45#14582778—21no—
46#14582776—21no—
47#14582756C2211yescharacteristic
48#14582754—21no—
49C4×C4⋊Dic43—21no—
50C4×(C2×D43)⋊C4C2211yescharacteristic
51#14582661C2211yescharacteristic, complemented
52#14582661C2211yescharacteristic, complemented
53#14582654C2211yescharacteristic, complemented
54#14582653C2211yescharacteristic, complemented
55C2×C4×D4×C43C2211yescharacteristic
56C2×#102×C43C2211yescharacteristic
57C2×#102×C43C2211yescharacteristic
58C2×#97×C43C2211yescharacteristic, complemented
59C4×C4⋊C4×C43C2211yescharacteristic, complemented
60C43×#340C2211yescharacteristic, complemented
61C43×#340C2211yescharacteristic, complemented
62C24×D43—21no—
63C22×Dic86C2311yescharacteristic
64C22×D172C2311yescharacteristic
65C22×C22⋊D43—21no—
66C2×D4×D43—22no—
67C2×D4×D43—22no—
68C2×D4×D43—22no—
69C2×D4×D43—41no—
70C2×D4×D43—41no—
71C2×D4×D43C2×C414yes—
72C23×Dic43—21no—
73C22×C4×D43C2311yescharacteristic
74C2×#10621873—41no—
75C2×#10621873—41no—
76C2×#10621873C2×C414yescomplemented
77C2×#10621883—22no—
78C2×#10621883—22no—
79C2×#10621883C2×C414yes—
80C2×#10621872—22no—
81C2×#10621872—22no—
82C2×#10621872—41no—
83C22×C43⋊C8C2311yescharacteristic
84C22×C43⋊C8C2311yescharacteristic
85#13063305—22no—
86#13063305C2×C414yescomplemented
87#13063290—22no—
88#13063290—41no—
89D4×Dic43—22no—
90D4×Dic43—41no—
91#13063283—22no—
92#13063283—41no—
93C2×C4⋊Dic43—21no—
94C2×C4⋊Dic43—21no—
95C2×C4⋊Dic43C2311yescharacteristic
96C2×C4⋊Dic43C2311yescharacteristic
97C2×Dic43⋊C4—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×(C2×D43)⋊C4—21no—
104C2×(C2×D43)⋊C4—21no—
105C2×(C2×D43)⋊C4—21no—
106C2×(C2×D43)⋊C4—44no—
107C2×(C2×D43)⋊C4D411yescharacteristic
108C2×(C2×D43)⋊C4D411yescharacteristic
109C2×C4×Dic43—21no—
110C2×C4×Dic43—21no—
111C2×C4×Dic43C2311yescharacteristic
112#13063259—41no—
113#13063256—22no—
114#13063250—22no—
115#13063248—41no—
116#13063247—22no—
117#13063246—22no—
118#13063245—22no—
119#13063245C2×C414yescomplemented
120(C2×D43)⋊C8C2×C414yescomplemented
121C8×Dic43—22no—
122C43⋊#95—21no—
123C43⋊#95—21no—
124C43⋊#95—21no—
125C43⋊#95—21no—
126C43⋊#95D411yescharacteristic
127C43⋊#95D411yescharacteristic
128C22×D4×C43C2311yescharacteristic
129C23×C4×C43—21no—
130C22×C8×C43C2311yescharacteristic
131C22×C8×C43C2311yescharacteristic
132C4×D4×C43—22no—
133C4×D4×C43—41no—
134C2×C4⋊C4×C43C2311yescharacteristic
135C2×C4⋊C4×C43C2311yescharacteristic
136C2×C4⋊C4×C43C2311yescharacteristic
137C2×C22⋊C4×C43—21no—
138C2×C42×C43—21no—
139C2×C42×C43C2311yescharacteristic
140#102×C43C2×C414yes—
141#102×C43D414yes—
142#97×C43—41no—
143#95×C43—21no—
144C24×C43—21no—
145C23×D43—21no—
146C23×D43—24no—
147C23×D43—42no—
148C23×D43—42no—
149C23×D43—42no—
150C23×D43—42no—
151C23×D43—81no—
152C23×D43—81no—
153C23×D43C2×D411yescharacteristic
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43—21no—
157C2×D4×C43C22×C412yes—
158C2×D4×C43C2×D412yes—
159C2×D4×C43#4112yes—
160C22×C4×C43—21no—
161C22×C4×C43—21no—
162C22×C4×C43—21no—
163C22×C4×C43—42no—
164C22×C4×C43—42no—
165C22×C4×C43—81no—
166C22×C4×C43C2×D411yescharacteristic
167C22×C4×C43C2×D411yescharacteristic
168C22×C4×C43C2411yescharacteristic
169C2×C22⋊D43—24no—
170C2×C22⋊D43—42no—
171C2×C22⋊D43—42no—
172C22×Dic43—21no—
173C22×Dic43—21no—
174C22×Dic43—21no—
175C22×Dic43—42no—
176C22×Dic43—42no—
177C22×Dic43—81no—
178C22×Dic43C2×D411yescharacteristic
179C22×Dic43C2×D411yescharacteristic
180C22×Dic43C2×D411yescharacteristic
181D4×D43—28no—
182D4×D43—44no—
183D4×D43—44no—
184D4×D43—44no—
185C2×D172—21no—
186C2×D172—21no—
187C2×D172—21no—
188C2×D172—21no—
189C2×D172—21no—
190C2×D172C22×C412yes—
191C2×C4×D43—21no—
192C2×C4×D43—21no—
193C2×C4×D43—21no—
194C2×C4×D43—21no—
195C2×C4×D43C22×C412yes—
196C2×C4×D43#4112yes—
197C2×Dic86—21no—
198C2×Dic86—21no—
199C2×Dic86—21no—
200C2×Dic86—21no—
201C2×Dic86—21no—
202C2×Dic86C22×C412yes—
203C2×C8×C43—21no—
204C2×C8×C43—21no—
205C2×C8×C43—21no—
206C2×C8×C43—21no—
207C2×C8×C43C22×C412yes—
208C2×C8×C43C2×D412yes—
209C4⋊C4×C43—21no—
210C4⋊C4×C43—21no—
211C4⋊C4×C43—21no—
212C4⋊C4×C43—21no—
213C4⋊C4×C43C22×C412yes—
214C4⋊C4×C43C2×D412yes—
215C22⋊C4×C43—42no—
216C42×C43—21no—
217C42×C43—21no—
218C42×C43—42no—
219C22⋊Dic43—42no—
220#10621883—28no—
221(C2×D43)⋊C4—22no—
222(C2×D43)⋊C4—24no—
223(C2×D43)⋊C4—41no—
224(C2×D43)⋊C4—42no—
225(C2×D43)⋊C4—42no—
226(C2×D43)⋊C4—42no—
227(C2×D43)⋊C4—42no—
228(C2×D43)⋊C4—81no—
229(C2×D43)⋊C4—81no—
230C4⋊Dic43—24no—
231C4⋊Dic43—21no—
232C4⋊Dic43—21no—
233C4⋊Dic43—21no—
234C4⋊Dic43—21no—
235C4⋊Dic43—42no—
236Dic43⋊C4—42no—
237C4×Dic43—21no—
238C4×Dic43—21no—
239C4×Dic43—42no—
240C4×Dic43—42no—
241C2×C43⋊C8—21no—
242C2×C43⋊C8—21no—
243C2×C43⋊C8—21no—
244C2×C43⋊C8—21no—
245C2×C43⋊C8—21no—
246C2×C43⋊C8C22×C412yes—
247#10621873—44no—
248#10621872—44no—
249C23×C43—22no—
250C23×C43—22no—
251C23×C43—22no—
252C23×C43—41no—
253C23×C43—41no—
254C23×C43—41no—
255C23×C43—41no—
256C23×C43C22×D411yescharacteristic
257C22×D43—21no—
258C22×D43—21no—
259C22×D43—21no—
260C22×D43—21no—
261C22×D43—21no—
262C22×D43—21no—
263C22×D43—22no—
264C22×D43—48no—
265C22×D43—48no—
266C22×D43—41no—
267C22×D43—41no—
268C22×D43—41no—
269C22×D43—41no—
270C22×D43—41no—
271C22×D43—41no—
272C22×D43—84no—
273C22×D43—84no—
274C22×D43—84no—
275C22×D43—84no—
276C22×D43—84no—
277C22×D43C4×D412yes—
278D4×C43—22no—
279D4×C43—22no—
280D4×C43—22no—
281D4×C43C4×D414yes—
282C2×C4×C43—22no—
283C2×C4×C43—22no—
284C2×C4×C43—21no—
285C2×C4×C43—21no—
286C2×C4×C43—21no—
287C2×C4×C43—21no—
288C2×C4×C43—21no—
289C2×C4×C43—21no—
290C2×C4×C43—41no—
291C2×C4×C43—41no—
292C2×C4×C43—41no—
293C2×C4×C43—41no—
294C2×C4×C43—41no—
295C2×C4×C43—41no—
296C2×C4×C43—41no—
297C2×C4×C43—84no—
298C2×C4×C43C23×C411yescharacteristic
299C2×C4×C43C22×D411yescharacteristic
300C2×C4×C43C2×#4111yescharacteristic
301C2×C4×C43C2×#4111yescharacteristic
302C2×C4×C43H(5,𝔽2)11yescharacteristic
303C2×C4×C43H(5,𝔽2)11yescharacteristic
304C22⋊D43—48no—
305C2×Dic43—21no—
306C2×Dic43—21no—
307C2×Dic43—21no—
308C2×Dic43—21no—
309C2×Dic43—22no—
310C2×Dic43—21no—
311C2×Dic43—21no—
312C2×Dic43—21no—
313C2×Dic43—41no—
314C2×Dic43—41no—
315C2×Dic43—41no—
316C2×Dic43—41no—
317C2×Dic43—41no—
318C2×Dic43—41no—
319C2×Dic43—41no—
320C2×Dic43—41no—
321C2×Dic43—84no—
322C2×Dic43C4×D412yes—
323C2×Dic43AGL(1,ℤ/8)12yes—
324D172—22no—
325D172—22no—
326D172—41no—
327D172—41no—
328C4×D43—22no—
329C4×D43—22no—
330C4×D43—22no—
331C4×D43—22no—
332Dic86—22no—
333Dic86—22no—
334Dic86—41no—
335Dic86—41no—
336C8×C43—22no—
337C8×C43—22no—
338C43⋊C8—22no—
339C43⋊C8—41no—
340#22884—431nomaximal, Sylow
341C22×C43—24no—
342C22×C43—42no—
343C22×C43—42no—
344C22×C43—42no—
345C22×C43—42no—
346C22×C43—42no—
347C22×C43—42no—
348C22×C43C2×C4×D411yescharacteristic
349C22×C43D4211yescharacteristic
350C22×C43#54611yescharacteristic
351C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
352C22×C43#57511yescharacteristic
353C22×C43#57711yescharacteristic
354C22×C43#57711yescharacteristic
355C2×D43—22no—
356C2×D43—22no—
357C2×D43—22no—
358C2×D43—41no—
359C2×D43—41no—
360C2×D43—41no—
361C2×D43—41no—
362C2×D43—42no—
363C2×D43—42no—
364C2×D43—42no—
365C2×D43—816no—
366C2×D43—81no—
367C2×D43—81no—
368C2×D43—81no—
369C2×D43—81no—
370C4×C43—42no—
371C4×C43—42no—
372C4×C43—41no—
373C4×C43—41no—
374C4×C43—81no—
375C4×C43C2×C4×D411yescharacteristic
376C4×C43#51811yescharacteristic
377C4×C43#54611yescharacteristic
378C4×C43#55111yescharacteristic
379Dic43—22no—
380Dic43—22no—
381Dic43—42no—
382Dic43—41no—
383Dic43—81no—
384Dic43—81no—
385C2×#450—431no—
386C2×C4×SD16—431no—
387C2×#418—431no—
388#2362—431no—
389D4×C22⋊C4—431no—
390#1973—431no—
391#1934—431no—
392#1926—431no—
393#1894—431no—
394#1880—431no—
395#1877—431no—
396#1862—431no—
397#1854—431no—
398#1762D4311yescharacteristic, complemented
399#1753—431no—
400C2×C43—44no—
401C2×C43#235811yescharacteristic
402C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
403C2×C43#294911yescharacteristic
404C2×C43#326511yescharacteristic
405C2×C43#326711yescharacteristic
406C2×C43#332311yescharacteristic
407C2×C43#332411yescharacteristic
408D43—42no—
409D43—82no—
410C23×D4—431no—
411C22×SD16—431no—
412C22×SD16—431no—
413C22×M16—431no—
414C2×C22⋊Q8—431no—
415C2×C4×Q8—431no—
416C2×C4×D4—431no—
417C2×C4×D4C2×D4311yescharacteristic
418C2×#117—431no—
419C22×C22⋊C4—861no—
420#450—438no—
421C4×SD16—864no—
422C2×#107—431no—
423C2×#106—431no—
424#418—864no—
425C2×#103—431no—
426C2×#103—431no—
427C2×#102—431no—
428C2×#102—431no—
429C2×#102—431no—
430C2×#102—431no—
431C2×#102C2×D4311yescharacteristic
432C2×#102C2×D4311yescharacteristic
433C2×C22⋊C8—431no—
434C2×#97C2×D4311yescharacteristic, complemented
435C2×C4×C8—431no—
436#391—431no—
437#390—431no—
438#390—431no—
439#389—431no—
440#388—861no—
441#388—861no—
442#387—861no—
443#386—861no—
444#386—861no—
445#380—431no—
446#379—861no—
447C4×C4⋊C4—861no—
448C4×C4⋊C4C2×D4311yescharacteristic, complemented
449C4×C22⋊C4—431no—
450#340—431no—
451#340—431no—
452#340C2×D4311yescharacteristic, complemented
453#340C2×D4311yescharacteristic, complemented
454#336—431no—
455#336—431no—
456C43#2288411yescharacteristic, complemented, Sylow
457C25—861no—
458C22×Q8—431no—
459C22×D4—434no—
460C22×D4—431no—
461C22×D4—862no—
462C22×D4—861no—
463C22×D4—862no—
464C22×D4—862no—
465C22×D4—1721no—
466C22×D4—1721no—
467C22×D4C22×D4311yescharacteristic
468C23×C4—21no—
469C23×C4—431no—
470C23×C4—861no—
471C2×SD16—434no—
472C2×SD16—434no—
473C2×SD16—862no—
474C2×SD16—862no—
475C2×SD16—1721no—
476C2×SD16—1721no—
477C2×M16—862no—
478C2×M16—862no—
479C2×M16—1721no—
480C22×C8—431no—
481C22×C8—431no—
482C22×C8C22×D4311yescharacteristic
483C22×C8C22×D4311yescharacteristic
484C22⋊Q8—434no—
485C22⋊Q8—862no—
486C4×Q8—862no—
487C4×Q8—1721no—
488C4×D4—22no—
489C4×D4—41no—
490C4×D4—862no—
491C4×D4—1721no—
492#117—862no—
493#117—1721no—
494C2×C4⋊C4—431no—
495C2×C4⋊C4—431no—
496C2×C4⋊C4—861no—
497C2×C4⋊C4—861no—
498C2×C4⋊C4—861no—
499C2×C4⋊C4C22×D4311yescharacteristic
500C2×C4⋊C4C22×D4311yescharacteristic
501C2×C4⋊C4C22×D4311yescharacteristic
502C2×C22⋊C4—21no—
503C2×C22⋊C4—431no—
504C2×C22⋊C4—431no—
505C2×C22⋊C4—861no—
506C2×C22⋊C4—861no—
507C2×C22⋊C4—861no—
508C2×C22⋊C4—861no—
509C2×C22⋊C4—861no—
510C2×C22⋊C4—861no—
511C2×C22⋊C4—861no—
512C2×C22⋊C4—861no—
513C2×C22⋊C4—1724no—
514C2×C42—21no—
515C2×C42—431no—
516C2×C42—861no—
517C2×C42—861no—
518C2×C42C22×D4311yescharacteristic
519#107—1721no—
520#106—862no—
521#103—862no—
522#103—1721no—
523#102—434no—
524#102—862no—
525#102—862no—
526#102—862no—
527#102C4×D4314yes—
528#102D17214yes—
529C22⋊C8—434no—
530#97—41no—
531C4×C8—862no—
532#95—21no—
533#95—431no—
534#95—431no—
535#95—861no—
536#95—861no—
537#95—861no—
538#95—861no—
539C24—21no—
540C24—431no—
541C24—864no—
542C24—861no—
543C24—3441no—
544C24—3441no—
545C24—1722no—
546C24—1722no—
547C24—1722no—
548C24—1722no—
549C2×Q8—432no—
550C2×Q8—861no—
551C2×Q8—861no—
552C2×Q8—861no—
553C2×Q8—861no—
554C2×Q8—861no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—432no—
559C2×D4—864no—
560C2×D4—868no—
561C2×D4—861no—
562C2×D4—861no—
563C2×D4—861no—
564C2×D4—861no—
565C2×D4—861no—
566C2×D4—1724no—
567C2×D4—1724no—
568C2×D4—1724no—
569C2×D4—1722no—
570C2×D4—1722no—
571C2×D4C2×C4×D4312yes—
572C2×D4C2×D17212yes—
573C2×D4#1062189812yes—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—42no—
578C22×C4—42no—
579C22×C4—81no—
580C22×C4—431no—
581C22×C4—431no—
582C22×C4—432no—
583C22×C4—432no—
584C22×C4—431no—
585C22×C4—861no—
586C22×C4—861no—
587C22×C4—861no—
588C22×C4—861no—
589C22×C4—861no—
590C22×C4—861no—
591C22×C4—861no—
592C22×C4—3441no—
593C22×C4—1722no—
594C22×C4—1722no—
595C22×C4D4×D4311yescharacteristic
596C22×C4D4×D4311yescharacteristic
597C22×C4C23×D4311yescharacteristic
598SD16—868no—
599SD16—1724no—
600M16—1724no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—432no—
606C2×C8—861no—
607C2×C8—861no—
608C2×C8—861no—
609C2×C8—861no—
610C2×C8—861no—
611C2×C8C2×C4×D4312yes—
612C2×C8C2×D17212yes—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—864no—
618C4⋊C4—861no—
619C4⋊C4—861no—
620C4⋊C4—861no—
621C4⋊C4—861no—
622C4⋊C4—1722no—
623C4⋊C4—1722no—
624C4⋊C4C2×C4×D4312yes—
625C4⋊C4C2×D17212yes—
626C22⋊C4—42no—
627C22⋊C4—862no—
628C22⋊C4—864no—
629C22⋊C4—3441no—
630C22⋊C4—3441no—
631C22⋊C4—1721no—
632C22⋊C4—1722no—
633C22⋊C4—1722no—
634C22⋊C4—1722no—
635C22⋊C4—1722no—
636C22⋊C4—1722no—
637C42—21no—
638C42—21no—
639C42—42no—
640C42—861no—
641C42—861no—
642C42—1722no—
643C42—1722no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—432no—
652C23—861no—
653C23—861no—
654C23—861no—
655C23—861no—
656C23—861no—
657C23—861no—
658C23—862no—
659C23—3444no—
660C23—3444no—
661C23—3444no—
662C23—3444no—
663C23—3444no—
664C23—1728no—
665C23—1728no—
666C23—1721no—
667C23—1721no—
668C23—1721no—
669C23—1721no—
670C23—1721no—
671C23—1721no—
672C23C2×D4×D4311yescharacteristic
673Q8—862no—
674Q8—862no—
675Q8—1721no—
676Q8—1721no—
677D4—22no—
678D4—22no—
679D4—22no—
680D4—862no—
681D4—862no—
682D4—1728no—
683D4—1721no—
684D4—1721no—
685D4C4×D17214yes—
686C2×C4—22no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—22no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—84no—
702C2×C4—432no—
703C2×C4—432no—
704C2×C4—861no—
705C2×C4—861no—
706C2×C4—861no—
707C2×C4—861no—
708C2×C4—862no—
709C2×C4—862no—
710C2×C4—862no—
711C2×C4—862no—
712C2×C4—862no—
713C2×C4—861no—
714C2×C4—861no—
715C2×C4—861no—
716C2×C4—3444no—
717C2×C4—1721no—
718C2×C4—1721no—
719C2×C4—1721no—
720C2×C4—1721no—
721C2×C4—1721no—
722C2×C4—1721no—
723C2×C4—1721no—
724C2×C4—1721no—
725C2×C4C22×C4×D4311yescharacteristic
726C2×C4C22×D17211yescharacteristic
727C2×C4#41×D4311yescharacteristic
728C2×C4C2×#1062189811yescharacteristic
729C2×C4#1306337011yescharacteristic
730C2×C4#1306337111yescharacteristic
731C8—22no—
732C8—22no—
733C8—862no—
734C8—1721no—
735C22—24no—
736C22—42no—
737C22—42no—
738C22—42no—
739C22—42no—
740C22—42no—
741C22—42no—
742C22—862no—
743C22—862no—
744C22—862no—
745C22—34416no—
746C22—3441no—
747C22—3441no—
748C22—3441no—
749C22—3441no—
750C22—1722no—
751C22—1722no—
752C22—1722no—
753C22—1721no—
754C22—1721no—
755C22—1721no—
756C22—1721no—
757C22C4×D4×D4311yescharacteristic
758C22D4×D17211yescharacteristic
759C22#1458353911yescharacteristic
760C22AGL(1,ℤ/8)×D4311yescharacteristic
761C22#1458369511yescharacteristic
762C22#1458370811yescharacteristic
763C22#1458370911yescharacteristic
764C4—41no—
765C4—41no—
766C4—42no—
767C4—42no—
768C4—81no—
769C4—862no—
770C4—862no—
771C4—3441no—
772C4—3441no—
773C4—1722no—
774C4—1721no—
775C4C2×C4×D17211yescharacteristic
776C4#1458337111yescharacteristic
777C4#1458354411yescharacteristic
778C4#1458357311yescharacteristic
779C2—44no—
780C2—3442no—
781C2—1722no—
782C2#1913757711yescharacteristic
783C2#1914340611yescharacteristic
784C2#1914345111yescharacteristic
785C2#1914609211yescharacteristic
786C2#1914612211yescharacteristic
787C2#1914681211yescharacteristic
788C2#1914682211yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1762C2
socleC23×C43C22×D4
prime radicalC22×D4×D43C22
cosocleC22×C4×C43C24
hypercenter#1762D43
hypocenterC43#22884
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1762

Complements

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

NH ≅ G/Ntype
2. C2×#14582990C2semidirect
4. #19137624C2semidirect
6. #19135476C2semidirect
7. #19135279C2semidirect
8. #19135222C2semidirect
9. #19135027C2semidirect
10. #19134951C2semidirect
11. #19134929C2semidirect
12. #19134844C2semidirect
13. #19134797C2semidirect
14. #19134380C2semidirect
15. C43×#1762C2semidirect
21. C2×#13063290C22semidirect
25. #14583051C4semidirect
27. C2×#13063259C22semidirect
28. C2×#13063256C22semidirect
30. C2×#13063250C22semidirect
31. C2×#13063248C22semidirect
37. C2×C8×Dic43C22semidirect
38. #14582805C22semidirect
41. #14582798C22semidirect
51. #14582661C22semidirect
52. #14582661C22semidirect
53. #14582654C22semidirect
54. #14582653C22semidirect
58. C2×#97×C43C22semidirect
59. C4×C4⋊C4×C43C22semidirect
60. C43×#340C22semidirect
61. C43×#340C22semidirect
76. C2×#10621873C2×C4semidirect
86. #13063305C2×C4semidirect
119. #13063245C2×C4semidirect
120. (C2×D43)⋊C8C2×C4semidirect
398. #1762D43semidirect
434. C2×#97C2×D43semidirect
448. C4×C4⋊C4C2×D43semidirect
452. #340C2×D43semidirect
453. #340C2×D43semidirect
456. C43#22884semidirect

Maximal subgroups

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

subgroupindex
C2×#145830512
C2×#145829902
C2×#145829022
#191376242
D4×(C2×D43)⋊C42
#191354762
#191352792
#191352222
#191350272
#191349512
#191349292
#191348442
#191347972
#191343802
C43×#17622
#2288443