Finite Group Databasebeta

← #25116849

Subgroups — #25116849

Order 11008.

1302 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583051C211yesmaximal, characteristic
2C2×#14582998C211yesmaximal, characteristic, complemented
3C2×#102×D43C211yesmaximal, characteristic
4#19137602C211yesmaximal, characteristic, complemented
5#19137416C211yesmaximal, characteristic
6#19135475C211yesmaximal, characteristic, complemented
7#19135294C211yesmaximal, characteristic, complemented
8#19135017C211yesmaximal, characteristic, complemented
9#19134947C211yesmaximal, characteristic, complemented
10#19134928C211yesmaximal, characteristic, complemented
11#19134843C211yesmaximal, characteristic, complemented
12#19134781C211yesmaximal, characteristic, complemented
13#19134423C211yesmaximal, characteristic, complemented
14#19134370C211yesmaximal, characteristic, complemented
15C43×#1925C211yesmaximal, characteristic, complemented
16C22×D4×D43C2211yescharacteristic
17C22×#10621873C2211yescharacteristic
18C22×#10621883C2211yescharacteristic
19C22×C8×D43C2211yescharacteristic
20C2×#13063305C2211yescharacteristic
21C2×#13063290C2211yescharacteristic, complemented
22C2×C4×D172C2211yescharacteristic
23C2×#13063287C2211yescharacteristic
24C2×C4⋊C4×D43C2211yescharacteristic
25C2×C22⋊C4×D43—21no—
26#14583051C418yescomplemented
27#14582998—24no—
28C2×#13063258C2211yescharacteristic, complemented
29C2×#13063250C2211yescharacteristic, complemented
30C2×#13063248C2211yescharacteristic, complemented
31C2×#13063247C2211yescharacteristic
32C2×#13063246C2211yescharacteristic
33C2×#13063245C2211yescharacteristic
34C2×#13063245C2211yescharacteristic
35#102×D43—24no—
36C2×(C2×D43)⋊C8C2211yescharacteristic
37C2×#13063236C2211yescharacteristic, complemented
38C2×#13063235C2211yescharacteristic, complemented
39#14582805C2211yescharacteristic, complemented
40#14582802C2211yescharacteristic
41#14582798C2211yescharacteristic, complemented
42#14582797—21no—
43#14582784—21no—
44#14582775—21no—
45#14582775—21no—
46#14582773—21no—
47#14582756C2211yescharacteristic
48#14582754—21no—
49C4×(C2×D43)⋊C4—21no—
50C4×(C2×D43)⋊C4C2211yescharacteristic
51#14582662C2211yescharacteristic, complemented
52#14582661C2211yescharacteristic, complemented
53#14582661C2211yescharacteristic, complemented
54#14582653C2211yescharacteristic, complemented
55C2×#107×C43C2211yescharacteristic, complemented
56C2×#102×C43C2211yescharacteristic
57C2×#102×C43C2211yescharacteristic
58C43×#390C2211yescharacteristic
59C4×C4⋊C4×C43C2211yescharacteristic, complemented
60C43×#340C2211yescharacteristic, complemented
61C43×#336C2211yescharacteristic, 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—
72C22×C4×D43—21no—
73C22×C4×D43—21no—
74C22×C4×D43—21no—
75C22×C4×D43C2311yescharacteristic
76C2×#10621873—22no—
77C2×#10621873—22no—
78C2×#10621873C2×C414yescomplemented
79C2×#10621883—41no—
80C2×#10621883—41no—
81C2×#10621883C2×C414yescomplemented
82C22×C43⋊C8C2311yescharacteristic
83C22×C43⋊C8C2311yescharacteristic
84C2×C8×D43—22no—
85C2×C8×D43—22no—
86C2×C8×D43—41no—
87#13063305—22no—
88#13063305C2×C414yescomplemented
89#13063290—22no—
90#13063290—41no—
91C4×D172—22no—
92C4×D172—41no—
93#13063287—22no—
94#13063287—41no—
95C2×C4⋊Dic43—21no—
96C2×C4⋊Dic43—21no—
97C2×C4⋊Dic43C2311yescharacteristic
98C2×C4⋊Dic43C2311yescharacteristic
99C2×Dic43⋊C4—21no—
100C2×Dic43⋊C4—21no—
101C4⋊C4×D43—22no—
102C4⋊C4×D43—41no—
103C2×C22⋊Dic43—21no—
104C2×C22⋊Dic43—21no—
105C2×(C2×D43)⋊C4—21no—
106C2×(C2×D43)⋊C4—21no—
107C2×(C2×D43)⋊C4—21no—
108C2×(C2×D43)⋊C4—21no—
109C2×(C2×D43)⋊C4D411yescharacteristic
110C2×(C2×D43)⋊C4D411yescharacteristic
111C22⋊C4×D43—44no—
112C2×C4×Dic43—21no—
113C2×C4×Dic43C2311yescharacteristic
114#13063258—41no—
115#13063250—41no—
116#13063248—22no—
117#13063247—22no—
118#13063246—22no—
119#13063245C2×C414yescomplemented
120#13063245D414yes—
121(C2×D43)⋊C8C2×C414yescomplemented
122#13063236—41no—
123#13063235—22no—
124C43⋊#95—21no—
125C43⋊#95—21no—
126C43⋊#95—21no—
127C43⋊#95—21no—
128C43⋊#95D411yescharacteristic
129C43⋊#95D411yescharacteristic
130C22×D4×C43C2311yescharacteristic
131C22×C8×C43C2311yescharacteristic
132C22×C8×C43C2311yescharacteristic
133C2×C4⋊C4×C43C2311yescharacteristic
134C2×C4⋊C4×C43C2311yescharacteristic
135C2×C4⋊C4×C43C2311yescharacteristic
136C2×C22⋊C4×C43—21no—
137C2×C22⋊C4×C43—21no—
138C2×C42×C43—21no—
139C2×C42×C43C2311yescharacteristic
140#107×C43—22no—
141#102×C43—22no—
142#102×C43C2×C414yescomplemented
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×C43—21no—
158C2×D4×C43—21no—
159C2×D4×C43C22×C412yes—
160C22×C4×C43—21no—
161C22×C4×C43—21no—
162C22×C4×C43—21no—
163C22×C4×C43C2×D411yescharacteristic
164C22×C4×C43C2×D411yescharacteristic
165C22×C4×C43C2411yescharacteristic
166C2×C22⋊D43—24no—
167C2×C22⋊D43—42no—
168C2×C22⋊D43—42no—
169C22×Dic43—21no—
170C22×Dic43—21no—
171C22×Dic43—21no—
172C22×Dic43C2×D411yescharacteristic
173C22×Dic43C2×D411yescharacteristic
174C22×Dic43C2×D411yescharacteristic
175D4×D43—28no—
176D4×D43—44no—
177D4×D43—44no—
178D4×D43—44no—
179C2×D172—21no—
180C2×D172—21no—
181C2×D172—21no—
182C2×D172C22×C412yes—
183C2×D172C2×D412yes—
184C2×D172#4112yes—
185C2×C4×D43—21no—
186C2×C4×D43—21no—
187C2×C4×D43—21no—
188C2×C4×D43—21no—
189C2×C4×D43—42no—
190C2×C4×D43—42no—
191C2×C4×D43—42no—
192C2×C4×D43—42no—
193C2×C4×D43—42no—
194C2×C4×D43—42no—
195C2×C4×D43—81no—
196C2×C4×D43—81no—
197C2×C4×D43—81no—
198C2×C4×D43C22×C412yes—
199C2×C4×D43#4112yes—
200C2×Dic86—21no—
201C2×Dic86—21no—
202C2×Dic86—21no—
203C2×Dic86—21no—
204C2×Dic86—21no—
205C2×Dic86C22×C412yes—
206C2×C8×C43—21no—
207C2×C8×C43—21no—
208C2×C8×C43—21no—
209C2×C8×C43—21no—
210C2×C8×C43—21no—
211C2×C8×C43C22×C412yes—
212C4⋊C4×C43—21no—
213C4⋊C4×C43—21no—
214C4⋊C4×C43—21no—
215C4⋊C4×C43—21no—
216C4⋊C4×C43C22×C412yes—
217C4⋊C4×C43C2×D412yes—
218C22⋊C4×C43—42no—
219C22⋊C4×C43—81no—
220C42×C43—21no—
221C42×C43—21no—
222C42×C43—81no—
223C22⋊Dic43—42no—
224C22⋊Dic43—81no—
225#10621883—44no—
226(C2×D43)⋊C4—24no—
227(C2×D43)⋊C4—22no—
228(C2×D43)⋊C4—22no—
229(C2×D43)⋊C4—42no—
230(C2×D43)⋊C4—42no—
231(C2×D43)⋊C4—42no—
232C4⋊Dic43—24no—
233C4⋊Dic43—21no—
234C4⋊Dic43—21no—
235C4⋊Dic43—21no—
236C4⋊Dic43—21no—
237C4⋊Dic43—81no—
238Dic43⋊C4—42no—
239Dic43⋊C4—42no—
240C4×Dic43—21no—
241C4×Dic43—21no—
242C4×Dic43—42no—
243C2×C43⋊C8—21no—
244C2×C43⋊C8—21no—
245C2×C43⋊C8—21no—
246C2×C43⋊C8—21no—
247C2×C43⋊C8C22×C412yes—
248C2×C43⋊C8C2×D412yes—
249#10621873—28no—
250C8×D43—44no—
251C23×C43—22no—
252C23×C43—41no—
253C23×C43—41no—
254C23×C43—41no—
255C23×C43—41no—
256C23×C43—41no—
257C23×C43—41no—
258C23×C43C22×D411yescharacteristic
259C22×D43—21no—
260C22×D43—21no—
261C22×D43—21no—
262C22×D43—21no—
263C22×D43—22no—
264C22×D43—22no—
265C22×D43—22no—
266C22×D43—48no—
267C22×D43—41no—
268C22×D43—41no—
269C22×D43—41no—
270C22×D43—41no—
271C22×D43—48no—
272C22×D43—84no—
273C22×D43—84no—
274C22×D43—84no—
275C22×D43—84no—
276C22×D43—84no—
277C22×D43C4×D412yes—
278C22×D43AGL(1,ℤ/8)12yes—
279C22×D43#13712yes—
280D4×C43—22no—
281D4×C43—22no—
282D4×C43—41no—
283D4×C43—41no—
284C2×C4×C43—22no—
285C2×C4×C43—22no—
286C2×C4×C43—21no—
287C2×C4×C43—21no—
288C2×C4×C43—21no—
289C2×C4×C43—21no—
290C2×C4×C43—21no—
291C2×C4×C43—21no—
292C2×C4×C43—41no—
293C2×C4×C43—41no—
294C2×C4×C43—41no—
295C2×C4×C43—41no—
296C2×C4×C43—41no—
297C2×C4×C43—41no—
298C2×C4×C43—41no—
299C2×C4×C43C23×C411yescharacteristic
300C2×C4×C43C22×D411yescharacteristic
301C2×C4×C43C2×#4111yescharacteristic
302C2×C4×C43C2×#4111yescharacteristic
303C2×C4×C43H(5,𝔽2)11yescharacteristic
304C2×C4×C43H(5,𝔽2)11yescharacteristic
305C22⋊D43—48no—
306C2×Dic43—21no—
307C2×Dic43—21no—
308C2×Dic43—22no—
309C2×Dic43—21no—
310C2×Dic43—21no—
311C2×Dic43—21no—
312C2×Dic43—21no—
313C2×Dic43—21no—
314C2×Dic43—21no—
315C2×Dic43—41no—
316C2×Dic43—41no—
317C2×Dic43—41no—
318C2×Dic43—41no—
319C2×Dic43—41no—
320C2×Dic43—41no—
321C2×Dic43—41no—
322C2×Dic43—41no—
323C2×Dic43C4×D412yes—
324D172—22no—
325D172—22no—
326D172—22no—
327D172C4×D414yes—
328C4×D43—22no—
329C4×D43—22no—
330C4×D43—22no—
331C4×D43—22no—
332C4×D43—84no—
333C4×D43—84no—
334C4×D43—84no—
335Dic86—22no—
336Dic86—22no—
337Dic86—41no—
338Dic86—41no—
339C8×C43—22no—
340C8×C43—41no—
341C43⋊C8—22no—
342C43⋊C8—22no—
343#22854—431nomaximal, Sylow
344C22×C43—42no—
345C22×C43—42no—
346C22×C43—42no—
347C22×C43—81no—
348C22×C43—81no—
349C22×C43—81no—
350C22×C43—81no—
351C22×C43C2×C4×D411yescharacteristic
352C22×C43D4211yescharacteristic
353C22×C43#54611yescharacteristic
354C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
355C22×C43C2×#13711yescharacteristic
356C22×C43#57611yescharacteristic
357C22×C43#57711yescharacteristic
358C2×D43—22no—
359C2×D43—22no—
360C2×D43—22no—
361C2×D43—22no—
362C2×D43—22no—
363C2×D43—22no—
364C2×D43—24no—
365C2×D43—42no—
366C2×D43—42no—
367C2×D43—42no—
368C2×D43—42no—
369C2×D43—42no—
370C2×D43—42no—
371C2×D43—816no—
372C2×D43#44014yescomplemented
373C4×C43—42no—
374C4×C43—42no—
375C4×C43—41no—
376C4×C43—41no—
377C4×C43—81no—
378C4×C43C2×C4×D411yescharacteristic
379C4×C43#51811yescharacteristic
380C4×C43#54611yescharacteristic
381C4×C43#55111yescharacteristic
382Dic43—22no—
383Dic43—42no—
384Dic43—41no—
385Dic43—41no—
386Dic43—81no—
387Dic43—81no—
388C2×#450—431no—
389C2×#440—431no—
390C22×#102—431no—
391#2360—431no—
392D4×C22⋊C4—431no—
393#1973—431no—
394#1936—431no—
395#1925D4311yescharacteristic, complemented
396#1892—431no—
397#1880—431no—
398#1877—431no—
399#1862—431no—
400#1852—431no—
401#1762—431no—
402#1752—431no—
403C2×C43—82no—
404C2×C43#235811yescharacteristic
405C2×C43C2×#44011yescharacteristic
406C2×C43#294611yescharacteristic
407C2×C43#326411yescharacteristic
408C2×C43#326611yescharacteristic
409C2×C43#331011yescharacteristic
410C2×C43#331411yescharacteristic
411D43—24no—
412D43—44no—
413C23×D4—431no—
414C22×SD16—431no—
415C22×SD16—431no—
416C23×C8—431no—
417C2×C22⋊Q8—431no—
418C2×C4×Q8—431no—
419C2×C4×D4—431no—
420C2×C4×D4—431no—
421C22×C4⋊C4—431no—
422C22×C22⋊C4—861no—
423#450—438no—
424#440—864no—
425C2×#107—431no—
426C2×#107C2×D4311yescharacteristic, complemented
427C2×#103—431no—
428C2×#103—431no—
429C2×#102—431no—
430C2×#102—431no—
431C2×#102—431no—
432C2×#102—431no—
433C2×#102—864no—
434C2×#102C2×D4311yescharacteristic
435C2×#102C2×D4311yescharacteristic
436C2×C22⋊C8—431no—
437C2×#97—431no—
438C2×#97—431no—
439#391—431no—
440#390—431no—
441#390C2×D4311yescharacteristic
442#389—431no—
443#389—861no—
444#387—861no—
445#386—861no—
446#386—861no—
447#385—861no—
448#380—431no—
449#379—861no—
450C4×C4⋊C4C2×D4311yescharacteristic, complemented
451C4×C22⋊C4—431no—
452C4×C22⋊C4—861no—
453#340—431no—
454#340—431no—
455#340—431no—
456#340C2×D4311yescharacteristic, complemented
457#336—431no—
458#336C2×D4311yescharacteristic, complemented
459C43#2285411yescharacteristic, complemented, Sylow
460C25—861no—
461C22×Q8—431no—
462C22×D4—434no—
463C22×D4—431no—
464C22×D4—862no—
465C22×D4—861no—
466C22×D4—862no—
467C22×D4—862no—
468C22×D4—1721no—
469C22×D4—1721no—
470C22×D4C22×D4311yescharacteristic
471C23×C4—431no—
472C23×C4—861no—
473C23×C4—861no—
474C23×C4—861no—
475C2×SD16—434no—
476C2×SD16—434no—
477C2×SD16—862no—
478C2×SD16—862no—
479C2×SD16—1721no—
480C2×SD16—1721no—
481C22×C8—431no—
482C22×C8—431no—
483C22×C8—862no—
484C22×C8—862no—
485C22×C8—1721no—
486C22×C8C22×D4311yescharacteristic
487C22×C8C22×D4311yescharacteristic
488C22⋊Q8—434no—
489C22⋊Q8—862no—
490C4×Q8—862no—
491C4×Q8—1721no—
492C4×D4—862no—
493C4×D4—862no—
494C4×D4—1721no—
495C4×D4—1721no—
496C2×C4⋊C4—431no—
497C2×C4⋊C4—431no—
498C2×C4⋊C4—861no—
499C2×C4⋊C4—862no—
500C2×C4⋊C4—861no—
501C2×C4⋊C4—861no—
502C2×C4⋊C4—861no—
503C2×C4⋊C4—1721no—
504C2×C4⋊C4C22×D4311yescharacteristic
505C2×C4⋊C4C22×D4311yescharacteristic
506C2×C4⋊C4C22×D4311yescharacteristic
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—431no—
510C2×C22⋊C4—431no—
511C2×C22⋊C4—861no—
512C2×C22⋊C4—861no—
513C2×C22⋊C4—861no—
514C2×C22⋊C4—861no—
515C2×C22⋊C4—861no—
516C2×C22⋊C4—861no—
517C2×C22⋊C4—1724no—
518C2×C42—21no—
519C2×C42—431no—
520C2×C42—861no—
521C2×C42C22×D4311yescharacteristic
522#107—22no—
523#107—1721no—
524#103—862no—
525#103—1721no—
526#102—22no—
527#102—434no—
528#102—434no—
529#102—862no—
530#102—862no—
531#102C4×D4314yescomplemented
532C22⋊C8—434no—
533#97—862no—
534#97—1721no—
535#95—21no—
536#95—431no—
537#95—431no—
538#95—861no—
539#95—861no—
540#95—861no—
541#95—861no—
542C24—21no—
543C24—431no—
544C24—864no—
545C24—861no—
546C24—3441no—
547C24—3441no—
548C24—1722no—
549C24—1722no—
550C24—1722no—
551C24—1722no—
552C2×Q8—432no—
553C2×Q8—861no—
554C2×Q8—861no—
555C2×Q8—861no—
556C2×Q8—861no—
557C2×Q8—861no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—432no—
564C2×D4—432no—
565C2×D4—432no—
566C2×D4—864no—
567C2×D4—868no—
568C2×D4—861no—
569C2×D4—861no—
570C2×D4—861no—
571C2×D4—1724no—
572C2×D4—1724no—
573C2×D4—1724no—
574C2×D4—1722no—
575C2×D4—1722no—
576C2×D4C2×C4×D4312yes—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—431no—
581C22×C4—432no—
582C22×C4—432no—
583C22×C4—431no—
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—3441no—
594C22×C4—3441no—
595C22×C4—1722no—
596C22×C4—1722no—
597C22×C4—1722no—
598C22×C4—1722no—
599C22×C4—1722no—
600C22×C4—1722no—
601C22×C4D4×D4311yescharacteristic
602C22×C4D4×D4311yescharacteristic
603C22×C4C23×D4311yescharacteristic
604SD16—868no—
605SD16—1724no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—432no—
612C2×C8—432no—
613C2×C8—861no—
614C2×C8—861no—
615C2×C8—861no—
616C2×C8—861no—
617C2×C8—1724no—
618C2×C8C2×C4×D4312yes—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—864no—
624C4⋊C4—861no—
625C4⋊C4—861no—
626C4⋊C4—861no—
627C4⋊C4—861no—
628C4⋊C4—3441no—
629C4⋊C4—1722no—
630C4⋊C4—1722no—
631C4⋊C4C2×C4×D4312yes—
632C4⋊C4D4×D4312yes—
633C22⋊C4—42no—
634C22⋊C4—81no—
635C22⋊C4—862no—
636C22⋊C4—862no—
637C22⋊C4—864no—
638C22⋊C4—3441no—
639C22⋊C4—1722no—
640C22⋊C4—1722no—
641C22⋊C4—1722no—
642C22⋊C4—1722no—
643C42—21no—
644C42—21no—
645C42—81no—
646C42—861no—
647C42—861no—
648C42—1722no—
649C23—22no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—432no—
657C23—432no—
658C23—432no—
659C23—861no—
660C23—861no—
661C23—861no—
662C23—861no—
663C23—862no—
664C23—862no—
665C23—862no—
666C23—3444no—
667C23—3444no—
668C23—3444no—
669C23—3444no—
670C23—3444no—
671C23—1728no—
672C23—1728no—
673C23—1721no—
674C23—1721no—
675C23—1721no—
676C23—1721no—
677C23C2×D4×D4311yescharacteristic
678Q8—862no—
679Q8—862no—
680Q8—1721no—
681Q8—1721no—
682D4—22no—
683D4—22no—
684D4—41no—
685D4—41no—
686D4—434no—
687D4—862no—
688D4—862no—
689D4—862no—
690D4—1728no—
691C2×C4—22no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—22no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—432no—
707C2×C4—861no—
708C2×C4—861no—
709C2×C4—862no—
710C2×C4—862no—
711C2×C4—862no—
712C2×C4—862no—
713C2×C4—862no—
714C2×C4—861no—
715C2×C4—861no—
716C2×C4—861no—
717C2×C4—861no—
718C2×C4—861no—
719C2×C4—861no—
720C2×C4—3444no—
721C2×C4—3444no—
722C2×C4—3444no—
723C2×C4—1721no—
724C2×C4—1721no—
725C2×C4—1721no—
726C2×C4—1721no—
727C2×C4—1721no—
728C2×C4—1721no—
729C2×C4—1721no—
730C2×C4—1721no—
731C2×C4C22×C4×D4311yescharacteristic
732C2×C4C2×D4×D4311yescharacteristic
733C2×C4#41×D4311yescharacteristic
734C2×C4#41×D4311yescharacteristic
735C2×C4#1306337111yescharacteristic
736C2×C4#1306337111yescharacteristic
737C8—22no—
738C8—41no—
739C8—862no—
740C8—862no—
741C22—42no—
742C22—42no—
743C22—42no—
744C22—81no—
745C22—81no—
746C22—81no—
747C22—81no—
748C22—434no—
749C22—862no—
750C22—862no—
751C22—862no—
752C22—862no—
753C22—862no—
754C22—862no—
755C22—864no—
756C22—34416no—
757C22—1722no—
758C22—1722no—
759C22—1722no—
760C22—1722no—
761C22—1722no—
762C22—1722no—
763C22C4×D4×D4311yescharacteristic
764C22#1458353311yescharacteristic
765C22#1458354111yescharacteristic
766C22AGL(1,ℤ/8)×D4311yescharacteristic
767C22#137×D4311yescharacteristic
768C22#1458370011yescharacteristic
769C22#1458370611yescharacteristic
770C4—42no—
771C4—41no—
772C4—41no—
773C4—42no—
774C4—81no—
775C4—862no—
776C4—3441no—
777C4—3441no—
778C4—1722no—
779C4—1721no—
780C4—1721no—
781C4C4×D4×D4311yescharacteristic
782C4#1458337311yescharacteristic
783C4#1458354211yescharacteristic
784C4#1458357411yescharacteristic
785C2—82no—
786C2—864no—
787C2—1724no—
788C2#1913757311yescharacteristic
789C2#440×D4311yescharacteristic
790C2#1914342011yescharacteristic
791C2#1914607011yescharacteristic
792C2#1914610011yescharacteristic
793C2#1914661911yescharacteristic
794C2#1914667911yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1925C2
socleC23×C43C22×D4
prime radicalC22×D4×D43C22
cosocleC22×C4×C43C24
hypercenter#1925D43
hypocenterC43#22854
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1925

Complements

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

NH ≅ G/Ntype
2. C2×#14582998C2semidirect
4. #19137602C2semidirect
6. #19135475C2semidirect
7. #19135294C2semidirect
8. #19135017C2semidirect
9. #19134947C2semidirect
10. #19134928C2semidirect
11. #19134843C2semidirect
12. #19134781C2semidirect
13. #19134423C2semidirect
14. #19134370C2semidirect
15. C43×#1925C2semidirect
21. C2×#13063290C22semidirect
26. #14583051C4semidirect
28. C2×#13063258C22semidirect
29. C2×#13063250C22semidirect
30. C2×#13063248C22semidirect
37. C2×#13063236C22semidirect
38. C2×#13063235C22semidirect
39. #14582805C22semidirect
41. #14582798C22semidirect
51. #14582662C22semidirect
52. #14582661C22semidirect
53. #14582661C22semidirect
54. #14582653C22semidirect
55. C2×#107×C43C22semidirect
59. C4×C4⋊C4×C43C22semidirect
60. C43×#340C22semidirect
61. C43×#336C22semidirect
78. C2×#10621873C2×C4semidirect
81. C2×#10621883C2×C4semidirect
88. #13063305C2×C4semidirect
119. #13063245C2×C4semidirect
121. (C2×D43)⋊C8C2×C4semidirect
142. #102×C43C2×C4semidirect
372. C2×D43#440semidirect
395. #1925D43semidirect
426. C2×#107C2×D43semidirect
450. C4×C4⋊C4C2×D43semidirect
456. #340C2×D43semidirect
458. #336C2×D43semidirect
459. C43#22854semidirect
531. #102C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145830512
C2×#145829982
C2×#102×D432
#191376022
#191374162
#191354752
#191352942
#191350172
#191349472
#191349282
#191348432
#191347812
#191344232
#191343702
C43×#19252
#2285443