Finite Group Databasebeta

← #25112409

Subgroups — #25112409

Order 11008.

1406 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
1C22×#13063357C211yesmaximal, characteristic
2C2×#14583006C211yesmaximal, characteristic, complemented
3#19137433C211yesmaximal, characteristic
4Q8×(C2×D43)⋊C4C211yesmaximal, characteristic, complemented
5#19135474C211yesmaximal, characteristic, complemented
6#19135449C211yesmaximal, characteristic, complemented
7#19134950C211yesmaximal, characteristic, complemented
8#19134948C211yesmaximal, characteristic, complemented
9#19134936C211yesmaximal, characteristic, complemented
10#19134934C211yesmaximal, characteristic, complemented
11#19134629C211yesmaximal, characteristic, complemented
12#19134534C211yesmaximal, characteristic
13#19134528C211yesmaximal, characteristic, complemented
14#19134378C211yesmaximal, characteristic, complemented
15C2×C4×Q16×C43C211yesmaximal, characteristic, complemented
16C22×#10621902C2211yescharacteristic
17C22×Q8×D43C2211yescharacteristic
18C2×#13063357—24no—
19C2×#13063357—24no—
20C2×#13063357C418yescomplemented
21C22×#10621885C2211yescharacteristic
22C22×#10621873C2211yescharacteristic
23C22×#10621884C2211yescharacteristic
24C22×#10621872C2211yescharacteristic
25C2×Q8×Dic43C2211yescharacteristic
26C2×Q8×Dic43C2211yescharacteristic
27#14583006—24no—
28C2×#13063257C2211yescharacteristic
29C2×#13063250C2211yescharacteristic
30C2×#13063249C2211yescharacteristic
31C2×#13063249C2211yescharacteristic
32C2×#13063248C2211yescharacteristic
33C2×#13063247C2211yescharacteristic
34C2×#13063245C2211yescharacteristic
35C2×(C2×D43)⋊C8C2211yescharacteristic
36C2×#13063235C2211yescharacteristic
37#14582805—21no—
38#14582805C2211yescharacteristic
39#14582804—21no—
40#14582804C2211yescharacteristic
41#14582801—21no—
42#14582801C2211yescharacteristic
43#14582800—21no—
44#14582800C2211yescharacteristic
45#14582756—21no—
46#14582756—21no—
47#14582756C2211yescharacteristic
48#14582756C2211yescharacteristic
49C4×(C2×D43)⋊C4—21no—
50C4×(C2×D43)⋊C4—21no—
51C4×(C2×D43)⋊C4C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582654C2211yescharacteristic
55#14582653C2211yescharacteristic
56C22×Q16×C43C2211yescharacteristic
57C2×C4×Q8×C43C2211yescharacteristic
58C2×C4×Q8×C43C2211yescharacteristic
59C4×Q16×C43—24no—
60C2×#107×C43C2211yescharacteristic
61C2×#103×C43C2211yescharacteristic
62C2×#103×C43C2211yescharacteristic
63C2×C4×C8×C43C2211yescharacteristic
64C2×#10621902—22no—
65C2×#10621902—22no—
66C2×#10621902—22no—
67C2×#10621902—41no—
68C2×#10621902—41no—
69C2×#10621902C2×C414yes—
70C22×Dic86—21no—
71C22×Dic86C2311yescharacteristic
72C2×Q8×D43—22no—
73C2×Q8×D43—22no—
74C2×Q8×D43—22no—
75C2×Q8×D43—41no—
76C2×Q8×D43—41no—
77C2×Q8×D43C2×C414yes—
78C22×D172—21no—
79C22×D172C2311yescharacteristic
80C22×C4×D43—21no—
81C22×C4×D43—21no—
82C22×C4×D43C2311yescharacteristic
83#13063357—232no—
84C2×#10621885—22no—
85C2×#10621885—22no—
86C2×#10621885C2×C414yes—
87C2×#10621873—22no—
88C2×#10621873—22no—
89C2×#10621873C2×C414yes—
90C2×#10621884—22no—
91C2×#10621884—22no—
92C2×#10621884C2×C414yes—
93C2×#10621872—22no—
94C2×#10621872—22no—
95C2×#10621872C2×C414yes—
96C22×C43⋊C8C2311yescharacteristic
97C22×C43⋊C8C2311yescharacteristic
98Q8×Dic43—22no—
99Q8×Dic43—22no—
100Q8×Dic43—41no—
101Q8×Dic43—41no—
102C2×C4⋊Dic43—21no—
103C2×C4⋊Dic43—21no—
104C2×C4⋊Dic43C2311yescharacteristic
105C2×C4⋊Dic43C2311yescharacteristic
106C2×(C2×D43)⋊C4—21no—
107C2×(C2×D43)⋊C4—21no—
108C2×(C2×D43)⋊C4—21no—
109C2×(C2×D43)⋊C4—21no—
110C2×(C2×D43)⋊C4—21no—
111C2×(C2×D43)⋊C4—21no—
112C2×(C2×D43)⋊C4D411yescharacteristic
113C2×(C2×D43)⋊C4D411yescharacteristic
114C2×C4×Dic43—21no—
115C2×C4×Dic43—21no—
116C2×C4×Dic43C2311yescharacteristic
117#13063257—22no—
118#13063250—41no—
119#13063249—22no—
120#13063249—22no—
121#13063248—41no—
122#13063247—41no—
123#13063245—41no—
124(C2×D43)⋊C8—22no—
125#13063235—22no—
126C43⋊#95—21no—
127C43⋊#95—21no—
128C43⋊#95—21no—
129C43⋊#95—21no—
130C43⋊#95—21no—
131C43⋊#95—21no—
132C43⋊#95D411yescharacteristic
133C43⋊#95D411yescharacteristic
134C22×Q8×C43C2311yescharacteristic
135C22×Q8×C43C2311yescharacteristic
136C2×Q16×C43C2×C414yes—
137C2×Q16×C43D414yes—
138C2×Q16×C43D414yes—
139C22×C8×C43C2311yescharacteristic
140C22×C8×C43C2311yescharacteristic
141C4×Q8×C43—22no—
142C4×Q8×C43—22no—
143C4×Q8×C43—41no—
144C4×Q8×C43—41no—
145C2×C4⋊C4×C43—21no—
146C2×C4⋊C4×C43—21no—
147C2×C4⋊C4×C43C2311yescharacteristic
148C2×C4⋊C4×C43C2311yescharacteristic
149C2×C42×C43—21no—
150C2×C42×C43—21no—
151C2×C42×C43C2311yescharacteristic
152#107×C43—22no—
153#103×C43—22no—
154#103×C43—22no—
155C4×C8×C43—22no—
156C23×D43—21no—
157C23×D43C2×D411yescharacteristic
158C2×Q8×C43—21no—
159C2×Q8×C43—21no—
160C2×Q8×C43—21no—
161C2×Q8×C43—21no—
162C2×Q8×C43—21no—
163C2×Q8×C43—21no—
164C2×Q8×C43C22×C412yes—
165C2×Q8×C43C22×C412yes—
166C2×Q8×C43C2×D412yes—
167C2×Q8×C43C2×D412yes—
168C2×Q8×C43C2×D412yes—
169C2×Q8×C43C2×D412yes—
170C22×C4×C43—21no—
171C22×C4×C43—21no—
172C22×C4×C43—21no—
173C22×C4×C43—21no—
174C22×C4×C43C2×D411yescharacteristic
175C22×C4×C43C2×D411yescharacteristic
176C22×C4×C43C2411yescharacteristic
177C22×Dic43—21no—
178C22×Dic43—21no—
179C22×Dic43—21no—
180C22×Dic43C2×D411yescharacteristic
181C22×Dic43C2×D411yescharacteristic
182C22×Dic43C2×D411yescharacteristic
183#10621902—28no—
184#10621902—44no—
185#10621902—44no—
186#10621902—44no—
187Q8×D43—28no—
188Q8×D43—44no—
189Q8×D43—44no—
190Q8×D43—44no—
191C2×D172—21no—
192C2×D172—24no—
193C2×D172—21no—
194C2×D172—21no—
195C2×D172—21no—
196C2×D172—21no—
197C2×D172—42no—
198C2×D172—42no—
199C2×D172C22×C412yes—
200C2×C4×D43—21no—
201C2×C4×D43—21no—
202C2×C4×D43—21no—
203C2×C4×D43—21no—
204C2×C4×D43—24no—
205C2×C4×D43—24no—
206C2×C4×D43—42no—
207C2×C4×D43—42no—
208C2×C4×D43—42no—
209C2×C4×D43—42no—
210C2×C4×D43C22×C412yes—
211C2×C4×D43#4112yes—
212C2×Dic86—21no—
213C2×Dic86—21no—
214C2×Dic86—21no—
215C2×Dic86—21no—
216C2×Dic86—21no—
217C2×Dic86—24no—
218C2×Dic86—42no—
219C2×Dic86—42no—
220C2×Dic86C22×C412yes—
221Q16×C43C22⋊C4116yescomplemented
222C2×C8×C43—21no—
223C2×C8×C43—21no—
224C2×C8×C43—21no—
225C2×C8×C43C22×C412yes—
226C2×C8×C43C2×D412yes—
227C2×C8×C43C2×D412yes—
228C4⋊C4×C43—21no—
229C4⋊C4×C43—21no—
230C4⋊C4×C43—21no—
231C4⋊C4×C43—21no—
232C4⋊C4×C43—42no—
233C4⋊C4×C43—42no—
234C42×C43—21no—
235C42×C43—21no—
236C42×C43—42no—
237C42×C43—42no—
238#10621885—28no—
239#10621884—28no—
240(C2×D43)⋊C4—22no—
241(C2×D43)⋊C4—41no—
242(C2×D43)⋊C4—42no—
243(C2×D43)⋊C4—42no—
244(C2×D43)⋊C4—42no—
245(C2×D43)⋊C4—81no—
246(C2×D43)⋊C4—81no—
247(C2×D43)⋊C4—81no—
248C4⋊Dic43—21no—
249C4⋊Dic43—21no—
250C4⋊Dic43—21no—
251C4⋊Dic43—21no—
252C4⋊Dic43—42no—
253C4⋊Dic43—42no—
254C4×Dic43—21no—
255C4×Dic43—21no—
256C4×Dic43—42no—
257C4×Dic43—42no—
258C2×C43⋊C8—21no—
259C2×C43⋊C8—21no—
260C2×C43⋊C8—21no—
261C2×C43⋊C8—21no—
262C2×C43⋊C8—21no—
263C2×C43⋊C8C22×C412yes—
264#10621873—28no—
265#10621872—28no—
266C23×C43C22×D411yescharacteristic
267C22×D43—21no—
268C22×D43—21no—
269C22×D43—21no—
270C22×D43—21no—
271C22×D43—21no—
272C22×D43—21no—
273C22×D43—22no—
274C22×D43—41no—
275C22×D43—41no—
276C22×D43—41no—
277C22×D43—41no—
278C22×D43—41no—
279C22×D43—41no—
280C22×D43C4×D412yes—
281Q8×C43—22no—
282Q8×C43—22no—
283Q8×C43—22no—
284Q8×C43—22no—
285Q8×C43—22no—
286Q8×C43—22no—
287Q8×C43C2×C22⋊C414yes—
288Q8×C43C2×C22⋊C414yes—
289C2×C4×C43—22no—
290C2×C4×C43—22no—
291C2×C4×C43—22no—
292C2×C4×C43—22no—
293C2×C4×C43—21no—
294C2×C4×C43—22no—
295C2×C4×C43—22no—
296C2×C4×C43—21no—
297C2×C4×C43—21no—
298C2×C4×C43—21no—
299C2×C4×C43—21no—
300C2×C4×C43—41no—
301C2×C4×C43—41no—
302C2×C4×C43—41no—
303C2×C4×C43—41no—
304C2×C4×C43—41no—
305C2×C4×C43—41no—
306C2×C4×C43#13712yescomplemented
307C2×C4×C43C23×C411yescharacteristic
308C2×C4×C43C22×D411yescharacteristic
309C2×C4×C43C22×D411yescharacteristic
310C2×C4×C43C2×#4111yescharacteristic
311C2×C4×C43H(5,𝔽2)11yescharacteristic
312C2×C4×C43H(5,𝔽2)11yescharacteristic
313C2×Dic43—21no—
314C2×Dic43—21no—
315C2×Dic43—22no—
316C2×Dic43—21no—
317C2×Dic43—21no—
318C2×Dic43—21no—
319C2×Dic43—21no—
320C2×Dic43—21no—
321C2×Dic43—21no—
322C2×Dic43—41no—
323C2×Dic43—41no—
324C2×Dic43—41no—
325C2×Dic43—41no—
326C2×Dic43—41no—
327C2×Dic43—41no—
328C2×Dic43—41no—
329C2×Dic43—41no—
330C2×Dic43C4×D412yes—
331D172—22no—
332D172—22no—
333D172—48no—
334D172—41no—
335D172—41no—
336C4×D43—22no—
337C4×D43—22no—
338C4×D43—22no—
339C4×D43—22no—
340C4×D43—48no—
341C4×D43—48no—
342Dic86—22no—
343Dic86—22no—
344Dic86—48no—
345Dic86—41no—
346Dic86—41no—
347C8×C43—41no—
348C8×C43C2×C22⋊C414yes—
349C43⋊C8—22no—
350C43⋊C8—41no—
351#22445—431nomaximal, Sylow
352C22×C43C2×C4×D411yescharacteristic
353C22×C43D4211yescharacteristic
354C22×C43D4211yescharacteristic
355C22×C43C2×#13711yescharacteristic
356C22×C43#57511yescharacteristic
357C22×C43#57711yescharacteristic
358C22×C43#57811yescharacteristic
359C2×D43—22no—
360C2×D43—22no—
361C2×D43—22no—
362C2×D43—41no—
363C2×D43—41no—
364C2×D43—41no—
365C2×D43—41no—
366C2×D43—42no—
367C2×D43—42no—
368C2×D43—42no—
369C2×D43—81no—
370C2×D43—81no—
371C2×D43—81no—
372C2×D43—81no—
373C4×C43—24no—
374C4×C43—24no—
375C4×C43—22no—
376C4×C43—41no—
377C4×C43—81no—
378C4×C43—81no—
379C4×C43C22×C22⋊C411yescharacteristic
380C4×C43#51811yescharacteristic
381C4×C43#54611yescharacteristic
382C4×C43#54611yescharacteristic
383Dic43—22no—
384Dic43—42no—
385Dic43—41no—
386Dic43—41no—
387Dic43—81no—
388Dic43—81no—
389C22×#137—431no—
390C2×#441—431no—
391C2×C4×Q16D4311yescharacteristic, complemented
392#2341—431no—
393Q8×C22⋊C4—431no—
394#1973—431no—
395#1968—431no—
396#1880—431no—
397#1880—431no—
398#1878—431no—
399#1878—431no—
400#1809—431no—
401#1788—431no—
402#1787—431no—
403#1753—431no—
404C2×C43D4×C22⋊C411yescharacteristic
405C2×C43C4×#13711yescharacteristic
406C2×C43#294711yescharacteristic
407C2×C43#327011yescharacteristic
408C2×C43#327111yescharacteristic
409C2×C43#327711yescharacteristic
410C2×C43#327811yescharacteristic
411D43—42no—
412D43—82no—
413C22×#41—431no—
414C23×Q8—431no—
415C2×#137—438no—
416C2×#137—864no—
417C2×#137—864no—
418C22×Q16—431no—
419C22×Q16C2×D4311yescharacteristic
420C22×SD16—431no—
421C22×SD16—431no—
422C22×M16—431no—
423C2×C4×Q8—431no—
424C2×C4×Q8—431no—
425C2×C4×Q8C2×D4311yescharacteristic
426C2×C4×Q8C2×D4311yescharacteristic
427#441—864no—
428C4×Q16—24no—
429C2×#107C2×D4311yescharacteristic
430C2×#106—431no—
431C2×#103—431no—
432C2×#103—431no—
433C2×#103—431no—
434C2×#103—431no—
435C2×#103C2×D4311yescharacteristic
436C2×#103C2×D4311yescharacteristic
437C2×#102—431no—
438C2×#102—431no—
439C2×C22⋊C8—431no—
440C2×#97—431no—
441C2×C4×C8C2×D4311yescharacteristic
442#391—431no—
443#391—431no—
444#391—861no—
445#391—861no—
446#390—431no—
447#390—431no—
448#390—861no—
449#390—861no—
450#380—431no—
451#380—431no—
452#380—861no—
453#380—861no—
454C4×C22⋊C4—431no—
455C4×C22⋊C4—861no—
456C4×C22⋊C4—861no—
457#340—431no—
458#340—431no—
459#336—431no—
460#336—431no—
461C43#2244511yescharacteristic, complemented, Sylow
462C2×#41—434no—
463C2×#41—862no—
464C2×#41—862no—
465C2×#41—862no—
466C2×#41—1721no—
467C2×#41—1721no—
468C22×Q8—434no—
469C22×Q8—431no—
470C22×Q8—861no—
471C22×Q8—862no—
472C22×Q8—862no—
473C22×Q8—862no—
474C22×Q8—1721no—
475C22×Q8—1721no—
476C22×Q8C22×D4311yescharacteristic
477C22×Q8C22×D4311yescharacteristic
478C22×D4—431no—
479C22×D4—861no—
480C23×C4—431no—
481C23×C4—861no—
482C23×C4—861no—
483#137—8632no—
484C2×Q16—434no—
485C2×Q16—862no—
486C2×Q16—862no—
487C2×Q16C4×D4314yes—
488C2×Q16D17214yes—
489C2×Q16C22⋊D4314yes—
490C2×SD16—434no—
491C2×SD16—434no—
492C2×SD16—862no—
493C2×SD16—862no—
494C2×SD16—862no—
495C2×SD16—862no—
496C2×M16—434no—
497C2×M16—862no—
498C2×M16—862no—
499C22×C8—431no—
500C22×C8—431no—
501C22×C8C22×D4311yescharacteristic
502C22×C8C22×D4311yescharacteristic
503C4×Q8—22no—
504C4×Q8—22no—
505C4×Q8—41no—
506C4×Q8—41no—
507C4×Q8—862no—
508C4×Q8—862no—
509C4×Q8—1721no—
510C4×Q8—1721no—
511C2×C4⋊C4—21no—
512C2×C4⋊C4—21no—
513C2×C4⋊C4—431no—
514C2×C4⋊C4—431no—
515C2×C4⋊C4—861no—
516C2×C4⋊C4—861no—
517C2×C4⋊C4C22×D4311yescharacteristic
518C2×C4⋊C4C22×D4311yescharacteristic
519C2×C22⋊C4—431no—
520C2×C22⋊C4—431no—
521C2×C22⋊C4—861no—
522C2×C22⋊C4—861no—
523C2×C22⋊C4—861no—
524C2×C22⋊C4—861no—
525C2×C22⋊C4—861no—
526C2×C22⋊C4—861no—
527C2×C42—21no—
528C2×C42—21no—
529C2×C42—431no—
530C2×C42—861no—
531C2×C42—861no—
532C2×C42C22×D4311yescharacteristic
533#107—22no—
534#106—862no—
535#103—22no—
536#103—22no—
537#103—862no—
538#103—862no—
539#103—1721no—
540#103—1721no—
541#102—1721no—
542#102—1721no—
543C22⋊C8—862no—
544#97—862no—
545C4×C8—22no—
546#95—431no—
547#95—431no—
548#95—861no—
549#95—861no—
550#95—861no—
551#95—861no—
552#95—861no—
553#95—861no—
554C24—431no—
555C24—861no—
556#41—868no—
557#41—1724no—
558#41—1724no—
559#41—1724no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—21no—
565C2×Q8—21no—
566C2×Q8—432no—
567C2×Q8—864no—
568C2×Q8—861no—
569C2×Q8—868no—
570C2×Q8—861no—
571C2×Q8—861no—
572C2×Q8—861no—
573C2×Q8—861no—
574C2×Q8—1722no—
575C2×Q8—1722no—
576C2×Q8—1724no—
577C2×Q8—1724no—
578C2×Q8—1724no—
579C2×Q8C2×C4×D4312yes—
580C2×Q8C2×C4×D4312yes—
581C2×Q8C2×D17212yes—
582C2×Q8C2×D17212yes—
583C2×Q8C2×C22⋊D4312yes—
584C2×Q8C2×C22⋊D4312yes—
585C2×D4—432no—
586C2×D4—864no—
587C2×D4—861no—
588C2×D4—861no—
589C2×D4—861no—
590C2×D4—861no—
591C2×D4—861no—
592C2×D4—1722no—
593C2×D4—1722no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—431no—
599C22×C4—432no—
600C22×C4—432no—
601C22×C4—431no—
602C22×C4—431no—
603C22×C4—864no—
604C22×C4—864no—
605C22×C4—861no—
606C22×C4—861no—
607C22×C4—861no—
608C22×C4—861no—
609C22×C4—861no—
610C22×C4—861no—
611C22×C4—861no—
612C22×C4—1722no—
613C22×C4—1722no—
614C22×C4—1722no—
615C22×C4—1722no—
616C22×C4D4×D4311yescharacteristic
617C22×C4D4×D4311yescharacteristic
618C22×C4C23×D4311yescharacteristic
619Q16—868no—
620Q16(C2×D43)⋊C4116yescomplemented
621SD16—868no—
622SD16—868no—
623M16—868no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—432no—
628C2×C8—861no—
629C2×C8—861no—
630C2×C8—861no—
631C2×C8—861no—
632C2×C8—861no—
633C2×C8C2×C4×D4312yes—
634C2×C8C2×D17212yes—
635C2×C8C2×C22⋊D4312yes—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—42no—
641C4⋊C4—42no—
642C4⋊C4—861no—
643C4⋊C4—861no—
644C4⋊C4—861no—
645C4⋊C4—861no—
646C4⋊C4—1722no—
647C4⋊C4—1722no—
648C22⋊C4—862no—
649C22⋊C4—3441no—
650C22⋊C4—3441no—
651C22⋊C4—3441no—
652C22⋊C4—1721no—
653C22⋊C4—1722no—
654C22⋊C4—1722no—
655C22⋊C4—1722no—
656C42—21no—
657C42—21no—
658C42—42no—
659C42—42no—
660C42—861no—
661C42—861no—
662C42—1722no—
663C42—1722no—
664C23—432no—
665C23—861no—
666C23—861no—
667C23—861no—
668C23—861no—
669C23—861no—
670C23—861no—
671C23—862no—
672C23—1721no—
673C23—1721no—
674C23—1721no—
675C23—1721no—
676C23—1721no—
677C23—1721no—
678C23C2×D4×D4311yescharacteristic
679Q8—22no—
680Q8—22no—
681Q8—22no—
682Q8—22no—
683Q8—22no—
684Q8—22no—
685Q8—862no—
686Q8—862no—
687Q8—1728no—
688Q8—1721no—
689Q8—1721no—
690Q8C2×(C2×D43)⋊C414yes—
691Q8C2×(C2×D43)⋊C414yes—
692D4—862no—
693D4—862no—
694D4—1728no—
695D4—1721no—
696D4—1721no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—432no—
715C2×C4—861no—
716C2×C4—861no—
717C2×C4—862no—
718C2×C4—862no—
719C2×C4—862no—
720C2×C4—862no—
721C2×C4—862no—
722C2×C4—861no—
723C2×C4—861no—
724C2×C4—861no—
725C2×C4—861no—
726C2×C4—861no—
727C2×C4—861no—
728C2×C4—1728no—
729C2×C4—1728no—
730C2×C4—1721no—
731C2×C4—1721no—
732C2×C4—1721no—
733C2×C4—1721no—
734C2×C4—1721no—
735C2×C4—1721no—
736C2×C4—1721no—
737C2×C4—1721no—
738C2×C4#1306335712yescomplemented
739C2×C4C22×C4×D4311yescharacteristic
740C2×C4C22×C22⋊D4311yescharacteristic
741C2×C4C22×D17211yescharacteristic
742C2×C4#41×D4311yescharacteristic
743C2×C4#1306337011yescharacteristic
744C2×C4#1306337111yescharacteristic
745C8—41no—
746C8—862no—
747C8—1721no—
748C8C2×(C2×D43)⋊C414yes—
749C22—862no—
750C22—862no—
751C22—862no—
752C22—3441no—
753C22—3441no—
754C22—3441no—
755C22—3441no—
756C22—1722no—
757C22—1722no—
758C22—1722no—
759C22—1721no—
760C22—1721no—
761C22—1721no—
762C22—1721no—
763C22C4×D4×D4311yescharacteristic
764C22D4×C22⋊D4311yescharacteristic
765C22D4×D17211yescharacteristic
766C22C2×#1306335711yescharacteristic
767C22#1458369611yescharacteristic
768C22#1458370611yescharacteristic
769C22#1458371211yescharacteristic
770C4—24no—
771C4—24no—
772C4—22no—
773C4—41no—
774C4—81no—
775C4—81no—
776C4—862no—
777C4—3441no—
778C4—3441no—
779C4—1721no—
780C4—1721no—
781C4—1722no—
782C4C22×(C2×D43)⋊C411yescharacteristic
783C4#1458337111yescharacteristic
784C4#1458353711yescharacteristic
785C4#1458354411yescharacteristic
786C2—3442no—
787C2—1722no—
788C2D4×(C2×D43)⋊C411yescharacteristic
789C2C4×#1306335711yescharacteristic
790C2#1914343311yescharacteristic
791C2#1914616511yescharacteristic
792C2#1914618011yescharacteristic
793C2#1914625111yescharacteristic
794C2#1914626211yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C4×Q16×C43C2
socleC23×C43C22×D4
prime radicalC22×#10621902C22
cosocleC22×C4×C43C24
hypercenterC2×C4×Q16D43
hypocenterC43#22445
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×Q16

Complements

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

NH ≅ G/Ntype
2. C2×#14583006C2semidirect
4. Q8×(C2×D43)⋊C4C2semidirect
5. #19135474C2semidirect
6. #19135449C2semidirect
7. #19134950C2semidirect
8. #19134948C2semidirect
9. #19134936C2semidirect
10. #19134934C2semidirect
11. #19134629C2semidirect
13. #19134528C2semidirect
14. #19134378C2semidirect
15. C2×C4×Q16×C43C2semidirect
20. C2×#13063357C4semidirect
221. Q16×C43C22⋊C4semidirect
306. C2×C4×C43#137semidirect
391. C2×C4×Q16D43semidirect
461. C43#22445semidirect
620. Q16(C2×D43)⋊C4semidirect
738. C2×C4#13063357semidirect

Maximal subgroups

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

subgroupindex
C22×#130633572
C2×#145830062
#191374332
Q8×(C2×D43)⋊C42
#191354742
#191354492
#191349502
#191349482
#191349362
#191349342
#191346292
#191345342
#191345282
#191343782
C2×C4×Q16×C432
#2244543