Finite Group Databasebeta

← #25112386

Subgroups — #25112386

Order 11008.

1434 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063354C211yesmaximal, characteristic
2C2×SD16×Dic43C211yesmaximal, characteristic, complemented
3Q8×(C2×D43)⋊C4C211yesmaximal, characteristic, complemented
4#19137420C211yesmaximal, characteristic
5#19135466C211yesmaximal, characteristic, complemented
6#19135454C211yesmaximal, characteristic, complemented
7#19134936C211yesmaximal, characteristic, complemented
8#19134934C211yesmaximal, characteristic, complemented
9#19134929C211yesmaximal, characteristic, complemented
10#19134927C211yesmaximal, characteristic, complemented
11#19134629C211yesmaximal, characteristic, complemented
12#19134532C211yesmaximal, characteristic
13#19134528C211yesmaximal, characteristic, complemented
14#19134380C211yesmaximal, characteristic, complemented
15C2×C43×#440C211yesmaximal, characteristic, complemented
16C22×#10621900C2211yescharacteristic
17C22×Q8×D43C2211yescharacteristic
18C2×#13063354—24no—
19C2×#13063354—24no—
20C2×#13063354C418yescomplemented
21C22×Dic172C2211yescharacteristic
22C22×#10621885C2211yescharacteristic
23C22×#10621883C2211yescharacteristic
24C22×#10621872C2211yescharacteristic
25C2×Q8×Dic43C2211yescharacteristic
26C2×D4×Dic43C2211yescharacteristic
27SD16×Dic43—24no—
28C2×#13063257C2211yescharacteristic
29C2×#13063250C2211yescharacteristic
30C2×#13063250C2211yescharacteristic
31C2×#13063249C2211yescharacteristic
32C2×#13063248C2211yescharacteristic
33C2×#13063248C2211yescharacteristic
34C2×#13063246C2211yescharacteristic
35C2×(C2×D43)⋊C8C2211yescharacteristic
36C2×C8×Dic43C2211yescharacteristic
37#14582805—21no—
38#14582805C2211yescharacteristic
39#14582805C2211yescharacteristic
40#14582804—21no—
41#14582804C2211yescharacteristic
42#14582804C2211yescharacteristic
43#14582778—21no—
44#14582776—21no—
45#14582760—21no—
46#14582756—21no—
47#14582756C2211yescharacteristic
48#14582756C2211yescharacteristic
49C4×(C2×D43)⋊C4—21no—
50C4×(C2×D43)⋊C4C2211yescharacteristic
51C2×C43⋊#95—21no—
52#14582661C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582654C2211yescharacteristic
55#14582653C2211yescharacteristic
56C22×SD16×C43C2211yescharacteristic
57C2×C4×Q8×C43C2211yescharacteristic
58C2×C4×D4×C43C2211yescharacteristic
59C43×#440—24no—
60C2×#107×C43C2211yescharacteristic
61C2×#103×C43C2211yescharacteristic
62C2×#102×C43C2211yescharacteristic
63C2×#97×C43C2211yescharacteristic
64C2×#10621900—22no—
65C2×#10621900—22no—
66C2×#10621900—22no—
67C2×#10621900—41no—
68C2×#10621900—41no—
69C2×#10621900C2×C414yes—
70C22×Dic86—21no—
71C22×Dic86C2311yescharacteristic
72C22×Dic86C2311yescharacteristic
73C2×Q8×D43—22no—
74C2×Q8×D43—22no—
75C2×Q8×D43—22no—
76C2×Q8×D43—41no—
77C2×Q8×D43—41no—
78C2×Q8×D43C2×C414yescomplemented
79C22×C22⋊D43—21no—
80C23×Dic43—21no—
81C23×Dic43—21no—
82C22×C4×D43—21no—
83C22×C4×D43C2311yescharacteristic
84#13063354—232no—
85C2×Dic172—22no—
86C2×Dic172—22no—
87C2×Dic172C2×C414yescomplemented
88C2×#10621885—22no—
89C2×#10621885—22no—
90C2×#10621885C2×C414yescomplemented
91C2×#10621883—22no—
92C2×#10621883—22no—
93C2×#10621883C2×C414yes—
94C2×#10621872—22no—
95C2×#10621872—22no—
96C2×#10621872C2×C414yescomplemented
97C22×C43⋊C8C2311yescharacteristic
98C22×C43⋊C8C2311yescharacteristic
99Q8×Dic43—22no—
100Q8×Dic43—41no—
101D4×Dic43—22no—
102D4×Dic43—41no—
103C2×C4⋊Dic43—21no—
104C2×C4⋊Dic43C2311yescharacteristic
105C2×C4⋊Dic43C2311yescharacteristic
106C2×C22⋊Dic43—21no—
107C2×(C2×D43)⋊C4—21no—
108C2×(C2×D43)⋊C4—21no—
109C2×(C2×D43)⋊C4D411yescharacteristic
110C2×(C2×D43)⋊C4D411yescharacteristic
111C2×C4×Dic43—21no—
112C2×C4×Dic43C2311yescharacteristic
113#13063257—22no—
114#13063250—41no—
115#13063250—41no—
116#13063249—22no—
117#13063248—41no—
118#13063248—41no—
119#13063246—22no—
120(C2×D43)⋊C8—22no—
121C8×Dic43—22no—
122C43⋊#95—21no—
123C43⋊#95—21no—
124C43⋊#95—21no—
125C43⋊#95—21no—
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×D4×C43C2311yescharacteristic
136C23×C4×C43—21no—
137C2×SD16×C43C2×C414yes—
138C2×SD16×C43D414yes—
139C2×SD16×C43D414yes—
140C22×C8×C43C2311yescharacteristic
141C22×C8×C43C2311yescharacteristic
142C4×Q8×C43—22no—
143C4×Q8×C43—41no—
144C4×D4×C43—22no—
145C4×D4×C43—41no—
146C2×C4⋊C4×C43—21no—
147C2×C4⋊C4×C43C2311yescharacteristic
148C2×C4⋊C4×C43C2311yescharacteristic
149C2×C22⋊C4×C43—21no—
150C2×C42×C43—21no—
151C2×C42×C43C2311yescharacteristic
152#107×C43—22no—
153#103×C43—22no—
154#102×C43—22no—
155#97×C43—22no—
156C24×C43—21no—
157C23×D43C2×D411yescharacteristic
158C2×Q8×C43—21no—
159C2×Q8×C43—21no—
160C2×Q8×C43—21no—
161C2×Q8×C43C22×C412yes—
162C2×Q8×C43C2×D412yes—
163C2×Q8×C43C2×D412yes—
164C2×D4×C43—21no—
165C2×D4×C43—21no—
166C2×D4×C43—21no—
167C2×D4×C43C22×C412yes—
168C2×D4×C43C2×D412yes—
169C2×D4×C43C2×D412yes—
170C22×C4×C43—21no—
171C22×C4×C43—21no—
172C22×C4×C43—21no—
173C22×C4×C43—42no—
174C22×C4×C43—42no—
175C22×C4×C43—81no—
176C22×C4×C43C2×D411yescharacteristic
177C22×C4×C43C2×D411yescharacteristic
178C22×C4×C43C2411yescharacteristic
179C2×C22⋊D43—24no—
180C2×C22⋊D43—42no—
181C2×C22⋊D43—42no—
182C22×Dic43—24no—
183C22×Dic43—21no—
184C22×Dic43—21no—
185C22×Dic43—21no—
186C22×Dic43—21no—
187C22×Dic43—42no—
188C22×Dic43—42no—
189C22×Dic43—42no—
190C22×Dic43—42no—
191C22×Dic43—81no—
192C22×Dic43C2×D411yescharacteristic
193C22×Dic43C2×D411yescharacteristic
194C22×Dic43C2×D411yescharacteristic
195Q8×D43—28no—
196Q8×D43—44no—
197Q8×D43—44no—
198Q8×D43—44no—
199#10621900—28no—
200#10621900—44no—
201#10621900—44no—
202#10621900—44no—
203C2×C4×D43—21no—
204C2×C4×D43—21no—
205C2×C4×D43—21no—
206C2×C4×D43—21no—
207C2×C4×D43—24no—
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—21no—
218C2×Dic86—21no—
219C2×Dic86—21no—
220C2×Dic86—21no—
221C2×Dic86—21no—
222C2×Dic86—24no—
223C2×Dic86—42no—
224C2×Dic86—42no—
225C2×Dic86C22×C412yes—
226C2×Dic86C22×C412yes—
227SD16×C43C22⋊C4116yescomplemented
228C2×C8×C43—21no—
229C2×C8×C43—21no—
230C2×C8×C43—21no—
231C2×C8×C43C22×C412yes—
232C2×C8×C43C2×D412yes—
233C2×C8×C43C2×D412yes—
234C4⋊C4×C43—21no—
235C4⋊C4×C43—21no—
236C4⋊C4×C43—21no—
237C4⋊C4×C43—21no—
238C4⋊C4×C43—42no—
239C22⋊C4×C43—42no—
240C42×C43—21no—
241C42×C43—21no—
242C42×C43—42no—
243C22⋊Dic43—42no—
244#10621885—28no—
245#10621883—28no—
246(C2×D43)⋊C4—22no—
247(C2×D43)⋊C4—41no—
248(C2×D43)⋊C4—42no—
249(C2×D43)⋊C4—81no—
250C4⋊Dic43—21no—
251C4⋊Dic43—21no—
252C4⋊Dic43—21no—
253C4⋊Dic43—21no—
254C4⋊Dic43—42no—
255C4×Dic43—21no—
256C4×Dic43—21no—
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—
264Dic172—28no—
265#10621872—28no—
266C23×C43—22no—
267C23×C43—22no—
268C23×C43—22no—
269C23×C43—41no—
270C23×C43—41no—
271C23×C43—41no—
272C23×C43—41no—
273C23×C43C22×D411yescharacteristic
274C22×D43—21no—
275C22×D43—21no—
276C22×D43—21no—
277C22×D43—21no—
278C22×D43—21no—
279C22×D43—21no—
280C22×D43C4×D412yes—
281Q8×C43—22no—
282Q8×C43—22no—
283Q8×C43—22no—
284Q8×C43C2×C22⋊C414yes—
285D4×C43—22no—
286D4×C43—22no—
287D4×C43—22no—
288D4×C43C2×C22⋊C414yes—
289C2×C4×C43—22no—
290C2×C4×C43—22no—
291C2×C4×C43—22no—
292C2×C4×C43—21no—
293C2×C4×C43—21no—
294C2×C4×C43—21no—
295C2×C4×C43—21no—
296C2×C4×C43—21no—
297C2×C4×C43—21no—
298C2×C4×C43—41no—
299C2×C4×C43—41no—
300C2×C4×C43—41no—
301C2×C4×C43—41no—
302C2×C4×C43—41no—
303C2×C4×C43—41no—
304C2×C4×C43—84no—
305C2×C4×C43C23×C411yescharacteristic
306C2×C4×C43C22×D411yescharacteristic
307C2×C4×C43C22×D411yescharacteristic
308C2×C4×C43C2×#4111yescharacteristic
309C2×C4×C43H(5,𝔽2)11yescharacteristic
310C2×C4×C43H(5,𝔽2)11yescharacteristic
311C22⋊D43—48no—
312C2×Dic43—21no—
313C2×Dic43—21no—
314C2×Dic43—21no—
315C2×Dic43—21no—
316C2×Dic43—22no—
317C2×Dic43—22no—
318C2×Dic43—21no—
319C2×Dic43—21no—
320C2×Dic43—21no—
321C2×Dic43—48no—
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×Dic43—41no—
331C2×Dic43—41no—
332C2×Dic43—84no—
333C2×Dic43C4×D412yes—
334C2×Dic43#13712yescomplemented
335C4×D43—22no—
336C4×D43—22no—
337C4×D43—22no—
338C4×D43—22no—
339C4×D43—48no—
340Dic86—22no—
341Dic86—22no—
342Dic86—22no—
343Dic86—22no—
344Dic86—48no—
345Dic86—41no—
346Dic86—41no—
347Dic86—41no—
348Dic86—41no—
349C8×C43—41no—
350C8×C43C2×C22⋊C414yes—
351C43⋊C8—22no—
352C43⋊C8—41no—
353#22444—431nomaximal, Sylow
354C22×C43—24no—
355C22×C43—42no—
356C22×C43—42no—
357C22×C43—42no—
358C22×C43—42no—
359C22×C43—42no—
360C22×C43—42no—
361C22×C43C2×C4×D411yescharacteristic
362C22×C43D4211yescharacteristic
363C22×C43D4211yescharacteristic
364C22×C43C2×#13711yescharacteristic
365C22×C43#57511yescharacteristic
366C22×C43#57711yescharacteristic
367C22×C43#57811yescharacteristic
368C2×D43—22no—
369C2×D43—22no—
370C2×D43—22no—
371C2×D43—41no—
372C2×D43—41no—
373C2×D43—41no—
374C2×D43—41no—
375C4×C43—24no—
376C4×C43—41no—
377C4×C43—41no—
378C4×C43—81no—
379C4×C43—81no—
380C4×C43C22×C22⋊C411yescharacteristic
381C4×C43#51811yescharacteristic
382C4×C43#54611yescharacteristic
383C4×C43#54611yescharacteristic
384Dic43—22no—
385Dic43—22no—
386Dic43—42no—
387Dic43—42no—
388Dic43—41no—
389Dic43—81no—
390Dic43—81no—
391C22×#137—431no—
392C2×#440D4311yescharacteristic, complemented
393C2×C4×SD16—431no—
394Q8×C22⋊C4—431no—
395#2339—431no—
396#1971—431no—
397#1969—431no—
398#1878—431no—
399#1878—431no—
400#1877—431no—
401#1877—431no—
402#1809—431no—
403#1788—431no—
404#1787—431no—
405#1753—431no—
406C2×C43—44no—
407C2×C43D4×C22⋊C411yescharacteristic
408C2×C43C4×#13711yescharacteristic
409C2×C43#294711yescharacteristic
410C2×C43#326611yescharacteristic
411C2×C43#326911yescharacteristic
412C2×C43#327511yescharacteristic
413C2×C43#327611yescharacteristic
414D43—42no—
415C22×#41—431no—
416C23×Q8—431no—
417C2×#137—438no—
418C2×#137—864no—
419C2×#137—864no—
420C22×Q16—431no—
421C22×Q16—431no—
422C22×SD16—431no—
423C22×SD16C2×D4311yescharacteristic
424C22×M16—431no—
425C2×C4×Q8—431no—
426C2×C4×Q8C2×D4311yescharacteristic
427C2×C4×D4—431no—
428C2×C4×D4C2×D4311yescharacteristic
429#440—24no—
430C4×SD16—864no—
431C2×#107C2×D4311yescharacteristic
432C2×#106—431no—
433C2×#103—431no—
434C2×#103—431no—
435C2×#103—431no—
436C2×#103—431no—
437C2×#103—431no—
438C2×#103C2×D4311yescharacteristic
439C2×#102—431no—
440C2×#102C2×D4311yescharacteristic
441C2×C22⋊C8—431no—
442C2×#97C2×D4311yescharacteristic
443C2×C4×C8—431no—
444#391—431no—
445#391—431no—
446#391—431no—
447#391—431no—
448#391—861no—
449#391—861no—
450#386—861no—
451#386—861no—
452#381—861no—
453#380—431no—
454#380—431no—
455#380—861no—
456C4×C22⋊C4—431no—
457C4×C22⋊C4—861no—
458C2×#95—861no—
459#340—431no—
460#340—431no—
461#336—431no—
462#336—431no—
463C43#2244411yescharacteristic, complemented, Sylow
464C2×#41—434no—
465C2×#41—862no—
466C2×#41—862no—
467C2×#41—862no—
468C2×#41—1721no—
469C2×#41—1721no—
470C22×Q8—434no—
471C22×Q8—431no—
472C22×Q8—431no—
473C22×Q8—861no—
474C22×Q8—862no—
475C22×Q8—862no—
476C22×Q8—862no—
477C22×Q8—1721no—
478C22×Q8—1721no—
479C22×Q8C22×D4311yescharacteristic
480C22×D4—861no—
481C22×D4C22×D4311yescharacteristic
482C23×C4—21no—
483C23×C4—431no—
484C23×C4—861no—
485C23×C4—861no—
486C23×C4—861no—
487#137—8632no—
488C2×Q16—434no—
489C2×Q16—434no—
490C2×Q16—862no—
491C2×Q16—862no—
492C2×Q16—862no—
493C2×Q16—862no—
494C2×SD16—434no—
495C2×SD16—862no—
496C2×SD16—862no—
497C2×SD16C4×D4314yes—
498C2×SD16D17214yes—
499C2×SD16C22⋊D4314yes—
500C2×M16—434no—
501C2×M16—862no—
502C2×M16—862no—
503C22×C8—431no—
504C22×C8—431no—
505C22×C8C22×D4311yescharacteristic
506C22×C8C22×D4311yescharacteristic
507C4×Q8—22no—
508C4×Q8—41no—
509C4×Q8—862no—
510C4×Q8—1721no—
511C4×D4—22no—
512C4×D4—41no—
513C4×D4—862no—
514C4×D4—1721no—
515C2×C4⋊C4—21no—
516C2×C4⋊C4—431no—
517C2×C4⋊C4—431no—
518C2×C4⋊C4—861no—
519C2×C4⋊C4C22×D4311yescharacteristic
520C2×C4⋊C4C22×D4311yescharacteristic
521C2×C22⋊C4—21no—
522C2×C22⋊C4—431no—
523C2×C22⋊C4—431no—
524C2×C22⋊C4—861no—
525C2×C22⋊C4—861no—
526C2×C22⋊C4—861no—
527C2×C42—21no—
528C2×C42—431no—
529C2×C42—861no—
530C2×C42C22×D4311yescharacteristic
531#107—22no—
532#106—862no—
533#103—22no—
534#103—862no—
535#103—1721no—
536#103—1721no—
537#103—1721no—
538#103—1721no—
539#102—22no—
540#102—862no—
541C22⋊C8—862no—
542#97—22no—
543C4×C8—862no—
544#95—431no—
545#95—431no—
546#95—861no—
547#95—861no—
548#95—861no—
549#95—861no—
550#95—861no—
551#95—861no—
552#95—861no—
553#95—861no—
554#95—861no—
555#95—861no—
556C24—21no—
557C24—431no—
558#41—868no—
559#41—1724no—
560#41—1724no—
561#41—1724no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—21no—
565C2×Q8—432no—
566C2×Q8—432no—
567C2×Q8—864no—
568C2×Q8—861no—
569C2×Q8—861no—
570C2×Q8—868no—
571C2×Q8—861no—
572C2×Q8—861no—
573C2×Q8—861no—
574C2×Q8—861no—
575C2×Q8—861no—
576C2×Q8—861no—
577C2×Q8—861no—
578C2×Q8—861no—
579C2×Q8—1722no—
580C2×Q8—1722no—
581C2×Q8—1724no—
582C2×Q8—1724no—
583C2×Q8—1724no—
584C2×Q8C2×C4×D4312yes—
585C2×Q8C2×D17212yes—
586C2×Q8C2×C22⋊D4312yes—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—864no—
591C2×D4—1722no—
592C2×D4—1722no—
593C2×D4C2×C4×D4312yes—
594C2×D4C2×D17212yes—
595C2×D4C2×C22⋊D4312yes—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—42no—
600C22×C4—42no—
601C22×C4—81no—
602C22×C4—431no—
603C22×C4—431no—
604C22×C4—432no—
605C22×C4—432no—
606C22×C4—431no—
607C22×C4—864no—
608C22×C4—864no—
609C22×C4—861no—
610C22×C4—861no—
611C22×C4—861no—
612C22×C4—861no—
613C22×C4—861no—
614C22×C4—861no—
615C22×C4—861no—
616C22×C4—861no—
617C22×C4—3441no—
618C22×C4—1722no—
619C22×C4—1722no—
620C22×C4—1722no—
621C22×C4—1722no—
622C22×C4—1722no—
623C22×C4—1722no—
624C22×C4D4×D4311yescharacteristic
625C22×C4D4×D4311yescharacteristic
626C22×C4C23×D4311yescharacteristic
627Q16—868no—
628Q16—868no—
629SD16—868no—
630SD16(C2×D43)⋊C4116yescomplemented
631M16—868no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—432no—
636C2×C8—861no—
637C2×C8—861no—
638C2×C8—861no—
639C2×C8—861no—
640C2×C8—861no—
641C2×C8C2×C4×D4312yes—
642C2×C8C2×D17212yes—
643C2×C8C2×C22⋊D4312yes—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—42no—
649C4⋊C4—861no—
650C4⋊C4—861no—
651C4⋊C4—861no—
652C4⋊C4—861no—
653C4⋊C4—1722no—
654C22⋊C4—42no—
655C22⋊C4—862no—
656C22⋊C4—3441no—
657C22⋊C4—1721no—
658C22⋊C4—1722no—
659C22⋊C4—1722no—
660C42—21no—
661C42—21no—
662C42—42no—
663C42—861no—
664C42—861no—
665C42—1722no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—432no—
674C23—861no—
675C23—861no—
676C23—861no—
677C23—861no—
678C23—861no—
679C23—861no—
680C23C2×D4×D4311yescharacteristic
681Q8—22no—
682Q8—22no—
683Q8—22no—
684Q8—862no—
685Q8—862no—
686Q8—862no—
687Q8—862no—
688Q8—1728no—
689Q8—1721no—
690Q8—1721no—
691Q8—1721no—
692Q8—1721no—
693Q8C2×(C2×D43)⋊C414yes—
694D4—22no—
695D4—22no—
696D4—22no—
697D4—1728no—
698D4C2×(C2×D43)⋊C414yes—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
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—84no—
715C2×C4—432no—
716C2×C4—432no—
717C2×C4—861no—
718C2×C4—861no—
719C2×C4—861no—
720C2×C4—861no—
721C2×C4—862no—
722C2×C4—862no—
723C2×C4—862no—
724C2×C4—862no—
725C2×C4—862no—
726C2×C4—862no—
727C2×C4—861no—
728C2×C4—861no—
729C2×C4—861no—
730C2×C4—3444no—
731C2×C4—1728no—
732C2×C4—1728no—
733C2×C4—1721no—
734C2×C4—1721no—
735C2×C4—1721no—
736C2×C4—1721no—
737C2×C4—1721no—
738C2×C4—1721no—
739C2×C4—1721no—
740C2×C4—1721no—
741C2×C4—1721no—
742C2×C4—1721no—
743C2×C4C22×C4×D4311yescharacteristic
744C2×C4C22×C22⋊D4311yescharacteristic
745C2×C4C22×D17211yescharacteristic
746C2×C4#41×D4311yescharacteristic
747C2×C4#1306337011yescharacteristic
748C2×C4#1306337111yescharacteristic
749C8—41no—
750C8—862no—
751C8—1721no—
752C8C2×(C2×D43)⋊C414yes—
753C22—24no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22—862no—
761C22—862no—
762C22—862no—
763C22—1721no—
764C22—1721no—
765C22—1721no—
766C22—1721no—
767C22C4×D4×D4311yescharacteristic
768C22D4×C22⋊D4311yescharacteristic
769C22D4×D17211yescharacteristic
770C22#137×D4311yescharacteristic
771C22#1458369511yescharacteristic
772C22#1458370911yescharacteristic
773C22#1458371511yescharacteristic
774C4—24no—
775C4—41no—
776C4—41no—
777C4—81no—
778C4—81no—
779C4—862no—
780C4—862no—
781C4—3441no—
782C4—3441no—
783C4—1722no—
784C4—1722no—
785C4—1721no—
786C4C22×(C2×D43)⋊C411yescharacteristic
787C4#1458337111yescharacteristic
788C4#1458353711yescharacteristic
789C4#1458354411yescharacteristic
790C2—44no—
791C2—1722no—
792C2D4×(C2×D43)⋊C411yescharacteristic
793C2#1914341711yescharacteristic
794C2#1914343511yescharacteristic
795C2#1914610711yescharacteristic
796C2#1914615211yescharacteristic
797C2#1914622611yescharacteristic
798C2#1914623511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#440C2
socleC23×C43C22×D4
prime radicalC22×#10621900C22
cosocleC22×C4×C43C24
hypercenterC2×#440D43
hypocenterC43#22444
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
2. C2×SD16×Dic43C2semidirect
3. Q8×(C2×D43)⋊C4C2semidirect
5. #19135466C2semidirect
6. #19135454C2semidirect
7. #19134936C2semidirect
8. #19134934C2semidirect
9. #19134929C2semidirect
10. #19134927C2semidirect
11. #19134629C2semidirect
13. #19134528C2semidirect
14. #19134380C2semidirect
15. C2×C43×#440C2semidirect
20. C2×#13063354C4semidirect
78. C2×Q8×D43C2×C4semidirect
87. C2×Dic172C2×C4semidirect
90. C2×#10621885C2×C4semidirect
96. C2×#10621872C2×C4semidirect
227. SD16×C43C22⋊C4semidirect
334. C2×Dic43#137semidirect
392. C2×#440D43semidirect
463. C43#22444semidirect
630. SD16(C2×D43)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×#130633542
C2×SD16×Dic432
Q8×(C2×D43)⋊C42
#191374202
#191354662
#191354542
#191349362
#191349342
#191349292
#191349272
#191346292
#191345322
#191345282
#191343802
C2×C43×#4402
#2244443