Finite Group Databasebeta

← #25002111

Subgroups — #25002111

Order 11008.

1350 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583379C211yesmaximal, characteristic
2C22×#13063253C211yesmaximal, characteristic
3C2×#14582901C211yesmaximal, characteristic
4C2×#14582667C211yesmaximal, characteristic, complemented
5#19134316C211yesmaximal, characteristic, complemented
6#19132825C211yesmaximal, characteristic, complemented
7C2×C43×#339C211yesmaximal, characteristic, complemented
8C22×#10621898C2211yescharacteristic
9C22×#10621877C2211yescharacteristic
10#14583379—22no—
11#14583379—22no—
12#14583379—22no—
13#14583379C414yescomplemented
14C2×C4×Dic86—21no—
15C2×C4×D172—21no—
16C2×(C22⋊D43)⋊C4—22no—
17C2×#13063283—21no—
18C22×C4⋊Dic43C2211yescharacteristic
19C22×C4⋊Dic43C2211yescharacteristic
20C2×C4⋊C4×D43—21no—
21C2×#13063253—22no—
22C2×#13063253—22no—
23C2×#13063253C414yescomplemented
24#14582901—22no—
25#14582901C414yescomplemented
26C2×#13063250—21no—
27C2×#13063247—21no—
28C2×C43⋊#95—22no—
29#14582667—22no—
30#14582661—21no—
31#14582661—21no—
32C22×M16×C43C2211yescharacteristic
33C2×#117×C43C2211yescharacteristic
34C22×C42×C43C2211yescharacteristic
35C43×#339—22no—
36C2×#10621898—21no—
37C2×#10621898—21no—
38C2×#10621898—21no—
39C2×#10621898—21no—
40C2×#10621898—21no—
41C2×#10621898—21no—
42C2×#10621898C2×C412yes—
43C2×#10621898C2×C412yes—
44C2×#10621898C2×C412yes—
45C2×#10621898D412yes—
46C2×#10621898D412yes—
47C2×#10621898Q812yes—
48C22×Dic86D411yescharacteristic
49C22×D172D411yescharacteristic
50C22×C22⋊D43—21no—
51C23×Dic43—21no—
52C23×Dic43D412yes—
53C22×C4×D43—21no—
54C22×C4×D43—22no—
55C2×#10621877—21no—
56C2×#10621877—21no—
57C2×#10621877—21no—
58C2×#10621877—21no—
59C2×#10621877—21no—
60C2×#10621877C2×C412yescomplemented
61C22×C43⋊C8—21no—
62C4×Dic86—24no—
63C4×Dic86—24no—
64C4×D172—24no—
65C4×D172—24no—
66(C22⋊D43)⋊C4—28no—
67(C22⋊D43)⋊C4—28no—
68#13063283—24no—
69#13063283—24no—
70C2×C4⋊Dic43—21no—
71C2×C4⋊Dic43—21no—
72C2×C4⋊Dic43—21no—
73C2×C4⋊Dic43—21no—
74C2×C4⋊Dic43—21no—
75C2×C4⋊Dic43—21no—
76C2×C4⋊Dic43—21no—
77C2×C4⋊Dic43—21no—
78C2×C4⋊Dic43—21no—
79C2×C4⋊Dic43C2×C412yes—
80C2×C4⋊Dic43C2×C412yescomplemented
81C2×C4⋊Dic43D412yes—
82C2×Dic43⋊C4—22no—
83C4⋊C4×D43—24no—
84C4⋊C4×D43—24no—
85C2×(C2×D43)⋊C4—22no—
86C2×C4×Dic43—22no—
87#13063253—28no—
88#13063250—24no—
89#13063247—24no—
90C43⋊#95—44no—
91C23×C4×C43—21no—
92C23×C4×C43C2311yescharacteristic
93C2×M16×C43—21no—
94C2×M16×C43—21no—
95C2×M16×C43—21no—
96C2×M16×C43—21no—
97C2×M16×C43—21no—
98C2×M16×C43C2×C412yescomplemented
99C22×C8×C43—21no—
100#117×C43—21no—
101#117×C43—21no—
102#117×C43C2×C412yes—
103#117×C43D412yes—
104C2×C4⋊C4×C43D411yescharacteristic
105C2×C4⋊C4×C43D411yescharacteristic
106C2×C22⋊C4×C43—21no—
107C2×C42×C43—21no—
108C2×C42×C43—21no—
109C2×C42×C43—21no—
110C2×C42×C43—21no—
111C2×C42×C43—21no—
112C2×C42×C43—21no—
113C2×C42×C43C2×C412yescomplemented
114C24×C43C2×D411yescharacteristic
115C23×D43—21no—
116C22×C4×C43—22no—
117C22×C4×C43—22no—
118C22×C4×C43—22no—
119C22×C4×C43—21no—
120C22×C4×C43—21no—
121C22×C4×C43—41no—
122C22×C4×C43—41no—
123C22×C4×C43—41no—
124C22×C4×C43—41no—
125C22×C4×C43C22×C411yescharacteristic
126C22×C4×C43C22×C411yescharacteristic
127C22×C4×C43C22×C411yescharacteristic
128C22×C4×C43C2×D411yescharacteristic
129C22×C4×C43C2×D411yescharacteristic
130C22×C4×C43C2×D411yescharacteristic
131C22×C4×C43C2×D411yescharacteristic
132C22×C4×C43C2×D411yescharacteristic
133C22×C4×C43C2×D411yescharacteristic
134C22×C4×C43C2×Q811yescharacteristic
135C22×C4×C43#4111yescharacteristic
136C22×C4×C43#4111yescharacteristic
137C22×C4×C43#4111yescharacteristic
138C22×C4×C43#4111yescharacteristic
139C2×C22⋊D43—22no—
140C2×C22⋊D43—22no—
141C2×C22⋊D43—22no—
142C2×C22⋊D43—22no—
143C2×C22⋊D43—22no—
144C2×C22⋊D43—22no—
145C22×Dic43—22no—
146C22×Dic43—21no—
147C22×Dic43—22no—
148C22×Dic43—22no—
149C22×Dic43—42no—
150C22×Dic43—42no—
151C22×Dic43—42no—
152C22×Dic43—42no—
153C22×Dic43—41no—
154C22×Dic43—41no—
155C22×Dic43C22⋊C414yes—
156#10621898—22no—
157#10621898—22no—
158#10621898—22no—
159#10621898—22no—
160#10621898—22no—
161#10621898—22no—
162#10621898—22no—
163#10621898—22no—
164#10621898—22no—
165#10621898—22no—
166#10621898—22no—
167#10621898—22no—
168#10621898C4214yes—
169#10621898C22⋊C414yes—
170#10621898C4⋊C414yes—
171#10621898C4⋊C414yes—
172C2×D172—21no—
173C2×D172—21no—
174C2×D172—21no—
175C2×D172C22⋊C412yes—
176C2×D172C22⋊C412yes—
177C2×D172C4⋊C412yes—
178C2×C4×D43—22no—
179C2×C4×D43—22no—
180C2×C4×D43—22no—
181C2×C4×D43—22no—
182C2×C4×D43—22no—
183C2×C4×D43—22no—
184C2×C4×D43—28no—
185C2×C4×D43—82no—
186C2×C4×D43—82no—
187C2×Dic86—21no—
188C2×Dic86—21no—
189C2×Dic86—21no—
190C2×Dic86C22⋊C412yes—
191C2×Dic86C22⋊C412yes—
192C2×Dic86C4⋊C412yes—
193M16×C43—22no—
194M16×C43—22no—
195M16×C43—41no—
196M16×C43—41no—
197C2×C8×C43—22no—
198C2×C8×C43—41no—
199C2×C8×C43—41no—
200C4⋊C4×C43—21no—
201C4⋊C4×C43—21no—
202C4⋊C4×C43C22⋊C412yes—
203C4⋊C4×C43C22⋊C412yes—
204C22⋊C4×C43—22no—
205C22⋊C4×C43—22no—
206C42×C43—22no—
207C42×C43—22no—
208C42×C43—22no—
209C42×C43—22no—
210C42×C43—41no—
211C42×C43—41no—
212(C2×D43)⋊C4—28no—
213C4⋊Dic43—22no—
214C4⋊Dic43—22no—
215C4⋊Dic43—22no—
216C4⋊Dic43—22no—
217C4⋊Dic43—22no—
218C4⋊Dic43—22no—
219C4⋊Dic43—41no—
220C4⋊Dic43—41no—
221Dic43⋊C4—28no—
222C4×Dic43—28no—
223#10621877—22no—
224#10621877—22no—
225#10621877—41no—
226#10621877—41no—
227C2×C43⋊C8—22no—
228C2×C43⋊C8—41no—
229C2×C43⋊C8—41no—
230C23×C43—21no—
231C23×C43—21no—
232C23×C43—21no—
233C23×C43—21no—
234C23×C43C2×C22⋊C411yescharacteristic
235C23×C43C4×D411yescharacteristic
236C23×C43C4×D411yescharacteristic
237C23×C43#12011yescharacteristic
238C23×C43#12011yescharacteristic
239C23×C43#12111yescharacteristic
240C23×C43C22⋊Q811yescharacteristic
241C22×D43—22no—
242C22×D43—22no—
243C22×D43—22no—
244C22×D43—41no—
245C22×D43—41no—
246C22×D43—41no—
247C22×D43—41no—
248C2×C4×C43—24no—
249C2×C4×C43—22no—
250C2×C4×C43—22no—
251C2×C4×C43—42no—
252C2×C4×C43—42no—
253C2×C4×C43—42no—
254C2×C4×C43—42no—
255C2×C4×C43—42no—
256C2×C4×C43—42no—
257C2×C4×C43—41no—
258C2×C4×C43—41no—
259C2×C4×C43—41no—
260C2×C4×C43—41no—
261C2×C4×C43C2×C4211yescharacteristic
262C2×C4×C43C2×C22⋊C411yescharacteristic
263C2×C4×C43C2×C22⋊C411yescharacteristic
264C2×C4×C43C2×C22⋊C411yescharacteristic
265C2×C4×C43C2×C22⋊C411yescharacteristic
266C2×C4×C43C2×C4⋊C411yescharacteristic
267C2×C4×C43C2×C4⋊C411yescharacteristic
268C2×C4×C43C2×C4⋊C411yescharacteristic
269C2×C4×C43#11711yescharacteristic
270C2×C4×C43#11711yescharacteristic
271C2×C4×C43C4×D411yescharacteristic
272C2×C4×C43C4×D411yescharacteristic
273C2×C4×C43C4×D411yescharacteristic
274C2×C4×C43C4×D411yescharacteristic
275C2×C4×C43C4×D411yescharacteristic
276C2×C4×C43C4×D411yescharacteristic
277C2×C4×C43#12011yescharacteristic
278C2×C4×C43#12011yescharacteristic
279C2×C4×C43#12111yescharacteristic
280C2×C4×C43#12111yescharacteristic
281C2×C4×C43#12111yescharacteristic
282C2×C4×C43C22⋊Q811yescharacteristic
283C2×C4×C43C22⋊Q811yescharacteristic
284C2×C4×C43C22⋊Q811yescharacteristic
285C2×C4×C43#12311yescharacteristic
286C2×C4×C43#12311yescharacteristic
287C2×C4×C43#12311yescharacteristic
288C2×C4×C43#12311yescharacteristic
289C22⋊D43—24no—
290C22⋊D43—24no—
291C22⋊D43—24no—
292C22⋊D43—24no—
293C2×Dic43—22no—
294C2×Dic43—22no—
295C2×Dic43—22no—
296C2×Dic43—24no—
297C2×Dic43—42no—
298C2×Dic43—42no—
299C2×Dic43—44no—
300C2×Dic43—44no—
301C2×Dic43—42no—
302C2×Dic43—82no—
303C2×Dic43—82no—
304C2×Dic43—81no—
305C2×Dic43—81no—
306D172—22no—
307D172—22no—
308D172—22no—
309D172#9514yescomplemented
310C4×D43—24no—
311C4×D43—24no—
312C4×D43—24no—
313C4×D43—24no—
314C4×D43—88no—
315Dic86—22no—
316Dic86—22no—
317Dic86—22no—
318Dic86#9514yescomplemented
319C8×C43—42no—
320C43⋊C8—42no—
321#10781—431nomaximal, Sylow
322C22×C43—21no—
323C22×C43—21no—
324C22×C43—21no—
325C22×C43—21no—
326C22×C43—21no—
327C22×C43—21no—
328C22×C43—21no—
329C22×C43—21no—
330C22×C43—21no—
331C22×C43—21no—
332C22×C43—21no—
333C22×C43—21no—
334C22×C43C4×C22⋊C411yescharacteristic
335C22×C43#37911yescharacteristic
336C22×C43#38011yescharacteristic
337C22×C43#38511yescharacteristic
338C22×C43#38511yescharacteristic
339C22×C43#38611yescharacteristic
340C22×C43#38611yescharacteristic
341C22×C43#45311yescharacteristic
342C22×C43#45411yescharacteristic
343C22×C43#45511yescharacteristic
344C22×C43#45611yescharacteristic
345C2×D43—24no—
346C2×D43—42no—
347C2×D43—42no—
348C2×D43—42no—
349C2×D43—42no—
350C2×D43—42no—
351C2×D43—42no—
352C4×C43—44no—
353C4×C43—42no—
354C4×C43—42no—
355C4×C43C2×#9511yescharacteristic
356C4×C43C4×C22⋊C411yescharacteristic
357C4×C43#38011yescharacteristic
358C4×C43#38111yescharacteristic
359C4×C43#38511yescharacteristic
360C4×C43#38511yescharacteristic
361C4×C43#38611yescharacteristic
362C4×C43#38611yescharacteristic
363Dic43—24no—
364Dic43—44no—
365Dic43—82no—
366C2×#520—431no—
367C22×#104—431no—
368C2×#417—431no—
369C2×#343—431no—
370#1736—431no—
371C2×#339D4311yescharacteristic, complemented
372C4⋊#95—431no—
373C2×C43—21no—
374C2×C43—21no—
375C2×C43—21no—
376C2×C43—21no—
377C2×C43C22⋊#9511yescharacteristic
378C2×C43#179211yescharacteristic
379C2×C43#179311yescharacteristic
380C2×C43#185911yescharacteristic
381C2×C43#186011yescharacteristic
382C2×C43#188211yescharacteristic
383C2×C43#188311yescharacteristic
384D43—44no—
385C22×#41—431no—
386C22×M16—431no—
387C22×M16C2×D4311yescharacteristic
388#520—434no—
389#520—862no—
390#520—862no—
391#520—862no—
392C2×C4×Q8—861no—
393C2×C4×D4—861no—
394C2×C4×D4—862no—
395C2×#117—861no—
396C2×#117C2×D4311yescharacteristic
397C22×C4⋊C4—431no—
398C22×C4⋊C4—431no—
399C22×C4⋊C4—861no—
400C22×C42C2×D4311yescharacteristic
401C2×#104—434no—
402C2×#104—862no—
403C2×#104—862no—
404#417—434no—
405#417—862no—
406C2×#103—861no—
407C2×#102—861no—
408C2×#95—862no—
409#343—862no—
410#340—861no—
411#340—861no—
412#339—22no—
413C43#1078111yescharacteristic, complemented, Sylow
414C2×#41—432no—
415C2×#41—432no—
416C2×#41—432no—
417C2×#41—432no—
418C2×#41—432no—
419C2×#41—432no—
420C2×#41—861no—
421C2×#41—861no—
422C2×#41—861no—
423C2×#41—861no—
424C2×#41—861no—
425C2×#41—861no—
426C22×Q8—431no—
427C22×D4—431no—
428C22×D4—861no—
429C23×C4—21no—
430C23×C4—432no—
431C23×C4—862no—
432C23×C4—861no—
433C23×C4—861no—
434C23×C4C22×D4311yescharacteristic
435C2×M16—21no—
436C2×M16—21no—
437C2×M16—21no—
438C2×M16—21no—
439C2×M16—21no—
440C2×M16—432no—
441C2×M16—861no—
442C2×M16—861no—
443C2×M16—861no—
444C2×M16—861no—
445C2×M16—861no—
446C2×M16C4×D4312yescomplemented
447C22×C8—21no—
448C22×C8—861no—
449C4×Q8—864no—
450C4×Q8—864no—
451C4×D4—864no—
452C4×D4—864no—
453C4×D4—868no—
454C4×D4—868no—
455#117—21no—
456#117—21no—
457#117—864no—
458#117—864no—
459#117C4×D4312yes—
460#117C22⋊D4312yes—
461C2×C4⋊C4—432no—
462C2×C4⋊C4—432no—
463C2×C4⋊C4—432no—
464C2×C4⋊C4—864no—
465C2×C4⋊C4—862no—
466C2×C4⋊C4—861no—
467C2×C4⋊C4—861no—
468C2×C4⋊C4—861no—
469C2×C4⋊C4—861no—
470C2×C4⋊C4—864no—
471C2×C4⋊C4—861no—
472C2×C4⋊C4—861no—
473C2×C4⋊C4—861no—
474C2×C4⋊C4—861no—
475C2×C4⋊C4—861no—
476C2×C4⋊C4D17211yescharacteristic
477C2×C4⋊C4D17211yescharacteristic
478C2×C22⋊C4—21no—
479C2×C22⋊C4—862no—
480C2×C42—21no—
481C2×C42—21no—
482C2×C42—21no—
483C2×C42—21no—
484C2×C42—21no—
485C2×C42—21no—
486C2×C42—862no—
487C2×C42C4×D4312yescomplemented
488#104—868no—
489#103—864no—
490#102—864no—
491#95—1724no—
492C24—861no—
493C24D4×D4311yescharacteristic
494#41—434no—
495#41—434no—
496#41—434no—
497#41—434no—
498#41—862no—
499#41—862no—
500#41—862no—
501#41—862no—
502#41—862no—
503#41—862no—
504#41—862no—
505#41—862no—
506#41—862no—
507#41—862no—
508#41—862no—
509#41—862no—
510C2×Q8—432no—
511C2×Q8—432no—
512C2×Q8—432no—
513C2×Q8—861no—
514C2×Q8—861no—
515C2×Q8—861no—
516C2×D4—432no—
517C2×D4—432no—
518C2×D4—432no—
519C2×D4—862no—
520C2×D4—862no—
521C2×D4—862no—
522C2×D4—862no—
523C2×D4—862no—
524C2×D4—862no—
525C2×D4—861no—
526C2×D4—861no—
527C2×D4—861no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—41no—
534C22×C4—41no—
535C22×C4—41no—
536C22×C4—41no—
537C22×C4—434no—
538C22×C4—868no—
539C22×C4—861no—
540C22×C4—862no—
541C22×C4—862no—
542C22×C4—862no—
543C22×C4—862no—
544C22×C4—862no—
545C22×C4—862no—
546C22×C4—862no—
547C22×C4—862no—
548C22×C4—862no—
549C22×C4—3442no—
550C22×C4—3442no—
551C22×C4—1722no—
552C22×C4—1722no—
553C22×C4—1721no—
554C22×C4—1721no—
555C22×C4—1722no—
556C22×C4—1722no—
557C22×C4C2×C4×D4311yescharacteristic
558C22×C4C2×C4×D4311yescharacteristic
559C22×C4C2×C4×D4311yescharacteristic
560C22×C4C2×D17211yescharacteristic
561C22×C4#1062189811yescharacteristic
562C22×C4#1062189811yescharacteristic
563C22×C4D4×D4311yescharacteristic
564C22×C4D4×D4311yescharacteristic
565C22×C4D4×D4311yescharacteristic
566C22×C4D4×D4311yescharacteristic
567C22×C4#1062190011yescharacteristic
568C22×C4Q8×D4311yescharacteristic
569C22×C4#1062190211yescharacteristic
570C22×C4C2×C22⋊D4311yescharacteristic
571M16—22no—
572M16—22no—
573M16—41no—
574M16—41no—
575M16—862no—
576M16—862no—
577M16—1721no—
578M16—1721no—
579C2×C8—22no—
580C2×C8—41no—
581C2×C8—41no—
582C2×C8—862no—
583C2×C8—1721no—
584C2×C8—1721no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—868no—
588C4⋊C4—862no—
589C4⋊C4—862no—
590C4⋊C4—862no—
591C4⋊C4—862no—
592C4⋊C4—862no—
593C4⋊C4—862no—
594C4⋊C4—1721no—
595C4⋊C4—1721no—
596C4⋊C4(C2×D43)⋊C412yes—
597C4⋊C4(C2×D43)⋊C412yes—
598C22⋊C4—22no—
599C22⋊C4—22no—
600C22⋊C4—868no—
601C42—22no—
602C42—22no—
603C42—22no—
604C42—22no—
605C42—41no—
606C42—41no—
607C42—868no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23—21no—
612C23—862no—
613C23—862no—
614C23—862no—
615C23—1721no—
616C23—1721no—
617C23—1721no—
618C23—1721no—
619C23C22⋊C4×D4311yescharacteristic
620C23(C22⋊D43)⋊C411yescharacteristic
621C23#1306328711yescharacteristic
622C23#1306329311yescharacteristic
623C23#1306329511yescharacteristic
624C23#1306329811yescharacteristic
625C23#1306330311yescharacteristic
626Q8—434no—
627Q8—862no—
628Q8—862no—
629Q8—862no—
630D4—434no—
631D4—864no—
632D4—864no—
633D4—864no—
634D4—864no—
635D4—862no—
636D4—862no—
637D4—862no—
638C2×C4—24no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—42no—
642C2×C4—42no—
643C2×C4—42no—
644C2×C4—42no—
645C2×C4—42no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—42no—
651C2×C4—862no—
652C2×C4—862no—
653C2×C4—862no—
654C2×C4—864no—
655C2×C4—864no—
656C2×C4—864no—
657C2×C4—864no—
658C2×C4—864no—
659C2×C4—3448no—
660C2×C4—3442no—
661C2×C4—3441no—
662C2×C4—3441no—
663C2×C4—3442no—
664C2×C4—1724no—
665C2×C4—1722no—
666C2×C4—1722no—
667C2×C4—1722no—
668C2×C4—1724no—
669C2×C4C42×D4311yescharacteristic
670C2×C4C22⋊C4×D4311yescharacteristic
671C2×C4C22⋊C4×D4311yescharacteristic
672C2×C4C22⋊C4×D4311yescharacteristic
673C2×C4C2×(C2×D43)⋊C411yescharacteristic
674C2×C4C4⋊C4×D4311yescharacteristic
675C2×C4C4⋊C4×D4311yescharacteristic
676C2×C4C4⋊C4×D4311yescharacteristic
677C2×C4#1306328211yescharacteristic
678C2×C4#1306328311yescharacteristic
679C2×C4(C22⋊D43)⋊C411yescharacteristic
680C2×C4C4×C22⋊D4311yescharacteristic
681C2×C4C4×C22⋊D4311yescharacteristic
682C2×C4#1306328711yescharacteristic
683C2×C4C4×D17211yescharacteristic
684C2×C4C4×D17211yescharacteristic
685C2×C4#1306329311yescharacteristic
686C2×C4#1306329511yescharacteristic
687C2×C4#1306329611yescharacteristic
688C2×C4#1306329811yescharacteristic
689C2×C4#1306330011yescharacteristic
690C2×C4#1306330111yescharacteristic
691C2×C4#1306330311yescharacteristic
692C2×C4#1306330511yescharacteristic
693C2×C4#1306330711yescharacteristic
694C2×C4#1306330711yescharacteristic
695C2×C4#1306331011yescharacteristic
696C2×C4#1306331011yescharacteristic
697C8—42no—
698C8—1722no—
699C22—21no—
700C22—21no—
701C22—21no—
702C22—21no—
703C22—21no—
704C22—21no—
705C22—21no—
706C22—21no—
707C22—21no—
708C22—21no—
709C22—21no—
710C22—21no—
711C22—864no—
712C22—1722no—
713C22—1722no—
714C22—1722no—
715C22—1722no—
716C22—1722no—
717C22—1722no—
718C22#1458274611yescharacteristic
719C22#1458275411yescharacteristic
720C22#1458275811yescharacteristic
721C22#1458277011yescharacteristic
722C22#1458277311yescharacteristic
723C22#1458277511yescharacteristic
724C22#1458277711yescharacteristic
725C22#1458306811yescharacteristic
726C22#1458307311yescharacteristic
727C22#1458307811yescharacteristic
728C22#1458308311yescharacteristic
729C4—44no—
730C4—42no—
731C4—42no—
732C4—864no—
733C4—3442no—
734C4—1724no—
735C4#95×D4311yescharacteristic
736C4C4×(C2×D43)⋊C411yescharacteristic
737C4#1458275611yescharacteristic
738C4#1458276111yescharacteristic
739C4#1458277011yescharacteristic
740C4#1458277311yescharacteristic
741C4#1458277511yescharacteristic
742C4#1458277711yescharacteristic
743C2—21no—
744C2—21no—
745C2—21no—
746C2—21no—
747C2—1724no—
748C2(C2×D43)⋊#9511yescharacteristic
749C2#1913455011yescharacteristic
750C2#1913455511yescharacteristic
751C2#1913482211yescharacteristic
752C2#1913482911yescharacteristic
753C2#1913496511yescharacteristic
754C2#1913497211yescharacteristic
subgroupG/H
centerC23#13063295
commutatorC2×C4×C43C2×C42
FrattiniC23×C4C22×D43
FittingC2×C43×#339C2
socleC23×C43#120
prime radicalC22×#10621898C22
cosocleC23×C4×C43C23
hypercenterC2×#339D43
hypocenterC43#10781
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#339

Complements

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

NH ≅ G/Ntype
4. C2×#14582667C2semidirect
5. #19134316C2semidirect
6. #19132825C2semidirect
7. C2×C43×#339C2semidirect
13. #14583379C4semidirect
23. C2×#13063253C4semidirect
25. #14582901C4semidirect
60. C2×#10621877C2×C4semidirect
80. C2×C4⋊Dic43C2×C4semidirect
98. C2×M16×C43C2×C4semidirect
113. C2×C42×C43C2×C4semidirect
309. D172#95semidirect
318. Dic86#95semidirect
371. C2×#339D43semidirect
413. C43#10781semidirect
446. C2×M16C4×D43semidirect
487. C2×C42C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145833792
C22×#130632532
C2×#145829012
C2×#145826672
#191343162
#191328252
C2×C43×#3392
#1078143