Finite Group Databasebeta

← #25116869

Subgroups — #25116869

Order 11008.

1170 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583038C211yesmaximal, characteristic
2C2×#14583002C211yesmaximal, characteristic, complemented
3#19137611C211yesmaximal, characteristic
4Q8×C22⋊Dic43C211yesmaximal, characteristic, complemented
5#19135473C211yesmaximal, characteristic, complemented
6#19135282C211yesmaximal, characteristic, complemented
7#19135239C211yesmaximal, characteristic, complemented
8#19135023C211yesmaximal, characteristic
9#19134948C211yesmaximal, characteristic, complemented
10#19134926C211yesmaximal, characteristic, complemented
11#19134847C211yesmaximal, characteristic, complemented
12#19134783C211yesmaximal, characteristic, complemented
13#19134427C211yesmaximal, characteristic, complemented
14#19134371C211yesmaximal, characteristic, complemented
15C22×#103×C43C211yesmaximal, characteristic, complemented
16C22×#10621884C2211yescharacteristic
17C22×#10621884C2211yescharacteristic
18C2×#13063299C2211yescharacteristic
19C2×Q8×Dic43C2211yescharacteristic
20C2×Q8×Dic43C2211yescharacteristic
21C2×#13063287C2211yescharacteristic
22C2×C4×C22⋊D43—21no—
23#14583038C418yescomplemented
24#14583002—24no—
25C2×#13063258C2211yescharacteristic
26C2×#13063258C2211yescharacteristic
27C2×#13063249C2211yescharacteristic
28C2×#13063249C2211yescharacteristic
29C2×#13063247C2211yescharacteristic
30C2×#13063247C2211yescharacteristic
31C2×C22⋊(C43⋊C8)C2211yescharacteristic
32C2×#13063235C2211yescharacteristic
33C2×#13063235C2211yescharacteristic
34#14582806—21no—
35#14582806—21no—
36#14582806C2211yescharacteristic
37#14582806C2211yescharacteristic
38#14582800C2211yescharacteristic
39#14582795C2211yescharacteristic
40#14582789—21no—
41#14582778—21no—
42#14582770—21no—
43#14582759—21no—
44#14582759C2211yescharacteristic
45C4⋊C4×Dic43C2211yescharacteristic
46C4×C22⋊Dic43—21no—
47C4×C22⋊Dic43C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582653C2211yescharacteristic
53#14582653C2211yescharacteristic
54C23×Q8×C43C2211yescharacteristic
55C23×C8×C43C2211yescharacteristic
56C22×C4⋊C4×C43C2211yescharacteristic
57C2×#103×C43—24no—
58C2×#103×C43C2211yescharacteristic
59C2×#103×C43C2211yescharacteristic
60C2×#103×C43C2211yescharacteristic
61C2×#103×C43C2211yescharacteristic
62C22×D172C2311yescharacteristic
63C22×C22⋊D43—21no—
64C22×C4×D43—21no—
65C2×#10621884—22no—
66C2×#10621884—22no—
67C2×#10621884—41no—
68C2×#10621884—41no—
69C2×#10621884C2×C414yescomplemented
70C2×#10621884C2×C414yescomplemented
71C22×C43⋊C8C2311yescharacteristic
72C22×C43⋊C8C2311yescharacteristic
73#13063299—22no—
74#13063299C2×C414yes—
75Q8×Dic43—22no—
76Q8×Dic43—22no—
77Q8×Dic43—41no—
78Q8×Dic43—41no—
79#13063287—22no—
80#13063287—41no—
81C4×C22⋊D43—44no—
82C2×C4⋊Dic43—21no—
83C2×C4⋊Dic43—21no—
84C2×C4⋊Dic43C2311yescharacteristic
85C2×C4⋊Dic43C2311yescharacteristic
86C2×C4⋊Dic43C2311yescharacteristic
87C2×Dic43⋊C4—21no—
88C2×C22⋊Dic43—21no—
89C2×C22⋊Dic43D411yescharacteristic
90C2×C22⋊Dic43D411yescharacteristic
91C2×(C2×D43)⋊C4—21no—
92C2×(C2×D43)⋊C4—21no—
93C2×(C2×D43)⋊C4—21no—
94C2×(C2×D43)⋊C4—21no—
95C2×C4×Dic43—21no—
96C2×C4×Dic43—21no—
97C2×C4×Dic43—21no—
98C2×C4×Dic43C2311yescharacteristic
99C2×C4×Dic43C2311yescharacteristic
100#13063258—22no—
101#13063258—41no—
102#13063249C2×C414yescomplemented
103#13063249C2×C414yescomplemented
104#13063247—22no—
105#13063247—41no—
106C22⋊(C43⋊C8)C2×C414yescomplemented
107#13063235—22no—
108#13063235—41no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C43⋊#95—21no—
114C43⋊#95—21no—
115C43⋊#95—21no—
116C43⋊#95D411yescharacteristic
117C43⋊#95D411yescharacteristic
118C22×Q8×C43—21no—
119C22×Q8×C43—22no—
120C22×Q8×C43—22no—
121C22×Q8×C43—22no—
122C22×Q8×C43—41no—
123C22×Q8×C43—41no—
124C22×Q8×C43C2×C414yescomplemented
125C22×Q8×C43C2311yescharacteristic
126C22×Q8×C43C2311yescharacteristic
127C23×C4×C43—21no—
128C23×C4×C43—21no—
129C23×C4×C43C2311yescharacteristic
130C22×C8×C43—22no—
131C22×C8×C43—22no—
132C22×C8×C43—41no—
133C22×C8×C43C2311yescharacteristic
134C22×C8×C43C2311yescharacteristic
135C2×C4⋊C4×C43—22no—
136C2×C4⋊C4×C43—21no—
137C2×C4⋊C4×C43—41no—
138C2×C4⋊C4×C43C2311yescharacteristic
139C2×C4⋊C4×C43C2311yescharacteristic
140#103×C43—22no—
141#103×C43—22no—
142#103×C43—22no—
143#103×C43D414yescomplemented
144C24×C43C2×D411yescharacteristic
145C23×D43—21no—
146C2×Q8×C43—24no—
147C2×Q8×C43—21no—
148C2×Q8×C43—21no—
149C2×Q8×C43—21no—
150C2×Q8×C43—21no—
151C2×Q8×C43—28no—
152C2×Q8×C43—21no—
153C2×Q8×C43—21no—
154C2×Q8×C43—21no—
155C2×Q8×C43—21no—
156C2×Q8×C43—42no—
157C2×Q8×C43—42no—
158C2×Q8×C43—44no—
159C2×Q8×C43—44no—
160C2×Q8×C43—44no—
161C2×Q8×C43C22×C412yes—
162C2×Q8×C43C22×C412yes—
163C2×Q8×C43C2×D412yes—
164C2×Q8×C43#4112yes—
165C22×C4×C43—21no—
166C22×C4×C43—21no—
167C22×C4×C43—21no—
168C22×C4×C43—21no—
169C22×C4×C43—24no—
170C22×C4×C43—21no—
171C22×C4×C43—21no—
172C22×C4×C43—21no—
173C22×C4×C43—21no—
174C22×C4×C43—42no—
175C22×C4×C43—42no—
176C22×C4×C43—42no—
177C22×C4×C43—42no—
178C22×C4×C43—81no—
179C22×C4×C43C22×C412yes—
180C22×C4×C43C2×D411yescharacteristic
181C22×C4×C43#4112yes—
182C22×C4×C43C2411yescharacteristic
183C2×C22⋊D43—24no—
184C2×C22⋊D43—42no—
185C2×C22⋊D43—42no—
186C22×Dic43—21no—
187C22×Dic43—21no—
188C22×Dic43—21no—
189C22×Dic43C2×D411yescharacteristic
190C22×Dic43C2×D411yescharacteristic
191C22×Dic43C2×D411yescharacteristic
192C22×Dic43C2×D411yescharacteristic
193C2×D172—21no—
194C2×D172—21no—
195C2×D172—21no—
196C2×D172—21no—
197C2×D172—21no—
198C2×D172C22×C412yes—
199C2×C4×D43—42no—
200C2×C4×D43—42no—
201C2×C4×D43—81no—
202C2×C8×C43—21no—
203C2×C8×C43—21no—
204C2×C8×C43—21no—
205C2×C8×C43—21no—
206C2×C8×C43—21no—
207C2×C8×C43—44no—
208C2×C8×C43C2×D412yes—
209C4⋊C4×C43—21no—
210C4⋊C4×C43—21no—
211C4⋊C4×C43—21no—
212C4⋊C4×C43—42no—
213C4⋊C4×C43C2×D412yes—
214C22⋊Dic43—22no—
215C22⋊Dic43—22no—
216C22⋊Dic43—42no—
217#10621884—28no—
218#10621884—44no—
219(C2×D43)⋊C4—24no—
220(C2×D43)⋊C4—42no—
221(C2×D43)⋊C4—42no—
222(C2×D43)⋊C4—81no—
223C4⋊Dic43—21no—
224C4⋊Dic43—21no—
225C4⋊Dic43—21no—
226C4⋊Dic43—21no—
227C4⋊Dic43—21no—
228C4⋊Dic43—42no—
229C4⋊Dic43—42no—
230C4⋊Dic43C22×C412yes—
231Dic43⋊C4—42no—
232C4×Dic43—21no—
233C4×Dic43—21no—
234C4×Dic43—21no—
235C4×Dic43—21no—
236C4×Dic43—42no—
237C4×Dic43—42no—
238C4×Dic43—42no—
239C2×C43⋊C8—21no—
240C2×C43⋊C8—21no—
241C2×C43⋊C8—21no—
242C2×C43⋊C8—21no—
243C2×C43⋊C8C22×C412yes—
244C2×C43⋊C8C22×C412yes—
245C23×C43—21no—
246C23×C43—21no—
247C23×C43—21no—
248C23×C43—21no—
249C23×C43C4×D412yes—
250C23×C43AGL(1,ℤ/8)12yes—
251C23×C43#13712yes—
252C23×C43C22×D411yescharacteristic
253C22×D43—22no—
254C22×D43—41no—
255C22×D43—41no—
256C22×D43—41no—
257C22×D43—41no—
258C22×D43—41no—
259C22×D43—41no—
260Q8×C43—22no—
261Q8×C43—22no—
262Q8×C43—22no—
263Q8×C43—22no—
264Q8×C43—22no—
265Q8×C43—48no—
266Q8×C43—41no—
267Q8×C43—41no—
268Q8×C43C4×D414yescomplemented
269C2×C4×C43—22no—
270C2×C4×C43—22no—
271C2×C4×C43—21no—
272C2×C4×C43—22no—
273C2×C4×C43—21no—
274C2×C4×C43—22no—
275C2×C4×C43—22no—
276C2×C4×C43—22no—
277C2×C4×C43—22no—
278C2×C4×C43—22no—
279C2×C4×C43—22no—
280C2×C4×C43—48no—
281C2×C4×C43—41no—
282C2×C4×C43—41no—
283C2×C4×C43—41no—
284C2×C4×C43—41no—
285C2×C4×C43—41no—
286C2×C4×C43—41no—
287C2×C4×C43—41no—
288C2×C4×C43—84no—
289C2×C4×C43C4×D412yes—
290C2×C4×C43C23×C411yescharacteristic
291C2×C4×C43C22×D411yescharacteristic
292C2×C4×C43C2×#4111yescharacteristic
293C2×C4×C43C2×#4111yescharacteristic
294C2×C4×C43H(5,𝔽2)11yescharacteristic
295C2×C4×C43H(5,𝔽2)11yescharacteristic
296C22⋊D43—48no—
297C2×Dic43—22no—
298C2×Dic43—21no—
299C2×Dic43—21no—
300C2×Dic43—21no—
301C2×Dic43—21no—
302C2×Dic43—21no—
303C2×Dic43—21no—
304C2×Dic43—21no—
305C2×Dic43—21no—
306C2×Dic43—21no—
307C2×Dic43—21no—
308C2×Dic43—21no—
309C2×Dic43—21no—
310C2×Dic43—41no—
311C2×Dic43—41no—
312C2×Dic43—41no—
313C2×Dic43—41no—
314C2×Dic43—41no—
315C2×Dic43—41no—
316C2×Dic43—41no—
317C2×Dic43—41no—
318D172—22no—
319D172—22no—
320D172—41no—
321D172—41no—
322C4×D43—84no—
323C8×C43—22no—
324C8×C43—41no—
325C43⋊C8—22no—
326C43⋊C8—22no—
327#22855—431nomaximal, Sylow
328C22×C43—22no—
329C22×C43—22no—
330C22×C43—22no—
331C22×C43—22no—
332C22×C43—22no—
333C22×C43—22no—
334C22×C43#44014yescomplemented
335C22×C43C2×C4×D411yescharacteristic
336C22×C43D4211yescharacteristic
337C22×C43#54611yescharacteristic
338C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
339C22×C43C2×#13711yescharacteristic
340C22×C43#57711yescharacteristic
341C22×C43#57811yescharacteristic
342C2×D43—42no—
343C2×D43—42no—
344C2×D43—42no—
345C2×D43—81no—
346C2×D43—81no—
347C2×D43—81no—
348C2×D43—81no—
349C4×C43—22no—
350C4×C43—24no—
351C4×C43—42no—
352C4×C43—42no—
353C4×C43—81no—
354C4×C43C2×C4×D411yescharacteristic
355C4×C43#51811yescharacteristic
356C4×C43#54611yescharacteristic
357C4×C43#55111yescharacteristic
358Dic43—42no—
359Dic43—41no—
360Dic43—41no—
361Dic43—41no—
362Dic43—41no—
363Dic43—81no—
364Dic43—81no—
365C2×#448—431no—
366C2×#440—431no—
367C22×#103D4311yescharacteristic, complemented
368#2361—431no—
369Q8×C22⋊C4—431no—
370#1973—431no—
371#1935—431no—
372#1928—431no—
373#1893—431no—
374#1880—431no—
375#1877—431no—
376#1863—431no—
377#1852—431no—
378#1763—431no—
379#1752—431no—
380C2×C43—24no—
381C2×C43#235811yescharacteristic
382C2×C43C2×#44011yescharacteristic
383C2×C43#294711yescharacteristic
384C2×C43#326511yescharacteristic
385C2×C43#327011yescharacteristic
386C2×C43#330811yescharacteristic
387C2×C43#332011yescharacteristic
388D43—82no—
389C23×Q8C2×D4311yescharacteristic
390C22×SD16—431no—
391C22×SD16—431no—
392C23×C8C2×D4311yescharacteristic
393C2×#121—431no—
394C2×C4×Q8—431no—
395C2×C4×Q8—431no—
396C2×C4×D4—431no—
397C2×C4×D4—861no—
398C22×C4⋊C4C2×D4311yescharacteristic
399#448—438no—
400#440—864no—
401C2×#107—431no—
402C2×#107—431no—
403C2×#103—24no—
404C2×#103—431no—
405C2×#103—431no—
406C2×#103C2×D4311yescharacteristic
407C2×#103C2×D4311yescharacteristic
408C2×#103C2×D4311yescharacteristic
409C2×#103C2×D4311yescharacteristic
410C2×#102—431no—
411C2×#102—431no—
412C2×C22⋊C8—431no—
413C2×#97—431no—
414C2×#97—431no—
415#391—431no—
416#391—431no—
417#391—861no—
418#391—861no—
419#390—431no—
420#389—431no—
421#388—861no—
422#386—861no—
423#385—861no—
424#380—431no—
425#380—861no—
426C4×C4⋊C4—431no—
427C4×C22⋊C4—431no—
428C4×C22⋊C4—861no—
429#340—431no—
430#340—431no—
431#340—431no—
432#340—431no—
433#336—431no—
434#336—431no—
435C43#2285511yescharacteristic, complemented, Sylow
436C22×Q8—21no—
437C22×Q8—22no—
438C22×Q8—22no—
439C22×Q8—22no—
440C22×Q8—41no—
441C22×Q8—41no—
442C22×Q8C4×D4314yescomplemented
443C22×Q8C22×D4311yescharacteristic
444C22×Q8C22×D4311yescharacteristic
445C22×D4—431no—
446C22×D4—861no—
447C23×C4—21no—
448C23×C4—21no—
449C23×C4—861no—
450C23×C4C22×D4311yescharacteristic
451C2×SD16—434no—
452C2×SD16—434no—
453C2×SD16—862no—
454C2×SD16—862no—
455C2×SD16—1721no—
456C2×SD16—1721no—
457C22×C8—22no—
458C22×C8—22no—
459C22×C8—41no—
460C22×C8—431no—
461C22×C8—431no—
462C22×C8C22×D4311yescharacteristic
463C22×C8C22×D4311yescharacteristic
464#121—434no—
465#121—862no—
466C4×Q8—862no—
467C4×Q8—862no—
468C4×Q8—1721no—
469C4×Q8—1721no—
470C4×D4—862no—
471C4×D4—1721no—
472C4×D4—1724no—
473C2×C4⋊C4—22no—
474C2×C4⋊C4—21no—
475C2×C4⋊C4—41no—
476C2×C4⋊C4—431no—
477C2×C4⋊C4—431no—
478C2×C4⋊C4—431no—
479C2×C4⋊C4—861no—
480C2×C4⋊C4—861no—
481C2×C4⋊C4—861no—
482C2×C4⋊C4C22×D4311yescharacteristic
483C2×C4⋊C4C22×D4311yescharacteristic
484C2×C22⋊C4—431no—
485C2×C22⋊C4—431no—
486C2×C22⋊C4—861no—
487C2×C22⋊C4—861no—
488C2×C22⋊C4—861no—
489C2×C22⋊C4—861no—
490C2×C22⋊C4—861no—
491C2×C42—431no—
492C2×C42—431no—
493C2×C42—861no—
494C2×C42—861no—
495C2×C42—861no—
496#107—862no—
497#107—1721no—
498#103—22no—
499#103—22no—
500#103—22no—
501#103—434no—
502#103—434no—
503#103C22⋊D4314yescomplemented
504#102—862no—
505#102—1721no—
506C22⋊C8—434no—
507#97—862no—
508#97—1721no—
509#95—431no—
510#95—431no—
511#95—861no—
512#95—861no—
513#95—861no—
514#95—861no—
515#95—861no—
516#95—861no—
517#95—861no—
518C24—861no—
519C24D4×D4311yescharacteristic
520C2×Q8—24no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—28no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—42no—
531C2×Q8—42no—
532C2×Q8—44no—
533C2×Q8—44no—
534C2×Q8—44no—
535C2×Q8C2×C4×D4312yes—
536C2×Q8C2×C4×D4312yes—
537C2×Q8#1062189812yes—
538C2×Q8C2×C22⋊D4312yes—
539C2×D4—432no—
540C2×D4—864no—
541C2×D4—861no—
542C2×D4—861no—
543C2×D4—861no—
544C2×D4—861no—
545C2×D4—861no—
546C2×D4—1722no—
547C2×D4—1722no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—24no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—42no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4—42no—
561C22×C4—81no—
562C22×C4—431no—
563C22×C4—431no—
564C22×C4—431no—
565C22×C4—431no—
566C22×C4—861no—
567C22×C4—861no—
568C22×C4—861no—
569C22×C4—3441no—
570C22×C4—1722no—
571C22×C4—1722no—
572C22×C4C2×C4×D4312yes—
573C22×C4D4×D4311yescharacteristic
574C22×C4#1062190012yes—
575C22×C4C23×D4311yescharacteristic
576SD16—868no—
577SD16—1724no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—44no—
584C2×C8—432no—
585C2×C8—432no—
586C2×C8—861no—
587C2×C8—861no—
588C2×C8—861no—
589C2×C8—861no—
590C2×C8C2×C22⋊D4312yes—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—42no—
595C4⋊C4—432no—
596C4⋊C4—861no—
597C4⋊C4—861no—
598C4⋊C4—861no—
599C4⋊C4—861no—
600C4⋊C4—861no—
601C4⋊C4—1722no—
602C4⋊C4—1722no—
603C4⋊C4—1722no—
604C4⋊C4C2×C22⋊D4312yes—
605C22⋊C4—862no—
606C22⋊C4—862no—
607C22⋊C4—864no—
608C22⋊C4—3441no—
609C22⋊C4—1722no—
610C22⋊C4—1722no—
611C22⋊C4—1722no—
612C42—861no—
613C42—861no—
614C42—861no—
615C42—861no—
616C42—1722no—
617C42—1722no—
618C42—1722no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—862no—
624C23—1721no—
625C23—1721no—
626C23—1721no—
627C23—1721no—
628C23—1721no—
629C23—1721no—
630C23(C22⋊D43)⋊C412yes—
631C23#1306335212yes—
632C23#1306335712yes—
633C23C2×D4×D4311yescharacteristic
634Q8—22no—
635Q8—22no—
636Q8—22no—
637Q8—22no—
638Q8—22no—
639Q8—48no—
640Q8—41no—
641Q8—41no—
642Q8C4×C22⋊D4314yescomplemented
643D4—862no—
644D4—862no—
645D4—1728no—
646D4—1721no—
647D4—1721no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—21no—
651C2×C4—22no—
652C2×C4—21no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—48no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—84no—
668C2×C4—862no—
669C2×C4—861no—
670C2×C4—861no—
671C2×C4—861no—
672C2×C4—861no—
673C2×C4—861no—
674C2×C4—861no—
675C2×C4—861no—
676C2×C4—861no—
677C2×C4—861no—
678C2×C4—861no—
679C2×C4—861no—
680C2×C4—861no—
681C2×C4—3444no—
682C2×C4—1721no—
683C2×C4—1721no—
684C2×C4—1721no—
685C2×C4—1721no—
686C2×C4—1721no—
687C2×C4—1721no—
688C2×C4—1721no—
689C2×C4—1721no—
690C2×C4(C22⋊D43)⋊C412yes—
691C2×C4C22×C4×D4311yescharacteristic
692C2×C4C22×C22⋊D4311yescharacteristic
693C2×C4C2×#1062190011yescharacteristic
694C2×C4C2×#1062189811yescharacteristic
695C2×C4#1306337011yescharacteristic
696C2×C4#1306337011yescharacteristic
697C8—22no—
698C8—41no—
699C8—862no—
700C8—862no—
701C22—22no—
702C22—22no—
703C22—22no—
704C22—22no—
705C22—22no—
706C22—22no—
707C22—3441no—
708C22—3441no—
709C22—3441no—
710C22—3441no—
711C22—1722no—
712C22—1722no—
713C22—1722no—
714C22#1458300214yescomplemented
715C22C2×(C22⋊D43)⋊C411yescharacteristic
716C22D4×C22⋊D4311yescharacteristic
717C22#1458353911yescharacteristic
718C22C2×#1306335211yescharacteristic
719C22C2×#1306335711yescharacteristic
720C22#1458370511yescharacteristic
721C22#1458371211yescharacteristic
722C4—22no—
723C4—24no—
724C4—42no—
725C4—42no—
726C4—81no—
727C4—3441no—
728C4—3441no—
729C4—1721no—
730C4—1721no—
731C4—1721no—
732C4—1721no—
733C4—1722no—
734C4C2×C4×C22⋊D4311yescharacteristic
735C4#1458337211yescharacteristic
736C4#1458354311yescharacteristic
737C4#1458357511yescharacteristic
738C2—24no—
739C2—3442no—
740C2#1913757411yescharacteristic
741C2C2×#1458300211yescharacteristic
742C2#1914343211yescharacteristic
743C2#1914609011yescharacteristic
744C2#1914616511yescharacteristic
745C2#1914658211yescharacteristic
746C2#1914676211yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC22×#103×C43C2
socleC23×C43C22×D4
prime radicalC2×#13063299C22
cosocleC22×C4×C43C24
hypercenterC22×#103D43
hypocenterC43#22855
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#103

Complements

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

NH ≅ G/Ntype
2. C2×#14583002C2semidirect
4. Q8×C22⋊Dic43C2semidirect
5. #19135473C2semidirect
6. #19135282C2semidirect
7. #19135239C2semidirect
9. #19134948C2semidirect
10. #19134926C2semidirect
11. #19134847C2semidirect
12. #19134783C2semidirect
13. #19134427C2semidirect
14. #19134371C2semidirect
15. C22×#103×C43C2semidirect
23. #14583038C4semidirect
69. C2×#10621884C2×C4semidirect
70. C2×#10621884C2×C4semidirect
102. #13063249C2×C4semidirect
103. #13063249C2×C4semidirect
106. C22⋊(C43⋊C8)C2×C4semidirect
124. C22×Q8×C43C2×C4semidirect
143. #103×C43D4semidirect
268. Q8×C43C4×D4semidirect
334. C22×C43#440semidirect
367. C22×#103D43semidirect
435. C43#22855semidirect
442. C22×Q8C4×D43semidirect
503. #103C22⋊D43semidirect
642. Q8C4×C22⋊D43semidirect
714. C22#14583002semidirect

Maximal subgroups

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

subgroupindex
C2×#145830382
C2×#145830022
#191376112
Q8×C22⋊Dic432
#191354732
#191352822
#191352392
#191350232
#191349482
#191349262
#191348472
#191347832
#191344272
#191343712
C22×#103×C432
#2285543