Finite Group Databasebeta

← #25116865

Subgroups — #25116865

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×#14582997C211yesmaximal, characteristic, complemented
3C22×#13063249C211yesmaximal, characteristic, complemented
4#19137609C211yesmaximal, characteristic
5#19135479C211yesmaximal, characteristic, complemented
6#19135288C211yesmaximal, characteristic, complemented
7#19135233C211yesmaximal, characteristic, complemented
8#19135021C211yesmaximal, characteristic
9#19134950C211yesmaximal, characteristic, complemented
10#19134932C211yesmaximal, characteristic, complemented
11#19134849C211yesmaximal, characteristic, complemented
12#19134782C211yesmaximal, characteristic, complemented
13#19134425C211yesmaximal, characteristic, complemented
14#19134373C211yesmaximal, characteristic, complemented
15Q8×C22⋊C4×C43C211yesmaximal, characteristic, complemented
16C22×#10621884C2211yescharacteristic
17C22×#10621884C2211yescharacteristic
18C23×C43⋊C8C2211yescharacteristic
19C2×#13063299C2211yescharacteristic
20C2×C4×D172C2211yescharacteristic
21C2×(C22⋊D43)⋊C4—21no—
22C22×C4⋊Dic43C2211yescharacteristic
23#14583038C418yescomplemented
24#14582997—24no—
25C2×#13063258C2211yescharacteristic
26C2×#13063258C2211yescharacteristic
27C2×#13063249—24no—
28C2×#13063249C2211yescharacteristic
29C2×#13063249C2211yescharacteristic
30C2×#13063249C2211yescharacteristic
31C2×#13063249C2211yescharacteristic
32C2×#13063249C2211yescharacteristic
33C2×#13063249C2211yescharacteristic
34C2×#13063245C2211yescharacteristic
35C2×#13063245C2211yescharacteristic
36C2×C22⋊(C43⋊C8)C2211yescharacteristic
37C2×#13063236C2211yescharacteristic
38C2×#13063236C2211yescharacteristic
39#14582801C2211yescharacteristic
40#14582797C2211yescharacteristic
41#14582791—21no—
42#14582776—21no—
43#14582773—21no—
44C4×C4⋊Dic43C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582654C2211yescharacteristic
50#14582654C2211yescharacteristic
51C23×Q8×C43C2211yescharacteristic
52C2×C4×Q8×C43C2211yescharacteristic
53C2×C4×Q8×C43C2211yescharacteristic
54C43×#391—21no—
55C43×#391—21no—
56C43×#391C2211yescharacteristic
57C43×#391C2211yescharacteristic
58C43×#380—21no—
59C43×#380C2211yescharacteristic
60C4×C22⋊C4×C43—21no—
61C4×C22⋊C4×C43C2211yescharacteristic
62C22×D172C2311yescharacteristic
63C22×C22⋊D43—21no—
64C23×Dic43—21no—
65C22×C4×D43—21no—
66C2×#10621884—22no—
67C2×#10621884—22no—
68C2×#10621884—41no—
69C2×#10621884—41no—
70C2×#10621884C2×C414yescomplemented
71C2×#10621884C2×C414yescomplemented
72C22×C43⋊C8—22no—
73C22×C43⋊C8—22no—
74C22×C43⋊C8—41no—
75C22×C43⋊C8C2311yescharacteristic
76C22×C43⋊C8C2311yescharacteristic
77C22×C43⋊C8C2311yescharacteristic
78C22×C43⋊C8C2311yescharacteristic
79#13063299—22no—
80#13063299C2×C414yes—
81C4×D172—22no—
82C4×D172—41no—
83(C22⋊D43)⋊C4—44no—
84C2×C4⋊Dic43—22no—
85C2×C4⋊Dic43—21no—
86C2×C4⋊Dic43—41no—
87C2×C4⋊Dic43C2311yescharacteristic
88C2×C4⋊Dic43C2311yescharacteristic
89C2×C4⋊Dic43C2311yescharacteristic
90C2×Dic43⋊C4—21no—
91C2×(C2×D43)⋊C4—21no—
92C2×(C2×D43)⋊C4—21no—
93C2×(C2×D43)⋊C4—21no—
94C2×(C2×D43)⋊C4—21no—
95C2×C4×Dic43—21no—
96#13063258—22no—
97#13063258—41no—
98#13063249—22no—
99#13063249—22no—
100#13063249—22no—
101#13063249C2×C414yescomplemented
102#13063249C2×C414yescomplemented
103#13063249D414yescomplemented
104#13063245—22no—
105#13063245—41no—
106C22⋊(C43⋊C8)C2×C414yescomplemented
107#13063236—22no—
108#13063236—41no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C22×Q8×C43—21no—
112C22×Q8×C43—22no—
113C22×Q8×C43—22no—
114C22×Q8×C43—22no—
115C22×Q8×C43—41no—
116C22×Q8×C43—41no—
117C22×Q8×C43C2×C414yescomplemented
118C22×Q8×C43C2311yescharacteristic
119C22×Q8×C43C2311yescharacteristic
120C23×C4×C43—21no—
121C23×C4×C43C2311yescharacteristic
122C4×Q8×C43—22no—
123C4×Q8×C43—22no—
124C4×Q8×C43—41no—
125C4×Q8×C43—41no—
126C2×C4⋊C4×C43—21no—
127C2×C4⋊C4×C43—21no—
128C2×C4⋊C4×C43C2311yescharacteristic
129C2×C4⋊C4×C43C2311yescharacteristic
130C2×C22⋊C4×C43—21no—
131C2×C22⋊C4×C43D411yescharacteristic
132C2×C22⋊C4×C43D411yescharacteristic
133C2×C42×C43—21no—
134C2×C42×C43—21no—
135C2×C42×C43C2311yescharacteristic
136C2×C42×C43C2311yescharacteristic
137#95×C43—21no—
138#95×C43—21no—
139#95×C43—21no—
140#95×C43—21no—
141#95×C43—21no—
142#95×C43D411yescharacteristic
143#95×C43D411yescharacteristic
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×C43C22×C412yes—
177C22×C4×C43C2×D411yescharacteristic
178C22×C4×C43C2×D411yescharacteristic
179C22×C4×C43C2×D411yescharacteristic
180C22×C4×C43C2×D411yescharacteristic
181C22×C4×C43C2×D411yescharacteristic
182C22×C4×C43#4112yes—
183C22×C4×C43C2411yescharacteristic
184C2×C22⋊D43—24no—
185C2×C22⋊D43—42no—
186C2×C22⋊D43—42no—
187C22×Dic43—21no—
188C22×Dic43—21no—
189C22×Dic43—21no—
190C22×Dic43—42no—
191C22×Dic43—42no—
192C22×Dic43—81no—
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—
202C4⋊C4×C43—21no—
203C4⋊C4×C43—21no—
204C4⋊C4×C43—21no—
205C4⋊C4×C43—21no—
206C4⋊C4×C43—42no—
207C4⋊C4×C43—42no—
208C22⋊C4×C43—22no—
209C22⋊C4×C43—22no—
210C22⋊C4×C43—42no—
211C42×C43—21no—
212C42×C43—21no—
213C42×C43—21no—
214C42×C43—21no—
215C42×C43—42no—
216C42×C43—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—42no—
228C4⋊Dic43C22×C412yes—
229C4⋊Dic43C2×D412yes—
230Dic43⋊C4—42no—
231C4×Dic43—42no—
232C2×C43⋊C8—21no—
233C2×C43⋊C8—21no—
234C2×C43⋊C8—21no—
235C2×C43⋊C8—21no—
236C2×C43⋊C8—21no—
237C2×C43⋊C8—21no—
238C2×C43⋊C8—21no—
239C2×C43⋊C8—21no—
240C2×C43⋊C8—21no—
241C2×C43⋊C8—44no—
242C2×C43⋊C8C22×C412yes—
243C2×C43⋊C8C22×C412yes—
244C2×C43⋊C8C2×D412yes—
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—21no—
271C2×C4×C43—22no—
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—21no—
280C2×C4×C43—21no—
281C2×C4×C43—21no—
282C2×C4×C43—21no—
283C2×C4×C43—21no—
284C2×C4×C43—21no—
285C2×C4×C43—21no—
286C2×C4×C43—21no—
287C2×C4×C43—21no—
288C2×C4×C43—21no—
289C2×C4×C43—21no—
290C2×C4×C43—21no—
291C2×C4×C43—48no—
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×C43—41no—
300C2×C4×C43C4×D412yes—
301C2×C4×C43C23×C411yescharacteristic
302C2×C4×C43C22×D411yescharacteristic
303C2×C4×C43C2×#4111yescharacteristic
304C2×C4×C43C2×#4111yescharacteristic
305C2×C4×C43H(5,𝔽2)11yescharacteristic
306C2×C4×C43H(5,𝔽2)11yescharacteristic
307C22⋊D43—48no—
308C2×Dic43—22no—
309C2×Dic43—22no—
310C2×Dic43—41no—
311C2×Dic43—41no—
312C2×Dic43—41no—
313C2×Dic43—41no—
314C2×Dic43—41no—
315C2×Dic43—41no—
316C2×Dic43—41no—
317C2×Dic43—84no—
318D172—22no—
319D172—22no—
320D172—41no—
321D172—41no—
322C4×D43—84no—
323C43⋊C8—22no—
324C43⋊C8—22no—
325C43⋊C8—22no—
326C43⋊C8—41no—
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—41no—
353C4×C43—41no—
354C4×C43—41no—
355C4×C43—41no—
356C4×C43—81no—
357C4×C43—81no—
358C4×C43C2×C4×D411yescharacteristic
359C4×C43#51811yescharacteristic
360C4×C43#54611yescharacteristic
361C4×C43#55111yescharacteristic
362Dic43—42no—
363Dic43—42no—
364Dic43—81no—
365C2×#448—431no—
366C2×#440—431no—
367C22×#103—431no—
368#2361—431no—
369Q8×C22⋊C4D4311yescharacteristic, complemented
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×C8—431no—
393C2×#121—431no—
394C2×C4×Q8C2×D4311yescharacteristic
395C2×C4×Q8C2×D4311yescharacteristic
396C2×C4×D4—431no—
397C2×C4×D4—861no—
398C22×C4⋊C4—431no—
399#448—438no—
400#440—864no—
401C2×#107—431no—
402C2×#107—431no—
403C2×#103—431no—
404C2×#103—431no—
405C2×#103—431no—
406C2×#103—431no—
407C2×#103—431no—
408C2×#103—431no—
409C2×#103—864no—
410C2×#102—431no—
411C2×#102—431no—
412C2×C22⋊C8—431no—
413C2×#97—431no—
414C2×#97—431no—
415#391—21no—
416#391—21no—
417#391C2×D4311yescharacteristic
418#391C2×D4311yescharacteristic
419#390—431no—
420#389—431no—
421#388—861no—
422#386—861no—
423#385—861no—
424#380—21no—
425#380C2×D4311yescharacteristic
426C4×C4⋊C4—431no—
427C4×C22⋊C4—21no—
428C4×C22⋊C4C2×D4311yescharacteristic
429#340—431no—
430#340—431no—
431#340—431no—
432#340—431no—
433#336—431no—
434#336—431no—
435C43#2285511yescharacteristic, complemented, Sylow
436C22×Q8—22no—
437C22×Q8—21no—
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—861no—
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—431no—
458C22×C8—431no—
459C22×C8—431no—
460C22×C8—431no—
461C22×C8—862no—
462C22×C8—862no—
463C22×C8—1721no—
464#121—434no—
465#121—862no—
466C4×Q8—22no—
467C4×Q8—22no—
468C4×Q8—41no—
469C4×Q8—41no—
470C4×D4—862no—
471C4×D4—1721no—
472C4×D4—1724no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—21no—
475C2×C4⋊C4—431no—
476C2×C4⋊C4—431no—
477C2×C4⋊C4—431no—
478C2×C4⋊C4—862no—
479C2×C4⋊C4—861no—
480C2×C4⋊C4—861no—
481C2×C4⋊C4—1721no—
482C2×C4⋊C4C22×D4311yescharacteristic
483C2×C4⋊C4C22×D4311yescharacteristic
484C2×C22⋊C4—21no—
485C2×C22⋊C4—861no—
486C2×C22⋊C4—861no—
487C2×C22⋊C4—861no—
488C2×C22⋊C4—861no—
489C2×C22⋊C4C22⋊D4311yescharacteristic
490C2×C22⋊C4C22⋊D4311yescharacteristic
491C2×C42—21no—
492C2×C42—21no—
493C2×C42—861no—
494C2×C42C22×D4311yescharacteristic
495C2×C42C22×D4311yescharacteristic
496#107—862no—
497#107—1721no—
498#103—434no—
499#103—434no—
500#103—434no—
501#103—862no—
502#103—862no—
503#103—862no—
504#102—862no—
505#102—1721no—
506C22⋊C8—434no—
507#97—862no—
508#97—1721no—
509#95—21no—
510#95—21no—
511#95—21no—
512#95—21no—
513#95—21no—
514#95—861no—
515#95—861no—
516#95C22⋊D4311yescharacteristic
517#95C22⋊D4311yescharacteristic
518C24—861no—
519C24C2×C22⋊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×Q8D4×D4312yes—
538C2×Q8#1062190012yes—
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—861no—
560C22×C4—861no—
561C22×C4—861no—
562C22×C4—3441no—
563C22×C4—3441no—
564C22×C4—1722no—
565C22×C4—1722no—
566C22×C4—1722no—
567C22×C4—1722no—
568C22×C4C2×C4×D4312yes—
569C22×C4#1062189812yes—
570C22×C4C2×C22⋊D4311yescharacteristic
571C22×C4C2×C22⋊D4311yescharacteristic
572C22×C4C2×C22⋊D4311yescharacteristic
573C22×C4C2×C22⋊D4311yescharacteristic
574C22×C4C2×C22⋊D4311yescharacteristic
575C22×C4C23×D4311yescharacteristic
576SD16—868no—
577SD16—1724no—
578C2×C8—432no—
579C2×C8—432no—
580C2×C8—432no—
581C2×C8—861no—
582C2×C8—861no—
583C2×C8—861no—
584C2×C8—861no—
585C2×C8—861no—
586C2×C8—861no—
587C2×C8—861no—
588C2×C8—861no—
589C2×C8—861no—
590C2×C8—1724no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—42no—
596C4⋊C4—42no—
597C4⋊C4—432no—
598C4⋊C4—432no—
599C4⋊C4—861no—
600C4⋊C4—861no—
601C4⋊C4—861no—
602C4⋊C4—861no—
603C4⋊C4—1722no—
604C4⋊C4—1722no—
605C22⋊C4—22no—
606C22⋊C4—22no—
607C22⋊C4—42no—
608C22⋊C4—864no—
609C22⋊C4—3441no—
610C22⋊C4—1722no—
611C22⋊C4—1722no—
612C42—21no—
613C42—21no—
614C42—21no—
615C42—21no—
616C42—42no—
617C42—42no—
618C42—1722no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—862no—
624C23—1721no—
625C23—1721no—
626C23—1721no—
627C23—1721no—
628C23—1721no—
629C23—1721no—
630C23C4×C22⋊D4312yes—
631C23#1306335012yes—
632C23#1306335612yes—
633C23C22×C22⋊D4311yescharacteristic
634Q8—22no—
635Q8—22no—
636Q8—22no—
637Q8—22no—
638Q8—22no—
639Q8—48no—
640Q8—41no—
641Q8—41no—
642Q8(C22⋊D43)⋊C414yescomplemented
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—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—48no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—862no—
680C2×C4—862no—
681C2×C4—3444no—
682C2×C4—3444no—
683C2×C4—1721no—
684C2×C4—1721no—
685C2×C4—1721no—
686C2×C4—1721no—
687C2×C4—1721no—
688C2×C4—1721no—
689C2×C4—1721no—
690C2×C4C4×C22⋊D4312yes—
691C2×C4C22×C4×D4311yescharacteristic
692C2×C4C2×D4×D4311yescharacteristic
693C2×C4C2×#1062190011yescharacteristic
694C2×C4C2×#1062189811yescharacteristic
695C2×C4#1306337011yescharacteristic
696C2×C4#1306337011yescharacteristic
697C8—862no—
698C8—862no—
699C8—862no—
700C8—1721no—
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#1458299714yescomplemented
715C22C2×C4×C22⋊D4311yescharacteristic
716C22D4×C22⋊D4311yescharacteristic
717C22#1458354311yescharacteristic
718C22C2×#1306335011yescharacteristic
719C22C2×#1306335611yescharacteristic
720C22#1458370711yescharacteristic
721C22#1458371411yescharacteristic
722C4—22no—
723C4—24no—
724C4—41no—
725C4—42no—
726C4—41no—
727C4—41no—
728C4—41no—
729C4—81no—
730C4—81no—
731C4—3441no—
732C4—1722no—
733C4—1722no—
734C4C2×(C22⋊D43)⋊C411yescharacteristic
735C4#1458337211yescharacteristic
736C4#1458353911yescharacteristic
737C4#1458357511yescharacteristic
738C2—24no—
739C2—3442no—
740C2#1913757411yescharacteristic
741C2C2×#1458299711yescharacteristic
742C2#1914343811yescharacteristic
743C2#1914609111yescharacteristic
744C2#1914616611yescharacteristic
745C2#1914658611yescharacteristic
746C2#1914676611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingQ8×C22⋊C4×C43C2
socleC23×C43C22×D4
prime radicalC2×#13063299C22
cosocleC22×C4×C43C24
hypercenterQ8×C22⋊C4D43
hypocenterC43#22855
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ Q8×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#14582997C2semidirect
3. C22×#13063249C2semidirect
5. #19135479C2semidirect
6. #19135288C2semidirect
7. #19135233C2semidirect
9. #19134950C2semidirect
10. #19134932C2semidirect
11. #19134849C2semidirect
12. #19134782C2semidirect
13. #19134425C2semidirect
14. #19134373C2semidirect
15. Q8×C22⋊C4×C43C2semidirect
23. #14583038C4semidirect
70. C2×#10621884C2×C4semidirect
71. C2×#10621884C2×C4semidirect
101. #13063249C2×C4semidirect
102. #13063249C2×C4semidirect
103. #13063249D4semidirect
106. C22⋊(C43⋊C8)C2×C4semidirect
117. C22×Q8×C43C2×C4semidirect
268. Q8×C43C4×D4semidirect
334. C22×C43#440semidirect
369. Q8×C22⋊C4D43semidirect
435. C43#22855semidirect
442. C22×Q8C4×D43semidirect
642. Q8(C22⋊D43)⋊C4semidirect
714. C22#14582997semidirect

Maximal subgroups

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

subgroupindex
C2×#145830382
C2×#145829972
C22×#130632492
#191376092
#191354792
#191352882
#191352332
#191350212
#191349502
#191349322
#191348492
#191347822
#191344252
#191343732
Q8×C22⋊C4×C432
#2285543