Finite Group Databasebeta

← #25116862

Subgroups — #25116862

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×#14583040C211yesmaximal, characteristic
2C2×#14582998C211yesmaximal, characteristic, complemented
3C22×#13063248C211yesmaximal, characteristic, complemented
4#19137611C211yesmaximal, characteristic
5#19137427C211yesmaximal, characteristic, complemented
6#19135474C211yesmaximal, characteristic, complemented
7#19135283C211yesmaximal, characteristic, complemented
8#19135235C211yesmaximal, characteristic, complemented
9#19135021C211yesmaximal, characteristic
10#19134951C211yesmaximal, characteristic, complemented
11#19134930C211yesmaximal, characteristic, complemented
12#19134846C211yesmaximal, characteristic, complemented
13#19134424C211yesmaximal, characteristic, complemented
14#19134374C211yesmaximal, characteristic, complemented
15C43×#1852C211yesmaximal, characteristic, complemented
16C23×Dic86C2211yescharacteristic
17C22×#10621873C2211yescharacteristic
18C22×#10621873C2211yescharacteristic
19C23×C43⋊C8C2211yescharacteristic
20C2×#13063299C2211yescharacteristic
21C2×#13063290C2211yescharacteristic
22C2×#13063290C2211yescharacteristic
23C2×#13063287C2211yescharacteristic
24C2×C4×C22⋊D43—21no—
25#14583040C418yescomplemented
26#14582998—24no—
27C2×#13063250C2211yescharacteristic
28C2×#13063250C2211yescharacteristic
29C2×#13063248—24no—
30C2×#13063248C2211yescharacteristic
31C2×#13063248C2211yescharacteristic
32C2×#13063248C2211yescharacteristic
33C2×#13063248C2211yescharacteristic
34C2×#13063245C2211yescharacteristic
35C2×#13063245C2211yescharacteristic
36C2×#13063235C2211yescharacteristic
37C2×#13063235C2211yescharacteristic
38#14582804C2211yescharacteristic
39#14582804C2211yescharacteristic
40#14582803—21no—
41#14582803—21no—
42#14582800C2211yescharacteristic
43#14582795C2211yescharacteristic
44#14582789—21no—
45#14582778—21no—
46#14582770—21no—
47#14582757—21no—
48C4⋊C4×Dic43C2211yescharacteristic
49C22⋊C4×Dic43—21no—
50C4×C22⋊Dic43C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582653C2211yescharacteristic
54#14582653C2211yescharacteristic
55C22×C4⋊C4×C43C2211yescharacteristic
56C2×#107×C43C2211yescharacteristic
57C2×#107×C43C2211yescharacteristic
58C2×C22⋊C8×C43C2211yescharacteristic
59C43×#380C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C43×#340C2211yescharacteristic
62C22×Dic86—22no—
63C22×Dic86—22no—
64C22×Dic86—21no—
65C22×Dic86—22no—
66C22×Dic86—41no—
67C22×Dic86—41no—
68C22×Dic86C2×C414yescomplemented
69C22×Dic86C2311yescharacteristic
70C22×Dic86C2311yescharacteristic
71C22×D172C2311yescharacteristic
72C22×C22⋊D43—21no—
73C23×Dic43—21no—
74C22×C4×D43—21no—
75C2×#10621873—22no—
76C2×#10621873—22no—
77C2×#10621873—41no—
78C2×#10621873—41no—
79C2×#10621873C2×C414yescomplemented
80C2×#10621873C2×C414yescomplemented
81C22×C43⋊C8—22no—
82C22×C43⋊C8—22no—
83C22×C43⋊C8—41no—
84C22×C43⋊C8C2311yescharacteristic
85C22×C43⋊C8C2311yescharacteristic
86#13063299—22no—
87#13063299C2×C414yes—
88#13063290—22no—
89#13063290—22no—
90#13063290—41no—
91#13063290—41no—
92#13063287—22no—
93#13063287—41no—
94C4×C22⋊D43—44no—
95C2×C4⋊Dic43C2311yescharacteristic
96C2×Dic43⋊C4—21no—
97C2×Dic43⋊C4—21no—
98C2×Dic43⋊C4—21no—
99C2×C22⋊Dic43D411yescharacteristic
100C2×C22⋊Dic43D411yescharacteristic
101C2×(C2×D43)⋊C4—21no—
102C2×(C2×D43)⋊C4—21no—
103C2×(C2×D43)⋊C4—21no—
104C2×(C2×D43)⋊C4—21no—
105C2×C4×Dic43—21no—
106C2×C4×Dic43—21no—
107C2×C4×Dic43—21no—
108C2×C4×Dic43C2311yescharacteristic
109C2×C4×Dic43C2311yescharacteristic
110#13063250C2×C414yescomplemented
111#13063250C2×C414yescomplemented
112#13063248—22no—
113#13063248—22no—
114#13063248—22no—
115#13063248D414yescomplemented
116#13063245—22no—
117#13063245—41no—
118#13063235—22no—
119#13063235—41no—
120C43⋊#95—21no—
121C43⋊#95—21no—
122C43⋊#95—21no—
123C43⋊#95—21no—
124C43⋊#95—21no—
125C43⋊#95—21no—
126C43⋊#95D411yescharacteristic
127C43⋊#95D411yescharacteristic
128C23×C4×C43—21no—
129C23×C4×C43C2311yescharacteristic
130C22×C8×C43C2311yescharacteristic
131C22×C8×C43C2311yescharacteristic
132C2×C4⋊C4×C43—22no—
133C2×C4⋊C4×C43—21no—
134C2×C4⋊C4×C43—41no—
135C2×C4⋊C4×C43C2311yescharacteristic
136C2×C4⋊C4×C43C2311yescharacteristic
137C2×C4⋊C4×C43C2311yescharacteristic
138C2×C4⋊C4×C43C2311yescharacteristic
139C2×C22⋊C4×C43—21no—
140#107×C43—22no—
141#107×C43—41no—
142C22⋊C8×C43C2×C414yescomplemented
143#95×C43—21no—
144C24×C43C2×D411yescharacteristic
145C23×D43—21no—
146C22×C4×C43—21no—
147C22×C4×C43—21no—
148C22×C4×C43—21no—
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43—21no—
154C22×C4×C43—42no—
155C22×C4×C43—42no—
156C22×C4×C43—81no—
157C22×C4×C43C22×C412yes—
158C22×C4×C43C2×D411yescharacteristic
159C22×C4×C43#4112yes—
160C22×C4×C43C2411yescharacteristic
161C2×C22⋊D43—24no—
162C2×C22⋊D43—42no—
163C2×C22⋊D43—42no—
164C22×Dic43—24no—
165C22×Dic43—21no—
166C22×Dic43—21no—
167C22×Dic43—21no—
168C22×Dic43—42no—
169C22×Dic43—42no—
170C22×Dic43C2×D411yescharacteristic
171C22×Dic43C2×D411yescharacteristic
172C22×Dic43C2×D411yescharacteristic
173C22×Dic43C2×D411yescharacteristic
174C2×D172—21no—
175C2×D172—21no—
176C2×D172—21no—
177C2×D172—21no—
178C2×D172—21no—
179C2×D172C22×C412yes—
180C2×C4×D43—42no—
181C2×C4×D43—42no—
182C2×C4×D43—81no—
183C2×Dic86—21no—
184C2×Dic86—21no—
185C2×Dic86—21no—
186C2×Dic86—21no—
187C2×Dic86—21no—
188C2×Dic86—21no—
189C2×Dic86—21no—
190C2×Dic86—28no—
191C2×Dic86—24no—
192C2×Dic86—21no—
193C2×Dic86—44no—
194C2×Dic86—44no—
195C2×Dic86—44no—
196C2×Dic86—42no—
197C2×Dic86—42no—
198C2×Dic86C22×C412yes—
199C2×Dic86C22×C412yes—
200C2×Dic86C2×D412yes—
201C2×Dic86#4112yes—
202C2×C8×C43—21no—
203C2×C8×C43—21no—
204C2×C8×C43—21no—
205C2×C8×C43—21no—
206C2×C8×C43C22×C412yes—
207C2×C8×C43C22×C412yes—
208C4⋊C4×C43—21no—
209C4⋊C4×C43—21no—
210C4⋊C4×C43—21no—
211C4⋊C4×C43—21no—
212C4⋊C4×C43—21no—
213C4⋊C4×C43—21no—
214C4⋊C4×C43—21no—
215C4⋊C4×C43—42no—
216C4⋊C4×C43C2×D412yes—
217C22⋊C4×C43—42no—
218C22⋊Dic43—22no—
219C22⋊Dic43—22no—
220(C2×D43)⋊C4—24no—
221(C2×D43)⋊C4—42no—
222(C2×D43)⋊C4—42no—
223(C2×D43)⋊C4—81no—
224C4⋊Dic43—21no—
225C4⋊Dic43C22×C412yes—
226Dic43⋊C4—42no—
227Dic43⋊C4—42no—
228Dic43⋊C4—42no—
229C4×Dic43—21no—
230C4×Dic43—21no—
231C4×Dic43—21no—
232C4×Dic43—21no—
233C4×Dic43—42no—
234C4×Dic43—42no—
235C4×Dic43—42no—
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⋊C8C2×D412yes—
243#10621873—28no—
244#10621873—44no—
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—
260C2×C4×C43—21no—
261C2×C4×C43—21no—
262C2×C4×C43—22no—
263C2×C4×C43—22no—
264C2×C4×C43—22no—
265C2×C4×C43—22no—
266C2×C4×C43—22no—
267C2×C4×C43—41no—
268C2×C4×C43—41no—
269C2×C4×C43—41no—
270C2×C4×C43—41no—
271C2×C4×C43—41no—
272C2×C4×C43—41no—
273C2×C4×C43—41no—
274C2×C4×C43—41no—
275C2×C4×C43—41no—
276C2×C4×C43—41no—
277C2×C4×C43—41no—
278C2×C4×C43—84no—
279C2×C4×C43C4×D412yes—
280C2×C4×C43C23×C411yescharacteristic
281C2×C4×C43C22×D411yescharacteristic
282C2×C4×C43C2×#4111yescharacteristic
283C2×C4×C43C2×#4111yescharacteristic
284C2×C4×C43H(5,𝔽2)11yescharacteristic
285C2×C4×C43H(5,𝔽2)11yescharacteristic
286C22⋊D43—48no—
287C2×Dic43—22no—
288C2×Dic43—22no—
289C2×Dic43—22no—
290C2×Dic43—22no—
291C2×Dic43—22no—
292C2×Dic43—21no—
293C2×Dic43—21no—
294C2×Dic43—21no—
295C2×Dic43—21no—
296C2×Dic43—21no—
297C2×Dic43—21no—
298C2×Dic43—21no—
299C2×Dic43—21no—
300C2×Dic43—21no—
301C2×Dic43—21no—
302C2×Dic43—21no—
303C2×Dic43—21no—
304C2×Dic43—48no—
305C2×Dic43—41no—
306C2×Dic43—41no—
307C2×Dic43—41no—
308C2×Dic43—41no—
309D172—22no—
310D172—22no—
311D172—41no—
312D172—41no—
313C4×D43—84no—
314Dic86—22no—
315Dic86—22no—
316Dic86—22no—
317Dic86—22no—
318Dic86—22no—
319Dic86—48no—
320Dic86—41no—
321Dic86—41no—
322Dic86C4×D414yescomplemented
323C8×C43—22no—
324C8×C43—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—42no—
351C4×C43—81no—
352C4×C43—81no—
353C4×C43—81no—
354C4×C43C2×C4×D411yescharacteristic
355C4×C43#51811yescharacteristic
356C4×C43#54611yescharacteristic
357C4×C43#55111yescharacteristic
358Dic43—24no—
359Dic43—42no—
360Dic43—42no—
361Dic43—41no—
362Dic43—41no—
363Dic43—41no—
364Dic43—41no—
365C2×#448—431no—
366C2×#440—431no—
367C22×#103—431no—
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#1852D4311yescharacteristic, complemented
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×Q8—431no—
390C22×SD16—431no—
391C22×SD16—431no—
392C23×C8—431no—
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×#107C2×D4311yescharacteristic
402C2×#107C2×D4311yescharacteristic
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⋊C8C2×D4311yescharacteristic
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—861no—
425#380C2×D4311yescharacteristic
426C4×C4⋊C4—431no—
427C4×C22⋊C4—431no—
428C4×C22⋊C4—861no—
429#340—431no—
430#340—431no—
431#340C2×D4311yescharacteristic
432#340C2×D4311yescharacteristic
433#336—431no—
434#336—431no—
435C43#2285511yescharacteristic, complemented, Sylow
436C22×Q8—434no—
437C22×Q8—431no—
438C22×Q8—431no—
439C22×Q8—862no—
440C22×Q8—862no—
441C22×Q8—861no—
442C22×Q8—862no—
443C22×Q8—1721no—
444C22×Q8—1721no—
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—862no—
460C22×C8—862no—
461C22×C8—1721no—
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—861no—
478C2×C4⋊C4—861no—
479C2×C4⋊C4—861no—
480C2×C4⋊C4C22×D4311yescharacteristic
481C2×C4⋊C4C22×D4311yescharacteristic
482C2×C4⋊C4C22×D4311yescharacteristic
483C2×C4⋊C4C22×D4311yescharacteristic
484C2×C22⋊C4—21no—
485C2×C22⋊C4—431no—
486C2×C22⋊C4—431no—
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—22no—
497#107—41no—
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⋊C8C4×D4314yescomplemented
507#97—862no—
508#97—1721no—
509#95—21no—
510#95—431no—
511#95—431no—
512#95—861no—
513#95—861no—
514#95—861no—
515#95—861no—
516#95—861no—
517#95—861no—
518C24—861no—
519C24D4×D4311yescharacteristic
520C2×Q8—432no—
521C2×Q8—432no—
522C2×Q8—432no—
523C2×Q8—432no—
524C2×Q8—868no—
525C2×Q8—864no—
526C2×Q8—861no—
527C2×Q8—861no—
528C2×Q8—861no—
529C2×Q8—861no—
530C2×Q8—861no—
531C2×Q8—861no—
532C2×Q8—861no—
533C2×Q8—861no—
534C2×Q8—1722no—
535C2×Q8—1722no—
536C2×Q8—1724no—
537C2×Q8—1724no—
538C2×Q8—1724no—
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—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—42no—
557C22×C4—42no—
558C22×C4—81no—
559C22×C4—431no—
560C22×C4—431no—
561C22×C4—431no—
562C22×C4—431no—
563C22×C4—861no—
564C22×C4—864no—
565C22×C4—861no—
566C22×C4—861no—
567C22×C4—3441no—
568C22×C4—1722no—
569C22×C4—1722no—
570C22×C4—1722no—
571C22×C4—1722no—
572C22×C4C2×C4×D4312yes—
573C22×C4D4×D4311yescharacteristic
574C22×C4#1062190212yes—
575C22×C4C23×D4311yescharacteristic
576SD16—868no—
577SD16—1724no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—432no—
583C2×C8—861no—
584C2×C8—861no—
585C2×C8—861no—
586C2×C8—861no—
587C2×C8—861no—
588C2×C8—1724no—
589C2×C8C2×C4×D4312yes—
590C2×C8C2×C4×D4312yes—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—42no—
599C4⋊C4—432no—
600C4⋊C4—861no—
601C4⋊C4—1722no—
602C4⋊C4—1722no—
603C4⋊C4—1722no—
604C4⋊C4D4×D4312yes—
605C22⋊C4—42no—
606C22⋊C4—862no—
607C22⋊C4—862no—
608C22⋊C4—864no—
609C22⋊C4—3441no—
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#1306328712yes—
631C23#1306334912yes—
632C23#1306335712yes—
633C23C2×D4×D4311yescharacteristic
634Q8—434no—
635Q8—862no—
636Q8—862no—
637Q8—862no—
638Q8—862no—
639Q8—862no—
640Q8—1728no—
641Q8—1721no—
642Q8—1721no—
643D4—862no—
644D4—862no—
645D4—1728no—
646D4—1721no—
647D4—1721no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—84no—
667C2×C4—862no—
668C2×C4—862no—
669C2×C4—862no—
670C2×C4—862no—
671C2×C4—862no—
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—861no—
682C2×C4—861no—
683C2×C4—861no—
684C2×C4—3444no—
685C2×C4—1728no—
686C2×C4—1721no—
687C2×C4—1721no—
688C2×C4—1721no—
689C2×C4—1721no—
690C2×C4#1306328712yes—
691C2×C4C22×C4×D4311yescharacteristic
692C2×C4C2×D4×D4311yescharacteristic
693C2×C4#41×D4311yescharacteristic
694C2×C4C2×#1062190211yescharacteristic
695C2×C4#1306337011yescharacteristic
696C2×C4#1306337111yescharacteristic
697C8—22no—
698C8—22no—
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#1458299814yescomplemented
715C22C2×#1306328711yescharacteristic
716C22#1458353111yescharacteristic
717C22#1458354111yescharacteristic
718C22C2×#1306334911yescharacteristic
719C22C2×#1306335711yescharacteristic
720C22#1458370911yescharacteristic
721C22#1458371511yescharacteristic
722C4—22no—
723C4—42no—
724C4—81no—
725C4—81no—
726C4—81no—
727C4—864no—
728C4—1721no—
729C4—1722no—
730C4—1721no—
731C4—1721no—
732C4—1721no—
733C4—1722no—
734C4C4×D4×D4311yescharacteristic
735C4#1458337111yescharacteristic
736C4#1458354011yescharacteristic
737C4#1458357611yescharacteristic
738C2—24no—
739C2—3442no—
740C2#1913757111yescharacteristic
741C2C2×#1458299811yescharacteristic
742C2#1914343611yescharacteristic
743C2#1914609411yescharacteristic
744C2#1914616911yescharacteristic
745C2#1914658411yescharacteristic
746C2#1914676411yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1852C2
socleC23×C43C22×D4
prime radicalC2×#13063299C22
cosocleC22×C4×C43C24
hypercenter#1852D43
hypocenterC43#22855
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1852

Complements

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

NH ≅ G/Ntype
2. C2×#14582998C2semidirect
3. C22×#13063248C2semidirect
5. #19137427C2semidirect
6. #19135474C2semidirect
7. #19135283C2semidirect
8. #19135235C2semidirect
10. #19134951C2semidirect
11. #19134930C2semidirect
12. #19134846C2semidirect
13. #19134424C2semidirect
14. #19134374C2semidirect
15. C43×#1852C2semidirect
25. #14583040C4semidirect
68. C22×Dic86C2×C4semidirect
79. C2×#10621873C2×C4semidirect
80. C2×#10621873C2×C4semidirect
110. #13063250C2×C4semidirect
111. #13063250C2×C4semidirect
115. #13063248D4semidirect
142. C22⋊C8×C43C2×C4semidirect
322. Dic86C4×D4semidirect
334. C22×C43#440semidirect
377. #1852D43semidirect
435. C43#22855semidirect
506. C22⋊C8C4×D43semidirect
714. C22#14582998semidirect

Maximal subgroups

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

subgroupindex
C2×#145830402
C2×#145829982
C22×#130632482
#191376112
#191374272
#191354742
#191352832
#191352352
#191350212
#191349512
#191349302
#191348462
#191344242
#191343742
C43×#18522
#2285543