Finite Group Databasebeta

← #25102371

Subgroups — #25102371

Order 11008.

1400 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583375C211yesmaximal, characteristic, complemented
2C2×#14583039C211yesmaximal, characteristic
3C2×#14582998C211yesmaximal, characteristic, complemented
4C2×#14582984C211yesmaximal, characteristic, complemented
5#19137286C211yesmaximal, characteristic
6#19134950C211yesmaximal, characteristic, complemented
7#19134949C211yesmaximal, characteristic, complemented
8#19134916C211yesmaximal, characteristic
9#19134862C211yesmaximal, characteristic, complemented
10#19134791C211yesmaximal, characteristic, complemented
11#19134528C211yesmaximal, characteristic, complemented
12#19134427C211yesmaximal, characteristic, complemented
13#19134414C211yesmaximal, characteristic, complemented
14#19134360C211yesmaximal, characteristic, complemented
15C43×#1863C211yesmaximal, characteristic, complemented
16C22×Q8×D43C2211yescharacteristic
17C22×#10621873C2211yescharacteristic
18C22×#10621884C2211yescharacteristic
19C2×#13063300C2211yescharacteristic
20#14583375—24no—
21#14583375—24no—
22C2×Q8×Dic43C2211yescharacteristic
23C2×C4×Dic86—21no—
24C2×C4×Dic86C2211yescharacteristic
25C2×#13063290—21no—
26C2×#13063290C2211yescharacteristic
27C2×#13063287C2211yescharacteristic
28C2×#13063283—21no—
29C2×#13063283C2211yescharacteristic
30C2×#13063282—21no—
31C2×#13063282C2211yescharacteristic
32#14583039C418yescomplemented
33#14582998—24no—
34#14582984—24no—
35C2×#13063256C2211yescharacteristic
36C2×#13063250C2211yescharacteristic
37C2×#13063249C2211yescharacteristic
38C2×#13063248C2211yescharacteristic
39C2×#13063248C2211yescharacteristic
40C2×#13063247C2211yescharacteristic
41C2×#13063245C2211yescharacteristic
42C2×(C2×D43)⋊C8C2211yescharacteristic
43C2×(C2×D43)⋊C8C2211yescharacteristic
44C2×#13063235C2211yescharacteristic
45C2×C8×Dic43C2211yescharacteristic
46#14582801C2211yescharacteristic
47#14582800—21no—
48#14582788—21no—
49#14582777—21no—
50#14582770—21no—
51#14582756C2211yescharacteristic
52C4⋊C4×Dic43C2211yescharacteristic
53#14582662C2211yescharacteristic
54#14582661C2211yescharacteristic
55#14582661C2211yescharacteristic
56#14582654C2211yescharacteristic
57C2×C4×Q8×C43C2211yescharacteristic
58C2×#107×C43C2211yescharacteristic
59C2×#103×C43C2211yescharacteristic
60C2×#103×C43C2211yescharacteristic
61C43×#389C2211yescharacteristic
62C43×#340C2211yescharacteristic
63C43×#336C2211yescharacteristic
64C22×Dic86—21no—
65C22×Dic86C2311yescharacteristic
66C2×Q8×D43—22no—
67C2×Q8×D43—22no—
68C2×Q8×D43—22no—
69C2×Q8×D43—22no—
70C2×Q8×D43—22no—
71C2×Q8×D43C2×C414yescomplemented
72C22×D172—21no—
73C22×D172C2311yescharacteristic
74C22×C4×D43—21no—
75C22×C4×D43—21no—
76C22×C4×D43C2311yescharacteristic
77C2×#10621873—22no—
78C2×#10621873—22no—
79C2×#10621873C2×C414yes—
80C2×#10621884—22no—
81C2×#10621884—22no—
82C2×#10621884C2×C414yes—
83C22×C43⋊C8C2311yescharacteristic
84C22×C43⋊C8C2311yescharacteristic
85#13063300—22no—
86#13063300C2×C414yes—
87Q8×Dic43—22no—
88Q8×Dic43D414yescomplemented
89C4×Dic86—28no—
90C4×Dic86—22no—
91C4×Dic86—22no—
92#13063290—28no—
93#13063290—22no—
94#13063290D414yescomplemented
95#13063287—22no—
96#13063287—22no—
97#13063283—28no—
98#13063283—22no—
99#13063283—22no—
100#13063282—28no—
101#13063282—22no—
102#13063282—22no—
103C2×C4⋊Dic43—21no—
104C2×C4⋊Dic43C2311yescharacteristic
105C2×C4⋊Dic43C2311yescharacteristic
106C2×Dic43⋊C4—21no—
107C2×Dic43⋊C4—21no—
108C2×Dic43⋊C4D411yescharacteristic
109C2×Dic43⋊C4D411yescharacteristic
110C2×(C2×D43)⋊C4—21no—
111C2×(C2×D43)⋊C4—21no—
112C2×(C2×D43)⋊C4—21no—
113C2×(C2×D43)⋊C4—21no—
114C2×(C2×D43)⋊C4—21no—
115C2×(C2×D43)⋊C4—21no—
116C2×(C2×D43)⋊C4D411yescharacteristic
117C2×(C2×D43)⋊C4D411yescharacteristic
118C2×C4×Dic43—21no—
119C2×C4×Dic43—21no—
120C2×C4×Dic43—21no—
121C2×C4×Dic43—21no—
122C2×C4×Dic43—21no—
123C2×C4×Dic43C2311yescharacteristic
124#13063256—22no—
125#13063250—22no—
126#13063249—22no—
127#13063248—22no—
128#13063248C2×C414yescomplemented
129#13063247—22no—
130#13063245—22no—
131(C2×D43)⋊C8—22no—
132(C2×D43)⋊C8C2×C414yescomplemented
133#13063235—22no—
134C8×Dic43—22no—
135C43⋊#95—21no—
136C43⋊#95—21no—
137C22×Q8×C43C2311yescharacteristic
138C22×C8×C43C2311yescharacteristic
139C22×C8×C43C2311yescharacteristic
140C4×Q8×C43—22no—
141C4×Q8×C43—22no—
142C2×C4⋊C4×C43—21no—
143C2×C4⋊C4×C43—21no—
144C2×C4⋊C4×C43C2311yescharacteristic
145C2×C4⋊C4×C43C2311yescharacteristic
146C2×C4⋊C4×C43C2311yescharacteristic
147C2×C42×C43—21no—
148C2×C42×C43C2311yescharacteristic
149#107×C43—22no—
150#103×C43—22no—
151#103×C43C2×C414yescomplemented
152#95×C43—21no—
153C23×D43—21no—
154C23×D43C2×D411yescharacteristic
155C2×Q8×C43—21no—
156C2×Q8×C43—21no—
157C2×Q8×C43—21no—
158C2×Q8×C43C22×C412yes—
159C2×Q8×C43C2×D412yes—
160C2×Q8×C43#4112yes—
161C22×C4×C43—21no—
162C22×C4×C43—21no—
163C22×C4×C43—21no—
164C22×C4×C43—21no—
165C22×C4×C43C2×D411yescharacteristic
166C22×C4×C43C2×D411yescharacteristic
167C22×C4×C43C2411yescharacteristic
168C22×Dic43—21no—
169C22×Dic43—21no—
170C22×Dic43—21no—
171C22×Dic43C2×D411yescharacteristic
172C22×Dic43C2×D411yescharacteristic
173C22×Dic43C2×D411yescharacteristic
174Q8×D43—28no—
175Q8×D43—28no—
176Q8×D43—28no—
177Q8×D43—28no—
178C2×D172—21no—
179C2×D172—24no—
180C2×D172—21no—
181C2×D172—21no—
182C2×D172—21no—
183C2×D172—21no—
184C2×D172—81no—
185C2×D172—81no—
186C2×D172C22×C412yes—
187C2×C4×D43—24no—
188C2×C4×D43—24no—
189C2×C4×D43—21no—
190C2×C4×D43—21no—
191C2×C4×D43—21no—
192C2×C4×D43—21no—
193C2×C4×D43—24no—
194C2×C4×D43—42no—
195C2×C4×D43—81no—
196C2×C4×D43—81no—
197C2×C4×D43C22×C412yes—
198C2×C4×D43#4112yes—
199C2×Dic86—24no—
200C2×Dic86—24no—
201C2×Dic86—21no—
202C2×Dic86—21no—
203C2×Dic86—21no—
204C2×Dic86—24no—
205C2×Dic86C22×C412yes—
206C2×Dic86C2×D412yes—
207C2×Dic86#4112yes—
208C2×C8×C43—21no—
209C2×C8×C43—21no—
210C2×C8×C43—21no—
211C2×C8×C43—21no—
212C2×C8×C43—21no—
213C2×C8×C43C22×C412yes—
214C4⋊C4×C43—24no—
215C4⋊C4×C43—21no—
216C4⋊C4×C43—21no—
217C4⋊C4×C43—21no—
218C4⋊C4×C43—21no—
219C4⋊C4×C43—81no—
220C4⋊C4×C43C22×C412yes—
221C4⋊C4×C43C2×D412yes—
222C42×C43—24no—
223C42×C43—21no—
224C42×C43—21no—
225#10621884—28no—
226(C2×D43)⋊C4—24no—
227(C2×D43)⋊C4—24no—
228(C2×D43)⋊C4—22no—
229(C2×D43)⋊C4—22no—
230(C2×D43)⋊C4—42no—
231(C2×D43)⋊C4—81no—
232(C2×D43)⋊C4—81no—
233(C2×D43)⋊C4—81no—
234C4⋊Dic43—21no—
235C4⋊Dic43—24no—
236C4⋊Dic43—21no—
237C4⋊Dic43—21no—
238C4⋊Dic43C2×D412yes—
239Dic43⋊C4—24no—
240Dic43⋊C4—24no—
241Dic43⋊C4—22no—
242Dic43⋊C4—22no—
243C4×Dic43—24no—
244C4×Dic43—24no—
245C4×Dic43—24no—
246C4×Dic43—24no—
247C4×Dic43—81no—
248C4×Dic43C2×D412yes—
249C4×Dic43C2×D412yes—
250C2×C43⋊C8—21no—
251C2×C43⋊C8—21no—
252C2×C43⋊C8—21no—
253C2×C43⋊C8—21no—
254C2×C43⋊C8—21no—
255C2×C43⋊C8C22×C412yes—
256#10621873—28no—
257C23×C43C22×D411yescharacteristic
258C22×D43—21no—
259C22×D43—21no—
260C22×D43—21no—
261C22×D43—21no—
262C22×D43—21no—
263C22×D43—21no—
264C22×D43—22no—
265C22×D43—41no—
266C22×D43—41no—
267C22×D43—41no—
268C22×D43—41no—
269C22×D43—41no—
270C22×D43—41no—
271C22×D43C4×D412yes—
272Q8×C43—22no—
273Q8×C43—22no—
274Q8×C43—22no—
275Q8×C43C4×D414yes—
276C2×C4×C43—22no—
277C2×C4×C43—22no—
278C2×C4×C43—22no—
279C2×C4×C43—22no—
280C2×C4×C43—21no—
281C2×C4×C43—22no—
282C2×C4×C43—21no—
283C2×C4×C43—21no—
284C2×C4×C43—21no—
285C2×C4×C43—21no—
286C2×C4×C43—21no—
287C2×C4×C43—41no—
288C2×C4×C43—41no—
289C2×C4×C43—41no—
290C2×C4×C43—41no—
291C2×C4×C43—41no—
292C2×C4×C43—41no—
293C2×C4×C43—41no—
294C2×C4×C43C23×C411yescharacteristic
295C2×C4×C43C22×D411yescharacteristic
296C2×C4×C43C22×D411yescharacteristic
297C2×C4×C43C2×#4111yescharacteristic
298C2×C4×C43C2×#4111yescharacteristic
299C2×C4×C43C2×#4111yescharacteristic
300C2×Dic43—22no—
301C2×Dic43—21no—
302C2×Dic43—22no—
303C2×Dic43—21no—
304C2×Dic43—22no—
305C2×Dic43—21no—
306C2×Dic43—21no—
307C2×Dic43—21no—
308C2×Dic43—21no—
309C2×Dic43—22no—
310C2×Dic43—41no—
311C2×Dic43—41no—
312C2×Dic43—41no—
313C2×Dic43—41no—
314C2×Dic43—41no—
315C2×Dic43C4×D412yes—
316C2×Dic43#12012yes—
317C2×Dic43#12012yes—
318D172—22no—
319D172—22no—
320D172—41no—
321D172—41no—
322D172—84no—
323C4×D43—216no—
324C4×D43—22no—
325C4×D43—22no—
326C4×D43—22no—
327C4×D43—22no—
328C4×D43—84no—
329Dic86—216no—
330Dic86—22no—
331Dic86—22no—
332Dic86—22no—
333Dic86C4×D414yes—
334C8×C43—22no—
335C8×C43—41no—
336C43⋊C8—22no—
337C43⋊C8—41no—
338#21462—431nomaximal, Sylow
339C22×C43C2×C4×D411yescharacteristic
340C22×C43C2×#12011yescharacteristic
341C22×C43#52511yescharacteristic
342C22×C43#57711yescharacteristic
343C22×C43#57711yescharacteristic
344C22×C43#57711yescharacteristic
345C22×C43#57811yescharacteristic
346C2×D43—22no—
347C2×D43—22no—
348C2×D43—22no—
349C2×D43—41no—
350C2×D43—41no—
351C2×D43—41no—
352C2×D43—41no—
353C2×D43—42no—
354C2×D43—42no—
355C2×D43—42no—
356C2×D43—81no—
357C2×D43—81no—
358C2×D43—81no—
359C2×D43—81no—
360C4×C43—24no—
361C4×C43—42no—
362C4×C43—41no—
363C4×C43—42no—
364C4×C43—41no—
365C4×C43—81no—
366C4×C43C2×C4×D411yescharacteristic
367C4×C43C2×C4×D411yescharacteristic
368C4×C43#52511yescharacteristic
369C4×C43#52511yescharacteristic
370Dic43—22no—
371Dic43—22no—
372Dic43—22no—
373Dic43—24no—
374Dic43—42no—
375Dic43—81no—
376C2×#519—431no—
377C2×#448—431no—
378C2×#440—431no—
379C2×C4×SD16—431no—
380#2324—431no—
381#1880—431no—
382#1880—431no—
383#1875—431no—
384#1865—431no—
385#1863D4311yescharacteristic, complemented
386#1854—431no—
387#1787—431no—
388#1763—431no—
389C4×#103—431no—
390#1750—431no—
391C2×C43C4×#12011yescharacteristic
392C2×C43#294711yescharacteristic
393C2×C43#294911yescharacteristic
394C2×C43#301011yescharacteristic
395C2×C43#301311yescharacteristic
396C2×C43#312111yescharacteristic
397C2×C43#312611yescharacteristic
398D43—42no—
399D43—82no—
400C23×Q8—431no—
401C22×SD16—431no—
402C22×SD16—431no—
403C2×#121—431no—
404#519—864no—
405#519—864no—
406C2×C4×Q8—431no—
407C2×C4×Q8—431no—
408C2×C4×Q8—431no—
409C2×C4×Q8—861no—
410C2×C4×Q8—861no—
411C2×C4×Q8C2×D4311yescharacteristic
412C2×C4×D4—431no—
413C2×#117—431no—
414C2×#117—431no—
415C2×#117—861no—
416C2×#117—861no—
417#448—438no—
418#440—864no—
419C4×SD16—864no—
420C2×#107C2×D4311yescharacteristic
421C2×#106—431no—
422C2×#103—431no—
423C2×#103—431no—
424C2×#103—431no—
425C2×#103—431no—
426C2×#103C2×D4311yescharacteristic
427C2×#103C2×D4311yescharacteristic
428C2×#102—431no—
429C2×#102—431no—
430C2×C22⋊C8—431no—
431C2×C22⋊C8—431no—
432C2×#97—431no—
433C2×C4×C8—431no—
434#390—431no—
435#390—861no—
436#389C2×D4311yescharacteristic
437#388—861no—
438#386—861no—
439#385—861no—
440#380—431no—
441C4×C4⋊C4—431no—
442#340—431no—
443#340—431no—
444#340—431no—
445#340C2×D4311yescharacteristic
446#336—431no—
447#336C2×D4311yescharacteristic
448C43#2146211yescharacteristic, complemented, Sylow
449C22×Q8—434no—
450C22×Q8—431no—
451C22×Q8—861no—
452C22×Q8—862no—
453C22×Q8—862no—
454C22×Q8—862no—
455C22×Q8—862no—
456C22×Q8—862no—
457C22×Q8C22×D4311yescharacteristic
458C22×D4—431no—
459C22×D4—861no—
460C23×C4—431no—
461C23×C4—861no—
462C23×C4—861no—
463C2×SD16—434no—
464C2×SD16—434no—
465C2×SD16—862no—
466C2×SD16—862no—
467C2×SD16—862no—
468C2×SD16—862no—
469C22×C8—431no—
470C22×C8—431no—
471C22×C8C22×D4311yescharacteristic
472C22×C8C22×D4311yescharacteristic
473#121—434no—
474#121—862no—
475C4×Q8—22no—
476C4×Q8—22no—
477C4×Q8—434no—
478C4×Q8—434no—
479C4×Q8—862no—
480C4×Q8—862no—
481C4×Q8—868no—
482C4×Q8—862no—
483C4×Q8—862no—
484C4×Q8—868no—
485C4×D4—862no—
486C4×D4—862no—
487#117—862no—
488#117—862no—
489#117—868no—
490#117—862no—
491#117—868no—
492#117—862no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—431no—
496C2×C4⋊C4—431no—
497C2×C4⋊C4—431no—
498C2×C4⋊C4—431no—
499C2×C4⋊C4—861no—
500C2×C4⋊C4—861no—
501C2×C4⋊C4—861no—
502C2×C4⋊C4C22×D4311yescharacteristic
503C2×C4⋊C4C22×D4311yescharacteristic
504C2×C4⋊C4C22×D4311yescharacteristic
505C2×C22⋊C4—431no—
506C2×C22⋊C4—431no—
507C2×C22⋊C4—861no—
508C2×C22⋊C4—861no—
509C2×C22⋊C4—861no—
510C2×C22⋊C4—861no—
511C2×C22⋊C4—861no—
512C2×C22⋊C4—861no—
513C2×C42—21no—
514C2×C42—431no—
515C2×C42—861no—
516C2×C42—861no—
517C2×C42—861no—
518C2×C42—861no—
519C2×C42—861no—
520C2×C42C22×D4311yescharacteristic
521#107—22no—
522#106—862no—
523#103—22no—
524#103—434no—
525#103—862no—
526#103—862no—
527#103—862no—
528#103C4×D4314yescomplemented
529#102—862no—
530#102—862no—
531C22⋊C8—434no—
532C22⋊C8—862no—
533#97—862no—
534C4×C8—862no—
535#95—21no—
536#95—861no—
537#95—861no—
538C24—431no—
539C24—861no—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8—432no—
544C2×Q8—432no—
545C2×Q8—432no—
546C2×Q8—864no—
547C2×Q8—864no—
548C2×Q8—864no—
549C2×Q8—868no—
550C2×Q8—868no—
551C2×Q8—868no—
552C2×Q8—868no—
553C2×Q8—861no—
554C2×Q8—861no—
555C2×Q8—861no—
556C2×Q8C2×C4×D4312yes—
557C2×Q8D4×D4312yes—
558C2×Q8#1062190212yes—
559C2×D4—432no—
560C2×D4—864no—
561C2×D4—861no—
562C2×D4—861no—
563C2×D4—861no—
564C2×D4—861no—
565C2×D4—861no—
566C2×D4—3441no—
567C2×D4—3441no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—431no—
573C22×C4—431no—
574C22×C4—431no—
575C22×C4—432no—
576C22×C4—432no—
577C22×C4—864no—
578C22×C4—864no—
579C22×C4—864no—
580C22×C4—861no—
581C22×C4—861no—
582C22×C4—861no—
583C22×C4—861no—
584C22×C4—861no—
585C22×C4—861no—
586C22×C4—861no—
587C22×C4—3441no—
588C22×C4—3441no—
589C22×C4—1722no—
590C22×C4D4×D4311yescharacteristic
591C22×C4D4×D4311yescharacteristic
592C22×C4C23×D4311yescharacteristic
593SD16—868no—
594SD16—868no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—432no—
601C2×C8—861no—
602C2×C8—861no—
603C2×C8—861no—
604C2×C8—861no—
605C2×C8—861no—
606C2×C8C2×C4×D4312yes—
607C4⋊C4—24no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—81no—
613C4⋊C4—432no—
614C4⋊C4—862no—
615C4⋊C4—862no—
616C4⋊C4—864no—
617C4⋊C4—864no—
618C4⋊C4—864no—
619C4⋊C4—861no—
620C4⋊C4—861no—
621C4⋊C4—861no—
622C4⋊C4C2×C4×D4312yes—
623C4⋊C4D4×D4312yes—
624C22⋊C4—862no—
625C22⋊C4—862no—
626C22⋊C4—864no—
627C22⋊C4—864no—
628C22⋊C4—3441no—
629C22⋊C4—3441no—
630C22⋊C4—3441no—
631C22⋊C4—1722no—
632C42—24no—
633C42—21no—
634C42—21no—
635C42—432no—
636C42—432no—
637C42—864no—
638C42—864no—
639C42—864no—
640C42—864no—
641C42—3441no—
642C23—432no—
643C23—861no—
644C23—861no—
645C23—861no—
646C23—861no—
647C23—861no—
648C23—861no—
649C23—862no—
650C23—1721no—
651C23—1721no—
652C23—1721no—
653C23—1721no—
654C23—1721no—
655C23—1721no—
656C23C2×D4×D4311yescharacteristic
657Q8—22no—
658Q8—22no—
659Q8—22no—
660Q8—434no—
661Q8—8616no—
662Q8—862no—
663Q8—862no—
664Q8—862no—
665Q8#1306328714yes—
666D4—862no—
667D4—862no—
668D4—3444no—
669D4—1721no—
670D4—1721no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—22no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—432no—
690C2×C4—432no—
691C2×C4—432no—
692C2×C4—8616no—
693C2×C4—862no—
694C2×C4—861no—
695C2×C4—862no—
696C2×C4—861no—
697C2×C4—862no—
698C2×C4—861no—
699C2×C4—861no—
700C2×C4—861no—
701C2×C4—861no—
702C2×C4—862no—
703C2×C4—862no—
704C2×C4—862no—
705C2×C4—862no—
706C2×C4—862no—
707C2×C4—3444no—
708C2×C4—1721no—
709C2×C4—1721no—
710C2×C4—1721no—
711C2×C4—1721no—
712C2×C4—1721no—
713C2×C4C22×C4×D4311yescharacteristic
714C2×C4C2×D4×D4311yescharacteristic
715C2×C4C2×D4×D4311yescharacteristic
716C2×C4#41×D4311yescharacteristic
717C2×C4#41×D4311yescharacteristic
718C2×C4C2×#1062190211yescharacteristic
719C8—22no—
720C8—41no—
721C8—862no—
722C8—1721no—
723C22—862no—
724C22—862no—
725C22—862no—
726C22—3441no—
727C22—3441no—
728C22—3441no—
729C22—3441no—
730C22—1722no—
731C22—1722no—
732C22—1722no—
733C22—1721no—
734C22—1721no—
735C22—1721no—
736C22—1721no—
737C22C4×D4×D4311yescharacteristic
738C22#120×D4311yescharacteristic
739C22#1458341211yescharacteristic
740C22#1458370611yescharacteristic
741C22#1458370811yescharacteristic
742C22#1458370911yescharacteristic
743C22#1458371211yescharacteristic
744C4—24no—
745C4—42no—
746C4—41no—
747C4—42no—
748C4—41no—
749C4—81no—
750C4—862no—
751C4—864no—
752C4—862no—
753C4—862no—
754C4—3441no—
755C4—1722no—
756C4C4×D4×D4311yescharacteristic
757C4C2×#1306328711yescharacteristic
758C4#1458340711yescharacteristic
759C4#1458341211yescharacteristic
760C2—3442no—
761C2—1722no—
762C2#1913709611yescharacteristic
763C2#1914343311yescharacteristic
764C2#1914345111yescharacteristic
765C2#1914387811yescharacteristic
766C2#1914391111yescharacteristic
767C2#1914482911yescharacteristic
768C2#1914488811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1863C2
socleC23×C43C22×D4
prime radicalC2×#13063300C22
cosocleC22×C4×C43C24
hypercenter#1863D43
hypocenterC43#21462
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1863

Complements

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

NH ≅ G/Ntype
1. C2×#14583375C2semidirect
3. C2×#14582998C2semidirect
4. C2×#14582984C2semidirect
6. #19134950C2semidirect
7. #19134949C2semidirect
9. #19134862C2semidirect
10. #19134791C2semidirect
11. #19134528C2semidirect
12. #19134427C2semidirect
13. #19134414C2semidirect
14. #19134360C2semidirect
15. C43×#1863C2semidirect
32. #14583039C4semidirect
71. C2×Q8×D43C2×C4semidirect
88. Q8×Dic43D4semidirect
94. #13063290D4semidirect
128. #13063248C2×C4semidirect
132. (C2×D43)⋊C8C2×C4semidirect
151. #103×C43C2×C4semidirect
385. #1863D43semidirect
448. C43#21462semidirect
528. #103C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145833752
C2×#145830392
C2×#145829982
C2×#145829842
#191372862
#191349502
#191349492
#191349162
#191348622
#191347912
#191345282
#191344272
#191344142
#191343602
C43×#18632
#2146243