Finite Group Databasebeta

← #25147698

Subgroups — #25147698

Order 11008.

1066 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583281C211yesmaximal, characteristic, complemented
2C2×#14583138C211yesmaximal, characteristic, complemented
3C2×#14583133C211yesmaximal, characteristic
4C2×C4×#10621882C211yesmaximal, characteristic, complemented
5#19138172C211yesmaximal, characteristic, complemented
6#19135836C211yesmaximal, characteristic, complemented
7#19135831C211yesmaximal, characteristic, complemented
8#19135598C211yesmaximal, characteristic, complemented
9#19135596C211yesmaximal, characteristic, complemented
10#19135455C211yesmaximal, characteristic, complemented
11#19135325C211yesmaximal, characteristic, complemented
12#19134932C211yesmaximal, characteristic, complemented
13#19134929C211yesmaximal, characteristic, complemented
14C22⋊C4×C43⋊C8C211yesmaximal, characteristic, complemented
15C43×#2427C211yesmaximal, characteristic, complemented
16C22×#10621885C2211yescharacteristic
17C22×#10621883C2211yescharacteristic
18C22×#10621884C2211yescharacteristic
19C22×#10621882C2211yescharacteristic
20C23×C43⋊C8C2211yescharacteristic
21C2×#13063313C2211yescharacteristic
22C2×#13063304C2211yescharacteristic
23C2×#13063299C2211yescharacteristic
24C2×C4×D172C2211yescharacteristic
25#14583281—24no—
26#14583138—24no—
27#14583133—24no—
28C4×#10621882—24no—
29C2×#13063258C2211yescharacteristic
30C2×#13063258C2211yescharacteristic
31C2×#13063249C2211yescharacteristic
32C2×#13063249C2211yescharacteristic
33C2×#13063248C2211yescharacteristic
34C2×#13063248C2211yescharacteristic
35C2×#13063246C2211yescharacteristic
36C2×#13063246C2211yescharacteristic
37C2×#13063245C2211yescharacteristic
38C2×#13063245C2211yescharacteristic
39C2×C22⋊(C43⋊C8)C2211yescharacteristic
40C2×C4×C43⋊C8C2211yescharacteristic
41C2×C4×C43⋊C8C2211yescharacteristic
42#14582828—21no—
43#14582814—21no—
44#14582805C2211yescharacteristic
45#14582797C2211yescharacteristic
46#14582775—21no—
47#14582758—21no—
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582654C2211yescharacteristic
51#14582654C2211yescharacteristic
52C2×#124×C43C2211yescharacteristic
53C2×C22⋊Q8×C43C2211yescharacteristic
54C2×#121×C43C2211yescharacteristic
55C2×C4×D4×C43C2211yescharacteristic
56C43×#397—21no—
57C43×#394—21no—
58C43×#391C2211yescharacteristic
59C43×#389C2211yescharacteristic
60C43×#386—21no—
61C43×#380—21no—
62C4×C22⋊C4×C43C2211yescharacteristic
63C22×Dic86C2311yescharacteristic
64C22×D172C2311yescharacteristic
65C22×C22⋊D43—21no—
66C22×C4×D43—21no—
67C2×#10621885—22no—
68C2×#10621885—22no—
69C2×#10621885—22no—
70C2×#10621883—22no—
71C2×#10621883—22no—
72C2×#10621883—41no—
73C2×#10621884—22no—
74C2×#10621884—22no—
75C2×#10621884—41no—
76C2×#10621882—22no—
77C2×#10621882—22no—
78C2×#10621882D414yes—
79C22×C43⋊C8—22no—
80C22×C43⋊C8—22no—
81C22×C43⋊C8—22no—
82C22×C43⋊C8C2311yescharacteristic
83C22×C43⋊C8C2311yescharacteristic
84C22×C43⋊C8C2311yescharacteristic
85C22×C43⋊C8C2311yescharacteristic
86#13063313—22no—
87#13063313—41no—
88#13063304—22no—
89#13063304—41no—
90#13063299—22no—
91#13063299—41no—
92C4×D172—22no—
93C4×D172—41no—
94C2×C4⋊Dic43C2311yescharacteristic
95C2×C4⋊Dic43C2311yescharacteristic
96C2×Dic43⋊C4—21no—
97C2×Dic43⋊C4—21no—
98C2×C22⋊Dic43—21no—
99C2×(C2×D43)⋊C4—21no—
100C2×(C2×D43)⋊C4—21no—
101C2×(C2×D43)⋊C4—21no—
102C2×(C2×D43)⋊C4—21no—
103#13063258—22no—
104#13063258D414yescomplemented
105#13063249—22no—
106#13063249—41no—
107#13063248—22no—
108#13063248—41no—
109#13063246—22no—
110#13063246—22no—
111#13063245—22no—
112#13063245—22no—
113C22⋊(C43⋊C8)—22no—
114C4×C43⋊C8—22no—
115C4×C43⋊C8—22no—
116C43⋊#95—21no—
117C43⋊#95—21no—
118C43⋊#95—21no—
119C22×Q8×C43C2311yescharacteristic
120C22×D4×C43—21no—
121C22×D4×C43C2311yescharacteristic
122C23×C4×C43—21no—
123C23×C4×C43C2311yescharacteristic
124#124×C43—22no—
125#124×C43—41no—
126C22⋊Q8×C43—22no—
127C22⋊Q8×C43—41no—
128#121×C43—22no—
129#121×C43—41no—
130C4×D4×C43—22no—
131C4×D4×C43—41no—
132C2×C4⋊C4×C43—21no—
133C2×C4⋊C4×C43—21no—
134C2×C4⋊C4×C43C2311yescharacteristic
135C2×C4⋊C4×C43C2311yescharacteristic
136C2×C22⋊C4×C43—21no—
137C2×C22⋊C4×C43—21no—
138C2×C22⋊C4×C43—21no—
139C2×C22⋊C4×C43—21no—
140C2×C22⋊C4×C43—21no—
141C2×C22⋊C4×C43D411yescharacteristic
142C2×C22⋊C4×C43D411yescharacteristic
143C2×C42×C43C2311yescharacteristic
144C2×C42×C43C2311yescharacteristic
145#95×C43—21no—
146#95×C43—21no—
147#95×C43—21no—
148#95×C43D411yescharacteristic
149#95×C43D411yescharacteristic
150C24×C43—21no—
151C24×C43C2×D411yescharacteristic
152C23×D43—21no—
153C2×Q8×C43—21no—
154C2×Q8×C43—21no—
155C2×Q8×C43—21no—
156C2×Q8×C43—21no—
157C2×Q8×C43—21no—
158C2×Q8×C43—21no—
159C2×D4×C43—21no—
160C2×D4×C43—21no—
161C2×D4×C43—21no—
162C2×D4×C43—21no—
163C2×D4×C43—21no—
164C2×D4×C43—42no—
165C2×D4×C43—42no—
166C2×D4×C43—81no—
167C2×D4×C43C2×D412yes—
168C22×C4×C43—21no—
169C22×C4×C43—21no—
170C22×C4×C43—21no—
171C22×C4×C43—21no—
172C22×C4×C43—21no—
173C22×C4×C43—21no—
174C22×C4×C43—21no—
175C22×C4×C43—21no—
176C22×C4×C43—21no—
177C22×C4×C43—42no—
178C22×C4×C43—42no—
179C22×C4×C43—81no—
180C22×C4×C43C2×D411yescharacteristic
181C22×C4×C43C2×D411yescharacteristic
182C22×C4×C43C2×D411yescharacteristic
183C22×C4×C43C2×D411yescharacteristic
184C22×C4×C43C2×D411yescharacteristic
185C22×C4×C43C2411yescharacteristic
186C2×C22⋊D43—42no—
187C2×C22⋊D43—42no—
188C2×C22⋊D43—81no—
189C22×Dic43—21no—
190C22×Dic43—21no—
191C22×Dic43—21no—
192C2×D172—21no—
193C2×D172—21no—
194C2×D172—21no—
195C2×D172—21no—
196C2×D172—21no—
197C2×D172C2×D412yes—
198C2×C4×D43—42no—
199C2×C4×D43—42no—
200C2×C4×D43—81no—
201C2×Dic86—21no—
202C2×Dic86—21no—
203C2×Dic86—21no—
204C2×Dic86—21no—
205C2×Dic86—21no—
206C2×Dic86—21no—
207C4⋊C4×C43—21no—
208C4⋊C4×C43—21no—
209C4⋊C4×C43—21no—
210C4⋊C4×C43—42no—
211C4⋊C4×C43—81no—
212C4⋊C4×C43C2×D412yes—
213C22⋊C4×C43—22no—
214C22⋊C4×C43—22no—
215C22⋊C4×C43—42no—
216C22⋊C4×C43—42no—
217C22⋊C4×C43—42no—
218C22⋊C4×C43—42no—
219C22⋊C4×C43—42no—
220C42×C43—21no—
221C42×C43—21no—
222C42×C43—21no—
223C42×C43—21no—
224C22⋊Dic43—42no—
225#10621885—44no—
226#10621884—44no—
227#10621883—44no—
228#10621882—28no—
229(C2×D43)⋊C4—42no—
230(C2×D43)⋊C4—42no—
231(C2×D43)⋊C4—42no—
232(C2×D43)⋊C4—42no—
233C4⋊Dic43—21no—
234C4⋊Dic43—21no—
235C4⋊Dic43—21no—
236C4⋊Dic43C2×D412yes—
237Dic43⋊C4—42no—
238Dic43⋊C4—81no—
239C2×C43⋊C8—21no—
240C2×C43⋊C8—21no—
241C2×C43⋊C8—21no—
242C2×C43⋊C8—21no—
243C2×C43⋊C8—21no—
244C2×C43⋊C8—21no—
245C2×C43⋊C8—21no—
246C2×C43⋊C8—21no—
247C2×C43⋊C8—44no—
248C2×C43⋊C8C2×D412yes—
249C2×C43⋊C8C2×D412yes—
250C2×C43⋊C8#4112yes—
251C2×C43⋊C8#4112yes—
252C23×C43—21no—
253C23×C43—21no—
254C23×C43—21no—
255C23×C43—21no—
256C23×C43—21no—
257C23×C43—21no—
258C23×C43—22no—
259C23×C43—41no—
260C23×C43—41no—
261C23×C43—41no—
262C23×C43—41no—
263C23×C43—41no—
264C23×C43—41no—
265C23×C43#13512yes—
266C23×C43C22×D411yescharacteristic
267C22×D43—22no—
268C22×D43—41no—
269C22×D43—41no—
270C22×D43—41no—
271C22×D43—41no—
272C22×D43—41no—
273C22×D43—41no—
274Q8×C43—41no—
275Q8×C43—41no—
276Q8×C43—41no—
277Q8×C43—41no—
278D4×C43—22no—
279D4×C43—22no—
280D4×C43—41no—
281D4×C43—41no—
282D4×C43—84no—
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—22no—
292C2×C4×C43—21no—
293C2×C4×C43—21no—
294C2×C4×C43—21no—
295C2×C4×C43—21no—
296C2×C4×C43—21no—
297C2×C4×C43—21no—
298C2×C4×C43—41no—
299C2×C4×C43—41no—
300C2×C4×C43—41no—
301C2×C4×C43—41no—
302C2×C4×C43—41no—
303C2×C4×C43—41no—
304C2×C4×C43—41no—
305C2×C4×C43—41no—
306C2×C4×C43—41no—
307C2×C4×C43—41no—
308C2×C4×C43—41no—
309C2×C4×C43—41no—
310C2×C4×C43—84no—
311C2×C4×C43#13512yes—
312C2×C4×C43C22×D411yescharacteristic
313C2×C4×C43C22×D411yescharacteristic
314C2×C4×C43C2×#4111yescharacteristic
315C2×C4×C43C2×#4111yescharacteristic
316C2×C4×C43H(5,𝔽2)11yescharacteristic
317C2×C4×C43H(5,𝔽2)11yescharacteristic
318C22⋊D43—84no—
319C2×Dic43—22no—
320C2×Dic43—41no—
321C2×Dic43—41no—
322C2×Dic43—41no—
323C2×Dic43—41no—
324C2×Dic43—41no—
325C2×Dic43—41no—
326C2×Dic43—41no—
327C2×Dic43—41no—
328D172—22no—
329D172—22no—
330D172—41no—
331D172—41no—
332C4×D43—84no—
333Dic86—41no—
334Dic86—41no—
335Dic86—41no—
336Dic86—41no—
337C43⋊C8—22no—
338C43⋊C8—41no—
339C43⋊C8—41no—
340C43⋊C8#12114yes—
341#25413—431nomaximal, Sylow
342C22×C43—22no—
343C22×C43—22no—
344C22×C43—22no—
345C22×C43—41no—
346C22×C43—41no—
347C22×C43—41no—
348C22×C43—41no—
349C22×C43—42no—
350C22×C43—42no—
351C22×C43—42no—
352C22×C43—81no—
353C22×C43—81no—
354C22×C43—81no—
355C22×C43—81no—
356C22×C43#53211yescharacteristic
357C22×C43D4211yescharacteristic
358C22×C43D4211yescharacteristic
359C22×C43C2×#13511yescharacteristic
360C22×C43C2×#13511yescharacteristic
361C22×C43#57611yescharacteristic
362C22×C43#57811yescharacteristic
363C2×D43—42no—
364C2×D43—42no—
365C2×D43—42no—
366C2×D43—81no—
367C2×D43—81no—
368C2×D43—81no—
369C2×D43—81no—
370C4×C43—22no—
371C4×C43—41no—
372C4×C43—41no—
373C4×C43—42no—
374C4×C43—41no—
375C4×C43—41no—
376C4×C43—81no—
377C4×C43—81no—
378C4×C43C2×#12111yescharacteristic
379C4×C43#54011yescharacteristic
380C4×C43#54611yescharacteristic
381C4×C43#55011yescharacteristic
382Dic43—42no—
383Dic43—81no—
384Dic43—81no—
385C2×#495—431no—
386C2×#467—431no—
387C2×#466—431no—
388C2×C4×D8—431no—
389#2427—431no—
390#2427D4311yescharacteristic, complemented
391#2042—431no—
392#2042—431no—
393#2000—431no—
394#2000—431no—
395#1969—431no—
396#1942—431no—
397#1877—431no—
398#1877—431no—
399C8×C22⋊C4—431no—
400C2×C43—42no—
401C2×C43—82no—
402C2×C43#242811yescharacteristic
403C2×C43#316811yescharacteristic
404C2×C43#317511yescharacteristic
405C2×C43#328011yescharacteristic
406C2×C43#328011yescharacteristic
407C2×C43#328311yescharacteristic
408C2×C43#328511yescharacteristic
409D43—82no—
410C22×Q16—431no—
411C22×SD16—431no—
412C22×SD16—431no—
413C22×D8—431no—
414C23×C8—431no—
415C2×#124—431no—
416C2×#124C2×D4311yescharacteristic
417C2×C22⋊Q8—431no—
418C2×C22⋊Q8C2×D4311yescharacteristic
419C2×#121—431no—
420C2×#121C2×D4311yescharacteristic
421C2×C4×D4—431no—
422C2×C4×D4C2×D4311yescharacteristic
423#495—864no—
424#467—864no—
425#466—864no—
426C4×D8—864no—
427C2×#107—431no—
428C2×#107—431no—
429C2×#103—431no—
430C2×#103—431no—
431C2×#103—431no—
432C2×#103—431no—
433C2×#102—431no—
434C2×#102—431no—
435C2×#102—431no—
436C2×#102—431no—
437C2×C22⋊C8—431no—
438C2×C4×C8—431no—
439C2×C4×C8—431no—
440#397—21no—
441#397—861no—
442#394—21no—
443#394—861no—
444#391—431no—
445#391C2×D4311yescharacteristic
446#389—431no—
447#389C2×D4311yescharacteristic
448#386—21no—
449#386—861no—
450#380—21no—
451#380—861no—
452C4×C22⋊C4C2×D4311yescharacteristic
453#340—431no—
454#340—431no—
455#336—431no—
456#336—431no—
457C43#2541311yescharacteristic, complemented, Sylow
458C22×Q8—431no—
459C22×Q8C22×D4311yescharacteristic
460C22×D4—21no—
461C22×D4—431no—
462C22×D4—861no—
463C22×D4C22×D4311yescharacteristic
464C23×C4—21no—
465C23×C4—861no—
466C23×C4C22×D4311yescharacteristic
467C2×Q16—862no—
468C2×Q16—862no—
469C2×Q16—862no—
470C2×SD16—862no—
471C2×SD16—862no—
472C2×SD16—862no—
473C2×SD16—862no—
474C2×SD16—1721no—
475C2×SD16—1721no—
476C2×D8—434no—
477C2×D8—862no—
478C2×D8—862no—
479C22×C8—431no—
480C22×C8—431no—
481C22×C8—431no—
482C22×C8—431no—
483C22×C8—862no—
484C22×C8—862no—
485C22×C8—862no—
486#124—22no—
487#124—41no—
488#124—862no—
489#124—1721no—
490C22⋊Q8—22no—
491C22⋊Q8—41no—
492C22⋊Q8—862no—
493C22⋊Q8—1721no—
494#121—22no—
495#121—41no—
496#121—862no—
497#121—1721no—
498C4×D4—22no—
499C4×D4—41no—
500C4×D4—862no—
501C4×D4—1721no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—431no—
505C2×C4⋊C4—431no—
506C2×C4⋊C4—861no—
507C2×C4⋊C4—861no—
508C2×C4⋊C4C22×D4311yescharacteristic
509C2×C4⋊C4C22×D4311yescharacteristic
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—861no—
516C2×C22⋊C4—861no—
517C2×C22⋊C4—861no—
518C2×C22⋊C4—861no—
519C2×C22⋊C4—861no—
520C2×C22⋊C4C22⋊D4311yescharacteristic
521C2×C22⋊C4C22⋊D4311yescharacteristic
522C2×C42C22×D4311yescharacteristic
523C2×C42C22×D4311yescharacteristic
524#107—434no—
525#107—862no—
526#103—862no—
527#103—862no—
528#103—1721no—
529#103—1721no—
530#102—862no—
531#102—862no—
532#102—862no—
533#102—862no—
534C22⋊C8—862no—
535C4×C8—862no—
536C4×C8—862no—
537#95—21no—
538#95—21no—
539#95—21no—
540#95—861no—
541#95—861no—
542#95—861no—
543#95C22⋊D4311yescharacteristic
544#95C22⋊D4311yescharacteristic
545C24—21no—
546C24—861no—
547C24C2×C22⋊D4311yescharacteristic
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8—861no—
555C2×Q8—861no—
556C2×Q8—861no—
557C2×Q8—861no—
558C2×Q8—861no—
559C2×Q8—861no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—42no—
566C2×D4—42no—
567C2×D4—81no—
568C2×D4—432no—
569C2×D4—861no—
570C2×D4—861no—
571C2×D4—861no—
572C2×D4—861no—
573C2×D4—861no—
574C2×D4—3441no—
575C2×D4—1722no—
576C2×D4—1722no—
577C2×D4D4×D4312yes—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—42no—
588C22×C4—42no—
589C22×C4—81no—
590C22×C4—861no—
591C22×C4—861no—
592C22×C4—861no—
593C22×C4—3441no—
594C22×C4—1722no—
595C22×C4—1722no—
596C22×C4C2×C22⋊D4311yescharacteristic
597C22×C4C2×C22⋊D4311yescharacteristic
598C22×C4C2×C22⋊D4311yescharacteristic
599C22×C4C2×C22⋊D4311yescharacteristic
600C22×C4C2×C22⋊D4311yescharacteristic
601C22×C4C23×D4311yescharacteristic
602Q16—1724no—
603SD16—1724no—
604SD16—1724no—
605D8—868no—
606C2×C8—432no—
607C2×C8—432no—
608C2×C8—432no—
609C2×C8—432no—
610C2×C8—861no—
611C2×C8—861no—
612C2×C8—861no—
613C2×C8—861no—
614C2×C8—861no—
615C2×C8—861no—
616C2×C8—861no—
617C2×C8—861no—
618C2×C8—1724no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—42no—
623C4⋊C4—81no—
624C4⋊C4—432no—
625C4⋊C4—861no—
626C4⋊C4—861no—
627C4⋊C4—861no—
628C4⋊C4—3441no—
629C4⋊C4—1722no—
630C4⋊C4D4×D4312yes—
631C22⋊C4—22no—
632C22⋊C4—22no—
633C22⋊C4—42no—
634C22⋊C4—42no—
635C22⋊C4—42no—
636C22⋊C4—42no—
637C22⋊C4—42no—
638C22⋊C4—1722no—
639C22⋊C4—1722no—
640C22⋊C4—1722no—
641C22⋊C4—1722no—
642C22⋊C4—1722no—
643C42—21no—
644C42—21no—
645C42—21no—
646C42—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—22no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—862no—
661C23—1721no—
662C23—1721no—
663C23—1721no—
664C23—1721no—
665C23—1721no—
666C23—1721no—
667C23#1306334512yes—
668C23C22×C22⋊D4311yescharacteristic
669Q8—41no—
670Q8—41no—
671Q8—41no—
672Q8—41no—
673Q8—1721no—
674Q8—1721no—
675Q8—1721no—
676Q8—1721no—
677D4—22no—
678D4—22no—
679D4—41no—
680D4—41no—
681D4—84no—
682D4—862no—
683D4—862no—
684D4—3444no—
685D4—1721no—
686D4—1721no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—22no—
701C2×C4—21no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—84no—
715C2×C4—862no—
716C2×C4—3444no—
717C2×C4—1721no—
718C2×C4—1721no—
719C2×C4—1721no—
720C2×C4—1721no—
721C2×C4—1721no—
722C2×C4—1721no—
723C2×C4—1721no—
724C2×C4—1721no—
725C2×C4#1306334512yes—
726C2×C4C2×D4×D4311yescharacteristic
727C2×C4C2×D4×D4311yescharacteristic
728C2×C4#41×D4311yescharacteristic
729C2×C4#41×D4311yescharacteristic
730C2×C4#1306337011yescharacteristic
731C2×C4#1306337011yescharacteristic
732C8—434no—
733C8—862no—
734C8—1721no—
735C8—1721no—
736C22—22no—
737C22—22no—
738C22—22no—
739C22—41no—
740C22—41no—
741C22—41no—
742C22—41no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—81no—
747C22—81no—
748C22—81no—
749C22—81no—
750C22—3441no—
751C22—3441no—
752C22—3441no—
753C22—3441no—
754C22—1722no—
755C22—1722no—
756C22—1722no—
757C22#1458344511yescharacteristic
758C22D4×C22⋊D4311yescharacteristic
759C22D4×C22⋊D4311yescharacteristic
760C22C2×#1306334511yescharacteristic
761C22C2×#1306334511yescharacteristic
762C22#1458370211yescharacteristic
763C22#1458371411yescharacteristic
764C4—22no—
765C4—41no—
766C4—42no—
767C4—41no—
768C4—41no—
769C4—41no—
770C4—81no—
771C4—81no—
772C4—3441no—
773C4—3441no—
774C4—1722no—
775C4#121×D4311yescharacteristic
776C4#1458349911yescharacteristic
777C4#1458353811yescharacteristic
778C4#1458356711yescharacteristic
779C2—42no—
780C2—82no—
781C2—3442no—
782C2#1913818011yescharacteristic
783C2#1914515911yescharacteristic
784C2#1914522811yescharacteristic
785C2#1914627611yescharacteristic
786C2#1914627611yescharacteristic
787C2#1914631311yescharacteristic
788C2#1914633211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2427C2
socleC23×C43C22×D4
prime radicalC2×#14583133C2
hypercenter#2427D43
hypocenterC43#25413
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2427

Complements

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

NH ≅ G/Ntype
1. C2×#14583281C2semidirect
2. C2×#14583138C2semidirect
4. C2×C4×#10621882C2semidirect
5. #19138172C2semidirect
6. #19135836C2semidirect
7. #19135831C2semidirect
8. #19135598C2semidirect
9. #19135596C2semidirect
10. #19135455C2semidirect
11. #19135325C2semidirect
12. #19134932C2semidirect
13. #19134929C2semidirect
14. C22⋊C4×C43⋊C8C2semidirect
15. C43×#2427C2semidirect
104. #13063258D4semidirect
390. #2427D43semidirect
457. C43#25413semidirect

Maximal subgroups

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

subgroupindex
C2×#145832812
C2×#145831382
C2×#145831332
C2×C4×#106218822
#191381722
#191358362
#191358312
#191355982
#191355962
#191354552
#191353252
#191349322
#191349292
C22⋊C4×C43⋊C82
C43×#24272
#2541343