Finite Group Databasebeta

← #25130574

Subgroups — #25130574

Order 11008.

1216 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583595C211yesmaximal, characteristic, complemented
2C2×#14583199C211yesmaximal, characteristic, complemented
3C2×C4×#10621882C211yesmaximal, characteristic, complemented
4#19135784C211yesmaximal, characteristic, complemented
5#19135777C211yesmaximal, characteristic, complemented
6#19135591C211yesmaximal, characteristic, complemented
7#19135591C211yesmaximal, characteristic, complemented
8#19135559C211yesmaximal, characteristic, complemented
9#19135390C211yesmaximal, characteristic, complemented
10#19134918C211yesmaximal, characteristic, complemented
11#19134913C211yesmaximal, characteristic, complemented
12#19134792C211yesmaximal, characteristic, complemented
13#19134782C211yesmaximal, characteristic, complemented
14#19134602C211yesmaximal, characteristic, complemented
15C43×#2535C211yesmaximal, characteristic, complemented
16C22×#10621882C2211yescharacteristic
17#14583595—24no—
18#14583595—24no—
19C2×#13063320—21no—
20C2×#13063317C2211yescharacteristic
21C2×#13063307—21no—
22C2×#13063299C2211yescharacteristic
23C2×#13063299C2211yescharacteristic
24C2×#13063297—21no—
25C2×C4×D172C2211yescharacteristic
26C2×(C22⋊D43)⋊C4—21no—
27C2×#13063284C2211yescharacteristic
28C22×C4⋊Dic43C2211yescharacteristic
29#14583199—24no—
30C4×#10621882—24no—
31C2×#13063258C2211yescharacteristic
32C2×#13063258C2211yescharacteristic
33C2×#13063256C2211yescharacteristic
34C2×C4⋊(C43⋊C8)C2211yescharacteristic
35C2×#13063246C2211yescharacteristic
36C2×#13063246C2211yescharacteristic
37C2×#13063246C2211yescharacteristic
38C2×#13063245C2211yescharacteristic
39C2×#13063245C2211yescharacteristic
40C2×#13063245C2211yescharacteristic
41C2×C22⋊(C43⋊C8)C2211yescharacteristic
42C2×C22⋊(C43⋊C8)C2211yescharacteristic
43C2×C22⋊(C43⋊C8)C2211yescharacteristic
44C2×C22⋊(C43⋊C8)C2211yescharacteristic
45C2×C4×C43⋊C8C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52C2×#121×C43C2211yescharacteristic
53C2×#121×C43C2211yescharacteristic
54C2×C4×D4×C43C2211yescharacteristic
55C2×C4×D4×C43C2211yescharacteristic
56C43×#397—21no—
57C43×#392—21no—
58C43×#386—21no—
59C43×#386—21no—
60C43×#382C2211yescharacteristic
61C43×#380C2211yescharacteristic
62C43×#380C2211yescharacteristic
63C22×D172C2311yescharacteristic
64C22×C22⋊D43—21no—
65C22×C22⋊D43—21no—
66C23×Dic43—21no—
67C22×C4×D43—21no—
68C2×#10621882—22no—
69C2×#10621882—22no—
70C2×#10621882—22no—
71C22×C43⋊C8C2311yescharacteristic
72C22×C43⋊C8C2311yescharacteristic
73C22×C43⋊C8C2311yescharacteristic
74C22×C43⋊C8C2311yescharacteristic
75#13063320—28no—
76#13063317—22no—
77#13063317D414yescomplemented
78#13063307—28no—
79#13063299—22no—
80#13063299—22no—
81#13063299—22no—
82#13063299—22no—
83#13063297—28no—
84C4×D172—22no—
85C4×D172D414yescomplemented
86(C22⋊D43)⋊C4—28no—
87#13063284—22no—
88#13063284—22no—
89C2×C4⋊Dic43—21no—
90C2×C4⋊Dic43—22no—
91C2×C4⋊Dic43—22no—
92C2×C4⋊Dic43C2311yescharacteristic
93C2×C4⋊Dic43C2311yescharacteristic
94C2×C4⋊Dic43C2311yescharacteristic
95C2×Dic43⋊C4—21no—
96C2×Dic43⋊C4—21no—
97C2×C22⋊Dic43—21no—
98C2×(C2×D43)⋊C4—21no—
99C2×(C2×D43)⋊C4—21no—
100C2×(C2×D43)⋊C4—21no—
101C2×C4×Dic43—21no—
102#13063258—22no—
103#13063258—22no—
104#13063256—22no—
105C4⋊(C43⋊C8)—22no—
106#13063246—22no—
107#13063246—22no—
108#13063246—22no—
109#13063245—22no—
110#13063245—41no—
111#13063245—41no—
112C22⋊(C43⋊C8)—22no—
113C22⋊(C43⋊C8)—22no—
114C22⋊(C43⋊C8)—41no—
115C22⋊(C43⋊C8)—41no—
116C4×C43⋊C8—22no—
117C22×D4×C43—21no—
118C22×D4×C43—21no—
119C22×D4×C43D411yescharacteristic
120C22×D4×C43C2311yescharacteristic
121C23×C4×C43—21no—
122C23×C4×C43C2311yescharacteristic
123C23×C4×C43C2311yescharacteristic
124#121×C43—22no—
125#121×C43—22no—
126#121×C43—41no—
127#121×C43—41no—
128C4×D4×C43—22no—
129C4×D4×C43—22no—
130C4×D4×C43—22no—
131C4×D4×C43—22no—
132C2×C4⋊C4×C43D411yescharacteristic
133C2×C4⋊C4×C43C2311yescharacteristic
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
144#95×C43—21no—
145#95×C43—21no—
146#95×C43—21no—
147#95×C43—21no—
148C24×C43—21no—
149C24×C43C2×D411yescharacteristic
150C24×C43C2×D411yescharacteristic
151C23×D43—21no—
152C2×D4×C43—22no—
153C2×D4×C43—21no—
154C2×D4×C43—22no—
155C2×D4×C43—21no—
156C2×D4×C43—21no—
157C2×D4×C43—21no—
158C2×D4×C43—21no—
159C2×D4×C43—41no—
160C2×D4×C43—42no—
161C2×D4×C43—42no—
162C2×D4×C43—42no—
163C2×D4×C43—42no—
164C2×D4×C43—81no—
165C2×D4×C43—81no—
166C2×D4×C43#4112yes—
167C22×C4×C43—21no—
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—21no—
178C22×C4×C43—21no—
179C22×C4×C43—21no—
180C22×C4×C43—21no—
181C22×C4×C43—21no—
182C22×C4×C43—42no—
183C22×C4×C43—81no—
184C22×C4×C43—81no—
185C22×C4×C43C2×D411yescharacteristic
186C22×C4×C43C2×D411yescharacteristic
187C22×C4×C43C2×D411yescharacteristic
188C22×C4×C43C2×D411yescharacteristic
189C22×C4×C43C2411yescharacteristic
190C2×C22⋊D43—24no—
191C2×C22⋊D43—24no—
192C2×C22⋊D43—42no—
193C2×C22⋊D43—42no—
194C2×C22⋊D43—81no—
195C2×C22⋊D43—81no—
196C22×Dic43—24no—
197C22×Dic43—21no—
198C22×Dic43—21no—
199C22×Dic43—21no—
200C22×Dic43—81no—
201C22×Dic43—81no—
202C2×D172—21no—
203C2×D172—21no—
204C2×D172—21no—
205C2×D172—21no—
206C2×D172—21no—
207C2×D172C2×D412yes—
208C2×C4×D43—24no—
209C2×C4×D43—81no—
210C2×C4×D43—81no—
211C4⋊C4×C43—22no—
212C4⋊C4×C43—21no—
213C4⋊C4×C43—21no—
214C4⋊C4×C43—21no—
215C4⋊C4×C43—21no—
216C4⋊C4×C43—21no—
217C4⋊C4×C43—21no—
218C22⋊C4×C43—22no—
219C22⋊C4×C43—22no—
220C22⋊C4×C43—42no—
221C22⋊C4×C43—42no—
222C22⋊C4×C43—42no—
223C22⋊C4×C43—81no—
224C22⋊C4×C43—81no—
225C42×C43C2×D412yes—
226C42×C43C2×D412yes—
227C22⋊Dic43—24no—
228#10621882—28no—
229(C2×D43)⋊C4—24no—
230(C2×D43)⋊C4—24no—
231(C2×D43)⋊C4—24no—
232C4⋊Dic43—24no—
233C4⋊Dic43—21no—
234C4⋊Dic43—21no—
235C4⋊Dic43—21no—
236C4⋊Dic43C2×D412yes—
237C4⋊Dic43C2×D412yes—
238C4⋊Dic43C2×D412yes—
239Dic43⋊C4—24no—
240Dic43⋊C4—24no—
241C4×Dic43—24no—
242C2×C43⋊C8—21no—
243C2×C43⋊C8—21no—
244C2×C43⋊C8—21no—
245C2×C43⋊C8—21no—
246C2×C43⋊C8—21no—
247C2×C43⋊C8—21no—
248C2×C43⋊C8—21no—
249C2×C43⋊C8—21no—
250C2×C43⋊C8—21no—
251C2×C43⋊C8—21no—
252C2×C43⋊C8—21no—
253C2×C43⋊C8#4112yes—
254C23×C43—21no—
255C23×C43—21no—
256C23×C43—21no—
257C23×C43—21no—
258C23×C43—21no—
259C23×C43—21no—
260C23×C43—21no—
261C23×C43—22no—
262C23×C43—21no—
263C23×C43—21no—
264C23×C43—21no—
265C23×C43—21no—
266C23×C43—21no—
267C23×C43—21no—
268C23×C43—41no—
269C23×C43—41no—
270C23×C43—41no—
271C23×C43—41no—
272C23×C43—41no—
273C23×C43—41no—
274C23×C43#13512yes—
275C23×C43C22×D411yescharacteristic
276C22×D43—22no—
277C22×D43—41no—
278C22×D43—41no—
279C22×D43—41no—
280C22×D43—41no—
281C22×D43—41no—
282C22×D43—41no—
283D4×C43—22no—
284D4×C43—22no—
285D4×C43—44no—
286D4×C43—41no—
287D4×C43—41no—
288D4×C43—84no—
289D4×C43—84no—
290C2×C4×C43—21no—
291C2×C4×C43—21no—
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—21no—
299C2×C4×C43—21no—
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—41no—
311C2×C4×C43—41no—
312C2×C4×C43—41no—
313C2×C4×C43—41no—
314C2×C4×C43—41no—
315C2×C4×C43—41no—
316C2×C4×C43—41no—
317C2×C4×C43—84no—
318C2×C4×C43#12012yes—
319C2×C4×C43#12012yes—
320C2×C4×C43C22×D411yescharacteristic
321C2×C4×C43C22×D411yescharacteristic
322C2×C4×C43C2×#4111yescharacteristic
323C2×C4×C43C2×#4111yescharacteristic
324C2×C4×C43H(5,𝔽2)11yescharacteristic
325C2×C4×C432−1+411yescharacteristic
326C22⋊D43—48no—
327C22⋊D43—84no—
328C2×Dic43—22no—
329C2×Dic43—22no—
330C2×Dic43—22no—
331C2×Dic43—41no—
332C2×Dic43—41no—
333C2×Dic43—41no—
334C2×Dic43—41no—
335C2×Dic43—41no—
336C2×Dic43—41no—
337C2×Dic43—84no—
338D172—22no—
339D172—22no—
340D172—41no—
341D172—41no—
342C4×D43—84no—
343C43⋊C8—22no—
344C43⋊C8—41no—
345C43⋊C8—41no—
346C43⋊C8—41no—
347#24124—431nomaximal, Sylow
348C22×C43—22no—
349C22×C43—22no—
350C22×C43—22no—
351C22×C43—41no—
352C22×C43—41no—
353C22×C43—41no—
354C22×C43—41no—
355C22×C43—41no—
356C22×C43—41no—
357C22×C43—41no—
358C22×C43—42no—
359C22×C43—41no—
360C22×C43—41no—
361C22×C43—41no—
362C22×C43—42no—
363C22×C43—41no—
364C22×C43—42no—
365C22×C43—81no—
366C22×C43—81no—
367C22×C43—81no—
368C22×C43—81no—
369C22×C43C2×#12011yescharacteristic
370C22×C43#54611yescharacteristic
371C22×C43#54711yescharacteristic
372C22×C43C2×#13511yescharacteristic
373C22×C43#57511yescharacteristic
374C22×C43#57611yescharacteristic
375C22×C43#57611yescharacteristic
376C2×D43—42no—
377C2×D43—42no—
378C2×D43—42no—
379C2×D43—81no—
380C2×D43—81no—
381C2×D43—81no—
382C2×D43—81no—
383C4×C43—22no—
384C4×C43—22no—
385C4×C43—41no—
386C4×C43—41no—
387C4×C43—81no—
388C4×C43—81no—
389C4×C43—81no—
390C4×C43#52511yescharacteristic
391C4×C43#53711yescharacteristic
392C4×C43#54811yescharacteristic
393C4×C43#55011yescharacteristic
394Dic43—42no—
395Dic43—42no—
396Dic43—42no—
397C2×#553—431no—
398C2×#478—431no—
399C2×C4×D8—431no—
400#2535D4311yescharacteristic, complemented
401#2034—431no—
402#2033—431no—
403#1999—431no—
404#1999—431no—
405#1991—431no—
406#1954—431no—
407#1875—431no—
408#1874—431no—
409#1854—431no—
410#1852—431no—
411#1804—431no—
412C2×C43—42no—
413C2×C43—81no—
414C2×C43—82no—
415C2×C43#240711yescharacteristic
416C2×C43#300211yescharacteristic
417C2×C43#300811yescharacteristic
418C2×C43#329711yescharacteristic
419C2×C43#332211yescharacteristic
420C2×C43#333911yescharacteristic
421C2×C43#335511yescharacteristic
422D43—82no—
423C22×D8—431no—
424#553—864no—
425#553—864no—
426C2×#126—861no—
427C2×#125—431no—
428C2×#123—861no—
429C2×#121—431no—
430C2×#121—431no—
431C2×#121—861no—
432C2×#121C2×D4311yescharacteristic
433C2×#121C2×D4311yescharacteristic
434C2×C4×D4—431no—
435C2×C4×D4—861no—
436C2×C4×D4C2×D4311yescharacteristic
437C2×C4×D4C2×D4311yescharacteristic
438C2×#117—431no—
439C22×C4⋊C4—431no—
440#478—864no—
441C4×D8—864no—
442C2×#107—431no—
443C2×#107—431no—
444C2×#106—431no—
445C2×C4⋊C8—431no—
446C2×#102—431no—
447C2×#102—431no—
448C2×#102—431no—
449C2×#102—431no—
450C2×#102—431no—
451C2×#102—431no—
452C2×C22⋊C8—431no—
453C2×C22⋊C8—431no—
454C2×C22⋊C8—431no—
455C2×C22⋊C8—431no—
456C2×C4×C8—431no—
457#397—21no—
458#392—21no—
459#386—21no—
460#386—21no—
461#382C2×D4311yescharacteristic
462#380C2×D4311yescharacteristic
463#380C2×D4311yescharacteristic
464#340—431no—
465#340—431no—
466#340—431no—
467#340—431no—
468#340—431no—
469#340—431no—
470C43#2412411yescharacteristic, complemented, Sylow
471C22×D4—21no—
472C22×D4—21no—
473C22×D4—431no—
474C22×D4—861no—
475C22×D4—861no—
476C22×D4C22⋊D4311yescharacteristic
477C22×D4C22×D4311yescharacteristic
478C23×C4—21no—
479C23×C4—861no—
480C23×C4—861no—
481C23×C4C22×D4311yescharacteristic
482C23×C4C22×D4311yescharacteristic
483C2×D8—862no—
484C2×D8—862no—
485C2×D8—862no—
486C22×C8—431no—
487C22×C8—431no—
488C22×C8—431no—
489C22×C8—431no—
490#126—868no—
491#125—434no—
492#125—862no—
493#123—868no—
494#121—22no—
495#121—22no—
496#121—41no—
497#121—41no—
498#121—862no—
499#121—862no—
500#121—862no—
501#121—862no—
502#121—868no—
503C4×D4—22no—
504C4×D4—22no—
505C4×D4—22no—
506C4×D4—22no—
507C4×D4—434no—
508C4×D4—868no—
509C4×D4—862no—
510#117—862no—
511#117—862no—
512C2×C4⋊C4—431no—
513C2×C4⋊C4—431no—
514C2×C4⋊C4—431no—
515C2×C4⋊C4—862no—
516C2×C4⋊C4—862no—
517C2×C4⋊C4—861no—
518C2×C4⋊C4—861no—
519C2×C4⋊C4—861no—
520C2×C4⋊C4C22⋊D4311yescharacteristic
521C2×C4⋊C4C22×D4311yescharacteristic
522C2×C4⋊C4C22×D4311yescharacteristic
523C2×C4⋊C4C22×D4311yescharacteristic
524C2×C22⋊C4—21no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—861no—
530C2×C22⋊C4—861no—
531C2×C22⋊C4—861no—
532C2×C22⋊C4—861no—
533C2×C22⋊C4C22⋊D4311yescharacteristic
534C2×C22⋊C4C22⋊D4311yescharacteristic
535C2×C42—861no—
536C2×C42C22×D4311yescharacteristic
537#107—862no—
538#107—862no—
539#106—862no—
540C4⋊C8—862no—
541#102—862no—
542#102—862no—
543#102—862no—
544#102—862no—
545#102—1721no—
546#102—1721no—
547C22⋊C8—862no—
548C22⋊C8—862no—
549C22⋊C8—1721no—
550C22⋊C8—1721no—
551C4×C8—862no—
552#95—21no—
553#95—21no—
554#95—21no—
555#95—21no—
556C24—21no—
557C24—861no—
558C24C2×C22⋊D4311yescharacteristic
559C24C2×C22⋊D4311yescharacteristic
560C2×D4—22no—
561C2×D4—22no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—41no—
568C2×D4—42no—
569C2×D4—42no—
570C2×D4—42no—
571C2×D4—42no—
572C2×D4—81no—
573C2×D4—81no—
574C2×D4—432no—
575C2×D4—864no—
576C2×D4—864no—
577C2×D4—861no—
578C2×D4—861no—
579C2×D4—861no—
580C2×D4—861no—
581C2×D4—861no—
582C2×D4—3441no—
583C2×D4—3441no—
584C2×D4—1722no—
585C2×D4—1722no—
586C2×D4#1062190012yes—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—42no—
603C22×C4—81no—
604C22×C4—81no—
605C22×C4—864no—
606C22×C4—861no—
607C22×C4—861no—
608C22×C4—861no—
609C22×C4—864no—
610C22×C4—3441no—
611C22×C4—3441no—
612C22×C4—3441no—
613C22×C4—3441no—
614C22×C4C2×C22⋊D4311yescharacteristic
615C22×C4C2×C22⋊D4311yescharacteristic
616C22×C4C2×C22⋊D4311yescharacteristic
617C22×C4C2×C22⋊D4311yescharacteristic
618C22×C4C23×D4311yescharacteristic
619D8—868no—
620C2×C8—432no—
621C2×C8—861no—
622C2×C8—861no—
623C2×C8—861no—
624C2×C8—861no—
625C2×C8—861no—
626C2×C8—861no—
627C2×C8—861no—
628C2×C8—861no—
629C2×C8—861no—
630C2×C8—861no—
631C2×C8—861no—
632C4⋊C4—22no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—432no—
640C4⋊C4—432no—
641C4⋊C4—432no—
642C4⋊C4—864no—
643C4⋊C4—864no—
644C4⋊C4—864no—
645C4⋊C4—861no—
646C4⋊C4—861no—
647C4⋊C4—861no—
648C22⋊C4—22no—
649C22⋊C4—22no—
650C22⋊C4—42no—
651C22⋊C4—42no—
652C22⋊C4—42no—
653C22⋊C4—81no—
654C22⋊C4—81no—
655C22⋊C4—864no—
656C22⋊C4—864no—
657C22⋊C4—864no—
658C22⋊C4—864no—
659C42—864no—
660C42D4×D4312yes—
661C42D4×D4312yes—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—22no—
674C23—21no—
675C23—21no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—862no—
683C23—1721no—
684C23—1721no—
685C23—1721no—
686C23—1721no—
687C23—1721no—
688C23—1721no—
689C23#1306334512yes—
690C23C22×C22⋊D4311yescharacteristic
691D4—22no—
692D4—22no—
693D4—44no—
694D4—41no—
695D4—41no—
696D4—84no—
697D4—84no—
698D4—862no—
699D4—862no—
700D4—3444no—
701D4—1728no—
702D4—1721no—
703D4—1721no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—84no—
732C2×C4—862no—
733C2×C4—862no—
734C2×C4—862no—
735C2×C4—3444no—
736C2×C4—3444no—
737C2×C4—1721no—
738C2×C4—1721no—
739C2×C4—1721no—
740C2×C4—1721no—
741C2×C4—1721no—
742C2×C4—1721no—
743C2×C4#1306329312yes—
744C2×C4#1306329312yes—
745C2×C4C2×D4×D4311yescharacteristic
746C2×C4C2×D4×D4311yescharacteristic
747C2×C4#41×D4311yescharacteristic
748C2×C4C2×#1062190011yescharacteristic
749C2×C4#1306337011yescharacteristic
750C2×C4#1306337211yescharacteristic
751C8—862no—
752C8—1721no—
753C8—1721no—
754C8—1721no—
755C22—22no—
756C22—22no—
757C22—22no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—42no—
764C22—41no—
765C22—41no—
766C22—42no—
767C22—41no—
768C22—41no—
769C22—42no—
770C22—41no—
771C22—41no—
772C22—81no—
773C22—81no—
774C22—81no—
775C22—81no—
776C22—3441no—
777C22—3441no—
778C22—3441no—
779C22—3441no—
780C22—1722no—
781C22—1722no—
782C22—1722no—
783C22C2×#1306329311yescharacteristic
784C22#1458354311yescharacteristic
785C22#1458354811yescharacteristic
786C22C2×#1306334511yescharacteristic
787C22#1458369711yescharacteristic
788C22#1458370211yescharacteristic
789C22#1458370211yescharacteristic
790C4—22no—
791C4—22no—
792C4—41no—
793C4—41no—
794C4—81no—
795C4—81no—
796C4—81no—
797C4—1722no—
798C4—1722no—
799C4—1722no—
800C4#1458340911yescharacteristic
801C4#1458347811yescharacteristic
802C4#1458355511yescharacteristic
803C4#1458356711yescharacteristic
804C2—42no—
805C2—81no—
806C2—82no—
807C2—3442no—
808C2#1913793611yescharacteristic
809C2#1914381111yescharacteristic
810C2#1914386111yescharacteristic
811C2#1914644511yescharacteristic
812C2#1914679611yescharacteristic
813C2#1914699111yescharacteristic
814C2#1914719511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2535C2
socleC23×C43C22×D4
hypercenter#2535D43
hypocenterC43#24124
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2535

Complements

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

NH ≅ G/Ntype
1. C2×#14583595C2semidirect
2. C2×#14583199C2semidirect
3. C2×C4×#10621882C2semidirect
4. #19135784C2semidirect
5. #19135777C2semidirect
6. #19135591C2semidirect
7. #19135591C2semidirect
8. #19135559C2semidirect
9. #19135390C2semidirect
10. #19134918C2semidirect
11. #19134913C2semidirect
12. #19134792C2semidirect
13. #19134782C2semidirect
14. #19134602C2semidirect
15. C43×#2535C2semidirect
77. #13063317D4semidirect
85. C4×D172D4semidirect
400. #2535D43semidirect
470. C43#24124semidirect

Maximal subgroups

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

subgroupindex
C2×#145835952
C2×#145831992
C2×C4×#106218822
#191357842
#191357772
#191355912
#191355592
#191353902
#191349182
#191349132
#191347922
#191347822
#191346022
C43×#25352
#2412443