Finite Group Databasebeta

← #25149849

Subgroups — #25149849

Order 11008.

1238 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583256C211yesmaximal, characteristic, complemented
2C2×#14583114C211yesmaximal, characteristic, complemented
3#19139534C211yesmaximal, characteristic, complemented
4#19135598C211yesmaximal, characteristic, complemented
5#19135598C211yesmaximal, characteristic, complemented
6#19135591C211yesmaximal, characteristic, complemented
7#19135591C211yesmaximal, characteristic, complemented
8#19135553C211yesmaximal, characteristic, complemented
9#19135390C211yesmaximal, characteristic, complemented
10#19134917C211yesmaximal, characteristic, complemented
11#19134912C211yesmaximal, characteristic, complemented
12#19134907C211yesmaximal, characteristic, complemented
13#19134902C211yesmaximal, characteristic, complemented
14C4×#13063246C211yesmaximal, characteristic, complemented
15C2×C43×#553C211yesmaximal, characteristic, complemented
16C22×#10621883C2211yescharacteristic
17C22×#10621882C2211yescharacteristic
18C2×#13063313C2211yescharacteristic
19C2×#13063304C2211yescharacteristic
20C2×#13063304C2211yescharacteristic
21C2×#13063299C2211yescharacteristic
22C2×#13063299C2211yescharacteristic
23#14583256—24no—
24#14583114—24no—
25C2×C4⋊(C43⋊C8)C2211yescharacteristic
26C2×#13063248C2211yescharacteristic
27C2×#13063248C2211yescharacteristic
28C2×#13063248C2211yescharacteristic
29C2×#13063246C2211yescharacteristic
30C2×#13063246C2211yescharacteristic
31C2×#13063245C2211yescharacteristic
32C2×#13063245C2211yescharacteristic
33C2×#13063245C2211yescharacteristic
34C2×C22⋊(C43⋊C8)C2211yescharacteristic
35C2×C22⋊(C43⋊C8)C2211yescharacteristic
36C2×C22⋊(C43⋊C8)C2211yescharacteristic
37C2×C22⋊(C43⋊C8)C2211yescharacteristic
38C2×C4×C43⋊C8C2211yescharacteristic
39#14582834—21no—
40#14582807—21no—
41#14582799—21no—
42#14582799—21no—
43C4×C4⋊Dic43C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50C43×#553—24no—
51C43×#553—24no—
52C2×#126×C43—21no—
53C2×#125×C43C2211yescharacteristic
54C2×#123×C43—21no—
55C2×#121×C43—21no—
56C2×#121×C43C2211yescharacteristic
57C2×#121×C43C2211yescharacteristic
58C2×C4×D4×C43—21no—
59C2×C4×D4×C43C2211yescharacteristic
60C2×C4×D4×C43C2211yescharacteristic
61C2×#117×C43C2211yescharacteristic
62C22×C4⋊C4×C43C2211yescharacteristic
63C22×Dic86C2311yescharacteristic
64C22×D172C2311yescharacteristic
65C22×C22⋊D43—21no—
66C22×C22⋊D43—21no—
67C2×#10621883—22no—
68C2×#10621883—41no—
69C2×#10621883—41no—
70C2×#10621882—22no—
71C2×#10621882—41no—
72C2×#10621882—41no—
73C22×C43⋊C8C2311yescharacteristic
74C22×C43⋊C8C2311yescharacteristic
75C22×C43⋊C8C2311yescharacteristic
76C22×C43⋊C8C2311yescharacteristic
77#13063313—22no—
78#13063313—22no—
79#13063304—22no—
80#13063304—22no—
81#13063304—41no—
82#13063304—41no—
83#13063299—22no—
84#13063299—22no—
85#13063299—41no—
86#13063299—41no—
87C2×C4⋊Dic43C2311yescharacteristic
88C2×C4⋊Dic43C2311yescharacteristic
89C2×Dic43⋊C4—21no—
90C2×Dic43⋊C4—21no—
91C2×C22⋊Dic43—21no—
92C2×C22⋊Dic43—21no—
93C2×(C2×D43)⋊C4—21no—
94C2×(C2×D43)⋊C4—21no—
95C2×(C2×D43)⋊C4—21no—
96C2×(C2×D43)⋊C4—21no—
97C2×C4×Dic43—21no—
98C4⋊(C43⋊C8)—22no—
99#13063248—22no—
100#13063248—22no—
101#13063248—22no—
102#13063246—22no—
103#13063246—22no—
104#13063245—22no—
105#13063245—22no—
106#13063245—22no—
107C22⋊(C43⋊C8)—41no—
108C22⋊(C43⋊C8)—41no—
109C22⋊(C43⋊C8)—41no—
110C22⋊(C43⋊C8)—41no—
111C4×C43⋊C8—22no—
112C43⋊#95—21no—
113C22×D4×C43—21no—
114C22×D4×C43—21no—
115C22×D4×C43D411yescharacteristic
116C22×D4×C43C2311yescharacteristic
117C23×C4×C43—21no—
118C23×C4×C43—21no—
119C23×C4×C43C2311yescharacteristic
120C23×C4×C43C2311yescharacteristic
121#126×C43—28no—
122#125×C43—22no—
123#125×C43D414yescomplemented
124#123×C43—28no—
125#121×C43—28no—
126#121×C43—22no—
127#121×C43—22no—
128#121×C43—22no—
129#121×C43—22no—
130C4×D4×C43—28no—
131C4×D4×C43—22no—
132C4×D4×C43—22no—
133C4×D4×C43—22no—
134C4×D4×C43D414yescomplemented
135#117×C43—22no—
136#117×C43—22no—
137C2×C4⋊C4×C43—21no—
138C2×C4⋊C4×C43—21no—
139C2×C4⋊C4×C43—21no—
140C2×C4⋊C4×C43—22no—
141C2×C4⋊C4×C43—22no—
142C2×C4⋊C4×C43D411yescharacteristic
143C2×C4⋊C4×C43C2311yescharacteristic
144C2×C4⋊C4×C43C2311yescharacteristic
145C2×C4⋊C4×C43C2311yescharacteristic
146C2×C22⋊C4×C43—21no—
147C2×C22⋊C4×C43—21no—
148C2×C22⋊C4×C43—21no—
149C2×C22⋊C4×C43—21no—
150C2×C22⋊C4×C43D411yescharacteristic
151C2×C22⋊C4×C43D411yescharacteristic
152C2×C42×C43—21no—
153C2×C42×C43C2311yescharacteristic
154C24×C43—21no—
155C24×C43C2×D411yescharacteristic
156C24×C43C2×D411yescharacteristic
157C23×D43—21no—
158C2×D4×C43—24no—
159C2×D4×C43—24no—
160C2×D4×C43—22no—
161C2×D4×C43—21no—
162C2×D4×C43—22no—
163C2×D4×C43—21no—
164C2×D4×C43—21no—
165C2×D4×C43—21no—
166C2×D4×C43—21no—
167C2×D4×C43—41no—
168C2×D4×C43—42no—
169C2×D4×C43—42no—
170C2×D4×C43—81no—
171C2×D4×C43—81no—
172C2×D4×C43C2×D412yes—
173C22×C4×C43—24no—
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—21no—
183C22×C4×C43—21no—
184C22×C4×C43—21no—
185C22×C4×C43—21no—
186C22×C4×C43—24no—
187C22×C4×C43—21no—
188C22×C4×C43—21no—
189C22×C4×C43—21no—
190C22×C4×C43—81no—
191C22×C4×C43—81no—
192C22×C4×C43—81no—
193C22×C4×C43—81no—
194C22×C4×C43C2×D411yescharacteristic
195C22×C4×C43C2×D411yescharacteristic
196C22×C4×C43C2×D411yescharacteristic
197C22×C4×C43C2×D411yescharacteristic
198C22×C4×C43C2411yescharacteristic
199C2×C22⋊D43—42no—
200C2×C22⋊D43—42no—
201C2×C22⋊D43—42no—
202C2×C22⋊D43—42no—
203C2×C22⋊D43—81no—
204C2×C22⋊D43—81no—
205C22×Dic43—21no—
206C22×Dic43—21no—
207C22×Dic43—21no—
208C2×D172—21no—
209C2×D172—21no—
210C2×D172—21no—
211C2×D172—21no—
212C2×D172—21no—
213C2×D172—21no—
214C2×Dic86—21no—
215C2×Dic86—21no—
216C2×Dic86—21no—
217C2×Dic86—21no—
218C2×Dic86—21no—
219C2×Dic86—21no—
220C4⋊C4×C43—24no—
221C4⋊C4×C43—24no—
222C4⋊C4×C43—24no—
223C4⋊C4×C43—22no—
224C4⋊C4×C43—21no—
225C4⋊C4×C43—21no—
226C4⋊C4×C43—21no—
227C4⋊C4×C43C2×D412yes—
228C4⋊C4×C43C2×D412yes—
229C4⋊C4×C43C2×D412yes—
230C22⋊C4×C43—24no—
231C22⋊C4×C43—24no—
232C22⋊C4×C43—24no—
233C22⋊C4×C43—24no—
234C22⋊C4×C43—22no—
235C22⋊C4×C43—22no—
236C42×C43—24no—
237C42×C43C2×D412yes—
238C42×C43C2×D412yes—
239C22⋊Dic43—42no—
240C22⋊Dic43—42no—
241#10621883—44no—
242#10621882—44no—
243(C2×D43)⋊C4—42no—
244(C2×D43)⋊C4—42no—
245(C2×D43)⋊C4—42no—
246(C2×D43)⋊C4—42no—
247C4⋊Dic43—21no—
248C4⋊Dic43—21no—
249C4⋊Dic43#4112yes—
250C4⋊Dic43#4112yes—
251Dic43⋊C4—42no—
252Dic43⋊C4—42no—
253C4×Dic43—81no—
254C2×C43⋊C8—21no—
255C2×C43⋊C8—21no—
256C2×C43⋊C8—21no—
257C2×C43⋊C8—21no—
258C2×C43⋊C8—21no—
259C2×C43⋊C8—21no—
260C2×C43⋊C8—21no—
261C2×C43⋊C8—21no—
262C2×C43⋊C8—21no—
263C2×C43⋊C8—21no—
264C2×C43⋊C8—21no—
265C2×C43⋊C8—21no—
266C23×C43—21no—
267C23×C43—21no—
268C23×C43—21no—
269C23×C43—21no—
270C23×C43—21no—
271C23×C43—21no—
272C23×C43—21no—
273C23×C43—22no—
274C23×C43—21no—
275C23×C43—21no—
276C23×C43—21no—
277C23×C43—21no—
278C23×C43—21no—
279C23×C43—21no—
280C23×C43—41no—
281C23×C43—41no—
282C23×C43—41no—
283C23×C43—41no—
284C23×C43—41no—
285C23×C43—41no—
286C23×C43#13512yes—
287C23×C43C22×D411yescharacteristic
288C22×D43—41no—
289C22×D43—41no—
290C22×D43—41no—
291C22×D43—41no—
292C22×D43—41no—
293C22×D43—41no—
294C22×D43—41no—
295D4×C43—22no—
296D4×C43—22no—
297D4×C43—44no—
298D4×C43—48no—
299D4×C43—41no—
300D4×C43—41no—
301D4×C43—84no—
302C2×C4×C43—21no—
303C2×C4×C43—21no—
304C2×C4×C43—21no—
305C2×C4×C43—21no—
306C2×C4×C43—21no—
307C2×C4×C43—22no—
308C2×C4×C43—22no—
309C2×C4×C43—21no—
310C2×C4×C43—22no—
311C2×C4×C43—21no—
312C2×C4×C43—21no—
313C2×C4×C43—21no—
314C2×C4×C43—21no—
315C2×C4×C43—41no—
316C2×C4×C43—41no—
317C2×C4×C43—41no—
318C2×C4×C43—41no—
319C2×C4×C43—41no—
320C2×C4×C43—41no—
321C2×C4×C43—41no—
322C2×C4×C43—41no—
323C2×C4×C43—41no—
324C2×C4×C43—41no—
325C2×C4×C43—41no—
326C2×C4×C43—41no—
327C2×C4×C43—41no—
328C2×C4×C43—41no—
329C2×C4×C43—84no—
330C2×C4×C43—84no—
331C2×C4×C43#12012yes—
332C2×C4×C43#12012yes—
333C2×C4×C43C22×D411yescharacteristic
334C2×C4×C43C22×D411yescharacteristic
335C2×C4×C43C2×#4111yescharacteristic
336C2×C4×C43C2×#4111yescharacteristic
337C2×C4×C43H(5,𝔽2)11yescharacteristic
338C2×C4×C43H(5,𝔽2)11yescharacteristic
339C22⋊D43—84no—
340C22⋊D43—84no—
341C2×Dic43—22no—
342C2×Dic43—22no—
343C2×Dic43—41no—
344C2×Dic43—41no—
345C2×Dic43—41no—
346C2×Dic43—41no—
347C2×Dic43—41no—
348C2×Dic43—41no—
349C2×Dic43—41no—
350D172—41no—
351D172—41no—
352D172—41no—
353D172—41no—
354Dic86—41no—
355Dic86—41no—
356Dic86—41no—
357Dic86—41no—
358C43⋊C8—41no—
359C43⋊C8—41no—
360C43⋊C8—41no—
361C43⋊C8—41no—
362#25575—431nomaximal, Sylow
363C22×C43—22no—
364C22×C43—22no—
365C22×C43—22no—
366C22×C43—41no—
367C22×C43—41no—
368C22×C43—41no—
369C22×C43—41no—
370C22×C43—41no—
371C22×C43—42no—
372C22×C43—41no—
373C22×C43—42no—
374C22×C43—41no—
375C22×C43—42no—
376C22×C43—41no—
377C22×C43—41no—
378C22×C43—41no—
379C22×C43—41no—
380C22×C43—81no—
381C22×C43—81no—
382C22×C43—81no—
383C22×C43—81no—
384C22×C43C2×#12011yescharacteristic
385C22×C43#54611yescharacteristic
386C22×C43#54611yescharacteristic
387C22×C43C2×#13511yescharacteristic
388C22×C43#57511yescharacteristic
389C22×C43#57611yescharacteristic
390C22×C43#57711yescharacteristic
391C2×D43—81no—
392C2×D43—81no—
393C2×D43—81no—
394C2×D43—81no—
395C2×D43—81no—
396C2×D43—81no—
397C2×D43—81no—
398C4×C43—22no—
399C4×C43—22no—
400C4×C43—41no—
401C4×C43—41no—
402C4×C43—42no—
403C4×C43—42no—
404C4×C43—42no—
405C4×C43#53211yescharacteristic
406C4×C43#53511yescharacteristic
407C4×C43#55011yescharacteristic
408C4×C43#55011yescharacteristic
409Dic43—42no—
410Dic43—42no—
411Dic43—81no—
412C2×#553D4311yescharacteristic, complemented
413C2×#488—431no—
414C2×#463—431no—
415#2540—431no—
416#2000—431no—
417#2000—431no—
418#1999—431no—
419#1999—431no—
420#1989—431no—
421#1954—431no—
422#1875—431no—
423#1874—431no—
424#1873—431no—
425#1872—431no—
426C4×#102—431no—
427C2×C43—42no—
428C2×C43—81no—
429C2×C43—82no—
430C2×C43#243111yescharacteristic
431C2×C43#300211yescharacteristic
432C2×C43#301211yescharacteristic
433C2×C43#329711yescharacteristic
434C2×C43#330111yescharacteristic
435C2×C43#332211yescharacteristic
436C2×C43#332611yescharacteristic
437D43—161no—
438C22×SD16—431no—
439C22×D8—431no—
440#553—24no—
441#553—24no—
442C2×#126—21no—
443C2×#125C2×D4311yescharacteristic
444C2×#124—431no—
445C2×#123—21no—
446C2×C22⋊Q8—431no—
447C2×C22⋊Q8—431no—
448C2×#121—21no—
449C2×#121—431no—
450C2×#121—431no—
451C2×#121C2×D4311yescharacteristic
452C2×#121C2×D4311yescharacteristic
453C2×C4×D4—21no—
454C2×C4×D4C2×D4311yescharacteristic
455C2×C4×D4C2×D4311yescharacteristic
456C2×#117C2×D4311yescharacteristic
457C22×C4⋊C4C2×D4311yescharacteristic
458#488—864no—
459#463—864no—
460C2×C4⋊C8—431no—
461C2×#103—431no—
462C2×#103—431no—
463C2×#103—431no—
464C2×#102—431no—
465C2×#102—431no—
466C2×#102—431no—
467C2×#102—431no—
468C2×#102—431no—
469C2×C22⋊C8—431no—
470C2×C22⋊C8—431no—
471C2×C22⋊C8—431no—
472C2×C22⋊C8—431no—
473C2×C4×C8—431no—
474#399—861no—
475#392—861no—
476#390—861no—
477#390—861no—
478C4×C4⋊C4—431no—
479#340—431no—
480#340—431no—
481#340—431no—
482#340—431no—
483#340—431no—
484#340—431no—
485C43#2557511yescharacteristic, complemented, Sylow
486C22×Q8—431no—
487C22×D4—21no—
488C22×D4—21no—
489C22×D4—431no—
490C22×D4—861no—
491C22×D4—861no—
492C22×D4C22⋊D4311yescharacteristic
493C22×D4C22×D4311yescharacteristic
494C23×C4—21no—
495C23×C4—21no—
496C23×C4C22×D4311yescharacteristic
497C23×C4C22×D4311yescharacteristic
498C2×SD16—862no—
499C2×SD16—1721no—
500C2×SD16—1721no—
501C2×D8—862no—
502C2×D8—1721no—
503C2×D8—1721no—
504C22×C8—431no—
505C22×C8—431no—
506C22×C8—431no—
507C22×C8—431no—
508#126—28no—
509#125—22no—
510#125C22⋊D4314yescomplemented
511#124—862no—
512#124—862no—
513#123—28no—
514C22⋊Q8—862no—
515C22⋊Q8—862no—
516C22⋊Q8—1721no—
517C22⋊Q8—1721no—
518#121—28no—
519#121—22no—
520#121—22no—
521#121—22no—
522#121—22no—
523#121—862no—
524#121—862no—
525#121—1721no—
526#121—1721no—
527C4×D4—28no—
528C4×D4—22no—
529C4×D4—22no—
530C4×D4—22no—
531C4×D4C22⋊D4314yescomplemented
532#117—22no—
533#117—22no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—22no—
538C2×C4⋊C4—22no—
539C2×C4⋊C4—431no—
540C2×C4⋊C4—431no—
541C2×C4⋊C4—861no—
542C2×C4⋊C4—861no—
543C2×C4⋊C4C22⋊D4311yescharacteristic
544C2×C4⋊C4C22×D4311yescharacteristic
545C2×C4⋊C4C22×D4311yescharacteristic
546C2×C4⋊C4C22×D4311yescharacteristic
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—861no—
552C2×C22⋊C4—861no—
553C2×C22⋊C4—861no—
554C2×C22⋊C4—861no—
555C2×C22⋊C4—861no—
556C2×C22⋊C4—861no—
557C2×C22⋊C4C22⋊D4311yescharacteristic
558C2×C22⋊C4C22⋊D4311yescharacteristic
559C2×C42—21no—
560C2×C42—861no—
561C2×C42C22×D4311yescharacteristic
562C4⋊C8—862no—
563#103—862no—
564#103—862no—
565#103—862no—
566#102—862no—
567#102—862no—
568#102—862no—
569#102—862no—
570#102—862no—
571C22⋊C8—1721no—
572C22⋊C8—1721no—
573C22⋊C8—1721no—
574C22⋊C8—1721no—
575C4×C8—862no—
576#95—861no—
577C24—21no—
578C24—861no—
579C24C2×C22⋊D4311yescharacteristic
580C24C2×C22⋊D4311yescharacteristic
581C2×Q8—861no—
582C2×Q8—861no—
583C2×Q8—861no—
584C2×Q8—861no—
585C2×Q8—861no—
586C2×Q8—861no—
587C2×D4—24no—
588C2×D4—22no—
589C2×D4—24no—
590C2×D4—22no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—41no—
597C2×D4—42no—
598C2×D4—42no—
599C2×D4—81no—
600C2×D4—81no—
601C2×D4—861no—
602C2×D4—861no—
603C2×D4—861no—
604C2×D4—861no—
605C2×D4—861no—
606C2×D4—861no—
607C2×D4—3441no—
608C2×D4—3441no—
609C2×D4—1722no—
610C2×D4—1722no—
611C2×D4—1722no—
612C2×D4—1722no—
613C2×D4C2×C22⋊D4312yes—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—24no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—24no—
631C22×C4—81no—
632C22×C4—81no—
633C22×C4—81no—
634C22×C4—81no—
635C22×C4—861no—
636C22×C4—861no—
637C22×C4—861no—
638C22×C4C2×C22⋊D4311yescharacteristic
639C22×C4C2×C22⋊D4311yescharacteristic
640C22×C4C2×C22⋊D4311yescharacteristic
641C22×C4C2×C22⋊D4311yescharacteristic
642C22×C4C23×D4311yescharacteristic
643SD16—1724no—
644D8—1724no—
645C2×C8—861no—
646C2×C8—861no—
647C2×C8—861no—
648C2×C8—861no—
649C2×C8—861no—
650C2×C8—861no—
651C2×C8—861no—
652C2×C8—861no—
653C2×C8—861no—
654C2×C8—861no—
655C2×C8—861no—
656C2×C8—861no—
657C4⋊C4—24no—
658C4⋊C4—24no—
659C4⋊C4—24no—
660C4⋊C4—22no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—432no—
665C4⋊C4—432no—
666C4⋊C4—861no—
667C4⋊C4—861no—
668C4⋊C4—1722no—
669C4⋊C4—1722no—
670C4⋊C4C2×C22⋊D4312yes—
671C4⋊C4C2×C22⋊D4312yes—
672C4⋊C4C2×C22⋊D4312yes—
673C22⋊C4—24no—
674C22⋊C4—24no—
675C22⋊C4—24no—
676C22⋊C4—24no—
677C22⋊C4—22no—
678C22⋊C4—22no—
679C22⋊C4—1722no—
680C22⋊C4—1722no—
681C22⋊C4—1722no—
682C22⋊C4—1722no—
683C22⋊C4—1722no—
684C22⋊C4—1722no—
685C42—24no—
686C42—3441no—
687C42C2×C22⋊D4312yes—
688C42C2×C22⋊D4312yes—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—22no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—1721no—
710C23—1721no—
711C23—1721no—
712C23—1721no—
713C23—1721no—
714C23—1721no—
715C23—1721no—
716C23#1306334512yes—
717C23C22×C22⋊D4311yescharacteristic
718Q8—1721no—
719Q8—1721no—
720Q8—1721no—
721Q8—1721no—
722D4—22no—
723D4—22no—
724D4—44no—
725D4—48no—
726D4—41no—
727D4—41no—
728D4—84no—
729D4—3444no—
730D4—3444no—
731D4—1721no—
732D4—1721no—
733D4—1721no—
734D4—1721no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—21no—
743C2×C4—22no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—84no—
763C2×C4—84no—
764C2×C4—862no—
765C2×C4—862no—
766C2×C4—1721no—
767C2×C4—1721no—
768C2×C4—1721no—
769C2×C4—1721no—
770C2×C4—1721no—
771C2×C4—1721no—
772C2×C4—1721no—
773C2×C4#1306329412yes—
774C2×C4#1306329412yes—
775C2×C4C22×C22⋊D4311yescharacteristic
776C2×C4C22×C22⋊D4311yescharacteristic
777C2×C4#41×D4311yescharacteristic
778C2×C4#41×D4311yescharacteristic
779C2×C4#1306337111yescharacteristic
780C2×C4#1306337111yescharacteristic
781C8—1721no—
782C8—1721no—
783C8—1721no—
784C8—1721no—
785C22—22no—
786C22—22no—
787C22—22no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—42no—
796C22—41no—
797C22—42no—
798C22—41no—
799C22—42no—
800C22—41no—
801C22—41no—
802C22—81no—
803C22—81no—
804C22—81no—
805C22—81no—
806C22—3441no—
807C22—3441no—
808C22—3441no—
809C22—3441no—
810C22—3441no—
811C22—3441no—
812C22—3441no—
813C22C2×#1306329411yescharacteristic
814C22#1458353711yescharacteristic
815C22#1458353711yescharacteristic
816C22C2×#1306334511yescharacteristic
817C22#1458369711yescharacteristic
818C22#1458370211yescharacteristic
819C22#1458371011yescharacteristic
820C4—22no—
821C4—22no—
822C4—42no—
823C4—41no—
824C4—41no—
825C4—42no—
826C4—42no—
827C4—3441no—
828C4—1722no—
829C4—1722no—
830C4#1458344511yescharacteristic
831C4#1458346311yescharacteristic
832C4#1458356811yescharacteristic
833C4#1458356811yescharacteristic
834C2—42no—
835C2—81no—
836C2—82no—
837C2—6881no—
838C2#1913821011yescharacteristic
839C2#1914381311yescharacteristic
840C2#1914389911yescharacteristic
841C2#1914643911yescharacteristic
842C2#1914649111yescharacteristic
843C2#1914679011yescharacteristic
844C2#1914684211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#553C2
socleC23×C43C22×D4
hypercenterC2×#553D43
hypocenterC43#25575
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#553

Complements

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

NH ≅ G/Ntype
1. C2×#14583256C2semidirect
2. C2×#14583114C2semidirect
3. #19139534C2semidirect
4. #19135598C2semidirect
5. #19135598C2semidirect
6. #19135591C2semidirect
7. #19135591C2semidirect
8. #19135553C2semidirect
9. #19135390C2semidirect
10. #19134917C2semidirect
11. #19134912C2semidirect
12. #19134907C2semidirect
13. #19134902C2semidirect
14. C4×#13063246C2semidirect
15. C2×C43×#553C2semidirect
123. #125×C43D4semidirect
134. C4×D4×C43D4semidirect
412. C2×#553D43semidirect
485. C43#25575semidirect
510. #125C22⋊D43semidirect
531. C4×D4C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145832562
C2×#145831142
#191395342
#191355982
#191355912
#191355532
#191353902
#191349172
#191349122
#191349072
#191349022
C4×#130632462
C2×C43×#5532
#2557543