Finite Group Databasebeta

← C2×#19146295 #25971818

Subgroups — C2×#19146295 #25971818

Order 11008.

2934 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063348C211yesmaximal, characteristic, complemented
2C23×#10621884C211yesmaximal, characteristic, complemented
3C2×#14583560C211yesmaximal, characteristic, complemented
4C2×#14583540C211yesmaximal, characteristic, complemented
5#19146295C2116yesmaximal, direct product factor
6C2×#14583284C211yesmaximal, characteristic, complemented
7C2×#14583131C211yesmaximal, characteristic, complemented
8C2×#14583130C211yesmaximal, characteristic, complemented
9C2×#14583123C211yesmaximal, characteristic, complemented
10C2×#14583117C211yesmaximal, characteristic, complemented
11C2×#14583060C211yesmaximal, characteristic, complemented
12C2×#14583047C211yesmaximal, characteristic, complemented
13C2×#14583035C211yesmaximal, characteristic, complemented
14C2×#14582984C211yesmaximal, characteristic, complemented
15C2×(C22⋊D43)⋊C8C211yesmaximal, characteristic, complemented
16C2×C43×#451C211yesmaximal, characteristic, complemented
17C22×#10621902C2211yescharacteristic
18C22×#10621902C2211yescharacteristic, complemented
19C23×D172C2211yescharacteristic
20C2×#13063348—28no—
21C2×#13063348C2218yescomplemented
22C22×#10621884—28no—
23C22×#10621884C2211yescharacteristic
24C22×#10621884C2211yescharacteristic
25C22×#10621884C2211yescharacteristic
26C22×#10621884C2211yescharacteristic
27C22×#10621884C2218yescomplemented
28C22×#10621884C2211yescharacteristic, complemented
29C22×D344C2211yescharacteristic
30C22×D344C2211yescharacteristic
31C23×C43⋊C8C2211yescharacteristic
32C22×C8×D43C2211yescharacteristic, complemented
33#14583560—24no—
34#14583560C2218yescomplemented
35#14583540—24no—
36#14583540C2218yescomplemented
37C2×#13063314—21no—
38C2×#13063314C2211yescharacteristic
39C2×#13063314C2211yescharacteristic, complemented
40C2×#13063310—21no—
41C2×#13063301—21no—
42C2×#13063301C2211yescharacteristic, complemented
43C2×#13063300—21no—
44C2×#13063300C2211yescharacteristic
45C2×#13063299—21no—
46C2×#13063299C2211yescharacteristic
47C2×#13063295—21no—
48C2×Q8×Dic43C2211yescharacteristic, complemented
49C2×#13063287C2211yescharacteristic
50C2×C4×C22⋊D43—21no—
51C2×C4×C22⋊D43C2211yescharacteristic
52C2×C22⋊C4×D43—21no—
53#14583284C2218yescomplemented
54#14583131C2218yescomplemented
55#14583130C2218yescomplemented
56#14583123C2218yescomplemented
57#14583117C2218yescomplemented
58#14583060C2218yescomplemented
59#14583047C2218yescomplemented
60#14583035C2218yescomplemented
61#14582984C2218yescomplemented
62(C22⋊D43)⋊C8C2218yescomplemented
63C2×#13063256C2211yescharacteristic, complemented
64C2×Dic43⋊C8C2211yescharacteristic, complemented
65C2×#13063249C2211yescharacteristic, complemented
66C2×#13063247C2211yescharacteristic
67C2×#13063247C2211yescharacteristic
68C2×#13063245C2211yescharacteristic, complemented
69C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
70C2×C8×Dic43C2211yescharacteristic, complemented
71C23×Q8×C43C2211yescharacteristic
72C22×Q16×C43C2211yescharacteristic, complemented
73C22×Q16×C43C2211yescharacteristic, complemented
74C2×C22⋊Q8×C43C2211yescharacteristic
75C43×#451C2218yescomplemented
76C2×#103×C43C2211yescharacteristic, complemented
77C2×#103×C43C2211yescharacteristic, complemented
78C2×C22⋊C8×C43C2211yescharacteristic
79C24×D43—21no—
80C2×#10621902—22no—
81C2×#10621902—22no—
82C2×#10621902—24no—
83C2×#10621902—24no—
84C2×#10621902—42no—
85C2×#10621902—42no—
86C2×#10621902C2314yes—
87C2×#10621902C2314yescomplemented
88C22×D172—24no—
89C22×D172—21no—
90C22×D172—21no—
91C22×D172—21no—
92C22×D172—22no—
93C22×D172—21no—
94C22×D172—42no—
95C22×D172C2311yescharacteristic
96C22×D172C2311yescharacteristic
97C22×D172C2314yes—
98C22×D172C2311yescharacteristic
99C22×C22⋊D43—21no—
100C22×C22⋊D43D411yescharacteristic
101C22×C4×D43—21no—
102C22×C4×D43—21no—
103C22×C4×D43—21no—
104C22×C4×D43C2311yescharacteristic
105#13063348—232no—
106C2×#10621884—24no—
107C2×#10621884—24no—
108C2×#10621884—232no—
109C2×#10621884—24no—
110C2×#10621884—24no—
111C2×#10621884D418yescomplemented
112C2×#10621884C2314yes—
113C2×#10621884C2314yes—
114C2×#10621884C2314yes—
115C2×#10621884C2314yes—
116C2×#10621884C2314yescomplemented
117C2×D344—24no—
118C2×D344—42no—
119C2×D344C2314yes—
120C2×D344C2314yes—
121C22×C43⋊C8—24no—
122C22×C43⋊C8C2311yescharacteristic
123C22×C43⋊C8C2314yes—
124C22×C43⋊C8C2311yescharacteristic
125C2×C8×D43—24no—
126C2×C8×D43C2314yescomplemented
127#13063314—28no—
128#13063314—22no—
129#13063314—22no—
130#13063314C2314yes—
131#13063314C2314yescomplemented
132#13063310—28no—
133#13063301—22no—
134#13063301—28no—
135#13063301C2314yescomplemented
136#13063300—22no—
137#13063300—28no—
138#13063300C2314yes—
139#13063299—22no—
140#13063299—28no—
141#13063299C2314yes—
142#13063295—28no—
143Q8×Dic43—22no—
144Q8×Dic43C2314yescomplemented
145#13063287—22no—
146#13063287C2314yes—
147C4×C22⋊D43—28no—
148C4×C22⋊D43D414yes—
149C4×C22⋊D43C2314yes—
150C2×C4⋊Dic43—21no—
151C2×C4⋊Dic43C2311yescharacteristic
152C2×Dic43⋊C4—21no—
153C2×Dic43⋊C4D411yescharacteristic
154C2×C22⋊Dic43D411yescharacteristic
155C2×(C2×D43)⋊C4—21no—
156C2×(C2×D43)⋊C4—21no—
157C2×(C2×D43)⋊C4—21no—
158C2×(C2×D43)⋊C4—21no—
159C2×(C2×D43)⋊C4—21no—
160C2×(C2×D43)⋊C4—21no—
161C2×(C2×D43)⋊C4—21no—
162C2×(C2×D43)⋊C4—21no—
163C2×(C2×D43)⋊C4D411yescharacteristic
164C22⋊C4×D43—28no—
165C2×C4×Dic43—21no—
166C2×C4×Dic43C2311yescharacteristic
167#13063256C2314yescomplemented
168Dic43⋊C8C2314yescomplemented
169#13063249C2314yescomplemented
170#13063247C2314yes—
171#13063247C2314yes—
172#13063245C2314yescomplemented
173(C2×D43)⋊C8C2314yescomplemented
174C8×Dic43C2314yescomplemented
175C22×Q8×C43—22no—
176C22×Q8×C43—21no—
177C22×Q8×C43—24no—
178C22×Q8×C43—42no—
179C22×Q8×C43C2311yescharacteristic
180C22×Q8×C43C2311yescharacteristic
181C22×Q8×C43C2314yes—
182C22×Q8×C43C2311yescharacteristic
183C23×C4×C43—21no—
184C23×C4×C43C2311yescharacteristic
185C2×Q16×C43—24no—
186C2×Q16×C43—42no—
187C2×Q16×C43C2314yescomplemented
188C2×Q16×C43C2314yescomplemented
189C22×C8×C43C2311yescharacteristic
190C22×C8×C43C2311yescharacteristic
191C22⋊Q8×C43—22no—
192C22⋊Q8×C43C2314yes—
193C2×C4⋊C4×C43—21no—
194C2×C4⋊C4×C43C2311yescharacteristic
195C2×C22⋊C4×C43—21no—
196#103×C43C2314yescomplemented
197#103×C43C2314yescomplemented
198C22⋊C8×C43C2314yes—
199C24×C43C2×D411yescharacteristic
200C23×D43—21no—
201C23×D43—21no—
202C23×D43—21no—
203C23×D43—24no—
204C23×D43—44no—
205C23×D43—44no—
206C23×D43—82no—
207C23×D43C2×D411yescharacteristic
208C2×Q8×C43—21no—
209C2×Q8×C43—21no—
210C2×Q8×C43—24no—
211C2×Q8×C43—21no—
212C2×Q8×C43—22no—
213C2×Q8×C43—28no—
214C2×Q8×C43—22no—
215C2×Q8×C43—22no—
216C2×Q8×C43—22no—
217C2×Q8×C43—22no—
218C2×Q8×C43—44no—
219C2×Q8×C43—44no—
220C2×Q8×C43—48no—
221C2×Q8×C43C2×D414yes—
222C2×Q8×C43C2412yes—
223C2×Q8×C43C2412yes—
224C2×Q8×C43C2412yes—
225C22×C4×C43—22no—
226C22×C4×C43—22no—
227C22×C4×C43—21no—
228C22×C4×C43—21no—
229C22×C4×C43—21no—
230C22×C4×C43—21no—
231C22×C4×C43—24no—
232C22×C4×C43—44no—
233C22×C4×C43C2×D411yescharacteristic
234C22×C4×C43C2×D412yes—
235C22×C4×C43C2412yes—
236C22×C4×C43C2411yescharacteristic
237C2×C22⋊D43—24no—
238C2×C22⋊D43—24no—
239C2×C22⋊D43—44no—
240C2×C22⋊D43C2×D414yes—
241C22×Dic43—21no—
242C22×Dic43C2×D411yescharacteristic
243C22×Dic43C2×D411yescharacteristic
244C22×Dic43C2×D411yescharacteristic
245#10621902—28no—
246#10621902—28no—
247#10621902—44no—
248#10621902—44no—
249#10621902—48no—
250#10621902—48no—
251C2×D172—21no—
252C2×D172—22no—
253C2×D172—21no—
254C2×D172—24no—
255C2×D172—21no—
256C2×D172—24no—
257C2×D172—24no—
258C2×D172—24no—
259C2×D172—22no—
260C2×D172—22no—
261C2×D172—22no—
262C2×D172—22no—
263C2×D172—28no—
264C2×D172—44no—
265C2×D172—44no—
266C2×D172—44no—
267C2×D172—44no—
268C2×D172—48no—
269C2×D172—82no—
270C2×D172C2×D414yes—
271C2×D172C2412yes—
272C2×D172C2412yes—
273C2×D172C2412yes—
274C2×C4×D43—22no—
275C2×C4×D43—22no—
276C2×C4×D43—24no—
277C2×C4×D43—24no—
278C2×C4×D43—24no—
279C2×C4×D43—44no—
280C2×C4×D43—44no—
281C2×C4×D43—82no—
282C2×C4×D43C2×D412yes—
283C2×C4×D43C2412yes—
284Q16×C43—28no—
285Q16×C43—44no—
286C2×C8×C43—22no—
287C2×C8×C43—22no—
288C2×C8×C43C2412yes—
289C2×C8×C43C2412yes—
290C4⋊C4×C43—24no—
291C4⋊C4×C43—21no—
292C4⋊C4×C43C2412yes—
293C22⋊C4×C43—24no—
294C22⋊Dic43C2×D414yes—
295#10621884—28no—
296#10621884—28no—
297#10621884—28no—
298#10621884—28no—
299#10621884C2×D4116yescomplemented
300(C2×D43)⋊C4—24no—
301(C2×D43)⋊C4—24no—
302(C2×D43)⋊C4—24no—
303(C2×D43)⋊C4—24no—
304(C2×D43)⋊C4—24no—
305(C2×D43)⋊C4—24no—
306(C2×D43)⋊C4—24no—
307(C2×D43)⋊C4—24no—
308(C2×D43)⋊C4C2×D414yes—
309C4⋊Dic43—21no—
310C4⋊Dic43—24no—
311C4⋊Dic43C2412yes—
312Dic43⋊C4—24no—
313Dic43⋊C4C2×D414yes—
314C4×Dic43—24no—
315C4×Dic43C2×D412yes—
316C4×Dic43C2412yes—
317C2×C43⋊C8—22no—
318C2×C43⋊C8—28no—
319C2×C43⋊C8C2×D414yes—
320C2×C43⋊C8C2412yes—
321C2×C43⋊C8C2412yes—
322D344—28no—
323D344—44no—
324C8×D43—28no—
325C23×C43—22no—
326C23×C43—22no—
327C23×C43#13514yescomplemented
328C23×C43C22×D412yes—
329C23×C43C22×D411yescharacteristic
330C22×D43—22no—
331C22×D43—24no—
332C22×D43—22no—
333C22×D43—22no—
334C22×D43—22no—
335C22×D43—22no—
336C22×D43—22no—
337C22×D43—48no—
338C22×D43—42no—
339C22×D43—42no—
340C22×D43—42no—
341C22×D43—42no—
342C22×D43—42no—
343C22×D43—42no—
344C22×D43—48no—
345C22×D43—42no—
346C22×D43—42no—
347C22×D43—84no—
348C22×D43—816no—
349C22×D43C22×D412yes—
350Q8×C43—24no—
351Q8×C43—22no—
352Q8×C43—22no—
353Q8×C43—22no—
354Q8×C43—22no—
355Q8×C43—22no—
356Q8×C43—48no—
357Q8×C43—42no—
358Q8×C43—42no—
359Q8×C43C22×D414yes—
360C2×C4×C43—24no—
361C2×C4×C43—22no—
362C2×C4×C43—22no—
363C2×C4×C43—24no—
364C2×C4×C43—22no—
365C2×C4×C43—22no—
366C2×C4×C43—22no—
367C2×C4×C43—22no—
368C2×C4×C43—22no—
369C2×C4×C43—48no—
370C2×C4×C43—42no—
371C2×C4×C43—42no—
372C2×C4×C43—42no—
373C2×C4×C43C22×D412yes—
374C2×C4×C43C22×D411yescharacteristic
375C2×C4×C43C22×D412yes—
376C2×C4×C43H(5,𝔽2)12yes—
377C2×C4×C43C2511yescharacteristic
378C22⋊D43—28no—
379C22⋊D43—48no—
380C2×Dic43—22no—
381C2×Dic43—22no—
382C2×Dic43—22no—
383C2×Dic43—22no—
384C2×Dic43—42no—
385C2×Dic43C22×D412yes—
386C2×Dic43C22×D412yes—
387C2×Dic43C22×D412yes—
388D172—24no—
389D172—22no—
390D172—22no—
391D172—22no—
392D172—22no—
393D172—22no—
394D172—48no—
395D172—48no—
396D172—48no—
397D172—42no—
398D172—42no—
399D172—84no—
400D172C22×D414yes—
401C4×D43—24no—
402C4×D43—22no—
403C4×D43—22no—
404C4×D43—48no—
405C4×D43—48no—
406C4×D43—84no—
407C8×C43—22no—
408C8×C43—22no—
409C43⋊C8—22no—
410C43⋊C8C22×D414yes—
411C2×#3282—431nomaximal, Sylow
412C22×C43—22no—
413C22×C43—28no—
414C22×C43—22no—
415C22×C43D4212yes—
416C22×C43C2×#13512yes—
417C22×C43C2×#13514yescomplemented
418C22×C43#57712yes—
419C22×C43C23×D411yescharacteristic
420C2×D43—24no—
421C2×D43—22no—
422C2×D43—22no—
423C2×D43—22no—
424C2×D43—44no—
425C2×D43—48no—
426C2×D43—42no—
427C2×D43—42no—
428C2×D43—42no—
429C2×D43—42no—
430C2×D43—42no—
431C2×D43—42no—
432C2×D43—42no—
433C2×D43—42no—
434C2×D43—816no—
435C2×D43—84no—
436C2×D43—84no—
437C4×C43—24no—
438C4×C43—22no—
439C4×C43—42no—
440C4×C43—42no—
441C4×C43—42no—
442C4×C43D4212yes—
443C4×C43C23×D411yescharacteristic
444C4×C43C2×H(5,𝔽2)11yescharacteristic
445Dic43—22no—
446Dic43—22no—
447Dic43—22no—
448Dic43—42no—
449C22×#135—431no—
450C23×SD16—431no—
451C2×#548—431no—
452C2×#546—431no—
453#3282—4316no—
454C2×#495—431no—
455C2×#465—431no—
456C2×#465—431no—
457C2×#464—431no—
458C2×#463—431no—
459C2×#452—431no—
460C2×#449—431no—
461C2×#451D4311yescharacteristic, complemented
462C2×#447—431no—
463C2×C4×SD16—431no—
464C2×C8×D4—431no—
465C2×C43—24no—
466C2×C43#328214yescomplemented
467C2×C43C2×D4211yescharacteristic
468C2×C43C22×#13511yescharacteristic
469C2×C43C2×#57711yescharacteristic
470D43—42no—
471D43—44no—
472D43—82no—
473D43—82no—
474C22×#41—431no—
475C22×#41—431no—
476C23×Q8C2×D4311yescharacteristic
477C23×D4—431no—
478C2×#135—438no—
479C2×#135—868no—
480C22×Q16C2×D4311yescharacteristic, complemented
481C22×Q16C2×D4311yescharacteristic, complemented
482C22×SD16—431no—
483C22×SD16—431no—
484C22×SD16—431no—
485C22×SD16—431no—
486C22×SD16—431no—
487C22×SD16—438no—
488C22×SD16—868no—
489C22×D8—431no—
490C22×D8—431no—
491C23×C8—431no—
492C23×C8—431no—
493#548—438no—
494#548—864no—
495#546—438no—
496#546—864no—
497C2×#124—431no—
498C2×#124—431no—
499C2×#124—861no—
500C2×#123—861no—
501C2×C22⋊Q8—431no—
502C2×C22⋊Q8—861no—
503C2×C22⋊Q8C2×D4311yescharacteristic
504C2×#121—431no—
505C2×#121—431no—
506C2×#121—861no—
507C2×#121—861no—
508C2×#120—861no—
509C2×C4×Q8—431no—
510C2×C4×D4—431no—
511C2×C4×D4—431no—
512C2×C4×D4—861no—
513C22×C22⋊C4—861no—
514#495—438no—
515#465—438no—
516#465—438no—
517#464—438no—
518#463—438no—
519#452—438no—
520#451C2×D4318yescomplemented
521#449—438no—
522#447—438no—
523C4×SD16—438no—
524C8×D4—438no—
525C2×#106—431no—
526C2×C4⋊C8—431no—
527C2×#103—431no—
528C2×#103C2×D4311yescharacteristic, complemented
529C2×#103C2×D4311yescharacteristic, complemented
530C2×#102—431no—
531C2×#102—431no—
532C2×#102—431no—
533C2×C22⋊C8—431no—
534C2×C22⋊C8C2×D4311yescharacteristic
535C2×C4×C8—431no—
536C43C2×#328211yescharacteristic, complemented, Sylow
537C25—861no—
538C2×#41—434no—
539C2×#41—434no—
540C2×#41—862no—
541C2×#41—862no—
542C2×#41—864no—
543C2×#41—864no—
544C2×#41—1722no—
545C2×#41—1722no—
546C22×Q8—21no—
547C22×Q8—22no—
548C22×Q8—24no—
549C22×Q8—42no—
550C22×Q8C22×D4311yescharacteristic
551C22×Q8C22×D4311yescharacteristic
552C22×Q8C22×D4314yes—
553C22×Q8C22×D4311yescharacteristic
554C22×D4—431no—
555C22×D4—431no—
556C22×D4—431no—
557C22×D4—431no—
558C22×D4—434no—
559C22×D4—864no—
560C22×D4—861no—
561C22×D4—861no—
562C22×D4—861no—
563C22×D4—861no—
564C22×D4—861no—
565C22×D4—862no—
566C22×D4—1722no—
567C23×C4—21no—
568C23×C4—431no—
569C23×C4—861no—
570C23×C4—861no—
571C23×C4—861no—
572C23×C4C22×D4311yescharacteristic
573#135—8632no—
574C2×Q16—24no—
575C2×Q16—42no—
576C2×Q16C22×D4314yescomplemented
577C2×Q16C22×D4314yescomplemented
578C2×SD16—438no—
579C2×SD16—434no—
580C2×SD16—434no—
581C2×SD16—434no—
582C2×SD16—434no—
583C2×SD16—434no—
584C2×SD16—864no—
585C2×SD16—864no—
586C2×SD16—8632no—
587C2×SD16—864no—
588C2×SD16—864no—
589C2×D8—434no—
590C2×D8—434no—
591C2×D8—864no—
592C2×D8—1722no—
593C22×C8—431no—
594C22×C8—431no—
595C22×C8—434no—
596C22×C8—434no—
597C22×C8—864no—
598C22×C8—864no—
599C22×C8C22×D4311yescharacteristic
600C22×C8C22×D4311yescharacteristic
601#124—434no—
602#124—434no—
603#124—862no—
604#124—862no—
605#124—868no—
606#123—868no—
607C22⋊Q8—22no—
608C22⋊Q8—434no—
609C22⋊Q8—868no—
610C22⋊Q8—862no—
611C22⋊Q8C22×D4314yes—
612#121—434no—
613#121—434no—
614#121—868no—
615#121—862no—
616#121—868no—
617#121—862no—
618#120—868no—
619C4×Q8—434no—
620C4×Q8—862no—
621C4×D4—434no—
622C4×D4—434no—
623C4×D4—434no—
624C4×D4—862no—
625C4×D4—868no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—431no—
628C2×C4⋊C4—431no—
629C2×C4⋊C4—861no—
630C2×C4⋊C4—861no—
631C2×C4⋊C4C22×D4311yescharacteristic
632C2×C22⋊C4—21no—
633C2×C22⋊C4—431no—
634C2×C22⋊C4—431no—
635C2×C22⋊C4—868no—
636C2×C22⋊C4—861no—
637C2×C22⋊C4—861no—
638C2×C22⋊C4—861no—
639C2×C22⋊C4—861no—
640C2×C22⋊C4—861no—
641C2×C22⋊C4—861no—
642C2×C22⋊C4—861no—
643C2×C22⋊C4—861no—
644C2×C42—431no—
645C2×C42—861no—
646#106—434no—
647C4⋊C8—434no—
648#103—434no—
649#103C22×D4314yescomplemented
650#103C22×D4314yescomplemented
651#102—434no—
652#102—434no—
653#102—434no—
654C22⋊C8—434no—
655C22⋊C8C22×D4314yes—
656C4×C8—434no—
657C24—431no—
658C24—861no—
659C24—864no—
660C24—861no—
661C24—861no—
662C24—3442no—
663C24—1724no—
664C24—1724no—
665C24D4×D4311yescharacteristic
666#41—868no—
667#41—868no—
668#41—1724no—
669#41—1724no—
670#41—1728no—
671#41—1728no—
672C2×Q8—21no—
673C2×Q8—21no—
674C2×Q8—24no—
675C2×Q8—21no—
676C2×Q8—22no—
677C2×Q8—28no—
678C2×Q8—22no—
679C2×Q8—22no—
680C2×Q8—22no—
681C2×Q8—22no—
682C2×Q8—44no—
683C2×Q8—44no—
684C2×Q8—48no—
685C2×Q8D4×D4314yes—
686C2×Q8C23×D4312yes—
687C2×Q8C23×D4312yes—
688C2×Q8C23×D4312yes—
689C2×D4—434no—
690C2×D4—434no—
691C2×D4—432no—
692C2×D4—432no—
693C2×D4—432no—
694C2×D4—868no—
695C2×D4—864no—
696C2×D4—864no—
697C2×D4—864no—
698C2×D4—864no—
699C2×D4—864no—
700C2×D4—861no—
701C2×D4—862no—
702C2×D4—862no—
703C2×D4—864no—
704C2×D4—861no—
705C2×D4—861no—
706C2×D4—862no—
707C2×D4—862no—
708C2×D4—862no—
709C2×D4—3442no—
710C2×D4—1724no—
711C2×D4—1728no—
712C2×D4—1724no—
713C2×D4—1724no—
714C2×D4—1724no—
715C2×D4—1724no—
716C22×C4—21no—
717C22×C4—22no—
718C22×C4—22no—
719C22×C4—24no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—44no—
724C22×C4—431no—
725C22×C4—431no—
726C22×C4—431no—
727C22×C4—432no—
728C22×C4—432no—
729C22×C4—864no—
730C22×C4—864no—
731C22×C4—864no—
732C22×C4—862no—
733C22×C4—862no—
734C22×C4—861no—
735C22×C4—3442no—
736C22×C4—1724no—
737C22×C4—1724no—
738C22×C4D4×D4312yes—
739C22×C4D4×D4311yescharacteristic
740C22×C4C23×D4312yes—
741C22×C4C23×D4311yescharacteristic
742Q16—28no—
743Q16—44no—
744SD16—4316no—
745SD16—868no—
746SD16—868no—
747SD16—868no—
748SD16—868no—
749D8—868no—
750D8—1724no—
751C2×C8—22no—
752C2×C8—22no—
753C2×C8—434no—
754C2×C8—432no—
755C2×C8—432no—
756C2×C8—868no—
757C2×C8—868no—
758C2×C8—862no—
759C2×C8C23×D4312yes—
760C2×C8C23×D4312yes—
761C4⋊C4—24no—
762C4⋊C4—21no—
763C4⋊C4—434no—
764C4⋊C4—432no—
765C4⋊C4—864no—
766C4⋊C4—864no—
767C4⋊C4—861no—
768C4⋊C4C23×D4312yes—
769C22⋊C4—24no—
770C22⋊C4—434no—
771C22⋊C4—434no—
772C22⋊C4—864no—
773C22⋊C4—864no—
774C22⋊C4—864no—
775C22⋊C4—864no—
776C22⋊C4—864no—
777C22⋊C4—864no—
778C22⋊C4—864no—
779C22⋊C4—864no—
780C42—432no—
781C42—432no—
782C42—864no—
783C23—22no—
784C23—22no—
785C23—432no—
786C23—862no—
787C23—862no—
788C23—862no—
789C23—862no—
790C23—864no—
791C23—862no—
792C23—862no—
793C23—34416no—
794C23—3444no—
795C23—1728no—
796C23—1722no—
797C23—1722no—
798C23—1728no—
799C23—1722no—
800C23—1722no—
801C23—1722no—
802C23—1722no—
803C23—1722no—
804C23—1722no—
805C23#1306334814yescomplemented
806C23C2×D4×D4312yes—
807C23C2×D4×D4311yescharacteristic
808Q8—22no—
809Q8—24no—
810Q8—22no—
811Q8—22no—
812Q8—22no—
813Q8—22no—
814Q8—48no—
815Q8—42no—
816Q8—42no—
817Q8C2×D4×D4314yes—
818D4—434no—
819D4—868no—
820D4—862no—
821D4—862no—
822D4—862no—
823D4—862no—
824D4—862no—
825D4—864no—
826D4—3444no—
827D4—1728no—
828D4—1728no—
829D4—1728no—
830D4—1728no—
831D4—1722no—
832D4—1722no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—24no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—24no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—48no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—432no—
847C2×C4—432no—
848C2×C4—432no—
849C2×C4—862no—
850C2×C4—862no—
851C2×C4—862no—
852C2×C4—862no—
853C2×C4—862no—
854C2×C4—864no—
855C2×C4—862no—
856C2×C4—3444no—
857C2×C4—1728no—
858C2×C4—1728no—
859C2×C4—1722no—
860C2×C4C2×D4×D4312yes—
861C2×C4C2×D4×D4312yes—
862C2×C4C2×D4×D4311yescharacteristic
863C2×C4#1306337012yes—
864C2×C4C24×D4311yescharacteristic
865C8—22no—
866C8—22no—
867C8—434no—
868C8—862no—
869C22—22no—
870C22—28no—
871C22—22no—
872C22—862no—
873C22—862no—
874C22—862no—
875C22—864no—
876C22—34416no—
877C22—3444no—
878C22—3444no—
879C22—1722no—
880C22—1722no—
881C22—1722no—
882C22—1722no—
883C22—1722no—
884C22—1722no—
885C22—1722no—
886C22—1722no—
887C22—1724no—
888C22—1728no—
889C22#1458353112yes—
890C22C2×#1306334812yes—
891C22C2×#1306334814yescomplemented
892C22#1458370812yes—
893C22C22×D4×D4311yescharacteristic
894C4—22no—
895C4—24no—
896C4—42no—
897C4—42no—
898C4—42no—
899C4—862no—
900C4—862no—
901C4—862no—
902C4—1722no—
903C4#1458353112yes—
904C4C22×D4×D4311yescharacteristic
905C4C2×#1306337011yescharacteristic
906C2—24no—
907C2—3442no—
908C2—3442no—
909C2—1722no—
910C2—1724no—
911C2#1914629514yesdirect product factor
912C2C2×#1458353111yescharacteristic
913C2C22×#1306334811yescharacteristic
914C2C2×#1458370811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#451C2
socleC23×C43C22×D4
hypercenterC2×#451D43
hypocenterC43C2×#3282
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#451

Complements

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

NH ≅ G/Ntype
1. C22×#13063348C2semidirect
2. C23×#10621884C2semidirect
3. C2×#14583560C2semidirect
4. C2×#14583540C2semidirect
5. #19146295C2direct (N × H)
6. C2×#14583284C2semidirect
7. C2×#14583131C2semidirect
8. C2×#14583130C2semidirect
9. C2×#14583123C2semidirect
10. C2×#14583117C2semidirect
11. C2×#14583060C2semidirect
12. C2×#14583047C2semidirect
13. C2×#14583035C2semidirect
14. C2×#14582984C2semidirect
15. C2×(C22⋊D43)⋊C8C2semidirect
16. C2×C43×#451C2semidirect
18. C22×#10621902C22semidirect
21. C2×#13063348C22semidirect
27. C22×#10621884C22semidirect
28. C22×#10621884C22semidirect
32. C22×C8×D43C22semidirect
34. #14583560C22semidirect
36. #14583540C22semidirect
39. C2×#13063314C22semidirect
42. C2×#13063301C22semidirect
48. C2×Q8×Dic43C22semidirect
53. #14583284C22semidirect
54. #14583131C22semidirect
55. #14583130C22semidirect
56. #14583123C22semidirect
57. #14583117C22semidirect
58. #14583060C22semidirect
59. #14583047C22semidirect
60. #14583035C22semidirect
61. #14582984C22semidirect
62. (C22⋊D43)⋊C8C22semidirect
63. C2×#13063256C22semidirect
64. C2×Dic43⋊C8C22semidirect
65. C2×#13063249C22semidirect
68. C2×#13063245C22semidirect
69. C2×(C2×D43)⋊C8C22semidirect
70. C2×C8×Dic43C22semidirect
72. C22×Q16×C43C22semidirect
73. C22×Q16×C43C22semidirect
75. C43×#451C22semidirect
76. C2×#103×C43C22semidirect
77. C2×#103×C43C22semidirect
87. C2×#10621902C23semidirect
111. C2×#10621884D4semidirect
116. C2×#10621884C23semidirect
126. C2×C8×D43C23semidirect
131. #13063314C23semidirect
135. #13063301C23semidirect
144. Q8×Dic43C23semidirect
167. #13063256C23semidirect
168. Dic43⋊C8C23semidirect
169. #13063249C23semidirect
172. #13063245C23semidirect
173. (C2×D43)⋊C8C23semidirect
174. C8×Dic43C23semidirect
187. C2×Q16×C43C23semidirect
188. C2×Q16×C43C23semidirect
196. #103×C43C23semidirect
197. #103×C43C23semidirect
299. #10621884C2×D4semidirect
327. C23×C43#135semidirect
417. C22×C43C2×#135semidirect
461. C2×#451D43semidirect
466. C2×C43#3282semidirect
480. C22×Q16C2×D43semidirect
481. C22×Q16C2×D43semidirect
520. #451C2×D43semidirect
528. C2×#103C2×D43semidirect
529. C2×#103C2×D43semidirect
536. C43C2×#3282semidirect
576. C2×Q16C22×D43semidirect
577. C2×Q16C22×D43semidirect
649. #103C22×D43semidirect
650. #103C22×D43semidirect
805. C23#13063348semidirect
891. C22C2×#13063348semidirect
911. C2#19146295direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130633482
C23×#106218842
C2×#145835602
C2×#145835402
#191462952
C2×#145832842
C2×#145831312
C2×#145831302
C2×#145831232
C2×#145831172
C2×#145830602
C2×#145830472
C2×#145830352
C2×#145829842
C2×(C22⋊D43)⋊C82
C2×C43×#4512
C2×#328243