Finite Group Databasebeta

← D43×#1520 #25063909

Subgroups — D43×#1520 #25063909

Order 11008.

1522 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C22⋊Q8×D43C211yesmaximal, characteristic
2C2×C22⋊C8×D43C211yesmaximal, characteristic
3#380×D43C211yesmaximal, characteristic
4#19133168C211yesmaximal, characteristic, complemented
5#19133167C211yesmaximal, characteristic, complemented
6#19133166C211yesmaximal, characteristic, complemented
7#19133165C214yesmaximal, complemented
8#328×D43C214yesmaximal, complemented
9C43×#1520C211yesmaximal, characteristic, complemented
10C22×Q8×D43C411yescharacteristic, complemented
11C23×C4×D43C2211yescharacteristic
12C22×C8×D43—21no—
13C2×#13063305C411yescharacteristic, complemented
14C2×#13063304C2211yescharacteristic
15C2×#13063303—21no—
16C2×#13063302—21no—
17C2×#13063301C411yescharacteristic, complemented
18C22⋊Q8×D43—21no—
19C22⋊Q8×D43—21no—
20C22⋊Q8×D43—21no—
21C22⋊Q8×D43—21no—
22C22⋊Q8×D43C412yescomplemented
23C22⋊Q8×D43C412yescomplemented
24C22⋊Q8×D43C2212yes—
25C22⋊Q8×D43C2212yes—
26C2×C4⋊C4×D43—21no—
27C2×C4⋊C4×D43—21no—
28C2×C4⋊C4×D43C411yescharacteristic, complemented
29C2×C22⋊C4×D43—21no—
30C2×C22⋊C4×D43—21no—
31C2×C22⋊(C43⋊C8)C2211yescharacteristic
32C2×(C2×D43)⋊C8—21no—
33C22⋊C8×D43—21no—
34C22⋊C8×D43—21no—
35C22⋊C8×D43C2212yes—
36C22⋊C8×D43C2212yes—
37#14582759C2211yescharacteristic
38#14582758C2212yes—
39#14582757—21no—
40#14582756—21no—
41#95×D43C2212yes—
42#14582637C2214yescomplemented
43#14582636C2214yescomplemented
44#14582635C2214yescomplemented
45C2×C22⋊Q8×C43C2211yescharacteristic
46C2×C22⋊C8×C43C2211yescharacteristic
47C43×#380C2211yescharacteristic
48C43×#328C2214yescomplemented
49C24×D43D411yescharacteristic
50C22×Dic86—21no—
51C22×Dic86C2×C411yescharacteristic, complemented
52C2×Q8×D43—21no—
53C2×Q8×D43—21no—
54C2×Q8×D43—44no—
55C2×Q8×D43C2×C412yes—
56C2×Q8×D43C2×C412yescomplemented
57C23×Dic43D411yescharacteristic
58C22×C4×D43—21no—
59C22×C4×D43—21no—
60C22×C4×D43—22no—
61C22×C4×D43—44no—
62C22×C4×D43C2×C411yescharacteristic
63C22×C4×D43C2×C411yescharacteristic
64C22×C4×D43C2×C411yescharacteristic
65C22×C4×D43C2×C411yescharacteristic
66C22×C4×D43D411yescharacteristic
67C22×C4×D43D411yescharacteristic
68C22×C4×D43D411yescharacteristic
69C22×C4×D43D411yescharacteristic
70C22×C4×D43D411yescharacteristic
71C22×C4×D43D411yescharacteristic
72C22×C4×D43C2311yescharacteristic
73C22×C4×D43C2311yescharacteristic
74C22×C43⋊C8—21no—
75C2×C8×D43—22no—
76C2×C8×D43—22no—
77C2×C8×D43—44no—
78#13063305—21no—
79#13063305—21no—
80#13063305C2×C412yes—
81#13063305C2×C412yescomplemented
82#13063304—21no—
83#13063304—21no—
84#13063304C2×C412yescomplemented
85#13063304C2312yes—
86#13063303—22no—
87#13063303—22no—
88#13063303—22no—
89#13063303—22no—
90#13063302—22no—
91#13063302—22no—
92#13063302—22no—
93#13063302—22no—
94#13063301—21no—
95#13063301—21no—
96#13063301C2×C412yes—
97#13063301C2×C412yescomplemented
98C2×C4⋊Dic43—21no—
99C2×C4⋊Dic43—21no—
100C2×C4⋊Dic43C2×C411yescharacteristic, complemented
101C2×Dic43⋊C4—21no—
102C2×Dic43⋊C4—21no—
103C2×Dic43⋊C4—21no—
104C2×Dic43⋊C4—22no—
105C4⋊C4×D43—22no—
106C4⋊C4×D43—22no—
107C4⋊C4×D43—21no—
108C4⋊C4×D43—21no—
109C4⋊C4×D43—22no—
110C4⋊C4×D43—22no—
111C4⋊C4×D43—44no—
112C4⋊C4×D43C2×C412yes—
113C4⋊C4×D43C2×C412yescomplemented
114C2×C22⋊Dic43—21no—
115C2×C22⋊Dic43—21no—
116C2×(C2×D43)⋊C4—21no—
117C2×(C2×D43)⋊C4—21no—
118C2×(C2×D43)⋊C4—22no—
119C22⋊C4×D43—22no—
120C22⋊C4×D43—22no—
121C22⋊C4×D43—22no—
122C22⋊C4×D43—22no—
123C22⋊C4×D43—44no—
124C22⋊(C43⋊C8)—21no—
125C22⋊(C43⋊C8)C2312yes—
126(C2×D43)⋊C8—22no—
127(C2×D43)⋊C8—22no—
128C43⋊#95—22no—
129C43⋊#95C2312yes—
130C22×Q8×C43C2×C411yescharacteristic, complemented
131C23×C4×C43C2311yescharacteristic
132C22×C8×C43—21no—
133C22⋊Q8×C43—21no—
134C22⋊Q8×C43—21no—
135C22⋊Q8×C43C2×C412yescomplemented
136C22⋊Q8×C43C2312yes—
137C2×C4⋊C4×C43—21no—
138C2×C4⋊C4×C43—21no—
139C2×C4⋊C4×C43C2×C411yescharacteristic, complemented
140C2×C22⋊C4×C43—21no—
141C2×C22⋊C4×C43—21no—
142C22⋊C8×C43—21no—
143C22⋊C8×C43C2312yes—
144#95×C43C2312yes—
145C24×C43C2×D411yescharacteristic
146C23×D43—42no—
147C23×D43—42no—
148C23×D43C22⋊C411yescharacteristic
149C23×D43C22⋊C411yescharacteristic
150C23×D43C22⋊C411yescharacteristic
151C23×D43C22⋊C411yescharacteristic
152C23×D43SD1614yes—
153C23×D43Q1614yes—
154C23×D43C2×D411yescharacteristic
155C23×D43C2×D411yescharacteristic
156C2×Q8×C43—21no—
157C2×Q8×C43—42no—
158C2×Q8×C43C22×C412yes—
159C22×C4×C43—21no—
160C22×C4×C43—21no—
161C22×C4×C43—22no—
162C22×C4×C43—42no—
163C22×C4×C43C22×C411yescharacteristic
164C22×C4×C43C22×C411yescharacteristic
165C22×C4×C43C2×D411yescharacteristic
166C22×C4×C43C2×D411yescharacteristic
167C22×C4×C43C2×D411yescharacteristic
168C22×C4×C43C2411yescharacteristic
169C22×Dic43—21no—
170C22×Dic43—21no—
171C22×Dic43—22no—
172C22×Dic43—42no—
173C22×Dic43C22⋊C411yescharacteristic
174C22×Dic43C22⋊C411yescharacteristic
175C22×Dic43C22⋊C411yescharacteristic
176C22×Dic43C22⋊C411yescharacteristic
177C22×Dic43C2×D411yescharacteristic
178C22×Dic43C2×D411yescharacteristic
179Q8×D43—44no—
180Q8×D43—44no—
181Q8×D43—44no—
182Q8×D43—44no—
183C2×C4×D43—24no—
184C2×C4×D43—24no—
185C2×C4×D43—24no—
186C2×C4×D43—22no—
187C2×C4×D43—22no—
188C2×C4×D43—22no—
189C2×C4×D43—22no—
190C2×C4×D43—42no—
191C2×C4×D43—42no—
192C2×C4×D43—42no—
193C2×C4×D43—44no—
194C2×C4×D43—44no—
195C2×C4×D43—44no—
196C2×C4×D43—44no—
197C2×C4×D43—42no—
198C2×C4×D43—42no—
199C2×C4×D43—42no—
200C2×C4×D43—42no—
201C2×C4×D43—42no—
202C2×C4×D43—42no—
203C2×C4×D43—44no—
204C2×C4×D43C22⋊C411yescharacteristic
205C2×C4×D43C22⋊C411yescharacteristic
206C2×C4×D43C22⋊C411yescharacteristic
207C2×C4×D43C22⋊C411yescharacteristic
208C2×C4×D43C22⋊C411yescharacteristic
209C2×C4×D43C22⋊C411yescharacteristic
210C2×C4×D43C22⋊C411yescharacteristic
211C2×C4×D43C22⋊C411yescharacteristic
212C2×C4×D43C22×C411yescharacteristic
213C2×C4×D43C22×C411yescharacteristic
214C2×C4×D43C22×C411yescharacteristic
215C2×C4×D43C22×C411yescharacteristic
216C2×C4×D43C2×D411yescharacteristic
217C2×C4×D43C2×D411yescharacteristic
218C2×C4×D43C2×D411yescharacteristic
219C2×C4×D43C2×D411yescharacteristic
220C2×Dic86—21no—
221C2×Dic86—22no—
222C2×Dic86—22no—
223C2×Dic86—44no—
224C2×Dic86—42no—
225C2×Dic86C22×C412yes—
226C2×C8×C43—22no—
227C2×C8×C43—42no—
228C4⋊C4×C43—22no—
229C4⋊C4×C43—21no—
230C4⋊C4×C43—22no—
231C4⋊C4×C43—42no—
232C4⋊C4×C43C22×C412yes—
233C22⋊C4×C43—22no—
234C22⋊C4×C43—22no—
235C22⋊C4×C43—42no—
236C22⋊Dic43—22no—
237C22⋊Dic43—22no—
238C22⋊Dic43—42no—
239(C2×D43)⋊C4—22no—
240(C2×D43)⋊C4—22no—
241(C2×D43)⋊C4—22no—
242(C2×D43)⋊C4—22no—
243(C2×D43)⋊C4—44no—
244C4⋊Dic43—21no—
245C4⋊Dic43—22no—
246C4⋊Dic43—22no—
247C4⋊Dic43—42no—
248C4⋊Dic43C22×C412yes—
249Dic43⋊C4—22no—
250Dic43⋊C4—22no—
251Dic43⋊C4—22no—
252Dic43⋊C4—22no—
253Dic43⋊C4—22no—
254Dic43⋊C4—22no—
255Dic43⋊C4—44no—
256C2×C43⋊C8—22no—
257C2×C43⋊C8—42no—
258C8×D43—44no—
259C8×D43—44no—
260C23×C43—41no—
261C23×C43—41no—
262C23×C43C2×C22⋊C411yescharacteristic
263C23×C43C2×C22⋊C411yescharacteristic
264C23×C43C2×SD1612yes—
265C23×C43C2×Q1612yes—
266C23×C43C22×D411yescharacteristic
267C22×D43—22no—
268C22×D43—22no—
269C22×D43—22no—
270C22×D43—22no—
271C22×D43—22no—
272C22×D43—22no—
273C22×D43—48no—
274C22×D43—48no—
275C22×D43—41no—
276C22×D43—41no—
277C22×D43—41no—
278C22×D43—41no—
279C22×D43—41no—
280C22×D43—41no—
281C22×D43#10314yes—
282C22×D43#10314yes—
283C22×D43#10314yes—
284C22×D43#10314yes—
285C22×D43C2×C22⋊C411yescharacteristic
286C22×D43C2×C22⋊C411yescharacteristic
287C22×D43C2×C22⋊C411yescharacteristic
288C22×D43C2×C22⋊C411yescharacteristic
289C22×D43C2×SD1612yes—
290C22×D43C2×SD1612yes—
291C22×D43C2×Q1612yes—
292C22×D43C2×Q1612yes—
293Q8×C43—42no—
294Q8×C43—42no—
295C2×C4×C43—22no—
296C2×C4×C43—22no—
297C2×C4×C43—22no—
298C2×C4×C43—22no—
299C2×C4×C43—22no—
300C2×C4×C43—41no—
301C2×C4×C43—41no—
302C2×C4×C43—41no—
303C2×C4×C43—42no—
304C2×C4×C43—42no—
305C2×C4×C43—42no—
306C2×C4×C43—42no—
307C2×C4×C43—42no—
308C2×C4×C43C2×C22⋊C411yescharacteristic
309C2×C4×C43C2×C22⋊C411yescharacteristic
310C2×C4×C43C23×C411yescharacteristic
311C2×C4×C43C22×D411yescharacteristic
312C2×Dic43—22no—
313C2×Dic43—22no—
314C2×Dic43—22no—
315C2×Dic43—22no—
316C2×Dic43—22no—
317C2×Dic43—41no—
318C2×Dic43—41no—
319C2×Dic43—41no—
320C2×Dic43—42no—
321C2×Dic43—42no—
322C2×Dic43—42no—
323C2×Dic43—42no—
324C2×Dic43—42no—
325C2×Dic43C2×C22⋊C411yescharacteristic
326C2×Dic43C2×C22⋊C411yescharacteristic
327C2×Dic43C2×C22⋊C411yescharacteristic
328C2×Dic43C2×C22⋊C411yescharacteristic
329C4×D43—22no—
330C4×D43—22no—
331C4×D43—22no—
332C4×D43—22no—
333C4×D43—22no—
334C4×D43—22no—
335C4×D43—22no—
336C4×D43—22no—
337C4×D43—22no—
338C4×D43—41no—
339C4×D43—41no—
340C4×D43—41no—
341C4×D43—41no—
342C4×D43—41no—
343C4×D43—41no—
344C4×D43—44no—
345C4×D43—44no—
346C4×D43—44no—
347C4×D43—44no—
348C4×D43—88no—
349C4×D43#9914yes—
350Dic86—44no—
351Dic86—42no—
352Dic86—44no—
353Dic86—42no—
354C8×C43—42no—
355C43⋊C8—42no—
356C2×#1520—431nomaximal, Sylow
357C22×C43—21no—
358C22×C43—21no—
359C22×C43—21no—
360C22×C43—21no—
361C22×C43—21no—
362C22×C43—21no—
363C22×C43—42no—
364C22×C43—42no—
365C22×C43C2×#10312yes—
366C22×C43C2×#10312yes—
367C22×C43C22×C22⋊C411yescharacteristic
368C22×C43C22×SD1611yescharacteristic
369C22×C43C22×Q1611yescharacteristic
370C2×D43—21no—
371C2×D43—21no—
372C2×D43—21no—
373C2×D43—21no—
374C2×D43—21no—
375C2×D43—21no—
376C2×D43—28no—
377C2×D43—28no—
378C2×D43—24no—
379C2×D43—24no—
380C2×D43—44no—
381C2×D43—44no—
382C2×D43—42no—
383C2×D43—42no—
384C2×D43C2×#9912yes—
385C2×D43C2×#10312yes—
386C2×D43C2×#10312yes—
387C2×D43C2×#10312yes—
388C2×D43C2×#10312yes—
389C2×D43#42112yes—
390C4×C43—21no—
391C4×C43—21no—
392C4×C43—21no—
393C4×C43—42no—
394C4×C43—42no—
395C4×C43—82no—
396C4×C43C2×#9912yes—
397Dic43—21no—
398Dic43—21no—
399Dic43—21no—
400Dic43—42no—
401Dic43—42no—
402Dic43—82no—
403Dic43C2×#9912yes—
404C22×C22⋊Q8—431no—
405C22×C22⋊C8—431no—
406C2×#380—431no—
407#1520—431no—
408#1520—431no—
409#1520—434no—
410#1520—431no—
411#1520D4311yescharacteristic, direct product factor
412C2×#328—434no—
413C2×C43—21no—
414C2×C43—21no—
415C2×C43—22no—
416C2×C43—22no—
417C2×C43C22×#9911yescharacteristic
418C2×C43C22×#10311yescharacteristic
419C2×C43C2×#42111yescharacteristic
420D43—22no—
421D43—22no—
422D43—22no—
423D43#152014yesdirect product factor
424C23×Q8—431no—
425C24×C4—431no—
426C23×C8—861no—
427C2×C22⋊Q8—431no—
428C2×C22⋊Q8—431no—
429C2×C22⋊Q8—432no—
430C2×C22⋊Q8—432no—
431C2×C22⋊Q8—432no—
432C2×C22⋊Q8—432no—
433C2×C22⋊Q8—431no—
434C2×C22⋊Q8—861no—
435C2×C22⋊Q8—861no—
436C2×C22⋊Q8—861no—
437C2×C22⋊Q8—861no—
438C2×C22⋊Q8—861no—
439C2×C22⋊Q8—861no—
440C2×C22⋊Q8C2×D4311yescharacteristic
441C22×C4⋊C4—431no—
442C22×C4⋊C4—861no—
443C22×C4⋊C4—861no—
444C22×C22⋊C4—861no—
445C22×C22⋊C4—861no—
446C2×C22⋊C8—431no—
447C2×C22⋊C8—432no—
448C2×C22⋊C8—432no—
449C2×C22⋊C8—861no—
450C2×C22⋊C8—861no—
451C2×C22⋊C8—861no—
452C2×C22⋊C8C2×D4311yescharacteristic
453#380—431no—
454#380—432no—
455#380—861no—
456#380—861no—
457#380C2×D4311yescharacteristic
458C2×#95—432no—
459#328—434no—
460#328—434no—
461#328—434no—
462#328C2×D4314yescomplemented
463C43C2×#152011yescharacteristic, complemented, Sylow
464C25—431no—
465C22×Q8—432no—
466C22×Q8—432no—
467C22×Q8—431no—
468C22×Q8—861no—
469C22×Q8—861no—
470C22×Q8—861no—
471C22×Q8—1724no—
472C22×Q8C4×D4311yescharacteristic, complemented
473C23×C4—431no—
474C23×C4—431no—
475C23×C4—431no—
476C23×C4—431no—
477C23×C4—431no—
478C23×C4—431no—
479C23×C4—431no—
480C23×C4—431no—
481C23×C4—431no—
482C23×C4—431no—
483C23×C4—431no—
484C23×C4—431no—
485C23×C4—431no—
486C23×C4—861no—
487C23×C4—861no—
488C23×C4—862no—
489C23×C4—1724no—
490C23×C4C22×D4311yescharacteristic
491C22×C8—21no—
492C22×C8—862no—
493C22×C8—862no—
494C22×C8—861no—
495C22×C8—1724no—
496C22⋊Q8—21no—
497C22⋊Q8—21no—
498C22⋊Q8—432no—
499C22⋊Q8—432no—
500C22⋊Q8—432no—
501C22⋊Q8—432no—
502C22⋊Q8—432no—
503C22⋊Q8—432no—
504C22⋊Q8—862no—
505C22⋊Q8—862no—
506C22⋊Q8—862no—
507C22⋊Q8—862no—
508C22⋊Q8—862no—
509C22⋊Q8—862no—
510C22⋊Q8—862no—
511C22⋊Q8—862no—
512C22⋊Q8—861no—
513C22⋊Q8—861no—
514C22⋊Q8—861no—
515C22⋊Q8—861no—
516C22⋊Q8—861no—
517C22⋊Q8—861no—
518C22⋊Q8C4×D4312yescomplemented
519C22⋊Q8C22×D4312yes—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—431no—
523C2×C4⋊C4—432no—
524C2×C4⋊C4—432no—
525C2×C4⋊C4—861no—
526C2×C4⋊C4—861no—
527C2×C4⋊C4—862no—
528C2×C4⋊C4—862no—
529C2×C4⋊C4—862no—
530C2×C4⋊C4—862no—
531C2×C4⋊C4—861no—
532C2×C4⋊C4—861no—
533C2×C4⋊C4—861no—
534C2×C4⋊C4—861no—
535C2×C4⋊C4—862no—
536C2×C4⋊C4—861no—
537C2×C4⋊C4—1724no—
538C2×C4⋊C4C4×D4311yescharacteristic, complemented
539C2×C22⋊C4—21no—
540C2×C22⋊C4—21no—
541C2×C22⋊C4—862no—
542C2×C22⋊C4—862no—
543C2×C22⋊C4—862no—
544C2×C22⋊C4—862no—
545C2×C22⋊C4—861no—
546C2×C22⋊C4—861no—
547C2×C22⋊C4—861no—
548C2×C22⋊C4—862no—
549C2×C22⋊C4—861no—
550C2×C22⋊C4—1724no—
551C22⋊C8—21no—
552C22⋊C8—432no—
553C22⋊C8—862no—
554C22⋊C8—862no—
555C22⋊C8—861no—
556C22⋊C8C22×D4312yes—
557#95—432no—
558#95—862no—
559#95C22×D4312yes—
560C24—431no—
561C24—431no—
562C24—431no—
563C24—431no—
564C24—431no—
565C24—434no—
566C24—434no—
567C24—431no—
568C24—1722no—
569C24—1722no—
570C24D4×D4311yescharacteristic
571C2×Q8—21no—
572C2×Q8—42no—
573C2×Q8—432no—
574C2×Q8—862no—
575C2×Q8—862no—
576C2×Q8—861no—
577C2×Q8—1722no—
578C2×Q8—1724no—
579C2×Q8—1724no—
580C2×Q8—1724no—
581C2×Q8—1724no—
582C2×Q8—1724no—
583C2×Q8C2×C4×D4312yes—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—22no—
587C22×C4—42no—
588C22×C4—431no—
589C22×C4—431no—
590C22×C4—431no—
591C22×C4—431no—
592C22×C4—431no—
593C22×C4—431no—
594C22×C4—431no—
595C22×C4—431no—
596C22×C4—431no—
597C22×C4—431no—
598C22×C4—431no—
599C22×C4—431no—
600C22×C4—431no—
601C22×C4—431no—
602C22×C4—431no—
603C22×C4—431no—
604C22×C4—431no—
605C22×C4—431no—
606C22×C4—431no—
607C22×C4—431no—
608C22×C4—431no—
609C22×C4—431no—
610C22×C4—864no—
611C22×C4—864no—
612C22×C4—864no—
613C22×C4—862no—
614C22×C4—862no—
615C22×C4—862no—
616C22×C4—862no—
617C22×C4—861no—
618C22×C4—861no—
619C22×C4—862no—
620C22×C4—1722no—
621C22×C4—1722no—
622C22×C4—1722no—
623C22×C4—1722no—
624C22×C4—1722no—
625C22×C4—1722no—
626C22×C4—1722no—
627C22×C4—1722no—
628C22×C4—1722no—
629C22×C4—1724no—
630C22×C4—1724no—
631C22×C4—1724no—
632C22×C4—1724no—
633C22×C4—1724no—
634C22×C4—1722no—
635C22×C4C2×C4×D4311yescharacteristic
636C22×C4C2×C4×D4311yescharacteristic
637C22×C4D4×D4311yescharacteristic
638C22×C4D4×D4311yescharacteristic
639C22×C4D4×D4311yescharacteristic
640C22×C4C23×D4311yescharacteristic
641C2×C8—22no—
642C2×C8—42no—
643C2×C8—862no—
644C2×C8—1724no—
645C2×C8—1724no—
646C2×C8—1722no—
647C4⋊C4—22no—
648C4⋊C4—21no—
649C4⋊C4—22no—
650C4⋊C4—42no—
651C4⋊C4—432no—
652C4⋊C4—862no—
653C4⋊C4—862no—
654C4⋊C4—862no—
655C4⋊C4—862no—
656C4⋊C4—862no—
657C4⋊C4—862no—
658C4⋊C4—861no—
659C4⋊C4—862no—
660C4⋊C4—862no—
661C4⋊C4—1722no—
662C4⋊C4—1724no—
663C4⋊C4C2×C4×D4312yes—
664C22⋊C4—22no—
665C22⋊C4—22no—
666C22⋊C4—42no—
667C22⋊C4—862no—
668C22⋊C4—862no—
669C22⋊C4—862no—
670C22⋊C4—862no—
671C22⋊C4—862no—
672C22⋊C4—862no—
673C22⋊C4—1724no—
674C22⋊C4—1722no—
675C23—41no—
676C23—41no—
677C23—431no—
678C23—431no—
679C23—431no—
680C23—431no—
681C23—434no—
682C23—434no—
683C23—432no—
684C23—432no—
685C23—434no—
686C23—434no—
687C23—432no—
688C23—432no—
689C23—862no—
690C23—862no—
691C23—862no—
692C23—862no—
693C23—862no—
694C23—862no—
695C23—1721no—
696C23—1721no—
697C23—1721no—
698C23—1721no—
699C23—1721no—
700C23—1721no—
701C23—1728no—
702C23—1728no—
703C23C22⋊C4×D4311yescharacteristic
704C23C22⋊C4×D4311yescharacteristic
705C23SD16×D4312yes—
706C23Q16×D4312yes—
707C23C2×D4×D4311yescharacteristic
708Q8—42no—
709Q8—42no—
710Q8—1722no—
711Q8—1724no—
712Q8—1724no—
713Q8—1722no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—431no—
728C2×C4—434no—
729C2×C4—431no—
730C2×C4—431no—
731C2×C4—431no—
732C2×C4—862no—
733C2×C4—862no—
734C2×C4—862no—
735C2×C4—862no—
736C2×C4—862no—
737C2×C4—862no—
738C2×C4—862no—
739C2×C4—862no—
740C2×C4—862no—
741C2×C4—862no—
742C2×C4—862no—
743C2×C4—862no—
744C2×C4—862no—
745C2×C4—862no—
746C2×C4—3448no—
747C2×C4—1721no—
748C2×C4—1721no—
749C2×C4—1721no—
750C2×C4—1721no—
751C2×C4—1721no—
752C2×C4—1721no—
753C2×C4—1724no—
754C2×C4—1724no—
755C2×C4—1724no—
756C2×C4—1724no—
757C2×C4—1721no—
758C2×C4—1721no—
759C2×C4—1721no—
760C2×C4—1722no—
761C2×C4—1722no—
762C2×C4—1722no—
763C2×C4—1722no—
764C2×C4—1722no—
765C2×C4C22⋊C4×D4311yescharacteristic
766C2×C4C22⋊C4×D4311yescharacteristic
767C2×C4C22×C4×D4311yescharacteristic
768C2×C4C2×D4×D4311yescharacteristic
769C8—42no—
770C8—1722no—
771C22—21no—
772C22—21no—
773C22—21no—
774C22—21no—
775C22—21no—
776C22—21no—
777C22—42no—
778C22—42no—
779C22—432no—
780C22—432no—
781C22—432no—
782C22—432no—
783C22—432no—
784C22—432no—
785C22—864no—
786C22—868no—
787C22—868no—
788C22—864no—
789C22—861no—
790C22—861no—
791C22—861no—
792C22—861no—
793C22—861no—
794C22—861no—
795C22—1722no—
796C22—1724no—
797C22—1724no—
798C22—1722no—
799C22#103×D4312yes—
800C22#103×D4312yes—
801C22C2×C22⋊C4×D4311yescharacteristic
802C22C2×SD16×D4311yescharacteristic
803C22C2×Q16×D4311yescharacteristic
804C4—21no—
805C4—21no—
806C4—21no—
807C4—42no—
808C4—42no—
809C4—82no—
810C4—432no—
811C4—861no—
812C4—861no—
813C4—861no—
814C4—3442no—
815C4—1722no—
816C4—1722no—
817C4#99×D4312yes—
818C2—21no—
819C2—22no—
820C2—22no—
821C2—21no—
822C2—434no—
823C2—862no—
824C2—862no—
825C2—862no—
826C2C2×#99×D4311yescharacteristic
827C2C2×#103×D4311yescharacteristic
828C2#421×D4311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1520C2
socleC22×C43C22×C22⋊C4
prime radicalC24×D43D4
cosocleC22×C4×C43C24
hypercenter#1520D43
hypocenterC43C2×#1520
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1520

Complements

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

NH ≅ G/Ntype
4. #19133168C2semidirect
5. #19133167C2semidirect
6. #19133166C2semidirect
7. #19133165C2semidirect
8. #328×D43C2semidirect
9. C43×#1520C2semidirect
10. C22×Q8×D43C4semidirect
13. C2×#13063305C4semidirect
17. C2×#13063301C4semidirect
22. C22⋊Q8×D43C4semidirect
23. C22⋊Q8×D43C4semidirect
28. C2×C4⋊C4×D43C4semidirect
42. #14582637C22semidirect
43. #14582636C22semidirect
44. #14582635C22semidirect
48. C43×#328C22semidirect
51. C22×Dic86C2×C4semidirect
56. C2×Q8×D43C2×C4semidirect
81. #13063305C2×C4semidirect
84. #13063304C2×C4semidirect
97. #13063301C2×C4semidirect
100. C2×C4⋊Dic43C2×C4semidirect
113. C4⋊C4×D43C2×C4semidirect
130. C22×Q8×C43C2×C4semidirect
135. C22⋊Q8×C43C2×C4semidirect
139. C2×C4⋊C4×C43C2×C4semidirect
411. #1520D43direct (N × H)
423. D43#1520direct (N × H)
462. #328C2×D43semidirect
463. C43C2×#1520semidirect
472. C22×Q8C4×D43semidirect
518. C22⋊Q8C4×D43semidirect
538. C2×C4⋊C4C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊Q8×D432
C2×C22⋊C8×D432
#380×D432
#191331682
#191331672
#191331662
#191331652
#328×D432
C43×#15202
C2×#152043