Finite Group Databasebeta

← D43×#1508 #25063715

Subgroups — D43×#1508 #25063715

Order 11008.

1554 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C22⋊Q8×D43C211yesmaximal, characteristic
2#407×D43C211yesmaximal, characteristic
3C4×C22⋊C4×D43C211yesmaximal, characteristic
4#19133116C211yesmaximal, characteristic, complemented
5#19133115C211yesmaximal, characteristic, complemented
6#19133114C211yesmaximal, characteristic, complemented
7#19133113C214yesmaximal, complemented
8#328×D43C214yesmaximal, complemented
9C43×#1508C211yesmaximal, characteristic, complemented
10C22×Q8×D43C411yescharacteristic, complemented
11C23×C4×D43C2211yescharacteristic
12C2×M16×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×D43C411yescharacteristic, complemented
28C2×C22⋊C4×D43—21no—
29C2×C22⋊C4×D43—21no—
30C2×C42×D43—21no—
31#14582863C2211yescharacteristic
32#14582862—21no—
33#14582861—21no—
34#14582861C2212yes—
35C22⋊C8×D43—21no—
36C22⋊C8×D43C2212yes—
37C22⋊C4×Dic43—21no—
38C4×(C2×D43)⋊C4—21no—
39C4×C22⋊Dic43C2211yescharacteristic
40#14582746C2212yes—
41#95×D43C2212yes—
42#14582637C2214yescomplemented
43#14582636C2214yescomplemented
44#14582635C2214yescomplemented
45C2×C22⋊Q8×C43C2211yescharacteristic
46C43×#407C2211yescharacteristic
47C4×C22⋊C4×C43C2211yescharacteristic
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
74C2×#10621877—21no—
75C2×#10621872—22no—
76M16×D43—44no—
77C2×C8×D43—22no—
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⋊Dic43C2×C411yescharacteristic, complemented
100C2×Dic43⋊C4—21no—
101C2×Dic43⋊C4—21no—
102C2×Dic43⋊C4—21no—
103C4⋊C4×D43—22no—
104C4⋊C4×D43—22no—
105C4⋊C4×D43—21no—
106C4⋊C4×D43—21no—
107C4⋊C4×D43—22no—
108C4⋊C4×D43—22no—
109C4⋊C4×D43C2×C412yes—
110C4⋊C4×D43C2×C412yescomplemented
111C2×C22⋊Dic43—21no—
112C2×C22⋊Dic43—21no—
113C2×(C2×D43)⋊C4—21no—
114C2×(C2×D43)⋊C4—21no—
115C2×(C2×D43)⋊C4—22no—
116C22⋊C4×D43—28no—
117C22⋊C4×D43—22no—
118C22⋊C4×D43—22no—
119C22⋊C4×D43—22no—
120C22⋊C4×D43—22no—
121C2×C4×Dic43—21no—
122C2×C4×Dic43—22no—
123C42×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
132C2×M16×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×C43C2×C411yescharacteristic, complemented
139C2×C22⋊C4×C43—21no—
140C2×C22⋊C4×C43—21no—
141C2×C42×C43—21no—
142C22⋊C8×C43—21no—
143C22⋊C8×C43C2312yes—
144#95×C43C2312yes—
145C24×C43C2×D411yescharacteristic
146C23×D43—24no—
147C23×D43—24no—
148C23×D43—42no—
149C23×D43C22⋊C411yescharacteristic
150C23×D43C22⋊C411yescharacteristic
151C23×D43C22⋊C411yescharacteristic
152C23×D43C22⋊C411yescharacteristic
153C23×D43C2×D411yescharacteristic
154C23×D43C2×D411yescharacteristic
155C2×Q8×C43—21no—
156C2×Q8×C43—42no—
157C2×Q8×C43C22×C412yes—
158C22×C4×C43—21no—
159C22×C4×C43—21no—
160C22×C4×C43—22no—
161C22×C4×C43—42no—
162C22×C4×C43C22×C411yescharacteristic
163C22×C4×C43C22×C411yescharacteristic
164C22×C4×C43C2×D411yescharacteristic
165C22×C4×C43C2×D411yescharacteristic
166C22×C4×C43C2×D411yescharacteristic
167C22×C4×C43C2411yescharacteristic
168C22×Dic43—21no—
169C22×Dic43—21no—
170C22×Dic43—22no—
171C22×Dic43—42no—
172C22×Dic43C22⋊C411yescharacteristic
173C22×Dic43C22⋊C411yescharacteristic
174C22×Dic43C22⋊C411yescharacteristic
175C22×Dic43C22⋊C411yescharacteristic
176C22×Dic43C2×D411yescharacteristic
177C22×Dic43C2×D411yescharacteristic
178Q8×D43—44no—
179Q8×D43—44no—
180Q8×D43—44no—
181Q8×D43—44no—
182C2×C4×D43—24no—
183C2×C4×D43—24no—
184C2×C4×D43—24no—
185C2×C4×D43—28no—
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—42no—
196C2×C4×D43—42no—
197C2×C4×D43—42no—
198C2×C4×D43—42no—
199C2×C4×D43—42no—
200C2×C4×D43—42no—
201C2×C4×D43—44no—
202C2×C4×D43—44no—
203C2×C4×D43C22⋊C411yescharacteristic
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×D43C2×D411yescharacteristic
216C2×C4×D43C2×D411yescharacteristic
217C2×C4×D43C2×D411yescharacteristic
218C2×C4×D43C2×D411yescharacteristic
219C2×Dic86—21no—
220C2×Dic86—22no—
221C2×Dic86—22no—
222C2×Dic86—44no—
223C2×Dic86—42no—
224C2×Dic86C22×C412yes—
225M16×C43—42no—
226C2×C8×C43—22no—
227C4⋊C4×C43—22no—
228C4⋊C4×C43—21no—
229C4⋊C4×C43—22no—
230C4⋊C4×C43C22×C412yes—
231C22⋊C4×C43—24no—
232C22⋊C4×C43—22no—
233C22⋊C4×C43—22no—
234C42×C43—42no—
235C22⋊Dic43—24no—
236C22⋊Dic43—22no—
237C22⋊Dic43—22no—
238(C2×D43)⋊C4—28no—
239(C2×D43)⋊C4—22no—
240(C2×D43)⋊C4—22no—
241(C2×D43)⋊C4—22no—
242(C2×D43)⋊C4—22no—
243C4⋊Dic43—21no—
244C4⋊Dic43—22no—
245C4⋊Dic43—22no—
246C4⋊Dic43C22×C412yes—
247Dic43⋊C4—22no—
248Dic43⋊C4—22no—
249Dic43⋊C4—22no—
250Dic43⋊C4—22no—
251Dic43⋊C4—22no—
252Dic43⋊C4—22no—
253C4×Dic43—44no—
254C4×Dic43—42no—
255#10621877—42no—
256C2×C43⋊C8—22no—
257#10621872—44no—
258C8×D43—44no—
259C23×C43—22no—
260C23×C43—22no—
261C23×C43—41no—
262C23×C43C2×C22⋊C411yescharacteristic
263C23×C43C2×C22⋊C411yescharacteristic
264C23×C43C22×D411yescharacteristic
265C22×D43—22no—
266C22×D43—22no—
267C22×D43—22no—
268C22×D43—22no—
269C22×D43—22no—
270C22×D43—22no—
271C22×D43—22no—
272C22×D43—22no—
273C22×D43—22no—
274C22×D43—22no—
275C22×D43—22no—
276C22×D43—22no—
277C22×D43—22no—
278C22×D43—41no—
279C22×D43—41no—
280C22×D43—41no—
281C22×D43—416no—
282C22×D43#10414yes—
283C22×D43C2×C22⋊C411yescharacteristic
284C22×D43C2×C22⋊C411yescharacteristic
285C22×D43C2×C22⋊C411yescharacteristic
286C22×D43C2×C22⋊C411yescharacteristic
287C22×D43#13714yes—
288Q8×C43—42no—
289Q8×C43—42no—
290C2×C4×C43—22no—
291C2×C4×C43—22no—
292C2×C4×C43—22no—
293C2×C4×C43—24no—
294C2×C4×C43—22no—
295C2×C4×C43—22no—
296C2×C4×C43—41no—
297C2×C4×C43—41no—
298C2×C4×C43—41no—
299C2×C4×C43—42no—
300C2×C4×C43—42no—
301C2×C4×C43—42no—
302C2×C4×C43—42no—
303C2×C4×C43C2×C22⋊C411yescharacteristic
304C2×C4×C43C2×C22⋊C411yescharacteristic
305C2×C4×C43C23×C411yescharacteristic
306C2×C4×C43C22×D411yescharacteristic
307C2×Dic43—22no—
308C2×Dic43—22no—
309C2×Dic43—22no—
310C2×Dic43—24no—
311C2×Dic43—22no—
312C2×Dic43—22no—
313C2×Dic43—41no—
314C2×Dic43—41no—
315C2×Dic43—41no—
316C2×Dic43—42no—
317C2×Dic43—42no—
318C2×Dic43—42no—
319C2×Dic43—42no—
320C2×Dic43C2×C22⋊C411yescharacteristic
321C2×Dic43C2×C22⋊C411yescharacteristic
322C2×Dic43C2×C22⋊C411yescharacteristic
323C2×Dic43C2×C22⋊C411yescharacteristic
324C4×D43—22no—
325C4×D43—22no—
326C4×D43—22no—
327C4×D43—22no—
328C4×D43—22no—
329C4×D43—22no—
330C4×D43—22no—
331C4×D43—22no—
332C4×D43—22no—
333C4×D43—41no—
334C4×D43—41no—
335C4×D43—41no—
336C4×D43—41no—
337C4×D43—41no—
338C4×D43—41no—
339C4×D43—416no—
340C4×D43—44no—
341C4×D43—44no—
342C4×D43—44no—
343C4×D43—44no—
344C4×D43#9914yes—
345Dic86—44no—
346Dic86—42no—
347Dic86—44no—
348Dic86—42no—
349C8×C43—42no—
350C43⋊C8—42no—
351C2×#1508—431nomaximal, Sylow
352C22×C43—21no—
353C22×C43—21no—
354C22×C43—21no—
355C22×C43—21no—
356C22×C43—21no—
357C22×C43—21no—
358C22×C43—21no—
359C22×C43—44no—
360C22×C43C2×#10412yes—
361C22×C43C22×C22⋊C411yescharacteristic
362C22×C43C2×#13712yes—
363C2×D43—21no—
364C2×D43—21no—
365C2×D43—21no—
366C2×D43—21no—
367C2×D43—28no—
368C2×D43—28no—
369C2×D43—21no—
370C2×D43—21no—
371C2×D43—21no—
372C2×D43—44no—
373C2×D43—44no—
374C2×D43—44no—
375C2×D43—44no—
376C2×D43C2×#9912yes—
377C2×D43#41912yes—
378C2×D43#41912yes—
379C2×D43C2×#10412yes—
380C2×D43C2×#10412yes—
381C4×C43—21no—
382C4×C43—21no—
383C4×C43—21no—
384C4×C43—44no—
385C4×C43—42no—
386C4×C43—42no—
387C4×C43C2×#9912yes—
388Dic43—21no—
389Dic43—21no—
390Dic43—21no—
391Dic43—44no—
392Dic43—42no—
393Dic43—42no—
394Dic43C2×#9912yes—
395C22×C22⋊Q8—431no—
396C2×#407—431no—
397C2×C4×C22⋊C4—431no—
398#1508—431no—
399#1508—431no—
400#1508—434no—
401#1508—431no—
402#1508D4311yescharacteristic, direct product factor
403C2×#328—434no—
404C2×C43—22no—
405C2×C43—22no—
406C2×C43—41no—
407C2×C43C22×#9911yescharacteristic
408C2×C43C2×#41911yescharacteristic
409C2×C43C22×#10411yescharacteristic
410D43—22no—
411D43—22no—
412D43—41no—
413D43#150814yesdirect product factor
414C23×Q8—431no—
415C24×C4—431no—
416C22×M16—861no—
417C2×C22⋊Q8—431no—
418C2×C22⋊Q8—431no—
419C2×C22⋊Q8—432no—
420C2×C22⋊Q8—432no—
421C2×C22⋊Q8—432no—
422C2×C22⋊Q8—432no—
423C2×C22⋊Q8—431no—
424C2×C22⋊Q8—861no—
425C2×C22⋊Q8—861no—
426C2×C22⋊Q8—861no—
427C2×C22⋊Q8—861no—
428C2×C22⋊Q8—861no—
429C2×C22⋊Q8—861no—
430C2×C22⋊Q8C2×D4311yescharacteristic
431C22×C4⋊C4—431no—
432C22×C4⋊C4—861no—
433C22×C22⋊C4—861no—
434C22×C22⋊C4—861no—
435C22×C42—861no—
436#407—431no—
437#407—432no—
438#407—861no—
439#407—861no—
440#407C2×D4311yescharacteristic
441C2×C22⋊C8—432no—
442C2×C22⋊C8—861no—
443C4×C22⋊C4—431no—
444C4×C22⋊C4—432no—
445C4×C22⋊C4—861no—
446C4×C22⋊C4—861no—
447C4×C22⋊C4C2×D4311yescharacteristic
448C2×#95—432no—
449#328—434no—
450#328—434no—
451#328—434no—
452#328C2×D4314yescomplemented
453C43C2×#150811yescharacteristic, complemented, Sylow
454C25—431no—
455C22×Q8—432no—
456C22×Q8—432no—
457C22×Q8—431no—
458C22×Q8—861no—
459C22×Q8—861no—
460C22×Q8—861no—
461C22×Q8—1724no—
462C22×Q8C4×D4311yescharacteristic, complemented
463C23×C4—431no—
464C23×C4—431no—
465C23×C4—431no—
466C23×C4—431no—
467C23×C4—431no—
468C23×C4—431no—
469C23×C4—431no—
470C23×C4—431no—
471C23×C4—431no—
472C23×C4—431no—
473C23×C4—431no—
474C23×C4—431no—
475C23×C4—431no—
476C23×C4—861no—
477C23×C4—861no—
478C23×C4—862no—
479C23×C4—1724no—
480C23×C4C22×D4311yescharacteristic
481C2×M16—21no—
482C2×M16—862no—
483C2×M16—861no—
484C2×M16—1724no—
485C22×C8—862no—
486C22⋊Q8—21no—
487C22⋊Q8—21no—
488C22⋊Q8—432no—
489C22⋊Q8—432no—
490C22⋊Q8—432no—
491C22⋊Q8—432no—
492C22⋊Q8—432no—
493C22⋊Q8—432no—
494C22⋊Q8—862no—
495C22⋊Q8—862no—
496C22⋊Q8—862no—
497C22⋊Q8—862no—
498C22⋊Q8—862no—
499C22⋊Q8—862no—
500C22⋊Q8—862no—
501C22⋊Q8—862no—
502C22⋊Q8—861no—
503C22⋊Q8—861no—
504C22⋊Q8—861no—
505C22⋊Q8—861no—
506C22⋊Q8—861no—
507C22⋊Q8—861no—
508C22⋊Q8C4×D4312yescomplemented
509C22⋊Q8C22×D4312yes—
510C2×C4⋊C4—21no—
511C2×C4⋊C4—431no—
512C2×C4⋊C4—432no—
513C2×C4⋊C4—432no—
514C2×C4⋊C4—861no—
515C2×C4⋊C4—861no—
516C2×C4⋊C4—862no—
517C2×C4⋊C4—862no—
518C2×C4⋊C4—862no—
519C2×C4⋊C4—862no—
520C2×C4⋊C4—861no—
521C2×C4⋊C4—861no—
522C2×C4⋊C4—861no—
523C2×C4⋊C4—861no—
524C2×C4⋊C4C4×D4311yescharacteristic, complemented
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—862no—
528C2×C22⋊C4—862no—
529C2×C22⋊C4—862no—
530C2×C22⋊C4—862no—
531C2×C22⋊C4—868no—
532C2×C22⋊C4—861no—
533C2×C22⋊C4—861no—
534C2×C22⋊C4—862no—
535C2×C22⋊C4—861no—
536C2×C22⋊C4—861no—
537C2×C42—21no—
538C2×C42—862no—
539C2×C42—861no—
540C2×C42—1724no—
541C22⋊C8—21no—
542C22⋊C8—432no—
543C22⋊C8—862no—
544C22⋊C8—862no—
545C22⋊C8—861no—
546C22⋊C8C22×D4312yes—
547#95—432no—
548#95—862no—
549#95C22×D4312yes—
550C24—431no—
551C24—431no—
552C24—431no—
553C24—431no—
554C24—431no—
555C24—431no—
556C24—864no—
557C24—864no—
558C24—1722no—
559C24D4×D4311yescharacteristic
560C2×Q8—21no—
561C2×Q8—42no—
562C2×Q8—432no—
563C2×Q8—862no—
564C2×Q8—862no—
565C2×Q8—861no—
566C2×Q8—1722no—
567C2×Q8—1724no—
568C2×Q8—1724no—
569C2×Q8—1724no—
570C2×Q8—1724no—
571C2×Q8—1724no—
572C2×Q8C2×C4×D4312yes—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—22no—
576C22×C4—42no—
577C22×C4—431no—
578C22×C4—431no—
579C22×C4—431no—
580C22×C4—431no—
581C22×C4—431no—
582C22×C4—431no—
583C22×C4—431no—
584C22×C4—431no—
585C22×C4—431no—
586C22×C4—431no—
587C22×C4—431no—
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—864no—
600C22×C4—864no—
601C22×C4—864no—
602C22×C4—862no—
603C22×C4—862no—
604C22×C4—862no—
605C22×C4—862no—
606C22×C4—868no—
607C22×C4—861no—
608C22×C4—861no—
609C22×C4—862no—
610C22×C4—1722no—
611C22×C4—1722no—
612C22×C4—1722no—
613C22×C4—1722no—
614C22×C4—1722no—
615C22×C4—1722no—
616C22×C4—1722no—
617C22×C4—1722no—
618C22×C4—1722no—
619C22×C4—1724no—
620C22×C4—1724no—
621C22×C4—1724no—
622C22×C4—1724no—
623C22×C4—1722no—
624C22×C4C2×C4×D4311yescharacteristic
625C22×C4C2×C4×D4311yescharacteristic
626C22×C4D4×D4311yescharacteristic
627C22×C4D4×D4311yescharacteristic
628C22×C4D4×D4311yescharacteristic
629C22×C4C23×D4311yescharacteristic
630M16—42no—
631M16—1724no—
632M16—1722no—
633C2×C8—22no—
634C2×C8—862no—
635C2×C8—1724no—
636C4⋊C4—22no—
637C4⋊C4—21no—
638C4⋊C4—22no—
639C4⋊C4—432no—
640C4⋊C4—862no—
641C4⋊C4—862no—
642C4⋊C4—862no—
643C4⋊C4—862no—
644C4⋊C4—862no—
645C4⋊C4—862no—
646C4⋊C4—861no—
647C4⋊C4—862no—
648C4⋊C4—862no—
649C4⋊C4C2×C4×D4312yes—
650C22⋊C4—24no—
651C22⋊C4—22no—
652C22⋊C4—22no—
653C22⋊C4—862no—
654C22⋊C4—862no—
655C22⋊C4—862no—
656C22⋊C4—862no—
657C22⋊C4—868no—
658C22⋊C4—864no—
659C22⋊C4—862no—
660C22⋊C4—862no—
661C42—42no—
662C42—1722no—
663C42—1724no—
664C23—22no—
665C23—22no—
666C23—41no—
667C23—431no—
668C23—431no—
669C23—431no—
670C23—434no—
671C23—434no—
672C23—431no—
673C23—862no—
674C23—862no—
675C23—862no—
676C23—862no—
677C23—862no—
678C23—862no—
679C23—862no—
680C23—862no—
681C23—862no—
682C23—862no—
683C23—862no—
684C23—862no—
685C23—862no—
686C23—1721no—
687C23—1721no—
688C23—1721no—
689C23—17216no—
690C23C22⋊C4×D4311yescharacteristic
691C23C22⋊C4×D4311yescharacteristic
692C23C2×D4×D4311yescharacteristic
693Q8—42no—
694Q8—42no—
695Q8—1722no—
696Q8—1724no—
697Q8—1724no—
698Q8—1722no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—24no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—431no—
713C2×C4—434no—
714C2×C4—431no—
715C2×C4—431no—
716C2×C4—431no—
717C2×C4—862no—
718C2×C4—862no—
719C2×C4—862no—
720C2×C4—862no—
721C2×C4—862no—
722C2×C4—862no—
723C2×C4—862no—
724C2×C4—862no—
725C2×C4—862no—
726C2×C4—862no—
727C2×C4—862no—
728C2×C4—862no—
729C2×C4—864no—
730C2×C4—862no—
731C2×C4—862no—
732C2×C4—1721no—
733C2×C4—1721no—
734C2×C4—1721no—
735C2×C4—1721no—
736C2×C4—1721no—
737C2×C4—1721no—
738C2×C4—1724no—
739C2×C4—1724no—
740C2×C4—1724no—
741C2×C4—1724no—
742C2×C4—17216no—
743C2×C4—1721no—
744C2×C4—1721no—
745C2×C4—1721no—
746C2×C4—1722no—
747C2×C4—1722no—
748C2×C4—1722no—
749C2×C4—1722no—
750C2×C4C22⋊C4×D4311yescharacteristic
751C2×C4C22⋊C4×D4311yescharacteristic
752C2×C4C22×C4×D4311yescharacteristic
753C2×C4C2×D4×D4311yescharacteristic
754C8—42no—
755C8—1722no—
756C22—21no—
757C22—21no—
758C22—21no—
759C22—21no—
760C22—21no—
761C22—21no—
762C22—21no—
763C22—44no—
764C22—432no—
765C22—432no—
766C22—432no—
767C22—432no—
768C22—432no—
769C22—868no—
770C22—868no—
771C22—861no—
772C22—861no—
773C22—861no—
774C22—861no—
775C22—861no—
776C22—861no—
777C22—861no—
778C22—1724no—
779C22—1724no—
780C22—1724no—
781C22—1724no—
782C22#104×D4312yes—
783C22C2×C22⋊C4×D4311yescharacteristic
784C22#137×D4312yes—
785C4—21no—
786C4—21no—
787C4—21no—
788C4—44no—
789C4—42no—
790C4—42no—
791C4—432no—
792C4—861no—
793C4—861no—
794C4—861no—
795C4—1724no—
796C4—1722no—
797C4—1722no—
798C4#99×D4312yes—
799C2—22no—
800C2—22no—
801C2—41no—
802C2—434no—
803C2—862no—
804C2—862no—
805C2—1721no—
806C2C2×#99×D4311yescharacteristic
807C2#419×D4311yescharacteristic
808C2C2×#104×D4311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1508C2
socleC22×C43C22×C22⋊C4
prime radicalC24×D43D4
cosocleC22×C4×C43C24
hypercenter#1508D43
hypocenterC43C2×#1508
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1508

Complements

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

NH ≅ G/Ntype
4. #19133116C2semidirect
5. #19133115C2semidirect
6. #19133114C2semidirect
7. #19133113C2semidirect
8. #328×D43C2semidirect
9. C43×#1508C2semidirect
10. C22×Q8×D43C4semidirect
13. C2×#13063305C4semidirect
17. C2×#13063301C4semidirect
22. C22⋊Q8×D43C4semidirect
23. C22⋊Q8×D43C4semidirect
27. 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
99. C2×C4⋊Dic43C2×C4semidirect
110. C4⋊C4×D43C2×C4semidirect
130. C22×Q8×C43C2×C4semidirect
135. C22⋊Q8×C43C2×C4semidirect
138. C2×C4⋊C4×C43C2×C4semidirect
402. #1508D43direct (N × H)
413. D43#1508direct (N × H)
452. #328C2×D43semidirect
453. C43C2×#1508semidirect
462. C22×Q8C4×D43semidirect
508. C22⋊Q8C4×D43semidirect
524. 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
#407×D432
C4×C22⋊C4×D432
#191331162
#191331152
#191331142
#191331132
#328×D432
C43×#15082
C2×#150843