Finite Group Databasebeta

← D43×#1511 #25063830

Subgroups — D43×#1511 #25063830

Order 11008.

1446 conjugacy classes of subgroups.

The subgroup lattice has 802 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
3#381×D43C211yesmaximal, characteristic
4#19133129C211yesmaximal, characteristic, complemented
5#19133128C211yesmaximal, characteristic, complemented
6#19133127C211yesmaximal, characteristic, complemented
7#19133126C214yesmaximal, complemented
8#328×D43C214yesmaximal, complemented
9C43×#1511C211yesmaximal, 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—
30#14582863C2211yescharacteristic
31#14582862—21no—
32#14582861—21no—
33#14582861C2212yes—
34C22⋊C8×D43—21no—
35C22⋊C8×D43C2212yes—
36#14582762C2211yescharacteristic
37#14582761—21no—
38#14582761C2212yes—
39#14582760—21no—
40#95×D43—21no—
41#95×D43C2212yes—
42#14582637C2214yescomplemented
43#14582636C2214yescomplemented
44#14582635C2214yescomplemented
45C2×C22⋊Q8×C43C2211yescharacteristic
46C43×#407C2211yescharacteristic
47C43×#381C2211yescharacteristic
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—22no—
117C22⋊C4×D43—22no—
118C22⋊C4×D43—22no—
119C22⋊C4×D43—22no—
120C22⋊C4×D43—44no—
121C22⋊(C43⋊C8)—21no—
122C22⋊(C43⋊C8)C2312yes—
123(C2×D43)⋊C8—22no—
124(C2×D43)⋊C8—22no—
125C43⋊#95—21no—
126C43⋊#95—22no—
127C43⋊#95—22no—
128C43⋊#95C2312yes—
129C22×Q8×C43C2×C411yescharacteristic, complemented
130C23×C4×C43C2311yescharacteristic
131C2×M16×C43—21no—
132C22⋊Q8×C43—21no—
133C22⋊Q8×C43—21no—
134C22⋊Q8×C43C2×C412yescomplemented
135C22⋊Q8×C43C2312yes—
136C2×C4⋊C4×C43—21no—
137C2×C4⋊C4×C43C2×C411yescharacteristic, complemented
138C2×C22⋊C4×C43—21no—
139C2×C22⋊C4×C43—21no—
140C22⋊C8×C43—21no—
141C22⋊C8×C43C2312yes—
142#95×C43—21no—
143#95×C43C2312yes—
144C24×C43C2×D411yescharacteristic
145C23×D43—24no—
146C23×D43—24no—
147C23×D43—42no—
148C23×D43C22⋊C411yescharacteristic
149C23×D43C22⋊C411yescharacteristic
150C23×D43C22⋊C411yescharacteristic
151C23×D43C22⋊C411yescharacteristic
152C23×D43C2×D411yescharacteristic
153C23×D43C2×D411yescharacteristic
154C2×Q8×C43—21no—
155C2×Q8×C43—42no—
156C2×Q8×C43C22×C412yes—
157C22×C4×C43—21no—
158C22×C4×C43—21no—
159C22×C4×C43—22no—
160C22×C4×C43—42no—
161C22×C4×C43C22×C411yescharacteristic
162C22×C4×C43C22×C411yescharacteristic
163C22×C4×C43C2×D411yescharacteristic
164C22×C4×C43C2×D411yescharacteristic
165C22×C4×C43C2×D411yescharacteristic
166C22×C4×C43C2411yescharacteristic
167C22×Dic43—21no—
168C22×Dic43—21no—
169C22×Dic43—22no—
170C22×Dic43—42no—
171C22×Dic43C22⋊C411yescharacteristic
172C22×Dic43C22⋊C411yescharacteristic
173C22×Dic43C22⋊C411yescharacteristic
174C22×Dic43C22⋊C411yescharacteristic
175C22×Dic43C2×D411yescharacteristic
176C22×Dic43C2×D411yescharacteristic
177Q8×D43—44no—
178Q8×D43—44no—
179Q8×D43—44no—
180Q8×D43—44no—
181C2×C4×D43—24no—
182C2×C4×D43—24no—
183C2×C4×D43—22no—
184C2×C4×D43—22no—
185C2×C4×D43—22no—
186C2×C4×D43—22no—
187C2×C4×D43—42no—
188C2×C4×D43—42no—
189C2×C4×D43—42no—
190C2×C4×D43—42no—
191C2×C4×D43—42no—
192C2×C4×D43—42no—
193C2×C4×D43—42no—
194C2×C4×D43—42no—
195C2×C4×D43—42no—
196C2×C4×D43—42no—
197C2×C4×D43—44no—
198C2×C4×D43—44no—
199C2×C4×D43—44no—
200C2×C4×D43—44no—
201C2×C4×D43—44no—
202C2×C4×D43C22⋊C411yescharacteristic
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×D43C2×D411yescharacteristic
215C2×C4×D43C2×D411yescharacteristic
216C2×C4×D43C2×D411yescharacteristic
217C2×C4×D43C2×D411yescharacteristic
218C2×Dic86—21no—
219C2×Dic86—22no—
220C2×Dic86—22no—
221C2×Dic86—44no—
222C2×Dic86—42no—
223C2×Dic86C22×C412yes—
224M16×C43—42no—
225C2×C8×C43—22no—
226C4⋊C4×C43—22no—
227C4⋊C4×C43—21no—
228C4⋊C4×C43—22no—
229C4⋊C4×C43C22×C412yes—
230C22⋊C4×C43—22no—
231C22⋊C4×C43—22no—
232C22⋊C4×C43—42no—
233C22⋊Dic43—22no—
234C22⋊Dic43—22no—
235C22⋊Dic43—42no—
236(C2×D43)⋊C4—22no—
237(C2×D43)⋊C4—22no—
238(C2×D43)⋊C4—22no—
239(C2×D43)⋊C4—22no—
240(C2×D43)⋊C4—44no—
241C4⋊Dic43—21no—
242C4⋊Dic43—22no—
243C4⋊Dic43—22no—
244C4⋊Dic43C22×C412yes—
245Dic43⋊C4—22no—
246Dic43⋊C4—22no—
247Dic43⋊C4—22no—
248Dic43⋊C4—22no—
249Dic43⋊C4—22no—
250Dic43⋊C4—22no—
251#10621877—42no—
252C2×C43⋊C8—22no—
253#10621872—44no—
254C8×D43—44no—
255C23×C43—22no—
256C23×C43—22no—
257C23×C43—41no—
258C23×C43C2×C22⋊C411yescharacteristic
259C23×C43C2×C22⋊C411yescharacteristic
260C23×C43C22×D411yescharacteristic
261C22×D43—22no—
262C22×D43—22no—
263C22×D43—22no—
264C22×D43—22no—
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—41no—
275C22×D43—41no—
276C22×D43—41no—
277C22×D43—416no—
278C22×D43#9914yes—
279C22×D43C2×C22⋊C411yescharacteristic
280C22×D43C2×C22⋊C411yescharacteristic
281C22×D43C2×C22⋊C411yescharacteristic
282C22×D43C2×C22⋊C411yescharacteristic
283C22×D43#13714yes—
284Q8×C43—42no—
285Q8×C43—42no—
286C2×C4×C43—22no—
287C2×C4×C43—22no—
288C2×C4×C43—22no—
289C2×C4×C43—22no—
290C2×C4×C43—41no—
291C2×C4×C43—41no—
292C2×C4×C43—41no—
293C2×C4×C43—41no—
294C2×C4×C43—42no—
295C2×C4×C43—42no—
296C2×C4×C43—42no—
297C2×C4×C43—42no—
298C2×C4×C43—42no—
299C2×C4×C43C2×C22⋊C411yescharacteristic
300C2×C4×C43C2×C22⋊C411yescharacteristic
301C2×C4×C43C23×C411yescharacteristic
302C2×C4×C43C22×D411yescharacteristic
303C2×Dic43—22no—
304C2×Dic43—22no—
305C2×Dic43—22no—
306C2×Dic43—22no—
307C2×Dic43—41no—
308C2×Dic43—41no—
309C2×Dic43—41no—
310C2×Dic43—41no—
311C2×Dic43—42no—
312C2×Dic43—42no—
313C2×Dic43—42no—
314C2×Dic43—42no—
315C2×Dic43—42no—
316C2×Dic43C2×C22⋊C411yescharacteristic
317C2×Dic43C2×C22⋊C411yescharacteristic
318C2×Dic43C2×C22⋊C411yescharacteristic
319C2×Dic43C2×C22⋊C411yescharacteristic
320C4×D43—22no—
321C4×D43—22no—
322C4×D43—22no—
323C4×D43—22no—
324C4×D43—22no—
325C4×D43—22no—
326C4×D43—22no—
327C4×D43—22no—
328C4×D43—41no—
329C4×D43—41no—
330C4×D43—41no—
331C4×D43—41no—
332C4×D43—41no—
333C4×D43—41no—
334C4×D43—41no—
335C4×D43—41no—
336C4×D43—44no—
337C4×D43—44no—
338C4×D43—44no—
339C4×D43—44no—
340C4×D43—88no—
341Dic86—44no—
342Dic86—44no—
343Dic86—42no—
344Dic86—42no—
345C8×C43—42no—
346C43⋊C8—42no—
347C2×#1511—431nomaximal, Sylow
348C22×C43—21no—
349C22×C43—21no—
350C22×C43—21no—
351C22×C43—21no—
352C22×C43—21no—
353C22×C43—21no—
354C22×C43—21no—
355C22×C43—44no—
356C22×C43C2×#9912yes—
357C22×C43C22×C22⋊C411yescharacteristic
358C22×C43C2×#13712yes—
359C2×D43—21no—
360C2×D43—21no—
361C2×D43—21no—
362C2×D43—21no—
363C2×D43—28no—
364C2×D43—28no—
365C2×D43—21no—
366C2×D43—21no—
367C2×D43—21no—
368C2×D43—44no—
369C2×D43—44no—
370C2×D43—44no—
371C2×D43—44no—
372C2×D43C2×#9912yes—
373C2×D43C2×#9912yes—
374C2×D43#41912yes—
375C2×D43#41912yes—
376C2×D43#42112yes—
377C4×C43—21no—
378C4×C43—21no—
379C4×C43—21no—
380C4×C43—21no—
381C4×C43—42no—
382C4×C43—42no—
383C4×C43—82no—
384Dic43—21no—
385Dic43—21no—
386Dic43—21no—
387Dic43—21no—
388Dic43—42no—
389Dic43—42no—
390Dic43—82no—
391C22×C22⋊Q8—431no—
392C2×#407—431no—
393C2×#381—431no—
394#1511—431no—
395#1511—431no—
396#1511—434no—
397#1511—431no—
398#1511D4311yescharacteristic, direct product factor
399C2×#328—434no—
400C2×C43—22no—
401C2×C43—22no—
402C2×C43—41no—
403C2×C43C22×#9911yescharacteristic
404C2×C43C2×#41911yescharacteristic
405C2×C43C2×#42111yescharacteristic
406D43—22no—
407D43—22no—
408D43—41no—
409D43#151114yesdirect product factor
410C23×Q8—431no—
411C24×C4—431no—
412C22×M16—861no—
413C2×C22⋊Q8—431no—
414C2×C22⋊Q8—431no—
415C2×C22⋊Q8—432no—
416C2×C22⋊Q8—432no—
417C2×C22⋊Q8—432no—
418C2×C22⋊Q8—432no—
419C2×C22⋊Q8—431no—
420C2×C22⋊Q8—861no—
421C2×C22⋊Q8—861no—
422C2×C22⋊Q8—861no—
423C2×C22⋊Q8—861no—
424C2×C22⋊Q8—861no—
425C2×C22⋊Q8—861no—
426C2×C22⋊Q8C2×D4311yescharacteristic
427C22×C4⋊C4—431no—
428C22×C4⋊C4—861no—
429C22×C22⋊C4—861no—
430C22×C22⋊C4—861no—
431#407—431no—
432#407—432no—
433#407—861no—
434#407—861no—
435#407C2×D4311yescharacteristic
436C2×C22⋊C8—432no—
437C2×C22⋊C8—861no—
438#381—431no—
439#381—432no—
440#381—861no—
441#381—861no—
442#381C2×D4311yescharacteristic
443C2×#95—432no—
444C2×#95—861no—
445#328—434no—
446#328—434no—
447#328—434no—
448#328C2×D4314yescomplemented
449C43C2×#151111yescharacteristic, complemented, Sylow
450C25—431no—
451C22×Q8—432no—
452C22×Q8—432no—
453C22×Q8—431no—
454C22×Q8—861no—
455C22×Q8—861no—
456C22×Q8—861no—
457C22×Q8—1724no—
458C22×Q8C4×D4311yescharacteristic, complemented
459C23×C4—431no—
460C23×C4—431no—
461C23×C4—431no—
462C23×C4—431no—
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—861no—
473C23×C4—861no—
474C23×C4—862no—
475C23×C4—1724no—
476C23×C4C22×D4311yescharacteristic
477C2×M16—21no—
478C2×M16—862no—
479C2×M16—861no—
480C2×M16—1724no—
481C22×C8—862no—
482C22⋊Q8—21no—
483C22⋊Q8—21no—
484C22⋊Q8—432no—
485C22⋊Q8—432no—
486C22⋊Q8—432no—
487C22⋊Q8—432no—
488C22⋊Q8—432no—
489C22⋊Q8—432no—
490C22⋊Q8—862no—
491C22⋊Q8—862no—
492C22⋊Q8—862no—
493C22⋊Q8—862no—
494C22⋊Q8—862no—
495C22⋊Q8—862no—
496C22⋊Q8—862no—
497C22⋊Q8—862no—
498C22⋊Q8—861no—
499C22⋊Q8—861no—
500C22⋊Q8—861no—
501C22⋊Q8—861no—
502C22⋊Q8—861no—
503C22⋊Q8—861no—
504C22⋊Q8C4×D4312yescomplemented
505C22⋊Q8C22×D4312yes—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—431no—
508C2×C4⋊C4—432no—
509C2×C4⋊C4—432no—
510C2×C4⋊C4—861no—
511C2×C4⋊C4—861no—
512C2×C4⋊C4—862no—
513C2×C4⋊C4—862no—
514C2×C4⋊C4—862no—
515C2×C4⋊C4—862no—
516C2×C4⋊C4—861no—
517C2×C4⋊C4—861no—
518C2×C4⋊C4—861no—
519C2×C4⋊C4—861no—
520C2×C4⋊C4C4×D4311yescharacteristic, complemented
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—862no—
524C2×C22⋊C4—862no—
525C2×C22⋊C4—862no—
526C2×C22⋊C4—862no—
527C2×C22⋊C4—861no—
528C2×C22⋊C4—861no—
529C2×C22⋊C4—861no—
530C2×C22⋊C4—862no—
531C2×C22⋊C4—861no—
532C2×C22⋊C4—1724no—
533C22⋊C8—21no—
534C22⋊C8—432no—
535C22⋊C8—862no—
536C22⋊C8—862no—
537C22⋊C8—861no—
538C22⋊C8C22×D4312yes—
539#95—21no—
540#95—432no—
541#95—862no—
542#95—862no—
543#95—861no—
544#95C22×D4312yes—
545C24—431no—
546C24—431no—
547C24—431no—
548C24—431no—
549C24—431no—
550C24—431no—
551C24—864no—
552C24—864no—
553C24—1722no—
554C24D4×D4311yescharacteristic
555C2×Q8—21no—
556C2×Q8—42no—
557C2×Q8—432no—
558C2×Q8—862no—
559C2×Q8—862no—
560C2×Q8—861no—
561C2×Q8—1722no—
562C2×Q8—1724no—
563C2×Q8—1724no—
564C2×Q8—1724no—
565C2×Q8—1724no—
566C2×Q8—1724no—
567C2×Q8C2×C4×D4312yes—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—22no—
571C22×C4—42no—
572C22×C4—431no—
573C22×C4—431no—
574C22×C4—431no—
575C22×C4—431no—
576C22×C4—431no—
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—864no—
595C22×C4—864no—
596C22×C4—862no—
597C22×C4—862no—
598C22×C4—862no—
599C22×C4—862no—
600C22×C4—861no—
601C22×C4—861no—
602C22×C4—862no—
603C22×C4—1722no—
604C22×C4—1722no—
605C22×C4—1722no—
606C22×C4—1722no—
607C22×C4—1722no—
608C22×C4—1722no—
609C22×C4—1722no—
610C22×C4—1722no—
611C22×C4—1722no—
612C22×C4—1722no—
613C22×C4—1724no—
614C22×C4—1724no—
615C22×C4—1724no—
616C22×C4—1724no—
617C22×C4—1724no—
618C22×C4—1722no—
619C22×C4C2×C4×D4311yescharacteristic
620C22×C4C2×C4×D4311yescharacteristic
621C22×C4D4×D4311yescharacteristic
622C22×C4D4×D4311yescharacteristic
623C22×C4D4×D4311yescharacteristic
624C22×C4C23×D4311yescharacteristic
625M16—42no—
626M16—1724no—
627M16—1722no—
628C2×C8—22no—
629C2×C8—862no—
630C2×C8—1724no—
631C4⋊C4—22no—
632C4⋊C4—21no—
633C4⋊C4—22no—
634C4⋊C4—432no—
635C4⋊C4—862no—
636C4⋊C4—862no—
637C4⋊C4—862no—
638C4⋊C4—862no—
639C4⋊C4—862no—
640C4⋊C4—862no—
641C4⋊C4—861no—
642C4⋊C4—862no—
643C4⋊C4—862no—
644C4⋊C4C2×C4×D4312yes—
645C22⋊C4—22no—
646C22⋊C4—22no—
647C22⋊C4—42no—
648C22⋊C4—862no—
649C22⋊C4—862no—
650C22⋊C4—862no—
651C22⋊C4—862no—
652C22⋊C4—862no—
653C22⋊C4—862no—
654C22⋊C4—1724no—
655C22⋊C4—1722no—
656C23—22no—
657C23—22no—
658C23—41no—
659C23—431no—
660C23—431no—
661C23—431no—
662C23—434no—
663C23—434no—
664C23—431no—
665C23—862no—
666C23—862no—
667C23—862no—
668C23—862no—
669C23—862no—
670C23—862no—
671C23—862no—
672C23—862no—
673C23—862no—
674C23—862no—
675C23—862no—
676C23—862no—
677C23—862no—
678C23—1721no—
679C23—1721no—
680C23—1721no—
681C23—17216no—
682C23C22⋊C4×D4311yescharacteristic
683C23C22⋊C4×D4311yescharacteristic
684C23C2×D4×D4311yescharacteristic
685Q8—42no—
686Q8—42no—
687Q8—1722no—
688Q8—1722no—
689Q8—1724no—
690Q8—1724no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—431no—
705C2×C4—431no—
706C2×C4—431no—
707C2×C4—431no—
708C2×C4—862no—
709C2×C4—862no—
710C2×C4—862no—
711C2×C4—862no—
712C2×C4—862no—
713C2×C4—862no—
714C2×C4—862no—
715C2×C4—862no—
716C2×C4—862no—
717C2×C4—862no—
718C2×C4—862no—
719C2×C4—862no—
720C2×C4—3448no—
721C2×C4—1721no—
722C2×C4—1721no—
723C2×C4—1721no—
724C2×C4—1721no—
725C2×C4—1721no—
726C2×C4—1721no—
727C2×C4—1721no—
728C2×C4—1721no—
729C2×C4—1724no—
730C2×C4—1724no—
731C2×C4—1724no—
732C2×C4—1724no—
733C2×C4—1721no—
734C2×C4—1721no—
735C2×C4—1721no—
736C2×C4—1721no—
737C2×C4—1722no—
738C2×C4—1722no—
739C2×C4—1722no—
740C2×C4—1722no—
741C2×C4—1722no—
742C2×C4C22⋊C4×D4311yescharacteristic
743C2×C4C22⋊C4×D4311yescharacteristic
744C2×C4C22×C4×D4311yescharacteristic
745C2×C4C2×D4×D4311yescharacteristic
746C8—42no—
747C8—1722no—
748C22—21no—
749C22—21no—
750C22—21no—
751C22—21no—
752C22—21no—
753C22—21no—
754C22—21no—
755C22—44no—
756C22—432no—
757C22—432no—
758C22—432no—
759C22—432no—
760C22—432no—
761C22—868no—
762C22—868no—
763C22—861no—
764C22—861no—
765C22—861no—
766C22—861no—
767C22—861no—
768C22—861no—
769C22—861no—
770C22—1724no—
771C22—1724no—
772C22—1724no—
773C22—1724no—
774C22#99×D4312yes—
775C22C2×C22⋊C4×D4311yescharacteristic
776C22#137×D4312yes—
777C4—21no—
778C4—21no—
779C4—21no—
780C4—21no—
781C4—42no—
782C4—42no—
783C4—82no—
784C4—861no—
785C4—861no—
786C4—861no—
787C4—861no—
788C4—3442no—
789C4—1722no—
790C4—1722no—
791C2—22no—
792C2—22no—
793C2—41no—
794C2—434no—
795C2—862no—
796C2—862no—
797C2—1721no—
798C2C2×#99×D4311yescharacteristic
799C2#419×D4311yescharacteristic
800C2#421×D4311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1511C2
socleC22×C43C22×C22⋊C4
prime radicalC24×D43D4
cosocleC22×C4×C43C24
hypercenter#1511D43
hypocenterC43C2×#1511
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1511

Complements

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

NH ≅ G/Ntype
4. #19133129C2semidirect
5. #19133128C2semidirect
6. #19133127C2semidirect
7. #19133126C2semidirect
8. #328×D43C2semidirect
9. C43×#1511C2semidirect
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
129. C22×Q8×C43C2×C4semidirect
134. C22⋊Q8×C43C2×C4semidirect
137. C2×C4⋊C4×C43C2×C4semidirect
398. #1511D43direct (N × H)
409. D43#1511direct (N × H)
448. #328C2×D43semidirect
449. C43C2×#1511semidirect
458. C22×Q8C4×D43semidirect
504. C22⋊Q8C4×D43semidirect
520. 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
#381×D432
#191331292
#191331282
#191331272
#191331262
#328×D432
C43×#15112
C2×#151143