Finite Group Databasebeta

← D43×#1436 #25017718

Subgroups — D43×#1436 #25017718

Order 11008.

3550 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊C4×D43C211yesmaximal, characteristic
2C22×C42×D43C211yesmaximal, characteristic
3C2×#95×D43C212yesmaximal
4C2×#95×D43C211yesmaximal, characteristic
5C2×#95×D43C212yesmaximal
6#19132830C211yesmaximal, characteristic, complemented
7#19132829C212yesmaximal, complemented
8#19132828C211yesmaximal, characteristic, complemented
9#19132827C211yesmaximal, characteristic, complemented
10#19132826C212yesmaximal, complemented
11C43×#1436C211yesmaximal, characteristic, complemented
12C23×C4×D43C2212yes—
13C23×C4×D43C2211yescharacteristic
14C23×C4×D43C2211yescharacteristic
15C23×C4×D43C2211yescharacteristic
16C23×C4×D43C2212yes—
17C22×C4⋊Dic43C2211yescharacteristic
18C22×Dic43⋊C4C2211yescharacteristic
19C22×Dic43⋊C4C2211yescharacteristic
20C2×C4⋊C4×D43—24no—
21C2×C4⋊C4×D43—24no—
22C2×C4⋊C4×D43C418yescomplemented
23C22×C4×Dic43C2212yes—
24C22×C4×Dic43C2211yescharacteristic
25C2×C42×D43—24no—
26C2×C42×D43—28no—
27C2×C43⋊#95C2212yes—
28C2×C43⋊#95C2212yes—
29C2×C43⋊#95C2211yescharacteristic
30C2×C43⋊#95C2212yes—
31C2×C43⋊#95C2212yes—
32C2×C43⋊#95C2212yes—
33C2×C43⋊#95C2212yes—
34C2×C43⋊#95C2212yes—
35#95×D43—24no—
36#95×D43—28no—
37#95×D43C4116yescomplemented
38C22×C4⋊C4×C43C2211yescharacteristic
39C22×C42×C43C2211yescharacteristic
40C2×#95×C43C2212yes—
41C2×#95×C43C2211yescharacteristic
42C2×#95×C43C2212yes—
43C24×D43C2311yescharacteristic
44C23×Dic43C2311yescharacteristic
45C23×Dic43C2312yes—
46C23×Dic43C2311yescharacteristic
47C23×Dic43C2311yescharacteristic
48C23×Dic43C2312yes—
49C22×C4×D43—24no—
50C22×C4×D43—24no—
51C22×C4×D43—24no—
52C22×C4×D43—22no—
53C22×C4×D43—22no—
54C22×C4×D43—24no—
55C22×C4×D43—24no—
56C22×C4×D43—24no—
57C22×C4×D43—24no—
58C22×C4×D43—22no—
59C22×C4×D43—22no—
60C22×C4×D43—24no—
61C22×C4×D43—24no—
62C22×C4×D43—24no—
63C22×C4×D43—24no—
64C22×C4×D43—24no—
65C22×C4×D43—24no—
66C22×C4×D43—24no—
67C22×C4×D43—24no—
68C22×C4×D43C2×C414yes—
69C22×C4×D43C2×C418yes—
70C22×C4×D43C2×C414yes—
71C22×C4×D43C2×C418yes—
72C22×C4×D43C2×C414yes—
73C22×C4×D43C2×C418yes—
74C22×C4×D43D414yes—
75C22×C4×D43D414yes—
76C22×C4×D43D418yes—
77C22×C4×D43Q818yes—
78C2×C4⋊Dic43—22no—
79C2×C4⋊Dic43—22no—
80C2×C4⋊Dic43C2×C414yescomplemented
81C2×Dic43⋊C4—22no—
82C2×Dic43⋊C4—22no—
83C2×Dic43⋊C4—22no—
84C2×Dic43⋊C4—22no—
85C2×Dic43⋊C4C2×C414yescomplemented
86C2×Dic43⋊C4C2×C414yescomplemented
87C4⋊C4×D43—232no—
88C2×C4×Dic43—22no—
89C2×C4×Dic43—24no—
90C2×C4×Dic43—24no—
91C2×C4×Dic43—24no—
92C2×C4×Dic43—24no—
93C42×D43—232no—
94C43⋊#95—22no—
95C43⋊#95—24no—
96C43⋊#95—24no—
97C43⋊#95—24no—
98C43⋊#95—24no—
99C43⋊#95C2×C418yescomplemented
100C43⋊#95C2×C418yescomplemented
101C43⋊#95C2×C418yescomplemented
102C23×C4×C43C2311yescharacteristic
103C23×C4×C43C2312yes—
104C23×C4×C43C2311yescharacteristic
105C23×C4×C43C2311yescharacteristic
106C23×C4×C43C2312yes—
107C2×C4⋊C4×C43—22no—
108C2×C4⋊C4×C43—22no—
109C2×C4⋊C4×C43C2×C414yescomplemented
110C2×C42×C43—22no—
111C2×C42×C43—24no—
112#95×C43—22no—
113#95×C43—24no—
114#95×C43C2×C418yescomplemented
115C24×C43C2411yescharacteristic
116C23×D43C22×C412yes—
117C23×D43C22×C414yes—
118C23×D43C2×D412yes—
119C23×D43C2×D412yes—
120C23×D43C2×D414yes—
121C23×D43C2×Q814yes—
122C23×D43#4114yes—
123C23×D43#4114yes—
124C23×D43#4114yes—
125C22×C4×C43—22no—
126C22×C4×C43—22no—
127C22×C4×C43—22no—
128C22×C4×C43—21no—
129C22×C4×C43—21no—
130C22×C4×C43—22no—
131C22×C4×C43—22no—
132C22×C4×C43—22no—
133C22×C4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43—22no—
136C22×C4×C43—22no—
137C22×C4×C43—22no—
138C22×C4×C43—22no—
139C22×C4×C43—22no—
140C22×C4×C43—22no—
141C22×C4×C43—22no—
142C22×C4×C43—22no—
143C22×C4×C43—22no—
144C22×C4×C43C22×C414yes—
145C22×C4×C43C22×C412yes—
146C22×C4×C43C22×C414yes—
147C22×C4×C43C22×C412yes—
148C22×C4×C43C22×C412yes—
149C22×C4×C43C22×C414yes—
150C22×C4×C43C2×D412yes—
151C22×C4×C43C2×D412yes—
152C22×C4×C43C2×D414yes—
153C22×C4×C43C2×Q814yes—
154C22×Dic43—22no—
155C22×Dic43—22no—
156C22×Dic43—22no—
157C22×Dic43—21no—
158C22×Dic43—21no—
159C22×Dic43—22no—
160C22×Dic43—22no—
161C22×Dic43—22no—
162C22×Dic43—21no—
163C22×Dic43—21no—
164C22×Dic43—22no—
165C22×Dic43—22no—
166C22×Dic43—22no—
167C22×Dic43—22no—
168C22×Dic43—22no—
169C22×Dic43—22no—
170C22×Dic43—22no—
171C22×Dic43—22no—
172C22×Dic43—22no—
173C22×Dic43C22×C414yes—
174C22×Dic43C22×C412yes—
175C22×Dic43C22×C414yes—
176C22×Dic43C22×C412yes—
177C22×Dic43C22×C412yes—
178C22×Dic43C22×C414yes—
179C22×Dic43C2×D412yes—
180C22×Dic43C2×D412yes—
181C22×Dic43C2×D414yes—
182C22×Dic43C2×Q814yes—
183C2×C4×D43—28no—
184C2×C4×D43—28no—
185C2×C4×D43—28no—
186C2×C4×D43—216no—
187C2×C4×D43—216no—
188C2×C4×D43—216no—
189C2×C4×D43—216no—
190C2×C4×D43—216no—
191C2×C4×D43—216no—
192C2×C4×D43—216no—
193C2×C4×D43—216no—
194C2×C4×D43—216no—
195C2×C4×D43—216no—
196C2×C4×D43—28no—
197C2×C4×D43—216no—
198C2×C4×D43—216no—
199C2×C4×D43—216no—
200C2×C4×D43—216no—
201C2×C4×D43—28no—
202C2×C4×D43—44no—
203C2×C4×D43—48no—
204C2×C4×D43—48no—
205C2×C4×D43—48no—
206C2×C4×D43—44no—
207C2×C4×D43—48no—
208C2×C4×D43—48no—
209C2×C4×D43C42116yescomplemented
210C2×C4×D43C22⋊C4116yes—
211C2×C4×D43C4⋊C4132yescomplemented
212C4⋊C4×C43—28no—
213C42×C43—28no—
214C4⋊Dic43—28no—
215Dic43⋊C4—28no—
216Dic43⋊C4—28no—
217C4×Dic43—28no—
218C4×Dic43—216no—
219C23×C43C23×C411yescharacteristic
220C23×C43C23×C412yes—
221C23×C43C22×D411yescharacteristic
222C23×C43C22×D411yescharacteristic
223C23×C43C22×D412yes—
224C23×C43C22×Q812yes—
225C23×C43C2×#4112yes—
226C23×C43C2×#4112yes—
227C23×C43C2×#4112yes—
228C22×D43C2×C4214yes—
229C22×D43C2×C22⋊C414yes—
230C22×D43C2×C4⋊C418yes—
231C22×D43#11714yes—
232C22×D43#11718yes—
233C22×D43C4×D418yes—
234C22×D43C4×D418yes—
235C22×D43C4×D418yes—
236C22×D43C4×D418yes—
237C22×D43C4×Q818yes—
238C22×D43C4×Q818yes—
239C22×D43#12014yes—
240C22×D43#12118yes—
241C22×D43C22⋊Q818yes—
242C22×D43C22⋊Q818yes—
243C22×D43#12318yes—
244C22×D43#12314yes—
245C22×D43#12414yes—
246C22×D43#12518yes—
247C22×D43#12618yes—
248C22×D43C4⋊Q814yes—
249C2×C4×C43—22no—
250C2×C4×C43—22no—
251C2×C4×C43—24no—
252C2×C4×C43—24no—
253C2×C4×C43—24no—
254C2×C4×C43—24no—
255C2×C4×C43—24no—
256C2×C4×C43—24no—
257C2×C4×C43—22no—
258C2×C4×C43—24no—
259C2×C4×C43—24no—
260C2×C4×C43—24no—
261C2×C4×C43—24no—
262C2×C4×C43—22no—
263C2×C4×C43—22no—
264C2×C4×C43—24no—
265C2×C4×C43—24no—
266C2×C4×C43—24no—
267C2×C4×C43—24no—
268C2×C4×C43—41no—
269C2×C4×C43—42no—
270C2×C4×C43—42no—
271C2×C4×C43—41no—
272C2×C4×C43—42no—
273C2×C4×C43—42no—
274C2×C4×C43—42no—
275C2×C4×C43C2×C4214yescomplemented
276C2×C4×C43C2×C22⋊C414yes—
277C2×C4×C43C2×C4⋊C418yescomplemented
278C2×Dic43—22no—
279C2×Dic43—22no—
280C2×Dic43—24no—
281C2×Dic43—24no—
282C2×Dic43—24no—
283C2×Dic43—24no—
284C2×Dic43—24no—
285C2×Dic43—24no—
286C2×Dic43—22no—
287C2×Dic43—24no—
288C2×Dic43—24no—
289C2×Dic43—24no—
290C2×Dic43—24no—
291C2×Dic43—22no—
292C2×Dic43—22no—
293C2×Dic43—24no—
294C2×Dic43—24no—
295C2×Dic43—24no—
296C2×Dic43—24no—
297C2×Dic43—41no—
298C2×Dic43—42no—
299C2×Dic43—42no—
300C2×Dic43—41no—
301C2×Dic43—42no—
302C2×Dic43—42no—
303C2×Dic43—42no—
304C2×Dic43C2×C4214yescomplemented
305C2×Dic43C2×C22⋊C414yes—
306C2×Dic43C2×C4⋊C418yescomplemented
307C4×D43—232no—
308C4×D43—264no—
309C4×D43—232no—
310C4×D43—416no—
311C4×D43—432no—
312C2×#1436—431nomaximal, Sylow
313C22×C43C22×C4211yescharacteristic
314C22×C43C22×C22⋊C411yescharacteristic
315C22×C43C22×C4⋊C412yes—
316C22×C43C2×#11711yescharacteristic
317C22×C43C2×#11712yes—
318C22×C43C2×C4×D412yes—
319C22×C43C2×C4×D412yes—
320C22×C43C2×C4×D412yes—
321C22×C43C2×C4×D412yes—
322C22×C43C2×C4×Q812yes—
323C22×C43C2×C4×Q812yes—
324C22×C43C2×#12011yescharacteristic
325C22×C43C2×#12112yes—
326C22×C43C2×C22⋊Q812yes—
327C22×C43C2×C22⋊Q812yes—
328C22×C43C2×#12312yes—
329C22×C43C2×#12311yescharacteristic
330C22×C43C2×#12411yescharacteristic
331C22×C43C2×#12512yes—
332C22×C43C2×#12612yes—
333C22×C43C2×C4⋊Q811yescharacteristic
334C2×D43C4×C22⋊C418yes—
335C2×D43C4×C4⋊C4116yes—
336C2×D43#385116yes—
337C2×D43#38618yes—
338C2×D43#387116yes—
339C2×D43#387116yes—
340C2×D43#388116yes—
341C2×D43#389116yes—
342C2×D43#39118yes—
343C4×C43—24no—
344C4×C43—28no—
345C4×C43—24no—
346C4×C43—42no—
347C4×C43—44no—
348Dic43—24no—
349Dic43—28no—
350Dic43—24no—
351Dic43—42no—
352Dic43—44no—
353C23×C4⋊C4—431no—
354C23×C42—431no—
355C22×#95—432no—
356C22×#95—431no—
357C22×#95—432no—
358#1436—431no—
359#1436—432no—
360#1436—432no—
361#1436—431no—
362#1436—431no—
363#1436D4311yescharacteristic, direct product factor
364C2×C43C2×C4×C22⋊C411yescharacteristic
365C2×C43C2×C4×C4⋊C412yes—
366C2×C43C2×#38512yes—
367C2×C43C2×#38611yescharacteristic
368C2×C43C2×#38712yes—
369C2×C43C2×#38712yes—
370C2×C43C2×#38812yes—
371C2×C43C2×#38912yes—
372C2×C43C2×#39111yescharacteristic
373D43#1436116yesdirect product factor
374C24×C4—431no—
375C24×C4—432no—
376C24×C4—431no—
377C24×C4—431no—
378C24×C4—432no—
379C22×C4⋊C4—431no—
380C22×C4⋊C4—431no—
381C22×C4⋊C4—431no—
382C22×C4⋊C4—438no—
383C22×C4⋊C4—864no—
384C22×C4⋊C4—864no—
385C22×C4⋊C4C2×D4311yescharacteristic
386C22×C42—432no—
387C22×C42—431no—
388C22×C42—864no—
389C22×C42—868no—
390C22×C42C2×D4311yescharacteristic
391C2×#95—432no—
392C2×#95—432no—
393C2×#95—432no—
394C2×#95—4316no—
395C2×#95—432no—
396C2×#95—432no—
397C2×#95—432no—
398C2×#95—432no—
399C2×#95—431no—
400C2×#95—864no—
401C2×#95—868no—
402C2×#95C2×D4312yes—
403C2×#95C2×D4311yescharacteristic
404C2×#95C2×D4312yes—
405C43C2×#143611yescharacteristic, complemented, Sylow
406C25—431no—
407C23×C4—431no—
408C23×C4—431no—
409C23×C4—432no—
410C23×C4—434no—
411C23×C4—434no—
412C23×C4—438no—
413C23×C4—438no—
414C23×C4—434no—
415C23×C4—434no—
416C23×C4—438no—
417C23×C4—438no—
418C23×C4—431no—
419C23×C4—432no—
420C23×C4—434no—
421C23×C4—438no—
422C23×C4—862no—
423C23×C4—862no—
424C23×C4—864no—
425C23×C4—864no—
426C23×C4—864no—
427C23×C4—864no—
428C23×C4—864no—
429C23×C4—864no—
430C23×C4—864no—
431C23×C4—862no—
432C23×C4—862no—
433C23×C4—864no—
434C23×C4—864no—
435C23×C4—864no—
436C23×C4—864no—
437C23×C4—864no—
438C23×C4—864no—
439C23×C4—864no—
440C23×C4—864no—
441C23×C4C22×D4311yescharacteristic
442C23×C4C22×D4312yes—
443C23×C4C22×D4311yescharacteristic
444C23×C4C22×D4311yescharacteristic
445C23×C4C22×D4312yes—
446C2×C4⋊C4—22no—
447C2×C4⋊C4—22no—
448C2×C4⋊C4—434no—
449C2×C4⋊C4—434no—
450C2×C4⋊C4—434no—
451C2×C4⋊C4—8632no—
452C2×C4⋊C4—862no—
453C2×C4⋊C4—862no—
454C2×C4⋊C4—862no—
455C2×C4⋊C4—862no—
456C2×C4⋊C4—862no—
457C2×C4⋊C4—862no—
458C2×C4⋊C4C4×D4314yescomplemented
459C2×C42—22no—
460C2×C42—24no—
461C2×C42—8632no—
462C2×C42—864no—
463C2×C42—864no—
464C2×C42—864no—
465C2×C42—862no—
466C2×C42—864no—
467#95—22no—
468#95—24no—
469#95—438no—
470#95—438no—
471#95—438no—
472#95—864no—
473#95—864no—
474#95—864no—
475#95—862no—
476#95—864no—
477#95C4×D4318yescomplemented
478C24—432no—
479C24—434no—
480C24—432no—
481C24—432no—
482C24—434no—
483C24—434no—
484C24—434no—
485C24—434no—
486C24—434no—
487C24C23×D4311yescharacteristic
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—434no—
508C22×C4—434no—
509C22×C4—432no—
510C22×C4—432no—
511C22×C4—434no—
512C22×C4—432no—
513C22×C4—432no—
514C22×C4—434no—
515C22×C4—4316no—
516C22×C4—4316no—
517C22×C4—4332no—
518C22×C4—434no—
519C22×C4—432no—
520C22×C4—868no—
521C22×C4—8616no—
522C22×C4—868no—
523C22×C4—868no—
524C22×C4—8616no—
525C22×C4—8616no—
526C22×C4—8616no—
527C22×C4—8616no—
528C22×C4—8616no—
529C22×C4—8616no—
530C22×C4—8616no—
531C22×C4—8616no—
532C22×C4—868no—
533C22×C4—8616no—
534C22×C4—868no—
535C22×C4—8616no—
536C22×C4—8616no—
537C22×C4—8616no—
538C22×C4—8616no—
539C22×C4—862no—
540C22×C4—862no—
541C22×C4—862no—
542C22×C4—861no—
543C22×C4—861no—
544C22×C4—862no—
545C22×C4—862no—
546C22×C4—862no—
547C22×C4—862no—
548C22×C4—862no—
549C22×C4—862no—
550C22×C4—862no—
551C22×C4—861no—
552C22×C4—861no—
553C22×C4—862no—
554C22×C4—862no—
555C22×C4—862no—
556C22×C4—862no—
557C22×C4—862no—
558C22×C4—1724no—
559C22×C4—1728no—
560C22×C4—1728no—
561C22×C4—1724no—
562C22×C4—1728no—
563C22×C4—1728no—
564C22×C4—1728no—
565C22×C4C2×C4×D4314yes—
566C22×C4C2×C4×D4312yes—
567C22×C4C2×C4×D4314yes—
568C22×C4C2×C4×D4312yes—
569C22×C4C2×C4×D4312yes—
570C22×C4C2×C4×D4314yes—
571C22×C4D4×D4312yes—
572C22×C4D4×D4312yes—
573C22×C4D4×D4314yes—
574C22×C4Q8×D4314yes—
575C4⋊C4—28no—
576C4⋊C4—868no—
577C4⋊C4—868no—
578C4⋊C4—868no—
579C42—28no—
580C42—8616no—
581C42—868no—
582C23—434no—
583C23—434no—
584C23—438no—
585C23—434no—
586C23—438no—
587C23—438no—
588C23—438no—
589C23—438no—
590C23—438no—
591C23—438no—
592C23—438no—
593C23—434no—
594C23—438no—
595C23—438no—
596C23—438no—
597C23—438no—
598C23—434no—
599C23—434no—
600C23—438no—
601C23—438no—
602C23—434no—
603C23C22×C4×D4311yescharacteristic
604C23C22×C4×D4312yes—
605C23C2×D4×D4311yescharacteristic
606C23C2×D4×D4311yescharacteristic
607C23C2×D4×D4312yes—
608C23C2×Q8×D4312yes—
609C23#41×D4312yes—
610C23#41×D4312yes—
611C23#41×D4312yes—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—24no—
615C2×C4—24no—
616C2×C4—24no—
617C2×C4—24no—
618C2×C4—24no—
619C2×C4—24no—
620C2×C4—22no—
621C2×C4—24no—
622C2×C4—24no—
623C2×C4—24no—
624C2×C4—24no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—24no—
628C2×C4—24no—
629C2×C4—24no—
630C2×C4—24no—
631C2×C4—41no—
632C2×C4—42no—
633C2×C4—42no—
634C2×C4—41no—
635C2×C4—42no—
636C2×C4—42no—
637C2×C4—42no—
638C2×C4—434no—
639C2×C4—434no—
640C2×C4—438no—
641C2×C4—8632no—
642C2×C4—8664no—
643C2×C4—8632no—
644C2×C4—862no—
645C2×C4—862no—
646C2×C4—864no—
647C2×C4—864no—
648C2×C4—864no—
649C2×C4—864no—
650C2×C4—864no—
651C2×C4—864no—
652C2×C4—862no—
653C2×C4—864no—
654C2×C4—864no—
655C2×C4—864no—
656C2×C4—864no—
657C2×C4—862no—
658C2×C4—862no—
659C2×C4—864no—
660C2×C4—864no—
661C2×C4—864no—
662C2×C4—864no—
663C2×C4—17216no—
664C2×C4—17232no—
665C2×C4—1721no—
666C2×C4—1722no—
667C2×C4—1722no—
668C2×C4—1721no—
669C2×C4—1722no—
670C2×C4—1722no—
671C2×C4—1722no—
672C2×C4C42×D4314yescomplemented
673C2×C4C22⋊C4×D4314yes—
674C2×C4C4⋊C4×D4318yescomplemented
675C22—4316no—
676C22—438no—
677C22—438no—
678C22—4316no—
679C22—4316no—
680C22—438no—
681C22—4316no—
682C22—4316no—
683C22—4316no—
684C22C2×C42×D4311yescharacteristic
685C22C2×C22⋊C4×D4311yescharacteristic
686C22C2×C4⋊C4×D4312yes—
687C22#117×D4311yescharacteristic
688C22#117×D4312yes—
689C22C4×D4×D4312yes—
690C22C4×D4×D4312yes—
691C22C4×D4×D4312yes—
692C22C4×D4×D4312yes—
693C22C4×Q8×D4312yes—
694C22C4×Q8×D4312yes—
695C22#120×D4311yescharacteristic
696C22#121×D4312yes—
697C22C22⋊Q8×D4312yes—
698C22C22⋊Q8×D4312yes—
699C22#123×D4312yes—
700C22#123×D4311yescharacteristic
701C22#124×D4311yescharacteristic
702C22#125×D4312yes—
703C22#126×D4312yes—
704C22C4⋊Q8×D4311yescharacteristic
705C4—24no—
706C4—28no—
707C4—24no—
708C4—42no—
709C4—44no—
710C4—864no—
711C4—868no—
712C4—864no—
713C4—1722no—
714C4—1724no—
715C2—4316no—
716C2C4×C22⋊C4×D4311yescharacteristic
717C2C4×C4⋊C4×D4312yes—
718C2#385×D4312yes—
719C2#386×D4311yescharacteristic
720C2#387×D4312yes—
721C2#387×D4312yes—
722C2#388×D4312yes—
723C2#389×D4312yes—
724C2#391×D4311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC22×C43C22×C42
FittingC43×#1436C2
socle, cosocleC24×C43C24
prime radicalC24×D43C23
hypercenter#1436D43
hypocenterC43C2×#1436
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
6. #19132830C2semidirect
7. #19132829C2semidirect
8. #19132828C2semidirect
9. #19132827C2semidirect
10. #19132826C2semidirect
11. C43×#1436C2semidirect
22. C2×C4⋊C4×D43C4semidirect
37. #95×D43C4semidirect
80. C2×C4⋊Dic43C2×C4semidirect
85. C2×Dic43⋊C4C2×C4semidirect
86. C2×Dic43⋊C4C2×C4semidirect
99. C43⋊#95C2×C4semidirect
100. C43⋊#95C2×C4semidirect
101. C43⋊#95C2×C4semidirect
109. C2×C4⋊C4×C43C2×C4semidirect
114. #95×C43C2×C4semidirect
209. C2×C4×D43C42semidirect
211. C2×C4×D43C4⋊C4semidirect
275. C2×C4×C43C2×C42semidirect
277. C2×C4×C43C2×C4⋊C4semidirect
304. C2×Dic43C2×C42semidirect
306. C2×Dic43C2×C4⋊C4semidirect
363. #1436D43direct (N × H)
373. D43#1436direct (N × H)
405. C43C2×#1436semidirect
458. C2×C4⋊C4C4×D43semidirect
477. #95C4×D43semidirect
672. C2×C4C42×D43semidirect
674. C2×C4C4⋊C4×D43semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊C4×D432
C22×C42×D432
C2×#95×D432
#191328302
#191328292
#191328282
#191328272
#191328262
C43×#14362
C2×#143643