Finite Group Databasebeta

← D43×#2035 #25124049

Subgroups — D43×#2035 #25124049

Order 11008.

1662 conjugacy classes of subgroups.

The subgroup lattice has 882 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C22⋊Q8×D43C211yesmaximal, characteristic
2C2×#106×D43C211yesmaximal, characteristic, complemented
3C2×#103×D43C211yesmaximal, characteristic, complemented
4C2×#103×D43C211yesmaximal, characteristic, complemented
5C2×C22⋊C8×D43C211yesmaximal, characteristic
6#380×D43C211yesmaximal, characteristic
7#19135794C211yesmaximal, characteristic, complemented
8#19135793C211yesmaximal, characteristic, complemented
9#19135792C211yesmaximal, characteristic, complemented
10#19135791C211yesmaximal, characteristic, complemented
11#19135790C211yesmaximal, characteristic, complemented
12#19135789C211yesmaximal, characteristic, complemented
13#19135788C211yesmaximal, characteristic, complemented
14#340×D43C211yesmaximal, characteristic, complemented
15C43×#2035C211yesmaximal, characteristic, complemented
16C22×Q8×D43C2211yescharacteristic
17C23×C4×D43C2211yescharacteristic
18C22×C8×D43C2211yescharacteristic
19C22×C8×D43C2211yescharacteristic
20C2×#13063305C2211yescharacteristic
21C2×#13063304C2211yescharacteristic
22C2×#13063303—21no—
23C2×#13063302—21no—
24C2×#13063301C2211yescharacteristic
25C22⋊Q8×D43—24no—
26C22⋊Q8×D43—24no—
27C2×C4⋊C4×D43—21no—
28C2×C4⋊C4×D43C2211yescharacteristic
29C2×C4⋊C4×D43C2211yescharacteristic
30C2×C4⋊C4×D43C2211yescharacteristic
31C2×C22⋊C4×D43—21no—
32C2×C22⋊C4×D43—21no—
33C2×#13063257C2211yescharacteristic, complemented
34C2×#13063256C2211yescharacteristic, complemented
35C2×#13063256C2211yescharacteristic, complemented
36#106×D43—24no—
37C2×#13063250C2211yescharacteristic, complemented
38C2×#13063250C2211yescharacteristic, complemented
39C2×#13063249C2211yescharacteristic, complemented
40C2×#13063249C2211yescharacteristic, complemented
41C2×#13063248C2211yescharacteristic, complemented
42C2×#13063248C2211yescharacteristic, complemented
43#103×D43—24no—
44#103×D43—24no—
45C2×C22⋊(C43⋊C8)C2211yescharacteristic
46C2×(C2×D43)⋊C8C2211yescharacteristic
47C2×(C2×D43)⋊C8C2211yescharacteristic
48C22⋊C8×D43—24no—
49#14582759C2211yescharacteristic
50#14582758—21no—
51#14582757—21no—
52#14582756C2211yescharacteristic
53#14582756C2211yescharacteristic
54#95×D43—21no—
55#14582662C2211yescharacteristic, complemented
56#14582661C2211yescharacteristic, complemented
57#14582661C2211yescharacteristic, complemented
58C2×C22⋊Q8×C43C2211yescharacteristic
59C2×#106×C43C2211yescharacteristic, complemented
60C2×#103×C43C2211yescharacteristic, complemented
61C2×#103×C43C2211yescharacteristic, complemented
62C2×C22⋊C8×C43C2211yescharacteristic
63C43×#380C2211yescharacteristic
64C43×#340C2211yescharacteristic, complemented
65C24×D43D411yescharacteristic
66C22×Dic86—21no—
67C22×Dic86C2311yescharacteristic
68C2×Q8×D43—22no—
69C2×Q8×D43—22no—
70C2×Q8×D43—22no—
71C2×Q8×D43—22no—
72C2×Q8×D43—22no—
73C2×Q8×D43D414yes—
74C23×Dic43D411yescharacteristic
75C22×C4×D43—21no—
76C22×C4×D43—21no—
77C22×C4×D43—22no—
78C22×C4×D43—22no—
79C22×C4×D43—22no—
80C22×C4×D43—22no—
81C22×C4×D43—22no—
82C22×C4×D43—22no—
83C22×C4×D43—21no—
84C22×C4×D43—21no—
85C22×C4×D43D411yescharacteristic
86C22×C4×D43D411yescharacteristic
87C22×C4×D43C2311yescharacteristic
88C22×C4×D43C2311yescharacteristic
89C22×C43⋊C8C2311yescharacteristic
90C22×C43⋊C8C2311yescharacteristic
91C2×C8×D43—22no—
92C2×C8×D43—22no—
93C2×C8×D43—22no—
94C2×C8×D43—22no—
95C2×C8×D43—22no—
96C2×C8×D43D414yes—
97#13063305—22no—
98#13063305—22no—
99#13063304—22no—
100#13063304—22no—
101#13063303—28no—
102#13063302—28no—
103#13063301—22no—
104#13063301—22no—
105C2×C4⋊Dic43—21no—
106C2×C4⋊Dic43C2311yescharacteristic
107C2×C4⋊Dic43C2311yescharacteristic
108C2×C4⋊Dic43C2311yescharacteristic
109C2×Dic43⋊C4—21no—
110C2×Dic43⋊C4—21no—
111C2×Dic43⋊C4—21no—
112C2×Dic43⋊C4—21no—
113C2×Dic43⋊C4—21no—
114C4⋊C4×D43—28no—
115C4⋊C4×D43—22no—
116C4⋊C4×D43—22no—
117C4⋊C4×D43—22no—
118C4⋊C4×D43—22no—
119C4⋊C4×D43—22no—
120C4⋊C4×D43D414yes—
121C2×C22⋊Dic43—21no—
122C2×C22⋊Dic43—21no—
123C2×(C2×D43)⋊C4—21no—
124C2×(C2×D43)⋊C4—21no—
125C2×(C2×D43)⋊C4—21no—
126C2×(C2×D43)⋊C4—21no—
127C22⋊C4×D43—28no—
128C22⋊C4×D43—44no—
129#13063257—22no—
130#13063256—22no—
131#13063256—22no—
132#13063250—22no—
133#13063250—22no—
134#13063249—22no—
135#13063249—22no—
136#13063248—22no—
137#13063248—22no—
138C22⋊(C43⋊C8)—22no—
139(C2×D43)⋊C8—22no—
140(C2×D43)⋊C8—22no—
141C43⋊#95—21no—
142C43⋊#95—21no—
143C43⋊#95—21no—
144C22×Q8×C43C2311yescharacteristic
145C23×C4×C43C2311yescharacteristic
146C22×C8×C43C2311yescharacteristic
147C22×C8×C43C2311yescharacteristic
148C22⋊Q8×C43—22no—
149C22⋊Q8×C43—22no—
150C2×C4⋊C4×C43—21no—
151C2×C4⋊C4×C43C2311yescharacteristic
152C2×C4⋊C4×C43C2311yescharacteristic
153C2×C4⋊C4×C43C2311yescharacteristic
154C2×C22⋊C4×C43—21no—
155C2×C22⋊C4×C43—21no—
156#106×C43—22no—
157#103×C43—22no—
158#103×C43—22no—
159C22⋊C8×C43—22no—
160#95×C43—21no—
161C24×C43C2×D411yescharacteristic
162C23×D43—22no—
163C23×D43—22no—
164C23×D43—22no—
165C23×D43—22no—
166C23×D43—22no—
167C23×D43—22no—
168C23×D43SD1614yes—
169C23×D43C2×D411yescharacteristic
170C23×D43C2×D411yescharacteristic
171C2×Q8×C43—21no—
172C2×Q8×C43—21no—
173C2×Q8×C43—21no—
174C2×Q8×C43—21no—
175C2×Q8×C43—21no—
176C2×Q8×C43C2×D412yes—
177C22×C4×C43—21no—
178C22×C4×C43—21no—
179C22×C4×C43—21no—
180C22×C4×C43—21no—
181C22×C4×C43—21no—
182C22×C4×C43—21no—
183C22×C4×C43—21no—
184C22×C4×C43—21no—
185C22×C4×C43—21no—
186C22×C4×C43—21no—
187C22×C4×C43C2×D411yescharacteristic
188C22×C4×C43C2411yescharacteristic
189C22×Dic43—22no—
190C22×Dic43—22no—
191C22×Dic43—22no—
192C22×Dic43—21no—
193C22×Dic43—21no—
194C22×Dic43—21no—
195C22×Dic43—21no—
196C22×Dic43C2×D411yescharacteristic
197C22×Dic43C2×D411yescharacteristic
198Q8×D43—28no—
199Q8×D43—28no—
200Q8×D43—44no—
201Q8×D43—44no—
202C2×C4×D43—21no—
203C2×C4×D43—21no—
204C2×C4×D43—21no—
205C2×C4×D43—21no—
206C2×C4×D43—21no—
207C2×C4×D43—21no—
208C2×C4×D43—22no—
209C2×C4×D43—22no—
210C2×C4×D43—22no—
211C2×C4×D43—24no—
212C2×C4×D43—24no—
213C2×C4×D43—22no—
214C2×C4×D43—22no—
215C2×C4×D43—22no—
216C2×C4×D43—44no—
217C2×C4×D43—44no—
218C2×C4×D43—44no—
219C2×C4×D43—44no—
220C2×C4×D43—42no—
221C2×C4×D43—42no—
222C2×C4×D43—42no—
223C2×C4×D43—42no—
224C2×C4×D43—42no—
225C2×C4×D43—42no—
226C2×C4×D43—42no—
227C2×C4×D43—42no—
228C2×C4×D43—42no—
229C2×C4×D43—42no—
230C2×C4×D43C2×D412yes—
231C2×C4×D43C2×D412yes—
232C2×C4×D43C2×D412yes—
233C2×C4×D43#4112yes—
234C2×C4×D43#4112yes—
235C2×C4×D43#4112yes—
236C2×Dic86—21no—
237C2×Dic86—21no—
238C2×Dic86—21no—
239C2×Dic86—21no—
240C2×Dic86—21no—
241C2×Dic86—24no—
242C2×Dic86—42no—
243C2×Dic86—42no—
244C2×Dic86C2×D412yes—
245C2×C8×C43—21no—
246C2×C8×C43—21no—
247C2×C8×C43—21no—
248C2×C8×C43—21no—
249C2×C8×C43—21no—
250C2×C8×C43C2×D412yes—
251C4⋊C4×C43—24no—
252C4⋊C4×C43—21no—
253C4⋊C4×C43—21no—
254C4⋊C4×C43—21no—
255C4⋊C4×C43—21no—
256C4⋊C4×C43—21no—
257C4⋊C4×C43C2×D412yes—
258C22⋊C4×C43—24no—
259C22⋊C4×C43—42no—
260C22⋊Dic43—24no—
261C22⋊Dic43—42no—
262(C2×D43)⋊C4—24no—
263(C2×D43)⋊C4—24no—
264(C2×D43)⋊C4—42no—
265(C2×D43)⋊C4—42no—
266C4⋊Dic43—24no—
267C4⋊Dic43—21no—
268C4⋊Dic43—21no—
269C4⋊Dic43—21no—
270C4⋊Dic43—21no—
271C4⋊Dic43—21no—
272C4⋊Dic43C2×D412yes—
273Dic43⋊C4—24no—
274Dic43⋊C4—24no—
275Dic43⋊C4—24no—
276Dic43⋊C4—42no—
277Dic43⋊C4—42no—
278C2×C43⋊C8—21no—
279C2×C43⋊C8—21no—
280C2×C43⋊C8—21no—
281C2×C43⋊C8—21no—
282C2×C43⋊C8—21no—
283C2×C43⋊C8C2×D412yes—
284C8×D43—28no—
285C8×D43—44no—
286C23×C43—21no—
287C23×C43—21no—
288C23×C43—21no—
289C23×C43—21no—
290C23×C43—21no—
291C23×C43—21no—
292C23×C43C2×SD1612yes—
293C23×C43C22×D411yescharacteristic
294C22×D43—21no—
295C22×D43—21no—
296C22×D43—21no—
297C22×D43—21no—
298C22×D43—21no—
299C22×D43—21no—
300C22×D43—28no—
301C22×D43—28no—
302C22×D43—28no—
303C22×D43—44no—
304C22×D43—44no—
305C22×D43—44no—
306C22×D43—44no—
307C22×D43#12012yes—
308C22×D43#12112yes—
309C22×D43#12312yes—
310C22×D43C2×SD1612yes—
311C22×D43C2×SD1612yes—
312C22×D43#13512yes—
313C22×D43#13712yes—
314C22×D43#13712yes—
315Q8×C43—22no—
316Q8×C43—22no—
317Q8×C43—41no—
318Q8×C43—41no—
319C2×C4×C43—21no—
320C2×C4×C43—22no—
321C2×C4×C43—22no—
322C2×C4×C43—21no—
323C2×C4×C43—21no—
324C2×C4×C43—41no—
325C2×C4×C43—41no—
326C2×C4×C43—41no—
327C2×C4×C43—41no—
328C2×C4×C43—41no—
329C2×C4×C43—41no—
330C2×C4×C43—41no—
331C2×C4×C43—41no—
332C2×C4×C43—41no—
333C2×C4×C43—41no—
334C2×C4×C43—41no—
335C2×C4×C43—41no—
336C2×C4×C43—41no—
337C2×C4×C43—41no—
338C2×C4×C43C22×D411yescharacteristic
339C2×C4×C43C22×D411yescharacteristic
340C2×C4×C43C22×D411yescharacteristic
341C2×C4×C43C2×#4111yescharacteristic
342C2×C4×C43C2×#4111yescharacteristic
343C2×C4×C43C2×#4111yescharacteristic
344C2×Dic43—22no—
345C2×Dic43—21no—
346C2×Dic43—22no—
347C2×Dic43—21no—
348C2×Dic43—21no—
349C2×Dic43—41no—
350C2×Dic43—41no—
351C2×Dic43—41no—
352C2×Dic43—41no—
353C2×Dic43—44no—
354C2×Dic43—41no—
355C2×Dic43—41no—
356C2×Dic43—41no—
357C2×Dic43—41no—
358C2×Dic43—41no—
359C2×Dic43—41no—
360C2×Dic43#12012yes—
361C2×Dic43#12112yes—
362C2×Dic43#12312yes—
363C4×D43—44no—
364C4×D43—48no—
365C4×D43—48no—
366C4×D43—41no—
367C4×D43—41no—
368C4×D43—41no—
369C4×D43—41no—
370C4×D43—44no—
371C4×D43—84no—
372C4×D43—84no—
373C4×D43#12114yes—
374C4×D43#12114yes—
375C4×D43#12314yes—
376C4×D43#12414yes—
377Dic86—22no—
378Dic86—22no—
379Dic86—41no—
380Dic86—41no—
381Dic86—48no—
382C8×C43—22no—
383C8×C43—41no—
384C43⋊C8—22no—
385C43⋊C8—41no—
386C2×#2035—431nomaximal, Sylow
387C22×C43—22no—
388C22×C43—22no—
389C22×C43—22no—
390C22×C43—41no—
391C22×C43—41no—
392C22×C43—41no—
393C22×C43—41no—
394C22×C43C2×#12011yescharacteristic
395C22×C43C2×#12111yescharacteristic
396C22×C43C2×#12311yescharacteristic
397C22×C43C22×SD1611yescharacteristic
398C22×C43C2×#13511yescharacteristic
399C22×C43C2×#13711yescharacteristic
400C22×C43C2×#13711yescharacteristic
401C2×D43—22no—
402C2×D43—22no—
403C2×D43—22no—
404C2×D43—41no—
405C2×D43—41no—
406C2×D43—41no—
407C2×D43—41no—
408C2×D43—416no—
409C2×D43#39414yes—
410C2×D43#44814yes—
411C2×D43#45214yes—
412C2×D43#46514yes—
413C2×D43#47014yes—
414C2×D43#48314yes—
415C2×D43#48514yes—
416C4×C43—42no—
417C4×C43—41no—
418C4×C43—42no—
419C4×C43—81no—
420C4×C43—81no—
421C4×C43C2×#12111yescharacteristic
422C4×C43C2×#12111yescharacteristic
423C4×C43C2×#12311yescharacteristic
424C4×C43C2×#12411yescharacteristic
425Dic43—42no—
426Dic43—41no—
427Dic43—42no—
428Dic43—81no—
429Dic43—81no—
430Dic43#39414yes—
431C22×C22⋊Q8—431no—
432C22×#106—431no—
433C22×#103—431no—
434C22×#103—431no—
435C22×C22⋊C8—431no—
436C2×#380—431no—
437#2035—431no—
438#2035—431no—
439#2035—431no—
440#2035—431no—
441#2035—431no—
442#2035—431no—
443#2035—431no—
444#2035D4311yescharacteristic, direct product factor
445C2×#340—431no—
446C2×C43—42no—
447C2×C43C2×#39411yescharacteristic
448C2×C43C2×#44811yescharacteristic
449C2×C43C2×#45211yescharacteristic
450C2×C43C2×#46511yescharacteristic
451C2×C43C2×#47011yescharacteristic
452C2×C43C2×#48311yescharacteristic
453C2×C43C2×#48511yescharacteristic
454D43—42no—
455D43#203518yesdirect product factor
456C23×Q8—431no—
457C24×C4—431no—
458C23×C8—431no—
459C23×C8—431no—
460C2×C22⋊Q8—431no—
461C2×C22⋊Q8—431no—
462C2×C22⋊Q8—431no—
463C2×C22⋊Q8—861no—
464C2×C22⋊Q8—861no—
465C2×C22⋊Q8—864no—
466C2×C22⋊Q8—864no—
467C2×C22⋊Q8C2×D4311yescharacteristic
468C22×C4⋊C4—431no—
469C22×C4⋊C4—431no—
470C22×C4⋊C4—431no—
471C22×C4⋊C4—861no—
472C22×C22⋊C4—861no—
473C22×C22⋊C4—861no—
474C2×#106—431no—
475C2×#106—431no—
476C2×#106—431no—
477C2×#106—864no—
478C2×#106C2×D4311yescharacteristic, complemented
479C2×#103—431no—
480C2×#103—431no—
481C2×#103—431no—
482C2×#103—431no—
483C2×#103—431no—
484C2×#103—431no—
485C2×#103—864no—
486C2×#103—864no—
487C2×#103C2×D4311yescharacteristic, complemented
488C2×#103C2×D4311yescharacteristic, complemented
489C2×C22⋊C8—431no—
490C2×C22⋊C8—431no—
491C2×C22⋊C8—431no—
492C2×C22⋊C8—864no—
493C2×C22⋊C8C2×D4311yescharacteristic
494#380—431no—
495#380—431no—
496#380—431no—
497#380—861no—
498#380—861no—
499#380C2×D4311yescharacteristic
500C2×#95—861no—
501#340—431no—
502#340—431no—
503#340—431no—
504#340C2×D4311yescharacteristic, complemented
505C43C2×#203511yescharacteristic, complemented, Sylow
506C25—431no—
507C22×Q8—434no—
508C22×Q8—431no—
509C22×Q8—861no—
510C22×Q8—862no—
511C22×Q8—862no—
512C22×Q8—862no—
513C22×Q8—862no—
514C22×Q8—862no—
515C22×Q8C22×D4311yescharacteristic
516C23×C4—431no—
517C23×C4—431no—
518C23×C4—431no—
519C23×C4—431no—
520C23×C4—431no—
521C23×C4—862no—
522C23×C4—862no—
523C23×C4—862no—
524C23×C4—862no—
525C23×C4—862no—
526C23×C4—862no—
527C23×C4—861no—
528C23×C4—861no—
529C23×C4—861no—
530C23×C4—861no—
531C23×C4C22×D4311yescharacteristic
532C22×C8—431no—
533C22×C8—434no—
534C22×C8—431no—
535C22×C8—862no—
536C22×C8—862no—
537C22×C8—862no—
538C22×C8—862no—
539C22×C8—862no—
540C22×C8C22×D4311yescharacteristic
541C22×C8C22×D4311yescharacteristic
542C22⋊Q8—22no—
543C22⋊Q8—22no—
544C22⋊Q8—868no—
545C22⋊Q8—862no—
546C22⋊Q8—868no—
547C22⋊Q8—862no—
548C22⋊Q8—862no—
549C22⋊Q8—862no—
550C22⋊Q8—862no—
551C22⋊Q8—862no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—431no—
554C2×C4⋊C4—434no—
555C2×C4⋊C4—431no—
556C2×C4⋊C4—431no—
557C2×C4⋊C4—862no—
558C2×C4⋊C4—868no—
559C2×C4⋊C4—862no—
560C2×C4⋊C4—862no—
561C2×C4⋊C4—862no—
562C2×C4⋊C4—862no—
563C2×C4⋊C4—861no—
564C2×C4⋊C4—861no—
565C2×C4⋊C4—861no—
566C2×C4⋊C4—861no—
567C2×C4⋊C4—861no—
568C2×C4⋊C4—861no—
569C2×C4⋊C4C22×D4311yescharacteristic
570C2×C4⋊C4C22×D4311yescharacteristic
571C2×C4⋊C4C22×D4311yescharacteristic
572C2×C22⋊C4—21no—
573C2×C22⋊C4—21no—
574C2×C22⋊C4—868no—
575C2×C22⋊C4—861no—
576C2×C22⋊C4—861no—
577C2×C22⋊C4—861no—
578C2×C22⋊C4—861no—
579C2×C22⋊C4—861no—
580C2×C22⋊C4—861no—
581C2×C22⋊C4—1724no—
582#106—22no—
583#106—862no—
584#106—862no—
585#106—862no—
586#103—22no—
587#103—22no—
588#103—862no—
589#103—862no—
590#103—862no—
591#103—862no—
592#103—862no—
593#103—862no—
594C22⋊C8—22no—
595C22⋊C8—862no—
596C22⋊C8—862no—
597C22⋊C8—862no—
598#95—21no—
599#95—861no—
600#95—861no—
601#95—861no—
602C24—431no—
603C24—434no—
604C24—431no—
605C24—862no—
606C24—862no—
607C24—862no—
608C24—862no—
609C24—862no—
610C24—862no—
611C24D4×D4311yescharacteristic
612C2×Q8—21no—
613C2×Q8—21no—
614C2×Q8—21no—
615C2×Q8—21no—
616C2×Q8—21no—
617C2×Q8—432no—
618C2×Q8—864no—
619C2×Q8—868no—
620C2×Q8—868no—
621C2×Q8—861no—
622C2×Q8—861no—
623C2×Q8—861no—
624C2×Q8—861no—
625C2×Q8—861no—
626C2×Q8—1722no—
627C2×Q8—1722no—
628C2×Q8—1724no—
629C2×Q8—1724no—
630C2×Q8D4×D4312yes—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—431no—
642C22×C4—432no—
643C22×C4—432no—
644C22×C4—432no—
645C22×C4—432no—
646C22×C4—432no—
647C22×C4—432no—
648C22×C4—431no—
649C22×C4—862no—
650C22×C4—862no—
651C22×C4—862no—
652C22×C4—864no—
653C22×C4—864no—
654C22×C4—862no—
655C22×C4—862no—
656C22×C4—862no—
657C22×C4—862no—
658C22×C4—862no—
659C22×C4—862no—
660C22×C4—861no—
661C22×C4—861no—
662C22×C4—861no—
663C22×C4—861no—
664C22×C4—861no—
665C22×C4—861no—
666C22×C4—861no—
667C22×C4—861no—
668C22×C4—861no—
669C22×C4—861no—
670C22×C4—1724no—
671C22×C4—1724no—
672C22×C4—1724no—
673C22×C4—1724no—
674C22×C4—1722no—
675C22×C4—1722no—
676C22×C4—1722no—
677C22×C4—1722no—
678C22×C4—1722no—
679C22×C4—1722no—
680C22×C4—1722no—
681C22×C4—1722no—
682C22×C4—1722no—
683C22×C4—1722no—
684C22×C4D4×D4311yescharacteristic
685C22×C4C23×D4311yescharacteristic
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—432no—
692C2×C8—868no—
693C2×C8—861no—
694C2×C8—861no—
695C2×C8—861no—
696C2×C8—861no—
697C2×C8—861no—
698C2×C8—1724no—
699C2×C8D4×D4312yes—
700C4⋊C4—24no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—21no—
706C4⋊C4—432no—
707C4⋊C4—864no—
708C4⋊C4—864no—
709C4⋊C4—864no—
710C4⋊C4—864no—
711C4⋊C4—861no—
712C4⋊C4—861no—
713C4⋊C4—861no—
714C4⋊C4—861no—
715C4⋊C4—861no—
716C4⋊C4—1722no—
717C4⋊C4—1722no—
718C4⋊C4D4×D4312yes—
719C22⋊C4—24no—
720C22⋊C4—42no—
721C22⋊C4—864no—
722C22⋊C4—864no—
723C22⋊C4—864no—
724C22⋊C4—1722no—
725C22⋊C4—1722no—
726C22⋊C4—1722no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—432no—
734C23—432no—
735C23—432no—
736C23—432no—
737C23—432no—
738C23—432no—
739C23—432no—
740C23—432no—
741C23—868no—
742C23—868no—
743C23—868no—
744C23—861no—
745C23—861no—
746C23—861no—
747C23—861no—
748C23—861no—
749C23—861no—
750C23—1724no—
751C23—1724no—
752C23—1724no—
753C23—1724no—
754C23SD16×D4312yes—
755C23C2×D4×D4311yescharacteristic
756Q8—22no—
757Q8—22no—
758Q8—41no—
759Q8—41no—
760Q8—862no—
761Q8—862no—
762Q8—1728no—
763Q8—1721no—
764Q8—1721no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—432no—
785C2×C4—432no—
786C2×C4—432no—
787C2×C4—434no—
788C2×C4—434no—
789C2×C4—434no—
790C2×C4—434no—
791C2×C4—862no—
792C2×C4—862no—
793C2×C4—861no—
794C2×C4—861no—
795C2×C4—861no—
796C2×C4—3444no—
797C2×C4—3444no—
798C2×C4—1724no—
799C2×C4—1724no—
800C2×C4—1728no—
801C2×C4—1728no—
802C2×C4—1724no—
803C2×C4—1721no—
804C2×C4—1721no—
805C2×C4—1721no—
806C2×C4—1721no—
807C2×C4—1721no—
808C2×C4—1721no—
809C2×C4—1721no—
810C2×C4—1721no—
811C2×C4—1721no—
812C2×C4—1721no—
813C2×C4—1721no—
814C2×C4—1721no—
815C2×C4—1721no—
816C2×C4—1721no—
817C2×C4C2×D4×D4311yescharacteristic
818C2×C4C2×D4×D4311yescharacteristic
819C2×C4C2×D4×D4311yescharacteristic
820C2×C4#41×D4311yescharacteristic
821C2×C4#41×D4311yescharacteristic
822C2×C4#41×D4311yescharacteristic
823C8—22no—
824C8—41no—
825C8—862no—
826C8—1721no—
827C22—22no—
828C22—22no—
829C22—22no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—434no—
835C22—434no—
836C22—434no—
837C22—434no—
838C22—434no—
839C22—434no—
840C22—434no—
841C22—862no—
842C22—862no—
843C22—862no—
844C22—17216no—
845C22—1721no—
846C22—1721no—
847C22—1721no—
848C22—1721no—
849C22#120×D4311yescharacteristic
850C22#121×D4311yescharacteristic
851C22#123×D4311yescharacteristic
852C22C2×SD16×D4311yescharacteristic
853C22#135×D4311yescharacteristic
854C22#137×D4311yescharacteristic
855C22#137×D4311yescharacteristic
856C4—41no—
857C4—42no—
858C4—42no—
859C4—81no—
860C4—81no—
861C4—434no—
862C4—3441no—
863C4—3441no—
864C4—1721no—
865C4—1722no—
866C4—1722no—
867C4#121×D4311yescharacteristic
868C4#121×D4311yescharacteristic
869C4#123×D4311yescharacteristic
870C4#124×D4311yescharacteristic
871C2—42no—
872C2—438no—
873C2—1722no—
874C2#394×D4311yescharacteristic
875C2#448×D4311yescharacteristic
876C2#452×D4311yescharacteristic
877C2#465×D4311yescharacteristic
878C2#470×D4311yescharacteristic
879C2#483×D4311yescharacteristic
880C2#485×D4311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2035C2
socleC23×C43C22×D4
prime radicalC24×D43D4
hypercenter#2035D43
hypocenterC43C2×#2035
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2035

Complements

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

NH ≅ G/Ntype
2. C2×#106×D43C2semidirect
3. C2×#103×D43C2semidirect
4. C2×#103×D43C2semidirect
7. #19135794C2semidirect
8. #19135793C2semidirect
9. #19135792C2semidirect
10. #19135791C2semidirect
11. #19135790C2semidirect
12. #19135789C2semidirect
13. #19135788C2semidirect
14. #340×D43C2semidirect
15. C43×#2035C2semidirect
33. C2×#13063257C22semidirect
34. C2×#13063256C22semidirect
35. C2×#13063256C22semidirect
37. C2×#13063250C22semidirect
38. C2×#13063250C22semidirect
39. C2×#13063249C22semidirect
40. C2×#13063249C22semidirect
41. C2×#13063248C22semidirect
42. C2×#13063248C22semidirect
55. #14582662C22semidirect
56. #14582661C22semidirect
57. #14582661C22semidirect
59. C2×#106×C43C22semidirect
60. C2×#103×C43C22semidirect
61. C2×#103×C43C22semidirect
64. C43×#340C22semidirect
444. #2035D43direct (N × H)
455. D43#2035direct (N × H)
478. C2×#106C2×D43semidirect
487. C2×#103C2×D43semidirect
488. C2×#103C2×D43semidirect
504. #340C2×D43semidirect
505. C43C2×#2035semidirect

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×#106×D432
C2×#103×D432
C2×C22⋊C8×D432
#380×D432
#191357942
#191357932
#191357922
#191357912
#191357902
#191357892
#191357882
#340×D432
C43×#20352
C2×#203543