Finite Group Databasebeta

← #25106415

Subgroups — #25106415

Order 11008.

1254 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583486C211yesmaximal, characteristic
2#19137208C211yesmaximal, characteristic, complemented
3#19137190C211yesmaximal, characteristic, complemented
4#19135580C211yesmaximal, characteristic, complemented
5#19135579C211yesmaximal, characteristic, complemented
6#19135432C211yesmaximal, characteristic, complemented
7#19135045C214yesmaximal, complemented
8#19134581C214yesmaximal, complemented
9C43×#1964C211yesmaximal, characteristic, complemented
10#14583486—22no—
11#14583486—22no—
12#14583486—22no—
13#14583486—22no—
14C2×#13063320C412yescomplemented
15C2×#13063311C412yescomplemented
16C2×#13063309C412yescomplemented
17C2×#13063304C2211yescharacteristic
18C2×#13063297C412yescomplemented
19C2×#13063293C2212yes—
20C2×D4×Dic43C2212yes—
21C22×(C2×D43)⋊C4C2211yescharacteristic
22C2×C22⋊C4×D43C2212yes—
23C2×#13063240C2214yes—
24#14582790—22no—
25#14582788—22no—
26#14582773—22no—
27#14582770—22no—
28#14582759C2211yescharacteristic
29#14582757C2212yes—
30#14582757C2212yes—
31#14582754C2212yes—
32C4×C22⋊Dic43C2211yescharacteristic
33#14582665C2214yes—
34#14582665C2214yes—
35C2×#121×C43C2211yescharacteristic
36C2×#99×C43C2214yes—
37C43×#380C2211yescharacteristic
38C4×C22⋊C4×C43C2211yescharacteristic
39C24×D43C2311yescharacteristic
40C22×Dic86C2×C411yescharacteristic, complemented
41C22×C22⋊D43C2×C412yes—
42C22×C22⋊D43C2×C412yes—
43C23×Dic43C2×C412yescomplemented
44C23×Dic43C2311yescharacteristic
45C22×C4×D43—22no—
46#13063320—24no—
47#13063320—24no—
48#13063311—24no—
49#13063311—24no—
50#13063309—24no—
51#13063309—24no—
52#13063304—21no—
53#13063304—21no—
54#13063304—21no—
55#13063304—21no—
56#13063297—24no—
57#13063297—24no—
58#13063293—24no—
59#13063293—24no—
60D4×Dic43—24no—
61D4×Dic43—24no—
62C2×C4⋊Dic43—21no—
63C2×C4⋊Dic43C2×C412yescomplemented
64C2×C4⋊Dic43C2×C411yescharacteristic, complemented
65C2×Dic43⋊C4—22no—
66C2×Dic43⋊C4—22no—
67C2×Dic43⋊C4C2×C412yescomplemented
68C2×C22⋊Dic43C2×C412yescomplemented
69C2×C22⋊Dic43C2312yes—
70C2×C22⋊Dic43C2312yes—
71C2×C22⋊Dic43C2312yes—
72C2×(C2×D43)⋊C4—22no—
73C2×(C2×D43)⋊C4—22no—
74C2×(C2×D43)⋊C4—22no—
75C2×(C2×D43)⋊C4C2×C412yes—
76C2×(C2×D43)⋊C4C2×C412yes—
77C2×(C2×D43)⋊C4C2×C412yes—
78C2×(C2×D43)⋊C4C2×C412yes—
79C2×(C2×D43)⋊C4D412yes—
80C2×(C2×D43)⋊C4D412yes—
81C2×(C2×D43)⋊C4D412yes—
82C2×(C2×D43)⋊C4D412yes—
83C22⋊C4×D43—44no—
84C2×C4×Dic43—21no—
85C2×C4×Dic43C2×C412yescomplemented
86#13063240—44no—
87C43⋊#95—21no—
88C43⋊#95—21no—
89C43⋊#95—22no—
90C43⋊#95—22no—
91C22×D4×C43C2×C411yescharacteristic, complemented
92C22×D4×C43C2312yes—
93C23×C4×C43C2311yescharacteristic
94#121×C43—21no—
95#121×C43—21no—
96#121×C43—21no—
97#121×C43—21no—
98C2×C4⋊C4×C43—21no—
99C2×C4⋊C4×C43C2×C411yescharacteristic, complemented
100C2×C22⋊C4×C43C2×C412yescomplemented
101C2×C22⋊C4×C43C2312yes—
102C2×C22⋊C4×C43C2312yes—
103C2×C42×C43—21no—
104#99×C43—44no—
105#95×C43—21no—
106#95×C43—21no—
107C24×C43C22×C412yes—
108C24×C43C2411yescharacteristic
109C23×D43—22no—
110C23×D43—22no—
111C23×D43—81no—
112C23×D43—81no—
113C23×D43C22×C412yes—
114C23×D43C2×D412yes—
115C23×D43C2×D412yes—
116C2×D4×C43—21no—
117C2×D4×C43—21no—
118C2×D4×C43—22no—
119C2×D4×C43—22no—
120C2×D4×C43—24no—
121C2×D4×C43—24no—
122C2×D4×C43—81no—
123C22×C4×C43—22no—
124C22×C4×C43—22no—
125C22×C4×C43—81no—
126C22×C4×C43C22×C412yes—
127C22×C4×C43C22×C411yescharacteristic
128C22×C4×C43C22×C411yescharacteristic
129C22×C4×C43C2×D411yescharacteristic
130C22×C4×C43C2×D411yescharacteristic
131C22×C4×C43C2×D411yescharacteristic
132C22×C4×C43C2×D411yescharacteristic
133C2×C22⋊D43—24no—
134C2×C22⋊D43—24no—
135C2×C22⋊D43—82no—
136C2×C22⋊D43—82no—
137C22×Dic43—24no—
138C22×Dic43—22no—
139C22×Dic43—22no—
140C22×Dic43—81no—
141C22×Dic43—82no—
142C22×Dic43C22×C412yes—
143C22×Dic43C22×C412yes—
144C22×Dic43C22×C412yes—
145C22×Dic43C2×D412yes—
146C22×Dic43C2×D412yes—
147C2×C4×D43—44no—
148C2×C4×D43—82no—
149C2×C4×D43—82no—
150C2×Dic86—21no—
151C2×Dic86—21no—
152C2×Dic86—81no—
153C4⋊C4×C43—21no—
154C4⋊C4×C43—21no—
155C4⋊C4×C43—81no—
156C22⋊C4×C43—22no—
157C22⋊C4×C43—22no—
158C22⋊C4×C43—22no—
159C22⋊C4×C43—24no—
160C22⋊C4×C43—22no—
161C42×C43—81no—
162C22⋊Dic43—24no—
163C22⋊Dic43—22no—
164C22⋊Dic43—22no—
165C22⋊Dic43—22no—
166C22⋊Dic43—24no—
167C22⋊Dic43—22no—
168(C2×D43)⋊C4—24no—
169(C2×D43)⋊C4—24no—
170(C2×D43)⋊C4—44no—
171(C2×D43)⋊C4—82no—
172(C2×D43)⋊C4—82no—
173(C2×D43)⋊C4C22⋊C414yes—
174(C2×D43)⋊C4C22⋊C414yes—
175(C2×D43)⋊C4C22⋊C414yes—
176(C2×D43)⋊C4C22⋊C414yes—
177C4⋊Dic43—21no—
178C4⋊Dic43—21no—
179C4⋊Dic43—24no—
180C4⋊Dic43—81no—
181Dic43⋊C4—22no—
182Dic43⋊C4—22no—
183Dic43⋊C4—82no—
184Dic43⋊C4—82no—
185C4×Dic43—24no—
186C4×Dic43—81no—
187C23×C43—22no—
188C23×C43—24no—
189C23×C43—41no—
190C23×C43—41no—
191C23×C43—42no—
192C23×C43—42no—
193C23×C43C23×C411yescharacteristic
194C23×C43C22×D411yescharacteristic
195C23×C43C22×D411yescharacteristic
196C23×C43H(5,𝔽2)12yes—
197C23×C432−1+412yes—
198C22×D43—22no—
199C22×D43—22no—
200C22×D43—24no—
201C22×D43—24no—
202C22×D43—42no—
203C22×D43—42no—
204C22×D43—42no—
205C22×D43—42no—
206C22×D43—42no—
207C22×D43—42no—
208C22×D43—84no—
209C22×D43—84no—
210C22×D43C2×C22⋊C414yes—
211D4×C43—42no—
212D4×C43—42no—
213D4×C43—44no—
214D4×C43—81no—
215D4×C43—81no—
216C2×C4×C43—22no—
217C2×C4×C43—24no—
218C2×C4×C43—41no—
219C2×C4×C43—41no—
220C2×C4×C43—41no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43—42no—
225C2×C4×C43—42no—
226C2×C4×C43—42no—
227C2×C4×C43—42no—
228C2×C4×C43—42no—
229C2×C4×C43—42no—
230C2×C4×C43C2×C22⋊C411yescharacteristic
231C2×C4×C43C2×C22⋊C411yescharacteristic
232C2×C4×C43C2×C22⋊C411yescharacteristic
233C2×C4×C43C2×C22⋊C411yescharacteristic
234C22⋊D43—84no—
235C22⋊D43—84no—
236C2×Dic43—22no—
237C2×Dic43—22no—
238C2×Dic43—42no—
239C2×Dic43—42no—
240C2×Dic43—42no—
241C2×Dic43—42no—
242C2×Dic43—42no—
243C2×Dic43—42no—
244C2×Dic43—42no—
245C2×Dic43—42no—
246C2×Dic43—42no—
247C2×Dic43—42no—
248C2×Dic43—42no—
249C2×Dic43—84no—
250C2×Dic43C2×C22⋊C414yes—
251C4×D43—88no—
252Dic86—81no—
253Dic86—81no—
254#21876—431nomaximal, Sylow
255C22×C43—21no—
256C22×C43—21no—
257C22×C43—21no—
258C22×C43—21no—
259C22×C43—21no—
260C22×C43—21no—
261C22×C43—42no—
262C22×C43—42no—
263C22×C43—42no—
264C22×C43—42no—
265C22×C43—42no—
266C22×C43—84no—
267C22×C43C22×C22⋊C411yescharacteristic
268C22×C43#52012yes—
269C22×C43#53511yescharacteristic
270C22×C43#53611yescharacteristic
271C22×C43#53712yes—
272C2×D43—24no—
273C2×D43—24no—
274C2×D43—24no—
275C2×D43—44no—
276C2×D43—44no—
277C2×D43—84no—
278C2×D43—84no—
279C4×C43—21no—
280C4×C43—21no—
281C4×C43—21no—
282C4×C43—21no—
283C4×C43—42no—
284C4×C43—82no—
285C4×C43—82no—
286Dic43—24no—
287Dic43—42no—
288Dic43—42no—
289Dic43—82no—
290Dic43—82no—
291C2×#538—431no—
292#2315—431no—
293#2312—431no—
294#1996—431no—
295#1996—431no—
296#1964—431no—
297#1964D4311yescharacteristic, complemented
298#1898—434no—
299#1799—434no—
300C2×C43—21no—
301C2×C43—22no—
302C2×C43—21no—
303C2×C43—22no—
304C2×C43—82no—
305C2×C43#231111yescharacteristic
306C2×C43#288311yescharacteristic
307C2×C43#288311yescharacteristic
308D43—44no—
309#538—862no—
310#538—862no—
311#538—862no—
312#538—862no—
313C2×#126—432no—
314C2×#124—432no—
315C2×#123—432no—
316C2×C22⋊Q8—431no—
317C2×#121—432no—
318C2×#121C2×D4311yescharacteristic
319C2×#120—432no—
320C2×C4×D4—432no—
321C22×C22⋊C4—431no—
322C22×C22⋊C4—432no—
323C2×#99—434no—
324C2×#99C2×D4314yes—
325#388—862no—
326#388—862no—
327#385—862no—
328#385—862no—
329#380—431no—
330#380—432no—
331#380—432no—
332#380C2×D4311yescharacteristic
333#379—432no—
334C4×C22⋊C4—431no—
335C4×C22⋊C4C2×D4311yescharacteristic
336#342—434no—
337#342—434no—
338C43#2187611yescharacteristic, complemented, Sylow
339C25—431no—
340C22×Q8—431no—
341C22×D4—432no—
342C22×D4—432no—
343C22×D4C4×D4311yescharacteristic, complemented
344C22×D4C22×D4312yes—
345C23×C4—431no—
346C23×C4—432no—
347C23×C4—862no—
348C23×C4C22×D4311yescharacteristic
349#126—864no—
350#126—864no—
351#124—864no—
352#124—864no—
353#123—864no—
354#123—864no—
355C22⋊Q8—861no—
356C22⋊Q8—861no—
357C22⋊Q8—861no—
358C22⋊Q8—861no—
359#121—21no—
360#121—21no—
361#121—21no—
362#121—21no—
363#121—864no—
364#121—864no—
365#120—864no—
366#120—864no—
367C4×D4—864no—
368C4×D4—864no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—432no—
371C2×C4⋊C4—432no—
372C2×C4⋊C4—431no—
373C2×C4⋊C4—862no—
374C2×C4⋊C4—862no—
375C2×C4⋊C4—861no—
376C2×C4⋊C4C4×D4311yescharacteristic, complemented
377C2×C22⋊C4—432no—
378C2×C22⋊C4—432no—
379C2×C22⋊C4—432no—
380C2×C22⋊C4—432no—
381C2×C22⋊C4—432no—
382C2×C22⋊C4—432no—
383C2×C22⋊C4—432no—
384C2×C22⋊C4—432no—
385C2×C22⋊C4—432no—
386C2×C22⋊C4—432no—
387C2×C22⋊C4—432no—
388C2×C22⋊C4—432no—
389C2×C22⋊C4—862no—
390C2×C22⋊C4—862no—
391C2×C22⋊C4—862no—
392C2×C22⋊C4—1724no—
393C2×C22⋊C4C4×D4312yescomplemented
394C2×C22⋊C4C22×D4312yes—
395C2×C22⋊C4C22×D4312yes—
396C2×C42—21no—
397C2×C42—432no—
398C2×C42—861no—
399#99—44no—
400#99—1724no—
401#95—21no—
402#95—21no—
403#95—862no—
404#95—862no—
405#95—861no—
406#95—861no—
407C24—432no—
408C24—432no—
409C24—432no—
410C24—862no—
411C24—862no—
412C24—3441no—
413C24—3441no—
414C24C2×C4×D4312yes—
415C24C23×D4311yescharacteristic
416C2×Q8—861no—
417C2×Q8—861no—
418C2×Q8—3441no—
419C2×D4—22no—
420C2×D4—22no—
421C2×D4—24no—
422C2×D4—24no—
423C2×D4—21no—
424C2×D4—21no—
425C2×D4—81no—
426C2×D4—864no—
427C2×D4—864no—
428C2×D4—3442no—
429C2×D4—3442no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—81no—
433C22×C4—432no—
434C22×C4—432no—
435C22×C4—432no—
436C22×C4—432no—
437C22×C4—432no—
438C22×C4—864no—
439C22×C4—862no—
440C22×C4—862no—
441C22×C4—3442no—
442C22×C4—3442no—
443C22×C4—3442no—
444C22×C4—3441no—
445C22×C4—1724no—
446C22×C4C2×C4×D4312yes—
447C22×C4C2×C4×D4311yescharacteristic
448C22×C4C2×C4×D4311yescharacteristic
449C22×C4D4×D4311yescharacteristic
450C22×C4D4×D4311yescharacteristic
451C22×C4D4×D4311yescharacteristic
452C22×C4D4×D4311yescharacteristic
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—81no—
456C4⋊C4—864no—
457C4⋊C4—862no—
458C4⋊C4—862no—
459C4⋊C4—861no—
460C4⋊C4—861no—
461C4⋊C4—3442no—
462C4⋊C4—3442no—
463C4⋊C4—3441no—
464C22⋊C4—22no—
465C22⋊C4—22no—
466C22⋊C4—22no—
467C22⋊C4—24no—
468C22⋊C4—22no—
469C22⋊C4—434no—
470C22⋊C4—434no—
471C22⋊C4—434no—
472C22⋊C4—434no—
473C22⋊C4—864no—
474C22⋊C4—864no—
475C22⋊C4—864no—
476C22⋊C4—862no—
477C22⋊C4—862no—
478C22⋊C4—862no—
479C22⋊C4—864no—
480C22⋊C4—862no—
481C22⋊C4—3442no—
482C22⋊C4—3442no—
483C22⋊C4—1724no—
484C42—81no—
485C42—864no—
486C42—3441no—
487C23—22no—
488C23—24no—
489C23—41no—
490C23—41no—
491C23—42no—
492C23—42no—
493C23—434no—
494C23—864no—
495C23—864no—
496C23—862no—
497C23—862no—
498C23—3444no—
499C23—3444no—
500C23—1722no—
501C23—1722no—
502C23—1722no—
503C23—1722no—
504C23—1722no—
505C23—1722no—
506C23C22×C4×D4311yescharacteristic
507C23C2×D4×D4311yescharacteristic
508C23C2×D4×D4311yescharacteristic
509C23#1306337012yes—
510C23#1306337212yes—
511Q8—3441no—
512Q8—3441no—
513D4—42no—
514D4—42no—
515D4—44no—
516D4—81no—
517D4—81no—
518D4—3444no—
519D4—3444no—
520C2×C4—22no—
521C2×C4—24no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—434no—
535C2×C4—862no—
536C2×C4—862no—
537C2×C4—3448no—
538C2×C4—3444no—
539C2×C4—1722no—
540C2×C4—1722no—
541C2×C4—1722no—
542C2×C4—1722no—
543C2×C4—1722no—
544C2×C4—1722no—
545C2×C4—1722no—
546C2×C4—1722no—
547C2×C4—1722no—
548C2×C4—1722no—
549C2×C4—1722no—
550C2×C4C22⋊C4×D4311yescharacteristic
551C2×C4C22⋊C4×D4311yescharacteristic
552C2×C4C22⋊C4×D4311yescharacteristic
553C2×C4C22⋊C4×D4311yescharacteristic
554C22—21no—
555C22—21no—
556C22—21no—
557C22—21no—
558C22—21no—
559C22—21no—
560C22—42no—
561C22—42no—
562C22—42no—
563C22—42no—
564C22—42no—
565C22—84no—
566C22—864no—
567C22—864no—
568C22—864no—
569C22—3444no—
570C22—3444no—
571C22—1724no—
572C22—1724no—
573C22C2×C22⋊C4×D4311yescharacteristic
574C22#1458337812yes—
575C22#1458346211yescharacteristic
576C22#1458346911yescharacteristic
577C22#1458347812yes—
578C4—21no—
579C4—21no—
580C4—21no—
581C4—21no—
582C4—42no—
583C4—82no—
584C4—82no—
585C4—864no—
586C4—3442no—
587C4—3442no—
588C4—1722no—
589C4—1722no—
590C2—21no—
591C2—22no—
592C2—22no—
593C2—21no—
594C2—82no—
595C2—1724no—
596C2#1913718511yescharacteristic
597C2#1914305311yescharacteristic
598C2#1914305411yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC24C23×D43
FittingC43×#1964C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#14583486C2
cosocleC24×C43C24
hypercenter#1964D43
hypocenterC43#21876
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1964

Complements

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

NH ≅ G/Ntype
2. #19137208C2semidirect
3. #19137190C2semidirect
4. #19135580C2semidirect
5. #19135579C2semidirect
6. #19135432C2semidirect
7. #19135045C2semidirect
8. #19134581C2semidirect
9. C43×#1964C2semidirect
14. C2×#13063320C4semidirect
15. C2×#13063311C4semidirect
16. C2×#13063309C4semidirect
18. C2×#13063297C4semidirect
40. C22×Dic86C2×C4semidirect
43. C23×Dic43C2×C4semidirect
63. C2×C4⋊Dic43C2×C4semidirect
64. C2×C4⋊Dic43C2×C4semidirect
67. C2×Dic43⋊C4C2×C4semidirect
68. C2×C22⋊Dic43C2×C4semidirect
85. C2×C4×Dic43C2×C4semidirect
91. C22×D4×C43C2×C4semidirect
99. C2×C4⋊C4×C43C2×C4semidirect
100. C2×C22⋊C4×C43C2×C4semidirect
297. #1964D43semidirect
338. C43#21876semidirect
343. C22×D4C4×D43semidirect
376. C2×C4⋊C4C4×D43semidirect
393. C2×C22⋊C4C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145834862
#191372082
#191371902
#191355802
#191355792
#191354322
#191350452
#191345812
C43×#19642
#2187643