Finite Group Databasebeta

← #24988793

Subgroups — #24988793

Order 11008.

798 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19135432C211yesmaximal, characteristic, complemented
2#19134694C211yesmaximal, characteristic, complemented
3#19134690C211yesmaximal, characteristic, complemented
4#19133138C211yesmaximal, characteristic, complemented
5#19133086C211yesmaximal, characteristic, complemented
6#19132955C211yesmaximal, characteristic, complemented
7C43×#3494C211yesmaximal, characteristic
8C2×#13063240—22no—
9#14582863C2211yescharacteristic
10C2×C22⋊(C43⋊C8)C2211yescharacteristic
11#14582759C2211yescharacteristic
12C4×C22⋊Dic43C2211yescharacteristic
13#14582661—21no—
14#14582661—21no—
15#14582658—21no—
16#14582658—21no—
17#14582636—21no—
18#14582636—21no—
19#14582633—21no—
20#14582633—21no—
21#14582623—22no—
22C43×#555—21no—
23C43×#553—21no—
24C43×#553—21no—
25C43×#551—22no—
26C43×#547—21no—
27C43×#546—22no—
28C43×#544C411yescharacteristic, complemented
29C43×#542—21no—
30C43×#540—21no—
31C43×#535C411yescharacteristic, complemented
32C43×#532—21no—
33C43×#529—21no—
34C43×#525C2211yescharacteristic
35C2×#121×C43C2211yescharacteristic
36C43×#520C411yescharacteristic, complemented
37C43×#518C411yescharacteristic, complemented
38C2×#117×C43C2211yescharacteristic
39C2×#10621877—21no—
40C22×C43⋊C8—21no—
41C2×C4⋊Dic43—21no—
42C2×C22⋊Dic43—21no—
43C2×C22⋊Dic43—21no—
44C2×C4×Dic43—21no—
45#13063240—44no—
46C22⋊(C43⋊C8)—21no—
47C22⋊(C43⋊C8)—21no—
48C22⋊(C43⋊C8)—21no—
49C22⋊(C43⋊C8)—21no—
50C43⋊#95—21no—
51C43⋊#95—21no—
52C2×#41×C43—22no—
53C2×#41×C43C2×C411yescharacteristic
54C22×D4×C43C2×C411yescharacteristic
55C22×D4×C43D412yes—
56C23×C4×C43C2311yescharacteristic
57C4⋊Q8×C43—21no—
58C4⋊Q8×C43—21no—
59#127×C43—21no—
60#126×C43—22no—
61#126×C43—22no—
62#125×C43—21no—
63#125×C43—21no—
64#124×C43—22no—
65#124×C43—22no—
66#124×C43—21no—
67#123×C43—22no—
68#123×C43—22no—
69#123×C43—22no—
70#123×C43—22no—
71#123×C43—21no—
72C22⋊Q8×C43—22no—
73C22⋊Q8×C43—22no—
74C22⋊Q8×C43D411yescharacteristic
75C22⋊Q8×C43D411yescharacteristic
76#121×C43—22no—
77#121×C43—22no—
78#121×C43—22no—
79#121×C43—21no—
80#121×C43—21no—
81#121×C43—21no—
82#121×C43—21no—
83#121×C43—21no—
84#121×C43—21no—
85#121×C43D411yescharacteristic
86#121×C43D411yescharacteristic
87#120×C43—22no—
88#120×C43—21no—
89C4×Q8×C43—21no—
90C4×D4×C43—22no—
91C4×D4×C43—22no—
92C4×D4×C43—21no—
93C4×D4×C43—22no—
94C4×D4×C43—21no—
95C4×D4×C43—21no—
96C4×D4×C43—21no—
97C4×D4×C43—21no—
98C4×D4×C43—21no—
99C4×D4×C43—21no—
100#117×C43—22no—
101#117×C43—21no—
102#117×C43—21no—
103#117×C43—21no—
104#117×C43C2×C411yescharacteristic
105#117×C43C2×C411yescharacteristic
106#117×C43C2×C411yescharacteristic
107#117×C43D411yescharacteristic
108#117×C43D411yescharacteristic
109C2×C4⋊C4×C43—21no—
110C2×C4⋊C4×C43C2×C411yescharacteristic
111C2×C4⋊C4×C43D411yescharacteristic
112C2×C4⋊C4×C43D411yescharacteristic
113C2×C22⋊C4×C43—22no—
114C2×C22⋊C4×C43—21no—
115C2×C22⋊C4×C43D412yes—
116C2×C42×C43—21no—
117C24×C43C22⋊C412yes—
118C24×C43C2×D411yescharacteristic
119#41×C43—42no—
120#41×C43—82no—
121#41×C43—82no—
122C2×Q8×C43—22no—
123C2×Q8×C43C22⋊C411yescharacteristic
124C2×D4×C43—22no—
125C2×D4×C43—22no—
126C2×D4×C43—21no—
127C2×D4×C43—21no—
128C2×D4×C43—21no—
129C2×D4×C43—21no—
130C2×D4×C43—22no—
131C2×D4×C43—21no—
132C2×D4×C43—22no—
133C2×D4×C43—42no—
134C2×D4×C43—42no—
135C2×D4×C43—42no—
136C2×D4×C43C22⋊C411yescharacteristic
137C22×C4×C43—22no—
138C22×C4×C43—22no—
139C22×C4×C43—22no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43—42no—
144C22×C4×C43C22⋊C412yes—
145C22×C4×C43C22×C411yescharacteristic
146C22×C4×C43C2×D411yescharacteristic
147C22×C4×C43C2×D411yescharacteristic
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2×D411yescharacteristic
151C22×Dic43—41no—
152C22×Dic43—41no—
153C4⋊C4×C43—22no—
154C4⋊C4×C43—22no—
155C4⋊C4×C43—22no—
156C4⋊C4×C43—22no—
157C4⋊C4×C43—21no—
158C4⋊C4×C43—21no—
159C4⋊C4×C43—21no—
160C4⋊C4×C43—21no—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43C22⋊C411yescharacteristic
164C4⋊C4×C43C22⋊C411yescharacteristic
165C4⋊C4×C43C22⋊C411yescharacteristic
166C4⋊C4×C43C22⋊C411yescharacteristic
167C4⋊C4×C43C22⋊C411yescharacteristic
168C4⋊C4×C43C22⋊C411yescharacteristic
169C22⋊C4×C43—22no—
170C22⋊C4×C43—22no—
171C22⋊C4×C43—22no—
172C22⋊C4×C43—22no—
173C22⋊C4×C43—22no—
174C22⋊C4×C43—22no—
175C22⋊C4×C43—22no—
176C22⋊C4×C43—21no—
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—
185C42×C43—22no—
186C42×C43—21no—
187C42×C43—21no—
188C42×C43—21no—
189C42×C43—21no—
190C42×C43—21no—
191C22⋊Dic43—22no—
192C22⋊Dic43—41no—
193C22⋊Dic43—42no—
194C4⋊Dic43—42no—
195C4×Dic43—42no—
196#10621877—42no—
197C2×C43⋊C8—42no—
198C2×C43⋊C8—41no—
199C2×C43⋊C8—41no—
200C23×C43—21no—
201C23×C43—21no—
202C23×C43—22no—
203C23×C43—21no—
204C23×C43—41no—
205C23×C43—41no—
206C23×C43—42no—
207C23×C43—42no—
208C23×C43—42no—
209C23×C43C2×C22⋊C411yescharacteristic
210C23×C43#12011yescharacteristic
211C23×C43#12011yescharacteristic
212Q8×C43—41no—
213Q8×C43—82no—
214D4×C43—41no—
215D4×C43—42no—
216D4×C43—42no—
217D4×C43—42no—
218D4×C43—41no—
219D4×C43—42no—
220D4×C43—41no—
221D4×C43—42no—
222D4×C43—81no—
223D4×C43—82no—
224D4×C43—82no—
225D4×C43—82no—
226C2×C4×C43—22no—
227C2×C4×C43—22no—
228C2×C4×C43—22no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—22no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43—42no—
243C2×C4×C43—42no—
244C2×C4×C43—81no—
245C2×C4×C43—82no—
246C2×C4×C43—82no—
247C2×C4×C43—82no—
248C2×C4×C43C2×C22⋊C411yescharacteristic
249C2×C4×C43C2×C22⋊C411yescharacteristic
250C2×C4×C43#12011yescharacteristic
251C2×C4×C43#12011yescharacteristic
252C2×Dic43—42no—
253C2×Dic43—81no—
254C2×Dic43—81no—
255C2×Dic43—81no—
256C2×Dic43—81no—
257C2×Dic43—81no—
258C43⋊C8—81no—
259C43⋊C8—81no—
260#8466—431nomaximal, Sylow
261C22×C43—21no—
262C22×C43—21no—
263C22×C43—21no—
264C22×C43—21no—
265C22×C43—21no—
266C22×C43—21no—
267C22×C43—21no—
268C22×C43—21no—
269C22×C43—42no—
270C22×C43—41no—
271C22×C43—42no—
272C22×C43—41no—
273C22×C43—42no—
274C22×C43—41no—
275C22×C43—81no—
276C22×C43—81no—
277C22×C43—162no—
278C22×C43#37911yescharacteristic
279C22×C43#45311yescharacteristic
280C22×C43#45511yescharacteristic
281C4×C43—21no—
282C4×C43—21no—
283C4×C43—21no—
284C4×C43—41no—
285C4×C43—41no—
286C4×C43—42no—
287C4×C43—41no—
288C4×C43—41no—
289C4×C43—41no—
290C4×C43—41no—
291C4×C43—41no—
292C4×C43#41012yes—
293Dic43—82no—
294Dic43—161no—
295#3494D4311yescharacteristic
296#1964—431no—
297#1826—431no—
298#1825—431no—
299#1513—431no—
300#1501—431no—
301#1471—431no—
302C2×C43—21no—
303C2×C43—21no—
304C2×C43—41no—
305C2×C43—41no—
306C2×C43—81no—
307C2×C43—82no—
308C2×C43#178211yescharacteristic
309C2×C43#179211yescharacteristic
310C2×C43#179411yescharacteristic
311#555—21no—
312#553—21no—
313#553—21no—
314#551—22no—
315#547—21no—
316#546—22no—
317#544Dic4311yescharacteristic, complemented
318#542—21no—
319#540—21no—
320#535Dic4311yescharacteristic, complemented
321#532—21no—
322#529—21no—
323#525C2×D4311yescharacteristic
324C2×#121C2×D4311yescharacteristic
325#520Dic4311yescharacteristic, complemented
326#518Dic4311yescharacteristic, complemented
327C2×#117C2×D4311yescharacteristic
328C2×#99—862no—
329#407—431no—
330C2×C22⋊C8—431no—
331#380—431no—
332C4×C22⋊C4—431no—
333#340—861no—
334#340—861no—
335#339—861no—
336#339—861no—
337#328—861no—
338#328—861no—
339#327—861no—
340#327—861no—
341#323—862no—
342C43#846611yescharacteristic, complemented, Sylow
343C2×#41—22no—
344C2×#41C2×Dic4311yescharacteristic
345C22×D4C2×Dic4311yescharacteristic
346C22×D4C22⋊D4312yes—
347C23×C4C22×D4311yescharacteristic
348C2×M16—861no—
349C22×C8—861no—
350C4⋊Q8—21no—
351C4⋊Q8—21no—
352#127—21no—
353#126—22no—
354#126—22no—
355#125—21no—
356#125—21no—
357#124—22no—
358#124—22no—
359#124—21no—
360#123—22no—
361#123—22no—
362#123—22no—
363#123—22no—
364#123—21no—
365C22⋊Q8—22no—
366C22⋊Q8—22no—
367C22⋊Q8C22⋊D4311yescharacteristic
368C22⋊Q8C22⋊D4311yescharacteristic
369#121—22no—
370#121—22no—
371#121—22no—
372#121—21no—
373#121—21no—
374#121—21no—
375#121—21no—
376#121—21no—
377#121—21no—
378#121C22⋊D4311yescharacteristic
379#121C22⋊D4311yescharacteristic
380#120—22no—
381#120—21no—
382C4×Q8—21no—
383C4×D4—22no—
384C4×D4—22no—
385C4×D4—21no—
386C4×D4—22no—
387C4×D4—21no—
388C4×D4—21no—
389C4×D4—21no—
390C4×D4—21no—
391C4×D4—21no—
392C4×D4—21no—
393#117—22no—
394#117—21no—
395#117—21no—
396#117—21no—
397#117C2×Dic4311yescharacteristic
398#117C2×Dic4311yescharacteristic
399#117C2×Dic4311yescharacteristic
400#117C22⋊D4311yescharacteristic
401#117C22⋊D4311yescharacteristic
402C2×C4⋊C4—21no—
403C2×C4⋊C4—861no—
404C2×C4⋊C4C2×Dic4311yescharacteristic
405C2×C4⋊C4C22⋊D4311yescharacteristic
406C2×C4⋊C4C22⋊D4311yescharacteristic
407C2×C22⋊C4—22no—
408C2×C22⋊C4—21no—
409C2×C22⋊C4—861no—
410C2×C22⋊C4—861no—
411C2×C22⋊C4C22⋊D4312yes—
412C2×C42—21no—
413C2×C42—861no—
414#99—1724no—
415C22⋊C8—861no—
416C22⋊C8—861no—
417C22⋊C8—861no—
418C22⋊C8—861no—
419#95—861no—
420#95—861no—
421C24C22⋊Dic4312yes—
422C24C2×C22⋊D4311yescharacteristic
423#41—42no—
424#41—82no—
425#41—82no—
426C2×Q8—22no—
427C2×Q8C22⋊Dic4311yescharacteristic
428C2×D4—21no—
429C2×D4—21no—
430C2×D4—22no—
431C2×D4—22no—
432C2×D4—22no—
433C2×D4—21no—
434C2×D4—22no—
435C2×D4—21no—
436C2×D4—21no—
437C2×D4—42no—
438C2×D4—42no—
439C2×D4—42no—
440C2×D4C22⋊Dic4311yescharacteristic
441C22×C4—21no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—42no—
448C22×C4—1721no—
449C22×C4—1721no—
450C22×C4C22⋊Dic4312yes—
451C22×C4C22×Dic4311yescharacteristic
452C22×C4C2×C22⋊D4311yescharacteristic
453C22×C4C2×C22⋊D4311yescharacteristic
454C22×C4C2×C22⋊D4311yescharacteristic
455C22×C4C2×C22⋊D4311yescharacteristic
456C22×C4C2×C22⋊D4311yescharacteristic
457M16—1722no—
458C2×C8—1722no—
459C2×C8—1721no—
460C2×C8—1721no—
461C4⋊C4—22no—
462C4⋊C4—22no—
463C4⋊C4—22no—
464C4⋊C4—22no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—1722no—
472C4⋊C4C22⋊Dic4311yescharacteristic
473C4⋊C4C22⋊Dic4311yescharacteristic
474C4⋊C4C22⋊Dic4311yescharacteristic
475C4⋊C4C22⋊Dic4311yescharacteristic
476C4⋊C4C22⋊Dic4311yescharacteristic
477C4⋊C4C22⋊Dic4311yescharacteristic
478C22⋊C4—22no—
479C22⋊C4—22no—
480C22⋊C4—22no—
481C22⋊C4—22no—
482C22⋊C4—22no—
483C22⋊C4—21no—
484C22⋊C4—21no—
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—21no—
489C22⋊C4—21no—
490C22⋊C4—22no—
491C22⋊C4—22no—
492C22⋊C4—21no—
493C22⋊C4—21no—
494C22⋊C4—862no—
495C22⋊C4—1722no—
496C22⋊C4—1721no—
497C42—22no—
498C42—21no—
499C42—21no—
500C42—21no—
501C42—21no—
502C42—21no—
503C42—1722no—
504C23—21no—
505C23—21no—
506C23—22no—
507C23—21no—
508C23—41no—
509C23—41no—
510C23—42no—
511C23—42no—
512C23—42no—
513C23C2×C22⋊Dic4311yescharacteristic
514C23#1306329411yescharacteristic
515C23#1306329411yescharacteristic
516Q8—41no—
517Q8—82no—
518D4—41no—
519D4—42no—
520D4—42no—
521D4—42no—
522D4—41no—
523D4—42no—
524D4—41no—
525D4—42no—
526D4—82no—
527D4—81no—
528D4—82no—
529D4—82no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—22no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—81no—
549C2×C4—82no—
550C2×C4—82no—
551C2×C4—82no—
552C2×C4—3441no—
553C2×C4—3441no—
554C2×C4—3441no—
555C2×C4—3441no—
556C2×C4—3441no—
557C2×C4—1722no—
558C2×C4C2×C22⋊Dic4311yescharacteristic
559C2×C4C2×C22⋊Dic4311yescharacteristic
560C2×C4#1306329411yescharacteristic
561C2×C4#1306329411yescharacteristic
562C8—3441no—
563C8—3441no—
564C22—21no—
565C22—21no—
566C22—21no—
567C22—21no—
568C22—21no—
569C22—21no—
570C22—21no—
571C22—21no—
572C22—41no—
573C22—42no—
574C22—41no—
575C22—42no—
576C22—42no—
577C22—41no—
578C22—81no—
579C22—81no—
580C22—162no—
581C22#1458275511yescharacteristic
582C22#1458306711yescharacteristic
583C22#1458307711yescharacteristic
584C4—21no—
585C4—21no—
586C4—21no—
587C4—41no—
588C4—41no—
589C4—41no—
590C4—42no—
591C4—41no—
592C4—41no—
593C4—41no—
594C4—41no—
595C4—3442no—
596C4—6881no—
597C4#1458287312yes—
598C2—21no—
599C2—21no—
600C2—41no—
601C2—41no—
602C2—82no—
603C2—81no—
604C2#1913451311yescharacteristic
605C2#1913454911yescharacteristic
606C2#1913455911yescharacteristic
subgroupG/H
centerC22#14582755
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
Fitting, prime radicalC43×#3494C2
socleC22×C43#379
cosocleC23×C4×C43C23
hypercenter#3494D43
hypocenterC43#8466
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3494

Complements

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

NH ≅ G/Ntype
1. #19135432C2semidirect
2. #19134694C2semidirect
3. #19134690C2semidirect
4. #19133138C2semidirect
5. #19133086C2semidirect
6. #19132955C2semidirect
28. C43×#544C4semidirect
31. C43×#535C4semidirect
36. C43×#520C4semidirect
37. C43×#518C4semidirect
317. #544Dic43semidirect
320. #535Dic43semidirect
325. #520Dic43semidirect
326. #518Dic43semidirect
342. C43#8466semidirect

Maximal subgroups

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

subgroupindex
#191354322
#191346942
#191346902
#191331382
#191330862
#191329552
C43×#34942
#846643