Finite Group Databasebeta

← #25108801

Subgroups — #25108801

Order 11008.

740 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583190C211yesmaximal, characteristic
2#19137343C211yesmaximal, characteristic, complemented
3#19137239C211yesmaximal, characteristic
4#19135546C211yesmaximal, characteristic, complemented
5#19135365C211yesmaximal, characteristic, complemented
6#19135338C211yesmaximal, characteristic, complemented
7#19135323C211yesmaximal, characteristic, complemented
8#19135292C211yesmaximal, characteristic
9#19135278C211yesmaximal, characteristic
10#19135223C211yesmaximal, characteristic
11#19135216C211yesmaximal, characteristic
12#19135181C211yesmaximal, characteristic, complemented
13#19135174C211yesmaximal, characteristic, complemented
14#19134606C211yesmaximal, characteristic
15C43×#1768C211yesmaximal, characteristic, complemented
16C2×#13063325C2211yescharacteristic
17C2×C4×D172C2211yescharacteristic
18#14583190C418yescomplemented
19C2×#13063259C2211yescharacteristic
20C2×#13063257C2211yescharacteristic
21C2×#13063257C2211yescharacteristic
22C2×#13063257C2211yescharacteristic
23C2×#13063247C2211yescharacteristic
24C2×#13063247C2211yescharacteristic
25C2×#13063247C2211yescharacteristic
26C2×#13063247C2211yescharacteristic
27#14582803—21no—
28#14582803—21no—
29#14582801C2211yescharacteristic
30#14582801C2211yescharacteristic
31#14582797C2211yescharacteristic
32#14582797C2211yescharacteristic
33#14582797C2211yescharacteristic
34#14582797C2211yescharacteristic
35#14582788—21no—
36#14582788—21no—
37#14582782—21no—
38#14582782—21no—
39#14582765C2211yescharacteristic
40#14582761—21no—
41#14582758—21no—
42C4×C4⋊Dic43C2211yescharacteristic
43C4×C4⋊Dic43C2211yescharacteristic
44C4×C4⋊Dic43C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582662C2211yescharacteristic
52#14582662C2211yescharacteristic
53C2×C4⋊C8×C43C2211yescharacteristic
54C2×C4⋊C8×C43C2211yescharacteristic
55C2×#97×C43C2211yescharacteristic
56C2×C4×C8×C43C2211yescharacteristic
57C43×#376C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C43×#336C2211yescharacteristic
60C22×Dic86—21no—
61C22×D172C2311yescharacteristic
62C22×C4×D43—21no—
63#13063325—22no—
64#13063325C2×C414yes—
65C4×D172—22no—
66C4×D172C2×C414yes—
67C2×C4⋊Dic43—21no—
68C2×C4⋊Dic43C2311yescharacteristic
69C2×C4⋊Dic43C2311yescharacteristic
70C2×C4⋊Dic43C2311yescharacteristic
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×Dic43⋊C4—21no—
76C2×Dic43⋊C4—21no—
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×(C2×D43)⋊C4—21no—
80C2×(C2×D43)⋊C4—21no—
81C2×(C2×D43)⋊C4—21no—
82C2×(C2×D43)⋊C4—21no—
83C2×(C2×D43)⋊C4—21no—
84C2×C4×Dic43—21no—
85C2×C4×Dic43—21no—
86C2×C4×Dic43—21no—
87#13063259—41no—
88#13063257—41no—
89#13063257C2×C414yes—
90#13063257C2×C414yes—
91#13063247—41no—
92#13063247—41no—
93#13063247C2×C414yes—
94#13063247C2×C414yes—
95C43⋊#95—21no—
96C43⋊#95—21no—
97C43⋊#95—21no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C22×C8×C43C2311yescharacteristic
105C22×C8×C43C2311yescharacteristic
106C22×C8×C43C2311yescharacteristic
107C22×C8×C43C2311yescharacteristic
108C2×C42×C43C2311yescharacteristic
109C2×C42×C43C2311yescharacteristic
110C2×C42×C43C2311yescharacteristic
111C4⋊C8×C43—22no—
112C4⋊C8×C43C2×C414yes—
113#97×C43—41no—
114C4×C8×C43—41no—
115#95×C43D411yescharacteristic
116#95×C43D411yescharacteristic
117#95×C43D411yescharacteristic
118#95×C43D411yescharacteristic
119C23×D43—21no—
120C22×C4×C43C2×D411yescharacteristic
121C22×C4×C43C2×D411yescharacteristic
122C22×C4×C43C2×D411yescharacteristic
123C22×C4×C43C2×D411yescharacteristic
124C22×C4×C43C2×D411yescharacteristic
125C22×C4×C43C2×D411yescharacteristic
126C22×C4×C43C2411yescharacteristic
127C22×Dic43—21no—
128C22×Dic43—21no—
129C22×Dic43—21no—
130C22×Dic43—21no—
131C22×Dic43—21no—
132C22×Dic43—21no—
133C22×Dic43—21no—
134C2×D172—21no—
135C2×D172—21no—
136C2×D172—21no—
137C2×D172—21no—
138C2×D172—21no—
139C2×D172C22×C412yes—
140C2×C4×D43—24no—
141C2×C4×D43—81no—
142C2×C4×D43—81no—
143C2×Dic86—24no—
144C2×Dic86—81no—
145C2×Dic86—81no—
146C2×C8×C43—21no—
147C2×C8×C43—21no—
148C2×C8×C43—21no—
149C2×C8×C43—21no—
150C2×C8×C43—21no—
151C2×C8×C43—21no—
152C2×C8×C43—21no—
153C2×C8×C43—21no—
154C2×C8×C43—21no—
155C2×C8×C43—21no—
156C2×C8×C43C22×C412yes—
157C2×C8×C43C22×C412yes—
158C42×C43—21no—
159C42×C43—21no—
160C42×C43—21no—
161C42×C43—21no—
162C42×C43C22×C412yes—
163C42×C43#4112yes—
164(C2×D43)⋊C4—24no—
165(C2×D43)⋊C4—81no—
166(C2×D43)⋊C4—81no—
167(C2×D43)⋊C4—81no—
168(C2×D43)⋊C4—81no—
169C4⋊Dic43—24no—
170C4⋊Dic43—21no—
171C4⋊Dic43—21no—
172C4⋊Dic43—21no—
173C4⋊Dic43—21no—
174C4⋊Dic43—21no—
175C4⋊Dic43—21no—
176C4⋊Dic43—21no—
177C4⋊Dic43—21no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43C22×C412yes—
182C4⋊Dic43C22×C412yes—
183C4⋊Dic43C22×C412yes—
184Dic43⋊C4—81no—
185Dic43⋊C4—81no—
186Dic43⋊C4—81no—
187Dic43⋊C4—81no—
188C4×Dic43—81no—
189C4×Dic43—81no—
190C4×Dic43—81no—
191C23×C43C22×D411yescharacteristic
192C22×D43—22no—
193C22×D43—41no—
194C22×D43—41no—
195C22×D43—41no—
196C22×D43—41no—
197C22×D43—41no—
198C22×D43—41no—
199C2×C4×C43—21no—
200C2×C4×C43—21no—
201C2×C4×C43—21no—
202C2×C4×C43—21no—
203C2×C4×C43—21no—
204C2×C4×C43—21no—
205C2×C4×C43—21no—
206C2×C4×C43—21no—
207C2×C4×C43—21no—
208C2×C4×C43—21no—
209C2×C4×C43—21no—
210C2×C4×C43—21no—
211C2×C4×C43—21no—
212C2×C4×C43—21no—
213C2×C4×C43—21no—
214C2×C4×C43—21no—
215C2×C4×C43C4×D412yes—
216C2×C4×C43C4×D412yes—
217C2×C4×C43C23×C411yescharacteristic
218C2×C4×C43C2×#4111yescharacteristic
219C2×C4×C43H(5,𝔽2)11yescharacteristic
220C2×C4×C432−1+411yescharacteristic
221C2×C4×C432−1+411yescharacteristic
222C2×C4×C432−1+411yescharacteristic
223C2×Dic43—22no—
224C2×Dic43—22no—
225C2×Dic43—22no—
226C2×Dic43—41no—
227C2×Dic43—41no—
228C2×Dic43—41no—
229C2×Dic43—41no—
230C2×Dic43—41no—
231C2×Dic43—41no—
232C2×Dic43—41no—
233C2×Dic43—41no—
234C2×Dic43—41no—
235C2×Dic43—41no—
236C2×Dic43—41no—
237C2×Dic43—41no—
238C2×Dic43—41no—
239C2×Dic43—41no—
240C2×Dic43—41no—
241C2×Dic43—41no—
242C2×Dic43—41no—
243C2×Dic43—41no—
244D172—22no—
245D172—22no—
246D172—41no—
247D172—41no—
248C4×D43—84no—
249Dic86—84no—
250C8×C43—22no—
251C8×C43—22no—
252C8×C43—41no—
253C8×C43—41no—
254#22123—431nomaximal, Sylow
255C22×C43C2×C4×D411yescharacteristic
256C22×C43#53611yescharacteristic
257C22×C43#53711yescharacteristic
258C22×C43#57611yescharacteristic
259C22×C43#57711yescharacteristic
260C22×C43#57711yescharacteristic
261C22×C43#57711yescharacteristic
262C2×D43—42no—
263C2×D43—42no—
264C2×D43—42no—
265C2×D43—81no—
266C2×D43—81no—
267C2×D43—81no—
268C2×D43—81no—
269C4×C43—22no—
270C4×C43—22no—
271C4×C43—41no—
272C4×C43—41no—
273C4×C43—41no—
274C4×C43—41no—
275C4×C43#51911yescharacteristic
276C4×C43#52011yescharacteristic
277C4×C43#54111yescharacteristic
278C4×C43#54211yescharacteristic
279Dic43—42no—
280Dic43—42no—
281Dic43—42no—
282Dic43—81no—
283Dic43—81no—
284Dic43—81no—
285Dic43—81no—
286C2×#476—431no—
287#2331—431no—
288#2319—431no—
289#1988—431no—
290#1949—431no—
291#1944—431no—
292#1941—431no—
293#1936—431no—
294#1934—431no—
295#1926—431no—
296#1925—431no—
297#1920—431no—
298#1919—431no—
299#1804—431no—
300#1768D4311yescharacteristic, complemented
301C2×C43#232311yescharacteristic
302C2×C43#294611yescharacteristic
303C2×C43#294911yescharacteristic
304C2×C43#324111yescharacteristic
305C2×C43#324411yescharacteristic
306C2×C43#325711yescharacteristic
307C2×C43#326311yescharacteristic
308D43—82no—
309C2×C4⋊Q8—431no—
310C2×C4×D4—431no—
311#476—438no—
312C2×#107—431no—
313C2×#106—431no—
314C2×#106—431no—
315C2×#106—431no—
316C2×C4⋊C8C2×D4311yescharacteristic
317C2×C4⋊C8C2×D4311yescharacteristic
318C2×#102—431no—
319C2×#102—431no—
320C2×#102—431no—
321C2×#102—431no—
322C2×#97C2×D4311yescharacteristic
323C2×C4×C8C2×D4311yescharacteristic
324#391—861no—
325#391—861no—
326#390—431no—
327#390—431no—
328#389—431no—
329#389—431no—
330#389—431no—
331#389—431no—
332#388—861no—
333#388—861no—
334#387—861no—
335#387—861no—
336#382—431no—
337#381—861no—
338#380—861no—
339C4×C4⋊C4—431no—
340C4×C4⋊C4—431no—
341C4×C4⋊C4—431no—
342#376C2×D4311yescharacteristic
343#340—431no—
344#340—431no—
345#340—431no—
346#340—431no—
347#340—431no—
348#340—431no—
349#340—431no—
350#340—431no—
351#336C2×D4311yescharacteristic
352#336C2×D4311yescharacteristic
353C43#2212311yescharacteristic, complemented, Sylow
354C22×Q8—861no—
355C22×D4—431no—
356C23×C4—861no—
357C22×C8C22×D4311yescharacteristic
358C22×C8C22×D4311yescharacteristic
359C22×C8C22×D4311yescharacteristic
360C22×C8C22×D4311yescharacteristic
361C4⋊Q8—434no—
362C4⋊Q8—862no—
363C4×D4—434no—
364C4×D4—862no—
365C2×C4⋊C4—431no—
366C2×C4⋊C4—431no—
367C2×C4⋊C4—431no—
368C2×C4⋊C4—431no—
369C2×C4⋊C4—431no—
370C2×C4⋊C4—431no—
371C2×C4⋊C4—431no—
372C2×C4⋊C4—861no—
373C2×C4⋊C4—861no—
374C2×C4⋊C4—861no—
375C2×C4⋊C4—861no—
376C2×C4⋊C4—861no—
377C2×C22⋊C4—861no—
378C2×C22⋊C4—861no—
379C2×C22⋊C4—861no—
380C2×C22⋊C4—861no—
381C2×C22⋊C4—861no—
382C2×C42—861no—
383C2×C42—861no—
384C2×C42—861no—
385C2×C42C22×D4311yescharacteristic
386C2×C42C22×D4311yescharacteristic
387C2×C42C22×D4311yescharacteristic
388#107—1721no—
389#106—434no—
390#106—434no—
391#106—1721no—
392C4⋊C8—22no—
393C4⋊C8C4×D4314yes—
394#102—434no—
395#102—434no—
396#102—1721no—
397#102—1721no—
398#97—41no—
399C4×C8—41no—
400#95—861no—
401#95—861no—
402#95—861no—
403#95—861no—
404#95—861no—
405#95—861no—
406#95—861no—
407#95—861no—
408#95—861no—
409#95D17211yescharacteristic
410#95D17211yescharacteristic
411#95D17211yescharacteristic
412#95D17211yescharacteristic
413C24—861no—
414C2×Q8—864no—
415C2×Q8—3441no—
416C2×Q8—3441no—
417C2×D4—432no—
418C2×D4—861no—
419C2×D4—861no—
420C2×D4—861no—
421C2×D4—861no—
422C2×D4—861no—
423C22×C4—861no—
424C22×C4—861no—
425C22×C4—861no—
426C22×C4—864no—
427C22×C4—861no—
428C22×C4—861no—
429C22×C4—861no—
430C22×C4—861no—
431C22×C4—3441no—
432C22×C4—3441no—
433C22×C4C2×D17211yescharacteristic
434C22×C4C2×D17211yescharacteristic
435C22×C4C2×D17211yescharacteristic
436C22×C4C2×D17211yescharacteristic
437C22×C4C2×D17211yescharacteristic
438C22×C4C2×D17211yescharacteristic
439C22×C4C23×D4311yescharacteristic
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8C2×C4×D4312yes—
451C2×C8C2×C4×D4312yes—
452C4⋊C4—432no—
453C4⋊C4—432no—
454C4⋊C4—432no—
455C4⋊C4—864no—
456C4⋊C4—861no—
457C4⋊C4—861no—
458C4⋊C4—861no—
459C4⋊C4—861no—
460C4⋊C4—861no—
461C4⋊C4—861no—
462C4⋊C4—861no—
463C4⋊C4—861no—
464C4⋊C4—861no—
465C4⋊C4—861no—
466C4⋊C4—861no—
467C4⋊C4—3441no—
468C4⋊C4—3441no—
469C4⋊C4—3441no—
470C4⋊C4—3441no—
471C22⋊C4—864no—
472C22⋊C4—3441no—
473C22⋊C4—3441no—
474C22⋊C4—3441no—
475C22⋊C4—3441no—
476C42—21no—
477C42—21no—
478C42—21no—
479C42—21no—
480C42—3441no—
481C42—3441no—
482C42—3441no—
483C42C2×C4×D4312yes—
484C42#1062189812yes—
485C23—862no—
486C23—1721no—
487C23—1721no—
488C23—1721no—
489C23—1721no—
490C23—1721no—
491C23—1721no—
492C23C22×D17211yescharacteristic
493Q8—3444no—
494D4—862no—
495D4—862no—
496D4—1721no—
497D4—1721no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—862no—
515C2×C4—862no—
516C2×C4—862no—
517C2×C4—3444no—
518C2×C4—1721no—
519C2×C4—1721no—
520C2×C4—1721no—
521C2×C4—1721no—
522C2×C4—1721no—
523C2×C4—1721no—
524C2×C4—1721no—
525C2×C4—1721no—
526C2×C4—1721no—
527C2×C4—1721no—
528C2×C4—1721no—
529C2×C4—1721no—
530C2×C4—1721no—
531C2×C4—1721no—
532C2×C4—1721no—
533C2×C4—1721no—
534C2×C4—1721no—
535C2×C4—1721no—
536C2×C4C4×D17212yes—
537C2×C4C4×D17212yes—
538C2×C4C22×C4×D4311yescharacteristic
539C2×C4C2×#1062189811yescharacteristic
540C2×C4#1306337011yescharacteristic
541C2×C4#1306337211yescharacteristic
542C2×C4#1306337211yescharacteristic
543C2×C4#1306337311yescharacteristic
544C8—22no—
545C8—22no—
546C8—41no—
547C8—41no—
548C22—3441no—
549C22—3441no—
550C22—3441no—
551C22—3441no—
552C22—1722no—
553C22—1722no—
554C22—1722no—
555C22C2×C4×D17211yescharacteristic
556C22#1458347511yescharacteristic
557C22#1458348011yescharacteristic
558C22#1458370411yescharacteristic
559C22#1458371111yescharacteristic
560C22#1458371111yescharacteristic
561C22#1458371111yescharacteristic
562C4—22no—
563C4—22no—
564C4—41no—
565C4—41no—
566C4—41no—
567C4—41no—
568C4—3441no—
569C4—3441no—
570C4—3441no—
571C4—3441no—
572C4—1722no—
573C4—1722no—
574C4—1722no—
575C4#1458337511yescharacteristic
576C4#1458337811yescharacteristic
577C4#1458350711yescharacteristic
578C4#1458351411yescharacteristic
579C2—3442no—
580C2#1913727811yescharacteristic
581C2#1914342911yescharacteristic
582C2#1914345611yescharacteristic
583C2#1914585011yescharacteristic
584C2#1914589511yescharacteristic
585C2#1914600811yescharacteristic
586C2#1914606611yescharacteristic
subgroupG/H
centerC23C22×D172
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1768C2
socleC23×C43C22×D4
prime radicalC22×D172C23
cosocleC22×C4×C43C24
hypercenter#1768D43
hypocenterC43#22123
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ #376 ◁ #1768

Complements

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

NH ≅ G/Ntype
2. #19137343C2semidirect
4. #19135546C2semidirect
5. #19135365C2semidirect
6. #19135338C2semidirect
7. #19135323C2semidirect
12. #19135181C2semidirect
13. #19135174C2semidirect
15. C43×#1768C2semidirect
18. #14583190C4semidirect
300. #1768D43semidirect
353. C43#22123semidirect

Maximal subgroups

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

subgroupindex
C2×#145831902
#191373432
#191372392
#191355462
#191353652
#191353382
#191353232
#191352922
#191352782
#191352232
#191352162
#191351812
#191351742
#191346062
C43×#17682
#2212343