Finite Group Databasebeta

← #25138063

Subgroups — #25138063

Order 11008.

706 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144411C211yesmaximal, characteristic, complemented
2C2×#14583190C211yesmaximal, characteristic, complemented
3C4×#13063353C211yesmaximal, characteristic
4#19143260C211yesmaximal, characteristic, complemented
5#19136042C212yesmaximal, complemented
6#19135889C212yesmaximal
7#19135584C211yesmaximal, characteristic, complemented
8#19135376C212yesmaximal, complemented
9#19135258C212yesmaximal, complemented
10#19134584C211yesmaximal, characteristic, complemented
11C43×#1950C211yesmaximal, characteristic, complemented
12C2×#13063353C2211yescharacteristic
13C2×#13063325C2211yescharacteristic
14C4×#10621898C2211yescharacteristic
15C2×C4×D172C2211yescharacteristic
16#14583195—21no—
17#14583190—21no—
18#14583190—21no—
19#14583190—21no—
20#14583190—22no—
21#14583185—21no—
22#14583180—21no—
23#14583012—21no—
24#14583001—21no—
25C4×#10621873—21no—
26C4×D344—21no—
27#14582959—22no—
28#14582955—21no—
29#14582951—21no—
30#14582941C2212yes—
31#14582941C2211yescharacteristic
32C2×#13063257C2212yes—
33#14582923C2211yescharacteristic
34#14582905C2211yescharacteristic
35#14582901C2211yescharacteristic
36#14582901C2212yes—
37C2×#13063247C2212yes—
38C2×#13063241C2212yes—
39#14582865C2212yes—
40#14582854C2212yes—
41#14582667C2212yes—
42#14582667C2212yes—
43#14582667C2212yes—
44C2×#108×C43C2212yes—
45C43×#423C2211yescharacteristic
46C2×C4⋊C8×C43C2211yescharacteristic
47C4×M16×C43C2211yescharacteristic
48C43×#341C2212yes—
49C2×#10621898C2311yescharacteristic
50C22×Dic86—21no—
51C22×D172C2311yescharacteristic
52C22×C4×D43—21no—
53#13063353—22no—
54#13063353—22no—
55C2×#10621873—21no—
56C2×D344—21no—
57C2×#10621877C2312yes—
58#13063325—21no—
59#13063325—21no—
60#13063325—21no—
61#13063325—21no—
62C4×Dic86D411yescharacteristic
63C4×Dic86D411yescharacteristic
64C4×D172—21no—
65C4×D172—21no—
66C4×D172—21no—
67C4×D172—21no—
68C4×D172D411yescharacteristic
69C4×D172D411yescharacteristic
70C4×C22⋊D43—21no—
71C4×C22⋊D43—21no—
72#13063284C2311yescharacteristic
73#13063282—21no—
74C2×C4⋊Dic43—21no—
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C4⋊Dic43C2312yes—
77C2×(C2×D43)⋊C4—21no—
78C42×D43—21no—
79#13063259—22no—
80#13063259—21no—
81#13063257—22no—
82#13063257—22no—
83#13063257—22no—
84#13063257—21no—
85C4⋊(C43⋊C8)—21no—
86C4⋊(C43⋊C8)—21no—
87#13063250—22no—
88#13063250—21no—
89#13063247—22no—
90#13063247—21no—
91#13063247—22no—
92#13063247—22no—
93#13063247—21no—
94#13063247—21no—
95#13063241—24no—
96(C2×D43)⋊C8—22no—
97(C2×D43)⋊C8—22no—
98#13063235—22no—
99C8×Dic43—22no—
100C2×M16×C43C2312yes—
101C2×M16×C43C2311yescharacteristic
102C2×M16×C43C2311yescharacteristic
103C22×C8×C43C2312yes—
104C2×C42×C43C2311yescharacteristic
105#108×C43—24no—
106C4⋊C8×C43—21no—
107C4⋊C8×C43—21no—
108C4⋊C8×C43D411yescharacteristic
109C4⋊C8×C43D411yescharacteristic
110C4⋊C8×C43D412yes—
111#97×C43—21no—
112C4×C8×C43—21no—
113C23×D43—21no—
114C22×C4×C43#4111yescharacteristic
115C22×C4×C43#4111yescharacteristic
116C22×C4×C43C2411yescharacteristic
117C2×C22⋊D43—21no—
118C22×Dic43—21no—
119C22×Dic43—22no—
120#10621898—21no—
121#10621898—21no—
122#10621898—21no—
123#10621898—21no—
124C2×D172—21no—
125C2×D172—21no—
126C2×D172—21no—
127C2×D172—21no—
128C2×D172—21no—
129C2×D172C2×D411yescharacteristic
130C2×D172#4112yes—
131C2×C4×D43—21no—
132C2×C4×D43—21no—
133C2×C4×D43—21no—
134C2×C4×D43—41no—
135C2×C4×D43—41no—
136C2×C4×D43—82no—
137C2×Dic86—41no—
138C2×Dic86—41no—
139C2×Dic86—82no—
140C2×Dic86C2×D411yescharacteristic
141M16×C43—21no—
142M16×C43—22no—
143M16×C43—22no—
144M16×C43—21no—
145M16×C43—21no—
146M16×C43#4112yes—
147C2×C8×C43—21no—
148C2×C8×C43—22no—
149C2×C8×C43—22no—
150C2×C8×C43—21no—
151C2×C8×C43—22no—
152C2×C8×C43C2×D412yes—
153C2×C8×C43C2×D412yes—
154C42×C43C2×D411yescharacteristic
155C42×C43C2×D411yescharacteristic
156C42×C43C2×D411yescharacteristic
157C42×C43C2×D411yescharacteristic
158C22⋊Dic43—21no—
159(C2×D43)⋊C4—21no—
160(C2×D43)⋊C4—21no—
161(C2×D43)⋊C4—41no—
162(C2×D43)⋊C4—41no—
163C4⋊Dic43—22no—
164C4⋊Dic43—21no—
165C4⋊Dic43—22no—
166C4⋊Dic43—21no—
167C4⋊Dic43—41no—
168C4⋊Dic43—41no—
169C4⋊Dic43C2×D411yescharacteristic
170C4⋊Dic43C2×D411yescharacteristic
171Dic43⋊C4—21no—
172Dic43⋊C4—21no—
173C4×Dic43—21no—
174C4×Dic43—21no—
175C4×Dic43—21no—
176#10621877—22no—
177#10621877—22no—
178C2×C43⋊C8—22no—
179D344—24no—
180#10621873—24no—
181C23×C43C2×#4111yescharacteristic
182C22×D43—21no—
183C22×D43—22no—
184C22×D43—41no—
185C22×D43—41no—
186C22×D43—81no—
187C22×D43—81no—
188C2×C4×C43—22no—
189C2×C4×C43—41no—
190C2×C4×C43#12111yescharacteristic
191C2×C4×C43#12111yescharacteristic
192C2×C4×C43#12111yescharacteristic
193C2×C4×C43#12111yescharacteristic
194C2×C4×C43C22×D411yescharacteristic
195C2×C4×C43C22×D411yescharacteristic
196C2×C4×C43C2×#4111yescharacteristic
197C2×C4×C43C2×#4111yescharacteristic
198C2×C4×C432−1+411yescharacteristic
199C2×C4×C432−1+411yescharacteristic
200C22⋊D43—41no—
201C22⋊D43—41no—
202C2×Dic43—21no—
203C2×Dic43—21no—
204C2×Dic43—21no—
205C2×Dic43—42no—
206C2×Dic43—41no—
207C2×Dic43—82no—
208C2×Dic43—81no—
209D172—22no—
210D172—21no—
211D172—21no—
212D172—22no—
213D172—41no—
214D172—41no—
215C4×D43—41no—
216C4×D43—41no—
217C4×D43—42no—
218C4×D43—81no—
219C4×D43—82no—
220C4×D43—82no—
221Dic86—21no—
222Dic86—21no—
223Dic86—82no—
224Dic86—82no—
225C8×C43—22no—
226C8×C43—22no—
227C8×C43—22no—
228C8×C43—42no—
229C8×C43—41no—
230C43⋊C8—42no—
231#24721—431nomaximal, Sylow
232C22×C43—21no—
233C22×C43—21no—
234C22×C43C2×#12111yescharacteristic
235C22×C43#55211yescharacteristic
236C22×C43#55611yescharacteristic
237C2×D43—42no—
238C2×D43—41no—
239C2×D43—41no—
240C2×D43—41no—
241C2×D43—82no—
242C2×D43—81no—
243C2×D43—81no—
244C2×D43—82no—
245C4×C43—21no—
246C4×C43—21no—
247C4×C43—21no—
248C4×C43#47112yes—
249C4×C43#52511yescharacteristic
250C4×C43#53611yescharacteristic
251C4×C43#54711yescharacteristic
252C4×C43#54811yescharacteristic
253Dic43—41no—
254Dic43—41no—
255Dic43—41no—
256Dic43—81no—
257Dic43—82no—
258#3079—431no—
259C2×#476—431no—
260C4×AGL(1,ℤ/8)—431no—
261#2925—431no—
262#2079—432no—
263#2051—432no—
264#1997—431no—
265#1951—432no—
266#1950D4311yescharacteristic, complemented
267#1931—432no—
268#1800—431no—
269C2×C43—21no—
270C2×C43—21no—
271C2×C43#241511yescharacteristic
272C2×C43C2×#47111yescharacteristic
273C2×C43#306811yescharacteristic
274D43—81no—
275D43—82no—
276C2×AGL(1,ℤ/8)—431no—
277C2×C4⋊Q8—431no—
278C4×#41—431no—
279C2×C4×D4—431no—
280#477—861no—
281#476—861no—
282#476—861no—
283#476—861no—
284#476—862no—
285#475—861no—
286#474—861no—
287#442—861no—
288#440—861no—
289C4×SD16—861no—
290C4×D8—861no—
291#433—862no—
292#432—861no—
293#431—861no—
294C2×#108C2×D4312yes—
295#428—432no—
296#428—431no—
297C2×#106—432no—
298#423—431no—
299#423C2×D4311yescharacteristic
300C2×C4⋊C8C2×D4311yescharacteristic
301#418—431no—
302#417—432no—
303#417—431no—
304C2×#102—432no—
305C2×#100—432no—
306#408—432no—
307#405—432no—
308C4×M16C2×D4311yescharacteristic
309#343—432no—
310#343—432no—
311#343—432no—
312#341C2×D4312yes—
313C43#2472111yescharacteristic, complemented, Sylow
314C2×#41—431no—
315C22×Q8—861no—
316C22×D4—431no—
317C23×C4—861no—
318AGL(1,ℤ/8)—862no—
319AGL(1,ℤ/8)—862no—
320C2×SD16—861no—
321C2×D8—861no—
322C2×M16—432no—
323C2×M16C22×D4311yescharacteristic
324C2×M16C22×D4312yes—
325C2×M16C22×D4311yescharacteristic
326C22×C8C22×D4312yes—
327C4⋊Q8—861no—
328C4⋊Q8—861no—
329C4⋊Q8—861no—
330C4⋊Q8—861no—
331C4×Q8—431no—
332C4×Q8—431no—
333C4×D4—431no—
334C4×D4—431no—
335C4×D4—861no—
336C4×D4—861no—
337C4×D4—861no—
338C4×D4—861no—
339C4×D4—861no—
340C4×D4—861no—
341#117—431no—
342#117—861no—
343C2×C4⋊C4—431no—
344C2×C4⋊C4—432no—
345C2×C4⋊C4—861no—
346C2×C22⋊C4—861no—
347C2×C42—861no—
348C2×C42C22×D4311yescharacteristic
349#108—24no—
350#107—861no—
351#107—862no—
352#106—861no—
353#106—862no—
354#106—862no—
355#106—862no—
356C4⋊C8—21no—
357C4⋊C8—21no—
358C4⋊C8—861no—
359C4⋊C8—861no—
360C4⋊C8D17211yescharacteristic
361C4⋊C8D17211yescharacteristic
362C4⋊C8D17212yes—
363#103—861no—
364#103—862no—
365#102—861no—
366#102—861no—
367#102—861no—
368#102—862no—
369#102—862no—
370#102—862no—
371#100—864no—
372C22⋊C8—862no—
373C22⋊C8—862no—
374#97—21no—
375#97—862no—
376C4×C8—21no—
377C4×C8—862no—
378C24—861no—
379#41—861no—
380#41—861no—
381#41—861no—
382#41—861no—
383C2×Q8—431no—
384C2×Q8—3442no—
385C2×Q8—1721no—
386C2×Q8—1721no—
387C2×D4—431no—
388C2×D4—432no—
389C2×D4—861no—
390C2×D4—861no—
391C2×D4—861no—
392C2×D4—861no—
393C2×D4—861no—
394C2×D4—861no—
395C22×C4—861no—
396C22×C4—861no—
397C22×C4—861no—
398C22×C4—861no—
399C22×C4—862no—
400C22×C4—3442no—
401C22×C4—1721no—
402C22×C4—1721no—
403C22×C4#1062190211yescharacteristic
404C22×C4#1062190211yescharacteristic
405C22×C4C23×D4311yescharacteristic
406SD16—864no—
407D8—864no—
408M16—21no—
409M16—22no—
410M16—22no—
411M16—21no—
412M16—21no—
413M16—862no—
414M16—862no—
415M16#1062190012yes—
416C2×C8—21no—
417C2×C8—22no—
418C2×C8—22no—
419C2×C8—21no—
420C2×C8—22no—
421C2×C8—862no—
422C2×C8C2×D17212yes—
423C2×C8C2×D17212yes—
424C4⋊C4—431no—
425C4⋊C4—431no—
426C4⋊C4—861no—
427C4⋊C4—861no—
428C4⋊C4—861no—
429C4⋊C4—862no—
430C4⋊C4—862no—
431C4⋊C4—861no—
432C4⋊C4—1721no—
433C4⋊C4—1721no—
434C22⋊C4—861no—
435C22⋊C4—861no—
436C22⋊C4—861no—
437C22⋊C4—1721no—
438C22⋊C4—1721no—
439C42—861no—
440C42—861no—
441C42—861no—
442C42C2×D17211yescharacteristic
443C42C2×D17211yescharacteristic
444C42D4×D4311yescharacteristic
445C42D4×D4311yescharacteristic
446C23—862no—
447C23—861no—
448C23—3441no—
449C23—3441no—
450C23—1721no—
451C23—1721no—
452C23C2×#1062190211yescharacteristic
453Q8—861no—
454Q8—861no—
455Q8—3442no—
456Q8—3442no—
457D4—862no—
458D4—861no—
459D4—862no—
460D4—861no—
461D4—1721no—
462D4—1721no—
463D4—1721no—
464D4—1721no—
465C2×C4—22no—
466C2×C4—41no—
467C2×C4—861no—
468C2×C4—861no—
469C2×C4—861no—
470C2×C4—3442no—
471C2×C4—3441no—
472C2×C4—3442no—
473C2×C4—3441no—
474C2×C4—3442no—
475C2×C4—1721no—
476C2×C4—1722no—
477C2×C4—1721no—
478C2×C4—1721no—
479C2×C4—1722no—
480C2×C4#1306330011yescharacteristic
481C2×C4#1306330011yescharacteristic
482C2×C4#1306330011yescharacteristic
483C2×C4#1306330011yescharacteristic
484C2×C4C2×D4×D4311yescharacteristic
485C2×C4C22×D17211yescharacteristic
486C2×C4#41×D4311yescharacteristic
487C2×C4C2×#1062190011yescharacteristic
488C2×C4#1306337211yescharacteristic
489C2×C4#1306337311yescharacteristic
490C8—22no—
491C8—22no—
492C8—22no—
493C8—42no—
494C8—41no—
495C8—1722no—
496C22—21no—
497C22—21no—
498C22—3442no—
499C22—3442no—
500C22—3441no—
501C22—3441no—
502C22—1721no—
503C22—1721no—
504C22—1721no—
505C22—1722no—
506C22C2×#1306330011yescharacteristic
507C22#1458358711yescharacteristic
508C22#1458362311yescharacteristic
509C4—21no—
510C4—21no—
511C4—21no—
512C4—3441no—
513C4—3442no—
514C4—1721no—
515C4—1721no—
516C4—1721no—
517C4#1458316312yes—
518C4#1458340911yescharacteristic
519C4#1458347211yescharacteristic
520C4#1458355311yescharacteristic
521C4#1458356111yescharacteristic
522C2—21no—
523C2—21no—
524C2—3442no—
525C2—3441no—
526C2#1913802211yescharacteristic
527C2C2×#1458316311yescharacteristic
528C2#1914432411yescharacteristic
subgroupG/H
centerC22C2×#13063300
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1950C2
socleC22×C43C2×#121
prime radicalC2×#13063353C22
hypercenter#1950D43
hypocenterC43#24721
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1950

Complements

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

NH ≅ G/Ntype
1. #19144411C2semidirect
2. C2×#14583190C2semidirect
4. #19143260C2semidirect
5. #19136042C2semidirect
7. #19135584C2semidirect
8. #19135376C2semidirect
9. #19135258C2semidirect
10. #19134584C2semidirect
11. C43×#1950C2semidirect
266. #1950D43semidirect
313. C43#24721semidirect

Maximal subgroups

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

subgroupindex
#191444112
C2×#145831902
C4×#130633532
#191432602
#191360422
#191358892
#191355842
#191353762
#191352582
#191345842
C43×#19502
#2472143