Finite Group Databasebeta

← #25147009

Subgroups — #25147009

Order 11008.

732 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144989C211yesmaximal, characteristic
2C2×#14583184C211yesmaximal, characteristic, complemented
3#19144067C211yesmaximal, characteristic
4#19143341C211yesmaximal, characteristic
5#19136044C212yesmaximal, complemented
6#19135894C212yesmaximal, complemented
7#19135584C211yesmaximal, characteristic, complemented
8#19135370C211yesmaximal, characteristic, complemented
9#19135107C212yesmaximal, complemented
10#19134653C212yesmaximal, complemented
11C4×#101×C43C211yesmaximal, characteristic, complemented
12C2×#13063356C2212yes—
13C2×#13063333C2212yes—
14#14583449C2211yescharacteristic
15C2×#13063325C2211yescharacteristic
16#14583259—22no—
17#14583250—21no—
18#14583246—21no—
19#14583184—21no—
20#14583184—22no—
21#14583184—21no—
22#14583121—22no—
23#14583109—21no—
24#14583099—21no—
25#14582978—21no—
26#14582972—22no—
27C8×D172—21no—
28C2×#13063260C2212yes—
29C2×#13063256C2212yes—
30#14582923C2211yescharacteristic
31C2×C4⋊(C43⋊C8)C2211yescharacteristic
32#14582901C2212yes—
33#14582901C2212yes—
34#14582898C2212yes—
35C2×#13063249C2212yes—
36#14582867C2212yes—
37#14582667C2212yes—
38#14582667C2212yes—
39#14582663C2212yes—
40C2×C4×Q8×C43C2211yescharacteristic
41C2×#101×C43C2211yescharacteristic
42C2×#101×C43C2211yescharacteristic
43C4×M16×C43C2211yescharacteristic
44C4×M16×C43C2211yescharacteristic
45C43×#343C2211yescharacteristic
46C43×#343C2211yescharacteristic
47C2×#10621898C2312yes—
48C22×Dic86—21no—
49#13063356—24no—
50#13063356—42no—
51C2×#10621885—22no—
52C2×#10621884—22no—
53#13063333—24no—
54#13063333—42no—
55C2×#10621877C2312yes—
56C2×#10621872—22no—
57C22×C43⋊C8C2312yes—
58C2×C8×D43—22no—
59#13063325—21no—
60#13063325—21no—
61#13063325—21no—
62#13063325—21no—
63#13063325D411yescharacteristic
64#13063322D411yescharacteristic
65#13063313D412yes—
66#13063299—21no—
67#13063299—21no—
68C4×D172—21no—
69C4×D172—21no—
70C2×C4⋊Dic43—21no—
71C2×C4⋊Dic43C2312yes—
72#13063260—42no—
73#13063256—22no—
74#13063256—22no—
75C4⋊(C43⋊C8)—21no—
76C4⋊(C43⋊C8)—21no—
77C4⋊(C43⋊C8)D411yescharacteristic
78C4⋊(C43⋊C8)D412yes—
79C4⋊(C43⋊C8)D411yescharacteristic
80#13063250—22no—
81#13063250—22no—
82#13063249—22no—
83#13063249—22no—
84#13063248—22no—
85#13063247—22no—
86#13063247—22no—
87#13063245—22no—
88(C2×D43)⋊C8—22no—
89(C2×D43)⋊C8—22no—
90C22×Q8×C43C2311yescharacteristic
91C2×M16×C43C2311yescharacteristic
92C2×M16×C43C2311yescharacteristic
93C2×M16×C43C2311yescharacteristic
94C2×M16×C43C2311yescharacteristic
95C4×Q8×C43—21no—
96C4×Q8×C43—21no—
97C4×Q8×C43—21no—
98C4×Q8×C43—21no—
99C2×C4⋊C4×C43—21no—
100C2×C4⋊C4×C43C2311yescharacteristic
101C2×C42×C43—21no—
102C2×C42×C43C2311yescharacteristic
103#101×C43—22no—
104#101×C43—22no—
105#97×C43—21no—
106#97×C43—21no—
107C4×C8×C43—21no—
108C4×C8×C43—21no—
109C2×Q8×C43—21no—
110C2×Q8×C43—21no—
111C2×Q8×C43—21no—
112C2×Q8×C43—21no—
113C2×Q8×C43—21no—
114C2×Q8×C43#4112yes—
115C22×C4×C43—21no—
116C22×C4×C43—21no—
117C22×C4×C43#4111yescharacteristic
118C22×C4×C43#4111yescharacteristic
119C22×C4×C43C2411yescharacteristic
120C2×C22⋊D43—22no—
121C22×Dic43—22no—
122#10621898—22no—
123#10621898—22no—
124#10621898—22no—
125#10621898—22no—
126C2×D172—21no—
127C2×D172—21no—
128C2×D172C2×D412yes—
129C2×C4×D43—22no—
130C2×Dic86—41no—
131C2×Dic86—41no—
132C2×Dic86—82no—
133C2×Dic86C2×D412yes—
134M16×C43—21no—
135M16×C43—21no—
136M16×C43—21no—
137M16×C43—21no—
138M16×C43—21no—
139M16×C43—21no—
140M16×C43—21no—
141M16×C43#4112yes—
142C2×C8×C43—21no—
143C2×C8×C43—21no—
144C2×C8×C43—21no—
145C2×C8×C43—21no—
146C4⋊C4×C43—21no—
147C4⋊C4×C43—21no—
148C4⋊C4×C43—41no—
149C4⋊C4×C43—41no—
150C42×C43—41no—
151C42×C43—41no—
152C42×C43C2×D411yescharacteristic
153C42×C43C2×D411yescharacteristic
154C42×C43C2×D411yescharacteristic
155C42×C43C2×D411yescharacteristic
156#10621885—44no—
157#10621884—44no—
158(C2×D43)⋊C4—22no—
159(C2×D43)⋊C4—22no—
160C4⋊Dic43—21no—
161C4⋊Dic43—21no—
162C4⋊Dic43—22no—
163C4⋊Dic43—22no—
164C4⋊Dic43—41no—
165C4⋊Dic43—41no—
166#10621877—22no—
167#10621877—22no—
168C2×C43⋊C8—22no—
169C2×C43⋊C8—22no—
170C2×C43⋊C8—22no—
171C2×C43⋊C8C2×D412yes—
172C2×C43⋊C8C2×D412yes—
173#10621872—44no—
174C8×D43—44no—
175C23×C43C2×#4111yescharacteristic
176C22×D43—22no—
177Q8×C43—22no—
178Q8×C43—22no—
179Q8×C43—41no—
180Q8×C43—41no—
181C2×C4×C43—22no—
182C2×C4×C43—22no—
183C2×C4×C43—41no—
184C2×C4×C43—41no—
185C2×C4×C43—41no—
186C2×C4×C43—41no—
187C2×C4×C43—81no—
188C2×C4×C43#12111yescharacteristic
189C2×C4×C43#12111yescharacteristic
190C2×C4×C43#12111yescharacteristic
191C2×C4×C43#12111yescharacteristic
192C2×C4×C43C22×D411yescharacteristic
193C2×C4×C43C22×D411yescharacteristic
194C2×C4×C43C2×#4111yescharacteristic
195C2×C4×C43C2×#4111yescharacteristic
196C2×C4×C43H(5,𝔽2)11yescharacteristic
197C2×C4×C432−1+411yescharacteristic
198C22⋊D43—42no—
199C22⋊D43—42no—
200C2×Dic43—22no—
201C2×Dic43—42no—
202C2×Dic43—82no—
203D172—22no—
204D172—22no—
205D172—42no—
206D172—81no—
207C4×D43—42no—
208C4×D43—42no—
209Dic86—22no—
210Dic86—22no—
211Dic86—82no—
212Dic86—82no—
213C8×C43—22no—
214C8×C43—41no—
215C8×C43—41no—
216C8×C43—41no—
217C43⋊C8—22no—
218C43⋊C8—22no—
219C43⋊C8—42no—
220#25361—431nomaximal, Sylow
221C22×C43—21no—
222C22×C43—21no—
223C22×C43C2×#12111yescharacteristic
224C22×C43#52911yescharacteristic
225C22×C43#54211yescharacteristic
226C2×D43—42no—
227C2×D43—42no—
228C2×D43—42no—
229C4×C43—21no—
230C4×C43—21no—
231C4×C43—21no—
232C4×C43—42no—
233C4×C43—81no—
234C4×C43#47112yes—
235C4×C43#54611yescharacteristic
236C4×C43#54611yescharacteristic
237C4×C43#54711yescharacteristic
238C4×C43#54811yescharacteristic
239Dic43—42no—
240Dic43—82no—
241#3141—431no—
242C2×#475—431no—
243#3037—431no—
244#2935—431no—
245#2079—432no—
246#2052—432no—
247#1997—431no—
248#1950—431no—
249#1908—432no—
250#1815—432no—
251C4×#101D4311yescharacteristic, complemented
252C2×C43—21no—
253C2×C43—21no—
254C2×C43#242711yescharacteristic
255C2×C43C2×#47111yescharacteristic
256C2×C43#306911yescharacteristic
257D43—82no—
258C2×#137—432no—
259C2×#131—432no—
260#532—431no—
261C2×C4⋊Q8—431no—
262C2×C4×Q8C2×D4311yescharacteristic
263#489—862no—
264#487—861no—
265#486—861no—
266#475—861no—
267#475—862no—
268#475—861no—
269#464—862no—
270#462—861no—
271#460—861no—
272#436—861no—
273#435—862no—
274C8×D4—861no—
275C2×#108—432no—
276C2×#106—432no—
277#423—431no—
278C2×C4⋊C8—431no—
279#417—432no—
280#417—432no—
281#417—432no—
282C2×#103—432no—
283C2×#101C2×D4311yescharacteristic
284C2×#101C2×D4311yescharacteristic
285#408—432no—
286C4×M16C2×D4311yescharacteristic
287C4×M16C2×D4311yescharacteristic
288#343—432no—
289#343—432no—
290#343C2×D4311yescharacteristic
291#343C2×D4311yescharacteristic
292#341—432no—
293C43#2536111yescharacteristic, complemented, Sylow
294C2×#41—432no—
295C22×Q8—861no—
296C22×Q8C22×D4311yescharacteristic
297#137—864no—
298#137—1722no—
299C2×Q16—862no—
300C2×SD16—862no—
301#131—864no—
302#131—1722no—
303C2×M16—432no—
304C2×M16—862no—
305C2×M16C22×D4311yescharacteristic
306C2×M16C22×D4311yescharacteristic
307C2×M16C22×D4311yescharacteristic
308C2×M16C22×D4311yescharacteristic
309C22×C8—432no—
310C22×C8—862no—
311C4⋊Q8—431no—
312C4⋊Q8—861no—
313C4⋊Q8—861no—
314C4⋊Q8—861no—
315C4⋊Q8—861no—
316#127—431no—
317#124—432no—
318#121—861no—
319#121—861no—
320C4×Q8—21no—
321C4×Q8—21no—
322C4×Q8—21no—
323C4×Q8—21no—
324C4×D4—861no—
325C4×D4—861no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—432no—
328C2×C4⋊C4—861no—
329C2×C4⋊C4C22×D4311yescharacteristic
330C2×C42—21no—
331C2×C42C22×D4311yescharacteristic
332#108—1722no—
333#106—862no—
334#106—862no—
335C4⋊C8—431no—
336C4⋊C8—432no—
337C4⋊C8—431no—
338C4⋊C8—861no—
339C4⋊C8—861no—
340#103—862no—
341#103—862no—
342#103—862no—
343#103—862no—
344#103—862no—
345#102—862no—
346#102—862no—
347#102—862no—
348#101—22no—
349#101—22no—
350C22⋊C8—862no—
351C22⋊C8—862no—
352#97—21no—
353#97—21no—
354C4×C8—21no—
355C4×C8—21no—
356#41—862no—
357#41—862no—
358#41—862no—
359#41—862no—
360C2×Q8—21no—
361C2×Q8—21no—
362C2×Q8—21no—
363C2×Q8—21no—
364C2×Q8—21no—
365C2×Q8—432no—
366C2×Q8—3442no—
367C2×Q8—1721no—
368C2×Q8—1721no—
369C2×Q8#1062189812yes—
370C2×D4—432no—
371C2×D4—862no—
372C2×D4—861no—
373C2×D4—861no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—862no—
377C22×C4—862no—
378C22×C4#1062189811yescharacteristic
379C22×C4#1062189811yescharacteristic
380C22×C4C23×D4311yescharacteristic
381Q16—1724no—
382SD16—1724no—
383M16—21no—
384M16—21no—
385M16—21no—
386M16—21no—
387M16—21no—
388M16—21no—
389M16—21no—
390M16—862no—
391M16—862no—
392M16—1724no—
393M16#1062189812yes—
394C2×C8—21no—
395C2×C8—21no—
396C2×C8—21no—
397C2×C8—21no—
398C2×C8—432no—
399C2×C8—432no—
400C2×C8—862no—
401C2×C8—862no—
402C2×C8—862no—
403C2×C8—1724no—
404C4⋊C4—21no—
405C4⋊C4—21no—
406C4⋊C4—41no—
407C4⋊C4—41no—
408C4⋊C4—861no—
409C4⋊C4—861no—
410C4⋊C4—862no—
411C4⋊C4—862no—
412C4⋊C4—1721no—
413C4⋊C4—1721no—
414C22⋊C4—862no—
415C22⋊C4—862no—
416C42—41no—
417C42—41no—
418C42D4×D4311yescharacteristic
419C42D4×D4311yescharacteristic
420C42D4×D4311yescharacteristic
421C42D4×D4311yescharacteristic
422C23—862no—
423C23C2×#1062189811yescharacteristic
424Q8—22no—
425Q8—22no—
426Q8—41no—
427Q8—41no—
428Q8—862no—
429Q8—862no—
430Q8—3442no—
431Q8—3442no—
432D4—862no—
433D4—862no—
434D4—3441no—
435D4—1722no—
436D4—1722no—
437D4—1722no—
438C2×C4—22no—
439C2×C4—22no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—81no—
445C2×C4—862no—
446C2×C4—3442no—
447C2×C4—1722no—
448C2×C4—1722no—
449C2×C4—1722no—
450C2×C4#1306329811yescharacteristic
451C2×C4#1306329811yescharacteristic
452C2×C4#1306329811yescharacteristic
453C2×C4#1306329811yescharacteristic
454C2×C4C2×D4×D4311yescharacteristic
455C2×C4C2×D4×D4311yescharacteristic
456C2×C4C2×#1062189811yescharacteristic
457C2×C4C2×#1062189811yescharacteristic
458C2×C4#1306337111yescharacteristic
459C2×C4#1306337211yescharacteristic
460C8—22no—
461C8—41no—
462C8—41no—
463C8—41no—
464C8—862no—
465C8—862no—
466C8—1722no—
467C22—21no—
468C22—21no—
469C22—1722no—
470C22—1722no—
471C22—1722no—
472C22C2×#1306329811yescharacteristic
473C22#1458343311yescharacteristic
474C22#1458352011yescharacteristic
475C4—21no—
476C4—21no—
477C4—21no—
478C4—42no—
479C4—81no—
480C4—3442no—
481C4—1722no—
482C4#1458316512yes—
483C4#1458354511yescharacteristic
484C4#1458354511yescharacteristic
485C4#1458355411yescharacteristic
486C4#1458355811yescharacteristic
487C2—21no—
488C2—21no—
489C2—3442no—
490C2#1913817211yescharacteristic
491C2C2×#1458316511yescharacteristic
492C2#1914433511yescharacteristic
subgroupG/H
centerC22C2×#13063298
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC4×#101×C43C2
socleC22×C43C2×#121
prime radical#14583449C22
hypercenterC4×#101D43
hypocenterC43#25361
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×#101

Complements

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

NH ≅ G/Ntype
2. C2×#14583184C2semidirect
5. #19136044C2semidirect
6. #19135894C2semidirect
7. #19135584C2semidirect
8. #19135370C2semidirect
9. #19135107C2semidirect
10. #19134653C2semidirect
11. C4×#101×C43C2semidirect
251. C4×#101D43semidirect
293. C43#25361semidirect

Maximal subgroups

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

subgroupindex
#191449892
C2×#145831842
#191440672
#191433412
#191360442
#191358942
#191355842
#191353702
#191351072
#191346532
C4×#101×C432
#2536143