Finite Group Databasebeta

← #25146979

Subgroups — #25146979

Order 11008.

764 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583176C211yesmaximal, characteristic, complemented
2#19144055C211yesmaximal, characteristic
3#19143339C211yesmaximal, characteristic, complemented
4#19136038C212yesmaximal, complemented
5#19135885C212yesmaximal, complemented
6#19135585C211yesmaximal, characteristic, complemented
7#19135370C211yesmaximal, characteristic, complemented
8#19135101C212yesmaximal, complemented
9#19134657C212yesmaximal, complemented
10C4×#13063241C211yesmaximal, characteristic, complemented
11C43×#3141C211yesmaximal, characteristic, complemented
12C2×#13063350C2212yes—
13C2×#13063332C2212yes—
14C2×C4×D172C2211yescharacteristic
15#14583176—21no—
16#14583176—22no—
17#14583176—21no—
18#14583111—22no—
19#14583101—21no—
20#14583091—21no—
21#14582977—21no—
22#14582971—22no—
23D4×C43⋊C8—21no—
24C2×#13063260C2212yes—
25C2×#13063258C2212yes—
26#14582923C2211yescharacteristic
27C2×C4⋊(C43⋊C8)C2211yescharacteristic
28#14582900C2212yes—
29C2×#13063245C2212yes—
30C2×#13063241C2211yescharacteristic
31C2×#13063241C2211yescharacteristic
32#14582866C2212yes—
33C4×#10621877C2211yescharacteristic
34#14582668C2212yes—
35#14582668C2212yes—
36#14582667C2211yescharacteristic
37#14582667C2211yescharacteristic
38#14582663C2212yes—
39C43×#532C2211yescharacteristic
40C2×C4⋊Q8×C43C2211yescharacteristic
41C43×#489—22no—
42C43×#487—21no—
43C43×#486—21no—
44C43×#417C2212yes—
45C43×#417C2212yes—
46C4×M16×C43C2211yescharacteristic
47C22×D172C2311yescharacteristic
48C22×C4×D43—21no—
49#13063350—24no—
50#13063350—42no—
51C2×#10621884—22no—
52C2×#10621882—22no—
53#13063332—24no—
54#13063332—42no—
55C2×#10621877—22no—
56C2×#10621877C2311yescharacteristic
57C2×#10621877C2312yes—
58C2×#10621877C2311yescharacteristic
59C22×C43⋊C8—22no—
60C22×C43⋊C8C2312yes—
61C4×D172—21no—
62C4×D172—21no—
63C4×D172—21no—
64C4×D172—21no—
65C2×C4⋊Dic43C2311yescharacteristic
66C2×(C2×D43)⋊C4—21no—
67#13063260—42no—
68#13063258—22no—
69#13063258—22no—
70C4⋊(C43⋊C8)—21no—
71C4⋊(C43⋊C8)—21no—
72C4⋊(C43⋊C8)D411yescharacteristic
73C4⋊(C43⋊C8)D412yes—
74C4⋊(C43⋊C8)D411yescharacteristic
75#13063249—22no—
76#13063246—22no—
77#13063245—22no—
78#13063245—22no—
79#13063241—22no—
80#13063241—22no—
81C22⋊(C43⋊C8)—22no—
82C22⋊(C43⋊C8)—22no—
83#13063236—21no—
84C4×C43⋊C8—21no—
85C2×#41×C43C2312yes—
86C22×Q8×C43—21no—
87C2×M16×C43C2311yescharacteristic
88C2×M16×C43C2311yescharacteristic
89C4⋊Q8×C43—21no—
90C4⋊Q8×C43—21no—
91C4⋊Q8×C43—21no—
92C4⋊Q8×C43—21no—
93C4⋊Q8×C43D411yescharacteristic
94#127×C43D411yescharacteristic
95#124×C43D412yes—
96#121×C43—21no—
97#121×C43—21no—
98C4×D4×C43—21no—
99C4×D4×C43—21no—
100C2×C4⋊C4×C43—21no—
101C2×C4⋊C4×C43C2312yes—
102C2×C42×C43C2311yescharacteristic
103#103×C43—22no—
104#103×C43—22no—
105#102×C43—22no—
106#102×C43—22no—
107#97×C43—21no—
108C4×C8×C43—21no—
109C23×D43—21no—
110#41×C43—22no—
111#41×C43—22no—
112#41×C43—22no—
113#41×C43—22no—
114C2×Q8×C43—41no—
115C2×Q8×C43—41no—
116C2×Q8×C43—82no—
117C2×Q8×C43C2×D412yes—
118C2×D4×C43—21no—
119C2×D4×C43—21no—
120C2×D4×C43—22no—
121C2×D4×C43C2×D412yes—
122C22×C4×C43—22no—
123C22×C4×C43—22no—
124C22×C4×C43#4111yescharacteristic
125C22×C4×C43#4111yescharacteristic
126C22×C4×C43C2411yescharacteristic
127C22×Dic43—21no—
128C2×D172—21no—
129C2×D172—21no—
130C2×D172—21no—
131C2×D172—21no—
132C2×D172—21no—
133C2×D172#4112yes—
134C2×C4×D43—41no—
135C2×C4×D43—41no—
136C2×C4×D43—82no—
137M16×C43—21no—
138M16×C43—21no—
139M16×C43—21no—
140M16×C43—21no—
141C2×C8×C43—21no—
142C2×C8×C43—21no—
143C4⋊C4×C43—21no—
144C4⋊C4×C43—21no—
145C4⋊C4×C43—22no—
146C4⋊C4×C43—22no—
147C4⋊C4×C43—41no—
148C4⋊C4×C43—41no—
149C22⋊C4×C43—22no—
150C22⋊C4×C43—22no—
151C42×C43C2×D411yescharacteristic
152C42×C43C2×D411yescharacteristic
153C42×C43C2×D411yescharacteristic
154C42×C43C2×D411yescharacteristic
155#10621884—44no—
156#10621882—44no—
157(C2×D43)⋊C4—41no—
158(C2×D43)⋊C4—41no—
159C4⋊Dic43—21no—
160C4⋊Dic43—21no—
161#10621877—21no—
162#10621877—21no—
163#10621877—22no—
164#10621877—22no—
165#10621877—21no—
166#10621877—44no—
167#10621877#4112yes—
168C2×C43⋊C8—21no—
169C2×C43⋊C8—22no—
170C2×C43⋊C8—22no—
171C2×C43⋊C8—21no—
172C2×C43⋊C8—22no—
173C2×C43⋊C8—44no—
174C2×C43⋊C8C2×D412yes—
175C2×C43⋊C8C2×D412yes—
176C23×C43—22no—
177C23×C43C2×#4111yescharacteristic
178C22×D43—22no—
179C22×D43—41no—
180C22×D43—41no—
181C22×D43—81no—
182C22×D43—81no—
183Q8×C43—22no—
184Q8×C43—22no—
185Q8×C43—82no—
186Q8×C43—82no—
187D4×C43—22no—
188D4×C43—22no—
189D4×C43—42no—
190D4×C43—42no—
191D4×C43—42no—
192D4×C43—81no—
193C2×C4×C43—22no—
194C2×C4×C43—22no—
195C2×C4×C43—41no—
196C2×C4×C43—42no—
197C2×C4×C43—42no—
198C2×C4×C43—42no—
199C2×C4×C43—82no—
200C2×C4×C43#12111yescharacteristic
201C2×C4×C43#12111yescharacteristic
202C2×C4×C43#12111yescharacteristic
203C2×C4×C43#12111yescharacteristic
204C2×C4×C43C22×D411yescharacteristic
205C2×C4×C43C22×D411yescharacteristic
206C2×C4×C43C2×#4111yescharacteristic
207C2×C4×C43C2×#4111yescharacteristic
208C2×C4×C43H(5,𝔽2)11yescharacteristic
209C2×C4×C432−1+411yescharacteristic
210C2×Dic43—41no—
211C2×Dic43—81no—
212D172—22no—
213D172—22no—
214D172—41no—
215D172—41no—
216C4×D43—82no—
217C4×D43—82no—
218C8×C43—41no—
219C8×C43—41no—
220C43⋊C8—22no—
221C43⋊C8—22no—
222C43⋊C8—22no—
223C43⋊C8—42no—
224C43⋊C8—41no—
225#25358—431nomaximal, Sylow
226C22×C43—21no—
227C22×C43—21no—
228C22×C43—42no—
229C22×C43—42no—
230C22×C43—42no—
231C22×C43C2×#12111yescharacteristic
232C22×C43#52911yescharacteristic
233C22×C43#54211yescharacteristic
234C2×D43—42no—
235C2×D43—82no—
236C2×D43—81no—
237C2×D43—81no—
238C2×D43—82no—
239C4×C43—21no—
240C4×C43—21no—
241C4×C43—21no—
242C4×C43—42no—
243C4×C43—82no—
244C4×C43#47212yes—
245C4×C43#54611yescharacteristic
246C4×C43#54611yescharacteristic
247C4×C43#54711yescharacteristic
248C4×C43#54811yescharacteristic
249Dic43—81no—
250#3141D4311yescharacteristic, complemented
251C2×#474—431no—
252#3036—431no—
253#2935—431no—
254#2078—432no—
255#2051—432no—
256#1997—431no—
257#1950—431no—
258#1907—432no—
259#1816—432no—
260C4×#100—431no—
261C2×C43—21no—
262C2×C43—21no—
263C2×C43—82no—
264C2×C43#242711yescharacteristic
265C2×C43C2×#47211yescharacteristic
266C2×C43#306911yescharacteristic
267D43—82no—
268C2×AGL(1,ℤ/8)—432no—
269C2×#131—432no—
270#532C2×D4311yescharacteristic
271C2×C4⋊Q8C2×D4311yescharacteristic
272C2×C4×D4—431no—
273#489—22no—
274#487—21no—
275#486—21no—
276#474—861no—
277#474—862no—
278#474—861no—
279#463—862no—
280#461—861no—
281#459—861no—
282#436—861no—
283#435—862no—
284C8×D4—861no—
285C2×#108—432no—
286C2×#107—432no—
287#423—431no—
288C2×C4⋊C8—431no—
289#417—432no—
290#417C2×D4312yes—
291#417C2×D4312yes—
292C2×#102—432no—
293C2×#100—431no—
294C2×#100—431no—
295#408—432no—
296C4×M16—431no—
297C4×M16C2×D4311yescharacteristic
298#343—431no—
299#343—431no—
300#343—432no—
301#343—432no—
302#341—432no—
303C43#2535811yescharacteristic, complemented, Sylow
304C2×#41C22×D4312yes—
305C22×Q8—21no—
306C22×D4—431no—
307C23×C4—861no—
308AGL(1,ℤ/8)—864no—
309AGL(1,ℤ/8)—1722no—
310C2×SD16—862no—
311C2×D8—862no—
312#131—864no—
313#131—1722no—
314C2×M16—431no—
315C2×M16—432no—
316C2×M16—431no—
317C2×M16—862no—
318C2×M16C22×D4311yescharacteristic
319C2×M16C22×D4311yescharacteristic
320C22×C8—432no—
321C22×C8—862no—
322C4⋊Q8—21no—
323C4⋊Q8—21no—
324C4⋊Q8—21no—
325C4⋊Q8—21no—
326C4⋊Q8C22⋊D4311yescharacteristic
327#127C22⋊D4311yescharacteristic
328#124C22⋊D4312yes—
329#121—21no—
330#121—21no—
331C4×D4—21no—
332C4×D4—21no—
333C4×D4—861no—
334C4×D4—861no—
335C4×D4—861no—
336C4×D4—861no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—431no—
339C2×C4⋊C4C22×D4312yes—
340C2×C22⋊C4—861no—
341C2×C42C22×D4311yescharacteristic
342#108—1722no—
343#107—862no—
344#107—862no—
345C4⋊C8—431no—
346C4⋊C8—432no—
347C4⋊C8—431no—
348C4⋊C8—861no—
349C4⋊C8—861no—
350#103—22no—
351#103—22no—
352#103—862no—
353#102—22no—
354#102—22no—
355#102—862no—
356#102—862no—
357#102—862no—
358#100—862no—
359#100—862no—
360C22⋊C8—862no—
361C22⋊C8—862no—
362#97—21no—
363#97—861no—
364C4×C8—21no—
365C4×C8—861no—
366C24—861no—
367#41—22no—
368#41—22no—
369#41—22no—
370#41—22no—
371C2×Q8—41no—
372C2×Q8—41no—
373C2×Q8—82no—
374C2×Q8C2×C22⋊D4312yes—
375C2×D4—22no—
376C2×D4—21no—
377C2×D4—21no—
378C2×D4—432no—
379C2×D4—861no—
380C2×D4—861no—
381C2×D4—861no—
382C2×D4—861no—
383C2×D4—861no—
384C2×D4C2×C22⋊D4312yes—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—861no—
388C22×C4—3442no—
389C22×C4—1721no—
390C22×C4—1721no—
391C22×C4#1062190011yescharacteristic
392C22×C4#1062190011yescharacteristic
393C22×C4C23×D4311yescharacteristic
394SD16—1724no—
395D8—1724no—
396M16—21no—
397M16—21no—
398M16—21no—
399M16—21no—
400M16—432no—
401M16—861no—
402M16—861no—
403M16—862no—
404M16—862no—
405M16—861no—
406M16—1724no—
407C2×C8—21no—
408C2×C8—21no—
409C2×C8—432no—
410C2×C8—432no—
411C2×C8—861no—
412C2×C8—862no—
413C2×C8—862no—
414C2×C8—861no—
415C2×C8—862no—
416C2×C8—1724no—
417C4⋊C4—21no—
418C4⋊C4—21no—
419C4⋊C4—22no—
420C4⋊C4—22no—
421C4⋊C4—41no—
422C4⋊C4—41no—
423C4⋊C4—861no—
424C4⋊C4—861no—
425C22⋊C4—22no—
426C22⋊C4—22no—
427C22⋊C4—1721no—
428C22⋊C4—1721no—
429C42D4×D4311yescharacteristic
430C42D4×D4311yescharacteristic
431C42C2×C22⋊D4311yescharacteristic
432C42C2×C22⋊D4311yescharacteristic
433C23—22no—
434C23—862no—
435C23—3441no—
436C23—3441no—
437C23—1721no—
438C23—1721no—
439C23C2×#1062190011yescharacteristic
440Q8—22no—
441Q8—22no—
442Q8—82no—
443Q8—82no—
444D4—22no—
445D4—22no—
446D4—42no—
447D4—42no—
448D4—42no—
449D4—81no—
450D4—862no—
451D4—862no—
452D4—1721no—
453D4—1721no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—41no—
457C2×C4—42no—
458C2×C4—42no—
459C2×C4—42no—
460C2×C4—82no—
461C2×C4—3442no—
462C2×C4—3442no—
463C2×C4—3441no—
464C2×C4—1721no—
465C2×C4#1306329711yescharacteristic
466C2×C4#1306329711yescharacteristic
467C2×C4#1306329711yescharacteristic
468C2×C4#1306329711yescharacteristic
469C2×C4C2×D4×D4311yescharacteristic
470C2×C4C22×C22⋊D4311yescharacteristic
471C2×C4#41×D4311yescharacteristic
472C2×C4#41×D4311yescharacteristic
473C2×C4#1306337111yescharacteristic
474C2×C4#1306337211yescharacteristic
475C8—41no—
476C8—41no—
477C8—862no—
478C8—862no—
479C8—862no—
480C8—1721no—
481C8—1722no—
482C22—21no—
483C22—21no—
484C22—42no—
485C22—42no—
486C22—42no—
487C22—3442no—
488C22—3442no—
489C22—3441no—
490C22—3441no—
491C22—1722no—
492C22C2×#1306329711yescharacteristic
493C22#1458342811yescharacteristic
494C22#1458351811yescharacteristic
495C4—21no—
496C4—21no—
497C4—21no—
498C4—42no—
499C4—82no—
500C4—3441no—
501C4#1458316712yes—
502C4#1458353711yescharacteristic
503C4#1458354211yescharacteristic
504C4#1458354811yescharacteristic
505C4#1458355711yescharacteristic
506C2—21no—
507C2—21no—
508C2—82no—
509C2—3442no—
510C2#1913817511yescharacteristic
511C2C2×#1458316711yescharacteristic
512C2#1914432911yescharacteristic
subgroupG/H
centerC22C2×#13063297
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#3141C2
socleC22×C43C2×#121
prime radical#19144055C2
hypercenter#3141D43
hypocenterC43#25358
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3141

Complements

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

NH ≅ G/Ntype
1. C2×#14583176C2semidirect
3. #19143339C2semidirect
4. #19136038C2semidirect
5. #19135885C2semidirect
6. #19135585C2semidirect
7. #19135370C2semidirect
8. #19135101C2semidirect
9. #19134657C2semidirect
10. C4×#13063241C2semidirect
11. C43×#3141C2semidirect
250. #3141D43semidirect
303. C43#25358semidirect

Maximal subgroups

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

subgroupindex
C2×#145831762
#191440552
#191433392
#191360382
#191358852
#191355852
#191353702
#191351012
#191346572
C4×#130632412
C43×#31412
#2535843