Finite Group Databasebeta

← #25082084

Subgroups — #25082084

Order 11008.

694 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145713C211yesmaximal, characteristic, complemented
2#19144083C211yesmaximal, characteristic, complemented
3#19144044C211yesmaximal, characteristic
4#19143704C211yesmaximal, characteristic, complemented
5#19134038C212yesmaximal, complemented
6#19134031C212yesmaximal, complemented
7#19133988C212yesmaximal, complemented
8#19133983C212yesmaximal, complemented
9#19133371C211yesmaximal, characteristic, complemented
10C2×#14582644C211yesmaximal, characteristic, complemented
11C43×#1547C211yesmaximal, characteristic, complemented
12C2×#13063358—21no—
13C2×#13063345—21no—
14C2×#13063325C2211yescharacteristic
15C4×#10621898C2211yescharacteristic
16#14583302C2212yes—
17#14583245C2212yes—
18#14583210—22no—
19#14583179—21no—
20#14583179—21no—
21#14583118—21no—
22#14583111—21no—
23#14583110—21no—
24#14583110C2212yes—
25#14583106C2211yescharacteristic
26#14583105—21no—
27#14583105C2212yes—
28#14583101C2211yescharacteristic
29#14583096C2211yescharacteristic
30#14583091C2211yescharacteristic
31#14583023C2212yes—
32#14582964C2212yes—
33C8×C22⋊D43—22no—
34#14582952C2211yescharacteristic
35#14582951—21no—
36C2×C4⋊(C43⋊C8)C2211yescharacteristic
37C4⋊C8×D43—21no—
38#14582909—21no—
39#14582895—21no—
40#14582651C2212yes—
41#14582651C2212yes—
42#14582644C2212yes—
43#14582644C2212yes—
44C43×#532C2211yescharacteristic
45C43×#423C2211yescharacteristic
46C2×C4⋊C8×C43C2211yescharacteristic
47C43×#332C2212yes—
48C43×#331C2212yes—
49C2×#10621898D411yescharacteristic
50C22×Dic86—21no—
51#13063358—44no—
52#13063345—44no—
53C2×Dic172—22no—
54C2×#10621885—21no—
55C2×#10621873—22no—
56C2×#10621883—21no—
57C2×#10621884—21no—
58C2×#10621882—21no—
59C22×C43⋊C8—21no—
60C2×C8×D43—22no—
61#13063325—21no—
62#13063325—21no—
63#13063325—21no—
64#13063325C2312yes—
65C4×Dic86D411yescharacteristic
66C4×Dic86C2311yescharacteristic
67C4×D172D411yescharacteristic
68C4×D172C2311yescharacteristic
69C4×C22⋊D43—21no—
70C4×C22⋊D43—21no—
71#13063284D411yescharacteristic
72#13063282—21no—
73C2×C4⋊Dic43—21no—
74C2×C4⋊Dic43—21no—
75C42×D43—21no—
76#13063258—22no—
77#13063258—22no—
78C4⋊(C43⋊C8)—21no—
79C4⋊(C43⋊C8)D411yescharacteristic
80C4⋊(C43⋊C8)D411yescharacteristic
81C4⋊(C43⋊C8)C2311yescharacteristic
82C4⋊(C43⋊C8)C2311yescharacteristic
83Dic43⋊C8—22no—
84#13063250—22no—
85#13063250—22no—
86#13063249—21no—
87#13063249—21no—
88#13063246—21no—
89#13063246—21no—
90#13063246—22no—
91#13063246—22no—
92C22⋊(C43⋊C8)D412yes—
93(C2×D43)⋊C8—22no—
94C4×C43⋊C8C2312yes—
95C8×Dic43—22no—
96C2×#41×C43—21no—
97C2×M16×C43—21no—
98C22×C8×C43—21no—
99C4⋊Q8×C43C2311yescharacteristic
100#127×C43C2311yescharacteristic
101#124×C43—21no—
102#121×C43—21no—
103#121×C43—21no—
104C4×D4×C43—21no—
105C4×D4×C43—21no—
106C2×C42×C43C2311yescharacteristic
107C4⋊C8×C43—21no—
108C4⋊C8×C43—21no—
109C4⋊C8×C43C2312yes—
110C4⋊C8×C43C2312yes—
111#41×C43—42no—
112#41×C43—42no—
113C2×Q8×C43—21no—
114C2×D4×C43—21no—
115C2×D4×C43—21no—
116C2×D4×C43—21no—
117C2×D4×C43—41no—
118C22×C4×C43—41no—
119C22×C4×C43C2×D411yescharacteristic
120C22×C4×C43C2×D411yescharacteristic
121C22×C4×C43#4111yescharacteristic
122C2×C22⋊D43—21no—
123C22×Dic43—41no—
124#10621898—22no—
125#10621898D814yes—
126C2×D172C2×D411yescharacteristic
127C2×C4×D43—21no—
128C2×C4×D43—21no—
129C2×C4×D43—21no—
130C2×Dic86—22no—
131C2×Dic86—42no—
132C2×Dic86—42no—
133C2×Dic86—41no—
134C2×Dic86C2×D411yescharacteristic
135M16×C43—42no—
136C2×C8×C43—22no—
137C2×C8×C43—22no—
138C2×C8×C43—81no—
139C4⋊C4×C43—21no—
140C4⋊C4×C43—21no—
141C22⋊C4×C43—41no—
142C22⋊C4×C43—41no—
143C42×C43C2×D411yescharacteristic
144C42×C43C2×D411yescharacteristic
145C42×C43#4111yescharacteristic
146C42×C43C2411yescharacteristic
147C22⋊Dic43—21no—
148#10621885—42no—
149#10621884—42no—
150#10621883—42no—
151#10621882—42no—
152(C2×D43)⋊C4—21no—
153(C2×D43)⋊C4—21no—
154C4⋊Dic43—22no—
155C4⋊Dic43—22no—
156C4⋊Dic43—41no—
157C4⋊Dic43—41no—
158C4⋊Dic43C2×D411yescharacteristic
159C4⋊Dic43C2×D411yescharacteristic
160Dic43⋊C4—21no—
161Dic43⋊C4—21no—
162C4×Dic43—21no—
163C4×Dic43—21no—
164C4×Dic43—21no—
165C2×C43⋊C8—21no—
166C2×C43⋊C8—21no—
167C2×C43⋊C8—42no—
168C2×C43⋊C8C2×D412yes—
169C2×C43⋊C8C2×D412yes—
170Dic172—44no—
171#10621873—44no—
172C8×D43—82no—
173C23×C43—41no—
174C23×C43#12111yescharacteristic
175C22×D43—21no—
176Q8×C43—41no—
177Q8×C43—41no—
178D4×C43—41no—
179D4×C43—41no—
180D4×C43—41no—
181D4×C43—41no—
182D4×C43—81no—
183D4×C43—82no—
184C2×C4×C43—21no—
185C2×C4×C43—21no—
186C2×C4×C43—41no—
187C2×C4×C43—41no—
188C2×C4×C43—82no—
189C2×C4×C43#12111yescharacteristic
190C2×C4×C43#12111yescharacteristic
191C2×C4×C43#12111yescharacteristic
192C2×C4×C43C2×D812yes—
193C2×C4×C43#13512yes—
194C2×C4×C43C22×D411yescharacteristic
195C2×C4×C43C22×D411yescharacteristic
196C2×C4×C43C2×#4111yescharacteristic
197C22⋊D43—24no—
198C2×Dic43—21no—
199C2×Dic43—21no—
200C2×Dic43—21no—
201C2×Dic43—42no—
202C2×Dic43—82no—
203D172—21no—
204D172C2×D812yes—
205C4×D43—24no—
206C4×D43—41no—
207C4×D43—41no—
208C4×D43—81no—
209Dic86—21no—
210Dic86—42no—
211Dic86—42no—
212Dic86—82no—
213Dic86C2×D812yes—
214C8×C43—42no—
215C8×C43—42no—
216C43⋊C8—22no—
217C43⋊C8—22no—
218C43⋊C8—41no—
219C43⋊C8—41no—
220#19416—431nomaximal, Sylow
221C22×C43—21no—
222C22×C43—21no—
223C22×C43—81no—
224C22×C43—81no—
225C22×C43—81no—
226C22×C43#46612yes—
227C22×C43C2×#12111yescharacteristic
228C2×D43—22no—
229C2×D43—41no—
230C2×D43—41no—
231C4×C43—21no—
232C4×C43—21no—
233C4×C43—21no—
234C4×C43—81no—
235C4×C43#46612yes—
236C4×C43C22×D811yescharacteristic
237C4×C43C2×#13511yescharacteristic
238C4×C43#57711yescharacteristic
239C4×C43#57811yescharacteristic
240Dic43—22no—
241Dic43—41no—
242Dic43—41no—
243Dic43—82no—
244#3226—431no—
245#3039—431no—
246#3035—431no—
247#2988—431no—
248#1682—432no—
249#1681—432no—
250#1674—432no—
251#1673—432no—
252#1571—431no—
253#1547D4311yescharacteristic, complemented
254C2×#332—431no—
255C2×C43—22no—
256C2×C43—161no—
257C2×C43#304611yescharacteristic
258C2×C43C2×#46611yescharacteristic
259C2×C43#306911yescharacteristic
260D43—42no—
261C2×#137—861no—
262C2×#135—861no—
263#532C2×D4311yescharacteristic
264C2×C4⋊Q8—431no—
265C4×#41—431no—
266#500—432no—
267#486—432no—
268#480—862no—
269#474—861no—
270#474—861no—
271#464—861no—
272#463—861no—
273#462—431no—
274#462—432no—
275#462—861no—
276#461—431no—
277#461—432no—
278#461—861no—
279#460—431no—
280#459—431no—
281C8×Q8—432no—
282C8×D4—432no—
283C8×D4—862no—
284#431—431no—
285#431—861no—
286#423C2×D4311yescharacteristic
287C2×C4⋊C8—431no—
288C2×C4⋊C8—861no—
289C2×C4⋊C8C2×D4311yescharacteristic
290#419—861no—
291#416—861no—
292#335—432no—
293#335—432no—
294#332—432no—
295#332—432no—
296#332C2×D4312yes—
297#331C2×D4312yes—
298C43#1941611yescharacteristic, complemented, Sylow
299C2×#41—21no—
300C2×#41—431no—
301C22×Q8—861no—
302#137—1724no—
303#135—1724no—
304C2×Q16—862no—
305C2×Q16—861no—
306C2×SD16—862no—
307C2×SD16—861no—
308C2×SD16—861no—
309C2×D8—861no—
310C2×M16—21no—
311C22×C8—21no—
312C22×C8—862no—
313C22×C8—861no—
314C4⋊Q8—432no—
315C4⋊Q8—861no—
316C4⋊Q8—861no—
317C4⋊Q8—861no—
318C4⋊Q8C22×D4311yescharacteristic
319#127C22×D4311yescharacteristic
320#124—21no—
321#121—21no—
322#121—21no—
323C4×Q8—431no—
324C4×Q8—431no—
325C4×D4—21no—
326C4×D4—21no—
327C4×D4—431no—
328C4×D4—431no—
329C4×D4—861no—
330C4×D4—861no—
331#117—431no—
332#117—861no—
333C2×C4⋊C4—861no—
334C2×C4⋊C4—861no—
335C2×C42—861no—
336C2×C42C22×D4311yescharacteristic
337#107—862no—
338#107—862no—
339C4⋊C8—21no—
340C4⋊C8—21no—
341C4⋊C8—431no—
342C4⋊C8—431no—
343C4⋊C8—431no—
344C4⋊C8—431no—
345C4⋊C8—862no—
346C4⋊C8—861no—
347C4⋊C8C22×D4312yes—
348C4⋊C8C22×D4312yes—
349#103—862no—
350#103—862no—
351#103—861no—
352#103—861no—
353#102—861no—
354#102—861no—
355#102—862no—
356#102—862no—
357C22⋊C8—432no—
358C22⋊C8—862no—
359C4×C8—432no—
360C4×C8—862no—
361#41—42no—
362#41—42no—
363#41—434no—
364#41—862no—
365C2×Q8—21no—
366C2×Q8—431no—
367C2×Q8—862no—
368C2×Q8—1722no—
369C2×Q8—1722no—
370C2×Q8—1721no—
371C2×D4—21no—
372C2×D4—21no—
373C2×D4—21no—
374C2×D4—41no—
375C2×D4—431no—
376C2×D4—861no—
377C22×C4—41no—
378C22×C4—861no—
379C22×C4—861no—
380C22×C4—861no—
381C22×C4—1721no—
382C22×C4#1062189811yescharacteristic
383C22×C4D4×D4311yescharacteristic
384C22×C4D4×D4311yescharacteristic
385Q16—1724no—
386Q16—1722no—
387SD16—1724no—
388SD16—1722no—
389SD16—1722no—
390D8—1722no—
391M16—42no—
392C2×C8—22no—
393C2×C8—22no—
394C2×C8—81no—
395C2×C8—432no—
396C2×C8—432no—
397C2×C8—861no—
398C2×C8—861no—
399C2×C8—3442no—
400C2×C8—1722no—
401C4⋊C4—21no—
402C4⋊C4—21no—
403C4⋊C4—431no—
404C4⋊C4—431no—
405C4⋊C4—861no—
406C4⋊C4—861no—
407C4⋊C4—862no—
408C4⋊C4—862no—
409C4⋊C4—1721no—
410C4⋊C4—1721no—
411C22⋊C4—41no—
412C22⋊C4—41no—
413C22⋊C4—861no—
414C22⋊C4—861no—
415C22⋊C4—861no—
416C42—861no—
417C42—861no—
418C42—861no—
419C42#1062189811yescharacteristic
420C42D4×D4311yescharacteristic
421C42D4×D4311yescharacteristic
422C42C23×D4311yescharacteristic
423C23—41no—
424C23—861no—
425C23#1306329811yescharacteristic
426Q8—41no—
427Q8—41no—
428Q8—432no—
429Q8—861no—
430Q8—3442no—
431Q8—1722no—
432Q8—1722no—
433D4—41no—
434D4—41no—
435D4—41no—
436D4—41no—
437D4—81no—
438D4—82no—
439D4—432no—
440D4—864no—
441D4—861no—
442C2×C4—21no—
443C2×C4—21no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—82no—
447C2×C4—861no—
448C2×C4—864no—
449C2×C4—861no—
450C2×C4—861no—
451C2×C4—3441no—
452C2×C4—3442no—
453C2×C4—1722no—
454C2×C4—1721no—
455C2×C4—1721no—
456C2×C4#1306329811yescharacteristic
457C2×C4#1306329811yescharacteristic
458C2×C4#1306329811yescharacteristic
459C2×C4D8×D4312yes—
460C2×C4#1306334612yes—
461C2×C4C2×D4×D4311yescharacteristic
462C2×C4C2×D4×D4311yescharacteristic
463C2×C4C2×#1062189811yescharacteristic
464C8—42no—
465C8—42no—
466C8—862no—
467C8—862no—
468C8—1721no—
469C8—1721no—
470C22—21no—
471C22—21no—
472C22—81no—
473C22—81no—
474C22—81no—
475C22—862no—
476C22—1721no—
477C22—1721no—
478C22#1458313412yes—
479C22C2×#1306329811yescharacteristic
480C4—21no—
481C4—21no—
482C4—21no—
483C4—81no—
484C4—862no—
485C4—3442no—
486C4—1721no—
487C4—1721no—
488C4#1458313412yes—
489C4C2×D8×D4311yescharacteristic
490C4C2×#1306334611yescharacteristic
491C4#1458370911yescharacteristic
492C4#1458371511yescharacteristic
493C2—22no—
494C2—161no—
495C2—1722no—
496C2#1914414411yescharacteristic
497C2C2×#1458313411yescharacteristic
498C2#1914433511yescharacteristic
subgroupG/H
centerC22C2×#13063298
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1547C2
socleC22×C43C2×#121
prime radical#19144044C2
hypercenter#1547D43
hypocenterC43#19416
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1547

Complements

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

NH ≅ G/Ntype
1. #19145713C2semidirect
2. #19144083C2semidirect
4. #19143704C2semidirect
5. #19134038C2semidirect
6. #19134031C2semidirect
7. #19133988C2semidirect
8. #19133983C2semidirect
9. #19133371C2semidirect
10. C2×#14582644C2semidirect
11. C43×#1547C2semidirect
253. #1547D43semidirect
298. C43#19416semidirect

Maximal subgroups

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

subgroupindex
#191457132
#191440832
#191440442
#191437042
#191340382
#191340312
#191339882
#191339832
#191333712
C2×#145826442
C43×#15472
#1941643