Finite Group Databasebeta

← #25082083

Subgroups — #25082083

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#19144082C211yesmaximal, characteristic, complemented
3#19143706C211yesmaximal, characteristic, complemented
4#19134037C212yesmaximal, complemented
5#19134030C212yesmaximal, complemented
6#19133987C212yesmaximal, complemented
7#19133982C212yesmaximal, complemented
8#19133369C211yesmaximal, characteristic, complemented
9#19133272C211yesmaximal, characteristic, complemented
10C2×#14582646C211yesmaximal, characteristic, complemented
11C43×#3035C211yesmaximal, characteristic
12C2×#13063355—21no—
13C2×#13063325C2211yescharacteristic
14#14583302C2212yes—
15#14583245C2212yes—
16#14583210—22no—
17#14583179—21no—
18#14583179—21no—
19#14583109—21no—
20#14583109C2212yes—
21#14583104—21no—
22#14583104C2212yes—
23Q8×C43⋊C8C2212yes—
24D4×C43⋊C8—22no—
25D4×C43⋊C8C2212yes—
26#14582952—21no—
27#14582952C2211yescharacteristic
28#14582923C2211yescharacteristic
29C2×C4⋊(C43⋊C8)—21no—
30C2×C4⋊(C43⋊C8)C2211yescharacteristic
31#14582907—21no—
32#14582651C2212yes—
33#14582651C2212yes—
34#14582646C2212yes—
35#14582646C2212yes—
36#14582645C2212yes—
37#14582643C2212yes—
38C2×#135×C43—21no—
39C43×#532C2211yescharacteristic
40C4×#41×C43C2211yescharacteristic
41C43×#464—21no—
42C43×#463—21no—
43C43×#462C2211yescharacteristic
44C43×#461C2211yescharacteristic
45C43×#460C2211yescharacteristic
46C43×#459C2211yescharacteristic
47C2×C4⋊C8×C43C2211yescharacteristic
48C43×#416—21no—
49C22×Dic86—21no—
50#13063355—44no—
51C2×#10621885—22no—
52C2×#10621883—22no—
53C2×#10621877—21no—
54C22×C43⋊C8—21no—
55C22×C43⋊C8—22no—
56#13063325—21no—
57#13063325—21no—
58#13063325—21no—
59#13063325C2312yes—
60C2×C4⋊Dic43—21no—
61C2×C4⋊Dic43—21no—
62#13063258—22no—
63#13063258—22no—
64C4⋊(C43⋊C8)—21no—
65C4⋊(C43⋊C8)—21no—
66C4⋊(C43⋊C8)—22no—
67C4⋊(C43⋊C8)D411yescharacteristic
68C4⋊(C43⋊C8)D411yescharacteristic
69C4⋊(C43⋊C8)C2312yes—
70C4⋊(C43⋊C8)C2312yes—
71#13063248—22no—
72#13063248—22no—
73#13063246—22no—
74#13063246—22no—
75C22⋊(C43⋊C8)—22no—
76C22⋊(C43⋊C8)D412yes—
77C4×C43⋊C8—22no—
78C4×C43⋊C8C2312yes—
79C2×#41×C43—21no—
80C2×#41×C43D411yescharacteristic
81#135×C43—44no—
82C2×Q16×C43—21no—
83C2×SD16×C43—21no—
84C2×SD16×C43—21no—
85C2×D8×C43—21no—
86C22×C8×C43—21no—
87C4⋊Q8×C43C2311yescharacteristic
88#127×C43C2311yescharacteristic
89#124×C43—21no—
90#121×C43—21no—
91#121×C43—21no—
92C4×Q8×C43D411yescharacteristic
93C4×Q8×C43C2311yescharacteristic
94C4×D4×C43—21no—
95C4×D4×C43—21no—
96C4×D4×C43—21no—
97C4×D4×C43—21no—
98C4×D4×C43D411yescharacteristic
99C4×D4×C43C2311yescharacteristic
100#117×C43—21no—
101#117×C43D411yescharacteristic
102C2×C42×C43—21no—
103C2×C42×C43C2311yescharacteristic
104C4⋊C8×C43—21no—
105C4⋊C8×C43C2311yescharacteristic
106C4⋊C8×C43C2311yescharacteristic
107#103×C43—21no—
108#103×C43—21no—
109#102×C43—21no—
110#102×C43—21no—
111#41×C43—22no—
112#41×C43—42no—
113#41×C43—42no—
114#41×C43D814yes—
115C2×Q8×C43—21no—
116C2×Q8×C43C2×D411yescharacteristic
117C2×D4×C43—21no—
118C2×D4×C43—21no—
119C2×D4×C43—21no—
120C2×D4×C43—21no—
121C2×D4×C43—41no—
122C2×D4×C43C2×D411yescharacteristic
123C22×C4×C43—21no—
124C22×C4×C43—21no—
125C22×C4×C43—21no—
126C22×C4×C43—41no—
127C22×C4×C43C2×D411yescharacteristic
128C22×C4×C43C2×D411yescharacteristic
129C22×C4×C43#4111yescharacteristic
130C22×Dic43—41no—
131C2×Dic86—22no—
132C2×Dic86—42no—
133C2×Dic86—42no—
134C2×Dic86—41no—
135Q16×C43—42no—
136SD16×C43—42no—
137SD16×C43—42no—
138D8×C43—42no—
139C2×C8×C43—21no—
140C2×C8×C43—21no—
141C2×C8×C43—42no—
142C4⋊C4×C43—21no—
143C4⋊C4×C43—21no—
144C4⋊C4×C43—21no—
145C4⋊C4×C43—21no—
146C4⋊C4×C43C2×D411yescharacteristic
147C4⋊C4×C43C2×D411yescharacteristic
148C22⋊C4×C43—21no—
149C22⋊C4×C43—21no—
150C22⋊C4×C43—21no—
151C22⋊C4×C43—41no—
152C22⋊C4×C43—41no—
153C42×C43—21no—
154C42×C43—21no—
155C42×C43—21no—
156C42×C43C2×D411yescharacteristic
157C42×C43C2×D411yescharacteristic
158C42×C43#4111yescharacteristic
159C42×C43C2411yescharacteristic
160#10621885—44no—
161#10621883—44no—
162C4⋊Dic43—22no—
163C4⋊Dic43—22no—
164C4⋊Dic43—41no—
165C4⋊Dic43—41no—
166#10621877—42no—
167C2×C43⋊C8—22no—
168C2×C43⋊C8—22no—
169C2×C43⋊C8—82no—
170C2×C43⋊C8—81no—
171C2×C43⋊C8C2×D412yes—
172C2×C43⋊C8C2×D412yes—
173C23×C43—21no—
174C23×C43—41no—
175C23×C43#12111yescharacteristic
176Q8×C43—21no—
177Q8×C43—41no—
178Q8×C43—41no—
179Q8×C43C2×D812yes—
180D4×C43—24no—
181D4×C43—21no—
182D4×C43—41no—
183D4×C43—41no—
184D4×C43—41no—
185D4×C43—41no—
186D4×C43—81no—
187D4×C43—82no—
188D4×C43C2×D812yes—
189C2×C4×C43—21no—
190C2×C4×C43—21no—
191C2×C4×C43—21no—
192C2×C4×C43—24no—
193C2×C4×C43—21no—
194C2×C4×C43—21no—
195C2×C4×C43—41no—
196C2×C4×C43—41no—
197C2×C4×C43—41no—
198C2×C4×C43—41no—
199C2×C4×C43—81no—
200C2×C4×C43—82no—
201C2×C4×C43#12111yescharacteristic
202C2×C4×C43#12111yescharacteristic
203C2×C4×C43#12111yescharacteristic
204C2×C4×C43C2×D812yes—
205C2×C4×C43#13512yes—
206C2×C4×C43C22×D411yescharacteristic
207C2×C4×C43C22×D411yescharacteristic
208C2×C4×C43C2×#4111yescharacteristic
209C2×Dic43—42no—
210C2×Dic43—82no—
211Dic86—42no—
212Dic86—42no—
213Dic86—82no—
214C8×C43—41no—
215C8×C43—41no—
216C43⋊C8—22no—
217C43⋊C8—22no—
218C43⋊C8—42no—
219C43⋊C8—42no—
220#19416—431nomaximal, Sylow
221C22×C43—21no—
222C22×C43—21no—
223C22×C43—22no—
224C22×C43—41no—
225C22×C43—41no—
226C22×C43—81no—
227C22×C43—81no—
228C22×C43—81no—
229C22×C43#46612yes—
230C22×C43C2×#12111yescharacteristic
231C4×C43—21no—
232C4×C43—22no—
233C4×C43—21no—
234C4×C43—21no—
235C4×C43—41no—
236C4×C43—41no—
237C4×C43—81no—
238C4×C43#46612yes—
239C4×C43C22×D811yescharacteristic
240C4×C43C2×#13511yescharacteristic
241C4×C43#57711yescharacteristic
242C4×C43#57811yescharacteristic
243Dic43—82no—
244#3226—431no—
245#3039—431no—
246#3035D4311yescharacteristic
247#2988—431no—
248#1682—432no—
249#1681—432no—
250#1674—432no—
251#1673—432no—
252#1571—431no—
253#1547—431no—
254C2×#332—431no—
255C2×C43—22no—
256C2×C43—42no—
257C2×C43—161no—
258C2×C43#304611yescharacteristic
259C2×C43C2×#46611yescharacteristic
260C2×C43#306911yescharacteristic
261C2×#137—861no—
262C2×#135—21no—
263#532C2×D4311yescharacteristic
264C2×C4⋊Q8—431no—
265C4×#41C2×D4311yescharacteristic
266#500—432no—
267#486—432no—
268#480—862no—
269#474—861no—
270#474—861no—
271#464—21no—
272#463—21no—
273#462—432no—
274#462—861no—
275#462C2×D4311yescharacteristic
276#461—432no—
277#461—861no—
278#461C2×D4311yescharacteristic
279#460C2×D4311yescharacteristic
280#459C2×D4311yescharacteristic
281C8×Q8—432no—
282C8×D4—432no—
283C8×D4—862no—
284#431—431no—
285#431—861no—
286#423—431no—
287C2×C4⋊C8—431no—
288C2×C4⋊C8—861no—
289C2×C4⋊C8C2×D4311yescharacteristic
290#419—861no—
291#416—21no—
292#335—432no—
293#335—432no—
294#332—432no—
295#332—432no—
296#332—432no—
297#331—432no—
298C43#1941611yescharacteristic, complemented, Sylow
299C2×#41—21no—
300C2×#41C22⋊D4311yescharacteristic
301C22×Q8—861no—
302#137—1724no—
303#135—44no—
304C2×Q16—21no—
305C2×Q16—862no—
306C2×SD16—21no—
307C2×SD16—21no—
308C2×SD16—862no—
309C2×D8—21no—
310C2×M16—861no—
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×Q8C22⋊D4311yescharacteristic
324C4×Q8C22×D4311yescharacteristic
325C4×D4—21no—
326C4×D4—21no—
327C4×D4—21no—
328C4×D4—21no—
329C4×D4C22⋊D4311yescharacteristic
330C4×D4C22×D4311yescharacteristic
331#117—21no—
332#117C22⋊D4311yescharacteristic
333C2×C4⋊C4—861no—
334C2×C4⋊C4—861no—
335C2×C42—21no—
336C2×C42C22×D4311yescharacteristic
337#107—862no—
338#107—862no—
339C4⋊C8—21no—
340C4⋊C8—431no—
341C4⋊C8—431no—
342C4⋊C8—432no—
343C4⋊C8—432no—
344C4⋊C8—862no—
345C4⋊C8—861no—
346C4⋊C8—861no—
347C4⋊C8C22×D4311yescharacteristic
348C4⋊C8C22×D4311yescharacteristic
349#103—21no—
350#103—21no—
351#103—862no—
352#103—862no—
353#102—21no—
354#102—21no—
355#102—862no—
356#102—862no—
357C22⋊C8—432no—
358C22⋊C8—862no—
359C4×C8—432no—
360C4×C8—862no—
361#41—22no—
362#41—42no—
363#41—42no—
364#41#1062188214yes—
365C2×Q8—21no—
366C2×Q8—862no—
367C2×Q8—1722no—
368C2×Q8—1722no—
369C2×Q8—1721no—
370C2×Q8C2×C22⋊D4311yescharacteristic
371C2×D4—21no—
372C2×D4—21no—
373C2×D4—21no—
374C2×D4—21no—
375C2×D4—41no—
376C2×D4C2×C22⋊D4311yescharacteristic
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—41no—
381C22×C4—1721no—
382C22×C4D4×D4311yescharacteristic
383C22×C4#1062190011yescharacteristic
384C22×C4C2×C22⋊D4311yescharacteristic
385Q16—42no—
386Q16—1724no—
387SD16—42no—
388SD16—42no—
389SD16—1724no—
390D8—42no—
391M16—1722no—
392C2×C8—21no—
393C2×C8—21no—
394C2×C8—42no—
395C2×C8—432no—
396C2×C8—432no—
397C2×C8—862no—
398C2×C8—862no—
399C2×C8—3442no—
400C2×C8—3441no—
401C4⋊C4—21no—
402C4⋊C4—21no—
403C4⋊C4—21no—
404C4⋊C4—21no—
405C4⋊C4—862no—
406C4⋊C4—862no—
407C4⋊C4—1721no—
408C4⋊C4—1721no—
409C4⋊C4C2×C22⋊D4311yescharacteristic
410C4⋊C4C2×C22⋊D4311yescharacteristic
411C22⋊C4—21no—
412C22⋊C4—21no—
413C22⋊C4—21no—
414C22⋊C4—41no—
415C22⋊C4—41no—
416C42—21no—
417C42—21no—
418C42—21no—
419C42D4×D4311yescharacteristic
420C42#1062190011yescharacteristic
421C42C2×C22⋊D4311yescharacteristic
422C42C23×D4311yescharacteristic
423C23—21no—
424C23—41no—
425C23#1306329711yescharacteristic
426Q8—21no—
427Q8—41no—
428Q8—41no—
429Q8—3442no—
430Q8—1722no—
431Q8—1722no—
432Q8C2×#1062188212yes—
433D4—24no—
434D4—21no—
435D4—41no—
436D4—41no—
437D4—41no—
438D4—41no—
439D4—81no—
440D4—82no—
441D4C2×#1062188212yes—
442C2×C4—21no—
443C2×C4—24no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—81no—
453C2×C4—82no—
454C2×C4—3442no—
455C2×C4—1722no—
456C2×C4#1306329711yescharacteristic
457C2×C4#1306329711yescharacteristic
458C2×C4#1306329711yescharacteristic
459C2×C4C2×#1062188212yes—
460C2×C4#1306334512yes—
461C2×C4C2×D4×D4311yescharacteristic
462C2×C4C22×C22⋊D4311yescharacteristic
463C2×C4C2×#1062190011yescharacteristic
464C8—41no—
465C8—41no—
466C8—862no—
467C8—862no—
468C8—1722no—
469C8—1722no—
470C22—21no—
471C22—21no—
472C22—22no—
473C22—41no—
474C22—41no—
475C22—81no—
476C22—81no—
477C22—81no—
478C22#1458313312yes—
479C22C2×#1306329711yescharacteristic
480C4—21no—
481C4—21no—
482C4—21no—
483C4—22no—
484C4—41no—
485C4—41no—
486C4—81no—
487C4—3442no—
488C4#1458313312yes—
489C4C22×#1062188211yescharacteristic
490C4C2×#1306334511yescharacteristic
491C4#1458370611yescharacteristic
492C4#1458371311yescharacteristic
493C2—22no—
494C2—42no—
495C2—161no—
496C2#1914414311yescharacteristic
497C2C2×#1458313311yescharacteristic
498C2#1914433411yescharacteristic
subgroupG/H
centerC22C2×#13063297
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
Fitting, prime radicalC43×#3035C2
socleC22×C43C2×#121
hypercenter#3035D43
hypocenterC43#19416
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3035

Complements

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

NH ≅ G/Ntype
1. #19145713C2semidirect
2. #19144082C2semidirect
3. #19143706C2semidirect
4. #19134037C2semidirect
5. #19134030C2semidirect
6. #19133987C2semidirect
7. #19133982C2semidirect
8. #19133369C2semidirect
9. #19133272C2semidirect
10. C2×#14582646C2semidirect
298. C43#19416semidirect

Maximal subgroups

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

subgroupindex
#191457132
#191440822
#191437062
#191340372
#191340302
#191339872
#191339822
#191333692
#191332722
C2×#145826462
C43×#30352
#1941643