Finite Group Databasebeta

← #25082085

Subgroups — #25082085

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#19145718C211yesmaximal, characteristic, complemented
2#19144082C211yesmaximal, characteristic, complemented
3#19144050C211yesmaximal, characteristic
4#19134039C212yesmaximal, complemented
5#19134032C212yesmaximal, complemented
6#19133989C212yesmaximal, complemented
7#19133984C212yesmaximal, complemented
8#19133370C211yesmaximal, characteristic, complemented
9#19133270C211yesmaximal, characteristic, complemented
10C2×#14582644C211yesmaximal, characteristic, complemented
11C43×#2988C211yesmaximal, characteristic, complemented
12C2×#13063355—21no—
13C2×#13063345—21no—
14#14583449C2211yescharacteristic
15C2×#13063325C2211yescharacteristic
16#14583304C2212yes—
17#14583246C2212yes—
18#14583213—22no—
19#14583180—21no—
20#14583180—21no—
21#14583121—21no—
22#14583114—21no—
23#14583109—21no—
24#14583109C2211yescharacteristic
25#14583109C2212yes—
26#14583104—21no—
27#14583104C2211yescharacteristic
28#14583104C2212yes—
29#14583099C2211yescharacteristic
30#14583094C2211yescharacteristic
31#14582923C2211yescharacteristic
32C2×C4⋊(C43⋊C8)C2211yescharacteristic
33#14582907—21no—
34#14582893—21no—
35#14582652C2212yes—
36#14582652C2212yes—
37#14582644C2212yes—
38#14582644C2212yes—
39#14582644C2212yes—
40#14582642C2212yes—
41C4×#41×C43C2211yescharacteristic
42C8×Q8×C43C2212yes—
43C8×D4×C43—22no—
44C8×D4×C43C2212yes—
45C43×#431—21no—
46C43×#431C2211yescharacteristic
47C2×C4⋊C8×C43—21no—
48C2×C4⋊C8×C43C2211yescharacteristic
49C2×#10621898—21no—
50C22×Dic86—21no—
51#13063355—44no—
52#13063345—44no—
53C2×#10621885—22no—
54C2×#10621885—21no—
55C2×#10621883—22no—
56C2×#10621883—21no—
57C2×#10621884—21no—
58C2×#10621882—21no—
59C2×#10621877—21no—
60C22×C43⋊C8—21no—
61#13063325—21no—
62#13063325—21no—
63#13063325—21no—
64#13063325C2311yescharacteristic
65#13063325C2312yes—
66#13063322C2311yescharacteristic
67#13063313—21no—
68#13063299—21no—
69#13063299—21no—
70C4×D172—21no—
71C4×D172—21no—
72C2×C4⋊Dic43—21no—
73C2×C4⋊Dic43—21no—
74#13063259—22no—
75#13063259—22no—
76C4⋊(C43⋊C8)—21no—
77C4⋊(C43⋊C8)—21no—
78C4⋊(C43⋊C8)C2311yescharacteristic
79C4⋊(C43⋊C8)C2311yescharacteristic
80C4⋊(C43⋊C8)C2312yes—
81#13063248—22no—
82#13063248—22no—
83#13063248—21no—
84#13063248—21no—
85#13063247—22no—
86#13063247—22no—
87#13063245—21no—
88#13063245—21no—
89C2×#41×C43D411yescharacteristic
90C22×C8×C43—21no—
91C22×C8×C43—22no—
92C4×Q8×C43D411yescharacteristic
93C4×Q8×C43C2311yescharacteristic
94C4×D4×C43—21no—
95C4×D4×C43—21no—
96C4×D4×C43D411yescharacteristic
97C4×D4×C43C2311yescharacteristic
98#117×C43—21no—
99#117×C43D411yescharacteristic
100C2×C42×C43—21no—
101C2×C42×C43C2311yescharacteristic
102C4⋊C8×C43—22no—
103C4⋊C8×C43—21no—
104C4⋊C8×C43D411yescharacteristic
105C4⋊C8×C43D411yescharacteristic
106C4⋊C8×C43C2312yes—
107C22⋊C8×C43—22no—
108C22⋊C8×C43D412yes—
109C4×C8×C43—22no—
110C4×C8×C43C2312yes—
111#41×C43—22no—
112#41×C43D814yes—
113C2×Q8×C43C2×D411yescharacteristic
114C2×D4×C43—21no—
115C2×D4×C43C2×D411yescharacteristic
116C22×C4×C43—21no—
117C22×C4×C43—21no—
118C22×C4×C43—21no—
119C22×C4×C43C2×D411yescharacteristic
120C22×C4×C43C2×D411yescharacteristic
121C22×C4×C43#4111yescharacteristic
122C2×C22⋊D43—41no—
123C22×Dic43—41no—
124#10621898—42no—
125#10621898—42no—
126C2×D172—21no—
127C2×D172—21no—
128C2×D172—21no—
129C2×C4×D43—41no—
130C2×Dic86—21no—
131C2×Dic86—22no—
132C2×Dic86—42no—
133C2×Dic86—42no—
134C2×Dic86—41no—
135C2×C8×C43—22no—
136C2×C8×C43—82no—
137C2×C8×C43—81no—
138C2×C8×C43C2×D412yes—
139C2×C8×C43C2×D412yes—
140C4⋊C4×C43—21no—
141C4⋊C4×C43—21no—
142C4⋊C4×C43C2×D411yescharacteristic
143C4⋊C4×C43C2×D411yescharacteristic
144C22⋊C4×C43—21no—
145C22⋊C4×C43—21no—
146C22⋊C4×C43—21no—
147C42×C43—21no—
148C42×C43—21no—
149C42×C43—21no—
150C42×C43C2×D411yescharacteristic
151C42×C43C2×D411yescharacteristic
152C42×C43#4111yescharacteristic
153C42×C43C2411yescharacteristic
154#10621885—42no—
155#10621885—44no—
156#10621884—42no—
157#10621883—42no—
158#10621883—44no—
159#10621882—42no—
160(C2×D43)⋊C4—41no—
161(C2×D43)⋊C4—41no—
162C4⋊Dic43—22no—
163C4⋊Dic43—21no—
164C4⋊Dic43—22no—
165C4⋊Dic43—21no—
166C4⋊Dic43—41no—
167C4⋊Dic43—41no—
168#10621877—42no—
169C2×C43⋊C8—21no—
170C2×C43⋊C8—21no—
171C2×C43⋊C8—22no—
172C2×C43⋊C8—42no—
173C23×C43—21no—
174C23×C43#12111yescharacteristic
175C22×D43—41no—
176Q8×C43—21no—
177Q8×C43C2×D812yes—
178D4×C43—24no—
179D4×C43—21no—
180D4×C43C2×D812yes—
181C2×C4×C43—21no—
182C2×C4×C43—21no—
183C2×C4×C43—21no—
184C2×C4×C43—24no—
185C2×C4×C43—21no—
186C2×C4×C43—21no—
187C2×C4×C43—41no—
188C2×C4×C43—41no—
189C2×C4×C43—41no—
190C2×C4×C43—81no—
191C2×C4×C43#12111yescharacteristic
192C2×C4×C43#12111yescharacteristic
193C2×C4×C43#12111yescharacteristic
194C2×C4×C43C2×D812yes—
195C2×C4×C43#13512yes—
196C2×C4×C43C22×D411yescharacteristic
197C2×C4×C43C22×D411yescharacteristic
198C2×C4×C43C2×#4111yescharacteristic
199C22⋊D43—82no—
200C2×Dic43—42no—
201C2×Dic43—41no—
202C2×Dic43—82no—
203D172—41no—
204D172—41no—
205D172—41no—
206D172—41no—
207D172—81no—
208C4×D43—82no—
209Dic86—42no—
210Dic86—41no—
211Dic86—42no—
212Dic86—41no—
213Dic86—82no—
214C8×C43—22no—
215C8×C43—22no—
216C8×C43—42no—
217C43⋊C8—41no—
218C43⋊C8—41no—
219C43⋊C8—42no—
220#19416—431nomaximal, Sylow
221C22×C43—21no—
222C22×C43—21no—
223C22×C43—22no—
224C22×C43—41no—
225C22×C43—41no—
226C22×C43#46612yes—
227C22×C43C2×#12111yescharacteristic
228C2×D43—81no—
229C2×D43—81no—
230C2×D43—81no—
231C4×C43—21no—
232C4×C43—22no—
233C4×C43—21no—
234C4×C43—21no—
235C4×C43—41no—
236C4×C43—41no—
237C4×C43#46612yes—
238C4×C43C22×D811yescharacteristic
239C4×C43C2×#13511yescharacteristic
240C4×C43#57711yescharacteristic
241C4×C43#57811yescharacteristic
242Dic43—82no—
243Dic43—81no—
244#3226—431no—
245#3039—431no—
246#3035—431no—
247#2988D4311yescharacteristic, complemented
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#304611yescharacteristic
258C2×C43C2×#46611yescharacteristic
259C2×C43#306911yescharacteristic
260D43—161no—
261C2×#137—861no—
262C2×#135—861no—
263#532—431no—
264C2×C4⋊Q8—431no—
265C4×#41C2×D4311yescharacteristic
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×Q8C2×D4312yes—
282C8×D4—22no—
283C8×D4C2×D4312yes—
284#431—21no—
285#431C2×D4311yescharacteristic
286#423—431no—
287C2×C4⋊C8—21no—
288C2×C4⋊C8—431no—
289C2×C4⋊C8C2×D4311yescharacteristic
290#419—861no—
291#416—861no—
292#335—432no—
293#335—432no—
294#332—432no—
295#332—432no—
296#332—432no—
297#331—432no—
298C43#1941611yescharacteristic, complemented, Sylow
299C2×#41—861no—
300C2×#41D17211yescharacteristic
301C22×Q8—861no—
302#137—1724no—
303#135—1724no—
304C2×Q16—861no—
305C2×Q16—862no—
306C2×SD16—861no—
307C2×SD16—861no—
308C2×SD16—862no—
309C2×D8—861no—
310C2×M16—861no—
311C22×C8—21no—
312C22×C8—22no—
313C22×C8—861no—
314C4⋊Q8—432no—
315C4⋊Q8—431no—
316C4⋊Q8—861no—
317C4⋊Q8—861no—
318C4⋊Q8—861no—
319#127—431no—
320#124—861no—
321#121—861no—
322#121—861no—
323C4×Q8D17211yescharacteristic
324C4×Q8C22×D4311yescharacteristic
325C4×D4—21no—
326C4×D4—21no—
327C4×D4—861no—
328C4×D4—861no—
329C4×D4D17211yescharacteristic
330C4×D4C22×D4311yescharacteristic
331#117—21no—
332#117D17211yescharacteristic
333C2×C4⋊C4—861no—
334C2×C4⋊C4—861no—
335C2×C42—21no—
336C2×C42C22×D4311yescharacteristic
337#107—862no—
338#107—862no—
339C4⋊C8—22no—
340C4⋊C8—21no—
341C4⋊C8—432no—
342C4⋊C8—431no—
343C4⋊C8—431no—
344C4⋊C8—861no—
345C4⋊C8—861no—
346C4⋊C8C22⋊D4311yescharacteristic
347C4⋊C8C22⋊D4311yescharacteristic
348C4⋊C8C22×D4312yes—
349#103—861no—
350#103—861no—
351#103—862no—
352#103—862no—
353#102—862no—
354#102—862no—
355#102—861no—
356#102—861no—
357C22⋊C8—22no—
358C22⋊C8C22⋊D4312yes—
359C4×C8—22no—
360C4×C8C22×D4312yes—
361#41—22no—
362#41—1722no—
363#41—1722no—
364#41D34414yes—
365C2×Q8—861no—
366C2×Q8—862no—
367C2×Q8—1722no—
368C2×Q8—1722no—
369C2×Q8—1721no—
370C2×Q8C2×D17211yescharacteristic
371C2×D4—21no—
372C2×D4—861no—
373C2×D4—861no—
374C2×D4—861no—
375C2×D4—1721no—
376C2×D4C2×D17211yescharacteristic
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—1721no—
381C22×C4—1721no—
382C22×C4C2×D17211yescharacteristic
383C22×C4#1062189811yescharacteristic
384C22×C4C2×C22⋊D4311yescharacteristic
385Q16—1722no—
386Q16—1724no—
387SD16—1722no—
388SD16—1722no—
389SD16—1724no—
390D8—1722no—
391M16—1722no—
392C2×C8—22no—
393C2×C8—82no—
394C2×C8—81no—
395C2×C8—861no—
396C2×C8—861no—
397C2×C8—862no—
398C2×C8—1722no—
399C2×C8C2×C22⋊D4312yes—
400C2×C8C2×C22⋊D4312yes—
401C4⋊C4—21no—
402C4⋊C4—21no—
403C4⋊C4—862no—
404C4⋊C4—861no—
405C4⋊C4—862no—
406C4⋊C4—861no—
407C4⋊C4—1721no—
408C4⋊C4—1721no—
409C4⋊C4C2×D17211yescharacteristic
410C4⋊C4C2×D17211yescharacteristic
411C22⋊C4—21no—
412C22⋊C4—21no—
413C22⋊C4—21no—
414C22⋊C4—1721no—
415C22⋊C4—1721no—
416C42—21no—
417C42—21no—
418C42—21no—
419C42C2×D17211yescharacteristic
420C42#1062189811yescharacteristic
421C42C2×C22⋊D4311yescharacteristic
422C42C23×D4311yescharacteristic
423C23—21no—
424C23—1721no—
425C23#1306329911yescharacteristic
426Q8—21no—
427Q8—3442no—
428Q8—1722no—
429Q8—1721no—
430Q8—1722no—
431Q8—1721no—
432Q8C2×D34412yes—
433D4—24no—
434D4—21no—
435D4—3441no—
436D4—3442no—
437D4—1721no—
438D4—1721no—
439D4—1721no—
440D4—1721no—
441D4C2×D34412yes—
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—81no—
452C2×C4—3442no—
453C2×C4—3442no—
454C2×C4—1721no—
455C2×C4—1722no—
456C2×C4#1306329911yescharacteristic
457C2×C4#1306329911yescharacteristic
458C2×C4#1306329911yescharacteristic
459C2×C4C2×D34412yes—
460C2×C4#1306334712yes—
461C2×C4C22×C22⋊D4311yescharacteristic
462C2×C4C22×D17211yescharacteristic
463C2×C4C2×#1062189811yescharacteristic
464C8—22no—
465C8—22no—
466C8—42no—
467C8—1721no—
468C8—1721no—
469C8—1722no—
470C22—21no—
471C22—21no—
472C22—22no—
473C22—41no—
474C22—41no—
475C22—3441no—
476C22—3441no—
477C22—3441no—
478C22#1458313512yes—
479C22C2×#1306329911yescharacteristic
480C4—21no—
481C4—21no—
482C4—21no—
483C4—22no—
484C4—41no—
485C4—41no—
486C4—3441no—
487C4—3442no—
488C4#1458313512yes—
489C4C22×D34411yescharacteristic
490C4C2×#1306334711yescharacteristic
491C4#1458371011yescharacteristic
492C4#1458371411yescharacteristic
493C2—22no—
494C2—42no—
495C2—6881no—
496C2#1914414511yescharacteristic
497C2C2×#1458313511yescharacteristic
498C2#1914433211yescharacteristic
subgroupG/H
centerC22C2×#13063299
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#2988C2
socleC22×C43C2×#121
prime radical#19144050C2
hypercenter#2988D43
hypocenterC43#19416
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2988

Complements

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

NH ≅ G/Ntype
1. #19145718C2semidirect
2. #19144082C2semidirect
4. #19134039C2semidirect
5. #19134032C2semidirect
6. #19133989C2semidirect
7. #19133984C2semidirect
8. #19133370C2semidirect
9. #19133270C2semidirect
10. C2×#14582644C2semidirect
11. C43×#2988C2semidirect
247. #2988D43semidirect
298. C43#19416semidirect

Maximal subgroups

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

subgroupindex
#191457182
#191440822
#191440502
#191340392
#191340322
#191339892
#191339842
#191333702
#191332702
C2×#145826442
C43×#29882
#1941643