Finite Group Databasebeta

← #25085906

Subgroups — #25085906

Order 11008.

684 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145336C211yesmaximal, characteristic
2#19145336C211yesmaximal, characteristic
3#19145142C211yesmaximal, characteristic
4#19145141C211yesmaximal, characteristic
5#19144977C211yesmaximal, characteristic
6#19134275C211yesmaximal, characteristic, complemented
7#19134269C211yesmaximal, characteristic, complemented
8#19134244C211yesmaximal, characteristic, complemented
9#19134243C211yesmaximal, characteristic, complemented
10#19134230C211yesmaximal, characteristic, complemented
11#19134226C211yesmaximal, characteristic, complemented
12#19134190C211yesmaximal, characteristic, complemented
13#19134189C211yesmaximal, characteristic, complemented
14#19132898C211yesmaximal, characteristic
15C43×#3185C211yesmaximal, characteristic
16#14583456C2211yescharacteristic
17C2×#13063325C2211yescharacteristic
18#14583309—22no—
19#14583308—22no—
20#14583304C2211yescharacteristic
21#14583304C2211yescharacteristic
22#14583302C2211yescharacteristic
23#14583302C2211yescharacteristic
24#14583297C2211yescharacteristic
25#14583297C2211yescharacteristic
26#14583295C2211yescharacteristic
27#14583295C2211yescharacteristic
28#14583295C2211yescharacteristic
29#14583295C2211yescharacteristic
30#14583278C2211yescharacteristic
31#14583278C2211yescharacteristic
32#14583269—22no—
33#14583251C2211yescharacteristic
34#14583251C2211yescharacteristic
35#14583251C2211yescharacteristic
36#14583251C2211yescharacteristic
37#14583251C2211yescharacteristic
38#14583251C2211yescharacteristic
39#14583249C2211yescharacteristic
40#14583249C2211yescharacteristic
41#14583155—22no—
42#14583155—22no—
43#14583004—22no—
44#14583004—22no—
45#14582942—22no—
46#14582941—22no—
47#14582907—22no—
48C4×#10621877C2211yescharacteristic
49C4×#10621877C2211yescharacteristic
50#14582621C2211yescharacteristic
51#14582621C2211yescharacteristic
52#14582620C2211yescharacteristic
53C8×C43⋊C8C2211yescharacteristic
54C43×#533C2211yescharacteristic
55C43×#533C2211yescharacteristic
56C43×#498C2211yescharacteristic
57C43×#494C2211yescharacteristic
58C43×#487C2211yescharacteristic
59C43×#487C2211yescharacteristic
60C43×#470—22no—
61C43×#441—22no—
62C4×M16×C43C2211yescharacteristic
63C22×Dic86—21no—
64C2×#10621885—22no—
65C2×#10621885—22no—
66C2×#10621877D412yes—
67C2×#10621877D412yes—
68#13063325—21no—
69#13063325—21no—
70#13063325—21no—
71#13063325C2311yescharacteristic
72#13063325C2311yescharacteristic
73#13063325C2311yescharacteristic
74#13063325C2311yescharacteristic
75#13063317—21no—
76#13063304—21no—
77#13063304—21no—
78C4×Dic86—21no—
79C4×Dic86—21no—
80#13063284—21no—
81C2×C4⋊Dic43—21no—
82C2×C4⋊Dic43—21no—
83#13063259—22no—
84#13063259—22no—
85#13063258—22no—
86#13063258—22no—
87#13063257—22no—
88#13063257—22no—
89#13063256—22no—
90#13063256—22no—
91#13063256—22no—
92#13063256—22no—
93#13063249—22no—
94#13063249—22no—
95#13063248—22no—
96#13063248—22no—
97#13063248—22no—
98#13063248—22no—
99#13063248—22no—
100#13063248—22no—
101#13063236D412yes—
102#13063236D412yes—
103C4×C43⋊C8C2311yescharacteristic
104C4×C43⋊C8C2311yescharacteristic
105C4×C43⋊C8C2311yescharacteristic
106C4×C43⋊C8C2311yescharacteristic
107C2×Q16×C43—22no—
108C2×M16×C43D412yes—
109C4⋊Q8×C43C2311yescharacteristic
110C4⋊Q8×C43C2311yescharacteristic
111C4⋊Q8×C43C2311yescharacteristic
112C4⋊Q8×C43C2311yescharacteristic
113#125×C43—21no—
114#125×C43—21no—
115C22⋊Q8×C43—21no—
116C22⋊Q8×C43—21no—
117C22⋊Q8×C43—21no—
118C22⋊Q8×C43—21no—
119C4×Q8×C43—21no—
120C4×Q8×C43—21no—
121C4×Q8×C43—21no—
122C4×Q8×C43—21no—
123#117×C43—21no—
124#117×C43—21no—
125C2×C42×C43C2311yescharacteristic
126#106×C43—22no—
127#103×C43—22no—
128#103×C43—22no—
129#97×C43D412yes—
130C4×C8×C43C2311yescharacteristic
131C4×C8×C43C2311yescharacteristic
132C2×Q8×C43—21no—
133C2×Q8×C43—21no—
134C2×Q8×C43—21no—
135C2×Q8×C43—21no—
136C22×C4×C43C2×D411yescharacteristic
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2×D411yescharacteristic
139C22×Dic43—41no—
140C2×Dic86—21no—
141C2×Dic86—21no—
142C2×Dic86—21no—
143C2×Dic86—21no—
144C2×Dic86—44no—
145C2×Dic86—41no—
146Q16×C43—44no—
147M16×C43—24no—
148C2×C8×C43C2×D412yes—
149C2×C8×C43C2×D412yes—
150C4⋊C4×C43—21no—
151C4⋊C4×C43—21no—
152C4⋊C4×C43—21no—
153C4⋊C4×C43—21no—
154C4⋊C4×C43—21no—
155C4⋊C4×C43—21no—
156C4⋊C4×C43—21no—
157C4⋊C4×C43—21no—
158C4⋊C4×C43—41no—
159C4⋊C4×C43—41no—
160C4⋊C4×C43—41no—
161C4⋊C4×C43—41no—
162C22⋊C4×C43—41no—
163C22⋊C4×C43—41no—
164C42×C43—41no—
165C42×C43—41no—
166C42×C43C2×D411yescharacteristic
167C42×C43C2×D411yescharacteristic
168C42×C43C2×D411yescharacteristic
169C42×C43C2411yescharacteristic
170C22⋊Dic43—41no—
171#10621885—44no—
172#10621885—44no—
173C4⋊Dic43—21no—
174C4⋊Dic43—21no—
175C4⋊Dic43—21no—
176C4⋊Dic43—21no—
177C4⋊Dic43—21no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—41no—
182C4⋊Dic43—41no—
183Dic43⋊C4—41no—
184Dic43⋊C4—41no—
185C4×Dic43—41no—
186#10621877—24no—
187#10621877—42no—
188C2×C43⋊C8C2×D412yes—
189C2×C43⋊C8C2×D412yes—
190C2×C43⋊C8C2×D412yes—
191C2×C43⋊C8C2×D412yes—
192C23×C43#12711yescharacteristic
193Q8×C43—42no—
194Q8×C43—42no—
195Q8×C43—42no—
196Q8×C43—42no—
197C2×C4×C43—22no—
198C2×C4×C43—22no—
199C2×C4×C43—22no—
200C2×C4×C43—41no—
201C2×C4×C43—41no—
202C2×C4×C43—41no—
203C2×C4×C43—41no—
204C2×C4×C43#12711yescharacteristic
205C2×C4×C43#12711yescharacteristic
206C2×C4×C43#12711yescharacteristic
207C2×C4×C43C22×D411yescharacteristic
208C2×C4×C43C22×D411yescharacteristic
209C2×C4×C43C22×D411yescharacteristic
210C2×Dic43—41no—
211C2×Dic43—41no—
212C2×Dic43—41no—
213C2×Dic43—41no—
214C2×Dic43—82no—
215Dic86—42no—
216Dic86—42no—
217Dic86—42no—
218Dic86—42no—
219Dic86—82no—
220C8×C43—22no—
221C8×C43#13714yes—
222C43⋊C8—22no—
223C43⋊C8—22no—
224C43⋊C8—22no—
225C43⋊C8#13714yes—
226#19751—431nomaximal, Sylow
227C22×C43—21no—
228C22×C43—21no—
229C22×C43—21no—
230C22×C43C2×#12711yescharacteristic
231C4×C43—21no—
232C4×C43—21no—
233C4×C43—21no—
234C4×C43—81no—
235C4×C43—81no—
236C4×C43—81no—
237C4×C43—81no—
238C4×C43C2×#13712yes—
239C4×C43C2×#13712yes—
240C4×C43#57512yes—
241Dic43—81no—
242Dic43—81no—
243Dic43—81no—
244Dic43—81no—
245#3185—431no—
246#3185—431no—
247#3185D4311yescharacteristic
248#3165—431no—
249#3165—431no—
250#3139—431no—
251#1723—431no—
252#1723—431no—
253#1718—431no—
254#1718—431no—
255#1716—431no—
256#1716—431no—
257#1707—431no—
258#1707—431no—
259#1455—431no—
260C2×C43—41no—
261C2×C43#315211yescharacteristic
262C2×C43#315211yescharacteristic
263C2×C43#315311yescharacteristic
264#533—431no—
265#533C2×D4311yescharacteristic
266#533C2×D4311yescharacteristic
267C2×C4⋊Q8—431no—
268#501—862no—
269#501—862no—
270#500—431no—
271#500—431no—
272#500—431no—
273#500—431no—
274#498—431no—
275#498—431no—
276#498—431no—
277#498—431no—
278#498—431no—
279#498—431no—
280#498C2×D4311yescharacteristic
281#494—431no—
282#494—431no—
283#494C2×D4311yescharacteristic
284#491—862no—
285#487—431no—
286#487—431no—
287#487—431no—
288#487—431no—
289#487—431no—
290#487—431no—
291#487—431no—
292#487—431no—
293#487C2×D4311yescharacteristic
294#487C2×D4311yescharacteristic
295#470—22no—
296#470—862no—
297#470—862no—
298#441—22no—
299#441—862no—
300#441—862no—
301#428—862no—
302#428—862no—
303#419—862no—
304C4×M16—431no—
305C4×M16—431no—
306C4×M16C2×D4311yescharacteristic
307#322—431no—
308#322—431no—
309#322—431no—
310C82—431no—
311C43#1975111yescharacteristic, complemented, Sylow
312C22×Q8—861no—
313C2×Q16—22no—
314C2×Q16—862no—
315C2×Q16—862no—
316C2×M16—432no—
317C2×M16—432no—
318C2×M16C22⋊D4312yes—
319C4⋊Q8—431no—
320C4⋊Q8—431no—
321C4⋊Q8—431no—
322C4⋊Q8—431no—
323C4⋊Q8—861no—
324C4⋊Q8—861no—
325C4⋊Q8—861no—
326C4⋊Q8C22×D4311yescharacteristic
327C4⋊Q8C22×D4311yescharacteristic
328C4⋊Q8C22×D4311yescharacteristic
329C4⋊Q8C22×D4311yescharacteristic
330#125—21no—
331#125—21no—
332#125—861no—
333C22⋊Q8—21no—
334C22⋊Q8—21no—
335C22⋊Q8—21no—
336C22⋊Q8—21no—
337C22⋊Q8—861no—
338C22⋊Q8—861no—
339C4×Q8—21no—
340C4×Q8—21no—
341C4×Q8—21no—
342C4×Q8—21no—
343C4×Q8—861no—
344C4×Q8—861no—
345#117—21no—
346#117—21no—
347#117—861no—
348C2×C4⋊C4—861no—
349C2×C4⋊C4—861no—
350C2×C42C22×D4311yescharacteristic
351#107—862no—
352#107—862no—
353#107—862no—
354#107—862no—
355#106—22no—
356#106—862no—
357#106—862no—
358#106—862no—
359#106—862no—
360#106—862no—
361#106—862no—
362#103—22no—
363#103—22no—
364#103—862no—
365#103—862no—
366#103—862no—
367#103—862no—
368#103—862no—
369#103—862no—
370#103—862no—
371#103—862no—
372#97—432no—
373#97—432no—
374#97C22⋊D4312yes—
375C4×C8—431no—
376C4×C8—431no—
377C4×C8—431no—
378C4×C8—431no—
379C4×C8C22×D4311yescharacteristic
380C4×C8C22×D4311yescharacteristic
381C2×Q8—21no—
382C2×Q8—21no—
383C2×Q8—21no—
384C2×Q8—21no—
385C2×Q8—861no—
386C2×Q8—861no—
387C2×Q8—861no—
388C2×Q8—861no—
389C2×Q8—1724no—
390C2×Q8—1721no—
391C22×C4—1721no—
392C22×C4D4×D4311yescharacteristic
393C22×C4D4×D4311yescharacteristic
394C22×C4C2×C22⋊D4311yescharacteristic
395Q16—44no—
396Q16—1724no—
397Q16—1724no—
398M16—24no—
399M16—864no—
400M16—1722no—
401C2×C8—432no—
402C2×C8—432no—
403C2×C8—432no—
404C2×C8—432no—
405C2×C8C2×C22⋊D4312yes—
406C2×C8C2×C22⋊D4312yes—
407C4⋊C4—21no—
408C4⋊C4—21no—
409C4⋊C4—21no—
410C4⋊C4—21no—
411C4⋊C4—21no—
412C4⋊C4—21no—
413C4⋊C4—21no—
414C4⋊C4—21no—
415C4⋊C4—41no—
416C4⋊C4—41no—
417C4⋊C4—41no—
418C4⋊C4—41no—
419C4⋊C4—861no—
420C4⋊C4—861no—
421C4⋊C4—861no—
422C4⋊C4—861no—
423C4⋊C4—861no—
424C4⋊C4—861no—
425C4⋊C4—861no—
426C4⋊C4—861no—
427C4⋊C4—1721no—
428C4⋊C4—1721no—
429C4⋊C4—1721no—
430C4⋊C4—1721no—
431C22⋊C4—41no—
432C22⋊C4—41no—
433C22⋊C4—1721no—
434C42—41no—
435C42—41no—
436C42—1721no—
437C42D4×D4311yescharacteristic
438C42D4×D4311yescharacteristic
439C42C2×C22⋊D4311yescharacteristic
440C42C23×D4311yescharacteristic
441C23#1306332111yescharacteristic
442Q8—42no—
443Q8—42no—
444Q8—42no—
445Q8—42no—
446Q8—3442no—
447Q8—1722no—
448Q8—1722no—
449Q8—1722no—
450Q8—1722no—
451C2×C4—22no—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—3442no—
459C2×C4—1721no—
460C2×C4—1721no—
461C2×C4—1721no—
462C2×C4—1721no—
463C2×C4#1306332111yescharacteristic
464C2×C4#1306332111yescharacteristic
465C2×C4#1306332111yescharacteristic
466C2×C4C2×D4×D4311yescharacteristic
467C2×C4C2×D4×D4311yescharacteristic
468C2×C4C22×C22⋊D4311yescharacteristic
469C8—22no—
470C8—434no—
471C8—862no—
472C8—862no—
473C8—862no—
474C8#1306335514yes—
475C22—21no—
476C22—21no—
477C22—21no—
478C22C2×#1306332111yescharacteristic
479C4—21no—
480C4—21no—
481C4—21no—
482C4—81no—
483C4—81no—
484C4—81no—
485C4—81no—
486C4—3441no—
487C4—3441no—
488C4—3441no—
489C4—3441no—
490C4#137×D4312yes—
491C4C2×#1306335512yes—
492C4#1458369812yes—
493C2—41no—
494C2#1914505011yescharacteristic
495C2#1914505511yescharacteristic
496C2#1914506211yescharacteristic
subgroupG/H
centerC22C2×#13063321
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3185C2
socleC22×C43C2×#127
prime radicalC23×C43#127
hypercenter#3185D43
hypocenterC43#19751
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3185

Complements

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

NH ≅ G/Ntype
6. #19134275C2semidirect
7. #19134269C2semidirect
8. #19134244C2semidirect
9. #19134243C2semidirect
10. #19134230C2semidirect
11. #19134226C2semidirect
12. #19134190C2semidirect
13. #19134189C2semidirect
311. C43#19751semidirect

Maximal subgroups

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

subgroupindex
#191453362
#191451422
#191451412
#191449772
#191342752
#191342692
#191342442
#191342432
#191342302
#191342262
#191341902
#191341892
#191328982
C43×#31852
#1975143