Finite Group Databasebeta

← #25082018

Subgroups — #25082018

Order 11008.

620 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144404C211yesmaximal, characteristic
2#19144377C211yesmaximal, characteristic
3#19143703C211yesmaximal, characteristic
4#19134050C212yesmaximal, complemented
5#19134043C212yesmaximal, complemented
6#19133962C212yesmaximal, complemented
7#19133957C212yesmaximal, complemented
8#19133370C211yesmaximal, characteristic, complemented
9#19133285C211yesmaximal, characteristic, complemented
10C2×#14582645C211yesmaximal, characteristic, complemented
11C43×#3209C211yesmaximal, characteristic, complemented
12C4×#10621898C2211yescharacteristic
13#14583203—21no—
14#14583196—21no—
15#14583191—21no—
16#14583191C2211yescharacteristic
17#14583186—21no—
18#14583186C2211yescharacteristic
19#14583181C2211yescharacteristic
20#14583181C2212yes—
21#14583176C2211yescharacteristic
22#14583176C2212yes—
23C8×Dic86C2212yes—
24C8×D172C2212yes—
25(C22⋊D43)⋊C8—22no—
26#14582951—21no—
27#14582939—21no—
28#14582935—21no—
29#14582923C2211yescharacteristic
30C2×C4⋊(C43⋊C8)C2211yescharacteristic
31C2×C4⋊(C43⋊C8)C2211yescharacteristic
32C4⋊C8×D43—21no—
33#14582898—21no—
34#14582893—21no—
35#14582652C2212yes—
36#14582652C2212yes—
37#14582648C2212yes—
38#14582645C2212yes—
39#14582645C2212yes—
40#14582645C2212yes—
41C43×#533C2211yescharacteristic
42C2×C4⋊Q8×C43C2211yescharacteristic
43C43×#494C2212yes—
44C43×#487C2212yes—
45C43×#462—21no—
46C43×#462—21no—
47C43×#451—22no—
48C43×#431C2211yescharacteristic
49C2×#10621898D411yescharacteristic
50C2×#10621877—21no—
51C22×C43⋊C8—21no—
52C22×C43⋊C8—21no—
53C2×C8×D43—22no—
54C4×Dic86D411yescharacteristic
55C4×Dic86C2311yescharacteristic
56C4×D172D411yescharacteristic
57C4×D172C2311yescharacteristic
58C4×C22⋊D43—21no—
59C4×C22⋊D43—21no—
60#13063284D411yescharacteristic
61#13063282—21no—
62C42×D43—21no—
63#13063258—21no—
64#13063258—22no—
65#13063258—21no—
66#13063256—22no—
67#13063256—21no—
68#13063256—21no—
69C4⋊(C43⋊C8)—21no—
70C4⋊(C43⋊C8)—21no—
71C4⋊(C43⋊C8)—21no—
72C4⋊(C43⋊C8)C2312yes—
73C4⋊(C43⋊C8)C2311yescharacteristic
74C4⋊(C43⋊C8)C2311yescharacteristic
75C4⋊(C43⋊C8)C2312yes—
76Dic43⋊C8—22no—
77#13063248—21no—
78#13063248—21no—
79#13063248—22no—
80#13063245—21no—
81#13063245—21no—
82#13063245—22no—
83(C2×D43)⋊C8—22no—
84C8×Dic43—22no—
85C22×Q8×C43—21no—
86C2×Q16×C43—22no—
87C2×Q16×C43—22no—
88C4⋊Q8×C43—21no—
89C4⋊Q8×C43—21no—
90C4⋊Q8×C43—21no—
91C4⋊Q8×C43C2312yes—
92C4⋊Q8×C43C2311yescharacteristic
93C4⋊Q8×C43C2311yescharacteristic
94#125×C43—21no—
95C22⋊Q8×C43—21no—
96C22⋊Q8×C43—21no—
97C4×Q8×C43—21no—
98C4×Q8×C43—21no—
99#117×C43—21no—
100C2×C4⋊C4×C43—21no—
101C2×C4⋊C4×C43—21no—
102C2×C42×C43C2311yescharacteristic
103C4⋊C8×C43D411yescharacteristic
104C4⋊C8×C43D411yescharacteristic
105#103×C43—22no—
106#103×C43—22no—
107C22⋊C8×C43D412yes—
108C4×C8×C43C2312yes—
109C2×Q8×C43—22no—
110C2×Q8×C43—21no—
111C2×Q8×C43—21no—
112C2×Q8×C43—41no—
113C2×Q8×C43—81no—
114C2×Q8×C43—81no—
115C22×C4×C43—41no—
116C22×C4×C43C2×D411yescharacteristic
117C22×C4×C43C2×D411yescharacteristic
118C22×C4×C43#4111yescharacteristic
119C2×C22⋊D43—21no—
120#10621898—22no—
121#10621898Q1614yescomplemented
122C2×D172C2×D411yescharacteristic
123C2×C4×D43—21no—
124C2×C4×D43—21no—
125C2×C4×D43—21no—
126C2×Dic86C2×D411yescharacteristic
127Q16×C43—82no—
128Q16×C43—82no—
129C2×C8×C43C2×D412yes—
130C2×C8×C43C2×D412yes—
131C4⋊C4×C43—21no—
132C4⋊C4×C43—22no—
133C4⋊C4×C43—21no—
134C4⋊C4×C43—21no—
135C4⋊C4×C43—22no—
136C4⋊C4×C43—21no—
137C4⋊C4×C43—41no—
138C4⋊C4×C43—41no—
139C4⋊C4×C43—41no—
140C4⋊C4×C43—41no—
141C22⋊C4×C43—41no—
142C42×C43—41no—
143C42×C43C2×D411yescharacteristic
144C42×C43C2×D411yescharacteristic
145C42×C43#4111yescharacteristic
146C42×C43C2411yescharacteristic
147C22⋊Dic43—21no—
148(C2×D43)⋊C4—21no—
149(C2×D43)⋊C4—21no—
150C4⋊Dic43C2×D411yescharacteristic
151C4⋊Dic43C2×D411yescharacteristic
152Dic43⋊C4—21no—
153Dic43⋊C4—21no—
154C4×Dic43—21no—
155C4×Dic43—21no—
156C4×Dic43—21no—
157#10621877—42no—
158C2×C43⋊C8—22no—
159C2×C43⋊C8—21no—
160C2×C43⋊C8—22no—
161C2×C43⋊C8—21no—
162C2×C43⋊C8—42no—
163C2×C43⋊C8—81no—
164C8×D43—82no—
165C23×C43#12111yescharacteristic
166C22×D43—21no—
167Q8×C43—41no—
168Q8×C43—42no—
169Q8×C43—41no—
170Q8×C43—42no—
171Q8×C43—81no—
172Q8×C43—82no—
173C2×C4×C43—21no—
174C2×C4×C43—21no—
175C2×C4×C43—41no—
176C2×C4×C43—41no—
177C2×C4×C43—41no—
178C2×C4×C43—42no—
179C2×C4×C43—82no—
180C2×C4×C43#12111yescharacteristic
181C2×C4×C43#12111yescharacteristic
182C2×C4×C43#12111yescharacteristic
183C2×C4×C43C2×Q1612yes—
184C2×C4×C43#13512yes—
185C2×C4×C43C22×D411yescharacteristic
186C2×C4×C43C22×D411yescharacteristic
187C2×C4×C43C2×#4111yescharacteristic
188C22⋊D43—24no—
189C2×Dic43—21no—
190C2×Dic43—21no—
191C2×Dic43—21no—
192D172—21no—
193D172C2×Q1612yes—
194C4×D43—24no—
195C4×D43—41no—
196C4×D43—41no—
197C4×D43—81no—
198Dic86—21no—
199Dic86C2×Q1612yes—
200C8×C43—22no—
201C8×C43—22no—
202C43⋊C8—41no—
203C43⋊C8—41no—
204C43⋊C8—42no—
205C43⋊C8—42no—
206#19411—431nomaximal, Sylow
207C22×C43—21no—
208C22×C43—21no—
209C22×C43#46712yes—
210C22×C43C2×#12111yescharacteristic
211C2×D43—22no—
212C2×D43—41no—
213C2×D43—41no—
214C4×C43—21no—
215C4×C43—21no—
216C4×C43—21no—
217C4×C43—82no—
218C4×C43—81no—
219C4×C43—81no—
220C4×C43#46712yes—
221C4×C43C22×Q1611yescharacteristic
222C4×C43C2×#13511yescharacteristic
223C4×C43#57611yescharacteristic
224C4×C43#57711yescharacteristic
225Dic43—22no—
226Dic43—41no—
227Dic43—41no—
228#3209D4311yescharacteristic, complemented
229#3079—431no—
230#3076—431no—
231#2988—431no—
232#1684—432no—
233#1683—432no—
234#1670—432no—
235#1669—432no—
236#1571—431no—
237#1550—431no—
238C2×#332—431no—
239C2×C43—22no—
240C2×C43#304511yescharacteristic
241C2×C43C2×#46711yescharacteristic
242C2×C43#306911yescharacteristic
243D43—42no—
244#533C2×D4311yescharacteristic
245C2×C4⋊Q8C2×D4311yescharacteristic
246C4×#41—431no—
247#494C2×D4312yes—
248#487C2×D4312yes—
249#479—861no—
250#478—861no—
251#477—431no—
252#477—861no—
253#476—431no—
254#476—861no—
255#475—431no—
256#475—432no—
257#474—431no—
258#474—432no—
259#462—21no—
260#462—21no—
261#451—22no—
262C8×Q8—432no—
263C8×D4—432no—
264C8×D4—862no—
265#431—861no—
266#431C2×D4311yescharacteristic
267#428—861no—
268#427—861no—
269#423—431no—
270C2×C4⋊C8—431no—
271C2×C4⋊C8—431no—
272C2×C4⋊C8—861no—
273#417—861no—
274#416—861no—
275#335—432no—
276#335—432no—
277#333—432no—
278#332—432no—
279#332—432no—
280#332—432no—
281C43#1941111yescharacteristic, complemented, Sylow
282C2×#41—431no—
283C22×Q8—21no—
284C2×Q16—22no—
285C2×Q16—22no—
286C2×M16—861no—
287C22×C8—861no—
288C22×C8—861no—
289C22×C8—862no—
290C4⋊Q8—21no—
291C4⋊Q8—21no—
292C4⋊Q8—21no—
293C4⋊Q8C22×D4312yes—
294C4⋊Q8C22×D4311yescharacteristic
295C4⋊Q8C22×D4311yescharacteristic
296#125—21no—
297C22⋊Q8—21no—
298C22⋊Q8—21no—
299C4×Q8—21no—
300C4×Q8—21no—
301C4×Q8—431no—
302C4×Q8—431no—
303C4×D4—431no—
304C4×D4—431no—
305C4×D4—861no—
306C4×D4—861no—
307#117—21no—
308#117—431no—
309#117—861no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—21no—
312C2×C42—861no—
313C2×C42C22×D4311yescharacteristic
314#107—861no—
315#107—861no—
316#107—862no—
317#106—861no—
318#106—861no—
319#106—862no—
320C4⋊C8—432no—
321C4⋊C8—431no—
322C4⋊C8—431no—
323C4⋊C8—432no—
324C4⋊C8—862no—
325C4⋊C8—861no—
326C4⋊C8—861no—
327C4⋊C8—861no—
328C4⋊C8C22⋊D4311yescharacteristic
329C4⋊C8C22⋊D4311yescharacteristic
330#103—22no—
331#103—22no—
332#103—861no—
333#103—861no—
334#103—862no—
335#102—861no—
336#102—861no—
337#102—862no—
338C22⋊C8—862no—
339C22⋊C8C22⋊D4312yes—
340C4×C8—862no—
341C4×C8C22×D4312yes—
342#41—434no—
343#41—862no—
344C2×Q8—22no—
345C2×Q8—21no—
346C2×Q8—21no—
347C2×Q8—41no—
348C2×Q8—81no—
349C2×Q8—81no—
350C2×Q8—431no—
351C2×D4—431no—
352C2×D4—861no—
353C22×C4—41no—
354C22×C4—861no—
355C22×C4—861no—
356C22×C4—861no—
357C22×C4D4×D4311yescharacteristic
358C22×C4#1062190011yescharacteristic
359C22×C4C2×C22⋊D4311yescharacteristic
360Q16—82no—
361Q16—82no—
362M16—1722no—
363C2×C8—861no—
364C2×C8—862no—
365C2×C8—861no—
366C2×C8—862no—
367C2×C8—3442no—
368C2×C8—3441no—
369C2×C8—1722no—
370C2×C8C2×C22⋊D4312yes—
371C2×C8C2×C22⋊D4312yes—
372C4⋊C4—22no—
373C4⋊C4—21no—
374C4⋊C4—21no—
375C4⋊C4—21no—
376C4⋊C4—22no—
377C4⋊C4—21no—
378C4⋊C4—41no—
379C4⋊C4—41no—
380C4⋊C4—41no—
381C4⋊C4—41no—
382C4⋊C4—431no—
383C4⋊C4—431no—
384C4⋊C4—861no—
385C4⋊C4—861no—
386C22⋊C4—41no—
387C22⋊C4—861no—
388C22⋊C4—861no—
389C22⋊C4—861no—
390C42—41no—
391C42—861no—
392C42—861no—
393C42—861no—
394C42D4×D4311yescharacteristic
395C42#1062190011yescharacteristic
396C42C2×C22⋊D4311yescharacteristic
397C42C23×D4311yescharacteristic
398C23—861no—
399C23#1306329611yescharacteristic
400Q8—41no—
401Q8—42no—
402Q8—41no—
403Q8—42no—
404Q8—81no—
405Q8—82no—
406Q8—432no—
407Q8—861no—
408D4—432no—
409D4—864no—
410D4—861no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—42no—
417C2×C4—82no—
418C2×C4—861no—
419C2×C4—864no—
420C2×C4—861no—
421C2×C4—861no—
422C2×C4—3441no—
423C2×C4—1721no—
424C2×C4—1721no—
425C2×C4#1306329611yescharacteristic
426C2×C4#1306329611yescharacteristic
427C2×C4#1306329611yescharacteristic
428C2×C4Q16×D4312yes—
429C2×C4#1306334812yes—
430C2×C4C2×D4×D4311yescharacteristic
431C2×C4C22×C22⋊D4311yescharacteristic
432C2×C4C2×#1062190011yescharacteristic
433C8—22no—
434C8—22no—
435C8—1721no—
436C8—1721no—
437C8—1722no—
438C8—1722no—
439C22—21no—
440C22—21no—
441C22—862no—
442C22—1721no—
443C22—1721no—
444C22#1458313712yes—
445C22C2×#1306329611yescharacteristic
446C4—21no—
447C4—21no—
448C4—21no—
449C4—81no—
450C4—82no—
451C4—81no—
452C4—862no—
453C4—1721no—
454C4—1721no—
455C4#1458313712yes—
456C4C2×Q16×D4311yescharacteristic
457C4C2×#1306334811yescharacteristic
458C4#1458370211yescharacteristic
459C4#1458371011yescharacteristic
460C2—22no—
461C2—1722no—
462C2#1914413011yescharacteristic
463C2C2×#1458313711yescharacteristic
464C2#1914432811yescharacteristic
subgroupG/H
centerC22C2×#13063296
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3209C2
socleC22×C43C2×#121
prime radicalC2×#10621898D4
hypercenter#3209D43
hypocenterC43#19411
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3209

Complements

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

NH ≅ G/Ntype
4. #19134050C2semidirect
5. #19134043C2semidirect
6. #19133962C2semidirect
7. #19133957C2semidirect
8. #19133370C2semidirect
9. #19133285C2semidirect
10. C2×#14582645C2semidirect
11. C43×#3209C2semidirect
121. #10621898Q16semidirect
228. #3209D43semidirect
281. C43#19411semidirect

Maximal subgroups

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

subgroupindex
#191444042
#191443772
#191437032
#191340502
#191340432
#191339622
#191339572
#191333702
#191332852
C2×#145826452
C43×#32092
#1941143