Finite Group Databasebeta

← #24992690

Subgroups — #24992690

Order 11008.

532 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144044C211yesmaximal, characteristic
2C8×#10621898C211yesmaximal, characteristic, complemented
3#19134612C211yesmaximal, characteristic, complemented
4#19133090C211yesmaximal, characteristic, complemented
5#19132490C211yesmaximal, characteristic, complemented
6#19132435C211yesmaximal, characteristic, complemented
7C43×#1492C211yesmaximal, characteristic, complemented
8C2×#13063345—21no—
9C4×#10621898C2211yescharacteristic
10#14583118—21no—
11#14583111—21no—
12#14583106C411yescharacteristic, complemented
13#14583101C411yescharacteristic, complemented
14#14583096C411yescharacteristic, complemented
15#14583091C411yescharacteristic, complemented
16C8×Dic86—21no—
17C8×D172—21no—
18C8×C22⋊D43—22no—
19#14582952C2211yescharacteristic
20#14582950—21no—
21C2×C4⋊(C43⋊C8)C2211yescharacteristic
22C2×#13063251—21no—
23#14582895—21no—
24C4×C8×D43—21no—
25C4×C4⋊Dic43C2211yescharacteristic
26#14582660—21no—
27#14582633—22no—
28C43×#532C2211yescharacteristic
29C43×#423C2211yescharacteristic
30C2×C4×C8×C43C2211yescharacteristic
31C43×D4⋊C8—21no—
32C43×D4⋊C8—21no—
33C2×#10621898D411yescharacteristic
34#13063345—42no—
35#13063345—42no—
36C2×#10621885—21no—
37C2×#10621883—21no—
38C2×#10621884—21no—
39C2×#10621882—21no—
40C22×C43⋊C8—21no—
41C2×C8×D43—22no—
42C4×Dic86C2×C411yescharacteristic
43C4×Dic86D411yescharacteristic
44C4×D172C2×C411yescharacteristic
45C4×D172D411yescharacteristic
46C4×C22⋊D43—21no—
47C4×C22⋊D43—21no—
48#13063284D411yescharacteristic
49#13063282—21no—
50C2×C4⋊Dic43—21no—
51C2×C4×Dic43—21no—
52C42×D43—21no—
53C4⋊(C43⋊C8)—21no—
54C4⋊(C43⋊C8)—21no—
55C4⋊(C43⋊C8)C2×C411yescharacteristic
56C4⋊(C43⋊C8)C2×C411yescharacteristic
57Dic43⋊C8—22no—
58#13063251—42no—
59#13063249—21no—
60#13063249—21no—
61#13063246—21no—
62#13063246—21no—
63C22⋊(C43⋊C8)D412yes—
64(C2×D43)⋊C8—22no—
65C4×C43⋊C8—21no—
66C8×Dic43—22no—
67C43⋊#95—21no—
68C2×#41×C43—21no—
69C2×M16×C43—21no—
70C22×C8×C43—21no—
71C4⋊Q8×C43C2×C411yescharacteristic
72#127×C43C2×C411yescharacteristic
73#124×C43—21no—
74#121×C43—21no—
75#121×C43—21no—
76C4×D4×C43—21no—
77C4×D4×C43—21no—
78C2×C42×C43C2311yescharacteristic
79C4⋊C8×C43—21no—
80C4⋊C8×C43—21no—
81C4×C8×C43—21no—
82C4×C8×C43D411yescharacteristic
83C4×C8×C43D411yescharacteristic
84#41×C43—41no—
85#41×C43—41no—
86#41×C43—41no—
87#41×C43—41no—
88C2×Q8×C43—21no—
89C2×D4×C43—21no—
90C2×D4×C43—21no—
91C2×D4×C43—21no—
92C2×D4×C43—41no—
93C22×C4×C43—41no—
94C22×C4×C43C2×D411yescharacteristic
95C22×C4×C43C2×D411yescharacteristic
96C22×C4×C43#4111yescharacteristic
97C2×C22⋊D43—21no—
98C22×Dic43—41no—
99#10621898—21no—
100#10621898—21no—
101#10621898D812yes—
102#10621898SD1612yes—
103C2×D172C22⋊C411yescharacteristic
104C2×C4×D43—21no—
105C2×C4×D43—21no—
106C2×C4×D43—21no—
107C2×Dic86C22⋊C411yescharacteristic
108M16×C43—41no—
109M16×C43—41no—
110C2×C8×C43—21no—
111C2×C8×C43—21no—
112C2×C8×C43—42no—
113C2×C8×C43—41no—
114C4⋊C4×C43—21no—
115C4⋊C4×C43—21no—
116C22⋊C4×C43—41no—
117C22⋊C4×C43—41no—
118C42×C43C22×C411yescharacteristic
119C42×C43C2×D411yescharacteristic
120C42×C43C2×D411yescharacteristic
121C42×C43#4111yescharacteristic
122C22⋊Dic43—21no—
123#10621885—42no—
124#10621884—42no—
125#10621883—42no—
126#10621882—42no—
127(C2×D43)⋊C4—21no—
128(C2×D43)⋊C4—21no—
129C4⋊Dic43—22no—
130C4⋊Dic43—41no—
131C4⋊Dic43C22⋊C411yescharacteristic
132C4⋊Dic43C22⋊C411yescharacteristic
133Dic43⋊C4—21no—
134Dic43⋊C4—21no—
135C4×Dic43—21no—
136C4×Dic43—21no—
137C4×Dic43—21no—
138C4×Dic43—41no—
139C4×Dic43—41no—
140C2×C43⋊C8—21no—
141C2×C43⋊C8—21no—
142C2×C43⋊C8—22no—
143C2×C43⋊C8—41no—
144C2×C43⋊C8—41no—
145C8×D43—44no—
146C23×C43—41no—
147C23×C43#12111yescharacteristic
148C22×D43—21no—
149Q8×C43—41no—
150Q8×C43—41no—
151D4×C43—41no—
152D4×C43—41no—
153D4×C43—41no—
154D4×C43—41no—
155D4×C43—81no—
156D4×C43—81no—
157D4×C43—81no—
158C2×C4×C43—21no—
159C2×C4×C43—21no—
160C2×C4×C43—41no—
161C2×C4×C43—41no—
162C2×C4×C43—81no—
163C2×C4×C43—81no—
164C2×C4×C43C2×C22⋊C411yescharacteristic
165C2×C4×C43C4×D411yescharacteristic
166C2×C4×C43C4×D411yescharacteristic
167C2×C4×C43#12011yescharacteristic
168C2×C4×C43#12111yescharacteristic
169C2×C4×C43#12311yescharacteristic
170C2×C4×C43C2×D811yescharacteristic
171C2×C4×C43C2×SD1611yescharacteristic
172C2×C4×C43#13511yescharacteristic
173C2×C4×C43#13511yescharacteristic
174C22⋊D43—22no—
175C22⋊D43—22no—
176C2×Dic43—21no—
177C2×Dic43—21no—
178C2×Dic43—21no—
179C2×Dic43—42no—
180C2×Dic43—81no—
181C2×Dic43—81no—
182D172—21no—
183D172#10212yes—
184C4×D43—22no—
185C4×D43—22no—
186C4×D43—42no—
187C4×D43—41no—
188C4×D43—41no—
189Dic86—21no—
190Dic86#10212yes—
191C8×C43—22no—
192C8×C43—41no—
193C8×C43—81no—
194C43⋊C8—42no—
195C43⋊C8—41no—
196C43⋊C8—41no—
197#9208—431nomaximal, Sylow
198C22×C43—21no—
199C22×C43—21no—
200C22×C43—81no—
201C22×C43—81no—
202C22×C43—81no—
203C22×C43#38611yescharacteristic
204C22×C43#46511yescharacteristic
205C22×C43#46611yescharacteristic
206C2×D43—22no—
207C2×D43—41no—
208C2×D43—41no—
209C4×C43—21no—
210C4×C43—21no—
211C4×C43—21no—
212C4×C43—81no—
213C4×C43C2×#10211yescharacteristic
214C4×C43#41611yescharacteristic
215C4×C43#44311yescharacteristic
216C4×C43#44411yescharacteristic
217C4×C43#46511yescharacteristic
218C4×C43#46611yescharacteristic
219Dic43—22no—
220Dic43—41no—
221Dic43—41no—
222Dic43—82no—
223#3035—431no—
224C8×#41—431no—
225#1806—431no—
226#1502—431no—
227#1492D4311yescharacteristic, complemented
228#1301—431no—
229#1279—431no—
230C2×C43—21no—
231C2×C43—21no—
232C2×C43—161no—
233C2×C43#187611yescharacteristic
234C2×C43#189311yescharacteristic
235C2×C43#190611yescharacteristic
236D43—42no—
237C2×#135—861no—
238#532C2×D4311yescharacteristic
239C4×#41—431no—
240#464—861no—
241#463—861no—
242#462—431no—
243#461—431no—
244#460—431no—
245#459—431no—
246C8×Q8—861no—
247C8×D4—861no—
248C8×D4—862no—
249#431—431no—
250#431—861no—
251#423C2×D4311yescharacteristic
252C2×C4⋊C8—431no—
253C2×#104—861no—
254#416—861no—
255C2×C4×C8—861no—
256C2×C4×C8C2×D4311yescharacteristic
257C4×C4⋊C4—431no—
258#339—861no—
259#327—862no—
260D4⋊C8—21no—
261D4⋊C8—21no—
262C43#920811yescharacteristic, complemented, Sylow
263C2×#41—21no—
264C2×#41—431no—
265#135—1722no—
266#135—1722no—
267C2×Q16—861no—
268C2×SD16—861no—
269C2×SD16—861no—
270C2×D8—861no—
271C2×M16—21no—
272C22×C8—21no—
273C22×C8—862no—
274C22×C8—861no—
275C4⋊Q8C4×D4311yescharacteristic
276#127C4×D4311yescharacteristic
277#124—21no—
278#121—21no—
279#121—21no—
280C4×Q8—431no—
281C4×Q8—431no—
282C4×D4—21no—
283C4×D4—21no—
284C4×D4—431no—
285C4×D4—431no—
286C4×D4—861no—
287C4×D4—861no—
288#117—431no—
289#117—861no—
290C2×C4⋊C4—861no—
291C2×C42—861no—
292C2×C42—861no—
293C2×C42C22×D4311yescharacteristic
294C4⋊C8—21no—
295C4⋊C8—21no—
296C4⋊C8—431no—
297C4⋊C8—431no—
298C4⋊C8—862no—
299C4⋊C8—861no—
300C4⋊C8—861no—
301#104—1722no—
302#103—861no—
303#103—861no—
304#102—861no—
305#102—861no—
306C22⋊C8—432no—
307C22⋊C8—862no—
308C4×C8—21no—
309C4×C8—862no—
310C4×C8—861no—
311C4×C8C22⋊D4311yescharacteristic
312C4×C8C22⋊D4311yescharacteristic
313#95—861no—
314#41—41no—
315#41—41no—
316#41—41no—
317#41—41no—
318#41—432no—
319#41—432no—
320#41—861no—
321#41—861no—
322C2×Q8—21no—
323C2×Q8—431no—
324C2×D4—21no—
325C2×D4—21no—
326C2×D4—21no—
327C2×D4—41no—
328C2×D4—431no—
329C2×D4—861no—
330C22×C4—41no—
331C22×C4—861no—
332C22×C4—861no—
333C22×C4—861no—
334C22×C4—1721no—
335C22×C4#1062189811yescharacteristic
336C22×C4D4×D4311yescharacteristic
337C22×C4D4×D4311yescharacteristic
338Q16—1722no—
339SD16—1722no—
340SD16—1722no—
341D8—1722no—
342M16—41no—
343M16—41no—
344C2×C8—21no—
345C2×C8—21no—
346C2×C8—42no—
347C2×C8—41no—
348C2×C8—861no—
349C2×C8—861no—
350C2×C8—862no—
351C2×C8—1724no—
352C2×C8—1721no—
353C2×C8—1721no—
354C4⋊C4—21no—
355C4⋊C4—21no—
356C4⋊C4—431no—
357C4⋊C4—431no—
358C4⋊C4—862no—
359C4⋊C4—861no—
360C4⋊C4—861no—
361C4⋊C4—1721no—
362C22⋊C4—41no—
363C22⋊C4—41no—
364C22⋊C4—861no—
365C22⋊C4—861no—
366C22⋊C4—861no—
367C42—861no—
368C42—861no—
369C42—861no—
370C42—1721no—
371C42—1721no—
372C42C2×C4×D4311yescharacteristic
373C42D4×D4311yescharacteristic
374C42#1062190011yescharacteristic
375C42C2×C22⋊D4311yescharacteristic
376C23—41no—
377C23—861no—
378C23#1306329811yescharacteristic
379Q8—41no—
380Q8—41no—
381Q8—432no—
382Q8—861no—
383D4—41no—
384D4—41no—
385D4—41no—
386D4—41no—
387D4—81no—
388D4—81no—
389D4—81no—
390D4—432no—
391D4—862no—
392D4—862no—
393D4—861no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—81no—
399C2×C4—81no—
400C2×C4—861no—
401C2×C4—862no—
402C2×C4—862no—
403C2×C4—861no—
404C2×C4—861no—
405C2×C4—3441no—
406C2×C4—3441no—
407C2×C4—1722no—
408C2×C4—1722no—
409C2×C4—1721no—
410C2×C4—1721no—
411C2×C4C22⋊C4×D4311yescharacteristic
412C2×C4(C22⋊D43)⋊C411yescharacteristic
413C2×C4C4×C22⋊D4311yescharacteristic
414C2×C4#1306329311yescharacteristic
415C2×C4#1306329611yescharacteristic
416C2×C4#1306330711yescharacteristic
417C2×C4D8×D4311yescharacteristic
418C2×C4SD16×D4311yescharacteristic
419C2×C4#1306334411yescharacteristic
420C2×C4#1306334611yescharacteristic
421C8—22no—
422C8—41no—
423C8—81no—
424C8—1722no—
425C8—1721no—
426C8—1721no—
427C22—21no—
428C22—21no—
429C22—81no—
430C22—81no—
431C22—81no—
432C22—862no—
433C22—1721no—
434C22—1721no—
435C22#1458277511yescharacteristic
436C22#1458312711yescharacteristic
437C22#1458313411yescharacteristic
438C4—21no—
439C4—21no—
440C4—21no—
441C4—81no—
442C4—862no—
443C4—3442no—
444C4—1721no—
445C4—1721no—
446C4#102×D4311yescharacteristic
447C4#1458289211yescharacteristic
448C4#1458301411yescharacteristic
449C4#1458301911yescharacteristic
450C4#1458312511yescharacteristic
451C4#1458313211yescharacteristic
452C2—21no—
453C2—21no—
454C2—161no—
455C2—1722no—
456C2#1913492511yescharacteristic
457C2#1913502011yescharacteristic
458C2#1913509911yescharacteristic
subgroupG/H
centerC2×C4#13063296
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1492C2
socleC22×C43#386
prime radical#19144044C2
cosocleC2×C42×C43C23
hypercenter#1492D43
hypocenterC43#9208
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1492

Complements

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

NH ≅ G/Ntype
2. C8×#10621898C2semidirect
3. #19134612C2semidirect
4. #19133090C2semidirect
5. #19132490C2semidirect
6. #19132435C2semidirect
7. C43×#1492C2semidirect
12. #14583106C4semidirect
13. #14583101C4semidirect
14. #14583096C4semidirect
15. #14583091C4semidirect
227. #1492D43semidirect
262. C43#9208semidirect

Maximal subgroups

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

subgroupindex
#191440442
C8×#106218982
#191346122
#191330902
#191324902
#191324352
C43×#14922
#920843