Finite Group Databasebeta

← #25080464

Subgroups — #25080464

Order 11008.

650 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145170C211yesmaximal, characteristic
2#19144717C211yesmaximal, characteristic, complemented
3C2×Q8×C43⋊C8C211yesmaximal, characteristic, complemented
4#19134013C212yesmaximal, complemented
5#19134009C212yesmaximal, complemented
6#19133997C212yesmaximal, complemented
7#19133953C212yesmaximal, complemented
8#19133356C211yesmaximal, characteristic, complemented
9#19133291C211yesmaximal, characteristic, complemented
10#19133290C211yesmaximal, characteristic, complemented
11C43×#3112C211yesmaximal, characteristic, complemented
12#14583449C2211yescharacteristic
13#14583302C2211yescharacteristic
14#14583275C2211yescharacteristic
15#14583247C2211yescharacteristic
16#14583245C2211yescharacteristic
17#14583212—21no—
18#14583194C2212yes—
19#14583133—21no—
20#14583133—21no—
21#14583099C2212yes—
22#14583038—21no—
23Q8×C43⋊C8—21no—
24Q8×C43⋊C8—21no—
25Q8×C43⋊C8C2212yes—
26Q8×C43⋊C8C2212yes—
27#14582997—22no—
28C4×#10621882—21no—
29C4×#10621882—21no—
30#14582956C2211yescharacteristic
31C2×C4⋊(C43⋊C8)—21no—
32C2×C4⋊(C43⋊C8)C2211yescharacteristic
33C2×C4×C43⋊C8—21no—
34C2×C4×C43⋊C8C2211yescharacteristic
35#14582651C2212yes—
36#14582649C2212yes—
37#14582648C2212yes—
38#14582647C2212yes—
39#14582643C2212yes—
40#14582642C2212yes—
41C43×#532C2211yescharacteristic
42C2×C4×Q8×C43C2211yescharacteristic
43C43×#480—21no—
44C43×#477C2212yes—
45C43×#460C2212yes—
46C43×#448—21no—
47C43×#440—22no—
48C43×#432C2211yescharacteristic
49C2×#10621898—21no—
50C2×#10621884—22no—
51C2×#10621882—21no—
52C2×#10621882—21no—
53C22×C43⋊C8—21no—
54C22×C43⋊C8D411yescharacteristic
55C22×C43⋊C8D411yescharacteristic
56#13063325C2311yescharacteristic
57#13063322C2311yescharacteristic
58#13063313—21no—
59#13063299—21no—
60#13063299—21no—
61C4×D172—21no—
62C4×D172—21no—
63#13063258—22no—
64#13063258—21no—
65#13063258—21no—
66C4⋊(C43⋊C8)—21no—
67C4⋊(C43⋊C8)—22no—
68C4⋊(C43⋊C8)—22no—
69C4⋊(C43⋊C8)C2312yes—
70C4⋊(C43⋊C8)C2312yes—
71#13063249—22no—
72#13063246—21no—
73#13063246—21no—
74#13063245—22no—
75#13063245—21no—
76#13063245—21no—
77C22⋊(C43⋊C8)—21no—
78#13063236—21no—
79C4×C43⋊C8—22no—
80C4×C43⋊C8—22no—
81C4×C43⋊C8D411yescharacteristic
82C4×C43⋊C8D411yescharacteristic
83C4×C43⋊C8C2311yescharacteristic
84C4×C43⋊C8C2311yescharacteristic
85C2×#41×C43—21no—
86C22×Q8×C43D411yescharacteristic
87C2×SD16×C43—22no—
88C4⋊Q8×C43C2311yescharacteristic
89#127×C43C2311yescharacteristic
90#124×C43—21no—
91#121×C43—21no—
92#121×C43—21no—
93C4×Q8×C43—21no—
94C4×Q8×C43—21no—
95C4×Q8×C43D412yes—
96C4×Q8×C43C2312yes—
97C4×D4×C43—21no—
98C4×D4×C43—21no—
99C2×C4⋊C4×C43—21no—
100C2×C4⋊C4×C43D411yescharacteristic
101C2×C42×C43—21no—
102C2×C42×C43C2311yescharacteristic
103#107×C43—22no—
104C4⋊C8×C43C2312yes—
105#103×C43—22no—
106#102×C43—22no—
107C22⋊C8×C43—21no—
108#97×C43—21no—
109#41×C43—82no—
110C2×Q8×C43—24no—
111C2×Q8×C43—21no—
112C2×Q8×C43—21no—
113C2×Q8×C43C2×D412yes—
114C2×D4×C43—21no—
115C2×D4×C43—21no—
116C2×D4×C43—21no—
117C2×D4×C43—41no—
118C22×C4×C43—21no—
119C22×C4×C43—21no—
120C22×C4×C43—41no—
121C22×C4×C43C2×D411yescharacteristic
122C22×C4×C43C2×D411yescharacteristic
123C22×C4×C43#4111yescharacteristic
124C2×C22⋊D43—41no—
125#10621898—82no—
126C2×D172—21no—
127C2×D172—21no—
128C2×D172—21no—
129C2×C4×D43—41no—
130C2×Dic86—21no—
131SD16×C43—44no—
132C2×C8×C43—22no—
133C4⋊C4×C43—22no—
134C4⋊C4×C43—21no—
135C4⋊C4×C43—22no—
136C4⋊C4×C43—21no—
137C4⋊C4×C43—21no—
138C4⋊C4×C43C2×D412yes—
139C22⋊C4×C43—41no—
140C22⋊C4×C43—41no—
141C42×C43—22no—
142C42×C43—22no—
143C42×C43C2×D411yescharacteristic
144C42×C43C2×D411yescharacteristic
145C42×C43#4111yescharacteristic
146C42×C43C2411yescharacteristic
147#10621884—44no—
148#10621882—42no—
149#10621882—42no—
150(C2×D43)⋊C4—41no—
151(C2×D43)⋊C4—41no—
152C4⋊Dic43—21no—
153C4⋊Dic43—21no—
154C2×C43⋊C8—22no—
155C2×C43⋊C8—22no—
156C2×C43⋊C8—22no—
157C2×C43⋊C8—41no—
158C2×C43⋊C8—42no—
159C2×C43⋊C8C2×D411yescharacteristic
160C2×C43⋊C8C2×D411yescharacteristic
161C2×C43⋊C8C2×D411yescharacteristic
162C2×C43⋊C8C2×D411yescharacteristic
163C23×C43—41no—
164C23×C43#12111yescharacteristic
165C22×D43—41no—
166Q8×C43—24no—
167Q8×C43—22no—
168Q8×C43—81no—
169Q8×C43#13514yes—
170D4×C43—42no—
171D4×C43—41no—
172D4×C43—41no—
173D4×C43—81no—
174D4×C43—82no—
175C2×C4×C43—24no—
176C2×C4×C43—22no—
177C2×C4×C43—22no—
178C2×C4×C43—22no—
179C2×C4×C43—21no—
180C2×C4×C43—21no—
181C2×C4×C43—22no—
182C2×C4×C43—42no—
183C2×C4×C43—41no—
184C2×C4×C43—82no—
185C2×C4×C43#12111yescharacteristic
186C2×C4×C43#12111yescharacteristic
187C2×C4×C43#12111yescharacteristic
188C2×C4×C43C22×D411yescharacteristic
189C2×C4×C43C22×D411yescharacteristic
190C2×C4×C43C2×#4111yescharacteristic
191C22⋊D43—82no—
192C2×Dic43—41no—
193D172—42no—
194D172—41no—
195D172—41no—
196D172—81no—
197C4×D43—82no—
198Dic86—81no—
199C8×C43—42no—
200C43⋊C8—21no—
201C43⋊C8—21no—
202C43⋊C8—21no—
203C43⋊C8—42no—
204C43⋊C8—42no—
205C43⋊C8#13712yes—
206#19264—431nomaximal, Sylow
207C22×C43—21no—
208C22×C43—21no—
209C22×C43—81no—
210C22×C43—81no—
211C22×C43—81no—
212C22×C43#47212yes—
213C22×C43C2×#12111yescharacteristic
214C2×D43—81no—
215C2×D43—81no—
216C2×D43—81no—
217C4×C43—21no—
218C4×C43—24no—
219C4×C43—21no—
220C4×C43—21no—
221C4×C43—21no—
222C4×C43—42no—
223C4×C43—81no—
224C4×C43C2×#13512yes—
225C4×C43C2×#13711yescharacteristic
226C4×C43#57511yescharacteristic
227Dic43—81no—
228#3169—431no—
229#3112—431no—
230#3112D4311yescharacteristic, complemented
231C2×C8×Q8—431no—
232#1678—432no—
233#1678—432no—
234#1676—432no—
235#1668—432no—
236#1568—431no—
237#1551—431no—
238#1551—431no—
239C2×C43—22no—
240C2×C43—161no—
241C2×C43#303711yescharacteristic
242C2×C43#305011yescharacteristic
243C2×C43C2×#47211yescharacteristic
244D43—161no—
245#532—431no—
246#532C2×D4311yescharacteristic
247C2×C4×Q8C2×D4311yescharacteristic
248#500—431no—
249#493—431no—
250#486—431no—
251#486—431no—
252#480—21no—
253#480—861no—
254#477—432no—
255#477C2×D4312yes—
256#466—861no—
257#466—861no—
258#460—432no—
259#460C2×D4312yes—
260#448—21no—
261#448—861no—
262C8×Q8—432no—
263C8×Q8—432no—
264C8×Q8—861no—
265C8×Q8—861no—
266#440—22no—
267#440—862no—
268C4×D8—861no—
269C4×D8—861no—
270#432—431no—
271#432C2×D4311yescharacteristic
272C2×C4⋊C8—431no—
273C2×C4⋊C8—861no—
274C2×C4×C8—431no—
275C2×C4×C8—861no—
276#335—432no—
277#334—432no—
278#333—432no—
279#333—432no—
280#331—432no—
281#331—432no—
282C43#1926411yescharacteristic, complemented, Sylow
283C2×#41—21no—
284C2×#41—861no—
285C22×Q8C22⋊D4311yescharacteristic
286C2×SD16—22no—
287C2×SD16—862no—
288C2×D8—861no—
289C2×D8—861no—
290C22×C8—431no—
291C22×C8—431no—
292C22×C8—861no—
293C4⋊Q8—431no—
294C4⋊Q8C22×D4311yescharacteristic
295#127—431no—
296#127C22×D4311yescharacteristic
297#124—21no—
298#124—861no—
299#121—21no—
300#121—21no—
301#121—861no—
302#121—861no—
303C4×Q8—21no—
304C4×Q8—21no—
305C4×Q8C22⋊D4312yes—
306C4×Q8C22×D4312yes—
307C4×D4—21no—
308C4×D4—21no—
309C4×D4—861no—
310C4×D4—861no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4C22⋊D4311yescharacteristic
313C2×C42—21no—
314C2×C42C22×D4311yescharacteristic
315#107—22no—
316#107—861no—
317#107—861no—
318#107—862no—
319C4⋊C8—432no—
320C4⋊C8—432no—
321C4⋊C8—862no—
322C4⋊C8—862no—
323C4⋊C8—861no—
324C4⋊C8C22×D4312yes—
325#103—22no—
326#103—862no—
327#102—22no—
328#102—861no—
329#102—861no—
330#102—861no—
331#102—861no—
332#102—862no—
333C22⋊C8—21no—
334C22⋊C8—861no—
335#97—21no—
336#97—861no—
337C4×C8—431no—
338C4×C8—431no—
339C4×C8—431no—
340C4×C8—431no—
341C4×C8—862no—
342C4×C8—862no—
343#41—82no—
344#41—3442no—
345C2×Q8—24no—
346C2×Q8—21no—
347C2×Q8—21no—
348C2×Q8—861no—
349C2×Q8C2×C22⋊D4312yes—
350C2×D4—21no—
351C2×D4—21no—
352C2×D4—21no—
353C2×D4—41no—
354C2×D4—861no—
355C2×D4—861no—
356C2×D4—861no—
357C2×D4—1721no—
358C22×C4—21no—
359C22×C4—21no—
360C22×C4—41no—
361C22×C4—1721no—
362C22×C4D4×D4311yescharacteristic
363C22×C4#1062190011yescharacteristic
364C22×C4C2×C22⋊D4311yescharacteristic
365SD16—44no—
366SD16—1724no—
367D8—1722no—
368D8—1722no—
369C2×C8—22no—
370C2×C8—431no—
371C2×C8—431no—
372C2×C8—431no—
373C2×C8—431no—
374C2×C8—862no—
375C2×C8—862no—
376C2×C8—862no—
377C2×C8—1721no—
378C2×C8—1722no—
379C4⋊C4—22no—
380C4⋊C4—21no—
381C4⋊C4—22no—
382C4⋊C4—21no—
383C4⋊C4—21no—
384C4⋊C4—861no—
385C4⋊C4—861no—
386C4⋊C4C2×C22⋊D4312yes—
387C22⋊C4—41no—
388C22⋊C4—41no—
389C22⋊C4—1721no—
390C22⋊C4—1721no—
391C42—22no—
392C42—22no—
393C42D4×D4311yescharacteristic
394C42#1062190011yescharacteristic
395C42C2×C22⋊D4311yescharacteristic
396C42C23×D4311yescharacteristic
397C23—41no—
398C23—1721no—
399C23#1306329711yescharacteristic
400Q8—24no—
401Q8—22no—
402Q8—81no—
403Q8—3441no—
404Q8#1306334514yes—
405D4—42no—
406D4—41no—
407D4—41no—
408D4—81no—
409D4—82no—
410D4—3441no—
411D4—3442no—
412D4—1722no—
413D4—1721no—
414D4—1721no—
415C2×C4—24no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—22no—
422C2×C4—42no—
423C2×C4—41no—
424C2×C4—82no—
425C2×C4—3442no—
426C2×C4—1721no—
427C2×C4#1306329711yescharacteristic
428C2×C4#1306329711yescharacteristic
429C2×C4#1306329711yescharacteristic
430C2×C4C2×D4×D4311yescharacteristic
431C2×C4C22×C22⋊D4311yescharacteristic
432C2×C4C2×#1062190011yescharacteristic
433C8—42no—
434C8—432no—
435C8—861no—
436C8—861no—
437C8—861no—
438C8—1722no—
439C8—1722no—
440C22—21no—
441C22—21no—
442C22—81no—
443C22—81no—
444C22—81no—
445C22—3441no—
446C22—3441no—
447C22—3441no—
448C22#1458316712yes—
449C22C2×#1306329711yescharacteristic
450C4—21no—
451C4—21no—
452C4—21no—
453C4—24no—
454C4—21no—
455C4—42no—
456C4—81no—
457C4—3441no—
458C4C2×#1306334512yes—
459C4#137×D4311yescharacteristic
460C4#1458369811yescharacteristic
461C2—22no—
462C2—161no—
463C2—6881no—
464C2#1914406411yescharacteristic
465C2#1914417311yescharacteristic
466C2C2×#1458316711yescharacteristic
subgroupG/H
centerC22C2×#13063297
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3112C2
socleC22×C43C2×#121
prime radical#19145170C2
hypercenter#3112D43
hypocenterC43#19264
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3112

Complements

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

NH ≅ G/Ntype
2. #19144717C2semidirect
3. C2×Q8×C43⋊C8C2semidirect
4. #19134013C2semidirect
5. #19134009C2semidirect
6. #19133997C2semidirect
7. #19133953C2semidirect
8. #19133356C2semidirect
9. #19133291C2semidirect
10. #19133290C2semidirect
11. C43×#3112C2semidirect
230. #3112D43semidirect
282. C43#19264semidirect

Maximal subgroups

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

subgroupindex
#191451702
#191447172
C2×Q8×C43⋊C82
#191340132
#191340092
#191339972
#191339532
#191333562
#191332912
#191332902
C43×#31122
#1926443