Finite Group Databasebeta

← #25080466

Subgroups — #25080466

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#19144718C211yesmaximal, characteristic, complemented
3#19144713C211yesmaximal, characteristic, complemented
4C2×#14583023C211yesmaximal, characteristic, complemented
5#19134014C212yesmaximal, complemented
6#19134010C212yesmaximal, complemented
7#19133998C212yesmaximal, complemented
8#19133954C212yesmaximal, complemented
9#19133356C211yesmaximal, characteristic, complemented
10#19133288C211yesmaximal, characteristic, complemented
11C43×#1551C211yesmaximal, characteristic, complemented
12#14583449C2211yescharacteristic
13C2×C4×Dic86C2211yescharacteristic
14#14583302C2211yescharacteristic
15#14583275C2211yescharacteristic
16#14583247C2211yescharacteristic
17#14583245C2211yescharacteristic
18#14583213—21no—
19#14583210—21no—
20#14583195C2212yes—
21#14583191C2212yes—
22#14583133—21no—
23#14583133—21no—
24#14583100C2212yes—
25#14583096C2212yes—
26#14583040—21no—
27#14583037—21no—
28#14583023—21no—
29#14583023—21no—
30#14583023C2212yes—
31#14583023C2212yes—
32#14583001—22no—
33#14582999—22no—
34C4×#10621882—21no—
35C4×#10621882—21no—
36#14582956C2211yescharacteristic
37C2×Dic43⋊C8—21no—
38C2×C4×C43⋊C8C2211yescharacteristic
39C2×C8×Dic43—21no—
40#14582651C2212yes—
41#14582649C2212yes—
42#14582647C2212yes—
43#14582642C2212yes—
44C43×#532C2211yescharacteristic
45C43×#432C2211yescharacteristic
46C2×C4⋊C8×C43C2211yescharacteristic
47C43×#333C2212yes—
48C43×#331C2212yes—
49C2×#10621898—21no—
50C22×Dic86D411yescharacteristic
51C2×#10621873—22no—
52C2×#10621883—22no—
53C2×#10621882—21no—
54C2×#10621882—21no—
55C22×C43⋊C8D411yescharacteristic
56C22×C43⋊C8D411yescharacteristic
57#13063325C2311yescharacteristic
58#13063322C2311yescharacteristic
59#13063313—21no—
60#13063299—21no—
61#13063299—21no—
62C4×Dic86—21no—
63C4×Dic86—21no—
64C4×Dic86D412yes—
65C4×Dic86C2312yes—
66C4×D172—21no—
67C4×D172—21no—
68C2×C4⋊Dic43D411yescharacteristic
69C2×Dic43⋊C4—21no—
70C2×C4×Dic43—21no—
71#13063259—22no—
72#13063258—22no—
73#13063258—21no—
74#13063258—21no—
75C4⋊(C43⋊C8)C2312yes—
76Dic43⋊C8—22no—
77Dic43⋊C8—22no—
78#13063250—22no—
79#13063248—22no—
80#13063247—22no—
81#13063246—22no—
82#13063246—21no—
83#13063246—21no—
84#13063245—21no—
85#13063245—21no—
86C22⋊(C43⋊C8)—21no—
87#13063236—21no—
88C4×C43⋊C8D411yescharacteristic
89C4×C43⋊C8D411yescharacteristic
90C4×C43⋊C8C2311yescharacteristic
91C4×C43⋊C8C2311yescharacteristic
92C8×Dic43—22no—
93C8×Dic43—22no—
94C2×#41×C43—21no—
95C22×C8×C43—21no—
96C4⋊Q8×C43C2311yescharacteristic
97#127×C43C2311yescharacteristic
98#124×C43—21no—
99#121×C43—21no—
100#121×C43—21no—
101C4×D4×C43—21no—
102C4×D4×C43—21no—
103C2×C42×C43C2311yescharacteristic
104C4⋊C8×C43—21no—
105C4⋊C8×C43C2312yes—
106C4⋊C8×C43C2312yes—
107C22⋊C8×C43—21no—
108#97×C43—21no—
109#41×C43—82no—
110C2×Q8×C43—21no—
111C2×D4×C43—21no—
112C2×D4×C43—21no—
113C2×D4×C43—21no—
114C2×D4×C43—41no—
115C22×C4×C43—41no—
116C22×C4×C43C2×D411yescharacteristic
117C22×C4×C43C2×D411yescharacteristic
118C22×C4×C43#4111yescharacteristic
119C2×C22⋊D43—41no—
120C22×Dic43—21no—
121C22×Dic43—21no—
122#10621898—82no—
123C2×D172—21no—
124C2×D172—21no—
125C2×D172—21no—
126C2×C4×D43—41no—
127C2×Dic86—21no—
128C2×Dic86—24no—
129C2×Dic86—21no—
130C2×Dic86C2×D412yes—
131C2×C8×C43—22no—
132C2×C8×C43—22no—
133C2×C8×C43—42no—
134C4⋊C4×C43—21no—
135C4⋊C4×C43—21no—
136C22⋊C4×C43—41no—
137C22⋊C4×C43—41no—
138C42×C43C2×D411yescharacteristic
139C42×C43C2×D411yescharacteristic
140C42×C43#4111yescharacteristic
141C42×C43C2411yescharacteristic
142#10621883—44no—
143#10621882—42no—
144#10621882—42no—
145(C2×D43)⋊C4—41no—
146(C2×D43)⋊C4—41no—
147C4⋊Dic43—21no—
148C4⋊Dic43—21no—
149C4⋊Dic43—21no—
150C4⋊Dic43C2×D412yes—
151Dic43⋊C4—22no—
152Dic43⋊C4—22no—
153C4×Dic43—22no—
154C4×Dic43—22no—
155C2×C43⋊C8—22no—
156C2×C43⋊C8—22no—
157C2×C43⋊C8—41no—
158C2×C43⋊C8C2×D411yescharacteristic
159C2×C43⋊C8C2×D411yescharacteristic
160C2×C43⋊C8C2×D411yescharacteristic
161C2×C43⋊C8C2×D411yescharacteristic
162#10621873—44no—
163C23×C43—41no—
164C23×C43#12111yescharacteristic
165C22×D43—41no—
166Q8×C43—81no—
167D4×C43—42no—
168D4×C43—41no—
169D4×C43—41no—
170D4×C43—81no—
171D4×C43—82no—
172C2×C4×C43—22no—
173C2×C4×C43—22no—
174C2×C4×C43—21no—
175C2×C4×C43—21no—
176C2×C4×C43—41no—
177C2×C4×C43—82no—
178C2×C4×C43#12111yescharacteristic
179C2×C4×C43#12111yescharacteristic
180C2×C4×C43#12111yescharacteristic
181C2×C4×C43C22×D411yescharacteristic
182C2×C4×C43C22×D411yescharacteristic
183C2×C4×C43C2×#4111yescharacteristic
184C22⋊D43—82no—
185C2×Dic43—24no—
186C2×Dic43—22no—
187C2×Dic43—22no—
188C2×Dic43—42no—
189C2×Dic43—41no—
190D172—42no—
191D172—41no—
192D172—41no—
193D172—81no—
194C4×D43—82no—
195Dic86—24no—
196Dic86—22no—
197Dic86—81no—
198Dic86#13514yes—
199C8×C43—42no—
200C8×C43—42no—
201C43⋊C8—21no—
202C43⋊C8—21no—
203C43⋊C8—21no—
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—21no—
219C4×C43—21no—
220C4×C43—21no—
221C4×C43—81no—
222C4×C43C2×#13512yes—
223C4×C43C2×#13711yescharacteristic
224C4×C43#57511yescharacteristic
225Dic43—24no—
226Dic43—42no—
227Dic43—81no—
228#3169—431no—
229#3112—431no—
230#3112—431no—
231C2×C8×Q8—431no—
232#1678—432no—
233#1678—432no—
234#1676—432no—
235#1668—432no—
236#1568—431no—
237#1551—431no—
238#1551D4311yescharacteristic, complemented
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×Q8—431no—
248#500—431no—
249#493—431no—
250#486—431no—
251#486—431no—
252#480—861no—
253#480—861no—
254#477—432no—
255#477—432no—
256#466—861no—
257#466—861no—
258#460—432no—
259#460—432no—
260#448—861no—
261#448—861no—
262C8×Q8—432no—
263C8×Q8—432no—
264C8×Q8—861no—
265C8×Q8—861no—
266#440—862no—
267#440—862no—
268C4×D8—861no—
269C4×D8—861no—
270#432—431no—
271#432C2×D4311yescharacteristic
272C2×C4⋊C8—861no—
273C2×C4⋊C8C2×D4311yescharacteristic
274C2×C4×C8—431no—
275C2×C4×C8—861no—
276#335—432no—
277#334—432no—
278#333—432no—
279#333C2×D4312yes—
280#331—432no—
281#331C2×D4312yes—
282C43#1926411yescharacteristic, complemented, Sylow
283C2×#41—21no—
284C2×#41—861no—
285C22×Q8—431no—
286C2×SD16—862no—
287C2×SD16—862no—
288C2×D8—861no—
289C2×D8—861no—
290C22×C8—21no—
291C22×C8—431no—
292C22×C8—431no—
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—432no—
304C4×Q8—432no—
305C4×Q8—861no—
306C4×Q8—861no—
307C4×D4—21no—
308C4×D4—21no—
309C4×D4—861no—
310C4×D4—861no—
311C2×C4⋊C4—431no—
312C2×C4⋊C4—861no—
313C2×C42—861no—
314C2×C42C22×D4311yescharacteristic
315#107—862no—
316#107—861no—
317#107—861no—
318#107—862no—
319C4⋊C8—21no—
320C4⋊C8—432no—
321C4⋊C8—862no—
322C4⋊C8—862no—
323C4⋊C8C22×D4312yes—
324C4⋊C8C22×D4312yes—
325#103—862no—
326#103—862no—
327#102—861no—
328#102—861no—
329#102—862no—
330#102—862no—
331#102—861no—
332#102—861no—
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—21no—
346C2×Q8—432no—
347C2×Q8—864no—
348C2×Q8—861no—
349C2×Q8—861no—
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—41no—
359C22×C4—861no—
360C22×C4—861no—
361C22×C4—1721no—
362C22×C4#1062189811yescharacteristic
363C22×C4D4×D4311yescharacteristic
364C22×C4D4×D4311yescharacteristic
365SD16—1724no—
366SD16—1724no—
367D8—1722no—
368D8—1722no—
369C2×C8—22no—
370C2×C8—22no—
371C2×C8—42no—
372C2×C8—431no—
373C2×C8—431no—
374C2×C8—431no—
375C2×C8—431no—
376C2×C8—862no—
377C2×C8—862no—
378C2×C8—1721no—
379C4⋊C4—21no—
380C4⋊C4—21no—
381C4⋊C4—432no—
382C4⋊C4—861no—
383C4⋊C4—862no—
384C4⋊C4—862no—
385C4⋊C4—861no—
386C4⋊C4—861no—
387C22⋊C4—41no—
388C22⋊C4—41no—
389C22⋊C4—1721no—
390C22⋊C4—1721no—
391C42—862no—
392C42—862no—
393C42#1062189811yescharacteristic
394C42D4×D4311yescharacteristic
395C42D4×D4311yescharacteristic
396C42C23×D4311yescharacteristic
397C23—41no—
398C23—1721no—
399C23#1306329811yescharacteristic
400Q8—81no—
401Q8—434no—
402Q8—864no—
403Q8—862no—
404Q8—3441no—
405D4—42no—
406D4—41no—
407D4—41no—
408D4—81no—
409D4—82no—
410D4—3441no—
411D4—3442no—
412D4—1722no—
413D4—1721no—
414D4—1721no—
415C2×C4—22no—
416C2×C4—22no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—41no—
420C2×C4—82no—
421C2×C4—864no—
422C2×C4—862no—
423C2×C4—862no—
424C2×C4—3442no—
425C2×C4—1721no—
426C2×C4—1722no—
427C2×C4#1306329811yescharacteristic
428C2×C4#1306329811yescharacteristic
429C2×C4#1306329811yescharacteristic
430C2×C4C2×D4×D4311yescharacteristic
431C2×C4C2×D4×D4311yescharacteristic
432C2×C4C2×#1062189811yescharacteristic
433C8—42no—
434C8—42no—
435C8—432no—
436C8—861no—
437C8—861no—
438C8—861no—
439C8—1722no—
440C22—21no—
441C22—21no—
442C22—81no—
443C22—81no—
444C22—81no—
445C22—3441no—
446C22—3441no—
447C22—3441no—
448C22#1458316812yes—
449C22C2×#1306329811yescharacteristic
450C4—21no—
451C4—21no—
452C4—21no—
453C4—21no—
454C4—81no—
455C4—864no—
456C4—3441no—
457C4—1722no—
458C4#135×D4312yes—
459C4#137×D4311yescharacteristic
460C4#1458369511yescharacteristic
461C2—22no—
462C2—161no—
463C2—6881no—
464C2#1914406611yescharacteristic
465C2#1914417511yescharacteristic
466C2C2×#1458316811yescharacteristic
subgroupG/H
centerC22C2×#13063298
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1551C2
socleC22×C43C2×#121
prime radical#19145170C2
hypercenter#1551D43
hypocenterC43#19264
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1551

Complements

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

NH ≅ G/Ntype
2. #19144718C2semidirect
3. #19144713C2semidirect
4. C2×#14583023C2semidirect
5. #19134014C2semidirect
6. #19134010C2semidirect
7. #19133998C2semidirect
8. #19133954C2semidirect
9. #19133356C2semidirect
10. #19133288C2semidirect
11. C43×#1551C2semidirect
238. #1551D43semidirect
282. C43#19264semidirect

Maximal subgroups

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

subgroupindex
#191451702
#191447182
#191447132
C2×#145830232
#191340142
#191340102
#191339982
#191339542
#191333562
#191332882
C43×#15512
#1926443