Finite Group Databasebeta

← #25081760

Subgroups — #25081760

Order 11008.

738 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145533C211yesmaximal, characteristic, complemented
2#19144388C211yesmaximal, characteristic, complemented
3C2×#14583095C211yesmaximal, characteristic
4#19143618C211yesmaximal, characteristic, complemented
5#19134007C214yesmaximal, complemented
6#19133939C214yesmaximal, complemented
7#19133365C211yesmaximal, characteristic, complemented
8#19133262C211yesmaximal, characteristic, complemented
9C43×#1542C211yesmaximal, characteristic, complemented
10C22×D344—21no—
11C2×#13063322C2211yescharacteristic
12C2×C4×D172C2211yescharacteristic
13#14583273C2212yescomplemented
14#14583247C2212yescomplemented
15#14583196—22no—
16#14583186C2212yescomplemented
17#14583176C2212yescomplemented
18#14583099—22no—
19#14583095—22no—
20#14583095C2214yes—
21#14583049—22no—
22C8×D172—22no—
23#14582964C2214yescomplemented
24#14582952C2211yescharacteristic
25#14582942—21no—
26#14582923C2211yescharacteristic
27#14582903—21no—
28C2×#13063247—21no—
29C22⋊C8×D43—22no—
30#14582649C2214yescomplemented
31#14582642C2214yescomplemented
32C43×#533C2211yescharacteristic
33C43×#431C2211yescharacteristic
34C2×C4⋊C8×C43C2211yescharacteristic
35C43×#333C2212yescomplemented
36C43×#332C2212yescomplemented
37C22×D172—21no—
38C22×D172—21no—
39C22×D172—21no—
40C22×D172D411yescharacteristic
41C22×C4×D43—21no—
42C2×#10621884—24no—
43C2×D344—24no—
44C2×D344—44no—
45C2×#10621877—21no—
46C2×C8×D43—24no—
47#13063322—21no—
48#13063322—21no—
49#13063322—21no—
50#13063322C2312yes—
51C4×D172—21no—
52C4×D172—21no—
53C4×D172D412yes—
54C4×D172C2312yes—
55C2×C4⋊Dic43D411yescharacteristic
56C2×(C2×D43)⋊C4—21no—
57#13063258—22no—
58#13063256—22no—
59C4⋊(C43⋊C8)—21no—
60C4⋊(C43⋊C8)D412yes—
61C4⋊(C43⋊C8)C2312yes—
62#13063247—24no—
63#13063245—22no—
64#13063245—22no—
65#13063245—24no—
66C22⋊(C43⋊C8)D412yes—
67(C2×D43)⋊C8—24no—
68C4×C43⋊C8C2312yes—
69C22×C8×C43—21no—
70C4⋊Q8×C43C2311yescharacteristic
71C4⋊Q8×C43C2311yescharacteristic
72#125×C43—21no—
73C22⋊Q8×C43—21no—
74C22⋊Q8×C43—21no—
75C4×Q8×C43—21no—
76C4×Q8×C43—21no—
77#117×C43—21no—
78C2×C42×C43C2311yescharacteristic
79C4⋊C8×C43—21no—
80C4⋊C8×C43C2312yes—
81C4⋊C8×C43C2312yes—
82C22⋊C8×C43—21no—
83C4×C8×C43—21no—
84C23×D43—21no—
85C23×D43—41no—
86C2×Q8×C43—21no—
87C2×Q8×C43—21no—
88C22×C4×C43C2×D411yescharacteristic
89C22×C4×C43C2×D411yescharacteristic
90C22×C4×C43#4111yescharacteristic
91C22×Dic43—21no—
92C2×D172—21no—
93C2×D172—22no—
94C2×D172—22no—
95C2×D172—22no—
96C2×D172—22no—
97C2×D172—41no—
98C2×D172—41no—
99C2×D172—41no—
100C2×D172—42no—
101C2×D172—42no—
102C2×D172—82no—
103C2×D172—82no—
104C2×D172SD1614yescomplemented
105C2×D172C2×D412yes—
106C2×C4×D43—22no—
107C2×C4×D43—22no—
108C2×C4×D43—82no—
109C2×C8×C43—22no—
110C2×C8×C43—22no—
111C2×C8×C43—42no—
112C4⋊C4×C43—21no—
113C4⋊C4×C43—21no—
114C4⋊C4×C43—21no—
115C4⋊C4×C43—21no—
116C4⋊C4×C43—41no—
117C4⋊C4×C43—41no—
118C22⋊C4×C43—41no—
119C42×C43—41no—
120C42×C43C2×D411yescharacteristic
121C42×C43C2×D411yescharacteristic
122C42×C43#4111yescharacteristic
123C42×C43C2411yescharacteristic
124#10621884—84no—
125(C2×D43)⋊C4—22no—
126(C2×D43)⋊C4—22no—
127C4⋊Dic43—21no—
128C4⋊Dic43C2×D412yes—
129#10621877—42no—
130C2×C43⋊C8—22no—
131C2×C43⋊C8C2×D414yes—
132D344—48no—
133C8×D43—84no—
134C23×C43#12111yescharacteristic
135C22×D43—22no—
136C22×D43—24no—
137C22×D43—42no—
138C22×D43—81no—
139C22×D43—81no—
140C22×D43—82no—
141C22×D43—82no—
142C22×D43—82no—
143Q8×C43—42no—
144Q8×C43—81no—
145C2×C4×C43—22no—
146C2×C4×C43—41no—
147C2×C4×C43—41no—
148C2×C4×C43—41no—
149C2×C4×C43#12111yescharacteristic
150C2×C4×C43#12111yescharacteristic
151C2×C4×C43#12111yescharacteristic
152C2×C4×C43C2×SD1612yes—
153C2×C4×C43#13512yes—
154C2×C4×C43C22×D411yescharacteristic
155C2×C4×C43C22×D411yescharacteristic
156C2×C4×C43C2×#4111yescharacteristic
157C2×Dic43—22no—
158C2×Dic43—81no—
159D172—22no—
160D172—24no—
161D172—42no—
162D172—42no—
163D172—44no—
164D172—82no—
165D172—82no—
166D172—82no—
167D172—82no—
168D172C2×SD1614yes—
169C4×D43—44no—
170C4×D43—82no—
171C8×C43—42no—
172C8×C43—42no—
173C43⋊C8—24no—
174C43⋊C8—42no—
175#19384—431nomaximal, Sylow
176C22×C43—21no—
177C22×C43—21no—
178C22×C43#46512yes—
179C22×C43C2×#12111yescharacteristic
180C2×D43—24no—
181C2×D43—42no—
182C2×D43—42no—
183C2×D43—84no—
184C2×D43—82no—
185C2×D43—82no—
186C2×D43—82no—
187C2×D43—164no—
188C4×C43—21no—
189C4×C43—21no—
190C4×C43—21no—
191C4×C43—81no—
192C4×C43—81no—
193C4×C43#46512yes—
194C4×C43C22×SD1611yescharacteristic
195C4×C43C2×#13511yescharacteristic
196C4×C43#57612yes—
197Dic43—42no—
198#3208—431no—
199#3077—431no—
200C2×#459—431no—
201#2972—431no—
202#1677—434no—
203#1665—434no—
204#1570—431no—
205#1545—431no—
206#1542D4311yescharacteristic, complemented
207C2×C43—22no—
208C2×C43#304111yescharacteristic
209C2×C43C2×#46511yescharacteristic
210C2×C43#306811yescharacteristic
211D43—44no—
212D43—162no—
213C22×D8—861no—
214#533C2×D4311yescharacteristic
215C2×#127—431no—
216C2×C4×D4—431no—
217#492—432no—
218#486—432no—
219#478—862no—
220#476—432no—
221#474—432no—
222#460—862no—
223#459—434no—
224#459—862no—
225#450—862no—
226C8×D4—434no—
227C8×D4—862no—
228#431—431no—
229#431C2×D4311yescharacteristic
230#428—861no—
231#423—431no—
232C2×C4⋊C8C2×D4311yescharacteristic
233#418—861no—
234C2×#102—861no—
235C2×C22⋊C8—862no—
236#334—434no—
237#333C2×D4312yescomplemented
238#332C2×D4312yescomplemented
239#331—434no—
240C43#1938411yescharacteristic, complemented, Sylow
241C22×D4—431no—
242C22×D4—861no—
243C22×D4—861no—
244C22×D4—861no—
245C23×C4—861no—
246C2×SD16—864no—
247C2×D8—864no—
248C2×D8—1724no—
249C2×M16—861no—
250C22×C8—21no—
251C22×C8—864no—
252C4⋊Q8C22×D4311yescharacteristic
253C4⋊Q8C22×D4311yescharacteristic
254#127—432no—
255#127—861no—
256#127—861no—
257#127—861no—
258#125—21no—
259C22⋊Q8—21no—
260C22⋊Q8—21no—
261C4×Q8—21no—
262C4×Q8—21no—
263C4×D4—432no—
264C4×D4—432no—
265C4×D4—861no—
266C4×D4—861no—
267#117—21no—
268C2×C4⋊C4—431no—
269C2×C22⋊C4—861no—
270C2×C42C22×D4311yescharacteristic
271#107—862no—
272#106—862no—
273C4⋊C8—21no—
274C4⋊C8—432no—
275C4⋊C8—432no—
276C4⋊C8—861no—
277C4⋊C8C22×D4312yes—
278C4⋊C8C22×D4312yes—
279#102—864no—
280#102—862no—
281#102—862no—
282#102—864no—
283C22⋊C8—21no—
284C22⋊C8—432no—
285C22⋊C8—864no—
286C4×C8—21no—
287C4×C8—432no—
288C24—861no—
289C24—1721no—
290C2×Q8—21no—
291C2×Q8—21no—
292C2×D4—434no—
293C2×D4—432no—
294C2×D4—861no—
295C2×D4—862no—
296C2×D4—862no—
297C2×D4—862no—
298C2×D4—862no—
299C2×D4—3442no—
300C2×D4—3442no—
301C2×D4—1721no—
302C2×D4—1721no—
303C2×D4—1721no—
304C2×D4—1722no—
305C2×D4—1722no—
306C22×C4—861no—
307C22×C4—862no—
308C22×C4—862no—
309C22×C4—3442no—
310C22×C4#1062189811yescharacteristic
311C22×C4D4×D4311yescharacteristic
312C22×C4D4×D4311yescharacteristic
313SD16—3444no—
314D8—1728no—
315M16—1722no—
316C2×C8—22no—
317C2×C8—22no—
318C2×C8—42no—
319C2×C8—434no—
320C2×C8—862no—
321C2×C8—3444no—
322C4⋊C4—21no—
323C4⋊C4—21no—
324C4⋊C4—21no—
325C4⋊C4—21no—
326C4⋊C4—41no—
327C4⋊C4—41no—
328C4⋊C4—432no—
329C4⋊C4—861no—
330C22⋊C4—41no—
331C22⋊C4—862no—
332C22⋊C4—862no—
333C42—41no—
334C42#1062189811yescharacteristic
335C42D4×D4311yescharacteristic
336C42D4×D4311yescharacteristic
337C42C23×D4311yescharacteristic
338C23—864no—
339C23—862no—
340C23—3441no—
341C23—3441no—
342C23—3442no—
343C23—3442no—
344C23—3442no—
345C23—1722no—
346C23#1306329811yescharacteristic
347Q8—42no—
348Q8—81no—
349D4—434no—
350D4—864no—
351D4—862no—
352D4—3442no—
353D4—3442no—
354D4—3442no—
355D4—3442no—
356D4—1722no—
357D4—1722no—
358D4—1724no—
359C2×C4—22no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—862no—
364C2×C4—3442no—
365C2×C4—3441no—
366C2×C4—1724no—
367C2×C4#1306329811yescharacteristic
368C2×C4#1306329811yescharacteristic
369C2×C4#1306329811yescharacteristic
370C2×C4SD16×D4312yes—
371C2×C4#1306334812yes—
372C2×C4C2×D4×D4311yescharacteristic
373C2×C4C2×D4×D4311yescharacteristic
374C2×C4C2×#1062189811yescharacteristic
375C8—42no—
376C8—42no—
377C8—864no—
378C8—1722no—
379C22—21no—
380C22—21no—
381C22—864no—
382C22—3444no—
383C22—3442no—
384C22—3442no—
385C22—3442no—
386C22—1722no—
387C22—1722no—
388C22—6884no—
389C22#1458313112yes—
390C22C2×#1306329811yescharacteristic
391C4—21no—
392C4—21no—
393C4—21no—
394C4—81no—
395C4—81no—
396C4—1722no—
397C4#1458313112yes—
398C4C2×SD16×D4311yescharacteristic
399C4C2×#1306334811yescharacteristic
400C4#1458370112yes—
401C2—22no—
402C2—1724no—
403C2—6882no—
404C2#1914410111yescharacteristic
405C2C2×#1458313111yescharacteristic
406C2#1914432611yescharacteristic
subgroupG/H
centerC22C2×#13063298
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1542C2
socleC22×C43C2×#121
prime radicalC2×#14583095C2
hypercenter#1542D43
hypocenterC43#19384
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1542

Complements

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

NH ≅ G/Ntype
1. #19145533C2semidirect
2. #19144388C2semidirect
4. #19143618C2semidirect
5. #19134007C2semidirect
6. #19133939C2semidirect
7. #19133365C2semidirect
8. #19133262C2semidirect
9. C43×#1542C2semidirect
13. #14583273C22semidirect
14. #14583247C22semidirect
16. #14583186C22semidirect
17. #14583176C22semidirect
23. #14582964C22semidirect
30. #14582649C22semidirect
31. #14582642C22semidirect
35. C43×#333C22semidirect
36. C43×#332C22semidirect
104. C2×D172SD16semidirect
206. #1542D43semidirect
237. #333C2×D43semidirect
238. #332C2×D43semidirect
240. C43#19384semidirect

Maximal subgroups

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

subgroupindex
#191455332
#191443882
C2×#145830952
#191436182
#191340072
#191339392
#191333652
#191332622
C43×#15422
#1938443