Finite Group Databasebeta

← #24991830

Subgroups — #24991830

Order 11008.

500 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145150C211yesmaximal, characteristic
2#19143339C211yesmaximal, characteristic
3#19135538C211yesmaximal, characteristic, complemented
4#19132999C211yesmaximal, characteristic, complemented
5#19132436C211yesmaximal, characteristic, complemented
6#19132431C211yesmaximal, characteristic, complemented
7C43×#1502C211yesmaximal, characteristic
8C2×#13063332—21no—
9#14583456C2211yescharacteristic
10#14583295C411yescharacteristic, complemented
11#14583271C411yescharacteristic, complemented
12#14583251C411yescharacteristic, complemented
13#14583245C411yescharacteristic, complemented
14#14583126—22no—
15C4×#10621883—22no—
16#14582977—21no—
17#14582971—22no—
18D4×C43⋊C8—21no—
19C2×C4⋊(C43⋊C8)C2211yescharacteristic
20#14582866—21no—
21C4×#10621877C2211yescharacteristic
22C2×C4×C43⋊C8C2211yescharacteristic
23#14582659—21no—
24#14582659—21no—
25#14582631—21no—
26#14582631—21no—
27C43×#532C2211yescharacteristic
28C43×#431C2211yescharacteristic
29C4×C4⋊C4×C43C2211yescharacteristic
30C43×#327—22no—
31C2×#10621883—22no—
32#13063332—42no—
33#13063332—42no—
34C2×#10621877—22no—
35C2×#10621877D411yescharacteristic
36C2×#10621877D411yescharacteristic
37C22×C43⋊C8—22no—
38C22×C43⋊C8—21no—
39C22×C43⋊C8—21no—
40#13063325C2×C411yescharacteristic
41#13063325C2×C411yescharacteristic
42#13063317—21no—
43#13063304—21no—
44#13063304—21no—
45C4×Dic86—21no—
46C4×Dic86—21no—
47#13063284—21no—
48#13063256—22no—
49C4⋊(C43⋊C8)—21no—
50C4⋊(C43⋊C8)D411yescharacteristic
51C4⋊(C43⋊C8)D411yescharacteristic
52#13063248—22no—
53#13063246—22no—
54C22⋊(C43⋊C8)—22no—
55C22⋊(C43⋊C8)—22no—
56#13063236—21no—
57C4×C43⋊C8—21no—
58C4×C43⋊C8—21no—
59C4×C43⋊C8C2×C411yescharacteristic
60C4×C43⋊C8C2×C411yescharacteristic
61C2×#41×C43—21no—
62C4⋊Q8×C43C2×C411yescharacteristic
63#127×C43C2×C411yescharacteristic
64#124×C43—21no—
65#121×C43—21no—
66#121×C43D412yes—
67C4×D4×C43—21no—
68C4×D4×C43D412yes—
69C2×C4⋊C4×C43—21no—
70C2×C42×C43—21no—
71C2×C42×C43C2311yescharacteristic
72C4⋊C8×C43—21no—
73C22⋊C8×C43—21no—
74C4×C8×C43—21no—
75#95×C43—21no—
76#41×C43—41no—
77#41×C43—41no—
78#41×C43—41no—
79#41×C43—41no—
80C2×Q8×C43—21no—
81C2×D4×C43—21no—
82C2×D4×C43—21no—
83C2×D4×C43—22no—
84C2×D4×C43C22⋊C412yes—
85C22×C4×C43—22no—
86C22×C4×C43—41no—
87C22×C4×C43C2×D411yescharacteristic
88C22×C4×C43C2×D411yescharacteristic
89C22×C4×C43#4111yescharacteristic
90C2×Dic86—21no—
91C2×Dic86—21no—
92C2×C8×C43—41no—
93C4⋊C4×C43—21no—
94C4⋊C4×C43—22no—
95C4⋊C4×C43—41no—
96C4⋊C4×C43C22⋊C412yes—
97C22⋊C4×C43—22no—
98C22⋊C4×C43—22no—
99C42×C43—41no—
100C42×C43—41no—
101C42×C43C22×C411yescharacteristic
102C42×C43C2×D411yescharacteristic
103C42×C43C2×D411yescharacteristic
104C42×C43#4111yescharacteristic
105C22⋊Dic43—41no—
106#10621883—44no—
107C4⋊Dic43—21no—
108C4⋊Dic43—21no—
109C4⋊Dic43—21no—
110C4⋊Dic43—21no—
111Dic43⋊C4—41no—
112Dic43⋊C4—41no—
113C4×Dic43—41no—
114#10621877—21no—
115#10621877—21no—
116#10621877—21no—
117#10621877—44no—
118#10621877SD1612yescomplemented
119C2×C43⋊C8—21no—
120C2×C43⋊C8—21no—
121C2×C43⋊C8—21no—
122C2×C43⋊C8—21no—
123C2×C43⋊C8—21no—
124C2×C43⋊C8—21no—
125C2×C43⋊C8—42no—
126C2×C43⋊C8—44no—
127C2×C43⋊C8—41no—
128C2×C43⋊C8—41no—
129C23×C43—22no—
130C23×C43#12111yescharacteristic
131Q8×C43—41no—
132Q8×C43—41no—
133D4×C43—42no—
134D4×C43—42no—
135D4×C43—42no—
136D4×C43—41no—
137D4×C43—41no—
138D4×C43—41no—
139D4×C43—41no—
140C2×C4×C43—21no—
141C2×C4×C43—21no—
142C2×C4×C43—22no—
143C2×C4×C43—41no—
144C2×C4×C43—42no—
145C2×C4×C43—42no—
146C2×C4×C43—42no—
147C2×C4×C43—81no—
148C2×C4×C43—81no—
149C2×C4×C43C2×C22⋊C411yescharacteristic
150C2×C4×C43C4×D411yescharacteristic
151C2×C4×C43C4×D411yescharacteristic
152C2×C4×C43#12011yescharacteristic
153C2×C4×C43#12111yescharacteristic
154C2×C4×C43#12311yescharacteristic
155C2×C4×C43C2×SD1611yescharacteristic
156C2×C4×C43#13511yescharacteristic
157C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
158C2×C4×C43#13711yescharacteristic
159C2×Dic43—41no—
160C2×Dic43—41no—
161Dic86—42no—
162Dic86—41no—
163Dic86—41no—
164C8×C43—81no—
165C43⋊C8—22no—
166C43⋊C8—22no—
167C43⋊C8—41no—
168C43⋊C8—41no—
169C43⋊C8—41no—
170C43⋊C8—41no—
171#9055—431nomaximal, Sylow
172C22×C43—21no—
173C22×C43—21no—
174C22×C43—42no—
175C22×C43—42no—
176C22×C43—42no—
177C22×C43#38611yescharacteristic
178C22×C43#46111yescharacteristic
179C22×C43#46311yescharacteristic
180C4×C43—21no—
181C4×C43—21no—
182C4×C43—21no—
183C4×C43—42no—
184C4×C43—82no—
185C4×C43C4×SD1611yescharacteristic
186C4×C43#44011yescharacteristic
187C4×C43#44311yescharacteristic
188C4×C43#44411yescharacteristic
189C4×C43#45011yescharacteristic
190C4×C43#45211yescharacteristic
191Dic43—81no—
192Dic43—81no—
193#3167—431no—
194#2935—431no—
195#1986—431no—
196#1502D4311yescharacteristic
197#1481—431no—
198#1279—431no—
199#1278—431no—
200C2×C43—21no—
201C2×C43—21no—
202C2×C43—82no—
203C2×C43#187611yescharacteristic
204C2×C43#187711yescharacteristic
205C2×C43#188411yescharacteristic
206C2×#131—861no—
207#533—431no—
208#532C2×D4311yescharacteristic
209#498—431no—
210#492—431no—
211#487—431no—
212#486—431no—
213#465—862no—
214C4×SD16—862no—
215#436—861no—
216#435—862no—
217C8×D4—861no—
218#431C2×D4311yescharacteristic
219C2×C4⋊C8—431no—
220#408—861no—
221C4×M16—431no—
222C2×C4×C8—431no—
223C4×C4⋊C4C2×D4311yescharacteristic
224#339—861no—
225#339—861no—
226#327—22no—
227Q8⋊C8—861no—
228Q8⋊C8—861no—
229C43#905511yescharacteristic, complemented, Sylow
230C2×#41—21no—
231C2×SD16—862no—
232#131—1722no—
233#131—1722no—
234C2×M16—431no—
235C2×M16—431no—
236C2×M16—862no—
237C22×C8—862no—
238C22×C8—861no—
239C22×C8—861no—
240C4⋊Q8—431no—
241C4⋊Q8—431no—
242C4⋊Q8C4×D4311yescharacteristic
243#127C4×D4311yescharacteristic
244#125—861no—
245#124—21no—
246C22⋊Q8—861no—
247C22⋊Q8—861no—
248#121—21no—
249#121C22⋊D4312yes—
250C4×Q8—861no—
251C4×Q8—861no—
252C4×D4—21no—
253C4×D4D17212yes—
254#117—861no—
255C2×C4⋊C4—21no—
256C2×C42—21no—
257C2×C42C22×D4311yescharacteristic
258#106—862no—
259C4⋊C8—21no—
260C4⋊C8—431no—
261C4⋊C8—431no—
262C4⋊C8—861no—
263#103—862no—
264#102—862no—
265C22⋊C8—21no—
266C22⋊C8—862no—
267C22⋊C8—862no—
268#97—861no—
269C4×C8—21no—
270C4×C8—431no—
271C4×C8—431no—
272C4×C8—861no—
273C4×C8—861no—
274#95—21no—
275#41—41no—
276#41—41no—
277#41—41no—
278#41—41no—
279C2×Q8—21no—
280C2×Q8—861no—
281C2×Q8—861no—
282C2×D4—22no—
283C2×D4—21no—
284C2×D4—21no—
285C2×D4(C2×D43)⋊C412yes—
286C22×C4—22no—
287C22×C4—41no—
288C22×C4D4×D4311yescharacteristic
289C22×C4#1062190011yescharacteristic
290C22×C4C2×C22⋊D4311yescharacteristic
291SD16—1724no—
292M16—432no—
293M16—861no—
294M16—861no—
295M16—861no—
296M16—1724no—
297C2×C8—41no—
298C2×C8—861no—
299C2×C8—861no—
300C2×C8—861no—
301C2×C8—861no—
302C2×C8—861no—
303C2×C8—861no—
304C2×C8—1724no—
305C2×C8—1722no—
306C2×C8—1721no—
307C2×C8—1721no—
308C4⋊C4—21no—
309C4⋊C4—22no—
310C4⋊C4—41no—
311C4⋊C4—861no—
312C4⋊C4—861no—
313C4⋊C4—861no—
314C4⋊C4—861no—
315C4⋊C4—1721no—
316C4⋊C4—1721no—
317C4⋊C4(C2×D43)⋊C412yes—
318C22⋊C4—22no—
319C22⋊C4—22no—
320C22⋊C4—1721no—
321C42—41no—
322C42—41no—
323C42—1721no—
324C42C2×C4×D4311yescharacteristic
325C42C2×D17211yescharacteristic
326C42D4×D4311yescharacteristic
327C42#1062190011yescharacteristic
328C23—22no—
329C23#1306329711yescharacteristic
330Q8—41no—
331Q8—41no—
332Q8—1722no—
333Q8—1721no—
334Q8—1721no—
335D4—42no—
336D4—42no—
337D4—42no—
338D4—41no—
339D4—41no—
340D4—41no—
341D4—41no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—22no—
345C2×C4—41no—
346C2×C4—42no—
347C2×C4—42no—
348C2×C4—42no—
349C2×C4—81no—
350C2×C4—81no—
351C2×C4—1721no—
352C2×C4—1721no—
353C2×C4C2×(C2×D43)⋊C411yescharacteristic
354C2×C4(C22⋊D43)⋊C411yescharacteristic
355C2×C4(C22⋊D43)⋊C411yescharacteristic
356C2×C4#1306329511yescharacteristic
357C2×C4#1306329711yescharacteristic
358C2×C4#1306330911yescharacteristic
359C2×C4SD16×D4311yescharacteristic
360C2×C4#1306334411yescharacteristic
361C2×C4#1306334911yescharacteristic
362C2×C4#1306335411yescharacteristic
363C8—81no—
364C8—862no—
365C8—862no—
366C8—1721no—
367C8—1721no—
368C8—1721no—
369C8—1721no—
370C22—21no—
371C22—21no—
372C22—42no—
373C22—42no—
374C22—42no—
375C22#1458277611yescharacteristic
376C22#1458310211yescharacteristic
377C22#1458311211yescharacteristic
378C4—21no—
379C4—21no—
380C4—21no—
381C4—42no—
382C4—82no—
383C4—3441no—
384C4—3441no—
385C4#1458299011yescharacteristic
386C4#1458299611yescharacteristic
387C4#1458301311yescharacteristic
388C4#1458301811yescharacteristic
389C4#1458305111yescharacteristic
390C4#1458306211yescharacteristic
391C2—21no—
392C2—21no—
393C2—82no—
394C2#1913492011yescharacteristic
395C2#1913492711yescharacteristic
396C2#1913497611yescharacteristic
subgroupG/H
centerC2×C4#13063295
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1502C2
socleC22×C43#386
prime radicalC43×#532C22
cosocleC2×C42×C43C23
hypercenter#1502D43
hypocenterC43#9055
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1502

Complements

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

NH ≅ G/Ntype
3. #19135538C2semidirect
4. #19132999C2semidirect
5. #19132436C2semidirect
6. #19132431C2semidirect
10. #14583295C4semidirect
11. #14583271C4semidirect
12. #14583251C4semidirect
13. #14583245C4semidirect
118. #10621877SD16semidirect
229. C43#9055semidirect

Maximal subgroups

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

subgroupindex
#191451502
#191433392
#191355382
#191329992
#191324362
#191324312
C43×#15022
#905543