Finite Group Databasebeta

← #24993256

Subgroups — #24993256

Order 11008.

490 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143313C211yesmaximal, characteristic
2#19135569C211yesmaximal, characteristic, complemented
3#19133280C211yesmaximal, characteristic, complemented
4#19133155C211yesmaximal, characteristic
5#19132454C211yesmaximal, characteristic, complemented
6#19132425C211yesmaximal, characteristic, complemented
7C43×#3206C211yesmaximal, characteristic
8C2×#13063332—21no—
9#14582971—22no—
10#14582971—22no—
11#14582952C2211yescharacteristic
12#14582923C2211yescharacteristic
13#14582866—21no—
14C2×#13063236C2211yescharacteristic
15#14582765C2211yescharacteristic
16#14582661—21no—
17#14582661—21no—
18#14582645—22no—
19#14582633—22no—
20C43×#532C2211yescharacteristic
21C2×C4⋊Q8×C43C2211yescharacteristic
22C43×#492C412yescomplemented
23C43×#487C412yescomplemented
24C43×#461—22no—
25C43×#448—22no—
26C43×#431C2211yescharacteristic
27#13063332—42no—
28#13063332—42no—
29C2×#10621877—22no—
30C2×#10621877—21no—
31C22×C43⋊C8—22no—
32C22×C43⋊C8D411yescharacteristic
33C22×C43⋊C8D411yescharacteristic
34C2×C4⋊Dic43—21no—
35C4⋊(C43⋊C8)—21no—
36C4⋊(C43⋊C8)—21no—
37C4⋊(C43⋊C8)D412yes—
38C22⋊(C43⋊C8)—24no—
39C22⋊(C43⋊C8)—21no—
40#13063236—21no—
41#13063236—21no—
42C4×C43⋊C8—21no—
43C43⋊#95—21no—
44C43⋊#95—21no—
45C2×#41×C43—21no—
46C22×Q8×C43—21no—
47C2×SD16×C43—24no—
48C4⋊Q8×C43—21no—
49C4⋊Q8×C43—21no—
50C4⋊Q8×C43—21no—
51C4⋊Q8×C43C2×C412yes—
52C4⋊Q8×C43C2×C411yescharacteristic
53#127×C43C2×C411yescharacteristic
54#124×C43—21no—
55#121×C43—21no—
56#121×C43D412yes—
57C4×D4×C43—21no—
58C4×D4×C43D412yes—
59C2×C4⋊C4×C43—21no—
60C2×C4⋊C4×C43—21no—
61C2×C42×C43C2311yescharacteristic
62C4⋊C8×C43—21no—
63#103×C43—24no—
64C22⋊C8×C43—21no—
65C4×C8×C43C2×C412yes—
66#41×C43—41no—
67#41×C43—41no—
68#41×C43—41no—
69#41×C43—41no—
70C2×Q8×C43—21no—
71C2×Q8×C43—22no—
72C2×Q8×C43—41no—
73C2×Q8×C43—82no—
74C2×D4×C43—21no—
75C2×D4×C43—21no—
76C2×D4×C43—22no—
77C2×D4×C43C22⋊C412yes—
78C22×C4×C43—22no—
79C22×C4×C43—41no—
80C22×C4×C43C2×D411yescharacteristic
81C22×C4×C43C2×D411yescharacteristic
82C22×C4×C43#4111yescharacteristic
83C22×Dic43—41no—
84SD16×C43—84no—
85C2×C8×C43—22no—
86C4⋊C4×C43—21no—
87C4⋊C4×C43—22no—
88C4⋊C4×C43—22no—
89C4⋊C4×C43—41no—
90C4⋊C4×C43—41no—
91C4⋊C4×C43C22⋊C412yes—
92C22⋊C4×C43—22no—
93C22⋊C4×C43—22no—
94C42×C43C22×C411yescharacteristic
95C42×C43C2×D411yescharacteristic
96C42×C43C2×D411yescharacteristic
97C42×C43#4111yescharacteristic
98C4⋊Dic43—41no—
99C4⋊Dic43—41no—
100#10621877—44no—
101#10621877—41no—
102#10621877—41no—
103C2×C43⋊C8—21no—
104C2×C43⋊C8—21no—
105C2×C43⋊C8—21no—
106C2×C43⋊C8—22no—
107C2×C43⋊C8—21no—
108C2×C43⋊C8—21no—
109C2×C43⋊C8—44no—
110C2×C43⋊C8—41no—
111C2×C43⋊C8SD1612yescomplemented
112C23×C43—22no—
113C23×C43#12111yescharacteristic
114Q8×C43—44no—
115Q8×C43—41no—
116Q8×C43—41no—
117Q8×C43—82no—
118D4×C43—42no—
119D4×C43—42no—
120D4×C43—42no—
121D4×C43—41no—
122D4×C43—41no—
123D4×C43—81no—
124C2×C4×C43—22no—
125C2×C4×C43—41no—
126C2×C4×C43—41no—
127C2×C4×C43—42no—
128C2×C4×C43—42no—
129C2×C4×C43—42no—
130C2×C4×C43—82no—
131C2×C4×C43C2×C22⋊C411yescharacteristic
132C2×C4×C43C4×D411yescharacteristic
133C2×C4×C43C4×D411yescharacteristic
134C2×C4×C43#12011yescharacteristic
135C2×C4×C43#12111yescharacteristic
136C2×C4×C43#12311yescharacteristic
137C2×C4×C43C2×SD1611yescharacteristic
138C2×C4×C43#13511yescharacteristic
139C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
140C2×C4×C43#13711yescharacteristic
141C2×Dic43—81no—
142C2×Dic43—81no—
143C2×Dic43—81no—
144C8×C43—42no—
145C43⋊C8—22no—
146C43⋊C8—42no—
147C43⋊C8—41no—
148C43⋊C8—81no—
149#9289—431nomaximal, Sylow
150C22×C43—21no—
151C22×C43—21no—
152C22×C43—42no—
153C22×C43—42no—
154C22×C43—42no—
155C22×C43#38611yescharacteristic
156C22×C43#46111yescharacteristic
157C22×C43#46311yescharacteristic
158C4×C43—21no—
159C4×C43—21no—
160C4×C43—21no—
161C4×C43—21no—
162C4×C43—42no—
163C4×C43—82no—
164C4×C43C4×SD1611yescharacteristic
165C4×C43#44011yescharacteristic
166C4×C43#45011yescharacteristic
167C4×C43#45211yescharacteristic
168Dic43—161no—
169#3206D4311yescharacteristic
170#2932—431no—
171#1993—431no—
172#1549—431no—
173#1517—431no—
174#1286—431no—
175#1275—431no—
176C2×C43—21no—
177C2×C43—21no—
178C2×C43—82no—
179C2×C43#187711yescharacteristic
180C2×C43#190211yescharacteristic
181C2×C43#191011yescharacteristic
182C2×#131—861no—
183#532C2×D4311yescharacteristic
184C2×C4⋊Q8C2×D4311yescharacteristic
185#492Dic4312yescomplemented
186#487Dic4312yescomplemented
187#461—22no—
188#448—22no—
189#435—862no—
190#435—862no—
191#431—431no—
192#431C2×D4311yescharacteristic
193#423—431no—
194#408—861no—
195C2×#97—431no—
196#382—431no—
197#340—861no—
198#340—861no—
199#332—862no—
200#327—862no—
201C43#928911yescharacteristic, complemented, Sylow
202C2×#41—21no—
203C22×Q8—21no—
204C2×SD16—24no—
205#131—1722no—
206#131—1722no—
207C2×M16—862no—
208C2×M16—861no—
209C22×C8—431no—
210C22×C8—431no—
211C22×C8—862no—
212C4⋊Q8—21no—
213C4⋊Q8—21no—
214C4⋊Q8—21no—
215C4⋊Q8C2×Dic4312yes—
216C4⋊Q8C2×Dic4311yescharacteristic
217#127C2×Dic4311yescharacteristic
218#124—21no—
219#121—21no—
220#121C22⋊D4312yes—
221C4×D4—21no—
222C4×D4C22⋊D4312yes—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—861no—
226C2×C42C22×D4311yescharacteristic
227C4⋊C8—21no—
228C4⋊C8—432no—
229C4⋊C8—861no—
230C4⋊C8—861no—
231#103—24no—
232C22⋊C8—21no—
233C22⋊C8—864no—
234C22⋊C8—861no—
235#97—861no—
236#97—861no—
237C4×C8—861no—
238C4×C8C2×Dic4312yes—
239#95—861no—
240#95—861no—
241#41—41no—
242#41—41no—
243#41—41no—
244#41—41no—
245C2×Q8—21no—
246C2×Q8—22no—
247C2×Q8—41no—
248C2×Q8—82no—
249C2×D4—22no—
250C2×D4—21no—
251C2×D4—21no—
252C2×D4C22⋊Dic4312yes—
253C22×C4—22no—
254C22×C4—41no—
255C22×C4—1721no—
256C22×C4D4×D4311yescharacteristic
257C22×C4#1062190011yescharacteristic
258C22×C4C2×C22⋊D4311yescharacteristic
259SD16—84no—
260M16—1724no—
261M16—1721no—
262M16—1721no—
263C2×C8—22no—
264C2×C8—432no—
265C2×C8—861no—
266C2×C8—861no—
267C2×C8—861no—
268C2×C8—862no—
269C2×C8—861no—
270C2×C8—861no—
271C2×C8—1724no—
272C2×C8—1721no—
273C4⋊C4—21no—
274C4⋊C4—22no—
275C4⋊C4—22no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—1721no—
279C4⋊C4—1721no—
280C4⋊C4C22⋊Dic4312yes—
281C22⋊C4—22no—
282C22⋊C4—22no—
283C42D4×D4311yescharacteristic
284C42#1062190011yescharacteristic
285C42C22×Dic4311yescharacteristic
286C42C2×C22⋊D4311yescharacteristic
287C23—22no—
288C23#1306329711yescharacteristic
289Q8—44no—
290Q8—41no—
291Q8—41no—
292Q8—82no—
293D4—42no—
294D4—42no—
295D4—42no—
296D4—41no—
297D4—41no—
298D4—81no—
299C2×C4—22no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—42no—
303C2×C4—42no—
304C2×C4—42no—
305C2×C4—82no—
306C2×C4—3441no—
307C2×C4—3441no—
308C2×C4—3441no—
309C2×C4C2×C22⋊Dic4311yescharacteristic
310C2×C4D4×Dic4311yescharacteristic
311C2×C4D4×Dic4311yescharacteristic
312C2×C4#1306329311yescharacteristic
313C2×C4#1306329711yescharacteristic
314C2×C4#1306330611yescharacteristic
315C2×C4SD16×D4311yescharacteristic
316C2×C4#1306334611yescharacteristic
317C2×C4#1306335211yescharacteristic
318C2×C4#1306335411yescharacteristic
319C8—42no—
320C8—862no—
321C8—3441no—
322C8—1722no—
323C8—1721no—
324C22—21no—
325C22—21no—
326C22—42no—
327C22—42no—
328C22—42no—
329C22#1458277911yescharacteristic
330C22#1458310211yescharacteristic
331C22#1458311611yescharacteristic
332C4—21no—
333C4—21no—
334C4—21no—
335C4—21no—
336C4—42no—
337C4—82no—
338C4—6881no—
339C4SD16×Dic4311yescharacteristic
340C4#1458300011yescharacteristic
341C4#1458304811yescharacteristic
342C4#1458305811yescharacteristic
343C2—21no—
344C2—21no—
345C2—82no—
346C2#1913493111yescharacteristic
347C2#1913507011yescharacteristic
348C2#1913512311yescharacteristic
subgroupG/H
centerC22#14582779
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#3206C2
socleC22×C43#386
prime radicalC43×#532C22
cosocleC2×C42×C43C23
hypercenter#3206D43
hypocenterC43#9289
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3206

Complements

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

NH ≅ G/Ntype
2. #19135569C2semidirect
3. #19133280C2semidirect
5. #19132454C2semidirect
6. #19132425C2semidirect
22. C43×#492C4semidirect
23. C43×#487C4semidirect
111. C2×C43⋊C8SD16semidirect
185. #492Dic43semidirect
186. #487Dic43semidirect
201. C43#9289semidirect

Maximal subgroups

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

subgroupindex
#191433132
#191355692
#191332802
#191331552
#191324542
#191324252
C43×#32062
#928943