Finite Group Databasebeta

← #24993338

Subgroups — #24993338

Order 11008.

492 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145520C211yesmaximal, characteristic
2#19135427C211yesmaximal, characteristic
3#19133276C211yesmaximal, characteristic, complemented
4#19133154C211yesmaximal, characteristic
5#19132453C211yesmaximal, characteristic, complemented
6#19132424C211yesmaximal, characteristic, complemented
7C43×#2331C211yesmaximal, characteristic, complemented
8#14583449C2211yescharacteristic
9#14583273C412yescomplemented
10#14583249C412yescomplemented
11#14583101—22no—
12#14583038—22no—
13#14582952C2211yescharacteristic
14#14582952C2211yescharacteristic
15#14582923C2211yescharacteristic
16C2×#13063253—21no—
17C2×#13063253—21no—
18#14582648—22no—
19#14582632—22no—
20C2×C4⋊Q8×C43C2211yescharacteristic
21C43×#391—22no—
22C43×#389—21no—
23C43×#387—22no—
24C43×#382C2211yescharacteristic
25C4×C4⋊C4×C43—21no—
26C43×#376C2211yescharacteristic
27C2×#10621898—21no—
28C2×#10621884—24no—
29C2×#10621877—21no—
30#13063325C2×C411yescharacteristic
31#13063322C2×C411yescharacteristic
32#13063313—21no—
33#13063299—21no—
34#13063299—21no—
35C4×D172—21no—
36C4×D172—21no—
37C4⋊(C43⋊C8)—21no—
38C4⋊(C43⋊C8)—21no—
39C4⋊(C43⋊C8)—21no—
40C4⋊(C43⋊C8)—21no—
41#13063253—42no—
42#13063253—42no—
43#13063249—24no—
44C22⋊(C43⋊C8)—21no—
45C22⋊(C43⋊C8)—21no—
46C4×C43⋊C8—21no—
47C4×C43⋊C8C2×C412yes—
48C22×Q8×C43D412yes—
49C4⋊Q8×C43—21no—
50C4⋊Q8×C43—21no—
51C4⋊Q8×C43C2×C412yes—
52C4⋊Q8×C43D412yes—
53C2×C4⋊C4×C43—21no—
54C2×C4⋊C4×C43—21no—
55C2×C4⋊C4×C43—21no—
56C2×C4⋊C4×C43—22no—
57C2×C42×C43—22no—
58C2×C42×C43D411yescharacteristic
59C2×C42×C43D411yescharacteristic
60C2×C42×C43C2311yescharacteristic
61#95×C43—22no—
62#95×C43—22no—
63#95×C43—21no—
64#95×C43—21no—
65#95×C43—21no—
66#95×C43D412yes—
67C2×Q8×C43—22no—
68C2×Q8×C43—82no—
69C2×Q8×C43C22⋊C414yes—
70C22×C4×C43—21no—
71C22×C4×C43—22no—
72C22×C4×C43—21no—
73C22×C4×C43—22no—
74C22×C4×C43C2×D411yescharacteristic
75C22×C4×C43C2×D411yescharacteristic
76C22×C4×C43C2×D411yescharacteristic
77C2×C22⋊D43—41no—
78#10621898—41no—
79#10621898—41no—
80#10621898—41no—
81#10621898—41no—
82C2×D172—21no—
83C2×D172—21no—
84C2×D172—21no—
85C2×C4×D43—41no—
86C2×Dic86—21no—
87C4⋊C4×C43—22no—
88C4⋊C4×C43—22no—
89C4⋊C4×C43—22no—
90C4⋊C4×C43—22no—
91C4⋊C4×C43—41no—
92C4⋊C4×C43—41no—
93C4⋊C4×C43—82no—
94C42×C43—21no—
95C42×C43—21no—
96C42×C43—21no—
97C42×C43—82no—
98C42×C43SD1612yescomplemented
99C42×C43C22×C411yescharacteristic
100C42×C43C2×D411yescharacteristic
101C42×C43#4111yescharacteristic
102C42×C43#4111yescharacteristic
103#10621884—84no—
104(C2×D43)⋊C4—41no—
105(C2×D43)⋊C4—41no—
106C4⋊Dic43—21no—
107C4⋊Dic43—21no—
108#10621877—41no—
109#10621877—41no—
110C2×C43⋊C8—22no—
111C2×C43⋊C8—41no—
112C2×C43⋊C8—41no—
113C23×C43#12011yescharacteristic
114C22×D43—41no—
115Q8×C43—44no—
116Q8×C43—82no—
117C2×C4×C43—24no—
118C2×C4×C43—22no—
119C2×C4×C43—41no—
120C2×C4×C43—41no—
121C2×C4×C43—41no—
122C2×C4×C43—42no—
123C2×C4×C43—42no—
124C2×C4×C43—41no—
125C2×C4×C43—42no—
126C2×C4×C43—41no—
127C2×C4×C43—41no—
128C2×C4×C43—42no—
129C2×C4×C43—41no—
130C2×C4×C43—42no—
131C2×C4×C43C2×C22⋊C411yescharacteristic
132C2×C4×C43C4×D411yescharacteristic
133C2×C4×C43C4×D411yescharacteristic
134C2×C4×C43#12111yescharacteristic
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
141C22⋊D43—81no—
142C22⋊D43—81no—
143C2×Dic43—41no—
144D172—42no—
145D172—41no—
146D172—41no—
147D172—81no—
148C4×D43—81no—
149C4×D43—81no—
150Dic86—41no—
151Dic86—41no—
152C43⋊C8—42no—
153C43⋊C8—81no—
154C43⋊C8—81no—
155#9301—431nomaximal, Sylow
156C22×C43—21no—
157C22×C43—21no—
158C22×C43#38611yescharacteristic
159C22×C43#44811yescharacteristic
160C22×C43#44911yescharacteristic
161C2×D43—81no—
162C2×D43—81no—
163C2×D43—81no—
164C4×C43—21no—
165C4×C43—21no—
166C4×C43—21no—
167C4×C43—21no—
168C4×C43—42no—
169C4×C43—44no—
170C4×C43—82no—
171C4×C43—81no—
172C4×C43C4×SD1611yescharacteristic
173C4×C43#44011yescharacteristic
174C4×C43#46011yescharacteristic
175C4×C43#46411yescharacteristic
176Dic43—81no—
177#3206—431no—
178#2331D4311yescharacteristic, complemented
179#1963—431no—
180#1548—431no—
181#1517—431no—
182#1286—431no—
183#1274—431no—
184C2×C43—21no—
185C2×C43—21no—
186C2×C43#188011yescharacteristic
187C2×C43#190511yescharacteristic
188C2×C43#191111yescharacteristic
189D43—161no—
190#532—431no—
191C2×C4⋊Q8C2×D4311yescharacteristic
192#492—432no—
193#487—432no—
194#461—862no—
195#448—862no—
196#431—431no—
197#431—431no—
198#423—431no—
199C2×#104—861no—
200C2×#104—861no—
201#391—22no—
202#389—21no—
203#387—22no—
204#382C2×D4311yescharacteristic
205C4×C4⋊C4—21no—
206#376C2×D4311yescharacteristic
207#333—862no—
208#327—862no—
209C43#930111yescharacteristic, complemented, Sylow
210C2×#41—861no—
211C22×Q8C22⋊D4312yes—
212C2×SD16—864no—
213C2×M16—861no—
214C4⋊Q8—21no—
215C4⋊Q8—21no—
216C4⋊Q8—431no—
217C4⋊Q8C4×D4312yes—
218C4⋊Q8D17212yes—
219#127—431no—
220#124—861no—
221#121—861no—
222#121—861no—
223C4×D4—861no—
224C4×D4—861no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—22no—
229C2×C42—22no—
230C2×C42C22⋊D4311yescharacteristic
231C2×C42C22⋊D4311yescharacteristic
232C2×C42C22×D4311yescharacteristic
233C4⋊C8—861no—
234C4⋊C8—861no—
235C4⋊C8—861no—
236C4⋊C8—861no—
237#104—1722no—
238#104—1722no—
239#103—864no—
240C22⋊C8—861no—
241C22⋊C8—861no—
242C4×C8—432no—
243C4×C8—861no—
244#95—22no—
245#95—22no—
246#95—21no—
247#95—21no—
248#95—21no—
249#95C22⋊D4312yes—
250#41—1721no—
251#41—1721no—
252#41—1721no—
253#41—1721no—
254C2×Q8—22no—
255C2×Q8—82no—
256C2×Q8—861no—
257C2×Q8(C2×D43)⋊C414yes—
258C2×D4—861no—
259C2×D4—861no—
260C2×D4—861no—
261C2×D4—1721no—
262C22×C4—21no—
263C22×C4—22no—
264C22×C4—21no—
265C22×C4—22no—
266C22×C4—1721no—
267C22×C4C2×C22⋊D4311yescharacteristic
268C22×C4C2×C22⋊D4311yescharacteristic
269C22×C4C2×C22⋊D4311yescharacteristic
270SD16—3444no—
271M16—1721no—
272M16—1721no—
273C2×C8—862no—
274C2×C8—1721no—
275C2×C8—1721no—
276C4⋊C4—22no—
277C4⋊C4—22no—
278C4⋊C4—22no—
279C4⋊C4—22no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—82no—
283C4⋊C4—861no—
284C4⋊C4—861no—
285C22⋊C4—1721no—
286C22⋊C4—1721no—
287C42—21no—
288C42—21no—
289C42—21no—
290C42—82no—
291C42#1062188412yescomplemented
292C42C2×C4×D4311yescharacteristic
293C42C2×D17211yescharacteristic
294C42#1062189811yescharacteristic
295C42#1062189811yescharacteristic
296C23—1721no—
297C23#1306329411yescharacteristic
298Q8—44no—
299Q8—82no—
300Q8—1721no—
301Q8—1721no—
302D4—3441no—
303D4—3441no—
304D4—3441no—
305D4—1722no—
306D4—1721no—
307D4—1721no—
308C2×C4—24no—
309C2×C4—22no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—41no—
316C2×C4—42no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—42no—
320C2×C4—41no—
321C2×C4—42no—
322C2×C4—3441no—
323C2×C4—3441no—
324C2×C4—1721no—
325C2×C4C2×(C2×D43)⋊C411yescharacteristic
326C2×C4C4×C22⋊D4311yescharacteristic
327C2×C4C4×C22⋊D4311yescharacteristic
328C2×C4#1306329911yescharacteristic
329C2×C4#1306329911yescharacteristic
330C2×C4#1306330811yescharacteristic
331C2×C4C2×#1062188411yescharacteristic
332C2×C4#1306334511yescharacteristic
333C2×C4#1306335011yescharacteristic
334C2×C4#1306335611yescharacteristic
335C8—3441no—
336C8—3441no—
337C8—1722no—
338C22—21no—
339C22—21no—
340C22—3441no—
341C22—3441no—
342C22—3441no—
343C22#1458277811yescharacteristic
344C22#1458303811yescharacteristic
345C22#1458304411yescharacteristic
346C4—21no—
347C4—21no—
348C4—21no—
349C4—21no—
350C4—42no—
351C4—44no—
352C4—82no—
353C4—81no—
354C4—3441no—
355C4C4×#1062188411yescharacteristic
356C4#1458299711yescharacteristic
357C4#1458309911yescharacteristic
358C4#1458312111yescharacteristic
359C2—21no—
360C2—21no—
361C2—6881no—
362C2#1913495011yescharacteristic
363C2#1913508911yescharacteristic
364C2#1913512711yescharacteristic
subgroupG/H
centerC22#14582778
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#2331C2
socleC22×C43#386
prime radical#14583449C22
cosocleC2×C42×C43C23
hypercenter#2331D43
hypocenterC43#9301
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2331

Complements

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

NH ≅ G/Ntype
3. #19133276C2semidirect
5. #19132453C2semidirect
6. #19132424C2semidirect
7. C43×#2331C2semidirect
9. #14583273C4semidirect
10. #14583249C4semidirect
98. C42×C43SD16semidirect
178. #2331D43semidirect
209. C43#9301semidirect
291. C42#10621884semidirect

Maximal subgroups

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

subgroupindex
#191455202
#191354272
#191332762
#191331542
#191324532
#191324242
C43×#23312
#930143