Finite Group Databasebeta

← #24993345

Subgroups — #24993345

Order 11008.

480 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145723C211yesmaximal, characteristic
2#19135427C211yesmaximal, characteristic
3#19133280C211yesmaximal, characteristic, complemented
4#19133154C211yesmaximal, characteristic
5#19132453C211yesmaximal, characteristic, complemented
6#19132424C211yesmaximal, characteristic, complemented
7C43×#2331C211yesmaximal, characteristic, complemented
8#14583449C2211yescharacteristic
9#14583295C412yescomplemented
10#14583247C412yescomplemented
11#14583217—22no—
12#14583186—22no—
13#14582952C2211yescharacteristic
14#14582952C2211yescharacteristic
15#14582923C2211yescharacteristic
16C2×#13063253—21no—
17C2×#13063253—21no—
18#14582645—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×#10621877—21no—
29#13063325C2×C411yescharacteristic
30#13063322C2×C411yescharacteristic
31#13063313—21no—
32#13063299—21no—
33#13063299—21no—
34C4×D172—21no—
35C4×D172—21no—
36#13063256—24no—
37C4⋊(C43⋊C8)—21no—
38C4⋊(C43⋊C8)—21no—
39C4⋊(C43⋊C8)—21no—
40C4⋊(C43⋊C8)—21no—
41#13063253—42no—
42#13063253—42no—
43#13063245—24no—
44C22⋊(C43⋊C8)—21no—
45C22⋊(C43⋊C8)—21no—
46C4×C43⋊C8—21no—
47C4×C43⋊C8C2×C412yes—
48C22×Q8×C43—21no—
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—22no—
56C2×C4⋊C4×C43D412yes—
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—22no—
69C2×Q8×C43—82no—
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—41no—
91C4⋊C4×C43—41no—
92C4⋊C4×C43—82no—
93C4⋊C4×C43C22⋊C414yes—
94C42×C43—21no—
95C42×C43—21no—
96C42×C43—21no—
97C42×C43—82no—
98C42×C43SD1612yes—
99C42×C43C22×C411yescharacteristic
100C42×C43C2×D411yescharacteristic
101C42×C43#4111yescharacteristic
102C42×C43#4111yescharacteristic
103(C2×D43)⋊C4—41no—
104(C2×D43)⋊C4—41no—
105C4⋊Dic43—21no—
106C4⋊Dic43—21no—
107#10621877—41no—
108#10621877—41no—
109C2×C43⋊C8—22no—
110C2×C43⋊C8—41no—
111C2×C43⋊C8—41no—
112C23×C43#12011yescharacteristic
113C22×D43—41no—
114Q8×C43—82no—
115Q8×C43—82no—
116C2×C4×C43—24no—
117C2×C4×C43—22no—
118C2×C4×C43—41no—
119C2×C4×C43—41no—
120C2×C4×C43—41no—
121C2×C4×C43—42no—
122C2×C4×C43—42no—
123C2×C4×C43—41no—
124C2×C4×C43—42no—
125C2×C4×C43—41no—
126C2×C4×C43—41no—
127C2×C4×C43—42no—
128C2×C4×C43—41no—
129C2×C4×C43—42no—
130C2×C4×C43C2×C22⋊C411yescharacteristic
131C2×C4×C43C4×D411yescharacteristic
132C2×C4×C43C4×D411yescharacteristic
133C2×C4×C43#12111yescharacteristic
134C2×C4×C43#12111yescharacteristic
135C2×C4×C43#12311yescharacteristic
136C2×C4×C43C2×SD1611yescharacteristic
137C2×C4×C43#13511yescharacteristic
138C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
139C2×C4×C43#13711yescharacteristic
140C22⋊D43—81no—
141C22⋊D43—81no—
142C2×Dic43—41no—
143D172—42no—
144D172—41no—
145D172—41no—
146D172—81no—
147C4×D43—81no—
148C4×D43—81no—
149Dic86—41no—
150Dic86—41no—
151C43⋊C8—42no—
152C43⋊C8—81no—
153C43⋊C8—81no—
154#9302—431nomaximal, Sylow
155C22×C43—21no—
156C22×C43—21no—
157C22×C43#38611yescharacteristic
158C22×C43#44811yescharacteristic
159C22×C43#44911yescharacteristic
160C2×D43—81no—
161C2×D43—81no—
162C2×D43—81no—
163C4×C43—21no—
164C4×C43—21no—
165C4×C43—21no—
166C4×C43—21no—
167C4×C43—42no—
168C4×C43—44no—
169C4×C43—82no—
170C4×C43—81no—
171C4×C43C4×SD1611yescharacteristic
172C4×C43#44011yescharacteristic
173C4×C43#46011yescharacteristic
174C4×C43#46411yescharacteristic
175Dic43—81no—
176#3227—431no—
177#2331D4311yescharacteristic, complemented
178#1963—431no—
179#1549—431no—
180#1517—431no—
181#1286—431no—
182#1274—431no—
183C2×C43—21no—
184C2×C43—21no—
185C2×C43#188011yescharacteristic
186C2×C43#190411yescharacteristic
187C2×C43#191211yescharacteristic
188D43—161no—
189#532—431no—
190C2×C4⋊Q8C2×D4311yescharacteristic
191#498—432no—
192#486—432no—
193#481—862no—
194#476—862no—
195#431—431no—
196#431—431no—
197#423—431no—
198C2×#104—861no—
199C2×#104—861no—
200#391—22no—
201#389—21no—
202#387—22no—
203#382C2×D4311yescharacteristic
204C4×C4⋊C4—21no—
205#376C2×D4311yescharacteristic
206#332—862no—
207#327—862no—
208C43#930211yescharacteristic, complemented, Sylow
209C2×#41—861no—
210C22×Q8—21no—
211C2×M16—861no—
212C4⋊Q8—21no—
213C4⋊Q8—21no—
214C4⋊Q8—431no—
215C4⋊Q8C4×D4312yes—
216C4⋊Q8D17212yes—
217#127—431no—
218#124—861no—
219#121—861no—
220#121—861no—
221C4×D4—861no—
222C4×D4—861no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—22no—
226C2×C4⋊C4C22⋊D4312yes—
227C2×C42—22no—
228C2×C42C22⋊D4311yescharacteristic
229C2×C42C22⋊D4311yescharacteristic
230C2×C42C22×D4311yescharacteristic
231#106—864no—
232C4⋊C8—861no—
233C4⋊C8—861no—
234C4⋊C8—861no—
235C4⋊C8—861no—
236#104—1722no—
237#104—1722no—
238#102—864no—
239C22⋊C8—861no—
240C22⋊C8—861no—
241C4×C8—432no—
242C4×C8—861no—
243#95—22no—
244#95—22no—
245#95—21no—
246#95—21no—
247#95—21no—
248#95C22⋊D4312yes—
249#41—1721no—
250#41—1721no—
251#41—1721no—
252#41—1721no—
253C2×Q8—22no—
254C2×Q8—22no—
255C2×Q8—82no—
256C2×Q8—861no—
257C2×D4—861no—
258C2×D4—861no—
259C2×D4—861no—
260C2×D4—1721no—
261C22×C4—21no—
262C22×C4—22no—
263C22×C4—21no—
264C22×C4—22no—
265C22×C4—1721no—
266C22×C4C2×C22⋊D4311yescharacteristic
267C22×C4C2×C22⋊D4311yescharacteristic
268C22×C4C2×C22⋊D4311yescharacteristic
269M16—1721no—
270M16—1721no—
271C2×C8—862no—
272C2×C8—1721no—
273C2×C8—1721no—
274C4⋊C4—22no—
275C4⋊C4—22no—
276C4⋊C4—22no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—82no—
280C4⋊C4—861no—
281C4⋊C4—861no—
282C4⋊C4(C2×D43)⋊C414yes—
283C22⋊C4—1721no—
284C22⋊C4—1721no—
285C42—21no—
286C42—21no—
287C42—21no—
288C42—82no—
289C42#1062188412yes—
290C42C2×C4×D4311yescharacteristic
291C42C2×D17211yescharacteristic
292C42#1062189811yescharacteristic
293C42#1062189811yescharacteristic
294C23—1721no—
295C23#1306329411yescharacteristic
296Q8—82no—
297Q8—82no—
298Q8—1721no—
299Q8—1721no—
300D4—3441no—
301D4—3441no—
302D4—3441no—
303D4—1722no—
304D4—1721no—
305D4—1721no—
306C2×C4—24no—
307C2×C4—22no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—41no—
314C2×C4—42no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—42no—
318C2×C4—41no—
319C2×C4—42no—
320C2×C4—3441no—
321C2×C4—3441no—
322C2×C4—1721no—
323C2×C4C2×(C2×D43)⋊C411yescharacteristic
324C2×C4C4×C22⋊D4311yescharacteristic
325C2×C4C4×C22⋊D4311yescharacteristic
326C2×C4#1306329911yescharacteristic
327C2×C4#1306329911yescharacteristic
328C2×C4#1306330811yescharacteristic
329C2×C4C2×#1062188411yescharacteristic
330C2×C4#1306334511yescharacteristic
331C2×C4#1306335011yescharacteristic
332C2×C4#1306335611yescharacteristic
333C8—3441no—
334C8—3441no—
335C8—1722no—
336C22—21no—
337C22—21no—
338C22—3441no—
339C22—3441no—
340C22—3441no—
341C22#1458277811yescharacteristic
342C22#1458303811yescharacteristic
343C22#1458304411yescharacteristic
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—42no—
349C4—44no—
350C4—82no—
351C4—81no—
352C4—3441no—
353C4C4×#1062188411yescharacteristic
354C4#1458299711yescharacteristic
355C4#1458309911yescharacteristic
356C4#1458312111yescharacteristic
357C2—21no—
358C2—21no—
359C2—6881no—
360C2#1913495011yescharacteristic
361C2#1913508211yescharacteristic
362C2#1913513211yescharacteristic
subgroupG/H
centerC22#14582778
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#2331C2
socleC22×C43#386
prime radical#14583449C22
cosocleC2×C42×C43C23
hypercenter#2331D43
hypocenterC43#9302
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. #19133280C2semidirect
5. #19132453C2semidirect
6. #19132424C2semidirect
7. C43×#2331C2semidirect
9. #14583295C4semidirect
10. #14583247C4semidirect
177. #2331D43semidirect
208. C43#9302semidirect

Maximal subgroups

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

subgroupindex
#191457232
#191354272
#191332802
#191331542
#191324532
#191324242
C43×#23312
#930243