Finite Group Databasebeta

← #24991797

Subgroups — #24991797

Order 11008.

476 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144599C211yesmaximal, characteristic
2#19135393C211yesmaximal, characteristic
3#19133252C211yesmaximal, characteristic, complemented
4#19133019C211yesmaximal, characteristic
5#19132490C211yesmaximal, characteristic, complemented
6#19132440C211yesmaximal, characteristic, complemented
7C43×#2961C211yesmaximal, characteristic, complemented
8C2×C4×D172C2211yescharacteristic
9#14583227C412yes—
10#14583186—21no—
11#14583101—21no—
12#14583049C412yes—
13C4×#10621884—22no—
14#14582952C2211yescharacteristic
15#14582952C2211yescharacteristic
16C2×C4⋊(C43⋊C8)C2211yescharacteristic
17C2×(C2×D43)⋊C8—21no—
18C2×(C2×D43)⋊C8—21no—
19#14582648—21no—
20#14582645—21no—
21#14582626—22no—
22C43×#533C2211yescharacteristic
23C43×#446—22no—
24C43×#446—22no—
25C43×#424—21no—
26C43×#423C2211yescharacteristic
27C43×#405—21no—
28C2×#97×C43C2211yescharacteristic
29C22×D172C2×C411yescharacteristic
30C22×C4×D43—21no—
31C2×#10621884—22no—
32C22×C43⋊C8—21no—
33C4×D172—21no—
34C4×D172—21no—
35C4×D172—21no—
36C4×D172—21no—
37C2×C4⋊Dic43C2×C411yescharacteristic
38C2×(C2×D43)⋊C4—21no—
39#13063256—22no—
40C4⋊(C43⋊C8)—21no—
41C4⋊(C43⋊C8)—21no—
42C4⋊(C43⋊C8)—21no—
43C4⋊(C43⋊C8)—21no—
44#13063249—22no—
45#13063245—22no—
46C22⋊(C43⋊C8)—21no—
47C22⋊(C43⋊C8)C2×C412yes—
48(C2×D43)⋊C8—42no—
49(C2×D43)⋊C8—42no—
50C4×C43⋊C8—21no—
51C4×C43⋊C8—21no—
52C2×M16×C43—21no—
53C22×C8×C43D411yescharacteristic
54C22×C8×C43D411yescharacteristic
55C4⋊Q8×C43D411yescharacteristic
56C4⋊Q8×C43D411yescharacteristic
57#125×C43—21no—
58C22⋊Q8×C43—21no—
59C22⋊Q8×C43C2×C412yes—
60C4×Q8×C43—21no—
61C4×Q8×C43D412yes—
62#117×C43—21no—
63C2×C42×C43C2311yescharacteristic
64C4⋊C8×C43—24no—
65C4⋊C8×C43—21no—
66C4⋊C8×C43D412yes—
67#97×C43—22no—
68#97×C43—21no—
69#97×C43—21no—
70C4×C8×C43—22no—
71C23×D43—21no—
72C2×Q8×C43—21no—
73C2×Q8×C43C22⋊C412yes—
74C22×C4×C43C22×C411yescharacteristic
75C22×C4×C43C2×D411yescharacteristic
76C22×C4×C43#4111yescharacteristic
77C22×Dic43—21no—
78C2×D172—21no—
79C2×D172—21no—
80C2×D172—42no—
81C2×C4×D43—41no—
82C2×C4×D43—41no—
83C2×C4×D43—41no—
84C2×C4×D43—41no—
85C2×C4×D43—41no—
86C2×C4×D43—41no—
87M16×C43—41no—
88M16×C43—41no—
89C2×C8×C43—21no—
90C2×C8×C43—21no—
91C2×C8×C43—22no—
92C2×C8×C43—21no—
93C2×C8×C43—21no—
94C2×C8×C43—21no—
95C2×C8×C43SD1612yescomplemented
96C4⋊C4×C43—22no—
97C4⋊C4×C43—21no—
98C4⋊C4×C43—21no—
99C4⋊C4×C43—21no—
100C4⋊C4×C43—22no—
101C4⋊C4×C43C22⋊C412yes—
102C22⋊C4×C43—22no—
103C42×C43—22no—
104C42×C43C2×D411yescharacteristic
105C42×C43C2×D411yescharacteristic
106C42×C43C2×D411yescharacteristic
107C42×C43#4111yescharacteristic
108#10621884—44no—
109(C2×D43)⋊C4—41no—
110(C2×D43)⋊C4—41no—
111C4⋊Dic43—21no—
112C4⋊Dic43—21no—
113C2×C43⋊C8—22no—
114C2×C43⋊C8—41no—
115C2×C43⋊C8—41no—
116C2×C43⋊C8—41no—
117C2×C43⋊C8—41no—
118C23×C43C4×D411yescharacteristic
119C22×D43—22no—
120C22×D43—41no—
121C22×D43—41no—
122C22×D43—41no—
123C22×D43—41no—
124C22×D43—41no—
125C22×D43—41no—
126Q8×C43—42no—
127Q8×C43—81no—
128C2×C4×C43—22no—
129C2×C4×C43—22no—
130C2×C4×C43—41no—
131C2×C4×C43—41no—
132C2×C4×C43C2×C22⋊C411yescharacteristic
133C2×C4×C43C4×D411yescharacteristic
134C2×C4×C43#12011yescharacteristic
135C2×C4×C43#12111yescharacteristic
136C2×C4×C43#12111yescharacteristic
137C2×C4×C43#12311yescharacteristic
138C2×C4×C43C2×SD1611yescharacteristic
139C2×C4×C43#13511yescharacteristic
140C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
141C2×C4×C43#13711yescharacteristic
142C2×Dic43—41no—
143C2×Dic43—41no—
144C2×Dic43—41no—
145D172—22no—
146D172—22no—
147D172—41no—
148D172—41no—
149C4×D43—81no—
150C4×D43—81no—
151C4×D43—81no—
152C4×D43—81no—
153C8×C43—22no—
154C8×C43—41no—
155C8×C43—42no—
156C43⋊C8—42no—
157C43⋊C8—81no—
158C43⋊C8—81no—
159#9050—431nomaximal, Sylow
160C22×C43—21no—
161C22×C43—21no—
162C22×C43#38611yescharacteristic
163C22×C43C4×SD1611yescharacteristic
164C22×C43#44011yescharacteristic
165C2×D43—42no—
166C2×D43—42no—
167C2×D43—42no—
168C2×D43—81no—
169C2×D43—81no—
170C2×D43—81no—
171C2×D43—81no—
172C4×C43—21no—
173C4×C43—21no—
174C4×C43—21no—
175C4×C43—21no—
176C4×C43—42no—
177C4×C43—42no—
178C4×C43#44811yescharacteristic
179C4×C43#44911yescharacteristic
180C4×C43#46011yescharacteristic
181C4×C43#46411yescharacteristic
182Dic43—81no—
183#3101—431no—
184#2961D4311yescharacteristic, complemented
185#1955—431no—
186#1542—431no—
187#1486—431no—
188#1301—431no—
189#1281—431no—
190C2×C43—21no—
191C2×C43—21no—
192C2×C43#188011yescharacteristic
193C2×C43#188111yescharacteristic
194C2×C43#189111yescharacteristic
195D43—82no—
196#533C2×D4311yescharacteristic
197C2×C4×D4—431no—
198#483—432no—
199#476—861no—
200#461—861no—
201#450—432no—
202#446—22no—
203#446—22no—
204C4×SD16—862no—
205#431—431no—
206#431—431no—
207#424—21no—
208#423C2×D4311yescharacteristic
209C2×C4⋊C8—431no—
210C2×C22⋊C8—861no—
211C2×C22⋊C8—861no—
212#405—21no—
213C2×#97C2×D4311yescharacteristic
214#333—861no—
215#332—861no—
216D4⋊C8—862no—
217C43#905011yescharacteristic, complemented, Sylow
218C22×D4—431no—
219C23×C4—861no—
220C2×SD16—862no—
221C2×M16—21no—
222C22×C8—861no—
223C22×C8C22⋊D4311yescharacteristic
224C22×C8C22⋊D4311yescharacteristic
225C4⋊Q8D17211yescharacteristic
226C4⋊Q8D17211yescharacteristic
227#125—21no—
228C22⋊Q8—21no—
229C22⋊Q8C4×D4312yes—
230C4×Q8—21no—
231C4×Q8C22⋊D4312yes—
232C4×D4—861no—
233C4×D4—861no—
234C4×D4—861no—
235C4×D4—861no—
236#117—21no—
237C2×C4⋊C4—431no—
238C2×C22⋊C4—861no—
239C2×C42C22×D4311yescharacteristic
240#106—862no—
241C4⋊C8—24no—
242C4⋊C8—21no—
243C4⋊C8—861no—
244C4⋊C8—861no—
245C4⋊C8—861no—
246C4⋊C8—861no—
247C4⋊C8C22⋊D4312yes—
248#103—862no—
249#102—862no—
250C22⋊C8—432no—
251C22⋊C8—861no—
252C22⋊C8—1722no—
253C22⋊C8—1722no—
254#97—22no—
255#97—21no—
256#97—21no—
257C4×C8—22no—
258C4×C8—861no—
259C4×C8—861no—
260C24—861no—
261C2×Q8—21no—
262C2×Q8(C2×D43)⋊C412yes—
263C2×D4—861no—
264C2×D4—861no—
265C2×D4—1722no—
266C22×C4—861no—
267C22×C4—1721no—
268C22×C4—1721no—
269C22×C4—1721no—
270C22×C4—1721no—
271C22×C4—1721no—
272C22×C4—1721no—
273C22×C4C2×C4×D4311yescharacteristic
274C22×C4#1062189811yescharacteristic
275C22×C4C2×C22⋊D4311yescharacteristic
276SD16—1724no—
277M16—41no—
278M16—41no—
279C2×C8—21no—
280C2×C8—21no—
281C2×C8—22no—
282C2×C8—21no—
283C2×C8—21no—
284C2×C8—21no—
285C2×C8—862no—
286C2×C8—1721no—
287C2×C8—1721no—
288C2×C8—1721no—
289C2×C8—1721no—
290C2×C8#1062188412yescomplemented
291C4⋊C4—22no—
292C4⋊C4—21no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—22no—
296C4⋊C4—861no—
297C4⋊C4—861no—
298C4⋊C4(C2×D43)⋊C412yes—
299C22⋊C4—22no—
300C22⋊C4—1721no—
301C22⋊C4—1721no—
302C42—22no—
303C42C2×D17211yescharacteristic
304C42#1062189811yescharacteristic
305C42C2×C22⋊D4311yescharacteristic
306C42C2×C22⋊D4311yescharacteristic
307C23—862no—
308C23—1721no—
309C23—1721no—
310C23—1721no—
311C23—1721no—
312C23—1721no—
313C23—1721no—
314C23C4×C22⋊D4311yescharacteristic
315Q8—42no—
316Q8—81no—
317D4—862no—
318D4—862no—
319D4—1721no—
320D4—1721no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—3441no—
326C2×C4—3441no—
327C2×C4—3441no—
328C2×C4—3441no—
329C2×C4—1721no—
330C2×C4—1721no—
331C2×C4—1721no—
332C2×C4C2×(C2×D43)⋊C411yescharacteristic
333C2×C4C4×C22⋊D4311yescharacteristic
334C2×C4#1306329411yescharacteristic
335C2×C4#1306329911yescharacteristic
336C2×C4#1306329911yescharacteristic
337C2×C4#1306330811yescharacteristic
338C2×C4C2×#1062188411yescharacteristic
339C2×C4#1306334511yescharacteristic
340C2×C4#1306335011yescharacteristic
341C2×C4#1306335611yescharacteristic
342C8—22no—
343C8—41no—
344C8—42no—
345C8—3441no—
346C8—3441no—
347C8—1722no—
348C22—21no—
349C22—21no—
350C22—3441no—
351C22—3441no—
352C22—3441no—
353C22—3441no—
354C22—1722no—
355C22—1722no—
356C22—1722no—
357C22#1458277811yescharacteristic
358C22C4×#1062188411yescharacteristic
359C22#1458299711yescharacteristic
360C4—21no—
361C4—21no—
362C4—21no—
363C4—21no—
364C4—42no—
365C4—42no—
366C4—3441no—
367C4#1458303811yescharacteristic
368C4#1458304411yescharacteristic
369C4#1458309911yescharacteristic
370C4#1458312111yescharacteristic
371C2—21no—
372C2—21no—
373C2—3442no—
374C2#1913495011yescharacteristic
375C2#1913495711yescharacteristic
376C2#1913501311yescharacteristic
subgroupG/H
centerC2×C4#13063294
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#2961C2
socleC22×C43#386
prime radicalC22×D172C2×C4
cosocleC2×C42×C43C23
hypercenter#2961D43
hypocenterC43#9050
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2961

Complements

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

NH ≅ G/Ntype
3. #19133252C2semidirect
5. #19132490C2semidirect
6. #19132440C2semidirect
7. C43×#2961C2semidirect
95. C2×C8×C43SD16semidirect
184. #2961D43semidirect
217. C43#9050semidirect
290. C2×C8#10621884semidirect

Maximal subgroups

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

subgroupindex
#191445992
#191353932
#191332522
#191330192
#191324902
#191324402
C43×#29612
#905043