Finite Group Databasebeta

← #24991087

Subgroups — #24991087

Order 11008.

426 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19135370C211yesmaximal, characteristic, complemented
2#19133365C211yesmaximal, characteristic, complemented
3#19133244C211yesmaximal, characteristic
4#19133046C211yesmaximal, characteristic
5#19132433C211yesmaximal, characteristic, complemented
6#19132429C211yesmaximal, characteristic, complemented
7C43×#2935C211yesmaximal, characteristic
8#14582952C2211yescharacteristic
9C2×#13063260—21no—
10#14582923C2211yescharacteristic
11C2×C4⋊(C43⋊C8)C2211yescharacteristic
12C2×C4×C43⋊C8C2211yescharacteristic
13#14582663—21no—
14#14582649—21no—
15#14582649—21no—
16#14582645C411yescharacteristic
17#14582645C411yescharacteristic
18#14582643C411yescharacteristic
19#14582643C411yescharacteristic
20D4⋊(C43⋊C8)—22no—
21C2×#131×C43—21no—
22C43×#532C2211yescharacteristic
23C43×#436—21no—
24C43×#435—22no—
25C8×D4×C43—21no—
26C2×C4⋊C8×C43C2211yescharacteristic
27C43×#408—21no—
28C4×M16×C43C2211yescharacteristic
29C2×#10621877—21no—
30C22×C43⋊C8—21no—
31C22×C43⋊C8—21no—
32#13063260—42no—
33C4⋊(C43⋊C8)—21no—
34C4⋊(C43⋊C8)—21no—
35C4⋊(C43⋊C8)—21no—
36C4⋊(C43⋊C8)C2×C411yescharacteristic
37C4⋊(C43⋊C8)C2×C411yescharacteristic
38C4⋊(C43⋊C8)C2×C411yescharacteristic
39C4⋊(C43⋊C8)C2×C411yescharacteristic
40C22⋊(C43⋊C8)—21no—
41C4×C43⋊C8—21no—
42C4×C43⋊C8—21no—
43C4×C43⋊C8—21no—
44C2×#41×C43—21no—
45#131×C43—42no—
46#131×C43—42no—
47C2×M16×C43—22no—
48C2×M16×C43D411yescharacteristic
49C2×M16×C43D411yescharacteristic
50C22×C8×C43—22no—
51C22×C8×C43—21no—
52C4⋊Q8×C43C2×C411yescharacteristic
53#127×C43C2×C411yescharacteristic
54#124×C43—21no—
55#121×C43—21no—
56#121×C43Q812yes—
57C4×D4×C43—21no—
58C4×D4×C43D412yes—
59C2×C42×C43C2311yescharacteristic
60C4⋊C8×C43—21no—
61C4⋊C8×C43D411yescharacteristic
62C4⋊C8×C43D411yescharacteristic
63C22⋊C8×C43—22no—
64C22⋊C8×C43—22no—
65#97×C43—21no—
66C4×C8×C43—21no—
67#41×C43—41no—
68#41×C43—41no—
69#41×C43—41no—
70#41×C43—41no—
71C2×Q8×C43—21no—
72C2×D4×C43—21no—
73C2×D4×C43—21no—
74C2×D4×C43—22no—
75C2×D4×C43C4⋊C412yes—
76C22×C4×C43—22no—
77C22×C4×C43C2×D411yescharacteristic
78C22×C4×C43C2×Q811yescharacteristic
79C22×C4×C43#4111yescharacteristic
80M16×C43—21no—
81M16×C43—21no—
82M16×C43—21no—
83M16×C43—44no—
84M16×C43SD1612yes—
85C2×C8×C43—21no—
86C2×C8×C43—21no—
87C2×C8×C43—21no—
88C2×C8×C43—21no—
89C2×C8×C43—44no—
90C2×C8×C43—41no—
91C2×C8×C43—41no—
92C4⋊C4×C43—21no—
93C4⋊C4×C43C4⋊C412yes—
94C22⋊C4×C43—22no—
95C22⋊C4×C43—22no—
96C42×C43C22×C411yescharacteristic
97C42×C43C2×D411yescharacteristic
98C42×C43C2×D411yescharacteristic
99C42×C43#4111yescharacteristic
100#10621877—41no—
101#10621877—41no—
102C2×C43⋊C8—22no—
103C2×C43⋊C8—21no—
104C2×C43⋊C8—21no—
105C2×C43⋊C8—21no—
106C2×C43⋊C8—21no—
107C2×C43⋊C8—41no—
108C2×C43⋊C8—41no—
109C2×C43⋊C8—41no—
110C2×C43⋊C8—41no—
111C2×C43⋊C8—41no—
112C23×C43—22no—
113C23×C43C22⋊Q811yescharacteristic
114Q8×C43—41no—
115Q8×C43—41no—
116D4×C43—42no—
117D4×C43—42no—
118D4×C43—42no—
119D4×C43—41no—
120D4×C43—41no—
121D4×C43—41no—
122D4×C43—41no—
123C2×C4×C43—21no—
124C2×C4×C43—21no—
125C2×C4×C43—22no—
126C2×C4×C43—41no—
127C2×C4×C43—42no—
128C2×C4×C43—42no—
129C2×C4×C43C2×C4⋊C411yescharacteristic
130C2×C4×C43C4×D411yescharacteristic
131C2×C4×C43C4×D411yescharacteristic
132C2×C4×C43#12011yescharacteristic
133C2×C4×C43C22⋊Q811yescharacteristic
134C2×C4×C43#12311yescharacteristic
135C2×C4×C43C2×SD1611yescharacteristic
136C2×C4×C43#13511yescharacteristic
137C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
138C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
139C8×C43—22no—
140C8×C43—41no—
141C8×C43—41no—
142C8×C43—41no—
143C43⋊C8—42no—
144C43⋊C8—41no—
145C43⋊C8—41no—
146C43⋊C8—41no—
147C43⋊C8—41no—
148C43⋊C8—81no—
149#8932—431nomaximal, Sylow
150C22×C43—21no—
151C22×C43—21no—
152C22×C43—42no—
153C22×C43—42no—
154C22×C43—42no—
155C22×C43#38511yescharacteristic
156C22×C43#47611yescharacteristic
157C22×C43#47811yescharacteristic
158C4×C43—21no—
159C4×C43—21no—
160C4×C43—21no—
161C4×C43—42no—
162C4×C43C4×SD1611yescharacteristic
163C4×C43#44211yescharacteristic
164C4×C43#44311yescharacteristic
165C4×C43#44411yescharacteristic
166C4×C43#44911yescharacteristic
167C4×C43#45011yescharacteristic
168#2935D4311yescharacteristic
169#1950—431no—
170#1570—431no—
171#1540—431no—
172#1492—431no—
173#1278—431no—
174#1277—431no—
175C2×C43—21no—
176C2×C43—21no—
177C2×C43—82no—
178C2×C43#185811yescharacteristic
179C2×C43#186411yescharacteristic
180C2×C43#186611yescharacteristic
181C2×#131—21no—
182#532C2×D4311yescharacteristic
183#436—21no—
184#435—22no—
185C8×D4—21no—
186#431—431no—
187C2×#108—861no—
188#423—431no—
189C2×C4⋊C8—431no—
190C2×C4⋊C8C2×D4311yescharacteristic
191#408—21no—
192C4×M16C2×D4311yescharacteristic
193C2×C4×C8—431no—
194#341—861no—
195#334—861no—
196#334—861no—
197#332—431no—
198#332—431no—
199#331—431no—
200#331—431no—
201D4⋊C8—862no—
202C43#893211yescharacteristic, complemented, Sylow
203C2×#41—21no—
204#131—42no—
205#131—42no—
206C2×M16—22no—
207C2×M16—861no—
208C2×M16C22⋊D4311yescharacteristic
209C2×M16C22⋊D4311yescharacteristic
210C22×C8—22no—
211C22×C8—21no—
212C22×C8—861no—
213C22×C8—861no—
214C4⋊Q8C4×D4311yescharacteristic
215#127C4×D4311yescharacteristic
216#124—21no—
217#121—21no—
218#121Dic8612yes—
219C4×D4—21no—
220C4×D4C22⋊D4312yes—
221C2×C42C22×D4311yescharacteristic
222#108—1722no—
223C4⋊C8—21no—
224C4⋊C8—431no—
225C4⋊C8—431no—
226C4⋊C8—431no—
227C4⋊C8—431no—
228C4⋊C8—861no—
229C4⋊C8—861no—
230C4⋊C8—861no—
231C4⋊C8C22⋊D4311yescharacteristic
232C4⋊C8C22⋊D4311yescharacteristic
233C22⋊C8—22no—
234C22⋊C8—22no—
235C22⋊C8—861no—
236#97—21no—
237C4×C8—21no—
238C4×C8—861no—
239C4×C8—861no—
240C4×C8—861no—
241#41—41no—
242#41—41no—
243#41—41no—
244#41—41no—
245C2×Q8—21no—
246C2×D4—22no—
247C2×D4—21no—
248C2×D4—21no—
249C2×D4Dic43⋊C412yes—
250C22×C4—22no—
251C22×C4C2×Dic8611yescharacteristic
252C22×C4#1062189811yescharacteristic
253C22×C4C2×C22⋊D4311yescharacteristic
254M16—21no—
255M16—21no—
256M16—21no—
257M16—44no—
258M16—1721no—
259M16—1721no—
260M16#1062188312yes—
261C2×C8—21no—
262C2×C8—21no—
263C2×C8—21no—
264C2×C8—21no—
265C2×C8—44no—
266C2×C8—41no—
267C2×C8—41no—
268C2×C8—862no—
269C2×C8—861no—
270C2×C8—861no—
271C2×C8—861no—
272C2×C8—861no—
273C2×C8—1721no—
274C2×C8—1721no—
275C2×C8—1721no—
276C2×C8—1721no—
277C2×C8—1721no—
278C4⋊C4—21no—
279C4⋊C4Dic43⋊C412yes—
280C22⋊C4—22no—
281C22⋊C4—22no—
282C42C2×C4×D4311yescharacteristic
283C42#1062189811yescharacteristic
284C42C2×C22⋊D4311yescharacteristic
285C42C2×C22⋊D4311yescharacteristic
286C23—22no—
287C23#1306330411yescharacteristic
288Q8—41no—
289Q8—41no—
290D4—42no—
291D4—42no—
292D4—42no—
293D4—41no—
294D4—41no—
295D4—41no—
296D4—41no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—22no—
300C2×C4—41no—
301C2×C4—42no—
302C2×C4—42no—
303C2×C4C2×Dic43⋊C411yescharacteristic
304C2×C4C4×C22⋊D4311yescharacteristic
305C2×C4C4×C22⋊D4311yescharacteristic
306C2×C4#1306329411yescharacteristic
307C2×C4#1306330411yescharacteristic
308C2×C4#1306330811yescharacteristic
309C2×C4C2×#1062188311yescharacteristic
310C2×C4#1306334511yescharacteristic
311C2×C4#1306335011yescharacteristic
312C2×C4#1306335111yescharacteristic
313C8—22no—
314C8—41no—
315C8—41no—
316C8—41no—
317C8—3441no—
318C8—1722no—
319C8—1721no—
320C8—1721no—
321C8—1721no—
322C8—1721no—
323C22—21no—
324C22—21no—
325C22—42no—
326C22—42no—
327C22—42no—
328C22#1458277211yescharacteristic
329C22#1458318911yescharacteristic
330C22#1458319911yescharacteristic
331C4—21no—
332C4—21no—
333C4—21no—
334C4—42no—
335C4C4×#1062188311yescharacteristic
336C4#1458300911yescharacteristic
337C4#1458301411yescharacteristic
338C4#1458301911yescharacteristic
339C4#1458304411yescharacteristic
340C4#1458305011yescharacteristic
341C2—21no—
342C2—21no—
343C2—82no—
344C2#1913481511yescharacteristic
345C2#1913485611yescharacteristic
346C2#1913487011yescharacteristic
subgroupG/H
centerC2×C4#13063294
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#2935C2
socleC22×C43#385
prime radicalC43×#532C22
cosocleC2×C42×C43C23
hypercenter#2935D43
hypocenterC43#8932
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2935

Complements

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

NH ≅ G/Ntype
1. #19135370C2semidirect
2. #19133365C2semidirect
5. #19132433C2semidirect
6. #19132429C2semidirect
202. C43#8932semidirect

Maximal subgroups

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

subgroupindex
#191353702
#191333652
#191332442
#191330462
#191324332
#191324292
C43×#29352
#893243