Finite Group Databasebeta

← #25013467

Subgroups — #25013467

Order 11008.

456 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143496C211yesmaximal, characteristic
2#19136224C211yesmaximal, characteristic, complemented
3C2×#14582683C211yesmaximal, characteristic, complemented
4#19136210C211yesmaximal, characteristic, complemented
5#19132685C211yesmaximal, characteristic, complemented
6#19132680C211yesmaximal, characteristic, complemented
7C43×#3407C211yesmaximal, characteristic, complemented
8#14583697C411yescharacteristic
9C2×#13063331C2211yescharacteristic
10C2×#13063265C2211yescharacteristic
11C22×C43⋊C16C2211yescharacteristic
12#14583019—22no—
13#14583014—22no—
14#14582947C411yescharacteristic
15#14582916C411yescharacteristic
16#14582915C411yescharacteristic
17#14582854C2211yescharacteristic
18#14582684—22no—
19#14582683—22no—
20(C2×D43)⋊C16—22no—
21C2×#131×C43C2211yescharacteristic
22C43×#504—22no—
23C43×#504—22no—
24C2×M32×C43—22no—
25C2×M32×C43C2211yescharacteristic
26C2×M32×C43C2211yescharacteristic
27C2×#10621898C2×C411yescharacteristic
28#13063356—21no—
29#13063355C812yes—
30#13063351—21no—
31#13063350C812yes—
32#13063345—22no—
33#13063331—21no—
34#13063331—21no—
35#13063331—21no—
36#13063331—21no—
37C2×#10621877C2×C411yescharacteristic
38C2×#10621877C2×C411yescharacteristic
39C2×#10621872—21no—
40C2×C8×D43—21no—
41#13063284C2×C411yescharacteristic
42#13063265—21no—
43#13063265—21no—
44C2×C43⋊C16—21no—
45C2×C43⋊C16—21no—
46C2×C43⋊C16—21no—
47C2×C43⋊C16—21no—
48#13063260—22no—
49#13063252—22no—
50#13063251—22no—
51#13063235—21no—
52C8×Dic43—21no—
53C2×#41×C43C2×C411yescharacteristic
54#131×C43—21no—
55#131×C43—21no—
56#131×C43D412yes—
57#131×C43D412yes—
58C2×M16×C43—21no—
59C2×M16×C43C2×C411yescharacteristic
60C22×C8×C43—21no—
61C22×C8×C43C2311yescharacteristic
62M32×C43—24no—
63M32×C43—21no—
64M32×C43—21no—
65M32×C43—21no—
66M32×C43D412yes—
67C2×C16×C43—24no—
68C2×C16×C43—21no—
69C2×C16×C43D412yes—
70#41×C43—21no—
71#41×C43—21no—
72#41×C43C22⋊C412yes—
73#41×C43C2×C812yes—
74C2×Q8×C43M1611yescharacteristic
75C2×D4×C43—21no—
76C2×D4×C43M1611yescharacteristic
77C22×C4×C43—21no—
78C22×C4×C43C22×C411yescharacteristic
79C2×C22⋊D43—21no—
80#10621898—21no—
81#10621898—21no—
82#10621898—21no—
83#10621898—21no—
84C2×D172C2×C811yescharacteristic
85C2×C4×D43—21no—
86C2×Dic86C2×C811yescharacteristic
87M16×C43—21no—
88M16×C43—22no—
89M16×C43—22no—
90M16×C43C22⋊C412yes—
91C2×C8×C43—21no—
92C2×C8×C43—22no—
93C2×C8×C43—22no—
94C2×C8×C43C2×D411yescharacteristic
95C2×C8×C43C2×D411yescharacteristic
96C2×C8×C43C2×D411yescharacteristic
97C2×C8×C43C2×D411yescharacteristic
98C2×C8×C43#4111yescharacteristic
99C2×C8×C43#4111yescharacteristic
100C22⋊Dic43—21no—
101#10621885—22no—
102#10621884—22no—
103#10621883—22no—
104#10621882—22no—
105C4⋊Dic43—21no—
106C4×Dic43—21no—
107#10621877—21no—
108#10621877—21no—
109#10621877—21no—
110#10621877C2×C812yes—
111C2×C43⋊C8—21no—
112C2×C43⋊C8—21no—
113#10621872—41no—
114#10621872—41no—
115C8×D43—41no—
116C8×D43—41no—
117C16×C43—22no—
118C16×C43—22no—
119C43⋊C16—41no—
120C43⋊C16—41no—
121C23×C43—21no—
122C23×C43#13111yescharacteristic
123C22×D43—21no—
124Q8×C43—21no—
125Q8×C43C22⋊C812yes—
126D4×C43—22no—
127D4×C43—22no—
128D4×C43—21no—
129D4×C43C22⋊C812yes—
130C2×C4×C43—21no—
131C2×C4×C43—22no—
132C2×C4×C43—22no—
133C2×C4×C43C2×C22⋊C411yescharacteristic
134C2×C4×C43C4×D411yescharacteristic
135C2×C4×C43C4×D411yescharacteristic
136C2×C4×C43C22×C811yescharacteristic
137C2×C4×C43C2×M1611yescharacteristic
138C2×C4×C43#13111yescharacteristic
139C22⋊D43—41no—
140C22⋊D43—41no—
141C2×Dic43—21no—
142C2×Dic43—41no—
143D172—21no—
144D172—21no—
145C4×D43—41no—
146C4×D43—41no—
147Dic86—21no—
148Dic86—21no—
149C8×C43—22no—
150C8×C43#12011yescharacteristic
151C8×C43#12111yescharacteristic
152C8×C43#12111yescharacteristic
153C8×C43#12311yescharacteristic
154C43⋊C8—22no—
155C43⋊C8—41no—
156#12979—431nomaximal, Sylow
157C22×C43—22no—
158C22×C43—41no—
159C22×C43—81no—
160C22×C43#40811yescharacteristic
161C22×C43C8×D411yescharacteristic
162C22×C43#43511yescharacteristic
163C2×D43—42no—
164C2×D43—41no—
165C4×C43—22no—
166C4×C43#38611yescharacteristic
167C4×C43C2×C22⋊C811yescharacteristic
168C4×C43C8×D411yescharacteristic
169C4×C43#43511yescharacteristic
170Dic43—41no—
171Dic43—81no—
172#3407D4311yescharacteristic, complemented
173#2955—431no—
174#2117—431no—
175C2×#350—431no—
176#2113—431no—
177#1379—431no—
178#1378—431no—
179C2×C43—21no—
180C2×C43—21no—
181C2×C43—21no—
182C2×C43—42no—
183C2×C43#186911yescharacteristic
184D43—81no—
185#575—431no—
186C2×#131—431no—
187C2×#131C2×D4311yescharacteristic
188#504—22no—
189#504—22no—
190C2×M32—22no—
191C2×M32—431no—
192C2×M32C2×D4311yescharacteristic
193C2×M32C2×D4311yescharacteristic
194C22×C16—431no—
195#444—862no—
196#443—862no—
197#430—431no—
198#421—431no—
199#421—431no—
200#405—431no—
201#350—862no—
202#350—862no—
203C22⋊C16—862no—
204C43#1297911yescharacteristic, complemented, Sylow
205C2×#41—431no—
206C2×#41C4×D4311yescharacteristic
207#137—432no—
208#137—861no—
209AGL(1,ℤ/8)—432no—
210AGL(1,ℤ/8)—861no—
211#135—862no—
212#131—21no—
213#131—21no—
214#131—861no—
215#131—861no—
216#131—861no—
217#131—861no—
218#131D17212yes—
219#131C22⋊D4312yes—
220C2×M16—21no—
221C2×M16—431no—
222C2×M16—431no—
223C2×M16—861no—
224C2×M16C4×D4311yescharacteristic
225C22×C8—21no—
226C22×C8—861no—
227C22×C8C22×D4311yescharacteristic
228#117—431no—
229M32—24no—
230M32—21no—
231M32—21no—
232M32—21no—
233M32—861no—
234M32—861no—
235M32C22⋊D4312yes—
236C2×C16—24no—
237C2×C16—21no—
238C2×C16—861no—
239C2×C16—861no—
240C2×C16—861no—
241C2×C16—861no—
242C2×C16C22⋊D4312yes—
243#108—862no—
244#104—862no—
245#104—862no—
246#97—861no—
247C4×C8—861no—
248#41—21no—
249#41—21no—
250#41—861no—
251#41—861no—
252#41—861no—
253#41—861no—
254#41C8×D4312yes—
255#41(C2×D43)⋊C412yes—
256C2×Q8—431no—
257C2×Q8#1062187211yescharacteristic
258C2×D4—21no—
259C2×D4—431no—
260C2×D4—861no—
261C2×D4#1062187211yescharacteristic
262C22×C4—21no—
263C22×C4—861no—
264C22×C4C2×C4×D4311yescharacteristic
265Q16—862no—
266SD16—862no—
267SD16—862no—
268D8—862no—
269M16—21no—
270M16—22no—
271M16—22no—
272M16—432no—
273M16—861no—
274M16—861no—
275M16—861no—
276M16—1721no—
277M16—1721no—
278M16(C2×D43)⋊C412yes—
279C2×C8—21no—
280C2×C8—22no—
281C2×C8—22no—
282C2×C8—861no—
283C2×C8—861no—
284C2×C8—1721no—
285C2×C8—1721no—
286C2×C8C2×D17211yescharacteristic
287C2×C8#1062189811yescharacteristic
288C2×C8#1062189811yescharacteristic
289C2×C8C2×C22⋊D4311yescharacteristic
290C2×C8C2×C22⋊D4311yescharacteristic
291C2×C8C2×C22⋊D4311yescharacteristic
292C4⋊C4—861no—
293C22⋊C4—861no—
294C42—861no—
295C16—22no—
296C16—22no—
297C16—1721no—
298C16—1721no—
299C23—21no—
300C23—861no—
301C23#1306333111yescharacteristic
302Q8—21no—
303Q8—861no—
304Q8—861no—
305Q8(C2×D43)⋊C812yes—
306D4—22no—
307D4—22no—
308D4—21no—
309D4—861no—
310D4—861no—
311D4—1721no—
312D4—1721no—
313D4(C2×D43)⋊C812yes—
314C2×C4—21no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—861no—
318C2×C4—1721no—
319C2×C4—1721no—
320C2×C4—1721no—
321C2×C4C2×(C2×D43)⋊C411yescharacteristic
322C2×C4C4×C22⋊D4311yescharacteristic
323C2×C4C4×C22⋊D4311yescharacteristic
324C2×C4C2×C8×D4311yescharacteristic
325C2×C4C2×#1062187211yescharacteristic
326C2×C4#1306333111yescharacteristic
327C8—22no—
328C8—862no—
329C8—1721no—
330C8#1306329411yescharacteristic
331C8#1306329911yescharacteristic
332C8#1306329911yescharacteristic
333C8#1306330811yescharacteristic
334C22—22no—
335C22—41no—
336C22—81no—
337C22—1722no—
338C22—1721no—
339C22#1458286511yescharacteristic
340C22C8×C22⋊D4311yescharacteristic
341C22#1458297011yescharacteristic
342C4—22no—
343C4—3441no—
344C4—1721no—
345C4#1458277811yescharacteristic
346C4C2×(C2×D43)⋊C811yescharacteristic
347C4C8×C22⋊D4311yescharacteristic
348C4#1458297011yescharacteristic
349C2—21no—
350C2—21no—
351C2—21no—
352C2—42no—
353C2—3441no—
354C2#1913488711yescharacteristic
subgroupG/H
centerC8#13063294
commutatorC2×C4×C43C22×C8
FrattiniC22×C8C22×D43
FittingC43×#3407C2
socleC2×C43#1869
prime radical#14583697C4
cosocleC22×C8×C43C23
hypercenter#3407D43
hypocenterC43#12979
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C8 ◁ C22×C8 ◁ #3407

Complements

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

NH ≅ G/Ntype
2. #19136224C2semidirect
3. C2×#14582683C2semidirect
4. #19136210C2semidirect
5. #19132685C2semidirect
6. #19132680C2semidirect
7. C43×#3407C2semidirect
172. #3407D43semidirect
204. C43#12979semidirect

Maximal subgroups

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

subgroupindex
#191434962
#191362242
C2×#145826832
#191362102
#191326852
#191326802
C43×#34072
#1297943