Finite Group Databasebeta

← #25013470

Subgroups — #25013470

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#19147697C211yesmaximal, characteristic, complemented
2#19143496C211yesmaximal, characteristic
3C2×#14582684C211yesmaximal, characteristic, complemented
4#19136209C211yesmaximal, characteristic, complemented
5#19132685C211yesmaximal, characteristic, complemented
6#19132682C211yesmaximal, characteristic, complemented
7C43×#2117C211yesmaximal, characteristic, complemented
8#14583697C411yescharacteristic
9C2×#13063331C2211yescharacteristic
10#14583317—22no—
11#14583315—22no—
12C2×#13063265C2211yescharacteristic
13M32×D43—22no—
14C22×C43⋊C16C2211yescharacteristic
15#14583019—22no—
16#14583014—22no—
17#14582947C411yescharacteristic
18#14582916C411yescharacteristic
19#14582915C411yescharacteristic
20#14582854C2211yescharacteristic
21#14582684—22no—
22C22⋊(C43⋊C16)—22no—
23C2×#131×C43C2211yescharacteristic
24C2×M32×C43C2211yescharacteristic
25C2×M32×C43C2211yescharacteristic
26C43×#350—22no—
27C2×#10621898C2×C411yescharacteristic
28#13063356C812yes—
29#13063355—21no—
30#13063351C812yes—
31#13063350—21no—
32#13063345—22no—
33#13063331—21no—
34#13063331—21no—
35#13063331D412yes—
36#13063331D412yes—
37C2×#10621877C2×C411yescharacteristic
38C2×#10621877C2×C411yescharacteristic
39C2×#10621872—21no—
40C2×C8×D43—21no—
41#13063284C2×C411yescharacteristic
42#13063265—21no—
43#13063265—21no—
44#13063264—24no—
45C2×C43⋊C16—21no—
46C2×C43⋊C16—21no—
47C2×C43⋊C16—21no—
48C2×C43⋊C16D412yes—
49C16×D43—24no—
50#13063260—22no—
51#13063252—22no—
52#13063251—22no—
53#13063235—21no—
54C8×Dic43—21no—
55C2×#41×C43C2×C411yescharacteristic
56#131×C43—21no—
57#131×C43—21no—
58#131×C43—21no—
59#131×C43—21no—
60C2×M16×C43—21no—
61C2×M16×C43C2×C411yescharacteristic
62C22×C8×C43—21no—
63C22×C8×C43C2311yescharacteristic
64M32×C43—21no—
65M32×C43—21no—
66M32×C43—21no—
67M32×C43D412yes—
68C2×C16×C43—21no—
69C2×C16×C43—21no—
70#41×C43—21no—
71#41×C43—21no—
72#41×C43—21no—
73#41×C43—21no—
74C2×Q8×C43C2×C811yescharacteristic
75C2×D4×C43—21no—
76C2×D4×C43C2×C811yescharacteristic
77C22×C4×C43—21no—
78C22×C4×C43C22×C411yescharacteristic
79C2×C22⋊D43—21no—
80#10621898—21no—
81#10621898—21no—
82#10621898C22⋊C412yes—
83#10621898C2×C812yes—
84C2×D172M1611yescharacteristic
85C2×C4×D43—21no—
86C2×Dic86M1611yescharacteristic
87M16×C43—21no—
88M16×C43—21no—
89M16×C43—41no—
90M16×C43—41no—
91C2×C8×C43—21no—
92C2×C8×C43—41no—
93C2×C8×C43—41no—
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#10621877C22⋊C412yes—
110#10621877C2×C812yes—
111C2×C43⋊C8—21no—
112C2×C43⋊C8—21no—
113#10621872—22no—
114#10621872—22no—
115C8×D43—22no—
116C8×D43—22no—
117C16×C43—22no—
118C16×C43—41no—
119C43⋊C16—22no—
120C43⋊C16—41no—
121C23×C43—21no—
122C23×C43#13111yescharacteristic
123C22×D43—21no—
124Q8×C43—21no—
125Q8×C43—21no—
126D4×C43—21no—
127D4×C43—21no—
128D4×C43—41no—
129D4×C43—41no—
130C2×C4×C43—21no—
131C2×C4×C43—41no—
132C2×C4×C43—41no—
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—22no—
140C22⋊D43—22no—
141C2×Dic43—21no—
142C2×Dic43—41no—
143D172—21no—
144D172C22⋊C812yes—
145C4×D43—22no—
146C4×D43—22no—
147Dic86—21no—
148Dic86C22⋊C812yes—
149C8×C43—41no—
150C8×C43#12011yescharacteristic
151C8×C43#12111yescharacteristic
152C8×C43#12111yescharacteristic
153C8×C43#12311yescharacteristic
154C43⋊C8—22no—
155C43⋊C8—22no—
156#12979—431nomaximal, Sylow
157C22×C43—41no—
158C22×C43—42no—
159C22×C43—41no—
160C22×C43#40811yescharacteristic
161C22×C43C8×D411yescharacteristic
162C22×C43#43511yescharacteristic
163C2×D43—22no—
164C2×D43—81no—
165C4×C43—41no—
166C4×C43#38611yescharacteristic
167C4×C43C2×C22⋊C811yescharacteristic
168C4×C43C8×D411yescharacteristic
169C4×C43#43511yescharacteristic
170Dic43—22no—
171Dic43—81no—
172#3407—431no—
173#2955—431no—
174#2117D4311yescharacteristic, complemented
175C2×#350—431no—
176#2113—431no—
177#1379—431no—
178#1378—431no—
179C2×C43—21no—
180C2×C43—21no—
181C2×C43—21no—
182C2×C43—81no—
183C2×C43#186911yescharacteristic
184D43—42no—
185#575—431no—
186C2×#131—431no—
187C2×#131C2×D4311yescharacteristic
188#504—862no—
189#504—862no—
190C2×M32—431no—
191C2×M32—862no—
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—22no—
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—21no—
215#131—21no—
216#131—432no—
217#131—432no—
218#131—861no—
219#131—861no—
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—21no—
230M32—21no—
231M32—21no—
232M32—864no—
233M32—861no—
234M32—861no—
235M32C22⋊D4312yes—
236C2×C16—21no—
237C2×C16—21no—
238C2×C16—432no—
239C2×C16—864no—
240C2×C16—861no—
241C2×C16—861no—
242C2×C16—861no—
243#108—862no—
244#104—862no—
245#104—862no—
246#97—861no—
247C4×C8—861no—
248#41—21no—
249#41—21no—
250#41—21no—
251#41—21no—
252#41—432no—
253#41—432no—
254#41—861no—
255#41—861no—
256C2×Q8—431no—
257C2×Q8C8×D4311yescharacteristic
258C2×D4—21no—
259C2×D4—431no—
260C2×D4—861no—
261C2×D4C8×D4311yescharacteristic
262C22×C4—21no—
263C22×C4—861no—
264C22×C4C2×C4×D4311yescharacteristic
265Q16—862no—
266SD16—862no—
267SD16—862no—
268D8—862no—
269M16—21no—
270M16—21no—
271M16—41no—
272M16—41no—
273M16—432no—
274M16—432no—
275M16—861no—
276M16—861no—
277M16—862no—
278M16—862no—
279C2×C8—21no—
280C2×C8—41no—
281C2×C8—41no—
282C2×C8—861no—
283C2×C8—861no—
284C2×C8—862no—
285C2×C8—862no—
286C2×C8#1062189811yescharacteristic
287C2×C8D4×D4311yescharacteristic
288C2×C8D4×D4311yescharacteristic
289C2×C8D4×D4311yescharacteristic
290C2×C8#1062190011yescharacteristic
291C2×C8C2×C22⋊D4311yescharacteristic
292C4⋊C4—861no—
293C22⋊C4—861no—
294C42—861no—
295C16—22no—
296C16—41no—
297C16—862no—
298C16—1721no—
299C23—21no—
300C23—861no—
301C23#1306333311yescharacteristic
302Q8—21no—
303Q8—21no—
304Q8—432no—
305Q8—861no—
306D4—21no—
307D4—21no—
308D4—41no—
309D4—41no—
310D4—432no—
311D4—862no—
312D4—862no—
313D4—861no—
314C2×C4—21no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—861no—
318C2×C4—862no—
319C2×C4—862no—
320C2×C4—1721no—
321C2×C4C22⋊C4×D4311yescharacteristic
322C2×C4(C22⋊D43)⋊C411yescharacteristic
323C2×C4C4×C22⋊D4311yescharacteristic
324C2×C4C2×C8×D4311yescharacteristic
325C2×C4M16×D4311yescharacteristic
326C2×C4#1306333111yescharacteristic
327C8—41no—
328C8—862no—
329C8—862no—
330C8#1306329311yescharacteristic
331C8#1306329611yescharacteristic
332C8#1306329811yescharacteristic
333C8#1306330711yescharacteristic
334C22—41no—
335C22—42no—
336C22—41no—
337C22—862no—
338C22—3441no—
339C22#1458286411yescharacteristic
340C22(C22⋊D43)⋊C811yescharacteristic
341C22#1458296811yescharacteristic
342C4—41no—
343C4—862no—
344C4—3441no—
345C4#1458277511yescharacteristic
346C4C22⋊C8×D4311yescharacteristic
347C4C8×C22⋊D4311yescharacteristic
348C4#1458297311yescharacteristic
349C2—21no—
350C2—21no—
351C2—21no—
352C2—81no—
353C2—1722no—
354C2#1913488411yescharacteristic
subgroupG/H
centerC8#13063293
commutatorC2×C4×C43C22×C8
FrattiniC22×C8C22×D43
FittingC43×#2117C2
socleC2×C43#1869
prime radical#14583697C4
cosocleC22×C8×C43C23
hypercenter#2117D43
hypocenterC43#12979
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C8 ◁ C22×C8 ◁ #2117

Complements

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

NH ≅ G/Ntype
1. #19147697C2semidirect
3. C2×#14582684C2semidirect
4. #19136209C2semidirect
5. #19132685C2semidirect
6. #19132682C2semidirect
7. C43×#2117C2semidirect
174. #2117D43semidirect
204. C43#12979semidirect

Maximal subgroups

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

subgroupindex
#191476972
#191434962
C2×#145826842
#191362092
#191326852
#191326822
C43×#21172
#1297943