Finite Group Databasebeta

← #25013738

Subgroups — #25013738

Order 11008.

466 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#19147729C211yesmaximal, characteristic
2#19136344C211yesmaximal, characteristic, complemented
3#19136322C211yesmaximal, characteristic, complemented
4#19135488C211yesmaximal, characteristic, complemented
5#19132706C211yesmaximal, characteristic, complemented
6#19132679C211yesmaximal, characteristic, complemented
7C2×C43×#444C211yesmaximal, characteristic, complemented
8C2×#13063347C2211yescharacteristic
9#14583340—21no—
10#14583339C412yescomplemented
11#14583335—21no—
12#14583334C412yescomplemented
13#14583329—22no—
14C2×#13063265C2211yescharacteristic
15C2×#13063265C2211yescharacteristic
16C2×#13063261C2211yescharacteristic
17C2×#13063253—21no—
18#14582865—21no—
19#14582715—21no—
20#14582712—21no—
21#14582705—22no—
22C2×#135×C43C2211yescharacteristic
23C2×#131×C43—21no—
24C43×#444—22no—
25C43×#444—22no—
26C2×#108×C43C2211yescharacteristic
27C2×#104×C43—21no—
28C2×#97×C43C2211yescharacteristic
29C2×#10621898—21no—
30#13063347—21no—
31#13063347—21no—
32#13063347—21no—
33#13063347—21no—
34C2×Dic172C2×C411yescharacteristic
35C2×#10621873—21no—
36C2×D344C2×C411yescharacteristic
37C2×#10621877—21no—
38#13063271—22no—
39#13063269—22no—
40#13063268—22no—
41#13063266—22no—
42#13063265—21no—
43#13063265—21no—
44#13063265—21no—
45#13063265C2×C412yes—
46C2×C43⋊C16—21no—
47C2×C43⋊C16—21no—
48#13063261—21no—
49#13063261—21no—
50#13063253—42no—
51(C2×D43)⋊C8—42no—
52C2×#41×C43—21no—
53#135×C43—21no—
54#135×C43—21no—
55#135×C43C2×C412yes—
56#135×C43D412yes—
57C2×Q16×C43D411yescharacteristic
58C2×SD16×C43—21no—
59C2×D8×C43D411yescharacteristic
60#131×C43—24no—
61#131×C43—42no—
62C2×M16×C43—21no—
63C2×M16×C43—41no—
64C22×C8×C43—41no—
65C22×C8×C43D411yescharacteristic
66C22×C8×C43C2311yescharacteristic
67C2×C42×C43D411yescharacteristic
68#108×C43—21no—
69#108×C43D412yes—
70#104×C43—24no—
71#97×C43—21no—
72#97×C43—21no—
73#41×C43—22no—
74#41×C43—22no—
75#41×C43—41no—
76#41×C43—41no—
77C2×Q8×C43—21no—
78C2×D4×C43—21no—
79C2×D4×C43—41no—
80C22×C4×C43—21no—
81C22×C4×C43—41no—
82C22×C4×C43C2×D411yescharacteristic
83C2×C22⋊D43—41no—
84#10621898—41no—
85#10621898—41no—
86#10621898—41no—
87#10621898—41no—
88C2×D172—21no—
89C2×C4×D43—41no—
90C2×Dic86—21no—
91Q16×C43—21no—
92Q16×C43C22⋊C412yes—
93SD16×C43—22no—
94SD16×C43—22no—
95D8×C43—21no—
96D8×C43C22⋊C412yes—
97M16×C43—22no—
98M16×C43—44no—
99M16×C43—41no—
100C2×C8×C43—21no—
101C2×C8×C43—21no—
102C2×C8×C43—44no—
103C2×C8×C43—41no—
104C2×C8×C43D812yes—
105C2×C8×C43C22×C411yescharacteristic
106C2×C8×C43C2×D411yescharacteristic
107C2×C8×C43C2×D411yescharacteristic
108C2×C8×C43C2×D411yescharacteristic
109C2×C8×C43#4111yescharacteristic
110C2×C8×C43#4111yescharacteristic
111C42×C43—21no—
112C42×C43—21no—
113#10621877—41no—
114#10621877—41no—
115C2×C43⋊C8—41no—
116Dic172—21no—
117Dic172—21no—
118D344—21no—
119D344—21no—
120#10621873—41no—
121#10621873—41no—
122C43⋊C16—22no—
123C43⋊C16—41no—
124C23×C43—41no—
125C23×C43#13511yescharacteristic
126C22×D43—41no—
127Q8×C43—22no—
128Q8×C43—41no—
129D4×C43—22no—
130D4×C43—42no—
131D4×C43—42no—
132D4×C43—41no—
133C2×C4×C43—41no—
134C2×C4×C43—42no—
135C2×C4×C43—42no—
136C2×C4×C43—41no—
137C2×C4×C43—81no—
138C2×C4×C43C4×D411yescharacteristic
139C2×C4×C43#12011yescharacteristic
140C2×C4×C43#12111yescharacteristic
141C2×C4×C43C2×D811yescharacteristic
142C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
143C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
144C22⋊D43—81no—
145C22⋊D43—81no—
146C2×Dic43—41no—
147D172—41no—
148D172—41no—
149C4×D43—81no—
150C4×D43—81no—
151Dic86—41no—
152Dic86—41no—
153C8×C43—22no—
154C8×C43—42no—
155C8×C43C2×C22⋊C411yescharacteristic
156C8×C43C4×D411yescharacteristic
157C8×C43#12111yescharacteristic
158C8×C43#12311yescharacteristic
159C43⋊C8—81no—
160#13024—431nomaximal, Sylow
161C22×C43—41no—
162C22×C43—42no—
163C22×C43—82no—
164C22×C43C4×D811yescharacteristic
165C22×C43#44911yescharacteristic
166C22×C43#46311yescharacteristic
167C2×D43—82no—
168C2×D43—81no—
169C4×C43—42no—
170C4×C43—81no—
171C4×C43#38611yescharacteristic
172C4×C43#44211yescharacteristic
173C4×C43#44711yescharacteristic
174C4×C43#45911yescharacteristic
175Dic43—81no—
176#3414—431no—
177C2×#444D4311yescharacteristic, complemented
178#2148—431no—
179#2143—431no—
180#1975—431no—
181#1388—431no—
182#1377—431no—
183C2×C43—21no—
184C2×C43—21no—
185C2×C43—21no—
186C2×C43—82no—
187C2×C43#187911yescharacteristic
188D43—161no—
189C2×#135—431no—
190C2×#135C2×D4311yescharacteristic
191C2×#131—21no—
192#510—432no—
193#510—861no—
194#509—432no—
195#509—861no—
196#508—862no—
197C2×M32—431no—
198C2×M32—431no—
199#444—22no—
200#444—22no—
201C2×#108—431no—
202C2×#108C2×D4311yescharacteristic
203C2×#104—21no—
204C2×#104—861no—
205#408—861no—
206C2×#97C2×D4311yescharacteristic
207#362—861no—
208#361—861no—
209#359—862no—
210C43#1302411yescharacteristic, complemented, Sylow
211C2×#41—21no—
212C2×#41—861no—
213#135—21no—
214#135—21no—
215#135—861no—
216#135—861no—
217#135—861no—
218#135—861no—
219#135C4×D4312yes—
220#135C22⋊D4312yes—
221C2×Q16—431no—
222C2×Q16D17211yescharacteristic
223C2×SD16—21no—
224C2×SD16—861no—
225C2×D8—431no—
226C2×D8D17211yescharacteristic
227#131—24no—
228#131—42no—
229C2×M16—21no—
230C2×M16—41no—
231C2×M16—861no—
232C22×C8—41no—
233C22×C8C22⋊D4311yescharacteristic
234C22×C8C22×D4311yescharacteristic
235C2×C42C22⋊D4311yescharacteristic
236Q32—862no—
237SD32—862no—
238SD32—862no—
239D16—862no—
240M32—432no—
241M32—861no—
242M32—861no—
243M32—861no—
244C2×C16—861no—
245C2×C16—861no—
246#108—21no—
247#108—861no—
248#108—861no—
249#108C22⋊D4312yes—
250#104—24no—
251#104—1722no—
252C22⋊C8—1722no—
253#97—21no—
254#97—21no—
255#41—22no—
256#41—22no—
257#41—41no—
258#41—41no—
259#41—1721no—
260#41—1721no—
261#41—1721no—
262#41—1721no—
263C2×Q8—21no—
264C2×Q8—861no—
265C2×D4—21no—
266C2×D4—41no—
267C2×D4—861no—
268C2×D4—1721no—
269C22×C4—21no—
270C22×C4—41no—
271C22×C4—1721no—
272C22×C4C2×C22⋊D4311yescharacteristic
273Q16—21no—
274Q16—861no—
275Q16—861no—
276Q16(C2×D43)⋊C412yes—
277SD16—22no—
278SD16—22no—
279SD16—1721no—
280SD16—1721no—
281D8—21no—
282D8—861no—
283D8—861no—
284D8(C2×D43)⋊C412yes—
285M16—22no—
286M16—44no—
287M16—41no—
288M16—1721no—
289M16—1721no—
290C2×C8—21no—
291C2×C8—21no—
292C2×C8—44no—
293C2×C8—41no—
294C2×C8—1721no—
295C2×C8#1062188212yes—
296C2×C8C2×C4×D4311yescharacteristic
297C2×C8C2×D17211yescharacteristic
298C2×C8#1062189811yescharacteristic
299C2×C8#1062189811yescharacteristic
300C2×C8C2×C22⋊D4311yescharacteristic
301C2×C8C2×C22⋊D4311yescharacteristic
302C42—21no—
303C42—21no—
304C16—862no—
305C16—1721no—
306C23—41no—
307C23—1721no—
308C23#1306334511yescharacteristic
309Q8—22no—
310Q8—41no—
311Q8—1721no—
312Q8—1721no—
313D4—22no—
314D4—42no—
315D4—42no—
316D4—41no—
317D4—3441no—
318D4—3441no—
319D4—1721no—
320D4—1721no—
321C2×C4—41no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—41no—
325C2×C4—81no—
326C2×C4—3441no—
327C2×C4—3441no—
328C2×C4—1721no—
329C2×C4C4×C22⋊D4311yescharacteristic
330C2×C4#1306329411yescharacteristic
331C2×C4#1306329911yescharacteristic
332C2×C4C2×#1062188211yescharacteristic
333C2×C4#1306335011yescharacteristic
334C2×C4#1306335111yescharacteristic
335C8—22no—
336C8—42no—
337C8—3441no—
338C8C2×(C2×D43)⋊C411yescharacteristic
339C8C4×C22⋊D4311yescharacteristic
340C8#1306329911yescharacteristic
341C8#1306330811yescharacteristic
342C22—41no—
343C22—42no—
344C22—82no—
345C22—3442no—
346C22—3441no—
347C22C4×#1062188211yescharacteristic
348C22#1458304411yescharacteristic
349C22#1458311411yescharacteristic
350C4—42no—
351C4—81no—
352C4—3441no—
353C4#1458277811yescharacteristic
354C4#1458300911yescharacteristic
355C4#1458303311yescharacteristic
356C4#1458309411yescharacteristic
357C2—21no—
358C2—21no—
359C2—21no—
360C2—82no—
361C2—6881no—
362C2#1913494311yescharacteristic
subgroupG/H
centerC4#14583033
commutatorC2×C8×C43C22×C4
FrattiniC22×C8C22×D43
FittingC2×C43×#444C2
socleC2×C43#1879
prime radical#19147729C2
cosocleC22×C8×C43C23
hypercenterC2×#444D43
hypocenterC43#13024
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×#97 ◁ C2×#444

Complements

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

NH ≅ G/Ntype
2. #19136344C2semidirect
3. #19136322C2semidirect
4. #19135488C2semidirect
5. #19132706C2semidirect
6. #19132679C2semidirect
7. C2×C43×#444C2semidirect
10. #14583339C4semidirect
12. #14583334C4semidirect
177. C2×#444D43semidirect
210. C43#13024semidirect

Maximal subgroups

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

subgroupindex
#191477292
#191363442
#191363222
#191354882
#191327062
#191326792
C2×C43×#4442
#1302443