Finite Group Databasebeta

← #25013766

Subgroups — #25013766

Order 11008.

476 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
1C2×#14583339C211yesmaximal, characteristic
2C2×#14582714C211yesmaximal, characteristic, complemented
3#19136307C211yesmaximal, characteristic
4#19135456C211yesmaximal, characteristic, complemented
5#19132705C211yesmaximal, characteristic, complemented
6#19132677C211yesmaximal, characteristic, complemented
7C2×C43×#443C211yesmaximal, characteristic
8C22×Dic172C2211yescharacteristic
9#14583339—22no—
10#14583339C414yescomplemented
11C2×#13063271—21no—
12C2×#13063269—21no—
13C2×#13063265C2211yescharacteristic
14C2×#13063265C2211yescharacteristic
15C2×#13063259C2211yescharacteristic
16C2×#13063250—21no—
17#14582805—21no—
18#14582714—22no—
19#14582703—21no—
20#14582700—21no—
21C2×#135×C43C2211yescharacteristic
22C2×#131×C43—21no—
23C43×#443—22no—
24C43×#443—22no—
25C2×#108×C43C2211yescharacteristic
26C2×#104×C43—21no—
27C2×C4×C8×C43C2211yescharacteristic
28C22×Dic86—21no—
29C2×Dic172—21no—
30C2×Dic172—21no—
31C2×Dic172—21no—
32C2×Dic172—21no—
33C2×Dic172—21no—
34C2×Dic172C2×C412yes—
35C2×C4⋊Dic43—21no—
36#13063271—24no—
37#13063269—24no—
38#13063265—21no—
39#13063265—21no—
40#13063265—21no—
41#13063265C2×C412yes—
42C2×C43⋊C16—21no—
43C2×C43⋊C16—21no—
44#13063259—21no—
45#13063259—21no—
46#13063250—41no—
47#13063250—41no—
48C43⋊#95—42no—
49C2×#41×C43—21no—
50#135×C43—21no—
51#135×C43—21no—
52#135×C43C2×C412yes—
53#135×C43D412yes—
54C2×Q16×C43D411yescharacteristic
55C2×SD16×C43—21no—
56C2×D8×C43D411yescharacteristic
57#131×C43—24no—
58#131×C43—42no—
59C2×M16×C43—21no—
60C2×M16×C43—41no—
61C22×C8×C43—41no—
62C22×C8×C43D411yescharacteristic
63C22×C8×C43C2311yescharacteristic
64C2×C42×C43D411yescharacteristic
65#108×C43—21no—
66#108×C43D412yes—
67#104×C43—24no—
68C4×C8×C43—21no—
69C4×C8×C43—21no—
70#41×C43—22no—
71#41×C43—22no—
72#41×C43—41no—
73#41×C43—41no—
74C2×Q8×C43—21no—
75C2×D4×C43—21no—
76C2×D4×C43—41no—
77C22×C4×C43—21no—
78C22×C4×C43—41no—
79C22×C4×C43C2×D411yescharacteristic
80C22×Dic43—41no—
81C22×Dic43—41no—
82C2×Dic86—22no—
83C2×Dic86—41no—
84C2×Dic86—41no—
85C2×Dic86—41no—
86C2×Dic86—41no—
87C2×Dic86—41no—
88Q16×C43—21no—
89Q16×C43C22⋊C412yes—
90SD16×C43—22no—
91SD16×C43—22no—
92D8×C43—21no—
93D8×C43C22⋊C412yes—
94M16×C43—22no—
95M16×C43—44no—
96M16×C43—41no—
97C2×C8×C43—21no—
98C2×C8×C43—21no—
99C2×C8×C43—44no—
100C2×C8×C43—41no—
101C2×C8×C43D811yescharacteristic
102C2×C8×C43D811yescharacteristic
103C2×C8×C43C22×C411yescharacteristic
104C2×C8×C43C2×D411yescharacteristic
105C2×C8×C43C2×D411yescharacteristic
106C2×C8×C43C2×D411yescharacteristic
107C2×C8×C43#4111yescharacteristic
108C2×C8×C43#4111yescharacteristic
109C42×C43—21no—
110C42×C43—21no—
111C4⋊Dic43—41no—
112C4⋊Dic43—41no—
113Dic172—22no—
114Dic172—22no—
115Dic172—41no—
116Dic172—41no—
117C43⋊C16—22no—
118C43⋊C16—41no—
119C23×C43—41no—
120C23×C43AGL(1,ℤ/8)11yescharacteristic
121Q8×C43—22no—
122Q8×C43—41no—
123D4×C43—22no—
124D4×C43—42no—
125D4×C43—42no—
126D4×C43—41no—
127C2×C4×C43—22no—
128C2×C4×C43—41no—
129C2×C4×C43—41no—
130C2×C4×C43—41no—
131C2×C4×C43—42no—
132C2×C4×C43—42no—
133C2×C4×C43C4×D411yescharacteristic
134C2×C4×C43#12011yescharacteristic
135C2×C4×C43#12111yescharacteristic
136C2×C4×C43C2×D811yescharacteristic
137C2×C4×C43#13511yescharacteristic
138C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
139C2×Dic43—42no—
140C2×Dic43—81no—
141C2×Dic43—81no—
142C2×Dic43—82no—
143C2×Dic43—81no—
144Dic86—42no—
145Dic86—42no—
146Dic86—81no—
147Dic86—81no—
148C8×C43—21no—
149C8×C43—21no—
150C8×C43—42no—
151C8×C43C2×C22⋊C411yescharacteristic
152C8×C43C4×D411yescharacteristic
153C8×C43#12111yescharacteristic
154C8×C43#12311yescharacteristic
155#13028—431nomaximal, Sylow
156C22×C43—21no—
157C22×C43—21no—
158C22×C43—42no—
159C22×C43—81no—
160C22×C43—81no—
161C22×C43#44211yescharacteristic
162C22×C43#44911yescharacteristic
163C22×C43#45911yescharacteristic
164C4×C43—42no—
165C4×C43—42no—
166C4×C43#38611yescharacteristic
167C4×C43C4×D811yescharacteristic
168C4×C43#44711yescharacteristic
169C4×C43#46311yescharacteristic
170Dic43—82no—
171Dic43—161no—
172C2×#510—431no—
173C2×#443D4311yescharacteristic
174C2×#362—431no—
175#2139—431no—
176#1969—431no—
177#1387—431no—
178#1376—431no—
179C2×C43—21no—
180C2×C43—21no—
181C2×C43—82no—
182C2×C43#187911yescharacteristic
183C2×C43#221211yescharacteristic
184C2×C43#221411yescharacteristic
185C2×#135C2×D4311yescharacteristic
186C22×Q16—431no—
187C2×#131—21no—
188#510—434no—
189#510—862no—
190C2×Q32—861no—
191C2×SD32—861no—
192C2×M32—431no—
193C2×M32—431no—
194#443—22no—
195#443—22no—
196C2×#108C2×D4311yescharacteristic
197C2×#107—431no—
198C2×#104—21no—
199C2×#103—861no—
200C2×C4×C8C2×D4311yescharacteristic
201#391—861no—
202#362—862no—
203#358—861no—
204#357—861no—
205C43#1302811yescharacteristic, complemented, Sylow
206C2×#41—21no—
207C22×Q8—861no—
208#135—21no—
209#135—21no—
210#135C4×D4312yes—
211#135C22⋊D4312yes—
212C2×Q16—432no—
213C2×Q16—861no—
214C2×Q16—861no—
215C2×Q16—861no—
216C2×Q16—861no—
217C2×Q16—861no—
218C2×Q16D17211yescharacteristic
219C2×SD16—21no—
220C2×D8D17211yescharacteristic
221#131—24no—
222#131—42no—
223C2×M16—21no—
224C2×M16—41no—
225C22×C8—41no—
226C22×C8C22⋊D4311yescharacteristic
227C22×C8C22×D4311yescharacteristic
228C2×C4⋊C4—861no—
229C2×C42C22⋊D4311yescharacteristic
230Q32—864no—
231SD32—864no—
232M32—432no—
233M32—861no—
234M32—861no—
235M32—861no—
236C2×C16—861no—
237C2×C16—861no—
238#108—21no—
239#108C22⋊D4312yes—
240#107—861no—
241#107—861no—
242#104—24no—
243#103—1721no—
244#103—1721no—
245C4×C8—21no—
246C4×C8—21no—
247#95—1722no—
248#41—22no—
249#41—22no—
250#41—41no—
251#41—41no—
252C2×Q8—21no—
253C2×Q8—862no—
254C2×Q8—1721no—
255C2×Q8—1721no—
256C2×Q8—1721no—
257C2×Q8—1721no—
258C2×Q8—1721no—
259C2×D4—21no—
260C2×D4—41no—
261C22×C4—21no—
262C22×C4—41no—
263C22×C4—1721no—
264C22×C4—1721no—
265C22×C4C2×C22⋊D4311yescharacteristic
266Q16—21no—
267Q16—862no—
268Q16—862no—
269Q16—1721no—
270Q16—1721no—
271Q16(C2×D43)⋊C412yes—
272SD16—22no—
273SD16—22no—
274D8—21no—
275D8(C2×D43)⋊C412yes—
276M16—22no—
277M16—44no—
278M16—41no—
279C2×C8—21no—
280C2×C8—21no—
281C2×C8—44no—
282C2×C8—41no—
283C2×C8#1062188211yescharacteristic
284C2×C8#1062188211yescharacteristic
285C2×C8C2×C4×D4311yescharacteristic
286C2×C8C2×D17211yescharacteristic
287C2×C8#1062189811yescharacteristic
288C2×C8#1062189811yescharacteristic
289C2×C8C2×C22⋊D4311yescharacteristic
290C2×C8C2×C22⋊D4311yescharacteristic
291C4⋊C4—1721no—
292C4⋊C4—1721no—
293C42—21no—
294C42—21no—
295C16—862no—
296C16—1721no—
297C23—41no—
298C23#1306335011yescharacteristic
299Q8—22no—
300Q8—41no—
301Q8—3441no—
302Q8—3441no—
303Q8—1722no—
304Q8—1722no—
305D4—22no—
306D4—42no—
307D4—42no—
308D4—41no—
309C2×C4—22no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—3441no—
316C2×C4—3441no—
317C2×C4—3442no—
318C2×C4—3441no—
319C2×C4—1722no—
320C2×C4C4×C22⋊D4311yescharacteristic
321C2×C4#1306329411yescharacteristic
322C2×C4#1306329911yescharacteristic
323C2×C4C2×#1062188211yescharacteristic
324C2×C4#1306334511yescharacteristic
325C2×C4#1306335111yescharacteristic
326C8—21no—
327C8—21no—
328C8—42no—
329C8C2×(C2×D43)⋊C411yescharacteristic
330C8C4×C22⋊D4311yescharacteristic
331C8#1306329911yescharacteristic
332C8#1306330811yescharacteristic
333C22—21no—
334C22—21no—
335C22—42no—
336C22—81no—
337C22—81no—
338C22#1458300911yescharacteristic
339C22#1458304411yescharacteristic
340C22#1458309411yescharacteristic
341C4—42no—
342C4—42no—
343C4—3442no—
344C4—6881no—
345C4#1458277811yescharacteristic
346C4C4×#1062188211yescharacteristic
347C4#1458303311yescharacteristic
348C4#1458311411yescharacteristic
349C2—21no—
350C2—21no—
351C2—82no—
352C2#1913494311yescharacteristic
353C2#1913666411yescharacteristic
354C2#1913667611yescharacteristic
subgroupG/H
centerC22#14583094
commutatorC2×C8×C43C22×C4
FrattiniC22×C8C22×D43
FittingC2×C43×#443C2
socleC22×C43#459
prime radicalC2×#135×C43C22
cosocleC22×C8×C43C23
hypercenterC2×#443D43
hypocenterC43#13028
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×C8 ◁ C2×#443

Complements

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

NH ≅ G/Ntype
2. C2×#14582714C2semidirect
4. #19135456C2semidirect
5. #19132705C2semidirect
6. #19132677C2semidirect
10. #14583339C4semidirect
205. C43#13028semidirect

Maximal subgroups

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

subgroupindex
C2×#145833392
C2×#145827142
#191363072
#191354562
#191327052
#191326772
C2×C43×#4432
#1302843