Finite Group Databasebeta

← #25013850

Subgroups — #25013850

Order 11008.

508 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×#14583334C211yesmaximal, characteristic
2C2×#14582711C211yesmaximal, characteristic, complemented
3C2×#14582709C211yesmaximal, characteristic, complemented
4#19135471C211yesmaximal, characteristic, complemented
5#19132695C211yesmaximal, characteristic, complemented
6#19132675C211yesmaximal, characteristic, complemented
7C2×C43×#444C211yesmaximal, characteristic, complemented
8C22×D344C2211yescharacteristic
9#14583334—22no—
10#14583334—22no—
11C2×#13063268C412yescomplemented
12C2×#13063266C412yescomplemented
13C2×#13063265C2211yescharacteristic
14C2×#13063265C2211yescharacteristic
15C2×#13063257C2211yescharacteristic
16C2×#13063247—21no—
17#14582801—21no—
18#14582711—22no—
19#14582709—22no—
20C2×#135×C43C2211yescharacteristic
21C2×#131×C43—21no—
22C43×#444—22no—
23C43×#444—22no—
24C2×#108×C43C2211yescharacteristic
25C2×#104×C43—21no—
26C2×#97×C43C2211yescharacteristic
27C22×D172—21no—
28C2×D344—21no—
29C2×D344—21no—
30C2×D344—21no—
31C2×D344—21no—
32C2×D344—21no—
33C2×D344C2×C412yes—
34C2×C4⋊Dic43—21no—
35C2×(C2×D43)⋊C4—42no—
36#13063268—24no—
37#13063266—24no—
38#13063265—21no—
39#13063265—21no—
40#13063265—21no—
41#13063265—21no—
42C2×C43⋊C16—21no—
43C2×C43⋊C16C2×C412yes—
44#13063257—21no—
45#13063257—21no—
46#13063247—42no—
47C2×#41×C43—21no—
48#135×C43—21no—
49#135×C43—21no—
50#135×C43D412yes—
51#135×C43D412yes—
52C2×Q16×C43C2×C411yescharacteristic
53C2×SD16×C43—21no—
54C2×D8×C43C2×C411yescharacteristic
55#131×C43—24no—
56#131×C43—42no—
57C2×M16×C43—21no—
58C2×M16×C43—41no—
59C22×C8×C43—41no—
60C22×C8×C43D411yescharacteristic
61C22×C8×C43C2311yescharacteristic
62C2×C42×C43D411yescharacteristic
63#108×C43—21no—
64#108×C43D412yes—
65#104×C43—24no—
66#97×C43—21no—
67#97×C43—21no—
68C23×D43—41no—
69#41×C43—22no—
70#41×C43—22no—
71#41×C43—41no—
72#41×C43—41no—
73C2×Q8×C43—21no—
74C2×D4×C43—21no—
75C2×D4×C43—41no—
76C22×C4×C43—21no—
77C22×C4×C43—41no—
78C22×C4×C43C2×D411yescharacteristic
79C22×Dic43—41no—
80C2×D172—22no—
81C2×D172—41no—
82C2×D172—41no—
83C2×D172—41no—
84C2×D172—41no—
85C2×D172—41no—
86Q16×C43—21no—
87Q16×C43C22⋊C412yescomplemented
88SD16×C43—22no—
89SD16×C43—22no—
90D8×C43—21no—
91D8×C43C22⋊C412yescomplemented
92M16×C43—22no—
93M16×C43—44no—
94M16×C43—41no—
95C2×C8×C43—21no—
96C2×C8×C43—21no—
97C2×C8×C43—44no—
98C2×C8×C43—41no—
99C2×C8×C43D812yes—
100C2×C8×C43C22×C411yescharacteristic
101C2×C8×C43C2×D411yescharacteristic
102C2×C8×C43C2×D411yescharacteristic
103C2×C8×C43C2×D411yescharacteristic
104C2×C8×C43#4111yescharacteristic
105C2×C8×C43#4111yescharacteristic
106C42×C43—21no—
107C42×C43—21no—
108(C2×D43)⋊C4—84no—
109C4⋊Dic43—41no—
110C4⋊Dic43—41no—
111D344—22no—
112D344—22no—
113D344—41no—
114D344—41no—
115C43⋊C16—22no—
116C43⋊C16—41no—
117C23×C43—41no—
118C23×C43AGL(1,ℤ/8)11yescharacteristic
119C22×D43—42no—
120C22×D43—82no—
121C22×D43—82no—
122C22×D43—81no—
123C22×D43—81no—
124Q8×C43—22no—
125Q8×C43—41no—
126D4×C43—22no—
127D4×C43—42no—
128D4×C43—42no—
129D4×C43—41no—
130C2×C4×C43—41no—
131C2×C4×C43—42no—
132C2×C4×C43—42no—
133C2×C4×C43—42no—
134C2×C4×C43—41no—
135C2×C4×C43C4×D411yescharacteristic
136C2×C4×C43#12011yescharacteristic
137C2×C4×C43#12111yescharacteristic
138C2×C4×C43C2×D811yescharacteristic
139C2×C4×C43#13511yescharacteristic
140C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
141C2×Dic43—82no—
142C2×Dic43—81no—
143D172—42no—
144D172—42no—
145D172—81no—
146D172—81no—
147C8×C43—22no—
148C8×C43—42no—
149C8×C43C2×C22⋊C411yescharacteristic
150C8×C43C4×D411yescharacteristic
151C8×C43#12111yescharacteristic
152C8×C43#12311yescharacteristic
153#13040—431nomaximal, Sylow
154C22×C43—22no—
155C22×C43—42no—
156C22×C43—82no—
157C22×C43#44211yescharacteristic
158C22×C43#44911yescharacteristic
159C22×C43#45911yescharacteristic
160C2×D43—82no—
161C2×D43—84no—
162C2×D43—161no—
163C2×D43—161no—
164C2×D43—162no—
165C4×C43—42no—
166C4×C43—81no—
167C4×C43#38611yescharacteristic
168C4×C43C4×D811yescharacteristic
169C4×C43#44711yescharacteristic
170C4×C43#46311yescharacteristic
171Dic43—161no—
172C2×#509—431no—
173C2×#444D4311yescharacteristic, complemented
174C2×#361—431no—
175C2×#360—431no—
176#1972—431no—
177#1383—431no—
178#1375—431no—
179C2×C43—21no—
180C2×C43—21no—
181C2×C43—82no—
182C2×C43#187911yescharacteristic
183C2×C43AGL(1,ℤ/16)12yes—
184D43—162no—
185C2×#135C2×D4311yescharacteristic
186C22×D8—431no—
187C2×#131—21no—
188#509—862no—
189#509—862no—
190C2×SD32—432no—
191C2×D16—432no—
192C2×M32—431no—
193C2×M32—431no—
194#444—22no—
195#444—22no—
196C2×#108C2×D4311yescharacteristic
197C2×#106—431no—
198C2×#104—21no—
199C2×#102—861no—
200C2×#97C2×D4311yescharacteristic
201#390—861no—
202#361—862no—
203#360—862no—
204C43#1304011yescharacteristic, complemented, Sylow
205C2×#41—21no—
206C22×D4—861no—
207#135—21no—
208#135—21no—
209#135D17212yes—
210#135C22⋊D4312yes—
211C2×Q16C4×D4311yescharacteristic
212C2×SD16—21no—
213C2×D8—432no—
214C2×D8—861no—
215C2×D8—861no—
216C2×D8—861no—
217C2×D8—861no—
218C2×D8—861no—
219C2×D8C4×D4311yescharacteristic
220#131—24no—
221#131—42no—
222C2×M16—21no—
223C2×M16—41no—
224C22×C8—41no—
225C22×C8C22⋊D4311yescharacteristic
226C22×C8C22×D4311yescharacteristic
227C2×C4⋊C4—861no—
228C2×C22⋊C4—1722no—
229C2×C42C22⋊D4311yescharacteristic
230SD32—864no—
231D16—864no—
232M32—861no—
233M32—861no—
234M32—861no—
235M32—861no—
236C2×C16—432no—
237C2×C16—861no—
238#108—21no—
239#108C22⋊D4312yes—
240#106—861no—
241#106—861no—
242#104—24no—
243#102—1722no—
244#97—21no—
245#97—21no—
246C24—1721no—
247#41—22no—
248#41—22no—
249#41—41no—
250#41—41no—
251C2×Q8—21no—
252C2×D4—21no—
253C2×D4—41no—
254C2×D4—862no—
255C2×D4—1721no—
256C2×D4—1721no—
257C2×D4—1721no—
258C2×D4—1721no—
259C2×D4—1721no—
260C22×C4—21no—
261C22×C4—41no—
262C22×C4—1721no—
263C22×C4C2×C22⋊D4311yescharacteristic
264Q16—21no—
265Q16(C2×D43)⋊C412yescomplemented
266SD16—22no—
267SD16—22no—
268D8—21no—
269D8—862no—
270D8—862no—
271D8—1721no—
272D8—1721no—
273D8(C2×D43)⋊C412yescomplemented
274M16—22no—
275M16—44no—
276M16—41no—
277C2×C8—21no—
278C2×C8—21no—
279C2×C8—44no—
280C2×C8—41no—
281C2×C8#1062188212yes—
282C2×C8C2×C4×D4311yescharacteristic
283C2×C8C2×D17211yescharacteristic
284C2×C8#1062189811yescharacteristic
285C2×C8#1062189811yescharacteristic
286C2×C8C2×C22⋊D4311yescharacteristic
287C2×C8C2×C22⋊D4311yescharacteristic
288C4⋊C4—1721no—
289C4⋊C4—1721no—
290C22⋊C4—3444no—
291C42—21no—
292C42—21no—
293C16—862no—
294C16—1721no—
295C23—41no—
296C23—3442no—
297C23—3442no—
298C23—3441no—
299C23—3441no—
300C23—1722no—
301C23#1306335011yescharacteristic
302Q8—22no—
303Q8—41no—
304D4—22no—
305D4—42no—
306D4—42no—
307D4—41no—
308D4—3441no—
309D4—3441no—
310D4—1722no—
311D4—1722no—
312C2×C4—41no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—41no—
317C2×C4—3442no—
318C2×C4—3441no—
319C2×C4C4×C22⋊D4311yescharacteristic
320C2×C4#1306329411yescharacteristic
321C2×C4#1306329911yescharacteristic
322C2×C4C2×#1062188211yescharacteristic
323C2×C4#1306334511yescharacteristic
324C2×C4#1306335111yescharacteristic
325C8—22no—
326C8—42no—
327C8C2×(C2×D43)⋊C411yescharacteristic
328C8C4×C22⋊D4311yescharacteristic
329C8#1306329911yescharacteristic
330C8#1306330811yescharacteristic
331C22—22no—
332C22—42no—
333C22—82no—
334C22—3442no—
335C22—3444no—
336C22—6882no—
337C22—6881no—
338C22—6881no—
339C22#1458300911yescharacteristic
340C22#1458304411yescharacteristic
341C22#1458309411yescharacteristic
342C4—42no—
343C4—81no—
344C4—6881no—
345C4#1458277811yescharacteristic
346C4C4×#1062188211yescharacteristic
347C4#1458303311yescharacteristic
348C4#1458311411yescharacteristic
349C2—21no—
350C2—21no—
351C2—82no—
352C2—6882no—
353C2#1913494311yescharacteristic
354C2#1913649312yes—
subgroupG/H
centerC22#14583009
commutatorC2×C8×C43C22×C4
FrattiniC22×C8C22×D43
FittingC2×C43×#444C2
socleC22×C43#442
prime radicalC2×#14583334C2
cosocleC22×C8×C43C23
hypercenterC2×#444D43
hypocenterC43#13040
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#97 ◁ C2×#444

Complements

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

NH ≅ G/Ntype
2. C2×#14582711C2semidirect
3. C2×#14582709C2semidirect
4. #19135471C2semidirect
5. #19132695C2semidirect
6. #19132675C2semidirect
7. C2×C43×#444C2semidirect
11. C2×#13063268C4semidirect
12. C2×#13063266C4semidirect
87. Q16×C43C22⋊C4semidirect
91. D8×C43C22⋊C4semidirect
173. C2×#444D43semidirect
204. C43#13040semidirect
265. Q16(C2×D43)⋊C4semidirect
273. D8(C2×D43)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×#145833342
C2×#145827112
C2×#145827092
#191354712
#191326952
#191326752
C2×C43×#4442
#1304043