Finite Group Databasebeta

← #25013650

Subgroups — #25013650

Order 11008.

476 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583329C211yesmaximal, characteristic
2C2×#14583017C211yesmaximal, characteristic, complemented
3C2×#14582706C211yesmaximal, characteristic, complemented
4C2×#14582705C211yesmaximal, characteristic, complemented
5#19132688C211yesmaximal, characteristic, complemented
6#19132673C211yesmaximal, characteristic, complemented
7C43×#1974C211yesmaximal, characteristic, complemented
8C2×#13063347C2211yescharacteristic
9C2×#13063331—21no—
10#14583329—22no—
11#14583329—22no—
12C2×#13063271C411yescharacteristic, complemented
13C2×#13063269C411yescharacteristic, complemented
14C2×#13063268C411yescharacteristic, complemented
15C2×#13063266C411yescharacteristic, complemented
16C22×C43⋊C16C2211yescharacteristic
17C22×C43⋊C16C2211yescharacteristic
18#14583017—22no—
19#14583017—22no—
20C2×#13063261C2211yescharacteristic
21C2×#13063253—21no—
22#14582706—22no—
23#14582705—22no—
24C2×#135×C43C2211yescharacteristic
25C2×#108×C43C2211yescharacteristic
26C2×#104×C43—21no—
27C43×#408—21no—
28C2×C4×C8×C43C2211yescharacteristic
29C2×#10621898—21no—
30#13063347—21no—
31#13063347—21no—
32#13063347D412yes—
33#13063347D412yes—
34C2×Dic172C2×C411yescharacteristic
35C2×#10621873—21no—
36C2×D344C2×C411yescharacteristic
37#13063331—24no—
38#13063331—42no—
39C2×#10621877—21no—
40C2×#10621872—41no—
41C2×C8×D43—41no—
42#13063271—22no—
43#13063269—22no—
44#13063268—22no—
45#13063266—22no—
46C2×C43⋊C16—21no—
47C2×C43⋊C16—21no—
48C2×C43⋊C16—21no—
49C2×C43⋊C16—21no—
50C2×C43⋊C16—21no—
51C2×C43⋊C16C2×C411yescharacteristic
52C2×C43⋊C16C2×C411yescharacteristic
53#13063261—21no—
54#13063261D412yes—
55#13063253—24no—
56C2×#41×C43—21no—
57#135×C43—21no—
58#135×C43—21no—
59#135×C43—21no—
60#135×C43—21no—
61C2×Q16×C43C2×C411yescharacteristic
62C2×SD16×C43—21no—
63C2×D8×C43C2×C411yescharacteristic
64C2×M16×C43—21no—
65C22×C8×C43D411yescharacteristic
66C22×C8×C43C2311yescharacteristic
67C2×C42×C43D411yescharacteristic
68#108×C43—21no—
69#108×C43—21no—
70#104×C43—42no—
71C22⋊C8×C43—41no—
72C22⋊C8×C43—41no—
73C4×C8×C43—21no—
74C4×C8×C43—21no—
75#41×C43—41no—
76#41×C43—41no—
77#41×C43—41no—
78#41×C43—41no—
79C2×Q8×C43—21no—
80C2×D4×C43—21no—
81C2×D4×C43—41no—
82C22×C4×C43—21no—
83C22×C4×C43—41no—
84C22×C4×C43C2×D411yescharacteristic
85C2×C22⋊D43—41no—
86#10621898—22no—
87#10621898—22no—
88#10621898—41no—
89#10621898—41no—
90C2×D172—21no—
91C2×C4×D43—41no—
92C2×Dic86—21no—
93Q16×C43—21no—
94Q16×C43—21no—
95SD16×C43—41no—
96SD16×C43—41no—
97D8×C43—21no—
98D8×C43—21no—
99M16×C43—41no—
100M16×C43—41no—
101C2×C8×C43—21no—
102C2×C8×C43—21no—
103C2×C8×C43—41no—
104C2×C8×C43D811yescharacteristic
105C2×C8×C43D811yescharacteristic
106C2×C8×C43C22×C411yescharacteristic
107C2×C8×C43C2×D411yescharacteristic
108C2×C8×C43C2×D411yescharacteristic
109C2×C8×C43C2×D411yescharacteristic
110C2×C8×C43#4111yescharacteristic
111C2×C8×C43#4111yescharacteristic
112C42×C43—21no—
113C42×C43—21no—
114#10621877—22no—
115#10621877—41no—
116C2×C43⋊C8—41no—
117Dic172—21no—
118Dic172C22⋊C412yes—
119D344—21no—
120D344C22⋊C412yes—
121#10621873—22no—
122#10621873—22no—
123#10621872—44no—
124C8×D43—44no—
125C43⋊C16—21no—
126C43⋊C16—21no—
127C43⋊C16—41no—
128C23×C43—41no—
129C23×C43#13511yescharacteristic
130C22×D43—41no—
131Q8×C43—41no—
132Q8×C43—41no—
133D4×C43—41no—
134D4×C43—41no—
135D4×C43—81no—
136D4×C43—81no—
137C2×C4×C43—22no—
138C2×C4×C43—41no—
139C2×C4×C43—41no—
140C2×C4×C43—41no—
141C2×C4×C43—81no—
142C2×C4×C43—81no—
143C2×C4×C43C4×D411yescharacteristic
144C2×C4×C43#12011yescharacteristic
145C2×C4×C43#12111yescharacteristic
146C2×C4×C43C2×D811yescharacteristic
147C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
148C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
149C22⋊D43—42no—
150C22⋊D43—42no—
151C2×Dic43—41no—
152D172—22no—
153D172—41no—
154C4×D43—42no—
155C4×D43—42no—
156Dic86—22no—
157Dic86—41no—
158C8×C43—21no—
159C8×C43—21no—
160C8×C43—81no—
161C8×C43C2×C22⋊C411yescharacteristic
162C8×C43C4×D411yescharacteristic
163C8×C43#12111yescharacteristic
164C8×C43#12311yescharacteristic
165C43⋊C8—42no—
166#13011—431nomaximal, Sylow
167C22×C43—21no—
168C22×C43—21no—
169C22×C43—81no—
170C22×C43—81no—
171C22×C43—81no—
172C22×C43C4×D811yescharacteristic
173C22×C43#44911yescharacteristic
174C22×C43#46311yescharacteristic
175C2×D43—42no—
176C2×D43—81no—
177C2×D43—81no—
178C4×C43—42no—
179C4×C43—81no—
180C4×C43#38611yescharacteristic
181C4×C43#44211yescharacteristic
182C4×C43#44711yescharacteristic
183C4×C43#45911yescharacteristic
184Dic43—42no—
185C2×#508—431no—
186C2×#443—431no—
187C2×#359—431no—
188C2×#359—431no—
189#1974D4311yescharacteristic, complemented
190#1381—431no—
191#1374—431no—
192C2×C43—21no—
193C2×C43—21no—
194C2×C43—161no—
195C2×C43#187911yescharacteristic
196C2×C43#217811yescharacteristic
197C2×C43#217911yescharacteristic
198D43—82no—
199C2×#135—431no—
200C2×#135C2×D4311yescharacteristic
201C2×#131—861no—
202#508—862no—
203#508—862no—
204C2×Q32—431no—
205C2×SD32—431no—
206C2×SD32—431no—
207C2×D16—431no—
208C22×C16—431no—
209C22×C16—431no—
210#443—862no—
211#443—862no—
212C2×#108—431no—
213C2×#108C2×D4311yescharacteristic
214C2×#104—21no—
215C2×#104—861no—
216#408—21no—
217C2×C4×C8C2×D4311yescharacteristic
218#359—862no—
219#359—862no—
220C43#1301111yescharacteristic, complemented, Sylow
221C2×#41—21no—
222C2×#41—861no—
223#135—21no—
224#135—21no—
225#135—21no—
226#135—21no—
227#135—432no—
228#135—432no—
229#135—861no—
230#135—861no—
231C2×Q16—431no—
232C2×Q16C4×D4311yescharacteristic
233C2×SD16—21no—
234C2×SD16—861no—
235C2×D8—431no—
236C2×D8C4×D4311yescharacteristic
237#131—864no—
238#131—1722no—
239C2×M16—21no—
240C2×M16—861no—
241C2×M16—1721no—
242C22×C8—1721no—
243C22×C8C22⋊D4311yescharacteristic
244C22×C8C22×D4311yescharacteristic
245C2×C42C22⋊D4311yescharacteristic
246Q32—862no—
247SD32—862no—
248SD32—862no—
249D16—862no—
250C2×C16—431no—
251C2×C16—431no—
252C2×C16—861no—
253C2×C16—861no—
254C2×C16—861no—
255C2×C16—861no—
256C2×C16—861no—
257#108—21no—
258#108—21no—
259#108—432no—
260#108—861no—
261#104—42no—
262#104—864no—
263C22⋊C8—41no—
264C22⋊C8—41no—
265C4×C8—21no—
266C4×C8—21no—
267#41—41no—
268#41—41no—
269#41—41no—
270#41—41no—
271#41—862no—
272#41—862no—
273#41—1721no—
274#41—1721no—
275C2×Q8—21no—
276C2×Q8—861no—
277C2×D4—21no—
278C2×D4—41no—
279C2×D4—861no—
280C2×D4—1721no—
281C22×C4—21no—
282C22×C4—41no—
283C22×C4—1721no—
284C22×C4C2×C22⋊D4311yescharacteristic
285Q16—21no—
286Q16—21no—
287Q16—432no—
288Q16—861no—
289SD16—41no—
290SD16—41no—
291SD16—862no—
292SD16—862no—
293D8—21no—
294D8—21no—
295D8—432no—
296D8—861no—
297M16—41no—
298M16—41no—
299M16—862no—
300M16—1724no—
301M16—1721no—
302C2×C8—21no—
303C2×C8—21no—
304C2×C8—41no—
305C2×C8—1724no—
306C2×C8—1721no—
307C2×C8#1062188211yescharacteristic
308C2×C8#1062188211yescharacteristic
309C2×C8C2×C4×D4311yescharacteristic
310C2×C8#1062189811yescharacteristic
311C2×C8D4×D4311yescharacteristic
312C2×C8D4×D4311yescharacteristic
313C2×C8D4×D4311yescharacteristic
314C2×C8#1062190011yescharacteristic
315C42—21no—
316C42—21no—
317C16—861no—
318C16—861no—
319C16—1721no—
320C23—41no—
321C23—1721no—
322C23#1306334511yescharacteristic
323Q8—41no—
324Q8—41no—
325Q8—862no—
326Q8—1721no—
327D4—41no—
328D4—41no—
329D4—81no—
330D4—81no—
331D4—862no—
332D4—1722no—
333D4—1722no—
334D4—1721no—
335C2×C4—22no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—81no—
340C2×C4—81no—
341C2×C4—1721no—
342C2×C4—1722no—
343C2×C4—1722no—
344C2×C4C4×C22⋊D4311yescharacteristic
345C2×C4#1306329311yescharacteristic
346C2×C4#1306329611yescharacteristic
347C2×C4C2×#1062188211yescharacteristic
348C2×C4#1306335011yescharacteristic
349C2×C4#1306335111yescharacteristic
350C8—21no—
351C8—21no—
352C8—81no—
353C8—1722no—
354C8C22⋊C4×D4311yescharacteristic
355C8(C22⋊D43)⋊C411yescharacteristic
356C8#1306329811yescharacteristic
357C8#1306330711yescharacteristic
358C22—21no—
359C22—21no—
360C22—81no—
361C22—81no—
362C22—81no—
363C22—3441no—
364C22—3441no—
365C22—1722no—
366C22C4×#1062188211yescharacteristic
367C22#1458304211yescharacteristic
368C22#1458311111yescharacteristic
369C4—42no—
370C4—81no—
371C4—1722no—
372C4#1458277511yescharacteristic
373C4#1458300911yescharacteristic
374C4#1458303211yescharacteristic
375C4#1458309111yescharacteristic
376C2—21no—
377C2—21no—
378C2—161no—
379C2—3442no—
380C2#1913494611yescharacteristic
381C2#1913647411yescharacteristic
382C2#1913647911yescharacteristic
subgroupG/H
centerC2×C4C2×#10621882
commutatorC2×C8×C43C22×C4
FrattiniC22×C8C22×D43
FittingC43×#1974C2
socleC22×C43C4×D8
prime radicalC2×#14583329C2
cosocleC22×C8×C43C23
hypercenter#1974D43
hypocenterC43#13011
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C2×C4×C8 ◁ #1974

Complements

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

NH ≅ G/Ntype
2. C2×#14583017C2semidirect
3. C2×#14582706C2semidirect
4. C2×#14582705C2semidirect
5. #19132688C2semidirect
6. #19132673C2semidirect
7. C43×#1974C2semidirect
12. C2×#13063271C4semidirect
13. C2×#13063269C4semidirect
14. C2×#13063268C4semidirect
15. C2×#13063266C4semidirect
189. #1974D43semidirect
220. C43#13011semidirect

Maximal subgroups

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

subgroupindex
C2×#145833292
C2×#145830172
C2×#145827062
C2×#145827052
#191326882
#191326732
C43×#19742
#1301143