Finite Group Databasebeta

← #24991832

Subgroups — #24991832

Order 11008.

500 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145150C211yesmaximal, characteristic
2#19135539C211yesmaximal, characteristic, complemented
3#19133090C211yesmaximal, characteristic
4#19132997C211yesmaximal, characteristic, complemented
5#19132434C211yesmaximal, characteristic, complemented
6#19132433C211yesmaximal, characteristic, complemented
7C43×#2935C211yesmaximal, characteristic
8#14583456C2211yescharacteristic
9#14583295C411yescharacteristic, complemented
10#14583271C411yescharacteristic, complemented
11#14583251C411yescharacteristic, complemented
12#14583245C411yescharacteristic, complemented
13#14583126—22no—
14C4×#10621883—22no—
15#14582952C2211yescharacteristic
16C2×C4×C43⋊C8C2211yescharacteristic
17C4×C4⋊Dic43C2211yescharacteristic
18#14582660—21no—
19#14582660—21no—
20#14582633—22no—
21#14582629—21no—
22#14582629—21no—
23C2×#131×C43—21no—
24C43×#532C2211yescharacteristic
25C43×#436—21no—
26C43×#435—22no—
27C8×D4×C43—21no—
28C2×C4⋊C8×C43C2211yescharacteristic
29C43×#408—21no—
30C4×M16×C43C2211yescharacteristic
31C2×#10621883—22no—
32C22×C43⋊C8—21no—
33#13063325C2×C411yescharacteristic
34#13063325C2×C411yescharacteristic
35#13063317—21no—
36#13063304—21no—
37#13063304—21no—
38C4×Dic86—21no—
39C4×Dic86—21no—
40#13063284—21no—
41C2×C4⋊Dic43—21no—
42C2×C4×Dic43—21no—
43#13063256—22no—
44C4⋊(C43⋊C8)—21no—
45#13063248—22no—
46#13063246—22no—
47C22⋊(C43⋊C8)—21no—
48C4×C43⋊C8—21no—
49C4×C43⋊C8—21no—
50C4×C43⋊C8C2×C411yescharacteristic
51C4×C43⋊C8C2×C411yescharacteristic
52C43⋊#95—21no—
53C2×#41×C43—21no—
54#131×C43—42no—
55#131×C43—42no—
56C2×M16×C43—22no—
57C2×M16×C43D411yescharacteristic
58C2×M16×C43D411yescharacteristic
59C22×C8×C43—22no—
60C22×C8×C43—21no—
61C4⋊Q8×C43C2×C411yescharacteristic
62#127×C43C2×C411yescharacteristic
63#124×C43—21no—
64#121×C43—21no—
65#121×C43D412yes—
66C4×D4×C43—21no—
67C4×D4×C43D412yes—
68C2×C42×C43C2311yescharacteristic
69C4⋊C8×C43—21no—
70C4⋊C8×C43D411yescharacteristic
71C4⋊C8×C43D411yescharacteristic
72C22⋊C8×C43—22no—
73C22⋊C8×C43—22no—
74#97×C43—21no—
75C4×C8×C43—21no—
76#41×C43—41no—
77#41×C43—41no—
78#41×C43—41no—
79#41×C43—41no—
80C2×Q8×C43—21no—
81C2×D4×C43—21no—
82C2×D4×C43—21no—
83C2×D4×C43—22no—
84C2×D4×C43C22⋊C412yes—
85C22×C4×C43—22no—
86C22×C4×C43C2×D411yescharacteristic
87C22×C4×C43C2×D411yescharacteristic
88C22×C4×C43#4111yescharacteristic
89C22×Dic43—41no—
90C2×Dic86—21no—
91C2×Dic86—21no—
92M16×C43—21no—
93M16×C43—21no—
94M16×C43—21no—
95M16×C43—44no—
96M16×C43SD1612yescomplemented
97C2×C8×C43—21no—
98C2×C8×C43—21no—
99C2×C8×C43—21no—
100C2×C8×C43—21no—
101C2×C8×C43—44no—
102C2×C8×C43—41no—
103C2×C8×C43—41no—
104C4⋊C4×C43—21no—
105C4⋊C4×C43C22⋊C412yes—
106C22⋊C4×C43—22no—
107C22⋊C4×C43—22no—
108C42×C43C22×C411yescharacteristic
109C42×C43C2×D411yescharacteristic
110C42×C43C2×D411yescharacteristic
111C42×C43#4111yescharacteristic
112C22⋊Dic43—41no—
113#10621883—44no—
114C4⋊Dic43—22no—
115C4⋊Dic43—21no—
116C4⋊Dic43—21no—
117C4⋊Dic43—21no—
118C4⋊Dic43—21no—
119C4⋊Dic43—41no—
120Dic43⋊C4—41no—
121Dic43⋊C4—41no—
122C4×Dic43—41no—
123C4×Dic43—41no—
124C4×Dic43—41no—
125C2×C43⋊C8—21no—
126C2×C43⋊C8—21no—
127C2×C43⋊C8—42no—
128C2×C43⋊C8—41no—
129C23×C43—22no—
130C23×C43#12111yescharacteristic
131Q8×C43—41no—
132Q8×C43—41no—
133D4×C43—42no—
134D4×C43—42no—
135D4×C43—42no—
136D4×C43—41no—
137D4×C43—41no—
138D4×C43—41no—
139D4×C43—41no—
140C2×C4×C43—21no—
141C2×C4×C43—21no—
142C2×C4×C43—22no—
143C2×C4×C43—41no—
144C2×C4×C43—42no—
145C2×C4×C43—42no—
146C2×C4×C43C2×C22⋊C411yescharacteristic
147C2×C4×C43C4×D411yescharacteristic
148C2×C4×C43C4×D411yescharacteristic
149C2×C4×C43#12011yescharacteristic
150C2×C4×C43#12111yescharacteristic
151C2×C4×C43#12311yescharacteristic
152C2×C4×C43C2×SD1611yescharacteristic
153C2×C4×C43#13511yescharacteristic
154C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
155C2×C4×C43#13711yescharacteristic
156C2×Dic43—42no—
157C2×Dic43—41no—
158C2×Dic43—41no—
159C2×Dic43—81no—
160C2×Dic43—81no—
161Dic86—42no—
162Dic86—41no—
163Dic86—41no—
164C8×C43—22no—
165C8×C43—41no—
166C8×C43—41no—
167C8×C43—41no—
168C43⋊C8—22no—
169C43⋊C8—41no—
170C43⋊C8—81no—
171#9055—431nomaximal, Sylow
172C22×C43—21no—
173C22×C43—21no—
174C22×C43—42no—
175C22×C43—42no—
176C22×C43—42no—
177C22×C43#38611yescharacteristic
178C22×C43#46111yescharacteristic
179C22×C43#46311yescharacteristic
180C4×C43—21no—
181C4×C43—21no—
182C4×C43—21no—
183C4×C43—42no—
184C4×C43C4×SD1611yescharacteristic
185C4×C43#44011yescharacteristic
186C4×C43#44311yescharacteristic
187C4×C43#44411yescharacteristic
188C4×C43#45011yescharacteristic
189C4×C43#45211yescharacteristic
190Dic43—82no—
191Dic43—81no—
192Dic43—81no—
193#3167—431no—
194#2935D4311yescharacteristic
195#1986—431no—
196#1502—431no—
197#1481—431no—
198#1279—431no—
199#1278—431no—
200C2×C43—21no—
201C2×C43—21no—
202C2×C43—82no—
203C2×C43#187611yescharacteristic
204C2×C43#187711yescharacteristic
205C2×C43#188411yescharacteristic
206C2×#131—21no—
207#533—431no—
208#532C2×D4311yescharacteristic
209#498—431no—
210#492—431no—
211#487—431no—
212#486—431no—
213#465—862no—
214C4×SD16—862no—
215#436—21no—
216#435—22no—
217C8×D4—21no—
218#431—431no—
219C2×C4⋊C8C2×D4311yescharacteristic
220#408—21no—
221C4×M16C2×D4311yescharacteristic
222C2×C4×C8—431no—
223C4×C4⋊C4—431no—
224#339—861no—
225#339—861no—
226#327—862no—
227Q8⋊C8—861no—
228Q8⋊C8—861no—
229C43#905511yescharacteristic, complemented, Sylow
230C2×#41—21no—
231C2×SD16—862no—
232#131—42no—
233#131—42no—
234C2×M16—22no—
235C2×M16C22⋊D4311yescharacteristic
236C2×M16C22⋊D4311yescharacteristic
237C22×C8—22no—
238C22×C8—21no—
239C22×C8—861no—
240C4⋊Q8—431no—
241C4⋊Q8—431no—
242C4⋊Q8C4×D4311yescharacteristic
243#127C4×D4311yescharacteristic
244#125—861no—
245#124—21no—
246C22⋊Q8—861no—
247C22⋊Q8—861no—
248#121—21no—
249#121D17212yes—
250C4×Q8—861no—
251C4×Q8—861no—
252C4×D4—21no—
253C4×D4C22⋊D4312yes—
254#117—861no—
255C2×C4⋊C4—861no—
256C2×C42—861no—
257C2×C42C22×D4311yescharacteristic
258#106—862no—
259C4⋊C8—21no—
260C4⋊C8—861no—
261C4⋊C8C22⋊D4311yescharacteristic
262C4⋊C8C22⋊D4311yescharacteristic
263#103—862no—
264#102—862no—
265C22⋊C8—22no—
266C22⋊C8—22no—
267C22⋊C8—861no—
268#97—21no—
269C4×C8—21no—
270C4×C8—431no—
271C4×C8—431no—
272C4×C8—861no—
273C4×C8—861no—
274#95—861no—
275#41—41no—
276#41—41no—
277#41—41no—
278#41—41no—
279C2×Q8—21no—
280C2×Q8—861no—
281C2×Q8—861no—
282C2×D4—22no—
283C2×D4—21no—
284C2×D4—21no—
285C2×D4(C2×D43)⋊C412yes—
286C22×C4—22no—
287C22×C4—1721no—
288C22×C4C2×D17211yescharacteristic
289C22×C4#1062189811yescharacteristic
290C22×C4C2×C22⋊D4311yescharacteristic
291SD16—1724no—
292M16—21no—
293M16—21no—
294M16—21no—
295M16—44no—
296M16#1062188312yescomplemented
297C2×C8—21no—
298C2×C8—21no—
299C2×C8—21no—
300C2×C8—21no—
301C2×C8—44no—
302C2×C8—41no—
303C2×C8—41no—
304C2×C8—861no—
305C2×C8—861no—
306C2×C8—1722no—
307C2×C8—1721no—
308C4⋊C4—21no—
309C4⋊C4—862no—
310C4⋊C4—861no—
311C4⋊C4—861no—
312C4⋊C4—861no—
313C4⋊C4—861no—
314C4⋊C4—1721no—
315C4⋊C4—1721no—
316C4⋊C4—1721no—
317C4⋊C4(C2×D43)⋊C412yes—
318C22⋊C4—22no—
319C22⋊C4—22no—
320C22⋊C4—1721no—
321C42—1721no—
322C42—1721no—
323C42—1721no—
324C42C2×C4×D4311yescharacteristic
325C42#1062189811yescharacteristic
326C42C2×C22⋊D4311yescharacteristic
327C42C2×C22⋊D4311yescharacteristic
328C23—22no—
329C23#1306329911yescharacteristic
330Q8—41no—
331Q8—41no—
332Q8—1722no—
333Q8—1721no—
334Q8—1721no—
335D4—42no—
336D4—42no—
337D4—42no—
338D4—41no—
339D4—41no—
340D4—41no—
341D4—41no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—22no—
345C2×C4—41no—
346C2×C4—42no—
347C2×C4—42no—
348C2×C4—3441no—
349C2×C4—3441no—
350C2×C4—1722no—
351C2×C4—1721no—
352C2×C4—1721no—
353C2×C4C2×(C2×D43)⋊C411yescharacteristic
354C2×C4C4×C22⋊D4311yescharacteristic
355C2×C4C4×C22⋊D4311yescharacteristic
356C2×C4#1306329411yescharacteristic
357C2×C4#1306329911yescharacteristic
358C2×C4#1306330811yescharacteristic
359C2×C4C2×#1062188311yescharacteristic
360C2×C4#1306334511yescharacteristic
361C2×C4#1306335111yescharacteristic
362C2×C4#1306335511yescharacteristic
363C8—22no—
364C8—41no—
365C8—41no—
366C8—41no—
367C8—862no—
368C8—3441no—
369C8—1721no—
370C22—21no—
371C22—21no—
372C22—42no—
373C22—42no—
374C22—42no—
375C22#1458277811yescharacteristic
376C22#1458310411yescharacteristic
377C22#1458311411yescharacteristic
378C4—21no—
379C4—21no—
380C4—21no—
381C4—42no—
382C4—3442no—
383C4—3441no—
384C4—3441no—
385C4C4×#1062188311yescharacteristic
386C4#1458299911yescharacteristic
387C4#1458301411yescharacteristic
388C4#1458301911yescharacteristic
389C4#1458305011yescharacteristic
390C4#1458306111yescharacteristic
391C2—21no—
392C2—21no—
393C2—82no—
394C2#1913492211yescharacteristic
395C2#1913492911yescharacteristic
396C2#1913497811yescharacteristic
subgroupG/H
centerC2×C4#13063294
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#2935C2
socleC22×C43#386
prime radicalC43×#532C22
cosocleC2×C42×C43C23
hypercenter#2935D43
hypocenterC43#9055
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2935

Complements

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

NH ≅ G/Ntype
2. #19135539C2semidirect
4. #19132997C2semidirect
5. #19132434C2semidirect
6. #19132433C2semidirect
9. #14583295C4semidirect
10. #14583271C4semidirect
11. #14583251C4semidirect
12. #14583245C4semidirect
96. M16×C43SD16semidirect
229. C43#9055semidirect
296. M16#10621883semidirect

Maximal subgroups

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

subgroupindex
#191451502
#191355392
#191330902
#191329972
#191324342
#191324332
C43×#29352
#905543