Finite Group Databasebeta

← #24991834

Subgroups — #24991834

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#19143339C211yesmaximal, characteristic
2#19135540C211yesmaximal, characteristic, complemented
3#19133090C211yesmaximal, characteristic
4#19132998C211yesmaximal, characteristic, complemented
5#19132435C211yesmaximal, characteristic, complemented
6#19132432C211yesmaximal, characteristic, complemented
7C43×#3167C211yesmaximal, characteristic
8C2×#13063332—21no—
9#14582977—21no—
10#14582971—22no—
11D4×C43⋊C8—21no—
12#14582952C2211yescharacteristic
13C2×C4⋊(C43⋊C8)C2211yescharacteristic
14#14582866—21no—
15C4×#10621877C2211yescharacteristic
16C4×C4⋊Dic43C2211yescharacteristic
17#14582658—21no—
18#14582658—21no—
19#14582633—22no—
20Q8⋊(C43⋊C8)—21no—
21Q8⋊(C43⋊C8)—21no—
22C43×#533C2211yescharacteristic
23C43×#532C2211yescharacteristic
24C43×#498C411yescharacteristic, complemented
25C43×#492C411yescharacteristic, complemented
26C43×#487C411yescharacteristic, complemented
27C43×#486C411yescharacteristic, complemented
28C43×#465—22no—
29C4×SD16×C43—22no—
30C2×C4×C8×C43C2211yescharacteristic
31#13063332—42no—
32#13063332—42no—
33C2×#10621877—22no—
34C2×#10621877D411yescharacteristic
35C2×#10621877D411yescharacteristic
36C22×C43⋊C8—22no—
37C22×C43⋊C8—21no—
38C2×C4⋊Dic43—21no—
39C2×C4×Dic43—21no—
40C4⋊(C43⋊C8)—21no—
41C4⋊(C43⋊C8)—21no—
42C4⋊(C43⋊C8)D411yescharacteristic
43C4⋊(C43⋊C8)D411yescharacteristic
44C22⋊(C43⋊C8)—22no—
45C22⋊(C43⋊C8)—22no—
46C22⋊(C43⋊C8)—21no—
47#13063236—21no—
48C4×C43⋊C8—21no—
49C4×C43⋊C8—21no—
50C43⋊#95—21no—
51C2×#41×C43—21no—
52C2×SD16×C43—22no—
53C22×C8×C43—21no—
54C4⋊Q8×C43C2×C411yescharacteristic
55C4⋊Q8×C43C2×C411yescharacteristic
56C4⋊Q8×C43C2×C411yescharacteristic
57#127×C43C2×C411yescharacteristic
58#125×C43—21no—
59#124×C43—21no—
60C22⋊Q8×C43—21no—
61C22⋊Q8×C43—21no—
62#121×C43—21no—
63#121×C43D412yes—
64C4×Q8×C43—21no—
65C4×Q8×C43—21no—
66C4×D4×C43—21no—
67C4×D4×C43D412yes—
68#117×C43—21no—
69C2×C42×C43C2311yescharacteristic
70#106×C43—22no—
71#103×C43—22no—
72#102×C43—22no—
73C4×C8×C43—21no—
74C4×C8×C43C2×C411yescharacteristic
75C4×C8×C43C2×C411yescharacteristic
76#41×C43—41no—
77#41×C43—41no—
78#41×C43—41no—
79#41×C43—41no—
80C2×Q8×C43—21no—
81C2×Q8×C43—21no—
82C2×Q8×C43—21no—
83C2×D4×C43—21no—
84C2×D4×C43—21no—
85C2×D4×C43—22no—
86C2×D4×C43C22⋊C412yes—
87C22×C4×C43—22no—
88C22×C4×C43C2×D411yescharacteristic
89C22×C4×C43C2×D411yescharacteristic
90C22×C4×C43#4111yescharacteristic
91C22×Dic43—41no—
92SD16×C43—44no—
93C2×C8×C43—21no—
94C2×C8×C43—21no—
95C2×C8×C43—42no—
96C4⋊C4×C43—21no—
97C4⋊C4×C43—21no—
98C4⋊C4×C43—21no—
99C4⋊C4×C43—21no—
100C4⋊C4×C43—21no—
101C4⋊C4×C43—41no—
102C4⋊C4×C43—41no—
103C4⋊C4×C43C22⋊C412yes—
104C22⋊C4×C43—22no—
105C22⋊C4×C43—22no—
106C22⋊C4×C43—41no—
107C42×C43—41no—
108C42×C43C22×C411yescharacteristic
109C42×C43C2×D411yescharacteristic
110C42×C43C2×D411yescharacteristic
111C42×C43#4111yescharacteristic
112C4⋊Dic43—22no—
113C4⋊Dic43—41no—
114C4×Dic43—41no—
115C4×Dic43—41no—
116#10621877—21no—
117#10621877—21no—
118#10621877—21no—
119#10621877—44no—
120#10621877SD1612yescomplemented
121C2×C43⋊C8—21no—
122C2×C43⋊C8—21no—
123C2×C43⋊C8—21no—
124C2×C43⋊C8—21no—
125C2×C43⋊C8—44no—
126C2×C43⋊C8—41no—
127C2×C43⋊C8—41no—
128C2×C43⋊C8—41no—
129C23×C43—22no—
130C23×C43#12111yescharacteristic
131Q8×C43—42no—
132Q8×C43—41no—
133Q8×C43—41no—
134Q8×C43—41no—
135Q8×C43—41no—
136D4×C43—42no—
137D4×C43—42no—
138D4×C43—42no—
139D4×C43—41no—
140D4×C43—41no—
141D4×C43—41no—
142D4×C43—41no—
143C2×C4×C43—21no—
144C2×C4×C43—21no—
145C2×C4×C43—22no—
146C2×C4×C43—41no—
147C2×C4×C43—42no—
148C2×C4×C43—42no—
149C2×C4×C43—41no—
150C2×C4×C43—41no—
151C2×C4×C43C2×C22⋊C411yescharacteristic
152C2×C4×C43C4×D411yescharacteristic
153C2×C4×C43C4×D411yescharacteristic
154C2×C4×C43#12011yescharacteristic
155C2×C4×C43#12111yescharacteristic
156C2×C4×C43#12311yescharacteristic
157C2×C4×C43C2×SD1611yescharacteristic
158C2×C4×C43#13511yescharacteristic
159C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
160C2×C4×C43#13711yescharacteristic
161C2×Dic43—42no—
162C2×Dic43—81no—
163C2×Dic43—81no—
164C8×C43—22no—
165C8×C43—41no—
166C43⋊C8—22no—
167C43⋊C8—41no—
168C43⋊C8—41no—
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×C43—81no—
185C4×C43—81no—
186C4×C43C4×SD1611yescharacteristic
187C4×C43#44011yescharacteristic
188C4×C43#44311yescharacteristic
189C4×C43#44411yescharacteristic
190C4×C43#45011yescharacteristic
191C4×C43#45211yescharacteristic
192Dic43—82no—
193#3167D4311yescharacteristic
194#2935—431no—
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—861no—
207#533C2×D4311yescharacteristic
208#532C2×D4311yescharacteristic
209#498Dic4311yescharacteristic, complemented
210#492Dic4311yescharacteristic, complemented
211#487Dic4311yescharacteristic, complemented
212#486Dic4311yescharacteristic, complemented
213#465—22no—
214C4×SD16—22no—
215#436—861no—
216#435—862no—
217C8×D4—861no—
218#431—431no—
219C2×C4⋊C8—431no—
220#408—861no—
221C4×M16—431no—
222C2×C4×C8C2×D4311yescharacteristic
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—22no—
232#131—1722no—
233#131—1722no—
234C2×M16—431no—
235C2×M16—431no—
236C2×M16—862no—
237C22×C8—21no—
238C22×C8—862no—
239C22×C8—861no—
240C4⋊Q8C2×Dic4311yescharacteristic
241C4⋊Q8C2×Dic4311yescharacteristic
242C4⋊Q8C2×Dic4311yescharacteristic
243#127C2×Dic4311yescharacteristic
244#125—21no—
245#124—21no—
246C22⋊Q8—21no—
247C22⋊Q8—21no—
248#121—21no—
249#121C22⋊D4312yes—
250C4×Q8—21no—
251C4×Q8—21no—
252C4×D4—21no—
253C4×D4C22⋊D4312yes—
254#117—21no—
255C2×C4⋊C4—861no—
256C2×C42—861no—
257C2×C42C22×D4311yescharacteristic
258#106—22no—
259C4⋊C8—431no—
260C4⋊C8—431no—
261C4⋊C8—861no—
262C4⋊C8—861no—
263#103—22no—
264#102—22no—
265C22⋊C8—862no—
266C22⋊C8—862no—
267C22⋊C8—861no—
268#97—861no—
269C4×C8—21no—
270C4×C8—861no—
271C4×C8—861no—
272C4×C8C2×Dic4311yescharacteristic
273C4×C8C2×Dic4311yescharacteristic
274#95—861no—
275#41—41no—
276#41—41no—
277#41—41no—
278#41—41no—
279C2×Q8—21no—
280C2×Q8—21no—
281C2×Q8—21no—
282C2×D4—22no—
283C2×D4—21no—
284C2×D4—21no—
285C2×D4C22⋊Dic4312yes—
286C22×C4—22no—
287C22×C4—1721no—
288C22×C4D4×D4311yescharacteristic
289C22×C4#1062190011yescharacteristic
290C22×C4C2×C22⋊D4311yescharacteristic
291SD16—44no—
292M16—432no—
293M16—861no—
294M16—861no—
295M16—861no—
296M16—1724no—
297C2×C8—21no—
298C2×C8—21no—
299C2×C8—42no—
300C2×C8—861no—
301C2×C8—861no—
302C2×C8—861no—
303C2×C8—861no—
304C2×C8—1724no—
305C2×C8—1721no—
306C2×C8—1721no—
307C2×C8—1721no—
308C4⋊C4—21no—
309C4⋊C4—21no—
310C4⋊C4—21no—
311C4⋊C4—21no—
312C4⋊C4—21no—
313C4⋊C4—41no—
314C4⋊C4—41no—
315C4⋊C4—862no—
316C4⋊C4—1721no—
317C4⋊C4C22⋊Dic4312yes—
318C22⋊C4—22no—
319C22⋊C4—22no—
320C22⋊C4—41no—
321C42—41no—
322C42—1721no—
323C42—1721no—
324C42D4×D4311yescharacteristic
325C42#1062190011yescharacteristic
326C42C22×Dic4311yescharacteristic
327C42C2×C22⋊D4311yescharacteristic
328C23—22no—
329C23#1306329711yescharacteristic
330Q8—42no—
331Q8—41no—
332Q8—41no—
333Q8—41no—
334Q8—41no—
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—41no—
349C2×C4—41no—
350C2×C4—3441no—
351C2×C4—3441no—
352C2×C4—1722no—
353C2×C4C2×C22⋊Dic4311yescharacteristic
354C2×C4D4×Dic4311yescharacteristic
355C2×C4D4×Dic4311yescharacteristic
356C2×C4#1306329311yescharacteristic
357C2×C4#1306329711yescharacteristic
358C2×C4#1306330611yescharacteristic
359C2×C4SD16×D4311yescharacteristic
360C2×C4#1306334611yescharacteristic
361C2×C4#1306335211yescharacteristic
362C2×C4#1306335411yescharacteristic
363C8—22no—
364C8—41no—
365C8—862no—
366C8—3441no—
367C8—1721no—
368C8—1721no—
369C8—1721no—
370C22—21no—
371C22—21no—
372C22—42no—
373C22—42no—
374C22—42no—
375C22#1458277911yescharacteristic
376C22#1458310211yescharacteristic
377C22#1458311611yescharacteristic
378C4—21no—
379C4—21no—
380C4—21no—
381C4—42no—
382C4—81no—
383C4—81no—
384C4—3442no—
385C4SD16×Dic4311yescharacteristic
386C4#1458300011yescharacteristic
387C4#1458301611yescharacteristic
388C4#1458302111yescharacteristic
389C4#1458304811yescharacteristic
390C4#1458305811yescharacteristic
391C2—21no—
392C2—21no—
393C2—82no—
394C2#1913492411yescharacteristic
395C2#1913493111yescharacteristic
396C2#1913497911yescharacteristic
subgroupG/H
centerC2×C4#13063293
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#3167C2
socleC22×C43#386
prime radicalC43×#532C22
cosocleC2×C42×C43C23
hypercenter#3167D43
hypocenterC43#9055
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3167

Complements

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

NH ≅ G/Ntype
2. #19135540C2semidirect
4. #19132998C2semidirect
5. #19132435C2semidirect
6. #19132432C2semidirect
24. C43×#498C4semidirect
25. C43×#492C4semidirect
26. C43×#487C4semidirect
27. C43×#486C4semidirect
120. #10621877SD16semidirect
209. #498Dic43semidirect
210. #492Dic43semidirect
211. #487Dic43semidirect
212. #486Dic43semidirect
229. C43#9055semidirect

Maximal subgroups

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

subgroupindex
#191433392
#191355402
#191330902
#191329982
#191324352
#191324322
C43×#31672
#905543