Finite Group Databasebeta

← #24991827

Subgroups — #24991827

Order 11008.

470 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143544C211yesmaximal, characteristic, complemented
2#19135515C211yesmaximal, characteristic
3#19133094C211yesmaximal, characteristic, complemented
4#19132994C211yesmaximal, characteristic
5#19132435C211yesmaximal, characteristic, complemented
6#19132432C211yesmaximal, characteristic, complemented
7C43×#3167C211yesmaximal, characteristic
8#14583030—21no—
9#14583030—22no—
10Q8×C43⋊C8—21no—
11#14582952C2211yescharacteristic
12#14582926—21no—
13C2×C4⋊(C43⋊C8)C2211yescharacteristic
14C2×#13063252—21no—
15C2×#13063252—21no—
16#14582855—21no—
17C4×#10621877C2211yescharacteristic
18C4×C4⋊Dic43C2211yescharacteristic
19#14582636—22no—
20D4⋊(C43⋊C8)—21no—
21D4⋊(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
31C2×#10621877D411yescharacteristic
32C2×#10621877D411yescharacteristic
33C22×C43⋊C8—21no—
34C2×C4⋊Dic43—21no—
35C2×C4×Dic43—21no—
36C4⋊(C43⋊C8)—22no—
37C4⋊(C43⋊C8)—22no—
38C4⋊(C43⋊C8)—21no—
39C4⋊(C43⋊C8)—21no—
40C4⋊(C43⋊C8)D411yescharacteristic
41C4⋊(C43⋊C8)D411yescharacteristic
42#13063252—42no—
43#13063252—42no—
44C22⋊(C43⋊C8)—21no—
45#13063236—22no—
46#13063236—21no—
47C4×C43⋊C8—22no—
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×C43D412yes—
62#121×C43—21no—
63#121×C43—21no—
64C4×Q8×C43—21no—
65C4×Q8×C43D412yes—
66C4×D4×C43—21no—
67C4×D4×C43—21no—
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×C43C22⋊C412yes—
83C2×D4×C43—21no—
84C2×D4×C43—21no—
85C2×D4×C43—21no—
86C2×D4×C43—41no—
87C22×C4×C43—41no—
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—22no—
100C4⋊C4×C43—22no—
101C4⋊C4×C43—21no—
102C4⋊C4×C43—21no—
103C4⋊C4×C43C22⋊C412yes—
104C22⋊C4×C43—22no—
105C22⋊C4×C43—41no—
106C22⋊C4×C43—41no—
107C42×C43—22no—
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#10621877SD1612yescomplemented
120C2×C43⋊C8—21no—
121C2×C43⋊C8—21no—
122C2×C43⋊C8—21no—
123C2×C43⋊C8—21no—
124C2×C43⋊C8—41no—
125C2×C43⋊C8—41no—
126C2×C43⋊C8—41no—
127C23×C43—41no—
128C23×C43#12111yescharacteristic
129Q8×C43—42no—
130Q8×C43—41no—
131Q8×C43—41no—
132Q8×C43—41no—
133Q8×C43—41no—
134D4×C43—42no—
135D4×C43—41no—
136D4×C43—41no—
137D4×C43—41no—
138D4×C43—41no—
139D4×C43—81no—
140D4×C43—81no—
141C2×C4×C43—21no—
142C2×C4×C43—21no—
143C2×C4×C43—22no—
144C2×C4×C43—22no—
145C2×C4×C43—41no—
146C2×C4×C43—41no—
147C2×C4×C43—81no—
148C2×C4×C43—81no—
149C2×C4×C43C2×C22⋊C411yescharacteristic
150C2×C4×C43C4×D411yescharacteristic
151C2×C4×C43C4×D411yescharacteristic
152C2×C4×C43#12011yescharacteristic
153C2×C4×C43#12111yescharacteristic
154C2×C4×C43#12311yescharacteristic
155C2×C4×C43C2×SD1611yescharacteristic
156C2×C4×C43#13511yescharacteristic
157C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
158C2×C4×C43#13711yescharacteristic
159C2×Dic43—42no—
160C2×Dic43—81no—
161C2×Dic43—81no—
162C8×C43—22no—
163C8×C43—41no—
164C43⋊C8—22no—
165C43⋊C8—41no—
166C43⋊C8—41no—
167C43⋊C8—41no—
168C43⋊C8—81no—
169#9054—431nomaximal, Sylow
170C22×C43—21no—
171C22×C43—21no—
172C22×C43—81no—
173C22×C43—81no—
174C22×C43—81no—
175C22×C43#38611yescharacteristic
176C22×C43#46011yescharacteristic
177C22×C43#46411yescharacteristic
178C4×C43—21no—
179C4×C43—21no—
180C4×C43—21no—
181C4×C43—42no—
182C4×C43—42no—
183C4×C43—81no—
184C4×C43C4×SD1611yescharacteristic
185C4×C43#44011yescharacteristic
186C4×C43#44311yescharacteristic
187C4×C43#44411yescharacteristic
188C4×C43#44811yescharacteristic
189C4×C43#44911yescharacteristic
190Dic43—82no—
191#3167D4311yescharacteristic
192#2962—431no—
193#1980—431no—
194#1503—431no—
195#1480—431no—
196#1279—431no—
197#1278—431no—
198C2×C43—21no—
199C2×C43—21no—
200C2×C43—161no—
201C2×C43#187611yescharacteristic
202C2×C43#188011yescharacteristic
203C2×C43#188411yescharacteristic
204#533C2×D4311yescharacteristic
205#532C2×D4311yescharacteristic
206#498Dic4311yescharacteristic, complemented
207#492Dic4311yescharacteristic, complemented
208#487Dic4311yescharacteristic, complemented
209#486Dic4311yescharacteristic, complemented
210#465—22no—
211#446—861no—
212#446—862no—
213C8×Q8—861no—
214C4×SD16—22no—
215#431—431no—
216#424—861no—
217C2×C4⋊C8—431no—
218C2×#104—861no—
219C2×#104—861no—
220#405—861no—
221C4×M16—431no—
222C2×C4×C8C2×D4311yescharacteristic
223C4×C4⋊C4—431no—
224#328—862no—
225D4⋊C8—861no—
226D4⋊C8—861no—
227C43#905411yescharacteristic, complemented, Sylow
228C2×#41—21no—
229C2×SD16—22no—
230C2×M16—431no—
231C2×M16—431no—
232C22×C8—21no—
233C22×C8—861no—
234C4⋊Q8C2×Dic4311yescharacteristic
235C4⋊Q8C2×Dic4311yescharacteristic
236C4⋊Q8C2×Dic4311yescharacteristic
237#127C2×Dic4311yescharacteristic
238#125—21no—
239#124—21no—
240C22⋊Q8—21no—
241C22⋊Q8C22⋊D4312yes—
242#121—21no—
243#121—21no—
244C4×Q8—21no—
245C4×Q8C22⋊D4312yes—
246C4×D4—21no—
247C4×D4—21no—
248#117—21no—
249C2×C4⋊C4—861no—
250C2×C42—861no—
251C2×C42C22×D4311yescharacteristic
252#106—22no—
253C4⋊C8—431no—
254C4⋊C8—431no—
255C4⋊C8—862no—
256C4⋊C8—862no—
257C4⋊C8—861no—
258C4⋊C8—861no—
259#104—1722no—
260#104—1722no—
261#103—22no—
262#102—22no—
263C22⋊C8—861no—
264#97—862no—
265#97—861no—
266C4×C8—21no—
267C4×C8—862no—
268C4×C8—861no—
269C4×C8—861no—
270C4×C8C2×Dic4311yescharacteristic
271C4×C8C2×Dic4311yescharacteristic
272#95—861no—
273#41—41no—
274#41—41no—
275#41—41no—
276#41—41no—
277C2×Q8—21no—
278C2×Q8—21no—
279C2×Q8C22⋊Dic4312yes—
280C2×D4—21no—
281C2×D4—21no—
282C2×D4—21no—
283C2×D4—41no—
284C22×C4—41no—
285C22×C4—1721no—
286C22×C4D4×D4311yescharacteristic
287C22×C4#1062190011yescharacteristic
288C22×C4C2×C22⋊D4311yescharacteristic
289SD16—44no—
290M16—432no—
291M16—861no—
292M16—861no—
293M16—861no—
294C2×C8—21no—
295C2×C8—21no—
296C2×C8—42no—
297C2×C8—861no—
298C2×C8—861no—
299C2×C8—861no—
300C2×C8—861no—
301C2×C8—1721no—
302C2×C8—1721no—
303C2×C8—1721no—
304C4⋊C4—21no—
305C4⋊C4—21no—
306C4⋊C4—21no—
307C4⋊C4—22no—
308C4⋊C4—22no—
309C4⋊C4—21no—
310C4⋊C4—21no—
311C4⋊C4—862no—
312C4⋊C4—1721no—
313C4⋊C4C22⋊Dic4312yes—
314C22⋊C4—22no—
315C22⋊C4—41no—
316C22⋊C4—41no—
317C42—22no—
318C42—1721no—
319C42—1721no—
320C42D4×D4311yescharacteristic
321C42#1062190011yescharacteristic
322C42C22×Dic4311yescharacteristic
323C42C2×C22⋊D4311yescharacteristic
324C23—41no—
325C23#1306329711yescharacteristic
326Q8—42no—
327Q8—41no—
328Q8—41no—
329Q8—41no—
330Q8—41no—
331D4—42no—
332D4—41no—
333D4—41no—
334D4—41no—
335D4—41no—
336D4—81no—
337D4—81no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—22no—
341C2×C4—22no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—81no—
345C2×C4—81no—
346C2×C4—3441no—
347C2×C4—3441no—
348C2×C4—1722no—
349C2×C4C2×C22⋊Dic4311yescharacteristic
350C2×C4D4×Dic4311yescharacteristic
351C2×C4D4×Dic4311yescharacteristic
352C2×C4#1306329311yescharacteristic
353C2×C4#1306329711yescharacteristic
354C2×C4#1306330611yescharacteristic
355C2×C4SD16×D4311yescharacteristic
356C2×C4#1306334611yescharacteristic
357C2×C4#1306335211yescharacteristic
358C2×C4#1306335411yescharacteristic
359C8—22no—
360C8—41no—
361C8—862no—
362C8—3441no—
363C8—1721no—
364C8—1721no—
365C8—1721no—
366C22—21no—
367C22—21no—
368C22—81no—
369C22—81no—
370C22—81no—
371C22#1458277911yescharacteristic
372C22#1458309711yescharacteristic
373C22#1458311911yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—42no—
378C4—42no—
379C4—81no—
380C4—3442no—
381C4SD16×Dic4311yescharacteristic
382C4#1458300011yescharacteristic
383C4#1458301611yescharacteristic
384C4#1458302111yescharacteristic
385C4#1458303611yescharacteristic
386C4#1458304311yescharacteristic
387C2—21no—
388C2—21no—
389C2—161no—
390C2#1913492411yescharacteristic
391C2#1913495211yescharacteristic
392C2#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#9054
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
1. #19143544C2semidirect
3. #19133094C2semidirect
5. #19132435C2semidirect
6. #19132432C2semidirect
24. C43×#498C4semidirect
25. C43×#492C4semidirect
26. C43×#487C4semidirect
27. C43×#486C4semidirect
119. #10621877SD16semidirect
206. #498Dic43semidirect
207. #492Dic43semidirect
208. #487Dic43semidirect
209. #486Dic43semidirect
227. C43#9054semidirect

Maximal subgroups

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

subgroupindex
#191435442
#191355152
#191330942
#191329942
#191324352
#191324322
C43×#31672
#905443