Finite Group Databasebeta

← #24992546

Subgroups — #24992546

Order 11008.

548 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144059C211yesmaximal, characteristic
2#19133154C211yesmaximal, characteristic, complemented
3#19133089C211yesmaximal, characteristic, complemented
4#19132986C211yesmaximal, characteristic, complemented
5#19132498C211yesmaximal, characteristic, complemented
6#19132453C211yesmaximal, characteristic, complemented
7C43×#2357C211yesmaximal, characteristic, complemented
8C2×#13063351—21no—
9#14583449C2211yescharacteristic
10#14583114—22no—
11#14583104C412yescomplemented
12#14583094C412yescomplemented
13#14582952C2211yescharacteristic
14#14582952C2211yescharacteristic
15#14582923C2211yescharacteristic
16#14582898—21no—
17#14582632—21no—
18#14582632—21no—
19#14582632—22no—
20D4⋊(C43⋊C8)—22no—
21C2×C4×D4×C43C2211yescharacteristic
22C43×#390—21no—
23C43×#388—22no—
24C43×#382C2211yescharacteristic
25C43×#381—21no—
26C4×C4⋊C4×C43—21no—
27C4×C4⋊C4×C43C2211yescharacteristic
28C4×C22⋊C4×C43—21no—
29C2×#10621898—21no—
30#13063351—42no—
31#13063351—42no—
32C2×#10621883—22no—
33C2×#10621882—22no—
34C2×#10621877—21no—
35#13063325C2×C411yescharacteristic
36#13063322C2×C411yescharacteristic
37#13063313—21no—
38#13063299—21no—
39#13063299—21no—
40C4×D172—21no—
41C4×D172—21no—
42C4⋊(C43⋊C8)—21no—
43C4⋊(C43⋊C8)—21no—
44C4⋊(C43⋊C8)—21no—
45C4⋊(C43⋊C8)C2×C412yes—
46#13063248—22no—
47#13063245—22no—
48C22⋊(C43⋊C8)—21no—
49C22⋊(C43⋊C8)—21no—
50C4×C43⋊C8—21no—
51C4×C43⋊C8—21no—
52C22×D4×C43D411yescharacteristic
53C23×C4×C43—21no—
54C4×D4×C43—21no—
55C4×D4×C43—21no—
56C4×D4×C43C2×C412yes—
57C4×D4×C43D412yes—
58C2×C4⋊C4×C43—21no—
59C2×C4⋊C4×C43—21no—
60C2×C4⋊C4×C43D411yescharacteristic
61C2×C22⋊C4×C43—21no—
62C2×C22⋊C4×C43—22no—
63C2×C22⋊C4×C43—22no—
64C2×C42×C43—21no—
65C2×C42×C43—22no—
66C2×C42×C43C2311yescharacteristic
67#95×C43—22no—
68#95×C43—21no—
69#95×C43D411yescharacteristic
70#95×C43D411yescharacteristic
71#95×C43D412yes—
72C24×C43—21no—
73C2×D4×C43—21no—
74C2×D4×C43—21no—
75C2×D4×C43—21no—
76C2×D4×C43—21no—
77C2×D4×C43—21no—
78C2×D4×C43C22⋊C412yes—
79C22×C4×C43—22no—
80C22×C4×C43—22no—
81C22×C4×C43—21no—
82C22×C4×C43—21no—
83C22×C4×C43—22no—
84C22×C4×C43—21no—
85C22×C4×C43—82no—
86C22×C4×C43C2×D411yescharacteristic
87C22×C4×C43C2×D411yescharacteristic
88C22×C4×C43C2×D411yescharacteristic
89C2×C22⋊D43—41no—
90#10621898—41no—
91#10621898—41no—
92#10621898—41no—
93#10621898—41no—
94C2×D172—21no—
95C2×D172—21no—
96C2×D172—21no—
97C2×C4×D43—41no—
98C2×Dic86—21no—
99C4⋊C4×C43—21no—
100C4⋊C4×C43—42no—
101C4⋊C4×C43—41no—
102C4⋊C4×C43—41no—
103C4⋊C4×C43C22⋊C412yes—
104C22⋊C4×C43—22no—
105C22⋊C4×C43—22no—
106C22⋊C4×C43—44no—
107C22⋊C4×C43—82no—
108C42×C43—41no—
109C42×C43—41no—
110C42×C43—82no—
111C42×C43C22×C411yescharacteristic
112C42×C43C2×D411yescharacteristic
113C42×C43#4111yescharacteristic
114C42×C43#4111yescharacteristic
115#10621883—44no—
116#10621882—44no—
117(C2×D43)⋊C4—41no—
118(C2×D43)⋊C4—41no—
119C4⋊Dic43—21no—
120C4⋊Dic43—21no—
121#10621877—41no—
122#10621877—41no—
123C2×C43⋊C8—22no—
124C2×C43⋊C8—41no—
125C2×C43⋊C8—41no—
126C23×C43—22no—
127C23×C43—42no—
128C23×C43—42no—
129C23×C43—41no—
130C23×C43—41no—
131C23×C43#12011yescharacteristic
132C22×D43—41no—
133D4×C43—22no—
134D4×C43—22no—
135D4×C43—41no—
136D4×C43—41no—
137C2×C4×C43—22no—
138C2×C4×C43—22no—
139C2×C4×C43—41no—
140C2×C4×C43—41no—
141C2×C4×C43—41no—
142C2×C4×C43—42no—
143C2×C4×C43—41no—
144C2×C4×C43—42no—
145C2×C4×C43—42no—
146C2×C4×C43—41no—
147C2×C4×C43—41no—
148C2×C4×C43—41no—
149C2×C4×C43—42no—
150C2×C4×C43—82no—
151C2×C4×C43—82no—
152C2×C4×C43C2×C22⋊C411yescharacteristic
153C2×C4×C43C4×D411yescharacteristic
154C2×C4×C43C4×D411yescharacteristic
155C2×C4×C43#12111yescharacteristic
156C2×C4×C43#12111yescharacteristic
157C2×C4×C43#12311yescharacteristic
158C2×C4×C43#13511yescharacteristic
159C2×C4×C43#13511yescharacteristic
160C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
161C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
162C22⋊D43—81no—
163C22⋊D43—81no—
164C2×Dic43—41no—
165D172—41no—
166D172—41no—
167D172—81no—
168D172—81no—
169C4×D43—81no—
170C4×D43—81no—
171Dic86—41no—
172Dic86—41no—
173C43⋊C8—42no—
174C43⋊C8—81no—
175C43⋊C8—81no—
176#9181—431nomaximal, Sylow
177C22×C43—21no—
178C22×C43—21no—
179C22×C43—42no—
180C22×C43—42no—
181C22×C43—42no—
182C22×C43—82no—
183C22×C43—82no—
184C22×C43#38611yescharacteristic
185C22×C43#44911yescharacteristic
186C22×C43#44911yescharacteristic
187C2×D43—81no—
188C2×D43—81no—
189C2×D43—81no—
190C4×C43—21no—
191C4×C43—21no—
192C4×C43—21no—
193C4×C43—21no—
194C4×C43—42no—
195C4×C43—42no—
196C4×C43—81no—
197C4×C43—82no—
198C4×C43#41611yescharacteristic
199C4×C43#41811yescharacteristic
200C4×C43#48211yescharacteristic
201C4×C43#48211yescharacteristic
202Dic43—81no—
203#3036—431no—
204#2357D4311yescharacteristic, complemented
205#1517—431no—
206#1502—431no—
207#1478—431no—
208#1303—431no—
209#1286—431no—
210C2×C43—21no—
211C2×C43—21no—
212C2×C43—82no—
213C2×C43#187511yescharacteristic
214C2×C43#190411yescharacteristic
215C2×C43#190611yescharacteristic
216D43—161no—
217C2×AGL(1,ℤ/8)—861no—
218#532—431no—
219C2×C4×D4C2×D4311yescharacteristic
220#463—862no—
221#461—432no—
222#459—432no—
223#431—431no—
224#431—431no—
225#423—431no—
226#417—861no—
227#390—21no—
228#388—22no—
229#382C2×D4311yescharacteristic
230#381—21no—
231C4×C4⋊C4—21no—
232C4×C4⋊C4C2×D4311yescharacteristic
233C4×C22⋊C4—21no—
234#327—861no—
235#327—861no—
236#327—862no—
237D4⋊C8—862no—
238C43#918111yescharacteristic, complemented, Sylow
239C2×#41—861no—
240C22×D4C22⋊D4311yescharacteristic
241C23×C4—21no—
242AGL(1,ℤ/8)—1722no—
243AGL(1,ℤ/8)—1722no—
244C2×SD16—862no—
245C2×D8—862no—
246C2×M16—861no—
247C4⋊Q8—431no—
248#127—431no—
249#124—861no—
250#121—861no—
251#121—861no—
252C4×D4—21no—
253C4×D4—21no—
254C4×D4—861no—
255C4×D4—861no—
256C4×D4C4×D4312yes—
257C4×D4D17212yes—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4C22⋊D4311yescharacteristic
261C2×C22⋊C4—21no—
262C2×C22⋊C4—22no—
263C2×C22⋊C4—22no—
264C2×C42—21no—
265C2×C42—22no—
266C2×C42C22×D4311yescharacteristic
267C4⋊C8—432no—
268C4⋊C8—861no—
269C4⋊C8—861no—
270C4⋊C8—861no—
271#103—862no—
272#102—862no—
273C22⋊C8—861no—
274C22⋊C8—861no—
275C4×C8—861no—
276C4×C8—861no—
277#95—22no—
278#95—21no—
279#95C22⋊D4311yescharacteristic
280#95C22⋊D4311yescharacteristic
281#95C22⋊D4312yes—
282C24—21no—
283#41—1721no—
284#41—1721no—
285#41—1721no—
286#41—1721no—
287C2×Q8—861no—
288C2×D4—21no—
289C2×D4—21no—
290C2×D4—21no—
291C2×D4—21no—
292C2×D4—21no—
293C2×D4—861no—
294C2×D4—861no—
295C2×D4—861no—
296C2×D4—1721no—
297C2×D4(C2×D43)⋊C412yes—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—22no—
301C22×C4—22no—
302C22×C4—22no—
303C22×C4—21no—
304C22×C4—82no—
305C22×C4—1721no—
306C22×C4C2×C22⋊D4311yescharacteristic
307C22×C4C2×C22⋊D4311yescharacteristic
308C22×C4C2×C22⋊D4311yescharacteristic
309SD16—1724no—
310D8—1724no—
311M16—1721no—
312M16—1721no—
313C2×C8—862no—
314C2×C8—1721no—
315C2×C8—1721no—
316C4⋊C4—21no—
317C4⋊C4—42no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C4⋊C4—861no—
321C4⋊C4—861no—
322C4⋊C4(C2×D43)⋊C412yes—
323C22⋊C4—22no—
324C22⋊C4—22no—
325C22⋊C4—44no—
326C22⋊C4—82no—
327C22⋊C4—1721no—
328C22⋊C4—1721no—
329C42—41no—
330C42—41no—
331C42—82no—
332C42C2×C4×D4311yescharacteristic
333C42C2×D17211yescharacteristic
334C42#1062189811yescharacteristic
335C42#1062189811yescharacteristic
336C23—22no—
337C23—42no—
338C23—42no—
339C23—41no—
340C23—41no—
341C23—1721no—
342C23#1306329411yescharacteristic
343Q8—1721no—
344Q8—1721no—
345D4—22no—
346D4—22no—
347D4—41no—
348D4—41no—
349D4—3441no—
350D4—3441no—
351D4—3441no—
352D4—3441no—
353D4—1721no—
354D4—1721no—
355C2×C4—22no—
356C2×C4—22no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—42no—
361C2×C4—41no—
362C2×C4—42no—
363C2×C4—42no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—42no—
368C2×C4—82no—
369C2×C4—82no—
370C2×C4—3441no—
371C2×C4—3441no—
372C2×C4—1721no—
373C2×C4C2×(C2×D43)⋊C411yescharacteristic
374C2×C4C4×C22⋊D4311yescharacteristic
375C2×C4C4×C22⋊D4311yescharacteristic
376C2×C4#1306329911yescharacteristic
377C2×C4#1306329911yescharacteristic
378C2×C4#1306330811yescharacteristic
379C2×C4#1306334511yescharacteristic
380C2×C4#1306334511yescharacteristic
381C2×C4#1306335011yescharacteristic
382C2×C4#1306335011yescharacteristic
383C8—3441no—
384C8—3441no—
385C8—1722no—
386C22—21no—
387C22—21no—
388C22—42no—
389C22—42no—
390C22—42no—
391C22—82no—
392C22—82no—
393C22—3441no—
394C22—3441no—
395C22—3441no—
396C22#1458277811yescharacteristic
397C22#1458304411yescharacteristic
398C22#1458304411yescharacteristic
399C4—21no—
400C4—21no—
401C4—21no—
402C4—21no—
403C4—42no—
404C4—42no—
405C4—81no—
406C4—82no—
407C4—3441no—
408C4#1458289311yescharacteristic
409C4#1458290311yescharacteristic
410C4#1458322311yescharacteristic
411C4#1458322311yescharacteristic
412C2—21no—
413C2—21no—
414C2—82no—
415C2—6881no—
416C2#1913491711yescharacteristic
417C2#1913508211yescharacteristic
418C2#1913509611yescharacteristic
subgroupG/H
centerC22#14582778
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#2357C2
socleC22×C43#386
prime radical#19144059C2
cosocleC2×C42×C43C23
hypercenter#2357D43
hypocenterC43#9181
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2357

Complements

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

NH ≅ G/Ntype
2. #19133154C2semidirect
3. #19133089C2semidirect
4. #19132986C2semidirect
5. #19132498C2semidirect
6. #19132453C2semidirect
7. C43×#2357C2semidirect
11. #14583104C4semidirect
12. #14583094C4semidirect
204. #2357D43semidirect
238. C43#9181semidirect

Maximal subgroups

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

subgroupindex
#191440592
#191331542
#191330892
#191329862
#191324982
#191324532
C43×#23572
#918143