Finite Group Databasebeta

← #24991835

Subgroups — #24991835

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#19145155C211yesmaximal, characteristic
2#19143338C211yesmaximal, characteristic
3#19135540C211yesmaximal, characteristic, complemented
4#19133091C211yesmaximal, characteristic
5#19132434C211yesmaximal, characteristic, complemented
6#19132431C211yesmaximal, characteristic, complemented
7C43×#1481C211yesmaximal, characteristic, complemented
8C2×#13063331—21no—
9#14583449C2211yescharacteristic
10#14583295C411yescharacteristic, complemented
11#14583273C411yescharacteristic, complemented
12#14583249C411yescharacteristic, complemented
13#14583247C411yescharacteristic, complemented
14#14583130—22no—
15C4×#10621884—22no—
16#14582976—21no—
17#14582969—22no—
18#14582964—21no—
19#14582865—21no—
20C4×#10621877C2211yescharacteristic
21C2×C4×C43⋊C8C2211yescharacteristic
22C4×C4⋊Dic43C2211yescharacteristic
23#14582658—21no—
24#14582658—21no—
25#14582634—22no—
26C43×#533C2211yescharacteristic
27C43×#431C2211yescharacteristic
28C2×C4⋊C8×C43C2211yescharacteristic
29C43×Q8⋊C8—21no—
30C43×Q8⋊C8—21no—
31C2×#10621898—21no—
32C2×#10621884—22no—
33#13063331—42no—
34#13063331—42no—
35C2×#10621877D411yescharacteristic
36C2×#10621877D411yescharacteristic
37C2×#10621872—22no—
38C22×C43⋊C8—21no—
39C2×C8×D43—22no—
40#13063325C2×C411yescharacteristic
41#13063322C2×C411yescharacteristic
42#13063313—21no—
43#13063299—21no—
44#13063299D412yes—
45C4×D172—21no—
46C4×D172D412yes—
47C2×C4⋊Dic43—21no—
48C2×C4×Dic43—21no—
49#13063256—22no—
50#13063249—22no—
51#13063245—22no—
52(C2×D43)⋊C8—22no—
53(C2×D43)⋊C8—22no—
54#13063236—21no—
55C4×C43⋊C8—21no—
56C4×C43⋊C8—21no—
57C4×C43⋊C8C2×C411yescharacteristic
58C4×C43⋊C8C2×C411yescharacteristic
59C43⋊#95—21no—
60C22×C8×C43—21no—
61C4⋊Q8×C43C2×C411yescharacteristic
62C4⋊Q8×C43C2×C411yescharacteristic
63#125×C43—21no—
64C22⋊Q8×C43—21no—
65C22⋊Q8×C43—21no—
66C4×Q8×C43—21no—
67C4×Q8×C43—21no—
68#117×C43—21no—
69C2×C42×C43C2311yescharacteristic
70C4⋊C8×C43—21no—
71C4⋊C8×C43—21no—
72C4⋊C8×C43D411yescharacteristic
73C4⋊C8×C43D411yescharacteristic
74C22⋊C8×C43—21no—
75C4×C8×C43—21no—
76C2×Q8×C43—21no—
77C2×Q8×C43—21no—
78C22×C4×C43C2×D411yescharacteristic
79C22×C4×C43C2×D411yescharacteristic
80C22×C4×C43#4111yescharacteristic
81C2×C22⋊D43—22no—
82C22×Dic43—41no—
83#10621898—41no—
84#10621898—41no—
85#10621898—41no—
86#10621898—41no—
87C2×D172—21no—
88C2×D172—21no—
89C2×D172C22⋊C412yes—
90C2×C4×D43—22no—
91C2×Dic86—21no—
92C2×C8×C43—21no—
93C2×C8×C43—21no—
94C2×C8×C43—41no—
95C2×C8×C43—41no—
96C2×C8×C43—41no—
97C4⋊C4×C43—21no—
98C4⋊C4×C43—21no—
99C4⋊C4×C43—21no—
100C4⋊C4×C43—21no—
101C4⋊C4×C43—41no—
102C4⋊C4×C43—41no—
103C22⋊C4×C43—41no—
104C42×C43—41no—
105C42×C43C22×C411yescharacteristic
106C42×C43C2×D411yescharacteristic
107C42×C43C2×D411yescharacteristic
108C42×C43#4111yescharacteristic
109#10621884—44no—
110(C2×D43)⋊C4—22no—
111(C2×D43)⋊C4—22no—
112C4⋊Dic43—21no—
113C4⋊Dic43—22no—
114C4⋊Dic43—41no—
115C4⋊Dic43C22⋊C412yes—
116C4×Dic43—41no—
117C4×Dic43—41no—
118#10621877—21no—
119#10621877—21no—
120#10621877—21no—
121#10621877SD1612yescomplemented
122C2×C43⋊C8—21no—
123C2×C43⋊C8—21no—
124C2×C43⋊C8—21no—
125C2×C43⋊C8—21no—
126C2×C43⋊C8—42no—
127#10621872—44no—
128C8×D43—44no—
129C23×C43#12111yescharacteristic
130C22×D43—22no—
131Q8×C43—42no—
132Q8×C43—41no—
133Q8×C43—41no—
134C2×C4×C43—21no—
135C2×C4×C43—21no—
136C2×C4×C43—41no—
137C2×C4×C43—41no—
138C2×C4×C43—41no—
139C2×C4×C43C2×C22⋊C411yescharacteristic
140C2×C4×C43C4×D411yescharacteristic
141C2×C4×C43C4×D411yescharacteristic
142C2×C4×C43#12011yescharacteristic
143C2×C4×C43#12111yescharacteristic
144C2×C4×C43#12311yescharacteristic
145C2×C4×C43C2×SD1611yescharacteristic
146C2×C4×C43#13511yescharacteristic
147C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
148C2×C4×C43#13711yescharacteristic
149C22⋊D43—42no—
150C22⋊D43—42no—
151C2×Dic43—22no—
152C2×Dic43—42no—
153C2×Dic43—81no—
154C2×Dic43—81no—
155D172—42no—
156D172—41no—
157D172—41no—
158D172—41no—
159D172—41no—
160C4×D43—42no—
161C4×D43—42no—
162Dic86—41no—
163Dic86—41no—
164C8×C43—41no—
165C8×C43—41no—
166C8×C43—81no—
167C43⋊C8—22no—
168C43⋊C8—22no—
169C43⋊C8—41no—
170C43⋊C8—41no—
171#9055—431nomaximal, Sylow
172C22×C43—21no—
173C22×C43—21no—
174C22×C43#38611yescharacteristic
175C22×C43#46111yescharacteristic
176C22×C43#46311yescharacteristic
177C2×D43—42no—
178C2×D43—42no—
179C2×D43—42no—
180C4×C43—21no—
181C4×C43—21no—
182C4×C43—21no—
183C4×C43—81no—
184C4×C43—81no—
185C4×C43C4×SD1611yescharacteristic
186C4×C43#44011yescharacteristic
187C4×C43#44311yescharacteristic
188C4×C43#44411yescharacteristic
189C4×C43#45011yescharacteristic
190C4×C43#45211yescharacteristic
191Dic43—42no—
192Dic43—82no—
193#3167—431no—
194#2935—431no—
195#1986—431no—
196#1502—431no—
197#1481D4311yescharacteristic, complemented
198#1279—431no—
199#1278—431no—
200C2×C43—21no—
201C2×C43—21no—
202C2×C43#187611yescharacteristic
203C2×C43#187711yescharacteristic
204C2×C43#188411yescharacteristic
205D43—82no—
206C2×#131—861no—
207#533C2×D4311yescharacteristic
208#532—431no—
209#498—431no—
210#492—431no—
211#487—431no—
212#486—431no—
213#465—862no—
214C4×SD16—862no—
215#436—861no—
216#435—862no—
217C8×D4—861no—
218#431C2×D4311yescharacteristic
219C2×C4⋊C8C2×D4311yescharacteristic
220#408—861no—
221C4×M16—431no—
222C2×C4×C8—431no—
223C4×C4⋊C4—431no—
224#339—861no—
225#339—861no—
226#327—862no—
227Q8⋊C8—21no—
228Q8⋊C8—21no—
229C43#905511yescharacteristic, complemented, Sylow
230C2×#41—861no—
231C2×SD16—862no—
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⋊Q8—431no—
241C4⋊Q8C4×D4311yescharacteristic
242C4⋊Q8C4×D4311yescharacteristic
243#127—431no—
244#125—21no—
245#124—861no—
246C22⋊Q8—21no—
247C22⋊Q8—21no—
248#121—432no—
249#121—861no—
250C4×Q8—21no—
251C4×Q8—21no—
252C4×D4—432no—
253C4×D4—861no—
254#117—21no—
255C2×C4⋊C4—861no—
256C2×C42—861no—
257C2×C42C22×D4311yescharacteristic
258#106—862no—
259C4⋊C8—21no—
260C4⋊C8—21no—
261C4⋊C8C22⋊D4311yescharacteristic
262C4⋊C8C22⋊D4311yescharacteristic
263#103—862no—
264#102—862no—
265C22⋊C8—21no—
266C22⋊C8—862no—
267C22⋊C8—862no—
268#97—861no—
269C4×C8—21no—
270C4×C8—431no—
271C4×C8—431no—
272C4×C8—861no—
273C4×C8—861no—
274#95—861no—
275#41—1721no—
276#41—1721no—
277#41—1721no—
278#41—1721no—
279C2×Q8—21no—
280C2×Q8—21no—
281C2×Q8—861no—
282C2×D4—432no—
283C2×D4—862no—
284C2×D4—861no—
285C2×D4—861no—
286C22×C4—862no—
287C22×C4—1721no—
288C22×C4#1062189811yescharacteristic
289C22×C4D4×D4311yescharacteristic
290C22×C4D4×D4311yescharacteristic
291SD16—1724no—
292M16—432no—
293M16—861no—
294M16—861no—
295M16—861no—
296M16—1724no—
297C2×C8—21no—
298C2×C8—21no—
299C2×C8—41no—
300C2×C8—41no—
301C2×C8—41no—
302C2×C8—861no—
303C2×C8—861no—
304C2×C8—861no—
305C2×C8—861no—
306C2×C8—1724no—
307C2×C8—1722no—
308C4⋊C4—21no—
309C4⋊C4—21no—
310C4⋊C4—21no—
311C4⋊C4—21no—
312C4⋊C4—41no—
313C4⋊C4—41no—
314C4⋊C4—432no—
315C4⋊C4—862no—
316C4⋊C4—861no—
317C4⋊C4—1721no—
318C22⋊C4—41no—
319C22⋊C4—862no—
320C22⋊C4—862no—
321C42—41no—
322C42—1721no—
323C42—1721no—
324C42C2×C4×D4311yescharacteristic
325C42D4×D4311yescharacteristic
326C42#1062190011yescharacteristic
327C42C2×C22⋊D4311yescharacteristic
328C23—862no—
329C23#1306329811yescharacteristic
330Q8—42no—
331Q8—41no—
332Q8—41no—
333Q8—1721no—
334Q8—1721no—
335D4—1722no—
336D4—1722no—
337D4—1722no—
338D4—1721no—
339D4—1721no—
340D4—1721no—
341D4—1721no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—862no—
348C2×C4—3441no—
349C2×C4—3441no—
350C2×C4—1722no—
351C2×C4—1722no—
352C2×C4—1722no—
353C2×C4C22⋊C4×D4311yescharacteristic
354C2×C4(C22⋊D43)⋊C411yescharacteristic
355C2×C4C4×C22⋊D4311yescharacteristic
356C2×C4#1306329311yescharacteristic
357C2×C4#1306329611yescharacteristic
358C2×C4#1306330711yescharacteristic
359C2×C4SD16×D4311yescharacteristic
360C2×C4#1306334811yescharacteristic
361C2×C4#1306335211yescharacteristic
362C2×C4#1306335711yescharacteristic
363C8—41no—
364C8—41no—
365C8—81no—
366C8—862no—
367C8—862no—
368C8—1721no—
369C8—1721no—
370C22—21no—
371C22—21no—
372C22—1722no—
373C22—1722no—
374C22—1722no—
375C22#1458277511yescharacteristic
376C22#1458310311yescharacteristic
377C22#1458311711yescharacteristic
378C4—21no—
379C4—21no—
380C4—21no—
381C4—81no—
382C4—81no—
383C4—3442no—
384C4—1722no—
385C4#1458298411yescharacteristic
386C4#1458300211yescharacteristic
387C4#1458301411yescharacteristic
388C4#1458301911yescharacteristic
389C4#1458304811yescharacteristic
390C4#1458306011yescharacteristic
391C2—21no—
392C2—21no—
393C2—3442no—
394C2#1913492511yescharacteristic
395C2#1913492611yescharacteristic
396C2#1913497511yescharacteristic
subgroupG/H
centerC2×C4#13063293
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1481C2
socleC22×C43#386
prime radical#14583449C22
cosocleC2×C42×C43C23
hypercenter#1481D43
hypocenterC43#9055
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1481

Complements

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

NH ≅ G/Ntype
3. #19135540C2semidirect
5. #19132434C2semidirect
6. #19132431C2semidirect
7. C43×#1481C2semidirect
10. #14583295C4semidirect
11. #14583273C4semidirect
12. #14583249C4semidirect
13. #14583247C4semidirect
121. #10621877SD16semidirect
197. #1481D43semidirect
229. C43#9055semidirect

Maximal subgroups

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

subgroupindex
#191451552
#191433382
#191355402
#191330912
#191324342
#191324312
C43×#14812
#905543