Finite Group Databasebeta

← #24993145

Subgroups — #24993145

Order 11008.

560 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145513C211yesmaximal, characteristic
2#19143341C211yesmaximal, characteristic, complemented
3#19133273C211yesmaximal, characteristic, complemented
4C2×#14582643C211yesmaximal, characteristic, complemented
5#19132490C211yesmaximal, characteristic, complemented
6#19132446C211yesmaximal, characteristic, complemented
7C43×#1965C211yesmaximal, characteristic, complemented
8C2×#13063333—21no—
9#14583449C2211yescharacteristic
10#14583275—21no—
11#14583245—21no—
12#14583091—22no—
13#14583033C414yes—
14#14582978—21no—
15#14582972—22no—
16C8×D172—21no—
17#14582952C2211yescharacteristic
18C2×C4⋊(C43⋊C8)C2211yescharacteristic
19C2×C4⋊(C43⋊C8)C2211yescharacteristic
20#14582867—21no—
21#14582646—21no—
22#14582643—21no—
23#14582643—21no—
24#14582642—21no—
25C2×#127×C43C2211yescharacteristic
26C43×#423C2211yescharacteristic
27C2×#100×C43—21no—
28C2×#100×C43—21no—
29C4×M16×C43C2211yescharacteristic
30C2×#10621898—21no—
31C2×#10621882—24no—
32#13063333—42no—
33#13063333—42no—
34C2×#10621872—22no—
35C22×C43⋊C8—21no—
36C22×C43⋊C8—21no—
37C2×C8×D43—22no—
38#13063325D411yescharacteristic
39#13063322D411yescharacteristic
40#13063313—21no—
41#13063299—21no—
42#13063299C2×C412yes—
43C4×D172—21no—
44C4×D172D412yes—
45C4⋊(C43⋊C8)—21no—
46C4⋊(C43⋊C8)—21no—
47C4⋊(C43⋊C8)—21no—
48C4⋊(C43⋊C8)—21no—
49C4⋊(C43⋊C8)D411yescharacteristic
50C4⋊(C43⋊C8)D411yescharacteristic
51#13063246—24no—
52C22⋊(C43⋊C8)C2×C412yes—
53(C2×D43)⋊C8—22no—
54(C2×D43)⋊C8—22no—
55C4×C43⋊C8—21no—
56C22×D4×C43—21no—
57C22×D4×C43—21no—
58C22×D4×C43C2×C412yes—
59C2×M16×C43—21no—
60C2×M16×C43D411yescharacteristic
61C2×M16×C43D411yescharacteristic
62#127×C43—21no—
63#127×C43—21no—
64#127×C43—21no—
65#127×C43—21no—
66C2×C42×C43C2311yescharacteristic
67C4⋊C8×C43—21no—
68C4⋊C8×C43—21no—
69#100×C43—42no—
70#100×C43—42no—
71#97×C43—21no—
72C4×C8×C43—21no—
73C24×C43—22no—
74C2×D4×C43—22no—
75C2×D4×C43—22no—
76C2×D4×C43—41no—
77C2×D4×C43—41no—
78C2×D4×C43—41no—
79C2×D4×C43—41no—
80C2×D4×C43—41no—
81C2×D4×C43—41no—
82C2×D4×C43—41no—
83C2×D4×C43—41no—
84C2×D4×C43—81no—
85C2×D4×C43—81no—
86C2×D4×C43—82no—
87C22×C4×C43C22×C411yescharacteristic
88C22×C4×C43C2×D411yescharacteristic
89C22×C4×C43#4111yescharacteristic
90C2×C22⋊D43—22no—
91#10621898—41no—
92#10621898—41no—
93#10621898—41no—
94#10621898—41no—
95C2×D172—21no—
96C2×D172—21no—
97C2×D172C22⋊C412yes—
98C2×C4×D43—22no—
99C2×Dic86—21no—
100M16×C43—21no—
101M16×C43—21no—
102M16×C43—21no—
103M16×C43—41no—
104M16×C43—41no—
105M16×C43D812yescomplemented
106C2×C8×C43—21no—
107C2×C8×C43—21no—
108C2×C8×C43—41no—
109C42×C43C2×D411yescharacteristic
110C42×C43C2×D411yescharacteristic
111C42×C43C2×D411yescharacteristic
112C42×C43#4111yescharacteristic
113#10621882—84no—
114(C2×D43)⋊C4—22no—
115(C2×D43)⋊C4—22no—
116C4⋊Dic43—21no—
117C4⋊Dic43C22⋊C412yes—
118C2×C43⋊C8—22no—
119C2×C43⋊C8—21no—
120C2×C43⋊C8—21no—
121C2×C43⋊C8—41no—
122C2×C43⋊C8—41no—
123C2×C43⋊C8—41no—
124C2×C43⋊C8—81no—
125#10621872—44no—
126C8×D43—44no—
127C23×C43—42no—
128C23×C43—42no—
129C23×C43—42no—
130C23×C43—82no—
131C23×C43—82no—
132C23×C43C4×D411yescharacteristic
133C22×D43—22no—
134D4×C43—44no—
135D4×C43—82no—
136D4×C43—82no—
137D4×C43—81no—
138D4×C43—81no—
139D4×C43—81no—
140D4×C43—81no—
141D4×C43—81no—
142D4×C43—81no—
143C2×C4×C43—21no—
144C2×C4×C43—21no—
145C2×C4×C43—41no—
146C2×C4×C43C2×C22⋊C411yescharacteristic
147C2×C4×C43C4×D411yescharacteristic
148C2×C4×C43#12011yescharacteristic
149C2×C4×C43#12111yescharacteristic
150C2×C4×C43#12111yescharacteristic
151C2×C4×C43#12311yescharacteristic
152C2×C4×C43C2×D811yescharacteristic
153C2×C4×C43#13511yescharacteristic
154C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
155C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
156C22⋊D43—42no—
157C22⋊D43—42no—
158C2×Dic43—22no—
159D172—42no—
160D172—41no—
161D172—41no—
162D172—41no—
163D172—41no—
164C4×D43—42no—
165C4×D43—42no—
166Dic86—41no—
167Dic86—41no—
168C8×C43—22no—
169C8×C43—41no—
170C8×C43—81no—
171C43⋊C8—42no—
172C43⋊C8—41no—
173C43⋊C8—41no—
174C43⋊C8—81no—
175#9273—431nomaximal, Sylow
176C22×C43—21no—
177C22×C43—21no—
178C22×C43—82no—
179C22×C43—82no—
180C22×C43—82no—
181C22×C43—162no—
182C22×C43—162no—
183C22×C43#38611yescharacteristic
184C22×C43C4×D811yescharacteristic
185C22×C43#44211yescharacteristic
186C2×D43—42no—
187C2×D43—42no—
188C2×D43—42no—
189C4×C43—21no—
190C4×C43—21no—
191C4×C43—21no—
192C4×C43#44711yescharacteristic
193C4×C43#44911yescharacteristic
194C4×C43#45911yescharacteristic
195C4×C43#46311yescharacteristic
196C4×C43#47111yescharacteristic
197C4×C43#47211yescharacteristic
198Dic43—42no—
199#3205—431no—
200#2935—431no—
201#1965D4311yescharacteristic, complemented
202#1547—431no—
203C2×#331—431no—
204#1301—431no—
205#1283—431no—
206C2×C43—21no—
207C2×C43—21no—
208C2×C43—162no—
209C2×C43#187911yescharacteristic
210C2×C43#190711yescharacteristic
211C2×C43#191411yescharacteristic
212D43—82no—
213C2×#131—861no—
214#532—431no—
215C2×#127C2×D4311yescharacteristic
216#493—861no—
217#486—861no—
218#459—862no—
219#447—434no—
220#436—861no—
221#435—862no—
222C8×D4—861no—
223#431—431no—
224#423C2×D4311yescharacteristic
225C2×C4⋊C8—431no—
226C2×C4⋊C8—431no—
227C2×#100—21no—
228C2×#100—21no—
229#408—861no—
230C4×M16C2×D4311yescharacteristic
231#332—861no—
232#331—861no—
233#331—861no—
234#331—861no—
235C43#927311yescharacteristic, complemented, Sylow
236C2×#41—861no—
237C22×D4—21no—
238C22×D4—21no—
239C22×D4C4×D4312yes—
240C2×D8—864no—
241#131—1722no—
242#131—1722no—
243C2×M16—21no—
244C2×M16—862no—
245C2×M16C22⋊D4311yescharacteristic
246C2×M16C22⋊D4311yescharacteristic
247C22×C8—862no—
248C22×C8—861no—
249C22×C8—861no—
250C4⋊Q8—431no—
251#127—21no—
252#127—21no—
253#127—21no—
254#127—21no—
255#127—431no—
256#124—861no—
257#121—432no—
258#121—861no—
259C4×D4—432no—
260C4×D4—861no—
261C2×C42C22×D4311yescharacteristic
262C4⋊C8—21no—
263C4⋊C8—21no—
264C4⋊C8—431no—
265C4⋊C8—431no—
266C4⋊C8—861no—
267C4⋊C8—861no—
268C4⋊C8—861no—
269C4⋊C8—861no—
270#102—864no—
271#100—42no—
272#100—42no—
273C22⋊C8—432no—
274C22⋊C8—862no—
275C22⋊C8—862no—
276#97—21no—
277C4×C8—21no—
278C4×C8—861no—
279C24—22no—
280#41—1721no—
281#41—1721no—
282#41—1721no—
283#41—1721no—
284C2×Q8—861no—
285C2×D4—22no—
286C2×D4—22no—
287C2×D4—41no—
288C2×D4—41no—
289C2×D4—41no—
290C2×D4—41no—
291C2×D4—41no—
292C2×D4—41no—
293C2×D4—41no—
294C2×D4—41no—
295C2×D4—81no—
296C2×D4—81no—
297C2×D4—82no—
298C2×D4—432no—
299C2×D4—862no—
300C2×D4—861no—
301C2×D4—861no—
302C22×C4—862no—
303C22×C4C2×C4×D4311yescharacteristic
304C22×C4#1062189811yescharacteristic
305C22×C4C2×C22⋊D4311yescharacteristic
306D8—3444no—
307M16—21no—
308M16—21no—
309M16—21no—
310M16—41no—
311M16—41no—
312M16—1724no—
313M16#1062188212yescomplemented
314C2×C8—21no—
315C2×C8—21no—
316C2×C8—41no—
317C2×C8—862no—
318C2×C8—861no—
319C2×C8—861no—
320C2×C8—3441no—
321C2×C8—1724no—
322C2×C8—1721no—
323C2×C8—1721no—
324C2×C8—1721no—
325C4⋊C4—432no—
326C4⋊C4—861no—
327C22⋊C4—862no—
328C22⋊C4—862no—
329C42D4×D4311yescharacteristic
330C42D4×D4311yescharacteristic
331C42D4×D4311yescharacteristic
332C42#1062190011yescharacteristic
333C23—42no—
334C23—42no—
335C23—42no—
336C23—82no—
337C23—82no—
338C23—862no—
339C23C4×C22⋊D4311yescharacteristic
340Q8—1721no—
341Q8—1721no—
342D4—44no—
343D4—82no—
344D4—82no—
345D4—81no—
346D4—81no—
347D4—81no—
348D4—81no—
349D4—81no—
350D4—81no—
351D4—1722no—
352D4—1722no—
353D4—1722no—
354D4—1721no—
355D4—1721no—
356D4—1721no—
357D4—1721no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—41no—
361C2×C4—862no—
362C2×C4—1722no—
363C2×C4—1722no—
364C2×C4C22⋊C4×D4311yescharacteristic
365C2×C4(C22⋊D43)⋊C411yescharacteristic
366C2×C4#1306329311yescharacteristic
367C2×C4#1306329611yescharacteristic
368C2×C4#1306329811yescharacteristic
369C2×C4#1306330711yescharacteristic
370C2×C4C2×#1062188211yescharacteristic
371C2×C4#1306334511yescharacteristic
372C2×C4#1306335011yescharacteristic
373C2×C4#1306335111yescharacteristic
374C8—22no—
375C8—41no—
376C8—81no—
377C8—3441no—
378C8—1722no—
379C8—1721no—
380C8—1721no—
381C22—21no—
382C22—21no—
383C22—82no—
384C22—82no—
385C22—82no—
386C22—162no—
387C22—162no—
388C22—1722no—
389C22—1722no—
390C22—1722no—
391C22#1458277511yescharacteristic
392C22C4×#1062188211yescharacteristic
393C22#1458300911yescharacteristic
394C4—21no—
395C4—21no—
396C4—21no—
397C4—1722no—
398C4#1458303211yescharacteristic
399C4#1458304211yescharacteristic
400C4#1458309111yescharacteristic
401C4#1458311111yescharacteristic
402C4#1458316111yescharacteristic
403C4#1458316811yescharacteristic
404C2—21no—
405C2—21no—
406C2—162no—
407C2—3442no—
408C2#1913494611yescharacteristic
409C2#1913510011yescharacteristic
410C2#1913513911yescharacteristic
subgroupG/H
centerC22#14582775
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1965C2
socleC22×C43#386
prime radical#19145513C2
cosocleC2×C42×C43C23
hypercenter#1965D43
hypocenterC43#9273
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1965

Complements

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

NH ≅ G/Ntype
2. #19143341C2semidirect
3. #19133273C2semidirect
4. C2×#14582643C2semidirect
5. #19132490C2semidirect
6. #19132446C2semidirect
7. C43×#1965C2semidirect
105. M16×C43D8semidirect
201. #1965D43semidirect
235. C43#9273semidirect
313. M16#10621882semidirect

Maximal subgroups

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

subgroupindex
#191455132
#191433412
#191332732
C2×#145826432
#191324902
#191324462
C43×#19652
#927343