Finite Group Databasebeta

← #24993324

Subgroups — #24993324

Order 11008.

632 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145513C211yesmaximal, characteristic
2#19135427C211yesmaximal, characteristic, complemented
3#19133263C211yesmaximal, characteristic, complemented
4#19133154C211yesmaximal, characteristic, complemented
5#19132453C211yesmaximal, characteristic, complemented
6#19132424C211yesmaximal, characteristic, complemented
7C43×#2328C211yesmaximal, characteristic, complemented
8#14583449C2211yescharacteristic
9#14583275C412yescomplemented
10#14583245C412yescomplemented
11#14583091—22no—
12#14583033—22no—
13#14582952C2211yescharacteristic
14#14582952C2211yescharacteristic
15#14582923C2211yescharacteristic
16C2×#13063253—21no—
17C2×#13063253—21no—
18#14582643—22no—
19#14582632—22no—
20C2×#127×C43C2211yescharacteristic
21C2×C4×D4×C43—21no—
22C43×#390—21no—
23C43×#386—22no—
24C43×#386—22no—
25C43×#382C2211yescharacteristic
26C43×#376C2211yescharacteristic
27C2×#10621898—21no—
28C2×#10621882—24no—
29C2×#10621877—21no—
30#13063325C2×C411yescharacteristic, complemented
31#13063322C2×C411yescharacteristic, complemented
32#13063313—21no—
33#13063299—21no—
34#13063299—21no—
35C4×D172—21no—
36C4×D172—21no—
37C4⋊(C43⋊C8)—21no—
38C4⋊(C43⋊C8)—21no—
39C4⋊(C43⋊C8)—21no—
40C4⋊(C43⋊C8)—21no—
41#13063253—42no—
42#13063253—42no—
43#13063246—24no—
44C22⋊(C43⋊C8)—21no—
45C22⋊(C43⋊C8)—21no—
46C4×C43⋊C8—21no—
47C4×C43⋊C8C2×C412yescomplemented
48C22×D4×C43—21no—
49C22×D4×C43—21no—
50C22×D4×C43D412yes—
51C23×C4×C43—22no—
52#127×C43—21no—
53#127×C43—21no—
54#127×C43C2×C412yes—
55#127×C43D412yes—
56C4×D4×C43—42no—
57C4×D4×C43—42no—
58C2×C4⋊C4×C43—21no—
59C2×C22⋊C4×C43—22no—
60C2×C22⋊C4×C43—22no—
61C2×C22⋊C4×C43—22no—
62C2×C42×C43D411yescharacteristic
63C2×C42×C43D411yescharacteristic
64C2×C42×C43C2311yescharacteristic
65#95×C43—21no—
66#95×C43—21no—
67#95×C43—21no—
68#95×C43D412yes—
69C24×C43—22no—
70C2×D4×C43—22no—
71C2×D4×C43—22no—
72C2×D4×C43—22no—
73C2×D4×C43—22no—
74C2×D4×C43—22no—
75C2×D4×C43—41no—
76C2×D4×C43—41no—
77C2×D4×C43—41no—
78C2×D4×C43—41no—
79C2×D4×C43—82no—
80C2×D4×C43—82no—
81C2×D4×C43C22⋊C414yes—
82C22×C4×C43—21no—
83C22×C4×C43—21no—
84C22×C4×C43—22no—
85C22×C4×C43—44no—
86C22×C4×C43—82no—
87C22×C4×C43—82no—
88C22×C4×C43C2×D411yescharacteristic
89C22×C4×C43C2×D411yescharacteristic
90C22×C4×C43C2×D411yescharacteristic
91C2×C22⋊D43—41no—
92#10621898—41no—
93#10621898—41no—
94#10621898—41no—
95#10621898—41no—
96C2×D172—21no—
97C2×D172—21no—
98C2×D172—21no—
99C2×C4×D43—41no—
100C2×Dic86—21no—
101C4⋊C4×C43—41no—
102C4⋊C4×C43—41no—
103C22⋊C4×C43—44no—
104C22⋊C4×C43—82no—
105C22⋊C4×C43—82no—
106C42×C43—21no—
107C42×C43—21no—
108C42×C43—21no—
109C42×C43D812yescomplemented
110C42×C43C22×C411yescharacteristic
111C42×C43C2×D411yescharacteristic
112C42×C43#4111yescharacteristic
113C42×C43#4111yescharacteristic
114#10621882—84no—
115(C2×D43)⋊C4—41no—
116(C2×D43)⋊C4—41no—
117C4⋊Dic43—21no—
118C4⋊Dic43—21no—
119#10621877—41no—
120#10621877—41no—
121C2×C43⋊C8—22no—
122C2×C43⋊C8—41no—
123C2×C43⋊C8—41no—
124C23×C43—24no—
125C23×C43—42no—
126C23×C43—42no—
127C23×C43—42no—
128C23×C43—42no—
129C23×C43—42no—
130C23×C43—42no—
131C23×C43#12011yescharacteristic
132C22×D43—41no—
133D4×C43—44no—
134D4×C43—42no—
135D4×C43—42no—
136D4×C43—42no—
137D4×C43—42no—
138D4×C43—82no—
139D4×C43—82no—
140D4×C43—82no—
141C2×C4×C43—22no—
142C2×C4×C43—41no—
143C2×C4×C43—41no—
144C2×C4×C43—41no—
145C2×C4×C43—41no—
146C2×C4×C43—41no—
147C2×C4×C43—41no—
148C2×C4×C43—42no—
149C2×C4×C43—42no—
150C2×C4×C43—42no—
151C2×C4×C43—41no—
152C2×C4×C43—88no—
153C2×C4×C43C2×C22⋊C411yescharacteristic
154C2×C4×C43C4×D411yescharacteristic
155C2×C4×C43C4×D411yescharacteristic
156C2×C4×C43#12111yescharacteristic
157C2×C4×C43#12111yescharacteristic
158C2×C4×C43#12311yescharacteristic
159C2×C4×C43C2×D811yescharacteristic
160C2×C4×C43#13511yescharacteristic
161C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
162C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
163C22⋊D43—81no—
164C22⋊D43—81no—
165C2×Dic43—41no—
166D172—42no—
167D172—41no—
168D172—41no—
169D172—81no—
170C4×D43—81no—
171C4×D43—81no—
172Dic86—41no—
173Dic86—41no—
174C43⋊C8—42no—
175C43⋊C8—81no—
176C43⋊C8—81no—
177#9299—431nomaximal, Sylow
178C22×C43—21no—
179C22×C43—21no—
180C22×C43—44no—
181C22×C43—44no—
182C22×C43—44no—
183C22×C43—82no—
184C22×C43—82no—
185C22×C43—82no—
186C22×C43—82no—
187C22×C43#38611yescharacteristic
188C22×C43#44711yescharacteristic
189C22×C43#44911yescharacteristic
190C2×D43—81no—
191C2×D43—81no—
192C2×D43—81no—
193C4×C43—21no—
194C4×C43—21no—
195C4×C43—21no—
196C4×C43—21no—
197C4×C43—42no—
198C4×C43—81no—
199C4×C43—82no—
200C4×C43C4×D811yescharacteristic
201C4×C43#44211yescharacteristic
202C4×C43#45911yescharacteristic
203C4×C43#46311yescharacteristic
204Dic43—81no—
205#3205—431no—
206#2328D4311yescharacteristic, complemented
207#1963—431no—
208#1545—431no—
209#1517—431no—
210#1286—431no—
211#1274—431no—
212C2×C43—21no—
213C2×C43—21no—
214C2×C43—84no—
215C2×C43#187911yescharacteristic
216C2×C43#190411yescharacteristic
217C2×C43#191111yescharacteristic
218D43—161no—
219#532—431no—
220C2×#127C2×D4311yescharacteristic
221C2×C4×D4—21no—
222#493—432no—
223#486—432no—
224#459—862no—
225#447—862no—
226#431—431no—
227#431—431no—
228#423—431no—
229C2×#104—861no—
230C2×#104—861no—
231#390—21no—
232#386—22no—
233#386—22no—
234#382C2×D4311yescharacteristic
235#376C2×D4311yescharacteristic
236#331—862no—
237#327—862no—
238C43#929911yescharacteristic, complemented, Sylow
239C2×#41—861no—
240C22×D4—21no—
241C22×D4—21no—
242C22×D4C22⋊D4312yes—
243C23×C4—22no—
244C2×D8—864no—
245C2×M16—861no—
246C4⋊Q8—431no—
247#127—21no—
248#127—21no—
249#127—431no—
250#127C4×D4312yes—
251#127D17212yes—
252#124—861no—
253#121—861no—
254#121—861no—
255C4×D4—42no—
256C4×D4—42no—
257C4×D4—861no—
258C4×D4—861no—
259C2×C4⋊C4—21no—
260C2×C22⋊C4—22no—
261C2×C22⋊C4—22no—
262C2×C22⋊C4—22no—
263C2×C42C22⋊D4311yescharacteristic
264C2×C42C22⋊D4311yescharacteristic
265C2×C42C22×D4311yescharacteristic
266C4⋊C8—861no—
267C4⋊C8—861no—
268C4⋊C8—861no—
269C4⋊C8—861no—
270#104—1722no—
271#104—1722no—
272#102—864no—
273C22⋊C8—861no—
274C22⋊C8—861no—
275C4×C8—432no—
276C4×C8—861no—
277#95—21no—
278#95—21no—
279#95—21no—
280#95C22⋊D4312yes—
281C24—22no—
282#41—1721no—
283#41—1721no—
284#41—1721no—
285#41—1721no—
286C2×Q8—861no—
287C2×D4—22no—
288C2×D4—22no—
289C2×D4—22no—
290C2×D4—22no—
291C2×D4—22no—
292C2×D4—41no—
293C2×D4—41no—
294C2×D4—41no—
295C2×D4—41no—
296C2×D4—82no—
297C2×D4—82no—
298C2×D4—861no—
299C2×D4—861no—
300C2×D4—861no—
301C2×D4—1721no—
302C2×D4(C2×D43)⋊C414yes—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—22no—
306C22×C4—44no—
307C22×C4—82no—
308C22×C4—82no—
309C22×C4—1721no—
310C22×C4C2×C22⋊D4311yescharacteristic
311C22×C4C2×C22⋊D4311yescharacteristic
312C22×C4C2×C22⋊D4311yescharacteristic
313D8—3444no—
314M16—1721no—
315M16—1721no—
316C2×C8—862no—
317C2×C8—1721no—
318C2×C8—1721no—
319C4⋊C4—41no—
320C4⋊C4—41no—
321C4⋊C4—861no—
322C4⋊C4—861no—
323C22⋊C4—44no—
324C22⋊C4—82no—
325C22⋊C4—82no—
326C22⋊C4—1721no—
327C22⋊C4—1721no—
328C42—21no—
329C42—21no—
330C42—21no—
331C42#1062188212yescomplemented
332C42C2×C4×D4311yescharacteristic
333C42C2×D17211yescharacteristic
334C42#1062189811yescharacteristic
335C42#1062189811yescharacteristic
336C23—24no—
337C23—42no—
338C23—42no—
339C23—42no—
340C23—42no—
341C23—42no—
342C23—42no—
343C23—1721no—
344C23#1306329411yescharacteristic
345Q8—1721no—
346Q8—1721no—
347D4—44no—
348D4—42no—
349D4—42no—
350D4—42no—
351D4—42no—
352D4—82no—
353D4—82no—
354D4—82no—
355D4—3441no—
356D4—3441no—
357D4—3441no—
358D4—1722no—
359D4—1721no—
360D4—1721no—
361C2×C4—22no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—42no—
369C2×C4—42no—
370C2×C4—41no—
371C2×C4—42no—
372C2×C4—88no—
373C2×C4—3441no—
374C2×C4—3441no—
375C2×C4—1721no—
376C2×C4C2×(C2×D43)⋊C411yescharacteristic
377C2×C4C4×C22⋊D4311yescharacteristic
378C2×C4C4×C22⋊D4311yescharacteristic
379C2×C4#1306329911yescharacteristic
380C2×C4#1306329911yescharacteristic
381C2×C4#1306330811yescharacteristic
382C2×C4C2×#1062188211yescharacteristic
383C2×C4#1306334511yescharacteristic
384C2×C4#1306335011yescharacteristic
385C2×C4#1306335111yescharacteristic
386C8—3441no—
387C8—3441no—
388C8—1722no—
389C22—21no—
390C22—21no—
391C22—44no—
392C22—44no—
393C22—44no—
394C22—82no—
395C22—82no—
396C22—82no—
397C22—82no—
398C22—3441no—
399C22—3441no—
400C22—3441no—
401C22#1458277811yescharacteristic
402C22#1458303311yescharacteristic
403C22#1458304411yescharacteristic
404C4—21no—
405C4—21no—
406C4—21no—
407C4—21no—
408C4—42no—
409C4—82no—
410C4—81no—
411C4—3441no—
412C4C4×#1062188211yescharacteristic
413C4#1458300911yescharacteristic
414C4#1458309411yescharacteristic
415C4#1458311411yescharacteristic
416C2—21no—
417C2—21no—
418C2—84no—
419C2—6881no—
420C2#1913494311yescharacteristic
421C2#1913508211yescharacteristic
422C2#1913512711yescharacteristic
subgroupG/H
centerC22#14582778
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#2328C2
socleC22×C43#386
prime radical#19145513C2
cosocleC2×C42×C43C23
hypercenter#2328D43
hypocenterC43#9299
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2328

Complements

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

NH ≅ G/Ntype
2. #19135427C2semidirect
3. #19133263C2semidirect
4. #19133154C2semidirect
5. #19132453C2semidirect
6. #19132424C2semidirect
7. C43×#2328C2semidirect
9. #14583275C4semidirect
10. #14583245C4semidirect
30. #13063325C2×C4semidirect
31. #13063322C2×C4semidirect
47. C4×C43⋊C8C2×C4semidirect
109. C42×C43D8semidirect
206. #2328D43semidirect
238. C43#9299semidirect
331. C42#10621882semidirect

Maximal subgroups

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

subgroupindex
#191455132
#191354272
#191332632
#191331542
#191324532
#191324242
C43×#23282
#929943