Finite Group Databasebeta

← #24992893

Subgroups — #24992893

Order 11008.

588 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144591C211yesmaximal, characteristic
2#19137059C211yesmaximal, characteristic, complemented
3#19133090C211yesmaximal, characteristic, complemented
4#19133019C211yesmaximal, characteristic, complemented
5#19132496C211yesmaximal, characteristic, complemented
6#19132428C211yesmaximal, characteristic, complemented
7C43×#1962C211yesmaximal, characteristic, complemented
8C2×C4×D172C2211yescharacteristic
9C2×#13063282—21no—
10#14583210—21no—
11#14583176C412yescomplemented
12#14583091C412yescomplemented
13#14583032—21no—
14C4×#10621882—22no—
15#14582952C2211yescharacteristic
16#14582952C2211yescharacteristic
17#14582801—21no—
18#14582797—21no—
19#14582790—22no—
20C4×C4⋊Dic43C2211yescharacteristic
21C4×(C2×D43)⋊C4—21no—
22#14582633—22no—
23#14582626—22no—
24C43×#532C2211yescharacteristic
25C43×#423C2211yescharacteristic
26C2×#104×C43—21no—
27C2×#104×C43—21no—
28C43×C43C2211yescharacteristic
29C22×D172D411yescharacteristic
30C22×C4×D43—21no—
31C2×#10621882—22no—
32C4×D172—21no—
33C4×D172—21no—
34C4×D172C2×C412yes—
35C4×D172D412yes—
36#13063282—42no—
37#13063282—42no—
38C2×C4⋊Dic43—21no—
39C2×C4⋊Dic43D411yescharacteristic
40C2×Dic43⋊C4—22no—
41C2×(C2×D43)⋊C4—21no—
42C2×(C2×D43)⋊C4—22no—
43C2×(C2×D43)⋊C4—22no—
44C2×C4×Dic43—21no—
45#13063258—22no—
46C4⋊(C43⋊C8)—21no—
47C4⋊(C43⋊C8)C2×C412yes—
48#13063246—22no—
49#13063245—22no—
50C22⋊(C43⋊C8)—21no—
51C22⋊(C43⋊C8)—21no—
52C4×C43⋊C8—21no—
53C4×C43⋊C8—21no—
54C43⋊#95—22no—
55C43⋊#95D412yes—
56C2×#41×C43—21no—
57C2×M16×C43—21no—
58C4⋊Q8×C43C2×C411yescharacteristic
59#127×C43C2×C411yescharacteristic
60#124×C43—21no—
61#121×C43—21no—
62#121×C43—21no—
63C4×D4×C43—21no—
64C4×D4×C43—21no—
65C2×C42×C43—21no—
66C2×C42×C43—21no—
67C2×C42×C43D411yescharacteristic
68C2×C42×C43D411yescharacteristic
69C2×C42×C43C2311yescharacteristic
70C4⋊C8×C43—21no—
71C4⋊C8×C43—21no—
72#104×C43—42no—
73#104×C43—42no—
74C23×D43—21no—
75#41×C43—41no—
76#41×C43—41no—
77#41×C43—41no—
78#41×C43—41no—
79C2×Q8×C43—21no—
80C2×D4×C43—21no—
81C2×D4×C43—21no—
82C2×D4×C43—21no—
83C2×D4×C43—41no—
84C22×C4×C43—21no—
85C22×C4×C43—21no—
86C22×C4×C43—41no—
87C22×C4×C43C2×D411yescharacteristic
88C22×C4×C43C2×D411yescharacteristic
89C22×C4×C43C2×D411yescharacteristic
90C22×Dic43—21no—
91C22×Dic43—22no—
92C2×D172—21no—
93C2×D172—42no—
94C2×D172C22⋊C412yes—
95C2×C4×D43—22no—
96C2×C4×D43—22no—
97C2×C4×D43—41no—
98C2×C4×D43—41no—
99C2×C4×D43—41no—
100C2×C4×D43—41no—
101M16×C43—41no—
102M16×C43—41no—
103C2×C8×C43—41no—
104C4⋊C4×C43—21no—
105C4⋊C4×C43—21no—
106C22⋊C4×C43—41no—
107C22⋊C4×C43—41no—
108C42×C43—21no—
109C42×C43—21no—
110C42×C43—21no—
111C42×C43—42no—
112C42×C43—42no—
113C42×C43D812yescomplemented
114C42×C43C22×C411yescharacteristic
115C42×C43C2×D411yescharacteristic
116C42×C43#4111yescharacteristic
117C42×C43#4111yescharacteristic
118#10621882—44no—
119(C2×D43)⋊C4—22no—
120(C2×D43)⋊C4—22no—
121(C2×D43)⋊C4—44no—
122(C2×D43)⋊C4—44no—
123C4⋊Dic43—21no—
124C4⋊Dic43—42no—
125C4⋊Dic43C22⋊C412yes—
126Dic43⋊C4—44no—
127C4×Dic43—41no—
128C4×Dic43—41no—
129C2×C43⋊C8—22no—
130C2×C43⋊C8—41no—
131C23×C43—41no—
132C23×C43#12011yescharacteristic
133C22×D43—22no—
134C22×D43—42no—
135C22×D43—42no—
136C22×D43—41no—
137C22×D43—41no—
138Q8×C43—41no—
139Q8×C43—41no—
140D4×C43—42no—
141D4×C43—41no—
142D4×C43—41no—
143D4×C43—81no—
144D4×C43—81no—
145D4×C43—81no—
146C2×C4×C43—22no—
147C2×C4×C43—22no—
148C2×C4×C43—22no—
149C2×C4×C43—41no—
150C2×C4×C43—41no—
151C2×C4×C43—41no—
152C2×C4×C43—41no—
153C2×C4×C43—41no—
154C2×C4×C43—41no—
155C2×C4×C43—81no—
156C2×C4×C43—81no—
157C2×C4×C43C2×C22⋊C411yescharacteristic
158C2×C4×C43C4×D411yescharacteristic
159C2×C4×C43C4×D411yescharacteristic
160C2×C4×C43#12111yescharacteristic
161C2×C4×C43#12111yescharacteristic
162C2×C4×C43#12311yescharacteristic
163C2×C4×C43C2×D811yescharacteristic
164C2×C4×C43#13511yescharacteristic
165C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
166C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
167C2×Dic43—22no—
168C2×Dic43—41no—
169C2×Dic43—41no—
170C2×Dic43—42no—
171C2×Dic43—42no—
172C2×Dic43—42no—
173D172—22no—
174D172—22no—
175D172—42no—
176C4×D43—42no—
177C4×D43—42no—
178C4×D43—42no—
179C4×D43—42no—
180C8×C43—81no—
181C43⋊C8—42no—
182C43⋊C8—81no—
183#9237—431nomaximal, Sylow
184C22×C43—21no—
185C22×C43—21no—
186C22×C43—81no—
187C22×C43—81no—
188C22×C43—81no—
189C22×C43#38611yescharacteristic
190C22×C43#44711yescharacteristic
191C22×C43#44911yescharacteristic
192C2×D43—42no—
193C2×D43—42no—
194C2×D43—42no—
195C2×D43—82no—
196C2×D43—82no—
197C4×C43—21no—
198C4×C43—21no—
199C4×C43—21no—
200C4×C43—42no—
201C4×C43—42no—
202C4×C43—81no—
203C4×C43#42112yes—
204C4×C43C4×D811yescharacteristic
205C4×C43#44211yescharacteristic
206C4×C43#45911yescharacteristic
207C4×C43#46311yescharacteristic
208Dic43—42no—
209Dic43—82no—
210#3100—431no—
211#2293—431no—
212#1962D4311yescharacteristic, complemented
213#1502—431no—
214#1486—431no—
215#1303—431no—
216#1276—431no—
217C2×C43—21no—
218C2×C43—21no—
219C2×C43—161no—
220C2×C43#187911yescharacteristic
221C2×C43#189711yescharacteristic
222C2×C43#190611yescharacteristic
223D43—82no—
224#532C2×D4311yescharacteristic
225C2×C4×D4—431no—
226C2×#117—861no—
227#480—861no—
228#474—432no—
229#459—432no—
230#447—861no—
231C4×D8—862no—
232#431—431no—
233#431—431no—
234#423C2×D4311yescharacteristic
235C2×#104—21no—
236C2×#104—21no—
237#390—861no—
238#389—861no—
239#388—862no—
240C4×C4⋊C4—431no—
241C4×C22⋊C4—861no—
242C43C2×D4311yescharacteristic
243#327—862no—
244D4⋊C8—862no—
245C43#923711yescharacteristic, complemented, Sylow
246C2×#41—21no—
247C22×D4—431no—
248C23×C4—861no—
249C2×D8—862no—
250C2×M16—21no—
251C4⋊Q8C4×D4311yescharacteristic
252#127C4×D4311yescharacteristic
253#124—21no—
254#121—21no—
255#121—21no—
256C4×D4—21no—
257C4×D4—21no—
258C4×D4—432no—
259C4×D4—432no—
260C4×D4—861no—
261C4×D4—861no—
262#117—1722no—
263#117—1722no—
264C2×C4⋊C4—431no—
265C2×C4⋊C4—862no—
266C2×C4⋊C4—861no—
267C2×C22⋊C4—861no—
268C2×C22⋊C4—862no—
269C2×C22⋊C4—862no—
270C2×C42—21no—
271C2×C42—21no—
272C2×C42—861no—
273C2×C42C22⋊D4311yescharacteristic
274C2×C42C22⋊D4311yescharacteristic
275C2×C42C22×D4311yescharacteristic
276#107—862no—
277C4⋊C8—21no—
278C4⋊C8—21no—
279C4⋊C8—432no—
280C4⋊C8—861no—
281#104—42no—
282#104—42no—
283#102—862no—
284#102—862no—
285C22⋊C8—861no—
286C22⋊C8—861no—
287C4×C8—861no—
288C4×C8—861no—
289#95—432no—
290#95—862no—
291C24—861no—
292#41—41no—
293#41—41no—
294#41—41no—
295#41—41no—
296C2×Q8—21no—
297C2×D4—21no—
298C2×D4—21no—
299C2×D4—21no—
300C2×D4—41no—
301C2×D4—432no—
302C2×D4—861no—
303C2×D4—1722no—
304C22×C4—21no—
305C22×C4—21no—
306C22×C4—41no—
307C22×C4—861no—
308C22×C4—862no—
309C22×C4—862no—
310C22×C4—862no—
311C22×C4—1721no—
312C22×C4—1721no—
313C22×C4—1721no—
314C22×C4—1721no—
315C22×C4D4×D4311yescharacteristic
316C22×C4D4×D4311yescharacteristic
317C22×C4C2×C22⋊D4311yescharacteristic
318D8—1724no—
319M16—41no—
320M16—41no—
321C2×C8—41no—
322C2×C8—862no—
323C2×C8—1721no—
324C4⋊C4—21no—
325C4⋊C4—21no—
326C4⋊C4—432no—
327C4⋊C4—861no—
328C4⋊C4—1724no—
329C4⋊C4—1722no—
330C22⋊C4—41no—
331C22⋊C4—41no—
332C22⋊C4—862no—
333C22⋊C4—862no—
334C22⋊C4—1724no—
335C22⋊C4—1724no—
336C42—21no—
337C42—21no—
338C42—21no—
339C42—42no—
340C42—42no—
341C42—1721no—
342C42—1721no—
343C42#1062188212yescomplemented
344C42C2×C4×D4311yescharacteristic
345C42#1062189811yescharacteristic
346C42D4×D4311yescharacteristic
347C42#1062190011yescharacteristic
348C23—41no—
349C23—862no—
350C23—1722no—
351C23—1722no—
352C23—1721no—
353C23—1721no—
354C23#1306329311yescharacteristic
355Q8—41no—
356Q8—41no—
357D4—42no—
358D4—41no—
359D4—41no—
360D4—81no—
361D4—81no—
362D4—81no—
363D4—862no—
364D4—862no—
365D4—1722no—
366C2×C4—22no—
367C2×C4—22no—
368C2×C4—22no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—81no—
376C2×C4—81no—
377C2×C4—862no—
378C2×C4—1722no—
379C2×C4—1722no—
380C2×C4—1722no—
381C2×C4—1721no—
382C2×C4—1721no—
383C2×C4—1722no—
384C2×C4—1722no—
385C2×C4—1722no—
386C2×C4—1722no—
387C2×C4C22⋊C4×D4311yescharacteristic
388C2×C4(C22⋊D43)⋊C411yescharacteristic
389C2×C4C4×C22⋊D4311yescharacteristic
390C2×C4#1306329611yescharacteristic
391C2×C4#1306329811yescharacteristic
392C2×C4#1306330711yescharacteristic
393C2×C4C2×#1062188211yescharacteristic
394C2×C4#1306334511yescharacteristic
395C2×C4#1306335011yescharacteristic
396C2×C4#1306335111yescharacteristic
397C8—81no—
398C8—3441no—
399C8—1722no—
400C22—21no—
401C22—21no—
402C22—81no—
403C22—81no—
404C22—81no—
405C22—3442no—
406C22—3442no—
407C22—1722no—
408C22—1722no—
409C22—1722no—
410C22#1458277511yescharacteristic
411C22#1458303211yescharacteristic
412C22#1458304211yescharacteristic
413C4—21no—
414C4—21no—
415C4—21no—
416C4—42no—
417C4—42no—
418C4—81no—
419C4—3442no—
420C4—1722no—
421C4#1458291412yes—
422C4C4×#1062188211yescharacteristic
423C4#1458300911yescharacteristic
424C4#1458309111yescharacteristic
425C4#1458311111yescharacteristic
426C2—21no—
427C2—21no—
428C2—161no—
429C2—3442no—
430C2#1913494611yescharacteristic
431C2#1913504011yescharacteristic
432C2#1913509911yescharacteristic
subgroupG/H
centerC2×C4#13063296
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1962C2
socleC22×C43#386
prime radical#19144591C2
cosocleC2×C42×C43C23
hypercenter#1962D43
hypocenterC43#9237
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1962

Complements

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

NH ≅ G/Ntype
2. #19137059C2semidirect
3. #19133090C2semidirect
4. #19133019C2semidirect
5. #19132496C2semidirect
6. #19132428C2semidirect
7. C43×#1962C2semidirect
11. #14583176C4semidirect
12. #14583091C4semidirect
113. C42×C43D8semidirect
212. #1962D43semidirect
245. C43#9237semidirect
343. C42#10621882semidirect

Maximal subgroups

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

subgroupindex
#191445912
#191370592
#191330902
#191330192
#191324962
#191324282
C43×#19622
#923743