Finite Group Databasebeta

← #24992848

Subgroups — #24992848

Order 11008.

686 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144603C211yesmaximal, characteristic
2#19135572C211yesmaximal, characteristic, complemented
3#19133093C211yesmaximal, characteristic, complemented
4#19133020C211yesmaximal, characteristic
5#19132498C211yesmaximal, characteristic, complemented
6#19132428C211yesmaximal, characteristic, complemented
7C42×D4×C43C211yesmaximal, characteristic
8#14583456C2211yescharacteristic
9#14583229—21no—
10#14583189C412yescomplemented
11#14583104C412yescomplemented
12#14583050—21no—
13C4×#10621883—22no—
14#14582952C2211yescharacteristic
15#14582952C2211yescharacteristic
16#14582923C2211yescharacteristic
17#14582659—21no—
18#14582659—21no—
19#14582635—22no—
20D4⋊(C43⋊C8)—22no—
21C2×C4×D4×C43—21no—
22C2×C4×D4×C43C2211yescharacteristic
23C22×C42×C43—21no—
24C4×C4⋊C4×C43—21no—
25C4×C4⋊C4×C43C2211yescharacteristic
26C4×C22⋊C4×C43—21no—
27C4×C22⋊C4×C43—22no—
28C43×C43C2211yescharacteristic
29C2×#10621883—22no—
30C2×#10621877—21no—
31#13063325C2×C411yescharacteristic, complemented
32#13063325C2×C411yescharacteristic, complemented
33#13063317—21no—
34#13063304—21no—
35#13063304—21no—
36C4×Dic86—21no—
37C4×Dic86—21no—
38#13063284—21no—
39#13063256—22no—
40C4⋊(C43⋊C8)—21no—
41C4⋊(C43⋊C8)—21no—
42C4⋊(C43⋊C8)—21no—
43C4⋊(C43⋊C8)C2×C412yescomplemented
44#13063248—22no—
45#13063246—22no—
46C22⋊(C43⋊C8)—21no—
47C22⋊(C43⋊C8)—21no—
48C4×C43⋊C8—21no—
49C4×C43⋊C8—21no—
50C22×D4×C43D411yescharacteristic
51C23×C4×C43—22no—
52C23×C4×C43—21no—
53C4×D4×C43—28no—
54C4×D4×C43—21no—
55C4×D4×C43—21no—
56C4×D4×C43C2×C412yes—
57C4×D4×C43D412yes—
58C2×C4⋊C4×C43—21no—
59C2×C4⋊C4×C43D411yescharacteristic
60C2×C22⋊C4×C43—22no—
61C2×C22⋊C4×C43—21no—
62C2×C42×C43—21no—
63C2×C42×C43—22no—
64C2×C42×C43—21no—
65C2×C42×C43—21no—
66C2×C42×C43—42no—
67C2×C42×C43—42no—
68C2×C42×C43D411yescharacteristic
69C2×C42×C43D411yescharacteristic
70C2×C42×C43C2311yescharacteristic
71#95×C43—22no—
72#95×C43D412yes—
73C24×C43—21no—
74C2×D4×C43—24no—
75C2×D4×C43—21no—
76C2×D4×C43C22⋊C412yes—
77C22×C4×C43—28no—
78C22×C4×C43—22no—
79C22×C4×C43—22no—
80C22×C4×C43—21no—
81C22×C4×C43—21no—
82C22×C4×C43—21no—
83C22×C4×C43—22no—
84C22×C4×C43—44no—
85C22×C4×C43—44no—
86C22×C4×C43—41no—
87C22×C4×C43—41no—
88C22×C4×C43—41no—
89C22×C4×C43—41no—
90C22×C4×C43C2×D411yescharacteristic
91C22×C4×C43C2×D411yescharacteristic
92C22×C4×C43C2×D411yescharacteristic
93C2×Dic86—21no—
94C2×Dic86—21no—
95C4⋊C4×C43—24no—
96C4⋊C4×C43—21no—
97C4⋊C4×C43C22⋊C412yes—
98C22⋊C4×C43—28no—
99C22⋊C4×C43—22no—
100C22⋊C4×C43—22no—
101C42×C43—24no—
102C42×C43—21no—
103C42×C43—21no—
104C42×C43—21no—
105C42×C43—42no—
106C42×C43—44no—
107C42×C43—41no—
108C42×C43—41no—
109C42×C43SD1612yescomplemented
110C42×C43C22×C411yescharacteristic
111C42×C43C2×D411yescharacteristic
112C42×C43#4111yescharacteristic
113C42×C43#4111yescharacteristic
114C22⋊Dic43—41no—
115#10621883—44no—
116C4⋊Dic43—21no—
117C4⋊Dic43—21no—
118C4⋊Dic43—21no—
119C4⋊Dic43—21no—
120Dic43⋊C4—41no—
121Dic43⋊C4—41no—
122C4×Dic43—41no—
123#10621877—41no—
124#10621877—41no—
125C2×C43⋊C8—22no—
126C2×C43⋊C8—41no—
127C2×C43⋊C8—41no—
128C23×C43—24no—
129C23×C43—22no—
130C23×C43—42no—
131C23×C43—41no—
132C23×C43—41no—
133C23×C43#12011yescharacteristic
134D4×C43—24no—
135D4×C43—22no—
136D4×C43#10414yes—
137C2×C4×C43—22no—
138C2×C4×C43—22no—
139C2×C4×C43—22no—
140C2×C4×C43—22no—
141C2×C4×C43—22no—
142C2×C4×C43—24no—
143C2×C4×C43—22no—
144C2×C4×C43—41no—
145C2×C4×C43—416no—
146C2×C4×C43—41no—
147C2×C4×C43—42no—
148C2×C4×C43—42no—
149C2×C4×C43—41no—
150C2×C4×C43—41no—
151C2×C4×C43—41no—
152C2×C4×C43—42no—
153C2×C4×C43—42no—
154C2×C4×C43—42no—
155C2×C4×C43—42no—
156C2×C4×C43C2×C22⋊C411yescharacteristic
157C2×C4×C43C4×D411yescharacteristic
158C2×C4×C43C4×D411yescharacteristic
159C2×C4×C43#12111yescharacteristic
160C2×C4×C43#12111yescharacteristic
161C2×C4×C43#12311yescharacteristic
162C2×C4×C43C2×SD1611yescharacteristic
163C2×C4×C43#13511yescharacteristic
164C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
165C2×C4×C43#13711yescharacteristic
166C2×Dic43—41no—
167C2×Dic43—41no—
168Dic86—42no—
169Dic86—81no—
170C43⋊C8—42no—
171C43⋊C8—81no—
172C43⋊C8—81no—
173#9231—431nomaximal, Sylow
174C22×C43—21no—
175C22×C43—21no—
176C22×C43—24no—
177C22×C43—44no—
178C22×C43—44no—
179C22×C43—42no—
180C22×C43—42no—
181C22×C43#38611yescharacteristic
182C22×C43#45011yescharacteristic
183C22×C43#45211yescharacteristic
184C4×C43—24no—
185C4×C43—21no—
186C4×C43—21no—
187C4×C43—21no—
188C4×C43—42no—
189C4×C43—44no—
190C4×C43—42no—
191C4×C43C2×#10412yes—
192C4×C43C4×SD1611yescharacteristic
193C4×C43#44011yescharacteristic
194C4×C43#46111yescharacteristic
195C4×C43#46311yescharacteristic
196Dic43—81no—
197Dic43—81no—
198#3101—431no—
199C42×D4D4311yescharacteristic
200#1994—431no—
201#1503—431no—
202#1486—431no—
203#1303—431no—
204#1276—431no—
205C2×C43—21no—
206C2×C43—21no—
207C2×C43—44no—
208C2×C43#187711yescharacteristic
209C2×C43#189611yescharacteristic
210C2×C43#190611yescharacteristic
211#533—431no—
212C2×C4×D4—21no—
213C2×C4×D4C2×D4311yescharacteristic
214C22×C42—21no—
215#483—861no—
216#476—432no—
217#461—432no—
218#450—861no—
219C4×SD16—862no—
220#431—431no—
221#431—431no—
222#423—431no—
223C4×C4⋊C4—21no—
224C4×C4⋊C4C2×D4311yescharacteristic
225C4×C22⋊C4—21no—
226C4×C22⋊C4—22no—
227C43C2×D4311yescharacteristic
228#339—861no—
229#339—861no—
230#328—862no—
231D4⋊C8—862no—
232C43#923111yescharacteristic, complemented, Sylow
233C22×D4C22⋊D4311yescharacteristic
234C23×C4—22no—
235C23×C4—21no—
236C2×SD16—862no—
237C2×M16—861no—
238C4⋊Q8—431no—
239C4⋊Q8—431no—
240#125—861no—
241C22⋊Q8—861no—
242C22⋊Q8—861no—
243C4×Q8—861no—
244C4×Q8—861no—
245C4×D4—28no—
246C4×D4—21no—
247C4×D4—21no—
248C4×D4C4×D4312yes—
249C4×D4D17212yes—
250#117—861no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4C22⋊D4311yescharacteristic
253C2×C22⋊C4—22no—
254C2×C22⋊C4—21no—
255C2×C42—21no—
256C2×C42—22no—
257C2×C42—21no—
258C2×C42—21no—
259C2×C42—42no—
260C2×C42—42no—
261C2×C42C22⋊D4311yescharacteristic
262C2×C42C22⋊D4311yescharacteristic
263C2×C42C22×D4311yescharacteristic
264#106—862no—
265C4⋊C8—432no—
266C4⋊C8—861no—
267C4⋊C8—861no—
268C4⋊C8—861no—
269#103—862no—
270#102—862no—
271C22⋊C8—861no—
272C22⋊C8—861no—
273C4×C8—861no—
274C4×C8—861no—
275#95—22no—
276#95C22⋊D4312yes—
277C24—21no—
278C2×Q8—861no—
279C2×Q8—861no—
280C2×D4—24no—
281C2×D4—21no—
282C2×D4(C2×D43)⋊C412yes—
283C22×C4—21no—
284C22×C4—28no—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—22no—
288C22×C4—22no—
289C22×C4—22no—
290C22×C4—44no—
291C22×C4—44no—
292C22×C4—41no—
293C22×C4—41no—
294C22×C4—41no—
295C22×C4—41no—
296C22×C4C2×C22⋊D4311yescharacteristic
297C22×C4C2×C22⋊D4311yescharacteristic
298C22×C4C2×C22⋊D4311yescharacteristic
299SD16—1724no—
300M16—1721no—
301M16—1721no—
302C2×C8—862no—
303C2×C8—1721no—
304C2×C8—1721no—
305C4⋊C4—24no—
306C4⋊C4—21no—
307C4⋊C4—861no—
308C4⋊C4—861no—
309C4⋊C4—861no—
310C4⋊C4—861no—
311C4⋊C4—1721no—
312C4⋊C4—1721no—
313C4⋊C4(C2×D43)⋊C412yes—
314C22⋊C4—28no—
315C22⋊C4—22no—
316C22⋊C4—22no—
317C22⋊C4—1721no—
318C42—24no—
319C42—21no—
320C42—21no—
321C42—21no—
322C42—44no—
323C42—42no—
324C42—41no—
325C42—41no—
326C42—1721no—
327C42#1062188312yescomplemented
328C42C2×C4×D4311yescharacteristic
329C42C2×D17211yescharacteristic
330C42#1062189811yescharacteristic
331C42#1062189811yescharacteristic
332C23—24no—
333C23—22no—
334C23—42no—
335C23—41no—
336C23—41no—
337C23#1306329411yescharacteristic
338Q8—3441no—
339Q8—1722no—
340D4—24no—
341D4—22no—
342D4#1306325314yes—
343C2×C4—22no—
344C2×C4—22no—
345C2×C4—22no—
346C2×C4—22no—
347C2×C4—22no—
348C2×C4—24no—
349C2×C4—22no—
350C2×C4—41no—
351C2×C4—416no—
352C2×C4—41no—
353C2×C4—42no—
354C2×C4—42no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—42no—
359C2×C4—42no—
360C2×C4—42no—
361C2×C4—42no—
362C2×C4—1721no—
363C2×C4—1721no—
364C2×C4C2×(C2×D43)⋊C411yescharacteristic
365C2×C4C4×C22⋊D4311yescharacteristic
366C2×C4C4×C22⋊D4311yescharacteristic
367C2×C4#1306329911yescharacteristic
368C2×C4#1306329911yescharacteristic
369C2×C4#1306330811yescharacteristic
370C2×C4C2×#1062188311yescharacteristic
371C2×C4#1306334511yescharacteristic
372C2×C4#1306335111yescharacteristic
373C2×C4#1306335511yescharacteristic
374C8—3441no—
375C8—3441no—
376C8—1722no—
377C22—21no—
378C22—21no—
379C22—24no—
380C22—44no—
381C22—44no—
382C22—42no—
383C22—42no—
384C22#1458277811yescharacteristic
385C22#1458305011yescharacteristic
386C22#1458306111yescharacteristic
387C4—24no—
388C4—21no—
389C4—21no—
390C4—21no—
391C4—44no—
392C4—42no—
393C4—42no—
394C4—3441no—
395C4—3441no—
396C4C2×#1306325312yes—
397C4C4×#1062188311yescharacteristic
398C4#1458299911yescharacteristic
399C4#1458310411yescharacteristic
400C4#1458311411yescharacteristic
401C2—21no—
402C2—21no—
403C2—44no—
404C2#1913492911yescharacteristic
405C2#1913503811yescharacteristic
406C2#1913509611yescharacteristic
subgroupG/H
centerC2×C4#13063299
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC42×D4×C43C2
socleC22×C43#386
prime radicalC22×D4×C43D4
cosocleC2×C42×C43C23
hypercenterC42×D4D43
hypocenterC43#9231
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C42×D4

Complements

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

NH ≅ G/Ntype
2. #19135572C2semidirect
3. #19133093C2semidirect
5. #19132498C2semidirect
6. #19132428C2semidirect
10. #14583189C4semidirect
11. #14583104C4semidirect
31. #13063325C2×C4semidirect
32. #13063325C2×C4semidirect
43. C4⋊(C43⋊C8)C2×C4semidirect
109. C42×C43SD16semidirect
232. C43#9231semidirect
327. C42#10621883semidirect

Maximal subgroups

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

subgroupindex
#191446032
#191355722
#191330932
#191330202
#191324982
#191324282
C42×D4×C432
#923143