Finite Group Databasebeta

← #24992849

Subgroups — #24992849

Order 11008.

686 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 686 conjugacy classes of subgroups — too many to draw. Only its 115 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144604C211yesmaximal, characteristic
2C4×#13063287C211yesmaximal, characteristic
3#19135571C211yesmaximal, characteristic, complemented
4#19133093C211yesmaximal, characteristic, complemented
5#19133019C211yesmaximal, characteristic
6#19132427C211yesmaximal, characteristic, complemented
7C43×#1303C211yesmaximal, characteristic, complemented
8#14583456C2211yescharacteristic
9C2×C4×D172C2211yescharacteristic
10C2×#13063287—21no—
11C2×C42×D43—21no—
12#14583230—21no—
13#14583190C412yescomplemented
14#14583105C412yescomplemented
15#14583052—21no—
16C4×#10621873—22no—
17#14582952C2211yescharacteristic
18C4⋊C4×Dic43—21no—
19C4×(C2×D43)⋊C4—21no—
20#14582746—22no—
21C42×Dic43C2211yescharacteristic
22#14582660—21no—
23#14582660—21no—
24#14582635—22no—
25#14582626—22no—
26C43×#431C2211yescharacteristic
27C43×#423C2211yescharacteristic
28C4×C4⋊C4×C43C2211yescharacteristic
29C22×D172D411yescharacteristic
30C22×C4×D43—22no—
31C22×C4×D43—21no—
32C2×#10621873—22no—
33#13063325C2×C411yescharacteristic, complemented
34#13063325C2×C411yescharacteristic, complemented
35#13063317—21no—
36#13063304—21no—
37#13063304—21no—
38C4×Dic86—21no—
39C4×Dic86—21no—
40C4×D172—21no—
41C4×D172—21no—
42C4×D172C2×C412yes—
43C4×D172D412yes—
44#13063287—28no—
45#13063284—21no—
46C2×C4⋊Dic43D411yescharacteristic
47C2×(C2×D43)⋊C4—22no—
48C2×(C2×D43)⋊C4—21no—
49C2×C4×Dic43—21no—
50C2×C4×Dic43—22no—
51C2×C4×Dic43—21no—
52C2×C4×Dic43D411yescharacteristic
53C2×C4×Dic43D411yescharacteristic
54C42×D43—42no—
55C42×D43—42no—
56#13063257—22no—
57C4⋊(C43⋊C8)—21no—
58#13063250—22no—
59#13063247—22no—
60C22⋊(C43⋊C8)—21no—
61C4×C43⋊C8—21no—
62C43⋊#95—22no—
63C2×M16×C43—21no—
64C2×C4⋊C4×C43—21no—
65C2×C42×C43—21no—
66C2×C42×C43C2311yescharacteristic
67C4⋊C8×C43—21no—
68C4⋊C8×C43—21no—
69C4⋊C8×C43C2×C412yescomplemented
70C22⋊C8×C43—21no—
71C4×C8×C43—21no—
72#95×C43D412yes—
73C23×D43—21no—
74C22×C4×C43—22no—
75C22×C4×C43C2×D411yescharacteristic
76C22×C4×C43C2×D411yescharacteristic
77C22×C4×C43C2×D411yescharacteristic
78C22×Dic43—21no—
79C22×Dic43—21no—
80C22×Dic43—21no—
81C2×D172—21no—
82C2×D172—24no—
83C2×D172C22⋊C412yes—
84C2×C4×D43—28no—
85C2×C4×D43—22no—
86C2×C4×D43—22no—
87C2×C4×D43—44no—
88C2×C4×D43—44no—
89C2×C4×D43—41no—
90C2×C4×D43—41no—
91C2×C4×D43—41no—
92C2×C4×D43—41no—
93C2×Dic86—21no—
94C2×Dic86—21no—
95M16×C43—41no—
96M16×C43—41no—
97C2×C8×C43—22no—
98C2×C8×C43—41no—
99C4⋊C4×C43—24no—
100C42×C43—41no—
101C42×C43—41no—
102C42×C43C22×C411yescharacteristic
103C42×C43C2×D411yescharacteristic
104C42×C43#4111yescharacteristic
105C42×C43#4111yescharacteristic
106C22⋊Dic43—41no—
107(C2×D43)⋊C4—28no—
108(C2×D43)⋊C4—22no—
109(C2×D43)⋊C4—22no—
110C4⋊Dic43—21no—
111C4⋊Dic43—21no—
112C4⋊Dic43—21no—
113C4⋊Dic43—21no—
114C4⋊Dic43—21no—
115C4⋊Dic43C22⋊C412yes—
116Dic43⋊C4—41no—
117Dic43⋊C4—41no—
118C4×Dic43—24no—
119C4×Dic43—21no—
120C4×Dic43—21no—
121C4×Dic43—21no—
122C4×Dic43—44no—
123C4×Dic43—42no—
124C4×Dic43—41no—
125C4×Dic43SD1612yescomplemented
126C2×C43⋊C8—41no—
127#10621873—44no—
128C23×C43#12011yescharacteristic
129C22×D43—24no—
130C22×D43—22no—
131C22×D43—42no—
132C22×D43—41no—
133C22×D43—41no—
134C2×C4×C43—22no—
135C2×C4×C43—24no—
136C2×C4×C43—41no—
137C2×C4×C43—42no—
138C2×C4×C43—42no—
139C2×C4×C43C2×C22⋊C411yescharacteristic
140C2×C4×C43C4×D411yescharacteristic
141C2×C4×C43C4×D411yescharacteristic
142C2×C4×C43#12111yescharacteristic
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
149C2×Dic43—22no—
150C2×Dic43—22no—
151C2×Dic43—22no—
152C2×Dic43—22no—
153C2×Dic43—22no—
154C2×Dic43—41no—
155C2×Dic43—41no—
156C2×Dic43—41no—
157C2×Dic43—41no—
158C2×Dic43—41no—
159C2×Dic43—41no—
160D172—24no—
161D172—22no—
162D172#10414yes—
163C4×D43—416no—
164C4×D43—42no—
165C4×D43—42no—
166C4×D43—42no—
167C4×D43—42no—
168Dic86—42no—
169Dic86—81no—
170C8×C43—42no—
171C8×C43—81no—
172C43⋊C8—81no—
173#9231—431nomaximal, Sylow
174C22×C43—21no—
175C22×C43—21no—
176C22×C43#38611yescharacteristic
177C22×C43#45011yescharacteristic
178C22×C43#45211yescharacteristic
179C2×D43—24no—
180C2×D43—44no—
181C2×D43—44no—
182C2×D43—42no—
183C2×D43—42no—
184C4×C43—21no—
185C4×C43—21no—
186C4×C43—21no—
187C4×C43—44no—
188C4×C43C2×#10412yes—
189C4×C43C4×SD1611yescharacteristic
190C4×C43#44011yescharacteristic
191C4×C43#46111yescharacteristic
192C4×C43#46311yescharacteristic
193Dic43—24no—
194Dic43—42no—
195Dic43—42no—
196Dic43—81no—
197Dic43—81no—
198#3101—431no—
199C42×D4—431no—
200#1994—431no—
201#1503—431no—
202#1486—431no—
203#1303D4311yescharacteristic, complemented
204#1276—431no—
205C2×C43—21no—
206C2×C43—21no—
207C2×C43#187711yescharacteristic
208C2×C43#189611yescharacteristic
209C2×C43#190611yescharacteristic
210D43—44no—
211#533—431no—
212C2×C4×D4—431no—
213C2×C4×D4—861no—
214C22×C42—861no—
215#483—861no—
216#476—432no—
217#461—432no—
218#450—861no—
219C4×SD16—862no—
220#431—431no—
221#431C2×D4311yescharacteristic
222#423C2×D4311yescharacteristic
223C4×C4⋊C4—861no—
224C4×C4⋊C4C2×D4311yescharacteristic
225C4×C22⋊C4—861no—
226C4×C22⋊C4—862no—
227C43—431no—
228#339—861no—
229#339—861no—
230#328—862no—
231D4⋊C8—862no—
232C43#923111yescharacteristic, complemented, Sylow
233C22×D4—431no—
234C23×C4—862no—
235C23×C4—861no—
236C2×SD16—862no—
237C2×M16—21no—
238C4⋊Q8—431no—
239C4⋊Q8—431no—
240#125—861no—
241C22⋊Q8—861no—
242C22⋊Q8—861no—
243C4×Q8—861no—
244C4×Q8—861no—
245C4×D4—432no—
246C4×D4—432no—
247C4×D4—868no—
248C4×D4—861no—
249C4×D4—861no—
250#117—861no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—431no—
253C2×C22⋊C4—862no—
254C2×C22⋊C4—861no—
255C2×C42—21no—
256C2×C42—431no—
257C2×C42—431no—
258C2×C42—861no—
259C2×C42—862no—
260C2×C42—861no—
261C2×C42—1722no—
262C2×C42—1722no—
263C2×C42C22×D4311yescharacteristic
264#106—862no—
265C4⋊C8—21no—
266C4⋊C8—21no—
267C4⋊C8—861no—
268C4⋊C8C4×D4312yescomplemented
269#103—862no—
270#102—862no—
271C22⋊C8—21no—
272C22⋊C8—861no—
273C4×C8—21no—
274C4×C8—861no—
275#95—862no—
276#95D17212yes—
277C24—861no—
278C2×Q8—861no—
279C2×Q8—861no—
280C2×D4—432no—
281C2×D4—864no—
282C2×D4—861no—
283C22×C4—22no—
284C22×C4—868no—
285C22×C4—861no—
286C22×C4—861no—
287C22×C4—861no—
288C22×C4—862no—
289C22×C4—862no—
290C22×C4—1724no—
291C22×C4—1724no—
292C22×C4—1721no—
293C22×C4—1721no—
294C22×C4—1721no—
295C22×C4—1721no—
296C22×C4C2×D17211yescharacteristic
297C22×C4D4×D4311yescharacteristic
298C22×C4D4×D4311yescharacteristic
299SD16—1724no—
300M16—41no—
301M16—41no—
302C2×C8—22no—
303C2×C8—41no—
304C2×C8—1721no—
305C4⋊C4—24no—
306C4⋊C4—432no—
307C4⋊C4—861no—
308C4⋊C4—861no—
309C4⋊C4—861no—
310C4⋊C4—861no—
311C4⋊C4—861no—
312C4⋊C4—1721no—
313C4⋊C4—1721no—
314C22⋊C4—868no—
315C22⋊C4—862no—
316C22⋊C4—862no—
317C22⋊C4—1721no—
318C42—41no—
319C42—41no—
320C42—432no—
321C42—864no—
322C42—861no—
323C42—861no—
324C42—861no—
325C42—1724no—
326C42—1722no—
327C42—1721no—
328C42C2×C4×D4311yescharacteristic
329C42#1062189811yescharacteristic
330C42D4×D4311yescharacteristic
331C42#1062190211yescharacteristic
332C23—864no—
333C23—862no—
334C23—1722no—
335C23—1721no—
336C23—1721no—
337C23#1306329511yescharacteristic
338Q8—3441no—
339Q8—1722no—
340D4—434no—
341D4—864no—
342D4—862no—
343C2×C4—22no—
344C2×C4—24no—
345C2×C4—41no—
346C2×C4—42no—
347C2×C4—42no—
348C2×C4—862no—
349C2×C4—862no—
350C2×C4—862no—
351C2×C4—862no—
352C2×C4—862no—
353C2×C4—17216no—
354C2×C4—1721no—
355C2×C4—1721no—
356C2×C4—1721no—
357C2×C4—1721no—
358C2×C4—1721no—
359C2×C4—1721no—
360C2×C4—1722no—
361C2×C4—1722no—
362C2×C4—1722no—
363C2×C4—1722no—
364C2×C4C22⋊C4×D4311yescharacteristic
365C2×C4#1306328711yescharacteristic
366C2×C4C4×D17211yescharacteristic
367C2×C4#1306329811yescharacteristic
368C2×C4#1306330011yescharacteristic
369C2×C4#1306331011yescharacteristic
370C2×C4SD16×D4311yescharacteristic
371C2×C4#1306334611yescharacteristic
372C2×C4#1306334911yescharacteristic
373C2×C4#1306335711yescharacteristic
374C8—42no—
375C8—81no—
376C8—3441no—
377C22—21no—
378C22—21no—
379C22—864no—
380C22—1724no—
381C22—1724no—
382C22—1722no—
383C22—1722no—
384C22#1458277711yescharacteristic
385C22#1458305111yescharacteristic
386C22#1458306411yescharacteristic
387C4—21no—
388C4—21no—
389C4—21no—
390C4—44no—
391C4—864no—
392C4—3441no—
393C4—3441no—
394C4—1722no—
395C4—1722no—
396C4#104×D4312yes—
397C4#1458298611yescharacteristic
398C4#1458299811yescharacteristic
399C4#1458310311yescharacteristic
400C4#1458311311yescharacteristic
401C2—21no—
402C2—21no—
403C2—1724no—
404C2#1913493011yescharacteristic
405C2#1913503711yescharacteristic
406C2#1913509711yescharacteristic
subgroupG/H
centerC2×C4#13063298
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1303C2
socleC22×C43#386
prime radicalC22×D172D4
cosocleC2×C42×C43C23
hypercenter#1303D43
hypocenterC43#9231
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1303

Complements

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

NH ≅ G/Ntype
3. #19135571C2semidirect
4. #19133093C2semidirect
6. #19132427C2semidirect
7. C43×#1303C2semidirect
13. #14583190C4semidirect
14. #14583105C4semidirect
33. #13063325C2×C4semidirect
34. #13063325C2×C4semidirect
69. C4⋊C8×C43C2×C4semidirect
125. C4×Dic43SD16semidirect
203. #1303D43semidirect
232. C43#9231semidirect
268. C4⋊C8C4×D43semidirect

Maximal subgroups

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

subgroupindex
#191446042
C4×#130632872
#191355712
#191330932
#191330192
#191324272
C43×#13032
#923143