Finite Group Databasebeta

← #24999150

Subgroups — #24999150

Order 11008.

658 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583273C211yesmaximal, characteristic
2C2×#14583181C211yesmaximal, characteristic, complemented
3C2×#14583100C211yesmaximal, characteristic
4#19135530C211yesmaximal, characteristic, complemented
5C2×#14582642C211yesmaximal, characteristic
6#19132429C211yesmaximal, characteristic, complemented
7C2×C43×#332C211yesmaximal, characteristic, complemented
8C22×#10621873—21no—
9C22×#10621884—22no—
10C2×#13063322C2211yescharacteristic
11C2×C4×Dic86C2211yescharacteristic
12#14583273—22no—
13#14583273—22no—
14#14583181—22no—
15#14583181—22no—
16#14583100—22no—
17#14583100—22no—
18C2×#13063256—21no—
19C2×C4⋊(C43⋊C8)C2211yescharacteristic
20C2×#13063248—21no—
21C2×#13063247—21no—
22C2×C4×C43⋊C8C2211yescharacteristic
23#14582653—22no—
24#14582642—22no—
25C2×C4⋊Q8×C43C2211yescharacteristic
26C2×C4⋊C8×C43C2211yescharacteristic
27C2×C4⋊C8×C43C2211yescharacteristic
28C43×#332—22no—
29C22×Dic86D411yescharacteristic
30C22×D172—21no—
31C22×D172—21no—
32C22×D172—21no—
33C2×#10621873—24no—
34C2×#10621873—42no—
35C2×#10621873—42no—
36C2×#10621884—28no—
37C2×#10621884—44no—
38C2×#10621884—44no—
39C22×C43⋊C8—21no—
40C22×C43⋊C8D412yes—
41#13063322—21no—
42#13063322—21no—
43#13063322—21no—
44#13063322D412yes—
45C4×Dic86—21no—
46C4×Dic86—21no—
47C4×Dic86—21no—
48C4×Dic86—21no—
49C2×C4⋊Dic43D411yescharacteristic
50C2×Dic43⋊C4—21no—
51C2×C4×Dic43—21no—
52#13063256—24no—
53C4⋊(C43⋊C8)—21no—
54C4⋊(C43⋊C8)D412yes—
55#13063248—24no—
56#13063247—24no—
57C4×C43⋊C8—21no—
58C4×C43⋊C8—21no—
59C22×Q8×C43—21no—
60C22×C8×C43—21no—
61C22×C8×C43—21no—
62C4⋊Q8×C43—21no—
63C4⋊Q8×C43—21no—
64C4⋊Q8×C43—21no—
65C4⋊Q8×C43D412yes—
66C2×C4⋊C4×C43—21no—
67C2×C4⋊C4×C43—21no—
68C2×C42×C43C2311yescharacteristic
69C4⋊C8×C43—21no—
70C4⋊C8×C43—21no—
71C4⋊C8×C43—21no—
72C4⋊C8×C43D412yes—
73C23×D43—41no—
74C2×Q8×C43—22no—
75C2×Q8×C43—41no—
76C2×Q8×C43—42no—
77C2×Q8×C43—42no—
78C22×C4×C43—41no—
79C22×C4×C43C2×D411yescharacteristic
80C22×C4×C43C2×D411yescharacteristic
81C22×C4×C43#4111yescharacteristic
82C22×Dic43—21no—
83C22×Dic43—21no—
84C2×D172—22no—
85C2×D172—22no—
86C2×D172—22no—
87C2×D172—41no—
88C2×D172—41no—
89C2×D172—41no—
90C2×D172—42no—
91C2×D172—41no—
92C2×D172—41no—
93C2×D172—42no—
94C2×D172—41no—
95C2×D172—41no—
96C2×D172—82no—
97C2×Dic86—21no—
98C2×Dic86—21no—
99C2×Dic86—21no—
100C2×Dic86—21no—
101C2×Dic86—21no—
102C2×Dic86SD1612yescomplemented
103C2×C8×C43—22no—
104C2×C8×C43—41no—
105C2×C8×C43—41no—
106C2×C8×C43—41no—
107C2×C8×C43—42no—
108C4⋊C4×C43—22no—
109C4⋊C4×C43—22no—
110C4⋊C4×C43—41no—
111C4⋊C4×C43—41no—
112C42×C43C2×D411yescharacteristic
113C42×C43C2×D411yescharacteristic
114C42×C43C2×D411yescharacteristic
115C42×C43C2×D411yescharacteristic
116#10621884—416no—
117C4⋊Dic43—21no—
118C4⋊Dic43—21no—
119Dic43⋊C4—41no—
120Dic43⋊C4—41no—
121C4×Dic43—41no—
122C4×Dic43—41no—
123C2×C43⋊C8—22no—
124C2×C43⋊C8—22no—
125C2×C43⋊C8—22no—
126C2×C43⋊C8—41no—
127C2×C43⋊C8—41no—
128C2×C43⋊C8SD1614yescomplemented
129#10621873—48no—
130C23×C43#12111yescharacteristic
131C22×D43—42no—
132C22×D43—82no—
133C22×D43—81no—
134C22×D43—81no—
135C22×D43—82no—
136Q8×C43—44no—
137Q8×C43—81no—
138Q8×C43—81no—
139C2×C4×C43—22no—
140C2×C4×C43—42no—
141C2×C4×C43—82no—
142C2×C4×C43#12011yescharacteristic
143C2×C4×C43#12011yescharacteristic
144C2×C4×C43#12011yescharacteristic
145C2×C4×C43#12111yescharacteristic
146C2×C4×C43#12111yescharacteristic
147C2×C4×C43#12711yescharacteristic
148C2×C4×C43C2×SD1611yescharacteristic
149C2×C4×C43C2×SD1612yes—
150C2×C4×C43#13511yescharacteristic
151C2×C4×C43AGL(1,ℤ/8)12yes—
152C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
153C2×C4×C43#13711yescharacteristic
154C2×Dic43—22no—
155C2×Dic43—41no—
156C2×Dic43—41no—
157C2×Dic43—41no—
158C2×Dic43—42no—
159D172—42no—
160D172—44no—
161D172—42no—
162D172—82no—
163D172—82no—
164D172—81no—
165D172—81no—
166D172—81no—
167D172—81no—
168Dic86—22no—
169Dic86—22no—
170Dic86—41no—
171Dic86—41no—
172C8×C43—42no—
173C8×C43—81no—
174C43⋊C8—24no—
175C43⋊C8—42no—
176#10268—431nomaximal, Sylow
177C22×C43#39211yescharacteristic
178C22×C43#46012yes—
179C22×C43#46511yescharacteristic
180C22×C43#46811yescharacteristic
181C22×C43#47112yes—
182C2×D43—82no—
183C2×D43—82no—
184C2×D43—82no—
185C2×D43—162no—
186C2×D43—162no—
187C4×C43—21no—
188C4×C43—21no—
189C4×C43—82no—
190C4×C43#44811yescharacteristic
191C4×C43#44911yescharacteristic
192C4×C43#45011yescharacteristic
193C4×C43#45012yes—
194C4×C43#45211yescharacteristic
195C4×C43#49211yescharacteristic
196C4×C43#49611yescharacteristic
197Dic43—42no—
198Dic43—81no—
199C2×#492—431no—
200C2×#475—431no—
201C2×#460—431no—
202#1984—431no—
203C2×#332D4311yescharacteristic, complemented
204C2×#331—431no—
205#1277—431no—
206C2×C43#166612yes—
207C2×C43#168612yes—
208C2×C43#200011yescharacteristic
209C2×C43#201411yescharacteristic
210C2×C43#201911yescharacteristic
211D43—162no—
212C22×SD16—861no—
213C22×SD16—862no—
214C2×C4⋊Q8C2×D4311yescharacteristic
215C2×#127—431no—
216C2×C4×Q8—431no—
217#492—862no—
218#492—862no—
219#475—862no—
220#475—862no—
221#460—862no—
222#460—862no—
223C2×#106—861no—
224C2×C4⋊C8—431no—
225C2×C4⋊C8C2×D4311yescharacteristic
226C2×C4⋊C8C2×D4311yescharacteristic
227C2×#103—861no—
228C2×#102—861no—
229C2×C4×C8—431no—
230#336—862no—
231#332—22no—
232#331—862no—
233C43#1026811yescharacteristic, complemented, Sylow
234C22×Q8—21no—
235C22×Q8—431no—
236C22×D4—861no—
237C22×D4—861no—
238C22×D4—861no—
239C2×SD16—864no—
240C2×SD16—868no—
241C2×SD16—1722no—
242C2×SD16—1722no—
243C2×SD16—1724no—
244C2×SD16—1724no—
245C22×C8—21no—
246C22×C8—21no—
247C22×C8—432no—
248C22×C8—861no—
249C4⋊Q8—21no—
250C4⋊Q8—21no—
251C4⋊Q8—21no—
252C4⋊Q8D17212yes—
253#127—432no—
254#127—861no—
255#127—861no—
256#127—861no—
257C4×Q8—861no—
258C4×Q8—861no—
259C4×Q8—861no—
260C4×Q8—861no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—431no—
264C2×C4⋊C4—861no—
265C2×C42—861no—
266C2×C42C22×D4311yescharacteristic
267#106—864no—
268C4⋊C8—21no—
269C4⋊C8—21no—
270C4⋊C8—21no—
271C4⋊C8—432no—
272C4⋊C8—861no—
273C4⋊C8C22⋊D4312yes—
274#103—864no—
275#102—864no—
276C4×C8—861no—
277C4×C8—861no—
278C24—1721no—
279C2×Q8—22no—
280C2×Q8—41no—
281C2×Q8—42no—
282C2×Q8—42no—
283C2×Q8—432no—
284C2×Q8—861no—
285C2×Q8—861no—
286C2×Q8—861no—
287C2×Q8—861no—
288C2×Q8—861no—
289C2×D4—862no—
290C2×D4—862no—
291C2×D4—862no—
292C2×D4—3442no—
293C2×D4—1721no—
294C2×D4—1721no—
295C2×D4—1721no—
296C2×D4—1721no—
297C2×D4—1722no—
298C2×D4—1721no—
299C2×D4—1722no—
300C2×D4—1721no—
301C2×D4—1721no—
302C22×C4—41no—
303C22×C4—861no—
304C22×C4—861no—
305C22×C4#1062189811yescharacteristic
306C22×C4D4×D4311yescharacteristic
307C22×C4D4×D4311yescharacteristic
308SD16—1728no—
309SD16—17216no—
310C2×C8—22no—
311C2×C8—41no—
312C2×C8—41no—
313C2×C8—41no—
314C2×C8—42no—
315C2×C8—434no—
316C2×C8—862no—
317C2×C8—862no—
318C2×C8—862no—
319C2×C8—1721no—
320C2×C8—1721no—
321C4⋊C4—22no—
322C4⋊C4—22no—
323C4⋊C4—41no—
324C4⋊C4—41no—
325C4⋊C4—861no—
326C4⋊C4—861no—
327C4⋊C4—1721no—
328C4⋊C4—1721no—
329C42—1721no—
330C42—1721no—
331C42C2×D17211yescharacteristic
332C42D4×D4311yescharacteristic
333C42D4×D4311yescharacteristic
334C42C2×C22⋊D4311yescharacteristic
335C23—3442no—
336C23—3441no—
337C23—3441no—
338C23—3442no—
339C23—1722no—
340C23#1306329811yescharacteristic
341Q8—44no—
342Q8—81no—
343Q8—81no—
344Q8—862no—
345Q8—862no—
346Q8—1721no—
347Q8—1721no—
348D4—3442no—
349D4—3442no—
350D4—3441no—
351D4—3441no—
352D4—3441no—
353D4—3441no—
354D4—1722no—
355D4—1724no—
356D4—1722no—
357C2×C4—22no—
358C2×C4—42no—
359C2×C4—82no—
360C2×C4—862no—
361C2×C4—1721no—
362C2×C4—1722no—
363C2×C4—1721no—
364C2×C4—1721no—
365C2×C4#1306329311yescharacteristic
366C2×C4#1306329511yescharacteristic
367C2×C4#1306329511yescharacteristic
368C2×C4#1306329811yescharacteristic
369C2×C4#1306329911yescharacteristic
370C2×C4#1306332111yescharacteristic
371C2×C4SD16×D4311yescharacteristic
372C2×C4SD16×D4312yes—
373C2×C4#1306334811yescharacteristic
374C2×C4#1306334912yes—
375C2×C4#1306335211yescharacteristic
376C2×C4#1306335711yescharacteristic
377C8—42no—
378C8—81no—
379C8—864no—
380C8—1722no—
381C22—3442no—
382C22—3442no—
383C22—3442no—
384C22—6882no—
385C22—6882no—
386C22#1458280811yescharacteristic
387C22#1458309812yes—
388C22#1458313111yescharacteristic
389C22#1458314811yescharacteristic
390C22#1458316512yes—
391C4—21no—
392C4—21no—
393C4—82no—
394C4—3441no—
395C4—1722no—
396C4#1458303911yescharacteristic
397C4#1458304711yescharacteristic
398C4#1458304811yescharacteristic
399C4#1458305112yes—
400C4#1458306011yescharacteristic
401C4#1458327011yescharacteristic
402C4#1458328711yescharacteristic
403C2—6882no—
404C2#1913394612yes—
405C2#1913407012yes—
406C2#1913559711yescharacteristic
407C2#1913568411yescharacteristic
408C2#1913570811yescharacteristic
subgroupG/H
centerC23#13063298
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC2×C43×#332C2
socleC23×C43#121
prime radicalC2×#13063322C22
hypercenterC2×#332D43
hypocenterC43#10268
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#332

Complements

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

NH ≅ G/Ntype
2. C2×#14583181C2semidirect
4. #19135530C2semidirect
6. #19132429C2semidirect
7. C2×C43×#332C2semidirect
102. C2×Dic86SD16semidirect
128. C2×C43⋊C8SD16semidirect
203. C2×#332D43semidirect
233. C43#10268semidirect

Maximal subgroups

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

subgroupindex
C2×#145832732
C2×#145831812
C2×#145831002
#191355302
C2×#145826422
#191324292
C2×C43×#3322
#1026843