Finite Group Databasebeta

← #24993437

Subgroups — #24993437

Order 11008.

480 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144411C211yesmaximal, characteristic
2#19143703C211yesmaximal, characteristic
3#19135543C211yesmaximal, characteristic, complemented
4#19134616C211yesmaximal, characteristic
5#19133275C211yesmaximal, characteristic, complemented
6#19132469C211yesmaximal, characteristic, complemented
7C43×#1303C211yesmaximal, characteristic, complemented
8C2×#13063325C2211yescharacteristic
9C4×#10621898C2211yescharacteristic
10#14583195—21no—
11#14583190—21no—
12#14583185C412yescomplemented
13#14583180C412yescomplemented
14C8×Dic86—21no—
15C8×D172—21no—
16(C22⋊D43)⋊C8—22no—
17#14582951—21no—
18#14582941—21no—
19#14582923C2211yescharacteristic
20C2×C4⋊(C43⋊C8)C2211yescharacteristic
21C4⋊C8×D43—21no—
22C2×#13063253—21no—
23#14582901—21no—
24#14582661—22no—
25#14582659—21no—
26#14582647—21no—
27#14582647—21no—
28C43×#431C2211yescharacteristic
29C43×#423C2211yescharacteristic
30C4×C4⋊C4×C43C2211yescharacteristic
31C2×#10621898D411yescharacteristic
32C22×Dic86—21no—
33C2×#10621877—21no—
34C22×C43⋊C8D412yes—
35C2×C8×D43—22no—
36#13063325—21no—
37#13063325—21no—
38#13063325—21no—
39#13063325C2×C412yes—
40C4×Dic86C2×C411yescharacteristic
41C4×Dic86D411yescharacteristic
42C4×D172C2×C411yescharacteristic
43C4×D172D411yescharacteristic
44C4×C22⋊D43—21no—
45C4×C22⋊D43—21no—
46#13063284D411yescharacteristic
47#13063282—21no—
48C2×C4⋊Dic43—21no—
49C2×C4⋊Dic43—21no—
50C42×D43—21no—
51#13063259—22no—
52#13063257—22no—
53C4⋊(C43⋊C8)—21no—
54C4⋊(C43⋊C8)—21no—
55C4⋊(C43⋊C8)—21no—
56C4⋊(C43⋊C8)—21no—
57Dic43⋊C8—22no—
58#13063253—42no—
59#13063250—22no—
60#13063247—22no—
61(C2×D43)⋊C8—22no—
62C8×Dic43—22no—
63C2×M16×C43—21no—
64C2×C4⋊C4×C43—21no—
65C2×C42×C43—21no—
66C2×C42×C43C2311yescharacteristic
67C4⋊C8×C43—21no—
68C4⋊C8×C43C2×C412yes—
69C4⋊C8×C43D411yescharacteristic
70C4⋊C8×C43D411yescharacteristic
71C22⋊C8×C43—21no—
72C4×C8×C43—21no—
73#95×C43—21no—
74C22×C4×C43—41no—
75C22×C4×C43C2×D411yescharacteristic
76C22×C4×C43C2×D411yescharacteristic
77C22×C4×C43#4111yescharacteristic
78C2×C22⋊D43—21no—
79C22×Dic43—41no—
80#10621898—21no—
81#10621898—21no—
82#10621898SD1612yes—
83#10621898Q1612yes—
84C2×D172C22⋊C411yescharacteristic
85C2×C4×D43—21no—
86C2×C4×D43—21no—
87C2×C4×D43—21no—
88C2×Dic86—22no—
89C2×Dic86—41no—
90C2×Dic86—82no—
91C2×Dic86C22⋊C411yescharacteristic
92M16×C43—41no—
93M16×C43—41no—
94C2×C8×C43—22no—
95C2×C8×C43—21no—
96C2×C8×C43—21no—
97C4⋊C4×C43—22no—
98C4⋊C4×C43—41no—
99C42×C43—41no—
100C42×C43—41no—
101C42×C43C22×C411yescharacteristic
102C42×C43C2×D411yescharacteristic
103C42×C43C2×D411yescharacteristic
104C42×C43#4111yescharacteristic
105C22⋊Dic43—21no—
106(C2×D43)⋊C4—21no—
107(C2×D43)⋊C4—21no—
108C4⋊Dic43—22no—
109C4⋊Dic43—22no—
110C4⋊Dic43—41no—
111C4⋊Dic43—41no—
112C4⋊Dic43C22⋊C411yescharacteristic
113C4⋊Dic43C22⋊C411yescharacteristic
114Dic43⋊C4—21no—
115Dic43⋊C4—21no—
116C4×Dic43—21no—
117C4×Dic43—21no—
118C4×Dic43—21no—
119#10621877—41no—
120#10621877—41no—
121C2×C43⋊C8—22no—
122C2×C43⋊C8—42no—
123C2×C43⋊C8—41no—
124C8×D43—82no—
125C23×C43#12111yescharacteristic
126C22×D43—21no—
127C2×C4×C43—21no—
128C2×C4×C43—21no—
129C2×C4×C43—41no—
130C2×C4×C43—42no—
131C2×C4×C43—81no—
132C2×C4×C43—81no—
133C2×C4×C43C2×C22⋊C411yescharacteristic
134C2×C4×C43C4×D411yescharacteristic
135C2×C4×C43C4×D411yescharacteristic
136C2×C4×C43#12011yescharacteristic
137C2×C4×C43#12111yescharacteristic
138C2×C4×C43#12311yescharacteristic
139C2×C4×C43C2×SD1611yescharacteristic
140C2×C4×C43C2×Q1611yescharacteristic
141C2×C4×C43#13511yescharacteristic
142C2×C4×C43#13511yescharacteristic
143C22⋊D43—22no—
144C22⋊D43—22no—
145C2×Dic43—21no—
146C2×Dic43—21no—
147C2×Dic43—21no—
148C2×Dic43—42no—
149C2×Dic43—82no—
150D172—21no—
151D172#10312yes—
152C4×D43—22no—
153C4×D43—22no—
154C4×D43—41no—
155C4×D43—41no—
156C4×D43—81no—
157Dic86—21no—
158Dic86—82no—
159Dic86—82no—
160Dic86#10312yes—
161C8×C43—42no—
162C8×C43—41no—
163C8×C43—41no—
164C43⋊C8—42no—
165C43⋊C8—81no—
166#9315—431nomaximal, Sylow
167C22×C43—21no—
168C22×C43—21no—
169C22×C43#38611yescharacteristic
170C22×C43#46511yescharacteristic
171C22×C43#46711yescharacteristic
172C2×D43—22no—
173C2×D43—41no—
174C2×D43—41no—
175C4×C43—21no—
176C4×C43—21no—
177C4×C43—21no—
178C4×C43—82no—
179C4×C43C2×#10311yescharacteristic
180C4×C43#41611yescharacteristic
181C4×C43#45511yescharacteristic
182C4×C43#45611yescharacteristic
183C4×C43#46511yescharacteristic
184C4×C43#46711yescharacteristic
185Dic43—22no—
186Dic43—41no—
187Dic43—41no—
188Dic43—82no—
189#3079—431no—
190#2988—431no—
191#1987—431no—
192#1806—431no—
193#1548—431no—
194#1303D4311yescharacteristic, complemented
195#1292—431no—
196C2×C43—21no—
197C2×C43—21no—
198C2×C43#188211yescharacteristic
199C2×C43#189211yescharacteristic
200C2×C43#190311yescharacteristic
201D43—42no—
202C2×C4⋊Q8—431no—
203C4×#41—431no—
204#477—861no—
205#476—861no—
206#475—432no—
207#474—432no—
208C8×Q8—861no—
209C8×D4—861no—
210C8×D4—862no—
211#431—861no—
212#431C2×D4311yescharacteristic
213#428—861no—
214#423—431no—
215#423C2×D4311yescharacteristic
216C2×C4⋊C8—431no—
217C2×C4⋊C8—861no—
218C2×#104—861no—
219#417—861no—
220C4×C4⋊C4C2×D4311yescharacteristic
221#340—862no—
222#339—861no—
223#333—861no—
224#333—861no—
225C43#931511yescharacteristic, complemented, Sylow
226C2×#41—431no—
227C22×Q8—861no—
228C2×M16—21no—
229C2×M16—861no—
230C22×C8—432no—
231C22×C8—862no—
232C4⋊Q8—432no—
233C4⋊Q8—861no—
234C4⋊Q8—861no—
235C4⋊Q8—861no—
236C4×Q8—431no—
237C4×Q8—431no—
238C4×D4—431no—
239C4×D4—431no—
240C4×D4—861no—
241C4×D4—861no—
242#117—431no—
243#117—861no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—861no—
246C2×C4⋊C4—861no—
247C2×C42—21no—
248C2×C42—861no—
249C2×C42C22×D4311yescharacteristic
250#107—862no—
251#106—862no—
252C4⋊C8—21no—
253C4⋊C8—862no—
254C4⋊C8—861no—
255C4⋊C8—861no—
256C4⋊C8—861no—
257C4⋊C8—861no—
258C4⋊C8C4×D4312yes—
259C4⋊C8D17211yescharacteristic
260C4⋊C8D17211yescharacteristic
261#104—1722no—
262#103—862no—
263#102—862no—
264C22⋊C8—21no—
265C22⋊C8—862no—
266C4×C8—21no—
267C4×C8—862no—
268#95—21no—
269#41—432no—
270#41—432no—
271#41—861no—
272#41—861no—
273C2×Q8—431no—
274C2×Q8—862no—
275C2×Q8—3442no—
276C2×Q8—1721no—
277C2×D4—431no—
278C2×D4—861no—
279C22×C4—41no—
280C22×C4—861no—
281C22×C4—861no—
282C22×C4—861no—
283C22×C4—1721no—
284C22×C4#1062189811yescharacteristic
285C22×C4D4×D4311yescharacteristic
286C22×C4D4×D4311yescharacteristic
287M16—41no—
288M16—41no—
289M16—1721no—
290M16—1721no—
291C2×C8—22no—
292C2×C8—21no—
293C2×C8—21no—
294C2×C8—862no—
295C2×C8—3442no—
296C2×C8—1721no—
297C2×C8—1722no—
298C4⋊C4—22no—
299C4⋊C4—41no—
300C4⋊C4—431no—
301C4⋊C4—431no—
302C4⋊C4—861no—
303C4⋊C4—861no—
304C4⋊C4—862no—
305C4⋊C4—862no—
306C4⋊C4—1721no—
307C4⋊C4—1721no—
308C22⋊C4—861no—
309C22⋊C4—861no—
310C22⋊C4—861no—
311C42—41no—
312C42—41no—
313C42—861no—
314C42—861no—
315C42—861no—
316C42C2×C4×D4311yescharacteristic
317C42C2×D17211yescharacteristic
318C42D4×D4311yescharacteristic
319C42#1062190211yescharacteristic
320C23—861no—
321C23#1306329811yescharacteristic
322Q8—432no—
323Q8—861no—
324Q8—3442no—
325Q8—3442no—
326D4—432no—
327D4—862no—
328D4—862no—
329D4—861no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—41no—
333C2×C4—42no—
334C2×C4—81no—
335C2×C4—81no—
336C2×C4—861no—
337C2×C4—862no—
338C2×C4—862no—
339C2×C4—861no—
340C2×C4—861no—
341C2×C4—3441no—
342C2×C4—3442no—
343C2×C4—1722no—
344C2×C4—1721no—
345C2×C4—1721no—
346C2×C4C22⋊C4×D4311yescharacteristic
347C2×C4#1306328711yescharacteristic
348C2×C4C4×D17211yescharacteristic
349C2×C4#1306329511yescharacteristic
350C2×C4#1306330011yescharacteristic
351C2×C4#1306331011yescharacteristic
352C2×C4SD16×D4311yescharacteristic
353C2×C4Q16×D4311yescharacteristic
354C2×C4#1306334411yescharacteristic
355C2×C4#1306334611yescharacteristic
356C8—41no—
357C8—41no—
358C8—42no—
359C8—3441no—
360C8—1722no—
361C22—21no—
362C22—21no—
363C22—862no—
364C22—1721no—
365C22—1721no—
366C22#1458277711yescharacteristic
367C22#1458312711yescharacteristic
368C22#1458313911yescharacteristic
369C4—21no—
370C4—21no—
371C4—21no—
372C4—82no—
373C4—862no—
374C4—3442no—
375C4—1721no—
376C4—1721no—
377C4#103×D4311yescharacteristic
378C4#1458289211yescharacteristic
379C4#1458307811yescharacteristic
380C4#1458308311yescharacteristic
381C4#1458312911yescharacteristic
382C4#1458314111yescharacteristic
383C2—21no—
384C2—21no—
385C2—1722no—
386C2#1913496511yescharacteristic
387C2#1913501711yescharacteristic
388C2#1913507411yescharacteristic
subgroupG/H
centerC22#14582777
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1303C2
socleC22×C43#386
prime radicalC2×#10621898D4
cosocleC2×C42×C43C23
hypercenter#1303D43
hypocenterC43#9315
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1303

Complements

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

NH ≅ G/Ntype
3. #19135543C2semidirect
5. #19133275C2semidirect
6. #19132469C2semidirect
7. C43×#1303C2semidirect
12. #14583185C4semidirect
13. #14583180C4semidirect
194. #1303D43semidirect
225. C43#9315semidirect

Maximal subgroups

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

subgroupindex
#191444112
#191437032
#191355432
#191346162
#191332752
#191324692
C43×#13032
#931543