Finite Group Databasebeta

← #24993481

Subgroups — #24993481

Order 11008.

474 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144404C211yesmaximal, characteristic
2#19143713C211yesmaximal, characteristic
3#19134616C211yesmaximal, characteristic
4#19133280C211yesmaximal, characteristic, complemented
5#19132498C211yesmaximal, characteristic, complemented
6#19132470C211yesmaximal, characteristic, complemented
7C43×#1981C211yesmaximal, characteristic, complemented
8C4×#10621898C2211yescharacteristic
9#14583191C412yescomplemented
10#14583186C412yescomplemented
11#14583181—21no—
12#14583176—21no—
13#14583026—21no—
14#14582976—21no—
15#14582970—22no—
16#14582955—21no—
17#14582952C2211yescharacteristic
18#14582939—21no—
19#14582923C2211yescharacteristic
20#14582923C2211yescharacteristic
21#14582921—21no—
22C2×#13063253—21no—
23#14582898—21no—
24#14582659—21no—
25#14582645—21no—
26#14582645—21no—
27C2×C4⋊Q8×C43C2211yescharacteristic
28C2×C4⋊C8×C43C2211yescharacteristic
29C2×#103×C43—22no—
30C4×C4⋊C4×C43C2211yescharacteristic
31C2×#10621898D411yescharacteristic
32C2×#10621877—21no—
33C2×#10621877—21no—
34C2×#10621872—22no—
35C4×Dic86C2×C411yescharacteristic
36C4×Dic86D411yescharacteristic
37C4×D172C2×C411yescharacteristic
38C4×D172D411yescharacteristic
39C4×C22⋊D43—21no—
40C4×C22⋊D43—21no—
41#13063284D411yescharacteristic
42#13063282—21no—
43C42×D43—21no—
44#13063258—22no—
45#13063256—22no—
46C4⋊(C43⋊C8)—21no—
47C4⋊(C43⋊C8)—21no—
48C4⋊(C43⋊C8)—21no—
49C4⋊(C43⋊C8)C2×C412yes—
50C4⋊(C43⋊C8)D411yescharacteristic
51C4⋊(C43⋊C8)D411yescharacteristic
52Dic43⋊C8—22no—
53#13063253—42no—
54#13063248—22no—
55#13063245—22no—
56C22⋊(C43⋊C8)—21no—
57(C2×D43)⋊C8—22no—
58#13063235—22no—
59C4×C43⋊C8—21no—
60C22×Q8×C43—21no—
61C22×C8×C43D412yes—
62C4⋊Q8×C43—21no—
63C4⋊Q8×C43—21no—
64C4⋊Q8×C43—21no—
65C4⋊Q8×C43C2×C412yes—
66C2×C4⋊C4×C43—21no—
67C2×C4⋊C4×C43—21no—
68C2×C4⋊C4×C43—21no—
69C2×C42×C43—21no—
70C2×C42×C43C2311yescharacteristic
71C4⋊C8×C43—21no—
72C4⋊C8×C43—21no—
73#103×C43—44no—
74#95×C43—21no—
75C2×Q8×C43—22no—
76C2×Q8×C43—42no—
77C2×Q8×C43—42no—
78C2×Q8×C43—41no—
79C22×C4×C43—41no—
80C22×C4×C43—41no—
81C22×C4×C43C2×D411yescharacteristic
82C22×C4×C43C2×D411yescharacteristic
83C22×C4×C43#4111yescharacteristic
84C2×C22⋊D43—21no—
85#10621898—21no—
86#10621898—21no—
87#10621898—21no—
88#10621898—21no—
89C2×D172C22⋊C411yescharacteristic
90C2×C4×D43—21no—
91C2×C4×D43—21no—
92C2×C4×D43—21no—
93C2×Dic86C22⋊C411yescharacteristic
94C2×C8×C43—22no—
95C2×C8×C43—42no—
96C4⋊C4×C43—22no—
97C4⋊C4×C43—22no—
98C4⋊C4×C43—22no—
99C4⋊C4×C43—41no—
100C4⋊C4×C43—41no—
101C4⋊C4×C43—41no—
102C42×C43—41no—
103C42×C43—41no—
104C42×C43C22×C411yescharacteristic
105C42×C43C2×D411yescharacteristic
106C42×C43C2×D411yescharacteristic
107C42×C43#4111yescharacteristic
108C22⋊Dic43—21no—
109(C2×D43)⋊C4—21no—
110(C2×D43)⋊C4—21no—
111C4⋊Dic43C22⋊C411yescharacteristic
112C4⋊Dic43C22⋊C411yescharacteristic
113Dic43⋊C4—21no—
114Dic43⋊C4—21no—
115C4×Dic43—21no—
116C4×Dic43—21no—
117C4×Dic43—21no—
118#10621877—41no—
119#10621877—41no—
120#10621877—41no—
121#10621877—41no—
122C2×C43⋊C8—22no—
123C2×C43⋊C8—21no—
124C2×C43⋊C8—21no—
125C2×C43⋊C8—41no—
126#10621872—82no—
127C23×C43#12111yescharacteristic
128C22×D43—21no—
129Q8×C43—44no—
130Q8×C43—81no—
131Q8×C43—81no—
132C2×C4×C43—21no—
133C2×C4×C43—21no—
134C2×C4×C43—41no—
135C2×C4×C43—42no—
136C2×C4×C43—42no—
137C2×C4×C43—81no—
138C2×C4×C43—82no—
139C2×C4×C43—81no—
140C2×C4×C43C2×C22⋊C411yescharacteristic
141C2×C4×C43C4×D411yescharacteristic
142C2×C4×C43C4×D411yescharacteristic
143C2×C4×C43#12011yescharacteristic
144C2×C4×C43#12111yescharacteristic
145C2×C4×C43#12311yescharacteristic
146C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
147C2×C4×C43#13711yescharacteristic
148C2×C4×C43#13711yescharacteristic
149C2×C4×C43#13711yescharacteristic
150C22⋊D43—41no—
151C22⋊D43—41no—
152C2×Dic43—21no—
153C2×Dic43—21no—
154C2×Dic43—21no—
155D172—21no—
156D172—21no—
157C4×D43—41no—
158C4×D43—41no—
159C4×D43—41no—
160C4×D43—41no—
161C4×D43—81no—
162Dic86—21no—
163Dic86—21no—
164C8×C43—42no—
165C43⋊C8—42no—
166C43⋊C8—41no—
167C43⋊C8—41no—
168C43⋊C8—81no—
169#9321—431nomaximal, Sylow
170C22×C43—21no—
171C22×C43—21no—
172C22×C43#38611yescharacteristic
173C22×C43#46811yescharacteristic
174C22×C43#47011yescharacteristic
175C2×D43—41no—
176C2×D43—41no—
177C2×D43—41no—
178C4×C43—21no—
179C4×C43—21no—
180C4×C43—21no—
181C4×C43—82no—
182C4×C43—82no—
183C4×C43#41711yescharacteristic
184C4×C43#41911yescharacteristic
185C4×C43#45311yescharacteristic
186C4×C43#45411yescharacteristic
187C4×C43#46811yescharacteristic
188C4×C43#47011yescharacteristic
189Dic43—41no—
190Dic43—41no—
191Dic43—41no—
192#3079—431no—
193#2989—431no—
194#1981D4311yescharacteristic, complemented
195#1806—431no—
196#1549—431no—
197#1303—431no—
198#1292—431no—
199C2×C43—21no—
200C2×C43—21no—
201C2×C43#188311yescharacteristic
202C2×C43#189411yescharacteristic
203C2×C43#190211yescharacteristic
204D43—81no—
205C2×C4⋊Q8C2×D4311yescharacteristic
206C4×#41—431no—
207#477—432no—
208#476—432no—
209#475—861no—
210#474—861no—
211#446—861no—
212#436—861no—
213#435—862no—
214#432—861no—
215#431—431no—
216#428—861no—
217#423—431no—
218#423—431no—
219#423—861no—
220C2×C4⋊C8C2×D4311yescharacteristic
221C2×#104—861no—
222#417—861no—
223C2×#103—22no—
224C4×C4⋊C4C2×D4311yescharacteristic
225#339—861no—
226#332—861no—
227#332—861no—
228C43#932111yescharacteristic, complemented, Sylow
229C2×#41—431no—
230C22×Q8—21no—
231C2×M16—862no—
232C2×M16—861no—
233C2×M16—861no—
234C22×C8C22⋊D4312yes—
235C4⋊Q8—21no—
236C4⋊Q8—21no—
237C4⋊Q8—21no—
238C4⋊Q8C4×D4312yes—
239C4×Q8—431no—
240C4×Q8—431no—
241C4×D4—431no—
242C4×D4—431no—
243C4×D4—861no—
244C4×D4—861no—
245#117—431no—
246#117—861no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C42—21no—
251C2×C42—861no—
252C2×C42C22×D4311yescharacteristic
253#107—862no—
254#106—862no—
255C4⋊C8—21no—
256C4⋊C8—21no—
257C4⋊C8—432no—
258C4⋊C8—431no—
259C4⋊C8—431no—
260C4⋊C8—862no—
261C4⋊C8—861no—
262C4⋊C8—861no—
263C4⋊C8—861no—
264#104—1722no—
265#103—44no—
266#103—862no—
267#102—862no—
268C22⋊C8—862no—
269C22⋊C8—861no—
270#97—862no—
271C4×C8—861no—
272#95—21no—
273#41—861no—
274#41—861no—
275#41—861no—
276#41—861no—
277C2×Q8—22no—
278C2×Q8—42no—
279C2×Q8—42no—
280C2×Q8—41no—
281C2×Q8—431no—
282C2×D4—431no—
283C2×D4—861no—
284C22×C4—41no—
285C22×C4—41no—
286C22×C4—861no—
287C22×C4—861no—
288C22×C4—861no—
289C22×C4D4×D4311yescharacteristic
290C22×C4#1062190011yescharacteristic
291C22×C4C2×C22⋊D4311yescharacteristic
292M16—3442no—
293M16—1721no—
294M16—1721no—
295M16—1721no—
296M16—1721no—
297C2×C8—22no—
298C2×C8—42no—
299C2×C8—862no—
300C2×C8—861no—
301C2×C8—861no—
302C2×C8—1721no—
303C4⋊C4—22no—
304C4⋊C4—22no—
305C4⋊C4—22no—
306C4⋊C4—41no—
307C4⋊C4—41no—
308C4⋊C4—41no—
309C4⋊C4—431no—
310C4⋊C4—431no—
311C4⋊C4—861no—
312C4⋊C4—861no—
313C22⋊C4—861no—
314C22⋊C4—861no—
315C22⋊C4—861no—
316C42—41no—
317C42—41no—
318C42—861no—
319C42—861no—
320C42—861no—
321C42C2×C4×D4311yescharacteristic
322C42#1062189811yescharacteristic
323C42D4×D4311yescharacteristic
324C42D4×D4311yescharacteristic
325C23—861no—
326C23#1306329611yescharacteristic
327Q8—44no—
328Q8—81no—
329Q8—81no—
330Q8—861no—
331Q8—861no—
332D4—861no—
333D4—861no—
334D4—1721no—
335D4—1721no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—41no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—82no—
342C2×C4—81no—
343C2×C4—81no—
344C2×C4—861no—
345C2×C4—861no—
346C2×C4—861no—
347C2×C4—3441no—
348C2×C4—1721no—
349C2×C4—1721no—
350C2×C4—1721no—
351C2×C4—1721no—
352C2×C4C22⋊C4×D4311yescharacteristic
353C2×C4(C22⋊D43)⋊C411yescharacteristic
354C2×C4C4×C22⋊D4311yescharacteristic
355C2×C4#1306329311yescharacteristic
356C2×C4#1306329811yescharacteristic
357C2×C4#1306330711yescharacteristic
358C2×C4#1306335211yescharacteristic
359C2×C4#1306335411yescharacteristic
360C2×C4#1306335711yescharacteristic
361C2×C4#1306335711yescharacteristic
362C8—42no—
363C8—3441no—
364C8—1721no—
365C8—1721no—
366C8—1722no—
367C22—21no—
368C22—21no—
369C22—1721no—
370C22—1721no—
371C22—1721no—
372C22#1458277511yescharacteristic
373C22#1458314211yescharacteristic
374C22#1458315411yescharacteristic
375C4—21no—
376C4—21no—
377C4—21no—
378C4—82no—
379C4—82no—
380C4—1721no—
381C4—1721no—
382C4—1721no—
383C4#1458289911yescharacteristic
384C4#1458290611yescharacteristic
385C4#1458306611yescharacteristic
386C4#1458307111yescharacteristic
387C4#1458314811yescharacteristic
388C4#1458315611yescharacteristic
389C2—21no—
390C2—21no—
391C2—3441no—
392C2#1913497411yescharacteristic
393C2#1913502511yescharacteristic
394C2#1913506511yescharacteristic
subgroupG/H
centerC22#14582775
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1981C2
socleC22×C43#386
prime radicalC2×#10621898D4
cosocleC2×C42×C43C23
hypercenter#1981D43
hypocenterC43#9321
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1981

Complements

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

NH ≅ G/Ntype
4. #19133280C2semidirect
5. #19132498C2semidirect
6. #19132470C2semidirect
7. C43×#1981C2semidirect
9. #14583191C4semidirect
10. #14583186C4semidirect
194. #1981D43semidirect
228. C43#9321semidirect

Maximal subgroups

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

subgroupindex
#191444042
#191437132
#191346162
#191332802
#191324982
#191324702
C43×#19812
#932143