Finite Group Databasebeta

← #24992504

Subgroups — #24992504

Order 11008.

566 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144392C211yesmaximal, characteristic
2#19133158C211yesmaximal, characteristic, complemented
3#19133093C211yesmaximal, characteristic, complemented
4#19132986C211yesmaximal, characteristic
5#19132498C211yesmaximal, characteristic, complemented
6#19132453C211yesmaximal, characteristic, complemented
7C43×#2349C211yesmaximal, characteristic
8#14583456C2211yescharacteristic
9#14583199—22no—
10#14583189C412yescomplemented
11#14583179C412yescomplemented
12#14582952C2211yescharacteristic
13#14582952C2211yescharacteristic
14#14582939—21no—
15#14582923C2211yescharacteristic
16#14582904—21no—
17#14582635—21no—
18#14582635—21no—
19#14582635—22no—
20D4⋊(C43⋊C8)—22no—
21C2×C4×D4×C43—21no—
22C2×C4×D4×C43C2211yescharacteristic
23C43×#389—21no—
24C43×#385—22no—
25C43×#382C2211yescharacteristic
26C43×#380—21no—
27C4×C4⋊C4×C43C2211yescharacteristic
28C2×#95×C43—21no—
29C2×#10621877—21no—
30#13063325C2×C411yescharacteristic, complemented
31#13063325C2×C411yescharacteristic, complemented
32#13063317—21no—
33#13063304—21no—
34#13063304—21no—
35C4×Dic86—21no—
36C4×Dic86—21no—
37#13063284—21no—
38#13063258—22no—
39#13063256—22no—
40C4⋊(C43⋊C8)—21no—
41C4⋊(C43⋊C8)—21no—
42C4⋊(C43⋊C8)—21no—
43C4⋊(C43⋊C8)C2×C412yescomplemented
44#13063246—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—21no—
52C23×C4×C43—22no—
53C4×D4×C43—21no—
54C4×D4×C43—21no—
55C4×D4×C43—42no—
56C4×D4×C43—42no—
57C4×D4×C43C2×C412yes—
58C4×D4×C43D412yes—
59C2×C4⋊C4×C43—21no—
60C2×C4⋊C4×C43—21no—
61C2×C4⋊C4×C43—22no—
62C2×C4⋊C4×C43D411yescharacteristic
63C2×C22⋊C4×C43—21no—
64C2×C22⋊C4×C43—22no—
65C2×C42×C43—21no—
66C2×C42×C43C2311yescharacteristic
67#95×C43—22no—
68#95×C43—21no—
69#95×C43D411yescharacteristic
70#95×C43D411yescharacteristic
71#95×C43D412yes—
72C24×C43—21no—
73C2×D4×C43—21no—
74C2×D4×C43—21no—
75C2×D4×C43—21no—
76C2×D4×C43C22⋊C412yes—
77C2×D4×C43SD1612yes—
78C2×D4×C43Q1612yes—
79C22×C4×C43—22no—
80C22×C4×C43—22no—
81C22×C4×C43—21no—
82C22×C4×C43—21no—
83C22×C4×C43—22no—
84C22×C4×C43—21no—
85C22×C4×C43—44no—
86C22×C4×C43—44no—
87C22×C4×C43—82no—
88C22×C4×C43—82no—
89C22×C4×C43C2×D411yescharacteristic
90C22×C4×C43C2×D411yescharacteristic
91C22×C4×C43C2×D411yescharacteristic
92C2×Dic86—21no—
93C2×Dic86—21no—
94C4⋊C4×C43—21no—
95C4⋊C4×C43—42no—
96C4⋊C4×C43—41no—
97C4⋊C4×C43—41no—
98C4⋊C4×C43—82no—
99C4⋊C4×C43C22⋊C412yes—
100C22⋊C4×C43—22no—
101C22⋊C4×C43—22no—
102C22⋊C4×C43—44no—
103C42×C43—41no—
104C42×C43—41no—
105C42×C43C22×C411yescharacteristic
106C42×C43C2×D411yescharacteristic
107C42×C43#4111yescharacteristic
108C42×C43#4111yescharacteristic
109C22⋊Dic43—41no—
110C4⋊Dic43—21no—
111C4⋊Dic43—21no—
112C4⋊Dic43—21no—
113C4⋊Dic43—21no—
114Dic43⋊C4—41no—
115Dic43⋊C4—41no—
116C4×Dic43—41no—
117#10621877—41no—
118#10621877—41no—
119C2×C43⋊C8—22no—
120C2×C43⋊C8—41no—
121C2×C43⋊C8—41no—
122C23×C43—22no—
123C23×C43—22no—
124C23×C43—22no—
125C23×C43—42no—
126C23×C43—42no—
127C23×C43#12011yescharacteristic
128D4×C43—22no—
129D4×C43—22no—
130D4×C43—22no—
131D4×C43#10314yes—
132C2×C4×C43—22no—
133C2×C4×C43—22no—
134C2×C4×C43—41no—
135C2×C4×C43—41no—
136C2×C4×C43—42no—
137C2×C4×C43—41no—
138C2×C4×C43—41no—
139C2×C4×C43—41no—
140C2×C4×C43—41no—
141C2×C4×C43—42no—
142C2×C4×C43—42no—
143C2×C4×C43—41no—
144C2×C4×C43—42no—
145C2×C4×C43—82no—
146C2×C4×C43—82no—
147C2×C4×C43—88no—
148C2×C4×C43C2×C22⋊C411yescharacteristic
149C2×C4×C43C4×D411yescharacteristic
150C2×C4×C43C4×D411yescharacteristic
151C2×C4×C43#12111yescharacteristic
152C2×C4×C43#12111yescharacteristic
153C2×C4×C43#12311yescharacteristic
154C2×C4×C43C2×SD1611yescharacteristic
155C2×C4×C43C2×Q1611yescharacteristic
156C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
157C2×C4×C43#13711yescharacteristic
158C2×Dic43—41no—
159C2×Dic43—41no—
160Dic86—81no—
161Dic86—81no—
162C43⋊C8—42no—
163C43⋊C8—81no—
164C43⋊C8—81no—
165#9175—431nomaximal, Sylow
166C22×C43—21no—
167C22×C43—21no—
168C22×C43—24no—
169C22×C43—44no—
170C22×C43—44no—
171C22×C43—42no—
172C22×C43—42no—
173C22×C43#38611yescharacteristic
174C22×C43#45011yescharacteristic
175C22×C43#45111yescharacteristic
176C4×C43—21no—
177C4×C43—21no—
178C4×C43—21no—
179C4×C43—21no—
180C4×C43—42no—
181C4×C43—42no—
182C4×C43—81no—
183C4×C43—82no—
184C4×C43C2×#10311yescharacteristic
185C4×C43#41711yescharacteristic
186C4×C43#48311yescharacteristic
187C4×C43#48411yescharacteristic
188Dic43—81no—
189Dic43—81no—
190#3077—431no—
191#2349D4311yescharacteristic
192#1518—431no—
193#1503—431no—
194#1478—431no—
195#1303—431no—
196#1286—431no—
197C2×C43—21no—
198C2×C43—21no—
199C2×C43—44no—
200C2×C43#187211yescharacteristic
201C2×C43#190411yescharacteristic
202C2×C43#190611yescharacteristic
203#533—431no—
204C2×C4×D4—21no—
205C2×C4×D4C2×D4311yescharacteristic
206#478—862no—
207#476—432no—
208#474—432no—
209#431—431no—
210#431—431no—
211#428—861no—
212#423—431no—
213#418—861no—
214#389—21no—
215#385—22no—
216#382C2×D4311yescharacteristic
217#380—21no—
218C4×C4⋊C4C2×D4311yescharacteristic
219C2×#95—21no—
220#328—861no—
221#328—861no—
222#328—862no—
223D4⋊C8—862no—
224C43#917511yescharacteristic, complemented, Sylow
225C22×D4C22⋊D4311yescharacteristic
226C23×C4—21no—
227C23×C4—22no—
228C2×M16—861no—
229C4⋊Q8—431no—
230C4⋊Q8—431no—
231#125—861no—
232C22⋊Q8—861no—
233C22⋊Q8—861no—
234C4×Q8—861no—
235C4×Q8—861no—
236C4×D4—21no—
237C4×D4—21no—
238C4×D4—42no—
239C4×D4—42no—
240C4×D4C4×D4312yes—
241C4×D4D17212yes—
242#117—861no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—22no—
246C2×C4⋊C4C22⋊D4311yescharacteristic
247C2×C22⋊C4—21no—
248C2×C22⋊C4—22no—
249C2×C42—21no—
250C2×C42C22×D4311yescharacteristic
251#107—862no—
252#106—862no—
253C4⋊C8—432no—
254C4⋊C8—861no—
255C4⋊C8—861no—
256C4⋊C8—861no—
257#102—862no—
258#102—862no—
259C22⋊C8—861no—
260C22⋊C8—861no—
261C4×C8—861no—
262C4×C8—861no—
263#95—22no—
264#95—21no—
265#95C22⋊D4311yescharacteristic
266#95C22⋊D4311yescharacteristic
267#95C22⋊D4312yes—
268C24—21no—
269C2×Q8—861no—
270C2×Q8—861no—
271C2×D4—21no—
272C2×D4—21no—
273C2×D4—21no—
274C2×D4(C2×D43)⋊C412yes—
275C2×D4#1062188312yes—
276C2×D4#1062188512yes—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—22no—
280C22×C4—22no—
281C22×C4—22no—
282C22×C4—21no—
283C22×C4—44no—
284C22×C4—44no—
285C22×C4—82no—
286C22×C4—82no—
287C22×C4C2×C22⋊D4311yescharacteristic
288C22×C4C2×C22⋊D4311yescharacteristic
289C22×C4C2×C22⋊D4311yescharacteristic
290M16—1721no—
291M16—1721no—
292C2×C8—862no—
293C2×C8—1721no—
294C2×C8—1721no—
295C4⋊C4—21no—
296C4⋊C4—42no—
297C4⋊C4—41no—
298C4⋊C4—41no—
299C4⋊C4—82no—
300C4⋊C4—861no—
301C4⋊C4—861no—
302C4⋊C4—861no—
303C4⋊C4—861no—
304C4⋊C4—1721no—
305C4⋊C4—1721no—
306C4⋊C4(C2×D43)⋊C412yes—
307C22⋊C4—22no—
308C22⋊C4—22no—
309C22⋊C4—44no—
310C22⋊C4—1721no—
311C42—41no—
312C42—41no—
313C42—1721no—
314C42C2×C4×D4311yescharacteristic
315C42C2×D17211yescharacteristic
316C42#1062189811yescharacteristic
317C42#1062189811yescharacteristic
318C23—22no—
319C23—22no—
320C23—22no—
321C23—42no—
322C23—42no—
323C23#1306329411yescharacteristic
324Q8—3441no—
325Q8—3441no—
326D4—22no—
327D4—22no—
328D4—22no—
329D4#1306324814yes—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—42no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—41no—
342C2×C4—42no—
343C2×C4—82no—
344C2×C4—82no—
345C2×C4—88no—
346C2×C4—1721no—
347C2×C4—1721no—
348C2×C4C2×(C2×D43)⋊C411yescharacteristic
349C2×C4C4×C22⋊D4311yescharacteristic
350C2×C4C4×C22⋊D4311yescharacteristic
351C2×C4#1306329911yescharacteristic
352C2×C4#1306329911yescharacteristic
353C2×C4#1306330811yescharacteristic
354C2×C4C2×#1062188311yescharacteristic
355C2×C4C2×#1062188511yescharacteristic
356C2×C4#1306335111yescharacteristic
357C2×C4#1306335611yescharacteristic
358C8—3441no—
359C8—3441no—
360C8—1722no—
361C22—21no—
362C22—21no—
363C22—24no—
364C22—44no—
365C22—44no—
366C22—42no—
367C22—42no—
368C22#1458277811yescharacteristic
369C22#1458305011yescharacteristic
370C22#1458305511yescharacteristic
371C4—21no—
372C4—21no—
373C4—21no—
374C4—21no—
375C4—42no—
376C4—42no—
377C4—82no—
378C4—81no—
379C4—3441no—
380C4—3441no—
381C4C2×#1306324811yescharacteristic
382C4#1458289811yescharacteristic
383C4#1458322911yescharacteristic
384C4#1458323411yescharacteristic
385C2—21no—
386C2—21no—
387C2—44no—
388C2#1913490211yescharacteristic
389C2#1913508211yescharacteristic
390C2#1913509611yescharacteristic
subgroupG/H
centerC22#14582778
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#2349C2
socleC22×C43#386
prime radicalC22×D4×C43D4
cosocleC2×C42×C43C23
hypercenter#2349D43
hypocenterC43#9175
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2349

Complements

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

NH ≅ G/Ntype
2. #19133158C2semidirect
3. #19133093C2semidirect
5. #19132498C2semidirect
6. #19132453C2semidirect
10. #14583189C4semidirect
11. #14583179C4semidirect
30. #13063325C2×C4semidirect
31. #13063325C2×C4semidirect
43. C4⋊(C43⋊C8)C2×C4semidirect
224. C43#9175semidirect

Maximal subgroups

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

subgroupindex
#191443922
#191331582
#191330932
#191329862
#191324982
#191324532
C43×#23492
#917543