Finite Group Databasebeta

← #24992507

Subgroups — #24992507

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#19144388C211yesmaximal, characteristic
2#19137506C211yesmaximal, characteristic
3#19133159C211yesmaximal, characteristic, complemented
4#19132985C211yesmaximal, characteristic
5#19132498C211yesmaximal, characteristic, complemented
6#19132454C211yesmaximal, characteristic, complemented
7C43×#1503C211yesmaximal, characteristic, complemented
8C2×C4×D172—21no—
9C2×C4×D172C2211yescharacteristic
10#14583196—22no—
11#14583186C412yescomplemented
12#14583176C412yescomplemented
13#14582952C2211yescharacteristic
14#14582942—21no—
15#14582923C2211yescharacteristic
16#14582903—21no—
17#14582797—21no—
18#14582770—22no—
19#14582765C2211yescharacteristic
20#14582758—21no—
21#95×D43—21no—
22#14582636—22no—
23#14582626—22no—
24C43×#533C2211yescharacteristic
25C43×#431C2211yescharacteristic
26C4×C4⋊C4×C43C2211yescharacteristic
27C43×#328—21no—
28C43×#328—21no—
29C22×D172D411yescharacteristic
30C22×C4×D43—21no—
31C22×C4×D43—22no—
32C2×#10621877—21no—
33C4×D172—21no—
34C4×D172—21no—
35C4×D172—42no—
36C4×D172—42no—
37C4×D172C2×C412yes—
38C4×D172D412yes—
39C2×C4⋊Dic43—21no—
40C2×C4⋊Dic43D411yescharacteristic
41C2×Dic43⋊C4—22no—
42C2×(C2×D43)⋊C4—21no—
43C2×(C2×D43)⋊C4—22no—
44#13063258—22no—
45#13063256—22no—
46C4⋊(C43⋊C8)—21no—
47C4⋊(C43⋊C8)—21no—
48C4⋊(C43⋊C8)C2×C412yescomplemented
49#13063245—22no—
50#13063245—22no—
51C22⋊(C43⋊C8)—21no—
52C4×C43⋊C8—21no—
53C43⋊#95—22no—
54C43⋊#95—21no—
55C43⋊#95D412yes—
56C4⋊Q8×C43C2×C411yescharacteristic, complemented
57C4⋊Q8×C43C2×C411yescharacteristic, complemented
58#125×C43—21no—
59C22⋊Q8×C43—21no—
60C22⋊Q8×C43—21no—
61C4×Q8×C43—21no—
62C4×Q8×C43—21no—
63#117×C43—21no—
64C2×C4⋊C4×C43—21no—
65C2×C42×C43—21no—
66C2×C42×C43C2311yescharacteristic
67C4⋊C8×C43—21no—
68C22⋊C8×C43—21no—
69C4×C8×C43—21no—
70#95×C43D411yescharacteristic
71#95×C43D411yescharacteristic
72C23×D43—21no—
73C2×Q8×C43—21no—
74C2×Q8×C43—21no—
75C22×C4×C43—21no—
76C22×C4×C43—21no—
77C22×C4×C43C2×D411yescharacteristic
78C22×C4×C43C2×D411yescharacteristic
79C22×C4×C43C2×D411yescharacteristic
80C22×Dic43—21no—
81C22×Dic43—22no—
82C2×D172—21no—
83C2×D172—21no—
84C2×D172—21no—
85C2×D172C22⋊C412yes—
86C2×D172SD1612yes—
87C2×D172Q1612yes—
88C2×C4×D43—22no—
89C2×C4×D43—22no—
90C2×C4×D43—44no—
91C2×C4×D43—44no—
92C2×C4×D43—82no—
93C2×C4×D43—82no—
94C2×C8×C43—41no—
95C4⋊C4×C43—21no—
96C4⋊C4×C43—21no—
97C4⋊C4×C43—21no—
98C4⋊C4×C43—21no—
99C4⋊C4×C43—42no—
100C4⋊C4×C43—41no—
101C4⋊C4×C43—41no—
102C22⋊C4×C43—41no—
103C42×C43—41no—
104C42×C43—41no—
105C42×C43—41no—
106C42×C43C22×C411yescharacteristic
107C42×C43C2×D411yescharacteristic
108C42×C43#4111yescharacteristic
109C42×C43#4111yescharacteristic
110(C2×D43)⋊C4—22no—
111(C2×D43)⋊C4—22no—
112(C2×D43)⋊C4—44no—
113C4⋊Dic43—21no—
114C4⋊Dic43—41no—
115C4⋊Dic43—41no—
116C4⋊Dic43C22⋊C412yes—
117Dic43⋊C4—82no—
118#10621877—41no—
119#10621877—41no—
120C2×C43⋊C8—22no—
121C2×C43⋊C8—41no—
122C23×C43#12011yescharacteristic
123C22×D43—22no—
124C22×D43—22no—
125C22×D43—22no—
126C22×D43—42no—
127C22×D43—42no—
128Q8×C43—81no—
129Q8×C43—81no—
130C2×C4×C43—22no—
131C2×C4×C43—41no—
132C2×C4×C43—41no—
133C2×C4×C43—41no—
134C2×C4×C43—41no—
135C2×C4×C43—41no—
136C2×C4×C43—41no—
137C2×C4×C43—41no—
138C2×C4×C43—41no—
139C2×C4×C43—41no—
140C2×C4×C43C2×C22⋊C411yescharacteristic
141C2×C4×C43C4×D411yescharacteristic
142C2×C4×C43C4×D411yescharacteristic
143C2×C4×C43#12111yescharacteristic
144C2×C4×C43#12111yescharacteristic
145C2×C4×C43#12311yescharacteristic
146C2×C4×C43C2×SD1611yescharacteristic
147C2×C4×C43C2×Q1611yescharacteristic
148C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
149C2×C4×C43#13711yescharacteristic
150C2×Dic43—22no—
151C2×Dic43—42no—
152C2×Dic43—42no—
153C2×Dic43—42no—
154C2×Dic43—42no—
155D172—22no—
156D172—22no—
157D172—22no—
158D172#10314yes—
159C4×D43—82no—
160C4×D43—82no—
161C4×D43—88no—
162C8×C43—81no—
163C43⋊C8—42no—
164C43⋊C8—81no—
165#9175—431nomaximal, Sylow
166C22×C43—21no—
167C22×C43—21no—
168C22×C43#38611yescharacteristic
169C22×C43#45011yescharacteristic
170C22×C43#45111yescharacteristic
171C2×D43—24no—
172C2×D43—44no—
173C2×D43—44no—
174C2×D43—42no—
175C2×D43—42no—
176C4×C43—21no—
177C4×C43—21no—
178C4×C43—21no—
179C4×C43—21no—
180C4×C43—42no—
181C4×C43—81no—
182C4×C43—81no—
183C4×C43—81no—
184C4×C43C2×#10311yescharacteristic
185C4×C43#41711yescharacteristic
186C4×C43#48311yescharacteristic
187C4×C43#48411yescharacteristic
188Dic43—42no—
189Dic43—82no—
190#3077—431no—
191#2349—431no—
192#1518—431no—
193#1503D4311yescharacteristic, complemented
194#1478—431no—
195#1303—431no—
196#1286—431no—
197C2×C43—21no—
198C2×C43—21no—
199C2×C43#187211yescharacteristic
200C2×C43#190411yescharacteristic
201C2×C43#190611yescharacteristic
202D43—44no—
203#533C2×D4311yescharacteristic
204C2×C4×D4—431no—
205C2×C4×D4—861no—
206#478—862no—
207#476—432no—
208#474—432no—
209#431—431no—
210#431C2×D4311yescharacteristic
211#428—861no—
212#423—431no—
213#418—861no—
214#389—861no—
215#385—862no—
216#382—431no—
217#380—861no—
218C4×C4⋊C4C2×D4311yescharacteristic
219C2×#95—861no—
220#328—21no—
221#328—21no—
222#328—862no—
223D4⋊C8—862no—
224C43#917511yescharacteristic, complemented, Sylow
225C22×D4—431no—
226C23×C4—862no—
227C23×C4—861no—
228C2×M16—861no—
229C4⋊Q8C4×D4311yescharacteristic, complemented
230C4⋊Q8C4×D4311yescharacteristic, complemented
231#125—21no—
232C22⋊Q8—21no—
233C22⋊Q8—21no—
234C4×Q8—21no—
235C4×Q8—21no—
236C4×D4—432no—
237C4×D4—432no—
238C4×D4—861no—
239C4×D4—861no—
240C4×D4—1722no—
241C4×D4—1722no—
242#117—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—431no—
245C2×C4⋊C4—862no—
246C2×C4⋊C4—861no—
247C2×C22⋊C4—861no—
248C2×C22⋊C4—862no—
249C2×C42—21no—
250C2×C42C22×D4311yescharacteristic
251#107—862no—
252#106—862no—
253C4⋊C8—21no—
254C4⋊C8—432no—
255C4⋊C8—861no—
256C4⋊C8—861no—
257#102—862no—
258#102—862no—
259C22⋊C8—21no—
260C22⋊C8—861no—
261C4×C8—21no—
262C4×C8—861no—
263#95—432no—
264#95—862no—
265#95—861no—
266#95C22⋊D4311yescharacteristic
267#95C22⋊D4311yescharacteristic
268C24—861no—
269C2×Q8—21no—
270C2×Q8—21no—
271C2×D4—432no—
272C2×D4—432no—
273C2×D4—432no—
274C2×D4—861no—
275C2×D4—861no—
276C2×D4—861no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—861no—
280C22×C4—862no—
281C22×C4—862no—
282C22×C4—862no—
283C22×C4—3442no—
284C22×C4—3442no—
285C22×C4—1724no—
286C22×C4—1724no—
287C22×C4D4×D4311yescharacteristic
288C22×C4D4×D4311yescharacteristic
289C22×C4C2×C22⋊D4311yescharacteristic
290M16—1721no—
291M16—1721no—
292C2×C8—41no—
293C2×C8—862no—
294C2×C8—1721no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—42no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—432no—
303C4⋊C4—861no—
304C4⋊C4—3442no—
305C4⋊C4—1721no—
306C4⋊C4—1721no—
307C22⋊C4—41no—
308C22⋊C4—862no—
309C22⋊C4—862no—
310C22⋊C4—1724no—
311C42—41no—
312C42—41no—
313C42—41no—
314C42C2×C4×D4311yescharacteristic
315C42#1062189811yescharacteristic
316C42D4×D4311yescharacteristic
317C42#1062190011yescharacteristic
318C23—862no—
319C23—862no—
320C23—862no—
321C23—1722no—
322C23—1722no—
323C23#1306329311yescharacteristic
324Q8—81no—
325Q8—81no—
326D4—434no—
327D4—862no—
328D4—862no—
329D4—862no—
330C2×C4—22no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—862no—
341C2×C4—3442no—
342C2×C4—3442no—
343C2×C4—3448no—
344C2×C4—1722no—
345C2×C4—1722no—
346C2×C4—1722no—
347C2×C4—1722no—
348C2×C4C22⋊C4×D4311yescharacteristic
349C2×C4(C22⋊D43)⋊C411yescharacteristic
350C2×C4C4×C22⋊D4311yescharacteristic
351C2×C4#1306329611yescharacteristic
352C2×C4#1306329811yescharacteristic
353C2×C4#1306330711yescharacteristic
354C2×C4SD16×D4311yescharacteristic
355C2×C4Q16×D4311yescharacteristic
356C2×C4#1306335211yescharacteristic
357C2×C4#1306335711yescharacteristic
358C8—81no—
359C8—3441no—
360C8—1722no—
361C22—21no—
362C22—21no—
363C22—864no—
364C22—1724no—
365C22—1724no—
366C22—1722no—
367C22—1722no—
368C22#1458277511yescharacteristic
369C22#1458304811yescharacteristic
370C22#1458305311yescharacteristic
371C4—21no—
372C4—21no—
373C4—21no—
374C4—21no—
375C4—42no—
376C4—81no—
377C4—81no—
378C4—81no—
379C4—3442no—
380C4—1722no—
381C4#103×D4311yescharacteristic
382C4#1458289911yescharacteristic
383C4#1458322811yescharacteristic
384C4#1458323311yescharacteristic
385C2—21no—
386C2—21no—
387C2—1724no—
388C2#1913489911yescharacteristic
389C2#1913508511yescharacteristic
390C2#1913509911yescharacteristic
subgroupG/H
centerC22#14582775
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1503C2
socleC22×C43#386
prime radicalC22×D172D4
cosocleC2×C42×C43C23
hypercenter#1503D43
hypocenterC43#9175
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1503

Complements

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

NH ≅ G/Ntype
3. #19133159C2semidirect
5. #19132498C2semidirect
6. #19132454C2semidirect
7. C43×#1503C2semidirect
11. #14583186C4semidirect
12. #14583176C4semidirect
48. C4⋊(C43⋊C8)C2×C4semidirect
56. C4⋊Q8×C43C2×C4semidirect
57. C4⋊Q8×C43C2×C4semidirect
193. #1503D43semidirect
224. C43#9175semidirect
229. C4⋊Q8C4×D43semidirect
230. C4⋊Q8C4×D43semidirect

Maximal subgroups

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

subgroupindex
#191443882
#191375062
#191331592
#191329852
#191324982
#191324542
C43×#15032
#917543