Finite Group Databasebeta

← #24993147

Subgroups — #24993147

Order 11008.

492 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145533C211yesmaximal, characteristic
2#19143544C211yesmaximal, characteristic, complemented
3#19135434C211yesmaximal, characteristic
4C2×#14582642C211yesmaximal, characteristic
5#19132490C211yesmaximal, characteristic, complemented
6#19132445C211yesmaximal, characteristic, complemented
7C43×#1550C211yesmaximal, characteristic, complemented
8C2×#13063322C2211yescharacteristic
9#14583273—21no—
10#14583247—21no—
11#14583099—22no—
12#14583049C414yes—
13#14583030—21no—
14#14583030—22no—
15Q8×C43⋊C8—21no—
16#14582952C2211yescharacteristic
17#14582926—21no—
18C2×C4⋊(C43⋊C8)C2211yescharacteristic
19C2×#13063241—21no—
20C2×#13063241—21no—
21#14582855—21no—
22C4×#10621877C2211yescharacteristic
23#14582642—21no—
24#14582642—21no—
25C43×#533C2211yescharacteristic
26C43×#423C2211yescharacteristic
27C2×C4⋊C8×C43C2211yescharacteristic
28C43×#333—21no—
29C43×#332—21no—
30C22×D172—21no—
31C22×D172—21no—
32C22×D172C2×C412yes—
33C2×#10621884—24no—
34C2×#10621877D411yescharacteristic
35C2×#10621877D411yescharacteristic
36C22×C43⋊C8—21no—
37#13063322—21no—
38#13063322—21no—
39#13063322—21no—
40#13063322—21no—
41C4⋊(C43⋊C8)—22no—
42C4⋊(C43⋊C8)—22no—
43C4⋊(C43⋊C8)—21no—
44C4⋊(C43⋊C8)—21no—
45C4⋊(C43⋊C8)D411yescharacteristic
46C4⋊(C43⋊C8)D411yescharacteristic
47#13063245—24no—
48#13063241—42no—
49#13063241—42no—
50C22⋊(C43⋊C8)C2×C412yes—
51#13063236—22no—
52#13063236—21no—
53C4×C43⋊C8—22no—
54C4×C43⋊C8—21no—
55C4×C43⋊C8—21no—
56C2×M16×C43—21no—
57C22×C8×C43—21no—
58C4⋊Q8×C43D411yescharacteristic
59C4⋊Q8×C43D411yescharacteristic
60#125×C43—21no—
61C22⋊Q8×C43—21no—
62C22⋊Q8×C43C2×C412yes—
63C4×Q8×C43—21no—
64C4×Q8×C43D412yes—
65#117×C43—21no—
66C2×C42×C43C2311yescharacteristic
67C4⋊C8×C43—21no—
68C4⋊C8×C43—21no—
69C4⋊C8×C43—21no—
70C4⋊C8×C43—21no—
71C23×D43—22no—
72C2×Q8×C43—21no—
73C2×Q8×C43C22⋊C412yes—
74C22×C4×C43C22×C411yescharacteristic
75C22×C4×C43C2×D411yescharacteristic
76C22×C4×C43#4111yescharacteristic
77C2×D172—22no—
78C2×D172—22no—
79C2×D172—41no—
80C2×D172—41no—
81C2×D172—41no—
82C2×D172—41no—
83C2×D172—41no—
84C2×D172—41no—
85C2×D172—41no—
86C2×D172—41no—
87C2×D172—81no—
88C2×D172—81no—
89C2×D172—82no—
90M16×C43—41no—
91M16×C43—41no—
92C2×C8×C43—41no—
93C2×C8×C43—41no—
94C2×C8×C43—81no—
95C4⋊C4×C43—22no—
96C4⋊C4×C43—21no—
97C4⋊C4×C43—21no—
98C4⋊C4×C43—21no—
99C4⋊C4×C43—22no—
100C4⋊C4×C43C22⋊C412yes—
101C22⋊C4×C43—22no—
102C42×C43—22no—
103C42×C43C2×D411yescharacteristic
104C42×C43C2×D411yescharacteristic
105C42×C43C2×D411yescharacteristic
106C42×C43#4111yescharacteristic
107#10621884—84no—
108#10621877—21no—
109#10621877—21no—
110#10621877—21no—
111#10621877SD1612yescomplemented
112C2×C43⋊C8—21no—
113C2×C43⋊C8—22no—
114C2×C43⋊C8—21no—
115C2×C43⋊C8—21no—
116C2×C43⋊C8—21no—
117C2×C43⋊C8—41no—
118C2×C43⋊C8—41no—
119C23×C43C4×D411yescharacteristic
120C22×D43—42no—
121C22×D43—42no—
122C22×D43—42no—
123C22×D43—82no—
124C22×D43—82no—
125Q8×C43—42no—
126Q8×C43—41no—
127Q8×C43—41no—
128C2×C4×C43—21no—
129C2×C4×C43—21no—
130C2×C4×C43—22no—
131C2×C4×C43—22no—
132C2×C4×C43—41no—
133C2×C4×C43C2×C22⋊C411yescharacteristic
134C2×C4×C43C4×D411yescharacteristic
135C2×C4×C43#12011yescharacteristic
136C2×C4×C43#12111yescharacteristic
137C2×C4×C43#12111yescharacteristic
138C2×C4×C43#12311yescharacteristic
139C2×C4×C43C2×SD1611yescharacteristic
140C2×C4×C43#13511yescharacteristic
141C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
142C2×C4×C43#13711yescharacteristic
143D172—44no—
144D172—82no—
145D172—82no—
146D172—81no—
147D172—81no—
148D172—81no—
149D172—81no—
150D172—81no—
151D172—81no—
152C8×C43—81no—
153C8×C43—81no—
154C43⋊C8—22no—
155C43⋊C8—42no—
156C43⋊C8—41no—
157C43⋊C8—41no—
158C43⋊C8—41no—
159#9274—431nomaximal, Sylow
160C22×C43—21no—
161C22×C43—21no—
162C22×C43#38611yescharacteristic
163C22×C43C4×SD1611yescharacteristic
164C22×C43#44011yescharacteristic
165C2×D43—82no—
166C2×D43—82no—
167C2×D43—82no—
168C2×D43—162no—
169C2×D43—162no—
170C4×C43—21no—
171C4×C43—21no—
172C4×C43—21no—
173C4×C43—42no—
174C4×C43—42no—
175C4×C43#44811yescharacteristic
176C4×C43#44911yescharacteristic
177C4×C43#46011yescharacteristic
178C4×C43#46411yescharacteristic
179C4×C43#47111yescharacteristic
180C4×C43#47211yescharacteristic
181#3208—431no—
182#2962—431no—
183#1965—431no—
184#1550D4311yescharacteristic, complemented
185C2×#331—431no—
186#1301—431no—
187#1283—431no—
188C2×C43—21no—
189C2×C43—21no—
190C2×C43#188011yescharacteristic
191C2×C43#190711yescharacteristic
192C2×C43#191411yescharacteristic
193D43—162no—
194#533C2×D4311yescharacteristic
195C2×#127—431no—
196#492—861no—
197#486—861no—
198#460—862no—
199#450—434no—
200#446—861no—
201#446—862no—
202C8×Q8—861no—
203#431—431no—
204#424—861no—
205#423C2×D4311yescharacteristic
206C2×C4⋊C8—431no—
207C2×C4⋊C8C2×D4311yescharacteristic
208C2×#100—861no—
209C2×#100—861no—
210#405—861no—
211C4×M16—431no—
212#333—21no—
213#332—21no—
214#331—861no—
215#331—861no—
216C43#927411yescharacteristic, complemented, Sylow
217C22×D4—432no—
218C22×D4—861no—
219C22×D4—861no—
220C2×SD16—864no—
221C2×M16—21no—
222C2×M16—431no—
223C2×M16—431no—
224C22×C8—21no—
225C22×C8—861no—
226C4⋊Q8C22⋊D4311yescharacteristic
227C4⋊Q8C22⋊D4311yescharacteristic
228#127—861no—
229#127—861no—
230#127—861no—
231#127—861no—
232#125—21no—
233C22⋊Q8—21no—
234C22⋊Q8C4×D4312yes—
235C4×Q8—21no—
236C4×Q8D17212yes—
237#117—21no—
238C2×C42C22×D4311yescharacteristic
239C4⋊C8—21no—
240C4⋊C8—21no—
241C4⋊C8—21no—
242C4⋊C8—21no—
243C4⋊C8—431no—
244C4⋊C8—431no—
245C4⋊C8—862no—
246C4⋊C8—862no—
247C4⋊C8—861no—
248C4⋊C8—861no—
249#102—864no—
250#100—1722no—
251#100—1722no—
252C22⋊C8—432no—
253#97—862no—
254#97—861no—
255C4×C8—862no—
256C4×C8—861no—
257C4×C8—861no—
258C24—862no—
259C2×Q8—21no—
260C2×Q8(C2×D43)⋊C412yes—
261C2×D4—862no—
262C2×D4—862no—
263C2×D4—3441no—
264C2×D4—3441no—
265C2×D4—3442no—
266C2×D4—1721no—
267C2×D4—1721no—
268C2×D4—1721no—
269C2×D4—1721no—
270C2×D4—1721no—
271C2×D4—1721no—
272C2×D4—1721no—
273C2×D4—1721no—
274C22×C4C2×C4×D4311yescharacteristic
275C22×C4D4×D4311yescharacteristic
276C22×C4#1062190011yescharacteristic
277SD16—3444no—
278M16—41no—
279M16—41no—
280M16—432no—
281M16—861no—
282M16—861no—
283M16—861no—
284C2×C8—41no—
285C2×C8—41no—
286C2×C8—81no—
287C2×C8—861no—
288C2×C8—862no—
289C2×C8—861no—
290C2×C8—861no—
291C2×C8—861no—
292C2×C8—1721no—
293C2×C8—1721no—
294C4⋊C4—22no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—22no—
299C4⋊C4(C2×D43)⋊C412yes—
300C22⋊C4—22no—
301C42—22no—
302C42C2×D17211yescharacteristic
303C42D4×D4311yescharacteristic
304C42#1062190011yescharacteristic
305C42C2×C22⋊D4311yescharacteristic
306C23—3442no—
307C23—3442no—
308C23—1722no—
309C23—1722no—
310C23—1722no—
311C23(C22⋊D43)⋊C411yescharacteristic
312Q8—42no—
313Q8—41no—
314Q8—41no—
315D4—3442no—
316D4—3442no—
317D4—3441no—
318D4—3441no—
319D4—3441no—
320D4—3441no—
321D4—3441no—
322D4—3441no—
323D4—1724no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—22no—
327C2×C4—22no—
328C2×C4—41no—
329C2×C4C2×(C2×D43)⋊C411yescharacteristic
330C2×C4(C22⋊D43)⋊C411yescharacteristic
331C2×C4#1306329511yescharacteristic
332C2×C4#1306329711yescharacteristic
333C2×C4#1306329711yescharacteristic
334C2×C4#1306330911yescharacteristic
335C2×C4SD16×D4311yescharacteristic
336C2×C4#1306334811yescharacteristic
337C2×C4#1306335211yescharacteristic
338C2×C4#1306335711yescharacteristic
339C8—81no—
340C8—81no—
341C8—862no—
342C8—1722no—
343C8—1721no—
344C8—1721no—
345C8—1721no—
346C22—21no—
347C22—21no—
348C22—3442no—
349C22—3442no—
350C22—3442no—
351C22—6882no—
352C22—6882no—
353C22#1458277611yescharacteristic
354C22#1458298411yescharacteristic
355C22#1458300211yescharacteristic
356C4—21no—
357C4—21no—
358C4—21no—
359C4—42no—
360C4—42no—
361C4#1458303911yescharacteristic
362C4#1458304711yescharacteristic
363C4#1458309711yescharacteristic
364C4#1458312311yescharacteristic
365C4#1458316411yescharacteristic
366C4#1458316711yescharacteristic
367C2—21no—
368C2—21no—
369C2—6882no—
370C2#1913494811yescharacteristic
371C2#1913510111yescharacteristic
372C2#1913514011yescharacteristic
subgroupG/H
centerC22#14582776
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1550C2
socleC22×C43#386
prime radicalC2×#13063322C22
cosocleC2×C42×C43C23
hypercenter#1550D43
hypocenterC43#9274
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1550

Complements

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

NH ≅ G/Ntype
2. #19143544C2semidirect
5. #19132490C2semidirect
6. #19132445C2semidirect
7. C43×#1550C2semidirect
111. #10621877SD16semidirect
184. #1550D43semidirect
216. C43#9274semidirect

Maximal subgroups

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

subgroupindex
#191455332
#191435442
#191354342
C2×#145826422
#191324902
#191324452
C43×#15502
#927443