Finite Group Databasebeta

← #24993103

Subgroups — #24993103

Order 11008.

492 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145520C211yesmaximal, characteristic
2#19143341C211yesmaximal, characteristic
3#19133273C211yesmaximal, characteristic
4C2×#14582648C211yesmaximal, characteristic, complemented
5#19132490C211yesmaximal, characteristic, complemented
6#19132446C211yesmaximal, characteristic, complemented
7C43×#1997C211yesmaximal, characteristic, complemented
8C2×#13063333—21no—
9#14583449C2211yescharacteristic
10#14583273—21no—
11#14583249—21no—
12#14583101—22no—
13#14583038C414yes—
14#14582978—21no—
15#14582972—22no—
16C8×D172—21no—
17#14582952C2211yescharacteristic
18C2×C4⋊(C43⋊C8)C2211yescharacteristic
19C2×C4⋊(C43⋊C8)C2211yescharacteristic
20#14582867—21no—
21#14582648—21no—
22#14582648—21no—
23#14582646—21no—
24#14582642—21no—
25C2×C4⋊Q8×C43C2211yescharacteristic
26C43×#423C2211yescharacteristic
27C4×M16×C43C2211yescharacteristic
28C43×#343—21no—
29C43×#343—21no—
30C2×#10621898—21no—
31C2×#10621884—24no—
32#13063333—42no—
33#13063333—42no—
34C2×#10621872—22no—
35C22×C43⋊C8—21no—
36C22×C43⋊C8—21no—
37C2×C8×D43—22no—
38#13063325D411yescharacteristic
39#13063322D411yescharacteristic
40#13063313—21no—
41#13063299—21no—
42#13063299C2×C412yes—
43C4×D172—21no—
44C4×D172D412yes—
45C4⋊(C43⋊C8)—21no—
46C4⋊(C43⋊C8)—21no—
47C4⋊(C43⋊C8)—21no—
48C4⋊(C43⋊C8)—21no—
49C4⋊(C43⋊C8)D411yescharacteristic
50C4⋊(C43⋊C8)D411yescharacteristic
51#13063249—24no—
52C22⋊(C43⋊C8)C2×C412yes—
53(C2×D43)⋊C8—22no—
54(C2×D43)⋊C8—22no—
55C4×C43⋊C8—21no—
56C22×Q8×C43C2×C412yes—
57C2×M16×C43—21no—
58C2×M16×C43D411yescharacteristic
59C2×M16×C43D411yescharacteristic
60C4⋊Q8×C43—21no—
61C4⋊Q8×C43—21no—
62C4⋊Q8×C43—21no—
63C4⋊Q8×C43—21no—
64C2×C4⋊C4×C43—21no—
65C2×C4⋊C4×C43—21no—
66C2×C42×C43C2311yescharacteristic
67C4⋊C8×C43—21no—
68C4⋊C8×C43—21no—
69#97×C43—21no—
70C4×C8×C43—21no—
71C2×Q8×C43—22no—
72C2×Q8×C43—22no—
73C2×Q8×C43—82no—
74C22×C4×C43—22no—
75C22×C4×C43C22×C411yescharacteristic
76C22×C4×C43C2×D411yescharacteristic
77C22×C4×C43#4111yescharacteristic
78C2×C22⋊D43—22no—
79#10621898—41no—
80#10621898—41no—
81#10621898—41no—
82#10621898—41no—
83C2×D172—21no—
84C2×D172—21no—
85C2×D172C22⋊C412yes—
86C2×C4×D43—22no—
87C2×Dic86—21no—
88M16×C43—21no—
89M16×C43—21no—
90M16×C43—21no—
91M16×C43—41no—
92M16×C43—41no—
93M16×C43SD1612yescomplemented
94C2×C8×C43—21no—
95C2×C8×C43—21no—
96C2×C8×C43—41no—
97C4⋊C4×C43—41no—
98C4⋊C4×C43—41no—
99C4⋊C4×C43—41no—
100C4⋊C4×C43—41no—
101C42×C43C2×D411yescharacteristic
102C42×C43C2×D411yescharacteristic
103C42×C43C2×D411yescharacteristic
104C42×C43#4111yescharacteristic
105#10621884—84no—
106(C2×D43)⋊C4—22no—
107(C2×D43)⋊C4—22no—
108C4⋊Dic43—21no—
109C4⋊Dic43C22⋊C412yes—
110C2×C43⋊C8—22no—
111C2×C43⋊C8—21no—
112C2×C43⋊C8—21no—
113C2×C43⋊C8—41no—
114C2×C43⋊C8—41no—
115C2×C43⋊C8—41no—
116C2×C43⋊C8—81no—
117#10621872—44no—
118C8×D43—44no—
119C23×C43C4×D411yescharacteristic
120C22×D43—22no—
121Q8×C43—44no—
122Q8×C43—82no—
123C2×C4×C43—21no—
124C2×C4×C43—21no—
125C2×C4×C43—41no—
126C2×C4×C43—42no—
127C2×C4×C43—82no—
128C2×C4×C43C2×C22⋊C411yescharacteristic
129C2×C4×C43C4×D411yescharacteristic
130C2×C4×C43#12011yescharacteristic
131C2×C4×C43#12111yescharacteristic
132C2×C4×C43#12111yescharacteristic
133C2×C4×C43#12311yescharacteristic
134C2×C4×C43C2×SD1611yescharacteristic
135C2×C4×C43#13511yescharacteristic
136C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
137C2×C4×C43#13711yescharacteristic
138C22⋊D43—42no—
139C22⋊D43—42no—
140C2×Dic43—22no—
141D172—42no—
142D172—41no—
143D172—41no—
144D172—41no—
145D172—41no—
146C4×D43—42no—
147C4×D43—42no—
148Dic86—41no—
149Dic86—41no—
150C8×C43—22no—
151C8×C43—41no—
152C8×C43—81no—
153C43⋊C8—42no—
154C43⋊C8—41no—
155C43⋊C8—41no—
156C43⋊C8—81no—
157#9267—431nomaximal, Sylow
158C22×C43—21no—
159C22×C43—21no—
160C22×C43#38611yescharacteristic
161C22×C43C4×SD1611yescharacteristic
162C22×C43#44011yescharacteristic
163C2×D43—42no—
164C2×D43—42no—
165C2×D43—42no—
166C4×C43—21no—
167C4×C43—21no—
168C4×C43—21no—
169C4×C43—82no—
170C4×C43#45011yescharacteristic
171C4×C43#45211yescharacteristic
172C4×C43#46111yescharacteristic
173C4×C43#46311yescharacteristic
174C4×C43#47111yescharacteristic
175C4×C43#47311yescharacteristic
176Dic43—42no—
177#3206—431no—
178#2935—431no—
179#1997D4311yescharacteristic, complemented
180#1547—431no—
181C2×#333—431no—
182#1301—431no—
183#1283—431no—
184C2×C43—21no—
185C2×C43—21no—
186C2×C43#187711yescharacteristic
187C2×C43#190811yescharacteristic
188C2×C43#191411yescharacteristic
189D43—82no—
190C2×#131—861no—
191#532—431no—
192C2×C4⋊Q8C2×D4311yescharacteristic
193#492—861no—
194#487—861no—
195#461—862no—
196#448—434no—
197#436—861no—
198#435—862no—
199C8×D4—861no—
200#431—431no—
201#423C2×D4311yescharacteristic
202C2×C4⋊C8—431no—
203C2×C4⋊C8—431no—
204#408—861no—
205C4×M16C2×D4311yescharacteristic
206#343—21no—
207#343—21no—
208#333—861no—
209#333—861no—
210#332—861no—
211#331—861no—
212C43#926711yescharacteristic, complemented, Sylow
213C2×#41—861no—
214C22×Q8C4×D4312yes—
215C2×SD16—864no—
216#131—1722no—
217#131—1722no—
218C2×M16—21no—
219C2×M16—862no—
220C2×M16C22⋊D4311yescharacteristic
221C2×M16C22⋊D4311yescharacteristic
222C22×C8—862no—
223C22×C8—861no—
224C22×C8—861no—
225C4⋊Q8—21no—
226C4⋊Q8—21no—
227C4⋊Q8—21no—
228C4⋊Q8—21no—
229C4⋊Q8—431no—
230#127—431no—
231#124—861no—
232#121—432no—
233#121—861no—
234C4×D4—432no—
235C4×D4—861no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—21no—
238C2×C42C22×D4311yescharacteristic
239C4⋊C8—21no—
240C4⋊C8—21no—
241C4⋊C8—431no—
242C4⋊C8—431no—
243C4⋊C8—861no—
244C4⋊C8—861no—
245C4⋊C8—861no—
246C4⋊C8—861no—
247#103—864no—
248C22⋊C8—432no—
249C22⋊C8—862no—
250C22⋊C8—862no—
251#97—21no—
252C4×C8—21no—
253C4×C8—861no—
254#41—1721no—
255#41—1721no—
256#41—1721no—
257#41—1721no—
258C2×Q8—22no—
259C2×Q8—22no—
260C2×Q8—82no—
261C2×Q8—861no—
262C2×D4—432no—
263C2×D4—862no—
264C2×D4—861no—
265C2×D4—861no—
266C22×C4—22no—
267C22×C4—862no—
268C22×C4C2×C4×D4311yescharacteristic
269C22×C4#1062189811yescharacteristic
270C22×C4C2×C22⋊D4311yescharacteristic
271SD16—3444no—
272M16—21no—
273M16—21no—
274M16—21no—
275M16—41no—
276M16—41no—
277M16—1724no—
278M16#1062188412yescomplemented
279C2×C8—21no—
280C2×C8—21no—
281C2×C8—41no—
282C2×C8—862no—
283C2×C8—861no—
284C2×C8—861no—
285C2×C8—3441no—
286C2×C8—1724no—
287C2×C8—1721no—
288C2×C8—1721no—
289C2×C8—1721no—
290C4⋊C4—41no—
291C4⋊C4—41no—
292C4⋊C4—41no—
293C4⋊C4—41no—
294C4⋊C4—432no—
295C4⋊C4—861no—
296C22⋊C4—862no—
297C22⋊C4—862no—
298C42D4×D4311yescharacteristic
299C42D4×D4311yescharacteristic
300C42D4×D4311yescharacteristic
301C42#1062190011yescharacteristic
302C23—862no—
303C23C4×C22⋊D4311yescharacteristic
304Q8—44no—
305Q8—82no—
306Q8—1721no—
307Q8—1721no—
308D4—1722no—
309D4—1722no—
310D4—1722no—
311D4—1721no—
312D4—1721no—
313D4—1721no—
314D4—1721no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—41no—
318C2×C4—42no—
319C2×C4—82no—
320C2×C4—862no—
321C2×C4—1722no—
322C2×C4—1722no—
323C2×C4C22⋊C4×D4311yescharacteristic
324C2×C4(C22⋊D43)⋊C411yescharacteristic
325C2×C4#1306329311yescharacteristic
326C2×C4#1306329611yescharacteristic
327C2×C4#1306329811yescharacteristic
328C2×C4#1306330711yescharacteristic
329C2×C4C2×#1062188411yescharacteristic
330C2×C4#1306334511yescharacteristic
331C2×C4#1306335011yescharacteristic
332C2×C4#1306335611yescharacteristic
333C8—22no—
334C8—41no—
335C8—81no—
336C8—3441no—
337C8—1722no—
338C8—1721no—
339C8—1721no—
340C22—21no—
341C22—21no—
342C22—1722no—
343C22—1722no—
344C22—1722no—
345C22#1458277511yescharacteristic
346C22C4×#1062188411yescharacteristic
347C22#1458299711yescharacteristic
348C4—21no—
349C4—21no—
350C4—21no—
351C4—82no—
352C4—1722no—
353C4#1458304911yescharacteristic
354C4#1458305911yescharacteristic
355C4#1458310111yescharacteristic
356C4#1458311111yescharacteristic
357C4#1458316511yescharacteristic
358C4#1458317311yescharacteristic
359C2—21no—
360C2—21no—
361C2—3442no—
362C2#1913493211yescharacteristic
363C2#1913510711yescharacteristic
364C2#1913513911yescharacteristic
subgroupG/H
centerC22#14582775
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1997C2
socleC22×C43#386
prime radical#14583449C22
cosocleC2×C42×C43C23
hypercenter#1997D43
hypocenterC43#9267
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1997

Complements

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

NH ≅ G/Ntype
4. C2×#14582648C2semidirect
5. #19132490C2semidirect
6. #19132446C2semidirect
7. C43×#1997C2semidirect
93. M16×C43SD16semidirect
179. #1997D43semidirect
212. C43#9267semidirect
278. M16#10621884semidirect

Maximal subgroups

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

subgroupindex
#191455202
#191433412
#191332732
C2×#145826482
#191324902
#191324462
C43×#19972
#926743