Finite Group Databasebeta

← #24993117

Subgroups — #24993117

Order 11008.

480 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145723C211yesmaximal, characteristic
2#19143341C211yesmaximal, characteristic
3#19133273C211yesmaximal, characteristic
4C2×#14582645C211yesmaximal, characteristic, complemented
5#19132490C211yesmaximal, characteristic, complemented
6#19132446C211yesmaximal, characteristic, complemented
7C43×#1997C211yesmaximal, characteristic, complemented
8C2×#13063333—21no—
9#14583449C2211yescharacteristic
10#14583295—21no—
11#14583247—21no—
12#14583217C414yes—
13#14583186—22no—
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#14582646—21no—
22#14582645—21no—
23#14582645—21no—
24#14582642—21no—
25C2×C4⋊Q8×C43C2211yescharacteristic
26C43×#423C2211yescharacteristic
27C4×M16×C43C2211yescharacteristic
28C43×#343—21no—
29C43×#343—21no—
30C2×#10621898—21no—
31#13063333—42no—
32#13063333—42no—
33C2×#10621872—22no—
34C22×C43⋊C8—21no—
35C22×C43⋊C8—21no—
36C2×C8×D43—22no—
37#13063325D411yescharacteristic
38#13063322D411yescharacteristic
39#13063313—21no—
40#13063299—21no—
41#13063299C2×C412yes—
42C4×D172—21no—
43C4×D172D412yes—
44#13063256—24no—
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#13063245—24no—
52C22⋊(C43⋊C8)C2×C412yes—
53(C2×D43)⋊C8—22no—
54(C2×D43)⋊C8—22no—
55C4×C43⋊C8—21no—
56C22×Q8×C43—21no—
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×C43C2×C412yes—
66C2×C42×C43C2311yescharacteristic
67C4⋊C8×C43—21no—
68C4⋊C8×C43—21no—
69#97×C43—21no—
70C4×C8×C43—21no—
71C2×Q8×C43—41no—
72C2×Q8×C43—41no—
73C2×Q8×C43—81no—
74C2×Q8×C43—81no—
75C22×C4×C43—22no—
76C22×C4×C43C22×C411yescharacteristic
77C22×C4×C43C2×D411yescharacteristic
78C22×C4×C43#4111yescharacteristic
79C2×C22⋊D43—22no—
80#10621898—41no—
81#10621898—41no—
82#10621898—41no—
83#10621898—41no—
84C2×D172—21no—
85C2×D172—21no—
86C2×D172C22⋊C412yes—
87C2×C4×D43—22no—
88C2×Dic86—21no—
89M16×C43—21no—
90M16×C43—21no—
91M16×C43—21no—
92M16×C43—41no—
93M16×C43—41no—
94M16×C43SD1612yes—
95C2×C8×C43—21no—
96C2×C8×C43—21no—
97C2×C8×C43—41no—
98C4⋊C4×C43—22no—
99C4⋊C4×C43—22no—
100C4⋊C4×C43—41no—
101C4⋊C4×C43—41no—
102C42×C43C2×D411yescharacteristic
103C42×C43C2×D411yescharacteristic
104C42×C43C2×D411yescharacteristic
105C42×C43#4111yescharacteristic
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—82no—
122Q8×C43—81no—
123Q8×C43—81no—
124C2×C4×C43—21no—
125C2×C4×C43—21no—
126C2×C4×C43—41no—
127C2×C4×C43—42no—
128C2×C4×C43—82no—
129C2×C4×C43C2×C22⋊C411yescharacteristic
130C2×C4×C43C4×D411yescharacteristic
131C2×C4×C43#12011yescharacteristic
132C2×C4×C43#12111yescharacteristic
133C2×C4×C43#12111yescharacteristic
134C2×C4×C43#12311yescharacteristic
135C2×C4×C43C2×SD1611yescharacteristic
136C2×C4×C43#13511yescharacteristic
137C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
138C2×C4×C43#13711yescharacteristic
139C22⋊D43—42no—
140C22⋊D43—42no—
141C2×Dic43—22no—
142D172—42no—
143D172—41no—
144D172—41no—
145D172—41no—
146D172—41no—
147C4×D43—42no—
148C4×D43—42no—
149Dic86—41no—
150Dic86—41no—
151C8×C43—22no—
152C8×C43—41no—
153C8×C43—81no—
154C43⋊C8—42no—
155C43⋊C8—41no—
156C43⋊C8—41no—
157C43⋊C8—81no—
158#9269—431nomaximal, Sylow
159C22×C43—21no—
160C22×C43—21no—
161C22×C43#38611yescharacteristic
162C22×C43C4×SD1611yescharacteristic
163C22×C43#44011yescharacteristic
164C2×D43—42no—
165C2×D43—42no—
166C2×D43—42no—
167C4×C43—21no—
168C4×C43—21no—
169C4×C43—21no—
170C4×C43—82no—
171C4×C43#45011yescharacteristic
172C4×C43#45211yescharacteristic
173C4×C43#46111yescharacteristic
174C4×C43#46311yescharacteristic
175C4×C43#47111yescharacteristic
176C4×C43#47211yescharacteristic
177Dic43—42no—
178#3227—431no—
179#2935—431no—
180#1997D4311yescharacteristic, complemented
181#1547—431no—
182C2×#332—431no—
183#1301—431no—
184#1283—431no—
185C2×C43—21no—
186C2×C43—21no—
187C2×C43#187711yescharacteristic
188C2×C43#190711yescharacteristic
189C2×C43#191511yescharacteristic
190D43—82no—
191C2×#131—861no—
192#532—431no—
193C2×C4⋊Q8C2×D4311yescharacteristic
194#498—861no—
195#486—861no—
196#481—434no—
197#476—862no—
198#436—861no—
199#435—862no—
200C8×D4—861no—
201#431—431no—
202#423C2×D4311yescharacteristic
203C2×C4⋊C8—431no—
204C2×C4⋊C8—431no—
205#408—861no—
206C4×M16C2×D4311yescharacteristic
207#343—21no—
208#343—21no—
209#332—861no—
210#332—861no—
211#332—861no—
212#331—861no—
213C43#926911yescharacteristic, complemented, Sylow
214C2×#41—861no—
215C22×Q8—21no—
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⋊C4C4×D4312yes—
238C2×C42C22×D4311yescharacteristic
239#106—864no—
240C4⋊C8—21no—
241C4⋊C8—21no—
242C4⋊C8—431no—
243C4⋊C8—431no—
244C4⋊C8—861no—
245C4⋊C8—861no—
246C4⋊C8—861no—
247C4⋊C8—861no—
248#102—864no—
249C22⋊C8—432no—
250C22⋊C8—862no—
251C22⋊C8—862no—
252#97—21no—
253C4×C8—21no—
254C4×C8—861no—
255#41—1721no—
256#41—1721no—
257#41—1721no—
258#41—1721no—
259C2×Q8—41no—
260C2×Q8—41no—
261C2×Q8—81no—
262C2×Q8—81no—
263C2×Q8—861no—
264C2×D4—432no—
265C2×D4—862no—
266C2×D4—861no—
267C2×D4—861no—
268C22×C4—22no—
269C22×C4—862no—
270C22×C4C2×C4×D4311yescharacteristic
271C22×C4#1062189811yescharacteristic
272C22×C4C2×C22⋊D4311yescharacteristic
273M16—21no—
274M16—21no—
275M16—21no—
276M16—41no—
277M16—41no—
278M16—1724no—
279M16#1062188412yes—
280C2×C8—21no—
281C2×C8—21no—
282C2×C8—41no—
283C2×C8—862no—
284C2×C8—861no—
285C2×C8—861no—
286C2×C8—3441no—
287C2×C8—1724no—
288C2×C8—1721no—
289C2×C8—1721no—
290C2×C8—1721no—
291C4⋊C4—22no—
292C4⋊C4—22no—
293C4⋊C4—41no—
294C4⋊C4—41no—
295C4⋊C4—432no—
296C4⋊C4—861no—
297C22⋊C4—862no—
298C22⋊C4—862no—
299C42D4×D4311yescharacteristic
300C42D4×D4311yescharacteristic
301C42D4×D4311yescharacteristic
302C42#1062190011yescharacteristic
303C23—862no—
304C23C4×C22⋊D4311yescharacteristic
305Q8—82no—
306Q8—81no—
307Q8—81no—
308Q8—1721no—
309Q8—1721no—
310D4—1722no—
311D4—1722no—
312D4—1722no—
313D4—1721no—
314D4—1721no—
315D4—1721no—
316D4—1721no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—41no—
320C2×C4—42no—
321C2×C4—82no—
322C2×C4—862no—
323C2×C4—1722no—
324C2×C4—1722no—
325C2×C4C22⋊C4×D4311yescharacteristic
326C2×C4(C22⋊D43)⋊C411yescharacteristic
327C2×C4#1306329311yescharacteristic
328C2×C4#1306329611yescharacteristic
329C2×C4#1306329811yescharacteristic
330C2×C4#1306330711yescharacteristic
331C2×C4C2×#1062188411yescharacteristic
332C2×C4#1306334511yescharacteristic
333C2×C4#1306335011yescharacteristic
334C2×C4#1306335611yescharacteristic
335C8—22no—
336C8—41no—
337C8—81no—
338C8—3441no—
339C8—1722no—
340C8—1721no—
341C8—1721no—
342C22—21no—
343C22—21no—
344C22—1722no—
345C22—1722no—
346C22—1722no—
347C22#1458277511yescharacteristic
348C22C4×#1062188411yescharacteristic
349C22#1458299711yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—82no—
354C4—1722no—
355C4#1458304911yescharacteristic
356C4#1458305911yescharacteristic
357C4#1458310111yescharacteristic
358C4#1458311111yescharacteristic
359C4#1458316111yescharacteristic
360C4#1458316811yescharacteristic
361C2—21no—
362C2—21no—
363C2—3442no—
364C2#1913493211yescharacteristic
365C2#1913510011yescharacteristic
366C2#1913514411yescharacteristic
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#9269
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×#14582645C2semidirect
5. #19132490C2semidirect
6. #19132446C2semidirect
7. C43×#1997C2semidirect
180. #1997D43semidirect
213. C43#9269semidirect

Maximal subgroups

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

subgroupindex
#191457232
#191433412
#191332732
C2×#145826452
#191324902
#191324462
C43×#19972
#926943