Finite Group Databasebeta

← #25013560

Subgroups — #25013560

Order 11008.

512 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583169C211yesmaximal, characteristic
2#19143195C211yesmaximal, characteristic, complemented
3#19136312C211yesmaximal, characteristic, complemented
4C2×#14582701C211yesmaximal, characteristic, complemented
5#19132704C211yesmaximal, characteristic, complemented
6#19132691C211yesmaximal, characteristic, complemented
7C2×C43×#350C211yesmaximal, characteristic, complemented
8C2×#13063350—21no—
9C22×D344C2211yescharacteristic
10#14583382—21no—
11#14583169—22no—
12#14583169C414yescomplemented
13C2×#13063261C2211yescharacteristic
14#14582941—22no—
15#14582941—21no—
16#14582937—21no—
17#14582937C2211yescharacteristic
18C2×#13063259—21no—
19C2×#13063259C2211yescharacteristic
20C2×#13063241—21no—
21#14582701—22no—
22#14582701—21no—
23#14582701—21no—
24C2×#131×C43C2211yescharacteristic
25C2×M32×C43C2211yescharacteristic
26C22×C16×C43C2211yescharacteristic
27C43×#350—22no—
28C22×D172—21no—
29#13063350—24no—
30#13063350—42no—
31C2×#10621884—41no—
32C2×D344—21no—
33C2×D344—21no—
34C2×D344—21no—
35C2×D344—21no—
36C2×D344—21no—
37C2×D344C2×C412yescomplemented
38C2×#10621882—41no—
39C2×#10621877—21no—
40Q8×Dic43—41no—
41D4×Dic43—42no—
42D4×Dic43—41no—
43#13063284—22no—
44#13063284—21no—
45C2×C4⋊Dic43—22no—
46C2×C4⋊Dic43—21no—
47#13063261—21no—
48#13063261C2×C412yescomplemented
49#13063259—22no—
50#13063259—21no—
51#13063259D411yescharacteristic
52#13063259D412yes—
53#13063259D411yescharacteristic
54#13063257—22no—
55#13063257—21no—
56#13063241—24no—
57C2×#41×C43D411yescharacteristic
58#131×C43—21no—
59#131×C43—21no—
60#131×C43C2×C412yes—
61#131×C43D412yes—
62C2×M16×C43—21no—
63C2×M16×C43D411yescharacteristic
64C22×C8×C43—21no—
65C22×C8×C43C2311yescharacteristic
66M32×C43—21no—
67M32×C43—21no—
68C2×C16×C43—21no—
69C2×C16×C43—21no—
70C2×C16×C43—21no—
71C2×C16×C43—21no—
72C23×D43—41no—
73#41×C43—21no—
74#41×C43—21no—
75#41×C43C22⋊C412yes—
76#41×C43SD1612yes—
77C2×Q8×C43D811yescharacteristic
78C2×D4×C43—21no—
79C2×D4×C43D811yescharacteristic
80C22×C4×C43—21no—
81C22×C4×C43C2×D411yescharacteristic
82C22×Dic43—42no—
83C22×Dic43—41no—
84C2×D172—22no—
85C2×D172—41no—
86C2×D172—41no—
87C2×D172—41no—
88C2×D172—41no—
89C2×D172—41no—
90M16×C43—21no—
91M16×C43—22no—
92M16×C43—22no—
93M16×C43C22⋊C412yes—
94C2×C8×C43—21no—
95C2×C8×C43—22no—
96C2×C8×C43—22no—
97C2×C8×C43C22×C411yescharacteristic
98C2×C8×C43C2×D411yescharacteristic
99C2×C8×C43C2×D411yescharacteristic
100C2×C8×C43C2×D411yescharacteristic
101C2×C8×C43#4111yescharacteristic
102C2×C8×C43#4111yescharacteristic
103C22⋊Dic43—42no—
104C22⋊Dic43—41no—
105#10621884—44no—
106#10621882—44no—
107C4⋊Dic43—21no—
108C4⋊Dic43—22no—
109C4⋊Dic43—21no—
110C4⋊Dic43—42no—
111C4⋊Dic43—41no—
112C4×Dic43—42no—
113C4×Dic43—41no—
114#10621877—22no—
115#10621877—41no—
116C2×C43⋊C8—41no—
117D344—22no—
118D344—22no—
119D344—41no—
120D344—41no—
121C16×C43—41no—
122C16×C43—41no—
123C23×C43—21no—
124C23×C43AGL(1,ℤ/8)11yescharacteristic
125C22×D43—42no—
126C22×D43—81no—
127C22×D43—81no—
128C22×D43—161no—
129C22×D43—161no—
130Q8×C43—21no—
131Q8×C43#10212yes—
132D4×C43—22no—
133D4×C43—22no—
134D4×C43—21no—
135D4×C43#10212yes—
136C2×C4×C43—21no—
137C2×C4×C43—22no—
138C2×C4×C43—22no—
139C2×C4×C43C2×C22⋊C411yescharacteristic
140C2×C4×C43#12011yescharacteristic
141C2×C4×C43#12311yescharacteristic
142C2×C4×C43C2×D811yescharacteristic
143C2×C4×C43C2×SD1611yescharacteristic
144C2×C4×C43#13711yescharacteristic
145C2×Dic43—41no—
146C2×Dic43—42no—
147C2×Dic43—41no—
148C2×Dic43—161no—
149C2×Dic43—162no—
150D172—42no—
151D172—42no—
152D172—81no—
153D172—81no—
154C8×C43—22no—
155C8×C43C4×D411yescharacteristic
156C8×C43C4×D411yescharacteristic
157C8×C43#12111yescharacteristic
158C8×C43#12111yescharacteristic
159C43⋊C8—42no—
160#12996—431nomaximal, Sylow
161C22×C43—21no—
162C22×C43—21no—
163C22×C43—22no—
164C22×C43—41no—
165C22×C43—41no—
166C22×C43#41711yescharacteristic
167C22×C43#44711yescharacteristic
168C22×C43#48111yescharacteristic
169C2×D43—82no—
170C2×D43—162no—
171C2×D43—161no—
172C2×D43—161no—
173C2×D43—162no—
174C4×C43—22no—
175C4×C43#38611yescharacteristic
176C4×C43C2×#10211yescharacteristic
177C4×C43#44811yescharacteristic
178C4×C43#48011yescharacteristic
179Dic43—82no—
180Dic43—81no—
181Dic43—81no—
182C2×#472—431no—
183#2913—431no—
184#2140—431no—
185C2×#357—431no—
186C2×#350D4311yescharacteristic, complemented
187#1387—431no—
188#1382—431no—
189C2×C43—21no—
190C2×C43—21no—
191C2×C43—42no—
192C2×C43#187411yescharacteristic
193C2×C43#219211yescharacteristic
194C2×C43#219311yescharacteristic
195D43—162no—
196C2×AGL(1,ℤ/8)—861no—
197C22×D8—431no—
198C2×#131C2×D4311yescharacteristic
199#520—861no—
200C2×M32C2×D4311yescharacteristic
201C22×C16C2×D4311yescharacteristic
202#472—434no—
203#472—862no—
204C2×#108—431no—
205#428—862no—
206#428—861no—
207#427—431no—
208#427—861no—
209C2×#107—431no—
210C2×#107—861no—
211C2×#100—861no—
212#357—862no—
213#357—861no—
214#357—861no—
215#350—22no—
216C43#1299611yescharacteristic, complemented, Sylow
217C2×#41D17211yescharacteristic
218C22×D4—861no—
219AGL(1,ℤ/8)—864no—
220AGL(1,ℤ/8)—1722no—
221C2×SD16—1721no—
222C2×D8—432no—
223C2×D8—861no—
224C2×D8—861no—
225C2×D8—861no—
226C2×D8—861no—
227C2×D8—861no—
228C2×D8—1721no—
229#131—21no—
230#131—21no—
231#131C4×D4312yes—
232#131C22⋊D4312yes—
233C2×M16—21no—
234C2×M16—861no—
235C2×M16D17211yescharacteristic
236C22×C8—21no—
237C22×C8C22×D4311yescharacteristic
238C4×Q8—1721no—
239C4×D4—1722no—
240C4×D4—1721no—
241#117—862no—
242#117—861no—
243C2×C4⋊C4—862no—
244C2×C4⋊C4—861no—
245M32—21no—
246M32—21no—
247C2×C16—21no—
248C2×C16—21no—
249C2×C16—21no—
250C2×C16—21no—
251#108—432no—
252#108—861no—
253#107—432no—
254#107—431no—
255#107—431no—
256#107—862no—
257#107—861no—
258#106—862no—
259#106—861no—
260#100—864no—
261C24—1721no—
262#41—21no—
263#41—21no—
264#41#1062187312yes—
265#41(C2×D43)⋊C412yes—
266C2×Q8D34411yescharacteristic
267C2×D4—21no—
268C2×D4—862no—
269C2×D4—1721no—
270C2×D4—1721no—
271C2×D4—1721no—
272C2×D4—1721no—
273C2×D4—1721no—
274C2×D4D34411yescharacteristic
275C22×C4—21no—
276C22×C4—1722no—
277C22×C4—1721no—
278C22×C4C2×D17211yescharacteristic
279SD16—1724no—
280D8—862no—
281D8—862no—
282D8—1724no—
283D8—1721no—
284D8—1721no—
285M16—21no—
286M16—22no—
287M16—22no—
288M16—862no—
289M16—1721no—
290M16(C2×D43)⋊C412yes—
291C2×C8—21no—
292C2×C8—22no—
293C2×C8—22no—
294C2×C8—1721no—
295C2×C8C2×C4×D4311yescharacteristic
296C2×C8D4×D4311yescharacteristic
297C2×C8D4×D4311yescharacteristic
298C2×C8#1062190011yescharacteristic
299C2×C8#1062190011yescharacteristic
300C2×C8C2×C22⋊D4311yescharacteristic
301C4⋊C4—861no—
302C4⋊C4—862no—
303C4⋊C4—861no—
304C4⋊C4—1722no—
305C4⋊C4—1721no—
306C22⋊C4—1722no—
307C22⋊C4—1721no—
308C42—1722no—
309C42—1721no—
310C16—41no—
311C16—41no—
312C23—21no—
313C23—3441no—
314C23—3441no—
315C23—1722no—
316C23—6881no—
317C23—6881no—
318C23#1306335311yescharacteristic
319Q8—21no—
320Q8#1306324712yes—
321D4—22no—
322D4—22no—
323D4—21no—
324D4—3441no—
325D4—3441no—
326D4—1722no—
327D4—1722no—
328D4#1306324712yes—
329C2×C4—21no—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—1721no—
333C2×C4—1722no—
334C2×C4—1721no—
335C2×C4—6881no—
336C2×C4—6882no—
337C2×C4C2×(C2×D43)⋊C411yescharacteristic
338C2×C4#1306329511yescharacteristic
339C2×C4#1306330911yescharacteristic
340C2×C4C2×D34411yescharacteristic
341C2×C4C2×#1062187311yescharacteristic
342C2×C4#1306335811yescharacteristic
343C8—22no—
344C8—1722no—
345C8(C22⋊D43)⋊C411yescharacteristic
346C8(C22⋊D43)⋊C411yescharacteristic
347C8#1306329711yescharacteristic
348C8#1306329711yescharacteristic
349C22—21no—
350C22—21no—
351C22—22no—
352C22—41no—
353C22—41no—
354C22—3442no—
355C22—6882no—
356C22—6882no—
357C22—6881no—
358C22—6881no—
359C22#1458290111yescharacteristic
360C22#1458303511yescharacteristic
361C22#1458321811yescharacteristic
362C4—22no—
363C4—3442no—
364C4—3441no—
365C4—3441no—
366C4#1458277611yescharacteristic
367C4C2×#1306324711yescharacteristic
368C4#1458304011yescharacteristic
369C4#1458321311yescharacteristic
370C2—21no—
371C2—21no—
372C2—42no—
373C2—6882no—
374C2#1913491011yescharacteristic
375C2#1913655411yescharacteristic
376C2#1913656111yescharacteristic
subgroupG/H
centerC22#14583035
commutatorC2×C8×C43C22×C4
FrattiniC22×C8C22×D43
FittingC2×C43×#350C2
socleC22×C43#447
prime radicalC2×#14583169C2
cosocleC22×C8×C43C23
hypercenterC2×#350D43
hypocenterC43#12996
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#131 ◁ C2×#350

Complements

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

NH ≅ G/Ntype
2. #19143195C2semidirect
3. #19136312C2semidirect
4. C2×#14582701C2semidirect
5. #19132704C2semidirect
6. #19132691C2semidirect
7. C2×C43×#350C2semidirect
12. #14583169C4semidirect
37. C2×D344C2×C4semidirect
48. #13063261C2×C4semidirect
186. C2×#350D43semidirect
216. C43#12996semidirect

Maximal subgroups

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

subgroupindex
C2×#145831692
#191431952
#191363122
C2×#145827012
#191327042
#191326912
C2×C43×#3502
#1299643