Finite Group Databasebeta

← #25013516

Subgroups — #25013516

Order 11008.

456 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583315C211yesmaximal, characteristic, complemented
2#19143496C211yesmaximal, characteristic
3#19136224C211yesmaximal, characteristic, complemented
4#19136216C211yesmaximal, characteristic, complemented
5#19132683C211yesmaximal, characteristic, complemented
6#19132680C211yesmaximal, characteristic, complemented
7C2×C43×#350C211yesmaximal, characteristic, complemented
8#14583697C411yescharacteristic
9C2×#13063331C2211yescharacteristic
10#14583315—22no—
11#14583315—22no—
12C2×#13063265C2211yescharacteristic
13C2×#13063265C2211yescharacteristic
14C2×#13063264—21no—
15C2×C16×D43—21no—
16#14583019—22no—
17#14583014—22no—
18#14582947C411yescharacteristic
19#14582916C411yescharacteristic
20#14582915C411yescharacteristic
21#14582854C2211yescharacteristic
22#14582684—22no—
23#14582681—22no—
24C2×#131×C43C2211yescharacteristic
25C2×M32×C43C2211yescharacteristic
26C22×C16×C43C2211yescharacteristic
27C43×#350—21no—
28C43×#350—21no—
29C2×#10621898C2×C411yescharacteristic
30#13063356C812yes—
31#13063355—21no—
32#13063351C812yes—
33#13063350—21no—
34#13063345—22no—
35#13063331—21no—
36#13063331—21no—
37#13063331D412yes—
38#13063331D412yes—
39C2×#10621877C2×C411yescharacteristic
40C2×#10621877C2×C411yescharacteristic
41C2×#10621872—21no—
42C2×C8×D43—21no—
43#13063284C2×C411yescharacteristic
44#13063265—21no—
45#13063265—21no—
46#13063265—21no—
47#13063265D412yes—
48#13063264—24no—
49C2×C43⋊C16—21no—
50C2×C43⋊C16—21no—
51C16×D43—24no—
52#13063260—22no—
53#13063252—22no—
54#13063251—22no—
55#13063235—21no—
56C8×Dic43—21no—
57C2×#41×C43C2×C411yescharacteristic
58#131×C43—21no—
59#131×C43—21no—
60#131×C43—21no—
61#131×C43—21no—
62C2×M16×C43—21no—
63C2×M16×C43C2×C411yescharacteristic
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×C43D411yescharacteristic
72C2×C16×C43D411yescharacteristic
73#41×C43—21no—
74#41×C43—21no—
75#41×C43—21no—
76#41×C43—21no—
77C2×Q8×C43C2×C811yescharacteristic
78C2×D4×C43—21no—
79C2×D4×C43C2×C811yescharacteristic
80C22×C4×C43—21no—
81C22×C4×C43C22×C411yescharacteristic
82C2×C22⋊D43—21no—
83#10621898—21no—
84#10621898—21no—
85#10621898C22⋊C412yes—
86#10621898C2×C812yes—
87C2×D172M1611yescharacteristic
88C2×C4×D43—21no—
89C2×Dic86M1611yescharacteristic
90M16×C43—21no—
91M16×C43—21no—
92M16×C43—41no—
93M16×C43—41no—
94C2×C8×C43—21no—
95C2×C8×C43—41no—
96C2×C8×C43—41no—
97C2×C8×C43C2×D411yescharacteristic
98C2×C8×C43C2×D411yescharacteristic
99C2×C8×C43C2×D411yescharacteristic
100C2×C8×C43C2×D411yescharacteristic
101C2×C8×C43#4111yescharacteristic
102C2×C8×C43#4111yescharacteristic
103C22⋊Dic43—21no—
104#10621885—22no—
105#10621884—22no—
106#10621883—22no—
107#10621882—22no—
108C4⋊Dic43—21no—
109C4×Dic43—21no—
110#10621877—21no—
111#10621877—21no—
112#10621877C22⋊C412yes—
113#10621877C2×C812yes—
114C2×C43⋊C8—21no—
115C2×C43⋊C8—21no—
116#10621872—22no—
117#10621872—22no—
118C8×D43—22no—
119C8×D43—22no—
120C16×C43—21no—
121C16×C43—21no—
122C16×C43—41no—
123C43⋊C16—22no—
124C43⋊C16—41no—
125C23×C43—21no—
126C23×C43#13111yescharacteristic
127C22×D43—21no—
128Q8×C43—21no—
129Q8×C43—21no—
130D4×C43—21no—
131D4×C43—21no—
132D4×C43—41no—
133D4×C43—41no—
134C2×C4×C43—21no—
135C2×C4×C43—41no—
136C2×C4×C43—41no—
137C2×C4×C43C2×C22⋊C411yescharacteristic
138C2×C4×C43C4×D411yescharacteristic
139C2×C4×C43C4×D411yescharacteristic
140C2×C4×C43C22×C811yescharacteristic
141C2×C4×C43C2×M1611yescharacteristic
142C2×C4×C43#13111yescharacteristic
143C22⋊D43—22no—
144C22⋊D43—22no—
145C2×Dic43—21no—
146C2×Dic43—41no—
147D172—21no—
148D172C22⋊C812yes—
149C4×D43—22no—
150C4×D43—22no—
151Dic86—21no—
152Dic86C22⋊C812yes—
153C8×C43—41no—
154C8×C43#12011yescharacteristic
155C8×C43#12111yescharacteristic
156C8×C43#12111yescharacteristic
157C8×C43#12311yescharacteristic
158C43⋊C8—22no—
159C43⋊C8—22no—
160#12987—431nomaximal, Sylow
161C22×C43—41no—
162C22×C43—41no—
163C22×C43—81no—
164C22×C43#40811yescharacteristic
165C22×C43C8×D411yescharacteristic
166C22×C43#43511yescharacteristic
167C2×D43—22no—
168C2×D43—42no—
169C4×C43—41no—
170C4×C43#38611yescharacteristic
171C4×C43C2×C22⋊C811yescharacteristic
172C4×C43C8×D411yescharacteristic
173C4×C43#43511yescharacteristic
174Dic43—22no—
175Dic43—81no—
176C2×#504—431no—
177#2955—431no—
178#2117—431no—
179C2×#350D4311yescharacteristic, complemented
180#2115—431no—
181#1379—431no—
182#1378—431no—
183C2×C43—21no—
184C2×C43—21no—
185C2×C43—21no—
186C2×C43—81no—
187C2×C43#186911yescharacteristic
188D43—42no—
189#575—431no—
190C2×#131—431no—
191C2×#131C2×D4311yescharacteristic
192#504—862no—
193#504—862no—
194C2×M32—431no—
195C2×M32—431no—
196C2×M32—861no—
197C2×M32C2×D4311yescharacteristic
198C22×C16—861no—
199C22×C16C2×D4311yescharacteristic
200#444—862no—
201#443—862no—
202#430—431no—
203#421—431no—
204#421—431no—
205#405—431no—
206#350—21no—
207#350—21no—
208#350—862no—
209#349—862no—
210C43#1298711yescharacteristic, complemented, Sylow
211C2×#41—431no—
212C2×#41C4×D4311yescharacteristic
213#137—432no—
214#137—861no—
215AGL(1,ℤ/8)—432no—
216AGL(1,ℤ/8)—861no—
217#135—862no—
218#131—21no—
219#131—21no—
220#131—21no—
221#131—21no—
222#131—432no—
223#131—432no—
224#131—861no—
225#131—861no—
226C2×M16—21no—
227C2×M16—431no—
228C2×M16—431no—
229C2×M16—861no—
230C2×M16C4×D4311yescharacteristic
231C22×C8—21no—
232C22×C8—861no—
233C22×C8C22×D4311yescharacteristic
234#117—431no—
235M32—21no—
236M32—21no—
237M32—432no—
238M32—864no—
239M32—861no—
240M32—861no—
241M32—861no—
242C2×C16—21no—
243C2×C16—21no—
244C2×C16—21no—
245C2×C16—864no—
246C2×C16—861no—
247C2×C16—861no—
248C2×C16C22⋊D4311yescharacteristic
249C2×C16C22⋊D4311yescharacteristic
250#108—862no—
251#104—862no—
252#104—862no—
253#97—861no—
254C4×C8—861no—
255#41—21no—
256#41—21no—
257#41—21no—
258#41—21no—
259#41—432no—
260#41—432no—
261#41—861no—
262#41—861no—
263C2×Q8—431no—
264C2×Q8C8×D4311yescharacteristic
265C2×D4—21no—
266C2×D4—431no—
267C2×D4—861no—
268C2×D4C8×D4311yescharacteristic
269C22×C4—21no—
270C22×C4—861no—
271C22×C4C2×C4×D4311yescharacteristic
272Q16—862no—
273SD16—862no—
274SD16—862no—
275D8—862no—
276M16—21no—
277M16—21no—
278M16—41no—
279M16—41no—
280M16—432no—
281M16—432no—
282M16—861no—
283M16—861no—
284M16—862no—
285M16—862no—
286C2×C8—21no—
287C2×C8—41no—
288C2×C8—41no—
289C2×C8—861no—
290C2×C8—861no—
291C2×C8—862no—
292C2×C8—862no—
293C2×C8#1062189811yescharacteristic
294C2×C8D4×D4311yescharacteristic
295C2×C8D4×D4311yescharacteristic
296C2×C8D4×D4311yescharacteristic
297C2×C8#1062190011yescharacteristic
298C2×C8C2×C22⋊D4311yescharacteristic
299C4⋊C4—861no—
300C22⋊C4—861no—
301C42—861no—
302C16—21no—
303C16—21no—
304C16—41no—
305C16—862no—
306C16—1721no—
307C23—21no—
308C23—861no—
309C23#1306333311yescharacteristic
310Q8—21no—
311Q8—21no—
312Q8—432no—
313Q8—861no—
314D4—21no—
315D4—21no—
316D4—41no—
317D4—41no—
318D4—432no—
319D4—862no—
320D4—862no—
321D4—861no—
322C2×C4—21no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—861no—
326C2×C4—862no—
327C2×C4—862no—
328C2×C4—1721no—
329C2×C4C22⋊C4×D4311yescharacteristic
330C2×C4(C22⋊D43)⋊C411yescharacteristic
331C2×C4C4×C22⋊D4311yescharacteristic
332C2×C4C2×C8×D4311yescharacteristic
333C2×C4M16×D4311yescharacteristic
334C2×C4#1306333111yescharacteristic
335C8—41no—
336C8—862no—
337C8—862no—
338C8#1306329311yescharacteristic
339C8#1306329611yescharacteristic
340C8#1306329811yescharacteristic
341C8#1306330711yescharacteristic
342C22—41no—
343C22—41no—
344C22—81no—
345C22—862no—
346C22—1722no—
347C22#1458286411yescharacteristic
348C22(C22⋊D43)⋊C811yescharacteristic
349C22#1458296811yescharacteristic
350C4—41no—
351C4—862no—
352C4—3441no—
353C4#1458277511yescharacteristic
354C4C22⋊C8×D4311yescharacteristic
355C4C8×C22⋊D4311yescharacteristic
356C4#1458297311yescharacteristic
357C2—21no—
358C2—21no—
359C2—21no—
360C2—81no—
361C2—1722no—
362C2#1913488411yescharacteristic
subgroupG/H
centerC8#13063296
commutatorC2×C4×C43C22×C8
FrattiniC22×C8C22×D43
FittingC2×C43×#350C2
socleC2×C43#1869
prime radical#14583697C4
cosocleC22×C8×C43C23
hypercenterC2×#350D43
hypocenterC43#12987
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C8 ◁ C22×C8 ◁ C2×#350

Complements

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

NH ≅ G/Ntype
1. C2×#14583315C2semidirect
3. #19136224C2semidirect
4. #19136216C2semidirect
5. #19132683C2semidirect
6. #19132680C2semidirect
7. C2×C43×#350C2semidirect
179. C2×#350D43semidirect
210. C43#12987semidirect

Maximal subgroups

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

subgroupindex
C2×#145833152
#191434962
#191362242
#191362162
#191326832
#191326802
C2×C43×#3502
#1298743