Finite Group Databasebeta

← #25079107

Subgroups — #25079107

Order 11008.

770 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144591C212yesmaximal, complemented
2C2×#14582978C211yesmaximal, characteristic, complemented
3#19134081C212yesmaximal, complemented
4#19134071C212yesmaximal, complemented
5#19134057C214yesmaximal, complemented
6#19133343C211yesmaximal, characteristic, complemented
7#19133244C212yesmaximal, complemented
8C43×#3147C211yesmaximal, characteristic, complemented
9C22×#10621872—21no—
10C2×C4×D172C2211yescharacteristic
11#14583210—22no—
12#14583176C2214yes—
13#14583091C2214yes—
14#14583032—22no—
15C4×#10621882—24no—
16#14582978—21no—
17#14582978—21no—
18#14582978C2212yes—
19#14582978C2212yes—
20#14582952C2212yes—
21C2×C4⋊(C43⋊C8)C2211yescharacteristic
22C2×(C2×D43)⋊C8—21no—
23#14582652C2212yescomplemented
24#14582650C2212yescomplemented
25#14582645C2214yescomplemented
26#14582643C2214yescomplemented
27C2×#135×C43—21no—
28C2×#135×C43—21no—
29C43×#532C2212yes—
30C43×#495—21no—
31C43×#495—21no—
32C43×#494C2211yescharacteristic, complemented
33C43×#493C2211yescharacteristic, complemented
34C43×#492C2212yescomplemented
35C2×C4×C8×C43C2211yescharacteristic
36C22×D172D411yescharacteristic
37C22×C4×D43—21no—
38C2×#10621882—24no—
39C2×#10621872—22no—
40C2×#10621872—22no—
41C2×#10621872—44no—
42C22×C43⋊C8—21no—
43C4×D172—21no—
44C4×D172—21no—
45C4×D172D412yes—
46C4×D172C2312yes—
47C2×C4⋊Dic43D411yescharacteristic
48C2×(C2×D43)⋊C4—21no—
49#13063258—24no—
50C4⋊(C43⋊C8)—21no—
51C4⋊(C43⋊C8)C2314yes—
52C4⋊(C43⋊C8)C2312yes—
53#13063246—24no—
54#13063245—24no—
55C22⋊(C43⋊C8)—22no—
56(C2×D43)⋊C8—22no—
57(C2×D43)⋊C8—22no—
58C4×C43⋊C8—22no—
59C2×#41×C43—22no—
60#135×C43—44no—
61#135×C43—44no—
62C2×Q16×C43—21no—
63C2×Q16×C43—21no—
64C2×SD16×C43—22no—
65C2×SD16×C43—22no—
66C2×D8×C43—21no—
67C2×D8×C43—21no—
68C22×C8×C43D411yescharacteristic
69C22×C8×C43D411yescharacteristic
70C4⋊Q8×C43C2312yes—
71#127×C43C2312yes—
72#124×C43—22no—
73#121×C43—22no—
74#121×C43—22no—
75C4×D4×C43—22no—
76C4×D4×C43—22no—
77C2×C42×C43C2311yescharacteristic
78C4×C8×C43D411yescharacteristic
79C4×C8×C43D411yescharacteristic
80C4×C8×C43C2311yescharacteristic
81C4×C8×C43C2311yescharacteristic
82C23×D43—21no—
83#41×C43—44no—
84#41×C43—44no—
85C2×Q8×C43—22no—
86C2×D4×C43—22no—
87C2×D4×C43—22no—
88C2×D4×C43—22no—
89C2×D4×C43—42no—
90C22×C4×C43—42no—
91C22×C4×C43C2×D411yescharacteristic
92C22×C4×C43C2×D411yescharacteristic
93C22×C4×C43#4111yescharacteristic
94C22×Dic43—21no—
95C2×D172—21no—
96C2×D172—42no—
97C2×D172C2×D412yes—
98C2×C4×D43—22no—
99C2×C4×D43—22no—
100C2×C4×D43—42no—
101C2×C4×D43—42no—
102Q16×C43—42no—
103Q16×C43—42no—
104SD16×C43—44no—
105SD16×C43—44no—
106D8×C43—42no—
107D8×C43—42no—
108C2×C8×C43—22no—
109C2×C8×C43D814yescomplemented
110C2×C8×C43C2×D411yescharacteristic
111C2×C8×C43C2×D411yescharacteristic
112C2×C8×C43C2×D411yescharacteristic
113C2×C8×C43C2×D411yescharacteristic
114C4⋊C4×C43—22no—
115C4⋊C4×C43—22no—
116C22⋊C4×C43—42no—
117C22⋊C4×C43—42no—
118C42×C43C2×D411yescharacteristic
119C42×C43C2×D411yescharacteristic
120C42×C43#4111yescharacteristic
121C42×C43C2411yescharacteristic
122#10621882—48no—
123(C2×D43)⋊C4—22no—
124(C2×D43)⋊C4—22no—
125C4⋊Dic43—21no—
126C4⋊Dic43C2×D412yes—
127C2×C43⋊C8—24no—
128C2×C43⋊C8—22no—
129C2×C43⋊C8—42no—
130#10621872—44no—
131#10621872—44no—
132C23×C43—42no—
133C23×C43#12111yescharacteristic
134C22×D43—22no—
135C22×D43—42no—
136C22×D43—42no—
137C22×D43—42no—
138Q8×C43—42no—
139Q8×C43—42no—
140D4×C43—42no—
141D4×C43—42no—
142D4×C43—44no—
143D4×C43—82no—
144D4×C43—84no—
145C2×C4×C43—22no—
146C2×C4×C43—41no—
147C2×C4×C43—42no—
148C2×C4×C43—84no—
149C2×C4×C43#12111yescharacteristic
150C2×C4×C43#12111yescharacteristic
151C2×C4×C43#12111yescharacteristic
152C2×C4×C43C2×D812yes—
153C2×C4×C43AGL(1,ℤ/8)12yes—
154C2×C4×C43C22×D411yescharacteristic
155C2×C4×C43C22×D411yescharacteristic
156C2×C4×C43C2×#4111yescharacteristic
157C2×Dic43—22no—
158C2×Dic43—42no—
159D172—24no—
160D172—42no—
161C4×D43—42no—
162C4×D43—42no—
163C4×D43—44no—
164C8×C43—21no—
165C8×C43—21no—
166C8×C43C2×D812yes—
167C8×C43C2×D812yes—
168C43⋊C8—42no—
169C43⋊C8—44no—
170#19133—431nomaximal, Sylow
171C22×C43—21no—
172C22×C43—21no—
173C22×C43—82no—
174C22×C43—82no—
175C22×C43—82no—
176C22×C43#45912yes—
177C22×C43C2×#12111yescharacteristic
178C2×D43—42no—
179C2×D43—42no—
180C2×D43—42no—
181C2×D43—84no—
182C4×C43—21no—
183C4×C43—21no—
184C4×C43—21no—
185C4×C43—82no—
186C4×C43#45912yes—
187C4×C43C22×D811yescharacteristic
188C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
189C4×C43#57512yes—
190Dic43—42no—
191#3147D4311yescharacteristic, complemented
192#3100—432no—
193C2×#436—431no—
194#1689—432no—
195#1687—432no—
196#1685—434no—
197#1564—431no—
198#1540—432no—
199C2×C43—22no—
200C2×C43—162no—
201C2×C43C2×#45911yescharacteristic
202C2×C43#305411yescharacteristic
203C2×C43#306711yescharacteristic
204D43—82no—
205C2×#135—21no—
206C2×#135—21no—
207C22×M16—861no—
208#532C2×D4312yes—
209C2×C4×D4—431no—
210#495—21no—
211#495—21no—
212#494C2×D4311yescharacteristic, complemented
213#493C2×D4311yescharacteristic, complemented
214#492C2×D4312yescomplemented
215#480—862no—
216#474—434no—
217#459—434no—
218#447—862no—
219C4×D8—864no—
220#436—432no—
221#436—432no—
222#436—861no—
223#436—861no—
224#431—432no—
225C2×C4⋊C8—431no—
226C2×C22⋊C8—861no—
227C2×C4×C8C2×D4311yescharacteristic
228#335—432no—
229#334—432no—
230#332—434no—
231#331—434no—
232C43#1913311yescharacteristic, complemented, Sylow
233C2×#41—22no—
234C22×D4—431no—
235C23×C4—861no—
236#135—44no—
237#135—44no—
238C2×Q16—21no—
239C2×Q16—21no—
240C2×SD16—22no—
241C2×SD16—22no—
242C2×D8—21no—
243C2×D8—21no—
244C2×D8—864no—
245C2×M16—862no—
246C2×M16—862no—
247C2×M16—1724no—
248C22×C8—861no—
249C22×C8C22⋊D4311yescharacteristic
250C22×C8C22⋊D4311yescharacteristic
251C4⋊Q8C22×D4312yes—
252#127C22×D4312yes—
253#124—22no—
254#121—22no—
255#121—22no—
256C4×D4—22no—
257C4×D4—22no—
258C4×D4—432no—
259C4×D4—432no—
260C4×D4—861no—
261C4×D4—861no—
262C2×C4⋊C4—431no—
263C2×C22⋊C4—861no—
264C2×C42C22×D4311yescharacteristic
265#107—864no—
266C4⋊C8—432no—
267C4⋊C8—434no—
268C4⋊C8—861no—
269#102—864no—
270#102—864no—
271C22⋊C8—862no—
272C22⋊C8—862no—
273C22⋊C8—862no—
274C4×C8—862no—
275C4×C8C22⋊D4311yescharacteristic
276C4×C8C22⋊D4311yescharacteristic
277C4×C8C22×D4311yescharacteristic
278C4×C8C22×D4311yescharacteristic
279C24—861no—
280#41—44no—
281#41—44no—
282C2×Q8—22no—
283C2×D4—22no—
284C2×D4—22no—
285C2×D4—22no—
286C2×D4—42no—
287C2×D4—432no—
288C2×D4—861no—
289C2×D4—1722no—
290C22×C4—42no—
291C22×C4—861no—
292C22×C4—862no—
293C22×C4—862no—
294C22×C4—1722no—
295C22×C4—1722no—
296C22×C4D4×D4311yescharacteristic
297C22×C4#1062190011yescharacteristic
298C22×C4C2×C22⋊D4311yescharacteristic
299Q16—42no—
300Q16—42no—
301SD16—44no—
302SD16—44no—
303D8—42no—
304D8—42no—
305D8—1728no—
306M16—1724no—
307M16—1724no—
308C2×C8—22no—
309C2×C8—864no—
310C2×C8—862no—
311C2×C8—1722no—
312C2×C8#1062188214yescomplemented
313C2×C8C2×C22⋊D4311yescharacteristic
314C2×C8C2×C22⋊D4311yescharacteristic
315C2×C8C2×C22⋊D4311yescharacteristic
316C2×C8C2×C22⋊D4311yescharacteristic
317C4⋊C4—22no—
318C4⋊C4—22no—
319C4⋊C4—432no—
320C4⋊C4—861no—
321C22⋊C4—42no—
322C22⋊C4—42no—
323C22⋊C4—862no—
324C22⋊C4—862no—
325C42D4×D4311yescharacteristic
326C42#1062190011yescharacteristic
327C42C2×C22⋊D4311yescharacteristic
328C42C23×D4311yescharacteristic
329C23—42no—
330C23—862no—
331C23—1722no—
332C23—1722no—
333C23—1722no—
334C23#1306329611yescharacteristic
335Q8—42no—
336Q8—42no—
337D4—42no—
338D4—42no—
339D4—44no—
340D4—82no—
341D4—84no—
342D4—864no—
343D4—1722no—
344C2×C4—22no—
345C2×C4—41no—
346C2×C4—42no—
347C2×C4—84no—
348C2×C4—862no—
349C2×C4—1722no—
350C2×C4—1724no—
351C2×C4—1722no—
352C2×C4—1722no—
353C2×C4#1306329611yescharacteristic
354C2×C4#1306329611yescharacteristic
355C2×C4#1306329611yescharacteristic
356C2×C4C2×#1062188212yes—
357C2×C4#1306335112yes—
358C2×C4C2×D4×D4311yescharacteristic
359C2×C4C22×C22⋊D4311yescharacteristic
360C2×C4C2×#1062190011yescharacteristic
361C8—21no—
362C8—21no—
363C8—1722no—
364C8—1724no—
365C8C2×#1062188212yes—
366C8C2×#1062188212yes—
367C22—21no—
368C22—21no—
369C22—82no—
370C22—82no—
371C22—82no—
372C22—3444no—
373C22—1722no—
374C22—1722no—
375C22—1722no—
376C22#1458309112yes—
377C22C2×#1306329611yescharacteristic
378C4—21no—
379C4—21no—
380C4—21no—
381C4—82no—
382C4—1722no—
383C4#1458309112yes—
384C4C22×#1062188211yescharacteristic
385C4C2×#1306335111yescharacteristic
386C4#1458369612yes—
387C2—22no—
388C2—162no—
389C2—3442no—
390C2C2×#1458309111yescharacteristic
391C2#1914420011yescharacteristic
392C2#1914431111yescharacteristic
subgroupG/H
centerC2×C4#13063296
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3147C2
socleC22×C43C2×#121
hypercenter#3147D43
hypocenterC43#19133
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3147

Complements

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

NH ≅ G/Ntype
1. #19144591C2semidirect
2. C2×#14582978C2semidirect
3. #19134081C2semidirect
4. #19134071C2semidirect
5. #19134057C2semidirect
6. #19133343C2semidirect
7. #19133244C2semidirect
8. C43×#3147C2semidirect
23. #14582652C22semidirect
24. #14582650C22semidirect
25. #14582645C22semidirect
26. #14582643C22semidirect
32. C43×#494C22semidirect
33. C43×#493C22semidirect
34. C43×#492C22semidirect
109. C2×C8×C43D8semidirect
191. #3147D43semidirect
212. #494C2×D43semidirect
213. #493C2×D43semidirect
214. #492C2×D43semidirect
232. C43#19133semidirect
312. C2×C8#10621882semidirect

Maximal subgroups

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

subgroupindex
#191445912
C2×#145829782
#191340812
#191340712
#191340572
#191333432
#191332442
C43×#31472
#1913343