Finite Group Databasebeta

← #25966135

Subgroups — #25966135

Order 11008.

3250 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583707C214yesmaximal, complemented
2#19148373C211yesmaximal, characteristic, complemented
3#19145073C2112yesmaximal, complemented
4#19145052C213yesmaximal, complemented
5#19145048C213yesmaximal, complemented
6#19145021C213yesmaximal, complemented
7C2×#14583273C213yesmaximal, complemented
8C4×#13063332C211yesmaximal, characteristic, complemented
9C43×#3499C211yesmaximal, characteristic, complemented
10C2×#13063371C2212yes—
11#14583707—232no—
12C2×#13063356C22112yescomplemented
13C2×#13063350C22112yescomplemented
14C2×#13063345C22112yescomplemented
15C22×#10621884C22112yescomplemented
16C2×#13063332C2212yes—
17#14583571—22no—
18D4×D172—26no—
19#14583468C2216yes—
20#14583449C2213yes—
21C2×#13063322C2213yes—
22#14583291C22112yescomplemented
23#14583289C22112yescomplemented
24#14583281C22112yescomplemented
25#14583278C2213yescomplemented
26#14583275C2213yescomplemented
27#14583273C2213yescomplemented
28#14583273C2216yescomplemented
29#14583273C22112yescomplemented
30#14583271C2211yescharacteristic, complemented
31#14582855C2216yescomplemented
32C4×#10621877C2213yescomplemented
33C2×C4×C43⋊C8C2213yescomplemented
34C2×2−1+4×C43C2212yes—
35D4×Q8×C43—22no—
36C43×#547—26no—
37C43×#536C2216yescomplemented
38C43×#532C2213yescomplemented
39C2×C4⋊Q8×C43C2213yescomplemented
40C4×#41×C43C2211yescharacteristic
41#13063371—216no—
42C2×#10621902—22no—
43C2×#10621898C2316yes—
44C22×D172—26no—
45C22×D172C2316yes—
46C2×D4×D43—26no—
47#13063356—248no—
48#13063350—248no—
49#13063345—248no—
50C2×#10621885C23112yes—
51C2×#10621883C2314yes—
52C2×#10621884—248no—
53C2×#10621884C23112yes—
54C2×#10621884C23124yes—
55C2×#10621882C23112yes—
56#13063332D4116yescomplemented
57C2×#10621877C2316yes—
58C22×C43⋊C8C2316yes—
59#13063325C2311yescharacteristic
60#13063322—26no—
61#13063322C2313yes—
62#13063322C2316yes—
63#13063313C2316yes—
64#13063300—212no—
65#13063299—26no—
66#13063295—212no—
67C4×D172—26no—
68#13063236C2316yes—
69C4×C43⋊C8C2311yescharacteristic
70C4×C43⋊C8C2313yes—
71C4×C43⋊C8C2316yes—
722−1+4×C43—216no—
73C2×#41×C43—26no—
74C2×#41×C43C2316yes—
75C2×#41×C43C2311yescharacteristic
76C22×Q8×C43—22no—
77C22×Q8×C43C2316yes—
78C4⋊Q8×C43—26no—
79C4⋊Q8×C43C2313yes—
80C4⋊Q8×C43C2316yes—
81#127×C43C2311yescharacteristic
82#124×C43C2316yes—
83#123×C43—212no—
84C22⋊Q8×C43—212no—
85#121×C43—26no—
86C4×Q8×C43D412yes—
87C4×D4×C43—26no—
88C4×D4×C43D416yes—
89#117×C43C2313yes—
90C2×C4⋊C4×C43—26no—
91C2×C42×C43C2313yes—
92C23×D43—26no—
93#41×C43—224no—
94#41×C43—424no—
95#41×C43C2×D418yes—
96C2×Q8×C43—26no—
97C2×Q8×C43—224no—
98C2×Q8×C43—48no—
99C2×Q8×C43C2×D411yescharacteristic
100C2×Q8×C43C2416yes—
101C2×D4×C43—22no—
102C2×D4×C43—26no—
103C2×D4×C43C2×D413yes—
104C2×D4×C43C2412yes—
105C22×C4×C43—26no—
106C22×C4×C43—26no—
107C22×C4×C43C2×D416yes—
108C22×C4×C43C2413yes—
109C2×C22⋊D43—26no—
110#10621902—48no—
111D4×D43—424no—
112#10621898—224no—
113C2×D172—26no—
114C2×D172—26no—
115C2×D172—212no—
116C2×D172—224no—
117C2×D172—812no—
118C2×D172C2416yes—
119C2×C4×D43—26no—
120C2×Dic86C2412yes—
121C4⋊C4×C43—26no—
122C4⋊C4×C43—212no—
123C4⋊C4×C43C2×D416yes—
124C22⋊C4×C43—212no—
125C22⋊C4×C43C2×D416yes—
126C42×C43C2×D416yes—
127C42×C43C2411yescharacteristic
128C42×C43C2413yes—
129#10621885—224no—
130#10621884—224no—
131#10621884—248no—
132#10621883—28no—
133#10621882—224no—
134(C2×D43)⋊C4—212no—
135C4⋊Dic43—22no—
136#10621877C2×D4124yescomplemented
137C2×C43⋊C8C2×D4124yescomplemented
138C2×C43⋊C8C2412yes—
139C2×C43⋊C8C2416yes—
140C23×C43—22no—
141C23×C43C22×D413yes—
142C22×D43—26no—
143C22×D43—412no—
144C22×D43—812no—
145Q8×C43—212no—
146Q8×C43—412no—
147Q8×C43#12714yes—
148D4×C43—24no—
149D4×C43—412no—
150D4×C43—44no—
151D4×C43#127112yes—
152C2×C4×C43—212no—
153C2×C4×C43—26no—
154C2×C4×C43—412no—
155C2×C4×C43—412no—
156C2×C4×C43C22×D4112yes—
157C2×C4×C43C22×D416yes—
158C2×C4×C43C22×D413yes—
159C2×C4×C43C22×D412yes—
160C2×C4×C43C2511yescharacteristic
161C22⋊D43—412no—
162C2×Dic43—22no—
163D172—212no—
164D172—412no—
165D172—412no—
166D172—812no—
167C4×D43—412no—
168Dic86—24no—
169C43⋊C8C22×D414yes—
170C43⋊C8C22×D4112yes—
171#60646—431nomaximal, Sylow
172C22×C43—26no—
173C22×C43—42no—
174C22×C43—44no—
175C22×C43C2×#12716yes—
176C22×C43C23×D411yescharacteristic
177C2×D43—46no—
178C2×D43—412no—
179C2×D43—1612no—
180C4×C43—26no—
181C4×C43—46no—
182C4×C43C2×#12716yes—
183C4×C43#57714yescomplemented
184C4×C43C23×D412yes—
185Dic43—42no—
186C2×#577—434no—
187#3499D4311yescharacteristic, complemented
188#3498—431no—
189#3154—4312no—
190#3152—433no—
191#3151—433no—
192#3147—433no—
193C2×#492—433no—
194C4×#131—431no—
195C2×C43—26no—
196C2×C43—82no—
197C2×C43C22×#12711yescharacteristic
198C2×C43C2×#57712yes—
199D43—86no—
200C2×2−1+4C2×D4312yes—
201C2×H(5,𝔽2)—432no—
202#577—8632no—
203C2×#137—4312no—
204C2×AGL(1,ℤ/8)—4312no—
205C2×#135—4312no—
206C22×SD16—4312no—
207C2×#131—432no—
208#550—862no—
209D4×Q8—22no—
210#547—26no—
211D42—866no—
212#536C2×D4316yescomplemented
213#535—436no—
214#532—433no—
215#532C2×D4313yescomplemented
216C2×C4⋊Q8C2×D4313yescomplemented
217C2×#127—433no—
218C4×#41C2×D4311yescharacteristic
219#497—4312no—
220#496—4312no—
221#495—4312no—
222#494—433no—
223#493—433no—
224#492—433no—
225#492—436no—
226#492—4312no—
227#492—431no—
228#405—436no—
229C4×M16—433no—
230C2×C4×C8—433no—
231C43#6064611yescharacteristic, complemented, Sylow
2322−1+4—216no—
233H(5,𝔽2)—8616no—
234C2×#41—26no—
235C2×#41—436no—
236C2×#41—862no—
237C2×#41C22×D4316yes—
238C2×#41C22×D4311yescharacteristic
239C22×Q8—22no—
240C22×Q8C22×D4316yes—
241C22×D4—436no—
242C22×D4—866no—
243C22×D4—866no—
244#137—8648no—
245AGL(1,ℤ/8)—8648no—
246#135—8648no—
247C2×Q16—4312no—
248C2×SD16—4312no—
249C2×SD16—4324no—
250C2×SD16—434no—
251C2×SD16—8648no—
252C2×D8—4312no—
253#131—4316no—
254C2×M16—436no—
255C22×C8—436no—
256C4⋊Q8—26no—
257C4⋊Q8—431no—
258C4⋊Q8C22×D4313yes—
259C4⋊Q8C22×D4316yes—
260#127—433no—
261#127—436no—
262#127—866no—
263#127C22×D4311yescharacteristic
264#124—436no—
265#124C22×D4316yes—
266#123—212no—
267C22⋊Q8—212no—
268#121—26no—
269#121—866no—
270#121—8612no—
271#120—8612no—
272C4×Q8C22⋊D4312yes—
273C4×D4—26no—
274C4×D4—866no—
275C4×D4C22⋊D4316yes—
276#117C22×D4313yes—
277C2×C4⋊C4—26no—
278C2×C42C22×D4313yes—
279#97—436no—
280C4×C8—431no—
281C4×C8—433no—
282C4×C8—436no—
283C24—866no—
284#41—224no—
285#41—424no—
286#41—8624no—
287#41—1728no—
288#41D4×D4318yes—
289C2×Q8—26no—
290C2×Q8—224no—
291C2×Q8—48no—
292C2×Q8—432no—
293C2×Q8C2×C22⋊D4311yescharacteristic
294C2×Q8C23×D4316yes—
295C2×D4—26no—
296C2×D4—22no—
297C2×D4—436no—
298C2×D4—866no—
299C2×D4—8624no—
300C2×D4—8612no—
301C2×D4—866no—
302C2×D4—866no—
303C2×D4—34412no—
304C2×D4—17224no—
305C2×D4C2×C22⋊D4313yes—
306C2×D4C23×D4312yes—
307C22×C4—26no—
308C22×C4—26no—
309C22×C4—866no—
310C22×C4C2×C22⋊D4316yes—
311C22×C4C23×D4313yes—
312Q16—8624no—
313SD16—868no—
314SD16—8624no—
315SD16—8648no—
316D8—8624no—
317M16—4324no—
318C2×C8—4324no—
319C2×C8—432no—
320C2×C8—436no—
321C4⋊C4—26no—
322C4⋊C4—212no—
323C4⋊C4—862no—
324C4⋊C4C2×C22⋊D4316yes—
325C22⋊C4—212no—
326C22⋊C4—8612no—
327C22⋊C4C2×C22⋊D4316yes—
328C42C2×C22⋊D4316yes—
329C42C23×D4311yescharacteristic
330C42C23×D4313yes—
331C23—22no—
332C23—866no—
333C23—34412no—
334C23—17212no—
335C23C22×C22⋊D4313yes—
336Q8—212no—
337Q8—412no—
338Q8—864no—
339Q8#1306332114yes—
340D4—24no—
341D4—412no—
342D4—44no—
343D4—8612no—
344D4—34412no—
345D4—17212no—
346D4—17212no—
347D4—17212no—
348D4#13063321112yes—
349C2×C4—212no—
350C2×C4—26no—
351C2×C4—412no—
352C2×C4—412no—
353C2×C4—862no—
354C2×C4—17212no—
355C2×C4C2×D4×D43112yes—
356C2×C4C22×C22⋊D4316yes—
357C2×C4C22×C22⋊D4313yes—
358C2×C4C22×C22⋊D4312yes—
359C2×C4C24×D4311yescharacteristic
360C8—434no—
361C8—4312no—
362C22—26no—
363C22—44no—
364C22—42no—
365C22—17212no—
366C22—1726no—
367C22—68812no—
368C22C2×#1306332116yes—
369C22C23×C22⋊D4311yescharacteristic
370C4—26no—
371C4—46no—
372C4—1722no—
373C4C2×#1306332116yes—
374C4#1458370714yescomplemented
375C4C22×D4×D4312yes—
376C2—26no—
377C2—82no—
378C2—3446no—
379C2C22×#1306332111yescharacteristic
380C2C2×#1458370712yes—
subgroupG/H
centerC22C23×C22⋊D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3499C2
socleC22×C43C23×D4
hypercenter#3499D43
hypocenterC43#60646
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C4×#41 ◁ #3499

Complements

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

NH ≅ G/Ntype
1. C2×#14583707C2semidirect
2. #19148373C2semidirect
3. #19145073C2semidirect
4. #19145052C2semidirect
5. #19145048C2semidirect
6. #19145021C2semidirect
7. C2×#14583273C2semidirect
8. C4×#13063332C2semidirect
9. C43×#3499C2semidirect
12. C2×#13063356C22semidirect
13. C2×#13063350C22semidirect
14. C2×#13063345C22semidirect
15. C22×#10621884C22semidirect
22. #14583291C22semidirect
23. #14583289C22semidirect
24. #14583281C22semidirect
25. #14583278C22semidirect
26. #14583275C22semidirect
27. #14583273C22semidirect
28. #14583273C22semidirect
29. #14583273C22semidirect
30. #14583271C22semidirect
31. #14582855C22semidirect
32. C4×#10621877C22semidirect
33. C2×C4×C43⋊C8C22semidirect
37. C43×#536C22semidirect
38. C43×#532C22semidirect
39. C2×C4⋊Q8×C43C22semidirect
56. #13063332D4semidirect
136. #10621877C2×D4semidirect
137. C2×C43⋊C8C2×D4semidirect
183. C4×C43#577semidirect
187. #3499D43semidirect
212. #536C2×D43semidirect
215. #532C2×D43semidirect
216. C2×C4⋊Q8C2×D43semidirect
231. C43#60646semidirect
374. C4#14583707semidirect

Maximal subgroups

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

subgroupindex
C2×#145837072
#191483732
#191450732
#191450522
#191450482
#191450212
C2×#145832732
C4×#130633322
C43×#34992
#6064643