Finite Group Databasebeta

← #11872842

Subgroups — #11872842

Order 1152.

836 conjugacy classes of subgroups; only the 156 normal subgroups are shown.

normal subgroups only

This group has 836 conjugacy classes of subgroups — too many to draw. Only its 156 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593996C211yesmaximal, characteristic
2#10593883C211yesmaximal, characteristic, complemented
3#10592408C211yesmaximal, characteristic, complemented
4C3×#4710C212yesmaximal, complemented
5#10590943C212yesmaximal
6#10590780C212yesmaximal, complemented
7#10590748C212yesmaximal, complemented
8#10590715C212yesmaximal, complemented
9C4×#3715C212yesmaximal, complemented
10#79787—32nomaximal
11C2×#3802C2211yescharacteristic
12#64081C2211yescharacteristic
13C2×C3×#204C2212yes—
14C3×C4×D12C2212yes—
15C3×C4×Dic6C2212yescomplemented
16D3×(C2×D3)⋊C4—22no—
17#63898C2212yes—
18#63879—22no—
19#63873C2211yescharacteristic, complemented
20#63872C2211yescharacteristic, complemented
21#63871C2212yes—
22#63868—22no—
23#63867—22no—
24#63849C2211yescharacteristic
25C2×#3715C2212yes—
26C32×#97C2211yescharacteristic, complemented
27#63647C2212yes—
28#63641C2212yescomplemented
29C4×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
30C3×#821C2212yes—
31C3×#818C2212yescomplemented
32C3×#816C2212yescomplemented
33#63574C2212yescomplemented
34#63565C2212yescomplemented
35#63562C2212yes—
36#5583—32no—
37#5545—32no—
38C3×#440—32no—
39#5169—32no—
40#5162—32no—
41C4×#215—32no—
42C4×#214—32no—
43#4891—32no—
44#4888—32no—
45#4818—32no—
46#4814—32no—
47#4776—32no—
48#4766—32no—
49#4710D312yescomplemented
50#4709—32no—
51#4709—61no—
52C22×D32—21no—
53C2×C4×C3⋊D3C2311yescharacteristic
54C2×C3×D12C2312yes—
55C2×C3×C4×D3—22no—
56C2×C3×Dic6C2312yes—
57C2×#625—21no—
58C2×D3×Dic3—22no—
59#3802—24no—
60C2×C32×C8C2312yes—
61C32×C42C2311yescharacteristic
62#3752D412yes—
63#3750D412yes—
64C4×C3⋊Dic3C2311yescharacteristic
65C2×C3⋊(C3⋊C8)C2312yes—
66C3×(C2×D3)⋊C4—22no—
67C3×C4⋊Dic3C2312yes—
68C3×C4⋊Dic3C2312yes—
69C3×Dic3⋊C4—22no—
70C3×C4×Dic3—22no—
71C3×#204—24no—
72#3724—22no—
73Dic3⋊Dic3—22no—
74Dic3⋊Dic3—22no—
75#3722—21no—
76#3722—22no—
77(C2×D3)⋊Dic3—22no—
78Dic32—21no—
79#3715—24no—
80#3123—91noSylow
81C2×D3×D4—32no—
82C2×C3×SD16—32no—
83C3×C4×Q8—32no—
84C3×C4×D4—32no—
85#946—32no—
86#944—32no—
87C2×#215—32no—
88D4×Dic3—32no—
89C2×#214—32no—
90C4×#67—62no—
91C2×(C2×D3)⋊C4—62no—
92C2×#204C2×D312yes—
93#898—62no—
94#897—32no—
95#893—32no—
96#892—32no—
97#890—32no—
98#889—62no—
99#67⋊C4—62no—
100D3×C22⋊C4—62no—
101#876—62no—
102C4×D12C2×D312yes—
103#872—32no—
104#872—61no—
105#870—62no—
106C4×Dic6C2×D312yescomplemented
107C3×#107—32no—
108C3×#103—32no—
109C3×#102—32no—
110C3×#97—21no—
111C3×#97C2×D312yescomplemented
112#835—32no—
113#832—32no—
114#821C2×D312yes—
115(C2×D3)⋊C8—32no—
116(C2×D3)⋊C8—32no—
117(C2×D3)⋊C8—62no—
118#818C2×D312yescomplemented
119#816C2×D312yescomplemented
120Dic3⋊C8—32no—
121Dic3⋊C8—32no—
122Dic3⋊C8—62no—
123#810—32no—
124#809—32no—
125#808—32no—
126#808—32no—
127C4×C3⋊C8—32no—
128C4×C3⋊C8—61no—
129C22×C3⋊D3C2×D411yescharacteristic
130C22×C3×D3—22no—
131C2×D32—24no—
132C2×D32—82no—
133C2×C32×C4C2×D412yes—
134C2×C32×C4C2411yescharacteristic
135C2×C3⋊Dic3C2×D411yescharacteristic
136C2×C3⋊Dic3C2×D412yes—
137C4×C3⋊D3—22no—
138C2×C3×Dic3—22no—
139C2×C3×Dic3—22no—
140C2×C3×Dic3—22no—
141C3×D12—22no—
142C3×D12#4114yes—
143C3×C4×D3—82no—
144C3×Dic6—22no—
145C3×Dic6—22no—
146#625—24no—
147D3×Dic3—82no—
148C32×C8—22no—
149C3⋊(C3⋊C8)—22no—
150#541—91no—
151#518—91no—
152#485—92no—
153#478—92no—
154#461—92no—
155#450—92no—
156#440—32no—
157C4×SD16—92no—
158#433—91no—
159C23×D3—62no—
160C2×C3×Q8—32no—
161C2×C3×D4—32no—
162C22×C3×C4—62no—
163C2×#67—62no—
164C22×Dic3—62no—
165D3×D4—64no—
166D3×D4—64no—
167C2×D12C22×D312yes—
168C2×C4×D3—22no—
169C2×C4×D3—32no—
170C2×C4×D3—61no—
171C2×C4×D3—62no—
172C2×Dic6C22×D312yes—
173C3×SD16—64no—
174C2×C3×C8—22no—
175C2×C3×C8C22×D312yes—
176C2×C3×C8C22×D312yes—
177C3×C4⋊C4—32no—
178C3×C4⋊C4—32no—
179C3×C4⋊C4—62no—
180C3×C22⋊C4—62no—
181C3×C42—21no—
182C3×C42—62no—
183C3×C42C22×D312yes—
184#217—62no—
185#215—64no—
186#214—64no—
187(C2×D3)⋊C4—22no—
188(C2×D3)⋊C4—32no—
189(C2×D3)⋊C4—32no—
190(C2×D3)⋊C4—62no—
191(C2×D3)⋊C4—62no—
192(C2×D3)⋊C4—62no—
193(C2×D3)⋊C4—62no—
194(C2×D3)⋊C4—62no—
195C4⋊Dic3—62no—
196C4⋊Dic3—62no—
197C4⋊Dic3C22×D312yes—
198C4⋊Dic3C22×D312yes—
199Dic3⋊C4—22no—
200Dic3⋊C4—32no—
201Dic3⋊C4—32no—
202Dic3⋊C4—62no—
203Dic3⋊C4—62no—
204Dic3⋊C4—62no—
205Dic3⋊C4—62no—
206Dic3⋊C4—62no—
207C4×Dic3—22no—
208C4×Dic3—32no—
209C4×Dic3—61no—
210C4×Dic3—62no—
211C2×C3⋊C8—32no—
212C2×C3⋊C8—32no—
213C2×C3⋊C8—62no—
214#204—24no—
215C22×C32C22×D411yescharacteristic
216C2×C3⋊D3—21no—
217C2×C3⋊D3—22no—
218C2×C3×D3—24no—
219C2×C3×D3—42no—
220C2×C3×D3—42no—
221D32—84no—
222C32×C4—22no—
223C32×C4C2×#4112yes—
224C3⋊Dic3—21no—
225C3⋊Dic3—22no—
226C3×Dic3—42no—
227C3×Dic3—42no—
228C3×Dic3—42no—
229C22×D4—91no—
230C2×SD16—32no—
231C2×SD16—92no—
232C4⋊Q8—91no—
233#126—182no—
234#125—91no—
235#125—182no—
236C22⋊Q8—92no—
237C4×Q8—32no—
238C4×D4—32no—
239C4×D4—92no—
240C4×D4—182no—
241#117—91no—
242#117—91no—
243C2×C22⋊C4—182no—
244#107—32no—
245#106—92no—
246C4⋊C8—92no—
247#103—32no—
248#103—92no—
249#102—32no—
250#102—92no—
251C22⋊C8—92no—
252#97D3211yescharacteristic, complemented
253C4×C8—91no—
254C23×C3—62no—
255C22×D3—22no—
256C22×D3—32no—
257C22×D3—61no—
258C22×D3—68no—
259C22×D3—242no—
260C22×D3—242no—
261C3×Q8—62no—
262C3×Q8—62no—
263C3×D4—34no—
264C3×D4—62no—
265C2×C3×C4—21no—
266C2×C3×C4—22no—
267C2×C3×C4—62no—
268C2×C3×C4—62no—
269C2×C3×C4—62no—
270C2×C3×C4—242no—
271C2×C3×C4D3×D412yes—
272C2×C3×C4D3×D412yes—
273C2×C3×C4C23×D312yes—
274#67—68no—
275C2×Dic3—22no—
276C2×Dic3—22no—
277C2×Dic3—22no—
278C2×Dic3—32no—
279C2×Dic3—32no—
280C2×Dic3—32no—
281C2×Dic3—62no—
282C2×Dic3—61no—
283C2×Dic3—242no—
284D12—22no—
285D12#23514yes—
286C4×D3—62no—
287C4×D3—62no—
288C4×D3—82no—
289C4×D3—122no—
290C4×D3—242no—
291Dic6—22no—
292Dic6—22no—
293C3×C8—22no—
294C3×C8—22no—
295C3×C8—42no—
296C3⋊C8—62no—
297C3⋊C8—62no—
298C3⋊C8—122no—
299C2×C32#52511yescharacteristic
300C2×C32#57712yes—
301C3⋊D3—41no—
302C3×D3—44no—
303C24—181no—
304C2×Q8—32no—
305C2×D4—32no—
306C2×D4—181no—
307C2×D4—184no—
308C22×C4—62no—
309C22×C4—91no—
310C22×C4—182no—
311SD16—64no—
312SD16—184no—
313C2×C8—92no—
314C2×C8C2×D3212yes—
315C4⋊C4—32no—
316C4⋊C4—32no—
317C4⋊C4—62no—
318C4⋊C4—92no—
319C4⋊C4—182no—
320C4⋊C4—182no—
321C4⋊C4—182no—
322C22⋊C4—62no—
323C22⋊C4—92no—
324C22⋊C4—181no—
325C22⋊C4—182no—
326C22⋊C4—182no—
327C42—62no—
328C42—91no—
329C42—181no—
330C42C2×D3211yescharacteristic
331C22×C3—21no—
332C22×C3—64no—
333C22×C3—122no—
334C22×C3—122no—
335C22×C3C2×D3×D412yes—
336C2×D3—24no—
337C2×D3—42no—
338C2×D3—42no—
339C2×D3—62no—
340C2×D3—62no—
341C2×D3—62no—
342C2×D3—121no—
343C2×D3—122no—
344C2×D3—248no—
345C3×C4—22no—
346C3×C4—22no—
347C3×C4—22no—
348C3×C4—42no—
349C3×C4—122no—
350C3×C4—122no—
351C3×C4—122no—
352C3×C4C2×#23512yes—
353C3×C4D3×#4112yes—
354Dic3—42no—
355Dic3—42no—
356Dic3—42no—
357Dic3—62no—
358Dic3—62no—
359Dic3—62no—
360Dic3—121no—
361Dic3—122no—
362C32#312311yescharacteristic, complemented, Sylow
363C23—62no—
364C23—91no—
365C23—184no—
366C23—722no—
367Q8—62no—
368Q8—62no—
369D4—34no—
370D4—62no—
371D4—184no—
372C2×C4—62no—
373C2×C4—62no—
374C2×C4—62no—
375C2×C4—92no—
376C2×C4—91no—
377C2×C4—182no—
378C2×C4—242no—
379C2×C4—722no—
380C2×C4#380212yes—
381C2×C4C22×D3211yescharacteristic
382C8—22no—
383C8—182no—
384C2×C3—22no—
385C2×C3—21no—
386C2×C3—124no—
387C2×C3#554712yes—
388C2×C3#577512yes—
389C2×C3#577812yes—
390D3—44no—
391D3—122no—
392D3—241no—
393C22—64no—
394C22—122no—
395C22—122no—
396C22—182no—
397C22—181no—
398C22—724no—
399C22C2×#380211yescharacteristic
400C4—22no—
401C4—122no—
402C4—122no—
403C4—122no—
404C4—182no—
405C4—181no—
406C4D3×#23512yes—
407C3—21no—
408C3#7978712yescomplemented
409C2—124no—
410C2—361no—
411C2#1059400611yescharacteristic
412C2#1059471912yes—
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#97C22
socleC22×C32C22×D4
prime radicalC2×#3802C22
hypercenter#97D32
hypocenterC32#3123
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #97

Complements

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

NH ≅ G/Ntype
2. #10593883C2semidirect
3. #10592408C2semidirect
4. C3×#4710C2semidirect
6. #10590780C2semidirect
7. #10590748C2semidirect
8. #10590715C2semidirect
9. C4×#3715C2semidirect
15. C3×C4×Dic6C22semidirect
19. #63873C22semidirect
20. #63872C22semidirect
26. C32×#97C22semidirect
28. #63641C22semidirect
29. C4×C3⋊(C3⋊C8)C22semidirect
31. C3×#818C22semidirect
32. C3×#816C22semidirect
33. #63574C22semidirect
34. #63565C22semidirect
49. #4710D3semidirect
106. C4×Dic6C2×D3semidirect
111. C3×#97C2×D3semidirect
118. #818C2×D3semidirect
119. #816C2×D3semidirect
252. #97D32semidirect
362. C32#3123semidirect
408. C3#79787semidirect

Maximal subgroups

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

subgroupindex
#105939962
#105938832
#105924082
C3×#47102
#105909432
#105907802
#105907482
#105907152
C4×#37152
#797873