Finite Group Databasebeta

← #11861240

Subgroups — #11861240

Order 1152.

957 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594708C212yesmaximal, complemented
2#10594684C211yesmaximal, characteristic
3C3⋊D3×#108C211yesmaximal, characteristic, complemented
4C3×#4894C212yesmaximal, complemented
5#10591009C212yesmaximal, complemented
6#10590975C214yesmaximal, complemented
7#10590916C212yesmaximal, complemented
8#10590703C211yesmaximal, characteristic, complemented
9#79899—32nomaximal
10#64306C2212yes—
11M16×C3⋊D3C2212yes—
12C2×C8×C3⋊D3C2211yescharacteristic
13C3×#907C2214yescomplemented
14C3×#904C2212yes—
15#63874C2211yescharacteristic
16#63822C2212yes—
17C2×#3712C2211yescharacteristic
18#63814C2214yescomplemented
19#63810C412yescomplemented
20#63809C412yescomplemented
21#63805—22no—
22#63803—22no—
23#63802C411yescharacteristic, complemented
24#63797C411yescharacteristic, complemented
25#63796C412yescomplemented
26D3×ΓL(1,𝔽25)—24no—
27C32×#108C2211yescharacteristic, complemented
28#63649C2212yescomplemented
29#63646C2211yescharacteristic, complemented
30C3×#825C2214yescomplemented
31C3×#815C2212yescomplemented
32#63569C2214yescomplemented
33Dic3×C3⋊C8C2212yescomplemented
34D3×#135—32no—
35#5750—34no—
36C3×#444—32no—
37#5197—32no—
38#5144—34no—
39#4894D312yescomplemented
40D3×#108—32no—
41D3×#108—61no—
42#4824—34no—
43#4821—34no—
44#4717—32no—
45#4708—32no—
46C2×C4×C3⋊D3C2311yescharacteristic
47C3×#235C2314yes—
48#3811—22no—
49#3805—22no—
50#3802C2×C412yes—
51C4×D32—22no—
52#3798—22no—
53#3797C2×C412yes—
54#3796C2×C414yes—
55C32×M16C2312yes—
56C2×C32×C8C2311yescharacteristic
57#3748C2312yes—
58C2×C3⋊(C3⋊C8)C2311yescharacteristic
59#3743—22no—
60C8×C3⋊D3—22no—
61C8×C3⋊D3C2×C411yescharacteristic
62C8×C3⋊D3C2×C411yescharacteristic
63C8×C3⋊D3C2×C411yescharacteristic
64C8×C3⋊D3C2×C411yescharacteristic
65C3×C4×Dic3C2312yes—
66C2×C3×C3⋊C8C2312yes—
67C3×Dic12C2×C412yes—
68C3×D24C2×C412yes—
69C3×#204C2×C414yes—
70C3×ΓL(1,𝔽25)—24no—
71C3×D3×C8—24no—
72#3724—21no—
73#3722—21no—
74#3718C2×C412yes—
75#3715C2×C414yes—
76#3713C2×C412yes—
77#3712D412yes—
78#3712D412yes—
79#3711—24no—
80D3×C3⋊C8—24no—
81#2957—91noSylow
82D3×#41—34no—
83C3×#135—32no—
84C3×#131—34no—
85#950—34no—
86#948—34no—
87#919—32no—
88D3×Q16—32no—
89#916—34no—
90D3×SD16—34no—
91#912—32no—
92D3×D8—32no—
93#907—64no—
94#907C2×D314yescomplemented
95D3×M16—34no—
96D3×M16—62no—
97D3×M16—64no—
98#904C2×D312yes—
99#901—34no—
100#901—64no—
101C2×ΓL(1,𝔽25)—32no—
102C2×ΓL(1,𝔽25)—64no—
103C2×D3×C8—32no—
104C2×D3×C8—61no—
105#872—32no—
106C3×#108—21no—
107C3×#108C2×D312yescomplemented
108C3×#104—34no—
109C3×#97—32no—
110#837—34no—
111#825C2×D314yescomplemented
112#822—34no—
113#822—62no—
114#819—32no—
115#819—61no—
116#815C2×D312yescomplemented
117C8×Dic3—32no—
118#805—34no—
119C4×C3⋊C8—32no—
120C22×C3⋊D3#4111yescharacteristic
121C2×D32—22no—
122C2×C32×C4C2411yescharacteristic
123C2×C3⋊Dic3#4111yescharacteristic
124C4×C3⋊D3C22×C411yescharacteristic
125C4×C3⋊D3C22×C411yescharacteristic
126C4×C3⋊D3C2×D411yescharacteristic
127C4×C3⋊D3C2×D411yescharacteristic
128C3×#67—24no—
129C2×C3×Dic3—22no—
130C3×D12C22×C414yes—
131C3×C4×D3—24no—
132C3×Dic6C22×C414yes—
133#627—22no—
134#626—24no—
135#625—22no—
136#624—22no—
137D3×Dic3—24no—
138C32×C8—22no—
139C32×C8C22×C411yescharacteristic
140C32×C8C22×C411yescharacteristic
141C3⋊(C3⋊C8)—22no—
142C3⋊(C3⋊C8)C22×C411yescharacteristic
143C3⋊(C3⋊C8)C22×C411yescharacteristic
144C3×C3⋊C8C2×D414yes—
145C2×#135—91no—
146#568—92no—
147#444—32no—
148#444—92no—
149#443—94no—
150C2×#108—91no—
151#421—92no—
152#405—91no—
153C3×#41—34no—
154#239—34no—
155D3×Q8—34no—
156#237—34no—
157#237—64no—
158D3×D4—34no—
159D3×D4—64no—
160#235—64no—
161#235C22×D314yes—
162C2×C4×D3—32no—
163C2×C4×D3—61no—
164C2×C4×D3—64no—
165C3×Q16—32no—
166C3×SD16—34no—
167C3×D8—32no—
168C3×M16—22no—
169C3×M16—64no—
170C3×M16C22×D314yes—
171C2×C3×C8—21no—
172C2×C3×C8—32no—
173C2×C3×C8—64no—
174C2×C3×C8C22×D312yes—
175C3×C42—32no—
176#216—34no—
177#215—34no—
178#214—34no—
179#213—34no—
180(C2×D3)⋊C4—62no—
181Dic3⋊C4—62no—
182C4×Dic3C22×D312yes—
183#208—34no—
184#208—62no—
185#208—64no—
186C2×C3⋊C8—32no—
187C2×C3⋊C8—61no—
188C2×C3⋊C8—64no—
189C2×C3⋊C8C22×D312yes—
190Dic12C4×D312yes—
191D24C4×D312yes—
192#204C4×D314yes—
193ΓL(1,𝔽25)—24no—
194ΓL(1,𝔽25)—34no—
195ΓL(1,𝔽25)—34no—
196ΓL(1,𝔽25)—64no—
197ΓL(1,𝔽25)—64no—
198ΓL(1,𝔽25)—122no—
199D3×C8—24no—
200D3×C8—32no—
201D3×C8—32no—
202D3×C8—32no—
203D3×C8—32no—
204D3×C8—61no—
205D3×C8—61no—
206D3×C8—61no—
207D3×C8—61no—
208D3×C8—64no—
209D3×C8—64no—
210D3×C8—122no—
211C22×C32C2×#4111yescharacteristic
212C2×C3⋊D3—41no—
213C2×C3⋊D3C4×D411yescharacteristic
214C2×C3⋊D3C4×D411yescharacteristic
215C2×C3×D3—24no—
216D32—82no—
217C32×C4C23×C411yescharacteristic
218C32×C4C22×D411yescharacteristic
219C3⋊Dic3C4×D411yescharacteristic
220C3⋊Dic3C4×D411yescharacteristic
221C3×Dic3—24no—
222C3×Dic3—42no—
223C2×#41—92no—
224#135—32no—
225#135—92no—
226#135—92no—
227#135—92no—
228C2×Q16—91no—
229C2×SD16—92no—
230C2×D8—91no—
231#131—34no—
232#131—94no—
233#131—182no—
234#131—182no—
235C2×M16—91no—
236C2×M16—92no—
237C2×M16—184no—
238C22×C8—91no—
239#117—91no—
240#108—92no—
241#108—91no—
242#108D3211yescharacteristic, complemented
243#104—34no—
244#104—94no—
245#97—32no—
246C4×C8—92no—
247C22×D3—32no—
248C22×D3—61no—
249C22×D3—64no—
250C3×Q8—34no—
251C3×D4—34no—
252C3×D4—64no—
253C2×C3×C4—21no—
254C2×C3×C4—64no—
255C2×C3×C4—62no—
256C2×C3×C4C23×D312yes—
257#67—24no—
258#67—64no—
259#67—64no—
260C2×Dic3—22no—
261C2×Dic3—32no—
262C2×Dic3—61no—
263C2×Dic3—64no—
264D12—64no—
265D12C2×C4×D314yes—
266C4×D3—24no—
267C4×D3—32no—
268C4×D3—32no—
269C4×D3—32no—
270C4×D3—32no—
271C4×D3—61no—
272C4×D3—61no—
273C4×D3—61no—
274C4×D3—61no—
275C4×D3—64no—
276C4×D3—64no—
277Dic6—64no—
278Dic6C2×C4×D314yes—
279C3×C8—24no—
280C3×C8—21no—
281C3×C8—21no—
282C3×C8—34no—
283C3×C8—42no—
284C3×C8C2×C4×D312yes—
285C3×C8C2×C4×D312yes—
286C3⋊C8—32no—
287C3⋊C8—32no—
288C3⋊C8—61no—
289C3⋊C8—61no—
290C3⋊C8—64no—
291C3⋊C8—122no—
292C3⋊C8D3×D414yes—
293C2×C32—21no—
294C2×C32C2×C4×D411yescharacteristic
295C3⋊D3—21no—
296C3⋊D3—21no—
297C3×D3—44no—
298#41—34no—
299#41—94no—
300#41—182no—
301#41—182no—
302C2×Q8—92no—
303C2×D4—92no—
304C2×D4—182no—
305C22×C4—91no—
306C22×C4—182no—
307Q16—32no—
308Q16—92no—
309SD16—34no—
310SD16—94no—
311D8—32no—
312D8—92no—
313M16—64no—
314M16—92no—
315M16—92no—
316M16—92no—
317M16—182no—
318M16—184no—
319M16C2×D3212yes—
320C2×C8—32no—
321C2×C8—64no—
322C2×C8—91no—
323C2×C8—91no—
324C2×C8—91no—
325C2×C8—91no—
326C2×C8—91no—
327C2×C8—182no—
328C2×C8—184no—
329C2×C8C2×D3211yescharacteristic
330C4⋊C4—181no—
331C22⋊C4—181no—
332C42—32no—
333C22×C3—21no—
334C22×C3—64no—
335C22×C3D3×#4112yes—
336C2×D3—24no—
337C2×D3—32no—
338C2×D3—32no—
339C2×D3—61no—
340C2×D3—61no—
341C2×D3—122no—
342C2×D3—122no—
343C2×D3—244no—
344C3×C4—21no—
345C3×C4—21no—
346C3×C4—64no—
347C3×C4—122no—
348C3×C4C22×C4×D312yes—
349C3×C4C2×D3×D412yes—
350Dic3—24no—
351Dic3—32no—
352Dic3—32no—
353Dic3—42no—
354Dic3—61no—
355Dic3—61no—
356C32#295711yescharacteristic, complemented, Sylow
357C23—91no—
358C23—182no—
359Q8—34no—
360Q8—182no—
361D4—34no—
362D4—64no—
363D4—184no—
364D4—182no—
365C2×C4—64no—
366C2×C4—62no—
367C2×C4—91no—
368C2×C4—91no—
369C2×C4—91no—
370C2×C4—91no—
371C2×C4—91no—
372C2×C4—182no—
373C2×C4—184no—
374C2×C4C22×D3211yescharacteristic
375C8—22no—
376C8—34no—
377C8—91no—
378C8—91no—
379C8—182no—
380C8C4×D3211yescharacteristic
381C8C4×D3211yescharacteristic
382C2×C3—22no—
383C2×C3—21no—
384C2×C3—41no—
385C2×C3—124no—
386C2×C3C4×D3×D412yes—
387D3—44no—
388D3—62no—
389D3—62no—
390D3—62no—
391D3—121no—
392C22—64no—
393C22—91no—
394C22—91no—
395C22—361no—
396C22—722no—
397C22#6431911yescharacteristic
398C4—64no—
399C4—91no—
400C4—91no—
401C4—122no—
402C4C2×C4×D3211yescharacteristic
403C4D32×D411yescharacteristic
404C3—21no—
405C3#7989912yescomplemented
406C2—21no—
407C2—124no—
408C2—181no—
409C2—181no—
410C2#1059460511yescharacteristic
subgroupG/H
centerC4D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#108C22
socleC2×C32C2×C4×D4
prime radical#10594684C2
cosocleC2×C32×C4C24
hypercenter#108D32
hypocenterC32#2957
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×C4 ◁ #108

Complements

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

NH ≅ G/Ntype
1. #10594708C2semidirect
3. C3⋊D3×#108C2semidirect
4. C3×#4894C2semidirect
5. #10591009C2semidirect
6. #10590975C2semidirect
7. #10590916C2semidirect
8. #10590703C2semidirect
13. C3×#907C22semidirect
18. #63814C22semidirect
19. #63810C4semidirect
20. #63809C4semidirect
23. #63802C4semidirect
24. #63797C4semidirect
25. #63796C4semidirect
27. C32×#108C22semidirect
28. #63649C22semidirect
29. #63646C22semidirect
30. C3×#825C22semidirect
31. C3×#815C22semidirect
32. #63569C22semidirect
33. Dic3×C3⋊C8C22semidirect
39. #4894D3semidirect
94. #907C2×D3semidirect
107. C3×#108C2×D3semidirect
111. #825C2×D3semidirect
116. #815C2×D3semidirect
242. #108D32semidirect
356. C32#2957semidirect
405. C3#79899semidirect

Maximal subgroups

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

subgroupindex
#105947082
#105946842
C3⋊D3×#1082
C3×#48942
#105910092
#105909752
#105909162
#105907032
#798993