Finite Group Databasebeta

← #11861216

Subgroups — #11861216

Order 1152.

1037 conjugacy classes of subgroups.

The subgroup lattice has 483 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3⋊D3×#135C211yesmaximal, characteristic
2#10595443C212yesmaximal, complemented
3C3×#5197C212yesmaximal, complemented
4#10591672C212yesmaximal, complemented
5#10591662C214yesmaximal, complemented
6#10590918C212yesmaximal, complemented
7#10590913C211yesmaximal, characteristic, complemented
8#10590703C211yesmaximal, characteristic, complemented
9#79899—32nomaximal
10#41×C3⋊D3C2212yes—
11C32×#135C2211yescharacteristic
12#64159C2212yes—
13#64128C411yescharacteristic, complemented
14Q16×C3⋊D3C411yescharacteristic, complemented
15#64125C412yescomplemented
16SD16×C3⋊D3C412yescomplemented
17#64121C411yescharacteristic, complemented
18D8×C3⋊D3C411yescharacteristic, complemented
19#64113C2211yescharacteristic
20C2×C8×C3⋊D3C2211yescharacteristic
21C3×#948C2214yescomplemented
22#63874C2211yescharacteristic
23C2×#3712—22no—
24C2×#3712C2211yescharacteristic
25#63818—22no—
26#63818C2212yes—
27#63817—24no—
28#63817C2214yescomplemented
29C3×#837C2214yescomplemented
30C3×#819C2212yescomplemented
31C3×#815C2212yescomplemented
32#63578C2212yescomplemented
33#63570C2214yescomplemented
34Dic3×C3⋊C8C2212yescomplemented
35D3×#135—32no—
36D3×#135—61no—
37#5750—34no—
38C3×#444—32no—
39#5197D312yescomplemented
40#5144—34no—
41#4894—32no—
42D3×#108—32no—
43#4824—34no—
44#4821—34no—
45#4717—32no—
46#4708—32no—
47C32×#41C2312yes—
48#3832C2×C412yes—
49Q8×C3⋊D3C2×C412yes—
50#3830—22no—
51#3830C2×C412yes—
52D4×C3⋊D3—22no—
53D4×C3⋊D3C2×C412yes—
54#3828—22no—
55#3828C2312yes—
56C2×C4×C3⋊D3—22no—
57C2×C4×C3⋊D3C2311yescharacteristic
58C32×Q16C2×C411yescharacteristic
59C32×SD16C2×C412yes—
60C32×D8C2×C411yescharacteristic
61C2×C32×C8C2311yescharacteristic
62#3756C2×C412yes—
63#3755C2×C412yes—
64#3754C2×C412yes—
65#3753C2×C412yes—
66C2×C3⋊(C3⋊C8)C2311yescharacteristic
67#3746C2×C411yescharacteristic
68#3745C2×C411yescharacteristic
69#3744C2×C412yes—
70C8×C3⋊D3C2×C411yescharacteristic
71C8×C3⋊D3C2×C411yescharacteristic
72C8×C3⋊D3C2×C411yescharacteristic
73C8×C3⋊D3C2×C411yescharacteristic
74C3×C4×Dic3C2312yes—
75C3×#208—24no—
76C3×#208C2314yes—
77C2×C3×C3⋊C8—24no—
78C2×C3×C3⋊C8C2312yes—
79#3724—21no—
80#3722—21no—
81#3712—22no—
82#3712—24no—
83#3712D412yes—
84#3712D412yes—
85#3710—22no—
86#3710—24no—
87#2957—91noSylow
88D3×#41—34no—
89D3×#41—62no—
90C3×#135—21no—
91C3×#135C2×D312yes—
92C3×#131—34no—
93#950—34no—
94#950—62no—
95#948C2×D314yescomplemented
96#919—32no—
97#919—61no—
98D3×Q16—32no—
99D3×Q16—61no—
100#916—34no—
101#916—62no—
102D3×SD16—34no—
103D3×SD16—62no—
104#912—32no—
105#912—61no—
106D3×D8—32no—
107D3×D8—61no—
108#907—34no—
109#907—64no—
110D3×M16—34no—
111D3×M16—64no—
112#904—32no—
113#904—61no—
114#901—34no—
115#901—64no—
116C2×ΓL(1,𝔽25)—32no—
117C2×ΓL(1,𝔽25)—64no—
118C2×D3×C8—32no—
119C2×D3×C8—61no—
120#872—32no—
121C3×#108—32no—
122C3×#104—34no—
123C3×#97—32no—
124#837C2×D314yescomplemented
125#825—34no—
126#822—34no—
127#819C2×D312yescomplemented
128#815C2×D312yescomplemented
129C8×Dic3—32no—
130#805—34no—
131C4×C3⋊C8—32no—
132C22×C3⋊D3—22no—
133C22×C3⋊D3#4111yescharacteristic
134C32×Q8C22×C412yes—
135C32×D4—22no—
136C32×D4C22×C412yes—
137C2×C32×C4—22no—
138C2×C32×C4C2411yescharacteristic
139#638—22no—
140#638—22no—
141#638—22no—
142C2×C3⋊Dic3—22no—
143C2×C3⋊Dic3#4111yescharacteristic
144C4⋊(C3⋊D3)—22no—
145C4⋊(C3⋊D3)C22×C412yes—
146C4×C3⋊D3—22no—
147C4×C3⋊D3—22no—
148C4×C3⋊D3—22no—
149C4×C3⋊D3C22×C411yescharacteristic
150C4×C3⋊D3C22×C411yescharacteristic
151C4×C3⋊D3C2×D411yescharacteristic
152C4×C3⋊D3C2×D411yescharacteristic
153#634—22no—
154#634C22×C412yes—
155C2×C3×Dic3—22no—
156C32×C8C22×C411yescharacteristic
157C32×C8C22×C411yescharacteristic
158C3⋊(C3⋊C8)C22×C411yescharacteristic
159C3⋊(C3⋊C8)C22×C411yescharacteristic
160C3×C3⋊C8—24no—
161C3×C3⋊C8C2×D414yes—
162C2×#135—91no—
163#568—92no—
164#444—32no—
165#444—92no—
166#443—94no—
167C2×#108—91no—
168#421—92no—
169#405—91no—
170C3×#41—22no—
171C3×#41C22×D314yes—
172#239—34no—
173#239—62no—
174D3×Q8—34no—
175D3×Q8—62no—
176#237—34no—
177#237—62no—
178#237—64no—
179#237—122no—
180D3×D4—34no—
181D3×D4—62no—
182D3×D4—64no—
183D3×D4—122no—
184#235—34no—
185#235—62no—
186#235—64no—
187#235—122no—
188C2×C4×D3—32no—
189C2×C4×D3—61no—
190C2×C4×D3—64no—
191C2×C4×D3—122no—
192C3×Q16—21no—
193C3×Q16C4×D312yes—
194C3×SD16—22no—
195C3×SD16C4×D314yes—
196C3×D8—21no—
197C3×D8C4×D312yes—
198C3×M16—34no—
199C3×M16—64no—
200C2×C3×C8—21no—
201C2×C3×C8—32no—
202C2×C3×C8—64no—
203C2×C3×C8C22×D312yes—
204C3×C42—32no—
205#216—34no—
206#216—62no—
207#215—34no—
208#215—62no—
209#214—34no—
210#214—62no—
211#213—34no—
212#213—62no—
213(C2×D3)⋊C4—62no—
214Dic3⋊C4—62no—
215C4×Dic3C22×D312yes—
216#208—24no—
217#208C22×D314yes—
218C2×C3⋊C8—24no—
219C2×C3⋊C8—32no—
220C2×C3⋊C8—61no—
221C2×C3⋊C8C22×D312yes—
222Dic12—32no—
223Dic12—61no—
224D24—32no—
225D24—61no—
226#204—34no—
227#204—62no—
228ΓL(1,𝔽25)—34no—
229ΓL(1,𝔽25)—34no—
230ΓL(1,𝔽25)—64no—
231ΓL(1,𝔽25)—64no—
232ΓL(1,𝔽25)—64no—
233D3×C8—32no—
234D3×C8—32no—
235D3×C8—32no—
236D3×C8—32no—
237D3×C8—61no—
238D3×C8—61no—
239D3×C8—61no—
240D3×C8—61no—
241D3×C8—64no—
242D3×C8—64no—
243D3×C8—64no—
244C22×C32—22no—
245C22×C32C2×#4111yescharacteristic
246C2×C3⋊D3—22no—
247C2×C3⋊D3—41no—
248C2×C3⋊D3—82no—
249C2×C3⋊D3C4×D411yescharacteristic
250C2×C3⋊D3C4×D411yescharacteristic
251C32×C4—22no—
252C32×C4C23×C411yescharacteristic
253C32×C4C22×D411yescharacteristic
254C3⋊Dic3—22no—
255C3⋊Dic3C4×D411yescharacteristic
256C3⋊Dic3C4×D411yescharacteristic
257C3×Dic3—42no—
258C2×#41—92no—
259#135—92no—
260#135—91no—
261#135—92no—
262#135—91no—
263#135—91no—
264#135D3211yescharacteristic
265C2×Q16—91no—
266C2×SD16—92no—
267C2×D8—91no—
268#131—34no—
269#131—94no—
270#131—184no—
271C2×M16—91no—
272C2×M16—92no—
273C2×M16—182no—
274C2×M16—182no—
275C22×C8—91no—
276#117—91no—
277#108—32no—
278#108—92no—
279#104—34no—
280#104—94no—
281#97—32no—
282C4×C8—92no—
283C22×D3—32no—
284C22×D3—61no—
285C22×D3—64no—
286C22×D3—122no—
287C3×Q8—22no—
288C3×Q8C2×C4×D314yes—
289C3×D4—24no—
290C3×D4—22no—
291C3×D4—42no—
292C3×D4C2×C4×D314yes—
293C2×C3×C4—24no—
294C2×C3×C4—21no—
295C2×C3×C4—42no—
296C2×C3×C4—62no—
297C2×C3×C4C23×D312yes—
298#67—64no—
299#67—64no—
300#67—64no—
301#67—122no—
302#67—122no—
303#67—122no—
304C2×Dic3—22no—
305C2×Dic3—32no—
306C2×Dic3—61no—
307C2×Dic3—64no—
308C2×Dic3—122no—
309D12—34no—
310D12—62no—
311D12—64no—
312D12—122no—
313C4×D3—32no—
314C4×D3—32no—
315C4×D3—32no—
316C4×D3—32no—
317C4×D3—61no—
318C4×D3—61no—
319C4×D3—61no—
320C4×D3—61no—
321C4×D3—64no—
322C4×D3—64no—
323C4×D3—64no—
324C4×D3—122no—
325C4×D3—122no—
326C4×D3—122no—
327Dic6—34no—
328Dic6—62no—
329Dic6—64no—
330Dic6—122no—
331C3×C8—21no—
332C3×C8—21no—
333C3×C8—34no—
334C3×C8—64no—
335C3×C8C2×C4×D312yes—
336C3×C8C2×C4×D312yes—
337C3⋊C8—24no—
338C3⋊C8—32no—
339C3⋊C8—32no—
340C3⋊C8—61no—
341C3⋊C8—61no—
342C3⋊C8D3×D414yes—
343C2×C32—21no—
344C2×C32—42no—
345C2×C32C2×C4×D411yescharacteristic
346C3⋊D3—21no—
347C3⋊D3—21no—
348C3⋊D3—42no—
349#41—92no—
350#41—92no—
351#41—92no—
352#41—182no—
353#41—182no—
354#41C2×D3212yes—
355C2×Q8—92no—
356C2×D4—92no—
357C2×D4—182no—
358C22×C4—91no—
359C22×C4—182no—
360Q16—92no—
361Q16—91no—
362Q16#62411yescharacteristic
363SD16—92no—
364SD16—92no—
365SD16—92no—
366SD16#62412yes—
367D8—92no—
368D8—91no—
369D8#62411yescharacteristic
370M16—34no—
371M16—64no—
372M16—92no—
373M16—92no—
374M16—184no—
375M16—182no—
376C2×C8—32no—
377C2×C8—64no—
378C2×C8—91no—
379C2×C8—91no—
380C2×C8—91no—
381C2×C8—91no—
382C2×C8—91no—
383C2×C8—184no—
384C2×C8—182no—
385C2×C8C2×D3211yescharacteristic
386C4⋊C4—181no—
387C22⋊C4—181no—
388C42—32no—
389C22×C3—24no—
390C22×C3—21no—
391C22×C3—42no—
392C22×C3D3×#4112yes—
393C2×D3—32no—
394C2×D3—32no—
395C2×D3—61no—
396C2×D3—61no—
397C2×D3—64no—
398C2×D3—122no—
399C2×D3—122no—
400C2×D3—122no—
401C2×D3—244no—
402C2×D3—244no—
403C3×C4—24no—
404C3×C4—21no—
405C3×C4—21no—
406C3×C4—42no—
407C3×C4—122no—
408C3×C4C22×C4×D312yes—
409C3×C4C2×D3×D412yes—
410Dic3—32no—
411Dic3—32no—
412Dic3—42no—
413Dic3—61no—
414Dic3—61no—
415Dic3—64no—
416Dic3—122no—
417C32#295711yescharacteristic, complemented, Sylow
418C23—91no—
419C23—182no—
420Q8—92no—
421Q8—182no—
422Q8C2×#62412yes—
423D4—22no—
424D4—92no—
425D4—182no—
426D4—182no—
427D4—182no—
428D4—182no—
429D4C2×#62412yes—
430C2×C4—22no—
431C2×C4—62no—
432C2×C4—91no—
433C2×C4—91no—
434C2×C4—91no—
435C2×C4—91no—
436C2×C4—91no—
437C2×C4—182no—
438C2×C4—182no—
439C2×C4—182no—
440C2×C4—182no—
441C2×C4C22×D3211yescharacteristic
442C8—34no—
443C8—64no—
444C8—91no—
445C8—91no—
446C8C2×#62411yescharacteristic
447C8C2×#62411yescharacteristic
448C2×C3—22no—
449C2×C3—21no—
450C2×C3—41no—
451C2×C3—44no—
452C2×C3—82no—
453C2×C3C4×D3×D412yes—
454D3—62no—
455D3—62no—
456D3—62no—
457D3—121no—
458D3—124no—
459D3—242no—
460C22—22no—
461C22—91no—
462C22—91no—
463C22—182no—
464C22—361no—
465C22—722no—
466C22#6431211yescharacteristic
467C4—22no—
468C4—91no—
469C4—91no—
470C4—122no—
471C4—182no—
472C4D32×D411yescharacteristic
473C4C22×#62411yescharacteristic
474C3—21no—
475C3#7989912yescomplemented
476C2—21no—
477C2—42no—
478C2—181no—
479C2—181no—
480C2—362no—
481C2D4×#62411yescharacteristic
subgroupG/H
centerC4D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#135C22
socleC2×C32C2×C4×D4
prime radicalC3⋊D3×#135C2
cosocleC2×C32×C4C24
hypercenter#135D32
hypocenterC32#2957
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×C4 ◁ #135

Complements

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

NH ≅ G/Ntype
2. #10595443C2semidirect
3. C3×#5197C2semidirect
4. #10591672C2semidirect
5. #10591662C2semidirect
6. #10590918C2semidirect
7. #10590913C2semidirect
8. #10590703C2semidirect
13. #64128C4semidirect
14. Q16×C3⋊D3C4semidirect
15. #64125C4semidirect
16. SD16×C3⋊D3C4semidirect
17. #64121C4semidirect
18. D8×C3⋊D3C4semidirect
21. C3×#948C22semidirect
28. #63817C22semidirect
29. C3×#837C22semidirect
30. C3×#819C22semidirect
31. C3×#815C22semidirect
32. #63578C22semidirect
33. #63570C22semidirect
34. Dic3×C3⋊C8C22semidirect
39. #5197D3semidirect
95. #948C2×D3semidirect
124. #837C2×D3semidirect
127. #819C2×D3semidirect
128. #815C2×D3semidirect
417. C32#2957semidirect
475. C3#79899semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×#1352
#105954432
C3×#51972
#105916722
#105916622
#105909182
#105909132
#105907032
#798993