Finite Group Databasebeta

← #11861214

Subgroups — #11861214

Order 1152.

1037 conjugacy classes of subgroups.

The subgroup lattice has 491 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3⋊D3×#135C211yesmaximal, characteristic
2#10595443C212yesmaximal, complemented
3C3×#5196C212yesmaximal, complemented
4#10591672C212yesmaximal, complemented
5#10591663C214yesmaximal, complemented
6#10590917C212yesmaximal, complemented
7#10590913C211yesmaximal, characteristic, complemented
8#10590700C211yesmaximal, characteristic, complemented
9#79890—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×C8×Dic3C2212yescomplemented
32#63578C2212yescomplemented
33#63570C2214yescomplemented
34#63554C2212yescomplemented
35D3×#135—32no—
36D3×#135—61no—
37#5750—34no—
38C3×#443—32no—
39#5196D312yescomplemented
40#5145—34no—
41#4895—32no—
42D3×#108—32no—
43#4823—34no—
44#4821—34no—
45#4700—32no—
46#4689—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#3712D411yescharacteristic
85#3712D411yescharacteristic
86#3710—22no—
87#3710—24no—
88#2957—91noSylow
89D3×#41—34no—
90D3×#41—62no—
91C3×#135—21no—
92C3×#135C2×D312yes—
93C3×#131—34no—
94#950—34no—
95#950—62no—
96#948C2×D314yescomplemented
97#919—32no—
98#919—61no—
99D3×Q16—32no—
100D3×Q16—61no—
101#916—34no—
102#916—62no—
103D3×SD16—34no—
104D3×SD16—62no—
105#912—32no—
106#912—61no—
107D3×D8—32no—
108D3×D8—61no—
109#907—34no—
110#907—64no—
111D3×M16—34no—
112D3×M16—64no—
113#904—32no—
114#904—61no—
115#901—34no—
116#901—64no—
117C2×ΓL(1,𝔽25)—32no—
118C2×ΓL(1,𝔽25)—64no—
119C2×D3×C8—32no—
120C2×D3×C8—61no—
121#872—32no—
122C3×#108—32no—
123C3×#104—34no—
124C3×C4×C8—32no—
125#837C2×D314yescomplemented
126#825—34no—
127#822—34no—
128#819C2×D312yescomplemented
129#815—32no—
130C8×Dic3C2×D312yescomplemented
131#805—34no—
132#803—32no—
133C22×C3⋊D3—22no—
134C22×C3⋊D3#4111yescharacteristic
135C32×Q8C22×C412yes—
136C32×D4—22no—
137C32×D4C22×C412yes—
138C2×C32×C4—22no—
139C2×C32×C4C2411yescharacteristic
140#638—22no—
141#638—22no—
142#638—22no—
143C2×C3⋊Dic3—22no—
144C2×C3⋊Dic3#4111yescharacteristic
145C4⋊(C3⋊D3)—22no—
146C4⋊(C3⋊D3)C22×C412yes—
147C4×C3⋊D3—22no—
148C4×C3⋊D3—22no—
149C4×C3⋊D3—22no—
150C4×C3⋊D3C22×C411yescharacteristic
151C4×C3⋊D3C22×C411yescharacteristic
152C4×C3⋊D3C2×D411yescharacteristic
153C4×C3⋊D3C2×D411yescharacteristic
154#634—22no—
155#634C22×C412yes—
156C2×C3×Dic3—22no—
157C32×C8C22×C411yescharacteristic
158C32×C8C22×C411yescharacteristic
159C3⋊(C3⋊C8)C22×C411yescharacteristic
160C3⋊(C3⋊C8)C22×C411yescharacteristic
161C3×C3⋊C8—24no—
162C3×C3⋊C8C2×D412yes—
163C3×C3⋊C8C2×D412yes—
164C2×#135—91no—
165#568—92no—
166#444—94no—
167#443—32no—
168#443—92no—
169C2×#108—91no—
170#421—92no—
171#405—91no—
172C3×#41—22no—
173C3×#41C22×D314yes—
174#239—34no—
175#239—62no—
176D3×Q8—34no—
177D3×Q8—62no—
178#237—34no—
179#237—62no—
180#237—64no—
181#237—122no—
182D3×D4—34no—
183D3×D4—62no—
184D3×D4—64no—
185D3×D4—122no—
186#235—34no—
187#235—62no—
188#235—64no—
189#235—122no—
190C2×C4×D3—32no—
191C2×C4×D3—61no—
192C2×C4×D3—64no—
193C2×C4×D3—122no—
194C3×Q16—21no—
195C3×Q16C4×D312yes—
196C3×SD16—22no—
197C3×SD16C4×D314yes—
198C3×D8—21no—
199C3×D8C4×D312yes—
200C3×M16—34no—
201C3×M16—64no—
202C2×C3×C8—21no—
203C2×C3×C8—32no—
204C2×C3×C8—64no—
205C2×C3×C8C22×D312yes—
206C3×C42—32no—
207#216—34no—
208#216—62no—
209#215—34no—
210#215—62no—
211#214—34no—
212#214—62no—
213#213—34no—
214#213—62no—
215(C2×D3)⋊C4—62no—
216Dic3⋊C4—62no—
217C4×Dic3C22×D312yes—
218#208—24no—
219#208C22×D314yes—
220C2×C3⋊C8—24no—
221C2×C3⋊C8—32no—
222C2×C3⋊C8—61no—
223C2×C3⋊C8C22×D312yes—
224Dic12—32no—
225Dic12—61no—
226D24—32no—
227D24—61no—
228#204—34no—
229#204—62no—
230ΓL(1,𝔽25)—32no—
231ΓL(1,𝔽25)—32no—
232ΓL(1,𝔽25)—32no—
233ΓL(1,𝔽25)—32no—
234ΓL(1,𝔽25)—64no—
235ΓL(1,𝔽25)—64no—
236ΓL(1,𝔽25)—64no—
237D3×C8—32no—
238D3×C8—32no—
239D3×C8—32no—
240D3×C8—32no—
241D3×C8—61no—
242D3×C8—61no—
243D3×C8—61no—
244D3×C8—61no—
245D3×C8—64no—
246D3×C8—64no—
247D3×C8—64no—
248C22×C32—22no—
249C22×C32C2×#4111yescharacteristic
250C2×C3⋊D3—22no—
251C2×C3⋊D3—41no—
252C2×C3⋊D3—82no—
253C2×C3⋊D3C4×D411yescharacteristic
254C2×C3⋊D3C4×D411yescharacteristic
255C32×C4—22no—
256C32×C4C23×C411yescharacteristic
257C32×C4C22×D411yescharacteristic
258C3⋊Dic3—22no—
259C3⋊Dic3C4×D411yescharacteristic
260C3⋊Dic3C4×D411yescharacteristic
261C3×Dic3—42no—
262C2×#41—92no—
263#135—92no—
264#135—91no—
265#135—92no—
266#135—91no—
267#135—91no—
268#135D3211yescharacteristic
269C2×Q16—91no—
270C2×SD16—92no—
271C2×D8—91no—
272#131—34no—
273#131—94no—
274#131—184no—
275C2×M16—91no—
276C2×M16—92no—
277C2×M16—182no—
278C2×M16—182no—
279C22×C8—91no—
280#117—91no—
281#108—32no—
282#108—92no—
283#104—34no—
284#104—94no—
285#97—92no—
286C4×C8—32no—
287C22×D3—32no—
288C22×D3—61no—
289C22×D3—64no—
290C22×D3—122no—
291C3×Q8—22no—
292C3×Q8C2×C4×D314yes—
293C3×D4—24no—
294C3×D4—22no—
295C3×D4—42no—
296C3×D4C2×C4×D314yes—
297C2×C3×C4—24no—
298C2×C3×C4—21no—
299C2×C3×C4—42no—
300C2×C3×C4—62no—
301C2×C3×C4C23×D312yes—
302#67—64no—
303#67—64no—
304#67—64no—
305#67—122no—
306#67—122no—
307#67—122no—
308C2×Dic3—22no—
309C2×Dic3—32no—
310C2×Dic3—61no—
311C2×Dic3—64no—
312C2×Dic3—122no—
313D12—34no—
314D12—62no—
315D12—64no—
316D12—122no—
317C4×D3—32no—
318C4×D3—32no—
319C4×D3—32no—
320C4×D3—32no—
321C4×D3—61no—
322C4×D3—61no—
323C4×D3—61no—
324C4×D3—61no—
325C4×D3—64no—
326C4×D3—64no—
327C4×D3—64no—
328C4×D3—122no—
329C4×D3—122no—
330C4×D3—122no—
331Dic6—34no—
332Dic6—62no—
333Dic6—64no—
334Dic6—122no—
335C3×C8—21no—
336C3×C8—21no—
337C3×C8—32no—
338C3×C8—32no—
339C3×C8—64no—
340C3×C8C2×C4×D312yes—
341C3×C8C2×C4×D312yes—
342C3⋊C8—24no—
343C3⋊C8—32no—
344C3⋊C8—32no—
345C3⋊C8—61no—
346C3⋊C8—61no—
347C3⋊C8D3×D412yes—
348C3⋊C8D3×D412yes—
349C2×C32—21no—
350C2×C32—42no—
351C2×C32C2×C4×D411yescharacteristic
352C3⋊D3—21no—
353C3⋊D3—21no—
354C3⋊D3—42no—
355#41—92no—
356#41—92no—
357#41—92no—
358#41—182no—
359#41—182no—
360#41C2×D3212yes—
361C2×Q8—92no—
362C2×D4—92no—
363C2×D4—182no—
364C22×C4—91no—
365C22×C4—182no—
366Q16—92no—
367Q16—91no—
368Q16#62411yescharacteristic
369SD16—92no—
370SD16—92no—
371SD16—92no—
372SD16#62412yes—
373D8—92no—
374D8—91no—
375D8#62411yescharacteristic
376M16—34no—
377M16—64no—
378M16—91no—
379M16—91no—
380M16—92no—
381M16—184no—
382M16—182no—
383C2×C8—32no—
384C2×C8—64no—
385C2×C8—91no—
386C2×C8—91no—
387C2×C8—91no—
388C2×C8—91no—
389C2×C8—91no—
390C2×C8—184no—
391C2×C8—182no—
392C2×C8C2×D3211yescharacteristic
393C4⋊C4—181no—
394C22⋊C4—181no—
395C42—32no—
396C22×C3—24no—
397C22×C3—21no—
398C22×C3—42no—
399C22×C3D3×#4112yes—
400C2×D3—32no—
401C2×D3—32no—
402C2×D3—61no—
403C2×D3—61no—
404C2×D3—64no—
405C2×D3—122no—
406C2×D3—122no—
407C2×D3—122no—
408C2×D3—244no—
409C2×D3—244no—
410C3×C4—24no—
411C3×C4—21no—
412C3×C4—21no—
413C3×C4—42no—
414C3×C4—122no—
415C3×C4C22×C4×D312yes—
416C3×C4C2×D3×D412yes—
417Dic3—32no—
418Dic3—32no—
419Dic3—42no—
420Dic3—61no—
421Dic3—61no—
422Dic3—64no—
423Dic3—122no—
424C32#295711yescharacteristic, complemented, Sylow
425C23—91no—
426C23—182no—
427Q8—92no—
428Q8—182no—
429Q8C2×#62412yes—
430D4—22no—
431D4—92no—
432D4—182no—
433D4—182no—
434D4—182no—
435D4—182no—
436D4C2×#62412yes—
437C2×C4—22no—
438C2×C4—62no—
439C2×C4—91no—
440C2×C4—91no—
441C2×C4—91no—
442C2×C4—91no—
443C2×C4—91no—
444C2×C4—182no—
445C2×C4—182no—
446C2×C4—182no—
447C2×C4—182no—
448C2×C4C22×D3211yescharacteristic
449C8—32no—
450C8—32no—
451C8—64no—
452C8—91no—
453C8—91no—
454C8C2×#62411yescharacteristic
455C8C2×#62411yescharacteristic
456C2×C3—22no—
457C2×C3—21no—
458C2×C3—41no—
459C2×C3—44no—
460C2×C3—82no—
461C2×C3C4×D3×D412yes—
462D3—62no—
463D3—62no—
464D3—62no—
465D3—121no—
466D3—124no—
467D3—242no—
468C22—22no—
469C22—91no—
470C22—91no—
471C22—182no—
472C22—361no—
473C22—722no—
474C22#6431211yescharacteristic
475C4—22no—
476C4—91no—
477C4—91no—
478C4—122no—
479C4—182no—
480C4D32×D411yescharacteristic
481C4C22×#62411yescharacteristic
482C3—21no—
483C3#7989012yescomplemented
484C2—21no—
485C2—42no—
486C2—181no—
487C2—181no—
488C2—362no—
489C2D4×#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×#5196C2semidirect
4. #10591672C2semidirect
5. #10591663C2semidirect
6. #10590917C2semidirect
7. #10590913C2semidirect
8. #10590700C2semidirect
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×C8×Dic3C22semidirect
32. #63578C22semidirect
33. #63570C22semidirect
34. #63554C22semidirect
39. #5196D3semidirect
96. #948C2×D3semidirect
125. #837C2×D3semidirect
128. #819C2×D3semidirect
130. C8×Dic3C2×D3semidirect
424. C32#2957semidirect
483. C3#79890semidirect

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×#51962
#105916722
#105916632
#105909172
#105909132
#105907002
#798903