Finite Group Databasebeta

← #11899416

Subgroups — #11899416

Order 1152.

762 conjugacy classes of subgroups.

The subgroup lattice has 531 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×#901C211yesmaximal, characteristic
2#10592600C211yesmaximal, characteristic, complemented
3C3×#4901C211yesmaximal, characteristic, complemented
4C2×C3×#798C211yesmaximal, characteristic, complemented
5#10590624C211yesmaximal, characteristic, complemented
6#10590621C211yesmaximal, characteristic, complemented
7D3×#812C211yesmaximal, characteristic, complemented
8#10590229C212yesmaximal, complemented
9#10590228C212yesmaximal, complemented
10#10590226C212yesmaximal, complemented
11D3×#798C212yesmaximal, complemented
12#82012—31nomaximal
13#82007—31nomaximal
14D3×#235C411yescharacteristic
15#64110C2211yescharacteristic
16C3×#901C2211yescharacteristic
17C2×C3×D3×C8C2211yescharacteristic
18#63817C411yescharacteristic
19#63814C411yescharacteristic
20D3×#208C411yescharacteristic
21#63804C412yes—
22#63803C2212yes—
23D3×ΓL(1,𝔽25)C412yes—
24D32×C8C2212yes—
25C2×C32×C16C2211yescharacteristic, complemented
26#63639C2211yescharacteristic, complemented
27#63625C2212yescomplemented
28C16×C3⋊D3C2212yescomplemented
29C3×#812C2211yescharacteristic, complemented
30C2×C3×C3⋊C16C2211yescharacteristic, complemented
31C3×#798C2211yescharacteristic
32C3×#798C2211yescharacteristic
33C3×#798C2212yescomplemented
34C3×#798C2211yescharacteristic, complemented
35C3×#798C2211yescharacteristic, complemented
36C3×D3×C16C2212yescomplemented
37#63544C2212yescomplemented
38#63543C2212yes—
39#63543C2212yescomplemented
40#63542C2212yescomplemented
41D3×C3⋊C16C2212yescomplemented
42D3×C3⋊C16C2212yescomplemented
43D3×#131—31no—
44C2×#901—31no—
45C3×#504—31no—
46C2×C3×M32—31no—
47#5140—31no—
48C2×#812—31no—
49#4907—31no—
50#4907—32no—
51#4907—32no—
52#4907—32no—
53D3×M32—31no—
54D3×M32—32no—
55D3×M32—32no—
56D3×M32—32no—
57#4901—31no—
58#4901—31no—
59#4901—31no—
60#4901—31no—
61#4901—32no—
62#4901—61no—
63#4901D311yescharacteristic, complemented
64C2×#798—32no—
65C2×#798D311yescharacteristic, complemented
66#3828C2×C411yescharacteristic
67C3×#235C2×C411yescharacteristic
68C2×C3×C4×D3C2×C411yescharacteristic
69D3×#67C812yes—
70#3804C812yes—
71D3×D12C811yescharacteristic
72C4×D32C2×C412yes—
73#3799C811yescharacteristic
74#3798C2×C412yes—
75#3795C811yescharacteristic
76D3×Dic6C811yescharacteristic
77C2×C32×C8C2311yescharacteristic
78#3748C2×C411yescharacteristic
79#3743C2×C412yes—
80C8×C3⋊D3C2312yes—
81C3×#208C2×C411yescharacteristic
82C2×C3×C3⋊C8C2×C411yescharacteristic
83C3×ΓL(1,𝔽25)C2×C412yes—
84C3×D3×C8C2×C411yescharacteristic
85C3×D3×C8C2×C411yescharacteristic
86C3×D3×C8C2311yescharacteristic
87C3×D3×C8C2311yescharacteristic
88C3×D3×C8C2312yes—
89#3712C2×C412yes—
90#3711C2×C412yes—
91#3711C2×C412yes—
92#3710C2×C412yes—
93D3×C3⋊C8C2×C412yes—
94D3×C3⋊C8C2×C412yes—
95C32×C16C2311yescharacteristic
96C32×C16C2311yescharacteristic
97C3⋊(C3⋊C16)C2312yes—
98C3×C3⋊C16C2311yescharacteristic
99C3×C3⋊C16C2312yes—
100C3×C3⋊C16C2311yescharacteristic
101#3407—91noSylow
102D3×#41—31no—
103C2×#235—31no—
104C3×#131—31no—
105C22×C3×C8—31no—
106#948—31no—
107C2×#208—31no—
108#907—31no—
109#907—32no—
110D3×M16—31no—
111D3×M16—32no—
112#901—31no—
113#901—31no—
114#901—31no—
115#901—31no—
116#901—32no—
117#901—32no—
118#901—32no—
119#901—61no—
120#901C2×D311yescharacteristic
121C2×ΓL(1,𝔽25)—32no—
122C2×D3×C8—32no—
123C2×D3×C8—32no—
124C2×D3×C8C2×D311yescharacteristic
125C3×M32—31no—
126C3×M32—31no—
127C3×M32—31no—
128C3×M32—31no—
129C3×M32—31no—
130C3×M32—32no—
131C2×C3×C16—21no—
132C2×C3×C16—31no—
133C2×C3×C16—32no—
134C2×C3×C16C2×D311yescharacteristic, complemented
135C2×C3×C16C2×D311yescharacteristic, complemented
136#812—31no—
137#812—31no—
138#812—32no—
139#812—32no—
140#812—61no—
141#812C2×D311yescharacteristic, complemented
142C2×C3⋊C16—32no—
143C2×C3⋊C16—32no—
144C2×C3⋊C16C2×D311yescharacteristic, complemented
145#798—32no—
146#798—32no—
147#798—32no—
148#798—32no—
149#798—32no—
150#798—32no—
151#798—62no—
152#798C2×D311yescharacteristic
153#798C2×D311yescharacteristic
154#798C2×D311yescharacteristic, complemented
155#798C2×D311yescharacteristic, complemented
156#798C2×D312yescomplemented
157D3×C16—32no—
158D3×C16—32no—
159D3×C16—32no—
160D3×C16—32no—
161D3×C16—32no—
162D3×C16—32no—
163D3×C16—62no—
164D3×C16C2×D312yescomplemented
165C22×C3×D3C2×C811yescharacteristic
166C2×D32C2×C812yes—
167C2×C32×C4C22×C411yescharacteristic
168#638C2×C812yes—
169C4⋊(C3⋊D3)C2×C811yescharacteristic
170C4×C3⋊D3C22×C412yes—
171#634C2×C811yescharacteristic
172C3×#67C2×C812yes—
173C2×C3×Dic3C2×C811yescharacteristic
174C3×D12C2×C811yescharacteristic
175C3×C4×D3C2×C811yescharacteristic
176C3×C4×D3C2×C811yescharacteristic
177C3×C4×D3C22×C411yescharacteristic
178C3×C4×D3C22×C412yes—
179C3×C4×D3C22×C411yescharacteristic
180C3×Dic6C2×C811yescharacteristic
181#627C2×C812yes—
182#626C2×C812yes—
183#626C2×C812yes—
184#625C2×C812yes—
185#624C2×C812yes—
186D3×Dic3C2×C812yes—
187D3×Dic3C2×C812yes—
188C32×C8C22×C411yescharacteristic
189C32×C8C2411yescharacteristic
190C3⋊(C3⋊C8)C22×C412yes—
191C3×C3⋊C8C22×C411yescharacteristic
192C3×C3⋊C8C22×C412yes—
193C3×C3⋊C8C22×C411yescharacteristic
194C2×#131—91no—
195#504—31no—
196#504—91no—
197#504—92no—
198#504—91no—
199#504—92no—
200#504—91no—
201C2×M32—31no—
202C2×M32—92no—
203C2×M32—92no—
204C2×M32—91no—
205C3×#41—31no—
206C22×C3×C4—31no—
207C2×#67—32no—
208#239—31no—
209D3×Q8—31no—
210#237—32no—
211#237—31no—
212D3×D4—32no—
213D3×D4—31no—
214#235—31no—
215#235—31no—
216#235—32no—
217#235—31no—
218#235—32no—
219#235—32no—
220#235—31no—
221#235—61no—
222#235C4×D311yescharacteristic
223C2×D12—31no—
224C2×C4×D3—32no—
225C2×C4×D3—32no—
226C2×C4×D3C4×D311yescharacteristic
227C2×Dic6—31no—
228C3×M16—31no—
229C3×M16—32no—
230C2×C3×C8—21no—
231C2×C3×C8—31no—
232C2×C3×C8—31no—
233C2×C3×C8—31no—
234C2×C3×C8—31no—
235C2×C3×C8—32no—
236C2×C3×C8—31no—
237C2×C3×C8C22×D311yescharacteristic
238C2×C3×C8C22×D311yescharacteristic
239#208—31no—
240#208—31no—
241#208—32no—
242#208—32no—
243#208—61no—
244#208C4×D311yescharacteristic
245C2×C3⋊C8—32no—
246C2×C3⋊C8—32no—
247C2×C3⋊C8C4×D311yescharacteristic
248ΓL(1,𝔽25)—32no—
249ΓL(1,𝔽25)—32no—
250ΓL(1,𝔽25)—32no—
251ΓL(1,𝔽25)—32no—
252ΓL(1,𝔽25)—32no—
253ΓL(1,𝔽25)—32no—
254ΓL(1,𝔽25)—62no—
255ΓL(1,𝔽25)C4×D312yes—
256D3×C8—32no—
257D3×C8—32no—
258D3×C8—32no—
259D3×C8—32no—
260D3×C8—32no—
261D3×C8—32no—
262D3×C8—62no—
263D3×C8C4×D311yescharacteristic
264D3×C8C4×D311yescharacteristic
265D3×C8C22×D311yescharacteristic
266D3×C8C22×D312yes—
267D3×C8C22×D311yescharacteristic
268C3×C16—21no—
269C3×C16—21no—
270C3×C16—31no—
271C3×C16—32no—
272C3×C16—31no—
273C3×C16C22×D311yescharacteristic
274C3×C16C22×D311yescharacteristic
275C3×C16C22×D311yescharacteristic
276C3×C16C22×D311yescharacteristic
277C3⋊C16—32no—
278C3⋊C16—32no—
279C3⋊C16—62no—
280C3⋊C16C22×D311yescharacteristic
281C3⋊C16C22×D312yes—
282C3⋊C16C22×D311yescharacteristic
283C22×C32C22×C811yescharacteristic
284C2×C3⋊D3C22×C812yes—
285C2×C3×D3—41no—
286C2×C3×D3C22×C811yescharacteristic
287C2×C3×D3C22×C812yes—
288C2×C3×D3C22×C811yescharacteristic
289D32—42no—
290C32×C4C22×C811yescharacteristic
291C32×C4C23×C411yescharacteristic
292C3⋊Dic3C22×C812yes—
293C3×Dic3C22×C811yescharacteristic
294C3×Dic3C22×C812yes—
295C3×Dic3C22×C811yescharacteristic
296C2×#41—91no—
297#131—31no—
298#131—92no—
299#131—91no—
300#131—92no—
301#131—91no—
302#131—91no—
303C2×M16—92no—
304C2×M16—91no—
305C22×C8—31no—
306C22×C8—92no—
307M32—31no—
308M32—31no—
309M32—31no—
310M32—31no—
311M32—31no—
312M32—32no—
313M32—92no—
314M32—92no—
315M32—92no—
316M32—91no—
317M32—92no—
318C2×C16—31no—
319C2×C16—32no—
320C2×C16—92no—
321C2×C16—92no—
322C2×C16—92no—
323C2×C16—92no—
324C2×C16D3211yescharacteristic, complemented
325C23×C3—31no—
326C22×D3—32no—
327C22×D3—32no—
328C22×D3D3×C811yescharacteristic
329C3×Q8—31no—
330C3×D4—32no—
331C3×D4—31no—
332C2×C3×C4—21no—
333C2×C3×C4—31no—
334C2×C3×C4—31no—
335C2×C3×C4—31no—
336C2×C3×C4—31no—
337C2×C3×C4—32no—
338C2×C3×C4—31no—
339C2×C3×C4C2×C4×D311yescharacteristic
340C2×C3×C4C2×C4×D311yescharacteristic
341#67—32no—
342#67—32no—
343#67—32no—
344#67—32no—
345#67—32no—
346#67—32no—
347#67—62no—
348#67D3×C812yes—
349C2×Dic3—32no—
350C2×Dic3—32no—
351C2×Dic3D3×C811yescharacteristic
352D12—32no—
353D12—32no—
354D12—31no—
355D12—31no—
356D12—61no—
357D12D3×C811yescharacteristic
358C4×D3—32no—
359C4×D3—32no—
360C4×D3—32no—
361C4×D3—32no—
362C4×D3—32no—
363C4×D3—32no—
364C4×D3—62no—
365C4×D3D3×C811yescharacteristic
366C4×D3D3×C811yescharacteristic
367C4×D3C2×C4×D311yescharacteristic
368C4×D3C2×C4×D312yes—
369C4×D3C2×C4×D311yescharacteristic
370Dic6—31no—
371Dic6—31no—
372Dic6—32no—
373Dic6—32no—
374Dic6—61no—
375Dic6D3×C811yescharacteristic
376C3×C8—21no—
377C3×C8—21no—
378C3×C8—31no—
379C3×C8—32no—
380C3×C8—31no—
381C3×C8C2×C4×D311yescharacteristic
382C3×C8C2×C4×D311yescharacteristic
383C3×C8C23×D311yescharacteristic
384C3×C8C23×D311yescharacteristic
385C3⋊C8—32no—
386C3⋊C8—32no—
387C3⋊C8—62no—
388C3⋊C8C2×C4×D311yescharacteristic
389C3⋊C8C2×C4×D312yes—
390C3⋊C8C2×C4×D311yescharacteristic
391C2×C32—21no—
392C2×C32C23×C811yescharacteristic
393C3⋊D3—22no—
394C3×D3—21no—
395C3×D3—22no—
396C3×D3—21no—
397#41—31no—
398#41—92no—
399#41—92no—
400#41—91no—
401#41—91no—
402#41—91no—
403C2×Q8—91no—
404C2×D4—91no—
405C2×D4—92no—
406C22×C4—31no—
407C22×C4—92no—
408M16—31no—
409M16—32no—
410M16—92no—
411M16—92no—
412M16—92no—
413M16—91no—
414M16—92no—
415C2×C8—31no—
416C2×C8—32no—
417C2×C8—31no—
418C2×C8—31no—
419C2×C8—31no—
420C2×C8—31no—
421C2×C8—92no—
422C2×C8—92no—
423C2×C8—92no—
424C2×C8—92no—
425C2×C8C2×D3211yescharacteristic
426C16—31no—
427C16—31no—
428C16—32no—
429C16—92no—
430C16C2×D3211yescharacteristic
431C16C2×D3211yescharacteristic
432C22×C3—21no—
433C22×C3—31no—
434C22×C3—32no—
435C22×C3—31no—
436C22×C3—121no—
437C22×C3C2×D3×C811yescharacteristic
438C22×C3C2×D3×C811yescharacteristic
439C2×D3—32no—
440C2×D3—32no—
441C2×D3—41no—
442C2×D3—62no—
443C2×D3—122no—
444C2×D3—122no—
445C2×D3C2×D3×C811yescharacteristic
446C2×D3C2×D3×C812yes—
447C2×D3C2×D3×C811yescharacteristic
448C3×C4—21no—
449C3×C4—21no—
450C3×C4—31no—
451C3×C4—32no—
452C3×C4—31no—
453C3×C4C2×D3×C811yescharacteristic
454C3×C4C2×D3×C811yescharacteristic
455C3×C4C22×C4×D311yescharacteristic
456C3×C4C22×C4×D311yescharacteristic
457Dic3—32no—
458Dic3—32no—
459Dic3—62no—
460Dic3C2×D3×C811yescharacteristic
461Dic3C2×D3×C812yes—
462Dic3C2×D3×C811yescharacteristic
463C32#340711yescharacteristic, complemented, Sylow
464C23—31no—
465C23—92no—
466Q8—31no—
467Q8—92no—
468Q8—91no—
469D4—32no—
470D4—31no—
471D4—92no—
472D4—92no—
473D4—92no—
474D4—92no—
475D4—91no—
476C2×C4—31no—
477C2×C4—31no—
478C2×C4—31no—
479C2×C4—31no—
480C2×C4—31no—
481C2×C4—32no—
482C2×C4—92no—
483C2×C4—92no—
484C2×C4—92no—
485C2×C4—92no—
486C2×C4C4×D3211yescharacteristic
487C8—31no—
488C8—31no—
489C8—32no—
490C8—92no—
491C8C4×D3211yescharacteristic
492C8C22×D3211yescharacteristic
493C2×C3—21no—
494C2×C3—21no—
495C2×C3—21no—
496C2×C3—41no—
497C2×C3—62no—
498C2×C3—61no—
499C2×C3—61no—
500C2×C3C22×D3×C811yescharacteristic
501C2×C3C22×D3×C811yescharacteristic
502D3—21no—
503D3—21no—
504D3—22no—
505D3—62no—
506D3—62no—
507D3—122no—
508C22—31no—
509C22—31no—
510C22—32no—
511C22—92no—
512C22—121no—
513C22—362no—
514C22D32×C811yescharacteristic
515C4—31no—
516C4—31no—
517C4—32no—
518C4—92no—
519C4D32×C811yescharacteristic
520C4C2×C4×D3211yescharacteristic
521C3—21no—
522C3#8200711yescharacteristic, complemented
523C3#8201211yescharacteristic, complemented
524C2—21no—
525C2—61no—
526C2—61no—
527C2—62no—
528C2—182no—
529C2C2×D32×C811yescharacteristic
subgroupG/H
center, FrattiniC8C22×D32
commutator, socleC2×C32C23×C8
FittingC2×C32×C16C22
prime radicalD3×#235C4
cosocleC32×C8C24
hypercenterC2×C16D32
hypocenterC32#3407
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C8 ◁ C2×C16

Complements

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

NH ≅ G/Ntype
2. #10592600C2semidirect
3. C3×#4901C2semidirect
4. C2×C3×#798C2semidirect
5. #10590624C2semidirect
6. #10590621C2semidirect
7. D3×#812C2semidirect
8. #10590229C2semidirect
9. #10590228C2semidirect
10. #10590226C2semidirect
11. D3×#798C2semidirect
25. C2×C32×C16C22semidirect
26. #63639C22semidirect
27. #63625C22semidirect
28. C16×C3⋊D3C22semidirect
29. C3×#812C22semidirect
30. C2×C3×C3⋊C16C22semidirect
33. C3×#798C22semidirect
34. C3×#798C22semidirect
35. C3×#798C22semidirect
36. C3×D3×C16C22semidirect
37. #63544C22semidirect
39. #63543C22semidirect
40. #63542C22semidirect
41. D3×C3⋊C16C22semidirect
42. D3×C3⋊C16C22semidirect
63. #4901D3semidirect
65. C2×#798D3semidirect
134. C2×C3×C16C2×D3semidirect
135. C2×C3×C16C2×D3semidirect
141. #812C2×D3semidirect
144. C2×C3⋊C16C2×D3semidirect
154. #798C2×D3semidirect
155. #798C2×D3semidirect
156. #798C2×D3semidirect
164. D3×C16C2×D3semidirect
324. C2×C16D32semidirect
463. C32#3407semidirect
522. C3#82007semidirect
523. C3#82012semidirect

Maximal subgroups

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

subgroupindex
D3×#9012
#105926002
C3×#49012
C2×C3×#7982
#105906242
#105906212
D3×#8122
#105902292
#105902282
#105902262
D3×#7982
#820123
#820073