Finite Group Databasebeta

← #11787810

Subgroups — #11787810

Order 1152.

775 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594982C211yesmaximal, characteristic
2C2×#63863C211yesmaximal, characteristic
3C2×C3×#823C211yesmaximal, characteristic
4C3×#5120C211yesmaximal, characteristic, complemented
5#10591100C211yesmaximal, characteristic, complemented
6#10589421C211yesmaximal, characteristic, complemented
7#10589160C211yesmaximal, characteristic, complemented
8#70343—31nomaximal
9#70069—31nomaximal
10C22×C3×D12C2211yescharacteristic
11C22×C3×Dic6C2211yescharacteristic
12C2×C32×M16C2211yescharacteristic
13#64135C2211yescharacteristic
14C2×C4×C3⋊Dic3C2211yescharacteristic
15C3×#926C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17D3×#217—22no—
18C2×(C2×D3)⋊Dic3—22no—
19#63898—22no—
20Dic3×D12—22no—
21#63863—22no—
22#63863C414yescomplemented
23C3×#823—22no—
24C3×#816—22no—
25#63566—22no—
26C2×#947—31no—
27#5798—31no—
28C2×#936—31no—
29#5521—31no—
30C3×#419—31no—
31C2×C3×#100—31no—
32#5225—31no—
33C2×#823D311yescharacteristic
34#5120—31no—
35#5120D311yescharacteristic, complemented
36#4555—31no—
37#4555—31no—
38#4555—31no—
39#4555—61no—
40#4532—31no—
41C23×C3×D3D412yes—
42C22×C32×C4C2311yescharacteristic
43C22×C3⋊Dic3—21no—
44C22×C3×Dic3—21no—
45C2×C3×D12—21no—
46C2×C3×D12—21no—
47C2×C3×D12—21no—
48C2×C3×D12—21no—
49C2×C3×D12C2×C412yes—
50C2×C3×D12D412yes—
51C2×C3×Dic6—21no—
52C2×C3×Dic6—21no—
53C2×C3×Dic6—21no—
54C2×C3×Dic6—21no—
55C2×C3×Dic6—21no—
56C2×C3×Dic6C2×C412yescomplemented
57C2×D3×Dic3—24no—
58C32×M16—21no—
59C32×M16—21no—
60C2×C32×C8—21no—
61#3757—21no—
62C4⋊(C3⋊Dic3)D412yes—
63C4×C3⋊Dic3—21no—
64C4×C3⋊Dic3—21no—
65C4×C3⋊Dic3C2×C412yescomplemented
66C3×#217—21no—
67C3×C4⋊Dic3D412yes—
68C3×C4×Dic3—21no—
69C3×#208—21no—
70C3×#208—21no—
71C2×C3×C3⋊C8—21no—
72(C2×D3)⋊Dic3—24no—
73(C2×D3)⋊Dic3—28no—
74#1885—91noSylow
75C22×C3×Q8—31no—
76C22×C3×D4—31no—
77C22×D12C2×D311yescharacteristic
78C22×Dic6C2×D311yescharacteristic
79C2×C3×M16—21no—
80C2×C3×M16—31no—
81C2×C3×M16C2×D311yescharacteristic
82C2×C3×M16C2×D311yescharacteristic
83C3×#117—31no—
84C2×#217—62no—
85C2×#217—62no—
86#947—34no—
87#947—62no—
88#936—34no—
89#936—62no—
90D4×Dic3—62no—
91D4×Dic3—62no—
92C2×(C2×D3)⋊C4—62no—
93#926—31no—
94#926—31no—
95#926—61no—
96#926C2×D311yescharacteristic
97C2×C4×Dic3—31no—
98C2×C4×Dic3—31no—
99C2×C4×Dic3—61no—
100C2×#208C2×D311yescharacteristic
101#893—62no—
102D3×C22⋊C4—62no—
103C4×D12—62no—
104C3×#103—62no—
105C3×#100—62no—
106#835—62no—
107#823—22no—
108#816—22no—
109#816—62no—
110C23×C32C2×D411yescharacteristic
111C22×C3×D3—22no—
112C22×C3×D3—22no—
113C22×C3×D3—44no—
114C22×C3×D3C22⋊C414yes—
115C2×C32×C4C22×C411yescharacteristic
116C2×C32×C4C2×D411yescharacteristic
117C2×C32×C4C2×D411yescharacteristic
118C2×C32×C4C2×D411yescharacteristic
119C2×C32×C4#4111yescharacteristic
120C2×C32×C4#4111yescharacteristic
121C2×C3⋊Dic3—22no—
122C2×C3⋊Dic3—22no—
123C2×C3⋊Dic3—42no—
124C2×C3×Dic3—22no—
125C2×C3×Dic3—22no—
126C2×C3×Dic3—41no—
127C2×C3×Dic3—41no—
128C3×D12—22no—
129C3×D12—22no—
130C3×D12—22no—
131C3×D12—22no—
132C3×Dic6—22no—
133C3×Dic6—22no—
134C3×Dic6—41no—
135C3×Dic6—41no—
136D3×Dic3—84no—
137C32×C8—41no—
138C3×C3⋊C8—41no—
139C2×#124—91no—
140#518—91no—
141#419—31no—
142#419—91no—
143C2×#100—31no—
144#339—91no—
145#339—91no—
146C24×C3—32no—
147C23×D3D1212yes—
148C2×C3×Q8—32no—
149C2×C3×Q8—61no—
150C2×C3×Q8—61no—
151C2×C3×Q8—61no—
152C2×C3×Q8—61no—
153C2×C3×Q8—61no—
154C2×C3×D4—32no—
155C2×C3×D4—32no—
156C2×C3×D4—61no—
157C2×C3×D4—61no—
158C2×C3×D4—61no—
159C2×C3×D4—61no—
160C22×C3×C4—21no—
161C22×C3×C4—61no—
162C22×C3×C4C22×D311yescharacteristic
163C22×C3×C4C22×D311yescharacteristic
164C22×Dic3—21no—
165C22×Dic3—64no—
166C22×Dic3—61no—
167C22×Dic3—61no—
168C22×Dic3—121no—
169C2×D12—21no—
170C2×D12—21no—
171C2×D12—21no—
172C2×D12—21no—
173C2×D12C4×D312yes—
174C2×D12#6712yes—
175C2×C4×D3—64no—
176C2×Dic6—21no—
177C2×Dic6—21no—
178C2×Dic6—21no—
179C2×Dic6—21no—
180C2×Dic6—21no—
181C2×Dic6C4×D312yescomplemented
182C3×M16—22no—
183C3×M16—21no—
184C3×M16—21no—
185C3×M16—21no—
186C3×M16—21no—
187C3×M16—41no—
188C3×M16—61no—
189C3×M16—61no—
190C2×C3×C8—21no—
191C2×C3×C8—21no—
192C2×C3×C8—41no—
193C2×C3×C8—61no—
194C3×C4⋊C4—32no—
195C3×C22⋊C4—61no—
196C3×C42—61no—
197#217—21no—
198#217—68no—
199#217—64no—
200#217—61no—
201#217—61no—
202#217—121no—
203(C2×D3)⋊C4—64no—
204(C2×D3)⋊C4—68no—
205C4⋊Dic3—32no—
206C4⋊Dic3—32no—
207C4⋊Dic3—62no—
208C4⋊Dic3#6712yes—
209C4×Dic3—21no—
210C4×Dic3—32no—
211C4×Dic3—32no—
212C4×Dic3—62no—
213C4×Dic3—61no—
214C4×Dic3—61no—
215C4×Dic3—61no—
216C4×Dic3—61no—
217C4×Dic3—121no—
218C4×Dic3—121no—
219#208—21no—
220#208—21no—
221C2×C3⋊C8—21no—
222C22×C32—22no—
223C22×C32C2×C22⋊C411yescharacteristic
224C22×C32#12011yescharacteristic
225C22×C32#12311yescharacteristic
226C2×C3×D3—24no—
227C2×C3×D3—44no—
228C2×C3×D3—44no—
229C2×C3×D3—82no—
230C32×C4C4×D411yescharacteristic
231C32×C4C4×D411yescharacteristic
232C32×C4#12111yescharacteristic
233C32×C4#12111yescharacteristic
234C3⋊Dic3—42no—
235C3⋊Dic3—42no—
236C3×Dic3—42no—
237C3×Dic3—42no—
238C22×Q8—31no—
239C22×D4—31no—
240C2×M16—31no—
241C2×M16D3211yescharacteristic
242#124—94no—
243#124—182no—
244C4×D4—182no—
245C4×D4—182no—
246#117—31no—
247#117—91no—
248C2×C22⋊C4—182no—
249C2×C22⋊C4—182no—
250C2×C42—91no—
251#103—62no—
252#103—182no—
253#100—62no—
254C23×C3—21no—
255C23×C3—34no—
256C23×C3—62no—
257C23×C3—62no—
258C23×C3—124no—
259C23×C3C2×D1211yescharacteristic
260C23×C3D3×D411yescharacteristic
261C22×D3—22no—
262C22×D3—22no—
263C22×D3—44no—
264C22×D3(C2×D3)⋊C414yes—
265C3×Q8—62no—
266C3×Q8—62no—
267C3×Q8—121no—
268C3×Q8—121no—
269C3×D4—62no—
270C3×D4—62no—
271C3×D4—62no—
272C3×D4—62no—
273C2×C3×C4—21no—
274C2×C3×C4—21no—
275C2×C3×C4—21no—
276C2×C3×C4—21no—
277C2×C3×C4—21no—
278C2×C3×C4—21no—
279C2×C3×C4—62no—
280C2×C3×C4—62no—
281C2×C3×C4—121no—
282C2×C3×C4—121no—
283C2×C3×C4C2×C4×D311yescharacteristic
284C2×C3×C4C2×C4×D311yescharacteristic
285C2×C3×C4#23511yescharacteristic
286C2×C3×C4D3×D411yescharacteristic
287C2×C3×C4D3×D411yescharacteristic
288C2×C3×C4D3×D411yescharacteristic
289C2×C3×C4D3×D411yescharacteristic
290C2×C3×C4#23711yescharacteristic
291C2×C3×C4#23711yescharacteristic
292C2×C3×C4#23711yescharacteristic
293C2×C3×C4C2×#6711yescharacteristic
294C2×C3×C4C2×#6711yescharacteristic
295C2×Dic3—22no—
296C2×Dic3—22no—
297C2×Dic3—41no—
298C2×Dic3—41no—
299C2×Dic3—62no—
300C2×Dic3—62no—
301C2×Dic3—62no—
302C2×Dic3—62no—
303C2×Dic3—122no—
304C2×Dic3—122no—
305C2×Dic3—122no—
306C2×Dic3—122no—
307C2×Dic3—124no—
308C2×Dic3—244no—
309D12—22no—
310D12—22no—
311D12—22no—
312D12—22no—
313C4×D3—244no—
314Dic6—22no—
315Dic6—22no—
316Dic6—41no—
317Dic6—41no—
318C3×C8—42no—
319C3×C8—41no—
320C3×C8—41no—
321C3×C8—121no—
322C3⋊C8—41no—
323C2×C32—21no—
324C2×C32—21no—
325C2×C32#38611yescharacteristic
326C2×C32#45512yes—
327C3×D3—44no—
328C24—32no—
329C2×Q8—32no—
330C2×Q8—61no—
331C2×Q8—61no—
332C2×Q8—61no—
333C2×Q8—61no—
334C2×Q8—61no—
335C2×D4—32no—
336C2×D4—32no—
337C2×D4—61no—
338C2×D4—61no—
339C2×D4—61no—
340C2×D4—61no—
341C22×C4—61no—
342C22×C4—184no—
343C22×C4—181no—
344C22×C4C2×D3211yescharacteristic
345M16—21no—
346M16—21no—
347M16—61no—
348M16—61no—
349C2×C8—21no—
350C2×C8—61no—
351C4⋊C4—32no—
352C4⋊C4—92no—
353C22⋊C4—61no—
354C22⋊C4—188no—
355C22⋊C4—184no—
356C22⋊C4—181no—
357C42—61no—
358C42—92no—
359C42—181no—
360C42—181no—
361C22×C3—22no—
362C22×C3—22no—
363C22×C3—21no—
364C22×C3—21no—
365C22×C3—21no—
366C22×C3—42no—
367C22×C3—64no—
368C22×C3—124no—
369C22×C3—124no—
370C22×C3—242no—
371C22×C3D3×C22⋊C411yescharacteristic
372C22×C3#88211yescharacteristic
373C22×C3#88311yescharacteristic
374C22×C3#88611yescharacteristic
375C22×C3C2×(C2×D3)⋊C411yescharacteristic
376C22×C3#93711yescharacteristic
377C2×D3—24no—
378C2×D3—44no—
379C2×D3—44no—
380C2×D3—82no—
381C3×C4—21no—
382C3×C4—21no—
383C3×C4—21no—
384C3×C4—21no—
385C3×C4—122no—
386C3×C4—122no—
387C3×C4#67⋊C411yescharacteristic
388C3×C4#67⋊C411yescharacteristic
389C3×C4#67⋊C411yescharacteristic
390C3×C4#88411yescharacteristic
391C3×C4C4×#6711yescharacteristic
392C3×C4#93811yescharacteristic
393C3×C4#93911yescharacteristic
394C3×C4#93911yescharacteristic
395Dic3—42no—
396Dic3—42no—
397Dic3—122no—
398Dic3—122no—
399Dic3—124no—
400Dic3—122no—
401Dic3—122no—
402Dic3—242no—
403C32#188511yescharacteristic, complemented, Sylow
404C23—34no—
405C23—62no—
406C23—62no—
407C23—124no—
408C23D3×D1211yescharacteristic
409Q8—62no—
410Q8—62no—
411Q8—121no—
412Q8—121no—
413D4—62no—
414D4—62no—
415D4—62no—
416D4—62no—
417C2×C4—62no—
418C2×C4—62no—
419C2×C4—121no—
420C2×C4—121no—
421C2×C4—182no—
422C2×C4—182no—
423C2×C4—362no—
424C2×C4—724no—
425C2×C4#379511yescharacteristic
426C2×C4C4×D3211yescharacteristic
427C2×C4#380211yescharacteristic
428C2×C4#380511yescharacteristic
429C2×C4D3×#6711yescharacteristic
430C2×C4D3×#6711yescharacteristic
431C8—41no—
432C8—121no—
433C2×C3—21no—
434C2×C3—21no—
435C2×C3—21no—
436C2×C3—21no—
437C2×C3—22no—
438C2×C3—21no—
439C2×C3—41no—
440C2×C3—41no—
441C2×C3—124no—
442C2×C3#474612yes—
443C2×C3#495611yescharacteristic
444C2×C3#495811yescharacteristic
445C2×C3#520212yes—
446D3—44no—
447C22—22no—
448C22—64no—
449C22—124no—
450C22—124no—
451C22—242no—
452C22#6389111yescharacteristic
453C22D3×(C2×D3)⋊C411yescharacteristic
454C22#6392211yescharacteristic
455C4—122no—
456C4—122no—
457C4—362no—
458C4—362no—
459C4#6387911yescharacteristic
460C4#6388511yescharacteristic
461C4#6390211yescharacteristic
462C4#6397011yescharacteristic
463C3—21no—
464C3#7006911yescharacteristic, complemented
465C3#7034311yescharacteristic, complemented
466C2—21no—
467C2—21no—
468C2—124no—
469C2#1059101212yes—
470C2#1059136311yescharacteristic
subgroupG/H
centerC22#63922
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32#120
prime radicalC22×C3×D12C22
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1885
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
4. C3×#5120C2semidirect
5. #10591100C2semidirect
6. #10589421C2semidirect
7. #10589160C2semidirect
22. #63863C4semidirect
35. #5120D3semidirect
56. C2×C3×Dic6C2×C4semidirect
65. C4×C3⋊Dic3C2×C4semidirect
181. C2×Dic6C4×D3semidirect
403. C32#1885semidirect
464. C3#70069semidirect
465. C3#70343semidirect

Maximal subgroups

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

subgroupindex
#105949822
C2×#638632
C2×C3×#8232
C3×#51202
#105911002
#105894212
#105891602
#703433
#700693