Finite Group Databasebeta

← #11787817

Subgroups — #11787817

Order 1152.

795 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#947C211yesmaximal, characteristic
2#10594982C211yesmaximal, characteristic
3#10592924C211yesmaximal, characteristic, complemented
4C3×#5225C211yesmaximal, characteristic, complemented
5C2×#63558C211yesmaximal, characteristic
6#10589162C211yesmaximal, characteristic, complemented
7#10589161C211yesmaximal, characteristic, complemented
8#71723—31nomaximal
9#70343—31nomaximal
10C22×C32×Q8C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
12#64135C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C3×#947—22no—
15C3×#947C414yescomplemented
16C2×C3×(C2×D3)⋊C4—22no—
17C3×#926C2211yescharacteristic
18C2×C3×C4×Dic3C2211yescharacteristic
19C2×C3×#208C2211yescharacteristic
20D3×#217—22no—
21#63898—22no—
22Dic3×D12—22no—
23#63662—22no—
24C3×#835—22no—
25#63558—22no—
26C2×C3×#124—31no—
27C2×#947D311yescharacteristic
28#5798—31no—
29#5521—31no—
30C3×#419—31no—
31#5225—31no—
32#5225—31no—
33#5225—61no—
34#5225D311yescharacteristic, complemented
35C2×#833—31no—
36C2×#823—31no—
37#4555—31no—
38#4532—31no—
39#4523—31no—
40#4523—31no—
41C23×C3×D3D412yes—
42C2×C32×Q8—21no—
43C2×C32×Q8—21no—
44C2×C32×Q8—21no—
45C2×C32×Q8—21no—
46C2×C32×Q8—21no—
47C2×C32×Q8C2×C412yescomplemented
48C22×C32×C4—21no—
49C22×C32×C4C2311yescharacteristic
50C22×C3×Dic3—21no—
51C2×C3×D12—21no—
52C2×C3×D12—21no—
53C2×C3×D12—21no—
54C2×C3×D12—21no—
55C2×C3×D12C2×C412yes—
56C2×C3×D12D412yes—
57C2×D3×Dic3—24no—
58#3757—21no—
59C4⋊(C3⋊Dic3)D412yes—
60C4×C3⋊Dic3—21no—
61#3748—21no—
62#3748—21no—
63C2×C3⋊(C3⋊C8)—21no—
64C3×#217—21no—
65C3×(C2×D3)⋊C4—28no—
66C3×C4⋊Dic3D412yes—
67C3×C4×Dic3—21no—
68C3×C4×Dic3—21no—
69C3×C4×Dic3C2×C412yescomplemented
70C3×#208—21no—
71C3×#208—21no—
72C2×C3×C3⋊C8—21no—
73(C2×D3)⋊Dic3—24no—
74#1885—91noSylow
75C22×C3×Q8—21no—
76C22×C3×Q8C2×D311yescharacteristic
77C22×C3×Q8C2×D311yescharacteristic
78C22×C3×D4—31no—
79C22×D12C2×D311yescharacteristic
80C2×C3×M16—31no—
81C3×#124—34no—
82C3×#124—62no—
83C3×#117—31no—
84C2×C3×C22⋊C4—62no—
85C2×C3×C42—31no—
86C2×#217—62no—
87#947—22no—
88#947Dic314yescomplemented
89D4×Dic3—62no—
90D4×Dic3—62no—
91C2×(C2×D3)⋊C4—22no—
92#926—31no—
93#926—31no—
94#926—61no—
95#926C2×D311yescharacteristic
96C2×C4×Dic3C2×D311yescharacteristic
97C2×#208—31no—
98C2×#208—31no—
99C2×#208—61no—
100C2×#208C2×D311yescharacteristic
101#893—62no—
102D3×C22⋊C4—62no—
103C4×D12—62no—
104C3×#103—62no—
105#835—22no—
106#835—62no—
107#835—62no—
108#835—64no—
109#833—62no—
110#823—62no—
111C23×C32C2×D411yescharacteristic
112C22×C3×D3—22no—
113C22×C3×D3—22no—
114C22×C3×D3—44no—
115C22×C3×D3C22⋊C414yes—
116C32×Q8—22no—
117C32×Q8—22no—
118C32×Q8—41no—
119C32×Q8—41no—
120C2×C32×C4—22no—
121C2×C32×C4—41no—
122C2×C32×C4—41no—
123C2×C32×C4C22×C411yescharacteristic
124C2×C32×C4C2×D411yescharacteristic
125C2×C32×C4C2×D411yescharacteristic
126C2×C32×C4C2×D411yescharacteristic
127C2×C32×C4#4111yescharacteristic
128C2×C32×C4#4111yescharacteristic
129C2×C3⋊Dic3—22no—
130C2×C3×Dic3—22no—
131C2×C3×Dic3—22no—
132C2×C3×Dic3—42no—
133C3×D12—22no—
134C3×D12—22no—
135C3×D12—22no—
136C3×D12—22no—
137D3×Dic3—84no—
138C3⋊(C3⋊C8)—41no—
139C3×C3⋊C8—41no—
140C2×#124—31no—
141#518—91no—
142#419—31no—
143#419—91no—
144C2×#100—91no—
145#339—91no—
146#339—91no—
147C24×C3—32no—
148C23×D3#6712yes—
149C2×C3×Q8—21no—
150C2×C3×Q8—21no—
151C2×C3×Q8—22no—
152C2×C3×Q8—22no—
153C2×C3×Q8—21no—
154C2×C3×Q8—21no—
155C2×C3×Q8—21no—
156C2×C3×Q8—21no—
157C2×C3×Q8—21no—
158C2×C3×Q8—21no—
159C2×C3×Q8—21no—
160C2×C3×Q8—21no—
161C2×C3×Q8—22no—
162C2×C3×Q8—41no—
163C2×C3×Q8—41no—
164C2×C3×Q8—41no—
165C2×C3×Q8C4×D312yescomplemented
166C2×C3×Q8C2×Dic312yescomplemented
167C2×C3×D4—32no—
168C2×C3×D4—32no—
169C2×C3×D4—61no—
170C2×C3×D4—61no—
171C2×C3×D4—61no—
172C2×C3×D4—61no—
173C22×C3×C4—21no—
174C22×C3×C4—21no—
175C22×C3×C4—21no—
176C22×C3×C4—41no—
177C22×C3×C4—61no—
178C22×C3×C4C22×D311yescharacteristic
179C22×C3×C4C22×D311yescharacteristic
180C22×Dic3—21no—
181C22×Dic3—64no—
182C2×D12—21no—
183C2×D12—21no—
184C2×D12—21no—
185C2×D12—21no—
186C2×D12C2×Dic312yes—
187C2×D12#6712yes—
188C2×C4×D3—64no—
189C3×M16—61no—
190C3×M16—61no—
191C2×C3×C8—61no—
192C3×C4⋊C4—32no—
193C3×C22⋊C4—68no—
194C3×C22⋊C4—61no—
195C3×C42—32no—
196C3×C42—61no—
197C3×C42—61no—
198#217—21no—
199#217—64no—
200#217—61no—
201#217—61no—
202#217—121no—
203(C2×D3)⋊C4—28no—
204(C2×D3)⋊C4—64no—
205C4⋊Dic3—32no—
206C4⋊Dic3—32no—
207C4⋊Dic3—62no—
208C4⋊Dic3#6712yes—
209C4×Dic3—21no—
210C4×Dic3—21no—
211C4×Dic3—61no—
212C4×Dic3—61no—
213C4×Dic3—121no—
214C4×Dic3C2×Dic312yescomplemented
215#208—21no—
216#208—21no—
217#208—61no—
218#208—61no—
219#208—61no—
220#208—61no—
221#208—121no—
222#208—121no—
223C2×C3⋊C8—21no—
224C2×C3⋊C8—62no—
225C2×C3⋊C8—61no—
226C2×C3⋊C8—61no—
227C22×C32—22no—
228C22×C32C2×C22⋊C411yescharacteristic
229C22×C32#12011yescharacteristic
230C22×C32#12311yescharacteristic
231C2×C3×D3—24no—
232C2×C3×D3—44no—
233C2×C3×D3—44no—
234C2×C3×D3—82no—
235C32×C4—42no—
236C32×C4C4×D411yescharacteristic
237C32×C4C4×D411yescharacteristic
238C32×C4#12111yescharacteristic
239C32×C4#12111yescharacteristic
240C3⋊Dic3—42no—
241C3×Dic3—42no—
242C3×Dic3—42no—
243C22×Q8D3211yescharacteristic
244C22×D4—31no—
245C2×M16—31no—
246C2×M16—91no—
247#124—34no—
248#124—62no—
249C4×D4—182no—
250C4×D4—182no—
251#117—31no—
252#117—91no—
253C2×C22⋊C4—62no—
254C2×C22⋊C4—182no—
255C2×C42—31no—
256#103—62no—
257#103—182no—
258#100—182no—
259C23×C3—21no—
260C23×C3—34no—
261C23×C3—62no—
262C23×C3—62no—
263C23×C3—124no—
264C23×C3D3×D411yescharacteristic
265C23×C3C2×#6711yescharacteristic
266C22×D3—22no—
267C22×D3—22no—
268C22×D3—44no—
269C22×D3#21714yes—
270C3×Q8—24no—
271C3×Q8—22no—
272C3×Q8—22no—
273C3×Q8—22no—
274C3×Q8—22no—
275C3×Q8—42no—
276C3×Q8—42no—
277C3×Q8—42no—
278C3×Q8—41no—
279C3×Q8—41no—
280C3×Q8—41no—
281C3×Q8—41no—
282C3×D4—62no—
283C3×D4—62no—
284C3×D4—62no—
285C3×D4—62no—
286C2×C3×C4—22no—
287C2×C3×C4—22no—
288C2×C3×C4—21no—
289C2×C3×C4—21no—
290C2×C3×C4—21no—
291C2×C3×C4—21no—
292C2×C3×C4—21no—
293C2×C3×C4—21no—
294C2×C3×C4—42no—
295C2×C3×C4—42no—
296C2×C3×C4—42no—
297C2×C3×C4—41no—
298C2×C3×C4—41no—
299C2×C3×C4—41no—
300C2×C3×C4—41no—
301C2×C3×C4—62no—
302C2×C3×C4—62no—
303C2×C3×C4—122no—
304C2×C3×C4C2×C4×D311yescharacteristic
305C2×C3×C4#23511yescharacteristic
306C2×C3×C4D3×D411yescharacteristic
307C2×C3×C4D3×D411yescharacteristic
308C2×C3×C4D3×D411yescharacteristic
309C2×C3×C4D3×D411yescharacteristic
310C2×C3×C4#23711yescharacteristic
311C2×C3×C4#23711yescharacteristic
312C2×C3×C4#23711yescharacteristic
313C2×C3×C4C22×Dic311yescharacteristic
314C2×C3×C4C2×#6711yescharacteristic
315C2×C3×C4C2×#6711yescharacteristic
316C2×Dic3—22no—
317C2×Dic3—22no—
318C2×Dic3—42no—
319C2×Dic3—62no—
320C2×Dic3—62no—
321C2×Dic3—122no—
322C2×Dic3—244no—
323D12—22no—
324D12—22no—
325D12—22no—
326D12—22no—
327C4×D3—244no—
328C3×C8—121no—
329C3⋊C8—41no—
330C3⋊C8—122no—
331C3⋊C8—121no—
332C3⋊C8—121no—
333C2×C32—21no—
334C2×C32—21no—
335C2×C32#38611yescharacteristic
336C2×C32#45512yes—
337C3×D3—44no—
338C24—32no—
339C2×Q8—21no—
340C2×Q8—21no—
341C2×Q8—21no—
342C2×Q8—21no—
343C2×Q8—21no—
344C2×Q8D3×Dic312yescomplemented
345C2×D4—32no—
346C2×D4—32no—
347C2×D4—61no—
348C2×D4—61no—
349C2×D4—61no—
350C2×D4—61no—
351C22×C4—21no—
352C22×C4—61no—
353C22×C4—184no—
354C22×C4C2×D3211yescharacteristic
355M16—61no—
356M16—61no—
357M16—181no—
358M16—181no—
359C2×C8—61no—
360C2×C8—181no—
361C4⋊C4—32no—
362C4⋊C4—92no—
363C22⋊C4—68no—
364C22⋊C4—61no—
365C22⋊C4—184no—
366C22⋊C4—181no—
367C42—32no—
368C42—61no—
369C42—61no—
370C42—181no—
371C22×C3—22no—
372C22×C3—22no—
373C22×C3—21no—
374C22×C3—21no—
375C22×C3—21no—
376C22×C3—42no—
377C22×C3—64no—
378C22×C3—124no—
379C22×C3—124no—
380C22×C3—242no—
381C22×C3D3×C22⋊C411yescharacteristic
382C22×C3#88311yescharacteristic
383C22×C3#93511yescharacteristic
384C22×C3#93711yescharacteristic
385C22×C3#93711yescharacteristic
386C22×C3C2×#21711yescharacteristic
387C2×D3—24no—
388C2×D3—44no—
389C2×D3—44no—
390C2×D3—82no—
391C3×C4—21no—
392C3×C4—21no—
393C3×C4—21no—
394C3×C4—21no—
395C3×C4—44no—
396C3×C4—42no—
397C3×C4—42no—
398C3×C4—122no—
399C3×C4—122no—
400C3×C4#67⋊C411yescharacteristic
401C3×C4#88411yescharacteristic
402C3×C4C4×#6711yescharacteristic
403C3×C4D4×Dic311yescharacteristic
404C3×C4D4×Dic311yescharacteristic
405C3×C4#93811yescharacteristic
406C3×C4#93911yescharacteristic
407C3×C4#93911yescharacteristic
408Dic3—42no—
409Dic3—42no—
410Dic3—122no—
411Dic3—122no—
412Dic3—242no—
413C32#188511yescharacteristic, complemented, Sylow
414C23—34no—
415C23—62no—
416C23—62no—
417C23—124no—
418C23D3×#6711yescharacteristic
419Q8—22no—
420Q8—22no—
421Q8—41no—
422Q8—41no—
423D4—62no—
424D4—62no—
425D4—62no—
426D4—62no—
427C2×C4—22no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—62no—
431C2×C4—62no—
432C2×C4—122no—
433C2×C4—182no—
434C2×C4—724no—
435C2×C4C2×D3×Dic311yescharacteristic
436C2×C4#380411yescharacteristic
437C2×C4#380511yescharacteristic
438C2×C4D3×#6711yescharacteristic
439C2×C4D3×#6711yescharacteristic
440C2×C4#381111yescharacteristic
441C8—121no—
442C8—361no—
443C2×C3—21no—
444C2×C3—21no—
445C2×C3—21no—
446C2×C3—21no—
447C2×C3—22no—
448C2×C3—21no—
449C2×C3—41no—
450C2×C3—41no—
451C2×C3—124no—
452C2×C3#495611yescharacteristic
453C2×C3#506112yes—
454C2×C3#520212yes—
455C2×C3#522011yescharacteristic
456D3—44no—
457C22—22no—
458C22—64no—
459C22—124no—
460C22—124no—
461C22—242no—
462C22D3×#21711yescharacteristic
463C22#6396911yescharacteristic
464C22#6398311yescharacteristic
465C4—42no—
466C4—122no—
467C4—122no—
468C4—362no—
469C4#6397011yescharacteristic
470C4#6397111yescharacteristic
471C4Dic3×#6711yescharacteristic
472C4#67⋊Dic311yescharacteristic
473C3—21no—
474C3#7034311yescharacteristic, complemented
475C3#7172311yescharacteristic, complemented
476C2—21no—
477C2—21no—
478C2—124no—
479C2#1059165912yes—
480C2#1059172111yescharacteristic
subgroupG/H
centerC22#63983
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC22×C32×Q8C22
socleC22×C32#120
prime radicalC22×C3×D12C22
cosocleC22×C32×C4C23
hypercenterC22×Q8D32
hypocenterC32#1885
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
3. #10592924C2semidirect
4. C3×#5225C2semidirect
6. #10589162C2semidirect
7. #10589161C2semidirect
15. C3×#947C4semidirect
34. #5225D3semidirect
47. C2×C32×Q8C2×C4semidirect
69. C3×C4×Dic3C2×C4semidirect
88. #947Dic3semidirect
165. C2×C3×Q8C4×D3semidirect
166. C2×C3×Q8C2×Dic3semidirect
214. C4×Dic3C2×Dic3semidirect
344. C2×Q8D3×Dic3semidirect
413. C32#1885semidirect
474. C3#70343semidirect
475. C3#71723semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9472
#105949822
#105929242
C3×#52252
C2×#635582
#105891622
#105891612
#717233
#703433