Finite Group Databasebeta

← #11860763

Subgroups — #11860763

Order 1152.

1133 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
1C22×#3755C211yesmaximal, characteristic
2C3×#5812C211yesmaximal, characteristic, complemented
3#10594996C211yesmaximal, characteristic
4C3×#5225C211yesmaximal, characteristic, complemented
5#10591540C214yesmaximal, complemented
6#10591536C214yesmaximal, complemented
7#10591138C211yesmaximal, characteristic, complemented
8#10591096C211yesmaximal, characteristic
9#10591057C211yesmaximal, characteristic, complemented
10#82548—31nomaximal
11#78947—31nomaximal
12C22×C32×Q8C2211yescharacteristic
13C22×C4⋊(C3⋊D3)C2211yescharacteristic
14C2×#3755C418yescomplemented
15C2×#3755C2212yes—
16C2×#3755C2212yes—
17C22×C3⋊(C3⋊C8)C2211yescharacteristic
18C3×Q8×Dic3—22no—
19C3×Q8×Dic3C2214yescomplemented
20C3×#926—22no—
21C3×#926C2211yescharacteristic
22C3×#926C2211yescharacteristic
23C3×#926C2211yescharacteristic
24C2×C3×#208C2211yescharacteristic
25#63974—22no—
26#63894—22no—
27#63894C2214yes—
28C3×#835C2214yescomplemented
29#63576C2212yescomplemented
30#63574C2212yescomplemented
31#63564C2214yes—
32#63554C2212yescomplemented
33Dic3×C3⋊C8C2212yescomplemented
34C3×#519—31no—
35#5812D311yescharacteristic, complemented
36C22×#215—31no—
37C22×#215—31no—
38C22×#215—61no—
39#5521—31no—
40#5521—31no—
41C3×#419—31no—
42#5225D311yescharacteristic, complemented
43#5131—31no—
44#5122—31no—
45#5026—34no—
46C4×#215—34no—
47#5001—31no—
48#4998—31no—
49#4998—31no—
50#4997—31no—
51#4817—34no—
52#4788—34no—
53C23×C3⋊D3—21no—
54C2×C32×Q8—21no—
55C2×C32×Q8—22no—
56C2×C32×Q8C2×C414yescomplemented
57C2×C32×Q8C2312yes—
58C22×C32×C4—21no—
59C22×C32×C4C2311yescharacteristic
60C2×C4⋊(C3⋊D3)—21no—
61C2×C4⋊(C3⋊D3)—22no—
62C2×C4⋊(C3⋊D3)C2×C414yes—
63C2×C4⋊(C3⋊D3)C2312yes—
64C2×#624—24no—
65#3755C2×C418yescomplemented
66#3755C2×C418yescomplemented
67C2×C3⋊(C3⋊C8)C2×C414yescomplemented
68C2×C3⋊(C3⋊C8)C2311yescharacteristic
69C2×C3⋊(C3⋊C8)C2311yescharacteristic
70C3×#217—21no—
71C3×#217—21no—
72C3×#217D412yes—
73C3×C4⋊Dic3—24no—
74C3×C4⋊Dic3D412yes—
75C3×C4⋊Dic3C2312yes—
76C3×C4⋊Dic3C2312yes—
77C3×C4×Dic3—21no—
78C3×C4×Dic3—21no—
79C3×C4×Dic3—24no—
80C3×C4×Dic3C2312yes—
81C3×#208—22no—
82C2×C3×C3⋊C8C2312yes—
83#3722—24no—
84#2949—91noSylow
85C22×C3×Q8—21no—
86C22×C3×Q8C2×D311yescharacteristic
87C22×C3×Q8C2×D311yescharacteristic
88C22×D12—31no—
89C22×D12—31no—
90C22×D12—61no—
91C2×C3×M16—31no—
92C3×C4×Q8—34no—
93C3×C4×Q8—62no—
94C3×#117—31no—
95C3×#117—31no—
96C3×#117—31no—
97C3×#117—62no—
98Q8×Dic3—22no—
99Q8×Dic3C2×D314yescomplemented
100C2×#215—38no—
101C2×#215—38no—
102C2×#215—32no—
103C2×#215—32no—
104C2×#215—32no—
105C2×#215—32no—
106C2×#215—68no—
107C2×#215—62no—
108C2×#215—62no—
109#926—22no—
110#926C2×D311yescharacteristic
111#926C2×D311yescharacteristic
112#926C2×D311yescharacteristic
113C2×#208C2×D311yescharacteristic
114C22×C3⋊C8—31no—
115C22×C3⋊C8—31no—
116C22×C3⋊C8—61no—
117#893—34no—
118#893—62no—
119D3×C22⋊C4—62no—
120D3×C22⋊C4—62no—
121C4×D12—34no—
122C4×D12—62no—
123C3×#103—34no—
124#835C2×D314yescomplemented
125#821—34no—
126#815—32no—
127C8×Dic3—32no—
128#809—34no—
129#808—32no—
130#808—32no—
131#807—32no—
132#807—32no—
133#803—32no—
134C4×C3⋊C8—32no—
135C23×C32C2×D411yescharacteristic
136C22×C3⋊D3—22no—
137C22×C3⋊D3—24no—
138C22×C3⋊D3—82no—
139C32×Q8—24no—
140C32×Q8—22no—
141C32×Q8C22×C414yes—
142C2×C32×C4—24no—
143C2×C32×C4—22no—
144C2×C32×C4C22×C412yes—
145C2×C32×C4C2×D411yescharacteristic
146C2×C32×C4#4112yes—
147C2×C32×C4C2411yescharacteristic
148C4⋊(C3⋊D3)—24no—
149C4⋊(C3⋊D3)—22no—
150C4⋊(C3⋊D3)C22×C414yes—
151C2×C3×Dic3—22no—
152C2×C3×Dic3—22no—
153C2×C3×Dic3C2×D414yes—
154#624—84no—
155C3⋊(C3⋊C8)C22×C412yes—
156C3⋊(C3⋊C8)C22×C412yes—
157C3×C3⋊C8—22no—
158C22×SD16—91no—
159#519—31no—
160#518—91no—
161#440—94no—
162C4×SD16—94no—
163#427—91no—
164#419—31no—
165#418—91no—
166#405—91no—
167C23×D3—61no—
168C23×D3—61no—
169C23×D3—121no—
170C2×C3×Q8—22no—
171C2×C3×Q8—21no—
172C2×C3×Q8—22no—
173C2×C3×Q8—21no—
174C2×C3×Q8—24no—
175C2×C3×Q8—22no—
176C2×C3×Q8—42no—
177C2×C3×Q8—41no—
178C2×C3×Q8C4×D314yescomplemented
179C2×C3×Q8C4×D314yescomplemented
180C2×C3×Q8C22×D312yes—
181C2×C3×Q8C22×D312yes—
182C22×C3×C4—21no—
183C22×C3×C4—21no—
184C22×C3×C4—21no—
185C22×C3×C4—41no—
186C22×C3×C4C22×D311yescharacteristic
187C22×C3×C4C22×D311yescharacteristic
188C2×D12—34no—
189C2×D12—34no—
190C2×D12—32no—
191C2×D12—32no—
192C2×D12—64no—
193C2×D12—62no—
194C2×D12—62no—
195C2×D12—61no—
196C2×D12—62no—
197C2×D12—61no—
198C2×D12—122no—
199C2×D12—121no—
200C2×C4×D3—64no—
201C2×C4×D3—64no—
202C3×M16—62no—
203C2×C3×C8—32no—
204C3×C4⋊C4—32no—
205C3×C4⋊C4—32no—
206C3×C4⋊C4—32no—
207C3×C4⋊C4—64no—
208C3×C22⋊C4—32no—
209C3×C22⋊C4—61no—
210C3×C22⋊C4—61no—
211C3×C42—32no—
212C3×C42—64no—
213C3×C42—61no—
214C3×C42—61no—
215#217—21no—
216#217—21no—
217#217#6712yes—
218#215—38no—
219#215—38no—
220#215—38no—
221#215—38no—
222#215—68no—
223#215—68no—
224(C2×D3)⋊C4—64no—
225(C2×D3)⋊C4—64no—
226C4⋊Dic3—24no—
227C4⋊Dic3#6712yes—
228C4⋊Dic3C22×D312yes—
229C4⋊Dic3C22×D312yes—
230C4×Dic3—21no—
231C4×Dic3—21no—
232C4×Dic3—24no—
233C4×Dic3C22×D312yes—
234#208—22no—
235C2×C3⋊C8—34no—
236C2×C3⋊C8—34no—
237C2×C3⋊C8—31no—
238C2×C3⋊C8—31no—
239C2×C3⋊C8—31no—
240C2×C3⋊C8—31no—
241C2×C3⋊C8—64no—
242C2×C3⋊C8—61no—
243C2×C3⋊C8—61no—
244C2×C3⋊C8C22×D312yes—
245C22×C32—22no—
246C22×C32C4×D412yes—
247C22×C32C22×D411yescharacteristic
248C2×C3⋊D3—24no—
249C2×C3⋊D3—44no—
250C2×C3⋊D3—84no—
251C32×C4—24no—
252C32×C4C4×D412yes—
253C32×C4C23×C411yescharacteristic
254C32×C4C2×#4111yescharacteristic
255C3×Dic3—24no—
256C3×Dic3—42no—
257C3×Dic3—42no—
258C22×Q8D3211yescharacteristic
259C22×D4—91no—
260C2×SD16—98no—
261C2×SD16—92no—
262C2×SD16—92no—
263C2×M16—31no—
264C22×C8—91no—
265C4×Q8—34no—
266C4×Q8—62no—
267C4×D4—94no—
268C4×D4—182no—
269#117—31no—
270#117—31no—
271#117—31no—
272#117—62no—
273C2×C22⋊C4—182no—
274#107—92no—
275#106—92no—
276#103—34no—
277#102—94no—
278#97—92no—
279C4×C8—92no—
280C23×C3—21no—
281C23×C3D3×D411yescharacteristic
282C23×C3C2×#6711yescharacteristic
283C22×D3—62no—
284C22×D3—62no—
285C22×D3—64no—
286C22×D3—64no—
287C22×D3—122no—
288C22×D3—124no—
289C22×D3—242no—
290C22×D3—242no—
291C22×D3—244no—
292C3×Q8—24no—
293C3×Q8—24no—
294C3×Q8—22no—
295C3×Q8—22no—
296C3×Q8—24no—
297C3×Q8—42no—
298C3×Q8—44no—
299C3×Q8C2×C4×D314yes—
300C3×Q8C2×C4×D314yes—
301C2×C3×C4—24no—
302C2×C3×C4—24no—
303C2×C3×C4—22no—
304C2×C3×C4—22no—
305C2×C3×C4—21no—
306C2×C3×C4—22no—
307C2×C3×C4—22no—
308C2×C3×C4—21no—
309C2×C3×C4—34no—
310C2×C3×C4—42no—
311C2×C3×C4—44no—
312C2×C3×C4—62no—
313C2×C3×C4—62no—
314C2×C3×C4C2×C4×D312yes—
315C2×C3×C4C2×C4×D312yes—
316C2×C3×C4#23512yes—
317C2×C3×C4D3×D411yescharacteristic
318C2×C3×C4#23712yes—
319C2×C3×C4C2×#6711yescharacteristic
320C2×C3×C4C23×D311yescharacteristic
321C2×C3×C4C23×D311yescharacteristic
322C2×Dic3—22no—
323C2×Dic3—22no—
324C2×Dic3C2×#6714yes—
325D12—34no—
326D12—34no—
327D12—64no—
328D12—64no—
329D12—64no—
330D12—62no—
331D12—62no—
332D12—122no—
333D12—124no—
334C4×D3—244no—
335C4×D3—244no—
336C3×C8—62no—
337C3⋊C8—22no—
338C3⋊C8—32no—
339C3⋊C8—32no—
340C3⋊C8—32no—
341C3⋊C8—32no—
342C3⋊C8—62no—
343C3⋊C8—62no—
344C2×C32—22no—
345C2×C32C2×C4×D411yescharacteristic
346C2×C32#57712yes—
347C3⋊D3—44no—
348C24—181no—
349C2×Q8—22no—
350C2×Q8—21no—
351C2×Q8#62414yescomplemented
352C2×Q8C2×D3212yes—
353C2×D4—92no—
354C2×D4—94no—
355C2×D4—182no—
356C2×D4—181no—
357C22×C4—21no—
358C22×C4—184no—
359C22×C4C2×D3211yescharacteristic
360SD16—98no—
361SD16—98no—
362M16—62no—
363C2×C8—32no—
364C2×C8—91no—
365C2×C8—91no—
366C2×C8—94no—
367C4⋊C4—32no—
368C4⋊C4—32no—
369C4⋊C4—32no—
370C4⋊C4—64no—
371C22⋊C4—32no—
372C22⋊C4—61no—
373C22⋊C4—61no—
374C22⋊C4—184no—
375C42—32no—
376C42—64no—
377C42—61no—
378C42—61no—
379C22×C3—24no—
380C22×C3—22no—
381C22×C3—22no—
382C22×C3—21no—
383C22×C3—22no—
384C22×C3#67⋊C412yes—
385C22×C3C4×#6712yes—
386C22×C3C2×D3×D411yescharacteristic
387C22×C3C22×#6711yescharacteristic
388C2×D3—64no—
389C2×D3—64no—
390C2×D3—124no—
391C2×D3—124no—
392C2×D3—124no—
393C2×D3—244no—
394C2×D3—244no—
395C2×D3—244no—
396C2×D3—248no—
397C3×C4—24no—
398C3×C4—24no—
399C3×C4—21no—
400C3×C4—21no—
401C3×C4—22no—
402C3×C4—44no—
403C3×C4—64no—
404C3×C4—122no—
405C3×C4—122no—
406C3×C4#67⋊C412yes—
407C3×C4C4×#6712yes—
408C3×C4C22×C4×D311yescharacteristic
409C3×C4C22×C4×D311yescharacteristic
410C3×C4C2×#23511yescharacteristic
411C3×C4C2×#23711yescharacteristic
412Dic3—24no—
413Dic3—42no—
414Dic3—42no—
415C32#294911yescharacteristic, complemented, Sylow
416C23—182no—
417C23—184no—
418C23—722no—
419C23D3×#6711yescharacteristic
420Q8—22no—
421Q8—24no—
422Q8C2×#62414yes—
423D4—94no—
424D4—182no—
425D4—184no—
426C2×C4—22no—
427C2×C4—24no—
428C2×C4—34no—
429C2×C4—62no—
430C2×C4—62no—
431C2×C4—724no—
432C2×C4#380412yes—
433C2×C4C2×#62412yes—
434C2×C4D3×#6711yescharacteristic
435C2×C4C22×D3211yescharacteristic
436C8—62no—
437C8—92no—
438C8—92no—
439C2×C3—24no—
440C2×C3—22no—
441C2×C3—22no—
442C2×C3—21no—
443C2×C3—22no—
444C2×C3C2×#67⋊C411yescharacteristic
445C2×C3#577812yes—
446C2×C3C2×C4×#6711yescharacteristic
447C2×C3#583712yes—
448D3—124no—
449D3—124no—
450D3—244no—
451C22—22no—
452C22—184no—
453C22—364no—
454C22—724no—
455C22#6395212yes—
456C22C2×D3×#6711yescharacteristic
457C4—24no—
458C4—64no—
459C4—122no—
460C4—122no—
461C4#6395212yes—
462C4C2×#380411yescharacteristic
463C4C22×#62411yescharacteristic
464C3—21no—
465C3#7894711yescharacteristic, complemented
466C3#8254811yescharacteristic, complemented
467C2—22no—
468C2—364no—
469C2#1059531912yes—
470C2C2×#6395211yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC22×C32C22×D4
prime radicalC22×C4⋊(C3⋊D3)C22
cosocleC2×C32×C4C24
hypercenterC22×Q8D32
hypocenterC32#2949
LCSG ▷ 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
2. C3×#5812C2semidirect
4. C3×#5225C2semidirect
5. #10591540C2semidirect
6. #10591536C2semidirect
7. #10591138C2semidirect
9. #10591057C2semidirect
14. C2×#3755C4semidirect
19. C3×Q8×Dic3C22semidirect
28. C3×#835C22semidirect
29. #63576C22semidirect
30. #63574C22semidirect
32. #63554C22semidirect
33. Dic3×C3⋊C8C22semidirect
35. #5812D3semidirect
42. #5225D3semidirect
56. C2×C32×Q8C2×C4semidirect
65. #3755C2×C4semidirect
66. #3755C2×C4semidirect
67. C2×C3⋊(C3⋊C8)C2×C4semidirect
99. Q8×Dic3C2×D3semidirect
124. #835C2×D3semidirect
178. C2×C3×Q8C4×D3semidirect
179. C2×C3×Q8C4×D3semidirect
351. C2×Q8#624semidirect
415. C32#2949semidirect
465. C3#78947semidirect
466. C3#82548semidirect

Maximal subgroups

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

subgroupindex
C22×#37552
C3×#58122
#105949962
C3×#52252
#105915402
#105915362
#105911382
#105910962
#105910572
#825483
#789473