Finite Group Databasebeta

← #11860761

Subgroups — #11860761

Order 1152.

1059 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5812C211yesmaximal, characteristic, complemented
2C22×C3×#215C211yesmaximal, characteristic
3#10594982C211yesmaximal, characteristic
4#10592924C211yesmaximal, characteristic, complemented
5#10591566C214yesmaximal, complemented
6Dic3×#215C214yesmaximal, complemented
7#10591122C211yesmaximal, characteristic, complemented
8#10591085C211yesmaximal, characteristic
9#10591055C211yesmaximal, characteristic, complemented
10#83843—31nomaximal
11#82548—31nomaximal
12C22×C32×Q8C2211yescharacteristic
13C22×C3×D12C2211yescharacteristic
14#64135C2211yescharacteristic
15C2×#3748C2211yescharacteristic
16C3×Q8×Dic3—22no—
17C3×Q8×Dic3C2214yescomplemented
18C2×C3×#215C418yescomplemented
19C2×C3×#215C2212yes—
20C2×C3×#215C2212yes—
21C3×#926—22no—
22C3×#926C2211yescharacteristic
23C3×#926C2211yescharacteristic
24C22×C3×C3⋊C8C2211yescharacteristic
25D3×#217—22no—
26#63898—22no—
27Dic3×D12C2214yes—
28#63662C2214yescomplemented
29#63575C2212yescomplemented
30#63573C2212yescomplemented
31#63562C2214yes—
32#63554C2212yescomplemented
33Dic3×C3⋊C8C2212yescomplemented
34C22×C3×SD16—31no—
35C3×#519—31no—
36#5812D311yescharacteristic, complemented
37C22×#215D311yescharacteristic
38#5798—31no—
39#5521—31no—
40#5225—31no—
41#5225—31no—
42#5225—61no—
43#5215—31no—
44#5164—34no—
45Dic3×SD16—34no—
46#5106—31no—
47#5101—31no—
48#5026—34no—
49C4×#215—34no—
50#5001—31no—
51#4998—31no—
52#4997—31no—
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×C3×D12—21no—
61C2×C3×D12—22no—
62C2×C3×D12C2×C414yes—
63C2×C3×D12C2312yes—
64C2×D3×Dic3—24no—
65#3757—21no—
66C4⋊(C3⋊Dic3)C2312yes—
67C4×C3⋊Dic3—21no—
68#3748—22no—
69C2×C3⋊(C3⋊C8)C2312yes—
70C3×#217—21no—
71C3×#217D412yes—
72C3×#215C2×C418yescomplemented
73C3×#215C2×C418yescomplemented
74C3×C4⋊Dic3—24no—
75C3×C4⋊Dic3D412yes—
76C3×C4⋊Dic3C2312yes—
77C3×C4×Dic3—21no—
78C3×C4×Dic3—24no—
79C3×C4×Dic3C2312yes—
80C2×C3×C3⋊C8C2×C414yescomplemented
81C2×C3×C3⋊C8C2311yescharacteristic
82C2×C3×C3⋊C8C2311yescharacteristic
83(C2×D3)⋊Dic3—24no—
84#2949—91noSylow
85C22×C3×Q8—21no—
86C22×C3×Q8C2×D311yescharacteristic
87C22×C3×Q8C2×D311yescharacteristic
88C22×C3×D4—31no—
89C22×D12C2×D311yescharacteristic
90C2×C3×SD16—38no—
91C2×C3×SD16—32no—
92C2×C3×SD16—32no—
93C22×C3×C8—31no—
94C3×C4×Q8—34no—
95C3×C4×Q8—62no—
96C3×#117—31no—
97C3×#117—31no—
98C3×#117—62no—
99C2×#217—62no—
100Q8×Dic3—22no—
101Q8×Dic3C2×D314yescomplemented
102C2×#215Dic318yescomplemented
103C2×#215C2×D312yes—
104C2×#215C2×D312yes—
105D4×Dic3—34no—
106D4×Dic3—62no—
107#926—22no—
108#926—31no—
109#926—31no—
110#926—61no—
111#926C2×D311yescharacteristic
112#926C2×D311yescharacteristic
113C2×#208—31no—
114C2×#208—31no—
115C2×#208—61no—
116C22×C3⋊C8C2×D311yescharacteristic
117#893—62no—
118D3×C22⋊C4—62no—
119C4×D12—34no—
120#835—34no—
121#835—34no—
122#835—64no—
123#832—34no—
124#818—32no—
125#817—32no—
126#815—32no—
127C8×Dic3—32no—
128#809—34no—
129#808—32no—
130#807—32no—
131#803—32no—
132C4×C3⋊C8—32no—
133C23×C32C2×D411yescharacteristic
134C22×C3×D3—22no—
135C22×C3×D3—24no—
136C22×C3×D3—82no—
137C32×Q8—24no—
138C32×Q8—22no—
139C32×Q8C22×C414yes—
140C2×C32×C4—24no—
141C2×C32×C4—22no—
142C2×C32×C4C22×C412yes—
143C2×C32×C4C2×D411yescharacteristic
144C2×C32×C4#4112yes—
145C2×C32×C4C2411yescharacteristic
146C2×C3⋊Dic3—22no—
147C2×C3×Dic3—22no—
148C2×C3×Dic3C2×D414yes—
149C3×D12—24no—
150C3×D12—22no—
151C3×D12C22×C414yes—
152D3×Dic3—84no—
153C3⋊(C3⋊C8)—22no—
154C3×C3⋊C8C22×C412yes—
155C3×C3⋊C8C22×C412yes—
156C22×SD16—31no—
157#519—31no—
158#518—91no—
159#440—94no—
160C4×SD16—94no—
161#427—91no—
162#419—91no—
163#418—91no—
164#405—91no—
165C24×C3—61no—
166C23×D3—21no—
167C2×C3×Q8—22no—
168C2×C3×Q8—21no—
169C2×C3×Q8—22no—
170C2×C3×Q8—21no—
171C2×C3×Q8—24no—
172C2×C3×Q8—22no—
173C2×C3×Q8—42no—
174C2×C3×Q8—41no—
175C2×C3×Q8C4×D314yescomplemented
176C2×C3×Q8C2×Dic314yescomplemented
177C2×C3×Q8C22×D312yes—
178C2×C3×Q8C22×D312yes—
179C2×C3×D4—34no—
180C2×C3×D4—32no—
181C2×C3×D4—62no—
182C2×C3×D4—61no—
183C22×C3×C4—21no—
184C22×C3×C4—21no—
185C22×C3×C4—21no—
186C22×C3×C4—41no—
187C22×C3×C4C22×D311yescharacteristic
188C22×C3×C4C22×D311yescharacteristic
189C22×Dic3—64no—
190C2×D12—21no—
191C2×D12—22no—
192C2×D12C2×Dic314yes—
193C2×D12C22×D312yes—
194C2×C4×D3—64no—
195C3×SD16—38no—
196C3×SD16—38no—
197C2×C3×C8—34no—
198C2×C3×C8—31no—
199C2×C3×C8—31no—
200C3×C4⋊C4—32no—
201C3×C4⋊C4—32no—
202C3×C4⋊C4—64no—
203C3×C22⋊C4—32no—
204C3×C22⋊C4—61no—
205C3×C42—32no—
206C3×C42—64no—
207C3×C42—61no—
208#217—21no—
209#217—61no—
210#217—61no—
211#217—64no—
212#217—121no—
213#217#6712yes—
214#215C2×Dic318yescomplemented
215#215C2×Dic318yescomplemented
216(C2×D3)⋊C4—64no—
217C4⋊Dic3—24no—
218C4⋊Dic3—32no—
219C4⋊Dic3—32no—
220C4⋊Dic3—62no—
221C4⋊Dic3#6712yes—
222C4⋊Dic3C22×D312yes—
223C4×Dic3—21no—
224C4×Dic3—24no—
225C4×Dic3—61no—
226C4×Dic3—61no—
227C4×Dic3—121no—
228C4×Dic3C22×D312yes—
229#208—62no—
230#208—62no—
231#208—122no—
232C2×C3⋊C8—32no—
233C2×C3⋊C8—32no—
234C2×C3⋊C8—62no—
235C2×C3⋊C8C2×Dic314yescomplemented
236C2×C3⋊C8C22×D311yescharacteristic
237C2×C3⋊C8C22×D311yescharacteristic
238C22×C32—22no—
239C22×C32C4×D412yes—
240C22×C32C22×D411yescharacteristic
241C2×C3×D3—24no—
242C2×C3×D3—44no—
243C2×C3×D3—84no—
244C32×C4—24no—
245C32×C4C4×D412yes—
246C32×C4C23×C411yescharacteristic
247C32×C4C2×#4111yescharacteristic
248C3⋊Dic3—42no—
249C3×Dic3—24no—
250C3×Dic3—42no—
251C22×Q8D3211yescharacteristic
252C22×D4—31no—
253C2×SD16—38no—
254C2×SD16—32no—
255C2×SD16—32no—
256C2×M16—91no—
257C22×C8—31no—
258C4×Q8—34no—
259C4×Q8—62no—
260C4×D4—94no—
261C4×D4—182no—
262#117—31no—
263#117—31no—
264#117—62no—
265#117—91no—
266C2×C22⋊C4—182no—
267#107—92no—
268#106—92no—
269#103—94no—
270#102—94no—
271#97—92no—
272C4×C8—92no—
273C23×C3—21no—
274C23×C3—62no—
275C23×C3—64no—
276C23×C3—242no—
277C23×C3D3×D411yescharacteristic
278C23×C3C2×#6711yescharacteristic
279C22×D3—22no—
280C22×D3—24no—
281C22×D3—82no—
282C3×Q8—24no—
283C3×Q8—24no—
284C3×Q8—22no—
285C3×Q8—22no—
286C3×Q8—24no—
287C3×Q8—42no—
288C3×Q8—44no—
289C3×Q8C2×C4×D314yes—
290C3×Q8C22×Dic314yes—
291C3×D4—34no—
292C3×D4—64no—
293C3×D4—62no—
294C2×C3×C4—24no—
295C2×C3×C4—24no—
296C2×C3×C4—22no—
297C2×C3×C4—22no—
298C2×C3×C4—21no—
299C2×C3×C4—22no—
300C2×C3×C4—22no—
301C2×C3×C4—21no—
302C2×C3×C4—34no—
303C2×C3×C4—42no—
304C2×C3×C4—44no—
305C2×C3×C4—62no—
306C2×C3×C4C2×C4×D312yes—
307C2×C3×C4#23512yes—
308C2×C3×C4D3×D411yescharacteristic
309C2×C3×C4#23712yes—
310C2×C3×C4C22×Dic312yes—
311C2×C3×C4C2×#6711yescharacteristic
312C2×C3×C4C23×D311yescharacteristic
313C2×C3×C4C23×D311yescharacteristic
314C2×Dic3—22no—
315C2×Dic3—62no—
316C2×Dic3—62no—
317C2×Dic3—122no—
318C2×Dic3—244no—
319C2×Dic3C2×#6714yes—
320D12—24no—
321D12—22no—
322D12C22×Dic314yes—
323C4×D3—244no—
324C3×C8—32no—
325C3×C8—32no—
326C3⋊C8—62no—
327C3⋊C8—62no—
328C3⋊C8—122no—
329C3⋊C8C22×Dic312yes—
330C3⋊C8C22×Dic312yes—
331C2×C32—22no—
332C2×C32C2×C4×D411yescharacteristic
333C2×C32#57712yes—
334C3×D3—44no—
335C24—61no—
336C2×Q8—22no—
337C2×Q8—21no—
338C2×Q8D3×Dic314yescomplemented
339C2×Q8C2×D3212yes—
340C2×D4—32no—
341C2×D4—34no—
342C2×D4—62no—
343C2×D4—61no—
344C22×C4—21no—
345C22×C4—184no—
346C22×C4C2×D3211yescharacteristic
347SD16—38no—
348SD16—38no—
349M16—182no—
350C2×C8—31no—
351C2×C8—31no—
352C2×C8—34no—
353C2×C8—92no—
354C4⋊C4—32no—
355C4⋊C4—32no—
356C4⋊C4—64no—
357C4⋊C4—92no—
358C22⋊C4—32no—
359C22⋊C4—61no—
360C22⋊C4—184no—
361C22⋊C4—181no—
362C42—32no—
363C42—64no—
364C42—61no—
365C42—181no—
366C22×C3—22no—
367C22×C3—22no—
368C22×C3—21no—
369C22×C3—22no—
370C22×C3—42no—
371C22×C3—64no—
372C22×C3—124no—
373C22×C3—244no—
374C22×C3C4×#6712yes—
375C22×C3D4×Dic312yes—
376C22×C3C2×D3×D411yescharacteristic
377C22×C3C22×#6711yescharacteristic
378C2×D3—24no—
379C2×D3—44no—
380C2×D3—84no—
381C3×C4—24no—
382C3×C4—24no—
383C3×C4—21no—
384C3×C4—21no—
385C3×C4—22no—
386C3×C4—44no—
387C3×C4—64no—
388C3×C4—122no—
389C3×C4C4×#6712yes—
390C3×C4D4×Dic312yes—
391C3×C4C22×C4×D311yescharacteristic
392C3×C4C2×#23511yescharacteristic
393C3×C4C2×#23711yescharacteristic
394C3×C4C23×Dic311yescharacteristic
395Dic3—24no—
396Dic3—42no—
397Dic3—122no—
398Dic3—122no—
399Dic3—242no—
400C32#294911yescharacteristic, complemented, Sylow
401C23—62no—
402C23—64no—
403C23—242no—
404C23D3×#6711yescharacteristic
405Q8—22no—
406Q8—24no—
407Q8C2×D3×Dic314yes—
408D4—34no—
409D4—62no—
410D4—64no—
411C2×C4—22no—
412C2×C4—24no—
413C2×C4—34no—
414C2×C4—62no—
415C2×C4—182no—
416C2×C4—724no—
417C2×C4C2×D3×Dic312yes—
418C2×C4#380412yes—
419C2×C4D3×#6711yescharacteristic
420C2×C4C22×D3211yescharacteristic
421C8—32no—
422C8—32no—
423C8—182no—
424C2×C3—22no—
425C2×C3—22no—
426C2×C3—21no—
427C2×C3—22no—
428C2×C3—42no—
429C2×C3—124no—
430C2×C3#576212yes—
431C2×C3C2×C4×#6711yescharacteristic
432C2×C3C2×D4×Dic311yescharacteristic
433C2×C3#583712yes—
434D3—44no—
435C22—22no—
436C22—64no—
437C22—124no—
438C22—244no—
439C22Dic3×#6712yes—
440C22C2×D3×#6711yescharacteristic
441C4—24no—
442C4—64no—
443C4—122no—
444C4—362no—
445C4Dic3×#6712yes—
446C4C22×D3×Dic311yescharacteristic
447C4C2×#380411yescharacteristic
448C3—21no—
449C3#8254811yescharacteristic, complemented
450C3#8384311yescharacteristic, complemented
451C2—22no—
452C2—124no—
453C2#1059531812yes—
454C2C2×Dic3×#6711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC22×C32C22×D4
prime radicalC22×C3×D12C22
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
1. C3×#5812C2semidirect
4. #10592924C2semidirect
5. #10591566C2semidirect
6. Dic3×#215C2semidirect
7. #10591122C2semidirect
9. #10591055C2semidirect
17. C3×Q8×Dic3C22semidirect
18. C2×C3×#215C4semidirect
28. #63662C22semidirect
29. #63575C22semidirect
30. #63573C22semidirect
32. #63554C22semidirect
33. Dic3×C3⋊C8C22semidirect
36. #5812D3semidirect
56. C2×C32×Q8C2×C4semidirect
72. C3×#215C2×C4semidirect
73. C3×#215C2×C4semidirect
80. C2×C3×C3⋊C8C2×C4semidirect
101. Q8×Dic3C2×D3semidirect
102. C2×#215Dic3semidirect
175. C2×C3×Q8C4×D3semidirect
176. C2×C3×Q8C2×Dic3semidirect
214. #215C2×Dic3semidirect
215. #215C2×Dic3semidirect
235. C2×C3⋊C8C2×Dic3semidirect
338. C2×Q8D3×Dic3semidirect
400. C32#2949semidirect
449. C3#82548semidirect
450. C3#83843semidirect

Maximal subgroups

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

subgroupindex
C3×#58122
C22×C3×#2152
#105949822
#105929242
#105915662
Dic3×#2152
#105911222
#105910852
#105910552
#838433
#825483