Finite Group Databasebeta

← C2×#10590537 #11873448

Subgroups — C2×#10590537 #11873448

Order 1152.

925 conjugacy classes of subgroups.

The subgroup lattice has 477 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#890C211yesmaximal, characteristic, complemented
2C2×#63864C211yesmaximal, characteristic
3C2×#63636C211yesmaximal, characteristic
4C2×C3×#810C211yesmaximal, characteristic, complemented
5C2×#63565C211yesmaximal, characteristic, complemented
6C2×#63564C211yesmaximal, characteristic
7C2×Dic3×C3⋊C8C211yesmaximal, characteristic, complemented
8#10590537C218yesmaximal, direct product factor
9C2×#5068—31nomaximal
10C2×#4800—31nomaximal
11C22×C4⋊(C3⋊D3)C2211yescharacteristic
12C22×C3×Dic6C2211yescharacteristic
13C2×C32×C4⋊C4C2211yescharacteristic
14C22×C3⋊(C3⋊C8)C2211yescharacteristic
15C2×C3×C4⋊Dic3—21no—
16C2×C3×C4⋊Dic3C2211yescharacteristic
17C2×C3×Dic3⋊C4—21no—
18C2×C3×C4×Dic3C2211yescharacteristic
19C22×C3×C3⋊C8C2211yescharacteristic
20C3×#890—22no—
21C3×#890C2214yescomplemented
22C2×#3722—21no—
23C2×#3722—21no—
24#63864—22no—
25#63864C2214yes—
26#63636C2214yes—
27C3×#810C2214yescomplemented
28#63565C2214yescomplemented
29#63564C2214yes—
30Dic3×C3⋊C8C2214yescomplemented
31C2×C3×#125—31no—
32C2×#947—31no—
33C2×#890D311yescharacteristic, complemented
34C2×#875—31no—
35C2×C3×#103—31no—
36C2×#835—31no—
37C2×#821—31no—
38C2×C8×Dic3—31no—
39#5068—38no—
40C2×#810—31no—
41C2×#810D311yescharacteristic, complemented
42C2×#809—31no—
43C2×#809—31no—
44C2×#809—31no—
45C2×#809—61no—
46C2×C4×C3⋊C8—31no—
47#4800—38no—
48C23×C3⋊D3—21no—
49C22×C32×C4—21no—
50C22×C32×C4C2311yescharacteristic
51C2×C4⋊(C3⋊D3)—22no—
52C2×C4⋊(C3⋊D3)—22no—
53C2×C4⋊(C3⋊D3)—21no—
54C2×C4⋊(C3⋊D3)C2312yes—
55C22×C3×Dic3—21no—
56C22×C3×Dic3—21no—
57C22×C3×Dic3D411yescharacteristic
58C22×C3×Dic3D411yescharacteristic
59C2×C3×Dic6—22no—
60C2×C3×Dic6—22no—
61C2×C3×Dic6—21no—
62C2×C3×Dic6C2312yes—
63C32×C4⋊C4—21no—
64C32×C4⋊C4C2312yes—
65C2×C3⋊(C3⋊C8)—22no—
66C2×C3⋊(C3⋊C8)C2312yes—
67C3×C4⋊Dic3—21no—
68C3×C4⋊Dic3—24no—
69C3×C4⋊Dic3C2312yes—
70C3×Dic3⋊C4—24no—
71C3×C4×Dic3D412yes—
72C3×C4×Dic3C2312yes—
73C2×C3×C3⋊C8—22no—
74C2×C3×C3⋊C8C2312yes—
75#3722—24no—
76#3722—24no—
77C2×#488—91noSylow
78C22×C3×Q8—31no—
79C22×D12—31no—
80C22×D12—31no—
81C22×D12—61no—
82C22×Dic6C2×D311yescharacteristic
83C22×C3×C8—31no—
84C3×#125—34no—
85C3×#125—62no—
86C2×C3×C4⋊C4—21no—
87C2×C3×C4⋊C4—31no—
88C2×C3×C4⋊C4—61no—
89C2×C3×C4⋊C4—61no—
90C2×C3×C4⋊C4C2×D311yescharacteristic
91C2×C3×C4⋊C4C2×D311yescharacteristic
92C2×C3×C42—31no—
93#947—34no—
94#947—62no—
95C2×(C2×D3)⋊C4—61no—
96C2×(C2×D3)⋊C4—61no—
97C2×(C2×D3)⋊C4—61no—
98C2×(C2×D3)⋊C4—61no—
99C2×C4⋊Dic3—21no—
100C2×C4⋊Dic3C2×D311yescharacteristic
101C2×Dic3⋊C4—21no—
102C2×C4×Dic3C2×D311yescharacteristic
103C22×C3⋊C8—31no—
104C22×C3⋊C8—31no—
105C22×C3⋊C8—61no—
106C22×C3⋊C8C2×D311yescharacteristic
107#890—22no—
108#890C2×D314yescomplemented
109#875—34no—
110#875—62no—
111C3×#103—34no—
112#835—34no—
113#821—34no—
114C8×Dic3—34no—
115#810—34no—
116#810C2×D314yescomplemented
117#809—34no—
118#809—34no—
119#809—34no—
120#809—64no—
121C4×C3⋊C8—34no—
122C23×C32C2×D411yescharacteristic
123C22×C3⋊D3—22no—
124C22×C3⋊D3—42no—
125C22×C3⋊D3—42no—
126C22×C3⋊D3—42no—
127C2×C32×C4—22no—
128C2×C32×C4—42no—
129C2×C32×C4C2×D411yescharacteristic
130C2×C32×C4#4112yes—
131C2×C32×C4#4112yes—
132C2×C32×C4C2411yescharacteristic
133C4⋊(C3⋊D3)—22no—
134C4⋊(C3⋊D3)—22no—
135C4⋊(C3⋊D3)—42no—
136C2×C3×Dic3—22no—
137C2×C3×Dic3—22no—
138C2×C3×Dic3—22no—
139C2×C3×Dic3—22no—
140C2×C3×Dic3—42no—
141C2×C3×Dic3—42no—
142C2×C3×Dic3C2×D412yes—
143C2×C3×Dic3C2×D412yes—
144C3×Dic6—22no—
145C3×Dic6—22no—
146C3×Dic6—42no—
147C3⋊(C3⋊C8)—22no—
148C3×C3⋊C8—22no—
149C2×#125—31no—
150C2×#124—91no—
151#488—98no—
152C2×#103—31no—
153C2×#103—91no—
154C2×#102—91no—
155C2×#102—91no—
156C2×C4×C8—91no—
157C23×D3—61no—
158C23×D3—61no—
159C23×D3—121no—
160C2×C3×Q8—32no—
161C2×C3×Q8—61no—
162C2×C3×Q8—62no—
163C2×C3×Q8—62no—
164C22×C3×C4—21no—
165C22×C3×C4—21no—
166C22×C3×C4—21no—
167C22×C3×C4—31no—
168C22×C3×C4—31no—
169C22×C3×C4—41no—
170C22×C3×C4—61no—
171C22×C3×C4—61no—
172C22×C3×C4C22×D311yescharacteristic
173C22×C3×C4C22×D311yescharacteristic
174C22×Dic3—21no—
175C22×Dic3—21no—
176C22×Dic3#6711yescharacteristic
177C22×Dic3#6711yescharacteristic
178C2×D12—32no—
179C2×D12—32no—
180C2×D12—62no—
181C2×D12—64no—
182C2×D12—62no—
183C2×D12—62no—
184C2×D12—62no—
185C2×D12—62no—
186C2×D12—61no—
187C2×D12—61no—
188C2×D12—122no—
189C2×D12—121no—
190C2×Dic6—22no—
191C2×Dic6—22no—
192C2×Dic6—21no—
193C2×Dic6C22×D312yes—
194C2×C3×C8—32no—
195C2×C3×C8—62no—
196C3×C4⋊C4—21no—
197C3×C4⋊C4—21no—
198C3×C4⋊C4—22no—
199C3×C4⋊C4—32no—
200C3×C4⋊C4—41no—
201C3×C4⋊C4—64no—
202C3×C4⋊C4—64no—
203C3×C4⋊C4—61no—
204C3×C4⋊C4C22×D312yes—
205C3×C4⋊C4C22×D312yes—
206C3×C42—32no—
207C3×C42—32no—
208(C2×D3)⋊C4—64no—
209(C2×D3)⋊C4—64no—
210(C2×D3)⋊C4—64no—
211(C2×D3)⋊C4—64no—
212C4⋊Dic3—21no—
213C4⋊Dic3—24no—
214C4⋊Dic3C22×D312yes—
215Dic3⋊C4—24no—
216C4×Dic3#6712yes—
217C4×Dic3C22×D312yes—
218C2×C3⋊C8—22no—
219C2×C3⋊C8—32no—
220C2×C3⋊C8—32no—
221C2×C3⋊C8—62no—
222C2×C3⋊C8—62no—
223C2×C3⋊C8—62no—
224C2×C3⋊C8—122no—
225C2×C3⋊C8C22×D312yes—
226C22×C32#12412yes—
227C22×C32#13512yes—
228C22×C32#13512yes—
229C22×C32C22×D411yescharacteristic
230C2×C3⋊D3—42no—
231C2×C3⋊D3—42no—
232C2×C3⋊D3—42no—
233C2×C3⋊D3—84no—
234C32×C4—42no—
235C32×C4#12412yes—
236C32×C4C2×#4111yescharacteristic
237C32×C4C2×#4111yescharacteristic
238C3×Dic3—22no—
239C3×Dic3—22no—
240C3×Dic3—42no—
241C3×Dic3—42no—
242C22×Q8—31no—
243C22×D4—91no—
244C22×C8—31no—
245C22×C8—91no—
246#125—34no—
247#125—62no—
248#124—94no—
249#124—182no—
250C2×C4⋊C4—31no—
251C2×C4⋊C4—61no—
252C2×C4⋊C4—61no—
253C2×C4⋊C4D3211yescharacteristic
254C2×C22⋊C4—181no—
255C2×C22⋊C4—181no—
256C2×C42—31no—
257#103—34no—
258#103—94no—
259#102—94no—
260#102—94no—
261C4×C8—94no—
262C23×C3—21no—
263C23×C3D3×D411yescharacteristic
264C23×C3C2×#6711yescharacteristic
265C22×D3—62no—
266C22×D3—62no—
267C22×D3—122no—
268C22×D3—124no—
269C22×D3—122no—
270C22×D3—122no—
271C22×D3—122no—
272C22×D3—122no—
273C22×D3—122no—
274C22×D3—122no—
275C22×D3—242no—
276C22×D3—242no—
277C3×Q8—62no—
278C3×Q8—62no—
279C3×Q8—122no—
280C2×C3×C4—22no—
281C2×C3×C4—22no—
282C2×C3×C4—21no—
283C2×C3×C4—22no—
284C2×C3×C4—22no—
285C2×C3×C4—21no—
286C2×C3×C4—32no—
287C2×C3×C4—32no—
288C2×C3×C4—42no—
289C2×C3×C4—42no—
290C2×C3×C4—42no—
291C2×C3×C4—62no—
292C2×C3×C4—62no—
293C2×C3×C4—62no—
294C2×C3×C4—62no—
295C2×C3×C4—82no—
296C2×C3×C4—122no—
297C2×C3×C4—122no—
298C2×C3×C4#23512yes—
299C2×C3×C4D3×D411yescharacteristic
300C2×C3×C4#23712yes—
301C2×C3×C4#23912yes—
302C2×C3×C4#23912yes—
303C2×C3×C4C2×#6711yescharacteristic
304C2×C3×C4C23×D311yescharacteristic
305C2×C3×C4C23×D311yescharacteristic
306C2×Dic3—22no—
307C2×Dic3—22no—
308C2×Dic3—22no—
309C2×Dic3—22no—
310C2×Dic3—42no—
311C2×Dic3—42no—
312C2×Dic3C2×#6712yes—
313C2×Dic3C2×#6712yes—
314D12—64no—
315D12—62no—
316D12—62no—
317D12—62no—
318D12—62no—
319D12—122no—
320D12—124no—
321D12—122no—
322D12—122no—
323Dic6—22no—
324Dic6—22no—
325Dic6—42no—
326C3×C8—62no—
327C3⋊C8—22no—
328C3⋊C8—62no—
329C3⋊C8—62no—
330C3⋊C8—122no—
331C2×C32#48814yescomplemented
332C2×C32C2×#12411yescharacteristic
333C2×C32C2×#13511yescharacteristic
334C2×C32C2×#13511yescharacteristic
335C3⋊D3—82no—
336C24—181no—
337C2×Q8—32no—
338C2×Q8—61no—
339C2×Q8—62no—
340C2×Q8—62no—
341C2×D4—92no—
342C2×D4—182no—
343C2×D4—182no—
344C2×D4—181no—
345C22×C4—21no—
346C22×C4—31no—
347C22×C4—31no—
348C22×C4—61no—
349C22×C4—61no—
350C22×C4C2×D3211yescharacteristic
351C2×C8—32no—
352C2×C8—62no—
353C2×C8—92no—
354C2×C8—182no—
355C4⋊C4—21no—
356C4⋊C4—32no—
357C4⋊C4—64no—
358C4⋊C4—64no—
359C4⋊C4—61no—
360C4⋊C4C2×D3212yes—
361C22⋊C4—184no—
362C22⋊C4—184no—
363C42—32no—
364C42—32no—
365C22×C3—21no—
366C22×C3—22no—
367C22×C3—22no—
368C22×C3—22no—
369C22×C3#88512yes—
370C22×C3#91612yes—
371C22×C3#91912yes—
372C22×C3#94712yes—
373C22×C3#95012yes—
374C22×C3#95012yes—
375C22×C3C2×D3×D411yescharacteristic
376C22×C3C22×#6711yescharacteristic
377C2×D3—124no—
378C2×D3—122no—
379C2×D3—122no—
380C2×D3—122no—
381C2×D3—122no—
382C2×D3—122no—
383C2×D3—122no—
384C2×D3—242no—
385C2×D3—242no—
386C2×D3—248no—
387C2×D3—244no—
388C2×D3—244no—
389C3×C4—21no—
390C3×C4—21no—
391C3×C4—22no—
392C3×C4—42no—
393C3×C4—42no—
394C3×C4—62no—
395C3×C4—62no—
396C3×C4—82no—
397C3×C4—122no—
398C3×C4—122no—
399C3×C4#88512yes—
400C3×C4#94712yes—
401C3×C4C2×#23511yescharacteristic
402C3×C4C2×#23711yescharacteristic
403C3×C4C2×#23911yescharacteristic
404C3×C4C2×#23911yescharacteristic
405Dic3—22no—
406Dic3—22no—
407Dic3—42no—
408Dic3—42no—
409C32C2×#48811yescharacteristic, complemented, Sylow
410C23—182no—
411C23—362no—
412C23—362no—
413C23—362no—
414C23D3×#6711yescharacteristic
415Q8—62no—
416Q8—62no—
417Q8—122no—
418D4—182no—
419D4—182no—
420D4—362no—
421C2×C4—22no—
422C2×C4—32no—
423C2×C4—32no—
424C2×C4—42no—
425C2×C4—62no—
426C2×C4—62no—
427C2×C4—62no—
428C2×C4—62no—
429C2×C4—122no—
430C2×C4—122no—
431C2×C4#379612yes—
432C2×C4#379912yes—
433C2×C4D3×#6711yescharacteristic
434C2×C4C22×D3211yescharacteristic
435C8—62no—
436C8—182no—
437C2×C3—21no—
438C2×C3—21no—
439C2×C3—24no—
440C2×C3—21no—
441C2×C3#480014yescomplemented
442C2×C3#506814yescomplemented
443C2×C3C2×#88511yescharacteristic
444C2×C3C2×#91611yescharacteristic
445C2×C3C2×#91911yescharacteristic
446C2×C3C2×#94711yescharacteristic
447C2×C3C2×#95011yescharacteristic
448C2×C3C2×#95011yescharacteristic
449D3—244no—
450D3—242no—
451D3—242no—
452C22—362no—
453C22—362no—
454C22—362no—
455C22—724no—
456C22#6390712yes—
457C22#6393512yes—
458C22#6394912yes—
459C22C2×D3×#6711yescharacteristic
460C4—42no—
461C4—62no—
462C4—62no—
463C4—122no—
464C4—122no—
465C4#6390712yes—
466C4C2×#379611yescharacteristic
467C4C2×#379911yescharacteristic
468C3—21no—
469C3C2×#480011yescharacteristic, complemented
470C3C2×#506811yescharacteristic, complemented
471C2—722no—
472C2#1059053714yesdirect product factor
473C2C2×#6390711yescharacteristic
474C2C2×#6393511yescharacteristic
475C2C2×#6394911yescharacteristic
subgroupG/H
centerC23D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC22×C4⋊(C3⋊D3)C22
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#488
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#890C2semidirect
4. C2×C3×#810C2semidirect
5. C2×#63565C2semidirect
7. C2×Dic3×C3⋊C8C2semidirect
8. #10590537C2direct (N × H)
21. C3×#890C22semidirect
27. C3×#810C22semidirect
28. #63565C22semidirect
30. Dic3×C3⋊C8C22semidirect
33. C2×#890D3semidirect
41. C2×#810D3semidirect
108. #890C2×D3semidirect
116. #810C2×D3semidirect
331. C2×C32#488semidirect
409. C32C2×#488semidirect
441. C2×C3#4800semidirect
442. C2×C3#5068semidirect
469. C3C2×#4800semidirect
470. C3C2×#5068semidirect
472. C2#10590537direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#8902
C2×#638642
C2×#636362
C2×C3×#8102
C2×#635652
C2×#635642
C2×Dic3×C3⋊C82
#105905372
C2×#50683
C2×#48003