Finite Group Databasebeta

← C2×#10591559 #11869507

Subgroups — C2×#10591559 #11869507

Order 1152.

913 conjugacy classes of subgroups.

The subgroup lattice has 471 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#946C211yesmaximal, characteristic
2C2×#63841C211yesmaximal, characteristic
3C2×#63662C211yesmaximal, characteristic, complemented
4C2×C3×#835C211yesmaximal, characteristic, complemented
5#10591559C218yesmaximal, direct product factor
6C2×#63576C211yesmaximal, characteristic, complemented
7C2×#63573C211yesmaximal, characteristic, complemented
8C2×(C2×D3)⋊(C3⋊C8)C211yesmaximal, characteristic
9C2×#5045—31nomaximal
10C2×#4815—31nomaximal
11C22×C32×Q8C2211yescharacteristic
12C22×C3×C4×D3C2211yescharacteristic
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C22×C3⋊(C3⋊C8)C2211yescharacteristic
15C3×#946—22no—
16C3×#946C2214yes—
17C2×C3×(C2×D3)⋊C4—21no—
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C2×C3×Dic3⋊C4—21no—
21C22×C3×C3⋊C8C2211yescharacteristic
22C2×(C2×D3)⋊Dic3—21no—
23C2×Dic32—21no—
24#63841—22no—
25#63841C2214yes—
26#63662C2214yescomplemented
27C3×#835C2214yescomplemented
28#63576C2214yescomplemented
29#63573C2214yescomplemented
30(C2×D3)⋊(C3⋊C8)C2214yes—
31C2×C3×C22⋊Q8—31no—
32C2×#946D311yescharacteristic
33C2×#926—31no—
34C2×#892—31no—
35C2×C3×#103—31no—
36C2×#835—31no—
37C2×#835—31no—
38C2×#835—61no—
39C2×#835D311yescharacteristic, complemented
40C2×#830—31no—
41C2×(C2×D3)⋊C8—31no—
42C2×#817—31no—
43#5045—38no—
44C2×#808—31no—
45C2×#807—31no—
46C2×#807—31no—
47#4815—38no—
48C23×C3×D3D411yescharacteristic
49C2×C32×Q8—21no—
50C2×C32×Q8—22no—
51C2×C32×Q8—22no—
52C2×C32×Q8C2312yes—
53C22×C32×C4—21no—
54C22×C32×C4C2311yescharacteristic
55C22×C3⋊Dic3—21no—
56C22×C3×Dic3—21no—
57C22×C3×Dic3—21no—
58C22×C3×Dic3D411yescharacteristic
59C2×C3×C4×D3—22no—
60C2×C3×C4×D3—22no—
61C2×C3×C4×D3D412yes—
62C2×C3×C4×D3C2312yes—
63C4⋊(C3⋊Dic3)—21no—
64C4⋊(C3⋊Dic3)C2312yes—
65C2×C3⋊(C3⋊C8)—22no—
66C2×C3⋊(C3⋊C8)C2312yes—
67C3×(C2×D3)⋊C4—24no—
68C3×C4⋊Dic3—21no—
69C3×C4⋊Dic3—21no—
70C3×C4⋊Dic3C2312yes—
71C3×C4⋊Dic3C2312yes—
72C3×Dic3⋊C4—24no—
73C2×C3×C3⋊C8—22no—
74C2×C3×C3⋊C8C2312yes—
75(C2×D3)⋊Dic3—24no—
76Dic32—24no—
77C2×#485—91noSylow
78C22×C3×Q8—21no—
79C22×C3×Q8C2×D311yescharacteristic
80C22×C3×Q8C2×D311yescharacteristic
81C23×C3×C4—31no—
82C22×C4×D3C2×D311yescharacteristic
83C22×C3×C8—31no—
84C3×C22⋊Q8—34no—
85C3×C22⋊Q8—62no—
86C2×C3×C4⋊C4—31no—
87C2×C3×C4⋊C4—31no—
88C2×C3×C4⋊C4—61no—
89C2×C3×C22⋊C4—61no—
90C2×#217—61no—
91#946—22no—
92#946C2×D314yes—
93C2×(C2×D3)⋊C4—21no—
94C2×(C2×D3)⋊C4—61no—
95#926—34no—
96#926—62no—
97C2×C4⋊Dic3—31no—
98C2×C4⋊Dic3—31no—
99C2×C4⋊Dic3—61no—
100C2×C4⋊Dic3C2×D311yescharacteristic
101C2×C4⋊Dic3C2×D311yescharacteristic
102C2×Dic3⋊C4—21no—
103C2×C4×Dic3—61no—
104C2×C4×Dic3—61no—
105C22×C3⋊C8—31no—
106C22×C3⋊C8—31no—
107C22×C3⋊C8—61no—
108C22×C3⋊C8C2×D311yescharacteristic
109#892—34no—
110#892—62no—
111C3×#103—34no—
112#835—34no—
113#835—34no—
114#835—64no—
115#835C2×D314yescomplemented
116#830—34no—
117(C2×D3)⋊C8—34no—
118#817—34no—
119#808—34no—
120#807—34no—
121#807—34no—
122C23×C32C2×D411yescharacteristic
123C22×C3×D3—22no—
124C22×C3×D3—22no—
125C22×C3×D3—22no—
126C22×C3×D3C2×D412yes—
127C32×Q8—22no—
128C32×Q8—22no—
129C32×Q8—42no—
130C2×C32×C4—22no—
131C2×C32×C4—42no—
132C2×C32×C4C2×D411yescharacteristic
133C2×C32×C4#4112yes—
134C2×C32×C4#4112yes—
135C2×C32×C4C2411yescharacteristic
136C2×C3⋊Dic3—22no—
137C2×C3⋊Dic3—42no—
138C2×C3×Dic3—22no—
139C2×C3×Dic3—22no—
140C2×C3×Dic3—22no—
141C2×C3×Dic3—42no—
142C2×C3×Dic3—42no—
143C2×C3×Dic3C2×D412yes—
144C3×C4×D3—24no—
145C3×C4×D3—22no—
146C3×C4×D3—22no—
147C3⋊(C3⋊C8)—22no—
148C3×C3⋊C8—22no—
149C2×C22⋊Q8—31no—
150C2×#117—91no—
151#485—98no—
152C2×#107—91no—
153C2×#106—91no—
154C2×#103—31no—
155C2×#103—91no—
156C2×C22⋊C8—91no—
157C24×C3—31no—
158C23×D3#6711yescharacteristic
159C2×C3×Q8—21no—
160C2×C3×Q8—21no—
161C2×C3×Q8—24no—
162C2×C3×Q8—22no—
163C2×C3×Q8—22no—
164C2×C3×Q8—22no—
165C2×C3×Q8—22no—
166C2×C3×Q8—22no—
167C2×C3×Q8—41no—
168C2×C3×Q8—42no—
169C2×C3×Q8C22×D312yes—
170C2×C3×Q8C22×D312yes—
171C22×C3×C4—21no—
172C22×C3×C4—21no—
173C22×C3×C4—21no—
174C22×C3×C4—31no—
175C22×C3×C4—32no—
176C22×C3×C4—32no—
177C22×C3×C4—41no—
178C22×C3×C4—62no—
179C22×C3×C4—62no—
180C22×C3×C4—61no—
181C22×C3×C4—61no—
182C22×C3×C4C22×D311yescharacteristic
183C22×C3×C4C22×D311yescharacteristic
184C22×Dic3—21no—
185C22×Dic3—21no—
186C22×Dic3—61no—
187C22×Dic3—61no—
188C22×Dic3—121no—
189C22×Dic3#6711yescharacteristic
190C2×C4×D3—22no—
191C2×C4×D3—22no—
192C2×C4×D3#6712yes—
193C2×C4×D3C22×D312yes—
194C2×C3×C8—32no—
195C2×C3×C8—62no—
196C3×C4⋊C4—32no—
197C3×C4⋊C4—32no—
198C3×C4⋊C4—64no—
199C3×C4⋊C4—61no—
200C3×C4⋊C4—61no—
201C3×C22⋊C4—64no—
202#217—64no—
203(C2×D3)⋊C4—24no—
204(C2×D3)⋊C4—64no—
205C4⋊Dic3—21no—
206C4⋊Dic3—21no—
207C4⋊Dic3—32no—
208C4⋊Dic3—32no—
209C4⋊Dic3—62no—
210C4⋊Dic3—61no—
211C4⋊Dic3—61no—
212C4⋊Dic3—121no—
213C4⋊Dic3C22×D312yes—
214C4⋊Dic3C22×D312yes—
215Dic3⋊C4—24no—
216C4×Dic3—64no—
217C4×Dic3—64no—
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#12312yes—
227C22×C32#13512yes—
228C22×C32#13712yes—
229C22×C32C22×D411yescharacteristic
230C2×C3×D3—22no—
231C2×C3×D3—22no—
232C2×C3×D3—22no—
233C2×C3×D3—44no—
234C32×C4—42no—
235C32×C4#12312yes—
236C32×C4C2×#4111yescharacteristic
237C32×C4C2×#4111yescharacteristic
238C3⋊Dic3—42no—
239C3×Dic3—22no—
240C3×Dic3—42no—
241C3×Dic3—42no—
242C22×Q8D3211yescharacteristic
243C23×C4—31no—
244C22×C8—31no—
245C22×C8—91no—
246C22⋊Q8—34no—
247C22⋊Q8—62no—
248#117—94no—
249#117—182no—
250C2×C4⋊C4—31no—
251C2×C4⋊C4—31no—
252C2×C4⋊C4—61no—
253C2×C4⋊C4—91no—
254C2×C22⋊C4—61no—
255C2×C22⋊C4—181no—
256C2×C42—181no—
257#107—94no—
258#106—94no—
259#103—34no—
260#103—94no—
261C22⋊C8—94no—
262C23×C3—21no—
263C23×C3—32no—
264C23×C3—62no—
265C23×C3—62no—
266C23×C3—62no—
267C23×C3D3×D411yescharacteristic
268C23×C3C2×#6711yescharacteristic
269C22×D3—22no—
270C22×D3—22no—
271C22×D3—22no—
272C22×D3C2×#6712yes—
273C3×Q8—24no—
274C3×Q8—22no—
275C3×Q8—22no—
276C3×Q8—22no—
277C3×Q8—22no—
278C3×Q8—42no—
279C3×Q8—44no—
280C3×Q8—42no—
281C3×Q8—42no—
282C2×C3×C4—22no—
283C2×C3×C4—22no—
284C2×C3×C4—21no—
285C2×C3×C4—22no—
286C2×C3×C4—22no—
287C2×C3×C4—21no—
288C2×C3×C4—32no—
289C2×C3×C4—42no—
290C2×C3×C4—44no—
291C2×C3×C4—42no—
292C2×C3×C4—42no—
293C2×C3×C4—62no—
294C2×C3×C4—64no—
295C2×C3×C4—62no—
296C2×C3×C4—62no—
297C2×C3×C4—62no—
298C2×C3×C4—62no—
299C2×C3×C4—122no—
300C2×C3×C4—122no—
301C2×C3×C4#23512yes—
302C2×C3×C4D3×D411yescharacteristic
303C2×C3×C4#23712yes—
304C2×C3×C4#23712yes—
305C2×C3×C4#23712yes—
306C2×C3×C4C2×#6711yescharacteristic
307C2×C3×C4C23×D311yescharacteristic
308C2×C3×C4C23×D311yescharacteristic
309C2×Dic3—22no—
310C2×Dic3—22no—
311C2×Dic3—22no—
312C2×Dic3—42no—
313C2×Dic3—42no—
314C2×Dic3—62no—
315C2×Dic3—62no—
316C2×Dic3—122no—
317C2×Dic3—122no—
318C2×Dic3—122no—
319C2×Dic3—242no—
320C2×Dic3C2×#6712yes—
321C4×D3—24no—
322C4×D3—22no—
323C4×D3—22no—
324C3×C8—62no—
325C3⋊C8—22no—
326C3⋊C8—62no—
327C3⋊C8—62no—
328C3⋊C8—122no—
329C2×C32#48514yescomplemented
330C2×C32C2×#12311yescharacteristic
331C2×C32C2×#13511yescharacteristic
332C2×C32C2×#13711yescharacteristic
333C3×D3—42no—
334C24—31no—
335C2×Q8—21no—
336C2×Q8—22no—
337C2×Q8—22no—
338C2×Q8C2×D3212yes—
339C22×C4—21no—
340C22×C4—31no—
341C22×C4—32no—
342C22×C4—32no—
343C22×C4—62no—
344C22×C4—62no—
345C22×C4—61no—
346C22×C4—61no—
347C22×C4—181no—
348C22×C4C2×D3211yescharacteristic
349C2×C8—32no—
350C2×C8—62no—
351C2×C8—92no—
352C2×C8—182no—
353C4⋊C4—32no—
354C4⋊C4—32no—
355C4⋊C4—64no—
356C4⋊C4—61no—
357C4⋊C4—61no—
358C4⋊C4—92no—
359C4⋊C4—181no—
360C22⋊C4—64no—
361C22⋊C4—184no—
362C42—184no—
363C22×C3—21no—
364C22×C3—22no—
365C22×C3—22no—
366C22×C3—22no—
367C22×C3—62no—
368C22×C3—62no—
369C22×C3—62no—
370C22×C3—124no—
371C22×C3#88312yes—
372C22×C3#91612yes—
373C22×C3#91812yes—
374C22×C3#93512yes—
375C22×C3#94212yes—
376C22×C3#95012yes—
377C22×C3C2×D3×D411yescharacteristic
378C22×C3C22×#6711yescharacteristic
379C2×D3—22no—
380C2×D3—22no—
381C2×D3—22no—
382C2×D3—44no—
383C3×C4—21no—
384C3×C4—21no—
385C3×C4—22no—
386C3×C4—44no—
387C3×C4—42no—
388C3×C4—42no—
389C3×C4—62no—
390C3×C4—122no—
391C3×C4—122no—
392C3×C4#88312yes—
393C3×C4#93512yes—
394C3×C4C2×#23511yescharacteristic
395C3×C4C2×#23711yescharacteristic
396C3×C4C2×#23711yescharacteristic
397C3×C4C2×#23711yescharacteristic
398Dic3—22no—
399Dic3—42no—
400Dic3—42no—
401Dic3—122no—
402Dic3—122no—
403Dic3—242no—
404C32C2×#48511yescharacteristic, complemented, Sylow
405C23—32no—
406C23—62no—
407C23—62no—
408C23—62no—
409C23D3×#6711yescharacteristic
410Q8—22no—
411Q8—22no—
412Q8—42no—
413C2×C4—22no—
414C2×C4—32no—
415C2×C4—42no—
416C2×C4—62no—
417C2×C4—62no—
418C2×C4—62no—
419C2×C4—64no—
420C2×C4—62no—
421C2×C4—62no—
422C2×C4—122no—
423C2×C4—122no—
424C2×C4—182no—
425C2×C4—362no—
426C2×C4#380412yes—
427C2×C4#380512yes—
428C2×C4D3×#6711yescharacteristic
429C2×C4C22×D3211yescharacteristic
430C8—62no—
431C8—182no—
432C2×C3—21no—
433C2×C3—21no—
434C2×C3—24no—
435C2×C3—21no—
436C2×C3—122no—
437C2×C3#481514yescomplemented
438C2×C3#504514yescomplemented
439C2×C3C2×#88311yescharacteristic
440C2×C3C2×#91611yescharacteristic
441C2×C3C2×#91811yescharacteristic
442C2×C3C2×#93511yescharacteristic
443C2×C3C2×#94211yescharacteristic
444C2×C3C2×#95011yescharacteristic
445D3—42no—
446C22—62no—
447C22—62no—
448C22—62no—
449C22—124no—
450C22#6394712yes—
451C22#6394812yes—
452C22#6396912yes—
453C22C2×D3×#6711yescharacteristic
454C4—42no—
455C4—62no—
456C4—122no—
457C4—122no—
458C4—362no—
459C4#6396912yes—
460C4C2×#380411yescharacteristic
461C4C2×#380511yescharacteristic
462C3—21no—
463C3C2×#481511yescharacteristic, complemented
464C3C2×#504511yescharacteristic, complemented
465C2—122no—
466C2#1059155914yesdirect product factor
467C2C2×#6394711yescharacteristic
468C2C2×#6394811yescharacteristic
469C2C2×#6396911yescharacteristic
subgroupG/H
centerC23D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC23×C32C2×D4
prime radicalC23×C3×D3D4
hypercenterC22×Q8D32
hypocenterC32C2×#485
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
3. C2×#63662C2semidirect
4. C2×C3×#835C2semidirect
5. #10591559C2direct (N × H)
6. C2×#63576C2semidirect
7. C2×#63573C2semidirect
26. #63662C22semidirect
27. C3×#835C22semidirect
28. #63576C22semidirect
29. #63573C22semidirect
39. C2×#835D3semidirect
115. #835C2×D3semidirect
329. C2×C32#485semidirect
404. C32C2×#485semidirect
437. C2×C3#4815semidirect
438. C2×C3#5045semidirect
463. C3C2×#4815semidirect
464. C3C2×#5045semidirect
466. C2#10591559direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#9462
C2×#638412
C2×#636622
C2×C3×#8352
#105915592
C2×#635762
C2×#635732
C2×(C2×D3)⋊(C3⋊C8)2
C2×#50453
C2×#48153