Finite Group Databasebeta

← C2×#10590579 #11866803

Subgroups — C2×#10590579 #11866803

Order 1152.

1105 conjugacy classes of subgroups.

The subgroup lattice has 507 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#897C211yesmaximal, characteristic
2C2×#63857C211yesmaximal, characteristic
3C22×#3719C211yesmaximal, characteristic, complemented
4C22×D3×C3⋊C8C211yesmaximal, characteristic
5C2×#63637C211yesmaximal, characteristic, complemented
6C2×C3×#807C211yesmaximal, characteristic, complemented
7C2×#63565C211yesmaximal, characteristic, complemented
8#10590579C218yesmaximal, direct product factor
9C2×#5051—31nomaximal
10C2×#4887—31nomaximal
11C22×#634C2211yescharacteristic
12C22×C3×C4×D3C2211yescharacteristic
13C22×C3×Dic6C2211yescharacteristic
14C2×C32×C4⋊C4C2211yescharacteristic
15C22×C3⋊(C3⋊C8)C2211yescharacteristic
16C2×C3×(C2×D3)⋊C4—21no—
17C2×C3×C4⋊Dic3—21no—
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C22×C3×C3⋊C8C2211yescharacteristic
20C3×#897—22no—
21C3×#897C2214yes—
22C2×Dic3⋊Dic3—21no—
23C2×(C2×D3)⋊Dic3—21no—
24#63857—22no—
25#63857C2214yes—
26C2×#3719—24no—
27C2×#3719C2214yescomplemented
28C2×D3×C3⋊C8—24no—
29C2×D3×C3⋊C8C2214yes—
30#63637C2214yescomplemented
31C3×#807C2214yescomplemented
32#63565C2214yescomplemented
33C2×C3×C22⋊Q8—31no—
34C22×#216—31no—
35C2×#924—31no—
36C23×C3⋊C8—31no—
37C22×Dic12—31no—
38C22×D3×C8—31no—
39C2×#897—31no—
40C2×#897D311yescharacteristic
41C2×C3×#107—31no—
42C2×#835—31no—
43#5051—38no—
44C2×#810—31no—
45C2×#810—31no—
46C2×#810—31no—
47C2×#810—61no—
48C2×#807D311yescharacteristic, complemented
49#4887—38no—
50C23×C3×D3D411yescharacteristic
51C22×C32×C4—21no—
52C22×C32×C4C2311yescharacteristic
53C22×C3⋊Dic3—21no—
54C2×#634—22no—
55C2×#634—22no—
56C2×#634—21no—
57C2×#634C2312yes—
58C22×C3×Dic3—21no—
59C22×C3×Dic3—21no—
60C22×C3×Dic3D411yescharacteristic
61C2×C3×C4×D3—22no—
62C2×C3×C4×D3—22no—
63C2×C3×C4×D3D412yes—
64C2×C3×C4×D3C2312yes—
65C2×C3×Dic6—22no—
66C2×C3×Dic6—22no—
67C2×C3×Dic6—21no—
68C2×C3×Dic6C2312yes—
69C32×C4⋊C4—21no—
70C32×C4⋊C4C2312yes—
71C2×C3⋊(C3⋊C8)—22no—
72C2×C3⋊(C3⋊C8)C2312yes—
73C3×(C2×D3)⋊C4—24no—
74C3×C4⋊Dic3—21no—
75C3×C4⋊Dic3—24no—
76C3×C4⋊Dic3C2312yes—
77C2×C3×C3⋊C8D414yes—
78C2×C3×C3⋊C8C2312yes—
79Dic3⋊Dic3—24no—
80(C2×D3)⋊Dic3—24no—
81#3719—28no—
82D3×C3⋊C8—28no—
83C2×#467—91noSylow
84C22×C3×Q8—31no—
85C23×C3×C4—31no—
86C22×C4×D3C2×D311yescharacteristic
87C22×Dic6—31no—
88C22×Dic6—31no—
89C22×Dic6—61no—
90C22×Dic6C2×D311yescharacteristic
91C22×C3×C8—31no—
92C3×C22⋊Q8—34no—
93C3×C22⋊Q8—62no—
94C2×C3×C4⋊C4—21no—
95C2×C3×C4⋊C4—31no—
96C2×C3×C4⋊C4—61no—
97C2×C3×C4⋊C4C2×D311yescharacteristic
98C2×C3×C4⋊C4C2×D311yescharacteristic
99C2×C3×C22⋊C4—61no—
100C2×#217—61no—
101C2×#216—34no—
102C2×#216—64no—
103C2×(C2×D3)⋊C4—21no—
104C2×(C2×D3)⋊C4—61no—
105C2×C4⋊Dic3—21no—
106C2×C4⋊Dic3—61no—
107C2×C4⋊Dic3C2×D311yescharacteristic
108#924—34no—
109#924—62no—
110C2×Dic3⋊C4—61no—
111C22×C3⋊C8—31no—
112C22×C3⋊C8—31no—
113C22×C3⋊C8—34no—
114C22×C3⋊C8—61no—
115C22×C3⋊C8—64no—
116C22×C3⋊C8C2×D311yescharacteristic
117C2×Dic12—34no—
118C2×Dic12—64no—
119C2×D3×C8—34no—
120C2×D3×C8—64no—
121#897—22no—
122#897—34no—
123#897—62no—
124#897C2×D314yes—
125C3×#107—34no—
126#835—34no—
127#810—34no—
128#810—34no—
129#810—34no—
130#810—64no—
131#807C2×D314yescomplemented
132C23×C32C2×D411yescharacteristic
133C22×C3×D3—22no—
134C22×C3×D3—22no—
135C22×C3×D3Q1614yescomplemented
136C22×C3×D3C2×D412yes—
137C2×C32×C4—22no—
138C2×C32×C4—42no—
139C2×C32×C4C2×D412yes—
140C2×C32×C4C2×D411yescharacteristic
141C2×C32×C4#4112yes—
142C2×C32×C4C2411yescharacteristic
143C2×C3⋊Dic3—22no—
144C2×C3⋊Dic3—42no—
145#634—22no—
146#634—22no—
147#634—42no—
148C2×C3×Dic3—22no—
149C2×C3×Dic3—22no—
150C2×C3×Dic3—22no—
151C2×C3×Dic3—42no—
152C2×C3×Dic3—42no—
153C2×C3×Dic3C2×D412yes—
154C3×C4×D3—24no—
155C3×C4×D3—22no—
156C3×C4×D3—22no—
157C3×Dic6—22no—
158C3×Dic6—22no—
159C3×Dic6—42no—
160C3⋊(C3⋊C8)—22no—
161C3×C3⋊C8C2×D414yes—
162C22×Q16—91no—
163C23×C8—91no—
164C2×C22⋊Q8—31no—
165C2×C22⋊Q8—91no—
166#467—98no—
167C2×#107—31no—
168C2×#103—91no—
169C2×#103—91no—
170C24×C3—31no—
171C23×D3#6711yescharacteristic
172C2×C3×Q8—32no—
173C2×C3×Q8—61no—
174C2×C3×Q8—62no—
175C2×C3×Q8—62no—
176C22×C3×C4—21no—
177C22×C3×C4—21no—
178C22×C3×C4—21no—
179C22×C3×C4—31no—
180C22×C3×C4—32no—
181C22×C3×C4—32no—
182C22×C3×C4—41no—
183C22×C3×C4—62no—
184C22×C3×C4—62no—
185C22×C3×C4—61no—
186C22×C3×C4—61no—
187C22×C3×C4C22×D311yescharacteristic
188C22×C3×C4C22×D311yescharacteristic
189C22×Dic3—21no—
190C22×Dic3—21no—
191C22×Dic3—61no—
192C22×Dic3—61no—
193C22×Dic3—121no—
194C22×Dic3#6711yescharacteristic
195C2×C4×D3—22no—
196C2×C4×D3—22no—
197C2×C4×D3#6712yes—
198C2×C4×D3C22×D312yes—
199C2×Dic6—22no—
200C2×Dic6—22no—
201C2×Dic6—21no—
202C2×Dic6—32no—
203C2×Dic6—32no—
204C2×Dic6—62no—
205C2×Dic6—64no—
206C2×Dic6—62no—
207C2×Dic6—62no—
208C2×Dic6—62no—
209C2×Dic6—62no—
210C2×Dic6—61no—
211C2×Dic6—61no—
212C2×Dic6—121no—
213C2×Dic6—122no—
214C2×Dic6C22×D312yes—
215C2×C3×C8—34no—
216C2×C3×C8—32no—
217C3×C4⋊C4—21no—
218C3×C4⋊C4—21no—
219C3×C4⋊C4—22no—
220C3×C4⋊C4—32no—
221C3×C4⋊C4—41no—
222C3×C4⋊C4—64no—
223C3×C4⋊C4—61no—
224C3×C4⋊C4C22×D312yes—
225C3×C4⋊C4C22×D312yes—
226C3×C22⋊C4—64no—
227#217—64no—
228#216—68no—
229(C2×D3)⋊C4—24no—
230(C2×D3)⋊C4—64no—
231C4⋊Dic3—21no—
232C4⋊Dic3—24no—
233C4⋊Dic3—64no—
234C4⋊Dic3C22×D312yes—
235Dic3⋊C4—64no—
236C2×C3⋊C8—32no—
237C2×C3⋊C8—32no—
238C2×C3⋊C8—62no—
239C2×C3⋊C8—62no—
240C2×C3⋊C8—62no—
241C2×C3⋊C8—68no—
242C2×C3⋊C8—122no—
243C2×C3⋊C8D1214yes—
244C2×C3⋊C8C22×D312yes—
245Dic12—68no—
246D3×C8—68no—
247C22×C32#12112yes—
248C22×C32C2×Q1612yes—
249C22×C32#13512yes—
250C22×C32C22×D411yescharacteristic
251C2×C3×D3—22no—
252C2×C3×D3—22no—
253C2×C3×D3—28no—
254C2×C3×D3C2×Q1614yescomplemented
255C32×C4—42no—
256C32×C4#12112yes—
257C32×C4C22×D411yescharacteristic
258C32×C4C2×#4111yescharacteristic
259C3⋊Dic3—42no—
260C3×Dic3—22no—
261C3×Dic3—42no—
262C3×Dic3—42no—
263C22×Q8—31no—
264C22×Q8—91no—
265C23×C4—31no—
266C2×Q16—94no—
267C2×Q16—184no—
268C22×C8—31no—
269C22×C8—94no—
270C22×C8—91no—
271C22×C8—184no—
272C22⋊Q8—34no—
273C22⋊Q8—62no—
274C22⋊Q8—94no—
275C22⋊Q8—182no—
276C2×C4⋊C4—31no—
277C2×C4⋊C4—61no—
278C2×C4⋊C4—181no—
279C2×C4⋊C4D3211yescharacteristic
280C2×C22⋊C4—61no—
281C2×C22⋊C4—181no—
282#107—34no—
283#103—94no—
284#103—94no—
285C23×C3—21no—
286C23×C3—34no—
287C23×C3—32no—
288C23×C3—62no—
289C23×C3—62no—
290C23×C3D3×D411yescharacteristic
291C23×C3C2×#6711yescharacteristic
292C22×D3—22no—
293C22×D3—22no—
294C22×D3#21614yescomplemented
295C22×D3C2×#6712yes—
296C3×Q8—62no—
297C3×Q8—62no—
298C3×Q8—122no—
299C2×C3×C4—22no—
300C2×C3×C4—22no—
301C2×C3×C4—21no—
302C2×C3×C4—22no—
303C2×C3×C4—22no—
304C2×C3×C4—21no—
305C2×C3×C4—32no—
306C2×C3×C4—42no—
307C2×C3×C4—42no—
308C2×C3×C4—42no—
309C2×C3×C4—62no—
310C2×C3×C4—64no—
311C2×C3×C4—62no—
312C2×C3×C4—62no—
313C2×C3×C4—62no—
314C2×C3×C4—62no—
315C2×C3×C4—82no—
316C2×C3×C4—122no—
317C2×C3×C4—122no—
318C2×C3×C4C2×D1212yes—
319C2×C3×C4D3×D412yes—
320C2×C3×C4D3×D411yescharacteristic
321C2×C3×C4#23712yes—
322C2×C3×C4#23912yes—
323C2×C3×C4C2×#6711yescharacteristic
324C2×C3×C4C23×D311yescharacteristic
325C2×C3×C4C23×D311yescharacteristic
326C2×Dic3—22no—
327C2×Dic3—22no—
328C2×Dic3—22no—
329C2×Dic3—42no—
330C2×Dic3—42no—
331C2×Dic3—62no—
332C2×Dic3—62no—
333C2×Dic3—122no—
334C2×Dic3—124no—
335C2×Dic3—122no—
336C2×Dic3—122no—
337C2×Dic3C2×#6712yes—
338C4×D3—24no—
339C4×D3—22no—
340C4×D3—22no—
341Dic6—22no—
342Dic6—22no—
343Dic6—42no—
344Dic6—64no—
345Dic6—62no—
346Dic6—62no—
347Dic6—62no—
348Dic6—62no—
349Dic6—122no—
350Dic6—124no—
351Dic6—122no—
352Dic6—122no—
353C3×C8—34no—
354C3⋊C8—62no—
355C3⋊C8—62no—
356C3⋊C8—122no—
357C3⋊C8C2×D1214yes—
358C2×C32#46714yescomplemented
359C2×C32C2×#12111yescharacteristic
360C2×C32C22×Q1611yescharacteristic
361C2×C32C2×#13511yescharacteristic
362C3×D3—24no—
363C24—31no—
364C2×Q8—32no—
365C2×Q8—61no—
366C2×Q8—62no—
367C2×Q8—62no—
368C2×Q8—92no—
369C2×Q8—181no—
370C2×Q8—182no—
371C2×Q8—182no—
372C22×C4—21no—
373C22×C4—31no—
374C22×C4—32no—
375C22×C4—32no—
376C22×C4—62no—
377C22×C4—62no—
378C22×C4—61no—
379C22×C4—61no—
380C22×C4—181no—
381C22×C4C2×D3211yescharacteristic
382Q16—188no—
383C2×C8—32no—
384C2×C8—34no—
385C2×C8—92no—
386C2×C8—188no—
387C2×C8—182no—
388C4⋊C4—21no—
389C4⋊C4—32no—
390C4⋊C4—64no—
391C4⋊C4—61no—
392C4⋊C4—184no—
393C4⋊C4C2×D3212yes—
394C22⋊C4—64no—
395C22⋊C4—184no—
396C22×C3—21no—
397C22×C3—22no—
398C22×C3—22no—
399C22×C3—22no—
400C22×C3—34no—
401C22×C3—68no—
402C22×C3—62no—
403C22×C3—62no—
404C22×C3#89512yes—
405C22×C3#91212yes—
406C22×C3D3×Q1612yes—
407C22×C3#93912yes—
408C22×C3C2×#21612yes—
409C22×C3#95012yes—
410C22×C3C2×D3×D411yescharacteristic
411C22×C3C22×#6711yescharacteristic
412C2×D3—22no—
413C2×D3—28no—
414C2×D3—22no—
415C2×D3C2×#21614yescomplemented
416C3×C4—21no—
417C3×C4—21no—
418C3×C4—22no—
419C3×C4—42no—
420C3×C4—42no—
421C3×C4—62no—
422C3×C4—82no—
423C3×C4—122no—
424C3×C4—122no—
425C3×C4#89512yes—
426C3×C4#93912yes—
427C3×C4C22×D1211yescharacteristic
428C3×C4C2×D3×D411yescharacteristic
429C3×C4C2×#23711yescharacteristic
430C3×C4C2×#23911yescharacteristic
431Dic3—22no—
432Dic3—42no—
433Dic3—42no—
434Dic3—124no—
435Dic3—122no—
436Dic3—122no—
437C32C2×#46711yescharacteristic, complemented, Sylow
438C23—32no—
439C23—34no—
440C23—62no—
441C23—62no—
442C23D3×#6711yescharacteristic
443Q8—62no—
444Q8—62no—
445Q8—122no—
446Q8—182no—
447Q8—182no—
448Q8—362no—
449C2×C4—22no—
450C2×C4—32no—
451C2×C4—42no—
452C2×C4—62no—
453C2×C4—62no—
454C2×C4—62no—
455C2×C4—64no—
456C2×C4—62no—
457C2×C4—62no—
458C2×C4—122no—
459C2×C4—122no—
460C2×C4—182no—
461C2×C4—362no—
462C2×C4#379612yes—
463C2×C4D3×D1212yes—
464C2×C4D3×#6711yescharacteristic
465C2×C4C22×D3211yescharacteristic
466C8—34no—
467C8—182no—
468C2×C3—21no—
469C2×C3—21no—
470C2×C3—24no—
471C2×C3—21no—
472C2×C3—64no—
473C2×C3#488714yescomplemented
474C2×C3#505114yescomplemented
475C2×C3C2×#89511yescharacteristic
476C2×C3C2×#91211yescharacteristic
477C2×C3C2×D3×Q1611yescharacteristic
478C2×C3C2×#93911yescharacteristic
479C2×C3C22×#21611yescharacteristic
480C2×C3C2×#95011yescharacteristic
481D3—24no—
482C22—34no—
483C22—62no—
484C22—62no—
485C22—68no—
486C22#6388612yes—
487C22#6393312yes—
488C22D3×#21612yes—
489C22C2×D3×#6711yescharacteristic
490C4—42no—
491C4—62no—
492C4—122no—
493C4—122no—
494C4—362no—
495C4#6388612yes—
496C4C2×#379611yescharacteristic
497C4C2×D3×D1211yescharacteristic
498C3—21no—
499C3C2×#488711yescharacteristic, complemented
500C3C2×#505111yescharacteristic, complemented
501C2—64no—
502C2#1059057914yesdirect product factor
503C2C2×#6388611yescharacteristic
504C2C2×#6393311yescharacteristic
505C2C2×D3×#21611yescharacteristic
subgroupG/H
centerC23D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC23×C3×D3D4
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#467
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
3. C22×#3719C2semidirect
5. C2×#63637C2semidirect
6. C2×C3×#807C2semidirect
7. C2×#63565C2semidirect
8. #10590579C2direct (N × H)
27. C2×#3719C22semidirect
30. #63637C22semidirect
31. C3×#807C22semidirect
32. #63565C22semidirect
48. C2×#807D3semidirect
131. #807C2×D3semidirect
135. C22×C3×D3Q16semidirect
254. C2×C3×D3C2×Q16semidirect
294. C22×D3#216semidirect
358. C2×C32#467semidirect
415. C2×D3C2×#216semidirect
437. C32C2×#467semidirect
473. C2×C3#4887semidirect
474. C2×C3#5051semidirect
499. C3C2×#4887semidirect
500. C3C2×#5051semidirect
502. C2#10590579direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#8972
C2×#638572
C22×#37192
C22×D3×C3⋊C82
C2×#636372
C2×C3×#8072
C2×#635652
#105905792
C2×#50513
C2×#48873