Finite Group Databasebeta

← C2×#10590859 #11865710

Subgroups — C2×#10590859 #11865710

Order 1152.

1081 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
1C22×C3×#204C211yesmaximal, characteristic
2C2×#63860C211yesmaximal, characteristic
3C2×Dic3×Dic6C211yesmaximal, characteristic, complemented
4C22×#3719C211yesmaximal, characteristic, complemented
5C2×#63643C211yesmaximal, characteristic, complemented
6C2×C3×Dic3⋊C8C211yesmaximal, characteristic, complemented
7C2×#63563C211yesmaximal, characteristic
8#10590859C218yesmaximal, direct product factor
9C2×#5166—31nomaximal
10C2×#4845—31nomaximal
11C22×#634C2211yescharacteristic
12C22×C3×D12C2211yescharacteristic
13C22×C3×Dic6C2211yescharacteristic
14C22×C32×C8C2211yescharacteristic
15C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
16C2×C3×C4×Dic3C2211yescharacteristic
17C22×C3×C3⋊C8C2211yescharacteristic
18C2×C3×#204—24no—
19C2×C3×#204C2214yes—
20C2×Dic3⋊Dic3—21no—
21C2×(C2×D3)⋊Dic3—21no—
22C2×(C2×D3)⋊Dic3—21no—
23C2×Dic32—21no—
24#63860—22no—
25#63860C2214yes—
26Dic3×Dic6—22no—
27Dic3×Dic6C2214yescomplemented
28C2×#3719—24no—
29C2×#3719C2214yescomplemented
30#63643C2214yescomplemented
31C3×Dic3⋊C8C2214yescomplemented
32#63563C2214yes—
33C22×C3×SD16—31no—
34C2×Q8×Dic3—31no—
35C22×#216—31no—
36C2×#936—31no—
37C22×Dic12—31no—
38C22×#204D311yescharacteristic
39C2×#875—31no—
40C2×C4×Dic6—31no—
41C2×C3×C4⋊C8—31no—
42C2×#832—31no—
43#5166—38no—
44C2×#821—31no—
45C2×#816—31no—
46C2×#816—31no—
47C2×#816—61no—
48C2×Dic3⋊C8D311yescharacteristic, complemented
49#4845—38no—
50C23×C3×D3—21no—
51C22×C32×C4C2311yescharacteristic
52C22×C3⋊Dic3—21no—
53C22×C3⋊Dic3—21no—
54C2×#634—22no—
55C2×#634—22no—
56C2×#634—21no—
57C2×#634C2312yes—
58C22×C3×Dic3—21no—
59C22×C3×Dic3D411yescharacteristic
60C22×C3×Dic3D411yescharacteristic
61C2×C3×D12—22no—
62C2×C3×D12—22no—
63C2×C3×D12—21no—
64C2×C3×D12C2312yes—
65C2×C3×Dic6—21no—
66C2×C3×Dic6—22no—
67C2×C3×Dic6D414yes—
68C2×C3×Dic6C2312yes—
69C2×C32×C8—22no—
70C2×C32×C8C2312yes—
71C4⋊(C3⋊Dic3)—21no—
72C4⋊(C3⋊Dic3)C2312yes—
73C3×C4×Dic3D412yes—
74C3×C4×Dic3C2312yes—
75C2×C3×C3⋊C8—22no—
76C2×C3×C3⋊C8C2312yes—
77C3×#204—28no—
78Dic3⋊Dic3—24no—
79(C2×D3)⋊Dic3—24no—
80(C2×D3)⋊Dic3—24no—
81Dic32—24no—
82#3719—28no—
83C2×#464—91noSylow
84C22×C3×Q8—31no—
85C22×C3×D4—31no—
86C22×D12C2×D311yescharacteristic
87C22×Dic6—31no—
88C22×Dic6—31no—
89C22×Dic6—61no—
90C22×Dic6C2×D311yescharacteristic
91C2×C3×SD16—34no—
92C2×C3×SD16—64no—
93C22×C3×C8—21no—
94C22×C3×C8—31no—
95C22×C3×C8C2×D311yescharacteristic
96C22×C3×C8C2×D311yescharacteristic
97C2×C3×C42—31no—
98C2×#217—61no—
99C2×#217—61no—
100Q8×Dic3—34no—
101Q8×Dic3—62no—
102C2×#216—34no—
103C2×#216—64no—
104#936—34no—
105#936—62no—
106C2×(C2×D3)⋊C4—61no—
107C2×(C2×D3)⋊C4—61no—
108C2×C4⋊Dic3—31no—
109C2×C4⋊Dic3—31no—
110C2×C4⋊Dic3—61no—
111C2×C4⋊Dic3—61no—
112C2×Dic3⋊C4—61no—
113C2×C4×Dic3—61no—
114C2×C4×Dic3—61no—
115C2×C4×Dic3C2×D311yescharacteristic
116C22×C3⋊C8C2×D311yescharacteristic
117C2×Dic12—34no—
118C2×Dic12—64no—
119C2×#204—24no—
120C2×#204C2×D314yes—
121#875—34no—
122#875—62no—
123C4×Dic6—34no—
124C4×Dic6—62no—
125C3×C4⋊C8—34no—
126#832—34no—
127#821—34no—
128#816—34no—
129#816—34no—
130#816—64no—
131Dic3⋊C8C2×D314yescomplemented
132C23×C32C2×D411yescharacteristic
133C22×C3×D3—22no—
134C22×C3×D3—42no—
135C22×C3×D3—42no—
136C22×C3×D3—42no—
137C2×C32×C4C2×D411yescharacteristic
138C2×C32×C4C2×D412yes—
139C2×C32×C4#4112yes—
140C2×C32×C4C2411yescharacteristic
141C2×C3⋊Dic3—22no—
142C2×C3⋊Dic3—22no—
143C2×C3⋊Dic3—42no—
144C2×C3⋊Dic3—42no—
145#634—22no—
146#634—22no—
147#634—42no—
148C2×C3×Dic3—24no—
149C2×C3×Dic3—22no—
150C2×C3×Dic3—22no—
151C2×C3×Dic3—22no—
152C2×C3×Dic3C2×D412yes—
153C2×C3×Dic3C2×D412yes—
154C3×D12—22no—
155C3×D12—22no—
156C3×D12—42no—
157C3×Dic6—24no—
158C3×Dic6—22no—
159C3×Dic6C2×D414yes—
160C32×C8—22no—
161C3×C3⋊C8—22no—
162C22×Q16—91no—
163C22×SD16—31no—
164C2×#124—91no—
165C2×C4×Q8—91no—
166#464—98no—
167C2×C4⋊C8—31no—
168C2×#103—91no—
169C2×#102—91no—
170C24×C3—61no—
171C23×D3—21no—
172C2×C3×Q8—34no—
173C2×C3×Q8—32no—
174C2×C3×Q8—61no—
175C2×C3×Q8—62no—
176C2×C3×D4—32no—
177C2×C3×D4—61no—
178C2×C3×D4—62no—
179C2×C3×D4—62no—
180C22×C3×C4—21no—
181C22×C3×C4—31no—
182C22×C3×C4—31no—
183C22×C3×C4—61no—
184C22×C3×C4C22×D311yescharacteristic
185C22×C3×C4C22×D311yescharacteristic
186C22×Dic3—21no—
187C22×Dic3—61no—
188C22×Dic3—61no—
189C22×Dic3—61no—
190C22×Dic3—61no—
191C22×Dic3—121no—
192C22×Dic3—121no—
193C22×Dic3D1211yescharacteristic
194C22×Dic3D1211yescharacteristic
195C2×D12—22no—
196C2×D12—22no—
197C2×D12—21no—
198C2×D12C22×D312yes—
199C2×Dic6—21no—
200C2×Dic6—22no—
201C2×Dic6—32no—
202C2×Dic6—32no—
203C2×Dic6—62no—
204C2×Dic6—64no—
205C2×Dic6—62no—
206C2×Dic6—62no—
207C2×Dic6—62no—
208C2×Dic6—62no—
209C2×Dic6—61no—
210C2×Dic6—61no—
211C2×Dic6—121no—
212C2×Dic6—122no—
213C2×Dic6#6714yes—
214C2×Dic6C22×D312yes—
215C3×SD16—68no—
216C2×C3×C8—22no—
217C2×C3×C8—22no—
218C2×C3×C8—22no—
219C2×C3×C8—32no—
220C2×C3×C8—42no—
221C2×C3×C8—62no—
222C2×C3×C8C22×D312yes—
223C2×C3×C8C22×D312yes—
224C3×C42—32no—
225C3×C42—32no—
226#217—64no—
227#217—64no—
228#216—68no—
229(C2×D3)⋊C4—64no—
230(C2×D3)⋊C4—64no—
231C4⋊Dic3—32no—
232C4⋊Dic3—32no—
233C4⋊Dic3—62no—
234C4⋊Dic3—61no—
235C4⋊Dic3—61no—
236C4⋊Dic3—64no—
237C4⋊Dic3—121no—
238Dic3⋊C4—64no—
239C4×Dic3—64no—
240C4×Dic3—64no—
241C4×Dic3D1212yes—
242C4×Dic3C22×D312yes—
243C2×C3⋊C8—22no—
244C2×C3⋊C8C22×D312yes—
245Dic12—68no—
246#204—28no—
247C22×C32#12112yes—
248C22×C32#13512yes—
249C22×C32#13712yes—
250C22×C32C22×D411yescharacteristic
251C2×C3×D3—42no—
252C2×C3×D3—42no—
253C2×C3×D3—42no—
254C2×C3×D3—84no—
255C32×C4#12112yes—
256C32×C4C22×D411yescharacteristic
257C32×C4C2×#4111yescharacteristic
258C3⋊Dic3—42no—
259C3⋊Dic3—42no—
260C3×Dic3—24no—
261C3×Dic3—22no—
262C3×Dic3—22no—
263C22×Q8—31no—
264C22×Q8—91no—
265C22×D4—31no—
266C2×Q16—94no—
267C2×Q16—184no—
268C2×SD16—34no—
269C2×SD16—64no—
270C22×C8—31no—
271C22×C8D3211yescharacteristic
272#124—94no—
273#124—182no—
274C4×Q8—94no—
275C4×Q8—182no—
276C2×C4⋊C4—91no—
277C2×C4⋊C4—181no—
278C2×C22⋊C4—181no—
279C2×C22⋊C4—181no—
280C2×C42—31no—
281C2×C42—181no—
282C4⋊C8—34no—
283#103—94no—
284#102—94no—
285C23×C3—21no—
286C23×C3—62no—
287C23×C3—122no—
288C23×C3—122no—
289C23×C3—122no—
290C23×C3C2×D1211yescharacteristic
291C23×C3D3×D411yescharacteristic
292C22×D3—22no—
293C22×D3—42no—
294C22×D3—42no—
295C22×D3—42no—
296C3×Q8—34no—
297C3×Q8—64no—
298C3×Q8—62no—
299C3×D4—62no—
300C3×D4—62no—
301C3×D4—122no—
302C2×C3×C4—21no—
303C2×C3×C4—22no—
304C2×C3×C4—21no—
305C2×C3×C4—22no—
306C2×C3×C4—32no—
307C2×C3×C4—32no—
308C2×C3×C4—64no—
309C2×C3×C4—62no—
310C2×C3×C4—62no—
311C2×C3×C4—62no—
312C2×C3×C4C2×D1211yescharacteristic
313C2×C3×C4D3×D411yescharacteristic
314C2×C3×C4D3×D412yes—
315C2×C3×C4#23712yes—
316C2×C3×C4#23912yes—
317C2×C3×C4C2×#6712yes—
318C2×C3×C4C23×D311yescharacteristic
319C2×C3×C4C23×D311yescharacteristic
320C2×Dic3—22no—
321C2×Dic3—22no—
322C2×Dic3—24no—
323C2×Dic3—22no—
324C2×Dic3—62no—
325C2×Dic3—62no—
326C2×Dic3—62no—
327C2×Dic3—62no—
328C2×Dic3—122no—
329C2×Dic3—122no—
330C2×Dic3—124no—
331C2×Dic3—122no—
332C2×Dic3—122no—
333C2×Dic3—122no—
334C2×Dic3—122no—
335C2×Dic3—242no—
336C2×Dic3C2×D1212yes—
337C2×Dic3C2×D1212yes—
338D12—22no—
339D12—22no—
340D12—42no—
341Dic6—24no—
342Dic6—22no—
343Dic6—64no—
344Dic6—62no—
345Dic6—62no—
346Dic6—62no—
347Dic6—62no—
348Dic6—122no—
349Dic6—124no—
350Dic6—122no—
351Dic6—122no—
352Dic6C2×#6714yes—
353C3×C8—22no—
354C3×C8—22no—
355C3×C8—42no—
356C3×C8—62no—
357C3⋊C8—22no—
358C2×C32#46414yescomplemented
359C2×C32C2×#12111yescharacteristic
360C2×C32C2×#13511yescharacteristic
361C2×C32C2×#13711yescharacteristic
362C3×D3—82no—
363C24—61no—
364C2×Q8—32no—
365C2×Q8—34no—
366C2×Q8—62no—
367C2×Q8—61no—
368C2×Q8—92no—
369C2×Q8—181no—
370C2×Q8—182no—
371C2×Q8—182no—
372C2×D4—32no—
373C2×D4—62no—
374C2×D4—61no—
375C2×D4—62no—
376C22×C4—31no—
377C22×C4—31no—
378C22×C4—61no—
379C22×C4—181no—
380C22×C4—181no—
381C22×C4C2×D3211yescharacteristic
382Q16—188no—
383SD16—68no—
384C2×C8—22no—
385C2×C8—32no—
386C2×C8—62no—
387C2×C8C2×D3212yes—
388C4⋊C4—92no—
389C4⋊C4—184no—
390C4⋊C4—181no—
391C22⋊C4—184no—
392C22⋊C4—184no—
393C42—32no—
394C42—32no—
395C42—184no—
396C22×C3—21no—
397C22×C3—22no—
398C22×C3—22no—
399C22×C3—22no—
400C22×C3—122no—
401C22×C3—122no—
402C22×C3—122no—
403C22×C3—244no—
404C22×C3#89512yes—
405C22×C3#90412yes—
406C22×C3#90912yes—
407C22×C3#91512yes—
408C22×C3#91612yes—
409C22×C3#93912yes—
410C22×C3C22×D1211yescharacteristic
411C22×C3C2×D3×D411yescharacteristic
412C2×D3—42no—
413C2×D3—42no—
414C2×D3—42no—
415C2×D3—84no—
416C3×C4—21no—
417C3×C4—21no—
418C3×C4—22no—
419C3×C4—62no—
420C3×C4—62no—
421C3×C4—64no—
422C3×C4#89512yes—
423C3×C4#93912yes—
424C3×C4C2×D3×D411yescharacteristic
425C3×C4C2×#23711yescharacteristic
426C3×C4C2×#23911yescharacteristic
427C3×C4C22×#6711yescharacteristic
428Dic3—22no—
429Dic3—22no—
430Dic3—24no—
431Dic3—124no—
432Dic3—122no—
433Dic3—122no—
434Dic3—122no—
435Dic3—122no—
436Dic3—242no—
437C32C2×#46411yescharacteristic, complemented, Sylow
438C23—62no—
439C23—122no—
440C23—122no—
441C23—122no—
442C23D3×D1211yescharacteristic
443Q8—34no—
444Q8—62no—
445Q8—64no—
446Q8—182no—
447Q8—182no—
448Q8—362no—
449D4—62no—
450D4—62no—
451D4—122no—
452C2×C4—32no—
453C2×C4—32no—
454C2×C4—62no—
455C2×C4—62no—
456C2×C4—62no—
457C2×C4—64no—
458C2×C4—182no—
459C2×C4—182no—
460C2×C4—362no—
461C2×C4—362no—
462C2×C4#379612yes—
463C2×C4D3×D1211yescharacteristic
464C2×C4D3×#6712yes—
465C2×C4C22×D3211yescharacteristic
466C8—22no—
467C8—62no—
468C2×C3—21no—
469C2×C3—21no—
470C2×C3—21no—
471C2×C3—24no—
472C2×C3—242no—
473C2×C3#484514yescomplemented
474C2×C3#516614yescomplemented
475C2×C3C2×#89511yescharacteristic
476C2×C3C2×#90411yescharacteristic
477C2×C3C2×#90911yescharacteristic
478C2×C3C2×#91511yescharacteristic
479C2×C3C2×#91611yescharacteristic
480C2×C3C2×#93911yescharacteristic
481D3—82no—
482C22—122no—
483C22—122no—
484C22—122no—
485C22—244no—
486C22#6380012yes—
487C22#6380612yes—
488C22#6388612yes—
489C22C2×D3×D1211yescharacteristic
490C4—64no—
491C4—62no—
492C4—62no—
493C4—362no—
494C4—362no—
495C4#6388612yes—
496C4C2×#379611yescharacteristic
497C4C2×D3×#6711yescharacteristic
498C3—21no—
499C3C2×#484511yescharacteristic, complemented
500C3C2×#516611yescharacteristic, complemented
501C2—242no—
502C2#1059085914yesdirect product factor
503C2C2×#6380011yescharacteristic
504C2C2×#6380611yescharacteristic
505C2C2×#6388611yescharacteristic
subgroupG/H
centerC23D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
hypercenterC22×C8D32
hypocenterC32C2×#464
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
3. C2×Dic3×Dic6C2semidirect
4. C22×#3719C2semidirect
5. C2×#63643C2semidirect
6. C2×C3×Dic3⋊C8C2semidirect
8. #10590859C2direct (N × H)
27. Dic3×Dic6C22semidirect
29. C2×#3719C22semidirect
30. #63643C22semidirect
31. C3×Dic3⋊C8C22semidirect
48. C2×Dic3⋊C8D3semidirect
131. Dic3⋊C8C2×D3semidirect
358. C2×C32#464semidirect
437. C32C2×#464semidirect
473. C2×C3#4845semidirect
474. C2×C3#5166semidirect
499. C3C2×#4845semidirect
500. C3C2×#5166semidirect
502. C2#10590859direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#2042
C2×#638602
C2×Dic3×Dic62
C22×#37192
C2×#636432
C2×C3×Dic3⋊C82
C2×#635632
#105908592
C2×#51663
C2×#48453