Finite Group Databasebeta

← C2×#10590801 #11865716

Subgroups — C2×#10590801 #11865716

Order 1152.

1101 conjugacy classes of subgroups.

The subgroup lattice has 513 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×Dic12C211yesmaximal, characteristic, complemented
2C2×#63864C211yesmaximal, characteristic
3C2×Dic3×Dic6C211yesmaximal, characteristic, complemented
4C22×#3717C211yesmaximal, characteristic
5C2×#63648C211yesmaximal, characteristic
6C2×C3×Dic3⋊C8C211yesmaximal, characteristic, complemented
7C2×#63566C211yesmaximal, characteristic, complemented
8#10590801C218yesmaximal, direct product factor
9C2×#5185—31nomaximal
10C2×#4845—31nomaximal
11C22×C4⋊(C3⋊D3)C2211yescharacteristic
12C22×C3×Dic6C2211yescharacteristic
13C22×C3×Dic6C2211yescharacteristic
14C22×C32×C8C2211yescharacteristic
15C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
16C2×C3×C4×Dic3C2211yescharacteristic
17C22×C3×C3⋊C8C2211yescharacteristic
18C2×C3×Dic12—24no—
19C2×C3×Dic12C2214yescomplemented
20C2×Dic3⋊Dic3—21no—
21C2×#3722—21no—
22C2×#3722—21no—
23C2×Dic32—21no—
24#63864—22no—
25#63864C2214yes—
26Dic3×Dic6—22no—
27Dic3×Dic6C2214yescomplemented
28C2×#3717—24no—
29C2×#3717C2214yes—
30#63648C2214yes—
31C3×Dic3⋊C8C2214yescomplemented
32#63566C2214yescomplemented
33C22×C3×Q16—31no—
34C2×#947—31no—
35C2×Q8×Dic3—31no—
36C22×#215—31no—
37C22×Dic12D311yescharacteristic, complemented
38C22×#204—31no—
39C2×#875—31no—
40C2×C4×Dic6—31no—
41C2×C3×C4⋊C8—31no—
42C2×#835—31no—
43#5185—38no—
44C2×#821—31no—
45C2×#821—31no—
46C2×#821—61no—
47C2×#816—31no—
48C2×Dic3⋊C8D311yescharacteristic, complemented
49#4845—38no—
50C23×C3⋊D3—21no—
51C22×C32×C4C2311yescharacteristic
52C22×C3⋊Dic3—21no—
53C2×C4⋊(C3⋊D3)—22no—
54C2×C4⋊(C3⋊D3)—22no—
55C2×C4⋊(C3⋊D3)—21no—
56C2×C4⋊(C3⋊D3)C2312yes—
57C22×C3×Dic3—21no—
58C22×C3×Dic3—21no—
59C22×C3×Dic3D411yescharacteristic
60C22×C3×Dic3D411yescharacteristic
61C2×C3×Dic6—21no—
62C2×C3×Dic6—22no—
63C2×C3×Dic6—22no—
64C2×C3×Dic6—22no—
65C2×C3×Dic6—21no—
66C2×C3×Dic6D414yes—
67C2×C3×Dic6C2312yes—
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×Dic12—28no—
78Dic3⋊Dic3—24no—
79#3722—24no—
80#3722—24no—
81Dic32—24no—
82#3717—28no—
83C2×#464—91noSylow
84C22×C3×Q8—31no—
85C22×C3×Q8—31no—
86C22×D12—31no—
87C22×D12—31no—
88C22×D12—61no—
89C22×Dic6C2×D311yescharacteristic
90C22×Dic6C2×D311yescharacteristic
91C2×C3×Q16—34no—
92C2×C3×Q16—64no—
93C22×C3×C8—21no—
94C22×C3×C8—31no—
95C22×C3×C8C2×D311yescharacteristic
96C22×C3×C8C2×D311yescharacteristic
97C2×C3×C42—31no—
98#947—34no—
99#947—62no—
100Q8×Dic3—34no—
101Q8×Dic3—62no—
102C2×#215—34no—
103C2×#215—64no—
104C2×(C2×D3)⋊C4—61no—
105C2×(C2×D3)⋊C4—61no—
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—24no—
118C2×Dic12C2×D314yescomplemented
119C2×#204—34no—
120C2×#204—64no—
121#875—34no—
122#875—62no—
123C4×Dic6—34no—
124C4×Dic6—62no—
125C3×C4⋊C8—34no—
126#835—34no—
127#821—34no—
128#821—34no—
129#821—64no—
130#816—34no—
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—42no—
143C4⋊(C3⋊D3)—22no—
144C4⋊(C3⋊D3)—22no—
145C4⋊(C3⋊D3)—42no—
146C2×C3×Dic3—24no—
147C2×C3×Dic3—22no—
148C2×C3×Dic3—22no—
149C2×C3×Dic3—22no—
150C2×C3×Dic3—22no—
151C2×C3×Dic3—42no—
152C2×C3×Dic3C2×D412yes—
153C2×C3×Dic3C2×D412yes—
154C3×Dic6—24no—
155C3×Dic6—22no—
156C3×Dic6—22no—
157C3×Dic6—22no—
158C3×Dic6—42no—
159C3×Dic6C2×D414yes—
160C32×C8—22no—
161C3×C3⋊C8—22no—
162C22×Q16—31no—
163C22×SD16—91no—
164C2×#124—91no—
165C2×C4×Q8—91no—
166#464—98no—
167C2×C4⋊C8—31no—
168C2×#103—91no—
169C2×#102—91no—
170C23×D3—61no—
171C23×D3—61no—
172C23×D3—121no—
173C2×C3×Q8—34no—
174C2×C3×Q8—32no—
175C2×C3×Q8—32no—
176C2×C3×Q8—61no—
177C2×C3×Q8—61no—
178C2×C3×Q8—62no—
179C2×C3×Q8—62no—
180C2×C3×Q8—62no—
181C22×C3×C4—21no—
182C22×C3×C4—31no—
183C22×C3×C4—31no—
184C22×C3×C4—61no—
185C22×C3×C4—61no—
186C22×C3×C4C22×D311yescharacteristic
187C22×C3×C4C22×D311yescharacteristic
188C22×Dic3—21no—
189C22×Dic3—21no—
190C22×Dic3—61no—
191C22×Dic3—61no—
192C22×Dic3—121no—
193C22×Dic3D1211yescharacteristic
194C22×Dic3D1211yescharacteristic
195C2×D12—32no—
196C2×D12—32no—
197C2×D12—62no—
198C2×D12—64no—
199C2×D12—62no—
200C2×D12—62no—
201C2×D12—62no—
202C2×D12—62no—
203C2×D12—61no—
204C2×D12—61no—
205C2×D12—121no—
206C2×D12—122no—
207C2×Dic6—21no—
208C2×Dic6—22no—
209C2×Dic6—22no—
210C2×Dic6—22no—
211C2×Dic6—21no—
212C2×Dic6#6714yes—
213C2×Dic6C22×D312yes—
214C2×Dic6C22×D312yes—
215C3×Q16—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#215—68no—
227(C2×D3)⋊C4—64no—
228(C2×D3)⋊C4—64no—
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—28no—
246#204—68no—
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—24no—
260C3×Dic3—22no—
261C3×Dic3—22no—
262C3×Dic3—42no—
263C22×Q8—31no—
264C22×Q8—31no—
265C22×D4—91no—
266C2×Q16—34no—
267C2×Q16—64no—
268C2×SD16—94no—
269C2×SD16—184no—
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×C3C2×D1211yescharacteristic
287C23×C3D3×D411yescharacteristic
288C22×D3—62no—
289C22×D3—62no—
290C22×D3—122no—
291C22×D3—124no—
292C22×D3—122no—
293C22×D3—122no—
294C22×D3—122no—
295C22×D3—122no—
296C22×D3—122no—
297C22×D3—122no—
298C22×D3—242no—
299C22×D3—242no—
300C3×Q8—34no—
301C3×Q8—64no—
302C3×Q8—62no—
303C3×Q8—62no—
304C3×Q8—62no—
305C3×Q8—122no—
306C2×C3×C4—21no—
307C2×C3×C4—22no—
308C2×C3×C4—21no—
309C2×C3×C4—22no—
310C2×C3×C4—32no—
311C2×C3×C4—32no—
312C2×C3×C4—64no—
313C2×C3×C4—62no—
314C2×C3×C4—62no—
315C2×C3×C4—62no—
316C2×C3×C4—62no—
317C2×C3×C4—122no—
318C2×C3×C4C2×D1211yescharacteristic
319C2×C3×C4D3×D411yescharacteristic
320C2×C3×C4D3×D412yes—
321C2×C3×C4#23712yes—
322C2×C3×C4#23912yes—
323C2×C3×C4C2×#6712yes—
324C2×C3×C4C23×D311yescharacteristic
325C2×C3×C4C23×D311yescharacteristic
326C2×Dic3—22no—
327C2×Dic3—22no—
328C2×Dic3—24no—
329C2×Dic3—22no—
330C2×Dic3—22no—
331C2×Dic3—42no—
332C2×Dic3—62no—
333C2×Dic3—62no—
334C2×Dic3—122no—
335C2×Dic3—122no—
336C2×Dic3—122no—
337C2×Dic3—242no—
338C2×Dic3C2×D1212yes—
339C2×Dic3C2×D1212yes—
340D12—64no—
341D12—62no—
342D12—62no—
343D12—62no—
344D12—62no—
345D12—122no—
346D12—124no—
347D12—122no—
348D12—122no—
349Dic6—24no—
350Dic6—22no—
351Dic6—22no—
352Dic6—22no—
353Dic6—42no—
354Dic6C2×#6714yes—
355C3×C8—22no—
356C3×C8—22no—
357C3×C8—42no—
358C3×C8—62no—
359C3⋊C8—22no—
360C2×C32#46414yescomplemented
361C2×C32C2×#12111yescharacteristic
362C2×C32C2×#13511yescharacteristic
363C2×C32C2×#13711yescharacteristic
364C3⋊D3—82no—
365C24—181no—
366C2×Q8—32no—
367C2×Q8—32no—
368C2×Q8—34no—
369C2×Q8—62no—
370C2×Q8—61no—
371C2×Q8—61no—
372C2×Q8—62no—
373C2×Q8—62no—
374C2×D4—92no—
375C2×D4—182no—
376C2×D4—181no—
377C2×D4—182no—
378C22×C4—31no—
379C22×C4—31no—
380C22×C4—61no—
381C22×C4—61no—
382C22×C4—181no—
383C22×C4C2×D3211yescharacteristic
384Q16—68no—
385SD16—188no—
386C2×C8—22no—
387C2×C8—32no—
388C2×C8—62no—
389C2×C8C2×D3212yes—
390C4⋊C4—92no—
391C4⋊C4—184no—
392C4⋊C4—181no—
393C22⋊C4—184no—
394C22⋊C4—184no—
395C42—32no—
396C42—32no—
397C42—184no—
398C22×C3—21no—
399C22×C3—22no—
400C22×C3—22no—
401C22×C3—22no—
402C22×C3#89512yes—
403C22×C3#90412yes—
404C22×C3#90912yes—
405C22×C3#91812yes—
406C22×C3#91912yes—
407C22×C3#93912yes—
408C22×C3C22×D1211yescharacteristic
409C22×C3C2×D3×D411yescharacteristic
410C2×D3—124no—
411C2×D3—122no—
412C2×D3—122no—
413C2×D3—122no—
414C2×D3—122no—
415C2×D3—122no—
416C2×D3—122no—
417C2×D3—242no—
418C2×D3—242no—
419C2×D3—248no—
420C2×D3—244no—
421C2×D3—244no—
422C3×C4—21no—
423C3×C4—21no—
424C3×C4—22no—
425C3×C4—64no—
426C3×C4—62no—
427C3×C4—62no—
428C3×C4—122no—
429C3×C4#89512yes—
430C3×C4#93912yes—
431C3×C4C2×D3×D411yescharacteristic
432C3×C4C2×#23711yescharacteristic
433C3×C4C2×#23911yescharacteristic
434C3×C4C22×#6711yescharacteristic
435Dic3—22no—
436Dic3—22no—
437Dic3—24no—
438Dic3—42no—
439Dic3—122no—
440Dic3—122no—
441Dic3—242no—
442C32C2×#46411yescharacteristic, complemented, Sylow
443C23—182no—
444C23—362no—
445C23—362no—
446C23—362no—
447C23D3×D1211yescharacteristic
448Q8—34no—
449Q8—62no—
450Q8—64no—
451Q8—62no—
452Q8—62no—
453Q8—122no—
454D4—182no—
455D4—182no—
456D4—362no—
457C2×C4—32no—
458C2×C4—32no—
459C2×C4—62no—
460C2×C4—62no—
461C2×C4—62no—
462C2×C4—64no—
463C2×C4—62no—
464C2×C4—122no—
465C2×C4—182no—
466C2×C4—362no—
467C2×C4#379612yes—
468C2×C4D3×D1211yescharacteristic
469C2×C4D3×#6712yes—
470C2×C4C22×D3211yescharacteristic
471C8—22no—
472C8—62no—
473C2×C3—21no—
474C2×C3—24no—
475C2×C3—21no—
476C2×C3—21no—
477C2×C3#484514yescomplemented
478C2×C3#518514yescomplemented
479C2×C3C2×#89511yescharacteristic
480C2×C3C2×#90411yescharacteristic
481C2×C3C2×#90911yescharacteristic
482C2×C3C2×#91811yescharacteristic
483C2×C3C2×#91911yescharacteristic
484C2×C3C2×#93911yescharacteristic
485D3—244no—
486D3—242no—
487D3—242no—
488C22—362no—
489C22—362no—
490C22—362no—
491C22—724no—
492C22#6380112yes—
493C22#6380812yes—
494C22#6388612yes—
495C22C2×D3×D1211yescharacteristic
496C4—64no—
497C4—62no—
498C4—62no—
499C4—122no—
500C4—362no—
501C4#6388612yes—
502C4C2×#379611yescharacteristic
503C4C2×D3×#6711yescharacteristic
504C3—21no—
505C3C2×#484511yescharacteristic, complemented
506C3C2×#518511yescharacteristic, complemented
507C2—722no—
508C2#1059080114yesdirect product factor
509C2C2×#6380111yescharacteristic
510C2C2×#6380811yescharacteristic
511C2C2×#6388611yescharacteristic
subgroupG/H
centerC23D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC22×C4⋊(C3⋊D3)C22
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
1. C22×C3×Dic12C2semidirect
3. C2×Dic3×Dic6C2semidirect
6. C2×C3×Dic3⋊C8C2semidirect
7. C2×#63566C2semidirect
8. #10590801C2direct (N × H)
19. C2×C3×Dic12C22semidirect
27. Dic3×Dic6C22semidirect
31. C3×Dic3⋊C8C22semidirect
32. #63566C22semidirect
37. C22×Dic12D3semidirect
48. C2×Dic3⋊C8D3semidirect
118. C2×Dic12C2×D3semidirect
131. Dic3⋊C8C2×D3semidirect
360. C2×C32#464semidirect
442. C32C2×#464semidirect
477. C2×C3#4845semidirect
478. C2×C3#5185semidirect
505. C3C2×#4845semidirect
506. C3C2×#5185semidirect
508. C2#10590801direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×Dic122
C2×#638642
C2×Dic3×Dic62
C22×#37172
C2×#636482
C2×C3×Dic3⋊C82
C2×#635662
#105908012
C2×#51853
C2×#48453