Finite Group Databasebeta

← C2×#10590501 #11866710

Subgroups — C2×#10590501 #11866710

Order 1152.

1193 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#897C211yesmaximal, characteristic, complemented
2C2×#63908C211yesmaximal, characteristic
3C22×#3715C211yesmaximal, characteristic, complemented
4C22×D3×C3⋊C8C211yesmaximal, characteristic, complemented
5C2×#63635C211yesmaximal, characteristic, complemented
6C2×C3×#809C211yesmaximal, characteristic, complemented
7C2×#63566C211yesmaximal, characteristic, complemented
8#10590501C218yesmaximal, direct product factor
9C2×#5048—31nomaximal
10C2×#4778—31nomaximal
11C22×C3×D12C2211yescharacteristic
12C22×C3×C4×D3C2211yescharacteristic
13C22×C3×Dic6C2211yescharacteristic
14C22×#625—21no—
15C2×C32×C4⋊C4C2211yescharacteristic
16C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
17C22×C3⋊(C3⋊C8)C2211yescharacteristic
18C2×C3×(C2×D3)⋊C4—21no—
19C2×C3×C4⋊Dic3—21no—
20C22×C3×C3⋊C8C2211yescharacteristic
21C3×#897—22no—
22C3×#897C2214yescomplemented
23C2×(C2×D3)⋊Dic3—21no—
24#63908—22no—
25#63908C2214yes—
26C2×#3715—24no—
27C2×#3715C2214yescomplemented
28C2×D3×C3⋊C8—24no—
29C2×D3×C3⋊C8C2214yescomplemented
30#63635C2214yescomplemented
31C3×#809C2214yescomplemented
32#63566C2214yescomplemented
33C2×C3×C22⋊Q8—31no—
34C22×#215—31no—
35C2×#938—31no—
36C22×#214—31no—
37C2×#930—31no—
38C23×C3⋊C8—31no—
39C22×D3×C8—31no—
40C2×#897D311yescharacteristic, complemented
41C2×C3×#102—31no—
42C2×#835—31no—
43C2×#816—31no—
44#5048—38no—
45C2×#809D311yescharacteristic, complemented
46C2×#808—31no—
47C2×#808—31no—
48C2×#808—61no—
49#4778—38no—
50C23×C3×D3—21no—
51C23×C3×D3D411yescharacteristic
52C22×C32×C4—21no—
53C22×C32×C4C2311yescharacteristic
54C22×C3⋊Dic3—21no—
55C22×C3×Dic3—21no—
56C22×C3×Dic3D411yescharacteristic
57C2×C3×D12—22no—
58C2×C3×D12—22no—
59C2×C3×D12—21no—
60C2×C3×D12C2312yes—
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—
69C2×#625—24no—
70C2×#625—44no—
71C32×C4⋊C4—21no—
72C32×C4⋊C4C2312yes—
73C4⋊(C3⋊Dic3)—21no—
74C4⋊(C3⋊Dic3)C2312yes—
75C2×C3⋊(C3⋊C8)D414yescomplemented
76C2×C3⋊(C3⋊C8)C2312yes—
77C3×(C2×D3)⋊C4—24no—
78C3×C4⋊Dic3—24no—
79C2×C3×C3⋊C8—22no—
80C2×C3×C3⋊C8C2312yes—
81(C2×D3)⋊Dic3—24no—
82#3715—28no—
83D3×C3⋊C8—28no—
84C2×#465—91noSylow
85C22×C3×Q8—31no—
86C22×C3×D4—31no—
87C23×C3×C4—31no—
88C22×#67—61no—
89C22×#67—61no—
90C22×D12C2×D311yescharacteristic
91C22×C4×D3C2×D311yescharacteristic
92C22×Dic6C2×D311yescharacteristic
93C22×C3×C8—31no—
94C3×C22⋊Q8—34no—
95C3×C22⋊Q8—62no—
96C2×C3×C4⋊C4—21no—
97C2×C3×C4⋊C4—61no—
98C2×C3×C4⋊C4C2×D311yescharacteristic
99C2×C3×C4⋊C4C2×D311yescharacteristic
100C2×C3×C22⋊C4—61no—
101C2×#217—61no—
102C2×#215—34no—
103C2×#215—64no—
104#938—34no—
105#938—62no—
106C2×#214—34no—
107C2×#214—64no—
108#930—34no—
109#930—62no—
110C2×(C2×D3)⋊C4—21no—
111C2×(C2×D3)⋊C4—61no—
112C2×C4⋊Dic3—21no—
113C2×C4⋊Dic3—31no—
114C2×C4⋊Dic3—31no—
115C2×C4⋊Dic3—61no—
116C22×C3⋊C8—31no—
117C22×C3⋊C8—31no—
118C22×C3⋊C8—34no—
119C22×C3⋊C8—61no—
120C22×C3⋊C8—64no—
121C22×C3⋊C8C2×D311yescharacteristic
122C2×D3×C8—34no—
123C2×D3×C8—64no—
124#897—22no—
125#897C2×D314yescomplemented
126C3×#102—34no—
127#835—34no—
128#816—34no—
129#809C2×D314yescomplemented
130#808—34no—
131#808—34no—
132#808—64no—
133C23×C32C2×D411yescharacteristic
134C22×C3×D3—22no—
135C22×C3×D3—22no—
136C22×C3×D3—22no—
137C22×C3×D3—42no—
138C22×C3×D3—42no—
139C22×C3×D3—42no—
140C22×C3×D3SD1614yescomplemented
141C22×C3×D3C2×D412yes—
142C2×C32×C4—22no—
143C2×C32×C4—42no—
144C2×C32×C4C2×D412yes—
145C2×C32×C4C2×D411yescharacteristic
146C2×C32×C4#4112yes—
147C2×C32×C4C2411yescharacteristic
148C2×C3⋊Dic3—22no—
149C2×C3⋊Dic3—42no—
150C2×C3×Dic3—22no—
151C2×C3×Dic3—22no—
152C2×C3×Dic3—42no—
153C2×C3×Dic3C2×D412yes—
154C3×D12—22no—
155C3×D12—22no—
156C3×D12—42no—
157C3×C4×D3—24no—
158C3×C4×D3—22no—
159C3×C4×D3—22no—
160C3×Dic6—22no—
161C3×Dic6—22no—
162C3×Dic6—42no—
163#625—48no—
164C3⋊(C3⋊C8)C2×D414yescomplemented
165C3×C3⋊C8—22no—
166C22×SD16—91no—
167C23×C8—91no—
168C2×C22⋊Q8—31no—
169C2×#121—91no—
170#465—98no—
171C2×#106—91no—
172C2×#103—91no—
173C2×#102—31no—
174C24×C3—31no—
175C24×C3—61no—
176C23×D3—21no—
177C23×D3#6711yescharacteristic
178C2×C3×Q8—32no—
179C2×C3×Q8—61no—
180C2×C3×Q8—62no—
181C2×C3×Q8—62no—
182C2×C3×D4—32no—
183C2×C3×D4—62no—
184C2×C3×D4—62no—
185C2×C3×D4—61no—
186C22×C3×C4—21no—
187C22×C3×C4—21no—
188C22×C3×C4—21no—
189C22×C3×C4—31no—
190C22×C3×C4—32no—
191C22×C3×C4—32no—
192C22×C3×C4—41no—
193C22×C3×C4—62no—
194C22×C3×C4—62no—
195C22×C3×C4—61no—
196C22×C3×C4C22×D311yescharacteristic
197C22×C3×C4C22×D311yescharacteristic
198C2×#67—64no—
199C2×#67—64no—
200C2×#67—124no—
201C2×#67—124no—
202C22×Dic3—21no—
203C22×Dic3—61no—
204C22×Dic3—61no—
205C22×Dic3—121no—
206C22×Dic3#6711yescharacteristic
207C2×D12—22no—
208C2×D12—22no—
209C2×D12—21no—
210C2×D12C22×D312yes—
211C2×C4×D3—22no—
212C2×C4×D3—22no—
213C2×C4×D3#6712yes—
214C2×C4×D3C22×D312yes—
215C2×Dic6—22no—
216C2×Dic6—22no—
217C2×Dic6—21no—
218C2×Dic6C22×D312yes—
219C2×C3×C8—32no—
220C2×C3×C8—62no—
221C3×C4⋊C4—21no—
222C3×C4⋊C4—21no—
223C3×C4⋊C4—22no—
224C3×C4⋊C4—41no—
225C3×C4⋊C4—64no—
226C3×C4⋊C4C22×D312yes—
227C3×C4⋊C4C22×D312yes—
228C3×C22⋊C4—64no—
229#217—64no—
230#215—68no—
231#214—68no—
232(C2×D3)⋊C4—24no—
233(C2×D3)⋊C4—64no—
234C4⋊Dic3—24no—
235C4⋊Dic3—32no—
236C4⋊Dic3—32no—
237C4⋊Dic3—62no—
238C4⋊Dic3—61no—
239C4⋊Dic3—61no—
240C4⋊Dic3—121no—
241C2×C3⋊C8—22no—
242C2×C3⋊C8—34no—
243C2×C3⋊C8—34no—
244C2×C3⋊C8—32no—
245C2×C3⋊C8—32no—
246C2×C3⋊C8—62no—
247C2×C3⋊C8—64no—
248C2×C3⋊C8—68no—
249C2×C3⋊C8C22×D312yes—
250D3×C8—68no—
251C22×C32#12112yes—
252C22×C32C2×SD1612yes—
253C22×C32#13512yes—
254C22×C32C22×D411yescharacteristic
255C2×C3×D3—22no—
256C2×C3×D3—22no—
257C2×C3×D3—28no—
258C2×C3×D3—42no—
259C2×C3×D3—42no—
260C2×C3×D3—42no—
261C2×C3×D3—84no—
262C2×C3×D3C2×SD1614yescomplemented
263C32×C4—42no—
264C32×C4#12112yes—
265C32×C4C22×D411yescharacteristic
266C32×C4C2×#4111yescharacteristic
267C3⋊Dic3—42no—
268C3×Dic3—22no—
269C3×Dic3—42no—
270C22×Q8—31no—
271C22×D4—31no—
272C22×D4—181no—
273C23×C4—31no—
274C2×SD16—94no—
275C2×SD16—184no—
276C22×C8—31no—
277C22×C8—94no—
278C22×C8—91no—
279C22×C8—184no—
280C22⋊Q8—34no—
281C22⋊Q8—62no—
282#121—94no—
283#121—182no—
284C2×C4⋊C4—61no—
285C2×C4⋊C4—91no—
286C2×C4⋊C4D3211yescharacteristic
287C2×C22⋊C4—61no—
288C2×C22⋊C4—181no—
289#106—94no—
290#103—94no—
291#102—34no—
292C23×C3—21no—
293C23×C3—34no—
294C23×C3—32no—
295C23×C3—62no—
296C23×C3—62no—
297C23×C3—62no—
298C23×C3—122no—
299C23×C3—122no—
300C23×C3—122no—
301C23×C3D3×D411yescharacteristic
302C23×C3C2×#6711yescharacteristic
303C22×D3—22no—
304C22×D3—22no—
305C22×D3—22no—
306C22×D3—42no—
307C22×D3—42no—
308C22×D3—42no—
309C22×D3#21514yescomplemented
310C22×D3C2×#6712yes—
311C3×Q8—62no—
312C3×Q8—62no—
313C3×Q8—122no—
314C3×D4—62no—
315C3×D4—62no—
316C3×D4—122no—
317C2×C3×C4—22no—
318C2×C3×C4—22no—
319C2×C3×C4—21no—
320C2×C3×C4—22no—
321C2×C3×C4—22no—
322C2×C3×C4—21no—
323C2×C3×C4—32no—
324C2×C3×C4—42no—
325C2×C3×C4—42no—
326C2×C3×C4—42no—
327C2×C3×C4—62no—
328C2×C3×C4—64no—
329C2×C3×C4—62no—
330C2×C3×C4—62no—
331C2×C3×C4—62no—
332C2×C3×C4—82no—
333C2×C3×C4—122no—
334C2×C3×C4#23512yes—
335C2×C3×C4D3×D412yes—
336C2×C3×C4D3×D412yes—
337C2×C3×C4D3×D411yescharacteristic
338C2×C3×C4#23712yes—
339C2×C3×C4C2×#6711yescharacteristic
340C2×C3×C4C23×D311yescharacteristic
341C2×C3×C4C23×D311yescharacteristic
342#67—128no—
343#67—128no—
344C2×Dic3—22no—
345C2×Dic3—22no—
346C2×Dic3—42no—
347C2×Dic3—62no—
348C2×Dic3—62no—
349C2×Dic3—122no—
350C2×Dic3—122no—
351C2×Dic3—122no—
352C2×Dic3—242no—
353C2×Dic3C2×#6712yes—
354D12—22no—
355D12—22no—
356D12—42no—
357C4×D3—24no—
358C4×D3—22no—
359C4×D3—22no—
360Dic6—22no—
361Dic6—22no—
362Dic6—42no—
363C3×C8—62no—
364C3⋊C8—22no—
365C3⋊C8—34no—
366C3⋊C8—34no—
367C3⋊C8—64no—
368C2×C32#46514yescomplemented
369C2×C32C2×#12111yescharacteristic
370C2×C32C22×SD1611yescharacteristic
371C2×C32C2×#13511yescharacteristic
372C3×D3—24no—
373C3×D3—82no—
374C24—31no—
375C24—61no—
376C2×Q8—32no—
377C2×Q8—61no—
378C2×Q8—62no—
379C2×Q8—62no—
380C2×D4—32no—
381C2×D4—62no—
382C2×D4—62no—
383C2×D4—61no—
384C2×D4—184no—
385C2×D4—364no—
386C22×C4—21no—
387C22×C4—31no—
388C22×C4—32no—
389C22×C4—32no—
390C22×C4—62no—
391C22×C4—62no—
392C22×C4—61no—
393C22×C4—181no—
394C22×C4C2×D3211yescharacteristic
395SD16—188no—
396C2×C8—32no—
397C2×C8—62no—
398C2×C8—92no—
399C2×C8—94no—
400C2×C8—188no—
401C4⋊C4—21no—
402C4⋊C4—64no—
403C4⋊C4—92no—
404C4⋊C4—181no—
405C4⋊C4C2×D3212yes—
406C22⋊C4—64no—
407C22⋊C4—184no—
408C22×C3—21no—
409C22×C3—22no—
410C22×C3—22no—
411C22×C3—22no—
412C22×C3—34no—
413C22×C3—62no—
414C22×C3—62no—
415C22×C3—68no—
416C22×C3—122no—
417C22×C3—122no—
418C22×C3—122no—
419C22×C3—244no—
420C22×C3#88412yes—
421C22×C3#91212yes—
422C22×C3D3×SD1612yes—
423C22×C3#93912yes—
424C22×C3C2×#21512yes—
425C22×C3#95012yes—
426C22×C3C2×D3×D411yescharacteristic
427C22×C3C22×#6711yescharacteristic
428C2×D3—22no—
429C2×D3—28no—
430C2×D3—22no—
431C2×D3—42no—
432C2×D3—42no—
433C2×D3—42no—
434C2×D3—84no—
435C2×D3C2×#21514yescomplemented
436C3×C4—21no—
437C3×C4—21no—
438C3×C4—22no—
439C3×C4—42no—
440C3×C4—42no—
441C3×C4—62no—
442C3×C4—82no—
443C3×C4—122no—
444C3×C4#88412yes—
445C3×C4#93912yes—
446C3×C4C2×#23511yescharacteristic
447C3×C4C2×D3×D411yescharacteristic
448C3×C4C2×D3×D411yescharacteristic
449C3×C4C2×#23711yescharacteristic
450Dic3—22no—
451Dic3—42no—
452Dic3—122no—
453Dic3—122no—
454Dic3—242no—
455C32C2×#46511yescharacteristic, complemented, Sylow
456C23—32no—
457C23—34no—
458C23—62no—
459C23—62no—
460C23—62no—
461C23—122no—
462C23—122no—
463C23—122no—
464C23D3×#6711yescharacteristic
465Q8—62no—
466Q8—62no—
467Q8—122no—
468D4—62no—
469D4—62no—
470D4—122no—
471D4—368no—
472C2×C4—22no—
473C2×C4—32no—
474C2×C4—42no—
475C2×C4—62no—
476C2×C4—62no—
477C2×C4—62no—
478C2×C4—64no—
479C2×C4—62no—
480C2×C4—122no—
481C2×C4—182no—
482C2×C4—362no—
483C2×C4#379512yes—
484C2×C4#380212yes—
485C2×C4D3×#6711yescharacteristic
486C2×C4C22×D3211yescharacteristic
487C8—62no—
488C8—94no—
489C2×C3—24no—
490C2×C3—21no—
491C2×C3—21no—
492C2×C3—21no—
493C2×C3—64no—
494C2×C3—242no—
495C2×C3#477814yescomplemented
496C2×C3#504814yescomplemented
497C2×C3C2×#88411yescharacteristic
498C2×C3C2×#91211yescharacteristic
499C2×C3C2×D3×SD1611yescharacteristic
500C2×C3C2×#93911yescharacteristic
501C2×C3C22×#21511yescharacteristic
502C2×C3C2×#95011yescharacteristic
503D3—24no—
504D3—82no—
505C22—34no—
506C22—68no—
507C22—62no—
508C22—62no—
509C22—122no—
510C22—122no—
511C22—122no—
512C22—244no—
513C22#6388512yes—
514C22#6393312yes—
515C22D3×#21512yes—
516C22C2×D3×#6711yescharacteristic
517C4—42no—
518C4—62no—
519C4—122no—
520C4—362no—
521C4#6388512yes—
522C4C2×#379511yescharacteristic
523C4C2×#380211yescharacteristic
524C3—21no—
525C3C2×#477811yescharacteristic, complemented
526C3C2×#504811yescharacteristic, complemented
527C2—64no—
528C2—242no—
529C2#1059050114yesdirect product factor
530C2C2×#6388511yescharacteristic
531C2C2×#6393311yescharacteristic
532C2C2×D3×#21511yescharacteristic
subgroupG/H
centerC23D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC2×#63908C2
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#465
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×#897C2semidirect
3. C22×#3715C2semidirect
4. C22×D3×C3⋊C8C2semidirect
5. C2×#63635C2semidirect
6. C2×C3×#809C2semidirect
7. C2×#63566C2semidirect
8. #10590501C2direct (N × H)
22. C3×#897C22semidirect
27. C2×#3715C22semidirect
29. C2×D3×C3⋊C8C22semidirect
30. #63635C22semidirect
31. C3×#809C22semidirect
32. #63566C22semidirect
40. C2×#897D3semidirect
45. C2×#809D3semidirect
75. C2×C3⋊(C3⋊C8)D4semidirect
125. #897C2×D3semidirect
129. #809C2×D3semidirect
140. C22×C3×D3SD16semidirect
164. C3⋊(C3⋊C8)C2×D4semidirect
262. C2×C3×D3C2×SD16semidirect
309. C22×D3#215semidirect
368. C2×C32#465semidirect
435. C2×D3C2×#215semidirect
455. C32C2×#465semidirect
495. C2×C3#4778semidirect
496. C2×C3#5048semidirect
525. C3C2×#4778semidirect
526. C3C2×#5048semidirect
529. C2#10590501direct (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×#639082
C22×#37152
C22×D3×C3⋊C82
C2×#636352
C2×C3×#8092
C2×#635662
#105905012
C2×#50483
C2×#47783