Finite Group Databasebeta

← C2×#10590368 #11865699

Subgroups — C2×#10590368 #11865699

Order 1152.

1165 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64084C211yesmaximal, characteristic
2C2×C3×C4×Dic6C211yesmaximal, characteristic, complemented
3C22×#3719C211yesmaximal, characteristic, complemented
4C22×#3717C211yesmaximal, characteristic
5C2×C3×C4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
6C2×#63567C211yesmaximal, characteristic, complemented
7C2×#63564C211yesmaximal, characteristic
8#10590368C218yesmaximal, direct product factor
9C2×#5028—31nomaximal
10C2×#4845—31nomaximal
11C22×C4⋊(C3⋊D3)C2211yescharacteristic
12C22×#634C2211yescharacteristic
13C22×C3×Dic6C2211yescharacteristic
14C2×C32×C42C2211yescharacteristic
15C2×#3752—21no—
16C2×#3752—21no—
17#64084—22no—
18#64084C2214yes—
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C2×C3×Dic3⋊C4—21no—
21C2×C3×C4×Dic3—21no—
22C22×C3×C3⋊C8C2211yescharacteristic
23C22×C3×C3⋊C8C2211yescharacteristic
24C3×C4×Dic6—22no—
25C3×C4×Dic6C2214yescomplemented
26C2×#3719—24no—
27C2×#3719C2214yescomplemented
28C2×#3717—24no—
29C2×#3717C2214yes—
30C3×C4⋊(C3⋊C8)C2214yescomplemented
31#63567C2214yescomplemented
32#63564C2214yes—
33C2×C3×C4×Q8—31no—
34C22×#216—31no—
35C22×#215—31no—
36C22×Dic12—31no—
37C22×#204—31no—
38C2×#875—31no—
39C2×#875—31no—
40C2×#875—61no—
41C2×C4×Dic6D311yescharacteristic, complemented
42C2×C3×C4⋊C8—31no—
43C2×#821—31no—
44C2×#816—31no—
45#5028—38no—
46C2×#810—31no—
47C2×#809—31no—
48C2×C4⋊(C3⋊C8)D311yescharacteristic, complemented
49#4845—38no—
50C23×C3⋊D3—21no—
51C22×C32×C4D411yescharacteristic
52C22×C32×C4D411yescharacteristic
53C22×C32×C4C2311yescharacteristic
54C22×C3⋊Dic3—21no—
55C2×C4⋊(C3⋊D3)—22no—
56C2×C4⋊(C3⋊D3)—22no—
57C2×C4⋊(C3⋊D3)—21no—
58C2×C4⋊(C3⋊D3)C2312yes—
59C2×#634—22no—
60C2×#634—22no—
61C2×#634—21no—
62C2×#634C2312yes—
63C22×C3×Dic3—21no—
64C22×C3×Dic3—21no—
65C2×C3×Dic6—21no—
66C2×C3×Dic6—22no—
67C2×C3×Dic6D414yes—
68C2×C3×Dic6C2312yes—
69C32×C42D412yes—
70C32×C42C2312yes—
71#3752—24no—
72#3752—24no—
73C3×C4⋊Dic3—21no—
74C3×C4⋊Dic3C2312yes—
75C3×Dic3⋊C4—24no—
76C3×C4×Dic3—24no—
77C2×C3×C3⋊C8—22no—
78C2×C3×C3⋊C8—22no—
79C2×C3×C3⋊C8C2312yes—
80C2×C3×C3⋊C8C2312yes—
81#3719—28no—
82#3717—28no—
83C2×#464—91noSylow
84C22×C3×Q8—31no—
85C22×D12—31no—
86C22×D12—31no—
87C22×D12—61no—
88C22×Dic6—31no—
89C22×Dic6—31no—
90C22×Dic6—61no—
91C22×Dic6C2×D311yescharacteristic
92C22×C3×C8—31no—
93C22×C3×C8—31no—
94C3×C4×Q8—34no—
95C3×C4×Q8—62no—
96C2×C3×C4⋊C4—31no—
97C2×C3×C4⋊C4—61no—
98C2×C3×C42—21no—
99C2×C3×C42—61no—
100C2×C3×C42C2×D311yescharacteristic
101C2×C3×C42C2×D311yescharacteristic
102C2×#216—34no—
103C2×#216—64no—
104C2×#215—34no—
105C2×#215—64no—
106C2×(C2×D3)⋊C4—62no—
107C2×(C2×D3)⋊C4—62no—
108C2×(C2×D3)⋊C4—61no—
109C2×(C2×D3)⋊C4—61no—
110C2×(C2×D3)⋊C4—61no—
111C2×(C2×D3)⋊C4—61no—
112C2×C4⋊Dic3C2×D311yescharacteristic
113C2×Dic3⋊C4—21no—
114C2×C4×Dic3—21no—
115C22×C3⋊C8C2×D311yescharacteristic
116C22×C3⋊C8C2×D311yescharacteristic
117C2×Dic12—34no—
118C2×Dic12—64no—
119C2×#204—34no—
120C2×#204—64no—
121#875—34no—
122#875—34no—
123#875—64no—
124#875—64no—
125#875—62no—
126#875—62no—
127C4×Dic6—22no—
128C4×Dic6C2×D314yescomplemented
129C3×C4⋊C8—34no—
130#821—34no—
131#816—34no—
132#810—34no—
133#809—34no—
134C4⋊(C3⋊C8)C2×D314yescomplemented
135C23×C32C2×D411yescharacteristic
136C22×C3⋊D3—22no—
137C22×C3⋊D3—42no—
138C22×C3⋊D3—42no—
139C22×C3⋊D3—42no—
140C2×C32×C4—22no—
141C2×C32×C4—22no—
142C2×C32×C4C2×D412yes—
143C2×C32×C4C2×D412yes—
144C2×C32×C4C2×D412yes—
145C2×C32×C4C2×D411yescharacteristic
146C2×C32×C4#4112yes—
147C2×C32×C4C2411yescharacteristic
148C2×C3⋊Dic3—22no—
149C2×C3⋊Dic3—42no—
150C4⋊(C3⋊D3)—22no—
151C4⋊(C3⋊D3)—22no—
152C4⋊(C3⋊D3)—42no—
153#634—22no—
154#634—22no—
155#634—42no—
156C2×C3×Dic3—24no—
157C2×C3×Dic3—22no—
158C2×C3×Dic3—22no—
159C2×C3×Dic3—42no—
160C3×Dic6—24no—
161C3×Dic6—22no—
162C3×Dic6C2×D414yes—
163C3×C3⋊C8—22no—
164C3×C3⋊C8—22no—
165C22×Q16—91no—
166C22×SD16—91no—
167C2×#124—91no—
168C2×C4×Q8—31no—
169#464—98no—
170C2×C4⋊C8—31no—
171C2×#103—91no—
172C2×#102—91no—
173C23×D3—62no—
174C23×D3—61no—
175C23×D3—61no—
176C2×C3×Q8—34no—
177C2×C3×Q8—32no—
178C2×C3×Q8—61no—
179C2×C3×Q8—62no—
180C22×C3×C4—21no—
181C22×C3×C4—21no—
182C22×C3×C4—21no—
183C22×C3×C4—61no—
184C22×C3×C4—61no—
185C22×C3×C4D1211yescharacteristic
186C22×C3×C4D1211yescharacteristic
187C22×C3×C4#6711yescharacteristic
188C22×C3×C4#6711yescharacteristic
189C22×C3×C4C22×D311yescharacteristic
190C22×C3×C4C22×D311yescharacteristic
191C22×Dic3—21no—
192C22×Dic3—21no—
193C22×Dic3—62no—
194C22×Dic3—61no—
195C22×Dic3—61no—
196C2×D12—32no—
197C2×D12—32no—
198C2×D12—62no—
199C2×D12—62no—
200C2×D12—62no—
201C2×D12—62no—
202C2×D12—62no—
203C2×D12—62no—
204C2×D12—61no—
205C2×D12—61no—
206C2×D12—122no—
207C2×D12—122no—
208C2×Dic6—22no—
209C2×Dic6—21no—
210C2×Dic6—32no—
211C2×Dic6—32no—
212C2×Dic6—62no—
213C2×Dic6—62no—
214C2×Dic6—62no—
215C2×Dic6—62no—
216C2×Dic6—62no—
217C2×Dic6—62no—
218C2×Dic6—61no—
219C2×Dic6—61no—
220C2×Dic6—122no—
221C2×Dic6—122no—
222C2×Dic6D1214yes—
223C2×Dic6C22×D312yes—
224C2×C3×C8—32no—
225C2×C3×C8—32no—
226C2×C3×C8—62no—
227C2×C3×C8—62no—
228C3×C4⋊C4—32no—
229C3×C4⋊C4—64no—
230C3×C4⋊C4—61no—
231C3×C42—22no—
232C3×C42—22no—
233C3×C42—64no—
234C3×C42D1212yes—
235C3×C42#6712yes—
236C3×C42C22×D312yes—
237C3×C42C22×D312yes—
238#216—68no—
239#215—68no—
240(C2×D3)⋊C4—68no—
241(C2×D3)⋊C4—68no—
242(C2×D3)⋊C4—64no—
243(C2×D3)⋊C4—64no—
244(C2×D3)⋊C4—64no—
245(C2×D3)⋊C4—64no—
246C4⋊Dic3—21no—
247C4⋊Dic3C22×D312yes—
248Dic3⋊C4—24no—
249C4×Dic3—24no—
250C2×C3⋊C8—22no—
251C2×C3⋊C8—22no—
252C2×C3⋊C8C22×D312yes—
253C2×C3⋊C8C22×D312yes—
254Dic12—68no—
255#204—68no—
256C22×C32#12112yes—
257C22×C32#13512yes—
258C22×C32#13712yes—
259C22×C32C22×D411yescharacteristic
260C2×C3⋊D3—42no—
261C2×C3⋊D3—42no—
262C2×C3⋊D3—42no—
263C2×C3⋊D3—84no—
264C32×C4—22no—
265C32×C4—22no—
266C32×C4#12112yes—
267C32×C4C22×D411yescharacteristic
268C32×C4C2×#4111yescharacteristic
269C3⋊Dic3—42no—
270C3×Dic3—24no—
271C3×Dic3—42no—
272C22×Q8—31no—
273C22×Q8—91no—
274C22×D4—91no—
275C2×Q16—94no—
276C2×Q16—184no—
277C2×SD16—94no—
278C2×SD16—184no—
279C22×C8—31no—
280C22×C8—31no—
281#124—94no—
282#124—182no—
283C4×Q8—34no—
284C4×Q8—62no—
285C2×C4⋊C4—31no—
286C2×C4⋊C4—61no—
287C2×C22⋊C4—181no—
288C2×C22⋊C4—181no—
289C2×C42—61no—
290C2×C42D3211yescharacteristic
291C4⋊C8—34no—
292#103—94no—
293#102—94no—
294C23×C3—21no—
295C23×C3C2×D1211yescharacteristic
296C23×C3C2×#6711yescharacteristic
297C22×D3—64no—
298C22×D3—62no—
299C22×D3—62no—
300C22×D3—124no—
301C22×D3—124no—
302C22×D3—124no—
303C22×D3—122no—
304C22×D3—122no—
305C22×D3—122no—
306C22×D3—122no—
307C22×D3—122no—
308C22×D3—122no—
309C3×Q8—34no—
310C3×Q8—64no—
311C3×Q8—62no—
312C2×C3×C4—22no—
313C2×C3×C4—22no—
314C2×C3×C4—22no—
315C2×C3×C4—22no—
316C2×C3×C4—21no—
317C2×C3×C4—22no—
318C2×C3×C4—22no—
319C2×C3×C4—21no—
320C2×C3×C4—22no—
321C2×C3×C4—22no—
322C2×C3×C4—42no—
323C2×C3×C4—42no—
324C2×C3×C4—64no—
325C2×C3×C4—62no—
326C2×C3×C4—62no—
327C2×C3×C4—122no—
328C2×C3×C4C2×D1212yes—
329C2×C3×C4C2×D1212yes—
330C2×C3×C4C2×D1212yes—
331C2×C3×C4C2×D1211yescharacteristic
332C2×C3×C4#23512yes—
333C2×C3×C4D3×D412yes—
334C2×C3×C4#23912yes—
335C2×C3×C4C2×#6712yes—
336C2×C3×C4C2×#6712yes—
337C2×C3×C4C2×#6711yescharacteristic
338C2×C3×C4C23×D311yescharacteristic
339C2×C3×C4C23×D311yescharacteristic
340C2×Dic3—24no—
341C2×Dic3—22no—
342C2×Dic3—22no—
343C2×Dic3—42no—
344C2×Dic3—64no—
345C2×Dic3—62no—
346C2×Dic3—62no—
347C2×Dic3—124no—
348C2×Dic3—122no—
349C2×Dic3—122no—
350D12—62no—
351D12—62no—
352D12—62no—
353D12—62no—
354D12—122no—
355D12—122no—
356D12—124no—
357D12—122no—
358D12—122no—
359Dic6—24no—
360Dic6—22no—
361Dic6—62no—
362Dic6—62no—
363Dic6—62no—
364Dic6—62no—
365Dic6—122no—
366Dic6—122no—
367Dic6—124no—
368Dic6—122no—
369Dic6—122no—
370Dic6C2×D1214yes—
371C3×C8—62no—
372C3×C8—62no—
373C3⋊C8—22no—
374C3⋊C8—22no—
375C2×C32#46414yescomplemented
376C2×C32C2×#12111yescharacteristic
377C2×C32C2×#13511yescharacteristic
378C2×C32C2×#13711yescharacteristic
379C3⋊D3—82no—
380C24—181no—
381C2×Q8—32no—
382C2×Q8—34no—
383C2×Q8—62no—
384C2×Q8—61no—
385C2×Q8—92no—
386C2×Q8—181no—
387C2×Q8—182no—
388C2×Q8—182no—
389C2×D4—92no—
390C2×D4—182no—
391C2×D4—182no—
392C2×D4—181no—
393C22×C4—61no—
394C22×C4—61no—
395C22×C4—181no—
396C22×C4#62611yescharacteristic
397C22×C4#62611yescharacteristic
398C22×C4C2×D3211yescharacteristic
399Q16—188no—
400SD16—188no—
401C2×C8—32no—
402C2×C8—32no—
403C2×C8—62no—
404C2×C8—62no—
405C4⋊C4—32no—
406C4⋊C4—61no—
407C4⋊C4—64no—
408C22⋊C4—184no—
409C22⋊C4—184no—
410C42—64no—
411C42#62612yes—
412C42C2×D3212yes—
413C22×C3—21no—
414C22×C3—22no—
415C22×C3—22no—
416C22×C3—22no—
417C22×C3#89512yes—
418C22×C3#90412yes—
419C22×C3#90912yes—
420C22×C3#93012yes—
421C22×C3#94212yes—
422C22×C3#95012yes—
423C22×C3C22×D1211yescharacteristic
424C22×C3C22×#6711yescharacteristic
425C2×D3—124no—
426C2×D3—124no—
427C2×D3—124no—
428C2×D3—122no—
429C2×D3—122no—
430C2×D3—122no—
431C2×D3—122no—
432C2×D3—122no—
433C2×D3—122no—
434C2×D3—248no—
435C2×D3—244no—
436C2×D3—244no—
437C3×C4—22no—
438C3×C4—22no—
439C3×C4—22no—
440C3×C4—22no—
441C3×C4—21no—
442C3×C4—21no—
443C3×C4—22no—
444C3×C4—42no—
445C3×C4—42no—
446C3×C4—64no—
447C3×C4—122no—
448C3×C4#89512yes—
449C3×C4#93012yes—
450C3×C4C22×D1211yescharacteristic
451C3×C4C2×#23511yescharacteristic
452C3×C4C2×D3×D411yescharacteristic
453C3×C4C2×#23911yescharacteristic
454Dic3—24no—
455Dic3—42no—
456Dic3—124no—
457Dic3—122no—
458Dic3—122no—
459C32C2×#46411yescharacteristic, complemented, Sylow
460C23—182no—
461C23—362no—
462C23—362no—
463C23—362no—
464C23C2×#62611yescharacteristic
465Q8—34no—
466Q8—62no—
467Q8—64no—
468Q8—182no—
469Q8—182no—
470Q8—362no—
471D4—182no—
472D4—182no—
473D4—362no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—62no—
477C2×C4—64no—
478C2×C4—62no—
479C2×C4—122no—
480C2×C4—182no—
481C2×C4—362no—
482C2×C4#379912yes—
483C2×C4D3×D1212yes—
484C2×C4C2×#62612yes—
485C2×C4C2×#62612yes—
486C2×C4C2×#62611yescharacteristic
487C2×C4C22×D3211yescharacteristic
488C8—62no—
489C8—62no—
490C2×C3—24no—
491C2×C3—21no—
492C2×C3—21no—
493C2×C3—21no—
494C2×C3#484514yescomplemented
495C2×C3#502814yescomplemented
496C2×C3C2×#89511yescharacteristic
497C2×C3C2×#90411yescharacteristic
498C2×C3C2×#90911yescharacteristic
499C2×C3C2×#93011yescharacteristic
500C2×C3C2×#94211yescharacteristic
501C2×C3C2×#95011yescharacteristic
502D3—244no—
503D3—242no—
504D3—242no—
505C22—362no—
506C22—362no—
507C22—362no—
508C22—724no—
509C22#6382912yes—
510C22#6383312yes—
511C22#6390912yes—
512C22C22×#62611yescharacteristic
513C4—22no—
514C4—22no—
515C4—64no—
516C4—122no—
517C4—362no—
518C4#6390912yes—
519C4C2×#379911yescharacteristic
520C4C2×D3×D1211yescharacteristic
521C3—21no—
522C3C2×#484511yescharacteristic, complemented
523C3C2×#502811yescharacteristic, complemented
524C2—722no—
525C2#1059036814yesdirect product factor
526C2C2×#6382911yescharacteristic
527C2C2×#6383311yescharacteristic
528C2C2×#6390911yescharacteristic
subgroupG/H
centerC23C2×#626
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C42C22
socleC23×C32C2×D4
prime radicalC22×C4⋊(C3⋊D3)C22
hypercenterC2×C42D32
hypocenterC32C2×#464
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C2×C3×C4×Dic6C2semidirect
3. C22×#3719C2semidirect
5. C2×C3×C4⋊(C3⋊C8)C2semidirect
6. C2×#63567C2semidirect
8. #10590368C2direct (N × H)
25. C3×C4×Dic6C22semidirect
27. C2×#3719C22semidirect
30. C3×C4⋊(C3⋊C8)C22semidirect
31. #63567C22semidirect
41. C2×C4×Dic6D3semidirect
48. C2×C4⋊(C3⋊C8)D3semidirect
128. C4×Dic6C2×D3semidirect
134. C4⋊(C3⋊C8)C2×D3semidirect
375. C2×C32#464semidirect
459. C32C2×#464semidirect
494. C2×C3#4845semidirect
495. C2×C3#5028semidirect
522. C3C2×#4845semidirect
523. C3C2×#5028semidirect
525. C2#10590368direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640842
C2×C3×C4×Dic62
C22×#37192
C22×#37172
C2×C3×C4⋊(C3⋊C8)2
C2×#635672
C2×#635642
#105903682
C2×#50283
C2×#48453