Finite Group Databasebeta

← C2×#10590604 #11863676

Subgroups — C2×#10590604 #11863676

Order 1152.

1561 conjugacy classes of subgroups.

The subgroup lattice has 563 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D3×Dic6C211yesmaximal, characteristic
2C2×C3×#897C211yesmaximal, characteristic
3C22×#3719C211yesmaximal, characteristic, complemented
4C22×#3718C211yesmaximal, characteristic, complemented
5C2×#63637C211yesmaximal, characteristic, complemented
6C2×C3×#810C211yesmaximal, characteristic, complemented
7C2×(C2×D3)⋊(C3⋊C8)C211yesmaximal, characteristic
8#10590604C218yesmaximal, direct product factor
9C2×#5050—31nomaximal
10C2×#4809—31nomaximal
11C22×#634C2211yescharacteristic
12C22×C3×C4×D3C2211yescharacteristic
13C22×C3×Dic6C2211yescharacteristic
14C22×C3×Dic6C2211yescharacteristic
15C22×#627—21no—
16C22×D3×Dic3—21no—
17C2×D3×Dic6—24no—
18C2×D3×Dic6—22no—
19C2×D3×Dic6—24no—
20C2×D3×Dic6C2214yes—
21C2×C32×C4⋊C4C2211yescharacteristic
22C22×C3⋊(C3⋊C8)C2211yescharacteristic
23C2×C3×(C2×D3)⋊C4—21no—
24C2×C3×C4⋊Dic3—21no—
25C22×C3×C3⋊C8C2211yescharacteristic
26C3×#897—22no—
27C3×#897C2214yes—
28C2×#3719—24no—
29C2×#3719C2214yescomplemented
30C2×#3718—24no—
31C2×#3718C2214yescomplemented
32#63637C2214yescomplemented
33C3×#810C2214yescomplemented
34(C2×D3)⋊(C3⋊C8)C2214yes—
35C22×D3×Q8—31no—
36C23×Dic6—31no—
37C2×C3×C22⋊Q8—31no—
38C22×#216—31no—
39C22×#216—31no—
40C22×#216—31no—
41C22×Dic12—31no—
42C2×#897D311yescharacteristic
43C2×C3×#103—31no—
44C2×#830—31no—
45C2×(C2×D3)⋊C8—31no—
46#5050—38no—
47C2×#810—31no—
48C2×#810—31no—
49C2×#810—61no—
50C2×#810D311yescharacteristic, complemented
51#4809—38no—
52C23×C3×D3D411yescharacteristic
53C22×C32×C4—21no—
54C22×C32×C4C2311yescharacteristic
55C22×C3⋊Dic3—21no—
56C2×#634—21no—
57C2×#634—22no—
58C2×#634D414yes—
59C2×#634C2312yes—
60C22×C3×Dic3—21no—
61C22×C3×Dic3—21no—
62C22×C3×Dic3D411yescharacteristic
63C2×C3×C4×D3—22no—
64C2×C3×C4×D3—22no—
65C2×C3×C4×D3D412yes—
66C2×C3×C4×D3C2312yes—
67C2×C3×Dic6—21no—
68C2×C3×Dic6—22no—
69C2×C3×Dic6—22no—
70C2×C3×Dic6—22no—
71C2×C3×Dic6—21no—
72C2×C3×Dic6D414yes—
73C2×C3×Dic6C2312yes—
74C2×C3×Dic6C2312yes—
75C2×#627—28no—
76C2×#627—24no—
77C2×D3×Dic3—28no—
78C2×D3×Dic3—24no—
79D3×Dic6—216no—
80D3×Dic6—28no—
81D3×Dic6—28no—
82C32×C4⋊C4—21no—
83C32×C4⋊C4C2312yes—
84C2×C3⋊(C3⋊C8)—22no—
85C2×C3⋊(C3⋊C8)C2312yes—
86C3×(C2×D3)⋊C4—24no—
87C3×C4⋊Dic3—24no—
88C2×C3×C3⋊C8—22no—
89C2×C3×C3⋊C8C2312yes—
90#3719—28no—
91#3718—28no—
92C2×#451—91noSylow
93C22×C3×Q8—31no—
94C22×C3×Q8—31no—
95C23×C3×C4—31no—
96C23×Dic3—61no—
97C2×D3×Q8—34no—
98C2×D3×Q8—64no—
99C2×D3×Q8—64no—
100C2×D3×Q8—62no—
101C22×C4×D3—61no—
102C22×C4×D3C2×D311yescharacteristic
103C22×Dic6—31no—
104C22×Dic6—31no—
105C22×Dic6—34no—
106C22×Dic6—61no—
107C22×Dic6—64no—
108C22×Dic6—62no—
109C22×Dic6—61no—
110C22×Dic6—61no—
111C22×Dic6—64no—
112C22×Dic6C2×D311yescharacteristic
113C22×Dic6C2×D311yescharacteristic
114C22×C3×C8—31no—
115C3×C22⋊Q8—34no—
116C3×C22⋊Q8—62no—
117C2×C3×C4⋊C4—21no—
118C2×C3×C4⋊C4—61no—
119C2×C3×C4⋊C4C2×D311yescharacteristic
120C2×C3×C4⋊C4C2×D311yescharacteristic
121C2×C3×C22⋊C4—61no—
122C2×#216—34no—
123C2×#216—34no—
124C2×#216—34no—
125C2×#216—64no—
126C2×#216—64no—
127C2×#216—64no—
128C2×(C2×D3)⋊C4—21no—
129C2×C4⋊Dic3—21no—
130C22×C3⋊C8—31no—
131C22×C3⋊C8—31no—
132C22×C3⋊C8—61no—
133C22×C3⋊C8C2×D311yescharacteristic
134C2×Dic12—34no—
135C2×Dic12—64no—
136#897—22no—
137#897C2×D314yes—
138C3×#103—34no—
139#830—34no—
140(C2×D3)⋊C8—34no—
141#810—34no—
142#810—34no—
143#810—64no—
144#810C2×D314yescomplemented
145C23×C32C2×D411yescharacteristic
146C22×C3×D3—22no—
147C22×C3×D3—22no—
148C22×C3×D3Q1614yescomplemented
149C22×C3×D3C2×D412yes—
150C2×C32×C4—22no—
151C2×C32×C4—42no—
152C2×C32×C4C2×D412yes—
153C2×C32×C4C2×D412yes—
154C2×C32×C4C2×D411yescharacteristic
155C2×C32×C4C2411yescharacteristic
156C2×C3⋊Dic3—24no—
157C2×C3⋊Dic3—22no—
158#634—24no—
159#634—22no—
160#634C2×D414yes—
161C2×C3×Dic3—24no—
162C2×C3×Dic3—22no—
163C2×C3×Dic3—22no—
164C2×C3×Dic3—22no—
165C2×C3×Dic3—42no—
166C2×C3×Dic3C2×D412yes—
167C3×C4×D3—24no—
168C3×C4×D3—22no—
169C3×C4×D3—22no—
170C3×Dic6—24no—
171C3×Dic6—22no—
172C3×Dic6—22no—
173C3×Dic6—22no—
174C3×Dic6—42no—
175C3×Dic6C2×D414yes—
176#627—216no—
177D3×Dic3—216no—
178C3⋊(C3⋊C8)—22no—
179C3×C3⋊C8—22no—
180C23×Q8—91no—
181C22×Q16—91no—
182C22×Q16—91no—
183C2×C22⋊Q8—31no—
184#451—98no—
185C2×#103—31no—
186C2×#103—91no—
187C2×C22⋊C8—91no—
188C24×C3—31no—
189C23×D3#6711yescharacteristic
190C2×C3×Q8—34no—
191C2×C3×Q8—32no—
192C2×C3×Q8—32no—
193C2×C3×Q8—62no—
194C2×C3×Q8—61no—
195C2×C3×Q8—61no—
196C2×C3×Q8—62no—
197C2×C3×Q8—62no—
198C22×C3×C4—21no—
199C22×C3×C4—21no—
200C22×C3×C4—21no—
201C22×C3×C4—31no—
202C22×C3×C4—32no—
203C22×C3×C4—32no—
204C22×C3×C4—41no—
205C22×C3×C4—61no—
206C22×C3×C4—62no—
207C22×C3×C4—62no—
208C22×C3×C4—61no—
209C22×C3×C4C22×D311yescharacteristic
210C22×C3×C4C22×D311yescharacteristic
211C22×Dic3—21no—
212C22×Dic3—21no—
213C22×Dic3—64no—
214C22×Dic3—68no—
215C22×Dic3—61no—
216C22×Dic3—61no—
217C22×Dic3—121no—
218C22×Dic3#6711yescharacteristic
219D3×Q8—68no—
220D3×Q8—68no—
221D3×Q8—616no—
222C2×C4×D3—22no—
223C2×C4×D3—22no—
224C2×C4×D3—68no—
225C2×C4×D3—64no—
226C2×C4×D3#6712yes—
227C2×C4×D3C22×D312yes—
228C2×Dic6—22no—
229C2×Dic6—21no—
230C2×Dic6—22no—
231C2×Dic6—22no—
232C2×Dic6—21no—
233C2×Dic6—34no—
234C2×Dic6—34no—
235C2×Dic6—32no—
236C2×Dic6—32no—
237C2×Dic6—62no—
238C2×Dic6—64no—
239C2×Dic6—68no—
240C2×Dic6—616no—
241C2×Dic6—64no—
242C2×Dic6—68no—
243C2×Dic6—68no—
244C2×Dic6—62no—
245C2×Dic6—61no—
246C2×Dic6—62no—
247C2×Dic6—61no—
248C2×Dic6—64no—
249C2×Dic6—68no—
250C2×Dic6—122no—
251C2×Dic6—121no—
252C2×Dic6D1214yes—
253C2×Dic6C22×D312yes—
254C2×Dic6C22×D312yes—
255C2×C3×C8—32no—
256C2×C3×C8—62no—
257C3×C4⋊C4—21no—
258C3×C4⋊C4—21no—
259C3×C4⋊C4—22no—
260C3×C4⋊C4—41no—
261C3×C4⋊C4—64no—
262C3×C4⋊C4C22×D312yes—
263C3×C4⋊C4C22×D312yes—
264C3×C22⋊C4—64no—
265#216—68no—
266#216—68no—
267#216—68no—
268(C2×D3)⋊C4—24no—
269C4⋊Dic3—24no—
270C2×C3⋊C8—22no—
271C2×C3⋊C8—32no—
272C2×C3⋊C8—32no—
273C2×C3⋊C8—62no—
274C2×C3⋊C8—62no—
275C2×C3⋊C8—62no—
276C2×C3⋊C8—122no—
277C2×C3⋊C8C22×D312yes—
278Dic12—68no—
279C22×C32#12012yes—
280C22×C32C2×Q1612yes—
281C22×C32#13712yes—
282C22×C32C22×D411yescharacteristic
283C2×C3×D3—22no—
284C2×C3×D3—22no—
285C2×C3×D3—28no—
286C2×C3×D3C2×Q1614yescomplemented
287C32×C4—42no—
288C32×C4#12012yes—
289C32×C4C22×D411yescharacteristic
290C32×C4C22×D411yescharacteristic
291C3⋊Dic3—24no—
292C3×Dic3—24no—
293C3×Dic3—22no—
294C3×Dic3—42no—
295C22×Q8—31no—
296C22×Q8—31no—
297C22×Q8—94no—
298C22×Q8—91no—
299C22×Q8—181no—
300C22×Q8—182no—
301C22×Q8—184no—
302C22×Q8—184no—
303C23×C4—31no—
304C23×C4—181no—
305C2×Q16—94no—
306C2×Q16—94no—
307C2×Q16—184no—
308C2×Q16—184no—
309C22×C8—31no—
310C22×C8—91no—
311C22⋊Q8—34no—
312C22⋊Q8—62no—
313C2×C4⋊C4—61no—
314C2×C4⋊C4D3211yescharacteristic
315C2×C22⋊C4—61no—
316#103—34no—
317#103—94no—
318C22⋊C8—94no—
319C23×C3—21no—
320C23×C3—34no—
321C23×C3—32no—
322C23×C3—62no—
323C23×C3—62no—
324C23×C3D3×D411yescharacteristic
325C23×C3C2×#6711yescharacteristic
326C22×D3—22no—
327C22×D3—22no—
328C22×D3#21614yescomplemented
329C22×D3C2×#6712yes—
330C3×Q8—34no—
331C3×Q8—64no—
332C3×Q8—62no—
333C3×Q8—62no—
334C3×Q8—62no—
335C3×Q8—122no—
336C2×C3×C4—22no—
337C2×C3×C4—22no—
338C2×C3×C4—21no—
339C2×C3×C4—22no—
340C2×C3×C4—22no—
341C2×C3×C4—21no—
342C2×C3×C4—32no—
343C2×C3×C4—42no—
344C2×C3×C4—42no—
345C2×C3×C4—42no—
346C2×C3×C4—62no—
347C2×C3×C4—64no—
348C2×C3×C4—62no—
349C2×C3×C4—64no—
350C2×C3×C4—62no—
351C2×C3×C4—62no—
352C2×C3×C4—62no—
353C2×C3×C4—82no—
354C2×C3×C4—122no—
355C2×C3×C4C2×D1212yes—
356C2×C3×C4D3×D412yes—
357C2×C3×C4D3×D412yes—
358C2×C3×C4D3×D412yes—
359C2×C3×C4D3×D411yescharacteristic
360C2×C3×C4C2×#6711yescharacteristic
361C2×C3×C4C23×D311yescharacteristic
362C2×C3×C4C23×D311yescharacteristic
363C2×Dic3—24no—
364C2×Dic3—22no—
365C2×Dic3—22no—
366C2×Dic3—22no—
367C2×Dic3—42no—
368C2×Dic3—616no—
369C2×Dic3—64no—
370C2×Dic3—64no—
371C2×Dic3—62no—
372C2×Dic3—62no—
373C2×Dic3—122no—
374C2×Dic3—124no—
375C2×Dic3C2×#6712yes—
376C4×D3—24no—
377C4×D3—22no—
378C4×D3—22no—
379C4×D3—616no—
380Dic6—24no—
381Dic6—22no—
382Dic6—22no—
383Dic6—22no—
384Dic6—34no—
385Dic6—34no—
386Dic6—42no—
387Dic6—64no—
388Dic6—616no—
389Dic6—616no—
390Dic6—64no—
391Dic6—64no—
392Dic6—62no—
393Dic6—62no—
394Dic6—122no—
395Dic6—124no—
396Dic6C2×D1214yes—
397C3×C8—62no—
398C3⋊C8—22no—
399C3⋊C8—62no—
400C3⋊C8—62no—
401C3⋊C8—122no—
402C2×C32#45114yescomplemented
403C2×C32C2×#12011yescharacteristic
404C2×C32C22×Q1611yescharacteristic
405C2×C32C2×#13711yescharacteristic
406C3×D3—24no—
407C24—31no—
408C2×Q8—32no—
409C2×Q8—32no—
410C2×Q8—34no—
411C2×Q8—62no—
412C2×Q8—61no—
413C2×Q8—61no—
414C2×Q8—62no—
415C2×Q8—62no—
416C2×Q8—92no—
417C2×Q8—94no—
418C2×Q8—184no—
419C2×Q8—188no—
420C2×Q8—188no—
421C2×Q8—188no—
422C2×Q8—1816no—
423C2×Q8—182no—
424C2×Q8—181no—
425C22×C4—21no—
426C22×C4—31no—
427C22×C4—32no—
428C22×C4—32no—
429C22×C4—61no—
430C22×C4—62no—
431C22×C4—62no—
432C22×C4—61no—
433C22×C4—184no—
434C22×C4—188no—
435C22×C4—181no—
436C22×C4C2×D3211yescharacteristic
437Q16—188no—
438Q16—188no—
439C2×C8—32no—
440C2×C8—62no—
441C2×C8—92no—
442C2×C8—182no—
443C4⋊C4—21no—
444C4⋊C4—64no—
445C4⋊C4C2×D3212yes—
446C22⋊C4—64no—
447C22×C3—21no—
448C22×C3—22no—
449C22×C3—22no—
450C22×C3—22no—
451C22×C3—34no—
452C22×C3—62no—
453C22×C3—62no—
454C22×C3—68no—
455C22×C3#88212yes—
456C22×C3#91512yes—
457C22×C3D3×Q1612yes—
458C22×C3#93712yes—
459C22×C3C2×#21612yes—
460C22×C3#95112yes—
461C22×C3C2×D3×D411yescharacteristic
462C22×C3C22×#6711yescharacteristic
463C2×D3—22no—
464C2×D3—28no—
465C2×D3—22no—
466C2×D3C2×#21614yescomplemented
467C3×C4—21no—
468C3×C4—21no—
469C3×C4—22no—
470C3×C4—42no—
471C3×C4—42no—
472C3×C4—62no—
473C3×C4—64no—
474C3×C4—82no—
475C3×C4—122no—
476C3×C4#88212yes—
477C3×C4#93712yes—
478C3×C4C22×D1211yescharacteristic
479C3×C4C2×D3×D411yescharacteristic
480C3×C4C2×D3×D411yescharacteristic
481C3×C4C2×D3×D411yescharacteristic
482Dic3—24no—
483Dic3—22no—
484Dic3—42no—
485Dic3—64no—
486Dic3—64no—
487Dic3—124no—
488C32C2×#45111yescharacteristic, complemented, Sylow
489C23—32no—
490C23—34no—
491C23—62no—
492C23—62no—
493C23D3×#6711yescharacteristic
494Q8—34no—
495Q8—62no—
496Q8—64no—
497Q8—62no—
498Q8—62no—
499Q8—94no—
500Q8—122no—
501Q8—1816no—
502Q8—182no—
503Q8—184no—
504C2×C4—22no—
505C2×C4—32no—
506C2×C4—42no—
507C2×C4—62no—
508C2×C4—62no—
509C2×C4—64no—
510C2×C4—62no—
511C2×C4—62no—
512C2×C4—64no—
513C2×C4—62no—
514C2×C4—122no—
515C2×C4—1816no—
516C2×C4—182no—
517C2×C4—184no—
518C2×C4D3×D1212yes—
519C2×C4#380212yes—
520C2×C4D3×#6711yescharacteristic
521C2×C4C22×D3211yescharacteristic
522C8—62no—
523C8—182no—
524C2×C3—21no—
525C2×C3—24no—
526C2×C3—21no—
527C2×C3—21no—
528C2×C3—64no—
529C2×C3#480914yescomplemented
530C2×C3#505014yescomplemented
531C2×C3C2×#88211yescharacteristic
532C2×C3C2×#91511yescharacteristic
533C2×C3C2×D3×Q1611yescharacteristic
534C2×C3C2×#93711yescharacteristic
535C2×C3C22×#21611yescharacteristic
536C2×C3C2×#95111yescharacteristic
537D3—24no—
538C22—34no—
539C22—62no—
540C22—68no—
541C22—62no—
542C22#6392212yes—
543C22#6392912yes—
544C22D3×#21612yes—
545C22C2×D3×#6711yescharacteristic
546C4—42no—
547C4—62no—
548C4—64no—
549C4—122no—
550C4—184no—
551C4#6392212yes—
552C4C2×D3×D1211yescharacteristic
553C4C2×#380211yescharacteristic
554C3—21no—
555C3C2×#480911yescharacteristic, complemented
556C3C2×#505011yescharacteristic, complemented
557C2—64no—
558C2#1059060414yesdirect product factor
559C2C2×#6392211yescharacteristic
560C2C2×#6392911yescharacteristic
561C2C2×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×#451
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
4. C22×#3718C2semidirect
5. C2×#63637C2semidirect
6. C2×C3×#810C2semidirect
8. #10590604C2direct (N × H)
29. C2×#3719C22semidirect
31. C2×#3718C22semidirect
32. #63637C22semidirect
33. C3×#810C22semidirect
50. C2×#810D3semidirect
144. #810C2×D3semidirect
148. C22×C3×D3Q16semidirect
286. C2×C3×D3C2×Q16semidirect
328. C22×D3#216semidirect
402. C2×C32#451semidirect
466. C2×D3C2×#216semidirect
488. C32C2×#451semidirect
529. C2×C3#4809semidirect
530. C2×C3#5050semidirect
555. C3C2×#4809semidirect
556. C3C2×#5050semidirect
558. C2#10590604direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D3×Dic62
C2×C3×#8972
C22×#37192
C22×#37182
C2×#636372
C2×C3×#8102
C2×(C2×D3)⋊(C3⋊C8)2
#105906042
C2×#50503
C2×#48093