Finite Group Databasebeta

← C2×#10590949 #11863675

Subgroups — C2×#10590949 #11863675

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
2C22×C3×Dic12C211yesmaximal, characteristic, complemented
3C2×#63856C211yesmaximal, characteristic
4C22×#3719C211yesmaximal, characteristic, complemented
5C2×#63643C211yesmaximal, characteristic, complemented
6C2×C3×(C2×D3)⋊C8C211yesmaximal, characteristic
7C2×#63566C211yesmaximal, characteristic, complemented
8#10590949C218yesmaximal, direct product factor
9C2×#5186—31nomaximal
10C2×#4739—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—
21C22×C32×C8C2211yescharacteristic
22C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
23C22×C3×C3⋊C8C2211yescharacteristic
24C2×C3×Dic12—24no—
25C2×C3×Dic12C2214yescomplemented
26C2×#3724—21no—
27C2×(C2×D3)⋊Dic3—21no—
28#63856—22no—
29#63856C2214yes—
30C2×#3719—24no—
31C2×#3719C2214yescomplemented
32#63643C2214yescomplemented
33C3×(C2×D3)⋊C8C2214yes—
34#63566C2214yescomplemented
35C22×D3×Q8—31no—
36C23×Dic6—31no—
37C22×C3×Q16—31no—
38C2×#946—31no—
39C22×#216—31no—
40C2×#924—31no—
41C22×Dic12—31no—
42C22×Dic12D311yescharacteristic, complemented
43C2×C3×C22⋊C8—31no—
44C2×#835—31no—
45#5186—38no—
46C2×(C2×D3)⋊C8D311yescharacteristic
47C2×#816—31no—
48C2×#816—31no—
49C2×#816—31no—
50C2×#816—61no—
51#4739—38no—
52C23×C3×D3D411yescharacteristic
53C22×C32×C4C2311yescharacteristic
54C22×C3⋊Dic3—21no—
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—
82C2×C32×C8—22no—
83C2×C32×C8C2312yes—
84C4⋊(C3⋊Dic3)—21no—
85C4⋊(C3⋊Dic3)C2312yes—
86C2×C3×C3⋊C8—22no—
87C2×C3×C3⋊C8C2312yes—
88C3×Dic12—28no—
89#3724—24no—
90(C2×D3)⋊Dic3—24no—
91#3719—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
114C2×C3×Q16—34no—
115C2×C3×Q16—64no—
116C22×C3×C8—21no—
117C22×C3×C8—31no—
118C22×C3×C8C2×D311yescharacteristic
119C22×C3×C8C2×D311yescharacteristic
120C2×#217—61no—
121#946—34no—
122#946—62no—
123C2×#216—34no—
124C2×#216—64no—
125C2×(C2×D3)⋊C4—61no—
126C2×C4⋊Dic3—31no—
127C2×C4⋊Dic3—31no—
128C2×C4⋊Dic3—61no—
129#924—34no—
130#924—62no—
131C2×Dic3⋊C4—61no—
132C2×Dic3⋊C4—61no—
133C22×C3⋊C8C2×D311yescharacteristic
134C2×Dic12—24no—
135C2×Dic12—34no—
136C2×Dic12—64no—
137C2×Dic12C2×D314yescomplemented
138C3×C22⋊C8—34no—
139#835—34no—
140(C2×D3)⋊C8C2×D314yes—
141#816—34no—
142#816—34no—
143#816—34no—
144#816—64no—
145C23×C32C2×D411yescharacteristic
146C22×C3×D3—22no—
147C22×C3×D3—22no—
148C22×C3×D3Q1614yescomplemented
149C22×C3×D3C2×D412yes—
150C2×C32×C4C2×D411yescharacteristic
151C2×C32×C4C2×D412yes—
152C2×C32×C4C2×D412yes—
153C2×C32×C4C2411yescharacteristic
154C2×C3⋊Dic3—24no—
155C2×C3⋊Dic3—22no—
156C2×C3⋊Dic3—22no—
157C2×C3⋊Dic3—42no—
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—
178C32×C8—22no—
179C3×C3⋊C8—22no—
180C23×Q8—91no—
181C22×Q16—31no—
182C22×Q16—91no—
183C2×C22⋊Q8—91no—
184#451—98no—
185C2×#103—91no—
186C2×#103—91no—
187C2×C22⋊C8—31no—
188C24×C3—31no—
189C23×D3D1211yescharacteristic
190C2×C3×Q8—34no—
191C2×C3×Q8—32no—
192C2×C3×Q8—32no—
193C2×C3×Q8—61no—
194C2×C3×Q8—61no—
195C2×C3×Q8—62no—
196C2×C3×Q8—62no—
197C2×C3×Q8—62no—
198C22×C3×C4—21no—
199C22×C3×C4—31no—
200C22×C3×C4—32no—
201C22×C3×C4—32no—
202C22×C3×C4—61no—
203C22×C3×C4—62no—
204C22×C3×C4—62no—
205C22×C3×C4—61no—
206C22×C3×C4C22×D311yescharacteristic
207C22×C3×C4C22×D311yescharacteristic
208C22×Dic3—21no—
209C22×Dic3—21no—
210C22×Dic3—64no—
211C22×Dic3—68no—
212C22×Dic3—61no—
213C22×Dic3—61no—
214C22×Dic3—61no—
215C22×Dic3—61no—
216C22×Dic3—121no—
217C22×Dic3—121no—
218C22×Dic3D1211yescharacteristic
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×D3D1212yes—
227C2×C4×D3C22×D312yes—
228C2×Dic6—21no—
229C2×Dic6—22no—
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—61no—
245C2×Dic6—61no—
246C2×Dic6—62no—
247C2×Dic6—62no—
248C2×Dic6—64no—
249C2×Dic6—68no—
250C2×Dic6—121no—
251C2×Dic6—122no—
252C2×Dic6#6714yes—
253C2×Dic6C22×D312yes—
254C2×Dic6C22×D312yes—
255C3×Q16—68no—
256C2×C3×C8—22no—
257C2×C3×C8—22no—
258C2×C3×C8—22no—
259C2×C3×C8—32no—
260C2×C3×C8—42no—
261C2×C3×C8—62no—
262C2×C3×C8C22×D312yes—
263C2×C3×C8C22×D312yes—
264#217—64no—
265#216—68no—
266(C2×D3)⋊C4—64no—
267C4⋊Dic3—32no—
268C4⋊Dic3—32no—
269C4⋊Dic3—62no—
270C4⋊Dic3—61no—
271C4⋊Dic3—61no—
272C4⋊Dic3—121no—
273Dic3⋊C4—64no—
274Dic3⋊C4—64no—
275C2×C3⋊C8—22no—
276C2×C3⋊C8C22×D312yes—
277Dic12—28no—
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#12012yes—
288C32×C4C22×D411yescharacteristic
289C32×C4C22×D411yescharacteristic
290C3⋊Dic3—24no—
291C3⋊Dic3—42no—
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—34no—
306C2×Q16—64no—
307C2×Q16—94no—
308C2×Q16—184no—
309C22×C8—31no—
310C22×C8D3211yescharacteristic
311C22⋊Q8—94no—
312C22⋊Q8—182no—
313C2×C4⋊C4—91no—
314C2×C4⋊C4—181no—
315C2×C22⋊C4—181no—
316#103—94no—
317#103—94no—
318C22⋊C8—34no—
319C23×C3—21no—
320C23×C3—34no—
321C23×C3—32no—
322C23×C3—62no—
323C23×C3—62no—
324C23×C3C2×D1211yescharacteristic
325C23×C3D3×D411yescharacteristic
326C22×D3—22no—
327C22×D3—22no—
328C22×D3Dic1214yescomplemented
329C22×D3C2×D1212yes—
330C3×Q8—34no—
331C3×Q8—64no—
332C3×Q8—62no—
333C3×Q8—62no—
334C3×Q8—62no—
335C3×Q8—122no—
336C2×C3×C4—21no—
337C2×C3×C4—21no—
338C2×C3×C4—22no—
339C2×C3×C4—22no—
340C2×C3×C4—32no—
341C2×C3×C4—64no—
342C2×C3×C4—62no—
343C2×C3×C4—62no—
344C2×C3×C4—64no—
345C2×C3×C4—62no—
346C2×C3×C4—62no—
347C2×C3×C4—62no—
348C2×C3×C4—122no—
349C2×C3×C4C2×D1211yescharacteristic
350C2×C3×C4D3×D411yescharacteristic
351C2×C3×C4D3×D412yes—
352C2×C3×C4D3×D412yes—
353C2×C3×C4D3×D412yes—
354C2×C3×C4C2×#6712yes—
355C2×C3×C4C23×D311yescharacteristic
356C2×C3×C4C23×D311yescharacteristic
357C2×Dic3—22no—
358C2×Dic3—24no—
359C2×Dic3—22no—
360C2×Dic3—22no—
361C2×Dic3—42no—
362C2×Dic3—616no—
363C2×Dic3—64no—
364C2×Dic3—64no—
365C2×Dic3—62no—
366C2×Dic3—62no—
367C2×Dic3—62no—
368C2×Dic3—62no—
369C2×Dic3—122no—
370C2×Dic3—124no—
371C2×Dic3—122no—
372C2×Dic3—122no—
373C2×Dic3—122no—
374C2×Dic3—242no—
375C2×Dic3C2×D1212yes—
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×#6714yes—
397C3×C8—22no—
398C3×C8—22no—
399C3×C8—42no—
400C3×C8—62no—
401C3⋊C8—22no—
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—61no—
412C2×Q8—61no—
413C2×Q8—62no—
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—181no—
424C2×Q8—182no—
425C22×C4—31no—
426C22×C4—32no—
427C22×C4—32no—
428C22×C4—61no—
429C22×C4—62no—
430C22×C4—62no—
431C22×C4—61no—
432C22×C4—184no—
433C22×C4—188no—
434C22×C4—181no—
435C22×C4—181no—
436C22×C4C2×D3211yescharacteristic
437Q16—68no—
438Q16—188no—
439C2×C8—22no—
440C2×C8—32no—
441C2×C8—62no—
442C2×C8C2×D3212yes—
443C4⋊C4—92no—
444C4⋊C4—184no—
445C4⋊C4—181no—
446C22⋊C4—184no—
447C22×C3—21no—
448C22×C3—22no—
449C22×C3—22no—
450C22×C3—22no—
451C22×C3—34no—
452C22×C3—68no—
453C22×C3—62no—
454C22×C3—62no—
455C22×C3#88212yes—
456C22×C3C2×Dic1212yes—
457C22×C3#90912yes—
458C22×C3D3×Q1612yes—
459C22×C3#91812yes—
460C22×C3#93712yes—
461C22×C3C22×D1211yescharacteristic
462C22×C3C2×D3×D411yescharacteristic
463C2×D3—22no—
464C2×D3—22no—
465C2×D3—28no—
466C2×D3C2×Dic1214yescomplemented
467C3×C4—21no—
468C3×C4—21no—
469C3×C4—22no—
470C3×C4—64no—
471C3×C4—62no—
472C3×C4—122no—
473C3×C4#88212yes—
474C3×C4#93712yes—
475C3×C4C2×D3×D411yescharacteristic
476C3×C4C2×D3×D411yescharacteristic
477C3×C4C2×D3×D411yescharacteristic
478C3×C4C22×#6711yescharacteristic
479Dic3—22no—
480Dic3—24no—
481Dic3—42no—
482Dic3—64no—
483Dic3—64no—
484Dic3—124no—
485Dic3—122no—
486Dic3—122no—
487Dic3—242no—
488C32C2×#45111yescharacteristic, complemented, Sylow
489C23—32no—
490C23—34no—
491C23—62no—
492C23—62no—
493C23D3×D1211yescharacteristic
494Q8—34no—
495Q8—62no—
496Q8—64no—
497Q8—62no—
498Q8—62no—
499Q8—94no—
500Q8—122no—
501Q8—1816no—
502Q8—182no—
503Q8—184no—
504C2×C4—32no—
505C2×C4—62no—
506C2×C4—62no—
507C2×C4—64no—
508C2×C4—62no—
509C2×C4—62no—
510C2×C4—64no—
511C2×C4—62no—
512C2×C4—122no—
513C2×C4—1816no—
514C2×C4—182no—
515C2×C4—184no—
516C2×C4—182no—
517C2×C4—362no—
518C2×C4D3×D1211yescharacteristic
519C2×C4#380212yes—
520C2×C4D3×#6712yes—
521C2×C4C22×D3211yescharacteristic
522C8—22no—
523C8—62no—
524C2×C3—21no—
525C2×C3—21no—
526C2×C3—24no—
527C2×C3—21no—
528C2×C3—64no—
529C2×C3#473914yescomplemented
530C2×C3#518614yescomplemented
531C2×C3C2×#88211yescharacteristic
532C2×C3C22×Dic1211yescharacteristic
533C2×C3C2×#90911yescharacteristic
534C2×C3C2×D3×Q1611yescharacteristic
535C2×C3C2×#91811yescharacteristic
536C2×C3C2×#93711yescharacteristic
537D3—24no—
538C22—34no—
539C22—62no—
540C22—68no—
541C22—62no—
542C22D3×Dic1212yes—
543C22#6380112yes—
544C22#6392212yes—
545C22C2×D3×D1211yescharacteristic
546C4—62no—
547C4—64no—
548C4—122no—
549C4—184no—
550C4—362no—
551C4#6392212yes—
552C4C2×#380211yescharacteristic
553C4C2×D3×#6711yescharacteristic
554C3—21no—
555C3C2×#473911yescharacteristic, complemented
556C3C2×#518611yescharacteristic, complemented
557C2—64no—
558C2#1059094914yesdirect product factor
559C2C2×D3×Dic1211yescharacteristic
560C2C2×#6380111yescharacteristic
561C2C2×#6392211yescharacteristic
subgroupG/H
centerC23D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC23×C3×D3D4
hypercenterC22×C8D32
hypocenterC32C2×#451
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
2. C22×C3×Dic12C2semidirect
4. C22×#3719C2semidirect
5. C2×#63643C2semidirect
7. C2×#63566C2semidirect
8. #10590949C2direct (N × H)
25. C2×C3×Dic12C22semidirect
31. C2×#3719C22semidirect
32. #63643C22semidirect
34. #63566C22semidirect
42. C22×Dic12D3semidirect
137. C2×Dic12C2×D3semidirect
148. C22×C3×D3Q16semidirect
286. C2×C3×D3C2×Q16semidirect
328. C22×D3Dic12semidirect
402. C2×C32#451semidirect
466. C2×D3C2×Dic12semidirect
488. C32C2×#451semidirect
529. C2×C3#4739semidirect
530. C2×C3#5186semidirect
555. C3C2×#4739semidirect
556. C3C2×#5186semidirect
558. C2#10590949direct (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
C22×C3×Dic122
C2×#638562
C22×#37192
C2×#636432
C2×C3×(C2×D3)⋊C82
C2×#635662
#105909492
C2×#51863
C2×#47393