Finite Group Databasebeta

← C2×#10591653 #11863665

Subgroups — C2×#10591653 #11863665

Order 1152.

1609 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D3×Dic6C211yesmaximal, characteristic
2C22×#3756C211yesmaximal, characteristic, complemented
3C2×C3×#946C211yesmaximal, characteristic
4C22×C3×#216C211yesmaximal, characteristic, complemented
5#10591653C218yesmaximal, direct product factor
6C2×#63567C211yesmaximal, characteristic, complemented
7C2×#63565C211yesmaximal, characteristic, complemented
8C2×(C2×D3)⋊(C3⋊C8)C211yesmaximal, characteristic
9C2×#5186—31nomaximal
10C2×#5050—31nomaximal
11C22×C32×Q8C2211yescharacteristic
12C22×#634C2211yescharacteristic
13C22×C3×C4×D3C2211yescharacteristic
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×#3756—24no—
22C2×#3756C2214yescomplemented
23C22×C3⋊(C3⋊C8)C2211yescharacteristic
24C3×#946—22no—
25C3×#946C2214yes—
26C2×C3×#216—24no—
27C2×C3×#216C2214yescomplemented
28C2×C3×(C2×D3)⋊C4—21no—
29C2×C3×C4⋊Dic3C2211yescharacteristic
30C2×C3×Dic3⋊C4—21no—
31C22×C3×C3⋊C8C2211yescharacteristic
32#63567C2214yescomplemented
33#63565C2214yescomplemented
34(C2×D3)⋊(C3⋊C8)C2214yes—
35C22×D3×Q8—31no—
36C23×Dic6—31no—
37C22×C3×Q16—31no—
38C2×C3×C22⋊Q8—31no—
39C2×#946D311yescharacteristic
40C22×#216—31no—
41C22×#216—31no—
42C22×#216—61no—
43C22×#216D311yescharacteristic, complemented
44C2×#835—31no—
45C2×#830—31no—
46#5186—38no—
47C2×(C2×D3)⋊C8—31no—
48C2×#816—31no—
49#5050—38no—
50C2×#810—31no—
51C2×#810—31no—
52C23×C3×D3D411yescharacteristic
53C2×C32×Q8—21no—
54C2×C32×Q8—22no—
55C2×C32×Q8—22no—
56C2×C32×Q8C2312yes—
57C22×C32×C4—21no—
58C22×C32×C4C2311yescharacteristic
59C22×C3⋊Dic3—21no—
60C2×#634—21no—
61C2×#634—22no—
62C2×#634D414yes—
63C2×#634C2312yes—
64C22×C3×Dic3—21no—
65C22×C3×Dic3—21no—
66C22×C3×Dic3D411yescharacteristic
67C2×C3×C4×D3—22no—
68C2×C3×C4×D3—22no—
69C2×C3×C4×D3D412yes—
70C2×C3×C4×D3C2312yes—
71C2×C3×Dic6—21no—
72C2×C3×Dic6—22no—
73C2×C3×Dic6D414yes—
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—
82#3756—28no—
83C2×C3⋊(C3⋊C8)—22no—
84C2×C3⋊(C3⋊C8)C2312yes—
85C3×#216—28no—
86C3×(C2×D3)⋊C4—24no—
87C3×C4⋊Dic3—21no—
88C3×C4⋊Dic3C2312yes—
89C3×Dic3⋊C4—24no—
90C2×C3×C3⋊C8—22no—
91C2×C3×C3⋊C8C2312yes—
92C2×#451—91noSylow
93C22×C3×Q8—21no—
94C22×C3×Q8—31no—
95C22×C3×Q8C2×D311yescharacteristic
96C22×C3×Q8C2×D311yescharacteristic
97C23×C3×C4—31no—
98C23×Dic3—61no—
99C2×D3×Q8—34no—
100C2×D3×Q8—64no—
101C2×D3×Q8—64no—
102C2×D3×Q8—62no—
103C22×C4×D3—61no—
104C22×C4×D3C2×D311yescharacteristic
105C22×Dic6—31no—
106C22×Dic6—31no—
107C22×Dic6—34no—
108C22×Dic6—61no—
109C22×Dic6—64no—
110C22×Dic6—62no—
111C22×Dic6—61no—
112C22×Dic6—61no—
113C22×Dic6—64no—
114C22×Dic6C2×D311yescharacteristic
115C2×C3×Q16—34no—
116C2×C3×Q16—64no—
117C22×C3×C8—31no—
118C3×C22⋊Q8—34no—
119C3×C22⋊Q8—62no—
120C2×C3×C4⋊C4—31no—
121C2×C3×C4⋊C4—61no—
122C2×C3×C22⋊C4—61no—
123#946—22no—
124#946C2×D314yes—
125C2×#216—24no—
126C2×#216—34no—
127C2×#216—34no—
128C2×#216—64no—
129C2×#216—64no—
130C2×#216—64no—
131C2×#216—68no—
132C2×#216C2×D314yescomplemented
133C2×(C2×D3)⋊C4—21no—
134C2×C4⋊Dic3C2×D311yescharacteristic
135C2×Dic3⋊C4—21no—
136C22×C3⋊C8—31no—
137C22×C3⋊C8—31no—
138C22×C3⋊C8—61no—
139C22×C3⋊C8C2×D311yescharacteristic
140#835—34no—
141#830—34no—
142(C2×D3)⋊C8—34no—
143#816—34no—
144#810—34no—
145#810—34no—
146C23×C32C2×D411yescharacteristic
147C22×C3×D3—22no—
148C22×C3×D3—22no—
149C22×C3×D3Q1614yescomplemented
150C22×C3×D3C2×D412yes—
151C32×Q8—22no—
152C32×Q8—22no—
153C32×Q8—42no—
154C2×C32×C4—22no—
155C2×C32×C4—42no—
156C2×C32×C4C2×D412yes—
157C2×C32×C4C2×D411yescharacteristic
158C2×C32×C4C2×D412yes—
159C2×C32×C4C2411yescharacteristic
160C2×C3⋊Dic3—24no—
161C2×C3⋊Dic3—22no—
162#634—24no—
163#634—22no—
164#634C2×D414yes—
165C2×C3×Dic3—24no—
166C2×C3×Dic3—22no—
167C2×C3×Dic3—22no—
168C2×C3×Dic3—22no—
169C2×C3×Dic3—42no—
170C2×C3×Dic3C2×D412yes—
171C3×C4×D3—24no—
172C3×C4×D3—22no—
173C3×C4×D3—22no—
174C3×Dic6—24no—
175C3×Dic6—22no—
176C3×Dic6C2×D414yes—
177#627—216no—
178D3×Dic3—216no—
179C3⋊(C3⋊C8)—22no—
180C3×C3⋊C8—22no—
181C23×Q8—91no—
182C22×Q16—31no—
183C22×Q16—91no—
184C2×C22⋊Q8—31no—
185#451—98no—
186C2×#103—91no—
187C2×#103—91no—
188C2×C22⋊C8—91no—
189C24×C3—31no—
190C23×D3#6711yescharacteristic
191C2×C3×Q8—21no—
192C2×C3×Q8—21no—
193C2×C3×Q8—24no—
194C2×C3×Q8—22no—
195C2×C3×Q8—22no—
196C2×C3×Q8—22no—
197C2×C3×Q8—22no—
198C2×C3×Q8—22no—
199C2×C3×Q8—34no—
200C2×C3×Q8—32no—
201C2×C3×Q8—41no—
202C2×C3×Q8—42no—
203C2×C3×Q8—62no—
204C2×C3×Q8—61no—
205C2×C3×Q8C22×D312yes—
206C2×C3×Q8C22×D312yes—
207C22×C3×C4—21no—
208C22×C3×C4—21no—
209C22×C3×C4—21no—
210C22×C3×C4—31no—
211C22×C3×C4—32no—
212C22×C3×C4—32no—
213C22×C3×C4—41no—
214C22×C3×C4—61no—
215C22×C3×C4—62no—
216C22×C3×C4—62no—
217C22×C3×C4—61no—
218C22×C3×C4C22×D311yescharacteristic
219C22×C3×C4C22×D311yescharacteristic
220C22×Dic3—21no—
221C22×Dic3—21no—
222C22×Dic3—64no—
223C22×Dic3—68no—
224C22×Dic3—61no—
225C22×Dic3—61no—
226C22×Dic3—121no—
227C22×Dic3#6711yescharacteristic
228D3×Q8—68no—
229D3×Q8—68no—
230D3×Q8—616no—
231C2×C4×D3—22no—
232C2×C4×D3—22no—
233C2×C4×D3—68no—
234C2×C4×D3—64no—
235C2×C4×D3#6712yes—
236C2×C4×D3C22×D312yes—
237C2×Dic6—21no—
238C2×Dic6—22no—
239C2×Dic6—34no—
240C2×Dic6—34no—
241C2×Dic6—32no—
242C2×Dic6—32no—
243C2×Dic6—64no—
244C2×Dic6—62no—
245C2×Dic6—68no—
246C2×Dic6—616no—
247C2×Dic6—64no—
248C2×Dic6—68no—
249C2×Dic6—68no—
250C2×Dic6—61no—
251C2×Dic6—62no—
252C2×Dic6—62no—
253C2×Dic6—61no—
254C2×Dic6—64no—
255C2×Dic6—68no—
256C2×Dic6—121no—
257C2×Dic6—122no—
258C2×Dic6#6714yes—
259C2×Dic6C22×D312yes—
260C3×Q16—68no—
261C2×C3×C8—32no—
262C2×C3×C8—62no—
263C3×C4⋊C4—32no—
264C3×C4⋊C4—64no—
265C3×C4⋊C4—61no—
266C3×C22⋊C4—64no—
267#216—28no—
268#216—68no—
269#216—68no—
270#216—616no—
271(C2×D3)⋊C4—24no—
272C4⋊Dic3—21no—
273C4⋊Dic3C22×D312yes—
274Dic3⋊C4—24no—
275C2×C3⋊C8—22no—
276C2×C3⋊C8—32no—
277C2×C3⋊C8—32no—
278C2×C3⋊C8—62no—
279C2×C3⋊C8—64no—
280C2×C3⋊C8—62no—
281C2×C3⋊C8—62no—
282C2×C3⋊C8C22×D312yes—
283C22×C32#12012yes—
284C22×C32C2×Q1612yes—
285C22×C32#13712yes—
286C22×C32C22×D411yescharacteristic
287C2×C3×D3—22no—
288C2×C3×D3—22no—
289C2×C3×D3—28no—
290C2×C3×D3C2×Q1614yescomplemented
291C32×C4—42no—
292C32×C4#12012yes—
293C32×C4C22×D411yescharacteristic
294C32×C4C22×D411yescharacteristic
295C3⋊Dic3—24no—
296C3×Dic3—24no—
297C3×Dic3—22no—
298C3×Dic3—42no—
299C22×Q8—31no—
300C22×Q8—94no—
301C22×Q8—91no—
302C22×Q8—181no—
303C22×Q8—182no—
304C22×Q8—184no—
305C22×Q8—184no—
306C22×Q8D3211yescharacteristic
307C23×C4—31no—
308C23×C4—181no—
309C2×Q16—34no—
310C2×Q16—64no—
311C2×Q16—94no—
312C2×Q16—184no—
313C22×C8—31no—
314C22×C8—91no—
315C22⋊Q8—34no—
316C22⋊Q8—62no—
317C2×C4⋊C4—31no—
318C2×C4⋊C4—61no—
319C2×C22⋊C4—61no—
320#103—94no—
321#103—94no—
322C22⋊C8—94no—
323C23×C3—21no—
324C23×C3—34no—
325C23×C3—32no—
326C23×C3—62no—
327C23×C3—62no—
328C23×C3D3×D411yescharacteristic
329C23×C3C2×#6711yescharacteristic
330C22×D3—22no—
331C22×D3—22no—
332C22×D3#21614yescomplemented
333C22×D3C2×#6712yes—
334C3×Q8—24no—
335C3×Q8—22no—
336C3×Q8—22no—
337C3×Q8—22no—
338C3×Q8—22no—
339C3×Q8—34no—
340C3×Q8—42no—
341C3×Q8—44no—
342C3×Q8—42no—
343C3×Q8—42no—
344C3×Q8—64no—
345C3×Q8—62no—
346C2×C3×C4—22no—
347C2×C3×C4—22no—
348C2×C3×C4—21no—
349C2×C3×C4—22no—
350C2×C3×C4—21no—
351C2×C3×C4—22no—
352C2×C3×C4—32no—
353C2×C3×C4—42no—
354C2×C3×C4—44no—
355C2×C3×C4—42no—
356C2×C3×C4—42no—
357C2×C3×C4—62no—
358C2×C3×C4—64no—
359C2×C3×C4—62no—
360C2×C3×C4—64no—
361C2×C3×C4—62no—
362C2×C3×C4—62no—
363C2×C3×C4—62no—
364C2×C3×C4—122no—
365C2×C3×C4D3×D411yescharacteristic
366C2×C3×C4D3×D412yes—
367C2×C3×C4D3×D412yes—
368C2×C3×C4D3×D412yes—
369C2×C3×C4C2×#6711yescharacteristic
370C2×C3×C4C2×#6712yes—
371C2×C3×C4C23×D311yescharacteristic
372C2×C3×C4C23×D311yescharacteristic
373C2×Dic3—24no—
374C2×Dic3—22no—
375C2×Dic3—22no—
376C2×Dic3—22no—
377C2×Dic3—42no—
378C2×Dic3—616no—
379C2×Dic3—64no—
380C2×Dic3—64no—
381C2×Dic3—62no—
382C2×Dic3—62no—
383C2×Dic3—122no—
384C2×Dic3—124no—
385C2×Dic3C2×#6712yes—
386C4×D3—24no—
387C4×D3—22no—
388C4×D3—22no—
389C4×D3—616no—
390Dic6—24no—
391Dic6—22no—
392Dic6—34no—
393Dic6—34no—
394Dic6—64no—
395Dic6—616no—
396Dic6—616no—
397Dic6—64no—
398Dic6—64no—
399Dic6—62no—
400Dic6—62no—
401Dic6—122no—
402Dic6—124no—
403Dic6C2×#6714yes—
404C3×C8—62no—
405C3⋊C8—22no—
406C3⋊C8—64no—
407C3⋊C8—62no—
408C3⋊C8—62no—
409C2×C32#45114yescomplemented
410C2×C32C2×#12011yescharacteristic
411C2×C32C22×Q1611yescharacteristic
412C2×C32C2×#13711yescharacteristic
413C3×D3—24no—
414C24—31no—
415C2×Q8—21no—
416C2×Q8—22no—
417C2×Q8—22no—
418C2×Q8—32no—
419C2×Q8—34no—
420C2×Q8—61no—
421C2×Q8—62no—
422C2×Q8—92no—
423C2×Q8—94no—
424C2×Q8—184no—
425C2×Q8—188no—
426C2×Q8—188no—
427C2×Q8—188no—
428C2×Q8—1816no—
429C2×Q8—181no—
430C2×Q8—182no—
431C2×Q8C2×D3212yes—
432C22×C4—21no—
433C22×C4—31no—
434C22×C4—32no—
435C22×C4—32no—
436C22×C4—61no—
437C22×C4—62no—
438C22×C4—62no—
439C22×C4—61no—
440C22×C4—184no—
441C22×C4—188no—
442C22×C4—181no—
443C22×C4C2×D3211yescharacteristic
444Q16—68no—
445Q16—188no—
446C2×C8—32no—
447C2×C8—62no—
448C2×C8—92no—
449C2×C8—182no—
450C4⋊C4—32no—
451C4⋊C4—64no—
452C4⋊C4—61no—
453C22⋊C4—64no—
454C22×C3—21no—
455C22×C3—22no—
456C22×C3—22no—
457C22×C3—22no—
458C22×C3—34no—
459C22×C3—68no—
460C22×C3—62no—
461C22×C3—62no—
462C22×C3D3×Q1612yes—
463C22×C3#91812yes—
464C22×C3#93712yes—
465C22×C3#93712yes—
466C22×C3C2×#21612yes—
467C22×C3#95112yes—
468C22×C3C2×D3×D411yescharacteristic
469C22×C3C22×#6711yescharacteristic
470C2×D3—22no—
471C2×D3—28no—
472C2×D3—22no—
473C2×D3C2×#21614yescomplemented
474C3×C4—21no—
475C3×C4—21no—
476C3×C4—22no—
477C3×C4—44no—
478C3×C4—42no—
479C3×C4—42no—
480C3×C4—62no—
481C3×C4—64no—
482C3×C4—122no—
483C3×C4#93712yes—
484C3×C4#93712yes—
485C3×C4C2×D3×D411yescharacteristic
486C3×C4C2×D3×D411yescharacteristic
487C3×C4C2×D3×D411yescharacteristic
488C3×C4C22×#6711yescharacteristic
489Dic3—24no—
490Dic3—22no—
491Dic3—42no—
492Dic3—64no—
493Dic3—64no—
494Dic3—124no—
495C32C2×#45111yescharacteristic, complemented, Sylow
496C23—32no—
497C23—34no—
498C23—62no—
499C23—62no—
500C23D3×#6711yescharacteristic
501Q8—22no—
502Q8—22no—
503Q8—34no—
504Q8—42no—
505Q8—62no—
506Q8—64no—
507Q8—94no—
508Q8—1816no—
509Q8—182no—
510Q8—184no—
511C2×C4—22no—
512C2×C4—32no—
513C2×C4—42no—
514C2×C4—62no—
515C2×C4—62no—
516C2×C4—64no—
517C2×C4—62no—
518C2×C4—62no—
519C2×C4—64no—
520C2×C4—62no—
521C2×C4—122no—
522C2×C4—1816no—
523C2×C4—182no—
524C2×C4—184no—
525C2×C4D3×#6712yes—
526C2×C4D3×#6711yescharacteristic
527C2×C4#381112yes—
528C2×C4C22×D3211yescharacteristic
529C8—62no—
530C8—182no—
531C2×C3—24no—
532C2×C3—21no—
533C2×C3—21no—
534C2×C3—21no—
535C2×C3—64no—
536C2×C3#505014yescomplemented
537C2×C3#518614yescomplemented
538C2×C3C2×D3×Q1611yescharacteristic
539C2×C3C2×#91811yescharacteristic
540C2×C3C2×#93711yescharacteristic
541C2×C3C2×#93711yescharacteristic
542C2×C3C22×#21611yescharacteristic
543C2×C3C2×#95111yescharacteristic
544D3—24no—
545C22—34no—
546C22—68no—
547C22—62no—
548C22—62no—
549C22D3×#21612yes—
550C22#6394312yes—
551C22#6398312yes—
552C22C2×D3×#6711yescharacteristic
553C4—42no—
554C4—62no—
555C4—64no—
556C4—122no—
557C4—184no—
558C4#6398312yes—
559C4C2×D3×#6711yescharacteristic
560C4C2×#381111yescharacteristic
561C3—21no—
562C3C2×#505011yescharacteristic, complemented
563C3C2×#518611yescharacteristic, complemented
564C2—64no—
565C2#1059165314yesdirect product factor
566C2C2×D3×#21611yescharacteristic
567C2C2×#6394311yescharacteristic
568C2C2×#6398311yescharacteristic
subgroupG/H
centerC23D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC23×C32C2×D4
prime radicalC23×C3×D3D4
hypercenterC22×Q8D32
hypocenterC32C2×#451
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
2. C22×#3756C2semidirect
4. C22×C3×#216C2semidirect
5. #10591653C2direct (N × H)
6. C2×#63567C2semidirect
7. C2×#63565C2semidirect
22. C2×#3756C22semidirect
27. C2×C3×#216C22semidirect
32. #63567C22semidirect
33. #63565C22semidirect
43. C22×#216D3semidirect
132. C2×#216C2×D3semidirect
149. C22×C3×D3Q16semidirect
290. C2×C3×D3C2×Q16semidirect
332. C22×D3#216semidirect
409. C2×C32#451semidirect
473. C2×D3C2×#216semidirect
495. C32C2×#451semidirect
536. C2×C3#5050semidirect
537. C2×C3#5186semidirect
562. C3C2×#5050semidirect
563. C3C2×#5186semidirect
565. C2#10591653direct (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×#37562
C2×C3×#9462
C22×C3×#2162
#105916532
C2×#635672
C2×#635652
C2×(C2×D3)⋊(C3⋊C8)2
C2×#51863
C2×#50503