Finite Group Databasebeta

← C2×#10591594 #11863669

Subgroups — C2×#10591594 #11863669

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×C3×D3×Q8C211yesmaximal, characteristic
2C22×C3×#216C211yesmaximal, characteristic, complemented
3C2×#63856C211yesmaximal, characteristic
4C22×#3718C211yesmaximal, characteristic, complemented
5C2×#63662C211yesmaximal, characteristic, complemented
6#10591594C218yesmaximal, direct product factor
7C2×#63566C211yesmaximal, characteristic, complemented
8C2×(C2×D3)⋊(C3⋊C8)C211yesmaximal, characteristic
9C2×#5228—31nomaximal
10C2×#5186—31nomaximal
11C22×C32×Q8C2211yescharacteristic
12C2×C3×D3×Q8—24no—
13C2×C3×D3×Q8—22no—
14C2×C3×D3×Q8—24no—
15C2×C3×D3×Q8C2214yes—
16C22×C3×C4×D3—21no—
17C22×C3×C4×D3C2211yescharacteristic
18C22×C3×Dic6—21no—
19C22×C3×Dic6C2211yescharacteristic
20C22×C3×Dic6C2211yescharacteristic
21C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
22C22×C3⋊(C3⋊C8)C2211yescharacteristic
23C2×C3×#216—24no—
24C2×C3×#216C2214yescomplemented
25C22×C3×C3⋊C8C2211yescharacteristic
26C2×#3724—21no—
27C2×(C2×D3)⋊Dic3—21no—
28#63856—22no—
29#63856C2214yes—
30C2×#3718—24no—
31C2×#3718C2214yescomplemented
32#63662C2214yescomplemented
33#63566C2214yescomplemented
34(C2×D3)⋊(C3⋊C8)C2214yes—
35C23×C3×Q8—31no—
36C22×D3×Q8D311yescharacteristic
37C22×C3×Q16—31no—
38C2×#946—31no—
39C22×#216—31no—
40C22×#216—31no—
41C22×#216D311yescharacteristic, complemented
42C2×#924—31no—
43#5228—38no—
44C2×#835—31no—
45C2×#835—31no—
46C2×#835—31no—
47C2×#835—61no—
48C2×#830—31no—
49#5186—38no—
50C2×(C2×D3)⋊C8—31no—
51C2×#816—31no—
52C23×C3×D3D411yescharacteristic
53C2×C32×Q8—22no—
54C2×C32×Q8—21no—
55C2×C32×Q8D414yes—
56C2×C32×Q8C2312yes—
57C22×C32×C4—21no—
58C22×C32×C4C2311yescharacteristic
59C22×C3⋊Dic3—21no—
60C22×C3×Dic3—21no—
61C22×C3×Dic3—21no—
62C22×C3×Dic3D411yescharacteristic
63C3×D3×Q8—216no—
64C3×D3×Q8—28no—
65C3×D3×Q8—28no—
66C2×C3×C4×D3—28no—
67C2×C3×C4×D3—24no—
68C2×C3×C4×D3—22no—
69C2×C3×C4×D3—22no—
70C2×C3×C4×D3D412yes—
71C2×C3×C4×D3C2312yes—
72C2×C3×Dic6—28no—
73C2×C3×Dic6—21no—
74C2×C3×Dic6—22no—
75C2×C3×Dic6—24no—
76C2×C3×Dic6—22no—
77C2×C3×Dic6—22no—
78C2×C3×Dic6—21no—
79C2×C3×Dic6D414yes—
80C2×C3×Dic6C2312yes—
81C2×C3×Dic6C2312yes—
82C4⋊(C3⋊Dic3)—21no—
83C4⋊(C3⋊Dic3)C2312yes—
84C2×C3⋊(C3⋊C8)—22no—
85C2×C3⋊(C3⋊C8)C2312yes—
86C3×#216—28no—
87C2×C3×C3⋊C8—22no—
88C2×C3×C3⋊C8C2312yes—
89#3724—24no—
90(C2×D3)⋊Dic3—24no—
91#3718—28no—
92C2×#451—91noSylow
93C22×C3×Q8—21no—
94C22×C3×Q8—34no—
95C22×C3×Q8—31no—
96C22×C3×Q8—31no—
97C22×C3×Q8—61no—
98C22×C3×Q8—62no—
99C22×C3×Q8—64no—
100C22×C3×Q8—64no—
101C22×C3×Q8C2×D311yescharacteristic
102C22×C3×Q8C2×D311yescharacteristic
103C23×C3×C4—31no—
104C23×C3×C4—61no—
105C2×D3×Q8—24no—
106C2×D3×Q8—22no—
107C2×D3×Q8—24no—
108C2×D3×Q8C2×D314yes—
109C22×C4×D3—21no—
110C22×C4×D3C2×D311yescharacteristic
111C22×Dic6—21no—
112C22×Dic6C2×D311yescharacteristic
113C22×Dic6C2×D311yescharacteristic
114C2×C3×Q16—34no—
115C2×C3×Q16—64no—
116C22×C3×C8—31no—
117C2×#217—61no—
118#946—34no—
119#946—62no—
120C2×#216—24no—
121C2×#216—34no—
122C2×#216—34no—
123C2×#216—64no—
124C2×#216—64no—
125C2×#216C2×D314yescomplemented
126C2×(C2×D3)⋊C4—61no—
127C2×C4⋊Dic3—31no—
128C2×C4⋊Dic3—31no—
129C2×C4⋊Dic3—61no—
130#924—34no—
131#924—62no—
132C2×Dic3⋊C4—61no—
133C2×Dic3⋊C4—61no—
134C22×C3⋊C8—31no—
135C22×C3⋊C8—31no—
136C22×C3⋊C8—61no—
137C22×C3⋊C8C2×D311yescharacteristic
138#835—34no—
139#835—34no—
140#835—34no—
141#835—64no—
142#830—34no—
143(C2×D3)⋊C8—34no—
144#816—34no—
145C23×C32C2×D411yescharacteristic
146C22×C3×D3—22no—
147C22×C3×D3—22no—
148C22×C3×D3Q1614yescomplemented
149C22×C3×D3C2×D412yes—
150C32×Q8—24no—
151C32×Q8—22no—
152C32×Q8C2×D414yes—
153C2×C32×C4—24no—
154C2×C32×C4—22no—
155C2×C32×C4C2×D411yescharacteristic
156C2×C32×C4C2×D412yes—
157C2×C32×C4C2×D412yes—
158C2×C32×C4C2411yescharacteristic
159C2×C3⋊Dic3—22no—
160C2×C3⋊Dic3—42no—
161C2×C3×Dic3—22no—
162C2×C3×Dic3—24no—
163C2×C3×Dic3—22no—
164C2×C3×Dic3—22no—
165C2×C3×Dic3—42no—
166C2×C3×Dic3C2×D412yes—
167C3×C4×D3—216no—
168C3×C4×D3—24no—
169C3×C4×D3—22no—
170C3×C4×D3—22no—
171C3×Dic6—216no—
172C3×Dic6—24no—
173C3×Dic6—22no—
174C3×Dic6—22no—
175C3×Dic6—22no—
176C3×Dic6—42no—
177C3×Dic6C2×D414yes—
178C3⋊(C3⋊C8)—22no—
179C3×C3⋊C8—22no—
180C23×Q8—31no—
181C22×Q16—31no—
182C22×Q16—91no—
183C2×C22⋊Q8—91no—
184#451—98no—
185C2×#103—91no—
186C2×#103—91no—
187C2×C22⋊C8—91no—
188C24×C3—31no—
189C23×D3#6711yescharacteristic
190C2×C3×Q8—22no—
191C2×C3×Q8—21no—
192C2×C3×Q8—22no—
193C2×C3×Q8—21no—
194C2×C3×Q8—24no—
195C2×C3×Q8—22no—
196C2×C3×Q8—34no—
197C2×C3×Q8—32no—
198C2×C3×Q8—32no—
199C2×C3×Q8—42no—
200C2×C3×Q8—41no—
201C2×C3×Q8—64no—
202C2×C3×Q8—68no—
203C2×C3×Q8—68no—
204C2×C3×Q8—616no—
205C2×C3×Q8—68no—
206C2×C3×Q8—61no—
207C2×C3×Q8—62no—
208C2×C3×Q8—61no—
209C2×C3×Q8—62no—
210C2×C3×Q8—62no—
211C2×C3×Q8#6714yes—
212C2×C3×Q8#6714yes—
213C2×C3×Q8C22×D312yes—
214C2×C3×Q8C22×D312yes—
215C22×C3×C4—21no—
216C22×C3×C4—21no—
217C22×C3×C4—21no—
218C22×C3×C4—31no—
219C22×C3×C4—32no—
220C22×C3×C4—32no—
221C22×C3×C4—41no—
222C22×C3×C4—64no—
223C22×C3×C4—68no—
224C22×C3×C4—61no—
225C22×C3×C4—62no—
226C22×C3×C4—62no—
227C22×C3×C4—61no—
228C22×C3×C4C22×D311yescharacteristic
229C22×C3×C4C22×D311yescharacteristic
230C22×Dic3—21no—
231C22×Dic3—21no—
232C22×Dic3—61no—
233C22×Dic3—61no—
234C22×Dic3—121no—
235C22×Dic3#6711yescharacteristic
236D3×Q8—216no—
237D3×Q8—28no—
238D3×Q8—28no—
239C2×C4×D3—28no—
240C2×C4×D3—24no—
241C2×C4×D3—22no—
242C2×C4×D3—22no—
243C2×C4×D3#6712yes—
244C2×C4×D3C22×D312yes—
245C2×Dic6—28no—
246C2×Dic6—22no—
247C2×Dic6—21no—
248C2×Dic6—24no—
249C2×Dic6—22no—
250C2×Dic6—22no—
251C2×Dic6—21no—
252C2×Dic6#6714yes—
253C2×Dic6C22×D312yes—
254C2×Dic6C22×D312yes—
255C3×Q16—68no—
256C2×C3×C8—32no—
257C2×C3×C8—62no—
258#217—64no—
259#216—28no—
260#216—68no—
261#216—68no—
262(C2×D3)⋊C4—64no—
263C4⋊Dic3—32no—
264C4⋊Dic3—32no—
265C4⋊Dic3—62no—
266C4⋊Dic3—61no—
267C4⋊Dic3—61no—
268C4⋊Dic3—121no—
269Dic3⋊C4—64no—
270Dic3⋊C4—64no—
271C2×C3⋊C8—22no—
272C2×C3⋊C8—32no—
273C2×C3⋊C8—32no—
274C2×C3⋊C8—62no—
275C2×C3⋊C8—62no—
276C2×C3⋊C8—62no—
277C2×C3⋊C8—122no—
278C2×C3⋊C8C22×D312yes—
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—24no—
288C32×C4#12012yes—
289C32×C4C22×D411yescharacteristic
290C32×C4C22×D411yescharacteristic
291C3⋊Dic3—42no—
292C3×Dic3—22no—
293C3×Dic3—24no—
294C3×Dic3—42no—
295C22×Q8—34no—
296C22×Q8—31no—
297C22×Q8—31no—
298C22×Q8—61no—
299C22×Q8—62no—
300C22×Q8—64no—
301C22×Q8—64no—
302C22×Q8D3211yescharacteristic
303C23×C4—31no—
304C23×C4—61no—
305C2×Q16—34no—
306C2×Q16—64no—
307C2×Q16—94no—
308C2×Q16—184no—
309C22×C8—31no—
310C22×C8—91no—
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—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—24no—
331C3×Q8—24no—
332C3×Q8—22no—
333C3×Q8—22no—
334C3×Q8—24no—
335C3×Q8—34no—
336C3×Q8—42no—
337C3×Q8—44no—
338C3×Q8—616no—
339C3×Q8—64no—
340C3×Q8—62no—
341C3×Q8—62no—
342C3×Q8—62no—
343C3×Q8—122no—
344C3×Q8C2×#6714yes—
345C3×Q8C2×#6714yes—
346C2×C3×C4—24no—
347C2×C3×C4—24no—
348C2×C3×C4—22no—
349C2×C3×C4—22no—
350C2×C3×C4—21no—
351C2×C3×C4—22no—
352C2×C3×C4—22no—
353C2×C3×C4—21no—
354C2×C3×C4—32no—
355C2×C3×C4—42no—
356C2×C3×C4—44no—
357C2×C3×C4—616no—
358C2×C3×C4—62no—
359C2×C3×C4—64no—
360C2×C3×C4—62no—
361C2×C3×C4—64no—
362C2×C3×C4—62no—
363C2×C3×C4—62no—
364C2×C3×C4—62no—
365C2×C3×C4—122no—
366C2×C3×C4D3×D411yescharacteristic
367C2×C3×C4D3×D412yes—
368C2×C3×C4C2×#6712yes—
369C2×C3×C4C2×#6712yes—
370C2×C3×C4C2×#6711yescharacteristic
371C2×C3×C4C2×#6712yes—
372C2×C3×C4C23×D311yescharacteristic
373C2×C3×C4C23×D311yescharacteristic
374C2×Dic3—22no—
375C2×Dic3—24no—
376C2×Dic3—22no—
377C2×Dic3—22no—
378C2×Dic3—42no—
379C2×Dic3—62no—
380C2×Dic3—62no—
381C2×Dic3—122no—
382C2×Dic3—122no—
383C2×Dic3—122no—
384C2×Dic3—242no—
385C2×Dic3C2×#6712yes—
386C4×D3—216no—
387C4×D3—24no—
388C4×D3—22no—
389C4×D3—22no—
390Dic6—216no—
391Dic6—24no—
392Dic6—22no—
393Dic6—22no—
394Dic6—22no—
395Dic6—42no—
396Dic6C2×#6714yes—
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—21no—
409C2×Q8—22no—
410C2×Q8—32no—
411C2×Q8—32no—
412C2×Q8—34no—
413C2×Q8—64no—
414C2×Q8—68no—
415C2×Q8—68no—
416C2×Q8—616no—
417C2×Q8—68no—
418C2×Q8—62no—
419C2×Q8—61no—
420C2×Q8—61no—
421C2×Q8—62no—
422C2×Q8—62no—
423C2×Q8#62514yes—
424C2×Q8C2×D3212yes—
425C22×C4—21no—
426C22×C4—31no—
427C22×C4—32no—
428C22×C4—32no—
429C22×C4—64no—
430C22×C4—68no—
431C22×C4—61no—
432C22×C4—62no—
433C22×C4—62no—
434C22×C4—61no—
435C22×C4—181no—
436C22×C4C2×D3211yescharacteristic
437Q16—68no—
438Q16—188no—
439C2×C8—32no—
440C2×C8—62no—
441C2×C8—92no—
442C2×C8—182no—
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×C3D3×Q1612yes—
456C22×C3#91812yes—
457C22×C3#93712yes—
458C22×C3#94212yes—
459C22×C3C2×#21612yes—
460C22×C3#95312yes—
461C22×C3C2×D3×D411yescharacteristic
462C22×C3C22×#6711yescharacteristic
463C2×D3—28no—
464C2×D3—22no—
465C2×D3—22no—
466C2×D3C2×#21614yescomplemented
467C3×C4—24no—
468C3×C4—24no—
469C3×C4—21no—
470C3×C4—21no—
471C3×C4—22no—
472C3×C4—44no—
473C3×C4—62no—
474C3×C4—64no—
475C3×C4—122no—
476C3×C4#93712yes—
477C3×C4#95312yes—
478C3×C4C2×D3×D411yescharacteristic
479C3×C4C22×#6711yescharacteristic
480C3×C4C22×#6711yescharacteristic
481C3×C4C22×#6711yescharacteristic
482Dic3—22no—
483Dic3—24no—
484Dic3—42no—
485Dic3—122no—
486Dic3—122no—
487Dic3—242no—
488C32C2×#45111yescharacteristic, complemented, Sylow
489C23—32no—
490C23—34no—
491C23—62no—
492C23—62no—
493C23D3×#6711yescharacteristic
494Q8—22no—
495Q8—24no—
496Q8—34no—
497Q8—616no—
498Q8—62no—
499Q8—64no—
500Q8—62no—
501Q8—62no—
502Q8—122no—
503Q8C2×#62514yes—
504C2×C4—22no—
505C2×C4—24no—
506C2×C4—32no—
507C2×C4—616no—
508C2×C4—62no—
509C2×C4—62no—
510C2×C4—64no—
511C2×C4—62no—
512C2×C4—62no—
513C2×C4—64no—
514C2×C4—62no—
515C2×C4—122no—
516C2×C4—182no—
517C2×C4—362no—
518C2×C4C2×#62512yes—
519C2×C4D3×#6712yes—
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#518614yescomplemented
530C2×C3#522814yescomplemented
531C2×C3C2×D3×Q1611yescharacteristic
532C2×C3C2×#91811yescharacteristic
533C2×C3C2×#93711yescharacteristic
534C2×C3C2×#94211yescharacteristic
535C2×C3C22×#21611yescharacteristic
536C2×C3C2×#95311yescharacteristic
537D3—24no—
538C22—34no—
539C22—62no—
540C22—68no—
541C22—62no—
542C22D3×#21612yes—
543C22#6394812yes—
544C22#6397612yes—
545C22C2×D3×#6711yescharacteristic
546C4—24no—
547C4—62no—
548C4—64no—
549C4—122no—
550C4—362no—
551C4#6397612yes—
552C4C22×#62511yescharacteristic
553C4C2×D3×#6711yescharacteristic
554C3—21no—
555C3C2×#518611yescharacteristic, complemented
556C3C2×#522811yescharacteristic, complemented
557C2—64no—
558C2#1059159414yesdirect product factor
559C2C2×D3×#21611yescharacteristic
560C2C2×#6394811yescharacteristic
561C2C2×#6397611yescharacteristic
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×C3×#216C2semidirect
4. C22×#3718C2semidirect
5. C2×#63662C2semidirect
6. #10591594C2direct (N × H)
7. C2×#63566C2semidirect
24. C2×C3×#216C22semidirect
31. C2×#3718C22semidirect
32. #63662C22semidirect
33. #63566C22semidirect
41. C22×#216D3semidirect
125. C2×#216C2×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#5186semidirect
530. C2×C3#5228semidirect
555. C3C2×#5186semidirect
556. C3C2×#5228semidirect
558. C2#10591594direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×D3×Q82
C22×C3×#2162
C2×#638562
C22×#37182
C2×#636622
#105915942
C2×#635662
C2×(C2×D3)⋊(C3⋊C8)2
C2×#52283
C2×#51863