Finite Group Databasebeta

← C2×#10591261 #11801736

Subgroups — C2×#10591261 #11801736

Order 1152.

2021 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×Dic6C211yesmaximal, characteristic
2C22×Dic3⋊Dic3C211yesmaximal, characteristic
3C22×Dic32C211yesmaximal, characteristic
4C2×#63658C211yesmaximal, characteristic
5C2×C3×C3⋊#95C211yesmaximal, characteristic
6C2×#63579C211yesmaximal, characteristic
7C2×#63579C211yesmaximal, characteristic
8#10591261C218yesmaximal, direct product factor
9C2×#5229—31nomaximal
10C2×#4646—31nomaximal
11C23×C32×C4C2211yescharacteristic
12C23×C3⋊Dic3C2211yescharacteristic
13C23×C3⋊Dic3C2211yescharacteristic
14C23×C3×Dic3C2211yescharacteristic
15C23×C3×Dic3C2211yescharacteristic
16C23×C3×Dic3C2211yescharacteristic
17C23×C3×Dic3C2211yescharacteristic
18C22×C3×Dic6—24no—
19C22×C3×Dic6—24no—
20C22×C3×Dic6C418yescomplemented
21C22×C3×Dic6C2214yes—
22C2×Dic3⋊Dic3—24no—
23C2×Dic3⋊Dic3C2214yes—
24C2×Dic32—24no—
25C2×Dic32C2214yes—
26#63658C2214yes—
27C3×C3⋊#95C2214yes—
28#63579C2214yes—
29#63579C2214yes—
30C23×C3×Q8—31no—
31C23×Dic6D311yescharacteristic
32C22×C4⋊Dic3—31no—
33C22×Dic3⋊C4—31no—
34C22×C4×Dic3—31no—
35C22×C4×Dic3—31no—
36C2×C3×#95—31no—
37#5229—38no—
38C2×C3⋊#95—31no—
39C2×C3⋊#95—31no—
40C2×C3⋊#95—31no—
41C2×C3⋊#95—31no—
42C2×C3⋊#95—31no—
43C2×C3⋊#95—31no—
44C2×C3⋊#95—61no—
45C2×C3⋊#95D311yescharacteristic
46#4646—38no—
47C24×C32C2311yescharacteristic
48C22×C32×C4—22no—
49C22×C32×C4—22no—
50C22×C32×C4C2×C414yes—
51C22×C32×C4C2312yes—
52C22×C3⋊Dic3—22no—
53C22×C3⋊Dic3—22no—
54C22×C3⋊Dic3—22no—
55C22×C3⋊Dic3—22no—
56C22×C3⋊Dic3—22no—
57C22×C3⋊Dic3Q814yescomplemented
58C22×C3⋊Dic3C2312yes—
59C22×C3⋊Dic3C2312yes—
60C22×C3×Dic3—22no—
61C22×C3×Dic3—22no—
62C22×C3×Dic3—22no—
63C22×C3×Dic3—22no—
64C22×C3×Dic3—22no—
65C22×C3×Dic3—22no—
66C22×C3×Dic3—22no—
67C22×C3×Dic3C2×C414yes—
68C22×C3×Dic3C2×C414yes—
69C22×C3×Dic3D414yes—
70C22×C3×Dic3D414yes—
71C22×C3×Dic3Q814yescomplemented
72C22×C3×Dic3C2312yes—
73C22×C3×Dic3C2312yes—
74C22×C3×Dic3C2312yes—
75C22×C3×Dic3C2312yes—
76C2×C3×Dic6—232no—
77C2×C3×Dic6—28no—
78C2×C3×Dic6—28no—
79C2×C3×Dic6C2×C4116yescomplemented
80Dic3⋊Dic3—28no—
81Dic32—28no—
82C2×#391—91noSylow
83C22×C3×Q8—38no—
84C22×C3×Q8—34no—
85C22×C3×Q8—64no—
86C22×C3×Q8—64no—
87C23×C3×C4—21no—
88C23×C3×C4—31no—
89C23×C3×C4—31no—
90C23×C3×C4—31no—
91C23×C3×C4—31no—
92C23×C3×C4C2×D311yescharacteristic
93C23×C3×C4C2×D311yescharacteristic
94C23×Dic3—31no—
95C23×Dic3—31no—
96C23×Dic3—31no—
97C23×Dic3—31no—
98C23×Dic3—61no—
99C23×Dic3—61no—
100C23×Dic3C2×D311yescharacteristic
101C23×Dic3C2×D311yescharacteristic
102C23×Dic3C2×D311yescharacteristic
103C23×Dic3C2×D311yescharacteristic
104C22×Dic6—24no—
105C22×Dic6—24no—
106C22×Dic6Dic318yescomplemented
107C22×Dic6C2×D314yes—
108C2×C4⋊Dic3—34no—
109C2×C4⋊Dic3—64no—
110C2×Dic3⋊C4—34no—
111C2×Dic3⋊C4—64no—
112C2×C4×Dic3—34no—
113C2×C4×Dic3—34no—
114C2×C4×Dic3—64no—
115C2×C4×Dic3—64no—
116C3×#95—34no—
117C3⋊#95—34no—
118C3⋊#95—34no—
119C3⋊#95—34no—
120C3⋊#95—34no—
121C3⋊#95—34no—
122C3⋊#95—34no—
123C3⋊#95—64no—
124C3⋊#95C2×D314yes—
125C23×C32C22×C412yes—
126C23×C32C2×D412yes—
127C23×C32C2×D412yes—
128C23×C32C2×Q812yes—
129C23×C32C2×Q812yes—
130C23×C32#4112yes—
131C23×C32#4112yes—
132C23×C32C2411yescharacteristic
133C2×C32×C4—28no—
134C2×C32×C4—22no—
135C2×C32×C4—22no—
136C2×C32×C4C22×C414yes—
137C2×C3⋊Dic3—22no—
138C2×C3⋊Dic3—28no—
139C2×C3⋊Dic3—22no—
140C2×C3⋊Dic3—22no—
141C2×C3⋊Dic3—22no—
142C2×C3⋊Dic3—22no—
143C2×C3⋊Dic3—44no—
144C2×C3⋊Dic3C2×Q814yescomplemented
145C2×C3×Dic3—28no—
146C2×C3×Dic3—28no—
147C2×C3×Dic3—22no—
148C2×C3×Dic3—22no—
149C2×C3×Dic3—22no—
150C2×C3×Dic3—22no—
151C2×C3×Dic3—22no—
152C2×C3×Dic3—22no—
153C2×C3×Dic3—22no—
154C2×C3×Dic3—44no—
155C2×C3×Dic3C22⋊C4116yes—
156C2×C3×Dic3C22×C414yes—
157C2×C3×Dic3C22×C414yes—
158C2×C3×Dic3C2×D414yes—
159C2×C3×Dic3C2×D414yes—
160C2×C3×Dic3C2×Q814yescomplemented
161C3×Dic6—232no—
162C23×Q8—31no—
163C22×C4⋊C4—91no—
164C22×C42—91no—
165#391—98no—
166C2×#95—31no—
167C2×#95—91no—
168C2×#95—91no—
169C2×#95—91no—
170C24×C3—21no—
171C24×C3C22×D311yescharacteristic
172C24×C3C22×D311yescharacteristic
173C2×C3×Q8—316no—
174C2×C3×Q8—632no—
175C2×C3×Q8—68no—
176C2×C3×Q8—68no—
177C22×C3×C4—22no—
178C22×C3×C4—22no—
179C22×C3×C4—22no—
180C22×C3×C4—22no—
181C22×C3×C4—24no—
182C22×C3×C4—22no—
183C22×C3×C4—34no—
184C22×C3×C4—34no—
185C22×C3×C4—34no—
186C22×C3×C4—32no—
187C22×C3×C4—34no—
188C22×C3×C4—34no—
189C22×C3×C4—32no—
190C22×C3×C4—32no—
191C22×C3×C4—32no—
192C22×C3×C4—42no—
193C22×C3×C4—42no—
194C22×C3×C4—62no—
195C22×C3×C4—62no—
196C22×C3×C4—62no—
197C22×C3×C4—62no—
198C22×C3×C4—62no—
199C22×C3×C4—62no—
200C22×C3×C4—62no—
201C22×C3×C4C4×D314yes—
202C22×C3×C4C2×Dic314yes—
203C22×C3×C4C22×D312yes—
204C22×C3×C4C22×D312yes—
205C22×Dic3—22no—
206C22×Dic3—22no—
207C22×Dic3—22no—
208C22×Dic3—22no—
209C22×Dic3—22no—
210C22×Dic3—22no—
211C22×Dic3—22no—
212C22×Dic3—34no—
213C22×Dic3—34no—
214C22×Dic3—32no—
215C22×Dic3—32no—
216C22×Dic3—32no—
217C22×Dic3—32no—
218C22×Dic3—62no—
219C22×Dic3—62no—
220C22×Dic3—64no—
221C22×Dic3—62no—
222C22×Dic3—62no—
223C22×Dic3—62no—
224C22×Dic3—62no—
225C22×Dic3—64no—
226C22×Dic3—62no—
227C22×Dic3—62no—
228C22×Dic3—62no—
229C22×Dic3—62no—
230C22×Dic3—62no—
231C22×Dic3—62no—
232C22×Dic3—122no—
233C22×Dic3—122no—
234C22×Dic3—122no—
235C22×Dic3—122no—
236C22×Dic3Dic614yescomplemented
237C22×Dic3C2×Dic314yes—
238C22×Dic3C2×Dic314yes—
239C22×Dic3#6714yes—
240C22×Dic3#6714yes—
241C22×Dic3C22×D312yes—
242C22×Dic3C22×D312yes—
243C22×Dic3C22×D312yes—
244C22×Dic3C22×D312yes—
245C2×Dic6—232no—
246C2×Dic6—28no—
247C2×Dic6—28no—
248C2×Dic6C2×Dic3116yescomplemented
249C4⋊Dic3—68no—
250Dic3⋊C4—68no—
251C4×Dic3—68no—
252C4×Dic3—68no—
253C22×C32C2×C22⋊C414yes—
254C22×C32C4×Q814yes—
255C22×C32C4×Q814yes—
256C22×C32C22⋊Q814yes—
257C22×C32C22⋊Q814yes—
258C22×C32#12414yes—
259C22×C32C4⋊Q814yes—
260C22×C32C23×C411yescharacteristic
261C22×C32C22×D411yescharacteristic
262C22×C32C22×D411yescharacteristic
263C22×C32C22×Q811yescharacteristic
264C22×C32C22×Q811yescharacteristic
265C22×C32C2×#4111yescharacteristic
266C22×C32C2×#4111yescharacteristic
267C32×C4—24no—
268C3⋊Dic3—24no—
269C3⋊Dic3—42no—
270C3×Dic3—24no—
271C3×Dic3—24no—
272C3×Dic3—42no—
273C3×Dic3C2×C22⋊C418yes—
274C22×Q8—38no—
275C22×Q8—34no—
276C22×Q8—64no—
277C22×Q8—64no—
278C23×C4—31no—
279C23×C4—31no—
280C23×C4—31no—
281C23×C4—31no—
282C23×C4—91no—
283C23×C4—91no—
284C23×C4D3211yescharacteristic
285C2×C4⋊C4—94no—
286C2×C4⋊C4—184no—
287C2×C42—94no—
288C2×C42—184no—
289#95—34no—
290#95—94no—
291#95—94no—
292#95—94no—
293C23×C3—21no—
294C23×C3—22no—
295C23×C3—22no—
296C23×C3—22no—
297C23×C3—22no—
298C23×C3—22no—
299C23×C3—22no—
300C23×C3—22no—
301C23×C3C2×Dic612yes—
302C23×C3C2×C4×D312yes—
303C23×C3#23512yes—
304C23×C3D3×D412yes—
305C23×C3D3×D412yes—
306C23×C3#23712yes—
307C23×C3D3×Q812yes—
308C23×C3D3×Q812yes—
309C23×C3D3×Q812yes—
310C23×C3#23912yes—
311C23×C3#23912yes—
312C23×C3C22×Dic312yes—
313C23×C3C2×#6712yes—
314C23×C3C2×#6712yes—
315C23×C3C23×D311yescharacteristic
316C23×C3C23×D311yescharacteristic
317C3×Q8—632no—
318C2×C3×C4—28no—
319C2×C3×C4—28no—
320C2×C3×C4—22no—
321C2×C3×C4—22no—
322C2×C3×C4—22no—
323C2×C3×C4—22no—
324C2×C3×C4—24no—
325C2×C3×C4—316no—
326C2×C3×C4—34no—
327C2×C3×C4—34no—
328C2×C3×C4—34no—
329C2×C3×C4—34no—
330C2×C3×C4—34no—
331C2×C3×C4—42no—
332C2×C3×C4—42no—
333C2×C3×C4—48no—
334C2×C3×C4—68no—
335C2×C3×C4—68no—
336C2×C3×C4—62no—
337C2×C3×C4—62no—
338C2×C3×C4—62no—
339C2×C3×C4—62no—
340C2×C3×C4—62no—
341C2×C3×C4—62no—
342C2×C3×C4—62no—
343C2×C3×C4—124no—
344C2×C3×C4C2×C4×D314yes—
345C2×C3×C4C22×Dic314yes—
346C2×Dic3—28no—
347C2×Dic3—28no—
348C2×Dic3—22no—
349C2×Dic3—22no—
350C2×Dic3—22no—
351C2×Dic3—22no—
352C2×Dic3—22no—
353C2×Dic3—22no—
354C2×Dic3—22no—
355C2×Dic3—34no—
356C2×Dic3—34no—
357C2×Dic3—44no—
358C2×Dic3—64no—
359C2×Dic3—68no—
360C2×Dic3—68no—
361C2×Dic3—62no—
362C2×Dic3—62no—
363C2×Dic3—62no—
364C2×Dic3—62no—
365C2×Dic3—64no—
366C2×Dic3—62no—
367C2×Dic3—62no—
368C2×Dic3—62no—
369C2×Dic3—62no—
370C2×Dic3—62no—
371C2×Dic3—62no—
372C2×Dic3—122no—
373C2×Dic3—122no—
374C2×Dic3—128no—
375C2×Dic3—122no—
376C2×Dic3—122no—
377C2×Dic3—128no—
378C2×Dic3—124no—
379C2×Dic3—124no—
380C2×Dic3#217116yes—
381C2×Dic3C2×Dic614yescomplemented
382C2×Dic3C22×Dic314yes—
383C2×Dic3C22×Dic314yes—
384C2×Dic3C2×#6714yes—
385C2×Dic3C2×#6714yes—
386Dic6—232no—
387C2×C32#39118yescomplemented
388C2×C32C22×C22⋊C411yescharacteristic
389C2×C32C2×C4×Q811yescharacteristic
390C2×C32C2×C4×Q811yescharacteristic
391C2×C32C2×C22⋊Q811yescharacteristic
392C2×C32C2×C22⋊Q811yescharacteristic
393C2×C32C2×#12411yescharacteristic
394C2×C32C2×C4⋊Q811yescharacteristic
395C24C2×D3211yescharacteristic
396C2×Q8—316no—
397C2×Q8—68no—
398C2×Q8—68no—
399C2×Q8—632no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—32no—
403C22×C4—34no—
404C22×C4—34no—
405C22×C4—34no—
406C22×C4—32no—
407C22×C4—32no—
408C22×C4—34no—
409C22×C4—34no—
410C22×C4—32no—
411C22×C4—62no—
412C22×C4—62no—
413C22×C4—62no—
414C22×C4—62no—
415C22×C4—62no—
416C22×C4—62no—
417C22×C4—62no—
418C22×C4—92no—
419C22×C4—94no—
420C22×C4—92no—
421C22×C4—182no—
422C22×C4—182no—
423C22×C4—182no—
424C22×C4—182no—
425C22×C4—182no—
426C22×C4D3×Dic314yes—
427C22×C4C2×D3212yes—
428C4⋊C4—188no—
429C42—188no—
430C22×C3—21no—
431C22×C3—21no—
432C22×C3—21no—
433C22×C3—21no—
434C22×C3—21no—
435C22×C3—21no—
436C22×C3—21no—
437C22×C3—24no—
438C22×C3—24no—
439C22×C3—24no—
440C22×C3—24no—
441C22×C3—24no—
442C22×C3—24no—
443C22×C3—24no—
444C22×C3C4×Dic614yes—
445C22×C3#87814yes—
446C22×C3D3×C22⋊C414yes—
447C22×C3#88514yes—
448C22×C3#88714yes—
449C22×C3#88814yes—
450C22×C3#89614yes—
451C22×C3#94414yes—
452C22×C3Q8×Dic314yes—
453C22×C3Q8×Dic314yes—
454C22×C3#94614yes—
455C22×C3#94614yes—
456C22×C3#94714yes—
457C22×C3C2×#21714yes—
458C22×C3C22×Dic611yescharacteristic
459C22×C3C22×C4×D311yescharacteristic
460C22×C3C2×#23511yescharacteristic
461C22×C3C2×D3×D411yescharacteristic
462C22×C3C2×D3×D411yescharacteristic
463C22×C3C2×#23711yescharacteristic
464C22×C3C2×D3×Q811yescharacteristic
465C22×C3C2×D3×Q811yescharacteristic
466C22×C3C2×D3×Q811yescharacteristic
467C22×C3C2×#23911yescharacteristic
468C22×C3C2×#23911yescharacteristic
469C22×C3C23×Dic311yescharacteristic
470C22×C3C22×#6711yescharacteristic
471C22×C3C22×#6711yescharacteristic
472C3×C4—24no—
473C3×C4—24no—
474C3×C4—38no—
475C3×C4—44no—
476C3×C4—64no—
477C3×C4—64no—
478C3×C4—122no—
479Dic3—24no—
480Dic3—24no—
481Dic3—42no—
482Dic3—64no—
483Dic3—64no—
484Dic3—124no—
485Dic3—124no—
486Dic3—122no—
487Dic3—122no—
488Dic3C2×#21718yes—
489C32C2×#39111yescharacteristic, complemented, Sylow
490C23D3×Dic612yes—
491C23#379612yes—
492C23#379712yes—
493C23#379912yes—
494C23C2×D3×Dic312yes—
495C23D3×#6712yes—
496C23D3×#6712yes—
497C23C22×D3211yescharacteristic
498Q8—632no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—28no—
502C2×C4—34no—
503C2×C4—34no—
504C2×C4—34no—
505C2×C4—316no—
506C2×C4—34no—
507C2×C4—34no—
508C2×C4—62no—
509C2×C4—62no—
510C2×C4—62no—
511C2×C4—62no—
512C2×C4—68no—
513C2×C4—68no—
514C2×C4—62no—
515C2×C4—62no—
516C2×C4—62no—
517C2×C4—94no—
518C2×C4—124no—
519C2×C4—182no—
520C2×C4—182no—
521C2×C4—188no—
522C2×C4—182no—
523C2×C4—182no—
524C2×C4—182no—
525C2×C4—364no—
526C2×C4C2×D3×Dic314yes—
527C2×C3—21no—
528C2×C3—21no—
529C2×C3—28no—
530C2×C3—21no—
531C2×C3—21no—
532C2×C3—21no—
533C2×C3—21no—
534C2×C3—21no—
535C2×C3#464618yescomplemented
536C2×C3#522918yescomplemented
537C2×C3C2×C4×Dic611yescharacteristic
538C2×C3C2×#87811yescharacteristic
539C2×C3C2×D3×C22⋊C411yescharacteristic
540C2×C3C2×#88511yescharacteristic
541C2×C3C2×#88711yescharacteristic
542C2×C3C2×#88811yescharacteristic
543C2×C3C2×#89611yescharacteristic
544C2×C3C2×#94411yescharacteristic
545C2×C3C2×Q8×Dic311yescharacteristic
546C2×C3C2×Q8×Dic311yescharacteristic
547C2×C3C2×#94611yescharacteristic
548C2×C3C2×#94611yescharacteristic
549C2×C3C2×#94711yescharacteristic
550C2×C3C22×#21711yescharacteristic
551C22#6383914yes—
552C22Dic3×Dic614yes—
553C22#6384314yes—
554C22#6388714yes—
555C22#6388814yes—
556C22#6390714yes—
557C22D3×#21714yes—
558C22C2×D3×Dic611yescharacteristic
559C22C2×#379611yescharacteristic
560C22C2×#379711yescharacteristic
561C22C2×#379911yescharacteristic
562C22C22×D3×Dic311yescharacteristic
563C22C2×D3×#6711yescharacteristic
564C22C2×D3×#6711yescharacteristic
565C4—24no—
566C4—38no—
567C4—64no—
568C4—64no—
569C4—122no—
570C4—184no—
571C4—362no—
572C3—21no—
573C3C2×#464611yescharacteristic, complemented
574C3C2×#522911yescharacteristic, complemented
575C2#1059126118yesdirect product factor
576C2C2×#6383911yescharacteristic
577C2C2×Dic3×Dic611yescharacteristic
578C2C2×#6384311yescharacteristic
579C2C2×#6388711yescharacteristic
580C2C2×#6388811yescharacteristic
581C2C2×#6390711yescharacteristic
582C2C2×D3×#21711yescharacteristic
subgroupG/H
centerC24C2×D32
commutatorC22×C32C23×C4
FrattiniC23C22×D32
FittingC23×C32×C4C22
socle, prime radicalC24×C32C23
cosocleC23×C32C24
hypercenterC23×C4D32
hypocenterC32C2×#391
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C24 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
8. #10591261C2direct (N × H)
20. C22×C3×Dic6C4semidirect
57. C22×C3⋊Dic3Q8semidirect
71. C22×C3×Dic3Q8semidirect
79. C2×C3×Dic6C2×C4semidirect
106. C22×Dic6Dic3semidirect
144. C2×C3⋊Dic3C2×Q8semidirect
160. C2×C3×Dic3C2×Q8semidirect
236. C22×Dic3Dic6semidirect
248. C2×Dic6C2×Dic3semidirect
381. C2×Dic3C2×Dic6semidirect
387. C2×C32#391semidirect
489. C32C2×#391semidirect
535. C2×C3#4646semidirect
536. C2×C3#5229semidirect
573. C3C2×#4646semidirect
574. C3C2×#5229semidirect
575. C2#10591261direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C3×Dic62
C22×Dic3⋊Dic32
C22×Dic322
C2×#636582
C2×C3×C3⋊#952
C2×#635792
#105912612
C2×#52293
C2×#46463