Finite Group Databasebeta

← C2×#10591656 #11863781

Subgroups — C2×#10591656 #11863781

Order 1152.

1681 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3796C211yesmaximal, characteristic
2C2×#64155C211yesmaximal, characteristic, complemented
3C22×C3×#216C211yesmaximal, characteristic, complemented
4C22×C3×#215C211yesmaximal, characteristic, complemented
5#10591656C218yesmaximal, direct product factor
6C2×#63566C211yesmaximal, characteristic, complemented
7C2×#63563C211yesmaximal, characteristic, complemented
8C2×#63557C211yesmaximal, characteristic, complemented
9C2×#5187—31nomaximal
10C2×#5173—31nomaximal
11C22×C32×Q8C2211yescharacteristic
12C22×C4×C3⋊D3C2211yescharacteristic
13C22×C3×D12C2211yescharacteristic
14C22×C3×Dic6C2211yescharacteristic
15C22×#626—21no—
16C22×D3×Dic3—21no—
17C2×#3796—22no—
18C2×#3796—24no—
19C2×#3796—24no—
20C2×#3796C2214yes—
21#64155—22no—
22#64155C2214yescomplemented
23C2×#3752—21no—
24C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
25C2×#3750—21no—
26C2×C3×#216—24no—
27C2×C3×#216C2214yescomplemented
28C2×C3×#215—24no—
29C2×C3×#215C2214yescomplemented
30C22×C3×C3⋊C8C2211yescharacteristic
31C22×C3×C3⋊C8C2211yescharacteristic
32#63566C2214yescomplemented
33#63563C2214yescomplemented
34#63557C2214yescomplemented
35C22×#239—31no—
36C22×#237—31no—
37C22×C3×Q16—31no—
38C22×C3×SD16—31no—
39C2×#946—31no—
40C2×#946—31no—
41C2×#946—61no—
42C22×#216D311yescharacteristic, complemented
43C22×#215D311yescharacteristic, complemented
44C2×#835—31no—
45C2×#832—31no—
46#5187—38no—
47#5173—38no—
48C2×#821—31no—
49C2×(C2×D3)⋊C8—31no—
50C2×(C2×D3)⋊C8—31no—
51C2×#816—31no—
52C23×C3⋊D3D411yescharacteristic
53C23×C3×D3—21no—
54C2×C32×Q8—21no—
55C2×C32×Q8—22no—
56C2×C32×Q8—22no—
57C2×C32×Q8C2312yes—
58C22×C32×C4—21no—
59C22×C32×C4C2311yescharacteristic
60C22×C3⋊Dic3—21no—
61C22×C3⋊Dic3D411yescharacteristic
62C2×C4×C3⋊D3—22no—
63C2×C4×C3⋊D3—22no—
64C2×C4×C3⋊D3D412yes—
65C2×C4×C3⋊D3C2312yes—
66C22×C3×Dic3—21no—
67C2×C3×D12—21no—
68C2×C3×D12—22no—
69C2×C3×D12D414yes—
70C2×C3×D12C2312yes—
71C2×C3×Dic6—21no—
72C2×C3×Dic6—22no—
73C2×C3×Dic6D414yes—
74C2×C3×Dic6C2312yes—
75C2×#626—28no—
76C2×#626—24no—
77C2×D3×Dic3—28no—
78C2×D3×Dic3—24no—
79#3796—216no—
80#3796—28no—
81#3796—28no—
82#3752—24no—
83C4⋊(C3⋊Dic3)—21no—
84C4⋊(C3⋊Dic3)C2312yes—
85#3750—24no—
86C3×#216—28no—
87C3×#215—28no—
88C2×C3×C3⋊C8—22no—
89C2×C3×C3⋊C8—22no—
90C2×C3×C3⋊C8C2312yes—
91C2×C3×C3⋊C8C2312yes—
92C2×#452—91noSylow
93C22×C3×Q8—21no—
94C22×C3×Q8—31no—
95C22×C3×Q8C2×D311yescharacteristic
96C22×C3×Q8C2×D311yescharacteristic
97C22×C3×D4—31no—
98C22×#67—61no—
99C23×Dic3—61no—
100C2×#239—34no—
101C2×#239—62no—
102C2×#239—64no—
103C2×#239—64no—
104C2×#237—34no—
105C2×#237—62no—
106C2×#237—64no—
107C2×#237—64no—
108C22×D12—61no—
109C22×D12C2×D311yescharacteristic
110C22×C4×D3—31no—
111C22×C4×D3—31no—
112C22×C4×D3—61no—
113C22×C4×D3—61no—
114C22×Dic6C2×D311yescharacteristic
115C2×C3×Q16—34no—
116C2×C3×Q16—64no—
117C2×C3×SD16—34no—
118C2×C3×SD16—64no—
119C22×C3×C8—31no—
120C22×C3×C8—31no—
121#946—34no—
122#946—34no—
123#946—64no—
124#946—62no—
125#946—62no—
126#946—64no—
127C2×#216—24no—
128C2×#216C2×D314yescomplemented
129C2×#215—24no—
130C2×#215C2×D314yescomplemented
131C2×(C2×D3)⋊C4—61no—
132C2×(C2×D3)⋊C4—61no—
133C2×(C2×D3)⋊C4—62no—
134C2×C4⋊Dic3—31no—
135C2×C4⋊Dic3—31no—
136C2×C4⋊Dic3—61no—
137C2×Dic3⋊C4—61no—
138C2×Dic3⋊C4—61no—
139C2×Dic3⋊C4—62no—
140C22×C3⋊C8C2×D311yescharacteristic
141C22×C3⋊C8C2×D311yescharacteristic
142#835—34no—
143#832—34no—
144#821—34no—
145(C2×D3)⋊C8—34no—
146(C2×D3)⋊C8—34no—
147#816—34no—
148C23×C32C2×D411yescharacteristic
149C22×C3⋊D3—22no—
150C22×C3⋊D3—22no—
151C22×C3⋊D3—22no—
152C22×C3⋊D3C2×D412yes—
153C22×C3×D3—24no—
154C22×C3×D3—22no—
155C22×C3×D3—42no—
156C22×C3×D3—42no—
157C32×Q8—22no—
158C32×Q8—22no—
159C32×Q8—42no—
160C2×C32×C4—22no—
161C2×C32×C4—42no—
162C2×C32×C4C2×D411yescharacteristic
163C2×C32×C4C2×D412yes—
164C2×C32×C4C2×D412yes—
165C2×C32×C4C2411yescharacteristic
166C2×C3⋊Dic3—22no—
167C2×C3⋊Dic3—22no—
168C2×C3⋊Dic3—42no—
169C2×C3⋊Dic3C2×D412yes—
170C4×C3⋊D3—24no—
171C4×C3⋊D3—22no—
172C4×C3⋊D3—22no—
173C2×C3×Dic3—24no—
174C2×C3×Dic3—22no—
175C3×D12—24no—
176C3×D12—22no—
177C3×D12C2×D414yes—
178C3×Dic6—24no—
179C3×Dic6—22no—
180C3×Dic6C2×D414yes—
181#626—216no—
182D3×Dic3—216no—
183C3×C3⋊C8—22no—
184C3×C3⋊C8—22no—
185C22×#41—91no—
186C22×Q16—31no—
187C22×SD16—31no—
188C2×C22⋊Q8—91no—
189#452—98no—
190C2×#103—91no—
191C2×#102—91no—
192C2×C22⋊C8—91no—
193C24×C3—61no—
194C23×D3—21no—
195C23×D3—31no—
196C23×D3—31no—
197C23×D3—61no—
198C2×C3×Q8—22no—
199C2×C3×Q8—21no—
200C2×C3×Q8—21no—
201C2×C3×Q8—22no—
202C2×C3×Q8—22no—
203C2×C3×Q8—22no—
204C2×C3×Q8—22no—
205C2×C3×Q8—22no—
206C2×C3×Q8—34no—
207C2×C3×Q8—32no—
208C2×C3×Q8—42no—
209C2×C3×Q8—42no—
210C2×C3×Q8—61no—
211C2×C3×Q8—62no—
212C2×C3×Q8C22×D312yes—
213C2×C3×Q8C22×D312yes—
214C2×C3×D4—34no—
215C2×C3×D4—32no—
216C2×C3×D4—61no—
217C2×C3×D4—62no—
218C22×C3×C4—22no—
219C22×C3×C4—21no—
220C22×C3×C4—21no—
221C22×C3×C4—21no—
222C22×C3×C4—61no—
223C22×C3×C4C22×D311yescharacteristic
224C22×C3×C4C22×D311yescharacteristic
225C2×#67—64no—
226C2×#67—68no—
227C22×Dic3—21no—
228C22×Dic3—31no—
229C22×Dic3—31no—
230C22×Dic3—61no—
231C22×Dic3—64no—
232C22×Dic3—68no—
233C22×Dic3—62no—
234C22×Dic3—61no—
235C22×Dic3—61no—
236#239—68no—
237#239—616no—
238#239—68no—
239#237—68no—
240#237—616no—
241#237—68no—
242C2×D12—22no—
243C2×D12—21no—
244C2×D12—64no—
245C2×D12—68no—
246C2×D12#6714yes—
247C2×D12C22×D312yes—
248C2×C4×D3—32no—
249C2×C4×D3—32no—
250C2×C4×D3—32no—
251C2×C4×D3—32no—
252C2×C4×D3—62no—
253C2×C4×D3—62no—
254C2×C4×D3—64no—
255C2×C4×D3—68no—
256C2×C4×D3—62no—
257C2×C4×D3—62no—
258C2×C4×D3—62no—
259C2×C4×D3—62no—
260C2×C4×D3—122no—
261C2×C4×D3—122no—
262C2×Dic6—22no—
263C2×Dic6—21no—
264C2×Dic6#6714yes—
265C2×Dic6C22×D312yes—
266C3×Q16—68no—
267C3×SD16—68no—
268C2×C3×C8—32no—
269C2×C3×C8—32no—
270C2×C3×C8—62no—
271C2×C3×C8—62no—
272#216—28no—
273#215—28no—
274(C2×D3)⋊C4—64no—
275(C2×D3)⋊C4—64no—
276(C2×D3)⋊C4—68no—
277C4⋊Dic3—32no—
278C4⋊Dic3—32no—
279C4⋊Dic3—62no—
280C4⋊Dic3—62no—
281C4⋊Dic3—61no—
282C4⋊Dic3—61no—
283Dic3⋊C4—64no—
284Dic3⋊C4—64no—
285Dic3⋊C4—68no—
286C2×C3⋊C8—22no—
287C2×C3⋊C8—22no—
288C2×C3⋊C8C22×D312yes—
289C2×C3⋊C8C22×D312yes—
290C22×C32#12012yes—
291C22×C32#13512yes—
292C22×C32#13712yes—
293C22×C32C22×D411yescharacteristic
294C2×C3⋊D3—22no—
295C2×C3⋊D3—22no—
296C2×C3⋊D3—22no—
297C2×C3⋊D3—44no—
298C2×C3×D3—24no—
299C2×C3×D3—42no—
300C2×C3×D3—42no—
301C2×C3×D3—48no—
302C32×C4—42no—
303C32×C4#12012yes—
304C32×C4C22×D411yescharacteristic
305C32×C4C22×D411yescharacteristic
306C3⋊Dic3—22no—
307C3⋊Dic3—42no—
308C3×Dic3—24no—
309C2×#41—94no—
310C2×#41—182no—
311C2×#41—184no—
312C2×#41—184no—
313C22×Q8—31no—
314C22×Q8D3211yescharacteristic
315C22×D4—31no—
316C22×D4—181no—
317C23×C4—91no—
318C23×C4—181no—
319C2×Q16—34no—
320C2×Q16—64no—
321C2×SD16—34no—
322C2×SD16—64no—
323C22×C8—31no—
324C22×C8—31no—
325C22⋊Q8—94no—
326C22⋊Q8—182no—
327C2×C4⋊C4—91no—
328C2×C4⋊C4—181no—
329C2×C22⋊C4—181no—
330#103—94no—
331#102—94no—
332C22⋊C8—94no—
333C23×C3—21no—
334C23×C3—64no—
335C23×C3—62no—
336C23×C3—122no—
337C23×C3—122no—
338C23×C3D3×D411yescharacteristic
339C23×C3D3×D411yescharacteristic
340C22×D3—24no—
341C22×D3—22no—
342C22×D3—32no—
343C22×D3—32no—
344C22×D3—42no—
345C22×D3—42no—
346C22×D3—62no—
347C22×D3—64no—
348C22×D3—62no—
349C22×D3—62no—
350C22×D3—62no—
351C22×D3—62no—
352C22×D3—62no—
353C22×D3—62no—
354C22×D3—122no—
355C22×D3—122no—
356C3×Q8—22no—
357C3×Q8—22no—
358C3×Q8—22no—
359C3×Q8—22no—
360C3×Q8—34no—
361C3×Q8—42no—
362C3×Q8—42no—
363C3×Q8—44no—
364C3×Q8—42no—
365C3×Q8—42no—
366C3×Q8—64no—
367C3×Q8—62no—
368C3×D4—34no—
369C3×D4—64no—
370C3×D4—62no—
371C2×C3×C4—24no—
372C2×C3×C4—22no—
373C2×C3×C4—22no—
374C2×C3×C4—21no—
375C2×C3×C4—22no—
376C2×C3×C4—22no—
377C2×C3×C4—21no—
378C2×C3×C4—44no—
379C2×C3×C4—42no—
380C2×C3×C4—42no—
381C2×C3×C4—64no—
382C2×C3×C4—62no—
383C2×C3×C4D3×D412yes—
384C2×C3×C4D3×D412yes—
385C2×C3×C4D3×D411yescharacteristic
386C2×C3×C4D3×D411yescharacteristic
387C2×C3×C4C2×#6712yes—
388C2×C3×C4C2×#6712yes—
389C2×C3×C4C23×D311yescharacteristic
390C2×C3×C4C23×D311yescharacteristic
391#67—616no—
392C2×Dic3—24no—
393C2×Dic3—22no—
394C2×Dic3—32no—
395C2×Dic3—32no—
396C2×Dic3—62no—
397C2×Dic3—616no—
398C2×Dic3—62no—
399C2×Dic3—62no—
400C2×Dic3—64no—
401C2×Dic3—62no—
402C2×Dic3—62no—
403C2×Dic3—122no—
404C2×Dic3—124no—
405C2×Dic3—122no—
406C2×Dic3—122no—
407D12—24no—
408D12—22no—
409D12—616no—
410D12C2×#6714yes—
411C4×D3—616no—
412C4×D3—64no—
413C4×D3—64no—
414C4×D3—62no—
415C4×D3—62no—
416C4×D3—62no—
417C4×D3—62no—
418C4×D3—122no—
419C4×D3—122no—
420C4×D3—124no—
421Dic6—24no—
422Dic6—22no—
423Dic6C2×#6714yes—
424C3×C8—62no—
425C3×C8—62no—
426C3⋊C8—22no—
427C3⋊C8—22no—
428C2×C32#45214yescomplemented
429C2×C32C2×#12011yescharacteristic
430C2×C32C2×#13511yescharacteristic
431C2×C32C2×#13711yescharacteristic
432C3⋊D3—42no—
433C3×D3—44no—
434C24—61no—
435C24—91no—
436#41—188no—
437#41—188no—
438#41—1816no—
439C2×Q8—21no—
440C2×Q8—22no—
441C2×Q8—22no—
442C2×Q8—32no—
443C2×Q8—34no—
444C2×Q8—62no—
445C2×Q8—61no—
446C2×Q8C2×D3212yes—
447C2×D4—32no—
448C2×D4—34no—
449C2×D4—62no—
450C2×D4—61no—
451C2×D4—184no—
452C2×D4—188no—
453C22×C4—21no—
454C22×C4—61no—
455C22×C4—91no—
456C22×C4—92no—
457C22×C4—92no—
458C22×C4—184no—
459C22×C4—188no—
460C22×C4—182no—
461C22×C4—182no—
462C22×C4—181no—
463C22×C4C2×D3211yescharacteristic
464Q16—68no—
465SD16—68no—
466C2×C8—32no—
467C2×C8—32no—
468C2×C8—62no—
469C2×C8—62no—
470C4⋊C4—92no—
471C4⋊C4—184no—
472C4⋊C4—181no—
473C22⋊C4—184no—
474C22×C3—21no—
475C22×C3—22no—
476C22×C3—22no—
477C22×C3—22no—
478C22×C3—64no—
479C22×C3—128no—
480C22×C3—122no—
481C22×C3—122no—
482C22×C3#91512yes—
483C22×C3#91612yes—
484C22×C3#91812yes—
485C22×C3#91912yes—
486C22×C3#93712yes—
487C22×C3#93712yes—
488C22×C3C2×D3×D411yescharacteristic
489C22×C3C2×D3×D411yescharacteristic
490C2×D3—24no—
491C2×D3—48no—
492C2×D3—42no—
493C2×D3—42no—
494C2×D3—64no—
495C2×D3—62no—
496C2×D3—62no—
497C2×D3—62no—
498C2×D3—62no—
499C2×D3—62no—
500C2×D3—62no—
501C2×D3—122no—
502C2×D3—122no—
503C2×D3—128no—
504C2×D3—124no—
505C2×D3—124no—
506C3×C4—21no—
507C3×C4—21no—
508C3×C4—22no—
509C3×C4—44no—
510C3×C4—42no—
511C3×C4—42no—
512C3×C4—64no—
513C3×C4#93712yes—
514C3×C4#93712yes—
515C3×C4C2×D3×D411yescharacteristic
516C3×C4C2×D3×D411yescharacteristic
517C3×C4C22×#6711yescharacteristic
518C3×C4C22×#6711yescharacteristic
519Dic3—24no—
520Dic3—62no—
521Dic3—62no—
522Dic3—122no—
523Dic3—124no—
524Dic3—122no—
525Dic3—122no—
526C32C2×#45211yescharacteristic, complemented, Sylow
527C23—62no—
528C23—64no—
529C23—92no—
530C23—122no—
531C23—122no—
532C23—182no—
533C23—182no—
534C23—182no—
535C23#381111yescharacteristic
536Q8—22no—
537Q8—22no—
538Q8—34no—
539Q8—42no—
540Q8—62no—
541Q8—64no—
542D4—34no—
543D4—62no—
544D4—64no—
545D4—1816no—
546C2×C4—22no—
547C2×C4—42no—
548C2×C4—62no—
549C2×C4—64no—
550C2×C4—92no—
551C2×C4—1816no—
552C2×C4—182no—
553C2×C4—182no—
554C2×C4—182no—
555C2×C4—184no—
556C2×C4—182no—
557C2×C4—362no—
558C2×C4D3×#6712yes—
559C2×C4D3×#6712yes—
560C2×C4#381111yescharacteristic
561C2×C4C22×D3211yescharacteristic
562C8—62no—
563C8—62no—
564C2×C3—21no—
565C2×C3—21no—
566C2×C3—24no—
567C2×C3—21no—
568C2×C3—124no—
569C2×C3#517314yescomplemented
570C2×C3#518714yescomplemented
571C2×C3C2×#91511yescharacteristic
572C2×C3C2×#91611yescharacteristic
573C2×C3C2×#91811yescharacteristic
574C2×C3C2×#91911yescharacteristic
575C2×C3C2×#93711yescharacteristic
576C2×C3C2×#93711yescharacteristic
577D3—44no—
578D3—124no—
579D3—122no—
580D3—122no—
581C22—64no—
582C22—122no—
583C22—122no—
584C22—128no—
585C22—182no—
586C22—182no—
587C22—182no—
588C22—364no—
589C22#6395012yes—
590C22#6395112yes—
591C22#6398312yes—
592C22C2×#381111yescharacteristic
593C4—42no—
594C4—64no—
595C4—182no—
596C4—362no—
597C4#6398312yes—
598C4C2×D3×#6711yescharacteristic
599C4C2×D3×#6711yescharacteristic
600C3—21no—
601C3C2×#517311yescharacteristic, complemented
602C3C2×#518711yescharacteristic, complemented
603C2—124no—
604C2—362no—
605C2#1059165614yesdirect product factor
606C2C2×#6395011yescharacteristic
607C2C2×#6395111yescharacteristic
608C2C2×#6398311yescharacteristic
subgroupG/H
centerC23#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC23×C32C2×D4
prime radicalC22×#3796C2
hypercenterC22×Q8D32
hypocenterC32C2×#452
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. C2×#64155C2semidirect
3. C22×C3×#216C2semidirect
4. C22×C3×#215C2semidirect
5. #10591656C2direct (N × H)
6. C2×#63566C2semidirect
7. C2×#63563C2semidirect
8. C2×#63557C2semidirect
22. #64155C22semidirect
27. C2×C3×#216C22semidirect
29. C2×C3×#215C22semidirect
32. #63566C22semidirect
33. #63563C22semidirect
34. #63557C22semidirect
42. C22×#216D3semidirect
43. C22×#215D3semidirect
128. C2×#216C2×D3semidirect
130. C2×#215C2×D3semidirect
428. C2×C32#452semidirect
526. C32C2×#452semidirect
569. C2×C3#5173semidirect
570. C2×C3#5187semidirect
601. C3C2×#5173semidirect
602. C3C2×#5187semidirect
605. C2#10591656direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37962
C2×#641552
C22×C3×#2162
C22×C3×#2152
#105916562
C2×#635662
C2×#635632
C2×#635572
C2×#51873
C2×#51733