Finite Group Databasebeta

← C2×#10591603 #11863668

Subgroups — C2×#10591603 #11863668

Order 1152.

1905 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Q8×C3⋊D3C211yesmaximal, characteristic
2C22×C3×#216C211yesmaximal, characteristic, complemented
3C2×#63871C211yesmaximal, characteristic
4C22×#3719C211yesmaximal, characteristic, complemented
5C2×C3×#835C211yesmaximal, characteristic, complemented
6#10591603C218yesmaximal, direct product factor
7C2×#63567C211yesmaximal, characteristic, complemented
8C2×#63557C211yesmaximal, characteristic
9C2×#5186—31nomaximal
10C2×#4809—31nomaximal
11C22×C32×Q8C2211yescharacteristic
12C2×Q8×C3⋊D3—24no—
13C2×Q8×C3⋊D3—22no—
14C2×Q8×C3⋊D3—24no—
15C2×Q8×C3⋊D3C2214yes—
16C22×C4×C3⋊D3—21no—
17C22×C4×C3⋊D3C2211yescharacteristic
18C22×#634—21no—
19C22×#634C2211yescharacteristic
20C22×C3×Dic6C2211yescharacteristic
21C2×C3×#216—24no—
22C2×C3×#216C2214yescomplemented
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C22×C3×C3⋊C8C2211yescharacteristic
25C22×C3×C3⋊C8C2211yescharacteristic
26C2×Dic3⋊Dic3—21no—
27C2×#3722—21no—
28#63871—22no—
29#63871C2214yes—
30C2×#3719—24no—
31C2×#3719C2214yescomplemented
32C3×#835C2214yescomplemented
33#63567C2214yescomplemented
34#63557C2214yes—
35C22×D3×Q8—31no—
36C22×D3×Q8—31no—
37C22×D3×Q8—61no—
38C22×C3×Q16—31no—
39C2×#946—31no—
40C22×#216—31no—
41C22×#216D311yescharacteristic, complemented
42C22×Dic12—31no—
43C2×#897—31no—
44C2×C3×#103—31no—
45C2×#835D311yescharacteristic, complemented
46#5186—38no—
47C2×(C2×D3)⋊C8—31no—
48C2×(C2×D3)⋊C8—31no—
49C2×#816—31no—
50C2×#810—31no—
51#4809—38no—
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⋊Dic3D411yescharacteristic
61Q8×C3⋊D3—216no—
62Q8×C3⋊D3—28no—
63Q8×C3⋊D3—28no—
64C2×C4×C3⋊D3—28no—
65C2×C4×C3⋊D3—24no—
66C2×C4×C3⋊D3—22no—
67C2×C4×C3⋊D3—22no—
68C2×C4×C3⋊D3D412yes—
69C2×C4×C3⋊D3C2312yes—
70C2×#634—28no—
71C2×#634—21no—
72C2×#634—22no—
73C2×#634—24no—
74C2×#634D414yes—
75C2×#634C2312yes—
76C22×C3×Dic3—21no—
77C22×C3×Dic3—21no—
78C2×C3×Dic6—22no—
79C2×C3×Dic6—22no—
80C2×C3×Dic6—21no—
81C2×C3×Dic6C2312yes—
82C3×#216—28no—
83C3×C4⋊Dic3—21no—
84C3×C4⋊Dic3C2312yes—
85C2×C3×C3⋊C8—22no—
86C2×C3×C3⋊C8—22no—
87C2×C3×C3⋊C8C2312yes—
88C2×C3×C3⋊C8C2312yes—
89Dic3⋊Dic3—24no—
90#3722—24no—
91#3719—28no—
92C2×#451—91noSylow
93C22×C3×Q8—21no—
94C22×C3×Q8—31no—
95C22×C3×Q8C2×D311yescharacteristic
96C22×C3×Q8C2×D311yescharacteristic
97C2×D3×Q8—34no—
98C2×D3×Q8—34no—
99C2×D3×Q8—64no—
100C2×D3×Q8—64no—
101C2×D3×Q8—64no—
102C2×D3×Q8—62no—
103C2×D3×Q8—62no—
104C2×D3×Q8—64no—
105C2×D3×Q8—68no—
106C2×D3×Q8—68no—
107C2×D3×Q8—64no—
108C2×D3×Q8—64no—
109C22×C4×D3—31no—
110C22×C4×D3—31no—
111C22×C4×D3—61no—
112C22×C4×D3—61no—
113C22×C4×D3—61no—
114C22×C4×D3—62no—
115C22×Dic6—31no—
116C22×Dic6—31no—
117C22×Dic6—61no—
118C22×Dic6—61no—
119C22×Dic6—61no—
120C22×Dic6—62no—
121C22×Dic6C2×D311yescharacteristic
122C2×C3×Q16—34no—
123C2×C3×Q16—64no—
124C22×C3×C8—31no—
125C22×C3×C8—31no—
126C2×C3×C4⋊C4—31no—
127#946—34no—
128#946—62no—
129C2×#216—24no—
130C2×#216—34no—
131C2×#216—64no—
132C2×#216C2×D314yescomplemented
133C2×(C2×D3)⋊C4—61no—
134C2×(C2×D3)⋊C4—61no—
135C2×C4⋊Dic3—61no—
136C2×C4⋊Dic3C2×D311yescharacteristic
137C2×Dic3⋊C4—61no—
138C22×C3⋊C8C2×D311yescharacteristic
139C22×C3⋊C8C2×D311yescharacteristic
140C2×Dic12—34no—
141C2×Dic12—64no—
142#897—34no—
143#897—62no—
144C3×#103—34no—
145#835C2×D314yescomplemented
146(C2×D3)⋊C8—34no—
147(C2×D3)⋊C8—34no—
148#816—34no—
149#810—34no—
150C23×C32C2×D411yescharacteristic
151C22×C3⋊D3—22no—
152C22×C3⋊D3—22no—
153C22×C3⋊D3Q1614yescomplemented
154C22×C3⋊D3C2×D412yes—
155C32×Q8—24no—
156C32×Q8—22no—
157C32×Q8C2×D414yes—
158C2×C32×C4—24no—
159C2×C32×C4—22no—
160C2×C32×C4C2×D412yes—
161C2×C32×C4C2×D411yescharacteristic
162C2×C32×C4C2×D412yes—
163C2×C32×C4C2411yescharacteristic
164C2×C3⋊Dic3—22no—
165C2×C3⋊Dic3—24no—
166C2×C3⋊Dic3—22no—
167C2×C3⋊Dic3C2×D412yes—
168C4×C3⋊D3—216no—
169C4×C3⋊D3—24no—
170C4×C3⋊D3—22no—
171C4×C3⋊D3—22no—
172#634—216no—
173#634—24no—
174#634—22no—
175#634C2×D414yes—
176C2×C3×Dic3—22no—
177C2×C3×Dic3—22no—
178C2×C3×Dic3—42no—
179C2×C3×Dic3—42no—
180C3×Dic6—22no—
181C3×Dic6—22no—
182C3×Dic6—42no—
183C3×C3⋊C8—22no—
184C3×C3⋊C8—22no—
185C23×Q8—91no—
186C22×Q16—31no—
187C22×Q16—91no—
188C2×C22⋊Q8—91no—
189#451—98no—
190C2×#103—31no—
191C2×#103—91no—
192C2×C22⋊C8—91no—
193C23×D3—31no—
194C23×D3—31no—
195C23×D3—61no—
196C2×C3×Q8—22no—
197C2×C3×Q8—24no—
198C2×C3×Q8—22no—
199C2×C3×Q8—22no—
200C2×C3×Q8—21no—
201C2×C3×Q8—21no—
202C2×C3×Q8—24no—
203C2×C3×Q8—22no—
204C2×C3×Q8—32no—
205C2×C3×Q8—61no—
206C2×C3×Q8—62no—
207C2×C3×Q8—62no—
208C2×C3×Q8D1214yes—
209C2×C3×Q8#6714yes—
210C2×C3×Q8C22×D312yes—
211C2×C3×Q8C22×D312yes—
212C22×C3×C4—22no—
213C22×C3×C4—21no—
214C22×C3×C4—21no—
215C22×C3×C4—21no—
216C22×C3×C4—61no—
217C22×C3×C4—61no—
218C22×C3×C4C22×D311yescharacteristic
219C22×C3×C4C22×D311yescharacteristic
220C22×Dic3—21no—
221C22×Dic3—21no—
222C22×Dic3—31no—
223C22×Dic3—31no—
224C22×Dic3—61no—
225C22×Dic3—62no—
226C22×Dic3—61no—
227C22×Dic3—61no—
228D3×Q8—68no—
229D3×Q8—68no—
230D3×Q8—616no—
231D3×Q8—632no—
232D3×Q8—616no—
233D3×Q8—616no—
234D3×Q8—616no—
235D3×Q8—68no—
236D3×Q8—68no—
237C2×C4×D3—32no—
238C2×C4×D3—32no—
239C2×C4×D3—32no—
240C2×C4×D3—32no—
241C2×C4×D3—62no—
242C2×C4×D3—62no—
243C2×C4×D3—64no—
244C2×C4×D3—64no—
245C2×C4×D3—68no—
246C2×C4×D3—616no—
247C2×C4×D3—68no—
248C2×C4×D3—68no—
249C2×C4×D3—64no—
250C2×C4×D3—64no—
251C2×C4×D3—62no—
252C2×C4×D3—62no—
253C2×C4×D3—62no—
254C2×C4×D3—62no—
255C2×Dic6—22no—
256C2×Dic6—22no—
257C2×Dic6—21no—
258C2×Dic6—34no—
259C2×Dic6—34no—
260C2×Dic6—32no—
261C2×Dic6—32no—
262C2×Dic6—64no—
263C2×Dic6—62no—
264C2×Dic6—64no—
265C2×Dic6—64no—
266C2×Dic6—68no—
267C2×Dic6—616no—
268C2×Dic6—68no—
269C2×Dic6—68no—
270C2×Dic6—64no—
271C2×Dic6—62no—
272C2×Dic6—62no—
273C2×Dic6—61no—
274C2×Dic6—61no—
275C2×Dic6—62no—
276C2×Dic6C22×D312yes—
277C3×Q16—68no—
278C2×C3×C8—32no—
279C2×C3×C8—32no—
280C2×C3×C8—62no—
281C2×C3×C8—62no—
282C3×C4⋊C4—32no—
283C3×C4⋊C4—61no—
284#216—28no—
285#216—68no—
286(C2×D3)⋊C4—64no—
287(C2×D3)⋊C4—64no—
288C4⋊Dic3—21no—
289C4⋊Dic3—64no—
290C4⋊Dic3C22×D312yes—
291Dic3⋊C4—64no—
292C2×C3⋊C8—22no—
293C2×C3⋊C8—22no—
294C2×C3⋊C8C22×D312yes—
295C2×C3⋊C8C22×D312yes—
296Dic12—68no—
297C22×C32#12012yes—
298C22×C32C2×Q1612yes—
299C22×C32#13712yes—
300C22×C32C22×D411yescharacteristic
301C2×C3⋊D3—22no—
302C2×C3⋊D3—22no—
303C2×C3⋊D3—28no—
304C2×C3⋊D3C2×Q1614yescomplemented
305C32×C4—24no—
306C32×C4#12012yes—
307C32×C4C22×D411yescharacteristic
308C32×C4C22×D411yescharacteristic
309C3⋊Dic3—22no—
310C3⋊Dic3—24no—
311C3×Dic3—42no—
312C3×Dic3—42no—
313C22×Q8—31no—
314C22×Q8—94no—
315C22×Q8—91no—
316C22×Q8—181no—
317C22×Q8—182no—
318C22×Q8—184no—
319C22×Q8—184no—
320C22×Q8D3211yescharacteristic
321C23×C4—91no—
322C23×C4—181no—
323C2×Q16—34no—
324C2×Q16—64no—
325C2×Q16—94no—
326C2×Q16—184no—
327C22×C8—31no—
328C22×C8—31no—
329C22⋊Q8—94no—
330C22⋊Q8—182no—
331C2×C4⋊C4—31no—
332C2×C4⋊C4—181no—
333C2×C22⋊C4—181no—
334#103—34no—
335#103—94no—
336C22⋊C8—94no—
337C23×C3—21no—
338C23×C3D3×D411yescharacteristic
339C23×C3D3×D411yescharacteristic
340C22×D3—34no—
341C22×D3—34no—
342C22×D3—32no—
343C22×D3—32no—
344C22×D3—64no—
345C22×D3—62no—
346C22×D3—64no—
347C22×D3—64no—
348C22×D3—62no—
349C22×D3—62no—
350C22×D3—62no—
351C22×D3—62no—
352C3×Q8—24no—
353C3×Q8—28no—
354C3×Q8—24no—
355C3×Q8—24no—
356C3×Q8—22no—
357C3×Q8—22no—
358C3×Q8—24no—
359C3×Q8—62no—
360C3×Q8—62no—
361C3×Q8—122no—
362C3×Q8C2×D1214yes—
363C3×Q8C2×#6714yes—
364C2×C3×C4—24no—
365C2×C3×C4—28no—
366C2×C3×C4—24no—
367C2×C3×C4—24no—
368C2×C3×C4—22no—
369C2×C3×C4—22no—
370C2×C3×C4—21no—
371C2×C3×C4—22no—
372C2×C3×C4—22no—
373C2×C3×C4—21no—
374C2×C3×C4—62no—
375C2×C3×C4—62no—
376C2×C3×C4—122no—
377C2×C3×C4—122no—
378C2×C3×C4C2×D1212yes—
379C2×C3×C4D3×D411yescharacteristic
380C2×C3×C4D3×D412yes—
381C2×C3×C4D3×D411yescharacteristic
382C2×C3×C4D3×D412yes—
383C2×C3×C4C2×#6712yes—
384C2×C3×C4C23×D311yescharacteristic
385C2×C3×C4C23×D311yescharacteristic
386C2×Dic3—22no—
387C2×Dic3—22no—
388C2×Dic3—32no—
389C2×Dic3—32no—
390C2×Dic3—42no—
391C2×Dic3—42no—
392C2×Dic3—62no—
393C2×Dic3—64no—
394C2×Dic3—64no—
395C2×Dic3—68no—
396C2×Dic3—64no—
397C2×Dic3—62no—
398C2×Dic3—64no—
399C2×Dic3—62no—
400C2×Dic3—62no—
401C2×Dic3—62no—
402C4×D3—632no—
403C4×D3—616no—
404C4×D3—616no—
405C4×D3—64no—
406C4×D3—64no—
407C4×D3—68no—
408C4×D3—64no—
409C4×D3—64no—
410C4×D3—62no—
411C4×D3—62no—
412C4×D3—62no—
413C4×D3—62no—
414Dic6—22no—
415Dic6—22no—
416Dic6—34no—
417Dic6—34no—
418Dic6—42no—
419Dic6—64no—
420Dic6—632no—
421Dic6—616no—
422Dic6—616no—
423Dic6—64no—
424Dic6—68no—
425Dic6—64no—
426Dic6—64no—
427Dic6—62no—
428Dic6—62no—
429C3×C8—62no—
430C3×C8—62no—
431C3⋊C8—22no—
432C3⋊C8—22no—
433C2×C32#45114yescomplemented
434C2×C32C2×#12011yescharacteristic
435C2×C32C22×Q1611yescharacteristic
436C2×C32C2×#13711yescharacteristic
437C3⋊D3—24no—
438C24—91no—
439C2×Q8—21no—
440C2×Q8—22no—
441C2×Q8—32no—
442C2×Q8—61no—
443C2×Q8—62no—
444C2×Q8—62no—
445C2×Q8—92no—
446C2×Q8—94no—
447C2×Q8—184no—
448C2×Q8—188no—
449C2×Q8—188no—
450C2×Q8—1816no—
451C2×Q8—188no—
452C2×Q8—182no—
453C2×Q8—181no—
454C2×Q8#62614yes—
455C2×Q8C2×D3212yes—
456C22×C4—21no—
457C22×C4—61no—
458C22×C4—61no—
459C22×C4—91no—
460C22×C4—92no—
461C22×C4—92no—
462C22×C4—184no—
463C22×C4—188no—
464C22×C4—181no—
465C22×C4—182no—
466C22×C4—182no—
467C22×C4C2×D3211yescharacteristic
468Q16—68no—
469Q16—188no—
470C2×C8—32no—
471C2×C8—32no—
472C2×C8—62no—
473C2×C8—62no—
474C4⋊C4—32no—
475C4⋊C4—61no—
476C4⋊C4—184no—
477C22⋊C4—184no—
478C22×C3—21no—
479C22×C3—22no—
480C22×C3—22no—
481C22×C3—22no—
482C22×C3#88212yes—
483C22×C3#91512yes—
484C22×C3D3×Q1612yes—
485C22×C3D3×Q1612yes—
486C22×C3#91812yes—
487C22×C3#93712yes—
488C22×C3C2×D3×D411yescharacteristic
489C22×C3C2×D3×D411yescharacteristic
490C2×D3—34no—
491C2×D3—34no—
492C2×D3—64no—
493C2×D3—64no—
494C2×D3—64no—
495C2×D3—616no—
496C2×D3—68no—
497C2×D3—62no—
498C2×D3—62no—
499C2×D3—62no—
500C2×D3—62no—
501C2×D3—68no—
502C3×C4—28no—
503C3×C4—24no—
504C3×C4—24no—
505C3×C4—21no—
506C3×C4—21no—
507C3×C4—22no—
508C3×C4—122no—
509C3×C4—122no—
510C3×C4#88212yes—
511C3×C4#93712yes—
512C3×C4C22×D1211yescharacteristic
513C3×C4C2×D3×D411yescharacteristic
514C3×C4C2×D3×D411yescharacteristic
515C3×C4C22×#6711yescharacteristic
516Dic3—42no—
517Dic3—42no—
518Dic3—64no—
519Dic3—68no—
520Dic3—64no—
521Dic3—62no—
522Dic3—64no—
523Dic3—62no—
524C32C2×#45111yescharacteristic, complemented, Sylow
525C23—92no—
526C23—94no—
527C23—182no—
528C23—182no—
529C23#381111yescharacteristic
530Q8—22no—
531Q8—24no—
532Q8—62no—
533Q8—62no—
534Q8—94no—
535Q8—122no—
536Q8—1816no—
537Q8—182no—
538Q8—184no—
539Q8C2×#62614yes—
540C2×C4—22no—
541C2×C4—24no—
542C2×C4—62no—
543C2×C4—62no—
544C2×C4—92no—
545C2×C4—122no—
546C2×C4—122no—
547C2×C4—1816no—
548C2×C4—182no—
549C2×C4—182no—
550C2×C4—184no—
551C2×C4—182no—
552C2×C4—182no—
553C2×C4—184no—
554C2×C4C2×#62612yes—
555C2×C4#381112yes—
556C2×C4#381111yescharacteristic
557C2×C4C22×D3211yescharacteristic
558C8—62no—
559C8—62no—
560C2×C3—21no—
561C2×C3—21no—
562C2×C3—24no—
563C2×C3—21no—
564C2×C3#480914yescomplemented
565C2×C3#518614yescomplemented
566C2×C3C2×#88211yescharacteristic
567C2×C3C2×#91511yescharacteristic
568C2×C3C2×D3×Q1611yescharacteristic
569C2×C3C2×D3×Q1611yescharacteristic
570C2×C3C2×#91811yescharacteristic
571C2×C3C2×#93711yescharacteristic
572D3—68no—
573D3—64no—
574D3—64no—
575C22—94no—
576C22—182no—
577C22—188no—
578C22—182no—
579C22#6394412yes—
580C22#6395112yes—
581C22#6398112yes—
582C22C2×#381111yescharacteristic
583C4—24no—
584C4—122no—
585C4—122no—
586C4—182no—
587C4—184no—
588C4#6398112yes—
589C4C22×#62611yescharacteristic
590C4C2×#381111yescharacteristic
591C3—21no—
592C3C2×#480911yescharacteristic, complemented
593C3C2×#518611yescharacteristic, complemented
594C2—184no—
595C2#1059160314yesdirect product factor
596C2C2×#6394411yescharacteristic
597C2C2×#6395111yescharacteristic
598C2C2×#6398111yescharacteristic
subgroupG/H
centerC23#3811
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×#3719C2semidirect
5. C2×C3×#835C2semidirect
6. #10591603C2direct (N × H)
7. C2×#63567C2semidirect
22. C2×C3×#216C22semidirect
31. C2×#3719C22semidirect
32. C3×#835C22semidirect
33. #63567C22semidirect
41. C22×#216D3semidirect
45. C2×#835D3semidirect
132. C2×#216C2×D3semidirect
145. #835C2×D3semidirect
153. C22×C3⋊D3Q16semidirect
304. C2×C3⋊D3C2×Q16semidirect
433. C2×C32#451semidirect
524. C32C2×#451semidirect
564. C2×C3#4809semidirect
565. C2×C3#5186semidirect
592. C3C2×#4809semidirect
593. C3C2×#5186semidirect
595. C2#10591603direct (N × H)

Maximal subgroups

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

subgroupindex
C22×Q8×C3⋊D32
C22×C3×#2162
C2×#638712
C22×#37192
C2×C3×#8352
#105916032
C2×#635672
C2×#635572
C2×#51863
C2×#48093