Finite Group Databasebeta

← C2×#10595167 #11900794

Subgroups — C2×#10595167 #11900794

Order 1152.

3901 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3830C211yesmaximal, characteristic, complemented
2C22×#3796C211yesmaximal, characteristic, complemented
3C2×C3×#940C211yesmaximal, characteristic, complemented
4C2×C3×#936C211yesmaximal, characteristic, complemented
5C2×#67⋊Dic3C214yesmaximal, complemented
6C2×#63958C214yesmaximal, complemented
7#10595167C2116yesmaximal, direct product factor
8C2×C4×#624C211yesmaximal, characteristic, complemented
9C2×#63866C211yesmaximal, characteristic, complemented
10C2×#63860C211yesmaximal, characteristic, complemented
11C2×#5716—31nomaximal
12C2×#5668—31nomaximal
13C22×C32×D4C2211yescharacteristic
14C22×#638C2212yes—
15C23×C3⋊Dic3C2212yes—
16C2×#3830—28no—
17C2×#3830C2218yescomplemented
18C22×C4×C3⋊D3C2211yescharacteristic
19C22×#634C2211yescharacteristic
20C22×C3×#67C2214yes—
21C22×C3×D12C2211yescharacteristic
22C22×C3×Dic6C2211yescharacteristic
23C22×#626C2212yes—
24C22×#624C2212yes—
25C22×D3×Dic3C2212yes—
26C2×#3796—28no—
27C2×#3796C2218yescomplemented
28C2×C3×#217C2214yes—
29C3×#940C2218yescomplemented
30C3×#936C2218yescomplemented
31C2×C3×C4×Dic3C2211yescharacteristic
32C2×C3×C4×Dic3C2211yescharacteristic
33#67⋊Dic3C22132yescomplemented
34C2×Dic3⋊Dic3C2214yes—
35C2×(C2×D3)⋊Dic3C2214yes—
36#63958C22132yescomplemented
37C2×Dic32C2212yes—
38C4×#624C2218yescomplemented
39#63866C2218yescomplemented
40#63860C2218yescomplemented
41C22×#239—31no—
42C22×#237—31no—
43C22×#237—31no—
44C22×#237—31no—
45C22×#237—61no—
46C2×C3×#127—31no—
47C2×C3×#124—31no—
48C2×#944—31no—
49C2×#940D311yescharacteristic, complemented
50C2×#938—34no—
51C2×#936—31no—
52C2×#936D311yescharacteristic, complemented
53C2×D4×Dic3—34no—
54#5716—316no—
55#5668—316no—
56C2×#884—34no—
57C2×#67⋊C4—34no—
58C2×#875—31no—
59C2×C42×D3—31no—
60C2×C42×D3—31no—
61C2×#869—31no—
62C24×C32C2312yes—
63C23×C3⋊D3C2311yescharacteristic
64C23×C3×D3C2312yes—
65C2×C32×D4—24no—
66C2×C32×D4C2314yes—
67C22×C32×C4C2311yescharacteristic
68C2×#638—28no—
69C2×#638C2318yes—
70C22×C3⋊Dic3—28no—
71C22×C3⋊Dic3C2312yes—
72C22×C3⋊Dic3C2318yes—
73C22×C3⋊Dic3C2311yescharacteristic
74#3830—232no—
75C2×C4×C3⋊D3D418yescomplemented
76C2×C4×C3⋊D3C2314yes—
77C2×#634—24no—
78C2×#634C2314yes—
79C2×C3×#67—216no—
80C2×C3×#67C23116yes—
81C22×C3×Dic3C2312yes—
82C22×C3×Dic3C2312yes—
83C22×C3×Dic3C2312yes—
84C2×C3×D12—24no—
85C2×C3×D12C2314yes—
86C2×C3×Dic6—24no—
87C2×C3×Dic6C2314yes—
88C2×#626—28no—
89C2×#626C2318yes—
90C2×#624—28no—
91C2×#624C2318yes—
92C2×D3×Dic3—28no—
93C2×D3×Dic3C2318yes—
94#3796—232no—
95C3×#217C23116yes—
96C3×C4×Dic3C2314yes—
97C3×C4×Dic3C2314yes—
98Dic3⋊Dic3C23116yes—
99(C2×D3)⋊Dic3C23116yes—
100Dic32C2318yes—
101C2×#532—91noSylow
102C22×C3×Q8—31no—
103C22×C3×D4—21no—
104C22×C3×D4—34no—
105C22×C3×D4—31no—
106C22×C3×D4C2×D311yescharacteristic
107C22×C3×D4C2×D311yescharacteristic
108C22×#67—32no—
109C22×#67—32no—
110C22×#67—32no—
111C22×#67—62no—
112C22×#67C2×D314yes—
113C23×Dic3—32no—
114C23×Dic3—32no—
115C23×Dic3—32no—
116C23×Dic3—62no—
117C2×#239—38no—
118C2×#239—68no—
119C2×#237—38no—
120C2×#237—38no—
121C2×#237—38no—
122C2×#237—68no—
123C2×#237—68no—
124C2×#237—68no—
125C2×#237—68no—
126C2×#237—616no—
127C22×D12—32no—
128C22×D12C2×D311yescharacteristic
129C22×C4×D3—31no—
130C22×C4×D3—31no—
131C22×C4×D3—32no—
132C22×C4×D3—32no—
133C22×C4×D3—32no—
134C22×C4×D3—61no—
135C22×Dic6—31no—
136C22×Dic6—31no—
137C22×Dic6—61no—
138C22×Dic6C2×D311yescharacteristic
139C3×#127—38no—
140C3×#124—38no—
141C2×C3×C22⋊C4—34no—
142C2×C3×C42—31no—
143C2×C3×C42—31no—
144C2×#217—34no—
145C2×#217C2×D314yes—
146#944—38no—
147#940C2×D318yescomplemented
148#938—332no—
149#936—38no—
150#936C2×D318yescomplemented
151D4×Dic3—332no—
152C2×(C2×D3)⋊C4—34no—
153C2×C4⋊Dic3—34no—
154C2×Dic3⋊C4—34no—
155C2×C4×Dic3—32no—
156C2×C4×Dic3—32no—
157C2×C4×Dic3C2×D311yescharacteristic
158C2×C4×Dic3C2×D311yescharacteristic
159#884—332no—
160#67⋊C4—332no—
161#875—38no—
162C42×D3—38no—
163C42×D3—38no—
164#869—38no—
165C23×C32—24no—
166C23×C32—28no—
167C23×C32C2414yes—
168C23×C32C2411yescharacteristic
169C22×C3⋊D3—24no—
170C22×C3⋊D3C2×D414yes—
171C22×C3⋊D3C2412yes—
172C22×C3×D3—24no—
173C22×C3×D3—28no—
174C22×C3×D3C2414yes—
175C32×D4—28no—
176C2×C32×C4C2×D414yes—
177C2×C32×C4C2412yes—
178#638—216no—
179C2×C3⋊Dic3—24no—
180C2×C3⋊Dic3—216no—
181C2×C3⋊Dic3C2×D414yes—
182C2×C3⋊Dic3C2414yes—
183C2×C3⋊Dic3C2412yes—
184C4×C3⋊D3C2×D4116yescomplemented
185#634—28no—
186C3×#67—232no—
187C2×C3×Dic3—24no—
188C2×C3×Dic3—24no—
189C2×C3×Dic3#4118yescomplemented
190C2×C3×Dic3C2414yes—
191C2×C3×Dic3C2414yes—
192C2×C3×Dic3C2414yes—
193C3×D12—28no—
194C3×Dic6—28no—
195#626—216no—
196#624—216no—
197D3×Dic3—216no—
198C22×#41—91no—
199C22×#41—91no—
200#532—916no—
201C2×C4⋊Q8—91no—
202C2×#127—31no—
203C2×#124—31no—
204C2×#124—91no—
205C2×#121—94no—
206C2×C4×D4—94no—
207C22×C42—91no—
208C24×C3—22no—
209C24×C3—32no—
210C24×C3C22×D312yes—
211C24×C3C22×D312yes—
212C23×D3—31no—
213C23×D3—31no—
214C23×D3—61no—
215C23×D3C22×D312yes—
216C2×C3×Q8—34no—
217C2×C3×Q8—64no—
218C2×C3×D4—28no—
219C2×C3×D4—24no—
220C2×C3×D4—24no—
221C2×C3×D4—24no—
222C2×C3×D4—316no—
223C2×C3×D4—34no—
224C2×C3×D4—616no—
225C2×C3×D4—64no—
226C2×C3×D4C22×D314yes—
227C2×C3×D4C22×D314yes—
228C22×C3×C4—21no—
229C22×C3×C4—32no—
230C22×C3×C4—32no—
231C22×C3×C4—32no—
232C22×C3×C4C22×D311yescharacteristic
233C22×C3×C4C22×D311yescharacteristic
234C2×#67—216no—
235C2×#67—38no—
236C2×#67—38no—
237C2×#67—38no—
238C2×#67—68no—
239C2×#67—68no—
240C2×#67—68no—
241C2×#67—68no—
242C2×#67—616no—
243C2×#67C22×D3116yes—
244C22×Dic3—31no—
245C22×Dic3—31no—
246C22×Dic3—38no—
247C22×Dic3—32no—
248C22×Dic3—32no—
249C22×Dic3—38no—
250C22×Dic3—38no—
251C22×Dic3—62no—
252C22×Dic3—61no—
253C22×Dic3—68no—
254C22×Dic3—68no—
255C22×Dic3—68no—
256C22×Dic3—68no—
257C22×Dic3—616no—
258C22×Dic3C22×D312yes—
259C22×Dic3C22×D312yes—
260C22×Dic3C22×D312yes—
261#239—632no—
262#237—632no—
263#237—632no—
264#237—632no—
265#237—664no—
266C2×D12—24no—
267C2×D12—38no—
268C2×D12—68no—
269C2×D12C22×D314yes—
270C2×C4×D3—38no—
271C2×C4×D3—38no—
272C2×C4×D3—34no—
273C2×C4×D3—34no—
274C2×C4×D3—38no—
275C2×C4×D3—38no—
276C2×C4×D3—38no—
277C2×C4×D3—68no—
278C2×C4×D3—64no—
279C2×C4×D3—68no—
280C2×C4×D3—68no—
281C2×C4×D3—68no—
282C2×Dic6—24no—
283C2×Dic6—34no—
284C2×Dic6—34no—
285C2×Dic6—64no—
286C2×Dic6—68no—
287C2×Dic6—64no—
288C2×Dic6—64no—
289C2×Dic6C22×D314yes—
290C3×C22⋊C4—316no—
291C3×C42—34no—
292C3×C42—34no—
293#217—316no—
294#217C22×D3116yes—
295(C2×D3)⋊C4—316no—
296C4⋊Dic3—316no—
297Dic3⋊C4—316no—
298C4×Dic3—38no—
299C4×Dic3—38no—
300C4×Dic3C22×D314yes—
301C4×Dic3C22×D314yes—
302C22×C32—24no—
303C22×C32—28no—
304C22×C32—48no—
305C22×C32C22×D412yes—
306C22×C32C2×#4114yes—
307C22×C32C2511yescharacteristic
308C2×C3⋊D3—28no—
309C2×C3⋊D3—24no—
310C2×C3⋊D3C22×D414yes—
311C2×C3×D3—24no—
312C2×C3×D3—28no—
313C2×C3×D3—48no—
314C32×C4C22×D414yes—
315C3⋊Dic3—24no—
316C3⋊Dic3C22×D414yes—
317C3×Dic3—24no—
318C3×Dic3—24no—
319C3×Dic3C2×#4118yescomplemented
320C2×#41—98no—
321C2×#41—98no—
322C2×#41—188no—
323C2×#41—188no—
324C22×Q8—31no—
325C22×Q8—91no—
326C22×D4—34no—
327C22×D4—31no—
328C22×D4—92no—
329C22×D4—92no—
330C22×D4D3211yescharacteristic
331C23×C4—92no—
332C23×C4—92no—
333C23×C4—91no—
334C23×C4—92no—
335C4⋊Q8—98no—
336#127—38no—
337#124—38no—
338#124—98no—
339#121—932no—
340C4×D4—932no—
341C2×C4⋊C4—94no—
342C2×C22⋊C4—34no—
343C2×C22⋊C4—94no—
344C2×C42—31no—
345C2×C42—31no—
346C2×C42—98no—
347C2×C42—92no—
348C23×C3—28no—
349C23×C3—24no—
350C23×C3—24no—
351C23×C3—28no—
352C23×C3—28no—
353C23×C3—24no—
354C23×C3—21no—
355C23×C3—34no—
356C23×C3—48no—
357C23×C3—64no—
358C23×C3—68no—
359C23×C3C23×D314yes—
360C23×C3C23×D314yes—
361C23×C3C23×D311yescharacteristic
362C23×C3C23×D311yescharacteristic
363C22×D3—24no—
364C22×D3—28no—
365C22×D3—34no—
366C22×D3—34no—
367C22×D3—32no—
368C22×D3—32no—
369C22×D3—64no—
370C22×D3—62no—
371C22×D3—64no—
372C22×D3—64no—
373C22×D3—124no—
374C22×D3C23×D314yes—
375C3×Q8—68no—
376C3×D4—216no—
377C3×D4—28no—
378C3×D4—28no—
379C3×D4—632no—
380C3×D4—68no—
381C2×C3×C4—22no—
382C2×C3×C4—24no—
383C2×C3×C4—38no—
384C2×C3×C4—34no—
385C2×C3×C4—34no—
386C2×C3×C4—34no—
387C2×C3×C4—64no—
388C2×C3×C4—64no—
389C2×C3×C4D3×D414yes—
390C2×C3×C4D3×D414yes—
391C2×C3×C4C23×D312yes—
392C2×C3×C4C23×D312yes—
393#67—232no—
394#67—616no—
395#67—616no—
396#67—616no—
397#67—632no—
398C2×Dic3—24no—
399C2×Dic3—24no—
400C2×Dic3—34no—
401C2×Dic3—34no—
402C2×Dic3—32no—
403C2×Dic3—32no—
404C2×Dic3—34no—
405C2×Dic3—34no—
406C2×Dic3—64no—
407C2×Dic3—64no—
408C2×Dic3—62no—
409C2×Dic3—616no—
410C2×Dic3—616no—
411C2×Dic3—616no—
412C2×Dic3—68no—
413C2×Dic3—632no—
414C2×Dic3—64no—
415C2×Dic3—64no—
416C2×Dic3#23718yescomplemented
417C2×Dic3C23×D314yes—
418C2×Dic3C23×D314yes—
419C2×Dic3C23×D314yes—
420D12—28no—
421D12—616no—
422C4×D3—316no—
423C4×D3—316no—
424C4×D3—616no—
425C4×D3—616no—
426C4×D3—616no—
427C4×D3—616no—
428Dic6—28no—
429Dic6—616no—
430Dic6—68no—
431Dic6—68no—
432C2×C32—44no—
433C2×C32#53214yescomplemented
434C2×C32C23×D411yescharacteristic
435C2×C32C22×#4112yes—
436C3⋊D3—24no—
437C3×D3—44no—
438C24—32no—
439C24—91no—
440C24C2×D3212yes—
441#41—1832no—
442#41—1832no—
443C2×Q8—34no—
444C2×Q8—64no—
445C2×Q8—94no—
446C2×Q8—184no—
447C2×D4—24no—
448C2×D4—316no—
449C2×D4—34no—
450C2×D4—616no—
451C2×D4—64no—
452C2×D4—98no—
453C2×D4—98no—
454C2×D4—188no—
455C2×D4—188no—
456C2×D4C2×D3214yes—
457C22×C4—32no—
458C22×C4—32no—
459C22×C4—32no—
460C22×C4—98no—
461C22×C4—98no—
462C22×C4—91no—
463C22×C4—94no—
464C22×C4—98no—
465C22×C4—98no—
466C22×C4—92no—
467C22×C4—188no—
468C22×C4—188no—
469C22×C4—188no—
470C22×C4C2×D3211yescharacteristic
471C4⋊C4—916no—
472C22⋊C4—316no—
473C22⋊C4—916no—
474C42—34no—
475C42—34no—
476C42—98no—
477C22×C3—28no—
478C22×C3—24no—
479C22×C3—24no—
480C22×C3—28no—
481C22×C3—28no—
482C22×C3—24no—
483C22×C3—22no—
484C22×C3—21no—
485C22×C3—48no—
486C22×C3—416no—
487C22×C3—48no—
488C22×C3—48no—
489C22×C3—64no—
490C22×C3—68no—
491C22×C3—128no—
492C22×C3C2×D3×D412yes—
493C22×C3C2×D3×D412yes—
494C22×C3C2×#23714yes—
495C22×C3D3×#4114yes—
496C22×C3C24×D311yescharacteristic
497C22×C3C24×D311yescharacteristic
498C2×D3—24no—
499C2×D3—28no—
500C2×D3—34no—
501C2×D3—34no—
502C2×D3—48no—
503C2×D3—64no—
504C2×D3—68no—
505C2×D3—64no—
506C2×D3—64no—
507C2×D3—68no—
508C2×D3—124no—
509C2×D3—128no—
510C3×C4—24no—
511C3×C4—38no—
512C3×C4—64no—
513C3×C4—64no—
514C3×C4C2×D3×D414yes—
515C3×C4C2×D3×D414yes—
516Dic3—24no—
517Dic3—24no—
518Dic3—34no—
519Dic3—34no—
520Dic3—64no—
521Dic3—68no—
522Dic3—64no—
523Dic3—64no—
524Dic3C2×#23718yescomplemented
525C32C2×#53211yescharacteristic, complemented, Sylow
526C23—28no—
527C23—24no—
528C23—34no—
529C23—68no—
530C23—64no—
531C23—94no—
532C23—92no—
533C23—184no—
534C23C22×D3214yes—
535C23C22×D3211yescharacteristic
536Q8—68no—
537Q8—188no—
538D4—28no—
539D4—632no—
540D4—68no—
541D4—1816no—
542D4—1816no—
543C2×C4—38no—
544C2×C4—34no—
545C2×C4—34no—
546C2×C4—34no—
547C2×C4—64no—
548C2×C4—64no—
549C2×C4—94no—
550C2×C4—92no—
551C2×C4—916no—
552C2×C4—94no—
553C2×C4—1816no—
554C2×C4—1816no—
555C2×C4—1816no—
556C2×C4—184no—
557C2×C4#381114yes—
558C2×C4C22×D3212yes—
559C2×C3—22no—
560C2×C3—24no—
561C2×C3—21no—
562C2×C3—48no—
563C2×C3—44no—
564C2×C3—44no—
565C2×C3—124no—
566C2×C3#566814yescomplemented
567C2×C3#571614yescomplemented
568C2×C3C22×D3×D411yescharacteristic
569C2×C3C22×D3×D411yescharacteristic
570C2×C3C22×#23712yes—
571C2×C3C2×D3×#4112yes—
572D3—44no—
573D3—64no—
574D3—64no—
575D3—124no—
576C22—28no—
577C22—24no—
578C22—48no—
579C22—68no—
580C22—64no—
581C22—94no—
582C22—128no—
583C22—184no—
584C22—188no—
585C22D3×#23714yes—
586C22C2×#381112yes—
587C22C23×D3211yescharacteristic
588C4—38no—
589C4—64no—
590C4—64no—
591C4—94no—
592C4—184no—
593C4C2×#381114yes—
594C3—21no—
595C3C2×#566811yescharacteristic, complemented
596C3C2×#571611yescharacteristic, complemented
597C2—44no—
598C2—124no—
599C2—184no—
600C2#1059516714yesdirect product factor
601C2C2×D3×#23712yes—
602C2C22×#381111yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC22×C32×D4C22
socleC23×C32C24
hypercenterC22×D4D32
hypocenterC32C2×#532
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×#3830C2semidirect
2. C22×#3796C2semidirect
3. C2×C3×#940C2semidirect
4. C2×C3×#936C2semidirect
5. C2×#67⋊Dic3C2semidirect
6. C2×#63958C2semidirect
7. #10595167C2direct (N × H)
8. C2×C4×#624C2semidirect
9. C2×#63866C2semidirect
10. C2×#63860C2semidirect
17. C2×#3830C22semidirect
27. C2×#3796C22semidirect
29. C3×#940C22semidirect
30. C3×#936C22semidirect
33. #67⋊Dic3C22semidirect
36. #63958C22semidirect
38. C4×#624C22semidirect
39. #63866C22semidirect
40. #63860C22semidirect
49. C2×#940D3semidirect
52. C2×#936D3semidirect
75. C2×C4×C3⋊D3D4semidirect
147. #940C2×D3semidirect
150. #936C2×D3semidirect
184. C4×C3⋊D3C2×D4semidirect
189. C2×C3×Dic3#41semidirect
319. C3×Dic3C2×#41semidirect
416. C2×Dic3#237semidirect
433. C2×C32#532semidirect
524. Dic3C2×#237semidirect
525. C32C2×#532semidirect
566. C2×C3#5668semidirect
567. C2×C3#5716semidirect
595. C3C2×#5668semidirect
596. C3C2×#5716semidirect
600. C2#10595167direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#38302
C22×#37962
C2×C3×#9402
C2×C3×#9362
C2×#67⋊Dic32
C2×#639582
#105951672
C2×C4×#6242
C2×#638662
C2×#638602
C2×#57163
C2×#56683