Finite Group Databasebeta

← C2×#79583 #11664911

Subgroups — C2×#79583 #11664911

Order 768.

2070 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5557C212yesmaximal, complemented
2C2×C3×C4×D8C211yesmaximal, characteristic, complemented
3C2×#5157C211yesmaximal, characteristic
4C2×#5155C211yesmaximal, characteristic, complemented
5C2×C4×#214C212yesmaximal, complemented
6#79583C2116yesmaximal, direct product factor
7C2×#4887C211yesmaximal, characteristic, complemented
8C2×#4878C211yesmaximal, characteristic, complemented
9C2×#4778C212yesmaximal, complemented
10C2×#4768C212yesmaximal, complemented
11C2×C4×Dic12C211yesmaximal, characteristic, complemented
12C2×C4×D3×C8C211yesmaximal, characteristic, complemented
13C2×#3168—31nomaximal, Sylow
14C22×C3×D8C2211yescharacteristic
15C2×C3×C4×D4C2212yes—
16C2×#938C2212yes—
17C2×#936C2212yes—
18C22×#214C2212yes—
19C2×C4×#67—22no—
20C2×#926—22no—
21C22×Dic12C2211yescharacteristic
22C22×D3×C8C2211yescharacteristic
23C22×D3×C8C2211yescharacteristic
24#5557—28no—
25#5557C22116yescomplemented
26C2×#897C2212yes—
27C2×#890C2212yes—
28C2×#883—22no—
29C2×#879—22no—
30C2×C42×D3C2211yescharacteristic
31C2×C4×Dic6C2212yes—
32C3×C4×D8C2218yescomplemented
33C2×C3×#107C2211yescharacteristic
34C2×C3×#102C2212yes—
35C2×C3×C4×C8C2211yescharacteristic
36C2×#832C2212yes—
37#5157C2218yes—
38#5155C2218yescomplemented
39C2×#818C2211yescharacteristic
40C2×#816C2212yes—
41C2×C8×Dic3C2211yescharacteristic
42C2×C8×Dic3C2211yescharacteristic
43C4×#214C22116yescomplemented
44C2×#810C2212yes—
45C2×#808C2212yes—
46C2×C4×C3⋊C8C2211yescharacteristic
47#4887C2218yescomplemented
48#4878C2218yescomplemented
49#4778C22116yescomplemented
50#4768C22116yescomplemented
51C4×Dic12C2218yescomplemented
52C4×D3×C8C2218yescomplemented
53C2×#529—32no—
54#3168—316no—
55C2×#499—31no—
56C2×#495—31no—
57C2×#488—32no—
58C2×#467—31no—
59C2×#466—31no—
60C2×#465—32no—
61C2×C4×Q16—31no—
62C2×C4×SD16—32no—
63C2×C4×D8D311yescharacteristic, complemented
64C22×C4×C8—31no—
65C22×C3×D4C2312yes—
66C23×C3×C4—22no—
67C22×#67—22no—
68C22×C4×D3D411yescharacteristic
69C22×C4×D3D411yescharacteristic
70C22×C4×D3C2311yescharacteristic
71C22×Dic6C2312yes—
72C2×C3×D8—24no—
73C2×C3×D8C2314yes—
74C22×C3×C8C2311yescharacteristic
75C22×C3×C8C2311yescharacteristic
76C3×C4×D4—24no—
77C3×C4×D4C2318yes—
78C2×C3×C4⋊C4C2312yes—
79C2×C3×C22⋊C4—22no—
80C2×C3×C42C2311yescharacteristic
81C2×#217—22no—
82C2×#217—22no—
83C2×#217—22no—
84#938—24no—
85#938C2318yes—
86#936—24no—
87#936C2318yes—
88C2×#214—28no—
89C2×#214C2318yes—
90C4×#67—216no—
91C2×(C2×D3)⋊C4—22no—
92#926—216no—
93C2×C4⋊Dic3—22no—
94C2×C4⋊Dic3—22no—
95C2×C4⋊Dic3C2312yes—
96C2×Dic3⋊C4—22no—
97C2×Dic3⋊C4—22no—
98C2×C4×Dic3—22no—
99C2×C4×Dic3D411yescharacteristic
100C2×C4×Dic3D411yescharacteristic
101C2×C4×Dic3C2311yescharacteristic
102C22×C3⋊C8C2311yescharacteristic
103C22×C3⋊C8C2311yescharacteristic
104C2×Dic12—24no—
105C2×Dic12C2314yes—
106C2×D3×C8—24no—
107C2×D3×C8—24no—
108C2×D3×C8C2314yes—
109C2×D3×C8C2314yes—
110#897—24no—
111#897C2318yes—
112#890—24no—
113#890C2318yes—
114#883—216no—
115#879—216no—
116C42×D3D414yes—
117C42×D3C2314yes—
118C4×Dic6—24no—
119C4×Dic6C2318yes—
120C3×#107C2314yes—
121C3×#102C2318yes—
122C3×C4×C8C2314yes—
123#832C2318yes—
124#818C2314yes—
125#816C2318yes—
126C8×Dic3C2314yes—
127C8×Dic3C2314yes—
128#810C2318yes—
129#808C2318yes—
130C4×C3⋊C8C2314yes—
131C22×Q16—31no—
132C22×SD16—32no—
133C22×D8C2×D311yescharacteristic
134C23×C8—31no—
135C23×C8—31no—
136#529—316no—
137#529—68no—
138C2×#126—62no—
139C2×#125—32no—
140C2×#124—32no—
141C2×#123—62no—
142C2×C22⋊Q8—32no—
143C2×#121—32no—
144C2×C4×Q8—32no—
145C2×C4×D4—62no—
146C2×C4×D4C2×D312yes—
147C2×#117—62no—
148C22×C42—31no—
149#499—38no—
150#495—38no—
151#488—316no—
152#467—38no—
153#466—38no—
154#465—316no—
155C4×Q16—38no—
156C4×SD16—316no—
157C4×D8C2×D318yescomplemented
158C2×#107—31no—
159C2×#107C2×D311yescharacteristic
160C2×#106—32no—
161C2×#103—32no—
162C2×#103—32no—
163C2×#102—32no—
164C2×#102C2×D312yes—
165C2×C4×C8—31no—
166C2×C4×C8—31no—
167C2×C4×C8—31no—
168C2×C4×C8—38no—
169C2×C4×C8C2×D311yescharacteristic
170C24×C3—22no—
171C23×D3C2×D411yescharacteristic
172C2×C3×D4—22no—
173C2×C3×D4—24no—
174C2×C3×D4—24no—
175C2×C3×D4C2414yes—
176C22×C3×C4—22no—
177C22×C3×C4—28no—
178C22×C3×C4—48no—
179C22×C3×C4C2×D411yescharacteristic
180C22×C3×C4C2×D411yescharacteristic
181C22×C3×C4C2411yescharacteristic
182C2×#67—28no—
183C2×#67—48no—
184C22×Dic3—22no—
185C22×Dic3—22no—
186C22×Dic3C2×D411yescharacteristic
187C22×Dic3C2×D411yescharacteristic
188C22×Dic3C2×D411yescharacteristic
189C2×C4×D3—24no—
190C2×C4×D3—24no—
191C2×C4×D3—22no—
192C2×C4×D3—22no—
193C2×C4×D3C2×D412yes—
194C2×C4×D3C2×D414yes—
195C2×C4×D3C2×D414yes—
196C2×C4×D3C2412yes—
197C2×Dic6—24no—
198C2×Dic6—24no—
199C2×Dic6—22no—
200C2×Dic6C2414yes—
201C3×D8—28no—
202C2×C3×C8—22no—
203C2×C3×C8#4114yes—
204C2×C3×C8C2412yes—
205C2×C3×C8C2412yes—
206C3×C4⋊C4—22no—
207C3×C4⋊C4C2414yes—
208C3×C22⋊C4—28no—
209C3×C42C2×D412yes—
210C3×C42C2412yes—
211#217—28no—
212#217—28no—
213#217—28no—
214#214—216no—
215(C2×D3)⋊C4—28no—
216C4⋊Dic3—22no—
217C4⋊Dic3—28no—
218C4⋊Dic3—28no—
219C4⋊Dic3C2414yes—
220Dic3⋊C4—28no—
221Dic3⋊C4—28no—
222C4×Dic3—28no—
223C4×Dic3C2×D412yes—
224C4×Dic3C2×D414yes—
225C4×Dic3C2×D414yes—
226C4×Dic3C2412yes—
227C2×C3⋊C8—22no—
228C2×C3⋊C8#4114yes—
229C2×C3⋊C8C2412yes—
230C2×C3⋊C8C2412yes—
231Dic12—28no—
232D3×C8—28no—
233D3×C8—28no—
234C22×Q8—32no—
235C22×D4—62no—
236C22×D4C22×D312yes—
237C23×C4—22no—
238C23×C4—31no—
239C23×C4—31no—
240C23×C4—31no—
241C2×Q16—34no—
242C2×Q16—64no—
243C2×SD16—38no—
244C2×SD16—68no—
245C2×D8—24no—
246C2×D8C22×D314yes—
247C22×C8—31no—
248C22×C8—31no—
249C22×C8—34no—
250C22×C8—34no—
251C22×C8—64no—
252C22×C8—64no—
253C22×C8C22×D311yescharacteristic
254C22×C8C22×D311yescharacteristic
255#126—616no—
256#125—38no—
257#125—64no—
258#124—38no—
259#124—64no—
260#123—616no—
261C22⋊Q8—38no—
262C22⋊Q8—64no—
263#121—38no—
264#121—64no—
265C4×Q8—38no—
266C4×Q8—64no—
267C4×D4—24no—
268C4×D4—616no—
269C4×D4C22×D318yes—
270#117—616no—
271C2×C4⋊C4—32no—
272C2×C4⋊C4—62no—
273C2×C4⋊C4—62no—
274C2×C4⋊C4—62no—
275C2×C4⋊C4—62no—
276C2×C4⋊C4C22×D312yes—
277C2×C22⋊C4—22no—
278C2×C22⋊C4—62no—
279C2×C22⋊C4—62no—
280C2×C22⋊C4—62no—
281C2×C22⋊C4—62no—
282C2×C42—31no—
283C2×C42—31no—
284C2×C42—31no—
285C2×C42—34no—
286C2×C42—34no—
287C2×C42—62no—
288C2×C42C22×D311yescharacteristic
289#107—34no—
290#107C22×D314yes—
291#106—38no—
292#103—38no—
293#103—38no—
294#102—38no—
295#102C22×D318yes—
296C4×C8—34no—
297C4×C8—34no—
298C4×C8—34no—
299C4×C8C22×D314yes—
300C23×C3—24no—
301C23×C3—44no—
302C23×C3—44no—
303C23×C3—44no—
304C23×C3C22×D411yescharacteristic
305C22×D3—22no—
306C22×D3—22no—
307C22×D3#13514yes—
308C22×D3C22×D412yes—
309C3×D4—24no—
310C3×D4—24no—
311C3×D4—44no—
312C2×C3×C4—22no—
313C2×C3×C4—24no—
314C2×C3×C4—44no—
315C2×C3×C4—416no—
316C2×C3×C4#13514yes—
317C2×C3×C4C22×D412yes—
318C2×C3×C4C22×D411yescharacteristic
319C2×C3×C4C22×D412yes—
320C2×C3×C4C2×#4112yes—
321C2×C3×C4C2×#4112yes—
322C2×C3×C4C2511yescharacteristic
323#67—416no—
324C2×Dic3—22no—
325C2×Dic3—22no—
326C2×Dic3—22no—
327C2×Dic3—24no—
328C2×Dic3—24no—
329C2×Dic3—44no—
330C2×Dic3—44no—
331C2×Dic3C22×D412yes—
332C2×Dic3C22×D412yes—
333C2×Dic3C22×D412yes—
334C4×D3—28no—
335C4×D3—24no—
336C4×D3—28no—
337C4×D3—22no—
338C4×D3—22no—
339Dic6—24no—
340Dic6—24no—
341Dic6—44no—
342C3×C8—22no—
343C3×C8C2×#4114yes—
344C3⋊C8—22no—
345C3⋊C8C2×#4114yes—
346C24—22no—
347C24—31no—
348C2×Q8—34no—
349C2×Q8—62no—
350C2×Q8—64no—
351C2×Q8—64no—
352C2×D4—24no—
353C2×D4—22no—
354C2×D4—24no—
355C2×D4—68no—
356C2×D4—128no—
357C2×D4C23×D314yes—
358C22×C4—22no—
359C22×C4—28no—
360C22×C4—31no—
361C22×C4—31no—
362C22×C4—31no—
363C22×C4—34no—
364C22×C4—32no—
365C22×C4—34no—
366C22×C4—32no—
367C22×C4—48no—
368C22×C4—64no—
369C22×C4—64no—
370C22×C4—62no—
371C22×C4—62no—
372C22×C4—62no—
373C22×C4—62no—
374C22×C4D3×D411yescharacteristic
375C22×C4D3×D411yescharacteristic
376C22×C4C23×D311yescharacteristic
377Q16—68no—
378SD16—616no—
379D8—28no—
380C2×C8—22no—
381C2×C8—34no—
382C2×C8—32no—
383C2×C8—32no—
384C2×C8—68no—
385C2×C8—62no—
386C2×C8—68no—
387C2×C8#23514yes—
388C2×C8C23×D312yes—
389C2×C8C23×D312yes—
390C4⋊C4—22no—
391C4⋊C4—34no—
392C4⋊C4—68no—
393C4⋊C4—68no—
394C4⋊C4—68no—
395C4⋊C4—62no—
396C4⋊C4—68no—
397C4⋊C4C23×D314yes—
398C22⋊C4—28no—
399C22⋊C4—68no—
400C22⋊C4—68no—
401C22⋊C4—68no—
402C22⋊C4—68no—
403C42—34no—
404C42—32no—
405C42—34no—
406C42—32no—
407C42—68no—
408C42D3×D412yes—
409C42C23×D312yes—
410C22×C3—44no—
411C22×C3—44no—
412C22×C3—44no—
413C22×C3—88no—
414C22×C3#53212yes—
415C22×C3C2×#13512yes—
416C22×C3C2×#13512yes—
417C22×C3C23×D411yescharacteristic
418C2×D3—28no—
419C2×D3—22no—
420C2×D3—22no—
421C2×D3C2×#13514yes—
422C3×C4—22no—
423C3×C4—44no—
424C3×C4#53212yes—
425C3×C4C2×#13514yes—
426C3×C4C22×#4111yescharacteristic
427C3×C4C22×#4111yescharacteristic
428Dic3—22no—
429Dic3—22no—
430Dic3—22no—
431Dic3—44no—
432Dic3—44no—
433C23—24no—
434C23—32no—
435C23—34no—
436C23—44no—
437C23—44no—
438C23—44no—
439C23—62no—
440C23—62no—
441C23C2×D3×D411yescharacteristic
442Q8—64no—
443Q8—64no—
444Q8—124no—
445D4—24no—
446D4—24no—
447D4—44no—
448D4—1216no—
449C2×C4—22no—
450C2×C4—24no—
451C2×C4—32no—
452C2×C4—32no—
453C2×C4—32no—
454C2×C4—44no—
455C2×C4—416no—
456C2×C4—68no—
457C2×C4—62no—
458C2×C4—62no—
459C2×C4—62no—
460C2×C4—62no—
461C2×C4—62no—
462C2×C4—68no—
463C2×C4—64no—
464C2×C4—64no—
465C2×C4—64no—
466C2×C4—124no—
467C2×C4—124no—
468C2×C4#91214yes—
469C2×C4C2×#23512yes—
470C2×C4C2×D3×D412yes—
471C2×C4C2×D3×D412yes—
472C2×C4C2×D3×D411yescharacteristic
473C2×C4D3×#4112yes—
474C2×C4C24×D311yescharacteristic
475C8—22no—
476C8—34no—
477C8—62no—
478C8C2×#23514yes—
479C2×C3—84no—
480C2×C3#316814yescomplemented
481C2×C3C2×#53211yescharacteristic
482C2×C3C22×#13511yescharacteristic
483C2×C3C22×#13511yescharacteristic
484D3—24no—
485C22—34no—
486C22—44no—
487C22—44no—
488C22—44no—
489C22—62no—
490C22—62no—
491C22—68no—
492C22—88no—
493C22#554812yes—
494C22C2×#91212yes—
495C22D3×#13512yes—
496C22C22×D3×D411yescharacteristic
497C4—22no—
498C4—44no—
499C4—62no—
500C4—62no—
501C4—62no—
502C4—124no—
503C4—124no—
504C4#554812yes—
505C4C2×#91214yes—
506C4C22×#23511yescharacteristic
507C4C2×D3×#4111yescharacteristic
508C3C2×#316811yescharacteristic, complemented, Sylow
509C2—64no—
510C2—84no—
511C2#7958314yesdirect product factor
512C2C2×#554811yescharacteristic
513C2C22×#91211yescharacteristic
514C2C2×D3×#13511yescharacteristic
subgroupG/H
centerC22×C4D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC2×C3×C4×D8C2
socleC23×C3C22×D4
prime radicalC2×#5157C2
hypercenterC2×C4×D8D3
hypocenterC3C2×#3168
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×D8

Complements

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

NH ≅ G/Ntype
1. C2×#5557C2semidirect
2. C2×C3×C4×D8C2semidirect
4. C2×#5155C2semidirect
5. C2×C4×#214C2semidirect
6. #79583C2direct (N × H)
7. C2×#4887C2semidirect
8. C2×#4878C2semidirect
9. C2×#4778C2semidirect
10. C2×#4768C2semidirect
11. C2×C4×Dic12C2semidirect
12. C2×C4×D3×C8C2semidirect
25. #5557C22semidirect
32. C3×C4×D8C22semidirect
38. #5155C22semidirect
43. C4×#214C22semidirect
47. #4887C22semidirect
48. #4878C22semidirect
49. #4778C22semidirect
50. #4768C22semidirect
51. C4×Dic12C22semidirect
52. C4×D3×C8C22semidirect
63. C2×C4×D8D3semidirect
157. C4×D8C2×D3semidirect
480. C2×C3#3168semidirect
508. C3C2×#3168semidirect
511. C2#79583direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#55572
C2×C3×C4×D82
C2×#51572
C2×#51552
C2×C4×#2142
#795832
C2×#48872
C2×#48782
C2×#47782
C2×#47682
C2×C4×Dic122
C2×C4×D3×C82
C2×#31683