Finite Group Databasebeta

← C2×#81593 #11664930

Subgroups — C2×#81593 #11664930

Order 768.

2006 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5728C211yesmaximal, characteristic
2C2×#5728C211yesmaximal, characteristic
3C2×C3×#487C211yesmaximal, characteristic, complemented
4C2×#5078C211yesmaximal, characteristic, complemented
5C2×#5092C211yesmaximal, characteristic, complemented
6#81593C2116yesmaximal, direct product factor
7C2×#4813C214yesmaximal
8C2×#4790C214yesmaximal, complemented
9C2×#4681C211yesmaximal, characteristic, complemented
10C2×C4×D3×C8C211yesmaximal, characteristic
11C2×#3170—31nomaximal, Sylow
12C2×C3×C4⋊Q8C2211yescharacteristic
13C2×C3×C4⋊Q8C2211yescharacteristic
14C2×#946—21no—
15C2×#946C2212yes—
16C2×Q8×Dic3—21no—
17C2×Q8×Dic3C2212yes—
18C22×#216C2214yes—
19C22×D3×C8C2212yes—
20#5728—24no—
21#5728—24no—
22#5728C2218yes—
23#5728C2218yes—
24C2×#897—21no—
25C2×#897C2212yes—
26C2×#892—21no—
27C2×#892—21no—
28C2×#890—21no—
29C2×#890—21no—
30C2×#887—21no—
31C2×#887C2212yes—
32C2×C42×D3C2211yescharacteristic
33C2×#869C2211yescharacteristic
34C2×#869C2211yescharacteristic
35C3×#487C2218yescomplemented
36C2×C3×#103C2214yes—
37C2×C3×C4×C8C2211yescharacteristic
38C2×#816C2214yes—
39C2×C8×Dic3C2212yes—
40#5092C2218yescomplemented
41#5078C2218yescomplemented
42C2×#807C2214yes—
43C2×C4×C3⋊C8C2211yescharacteristic
44#4813C22132yes—
45#4790C22132yescomplemented
46C4×D3×C8C2218yes—
47#4681C2218yescomplemented
48C2×#533—31no—
49C2×#533—31no—
50#3170—316no—
51C2×#500—31no—
52C2×#494—31no—
53C2×#487—31no—
54C2×#487D311yescharacteristic, complemented
55C2×#467—34no—
56C2×C4×Q16—34no—
57C22×C4×C8—31no—
58C22×C3×Q8—21no—
59C22×C3×Q8C2312yes—
60C22×C4×D3D411yescharacteristic
61C22×C4×D3D411yescharacteristic
62C22×C4×D3C2311yescharacteristic
63C22×Dic6—21no—
64C22×Dic6C2312yes—
65C22×C3×C8C2312yes—
66C3×C4⋊Q8—22no—
67C3×C4⋊Q8—22no—
68C3×C4⋊Q8C2314yes—
69C3×C4⋊Q8C2314yes—
70C2×C3×C4⋊C4—21no—
71C2×C3×C4⋊C4—21no—
72C2×C3×C4⋊C4—21no—
73C2×C3×C4⋊C4C2312yes—
74C2×C3×C42C2311yescharacteristic
75#946—24no—
76#946—28no—
77#946C2318yes—
78Q8×Dic3—24no—
79Q8×Dic3—28no—
80Q8×Dic3C2318yes—
81C2×#216—216no—
82C2×#216C23116yes—
83C2×(C2×D3)⋊C4—22no—
84C2×(C2×D3)⋊C4—22no—
85C2×C4⋊Dic3—21no—
86C2×C4⋊Dic3—21no—
87C2×C4⋊Dic3—21no—
88C2×C4⋊Dic3—22no—
89C2×C4⋊Dic3—22no—
90C2×C4⋊Dic3C2312yes—
91C2×Dic3⋊C4—22no—
92C2×Dic3⋊C4—22no—
93C2×C4×Dic3—22no—
94C2×C4×Dic3—22no—
95C2×C4×Dic3D411yescharacteristic
96C2×C4×Dic3D411yescharacteristic
97C2×C4×Dic3C2311yescharacteristic
98C22×C3⋊C8C2312yes—
99C2×D3×C8—28no—
100C2×D3×C8C2318yes—
101#897—24no—
102#897—28no—
103#897C2318yes—
104#892—28no—
105#892—28no—
106#890—28no—
107#890—28no—
108#887—24no—
109#887—28no—
110#887C2318yes—
111C42×D3D414yes—
112C42×D3C2314yes—
113#869—22no—
114#869—22no—
115#869C2314yes—
116#869C2314yes—
117C3×#103C23116yes—
118C3×C4×C8C2314yes—
119#816C23116yes—
120C8×Dic3C2318yes—
121#807C23116yes—
122C4×C3⋊C8C2314yes—
123C22×Q16—34no—
124C23×C8—32no—
125#533—38no—
126#533—38no—
127#533—64no—
128#533—64no—
129C2×C4⋊Q8—31no—
130C2×C4⋊Q8—31no—
131C2×C4⋊Q8C2×D311yescharacteristic
132C2×C4⋊Q8C2×D311yescharacteristic
133C2×#125—61no—
134C2×#125—61no—
135C2×C22⋊Q8—32no—
136C2×C22⋊Q8—32no—
137C2×C22⋊Q8—61no—
138C2×C22⋊Q8—61no—
139C2×C4×Q8—32no—
140C2×C4×Q8—32no—
141C2×C4×Q8—61no—
142C2×C4×Q8—61no—
143C2×#117—61no—
144C2×#117—61no—
145C22×C42—31no—
146#500—38no—
147#494—38no—
148#487—38no—
149#487C2×D318yescomplemented
150#467—332no—
151C4×Q16—332no—
152C2×#107—34no—
153C2×#103—34no—
154C2×#103C2×D314yes—
155C2×C4×C8—32no—
156C2×C4×C8—31no—
157C2×C4×C8—38no—
158C2×C4×C8C2×D311yescharacteristic
159C23×D3C2×D411yescharacteristic
160C2×C3×Q8—22no—
161C2×C3×Q8—24no—
162C2×C3×Q8—28no—
163C2×C3×Q8—44no—
164C2×C3×Q8C2414yes—
165C22×C3×C4—22no—
166C22×C3×C4—22no—
167C22×C3×C4C2×D411yescharacteristic
168C22×C3×C4C2×D411yescharacteristic
169C22×C3×C4C2411yescharacteristic
170C22×Dic3—22no—
171C22×Dic3—22no—
172C22×Dic3C2×D411yescharacteristic
173C22×Dic3C2×D411yescharacteristic
174C22×Dic3C2×D411yescharacteristic
175C2×C4×D3—24no—
176C2×C4×D3—24no—
177C2×C4×D3Q1618yescomplemented
178C2×C4×D3C2×D412yes—
179C2×C4×D3C2×D414yes—
180C2×C4×D3C2×D414yes—
181C2×C4×D3C2412yes—
182C2×Dic6—28no—
183C2×Dic6—22no—
184C2×Dic6—24no—
185C2×Dic6—44no—
186C2×Dic6C2414yes—
187C2×C3×C8—24no—
188C2×C3×C8C2414yes—
189C3×C4⋊C4—24no—
190C3×C4⋊C4—22no—
191C3×C4⋊C4—24no—
192C3×C4⋊C4—24no—
193C3×C4⋊C4C2414yes—
194C3×C42C2×D412yes—
195C3×C42C2412yes—
196#216—232no—
197(C2×D3)⋊C4—28no—
198(C2×D3)⋊C4—28no—
199C4⋊Dic3—22no—
200C4⋊Dic3—24no—
201C4⋊Dic3—24no—
202C4⋊Dic3—24no—
203C4⋊Dic3—28no—
204C4⋊Dic3—28no—
205C4⋊Dic3C2414yes—
206Dic3⋊C4—28no—
207Dic3⋊C4—28no—
208C4×Dic3—28no—
209C4×Dic3—28no—
210C4×Dic3C2×D412yes—
211C4×Dic3C2×D414yes—
212C4×Dic3C2×D414yes—
213C4×Dic3C2412yes—
214C2×C3⋊C8#4118yes—
215C2×C3⋊C8C2414yes—
216D3×C8—216no—
217C22×Q8—21no—
218C22×Q8—32no—
219C22×Q8—61no—
220C22×Q8C22×D312yes—
221C23×C4—31no—
222C23×C4—31no—
223C23×C4—31no—
224C2×Q16—316no—
225C2×Q16—616no—
226C22×C8—32no—
227C22×C8—38no—
228C22×C8—68no—
229C22×C8C22×D312yes—
230C4⋊Q8—22no—
231C4⋊Q8—22no—
232C4⋊Q8—34no—
233C4⋊Q8—34no—
234C4⋊Q8—62no—
235C4⋊Q8—62no—
236C4⋊Q8C22×D314yes—
237C4⋊Q8C22×D314yes—
238#125—68no—
239#125—68no—
240C22⋊Q8—38no—
241C22⋊Q8—38no—
242C22⋊Q8—64no—
243C22⋊Q8—68no—
244C22⋊Q8—64no—
245C22⋊Q8—68no—
246C4×Q8—38no—
247C4×Q8—38no—
248C4×Q8—64no—
249C4×Q8—68no—
250C4×Q8—64no—
251C4×Q8—68no—
252#117—68no—
253#117—68no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—32no—
258C2×C4⋊C4—62no—
259C2×C4⋊C4—62no—
260C2×C4⋊C4—62no—
261C2×C4⋊C4—62no—
262C2×C4⋊C4—61no—
263C2×C4⋊C4—61no—
264C2×C4⋊C4—61no—
265C2×C4⋊C4C22×D312yes—
266C2×C22⋊C4—62no—
267C2×C22⋊C4—62no—
268C2×C42—31no—
269C2×C42—31no—
270C2×C42—31no—
271C2×C42—34no—
272C2×C42—34no—
273C2×C42—62no—
274C2×C42—62no—
275C2×C42C22×D311yescharacteristic
276#107—316no—
277#103—316no—
278#103C22×D3116yes—
279C4×C8—38no—
280C4×C8—34no—
281C4×C8C22×D314yes—
282C23×C3C22×D411yescharacteristic
283C22×D3—22no—
284C22×D3—22no—
285C22×D3C2×Q1614yes—
286C22×D3C22×D412yes—
287C3×Q8—28no—
288C3×Q8—44no—
289C3×Q8—48no—
290C2×C3×C4—24no—
291C2×C3×C4—24no—
292C2×C3×C4—44no—
293C2×C3×C4—44no—
294C2×C3×C4C2×Q1614yes—
295C2×C3×C4#13514yes—
296C2×C3×C4C22×D411yescharacteristic
297C2×C3×C4C22×D412yes—
298C2×C3×C4C22×D412yes—
299C2×C3×C4C2×#4114yes—
300C2×C3×C4C2511yescharacteristic
301C2×Dic3—22no—
302C2×Dic3—22no—
303C2×Dic3—24no—
304C2×Dic3—24no—
305C2×Dic3—44no—
306C2×Dic3—44no—
307C2×Dic3C2×Q1614yes—
308C2×Dic3C22×D412yes—
309C2×Dic3C22×D412yes—
310C2×Dic3C22×D412yes—
311C4×D3—24no—
312C4×D3—28no—
313C4×D3—24no—
314C4×D3C2×Q16116yescomplemented
315Dic6—28no—
316Dic6—44no—
317Dic6—48no—
318C3×C8—24no—
319C3⋊C8C2×#4118yes—
320C24—31no—
321C2×Q8—22no—
322C2×Q8—24no—
323C2×Q8—28no—
324C2×Q8—34no—
325C2×Q8—44no—
326C2×Q8—64no—
327C2×Q8—62no—
328C2×Q8—68no—
329C2×Q8—124no—
330C2×Q8C23×D314yes—
331C22×C4—22no—
332C22×C4—22no—
333C22×C4—31no—
334C22×C4—38no—
335C22×C4—34no—
336C22×C4—31no—
337C22×C4—31no—
338C22×C4—32no—
339C22×C4—34no—
340C22×C4—32no—
341C22×C4—64no—
342C22×C4—64no—
343C22×C4—62no—
344C22×C4—62no—
345C22×C4D3×D411yescharacteristic
346C22×C4D3×D411yescharacteristic
347C22×C4C23×D311yescharacteristic
348Q16—632no—
349C2×C8—24no—
350C2×C8—38no—
351C2×C8—34no—
352C2×C8—616no—
353C2×C8C23×D314yes—
354C4⋊C4—24no—
355C4⋊C4—24no—
356C4⋊C4—24no—
357C4⋊C4—22no—
358C4⋊C4—34no—
359C4⋊C4—68no—
360C4⋊C4—68no—
361C4⋊C4—68no—
362C4⋊C4—68no—
363C4⋊C4—62no—
364C4⋊C4—64no—
365C4⋊C4—64no—
366C4⋊C4—64no—
367C4⋊C4C23×D314yes—
368C22⋊C4—68no—
369C22⋊C4—68no—
370C42—32no—
371C42—34no—
372C42—34no—
373C42—32no—
374C42—68no—
375C42—68no—
376C42D3×D412yes—
377C42C23×D312yes—
378C22×C3#53212yes—
379C22×C3C22×Q1612yes—
380C22×C3C2×#13512yes—
381C22×C3C23×D411yescharacteristic
382C2×D3—28no—
383C2×D3—22no—
384C2×D3—22no—
385C2×D3C22×Q1614yes—
386C3×C4—44no—
387C3×C4—44no—
388C3×C4#53212yes—
389C3×C4C22×Q1614yes—
390C3×C4C2×#13514yes—
391C3×C4C22×#4112yes—
392Dic3—22no—
393Dic3—22no—
394Dic3—44no—
395Dic3—44no—
396Dic3C22×Q1614yes—
397C23—32no—
398C23—34no—
399C23—62no—
400C23—62no—
401C23C2×D3×D411yescharacteristic
402Q8—28no—
403Q8—44no—
404Q8—48no—
405Q8—68no—
406Q8—124no—
407Q8—128no—
408C2×C4—24no—
409C2×C4—24no—
410C2×C4—32no—
411C2×C4—34no—
412C2×C4—316no—
413C2×C4—32no—
414C2×C4—32no—
415C2×C4—44no—
416C2×C4—44no—
417C2×C4—62no—
418C2×C4—62no—
419C2×C4—64no—
420C2×C4—64no—
421C2×C4—68no—
422C2×C4—64no—
423C2×C4—64no—
424C2×C4—124no—
425C2×C4—124no—
426C2×C4#91614yes—
427C2×C4D3×Q1614yes—
428C2×C4C2×D3×D411yescharacteristic
429C2×C4C2×D3×D412yes—
430C2×C4C2×D3×D412yes—
431C2×C4D3×#4114yes—
432C2×C4C24×D311yescharacteristic
433C8—24no—
434C8—38no—
435C2×C3#317014yescomplemented
436C2×C3C2×#53211yescharacteristic
437C2×C3C23×Q1611yescharacteristic
438C2×C3C22×#13511yescharacteristic
439D3—24no—
440C22—34no—
441C22—62no—
442C22—62no—
443C22—68no—
444C22#566812yes—
445C22C2×#91612yes—
446C22C2×D3×Q1612yes—
447C22C22×D3×D411yescharacteristic
448C4—34no—
449C4—44no—
450C4—44no—
451C4—62no—
452C4—62no—
453C4—124no—
454C4—124no—
455C4#566812yes—
456C4C2×#91614yes—
457C4C2×D3×Q1614yes—
458C4C2×D3×#4112yes—
459C3C2×#317011yescharacteristic, complemented, Sylow
460C2—64no—
461C2#8159314yesdirect product factor
462C2C2×#566811yescharacteristic
463C2C22×#91611yescharacteristic
464C2C22×D3×Q1611yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC2×C3×#487C2
socleC23×C3C22×D4
prime radicalC23×D3C2×D4
hypercenterC2×#487D3
hypocenterC3C2×#3170
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#487

Complements

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

NH ≅ G/Ntype
3. C2×C3×#487C2semidirect
4. C2×#5078C2semidirect
5. C2×#5092C2semidirect
6. #81593C2direct (N × H)
8. C2×#4790C2semidirect
9. C2×#4681C2semidirect
35. C3×#487C22semidirect
40. #5092C22semidirect
41. #5078C22semidirect
45. #4790C22semidirect
47. #4681C22semidirect
54. C2×#487D3semidirect
149. #487C2×D3semidirect
177. C2×C4×D3Q16semidirect
314. C4×D3C2×Q16semidirect
435. C2×C3#3170semidirect
459. C3C2×#3170semidirect
461. C2#81593direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#57282
C2×C3×#4872
C2×#50782
C2×#50922
#815932
C2×#48132
C2×#47902
C2×#46812
C2×C4×D3×C82
C2×#31703