Finite Group Databasebeta

← C2×#10591446 #11860068

Subgroups — C2×#10591446 #11860068

Order 1152.

1301 conjugacy classes of subgroups.

The subgroup lattice has 507 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×C3⋊Dic3C211yesmaximal, characteristic
2C22×C3×#214C211yesmaximal, characteristic
3C2×#63843C211yesmaximal, characteristic, complemented
4C2×C3×#832C211yesmaximal, characteristic
5#10591446C218yesmaximal, direct product factor
6C2×#63575C211yesmaximal, characteristic, complemented
7C2×#63566C211yesmaximal, characteristic, complemented
8C2×#63555C211yesmaximal, characteristic, complemented
9C2×#5164—31nomaximal
10C2×#4757—31nomaximal
11C22×C32×D4C2211yescharacteristic
12C23×C3⋊Dic3—21no—
13C22×C3×Dic6C2211yescharacteristic
14C2×#3757—21no—
15D4×C3⋊Dic3—22no—
16D4×C3⋊Dic3C2214yes—
17C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
18C2×C4×C3⋊Dic3C2211yescharacteristic
19C2×C3×#214C418yescomplemented
20C2×C3×#214C2214yes—
21C2×C3×C4⋊Dic3C2211yescharacteristic
22C22×C3×C3⋊C8C2211yescharacteristic
23C22×C3×C3⋊C8C2211yescharacteristic
24C2×Dic3⋊Dic3—21no—
25C2×Dic32—21no—
26#63843—22no—
27#63843C2214yescomplemented
28C3×#832C2214yes—
29#63575C2214yescomplemented
30#63566C2214yescomplemented
31#63555C2214yescomplemented
32C22×C3×SD16—31no—
33C2×Q8×Dic3—31no—
34C2×D4×Dic3—31no—
35C2×D4×Dic3—31no—
36C2×D4×Dic3—61no—
37C22×#214D311yescharacteristic
38C2×#887—31no—
39C2×C3×#102—31no—
40C2×#835—31no—
41C2×#832D311yescharacteristic
42#5164—38no—
43C2×#818—31no—
44C2×#816—31no—
45C2×#815—31no—
46C2×#815—31no—
47C2×#807—31no—
48#4757—38no—
49C24×C32—21no—
50C2×C32×D4—21no—
51C2×C32×D4—22no—
52C2×C32×D4C2×C414yes—
53C2×C32×D4C2312yes—
54C22×C32×C4C2311yescharacteristic
55C22×C3⋊Dic3—21no—
56C22×C3⋊Dic3—24no—
57C22×C3⋊Dic3—44no—
58C22×C3⋊Dic3D411yescharacteristic
59C22×C3⋊Dic3D411yescharacteristic
60C22×C3×Dic3—21no—
61C22×C3×Dic3—21no—
62C2×C3×Dic6—21no—
63C2×C3×Dic6—22no—
64C2×C3×Dic6C2×C414yescomplemented
65C2×C3×Dic6C2312yes—
66#3757—24no—
67C4⋊(C3⋊Dic3)—21no—
68C4⋊(C3⋊Dic3)C2312yes—
69C4×C3⋊Dic3D412yes—
70C4×C3⋊Dic3C2312yes—
71C3×#214C2×C4116yescomplemented
72C3×C4⋊Dic3—21no—
73C3×C4⋊Dic3C2312yes—
74C2×C3×C3⋊C8—22no—
75C2×C3×C3⋊C8C2×C414yescomplemented
76C2×C3×C3⋊C8C2312yes—
77C2×C3×C3⋊C8C2312yes—
78Dic3⋊Dic3—24no—
79Dic32—24no—
80C2×#440—91noSylow
81C22×C3×Q8—31no—
82C22×C3×D4—21no—
83C22×C3×D4C2×D311yescharacteristic
84C22×C3×D4C2×D311yescharacteristic
85C23×Dic3—61no—
86C23×Dic3—61no—
87C23×Dic3—62no—
88C22×Dic6C2×D311yescharacteristic
89C2×C3×SD16—38no—
90C2×C3×SD16—34no—
91C22×C3×C8—31no—
92C22×C3×C8—31no—
93C2×C3×C4⋊C4—31no—
94C2×#217—61no—
95C2×#217—61no—
96C2×#217—62no—
97Q8×Dic3—34no—
98Q8×Dic3—62no—
99D4×Dic3—34no—
100D4×Dic3—34no—
101D4×Dic3—64no—
102D4×Dic3—62no—
103D4×Dic3—62no—
104D4×Dic3—64no—
105C2×#214Dic318yescomplemented
106C2×#214C2×D314yes—
107C2×C4⋊Dic3—31no—
108C2×C4⋊Dic3—31no—
109C2×C4⋊Dic3—61no—
110C2×C4⋊Dic3—61no—
111C2×C4⋊Dic3C2×D311yescharacteristic
112C2×Dic3⋊C4—61no—
113C2×C4×Dic3—31no—
114C2×C4×Dic3—31no—
115C2×C4×Dic3—61no—
116C2×C4×Dic3—61no—
117C2×C4×Dic3—61no—
118C22×C3⋊C8C2×D311yescharacteristic
119C22×C3⋊C8C2×D311yescharacteristic
120#887—34no—
121#887—62no—
122C3×#102—34no—
123#835—34no—
124#832C2×D314yes—
125#818—34no—
126#816—34no—
127#815—34no—
128#815—34no—
129#807—34no—
130C23×C32—24no—
131C23×C32—22no—
132C23×C32—42no—
133C23×C32—42no—
134C23×C32C2×D411yescharacteristic
135C32×D4—24no—
136C32×D4—22no—
137C32×D4C22×C414yes—
138C2×C32×C4C22×C412yes—
139C2×C32×C4C2×D411yescharacteristic
140C2×C32×C4#4112yes—
141C2×C32×C4C2411yescharacteristic
142C2×C3⋊Dic3—22no—
143C2×C3⋊Dic3—22no—
144C2×C3⋊Dic3—22no—
145C2×C3⋊Dic3—48no—
146C2×C3⋊Dic3—42no—
147C2×C3⋊Dic3C2×D412yes—
148C2×C3⋊Dic3C2×D412yes—
149C2×C3×Dic3—24no—
150C2×C3×Dic3—22no—
151C2×C3×Dic3—22no—
152C2×C3×Dic3—42no—
153C3×Dic6—24no—
154C3×Dic6—22no—
155C3×Dic6C22×C414yescomplemented
156C3×C3⋊C8—22no—
157C3×C3⋊C8C22×C414yescomplemented
158C22×SD16—31no—
159C2×C4×Q8—91no—
160C2×C4×D4—91no—
161#440—98no—
162C2×#107—91no—
163C2×#103—91no—
164C2×#102—31no—
165C2×#97—91no—
166C24×C3—22no—
167C24×C3—21no—
168C24×C3—21no—
169C2×C3×Q8—34no—
170C2×C3×Q8—32no—
171C2×C3×Q8—61no—
172C2×C3×Q8—62no—
173C2×C3×D4—22no—
174C2×C3×D4—24no—
175C2×C3×D4—21no—
176C2×C3×D4—21no—
177C2×C3×D4—22no—
178C2×C3×D4—22no—
179C2×C3×D4—24no—
180C2×C3×D4—22no—
181C2×C3×D4C4×D314yes—
182C2×C3×D4C2×Dic314yes—
183C2×C3×D4C22×D312yes—
184C2×C3×D4C22×D312yes—
185C22×C3×C4—21no—
186C22×C3×C4—61no—
187C22×C3×C4—61no—
188C22×C3×C4C22×D311yescharacteristic
189C22×C3×C4C22×D311yescharacteristic
190C22×Dic3—21no—
191C22×Dic3—21no—
192C22×Dic3—31no—
193C22×Dic3—31no—
194C22×Dic3—31no—
195C22×Dic3—31no—
196C22×Dic3—61no—
197C22×Dic3—61no—
198C22×Dic3—64no—
199C22×Dic3—64no—
200C22×Dic3—62no—
201C22×Dic3—68no—
202C22×Dic3—61no—
203C22×Dic3—61no—
204C22×Dic3—128no—
205C22×Dic3—124no—
206C22×Dic3—124no—
207C2×Dic6—21no—
208C2×Dic6—22no—
209C2×Dic6C2×Dic314yescomplemented
210C2×Dic6C22×D312yes—
211C3×SD16—316no—
212C2×C3×C8—34no—
213C2×C3×C8—32no—
214C2×C3×C8—32no—
215C2×C3×C8—62no—
216C3×C4⋊C4—32no—
217C3×C4⋊C4—61no—
218#217—64no—
219#217—64no—
220#217—68no—
221#214C2×Dic3116yescomplemented
222C4⋊Dic3—21no—
223C4⋊Dic3—32no—
224C4⋊Dic3—32no—
225C4⋊Dic3—62no—
226C4⋊Dic3—64no—
227C4⋊Dic3—62no—
228C4⋊Dic3—61no—
229C4⋊Dic3—61no—
230C4⋊Dic3C22×D312yes—
231Dic3⋊C4—64no—
232C4×Dic3—32no—
233C4×Dic3—32no—
234C4×Dic3—32no—
235C4×Dic3—32no—
236C4×Dic3—62no—
237C4×Dic3—62no—
238C4×Dic3—64no—
239C4×Dic3—64no—
240C2×C3⋊C8—22no—
241C2×C3⋊C8C2×Dic314yescomplemented
242C2×C3⋊C8C22×D312yes—
243C2×C3⋊C8C22×D312yes—
244C22×C32—24no—
245C22×C32—42no—
246C22×C32—42no—
247C22×C32—48no—
248C22×C32C4×D412yes—
249C22×C32AGL(1,ℤ/8)12yes—
250C22×C32#13712yes—
251C22×C32C22×D411yescharacteristic
252C32×C4C4×D412yes—
253C32×C4C23×C411yescharacteristic
254C32×C4C2×#4111yescharacteristic
255C3⋊Dic3—22no—
256C3⋊Dic3—22no—
257C3⋊Dic3—42no—
258C3×Dic3—24no—
259C3×Dic3—42no—
260C22×Q8—31no—
261C22×D4D3211yescharacteristic
262C23×C4—181no—
263C2×SD16—38no—
264C2×SD16—34no—
265C22×C8—31no—
266C22×C8—31no—
267C4×Q8—94no—
268C4×Q8—182no—
269C4×D4—94no—
270C4×D4—182no—
271C2×C4⋊C4—31no—
272C2×C4⋊C4—91no—
273C2×C4⋊C4—181no—
274C2×C22⋊C4—181no—
275C2×C42—91no—
276C2×C42—181no—
277#107—94no—
278#103—94no—
279#102—34no—
280#97—94no—
281C23×C3—24no—
282C23×C3—28no—
283C23×C3—24no—
284C23×C3—24no—
285C23×C3—22no—
286C23×C3—22no—
287C23×C3—21no—
288C23×C3—44no—
289C23×C3—44no—
290C23×C3—42no—
291C23×C3—42no—
292C23×C3—42no—
293C23×C3—42no—
294C23×C3D3×D411yescharacteristic
295C23×C3D3×D411yescharacteristic
296C3×Q8—34no—
297C3×Q8—64no—
298C3×Q8—62no—
299C3×D4—24no—
300C3×D4—28no—
301C3×D4—24no—
302C3×D4—24no—
303C3×D4—22no—
304C3×D4—22no—
305C3×D4—24no—
306C3×D4C2×C4×D314yes—
307C3×D4C22×Dic314yes—
308C2×C3×C4—21no—
309C2×C3×C4—22no—
310C2×C3×C4—22no—
311C2×C3×C4—21no—
312C2×C3×C4—64no—
313C2×C3×C4—62no—
314C2×C3×C4—62no—
315C2×C3×C4—122no—
316C2×C3×C4C2×C4×D312yes—
317C2×C3×C4D3×D411yescharacteristic
318C2×C3×C4D3×D411yescharacteristic
319C2×C3×C4#23712yes—
320C2×C3×C4#23712yes—
321C2×C3×C4C22×Dic312yes—
322C2×C3×C4C23×D311yescharacteristic
323C2×C3×C4C23×D311yescharacteristic
324C2×Dic3—24no—
325C2×Dic3—22no—
326C2×Dic3—22no—
327C2×Dic3—32no—
328C2×Dic3—32no—
329C2×Dic3—32no—
330C2×Dic3—32no—
331C2×Dic3—42no—
332C2×Dic3—62no—
333C2×Dic3—62no—
334C2×Dic3—64no—
335C2×Dic3—62no—
336C2×Dic3—62no—
337C2×Dic3—62no—
338C2×Dic3—62no—
339C2×Dic3—64no—
340C2×Dic3—62no—
341C2×Dic3—62no—
342C2×Dic3—122no—
343C2×Dic3—1216no—
344C2×Dic3—128no—
345C2×Dic3—128no—
346C2×Dic3—124no—
347C2×Dic3—122no—
348C2×Dic3—122no—
349Dic6—24no—
350Dic6—22no—
351Dic6C22×Dic314yescomplemented
352C3×C8—34no—
353C3×C8—62no—
354C3⋊C8—22no—
355C3⋊C8C22×Dic314yescomplemented
356C2×C32—44no—
357C2×C32#44014yescomplemented
358C2×C32C2×C4×D411yescharacteristic
359C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
360C2×C32C2×#13711yescharacteristic
361C24—21no—
362C2×Q8—32no—
363C2×Q8—34no—
364C2×Q8—62no—
365C2×Q8—61no—
366C2×D4—22no—
367C2×D4—21no—
368C2×D4D3×Dic314yes—
369C2×D4C2×D3212yes—
370C22×C4—61no—
371C22×C4—61no—
372C22×C4—91no—
373C22×C4—91no—
374C22×C4—184no—
375C22×C4—181no—
376C22×C4—364no—
377C22×C4C2×D3211yescharacteristic
378SD16—316no—
379C2×C8—32no—
380C2×C8—34no—
381C2×C8—32no—
382C2×C8—62no—
383C4⋊C4—32no—
384C4⋊C4—61no—
385C4⋊C4—92no—
386C4⋊C4—184no—
387C4⋊C4—181no—
388C22⋊C4—184no—
389C42—92no—
390C42—92no—
391C42—184no—
392C22×C3—28no—
393C22×C3—24no—
394C22×C3—24no—
395C22×C3—21no—
396C22×C3—22no—
397C22×C3—22no—
398C22×C3—22no—
399C22×C3—44no—
400C22×C3—44no—
401C22×C3—416no—
402C22×C3—48no—
403C22×C3—42no—
404C22×C3—42no—
405C22×C3—42no—
406C22×C3—42no—
407C22×C3—48no—
408C22×C3#67⋊C412yes—
409C22×C3#91112yes—
410C22×C3#91412yes—
411C22×C3#91512yes—
412C22×C3#91512yes—
413C22×C3D4×Dic312yes—
414C22×C3C2×D3×D411yescharacteristic
415C22×C3C2×D3×D411yescharacteristic
416C3×C4—21no—
417C3×C4—21no—
418C3×C4—22no—
419C3×C4—64no—
420C3×C4—122no—
421C3×C4#67⋊C412yes—
422C3×C4D4×Dic312yes—
423C3×C4C22×C4×D311yescharacteristic
424C3×C4C2×#23711yescharacteristic
425C3×C4C2×#23711yescharacteristic
426C3×C4C23×Dic311yescharacteristic
427Dic3—24no—
428Dic3—42no—
429Dic3—64no—
430Dic3—62no—
431Dic3—62no—
432Dic3—62no—
433Dic3—62no—
434Dic3—122no—
435Dic3—124no—
436Dic3—122no—
437Dic3—122no—
438C32C2×#44011yescharacteristic, complemented, Sylow
439C23—22no—
440C23—24no—
441C23—42no—
442C23—42no—
443C23#381111yescharacteristic
444Q8—34no—
445Q8—62no—
446Q8—64no—
447D4—22no—
448D4—24no—
449D4C2×D3×Dic314yes—
450C2×C4—62no—
451C2×C4—64no—
452C2×C4—62no—
453C2×C4—92no—
454C2×C4—92no—
455C2×C4—122no—
456C2×C4—182no—
457C2×C4—182no—
458C2×C4—182no—
459C2×C4—368no—
460C2×C4—362no—
461C2×C4C2×D3×Dic312yes—
462C2×C4#380512yes—
463C2×C4#381111yescharacteristic
464C2×C4C22×D3211yescharacteristic
465C8—34no—
466C8—62no—
467C2×C3—21no—
468C2×C3—21no—
469C2×C3—21no—
470C2×C3—24no—
471C2×C3—48no—
472C2×C3—44no—
473C2×C3—44no—
474C2×C3#475714yescomplemented
475C2×C3#516414yescomplemented
476C2×C3C2×#67⋊C411yescharacteristic
477C2×C3C2×#91111yescharacteristic
478C2×C3C2×#91411yescharacteristic
479C2×C3C2×#91511yescharacteristic
480C2×C3C2×#91511yescharacteristic
481C2×C3C2×D4×Dic311yescharacteristic
482C22—24no—
483C22—42no—
484C22—42no—
485C22—48no—
486C22#6393112yes—
487C22#6393712yes—
488C22#67⋊Dic312yes—
489C22C2×#381111yescharacteristic
490C4—64no—
491C4—122no—
492C4—182no—
493C4—182no—
494C4—362no—
495C4#67⋊Dic312yes—
496C4C22×D3×Dic311yescharacteristic
497C4C2×#380511yescharacteristic
498C3—21no—
499C3C2×#475711yescharacteristic, complemented
500C3C2×#516411yescharacteristic, complemented
501C2—44no—
502C2#1059144614yesdirect product factor
503C2C2×#6393111yescharacteristic
504C2C2×#6393711yescharacteristic
505C2C2×#67⋊Dic311yescharacteristic
subgroupG/H
centerC23#3811
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
Fitting, prime radicalC22×C32×D4C22
socleC23×C32C2×D4
cosocleC2×C32×C4C24
hypercenterC22×D4D32
hypocenterC32C2×#440
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
3. C2×#63843C2semidirect
5. #10591446C2direct (N × H)
6. C2×#63575C2semidirect
7. C2×#63566C2semidirect
8. C2×#63555C2semidirect
19. C2×C3×#214C4semidirect
27. #63843C22semidirect
29. #63575C22semidirect
30. #63566C22semidirect
31. #63555C22semidirect
64. C2×C3×Dic6C2×C4semidirect
71. C3×#214C2×C4semidirect
75. C2×C3×C3⋊C8C2×C4semidirect
105. C2×#214Dic3semidirect
155. C3×Dic6C22×C4semidirect
157. C3×C3⋊C8C22×C4semidirect
209. C2×Dic6C2×Dic3semidirect
221. #214C2×Dic3semidirect
241. C2×C3⋊C8C2×Dic3semidirect
351. Dic6C22×Dic3semidirect
355. C3⋊C8C22×Dic3semidirect
357. C2×C32#440semidirect
438. C32C2×#440semidirect
474. C2×C3#4757semidirect
475. C2×C3#5164semidirect
499. C3C2×#4757semidirect
500. C3C2×#5164semidirect
502. C2#10591446direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D4×C3⋊Dic32
C22×C3×#2142
C2×#638432
C2×C3×#8322
#105914462
C2×#635752
C2×#635662
C2×#635552
C2×#51643
C2×#47573