Finite Group Databasebeta

← C2×#10591440 #11860067

Subgroups — C2×#10591440 #11860067

Order 1152.

1189 conjugacy classes of subgroups.

The subgroup lattice has 493 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D4×Dic3C211yesmaximal, characteristic
2C22×C3×#214C211yesmaximal, characteristic
3C2×Dic3×Dic6C211yesmaximal, characteristic, complemented
4C2×#63659C211yesmaximal, characteristic
5#10591440C218yesmaximal, direct product factor
6C2×#63575C211yesmaximal, characteristic, complemented
7C2×#63565C211yesmaximal, characteristic, complemented
8C2×#63554C211yesmaximal, characteristic, complemented
9C2×#5164—31nomaximal
10C2×#5018—31nomaximal
11C22×C32×D4C2211yescharacteristic
12C23×C3×Dic3—21no—
13C22×C3×Dic6C2211yescharacteristic
14C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
15C22×C3⋊(C3⋊C8)C2211yescharacteristic
16C2×C3×#217—21no—
17C3×D4×Dic3—22no—
18C3×D4×Dic3C2214yes—
19C2×C3×#214C418yescomplemented
20C2×C3×#214C2214yes—
21C2×C3×C4⋊Dic3C2211yescharacteristic
22C2×C3×C4×Dic3C2211yescharacteristic
23C22×C3×C3⋊C8C2211yescharacteristic
24C2×Dic3⋊Dic3—21no—
25C2×Dic32—21no—
26Dic3×Dic6—22no—
27Dic3×Dic6C2214yescomplemented
28#63659C2214yes—
29#63575C2214yescomplemented
30#63565C2214yescomplemented
31#63554C2214yescomplemented
32C22×C3×SD16—31no—
33C2×C3×C4×D4—31no—
34C2×Q8×Dic3—31no—
35C2×D4×Dic3D311yescharacteristic
36C22×#214D311yescharacteristic
37C2×C4×Dic6—31no—
38C2×#835—31no—
39C2×#832—31no—
40C2×#832—31no—
41C2×#832—61no—
42#5164—38no—
43C2×#818—31no—
44C2×#815—31no—
45#5018—38no—
46C2×#810—31no—
47C2×#807—31no—
48C2×#803—31no—
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—21no—
57C22×C3×Dic3—21no—
58C22×C3×Dic3—24no—
59C22×C3×Dic3—44no—
60C22×C3×Dic3D411yescharacteristic
61C22×C3×Dic3D411yescharacteristic
62C2×C3×Dic6—21no—
63C2×C3×Dic6—22no—
64C2×C3×Dic6C2×C414yescomplemented
65C2×C3×Dic6C2312yes—
66C4⋊(C3⋊Dic3)—21no—
67C4⋊(C3⋊Dic3)C2312yes—
68C2×C3⋊(C3⋊C8)—22no—
69C2×C3⋊(C3⋊C8)C2312yes—
70C3×#217—24no—
71C3×#214C2×C4116yescomplemented
72C3×C4⋊Dic3—21no—
73C3×C4⋊Dic3C2312yes—
74C3×C4×Dic3D412yes—
75C3×C4×Dic3C2312yes—
76C2×C3×C3⋊C8C2×C414yescomplemented
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×C3×C4—61no—
86C23×Dic3—21no—
87C22×Dic6C2×D311yescharacteristic
88C2×C3×SD16—38no—
89C2×C3×SD16—34no—
90C22×C3×C8—31no—
91C3×C4×D4—34no—
92C3×C4×D4—62no—
93C2×C3×C4⋊C4—31no—
94C2×C3×C22⋊C4—61no—
95C2×C3×C42—31no—
96C2×#217—21no—
97Q8×Dic3—34no—
98Q8×Dic3—62no—
99D4×Dic3—22no—
100D4×Dic3C2×D314yes—
101C2×#214Dic318yescomplemented
102C2×#214C2×D314yes—
103C2×C4⋊Dic3—31no—
104C2×C4⋊Dic3—31no—
105C2×C4⋊Dic3—61no—
106C2×C4⋊Dic3—61no—
107C2×C4⋊Dic3C2×D311yescharacteristic
108C2×Dic3⋊C4—61no—
109C2×C4×Dic3—61no—
110C2×C4×Dic3—61no—
111C2×C4×Dic3C2×D311yescharacteristic
112C22×C3⋊C8—31no—
113C22×C3⋊C8—31no—
114C22×C3⋊C8—61no—
115C22×C3⋊C8C2×D311yescharacteristic
116C4×Dic6—34no—
117C4×Dic6—62no—
118#835—34no—
119#832—34no—
120#832—34no—
121#832—64no—
122#818—34no—
123#815—34no—
124#810—34no—
125#807—34no—
126#803—34no—
127C23×C32—24no—
128C23×C32—22no—
129C23×C32—42no—
130C23×C32—42no—
131C23×C32C2×D411yescharacteristic
132C32×D4—24no—
133C32×D4—22no—
134C32×D4C22×C414yes—
135C2×C32×C4C22×C412yes—
136C2×C32×C4C2×D411yescharacteristic
137C2×C32×C4#4112yes—
138C2×C32×C4C2411yescharacteristic
139C2×C3⋊Dic3—22no—
140C2×C3⋊Dic3—42no—
141C2×C3×Dic3—24no—
142C2×C3×Dic3—22no—
143C2×C3×Dic3—22no—
144C2×C3×Dic3—22no—
145C2×C3×Dic3—22no—
146C2×C3×Dic3—48no—
147C2×C3×Dic3—42no—
148C2×C3×Dic3C2×D412yes—
149C2×C3×Dic3C2×D412yes—
150C3×Dic6—24no—
151C3×Dic6—22no—
152C3×Dic6C22×C414yescomplemented
153C3⋊(C3⋊C8)—22no—
154C3×C3⋊C8C22×C414yescomplemented
155C22×SD16—31no—
156C2×C4×Q8—91no—
157C2×C4×D4—31no—
158#440—98no—
159C2×#107—91no—
160C2×#103—91no—
161C2×#102—91no—
162C2×#97—91no—
163C24×C3—21no—
164C24×C3—21no—
165C24×C3—41no—
166C2×C3×Q8—34no—
167C2×C3×Q8—32no—
168C2×C3×Q8—62no—
169C2×C3×Q8—61no—
170C2×C3×D4—22no—
171C2×C3×D4—21no—
172C2×C3×D4—22no—
173C2×C3×D4—21no—
174C2×C3×D4—24no—
175C2×C3×D4—22no—
176C2×C3×D4—42no—
177C2×C3×D4—41no—
178C2×C3×D4C4×D314yes—
179C2×C3×D4C2×Dic314yes—
180C2×C3×D4C22×D312yes—
181C2×C3×D4C22×D312yes—
182C22×C3×C4—21no—
183C22×C3×C4—31no—
184C22×C3×C4—31no—
185C22×C3×C4—64no—
186C22×C3×C4—61no—
187C22×C3×C4—61no—
188C22×C3×C4—124no—
189C22×C3×C4C22×D311yescharacteristic
190C22×C3×C4C22×D311yescharacteristic
191C22×Dic3—21no—
192C22×Dic3—21no—
193C22×Dic3—24no—
194C22×Dic3—44no—
195C22×Dic3—61no—
196C22×Dic3—61no—
197C22×Dic3—121no—
198C22×Dic3#6711yescharacteristic
199C22×Dic3#6711yescharacteristic
200C2×Dic6—21no—
201C2×Dic6—22no—
202C2×Dic6C2×Dic314yescomplemented
203C2×Dic6C22×D312yes—
204C3×SD16—316no—
205C2×C3×C8—34no—
206C2×C3×C8—32no—
207C3×C4⋊C4—32no—
208C3×C4⋊C4—61no—
209C3×C22⋊C4—64no—
210C3×C42—32no—
211C3×C42—32no—
212#217—24no—
213#214C2×Dic3116yescomplemented
214C4⋊Dic3—21no—
215C4⋊Dic3—32no—
216C4⋊Dic3—32no—
217C4⋊Dic3—62no—
218C4⋊Dic3—61no—
219C4⋊Dic3—61no—
220C4⋊Dic3—64no—
221C4⋊Dic3—121no—
222C4⋊Dic3C22×D312yes—
223Dic3⋊C4—64no—
224C4×Dic3—64no—
225C4×Dic3—64no—
226C4×Dic3#6712yes—
227C4×Dic3C22×D312yes—
228C2×C3⋊C8—32no—
229C2×C3⋊C8—32no—
230C2×C3⋊C8—62no—
231C2×C3⋊C8—62no—
232C2×C3⋊C8—62no—
233C2×C3⋊C8—122no—
234C2×C3⋊C8C2×Dic314yescomplemented
235C2×C3⋊C8C22×D312yes—
236C22×C32—24no—
237C22×C32—42no—
238C22×C32—42no—
239C22×C32—48no—
240C22×C32C4×D412yes—
241C22×C32AGL(1,ℤ/8)12yes—
242C22×C32#13712yes—
243C22×C32C22×D411yescharacteristic
244C32×C4C4×D412yes—
245C32×C4C23×C411yescharacteristic
246C32×C4C2×#4111yescharacteristic
247C3⋊Dic3—42no—
248C3×Dic3—24no—
249C3×Dic3—22no—
250C3×Dic3—22no—
251C3×Dic3—42no—
252C22×Q8—31no—
253C22×D4D3211yescharacteristic
254C23×C4—61no—
255C2×SD16—38no—
256C2×SD16—34no—
257C22×C8—31no—
258C22×C8—91no—
259C4×Q8—94no—
260C4×Q8—182no—
261C4×D4—34no—
262C4×D4—62no—
263C2×C4⋊C4—31no—
264C2×C4⋊C4—91no—
265C2×C4⋊C4—181no—
266C2×C22⋊C4—61no—
267C2×C42—31no—
268C2×C42—181no—
269#107—94no—
270#103—94no—
271#102—94no—
272#97—94no—
273C23×C3—24no—
274C23×C3—24no—
275C23×C3—22no—
276C23×C3—22no—
277C23×C3—21no—
278C23×C3—42no—
279C23×C3—44no—
280C23×C3—42no—
281C23×C3—42no—
282C23×C3—42no—
283C23×C3—42no—
284C23×C3—82no—
285C23×C3—82no—
286C23×C3D3×D411yescharacteristic
287C23×C3C2×#6711yescharacteristic
288C3×Q8—34no—
289C3×Q8—64no—
290C3×Q8—62no—
291C3×D4—24no—
292C3×D4—24no—
293C3×D4—22no—
294C3×D4—22no—
295C3×D4—24no—
296C3×D4—42no—
297C3×D4—44no—
298C3×D4C2×C4×D314yes—
299C3×D4C22×Dic314yes—
300C2×C3×C4—21no—
301C2×C3×C4—22no—
302C2×C3×C4—22no—
303C2×C3×C4—21no—
304C2×C3×C4—32no—
305C2×C3×C4—32no—
306C2×C3×C4—62no—
307C2×C3×C4—62no—
308C2×C3×C4—64no—
309C2×C3×C4—62no—
310C2×C3×C4—62no—
311C2×C3×C4—128no—
312C2×C3×C4—122no—
313C2×C3×C4C2×C4×D312yes—
314C2×C3×C4#23512yes—
315C2×C3×C4D3×D411yescharacteristic
316C2×C3×C4#23712yes—
317C2×C3×C4C22×Dic312yes—
318C2×C3×C4C2×#6711yescharacteristic
319C2×C3×C4C23×D311yescharacteristic
320C2×C3×C4C23×D311yescharacteristic
321C2×Dic3—22no—
322C2×Dic3—24no—
323C2×Dic3—22no—
324C2×Dic3—22no—
325C2×Dic3—22no—
326C2×Dic3—48no—
327C2×Dic3—42no—
328C2×Dic3—62no—
329C2×Dic3—62no—
330C2×Dic3—122no—
331C2×Dic3—122no—
332C2×Dic3—122no—
333C2×Dic3—242no—
334C2×Dic3C2×#6712yes—
335C2×Dic3C2×#6712yes—
336Dic6—24no—
337Dic6—22no—
338Dic6C22×Dic314yescomplemented
339C3×C8—34no—
340C3⋊C8—62no—
341C3⋊C8—62no—
342C3⋊C8—122no—
343C3⋊C8C22×Dic314yescomplemented
344C2×C32—44no—
345C2×C32#44014yescomplemented
346C2×C32C2×C4×D411yescharacteristic
347C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
348C2×C32C2×#13711yescharacteristic
349C24—21no—
350C2×Q8—32no—
351C2×Q8—34no—
352C2×Q8—62no—
353C2×Q8—61no—
354C2×D4—22no—
355C2×D4—21no—
356C2×D4D3×Dic314yes—
357C2×D4C2×D3212yes—
358C22×C4—31no—
359C22×C4—31no—
360C22×C4—64no—
361C22×C4—61no—
362C22×C4—61no—
363C22×C4—124no—
364C22×C4—181no—
365C22×C4C2×D3211yescharacteristic
366SD16—316no—
367C2×C8—32no—
368C2×C8—34no—
369C2×C8—92no—
370C2×C8—182no—
371C4⋊C4—32no—
372C4⋊C4—61no—
373C4⋊C4—92no—
374C4⋊C4—184no—
375C4⋊C4—181no—
376C22⋊C4—64no—
377C42—32no—
378C42—32no—
379C42—184no—
380C22×C3—24no—
381C22×C3—24no—
382C22×C3—21no—
383C22×C3—22no—
384C22×C3—22no—
385C22×C3—22no—
386C22×C3—44no—
387C22×C3—48no—
388C22×C3—42no—
389C22×C3—42no—
390C22×C3—48no—
391C22×C3—42no—
392C22×C3—42no—
393C22×C3—82no—
394C22×C3—82no—
395C22×C3—88no—
396C22×C3#91412yes—
397C22×C3#91512yes—
398C22×C3C4×#6712yes—
399C22×C3#93212yes—
400C22×C3D4×Dic312yes—
401C22×C3#95112yes—
402C22×C3C2×D3×D411yescharacteristic
403C22×C3C22×#6711yescharacteristic
404C3×C4—21no—
405C3×C4—21no—
406C3×C4—22no—
407C3×C4—62no—
408C3×C4—62no—
409C3×C4—64no—
410C3×C4—122no—
411C3×C4C4×#6712yes—
412C3×C4D4×Dic312yes—
413C3×C4C22×C4×D311yescharacteristic
414C3×C4C2×#23511yescharacteristic
415C3×C4C2×#23711yescharacteristic
416C3×C4C23×Dic311yescharacteristic
417Dic3—22no—
418Dic3—24no—
419Dic3—22no—
420Dic3—42no—
421Dic3—122no—
422Dic3—122no—
423Dic3—242no—
424C32C2×#44011yescharacteristic, complemented, Sylow
425C23—22no—
426C23—24no—
427C23—42no—
428C23—42no—
429C23D3×#6711yescharacteristic
430Q8—34no—
431Q8—62no—
432Q8—64no—
433D4—22no—
434D4—24no—
435D4C2×D3×Dic314yes—
436C2×C4—32no—
437C2×C4—32no—
438C2×C4—62no—
439C2×C4—62no—
440C2×C4—62no—
441C2×C4—64no—
442C2×C4—62no—
443C2×C4—128no—
444C2×C4—122no—
445C2×C4—182no—
446C2×C4—362no—
447C2×C4C2×D3×Dic312yes—
448C2×C4#380412yes—
449C2×C4D3×#6711yescharacteristic
450C2×C4C22×D3211yescharacteristic
451C8—34no—
452C8—182no—
453C2×C3—21no—
454C2×C3—21no—
455C2×C3—21no—
456C2×C3—24no—
457C2×C3—44no—
458C2×C3—44no—
459C2×C3—84no—
460C2×C3#501814yescomplemented
461C2×C3#516414yescomplemented
462C2×C3C2×#91411yescharacteristic
463C2×C3C2×#91511yescharacteristic
464C2×C3C2×C4×#6711yescharacteristic
465C2×C3C2×#93211yescharacteristic
466C2×C3C2×D4×Dic311yescharacteristic
467C2×C3C2×#95111yescharacteristic
468C22—24no—
469C22—42no—
470C22—42no—
471C22—48no—
472C22#6392912yes—
473C22#6393412yes—
474C22Dic3×#6712yes—
475C22C2×D3×#6711yescharacteristic
476C4—62no—
477C4—62no—
478C4—64no—
479C4—122no—
480C4—362no—
481C4Dic3×#6712yes—
482C4C22×D3×Dic311yescharacteristic
483C4C2×#380411yescharacteristic
484C3—21no—
485C3C2×#501811yescharacteristic, complemented
486C3C2×#516411yescharacteristic, complemented
487C2—44no—
488C2#1059144014yesdirect product factor
489C2C2×#6392911yescharacteristic
490C2C2×#6393411yescharacteristic
491C2C2×Dic3×#6711yescharacteristic
subgroupG/H
centerC23D3×#67
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×Dic3×Dic6C2semidirect
5. #10591440C2direct (N × H)
6. C2×#63575C2semidirect
7. C2×#63565C2semidirect
8. C2×#63554C2semidirect
19. C2×C3×#214C4semidirect
27. Dic3×Dic6C22semidirect
29. #63575C22semidirect
30. #63565C22semidirect
31. #63554C22semidirect
64. C2×C3×Dic6C2×C4semidirect
71. C3×#214C2×C4semidirect
76. C2×C3×C3⋊C8C2×C4semidirect
101. C2×#214Dic3semidirect
152. C3×Dic6C22×C4semidirect
154. C3×C3⋊C8C22×C4semidirect
202. C2×Dic6C2×Dic3semidirect
213. #214C2×Dic3semidirect
234. C2×C3⋊C8C2×Dic3semidirect
338. Dic6C22×Dic3semidirect
343. C3⋊C8C22×Dic3semidirect
345. C2×C32#440semidirect
424. C32C2×#440semidirect
460. C2×C3#5018semidirect
461. C2×C3#5164semidirect
485. C3C2×#5018semidirect
486. C3C2×#5164semidirect
488. C2#10591440direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×D4×Dic32
C22×C3×#2142
C2×Dic3×Dic62
C2×#636592
#105914402
C2×#635752
C2×#635652
C2×#635542
C2×#51643
C2×#50183