Finite Group Databasebeta

← C2×#10590766 #11860084

Subgroups — C2×#10590766 #11860084

Order 1152.

1153 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#204C211yesmaximal, characteristic
2C2×Dic3×D12C211yesmaximal, characteristic
3C2×Dic3×Dic6C211yesmaximal, characteristic, complemented
4C2×#63645C211yesmaximal, characteristic, complemented
5C2×C3×#815C211yesmaximal, characteristic, complemented
6C2×#63566C211yesmaximal, characteristic, complemented
7C2×#63563C211yesmaximal, characteristic
8#10590766C218yesmaximal, direct product factor
9C2×#5164—31nomaximal
10C2×#4710—31nomaximal
11C22×C3×D12C2211yescharacteristic
12C22×C3×Dic6C2211yescharacteristic
13C22×D3×Dic3—21no—
14C22×C32×C8C2211yescharacteristic
15C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
16C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
17C2×C3×C4×Dic3C2211yescharacteristic
18C22×C3×C3⋊C8C2211yescharacteristic
19C2×C3×#204C418yescomplemented
20C2×C3×#204C2214yes—
21C2×Dic3⋊Dic3—21no—
22C2×(C2×D3)⋊Dic3—21no—
23C2×Dic32—21no—
24Dic3×D12—22no—
25Dic3×D12C2214yes—
26Dic3×Dic6—22no—
27Dic3×Dic6C2214yescomplemented
28#63645C2214yescomplemented
29C3×#815C2214yescomplemented
30#63566C2214yescomplemented
31#63563C2214yes—
32C22×C3×SD16—31no—
33C2×Q8×Dic3—31no—
34C2×D4×Dic3—31no—
35C22×#204D311yescharacteristic
36C2×C4×D12—31no—
37C2×C4×Dic6—31no—
38C2×C3×#97—31no—
39C2×#835—31no—
40C2×#832—31no—
41#5164—38no—
42C2×#821—31no—
43C2×#818—31no—
44C2×#818—31no—
45C2×#818—61no—
46C2×#816—31no—
47C2×#815D311yescharacteristic, complemented
48#4710—38no—
49C23×C3×D3—21no—
50C22×C32×C4C2311yescharacteristic
51C22×C3⋊Dic3—21no—
52C22×C3⋊Dic3—21no—
53C22×C3×Dic3—21no—
54C22×C3×Dic3D411yescharacteristic
55C22×C3×Dic3D411yescharacteristic
56C2×C3×D12—21no—
57C2×C3×D12—22no—
58C2×C3×D12C2×C414yes—
59C2×C3×D12C2312yes—
60C2×C3×Dic6—21no—
61C2×C3×Dic6—22no—
62C2×C3×Dic6C2×C414yescomplemented
63C2×C3×Dic6C2312yes—
64C2×D3×Dic3—24no—
65C2×D3×Dic3—44no—
66C2×C32×C8C2×C414yescomplemented
67C2×C32×C8C2312yes—
68C4⋊(C3⋊Dic3)—21no—
69C4⋊(C3⋊Dic3)—21no—
70C4⋊(C3⋊Dic3)C2312yes—
71C4⋊(C3⋊Dic3)C2312yes—
72C3×C4×Dic3D412yes—
73C3×C4×Dic3C2312yes—
74C2×C3×C3⋊C8—22no—
75C2×C3×C3⋊C8C2312yes—
76C3×#204C2×C4116yescomplemented
77Dic3⋊Dic3—24no—
78(C2×D3)⋊Dic3—24no—
79Dic32—24no—
80C2×#440—91noSylow
81C22×C3×Q8—31no—
82C22×C3×D4—31no—
83C23×Dic3—61no—
84C22×D12C2×D311yescharacteristic
85C22×C4×D3—61no—
86C22×Dic6C2×D311yescharacteristic
87C2×C3×SD16—38no—
88C2×C3×SD16—34no—
89C22×C3×C8—21no—
90C22×C3×C8—31no—
91C22×C3×C8C2×D311yescharacteristic
92C22×C3×C8C2×D311yescharacteristic
93C2×C3×C42—31no—
94C2×#217—61no—
95Q8×Dic3—34no—
96Q8×Dic3—62no—
97D4×Dic3—34no—
98D4×Dic3—62no—
99C2×(C2×D3)⋊C4—61no—
100C2×C4⋊Dic3—31no—
101C2×C4⋊Dic3—31no—
102C2×C4⋊Dic3—31no—
103C2×C4⋊Dic3—31no—
104C2×C4⋊Dic3—61no—
105C2×C4⋊Dic3—61no—
106C2×C4⋊Dic3—61no—
107C2×Dic3⋊C4—61no—
108C2×C4×Dic3—61no—
109C2×C4×Dic3—61no—
110C2×C4×Dic3C2×D311yescharacteristic
111C22×C3⋊C8C2×D311yescharacteristic
112C2×#204Dic318yescomplemented
113C2×#204C2×D314yes—
114C4×D12—34no—
115C4×D12—62no—
116C4×Dic6—34no—
117C4×Dic6—62no—
118C3×#97—34no—
119#835—34no—
120#832—34no—
121#821—34no—
122#818—34no—
123#818—34no—
124#818—64no—
125#816—34no—
126#815C2×D314yescomplemented
127C23×C32C2×D411yescharacteristic
128C22×C3×D3—24no—
129C22×C3×D3—22no—
130C22×C3×D3—42no—
131C22×C3×D3—42no—
132C2×C32×C4C22×C412yes—
133C2×C32×C4C2×D411yescharacteristic
134C2×C32×C4#4112yes—
135C2×C32×C4C2411yescharacteristic
136C2×C3⋊Dic3—22no—
137C2×C3⋊Dic3—22no—
138C2×C3⋊Dic3—42no—
139C2×C3⋊Dic3—42no—
140C2×C3×Dic3—24no—
141C2×C3×Dic3—22no—
142C2×C3×Dic3—22no—
143C2×C3×Dic3—22no—
144C2×C3×Dic3C2×D412yes—
145C2×C3×Dic3C2×D412yes—
146C3×D12—24no—
147C3×D12—22no—
148C3×D12C22×C414yes—
149C3×Dic6—24no—
150C3×Dic6—22no—
151C3×Dic6C22×C414yescomplemented
152D3×Dic3—48no—
153C32×C8C22×C414yescomplemented
154C3×C3⋊C8—22no—
155C22×SD16—31no—
156C2×C4×Q8—91no—
157C2×C4×D4—91no—
158#440—98no—
159C2×#107—91no—
160C2×#103—91no—
161C2×#102—91no—
162C2×#97—31no—
163C24×C3—61no—
164C23×D3—21no—
165C2×C3×Q8—34no—
166C2×C3×Q8—32no—
167C2×C3×Q8—61no—
168C2×C3×Q8—62no—
169C2×C3×D4—34no—
170C2×C3×D4—32no—
171C2×C3×D4—61no—
172C2×C3×D4—62no—
173C22×C3×C4—21no—
174C22×C3×C4—31no—
175C22×C3×C4—31no—
176C22×C3×C4—61no—
177C22×C3×C4C22×D311yescharacteristic
178C22×C3×C4C22×D311yescharacteristic
179C22×Dic3—21no—
180C22×Dic3—61no—
181C22×Dic3—61no—
182C22×Dic3—61no—
183C22×Dic3—61no—
184C22×Dic3—64no—
185C22×Dic3—121no—
186C22×Dic3—121no—
187C22×Dic3—124no—
188C22×Dic3D1211yescharacteristic
189C22×Dic3D1211yescharacteristic
190C2×D12—21no—
191C2×D12—22no—
192C2×D12C2×Dic314yes—
193C2×D12C22×D312yes—
194C2×C4×D3—64no—
195C2×C4×D3—124no—
196C2×Dic6—21no—
197C2×Dic6—22no—
198C2×Dic6C2×Dic314yescomplemented
199C2×Dic6C22×D312yes—
200C3×SD16—316no—
201C2×C3×C8—24no—
202C2×C3×C8—22no—
203C2×C3×C8—32no—
204C2×C3×C8—62no—
205C2×C3×C8C4×D314yescomplemented
206C2×C3×C8C2×Dic314yescomplemented
207C2×C3×C8C22×D312yes—
208C2×C3×C8C22×D312yes—
209C3×C42—32no—
210C3×C42—32no—
211#217—64no—
212(C2×D3)⋊C4—64no—
213C4⋊Dic3—32no—
214C4⋊Dic3—32no—
215C4⋊Dic3—32no—
216C4⋊Dic3—32no—
217C4⋊Dic3—62no—
218C4⋊Dic3—62no—
219C4⋊Dic3—61no—
220C4⋊Dic3—61no—
221C4⋊Dic3—61no—
222C4⋊Dic3—61no—
223C4⋊Dic3—64no—
224C4⋊Dic3—121no—
225C4⋊Dic3—121no—
226Dic3⋊C4—64no—
227C4×Dic3—64no—
228C4×Dic3—64no—
229C4×Dic3D1212yes—
230C4×Dic3C22×D312yes—
231C2×C3⋊C8—22no—
232C2×C3⋊C8C22×D312yes—
233#204C2×Dic3116yescomplemented
234C22×C32C4×D412yes—
235C22×C32AGL(1,ℤ/8)12yes—
236C22×C32#13712yes—
237C22×C32C22×D411yescharacteristic
238C2×C3×D3—24no—
239C2×C3×D3—42no—
240C2×C3×D3—42no—
241C2×C3×D3—48no—
242C32×C4C4×D412yes—
243C32×C4C23×C411yescharacteristic
244C32×C4C2×#4111yescharacteristic
245C3⋊Dic3—42no—
246C3⋊Dic3—42no—
247C3×Dic3—24no—
248C3×Dic3—22no—
249C3×Dic3—22no—
250C22×Q8—31no—
251C22×D4—31no—
252C23×C4—181no—
253C2×SD16—38no—
254C2×SD16—34no—
255C22×C8—31no—
256C22×C8D3211yescharacteristic
257C4×Q8—94no—
258C4×Q8—182no—
259C4×D4—94no—
260C4×D4—182no—
261C2×C4⋊C4—91no—
262C2×C4⋊C4—91no—
263C2×C4⋊C4—181no—
264C2×C22⋊C4—181no—
265C2×C42—31no—
266C2×C42—181no—
267#107—94no—
268#103—94no—
269#102—94no—
270#97—34no—
271C23×C3—21no—
272C23×C3—64no—
273C23×C3—62no—
274C23×C3—122no—
275C23×C3—122no—
276C23×C3C2×D1211yescharacteristic
277C23×C3D3×D411yescharacteristic
278C22×D3—24no—
279C22×D3—22no—
280C22×D3—42no—
281C22×D3—42no—
282C3×Q8—34no—
283C3×Q8—64no—
284C3×Q8—62no—
285C3×D4—34no—
286C3×D4—64no—
287C3×D4—62no—
288C2×C3×C4—21no—
289C2×C3×C4—22no—
290C2×C3×C4—21no—
291C2×C3×C4—22no—
292C2×C3×C4—32no—
293C2×C3×C4—32no—
294C2×C3×C4—64no—
295C2×C3×C4—62no—
296C2×C3×C4—62no—
297C2×C3×C4—62no—
298C2×C3×C4C2×C4×D312yes—
299C2×C3×C4C2×D1211yescharacteristic
300C2×C3×C4#23512yes—
301C2×C3×C4D3×D411yescharacteristic
302C2×C3×C4#23712yes—
303C2×C3×C4C22×Dic312yes—
304C2×C3×C4C23×D311yescharacteristic
305C2×C3×C4C23×D311yescharacteristic
306C2×Dic3—22no—
307C2×Dic3—22no—
308C2×Dic3—24no—
309C2×Dic3—22no—
310C2×Dic3—62no—
311C2×Dic3—62no—
312C2×Dic3—62no—
313C2×Dic3—62no—
314C2×Dic3—122no—
315C2×Dic3—122no—
316C2×Dic3—128no—
317C2×Dic3—122no—
318C2×Dic3—122no—
319C2×Dic3—122no—
320C2×Dic3—122no—
321C2×Dic3—242no—
322C2×Dic3—242no—
323C2×Dic3C2×D1212yes—
324C2×Dic3C2×D1212yes—
325D12—24no—
326D12—22no—
327D12C22×Dic314yes—
328C4×D3—128no—
329Dic6—24no—
330Dic6—22no—
331Dic6C22×Dic314yescomplemented
332C3×C8—24no—
333C3×C8—62no—
334C3×C8C2×C4×D314yescomplemented
335C3×C8C22×Dic314yescomplemented
336C3⋊C8—22no—
337C2×C32#44014yescomplemented
338C2×C32C2×C4×D411yescharacteristic
339C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
340C2×C32C2×#13711yescharacteristic
341C3×D3—44no—
342C24—61no—
343C2×Q8—32no—
344C2×Q8—34no—
345C2×Q8—62no—
346C2×Q8—61no—
347C2×D4—32no—
348C2×D4—34no—
349C2×D4—62no—
350C2×D4—61no—
351C22×C4—31no—
352C22×C4—31no—
353C22×C4—61no—
354C22×C4—184no—
355C22×C4—181no—
356C22×C4—181no—
357C22×C4—364no—
358C22×C4C2×D3211yescharacteristic
359SD16—316no—
360C2×C8—32no—
361C2×C8—62no—
362C2×C8D3×Dic314yescomplemented
363C2×C8C2×D3212yes—
364C4⋊C4—92no—
365C4⋊C4—92no—
366C4⋊C4—184no—
367C4⋊C4—181no—
368C4⋊C4—181no—
369C22⋊C4—184no—
370C42—32no—
371C42—32no—
372C42—184no—
373C22×C3—21no—
374C22×C3—22no—
375C22×C3—22no—
376C22×C3—22no—
377C22×C3—64no—
378C22×C3—128no—
379C22×C3—122no—
380C22×C3—122no—
381C22×C3C4×D1212yes—
382C22×C3#90812yes—
383C22×C3#90912yes—
384C22×C3#91412yes—
385C22×C3#91512yes—
386C22×C3D4×Dic312yes—
387C22×C3C22×D1211yescharacteristic
388C22×C3C2×D3×D411yescharacteristic
389C2×D3—24no—
390C2×D3—48no—
391C2×D3—42no—
392C2×D3—42no—
393C3×C4—21no—
394C3×C4—21no—
395C3×C4—22no—
396C3×C4—64no—
397C3×C4—62no—
398C3×C4—62no—
399C3×C4C4×D1212yes—
400C3×C4D4×Dic312yes—
401C3×C4C22×C4×D311yescharacteristic
402C3×C4C2×#23511yescharacteristic
403C3×C4C2×#23711yescharacteristic
404C3×C4C23×Dic311yescharacteristic
405Dic3—22no—
406Dic3—22no—
407Dic3—24no—
408Dic3—122no—
409Dic3—122no—
410Dic3—122no—
411Dic3—122no—
412Dic3—242no—
413Dic3—242no—
414C32C2×#44011yescharacteristic, complemented, Sylow
415C23—62no—
416C23—64no—
417C23—122no—
418C23—122no—
419C23D3×D1211yescharacteristic
420Q8—34no—
421Q8—62no—
422Q8—64no—
423D4—34no—
424D4—62no—
425D4—64no—
426C2×C4—32no—
427C2×C4—32no—
428C2×C4—62no—
429C2×C4—62no—
430C2×C4—62no—
431C2×C4—64no—
432C2×C4—182no—
433C2×C4—182no—
434C2×C4—368no—
435C2×C4—362no—
436C2×C4—362no—
437C2×C4#379512yes—
438C2×C4D3×D1211yescharacteristic
439C2×C4C2×D3×Dic312yes—
440C2×C4C22×D3211yescharacteristic
441C8—62no—
442C8C2×D3×Dic314yescomplemented
443C2×C3—24no—
444C2×C3—21no—
445C2×C3—21no—
446C2×C3—21no—
447C2×C3—124no—
448C2×C3#471014yescomplemented
449C2×C3#516414yescomplemented
450C2×C3C2×C4×D1211yescharacteristic
451C2×C3C2×#90811yescharacteristic
452C2×C3C2×#90911yescharacteristic
453C2×C3C2×#91411yescharacteristic
454C2×C3C2×#91511yescharacteristic
455C2×C3C2×D4×Dic311yescharacteristic
456D3—44no—
457C22—64no—
458C22—128no—
459C22—122no—
460C22—122no—
461C22#6379412yes—
462C22#6380012yes—
463C22Dic3×D1212yes—
464C22C2×D3×D1211yescharacteristic
465C4—64no—
466C4—62no—
467C4—62no—
468C4—362no—
469C4—362no—
470C4Dic3×D1212yes—
471C4C2×#379511yescharacteristic
472C4C22×D3×Dic311yescharacteristic
473C3—21no—
474C3C2×#471011yescharacteristic, complemented
475C3C2×#516411yescharacteristic, complemented
476C2—124no—
477C2#1059076614yesdirect product factor
478C2C2×#6379411yescharacteristic
479C2C2×#6380011yescharacteristic
480C2C2×Dic3×D1211yescharacteristic
subgroupG/H
centerC23D3×D12
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
cosocleC2×C32×C4C24
hypercenterC22×C8D32
hypocenterC32C2×#440
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
3. C2×Dic3×Dic6C2semidirect
4. C2×#63645C2semidirect
5. C2×C3×#815C2semidirect
6. C2×#63566C2semidirect
8. #10590766C2direct (N × H)
19. C2×C3×#204C4semidirect
27. Dic3×Dic6C22semidirect
28. #63645C22semidirect
29. C3×#815C22semidirect
30. #63566C22semidirect
47. C2×#815D3semidirect
62. C2×C3×Dic6C2×C4semidirect
66. C2×C32×C8C2×C4semidirect
76. C3×#204C2×C4semidirect
112. C2×#204Dic3semidirect
126. #815C2×D3semidirect
151. C3×Dic6C22×C4semidirect
153. C32×C8C22×C4semidirect
198. C2×Dic6C2×Dic3semidirect
205. C2×C3×C8C4×D3semidirect
206. C2×C3×C8C2×Dic3semidirect
233. #204C2×Dic3semidirect
331. Dic6C22×Dic3semidirect
334. C3×C8C2×C4×D3semidirect
335. C3×C8C22×Dic3semidirect
337. C2×C32#440semidirect
362. C2×C8D3×Dic3semidirect
414. C32C2×#440semidirect
442. C8C2×D3×Dic3semidirect
448. C2×C3#4710semidirect
449. C2×C3#5164semidirect
474. C3C2×#4710semidirect
475. C3C2×#5164semidirect
477. C2#10590766direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#2042
C2×Dic3×D122
C2×Dic3×Dic62
C2×#636452
C2×C3×#8152
C2×#635662
C2×#635632
#105907662
C2×#51643
C2×#47103