Finite Group Databasebeta

← C2×#10591540 #11860076

Subgroups — C2×#10591540 #11860076

Order 1152.

1237 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3755C211yesmaximal, characteristic
2C2×C3×Q8×Dic3C211yesmaximal, characteristic, complemented
3C2×#63894C211yesmaximal, characteristic
4C2×C3×#835C211yesmaximal, characteristic, complemented
5#10591540C218yesmaximal, direct product factor
6C2×#63576C211yesmaximal, characteristic, complemented
7C2×#63564C211yesmaximal, characteristic
8C2×#63554C211yesmaximal, characteristic, complemented
9C2×#5026—31nomaximal
10C2×#4817—31nomaximal
11C22×C32×Q8C2211yescharacteristic
12C22×C4⋊(C3⋊D3)C2211yescharacteristic
13C22×#624—21no—
14C2×#3755C418yescomplemented
15C2×#3755C2214yes—
16C22×C3⋊(C3⋊C8)C2211yescharacteristic
17C3×Q8×Dic3—22no—
18C3×Q8×Dic3C2214yescomplemented
19C2×C3×C4⋊Dic3—21no—
20C2×C3×C4⋊Dic3C2211yescharacteristic
21C2×C3×C4⋊Dic3C2211yescharacteristic
22C2×C3×C4×Dic3—21no—
23C2×C3×C4×Dic3C2211yescharacteristic
24C22×C3×C3⋊C8C2211yescharacteristic
25C2×#3722—21no—
26#63894—22no—
27#63894C2214yes—
28C3×#835C2214yescomplemented
29#63576C2214yescomplemented
30#63564C2214yes—
31#63554C2214yescomplemented
32C2×C3×C4×Q8—31no—
33C2×Q8×Dic3D311yescharacteristic, complemented
34C22×#215—31no—
35C22×#215—31no—
36C22×#215—61no—
37C2×#893—31no—
38C2×C4×D12—31no—
39C2×C3×#103—31no—
40C2×#835D311yescharacteristic, complemented
41C2×#821—31no—
42C2×#815—31no—
43#5026—38no—
44C2×#809—31no—
45C2×#807—31no—
46C2×#807—31no—
47C2×#803—31no—
48#4817—38no—
49C23×C3⋊D3—21no—
50C2×C32×Q8—21no—
51C2×C32×Q8—22no—
52C2×C32×Q8C2×C414yescomplemented
53C2×C32×Q8C2312yes—
54C22×C32×C4—21no—
55C22×C32×C4C2311yescharacteristic
56C2×C4⋊(C3⋊D3)—21no—
57C2×C4⋊(C3⋊D3)—22no—
58C2×C4⋊(C3⋊D3)C2×C414yes—
59C2×C4⋊(C3⋊D3)C2312yes—
60C22×C3×Dic3—21no—
61C22×C3×Dic3—21no—
62C22×C3×Dic3D411yescharacteristic
63C22×C3×Dic3D411yescharacteristic
64C2×#624—24no—
65C2×#624—44no—
66#3755C2×C4116yescomplemented
67C2×C3⋊(C3⋊C8)C2×C414yescomplemented
68C2×C3⋊(C3⋊C8)C2312yes—
69C3×C4⋊Dic3—21no—
70C3×C4⋊Dic3—21no—
71C3×C4⋊Dic3—24no—
72C3×C4⋊Dic3C2312yes—
73C3×C4⋊Dic3C2312yes—
74C3×C4×Dic3—24no—
75C3×C4×Dic3D412yes—
76C3×C4×Dic3C2312yes—
77C2×C3×C3⋊C8—22no—
78C2×C3×C3⋊C8C2312yes—
79#3722—24no—
80C2×#440—91noSylow
81C22×C3×Q8—21no—
82C22×C3×Q8C2×D311yescharacteristic
83C22×C3×Q8C2×D311yescharacteristic
84C22×D12—31no—
85C22×D12—31no—
86C22×D12—61no—
87C22×C4×D3—61no—
88C22×C4×D3—61no—
89C22×C3×C8—31no—
90C3×C4×Q8—34no—
91C3×C4×Q8—62no—
92C2×C3×C4⋊C4—31no—
93C2×C3×C4⋊C4—31no—
94C2×C3×C4⋊C4—61no—
95C2×C3×C42—31no—
96C2×C3×C42—61no—
97Q8×Dic3—22no—
98Q8×Dic3C2×D314yescomplemented
99C2×#215—38no—
100C2×#215—38no—
101C2×#215—34no—
102C2×#215—34no—
103C2×#215—68no—
104C2×#215—64no—
105C2×(C2×D3)⋊C4—61no—
106C2×(C2×D3)⋊C4—61no—
107C2×C4⋊Dic3—21no—
108C2×C4⋊Dic3C2×D311yescharacteristic
109C2×C4⋊Dic3C2×D311yescharacteristic
110C2×C4×Dic3—21no—
111C2×C4×Dic3C2×D311yescharacteristic
112C22×C3⋊C8—31no—
113C22×C3⋊C8—31no—
114C22×C3⋊C8—61no—
115C22×C3⋊C8C2×D311yescharacteristic
116#893—34no—
117#893—62no—
118C4×D12—34no—
119C4×D12—62no—
120C3×#103—34no—
121#835C2×D314yescomplemented
122#821—34no—
123#815—34no—
124#809—34no—
125#807—34no—
126#807—34no—
127#803—34no—
128C23×C32C2×D411yescharacteristic
129C22×C3⋊D3—24no—
130C22×C3⋊D3—22no—
131C22×C3⋊D3—42no—
132C22×C3⋊D3—42no—
133C32×Q8—24no—
134C32×Q8—22no—
135C32×Q8C22×C414yescomplemented
136C2×C32×C4—24no—
137C2×C32×C4—22no—
138C2×C32×C4C22×C412yes—
139C2×C32×C4C2×D411yescharacteristic
140C2×C32×C4#4112yes—
141C2×C32×C4C2411yescharacteristic
142C4⋊(C3⋊D3)—24no—
143C4⋊(C3⋊D3)—22no—
144C4⋊(C3⋊D3)C22×C414yes—
145C2×C3×Dic3—22no—
146C2×C3×Dic3—22no—
147C2×C3×Dic3—22no—
148C2×C3×Dic3—22no—
149C2×C3×Dic3—42no—
150C2×C3×Dic3—42no—
151C2×C3×Dic3C2×D412yes—
152C2×C3×Dic3C2×D412yes—
153#624—48no—
154C3⋊(C3⋊C8)C22×C414yescomplemented
155C3×C3⋊C8—22no—
156C22×SD16—91no—
157C2×C4×Q8—31no—
158C2×C4×D4—91no—
159#440—98no—
160C2×#107—91no—
161C2×#103—31no—
162C2×#102—91no—
163C2×#97—91no—
164C23×D3—61no—
165C23×D3—61no—
166C23×D3—121no—
167C2×C3×Q8—22no—
168C2×C3×Q8—21no—
169C2×C3×Q8—22no—
170C2×C3×Q8—21no—
171C2×C3×Q8—24no—
172C2×C3×Q8—22no—
173C2×C3×Q8—42no—
174C2×C3×Q8—41no—
175C2×C3×Q8C4×D314yescomplemented
176C2×C3×Q8C4×D314yescomplemented
177C2×C3×Q8C22×D312yes—
178C2×C3×Q8C22×D312yes—
179C22×C3×C4—21no—
180C22×C3×C4—21no—
181C22×C3×C4—21no—
182C22×C3×C4—31no—
183C22×C3×C4—31no—
184C22×C3×C4—41no—
185C22×C3×C4—61no—
186C22×C3×C4—61no—
187C22×C3×C4C22×D311yescharacteristic
188C22×C3×C4C22×D311yescharacteristic
189C22×Dic3—21no—
190C22×Dic3—21no—
191C22×Dic3#6711yescharacteristic
192C22×Dic3#6711yescharacteristic
193C2×D12—34no—
194C2×D12—34no—
195C2×D12—32no—
196C2×D12—32no—
197C2×D12—64no—
198C2×D12—62no—
199C2×D12—62no—
200C2×D12—61no—
201C2×D12—62no—
202C2×D12—61no—
203C2×D12—122no—
204C2×D12—121no—
205C2×C4×D3—64no—
206C2×C4×D3—64no—
207C2×C4×D3—124no—
208C2×C4×D3—124no—
209C2×C3×C8—32no—
210C2×C3×C8—62no—
211C3×C4⋊C4—32no—
212C3×C4⋊C4—32no—
213C3×C4⋊C4—64no—
214C3×C4⋊C4—61no—
215C3×C4⋊C4—61no—
216C3×C42—32no—
217C3×C42—32no—
218C3×C42—64no—
219#215—316no—
220#215—316no—
221#215—616no—
222(C2×D3)⋊C4—64no—
223(C2×D3)⋊C4—64no—
224C4⋊Dic3—21no—
225C4⋊Dic3—21no—
226C4⋊Dic3—24no—
227C4⋊Dic3C22×D312yes—
228C4⋊Dic3C22×D312yes—
229C4×Dic3—24no—
230C4×Dic3#6712yes—
231C4×Dic3C22×D312yes—
232C2×C3⋊C8—22no—
233C2×C3⋊C8—34no—
234C2×C3⋊C8—34no—
235C2×C3⋊C8—32no—
236C2×C3⋊C8—32no—
237C2×C3⋊C8—64no—
238C2×C3⋊C8—62no—
239C2×C3⋊C8C22×D312yes—
240C22×C32C4×D412yes—
241C22×C32AGL(1,ℤ/8)12yes—
242C22×C32#13712yes—
243C22×C32C22×D411yescharacteristic
244C2×C3⋊D3—24no—
245C2×C3⋊D3—42no—
246C2×C3⋊D3—42no—
247C2×C3⋊D3—48no—
248C32×C4—24no—
249C32×C4C4×D412yes—
250C32×C4C23×C411yescharacteristic
251C32×C4C2×#4111yescharacteristic
252C3×Dic3—22no—
253C3×Dic3—22no—
254C3×Dic3—42no—
255C3×Dic3—42no—
256C22×Q8D3211yescharacteristic
257C22×D4—91no—
258C23×C4—181no—
259C2×SD16—98no—
260C2×SD16—94no—
261C22×C8—31no—
262C22×C8—91no—
263C4×Q8—34no—
264C4×Q8—62no—
265C4×D4—94no—
266C4×D4—182no—
267C2×C4⋊C4—31no—
268C2×C4⋊C4—31no—
269C2×C4⋊C4—61no—
270C2×C22⋊C4—181no—
271C2×C42—31no—
272C2×C42—61no—
273#107—94no—
274#103—34no—
275#102—94no—
276#97—94no—
277C23×C3—21no—
278C23×C3D3×D411yescharacteristic
279C23×C3C2×#6711yescharacteristic
280C22×D3—64no—
281C22×D3—64no—
282C22×D3—62no—
283C22×D3—62no—
284C22×D3—122no—
285C22×D3—124no—
286C22×D3—122no—
287C22×D3—122no—
288C22×D3—122no—
289C22×D3—122no—
290C22×D3—242no—
291C22×D3—242no—
292C3×Q8—24no—
293C3×Q8—24no—
294C3×Q8—22no—
295C3×Q8—22no—
296C3×Q8—24no—
297C3×Q8—42no—
298C3×Q8—44no—
299C3×Q8C2×C4×D314yescomplemented
300C3×Q8C2×C4×D314yescomplemented
301C2×C3×C4—24no—
302C2×C3×C4—24no—
303C2×C3×C4—22no—
304C2×C3×C4—22no—
305C2×C3×C4—21no—
306C2×C3×C4—22no—
307C2×C3×C4—22no—
308C2×C3×C4—21no—
309C2×C3×C4—32no—
310C2×C3×C4—32no—
311C2×C3×C4—42no—
312C2×C3×C4—44no—
313C2×C3×C4—62no—
314C2×C3×C4—62no—
315C2×C3×C4—62no—
316C2×C3×C4—62no—
317C2×C3×C4—122no—
318C2×C3×C4—122no—
319C2×C3×C4C2×C4×D312yes—
320C2×C3×C4C2×C4×D312yes—
321C2×C3×C4#23512yes—
322C2×C3×C4D3×D411yescharacteristic
323C2×C3×C4#23712yes—
324C2×C3×C4C2×#6711yescharacteristic
325C2×C3×C4C23×D311yescharacteristic
326C2×C3×C4C23×D311yescharacteristic
327C2×Dic3—22no—
328C2×Dic3—22no—
329C2×Dic3—22no—
330C2×Dic3—22no—
331C2×Dic3—42no—
332C2×Dic3—42no—
333C2×Dic3C2×#6712yes—
334C2×Dic3C2×#6712yes—
335D12—34no—
336D12—34no—
337D12—64no—
338D12—64no—
339D12—64no—
340D12—62no—
341D12—62no—
342D12—122no—
343D12—124no—
344C4×D3—128no—
345C4×D3—128no—
346C3×C8—62no—
347C3⋊C8—22no—
348C3⋊C8—34no—
349C3⋊C8—34no—
350C3⋊C8—64no—
351C2×C32#44014yescomplemented
352C2×C32C2×C4×D411yescharacteristic
353C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
354C2×C32C2×#13711yescharacteristic
355C3⋊D3—44no—
356C24—181no—
357C2×Q8—22no—
358C2×Q8—21no—
359C2×Q8#62414yescomplemented
360C2×Q8C2×D3212yes—
361C2×D4—92no—
362C2×D4—94no—
363C2×D4—182no—
364C2×D4—181no—
365C22×C4—21no—
366C22×C4—31no—
367C22×C4—31no—
368C22×C4—61no—
369C22×C4—61no—
370C22×C4—184no—
371C22×C4—364no—
372C22×C4C2×D3211yescharacteristic
373SD16—916no—
374C2×C8—32no—
375C2×C8—62no—
376C2×C8—92no—
377C2×C8—94no—
378C4⋊C4—32no—
379C4⋊C4—32no—
380C4⋊C4—64no—
381C4⋊C4—61no—
382C4⋊C4—61no—
383C22⋊C4—184no—
384C42—32no—
385C42—32no—
386C42—64no—
387C22×C3—21no—
388C22×C3—22no—
389C22×C3—22no—
390C22×C3—22no—
391C22×C3#67⋊C412yes—
392C22×C3#91412yes—
393C22×C3#91812yes—
394C22×C3C4×#6712yes—
395C22×C3#94212yes—
396C22×C3#94912yes—
397C22×C3C2×D3×D411yescharacteristic
398C22×C3C22×#6711yescharacteristic
399C2×D3—64no—
400C2×D3—64no—
401C2×D3—124no—
402C2×D3—122no—
403C2×D3—122no—
404C2×D3—128no—
405C2×D3—122no—
406C2×D3—122no—
407C2×D3—128no—
408C2×D3—242no—
409C2×D3—248no—
410C2×D3—242no—
411C3×C4—24no—
412C3×C4—24no—
413C3×C4—21no—
414C3×C4—21no—
415C3×C4—22no—
416C3×C4—44no—
417C3×C4—62no—
418C3×C4—62no—
419C3×C4—122no—
420C3×C4—122no—
421C3×C4#67⋊C412yes—
422C3×C4C4×#6712yes—
423C3×C4C22×C4×D311yescharacteristic
424C3×C4C22×C4×D311yescharacteristic
425C3×C4C2×#23511yescharacteristic
426C3×C4C2×#23711yescharacteristic
427Dic3—22no—
428Dic3—22no—
429Dic3—42no—
430Dic3—42no—
431C32C2×#44011yescharacteristic, complemented, Sylow
432C23—182no—
433C23—184no—
434C23—362no—
435C23—362no—
436C23D3×#6711yescharacteristic
437Q8—22no—
438Q8—24no—
439Q8C2×#62414yescomplemented
440D4—94no—
441D4—182no—
442D4—184no—
443C2×C4—22no—
444C2×C4—24no—
445C2×C4—32no—
446C2×C4—32no—
447C2×C4—62no—
448C2×C4—62no—
449C2×C4—62no—
450C2×C4—62no—
451C2×C4—122no—
452C2×C4—122no—
453C2×C4—368no—
454C2×C4#380412yes—
455C2×C4C2×#62412yes—
456C2×C4D3×#6711yescharacteristic
457C2×C4C22×D3211yescharacteristic
458C8—62no—
459C8—94no—
460C2×C3—21no—
461C2×C3—24no—
462C2×C3—21no—
463C2×C3—21no—
464C2×C3#481714yescomplemented
465C2×C3#502614yescomplemented
466C2×C3C2×#67⋊C411yescharacteristic
467C2×C3C2×#91411yescharacteristic
468C2×C3C2×#91811yescharacteristic
469C2×C3C2×C4×#6711yescharacteristic
470C2×C3C2×#94211yescharacteristic
471C2×C3C2×#94911yescharacteristic
472D3—124no—
473D3—124no—
474D3—244no—
475C22—184no—
476C22—362no—
477C22—368no—
478C22—362no—
479C22#6393912yes—
480C22#6394812yes—
481C22#6395212yes—
482C22C2×D3×#6711yescharacteristic
483C4—24no—
484C4—62no—
485C4—62no—
486C4—122no—
487C4—122no—
488C4#6395212yes—
489C4C2×#380411yescharacteristic
490C4C22×#62411yescharacteristic
491C3—21no—
492C3C2×#481711yescharacteristic, complemented
493C3C2×#502611yescharacteristic, complemented
494C2—364no—
495C2#1059154014yesdirect product factor
496C2C2×#6393911yescharacteristic
497C2C2×#6394811yescharacteristic
498C2C2×#6395211yescharacteristic
subgroupG/H
centerC23D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC23×C32C2×D4
prime radicalC22×C4⋊(C3⋊D3)C22
cosocleC2×C32×C4C24
hypercenterC22×Q8D32
hypocenterC32C2×#440
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
2. C2×C3×Q8×Dic3C2semidirect
4. C2×C3×#835C2semidirect
5. #10591540C2direct (N × H)
6. C2×#63576C2semidirect
8. C2×#63554C2semidirect
14. C2×#3755C4semidirect
18. C3×Q8×Dic3C22semidirect
28. C3×#835C22semidirect
29. #63576C22semidirect
31. #63554C22semidirect
33. C2×Q8×Dic3D3semidirect
40. C2×#835D3semidirect
52. C2×C32×Q8C2×C4semidirect
66. #3755C2×C4semidirect
67. C2×C3⋊(C3⋊C8)C2×C4semidirect
98. Q8×Dic3C2×D3semidirect
121. #835C2×D3semidirect
135. C32×Q8C22×C4semidirect
154. C3⋊(C3⋊C8)C22×C4semidirect
175. C2×C3×Q8C4×D3semidirect
176. C2×C3×Q8C4×D3semidirect
299. C3×Q8C2×C4×D3semidirect
300. C3×Q8C2×C4×D3semidirect
351. C2×C32#440semidirect
359. C2×Q8#624semidirect
431. C32C2×#440semidirect
439. Q8C2×#624semidirect
464. C2×C3#4817semidirect
465. C2×C3#5026semidirect
492. C3C2×#4817semidirect
493. C3C2×#5026semidirect
495. C2#10591540direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37552
C2×C3×Q8×Dic32
C2×#638942
C2×C3×#8352
#105915402
C2×#635762
C2×#635642
C2×#635542
C2×#50263
C2×#48173