Finite Group Databasebeta

← C2×#10590457 #11860064

Subgroups — C2×#10590457 #11860064

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×#887C211yesmaximal, characteristic, complemented
2C2×#63894C211yesmaximal, characteristic
3C22×#3717C211yesmaximal, characteristic
4C2×#63636C211yesmaximal, characteristic
5C2×C3×#807C211yesmaximal, characteristic, complemented
6C2×#63565C211yesmaximal, characteristic, complemented
7C2×#63554C211yesmaximal, characteristic, complemented
8#10590457C218yesmaximal, direct product factor
9C2×#5026—31nomaximal
10C2×#4889—31nomaximal
11C22×C4⋊(C3⋊D3)C2211yescharacteristic
12C22×C3×Dic6C2211yescharacteristic
13C22×#624—21no—
14C2×C32×C4⋊C4C2211yescharacteristic
15C22×C3⋊(C3⋊C8)C2211yescharacteristic
16C2×C3×C4⋊Dic3C2211yescharacteristic
17C2×C3×Dic3⋊C4—21no—
18C2×C3×C4×Dic3—21no—
19C2×C3×C4×Dic3C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21C3×#887—22no—
22C3×#887C2214yescomplemented
23C2×#3722—21no—
24#63894—22no—
25#63894C2214yes—
26C2×#3717C418yescomplemented
27C2×#3717C2214yes—
28#63636C2214yes—
29C3×#807C2214yescomplemented
30#63565C2214yescomplemented
31#63554C2214yescomplemented
32C2×C3×C4×Q8—31no—
33C22×#215—31no—
34C22×#204—31no—
35C2×#893—31no—
36C2×#887D311yescharacteristic, complemented
37C2×C4×D12—31no—
38C2×C3×#107—31no—
39C2×#835—31no—
40C2×#815—31no—
41#5026—38no—
42C2×#810—31no—
43C2×#809—31no—
44C2×#809—31no—
45C2×#809—61no—
46C2×#807D311yescharacteristic, complemented
47C2×#803—31no—
48#4889—38no—
49C23×C3⋊D3—21no—
50C22×C32×C4—21no—
51C22×C32×C4C2311yescharacteristic
52C2×C4⋊(C3⋊D3)—21no—
53C2×C4⋊(C3⋊D3)—22no—
54C2×C4⋊(C3⋊D3)C2×C414yes—
55C2×C4⋊(C3⋊D3)C2312yes—
56C22×C3×Dic3—21no—
57C22×C3×Dic3—21no—
58C22×C3×Dic3D411yescharacteristic
59C22×C3×Dic3D411yescharacteristic
60C2×C3×Dic6—21no—
61C2×C3×Dic6—22no—
62C2×C3×Dic6C2×C414yescomplemented
63C2×C3×Dic6C2312yes—
64C2×#624—24no—
65C2×#624—44no—
66C32×C4⋊C4—21no—
67C32×C4⋊C4C2312yes—
68C2×C3⋊(C3⋊C8)—22no—
69C2×C3⋊(C3⋊C8)C2312yes—
70C3×C4⋊Dic3—21no—
71C3×C4⋊Dic3C2312yes—
72C3×Dic3⋊C4—24no—
73C3×C4×Dic3—24no—
74C3×C4×Dic3D412yes—
75C3×C4×Dic3C2312yes—
76C2×C3×C3⋊C8C2×C414yescomplemented
77C2×C3×C3⋊C8C2312yes—
78#3722—24no—
79#3717C2×C4116yescomplemented
80C2×#440—91noSylow
81C22×C3×Q8—31no—
82C22×D12—31no—
83C22×D12—31no—
84C22×D12—61no—
85C22×C4×D3—61no—
86C22×C4×D3—61no—
87C22×Dic6C2×D311yescharacteristic
88C22×C3×C8—31no—
89C3×C4×Q8—34no—
90C3×C4×Q8—62no—
91C2×C3×C4⋊C4—21no—
92C2×C3×C4⋊C4—31no—
93C2×C3×C4⋊C4—61no—
94C2×C3×C4⋊C4C2×D311yescharacteristic
95C2×C3×C4⋊C4C2×D311yescharacteristic
96C2×C3×C42—31no—
97C2×C3×C42—61no—
98C2×#215—38no—
99C2×#215—34no—
100C2×(C2×D3)⋊C4—61no—
101C2×(C2×D3)⋊C4—61no—
102C2×C4⋊Dic3C2×D311yescharacteristic
103C2×Dic3⋊C4—21no—
104C2×C4×Dic3—21no—
105C2×C4×Dic3C2×D311yescharacteristic
106C22×C3⋊C8—31no—
107C22×C3⋊C8—31no—
108C22×C3⋊C8—61no—
109C22×C3⋊C8C2×D311yescharacteristic
110C2×#204—38no—
111C2×#204—34no—
112#893—34no—
113#893—62no—
114#887—22no—
115#887C2×D314yescomplemented
116C4×D12—34no—
117C4×D12—62no—
118C3×#107—34no—
119#835—34no—
120#815—34no—
121#810—34no—
122#809—34no—
123#809—34no—
124#809—64no—
125#807C2×D314yescomplemented
126#803—34no—
127C23×C32C2×D411yescharacteristic
128C22×C3⋊D3—24no—
129C22×C3⋊D3—22no—
130C22×C3⋊D3—42no—
131C22×C3⋊D3—42no—
132C2×C32×C4—22no—
133C2×C32×C4—42no—
134C2×C32×C4C22×C412yes—
135C2×C32×C4C2×D411yescharacteristic
136C2×C32×C4#4112yes—
137C2×C32×C4C2411yescharacteristic
138C4⋊(C3⋊D3)—24no—
139C4⋊(C3⋊D3)—22no—
140C4⋊(C3⋊D3)C22×C414yes—
141C2×C3×Dic3—24no—
142C2×C3×Dic3—22no—
143C2×C3×Dic3—22no—
144C2×C3×Dic3—22no—
145C2×C3×Dic3—22no—
146C2×C3×Dic3—42no—
147C2×C3×Dic3C2×D412yes—
148C2×C3×Dic3C2×D412yes—
149C3×Dic6—24no—
150C3×Dic6—22no—
151C3×Dic6C22×C414yescomplemented
152#624—48no—
153C3⋊(C3⋊C8)—22no—
154C3×C3⋊C8C22×C414yescomplemented
155C22×SD16—91no—
156C2×C4×Q8—31no—
157C2×C4×D4—91no—
158#440—98no—
159C2×#107—31no—
160C2×#103—91no—
161C2×#102—91no—
162C2×#97—91no—
163C23×D3—61no—
164C23×D3—61no—
165C23×D3—121no—
166C2×C3×Q8—34no—
167C2×C3×Q8—32no—
168C2×C3×Q8—61no—
169C2×C3×Q8—62no—
170C22×C3×C4—21no—
171C22×C3×C4—21no—
172C22×C3×C4—21no—
173C22×C3×C4—31no—
174C22×C3×C4—31no—
175C22×C3×C4—41no—
176C22×C3×C4—61no—
177C22×C3×C4—61no—
178C22×C3×C4C22×D311yescharacteristic
179C22×C3×C4C22×D311yescharacteristic
180C22×Dic3—21no—
181C22×Dic3—21no—
182C22×Dic3#6711yescharacteristic
183C22×Dic3#6711yescharacteristic
184C2×D12—34no—
185C2×D12—34no—
186C2×D12—32no—
187C2×D12—32no—
188C2×D12—62no—
189C2×D12—64no—
190C2×D12—62no—
191C2×D12—61no—
192C2×D12—62no—
193C2×D12—61no—
194C2×D12—122no—
195C2×D12—121no—
196C2×C4×D3—64no—
197C2×C4×D3—64no—
198C2×C4×D3—124no—
199C2×C4×D3—124no—
200C2×Dic6—22no—
201C2×Dic6—21no—
202C2×Dic6C4×D314yescomplemented
203C2×Dic6C22×D312yes—
204C2×C3×C8—34no—
205C2×C3×C8—32no—
206C3×C4⋊C4—21no—
207C3×C4⋊C4—21no—
208C3×C4⋊C4—22no—
209C3×C4⋊C4—32no—
210C3×C4⋊C4—41no—
211C3×C4⋊C4—64no—
212C3×C4⋊C4—61no—
213C3×C4⋊C4C22×D312yes—
214C3×C4⋊C4C22×D312yes—
215C3×C42—32no—
216C3×C42—32no—
217C3×C42—64no—
218#215—316no—
219(C2×D3)⋊C4—64no—
220(C2×D3)⋊C4—64no—
221C4⋊Dic3—21no—
222C4⋊Dic3C22×D312yes—
223Dic3⋊C4—24no—
224C4×Dic3—24no—
225C4×Dic3#6712yes—
226C4×Dic3C22×D312yes—
227C2×C3⋊C8—32no—
228C2×C3⋊C8—32no—
229C2×C3⋊C8—62no—
230C2×C3⋊C8—62no—
231C2×C3⋊C8—62no—
232C2×C3⋊C8—122no—
233C2×C3⋊C8C4×D314yescomplemented
234C2×C3⋊C8C22×D312yes—
235#204—316no—
236C22×C32C4×D412yes—
237C22×C32AGL(1,ℤ/8)12yes—
238C22×C32#13712yes—
239C22×C32C22×D411yescharacteristic
240C2×C3⋊D3—24no—
241C2×C3⋊D3—42no—
242C2×C3⋊D3—42no—
243C2×C3⋊D3—48no—
244C32×C4—42no—
245C32×C4C4×D412yes—
246C32×C4C23×C411yescharacteristic
247C32×C4C2×#4111yescharacteristic
248C3×Dic3—24no—
249C3×Dic3—22no—
250C3×Dic3—22no—
251C3×Dic3—42no—
252C22×Q8—31no—
253C22×D4—91no—
254C23×C4—181no—
255C2×SD16—98no—
256C2×SD16—94no—
257C22×C8—31no—
258C22×C8—91no—
259C4×Q8—34no—
260C4×Q8—62no—
261C4×D4—94no—
262C4×D4—182no—
263C2×C4⋊C4—31no—
264C2×C4⋊C4—61no—
265C2×C4⋊C4D3211yescharacteristic
266C2×C22⋊C4—181no—
267C2×C42—31no—
268C2×C42—61no—
269#107—34no—
270#103—94no—
271#102—94no—
272#97—94no—
273C23×C3—21no—
274C23×C3D3×D411yescharacteristic
275C23×C3C2×#6711yescharacteristic
276C22×D3—64no—
277C22×D3—64no—
278C22×D3—62no—
279C22×D3—62no—
280C22×D3—122no—
281C22×D3—124no—
282C22×D3—122no—
283C22×D3—122no—
284C22×D3—122no—
285C22×D3—122no—
286C22×D3—242no—
287C22×D3—242no—
288C3×Q8—34no—
289C3×Q8—64no—
290C3×Q8—62no—
291C2×C3×C4—22no—
292C2×C3×C4—22no—
293C2×C3×C4—21no—
294C2×C3×C4—22no—
295C2×C3×C4—22no—
296C2×C3×C4—21no—
297C2×C3×C4—32no—
298C2×C3×C4—32no—
299C2×C3×C4—42no—
300C2×C3×C4—42no—
301C2×C3×C4—42no—
302C2×C3×C4—64no—
303C2×C3×C4—62no—
304C2×C3×C4—62no—
305C2×C3×C4—62no—
306C2×C3×C4—62no—
307C2×C3×C4—82no—
308C2×C3×C4—122no—
309C2×C3×C4C2×C4×D312yes—
310C2×C3×C4C2×C4×D312yes—
311C2×C3×C4#23512yes—
312C2×C3×C4D3×D411yescharacteristic
313C2×C3×C4#23912yes—
314C2×C3×C4C2×#6711yescharacteristic
315C2×C3×C4C23×D311yescharacteristic
316C2×C3×C4C23×D311yescharacteristic
317C2×Dic3—24no—
318C2×Dic3—22no—
319C2×Dic3—22no—
320C2×Dic3—22no—
321C2×Dic3—22no—
322C2×Dic3—42no—
323C2×Dic3C2×#6712yes—
324C2×Dic3C2×#6712yes—
325D12—34no—
326D12—34no—
327D12—64no—
328D12—64no—
329D12—64no—
330D12—62no—
331D12—62no—
332D12—122no—
333D12—124no—
334C4×D3—128no—
335C4×D3—128no—
336Dic6—24no—
337Dic6—22no—
338Dic6C2×C4×D314yescomplemented
339C3×C8—34no—
340C3⋊C8—62no—
341C3⋊C8—62no—
342C3⋊C8—122no—
343C3⋊C8C2×C4×D314yescomplemented
344C2×C32#44014yescomplemented
345C2×C32C2×C4×D411yescharacteristic
346C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
347C2×C32C2×#13711yescharacteristic
348C3⋊D3—44no—
349C24—181no—
350C2×Q8—32no—
351C2×Q8—34no—
352C2×Q8—62no—
353C2×Q8—61no—
354C2×D4—92no—
355C2×D4—94no—
356C2×D4—182no—
357C2×D4—181no—
358C22×C4—21no—
359C22×C4—31no—
360C22×C4—31no—
361C22×C4—61no—
362C22×C4—61no—
363C22×C4—184no—
364C22×C4—364no—
365C22×C4C2×D3211yescharacteristic
366SD16—916no—
367C2×C8—32no—
368C2×C8—34no—
369C2×C8—92no—
370C2×C8—182no—
371C4⋊C4—21no—
372C4⋊C4—32no—
373C4⋊C4—64no—
374C4⋊C4—61no—
375C4⋊C4C2×D3212yes—
376C22⋊C4—184no—
377C42—32no—
378C42—32no—
379C42—64no—
380C22×C3—21no—
381C22×C3—22no—
382C22×C3—22no—
383C22×C3—22no—
384C22×C3#89312yes—
385C22×C3#91112yes—
386C22×C3#91812yes—
387C22×C3C4×#6712yes—
388C22×C3#94212yes—
389C22×C3#94912yes—
390C22×C3C2×D3×D411yescharacteristic
391C22×C3C22×#6711yescharacteristic
392C2×D3—64no—
393C2×D3—64no—
394C2×D3—124no—
395C2×D3—128no—
396C2×D3—122no—
397C2×D3—122no—
398C2×D3—128no—
399C2×D3—122no—
400C2×D3—122no—
401C2×D3—242no—
402C2×D3—242no—
403C2×D3—248no—
404C3×C4—21no—
405C3×C4—21no—
406C3×C4—22no—
407C3×C4—42no—
408C3×C4—42no—
409C3×C4—62no—
410C3×C4—64no—
411C3×C4—62no—
412C3×C4—82no—
413C3×C4—122no—
414C3×C4#89312yes—
415C3×C4C4×#6712yes—
416C3×C4C22×C4×D311yescharacteristic
417C3×C4C22×C4×D311yescharacteristic
418C3×C4C2×#23511yescharacteristic
419C3×C4C2×#23911yescharacteristic
420Dic3—24no—
421Dic3—22no—
422Dic3—22no—
423Dic3—42no—
424C32C2×#44011yescharacteristic, complemented, Sylow
425C23—182no—
426C23—184no—
427C23—362no—
428C23—362no—
429C23D3×#6711yescharacteristic
430Q8—34no—
431Q8—62no—
432Q8—64no—
433D4—94no—
434D4—182no—
435D4—184no—
436C2×C4—22no—
437C2×C4—32no—
438C2×C4—32no—
439C2×C4—42no—
440C2×C4—62no—
441C2×C4—64no—
442C2×C4—62no—
443C2×C4—62no—
444C2×C4—62no—
445C2×C4—122no—
446C2×C4—368no—
447C2×C4#379912yes—
448C2×C4C4×D3212yes—
449C2×C4D3×#6711yescharacteristic
450C2×C4C22×D3211yescharacteristic
451C8—34no—
452C8—182no—
453C2×C3—21no—
454C2×C3—21no—
455C2×C3—21no—
456C2×C3—24no—
457C2×C3#488914yescomplemented
458C2×C3#502614yescomplemented
459C2×C3C2×#89311yescharacteristic
460C2×C3C2×#91111yescharacteristic
461C2×C3C2×#91811yescharacteristic
462C2×C3C2×C4×#6711yescharacteristic
463C2×C3C2×#94211yescharacteristic
464C2×C3C2×#94911yescharacteristic
465D3—124no—
466D3—124no—
467D3—244no—
468C22—184no—
469C22—362no—
470C22—362no—
471C22—368no—
472C22#6390412yes—
473C22#6392512yes—
474C22#6394812yes—
475C22C2×D3×#6711yescharacteristic
476C4—42no—
477C4—62no—
478C4—62no—
479C4—64no—
480C4—122no—
481C4#6390412yes—
482C4C2×#379911yescharacteristic
483C4C2×C4×D3211yescharacteristic
484C3—21no—
485C3C2×#488911yescharacteristic, complemented
486C3C2×#502611yescharacteristic, complemented
487C2—364no—
488C2#1059045714yesdirect product factor
489C2C2×#6390411yescharacteristic
490C2C2×#6392511yescharacteristic
491C2C2×#6394811yescharacteristic
subgroupG/H
centerC23D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC22×C4⋊(C3⋊D3)C22
cosocleC2×C32×C4C24
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#440
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#887C2semidirect
5. C2×C3×#807C2semidirect
6. C2×#63565C2semidirect
7. C2×#63554C2semidirect
8. #10590457C2direct (N × H)
22. C3×#887C22semidirect
26. C2×#3717C4semidirect
29. C3×#807C22semidirect
30. #63565C22semidirect
31. #63554C22semidirect
36. C2×#887D3semidirect
46. C2×#807D3semidirect
62. C2×C3×Dic6C2×C4semidirect
76. C2×C3×C3⋊C8C2×C4semidirect
79. #3717C2×C4semidirect
115. #887C2×D3semidirect
125. #807C2×D3semidirect
151. C3×Dic6C22×C4semidirect
154. C3×C3⋊C8C22×C4semidirect
202. C2×Dic6C4×D3semidirect
233. C2×C3⋊C8C4×D3semidirect
338. Dic6C2×C4×D3semidirect
343. C3⋊C8C2×C4×D3semidirect
344. C2×C32#440semidirect
424. C32C2×#440semidirect
457. C2×C3#4889semidirect
458. C2×C3#5026semidirect
485. C3C2×#4889semidirect
486. C3C2×#5026semidirect
488. C2#10590457direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#8872
C2×#638942
C22×#37172
C2×#636362
C2×C3×#8072
C2×#635652
C2×#635542
#105904572
C2×#50263
C2×#48893