Finite Group Databasebeta

← C2×#10590550 #11873583

Subgroups — C2×#10590550 #11873583

Order 1152.

1077 conjugacy classes of subgroups.

The subgroup lattice has 517 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#890C211yesmaximal, characteristic, complemented
2C2×#63911C211yesmaximal, characteristic
3C2×#63636C211yesmaximal, characteristic, complemented
4C2×C3×#809C211yesmaximal, characteristic, complemented
5C2×#63564C211yesmaximal, characteristic, complemented
6C2×#63562C211yesmaximal, characteristic, complemented
7C2×#63554C211yesmaximal, characteristic, complemented
8#10590550C218yesmaximal, direct product factor
9C2×#5067—31nomaximal
10C2×#4764—31nomaximal
11C22×C4⋊(C3⋊D3)C2211yescharacteristic
12C22×C3×D12C2211yescharacteristic
13C22×#626—21no—
14C22×#626—21no—
15C2×C32×C4⋊C4C2211yescharacteristic
16C22×C3⋊(C3⋊C8)C2211yescharacteristic
17C2×C3×C4⋊Dic3—21no—
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C2×C3×Dic3⋊C4—21no—
20C2×C3×C4×Dic3C2211yescharacteristic
21C22×C3×C3⋊C8C2211yescharacteristic
22C3×#890—22no—
23C3×#890C2214yescomplemented
24#63911—22no—
25#63911C2214yes—
26#63636C2214yescomplemented
27C3×#809C2214yescomplemented
28#63564C2214yescomplemented
29#63562C2214yescomplemented
30#63554C2214yescomplemented
31C2×C3×#125—31no—
32C2×#940—31no—
33C2×#890D311yescharacteristic, complemented
34C2×#874—31no—
35C2×C3×#102—31no—
36C2×#832—31no—
37C2×#821—31no—
38C2×#815—31no—
39#5067—38no—
40C2×#809—31no—
41C2×#809—31no—
42C2×#809—31no—
43C2×#809—31no—
44C2×#809—61no—
45C2×#809D311yescharacteristic, complemented
46C2×#803—31no—
47#4764—38no—
48C23×C3⋊D3—21no—
49C23×C3×D3—21no—
50C22×C32×C4—21no—
51C22×C32×C4C2311yescharacteristic
52C2×C4⋊(C3⋊D3)—22no—
53C2×C4⋊(C3⋊D3)—22no—
54C2×C4⋊(C3⋊D3)—21no—
55C2×C4⋊(C3⋊D3)C2312yes—
56C22×C3×Dic3—21no—
57C22×C3×Dic3D411yescharacteristic
58C22×C3×Dic3D411yescharacteristic
59C2×C3×D12—22no—
60C2×C3×D12—22no—
61C2×C3×D12—21no—
62C2×C3×D12C2312yes—
63C2×#626—24no—
64C2×#626—24no—
65C2×#626—44no—
66C2×#626—44no—
67C32×C4⋊C4—21no—
68C32×C4⋊C4C2312yes—
69C2×C3⋊(C3⋊C8)—22no—
70C2×C3⋊(C3⋊C8)C2312yes—
71C3×C4⋊Dic3—21no—
72C3×C4⋊Dic3—24no—
73C3×C4⋊Dic3C2312yes—
74C3×Dic3⋊C4—24no—
75C3×C4×Dic3D412yes—
76C3×C4×Dic3C2312yes—
77C2×C3×C3⋊C8—22no—
78C2×C3×C3⋊C8C2312yes—
79C2×#490—91noSylow
80C22×C3×D4—31no—
81C22×#67—61no—
82C22×#67—61no—
83C22×D12—31no—
84C22×D12—31no—
85C22×D12—61no—
86C22×D12—61no—
87C22×D12—61no—
88C22×D12C2×D311yescharacteristic
89C22×C3×C8—31no—
90C3×#125—34no—
91C3×#125—62no—
92C2×C3×C4⋊C4—21no—
93C2×C3×C4⋊C4—31no—
94C2×C3×C4⋊C4—61no—
95C2×C3×C4⋊C4—61no—
96C2×C3×C4⋊C4C2×D311yescharacteristic
97C2×C3×C4⋊C4C2×D311yescharacteristic
98C2×C3×C42—31no—
99#940—34no—
100#940—62no—
101C2×C4⋊Dic3—21no—
102C2×C4⋊Dic3C2×D311yescharacteristic
103C2×Dic3⋊C4—21no—
104C2×C4×Dic3C2×D311yescharacteristic
105C22×C3⋊C8—31no—
106C22×C3⋊C8—31no—
107C22×C3⋊C8—61no—
108C22×C3⋊C8C2×D311yescharacteristic
109#890—22no—
110#890C2×D314yescomplemented
111#874—34no—
112#874—62no—
113C3×#102—34no—
114#832—34no—
115#821—34no—
116#815—34no—
117#809—34no—
118#809—34no—
119#809—34no—
120#809—34no—
121#809—64no—
122#809C2×D314yescomplemented
123#803—34no—
124C23×C32C2×D411yescharacteristic
125C22×C3⋊D3—22no—
126C22×C3⋊D3—42no—
127C22×C3⋊D3—42no—
128C22×C3⋊D3—42no—
129C22×C3×D3—22no—
130C22×C3×D3—42no—
131C22×C3×D3—42no—
132C22×C3×D3—42no—
133C2×C32×C4—22no—
134C2×C32×C4—42no—
135C2×C32×C4C2×D411yescharacteristic
136C2×C32×C4#4112yes—
137C2×C32×C4#4112yes—
138C2×C32×C4C2411yescharacteristic
139C4⋊(C3⋊D3)—22no—
140C4⋊(C3⋊D3)—22no—
141C4⋊(C3⋊D3)—42no—
142C2×C3×Dic3—22no—
143C2×C3×Dic3—22no—
144C2×C3×Dic3—22no—
145C2×C3×Dic3—42no—
146C2×C3×Dic3C2×D412yes—
147C2×C3×Dic3C2×D412yes—
148C3×D12—22no—
149C3×D12—22no—
150C3×D12—42no—
151#626—48no—
152#626—48no—
153C3⋊(C3⋊C8)—22no—
154C3×C3⋊C8—22no—
155C2×#127—91no—
156C2×#125—31no—
157#490—98no—
158C2×#102—31no—
159C2×#102—91no—
160C2×#102—91no—
161C2×#102—91no—
162C2×#97—91no—
163C24×C3—61no—
164C23×D3—21no—
165C23×D3—61no—
166C23×D3—61no—
167C23×D3—121no—
168C2×C3×D4—32no—
169C2×C3×D4—62no—
170C2×C3×D4—62no—
171C2×C3×D4—61no—
172C22×C3×C4—21no—
173C22×C3×C4—21no—
174C22×C3×C4—21no—
175C22×C3×C4—31no—
176C22×C3×C4—31no—
177C22×C3×C4—41no—
178C22×C3×C4—61no—
179C22×C3×C4C22×D311yescharacteristic
180C22×C3×C4C22×D311yescharacteristic
181C2×#67—64no—
182C2×#67—64no—
183C2×#67—124no—
184C2×#67—124no—
185C22×Dic3—21no—
186C22×Dic3#6711yescharacteristic
187C22×Dic3#6711yescharacteristic
188C2×D12—22no—
189C2×D12—22no—
190C2×D12—21no—
191C2×D12—32no—
192C2×D12—32no—
193C2×D12—62no—
194C2×D12—64no—
195C2×D12—62no—
196C2×D12—62no—
197C2×D12—62no—
198C2×D12—62no—
199C2×D12—64no—
200C2×D12—64no—
201C2×D12—61no—
202C2×D12—61no—
203C2×D12—122no—
204C2×D12—121no—
205C2×D12—124no—
206C2×D12—124no—
207C2×D12C22×D312yes—
208C2×C3×C8—32no—
209C2×C3×C8—62no—
210C3×C4⋊C4—21no—
211C3×C4⋊C4—21no—
212C3×C4⋊C4—22no—
213C3×C4⋊C4—32no—
214C3×C4⋊C4—41no—
215C3×C4⋊C4—64no—
216C3×C4⋊C4—64no—
217C3×C4⋊C4—61no—
218C3×C4⋊C4C22×D312yes—
219C3×C4⋊C4C22×D312yes—
220C3×C42—32no—
221C3×C42—32no—
222C4⋊Dic3—21no—
223C4⋊Dic3—24no—
224C4⋊Dic3C22×D312yes—
225Dic3⋊C4—24no—
226C4×Dic3#6712yes—
227C4×Dic3C22×D312yes—
228C2×C3⋊C8—22no—
229C2×C3⋊C8—32no—
230C2×C3⋊C8—32no—
231C2×C3⋊C8—62no—
232C2×C3⋊C8—62no—
233C2×C3⋊C8—62no—
234C2×C3⋊C8—122no—
235C2×C3⋊C8C22×D312yes—
236C22×C32#12412yes—
237C22×C32AGL(1,ℤ/8)12yes—
238C22×C32AGL(1,ℤ/8)12yes—
239C22×C32C22×D411yescharacteristic
240C2×C3⋊D3—42no—
241C2×C3⋊D3—42no—
242C2×C3⋊D3—42no—
243C2×C3⋊D3—84no—
244C2×C3×D3—42no—
245C2×C3×D3—42no—
246C2×C3×D3—42no—
247C2×C3×D3—84no—
248C32×C4—42no—
249C32×C4#12412yes—
250C32×C4C2×#4111yescharacteristic
251C32×C4C2×#4111yescharacteristic
252C3×Dic3—22no—
253C3×Dic3—22no—
254C3×Dic3—42no—
255C22×D4—31no—
256C22×D4—91no—
257C22×D4—181no—
258C22×D4—181no—
259C22×C8—31no—
260C22×C8—91no—
261#127—94no—
262#127—182no—
263#125—34no—
264#125—62no—
265C2×C4⋊C4—31no—
266C2×C4⋊C4—61no—
267C2×C4⋊C4—61no—
268C2×C4⋊C4D3211yescharacteristic
269C2×C42—31no—
270#102—34no—
271#102—94no—
272#102—94no—
273#102—94no—
274#97—94no—
275C23×C3—21no—
276C23×C3—62no—
277C23×C3—122no—
278C23×C3—122no—
279C23×C3—122no—
280C23×C3D3×D411yescharacteristic
281C23×C3C2×#6711yescharacteristic
282C22×D3—22no—
283C22×D3—42no—
284C22×D3—42no—
285C22×D3—42no—
286C22×D3—62no—
287C22×D3—62no—
288C22×D3—122no—
289C22×D3—124no—
290C22×D3—122no—
291C22×D3—122no—
292C22×D3—122no—
293C22×D3—122no—
294C22×D3—122no—
295C22×D3—122no—
296C22×D3—242no—
297C22×D3—242no—
298C3×D4—62no—
299C3×D4—62no—
300C3×D4—122no—
301C2×C3×C4—22no—
302C2×C3×C4—22no—
303C2×C3×C4—21no—
304C2×C3×C4—22no—
305C2×C3×C4—22no—
306C2×C3×C4—21no—
307C2×C3×C4—32no—
308C2×C3×C4—32no—
309C2×C3×C4—42no—
310C2×C3×C4—42no—
311C2×C3×C4—42no—
312C2×C3×C4—62no—
313C2×C3×C4—62no—
314C2×C3×C4—62no—
315C2×C3×C4—82no—
316C2×C3×C4—122no—
317C2×C3×C4#23512yes—
318C2×C3×C4D3×D411yescharacteristic
319C2×C3×C4#23712yes—
320C2×C3×C4#23912yes—
321C2×C3×C4#23912yes—
322C2×C3×C4C2×#6711yescharacteristic
323C2×C3×C4C23×D311yescharacteristic
324C2×C3×C4C23×D311yescharacteristic
325#67—128no—
326#67—128no—
327C2×Dic3—22no—
328C2×Dic3—22no—
329C2×Dic3—22no—
330C2×Dic3—42no—
331C2×Dic3C2×#6712yes—
332C2×Dic3C2×#6712yes—
333D12—22no—
334D12—22no—
335D12—42no—
336D12—64no—
337D12—62no—
338D12—62no—
339D12—62no—
340D12—62no—
341D12—122no—
342D12—124no—
343D12—128no—
344D12—128no—
345D12—122no—
346D12—122no—
347C3×C8—62no—
348C3⋊C8—22no—
349C3⋊C8—62no—
350C3⋊C8—62no—
351C3⋊C8—122no—
352C2×C32#49014yescomplemented
353C2×C32C2×#12411yescharacteristic
354C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
355C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
356C3⋊D3—82no—
357C3×D3—82no—
358C24—61no—
359C24—181no—
360C2×D4—32no—
361C2×D4—62no—
362C2×D4—62no—
363C2×D4—61no—
364C2×D4—92no—
365C2×D4—184no—
366C2×D4—184no—
367C2×D4—182no—
368C2×D4—182no—
369C2×D4—181no—
370C2×D4—364no—
371C2×D4—364no—
372C22×C4—21no—
373C22×C4—31no—
374C22×C4—31no—
375C22×C4—61no—
376C22×C4C2×D3211yescharacteristic
377C2×C8—32no—
378C2×C8—62no—
379C2×C8—92no—
380C2×C8—182no—
381C4⋊C4—21no—
382C4⋊C4—32no—
383C4⋊C4—64no—
384C4⋊C4—64no—
385C4⋊C4—61no—
386C4⋊C4C2×D3212yes—
387C42—32no—
388C42—32no—
389C22×C3—21no—
390C22×C3—22no—
391C22×C3—22no—
392C22×C3—22no—
393C22×C3—122no—
394C22×C3—122no—
395C22×C3—122no—
396C22×C3—244no—
397C22×C3#88512yes—
398C22×C3#91112yes—
399C22×C3#91412yes—
400C22×C3#94712yes—
401C22×C3#94912yes—
402C22×C3#94912yes—
403C22×C3C2×D3×D411yescharacteristic
404C22×C3C22×#6711yescharacteristic
405C2×D3—42no—
406C2×D3—42no—
407C2×D3—42no—
408C2×D3—84no—
409C2×D3—124no—
410C2×D3—122no—
411C2×D3—122no—
412C2×D3—122no—
413C2×D3—122no—
414C2×D3—122no—
415C2×D3—122no—
416C2×D3—242no—
417C2×D3—242no—
418C2×D3—248no—
419C2×D3—244no—
420C2×D3—244no—
421C3×C4—21no—
422C3×C4—21no—
423C3×C4—22no—
424C3×C4—42no—
425C3×C4—42no—
426C3×C4—62no—
427C3×C4—62no—
428C3×C4—82no—
429C3×C4—122no—
430C3×C4#88512yes—
431C3×C4#94712yes—
432C3×C4C2×#23511yescharacteristic
433C3×C4C2×#23711yescharacteristic
434C3×C4C2×#23911yescharacteristic
435C3×C4C2×#23911yescharacteristic
436Dic3—22no—
437Dic3—22no—
438Dic3—42no—
439C32C2×#49011yescharacteristic, complemented, Sylow
440C23—62no—
441C23—122no—
442C23—122no—
443C23—122no—
444C23—182no—
445C23—362no—
446C23—362no—
447C23—362no—
448C23D3×#6711yescharacteristic
449D4—62no—
450D4—62no—
451D4—122no—
452D4—182no—
453D4—182no—
454D4—368no—
455D4—368no—
456D4—362no—
457C2×C4—22no—
458C2×C4—32no—
459C2×C4—32no—
460C2×C4—42no—
461C2×C4—62no—
462C2×C4—62no—
463C2×C4—62no—
464C2×C4—122no—
465C2×C4#379612yes—
466C2×C4#379912yes—
467C2×C4D3×#6711yescharacteristic
468C2×C4C22×D3211yescharacteristic
469C8—62no—
470C8—182no—
471C2×C3—21no—
472C2×C3—24no—
473C2×C3—21no—
474C2×C3—21no—
475C2×C3—242no—
476C2×C3#476414yescomplemented
477C2×C3#506714yescomplemented
478C2×C3C2×#88511yescharacteristic
479C2×C3C2×#91111yescharacteristic
480C2×C3C2×#91411yescharacteristic
481C2×C3C2×#94711yescharacteristic
482C2×C3C2×#94911yescharacteristic
483C2×C3C2×#94911yescharacteristic
484D3—82no—
485D3—244no—
486D3—242no—
487D3—242no—
488C22—122no—
489C22—122no—
490C22—122no—
491C22—244no—
492C22—362no—
493C22—362no—
494C22—362no—
495C22—724no—
496C22#6390712yes—
497C22#6392512yes—
498C22#6393912yes—
499C22C2×D3×#6711yescharacteristic
500C4—42no—
501C4—62no—
502C4—62no—
503C4—122no—
504C4#6390712yes—
505C4C2×#379611yescharacteristic
506C4C2×#379911yescharacteristic
507C3—21no—
508C3C2×#476411yescharacteristic, complemented
509C3C2×#506711yescharacteristic, complemented
510C2—242no—
511C2—722no—
512C2#1059055014yesdirect product factor
513C2C2×#6390711yescharacteristic
514C2C2×#6392511yescharacteristic
515C2C2×#6393911yescharacteristic
subgroupG/H
centerC23D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC2×#63911C2
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#490
LCSG ▷ C2×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×#890C2semidirect
3. C2×#63636C2semidirect
4. C2×C3×#809C2semidirect
5. C2×#63564C2semidirect
6. C2×#63562C2semidirect
7. C2×#63554C2semidirect
8. #10590550C2direct (N × H)
23. C3×#890C22semidirect
26. #63636C22semidirect
27. C3×#809C22semidirect
28. #63564C22semidirect
29. #63562C22semidirect
30. #63554C22semidirect
33. C2×#890D3semidirect
45. C2×#809D3semidirect
110. #890C2×D3semidirect
122. #809C2×D3semidirect
352. C2×C32#490semidirect
439. C32C2×#490semidirect
476. C2×C3#4764semidirect
477. C2×C3#5067semidirect
508. C3C2×#4764semidirect
509. C3C2×#5067semidirect
512. C2#10590550direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#8902
C2×#639112
C2×#636362
C2×C3×#8092
C2×#635642
C2×#635622
C2×#635542
#105905502
C2×#50673
C2×#47643