Finite Group Databasebeta

← C2×#10590473 #11868358

Subgroups — C2×#10590473 #11868358

Order 1152.

1009 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64099C211yesmaximal, characteristic, complemented
2C2×#63898C211yesmaximal, characteristic
3C2×C3×#809C211yesmaximal, characteristic
4C2×C3×#807C211yesmaximal, characteristic, complemented
5C2×#63573C211yesmaximal, characteristic, complemented
6C2×#63572C211yesmaximal, characteristic, complemented
7C2×#63563C211yesmaximal, characteristic
8#10590473C218yesmaximal, direct product factor
9C2×#4891—31nomaximal
10C2×#4763—31nomaximal
11C22×C3×D12C2211yescharacteristic
12C22×D3×Dic3—21no—
13C2×C32×C4⋊C4C2211yescharacteristic
14C2×C4⋊(C3⋊Dic3)—21no—
15C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
16C2×#3750—21no—
17C2×C4×C3⋊Dic3C2211yescharacteristic
18#64099—22no—
19#64099C2214yescomplemented
20C2×C3×C4⋊Dic3C2211yescharacteristic
21C22×C3×C3⋊C8C2211yescharacteristic
22C22×C3×C3⋊C8C2211yescharacteristic
23C2×(C2×D3)⋊Dic3—21no—
24#63898—22no—
25#63898C2214yes—
26C3×#809C2214yes—
27C3×#807C2214yescomplemented
28#63573C2214yescomplemented
29#63572C2214yescomplemented
30#63563C2214yes—
31C2×D4×Dic3—31no—
32C2×#893—31no—
33C2×#890—31no—
34C2×#890—31no—
35C2×#890—61no—
36C2×C3×#107—31no—
37C2×C3×#102—31no—
38C2×#832—31no—
39C2×#821—31no—
40C2×#817—31no—
41C2×Dic3⋊C8—31no—
42C2×Dic3⋊C8—31no—
43C2×#809D311yescharacteristic
44C2×#808—31no—
45C2×#807D311yescharacteristic, complemented
46#4891—38no—
47#4763—38no—
48C23×C3×D3—21no—
49C22×C32×C4—21no—
50C22×C32×C4C2311yescharacteristic
51C22×C3⋊Dic3—21no—
52C22×C3⋊Dic3D411yescharacteristic
53C22×C3⋊Dic3D411yescharacteristic
54C22×C3×Dic3—21no—
55C2×C3×D12—21no—
56C2×C3×D12—22no—
57C2×C3×D12Q814yes—
58C2×C3×D12C2312yes—
59C2×D3×Dic3—24no—
60C2×D3×Dic3—44no—
61C32×C4⋊C4—21no—
62C32×C4⋊C4C2312yes—
63C4⋊(C3⋊Dic3)—21no—
64C4⋊(C3⋊Dic3)—24no—
65C4⋊(C3⋊Dic3)C2312yes—
66#3750—24no—
67C4×C3⋊Dic3D412yes—
68C4×C3⋊Dic3C2312yes—
69C3×C4⋊Dic3—21no—
70C3×C4⋊Dic3C2312yes—
71C2×C3×C3⋊C8—22no—
72C2×C3×C3⋊C8—22no—
73C2×C3×C3⋊C8C2312yes—
74C2×C3×C3⋊C8C2312yes—
75(C2×D3)⋊Dic3—24no—
76C2×#478—91noSylow
77C22×C3×D4—31no—
78C23×Dic3—61no—
79C22×D12C2×D311yescharacteristic
80C22×C4×D3—61no—
81C22×C3×C8—31no—
82C22×C3×C8—31no—
83C2×C3×C4⋊C4—21no—
84C2×C3×C4⋊C4—31no—
85C2×C3×C4⋊C4C2×D311yescharacteristic
86C2×C3×C4⋊C4C2×D311yescharacteristic
87C2×#217—61no—
88D4×Dic3—34no—
89D4×Dic3—62no—
90C2×(C2×D3)⋊C4—61no—
91C2×C4⋊Dic3—31no—
92C2×C4⋊Dic3—31no—
93C2×C4⋊Dic3—61no—
94C2×C4⋊Dic3—61no—
95C2×C4⋊Dic3—61no—
96C2×C4⋊Dic3—62no—
97C2×C4⋊Dic3C2×D311yescharacteristic
98C2×Dic3⋊C4—61no—
99C2×Dic3⋊C4—61no—
100C2×Dic3⋊C4—62no—
101C2×C4×Dic3—31no—
102C2×C4×Dic3—31no—
103C2×C4×Dic3—61no—
104C22×C3⋊C8C2×D311yescharacteristic
105C22×C3⋊C8C2×D311yescharacteristic
106#893—34no—
107#893—62no—
108#890—34no—
109#890—34no—
110#890—64no—
111#890—62no—
112#890—62no—
113#890—64no—
114C3×#107—34no—
115C3×#102—34no—
116#832—34no—
117#821—34no—
118#817—34no—
119Dic3⋊C8—34no—
120Dic3⋊C8—34no—
121#809C2×D314yes—
122#808—34no—
123#807C2×D314yescomplemented
124C23×C32C2×D411yescharacteristic
125C22×C3×D3—24no—
126C22×C3×D3—22no—
127C22×C3×D3—42no—
128C22×C3×D3—42no—
129C2×C32×C4—22no—
130C2×C32×C4—42no—
131C2×C32×C4C2×D411yescharacteristic
132C2×C32×C4C2×Q812yes—
133C2×C32×C4#4112yes—
134C2×C32×C4C2411yescharacteristic
135C2×C3⋊Dic3—22no—
136C2×C3⋊Dic3—22no—
137C2×C3⋊Dic3—22no—
138C2×C3⋊Dic3—42no—
139C2×C3⋊Dic3C2×D412yes—
140C2×C3⋊Dic3C2×D412yes—
141C2×C3×Dic3—22no—
142C2×C3×Dic3—42no—
143C3×D12—24no—
144C3×D12—22no—
145C3×D12C2×Q814yes—
146D3×Dic3—48no—
147C3×C3⋊C8—22no—
148C3×C3⋊C8—22no—
149C2×#125—91no—
150C2×C4×D4—91no—
151#478—98no—
152C2×#107—31no—
153C2×#106—91no—
154C2×C4⋊C8—91no—
155C2×#102—31no—
156C2×#102—91no—
157C24×C3—61no—
158C23×D3—21no—
159C2×C3×D4—34no—
160C2×C3×D4—32no—
161C2×C3×D4—62no—
162C2×C3×D4—61no—
163C22×C3×C4—22no—
164C22×C3×C4—21no—
165C22×C3×C4—21no—
166C22×C3×C4—21no—
167C22×C3×C4—61no—
168C22×C3×C4C22×D311yescharacteristic
169C22×C3×C4C22×D311yescharacteristic
170C22×Dic3—21no—
171C22×Dic3—31no—
172C22×Dic3—31no—
173C22×Dic3—31no—
174C22×Dic3—31no—
175C22×Dic3—61no—
176C22×Dic3—61no—
177C22×Dic3—64no—
178C22×Dic3—62no—
179C22×Dic3—61no—
180C22×Dic3—61no—
181C22×Dic3—124no—
182C2×D12—21no—
183C2×D12—22no—
184C2×D12Dic614yes—
185C2×D12C22×D312yes—
186C2×C4×D3—64no—
187C2×C4×D3—124no—
188C2×C3×C8—32no—
189C2×C3×C8—32no—
190C2×C3×C8—62no—
191C2×C3×C8—62no—
192C3×C4⋊C4—22no—
193C3×C4⋊C4—21no—
194C3×C4⋊C4—21no—
195C3×C4⋊C4—22no—
196C3×C4⋊C4—32no—
197C3×C4⋊C4—61no—
198C3×C4⋊C4C22×D312yes—
199C3×C4⋊C4C22×D312yes—
200#217—64no—
201(C2×D3)⋊C4—64no—
202C4⋊Dic3—21no—
203C4⋊Dic3—32no—
204C4⋊Dic3—32no—
205C4⋊Dic3—62no—
206C4⋊Dic3—64no—
207C4⋊Dic3—64no—
208C4⋊Dic3—68no—
209C4⋊Dic3—62no—
210C4⋊Dic3—61no—
211C4⋊Dic3—61no—
212C4⋊Dic3C22×D312yes—
213Dic3⋊C4—64no—
214Dic3⋊C4—64no—
215Dic3⋊C4—68no—
216C4×Dic3—32no—
217C4×Dic3—32no—
218C4×Dic3—32no—
219C4×Dic3—32no—
220C4×Dic3—62no—
221C4×Dic3—62no—
222C2×C3⋊C8—22no—
223C2×C3⋊C8—22no—
224C2×C3⋊C8C22×D312yes—
225C2×C3⋊C8C22×D312yes—
226C22×C32C22⋊Q812yes—
227C22×C32#13512yes—
228C22×C32AGL(1,ℤ/8)12yes—
229C22×C32C22×D411yescharacteristic
230C2×C3×D3—24no—
231C2×C3×D3—42no—
232C2×C3×D3—42no—
233C2×C3×D3—48no—
234C32×C4—42no—
235C32×C4C22⋊Q812yes—
236C32×C4C22×Q811yescharacteristic
237C32×C4C2×#4111yescharacteristic
238C3⋊Dic3—22no—
239C3⋊Dic3—22no—
240C3⋊Dic3—42no—
241C3×Dic3—42no—
242C22×D4—31no—
243C23×C4—181no—
244C22×C8—31no—
245C22×C8—31no—
246#125—94no—
247#125—182no—
248C4×D4—94no—
249C4×D4—182no—
250C2×C4⋊C4—31no—
251C2×C4⋊C4—91no—
252C2×C4⋊C4—181no—
253C2×C4⋊C4—181no—
254C2×C4⋊C4D3211yescharacteristic
255C2×C22⋊C4—181no—
256C2×C42—91no—
257#107—34no—
258#106—94no—
259C4⋊C8—94no—
260#102—34no—
261#102—94no—
262C23×C3—21no—
263C23×C3—64no—
264C23×C3—62no—
265C23×C3—122no—
266C23×C3—122no—
267C23×C3D3×D411yescharacteristic
268C23×C3D3×D411yescharacteristic
269C22×D3—24no—
270C22×D3—22no—
271C22×D3—42no—
272C22×D3—42no—
273C3×D4—34no—
274C3×D4—64no—
275C3×D4—62no—
276C2×C3×C4—24no—
277C2×C3×C4—22no—
278C2×C3×C4—22no—
279C2×C3×C4—21no—
280C2×C3×C4—22no—
281C2×C3×C4—22no—
282C2×C3×C4—21no—
283C2×C3×C4—44no—
284C2×C3×C4—42no—
285C2×C3×C4—42no—
286C2×C3×C4—62no—
287C2×C3×C4—122no—
288C2×C3×C4C2×Dic612yes—
289C2×C3×C4#23512yes—
290C2×C3×C4D3×D411yescharacteristic
291C2×C3×C4D3×D411yescharacteristic
292C2×C3×C4#23712yes—
293C2×C3×C4D3×Q812yes—
294C2×C3×C4C23×D311yescharacteristic
295C2×C3×C4C23×D311yescharacteristic
296C2×Dic3—22no—
297C2×Dic3—32no—
298C2×Dic3—32no—
299C2×Dic3—32no—
300C2×Dic3—32no—
301C2×Dic3—42no—
302C2×Dic3—62no—
303C2×Dic3—62no—
304C2×Dic3—62no—
305C2×Dic3—62no—
306C2×Dic3—62no—
307C2×Dic3—62no—
308C2×Dic3—64no—
309C2×Dic3—62no—
310C2×Dic3—62no—
311C2×Dic3—122no—
312C2×Dic3—122no—
313C2×Dic3—128no—
314C2×Dic3—124no—
315C2×Dic3—122no—
316C2×Dic3—122no—
317D12—24no—
318D12—22no—
319D12C2×Dic614yes—
320C4×D3—128no—
321C3×C8—62no—
322C3×C8—62no—
323C3⋊C8—22no—
324C3⋊C8—22no—
325C2×C32#47814yescomplemented
326C2×C32C2×C22⋊Q811yescharacteristic
327C2×C32C2×#13511yescharacteristic
328C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
329C3×D3—44no—
330C24—61no—
331C2×D4—32no—
332C2×D4—34no—
333C2×D4—62no—
334C2×D4—61no—
335C22×C4—21no—
336C22×C4—61no—
337C22×C4—91no—
338C22×C4—91no—
339C22×C4—184no—
340C22×C4—181no—
341C22×C4—364no—
342C22×C4C2×D3211yescharacteristic
343C2×C8—32no—
344C2×C8—32no—
345C2×C8—62no—
346C2×C8—62no—
347C4⋊C4—21no—
348C4⋊C4—32no—
349C4⋊C4—61no—
350C4⋊C4—92no—
351C4⋊C4—184no—
352C4⋊C4—184no—
353C4⋊C4—181no—
354C4⋊C4C2×D3212yes—
355C22⋊C4—184no—
356C42—92no—
357C42—92no—
358C22×C3—21no—
359C22×C3—22no—
360C22×C3—22no—
361C22×C3—22no—
362C22×C3—64no—
363C22×C3—128no—
364C22×C3—122no—
365C22×C3—122no—
366C22×C3#87812yes—
367C22×C3#89612yes—
368C22×C3#91112yes—
369C22×C3#91112yes—
370C22×C3#91612yes—
371C22×C3#91912yes—
372C22×C3C2×D3×D411yescharacteristic
373C22×C3C2×D3×D411yescharacteristic
374C2×D3—24no—
375C2×D3—42no—
376C2×D3—42no—
377C2×D3—48no—
378C3×C4—21no—
379C3×C4—21no—
380C3×C4—22no—
381C3×C4—44no—
382C3×C4—42no—
383C3×C4—42no—
384C3×C4—122no—
385C3×C4#87812yes—
386C3×C4#89612yes—
387C3×C4C22×Dic611yescharacteristic
388C3×C4C2×#23511yescharacteristic
389C3×C4C2×#23711yescharacteristic
390C3×C4C2×D3×Q811yescharacteristic
391Dic3—42no—
392Dic3—62no—
393Dic3—62no—
394Dic3—62no—
395Dic3—62no—
396Dic3—122no—
397Dic3—122no—
398Dic3—124no—
399Dic3—122no—
400Dic3—122no—
401C32C2×#47811yescharacteristic, complemented, Sylow
402C23—62no—
403C23—64no—
404C23—122no—
405C23—122no—
406C23#381111yescharacteristic
407D4—34no—
408D4—62no—
409D4—64no—
410C2×C4—22no—
411C2×C4—42no—
412C2×C4—62no—
413C2×C4—92no—
414C2×C4—92no—
415C2×C4—122no—
416C2×C4—182no—
417C2×C4—182no—
418C2×C4—182no—
419C2×C4—368no—
420C2×C4—362no—
421C2×C4D3×Dic612yes—
422C2×C4#379512yes—
423C2×C4#381111yescharacteristic
424C2×C4C22×D3211yescharacteristic
425C8—62no—
426C8—62no—
427C2×C3—21no—
428C2×C3—24no—
429C2×C3—21no—
430C2×C3—21no—
431C2×C3—124no—
432C2×C3#476314yescomplemented
433C2×C3#489114yescomplemented
434C2×C3C2×#87811yescharacteristic
435C2×C3C2×#89611yescharacteristic
436C2×C3C2×#91111yescharacteristic
437C2×C3C2×#91111yescharacteristic
438C2×C3C2×#91611yescharacteristic
439C2×C3C2×#91911yescharacteristic
440D3—44no—
441C22—64no—
442C22—122no—
443C22—128no—
444C22—122no—
445C22#6389612yes—
446C22#6392712yes—
447C22#6395012yes—
448C22C2×#381111yescharacteristic
449C4—42no—
450C4—122no—
451C4—182no—
452C4—182no—
453C4—362no—
454C4#6389612yes—
455C4C2×D3×Dic611yescharacteristic
456C4C2×#379511yescharacteristic
457C3—21no—
458C3C2×#476311yescharacteristic, complemented
459C3C2×#489111yescharacteristic, complemented
460C2—124no—
461C2#1059047314yesdirect product factor
462C2C2×#6389611yescharacteristic
463C2C2×#6392711yescharacteristic
464C2C2×#6395011yescharacteristic
subgroupG/H
centerC23#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#478
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×#64099C2semidirect
4. C2×C3×#807C2semidirect
5. C2×#63573C2semidirect
6. C2×#63572C2semidirect
8. #10590473C2direct (N × H)
19. #64099C22semidirect
27. C3×#807C22semidirect
28. #63573C22semidirect
29. #63572C22semidirect
45. C2×#807D3semidirect
123. #807C2×D3semidirect
325. C2×C32#478semidirect
401. C32C2×#478semidirect
432. C2×C3#4763semidirect
433. C2×C3#4891semidirect
458. C3C2×#4763semidirect
459. C3C2×#4891semidirect
461. C2#10590473direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640992
C2×#638982
C2×C3×#8092
C2×C3×#8072
C2×#635732
C2×#635722
C2×#635632
#105904732
C2×#48913
C2×#47633