Finite Group Databasebeta

← C2×#10590651 #11869455

Subgroups — C2×#10590651 #11869455

Order 1152.

1037 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63916C211yesmaximal, characteristic
2C2×#63849C211yesmaximal, characteristic, complemented
3C2×#63647C211yesmaximal, characteristic, complemented
4C2×C3×#821C211yesmaximal, characteristic, complemented
5C2×C3×#818C211yesmaximal, characteristic, complemented
6C2×#63574C211yesmaximal, characteristic, complemented
7C2×#63562C211yesmaximal, characteristic, complemented
8#10590651C218yesmaximal, direct product factor
9C2×#4885—31nomaximal
10C2×#4784—31nomaximal
11C22×C4×C3⋊D3C2211yescharacteristic
12C22×C3×D12C2211yescharacteristic
13C22×#626—21no—
14C22×C32×C8C2211yescharacteristic
15C22×C3⋊(C3⋊C8)C2211yescharacteristic
16C2×C3×C4⋊Dic3C2211yescharacteristic
17C2×C3×C4⋊Dic3C2211yescharacteristic
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C2×#3722—21no—
20C2×(C2×D3)⋊Dic3—21no—
21C2×Dic32—21no—
22#63916—22no—
23#63916C2214yes—
24#63849—22no—
25#63849C2214yescomplemented
26#63647C2214yescomplemented
27C3×#821C2214yescomplemented
28C3×#818C2214yescomplemented
29#63574C2214yescomplemented
30#63562C2214yescomplemented
31C2×#938—31no—
32C2×#895—31no—
33C2×#892—31no—
34C2×#892—31no—
35C2×C3×#107—31no—
36C2×C3×#102—31no—
37C2×#832—31no—
38C2×#821D311yescharacteristic, complemented
39C2×(C2×D3)⋊C8—31no—
40C2×(C2×D3)⋊C8—31no—
41C2×(C2×D3)⋊C8—61no—
42C2×#818D311yescharacteristic, complemented
43C2×#809—31no—
44C2×#808—31no—
45C2×#808—31no—
46#4885—38no—
47#4784—38no—
48C23×C3⋊D3D411yescharacteristic
49C23×C3×D3—21no—
50C22×C32×C4C2311yescharacteristic
51C22×C3⋊Dic3D411yescharacteristic
52C2×C4×C3⋊D3—22no—
53C2×C4×C3⋊D3—22no—
54C2×C4×C3⋊D3D412yes—
55C2×C4×C3⋊D3C2312yes—
56C22×C3×Dic3—21no—
57C22×C3×Dic3—21no—
58C22×C3×Dic3—21no—
59C2×C3×D12—22no—
60C2×C3×D12—22no—
61C2×C3×D12—21no—
62C2×C3×D12C2312yes—
63C2×#626—24no—
64C2×#626—44no—
65C2×C32×C8—22no—
66C2×C32×C8C2312yes—
67C2×C3⋊(C3⋊C8)—22no—
68C2×C3⋊(C3⋊C8)C2312yes—
69C3×C4⋊Dic3—21no—
70C3×C4⋊Dic3—21no—
71C3×C4⋊Dic3—21no—
72C3×C4⋊Dic3C2312yes—
73C3×C4⋊Dic3C2312yes—
74C3×C4⋊Dic3C2312yes—
75#3722—24no—
76(C2×D3)⋊Dic3—24no—
77Dic32—24no—
78C2×#482—91noSylow
79C22×C3×D4—31no—
80C22×#67—61no—
81C22×D12—61no—
82C22×D12C2×D311yescharacteristic
83C22×C4×D3—31no—
84C22×C4×D3—31no—
85C22×C4×D3—61no—
86C22×C3×C8—21no—
87C22×C3×C8C2×D311yescharacteristic
88C22×C3×C8C2×D311yescharacteristic
89C2×C3×C4⋊C4—31no—
90C2×C3×C4⋊C4—31no—
91C2×C3×C4⋊C4—31no—
92C2×#217—61no—
93#938—34no—
94#938—62no—
95C2×(C2×D3)⋊C4—61no—
96C2×(C2×D3)⋊C4—61no—
97C2×(C2×D3)⋊C4—61no—
98C2×C4⋊Dic3C2×D311yescharacteristic
99C2×C4⋊Dic3C2×D311yescharacteristic
100C2×C4⋊Dic3C2×D311yescharacteristic
101C2×C4×Dic3—61no—
102C2×C4×Dic3—61no—
103C22×C3⋊C8—31no—
104C22×C3⋊C8—31no—
105C22×C3⋊C8—61no—
106#895—34no—
107#895—62no—
108#892—34no—
109#892—34no—
110#892—62no—
111#892—62no—
112C3×#107—34no—
113C3×#102—34no—
114#832—34no—
115#821C2×D314yescomplemented
116(C2×D3)⋊C8—34no—
117(C2×D3)⋊C8—34no—
118(C2×D3)⋊C8—64no—
119#818C2×D314yescomplemented
120#809—34no—
121#808—34no—
122#808—34no—
123C23×C32C2×D411yescharacteristic
124C22×C3⋊D3—22no—
125C22×C3⋊D3—22no—
126C22×C3⋊D3—22no—
127C22×C3⋊D3C2×D412yes—
128C22×C3×D3—22no—
129C22×C3×D3—42no—
130C22×C3×D3—42no—
131C22×C3×D3—42no—
132C2×C32×C4C2×D411yescharacteristic
133C2×C32×C4#4112yes—
134C2×C32×C4#4112yes—
135C2×C32×C4C2411yescharacteristic
136C2×C3⋊Dic3—22no—
137C2×C3⋊Dic3C2×D412yes—
138C4×C3⋊D3—24no—
139C4×C3⋊D3—22no—
140C4×C3⋊D3—22no—
141C2×C3×Dic3—22no—
142C2×C3×Dic3—22no—
143C2×C3×Dic3—22no—
144C2×C3×Dic3—42no—
145C2×C3×Dic3—42no—
146C2×C3×Dic3—42no—
147C3×D12—22no—
148C3×D12—22no—
149C3×D12—42no—
150#626—48no—
151C32×C8—22no—
152C3⋊(C3⋊C8)—22no—
153C2×#121—91no—
154C2×#117—91no—
155#482—98no—
156C2×#107—31no—
157C2×#106—91no—
158C2×#102—31no—
159C2×#102—91no—
160C2×C22⋊C8—91no—
161C24×C3—61no—
162C23×D3—21no—
163C23×D3—31no—
164C23×D3—31no—
165C23×D3—61no—
166C2×C3×D4—32no—
167C2×C3×D4—62no—
168C2×C3×D4—61no—
169C2×C3×D4—62no—
170C22×C3×C4—21no—
171C22×C3×C4—61no—
172C22×C3×C4—61no—
173C22×C3×C4—61no—
174C22×C3×C4C22×D311yescharacteristic
175C22×C3×C4C22×D311yescharacteristic
176C2×#67—64no—
177C2×#67—124no—
178C22×Dic3—21no—
179C22×Dic3—21no—
180C22×Dic3—21no—
181C22×Dic3—31no—
182C22×Dic3—31no—
183C22×Dic3—61no—
184C2×D12—22no—
185C2×D12—22no—
186C2×D12—21no—
187C2×D12—64no—
188C2×D12—124no—
189C2×D12C22×D312yes—
190C2×C4×D3—32no—
191C2×C4×D3—32no—
192C2×C4×D3—32no—
193C2×C4×D3—32no—
194C2×C4×D3—62no—
195C2×C4×D3—62no—
196C2×C4×D3—62no—
197C2×C4×D3—62no—
198C2×C4×D3—62no—
199C2×C4×D3—62no—
200C2×C4×D3—122no—
201C2×C4×D3—122no—
202C2×C3×C8—22no—
203C2×C3×C8—22no—
204C2×C3×C8—22no—
205C2×C3×C8—42no—
206C2×C3×C8C22×D312yes—
207C2×C3×C8C22×D312yes—
208C3×C4⋊C4—32no—
209C3×C4⋊C4—32no—
210C3×C4⋊C4—32no—
211C3×C4⋊C4—61no—
212C3×C4⋊C4—61no—
213C3×C4⋊C4—61no—
214#217—64no—
215(C2×D3)⋊C4—64no—
216(C2×D3)⋊C4—64no—
217(C2×D3)⋊C4—64no—
218C4⋊Dic3—21no—
219C4⋊Dic3—21no—
220C4⋊Dic3—21no—
221C4⋊Dic3C22×D312yes—
222C4⋊Dic3C22×D312yes—
223C4⋊Dic3C22×D312yes—
224C4×Dic3—64no—
225C4×Dic3—64no—
226C2×C3⋊C8—32no—
227C2×C3⋊C8—32no—
228C2×C3⋊C8—62no—
229C2×C3⋊C8—62no—
230C2×C3⋊C8—62no—
231C2×C3⋊C8—122no—
232C22×C32#12312yes—
233C22×C32#13512yes—
234C22×C32AGL(1,ℤ/8)12yes—
235C22×C32C22×D411yescharacteristic
236C2×C3⋊D3—22no—
237C2×C3⋊D3—22no—
238C2×C3⋊D3—22no—
239C2×C3⋊D3—44no—
240C2×C3×D3—42no—
241C2×C3×D3—42no—
242C2×C3×D3—42no—
243C2×C3×D3—84no—
244C32×C4#12312yes—
245C32×C4C2×#4111yescharacteristic
246C32×C4C2×#4111yescharacteristic
247C3⋊Dic3—22no—
248C3×Dic3—42no—
249C3×Dic3—42no—
250C3×Dic3—42no—
251C22×D4—31no—
252C22×D4—181no—
253C23×C4—91no—
254C22×C8—91no—
255C22×C8D3211yescharacteristic
256#121—94no—
257#121—182no—
258#117—94no—
259#117—182no—
260C2×C4⋊C4—31no—
261C2×C4⋊C4—31no—
262C2×C4⋊C4—31no—
263C2×C22⋊C4—181no—
264C2×C22⋊C4—181no—
265C2×C42—181no—
266#107—34no—
267#106—94no—
268#102—34no—
269#102—94no—
270C22⋊C8—94no—
271C23×C3—21no—
272C23×C3—62no—
273C23×C3—122no—
274C23×C3—122no—
275C23×C3—122no—
276C23×C3D3×D411yescharacteristic
277C23×C3D3×D411yescharacteristic
278C22×D3—22no—
279C22×D3—32no—
280C22×D3—32no—
281C22×D3—42no—
282C22×D3—42no—
283C22×D3—42no—
284C22×D3—62no—
285C22×D3—64no—
286C22×D3—62no—
287C22×D3—62no—
288C22×D3—62no—
289C22×D3—62no—
290C22×D3—62no—
291C22×D3—62no—
292C22×D3—122no—
293C22×D3—122no—
294C3×D4—62no—
295C3×D4—62no—
296C3×D4—122no—
297C2×C3×C4—21no—
298C2×C3×C4—22no—
299C2×C3×C4—21no—
300C2×C3×C4—22no—
301C2×C3×C4—62no—
302C2×C3×C4—62no—
303C2×C3×C4—62no—
304C2×C3×C4—122no—
305C2×C3×C4—122no—
306C2×C3×C4—122no—
307C2×C3×C4#23512yes—
308C2×C3×C4#23512yes—
309C2×C3×C4D3×D411yescharacteristic
310C2×C3×C4D3×D411yescharacteristic
311C2×C3×C4#23712yes—
312C2×C3×C4#23912yes—
313C2×C3×C4C23×D311yescharacteristic
314C2×C3×C4C23×D311yescharacteristic
315#67—128no—
316C2×Dic3—22no—
317C2×Dic3—22no—
318C2×Dic3—22no—
319C2×Dic3—32no—
320C2×Dic3—32no—
321C2×Dic3—42no—
322C2×Dic3—42no—
323C2×Dic3—42no—
324C2×Dic3—62no—
325C2×Dic3—62no—
326C2×Dic3—62no—
327C2×Dic3—122no—
328D12—22no—
329D12—22no—
330D12—42no—
331D12—128no—
332C4×D3—64no—
333C4×D3—64no—
334C4×D3—62no—
335C4×D3—62no—
336C4×D3—62no—
337C4×D3—62no—
338C4×D3—122no—
339C4×D3—122no—
340C4×D3—124no—
341C3×C8—22no—
342C3×C8—22no—
343C3×C8—42no—
344C3⋊C8—62no—
345C3⋊C8—62no—
346C3⋊C8—122no—
347C2×C32#48214yescomplemented
348C2×C32C2×#12311yescharacteristic
349C2×C32C2×#13511yescharacteristic
350C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
351C3⋊D3—42no—
352C3×D3—82no—
353C24—61no—
354C24—91no—
355C2×D4—32no—
356C2×D4—62no—
357C2×D4—61no—
358C2×D4—62no—
359C2×D4—184no—
360C2×D4—364no—
361C22×C4—61no—
362C22×C4—61no—
363C22×C4—61no—
364C22×C4—91no—
365C22×C4—92no—
366C22×C4—92no—
367C22×C4—182no—
368C22×C4—182no—
369C22×C4C2×D3211yescharacteristic
370C2×C8—22no—
371C2×C8—92no—
372C2×C8—182no—
373C2×C8C2×D3212yes—
374C4⋊C4—32no—
375C4⋊C4—32no—
376C4⋊C4—32no—
377C4⋊C4—61no—
378C4⋊C4—61no—
379C4⋊C4—61no—
380C22⋊C4—184no—
381C22⋊C4—184no—
382C42—184no—
383C22×C3—21no—
384C22×C3—22no—
385C22×C3—22no—
386C22×C3—22no—
387C22×C3—122no—
388C22×C3—122no—
389C22×C3—122no—
390C22×C3—244no—
391C22×C3#88312yes—
392C22×C3#89412yes—
393C22×C3#91112yes—
394C22×C3#91212yes—
395C22×C3#91412yes—
396C22×C3#91912yes—
397C22×C3C2×D3×D411yescharacteristic
398C22×C3C2×D3×D411yescharacteristic
399C2×D3—42no—
400C2×D3—42no—
401C2×D3—42no—
402C2×D3—64no—
403C2×D3—62no—
404C2×D3—62no—
405C2×D3—62no—
406C2×D3—62no—
407C2×D3—62no—
408C2×D3—62no—
409C2×D3—84no—
410C2×D3—122no—
411C2×D3—122no—
412C2×D3—128no—
413C2×D3—124no—
414C2×D3—124no—
415C3×C4—21no—
416C3×C4—21no—
417C3×C4—22no—
418C3×C4—122no—
419C3×C4—122no—
420C3×C4—122no—
421C3×C4#88312yes—
422C3×C4#89412yes—
423C3×C4C2×#23511yescharacteristic
424C3×C4C2×#23511yescharacteristic
425C3×C4C2×#23711yescharacteristic
426C3×C4C2×#23911yescharacteristic
427Dic3—42no—
428Dic3—42no—
429Dic3—42no—
430Dic3—62no—
431Dic3—62no—
432Dic3—122no—
433C32C2×#48211yescharacteristic, complemented, Sylow
434C23—62no—
435C23—92no—
436C23—122no—
437C23—122no—
438C23—122no—
439C23—182no—
440C23—182no—
441C23—182no—
442C23#380211yescharacteristic
443D4—62no—
444D4—62no—
445D4—122no—
446D4—368no—
447C2×C4—62no—
448C2×C4—62no—
449C2×C4—62no—
450C2×C4—92no—
451C2×C4—122no—
452C2×C4—122no—
453C2×C4—122no—
454C2×C4—182no—
455C2×C4—182no—
456C2×C4—182no—
457C2×C4—184no—
458C2×C4#379912yes—
459C2×C4#380211yescharacteristic
460C2×C4#380412yes—
461C2×C4C22×D3211yescharacteristic
462C8—22no—
463C8—182no—
464C2×C3—21no—
465C2×C3—21no—
466C2×C3—21no—
467C2×C3—24no—
468C2×C3—242no—
469C2×C3#478414yescomplemented
470C2×C3#488514yescomplemented
471C2×C3C2×#88311yescharacteristic
472C2×C3C2×#89411yescharacteristic
473C2×C3C2×#91111yescharacteristic
474C2×C3C2×#91211yescharacteristic
475C2×C3C2×#91411yescharacteristic
476C2×C3C2×#91911yescharacteristic
477D3—82no—
478D3—124no—
479D3—122no—
480D3—122no—
481C22—122no—
482C22—122no—
483C22—122no—
484C22—182no—
485C22—182no—
486C22—182no—
487C22—244no—
488C22—364no—
489C22#6379812yes—
490C22#6381012yes—
491C22#6385412yes—
492C22C2×#380211yescharacteristic
493C4—122no—
494C4—122no—
495C4—122no—
496C4—182no—
497C4#6385412yes—
498C4C2×#379911yescharacteristic
499C4C2×#380411yescharacteristic
500C3—21no—
501C3C2×#478411yescharacteristic, complemented
502C3C2×#488511yescharacteristic, complemented
503C2—242no—
504C2—362no—
505C2#1059065114yesdirect product factor
506C2C2×#6379811yescharacteristic
507C2C2×#6381011yescharacteristic
508C2C2×#6385411yescharacteristic
subgroupG/H
centerC23#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC2×#63916C2
hypercenterC22×C8D32
hypocenterC32C2×#482
LCSG ▷ C2×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
2. C2×#63849C2semidirect
3. C2×#63647C2semidirect
4. C2×C3×#821C2semidirect
5. C2×C3×#818C2semidirect
6. C2×#63574C2semidirect
7. C2×#63562C2semidirect
8. #10590651C2direct (N × H)
25. #63849C22semidirect
26. #63647C22semidirect
27. C3×#821C22semidirect
28. C3×#818C22semidirect
29. #63574C22semidirect
30. #63562C22semidirect
38. C2×#821D3semidirect
42. C2×#818D3semidirect
115. #821C2×D3semidirect
119. #818C2×D3semidirect
347. C2×C32#482semidirect
433. C32C2×#482semidirect
469. C2×C3#4784semidirect
470. C2×C3#4885semidirect
501. C3C2×#4784semidirect
502. C3C2×#4885semidirect
505. C2#10590651direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#639162
C2×#638492
C2×#636472
C2×C3×#8212
C2×C3×#8182
C2×#635742
C2×#635622
#105906512
C2×#48853
C2×#47843