Finite Group Databasebeta

← C2×#10594605 #11899900

Subgroups — C2×#10594605 #11899900

Order 1152.

5265 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3802C211yesmaximal, characteristic
2C22×C4×D32C212yesmaximal, complemented
3C2×C4⋊C4×C3⋊D3C211yesmaximal, characteristic, complemented
4C2×C3×#893C212yesmaximal, complemented
5C2×#63921C212yesmaximal, complemented
6C2×Dic3×D12C212yesmaximal, complemented
7C2×C4×#624C211yesmaximal, characteristic, complemented
8C2×#63879C214yesmaximal, complemented
9#10594605C2116yesmaximal, direct product factor
10C2×C4×D3×D4—32nomaximal
11C23×D32C2212yes—
12C22×C4×C3⋊D3C2212yes—
13C22×C4×C3⋊D3C2211yescharacteristic
14C22×C3×D12C2212yes—
15C22×C3×C4×D3C2214yescomplemented
16C22×#625C2212yes—
17C22×#624C2211yescharacteristic
18C22×#624C2211yescharacteristic
19C22×D3×Dic3C2214yescomplemented
20C2×#3802C4116yescomplemented
21C2×#3802C2218yes—
22C2×C4×D32—216no—
23C2×C4×D32C22116yescomplemented
24C2×C32×C4⋊C4C2211yescharacteristic, complemented
25C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
26C2×#3750C2212yescomplemented
27C4⋊C4×C3⋊D3C2218yescomplemented
28C2×C3×(C2×D3)⋊C4C2214yescomplemented
29C2×C3×C4×Dic3C2212yescomplemented
30C3×#893C22116yescomplemented
31C2×(C2×D3)⋊Dic3C2214yescomplemented
32C2×Dic32C2212yescomplemented
33#63921C22116yescomplemented
34Dic3×D12C22116yescomplemented
35C4×#624C2218yescomplemented
36#63879C22132yescomplemented
37C22×D3×D4—32no—
38C23×C4×D3—34no—
39C2×C3×C4×D4—32no—
40C2×D4×Dic3—32no—
41C2×C4×#67—34no—
42C4×D3×D4—332no—
43C2×#893D312yescomplemented
44C2×D3×C4⋊C4—32no—
45C2×D3×C4⋊C4—61no—
46C2×#67⋊C4—34no—
47C2×D3×C22⋊C4—34no—
48C2×C4×D12—32no—
49C2×C42×D3—32no—
50C23×C3⋊D3C2311yescharacteristic
51C23×C3×D3C2314yes—
52C22×D32—28no—
53C22×D32—28no—
54C22×D32C2×C4116yescomplemented
55C22×D32C2318yes—
56C22×C32×C4C2312yes—
57C22×C32×C4C2311yescharacteristic
58C22×C3⋊Dic3C2312yes—
59C22×C3⋊Dic3C2311yescharacteristic
60C2×C4×C3⋊D3—28no—
61C2×C4×C3⋊D3C2×C418yescomplemented
62C2×C4×C3⋊D3C2318yes—
63C2×C4×C3⋊D3C2314yes—
64C22×C3×Dic3C2312yes—
65C22×C3×Dic3C2312yes—
66C2×C3×D12C2×C4116yescomplemented
67C2×C3×D12C2318yes—
68C2×C3×C4×D3—216no—
69C2×C3×C4×D3C23116yescomplemented
70C2×#625C2×C4116yescomplemented
71C2×#625C2318yes—
72C2×#624—24no—
73C2×#624D418yescomplemented
74C2×#624C2314yes—
75C2×#624C2314yes—
76C2×D3×Dic3—216no—
77C2×D3×Dic3C23116yescomplemented
78#3802C2×C4164yescomplemented
79C4×D32—264no—
80C32×C4⋊C4C2314yescomplemented
81C4⋊(C3⋊Dic3)C2314yescomplemented
82#3750C2318yescomplemented
83C3×(C2×D3)⋊C4C23116yescomplemented
84C3×C4×Dic3C2318yescomplemented
85(C2×D3)⋊Dic3C23116yescomplemented
86Dic32C2318yescomplemented
87C22×C4×D4—91noSylow
88C24×D3—34no—
89C22×C3×D4—32no—
90C23×C3×C4—34no—
91C22×#67—34no—
92C23×Dic3—34no—
93C2×D3×D4—332no—
94C2×D3×D4—316no—
95C22×D12C2×D312yes—
96C22×C4×D3—32no—
97C22×C4×D3—32no—
98C22×C4×D3—34no—
99C22×C4×D3—34no—
100C22×C4×D3—32no—
101C22×C4×D3—332no—
102C22×C4×D3—61no—
103C22×C4×D3—62no—
104C22×C4×D3—632no—
105C22×C4×D3C2×D314yescomplemented
106C3×C4×D4—316no—
107C2×C3×C4⋊C4—21no—
108C2×C3×C4⋊C4C2×D312yescomplemented
109C2×C3×C22⋊C4—34no—
110C2×C3×C42—32no—
111C2×#217—34no—
112D4×Dic3—316no—
113C4×#67—332no—
114C2×(C2×D3)⋊C4—34no—
115C2×(C2×D3)⋊C4C2×D314yescomplemented
116C2×C4⋊Dic3—32no—
117C2×C4⋊Dic3—61no—
118C2×Dic3⋊C4—34no—
119C2×Dic3⋊C4—62no—
120C2×C4×Dic3—32no—
121C2×C4×Dic3—32no—
122C2×C4×Dic3C2×D312yescomplemented
123#893C2×D3116yescomplemented
124D3×C4⋊C4—316no—
125D3×C4⋊C4—68no—
126#67⋊C4—332no—
127D3×C22⋊C4—332no—
128C4×D12—316no—
129C42×D3—316no—
130C23×C32C2411yescharacteristic
131C22×C3⋊D3C22×C414yes—
132C22×C3⋊D3C2×D414yes—
133C22×C3⋊D3#4114yes—
134C22×C3⋊D3C2412yes—
135C22×C3×D3—28no—
136C22×C3×D3—28no—
137C22×C3×D3C22×C4116yescomplemented
138C22×C3×D3C2418yes—
139C2×D32—264no—
140C2×D32—216no—
141C2×D32—216no—
142C2×D32C22×C4132yescomplemented
143C2×C32×C4—24no—
144C2×C32×C4C22×C414yescomplemented
145C2×C32×C4C2414yes—
146C2×C32×C4C2412yes—
147C2×C3⋊Dic3—24no—
148C2×C3⋊Dic3C22×C414yescomplemented
149C2×C3⋊Dic3C2414yes—
150C2×C3⋊Dic3C2412yes—
151C4×C3⋊D3—216no—
152C4×C3⋊D3C22×C4116yescomplemented
153C2×C3×Dic3—24no—
154C2×C3×Dic3C2×D418yescomplemented
155C2×C3×Dic3C2414yes—
156C2×C3×Dic3C2414yes—
157C3×D12C22×C4132yescomplemented
158C3×C4×D3—232no—
159#625C22×C4132yescomplemented
160#624—28no—
161#624C2×D4116yescomplemented
162D3×Dic3—232no—
163C23×D4—91no—
164C24×C4—92no—
165C2×C4×D4—32no—
166C2×C4×D4—92no—
167C2×C4×D4—94no—
168C2×C4×D4—916no—
169C22×C4⋊C4—91no—
170C22×C22⋊C4—92no—
171C22×C42—91no—
172C24×C3—34no—
173C23×D3—32no—
174C23×D3—332no—
175C23×D3—316no—
176C23×D3—61no—
177C23×D3—616no—
178C23×D3—616no—
179C23×D3C22×D314yes—
180C2×C3×D4—316no—
181C2×C3×D4—38no—
182C22×C3×C4—21no—
183C22×C3×C4—22no—
184C22×C3×C4—32no—
185C22×C3×C4—32no—
186C22×C3×C4—316no—
187C22×C3×C4—616no—
188C22×C3×C4C22×D314yes—
189C22×C3×C4C22×D312yes—
190C2×#67—332no—
191C2×#67—316no—
192C22×Dic3—32no—
193C22×Dic3—34no—
194C22×Dic3—316no—
195C22×Dic3—61no—
196C22×Dic3—62no—
197C22×Dic3—616no—
198C22×Dic3C22×D312yes—
199C22×Dic3C22×D312yes—
200D3×D4—3128no—
201C2×D12C4×D3116yescomplemented
202C2×D12C22×D318yes—
203C2×C4×D3—216no—
204C2×C4×D3—316no—
205C2×C4×D3—38no—
206C2×C4×D3—316no—
207C2×C4×D3—38no—
208C2×C4×D3—316no—
209C2×C4×D3—316no—
210C2×C4×D3—38no—
211C2×C4×D3—64no—
212C2×C4×D3—68no—
213C2×C4×D3—68no—
214C2×C4×D3—6128no—
215C2×C4×D3—68no—
216C2×C4×D3—616no—
217C2×C4×D3—616no—
218C2×C4×D3—128no—
219C2×C4×D3C22×D3116yescomplemented
220C3×C4⋊C4—24no—
221C3×C4⋊C4C22×D318yescomplemented
222C3×C22⋊C4—316no—
223C3×C42—38no—
224#217—316no—
225(C2×D3)⋊C4—316no—
226(C2×D3)⋊C4C22×D3116yescomplemented
227C4⋊Dic3—38no—
228C4⋊Dic3—64no—
229Dic3⋊C4—316no—
230Dic3⋊C4—68no—
231C4×Dic3—38no—
232C4×Dic3—38no—
233C4×Dic3C22×D318yescomplemented
234C22×C32C23×C412yes—
235C22×C32C22×D412yes—
236C22×C32C2×#4112yes—
237C22×C32C2511yescharacteristic
238C2×C3⋊D3C4×D4116yescomplemented
239C2×C3⋊D3C23×C414yes—
240C2×C3⋊D3C22×D414yes—
241C2×C3⋊D3C2×#4114yes—
242C2×C3×D3—232no—
243C2×C3×D3—28no—
244C2×C3×D3—28no—
245C2×C3×D3C23×C4116yescomplemented
246D32—264no—
247C32×C4—24no—
248C32×C4C23×C414yescomplemented
249C3⋊Dic3—24no—
250C3⋊Dic3C23×C414yescomplemented
251C3×Dic3—24no—
252C3×Dic3C22×D418yescomplemented
253C25—92no—
254C22×D4—32no—
255C22×D4—98no—
256C22×D4—916no—
257C22×D4—92no—
258C23×C4—34no—
259C23×C4—91no—
260C23×C4—91no—
261C23×C4—916no—
262C23×C4—94no—
263C23×C4—91no—
264C23×C4—92no—
265C23×C4—1816no—
266C4×D4—316no—
267C4×D4—916no—
268C4×D4—932no—
269C2×C4⋊C4—92no—
270C2×C4⋊C4—91no—
271C2×C4⋊C4—98no—
272C2×C4⋊C4D3211yescharacteristic, complemented
273C2×C22⋊C4—34no—
274C2×C22⋊C4—916no—
275C2×C22⋊C4—94no—
276C2×C42—32no—
277C2×C42—98no—
278C2×C42—92no—
279C23×C3—21no—
280C23×C3—316no—
281C23×C3—38no—
282C23×C3—68no—
283C23×C3—68no—
284C23×C3C23×D312yes—
285C22×D3—28no—
286C22×D3—28no—
287C22×D3—38no—
288C22×D3—38no—
289C22×D3—38no—
290C22×D3—34no—
291C22×D3—364no—
292C22×D3—64no—
293C22×D3—64no—
294C22×D3—64no—
295C22×D3—62no—
296C22×D3—632no—
297C22×D3—632no—
298C22×D3—6128no—
299C22×D3C2×C4×D3116yescomplemented
300C22×D3C23×D318yes—
301C3×D4—332no—
302C2×C3×C4—28no—
303C2×C3×C4—22no—
304C2×C3×C4—24no—
305C2×C3×C4—24no—
306C2×C3×C4—38no—
307C2×C3×C4—34no—
308C2×C3×C4—34no—
309C2×C3×C4—44no—
310C2×C3×C4—632no—
311C2×C3×C4—64no—
312C2×C3×C4C2×C4×D318yescomplemented
313C2×C3×C4C23×D318yes—
314C2×C3×C4C23×D314yes—
315#67—364no—
316C2×Dic3—24no—
317C2×Dic3—38no—
318C2×Dic3—34no—
319C2×Dic3—38no—
320C2×Dic3—64no—
321C2×Dic3—62no—
322C2×Dic3—64no—
323C2×Dic3—68no—
324C2×Dic3—632no—
325C2×Dic3—124no—
326C2×Dic3D3×D418yescomplemented
327C2×Dic3C23×D314yes—
328C2×Dic3C23×D314yes—
329D12C2×C4×D3132yescomplemented
330C4×D3—232no—
331C4×D3—332no—
332C4×D3—332no—
333C4×D3—616no—
334C4×D3—616no—
335C4×D3—632no—
336C4×D3—632no—
337C4×D3—1216no—
338C2×C32C2×C4×D414yescomplemented
339C2×C32C24×C411yescharacteristic
340C2×C32C23×D411yescharacteristic
341C2×C32C22×#4111yescharacteristic
342C3⋊D3C2×C4×D418yescomplemented
343C3×D3—216no—
344C24—34no—
345C24—98no—
346C24—916no—
347C24—91no—
348C24—188no—
349C24—188no—
350C2×D4—38no—
351C2×D4—316no—
352C2×D4—964no—
353C2×D4—98no—
354C2×D4—916no—
355C22×C4—32no—
356C22×C4—32no—
357C22×C4—316no—
358C22×C4—616no—
359C22×C4—94no—
360C22×C4—98no—
361C22×C4—94no—
362C22×C4—916no—
363C22×C4—91no—
364C22×C4—94no—
365C22×C4—98no—
366C22×C4—92no—
367C22×C4—98no—
368C22×C4—188no—
369C22×C4—1816no—
370C22×C4—1864no—
371C22×C4—184no—
372C22×C4C2×D3212yes—
373C22×C4C2×D3211yescharacteristic
374C4⋊C4—98no—
375C4⋊C4—94no—
376C4⋊C4C2×D3214yescomplemented
377C22⋊C4—316no—
378C22⋊C4—916no—
379C42—38no—
380C42—98no—
381C22×C3—22no—
382C22×C3—22no—
383C22×C3—22no—
384C22×C3—21no—
385C22×C3—316no—
386C22×C3—68no—
387C22×C3—68no—
388C22×C3—632no—
389C22×C3C22×C4×D314yes—
390C22×C3C2×D3×D414yes—
391C22×C3D3×#4114yes—
392C22×C3C24×D312yes—
393C2×D3—28no—
394C2×D3—28no—
395C2×D3—232no—
396C2×D3—38no—
397C2×D3—38no—
398C2×D3—38no—
399C2×D3—332no—
400C2×D3—64no—
401C2×D3—64no—
402C2×D3—616no—
403C2×D3—64no—
404C2×D3—6128no—
405C2×D3C22×C4×D3116yescomplemented
406C3×C4—28no—
407C3×C4—24no—
408C3×C4—38no—
409C3×C4—44no—
410C3×C4—64no—
411C3×C4C22×C4×D318yescomplemented
412Dic3—24no—
413Dic3—38no—
414Dic3—64no—
415Dic3—68no—
416Dic3—124no—
417Dic3C2×D3×D418yescomplemented
418C32C22×C4×D411yescharacteristic, complemented, Sylow
419C23—316no—
420C23—38no—
421C23—68no—
422C23—68no—
423C23—932no—
424C23—94no—
425C23—94no—
426C23—94no—
427C23—92no—
428C23—1816no—
429C23—1864no—
430C23—1816no—
431C23C22×D3211yescharacteristic
432D4—332no—
433D4—932no—
434C2×C4—24no—
435C2×C4—38no—
436C2×C4—34no—
437C2×C4—34no—
438C2×C4—632no—
439C2×C4—64no—
440C2×C4—916no—
441C2×C4—94no—
442C2×C4—92no—
443C2×C4—916no—
444C2×C4—94no—
445C2×C4—1816no—
446C2×C4—1832no—
447C2×C4—188no—
448C2×C4—184no—
449C2×C4C4×D3214yescomplemented
450C2×C4C22×D3214yes—
451C2×C4C22×D3212yes—
452C2×C3—24no—
453C2×C3—21no—
454C2×C3—21no—
455C2×C3—21no—
456C2×C3—616no—
457C2×C3C4×D3×D418yescomplemented
458C2×C3C23×C4×D312yes—
459C2×C3C22×D3×D412yes—
460C2×C3C2×D3×#4112yes—
461D3—216no—
462D3—316no—
463D3—68no—
464C22—316no—
465C22—632no—
466C22—68no—
467C22—68no—
468C22—916no—
469C22—94no—
470C22—94no—
471C22—94no—
472C22—1864no—
473C22C2×C4×D3212yes—
474C22D32×D412yes—
475C22#6431912yes—
476C22C23×D3211yescharacteristic
477C4—24no—
478C4—38no—
479C4—64no—
480C4—94no—
481C4—184no—
482C4C2×C4×D3214yescomplemented
483C3—21no—
484C3C2×C4×D3×D412yescomplemented
485C2—616no—
486C2—98no—
487C2#1059460514yesdirect product factor
488C2C22×C4×D3211yescharacteristic
489C2C2×D32×D411yescharacteristic
490C2C2×#6431911yescharacteristic
subgroupG/H
centerC23C22×D32
commutatorC2×C32C24×C4
FrattiniC22C23×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C24
prime radicalC22×#3802C2
cosocleC22×C32C25
hypercenterC2×C4⋊C4D32
hypocenterC32C22×C4×D4
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×C4×D32C2semidirect
3. C2×C4⋊C4×C3⋊D3C2semidirect
4. C2×C3×#893C2semidirect
5. C2×#63921C2semidirect
6. C2×Dic3×D12C2semidirect
7. C2×C4×#624C2semidirect
8. C2×#63879C2semidirect
9. #10594605C2direct (N × H)
15. C22×C3×C4×D3C22semidirect
19. C22×D3×Dic3C22semidirect
20. C2×#3802C4semidirect
23. C2×C4×D32C22semidirect
24. C2×C32×C4⋊C4C22semidirect
25. C2×C4⋊(C3⋊Dic3)C22semidirect
26. C2×#3750C22semidirect
27. C4⋊C4×C3⋊D3C22semidirect
28. C2×C3×(C2×D3)⋊C4C22semidirect
29. C2×C3×C4×Dic3C22semidirect
30. C3×#893C22semidirect
31. C2×(C2×D3)⋊Dic3C22semidirect
32. C2×Dic32C22semidirect
33. #63921C22semidirect
34. Dic3×D12C22semidirect
35. C4×#624C22semidirect
36. #63879C22semidirect
43. C2×#893D3semidirect
54. C22×D32C2×C4semidirect
61. C2×C4×C3⋊D3C2×C4semidirect
66. C2×C3×D12C2×C4semidirect
69. C2×C3×C4×D3C23semidirect
70. C2×#625C2×C4semidirect
73. C2×#624D4semidirect
77. C2×D3×Dic3C23semidirect
78. #3802C2×C4semidirect
80. C32×C4⋊C4C23semidirect
81. C4⋊(C3⋊Dic3)C23semidirect
82. #3750C23semidirect
83. C3×(C2×D3)⋊C4C23semidirect
84. C3×C4×Dic3C23semidirect
85. (C2×D3)⋊Dic3C23semidirect
86. Dic32C23semidirect
105. C22×C4×D3C2×D3semidirect
108. C2×C3×C4⋊C4C2×D3semidirect
115. C2×(C2×D3)⋊C4C2×D3semidirect
122. C2×C4×Dic3C2×D3semidirect
123. #893C2×D3semidirect
137. C22×C3×D3C22×C4semidirect
142. C2×D32C22×C4semidirect
144. C2×C32×C4C22×C4semidirect
148. C2×C3⋊Dic3C22×C4semidirect
152. C4×C3⋊D3C22×C4semidirect
154. C2×C3×Dic3C2×D4semidirect
157. C3×D12C22×C4semidirect
159. #625C22×C4semidirect
161. #624C2×D4semidirect
201. C2×D12C4×D3semidirect
219. C2×C4×D3C22×D3semidirect
221. C3×C4⋊C4C22×D3semidirect
226. (C2×D3)⋊C4C22×D3semidirect
233. C4×Dic3C22×D3semidirect
238. C2×C3⋊D3C4×D4semidirect
245. C2×C3×D3C23×C4semidirect
248. C32×C4C23×C4semidirect
250. C3⋊Dic3C23×C4semidirect
252. C3×Dic3C22×D4semidirect
272. C2×C4⋊C4D32semidirect
299. C22×D3C2×C4×D3semidirect
312. C2×C3×C4C2×C4×D3semidirect
326. C2×Dic3D3×D4semidirect
329. D12C2×C4×D3semidirect
338. C2×C32C2×C4×D4semidirect
342. C3⋊D3C2×C4×D4semidirect
376. C4⋊C4C2×D32semidirect
405. C2×D3C22×C4×D3semidirect
411. C3×C4C22×C4×D3semidirect
417. Dic3C2×D3×D4semidirect
418. C32C22×C4×D4semidirect
449. C2×C4C4×D32semidirect
457. C2×C3C4×D3×D4semidirect
482. C4C2×C4×D32semidirect
484. C3C2×C4×D3×D4semidirect
487. C2#10594605direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#38022
C22×C4×D322
C2×C4⋊C4×C3⋊D32
C2×C3×#8932
C2×#639212
C2×Dic3×D122
C2×C4×#6242
C2×#638792
#105946052
C2×C4×D3×D43