Finite Group Databasebeta

← C2×#10590681 #11858482

Subgroups — C2×#10590681 #11858482

Order 1152.

1137 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×ΓL(1,𝔽25)C211yesmaximal, characteristic
2C2×D3×C4⋊Dic3C211yesmaximal, characteristic
3C2×#63841C211yesmaximal, characteristic
4C2×#63645C211yesmaximal, characteristic, complemented
5C2×C3×#817C211yesmaximal, characteristic, complemented
6C2×#63575C211yesmaximal, characteristic, complemented
7C2×#63573C211yesmaximal, characteristic, complemented
8#10590681C218yesmaximal, direct product factor
9C2×#5121—31nomaximal
10C2×#4861—31nomaximal
11C22×C3×C4×D3C2211yescharacteristic
12C22×D3×Dic3—21no—
13C22×C32×C8C2211yescharacteristic
14C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
15C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
16C2×C3×C4⋊Dic3C2211yescharacteristic
17C2×C3×C4⋊Dic3C2211yescharacteristic
18C22×C3×C3⋊C8C2211yescharacteristic
19C2×C3×ΓL(1,𝔽25)C418yescomplemented
20C2×C3×ΓL(1,𝔽25)C2214yes—
21C2×Dic3⋊Dic3—21no—
22C2×(C2×D3)⋊Dic3—21no—
23C2×Dic32—21no—
24D3×C4⋊Dic3—22no—
25D3×C4⋊Dic3C2214yes—
26#63841—22no—
27#63841C2214yes—
28#63645C2214yescomplemented
29C3×#817C2214yescomplemented
30#63575C2214yescomplemented
31#63573C2214yescomplemented
32C22×C3×M16—31no—
33C2×#926—31no—
34C22×C4⋊Dic3—31no—
35C22×ΓL(1,𝔽25)D311yescharacteristic
36C2×#892—31no—
37C2×D3×C4⋊C4—31no—
38C2×C3×#106—31no—
39#5121—38no—
40C2×#818—31no—
41C2×#818—31no—
42C2×#818—31no—
43C2×#818—61no—
44C2×#817—31no—
45C2×#817D311yescharacteristic, complemented
46C2×#808—31no—
47C2×#807—31no—
48#4861—38no—
49C23×C3×D3D411yescharacteristic
50C22×C32×C4C2311yescharacteristic
51C22×C3⋊Dic3—21no—
52C22×C3⋊Dic3—21no—
53C22×C3×Dic3—21no—
54C22×C3×Dic3—21no—
55C22×C3×Dic3D411yescharacteristic
56C2×C3×C4×D3C2×C414yes—
57C2×C3×C4×D3D412yes—
58C2×C3×C4×D3Q814yes—
59C2×C3×C4×D3C2312yes—
60C2×D3×Dic3—24no—
61C2×D3×Dic3—44no—
62C2×C32×C8C2×C414yescomplemented
63C2×C32×C8C2312yes—
64C4⋊(C3⋊Dic3)—21no—
65C4⋊(C3⋊Dic3)—21no—
66C4⋊(C3⋊Dic3)C2312yes—
67C4⋊(C3⋊Dic3)C2312yes—
68C3×C4⋊Dic3—21no—
69C3×C4⋊Dic3—21no—
70C3×C4⋊Dic3C2312yes—
71C3×C4⋊Dic3C2312yes—
72C2×C3×C3⋊C8C2×C414yescomplemented
73C2×C3×C3⋊C8C2312yes—
74C3×ΓL(1,𝔽25)C2×C4116yescomplemented
75Dic3⋊Dic3—24no—
76(C2×D3)⋊Dic3—24no—
77Dic32—24no—
78C2×#428—91noSylow
79C23×C3×C4—31no—
80C23×Dic3—61no—
81C22×C4×D3—61no—
82C22×C4×D3C2×D311yescharacteristic
83C2×C3×M16—38no—
84C2×C3×M16—34no—
85C22×C3×C8—21no—
86C22×C3×C8—31no—
87C22×C3×C8C2×D311yescharacteristic
88C22×C3×C8C2×D311yescharacteristic
89C2×C3×C4⋊C4—31no—
90C2×C3×C4⋊C4—31no—
91C2×#217—61no—
92C2×(C2×D3)⋊C4—61no—
93#926—34no—
94#926—62no—
95C2×C4⋊Dic3—31no—
96C2×C4⋊Dic3—31no—
97C2×C4⋊Dic3—31no—
98C2×C4⋊Dic3—31no—
99C2×C4⋊Dic3—34no—
100C2×C4⋊Dic3—61no—
101C2×C4⋊Dic3—61no—
102C2×C4⋊Dic3—62no—
103C2×C4⋊Dic3—61no—
104C2×C4⋊Dic3C2×D311yescharacteristic
105C2×C4⋊Dic3C2×D311yescharacteristic
106C2×Dic3⋊C4—61no—
107C2×C4×Dic3—61no—
108C2×C4×Dic3—61no—
109C22×C3⋊C8C2×D311yescharacteristic
110C2×ΓL(1,𝔽25)Dic318yescomplemented
111C2×ΓL(1,𝔽25)C2×D314yes—
112#892—34no—
113#892—62no—
114D3×C4⋊C4—34no—
115D3×C4⋊C4—62no—
116C3×#106—34no—
117#818—34no—
118#818—34no—
119#818—34no—
120#818—64no—
121#817—34no—
122#817C2×D314yescomplemented
123#808—34no—
124#807—34no—
125C23×C32C2×D411yescharacteristic
126C22×C3×D3—22no—
127C22×C3×D3—22no—
128C22×C3×D3C4⋊C414yes—
129C22×C3×D3C2×D412yes—
130C2×C32×C4C22×C412yes—
131C2×C32×C4C2×D411yescharacteristic
132C2×C32×C4C2×Q812yes—
133C2×C32×C4C2411yescharacteristic
134C2×C3⋊Dic3—22no—
135C2×C3⋊Dic3—22no—
136C2×C3⋊Dic3—42no—
137C2×C3⋊Dic3—42no—
138C2×C3×Dic3—22no—
139C2×C3×Dic3—22no—
140C2×C3×Dic3—42no—
141C2×C3×Dic3—42no—
142C2×C3×Dic3C4⋊C414yes—
143C2×C3×Dic3C2×D412yes—
144C3×C4×D3C4⋊C418yes—
145C3×C4×D3C22×C414yes—
146C3×C4×D3C2×Q814yes—
147D3×Dic3—48no—
148C32×C8C22×C414yescomplemented
149C3×C3⋊C8C22×C414yescomplemented
150C22×M16—31no—
151C2×#117—91no—
152C22×C4⋊C4—91no—
153#428—98no—
154C2×#107—91no—
155C2×#107—91no—
156C2×#106—31no—
157C2×#106—91no—
158C24×C3—31no—
159C23×D3D1211yescharacteristic
160C22×C3×C4—21no—
161C22×C3×C4—31no—
162C22×C3×C4—34no—
163C22×C3×C4—32no—
164C22×C3×C4—34no—
165C22×C3×C4—32no—
166C22×C3×C4—61no—
167C22×C3×C4—61no—
168C22×C3×C4C22×D311yescharacteristic
169C22×C3×C4C22×D311yescharacteristic
170C22×Dic3—21no—
171C22×Dic3—21no—
172C22×Dic3—64no—
173C22×Dic3—61no—
174C22×Dic3—61no—
175C22×Dic3—61no—
176C22×Dic3—61no—
177C22×Dic3—121no—
178C22×Dic3—121no—
179C22×Dic3—124no—
180C22×Dic3D1211yescharacteristic
181C2×C4×D3—64no—
182C2×C4×D3—124no—
183C2×C4×D3Dic614yes—
184C2×C4×D3D1212yes—
185C2×C4×D3C2×Dic314yes—
186C2×C4×D3C22×D312yes—
187C3×M16—316no—
188C2×C3×C8—24no—
189C2×C3×C8—22no—
190C2×C3×C8—34no—
191C2×C3×C8—32no—
192C2×C3×C8C4×D314yescomplemented
193C2×C3×C8C2×Dic314yescomplemented
194C2×C3×C8C22×D312yes—
195C2×C3×C8C22×D312yes—
196C3×C4⋊C4—32no—
197C3×C4⋊C4—32no—
198C3×C4⋊C4—61no—
199C3×C4⋊C4—61no—
200#217—64no—
201(C2×D3)⋊C4—64no—
202C4⋊Dic3—21no—
203C4⋊Dic3—21no—
204C4⋊Dic3—32no—
205C4⋊Dic3—32no—
206C4⋊Dic3—32no—
207C4⋊Dic3—32no—
208C4⋊Dic3—62no—
209C4⋊Dic3—62no—
210C4⋊Dic3—64no—
211C4⋊Dic3—61no—
212C4⋊Dic3—61no—
213C4⋊Dic3—61no—
214C4⋊Dic3—61no—
215C4⋊Dic3—121no—
216C4⋊Dic3—121no—
217C4⋊Dic3C22×D312yes—
218C4⋊Dic3C22×D312yes—
219Dic3⋊C4—64no—
220C4×Dic3—64no—
221C4×Dic3—64no—
222C2×C3⋊C8C2×Dic314yescomplemented
223C2×C3⋊C8C22×D312yes—
224ΓL(1,𝔽25)C2×Dic3116yescomplemented
225C22×C32C2×C4⋊C412yes—
226C22×C32AGL(1,ℤ/8)12yes—
227C22×C32#13712yes—
228C22×C32C22×D411yescharacteristic
229C2×C3×D3—22no—
230C2×C3×D3—22no—
231C2×C3×D3—28no—
232C2×C3×D3C2×C4⋊C414yes—
233C32×C4C2×C4⋊C412yes—
234C32×C4C23×C411yescharacteristic
235C32×C4C22×Q811yescharacteristic
236C3⋊Dic3—42no—
237C3⋊Dic3—42no—
238C3×Dic3—42no—
239C3×Dic3—42no—
240C3×Dic3C2×C4⋊C414yes—
241C23×C4—31no—
242C23×C4—181no—
243C2×M16—38no—
244C2×M16—34no—
245C22×C8—31no—
246C22×C8D3211yescharacteristic
247#117—94no—
248#117—182no—
249C2×C4⋊C4—31no—
250C2×C4⋊C4—31no—
251C2×C4⋊C4—94no—
252C2×C4⋊C4—91no—
253C2×C4⋊C4—91no—
254C2×C4⋊C4—182no—
255C2×C4⋊C4—181no—
256C2×C22⋊C4—181no—
257C2×C42—181no—
258#107—94no—
259#107—94no—
260#106—34no—
261#106—94no—
262C23×C3—21no—
263C23×C3—34no—
264C23×C3—32no—
265C23×C3—62no—
266C23×C3—62no—
267C23×C3C2×D1211yescharacteristic
268C23×C3D3×D411yescharacteristic
269C22×D3—22no—
270C22×D3—22no—
271C22×D3C4⋊Dic314yes—
272C22×D3C2×D1212yes—
273C2×C3×C4—21no—
274C2×C3×C4—22no—
275C2×C3×C4—21no—
276C2×C3×C4—22no—
277C2×C3×C4—34no—
278C2×C3×C4—32no—
279C2×C3×C4—38no—
280C2×C3×C4—34no—
281C2×C3×C4—34no—
282C2×C3×C4—62no—
283C2×C3×C4—62no—
284C2×C3×C4—122no—
285C2×C3×C4—122no—
286C2×C3×C4C2×Dic612yes—
287C2×C3×C4C2×C4×D312yes—
288C2×C3×C4C2×D1211yescharacteristic
289C2×C3×C4D3×D411yescharacteristic
290C2×C3×C4D3×Q812yes—
291C2×C3×C4C22×Dic312yes—
292C2×C3×C4C23×D311yescharacteristic
293C2×C3×C4C23×D311yescharacteristic
294C2×Dic3—22no—
295C2×Dic3—22no—
296C2×Dic3—42no—
297C2×Dic3—42no—
298C2×Dic3—62no—
299C2×Dic3—62no—
300C2×Dic3—62no—
301C2×Dic3—62no—
302C2×Dic3—122no—
303C2×Dic3—122no—
304C2×Dic3—128no—
305C2×Dic3—122no—
306C2×Dic3—122no—
307C2×Dic3—122no—
308C2×Dic3—122no—
309C2×Dic3—242no—
310C2×Dic3—242no—
311C2×Dic3C4⋊Dic314yes—
312C2×Dic3C2×D1212yes—
313C4×D3—128no—
314C4×D3C4⋊Dic318yes—
315C4×D3C2×Dic614yes—
316C4×D3C22×Dic314yes—
317C3×C8—24no—
318C3×C8—34no—
319C3×C8C2×C4×D314yescomplemented
320C3×C8C22×Dic314yescomplemented
321C3⋊C8C22×Dic314yescomplemented
322C2×C32#42814yescomplemented
323C2×C32C22×C4⋊C411yescharacteristic
324C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
325C2×C32C2×#13711yescharacteristic
326C3×D3—24no—
327C24—31no—
328C22×C4—31no—
329C22×C4—32no—
330C22×C4—34no—
331C22×C4—32no—
332C22×C4—34no—
333C22×C4—61no—
334C22×C4—61no—
335C22×C4—184no—
336C22×C4—181no—
337C22×C4—181no—
338C22×C4—364no—
339C22×C4C2×D3211yescharacteristic
340M16—316no—
341C2×C8—32no—
342C2×C8—34no—
343C2×C8D3×Dic314yescomplemented
344C2×C8C2×D3212yes—
345C4⋊C4—32no—
346C4⋊C4—32no—
347C4⋊C4—61no—
348C4⋊C4—61no—
349C4⋊C4—92no—
350C4⋊C4—92no—
351C4⋊C4—184no—
352C4⋊C4—181no—
353C4⋊C4—181no—
354C22⋊C4—184no—
355C42—184no—
356C22×C3—21no—
357C22×C3—22no—
358C22×C3—22no—
359C22×C3—22no—
360C22×C3—34no—
361C22×C3—62no—
362C22×C3—62no—
363C22×C3—68no—
364C22×C3D3×C4⋊C412yes—
365C22×C3#90812yes—
366C22×C3#90912yes—
367C22×C3#91412yes—
368C22×C3#91512yes—
369C22×C3C2×C4⋊Dic312yes—
370C22×C3C22×D1211yescharacteristic
371C22×C3C2×D3×D411yescharacteristic
372C2×D3—28no—
373C2×D3—22no—
374C2×D3—22no—
375C2×D3C2×C4⋊Dic314yes—
376C3×C4—21no—
377C3×C4—21no—
378C3×C4—22no—
379C3×C4—34no—
380C3×C4—122no—
381C3×C4—122no—
382C3×C4D3×C4⋊C412yes—
383C3×C4C2×C4⋊Dic312yes—
384C3×C4C22×Dic611yescharacteristic
385C3×C4C22×C4×D311yescharacteristic
386C3×C4C2×D3×Q811yescharacteristic
387C3×C4C23×Dic311yescharacteristic
388Dic3—42no—
389Dic3—42no—
390Dic3—122no—
391Dic3—122no—
392Dic3—122no—
393Dic3—122no—
394Dic3—242no—
395Dic3—242no—
396Dic3C2×C4⋊Dic314yes—
397C32C2×#42811yescharacteristic, complemented, Sylow
398C23—32no—
399C23—34no—
400C23—62no—
401C23—62no—
402C23D3×D1211yescharacteristic
403C2×C4—32no—
404C2×C4—34no—
405C2×C4—34no—
406C2×C4—34no—
407C2×C4—38no—
408C2×C4—62no—
409C2×C4—62no—
410C2×C4—122no—
411C2×C4—122no—
412C2×C4—182no—
413C2×C4—182no—
414C2×C4—368no—
415C2×C4—362no—
416C2×C4—362no—
417C2×C4D3×Dic612yes—
418C2×C4D3×D1211yescharacteristic
419C2×C4C2×D3×Dic312yes—
420C2×C4C22×D3211yescharacteristic
421C8—34no—
422C8C2×D3×Dic314yescomplemented
423C2×C3—21no—
424C2×C3—21no—
425C2×C3—21no—
426C2×C3—24no—
427C2×C3—64no—
428C2×C3#486114yescomplemented
429C2×C3#512114yescomplemented
430C2×C3C2×D3×C4⋊C411yescharacteristic
431C2×C3C2×#90811yescharacteristic
432C2×C3C2×#90911yescharacteristic
433C2×C3C2×#91411yescharacteristic
434C2×C3C2×#91511yescharacteristic
435C2×C3C22×C4⋊Dic311yescharacteristic
436D3—24no—
437C22—34no—
438C22—62no—
439C22—62no—
440C22—68no—
441C22#6379412yes—
442C22#6380012yes—
443C22D3×C4⋊Dic312yes—
444C22C2×D3×D1211yescharacteristic
445C4—34no—
446C4—122no—
447C4—122no—
448C4—362no—
449C4—362no—
450C4D3×C4⋊Dic312yes—
451C4C2×D3×Dic611yescharacteristic
452C4C22×D3×Dic311yescharacteristic
453C3—21no—
454C3C2×#486111yescharacteristic, complemented
455C3C2×#512111yescharacteristic, complemented
456C2—64no—
457C2#1059068114yesdirect product factor
458C2C2×#6379411yescharacteristic
459C2C2×#6380011yescharacteristic
460C2C2×D3×C4⋊Dic311yescharacteristic
subgroupG/H
centerC23D3×D12
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC23×C3×D3D4
cosocleC2×C32×C4C24
hypercenterC22×C8D32
hypocenterC32C2×#428
LCSG ▷ 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
4. C2×#63645C2semidirect
5. C2×C3×#817C2semidirect
6. C2×#63575C2semidirect
7. C2×#63573C2semidirect
8. #10590681C2direct (N × H)
19. C2×C3×ΓL(1,𝔽25)C4semidirect
28. #63645C22semidirect
29. C3×#817C22semidirect
30. #63575C22semidirect
31. #63573C22semidirect
45. C2×#817D3semidirect
62. C2×C32×C8C2×C4semidirect
72. C2×C3×C3⋊C8C2×C4semidirect
74. C3×ΓL(1,𝔽25)C2×C4semidirect
110. C2×ΓL(1,𝔽25)Dic3semidirect
122. #817C2×D3semidirect
148. C32×C8C22×C4semidirect
149. C3×C3⋊C8C22×C4semidirect
192. C2×C3×C8C4×D3semidirect
193. C2×C3×C8C2×Dic3semidirect
222. C2×C3⋊C8C2×Dic3semidirect
224. ΓL(1,𝔽25)C2×Dic3semidirect
319. C3×C8C2×C4×D3semidirect
320. C3×C8C22×Dic3semidirect
321. C3⋊C8C22×Dic3semidirect
322. C2×C32#428semidirect
343. C2×C8D3×Dic3semidirect
397. C32C2×#428semidirect
422. C8C2×D3×Dic3semidirect
428. C2×C3#4861semidirect
429. C2×C3#5121semidirect
454. C3C2×#4861semidirect
455. C3C2×#5121semidirect
457. C2#10590681direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×ΓL(1,𝔽25)2
C2×D3×C4⋊Dic32
C2×#638412
C2×#636452
C2×C3×#8172
C2×#635752
C2×#635732
#105906812
C2×#51213
C2×#48613