Finite Group Databasebeta

← C2×#10590688 #11858481

Subgroups — C2×#10590688 #11858481

Order 1152.

1221 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3743C211yesmaximal, characteristic
2C2×#63900C211yesmaximal, characteristic
3C2×#63849C211yesmaximal, characteristic
4C2×C3×#818C211yesmaximal, characteristic, complemented
5C2×C3×#817C211yesmaximal, characteristic, complemented
6C2×#63576C211yesmaximal, characteristic, complemented
7C2×#63574C211yesmaximal, characteristic, complemented
8#10590688C218yesmaximal, direct product factor
9C2×#4881—31nomaximal
10C2×#4861—31nomaximal
11C22×C4×C3⋊D3C2211yescharacteristic
12C22×#624—21no—
13C22×C32×C8C2211yescharacteristic
14C22×C3⋊(C3⋊C8)C2211yescharacteristic
15C2×#3743C418yescomplemented
16C2×#3743C2214yes—
17C2×C3×C4⋊Dic3C2211yescharacteristic
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C2×C3×C4⋊Dic3C2211yescharacteristic
21C2×#3724—21no—
22C2×#3722—21no—
23C2×Dic32—21no—
24#63900—22no—
25#63900C2214yes—
26#63849—22no—
27#63849C2214yes—
28C3×#818C2214yescomplemented
29C3×#817C2214yescomplemented
30#63576C2214yescomplemented
31#63574C2214yescomplemented
32C22×ΓL(1,𝔽25)—31no—
33C22×ΓL(1,𝔽25)—31no—
34C22×ΓL(1,𝔽25)—61no—
35C2×#892—31no—
36C2×#892—31no—
37C2×D3×C4⋊C4—31no—
38C2×D3×C4⋊C4—31no—
39C2×C3×#107—31no—
40C2×C3×#106—31no—
41C2×#818D311yescharacteristic, complemented
42C2×#817D311yescharacteristic, complemented
43C2×#808—31no—
44C2×#808—31no—
45C2×#807—31no—
46C2×#807—31no—
47#4881—38no—
48#4861—38no—
49C23×C3⋊D3D411yescharacteristic
50C22×C32×C4C2311yescharacteristic
51C22×C3⋊Dic3D411yescharacteristic
52C2×C4×C3⋊D3C2×C414yes—
53C2×C4×C3⋊D3D412yes—
54C2×C4×C3⋊D3Q814yes—
55C2×C4×C3⋊D3C2312yes—
56C22×C3×Dic3—21no—
57C22×C3×Dic3—21no—
58C22×C3×Dic3—21no—
59C22×C3×Dic3—21no—
60C2×#624—24no—
61C2×#624—44no—
62C2×C32×C8C2×C414yescomplemented
63C2×C32×C8C2312yes—
64C2×C3⋊(C3⋊C8)C2×C414yescomplemented
65C2×C3⋊(C3⋊C8)C2312yes—
66#3743C2×C4116yescomplemented
67C3×C4⋊Dic3—21no—
68C3×C4⋊Dic3—21no—
69C3×C4⋊Dic3—21no—
70C3×C4⋊Dic3—21no—
71C3×C4⋊Dic3C2312yes—
72C3×C4⋊Dic3C2312yes—
73C3×C4⋊Dic3C2312yes—
74C3×C4⋊Dic3C2312yes—
75#3724—24no—
76#3722—24no—
77Dic32—24no—
78C2×#428—91noSylow
79C22×C4×D3—31no—
80C22×C4×D3—31no—
81C22×C4×D3—61no—
82C22×C4×D3—61no—
83C22×C4×D3—61no—
84C22×C3×C8—21no—
85C22×C3×C8C2×D311yescharacteristic
86C22×C3×C8C2×D311yescharacteristic
87C2×C3×C4⋊C4—31no—
88C2×C3×C4⋊C4—31no—
89C2×C3×C4⋊C4—31no—
90C2×C3×C4⋊C4—31no—
91C2×(C2×D3)⋊C4—61no—
92C2×(C2×D3)⋊C4—61no—
93C2×C4⋊Dic3C2×D311yescharacteristic
94C2×C4⋊Dic3C2×D311yescharacteristic
95C2×C4⋊Dic3C2×D311yescharacteristic
96C2×C4⋊Dic3C2×D311yescharacteristic
97C2×Dic3⋊C4—61no—
98C2×Dic3⋊C4—61no—
99C2×C4×Dic3—61no—
100C2×C4×Dic3—61no—
101C22×C3⋊C8—31no—
102C22×C3⋊C8—31no—
103C22×C3⋊C8—61no—
104C2×ΓL(1,𝔽25)—38no—
105C2×ΓL(1,𝔽25)—38no—
106C2×ΓL(1,𝔽25)—34no—
107C2×ΓL(1,𝔽25)—34no—
108C2×ΓL(1,𝔽25)—68no—
109C2×ΓL(1,𝔽25)—64no—
110#892—34no—
111#892—34no—
112#892—62no—
113#892—62no—
114D3×C4⋊C4—34no—
115D3×C4⋊C4—34no—
116D3×C4⋊C4—62no—
117D3×C4⋊C4—62no—
118C3×#107—34no—
119C3×#106—34no—
120#818C2×D314yescomplemented
121#817C2×D314yescomplemented
122#808—34no—
123#808—34no—
124#807—34no—
125#807—34no—
126C23×C32C2×D411yescharacteristic
127C22×C3⋊D3—22no—
128C22×C3⋊D3—22no—
129C22×C3⋊D3C4⋊C414yes—
130C22×C3⋊D3C2×D412yes—
131C2×C32×C4C22×C412yes—
132C2×C32×C4C2×D411yescharacteristic
133C2×C32×C4C2×Q812yes—
134C2×C32×C4C2411yescharacteristic
135C2×C3⋊Dic3C4⋊C414yes—
136C2×C3⋊Dic3C2×D412yes—
137C4×C3⋊D3C4⋊C418yes—
138C4×C3⋊D3C22×C414yes—
139C4×C3⋊D3C2×Q814yes—
140C2×C3×Dic3—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—
147C2×C3×Dic3—42no—
148#624—48no—
149C32×C8C22×C414yescomplemented
150C3⋊(C3⋊C8)C22×C414yescomplemented
151C22×M16—91no—
152C2×#117—91no—
153C22×C4⋊C4—91no—
154#428—98no—
155C2×#107—31no—
156C2×#107—91no—
157C2×#106—31no—
158C2×#106—91no—
159C23×D3—31no—
160C23×D3—31no—
161C23×D3—61no—
162C22×C3×C4—21no—
163C22×C3×C4—61no—
164C22×C3×C4—61no—
165C22×C3×C4—61no—
166C22×C3×C4—61no—
167C22×C3×C4C22×D311yescharacteristic
168C22×C3×C4C22×D311yescharacteristic
169C22×Dic3—21no—
170C22×Dic3—21no—
171C22×Dic3—21no—
172C22×Dic3—21no—
173C22×Dic3—31no—
174C22×Dic3—31no—
175C22×Dic3—61no—
176C2×C4×D3—34no—
177C2×C4×D3—34no—
178C2×C4×D3—32no—
179C2×C4×D3—32no—
180C2×C4×D3—34no—
181C2×C4×D3—34no—
182C2×C4×D3—32no—
183C2×C4×D3—32no—
184C2×C4×D3—64no—
185C2×C4×D3—62no—
186C2×C4×D3—62no—
187C2×C4×D3—64no—
188C2×C4×D3—64no—
189C2×C4×D3—64no—
190C2×C4×D3—124no—
191C2×C4×D3—124no—
192C2×C3×C8—24no—
193C2×C3×C8—22no—
194C2×C3×C8C4×D314yescomplemented
195C2×C3×C8C4×D314yescomplemented
196C2×C3×C8C22×D312yes—
197C2×C3×C8C22×D312yes—
198C3×C4⋊C4—32no—
199C3×C4⋊C4—32no—
200C3×C4⋊C4—32no—
201C3×C4⋊C4—32no—
202C3×C4⋊C4—61no—
203C3×C4⋊C4—61no—
204C3×C4⋊C4—61no—
205C3×C4⋊C4—61no—
206(C2×D3)⋊C4—64no—
207(C2×D3)⋊C4—64no—
208C4⋊Dic3—21no—
209C4⋊Dic3—21no—
210C4⋊Dic3—21no—
211C4⋊Dic3—21no—
212C4⋊Dic3C22×D312yes—
213C4⋊Dic3C22×D312yes—
214C4⋊Dic3C22×D312yes—
215C4⋊Dic3C22×D312yes—
216Dic3⋊C4—64no—
217Dic3⋊C4—64no—
218C4×Dic3—64no—
219C4×Dic3—64no—
220C2×C3⋊C8—34no—
221C2×C3⋊C8—34no—
222C2×C3⋊C8—32no—
223C2×C3⋊C8—32no—
224C2×C3⋊C8—64no—
225C2×C3⋊C8—62no—
226ΓL(1,𝔽25)—316no—
227ΓL(1,𝔽25)—316no—
228ΓL(1,𝔽25)—616no—
229C22×C32C2×C4⋊C412yes—
230C22×C32AGL(1,ℤ/8)12yes—
231C22×C32#13712yes—
232C22×C32C22×D411yescharacteristic
233C2×C3⋊D3—22no—
234C2×C3⋊D3—22no—
235C2×C3⋊D3—28no—
236C2×C3⋊D3C2×C4⋊C414yes—
237C32×C4C2×C4⋊C412yes—
238C32×C4C23×C411yescharacteristic
239C32×C4C22×Q811yescharacteristic
240C3⋊Dic3C2×C4⋊C414yes—
241C3×Dic3—42no—
242C3×Dic3—42no—
243C3×Dic3—42no—
244C3×Dic3—42no—
245C23×C4—91no—
246C23×C4—181no—
247C2×M16—98no—
248C2×M16—94no—
249C22×C8—91no—
250C22×C8D3211yescharacteristic
251#117—94no—
252#117—182no—
253C2×C4⋊C4—31no—
254C2×C4⋊C4—31no—
255C2×C4⋊C4—31no—
256C2×C4⋊C4—31no—
257C2×C4⋊C4—94no—
258C2×C4⋊C4—182no—
259C2×C4⋊C4—181no—
260C2×C22⋊C4—181no—
261C2×C42—181no—
262#107—34no—
263#107—94no—
264#106—34no—
265#106—94no—
266C23×C3—21no—
267C23×C3D3×D411yescharacteristic
268C23×C3D3×D411yescharacteristic
269C22×D3—34no—
270C22×D3—34no—
271C22×D3—32no—
272C22×D3—32no—
273C22×D3—64no—
274C22×D3—62no—
275C22×D3—62no—
276C22×D3—62no—
277C22×D3—62no—
278C22×D3—62no—
279C22×D3—122no—
280C22×D3—122no—
281C2×C3×C4—21no—
282C2×C3×C4—22no—
283C2×C3×C4—21no—
284C2×C3×C4—22no—
285C2×C3×C4—62no—
286C2×C3×C4—62no—
287C2×C3×C4—62no—
288C2×C3×C4—62no—
289C2×C3×C4—122no—
290C2×C3×C4—122no—
291C2×C3×C4—122no—
292C2×C3×C4—122no—
293C2×C3×C4C2×C4×D312yes—
294C2×C3×C4C2×C4×D312yes—
295C2×C3×C4D3×D411yescharacteristic
296C2×C3×C4D3×D411yescharacteristic
297C2×C3×C4D3×Q812yes—
298C2×C3×C4D3×Q812yes—
299C2×C3×C4C23×D311yescharacteristic
300C2×C3×C4C23×D311yescharacteristic
301C2×Dic3—22no—
302C2×Dic3—22no—
303C2×Dic3—22no—
304C2×Dic3—22no—
305C2×Dic3—34no—
306C2×Dic3—34no—
307C2×Dic3—32no—
308C2×Dic3—32no—
309C2×Dic3—42no—
310C2×Dic3—42no—
311C2×Dic3—42no—
312C2×Dic3—42no—
313C2×Dic3—64no—
314C2×Dic3—62no—
315C4×D3—38no—
316C4×D3—38no—
317C4×D3—34no—
318C4×D3—34no—
319C4×D3—34no—
320C4×D3—34no—
321C4×D3—68no—
322C4×D3—64no—
323C4×D3—64no—
324C4×D3—128no—
325C4×D3—128no—
326C3×C8—24no—
327C3×C8C2×C4×D314yescomplemented
328C3×C8C2×C4×D314yescomplemented
329C3⋊C8—34no—
330C3⋊C8—34no—
331C3⋊C8—64no—
332C2×C32#42814yescomplemented
333C2×C32C22×C4⋊C411yescharacteristic
334C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
335C2×C32C2×#13711yescharacteristic
336C3⋊D3—24no—
337C24—91no—
338C22×C4—61no—
339C22×C4—61no—
340C22×C4—61no—
341C22×C4—61no—
342C22×C4—91no—
343C22×C4—92no—
344C22×C4—94no—
345C22×C4—92no—
346C22×C4—94no—
347C22×C4—184no—
348C22×C4—364no—
349C22×C4C2×D3211yescharacteristic
350M16—916no—
351C2×C8—92no—
352C2×C8—94no—
353C2×C8#62414yescomplemented
354C2×C8C2×D3212yes—
355C4⋊C4—32no—
356C4⋊C4—32no—
357C4⋊C4—32no—
358C4⋊C4—32no—
359C4⋊C4—61no—
360C4⋊C4—61no—
361C4⋊C4—61no—
362C4⋊C4—61no—
363C4⋊C4—184no—
364C22⋊C4—184no—
365C42—184no—
366C22×C3—21no—
367C22×C3—22no—
368C22×C3—22no—
369C22×C3—22no—
370C22×C3D3×C4⋊C412yes—
371C22×C3D3×C4⋊C412yes—
372C22×C3#91112yes—
373C22×C3#91412yes—
374C22×C3#91512yes—
375C22×C3#91812yes—
376C22×C3C2×D3×D411yescharacteristic
377C22×C3C2×D3×D411yescharacteristic
378C2×D3—34no—
379C2×D3—34no—
380C2×D3—64no—
381C2×D3—68no—
382C2×D3—62no—
383C2×D3—62no—
384C2×D3—62no—
385C2×D3—62no—
386C2×D3—68no—
387C2×D3—122no—
388C2×D3—122no—
389C2×D3—128no—
390C3×C4—21no—
391C3×C4—21no—
392C3×C4—22no—
393C3×C4—122no—
394C3×C4—122no—
395C3×C4—122no—
396C3×C4—122no—
397C3×C4D3×C4⋊C412yes—
398C3×C4D3×C4⋊C412yes—
399C3×C4C22×C4×D311yescharacteristic
400C3×C4C22×C4×D311yescharacteristic
401C3×C4C2×D3×Q811yescharacteristic
402C3×C4C2×D3×Q811yescharacteristic
403Dic3—34no—
404Dic3—34no—
405Dic3—42no—
406Dic3—42no—
407Dic3—42no—
408Dic3—42no—
409Dic3—64no—
410C32C2×#42811yescharacteristic, complemented, Sylow
411C23—92no—
412C23—94no—
413C23—182no—
414C23—182no—
415C23#380211yescharacteristic
416C2×C4—62no—
417C2×C4—62no—
418C2×C4—62no—
419C2×C4—62no—
420C2×C4—92no—
421C2×C4—94no—
422C2×C4—94no—
423C2×C4—94no—
424C2×C4—98no—
425C2×C4—122no—
426C2×C4—122no—
427C2×C4—122no—
428C2×C4—122no—
429C2×C4—368no—
430C2×C4#379712yes—
431C2×C4#380211yescharacteristic
432C2×C4C2×#62412yes—
433C2×C4C22×D3211yescharacteristic
434C8—94no—
435C8C2×#62414yescomplemented
436C2×C3—21no—
437C2×C3—21no—
438C2×C3—21no—
439C2×C3—24no—
440C2×C3#486114yescomplemented
441C2×C3#488114yescomplemented
442C2×C3C2×D3×C4⋊C411yescharacteristic
443C2×C3C2×D3×C4⋊C411yescharacteristic
444C2×C3C2×#91111yescharacteristic
445C2×C3C2×#91411yescharacteristic
446C2×C3C2×#91511yescharacteristic
447C2×C3C2×#91811yescharacteristic
448D3—64no—
449D3—64no—
450D3—124no—
451C22—94no—
452C22—182no—
453C22—182no—
454C22—188no—
455C22#6379812yes—
456C22#6381112yes—
457C22#6390012yes—
458C22C2×#380211yescharacteristic
459C4—94no—
460C4—122no—
461C4—122no—
462C4—122no—
463C4—122no—
464C4#6390012yes—
465C4C2×#379711yescharacteristic
466C4C22×#62411yescharacteristic
467C3—21no—
468C3C2×#486111yescharacteristic, complemented
469C3C2×#488111yescharacteristic, complemented
470C2—184no—
471C2#1059068814yesdirect product factor
472C2C2×#6379811yescharacteristic
473C2C2×#6381111yescharacteristic
474C2C2×#6390011yescharacteristic
subgroupG/H
centerC23#3802
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×C3×#818C2semidirect
5. C2×C3×#817C2semidirect
6. C2×#63576C2semidirect
7. C2×#63574C2semidirect
8. #10590688C2direct (N × H)
15. C2×#3743C4semidirect
28. C3×#818C22semidirect
29. C3×#817C22semidirect
30. #63576C22semidirect
31. #63574C22semidirect
41. C2×#818D3semidirect
42. C2×#817D3semidirect
62. C2×C32×C8C2×C4semidirect
64. C2×C3⋊(C3⋊C8)C2×C4semidirect
66. #3743C2×C4semidirect
120. #818C2×D3semidirect
121. #817C2×D3semidirect
149. C32×C8C22×C4semidirect
150. C3⋊(C3⋊C8)C22×C4semidirect
194. C2×C3×C8C4×D3semidirect
195. C2×C3×C8C4×D3semidirect
327. C3×C8C2×C4×D3semidirect
328. C3×C8C2×C4×D3semidirect
332. C2×C32#428semidirect
353. C2×C8#624semidirect
410. C32C2×#428semidirect
435. C8C2×#624semidirect
440. C2×C3#4861semidirect
441. C2×C3#4881semidirect
468. C3C2×#4861semidirect
469. C3C2×#4881semidirect
471. C2#10590688direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37432
C2×#639002
C2×#638492
C2×C3×#8182
C2×C3×#8172
C2×#635762
C2×#635742
#105906882
C2×#48813
C2×#48613