Finite Group Databasebeta

← C2×#10590571 #11858433

Subgroups — C2×#10590571 #11858433

Order 1152.

1089 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#892C211yesmaximal, characteristic
2C2×#63841C211yesmaximal, characteristic
3C22×D3×C3⋊C8C211yesmaximal, characteristic
4C2×#63635C211yesmaximal, characteristic, complemented
5C2×C3×#807C211yesmaximal, characteristic, complemented
6C2×#63575C211yesmaximal, characteristic, complemented
7C2×#63574C211yesmaximal, characteristic, complemented
8#10590571C218yesmaximal, direct product factor
9C2×#4998—31nomaximal
10C2×#4880—31nomaximal
11C22×C3×C4×D3C2211yescharacteristic
12C2×C32×C4⋊C4C2211yescharacteristic
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C22×C3⋊(C3⋊C8)C2211yescharacteristic
15C2×C3×(C2×D3)⋊C4—21no—
16C2×C3×C4⋊Dic3C2211yescharacteristic
17C2×C3×C4⋊Dic3C2211yescharacteristic
18C2×C3×C4×Dic3—21no—
19C22×C3×C3⋊C8C2211yescharacteristic
20C3×#892—22no—
21C3×#892C2214yes—
22C2×(C2×D3)⋊Dic3—21no—
23C2×Dic32—21no—
24#63841—22no—
25#63841C2214yes—
26C2×D3×C3⋊C8C418yescomplemented
27C2×D3×C3⋊C8C2214yes—
28#63635C2214yescomplemented
29C3×#807C2214yescomplemented
30#63575C2214yescomplemented
31#63574C2214yescomplemented
32C2×C3×#117—31no—
33C2×#926—31no—
34C23×C3⋊C8—31no—
35C22×D3×C8—31no—
36C2×#892—31no—
37C2×#892D311yescharacteristic
38C2×C3×#107—31no—
39C2×#818—31no—
40#4998—38no—
41C2×#808—31no—
42C2×#808—31no—
43C2×#808—31no—
44C2×#808—31no—
45C2×#808—61no—
46C2×#807—31no—
47C2×#807D311yescharacteristic, complemented
48#4880—38no—
49C23×C3×D3D411yescharacteristic
50C22×C32×C4—21no—
51C22×C32×C4C2311yescharacteristic
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—
60C32×C4⋊C4—21no—
61C32×C4⋊C4C2312yes—
62C4⋊(C3⋊Dic3)—21no—
63C4⋊(C3⋊Dic3)C2312yes—
64C2×C3⋊(C3⋊C8)C2×C414yes—
65C2×C3⋊(C3⋊C8)C2312yes—
66C3×(C2×D3)⋊C4—24no—
67C3×C4⋊Dic3—21no—
68C3×C4⋊Dic3—21no—
69C3×C4⋊Dic3C2312yes—
70C3×C4⋊Dic3C2312yes—
71C3×C4×Dic3—24no—
72C2×C3×C3⋊C8C2×C414yes—
73C2×C3×C3⋊C8C2312yes—
74(C2×D3)⋊Dic3—24no—
75Dic32—24no—
76D3×C3⋊C8C2×C4116yescomplemented
77C2×#427—91noSylow
78C23×C3×C4—31no—
79C22×C4×D3C2×D311yescharacteristic
80C22×C3×C8—31no—
81C3×#117—34no—
82C3×#117—62no—
83C2×C3×C4⋊C4—21no—
84C2×C3×C4⋊C4—31no—
85C2×C3×C4⋊C4—31no—
86C2×C3×C4⋊C4C2×D311yescharacteristic
87C2×C3×C4⋊C4C2×D311yescharacteristic
88C2×C3×C22⋊C4—61no—
89C2×C3×C42—61no—
90C2×#217—61no—
91C2×(C2×D3)⋊C4—21no—
92C2×(C2×D3)⋊C4—61no—
93#926—34no—
94#926—62no—
95C2×C4⋊Dic3—31no—
96C2×C4⋊Dic3—31no—
97C2×C4⋊Dic3—61no—
98C2×C4⋊Dic3C2×D311yescharacteristic
99C2×C4⋊Dic3C2×D311yescharacteristic
100C2×C4×Dic3—21no—
101C2×C4×Dic3—61no—
102C2×C4×Dic3—61no—
103C22×C3⋊C8—31no—
104C22×C3⋊C8—31no—
105C22×C3⋊C8—38no—
106C22×C3⋊C8—34no—
107C22×C3⋊C8—61no—
108C22×C3⋊C8C2×D311yescharacteristic
109C2×D3×C8—38no—
110C2×D3×C8—34no—
111#892—22no—
112#892—34no—
113#892—62no—
114#892C2×D314yes—
115C3×#107—34no—
116#818—34no—
117#808—34no—
118#808—34no—
119#808—34no—
120#808—34no—
121#808—64no—
122#807—34no—
123#807C2×D314yescomplemented
124C23×C32C2×D411yescharacteristic
125C22×C3×D3—22no—
126C22×C3×D3—22no—
127C22×C3×D3C4⋊C414yes—
128C22×C3×D3C2×D412yes—
129C2×C32×C4—22no—
130C2×C32×C4—42no—
131C2×C32×C4C22×C412yes—
132C2×C32×C4C2×D411yescharacteristic
133C2×C32×C4C2×Q812yes—
134C2×C32×C4C2411yescharacteristic
135C2×C3⋊Dic3—22no—
136C2×C3⋊Dic3—42no—
137C2×C3×Dic3—22no—
138C2×C3×Dic3—22no—
139C2×C3×Dic3—42no—
140C2×C3×Dic3—42no—
141C2×C3×Dic3C4⋊C414yes—
142C2×C3×Dic3C2×D412yes—
143C3×C4×D3C4⋊C418yes—
144C3×C4×D3C22×C414yes—
145C3×C4×D3C2×Q814yes—
146C3⋊(C3⋊C8)C22×C414yes—
147C3×C3⋊C8C22×C414yes—
148C23×C8—91no—
149C2×#117—31no—
150C2×#117—91no—
151#427—98no—
152C2×#107—31no—
153C2×#107—91no—
154C2×#106—91no—
155C2×#106—91no—
156C24×C3—31no—
157C23×D3#6711yescharacteristic
158C22×C3×C4—21no—
159C22×C3×C4—21no—
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—41no—
167C22×C3×C4—61no—
168C22×C3×C4—61no—
169C22×C3×C4C22×D311yescharacteristic
170C22×C3×C4C22×D311yescharacteristic
171C22×Dic3—21no—
172C22×Dic3—21no—
173C22×Dic3—61no—
174C22×Dic3—61no—
175C22×Dic3—121no—
176C22×Dic3#6711yescharacteristic
177C2×C4×D3Dic614yes—
178C2×C4×D3C4×D314yes—
179C2×C4×D3#6712yes—
180C2×C4×D3C22×D312yes—
181C2×C3×C8—34no—
182C2×C3×C8—32no—
183C3×C4⋊C4—21no—
184C3×C4⋊C4—21no—
185C3×C4⋊C4—22no—
186C3×C4⋊C4—32no—
187C3×C4⋊C4—32no—
188C3×C4⋊C4—41no—
189C3×C4⋊C4—61no—
190C3×C4⋊C4—61no—
191C3×C4⋊C4C22×D312yes—
192C3×C4⋊C4C22×D312yes—
193C3×C22⋊C4—64no—
194C3×C42—64no—
195#217—64no—
196(C2×D3)⋊C4—24no—
197(C2×D3)⋊C4—64no—
198C4⋊Dic3—21no—
199C4⋊Dic3—21no—
200C4⋊Dic3—32no—
201C4⋊Dic3—32no—
202C4⋊Dic3—62no—
203C4⋊Dic3—61no—
204C4⋊Dic3—61no—
205C4⋊Dic3—121no—
206C4⋊Dic3C22×D312yes—
207C4⋊Dic3C22×D312yes—
208C4×Dic3—24no—
209C4×Dic3—64no—
210C4×Dic3—64no—
211C2×C3⋊C8—34no—
212C2×C3⋊C8—34no—
213C2×C3⋊C8—32no—
214C2×C3⋊C8—32no—
215C2×C3⋊C8—316no—
216C2×C3⋊C8—62no—
217C2×C3⋊C8—64no—
218C2×C3⋊C8C4×D314yes—
219C2×C3⋊C8C22×D312yes—
220D3×C8—316no—
221C22×C32C2×C4⋊C412yes—
222C22×C32#13512yes—
223C22×C32#13512yes—
224C22×C32C22×D411yescharacteristic
225C2×C3×D3—22no—
226C2×C3×D3—22no—
227C2×C3×D3—28no—
228C2×C3×D3C2×C4⋊C414yes—
229C32×C4—42no—
230C32×C4C2×C4⋊C412yes—
231C32×C4C23×C411yescharacteristic
232C32×C4C22×Q811yescharacteristic
233C3⋊Dic3—42no—
234C3×Dic3—42no—
235C3×Dic3—42no—
236C3×Dic3C2×C4⋊C414yes—
237C23×C4—31no—
238C22×C8—31no—
239C22×C8—98no—
240C22×C8—94no—
241C22×C8—91no—
242#117—34no—
243#117—62no—
244#117—94no—
245#117—182no—
246C2×C4⋊C4—31no—
247C2×C4⋊C4—31no—
248C2×C4⋊C4—91no—
249C2×C4⋊C4D3211yescharacteristic
250C2×C22⋊C4—61no—
251C2×C22⋊C4—181no—
252C2×C42—61no—
253C2×C42—181no—
254#107—34no—
255#107—94no—
256#106—94no—
257#106—94no—
258C23×C3—21no—
259C23×C3—34no—
260C23×C3—32no—
261C23×C3—62no—
262C23×C3—62no—
263C23×C3D3×D411yescharacteristic
264C23×C3C2×#6711yescharacteristic
265C22×D3—22no—
266C22×D3—22no—
267C22×D3Dic3⋊C414yes—
268C22×D3C2×#6712yes—
269C2×C3×C4—22no—
270C2×C3×C4—22no—
271C2×C3×C4—21no—
272C2×C3×C4—22no—
273C2×C3×C4—22no—
274C2×C3×C4—21no—
275C2×C3×C4—34no—
276C2×C3×C4—32no—
277C2×C3×C4—38no—
278C2×C3×C4—34no—
279C2×C3×C4—34no—
280C2×C3×C4—42no—
281C2×C3×C4—42no—
282C2×C3×C4—42no—
283C2×C3×C4—62no—
284C2×C3×C4—62no—
285C2×C3×C4—82no—
286C2×C3×C4—122no—
287C2×C3×C4—122no—
288C2×C3×C4C2×Dic612yes—
289C2×C3×C4C2×C4×D312yes—
290C2×C3×C4C2×C4×D312yes—
291C2×C3×C4D3×D411yescharacteristic
292C2×C3×C4D3×Q812yes—
293C2×C3×C4C2×#6711yescharacteristic
294C2×C3×C4C23×D311yescharacteristic
295C2×C3×C4C23×D311yescharacteristic
296C2×Dic3—22no—
297C2×Dic3—22no—
298C2×Dic3—42no—
299C2×Dic3—42no—
300C2×Dic3—62no—
301C2×Dic3—62no—
302C2×Dic3—122no—
303C2×Dic3—122no—
304C2×Dic3—122no—
305C2×Dic3—242no—
306C2×Dic3Dic3⋊C414yes—
307C2×Dic3C2×#6712yes—
308C4×D3Dic3⋊C418yes—
309C4×D3C2×Dic614yes—
310C4×D3C2×C4×D314yes—
311C3×C8—34no—
312C3⋊C8—34no—
313C3⋊C8—34no—
314C3⋊C8—64no—
315C3⋊C8C2×C4×D314yes—
316C2×C32#42714yescomplemented
317C2×C32C22×C4⋊C411yescharacteristic
318C2×C32C2×#13511yescharacteristic
319C2×C32C2×#13511yescharacteristic
320C3×D3—24no—
321C24—31no—
322C22×C4—21no—
323C22×C4—31no—
324C22×C4—32no—
325C22×C4—34no—
326C22×C4—34no—
327C22×C4—32no—
328C22×C4—61no—
329C22×C4—61no—
330C22×C4—181no—
331C22×C4C2×D3211yescharacteristic
332C2×C8—32no—
333C2×C8—34no—
334C2×C8—916no—
335C2×C8—92no—
336C2×C8—94no—
337C4⋊C4—21no—
338C4⋊C4—32no—
339C4⋊C4—32no—
340C4⋊C4—61no—
341C4⋊C4—61no—
342C4⋊C4—92no—
343C4⋊C4—181no—
344C4⋊C4C2×D3212yes—
345C22⋊C4—64no—
346C22⋊C4—184no—
347C42—64no—
348C42—184no—
349C22×C3—21no—
350C22×C3—22no—
351C22×C3—22no—
352C22×C3—22no—
353C22×C3—34no—
354C22×C3—68no—
355C22×C3—62no—
356C22×C3—62no—
357C22×C3D3×C4⋊C412yes—
358C22×C3#91212yes—
359C22×C3#91912yes—
360C22×C3C2×Dic3⋊C412yes—
361C22×C3#95012yes—
362C22×C3#95012yes—
363C22×C3C2×D3×D411yescharacteristic
364C22×C3C22×#6711yescharacteristic
365C2×D3—28no—
366C2×D3—22no—
367C2×D3—22no—
368C2×D3C2×Dic3⋊C414yes—
369C3×C4—21no—
370C3×C4—21no—
371C3×C4—22no—
372C3×C4—34no—
373C3×C4—42no—
374C3×C4—42no—
375C3×C4—82no—
376C3×C4—122no—
377C3×C4—122no—
378C3×C4D3×C4⋊C412yes—
379C3×C4C2×Dic3⋊C412yes—
380C3×C4C22×Dic611yescharacteristic
381C3×C4C22×C4×D311yescharacteristic
382C3×C4C22×C4×D311yescharacteristic
383C3×C4C2×D3×Q811yescharacteristic
384Dic3—42no—
385Dic3—42no—
386Dic3—122no—
387Dic3—122no—
388Dic3—242no—
389Dic3C2×Dic3⋊C414yes—
390C32C2×#42711yescharacteristic, complemented, Sylow
391C23—32no—
392C23—34no—
393C23—62no—
394C23—62no—
395C23D3×#6711yescharacteristic
396C2×C4—22no—
397C2×C4—32no—
398C2×C4—34no—
399C2×C4—34no—
400C2×C4—34no—
401C2×C4—38no—
402C2×C4—42no—
403C2×C4—62no—
404C2×C4—62no—
405C2×C4—122no—
406C2×C4—122no—
407C2×C4—182no—
408C2×C4—362no—
409C2×C4D3×Dic612yes—
410C2×C4C4×D3212yes—
411C2×C4D3×#6711yescharacteristic
412C2×C4C22×D3211yescharacteristic
413C8—34no—
414C8—94no—
415C2×C3—21no—
416C2×C3—21no—
417C2×C3—21no—
418C2×C3—24no—
419C2×C3—64no—
420C2×C3#488014yescomplemented
421C2×C3#499814yescomplemented
422C2×C3C2×D3×C4⋊C411yescharacteristic
423C2×C3C2×#91211yescharacteristic
424C2×C3C2×#91911yescharacteristic
425C2×C3C22×Dic3⋊C411yescharacteristic
426C2×C3C2×#95011yescharacteristic
427C2×C3C2×#95011yescharacteristic
428D3—24no—
429C22—34no—
430C22—62no—
431C22—62no—
432C22—68no—
433C22D3×Dic3⋊C412yes—
434C22#6393312yes—
435C22#6394912yes—
436C22C2×D3×#6711yescharacteristic
437C4—34no—
438C4—42no—
439C4—122no—
440C4—122no—
441C4—362no—
442C4D3×Dic3⋊C412yes—
443C4C2×D3×Dic611yescharacteristic
444C4C2×C4×D3211yescharacteristic
445C3—21no—
446C3C2×#488011yescharacteristic, complemented
447C3C2×#499811yescharacteristic, complemented
448C2—64no—
449C2#1059057114yesdirect product factor
450C2C2×D3×Dic3⋊C411yescharacteristic
451C2C2×#6393311yescharacteristic
452C2C2×#6394911yescharacteristic
subgroupG/H
centerC23D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC23×C3×D3D4
cosocleC2×C32×C4C24
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#427
LCSG ▷ 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
4. C2×#63635C2semidirect
5. C2×C3×#807C2semidirect
6. C2×#63575C2semidirect
7. C2×#63574C2semidirect
8. #10590571C2direct (N × H)
26. C2×D3×C3⋊C8C4semidirect
28. #63635C22semidirect
29. C3×#807C22semidirect
30. #63575C22semidirect
31. #63574C22semidirect
47. C2×#807D3semidirect
76. D3×C3⋊C8C2×C4semidirect
123. #807C2×D3semidirect
316. C2×C32#427semidirect
390. C32C2×#427semidirect
420. C2×C3#4880semidirect
421. C2×C3#4998semidirect
446. C3C2×#4880semidirect
447. C3C2×#4998semidirect
449. C2#10590571direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#8922
C2×#638412
C22×D3×C3⋊C82
C2×#636352
C2×C3×#8072
C2×#635752
C2×#635742
#105905712
C2×#49983
C2×#48803