Finite Group Databasebeta

← C2×#10590748 #11865496

Subgroups — C2×#10590748 #11865496

Order 1152.

1157 conjugacy classes of subgroups.

The subgroup lattice has 511 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#204C211yesmaximal, characteristic
2C2×#63898C211yesmaximal, characteristic
3C2×#63873C211yesmaximal, characteristic, complemented
4C22×#3715C211yesmaximal, characteristic
5C2×#63641C211yesmaximal, characteristic, complemented
6C2×C3×#816C211yesmaximal, characteristic, complemented
7C2×#63565C211yesmaximal, characteristic, complemented
8#10590748C218yesmaximal, direct product factor
9C2×#5162—31nomaximal
10C2×#4818—31nomaximal
11C22×C3×D12C2211yescharacteristic
12C22×C3×Dic6C2211yescharacteristic
13C22×C3×Dic6C2211yescharacteristic
14C22×D3×Dic3—21no—
15C22×C32×C8C2211yescharacteristic
16C2×C4×C3⋊Dic3C2211yescharacteristic
17C22×C3⋊(C3⋊C8)C2211yescharacteristic
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C2×C3×#204—24no—
20C2×C3×#204C2214yes—
21C2×#3724—21no—
22C2×#3724—21no—
23C2×(C2×D3)⋊Dic3—21no—
24#63898—22no—
25#63898C2214yes—
26#63873—22no—
27#63873C2214yescomplemented
28C2×#3715—24no—
29C2×#3715C2214yes—
30#63641C2214yescomplemented
31C3×#816C2214yescomplemented
32#63565C2214yescomplemented
33C22×C3×SD16—31no—
34C2×#944—31no—
35C2×#944—31no—
36C22×#215—31no—
37C2×D4×Dic3—31no—
38C22×#214—31no—
39C22×#204D311yescharacteristic
40C2×#893—31no—
41C2×C3×#103—31no—
42C2×#835—31no—
43#5162—38no—
44C2×#816D311yescharacteristic, complemented
45C2×Dic3⋊C8—31no—
46C2×Dic3⋊C8—31no—
47C2×Dic3⋊C8—61no—
48C2×#810—31no—
49#4818—38no—
50C23×C3×D3—21no—
51C22×C32×C4C2311yescharacteristic
52C22×C3⋊Dic3D411yescharacteristic
53C22×C3⋊Dic3D411yescharacteristic
54C22×C3×Dic3—21no—
55C22×C3×Dic3—21no—
56C22×C3×Dic3—21no—
57C2×C3×D12—21no—
58C2×C3×D12—22no—
59C2×C3×D12D414yes—
60C2×C3×D12C2312yes—
61C2×C3×Dic6—22no—
62C2×C3×Dic6—22no—
63C2×C3×Dic6—22no—
64C2×C3×Dic6—22no—
65C2×C3×Dic6—21no—
66C2×C3×Dic6—21no—
67C2×C3×Dic6C2312yes—
68C2×C3×Dic6C2312yes—
69C2×D3×Dic3—24no—
70C2×D3×Dic3—44no—
71C2×C32×C8—22no—
72C2×C32×C8C2312yes—
73C4×C3⋊Dic3D412yes—
74C4×C3⋊Dic3C2312yes—
75C2×C3⋊(C3⋊C8)—22no—
76C2×C3⋊(C3⋊C8)C2312yes—
77C3×C4⋊Dic3—21no—
78C3×C4⋊Dic3C2312yes—
79C3×#204—28no—
80#3724—24no—
81#3724—24no—
82(C2×D3)⋊Dic3—24no—
83#3715—28no—
84C2×#461—91noSylow
85C22×C3×Q8—31no—
86C22×C3×Q8—31no—
87C22×C3×D4—31no—
88C23×Dic3—61no—
89C22×D12C2×D311yescharacteristic
90C22×C4×D3—61no—
91C22×Dic6C2×D311yescharacteristic
92C22×Dic6C2×D311yescharacteristic
93C2×C3×SD16—34no—
94C2×C3×SD16—64no—
95C22×C3×C8—21no—
96C22×C3×C8C2×D311yescharacteristic
97C22×C3×C8C2×D311yescharacteristic
98C2×C3×C4⋊C4—31no—
99C2×#217—61no—
100#944—34no—
101#944—34no—
102#944—62no—
103#944—62no—
104C2×#215—34no—
105C2×#215—64no—
106D4×Dic3—34no—
107D4×Dic3—62no—
108C2×#214—34no—
109C2×#214—64no—
110C2×(C2×D3)⋊C4—61no—
111C2×C4⋊Dic3C2×D311yescharacteristic
112C2×Dic3⋊C4—61no—
113C2×Dic3⋊C4—61no—
114C2×Dic3⋊C4—61no—
115C2×Dic3⋊C4—61no—
116C2×C4×Dic3—31no—
117C2×C4×Dic3—31no—
118C2×C4×Dic3—61no—
119C22×C3⋊C8—31no—
120C22×C3⋊C8—31no—
121C22×C3⋊C8—61no—
122C2×#204—24no—
123C2×#204C2×D314yes—
124#893—34no—
125#893—62no—
126C3×#103—34no—
127#835—34no—
128#816C2×D314yescomplemented
129Dic3⋊C8—34no—
130Dic3⋊C8—34no—
131Dic3⋊C8—64no—
132#810—34no—
133C23×C32C2×D411yescharacteristic
134C22×C3×D3—24no—
135C22×C3×D3—22no—
136C22×C3×D3—42no—
137C22×C3×D3—42no—
138C2×C32×C4C2×D411yescharacteristic
139C2×C32×C4C2×D412yes—
140C2×C32×C4#4112yes—
141C2×C32×C4C2411yescharacteristic
142C2×C3⋊Dic3—22no—
143C2×C3⋊Dic3SD1614yescomplemented
144C2×C3⋊Dic3C2×D412yes—
145C2×C3⋊Dic3C2×D412yes—
146C2×C3×Dic3—22no—
147C2×C3×Dic3—22no—
148C2×C3×Dic3—22no—
149C2×C3×Dic3—42no—
150C2×C3×Dic3—42no—
151C2×C3×Dic3—42no—
152C3×D12—24no—
153C3×D12—22no—
154C3×D12C2×D414yes—
155C3×Dic6—22no—
156C3×Dic6—22no—
157C3×Dic6—22no—
158C3×Dic6—22no—
159C3×Dic6—42no—
160C3×Dic6—42no—
161D3×Dic3—48no—
162C32×C8—22no—
163C3⋊(C3⋊C8)—22no—
164C22×SD16—31no—
165C22×SD16—91no—
166C2×C4⋊Q8—91no—
167C2×C4×D4—91no—
168#461—98no—
169C2×C4⋊C8—91no—
170C2×#103—31no—
171C2×#103—91no—
172C24×C3—61no—
173C23×D3—21no—
174C2×C3×Q8—32no—
175C2×C3×Q8—32no—
176C2×C3×Q8—61no—
177C2×C3×Q8—61no—
178C2×C3×Q8—62no—
179C2×C3×Q8—62no—
180C2×C3×Q8—62no—
181C2×C3×Q8—62no—
182C2×C3×D4—34no—
183C2×C3×D4—32no—
184C2×C3×D4—62no—
185C2×C3×D4—61no—
186C22×C3×C4—21no—
187C22×C3×C4—61no—
188C22×C3×C4—61no—
189C22×C3×C4—61no—
190C22×C3×C4C22×D311yescharacteristic
191C22×C3×C4C22×D311yescharacteristic
192C22×Dic3—21no—
193C22×Dic3—21no—
194C22×Dic3—21no—
195C22×Dic3—31no—
196C22×Dic3—31no—
197C22×Dic3—31no—
198C22×Dic3—31no—
199C22×Dic3—61no—
200C22×Dic3—61no—
201C22×Dic3—64no—
202C22×Dic3—124no—
203C2×D12—21no—
204C2×D12—22no—
205C2×D12#6714yes—
206C2×D12C22×D312yes—
207C2×C4×D3—64no—
208C2×C4×D3—124no—
209C2×Dic6—22no—
210C2×Dic6—22no—
211C2×Dic6—22no—
212C2×Dic6—22no—
213C2×Dic6—21no—
214C2×Dic6—21no—
215C2×Dic6C22×D312yes—
216C2×Dic6C22×D312yes—
217C3×SD16—68no—
218C2×C3×C8—22no—
219C2×C3×C8—22no—
220C2×C3×C8—22no—
221C2×C3×C8—42no—
222C2×C3×C8C22×D312yes—
223C2×C3×C8C22×D312yes—
224C3×C4⋊C4—32no—
225C3×C4⋊C4—61no—
226#217—64no—
227#215—68no—
228#214—68no—
229(C2×D3)⋊C4—64no—
230C4⋊Dic3—21no—
231C4⋊Dic3C22×D312yes—
232Dic3⋊C4—64no—
233Dic3⋊C4—64no—
234Dic3⋊C4—64no—
235Dic3⋊C4—64no—
236C4×Dic3—32no—
237C4×Dic3—32no—
238C4×Dic3—32no—
239C4×Dic3—32no—
240C4×Dic3—62no—
241C4×Dic3—62no—
242C2×C3⋊C8—32no—
243C2×C3⋊C8—32no—
244C2×C3⋊C8—62no—
245C2×C3⋊C8—62no—
246C2×C3⋊C8—62no—
247C2×C3⋊C8—122no—
248#204—28no—
249C22×C32#12112yes—
250C22×C32C2×SD1612yes—
251C22×C32#13712yes—
252C22×C32C22×D411yescharacteristic
253C2×C3×D3—24no—
254C2×C3×D3—42no—
255C2×C3×D3—42no—
256C2×C3×D3—48no—
257C32×C4#12112yes—
258C32×C4C22×D411yescharacteristic
259C32×C4C2×#4111yescharacteristic
260C3⋊Dic3—22no—
261C3⋊Dic3C2×SD1614yescomplemented
262C3×Dic3—42no—
263C3×Dic3—42no—
264C3×Dic3—42no—
265C22×Q8—31no—
266C22×Q8—31no—
267C22×D4—31no—
268C23×C4—181no—
269C2×SD16—34no—
270C2×SD16—64no—
271C2×SD16—94no—
272C2×SD16—184no—
273C22×C8—91no—
274C22×C8D3211yescharacteristic
275C4⋊Q8—94no—
276C4⋊Q8—182no—
277C4×D4—94no—
278C4×D4—182no—
279C2×C4⋊C4—31no—
280C2×C4⋊C4—181no—
281C2×C4⋊C4—181no—
282C2×C22⋊C4—181no—
283C2×C42—91no—
284C4⋊C8—94no—
285#103—34no—
286#103—94no—
287C23×C3—21no—
288C23×C3—64no—
289C23×C3—62no—
290C23×C3—122no—
291C23×C3—122no—
292C23×C3D3×D411yescharacteristic
293C23×C3D3×D411yescharacteristic
294C22×D3—24no—
295C22×D3—22no—
296C22×D3—42no—
297C22×D3—42no—
298C3×Q8—62no—
299C3×Q8—62no—
300C3×Q8—62no—
301C3×Q8—62no—
302C3×Q8—122no—
303C3×Q8—122no—
304C3×D4—34no—
305C3×D4—64no—
306C3×D4—62no—
307C2×C3×C4—21no—
308C2×C3×C4—22no—
309C2×C3×C4—21no—
310C2×C3×C4—22no—
311C2×C3×C4—62no—
312C2×C3×C4—62no—
313C2×C3×C4—62no—
314C2×C3×C4—122no—
315C2×C3×C4—122no—
316C2×C3×C4—122no—
317C2×C3×C4#23512yes—
318C2×C3×C4D3×D411yescharacteristic
319C2×C3×C4D3×D411yescharacteristic
320C2×C3×C4D3×D412yes—
321C2×C3×C4#23712yes—
322C2×C3×C4C2×#6712yes—
323C2×C3×C4C23×D311yescharacteristic
324C2×C3×C4C23×D311yescharacteristic
325C2×Dic3—22no—
326C2×Dic3—22no—
327C2×Dic3—22no—
328C2×Dic3—34no—
329C2×Dic3—34no—
330C2×Dic3—32no—
331C2×Dic3—32no—
332C2×Dic3—32no—
333C2×Dic3—32no—
334C2×Dic3—42no—
335C2×Dic3—42no—
336C2×Dic3—42no—
337C2×Dic3—64no—
338C2×Dic3—62no—
339C2×Dic3—62no—
340C2×Dic3—62no—
341C2×Dic3—62no—
342C2×Dic3—122no—
343C2×Dic3—128no—
344D12—24no—
345D12—22no—
346D12C2×#6714yes—
347C4×D3—128no—
348Dic6—22no—
349Dic6—22no—
350Dic6—22no—
351Dic6—22no—
352Dic6—42no—
353Dic6—42no—
354C3×C8—22no—
355C3×C8—22no—
356C3×C8—42no—
357C3⋊C8—62no—
358C3⋊C8—62no—
359C3⋊C8—122no—
360C2×C32#46114yescomplemented
361C2×C32C2×#12111yescharacteristic
362C2×C32C22×SD1611yescharacteristic
363C2×C32C2×#13711yescharacteristic
364C3×D3—44no—
365C24—61no—
366C2×Q8—32no—
367C2×Q8—32no—
368C2×Q8—61no—
369C2×Q8—61no—
370C2×Q8—62no—
371C2×Q8—62no—
372C2×Q8—62no—
373C2×Q8—62no—
374C2×D4—32no—
375C2×D4—34no—
376C2×D4—62no—
377C2×D4—61no—
378C22×C4—61no—
379C22×C4—61no—
380C22×C4—61no—
381C22×C4—91no—
382C22×C4—91no—
383C22×C4—184no—
384C22×C4—364no—
385C22×C4C2×D3211yescharacteristic
386SD16—68no—
387SD16—188no—
388C2×C8—22no—
389C2×C8—92no—
390C2×C8—182no—
391C2×C8C2×D3212yes—
392C4⋊C4—32no—
393C4⋊C4—61no—
394C4⋊C4—184no—
395C4⋊C4—184no—
396C22⋊C4—184no—
397C42—92no—
398C42—92no—
399C22×C3—21no—
400C22×C3—22no—
401C22×C3—22no—
402C22×C3—22no—
403C22×C3—64no—
404C22×C3—122no—
405C22×C3—122no—
406C22×C3—128no—
407C22×C3#88412yes—
408C22×C3D3×SD1612yes—
409C22×C3D3×SD1612yes—
410C22×C3#91512yes—
411C22×C3#91812yes—
412C22×C3#93912yes—
413C22×C3C2×D3×D411yescharacteristic
414C22×C3C2×D3×D411yescharacteristic
415C2×D3—24no—
416C2×D3—48no—
417C2×D3—42no—
418C2×D3—42no—
419C3×C4—21no—
420C3×C4—21no—
421C3×C4—22no—
422C3×C4—122no—
423C3×C4—122no—
424C3×C4—122no—
425C3×C4#88412yes—
426C3×C4#93912yes—
427C3×C4C2×#23511yescharacteristic
428C3×C4C2×D3×D411yescharacteristic
429C3×C4C2×#23711yescharacteristic
430C3×C4C22×#6711yescharacteristic
431Dic3—34no—
432Dic3—34no—
433Dic3—42no—
434Dic3—42no—
435Dic3—42no—
436Dic3—64no—
437Dic3—62no—
438Dic3—62no—
439Dic3—122no—
440C32C2×#46111yescharacteristic, complemented, Sylow
441C23—62no—
442C23—64no—
443C23—122no—
444C23—122no—
445C23#380211yescharacteristic
446Q8—62no—
447Q8—62no—
448Q8—62no—
449Q8—62no—
450Q8—122no—
451Q8—122no—
452D4—34no—
453D4—62no—
454D4—64no—
455C2×C4—62no—
456C2×C4—62no—
457C2×C4—62no—
458C2×C4—92no—
459C2×C4—94no—
460C2×C4—92no—
461C2×C4—122no—
462C2×C4—122no—
463C2×C4—122no—
464C2×C4—182no—
465C2×C4—368no—
466C2×C4#379512yes—
467C2×C4#380211yescharacteristic
468C2×C4D3×#6712yes—
469C2×C4C22×D3211yescharacteristic
470C8—22no—
471C8—182no—
472C2×C3—24no—
473C2×C3—21no—
474C2×C3—21no—
475C2×C3—21no—
476C2×C3—124no—
477C2×C3#481814yescomplemented
478C2×C3#516214yescomplemented
479C2×C3C2×#88411yescharacteristic
480C2×C3C2×D3×SD1611yescharacteristic
481C2×C3C2×D3×SD1611yescharacteristic
482C2×C3C2×#91511yescharacteristic
483C2×C3C2×#91811yescharacteristic
484C2×C3C2×#93911yescharacteristic
485D3—44no—
486C22—64no—
487C22—128no—
488C22—122no—
489C22—122no—
490C22#6379612yes—
491C22#6381112yes—
492C22#6388512yes—
493C22C2×#380211yescharacteristic
494C4—94no—
495C4—122no—
496C4—122no—
497C4—122no—
498C4—182no—
499C4#6388512yes—
500C4C2×#379511yescharacteristic
501C4C2×D3×#6711yescharacteristic
502C3—21no—
503C3C2×#481811yescharacteristic, complemented
504C3C2×#516211yescharacteristic, complemented
505C2—124no—
506C2#1059074814yesdirect product factor
507C2C2×#6379611yescharacteristic
508C2C2×#6381111yescharacteristic
509C2C2×#6388511yescharacteristic
subgroupG/H
centerC23#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
hypercenterC22×C8D32
hypocenterC32C2×#461
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
3. C2×#63873C2semidirect
5. C2×#63641C2semidirect
6. C2×C3×#816C2semidirect
7. C2×#63565C2semidirect
8. #10590748C2direct (N × H)
27. #63873C22semidirect
30. #63641C22semidirect
31. C3×#816C22semidirect
32. #63565C22semidirect
44. C2×#816D3semidirect
128. #816C2×D3semidirect
143. C2×C3⋊Dic3SD16semidirect
261. C3⋊Dic3C2×SD16semidirect
360. C2×C32#461semidirect
440. C32C2×#461semidirect
477. C2×C3#4818semidirect
478. C2×C3#5162semidirect
503. C3C2×#4818semidirect
504. C3C2×#5162semidirect
506. C2#10590748direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#2042
C2×#638982
C2×#638732
C22×#37152
C2×#636412
C2×C3×#8162
C2×#635652
#105907482
C2×#51623
C2×#48183