Finite Group Databasebeta

← C2×#10590538 #11865712

Subgroups — C2×#10590538 #11865712

Order 1152.

1149 conjugacy classes of subgroups.

The subgroup lattice has 519 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64096C211yesmaximal, characteristic, complemented
2C2×#63863C211yesmaximal, characteristic
3C22×#3719C211yesmaximal, characteristic, complemented
4C22×#3716C211yesmaximal, characteristic
5C2×C3×#810C211yesmaximal, characteristic, complemented
6C2×C3×#809C211yesmaximal, characteristic
7C2×#63572C211yesmaximal, characteristic, complemented
8#10590538C218yesmaximal, direct product factor
9C2×#4798—31nomaximal
10C2×#4767—31nomaximal
11C22×#634C2211yescharacteristic
12C22×C3×D12C2211yescharacteristic
13C22×C3×Dic6C2211yescharacteristic
14C2×C32×C4⋊C4C2211yescharacteristic
15C2×#3750—21no—
16C2×C4×C3⋊Dic3—21no—
17C2×C4×C3⋊Dic3C2211yescharacteristic
18#64096—22no—
19#64096C2214yescomplemented
20C22×C3×C3⋊C8C2211yescharacteristic
21C22×C3×C3⋊C8C2211yescharacteristic
22C2×(C2×D3)⋊Dic3—21no—
23C2×(C2×D3)⋊Dic3—21no—
24#63863—22no—
25#63863C2214yes—
26C2×#3719—24no—
27C2×#3719C2214yescomplemented
28C2×#3716—24no—
29C2×#3716C2214yes—
30C3×#810C2214yescomplemented
31C3×#809C2214yes—
32#63572C2214yescomplemented
33C2×#947—31no—
34C22×#216—31no—
35C2×#936—31no—
36C22×#214—31no—
37C22×Dic12—31no—
38C22×#204—31no—
39C2×#887—31no—
40C2×#887—31no—
41C2×#887—61no—
42C2×C3×#103—31no—
43C2×C3×#102—31no—
44C2×Dic3⋊C8—31no—
45C2×Dic3⋊C8—31no—
46C2×#810D311yescharacteristic, complemented
47C2×#809D311yescharacteristic
48#4798—38no—
49#4767—38no—
50C23×C3×D3—21no—
51C22×C32×C4—21no—
52C22×C32×C4C2311yescharacteristic
53C22×C3⋊Dic3—21no—
54C22×C3⋊Dic3D411yescharacteristic
55C22×C3⋊Dic3D411yescharacteristic
56C2×#634—21no—
57C2×#634—22no—
58C2×#634D414yes—
59C2×#634C2312yes—
60C22×C3×Dic3—21no—
61C2×C3×D12—22no—
62C2×C3×D12—22no—
63C2×C3×D12—21no—
64C2×C3×D12C2312yes—
65C2×C3×Dic6—22no—
66C2×C3×Dic6—22no—
67C2×C3×Dic6—21no—
68C2×C3×Dic6C2312yes—
69C32×C4⋊C4—21no—
70C32×C4⋊C4C2312yes—
71#3750—24no—
72C4×C3⋊Dic3—24no—
73C4×C3⋊Dic3D412yes—
74C4×C3⋊Dic3C2312yes—
75C2×C3×C3⋊C8—22no—
76C2×C3×C3⋊C8—22no—
77C2×C3×C3⋊C8C2312yes—
78C2×C3×C3⋊C8C2312yes—
79(C2×D3)⋊Dic3—24no—
80(C2×D3)⋊Dic3—24no—
81#3719—28no—
82#3716—28no—
83C2×#464—91noSylow
84C22×C3×Q8—31no—
85C22×C3×D4—31no—
86C22×D12C2×D311yescharacteristic
87C22×Dic6—31no—
88C22×Dic6—31no—
89C22×Dic6—61no—
90C22×Dic6C2×D311yescharacteristic
91C22×C3×C8—31no—
92C22×C3×C8—31no—
93C2×C3×C4⋊C4—21no—
94C2×C3×C4⋊C4C2×D311yescharacteristic
95C2×C3×C4⋊C4C2×D311yescharacteristic
96C2×#217—61no—
97C2×#217—61no—
98#947—34no—
99#947—62no—
100C2×#216—34no—
101C2×#216—64no—
102#936—34no—
103#936—62no—
104C2×#214—34no—
105C2×#214—64no—
106C2×(C2×D3)⋊C4—61no—
107C2×(C2×D3)⋊C4—61no—
108C2×Dic3⋊C4—61no—
109C2×Dic3⋊C4—61no—
110C2×Dic3⋊C4—62no—
111C2×C4×Dic3—31no—
112C2×C4×Dic3—31no—
113C2×C4×Dic3—61no—
114C2×C4×Dic3—61no—
115C2×C4×Dic3—61no—
116C2×C4×Dic3—62no—
117C22×C3⋊C8C2×D311yescharacteristic
118C22×C3⋊C8C2×D311yescharacteristic
119C2×Dic12—34no—
120C2×Dic12—64no—
121C2×#204—34no—
122C2×#204—64no—
123#887—34no—
124#887—34no—
125#887—64no—
126#887—62no—
127#887—62no—
128#887—64no—
129C3×#103—34no—
130C3×#102—34no—
131Dic3⋊C8—34no—
132Dic3⋊C8—34no—
133#810C2×D314yescomplemented
134#809C2×D314yes—
135C23×C32C2×D411yescharacteristic
136C22×C3×D3—22no—
137C22×C3×D3—42no—
138C22×C3×D3—42no—
139C22×C3×D3—42no—
140C2×C32×C4—22no—
141C2×C32×C4—42no—
142C2×C32×C4C2×D411yescharacteristic
143C2×C32×C4C2×D412yes—
144C2×C32×C4#4112yes—
145C2×C32×C4C2411yescharacteristic
146C2×C3⋊Dic3—24no—
147C2×C3⋊Dic3—22no—
148C2×C3⋊Dic3—22no—
149C2×C3⋊Dic3—22no—
150C2×C3⋊Dic3C2×D412yes—
151C2×C3⋊Dic3C2×D412yes—
152#634—24no—
153#634—22no—
154#634C2×D414yes—
155C2×C3×Dic3—22no—
156C2×C3×Dic3—42no—
157C3×D12—22no—
158C3×D12—22no—
159C3×D12—42no—
160C3×Dic6—22no—
161C3×Dic6—22no—
162C3×Dic6—42no—
163C3×C3⋊C8—22no—
164C3×C3⋊C8—22no—
165C22×Q16—91no—
166C22×SD16—91no—
167C2×#124—91no—
168C2×C4×Q8—91no—
169#464—98no—
170C2×C4⋊C8—91no—
171C2×#103—31no—
172C2×#102—31no—
173C24×C3—61no—
174C23×D3—21no—
175C2×C3×Q8—32no—
176C2×C3×Q8—61no—
177C2×C3×Q8—62no—
178C2×C3×Q8—62no—
179C2×C3×D4—32no—
180C2×C3×D4—62no—
181C2×C3×D4—62no—
182C2×C3×D4—61no—
183C22×C3×C4—22no—
184C22×C3×C4—21no—
185C22×C3×C4—21no—
186C22×C3×C4—21no—
187C22×C3×C4—61no—
188C22×C3×C4C22×D311yescharacteristic
189C22×C3×C4C22×D311yescharacteristic
190C22×Dic3—21no—
191C22×Dic3—31no—
192C22×Dic3—31no—
193C22×Dic3—31no—
194C22×Dic3—31no—
195C22×Dic3—61no—
196C22×Dic3—61no—
197C22×Dic3—62no—
198C22×Dic3—61no—
199C22×Dic3—61no—
200C2×D12—22no—
201C2×D12—22no—
202C2×D12—21no—
203C2×D12C22×D312yes—
204C2×Dic6—22no—
205C2×Dic6—22no—
206C2×Dic6—21no—
207C2×Dic6—34no—
208C2×Dic6—34no—
209C2×Dic6—32no—
210C2×Dic6—32no—
211C2×Dic6—62no—
212C2×Dic6—64no—
213C2×Dic6—62no—
214C2×Dic6—64no—
215C2×Dic6—62no—
216C2×Dic6—62no—
217C2×Dic6—61no—
218C2×Dic6—61no—
219C2×Dic6C22×D312yes—
220C2×C3×C8—32no—
221C2×C3×C8—32no—
222C2×C3×C8—62no—
223C2×C3×C8—62no—
224C3×C4⋊C4—22no—
225C3×C4⋊C4—21no—
226C3×C4⋊C4—21no—
227C3×C4⋊C4—22no—
228C3×C4⋊C4C22×D312yes—
229C3×C4⋊C4C22×D312yes—
230#217—64no—
231#217—64no—
232#216—68no—
233#214—68no—
234(C2×D3)⋊C4—64no—
235(C2×D3)⋊C4—64no—
236Dic3⋊C4—64no—
237Dic3⋊C4—64no—
238Dic3⋊C4—68no—
239C4×Dic3—32no—
240C4×Dic3—32no—
241C4×Dic3—32no—
242C4×Dic3—32no—
243C4×Dic3—62no—
244C4×Dic3—62no—
245C4×Dic3—64no—
246C4×Dic3—64no—
247C4×Dic3—68no—
248C2×C3⋊C8—22no—
249C2×C3⋊C8—22no—
250C2×C3⋊C8C22×D312yes—
251C2×C3⋊C8C22×D312yes—
252Dic12—68no—
253#204—68no—
254C22×C32#12112yes—
255C22×C32#13512yes—
256C22×C32#13712yes—
257C22×C32C22×D411yescharacteristic
258C2×C3×D3—42no—
259C2×C3×D3—42no—
260C2×C3×D3—42no—
261C2×C3×D3—84no—
262C32×C4—42no—
263C32×C4#12112yes—
264C32×C4C22×D411yescharacteristic
265C32×C4C2×#4111yescharacteristic
266C3⋊Dic3—24no—
267C3⋊Dic3—22no—
268C3⋊Dic3—22no—
269C3×Dic3—42no—
270C22×Q8—31no—
271C22×Q8—91no—
272C22×D4—31no—
273C2×Q16—94no—
274C2×Q16—184no—
275C2×SD16—94no—
276C2×SD16—184no—
277C22×C8—31no—
278C22×C8—31no—
279#124—94no—
280#124—182no—
281C4×Q8—94no—
282C4×Q8—182no—
283C2×C4⋊C4—181no—
284C2×C4⋊C4D3211yescharacteristic
285C2×C22⋊C4—181no—
286C2×C22⋊C4—181no—
287C2×C42—91no—
288C2×C42—181no—
289C4⋊C8—94no—
290#103—34no—
291#102—34no—
292C23×C3—21no—
293C23×C3—62no—
294C23×C3—122no—
295C23×C3—122no—
296C23×C3—122no—
297C23×C3D3×D411yescharacteristic
298C23×C3D3×D411yescharacteristic
299C22×D3—22no—
300C22×D3—42no—
301C22×D3—42no—
302C22×D3—42no—
303C3×Q8—62no—
304C3×Q8—62no—
305C3×Q8—122no—
306C3×D4—62no—
307C3×D4—62no—
308C3×D4—122no—
309C2×C3×C4—24no—
310C2×C3×C4—22no—
311C2×C3×C4—22no—
312C2×C3×C4—21no—
313C2×C3×C4—22no—
314C2×C3×C4—22no—
315C2×C3×C4—21no—
316C2×C3×C4—44no—
317C2×C3×C4—42no—
318C2×C3×C4—42no—
319C2×C3×C4—62no—
320C2×C3×C4—122no—
321C2×C3×C4#23512yes—
322C2×C3×C4#23512yes—
323C2×C3×C4D3×D412yes—
324C2×C3×C4D3×D412yes—
325C2×C3×C4D3×D411yescharacteristic
326C2×C3×C4D3×D411yescharacteristic
327C2×C3×C4C23×D311yescharacteristic
328C2×C3×C4C23×D311yescharacteristic
329C2×Dic3—22no—
330C2×Dic3—32no—
331C2×Dic3—32no—
332C2×Dic3—32no—
333C2×Dic3—32no—
334C2×Dic3—42no—
335C2×Dic3—62no—
336C2×Dic3—62no—
337C2×Dic3—64no—
338C2×Dic3—68no—
339C2×Dic3—64no—
340C2×Dic3—64no—
341C2×Dic3—64no—
342C2×Dic3—62no—
343C2×Dic3—62no—
344C2×Dic3—62no—
345C2×Dic3—62no—
346C2×Dic3—62no—
347C2×Dic3—62no—
348C2×Dic3—122no—
349D12—22no—
350D12—22no—
351D12—42no—
352Dic6—22no—
353Dic6—22no—
354Dic6—34no—
355Dic6—34no—
356Dic6—42no—
357Dic6—64no—
358Dic6—64no—
359Dic6—68no—
360Dic6—64no—
361Dic6—64no—
362Dic6—62no—
363Dic6—62no—
364C3×C8—62no—
365C3×C8—62no—
366C3⋊C8—22no—
367C3⋊C8—22no—
368C2×C32#46414yescomplemented
369C2×C32C2×#12111yescharacteristic
370C2×C32C2×#13511yescharacteristic
371C2×C32C2×#13711yescharacteristic
372C3×D3—82no—
373C24—61no—
374C2×Q8—32no—
375C2×Q8—61no—
376C2×Q8—62no—
377C2×Q8—62no—
378C2×Q8—92no—
379C2×Q8—94no—
380C2×Q8—182no—
381C2×Q8—181no—
382C2×D4—32no—
383C2×D4—62no—
384C2×D4—62no—
385C2×D4—61no—
386C22×C4—21no—
387C22×C4—61no—
388C22×C4—91no—
389C22×C4—91no—
390C22×C4—181no—
391C22×C4C2×D3211yescharacteristic
392Q16—188no—
393SD16—188no—
394C2×C8—32no—
395C2×C8—32no—
396C2×C8—62no—
397C2×C8—62no—
398C4⋊C4—21no—
399C4⋊C4—184no—
400C4⋊C4C2×D3212yes—
401C22⋊C4—184no—
402C22⋊C4—184no—
403C42—92no—
404C42—92no—
405C42—184no—
406C22×C3—21no—
407C22×C3—22no—
408C22×C3—22no—
409C22×C3—22no—
410C22×C3—122no—
411C22×C3—122no—
412C22×C3—122no—
413C22×C3—244no—
414C22×C3#88412yes—
415C22×C3#88412yes—
416C22×C3#91212yes—
417C22×C3#91512yes—
418C22×C3#91612yes—
419C22×C3#91812yes—
420C22×C3C2×D3×D411yescharacteristic
421C22×C3C2×D3×D411yescharacteristic
422C2×D3—42no—
423C2×D3—42no—
424C2×D3—42no—
425C2×D3—84no—
426C3×C4—21no—
427C3×C4—21no—
428C3×C4—22no—
429C3×C4—44no—
430C3×C4—42no—
431C3×C4—42no—
432C3×C4—122no—
433C3×C4#88412yes—
434C3×C4#88412yes—
435C3×C4C2×#23511yescharacteristic
436C3×C4C2×#23511yescharacteristic
437C3×C4C2×D3×D411yescharacteristic
438C3×C4C2×D3×D411yescharacteristic
439Dic3—42no—
440Dic3—68no—
441Dic3—64no—
442Dic3—64no—
443Dic3—64no—
444Dic3—62no—
445Dic3—62no—
446Dic3—62no—
447Dic3—62no—
448Dic3—122no—
449C32C2×#46411yescharacteristic, complemented, Sylow
450C23—62no—
451C23—122no—
452C23—122no—
453C23—122no—
454C23#381111yescharacteristic
455Q8—62no—
456Q8—62no—
457Q8—94no—
458Q8—122no—
459Q8—182no—
460Q8—184no—
461D4—62no—
462D4—62no—
463D4—122no—
464C2×C4—22no—
465C2×C4—42no—
466C2×C4—62no—
467C2×C4—92no—
468C2×C4—92no—
469C2×C4—122no—
470C2×C4—182no—
471C2×C4—184no—
472C2×C4—182no—
473C2×C4—182no—
474C2×C4#379812yes—
475C2×C4#380212yes—
476C2×C4#381111yescharacteristic
477C2×C4C22×D3211yescharacteristic
478C8—62no—
479C8—62no—
480C2×C3—21no—
481C2×C3—21no—
482C2×C3—24no—
483C2×C3—21no—
484C2×C3—242no—
485C2×C3#476714yescomplemented
486C2×C3#479814yescomplemented
487C2×C3C2×#88411yescharacteristic
488C2×C3C2×#88411yescharacteristic
489C2×C3C2×#91211yescharacteristic
490C2×C3C2×#91511yescharacteristic
491C2×C3C2×#91611yescharacteristic
492C2×C3C2×#91811yescharacteristic
493D3—82no—
494C22—122no—
495C22—122no—
496C22—122no—
497C22—244no—
498C22#6391212yes—
499C22#6393612yes—
500C22#6395112yes—
501C22C2×#381111yescharacteristic
502C4—42no—
503C4—122no—
504C4—182no—
505C4—182no—
506C4—184no—
507C4#6391212yes—
508C4C2×#379811yescharacteristic
509C4C2×#380211yescharacteristic
510C3—21no—
511C3C2×#476711yescharacteristic, complemented
512C3C2×#479811yescharacteristic, complemented
513C2—242no—
514C2#1059053814yesdirect product factor
515C2C2×#6391211yescharacteristic
516C2C2×#6393611yescharacteristic
517C2C2×#6395111yescharacteristic
subgroupG/H
centerC23#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#464
LCSG ▷ C2×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
1. C2×#64096C2semidirect
3. C22×#3719C2semidirect
5. C2×C3×#810C2semidirect
7. C2×#63572C2semidirect
8. #10590538C2direct (N × H)
19. #64096C22semidirect
27. C2×#3719C22semidirect
30. C3×#810C22semidirect
32. #63572C22semidirect
46. C2×#810D3semidirect
133. #810C2×D3semidirect
368. C2×C32#464semidirect
449. C32C2×#464semidirect
485. C2×C3#4767semidirect
486. C2×C3#4798semidirect
511. C3C2×#4767semidirect
512. C3C2×#4798semidirect
514. C2#10590538direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640962
C2×#638632
C22×#37192
C22×#37162
C2×C3×#8102
C2×C3×#8092
C2×#635722
#105905382
C2×#47983
C2×#47673