Finite Group Databasebeta

← C2×#10590585 #11866935

Subgroups — C2×#10590585 #11866935

Order 1152.

1189 conjugacy classes of subgroups.

The subgroup lattice has 545 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#897C211yesmaximal, characteristic, complemented
2C2×#63909C211yesmaximal, characteristic
3C22×#3717C211yesmaximal, characteristic, complemented
4C22×#3711C211yesmaximal, characteristic, complemented
5C2×#63636C211yesmaximal, characteristic, complemented
6C2×C3×#807C211yesmaximal, characteristic, complemented
7C2×#63565C211yesmaximal, characteristic, complemented
8#10590585C218yesmaximal, direct product factor
9C2×#5049—31nomaximal
10C2×#4886—31nomaximal
11C22×C4⋊(C3⋊D3)C2211yescharacteristic
12C22×C3×C4×D3C2211yescharacteristic
13C22×C3×Dic6C2211yescharacteristic
14C22×#626—21no—
15C2×C32×C4⋊C4C2211yescharacteristic
16C22×C3⋊(C3⋊C8)C2211yescharacteristic
17C2×C3×(C2×D3)⋊C4—21no—
18C2×C3×C4⋊Dic3—21no—
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21C3×#897—22no—
22C3×#897C2214yescomplemented
23C2×#3722—21no—
24#63909—22no—
25#63909C2214yes—
26C2×#3717—24no—
27C2×#3717C2214yescomplemented
28C2×#3711—24no—
29C2×#3711C2214yescomplemented
30#63636C2214yescomplemented
31C3×#807C2214yescomplemented
32#63565C2214yescomplemented
33C2×C3×C22⋊Q8—31no—
34C22×#215—31no—
35C2×#930—31no—
36C22×#208—31no—
37C22×#204—31no—
38C22×ΓL(1,𝔽25)—31no—
39C2×#897D311yescharacteristic, complemented
40C2×#895—31no—
41C2×C3×#107—31no—
42C2×#835—31no—
43#5049—38no—
44C2×#810—31no—
45C2×#809—31no—
46C2×#809—31no—
47C2×#809—61no—
48C2×#807D311yescharacteristic, complemented
49#4886—38no—
50C23×C3⋊D3—21no—
51C23×C3×D3D411yescharacteristic
52C22×C32×C4—21no—
53C22×C32×C4C2311yescharacteristic
54C2×C4⋊(C3⋊D3)—22no—
55C2×C4⋊(C3⋊D3)—22no—
56C2×C4⋊(C3⋊D3)—21no—
57C2×C4⋊(C3⋊D3)C2312yes—
58C22×C3×Dic3—21no—
59C22×C3×Dic3—21no—
60C22×C3×Dic3D411yescharacteristic
61C2×C3×C4×D3—22no—
62C2×C3×C4×D3—22no—
63C2×C3×C4×D3D412yes—
64C2×C3×C4×D3C2312yes—
65C2×C3×Dic6—22no—
66C2×C3×Dic6—22no—
67C2×C3×Dic6—21no—
68C2×C3×Dic6C2312yes—
69C2×#626—24no—
70C2×#626—44no—
71C32×C4⋊C4—21no—
72C32×C4⋊C4C2312yes—
73C2×C3⋊(C3⋊C8)—22no—
74C2×C3⋊(C3⋊C8)C2312yes—
75C3×(C2×D3)⋊C4—24no—
76C3×C4⋊Dic3—21no—
77C3×C4⋊Dic3—24no—
78C3×C4⋊Dic3C2312yes—
79C2×C3×C3⋊C8D414yescomplemented
80C2×C3×C3⋊C8C2312yes—
81#3722—24no—
82#3717—28no—
83#3711—28no—
84C2×#468—91noSylow
85C22×C3×Q8—31no—
86C23×C3×C4—31no—
87C22×#67—61no—
88C22×D12—31no—
89C22×D12—31no—
90C22×D12—61no—
91C22×D12—61no—
92C22×C4×D3C2×D311yescharacteristic
93C22×Dic6C2×D311yescharacteristic
94C22×C3×C8—31no—
95C3×C22⋊Q8—34no—
96C3×C22⋊Q8—62no—
97C2×C3×C4⋊C4—21no—
98C2×C3×C4⋊C4—31no—
99C2×C3×C4⋊C4—61no—
100C2×C3×C4⋊C4C2×D311yescharacteristic
101C2×C3×C4⋊C4C2×D311yescharacteristic
102C2×C3×C22⋊C4—61no—
103C2×#215—34no—
104C2×#215—64no—
105#930—34no—
106#930—62no—
107C2×(C2×D3)⋊C4—21no—
108C2×(C2×D3)⋊C4—61no—
109C2×(C2×D3)⋊C4—61no—
110C2×C4⋊Dic3—21no—
111C2×C4⋊Dic3C2×D311yescharacteristic
112C2×#208—34no—
113C2×#208—64no—
114C22×C3⋊C8—31no—
115C22×C3⋊C8—31no—
116C22×C3⋊C8—61no—
117C22×C3⋊C8C2×D311yescharacteristic
118C2×#204—34no—
119C2×#204—64no—
120C2×ΓL(1,𝔽25)—34no—
121C2×ΓL(1,𝔽25)—64no—
122#897—22no—
123#897C2×D314yescomplemented
124#895—34no—
125#895—62no—
126C3×#107—34no—
127#835—34no—
128#810—34no—
129#809—34no—
130#809—34no—
131#809—64no—
132#807C2×D314yescomplemented
133C23×C32C2×D411yescharacteristic
134C22×C3⋊D3—22no—
135C22×C3⋊D3—42no—
136C22×C3⋊D3—42no—
137C22×C3⋊D3—42no—
138C22×C3×D3—22no—
139C22×C3×D3—22no—
140C22×C3×D3—22no—
141C22×C3×D3C2×D412yes—
142C2×C32×C4—22no—
143C2×C32×C4—42no—
144C2×C32×C4C2×D412yes—
145C2×C32×C4C2×D411yescharacteristic
146C2×C32×C4#4112yes—
147C2×C32×C4C2411yescharacteristic
148C4⋊(C3⋊D3)—22no—
149C4⋊(C3⋊D3)—22no—
150C4⋊(C3⋊D3)—42no—
151C2×C3×Dic3—22no—
152C2×C3×Dic3—22no—
153C2×C3×Dic3—22no—
154C2×C3×Dic3—42no—
155C2×C3×Dic3—42no—
156C2×C3×Dic3C2×D412yes—
157C3×C4×D3—24no—
158C3×C4×D3—22no—
159C3×C4×D3—22no—
160C3×Dic6—22no—
161C3×Dic6—22no—
162C3×Dic6—42no—
163#626—48no—
164C3⋊(C3⋊C8)—22no—
165C3×C3⋊C8C2×D414yescomplemented
166C22×SD16—91no—
167C22×M16—91no—
168C2×C22⋊Q8—31no—
169C2×#121—91no—
170#468—98no—
171C2×#107—31no—
172C2×#103—91no—
173C2×#102—91no—
174C24×C3—31no—
175C23×D3—61no—
176C23×D3—61no—
177C23×D3—121no—
178C23×D3#6711yescharacteristic
179C2×C3×Q8—32no—
180C2×C3×Q8—61no—
181C2×C3×Q8—62no—
182C2×C3×Q8—62no—
183C22×C3×C4—21no—
184C22×C3×C4—21no—
185C22×C3×C4—21no—
186C22×C3×C4—31no—
187C22×C3×C4—32no—
188C22×C3×C4—32no—
189C22×C3×C4—41no—
190C22×C3×C4—62no—
191C22×C3×C4—62no—
192C22×C3×C4—61no—
193C22×C3×C4—61no—
194C22×C3×C4C22×D311yescharacteristic
195C22×C3×C4C22×D311yescharacteristic
196C2×#67—64no—
197C2×#67—124no—
198C22×Dic3—21no—
199C22×Dic3—21no—
200C22×Dic3#6711yescharacteristic
201C2×D12—32no—
202C2×D12—32no—
203C2×D12—62no—
204C2×D12—64no—
205C2×D12—62no—
206C2×D12—62no—
207C2×D12—62no—
208C2×D12—62no—
209C2×D12—64no—
210C2×D12—61no—
211C2×D12—61no—
212C2×D12—122no—
213C2×D12—121no—
214C2×D12—124no—
215C2×C4×D3—22no—
216C2×C4×D3—22no—
217C2×C4×D3#6712yes—
218C2×C4×D3C22×D312yes—
219C2×Dic6—22no—
220C2×Dic6—22no—
221C2×Dic6—21no—
222C2×Dic6C22×D312yes—
223C2×C3×C8—34no—
224C2×C3×C8—32no—
225C3×C4⋊C4—21no—
226C3×C4⋊C4—21no—
227C3×C4⋊C4—22no—
228C3×C4⋊C4—32no—
229C3×C4⋊C4—41no—
230C3×C4⋊C4—64no—
231C3×C4⋊C4—61no—
232C3×C4⋊C4C22×D312yes—
233C3×C4⋊C4C22×D312yes—
234C3×C22⋊C4—64no—
235#215—68no—
236(C2×D3)⋊C4—24no—
237(C2×D3)⋊C4—64no—
238(C2×D3)⋊C4—64no—
239C4⋊Dic3—21no—
240C4⋊Dic3—24no—
241C4⋊Dic3C22×D312yes—
242#208—68no—
243C2×C3⋊C8—32no—
244C2×C3⋊C8—32no—
245C2×C3⋊C8—62no—
246C2×C3⋊C8—62no—
247C2×C3⋊C8—62no—
248C2×C3⋊C8—122no—
249C2×C3⋊C8D1214yescomplemented
250C2×C3⋊C8C22×D312yes—
251#204—68no—
252ΓL(1,𝔽25)—68no—
253C22×C32#12112yes—
254C22×C32AGL(1,ℤ/8)12yes—
255C22×C32#13712yes—
256C22×C32C22×D411yescharacteristic
257C2×C3⋊D3—42no—
258C2×C3⋊D3—42no—
259C2×C3⋊D3—42no—
260C2×C3⋊D3—84no—
261C2×C3×D3—22no—
262C2×C3×D3—22no—
263C2×C3×D3—22no—
264C2×C3×D3—44no—
265C32×C4—42no—
266C32×C4#12112yes—
267C32×C4C22×D411yescharacteristic
268C32×C4C2×#4111yescharacteristic
269C3×Dic3—22no—
270C3×Dic3—42no—
271C3×Dic3—42no—
272C22×Q8—31no—
273C22×D4—91no—
274C22×D4—181no—
275C23×C4—31no—
276C2×SD16—94no—
277C2×SD16—184no—
278C2×M16—94no—
279C2×M16—184no—
280C22×C8—31no—
281C22×C8—91no—
282C22⋊Q8—34no—
283C22⋊Q8—62no—
284#121—94no—
285#121—182no—
286C2×C4⋊C4—31no—
287C2×C4⋊C4—61no—
288C2×C4⋊C4D3211yescharacteristic
289C2×C22⋊C4—61no—
290C2×C22⋊C4—181no—
291#107—34no—
292#103—94no—
293#102—94no—
294C23×C3—21no—
295C23×C3—32no—
296C23×C3—62no—
297C23×C3—62no—
298C23×C3—62no—
299C23×C3D3×D411yescharacteristic
300C23×C3C2×#6711yescharacteristic
301C22×D3—22no—
302C22×D3—22no—
303C22×D3—22no—
304C22×D3—62no—
305C22×D3—62no—
306C22×D3—122no—
307C22×D3—124no—
308C22×D3—122no—
309C22×D3—122no—
310C22×D3—122no—
311C22×D3—122no—
312C22×D3—122no—
313C22×D3—122no—
314C22×D3—242no—
315C22×D3—242no—
316C22×D3C2×#6712yes—
317C3×Q8—62no—
318C3×Q8—62no—
319C3×Q8—122no—
320C2×C3×C4—22no—
321C2×C3×C4—22no—
322C2×C3×C4—21no—
323C2×C3×C4—22no—
324C2×C3×C4—22no—
325C2×C3×C4—21no—
326C2×C3×C4—32no—
327C2×C3×C4—42no—
328C2×C3×C4—42no—
329C2×C3×C4—42no—
330C2×C3×C4—62no—
331C2×C3×C4—64no—
332C2×C3×C4—62no—
333C2×C3×C4—62no—
334C2×C3×C4—62no—
335C2×C3×C4—62no—
336C2×C3×C4—82no—
337C2×C3×C4—122no—
338C2×C3×C4—122no—
339C2×C3×C4C2×D1212yes—
340C2×C3×C4D3×D412yes—
341C2×C3×C4D3×D411yescharacteristic
342C2×C3×C4#23712yes—
343C2×C3×C4#23912yes—
344C2×C3×C4C2×#6711yescharacteristic
345C2×C3×C4C23×D311yescharacteristic
346C2×C3×C4C23×D311yescharacteristic
347#67—128no—
348C2×Dic3—22no—
349C2×Dic3—22no—
350C2×Dic3—22no—
351C2×Dic3—42no—
352C2×Dic3—42no—
353C2×Dic3C2×#6712yes—
354D12—64no—
355D12—62no—
356D12—62no—
357D12—62no—
358D12—62no—
359D12—122no—
360D12—124no—
361D12—128no—
362D12—122no—
363D12—122no—
364C4×D3—24no—
365C4×D3—22no—
366C4×D3—22no—
367Dic6—22no—
368Dic6—22no—
369Dic6—42no—
370C3×C8—34no—
371C3⋊C8—62no—
372C3⋊C8—62no—
373C3⋊C8—122no—
374C3⋊C8C2×D1214yescomplemented
375C2×C32#46814yescomplemented
376C2×C32C2×#12111yescharacteristic
377C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
378C2×C32C2×#13711yescharacteristic
379C3⋊D3—82no—
380C3×D3—42no—
381C24—31no—
382C24—181no—
383C2×Q8—32no—
384C2×Q8—61no—
385C2×Q8—62no—
386C2×Q8—62no—
387C2×D4—92no—
388C2×D4—184no—
389C2×D4—182no—
390C2×D4—182no—
391C2×D4—181no—
392C2×D4—364no—
393C22×C4—21no—
394C22×C4—31no—
395C22×C4—32no—
396C22×C4—32no—
397C22×C4—62no—
398C22×C4—62no—
399C22×C4—61no—
400C22×C4—61no—
401C22×C4C2×D3211yescharacteristic
402SD16—188no—
403M16—188no—
404C2×C8—32no—
405C2×C8—34no—
406C2×C8—92no—
407C2×C8—182no—
408C4⋊C4—21no—
409C4⋊C4—32no—
410C4⋊C4—64no—
411C4⋊C4—61no—
412C4⋊C4C2×D3212yes—
413C22⋊C4—64no—
414C22⋊C4—184no—
415C22×C3—21no—
416C22×C3—22no—
417C22×C3—22no—
418C22×C3—22no—
419C22×C3—62no—
420C22×C3—62no—
421C22×C3—62no—
422C22×C3—124no—
423C22×C3#89512yes—
424C22×C3#91112yes—
425C22×C3#91812yes—
426C22×C3#93912yes—
427C22×C3#94212yes—
428C22×C3#94912yes—
429C22×C3C2×D3×D411yescharacteristic
430C22×C3C22×#6711yescharacteristic
431C2×D3—22no—
432C2×D3—22no—
433C2×D3—22no—
434C2×D3—44no—
435C2×D3—124no—
436C2×D3—122no—
437C2×D3—122no—
438C2×D3—122no—
439C2×D3—122no—
440C2×D3—122no—
441C2×D3—122no—
442C2×D3—242no—
443C2×D3—242no—
444C2×D3—248no—
445C2×D3—244no—
446C2×D3—244no—
447C3×C4—21no—
448C3×C4—21no—
449C3×C4—22no—
450C3×C4—42no—
451C3×C4—42no—
452C3×C4—62no—
453C3×C4—82no—
454C3×C4—122no—
455C3×C4—122no—
456C3×C4#89512yes—
457C3×C4#93912yes—
458C3×C4C22×D1211yescharacteristic
459C3×C4C2×D3×D411yescharacteristic
460C3×C4C2×#23711yescharacteristic
461C3×C4C2×#23911yescharacteristic
462Dic3—22no—
463Dic3—42no—
464Dic3—42no—
465C32C2×#46811yescharacteristic, complemented, Sylow
466C23—32no—
467C23—62no—
468C23—62no—
469C23—62no—
470C23—182no—
471C23—362no—
472C23—362no—
473C23—362no—
474C23D3×#6711yescharacteristic
475Q8—62no—
476Q8—62no—
477Q8—122no—
478D4—182no—
479D4—182no—
480D4—368no—
481D4—362no—
482C2×C4—22no—
483C2×C4—32no—
484C2×C4—42no—
485C2×C4—62no—
486C2×C4—62no—
487C2×C4—62no—
488C2×C4—64no—
489C2×C4—62no—
490C2×C4—62no—
491C2×C4—122no—
492C2×C4—122no—
493C2×C4#379612yes—
494C2×C4D3×D1212yes—
495C2×C4D3×#6711yescharacteristic
496C2×C4C22×D3211yescharacteristic
497C8—34no—
498C8—182no—
499C2×C3—21no—
500C2×C3—21no—
501C2×C3—21no—
502C2×C3—24no—
503C2×C3—122no—
504C2×C3#488614yescomplemented
505C2×C3#504914yescomplemented
506C2×C3C2×#89511yescharacteristic
507C2×C3C2×#91111yescharacteristic
508C2×C3C2×#91811yescharacteristic
509C2×C3C2×#93911yescharacteristic
510C2×C3C2×#94211yescharacteristic
511C2×C3C2×#94911yescharacteristic
512D3—42no—
513D3—244no—
514D3—242no—
515D3—242no—
516C22—62no—
517C22—62no—
518C22—62no—
519C22—124no—
520C22—362no—
521C22—362no—
522C22—362no—
523C22—724no—
524C22#6388612yes—
525C22#6392512yes—
526C22#6394812yes—
527C22C2×D3×#6711yescharacteristic
528C4—42no—
529C4—62no—
530C4—122no—
531C4—122no—
532C4#6388612yes—
533C4C2×#379611yescharacteristic
534C4C2×D3×D1211yescharacteristic
535C3—21no—
536C3C2×#488611yescharacteristic, complemented
537C3C2×#504911yescharacteristic, complemented
538C2—122no—
539C2—722no—
540C2#1059058514yesdirect product factor
541C2C2×#6388611yescharacteristic
542C2C2×#6392511yescharacteristic
543C2C2×#6394811yescharacteristic
subgroupG/H
centerC23D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC2×#63909C2
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#468
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×C3×#897C2semidirect
3. C22×#3717C2semidirect
4. C22×#3711C2semidirect
5. C2×#63636C2semidirect
6. C2×C3×#807C2semidirect
7. C2×#63565C2semidirect
8. #10590585C2direct (N × H)
22. C3×#897C22semidirect
27. C2×#3717C22semidirect
29. C2×#3711C22semidirect
30. #63636C22semidirect
31. C3×#807C22semidirect
32. #63565C22semidirect
39. C2×#897D3semidirect
48. C2×#807D3semidirect
79. C2×C3×C3⋊C8D4semidirect
123. #897C2×D3semidirect
132. #807C2×D3semidirect
165. C3×C3⋊C8C2×D4semidirect
249. C2×C3⋊C8D12semidirect
374. C3⋊C8C2×D12semidirect
375. C2×C32#468semidirect
465. C32C2×#468semidirect
504. C2×C3#4886semidirect
505. C2×C3#5049semidirect
536. C3C2×#4886semidirect
537. C3C2×#5049semidirect
540. C2#10590585direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#8972
C2×#639092
C22×#37172
C22×#37112
C2×#636362
C2×C3×#8072
C2×#635652
#105905852
C2×#50493
C2×#48863