Finite Group Databasebeta

← C2×#10590876 #11865605

Subgroups — C2×#10590876 #11865605

Order 1152.

1237 conjugacy classes of subgroups.

The subgroup lattice has 543 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#204C211yesmaximal, characteristic, complemented
2C2×#63914C211yesmaximal, characteristic
3C2×#63843C211yesmaximal, characteristic, complemented
4C22×#3715C211yesmaximal, characteristic, complemented
5C2×#63641C211yesmaximal, characteristic, complemented
6C2×C3×#821C211yesmaximal, characteristic, complemented
7C2×#63562C211yesmaximal, characteristic, complemented
8#10590876C218yesmaximal, direct product factor
9C2×#5163—31nomaximal
10C2×#4762—31nomaximal
11C22×C3×D12C2211yescharacteristic
12C22×C3×D12C2211yescharacteristic
13C22×C3×Dic6C2211yescharacteristic
14C22×#625—21no—
15C22×#625—21no—
16C22×C32×C8C2211yescharacteristic
17C2×C4×C3⋊Dic3C2211yescharacteristic
18C22×C3⋊(C3⋊C8)C2211yescharacteristic
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C2×C3×#204—24no—
21C2×C3×#204C2214yescomplemented
22C2×Dic3⋊Dic3—21no—
23C2×Dic32—21no—
24#63914—22no—
25#63914C2214yes—
26#63843—22no—
27#63843C2214yescomplemented
28C2×#3715—24no—
29C2×#3715C2214yescomplemented
30#63641C2214yescomplemented
31C3×#821C2214yescomplemented
32#63562C2214yescomplemented
33C22×C3×SD16—31no—
34C2×Q8×Dic3—31no—
35C22×#215—31no—
36C2×#940—31no—
37C2×#940—31no—
38C22×#214—31no—
39C22×#204D311yescharacteristic, complemented
40C2×#887—31no—
41C2×C3×#102—31no—
42C2×#832—31no—
43#5163—38no—
44C2×#821D311yescharacteristic, complemented
45C2×Dic3⋊C8—31no—
46C2×Dic3⋊C8—31no—
47C2×Dic3⋊C8—61no—
48C2×#809—31no—
49#4762—38no—
50C23×C3×D3—21no—
51C23×C3×D3—21no—
52C22×C32×C4C2311yescharacteristic
53C22×C3⋊Dic3D411yescharacteristic
54C22×C3⋊Dic3D411yescharacteristic
55C22×C3×Dic3—21no—
56C22×C3×Dic3—21no—
57C2×C3×D12—22no—
58C2×C3×D12—22no—
59C2×C3×D12—22no—
60C2×C3×D12—22no—
61C2×C3×D12—21no—
62C2×C3×D12—21no—
63C2×C3×D12C2312yes—
64C2×C3×D12C2312yes—
65C2×C3×Dic6—21no—
66C2×C3×Dic6—22no—
67C2×C3×Dic6D414yescomplemented
68C2×C3×Dic6C2312yes—
69C2×#625—24no—
70C2×#625—24no—
71C2×#625—44no—
72C2×#625—44no—
73C2×C32×C8—22no—
74C2×C32×C8C2312yes—
75C4×C3⋊Dic3D412yes—
76C4×C3⋊Dic3C2312yes—
77C2×C3⋊(C3⋊C8)—22no—
78C2×C3⋊(C3⋊C8)C2312yes—
79C3×C4⋊Dic3—21no—
80C3×C4⋊Dic3C2312yes—
81C3×#204—28no—
82Dic3⋊Dic3—24no—
83Dic32—24no—
84#3715—28no—
85C2×#460—91noSylow
86C22×C3×Q8—31no—
87C22×C3×D4—31no—
88C22×C3×D4—31no—
89C22×#67—61no—
90C22×#67—61no—
91C22×#67—61no—
92C22×#67—61no—
93C22×D12C2×D311yescharacteristic
94C22×D12C2×D311yescharacteristic
95C22×Dic6C2×D311yescharacteristic
96C2×C3×SD16—34no—
97C2×C3×SD16—64no—
98C22×C3×C8—21no—
99C22×C3×C8C2×D311yescharacteristic
100C22×C3×C8C2×D311yescharacteristic
101C2×C3×C4⋊C4—31no—
102Q8×Dic3—34no—
103Q8×Dic3—62no—
104C2×#215—34no—
105C2×#215—64no—
106#940—34no—
107#940—34no—
108#940—62no—
109#940—62no—
110C2×#214—34no—
111C2×#214—64no—
112C2×C4⋊Dic3—61no—
113C2×C4⋊Dic3C2×D311yescharacteristic
114C2×Dic3⋊C4—61no—
115C2×C4×Dic3—31no—
116C2×C4×Dic3—31no—
117C2×C4×Dic3—61no—
118C2×C4×Dic3—61no—
119C2×C4×Dic3—61no—
120C22×C3⋊C8—31no—
121C22×C3⋊C8—31no—
122C22×C3⋊C8—61no—
123C2×#204—24no—
124C2×#204C2×D314yescomplemented
125#887—34no—
126#887—62no—
127C3×#102—34no—
128#832—34no—
129#821C2×D314yescomplemented
130Dic3⋊C8—34no—
131Dic3⋊C8—34no—
132Dic3⋊C8—64no—
133#809—34no—
134C23×C32C2×D411yescharacteristic
135C22×C3×D3—22no—
136C22×C3×D3—22no—
137C22×C3×D3—42no—
138C22×C3×D3—42no—
139C22×C3×D3—42no—
140C22×C3×D3—42no—
141C22×C3×D3—42no—
142C22×C3×D3—42no—
143C2×C32×C4C2×D411yescharacteristic
144C2×C32×C4C2×D412yes—
145C2×C32×C4#4112yes—
146C2×C32×C4C2411yescharacteristic
147C2×C3⋊Dic3—22no—
148C2×C3⋊Dic3SD1614yescomplemented
149C2×C3⋊Dic3C2×D412yes—
150C2×C3⋊Dic3C2×D412yes—
151C2×C3×Dic3—24no—
152C2×C3×Dic3—22no—
153C2×C3×Dic3—22no—
154C2×C3×Dic3—42no—
155C3×D12—22no—
156C3×D12—22no—
157C3×D12—22no—
158C3×D12—22no—
159C3×D12—42no—
160C3×D12—42no—
161C3×Dic6—24no—
162C3×Dic6—22no—
163C3×Dic6C2×D414yescomplemented
164#625—48no—
165#625—48no—
166C32×C8—22no—
167C3⋊(C3⋊C8)—22no—
168C22×SD16—31no—
169C22×SD16—91no—
170C2×#127—91no—
171C2×C4×Q8—91no—
172#460—98no—
173C2×C4⋊C8—91no—
174C2×#102—31no—
175C2×#102—91no—
176C24×C3—61no—
177C24×C3—61no—
178C23×D3—21no—
179C23×D3—21no—
180C2×C3×Q8—34no—
181C2×C3×Q8—32no—
182C2×C3×Q8—62no—
183C2×C3×Q8—61no—
184C2×C3×D4—32no—
185C2×C3×D4—32no—
186C2×C3×D4—62no—
187C2×C3×D4—62no—
188C2×C3×D4—61no—
189C2×C3×D4—61no—
190C2×C3×D4—62no—
191C2×C3×D4—62no—
192C22×C3×C4—21no—
193C22×C3×C4—61no—
194C22×C3×C4—61no—
195C22×C3×C4C22×D311yescharacteristic
196C22×C3×C4C22×D311yescharacteristic
197C2×#67—64no—
198C2×#67—64no—
199C2×#67—64no—
200C2×#67—64no—
201C2×#67—124no—
202C2×#67—124no—
203C2×#67—124no—
204C2×#67—124no—
205C22×Dic3—21no—
206C22×Dic3—21no—
207C22×Dic3—31no—
208C22×Dic3—31no—
209C22×Dic3—31no—
210C22×Dic3—31no—
211C22×Dic3—61no—
212C22×Dic3—61no—
213C2×D12—22no—
214C2×D12—22no—
215C2×D12—22no—
216C2×D12—22no—
217C2×D12—21no—
218C2×D12—21no—
219C2×D12C22×D312yes—
220C2×D12C22×D312yes—
221C2×Dic6—21no—
222C2×Dic6—22no—
223C2×Dic6#6714yescomplemented
224C2×Dic6C22×D312yes—
225C3×SD16—68no—
226C2×C3×C8—22no—
227C2×C3×C8—22no—
228C2×C3×C8—22no—
229C2×C3×C8—42no—
230C2×C3×C8C22×D312yes—
231C2×C3×C8C22×D312yes—
232C3×C4⋊C4—32no—
233C3×C4⋊C4—61no—
234#215—68no—
235#214—68no—
236C4⋊Dic3—21no—
237C4⋊Dic3—64no—
238C4⋊Dic3C22×D312yes—
239Dic3⋊C4—64no—
240C4×Dic3—32no—
241C4×Dic3—32no—
242C4×Dic3—32no—
243C4×Dic3—32no—
244C4×Dic3—62no—
245C4×Dic3—62no—
246C4×Dic3—64no—
247C4×Dic3—64no—
248C2×C3⋊C8—32no—
249C2×C3⋊C8—32no—
250C2×C3⋊C8—62no—
251C2×C3⋊C8—62no—
252C2×C3⋊C8—62no—
253C2×C3⋊C8—122no—
254#204—28no—
255C22×C32#12112yes—
256C22×C32C2×SD1612yes—
257C22×C32AGL(1,ℤ/8)12yes—
258C22×C32C22×D411yescharacteristic
259C2×C3×D3—42no—
260C2×C3×D3—42no—
261C2×C3×D3—42no—
262C2×C3×D3—42no—
263C2×C3×D3—42no—
264C2×C3×D3—42no—
265C2×C3×D3—84no—
266C2×C3×D3—84no—
267C32×C4#12112yes—
268C32×C4C22×D411yescharacteristic
269C32×C4C2×#4111yescharacteristic
270C3⋊Dic3—22no—
271C3⋊Dic3C2×SD1614yescomplemented
272C3×Dic3—24no—
273C3×Dic3—42no—
274C22×Q8—31no—
275C22×D4—31no—
276C22×D4—31no—
277C22×D4—181no—
278C22×D4—181no—
279C2×SD16—34no—
280C2×SD16—64no—
281C2×SD16—94no—
282C2×SD16—184no—
283C22×C8—91no—
284C22×C8D3211yescharacteristic
285#127—94no—
286#127—182no—
287C4×Q8—94no—
288C4×Q8—182no—
289C2×C4⋊C4—31no—
290C2×C4⋊C4—181no—
291C2×C42—91no—
292C2×C42—181no—
293C4⋊C8—94no—
294#102—34no—
295#102—94no—
296C23×C3—21no—
297C23×C3—62no—
298C23×C3—62no—
299C23×C3—122no—
300C23×C3—122no—
301C23×C3—122no—
302C23×C3—122no—
303C23×C3—122no—
304C23×C3—122no—
305C23×C3D3×D411yescharacteristic
306C23×C3D3×D411yescharacteristic
307C22×D3—22no—
308C22×D3—22no—
309C22×D3—42no—
310C22×D3—42no—
311C22×D3—42no—
312C22×D3—42no—
313C22×D3—42no—
314C22×D3—42no—
315C3×Q8—34no—
316C3×Q8—64no—
317C3×Q8—62no—
318C3×D4—62no—
319C3×D4—62no—
320C3×D4—62no—
321C3×D4—62no—
322C3×D4—122no—
323C3×D4—122no—
324C2×C3×C4—21no—
325C2×C3×C4—22no—
326C2×C3×C4—21no—
327C2×C3×C4—22no—
328C2×C3×C4—64no—
329C2×C3×C4—62no—
330C2×C3×C4—62no—
331C2×C3×C4—122no—
332C2×C3×C4#23512yes—
333C2×C3×C4D3×D411yescharacteristic
334C2×C3×C4D3×D411yescharacteristic
335C2×C3×C4D3×D412yes—
336C2×C3×C4#23712yes—
337C2×C3×C4C2×#6712yes—
338C2×C3×C4C23×D311yescharacteristic
339C2×C3×C4C23×D311yescharacteristic
340#67—128no—
341#67—128no—
342#67—128no—
343#67—128no—
344C2×Dic3—24no—
345C2×Dic3—22no—
346C2×Dic3—22no—
347C2×Dic3—34no—
348C2×Dic3—34no—
349C2×Dic3—32no—
350C2×Dic3—32no—
351C2×Dic3—32no—
352C2×Dic3—32no—
353C2×Dic3—42no—
354C2×Dic3—64no—
355C2×Dic3—62no—
356C2×Dic3—62no—
357C2×Dic3—62no—
358C2×Dic3—62no—
359C2×Dic3—122no—
360D12—22no—
361D12—22no—
362D12—22no—
363D12—22no—
364D12—42no—
365D12—42no—
366Dic6—24no—
367Dic6—22no—
368Dic6C2×#6714yescomplemented
369C3×C8—22no—
370C3×C8—22no—
371C3×C8—42no—
372C3⋊C8—62no—
373C3⋊C8—62no—
374C3⋊C8—122no—
375C2×C32#46014yescomplemented
376C2×C32C2×#12111yescharacteristic
377C2×C32C22×SD1611yescharacteristic
378C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
379C3×D3—82no—
380C3×D3—82no—
381C24—61no—
382C24—61no—
383C2×Q8—32no—
384C2×Q8—34no—
385C2×Q8—62no—
386C2×Q8—61no—
387C2×D4—32no—
388C2×D4—32no—
389C2×D4—62no—
390C2×D4—62no—
391C2×D4—61no—
392C2×D4—61no—
393C2×D4—62no—
394C2×D4—62no—
395C2×D4—184no—
396C2×D4—184no—
397C2×D4—364no—
398C2×D4—364no—
399C22×C4—61no—
400C22×C4—61no—
401C22×C4—91no—
402C22×C4—91no—
403C22×C4C2×D3211yescharacteristic
404SD16—68no—
405SD16—188no—
406C2×C8—22no—
407C2×C8—92no—
408C2×C8—182no—
409C2×C8C2×D3212yes—
410C4⋊C4—32no—
411C4⋊C4—61no—
412C4⋊C4—184no—
413C42—92no—
414C42—92no—
415C42—184no—
416C22×C3—21no—
417C22×C3—22no—
418C22×C3—22no—
419C22×C3—22no—
420C22×C3—122no—
421C22×C3—122no—
422C22×C3—122no—
423C22×C3—122no—
424C22×C3—122no—
425C22×C3—122no—
426C22×C3—244no—
427C22×C3—244no—
428C22×C3#88412yes—
429C22×C3#91112yes—
430C22×C3D3×SD1612yes—
431C22×C3D3×SD1612yes—
432C22×C3#91412yes—
433C22×C3#93912yes—
434C22×C3C2×D3×D411yescharacteristic
435C22×C3C2×D3×D411yescharacteristic
436C2×D3—42no—
437C2×D3—42no—
438C2×D3—42no—
439C2×D3—42no—
440C2×D3—42no—
441C2×D3—42no—
442C2×D3—84no—
443C2×D3—84no—
444C3×C4—21no—
445C3×C4—21no—
446C3×C4—22no—
447C3×C4—64no—
448C3×C4—122no—
449C3×C4#88412yes—
450C3×C4#93912yes—
451C3×C4C2×#23511yescharacteristic
452C3×C4C2×D3×D411yescharacteristic
453C3×C4C2×#23711yescharacteristic
454C3×C4C22×#6711yescharacteristic
455Dic3—24no—
456Dic3—34no—
457Dic3—34no—
458Dic3—42no—
459Dic3—64no—
460Dic3—62no—
461Dic3—62no—
462Dic3—122no—
463C32C2×#46011yescharacteristic, complemented, Sylow
464C23—62no—
465C23—62no—
466C23—122no—
467C23—122no—
468C23—122no—
469C23—122no—
470C23—122no—
471C23—122no—
472C23#380211yescharacteristic
473Q8—34no—
474Q8—62no—
475Q8—64no—
476D4—62no—
477D4—62no—
478D4—62no—
479D4—62no—
480D4—122no—
481D4—122no—
482D4—368no—
483D4—368no—
484C2×C4—62no—
485C2×C4—64no—
486C2×C4—62no—
487C2×C4—92no—
488C2×C4—94no—
489C2×C4—92no—
490C2×C4—122no—
491C2×C4—182no—
492C2×C4#379512yes—
493C2×C4#380211yescharacteristic
494C2×C4D3×#6712yes—
495C2×C4C22×D3211yescharacteristic
496C8—22no—
497C8—182no—
498C2×C3—21no—
499C2×C3—21no—
500C2×C3—21no—
501C2×C3—24no—
502C2×C3—242no—
503C2×C3—242no—
504C2×C3#476214yescomplemented
505C2×C3#516314yescomplemented
506C2×C3C2×#88411yescharacteristic
507C2×C3C2×#91111yescharacteristic
508C2×C3C2×D3×SD1611yescharacteristic
509C2×C3C2×D3×SD1611yescharacteristic
510C2×C3C2×#91411yescharacteristic
511C2×C3C2×#93911yescharacteristic
512D3—82no—
513D3—82no—
514C22—122no—
515C22—122no—
516C22—122no—
517C22—122no—
518C22—122no—
519C22—122no—
520C22—244no—
521C22—244no—
522C22#6379612yes—
523C22#6379812yes—
524C22#6388512yes—
525C22C2×#380211yescharacteristic
526C4—64no—
527C4—94no—
528C4—122no—
529C4—182no—
530C4#6388512yes—
531C4C2×#379511yescharacteristic
532C4C2×D3×#6711yescharacteristic
533C3—21no—
534C3C2×#476211yescharacteristic, complemented
535C3C2×#516311yescharacteristic, complemented
536C2—242no—
537C2—242no—
538C2#1059087614yesdirect product factor
539C2C2×#6379611yescharacteristic
540C2C2×#6379811yescharacteristic
541C2C2×#6388511yescharacteristic
subgroupG/H
centerC23#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC2×#63914C2
hypercenterC22×C8D32
hypocenterC32C2×#460
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
1. C22×C3×#204C2semidirect
3. C2×#63843C2semidirect
4. C22×#3715C2semidirect
5. C2×#63641C2semidirect
6. C2×C3×#821C2semidirect
7. C2×#63562C2semidirect
8. #10590876C2direct (N × H)
21. C2×C3×#204C22semidirect
27. #63843C22semidirect
29. C2×#3715C22semidirect
30. #63641C22semidirect
31. C3×#821C22semidirect
32. #63562C22semidirect
39. C22×#204D3semidirect
44. C2×#821D3semidirect
67. C2×C3×Dic6D4semidirect
124. C2×#204C2×D3semidirect
129. #821C2×D3semidirect
148. C2×C3⋊Dic3SD16semidirect
163. C3×Dic6C2×D4semidirect
223. C2×Dic6#67semidirect
271. C3⋊Dic3C2×SD16semidirect
368. Dic6C2×#67semidirect
375. C2×C32#460semidirect
463. C32C2×#460semidirect
504. C2×C3#4762semidirect
505. C2×C3#5163semidirect
534. C3C2×#4762semidirect
535. C3C2×#5163semidirect
538. C2#10590876direct (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×#639142
C2×#638432
C22×#37152
C2×#636412
C2×C3×#8212
C2×#635622
#105908762
C2×#51633
C2×#47623