Finite Group Databasebeta

← C2×#10590770 #11865555

Subgroups — C2×#10590770 #11865555

Order 1152.

1297 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3745C211yesmaximal, characteristic
2C2×#63894C211yesmaximal, characteristic, complemented
3C2×#63864C211yesmaximal, characteristic, complemented
4C22×#3717C211yesmaximal, characteristic, complemented
5C2×C3×#816C211yesmaximal, characteristic, complemented
6C2×C3×Dic3⋊C8C211yesmaximal, characteristic, complemented
7C2×#63564C211yesmaximal, characteristic, complemented
8#10590770C218yesmaximal, direct product factor
9C2×#4844—31nomaximal
10C2×#4819—31nomaximal
11C22×C4⋊(C3⋊D3)C2211yescharacteristic
12C22×C4⋊(C3⋊D3)C2211yescharacteristic
13C22×C3×Dic6C2211yescharacteristic
14C22×#624—21no—
15C22×C32×C8C2211yescharacteristic
16C2×#3745—24no—
17C2×#3745C2214yes—
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C2×C3×C4×Dic3C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21C2×#3722—21no—
22C2×#3722—21no—
23C2×#3722—21no—
24#63894—22no—
25#63894C2214yescomplemented
26#63864—22no—
27#63864C2214yescomplemented
28C2×#3717—24no—
29C2×#3717C2214yescomplemented
30C3×#816C2214yescomplemented
31C3×Dic3⋊C8C2214yescomplemented
32#63564C2214yescomplemented
33C2×#947—31no—
34C22×#215—31no—
35C22×D24—31no—
36C22×D24—31no—
37C22×D24—61no—
38C22×#204—31no—
39C2×#893—31no—
40C2×#875—31no—
41C2×C4×D12—31no—
42C2×C3×C4⋊C8—31no—
43C2×C3×#103—31no—
44C2×#821—31no—
45C2×#816D311yescharacteristic, complemented
46C2×Dic3⋊C8D311yescharacteristic, complemented
47C2×#809—31no—
48#4844—38no—
49#4819—38no—
50C23×C3⋊D3—21no—
51C23×C3⋊D3—21no—
52C22×C32×C4C2311yescharacteristic
53C2×C4⋊(C3⋊D3)—21no—
54C2×C4⋊(C3⋊D3)—22no—
55C2×C4⋊(C3⋊D3)—22no—
56C2×C4⋊(C3⋊D3)—22no—
57C2×C4⋊(C3⋊D3)—21no—
58C2×C4⋊(C3⋊D3)D414yes—
59C2×C4⋊(C3⋊D3)C2312yes—
60C2×C4⋊(C3⋊D3)C2312yes—
61C22×C3×Dic3—21no—
62C22×C3×Dic3—21no—
63C22×C3×Dic3D411yescharacteristic
64C22×C3×Dic3D411yescharacteristic
65C2×C3×Dic6—22no—
66C2×C3×Dic6—22no—
67C2×C3×Dic6—21no—
68C2×C3×Dic6C2312yes—
69C2×#624—24no—
70C2×#624—44no—
71C2×C32×C8—22no—
72C2×C32×C8C2312yes—
73#3745—28no—
74C3×C4⋊Dic3—21no—
75C3×C4⋊Dic3C2312yes—
76C3×C4×Dic3D412yes—
77C3×C4×Dic3C2312yes—
78C2×C3×C3⋊C8—22no—
79C2×C3×C3⋊C8C2312yes—
80#3722—24no—
81#3722—24no—
82#3722—24no—
83#3717—28no—
84C2×#463—91noSylow
85C22×C3×Q8—31no—
86C22×D12—31no—
87C22×D12—31no—
88C22×D12—31no—
89C22×D12—31no—
90C22×D12—61no—
91C22×D12—61no—
92C22×C4×D3—61no—
93C22×C4×D3—61no—
94C22×Dic6C2×D311yescharacteristic
95C22×C3×C8—21no—
96C22×C3×C8—31no—
97C22×C3×C8C2×D311yescharacteristic
98C22×C3×C8C2×D311yescharacteristic
99C2×C3×C4⋊C4—31no—
100C2×C3×C42—31no—
101#947—34no—
102#947—62no—
103C2×#215—34no—
104C2×#215—64no—
105C2×(C2×D3)⋊C4—61no—
106C2×(C2×D3)⋊C4—61no—
107C2×(C2×D3)⋊C4—61no—
108C2×(C2×D3)⋊C4—61no—
109C2×(C2×D3)⋊C4—61no—
110C2×(C2×D3)⋊C4—61no—
111C2×C4⋊Dic3C2×D311yescharacteristic
112C2×C4×Dic3C2×D311yescharacteristic
113C22×C3⋊C8C2×D311yescharacteristic
114C2×D24—34no—
115C2×D24—34no—
116C2×D24—64no—
117C2×D24—64no—
118C2×D24—64no—
119C2×D24—68no—
120C2×#204—34no—
121C2×#204—64no—
122#893—34no—
123#893—62no—
124#875—34no—
125#875—62no—
126C4×D12—34no—
127C4×D12—62no—
128C3×C4⋊C8—34no—
129C3×#103—34no—
130#821—34no—
131#816C2×D314yescomplemented
132Dic3⋊C8C2×D314yescomplemented
133#809—34no—
134C23×C32C2×D411yescharacteristic
135C22×C3⋊D3—24no—
136C22×C3⋊D3—22no—
137C22×C3⋊D3—22no—
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
147C4⋊(C3⋊D3)—22no—
148C4⋊(C3⋊D3)—24no—
149C4⋊(C3⋊D3)—22no—
150C4⋊(C3⋊D3)—22no—
151C4⋊(C3⋊D3)—42no—
152C4⋊(C3⋊D3)C2×D414yes—
153C2×C3×Dic3—22no—
154C2×C3×Dic3—22no—
155C2×C3×Dic3—22no—
156C2×C3×Dic3—22no—
157C2×C3×Dic3—42no—
158C2×C3×Dic3—42no—
159C2×C3×Dic3C2×D412yes—
160C2×C3×Dic3C2×D412yes—
161C3×Dic6—22no—
162C3×Dic6—22no—
163C3×Dic6—42no—
164#624—48no—
165C32×C8—22no—
166C3×C3⋊C8—22no—
167C22×SD16—91no—
168C22×D8—91no—
169C2×#124—91no—
170C2×C4×D4—91no—
171#463—98no—
172C2×C4⋊C8—31no—
173C2×#103—31no—
174C2×#102—91no—
175C23×D3—61no—
176C23×D3—61no—
177C23×D3—61no—
178C23×D3—61no—
179C23×D3—121no—
180C23×D3—121no—
181C2×C3×Q8—32no—
182C2×C3×Q8—61no—
183C2×C3×Q8—62no—
184C2×C3×Q8—62no—
185C22×C3×C4—21no—
186C22×C3×C4—31no—
187C22×C3×C4—31no—
188C22×C3×C4—61no—
189C22×C3×C4—61no—
190C22×C3×C4C22×D311yescharacteristic
191C22×C3×C4C22×D311yescharacteristic
192C22×Dic3—21no—
193C22×Dic3—21no—
194C22×Dic3D1211yescharacteristic
195C22×Dic3D1211yescharacteristic
196C2×D12—34no—
197C2×D12—34no—
198C2×D12—32no—
199C2×D12—32no—
200C2×D12—32no—
201C2×D12—32no—
202C2×D12—64no—
203C2×D12—62no—
204C2×D12—62no—
205C2×D12—61no—
206C2×D12—62no—
207C2×D12—61no—
208C2×D12—62no—
209C2×D12—64no—
210C2×D12—62no—
211C2×D12—62no—
212C2×D12—62no—
213C2×D12—62no—
214C2×D12—61no—
215C2×D12—61no—
216C2×D12—122no—
217C2×D12—122no—
218C2×D12—121no—
219C2×D12—121no—
220C2×C4×D3—64no—
221C2×C4×D3—64no—
222C2×C4×D3—124no—
223C2×C4×D3—124no—
224C2×Dic6—22no—
225C2×Dic6—22no—
226C2×Dic6—21no—
227C2×Dic6C22×D312yes—
228C2×C3×C8—24no—
229C2×C3×C8—22no—
230C2×C3×C8—22no—
231C2×C3×C8—22no—
232C2×C3×C8—32no—
233C2×C3×C8—62no—
234C2×C3×C8C22×D312yes—
235C2×C3×C8C22×D312yes—
236C3×C4⋊C4—32no—
237C3×C4⋊C4—61no—
238C3×C42—32no—
239C3×C42—32no—
240#215—68no—
241(C2×D3)⋊C4—64no—
242(C2×D3)⋊C4—64no—
243(C2×D3)⋊C4—64no—
244(C2×D3)⋊C4—64no—
245(C2×D3)⋊C4—64no—
246(C2×D3)⋊C4—64no—
247C4⋊Dic3—21no—
248C4⋊Dic3C22×D312yes—
249C4×Dic3D1212yes—
250C4×Dic3C22×D312yes—
251C2×C3⋊C8—22no—
252C2×C3⋊C8C22×D312yes—
253D24—68no—
254D24—68no—
255D24—616no—
256#204—68no—
257C22×C32#12112yes—
258C22×C32#13512yes—
259C22×C32AGL(1,ℤ/8)12yes—
260C22×C32C22×D411yescharacteristic
261C2×C3⋊D3—24no—
262C2×C3⋊D3—42no—
263C2×C3⋊D3—42no—
264C2×C3⋊D3—42no—
265C2×C3⋊D3—48no—
266C2×C3⋊D3—42no—
267C2×C3⋊D3—42no—
268C2×C3⋊D3—84no—
269C32×C4#12112yes—
270C32×C4C22×D411yescharacteristic
271C32×C4C2×#4111yescharacteristic
272C3×Dic3—22no—
273C3×Dic3—22no—
274C3×Dic3—42no—
275C3×Dic3—42no—
276C22×Q8—31no—
277C22×D4—91no—
278C22×D4—91no—
279C23×C4—181no—
280C2×SD16—94no—
281C2×SD16—184no—
282C2×D8—94no—
283C2×D8—184no—
284C22×C8—31no—
285C22×C8D3211yescharacteristic
286#124—94no—
287#124—182no—
288C4×D4—94no—
289C4×D4—182no—
290C2×C4⋊C4—31no—
291C2×C22⋊C4—181no—
292C2×C22⋊C4—181no—
293C2×C22⋊C4—181no—
294C2×C42—31no—
295C4⋊C8—34no—
296#103—34no—
297#102—94no—
298C23×C3—21no—
299C23×C3C2×D1211yescharacteristic
300C23×C3D3×D411yescharacteristic
301C22×D3—64no—
302C22×D3—64no—
303C22×D3—62no—
304C22×D3—62no—
305C22×D3—62no—
306C22×D3—62no—
307C22×D3—122no—
308C22×D3—124no—
309C22×D3—122no—
310C22×D3—122no—
311C22×D3—122no—
312C22×D3—122no—
313C22×D3—122no—
314C22×D3—124no—
315C22×D3—122no—
316C22×D3—122no—
317C22×D3—122no—
318C22×D3—122no—
319C22×D3—122no—
320C22×D3—122no—
321C22×D3—242no—
322C22×D3—242no—
323C22×D3—242no—
324C22×D3—242no—
325C3×Q8—62no—
326C3×Q8—62no—
327C3×Q8—122no—
328C2×C3×C4—21no—
329C2×C3×C4—22no—
330C2×C3×C4—21no—
331C2×C3×C4—22no—
332C2×C3×C4—32no—
333C2×C3×C4—32no—
334C2×C3×C4—62no—
335C2×C3×C4—62no—
336C2×C3×C4—62no—
337C2×C3×C4—62no—
338C2×C3×C4—122no—
339C2×C3×C4—122no—
340C2×C3×C4C2×D1211yescharacteristic
341C2×C3×C4#23512yes—
342C2×C3×C4D3×D411yescharacteristic
343C2×C3×C4D3×D412yes—
344C2×C3×C4D3×D412yes—
345C2×C3×C4#23912yes—
346C2×C3×C4C23×D311yescharacteristic
347C2×C3×C4C23×D311yescharacteristic
348C2×Dic3—22no—
349C2×Dic3—22no—
350C2×Dic3—22no—
351C2×Dic3—22no—
352C2×Dic3—42no—
353C2×Dic3—42no—
354C2×Dic3C2×D1212yes—
355C2×Dic3C2×D1212yes—
356D12—34no—
357D12—34no—
358D12—64no—
359D12—64no—
360D12—64no—
361D12—64no—
362D12—62no—
363D12—62no—
364D12—62no—
365D12—62no—
366D12—62no—
367D12—62no—
368D12—122no—
369D12—122no—
370D12—124no—
371D12—124no—
372D12—122no—
373D12—122no—
374C4×D3—128no—
375C4×D3—128no—
376Dic6—22no—
377Dic6—22no—
378Dic6—42no—
379C3×C8—24no—
380C3×C8—22no—
381C3×C8—22no—
382C3×C8—62no—
383C3⋊C8—22no—
384C2×C32#46314yescomplemented
385C2×C32C2×#12111yescharacteristic
386C2×C32C2×#13511yescharacteristic
387C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
388C3⋊D3—44no—
389C3⋊D3—82no—
390C24—181no—
391C24—181no—
392C2×Q8—32no—
393C2×Q8—61no—
394C2×Q8—62no—
395C2×Q8—62no—
396C2×D4—92no—
397C2×D4—92no—
398C2×D4—94no—
399C2×D4—182no—
400C2×D4—182no—
401C2×D4—181no—
402C2×D4—181no—
403C2×D4—182no—
404C22×C4—31no—
405C22×C4—31no—
406C22×C4—61no—
407C22×C4—61no—
408C22×C4—184no—
409C22×C4—364no—
410C22×C4C2×D3211yescharacteristic
411SD16—188no—
412D8—188no—
413C2×C8—22no—
414C2×C8—32no—
415C2×C8—62no—
416C2×C8C2×D3212yes—
417C4⋊C4—32no—
418C4⋊C4—61no—
419C22⋊C4—184no—
420C22⋊C4—184no—
421C22⋊C4—184no—
422C42—32no—
423C42—32no—
424C22×C3—21no—
425C22×C3—22no—
426C22×C3—22no—
427C22×C3—22no—
428C22×C3#88412yes—
429C22×C3#89512yes—
430C22×C3#90412yes—
431C22×C3#90812yes—
432C22×C3#91412yes—
433C22×C3#91912yes—
434C22×C3C22×D1211yescharacteristic
435C22×C3C2×D3×D411yescharacteristic
436C2×D3—64no—
437C2×D3—64no—
438C2×D3—124no—
439C2×D3—122no—
440C2×D3—122no—
441C2×D3—122no—
442C2×D3—122no—
443C2×D3—128no—
444C2×D3—128no—
445C2×D3—124no—
446C2×D3—122no—
447C2×D3—122no—
448C2×D3—122no—
449C2×D3—122no—
450C2×D3—122no—
451C2×D3—122no—
452C2×D3—248no—
453C2×D3—242no—
454C2×D3—242no—
455C2×D3—242no—
456C2×D3—242no—
457C2×D3—248no—
458C2×D3—244no—
459C2×D3—244no—
460C3×C4—21no—
461C3×C4—21no—
462C3×C4—22no—
463C3×C4—62no—
464C3×C4—62no—
465C3×C4—122no—
466C3×C4—122no—
467C3×C4#88412yes—
468C3×C4#89512yes—
469C3×C4C2×#23511yescharacteristic
470C3×C4C2×D3×D411yescharacteristic
471C3×C4C2×D3×D411yescharacteristic
472C3×C4C2×#23911yescharacteristic
473Dic3—22no—
474Dic3—22no—
475Dic3—42no—
476Dic3—42no—
477C32C2×#46311yescharacteristic, complemented, Sylow
478C23—182no—
479C23—184no—
480C23—182no—
481C23—362no—
482C23—362no—
483C23—362no—
484C23—362no—
485C23—362no—
486C23D3×D1211yescharacteristic
487Q8—62no—
488Q8—62no—
489Q8—122no—
490D4—94no—
491D4—182no—
492D4—182no—
493D4—182no—
494D4—184no—
495D4—362no—
496C2×C4—32no—
497C2×C4—32no—
498C2×C4—62no—
499C2×C4—62no—
500C2×C4—62no—
501C2×C4—62no—
502C2×C4—122no—
503C2×C4—122no—
504C2×C4—368no—
505C2×C4#379912yes—
506C2×C4D3×D1211yescharacteristic
507C2×C4#381112yes—
508C2×C4C22×D3211yescharacteristic
509C8—22no—
510C8—62no—
511C2×C3—24no—
512C2×C3—21no—
513C2×C3—21no—
514C2×C3—21no—
515C2×C3#481914yescomplemented
516C2×C3#484414yescomplemented
517C2×C3C2×#88411yescharacteristic
518C2×C3C2×#89511yescharacteristic
519C2×C3C2×#90411yescharacteristic
520C2×C3C2×#90811yescharacteristic
521C2×C3C2×#91411yescharacteristic
522C2×C3C2×#91911yescharacteristic
523D3—124no—
524D3—124no—
525D3—244no—
526D3—244no—
527D3—242no—
528D3—242no—
529C22—184no—
530C22—368no—
531C22—362no—
532C22—362no—
533C22—362no—
534C22—362no—
535C22—362no—
536C22—724no—
537C22#6379412yes—
538C22#6380812yes—
539C22#6391012yes—
540C22C2×D3×D1211yescharacteristic
541C4—62no—
542C4—62no—
543C4—122no—
544C4—122no—
545C4#6391012yes—
546C4C2×#379911yescharacteristic
547C4C2×#381111yescharacteristic
548C3—21no—
549C3C2×#481911yescharacteristic, complemented
550C3C2×#484411yescharacteristic, complemented
551C2—364no—
552C2—722no—
553C2#1059077014yesdirect product factor
554C2C2×#6379411yescharacteristic
555C2C2×#6380811yescharacteristic
556C2C2×#6391011yescharacteristic
subgroupG/H
centerC23D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC22×#3745C2
hypercenterC22×C8D32
hypocenterC32C2×#463
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
2. C2×#63894C2semidirect
3. C2×#63864C2semidirect
4. C22×#3717C2semidirect
5. C2×C3×#816C2semidirect
6. C2×C3×Dic3⋊C8C2semidirect
7. C2×#63564C2semidirect
8. #10590770C2direct (N × H)
25. #63894C22semidirect
27. #63864C22semidirect
29. C2×#3717C22semidirect
30. C3×#816C22semidirect
31. C3×Dic3⋊C8C22semidirect
32. #63564C22semidirect
45. C2×#816D3semidirect
46. C2×Dic3⋊C8D3semidirect
131. #816C2×D3semidirect
132. Dic3⋊C8C2×D3semidirect
384. C2×C32#463semidirect
477. C32C2×#463semidirect
515. C2×C3#4819semidirect
516. C2×C3#4844semidirect
549. C3C2×#4819semidirect
550. C3C2×#4844semidirect
553. C2#10590770direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37452
C2×#638942
C2×#638642
C22×#37172
C2×C3×#8162
C2×C3×Dic3⋊C82
C2×#635642
#105907702
C2×#48443
C2×#48193