Finite Group Databasebeta

← C2×#10594692 #11918939

Subgroups — C2×#10594692 #11918939

Order 1152.

2945 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64298C212yesmaximal, complemented
2C22×#3746C211yesmaximal, characteristic, complemented
3C2×C3×#904C211yesmaximal, characteristic, complemented
4C2×C3×#901C211yesmaximal, characteristic, complemented
5C2×#63831C212yesmaximal, complemented
6C2×#63807C212yesmaximal, complemented
7#10594692C2116yesmaximal, direct product factor
8C2×#63800C214yesmaximal, complemented
9C2×D3×Dic12C212yesmaximal, complemented
10C2×#5771—31nomaximal
11C2×#5753—31nomaximal
12C22×#634C2212yes—
13C2×C3×#235C2211yescharacteristic
14C2×C3×#235C2212yes—
15C2×#3805—24no—
16#64298—28no—
17#64298C22116yescomplemented
18C2×#3795—22no—
19C2×#3795C2214yes—
20C2×D3×Dic6—22no—
21C2×D3×Dic6C2214yes—
22C22×C32×C8C2211yescharacteristic
23C2×#3746C2212yes—
24C2×#3746C2212yes—
25C2×#3746C2218yescomplemented
26C2×C3×#208C2211yescharacteristic
27C2×C3×Dic12C2211yescharacteristic
28C3×#904C2218yescomplemented
29C2×C3×D24C2211yescharacteristic
30C2×C3×#204C2212yes—
31C3×#901C2218yescomplemented
32C2×C3×ΓL(1,𝔽25)C2212yes—
33C2×C3×D3×C8C2212yes—
34C2×#3719C2214yes—
35#63831C22116yescomplemented
36C2×#3716C2214yes—
37#63807C22116yescomplemented
38#63800C22132yescomplemented
39D3×Dic12C22116yescomplemented
40C2×#1010—32no—
41C2×#1010—32no—
42C2×C3×#135—31no—
43C2×C3×#131—31no—
44C2×#951—32no—
45#5771—316no—
46C2×D3×Q16—32no—
47C2×#915—34no—
48C2×#912—32no—
49#5753—316no—
50C2×#909—32no—
51C2×#909—34no—
52C22×Dic12—31no—
53C22×Dic12—31no—
54C22×Dic12—32no—
55C22×Dic12—61no—
56C2×#904—32no—
57C2×#904D311yescharacteristic, complemented
58C2×#901D311yescharacteristic, complemented
59C22×C32×C4C2311yescharacteristic
60C22×C3⋊Dic3—22no—
61C2×#634—22no—
62C2×#634—24no—
63C2×#634C2314yes—
64C2×#634C2318yes—
65C2×C3×#67—22no—
66C2×C3×#67D412yes—
67C3×#235—24no—
68C3×#235D414yes—
69C3×#235C2314yes—
70C3×#235C2318yes—
71C2×C3×D12D411yescharacteristic
72C2×C3×D12C2312yes—
73C2×C3×C4×D3—22no—
74C2×C3×C4×D3C2312yes—
75C2×C3×Dic6D411yescharacteristic
76C2×C3×Dic6C2312yes—
77C2×#627—24no—
78C2×#625—24no—
79#3805—232no—
80C2×D3×Dic3—24no—
81C2×D3×Dic3—24no—
82#3795—216no—
83#3795—28no—
84#3795C23116yes—
85D3×Dic6—28no—
86D3×Dic6—216no—
87D3×Dic6C23116yes—
88C2×C32×C8C2311yescharacteristic
89C2×C32×C8C2311yescharacteristic
90C2×C32×C8C2314yes—
91#3746C2318yes—
92#3746C2318yes—
93C3×#208C2314yes—
94C2×C3×C3⋊C8C2312yes—
95C3×Dic12C2314yes—
96C3×D24C2314yes—
97C3×#204C2318yes—
98C3×ΓL(1,𝔽25)C2318yes—
99C3×D3×C8C2318yes—
100#3719C23116yes—
101#3716C23116yes—
102C2×#578—91noSylow
103C2×C3×#41—31no—
104C2×C3×#41—32no—
105#1010—316no—
106#1010—316no—
107#1010—68no—
108#1010—68no—
109C2×D3×Q8—34no—
110C2×D3×Q8—62no—
111C2×#237—34no—
112C2×#237—62no—
113C2×#237—64no—
114C2×#237—64no—
115C2×#235—34no—
116C2×#235—62no—
117C2×#235C2×D311yescharacteristic
118C2×#235C2×D312yes—
119C22×Dic6—32no—
120C22×Dic6—32no—
121C22×Dic6—34no—
122C22×Dic6—62no—
123C22×Dic6—62no—
124C3×#135—38no—
125C2×C3×Q16—31no—
126C2×C3×SD16—32no—
127C2×C3×D8—31no—
128C3×#131—38no—
129C2×C3×M16—31no—
130C2×C3×M16—32no—
131C22×C3×C8—21no—
132C22×C3×C8—32no—
133C22×C3×C8C2×D311yescharacteristic
134C22×C3×C8C2×D311yescharacteristic
135#951—316no—
136C2×#216—34no—
137C2×#214—34no—
138C2×#208C2×D311yescharacteristic
139D3×Q16—316no—
140#915—332no—
141#912—316no—
142#909—316no—
143#909—332no—
144C2×Dic12—34no—
145C2×Dic12—32no—
146C2×Dic12—32no—
147C2×Dic12—32no—
148C2×Dic12—32no—
149C2×Dic12—38no—
150C2×Dic12—38no—
151C2×Dic12—316no—
152C2×Dic12—62no—
153C2×Dic12—62no—
154C2×Dic12—68no—
155C2×Dic12C2×D311yescharacteristic
156#904—316no—
157#904C2×D318yescomplemented
158C2×D24C2×D311yescharacteristic
159C2×#204—34no—
160C2×#204C2×D312yes—
161#901C2×D318yescomplemented
162C2×ΓL(1,𝔽25)C2×D312yes—
163C2×D3×C8C2×D312yes—
164C23×C32C2×D411yescharacteristic
165C22×C3×D3—22no—
166C22×C3×D3C2×D412yes—
167C2×C32×C4C2×D411yescharacteristic
168C2×C32×C4C2×D412yes—
169C2×C32×C4C2411yescharacteristic
170C2×C32×C4C2412yes—
171C2×C3⋊Dic3—24no—
172C2×C3⋊Dic3—28no—
173#634—28no—
174#634—24no—
175#634C2418yes—
176C3×#67—28no—
177C3×#67C2×D418yes—
178C2×C3×Dic3—22no—
179C2×C3×Dic3C2×D412yes—
180C3×D12—22no—
181C3×D12C2×D414yes—
182C3×D12C2414yes—
183C3×C4×D3—28no—
184C3×C4×D3C2×D414yes—
185C3×C4×D3C2414yes—
186C3×Dic6—22no—
187C3×Dic6C2×D414yes—
188C3×Dic6C2414yes—
189#627—216no—
190#625—216no—
191D3×Dic3—216no—
192D3×Dic3—216no—
193C32×C8C2412yes—
194C32×C8C2412yes—
195C3×C3⋊C8C2414yes—
196C2×2−1+4—92no—
197#578—916no—
198C2×#137—94no—
199C2×#137—92no—
200C2×#135—31no—
201C2×#135—92no—
202C22×Q16—92no—
203C22×Q16—91no—
204C2×#131—31no—
205C3×#41—34no—
206C3×#41—34no—
207C3×#41—38no—
208C3×#41—64no—
209C2×C3×Q8—31no—
210C2×C3×Q8—32no—
211C2×C3×D4—32no—
212C2×C3×D4—31no—
213C2×C3×D4—32no—
214C2×C3×D4—62no—
215C22×C3×C4—21no—
216C22×C3×C4—32no—
217C22×C3×C4—62no—
218C22×C3×C4C22×D311yescharacteristic
219C22×C3×C4C22×D311yescharacteristic
220C2×#67—22no—
221C2×#67—64no—
222C2×#67—64no—
223C2×#67D1212yes—
224C22×Dic3—64no—
225C22×Dic3—62no—
226C22×Dic3—62no—
227C22×Dic3—64no—
228C22×Dic3—122no—
229D3×Q8—316no—
230D3×Q8—616no—
231D3×Q8—68no—
232#237—316no—
233#237—616no—
234#237—632no—
235#237—632no—
236#237—68no—
237#235—24no—
238#235—316no—
239#235—68no—
240#235—616no—
241#235D1214yes—
242#235C22×D314yes—
243#235C22×D318yes—
244C2×D12D1211yescharacteristic
245C2×D12C22×D312yes—
246C2×C4×D3—22no—
247C2×C4×D3—64no—
248C2×C4×D3—64no—
249C2×C4×D3C22×D312yes—
250C2×Dic6—34no—
251C2×Dic6—38no—
252C2×Dic6—34no—
253C2×Dic6—38no—
254C2×Dic6—316no—
255C2×Dic6—64no—
256C2×Dic6—68no—
257C2×Dic6—68no—
258C2×Dic6—64no—
259C2×Dic6—62no—
260C2×Dic6—64no—
261C2×Dic6—62no—
262C2×Dic6—64no—
263C2×Dic6—64no—
264C2×Dic6—616no—
265C2×Dic6—122no—
266C2×Dic6—124no—
267C2×Dic6D1211yescharacteristic
268C2×Dic6C22×D312yes—
269C3×Q16—34no—
270C3×SD16—38no—
271C3×D8—34no—
272C3×M16—34no—
273C3×M16—38no—
274C2×C3×C8—21no—
275C2×C3×C8—21no—
276C2×C3×C8—24no—
277C2×C3×C8—32no—
278C2×C3×C8—38no—
279C2×C3×C8C22×D311yescharacteristic
280C2×C3×C8C22×D311yescharacteristic
281C2×C3×C8C22×D314yes—
282C2×C3×C8C22×D311yescharacteristic
283C2×C3×C8C22×D311yescharacteristic
284C2×C3×C8C22×D314yes—
285#216—316no—
286#214—316no—
287#208C22×D314yes—
288C2×C3⋊C8C22×D312yes—
289Dic12—316no—
290Dic12—38no—
291Dic12—38no—
292Dic12—38no—
293Dic12—38no—
294Dic12—68no—
295Dic12—68no—
296Dic12C22×D314yes—
297D24C22×D314yes—
298#204—316no—
299#204C22×D318yes—
300ΓL(1,𝔽25)C22×D318yes—
301D3×C8C22×D318yes—
302C22×C32—22no—
303C22×C32C22×D412yes—
304C22×C32C22×D411yescharacteristic
305C2×C3×D3—24no—
306C2×C3×D3—24no—
307C2×C3×D3—44no—
308C2×C3×D3C22×D414yes—
309C32×C4C22×D411yescharacteristic
310C32×C4C22×D412yes—
311C32×C4C2511yescharacteristic
312C3⋊Dic3—28no—
313C3×Dic3—24no—
314C3×Dic3C22×D414yes—
3152−1+4—916no—
3162−1+4—188no—
317C2×#41—31no—
318C2×#41—32no—
319C2×#41—94no—
320C2×#41—182no—
321C2×#41—184no—
322C22×Q8—94no—
323C22×Q8—92no—
324C22×Q8—182no—
325#137—932no—
326#137—916no—
327#135—38no—
328#135—916no—
329C2×Q16—31no—
330C2×Q16—916no—
331C2×Q16—94no—
332C2×Q16—92no—
333C2×Q16—92no—
334C2×Q16—98no—
335C2×SD16—32no—
336C2×SD16—94no—
337C2×D8—31no—
338#131—38no—
339C2×M16—31no—
340C2×M16—32no—
341C22×C8—32no—
342C22×C8D3211yescharacteristic
343C23×C3—21no—
344C23×C3—32no—
345C23×C3—62no—
346C23×C3C2×D1211yescharacteristic
347C23×C3D3×D411yescharacteristic
348C22×D3—22no—
349C22×D3C2×D1212yes—
350C3×Q8—34no—
351C3×Q8—34no—
352C3×Q8—62no—
353C3×D4—38no—
354C3×D4—34no—
355C3×D4—34no—
356C3×D4—68no—
357C3×D4—62no—
358C2×C3×C4—22no—
359C2×C3×C4—21no—
360C2×C3×C4—22no—
361C2×C3×C4—21no—
362C2×C3×C4—32no—
363C2×C3×C4—34no—
364C2×C3×C4—34no—
365C2×C3×C4—62no—
366C2×C3×C4—68no—
367C2×C3×C4C2×D1211yescharacteristic
368C2×C3×C4C2×D1212yes—
369C2×C3×C4D3×D411yescharacteristic
370C2×C3×C4D3×D412yes—
371C2×C3×C4C23×D311yescharacteristic
372C2×C3×C4C23×D312yes—
373C2×C3×C4C23×D311yescharacteristic
374C2×C3×C4C23×D312yes—
375#67—28no—
376#67—616no—
377#67—616no—
378#67C2×D1218yes—
379C2×Dic3—22no—
380C2×Dic3—616no—
381C2×Dic3—64no—
382C2×Dic3—68no—
383C2×Dic3—64no—
384C2×Dic3—68no—
385C2×Dic3—616no—
386C2×Dic3—128no—
387C2×Dic3—124no—
388C2×Dic3C2×D1212yes—
389D12—22no—
390D12C2×D1214yes—
391D12C23×D314yes—
392C4×D3—28no—
393C4×D3—616no—
394C4×D3—616no—
395C4×D3C2×D1214yes—
396C4×D3C23×D314yes—
397Dic6—22no—
398Dic6—38no—
399Dic6—38no—
400Dic6—68no—
401Dic6—616no—
402Dic6—68no—
403Dic6—64no—
404Dic6—64no—
405Dic6—68no—
406Dic6—616no—
407Dic6—124no—
408Dic6—128no—
409Dic6C2×D1214yes—
410Dic6C23×D314yes—
411C3×C8—22no—
412C3×C8—22no—
413C3×C8—34no—
414C3×C8C23×D312yes—
415C3×C8C23×D312yes—
416C3×C8C23×D312yes—
417C3×C8C23×D312yes—
418C3⋊C8C23×D314yes—
419C2×C32—22no—
420C2×C32#57812yescomplemented
421C2×C32C23×D411yescharacteristic
422C3×D3—24no—
423C3×D3—44no—
424#41—34no—
425#41—34no—
426#41—38no—
427#41—64no—
428#41—916no—
429#41—188no—
430#41—1816no—
431#41—1832no—
432C2×Q8—31no—
433C2×Q8—32no—
434C2×Q8—916no—
435C2×Q8—94no—
436C2×Q8—98no—
437C2×Q8—184no—
438C2×Q8—188no—
439C2×Q8—1816no—
440C2×Q8—182no—
441C2×Q8—184no—
442C2×D4—32no—
443C2×D4—32no—
444C2×D4—31no—
445C2×D4—62no—
446C2×D4—184no—
447C22×C4—32no—
448C22×C4—62no—
449C22×C4—184no—
450C22×C4—184no—
451C22×C4—182no—
452C22×C4C2×D3211yescharacteristic
453Q16—34no—
454Q16—916no—
455Q16—98no—
456Q16—98no—
457SD16—38no—
458SD16—916no—
459D8—34no—
460M16—34no—
461M16—38no—
462C2×C8—32no—
463C2×C8—38no—
464C2×C8C2×D3211yescharacteristic
465C2×C8C2×D3211yescharacteristic
466C2×C8C2×D3214yes—
467C22×C3—24no—
468C22×C3—22no—
469C22×C3—22no—
470C22×C3—22no—
471C22×C3—21no—
472C22×C3—34no—
473C22×C3—64no—
474C22×C3—64no—
475C22×C3—124no—
476C22×C3C22×D1212yes—
477C22×C3C22×D1211yescharacteristic
478C22×C3C2×D3×D412yes—
479C22×C3C2×D3×D411yescharacteristic
480C2×D3—24no—
481C2×D3—24no—
482C2×D3—44no—
483C2×D3C22×D1214yes—
484C3×C4—21no—
485C3×C4—22no—
486C3×C4—21no—
487C3×C4—34no—
488C3×C4—64no—
489C3×C4C22×D1212yes—
490C3×C4C22×D1211yescharacteristic
491C3×C4C2×D3×D411yescharacteristic
492C3×C4C2×D3×D412yes—
493C3×C4C24×D311yescharacteristic
494C3×C4C24×D311yescharacteristic
495Dic3—24no—
496Dic3—68no—
497Dic3—68no—
498Dic3—128no—
499Dic3C22×D1214yes—
500C32C2×#57811yescharacteristic, complemented, Sylow
501C23—32no—
502C23—62no—
503C23D3×D1211yescharacteristic
504Q8—34no—
505Q8—34no—
506Q8—62no—
507Q8—98no—
508Q8—1816no—
509Q8—184no—
510Q8—188no—
511D4—38no—
512D4—34no—
513D4—34no—
514D4—68no—
515D4—62no—
516D4—1816no—
517C2×C4—32no—
518C2×C4—34no—
519C2×C4—34no—
520C2×C4—62no—
521C2×C4—68no—
522C2×C4—1816no—
523C2×C4—1816no—
524C2×C4—188no—
525C2×C4—184no—
526C2×C4D3×D1212yes—
527C2×C4D3×D1211yescharacteristic
528C2×C4C22×D3212yes—
529C2×C4C22×D3211yescharacteristic
530C8—34no—
531C8C22×D3212yes—
532C8C22×D3212yes—
533C2×C3—24no—
534C2×C3—22no—
535C2×C3—22no—
536C2×C3—21no—
537C2×C3—22no—
538C2×C3—64no—
539C2×C3—124no—
540C2×C3#575312yescomplemented
541C2×C3#577112yescomplemented
542C2×C3C23×D1211yescharacteristic
543C2×C3C22×D3×D411yescharacteristic
544D3—24no—
545D3—44no—
546C22—22no—
547C22—34no—
548C22—64no—
549C22—64no—
550C22—124no—
551C22C2×D3×D1212yes—
552C22C2×D3×D1211yescharacteristic
553C4—34no—
554C4—64no—
555C4—188no—
556C4C2×D3×D1211yescharacteristic
557C4C2×D3×D1212yes—
558C4C23×D3211yescharacteristic
559C3—21no—
560C3C2×#575311yescharacteristic, complemented
561C3C2×#577111yescharacteristic, complemented
562C2—22no—
563C2—64no—
564C2—124no—
565C2#1059469212yesdirect product factor
566C2C22×D3×D1211yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC32×C4C25
FrattiniC4C23×D32
FittingC22×C32×C8C22
socleC22×C32C22×D4
hypercenterC22×C8D32
hypocenterC32C2×#578
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#64298C2semidirect
2. C22×#3746C2semidirect
3. C2×C3×#904C2semidirect
4. C2×C3×#901C2semidirect
5. C2×#63831C2semidirect
6. C2×#63807C2semidirect
7. #10594692C2direct (N × H)
8. C2×#63800C2semidirect
9. C2×D3×Dic12C2semidirect
17. #64298C22semidirect
25. C2×#3746C22semidirect
28. C3×#904C22semidirect
31. C3×#901C22semidirect
35. #63831C22semidirect
37. #63807C22semidirect
38. #63800C22semidirect
39. D3×Dic12C22semidirect
57. C2×#904D3semidirect
58. C2×#901D3semidirect
157. #904C2×D3semidirect
161. #901C2×D3semidirect
420. C2×C32#578semidirect
500. C32C2×#578semidirect
540. C2×C3#5753semidirect
541. C2×C3#5771semidirect
560. C3C2×#5753semidirect
561. C3C2×#5771semidirect
565. C2#10594692direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#642982
C22×#37462
C2×C3×#9042
C2×C3×#9012
C2×#638312
C2×#638072
#105946922
C2×#638002
C2×D3×Dic122
C2×#57713
C2×#57533