Finite Group Databasebeta

← C2×#10590608 #11857795

Subgroups — C2×#10590608 #11857795

Order 1152.

1665 conjugacy classes of subgroups.

The subgroup lattice has 559 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3795C211yesmaximal, characteristic
2C2×C3×#892C211yesmaximal, characteristic, complemented
3C22×D3×C3⋊C8C211yesmaximal, characteristic, complemented
4C2×#63637C211yesmaximal, characteristic, complemented
5C2×C3×#809C211yesmaximal, characteristic, complemented
6C2×#63567C211yesmaximal, characteristic, complemented
7C2×#63562C211yesmaximal, characteristic, complemented
8#10590608C218yesmaximal, direct product factor
9C2×#5002—31nomaximal
10C2×#4772—31nomaximal
11C22×#634C2211yescharacteristic
12C22×C3×D12C2211yescharacteristic
13C22×C3×C4×D3C2211yescharacteristic
14C22×#625—21no—
15C22×D3×Dic3—21no—
16C2×#3795—22no—
17C2×#3795—24no—
18C2×#3795C418yescomplemented
19C2×#3795C2214yes—
20C2×C32×C4⋊C4C2211yescharacteristic
21C22×C3⋊(C3⋊C8)C2211yescharacteristic
22C2×C3×(C2×D3)⋊C4—21no—
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C2×C3×C4×Dic3—21no—
25C22×C3×C3⋊C8C2211yescharacteristic
26C3×#892—22no—
27C3×#892C2214yescomplemented
28C2×D3×C3⋊C8—24no—
29C2×D3×C3⋊C8C2214yescomplemented
30#63637C2214yescomplemented
31C3×#809C2214yescomplemented
32#63567C2214yescomplemented
33#63562C2214yescomplemented
34C22×#237—31no—
35C22×#235—31no—
36C2×C3×#117—31no—
37C23×C3⋊C8—31no—
38C22×D3×C8—31no—
39C2×#892D311yescharacteristic, complemented
40C2×C3×#102—31no—
41C2×#832—31no—
42C2×#816—31no—
43#5002—38no—
44C2×#810—31no—
45C2×#810—31no—
46C2×#810—31no—
47C2×#810—61no—
48C2×#809—31no—
49C2×#809D311yescharacteristic, complemented
50#4772—38no—
51C23×C3×D3—21no—
52C23×C3×D3D411yescharacteristic
53C22×C32×C4—21no—
54C22×C32×C4C2311yescharacteristic
55C22×C3⋊Dic3—21no—
56C2×#634—21no—
57C2×#634—22no—
58C2×#634C2×C414yes—
59C2×#634C2312yes—
60C22×C3×Dic3—21no—
61C22×C3×Dic3D411yescharacteristic
62C2×C3×D12—21no—
63C2×C3×D12—22no—
64C2×C3×D12C2×C414yes—
65C2×C3×D12C2312yes—
66C2×C3×C4×D3C2×C414yes—
67C2×C3×C4×D3D412yes—
68C2×C3×C4×D3D414yes—
69C2×C3×C4×D3C2312yes—
70C2×#625—28no—
71C2×#625—24no—
72C2×D3×Dic3—28no—
73C2×D3×Dic3—24no—
74#3795—216no—
75#3795—28no—
76#3795C2×C4116yescomplemented
77C32×C4⋊C4—21no—
78C32×C4⋊C4C2312yes—
79C2×C3⋊(C3⋊C8)—22no—
80C2×C3⋊(C3⋊C8)C2312yes—
81C3×(C2×D3)⋊C4—24no—
82C3×C4⋊Dic3—21no—
83C3×C4⋊Dic3C2312yes—
84C3×C4×Dic3—24no—
85C2×C3×C3⋊C8—22no—
86C2×C3×C3⋊C8C2312yes—
87D3×C3⋊C8—28no—
88C2×#416—91noSylow
89C22×C3×D4—31no—
90C23×C3×C4—31no—
91C22×#67—61no—
92C22×#67—61no—
93C23×Dic3—61no—
94C2×#237—38no—
95C2×#237—34no—
96C2×#237—64no—
97C2×#237—62no—
98C2×#235—38no—
99C2×#235—34no—
100C2×#235—64no—
101C2×#235—62no—
102C22×D12C2×D311yescharacteristic
103C22×C4×D3—61no—
104C22×C4×D3C2×D311yescharacteristic
105C22×Dic6—31no—
106C22×Dic6—31no—
107C22×Dic6—61no—
108C22×C3×C8—31no—
109C3×#117—34no—
110C3×#117—62no—
111C2×C3×C4⋊C4—21no—
112C2×C3×C4⋊C4—31no—
113C2×C3×C4⋊C4C2×D311yescharacteristic
114C2×C3×C4⋊C4C2×D311yescharacteristic
115C2×C3×C22⋊C4—61no—
116C2×C3×C42—61no—
117C2×(C2×D3)⋊C4—21no—
118C2×C4⋊Dic3C2×D311yescharacteristic
119C2×C4×Dic3—21no—
120C22×C3⋊C8—31no—
121C22×C3⋊C8—31no—
122C22×C3⋊C8—34no—
123C22×C3⋊C8—61no—
124C22×C3⋊C8—64no—
125C22×C3⋊C8C2×D311yescharacteristic
126C2×D3×C8—34no—
127C2×D3×C8—64no—
128#892—22no—
129#892C2×D314yescomplemented
130C3×#102—34no—
131#832—34no—
132#816—34no—
133#810—34no—
134#810—34no—
135#810—34no—
136#810—64no—
137#809—34no—
138#809C2×D314yescomplemented
139C23×C32C2×D411yescharacteristic
140C22×C3×D3—22no—
141C22×C3×D3—22no—
142C22×C3×D3—24no—
143C22×C3×D3—22no—
144C22×C3×D3—42no—
145C22×C3×D3—42no—
146C22×C3×D3C22⋊C414yes—
147C22×C3×D3C2×D412yes—
148C2×C32×C4—22no—
149C2×C32×C4—42no—
150C2×C32×C4C22×C412yes—
151C2×C32×C4C2×D412yes—
152C2×C32×C4C2×D411yescharacteristic
153C2×C32×C4C2411yescharacteristic
154C2×C3⋊Dic3—24no—
155C2×C3⋊Dic3—22no—
156#634—24no—
157#634—22no—
158#634C22×C414yes—
159C2×C3×Dic3—22no—
160C2×C3×Dic3—42no—
161C2×C3×Dic3C22⋊C414yes—
162C2×C3×Dic3C2×D412yes—
163C3×D12—24no—
164C3×D12—22no—
165C3×D12C22×C414yes—
166C3×C4×D3C22⋊C418yes—
167C3×C4×D3C22×C414yes—
168C3×C4×D3C2×D414yes—
169#625—216no—
170D3×Dic3—216no—
171C3⋊(C3⋊C8)—22no—
172C3×C3⋊C8—22no—
173C22×#41—91no—
174C23×C8—91no—
175C2×#117—31no—
176#416—98no—
177C2×#103—91no—
178C2×#103—91no—
179C2×#102—31no—
180C2×#102—91no—
181C24×C3—31no—
182C24×C3—61no—
183C23×D3—21no—
184C23×D3#6711yescharacteristic
185C2×C3×D4—34no—
186C2×C3×D4—32no—
187C2×C3×D4—62no—
188C2×C3×D4—61no—
189C22×C3×C4—21no—
190C22×C3×C4—21no—
191C22×C3×C4—21no—
192C22×C3×C4—31no—
193C22×C3×C4—34no—
194C22×C3×C4—34no—
195C22×C3×C4—32no—
196C22×C3×C4—32no—
197C22×C3×C4—41no—
198C22×C3×C4—61no—
199C22×C3×C4C22×D311yescharacteristic
200C22×C3×C4C22×D311yescharacteristic
201C2×#67—68no—
202C2×#67—64no—
203C2×#67—68no—
204C2×#67—64no—
205C22×Dic3—21no—
206C22×Dic3—61no—
207C22×Dic3—61no—
208C22×Dic3—68no—
209C22×Dic3—64no—
210C22×Dic3—121no—
211C22×Dic3#6711yescharacteristic
212#237—316no—
213#237—616no—
214#237—68no—
215#235—316no—
216#235—616no—
217#235—68no—
218C2×D12—22no—
219C2×D12—21no—
220C2×D12C4×D314yes—
221C2×D12C22×D312yes—
222C2×C4×D3—68no—
223C2×C4×D3—64no—
224C2×C4×D3C4×D314yes—
225C2×C4×D3D1214yes—
226C2×C4×D3#6712yes—
227C2×C4×D3C22×D312yes—
228C2×Dic6—34no—
229C2×Dic6—34no—
230C2×Dic6—32no—
231C2×Dic6—32no—
232C2×Dic6—62no—
233C2×Dic6—64no—
234C2×Dic6—62no—
235C2×Dic6—62no—
236C2×Dic6—61no—
237C2×Dic6—61no—
238C2×Dic6—122no—
239C2×Dic6—121no—
240C2×C3×C8—32no—
241C2×C3×C8—62no—
242C3×C4⋊C4—21no—
243C3×C4⋊C4—21no—
244C3×C4⋊C4—22no—
245C3×C4⋊C4—32no—
246C3×C4⋊C4—41no—
247C3×C4⋊C4—61no—
248C3×C4⋊C4C22×D312yes—
249C3×C4⋊C4C22×D312yes—
250C3×C22⋊C4—64no—
251C3×C42—64no—
252(C2×D3)⋊C4—24no—
253C4⋊Dic3—21no—
254C4⋊Dic3C22×D312yes—
255C4×Dic3—24no—
256C2×C3⋊C8—22no—
257C2×C3⋊C8—32no—
258C2×C3⋊C8—32no—
259C2×C3⋊C8—62no—
260C2×C3⋊C8—68no—
261C2×C3⋊C8—62no—
262C2×C3⋊C8—62no—
263C2×C3⋊C8—122no—
264C2×C3⋊C8C22×D312yes—
265D3×C8—68no—
266C22×C32C2×C22⋊C412yes—
267C22×C32#13512yes—
268C22×C32#13512yes—
269C22×C32C22×D411yescharacteristic
270C2×C3×D3—22no—
271C2×C3×D3—22no—
272C2×C3×D3—28no—
273C2×C3×D3—24no—
274C2×C3×D3—42no—
275C2×C3×D3—42no—
276C2×C3×D3—48no—
277C2×C3×D3C2×C22⋊C414yes—
278C32×C4—42no—
279C32×C4C2×C22⋊C412yes—
280C32×C4C23×C411yescharacteristic
281C32×C4C22×D411yescharacteristic
282C3⋊Dic3—24no—
283C3×Dic3—42no—
284C3×Dic3C2×C22⋊C414yes—
285C2×#41—94no—
286C2×#41—98no—
287C2×#41—184no—
288C2×#41—182no—
289C22×Q8—91no—
290C22×D4—31no—
291C22×D4—181no—
292C23×C4—31no—
293C23×C4—181no—
294C22×C8—31no—
295C22×C8—94no—
296C22×C8—91no—
297C22×C8—184no—
298#117—34no—
299#117—62no—
300C2×C4⋊C4—31no—
301C2×C4⋊C4D3211yescharacteristic
302C2×C22⋊C4—61no—
303C2×C42—61no—
304#103—94no—
305#103—94no—
306#102—34no—
307#102—94no—
308C23×C3—21no—
309C23×C3—34no—
310C23×C3—32no—
311C23×C3—62no—
312C23×C3—62no—
313C23×C3—64no—
314C23×C3—62no—
315C23×C3—122no—
316C23×C3—122no—
317C23×C3D3×D411yescharacteristic
318C23×C3C2×#6711yescharacteristic
319C22×D3—22no—
320C22×D3—22no—
321C22×D3—24no—
322C22×D3—22no—
323C22×D3—42no—
324C22×D3—42no—
325C22×D3(C2×D3)⋊C414yes—
326C22×D3C2×#6712yes—
327C3×D4—34no—
328C3×D4—64no—
329C3×D4—62no—
330C2×C3×C4—22no—
331C2×C3×C4—22no—
332C2×C3×C4—21no—
333C2×C3×C4—22no—
334C2×C3×C4—22no—
335C2×C3×C4—21no—
336C2×C3×C4—34no—
337C2×C3×C4—32no—
338C2×C3×C4—38no—
339C2×C3×C4—34no—
340C2×C3×C4—34no—
341C2×C3×C4—42no—
342C2×C3×C4—42no—
343C2×C3×C4—42no—
344C2×C3×C4—62no—
345C2×C3×C4—82no—
346C2×C3×C4—122no—
347C2×C3×C4C2×C4×D312yes—
348C2×C3×C4C2×C4×D312yes—
349C2×C3×C4C2×D1212yes—
350C2×C3×C4D3×D412yes—
351C2×C3×C4D3×D411yescharacteristic
352C2×C3×C4C2×#6711yescharacteristic
353C2×C3×C4C23×D311yescharacteristic
354C2×C3×C4C23×D311yescharacteristic
355#67—616no—
356#67—616no—
357C2×Dic3—22no—
358C2×Dic3—42no—
359C2×Dic3—64no—
360C2×Dic3—64no—
361C2×Dic3—62no—
362C2×Dic3—62no—
363C2×Dic3—616no—
364C2×Dic3—122no—
365C2×Dic3—124no—
366C2×Dic3(C2×D3)⋊C414yes—
367C2×Dic3C2×#6712yes—
368D12—24no—
369D12—22no—
370D12C2×C4×D314yes—
371C4×D3—616no—
372C4×D3(C2×D3)⋊C418yes—
373C4×D3C2×C4×D314yes—
374C4×D3C2×D1214yes—
375Dic6—34no—
376Dic6—34no—
377Dic6—64no—
378Dic6—64no—
379Dic6—64no—
380Dic6—62no—
381Dic6—62no—
382Dic6—122no—
383Dic6—124no—
384C3×C8—62no—
385C3⋊C8—22no—
386C3⋊C8—62no—
387C3⋊C8—62no—
388C3⋊C8—122no—
389C2×C32#41614yescomplemented
390C2×C32C22×C22⋊C411yescharacteristic
391C2×C32C2×#13511yescharacteristic
392C2×C32C2×#13511yescharacteristic
393C3×D3—24no—
394C3×D3—44no—
395C24—31no—
396C24—61no—
397#41—916no—
398#41—188no—
399#41—1816no—
400C2×Q8—92no—
401C2×Q8—94no—
402C2×Q8—182no—
403C2×Q8—181no—
404C2×D4—32no—
405C2×D4—34no—
406C2×D4—62no—
407C2×D4—61no—
408C2×D4—184no—
409C2×D4—188no—
410C22×C4—21no—
411C22×C4—31no—
412C22×C4—32no—
413C22×C4—34no—
414C22×C4—34no—
415C22×C4—32no—
416C22×C4—61no—
417C22×C4—184no—
418C22×C4—188no—
419C22×C4—181no—
420C22×C4C2×D3211yescharacteristic
421C2×C8—32no—
422C2×C8—62no—
423C2×C8—92no—
424C2×C8—188no—
425C2×C8—182no—
426C4⋊C4—21no—
427C4⋊C4—32no—
428C4⋊C4—61no—
429C4⋊C4C2×D3212yes—
430C22⋊C4—64no—
431C42—64no—
432C22×C3—21no—
433C22×C3—22no—
434C22×C3—22no—
435C22×C3—22no—
436C22×C3—34no—
437C22×C3—62no—
438C22×C3—62no—
439C22×C3—68no—
440C22×C3—64no—
441C22×C3—128no—
442C22×C3—122no—
443C22×C3—122no—
444C22×C3D3×C22⋊C412yes—
445C22×C3#91212yes—
446C22×C3#91612yes—
447C22×C3C2×(C2×D3)⋊C412yes—
448C22×C3#95012yes—
449C22×C3#95012yes—
450C22×C3C2×D3×D411yescharacteristic
451C22×C3C22×#6711yescharacteristic
452C2×D3—28no—
453C2×D3—22no—
454C2×D3—22no—
455C2×D3—24no—
456C2×D3—42no—
457C2×D3—42no—
458C2×D3—48no—
459C2×D3C2×(C2×D3)⋊C414yes—
460C3×C4—21no—
461C3×C4—21no—
462C3×C4—22no—
463C3×C4—34no—
464C3×C4—42no—
465C3×C4—42no—
466C3×C4—82no—
467C3×C4—122no—
468C3×C4D3×C22⋊C412yes—
469C3×C4C2×(C2×D3)⋊C412yes—
470C3×C4C22×C4×D311yescharacteristic
471C3×C4C22×C4×D311yescharacteristic
472C3×C4C22×D1211yescharacteristic
473C3×C4C2×D3×D411yescharacteristic
474Dic3—42no—
475Dic3—64no—
476Dic3—64no—
477Dic3—124no—
478Dic3C2×(C2×D3)⋊C414yes—
479C32C2×#41611yescharacteristic, complemented, Sylow
480C23—32no—
481C23—34no—
482C23—62no—
483C23—62no—
484C23—62no—
485C23—64no—
486C23—122no—
487C23—122no—
488C23D3×#6711yescharacteristic
489Q8—94no—
490Q8—182no—
491Q8—184no—
492D4—34no—
493D4—62no—
494D4—64no—
495D4—1816no—
496C2×C4—22no—
497C2×C4—32no—
498C2×C4—34no—
499C2×C4—34no—
500C2×C4—34no—
501C2×C4—38no—
502C2×C4—42no—
503C2×C4—62no—
504C2×C4—122no—
505C2×C4—1816no—
506C2×C4—182no—
507C2×C4—184no—
508C2×C4C4×D3212yes—
509C2×C4D3×D1212yes—
510C2×C4D3×#6711yescharacteristic
511C2×C4C22×D3211yescharacteristic
512C8—62no—
513C8—182no—
514C2×C3—21no—
515C2×C3—21no—
516C2×C3—24no—
517C2×C3—21no—
518C2×C3—64no—
519C2×C3—124no—
520C2×C3#477214yescomplemented
521C2×C3#500214yescomplemented
522C2×C3C2×D3×C22⋊C411yescharacteristic
523C2×C3C2×#91211yescharacteristic
524C2×C3C2×#91611yescharacteristic
525C2×C3C22×(C2×D3)⋊C411yescharacteristic
526C2×C3C2×#95011yescharacteristic
527C2×C3C2×#95011yescharacteristic
528D3—24no—
529D3—44no—
530C22—34no—
531C22—62no—
532C22—62no—
533C22—68no—
534C22—64no—
535C22—122no—
536C22—122no—
537C22—128no—
538C22D3×(C2×D3)⋊C412yes—
539C22#6393312yes—
540C22#6394712yes—
541C22C2×D3×#6711yescharacteristic
542C4—34no—
543C4—42no—
544C4—122no—
545C4—184no—
546C4D3×(C2×D3)⋊C412yes—
547C4C2×C4×D3211yescharacteristic
548C4C2×D3×D1211yescharacteristic
549C3—21no—
550C3C2×#477211yescharacteristic, complemented
551C3C2×#500211yescharacteristic, complemented
552C2—64no—
553C2—124no—
554C2#1059060814yesdirect product factor
555C2C2×D3×(C2×D3)⋊C411yescharacteristic
556C2C2×#6393311yescharacteristic
557C2C2×#6394711yescharacteristic
subgroupG/H
centerC23D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC22×#3795C2
cosocleC2×C32×C4C24
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#416
LCSG ▷ 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
2. C2×C3×#892C2semidirect
3. C22×D3×C3⋊C8C2semidirect
4. C2×#63637C2semidirect
5. C2×C3×#809C2semidirect
6. C2×#63567C2semidirect
7. C2×#63562C2semidirect
8. #10590608C2direct (N × H)
18. C2×#3795C4semidirect
27. C3×#892C22semidirect
29. C2×D3×C3⋊C8C22semidirect
30. #63637C22semidirect
31. C3×#809C22semidirect
32. #63567C22semidirect
33. #63562C22semidirect
39. C2×#892D3semidirect
49. C2×#809D3semidirect
76. #3795C2×C4semidirect
129. #892C2×D3semidirect
138. #809C2×D3semidirect
389. C2×C32#416semidirect
479. C32C2×#416semidirect
520. C2×C3#4772semidirect
521. C2×C3#5002semidirect
550. C3C2×#4772semidirect
551. C3C2×#5002semidirect
554. C2#10590608direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37952
C2×C3×#8922
C22×D3×C3⋊C82
C2×#636372
C2×C3×#8092
C2×#635672
C2×#635622
#105906082
C2×#50023
C2×#47723