Finite Group Databasebeta

← C2×#10591617 #11865603

Subgroups — C2×#10591617 #11865603

Order 1152.

1317 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3755C211yesmaximal, characteristic, complemented
2C2×C3×Q8×Dic3C211yesmaximal, characteristic, complemented
3C22×C3×#215C211yesmaximal, characteristic, complemented
4C2×#63911C211yesmaximal, characteristic
5#10591617C218yesmaximal, direct product factor
6C2×Dic3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
7C2×#63564C211yesmaximal, characteristic, complemented
8C2×#63562C211yesmaximal, characteristic, complemented
9C2×#5163—31nomaximal
10C2×#5027—31nomaximal
11C22×C32×Q8C2211yescharacteristic
12C22×C4⋊(C3⋊D3)C2211yescharacteristic
13C22×C3×D12C2211yescharacteristic
14C22×#626—21no—
15C22×#626—21no—
16C2×#3755—24no—
17C2×#3755C2214yescomplemented
18C22×C3⋊(C3⋊C8)C2211yescharacteristic
19C3×Q8×Dic3—22no—
20C3×Q8×Dic3C2214yescomplemented
21C2×C3×#215—24no—
22C2×C3×#215C2214yescomplemented
23C2×C3×C4⋊Dic3—21no—
24C2×C3×C4⋊Dic3C2211yescharacteristic
25C2×C3×C4×Dic3—21no—
26C2×C3×C4×Dic3C2211yescharacteristic
27C22×C3×C3⋊C8C2211yescharacteristic
28#63911—22no—
29#63911C2214yes—
30Dic3⋊(C3⋊C8)C2214yescomplemented
31#63564C2214yescomplemented
32#63562C2214yescomplemented
33C22×C3×SD16—31no—
34C2×C3×C4×Q8—31no—
35C2×Q8×Dic3D311yescharacteristic, complemented
36C22×#215—31no—
37C22×#215—31no—
38C22×#215—61no—
39C22×#215D311yescharacteristic, complemented
40C2×#940—31no—
41C2×#874—31no—
42C2×#832—31no—
43#5163—38no—
44C2×#821—31no—
45C2×Dic3⋊C8—31no—
46#5027—38no—
47C2×#809—31no—
48C2×#809—31no—
49C2×C4⋊(C3⋊C8)—31no—
50C23×C3⋊D3—21no—
51C23×C3×D3—21no—
52C2×C32×Q8—21no—
53C2×C32×Q8—22no—
54C2×C32×Q8D414yescomplemented
55C2×C32×Q8C2312yes—
56C22×C32×C4—21no—
57C22×C32×C4C2311yescharacteristic
58C2×C4⋊(C3⋊D3)—22no—
59C2×C4⋊(C3⋊D3)—22no—
60C2×C4⋊(C3⋊D3)—21no—
61C2×C4⋊(C3⋊D3)C2312yes—
62C22×C3×Dic3—21no—
63C22×C3×Dic3D411yescharacteristic
64C22×C3×Dic3D411yescharacteristic
65C2×C3×D12—22no—
66C2×C3×D12—22no—
67C2×C3×D12—21no—
68C2×C3×D12C2312yes—
69C2×#626—24no—
70C2×#626—24no—
71C2×#626—44no—
72C2×#626—44no—
73#3755—28no—
74C2×C3⋊(C3⋊C8)—22no—
75C2×C3⋊(C3⋊C8)C2312yes—
76C3×#215—28no—
77C3×C4⋊Dic3—21no—
78C3×C4⋊Dic3—24no—
79C3×C4⋊Dic3C2312yes—
80C3×C4×Dic3—24no—
81C3×C4×Dic3D412yes—
82C3×C4×Dic3C2312yes—
83C2×C3×C3⋊C8—22no—
84C2×C3×C3⋊C8C2312yes—
85C2×#460—91noSylow
86C22×C3×Q8—21no—
87C22×C3×Q8C2×D311yescharacteristic
88C22×C3×Q8C2×D311yescharacteristic
89C22×C3×D4—31no—
90C22×#67—61no—
91C22×#67—61no—
92C22×D12—31no—
93C22×D12—31no—
94C22×D12—61no—
95C22×D12—61no—
96C22×D12—61no—
97C22×D12C2×D311yescharacteristic
98C2×C3×SD16—34no—
99C2×C3×SD16—64no—
100C22×C3×C8—31no—
101C3×C4×Q8—34no—
102C3×C4×Q8—62no—
103C2×C3×C4⋊C4—31no—
104C2×C3×C4⋊C4—61no—
105C2×C3×C42—31no—
106C2×C3×C42—61no—
107Q8×Dic3—22no—
108Q8×Dic3C2×D314yescomplemented
109C2×#215—24no—
110C2×#215—34no—
111C2×#215—34no—
112C2×#215—64no—
113C2×#215—68no—
114C2×#215—64no—
115C2×#215—64no—
116C2×#215C2×D314yescomplemented
117#940—34no—
118#940—62no—
119C2×C4⋊Dic3—21no—
120C2×C4⋊Dic3C2×D311yescharacteristic
121C2×C4×Dic3—21no—
122C2×C4×Dic3C2×D311yescharacteristic
123C22×C3⋊C8—31no—
124C22×C3⋊C8—31no—
125C22×C3⋊C8—61no—
126C22×C3⋊C8C2×D311yescharacteristic
127#874—34no—
128#874—62no—
129#832—34no—
130#821—34no—
131Dic3⋊C8—34no—
132#809—34no—
133#809—34no—
134C4⋊(C3⋊C8)—34no—
135C23×C32C2×D411yescharacteristic
136C22×C3⋊D3—22no—
137C22×C3⋊D3—42no—
138C22×C3⋊D3—42no—
139C22×C3⋊D3—42no—
140C22×C3×D3—22no—
141C22×C3×D3—42no—
142C22×C3×D3—42no—
143C22×C3×D3—42no—
144C32×Q8—24no—
145C32×Q8—22no—
146C32×Q8C2×D414yescomplemented
147C2×C32×C4—24no—
148C2×C32×C4—22no—
149C2×C32×C4C2×D412yes—
150C2×C32×C4C2×D411yescharacteristic
151C2×C32×C4#4112yes—
152C2×C32×C4C2411yescharacteristic
153C4⋊(C3⋊D3)—22no—
154C4⋊(C3⋊D3)—22no—
155C4⋊(C3⋊D3)—42no—
156C2×C3×Dic3—22no—
157C2×C3×Dic3—22no—
158C2×C3×Dic3—42no—
159C2×C3×Dic3SD1614yescomplemented
160C2×C3×Dic3C2×D412yes—
161C2×C3×Dic3C2×D412yes—
162C3×D12—22no—
163C3×D12—22no—
164C3×D12—42no—
165#626—48no—
166#626—48no—
167C3⋊(C3⋊C8)—22no—
168C3×C3⋊C8—22no—
169C22×SD16—31no—
170C22×SD16—91no—
171C2×#127—91no—
172C2×C4×Q8—31no—
173#460—98no—
174C2×C4⋊C8—91no—
175C2×#102—91no—
176C2×#102—91no—
177C24×C3—61no—
178C23×D3—21no—
179C23×D3—61no—
180C23×D3—61no—
181C23×D3—121no—
182C2×C3×Q8—22no—
183C2×C3×Q8—21no—
184C2×C3×Q8—22no—
185C2×C3×Q8—21no—
186C2×C3×Q8—24no—
187C2×C3×Q8—22no—
188C2×C3×Q8—42no—
189C2×C3×Q8—41no—
190C2×C3×Q8D1214yescomplemented
191C2×C3×Q8#6714yescomplemented
192C2×C3×Q8C22×D312yes—
193C2×C3×Q8C22×D312yes—
194C2×C3×D4—32no—
195C2×C3×D4—62no—
196C2×C3×D4—62no—
197C2×C3×D4—61no—
198C22×C3×C4—21no—
199C22×C3×C4—21no—
200C22×C3×C4—21no—
201C22×C3×C4—31no—
202C22×C3×C4—31no—
203C22×C3×C4—41no—
204C22×C3×C4—61no—
205C22×C3×C4C22×D311yescharacteristic
206C22×C3×C4C22×D311yescharacteristic
207C2×#67—64no—
208C2×#67—64no—
209C2×#67—124no—
210C2×#67—124no—
211C22×Dic3—21no—
212C22×Dic3#6711yescharacteristic
213C22×Dic3#6711yescharacteristic
214C2×D12—22no—
215C2×D12—22no—
216C2×D12—21no—
217C2×D12—32no—
218C2×D12—32no—
219C2×D12—62no—
220C2×D12—64no—
221C2×D12—62no—
222C2×D12—62no—
223C2×D12—62no—
224C2×D12—62no—
225C2×D12—64no—
226C2×D12—64no—
227C2×D12—61no—
228C2×D12—61no—
229C2×D12—122no—
230C2×D12—121no—
231C2×D12—124no—
232C2×D12—124no—
233C2×D12C22×D312yes—
234C3×SD16—68no—
235C2×C3×C8—32no—
236C2×C3×C8—62no—
237C3×C4⋊C4—32no—
238C3×C4⋊C4—64no—
239C3×C4⋊C4—61no—
240C3×C42—32no—
241C3×C42—32no—
242C3×C42—64no—
243#215—28no—
244#215—616no—
245#215—68no—
246#215—68no—
247C4⋊Dic3—21no—
248C4⋊Dic3—24no—
249C4⋊Dic3C22×D312yes—
250C4×Dic3—24no—
251C4×Dic3#6712yes—
252C4×Dic3C22×D312yes—
253C2×C3⋊C8—22no—
254C2×C3⋊C8—32no—
255C2×C3⋊C8—32no—
256C2×C3⋊C8—62no—
257C2×C3⋊C8—64no—
258C2×C3⋊C8—62no—
259C2×C3⋊C8—62no—
260C2×C3⋊C8C22×D312yes—
261C22×C32#12112yes—
262C22×C32C2×SD1612yes—
263C22×C32AGL(1,ℤ/8)12yes—
264C22×C32C22×D411yescharacteristic
265C2×C3⋊D3—42no—
266C2×C3⋊D3—42no—
267C2×C3⋊D3—42no—
268C2×C3⋊D3—84no—
269C2×C3×D3—42no—
270C2×C3×D3—42no—
271C2×C3×D3—42no—
272C2×C3×D3—84no—
273C32×C4—24no—
274C32×C4#12112yes—
275C32×C4C22×D411yescharacteristic
276C32×C4C2×#4111yescharacteristic
277C3×Dic3—22no—
278C3×Dic3—42no—
279C3×Dic3C2×SD1614yescomplemented
280C22×Q8D3211yescharacteristic
281C22×D4—31no—
282C22×D4—91no—
283C22×D4—181no—
284C22×D4—181no—
285C2×SD16—34no—
286C2×SD16—64no—
287C2×SD16—94no—
288C2×SD16—184no—
289C22×C8—31no—
290C22×C8—91no—
291#127—94no—
292#127—182no—
293C4×Q8—34no—
294C4×Q8—62no—
295C2×C4⋊C4—31no—
296C2×C4⋊C4—61no—
297C2×C42—31no—
298C2×C42—61no—
299C4⋊C8—94no—
300#102—94no—
301#102—94no—
302C23×C3—21no—
303C23×C3—62no—
304C23×C3—122no—
305C23×C3—122no—
306C23×C3—122no—
307C23×C3D3×D411yescharacteristic
308C23×C3C2×#6711yescharacteristic
309C22×D3—22no—
310C22×D3—42no—
311C22×D3—42no—
312C22×D3—42no—
313C22×D3—62no—
314C22×D3—62no—
315C22×D3—122no—
316C22×D3—124no—
317C22×D3—122no—
318C22×D3—122no—
319C22×D3—122no—
320C22×D3—122no—
321C22×D3—122no—
322C22×D3—122no—
323C22×D3—242no—
324C22×D3—242no—
325C3×Q8—24no—
326C3×Q8—24no—
327C3×Q8—22no—
328C3×Q8—22no—
329C3×Q8—24no—
330C3×Q8—42no—
331C3×Q8—44no—
332C3×Q8C2×D1214yescomplemented
333C3×Q8C2×#6714yescomplemented
334C3×D4—62no—
335C3×D4—62no—
336C3×D4—122no—
337C2×C3×C4—24no—
338C2×C3×C4—24no—
339C2×C3×C4—22no—
340C2×C3×C4—22no—
341C2×C3×C4—21no—
342C2×C3×C4—22no—
343C2×C3×C4—22no—
344C2×C3×C4—21no—
345C2×C3×C4—34no—
346C2×C3×C4—32no—
347C2×C3×C4—32no—
348C2×C3×C4—42no—
349C2×C3×C4—44no—
350C2×C3×C4—62no—
351C2×C3×C4—62no—
352C2×C3×C4—122no—
353C2×C3×C4C2×D1212yes—
354C2×C3×C4#23512yes—
355C2×C3×C4D3×D411yescharacteristic
356C2×C3×C4#23712yes—
357C2×C3×C4C2×#6712yes—
358C2×C3×C4C2×#6711yescharacteristic
359C2×C3×C4C23×D311yescharacteristic
360C2×C3×C4C23×D311yescharacteristic
361#67—128no—
362#67—128no—
363C2×Dic3—22no—
364C2×Dic3—22no—
365C2×Dic3—42no—
366C2×Dic3#21514yescomplemented
367C2×Dic3C2×#6712yes—
368C2×Dic3C2×#6712yes—
369D12—22no—
370D12—22no—
371D12—42no—
372D12—64no—
373D12—62no—
374D12—62no—
375D12—62no—
376D12—62no—
377D12—122no—
378D12—124no—
379D12—128no—
380D12—128no—
381D12—122no—
382D12—122no—
383C3×C8—62no—
384C3⋊C8—22no—
385C3⋊C8—64no—
386C3⋊C8—62no—
387C3⋊C8—62no—
388C2×C32#46014yescomplemented
389C2×C32C2×#12111yescharacteristic
390C2×C32C22×SD1611yescharacteristic
391C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
392C3⋊D3—82no—
393C3×D3—82no—
394C24—61no—
395C24—181no—
396C2×Q8—22no—
397C2×Q8—21no—
398C2×Q8#62614yescomplemented
399C2×Q8C2×D3212yes—
400C2×D4—32no—
401C2×D4—62no—
402C2×D4—62no—
403C2×D4—61no—
404C2×D4—92no—
405C2×D4—184no—
406C2×D4—184no—
407C2×D4—182no—
408C2×D4—182no—
409C2×D4—181no—
410C2×D4—364no—
411C2×D4—364no—
412C22×C4—21no—
413C22×C4—31no—
414C22×C4—31no—
415C22×C4—61no—
416C22×C4C2×D3211yescharacteristic
417SD16—68no—
418SD16—188no—
419C2×C8—32no—
420C2×C8—62no—
421C2×C8—92no—
422C2×C8—182no—
423C4⋊C4—32no—
424C4⋊C4—64no—
425C4⋊C4—61no—
426C42—32no—
427C42—32no—
428C42—64no—
429C22×C3—21no—
430C22×C3—22no—
431C22×C3—22no—
432C22×C3—22no—
433C22×C3—122no—
434C22×C3—122no—
435C22×C3—122no—
436C22×C3—244no—
437C22×C3D3×SD1612yes—
438C22×C3#91412yes—
439C22×C3#93012yes—
440C22×C3#93912yes—
441C22×C3C2×#21512yes—
442C22×C3#94912yes—
443C22×C3C2×D3×D411yescharacteristic
444C22×C3C22×#6711yescharacteristic
445C2×D3—42no—
446C2×D3—42no—
447C2×D3—42no—
448C2×D3—84no—
449C2×D3—124no—
450C2×D3—122no—
451C2×D3—122no—
452C2×D3—122no—
453C2×D3—122no—
454C2×D3—122no—
455C2×D3—122no—
456C2×D3—242no—
457C2×D3—242no—
458C2×D3—248no—
459C2×D3—244no—
460C2×D3—244no—
461C3×C4—24no—
462C3×C4—24no—
463C3×C4—21no—
464C3×C4—21no—
465C3×C4—22no—
466C3×C4—34no—
467C3×C4—44no—
468C3×C4—62no—
469C3×C4—122no—
470C3×C4#93012yes—
471C3×C4#93912yes—
472C3×C4C22×D1211yescharacteristic
473C3×C4C2×#23511yescharacteristic
474C3×C4C2×#23711yescharacteristic
475C3×C4C22×#6711yescharacteristic
476Dic3—22no—
477Dic3—42no—
478Dic3C2×#21514yescomplemented
479C32C2×#46011yescharacteristic, complemented, Sylow
480C23—62no—
481C23—122no—
482C23—122no—
483C23—122no—
484C23—182no—
485C23—362no—
486C23—362no—
487C23—362no—
488C23D3×#6711yescharacteristic
489Q8—22no—
490Q8—24no—
491Q8C2×#62614yescomplemented
492D4—62no—
493D4—62no—
494D4—122no—
495D4—182no—
496D4—182no—
497D4—368no—
498D4—368no—
499D4—362no—
500C2×C4—22no—
501C2×C4—24no—
502C2×C4—32no—
503C2×C4—34no—
504C2×C4—32no—
505C2×C4—62no—
506C2×C4—62no—
507C2×C4—122no—
508C2×C4#380412yes—
509C2×C4C2×#62612yes—
510C2×C4D3×#6711yescharacteristic
511C2×C4C22×D3211yescharacteristic
512C8—62no—
513C8—182no—
514C2×C3—24no—
515C2×C3—21no—
516C2×C3—21no—
517C2×C3—21no—
518C2×C3—242no—
519C2×C3#502714yescomplemented
520C2×C3#516314yescomplemented
521C2×C3C2×D3×SD1611yescharacteristic
522C2×C3C2×#91411yescharacteristic
523C2×C3C2×#93011yescharacteristic
524C2×C3C2×#93911yescharacteristic
525C2×C3C22×#21511yescharacteristic
526C2×C3C2×#94911yescharacteristic
527D3—82no—
528D3—244no—
529D3—242no—
530D3—242no—
531C22—122no—
532C22—122no—
533C22—122no—
534C22—244no—
535C22—362no—
536C22—362no—
537C22—362no—
538C22—724no—
539C22D3×#21512yes—
540C22#6393912yes—
541C22#6397812yes—
542C22C2×D3×#6711yescharacteristic
543C4—24no—
544C4—34no—
545C4—62no—
546C4—122no—
547C4#6397812yes—
548C4C2×#380411yescharacteristic
549C4C22×#62611yescharacteristic
550C3—21no—
551C3C2×#502711yescharacteristic, complemented
552C3C2×#516311yescharacteristic, complemented
553C2—242no—
554C2—722no—
555C2#1059161714yesdirect product factor
556C2C2×D3×#21511yescharacteristic
557C2C2×#6393911yescharacteristic
558C2C2×#6397811yescharacteristic
subgroupG/H
centerC23D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC23×C32C2×D4
prime radicalC2×#63911C2
hypercenterC22×Q8D32
hypocenterC32C2×#460
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C22×#3755C2semidirect
2. C2×C3×Q8×Dic3C2semidirect
3. C22×C3×#215C2semidirect
5. #10591617C2direct (N × H)
6. C2×Dic3⋊(C3⋊C8)C2semidirect
7. C2×#63564C2semidirect
8. C2×#63562C2semidirect
17. C2×#3755C22semidirect
20. C3×Q8×Dic3C22semidirect
22. C2×C3×#215C22semidirect
30. Dic3⋊(C3⋊C8)C22semidirect
31. #63564C22semidirect
32. #63562C22semidirect
35. C2×Q8×Dic3D3semidirect
39. C22×#215D3semidirect
54. C2×C32×Q8D4semidirect
108. Q8×Dic3C2×D3semidirect
116. C2×#215C2×D3semidirect
146. C32×Q8C2×D4semidirect
159. C2×C3×Dic3SD16semidirect
190. C2×C3×Q8D12semidirect
191. C2×C3×Q8#67semidirect
279. C3×Dic3C2×SD16semidirect
332. C3×Q8C2×D12semidirect
333. C3×Q8C2×#67semidirect
366. C2×Dic3#215semidirect
388. C2×C32#460semidirect
398. C2×Q8#626semidirect
478. Dic3C2×#215semidirect
479. C32C2×#460semidirect
491. Q8C2×#626semidirect
519. C2×C3#5027semidirect
520. C2×C3#5163semidirect
551. C3C2×#5027semidirect
552. C3C2×#5163semidirect
555. C2#10591617direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37552
C2×C3×Q8×Dic32
C22×C3×#2152
C2×#639112
#105916172
C2×Dic3⋊(C3⋊C8)2
C2×#635642
C2×#635622
C2×#51633
C2×#50273