Finite Group Databasebeta

← C2×#10591420 #11857796

Subgroups — C2×#10591420 #11857796

Order 1152.

1685 conjugacy classes of subgroups.

The subgroup lattice has 565 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#237C211yesmaximal, characteristic
2C2×#63841C211yesmaximal, characteristic, complemented
3C22×D3×C3⋊C8C211yesmaximal, characteristic, complemented
4C2×#63659C211yesmaximal, characteristic, complemented
5C2×C3×#832C211yesmaximal, characteristic, complemented
6#10591420C218yesmaximal, direct product factor
7C2×#63566C211yesmaximal, characteristic, complemented
8C2×#63565C211yesmaximal, characteristic, complemented
9C2×#5233—31nomaximal
10C2×#4772—31nomaximal
11C22×C32×D4C2211yescharacteristic
12C22×C3×#67—21no—
13C23×C3×Dic3—21no—
14C2×C3×#237—22no—
15C2×C3×#237—24no—
16C2×C3×#237C418yescomplemented
17C2×C3×#237C2214yes—
18C22×C3×C4×D3C2211yescharacteristic
19C22×C3×Dic6C2211yescharacteristic
20C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
21C22×C3⋊(C3⋊C8)C2211yescharacteristic
22C2×C3×C4⋊Dic3C2211yescharacteristic
23C22×C3×C3⋊C8C2211yescharacteristic
24C2×(C2×D3)⋊Dic3—21no—
25C2×Dic32—21no—
26#63841—22no—
27#63841C2214yescomplemented
28C2×D3×C3⋊C8—24no—
29C2×D3×C3⋊C8C2214yescomplemented
30#63659C2214yescomplemented
31C3×#832C2214yescomplemented
32#63566C2214yescomplemented
33#63565C2214yescomplemented
34C22×C3×#41—31no—
35C22×#237D311yescharacteristic
36C2×#926—31no—
37C23×C3⋊C8—31no—
38C22×D3×C8—31no—
39C2×#892—31no—
40C2×C3×#102—31no—
41#5233—38no—
42C2×#835—31no—
43C2×#835—31no—
44C2×#832—31no—
45C2×#832—31no—
46C2×#832—61no—
47C2×#832D311yescharacteristic, complemented
48C2×#816—31no—
49C2×#810—31no—
50#4772—38no—
51C24×C32—21no—
52C23×C3×D3D411yescharacteristic
53C2×C32×D4—21no—
54C2×C32×D4—22no—
55C2×C32×D4C2×C414yes—
56C2×C32×D4C2312yes—
57C22×C32×C4C2311yescharacteristic
58C22×C3⋊Dic3—21no—
59C2×C3×#67—28no—
60C2×C3×#67—24no—
61C22×C3×Dic3—21no—
62C22×C3×Dic3—28no—
63C22×C3×Dic3—24no—
64C22×C3×Dic3—21no—
65C22×C3×Dic3D411yescharacteristic
66C3×#237—216no—
67C3×#237—28no—
68C3×#237C2×C4116yescomplemented
69C2×C3×C4×D3C2×C414yes—
70C2×C3×C4×D3D412yes—
71C2×C3×C4×D3D414yes—
72C2×C3×C4×D3C2312yes—
73C2×C3×Dic6—21no—
74C2×C3×Dic6—22no—
75C2×C3×Dic6C2×C414yes—
76C2×C3×Dic6C2312yes—
77C4⋊(C3⋊Dic3)—21no—
78C4⋊(C3⋊Dic3)C2312yes—
79C2×C3⋊(C3⋊C8)—22no—
80C2×C3⋊(C3⋊C8)C2312yes—
81C3×C4⋊Dic3—21no—
82C3×C4⋊Dic3C2312yes—
83C2×C3×C3⋊C8—22no—
84C2×C3×C3⋊C8C2312yes—
85(C2×D3)⋊Dic3—24no—
86Dic32—24no—
87D3×C3⋊C8—28no—
88C2×#416—91noSylow
89C2×C3×#41—38no—
90C2×C3×#41—34no—
91C2×C3×#41—64no—
92C2×C3×#41—62no—
93C22×C3×Q8—31no—
94C22×C3×D4—21no—
95C22×C3×D4—61no—
96C22×C3×D4C2×D311yescharacteristic
97C22×C3×D4C2×D311yescharacteristic
98C23×C3×C4—31no—
99C23×C3×C4—61no—
100C22×#67—21no—
101C23×Dic3—21no—
102C2×#237—22no—
103C2×#237—24no—
104C2×#237Dic318yescomplemented
105C2×#237C2×D314yes—
106C22×C4×D3C2×D311yescharacteristic
107C22×Dic6C2×D311yescharacteristic
108C22×C3×C8—31no—
109C2×C3×C4⋊C4—31no—
110C2×#217—61no—
111C2×(C2×D3)⋊C4—61no—
112#926—34no—
113#926—62no—
114C2×C4⋊Dic3—31no—
115C2×C4⋊Dic3—31no—
116C2×C4⋊Dic3—61no—
117C2×C4⋊Dic3C2×D311yescharacteristic
118C2×C4×Dic3—61no—
119C2×C4×Dic3—61no—
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—34no—
129#892—62no—
130C3×#102—34no—
131#835—34no—
132#835—34no—
133#832—34no—
134#832—34no—
135#832—64no—
136#832C2×D314yescomplemented
137#816—34no—
138#810—34no—
139C23×C32—24no—
140C23×C32—22no—
141C23×C32—42no—
142C23×C32—42no—
143C23×C32C2×D411yescharacteristic
144C22×C3×D3—22no—
145C22×C3×D3—22no—
146C22×C3×D3C22⋊C414yes—
147C22×C3×D3C2×D412yes—
148C32×D4—24no—
149C32×D4—22no—
150C32×D4C22×C414yes—
151C2×C32×C4C22×C412yes—
152C2×C32×C4C2×D411yescharacteristic
153C2×C32×C4C2×D412yes—
154C2×C32×C4C2411yescharacteristic
155C2×C3⋊Dic3—22no—
156C2×C3⋊Dic3—42no—
157C3×#67—216no—
158C2×C3×Dic3—24no—
159C2×C3×Dic3—22no—
160C2×C3×Dic3—216no—
161C2×C3×Dic3—22no—
162C2×C3×Dic3—42no—
163C2×C3×Dic3C22⋊C414yes—
164C2×C3×Dic3C2×D412yes—
165C3×C4×D3C22⋊C418yes—
166C3×C4×D3C22×C414yes—
167C3×C4×D3C2×D414yes—
168C3×Dic6—24no—
169C3×Dic6—22no—
170C3×Dic6C22×C414yes—
171C3⋊(C3⋊C8)—22no—
172C3×C3⋊C8—22no—
173C22×#41—31no—
174C23×C8—91no—
175C2×#117—91no—
176#416—98no—
177C2×#103—91no—
178C2×#103—91no—
179C2×#102—31no—
180C2×#102—91no—
181C24×C3—21no—
182C24×C3—21no—
183C24×C3—31no—
184C24×C3—41no—
185C23×D3#6711yescharacteristic
186C3×#41—316no—
187C3×#41—616no—
188C3×#41—68no—
189C2×C3×Q8—34no—
190C2×C3×Q8—32no—
191C2×C3×Q8—62no—
192C2×C3×Q8—61no—
193C2×C3×D4—21no—
194C2×C3×D4—22no—
195C2×C3×D4—21no—
196C2×C3×D4—22no—
197C2×C3×D4—24no—
198C2×C3×D4—22no—
199C2×C3×D4—42no—
200C2×C3×D4—41no—
201C2×C3×D4—68no—
202C2×C3×D4—64no—
203C2×C3×D4C4×D314yes—
204C2×C3×D4C2×Dic314yes—
205C2×C3×D4C22×D312yes—
206C2×C3×D4C22×D312yes—
207C22×C3×C4—21no—
208C22×C3×C4—31no—
209C22×C3×C4—34no—
210C22×C3×C4—34no—
211C22×C3×C4—32no—
212C22×C3×C4—32no—
213C22×C3×C4—68no—
214C22×C3×C4—64no—
215C22×C3×C4—61no—
216C22×C3×C4—61no—
217C22×C3×C4C22×D311yescharacteristic
218C22×C3×C4C22×D311yescharacteristic
219C2×#67—28no—
220C2×#67—24no—
221C22×Dic3—21no—
222C22×Dic3—28no—
223C22×Dic3—24no—
224C22×Dic3—21no—
225C22×Dic3—61no—
226C22×Dic3—61no—
227C22×Dic3—121no—
228C22×Dic3#6711yescharacteristic
229#237—216no—
230#237—28no—
231#237C2×Dic3116yescomplemented
232C2×C4×D3C2×Dic314yes—
233C2×C4×D3#6712yes—
234C2×C4×D3#6714yes—
235C2×C4×D3C22×D312yes—
236C2×Dic6—21no—
237C2×Dic6—22no—
238C2×Dic6C2×Dic314yes—
239C2×Dic6C22×D312yes—
240C2×C3×C8—32no—
241C2×C3×C8—62no—
242C3×C4⋊C4—32no—
243C3×C4⋊C4—61no—
244#217—64no—
245(C2×D3)⋊C4—64no—
246C4⋊Dic3—21no—
247C4⋊Dic3—32no—
248C4⋊Dic3—32no—
249C4⋊Dic3—62no—
250C4⋊Dic3—61no—
251C4⋊Dic3—61no—
252C4⋊Dic3—121no—
253C4⋊Dic3C22×D312yes—
254C4×Dic3—64no—
255C4×Dic3—64no—
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×C32—24no—
267C22×C32—42no—
268C22×C32—42no—
269C22×C32—48no—
270C22×C32C2×C22⋊C412yes—
271C22×C32#13512yes—
272C22×C32#13512yes—
273C22×C32C22×D411yescharacteristic
274C2×C3×D3—22no—
275C2×C3×D3—22no—
276C2×C3×D3—28no—
277C2×C3×D3C2×C22⋊C414yes—
278C32×C4C2×C22⋊C412yes—
279C32×C4C23×C411yescharacteristic
280C32×C4C22×D411yescharacteristic
281C3⋊Dic3—42no—
282C3×Dic3—24no—
283C3×Dic3—42no—
284C3×Dic3C2×C22⋊C414yes—
285C2×#41—38no—
286C2×#41—34no—
287C2×#41—62no—
288C2×#41—64no—
289C22×Q8—31no—
290C22×D4—61no—
291C22×D4D3211yescharacteristic
292C23×C4—31no—
293C23×C4—61no—
294C22×C8—31no—
295C22×C8—94no—
296C22×C8—91no—
297C22×C8—184no—
298#117—94no—
299#117—182no—
300C2×C4⋊C4—31no—
301C2×C4⋊C4—91no—
302C2×C22⋊C4—181no—
303C2×C42—181no—
304#103—94no—
305#103—94no—
306#102—34no—
307#102—94no—
308C23×C3—24no—
309C23×C3—24no—
310C23×C3—22no—
311C23×C3—22no—
312C23×C3—21no—
313C23×C3—34no—
314C23×C3—32no—
315C23×C3—42no—
316C23×C3—44no—
317C23×C3—42no—
318C23×C3—42no—
319C23×C3—42no—
320C23×C3—42no—
321C23×C3—62no—
322C23×C3—62no—
323C23×C3—82no—
324C23×C3—82no—
325C23×C3D3×D411yescharacteristic
326C23×C3C2×#6711yescharacteristic
327C22×D3—22no—
328C22×D3—22no—
329C22×D3#21714yes—
330C22×D3C2×#6712yes—
331C3×Q8—34no—
332C3×Q8—64no—
333C3×Q8—62no—
334C3×D4—24no—
335C3×D4—24no—
336C3×D4—22no—
337C3×D4—22no—
338C3×D4—24no—
339C3×D4—42no—
340C3×D4—44no—
341C3×D4—616no—
342C3×D4C2×C4×D314yes—
343C3×D4C22×Dic314yes—
344C2×C3×C4—21no—
345C2×C3×C4—22no—
346C2×C3×C4—22no—
347C2×C3×C4—21no—
348C2×C3×C4—34no—
349C2×C3×C4—32no—
350C2×C3×C4—38no—
351C2×C3×C4—34no—
352C2×C3×C4—34no—
353C2×C3×C4—616no—
354C2×C3×C4—64no—
355C2×C3×C4—62no—
356C2×C3×C4—62no—
357C2×C3×C4—122no—
358C2×C3×C4C2×C4×D312yes—
359C2×C3×C4D3×D411yescharacteristic
360C2×C3×C4D3×D412yes—
361C2×C3×C4C22×Dic312yes—
362C2×C3×C4C2×#6711yescharacteristic
363C2×C3×C4C2×#6712yes—
364C2×C3×C4C23×D311yescharacteristic
365C2×C3×C4C23×D311yescharacteristic
366#67—216no—
367C2×Dic3—24no—
368C2×Dic3—22no—
369C2×Dic3—216no—
370C2×Dic3—22no—
371C2×Dic3—42no—
372C2×Dic3—62no—
373C2×Dic3—62no—
374C2×Dic3—122no—
375C2×Dic3—122no—
376C2×Dic3—122no—
377C2×Dic3—242no—
378C2×Dic3#21714yes—
379C2×Dic3C2×#6712yes—
380C4×D3#21718yes—
381C4×D3C22×Dic314yes—
382C4×D3C2×#6714yes—
383Dic6—24no—
384Dic6—22no—
385Dic6C22×Dic314yes—
386C3×C8—62no—
387C3⋊C8—22no—
388C3⋊C8—62no—
389C3⋊C8—62no—
390C3⋊C8—122no—
391C2×C32—44no—
392C2×C32#41614yescomplemented
393C2×C32C22×C22⋊C411yescharacteristic
394C2×C32C2×#13511yescharacteristic
395C2×C32C2×#13511yescharacteristic
396C3×D3—24no—
397C24—21no—
398C24—31no—
399#41—316no—
400#41—68no—
401#41—616no—
402C2×Q8—32no—
403C2×Q8—34no—
404C2×Q8—61no—
405C2×Q8—62no—
406C2×D4—22no—
407C2×D4—21no—
408C2×D4—64no—
409C2×D4—68no—
410C2×D4D3×Dic314yes—
411C2×D4C2×D3212yes—
412C22×C4—31no—
413C22×C4—32no—
414C22×C4—34no—
415C22×C4—32no—
416C22×C4—34no—
417C22×C4—64no—
418C22×C4—68no—
419C22×C4—61no—
420C22×C4—61no—
421C22×C4—181no—
422C22×C4C2×D3211yescharacteristic
423C2×C8—32no—
424C2×C8—62no—
425C2×C8—92no—
426C2×C8—188no—
427C2×C8—182no—
428C4⋊C4—32no—
429C4⋊C4—61no—
430C4⋊C4—92no—
431C4⋊C4—181no—
432C22⋊C4—184no—
433C42—184no—
434C22×C3—24no—
435C22×C3—24no—
436C22×C3—21no—
437C22×C3—22no—
438C22×C3—22no—
439C22×C3—22no—
440C22×C3—34no—
441C22×C3—44no—
442C22×C3—48no—
443C22×C3—42no—
444C22×C3—42no—
445C22×C3—48no—
446C22×C3—42no—
447C22×C3—42no—
448C22×C3—62no—
449C22×C3—62no—
450C22×C3—68no—
451C22×C3—82no—
452C22×C3—82no—
453C22×C3—88no—
454C22×C3D3×C22⋊C412yes—
455C22×C3#91212yes—
456C22×C3#91612yes—
457C22×C3#95012yes—
458C22×C3#95012yes—
459C22×C3C2×#21712yes—
460C22×C3C2×D3×D411yescharacteristic
461C22×C3C22×#6711yescharacteristic
462C2×D3—28no—
463C2×D3—22no—
464C2×D3—22no—
465C2×D3C2×#21714yes—
466C3×C4—21no—
467C3×C4—21no—
468C3×C4—22no—
469C3×C4—34no—
470C3×C4—64no—
471C3×C4—122no—
472C3×C4D3×C22⋊C412yes—
473C3×C4C2×#21712yes—
474C3×C4C22×C4×D311yescharacteristic
475C3×C4C2×D3×D411yescharacteristic
476C3×C4C23×Dic311yescharacteristic
477C3×C4C22×#6711yescharacteristic
478Dic3—24no—
479Dic3—42no—
480Dic3—122no—
481Dic3—122no—
482Dic3—242no—
483Dic3C2×#21714yes—
484C32C2×#41611yescharacteristic, complemented, Sylow
485C23—22no—
486C23—24no—
487C23—32no—
488C23—34no—
489C23—42no—
490C23—42no—
491C23—62no—
492C23—62no—
493C23D3×#6711yescharacteristic
494Q8—34no—
495Q8—62no—
496Q8—64no—
497D4—22no—
498D4—24no—
499D4—616no—
500D4C2×D3×Dic314yes—
501C2×C4—32no—
502C2×C4—34no—
503C2×C4—34no—
504C2×C4—34no—
505C2×C4—38no—
506C2×C4—616no—
507C2×C4—62no—
508C2×C4—64no—
509C2×C4—62no—
510C2×C4—122no—
511C2×C4—182no—
512C2×C4—362no—
513C2×C4C2×D3×Dic312yes—
514C2×C4D3×#6712yes—
515C2×C4D3×#6711yescharacteristic
516C2×C4C22×D3211yescharacteristic
517C8—62no—
518C8—182no—
519C2×C3—21no—
520C2×C3—21no—
521C2×C3—21no—
522C2×C3—24no—
523C2×C3—44no—
524C2×C3—44no—
525C2×C3—64no—
526C2×C3—84no—
527C2×C3#477214yescomplemented
528C2×C3#523314yescomplemented
529C2×C3C2×D3×C22⋊C411yescharacteristic
530C2×C3C2×#91211yescharacteristic
531C2×C3C2×#91611yescharacteristic
532C2×C3C2×#95011yescharacteristic
533C2×C3C2×#95011yescharacteristic
534C2×C3C22×#21711yescharacteristic
535D3—24no—
536C22—24no—
537C22—34no—
538C22—42no—
539C22—42no—
540C22—48no—
541C22—62no—
542C22—62no—
543C22—68no—
544C22#6393312yes—
545C22#6393512yes—
546C22D3×#21712yes—
547C22C2×D3×#6711yescharacteristic
548C4—34no—
549C4—64no—
550C4—122no—
551C4—362no—
552C4D3×#21712yes—
553C4C22×D3×Dic311yescharacteristic
554C4C2×D3×#6711yescharacteristic
555C3—21no—
556C3C2×#477211yescharacteristic, complemented
557C3C2×#523311yescharacteristic, complemented
558C2—44no—
559C2—64no—
560C2#1059142014yesdirect product factor
561C2C2×#6393311yescharacteristic
562C2C2×#6393511yescharacteristic
563C2C2×D3×#21711yescharacteristic
subgroupG/H
centerC23D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC23×C32C2×D4
prime radicalC22×C3×#237C2
cosocleC2×C32×C4C24
hypercenterC22×D4D32
hypocenterC32C2×#416
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C2×#63841C2semidirect
3. C22×D3×C3⋊C8C2semidirect
4. C2×#63659C2semidirect
5. C2×C3×#832C2semidirect
6. #10591420C2direct (N × H)
7. C2×#63566C2semidirect
8. C2×#63565C2semidirect
16. C2×C3×#237C4semidirect
27. #63841C22semidirect
29. C2×D3×C3⋊C8C22semidirect
30. #63659C22semidirect
31. C3×#832C22semidirect
32. #63566C22semidirect
33. #63565C22semidirect
47. C2×#832D3semidirect
68. C3×#237C2×C4semidirect
104. C2×#237Dic3semidirect
136. #832C2×D3semidirect
231. #237C2×Dic3semidirect
392. C2×C32#416semidirect
484. C32C2×#416semidirect
527. C2×C3#4772semidirect
528. C2×C3#5233semidirect
556. C3C2×#4772semidirect
557. C3C2×#5233semidirect
560. C2#10591420direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#2372
C2×#638412
C22×D3×C3⋊C82
C2×#636592
C2×C3×#8322
#105914202
C2×#635662
C2×#635652
C2×#52333
C2×#47723