Finite Group Databasebeta

← C2×#10590950 #11863674

Subgroups — C2×#10590950 #11863674

Order 1152.

1581 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3797C211yesmaximal, characteristic
2C22×C3×Dic12C211yesmaximal, characteristic, complemented
3C2×#63871C211yesmaximal, characteristic
4C22×#3718C211yesmaximal, characteristic, complemented
5C2×#63647C211yesmaximal, characteristic
6C2×C3×#816C211yesmaximal, characteristic, complemented
7C2×#63565C211yesmaximal, characteristic, complemented
8#10590950C218yesmaximal, direct product factor
9C2×#5186—31nomaximal
10C2×#4809—31nomaximal
11C22×C4×C3⋊D3C2211yescharacteristic
12C22×C3×Dic6C2211yescharacteristic
13C22×C3×Dic6C2211yescharacteristic
14C22×C3×Dic6C2211yescharacteristic
15C22×#627—21no—
16C22×#624—21no—
17C2×#3797—22no—
18C2×#3797—24no—
19C2×#3797—24no—
20C2×#3797C2214yes—
21C22×C32×C8C2211yescharacteristic
22C22×C3⋊(C3⋊C8)C2211yescharacteristic
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C2×C3×Dic12—24no—
25C2×C3×Dic12C2214yescomplemented
26C2×Dic3⋊Dic3—21no—
27C2×#3722—21no—
28#63871—22no—
29#63871C2214yes—
30C2×#3718—24no—
31C2×#3718C2214yescomplemented
32#63647C2214yes—
33C3×#816C2214yescomplemented
34#63565C2214yescomplemented
35C22×D3×Q8—31no—
36C22×D3×Q8—31no—
37C22×C3×Q16—31no—
38C2×#946—31no—
39C22×#216—31no—
40C22×#216—31no—
41C22×Dic12D311yescharacteristic, complemented
42C2×#897—31no—
43C2×C3×#103—31no—
44C2×#835—31no—
45#5186—38no—
46C2×(C2×D3)⋊C8—31no—
47C2×(C2×D3)⋊C8—31no—
48C2×(C2×D3)⋊C8—61no—
49C2×#816D311yescharacteristic, complemented
50C2×#810—31no—
51#4809—38no—
52C23×C3⋊D3D411yescharacteristic
53C22×C32×C4C2311yescharacteristic
54C22×C3⋊Dic3D411yescharacteristic
55C2×C4×C3⋊D3—22no—
56C2×C4×C3⋊D3—22no—
57C2×C4×C3⋊D3D412yes—
58C2×C4×C3⋊D3C2312yes—
59C22×C3×Dic3—21no—
60C22×C3×Dic3—21no—
61C22×C3×Dic3—21no—
62C22×C3×Dic3—21no—
63C2×C3×Dic6—21no—
64C2×C3×Dic6—21no—
65C2×C3×Dic6—22no—
66C2×C3×Dic6—22no—
67C2×C3×Dic6—22no—
68C2×C3×Dic6—22no—
69C2×C3×Dic6—21no—
70C2×C3×Dic6D414yes—
71C2×C3×Dic6D414yes—
72C2×C3×Dic6C2312yes—
73C2×C3×Dic6C2312yes—
74C2×C3×Dic6C2312yes—
75C2×#627—28no—
76C2×#627—24no—
77C2×#624—28no—
78C2×#624—24no—
79#3797—216no—
80#3797—28no—
81#3797—28no—
82C2×C32×C8—22no—
83C2×C32×C8C2312yes—
84C2×C3⋊(C3⋊C8)—22no—
85C2×C3⋊(C3⋊C8)C2312yes—
86C3×C4⋊Dic3—21no—
87C3×C4⋊Dic3C2312yes—
88C3×Dic12—28no—
89Dic3⋊Dic3—24no—
90#3722—24no—
91#3718—28no—
92C2×#451—91noSylow
93C22×C3×Q8—31no—
94C22×C3×Q8—31no—
95C22×C3×Q8—31no—
96C2×D3×Q8—34no—
97C2×D3×Q8—34no—
98C2×D3×Q8—62no—
99C2×D3×Q8—62no—
100C2×D3×Q8—64no—
101C2×D3×Q8—64no—
102C2×D3×Q8—64no—
103C2×D3×Q8—64no—
104C22×C4×D3—31no—
105C22×C4×D3—31no—
106C22×C4×D3—61no—
107C22×C4×D3—61no—
108C22×C4×D3—61no—
109C22×Dic6—61no—
110C22×Dic6—61no—
111C22×Dic6C2×D311yescharacteristic
112C22×Dic6C2×D311yescharacteristic
113C22×Dic6C2×D311yescharacteristic
114C2×C3×Q16—34no—
115C2×C3×Q16—64no—
116C22×C3×C8—21no—
117C22×C3×C8C2×D311yescharacteristic
118C22×C3×C8C2×D311yescharacteristic
119C2×C3×C4⋊C4—31no—
120#946—34no—
121#946—62no—
122C2×#216—34no—
123C2×#216—34no—
124C2×#216—64no—
125C2×#216—64no—
126C2×(C2×D3)⋊C4—61no—
127C2×(C2×D3)⋊C4—61no—
128C2×C4⋊Dic3—61no—
129C2×C4⋊Dic3C2×D311yescharacteristic
130C2×Dic3⋊C4—61no—
131C22×C3⋊C8—31no—
132C22×C3⋊C8—31no—
133C22×C3⋊C8—61no—
134C2×Dic12—24no—
135C2×Dic12C2×D314yescomplemented
136#897—34no—
137#897—62no—
138C3×#103—34no—
139#835—34no—
140(C2×D3)⋊C8—34no—
141(C2×D3)⋊C8—34no—
142(C2×D3)⋊C8—64no—
143#816C2×D314yescomplemented
144#810—34no—
145C23×C32C2×D411yescharacteristic
146C22×C3⋊D3—22no—
147C22×C3⋊D3—22no—
148C22×C3⋊D3Q1614yescomplemented
149C22×C3⋊D3C2×D412yes—
150C2×C32×C4C2×D412yes—
151C2×C32×C4C2×D411yescharacteristic
152C2×C32×C4C2×D412yes—
153C2×C32×C4C2411yescharacteristic
154C2×C3⋊Dic3—22no—
155C2×C3⋊Dic3C2×D412yes—
156C4×C3⋊D3—24no—
157C4×C3⋊D3—22no—
158C4×C3⋊D3—22no—
159C2×C3×Dic3—24no—
160C2×C3×Dic3—24no—
161C2×C3×Dic3—22no—
162C2×C3×Dic3—22no—
163C2×C3×Dic3—22no—
164C2×C3×Dic3—22no—
165C2×C3×Dic3—42no—
166C2×C3×Dic3—42no—
167C3×Dic6—24no—
168C3×Dic6—24no—
169C3×Dic6—22no—
170C3×Dic6—22no—
171C3×Dic6—22no—
172C3×Dic6—22no—
173C3×Dic6—42no—
174C3×Dic6C2×D414yes—
175C3×Dic6C2×D414yes—
176#627—216no—
177#624—216no—
178C32×C8—22no—
179C3⋊(C3⋊C8)—22no—
180C23×Q8—91no—
181C22×Q16—31no—
182C22×Q16—91no—
183C2×C22⋊Q8—91no—
184#451—98no—
185C2×#103—31no—
186C2×#103—91no—
187C2×C22⋊C8—91no—
188C23×D3—31no—
189C23×D3—31no—
190C23×D3—61no—
191C2×C3×Q8—34no—
192C2×C3×Q8—34no—
193C2×C3×Q8—32no—
194C2×C3×Q8—32no—
195C2×C3×Q8—32no—
196C2×C3×Q8—62no—
197C2×C3×Q8—61no—
198C2×C3×Q8—61no—
199C2×C3×Q8—61no—
200C2×C3×Q8—62no—
201C2×C3×Q8—62no—
202C2×C3×Q8—62no—
203C22×C3×C4—21no—
204C22×C3×C4—61no—
205C22×C3×C4—61no—
206C22×C3×C4—61no—
207C22×C3×C4—61no—
208C22×C3×C4C22×D311yescharacteristic
209C22×C3×C4C22×D311yescharacteristic
210C22×Dic3—21no—
211C22×Dic3—21no—
212C22×Dic3—21no—
213C22×Dic3—21no—
214C22×Dic3—31no—
215C22×Dic3—31no—
216C22×Dic3—61no—
217D3×Q8—68no—
218D3×Q8—68no—
219D3×Q8—616no—
220D3×Q8—616no—
221D3×Q8—68no—
222D3×Q8—68no—
223C2×C4×D3—32no—
224C2×C4×D3—32no—
225C2×C4×D3—32no—
226C2×C4×D3—32no—
227C2×C4×D3—62no—
228C2×C4×D3—62no—
229C2×C4×D3—64no—
230C2×C4×D3—64no—
231C2×C4×D3—68no—
232C2×C4×D3—68no—
233C2×C4×D3—62no—
234C2×C4×D3—62no—
235C2×C4×D3—62no—
236C2×C4×D3—62no—
237C2×C4×D3—122no—
238C2×C4×D3—122no—
239C2×Dic6—22no—
240C2×Dic6—21no—
241C2×Dic6—21no—
242C2×Dic6—22no—
243C2×Dic6—22no—
244C2×Dic6—22no—
245C2×Dic6—21no—
246C2×Dic6—64no—
247C2×Dic6—64no—
248C2×Dic6—68no—
249C2×Dic6—68no—
250C2×Dic6D1214yes—
251C2×Dic6#6714yes—
252C2×Dic6C22×D312yes—
253C2×Dic6C22×D312yes—
254C2×Dic6C22×D312yes—
255C3×Q16—68no—
256C2×C3×C8—22no—
257C2×C3×C8—22no—
258C2×C3×C8—22no—
259C2×C3×C8—42no—
260C2×C3×C8C22×D312yes—
261C2×C3×C8C22×D312yes—
262C3×C4⋊C4—32no—
263C3×C4⋊C4—61no—
264#216—68no—
265#216—68no—
266(C2×D3)⋊C4—64no—
267(C2×D3)⋊C4—64no—
268C4⋊Dic3—21no—
269C4⋊Dic3—64no—
270C4⋊Dic3C22×D312yes—
271Dic3⋊C4—64no—
272C2×C3⋊C8—32no—
273C2×C3⋊C8—32no—
274C2×C3⋊C8—62no—
275C2×C3⋊C8—62no—
276C2×C3⋊C8—62no—
277C2×C3⋊C8—122no—
278Dic12—28no—
279C22×C32#12012yes—
280C22×C32C2×Q1612yes—
281C22×C32#13712yes—
282C22×C32C22×D411yescharacteristic
283C2×C3⋊D3—22no—
284C2×C3⋊D3—22no—
285C2×C3⋊D3—28no—
286C2×C3⋊D3C2×Q1614yescomplemented
287C32×C4#12012yes—
288C32×C4C22×D411yescharacteristic
289C32×C4C22×D411yescharacteristic
290C3⋊Dic3—22no—
291C3×Dic3—24no—
292C3×Dic3—24no—
293C3×Dic3—42no—
294C3×Dic3—42no—
295C22×Q8—31no—
296C22×Q8—31no—
297C22×Q8—31no—
298C22×Q8—94no—
299C22×Q8—181no—
300C22×Q8—182no—
301C22×Q8—184no—
302C22×Q8—184no—
303C23×C4—91no—
304C23×C4—181no—
305C2×Q16—34no—
306C2×Q16—64no—
307C2×Q16—94no—
308C2×Q16—184no—
309C22×C8—91no—
310C22×C8D3211yescharacteristic
311C22⋊Q8—94no—
312C22⋊Q8—182no—
313C2×C4⋊C4—31no—
314C2×C4⋊C4—181no—
315C2×C22⋊C4—181no—
316#103—34no—
317#103—94no—
318C22⋊C8—94no—
319C23×C3—21no—
320C23×C3D3×D411yescharacteristic
321C23×C3D3×D411yescharacteristic
322C22×D3—34no—
323C22×D3—34no—
324C22×D3—32no—
325C22×D3—32no—
326C22×D3—64no—
327C22×D3—62no—
328C22×D3—62no—
329C22×D3—62no—
330C22×D3—62no—
331C22×D3—62no—
332C22×D3—122no—
333C22×D3—122no—
334C3×Q8—34no—
335C3×Q8—34no—
336C3×Q8—64no—
337C3×Q8—64no—
338C3×Q8—62no—
339C3×Q8—62no—
340C3×Q8—62no—
341C3×Q8—62no—
342C3×Q8—122no—
343C2×C3×C4—21no—
344C2×C3×C4—22no—
345C2×C3×C4—21no—
346C2×C3×C4—22no—
347C2×C3×C4—64no—
348C2×C3×C4—64no—
349C2×C3×C4—62no—
350C2×C3×C4—62no—
351C2×C3×C4—62no—
352C2×C3×C4—62no—
353C2×C3×C4—122no—
354C2×C3×C4—122no—
355C2×C3×C4C2×D1212yes—
356C2×C3×C4D3×D412yes—
357C2×C3×C4D3×D411yescharacteristic
358C2×C3×C4D3×D411yescharacteristic
359C2×C3×C4D3×D412yes—
360C2×C3×C4C2×#6712yes—
361C2×C3×C4C23×D311yescharacteristic
362C2×C3×C4C23×D311yescharacteristic
363C2×Dic3—24no—
364C2×Dic3—24no—
365C2×Dic3—22no—
366C2×Dic3—22no—
367C2×Dic3—22no—
368C2×Dic3—22no—
369C2×Dic3—32no—
370C2×Dic3—32no—
371C2×Dic3—42no—
372C2×Dic3—42no—
373C2×Dic3—62no—
374C2×Dic3—62no—
375C2×Dic3—62no—
376C2×Dic3—122no—
377C4×D3—616no—
378C4×D3—616no—
379C4×D3—64no—
380C4×D3—64no—
381C4×D3—62no—
382C4×D3—62no—
383C4×D3—62no—
384C4×D3—62no—
385C4×D3—122no—
386C4×D3—122no—
387C4×D3—124no—
388Dic6—24no—
389Dic6—24no—
390Dic6—22no—
391Dic6—22no—
392Dic6—22no—
393Dic6—22no—
394Dic6—42no—
395Dic6—616no—
396Dic6—616no—
397Dic6C2×D1214yes—
398Dic6C2×#6714yes—
399C3×C8—22no—
400C3×C8—22no—
401C3×C8—42no—
402C3⋊C8—62no—
403C3⋊C8—62no—
404C3⋊C8—122no—
405C2×C32#45114yescomplemented
406C2×C32C2×#12011yescharacteristic
407C2×C32C22×Q1611yescharacteristic
408C2×C32C2×#13711yescharacteristic
409C3⋊D3—24no—
410C24—91no—
411C2×Q8—32no—
412C2×Q8—32no—
413C2×Q8—32no—
414C2×Q8—34no—
415C2×Q8—34no—
416C2×Q8—62no—
417C2×Q8—61no—
418C2×Q8—61no—
419C2×Q8—61no—
420C2×Q8—62no—
421C2×Q8—62no—
422C2×Q8—62no—
423C2×Q8—184no—
424C2×Q8—188no—
425C2×Q8—188no—
426C2×Q8—188no—
427C2×Q8—1816no—
428C22×C4—61no—
429C22×C4—61no—
430C22×C4—61no—
431C22×C4—61no—
432C22×C4—91no—
433C22×C4—92no—
434C22×C4—92no—
435C22×C4—184no—
436C22×C4—188no—
437C22×C4—182no—
438C22×C4—182no—
439C22×C4C2×D3211yescharacteristic
440Q16—68no—
441Q16—188no—
442C2×C8—22no—
443C2×C8—92no—
444C2×C8—182no—
445C2×C8C2×D3212yes—
446C4⋊C4—32no—
447C4⋊C4—61no—
448C4⋊C4—184no—
449C22⋊C4—184no—
450C22×C3—21no—
451C22×C3—22no—
452C22×C3—22no—
453C22×C3—22no—
454C22×C3#88212yes—
455C22×C3#91512yes—
456C22×C3D3×Q1612yes—
457C22×C3D3×Q1612yes—
458C22×C3#91812yes—
459C22×C3#93712yes—
460C22×C3C2×D3×D411yescharacteristic
461C22×C3C2×D3×D411yescharacteristic
462C2×D3—34no—
463C2×D3—34no—
464C2×D3—64no—
465C2×D3—68no—
466C2×D3—62no—
467C2×D3—62no—
468C2×D3—62no—
469C2×D3—62no—
470C2×D3—68no—
471C2×D3—122no—
472C2×D3—122no—
473C2×D3—128no—
474C3×C4—21no—
475C3×C4—21no—
476C3×C4—22no—
477C3×C4—64no—
478C3×C4—64no—
479C3×C4—122no—
480C3×C4—122no—
481C3×C4#88212yes—
482C3×C4#93712yes—
483C3×C4C22×D1211yescharacteristic
484C3×C4C2×D3×D411yescharacteristic
485C3×C4C2×D3×D411yescharacteristic
486C3×C4C22×#6711yescharacteristic
487Dic3—24no—
488Dic3—24no—
489Dic3—42no—
490Dic3—42no—
491Dic3—62no—
492Dic3—62no—
493Dic3—122no—
494C32C2×#45111yescharacteristic, complemented, Sylow
495C23—92no—
496C23—94no—
497C23—182no—
498C23—182no—
499C23#380211yescharacteristic
500Q8—34no—
501Q8—34no—
502Q8—62no—
503Q8—62no—
504Q8—64no—
505Q8—64no—
506Q8—62no—
507Q8—62no—
508Q8—122no—
509Q8—1816no—
510C2×C4—62no—
511C2×C4—62no—
512C2×C4—64no—
513C2×C4—64no—
514C2×C4—62no—
515C2×C4—62no—
516C2×C4—92no—
517C2×C4—122no—
518C2×C4—122no—
519C2×C4—1816no—
520C2×C4—182no—
521C2×C4—182no—
522C2×C4—182no—
523C2×C4—184no—
524C2×C4D3×D1212yes—
525C2×C4#380211yescharacteristic
526C2×C4D3×#6712yes—
527C2×C4C22×D3211yescharacteristic
528C8—22no—
529C8—182no—
530C2×C3—21no—
531C2×C3—21no—
532C2×C3—24no—
533C2×C3—21no—
534C2×C3#480914yescomplemented
535C2×C3#518614yescomplemented
536C2×C3C2×#88211yescharacteristic
537C2×C3C2×#91511yescharacteristic
538C2×C3C2×D3×Q1611yescharacteristic
539C2×C3C2×D3×Q1611yescharacteristic
540C2×C3C2×#91811yescharacteristic
541C2×C3C2×#93711yescharacteristic
542D3—64no—
543D3—64no—
544D3—124no—
545C22—94no—
546C22—182no—
547C22—188no—
548C22—182no—
549C22#6380212yes—
550C22#6381112yes—
551C22#6392212yes—
552C22C2×#380211yescharacteristic
553C4—64no—
554C4—64no—
555C4—122no—
556C4—122no—
557C4—182no—
558C4#6392212yes—
559C4C2×D3×D1211yescharacteristic
560C4C2×D3×#6711yescharacteristic
561C3—21no—
562C3C2×#480911yescharacteristic, complemented
563C3C2×#518611yescharacteristic, complemented
564C2—184no—
565C2#1059095014yesdirect product factor
566C2C2×#6380211yescharacteristic
567C2C2×#6381111yescharacteristic
568C2C2×#6392211yescharacteristic
subgroupG/H
centerC23#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC23×C3⋊D3D4
hypercenterC22×C8D32
hypocenterC32C2×#451
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. C22×C3×Dic12C2semidirect
4. C22×#3718C2semidirect
6. C2×C3×#816C2semidirect
7. C2×#63565C2semidirect
8. #10590950C2direct (N × H)
25. C2×C3×Dic12C22semidirect
31. C2×#3718C22semidirect
33. C3×#816C22semidirect
34. #63565C22semidirect
41. C22×Dic12D3semidirect
49. C2×#816D3semidirect
135. C2×Dic12C2×D3semidirect
143. #816C2×D3semidirect
148. C22×C3⋊D3Q16semidirect
286. C2×C3⋊D3C2×Q16semidirect
405. C2×C32#451semidirect
494. C32C2×#451semidirect
534. C2×C3#4809semidirect
535. C2×C3#5186semidirect
562. C3C2×#4809semidirect
563. C3C2×#5186semidirect
565. C2#10590950direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37972
C22×C3×Dic122
C2×#638712
C22×#37182
C2×#636472
C2×C3×#8162
C2×#635652
#105909502
C2×#51863
C2×#48093