Finite Group Databasebeta

← C2×#13077462 #15617885

Subgroups — C2×#13077462 #15617885

Order 2816.

2730 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#67004C211yesmaximal, characteristic
2C2×#10623358C211yesmaximal, characteristic
3C2×#10623047C211yesmaximal, characteristic, complemented
4#13077462C2116yesmaximal, direct product factor
5C2×#10622402C212yesmaximal, complemented
6C2×#10622370C212yesmaximal, complemented
7C2×#10622403C212yesmaximal, complemented
8C2×#10622371C212yesmaximal, complemented
9C2×#10622608C211yesmaximal, characteristic, complemented
10C22×#66880C211yesmaximal, characteristic, complemented
11C2×#10622714C211yesmaximal, characteristic, complemented
12C2×C11×#416C211yesmaximal, characteristic
13C22×C11×#41C2211yescharacteristic
14C23×Dic22C2211yescharacteristic
15C23×C8×C11C2211yescharacteristic
16C2×C11×#117C2211yescharacteristic
17#10623358—24no—
18#10623358C2218yes—
19C2×#67004C4116yescomplemented
20C2×#67004C2218yes—
21C2×Q8×Dic11C2212yes—
22C22×#4326C2212yes—
23C2×D4×Dic11—22no—
24C2×D4×Dic11C2212yes—
25C22×#4324C2212yes—
26C2×#66979—21no—
27C2×#66979C2211yescharacteristic
28C22×C4⋊Dic11—21no—
29C22×C4⋊Dic11C2211yescharacteristic
30C22×#4318C2211yescharacteristic
31#10623047—24no—
32#10623047C2218yescomplemented
33C2×#66940C2212yes—
34C2×#66940C2212yes—
35C2×#66930—22no—
36C2×C4×Dic22—21no—
37C2×C4×Dic22—21no—
38C11×#416C2218yes—
39C2×C11×#103C2211yescharacteristic
40C2×C11×#103C2211yescharacteristic
41C2×C11×#102C2211yescharacteristic
42C2×C11×#102C2211yescharacteristic
43C2×#66880C2212yes—
44C2×#66880C2212yes—
45C2×#66880C2218yescomplemented
46#10622714C2218yescomplemented
47C2×#66879C2212yes—
48C2×C8×Dic11C2212yes—
49#10622608C2218yescomplemented
50C2×#66872C2212yes—
51C2×#66871C2212yes—
52#10622403C22116yescomplemented
53#10622402C22116yescomplemented
54#10622371C22116yescomplemented
55#10622370C22116yescomplemented
56C2×C11×#41—22no—
57C2×C11×#41—24no—
58C2×C11×#41C2×C418yes—
59C2×C11×#41C2314yes—
60C22×Q8×C11C2311yescharacteristic
61C22×D4×C11—21no—
62C22×D4×C11C2311yescharacteristic
63C23×C4×C11—21no—
64C23×C4×C11C2311yescharacteristic
65C23×Dic11—21no—
66C23×Dic11—21no—
67C23×Dic11—22no—
68C22×Dic22—21no—
69C22×Dic22—22no—
70C22×Dic22—24no—
71C22×Dic22C2×C418yescomplemented
72C22×Dic22C2312yes—
73C22×Dic22C2314yes—
74C22×C8×C11—24no—
75C22×C8×C11C2311yescharacteristic
76C22×C8×C11C2311yescharacteristic
77C22×C8×C11C2314yes—
78C11×#117—22no—
79C11×#117C2314yes—
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C11×C22⋊C4—21no—
83C2×C42×C11—21no—
84C2×C22⋊Dic11—22no—
85C2×C22⋊Dic11D412yes—
86#67004C2×C4164yescomplemented
87Q8×Dic11—24no—
88Q8×Dic11C2318yes—
89C2×#4326C2×C4116yescomplemented
90C2×#4326C2318yes—
91D4×Dic11—216no—
92D4×Dic11—24no—
93D4×Dic11C2318yes—
94C2×#4324C2×C4116yescomplemented
95C2×#4324C2318yes—
96#66979—28no—
97#66979D414yes—
98#66979C2314yes—
99C2×C4⋊Dic11—21no—
100C2×C4⋊Dic11—22no—
101C2×C4⋊Dic11—22no—
102C2×C4⋊Dic11—28no—
103C2×C4⋊Dic11D411yescharacteristic
104C2×C4⋊Dic11D411yescharacteristic
105C2×C4⋊Dic11C2312yes—
106C2×C4⋊Dic11C2314yes—
107C2×Dic11⋊C4—22no—
108C2×Dic11⋊C4—22no—
109C2×C4×Dic11—22no—
110C2×C4×Dic11—22no—
111C2×C4×Dic11—22no—
112C2×C4×Dic11C2312yes—
113C2×#4318C2×C418yescomplemented
114C2×#4318C2314yes—
115C22×C11⋊C8C2312yes—
116#66940—24no—
117#66940—24no—
118#66940C2318yes—
119#66940C2318yes—
120#66930—216no—
121C4×Dic22—28no—
122C4×Dic22—28no—
123C11×#103C2314yes—
124C11×#103C2314yes—
125C11×#102C2314yes—
126C11×#102C2314yes—
127#66880C2318yes—
128#66880C2318yes—
129#66879C2318yes—
130C8×Dic11C2318yes—
131#66872C2318yes—
132#66871C2318yes—
133C2×#2947—111nomaximal, Sylow
134C24×C11—21no—
135C24×C11C2×D411yescharacteristic
136C11×#41—216no—
137C11×#41—28no—
138C11×#41C22×C4116yes—
139C2×Q8×C11—21no—
140C2×Q8×C11—22no—
141C2×Q8×C11C22×C414yes—
142C2×Q8×C11C2412yes—
143C2×D4×C11—28no—
144C2×D4×C11—24no—
145C2×D4×C11—21no—
146C2×D4×C11—22no—
147C2×D4×C11C22×C414yes—
148C2×D4×C11C2412yes—
149C22×C4×C11—21no—
150C22×C4×C11—28no—
151C22×C4×C11—24no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11C22×C414yes—
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D412yes—
157C22×C4×C11#4114yes—
158C22×C4×C11C2411yescharacteristic
159C22×C4×C11C2412yes—
160C22×Dic11—28no—
161C22×Dic11—28no—
162C22×Dic11—24no—
163C22×Dic11—22no—
164C22×Dic11—22no—
165C22×Dic11—24no—
166C22×Dic11—82no—
167C22×Dic11—84no—
168C22×Dic11C2×D412yes—
169C22×Dic11C2×D412yes—
170C2×Dic22—28no—
171C2×Dic22—216no—
172C2×Dic22—24no—
173C2×Dic22—22no—
174C2×Dic22—24no—
175C2×Dic22—28no—
176C2×Dic22C22×C418yes—
177C2×Dic22C22×C4116yescomplemented
178C2×Dic22C2414yes—
179C2×C8×C11—22no—
180C2×C8×C11—22no—
181C2×C8×C11—28no—
182C2×C8×C11C2412yes—
183C2×C8×C11C2412yes—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4C2412yes—
187C11×C4⋊C4C2412yes—
188C11×C22⋊C4—24no—
189C42×C11—24no—
190C22⋊Dic11—28no—
191C22⋊Dic11C2×D418yes—
192#4326C22×C4132yescomplemented
193#4324C22×C4132yescomplemented
194C4⋊Dic11—28no—
195C4⋊Dic11—24no—
196C4⋊Dic11—22no—
197C4⋊Dic11C2×D414yes—
198C4⋊Dic11C2×D414yes—
199C4⋊Dic11C2414yes—
200Dic11⋊C4—28no—
201Dic11⋊C4—28no—
202C4×Dic11—28no—
203C4×Dic11—28no—
204C4×Dic11—28no—
205C4×Dic11C2×D414yes—
206C4×Dic11C2414yes—
207#4318C22×C4116yescomplemented
208C2×C11⋊C8C22×C418yes—
209C2×C11⋊C8C2414yes—
210C22×#137—111no—
211C2×#520—111no—
212C2×#519—111no—
213#2947—1116no—
214C2×#441—112no—
215C2×#440—112no—
216C2×C4×Q16—112no—
217C2×C4×SD16—112no—
218C2×#428—111no—
219C2×#416D1111yescharacteristic
220C22×#103—111no—
221C2×#405—111no—
222C23×C11—22no—
223C23×C11—22no—
224C23×C11—24no—
225C23×C11—22no—
226C23×C11—42no—
227C23×C11—42no—
228C23×C11C4×D414yes—
229C23×C11C22×D412yes—
230C23×C11C22×D411yescharacteristic
231Q8×C11—24no—
232Q8×C11—22no—
233Q8×C11C23×C414yes—
234D4×C11—216no—
235D4×C11—24no—
236D4×C11—22no—
237D4×C11C23×C414yes—
238C2×C4×C11—24no—
239C2×C4×C11—22no—
240C2×C4×C11—216no—
241C2×C4×C11—22no—
242C2×C4×C11—22no—
243C2×C4×C11—42no—
244C2×C4×C11—42no—
245C2×C4×C11C4×D414yes—
246C2×C4×C11C4×D418yes—
247C2×C4×C11C23×C412yes—
248C2×C4×C11C23×C414yes—
249C2×C4×C11C22×D411yescharacteristic
250C2×C4×C11C22×D412yes—
251C2×C4×C11C2×#4112yes—
252C2×C4×C11C2×#4114yes—
253C2×C4×C11C2511yescharacteristic
254C2×Dic11—28no—
255C2×Dic11—216no—
256C2×Dic11—24no—
257C2×Dic11—24no—
258C2×Dic11—24no—
259C2×Dic11—24no—
260C2×Dic11—44no—
261C2×Dic11—88no—
262C2×Dic11—84no—
263C2×Dic11C22×D414yes—
264C2×Dic11C22×D414yes—
265Dic22—28no—
266Dic22—216no—
267Dic22—24no—
268Dic22C23×C418yes—
269C8×C11—22no—
270C8×C11—22no—
271C11⋊C8C23×C418yes—
272C22×#41C2×D1111yescharacteristic
273C23×Q8—111no—
274C2×#137—118no—
275C2×#137—1116no—
276C22×Q16—112no—
277C22×SD16—112no—
278C22×M16—111no—
279C23×C8C2×D1111yescharacteristic
280#520—118no—
281#520—224no—
282#519—118no—
283#519—224no—
284C2×C4×Q8—112no—
285C2×C4×Q8—112no—
286C2×C4×Q8—112no—
287C2×C4×Q8—221no—
288C2×C4×Q8—221no—
289C2×C4×D4—112no—
290C2×C4×D4—222no—
291C2×#117—111no—
292C2×#117—222no—
293C2×#117—221no—
294C2×#117C2×D1111yescharacteristic
295C22×C4⋊C4—111no—
296C22×C4⋊C4—221no—
297#441—1116no—
298#440—1116no—
299C4×Q16—1116no—
300C4×SD16—1116no—
301#428—118no—
302C2×#107—112no—
303C2×#106—112no—
304#416C2×D1118yes—
305C2×#103—112no—
306C2×#103—112no—
307C2×#103—118no—
308C2×#103C2×D1111yescharacteristic
309C2×#103C2×D1111yescharacteristic
310C2×#102C2×D1111yescharacteristic
311C2×#102C2×D1111yescharacteristic
312#405—118no—
313C2×#97—112no—
314C2×C4×C8—112no—
315C22×C11—28no—
316C22×C11—22no—
317C22×C11—22no—
318C22×C11—24no—
319C22×C11—48no—
320C22×C11—42no—
321C22×C11—42no—
322C22×C11C2×C4×D414yes—
323C22×C11C2×C4×D412yes—
324C22×C11#57712yes—
325C22×C11#57812yes—
326C22×C11C23×D411yescharacteristic
327C4×C11—24no—
328C4×C11—42no—
329C4×C11—42no—
330C4×C11C2×C4×D414yes—
331C4×C11C2×C4×D412yes—
332C4×C11C24×C411yescharacteristic
333C4×C11C22×#4111yescharacteristic
334Dic11—28no—
335Dic11—24no—
336Dic11—24no—
337Dic11—44no—
338C2×#41—22no—
339C2×#41—24no—
340C2×#41C4×D1118yes—
341C2×#41C22×D1114yes—
342C22×Q8—118no—
343C22×Q8—112no—
344C22×Q8—114no—
345C22×Q8—221no—
346C22×Q8—222no—
347C22×Q8—224no—
348C22×Q8C22×D1111yescharacteristic
349C22×D4—21no—
350C22×D4C22×D1111yescharacteristic
351C23×C4—21no—
352C23×C4—222no—
353C23×C4—221no—
354C23×C4—221no—
355C23×C4C22×D1111yescharacteristic
356#137—1164no—
357C2×Q16—1116no—
358C2×Q16—118no—
359C2×SD16—1116no—
360C2×SD16—118no—
361C2×M16—118no—
362C2×M16—114no—
363C22×C8—24no—
364C22×C8—112no—
365C22×C8C22×D1111yescharacteristic
366C22×C8C22×D1111yescharacteristic
367C22×C8C22×D1114yes—
368C4×Q8—118no—
369C4×Q8—118no—
370C4×Q8—118no—
371C4×Q8—228no—
372C4×Q8—228no—
373C4×Q8—224no—
374C4×Q8—224no—
375C4×Q8—224no—
376C4×D4—118no—
377C4×D4—224no—
378C4×D4—2216no—
379#117—22no—
380#117—114no—
381#117—114no—
382#117—2216no—
383#117—228no—
384#117C22×D1114yes—
385C2×C4⋊C4—111no—
386C2×C4⋊C4—111no—
387C2×C4⋊C4—112no—
388C2×C4⋊C4—114no—
389C2×C4⋊C4—228no—
390C2×C4⋊C4—222no—
391C2×C4⋊C4—222no—
392C2×C4⋊C4—222no—
393C2×C4⋊C4—221no—
394C2×C4⋊C4—222no—
395C2×C4⋊C4C22×D1111yescharacteristic
396C2×C4⋊C4C22×D1111yescharacteristic
397C2×C22⋊C4—21no—
398C2×C22⋊C4—112no—
399C2×C22⋊C4—222no—
400C2×C42—21no—
401C2×C42—112no—
402C2×C42—222no—
403C2×C42—222no—
404C2×C42—222no—
405#107—118no—
406#106—118no—
407#103—118no—
408#103—118no—
409#103C22×D1114yes—
410#103C22×D1114yes—
411#102C22×D1114yes—
412#102C22×D1114yes—
413#97—118no—
414C4×C8—118no—
415C2×C11—24no—
416C2×C11—44no—
417C2×C11#294714yescomplemented
418C2×C11C22×C4×D411yescharacteristic
419C2×C11C2×#57711yescharacteristic
420C2×C11C2×#57811yescharacteristic
421C24—21no—
422C24D4×D1111yescharacteristic
423#41—216no—
424#41—28no—
425#41C2×C4×D11116yes—
426C2×Q8—21no—
427C2×Q8—22no—
428C2×Q8—118no—
429C2×Q8—1116no—
430C2×Q8—114no—
431C2×Q8—228no—
432C2×Q8—2216no—
433C2×Q8—224no—
434C2×Q8—222no—
435C2×Q8—224no—
436C2×Q8—228no—
437C2×Q8C2×C4×D1114yes—
438C2×Q8C23×D1112yes—
439C2×D4—28no—
440C2×D4—24no—
441C2×D4—21no—
442C2×D4—22no—
443C2×D4C2×C4×D1114yes—
444C2×D4C23×D1112yes—
445C22×C4—21no—
446C22×C4—28no—
447C22×C4—24no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—112no—
451C22×C4—112no—
452C22×C4—228no—
453C22×C4—228no—
454C22×C4—224no—
455C22×C4—222no—
456C22×C4—222no—
457C22×C4—224no—
458C22×C4—884no—
459C22×C4—882no—
460C22×C4C2×C4×D1114yes—
461C22×C4D4×D1112yes—
462C22×C4D4×D1111yescharacteristic
463C22×C4#434114yes—
464C22×C4C23×D1112yes—
465C22×C4C23×D1111yescharacteristic
466Q16—1132no—
467SD16—1132no—
468M16—1116no—
469C2×C8—22no—
470C2×C8—22no—
471C2×C8—28no—
472C2×C8—118no—
473C2×C8—114no—
474C2×C8C23×D1112yes—
475C2×C8C23×D1112yes—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—114no—
479C4⋊C4—114no—
480C4⋊C4—114no—
481C4⋊C4—228no—
482C4⋊C4—228no—
483C4⋊C4—228no—
484C4⋊C4—224no—
485C4⋊C4—222no—
486C4⋊C4C23×D1112yes—
487C4⋊C4C23×D1112yes—
488C22⋊C4—24no—
489C22⋊C4—118no—
490C22⋊C4—228no—
491C42—24no—
492C42—114no—
493C42—114no—
494C42—228no—
495C42—228no—
496C42—228no—
497C11C2×#294711yescharacteristic, complemented, Sylow
498C23—22no—
499C23—22no—
500C23—24no—
501C23—22no—
502C23—42no—
503C23—42no—
504C23(C22⋊D11)⋊C414yes—
505C23C2×D4×D1112yes—
506C23C2×D4×D1111yescharacteristic
507Q8—24no—
508Q8—22no—
509Q8—118no—
510Q8—2216no—
511Q8—228no—
512Q8—224no—
513Q8C22×C4×D1114yes—
514D4—216no—
515D4—24no—
516D4—22no—
517D4C22×C4×D1114yes—
518C2×C4—24no—
519C2×C4—22no—
520C2×C4—216no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—114no—
526C2×C4—114no—
527C2×C4—2216no—
528C2×C4—228no—
529C2×C4—224no—
530C2×C4—224no—
531C2×C4—224no—
532C2×C4—224no—
533C2×C4—444no—
534C2×C4—888no—
535C2×C4—884no—
536C2×C4(C22⋊D11)⋊C414yes—
537C2×C4(C22⋊D11)⋊C418yes—
538C2×C4C22×C4×D1112yes—
539C2×C4C22×C4×D1114yes—
540C2×C4C2×D4×D1112yes—
541C2×C4C2×D4×D1111yescharacteristic
542C2×C4C2×#434112yes—
543C2×C4C2×#434114yes—
544C2×C4C24×D1111yescharacteristic
545C8—22no—
546C8—22no—
547C8—118no—
548C22—28no—
549C22—22no—
550C22—22no—
551C22—24no—
552C22—48no—
553C22—42no—
554C22—42no—
555C22C2×(C22⋊D11)⋊C414yes—
556C22C2×(C22⋊D11)⋊C412yes—
557C22#1062330112yes—
558C22#1062330212yes—
559C22C22×D4×D1111yescharacteristic
560C4—24no—
561C4—42no—
562C4—42no—
563C4—228no—
564C4—224no—
565C4—224no—
566C4—444no—
567C4C2×(C22⋊D11)⋊C414yes—
568C4C2×(C22⋊D11)⋊C412yes—
569C4C23×C4×D1111yescharacteristic
570C4C22×#434111yescharacteristic
571C2—24no—
572C2—44no—
573C2#1307746214yesdirect product factor
574C2C22×(C22⋊D11)⋊C411yescharacteristic
575C2C2×#1062330111yescharacteristic
576C2C2×#1062330211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC4×C11C24×C4
FrattiniC2×C4C24×D11
FittingC2×C11×#416C2
socleC23×C11C22×D4
prime radicalC22×C11×#41C22
cosocleC2×C4×C11C25
hypercenterC2×#416D11
hypocenterC11C2×#2947
LCSG ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#416

Complements

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

NH ≅ G/Ntype
3. C2×#10623047C2semidirect
4. #13077462C2direct (N × H)
5. C2×#10622402C2semidirect
6. C2×#10622370C2semidirect
7. C2×#10622403C2semidirect
8. C2×#10622371C2semidirect
9. C2×#10622608C2semidirect
10. C22×#66880C2semidirect
11. C2×#10622714C2semidirect
19. C2×#67004C4semidirect
32. #10623047C22semidirect
45. C2×#66880C22semidirect
46. #10622714C22semidirect
49. #10622608C22semidirect
52. #10622403C22semidirect
53. #10622402C22semidirect
54. #10622371C22semidirect
55. #10622370C22semidirect
71. C22×Dic22C2×C4semidirect
86. #67004C2×C4semidirect
89. C2×#4326C2×C4semidirect
94. C2×#4324C2×C4semidirect
113. C2×#4318C2×C4semidirect
177. C2×Dic22C22×C4semidirect
192. #4326C22×C4semidirect
193. #4324C22×C4semidirect
207. #4318C22×C4semidirect
417. C2×C11#2947semidirect
497. C11C2×#2947semidirect
573. C2#13077462direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#670042
C2×#106233582
C2×#106230472
#130774622
C2×#106224022
C2×#106223702
C2×#106224032
C2×#106223712
C2×#106226082
C22×#668802
C2×#106227142
C2×C11×#4162
C2×#294711