Finite Group Databasebeta

← C2×#13078779 #15621912

Subgroups — C2×#13078779 #15621912

Order 2816.

2150 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623001C211yesmaximal, characteristic, complemented
2C2×C4×#4339C211yesmaximal, characteristic
3#13078779C2116yesmaximal, direct product factor
4C2×#10622336C212yesmaximal, complemented
5C2×#10622463C211yesmaximal, characteristic, complemented
6C2×#10622455C211yesmaximal, characteristic, complemented
7C2×#10622462C211yesmaximal, characteristic, complemented
8C2×#10622454C211yesmaximal, characteristic, complemented
9C2×#10622346C212yesmaximal
10C2×#10622329C212yesmaximal, complemented
11C2×#10622323C212yesmaximal, complemented
12C2×C11×#432C211yesmaximal, characteristic, complemented
13C22×#4339C2211yescharacteristic
14C22×C42×C11C2211yescharacteristic
15C2×C4×C22⋊D11—21no—
16C2×C4×C22⋊D11—21no—
17C2×#66979—21no—
18C2×#66979C2211yescharacteristic
19C2×#66977—21no—
20C2×#66977C2212yes—
21C22×Dic44C2212yes—
22C22×#4314C2212yes—
23C4×#4339—24no—
24C4×#4339C2218yes—
25C2×C4×D44C2211yescharacteristic
26C2×C4×D44C2211yescharacteristic
27C2×#66925—21no—
28C2×C42×D11—21no—
29#10623001—24no—
30#10623001C2218yescomplemented
31C2×#66923—21no—
32C2×#66922C2211yescharacteristic
33C2×#66922C2211yescharacteristic
34C2×C4×Dic22—21no—
35C2×C4×Dic22C2211yescharacteristic
36C2×C4×Dic22C2212yes—
37C2×C4×Dic22C2211yescharacteristic
38C11×#432C2218yescomplemented
39C2×C11×C4⋊C8C2211yescharacteristic
40C2×C11×C4⋊C8C2211yescharacteristic
41C2×C11×C22⋊C8C2212yes—
42C2×C11×#97C2212yes—
43C2×#66885C2212yes—
44C2×#66882C2212yes—
45C2×#66881C2212yes—
46C2×#66880C2212yes—
47C2×#66880C2212yes—
48C2×#66880C2212yes—
49#10622463C2218yescomplemented
50#10622462C2218yescomplemented
51#10622455C2218yescomplemented
52#10622454C2218yescomplemented
53#10622346C22116yes—
54#10622336C22116yescomplemented
55#10622329C22116yescomplemented
56#10622323C22116yescomplemented
57C23×C4×C11D411yescharacteristic
58C23×C4×C11D411yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C22×C22⋊D11—21no—
61C2×#4339—22no—
62C2×#4339—24no—
63C2×#4339—24no—
64C2×#4339C2314yes—
65C22×D44C2311yescharacteristic
66C22×C4×D11—21no—
67C22×C4×D11—21no—
68C22×C4×D11—21no—
69C22×Dic22—21no—
70C22×Dic22C2312yes—
71C22×Dic22C2311yescharacteristic
72C22×C8×C11C2312yes—
73C22×C8×C11C2312yes—
74C2×C42×C11D411yescharacteristic
75C2×C42×C11D411yescharacteristic
76C2×C42×C11D414yes—
77C2×C42×C11C2311yescharacteristic
78C2×C42×C11C2311yescharacteristic
79C2×C42×C11C2314yes—
80C2×C22⋊Dic11—22no—
81C2×C22⋊Dic11—21no—
82C4×C22⋊D11—28no—
83C4×C22⋊D11—28no—
84C2×(C2×D11)⋊C4—21no—
85C2×(C2×D11)⋊C4—21no—
86#66979—28no—
87#66979—22no—
88#66979C2314yes—
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11—21no—
91C2×C4⋊Dic11—21no—
92C2×C4⋊Dic11C2312yes—
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95#66977—24no—
96#66977—28no—
97#66977C2318yes—
98C2×Dic11⋊C4—22no—
99C2×Dic11⋊C4—22no—
100C2×Dic11⋊C4—21no—
101C2×Dic11⋊C4—21no—
102C2×C4×Dic11—22no—
103C2×C4×Dic11—21no—
104C2×C4×Dic11—21no—
105C2×C4×Dic11—21no—
106C2×Dic44—28no—
107C2×Dic44C2318yes—
108C2×#4314—28no—
109C2×#4314C2318yes—
110C4×D44—22no—
111C4×D44—22no—
112C4×D44C2314yes—
113C4×D44C2314yes—
114#66925—28no—
115C42×D11—28no—
116#66923—28no—
117#66922—22no—
118#66922—22no—
119#66922C2314yes—
120#66922C2314yes—
121C4×Dic22—28no—
122C4×Dic22—24no—
123C4×Dic22—22no—
124C4×Dic22—22no—
125C4×Dic22C2318yes—
126C4×Dic22C2314yes—
127C4×Dic22C2314yes—
128C11×C4⋊C8C2314yes—
129C11×C4⋊C8C2314yes—
130C11×C22⋊C8C2318yes—
131C11×#97C2318yes—
132#66885C2318yes—
133#66882C2318yes—
134#66881C2318yes—
135#66880C2318yes—
136#66880C2318yes—
137#66880C2318yes—
138C2×#3116—111nomaximal, Sylow
139C24×C11C2×D411yescharacteristic
140C23×D11—21no—
141C22×C4×C11—24no—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11—42no—
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D412yes—
150C22×C4×C11C2×D414yes—
151C22×C4×C11C2×D414yes—
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2412yes—
154C22×C4×C11C2411yescharacteristic
155C2×C22⋊D11—28no—
156C2×C22⋊D11—24no—
157C22×Dic11—21no—
158C22×Dic11—21no—
159C22×Dic11—21no—
160C22×Dic11—22no—
161C22×Dic11—22no—
162#4339—216no—
163#4339—28no—
164#4339—28no—
165C2×D44—21no—
166C2×D44—22no—
167C2×D44#4114yes—
168C2×D44C2412yes—
169C2×C4×D11—28no—
170C2×C4×D11—24no—
171C2×C4×D11—24no—
172C2×C4×D11—24no—
173C2×C4×D11—44no—
174C2×C4×D11—44no—
175C2×Dic22—21no—
176C2×Dic22—22no—
177C2×Dic22—24no—
178C2×Dic22—22no—
179C2×Dic22—24no—
180C2×Dic22—24no—
181C2×Dic22—44no—
182C2×Dic22#4114yes—
183C2×Dic22C2414yes—
184C2×Dic22C2412yes—
185C2×C8×C11—24no—
186C2×C8×C11—24no—
187C2×C8×C11C2414yes—
188C2×C8×C11C2414yes—
189C42×C11C2×D412yes—
190C42×C11C2×D414yes—
191C42×C11C2×D412yes—
192C42×C11C2×D414yes—
193C42×C11C2412yes—
194C42×C11C2412yes—
195C22⋊Dic11—28no—
196C22⋊Dic11—24no—
197(C2×D11)⋊C4—24no—
198(C2×D11)⋊C4—24no—
199C4⋊Dic11—22no—
200C4⋊Dic11—24no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11—24no—
204C4⋊Dic11—24no—
205C4⋊Dic11C2412yes—
206C4⋊Dic11C2412yes—
207C4⋊Dic11C2414yes—
208Dic11⋊C4—28no—
209Dic11⋊C4—28no—
210Dic11⋊C4—24no—
211Dic11⋊C4—24no—
212C4×Dic11—28no—
213C4×Dic11—24no—
214C4×Dic11—24no—
215C4×Dic11—24no—
216Dic44—216no—
217#4314—216no—
218C2×#533—111no—
219C2×C4×#41—111no—
220#3116—1116no—
221C2×#485—112no—
222C2×#477—111no—
223C2×#476—111no—
224C2×#462—111no—
225C2×#461—111no—
226C2×#452—112no—
227C2×#441—112no—
228C2×#440—112no—
229C2×#432D1111yescharacteristic, complemented
230C23×C11—22no—
231C23×C11—22no—
232C23×C11—22no—
233C23×C11C22×D412yes—
234C23×C11C22×D411yescharacteristic
235C22×D11—24no—
236C22×D11—22no—
237C22×D11—42no—
238C22×D11—42no—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11—22no—
242C2×C4×C11—22no—
243C2×C4×C11—24no—
244C2×C4×C11—28no—
245C2×C4×C11—22no—
246C2×C4×C11—22no—
247C2×C4×C11—44no—
248C2×C4×C11#13714yes—
249C2×C4×C11C22×D412yes—
250C2×C4×C11C22×D412yes—
251C2×C4×C11C22×D412yes—
252C2×C4×C11C22×D412yes—
253C2×C4×C11C22×D411yescharacteristic
254C2×C4×C11C22×D412yes—
255C2×C4×C11C2×#4112yes—
256C2×C4×C11C2×#4112yes—
257C2×C4×C11C2511yescharacteristic
258C22⋊D11—216no—
259C2×Dic11—24no—
260C2×Dic11—22no—
261C2×Dic11—22no—
262C2×Dic11—22no—
263C2×Dic11—24no—
264C2×Dic11—24no—
265C2×Dic11—44no—
266C2×Dic11—42no—
267C2×Dic11—44no—
268C2×Dic11—42no—
269D44—24no—
270D44—22no—
271D44C2×#4114yes—
272C4×D11—216no—
273C4×D11—48no—
274C4×D11—48no—
275Dic22—24no—
276Dic22—22no—
277Dic22—24no—
278Dic22—24no—
279Dic22—48no—
280Dic22—44no—
281Dic22C2×#4114yes—
282C8×C11—24no—
283C8×C11—24no—
284C22×#41—111no—
285C22×Q16—112no—
286C22×SD16—112no—
287#533—118no—
288#533—224no—
289C2×C4⋊Q8—111no—
290C2×C4⋊Q8—111no—
291C2×#125—221no—
292C2×C22⋊Q8—112no—
293C2×C22⋊Q8—221no—
294C4×#41—118no—
295C4×#41—224no—
296C2×C4×Q8—111no—
297C2×C4×Q8—111no—
298C2×C4×Q8—112no—
299C2×C4×Q8—221no—
300C2×C4×D4—111no—
301C2×C4×D4—111no—
302C2×C4×D4—221no—
303C2×C4×D4—221no—
304C2×#117—111no—
305C2×#117—221no—
306C2×#117—221no—
307C22×C42—221no—
308C22×C42C2×D1111yescharacteristic
309#485—1116no—
310#477—118no—
311#476—118no—
312#462—118no—
313#461—118no—
314#452—1116no—
315#441—1116no—
316#440—1116no—
317#432C2×D1118yescomplemented
318C2×#107—112no—
319C2×#106—112no—
320C2×C4⋊C8C2×D1111yescharacteristic
321C2×C4⋊C8C2×D1111yescharacteristic
322C2×#103—112no—
323C2×#103—112no—
324C2×#103—112no—
325C2×#102—112no—
326C2×C22⋊C8C2×D1112yes—
327C2×#97C2×D1112yes—
328C22×C11—22no—
329C22×C11—22no—
330C22×C11—22no—
331C22×C11—44no—
332C22×C11#52512yes—
333C22×C11C2×#13712yes—
334C22×C11#57512yes—
335C22×C11C23×D411yescharacteristic
336C2×D11—24no—
337C2×D11—48no—
338C2×D11—42no—
339C2×D11—42no—
340C4×C11—22no—
341C4×C11—22no—
342C4×C11—22no—
343C4×C11—22no—
344C4×C11#52512yes—
345C4×C11C2×#13714yes—
346C4×C11C22×#4111yescharacteristic
347C4×C11C22×#4111yescharacteristic
348Dic11—24no—
349Dic11—44no—
350Dic11—42no—
351Dic11—44no—
352Dic11—42no—
353C2×#41—114no—
354C2×#41—224no—
355C2×#41—224no—
356C2×#41—222no—
357C22×Q8—111no—
358C22×Q8—112no—
359C22×Q8—221no—
360C22×D4—111no—
361C22×D4—221no—
362C23×C4—221no—
363C23×C4—221no—
364C23×C4—221no—
365C23×C4D4411yescharacteristic
366C23×C4D4411yescharacteristic
367C23×C4C22×D1111yescharacteristic
368C2×Q16—118no—
369C2×Q16—228no—
370C2×SD16—118no—
371C2×SD16—228no—
372C22×C8C22×D1112yes—
373C22×C8C22×D1112yes—
374C4⋊Q8—114no—
375C4⋊Q8—114no—
376C4⋊Q8—222no—
377C4⋊Q8—222no—
378#125—228no—
379C22⋊Q8—118no—
380C22⋊Q8—224no—
381C22⋊Q8—228no—
382C4×Q8—114no—
383C4×Q8—114no—
384C4×Q8—118no—
385C4×Q8—222no—
386C4×Q8—222no—
387C4×Q8—224no—
388C4×Q8—228no—
389C4×D4—114no—
390C4×D4—114no—
391C4×D4—228no—
392C4×D4—228no—
393C4×D4—222no—
394C4×D4—222no—
395#117—114no—
396#117—222no—
397#117—228no—
398#117—228no—
399C2×C4⋊C4—111no—
400C2×C4⋊C4—111no—
401C2×C4⋊C4—112no—
402C2×C4⋊C4—221no—
403C2×C4⋊C4—221no—
404C2×C4⋊C4—221no—
405C2×C4⋊C4—221no—
406C2×C4⋊C4—222no—
407C2×C4⋊C4—222no—
408C2×C4⋊C4—221no—
409C2×C22⋊C4—221no—
410C2×C22⋊C4—222no—
411C2×C22⋊C4—221no—
412C2×C22⋊C4—221no—
413C2×C42—221no—
414C2×C42—222no—
415C2×C42—221no—
416C2×C42—221no—
417C2×C42—228no—
418C2×C42D4411yescharacteristic
419C2×C42D4414yes—
420C2×C42D4411yescharacteristic
421C2×C42C22×D1111yescharacteristic
422C2×C42C22×D1111yescharacteristic
423C2×C42C22×D1114yes—
424#107—118no—
425#106—118no—
426C4⋊C8C22×D1114yes—
427C4⋊C8C22×D1114yes—
428#103—118no—
429#103—118no—
430#103—118no—
431#102—118no—
432C22⋊C8C22×D1118yes—
433#97C22×D1118yes—
434C2×C11—42no—
435C2×C11#311614yescomplemented
436C2×C11C2×#52511yescharacteristic
437C2×C11C22×#13711yescharacteristic
438C2×C11C2×#57511yescharacteristic
439D11—44no—
440C24—221no—
441C24C2×D4411yescharacteristic
442#41—228no—
443#41—228no—
444#41—2216no—
445C2×Q8—114no—
446C2×Q8—112no—
447C2×Q8—114no—
448C2×Q8—221no—
449C2×Q8—224no—
450C2×Q8—222no—
451C2×Q8—222no—
452C2×Q8—224no—
453C2×Q8—224no—
454C2×Q8—444no—
455C2×D4—114no—
456C2×D4—112no—
457C2×D4—228no—
458C2×D4—224no—
459C2×D4—221no—
460C2×D4—222no—
461C22×C4—24no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—42no—
465C22×C4—228no—
466C22×C4—221no—
467C22×C4—224no—
468C22×C4—221no—
469C22×C4—221no—
470C22×C4—222no—
471C22×C4—222no—
472C22×C4—224no—
473C22×C4—224no—
474C22×C4—444no—
475C22×C4—444no—
476C22×C4C2×D4414yes—
477C22×C4C2×D4412yes—
478C22×C4C2×D4411yescharacteristic
479C22×C4C2×D4411yescharacteristic
480C22×C4C2×D4411yescharacteristic
481C22×C4C2×D4411yescharacteristic
482C22×C4C2×D4414yes—
483C22×C4C2×D4411yescharacteristic
484C22×C4C23×D1112yes—
485C22×C4C23×D1111yescharacteristic
486Q16—2216no—
487SD16—2216no—
488C2×C8—24no—
489C2×C8—24no—
490C2×C8C23×D1114yes—
491C2×C8C23×D1114yes—
492C4⋊C4—114no—
493C4⋊C4—112no—
494C4⋊C4—112no—
495C4⋊C4—221no—
496C4⋊C4—221no—
497C4⋊C4—222no—
498C4⋊C4—224no—
499C4⋊C4—224no—
500C4⋊C4—224no—
501C4⋊C4—224no—
502C4⋊C4—228no—
503C4⋊C4—228no—
504C4⋊C4—224no—
505C22⋊C4—224no—
506C22⋊C4—228no—
507C22⋊C4—224no—
508C22⋊C4—224no—
509C42—224no—
510C42—224no—
511C42—224no—
512C42—228no—
513C42C2×D4414yes—
514C42C2×D4414yes—
515C42C2×D4412yes—
516C42C2×D4412yes—
517C42C23×D1112yes—
518C42C23×D1112yes—
519C11C2×#311611yescharacteristic, complemented, Sylow
520C23—22no—
521C23—22no—
522C23—22no—
523C23—224no—
524C23—222no—
525C23—442no—
526C23—442no—
527C23C22×D4412yes—
528C23C22×D4411yescharacteristic
529Q8—114no—
530Q8—224no—
531Q8—222no—
532Q8—224no—
533Q8—224no—
534Q8—448no—
535Q8—444no—
536D4—114no—
537D4—2216no—
538D4—224no—
539D4—222no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—28no—
545C2×C4—24no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—44no—
549C2×C4—2216no—
550C2×C4—224no—
551C2×C4—222no—
552C2×C4—222no—
553C2×C4—222no—
554C2×C4—224no—
555C2×C4—224no—
556C2×C4—448no—
557C2×C4—442no—
558C2×C4—442no—
559C2×C4—444no—
560C2×C4—444no—
561C2×C4—448no—
562C2×C4#6696214yes—
563C2×C4C22×D4412yes—
564C2×C4C22×D4412yes—
565C2×C4C22×D4412yes—
566C2×C4C22×D4412yes—
567C2×C4C22×D4412yes—
568C2×C4C22×D4411yescharacteristic
569C2×C4#41×D1112yes—
570C2×C4#41×D1112yes—
571C2×C4C24×D1111yescharacteristic
572C8—24no—
573C8—24no—
574C22—22no—
575C22—22no—
576C22—22no—
577C22—44no—
578C22—224no—
579C22—442no—
580C22—442no—
581C22—448no—
582C22#1062305512yes—
583C22C2×#6696212yes—
584C22#1062327912yes—
585C22C23×D4411yescharacteristic
586C4—22no—
587C4—22no—
588C4—22no—
589C4—22no—
590C4—224no—
591C4—444no—
592C4—442no—
593C4—442no—
594C4—444no—
595C4#1062305512yes—
596C4C2×#6696214yes—
597C4C2×#41×D1111yescharacteristic
598C4C2×#41×D1111yescharacteristic
599C2—42no—
600C2—444no—
601C2#1307877914yesdirect product factor
602C2C2×#1062305511yescharacteristic
603C2C22×#6696211yescharacteristic
604C2C2×#1062327911yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#432C2
socleC23×C11C22×D4
prime radicalC22×#4339C22
hypercenterC2×#432D11
hypocenterC11C2×#3116
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#432

Complements

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

NH ≅ G/Ntype
1. C2×#10623001C2semidirect
3. #13078779C2direct (N × H)
4. C2×#10622336C2semidirect
5. C2×#10622463C2semidirect
6. C2×#10622455C2semidirect
7. C2×#10622462C2semidirect
8. C2×#10622454C2semidirect
10. C2×#10622329C2semidirect
11. C2×#10622323C2semidirect
12. C2×C11×#432C2semidirect
30. #10623001C22semidirect
38. C11×#432C22semidirect
49. #10622463C22semidirect
50. #10622462C22semidirect
51. #10622455C22semidirect
52. #10622454C22semidirect
54. #10622336C22semidirect
55. #10622329C22semidirect
56. #10622323C22semidirect
229. C2×#432D11semidirect
317. #432C2×D11semidirect
435. C2×C11#3116semidirect
519. C11C2×#3116semidirect
601. C2#13078779direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230012
C2×C4×#43392
#130787792
C2×#106223362
C2×#106224632
C2×#106224552
C2×#106224622
C2×#106224542
C2×#106223462
C2×#106223292
C2×#106223232
C2×C11×#4322
C2×#311611