Finite Group Databasebeta

← C2×#13079983 #15626623

Subgroups — C2×#13079983 #15626623

Order 2816.

1898 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623010C211yesmaximal, characteristic
2#13079983C2116yesmaximal, direct product factor
3C2×#10622635C212yesmaximal, complemented
4C2×#10622704C211yesmaximal, characteristic, complemented
5C2×#10622697C211yesmaximal, characteristic, complemented
6C2×#10622665C212yesmaximal, complemented
7C2×#10622662C212yesmaximal
8C2×#10622641C212yesmaximal, complemented
9C2×#10622703C211yesmaximal, characteristic, complemented
10C2×#10622696C211yesmaximal, characteristic, complemented
11C2×#10622537C211yesmaximal, characteristic, complemented
12C2×C11×#533C211yesmaximal, characteristic, complemented
13C11×#533—24no—
14C11×#533C2218yescomplemented
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×C11×#125—21no—
18C2×C11×C22⋊Q8—21no—
19C2×C11×C22⋊Q8C2212yes—
20C2×C4×Q8×C11—21no—
21C2×C4×Q8×C11C2212yes—
22C2×C11×#117—21no—
23C22×C42×C11C2211yescharacteristic
24C22×#4326C2212yes—
25C22×#4325C2212yes—
26C2×#66983C2211yescharacteristic
27C2×#66982—21no—
28C2×C4×C22⋊D11—21no—
29C2×#66977C2211yescharacteristic
30C22×#4318C2212yes—
31#10623010—24no—
32#10623010C2218yes—
33C2×#66929—21no—
34C2×#66928C2211yescharacteristic
35C2×C4×D44C2211yescharacteristic
36C2×#66925—21no—
37C2×#66923C2211yescharacteristic
38C2×C4×Dic22C2211yescharacteristic
39C2×#66899C2212yes—
40C2×#66899C2212yes—
41#10622704C2218yescomplemented
42#10622703C2218yescomplemented
43#10622697C2218yescomplemented
44#10622696C2218yescomplemented
45#10622665C22116yescomplemented
46#10622662C22116yes—
47#10622641C22116yescomplemented
48#10622635C22116yescomplemented
49C2×#66874C2212yes—
50C2×#66873C2212yes—
51C2×#66872C2212yes—
52C2×#66871C2212yes—
53#10622537C2218yescomplemented
54C2×C4⋊(C11⋊C8)C2211yescharacteristic
55C2×C4⋊(C11⋊C8)C2211yescharacteristic
56C2×C4⋊(C11⋊C8)C2212yes—
57C22×Q8×C11—21no—
58C22×Q8×C11C2312yes—
59C23×C4×C11D411yescharacteristic
60C23×C4×C11D411yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C22×C22⋊D11—21no—
63C22×D44C2311yescharacteristic
64C22×C4×D11—21no—
65C22×Dic22C2311yescharacteristic
66C11×C4⋊Q8—22no—
67C11×C4⋊Q8—22no—
68C11×C4⋊Q8C2314yes—
69C11×C4⋊Q8C2314yes—
70C11×#125—28no—
71C11×C22⋊Q8—28no—
72C11×C22⋊Q8—24no—
73C11×C22⋊Q8C2318yes—
74C4×Q8×C11—28no—
75C4×Q8×C11—24no—
76C4×Q8×C11C2318yes—
77C11×#117—28no—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4—22no—
82C2×C11×C4⋊C4—22no—
83C2×C11×C4⋊C4C2312yes—
84C2×C11×C22⋊C4—22no—
85C2×C42×C11—22no—
86C2×C42×C11D411yescharacteristic
87C2×C42×C11D411yescharacteristic
88C2×C42×C11D414yes—
89C2×C42×C11C2311yescharacteristic
90C2×C42×C11C2311yescharacteristic
91C2×C42×C11C2314yes—
92C2×C22⋊Dic11—21no—
93C2×#4326—44no—
94C2×#4326C2318yes—
95C2×#4325—44no—
96C2×#4325C2318yes—
97#66983—22no—
98#66983C2314yes—
99#66982—28no—
100C4×C22⋊D11—28no—
101C2×(C2×D11)⋊C4—21no—
102C2×(C2×D11)⋊C4—21no—
103C2×(C2×D11)⋊C4—21no—
104C2×(C2×D11)⋊C4—21no—
105C2×C4⋊Dic11C2311yescharacteristic
106C2×C4⋊Dic11C2311yescharacteristic
107#66977—22no—
108#66977C2314yes—
109C2×Dic11⋊C4—21no—
110C2×Dic11⋊C4—21no—
111C2×Dic11⋊C4—21no—
112C2×Dic11⋊C4—21no—
113C2×C4×Dic11—21no—
114C2×#4318—44no—
115C2×#4318C2318yes—
116C22×C11⋊C8C2312yes—
117C22×C11⋊C8C2312yes—
118#66929—28no—
119#66928—22no—
120#66928C2314yes—
121C4×D44—22no—
122C4×D44C2314yes—
123#66925—28no—
124#66923—22no—
125#66923C2314yes—
126C4×Dic22—22no—
127C4×Dic22C2314yes—
128#66899C2318yes—
129#66899C2318yes—
130#66874C2318yes—
131#66873C2318yes—
132#66872C2318yes—
133#66871C2318yes—
134C4⋊(C11⋊C8)C2318yes—
135C4⋊(C11⋊C8)C2314yes—
136C4⋊(C11⋊C8)C2314yes—
137C2×#3252—111nomaximal, Sylow
138C24×C11C2×D411yescharacteristic
139C23×D11—21no—
140C2×Q8×C11—22no—
141C2×Q8×C11—24no—
142C2×Q8×C11—24no—
143C2×Q8×C11—24no—
144C2×Q8×C11—44no—
145C2×Q8×C11C2414yes—
146C22×C4×C11—24no—
147C22×C4×C11—22no—
148C22×C4×C11—22no—
149C22×C4×C11—22no—
150C22×C4×C11—22no—
151C22×C4×C11—42no—
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D412yes—
157C22×C4×C11C2×D414yes—
158C22×C4×C11C2×D414yes—
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11C2412yes—
161C22×C4×C11C2411yescharacteristic
162C2×C22⋊D11—24no—
163C2×C22⋊D11—44no—
164C22×Dic11—21no—
165C22×Dic11—21no—
166C22×Dic11—21no—
167C2×D44—21no—
168C2×D44—22no—
169C2×D44—22no—
170C2×D44C2412yes—
171C2×C4×D11—24no—
172C2×C4×D11—44no—
173C2×Dic22—21no—
174C2×Dic22—22no—
175C2×Dic22—22no—
176C2×Dic22C2412yes—
177C11×C4⋊C4—24no—
178C11×C4⋊C4—24no—
179C11×C4⋊C4—24no—
180C11×C4⋊C4—28no—
181C11×C4⋊C4—28no—
182C11×C4⋊C4—22no—
183C11×C4⋊C4C2414yes—
184C11×C22⋊C4—28no—
185C42×C11—28no—
186C42×C11C2×D412yes—
187C42×C11C2×D412yes—
188C42×C11C2×D414yes—
189C42×C11C2×D414yes—
190C42×C11C2412yes—
191C42×C11C2412yes—
192C22⋊Dic11—24no—
193#4326—48no—
194#4325—48no—
195(C2×D11)⋊C4—24no—
196(C2×D11)⋊C4—24no—
197(C2×D11)⋊C4—24no—
198(C2×D11)⋊C4—24no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11C2412yes—
202C4⋊Dic11C2412yes—
203Dic11⋊C4—24no—
204Dic11⋊C4—24no—
205Dic11⋊C4—24no—
206Dic11⋊C4—24no—
207C4×Dic11—24no—
208#4318—48no—
209C2×C11⋊C8—24no—
210C2×C11⋊C8—24no—
211C2×C11⋊C8C2414yes—
212C2×C11⋊C8C2414yes—
213C2×#533D1111yescharacteristic, complemented
214C2×#529—111no—
215#3252—1116no—
216C2×#479—112no—
217C2×#477—111no—
218C2×#476—111no—
219C2×#470—112no—
220C2×#468—112no—
221C2×#464—112no—
222C2×#462—111no—
223C2×#461—111no—
224C2×#423—111no—
225C23×C11—22no—
226C23×C11—22no—
227C23×C11—22no—
228C23×C11C22×D412yes—
229C23×C11C22×D411yescharacteristic
230C22×D11—22no—
231C22×D11—42no—
232C22×D11—42no—
233C22×D11—42no—
234Q8×C11—24no—
235Q8×C11—24no—
236Q8×C11—48no—
237Q8×C11—44no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11—22no—
242C2×C4×C11—24no—
243C2×C4×C11—28no—
244C2×C4×C11—22no—
245C2×C4×C11—22no—
246C2×C4×C11—24no—
247C2×C4×C11—24no—
248C2×C4×C11—44no—
249C2×C4×C11—44no—
250C2×C4×C11—44no—
251C2×C4×C11#13714yes—
252C2×C4×C11C22×D412yes—
253C2×C4×C11C22×D412yes—
254C2×C4×C11C22×D412yes—
255C2×C4×C11C22×D412yes—
256C2×C4×C11C22×D411yescharacteristic
257C2×C4×C11C22×D412yes—
258C2×C4×C11H(5,𝔽2)12yes—
259C2×C4×C112−1+412yes—
260C2×C4×C11C2511yescharacteristic
261C22⋊D11—48no—
262C2×Dic11—22no—
263C2×Dic11—22no—
264C2×Dic11—22no—
265C2×Dic11—42no—
266C2×Dic11—42no—
267C2×Dic11—42no—
268D44—22no—
269D44—22no—
270D44—42no—
271C4×D11—48no—
272Dic22—22no—
273Dic22—22no—
274Dic22—42no—
275C11⋊C8—24no—
276C11⋊C8—24no—
277C22×Q16—112no—
278C22×SD16—112no—
279C22×M16—112no—
280#533—24no—
281#533C2×D1118yescomplemented
282C2×C4⋊Q8C2×D1111yescharacteristic
283C2×C4⋊Q8C2×D1111yescharacteristic
284#529—118no—
285#529—224no—
286C2×#126—221no—
287C2×#125—21no—
288C2×#125—111no—
289C2×#124—111no—
290C2×#123—221no—
291C2×C22⋊Q8—21no—
292C2×C22⋊Q8—111no—
293C2×C22⋊Q8C2×D1112yes—
294C2×#121—111no—
295C2×C4×Q8—21no—
296C2×C4×Q8—111no—
297C2×C4×Q8C2×D1112yes—
298C2×C4×D4—111no—
299C2×C4×D4—221no—
300C2×#117—21no—
301C2×#117—221no—
302C22×C42C2×D1111yescharacteristic
303#479—1116no—
304#477—118no—
305#476—118no—
306#470—1116no—
307#468—1116no—
308#464—1116no—
309#462—118no—
310#461—118no—
311C2×#107—112no—
312C2×#106—112no—
313#423—118no—
314C2×C4⋊C8—111no—
315C2×C4⋊C8—112no—
316C2×C4⋊C8—111no—
317C2×#103—112no—
318C2×#103—112no—
319C2×#103—112no—
320C2×#102—112no—
321C22×C11—22no—
322C22×C11—22no—
323C22×C11—22no—
324C22×C11—44no—
325C22×C11#53712yes—
326C22×C11C2×#13712yes—
327C22×C11#57512yes—
328C22×C11C23×D411yescharacteristic
329C2×D11—42no—
330C2×D11—42no—
331C2×D11—42no—
332C2×D11—84no—
333C4×C11—22no—
334C4×C11—22no—
335C4×C11—22no—
336C4×C11—22no—
337C4×C11—44no—
338C4×C11—44no—
339C4×C11#53712yes—
340C4×C11C2×#13714yes—
341C4×C11C2×H(5,𝔽2)11yescharacteristic
342C4×C11C2×2−1+411yescharacteristic
343Dic11—42no—
344Dic11—42no—
345Dic11—42no—
346C22×Q8—21no—
347C22×Q8—111no—
348C22×Q8C22×D1112yes—
349C22×D4—111no—
350C22×D4—221no—
351C23×C4—221no—
352C23×C4C22⋊D1111yescharacteristic
353C23×C4C22⋊D1111yescharacteristic
354C23×C4C22×D1111yescharacteristic
355C2×Q16—118no—
356C2×Q16—444no—
357C2×SD16—118no—
358C2×SD16—444no—
359C2×M16—118no—
360C2×M16—444no—
361C22×C8—112no—
362C22×C8—112no—
363C4⋊Q8—22no—
364C4⋊Q8—22no—
365C4⋊Q8C22×D1114yes—
366C4⋊Q8C22×D1114yes—
367#126—228no—
368#125—28no—
369#125—114no—
370#125—222no—
371#124—114no—
372#124—222no—
373#123—228no—
374C22⋊Q8—28no—
375C22⋊Q8—24no—
376C22⋊Q8—114no—
377C22⋊Q8—222no—
378C22⋊Q8C22×D1118yes—
379#121—114no—
380#121—222no—
381C4×Q8—28no—
382C4×Q8—24no—
383C4×Q8—114no—
384C4×Q8—222no—
385C4×Q8C22×D1118yes—
386C4×D4—114no—
387C4×D4—228no—
388C4×D4—222no—
389#117—28no—
390#117—228no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—111no—
397C2×C4⋊C4—111no—
398C2×C4⋊C4—221no—
399C2×C4⋊C4—221no—
400C2×C4⋊C4—221no—
401C2×C4⋊C4—221no—
402C2×C4⋊C4C22×D1112yes—
403C2×C22⋊C4—22no—
404C2×C22⋊C4—221no—
405C2×C22⋊C4—221no—
406C2×C22⋊C4—221no—
407C2×C22⋊C4—221no—
408C2×C22⋊C4—221no—
409C2×C42—22no—
410C2×C42—221no—
411C2×C42C22⋊D1111yescharacteristic
412C2×C42C22⋊D1111yescharacteristic
413C2×C42C22⋊D1114yes—
414C2×C42C22×D1111yescharacteristic
415C2×C42C22×D1111yescharacteristic
416C2×C42C22×D1114yes—
417#107—118no—
418#106—118no—
419C4⋊C8—114no—
420C4⋊C8—114no—
421C4⋊C8—118no—
422#103—118no—
423#103—118no—
424#103—118no—
425#102—118no—
426C2×C11—42no—
427C2×C11#325214yescomplemented
428C2×C11C2×#53711yescharacteristic
429C2×C11C22×#13711yescharacteristic
430C2×C11C2×#57511yescharacteristic
431D11—82no—
432C24—221no—
433C24C2×C22⋊D1111yescharacteristic
434C2×Q8—22no—
435C2×Q8—24no—
436C2×Q8—24no—
437C2×Q8—24no—
438C2×Q8—44no—
439C2×Q8—112no—
440C2×Q8—221no—
441C2×Q8—222no—
442C2×Q8—222no—
443C2×Q8C23×D1114yes—
444C2×D4—112no—
445C2×D4—224no—
446C2×D4—222no—
447C2×D4—222no—
448C2×D4—221no—
449C2×D4—444no—
450C22×C4—24no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—42no—
456C22×C4—221no—
457C22×C4—221no—
458C22×C4—221no—
459C22×C4—224no—
460C22×C4—444no—
461C22×C4C2×C22⋊D1114yes—
462C22×C4C2×C22⋊D1112yes—
463C22×C4C2×C22⋊D1111yescharacteristic
464C22×C4C2×C22⋊D1111yescharacteristic
465C22×C4C2×C22⋊D1111yescharacteristic
466C22×C4C2×C22⋊D1111yescharacteristic
467C22×C4C2×C22⋊D1114yes—
468C22×C4C2×C22⋊D1111yescharacteristic
469C22×C4C23×D1112yes—
470C22×C4C23×D1111yescharacteristic
471Q16—448no—
472SD16—448no—
473M16—448no—
474C2×C8—114no—
475C2×C8—114no—
476C2×C8—224no—
477C2×C8—224no—
478C4⋊C4—24no—
479C4⋊C4—24no—
480C4⋊C4—24no—
481C4⋊C4—28no—
482C4⋊C4—28no—
483C4⋊C4—22no—
484C4⋊C4—112no—
485C4⋊C4—112no—
486C4⋊C4—221no—
487C4⋊C4—221no—
488C4⋊C4—224no—
489C4⋊C4—224no—
490C4⋊C4—224no—
491C4⋊C4—224no—
492C4⋊C4C23×D1114yes—
493C22⋊C4—28no—
494C22⋊C4—224no—
495C22⋊C4—224no—
496C22⋊C4—224no—
497C22⋊C4—224no—
498C22⋊C4—224no—
499C42—28no—
500C42—224no—
501C42C2×C22⋊D1114yes—
502C42C2×C22⋊D1112yes—
503C42C2×C22⋊D1112yes—
504C42C2×C22⋊D1114yes—
505C42C23×D1112yes—
506C42C23×D1112yes—
507C11C2×#325211yescharacteristic, complemented, Sylow
508C23—22no—
509C23—22no—
510C23—22no—
511C23—222no—
512C23—442no—
513C23—442no—
514C23—442no—
515C23C22×C22⋊D1112yes—
516C23C22×C22⋊D1111yescharacteristic
517Q8—24no—
518Q8—24no—
519Q8—48no—
520Q8—44no—
521Q8—222no—
522Q8—222no—
523Q8—442no—
524D4—222no—
525D4—222no—
526D4—448no—
527D4—442no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—28no—
533C2×C4—24no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—24no—
537C2×C4—24no—
538C2×C4—44no—
539C2×C4—44no—
540C2×C4—44no—
541C2×C4—222no—
542C2×C4—222no—
543C2×C4—222no—
544C2×C4—442no—
545C2×C4—442no—
546C2×C4—442no—
547C2×C4—448no—
548C2×C4#6699514yes—
549C2×C4#6704212yes—
550C2×C4#6704312yes—
551C2×C4C22×C22⋊D1112yes—
552C2×C4C22×C22⋊D1112yes—
553C2×C4C22×C22⋊D1112yes—
554C2×C4C22×C22⋊D1112yes—
555C2×C4C22×C22⋊D1112yes—
556C2×C4C22×C22⋊D1111yescharacteristic
557C2×C4C24×D1111yescharacteristic
558C8—224no—
559C8—224no—
560C22—22no—
561C22—22no—
562C22—22no—
563C22—44no—
564C22—442no—
565C22—442no—
566C22—442no—
567C22—884no—
568C22C2×#6699512yes—
569C22#1062335312yes—
570C22#1062336412yes—
571C22C23×C22⋊D1111yescharacteristic
572C4—22no—
573C4—22no—
574C4—22no—
575C4—22no—
576C4—44no—
577C4—44no—
578C4—442no—
579C4—442no—
580C4—442no—
581C4C2×#6699514yes—
582C4#1062336412yes—
583C4C2×#6704211yescharacteristic
584C4C2×#6704311yescharacteristic
585C2—42no—
586C2—882no—
587C2#1307998314yesdirect product factor
588C2C2×#1062336411yescharacteristic
589C2C22×#6699511yescharacteristic
590C2C2×#1062335311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#533C2
socleC23×C11C22×D4
prime radicalC2×#66983C22
hypercenterC2×#533D11
hypocenterC11C2×#3252
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
2. #13079983C2direct (N × H)
3. C2×#10622635C2semidirect
4. C2×#10622704C2semidirect
5. C2×#10622697C2semidirect
6. C2×#10622665C2semidirect
8. C2×#10622641C2semidirect
9. C2×#10622703C2semidirect
10. C2×#10622696C2semidirect
11. C2×#10622537C2semidirect
12. C2×C11×#533C2semidirect
14. C11×#533C22semidirect
41. #10622704C22semidirect
42. #10622703C22semidirect
43. #10622697C22semidirect
44. #10622696C22semidirect
45. #10622665C22semidirect
47. #10622641C22semidirect
48. #10622635C22semidirect
53. #10622537C22semidirect
213. C2×#533D11semidirect
281. #533C2×D11semidirect
427. C2×C11#3252semidirect
507. C11C2×#3252semidirect
587. C2#13079983direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230102
#130799832
C2×#106226352
C2×#106227042
C2×#106226972
C2×#106226652
C2×#106226622
C2×#106226412
C2×#106227032
C2×#106226962
C2×#106225372
C2×C11×#5332
C2×#325211