Finite Group Databasebeta

← C2×#13079563 #15624963

Subgroups — C2×#13079563 #15624963

Order 2816.

2134 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623109C211yesmaximal, characteristic
2C2×D11×C4⋊Q8C211yesmaximal, characteristic
3#13079563C2116yesmaximal, direct product factor
4C2×#10622794C212yesmaximal, complemented
5C2×#10622405C212yesmaximal, complemented
6C2×#10622462C211yesmaximal, characteristic, complemented
7C2×#10622644C211yesmaximal, characteristic, complemented
8C2×#10622703C211yesmaximal, characteristic, complemented
9C2×#10622421C212yesmaximal
10C2×#10622799C212yesmaximal
11C2×#10622446C211yesmaximal, characteristic
12C2×C11×#462C211yesmaximal, characteristic, complemented
13C22×Q8×D11C2212yes—
14C22×C11×Q16C2212yes—
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×C4×Q8×C11C2211yescharacteristic
17C2×#66999C2211yescharacteristic
18C2×#66997C2212yes—
19C2×#66997C2211yescharacteristic
20C22×#4326C2212yes—
21C22×#4326C2212yes—
22C22×Dic44C2212yes—
23D11×C4⋊Q8—24no—
24D11×C4⋊Q8C2218yes—
25#10623109—24no—
26#10623109C2218yes—
27C2×#66950C2211yescharacteristic
28C2×#66949—21no—
29C2×C4⋊C4×D11—21no—
30C2×C4⋊C4×D11—21no—
31C2×#66942—21no—
32C2×#66941—21no—
33C2×#66941—21no—
34C2×#66941C2211yescharacteristic
35C2×#66925—21no—
36C2×C42×D11C2211yescharacteristic
37C2×#66922C2211yescharacteristic
38C2×C4×Dic22—21no—
39C2×C4×Dic22C2211yescharacteristic
40C11×#462C2218yescomplemented
41C2×C11×C4⋊C8C2211yescharacteristic
42C2×C11×#103C2212yes—
43C2×#66899C2212yes—
44#10622799C22116yes—
45#10622794C22116yescomplemented
46C2×(C2×D11)⋊C8C2212yes—
47C2×#66880C2212yes—
48C2×C8×Dic11C2212yes—
49#10622703C2218yescomplemented
50#10622644C2218yescomplemented
51C2×#66874C2212yes—
52C2×C4⋊(C11⋊C8)C2211yescharacteristic
53#10622462C2218yescomplemented
54#10622446C2218yes—
55#10622421C22116yes—
56#10622405C22116yescomplemented
57C22×Q8×C11C2311yescharacteristic
58C22×Q8×C11C2312yes—
59C2×Q8×D11—24no—
60C2×Q8×D11—44no—
61C2×Q8×D11—44no—
62C2×Q8×D11C2318yes—
63C22×C4×D11—22no—
64C22×C4×D11D411yescharacteristic
65C22×C4×D11D411yescharacteristic
66C22×C4×D11C2311yescharacteristic
67C22×Dic22—21no—
68C22×Dic22—22no—
69C22×Dic22C2311yescharacteristic
70C22×Dic22C2312yes—
71C2×C11×Q16—44no—
72C2×C11×Q16C2318yes—
73C22×C8×C11C2312yes—
74C11×C4⋊Q8—22no—
75C11×C4⋊Q8C2314yes—
76C4×Q8×C11—22no—
77C4×Q8×C11C2314yes—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C42×C11—21no—
83C2×C42×C11C2311yescharacteristic
84#66999—22no—
85#66999C2314yes—
86#66997—24no—
87#66997—22no—
88#66997C2318yes—
89#66997C2314yes—
90C2×#4326—44no—
91C2×#4326—44no—
92C2×#4326C2318yes—
93C2×#4326C2318yes—
94C2×(C2×D11)⋊C4—21no—
95C2×(C2×D11)⋊C4—21no—
96C2×C4⋊Dic11—21no—
97C2×C4⋊Dic11—21no—
98C2×C4⋊Dic11—21no—
99C2×C4⋊Dic11C2311yescharacteristic
100C2×Dic11⋊C4—21no—
101C2×Dic11⋊C4—21no—
102C2×Dic11⋊C4—21no—
103C2×Dic11⋊C4—21no—
104C2×Dic11⋊C4—21no—
105C2×Dic11⋊C4—22no—
106C2×Dic11⋊C4—22no—
107C2×C4×Dic11—21no—
108C2×C4×Dic11D411yescharacteristic
109C2×C4×Dic11D411yescharacteristic
110C2×C4×Dic11C2311yescharacteristic
111C22×C11⋊C8C2312yes—
112C2×Dic44—44no—
113C2×Dic44C2318yes—
114#66950—22no—
115#66950C2314yes—
116#66949—28no—
117C4⋊C4×D11—28no—
118C4⋊C4×D11—28no—
119#66942—28no—
120#66941—28no—
121#66941—28no—
122#66941—22no—
123#66941C2314yes—
124#66925—28no—
125C42×D11D414yes—
126C42×D11C2314yes—
127#66922—22no—
128#66922C2314yes—
129C4×Dic22—22no—
130C4×Dic22—28no—
131C4×Dic22C2314yes—
132C11×C4⋊C8C2314yes—
133C11×#103C2318yes—
134#66899C2318yes—
135(C2×D11)⋊C8C2318yes—
136#66880C2318yes—
137C8×Dic11C2318yes—
138#66874C2318yes—
139C4⋊(C11⋊C8)C2314yes—
140C2×#3209—111nomaximal, Sylow
141C23×D11C2×D411yescharacteristic
142C2×Q8×C11—21no—
143C2×Q8×C11—22no—
144C2×Q8×C11—22no—
145C2×Q8×C11—24no—
146C2×Q8×C11—22no—
147C2×Q8×C11—24no—
148C2×Q8×C11C2414yes—
149C2×Q8×C11C2412yes—
150C22×C4×C11—21no—
151C22×C4×C11—22no—
152C22×C4×C11—21no—
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2411yescharacteristic
156C22×Dic11—21no—
157C22×Dic11—21no—
158C22×Dic11—22no—
159C22×Dic11C2×D411yescharacteristic
160C22×Dic11C2×D411yescharacteristic
161C22×Dic11C2×D411yescharacteristic
162Q8×D11—48no—
163Q8×D11—48no—
164Q8×D11—416no—
165C2×C4×D11—24no—
166C2×C4×D11—28no—
167C2×C4×D11—22no—
168C2×C4×D11—22no—
169C2×C4×D11—48no—
170C2×C4×D11Q1618yescomplemented
171C2×C4×D11C2×D412yes—
172C2×C4×D11C2×D414yes—
173C2×C4×D11C2×D414yes—
174C2×C4×D11C2412yes—
175C2×Dic22—24no—
176C2×Dic22—28no—
177C2×Dic22—21no—
178C2×Dic22—22no—
179C2×Dic22—22no—
180C2×Dic22—24no—
181C2×Dic22—22no—
182C2×Dic22—24no—
183C2×Dic22—48no—
184C2×Dic22—44no—
185C2×Dic22C2414yes—
186C2×Dic22C2412yes—
187C11×Q16—48no—
188C2×C8×C11—24no—
189C2×C8×C11C2414yes—
190C11×C4⋊C4—24no—
191C11×C4⋊C4—24no—
192C11×C4⋊C4—21no—
193C11×C4⋊C4—24no—
194C11×C4⋊C4C2412yes—
195C42×C11—24no—
196C42×C11C2×D412yes—
197C42×C11C2412yes—
198#4326—48no—
199#4326—48no—
200(C2×D11)⋊C4—24no—
201(C2×D11)⋊C4—24no—
202C4⋊Dic11—24no—
203C4⋊Dic11—21no—
204C4⋊Dic11—24no—
205C4⋊Dic11—24no—
206C4⋊Dic11C2412yes—
207Dic11⋊C4—24no—
208Dic11⋊C4—24no—
209Dic11⋊C4—24no—
210Dic11⋊C4—24no—
211Dic11⋊C4—28no—
212Dic11⋊C4—28no—
213Dic11⋊C4—24no—
214C4×Dic11—24no—
215C4×Dic11C2×D414yes—
216C4×Dic11C2×D412yes—
217C4×Dic11C2×D414yes—
218C4×Dic11C2412yes—
219C2×C11⋊C8—24no—
220C2×C11⋊C8C2414yes—
221Dic44—48no—
222C2×#533—111no—
223C22×C4⋊Q8—111no—
224#3209—1116no—
225C2×#494—112no—
226C2×#487—112no—
227C2×#462—111no—
228C2×#462—111no—
229C2×#462—111no—
230C2×#462D1111yescharacteristic, complemented
231C2×#451—112no—
232C2×#451—112no—
233C2×#431—111no—
234C23×C11C22×D411yescharacteristic
235C22×D11—22no—
236C22×D11—22no—
237C22×D11C2×Q1614yes—
238C22×D11C22×D412yes—
239Q8×C11—22no—
240Q8×C11—24no—
241Q8×C11—22no—
242Q8×C11—24no—
243Q8×C11—44no—
244Q8×C11—42no—
245C2×C4×C11—22no—
246C2×C4×C11—22no—
247C2×C4×C11—24no—
248C2×C4×C11—22no—
249C2×C4×C11—44no—
250C2×C4×C11—42no—
251C2×C4×C11—42no—
252C2×C4×C11C2×Q1614yes—
253C2×C4×C11C22×D412yes—
254C2×C4×C11C22×D411yescharacteristic
255C2×C4×C11C22×D412yes—
256C2×C4×C11H(5,𝔽2)12yes—
257C2×C4×C11H(5,𝔽2)12yes—
258C2×C4×C11C2511yescharacteristic
259C2×Dic11—22no—
260C2×Dic11—22no—
261C2×Dic11—22no—
262C2×Dic11—24no—
263C2×Dic11—44no—
264C2×Dic11—42no—
265C2×Dic11—42no—
266C2×Dic11C2×Q1614yes—
267C2×Dic11#13714yes—
268C2×Dic11C22×D412yes—
269C2×Dic11C22×D412yes—
270C2×Dic11C22×D412yes—
271C4×D11—24no—
272C4×D11—22no—
273C4×D11—22no—
274C4×D11—28no—
275C4×D11—416no—
276C4×D11C2×Q16116yescomplemented
277Dic22—22no—
278Dic22—24no—
279Dic22—22no—
280Dic22—24no—
281Dic22—416no—
282Dic22—42no—
283Dic22—44no—
284Dic22—48no—
285C8×C11—24no—
286C11⋊C8—24no—
287C23×Q8—112no—
288C22×Q16—112no—
289C22×Q16—112no—
290C22×Q16—112no—
291C22×Q16C2×D1112yes—
292#533—118no—
293#533—224no—
294C2×C4⋊Q8—111no—
295C2×C4⋊Q8—112no—
296C2×C4⋊Q8—111no—
297C2×C4⋊Q8—118no—
298C2×C4⋊Q8—111no—
299C2×C4⋊Q8—221no—
300C2×C4⋊Q8—221no—
301C2×C4⋊Q8—224no—
302C2×C4⋊Q8C2×D1111yescharacteristic
303C2×#125—221no—
304C2×C22⋊Q8—111no—
305C2×C22⋊Q8—111no—
306C2×C22⋊Q8—221no—
307C2×C4×Q8—111no—
308C2×C4×Q8—221no—
309C2×C4×Q8C2×D1111yescharacteristic
310C2×#117—221no—
311C22×C4⋊C4—221no—
312C22×C4⋊C4—221no—
313C22×C42—111no—
314#494—1116no—
315#487—1116no—
316#462—118no—
317#462—118no—
318#462—118no—
319#462C2×D1118yescomplemented
320#451—1116no—
321#451—1116no—
322#431—118no—
323C2×C4⋊C8—111no—
324C2×C4⋊C8C2×D1111yescharacteristic
325C2×#103—112no—
326C2×#103—112no—
327C2×#103—112no—
328C2×#103C2×D1112yes—
329C2×C22⋊C8—112no—
330C2×C4×C8—112no—
331C22×C11#53512yes—
332C22×C11C22×Q1612yes—
333C22×C11C2×#13712yes—
334C22×C11C23×D411yescharacteristic
335C2×D11—22no—
336C2×D11—28no—
337C2×D11—22no—
338C2×D11C22×Q1614yes—
339C4×C11—22no—
340C4×C11—42no—
341C4×C11—44no—
342C4×C11—42no—
343C4×C11#53512yes—
344C4×C11C22×Q1614yes—
345C4×C11C2×H(5,𝔽2)11yescharacteristic
346C4×C11C2×H(5,𝔽2)11yescharacteristic
347Dic11—22no—
348Dic11—44no—
349Dic11—42no—
350Dic11—42no—
351Dic11C22×Q1614yes—
352Dic11C2×#13714yes—
353C22×Q8—118no—
354C22×Q8—111no—
355C22×Q8—112no—
356C22×Q8—221no—
357C22×Q8—222no—
358C22×Q8—224no—
359C22×Q8—444no—
360C22×Q8—444no—
361C22×Q8C22×D1111yescharacteristic
362C22×Q8C22×D1112yes—
363C23×C4—111no—
364C23×C4—111no—
365C23×C4—111no—
366C23×C4—222no—
367C2×Q16—44no—
368C2×Q16—118no—
369C2×Q16—118no—
370C2×Q16—118no—
371C2×Q16—444no—
372C2×Q16—444no—
373C2×Q16—444no—
374C2×Q16C22×D1118yes—
375C22×C8—112no—
376C22×C8C22×D1112yes—
377C4⋊Q8—22no—
378C4⋊Q8—114no—
379C4⋊Q8—118no—
380C4⋊Q8—114no—
381C4⋊Q8—114no—
382C4⋊Q8—228no—
383C4⋊Q8—228no—
384C4⋊Q8—222no—
385C4⋊Q8—224no—
386C4⋊Q8—222no—
387C4⋊Q8—222no—
388C4⋊Q8C22×D1114yes—
389#125—228no—
390C22⋊Q8—114no—
391C22⋊Q8—114no—
392C22⋊Q8—222no—
393C22⋊Q8—228no—
394C22⋊Q8—222no—
395C4×Q8—22no—
396C4×Q8—114no—
397C4×Q8—228no—
398C4×Q8—222no—
399C4×Q8C22×D1114yes—
400#117—228no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—111no—
405C2×C4⋊C4—228no—
406C2×C4⋊C4—228no—
407C2×C4⋊C4—222no—
408C2×C4⋊C4—222no—
409C2×C4⋊C4—221no—
410C2×C4⋊C4—221no—
411C2×C4⋊C4—221no—
412C2×C4⋊C4—221no—
413C2×C4⋊C4—221no—
414C2×C4⋊C4—221no—
415C2×C4⋊C4—221no—
416C2×C4⋊C4—221no—
417C2×C4⋊C4C22×D1111yescharacteristic
418C2×C22⋊C4—221no—
419C2×C22⋊C4—221no—
420C2×C42—21no—
421C2×C42—111no—
422C2×C42—111no—
423C2×C42—111no—
424C2×C42—114no—
425C2×C42—114no—
426C2×C42—221no—
427C2×C42C22×D1111yescharacteristic
428C4⋊C8—114no—
429C4⋊C8C22×D1114yes—
430#103—118no—
431#103—118no—
432#103—118no—
433#103C22×D1118yes—
434C22⋊C8—118no—
435C4×C8—118no—
436C2×C11#320914yescomplemented
437C2×C11C2×#53511yescharacteristic
438C2×C11C23×Q1611yescharacteristic
439C2×C11C22×#13711yescharacteristic
440D11—24no—
441C24—111no—
442C2×Q8—21no—
443C2×Q8—22no—
444C2×Q8—22no—
445C2×Q8—24no—
446C2×Q8—22no—
447C2×Q8—24no—
448C2×Q8—114no—
449C2×Q8—112no—
450C2×Q8—224no—
451C2×Q8—228no—
452C2×Q8—221no—
453C2×Q8—222no—
454C2×Q8—222no—
455C2×Q8—224no—
456C2×Q8—222no—
457C2×Q8—224no—
458C2×Q8—444no—
459C2×Q8—448no—
460C2×Q8—448no—
461C2×Q8—448no—
462C2×Q8—4416no—
463C2×Q8C23×D1114yes—
464C2×Q8C23×D1112yes—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—22no—
468C22×C4—111no—
469C22×C4—111no—
470C22×C4—118no—
471C22×C4—114no—
472C22×C4—111no—
473C22×C4—114no—
474C22×C4—112no—
475C22×C4—112no—
476C22×C4—224no—
477C22×C4—228no—
478C22×C4—222no—
479C22×C4—222no—
480C22×C4—221no—
481C22×C4—221no—
482C22×C4—222no—
483C22×C4—448no—
484C22×C4D4×D1111yescharacteristic
485C22×C4D4×D1111yescharacteristic
486C22×C4C23×D1111yescharacteristic
487Q16—48no—
488Q16—448no—
489Q16—448no—
490Q16—448no—
491C2×C8—24no—
492C2×C8—114no—
493C2×C8—224no—
494C2×C8C23×D1114yes—
495C4⋊C4—24no—
496C4⋊C4—24no—
497C4⋊C4—24no—
498C4⋊C4—21no—
499C4⋊C4—112no—
500C4⋊C4—228no—
501C4⋊C4—228no—
502C4⋊C4—224no—
503C4⋊C4—224no—
504C4⋊C4—224no—
505C4⋊C4—224no—
506C4⋊C4—224no—
507C4⋊C4—221no—
508C4⋊C4—224no—
509C4⋊C4—224no—
510C4⋊C4—224no—
511C4⋊C4C23×D1112yes—
512C22⋊C4—224no—
513C22⋊C4—224no—
514C42—24no—
515C42—114no—
516C42—114no—
517C42—112no—
518C42—112no—
519C42—224no—
520C42D4×D1112yes—
521C42C23×D1112yes—
522C11C2×#320911yescharacteristic, complemented, Sylow
523C23—114no—
524C23—112no—
525C23—222no—
526C23—222no—
527C23C2×D4×D1111yescharacteristic
528Q8—22no—
529Q8—24no—
530Q8—22no—
531Q8—24no—
532Q8—42no—
533Q8—44no—
534Q8—222no—
535Q8—224no—
536Q8—222no—
537Q8—224no—
538Q8—448no—
539Q8—4416no—
540Q8—444no—
541Q8—442no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—24no—
546C2×C4—42no—
547C2×C4—44no—
548C2×C4—42no—
549C2×C4—114no—
550C2×C4—114no—
551C2×C4—112no—
552C2×C4—112no—
553C2×C4—1116no—
554C2×C4—112no—
555C2×C4—228no—
556C2×C4—222no—
557C2×C4—224no—
558C2×C4—222no—
559C2×C4—222no—
560C2×C4—222no—
561C2×C4—222no—
562C2×C4—224no—
563C2×C4—4416no—
564C2×C4—442no—
565C2×C4—444no—
566C2×C4—442no—
567C2×C4Q16×D1114yes—
568C2×C4C2×D4×D1112yes—
569C2×C4C2×D4×D1112yes—
570C2×C4C2×D4×D1111yescharacteristic
571C2×C4#6703712yes—
572C2×C4#6704212yes—
573C2×C4C24×D1111yescharacteristic
574C8—24no—
575C8—224no—
576C22—114no—
577C22—228no—
578C22—222no—
579C22—222no—
580C22#1062313812yes—
581C22C2×Q16×D1112yes—
582C22D11×#13712yes—
583C22C22×D4×D1111yescharacteristic
584C4—22no—
585C4—44no—
586C4—42no—
587C4—42no—
588C4—114no—
589C4—114no—
590C4—222no—
591C4—444no—
592C4—442no—
593C4—442no—
594C4#1062313812yes—
595C4C2×Q16×D1114yes—
596C4C2×#6703711yescharacteristic
597C4C2×#6704211yescharacteristic
598C2—224no—
599C2#1307956314yesdirect product factor
600C2C2×#1062313811yescharacteristic
601C2C22×Q16×D1111yescharacteristic
602C2C2×D11×#13711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#462C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
hypercenterC2×#462D11
hypocenterC11C2×#3209
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#462

Complements

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

NH ≅ G/Ntype
3. #13079563C2direct (N × H)
4. C2×#10622794C2semidirect
5. C2×#10622405C2semidirect
6. C2×#10622462C2semidirect
7. C2×#10622644C2semidirect
8. C2×#10622703C2semidirect
12. C2×C11×#462C2semidirect
40. C11×#462C22semidirect
45. #10622794C22semidirect
49. #10622703C22semidirect
50. #10622644C22semidirect
53. #10622462C22semidirect
56. #10622405C22semidirect
170. C2×C4×D11Q16semidirect
230. C2×#462D11semidirect
276. C4×D11C2×Q16semidirect
319. #462C2×D11semidirect
436. C2×C11#3209semidirect
522. C11C2×#3209semidirect
599. C2#13079563direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231092
C2×D11×C4⋊Q82
#130795632
C2×#106227942
C2×#106224052
C2×#106224622
C2×#106226442
C2×#106227032
C2×#106224212
C2×#106227992
C2×#106224462
C2×C11×#4622
C2×#320911