Finite Group Databasebeta

← C2×#13078783 #15621917

Subgroups — C2×#13078783 #15621917

Order 2816.

2150 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×Dic22C211yesmaximal, characteristic, complemented
2#13078783C2116yesmaximal, direct product factor
3C2×#10622657C211yesmaximal, characteristic, complemented
4C2×#10622647C211yesmaximal, characteristic
5C2×#10622676C212yesmaximal, complemented
6C2×#10622667C212yesmaximal, complemented
7C2×#10622663C211yesmaximal, characteristic, complemented
8C2×#10622653C211yesmaximal, characteristic
9C2×#10622643C212yesmaximal, complemented
10C2×#10622631C212yesmaximal, complemented
11C2×#10622539C211yesmaximal, characteristic, complemented
12C2×C11×#529C211yesmaximal, characteristic
13C23×Dic22C2211yescharacteristic
14C11×#529—24no—
15C11×#529C2218yes—
16C2×C11×#126—21no—
17C2×C11×#125C2211yescharacteristic
18C2×C11×#124C2211yescharacteristic
19C2×C11×#123—21no—
20C2×C11×C22⋊Q8C2211yescharacteristic
21C2×C11×#121C2211yescharacteristic
22C2×C4×Q8×C11C2211yescharacteristic
23C2×C4×D4×C11—21no—
24C2×C4×D4×C11C2211yescharacteristic
25C2×C11×#117—21no—
26C22×C42×C11C2211yescharacteristic
27C22×#4326C2212yes—
28C22×#4324C2212yes—
29C22×C4⋊Dic11C2211yescharacteristic
30C22×Dic11⋊C4—21no—
31C22×C4×Dic11—21no—
32C2×C4×Dic22—24no—
33C2×C4×Dic22—21no—
34C2×C4×Dic22—21no—
35C2×C4×Dic22C2212yes—
36C2×C4×Dic22C2212yes—
37C2×C4×Dic22C2218yescomplemented
38C2×#66899C2212yes—
39C2×#66896C2212yes—
40C2×C22⋊(C11⋊C8)C2211yescharacteristic
41C2×C22⋊(C11⋊C8)C2211yescharacteristic
42#10622676C22116yescomplemented
43#10622667C22116yescomplemented
44#10622663C2218yescomplemented
45#10622657C2218yescomplemented
46#10622653C2218yes—
47#10622647C2218yes—
48#10622643C22116yescomplemented
49#10622631C22116yescomplemented
50C2×#66874C2212yes—
51C2×#66874C2212yes—
52C2×#66872C2212yes—
53C2×#66871C2212yes—
54#10622539C2218yescomplemented
55C2×C4⋊(C11⋊C8)C2212yes—
56C2×#66867C2212yes—
57C22×Q8×C11C2311yescharacteristic
58C22×D4×C11—21no—
59C22×D4×C11C2311yescharacteristic
60C23×C4×C11—21no—
61C23×C4×C11D411yescharacteristic
62C23×C4×C11D411yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×Dic11—21no—
65C23×Dic11—21no—
66C22×Dic22—21no—
67C22×Dic22—22no—
68C22×Dic22—28no—
69C22×Dic22C2314yes—
70C22×Dic22C2312yes—
71C11×#126—28no—
72C11×#125—22no—
73C11×#125C2314yes—
74C11×#124—22no—
75C11×#124C2314yes—
76C11×#123—28no—
77C11×C22⋊Q8—22no—
78C11×C22⋊Q8C2314yes—
79C11×#121—22no—
80C11×#121C2314yes—
81C4×Q8×C11—22no—
82C4×Q8×C11C2314yes—
83C4×D4×C11—28no—
84C4×D4×C11—22no—
85C4×D4×C11C2314yes—
86C11×#117—28no—
87C2×C11×C4⋊C4—21no—
88C2×C11×C4⋊C4—21no—
89C2×C11×C4⋊C4—21no—
90C2×C11×C4⋊C4—21no—
91C2×C11×C4⋊C4C2311yescharacteristic
92C2×C11×C4⋊C4C2311yescharacteristic
93C2×C11×C22⋊C4—21no—
94C2×C11×C22⋊C4—21no—
95C2×C11×C22⋊C4—21no—
96C2×C11×C22⋊C4—21no—
97C2×C11×C22⋊C4—21no—
98C2×C42×C11—21no—
99C2×C42×C11D411yescharacteristic
100C2×C42×C11D411yescharacteristic
101C2×C42×C11D414yes—
102C2×C42×C11C2311yescharacteristic
103C2×C42×C11C2311yescharacteristic
104C2×C42×C11C2314yes—
105C2×#4326—28no—
106C2×#4326C2318yes—
107C2×#4324—28no—
108C2×#4324C2318yes—
109C2×C4⋊Dic11—21no—
110C2×C4⋊Dic11—22no—
111C2×C4⋊Dic11C2312yes—
112C2×C4⋊Dic11C2314yes—
113C2×Dic11⋊C4—22no—
114C2×Dic11⋊C4—22no—
115C2×Dic11⋊C4—28no—
116C2×C4×Dic11—22no—
117C2×C4×Dic11—22no—
118C2×C4×Dic11—28no—
119C22×C11⋊C8C2312yes—
120C22×C11⋊C8C2312yes—
121C4×Dic22—24no—
122C4×Dic22—24no—
123C4×Dic22—28no—
124C4×Dic22—28no—
125C4×Dic22C2318yes—
126C4×Dic22C2318yes—
127#66899C2318yes—
128#66896C2318yes—
129C22⋊(C11⋊C8)C2314yes—
130C22⋊(C11⋊C8)C2314yes—
131#66874C2318yes—
132#66874C2318yes—
133#66872C2318yes—
134#66871C2318yes—
135C4⋊(C11⋊C8)C2318yes—
136#66867C2318yes—
137C2×#3117—111nomaximal, Sylow
138C24×C11—21no—
139C24×C11C2×D411yescharacteristic
140C2×Q8×C11—21no—
141C2×Q8×C11—24no—
142C2×Q8×C11C2412yes—
143C2×D4×C11—24no—
144C2×D4×C11—21no—
145C2×D4×C11—24no—
146C2×D4×C11—44no—
147C2×D4×C11C2412yes—
148C22×C4×C11—24no—
149C22×C4×C11—24no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—24no—
154C22×C4×C11—42no—
155C22×C4×C11—44no—
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D414yes—
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11C2×D411yescharacteristic
161C22×C4×C11C2×D411yescharacteristic
162C22×C4×C11C2×D412yes—
163C22×C4×C11C2×D414yes—
164C22×C4×C11C2412yes—
165C22×C4×C11C2411yescharacteristic
166C22×Dic11—28no—
167C22×Dic11—24no—
168C22×Dic11—22no—
169C22×Dic11—24no—
170C22×Dic11—22no—
171C22×Dic11—44no—
172C2×Dic22—28no—
173C2×Dic22—216no—
174C2×Dic22—216no—
175C2×Dic22—24no—
176C2×Dic22—22no—
177C2×Dic22—24no—
178C2×Dic22#4118yes—
179C2×Dic22C2414yes—
180C11×C4⋊C4—24no—
181C11×C4⋊C4—24no—
182C11×C4⋊C4—24no—
183C11×C4⋊C4—24no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4C2412yes—
187C11×C4⋊C4C2412yes—
188C11×C22⋊C4—24no—
189C11×C22⋊C4—24no—
190C11×C22⋊C4—24no—
191C11×C22⋊C4—24no—
192C11×C22⋊C4—24no—
193C42×C11—24no—
194C42×C11C2×D414yes—
195C42×C11C2×D412yes—
196C42×C11C2×D412yes—
197C42×C11C2×D414yes—
198C42×C11C2412yes—
199C42×C11C2412yes—
200#4326—216no—
201#4324—216no—
202C4⋊Dic11—24no—
203C4⋊Dic11—22no—
204C4⋊Dic11C2414yes—
205Dic11⋊C4—28no—
206Dic11⋊C4—28no—
207C4×Dic11—28no—
208C4×Dic11—28no—
209C2×C11⋊C8—24no—
210C2×C11⋊C8—24no—
211C2×C11⋊C8C2414yes—
212C2×C11⋊C8C2414yes—
213C2×#529D1111yescharacteristic
214C22×C4×Q8—111no—
215#3117—1116no—
216C2×#484—111no—
217C2×#481—111no—
218C2×#479—112no—
219C2×#464—112no—
220C2×#451—111no—
221C2×#448—111no—
222C2×#441—112no—
223C2×#440—112no—
224C2×#432—111no—
225C23×C11—22no—
226C23×C11—22no—
227C23×C11—22no—
228C23×C11—42no—
229C23×C11—42no—
230C23×C11—42no—
231C23×C11#13714yes—
232C23×C11C22×D412yes—
233C23×C11C22×D411yescharacteristic
234Q8×C11—24no—
235Q8×C11—42no—
236D4×C11—24no—
237D4×C11—48no—
238D4×C11—42no—
239C2×C4×C11—22no—
240C2×C4×C11—28no—
241C2×C4×C11—22no—
242C2×C4×C11—22no—
243C2×C4×C11—22no—
244C2×C4×C11—22no—
245C2×C4×C11—24no—
246C2×C4×C11—24no—
247C2×C4×C11—22no—
248C2×C4×C11—22no—
249C2×C4×C11—22no—
250C2×C4×C11—44no—
251C2×C4×C11—48no—
252C2×C4×C11—42no—
253C2×C4×C11—42no—
254C2×C4×C11—42no—
255C2×C4×C11C22×D412yes—
256C2×C4×C11C22×D412yes—
257C2×C4×C11C22×D412yes—
258C2×C4×C11C22×D412yes—
259C2×C4×C11C22×D412yes—
260C2×C4×C11C22×D411yescharacteristic
261C2×C4×C11C2×#4114yes—
262C2×C4×C11C2511yescharacteristic
263C2×Dic11—216no—
264C2×Dic11—28no—
265C2×Dic11—24no—
266C2×Dic11—24no—
267C2×Dic11—48no—
268C2×Dic11—44no—
269Dic22—216no—
270Dic22—28no—
271Dic22—24no—
272Dic22C2×#4118yes—
273C11⋊C8—24no—
274C11⋊C8—24no—
275C23×Q8—111no—
276C22×Q16—112no—
277C22×SD16—112no—
278#529—24no—
279#529C2×D1118yes—
280C2×#126—21no—
281C2×#125C2×D1111yescharacteristic
282C2×#124C2×D1111yescharacteristic
283C2×#123—21no—
284C2×C22⋊Q8C2×D1111yescharacteristic
285C2×#121C2×D1111yescharacteristic
286C2×C4×Q8—112no—
287C2×C4×Q8—112no—
288C2×C4×Q8—118no—
289C2×C4×Q8—221no—
290C2×C4×Q8—221no—
291C2×C4×Q8—224no—
292C2×C4×Q8C2×D1111yescharacteristic
293C2×C4×D4—21no—
294C2×C4×D4C2×D1111yescharacteristic
295C2×#117—21no—
296C22×C4⋊C4—111no—
297C22×C4⋊C4—221no—
298C22×C42—221no—
299C22×C42C2×D1111yescharacteristic
300#484—118no—
301#481—118no—
302#479—1116no—
303#464—1116no—
304#451—118no—
305#448—118no—
306#441—1116no—
307#440—1116no—
308#432—118no—
309C2×#107—112no—
310C2×#106—112no—
311C2×C4⋊C8—112no—
312C2×#103—112no—
313C2×#103—112no—
314C2×#103—112no—
315C2×#102—112no—
316C2×C22⋊C8—111no—
317C2×C22⋊C8—111no—
318C2×#97—112no—
319C22×C11—28no—
320C22×C11—22no—
321C22×C11—22no—
322C22×C11—42no—
323C22×C11—42no—
324C22×C11—42no—
325C22×C11—84no—
326C22×C11#52512yes—
327C22×C11C2×#13714yes—
328C22×C11C2×#13712yes—
329C22×C11#57512yes—
330C22×C11C23×D411yescharacteristic
331C4×C11—22no—
332C4×C11—22no—
333C4×C11—22no—
334C4×C11—22no—
335C4×C11—22no—
336C4×C11—42no—
337C4×C11—42no—
338C4×C11—42no—
339C4×C11#52512yes—
340C4×C11C22×#4112yes—
341Dic11—28no—
342Dic11—44no—
343C22×Q8—112no—
344C22×Q8—114no—
345C22×Q8—228no—
346C22×Q8—222no—
347C22×Q8—221no—
348C22×Q8C22×D1111yescharacteristic
349C22×D4—21no—
350C22×D4C22×D1111yescharacteristic
351C23×C4—21no—
352C23×C4—221no—
353C23×C4—221no—
354C23×C4C22⋊D1111yescharacteristic
355C23×C4C22⋊D1111yescharacteristic
356C23×C4C22×D1111yescharacteristic
357C2×Q16—118no—
358C2×Q16—228no—
359C2×SD16—118no—
360C2×SD16—228no—
361C22×C8—112no—
362C22×C8—112no—
363#126—28no—
364#125—22no—
365#125C22×D1114yes—
366#124—22no—
367#124C22×D1114yes—
368#123—28no—
369C22⋊Q8—22no—
370C22⋊Q8C22×D1114yes—
371#121—22no—
372#121C22×D1114yes—
373C4×Q8—22no—
374C4×Q8—118no—
375C4×Q8—118no—
376C4×Q8—228no—
377C4×Q8—224no—
378C4×Q8—224no—
379C4×Q8—228no—
380C4×Q8C22×D1114yes—
381C4×D4—28no—
382C4×D4—22no—
383C4×D4C22×D1114yes—
384#117—28no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—112no—
390C2×C4⋊C4—114no—
391C2×C4⋊C4—222no—
392C2×C4⋊C4—221no—
393C2×C4⋊C4—228no—
394C2×C4⋊C4—222no—
395C2×C4⋊C4—222no—
396C2×C4⋊C4C22×D1111yescharacteristic
397C2×C4⋊C4C22×D1111yescharacteristic
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—21no—
401C2×C22⋊C4—21no—
402C2×C22⋊C4—21no—
403C2×C42—21no—
404C2×C42—228no—
405C2×C42—222no—
406C2×C42—222no—
407C2×C42C22⋊D1111yescharacteristic
408C2×C42C22⋊D1111yescharacteristic
409C2×C42C22⋊D1114yes—
410C2×C42C22×D1111yescharacteristic
411C2×C42C22×D1111yescharacteristic
412C2×C42C22×D1114yes—
413#107—118no—
414#106—118no—
415C4⋊C8—118no—
416#103—118no—
417#103—118no—
418#103—118no—
419#102—118no—
420C22⋊C8—114no—
421C22⋊C8—114no—
422#97—118no—
423C2×C11—24no—
424C2×C11—82no—
425C2×C11#311714yescomplemented
426C2×C11C2×#52511yescharacteristic
427C2×C11C22×#13711yescharacteristic
428C2×C11C2×#57511yescharacteristic
429C24—21no—
430C24C2×C22⋊D1111yescharacteristic
431C2×Q8—21no—
432C2×Q8—24no—
433C2×Q8—118no—
434C2×Q8—114no—
435C2×Q8—2216no—
436C2×Q8—228no—
437C2×Q8—2216no—
438C2×Q8—224no—
439C2×Q8—224no—
440C2×Q8—222no—
441C2×Q8C23×D1112yes—
442C2×D4—24no—
443C2×D4—24no—
444C2×D4—21no—
445C2×D4—44no—
446C2×D4C23×D1112yes—
447C22×C4—24no—
448C22×C4—24no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—24no—
453C22×C4—42no—
454C22×C4—44no—
455C22×C4—228no—
456C22×C4—224no—
457C22×C4—222no—
458C22×C4—224no—
459C22×C4—222no—
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⋊D1111yescharacteristic
468C22×C4C2×C22⋊D1114yes—
469C22×C4C23×D1112yes—
470C22×C4C23×D1111yescharacteristic
471Q16—2216no—
472SD16—2216no—
473C2×C8—114no—
474C2×C8—114no—
475C2×C8—224no—
476C2×C8—224no—
477C4⋊C4—24no—
478C4⋊C4—24no—
479C4⋊C4—24no—
480C4⋊C4—24no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—114no—
484C4⋊C4—224no—
485C4⋊C4—222no—
486C4⋊C4—228no—
487C4⋊C4—228no—
488C4⋊C4C23×D1112yes—
489C4⋊C4C23×D1112yes—
490C22⋊C4—24no—
491C22⋊C4—24no—
492C22⋊C4—24no—
493C22⋊C4—24no—
494C22⋊C4—24no—
495C42—24no—
496C42—228no—
497C42—228no—
498C42C2×C22⋊D1114yes—
499C42C2×C22⋊D1112yes—
500C42C2×C22⋊D1112yes—
501C42C2×C22⋊D1114yes—
502C42C23×D1112yes—
503C42C23×D1112yes—
504C11C2×#311711yescharacteristic, complemented, Sylow
505C23—22no—
506C23—22no—
507C23—22no—
508C23—42no—
509C23—42no—
510C23—42no—
511C23#6700414yes—
512C23C22×C22⋊D1112yes—
513C23C22×C22⋊D1111yescharacteristic
514Q8—24no—
515Q8—42no—
516Q8—118no—
517Q8—2216no—
518Q8—228no—
519Q8—224no—
520D4—24no—
521D4—48no—
522D4—42no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—28no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—24no—
530C2×C4—24no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—44no—
535C2×C4—48no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—2216no—
540C2×C4—228no—
541C2×C4—224no—
542C2×C4—224no—
543C2×C4—448no—
544C2×C4—444no—
545C2×C4#41×D1114yes—
546C2×C4C22×C22⋊D1112yes—
547C2×C4C22×C22⋊D1112yes—
548C2×C4C22×C22⋊D1112yes—
549C2×C4C22×C22⋊D1112yes—
550C2×C4C22×C22⋊D1112yes—
551C2×C4C22×C22⋊D1111yescharacteristic
552C2×C4C24×D1111yescharacteristic
553C8—224no—
554C8—224no—
555C22—22no—
556C22—22no—
557C22—28no—
558C22—42no—
559C22—42no—
560C22—42no—
561C22—84no—
562C22#1062335312yes—
563C22C2×#6700414yes—
564C22C2×#6700412yes—
565C22#1062335912yes—
566C22C23×C22⋊D1111yescharacteristic
567C4—22no—
568C4—22no—
569C4—22no—
570C4—22no—
571C4—22no—
572C4—42no—
573C4—42no—
574C4—42no—
575C4—228no—
576C4—444no—
577C4#1062335912yes—
578C4C2×#41×D1112yes—
579C2—24no—
580C2—82no—
581C2#1307878314yesdirect product factor
582C2C2×#1062335911yescharacteristic
583C2C22×#6700411yescharacteristic
584C2C2×#1062335311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#529C2
socleC23×C11C22×D4
prime radicalC2×C11×#121C22
hypercenterC2×#529D11
hypocenterC11C2×#3117
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
1. C22×C4×Dic22C2semidirect
2. #13078783C2direct (N × H)
3. C2×#10622657C2semidirect
5. C2×#10622676C2semidirect
6. C2×#10622667C2semidirect
7. C2×#10622663C2semidirect
9. C2×#10622643C2semidirect
10. C2×#10622631C2semidirect
11. C2×#10622539C2semidirect
37. C2×C4×Dic22C22semidirect
42. #10622676C22semidirect
43. #10622667C22semidirect
44. #10622663C22semidirect
45. #10622657C22semidirect
48. #10622643C22semidirect
49. #10622631C22semidirect
54. #10622539C22semidirect
425. C2×C11#3117semidirect
504. C11C2×#3117semidirect
581. C2#13078783direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×Dic222
#130787832
C2×#106226572
C2×#106226472
C2×#106226762
C2×#106226672
C2×#106226632
C2×#106226532
C2×#106226432
C2×#106226312
C2×#106225392
C2×C11×#5292
C2×#311711