Finite Group Databasebeta

← C2×#13078787 #15621921

Subgroups — C2×#13078787 #15621921

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
1C2×#10623010C211yesmaximal, characteristic
2#13078787C2116yesmaximal, direct product factor
3C2×#10622583C211yesmaximal, characteristic, complemented
4C2×#10622581C211yesmaximal, characteristic
5C2×#10622635C212yesmaximal, complemented
6C2×#10622641C212yesmaximal, complemented
7C2×#10622841C211yesmaximal, characteristic, complemented
8C2×#10622840C211yesmaximal, characteristic
9C2×#10622643C212yesmaximal, complemented
10C2×#10622639C212yesmaximal, complemented
11C2×#10622539C211yesmaximal, characteristic, complemented
12C22×C4×Q8×C11C211yesmaximal, characteristic, complemented
13C23×Q8×C11C2211yescharacteristic
14C2×C4×Q8×C11—21no—
15C2×C4×Q8×C11—21no—
16C2×C4×Q8×C11—24no—
17C2×C4×Q8×C11C2212yes—
18C2×C4×Q8×C11C2212yes—
19C2×C4×Q8×C11C2218yescomplemented
20C22×C11×C4⋊C4—21no—
21C22×C11×C4⋊C4C2211yescharacteristic
22C22×C42×C11—21no—
23C22×C42×C11C2211yescharacteristic
24C22×#4326C2212yes—
25C22×#4325C2212yes—
26C2×#66983C2211yescharacteristic
27C2×#66982—21no—
28C2×C4×C22⋊D11—21no—
29C2×#66977C2211yescharacteristic
30#10623010—24no—
31#10623010C2218yes—
32C2×#66929—21no—
33C2×#66928C2211yescharacteristic
34C2×C4×D44C2211yescharacteristic
35C2×#66925—21no—
36C2×#66923C2211yescharacteristic
37C2×C4×Dic22C2211yescharacteristic
38#10622841C2218yescomplemented
39#10622840C2218yes—
40C2×#66899C2212yes—
41C2×#66899C2212yes—
42C2×C22⋊(C11⋊C8)C2211yescharacteristic
43C2×C22⋊(C11⋊C8)C2211yescharacteristic
44#10622643C22116yescomplemented
45#10622641C22116yescomplemented
46#10622639C22116yescomplemented
47#10622635C22116yescomplemented
48#10622583C2218yescomplemented
49C2×#66874C2212yes—
50#10622581C2218yes—
51C2×#66873C2212yes—
52C2×#66872C2212yes—
53C2×#66871C2212yes—
54#10622539C2218yescomplemented
55C2×C4⋊(C11⋊C8)C2212yes—
56C2×#66867C2212yes—
57C22×Q8×C11—28no—
58C22×Q8×C11—21no—
59C22×Q8×C11—22no—
60C22×Q8×C11C2314yes—
61C22×Q8×C11C2312yes—
62C23×C4×C11—21no—
63C23×C4×C11—21no—
64C23×C4×C11D411yescharacteristic
65C23×C4×C11D411yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C22×C22⋊D11—21no—
68C22×D44C2311yescharacteristic
69C22×C4×D11—21no—
70C22×Dic22C2311yescharacteristic
71C4×Q8×C11—24no—
72C4×Q8×C11—24no—
73C4×Q8×C11—28no—
74C4×Q8×C11—28no—
75C4×Q8×C11C2318yes—
76C4×Q8×C11C2318yes—
77C2×C11×C4⋊C4—22no—
78C2×C11×C4⋊C4—22no—
79C2×C11×C4⋊C4—28no—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4—22no—
82C2×C11×C4⋊C4C2312yes—
83C2×C11×C4⋊C4C2314yes—
84C2×C42×C11—22no—
85C2×C42×C11—22no—
86C2×C42×C11—28no—
87C2×C42×C11D411yescharacteristic
88C2×C42×C11D411yescharacteristic
89C2×C42×C11D414yes—
90C2×C42×C11C2311yescharacteristic
91C2×C42×C11C2311yescharacteristic
92C2×C42×C11C2314yes—
93C2×C22⋊Dic11—21no—
94C2×#4326—28no—
95C2×#4326C2318yes—
96C2×#4325—28no—
97C2×#4325C2318yes—
98#66983—22no—
99#66983C2314yes—
100#66982—28no—
101C4×C22⋊D11—28no—
102C2×(C2×D11)⋊C4—21no—
103C2×(C2×D11)⋊C4—21no—
104C2×(C2×D11)⋊C4—21no—
105C2×(C2×D11)⋊C4—21no—
106C2×C4⋊Dic11C2311yescharacteristic
107C2×C4⋊Dic11C2311yescharacteristic
108#66977—22no—
109#66977C2314yes—
110C2×Dic11⋊C4—21no—
111C2×Dic11⋊C4—21no—
112C2×Dic11⋊C4—21no—
113C2×Dic11⋊C4—21no—
114C2×C4×Dic11—21no—
115C22×C11⋊C8C2312yes—
116C22×C11⋊C8C2312yes—
117#66929—28no—
118#66928—22no—
119#66928C2314yes—
120C4×D44—22no—
121C4×D44C2314yes—
122#66925—28no—
123#66923—22no—
124#66923C2314yes—
125C4×Dic22—22no—
126C4×Dic22C2314yes—
127#66899C2318yes—
128#66899C2318yes—
129C22⋊(C11⋊C8)C2314yes—
130C22⋊(C11⋊C8)C2314yes—
131#66874C2318yes—
132#66873C2318yes—
133#66872C2318yes—
134#66871C2318yes—
135C4⋊(C11⋊C8)C2318yes—
136#66867C2318yes—
137C2×#3117—111nomaximal, Sylow
138C24×C11C2×D411yescharacteristic
139C23×D11—21no—
140C2×Q8×C11—216no—
141C2×Q8×C11—28no—
142C2×Q8×C11—216no—
143C2×Q8×C11—24no—
144C2×Q8×C11—22no—
145C2×Q8×C11—24no—
146C2×Q8×C11#4118yes—
147C2×Q8×C11C2414yes—
148C22×C4×C11—28no—
149C22×C4×C11—24no—
150C22×C4×C11—24no—
151C22×C4×C11—22no—
152C22×C4×C11—24no—
153C22×C4×C11—24no—
154C22×C4×C11—22no—
155C22×C4×C11—42no—
156C22×C4×C11—44no—
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11C2×D411yescharacteristic
161C22×C4×C11C2×D411yescharacteristic
162C22×C4×C11C2×D412yes—
163C22×C4×C11C2×D414yes—
164C22×C4×C11C2×D414yes—
165C22×C4×C11C2412yes—
166C22×C4×C11C2411yescharacteristic
167C2×C22⋊D11—24no—
168C2×C22⋊D11—44no—
169C22×Dic11—21no—
170C22×Dic11—21no—
171C22×Dic11—21no—
172C2×D44—21no—
173C2×D44—24no—
174C2×D44C2412yes—
175C2×C4×D11—24no—
176C2×C4×D11—44no—
177C2×Dic22—21no—
178C2×Dic22—24no—
179C2×Dic22C2412yes—
180C11×C4⋊C4—28no—
181C11×C4⋊C4—28no—
182C11×C4⋊C4—24no—
183C11×C4⋊C4—22no—
184C11×C4⋊C4C2414yes—
185C42×C11—28no—
186C42×C11—28no—
187C42×C11C2×D412yes—
188C42×C11C2×D412yes—
189C42×C11C2×D414yes—
190C42×C11C2×D414yes—
191C42×C11C2412yes—
192C42×C11C2412yes—
193C22⋊Dic11—24no—
194#4326—216no—
195#4325—216no—
196(C2×D11)⋊C4—24no—
197(C2×D11)⋊C4—24no—
198(C2×D11)⋊C4—24no—
199(C2×D11)⋊C4—24no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11C2412yes—
203C4⋊Dic11C2412yes—
204Dic11⋊C4—24no—
205Dic11⋊C4—24no—
206Dic11⋊C4—24no—
207Dic11⋊C4—24no—
208C4×Dic11—24no—
209C2×C11⋊C8—24no—
210C2×C11⋊C8—24no—
211C2×C11⋊C8C2414yes—
212C2×C11⋊C8C2414yes—
213C2×#529—111no—
214C22×C4×Q8D1111yescharacteristic, complemented
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#13714yes—
228C23×C11C22×D412yes—
229C23×C11C22×D411yescharacteristic
230C22×D11—22no—
231C22×D11—42no—
232C22×D11—42no—
233C22×D11—42no—
234Q8×C11—216no—
235Q8×C11—28no—
236Q8×C11—24no—
237Q8×C11C2×#4118yes—
238C2×C4×C11—216no—
239C2×C4×C11—28no—
240C2×C4×C11—22no—
241C2×C4×C11—28no—
242C2×C4×C11—22no—
243C2×C4×C11—22no—
244C2×C4×C11—22no—
245C2×C4×C11—22no—
246C2×C4×C11—24no—
247C2×C4×C11—24no—
248C2×C4×C11—24no—
249C2×C4×C11—24no—
250C2×C4×C11—44no—
251C2×C4×C11—48no—
252C2×C4×C11—44no—
253C2×C4×C11C22×D412yes—
254C2×C4×C11C22×D412yes—
255C2×C4×C11C22×D412yes—
256C2×C4×C11C22×D412yes—
257C2×C4×C11C22×D412yes—
258C2×C4×C11C22×D411yescharacteristic
259C2×C4×C11C2×#4114yes—
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—24no—
269D44—42no—
270C4×D11—48no—
271Dic22—24no—
272Dic22—42no—
273C11⋊C8—24no—
274C11⋊C8—24no—
275C23×Q8C2×D1111yescharacteristic
276C22×Q16—112no—
277C22×SD16—112no—
278#529—118no—
279#529—224no—
280C2×#126—221no—
281C2×#125—111no—
282C2×#124—111no—
283C2×#123—221no—
284C2×C22⋊Q8—111no—
285C2×#121—111no—
286C2×C4×Q8—21no—
287C2×C4×Q8—21no—
288C2×C4×Q8—24no—
289C2×C4×Q8—111no—
290C2×C4×Q8C2×D1112yes—
291C2×C4×Q8C2×D1112yes—
292C2×C4×Q8C2×D1118yescomplemented
293C2×C4×D4—111no—
294C2×C4×D4—221no—
295C2×#117—221no—
296C22×C4⋊C4—21no—
297C22×C4⋊C4C2×D1111yescharacteristic
298C22×C42—21no—
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#52512yes—
323C22×C11C2×#13714yes—
324C22×C11C2×#13712yes—
325C22×C11#57512yes—
326C22×C11C23×D411yescharacteristic
327C2×D11—42no—
328C2×D11—42no—
329C2×D11—42no—
330C2×D11—84no—
331C4×C11—28no—
332C4×C11—22no—
333C4×C11—22no—
334C4×C11—22no—
335C4×C11—22no—
336C4×C11—22no—
337C4×C11—44no—
338C4×C11#52512yes—
339C4×C11C22×#4112yes—
340Dic11—42no—
341Dic11—42no—
342Dic11—42no—
343C22×Q8—28no—
344C22×Q8—22no—
345C22×Q8—21no—
346C22×Q8—111no—
347C22×Q8C22×D1114yes—
348C22×Q8C22×D1112yes—
349C22×D4—111no—
350C22×D4—221no—
351C23×C4—21no—
352C23×C4—21no—
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—228no—
364#125—114no—
365#125—222no—
366#124—114no—
367#124—222no—
368#123—228no—
369C22⋊Q8—114no—
370C22⋊Q8—222no—
371#121—114no—
372#121—222no—
373C4×Q8—24no—
374C4×Q8—24no—
375C4×Q8—28no—
376C4×Q8—28no—
377C4×Q8—114no—
378C4×Q8—222no—
379C4×Q8C22×D1118yes—
380C4×Q8C22×D1118yes—
381C4×D4—114no—
382C4×D4—228no—
383C4×D4—222no—
384#117—228no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—28no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—111no—
391C2×C4⋊C4—111no—
392C2×C4⋊C4—221no—
393C2×C4⋊C4—221no—
394C2×C4⋊C4—221no—
395C2×C4⋊C4—221no—
396C2×C4⋊C4C22×D1112yes—
397C2×C4⋊C4C22×D1114yes—
398C2×C22⋊C4—221no—
399C2×C22⋊C4—221no—
400C2×C22⋊C4—221no—
401C2×C22⋊C4—221no—
402C2×C22⋊C4—221no—
403C2×C42—22no—
404C2×C42—22no—
405C2×C42—28no—
406C2×C42—221no—
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#311714yescomplemented
425C2×C11C2×#52511yescharacteristic
426C2×C11C22×#13711yescharacteristic
427C2×C11C2×#57511yescharacteristic
428D11—82no—
429C24—221no—
430C24C2×C22⋊D1111yescharacteristic
431C2×Q8—216no—
432C2×Q8—28no—
433C2×Q8—216no—
434C2×Q8—24no—
435C2×Q8—24no—
436C2×Q8—22no—
437C2×Q8—112no—
438C2×Q8—221no—
439C2×Q8—224no—
440C2×Q8#433918yes—
441C2×Q8C23×D1114yes—
442C2×D4—112no—
443C2×D4—224no—
444C2×D4—224no—
445C2×D4—221no—
446C2×D4—444no—
447C22×C4—28no—
448C22×C4—24no—
449C22×C4—24no—
450C22×C4—22no—
451C22×C4—24no—
452C22×C4—24no—
453C22×C4—22no—
454C22×C4—42no—
455C22×C4—44no—
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⋊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—28no—
478C4⋊C4—28no—
479C4⋊C4—24no—
480C4⋊C4—22no—
481C4⋊C4—112no—
482C4⋊C4—112no—
483C4⋊C4—221no—
484C4⋊C4—221no—
485C4⋊C4—224no—
486C4⋊C4—224no—
487C4⋊C4—224no—
488C4⋊C4—224no—
489C4⋊C4C23×D1114yes—
490C22⋊C4—224no—
491C22⋊C4—224no—
492C22⋊C4—224no—
493C22⋊C4—224no—
494C22⋊C4—224no—
495C42—28no—
496C42—28no—
497C42—224no—
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—222no—
508C23—442no—
509C23—442no—
510C23—442no—
511C23#6699514yes—
512C23C22×C22⋊D1112yes—
513C23C22×C22⋊D1111yescharacteristic
514Q8—216no—
515Q8—28no—
516Q8—24no—
517Q8—224no—
518Q8—442no—
519Q8C2×#433918yes—
520D4—224no—
521D4—448no—
522D4—442no—
523C2×C4—216no—
524C2×C4—28no—
525C2×C4—22no—
526C2×C4—28no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—24no—
532C2×C4—24no—
533C2×C4—24no—
534C2×C4—24no—
535C2×C4—44no—
536C2×C4—48no—
537C2×C4—44no—
538C2×C4—222no—
539C2×C4—222no—
540C2×C4—222no—
541C2×C4—448no—
542C2×C4—442no—
543C2×C4—442no—
544C2×C4—442no—
545C2×C4C2×#433914yes—
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—28no—
557C22—22no—
558C22—442no—
559C22—442no—
560C22—442no—
561C22—884no—
562C22#1062332212yes—
563C22C2×#6699514yes—
564C22C2×#6699512yes—
565C22#1062335312yes—
566C22C23×C22⋊D1111yescharacteristic
567C4—28no—
568C4—22no—
569C4—22no—
570C4—22no—
571C4—22no—
572C4—22no—
573C4—44no—
574C4—442no—
575C4—442no—
576C4—442no—
577C4#1062332212yes—
578C4C22×#433912yes—
579C2—24no—
580C2—882no—
581C2#1307878714yesdirect product factor
582C2C2×#1062332211yescharacteristic
583C2C22×#6699511yescharacteristic
584C2C2×#1062335311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC22×C4×Q8×C11C2
socleC23×C11C22×D4
prime radicalC2×#66983C22
hypercenterC22×C4×Q8D11
hypocenterC11C2×#3117
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C22×C4×Q8

Complements

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

NH ≅ G/Ntype
2. #13078787C2direct (N × H)
3. C2×#10622583C2semidirect
5. C2×#10622635C2semidirect
6. C2×#10622641C2semidirect
7. C2×#10622841C2semidirect
9. C2×#10622643C2semidirect
10. C2×#10622639C2semidirect
11. C2×#10622539C2semidirect
12. C22×C4×Q8×C11C2semidirect
19. C2×C4×Q8×C11C22semidirect
38. #10622841C22semidirect
44. #10622643C22semidirect
45. #10622641C22semidirect
46. #10622639C22semidirect
47. #10622635C22semidirect
48. #10622583C22semidirect
54. #10622539C22semidirect
214. C22×C4×Q8D11semidirect
292. C2×C4×Q8C2×D11semidirect
424. C2×C11#3117semidirect
504. C11C2×#3117semidirect
581. C2#13078787direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230102
#130787872
C2×#106225832
C2×#106225812
C2×#106226352
C2×#106226412
C2×#106228412
C2×#106228402
C2×#106226432
C2×#106226392
C2×#106225392
C22×C4×Q8×C112
C2×#311711