Finite Group Databasebeta

← C2×#13079326 #15623697

Subgroups — C2×#13079326 #15623697

Order 2816.

1998 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623001C211yesmaximal, characteristic, complemented
2#13079326C2116yesmaximal, direct product factor
3C2×#10622678C211yesmaximal, characteristic, complemented
4C2×#10622673C211yesmaximal, characteristic, complemented
5C2×#10622682C211yesmaximal, characteristic, complemented
6C2×#10622668C211yesmaximal, characteristic, complemented
7C2×#10622664C212yesmaximal, complemented
8C2×#10622654C212yesmaximal
9C2×#10622643C212yesmaximal, complemented
10C2×#10622631C212yesmaximal, complemented
11C22×#66867C211yesmaximal, characteristic, complemented
12C2×C11×#529C211yesmaximal, characteristic
13C11×#529—24no—
14C11×#529C2218yes—
15C2×C11×#126—21no—
16C2×C11×#125C2211yescharacteristic
17C2×C11×#124C2211yescharacteristic
18C2×C11×#123—21no—
19C2×C11×C22⋊Q8C2211yescharacteristic
20C2×C11×#121C2211yescharacteristic
21C2×C4×Q8×C11C2211yescharacteristic
22C2×C4×D4×C11—21no—
23C2×C4×D4×C11C2211yescharacteristic
24C2×C11×#117—21no—
25C22×C42×C11C2211yescharacteristic
26C22×#4326C2212yes—
27C22×#4324C2212yes—
28C2×#66979—21no—
29C2×#66977—21no—
30C2×#66977C2212yes—
31C23×C11⋊C8C2212yes—
32#10623001—24no—
33#10623001C2218yescomplemented
34C2×#66923—21no—
35C2×#66922C2211yescharacteristic
36C2×#66922C2211yescharacteristic
37C2×C4×Dic22—21no—
38C2×C4×Dic22C2212yes—
39C2×#66899C2212yes—
40C2×#66896C2212yes—
41#10622682C2218yescomplemented
42#10622678C2218yescomplemented
43#10622673C2218yescomplemented
44#10622668C2218yescomplemented
45#10622664C22116yescomplemented
46#10622654C22116yes—
47#10622643C22116yescomplemented
48#10622631C22116yescomplemented
49C2×#66874C2212yes—
50C2×#66874C2212yes—
51C2×#66872C2212yes—
52C2×#66871C2212yes—
53C2×#66867C2211yescharacteristic
54C2×#66867C2212yes—
55C2×#66867C2211yescharacteristic
56C2×#66867C2218yescomplemented
57C22×Q8×C11C2311yescharacteristic
58C22×D4×C11—21no—
59C22×D4×C11C2311yescharacteristic
60C23×C4×C11—21no—
61C23×C4×C11D411yescharacteristic
62C23×C4×C11D411yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C22×Dic22—21no—
65C22×Dic22C2312yes—
66C11×#126—28no—
67C11×#125—22no—
68C11×#125C2314yes—
69C11×#124—22no—
70C11×#124C2314yes—
71C11×#123—28no—
72C11×C22⋊Q8—22no—
73C11×C22⋊Q8C2314yes—
74C11×#121—22no—
75C11×#121C2314yes—
76C4×Q8×C11—22no—
77C4×Q8×C11C2314yes—
78C4×D4×C11—28no—
79C4×D4×C11—22no—
80C4×D4×C11C2314yes—
81C11×#117—28no—
82C2×C11×C4⋊C4—21no—
83C2×C11×C4⋊C4—21no—
84C2×C11×C4⋊C4—21no—
85C2×C11×C4⋊C4—21no—
86C2×C11×C4⋊C4C2311yescharacteristic
87C2×C11×C4⋊C4C2311yescharacteristic
88C2×C11×C22⋊C4—21no—
89C2×C11×C22⋊C4—21no—
90C2×C11×C22⋊C4—21no—
91C2×C11×C22⋊C4—21no—
92C2×C11×C22⋊C4—21no—
93C2×C42×C11—21no—
94C2×C42×C11D411yescharacteristic
95C2×C42×C11D411yescharacteristic
96C2×C42×C11D414yes—
97C2×C42×C11C2311yescharacteristic
98C2×C42×C11C2311yescharacteristic
99C2×C42×C11C2314yes—
100C2×C22⋊Dic11—22no—
101C2×#4326—28no—
102C2×#4326C2318yes—
103C2×#4324—28no—
104C2×#4324C2318yes—
105#66979—28no—
106C2×C4⋊Dic11—21no—
107C2×C4⋊Dic11—21no—
108C2×C4⋊Dic11—21no—
109C2×C4⋊Dic11C2312yes—
110#66977—24no—
111#66977—28no—
112#66977C2318yes—
113C2×Dic11⋊C4—22no—
114C2×Dic11⋊C4—22no—
115C2×C4×Dic11—22no—
116C22×C11⋊C8—28no—
117C22×C11⋊C8C2312yes—
118C22×C11⋊C8C2318yes—
119C22×C11⋊C8C2312yes—
120#66923—28no—
121#66922—22no—
122#66922—22no—
123#66922C2314yes—
124#66922C2314yes—
125C4×Dic22—28no—
126C4×Dic22—24no—
127C4×Dic22C2318yes—
128#66899C2318yes—
129#66896C2318yes—
130#66874C2318yes—
131#66874C2318yes—
132#66872C2318yes—
133#66871C2318yes—
134#66867C2318yes—
135#66867C2314yes—
136#66867C2314yes—
137C2×#3181—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×D411yescharacteristic
159C22×C4×C11C2×D412yes—
160C22×C4×C11C2×D411yescharacteristic
161C22×C4×C11C2×D411yescharacteristic
162C22×C4×C11C2×D414yes—
163C22×C4×C11C2×D414yes—
164C22×C4×C11C2412yes—
165C22×C4×C11C2411yescharacteristic
166C22×Dic11—22no—
167C22×Dic11—22no—
168C2×Dic22—22no—
169C2×Dic22—24no—
170C2×Dic22—24no—
171C2×Dic22—24no—
172C2×Dic22—44no—
173C2×Dic22C2414yes—
174C11×C4⋊C4—24no—
175C11×C4⋊C4—24no—
176C11×C4⋊C4—24no—
177C11×C4⋊C4—24no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4C2412yes—
181C11×C4⋊C4C2412yes—
182C11×C22⋊C4—24no—
183C11×C22⋊C4—24no—
184C11×C22⋊C4—24no—
185C11×C22⋊C4—24no—
186C11×C22⋊C4—24no—
187C42×C11—24no—
188C42×C11C2×D412yes—
189C42×C11C2×D414yes—
190C42×C11C2×D412yes—
191C42×C11C2×D414yes—
192C42×C11C2412yes—
193C42×C11C2412yes—
194C22⋊Dic11—28no—
195#4326—216no—
196#4324—216no—
197C4⋊Dic11—22no—
198C4⋊Dic11—24no—
199C4⋊Dic11—24no—
200C4⋊Dic11—24no—
201C4⋊Dic11C2414yes—
202Dic11⋊C4—28no—
203Dic11⋊C4—28no—
204C4×Dic11—28no—
205C2×C11⋊C8—216no—
206C2×C11⋊C8—24no—
207C2×C11⋊C8#4118yes—
208C2×C11⋊C8C2414yes—
209C2×C11⋊C8C2414yes—
210C2×#533—111no—
211C2×#529D1111yescharacteristic
212#3181—1116no—
213C2×#501—111no—
214C2×#497—111no—
215C2×#491—111no—
216C2×#489—111no—
217C2×#467—112no—
218C2×#465—112no—
219C2×#441—112no—
220C2×#440—112no—
221C22×#97—111no—
222C23×C11—22no—
223C23×C11—22no—
224C23×C11—22no—
225C23×C11—42no—
226C23×C11—42no—
227C23×C11—42no—
228C23×C11#13714yes—
229C23×C11C22×D412yes—
230C23×C11C22×D411yescharacteristic
231Q8×C11—24no—
232Q8×C11—42no—
233D4×C11—24no—
234D4×C11—48no—
235D4×C11—42no—
236C2×C4×C11—22no—
237C2×C4×C11—28no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11—22no—
242C2×C4×C11—24no—
243C2×C4×C11—24no—
244C2×C4×C11—22no—
245C2×C4×C11—22no—
246C2×C4×C11—22no—
247C2×C4×C11—44no—
248C2×C4×C11—48no—
249C2×C4×C11—42no—
250C2×C4×C11—42no—
251C2×C4×C11—42no—
252C2×C4×C11C22×D412yes—
253C2×C4×C11C22×D412yes—
254C2×C4×C11C22×D412yes—
255C2×C4×C11C22×D412yes—
256C2×C4×C11C22×D412yes—
257C2×C4×C11C22×D411yescharacteristic
258C2×C4×C11C2×#4114yes—
259C2×C4×C11C2511yescharacteristic
260C2×Dic11—24no—
261C2×Dic11—24no—
262C2×Dic11—44no—
263C2×Dic11—44no—
264Dic22—24no—
265Dic22—24no—
266Dic22—48no—
267Dic22—44no—
268C11⋊C8—24no—
269C11⋊C8C2×#4118yes—
270C22×Q16—112no—
271C22×SD16—112no—
272C23×C8—112no—
273#533—118no—
274#533—224no—
275C2×C4⋊Q8—111no—
276C2×C4⋊Q8—111no—
277#529—24no—
278#529C2×D1118yes—
279C2×#126—21no—
280C2×#125—221no—
281C2×#125C2×D1111yescharacteristic
282C2×#124C2×D1111yescharacteristic
283C2×#123—21no—
284C2×C22⋊Q8—112no—
285C2×C22⋊Q8—221no—
286C2×C22⋊Q8C2×D1111yescharacteristic
287C2×#121C2×D1111yescharacteristic
288C2×C4×Q8—112no—
289C2×C4×Q8—221no—
290C2×C4×Q8C2×D1111yescharacteristic
291C2×C4×D4—21no—
292C2×C4×D4C2×D1111yescharacteristic
293C2×#117—21no—
294C2×#117—221no—
295C22×C42C2×D1111yescharacteristic
296#501—118no—
297#497—118no—
298#491—118no—
299#489—118no—
300#467—1116no—
301#465—1116no—
302#441—1116no—
303#440—1116no—
304C2×#107—112no—
305C2×#106—112no—
306C2×#103—112no—
307C2×#103—112no—
308C2×#103—112no—
309C2×#102—112no—
310C2×#97—111no—
311C2×#97—111no—
312C2×#97—112no—
313C2×#97—118no—
314C22×C11—28no—
315C22×C11—22no—
316C22×C11—22no—
317C22×C11—42no—
318C22×C11—42no—
319C22×C11—42no—
320C22×C11—84no—
321C22×C11#53212yes—
322C22×C11C2×#13714yes—
323C22×C11C2×#13712yes—
324C22×C11#57512yes—
325C22×C11C23×D411yescharacteristic
326C4×C11—22no—
327C4×C11—22no—
328C4×C11—22no—
329C4×C11—22no—
330C4×C11—22no—
331C4×C11—42no—
332C4×C11—42no—
333C4×C11—42no—
334C4×C11#53212yes—
335C4×C11C22×#4112yes—
336Dic11—44no—
337Dic11—44no—
338C22×Q8—112no—
339C22×Q8—221no—
340C22×Q8C22×D1111yescharacteristic
341C22×D4—21no—
342C22×D4C22×D1111yescharacteristic
343C23×C4—21no—
344C23×C4C22⋊D1111yescharacteristic
345C23×C4C22⋊D1111yescharacteristic
346C23×C4C22×D1111yescharacteristic
347C2×Q16—118no—
348C2×Q16—228no—
349C2×SD16—118no—
350C2×SD16—228no—
351C22×C8—112no—
352C22×C8—112no—
353C22×C8—118no—
354C22×C8—228no—
355C4⋊Q8—114no—
356C4⋊Q8—114no—
357C4⋊Q8—222no—
358C4⋊Q8—222no—
359#126—28no—
360#125—22no—
361#125—228no—
362#125C22×D1114yes—
363#124—22no—
364#124C22×D1114yes—
365#123—28no—
366C22⋊Q8—22no—
367C22⋊Q8—118no—
368C22⋊Q8—224no—
369C22⋊Q8—228no—
370C22⋊Q8C22×D1114yes—
371#121—22no—
372#121C22×D1114yes—
373C4×Q8—22no—
374C4×Q8—118no—
375C4×Q8—224no—
376C4×Q8—228no—
377C4×Q8C22×D1114yes—
378C4×D4—28no—
379C4×D4—22no—
380C4×D4C22×D1114yes—
381#117—28no—
382#117—228no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—112no—
388C2×C4⋊C4—221no—
389C2×C4⋊C4—221no—
390C2×C4⋊C4—222no—
391C2×C4⋊C4—222no—
392C2×C4⋊C4—221no—
393C2×C4⋊C4C22×D1111yescharacteristic
394C2×C4⋊C4C22×D1111yescharacteristic
395C2×C22⋊C4—21no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—21no—
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—222no—
401C2×C42—21no—
402C2×C42—222no—
403C2×C42C22⋊D1111yescharacteristic
404C2×C42C22⋊D1111yescharacteristic
405C2×C42C22⋊D1114yes—
406C2×C42C22×D1111yescharacteristic
407C2×C42C22×D1111yescharacteristic
408C2×C42C22×D1114yes—
409#107—118no—
410#106—118no—
411#103—118no—
412#103—118no—
413#103—118no—
414#102—118no—
415#97—118no—
416#97—114no—
417#97—114no—
418C2×C11—24no—
419C2×C11—82no—
420C2×C11#318114yescomplemented
421C2×C11C2×#53211yescharacteristic
422C2×C11C22×#13711yescharacteristic
423C2×C11C2×#57511yescharacteristic
424C24—21no—
425C24C2×C22⋊D1111yescharacteristic
426C2×Q8—21no—
427C2×Q8—24no—
428C2×Q8—114no—
429C2×Q8—224no—
430C2×Q8—222no—
431C2×Q8—224no—
432C2×Q8—224no—
433C2×Q8—444no—
434C2×Q8C23×D1112yes—
435C2×D4—24no—
436C2×D4—24no—
437C2×D4—21no—
438C2×D4—44no—
439C2×D4C23×D1112yes—
440C22×C4—24no—
441C22×C4—24no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—24no—
446C22×C4—42no—
447C22×C4—44no—
448C22×C4—222no—
449C22×C4—222no—
450C22×C4C2×C22⋊D1114yes—
451C22×C4C2×C22⋊D1112yes—
452C22×C4C2×C22⋊D1111yescharacteristic
453C22×C4C2×C22⋊D1111yescharacteristic
454C22×C4C2×C22⋊D1111yescharacteristic
455C22×C4C2×C22⋊D1111yescharacteristic
456C22×C4C2×C22⋊D1111yescharacteristic
457C22×C4C2×C22⋊D1114yes—
458C22×C4C23×D1112yes—
459C22×C4C23×D1111yescharacteristic
460Q16—2216no—
461SD16—2216no—
462C2×C8—118no—
463C2×C8—114no—
464C2×C8—114no—
465C2×C8—2216no—
466C2×C8—224no—
467C4⋊C4—24no—
468C4⋊C4—24no—
469C4⋊C4—24no—
470C4⋊C4—24no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—114no—
474C4⋊C4—222no—
475C4⋊C4—224no—
476C4⋊C4—224no—
477C4⋊C4—228no—
478C4⋊C4—228no—
479C4⋊C4—224no—
480C4⋊C4C23×D1112yes—
481C4⋊C4C23×D1112yes—
482C22⋊C4—24no—
483C22⋊C4—24no—
484C22⋊C4—24no—
485C22⋊C4—24no—
486C22⋊C4—24no—
487C22⋊C4—228no—
488C42—24no—
489C42—228no—
490C42C2×C22⋊D1114yes—
491C42C2×C22⋊D1112yes—
492C42C2×C22⋊D1114yes—
493C42C2×C22⋊D1112yes—
494C42C23×D1112yes—
495C42C23×D1112yes—
496C11C2×#318111yescharacteristic, complemented, Sylow
497C23—22no—
498C23—22no—
499C23—22no—
500C23—42no—
501C23—42no—
502C23—42no—
503C23#6700414yes—
504C23C22×C22⋊D1112yes—
505C23C22×C22⋊D1111yescharacteristic
506Q8—24no—
507Q8—42no—
508Q8—224no—
509Q8—224no—
510Q8—448no—
511Q8—444no—
512D4—24no—
513D4—48no—
514D4—42no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—28no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—24no—
522C2×C4—24no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—44no—
527C2×C4—48no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—224no—
532C2×C4—224no—
533C2×C4—444no—
534C2×C4—444no—
535C2×C4#41×D1114yes—
536C2×C4C22×C22⋊D1112yes—
537C2×C4C22×C22⋊D1112yes—
538C2×C4C22×C22⋊D1112yes—
539C2×C4C22×C22⋊D1112yes—
540C2×C4C22×C22⋊D1112yes—
541C2×C4C22×C22⋊D1111yescharacteristic
542C2×C4C24×D1111yescharacteristic
543C8—118no—
544C8—224no—
545C22—28no—
546C22—22no—
547C22—22no—
548C22—42no—
549C22—42no—
550C22—42no—
551C22—84no—
552C22#1062335312yes—
553C22C2×#6700414yes—
554C22C2×#6700412yes—
555C22#1062336312yes—
556C22C23×C22⋊D1111yescharacteristic
557C4—22no—
558C4—22no—
559C4—22no—
560C4—22no—
561C4—22no—
562C4—42no—
563C4—42no—
564C4—42no—
565C4—444no—
566C4—444no—
567C4#1062336312yes—
568C4C2×#41×D1112yes—
569C2—24no—
570C2—82no—
571C2#1307932614yesdirect product factor
572C2C2×#1062336311yescharacteristic
573C2C22×#6700411yescharacteristic
574C2C2×#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×#3181
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. C2×#10623001C2semidirect
2. #13079326C2direct (N × H)
3. C2×#10622678C2semidirect
4. C2×#10622673C2semidirect
5. C2×#10622682C2semidirect
6. C2×#10622668C2semidirect
7. C2×#10622664C2semidirect
9. C2×#10622643C2semidirect
10. C2×#10622631C2semidirect
11. C22×#66867C2semidirect
33. #10623001C22semidirect
41. #10622682C22semidirect
42. #10622678C22semidirect
43. #10622673C22semidirect
44. #10622668C22semidirect
45. #10622664C22semidirect
47. #10622643C22semidirect
48. #10622631C22semidirect
56. C2×#66867C22semidirect
420. C2×C11#3181semidirect
496. C11C2×#3181semidirect
571. C2#13079326direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230012
#130793262
C2×#106226782
C2×#106226732
C2×#106226822
C2×#106226682
C2×#106226642
C2×#106226542
C2×#106226432
C2×#106226312
C22×#668672
C2×C11×#5292
C2×#318111