Finite Group Databasebeta

← C2×#13067009 #14720133

Subgroups — C2×#13067009 #14720133

Order 2816.

1282 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×Q8×D11C211yesmaximal, characteristic
2C2×#10622446C211yesmaximal, characteristic
3C2×#10622298C211yesmaximal, characteristic
4#13067009C218yesmaximal, direct product factor
5C2×#10622094C211yesmaximal, characteristic, complemented
6C2×Q8⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
7C2×#10622122C211yesmaximal, characteristic, complemented
8C2×C11×Q8⋊C8C211yesmaximal, characteristic, complemented
9C22×Q8×D11C411yescharacteristic
10C2×C4×Q8×C11C2211yescharacteristic
11C2×Q8×Dic11C411yescharacteristic
12C4×Q8×D11—22no—
13C4×Q8×D11—22no—
14C4×Q8×D11C414yes—
15C4×Q8×D11C2214yes—
16C2×C4⋊C4×D11—21no—
17C2×C4⋊C4×D11C411yescharacteristic
18C2×#66940—21no—
19C2×#66940C411yescharacteristic
20C2×C42×D11—21no—
21C2×C42×D11C2211yescharacteristic
22C2×C4×Dic22—21no—
23C2×C4×Dic22C2211yescharacteristic
24C2×C11×C4⋊C8C2211yescharacteristic
25C2×C4×C8×C11C2211yescharacteristic
26C2×(C2×D11)⋊C8—21no—
27C2×(C2×D11)⋊C8—21no—
28C2×Dic11⋊C8—21no—
29C2×C8×Dic11—21no—
30C2×C4⋊(C11⋊C8)C2211yescharacteristic
31C2×C4×C11⋊C8C2211yescharacteristic
32#10622446—22no—
33#10622446C2214yes—
34#10622298—22no—
35#10622298C2214yes—
36C11×Q8⋊C8C2214yescomplemented
37Q8⋊(C11⋊C8)C2214yescomplemented
38#10622122C2214yescomplemented
39#10622094C2214yescomplemented
40C22×Q8×C11C2×C411yescharacteristic
41C2×Q8×D11—22no—
42C2×Q8×D11—24no—
43C2×Q8×D11C818yescomplemented
44C2×Q8×D11C2×C414yes—
45C22×C4×D11—21no—
46C22×C4×D11—21no—
47C22×C4×D11C2×C411yescharacteristic
48C22×C4×D11D411yescharacteristic
49C22×C4×D11D411yescharacteristic
50C22×Dic22—21no—
51C22×Dic22C2×C411yescharacteristic
52C22×C8×C11—21no—
53C22×C8×C11—21no—
54C4×Q8×C11—21no—
55C4×Q8×C11—21no—
56C4×Q8×C11C2×C412yes—
57C4×Q8×C11C2312yes—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4C2×C411yescharacteristic
60C2×C42×C11—21no—
61C2×C42×C11C2311yescharacteristic
62Q8×Dic11—22no—
63Q8×Dic11C2×C414yes—
64C2×C4⋊Dic11—21no—
65C2×C4⋊Dic11C2×C411yescharacteristic
66C2×Dic11⋊C4—21no—
67C2×Dic11⋊C4—21no—
68C2×Dic11⋊C4—21no—
69C2×C4×Dic11—21no—
70C2×C4×Dic11—21no—
71C2×C4×Dic11—21no—
72C2×C4×Dic11C2×C411yescharacteristic
73C2×C4×Dic11D411yescharacteristic
74C2×C4×Dic11D411yescharacteristic
75C22×C11⋊C8—21no—
76C22×C11⋊C8—21no—
77C4⋊C4×D11—24no—
78C4⋊C4×D11—22no—
79C4⋊C4×D11—24no—
80C4⋊C4×D11C2×C414yes—
81#66940—24no—
82#66940—22no—
83#66940—24no—
84#66940C2×C414yes—
85C42×D11—24no—
86C42×D11—24no—
87C42×D11C2×C412yes—
88C42×D11D412yes—
89C42×D11D412yes—
90C42×D11C2312yes—
91C4×Dic22—21no—
92C4×Dic22—21no—
93C4×Dic22—24no—
94C4×Dic22—24no—
95C4×Dic22C2×C412yes—
96C4×Dic22C2312yes—
97C11×C4⋊C8—21no—
98C11×C4⋊C8C2312yes—
99C4×C8×C11—21no—
100C4×C8×C11C2312yes—
101(C2×D11)⋊C8—24no—
102(C2×D11)⋊C8—24no—
103Dic11⋊C8—24no—
104C8×Dic11—24no—
105C4⋊(C11⋊C8)—21no—
106C4⋊(C11⋊C8)C2312yes—
107C4×C11⋊C8—21no—
108C4×C11⋊C8C2312yes—
109C2×#1479—111nomaximal, Sylow
110C23×D11C22⋊C411yescharacteristic
111C2×Q8×C11—21no—
112C2×Q8×C11—22no—
113C2×Q8×C11C2×C814yes—
114C2×Q8×C11C22×C412yes—
115C22×C4×C11—21no—
116C22×C4×C11—21no—
117C22×C4×C11C22×C411yescharacteristic
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2×D411yescharacteristic
120C22×Dic11—21no—
121C22×Dic11—21no—
122C22×Dic11C22⋊C411yescharacteristic
123C22×Dic11C22⋊C411yescharacteristic
124C22×Dic11C22⋊C411yescharacteristic
125Q8×D11—216no—
126Q8×D11—28no—
127Q8×D11C2×C8116yescomplemented
128C2×C4×D11—28no—
129C2×C4×D11—24no—
130C2×C4×D11—24no—
131C2×C4×D11—22no—
132C2×C4×D11—22no—
133C2×C4×D11—42no—
134C2×C4×D11—44no—
135C2×C4×D11C22⋊C412yes—
136C2×C4×D11C22⋊C412yes—
137C2×C4×D11C22⋊C412yes—
138C2×C4×D11C2×C814yes—
139C2×C4×D11M1614yes—
140C2×C4×D11C22×C412yes—
141C2×C4×D11C2×D412yes—
142C2×C4×D11C2×D412yes—
143C2×Dic22—28no—
144C2×Dic22—24no—
145C2×Dic22—21no—
146C2×Dic22—22no—
147C2×Dic22C2×C814yes—
148C2×Dic22C22×C412yes—
149C2×C8×C11—22no—
150C2×C8×C11—22no—
151C2×C8×C11—42no—
152C2×C8×C11—42no—
153C11×C4⋊C4—22no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—22no—
156C11×C4⋊C4C22×C412yes—
157C42×C11—22no—
158C42×C11—22no—
159C42×C11C22×C411yescharacteristic
160C42×C11C2×D411yescharacteristic
161C42×C11C2×D411yescharacteristic
162C42×C11C2411yescharacteristic
163C4⋊Dic11—24no—
164C4⋊Dic11—21no—
165C4⋊Dic11C22×C412yes—
166Dic11⋊C4—24no—
167Dic11⋊C4—24no—
168Dic11⋊C4—22no—
169Dic11⋊C4—22no—
170C4×Dic11—24no—
171C4×Dic11—24no—
172C4×Dic11—22no—
173C4×Dic11—22no—
174C4×Dic11C22⋊C412yes—
175C4×Dic11C22⋊C412yes—
176C4×Dic11C22⋊C412yes—
177C4×Dic11C22×C412yes—
178C4×Dic11C2×D412yes—
179C4×Dic11C2×D412yes—
180C2×C11⋊C8—22no—
181C2×C11⋊C8—22no—
182C2×C11⋊C8—42no—
183C2×C11⋊C8—42no—
184C22×C4×Q8—111no—
185C2×#431—111no—
186C2×#431—111no—
187#1479—118no—
188C2×Q8⋊C8—111no—
189C2×Q8⋊C8—111no—
190C2×Q8⋊C8—111no—
191C2×Q8⋊C8D1111yescharacteristic, complemented
192C23×C11C2×C22⋊C411yescharacteristic
193C22×D11—22no—
194C22×D11—22no—
195C22×D11C22⋊C814yes—
196C22×D11C2×C22⋊C412yes—
197Q8×C11—22no—
198Q8×C11—24no—
199Q8×C11C22×C814yes—
200C2×C4×C11—22no—
201C2×C4×C11—24no—
202C2×C4×C11—22no—
203C2×C4×C11—22no—
204C2×C4×C11—42no—
205C2×C4×C11C2×C22⋊C411yescharacteristic
206C2×C4×C11C2×C22⋊C411yescharacteristic
207C2×C4×C11C2×C22⋊C411yescharacteristic
208C2×C4×C11C22×C812yes—
209C2×C4×C11C2×M1612yes—
210C2×C4×C11#13712yes—
211C2×C4×C11#13712yes—
212C2×C4×C11C23×C411yescharacteristic
213C2×C4×C11C22×D411yescharacteristic
214C2×C4×C11C22×D411yescharacteristic
215C2×Dic11—22no—
216C2×Dic11—24no—
217C2×Dic11—22no—
218C2×Dic11—22no—
219C2×Dic11—22no—
220C2×Dic11—42no—
221C2×Dic11C22⋊C814yes—
222C2×Dic11C2×C22⋊C412yes—
223C2×Dic11C2×C22⋊C412yes—
224C2×Dic11C2×C22⋊C412yes—
225C4×D11—216no—
226C4×D11—22no—
227C4×D11—22no—
228C4×D11—24no—
229C4×D11—42no—
230C4×D11—42no—
231C4×D11—48no—
232C4×D11C22⋊C818yes—
233C4×D11C22×C814yes—
234C4×D11C2×M1614yes—
235Dic22—22no—
236Dic22—24no—
237Dic22—216no—
238Dic22C22×C814yes—
239C8×C11—42no—
240C8×C11—42no—
241C11⋊C8—42no—
242C11⋊C8—42no—
243C23×Q8—111no—
244C2×C4×Q8—111no—
245C2×C4×Q8—114no—
246C2×C4×Q8—114no—
247C2×C4×Q8—111no—
248C2×C4×Q8—111no—
249C2×C4×Q8—221no—
250C2×C4×Q8—221no—
251C2×C4×Q8—222no—
252C2×C4×Q8—222no—
253C2×C4×Q8C2×D1111yescharacteristic
254C22×C4⋊C4—111no—
255C22×C4⋊C4—221no—
256C22×C42—111no—
257C22×C42—221no—
258#431—114no—
259#431—114no—
260#431—222no—
261#431—222no—
262C2×C4⋊C8—111no—
263C2×C4⋊C8—221no—
264C2×C4⋊C8C2×D1111yescharacteristic
265C2×C22⋊C8—221no—
266C2×C22⋊C8—221no—
267C2×C4×C8—111no—
268C2×C4×C8—221no—
269C2×C4×C8C2×D1111yescharacteristic
270Q8⋊C8—114no—
271Q8⋊C8—114no—
272Q8⋊C8—114no—
273Q8⋊C8C2×D1114yescomplemented
274C22×C11C2×C22⋊C812yes—
275C22×C11#41912yes—
276C22×C11#42112yes—
277C22×C11C22×C22⋊C411yescharacteristic
278C2×D11—22no—
279C2×D11—22no—
280C2×D11—28no—
281C2×D11C2×C22⋊C814yes—
282C4×C11—24no—
283C4×C11—21no—
284C4×C11—21no—
285C4×C11—42no—
286C4×C11C2×C22⋊C812yes—
287C4×C11#41912yes—
288C4×C11C23×C811yescharacteristic
289C4×C11C22×M1611yescharacteristic
290C4×C11C2×#13711yescharacteristic
291C4×C11C2×#13711yescharacteristic
292Dic11—24no—
293Dic11—22no—
294Dic11—22no—
295Dic11—42no—
296Dic11C2×C22⋊C814yes—
297C22×Q8—118no—
298C22×Q8—114no—
299C22×Q8—111no—
300C22×Q8—221no—
301C22×Q8—222no—
302C22×Q8—224no—
303C22×Q8C4×D1111yescharacteristic
304C23×C4—111no—
305C23×C4—111no—
306C23×C4—111no—
307C23×C4—221no—
308C23×C4—221no—
309C22×C8—21no—
310C22×C8—21no—
311C22×C8—221no—
312C22×C8—221no—
313C4×Q8—21no—
314C4×Q8—21no—
315C4×Q8—114no—
316C4×Q8—114no—
317C4×Q8—112no—
318C4×Q8—112no—
319C4×Q8—224no—
320C4×Q8—224no—
321C4×Q8—224no—
322C4×Q8—222no—
323C4×Q8—224no—
324C4×Q8—222no—
325C4×Q8—221no—
326C4×Q8—221no—
327C4×Q8C4×D1112yes—
328C4×Q8C22×D1112yes—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—111no—
331C2×C4⋊C4—114no—
332C2×C4⋊C4—222no—
333C2×C4⋊C4—224no—
334C2×C4⋊C4—224no—
335C2×C4⋊C4—221no—
336C2×C4⋊C4—221no—
337C2×C4⋊C4—221no—
338C2×C4⋊C4—221no—
339C2×C4⋊C4C4×D1111yescharacteristic
340C2×C42—21no—
341C2×C42—111no—
342C2×C42—111no—
343C2×C42—111no—
344C2×C42—112no—
345C2×C42—112no—
346C2×C42—112no—
347C2×C42—112no—
348C2×C42—224no—
349C2×C42—224no—
350C2×C42—221no—
351C2×C42—221no—
352C2×C42—221no—
353C2×C42C22×D1111yescharacteristic
354C4⋊C8—21no—
355C4⋊C8—112no—
356C4⋊C8—224no—
357C4⋊C8—221no—
358C4⋊C8C22×D1112yes—
359C22⋊C8—224no—
360C22⋊C8—224no—
361C4×C8—21no—
362C4×C8—112no—
363C4×C8—224no—
364C4×C8—221no—
365C4×C8C22×D1112yes—
366C2×C11#147914yescomplemented
367C2×C11C22×C22⋊C811yescharacteristic
368C2×C11C2×#41911yescharacteristic
369C2×C11C2×#42111yescharacteristic
370D11—24no—
371C24—111no—
372C2×Q8—21no—
373C2×Q8—22no—
374C2×Q8—1116no—
375C2×Q8—114no—
376C2×Q8—112no—
377C2×Q8—224no—
378C2×Q8—228no—
379C2×Q8—228no—
380C2×Q8—2216no—
381C2×Q8—221no—
382C2×Q8—222no—
383C2×Q8C8×D1114yes—
384C2×Q8C2×C4×D1112yes—
385C22×C4—21no—
386C22×C4—21no—
387C22×C4—111no—
388C22×C4—112no—
389C22×C4—114no—
390C22×C4—114no—
391C22×C4—112no—
392C22×C4—111no—
393C22×C4—111no—
394C22×C4—112no—
395C22×C4—112no—
396C22×C4—112no—
397C22×C4—112no—
398C22×C4—224no—
399C22×C4—228no—
400C22×C4—224no—
401C22×C4—221no—
402C22×C4—222no—
403C22×C4—222no—
404C22×C4—221no—
405C22×C4—442no—
406C22×C4—444no—
407C22×C4C2×C4×D1111yescharacteristic
408C22×C4D4×D1111yescharacteristic
409C22×C4D4×D1111yescharacteristic
410C2×C8—22no—
411C2×C8—22no—
412C2×C8—42no—
413C2×C8—42no—
414C2×C8—222no—
415C2×C8—222no—
416C2×C8—442no—
417C2×C8—442no—
418C4⋊C4—22no—
419C4⋊C4—21no—
420C4⋊C4—22no—
421C4⋊C4—112no—
422C4⋊C4—224no—
423C4⋊C4—224no—
424C4⋊C4—224no—
425C4⋊C4—221no—
426C4⋊C4—222no—
427C4⋊C4—222no—
428C4⋊C4C2×C4×D1112yes—
429C42—22no—
430C42—22no—
431C42—112no—
432C42—112no—
433C42—112no—
434C42—112no—
435C42—112no—
436C42—112no—
437C42—224no—
438C42—224no—
439C42—222no—
440C42—222no—
441C42C2×C4×D1111yescharacteristic
442C42D4×D1111yescharacteristic
443C42D4×D1111yescharacteristic
444C42C23×D1111yescharacteristic
445C11C2×#147911yescharacteristic, complemented, Sylow
446C23—112no—
447C23—114no—
448C23—222no—
449C23—222no—
450C23C22⋊C4×D1111yescharacteristic
451Q8—22no—
452Q8—24no—
453Q8—114no—
454Q8—2216no—
455Q8—222no—
456Q8—224no—
457Q8C2×C8×D1114yes—
458C2×C4—22no—
459C2×C4—24no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—42no—
463C2×C4—112no—
464C2×C4—114no—
465C2×C4—114no—
466C2×C4—114no—
467C2×C4—118no—
468C2×C4—112no—
469C2×C4—112no—
470C2×C4—2216no—
471C2×C4—222no—
472C2×C4—224no—
473C2×C4—222no—
474C2×C4—222no—
475C2×C4—222no—
476C2×C4—222no—
477C2×C4—224no—
478C2×C4—222no—
479C2×C4—442no—
480C2×C4—442no—
481C2×C4—448no—
482C2×C4—442no—
483C2×C4C22⋊C4×D1111yescharacteristic
484C2×C4C22⋊C4×D1111yescharacteristic
485C2×C4C22⋊C4×D1111yescharacteristic
486C2×C4C2×C8×D1112yes—
487C2×C4M16×D1112yes—
488C2×C4#6696812yes—
489C2×C4#6697112yes—
490C2×C4C22×C4×D1111yescharacteristic
491C2×C4C2×D4×D1111yescharacteristic
492C2×C4C2×D4×D1111yescharacteristic
493C8—42no—
494C8—42no—
495C8—442no—
496C8—442no—
497C22—114no—
498C22—228no—
499C22—222no—
500C22—222no—
501C22D11×C22⋊C812yes—
502C22#1062241512yes—
503C22#1062243412yes—
504C22C2×C22⋊C4×D1111yescharacteristic
505C4—24no—
506C4—21no—
507C4—21no—
508C4—42no—
509C4—114no—
510C4—224no—
511C4—222no—
512C4—222no—
513C4—442no—
514C4D11×C22⋊C812yes—
515C4#1062241512yes—
516C4C22×C8×D1111yescharacteristic
517C4C2×M16×D1111yescharacteristic
518C4C2×#6696811yescharacteristic
519C4C2×#6697111yescharacteristic
520C2—224no—
521C2#1306700914yesdirect product factor
522C2C2×D11×C22⋊C811yescharacteristic
523C2C2×#1062241511yescharacteristic
524C2C2×#1062243411yescharacteristic
subgroupG/H
centerC22×C4D4×D11
commutatorC4×C11C23×C8
FrattiniC42C23×D11
FittingC2×C11×Q8⋊C8C2
socleC23×C11C2×C22⋊C4
prime radicalC23×D11C22⋊C4
cosocleC42×C11C24
hypercenterC2×Q8⋊C8D11
hypocenterC11C2×#1479
LCSG ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×Q8⋊C8

Complements

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

NH ≅ G/Ntype
4. #13067009C2direct (N × H)
5. C2×#10622094C2semidirect
6. C2×Q8⋊(C11⋊C8)C2semidirect
7. C2×#10622122C2semidirect
8. C2×C11×Q8⋊C8C2semidirect
36. C11×Q8⋊C8C22semidirect
37. Q8⋊(C11⋊C8)C22semidirect
38. #10622122C22semidirect
39. #10622094C22semidirect
43. C2×Q8×D11C8semidirect
127. Q8×D11C2×C8semidirect
191. C2×Q8⋊C8D11semidirect
273. Q8⋊C8C2×D11semidirect
366. C2×C11#1479semidirect
445. C11C2×#1479semidirect
521. C2#13067009direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×Q8×D112
C2×#106224462
C2×#106222982
#130670092
C2×#106220942
C2×Q8⋊(C11⋊C8)2
C2×#106221222
C2×C11×Q8⋊C82
C2×#147911