Finite Group Databasebeta

← C2×#13067126 #14720921

Subgroups — C2×#13067126 #14720921

Order 2816.

1130 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623153C211yesmaximal, characteristic
2C2×#10622332C211yesmaximal, characteristic
3C2×#10622261C211yesmaximal, characteristic
4#13067126C218yesmaximal, direct product factor
5C2×#10622105C211yesmaximal, characteristic
6C2×#10622176C211yesmaximal, characteristic
7C2×#10622090C211yesmaximal, characteristic
8C2×C11×#328C211yesmaximal, characteristic
9C2×C11×C22⋊Q8C2211yescharacteristic
10C2×Q8×Dic11C411yescharacteristic, complemented
11C2×#66997C411yescharacteristic, complemented
12C2×#66977C2211yescharacteristic
13C22×C4×Dic11—21no—
14C22×C4×Dic11C2211yescharacteristic
15#10623153—22no—
16#10623153—22no—
17#10623153C414yescomplemented
18#10623153C2214yes—
19C2×#66942—21no—
20C2×#66941C411yescharacteristic, complemented
21C2×#66940—21no—
22C2×#66940C411yescharacteristic, complemented
23C2×#66931—21no—
24C2×#66930—21no—
25C2×C11×C22⋊C8C2211yescharacteristic
26C2×C11×#95C2211yescharacteristic
27C2×C11⋊#95—21no—
28C2×C11⋊#95C2211yescharacteristic
29C2×C22⋊(C11⋊C8)C2211yescharacteristic
30C2×#66879—21no—
31C2×Dic11⋊C8—21no—
32#10622332—22no—
33#10622332C2214yes—
34#10622261—22no—
35#10622261C2214yes—
36C11×#328C2214yes—
37#10622176C2214yes—
38#10622105C2214yes—
39#10622090C2214yes—
40C22×Q8×C11C2×C411yescharacteristic
41C23×C4×C11—21no—
42C23×C4×C11C2311yescharacteristic
43C23×Dic11—21no—
44C23×Dic11D411yescharacteristic
45C23×Dic11D411yescharacteristic
46C22×Dic22—21no—
47C22×Dic22C2×C411yescharacteristic
48C22×C8×C11—21no—
49C11×C22⋊Q8—21no—
50C11×C22⋊Q8—21no—
51C11×C22⋊Q8C2×C412yes—
52C11×C22⋊Q8C2312yes—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4C2×C411yescharacteristic
55C2×C11×C22⋊C4—21no—
56C2×C22⋊Dic11—21no—
57Q8×Dic11—22no—
58Q8×Dic11C2×C414yescomplemented
59#66997—22no—
60#66997C2×C414yescomplemented
61C2×C4⋊Dic11—21no—
62C2×C4⋊Dic11C2×C411yescharacteristic
63#66977—21no—
64#66977—21no—
65#66977C2×C412yes—
66#66977C2312yes—
67C2×Dic11⋊C4—21no—
68C2×Dic11⋊C4—21no—
69C2×Dic11⋊C4—21no—
70C2×Dic11⋊C4—21no—
71C2×Dic11⋊C4—21no—
72C2×C4×Dic11—28no—
73C2×C4×Dic11—21no—
74C2×C4×Dic11—21no—
75C2×C4×Dic11—24no—
76C2×C4×Dic11C2×C411yescharacteristic
77C2×C4×Dic11C2×C411yescharacteristic
78C2×C4×Dic11C2×C412yes—
79C2×C4×Dic11D412yes—
80C2×C4×Dic11D411yescharacteristic
81C2×C4×Dic11D411yescharacteristic
82C2×C4×Dic11D412yes—
83C2×C4×Dic11C2312yes—
84C22×C11⋊C8—21no—
85#66942—24no—
86#66942—24no—
87#66941—22no—
88#66941C2×C414yescomplemented
89#66940—24no—
90#66940—22no—
91#66940—24no—
92#66940C2×C414yescomplemented
93#66931—24no—
94#66931—24no—
95#66930—24no—
96#66930—24no—
97C11×C22⋊C8—21no—
98C11×C22⋊C8C2312yes—
99C11×#95—21no—
100C11×#95C2312yes—
101C11⋊#95—21no—
102C11⋊#95—24no—
103C11⋊#95C2312yes—
104C22⋊(C11⋊C8)—21no—
105C22⋊(C11⋊C8)C2312yes—
106#66879—24no—
107Dic11⋊C8—24no—
108C2×#1506—111nomaximal, Sylow
109C24×C11C2×D411yescharacteristic
110C2×Q8×C11—21no—
111C2×Q8×C11—42no—
112C2×Q8×C11C22×C412yes—
113C22×C4×C11—24no—
114C22×C4×C11—21no—
115C22×C4×C11—21no—
116C22×C4×C11—22no—
117C22×C4×C11—42no—
118C22×C4×C11—42no—
119C22×C4×C11—42no—
120C22×C4×C11C22×C411yescharacteristic
121C22×C4×C11C22×C411yescharacteristic
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2411yescharacteristic
126C22×Dic11—24no—
127C22×Dic11—24no—
128C22×Dic11—21no—
129C22×Dic11—21no—
130C22×Dic11—22no—
131C22×Dic11—22no—
132C22×Dic11—22no—
133C22×Dic11—42no—
134C22×Dic11—42no—
135C22×Dic11C22⋊C412yes—
136C22×Dic11C22⋊C412yes—
137C22×Dic11C22⋊C411yescharacteristic
138C22×Dic11C22⋊C411yescharacteristic
139C22×Dic11C22⋊C411yescharacteristic
140C22×Dic11C22⋊C411yescharacteristic
141C22×Dic11C2×D412yes—
142C22×Dic11C2×D412yes—
143C2×Dic22—24no—
144C2×Dic22—21no—
145C2×Dic22—42no—
146C2×Dic22—44no—
147C2×Dic22C22×C412yes—
148C2×C8×C11—22no—
149C2×C8×C11—42no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—22no—
153C11×C4⋊C4C22×C412yes—
154C11×C22⋊C4—22no—
155C11×C22⋊C4—22no—
156C22⋊Dic11—22no—
157C22⋊Dic11—22no—
158C4⋊Dic11—24no—
159C4⋊Dic11—21no—
160C4⋊Dic11C22×C412yes—
161Dic11⋊C4—24no—
162Dic11⋊C4—24no—
163Dic11⋊C4—24no—
164Dic11⋊C4—24no—
165Dic11⋊C4—22no—
166Dic11⋊C4—22no—
167C4×Dic11—216no—
168C4×Dic11—24no—
169C4×Dic11—24no—
170C4×Dic11C22⋊C412yes—
171C4×Dic11C22⋊C412yes—
172C4×Dic11C22⋊C412yes—
173C4×Dic11C22⋊C412yes—
174C4×Dic11C22×C412yes—
175C4×Dic11C22×C412yes—
176C4×Dic11C2×D412yes—
177C4×Dic11C2×D412yes—
178C2×C11⋊C8—22no—
179C2×C11⋊C8—42no—
180C2×#533—111no—
181C2×#432—111no—
182C2×#376—111no—
183#1506—118no—
184C2×#328—111no—
185C2×#328—111no—
186C2×#328—111no—
187C2×#328D1111yescharacteristic
188C23×C11—22no—
189C23×C11—22no—
190C23×C11C2×C22⋊C411yescharacteristic
191C23×C11C2×C22⋊C411yescharacteristic
192C23×C11#13712yes—
193C23×C11#13712yes—
194C23×C11C22×D411yescharacteristic
195Q8×C11—42no—
196Q8×C11—42no—
197C2×C4×C11—22no—
198C2×C4×C11—22no—
199C2×C4×C11—24no—
200C2×C4×C11—22no—
201C2×C4×C11—22no—
202C2×C4×C11—41no—
203C2×C4×C11—41no—
204C2×C4×C11—41no—
205C2×C4×C11—41no—
206C2×C4×C11—42no—
207C2×C4×C11—48no—
208C2×C4×C11—42no—
209C2×C4×C11—42no—
210C2×C4×C11—42no—
211C2×C4×C11C2×C22⋊C411yescharacteristic
212C2×C4×C11C2×C22⋊C411yescharacteristic
213C2×C4×C11C23×C411yescharacteristic
214C2×C4×C11C22×D411yescharacteristic
215C2×Dic11—22no—
216C2×Dic11—22no—
217C2×Dic11—24no—
218C2×Dic11—22no—
219C2×Dic11—22no—
220C2×Dic11—22no—
221C2×Dic11—24no—
222C2×Dic11—24no—
223C2×Dic11—24no—
224C2×Dic11—22no—
225C2×Dic11—22no—
226C2×Dic11—42no—
227C2×Dic11—48no—
228C2×Dic11—42no—
229C2×Dic11—42no—
230C2×Dic11—42no—
231C2×Dic11#10414yes—
232C2×Dic11C2×C22⋊C412yes—
233C2×Dic11C2×C22⋊C412yes—
234C2×Dic11C2×C22⋊C412yes—
235C2×Dic11C2×C22⋊C412yes—
236Dic22—42no—
237Dic22—48no—
238Dic22—42no—
239C8×C11—42no—
240C11⋊C8—42no—
241#533—114no—
242#533—114no—
243#533—222no—
244#533—222no—
245C2×C4⋊Q8—111no—
246C2×C4⋊Q8—111no—
247C2×#125—221no—
248C2×C22⋊Q8—111no—
249C2×C22⋊Q8—221no—
250C2×C22⋊Q8C2×D1111yescharacteristic
251C2×C4×Q8—111no—
252C2×C4×Q8—111no—
253C2×C4×Q8—221no—
254C2×#117—221no—
255C22×C42—111no—
256C22×C42—221no—
257#432—114no—
258#432—222no—
259C2×C4⋊C8—221no—
260C2×C22⋊C8—111no—
261C2×C22⋊C8C2×D1111yescharacteristic
262C2×#97—221no—
263#376—114no—
264#376—222no—
265C2×#95—111no—
266C2×#95—221no—
267C2×#95C2×D1111yescharacteristic
268#328—114no—
269#328—114no—
270#328—114no—
271#328C2×D1114yes—
272C22×C11—21no—
273C22×C11—21no—
274C22×C11—21no—
275C22×C11—21no—
276C22×C11—24no—
277C22×C11—24no—
278C22×C11#41012yes—
279C22×C11#41912yes—
280C22×C11#41912yes—
281C22×C11C2×#10412yes—
282C22×C11C22×C22⋊C411yescharacteristic
283C22×C11C2×#13711yescharacteristic
284C22×C11C2×#13711yescharacteristic
285C4×C11—21no—
286C4×C11—21no—
287C4×C11—21no—
288C4×C11—21no—
289C4×C11—44no—
290C4×C11—42no—
291C4×C11—42no—
292Dic11—22no—
293Dic11—22no—
294Dic11—22no—
295Dic11—44no—
296Dic11—42no—
297Dic11—42no—
298Dic11C2×#10414yes—
299C22×Q8—111no—
300C22×Q8—221no—
301C22×Q8C4×D1111yescharacteristic
302C23×C4—21no—
303C23×C4—111no—
304C23×C4—111no—
305C23×C4—221no—
306C23×C4C22×D1111yescharacteristic
307C22×C8—21no—
308C22×C8—221no—
309C4⋊Q8—114no—
310C4⋊Q8—114no—
311C4⋊Q8—222no—
312C4⋊Q8—222no—
313#125—224no—
314#125—224no—
315C22⋊Q8—21no—
316C22⋊Q8—21no—
317C22⋊Q8—112no—
318C22⋊Q8—112no—
319C22⋊Q8—224no—
320C22⋊Q8—224no—
321C22⋊Q8—221no—
322C22⋊Q8—221no—
323C22⋊Q8C4×D1112yes—
324C22⋊Q8C22×D1112yes—
325C4×Q8—114no—
326C4×Q8—114no—
327C4×Q8—222no—
328C4×Q8—224no—
329C4×Q8—224no—
330C4×Q8—222no—
331#117—224no—
332#117—224no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—111no—
335C2×C4⋊C4—221no—
336C2×C4⋊C4—221no—
337C2×C4⋊C4—221no—
338C2×C4⋊C4—221no—
339C2×C4⋊C4—221no—
340C2×C4⋊C4—221no—
341C2×C4⋊C4C4×D1111yescharacteristic
342C2×C22⋊C4—21no—
343C2×C22⋊C4—221no—
344C2×C42—111no—
345C2×C42—111no—
346C2×C42—112no—
347C2×C42—111no—
348C2×C42—111no—
349C2×C42—112no—
350C2×C42—112no—
351C2×C42—112no—
352C2×C42—221no—
353C2×C42—221no—
354C2×C42—224no—
355C2×C42—228no—
356C4⋊C8—224no—
357C22⋊C8—21no—
358C22⋊C8—112no—
359C22⋊C8—221no—
360C22⋊C8C22×D1112yes—
361#97—224no—
362#95—21no—
363#95—112no—
364#95—224no—
365#95—221no—
366#95C22×D1112yes—
367C2×C11—21no—
368C2×C11—21no—
369C2×C11—22no—
370C2×C11#150614yescomplemented
371C2×C11C2×#41011yescharacteristic
372C2×C11C2×#41911yescharacteristic
373C2×C11C22×#10411yescharacteristic
374C24D4×D1111yescharacteristic
375C2×Q8—21no—
376C2×Q8—42no—
377C2×Q8—112no—
378C2×Q8—224no—
379C2×Q8—221no—
380C2×Q8—442no—
381C2×Q8—444no—
382C2×Q8C2×C4×D1112yes—
383C22×C4—24no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—22no—
387C22×C4—42no—
388C22×C4—42no—
389C22×C4—42no—
390C22×C4—111no—
391C22×C4—112no—
392C22×C4—112no—
393C22×C4—111no—
394C22×C4—111no—
395C22×C4—111no—
396C22×C4—112no—
397C22×C4—112no—
398C22×C4—224no—
399C22×C4—222no—
400C22×C4—222no—
401C22×C4—224no—
402C22×C4—221no—
403C22×C4—221no—
404C22×C4—222no—
405C22×C4—442no—
406C22×C4—442no—
407C22×C4C2×C4×D1111yescharacteristic
408C22×C4C2×C4×D1111yescharacteristic
409C22×C4D4×D1111yescharacteristic
410C22×C4D4×D1111yescharacteristic
411C22×C4D4×D1111yescharacteristic
412C22×C4C23×D1111yescharacteristic
413C2×C8—22no—
414C2×C8—42no—
415C2×C8—222no—
416C2×C8—442no—
417C4⋊C4—22no—
418C4⋊C4—21no—
419C4⋊C4—22no—
420C4⋊C4—112no—
421C4⋊C4—224no—
422C4⋊C4—224no—
423C4⋊C4—224no—
424C4⋊C4—224no—
425C4⋊C4—224no—
426C4⋊C4—221no—
427C4⋊C4—222no—
428C4⋊C4—222no—
429C4⋊C4C2×C4×D1112yes—
430C22⋊C4—22no—
431C22⋊C4—22no—
432C22⋊C4—222no—
433C22⋊C4—222no—
434C42—112no—
435C42—112no—
436C42—112no—
437C42—112no—
438C42—112no—
439C42—112no—
440C42—112no—
441C42—112no—
442C42—224no—
443C42—224no—
444C42—2216no—
445C11C2×#150611yescharacteristic, complemented, Sylow
446C23—22no—
447C23—22no—
448C23C22⋊C4×D1111yescharacteristic
449C23C22⋊C4×D1111yescharacteristic
450C23#6696812yes—
451C23#6697112yes—
452C23C2×D4×D1111yescharacteristic
453Q8—42no—
454Q8—42no—
455Q8—442no—
456Q8—442no—
457Q8—448no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—24no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—42no—
468C2×C4—48no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—42no—
472C2×C4—112no—
473C2×C4—114no—
474C2×C4—112no—
475C2×C4—112no—
476C2×C4—112no—
477C2×C4—224no—
478C2×C4—224no—
479C2×C4—222no—
480C2×C4—222no—
481C2×C4—224no—
482C2×C4—222no—
483C2×C4—222no—
484C2×C4—222no—
485C2×C4—224no—
486C2×C4—222no—
487C2×C4—222no—
488C2×C4—442no—
489C2×C4—448no—
490C2×C4—442no—
491C2×C4—442no—
492C2×C4—442no—
493C2×C4C22⋊C4×D1111yescharacteristic
494C2×C4C22⋊C4×D1111yescharacteristic
495C2×C4C22×C4×D1111yescharacteristic
496C2×C4C2×D4×D1111yescharacteristic
497C8—42no—
498C8—442no—
499C22—21no—
500C22—21no—
501C22—24no—
502C22—24no—
503C22—21no—
504C22—21no—
505C22#1062235312yes—
506C22#1062241512yes—
507C22#1062241512yes—
508C22D11×#10412yes—
509C22C2×C22⋊C4×D1111yescharacteristic
510C22C2×#6696811yescharacteristic
511C22C2×#6697111yescharacteristic
512C4—21no—
513C4—21no—
514C4—21no—
515C4—21no—
516C4—44no—
517C4—42no—
518C4—42no—
519C4—114no—
520C4—222no—
521C4—222no—
522C4—222no—
523C4—444no—
524C4—442no—
525C4—442no—
526C2—21no—
527C2—21no—
528C2—22no—
529C2#1306712614yesdirect product factor
530C2C2×#1062235311yescharacteristic
531C2C2×#1062241511yescharacteristic
532C2C2×D11×#10411yescharacteristic
subgroupG/H
centerC23C22⋊C4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#328C2
socleC23×C11C2×C22⋊C4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenterC2×#328D11
hypocenterC11C2×#1506
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#328

Complements

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

NH ≅ G/Ntype
4. #13067126C2direct (N × H)
10. C2×Q8×Dic11C4semidirect
11. C2×#66997C4semidirect
17. #10623153C4semidirect
20. C2×#66941C4semidirect
22. C2×#66940C4semidirect
58. Q8×Dic11C2×C4semidirect
60. #66997C2×C4semidirect
88. #66941C2×C4semidirect
92. #66940C2×C4semidirect
370. C2×C11#1506semidirect
445. C11C2×#1506semidirect
529. C2#13067126direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231532
C2×#106223322
C2×#106222612
#130671262
C2×#106221052
C2×#106221762
C2×#106220902
C2×C11×#3282
C2×#150611