Finite Group Databasebeta

← C2×#13067719 #14729486

Subgroups — C2×#13067719 #14729486

Order 2816.

1290 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622701C211yesmaximal, characteristic, complemented
2C2×#10622640C211yesmaximal, characteristic, complemented
3C2×#10622628C211yesmaximal, characteristic
4#13067719C218yesmaximal, direct product factor
5C2×#10622185C211yesmaximal, characteristic, complemented
6C2×Q8⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
7C2×D4⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
8C2×D4×Q8×C11C211yesmaximal, characteristic, complemented
9C23×Q8×C11—21no—
10D4×Q8×C11—22no—
11D4×Q8×C11—22no—
12D4×Q8×C11—22no—
13D4×Q8×C11C2214yescomplemented
14C2×C11×C4⋊Q8—21no—
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×C11×C22⋊Q8—21no—
17C2×C11×C22⋊Q8—22no—
18C2×C4×Q8×C11C2211yescharacteristic
19C2×C4×D4×C11—21no—
20C2×C4×D4×C11C2211yescharacteristic
21C22×#4325—21no—
22C22×#4323—21no—
23C2×#66927C2211yescharacteristic
24#10622701—22no—
25#10622701C2214yescomplemented
26#10622640—22no—
27#10622640C2214yescomplemented
28#10622628—22no—
29#10622628C2214yes—
30C2×#66873—21no—
31C2×#66873—21no—
32C2×#66873—22no—
33C2×C4⋊(C11⋊C8)C2211yescharacteristic
34C2×C4⋊(C11⋊C8)C2211yescharacteristic
35C2×C4×C11⋊C8C2211yescharacteristic
36#10622185C2214yescomplemented
37Q8⋊(C11⋊C8)C2214yescomplemented
38D4⋊(C11⋊C8)C2214yescomplemented
39C22×Q8×C11—22no—
40C22×Q8×C11—24no—
41C22×Q8×C11—24no—
42C22×Q8×C11—21no—
43C22×Q8×C11—44no—
44C22×Q8×C11—44no—
45C22×Q8×C11D411yescharacteristic
46C22×D4×C11D411yescharacteristic
47C23×C4×C11—22no—
48C23×C4×C11—21no—
49C22×D44—21no—
50C22×D44—21no—
51C22×D44—21no—
52C11×C4⋊Q8—24no—
53C11×C4⋊Q8—24no—
54C11×C4⋊Q8—21no—
55C11×C4⋊Q8—21no—
56C11×C4⋊Q8D412yes—
57C11×C4⋊Q8C2312yes—
58C11×C22⋊Q8—24no—
59C11×C22⋊Q8—28no—
60C11×C22⋊Q8—24no—
61C11×C22⋊Q8—28no—
62C4×Q8×C11—21no—
63C4×Q8×C11—21no—
64C4×Q8×C11D412yes—
65C4×Q8×C11C2312yes—
66C4×D4×C11—24no—
67C4×D4×C11—24no—
68C4×D4×C11—21no—
69C4×D4×C11—21no—
70C4×D4×C11D412yes—
71C4×D4×C11C2312yes—
72C2×C11×C4⋊C4—22no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4D411yescharacteristic
76C2×C11×C4⋊C4D411yescharacteristic
77C2×C11×C4⋊C4D412yes—
78C2×C11×C22⋊C4—22no—
79C2×C11×C22⋊C4—21no—
80C2×C42×C11—21no—
81C2×C42×C11C2311yescharacteristic
82C2×#4325—24no—
83C2×#4325—44no—
84C2×#4323—24no—
85C2×#4323—44no—
86C22×C11⋊C8—21no—
87C22×C11⋊C8—21no—
88C22×C11⋊C8—21no—
89#66927—21no—
90#66927—21no—
91#66927—21no—
92#66927C2312yes—
93#66873—24no—
94#66873—24no—
95#66873—28no—
96C4⋊(C11⋊C8)—21no—
97C4⋊(C11⋊C8)—21no—
98C4⋊(C11⋊C8)C2312yes—
99C4⋊(C11⋊C8)C2312yes—
100C4×C11⋊C8—21no—
101C4×C11⋊C8C2312yes—
102C2×#1627—111nomaximal, Sylow
103C24×C11—21no—
104C23×D11—41no—
105C2×Q8×C11—28no—
106C2×Q8×C11—21no—
107C2×Q8×C11—22no—
108C2×Q8×C11—22no—
109C2×Q8×C11—22no—
110C2×Q8×C11—48no—
111C2×Q8×C11—48no—
112C2×Q8×C11—416no—
113C2×Q8×C11—48no—
114C2×Q8×C11—42no—
115C2×Q8×C11—42no—
116C2×Q8×C11D814yescomplemented
117C2×Q8×C11C2×D412yes—
118C2×D4×C11—21no—
119C2×D4×C11—22no—
120C2×D4×C11SD1614yescomplemented
121C2×D4×C11C2×D412yes—
122C22×C4×C11—21no—
123C22×C4×C11—28no—
124C22×C4×C11—21no—
125C22×C4×C11—22no—
126C22×C4×C11—21no—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11—48no—
130C22×C4×C11—42no—
131C22×C4×C11—42no—
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2×D411yescharacteristic
135C2×D44—22no—
136C2×D44—22no—
137C2×D44—22no—
138C2×D44—44no—
139C2×D44—41no—
140C2×D44—41no—
141C2×D44—41no—
142C2×D44—42no—
143C2×D44—42no—
144C2×D44—42no—
145C2×D44—42no—
146C11×C4⋊C4—28no—
147C11×C4⋊C4—22no—
148C11×C4⋊C4—22no—
149C11×C4⋊C4—21no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—22no—
153C11×C4⋊C4—22no—
154C11×C4⋊C4C2×D412yes—
155C11×C4⋊C4C2×D412yes—
156C11×C4⋊C4C2×D414yes—
157C11×C22⋊C4—28no—
158C11×C22⋊C4—22no—
159C11×C22⋊C4—22no—
160C42×C11—22no—
161C42×C11—22no—
162C42×C11C2×D411yescharacteristic
163C42×C11C2×D411yescharacteristic
164C42×C11C2×D411yescharacteristic
165C42×C11C2411yescharacteristic
166#4325—48no—
167#4323—48no—
168C2×C11⋊C8—22no—
169C2×C11⋊C8—22no—
170C2×C11⋊C8—22no—
171C2×C11⋊C8—42no—
172C2×C11⋊C8—42no—
173C2×C11⋊C8—42no—
174C2×D4×Q8D1111yescharacteristic, complemented
175C2×#486—111no—
176C2×#460—111no—
177C2×#459—111no—
178#1627—118no—
179C2×#332—111no—
180C2×Q8⋊C8—111no—
181C2×D4⋊C8—111no—
182C23×C11—22no—
183C23×C11—24no—
184C23×C11—42no—
185C23×C11—42no—
186C23×C11#12011yescharacteristic
187C22×D11—42no—
188C22×D11—82no—
189C22×D11—82no—
190C22×D11—82no—
191Q8×C11—22no—
192Q8×C11—24no—
193Q8×C11—416no—
194Q8×C11—42no—
195Q8×C11—42no—
196Q8×C11—44no—
197Q8×C11C2×D814yescomplemented
198D4×C11—22no—
199D4×C11—24no—
200D4×C11C2×SD1614yescomplemented
201C2×C4×C11—22no—
202C2×C4×C11—24no—
203C2×C4×C11—22no—
204C2×C4×C11—22no—
205C2×C4×C11—24no—
206C2×C4×C11—22no—
207C2×C4×C11—416no—
208C2×C4×C11—44no—
209C2×C4×C11—42no—
210C2×C4×C11—42no—
211C2×C4×C11—42no—
212C2×C4×C11—42no—
213C2×C4×C11—44no—
214C2×C4×C11#12011yescharacteristic
215C2×C4×C11#12011yescharacteristic
216C2×C4×C11#12011yescharacteristic
217C2×C4×C11C2×D812yes—
218C2×C4×C11C2×SD1612yes—
219C2×C4×C11AGL(1,ℤ/8)12yes—
220C2×C4×C11#13712yes—
221C2×C4×C11C22×D411yescharacteristic
222C2×C4×C11C22×D411yescharacteristic
223C2×C4×C11C22×D411yescharacteristic
224D44—44no—
225D44—42no—
226D44—42no—
227D44—42no—
228D44—42no—
229D44—82no—
230D44—82no—
231D44—82no—
232C11⋊C8—42no—
233C11⋊C8—42no—
234C11⋊C8—42no—
235C23×Q8—21no—
236C22×SD16—221no—
237C22×D8—221no—
238D4×Q8—22no—
239D4×Q8—22no—
240D4×Q8—22no—
241D4×Q8C2×D1114yescomplemented
242C2×C4⋊Q8—21no—
243C2×C4⋊Q8C2×D1111yescharacteristic
244C2×#127—111no—
245C2×C22⋊Q8—21no—
246C2×C22⋊Q8—22no—
247C2×C4×Q8C2×D1111yescharacteristic
248C2×C4×D4—21no—
249C2×C4×D4C2×D1111yescharacteristic
250#486—114no—
251#486—222no—
252#460—114no—
253#460—222no—
254#459—114no—
255#459—222no—
256C2×C4⋊C8—111no—
257C2×C4⋊C8—111no—
258C2×#102—222no—
259C2×#102—221no—
260C2×#102—221no—
261C2×C4×C8—111no—
262#332—114no—
263Q8⋊C8—114no—
264D4⋊C8—114no—
265C22×C11—24no—
266C22×C11—48no—
267C22×C11—42no—
268C22×C11—42no—
269C22×C11#44712yes—
270C22×C11#44812yes—
271C22×C11#45412yes—
272C22×C11C2×#12011yescharacteristic
273C2×D11—82no—
274C2×D11—82no—
275C2×D11—82no—
276C2×D11—164no—
277C4×C11—24no—
278C4×C11—21no—
279C4×C11—21no—
280C4×C11—44no—
281C4×C11—42no—
282C4×C11—42no—
283C4×C11#44712yes—
284C4×C11#44812yes—
285C4×C11C22×D811yescharacteristic
286C4×C11C22×SD1611yescharacteristic
287C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
288C4×C11C2×#13711yescharacteristic
289C22×Q8—22no—
290C22×Q8—24no—
291C22×Q8—24no—
292C22×Q8—21no—
293C22×Q8—44no—
294C22×Q8—44no—
295C22×Q8C22⋊D1111yescharacteristic
296C22×D4—221no—
297C22×D4—221no—
298C22×D4—221no—
299C22×D4C22⋊D1111yescharacteristic
300C23×C4—22no—
301C23×C4—21no—
302C2×SD16—224no—
303C2×SD16—444no—
304C2×D8—224no—
305C2×D8—444no—
306C22×C8—221no—
307C22×C8—221no—
308C22×C8—221no—
309C4⋊Q8—24no—
310C4⋊Q8—24no—
311C4⋊Q8—21no—
312C4⋊Q8—21no—
313C4⋊Q8C22⋊D1112yes—
314C4⋊Q8C22×D1112yes—
315#127—112no—
316#127—221no—
317#127—221no—
318#127—221no—
319C22⋊Q8—24no—
320C22⋊Q8—28no—
321C22⋊Q8—24no—
322C22⋊Q8—28no—
323C4×Q8—21no—
324C4×Q8—21no—
325C4×Q8C22⋊D1112yes—
326C4×Q8C22×D1112yes—
327C4×D4—24no—
328C4×D4—24no—
329C4×D4—21no—
330C4×D4—21no—
331C4×D4C22⋊D1112yes—
332C4×D4C22×D1112yes—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4C22⋊D1111yescharacteristic
337C2×C4⋊C4C22⋊D1111yescharacteristic
338C2×C4⋊C4C22⋊D1112yes—
339C2×C22⋊C4—22no—
340C2×C22⋊C4—21no—
341C2×C42—21no—
342C2×C42C22×D1111yescharacteristic
343C4⋊C8—112no—
344C4⋊C8—112no—
345C4⋊C8—221no—
346C4⋊C8—221no—
347#102—224no—
348#102—224no—
349#102—228no—
350C4×C8—112no—
351C4×C8—221no—
352C2×C11—44no—
353C2×C11#162714yescomplemented
354C2×C11C2×#44711yescharacteristic
355C2×C11C2×#44811yescharacteristic
356C2×C11C2×#45411yescharacteristic
357D11—162no—
358C24—21no—
359C24—441no—
360C2×Q8—28no—
361C2×Q8—22no—
362C2×Q8—21no—
363C2×Q8—22no—
364C2×Q8—22no—
365C2×Q8—48no—
366C2×Q8—48no—
367C2×Q8—416no—
368C2×Q8—48no—
369C2×Q8—42no—
370C2×Q8—42no—
371C2×Q8#432314yescomplemented
372C2×Q8C2×C22⋊D1112yes—
373C2×D4—22no—
374C2×D4—21no—
375C2×D4—222no—
376C2×D4—222no—
377C2×D4—222no—
378C2×D4—444no—
379C2×D4—442no—
380C2×D4—442no—
381C2×D4—442no—
382C2×D4—442no—
383C2×D4—441no—
384C2×D4—441no—
385C2×D4—441no—
386C2×D4#432514yescomplemented
387C2×D4C2×C22⋊D1112yes—
388C22×C4—21no—
389C22×C4—28no—
390C22×C4—21no—
391C22×C4—22no—
392C22×C4—21no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—48no—
396C22×C4—42no—
397C22×C4—42no—
398C22×C4C2×C22⋊D1111yescharacteristic
399C22×C4C2×C22⋊D1111yescharacteristic
400C22×C4C2×C22⋊D1111yescharacteristic
401SD16—448no—
402D8—448no—
403C2×C8—222no—
404C2×C8—222no—
405C2×C8—222no—
406C2×C8—442no—
407C2×C8—442no—
408C2×C8—442no—
409C4⋊C4—28no—
410C4⋊C4—22no—
411C4⋊C4—22no—
412C4⋊C4—21no—
413C4⋊C4—21no—
414C4⋊C4—22no—
415C4⋊C4—22no—
416C4⋊C4—22no—
417C4⋊C4C2×C22⋊D1112yes—
418C4⋊C4C2×C22⋊D1112yes—
419C4⋊C4C2×C22⋊D1114yes—
420C22⋊C4—28no—
421C22⋊C4—22no—
422C22⋊C4—22no—
423C42—22no—
424C42—22no—
425C42C2×C22⋊D1111yescharacteristic
426C42C2×C22⋊D1111yescharacteristic
427C42C2×C22⋊D1111yescharacteristic
428C42C23×D1111yescharacteristic
429C11C2×#162711yescharacteristic, complemented, Sylow
430C23—24no—
431C23—22no—
432C23—42no—
433C23—42no—
434C23—442no—
435C23—882no—
436C23—882no—
437C23—882no—
438C23#6700611yescharacteristic
439Q8—22no—
440Q8—24no—
441Q8—416no—
442Q8—42no—
443Q8—42no—
444Q8—44no—
445Q8C2×#432314yescomplemented
446D4—22no—
447D4—24no—
448D4—444no—
449D4—442no—
450D4—442no—
451D4—442no—
452D4—442no—
453D4—882no—
454D4—882no—
455D4—882no—
456D4C2×#432514yescomplemented
457C2×C4—24no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—24no—
462C2×C4—22no—
463C2×C4—416no—
464C2×C4—44no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—44no—
470C2×C4C2×#432312yes—
471C2×C4#6698512yes—
472C2×C4C2×#432512yes—
473C2×C4#6699512yes—
474C2×C4#6700611yescharacteristic
475C2×C4#6700611yescharacteristic
476C2×C4#6700611yescharacteristic
477C2×C4C22×C22⋊D1111yescharacteristic
478C2×C4C22×C22⋊D1111yescharacteristic
479C2×C4C22×C22⋊D1111yescharacteristic
480C8—442no—
481C8—442no—
482C8—442no—
483C22—24no—
484C22—42no—
485C22—42no—
486C22—48no—
487C22—882no—
488C22—882no—
489C22—882no—
490C22—1764no—
491C22#1062283012yes—
492C22#1062284012yes—
493C22#1062285812yes—
494C22C2×#6700611yescharacteristic
495C4—24no—
496C4—21no—
497C4—21no—
498C4—44no—
499C4—42no—
500C4—42no—
501C4#1062283012yes—
502C4#1062284012yes—
503C4C22×#432311yescharacteristic
504C4C2×#6698511yescharacteristic
505C4C22×#432511yescharacteristic
506C4C2×#6699511yescharacteristic
507C2—44no—
508C2—1762no—
509C2#1306771914yesdirect product factor
510C2C2×#1062283011yescharacteristic
511C2C2×#1062284011yescharacteristic
512C2C2×#1062285811yescharacteristic
subgroupG/H
centerC23#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×D4×Q8×C11C2
socleC23×C11#120
prime radicalC2×#10622628C2
hypercenterC2×D4×Q8D11
hypocenterC11C2×#1627
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×D4×Q8

Complements

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

NH ≅ G/Ntype
1. C2×#10622701C2semidirect
2. C2×#10622640C2semidirect
4. #13067719C2direct (N × H)
5. C2×#10622185C2semidirect
6. C2×Q8⋊(C11⋊C8)C2semidirect
7. C2×D4⋊(C11⋊C8)C2semidirect
8. C2×D4×Q8×C11C2semidirect
13. D4×Q8×C11C22semidirect
25. #10622701C22semidirect
27. #10622640C22semidirect
36. #10622185C22semidirect
37. Q8⋊(C11⋊C8)C22semidirect
38. D4⋊(C11⋊C8)C22semidirect
116. C2×Q8×C11D8semidirect
120. C2×D4×C11SD16semidirect
174. C2×D4×Q8D11semidirect
197. Q8×C11C2×D8semidirect
200. D4×C11C2×SD16semidirect
241. D4×Q8C2×D11semidirect
353. C2×C11#1627semidirect
371. C2×Q8#4323semidirect
386. C2×D4#4325semidirect
429. C11C2×#1627semidirect
445. Q8C2×#4323semidirect
456. D4C2×#4325semidirect
509. C2#13067719direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106227012
C2×#106226402
C2×#106226282
#130677192
C2×#106221852
C2×Q8⋊(C11⋊C8)2
C2×D4⋊(C11⋊C8)2
C2×D4×Q8×C112
C2×#162711