Finite Group Databasebeta

← C2×#13066982 #14719747

Subgroups — C2×#13066982 #14719747

Order 2816.

1066 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66932C211yesmaximal, characteristic
2C2×#10622332C211yesmaximal, characteristic, complemented
3C2×#10622331C211yesmaximal, characteristic, complemented
4#13066982C218yesmaximal, direct product factor
5C2×#10622107C211yesmaximal, characteristic, complemented
6C2×#10622107C211yesmaximal, characteristic, complemented
7C2×#10622163C211yesmaximal, characteristic
8C2×C11×#323C211yesmaximal, characteristic
9C22×C11×C22⋊C4C2211yescharacteristic
10C22×C22⋊Dic11C411yescharacteristic
11C22×C22⋊Dic11C411yescharacteristic
12C22×C4⋊Dic11C411yescharacteristic
13C22×Dic11⋊C4C411yescharacteristic
14C22×Dic11⋊C4C2211yescharacteristic
15C22×C4×Dic11C2211yescharacteristic
16C2×#66932—22no—
17C2×#66932—22no—
18C2×#66932—21no—
19C2×#66932—21no—
20C2×#66932—21no—
21C2×#66932—21no—
22C2×#66932C414yes—
23C2×#66932C2214yes—
24C2×C11×C22⋊C8C2211yescharacteristic
25C2×C11×C22⋊C8C2211yescharacteristic
26C2×C22⋊(C11⋊C8)C2211yescharacteristic
27C2×C22⋊(C11⋊C8)C2211yescharacteristic
28C2×#66879—21no—
29C2×Dic11⋊C8—21no—
30C2×Dic11⋊C8—21no—
31C2×C8×Dic11—21no—
32#10622332—22no—
33#10622332C2214yescomplemented
34#10622331—22no—
35#10622331C2214yescomplemented
36C11×#323C2214yes—
37#10622163C2214yes—
38#10622107C2214yescomplemented
39#10622107C2214yescomplemented
40C25×C11C2×C411yescharacteristic
41C23×C4×C11C2×C411yescharacteristic
42C23×C4×C11C2311yescharacteristic
43C23×Dic11C2×C411yescharacteristic
44C23×Dic11C2×C411yescharacteristic
45C23×Dic11C2×C411yescharacteristic
46C23×Dic11C2×C411yescharacteristic
47C22×C8×C11—21no—
48C22×C8×C11—21no—
49C2×C11×C22⋊C4—21no—
50C2×C11×C22⋊C4—21no—
51C2×C11×C22⋊C4—21no—
52C2×C11×C22⋊C4—21no—
53C2×C11×C22⋊C4C2×C412yes—
54C2×C11×C22⋊C4C2312yes—
55C2×C22⋊Dic11—22no—
56C2×C22⋊Dic11—21no—
57C2×C22⋊Dic11—21no—
58C2×C22⋊Dic11—21no—
59C2×C22⋊Dic11—21no—
60C2×C22⋊Dic11—22no—
61C2×C22⋊Dic11C2×C414yes—
62C2×C22⋊Dic11C2×C414yes—
63C2×C4⋊Dic11—22no—
64C2×C4⋊Dic11—21no—
65C2×C4⋊Dic11—21no—
66C2×C4⋊Dic11C2×C414yes—
67C2×Dic11⋊C4—21no—
68C2×Dic11⋊C4—21no—
69C2×Dic11⋊C4—21no—
70C2×Dic11⋊C4—21no—
71C2×Dic11⋊C4—21no—
72C2×Dic11⋊C4—21no—
73C2×Dic11⋊C4—22no—
74C2×Dic11⋊C4C2×C412yes—
75C2×Dic11⋊C4C2×C414yes—
76C2×Dic11⋊C4C2312yes—
77C2×C4×Dic11C2×C412yes—
78C2×C4×Dic11D412yes—
79C2×C4×Dic11D412yes—
80C2×C4×Dic11D411yescharacteristic
81C2×C4×Dic11D411yescharacteristic
82C2×C4×Dic11D411yescharacteristic
83C2×C4×Dic11D411yescharacteristic
84C2×C4×Dic11C2312yes—
85C22×C11⋊C8—21no—
86C22×C11⋊C8—21no—
87#66932—24no—
88#66932—24no—
89#66932—24no—
90#66932—24no—
91#66932—24no—
92#66932—24no—
93#66932—24no—
94#66932—24no—
95C11×C22⋊C8—21no—
96C11×C22⋊C8—21no—
97C11×C22⋊C8C2312yes—
98C11×C22⋊C8C2312yes—
99C22⋊(C11⋊C8)—21no—
100C22⋊(C11⋊C8)—21no—
101C22⋊(C11⋊C8)C2312yes—
102C22⋊(C11⋊C8)C2312yes—
103#66879—24no—
104Dic11⋊C8—24no—
105Dic11⋊C8—24no—
106C8×Dic11—24no—
107C2×#1473—111nomaximal, Sylow
108C24×C11—21no—
109C24×C11—21no—
110C24×C11—22no—
111C24×C11—22no—
112C24×C11—42no—
113C24×C11—42no—
114C24×C11C22×C411yescharacteristic
115C24×C11C22×C412yes—
116C22×C4×C11—21no—
117C22×C4×C11—21no—
118C22×C4×C11—42no—
119C22×C4×C11—42no—
120C22×C4×C11C22×C412yes—
121C22×C4×C11C22×C411yescharacteristic
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2411yescharacteristic
127C22×Dic11—21no—
128C22×Dic11—21no—
129C22×Dic11—21no—
130C22×Dic11—21no—
131C22×Dic11—22no—
132C22×Dic11—22no—
133C22×Dic11—22no—
134C22×Dic11—22no—
135C22×Dic11—42no—
136C22×Dic11—42no—
137C22×Dic11C22⋊C411yescharacteristic
138C22×Dic11C22⋊C411yescharacteristic
139C22×Dic11C22⋊C412yes—
140C22×Dic11C22⋊C411yescharacteristic
141C22×Dic11C22⋊C411yescharacteristic
142C22×Dic11C22⋊C412yes—
143C22×Dic11C22×C412yes—
144C22×Dic11C22×C412yes—
145C22×Dic11C22×C412yes—
146C22×Dic11C22×C412yes—
147C2×C8×C11—22no—
148C2×C8×C11—22no—
149C2×C8×C11—42no—
150C2×C8×C11—42no—
151C11×C22⋊C4—22no—
152C11×C22⋊C4—22no—
153C11×C22⋊C4—22no—
154C11×C22⋊C4—22no—
155C22⋊Dic11—24no—
156C22⋊Dic11—24no—
157C22⋊Dic11—24no—
158C22⋊Dic11—24no—
159C4⋊Dic11—24no—
160C4⋊Dic11—24no—
161Dic11⋊C4—24no—
162Dic11⋊C4—24no—
163Dic11⋊C4—22no—
164Dic11⋊C4—22no—
165Dic11⋊C4—22no—
166Dic11⋊C4—22no—
167C4×Dic11C22⋊C412yes—
168C4×Dic11C22⋊C412yes—
169C4×Dic11C22⋊C412yes—
170C4×Dic11C22⋊C412yes—
171C4×Dic11C2×D412yes—
172C4×Dic11C2×D412yes—
173C4×Dic11C2×D412yes—
174C4×Dic11C2×D412yes—
175C2×C11⋊C8—22no—
176C2×C11⋊C8—22no—
177C2×C11⋊C8—42no—
178C2×C11⋊C8—42no—
179C22×#126—111no—
180C2×#432—111no—
181C2×#431—111no—
182#1473—118no—
183C2×#324—111no—
184C2×#324—111no—
185C2×#323—111no—
186C2×#323D1111yescharacteristic
187C23×C11—22no—
188C23×C11—22no—
189C23×C11—22no—
190C23×C11—22no—
191C23×C11—22no—
192C23×C11—42no—
193C23×C11—42no—
194C23×C11—42no—
195C23×C11—42no—
196C23×C11—42no—
197C23×C11—42no—
198C23×C11—42no—
199C23×C11—42no—
200C23×C11—84no—
201C23×C11—84no—
202C23×C11C2×C22⋊C411yescharacteristic
203C23×C11C2×C22⋊C411yescharacteristic
204C23×C11#13112yes—
205C23×C11#13112yes—
206C23×C11C23×C411yescharacteristic
207C2×C4×C11—22no—
208C2×C4×C11—22no—
209C2×C4×C11—22no—
210C2×C4×C11—41no—
211C2×C4×C11—41no—
212C2×C4×C11—41no—
213C2×C4×C11—41no—
214C2×C4×C11—42no—
215C2×C4×C11—42no—
216C2×C4×C11—42no—
217C2×C4×C11C2×C22⋊C411yescharacteristic
218C2×C4×C11C2×C22⋊C411yescharacteristic
219C2×C4×C11C22×D411yescharacteristic
220C2×C4×C11C22×D411yescharacteristic
221C2×Dic11—22no—
222C2×Dic11—22no—
223C2×Dic11—24no—
224C2×Dic11—22no—
225C2×Dic11—22no—
226C2×Dic11—22no—
227C2×Dic11—22no—
228C2×Dic11—22no—
229C2×Dic11—22no—
230C2×Dic11—22no—
231C2×Dic11—22no—
232C2×Dic11—42no—
233C2×Dic11—42no—
234C2×Dic11—42no—
235C2×Dic11—42no—
236C2×Dic11—42no—
237C2×Dic11—42no—
238C2×Dic11—42no—
239C2×Dic11C2×C22⋊C412yes—
240C2×Dic11C2×C22⋊C412yes—
241C2×Dic11C2×C22⋊C412yes—
242C2×Dic11C2×C22⋊C412yes—
243C8×C11—42no—
244C8×C11—42no—
245C11⋊C8—42no—
246C11⋊C8—42no—
247C2×#126—114no—
248C2×#126—114no—
249C2×#126—221no—
250C2×#126—221no—
251C2×#126—221no—
252C2×#126—221no—
253C2×#126—222no—
254C2×#126—222no—
255C22×C4⋊C4—111no—
256C22×C4⋊C4—111no—
257C22×C4⋊C4—111no—
258C22×C22⋊C4—111no—
259C22×C22⋊C4—111no—
260C22×C22⋊C4C2×D1111yescharacteristic
261C22×C42—111no—
262#432—114no—
263#432—222no—
264#431—114no—
265#431—222no—
266C2×C4⋊C8—221no—
267C2×C4⋊C8—221no—
268C2×C22⋊C8—111no—
269C2×C22⋊C8—111no—
270C2×C22⋊C8C2×D1111yescharacteristic
271C2×C22⋊C8C2×D1111yescharacteristic
272C2×#97—221no—
273C2×C4×C8—221no—
274#324—114no—
275#324—114no—
276#323—114no—
277#323C2×D1114yes—
278C22×C11—21no—
279C22×C11—21no—
280C22×C11—21no—
281C22×C11—21no—
282C22×C11—24no—
283C22×C11—24no—
284C22×C11—42no—
285C22×C11—42no—
286C22×C11—42no—
287C22×C11—82no—
288C22×C11—82no—
289C22×C11—84no—
290C22×C11—84no—
291C22×C11#40812yes—
292C22×C11#40812yes—
293C22×C11#41012yes—
294C22×C11#41312yes—
295C22×C11C22×C22⋊C411yescharacteristic
296C22×C11C2×#13111yescharacteristic
297C22×C11C2×#13111yescharacteristic
298C4×C11—21no—
299C4×C11—21no—
300C4×C11—21no—
301C4×C11—21no—
302C4×C11—42no—
303Dic11—22no—
304Dic11—22no—
305Dic11—22no—
306Dic11—22no—
307Dic11—42no—
308Dic11—42no—
309C25C4×D1111yescharacteristic
310C23×C4—111no—
311C23×C4—111no—
312C23×C4—111no—
313C23×C4—111no—
314C23×C4C4×D1111yescharacteristic
315C23×C4C22×D1111yescharacteristic
316C22×C8—21no—
317C22×C8—21no—
318C22×C8—221no—
319C22×C8—221no—
320#126—224no—
321#126—224no—
322#126—224no—
323#126—224no—
324#126—224no—
325#126—224no—
326#126—224no—
327#126—224no—
328C2×C4⋊C4—114no—
329C2×C4⋊C4—112no—
330C2×C4⋊C4—114no—
331C2×C4⋊C4—112no—
332C2×C4⋊C4—222no—
333C2×C4⋊C4—221no—
334C2×C4⋊C4—221no—
335C2×C4⋊C4—222no—
336C2×C4⋊C4—221no—
337C2×C4⋊C4—221no—
338C2×C4⋊C4—221no—
339C2×C4⋊C4—221no—
340C2×C4⋊C4—221no—
341C2×C4⋊C4—221no—
342C2×C22⋊C4—21no—
343C2×C22⋊C4—21no—
344C2×C22⋊C4—21no—
345C2×C22⋊C4—21no—
346C2×C22⋊C4—114no—
347C2×C22⋊C4—114no—
348C2×C22⋊C4—222no—
349C2×C22⋊C4—221no—
350C2×C22⋊C4—221no—
351C2×C22⋊C4—221no—
352C2×C22⋊C4—221no—
353C2×C22⋊C4—222no—
354C2×C22⋊C4C4×D1112yes—
355C2×C22⋊C4C22×D1112yes—
356C2×C42—112no—
357C2×C42—111no—
358C2×C42—111no—
359C2×C42—111no—
360C2×C42—111no—
361C2×C42—112no—
362C2×C42—112no—
363C2×C42—112no—
364C4⋊C8—224no—
365C4⋊C8—224no—
366C22⋊C8—21no—
367C22⋊C8—21no—
368C22⋊C8—112no—
369C22⋊C8—112no—
370C22⋊C8—221no—
371C22⋊C8—221no—
372C22⋊C8C22×D1112yes—
373C22⋊C8C22×D1112yes—
374#97—224no—
375C4×C8—224no—
376C2×C11—21no—
377C2×C11—21no—
378C2×C11—22no—
379C2×C11—82no—
380C2×C11#147314yescomplemented
381C2×C11C2×#40811yescharacteristic
382C2×C11C2×#41011yescharacteristic
383C2×C11C2×#41311yescharacteristic
384C24—21no—
385C24—21no—
386C24—22no—
387C24—22no—
388C24—42no—
389C24—42no—
390C24C2×C4×D1111yescharacteristic
391C24C2×C4×D1112yes—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—42no—
395C22×C4—42no—
396C22×C4—112no—
397C22×C4—111no—
398C22×C4—111no—
399C22×C4—111no—
400C22×C4—111no—
401C22×C4—112no—
402C22×C4—112no—
403C22×C4—112no—
404C22×C4—112no—
405C22×C4—112no—
406C22×C4—222no—
407C22×C4—222no—
408C22×C4—221no—
409C22×C4—221no—
410C22×C4—221no—
411C22×C4—221no—
412C22×C4—222no—
413C22×C4—222no—
414C22×C4—442no—
415C22×C4—442no—
416C22×C4C2×C4×D1112yes—
417C22×C4C2×C4×D1111yescharacteristic
418C22×C4D4×D1111yescharacteristic
419C22×C4D4×D1111yescharacteristic
420C22×C4D4×D1111yescharacteristic
421C22×C4D4×D1111yescharacteristic
422C22×C4C23×D1111yescharacteristic
423C2×C8—22no—
424C2×C8—22no—
425C2×C8—42no—
426C2×C8—42no—
427C2×C8—222no—
428C2×C8—222no—
429C2×C8—442no—
430C2×C8—442no—
431C4⋊C4—224no—
432C4⋊C4—224no—
433C4⋊C4—224no—
434C4⋊C4—224no—
435C4⋊C4—222no—
436C4⋊C4—222no—
437C4⋊C4—222no—
438C4⋊C4—222no—
439C22⋊C4—22no—
440C22⋊C4—22no—
441C22⋊C4—22no—
442C22⋊C4—22no—
443C22⋊C4—224no—
444C22⋊C4—224no—
445C22⋊C4—224no—
446C22⋊C4—224no—
447C42—112no—
448C42—112no—
449C42—112no—
450C42—112no—
451C42—112no—
452C42—112no—
453C42—112no—
454C42—112no—
455C11C2×#147311yescharacteristic, complemented, Sylow
456C23—22no—
457C23—22no—
458C23—22no—
459C23—22no—
460C23—22no—
461C23—42no—
462C23—42no—
463C23—42no—
464C23—42no—
465C23—42no—
466C23—42no—
467C23—42no—
468C23—42no—
469C23—84no—
470C23—84no—
471C23C22⋊C4×D1111yescharacteristic
472C23C22⋊C4×D1111yescharacteristic
473C23#6695412yes—
474C23#6696012yes—
475C23C22×C4×D1111yescharacteristic
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—112no—
487C2×C4—112no—
488C2×C4—112no—
489C2×C4—112no—
490C2×C4—222no—
491C2×C4—222no—
492C2×C4—224no—
493C2×C4—222no—
494C2×C4—222no—
495C2×C4—222no—
496C2×C4—222no—
497C2×C4—222no—
498C2×C4—222no—
499C2×C4—222no—
500C2×C4—222no—
501C2×C4—442no—
502C2×C4—442no—
503C2×C4—442no—
504C2×C4—442no—
505C2×C4—442no—
506C2×C4—442no—
507C2×C4—442no—
508C2×C4C22⋊C4×D1111yescharacteristic
509C2×C4C22⋊C4×D1111yescharacteristic
510C2×C4C2×D4×D1111yescharacteristic
511C2×C4C2×D4×D1111yescharacteristic
512C8—42no—
513C8—42no—
514C8—442no—
515C8—442no—
516C22—21no—
517C22—21no—
518C22—21no—
519C22—21no—
520C22—24no—
521C22—24no—
522C22—42no—
523C22—42no—
524C22—42no—
525C22—82no—
526C22—82no—
527C22—84no—
528C22—84no—
529C22#1062234012yes—
530C22#1062234012yes—
531C22#1062235312yes—
532C22#1062235812yes—
533C22C2×C22⋊C4×D1111yescharacteristic
534C22C2×#6695411yescharacteristic
535C22C2×#6696011yescharacteristic
536C4—21no—
537C4—21no—
538C4—21no—
539C4—21no—
540C4—42no—
541C4—222no—
542C4—222no—
543C4—222no—
544C4—222no—
545C4—442no—
546C4—442no—
547C2—21no—
548C2—21no—
549C2—22no—
550C2—82no—
551C2#1306698214yesdirect product factor
552C2C2×#1062234011yescharacteristic
553C2C2×#1062235311yescharacteristic
554C2C2×#1062235811yescharacteristic
subgroupG/H
centerC23C22⋊C4×D11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#323C2
socleC23×C11C2×C22⋊C4
prime radicalC25×C11C2×C4
cosocleC22×C4×C11C24
hypercenterC2×#323D11
hypocenterC11C2×#1473
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#323

Complements

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

NH ≅ G/Ntype
2. C2×#10622332C2semidirect
3. C2×#10622331C2semidirect
4. #13066982C2direct (N × H)
5. C2×#10622107C2semidirect
6. C2×#10622107C2semidirect
33. #10622332C22semidirect
35. #10622331C22semidirect
38. #10622107C22semidirect
39. #10622107C22semidirect
380. C2×C11#1473semidirect
455. C11C2×#1473semidirect
551. C2#13066982direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669322
C2×#106223322
C2×#106223312
#130669822
C2×#106221072
C2×#106221632
C2×C11×#3232
C2×#147311