Finite Group Databasebeta

← C2×#13073778 #14925060

Subgroups — C2×#13073778 #14925060

Order 2816.

3006 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66942C211yesmaximal, characteristic, complemented
2C22×#66946C211yesmaximal, characteristic
3#13073778C2116yesmaximal, direct product factor
4C2×#10622595C211yesmaximal, characteristic, complemented
5C2×#10622285C211yesmaximal, characteristic
6C2×#10622604C211yesmaximal, characteristic
7C2×#10622283C212yesmaximal, complemented
8C2×#10622282C212yesmaximal, complemented
9C2×#10622280C212yesmaximal, complemented
10C2×#10622280C212yesmaximal, complemented
11C2×#10622262C211yesmaximal, characteristic, complemented
12C2×C11×#400C211yesmaximal, characteristic, complemented
13C23×D44C2211yescharacteristic
14C23×C4×D11C2212yes—
15C22×C11×C4⋊C4C2211yescharacteristic
16C22×C11×C4⋊C4C2211yescharacteristic
17C22×(C2×D11)⋊C4C2212yes—
18C22×(C2×D11)⋊C4C2212yes—
19C22×(C2×D11)⋊C4C2212yes—
20C22×(C2×D11)⋊C4C2212yes—
21C22×(C2×D11)⋊C4C2212yes—
22C22×C4⋊Dic11C2211yescharacteristic
23C22×Dic11⋊C4C2211yescharacteristic
24C22×Dic11⋊C4C2211yescharacteristic
25C22×Dic11⋊C4C2211yescharacteristic
26C22×Dic11⋊C4C2211yescharacteristic
27C22×Dic11⋊C4C2212yes—
28C22×C4×Dic11C2212yes—
29C22×C4×Dic11C2211yescharacteristic
30C2×#66946—28no—
31C2×#66946C2218yes—
32C2×#66942—28no—
33C2×#66942C2218yescomplemented
34C11×#400C2218yescomplemented
35C2×C11×#95C2211yescharacteristic
36C2×C11×#95C2212yes—
37C2×C11×#95C2212yes—
38C2×C11⋊#95C2211yescharacteristic
39C2×C11⋊#95C2212yes—
40C2×C11⋊#95C2212yes—
41#10622604C2218yes—
42#10622595C2218yescomplemented
43#10622285C2218yes—
44#10622283C22116yescomplemented
45#10622282C22116yescomplemented
46#10622280C22116yescomplemented
47#10622280C22116yescomplemented
48#10622262C2218yescomplemented
49C24×D11C2312yes—
50C23×C4×C11C2312yes—
51C23×C4×C11C2311yescharacteristic
52C23×C4×C11C2311yescharacteristic
53C23×C4×C11C2312yes—
54C23×C4×C11C2311yescharacteristic
55C23×Dic11C2312yes—
56C23×Dic11C2311yescharacteristic
57C23×Dic11C2311yescharacteristic
58C23×Dic11C2311yescharacteristic
59C23×Dic11C2311yescharacteristic
60C22×D44—28no—
61C22×D44—24no—
62C22×D44C2314yes—
63C22×C4×D11—28no—
64C22×C4×D11—28no—
65C22×C4×D11—28no—
66C22×C4×D11C2318yes—
67C2×C11×C4⋊C4—24no—
68C2×C11×C4⋊C4—24no—
69C2×C11×C4⋊C4C2314yes—
70C2×C11×C4⋊C4C2314yes—
71C2×(C2×D11)⋊C4—28no—
72C2×(C2×D11)⋊C4—28no—
73C2×(C2×D11)⋊C4—28no—
74C2×(C2×D11)⋊C4—44no—
75C2×(C2×D11)⋊C4—44no—
76C2×(C2×D11)⋊C4C2318yes—
77C2×(C2×D11)⋊C4C2318yes—
78C2×(C2×D11)⋊C4C2318yes—
79C2×(C2×D11)⋊C4C2318yes—
80C2×(C2×D11)⋊C4C2318yes—
81C2×C4⋊Dic11—24no—
82C2×C4⋊Dic11C2314yes—
83C2×Dic11⋊C4—24no—
84C2×Dic11⋊C4—24no—
85C2×Dic11⋊C4—24no—
86C2×Dic11⋊C4—24no—
87C2×Dic11⋊C4—28no—
88C2×Dic11⋊C4C2314yes—
89C2×Dic11⋊C4C2314yes—
90C2×Dic11⋊C4C2314yes—
91C2×Dic11⋊C4C2314yes—
92C2×Dic11⋊C4C2318yes—
93C2×C4×Dic11—44no—
94C2×C4×Dic11D418yes—
95C2×C4×Dic11C2318yes—
96C2×C4×Dic11C2314yes—
97#66946—232no—
98#66942—232no—
99C11×#95C2314yes—
100C11×#95C2318yes—
101C11×#95C2318yes—
102C11⋊#95C2314yes—
103C11⋊#95C2318yes—
104C11⋊#95C2318yes—
105C2×#2562—111nomaximal, Sylow
106C24×C11C2411yescharacteristic
107C23×D11—24no—
108C23×D11—24no—
109C23×D11—24no—
110C23×D11—24no—
111C23×D11—24no—
112C23×D11—24no—
113C23×D11#4118yes—
114C23×D11C2414yes—
115C22×C4×C11—24no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—24no—
119C22×C4×C11—24no—
120C22×C4×C11—24no—
121C22×C4×C11—24no—
122C22×C4×C11—24no—
123C22×C4×C11—24no—
124C22×C4×C11—24no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11C2×D414yes—
128C22×C4×C11C2414yes—
129C22×C4×C11C2414yes—
130C22×C4×C11C2412yes—
131C22×C4×C11C2412yes—
132C22×C4×C11C2412yes—
133C22×Dic11—22no—
134C22×Dic11—22no—
135C22×Dic11—24no—
136C22×Dic11—24no—
137C22×Dic11—24no—
138C22×Dic11—22no—
139C22×Dic11—24no—
140C22×Dic11—22no—
141C22×Dic11—22no—
142C22×Dic11—22no—
143C22×Dic11C2×D414yes—
144C22×Dic11C2×D414yes—
145C22×Dic11#4118yes—
146C22×Dic11C2414yes—
147C22×Dic11C2412yes—
148C22×Dic11C2412yes—
149C22×Dic11C2412yes—
150C22×Dic11C2412yes—
151C2×D44—232no—
152C2×D44—216no—
153C2×D44—28no—
154C2×C4×D11—216no—
155C2×C4×D11—216no—
156C2×C4×D11—216no—
157C2×C4×D11—432no—
158C11×C4⋊C4—28no—
159C11×C4⋊C4—28no—
160(C2×D11)⋊C4—216no—
161(C2×D11)⋊C4—216no—
162(C2×D11)⋊C4—216no—
163(C2×D11)⋊C4—48no—
164(C2×D11)⋊C4—48no—
165C4⋊Dic11—28no—
166Dic11⋊C4—28no—
167Dic11⋊C4—28no—
168Dic11⋊C4—28no—
169Dic11⋊C4—216no—
170Dic11⋊C4—28no—
171C4×Dic11—48no—
172C4×Dic11C2×D4116yes—
173C22×#125—111no—
174C22×C4×D4—111no—
175#2562—1116no—
176C2×#400—111no—
177C2×#400D1111yescharacteristic, complemented
178C2×#394—111no—
179C2×#394—111no—
180C2×#388—112no—
181C2×#388—112no—
182C2×#380—112no—
183C2×#380—112no—
184C2×C4×C4⋊C4—111no—
185C23×C11C22×D412yes—
186C23×C11C2×#4114yes—
187C23×C11C2×#4114yes—
188C23×C11H(5,𝔽2)12yes—
189C23×C112−1+412yes—
190C23×C11C2511yescharacteristic
191C22×D11—216no—
192C22×D11—216no—
193C22×D11—216no—
194C22×D11—24no—
195C22×D11—24no—
196C22×D11—24no—
197C22×D11—24no—
198C22×D11—24no—
199C22×D11—24no—
200C22×D11—48no—
201C22×D11—48no—
202C22×D11—48no—
203C22×D11—48no—
204C22×D11C2×#4118yes—
205C2×C4×C11—28no—
206C2×C4×C11—24no—
207C2×C4×C11—22no—
208C2×C4×C11—22no—
209C2×C4×C11—24no—
210C2×C4×C11—24no—
211C2×C4×C11—24no—
212C2×C4×C11—24no—
213C2×C4×C11—24no—
214C2×C4×C11—24no—
215C2×C4×C11—24no—
216C2×C4×C11—22no—
217C2×C4×C11—22no—
218C2×C4×C11—44no—
219C2×C4×C11—48no—
220C2×C4×C11—44no—
221C2×C4×C11—48no—
222C2×C4×C11C22×D414yes—
223C2×Dic11—28no—
224C2×Dic11—22no—
225C2×Dic11—22no—
226C2×Dic11—22no—
227C2×Dic11—22no—
228C2×Dic11—24no—
229C2×Dic11—24no—
230C2×Dic11—24no—
231C2×Dic11—24no—
232C2×Dic11—22no—
233C2×Dic11—22no—
234C2×Dic11—44no—
235C2×Dic11—44no—
236C2×Dic11—48no—
237C2×Dic11#124116yes—
238C2×Dic11C22×D414yes—
239C2×Dic11C22×D414yes—
240C2×Dic11C2×#4118yes—
241D44—232no—
242C4×D11—432no—
243C23×D4—111no—
244C24×C4—112no—
245C2×#125—118no—
246C2×#125—228no—
247C2×C4×D4—118no—
248C2×C4×D4—228no—
249C22×C4⋊C4—111no—
250C22×C4⋊C4—111no—
251C22×C4⋊C4—111no—
252C22×C4⋊C4—111no—
253C22×C4⋊C4—112no—
254C22×C4⋊C4—111no—
255C22×C4⋊C4C2×D1111yescharacteristic
256C22×C4⋊C4C2×D1111yescharacteristic
257C22×C22⋊C4—112no—
258C22×C22⋊C4—112no—
259C22×C22⋊C4—112no—
260C22×C22⋊C4—112no—
261C22×C22⋊C4—112no—
262C22×C42—111no—
263C22×C42—112no—
264#400—118no—
265#400C2×D1118yescomplemented
266#394—118no—
267#394—118no—
268#388—1116no—
269#388—1116no—
270#380—1116no—
271#380—1116no—
272C4×C4⋊C4—118no—
273C2×#95—111no—
274C2×#95—112no—
275C2×#95—112no—
276C2×#95C2×D1111yescharacteristic
277C2×#95C2×D1112yes—
278C2×#95C2×D1112yes—
279C22×C11#52514yes—
280C22×C11C2×#12414yes—
281C22×C11#53714yes—
282C22×C11#55218yes—
283C22×C11#55318yes—
284C22×C11C23×D411yescharacteristic
285C22×C11C22×#4112yes—
286C22×C11C22×#4112yes—
287C22×C11C2×H(5,𝔽2)11yescharacteristic
288C22×C11C2×2−1+411yescharacteristic
289C2×D11—28no—
290C2×D11—28no—
291C2×D11—28no—
292C2×D11—432no—
293C2×D11—44no—
294C2×D11—44no—
295C2×D11—44no—
296C2×D11—44no—
297C4×C11—24no—
298C4×C11—42no—
299C4×C11—44no—
300C4×C11—42no—
301C4×C11—44no—
302Dic11—24no—
303Dic11—42no—
304Dic11—42no—
305Dic11—44no—
306Dic11C2×#12418yes—
307C25—112no—
308C22×D4—114no—
309C22×D4—228no—
310C22×D4—224no—
311C23×C4—111no—
312C23×C4—111no—
313C23×C4—111no—
314C23×C4—111no—
315C23×C4—112no—
316C23×C4—118no—
317C23×C4—228no—
318C23×C4—228no—
319C23×C4—228no—
320C23×C4C22×D1111yescharacteristic
321C23×C4C22×D1111yescharacteristic
322C23×C4C22×D1112yes—
323C23×C4C22×D1112yes—
324C23×C4C22×D1111yescharacteristic
325#125—2232no—
326C4×D4—2232no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—114no—
330C2×C4⋊C4—114no—
331C2×C4⋊C4—114no—
332C2×C4⋊C4—114no—
333C2×C4⋊C4—114no—
334C2×C4⋊C4—118no—
335C2×C4⋊C4—224no—
336C2×C4⋊C4—224no—
337C2×C4⋊C4—224no—
338C2×C4⋊C4—224no—
339C2×C4⋊C4—228no—
340C2×C4⋊C4—224no—
341C2×C4⋊C4C22×D1114yes—
342C2×C4⋊C4C22×D1114yes—
343C2×C22⋊C4—118no—
344C2×C22⋊C4—118no—
345C2×C22⋊C4—118no—
346C2×C22⋊C4—118no—
347C2×C22⋊C4—118no—
348C2×C22⋊C4—228no—
349C2×C22⋊C4—228no—
350C2×C22⋊C4—228no—
351C2×C22⋊C4—444no—
352C2×C22⋊C4—444no—
353C2×C42—118no—
354C2×C42—114no—
355C2×C42—118no—
356C2×C42—444no—
357#95—114no—
358#95—118no—
359#95—118no—
360#95C22×D1114yes—
361#95C22×D1118yes—
362#95C22×D1118yes—
363C2×C11#256218yescomplemented
364C2×C11C2×#52511yescharacteristic
365C2×C11C22×#12411yescharacteristic
366C2×C11C2×#53711yescharacteristic
367C2×C11C2×#55212yes—
368C2×C11C2×#55312yes—
369D11—48no—
370C24—118no—
371C24—114no—
372C24—224no—
373C24—224no—
374C24—224no—
375C24—224no—
376C24—224no—
377C24—224no—
378C24C23×D1111yescharacteristic
379C2×D4—2216no—
380C2×D4—2232no—
381C2×D4—228no—
382C22×C4—24no—
383C22×C4—24no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—24no—
388C22×C4—24no—
389C22×C4—24no—
390C22×C4—24no—
391C22×C4—24no—
392C22×C4—24no—
393C22×C4—22no—
394C22×C4—114no—
395C22×C4—118no—
396C22×C4—112no—
397C22×C4—114no—
398C22×C4—112no—
399C22×C4—114no—
400C22×C4—112no—
401C22×C4—112no—
402C22×C4—2216no—
403C22×C4—2216no—
404C22×C4—2216no—
405C22×C4—222no—
406C22×C4—222no—
407C22×C4—222no—
408C22×C4—222no—
409C22×C4—222no—
410C22×C4—224no—
411C22×C4—224no—
412C22×C4—224no—
413C22×C4—224no—
414C22×C4—222no—
415C22×C4—4432no—
416C22×C4D4×D1114yes—
417C22×C4C23×D1114yes—
418C22×C4C23×D1114yes—
419C22×C4C23×D1112yes—
420C22×C4C23×D1112yes—
421C22×C4C23×D1112yes—
422C4⋊C4—28no—
423C4⋊C4—28no—
424C4⋊C4—228no—
425C4⋊C4—228no—
426C4⋊C4—228no—
427C4⋊C4—228no—
428C4⋊C4—2216no—
429C4⋊C4—228no—
430C22⋊C4—2216no—
431C22⋊C4—2216no—
432C22⋊C4—2216no—
433C22⋊C4—448no—
434C22⋊C4—448no—
435C42—1116no—
436C42—448no—
437C11C2×#256211yescharacteristic, complemented, Sylow
438C23—118no—
439C23—2216no—
440C23—2216no—
441C23—224no—
442C23—224no—
443C23—224no—
444C23—224no—
445C23—224no—
446C23—224no—
447C23—2216no—
448C23—448no—
449C23—448no—
450C23—448no—
451C23—448no—
452C23C2×D4×D1112yes—
453C23#6704012yes—
454C23#41×D1114yes—
455C23#41×D1114yes—
456C23#6704212yes—
457C23C24×D1111yescharacteristic
458D4—2232no—
459C2×C4—28no—
460C2×C4—24no—
461C2×C4—24no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—24no—
466C2×C4—24no—
467C2×C4—24no—
468C2×C4—24no—
469C2×C4—24no—
470C2×C4—24no—
471C2×C4—22no—
472C2×C4—48no—
473C2×C4—44no—
474C2×C4—44no—
475C2×C4—48no—
476C2×C4—114no—
477C2×C4—118no—
478C2×C4—1116no—
479C2×C4—114no—
480C2×C4—228no—
481C2×C4—222no—
482C2×C4—222no—
483C2×C4—222no—
484C2×C4—222no—
485C2×C4—222no—
486C2×C4—224no—
487C2×C4—224no—
488C2×C4—224no—
489C2×C4—224no—
490C2×C4—222no—
491C2×C4—4432no—
492C2×C4—448no—
493C2×C4—444no—
494C2×C4—444no—
495C2×C4C2×D4×D1114yes—
496C22—228no—
497C22—228no—
498C22—228no—
499C22—444no—
500C22—444no—
501C22—444no—
502C22—444no—
503C22—4432no—
504C22#1062316014yes—
505C22#1062318714yes—
506C22D11×#12414yes—
507C22#1062322418yes—
508C22#1062324018yes—
509C22C22×D4×D1111yescharacteristic
510C22C2×#6704011yescharacteristic
511C22C2×#41×D1112yes—
512C22C2×#41×D1112yes—
513C22C2×#6704211yescharacteristic
514C4—24no—
515C4—44no—
516C4—44no—
517C4—42no—
518C4—42no—
519C4—118no—
520C4—224no—
521C4—444no—
522C4—442no—
523C4—442no—
524C2—448no—
525C2#1307377818yesdirect product factor
526C2C2×#1062318711yescharacteristic
527C2C2×D11×#12411yescharacteristic
528C2C2×#1062316011yescharacteristic
529C2C2×#1062322412yes—
530C2C2×#1062324012yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#400C2
socleC24×C11C24
prime radicalC23×D44C22
hypercenterC2×#400D11
hypocenterC11C2×#2562
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#400

Complements

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

NH ≅ G/Ntype
1. C22×#66942C2semidirect
3. #13073778C2direct (N × H)
4. C2×#10622595C2semidirect
7. C2×#10622283C2semidirect
8. C2×#10622282C2semidirect
9. C2×#10622280C2semidirect
10. C2×#10622280C2semidirect
11. C2×#10622262C2semidirect
12. C2×C11×#400C2semidirect
33. C2×#66942C22semidirect
34. C11×#400C22semidirect
42. #10622595C22semidirect
44. #10622283C22semidirect
45. #10622282C22semidirect
46. #10622280C22semidirect
47. #10622280C22semidirect
48. #10622262C22semidirect
177. C2×#400D11semidirect
265. #400C2×D11semidirect
363. C2×C11#2562semidirect
437. C11C2×#2562semidirect
525. C2#13073778direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669422
C22×#669462
#130737782
C2×#106225952
C2×#106222852
C2×#106226042
C2×#106222832
C2×#106222822
C2×#106222802
C2×#106222622
C2×C11×#4002
C2×#256211