Finite Group Databasebeta

← C2×#13066954 #14719630

Subgroups — C2×#13066954 #14719630

Order 2816.

1738 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622820C212yesmaximal, complemented
2#13066954C218yesmaximal, direct product factor
3C2×#10622166C212yesmaximal, complemented
4C2×#10622163C212yesmaximal, complemented
5C22×C4×D4×C11C211yesmaximal, characteristic
6C23×D4×C11C411yescharacteristic
7C24×C4×C11C411yescharacteristic
8C24×C4×C11C2211yescharacteristic
9C2×C4×D4×C11—22no—
10C2×C4×D4×C11—22no—
11C2×C4×D4×C11—24no—
12C2×C4×D4×C11C414yes—
13C2×C4×D4×C11C2214yes—
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C11×C22⋊C4C411yescharacteristic
16C22×C11×C22⋊C4C2211yescharacteristic
17C22×C42×C11C411yescharacteristic
18C22×#4318—22no—
19#10622820—24no—
20#10622820C2218yescomplemented
21C2×C22⋊(C11⋊C8)—22no—
22C2×C22⋊(C11⋊C8)C2214yes—
23#10622166C2218yescomplemented
24#10622163C2218yescomplemented
25C25×C11C2×C411yescharacteristic
26C25×C11C2×C411yescharacteristic
27C22×D4×C11—22no—
28C22×D4×C11—22no—
29C22×D4×C11—24no—
30C22×D4×C11—24no—
31C22×D4×C11C2×C414yes—
32C23×C4×C11—22no—
33C23×C4×C11—21no—
34C23×C4×C11—21no—
35C23×C4×C11—44no—
36C23×C4×C11—44no—
37C23×C4×C11C2×C411yescharacteristic
38C23×C4×C11C2×C411yescharacteristic
39C23×C4×C11C2×C411yescharacteristic
40C23×C4×C11C2×C411yescharacteristic
41C23×C4×C11C2×C414yes—
42C23×C4×C11C2×C412yes—
43C23×C4×C11D412yes—
44C23×C4×C11D412yes—
45C23×C4×C11D414yes—
46C23×C4×C11C2311yescharacteristic
47C23×C4×C11C2312yes—
48C4×D4×C11—28no—
49C4×D4×C11—28no—
50C4×D4×C11—28no—
51C4×D4×C11—28no—
52C2×C11×C4⋊C4—22no—
53C2×C11×C4⋊C4—22no—
54C2×C11×C4⋊C4C2×C412yes—
55C2×C11×C4⋊C4C2312yes—
56C2×C11×C22⋊C4—22no—
57C2×C11×C22⋊C4—22no—
58C2×C11×C22⋊C4—22no—
59C2×C11×C22⋊C4—22no—
60C2×C11×C22⋊C4C2×C414yes—
61C2×C11×C22⋊C4C2×C412yes—
62C2×C11×C22⋊C4C2312yes—
63C2×C42×C11—22no—
64C2×C42×C11—21no—
65C2×C42×C11—21no—
66C2×C42×C11C2×C414yes—
67C2×#4318—28no—
68C2×#4318—48no—
69C22×C11⋊C8—24no—
70C22⋊(C11⋊C8)—28no—
71C22⋊(C11⋊C8)—24no—
72C22⋊(C11⋊C8)C2318yes—
73C2×#1465—111nomaximal, Sylow
74C24×C11—21no—
75C24×C11—21no—
76C24×C11—22no—
77C24×C11—22no—
78C24×C11—22no—
79C24×C11—42no—
80C24×C11—42no—
81C24×C11—42no—
82C24×C11—42no—
83C24×C11C22⋊C412yes—
84C24×C11C22⋊C412yes—
85C24×C11M1614yescomplemented
86C24×C11C22×C411yescharacteristic
87C24×C11C22×C412yes—
88C24×C11C22×C412yes—
89C2×D4×C11—216no—
90C2×D4×C11—216no—
91C2×D4×C11—28no—
92C2×D4×C11—28no—
93C2×D4×C11—28no—
94C22×C4×C11—21no—
95C22×C4×C11—21no—
96C22×C4×C11—22no—
97C22×C4×C11—28no—
98C22×C4×C11—24no—
99C22×C4×C11—21no—
100C22×C4×C11—21no—
101C22×C4×C11—21no—
102C22×C4×C11—21no—
103C22×C4×C11—24no—
104C22×C4×C11—24no—
105C22×C4×C11—44no—
106C22×C4×C11—48no—
107C22×C4×C11—44no—
108C22×C4×C11—44no—
109C22×C4×C11—42no—
110C22×C4×C11—44no—
111C22×C4×C11—48no—
112C22×C4×C11—48no—
113C22×C4×C11—44no—
114C22×C4×C11—42no—
115C22×C4×C11—42no—
116C22×C4×C11C22⋊C411yescharacteristic
117C22×C4×C11C22⋊C412yes—
118C22×C4×C11C22⋊C414yes—
119C22×C4×C11C22⋊C414yes—
120C22×C4×C11C22⋊C411yescharacteristic
121C22×C4×C11M1614yescomplemented
122C22×C4×C11C22×C412yes—
123C22×C4×C11C22×C412yes—
124C22×C4×C11C22×C412yes—
125C22×C4×C11C22×C412yes—
126C22×C4×C11C22×C411yescharacteristic
127C22×C4×C11C2×D412yes—
128C22×C4×C11C2×D414yes—
129C22×C4×C11C2×D412yes—
130C22×C4×C11C2×D414yes—
131C22×C4×C11C2411yescharacteristic
132C11×C4⋊C4—24no—
133C11×C4⋊C4—24no—
134C11×C22⋊C4—28no—
135C11×C22⋊C4—24no—
136C11×C22⋊C4—24no—
137C42×C11—24no—
138C42×C11—24no—
139#4318—416no—
140C2×C11⋊C8—28no—
141C2×C11⋊C8—48no—
142C22×C4×D4D1111yescharacteristic
143C2×#407—112no—
144#1465—118no—
145C2×#324—112no—
146C2×#323—112no—
147C23×C11—22no—
148C23×C11—22no—
149C23×C11—22no—
150C23×C11—22no—
151C23×C11—22no—
152C23×C11—22no—
153C23×C11—24no—
154C23×C11—24no—
155C23×C11—24no—
156C23×C11—24no—
157C23×C11—24no—
158C23×C11—24no—
159C23×C11—42no—
160C23×C11—42no—
161C23×C11—42no—
162C23×C11—42no—
163C23×C11—42no—
164C23×C11—48no—
165C23×C11—42no—
166C23×C11—42no—
167C23×C11—42no—
168C23×C11—48no—
169C23×C11—48no—
170C23×C11—48no—
171C23×C11—42no—
172C23×C11—42no—
173C23×C11C2×C22⋊C414yes—
174C23×C11C2×C22⋊C411yescharacteristic
175C23×C11C2×C22⋊C411yescharacteristic
176C23×C11C2×M1612yes—
177C23×C11C2×M1612yes—
178C23×C11C2×M1614yescomplemented
179C23×C11C23×C411yescharacteristic
180D4×C11—232no—
181C2×C4×C11—22no—
182C2×C4×C11—22no—
183C2×C4×C11—24no—
184C2×C4×C11—24no—
185C2×C4×C11—24no—
186C2×C4×C11—22no—
187C2×C4×C11—28no—
188C2×C4×C11—24no—
189C2×C4×C11—24no—
190C2×C4×C11—28no—
191C2×C4×C11—22no—
192C2×C4×C11—22no—
193C2×C4×C11—44no—
194C2×C4×C11—41no—
195C2×C4×C11—44no—
196C2×C4×C11—42no—
197C2×C4×C11—41no—
198C2×C4×C11—48no—
199C2×C4×C11—42no—
200C2×C4×C11—42no—
201C2×C4×C11—42no—
202C2×C4×C11—42no—
203C2×C4×C11—48no—
204C2×C4×C11—42no—
205C2×C4×C11—42no—
206C2×C4×C11#9914yes—
207C2×C4×C11C2×C22⋊C412yes—
208C2×C4×C11C2×C22⋊C412yes—
209C2×C4×C11C2×C22⋊C412yes—
210C2×C4×C11C2×M1614yescomplemented
211C2×C4×C11C22×D412yes—
212C11⋊C8—48no—
213C23×D4Dic1111yescharacteristic
214C24×C4Dic1111yescharacteristic
215C24×C4C2×D1111yescharacteristic
216C22×M16—222no—
217C2×C4×D4—22no—
218C2×C4×D4—22no—
219C2×C4×D4—24no—
220C2×C4×D4Dic1114yes—
221C2×C4×D4C2×D1114yes—
222C22×C4⋊C4C2×D1111yescharacteristic
223C22×C22⋊C4Dic1111yescharacteristic
224C22×C22⋊C4C2×D1111yescharacteristic
225C22×C42Dic1111yescharacteristic
226#407—118no—
227#407—224no—
228C2×C22⋊C8—114no—
229C2×C22⋊C8—222no—
230#324—118no—
231#323—118no—
232C22×C11—21no—
233C22×C11—21no—
234C22×C11—21no—
235C22×C11—21no—
236C22×C11—24no—
237C22×C11—24no—
238C22×C11—24no—
239C22×C11—24no—
240C22×C11—24no—
241C22×C11—24no—
242C22×C11—44no—
243C22×C11—44no—
244C22×C11—44no—
245C22×C11—44no—
246C22×C11—48no—
247C22×C11—48no—
248C22×C11—42no—
249C22×C11—42no—
250C22×C11—48no—
251C22×C11—48no—
252C22×C11#40712yes—
253C22×C11#40712yes—
254C22×C11C2×#9912yes—
255C22×C11#41312yes—
256C22×C11C22×C22⋊C411yescharacteristic
257C22×C11C22×M1611yescharacteristic
258C22×C11C22×M1611yescharacteristic
259C4×C11—24no—
260C4×C11—22no—
261C4×C11—22no—
262C4×C11—22no—
263C4×C11—42no—
264C4×C11—42no—
265C4×C11C2×#9914yes—
266C25C2×Dic1111yescharacteristic
267C25C2×Dic1111yescharacteristic
268C22×D4—24no—
269C22×D4—22no—
270C22×D4—22no—
271C22×D4—24no—
272C22×D4C2×Dic1114yes—
273C23×C4—22no—
274C23×C4—21no—
275C23×C4—21no—
276C23×C4—44no—
277C23×C4—44no—
278C23×C4C2×Dic1111yescharacteristic
279C23×C4C2×Dic1111yescharacteristic
280C23×C4C2×Dic1111yescharacteristic
281C23×C4C2×Dic1111yescharacteristic
282C23×C4C2×Dic1114yes—
283C23×C4C2×Dic1112yes—
284C23×C4C22⋊D1112yes—
285C23×C4C22⋊D1112yes—
286C23×C4C22⋊D1114yes—
287C23×C4C22×D1111yescharacteristic
288C23×C4C22×D1112yes—
289C2×M16—228no—
290C2×M16—448no—
291C22×C8—224no—
292C4×D4—28no—
293C4×D4—28no—
294C4×D4—28no—
295C4×D4—28no—
296C2×C4⋊C4—22no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4C2×Dic1112yes—
299C2×C4⋊C4C22×D1112yes—
300C2×C22⋊C4—22no—
301C2×C22⋊C4—22no—
302C2×C22⋊C4—22no—
303C2×C22⋊C4—22no—
304C2×C22⋊C4C2×Dic1114yes—
305C2×C22⋊C4C2×Dic1112yes—
306C2×C22⋊C4C22×D1112yes—
307C2×C42—22no—
308C2×C42—21no—
309C2×C42—21no—
310C2×C42C2×Dic1114yes—
311C22⋊C8—118no—
312C22⋊C8—224no—
313C22⋊C8—228no—
314C2×C11—21no—
315C2×C11—21no—
316C2×C11—22no—
317C2×C11—44no—
318C2×C11—44no—
319C2×C11#146514yescomplemented
320C2×C11C2×#40711yescharacteristic
321C2×C11C22×#9911yescharacteristic
322C2×C11C2×#41311yescharacteristic
323C24—22no—
324C24—22no—
325C24—22no—
326C24—21no—
327C24—21no—
328C24—42no—
329C24—42no—
330C24—42no—
331C24—42no—
332C24#431814yescomplemented
333C24C22⋊Dic1112yes—
334C24C22⋊Dic1112yes—
335C24C22×Dic1111yescharacteristic
336C24C22×Dic1112yes—
337C24C22×Dic1112yes—
338C2×D4—216no—
339C2×D4—216no—
340C2×D4—28no—
341C2×D4—28no—
342C2×D4—28no—
343C22×C4—22no—
344C22×C4—21no—
345C22×C4—21no—
346C22×C4—28no—
347C22×C4—24no—
348C22×C4—21no—
349C22×C4—21no—
350C22×C4—21no—
351C22×C4—21no—
352C22×C4—24no—
353C22×C4—24no—
354C22×C4—44no—
355C22×C4—44no—
356C22×C4—48no—
357C22×C4—42no—
358C22×C4—44no—
359C22×C4—44no—
360C22×C4—48no—
361C22×C4—48no—
362C22×C4—44no—
363C22×C4—42no—
364C22×C4—42no—
365C22×C4#431814yescomplemented
366C22×C4C22⋊Dic1112yes—
367C22×C4C22⋊Dic1114yes—
368C22×C4C22⋊Dic1111yescharacteristic
369C22×C4C22⋊Dic1114yes—
370C22×C4C22⋊Dic1111yescharacteristic
371C22×C4C22×Dic1112yes—
372C22×C4C22×Dic1112yes—
373C22×C4C22×Dic1112yes—
374C22×C4C22×Dic1112yes—
375C22×C4C22×Dic1111yescharacteristic
376C22×C4C2×C22⋊D1114yes—
377C22×C4C2×C22⋊D1112yes—
378C22×C4C2×C22⋊D1112yes—
379C22×C4C2×C22⋊D1114yes—
380C22×C4C23×D1111yescharacteristic
381M16—4416no—
382C2×C8—228no—
383C2×C8—448no—
384C4⋊C4—24no—
385C4⋊C4—24no—
386C22⋊C4—28no—
387C22⋊C4—24no—
388C22⋊C4—24no—
389C42—24no—
390C42—24no—
391C11C2×#146511yescharacteristic, complemented, Sylow
392C23—22no—
393C23—22no—
394C23—22no—
395C23—22no—
396C23—22no—
397C23—24no—
398C23—24no—
399C23—24no—
400C23—24no—
401C23—24no—
402C23—24no—
403C23—22no—
404C23—42no—
405C23—42no—
406C23—42no—
407C23—42no—
408C23—42no—
409C23—48no—
410C23—42no—
411C23—42no—
412C23—42no—
413C23—48no—
414C23—48no—
415C23—48no—
416C23—42no—
417C23—42no—
418C23C2×#431812yes—
419C23C2×#431812yes—
420C23C2×#431814yescomplemented
421C23C2×C22⋊Dic1114yes—
422C23C2×C22⋊Dic1111yescharacteristic
423C23C2×C22⋊Dic1111yescharacteristic
424C23C23×Dic1111yescharacteristic
425D4—232no—
426C2×C4—22no—
427C2×C4—24no—
428C2×C4—24no—
429C2×C4—24no—
430C2×C4—22no—
431C2×C4—22no—
432C2×C4—28no—
433C2×C4—24no—
434C2×C4—24no—
435C2×C4—28no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—44no—
439C2×C4—41no—
440C2×C4—44no—
441C2×C4—42no—
442C2×C4—41no—
443C2×C4—48no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—42no—
447C2×C4—42no—
448C2×C4—48no—
449C2×C4—42no—
450C2×C4—42no—
451C2×C4#6689814yes—
452C2×C4C2×#431814yescomplemented
453C2×C4C2×C22⋊Dic1112yes—
454C2×C4C2×C22⋊Dic1112yes—
455C2×C4C2×C22⋊Dic1112yes—
456C2×C4C22×C22⋊D1112yes—
457C8—448no—
458C22—21no—
459C22—21no—
460C22—21no—
461C22—21no—
462C22—24no—
463C22—24no—
464C22—24no—
465C22—24no—
466C22—24no—
467C22—24no—
468C22—44no—
469C22—44no—
470C22—44no—
471C22—44no—
472C22—48no—
473C22—48no—
474C22—42no—
475C22—42no—
476C22—48no—
477C22—48no—
478C22#1062282012yes—
479C22#1062282012yes—
480C22C2×#6689812yes—
481C22#1062285012yes—
482C22C22×#431811yescharacteristic
483C22C22×#431811yescharacteristic
484C22C22×C22⋊Dic1111yescharacteristic
485C4—24no—
486C4—22no—
487C4—22no—
488C4—22no—
489C4—42no—
490C4—42no—
491C4C2×#6689814yes—
492C2—21no—
493C2—21no—
494C2—22no—
495C2—44no—
496C2—44no—
497C2#1306695414yesdirect product factor
498C2C2×#1062282011yescharacteristic
499C2C22×#6689811yescharacteristic
500C2C2×#1062285011yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC22×C4×D4×C11C2
socleC23×C11C2×C22⋊C4
prime radicalC23×D4×C11C4
cosocleC22×C4×C11C24
hypercenterC22×C4×D4D11
hypocenterC11C2×#1465
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C24×C4 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×#10622820C2semidirect
2. #13066954C2direct (N × H)
3. C2×#10622166C2semidirect
4. C2×#10622163C2semidirect
20. #10622820C22semidirect
23. #10622166C22semidirect
24. #10622163C22semidirect
85. C24×C11M16semidirect
121. C22×C4×C11M16semidirect
178. C23×C11C2×M16semidirect
210. C2×C4×C11C2×M16semidirect
319. C2×C11#1465semidirect
332. C24#4318semidirect
365. C22×C4#4318semidirect
391. C11C2×#1465semidirect
420. C23C2×#4318semidirect
452. C2×C4C2×#4318semidirect
497. C2#13066954direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106228202
#130669542
C2×#106221662
C2×#106221632
C22×C4×D4×C112
C2×#146511