Finite Group Databasebeta

← C2×#13074433 #14920144

Subgroups — C2×#13074433 #14920144

Order 2816.

2894 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66931C211yesmaximal, characteristic
2C23×C4⋊Dic11C211yesmaximal, characteristic
3#13074433C2116yesmaximal, direct product factor
4C2×#10622273C212yesmaximal, complemented
5C2×#10622270C212yesmaximal, complemented
6C2×#10622274C212yesmaximal, complemented
7C2×#10622269C212yesmaximal, complemented
8C2×#10622563C211yesmaximal, characteristic
9C2×#10622559C211yesmaximal, characteristic
10C2×#10622824C211yesmaximal, characteristic
11C2×#10622555C211yesmaximal, characteristic
12C2×C11×#381C211yesmaximal, characteristic
13C24×C4×C11C2211yescharacteristic
14C24×Dic11C2211yescharacteristic
15C24×Dic11C2211yescharacteristic
16C23×Dic22C2211yescharacteristic
17C22×C11×C22⋊C4C2211yescharacteristic
18C22×C11×C22⋊C4C2211yescharacteristic
19C22×C22⋊Dic11C2211yescharacteristic
20C22×C22⋊Dic11C2211yescharacteristic
21C22×C4⋊Dic11—28no—
22C22×C4⋊Dic11C2218yes—
23C22×C4⋊Dic11C2212yes—
24C22×C4⋊Dic11C2212yes—
25C22×C4⋊Dic11C2211yescharacteristic
26C22×C4⋊Dic11C2212yes—
27C22×Dic11⋊C4C2211yescharacteristic
28C22×Dic11⋊C4C2211yescharacteristic
29C22×Dic11⋊C4C2212yes—
30C22×Dic11⋊C4C2212yes—
31C2×#66931—28no—
32C2×#66931C2218yes—
33C11×#381C2218yes—
34C2×C11×#95C2212yes—
35C2×C11×#95C2212yes—
36#10622824C2218yes—
37C2×C11⋊#95C2212yes—
38C2×C11⋊#95C2212yes—
39C2×C11⋊#95C2212yes—
40C2×C11⋊#95C2212yes—
41C2×C11⋊#95C2212yes—
42#10622563C2218yes—
43#10622559C2218yes—
44#10622555C2218yes—
45#10622274C22116yescomplemented
46#10622273C22116yescomplemented
47#10622270C22116yescomplemented
48#10622269C22116yescomplemented
49C25×C11C2311yescharacteristic
50C23×C4×C11—24no—
51C23×C4×C11—24no—
52C23×C4×C11Q818yescomplemented
53C23×C4×C11C2311yescharacteristic
54C23×C4×C11C2311yescharacteristic
55C23×C4×C11C2312yes—
56C23×C4×C11C2312yes—
57C23×C4×C11C2314yes—
58C23×Dic11—24no—
59C23×Dic11—44no—
60C23×Dic11—44no—
61C23×Dic11D418yes—
62C23×Dic11C2311yescharacteristic
63C23×Dic11C2312yes—
64C23×Dic11C2312yes—
65C23×Dic11C2311yescharacteristic
66C23×Dic11C2311yescharacteristic
67C23×Dic11C2311yescharacteristic
68C23×Dic11C2314yes—
69C23×Dic11C2314yes—
70C22×Dic22—24no—
71C22×Dic22—44no—
72C22×Dic22C2314yes—
73C2×C11×C22⋊C4—24no—
74C2×C11×C22⋊C4—24no—
75C2×C11×C22⋊C4C2314yes—
76C2×C11×C22⋊C4C2314yes—
77C2×C22⋊Dic11—24no—
78C2×C22⋊Dic11—24no—
79C2×C22⋊Dic11C2314yes—
80C2×C22⋊Dic11C2314yes—
81C2×C4⋊Dic11—24no—
82C2×C4⋊Dic11—28no—
83C2×C4⋊Dic11—28no—
84C2×C4⋊Dic11—232no—
85C2×C4⋊Dic11—44no—
86C2×C4⋊Dic11C2314yes—
87C2×C4⋊Dic11C2318yes—
88C2×C4⋊Dic11C2318yes—
89C2×C4⋊Dic11C2318yes—
90C2×Dic11⋊C4—24no—
91C2×Dic11⋊C4—24no—
92C2×Dic11⋊C4—44no—
93C2×Dic11⋊C4—44no—
94C2×Dic11⋊C4C2314yes—
95C2×Dic11⋊C4C2314yes—
96C2×Dic11⋊C4C2318yes—
97C2×Dic11⋊C4C2318yes—
98#66931—232no—
99C11×#95C2318yes—
100C11×#95C2318yes—
101C11⋊#95C2318yes—
102C11⋊#95C2318yes—
103C11⋊#95C2318yes—
104C11⋊#95C2318yes—
105C11⋊#95C2318yes—
106C2×#2627—111nomaximal, Sylow
107C24×C11—24no—
108C24×C11—24no—
109C24×C11C2×D414yes—
110C24×C11C2×Q814yes—
111C24×C11#4114yes—
112C24×C11C2412yes—
113C24×C11C2411yescharacteristic
114C22×C4×C11—232no—
115C22×C4×C11—24no—
116C22×C4×C11—28no—
117C22×C4×C11—24no—
118C22×C4×C11—28no—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—24no—
122C22×C4×C11—24no—
123C22×C4×C11—24no—
124C22×C4×C11—24no—
125C22×C4×C11—24no—
126C22×C4×C11C2×Q818yes—
127C22×C4×C11C2×Q8116yescomplemented
128C22×C4×C11C2412yes—
129C22×C4×C11C2414yes—
130C22×C4×C11C2412yes—
131C22×C4×C11C2414yes—
132C22×Dic11—22no—
133C22×Dic11—28no—
134C22×Dic11—24no—
135C22×Dic11—22no—
136C22×Dic11—24no—
137C22×Dic11—24no—
138C22×Dic11—24no—
139C22×Dic11—24no—
140C22×Dic11—24no—
141C22×Dic11—24no—
142C22×Dic11—24no—
143C22×Dic11—24no—
144C22×Dic11—24no—
145C22×Dic11—416no—
146C22×Dic11—48no—
147C22×Dic11—48no—
148C22×Dic11—416no—
149C22×Dic11C2×D414yes—
150C22×Dic11C2×D414yes—
151C22×Dic11C2×D4116yes—
152C22×Dic11C2412yes—
153C22×Dic11C2414yes—
154C22×Dic11C2414yes—
155C22×Dic11C2412yes—
156C22×Dic11C2412yes—
157C22×Dic11C2412yes—
158C2×Dic22—28no—
159C2×Dic22—48no—
160C2×Dic22—416no—
161C11×C22⋊C4—28no—
162C11×C22⋊C4—28no—
163C22⋊Dic11—28no—
164C22⋊Dic11—28no—
165C4⋊Dic11—28no—
166C4⋊Dic11—216no—
167C4⋊Dic11—216no—
168C4⋊Dic11—48no—
169Dic11⋊C4—28no—
170Dic11⋊C4—28no—
171Dic11⋊C4—48no—
172Dic11⋊C4—48no—
173C22×C22⋊Q8—111no—
174C23×C4⋊C4—111no—
175#2627—1116no—
176C2×#400—112no—
177C2×#398—112no—
178C2×#398—112no—
179C2×#395—112no—
180C2×#385—111no—
181C2×#385—111no—
182C2×#381—111no—
183C2×#381D1111yescharacteristic
184C2×#380—111no—
185C23×C11—28no—
186C23×C11—28no—
187C23×C11—216no—
188C23×C11—216no—
189C23×C11—24no—
190C23×C11—24no—
191C23×C11C22⋊Q8116yes—
192C23×C11C22×D414yes—
193C23×C11C22×D412yes—
194C23×C11C22×Q814yes—
195C23×C11C22×Q812yes—
196C23×C11C2×#4114yes—
197C23×C11C2×#4112yes—
198C23×C11H(5,𝔽2)14yes—
199C23×C112−1+414yes—
200C23×C11C2511yescharacteristic
201C2×C4×C11—216no—
202C2×C4×C11—232no—
203C2×C4×C11—24no—
204C2×C4×C11—24no—
205C2×C4×C11—22no—
206C2×C4×C11—22no—
207C2×C4×C11—24no—
208C2×C4×C11—24no—
209C2×C4×C11—24no—
210C2×C4×C11—24no—
211C2×C4×C11—24no—
212C2×C4×C11—44no—
213C2×C4×C11—44no—
214C2×C4×C11—48no—
215C2×C4×C11C22×Q818yes—
216C2×Dic11—28no—
217C2×Dic11—28no—
218C2×Dic11—24no—
219C2×Dic11—24no—
220C2×Dic11—22no—
221C2×Dic11—24no—
222C2×Dic11—22no—
223C2×Dic11—24no—
224C2×Dic11—24no—
225C2×Dic11—24no—
226C2×Dic11—24no—
227C2×Dic11—24no—
228C2×Dic11—24no—
229C2×Dic11—24no—
230C2×Dic11—416no—
231C2×Dic11—416no—
232C2×Dic11—44no—
233C2×Dic11—48no—
234C2×Dic11—44no—
235C2×Dic11—48no—
236C2×Dic11C22×D414yes—
237C2×Dic11C22×D414yes—
238Dic22—416no—
239C23×Q8—111no—
240C24×C4—111no—
241C24×C4—111no—
242C24×C4C2×D1111yescharacteristic
243C2×C22⋊Q8—118no—
244C2×C22⋊Q8—228no—
245C22×C4⋊C4—118no—
246C22×C4⋊C4—111no—
247C22×C4⋊C4—111no—
248C22×C4⋊C4—112no—
249C22×C4⋊C4—112no—
250C22×C4⋊C4—111no—
251C22×C4⋊C4—112no—
252C22×C4⋊C4—112no—
253C22×C4⋊C4—112no—
254C22×C4⋊C4—228no—
255C22×C22⋊C4—111no—
256C22×C22⋊C4—111no—
257C22×C22⋊C4C2×D1111yescharacteristic
258C22×C22⋊C4C2×D1111yescharacteristic
259#400—1116no—
260#398—1116no—
261#398—1116no—
262#395—1116no—
263#385—118no—
264#385—118no—
265#381—118no—
266#381C2×D1118yes—
267#380—118no—
268C2×#95—112no—
269C2×#95—112no—
270C2×#95—112no—
271C2×#95—112no—
272C2×#95—112no—
273C2×#95C2×D1112yes—
274C2×#95C2×D1112yes—
275C22×C11—232no—
276C22×C11—24no—
277C22×C11—24no—
278C22×C11—28no—
279C22×C11—28no—
280C22×C11C2×C22⋊Q818yes—
281C22×C11C2×C22⋊Q814yes—
282C22×C11#53414yes—
283C22×C11#53614yes—
284C22×C11#53918yes—
285C22×C11#54418yes—
286C22×C11C23×D411yescharacteristic
287C22×C11C23×Q811yescharacteristic
288C22×C11C22×#4111yescharacteristic
289C22×C11C2×H(5,𝔽2)12yes—
290C22×C11C2×2−1+412yes—
291C4×C11—28no—
292C4×C11—42no—
293C4×C11—42no—
294C4×C11—44no—
295Dic11—24no—
296Dic11—24no—
297Dic11—42no—
298Dic11—44no—
299Dic11—42no—
300Dic11—44no—
301C25C22×D1111yescharacteristic
302C22×Q8—114no—
303C22×Q8—224no—
304C22×Q8—444no—
305C23×C4—24no—
306C23×C4—24no—
307C23×C4—111no—
308C23×C4—111no—
309C23×C4—118no—
310C23×C4—114no—
311C23×C4—111no—
312C23×C4—111no—
313C23×C4—112no—
314C23×C4—112no—
315C23×C4—114no—
316C23×C4—224no—
317C23×C4—444no—
318C23×C4—444no—
319C23×C4Dic2218yescomplemented
320C23×C4C22×D1111yescharacteristic
321C23×C4C22×D1111yescharacteristic
322C23×C4C22×D1112yes—
323C23×C4C22×D1112yes—
324C23×C4C22×D1114yes—
325C22⋊Q8—2232no—
326C2×C4⋊C4—118no—
327C2×C4⋊C4—118no—
328C2×C4⋊C4—114no—
329C2×C4⋊C4—114no—
330C2×C4⋊C4—114no—
331C2×C4⋊C4—118no—
332C2×C4⋊C4—118no—
333C2×C4⋊C4—118no—
334C2×C4⋊C4—228no—
335C2×C4⋊C4—228no—
336C2×C4⋊C4—2232no—
337C2×C4⋊C4—224no—
338C2×C4⋊C4—224no—
339C2×C4⋊C4—224no—
340C2×C4⋊C4—444no—
341C2×C4⋊C4—444no—
342C2×C4⋊C4—444no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—114no—
346C2×C22⋊C4—114no—
347C2×C22⋊C4—224no—
348C2×C22⋊C4—224no—
349C2×C22⋊C4C22×D1114yes—
350C2×C22⋊C4C22×D1114yes—
351#95—118no—
352#95—118no—
353#95—118no—
354#95—118no—
355#95—118no—
356#95C22×D1118yes—
357#95C22×D1118yes—
358C2×C11—28no—
359C2×C11#262718yescomplemented
360C2×C11C22×C22⋊Q811yescharacteristic
361C2×C11C2×#53411yescharacteristic
362C2×C11C2×#53611yescharacteristic
363C2×C11C2×#53912yes—
364C2×C11C2×#54412yes—
365C24—24no—
366C24—24no—
367C24C2×Dic2214yes—
368C24D4×D1114yes—
369C24#434114yes—
370C24C23×D1112yes—
371C24C23×D1111yescharacteristic
372C2×Q8—228no—
373C2×Q8—448no—
374C2×Q8—4416no—
375C22×C4—232no—
376C22×C4—24no—
377C22×C4—28no—
378C22×C4—24no—
379C22×C4—28no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—24no—
383C22×C4—24no—
384C22×C4—24no—
385C22×C4—24no—
386C22×C4—24no—
387C22×C4—114no—
388C22×C4—114no—
389C22×C4—112no—
390C22×C4—112no—
391C22×C4—1116no—
392C22×C4—112no—
393C22×C4—114no—
394C22×C4—112no—
395C22×C4—114no—
396C22×C4—224no—
397C22×C4—224no—
398C22×C4—222no—
399C22×C4—222no—
400C22×C4—228no—
401C22×C4—224no—
402C22×C4—224no—
403C22×C4—224no—
404C22×C4—224no—
405C22×C4—224no—
406C22×C4—224no—
407C22×C4—224no—
408C22×C4—224no—
409C22×C4—4416no—
410C22×C4—448no—
411C22×C4—448no—
412C22×C4—4416no—
413C22×C4C2×Dic2218yes—
414C22×C4C2×Dic22116yescomplemented
415C22×C4C23×D1112yes—
416C22×C4C23×D1114yes—
417C22×C4C23×D1112yes—
418C22×C4C23×D1114yes—
419C4⋊C4—2216no—
420C4⋊C4—2216no—
421C4⋊C4—228no—
422C4⋊C4—228no—
423C4⋊C4—228no—
424C4⋊C4—448no—
425C4⋊C4—448no—
426C4⋊C4—448no—
427C22⋊C4—28no—
428C22⋊C4—28no—
429C22⋊C4—228no—
430C22⋊C4—228no—
431C11C2×#262711yescharacteristic, complemented, Sylow
432C23—216no—
433C23—28no—
434C23—28no—
435C23—24no—
436C23—216no—
437C23—24no—
438C23#66931116yes—
439C23C22×Dic2214yes—
440C23C22×Dic2212yes—
441C23C2×D4×D1114yes—
442C23C2×D4×D1112yes—
443C23C2×#434114yes—
444C23C2×#434112yes—
445C23#6704214yes—
446C23#6704314yes—
447C23C24×D1111yescharacteristic
448Q8—4416no—
449C2×C4—216no—
450C2×C4—232no—
451C2×C4—24no—
452C2×C4—24no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—24no—
456C2×C4—24no—
457C2×C4—24no—
458C2×C4—24no—
459C2×C4—24no—
460C2×C4—44no—
461C2×C4—44no—
462C2×C4—48no—
463C2×C4—114no—
464C2×C4—114no—
465C2×C4—228no—
466C2×C4—228no—
467C2×C4—224no—
468C2×C4—224no—
469C2×C4—222no—
470C2×C4—222no—
471C2×C4—224no—
472C2×C4—224no—
473C2×C4—224no—
474C2×C4—224no—
475C2×C4—224no—
476C2×C4—224no—
477C2×C4—224no—
478C2×C4—224no—
479C2×C4—4416no—
480C2×C4—4416no—
481C2×C4—444no—
482C2×C4—448no—
483C2×C4—444no—
484C2×C4—448no—
485C2×C4C22×Dic2218yes—
486C22—232no—
487C22—24no—
488C22—24no—
489C22—28no—
490C22—28no—
491C22C2×#6693118yes—
492C22C2×#6693114yes—
493C22#1062305018yes—
494C22#1062317914yes—
495C22#1062318414yes—
496C22#1062319618yes—
497C22C23×Dic2211yescharacteristic
498C22C22×D4×D1111yescharacteristic
499C22C22×#434111yescharacteristic
500C22C2×#6704212yes—
501C22C2×#6704312yes—
502C4—28no—
503C4—42no—
504C4—42no—
505C4—44no—
506C4—224no—
507C4—224no—
508C4—444no—
509C4—442no—
510C4—442no—
511C4—444no—
512C2—28no—
513C2#1307443318yesdirect product factor
514C2C22×#6693111yescharacteristic
515C2C2×#1062318411yescharacteristic
516C2C2×#1062317911yescharacteristic
517C2C2×#1062319612yes—
518C2C2×#1062305012yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#381C2
socleC24×C11C24
prime radicalC25×C11C23
hypercenterC2×#381D11
hypocenterC11C2×#2627
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#381

Complements

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

NH ≅ G/Ntype
3. #13074433C2direct (N × H)
4. C2×#10622273C2semidirect
5. C2×#10622270C2semidirect
6. C2×#10622274C2semidirect
7. C2×#10622269C2semidirect
45. #10622274C22semidirect
46. #10622273C22semidirect
47. #10622270C22semidirect
48. #10622269C22semidirect
52. C23×C4×C11Q8semidirect
127. C22×C4×C11C2×Q8semidirect
319. C23×C4Dic22semidirect
359. C2×C11#2627semidirect
414. C22×C4C2×Dic22semidirect
431. C11C2×#2627semidirect
513. C2#13074433direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669312
C23×C4⋊Dic112
#130744332
C2×#106222732
C2×#106222702
C2×#106222742
C2×#106222692
C2×#106225632
C2×#106225592
C2×#106228242
C2×#106225552
C2×C11×#3812
C2×#262711