Finite Group Databasebeta

← C2×#13073992 #14924002

Subgroups — C2×#13073992 #14924002

Order 2816.

3094 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×#66999C211yesmaximal, characteristic
2C22×C4⋊C4×D11C211yesmaximal, characteristic
3#13073992C2116yesmaximal, direct product factor
4C2×#10622274C211yesmaximal, characteristic, complemented
5C2×#10622596C211yesmaximal, characteristic, complemented
6C2×#10622842C211yesmaximal, characteristic, complemented
7C2×#10622260C212yesmaximal, complemented
8C2×#10622586C212yesmaximal, complemented
9C2×#10622281C212yesmaximal
10C2×#10622602C212yesmaximal
11C2×#10622279C211yesmaximal, characteristic
12C2×C11×#395C211yesmaximal, characteristic, complemented
13C23×Q8×C11C2211yescharacteristic
14C23×C4×D11C2211yescharacteristic
15C23×C4×D11C2211yescharacteristic
16C23×C4×D11C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C4⋊C4C2212yes—
19C2×#66999—28no—
20C2×#66999C2218yes—
21C22×(C2×D11)⋊C4C2212yes—
22C22×(C2×D11)⋊C4C2212yes—
23C22×C4⋊Dic11C2211yescharacteristic
24C22×C4⋊Dic11C2212yes—
25C22×C4⋊Dic11C2211yescharacteristic
26C22×Dic11⋊C4C2211yescharacteristic
27C22×Dic11⋊C4C2211yescharacteristic
28C22×Dic11⋊C4C2212yes—
29C22×Dic11⋊C4C2212yes—
30C22×Dic11⋊C4C2212yes—
31C22×C4×Dic11C2212yes—
32C2×C4⋊C4×D11—28no—
33C2×C4⋊C4×D11C2218yes—
34C11×#395C2218yescomplemented
35C2×C11×#95C2211yescharacteristic
36C2×C11×#95C2212yes—
37#10622842C2218yescomplemented
38C2×C11⋊#95C2211yescharacteristic
39C2×C11⋊#95C2212yes—
40C2×C11⋊#95C2212yes—
41C2×C11⋊#95C2212yes—
42#10622602C22116yes—
43#10622596C2218yescomplemented
44#10622586C22116yescomplemented
45#10622281C22116yes—
46#10622279C2218yes—
47#10622274C2218yescomplemented
48#10622260C22116yescomplemented
49C24×D11C2311yescharacteristic
50C22×Q8×C11—24no—
51C22×Q8×C11—44no—
52C22×Q8×C11C2314yes—
53C23×C4×C11C2312yes—
54C23×C4×C11C2311yescharacteristic
55C23×C4×C11C2311yescharacteristic
56C23×C4×C11C2312yes—
57C23×C4×C11C2311yescharacteristic
58C23×Dic11C2311yescharacteristic
59C23×Dic11C2312yes—
60C23×Dic11C2311yescharacteristic
61C23×Dic11C2312yes—
62C23×Dic11C2311yescharacteristic
63C22×C4×D11—24no—
64C22×C4×D11—24no—
65C22×C4×D11—24no—
66C22×C4×D11—24no—
67C22×C4×D11—44no—
68C22×C4×D11—44no—
69C22×C4×D11D418yes—
70C22×C4×D11C2314yes—
71C22×C4×D11C2314yes—
72C22×C4×D11C2314yes—
73C2×C11×C4⋊C4—24no—
74C2×C11×C4⋊C4—44no—
75C2×C11×C4⋊C4C2314yes—
76C2×C11×C4⋊C4C2318yes—
77#66999—232no—
78C2×(C2×D11)⋊C4—28no—
79C2×(C2×D11)⋊C4Q8116yescomplemented
80C2×(C2×D11)⋊C4C2318yes—
81C2×(C2×D11)⋊C4C2318yes—
82C2×C4⋊Dic11—24no—
83C2×C4⋊Dic11—24no—
84C2×C4⋊Dic11—28no—
85C2×C4⋊Dic11C2314yes—
86C2×C4⋊Dic11C2318yes—
87C2×C4⋊Dic11C2314yes—
88C2×Dic11⋊C4—24no—
89C2×Dic11⋊C4—28no—
90C2×Dic11⋊C4—24no—
91C2×Dic11⋊C4—28no—
92C2×Dic11⋊C4—44no—
93C2×Dic11⋊C4C2318yes—
94C2×Dic11⋊C4C2318yes—
95C2×Dic11⋊C4C2314yes—
96C2×Dic11⋊C4C2314yes—
97C2×Dic11⋊C4C2318yes—
98C2×C4×Dic11—44no—
99C2×C4×Dic11C2318yes—
100C4⋊C4×D11—232no—
101C11×#95C2318yes—
102C11×#95C2314yes—
103C11⋊#95C2318yes—
104C11⋊#95C2314yes—
105C11⋊#95C2318yes—
106C11⋊#95C2318yes—
107C2×#2583—111nomaximal, Sylow
108C24×C11C2411yescharacteristic
109C23×D11—22no—
110C23×D11—22no—
111C23×D11—24no—
112C23×D11C2×D414yes—
113C23×D11C2×Q818yes—
114C23×D11C2412yes—
115C2×Q8×C11—28no—
116C2×Q8×C11—48no—
117C2×Q8×C11—416no—
118C22×C4×C11—22no—
119C22×C4×C11—24no—
120C22×C4×C11—22no—
121C22×C4×C11—24no—
122C22×C4×C11—24no—
123C22×C4×C11—24no—
124C22×C4×C11—22no—
125C22×C4×C11—24no—
126C22×C4×C11—24no—
127C22×C4×C11—24no—
128C22×C4×C11C2×D414yes—
129C22×C4×C11C2×Q818yes—
130C22×C4×C11#4114yes—
131C22×C4×C11C2412yes—
132C22×C4×C11C2414yes—
133C22×C4×C11C2412yes—
134C22×C4×C11C2414yes—
135C22×C4×C11C2412yes—
136C22×Dic11—22no—
137C22×Dic11—24no—
138C22×Dic11—22no—
139C22×Dic11—24no—
140C22×Dic11—22no—
141C22×Dic11—24no—
142C22×Dic11—24no—
143C22×Dic11—24no—
144C22×Dic11—24no—
145C22×Dic11—24no—
146C22×Dic11C2×D414yes—
147C22×Dic11C2×Q818yes—
148C22×Dic11#4114yes—
149C22×Dic11C2412yes—
150C22×Dic11C2414yes—
151C22×Dic11C2412yes—
152C22×Dic11C2414yes—
153C22×Dic11C2412yes—
154C2×C4×D11—232no—
155C2×C4×D11—28no—
156C2×C4×D11—28no—
157C2×C4×D11—28no—
158C2×C4×D11—28no—
159C2×C4×D11—416no—
160C2×C4×D11—48no—
161C2×C4×D11—48no—
162C2×C4×D11—416no—
163C2×C4×D11C2×D4116yes—
164C11×C4⋊C4—28no—
165C11×C4⋊C4—48no—
166(C2×D11)⋊C4—216no—
167(C2×D11)⋊C4C2×Q8132yescomplemented
168C4⋊Dic11—28no—
169C4⋊Dic11—216no—
170C4⋊Dic11—28no—
171Dic11⋊C4—28no—
172Dic11⋊C4—216no—
173Dic11⋊C4—28no—
174Dic11⋊C4—216no—
175Dic11⋊C4—48no—
176C4×Dic11—48no—
177C22×C22⋊Q8—111no—
178C23×C4⋊C4—111no—
179#2583—1116no—
180C2×#398—111no—
181C2×#398—111no—
182C2×#395—111no—
183C2×#395D1111yescharacteristic, complemented
184C2×#389—112no—
185C2×#389—112no—
186C2×#385—112no—
187C2×#385—112no—
188C2×C4×C22⋊C4—111no—
189C23×C11C22×D412yes—
190C23×C11C22×Q814yes—
191C23×C11C2×#4112yes—
192C23×C11C2×#4112yes—
193C23×C11H(5,𝔽2)14yes—
194C23×C11C2511yescharacteristic
195C22×D11—28no—
196C22×D11—28no—
197C22×D11—216no—
198C22×D11—216no—
199C22×D11—22no—
200C22×D11—22no—
201C22×D11—24no—
202C22×D11C4⋊Q8116yes—
203C22×D11C22×D414yes—
204C22×D11C22×Q818yes—
205Q8×C11—416no—
206C2×C4×C11—28no—
207C2×C4×C11—28no—
208C2×C4×C11—216no—
209C2×C4×C11—22no—
210C2×C4×C11—24no—
211C2×C4×C11—22no—
212C2×C4×C11—24no—
213C2×C4×C11—24no—
214C2×C4×C11—24no—
215C2×C4×C11—22no—
216C2×C4×C11—24no—
217C2×C4×C11—24no—
218C2×C4×C11—24no—
219C2×C4×C11—44no—
220C2×C4×C11—48no—
221C2×C4×C11C22×D414yes—
222C2×C4×C11C22×Q818yes—
223C2×C4×C11C2×#4114yes—
224C2×Dic11—28no—
225C2×Dic11—28no—
226C2×Dic11—216no—
227C2×Dic11—22no—
228C2×Dic11—24no—
229C2×Dic11—22no—
230C2×Dic11—24no—
231C2×Dic11—24no—
232C2×Dic11—24no—
233C2×Dic11—22no—
234C2×Dic11—24no—
235C2×Dic11—24no—
236C2×Dic11—24no—
237C2×Dic11—48no—
238C2×Dic11—44no—
239C2×Dic11C22×D414yes—
240C2×Dic11C22×Q818yes—
241C2×Dic11C2×#4114yes—
242C4×D11—232no—
243C4×D11—416no—
244C4×D11—416no—
245C23×Q8C2×D1111yescharacteristic
246C24×C4—111no—
247C24×C4—111no—
248C24×C4—111no—
249C2×C22⋊Q8—118no—
250C2×C22⋊Q8—228no—
251C22×C4⋊C4—111no—
252C22×C4⋊C4—112no—
253C22×C4⋊C4—111no—
254C22×C4⋊C4—112no—
255C22×C4⋊C4—111no—
256C22×C4⋊C4—112no—
257C22×C4⋊C4—111no—
258C22×C4⋊C4—112no—
259C22×C4⋊C4—118no—
260C22×C4⋊C4—228no—
261C22×C4⋊C4C2×D1111yescharacteristic
262C22×C4⋊C4C2×D1112yes—
263C22×C22⋊C4—112no—
264C22×C22⋊C4—112no—
265C22×C42—112no—
266#398—118no—
267#398—118no—
268#395—118no—
269#395C2×D1118yescomplemented
270#389—1116no—
271#389—1116no—
272#385—1116no—
273#385—1116no—
274C4×C22⋊C4—118no—
275C2×#95—111no—
276C2×#95—112no—
277C2×#95—112no—
278C2×#95—112no—
279C2×#95C2×D1111yescharacteristic
280C2×#95C2×D1112yes—
281C22×C11#52514yes—
282C22×C11C2×C4⋊Q814yes—
283C22×C11#53414yes—
284C22×C11#55418yes—
285C22×C11#55418yes—
286C22×C11C23×D411yescharacteristic
287C22×C11C23×Q812yes—
288C22×C11C22×#4111yescharacteristic
289C22×C11C22×#4111yescharacteristic
290C22×C11C2×H(5,𝔽2)12yes—
291C2×D11—232no—
292C2×D11—24no—
293C2×D11—24no—
294C2×D11—28no—
295C2×D11—28no—
296C2×D11C2×C4⋊Q818yes—
297C4×C11—24no—
298C4×C11—24no—
299C4×C11—28no—
300C4×C11—44no—
301C4×C11—42no—
302Dic11—24no—
303Dic11—24no—
304Dic11—28no—
305Dic11—44no—
306Dic11—42no—
307C25—111no—
308C22×Q8—24no—
309C22×Q8—44no—
310C22×Q8C22×D1114yes—
311C23×C4—112no—
312C23×C4—111no—
313C23×C4—111no—
314C23×C4—118no—
315C23×C4—114no—
316C23×C4—112no—
317C23×C4—111no—
318C23×C4—114no—
319C23×C4—114no—
320C23×C4—224no—
321C23×C4—224no—
322C23×C4—224no—
323C23×C4—224no—
324C23×C4—444no—
325C23×C4—444no—
326C23×C4C22×D1112yes—
327C23×C4C22×D1111yescharacteristic
328C23×C4C22×D1111yescharacteristic
329C23×C4C22×D1112yes—
330C23×C4C22×D1111yescharacteristic
331C22⋊Q8—2232no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4—44no—
334C2×C4⋊C4—114no—
335C2×C4⋊C4—114no—
336C2×C4⋊C4—114no—
337C2×C4⋊C4—118no—
338C2×C4⋊C4—114no—
339C2×C4⋊C4—118no—
340C2×C4⋊C4—118no—
341C2×C4⋊C4—118no—
342C2×C4⋊C4—2232no—
343C2×C4⋊C4—224no—
344C2×C4⋊C4—224no—
345C2×C4⋊C4—228no—
346C2×C4⋊C4—228no—
347C2×C4⋊C4—224no—
348C2×C4⋊C4—224no—
349C2×C4⋊C4—228no—
350C2×C4⋊C4—444no—
351C2×C4⋊C4C22×D1114yes—
352C2×C4⋊C4C22×D1118yes—
353C2×C22⋊C4—1116no—
354C2×C22⋊C4—118no—
355C2×C22⋊C4—118no—
356C2×C22⋊C4—228no—
357C2×C42—118no—
358C2×C42—444no—
359#95—114no—
360#95—118no—
361#95—118no—
362#95—118no—
363#95C22×D1114yes—
364#95C22×D1118yes—
365C2×C11#258318yescomplemented
366C2×C11C2×#52511yescharacteristic
367C2×C11C22×C4⋊Q811yescharacteristic
368C2×C11C2×#53411yescharacteristic
369C2×C11C2×#55412yes—
370C2×C11C2×#55412yes—
371D11—28no—
372C24—114no—
373C24—118no—
374C24—112no—
375C24—224no—
376C24—222no—
377C24—222no—
378C24C23×D1111yescharacteristic
379C2×Q8—28no—
380C2×Q8—48no—
381C2×Q8—416no—
382C22×C4—22no—
383C22×C4—24no—
384C22×C4—24no—
385C22×C4—24no—
386C22×C4—22no—
387C22×C4—24no—
388C22×C4—22no—
389C22×C4—24no—
390C22×C4—24no—
391C22×C4—24no—
392C22×C4—114no—
393C22×C4—118no—
394C22×C4—114no—
395C22×C4—114no—
396C22×C4—112no—
397C22×C4—112no—
398C22×C4—1116no—
399C22×C4—114no—
400C22×C4—112no—
401C22×C4—228no—
402C22×C4—228no—
403C22×C4—2232no—
404C22×C4—228no—
405C22×C4—222no—
406C22×C4—224no—
407C22×C4—224no—
408C22×C4—224no—
409C22×C4—222no—
410C22×C4—228no—
411C22×C4—224no—
412C22×C4—222no—
413C22×C4—224no—
414C22×C4—224no—
415C22×C4—224no—
416C22×C4—4416no—
417C22×C4—448no—
418C22×C4—448no—
419C22×C4—4416no—
420C22×C4D4×D1114yes—
421C22×C4Q8×D1118yes—
422C22×C4#434314yes—
423C22×C4C23×D1112yes—
424C22×C4C23×D1114yes—
425C22×C4C23×D1112yes—
426C22×C4C23×D1114yes—
427C22×C4C23×D1112yes—
428C4⋊C4—28no—
429C4⋊C4—48no—
430C4⋊C4—228no—
431C4⋊C4—228no—
432C4⋊C4—2216no—
433C4⋊C4—2216no—
434C4⋊C4—228no—
435C4⋊C4—228no—
436C4⋊C4—2216no—
437C4⋊C4—448no—
438C22⋊C4—1132no—
439C22⋊C4—2216no—
440C42—448no—
441C11C2×#258311yescharacteristic, complemented, Sylow
442C23—1116no—
443C23—114no—
444C23—118no—
445C23—2216no—
446C23—228no—
447C23—228no—
448C23—2216no—
449C23—224no—
450C23—222no—
451C23—222no—
452C23C2×D4×D1112yes—
453C23#6703714yes—
454C23C2×Q8×D1114yes—
455C23C2×#434312yes—
456C23#41×D1112yes—
457C23C24×D1111yescharacteristic
458Q8—416no—
459C2×C4—28no—
460C2×C4—28no—
461C2×C4—216no—
462C2×C4—22no—
463C2×C4—24no—
464C2×C4—24no—
465C2×C4—24no—
466C2×C4—22no—
467C2×C4—24no—
468C2×C4—22no—
469C2×C4—24no—
470C2×C4—24no—
471C2×C4—24no—
472C2×C4—44no—
473C2×C4—48no—
474C2×C4—114no—
475C2×C4—118no—
476C2×C4—114no—
477C2×C4—2232no—
478C2×C4—2216no—
479C2×C4—228no—
480C2×C4—228no—
481C2×C4—222no—
482C2×C4—224no—
483C2×C4—224no—
484C2×C4—224no—
485C2×C4—222no—
486C2×C4—224no—
487C2×C4—222no—
488C2×C4—224no—
489C2×C4—224no—
490C2×C4—224no—
491C2×C4—4416no—
492C2×C4—4416no—
493C2×C4—444no—
494C2×C4—448no—
495C2×C4C2×D4×D1114yes—
496C2×C4C2×Q8×D1118yes—
497C2×C4C2×#434314yes—
498C22—118no—
499C22—224no—
500C22—228no—
501C22—228no—
502C22—224no—
503C22—2232no—
504C22#1062312014yes—
505C22#1062315814yes—
506C22#1062316718yes—
507C22D11×C4⋊Q814yes—
508C22#1062326118yes—
509C22C22×D4×D1111yescharacteristic
510C22C2×#6703712yes—
511C22C22×Q8×D1112yes—
512C22C22×#434311yescharacteristic
513C22C2×#41×D1111yescharacteristic
514C4—24no—
515C4—28no—
516C4—24no—
517C4—42no—
518C4—44no—
519C4—224no—
520C4—228no—
521C4—224no—
522C4—444no—
523C4—442no—
524C2—228no—
525C2#1307399218yesdirect product factor
526C2C2×#1062315811yescharacteristic
527C2C2×D11×C4⋊Q811yescharacteristic
528C2C2×#1062312011yescharacteristic
529C2C2×#1062316712yes—
530C2C2×#1062326112yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#395C2
socleC24×C11C24
prime radicalC24×D11C23
hypercenterC2×#395D11
hypocenterC11C2×#2583
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#395

Complements

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

NH ≅ G/Ntype
3. #13073992C2direct (N × H)
4. C2×#10622274C2semidirect
5. C2×#10622596C2semidirect
6. C2×#10622842C2semidirect
7. C2×#10622260C2semidirect
8. C2×#10622586C2semidirect
12. C2×C11×#395C2semidirect
34. C11×#395C22semidirect
37. #10622842C22semidirect
43. #10622596C22semidirect
44. #10622586C22semidirect
47. #10622274C22semidirect
48. #10622260C22semidirect
79. C2×(C2×D11)⋊C4Q8semidirect
167. (C2×D11)⋊C4C2×Q8semidirect
183. C2×#395D11semidirect
269. #395C2×D11semidirect
365. C2×C11#2583semidirect
441. C11C2×#2583semidirect
525. C2#13073992direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669992
C22×C4⋊C4×D112
#130739922
C2×#106222742
C2×#106225962
C2×#106228422
C2×#106222602
C2×#106225862
C2×#106222812
C2×#106226022
C2×#106222792
C2×C11×#3952
C2×#258311