Finite Group Databasebeta

← C2×#13074534 #14920178

Subgroups — C2×#13074534 #14920178

Order 2816.

2958 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×C4×C22⋊D11C211yesmaximal, characteristic
2#13074534C2116yesmaximal, direct product factor
3C2×#10622593C211yesmaximal, characteristic, complemented
4C2×#10622565C212yesmaximal, complemented
5C2×#10622606C211yesmaximal, characteristic, complemented
6C2×#10622842C211yesmaximal, characteristic, complemented
7C2×#10622572C212yesmaximal
8C2×#10622844C211yesmaximal, characteristic, complemented
9C2×#10622591C212yesmaximal, complemented
10C2×#10622602C212yesmaximal, complemented
11C2×#10622824C211yesmaximal, characteristic, complemented
12C22×C11×C22⋊Q8C211yesmaximal, characteristic, complemented
13C23×Q8×C11C2211yescharacteristic
14C24×C4×C11C2211yescharacteristic
15C23×C22⋊D11C2211yescharacteristic
16C23×C4×D11C2211yescharacteristic
17C2×C11×C22⋊Q8—28no—
18C2×C11×C22⋊Q8C2218yescomplemented
19C22×C11×C4⋊C4C2212yes—
20C22×C11×C4⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4C2212yes—
22C22×C22⋊Dic11C2211yescharacteristic
23C22×C22⋊Dic11C2212yes—
24C2×C4×C22⋊D11—28no—
25C2×C4×C22⋊D11C2218yes—
26C22×(C2×D11)⋊C4C2212yes—
27C22×(C2×D11)⋊C4C2211yescharacteristic
28C22×(C2×D11)⋊C4C2212yes—
29C22×Dic11⋊C4C2211yescharacteristic
30C22×Dic11⋊C4C2212yes—
31C22×Dic11⋊C4C2212yes—
32C22×C4×Dic11C2211yescharacteristic
33#10622844C2218yescomplemented
34#10622842C2218yescomplemented
35#10622824C2218yescomplemented
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2211yescharacteristic
38C2×C11⋊#95C2211yescharacteristic
39C2×C11⋊#95C2212yes—
40C2×C11⋊#95C2212yes—
41C2×C11⋊#95C2212yes—
42C2×C11⋊#95C2212yes—
43#10622606C2218yescomplemented
44#10622602C22116yescomplemented
45#10622593C2218yescomplemented
46#10622591C22116yescomplemented
47#10622572C22116yes—
48#10622565C22116yescomplemented
49C25×C11C2311yescharacteristic
50C24×D11C2311yescharacteristic
51C22×Q8×C11—24no—
52C22×Q8×C11—44no—
53C22×Q8×C11C2314yes—
54C23×C4×C11—44no—
55C23×C4×C11D418yes—
56C23×C4×C11C2312yes—
57C23×C4×C11C2312yes—
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2314yes—
61C22×C22⋊D11—24no—
62C22×C22⋊D11—24no—
63C22×C22⋊D11—24no—
64C22×C22⋊D11C2314yes—
65C23×Dic11C2311yescharacteristic
66C23×Dic11C2311yescharacteristic
67C23×Dic11C2312yes—
68C23×Dic11C2312yes—
69C23×Dic11C2311yescharacteristic
70C22×C4×D11—24no—
71C22×C4×D11—44no—
72C22×C4×D11C2314yes—
73C11×C22⋊Q8—232no—
74C2×C11×C4⋊C4—24no—
75C2×C11×C4⋊C4—28no—
76C2×C11×C4⋊C4C2318yes—
77C2×C11×C4⋊C4C2314yes—
78C2×C11×C22⋊C4—28no—
79C2×C11×C22⋊C4C2318yes—
80C2×C22⋊Dic11—24no—
81C2×C22⋊Dic11—44no—
82C2×C22⋊Dic11C2314yes—
83C2×C22⋊Dic11C2318yes—
84C4×C22⋊D11—232no—
85C2×(C2×D11)⋊C4—28no—
86C2×(C2×D11)⋊C4—24no—
87C2×(C2×D11)⋊C4—44no—
88C2×(C2×D11)⋊C4C2314yes—
89C2×(C2×D11)⋊C4C2318yes—
90C2×(C2×D11)⋊C4C2318yes—
91C2×Dic11⋊C4—24no—
92C2×Dic11⋊C4—28no—
93C2×Dic11⋊C4—44no—
94C2×Dic11⋊C4C2314yes—
95C2×Dic11⋊C4C2318yes—
96C2×Dic11⋊C4C2318yes—
97C2×C4×Dic11—24no—
98C2×C4×Dic11C2314yes—
99C11⋊#95C2318yes—
100C11⋊#95C2318yes—
101C11⋊#95C2318yes—
102C11⋊#95C2314yes—
103C11⋊#95C2314yes—
104C11⋊#95C2318yes—
105C11⋊#95C2318yes—
106C2×#2638—111nomaximal, Sylow
107C24×C11—22no—
108C24×C11—22no—
109C24×C11—24no—
110C24×C11—24no—
111C24×C11C2×D414yes—
112C24×C11C2412yes—
113C24×C11C2411yescharacteristic
114C23×D11—22no—
115C23×D11—22no—
116C23×D11—24no—
117C23×D11—24no—
118C23×D11#4114yes—
119C23×D11C2412yes—
120C2×Q8×C11—28no—
121C2×Q8×C11—48no—
122C2×Q8×C11—416no—
123C22×C4×C11—24no—
124C22×C4×C11—24no—
125C22×C4×C11—24no—
126C22×C4×C11—24no—
127C22×C4×C11—24no—
128C22×C4×C11—24no—
129C22×C4×C11—24no—
130C22×C4×C11—24no—
131C22×C4×C11—416no—
132C22×C4×C11—48no—
133C22×C4×C11C2×D414yes—
134C22×C4×C11C2×D414yes—
135C22×C4×C11C2×D4116yes—
136C22×C4×C11C2414yes—
137C22×C4×C11C2414yes—
138C22×C4×C11C2412yes—
139C22×C4×C11C2412yes—
140C2×C22⋊D11—232no—
141C2×C22⋊D11—28no—
142C2×C22⋊D11—28no—
143C2×C22⋊D11—28no—
144C22×Dic11—22no—
145C22×Dic11—22no—
146C22×Dic11—22no—
147C22×Dic11—22no—
148C22×Dic11—24no—
149C22×Dic11—24no—
150C22×Dic11—24no—
151C22×Dic11—24no—
152C22×Dic11—24no—
153C22×Dic11—24no—
154C22×Dic11—24no—
155C22×Dic11—24no—
156C22×Dic11#4114yes—
157C22×Dic11C2412yes—
158C22×Dic11C2414yes—
159C22×Dic11C2414yes—
160C22×Dic11C2412yes—
161C22×Dic11C2412yes—
162C2×C4×D11—28no—
163C2×C4×D11—48no—
164C2×C4×D11—416no—
165C11×C4⋊C4—28no—
166C11×C4⋊C4—216no—
167C11×C22⋊C4—216no—
168C22⋊Dic11—28no—
169C22⋊Dic11—48no—
170(C2×D11)⋊C4—216no—
171(C2×D11)⋊C4—28no—
172(C2×D11)⋊C4—48no—
173Dic11⋊C4—216no—
174Dic11⋊C4—28no—
175Dic11⋊C4—48no—
176C4×Dic11—28no—
177C22×C22⋊Q8D1111yescharacteristic, complemented
178C22×C4×D4—111no—
179#2638—1116no—
180C2×#398—111no—
181C2×#397—111no—
182C2×#397—112no—
183C2×#395—111no—
184C2×#394—112no—
185C2×#393—111no—
186C2×#387—112no—
187C2×#385—112no—
188C2×#381—111no—
189C23×C11—28no—
190C23×C11—28no—
191C23×C11—28no—
192C23×C11—22no—
193C23×C11—22no—
194C23×C11—24no—
195C23×C11—24no—
196C23×C11—48no—
197C23×C11—48no—
198C23×C11C22×D414yes—
199C23×C11C22×D412yes—
200C23×C11C2×#4112yes—
201C23×C11C2×#4112yes—
202C23×C11H(5,𝔽2)14yes—
203C23×C112−1+414yes—
204C23×C11C2511yescharacteristic
205C22×D11—28no—
206C22×D11—216no—
207C22×D11—22no—
208C22×D11—22no—
209C22×D11—24no—
210C22×D11—24no—
211C22×D11—44no—
212C22×D11—44no—
213C22×D11—48no—
214C22×D11C2×#4114yes—
215Q8×C11—416no—
216C2×C4×C11—28no—
217C2×C4×C11—28no—
218C2×C4×C11—24no—
219C2×C4×C11—24no—
220C2×C4×C11—24no—
221C2×C4×C11—24no—
222C2×C4×C11—24no—
223C2×C4×C11—24no—
224C2×C4×C11—24no—
225C2×C4×C11—24no—
226C2×C4×C11—416no—
227C2×C4×C11—48no—
228C2×C4×C11—48no—
229C2×C4×C11C22×D414yes—
230C2×C4×C11C22×D414yes—
231C22⋊D11—232no—
232C2×Dic11—28no—
233C2×Dic11—22no—
234C2×Dic11—22no—
235C2×Dic11—22no—
236C2×Dic11—22no—
237C2×Dic11—24no—
238C2×Dic11—24no—
239C2×Dic11—24no—
240C2×Dic11—24no—
241C2×Dic11—24no—
242C2×Dic11—24no—
243C2×Dic11—24no—
244C2×Dic11—24no—
245C2×Dic11—44no—
246C2×Dic11—44no—
247C2×Dic11—48no—
248C2×Dic11—48no—
249C2×Dic11C2×#4114yes—
250C4×D11—416no—
251C23×Q8C2×D1111yescharacteristic
252C23×D4—111no—
253C24×C4—111no—
254C24×C4C2×D1111yescharacteristic
255C2×C22⋊Q8—28no—
256C2×C22⋊Q8C2×D1118yescomplemented
257C2×C4×D4—118no—
258C2×C4×D4—228no—
259C22×C4⋊C4—112no—
260C22×C4⋊C4—111no—
261C22×C4⋊C4—112no—
262C22×C4⋊C4C2×D1111yescharacteristic
263C22×C4⋊C4C2×D1112yes—
264C22×C22⋊C4—111no—
265C22×C22⋊C4—111no—
266C22×C22⋊C4—112no—
267C22×C22⋊C4—112no—
268C22×C22⋊C4—112no—
269C22×C22⋊C4C2×D1112yes—
270C22×C42—111no—
271#398—118no—
272#397—118no—
273#397—1116no—
274#395—118no—
275#394—1116no—
276#393—118no—
277#387—1116no—
278#385—1116no—
279#381—118no—
280C2×#95—112no—
281C2×#95—111no—
282C2×#95—112no—
283C2×#95—111no—
284C2×#95—112no—
285C2×#95—112no—
286C2×#95—112no—
287C22×C11—24no—
288C22×C11—24no—
289C22×C11—24no—
290C22×C11—416no—
291C22×C11—44no—
292C22×C11—44no—
293C22×C11#52514yes—
294C22×C11#53414yes—
295C22×C11#53614yes—
296C22×C11#53918yes—
297C22×C11#54218yes—
298C22×C11C23×D411yescharacteristic
299C22×C11C22×#4111yescharacteristic
300C22×C11C22×#4111yescharacteristic
301C22×C11C2×H(5,𝔽2)12yes—
302C22×C11C2×2−1+412yes—
303C2×D11—24no—
304C2×D11—28no—
305C2×D11—416no—
306C2×D11—42no—
307C2×D11—42no—
308C2×D11—44no—
309C4×C11—24no—
310C4×C11—24no—
311C4×C11—44no—
312C4×C11—44no—
313Dic11—24no—
314Dic11—42no—
315Dic11—42no—
316Dic11—44no—
317Dic11—44no—
318C25—111no—
319C25C22×D1111yescharacteristic
320C22×Q8—24no—
321C22×Q8—44no—
322C22×Q8C22×D1114yes—
323C22×D4—114no—
324C22×D4—224no—
325C22×D4—224no—
326C22×D4—224no—
327C23×C4—44no—
328C23×C4—111no—
329C23×C4—112no—
330C23×C4—112no—
331C23×C4—111no—
332C23×C4—111no—
333C23×C4—114no—
334C23×C4—224no—
335C23×C4—444no—
336C23×C4C22⋊D1118yes—
337C23×C4C22×D1112yes—
338C23×C4C22×D1112yes—
339C23×C4C22×D1111yescharacteristic
340C23×C4C22×D1111yescharacteristic
341C23×C4C22×D1114yes—
342C22⋊Q8—232no—
343C4×D4—2232no—
344C2×C4⋊C4—24no—
345C2×C4⋊C4—28no—
346C2×C4⋊C4—114no—
347C2×C4⋊C4—118no—
348C2×C4⋊C4—118no—
349C2×C4⋊C4—228no—
350C2×C4⋊C4—224no—
351C2×C4⋊C4—444no—
352C2×C4⋊C4C22×D1118yes—
353C2×C4⋊C4C22×D1114yes—
354C2×C22⋊C4—28no—
355C2×C22⋊C4—114no—
356C2×C22⋊C4—114no—
357C2×C22⋊C4—118no—
358C2×C22⋊C4—118no—
359C2×C22⋊C4—118no—
360C2×C22⋊C4—228no—
361C2×C22⋊C4—224no—
362C2×C22⋊C4—224no—
363C2×C22⋊C4—444no—
364C2×C22⋊C4—444no—
365C2×C22⋊C4C22×D1118yes—
366C2×C42—114no—
367C2×C42—224no—
368#95—118no—
369#95—114no—
370#95—114no—
371#95—118no—
372#95—118no—
373#95—118no—
374#95—118no—
375C2×C11—44no—
376C2×C11#263818yescomplemented
377C2×C11C2×#52511yescharacteristic
378C2×C11C2×#53411yescharacteristic
379C2×C11C2×#53611yescharacteristic
380C2×C11C2×#53912yes—
381C2×C11C2×#54212yes—
382D11—44no—
383C24—24no—
384C24—24no—
385C24—22no—
386C24—22no—
387C24—114no—
388C24—112no—
389C24—224no—
390C24—224no—
391C24—222no—
392C24—222no—
393C24C2×C22⋊D1114yes—
394C24C23×D1112yes—
395C24C23×D1111yescharacteristic
396C2×Q8—28no—
397C2×Q8—48no—
398C2×Q8—416no—
399C2×D4—228no—
400C2×D4—228no—
401C2×D4—2232no—
402C2×D4—228no—
403C22×C4—24no—
404C22×C4—24no—
405C22×C4—24no—
406C22×C4—24no—
407C22×C4—24no—
408C22×C4—24no—
409C22×C4—24no—
410C22×C4—24no—
411C22×C4—48no—
412C22×C4—416no—
413C22×C4—114no—
414C22×C4—112no—
415C22×C4—112no—
416C22×C4—114no—
417C22×C4—114no—
418C22×C4—112no—
419C22×C4—222no—
420C22×C4—222no—
421C22×C4—224no—
422C22×C4—224no—
423C22×C4—224no—
424C22×C4—224no—
425C22×C4—224no—
426C22×C4—224no—
427C22×C4—224no—
428C22×C4—224no—
429C22×C4—222no—
430C22×C4—222no—
431C22×C4—228no—
432C22×C4—448no—
433C22×C4—4416no—
434C22×C4C2×C22⋊D1114yes—
435C22×C4C2×C22⋊D1114yes—
436C22×C4C2×C22⋊D11116yes—
437C22×C4C23×D1114yes—
438C22×C4C23×D1114yes—
439C22×C4C23×D1112yes—
440C22×C4C23×D1112yes—
441C4⋊C4—28no—
442C4⋊C4—216no—
443C4⋊C4—2216no—
444C4⋊C4—228no—
445C4⋊C4—448no—
446C22⋊C4—216no—
447C22⋊C4—2216no—
448C22⋊C4—228no—
449C22⋊C4—228no—
450C22⋊C4—448no—
451C22⋊C4—448no—
452C42—228no—
453C11C2×#263811yescharacteristic, complemented, Sylow
454C23—28no—
455C23—28no—
456C23—28no—
457C23—24no—
458C23—24no—
459C23—22no—
460C23—22no—
461C23—48no—
462C23—48no—
463C23—114no—
464C23—228no—
465C23—2216no—
466C23—224no—
467C23—224no—
468C23—222no—
469C23—222no—
470C23—444no—
471C23—444no—
472C23—448no—
473C23#6703714yes—
474C23#6704014yes—
475C23#41×D1112yes—
476C23#41×D1112yes—
477C23C22×C22⋊D1114yes—
478C23C22×C22⋊D1112yes—
479C23C24×D1111yescharacteristic
480Q8—416no—
481D4—2232no—
482C2×C4—28no—
483C2×C4—28no—
484C2×C4—24no—
485C2×C4—24no—
486C2×C4—24no—
487C2×C4—24no—
488C2×C4—24no—
489C2×C4—24no—
490C2×C4—24no—
491C2×C4—24no—
492C2×C4—416no—
493C2×C4—48no—
494C2×C4—48no—
495C2×C4—114no—
496C2×C4—228no—
497C2×C4—222no—
498C2×C4—222no—
499C2×C4—224no—
500C2×C4—224no—
501C2×C4—224no—
502C2×C4—224no—
503C2×C4—224no—
504C2×C4—224no—
505C2×C4—224no—
506C2×C4—224no—
507C2×C4—222no—
508C2×C4—222no—
509C2×C4—4416no—
510C2×C4—444no—
511C2×C4—444no—
512C2×C4—448no—
513C2×C4—448no—
514C2×C4C22×C22⋊D1114yes—
515C2×C4C22×C22⋊D1114yes—
516C22—24no—
517C22—24no—
518C22—24no—
519C22—416no—
520C22—44no—
521C22—44no—
522C22—228no—
523C22—224no—
524C22—442no—
525C22—442no—
526C22—4416no—
527C22—444no—
528C22#1062316918yes—
529C22#1062317118yes—
530C22#1062333514yes—
531C22#1062334714yes—
532C22#1062335914yes—
533C22C2×#6703712yes—
534C22C2×#6704012yes—
535C22C2×#41×D1111yescharacteristic
536C22C2×#41×D1111yescharacteristic
537C22C23×C22⋊D1111yescharacteristic
538C4—24no—
539C4—24no—
540C4—44no—
541C4—44no—
542C4—224no—
543C4—442no—
544C4—442no—
545C4—444no—
546C4—444no—
547C2—44no—
548C2—444no—
549C2#1307453418yesdirect product factor
550C2C2×#1062335911yescharacteristic
551C2C2×#1062333511yescharacteristic
552C2C2×#1062334711yescharacteristic
553C2C2×#1062316912yes—
554C2C2×#1062317112yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC22×C11×C22⋊Q8C2
socleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenterC22×C22⋊Q8D11
hypocenterC11C2×#2638
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. #13074534C2direct (N × H)
3. C2×#10622593C2semidirect
4. C2×#10622565C2semidirect
5. C2×#10622606C2semidirect
6. C2×#10622842C2semidirect
8. C2×#10622844C2semidirect
9. C2×#10622591C2semidirect
10. C2×#10622602C2semidirect
11. C2×#10622824C2semidirect
12. C22×C11×C22⋊Q8C2semidirect
18. C2×C11×C22⋊Q8C22semidirect
33. #10622844C22semidirect
34. #10622842C22semidirect
35. #10622824C22semidirect
43. #10622606C22semidirect
44. #10622602C22semidirect
45. #10622593C22semidirect
46. #10622591C22semidirect
48. #10622565C22semidirect
177. C22×C22⋊Q8D11semidirect
256. C2×C22⋊Q8C2×D11semidirect
376. C2×C11#2638semidirect
453. C11C2×#2638semidirect
549. C2#13074534direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D112
#130745342
C2×#106225932
C2×#106225652
C2×#106226062
C2×#106228422
C2×#106225722
C2×#106228442
C2×#106225912
C2×#106226022
C2×#106228242
C22×C11×C22⋊Q82
C2×#263811