Finite Group Databasebeta

← C2×#13071642 #14913313

Subgroups — C2×#13071642 #14913313

Order 2816.

3310 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66950C211yesmaximal, characteristic
2C22×C4×Dic22C211yesmaximal, characteristic, complemented
3C22×#66945C211yesmaximal, characteristic
4#13071642C2116yesmaximal, direct product factor
5C2×#10622587C211yesmaximal, characteristic, complemented
6C2×#10622603C212yesmaximal
7C2×#10622282C212yesmaximal
8C2×#10622267C212yesmaximal, complemented
9C2×C4⋊C4×Dic11C211yesmaximal, characteristic, complemented
10C2×C4⋊C4×Dic11C212yesmaximal, complemented
11C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic
12C2×C11×#389C211yesmaximal, characteristic, complemented
13C23×C4×D11C2211yescharacteristic
14C23×Dic22C2211yescharacteristic
15C22×C11×C4⋊C4C2212yes—
16C22×C11×C4⋊C4C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C42×C11C2211yescharacteristic
19C22×(C2×D11)⋊C4C2211yescharacteristic
20C22×(C2×D11)⋊C4C2211yescharacteristic
21C22×(C2×D11)⋊C4C2212yes—
22C22×(C2×D11)⋊C4C2212yes—
23C22×C4⋊Dic11C2212yes—
24C22×C4⋊Dic11C2211yescharacteristic
25C22×Dic11⋊C4C2212yes—
26C22×C4×Dic11C2211yescharacteristic
27C22×C4×Dic11C2212yes—
28C22×C4×Dic11C2212yes—
29C22×C4×Dic11C2212yes—
30C2×#66950C4116yescomplemented
31C2×#66950C2218yes—
32C2×#66945—28no—
33C2×#66945C2218yes—
34C2×C4×Dic22—28no—
35C2×C4×Dic22C2218yescomplemented
36C11×#389C2218yescomplemented
37C2×C11×#95C2212yes—
38C2×C11⋊#95C2211yescharacteristic
39C2×C11⋊#95C2211yescharacteristic
40C2×C11⋊#95C2212yes—
41C2×C11⋊#95C2212yes—
42C2×C11⋊#95C2212yes—
43#10622603C22116yes—
44C4⋊C4×Dic11C2218yescomplemented
45C4⋊C4×Dic11C22116yescomplemented
46#10622587C2218yescomplemented
47C4×(C2×D11)⋊C4C2218yes—
48#10622282C22116yes—
49#10622267C22116yescomplemented
50C24×D11C2311yescharacteristic
51C23×C4×C11C2312yes—
52C23×C4×C11C2311yescharacteristic
53C23×C4×C11C2312yes—
54C23×C4×C11C2311yescharacteristic
55C23×C4×C11C2311yescharacteristic
56C23×Dic11C2311yescharacteristic
57C23×Dic11C2311yescharacteristic
58C23×Dic11C2312yes—
59C23×Dic11C2312yes—
60C23×Dic11C2311yescharacteristic
61C22×C4×D11—24no—
62C22×C4×D11—24no—
63C22×C4×D11C2×C418yes—
64C22×C4×D11C2314yes—
65C22×Dic22—24no—
66C22×Dic22—24no—
67C22×Dic22C2×C418yes—
68C22×Dic22C2314yes—
69C2×C11×C4⋊C4—24no—
70C2×C11×C4⋊C4—28no—
71C2×C11×C4⋊C4C2×C418yes—
72C2×C11×C4⋊C4C2314yes—
73C2×C11×C4⋊C4C2318yes—
74C2×C11×C4⋊C4C2314yes—
75C2×C42×C11—24no—
76C2×C42×C11C2314yes—
77C2×(C2×D11)⋊C4—24no—
78C2×(C2×D11)⋊C4—28no—
79C2×(C2×D11)⋊C4—24no—
80C2×(C2×D11)⋊C4C2×C4116yes—
81C2×(C2×D11)⋊C4C2318yes—
82C2×(C2×D11)⋊C4C2314yes—
83C2×(C2×D11)⋊C4C2314yes—
84C2×(C2×D11)⋊C4C2318yes—
85C2×C4⋊Dic11C2×C4116yes—
86C2×C4⋊Dic11D418yes—
87C2×C4⋊Dic11C2318yes—
88C2×C4⋊Dic11C2314yes—
89C2×Dic11⋊C4—28no—
90C2×Dic11⋊C4C2318yes—
91C2×C4×Dic11—24no—
92C2×C4×Dic11—28no—
93C2×C4×Dic11—28no—
94C2×C4×Dic11—28no—
95C2×C4×Dic11C2318yes—
96C2×C4×Dic11C2318yes—
97C2×C4×Dic11C2318yes—
98C2×C4×Dic11C2314yes—
99#66950C2×C4164yescomplemented
100#66945—232no—
101C4×Dic22—232no—
102C11×#95C2318yes—
103C11⋊#95C2314yes—
104C11⋊#95C2318yes—
105C11⋊#95C2318yes—
106C11⋊#95C2318yes—
107C11⋊#95C2314yes—
108C2×#2362—111nomaximal, Sylow
109C24×C11C2411yescharacteristic
110C23×D11—22no—
111C23×D11—22no—
112C23×D11—22no—
113C23×D11—22no—
114C23×D11—22no—
115C23×D11—22no—
116C23×D11C22×C414yes—
117C23×D11C2412yes—
118C22×C4×C11—22no—
119C22×C4×C11—24no—
120C22×C4×C11—24no—
121C22×C4×C11—22no—
122C22×C4×C11—24no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—24no—
126C22×C4×C11—22no—
127C22×C4×C11—24no—
128C22×C4×C11C22×C418yes—
129C22×C4×C11C22×C414yes—
130C22×C4×C11C2×D414yes—
131C22×C4×C11#4114yes—
132C22×C4×C11#4114yes—
133C22×C4×C11C2414yes—
134C22×C4×C11C2412yes—
135C22×C4×C11C2414yes—
136C22×C4×C11C2412yes—
137C22×C4×C11C2412yes—
138C22×Dic11—22no—
139C22×Dic11—24no—
140C22×Dic11—22no—
141C22×Dic11—24no—
142C22×Dic11—24no—
143C22×Dic11—22no—
144C22×Dic11—22no—
145C22×Dic11—22no—
146C22×Dic11—24no—
147C22×Dic11—22no—
148C22×Dic11—22no—
149C22×Dic11C22×C414yes—
150C22×Dic11C22×C418yes—
151C22×Dic11C2×D418yes—
152C22×Dic11#4114yes—
153C22×Dic11C2412yes—
154C22×Dic11C2412yes—
155C22×Dic11C2414yes—
156C22×Dic11C2414yes—
157C22×Dic11C2412yes—
158C2×C4×D11—232no—
159C2×C4×D11—28no—
160C2×C4×D11—28no—
161C2×C4×D11C22×C4116yes—
162C2×Dic22—232no—
163C2×Dic22—28no—
164C2×Dic22—28no—
165C2×Dic22C22×C4116yes—
166C11×C4⋊C4—28no—
167C11×C4⋊C4—216no—
168C11×C4⋊C4C22×C4116yes—
169C42×C11—28no—
170(C2×D11)⋊C4—216no—
171(C2×D11)⋊C4—28no—
172(C2×D11)⋊C4—28no—
173(C2×D11)⋊C4C22×C4132yes—
174C4⋊Dic11C22×C4132yes—
175C4⋊Dic11C2×D4116yes—
176Dic11⋊C4—216no—
177C4×Dic11—216no—
178C4×Dic11—216no—
179C4×Dic11—216no—
180C4×Dic11—28no—
181C22×C22⋊Q8—111no—
182C22×C4×Q8—111no—
183C22×#117—111no—
184#2362—1116no—
185C2×#391—111no—
186C2×#389D1111yescharacteristic, complemented
187C2×#388—112no—
188C2×#388—112no—
189C2×#387—112no—
190C2×C4×C4⋊C4—111no—
191C2×C4×C4⋊C4—112no—
192C2×C4×C22⋊C4—111no—
193C23×C11C23×C412yes—
194C23×C11C22×D412yes—
195C23×C11C2×#4112yes—
196C23×C11C2×#4112yes—
197C23×C11C2×#4112yes—
198C23×C112−1+412yes—
199C23×C112−1+412yes—
200C23×C11C2511yescharacteristic
201C22×D11—28no—
202C22×D11—28no—
203C22×D11—28no—
204C22×D11—22no—
205C22×D11—22no—
206C22×D11—22no—
207C22×D11—22no—
208C22×D11—22no—
209C22×D11—22no—
210C22×D11—44no—
211C22×D11—44no—
212C22×D11—44no—
213C22×D11—44no—
214C22×D11C23×C414yes—
215C2×C4×C11—216no—
216C2×C4×C11—28no—
217C2×C4×C11—22no—
218C2×C4×C11—24no—
219C2×C4×C11—24no—
220C2×C4×C11—22no—
221C2×C4×C11—24no—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11—24no—
225C2×C4×C11—22no—
226C2×C4×C11—24no—
227C2×C4×C11—44no—
228C2×C4×C11—48no—
229C2×C4×C11C4×D4116yes—
230C2×C4×C11C23×C418yes—
231C2×C4×C11C23×C414yes—
232C2×C4×C11C22×D414yes—
233C2×C4×C11C2×#4114yes—
234C2×C4×C11C2×#4114yes—
235C2×Dic11—216no—
236C2×Dic11—28no—
237C2×Dic11—216no—
238C2×Dic11—28no—
239C2×Dic11—22no—
240C2×Dic11—24no—
241C2×Dic11—22no—
242C2×Dic11—24no—
243C2×Dic11—24no—
244C2×Dic11—22no—
245C2×Dic11—24no—
246C2×Dic11—22no—
247C2×Dic11—22no—
248C2×Dic11—22no—
249C2×Dic11—22no—
250C2×Dic11—44no—
251C2×Dic11C23×C414yes—
252C2×Dic11C23×C418yes—
253C2×Dic11C22×D418yes—
254C2×Dic11C2×#4114yes—
255C4×D11—232no—
256Dic22—232no—
257C23×Q8—111no—
258C24×C4—111no—
259C2×C22⋊Q8—118no—
260C2×C22⋊Q8—1116no—
261C2×C4×Q8—118no—
262C2×C4×Q8—228no—
263C2×#117—118no—
264C2×#117—228no—
265C22×C4⋊C4—111no—
266C22×C4⋊C4—112no—
267C22×C4⋊C4—112no—
268C22×C4⋊C4C2×D1111yescharacteristic
269C22×C4⋊C4C2×D1112yes—
270C22×C4⋊C4C2×D1111yescharacteristic
271C22×C22⋊C4—112no—
272C22×C22⋊C4—112no—
273C22×C22⋊C4—111no—
274C22×C22⋊C4—111no—
275C22×C42—112no—
276C22×C42—112no—
277C22×C42—111no—
278C22×C42—112no—
279C22×C42C2×D1111yescharacteristic
280#391—118no—
281#389C2×D1118yescomplemented
282#388—1116no—
283#388—1116no—
284#387—1116no—
285C4×C4⋊C4—1116no—
286C4×C4⋊C4—118no—
287C4×C22⋊C4—118no—
288C2×#95—111no—
289C2×#95—111no—
290C2×#95—112no—
291C2×#95—112no—
292C2×#95—112no—
293C2×#95C2×D1112yes—
294C22×C11C2×C4×D414yes—
295C22×C11C4×#4114yes—
296C22×C11#51914yes—
297C22×C11#54714yes—
298C22×C11#54814yes—
299C22×C11#55214yes—
300C22×C11#55614yes—
301C22×C11C24×C411yescharacteristic
302C22×C11C23×D411yescharacteristic
303C22×C11C22×#4111yescharacteristic
304C22×C11C22×#4111yescharacteristic
305C22×C11C22×#4111yescharacteristic
306C22×C11C2×2−1+411yescharacteristic
307C22×C11C2×2−1+411yescharacteristic
308C2×D11—24no—
309C2×D11—24no—
310C2×D11—24no—
311C2×D11—416no—
312C2×D11—42no—
313C2×D11—42no—
314C2×D11—42no—
315C2×D11—42no—
316C4×C11—28no—
317C4×C11—24no—
318C4×C11—42no—
319C4×C11—44no—
320C4×C11C2×C4×D418yes—
321Dic11—28no—
322Dic11—24no—
323Dic11—28no—
324Dic11—24no—
325Dic11—42no—
326C25—111no—
327C22×Q8—118no—
328C22×Q8—114no—
329C22×Q8—224no—
330C22×Q8—224no—
331C23×C4—112no—
332C23×C4—112no—
333C23×C4—111no—
334C23×C4—111no—
335C23×C4—118no—
336C23×C4—114no—
337C23×C4—111no—
338C23×C4—224no—
339C23×C4—224no—
340C23×C4C22×D1111yescharacteristic
341C23×C4C22×D1112yes—
342C23×C4C22×D1112yes—
343C23×C4C22×D1111yescharacteristic
344C23×C4C22×D1111yescharacteristic
345C22⋊Q8—1164no—
346C4×Q8—2232no—
347#117—2232no—
348C2×C4⋊C4—24no—
349C2×C4⋊C4—28no—
350C2×C4⋊C4—1116no—
351C2×C4⋊C4—118no—
352C2×C4⋊C4—114no—
353C2×C4⋊C4—118no—
354C2×C4⋊C4—118no—
355C2×C4⋊C4—228no—
356C2×C4⋊C4C4×D1118yes—
357C2×C4⋊C4C22×D1114yes—
358C2×C4⋊C4C22×D1118yes—
359C2×C4⋊C4C22×D1114yes—
360C2×C22⋊C4—1116no—
361C2×C22⋊C4—118no—
362C2×C22⋊C4—118no—
363C2×C22⋊C4—114no—
364C2×C22⋊C4—114no—
365C2×C22⋊C4—228no—
366C2×C22⋊C4—224no—
367C2×C22⋊C4—224no—
368C2×C42—24no—
369C2×C42—118no—
370C2×C42—118no—
371C2×C42—114no—
372C2×C42—118no—
373C2×C42—228no—
374C2×C42—228no—
375C2×C42—228no—
376C2×C42—224no—
377C2×C42C22×D1114yes—
378#95—114no—
379#95—114no—
380#95—118no—
381#95—118no—
382#95—118no—
383#95C22×D1118yes—
384C2×C11#236218yescomplemented
385C2×C11C22×C4×D411yescharacteristic
386C2×C11C2×C4×#4111yescharacteristic
387C2×C11C2×#51911yescharacteristic
388C2×C11C2×#54711yescharacteristic
389C2×C11C2×#54811yescharacteristic
390C2×C11C2×#55211yescharacteristic
391C2×C11C2×#55611yescharacteristic
392D11—44no—
393C24—114no—
394C24—112no—
395C24—222no—
396C24—222no—
397C24—222no—
398C24—222no—
399C24—222no—
400C24—222no—
401C24C23×D1111yescharacteristic
402C2×Q8—1116no—
403C2×Q8—2232no—
404C2×Q8—228no—
405C2×Q8—228no—
406C22×C4—22no—
407C22×C4—24no—
408C22×C4—24no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—24no—
412C22×C4—24no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—24no—
416C22×C4—118no—
417C22×C4—114no—
418C22×C4—118no—
419C22×C4—114no—
420C22×C4—112no—
421C22×C4—112no—
422C22×C4—114no—
423C22×C4—114no—
424C22×C4—1116no—
425C22×C4—112no—
426C22×C4—222no—
427C22×C4—224no—
428C22×C4—222no—
429C22×C4—222no—
430C22×C4—224no—
431C22×C4—224no—
432C22×C4—224no—
433C22×C4—222no—
434C22×C4—2232no—
435C22×C4—228no—
436C22×C4—228no—
437C22×C4—222no—
438C22×C4—222no—
439C22×C4—222no—
440C22×C4C2×C4×D1118yes—
441C22×C4C2×C4×D1114yes—
442C22×C4D4×D1114yes—
443C22×C4#434114yes—
444C22×C4#434314yes—
445C22×C4C23×D1114yes—
446C22×C4C23×D1112yes—
447C22×C4C23×D1114yes—
448C22×C4C23×D1112yes—
449C22×C4C23×D1112yes—
450C4⋊C4—28no—
451C4⋊C4—216no—
452C4⋊C4—1132no—
453C4⋊C4—1116no—
454C4⋊C4—2216no—
455C4⋊C4C2×C4×D11116yes—
456C22⋊C4—1132no—
457C22⋊C4—2216no—
458C22⋊C4—228no—
459C22⋊C4—228no—
460C42—28no—
461C42—2216no—
462C42—2216no—
463C42—2216no—
464C42—228no—
465C11C2×#236211yescharacteristic, complemented, Sylow
466C23—114no—
467C23—228no—
468C23—228no—
469C23—228no—
470C23—222no—
471C23—222no—
472C23—222no—
473C23—222no—
474C23—222no—
475C23—222no—
476C23—444no—
477C23—444no—
478C23—444no—
479C23—444no—
480C23C22×C4×D1112yes—
481C23C2×D4×D1112yes—
482C23C2×#434112yes—
483C23C2×#434312yes—
484C23#6704012yes—
485C23#41×D1112yes—
486C23#6704312yes—
487C23C24×D1111yescharacteristic
488Q8—2232no—
489C2×C4—216no—
490C2×C4—28no—
491C2×C4—22no—
492C2×C4—24no—
493C2×C4—24no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—24no—
497C2×C4—24no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—24no—
501C2×C4—48no—
502C2×C4—44no—
503C2×C4—118no—
504C2×C4—114no—
505C2×C4—118no—
506C2×C4—114no—
507C2×C4—228no—
508C2×C4—2216no—
509C2×C4—2216no—
510C2×C4—222no—
511C2×C4—224no—
512C2×C4—222no—
513C2×C4—222no—
514C2×C4—224no—
515C2×C4—224no—
516C2×C4—224no—
517C2×C4—222no—
518C2×C4—228no—
519C2×C4—2232no—
520C2×C4—222no—
521C2×C4—222no—
522C2×C4—222no—
523C2×C4—444no—
524C2×C4#66946116yes—
525C2×C4C22×C4×D1118yes—
526C2×C4C22×C4×D1114yes—
527C2×C4C2×D4×D1114yes—
528C2×C4C2×#434114yes—
529C2×C4C2×#434314yes—
530C22—224no—
531C22—224no—
532C22—224no—
533C22—442no—
534C22—4416no—
535C22—442no—
536C22—442no—
537C22—442no—
538C22C2×#6694614yes—
539C22C4×#434114yes—
540C22#1062310314yes—
541C22#1062312914yes—
542C22#1062316214yes—
543C22#1062322514yes—
544C22#1062326314yes—
545C22C23×C4×D1111yescharacteristic
546C22C22×D4×D1111yescharacteristic
547C22C22×#434111yescharacteristic
548C22C22×#434311yescharacteristic
549C22C2×#6704011yescharacteristic
550C22C2×#41×D1111yescharacteristic
551C22C2×#6704311yescharacteristic
552C4—28no—
553C4—24no—
554C4—42no—
555C4—44no—
556C4—224no—
557C4—224no—
558C4—228no—
559C4—228no—
560C4—442no—
561C4C2×#6694618yes—
562C2—444no—
563C2#1307164218yesdirect product factor
564C2C22×#6694611yescharacteristic
565C2C2×C4×#434111yescharacteristic
566C2C2×#1062310311yescharacteristic
567C2C2×#1062316211yescharacteristic
568C2C2×#1062312911yescharacteristic
569C2C2×#1062322511yescharacteristic
570C2C2×#1062326311yescharacteristic
subgroupG/H
centerC24C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC2×C11×#389C2
socleC24×C11C24
prime radicalC24×D11C23
cosocleC23×C11C25
hypercenterC2×#389D11
hypocenterC11C2×#2362
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
2. C22×C4×Dic22C2semidirect
4. #13071642C2direct (N × H)
5. C2×#10622587C2semidirect
8. C2×#10622267C2semidirect
9. C2×C4⋊C4×Dic11C2semidirect
10. C2×C4⋊C4×Dic11C2semidirect
12. C2×C11×#389C2semidirect
30. C2×#66950C4semidirect
35. C2×C4×Dic22C22semidirect
36. C11×#389C22semidirect
44. C4⋊C4×Dic11C22semidirect
45. C4⋊C4×Dic11C22semidirect
46. #10622587C22semidirect
49. #10622267C22semidirect
99. #66950C2×C4semidirect
186. C2×#389D11semidirect
281. #389C2×D11semidirect
384. C2×C11#2362semidirect
465. C11C2×#2362semidirect
563. C2#13071642direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669502
C22×C4×Dic222
C22×#669452
#130716422
C2×#106225872
C2×#106226032
C2×#106222822
C2×#106222672
C2×C4⋊C4×Dic112
C2×C4×(C2×D11)⋊C42
C2×C11×#3892
C2×#236211