Finite Group Databasebeta

← C2×#13071641 #14913312

Subgroups — C2×#13071641 #14913312

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×#66977C211yesmaximal, characteristic
2C22×C4×Dic22C211yesmaximal, characteristic, complemented
3C22×#66979C211yesmaximal, characteristic
4#13071641C2116yesmaximal, direct product factor
5C2×#10622542C211yesmaximal, characteristic, complemented
6C2×#10622541C211yesmaximal, characteristic, complemented
7C2×#10622558C212yesmaximal
8C2×#10622557C212yesmaximal
9C2×#10622265C212yesmaximal, complemented
10C2×C4×C4⋊Dic11C211yesmaximal, characteristic, complemented
11C2×#10622262C212yesmaximal, complemented
12C2×C4×C11×C22⋊C4C211yesmaximal, characteristic
13C24×C4×C11C2211yescharacteristic
14C23×Dic22C2211yescharacteristic
15C22×C11×C22⋊C4C2211yescharacteristic
16C22×C11×C22⋊C4C2211yescharacteristic
17C22×C42×C11C2211yescharacteristic
18C22×C42×C11C2211yescharacteristic
19C22×C22⋊Dic11C2212yes—
20C22×C22⋊Dic11C2212yes—
21C2×#66979—28no—
22C2×#66979C2218yes—
23C22×C4⋊Dic11C2211yescharacteristic
24C22×C4⋊Dic11C2211yescharacteristic
25C22×C4⋊Dic11C2211yescharacteristic
26C2×#66977C4116yescomplemented
27C2×#66977C2218yes—
28C22×Dic11⋊C4C2212yes—
29C22×Dic11⋊C4C2212yes—
30C22×Dic11⋊C4C2212yes—
31C22×C4×Dic11C2212yes—
32C22×C4×Dic11C2212yes—
33C22×C4×Dic11C2212yes—
34C2×C4×Dic22—28no—
35C2×C4×Dic22C2218yescomplemented
36C4×C11×C22⋊C4C2218yes—
37C2×C11×#95C2211yescharacteristic
38C2×C11×#95C2211yescharacteristic
39C2×C11⋊#95C2212yes—
40C2×C11⋊#95C2212yes—
41C2×C11⋊#95C2212yes—
42C2×C11⋊#95C2212yes—
43#10622558C22116yes—
44#10622557C22116yes—
45C4×C4⋊Dic11C2218yescomplemented
46#10622542C2218yescomplemented
47#10622541C2218yescomplemented
48#10622265C22116yescomplemented
49#10622262C22116yescomplemented
50C25×C11C2311yescharacteristic
51C23×C4×C11—24no—
52C23×C4×C11—24no—
53C23×C4×C11C2×C418yes—
54C23×C4×C11C2311yescharacteristic
55C23×C4×C11C2311yescharacteristic
56C23×C4×C11C2311yescharacteristic
57C23×C4×C11C2314yes—
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×Dic11C2312yes—
62C23×Dic11C2312yes—
63C23×Dic11C2312yes—
64C23×Dic11C2312yes—
65C22×Dic22—24no—
66C22×Dic22—24no—
67C22×Dic22C2×C418yes—
68C22×Dic22C2314yes—
69C2×C11×C22⋊C4—24no—
70C2×C11×C22⋊C4—24no—
71C2×C11×C22⋊C4C2314yes—
72C2×C11×C22⋊C4C2314yes—
73C2×C42×C11—24no—
74C2×C42×C11—24no—
75C2×C42×C11C2314yes—
76C2×C42×C11C2314yes—
77C2×C22⋊Dic11—28no—
78C2×C22⋊Dic11C2×C4116yes—
79C2×C22⋊Dic11C2318yes—
80C2×C22⋊Dic11C2318yes—
81#66979—232no—
82C2×C4⋊Dic11—24no—
83C2×C4⋊Dic11C2×C418yes—
84C2×C4⋊Dic11D418yes—
85C2×C4⋊Dic11C2314yes—
86C2×C4⋊Dic11C2314yes—
87C2×C4⋊Dic11C2314yes—
88#66977C2×C4164yescomplemented
89C2×Dic11⋊C4—28no—
90C2×Dic11⋊C4—28no—
91C2×Dic11⋊C4C2×C4116yes—
92C2×Dic11⋊C4C2318yes—
93C2×Dic11⋊C4C2318yes—
94C2×Dic11⋊C4C2318yes—
95C2×C4×Dic11—28no—
96C2×C4×Dic11—28no—
97C2×C4×Dic11—28no—
98C2×C4×Dic11C2318yes—
99C2×C4×Dic11C2318yes—
100C2×C4×Dic11C2318yes—
101C4×Dic22—232no—
102C11×#95C2314yes—
103C11×#95C2314yes—
104C11⋊#95C2318yes—
105C11⋊#95C2318yes—
106C11⋊#95C2318yes—
107C11⋊#95C2318yes—
108C2×#2362—111nomaximal, Sylow
109C24×C11—22no—
110C24×C11—22no—
111C24×C11—22no—
112C24×C11—22no—
113C24×C11—22no—
114C24×C11—22no—
115C24×C11C22×C414yes—
116C24×C11C2412yes—
117C24×C11C2411yescharacteristic
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—232no—
125C22×C4×C11—28no—
126C22×C4×C11—28no—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11C22×C414yes—
134C22×C4×C11C22×C4116yes—
135C22×C4×C11C22×C414yes—
136C22×C4×C11C2×D414yes—
137C22×C4×C11#4114yes—
138C22×C4×C11#4114yes—
139C22×C4×C11#4114yes—
140C22×C4×C11C2412yes—
141C22×C4×C11C2412yes—
142C22×C4×C11C2412yes—
143C22×C4×C11C2412yes—
144C22×C4×C11C2412yes—
145C22×C4×C11C2412yes—
146C22×Dic11—24no—
147C22×Dic11—24no—
148C22×Dic11—24no—
149C22×Dic11—24no—
150C22×Dic11—24no—
151C22×Dic11—24no—
152C22×Dic11—24no—
153C22×Dic11—24no—
154C22×Dic11—24no—
155C22×Dic11C22×C418yes—
156C22×Dic11C22×C418yes—
157C22×Dic11C2×D418yes—
158C22×Dic11C2414yes—
159C22×Dic11C2414yes—
160C22×Dic11C2414yes—
161C22×Dic11C2414yes—
162C2×Dic22—232no—
163C2×Dic22—28no—
164C2×Dic22—28no—
165C2×Dic22C22×C4116yes—
166C11×C22⋊C4—28no—
167C11×C22⋊C4—28no—
168C42×C11—28no—
169C42×C11—28no—
170C22⋊Dic11—216no—
171C22⋊Dic11C22×C4132yes—
172C4⋊Dic11—28no—
173C4⋊Dic11C22×C4116yes—
174C4⋊Dic11C2×D4116yes—
175Dic11⋊C4—216no—
176Dic11⋊C4—216no—
177Dic11⋊C4C22×C4132yes—
178C4×Dic11—216no—
179C4×Dic11—216no—
180C4×Dic11—216no—
181C22×C22⋊Q8—111no—
182C22×C4×Q8—111no—
183C22×#117—111no—
184#2362—1116no—
185C2×#391—111no—
186C2×#389—111no—
187C2×#388—112no—
188C2×#388—112no—
189C2×#387—112no—
190C2×C4×C4⋊C4—111no—
191C2×C4×C4⋊C4—112no—
192C2×C4×C22⋊C4D1111yescharacteristic
193C23×C11—28no—
194C23×C11—28no—
195C23×C11—28no—
196C23×C11—22no—
197C23×C11—22no—
198C23×C11—22no—
199C23×C11—22no—
200C23×C11—22no—
201C23×C11—22no—
202C23×C11—44no—
203C23×C11—44no—
204C23×C11—44no—
205C23×C11—44no—
206C23×C11C23×C414yes—
207C23×C11C23×C412yes—
208C23×C11C22×D412yes—
209C23×C11C2×#4112yes—
210C23×C11C2×#4112yes—
211C23×C11C2×#4112yes—
212C23×C112−1+412yes—
213C23×C112−1+412yes—
214C23×C11C2511yescharacteristic
215C2×C4×C11—28no—
216C2×C4×C11—28no—
217C2×C4×C11—28no—
218C2×C4×C11—22no—
219C2×C4×C11—22no—
220C2×C4×C11—22no—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11—232no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—44no—
232C2×C4×C11—44no—
233C2×C4×C11C4×D4116yes—
234C2×C4×C11C23×C414yes—
235C2×C4×C11C23×C414yes—
236C2×C4×C11C22×D414yes—
237C2×C4×C11C2×#4114yes—
238C2×C4×C11C2×#4114yes—
239C2×C4×C11C2×#4114yes—
240C2×Dic11—216no—
241C2×Dic11—216no—
242C2×Dic11—216no—
243C2×Dic11—24no—
244C2×Dic11—24no—
245C2×Dic11—24no—
246C2×Dic11—24no—
247C2×Dic11—24no—
248C2×Dic11—24no—
249C2×Dic11—24no—
250C2×Dic11—24no—
251C2×Dic11—24no—
252C2×Dic11—48no—
253C2×Dic11C23×C418yes—
254C2×Dic11C23×C418yes—
255C2×Dic11C22×D418yes—
256Dic22—232no—
257C23×Q8—111no—
258C24×C4C2×D1111yescharacteristic
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—112no—
266C22×C4⋊C4—111no—
267C22×C4⋊C4—111no—
268C22×C4⋊C4—112no—
269C22×C4⋊C4—112no—
270C22×C4⋊C4—111no—
271C22×C22⋊C4—112no—
272C22×C22⋊C4—112no—
273C22×C22⋊C4C2×D1111yescharacteristic
274C22×C22⋊C4C2×D1111yescharacteristic
275C22×C42—112no—
276C22×C42—112no—
277C22×C42—112no—
278C22×C42C2×D1111yescharacteristic
279C22×C42C2×D1111yescharacteristic
280#391—118no—
281#389—118no—
282#388—1116no—
283#388—1116no—
284#387—1116no—
285C4×C4⋊C4—118no—
286C4×C4⋊C4—1116no—
287C4×C22⋊C4C2×D1118yes—
288C2×#95—112no—
289C2×#95—112no—
290C2×#95—112no—
291C2×#95—112no—
292C2×#95C2×D1111yescharacteristic
293C2×#95C2×D1111yescharacteristic
294C22×C11—24no—
295C22×C11—24no—
296C22×C11—24no—
297C22×C11—416no—
298C22×C11—42no—
299C22×C11—42no—
300C22×C11—42no—
301C22×C11—42no—
302C22×C11C2×C4×D414yes—
303C22×C11C4×#4114yes—
304C22×C11#51914yes—
305C22×C11#54714yes—
306C22×C11#54814yes—
307C22×C11#55214yes—
308C22×C11#55614yes—
309C22×C11C24×C411yescharacteristic
310C22×C11C23×D411yescharacteristic
311C22×C11C22×#4111yescharacteristic
312C22×C11C22×#4111yescharacteristic
313C22×C11C22×#4111yescharacteristic
314C22×C11C2×2−1+411yescharacteristic
315C22×C11C2×2−1+411yescharacteristic
316C4×C11—24no—
317C4×C11—24no—
318C4×C11—24no—
319C4×C11—42no—
320C4×C11—42no—
321C4×C11C2×C4×D418yes—
322Dic11—28no—
323Dic11—28no—
324Dic11—28no—
325Dic11—44no—
326C25C22×D1111yescharacteristic
327C22×Q8—118no—
328C22×Q8—114no—
329C22×Q8—224no—
330C22×Q8—224no—
331C23×C4—24no—
332C23×C4—24no—
333C23×C4—112no—
334C23×C4—112no—
335C23×C4—112no—
336C23×C4—112no—
337C23×C4C4×D1118yes—
338C23×C4C22×D1111yescharacteristic
339C23×C4C22×D1111yescharacteristic
340C23×C4C22×D1114yes—
341C23×C4C22×D1111yescharacteristic
342C23×C4C22×D1111yescharacteristic
343C23×C4C22×D1111yescharacteristic
344C23×C4C22×D1111yescharacteristic
345C22⋊Q8—1164no—
346C4×Q8—2232no—
347#117—2232no—
348C2×C4⋊C4—1116no—
349C2×C4⋊C4—118no—
350C2×C4⋊C4—118no—
351C2×C4⋊C4—114no—
352C2×C4⋊C4—118no—
353C2×C4⋊C4—114no—
354C2×C4⋊C4—114no—
355C2×C4⋊C4—118no—
356C2×C4⋊C4—118no—
357C2×C4⋊C4—228no—
358C2×C4⋊C4—228no—
359C2×C4⋊C4—224no—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—1116no—
363C2×C22⋊C4—118no—
364C2×C22⋊C4—118no—
365C2×C22⋊C4—228no—
366C2×C22⋊C4C22×D1114yes—
367C2×C22⋊C4C22×D1114yes—
368C2×C42—24no—
369C2×C42—24no—
370C2×C42—118no—
371C2×C42—118no—
372C2×C42—118no—
373C2×C42—228no—
374C2×C42—228no—
375C2×C42—228no—
376C2×C42C22×D1114yes—
377C2×C42C22×D1114yes—
378#95—118no—
379#95—118no—
380#95—118no—
381#95—118no—
382#95C22×D1114yes—
383#95C22×D1114yes—
384C2×C11—44no—
385C2×C11#236218yescomplemented
386C2×C11C22×C4×D411yescharacteristic
387C2×C11C2×C4×#4111yescharacteristic
388C2×C11C2×#51911yescharacteristic
389C2×C11C2×#54711yescharacteristic
390C2×C11C2×#54811yescharacteristic
391C2×C11C2×#55211yescharacteristic
392C2×C11C2×#55611yescharacteristic
393C24—22no—
394C24—22no—
395C24—22no—
396C24—22no—
397C24—22no—
398C24—22no—
399C24C2×C4×D1114yes—
400C24C23×D1112yes—
401C24C23×D1111yescharacteristic
402C2×Q8—1116no—
403C2×Q8—2232no—
404C2×Q8—228no—
405C2×Q8—228no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—232no—
413C22×C4—28no—
414C22×C4—28no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—118no—
422C22×C4—118no—
423C22×C4—118no—
424C22×C4—114no—
425C22×C4—114no—
426C22×C4—114no—
427C22×C4—114no—
428C22×C4—224no—
429C22×C4—224no—
430C22×C4—224no—
431C22×C4—224no—
432C22×C4—224no—
433C22×C4—224no—
434C22×C4—224no—
435C22×C4—224no—
436C22×C4—224no—
437C22×C4C2×C4×D1114yes—
438C22×C4C2×C4×D11116yes—
439C22×C4C2×C4×D1114yes—
440C22×C4#433914yes—
441C22×C4#433914yes—
442C22×C4D4×D1114yes—
443C22×C4#434114yes—
444C22×C4C23×D1112yes—
445C22×C4C23×D1112yes—
446C22×C4C23×D1112yes—
447C22×C4C23×D1112yes—
448C22×C4C23×D1112yes—
449C22×C4C23×D1112yes—
450C4⋊C4—1132no—
451C4⋊C4—1116no—
452C4⋊C4—1116no—
453C4⋊C4—2216no—
454C4⋊C4—2216no—
455C4⋊C4—228no—
456C22⋊C4—28no—
457C22⋊C4—28no—
458C22⋊C4—1132no—
459C22⋊C4—2216no—
460C42—28no—
461C42—28no—
462C42—2216no—
463C42—2216no—
464C42—2216no—
465C11C2×#236211yescharacteristic, complemented, Sylow
466C23—28no—
467C23—28no—
468C23—28no—
469C23—22no—
470C23—22no—
471C23—22no—
472C23—22no—
473C23—22no—
474C23—22no—
475C23—44no—
476C23—44no—
477C23—44no—
478C23—44no—
479C23C22×C4×D1114yes—
480C23C22×C4×D1112yes—
481C23C2×#433912yes—
482C23C2×#433912yes—
483C23C2×D4×D1112yes—
484C23C2×#434112yes—
485C23#6704312yes—
486C23#6704312yes—
487C23C24×D1111yescharacteristic
488Q8—2232no—
489C2×C4—28no—
490C2×C4—28no—
491C2×C4—28no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—232no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—44no—
506C2×C4—44no—
507C2×C4—118no—
508C2×C4—118no—
509C2×C4—118no—
510C2×C4—2216no—
511C2×C4—2216no—
512C2×C4—2216no—
513C2×C4—224no—
514C2×C4—224no—
515C2×C4—224no—
516C2×C4—224no—
517C2×C4—224no—
518C2×C4—224no—
519C2×C4—224no—
520C2×C4—224no—
521C2×C4—224no—
522C2×C4—448no—
523C2×C4(C22⋊D11)⋊C4116yes—
524C2×C4C22×C4×D1114yes—
525C2×C4C22×C4×D1114yes—
526C2×C4C2×#433914yes—
527C2×C4C2×#433914yes—
528C2×C4C2×D4×D1114yes—
529C2×C4C2×#434114yes—
530C22—24no—
531C22—24no—
532C22—24no—
533C22—42no—
534C22—416no—
535C22—42no—
536C22—42no—
537C22—42no—
538C22C4×#433914yes—
539C22C2×(C22⋊D11)⋊C414yes—
540C22#1062304714yes—
541C22#1062307214yes—
542C22#1062307314yes—
543C22#1062308214yes—
544C22#1062308314yes—
545C22C23×C4×D1111yescharacteristic
546C22C22×#433911yescharacteristic
547C22C22×#433911yescharacteristic
548C22C22×D4×D1111yescharacteristic
549C22C22×#434111yescharacteristic
550C22C2×#6704311yescharacteristic
551C22C2×#6704311yescharacteristic
552C4—24no—
553C4—24no—
554C4—24no—
555C4—42no—
556C4—42no—
557C4—228no—
558C4—228no—
559C4—228no—
560C4—444no—
561C4C2×(C22⋊D11)⋊C418yes—
562C2—44no—
563C2#1307164118yesdirect product factor
564C2C22×(C22⋊D11)⋊C411yescharacteristic
565C2C2×C4×#433911yescharacteristic
566C2C2×#1062304711yescharacteristic
567C2C2×#1062308211yescharacteristic
568C2C2×#1062308311yescharacteristic
569C2C2×#1062307211yescharacteristic
570C2C2×#1062307311yescharacteristic
subgroupG/H
centerC24C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC2×C4×C11×C22⋊C4C2
socleC24×C11C24
prime radicalC25×C11C23
cosocleC23×C11C25
hypercenterC2×C4×C22⋊C4D11
hypocenterC11C2×#2362
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×C4×Dic22C2semidirect
4. #13071641C2direct (N × H)
5. C2×#10622542C2semidirect
6. C2×#10622541C2semidirect
9. C2×#10622265C2semidirect
10. C2×C4×C4⋊Dic11C2semidirect
11. C2×#10622262C2semidirect
26. C2×#66977C4semidirect
35. C2×C4×Dic22C22semidirect
45. C4×C4⋊Dic11C22semidirect
46. #10622542C22semidirect
47. #10622541C22semidirect
48. #10622265C22semidirect
49. #10622262C22semidirect
88. #66977C2×C4semidirect
385. C2×C11#2362semidirect
465. C11C2×#2362semidirect
563. C2#13071641direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669772
C22×C4×Dic222
C22×#669792
#130716412
C2×#106225422
C2×#106225412
C2×#106225582
C2×#106225572
C2×#106222652
C2×C4×C4⋊Dic112
C2×#106222622
C2×C4×C11×C22⋊C42
C2×#236211