Finite Group Databasebeta

← C2×#13071144 #14912216

Subgroups — C2×#13071144 #14912216

Order 2816.

3854 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66977C211yesmaximal, characteristic
2C22×#66940C211yesmaximal, characteristic, complemented
3C23×C4×Dic11C211yesmaximal, characteristic
4#13071144C2116yesmaximal, direct product factor
5C2×#10622587C211yesmaximal, characteristic, complemented
6C2×#10622586C211yesmaximal, characteristic, complemented
7C2×#10622265C212yesmaximal, complemented
8C2×#10622559C212yesmaximal
9C2×C4⋊C4×Dic11C211yesmaximal, characteristic, complemented
10C2×#10622262C212yesmaximal, complemented
11C2×C22⋊C4×Dic11C212yesmaximal
12C2×C11×#380C211yesmaximal, characteristic
13C24×C4×C11C2211yescharacteristic
14C24×Dic11C2211yescharacteristic
15C24×Dic11C2211yescharacteristic
16C23×Dic22C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C11×C22⋊C4C2212yes—
20C22×C22⋊Dic11C2212yes—
21C22×C4⋊Dic11C2211yescharacteristic
22C2×#66977C4116yescomplemented
23C2×#66977C2218yes—
24C22×Dic11⋊C4C2212yes—
25C22×Dic11⋊C4C2212yes—
26C22×Dic11⋊C4C2212yes—
27C22×C4×Dic11—28no—
28C22×C4×Dic11C2218yes—
29C22×C4×Dic11C2212yes—
30C22×C4×Dic11C2212yes—
31C22×C4×Dic11C2211yescharacteristic
32C22×C4×Dic11C2211yescharacteristic
33C22×C4×Dic11C2211yescharacteristic
34C22×C4×Dic11C2211yescharacteristic
35C2×#66940—28no—
36C2×#66940C2218yescomplemented
37C11×#380C2218yes—
38C2×C11×#95C2212yes—
39C2×C11⋊#95C2212yes—
40C2×C11⋊#95C2212yes—
41C2×C11⋊#95C2212yes—
42C2×C11⋊#95C2212yes—
43C4⋊C4×Dic11C2218yescomplemented
44#10622587C2218yescomplemented
45#10622586C2218yescomplemented
46#10622559C22116yes—
47C22⋊C4×Dic11C22116yes—
48#10622265C22116yescomplemented
49#10622262C22116yescomplemented
50C25×C11C2311yescharacteristic
51C23×C4×C11—24no—
52C23×C4×C11—24no—
53C23×C4×C11C2×C418yes—
54C23×C4×C11C2312yes—
55C23×C4×C11C2312yes—
56C23×C4×C11C2311yescharacteristic
57C23×C4×C11C2314yes—
58C23×C4×C11C2311yescharacteristic
59C23×Dic11—24no—
60C23×Dic11—24no—
61C23×Dic11—24no—
62C23×Dic11—24no—
63C23×Dic11—24no—
64C23×Dic11Q818yescomplemented
65C23×Dic11C2314yes—
66C23×Dic11C2312yes—
67C23×Dic11C2312yes—
68C23×Dic11C2311yescharacteristic
69C23×Dic11C2311yescharacteristic
70C23×Dic11C2314yes—
71C23×Dic11C2311yescharacteristic
72C23×Dic11C2311yescharacteristic
73C22×Dic22—24no—
74C22×Dic22—24no—
75C22×Dic22C2×C418yescomplemented
76C22×Dic22C2314yes—
77C2×C11×C4⋊C4—24no—
78C2×C11×C4⋊C4—24no—
79C2×C11×C4⋊C4C2314yes—
80C2×C11×C4⋊C4C2314yes—
81C2×C11×C22⋊C4—28no—
82C2×C11×C22⋊C4C2318yes—
83C2×C22⋊Dic11C2×C4116yes—
84C2×C22⋊Dic11C2318yes—
85C2×C4⋊Dic11C2×C418yescomplemented
86C2×C4⋊Dic11C2314yes—
87#66977C2×C4164yescomplemented
88C2×Dic11⋊C4—28no—
89C2×Dic11⋊C4—28no—
90C2×Dic11⋊C4C2×C4116yescomplemented
91C2×Dic11⋊C4C2318yes—
92C2×Dic11⋊C4C2318yes—
93C2×Dic11⋊C4C2318yes—
94C2×C4×Dic11—24no—
95C2×C4×Dic11—28no—
96C2×C4×Dic11—24no—
97C2×C4×Dic11—24no—
98C2×C4×Dic11—28no—
99C2×C4×Dic11—232no—
100C2×C4×Dic11D418yes—
101C2×C4×Dic11C2318yes—
102C2×C4×Dic11C2314yes—
103C2×C4×Dic11C2318yes—
104C2×C4×Dic11C2314yes—
105C2×C4×Dic11C2314yes—
106C2×C4×Dic11C2314yes—
107#66940—232no—
108C11×#95C2318yes—
109C11⋊#95C2318yes—
110C11⋊#95C2318yes—
111C11⋊#95C2318yes—
112C11⋊#95C2318yes—
113C2×C4×C22⋊Q8—111nomaximal, Sylow
114C24×C11—22no—
115C24×C11—22no—
116C24×C11—22no—
117C24×C11—22no—
118C24×C11C22×C414yes—
119C24×C11C2×Q814yes—
120C24×C11#4114yes—
121C24×C11C2412yes—
122C24×C11C2411yescharacteristic
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—232no—
126C22×C4×C11—28no—
127C22×C4×C11—28no—
128C22×C4×C11—24no—
129C22×C4×C11—24no—
130C22×C4×C11—24no—
131C22×C4×C11—24no—
132C22×C4×C11—24no—
133C22×C4×C11—24no—
134C22×C4×C11C22×C414yes—
135C22×C4×C11C22×C4116yes—
136C22×C4×C11C22×C414yes—
137C22×C4×C11C2×D414yes—
138C22×C4×C11#4114yes—
139C22×C4×C11C2414yes—
140C22×C4×C11C2414yes—
141C22×C4×C11C2412yes—
142C22×C4×C11C2412yes—
143C22×Dic11—232no—
144C22×Dic11—232no—
145C22×Dic11—28no—
146C22×Dic11—28no—
147C22×Dic11—28no—
148C22×Dic11—28no—
149C22×Dic11—22no—
150C22×Dic11—22no—
151C22×Dic11—24no—
152C22×Dic11—24no—
153C22×Dic11—24no—
154C22×Dic11—24no—
155C22×Dic11—28no—
156C22×Dic11—22no—
157C22×Dic11—22no—
158C22×Dic11—22no—
159C22×Dic11—22no—
160C22×Dic11C22×C418yes—
161C22×Dic11C22×C418yes—
162C22×Dic11C2×D414yes—
163C22×Dic11C2×D414yes—
164C22×Dic11C2×Q814yes—
165C22×Dic11C2×Q814yes—
166C22×Dic11C2×Q8116yescomplemented
167C22×Dic11#4114yes—
168C22×Dic11#4114yes—
169C22×Dic11C2414yes—
170C22×Dic11C2414yes—
171C22×Dic11C2412yes—
172C22×Dic11C2412yes—
173C22×Dic11C2412yes—
174C22×Dic11C2412yes—
175C2×Dic22—232no—
176C2×Dic22—28no—
177C2×Dic22—28no—
178C2×Dic22C22×C4116yescomplemented
179C11×C4⋊C4—28no—
180C11×C4⋊C4—28no—
181C11×C22⋊C4—216no—
182C22⋊Dic11C22×C4132yes—
183C4⋊Dic11C22×C4116yescomplemented
184Dic11⋊C4—216no—
185Dic11⋊C4—216no—
186Dic11⋊C4C22×C4132yescomplemented
187C4×Dic11—216no—
188C4×Dic11—28no—
189C4×Dic11—28no—
190C4×Dic11—216no—
191C4×Dic11—28no—
192C4×Dic11C2×D4116yes—
193C22×C22⋊Q8—111no—
194C22×C4×Q8—111no—
195C23×C42—111no—
196C4×C22⋊Q8—1116no—
197C2×#391—111no—
198C2×#389—111no—
199C2×#387—112no—
200C2×#385—112no—
201C2×#380D1111yescharacteristic
202C2×C4×C4⋊C4—112no—
203C2×C4×C4⋊C4—111no—
204C2×C4×C22⋊C4—112no—
205C23×C11—28no—
206C23×C11—28no—
207C23×C11—28no—
208C23×C11—28no—
209C23×C11—28no—
210C23×C11—28no—
211C23×C11—22no—
212C23×C11—22no—
213C23×C11—22no—
214C23×C11—22no—
215C23×C11C4×Q8116yescomplemented
216C23×C11C23×C414yes—
217C23×C11C23×C412yes—
218C23×C11C22×D412yes—
219C23×C11C22×Q814yes—
220C23×C11C22×Q812yes—
221C23×C11C2×#4114yes—
222C23×C11C2×#4112yes—
223C23×C11C2×#4112yes—
224C23×C11C2×#4112yes—
225C23×C11C2×#4112yes—
226C23×C11C2511yescharacteristic
227C2×C4×C11—28no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—232no—
231C2×C4×C11—24no—
232C2×C4×C11—24no—
233C2×C4×C11—24no—
234C2×C4×C11—24no—
235C2×C4×C11—24no—
236C2×C4×C11—24no—
237C2×C4×C11—48no—
238C2×C4×C11—48no—
239C2×C4×C11C4×D4116yes—
240C2×C4×C11C23×C414yes—
241C2×C4×C11C23×C414yes—
242C2×C4×C11C22×D414yes—
243C2×C4×C11C2×#4114yes—
244C2×Dic11—232no—
245C2×Dic11—216no—
246C2×Dic11—216no—
247C2×Dic11—28no—
248C2×Dic11—28no—
249C2×Dic11—28no—
250C2×Dic11—22no—
251C2×Dic11—22no—
252C2×Dic11—24no—
253C2×Dic11—24no—
254C2×Dic11—24no—
255C2×Dic11—24no—
256C2×Dic11—22no—
257C2×Dic11—22no—
258C2×Dic11—22no—
259C2×Dic11—22no—
260C2×Dic11—232no—
261C2×Dic11C22⋊Q8116yescomplemented
262C2×Dic11C23×C418yes—
263C2×Dic11C23×C418yes—
264C2×Dic11C22×D414yes—
265C2×Dic11C22×D414yes—
266C2×Dic11C22×Q814yes—
267C2×Dic11C22×Q814yes—
268C2×Dic11C2×#4114yes—
269C2×Dic11C2×#4114yes—
270Dic22—232no—
271C23×Q8—111no—
272C24×C4—111no—
273C24×C4—111no—
274C24×C4C2×D1111yescharacteristic
275C2×C22⋊Q8—118no—
276C2×C22⋊Q8—1116no—
277C2×C4×Q8—118no—
278C2×C4×Q8—228no—
279C22×C4⋊C4—112no—
280C22×C4⋊C4—111no—
281C22×C4⋊C4—112no—
282C22×C4⋊C4—112no—
283C22×C4⋊C4C2×D1111yescharacteristic
284C22×C4⋊C4C2×D1111yescharacteristic
285C22×C22⋊C4—112no—
286C22×C22⋊C4C2×D1112yes—
287C22×C42—111no—
288C22×C42—111no—
289C22×C42—111no—
290C22×C42—111no—
291C22×C42—118no—
292C22×C42—112no—
293C22×C42—112no—
294C22×C42—228no—
295#391—118no—
296#389—118no—
297#387—1116no—
298#385—1116no—
299#380C2×D1118yes—
300C4×C4⋊C4—118no—
301C4×C4⋊C4—1116no—
302C4×C22⋊C4—1116no—
303C2×#95—112no—
304C2×#95—112no—
305C2×#95—112no—
306C2×#95—112no—
307C2×#95C2×D1112yes—
308C22×C11—24no—
309C22×C11—24no—
310C22×C11—24no—
311C22×C11—24no—
312C22×C11—24no—
313C22×C11—24no—
314C22×C11—232no—
315C22×C11C2×C4×D414yes—
316C22×C11C2×C4×Q814yes—
317C22×C11C2×C4×Q818yescomplemented
318C22×C11C4×#4114yes—
319C22×C11C2×C22⋊Q814yes—
320C22×C11#52514yes—
321C22×C11#52914yes—
322C22×C11#53314yes—
323C22×C11C24×C411yescharacteristic
324C22×C11C23×D411yescharacteristic
325C22×C11C23×Q811yescharacteristic
326C22×C11C22×#4111yescharacteristic
327C22×C11C22×#4111yescharacteristic
328C22×C11C22×#4111yescharacteristic
329C22×C11C22×#4111yescharacteristic
330C4×C11—24no—
331C4×C11—44no—
332C4×C11—44no—
333C4×C11C2×C4×D418yes—
334Dic11—28no—
335Dic11—28no—
336Dic11—24no—
337Dic11—24no—
338Dic11—24no—
339Dic11C2×C22⋊Q818yescomplemented
340C25C22×D1111yescharacteristic
341C22×Q8—118no—
342C22×Q8—114no—
343C22×Q8—224no—
344C22×Q8—224no—
345C23×C4—24no—
346C23×C4—24no—
347C23×C4—111no—
348C23×C4—118no—
349C23×C4—114no—
350C23×C4—112no—
351C23×C4—112no—
352C23×C4—111no—
353C23×C4—111no—
354C23×C4—111no—
355C23×C4—114no—
356C23×C4—224no—
357C23×C4—224no—
358C23×C4—224no—
359C23×C4—224no—
360C23×C4—224no—
361C23×C4C4×D1118yes—
362C23×C4C22×D1112yes—
363C23×C4C22×D1112yes—
364C23×C4C22×D1114yes—
365C23×C4C22×D1111yescharacteristic
366C23×C4C22×D1111yescharacteristic
367C22⋊Q8—1164no—
368C4×Q8—2232no—
369C2×C4⋊C4—24no—
370C2×C4⋊C4—24no—
371C2×C4⋊C4—1116no—
372C2×C4⋊C4—118no—
373C2×C4⋊C4—118no—
374C2×C4⋊C4—114no—
375C2×C4⋊C4—118no—
376C2×C4⋊C4—118no—
377C2×C4⋊C4—228no—
378C2×C4⋊C4—228no—
379C2×C4⋊C4C22×D1114yes—
380C2×C4⋊C4C22×D1114yes—
381C2×C22⋊C4—28no—
382C2×C22⋊C4—1116no—
383C2×C22⋊C4—118no—
384C2×C22⋊C4C22×D1118yes—
385C2×C42—118no—
386C2×C42—114no—
387C2×C42—118no—
388C2×C42—118no—
389C2×C42—114no—
390C2×C42—114no—
391C2×C42—114no—
392C2×C42—2232no—
393C2×C42—228no—
394C2×C42—228no—
395C2×C42—224no—
396C2×C42—224no—
397C2×C42—224no—
398#95—118no—
399#95—118no—
400#95—118no—
401#95—118no—
402#95C22×D1118yes—
403C2×C11—28no—
404C2×C11C4×C22⋊Q818yescomplemented
405C2×C11C22×C4×D411yescharacteristic
406C2×C11C22×C4×Q811yescharacteristic
407C2×C11C2×C4×#4111yescharacteristic
408C2×C11C22×C22⋊Q811yescharacteristic
409C2×C11C2×#52511yescharacteristic
410C2×C11C2×#52911yescharacteristic
411C2×C11C2×#53311yescharacteristic
412C24—22no—
413C24—22no—
414C24—22no—
415C24—22no—
416C24C2×C4×D1114yes—
417C24#434114yes—
418C24Q8×D1114yes—
419C24C23×D1112yes—
420C24C23×D1111yescharacteristic
421C2×Q8—1116no—
422C2×Q8—2232no—
423C2×Q8—228no—
424C2×Q8—228no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—232no—
428C22×C4—28no—
429C22×C4—28no—
430C22×C4—24no—
431C22×C4—24no—
432C22×C4—24no—
433C22×C4—24no—
434C22×C4—24no—
435C22×C4—24no—
436C22×C4—114no—
437C22×C4—114no—
438C22×C4—114no—
439C22×C4—112no—
440C22×C4—118no—
441C22×C4—118no—
442C22×C4—114no—
443C22×C4—114no—
444C22×C4—1116no—
445C22×C4—114no—
446C22×C4—112no—
447C22×C4—112no—
448C22×C4—112no—
449C22×C4—114no—
450C22×C4—114no—
451C22×C4—228no—
452C22×C4—228no—
453C22×C4—2232no—
454C22×C4—228no—
455C22×C4—228no—
456C22×C4—2232no—
457C22×C4—222no—
458C22×C4—222no—
459C22×C4—224no—
460C22×C4—228no—
461C22×C4—222no—
462C22×C4—222no—
463C22×C4—224no—
464C22×C4—224no—
465C22×C4—224no—
466C22×C4—222no—
467C22×C4—222no—
468C22×C4C2×C4×D1114yes—
469C22×C4C2×C4×D11116yes—
470C22×C4C2×C4×D1114yes—
471C22×C4D4×D1114yes—
472C22×C4#434114yes—
473C22×C4C23×D1114yes—
474C22×C4C23×D1114yes—
475C22×C4C23×D1112yes—
476C22×C4C23×D1112yes—
477C4⋊C4—28no—
478C4⋊C4—28no—
479C4⋊C4—1132no—
480C4⋊C4—1116no—
481C4⋊C4—2216no—
482C4⋊C4—2216no—
483C22⋊C4—216no—
484C22⋊C4—1132no—
485C42—1116no—
486C42—228no—
487C42—228no—
488C42—2216no—
489C42—2216no—
490C42—228no—
491C11C2×C4×C22⋊Q811yescharacteristic, complemented, Sylow
492C23—28no—
493C23—28no—
494C23—28no—
495C23—28no—
496C23—28no—
497C23—28no—
498C23—22no—
499C23—22no—
500C23—22no—
501C23—22no—
502C23#66940116yescomplemented
503C23C22×C4×D1114yes—
504C23C22×C4×D1112yes—
505C23C2×D4×D1112yes—
506C23C2×#434114yes—
507C23C2×#434112yes—
508C23C2×#434112yes—
509C23C2×Q8×D1114yes—
510C23C2×Q8×D1112yes—
511C23#41×D1112yes—
512C23#41×D1112yes—
513C23C24×D1111yescharacteristic
514Q8—2232no—
515C2×C4—28no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—232no—
519C2×C4—24no—
520C2×C4—24no—
521C2×C4—24no—
522C2×C4—24no—
523C2×C4—24no—
524C2×C4—24no—
525C2×C4—48no—
526C2×C4—48no—
527C2×C4—1116no—
528C2×C4—114no—
529C2×C4—114no—
530C2×C4—114no—
531C2×C4—118no—
532C2×C4—118no—
533C2×C4—114no—
534C2×C4—114no—
535C2×C4—114no—
536C2×C4—2232no—
537C2×C4—2232no—
538C2×C4—2216no—
539C2×C4—2216no—
540C2×C4—228no—
541C2×C4—228no—
542C2×C4—228no—
543C2×C4—222no—
544C2×C4—222no—
545C2×C4—224no—
546C2×C4—222no—
547C2×C4—222no—
548C2×C4—224no—
549C2×C4—224no—
550C2×C4—224no—
551C2×C4—222no—
552C2×C4—222no—
553C2×C4(C22⋊D11)⋊C4116yes—
554C2×C4C22×C4×D1114yes—
555C2×C4C22×C4×D1114yes—
556C2×C4C2×D4×D1114yes—
557C2×C4C2×#434114yes—
558C22—24no—
559C22—24no—
560C22—232no—
561C22—24no—
562C22—24no—
563C22—24no—
564C22—24no—
565C22C2×(C22⋊D11)⋊C414yes—
566C22C2×#6694014yes—
567C22C2×#6694018yescomplemented
568C22#1062305314yes—
569C22#1062313114yes—
570C22#1062313714yes—
571C22#1062315314yes—
572C22D11×C22⋊Q814yes—
573C22C23×C4×D1111yescharacteristic
574C22C22×D4×D1111yescharacteristic
575C22C22×#434111yescharacteristic
576C22C22×#434111yescharacteristic
577C22C22×Q8×D1111yescharacteristic
578C22C2×#41×D1111yescharacteristic
579C22C2×#41×D1111yescharacteristic
580C4—24no—
581C4—44no—
582C4—44no—
583C4—118no—
584C4—224no—
585C4—224no—
586C4—228no—
587C4—228no—
588C4—224no—
589C4C2×(C22⋊D11)⋊C418yes—
590C2—28no—
591C2#1307114418yesdirect product factor
592C2C22×(C22⋊D11)⋊C411yescharacteristic
593C2C22×#6694011yescharacteristic
594C2C2×#1062305311yescharacteristic
595C2C2×D11×C22⋊Q811yescharacteristic
596C2C2×#1062313711yescharacteristic
597C2C2×#1062313111yescharacteristic
598C2C2×#1062315311yescharacteristic
subgroupG/H
centerC24C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC2×C11×#380C2
socleC24×C11C24
prime radicalC25×C11C23
cosocleC23×C11C25
hypercenterC2×#380D11
hypocenterC11C2×C4×C22⋊Q8
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
2. C22×#66940C2semidirect
4. #13071144C2direct (N × H)
5. C2×#10622587C2semidirect
6. C2×#10622586C2semidirect
7. C2×#10622265C2semidirect
9. C2×C4⋊C4×Dic11C2semidirect
10. C2×#10622262C2semidirect
22. C2×#66977C4semidirect
36. C2×#66940C22semidirect
43. C4⋊C4×Dic11C22semidirect
44. #10622587C22semidirect
45. #10622586C22semidirect
48. #10622265C22semidirect
49. #10622262C22semidirect
64. C23×Dic11Q8semidirect
75. C22×Dic22C2×C4semidirect
85. C2×C4⋊Dic11C2×C4semidirect
87. #66977C2×C4semidirect
90. C2×Dic11⋊C4C2×C4semidirect
166. C22×Dic11C2×Q8semidirect
178. C2×Dic22C22×C4semidirect
183. C4⋊Dic11C22×C4semidirect
186. Dic11⋊C4C22×C4semidirect
215. C23×C11C4×Q8semidirect
261. C2×Dic11C22⋊Q8semidirect
317. C22×C11C2×C4×Q8semidirect
339. Dic11C2×C22⋊Q8semidirect
404. C2×C11C4×C22⋊Q8semidirect
491. C11C2×C4×C22⋊Q8semidirect
502. C23#66940semidirect
567. C22C2×#66940semidirect
591. C2#13071144direct (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×#669402
C23×C4×Dic112
#130711442
C2×#106225872
C2×#106225862
C2×#106222652
C2×#106225592
C2×C4⋊C4×Dic112
C2×#106222622
C2×C22⋊C4×Dic112
C2×C11×#3802
C2×C4×C22⋊Q811