Finite Group Databasebeta

← C2×#13071621 #14913290

Subgroups — C2×#13071621 #14913290

Order 2816.

3614 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66977C211yesmaximal, characteristic
2C22×#66940C211yesmaximal, characteristic, complemented
3#13071621C2116yesmaximal, direct product factor
4C2×#10622587C211yesmaximal, characteristic, complemented
5C2×#10622586C211yesmaximal, characteristic, complemented
6C2×#10622585C212yesmaximal, complemented
7C2×#10622591C212yesmaximal, complemented
8C2×#10622823C212yesmaximal
9C2×C4⋊C4×Dic11C211yesmaximal, characteristic, complemented
10C2×C4×C22⋊Dic11C211yesmaximal, characteristic
11C2×C4×C22⋊Dic11C212yesmaximal
12C23×C11×C4⋊C4C211yesmaximal, characteristic
13C24×C4×C11C2212yes—
14C24×C4×C11C2211yescharacteristic
15C23×Dic22C2211yescharacteristic
16C22×C11×C4⋊C4—28no—
17C22×C11×C4⋊C4C2218yes—
18C22×C11×C4⋊C4C2212yes—
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×C11×C4⋊C4C2211yescharacteristic
21C22×C22⋊Dic11C2211yescharacteristic
22C22×C22⋊Dic11C2212yes—
23C22×C22⋊Dic11C2211yescharacteristic
24C22×C4⋊Dic11C2211yescharacteristic
25C2×#66977C4116yescomplemented
26C2×#66977C2218yes—
27C22×Dic11⋊C4C2212yes—
28C22×Dic11⋊C4C2212yes—
29C22×Dic11⋊C4C2212yes—
30C22×C4×Dic11C2211yescharacteristic
31C22×C4×Dic11C2212yes—
32C22×C4×Dic11C2211yescharacteristic
33C22×C4×Dic11C2212yes—
34C2×#66940—28no—
35C2×#66940C2218yescomplemented
36#10622823C22116yes—
37C4×C22⋊Dic11C2218yes—
38C4×C22⋊Dic11C22116yes—
39C2×C11⋊#95C2211yescharacteristic
40C2×C11⋊#95C2212yes—
41C2×C11⋊#95C2211yescharacteristic
42C2×C11⋊#95C2212yes—
43C2×C11⋊#95C2212yes—
44C2×C11⋊#95C2212yes—
45#10622591C22116yescomplemented
46C4⋊C4×Dic11C2218yescomplemented
47#10622587C2218yescomplemented
48#10622586C2218yescomplemented
49#10622585C22116yescomplemented
50C25×C11C2311yescharacteristic
51C23×C4×C11—24no—
52C23×C4×C11—24no—
53C23×C4×C11—28no—
54C23×C4×C11—28no—
55C23×C4×C11—44no—
56C23×C4×C11C2×C418yes—
57C23×C4×C11C2312yes—
58C23×C4×C11C2318yes—
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2314yes—
61C23×C4×C11C2312yes—
62C23×C4×C11C2311yescharacteristic
63C23×Dic11C2311yescharacteristic
64C23×Dic11C2311yescharacteristic
65C23×Dic11C2312yes—
66C23×Dic11C2312yes—
67C23×Dic11C2311yescharacteristic
68C23×Dic11C2311yescharacteristic
69C22×Dic22—24no—
70C22×Dic22—24no—
71C22×Dic22C2×C418yescomplemented
72C22×Dic22C2314yes—
73C2×C11×C4⋊C4—28no—
74C2×C11×C4⋊C4—24no—
75C2×C11×C4⋊C4—232no—
76C2×C11×C4⋊C4D418yes—
77C2×C11×C4⋊C4C2318yes—
78C2×C11×C4⋊C4C2314yes—
79C2×C11×C4⋊C4C2314yes—
80C2×C22⋊Dic11—24no—
81C2×C22⋊Dic11C2×C4116yes—
82C2×C22⋊Dic11Q818yescomplemented
83C2×C22⋊Dic11C2314yes—
84C2×C22⋊Dic11C2318yes—
85C2×C22⋊Dic11C2314yes—
86C2×C4⋊Dic11C2×C418yescomplemented
87C2×C4⋊Dic11C2314yes—
88#66977C2×C4164yescomplemented
89C2×Dic11⋊C4—28no—
90C2×Dic11⋊C4—44no—
91C2×Dic11⋊C4C2×C4116yescomplemented
92C2×Dic11⋊C4C2318yes—
93C2×Dic11⋊C4C2318yes—
94C2×Dic11⋊C4C2318yes—
95C2×C4×Dic11—28no—
96C2×C4×Dic11—24no—
97C2×C4×Dic11—24no—
98C2×C4×Dic11—44no—
99C2×C4×Dic11C2314yes—
100C2×C4×Dic11C2318yes—
101C2×C4×Dic11C2314yes—
102C2×C4×Dic11C2318yes—
103#66940—232no—
104C11⋊#95C2314yes—
105C11⋊#95C2318yes—
106C11⋊#95C2318yes—
107C11⋊#95C2314yes—
108C11⋊#95C2318yes—
109C11⋊#95C2318yes—
110C2×#2360—111nomaximal, Sylow
111C24×C11—22no—
112C24×C11—22no—
113C24×C11—22no—
114C24×C11—22no—
115C24×C11C22×C414yes—
116C24×C11C2×Q814yes—
117C24×C11#4114yes—
118C24×C11C2412yes—
119C24×C11C2411yescharacteristic
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—24no—
123C22×C4×C11—24no—
124C22×C4×C11—232no—
125C22×C4×C11—28no—
126C22×C4×C11—28no—
127C22×C4×C11—24no—
128C22×C4×C11—216no—
129C22×C4×C11—24no—
130C22×C4×C11—24no—
131C22×C4×C11—216no—
132C22×C4×C11—48no—
133C22×C4×C11—432no—
134C22×C4×C11C22×C414yes—
135C22×C4×C11C22×C4116yes—
136C22×C4×C11C22×C414yes—
137C22×C4×C11C2×D418yes—
138C22×C4×C11C2×D414yes—
139C22×C4×C11#4114yes—
140C22×C4×C11C2414yes—
141C22×C4×C11C2412yes—
142C22×C4×C11C2414yes—
143C22×C4×C11C2412yes—
144C22×Dic11—22no—
145C22×Dic11—24no—
146C22×Dic11—22no—
147C22×Dic11—22no—
148C22×Dic11—24no—
149C22×Dic11—22no—
150C22×Dic11—22no—
151C22×Dic11—22no—
152C22×Dic11—22no—
153C22×Dic11—24no—
154C22×Dic11—22no—
155C22×Dic11—24no—
156C22×Dic11—22no—
157C22×Dic11—22no—
158C22×Dic11C22×C418yes—
159C22×Dic11C22×C418yes—
160C22×Dic11C2×Q814yes—
161C22×Dic11C2×Q814yes—
162C22×Dic11C2412yes—
163C22×Dic11C2412yes—
164C22×Dic11C2414yes—
165C22×Dic11C2414yes—
166C22×Dic11C2412yes—
167C22×Dic11C2412yes—
168C2×Dic22—232no—
169C2×Dic22—28no—
170C2×Dic22—28no—
171C2×Dic22C22×C4116yescomplemented
172C11×C4⋊C4—216no—
173C11×C4⋊C4—28no—
174C11×C4⋊C4C2×D4116yes—
175C22⋊Dic11—28no—
176C22⋊Dic11C22×C4132yes—
177C22⋊Dic11C2×Q8116yescomplemented
178C4⋊Dic11C22×C4116yescomplemented
179Dic11⋊C4—216no—
180Dic11⋊C4—48no—
181Dic11⋊C4C22×C4132yescomplemented
182C4×Dic11—216no—
183C4×Dic11—28no—
184C4×Dic11—28no—
185C4×Dic11—48no—
186C22×C22⋊Q8—111no—
187C22×C4×Q8—111no—
188C23×C4⋊C4D1111yescharacteristic
189#2360—1116no—
190C2×#391—111no—
191C2×#389—112no—
192C2×#389—111no—
193C2×#387—112no—
194C2×#385—112no—
195C2×C4×C4⋊C4—111no—
196C2×C4×C22⋊C4—112no—
197C2×C4×C22⋊C4—111no—
198C23×C11—28no—
199C23×C11—28no—
200C23×C11—28no—
201C23×C11—28no—
202C23×C11—28no—
203C23×C11—28no—
204C23×C11—22no—
205C23×C11—22no—
206C23×C11—22no—
207C23×C11—22no—
208C23×C11C4×Q8116yescomplemented
209C23×C11C23×C414yes—
210C23×C11C23×C412yes—
211C23×C11C22×D412yes—
212C23×C11C22×Q814yes—
213C23×C11C22×Q812yes—
214C23×C11C2×#4112yes—
215C23×C11C2×#4114yes—
216C23×C11C2×#4112yes—
217C23×C11H(5,𝔽2)12yes—
218C23×C112−1+412yes—
219C23×C11C2511yescharacteristic
220C2×C4×C11—28no—
221C2×C4×C11—216no—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11—24no—
225C2×C4×C11—24no—
226C2×C4×C11—232no—
227C2×C4×C11—24no—
228C2×C4×C11—24no—
229C2×C4×C11—24no—
230C2×C4×C11—432no—
231C2×C4×C11—48no—
232C2×C4×C11C4×D4116yes—
233C2×C4×C11C23×C414yes—
234C2×C4×C11C23×C414yes—
235C2×C4×C11C22×D418yes—
236C2×C4×C11C22×D414yes—
237C2×C4×C11C2×#4114yes—
238C2×Dic11—216no—
239C2×Dic11—216no—
240C2×Dic11—28no—
241C2×Dic11—28no—
242C2×Dic11—22no—
243C2×Dic11—24no—
244C2×Dic11—22no—
245C2×Dic11—24no—
246C2×Dic11—22no—
247C2×Dic11—24no—
248C2×Dic11—24no—
249C2×Dic11—22no—
250C2×Dic11—22no—
251C2×Dic11—22no—
252C2×Dic11—22no—
253C2×Dic11—22no—
254C2×Dic11—22no—
255C2×Dic11—22no—
256C2×Dic11—44no—
257C2×Dic11—44no—
258C2×Dic11C23×C418yes—
259C2×Dic11C23×C418yes—
260C2×Dic11C22×Q814yes—
261C2×Dic11C22×Q814yes—
262Dic22—232no—
263C23×Q8—111no—
264C24×C4C2×D1112yes—
265C24×C4C2×D1111yescharacteristic
266C2×C22⋊Q8—118no—
267C2×C22⋊Q8—1116no—
268C2×C4×Q8—118no—
269C2×C4×Q8—228no—
270C22×C4⋊C4—28no—
271C22×C4⋊C4—112no—
272C22×C4⋊C4—111no—
273C22×C4⋊C4—112no—
274C22×C4⋊C4—112no—
275C22×C4⋊C4C2×D1118yes—
276C22×C4⋊C4C2×D1112yes—
277C22×C4⋊C4C2×D1111yescharacteristic
278C22×C4⋊C4C2×D1111yescharacteristic
279C22×C22⋊C4—112no—
280C22×C22⋊C4—111no—
281C22×C22⋊C4—111no—
282C22×C42—112no—
283C22×C42—111no—
284C22×C42—111no—
285C22×C42—112no—
286#391—118no—
287#389—1116no—
288#389—118no—
289#387—1116no—
290#385—1116no—
291C4×C4⋊C4—118no—
292C4×C22⋊C4—118no—
293C4×C22⋊C4—1116no—
294C2×#95—111no—
295C2×#95—112no—
296C2×#95—111no—
297C2×#95—112no—
298C2×#95—112no—
299C2×#95—112no—
300C22×C11—232no—
301C22×C11—24no—
302C22×C11—24no—
303C22×C11—24no—
304C22×C11—24no—
305C22×C11—24no—
306C22×C11—24no—
307C22×C11C2×C4×D414yes—
308C22×C11C2×C4×Q814yes—
309C22×C11C2×C4×Q818yescomplemented
310C22×C11#52014yes—
311C22×C11#54614yes—
312C22×C11D4×Q814yes—
313C22×C11#55214yes—
314C22×C11#55414yes—
315C22×C11C24×C411yescharacteristic
316C22×C11C23×D411yescharacteristic
317C22×C11C23×Q811yescharacteristic
318C22×C11C22×#4111yescharacteristic
319C22×C11C22×#4111yescharacteristic
320C22×C11C2×H(5,𝔽2)11yescharacteristic
321C22×C11C2×2−1+411yescharacteristic
322C4×C11—24no—
323C4×C11—28no—
324C4×C11—44no—
325C4×C11C2×C4×D418yes—
326Dic11—28no—
327Dic11—28no—
328Dic11—24no—
329Dic11—24no—
330Dic11—42no—
331Dic11—42no—
332C25C22×D1111yescharacteristic
333C22×Q8—118no—
334C22×Q8—114no—
335C22×Q8—224no—
336C22×Q8—224no—
337C23×C4—24no—
338C23×C4—24no—
339C23×C4—28no—
340C23×C4—28no—
341C23×C4—44no—
342C23×C4—112no—
343C23×C4—112no—
344C23×C4—111no—
345C23×C4—111no—
346C23×C4—111no—
347C23×C4—111no—
348C23×C4C4×D1118yes—
349C23×C4C22×D1112yes—
350C23×C4C22×D1118yes—
351C23×C4C22×D1114yes—
352C23×C4C22×D1111yescharacteristic
353C23×C4C22×D1112yes—
354C23×C4C22×D1111yescharacteristic
355C22⋊Q8—1164no—
356C4×Q8—2232no—
357C2×C4⋊C4—28no—
358C2×C4⋊C4—24no—
359C2×C4⋊C4—232no—
360C2×C4⋊C4—1116no—
361C2×C4⋊C4—118no—
362C2×C4⋊C4—114no—
363C2×C4⋊C4—118no—
364C2×C4⋊C4—118no—
365C2×C4⋊C4—118no—
366C2×C4⋊C4—228no—
367C2×C4⋊C4—444no—
368C2×C4⋊C4C22⋊D1118yes—
369C2×C4⋊C4C22×D1118yes—
370C2×C4⋊C4C22×D1114yes—
371C2×C4⋊C4C22×D1114yes—
372C2×C22⋊C4—1116no—
373C2×C22⋊C4—118no—
374C2×C22⋊C4—118no—
375C2×C22⋊C4—114no—
376C2×C22⋊C4—114no—
377C2×C22⋊C4—224no—
378C2×C42—118no—
379C2×C42—114no—
380C2×C42—114no—
381C2×C42—118no—
382C2×C42—224no—
383C2×C42—228no—
384C2×C42—224no—
385C2×C42—444no—
386#95—114no—
387#95—118no—
388#95—114no—
389#95—118no—
390#95—118no—
391#95—118no—
392C2×C11—28no—
393C2×C11#236018yescomplemented
394C2×C11C22×C4×D411yescharacteristic
395C2×C11C22×C4×Q811yescharacteristic
396C2×C11C2×#52011yescharacteristic
397C2×C11C2×#54611yescharacteristic
398C2×C11C2×D4×Q811yescharacteristic
399C2×C11C2×#55211yescharacteristic
400C2×C11C2×#55411yescharacteristic
401C24—22no—
402C24—22no—
403C24—22no—
404C24—22no—
405C24C2×C4×D1114yes—
406C24#434114yes—
407C24Q8×D1114yes—
408C24C23×D1112yes—
409C24C23×D1111yescharacteristic
410C2×Q8—1116no—
411C2×Q8—2232no—
412C2×Q8—228no—
413C2×Q8—228no—
414C22×C4—22no—
415C22×C4—24no—
416C22×C4—24no—
417C22×C4—22no—
418C22×C4—232no—
419C22×C4—28no—
420C22×C4—28no—
421C22×C4—216no—
422C22×C4—24no—
423C22×C4—24no—
424C22×C4—24no—
425C22×C4—216no—
426C22×C4—48no—
427C22×C4—432no—
428C22×C4—118no—
429C22×C4—118no—
430C22×C4—114no—
431C22×C4—114no—
432C22×C4—112no—
433C22×C4—112no—
434C22×C4—114no—
435C22×C4—114no—
436C22×C4—112no—
437C22×C4—112no—
438C22×C4—222no—
439C22×C4—224no—
440C22×C4—222no—
441C22×C4—224no—
442C22×C4—224no—
443C22×C4—222no—
444C22×C4—222no—
445C22×C4—224no—
446C22×C4—222no—
447C22×C4—222no—
448C22×C4—222no—
449C22×C4—222no—
450C22×C4—222no—
451C22×C4—222no—
452C22×C4C2×C4×D1114yes—
453C22×C4C2×C4×D11116yes—
454C22×C4C2×C4×D1114yes—
455C22×C4#433914yes—
456C22×C4C2×C22⋊D1118yes—
457C22×C4C2×C22⋊D1114yes—
458C22×C4C23×D1114yes—
459C22×C4C23×D1112yes—
460C22×C4C23×D1114yes—
461C22×C4C23×D1112yes—
462C4⋊C4—216no—
463C4⋊C4—28no—
464C4⋊C4—1132no—
465C4⋊C4—1116no—
466C4⋊C4—2216no—
467C4⋊C4—448no—
468C4⋊C4C2×C22⋊D11116yes—
469C22⋊C4—1132no—
470C22⋊C4—1116no—
471C22⋊C4—228no—
472C42—228no—
473C42—2216no—
474C42—228no—
475C42—448no—
476C11C2×#236011yescharacteristic, complemented, Sylow
477C23—28no—
478C23—28no—
479C23—28no—
480C23—28no—
481C23—28no—
482C23—28no—
483C23—22no—
484C23—22no—
485C23—22no—
486C23—22no—
487C23#66940116yescomplemented
488C23C22×C4×D1114yes—
489C23C22×C4×D1112yes—
490C23C2×#433912yes—
491C23C2×#434114yes—
492C23C2×#434112yes—
493C23#6703712yes—
494C23C2×Q8×D1114yes—
495C23C2×Q8×D1112yes—
496C23#6704012yes—
497C23C22×C22⋊D1112yes—
498C23C24×D1111yescharacteristic
499Q8—2232no—
500C2×C4—28no—
501C2×C4—216no—
502C2×C4—22no—
503C2×C4—24no—
504C2×C4—24no—
505C2×C4—22no—
506C2×C4—232no—
507C2×C4—24no—
508C2×C4—24no—
509C2×C4—24no—
510C2×C4—432no—
511C2×C4—48no—
512C2×C4—118no—
513C2×C4—118no—
514C2×C4—114no—
515C2×C4—114no—
516C2×C4—2216no—
517C2×C4—228no—
518C2×C4—2216no—
519C2×C4—228no—
520C2×C4—222no—
521C2×C4—224no—
522C2×C4—222no—
523C2×C4—224no—
524C2×C4—224no—
525C2×C4—222no—
526C2×C4—222no—
527C2×C4—224no—
528C2×C4—222no—
529C2×C4—222no—
530C2×C4—222no—
531C2×C4—222no—
532C2×C4—222no—
533C2×C4—222no—
534C2×C4—444no—
535C2×C4—444no—
536C2×C4C4×C22⋊D11116yes—
537C2×C4C22×C4×D1114yes—
538C2×C4C22×C4×D1114yes—
539C2×C4C2×#433914yes—
540C2×C4C22×C22⋊D1118yes—
541C2×C4C22×C22⋊D1114yes—
542C22—232no—
543C22—24no—
544C22—24no—
545C22—24no—
546C22—24no—
547C22—24no—
548C22—24no—
549C22C2×#6694014yes—
550C22C2×#6694018yescomplemented
551C22#1062303514yes—
552C22#1062304214yes—
553C22#1062304414yes—
554C22C2×C4×C22⋊D1114yes—
555C22#1062333714yes—
556C22Q8×C22⋊D1114yes—
557C22C23×C4×D1111yescharacteristic
558C22C22×#433911yescharacteristic
559C22C22×#434111yescharacteristic
560C22C2×#6703711yescharacteristic
561C22C22×Q8×D1111yescharacteristic
562C22C2×#6704011yescharacteristic
563C22C23×C22⋊D1111yescharacteristic
564C4—24no—
565C4—28no—
566C4—44no—
567C4—224no—
568C4—228no—
569C4—228no—
570C4—224no—
571C4—442no—
572C4—442no—
573C4C2×C4×C22⋊D1118yes—
574C2—28no—
575C2#1307162118yesdirect product factor
576C2C22×C4×C22⋊D1111yescharacteristic
577C2C22×#6694011yescharacteristic
578C2C2×#1062303511yescharacteristic
579C2C2×#1062333711yescharacteristic
580C2C2×Q8×C22⋊D1111yescharacteristic
581C2C2×#1062304411yescharacteristic
582C2C2×#1062304211yescharacteristic
subgroupG/H
centerC24C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC23×C11×C4⋊C4C2
socleC24×C11C24
prime radicalC25×C11C23
cosocleC23×C11C25
hypercenterC23×C4⋊C4D11
hypocenterC11C2×#2360
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C23×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×#66940C2semidirect
3. #13071621C2direct (N × H)
4. C2×#10622587C2semidirect
5. C2×#10622586C2semidirect
6. C2×#10622585C2semidirect
7. C2×#10622591C2semidirect
9. C2×C4⋊C4×Dic11C2semidirect
25. C2×#66977C4semidirect
35. C2×#66940C22semidirect
45. #10622591C22semidirect
46. C4⋊C4×Dic11C22semidirect
47. #10622587C22semidirect
48. #10622586C22semidirect
49. #10622585C22semidirect
71. C22×Dic22C2×C4semidirect
82. C2×C22⋊Dic11Q8semidirect
86. C2×C4⋊Dic11C2×C4semidirect
88. #66977C2×C4semidirect
91. C2×Dic11⋊C4C2×C4semidirect
171. C2×Dic22C22×C4semidirect
177. C22⋊Dic11C2×Q8semidirect
178. C4⋊Dic11C22×C4semidirect
181. Dic11⋊C4C22×C4semidirect
208. C23×C11C4×Q8semidirect
309. C22×C11C2×C4×Q8semidirect
393. C2×C11#2360semidirect
476. C11C2×#2360semidirect
487. C23#66940semidirect
550. C22C2×#66940semidirect
575. C2#13071621direct (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
#130716212
C2×#106225872
C2×#106225862
C2×#106225852
C2×#106225912
C2×#106228232
C2×C4⋊C4×Dic112
C2×C4×C22⋊Dic112
C23×C11×C4⋊C42
C2×#236011