Finite Group Databasebeta

← C2×#13072921 #14922820

Subgroups — C2×#13072921 #14922820

Order 2816.

3678 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66988C211yesmaximal, characteristic
2C22×D4×Dic11C211yesmaximal, characteristic
3C23×Dic11⋊C4C211yesmaximal, characteristic, complemented
4#13072921C2116yesmaximal, direct product factor
5C2×#10622597C212yesmaximal, complemented
6C2×#10622565C212yesmaximal, complemented
7C2×#10622585C212yesmaximal, complemented
8C2×#10622824C211yesmaximal, characteristic, complemented
9C2×#10622556C211yesmaximal, characteristic, complemented
10C2×#10622555C211yesmaximal, characteristic, complemented
11C2×#10622555C212yesmaximal, complemented
12C22×C11×#123C211yesmaximal, characteristic
13C23×D4×C11C2211yescharacteristic
14C24×C4×C11C2211yescharacteristic
15C24×Dic11C2211yescharacteristic
16C24×Dic11C2211yescharacteristic
17C24×Dic11C2211yescharacteristic
18C2×C11×#123—28no—
19C2×C11×#123C2218yes—
20C22×C11×C4⋊C4C2212yes—
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4C2212yes—
23C22×C22⋊Dic11C2211yescharacteristic
24C22×C22⋊Dic11C2212yes—
25C22×C22⋊Dic11C2211yescharacteristic
26C22×C22⋊Dic11C2211yescharacteristic
27C2×#66988—28no—
28C2×#66988C2218yes—
29C2×D4×Dic11—28no—
30C2×D4×Dic11C2218yes—
31C22×C4⋊Dic11C2211yescharacteristic
32C22×Dic11⋊C4—28no—
33C22×Dic11⋊C4C2212yes—
34C22×Dic11⋊C4C2212yes—
35C22×Dic11⋊C4C2212yes—
36C22×Dic11⋊C4C2212yes—
37C22×Dic11⋊C4C2218yescomplemented
38C22×C4×Dic11C2211yescharacteristic
39#10622824C2218yescomplemented
40C2×C11⋊#95C2212yes—
41C2×C11⋊#95C2212yes—
42C2×C11⋊#95C2212yes—
43C2×C11⋊#95C2212yes—
44C2×C11⋊#95C2212yes—
45#10622597C22116yescomplemented
46#10622585C22116yescomplemented
47#10622565C22116yescomplemented
48#10622556C2218yescomplemented
49#10622555C22116yescomplemented
50#10622555C2218yescomplemented
51C25×C11C2311yescharacteristic
52C25×C11C2311yescharacteristic
53C22×D4×C11—24no—
54C22×D4×C11—24no—
55C22×D4×C11D418yes—
56C22×D4×C11C2314yes—
57C23×C4×C11—24no—
58C23×C4×C11—24no—
59C23×C4×C11—24no—
60C23×C4×C11C2312yes—
61C23×C4×C11C2312yes—
62C23×C4×C11C2314yes—
63C23×C4×C11C2311yescharacteristic
64C23×Dic11—28no—
65C23×Dic11—24no—
66C23×Dic11—24no—
67C23×Dic11—24no—
68C23×Dic11—24no—
69C23×Dic11—28no—
70C23×Dic11D418yes—
71C23×Dic11C2311yescharacteristic
72C23×Dic11C2312yes—
73C23×Dic11C2312yes—
74C23×Dic11C2314yes—
75C23×Dic11C2311yescharacteristic
76C23×Dic11C2314yes—
77C23×Dic11C2311yescharacteristic
78C23×Dic11C2314yes—
79C23×Dic11C2311yescharacteristic
80C11×#123—232no—
81C2×C11×C4⋊C4—28no—
82C2×C11×C4⋊C4C2318yes—
83C2×C11×C22⋊C4—24no—
84C2×C11×C22⋊C4—28no—
85C2×C11×C22⋊C4C2314yes—
86C2×C11×C22⋊C4C2318yes—
87C2×C22⋊Dic11—24no—
88C2×C22⋊Dic11—24no—
89C2×C22⋊Dic11—28no—
90C2×C22⋊Dic11—24no—
91C2×C22⋊Dic11C2318yes—
92C2×C22⋊Dic11C2314yes—
93C2×C22⋊Dic11C2314yes—
94C2×C22⋊Dic11C2314yes—
95#66988—232no—
96D4×Dic11—232no—
97C2×C4⋊Dic11—24no—
98C2×C4⋊Dic11C2314yes—
99C2×Dic11⋊C4—28no—
100C2×Dic11⋊C4—28no—
101C2×Dic11⋊C4—28no—
102C2×Dic11⋊C4—232no—
103C2×Dic11⋊C4—28no—
104C2×Dic11⋊C4C2318yes—
105C2×Dic11⋊C4C2318yes—
106C2×Dic11⋊C4C2318yes—
107C2×Dic11⋊C4C2318yes—
108C2×C4×Dic11—24no—
109C2×C4×Dic11C2314yes—
110C11⋊#95C2318yes—
111C11⋊#95C2318yes—
112C11⋊#95C2318yes—
113C11⋊#95C2318yes—
114C11⋊#95C2318yes—
115C2×#2486—111nomaximal, Sylow
116C24×C11—24no—
117C24×C11—24no—
118C24×C11—22no—
119C24×C11—24no—
120C24×C11—22no—
121C24×C11—24no—
122C24×C11C2×D414yes—
123C24×C11C2×D414yes—
124C24×C11C2×D414yes—
125C24×C11#4114yes—
126C24×C11C2412yes—
127C24×C11C2412yes—
128C24×C11C2411yescharacteristic
129C2×D4×C11—232no—
130C2×D4×C11—28no—
131C2×D4×C11—28no—
132C2×D4×C11C2×D4116yes—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—28no—
136C22×C4×C11—24no—
137C22×C4×C11—24no—
138C22×C4×C11—24no—
139C22×C4×C11—28no—
140C22×C4×C11—24no—
141C22×C4×C11—28no—
142C22×C4×C11—24no—
143C22×C4×C11—24no—
144C22×C4×C11—416no—
145C22×C4×C11C2×D414yes—
146C22×C4×C11C2414yes—
147C22×C4×C11C2414yes—
148C22×C4×C11C2412yes—
149C22×Dic11—232no—
150C22×Dic11—216no—
151C22×Dic11—28no—
152C22×Dic11—216no—
153C22×Dic11—22no—
154C22×Dic11—28no—
155C22×Dic11—24no—
156C22×Dic11—24no—
157C22×Dic11—24no—
158C22×Dic11—22no—
159C22×Dic11—28no—
160C22×Dic11—24no—
161C22×Dic11—24no—
162C22×Dic11—28no—
163C22×Dic11—24no—
164C22×Dic11—24no—
165C22×Dic11—24no—
166C22×Dic11—24no—
167C22×Dic11—416no—
168C22×Dic11—416no—
169C22×Dic11C2×D414yes—
170C22×Dic11C2×D4116yes—
171C22×Dic11C2×D414yes—
172C22×Dic11#4118yes—
173C22×Dic11C2412yes—
174C22×Dic11C2412yes—
175C22×Dic11C2414yes—
176C22×Dic11C2414yes—
177C22×Dic11C2412yes—
178C22×Dic11C2412yes—
179C11×C4⋊C4—216no—
180C11×C22⋊C4—28no—
181C11×C22⋊C4—216no—
182C22⋊Dic11—28no—
183C22⋊Dic11—28no—
184C22⋊Dic11—216no—
185C22⋊Dic11—28no—
186C4⋊Dic11—28no—
187Dic11⋊C4—216no—
188Dic11⋊C4—216no—
189Dic11⋊C4—216no—
190Dic11⋊C4—216no—
191C4×Dic11—28no—
192C22×#123—111no—
193C22×#123D1111yescharacteristic
194C22×C4×D4—111no—
195C23×C4⋊C4—111no—
196#2486—1116no—
197C2×#398—112no—
198C2×#397—112no—
199C2×#389—112no—
200C2×#381—111no—
201C2×#381—111no—
202C2×#380—112no—
203C2×#380—111no—
204C23×C11—28no—
205C23×C11—28no—
206C23×C11—216no—
207C23×C11—216no—
208C23×C11—24no—
209C23×C11—24no—
210C23×C11—28no—
211C23×C11—216no—
212C23×C11—22no—
213C23×C11—24no—
214C23×C11—22no—
215C23×C11—24no—
216C23×C11—44no—
217C23×C11—44no—
218C23×C11—48no—
219C23×C11#121116yes—
220C23×C11C22×D414yes—
221C23×C11C22×D412yes—
222C23×C11C22×D414yes—
223C23×C11C22×D414yes—
224C23×C11C22×D412yes—
225C23×C11C2×#4114yes—
226C23×C11C2×#4112yes—
227C23×C11C2×#4114yes—
228C23×C112−1+414yes—
229C23×C11C2511yescharacteristic
230D4×C11—232no—
231C2×C4×C11—28no—
232C2×C4×C11—22no—
233C2×C4×C11—22no—
234C2×C4×C11—24no—
235C2×C4×C11—24no—
236C2×C4×C11—24no—
237C2×C4×C11—24no—
238C2×C4×C11—24no—
239C2×C4×C11—24no—
240C2×C4×C11—416no—
241C2×C4×C11—48no—
242C2×C4×C11—48no—
243C2×C4×C11C22×D414yes—
244C2×Dic11—28no—
245C2×Dic11—24no—
246C2×Dic11—232no—
247C2×Dic11—22no—
248C2×Dic11—24no—
249C2×Dic11—24no—
250C2×Dic11—24no—
251C2×Dic11—22no—
252C2×Dic11—24no—
253C2×Dic11—24no—
254C2×Dic11—24no—
255C2×Dic11—24no—
256C2×Dic11—24no—
257C2×Dic11—416no—
258C2×Dic11—48no—
259C2×Dic11—44no—
260C2×Dic11—44no—
261C2×Dic11—48no—
262C2×Dic11—416no—
263C2×Dic11#123116yescomplemented
264C2×Dic11C22×D414yes—
265C2×Dic11C22×D414yes—
266C2×Dic11C2×#4118yes—
267C23×D4C2×D1111yescharacteristic
268C24×C4—111no—
269C24×C4—111no—
270C24×C4—111no—
271C24×C4C2×D1111yescharacteristic
272C2×#123—28no—
273C2×#123—118no—
274C2×#123—228no—
275C2×#123C2×D1118yes—
276C2×C4×D4—118no—
277C2×C4×D4—228no—
278C22×C4⋊C4—112no—
279C22×C4⋊C4—112no—
280C22×C4⋊C4—112no—
281C22×C4⋊C4—112no—
282C22×C4⋊C4—118no—
283C22×C4⋊C4—111no—
284C22×C4⋊C4—228no—
285C22×C4⋊C4C2×D1112yes—
286C22×C22⋊C4—111no—
287C22×C22⋊C4—112no—
288C22×C22⋊C4—111no—
289C22×C22⋊C4—111no—
290C22×C22⋊C4C2×D1112yes—
291C22×C22⋊C4C2×D1111yescharacteristic
292C22×C42—111no—
293#398—1116no—
294#397—1116no—
295#389—1116no—
296#381—118no—
297#381—118no—
298#380—1116no—
299#380—118no—
300C2×#95—112no—
301C2×#95—112no—
302C2×#95—112no—
303C2×#95—112no—
304C2×#95—112no—
305C22×C11—24no—
306C22×C11—24no—
307C22×C11—28no—
308C22×C11—28no—
309C22×C11—232no—
310C22×C11—24no—
311C22×C11—28no—
312C22×C11—42no—
313C22×C11—42no—
314C22×C11—44no—
315C22×C11—416no—
316C22×C11C2×#12118yes—
317C22×C11C2×#12114yes—
318C22×C11C2×#12314yes—
319C22×C11#53614yes—
320C22×C11#54718yes—
321C22×C11#55218yes—
322C22×C11C23×D411yescharacteristic
323C22×C11C23×D411yescharacteristic
324C22×C11C22×#4111yescharacteristic
325C22×C11C22×#4112yes—
326C22×C11C2×2−1+412yes—
327C4×C11—24no—
328C4×C11—44no—
329C4×C11—44no—
330Dic11—24no—
331Dic11—44no—
332Dic11—42no—
333Dic11—42no—
334Dic11—44no—
335Dic11C2×#12318yescomplemented
336C25C22×D1111yescharacteristic
337C25C22×D1111yescharacteristic
338C22×D4—24no—
339C22×D4—24no—
340C22×D4C22⋊D1118yes—
341C22×D4C22×D1114yes—
342C23×C4—24no—
343C23×C4—24no—
344C23×C4—24no—
345C23×C4—111no—
346C23×C4—118no—
347C23×C4—114no—
348C23×C4—111no—
349C23×C4—114no—
350C23×C4—114no—
351C23×C4—112no—
352C23×C4—111no—
353C23×C4—112no—
354C23×C4—111no—
355C23×C4—228no—
356C23×C4—224no—
357C23×C4—228no—
358C23×C4—224no—
359C23×C4—224no—
360C23×C4—224no—
361C23×C4C22×D1114yes—
362C23×C4C22×D1112yes—
363C23×C4C22×D1112yes—
364C23×C4C22×D1111yescharacteristic
365#123—232no—
366#123—2232no—
367C4×D4—2232no—
368C2×C4⋊C4—28no—
369C2×C4⋊C4—118no—
370C2×C4⋊C4—118no—
371C2×C4⋊C4—114no—
372C2×C4⋊C4—118no—
373C2×C4⋊C4—118no—
374C2×C4⋊C4—228no—
375C2×C4⋊C4—228no—
376C2×C4⋊C4—2232no—
377C2×C4⋊C4—224no—
378C2×C4⋊C4—228no—
379C2×C4⋊C4—228no—
380C2×C4⋊C4C22×D1118yes—
381C2×C22⋊C4—24no—
382C2×C22⋊C4—28no—
383C2×C22⋊C4—114no—
384C2×C22⋊C4—114no—
385C2×C22⋊C4—114no—
386C2×C22⋊C4—118no—
387C2×C22⋊C4—224no—
388C2×C22⋊C4—224no—
389C2×C22⋊C4—224no—
390C2×C22⋊C4—228no—
391C2×C22⋊C4C22×D1114yes—
392C2×C22⋊C4C22×D1118yes—
393C2×C42—114no—
394C2×C42—224no—
395#95—118no—
396#95—118no—
397#95—118no—
398#95—118no—
399#95—118no—
400C2×C11—28no—
401C2×C11—44no—
402C2×C11#248618yescomplemented
403C2×C11C22×#12111yescharacteristic
404C2×C11C22×#12311yescharacteristic
405C2×C11C2×#53611yescharacteristic
406C2×C11C2×#54712yes—
407C2×C11C2×#55212yes—
408C24—24no—
409C24—24no—
410C24—22no—
411C24—22no—
412C24—24no—
413C24—24no—
414C24D4×D1114yes—
415C24#434114yes—
416C24C2×C22⋊D1114yes—
417C24C2×C22⋊D1114yes—
418C24C23×D1112yes—
419C24C23×D1112yes—
420C24C23×D1111yescharacteristic
421C2×D4—232no—
422C2×D4—28no—
423C2×D4—28no—
424C2×D4C2×C22⋊D11116yes—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—28no—
428C22×C4—24no—
429C22×C4—28no—
430C22×C4—24no—
431C22×C4—24no—
432C22×C4—24no—
433C22×C4—24no—
434C22×C4—24no—
435C22×C4—28no—
436C22×C4—416no—
437C22×C4—114no—
438C22×C4—118no—
439C22×C4—112no—
440C22×C4—114no—
441C22×C4—1116no—
442C22×C4—112no—
443C22×C4—112no—
444C22×C4—112no—
445C22×C4—114no—
446C22×C4—114no—
447C22×C4—2232no—
448C22×C4—2216no—
449C22×C4—228no—
450C22×C4—2216no—
451C22×C4—224no—
452C22×C4—222no—
453C22×C4—222no—
454C22×C4—228no—
455C22×C4—224no—
456C22×C4—228no—
457C22×C4—224no—
458C22×C4—224no—
459C22×C4—224no—
460C22×C4—224no—
461C22×C4—224no—
462C22×C4—224no—
463C22×C4—224no—
464C22×C4—228no—
465C22×C4—4416no—
466C22×C4—4416no—
467C22×C4C2×C22⋊D1114yes—
468C22×C4C23×D1114yes—
469C22×C4C23×D1114yes—
470C22×C4C23×D1112yes—
471C4⋊C4—216no—
472C4⋊C4—2216no—
473C4⋊C4—2216no—
474C4⋊C4—228no—
475C4⋊C4—2216no—
476C4⋊C4—2216no—
477C22⋊C4—28no—
478C22⋊C4—216no—
479C22⋊C4—228no—
480C22⋊C4—228no—
481C22⋊C4—228no—
482C22⋊C4—2216no—
483C42—228no—
484C11C2×#248611yescharacteristic, complemented, Sylow
485C23—216no—
486C23—28no—
487C23—216no—
488C23—28no—
489C23—24no—
490C23—24no—
491C23—28no—
492C23—216no—
493C23—22no—
494C23—22no—
495C23—24no—
496C23—24no—
497C23—44no—
498C23—48no—
499C23—44no—
500C23#66992116yes—
501C23C2×D4×D1114yes—
502C23C2×D4×D1112yes—
503C23C2×#434114yes—
504C23C2×#434112yes—
505C23#41×D1114yes—
506C23#6704314yes—
507C23C22×C22⋊D1114yes—
508C23C22×C22⋊D1114yes—
509C23C22×C22⋊D1112yes—
510C23C24×D1111yescharacteristic
511D4—232no—
512C2×C4—28no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—24no—
516C2×C4—24no—
517C2×C4—24no—
518C2×C4—24no—
519C2×C4—24no—
520C2×C4—24no—
521C2×C4—416no—
522C2×C4—48no—
523C2×C4—48no—
524C2×C4—1116no—
525C2×C4—114no—
526C2×C4—118no—
527C2×C4—114no—
528C2×C4—2232no—
529C2×C4—228no—
530C2×C4—224no—
531C2×C4—222no—
532C2×C4—222no—
533C2×C4—224no—
534C2×C4—224no—
535C2×C4—224no—
536C2×C4—224no—
537C2×C4—224no—
538C2×C4—224no—
539C2×C4—224no—
540C2×C4—224no—
541C2×C4—4416no—
542C2×C4—4416no—
543C2×C4—448no—
544C2×C4—448no—
545C2×C4—444no—
546C2×C4—444no—
547C2×C4C22×C22⋊D1114yes—
548C22—28no—
549C22—232no—
550C22—24no—
551C22—28no—
552C22—24no—
553C22—28no—
554C22—24no—
555C22—44no—
556C22—416no—
557C22—42no—
558C22—42no—
559C22#1062317914yes—
560C22#1062318118yes—
561C22D11×#12314yes—
562C22C2×#6699218yes—
563C22C2×#6699214yes—
564C22#1062335518yes—
565C22C22×D4×D1111yescharacteristic
566C22C22×#434111yescharacteristic
567C22C2×#41×D1112yes—
568C22C2×#6704312yes—
569C22C23×C22⋊D1111yescharacteristic
570C4—24no—
571C4—44no—
572C4—44no—
573C4—118no—
574C4—224no—
575C4—442no—
576C4—444no—
577C4—444no—
578C4—442no—
579C2—28no—
580C2—44no—
581C2#1307292118yesdirect product factor
582C2C22×#6699211yescharacteristic
583C2C2×D11×#12311yescharacteristic
584C2C2×#1062317911yescharacteristic
585C2C2×#1062335512yes—
586C2C2×#1062318112yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC22×C11×#123C2
socleC24×C11C24
prime radicalC23×D4×C11C22
hypercenterC22×#123D11
hypocenterC11C2×#2486
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×#123

Complements

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

NH ≅ G/Ntype
3. C23×Dic11⋊C4C2semidirect
4. #13072921C2direct (N × H)
5. C2×#10622597C2semidirect
6. C2×#10622565C2semidirect
7. C2×#10622585C2semidirect
8. C2×#10622824C2semidirect
9. C2×#10622556C2semidirect
10. C2×#10622555C2semidirect
11. C2×#10622555C2semidirect
37. C22×Dic11⋊C4C22semidirect
39. #10622824C22semidirect
45. #10622597C22semidirect
46. #10622585C22semidirect
47. #10622565C22semidirect
48. #10622556C22semidirect
49. #10622555C22semidirect
50. #10622555C22semidirect
263. C2×Dic11#123semidirect
335. Dic11C2×#123semidirect
402. C2×C11#2486semidirect
484. C11C2×#2486semidirect
581. C2#13072921direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669882
C22×D4×Dic112
C23×Dic11⋊C42
#130729212
C2×#106225972
C2×#106225652
C2×#106225852
C2×#106228242
C2×#106225562
C2×#106225552
C22×C11×#1232
C2×#248611