Finite Group Databasebeta

← C2×C4×#66988 #14912205

Subgroups — C2×C4×#66988 #14912205

Order 2816.

4070 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66988C211yesmaximal, characteristic
2C23×C4×Dic11C211yesmaximal, characteristic, complemented
3C4×#66988C2116yesmaximal, direct product factor
4C2×#10622557C212yesmaximal, complemented
5C2×#10622591C212yesmaximal, complemented
6C2×#10622833C211yesmaximal, characteristic
7C2×#10622559C211yesmaximal, characteristic, complemented
8C2×#10622556C211yesmaximal, characteristic, complemented
9C2×C4×Dic11⋊C4C212yesmaximal, complemented
10C2×C4×C22⋊Dic11C211yesmaximal, characteristic, complemented
11C2×C4×C22⋊Dic11C212yesmaximal, complemented
12C22×C4×D4×C11C211yesmaximal, characteristic
13C23×D4×C11C2211yescharacteristic
14C24×C4×C11C2211yescharacteristic
15C24×C4×C11C2211yescharacteristic
16C24×Dic11C2211yescharacteristic
17C24×Dic11C2211yescharacteristic
18C2×C4×D4×C11—28no—
19C2×C4×D4×C11C2218yes—
20C22×C11×C4⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C42×C11C2211yescharacteristic
24C22×C22⋊Dic11C2211yescharacteristic
25C22×C22⋊Dic11C2212yes—
26C22×C22⋊Dic11C2211yescharacteristic
27C22×C22⋊Dic11C2212yes—
28C2×#66988C4116yesdirect product factor
29C2×#66988C2218yes—
30C22×Dic11⋊C4C2212yes—
31C22×Dic11⋊C4C2212yes—
32C22×C4×Dic11—28no—
33C22×C4×Dic11C2212yes—
34C22×C4×Dic11C2212yes—
35C22×C4×Dic11C2212yes—
36C22×C4×Dic11C2218yescomplemented
37#10622833C2218yes—
38C4×C22⋊Dic11C22116yescomplemented
39C4×C22⋊Dic11C2218yescomplemented
40C2×C11⋊#95C2212yes—
41C2×C11⋊#95C2212yes—
42C2×C11⋊#95C2212yes—
43C2×C11⋊#95C2212yes—
44C2×C11⋊#95C2212yes—
45#10622591C22116yescomplemented
46#10622559C2218yescomplemented
47#10622557C22116yescomplemented
48#10622556C2218yescomplemented
49C4×Dic11⋊C4C22116yescomplemented
50C25×C11C2311yescharacteristic
51C25×C11C2311yescharacteristic
52C22×D4×C11—24no—
53C22×D4×C11—24no—
54C22×D4×C11C2×C418yes—
55C22×D4×C11C2314yes—
56C23×C4×C11—28no—
57C23×C4×C11—24no—
58C23×C4×C11—28no—
59C23×C4×C11D418yes—
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2314yes—
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2314yes—
66C23×C4×C11C2311yescharacteristic
67C23×Dic11—24no—
68C23×Dic11—24no—
69C23×Dic11—24no—
70C23×Dic11—28no—
71C23×Dic11C2×C418yescomplemented
72C23×Dic11C2312yes—
73C23×Dic11C2314yes—
74C23×Dic11C2312yes—
75C23×Dic11C2312yes—
76C23×Dic11C2314yes—
77C23×Dic11C2312yes—
78C4×D4×C11—232no—
79C2×C11×C4⋊C4—24no—
80C2×C11×C4⋊C4C2314yes—
81C2×C11×C22⋊C4—24no—
82C2×C11×C22⋊C4—24no—
83C2×C11×C22⋊C4C2314yes—
84C2×C11×C22⋊C4C2314yes—
85C2×C42×C11—24no—
86C2×C42×C11C2314yes—
87C2×C22⋊Dic11—24no—
88C2×C22⋊Dic11—28no—
89C2×C22⋊Dic11C2×C418yescomplemented
90C2×C22⋊Dic11C2×C4116yescomplemented
91C2×C22⋊Dic11C2314yes—
92C2×C22⋊Dic11C2318yes—
93C2×C22⋊Dic11C2318yes—
94C2×C22⋊Dic11C2314yes—
95#66988C2×C4164yesdirect product factor
96C2×Dic11⋊C4—28no—
97C2×Dic11⋊C4C2×C4116yescomplemented
98C2×Dic11⋊C4C2318yes—
99C2×Dic11⋊C4C2318yes—
100C2×C4×Dic11—28no—
101C2×C4×Dic11—28no—
102C2×C4×Dic11—232no—
103C2×C4×Dic11—28no—
104C2×C4×Dic11C2318yes—
105C2×C4×Dic11C2318yes—
106C2×C4×Dic11C2318yes—
107C11⋊#95C2318yes—
108C11⋊#95C2318yes—
109C11⋊#95C2318yes—
110C11⋊#95C2318yes—
111C11⋊#95C2318yes—
112C2×C4×#123—111nomaximal, Sylow
113C24×C11—24no—
114C24×C11—24no—
115C24×C11—22no—
116C24×C11—24no—
117C24×C11—24no—
118C24×C11—22no—
119C24×C11C22×C414yes—
120C24×C11C22×C414yes—
121C24×C11C2×D414yes—
122C24×C11#4114yes—
123C24×C11C2412yes—
124C24×C11C2412yes—
125C24×C11C2411yescharacteristic
126C2×D4×C11—232no—
127C2×D4×C11—28no—
128C2×D4×C11—28no—
129C2×D4×C11C22×C4116yes—
130C22×C4×C11—22no—
131C22×C4×C11—24no—
132C22×C4×C11—22no—
133C22×C4×C11—232no—
134C22×C4×C11—216no—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11—24no—
138C22×C4×C11—24no—
139C22×C4×C11—28no—
140C22×C4×C11—216no—
141C22×C4×C11—416no—
142C22×C4×C11C22×C414yes—
143C22×C4×C11C2×D414yes—
144C22×C4×C11C2×D4116yes—
145C22×C4×C11C2×D414yes—
146C22×C4×C11#4118yes—
147C22×C4×C11C2412yes—
148C22×C4×C11C2412yes—
149C22×C4×C11C2412yes—
150C22×C4×C11C2412yes—
151C22×C4×C11C2412yes—
152C22×Dic11—232no—
153C22×Dic11—216no—
154C22×Dic11—232no—
155C22×Dic11—28no—
156C22×Dic11—28no—
157C22×Dic11—24no—
158C22×Dic11—24no—
159C22×Dic11—24no—
160C22×Dic11—24no—
161C22×Dic11—28no—
162C22×Dic11—24no—
163C22×Dic11—24no—
164C22×Dic11—24no—
165C22×Dic11—24no—
166C22×Dic11—24no—
167C22×Dic11C22×C418yes—
168C22×Dic11C22×C418yes—
169C22×Dic11C22×C4116yescomplemented
170C22×Dic11#4118yes—
171C22×Dic11C2414yes—
172C22×Dic11C2414yes—
173C22×Dic11C2414yes—
174C22×Dic11C2414yes—
175C11×C4⋊C4—28no—
176C11×C22⋊C4—28no—
177C11×C22⋊C4—28no—
178C42×C11—28no—
179C22⋊Dic11—216no—
180C22⋊Dic11—28no—
181C22⋊Dic11C22×C4132yescomplemented
182C22⋊Dic11C22×C4116yescomplemented
183Dic11⋊C4—216no—
184Dic11⋊C4C22×C4132yescomplemented
185C4×Dic11—216no—
186C4×Dic11—216no—
187C4×Dic11—216no—
188C22×#123—111no—
189C22×C4×D4D1111yescharacteristic
190C23×C42—111no—
191C4×#123—1116no—
192C2×#388—112no—
193C2×#387—112no—
194C2×#386—111no—
195C2×#385—111no—
196C2×#381—111no—
197C2×C4×C4⋊C4—112no—
198C2×C4×C22⋊C4—111no—
199C2×C4×C22⋊C4—112no—
200C23×C11—216no—
201C23×C11—28no—
202C23×C11—28no—
203C23×C11—216no—
204C23×C11—24no—
205C23×C11—24no—
206C23×C11—28no—
207C23×C11—216no—
208C23×C11—22no—
209C23×C11—24no—
210C23×C11—24no—
211C23×C11—22no—
212C23×C11—44no—
213C23×C11—44no—
214C23×C11—48no—
215C23×C11C4×D4116yes—
216C23×C11C23×C414yes—
217C23×C11C23×C414yes—
218C23×C11C23×C412yes—
219C23×C11C22×D414yes—
220C23×C11C22×D412yes—
221C23×C11C2×#4114yes—
222C23×C11C2×#4112yes—
223C23×C11C2×#4114yes—
224C23×C11C2×#4114yes—
225C23×C11C2511yescharacteristic
226D4×C11—232no—
227C2×C4×C11—28no—
228C2×C4×C11—28no—
229C2×C4×C11—22no—
230C2×C4×C11—24no—
231C2×C4×C11—22no—
232C2×C4×C11—232no—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—24no—
236C2×C4×C11—24no—
237C2×C4×C11—44no—
238C2×C4×C11—44no—
239C2×C4×C11—416no—
240C2×C4×C11#123116yescomplemented
241C2×C4×C11C23×C414yes—
242C2×C4×C11C22×D414yes—
243C2×C4×C11C22×D414yes—
244C2×C4×C11C2×#4118yes—
245C2×Dic11—232no—
246C2×Dic11—216no—
247C2×Dic11—232no—
248C2×Dic11—216no—
249C2×Dic11—216no—
250C2×Dic11—24no—
251C2×Dic11—24no—
252C2×Dic11—24no—
253C2×Dic11—24no—
254C2×Dic11—24no—
255C2×Dic11—24no—
256C2×Dic11—24no—
257C2×Dic11—24no—
258C2×Dic11—24no—
259C2×Dic11—48no—
260C2×Dic11C23×C418yes—
261C2×Dic11C23×C418yes—
262C2×Dic11C2×#4118yes—
263C23×D4C2×D1111yescharacteristic
264C24×C4—111no—
265C24×C4—111no—
266C24×C4C2×D1111yescharacteristic
267C24×C4C2×D1111yescharacteristic
268C2×#123—118no—
269C2×#123—1116no—
270C2×C4×D4—28no—
271C2×C4×D4C2×D1118yes—
272C22×C4⋊C4—112no—
273C22×C4⋊C4—112no—
274C22×C4⋊C4C2×D1111yescharacteristic
275C22×C22⋊C4—111no—
276C22×C22⋊C4—112no—
277C22×C22⋊C4—111no—
278C22×C22⋊C4—112no—
279C22×C22⋊C4C2×D1111yescharacteristic
280C22×C22⋊C4C2×D1111yescharacteristic
281C22×C42—112no—
282C22×C42—118no—
283C22×C42—112no—
284C22×C42—112no—
285C22×C42—228no—
286C22×C42C2×D1111yescharacteristic
287#388—1116no—
288#387—1116no—
289#386—118no—
290#385—118no—
291#381—118no—
292C4×C4⋊C4—1116no—
293C4×C22⋊C4—1116no—
294C4×C22⋊C4—118no—
295C2×#95—112no—
296C2×#95—112no—
297C2×#95—112no—
298C2×#95—112no—
299C2×#95—112no—
300C22×C11—28no—
301C22×C11—24no—
302C22×C11—24no—
303C22×C11—28no—
304C22×C11—232no—
305C22×C11—24no—
306C22×C11—28no—
307C22×C11—42no—
308C22×C11—42no—
309C22×C11—44no—
310C22×C11—416no—
311C22×C11C2×C4×D418yes—
312C22×C11C2×C4×D414yes—
313C22×C11C4×#4118yes—
314C22×C11C2×#12314yes—
315C22×C11#52514yes—
316C22×C11#52918yes—
317C22×C11C24×C411yescharacteristic
318C22×C11C23×D411yescharacteristic
319C22×C11C22×#4111yescharacteristic
320C22×C11C22×#4112yes—
321C22×C11C22×#4112yes—
322C4×C11—24no—
323C4×C11—24no—
324C4×C11—42no—
325C4×C11—42no—
326C4×C11C2×#12318yescomplemented
327Dic11—28no—
328Dic11—28no—
329Dic11—28no—
330Dic11—44no—
331C25C22×D1111yescharacteristic
332C25C22×D1111yescharacteristic
333C22×D4—24no—
334C22×D4—24no—
335C22×D4C4×D1118yes—
336C22×D4C22×D1114yes—
337C23×C4—28no—
338C23×C4—28no—
339C23×C4—24no—
340C23×C4—118no—
341C23×C4—112no—
342C23×C4—112no—
343C23×C4—112no—
344C23×C4—114no—
345C23×C4—112no—
346C23×C4—114no—
347C23×C4—228no—
348C23×C4—224no—
349C23×C4—224no—
350C23×C4—224no—
351C23×C4C22⋊D1118yes—
352C23×C4C22×D1111yescharacteristic
353C23×C4C22×D1111yescharacteristic
354C23×C4C22×D1114yes—
355C23×C4C22×D1111yescharacteristic
356C23×C4C22×D1111yescharacteristic
357C23×C4C22×D1114yes—
358C23×C4C22×D1111yescharacteristic
359#123—1164no—
360C4×D4—232no—
361C2×C4⋊C4—24no—
362C2×C4⋊C4—1116no—
363C2×C4⋊C4—118no—
364C2×C4⋊C4—118no—
365C2×C4⋊C4—228no—
366C2×C4⋊C4C22×D1114yes—
367C2×C22⋊C4—24no—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—118no—
370C2×C22⋊C4—1116no—
371C2×C22⋊C4—114no—
372C2×C22⋊C4—118no—
373C2×C22⋊C4—114no—
374C2×C22⋊C4—118no—
375C2×C22⋊C4—228no—
376C2×C22⋊C4—224no—
377C2×C22⋊C4C22×D1114yes—
378C2×C22⋊C4C22×D1114yes—
379C2×C42—24no—
380C2×C42—118no—
381C2×C42—118no—
382C2×C42—118no—
383C2×C42—228no—
384C2×C42—228no—
385C2×C42—2232no—
386C2×C42—228no—
387C2×C42C22×D1114yes—
388#95—118no—
389#95—118no—
390#95—118no—
391#95—118no—
392#95—118no—
393C2×C11—28no—
394C2×C11—44no—
395C2×C11C4×#12318yescomplemented
396C2×C11C22×C4×D411yescharacteristic
397C2×C11C2×C4×#4112yes—
398C2×C11C22×#12311yescharacteristic
399C2×C11C2×#52511yescharacteristic
400C2×C11C2×#52912yes—
401C24—24no—
402C24—24no—
403C24—22no—
404C24—24no—
405C24—24no—
406C24—22no—
407C24C2×C4×D1114yes—
408C24C2×C4×D1114yes—
409C24#433914yes—
410C24C2×C22⋊D1114yes—
411C24C23×D1112yes—
412C24C23×D1112yes—
413C24C23×D1111yescharacteristic
414C2×D4—232no—
415C2×D4—28no—
416C2×D4—28no—
417C2×D4C2×C4×D11116yes—
418C22×C4—22no—
419C22×C4—24no—
420C22×C4—22no—
421C22×C4—232no—
422C22×C4—216no—
423C22×C4—24no—
424C22×C4—24no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—216no—
428C22×C4—28no—
429C22×C4—416no—
430C22×C4—118no—
431C22×C4—118no—
432C22×C4—1116no—
433C22×C4—118no—
434C22×C4—114no—
435C22×C4—114no—
436C22×C4—114no—
437C22×C4—114no—
438C22×C4—2216no—
439C22×C4—2232no—
440C22×C4—2232no—
441C22×C4—228no—
442C22×C4—224no—
443C22×C4—224no—
444C22×C4—224no—
445C22×C4—224no—
446C22×C4—228no—
447C22×C4—228no—
448C22×C4—224no—
449C22×C4—224no—
450C22×C4—224no—
451C22×C4—224no—
452C22×C4—224no—
453C22×C4C2×C4×D1114yes—
454C22×C4#434118yes—
455C22×C4C2×C22⋊D1114yes—
456C22×C4C2×C22⋊D11116yes—
457C22×C4C2×C22⋊D1114yes—
458C22×C4C23×D1112yes—
459C22×C4C23×D1112yes—
460C22×C4C23×D1112yes—
461C22×C4C23×D1112yes—
462C22×C4C23×D1112yes—
463C4⋊C4—28no—
464C4⋊C4—1132no—
465C4⋊C4—2216no—
466C22⋊C4—28no—
467C22⋊C4—28no—
468C22⋊C4—1116no—
469C22⋊C4—1132no—
470C22⋊C4—2216no—
471C22⋊C4—228no—
472C42—28no—
473C42—2216no—
474C42—2216no—
475C42—2216no—
476C11C2×C4×#12311yescharacteristic, complemented, Sylow
477C23—216no—
478C23—216no—
479C23—28no—
480C23—28no—
481C23—24no—
482C23—24no—
483C23—28no—
484C23—216no—
485C23—22no—
486C23—24no—
487C23—24no—
488C23—22no—
489C23—48no—
490C23—44no—
491C23—44no—
492C23C4×C22⋊D11116yes—
493C23C22×C4×D1114yes—
494C23C22×C4×D1114yes—
495C23C22×C4×D1112yes—
496C23C2×#433914yes—
497C23C2×#433912yes—
498C23C2×#434114yes—
499C23#41×D1114yes—
500C23C22×C22⋊D1114yes—
501C23C22×C22⋊D1112yes—
502C23C24×D1111yescharacteristic
503D4—232no—
504C2×C4—28no—
505C2×C4—28no—
506C2×C4—22no—
507C2×C4—24no—
508C2×C4—22no—
509C2×C4—232no—
510C2×C4—24no—
511C2×C4—24no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—44no—
515C2×C4—44no—
516C2×C4—416no—
517C2×C4—118no—
518C2×C4—118no—
519C2×C4—118no—
520C2×C4—2232no—
521C2×C4—2232no—
522C2×C4—2216no—
523C2×C4—2216no—
524C2×C4—2216no—
525C2×C4—224no—
526C2×C4—224no—
527C2×C4—224no—
528C2×C4—224no—
529C2×C4—224no—
530C2×C4—224no—
531C2×C4—224no—
532C2×C4—224no—
533C2×C4—224no—
534C2×C4—448no—
535C2×C4#66988116yesdirect product factor
536C2×C4C22×C4×D1114yes—
537C2×C4C2×#434118yes—
538C2×C4C22×C22⋊D1114yes—
539C2×C4C22×C22⋊D1114yes—
540C22—28no—
541C22—232no—
542C22—28no—
543C22—24no—
544C22—24no—
545C22—24no—
546C22—28no—
547C22—44no—
548C22—416no—
549C22—42no—
550C22—42no—
551C22C4×#434118yes—
552C22#1062306918yes—
553C22C2×C4×C22⋊D1118yes—
554C22C2×C4×C22⋊D1114yes—
555C22C2×#6698814yes—
556C22#1062335914yes—
557C22C23×C4×D1111yescharacteristic
558C22C22×#433911yescharacteristic
559C22C22×#434112yes—
560C22C2×#41×D1112yes—
561C22C23×C22⋊D1111yescharacteristic
562C4—24no—
563C4—24no—
564C4—42no—
565C4—42no—
566C4—228no—
567C4—228no—
568C4—228no—
569C4—444no—
570C4C2×#6698818yesdirect product factor
571C2—28no—
572C2—44no—
573C2C4×#6698818yesdirect product factor
574C2C22×C4×C22⋊D1111yescharacteristic
575C2C2×C4×#434112yes—
576C2C22×#6698811yescharacteristic
577C2C2×#1062335911yescharacteristic
578C2C2×#1062306912yes—
subgroupG/H
centerC23×C4C22×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC22×C4×D4×C11C2
socleC24×C11C24
prime radicalC23×D4×C11C22
cosocleC23×C11C25
hypercenterC22×C4×D4D11
hypocenterC11C2×C4×#123
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23×C4 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
2. C23×C4×Dic11C2semidirect
3. C4×#66988C2direct (N × H)
4. C2×#10622557C2semidirect
5. C2×#10622591C2semidirect
7. C2×#10622559C2semidirect
8. C2×#10622556C2semidirect
9. C2×C4×Dic11⋊C4C2semidirect
10. C2×C4×C22⋊Dic11C2semidirect
11. C2×C4×C22⋊Dic11C2semidirect
28. C2×#66988C4direct (N × H)
36. C22×C4×Dic11C22semidirect
38. C4×C22⋊Dic11C22semidirect
39. C4×C22⋊Dic11C22semidirect
45. #10622591C22semidirect
46. #10622559C22semidirect
47. #10622557C22semidirect
48. #10622556C22semidirect
49. C4×Dic11⋊C4C22semidirect
71. C23×Dic11C2×C4semidirect
89. C2×C22⋊Dic11C2×C4semidirect
90. C2×C22⋊Dic11C2×C4semidirect
95. #66988C2×C4direct (N × H)
97. C2×Dic11⋊C4C2×C4semidirect
169. C22×Dic11C22×C4semidirect
181. C22⋊Dic11C22×C4semidirect
182. C22⋊Dic11C22×C4semidirect
184. Dic11⋊C4C22×C4semidirect
240. C2×C4×C11#123semidirect
326. C4×C11C2×#123semidirect
395. C2×C11C4×#123semidirect
476. C11C2×C4×#123semidirect
535. C2×C4#66988direct (N × H)
570. C4C2×#66988direct (N × H)
573. C2C4×#66988direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669882
C23×C4×Dic112
C4×#669882
C2×#106225572
C2×#106225912
C2×#106228332
C2×#106225592
C2×#106225562
C2×C4×Dic11⋊C42
C2×C4×C22⋊Dic112
C22×C4×D4×C112
C2×C4×#12311