Finite Group Databasebeta

← C2×#13071097 #14912153

Subgroups — C2×#13071097 #14912153

Order 2816.

3854 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66945C211yesmaximal, characteristic
2C22×#66945C211yesmaximal, characteristic
3C22×C42×D11C211yesmaximal, characteristic
4#13071097C2116yesmaximal, direct product factor
5C2×#10622598C211yesmaximal, characteristic, complemented
6C2×#10622541C211yesmaximal, characteristic, complemented
7C2×#10622586C211yesmaximal, characteristic, complemented
8C2×#10622281C212yesmaximal
9C2×#10622602C212yesmaximal
10C2×C4⋊C4×Dic11C212yesmaximal, complemented
11C2×#10622262C212yesmaximal, complemented
12C2×C11×#389C211yesmaximal, characteristic, complemented
13C23×C4×D11C2211yescharacteristic
14C23×C4×D11C2211yescharacteristic
15C23×C4×D11C2211yescharacteristic
16C22×C11×C4⋊C4C2212yes—
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C42×C11C2211yescharacteristic
20C22×(C2×D11)⋊C4C2212yes—
21C22×(C2×D11)⋊C4C2212yes—
22C22×C4⋊Dic11C2212yes—
23C22×C4⋊Dic11C2211yescharacteristic
24C22×C4⋊Dic11C2211yescharacteristic
25C22×Dic11⋊C4C2212yes—
26C22×Dic11⋊C4C2212yes—
27C22×C4×Dic11C2211yescharacteristic
28C22×C4×Dic11C2212yes—
29C22×C4×Dic11C2211yescharacteristic
30C22×C4×Dic11C2211yescharacteristic
31C22×C4×Dic11C2212yes—
32C2×#66945—28no—
33C2×#66945C4116yescomplemented
34C2×#66945C2218yes—
35C2×#66945C2218yes—
36C2×C42×D11—28no—
37C2×C42×D11C2218yes—
38C11×#389C2218yescomplemented
39C2×C11×#95C2212yes—
40C2×C11⋊#95C2212yes—
41C2×C11⋊#95C2212yes—
42C2×C11⋊#95C2212yes—
43#10622602C22116yes—
44#10622598C2218yescomplemented
45C4⋊C4×Dic11C22116yescomplemented
46#10622586C2218yescomplemented
47#10622541C2218yescomplemented
48#10622281C22116yes—
49#10622262C22116yescomplemented
50C24×D11C2311yescharacteristic
51C23×C4×C11C2312yes—
52C23×C4×C11C2312yes—
53C23×C4×C11C2311yescharacteristic
54C23×C4×C11C2311yescharacteristic
55C23×C4×C11C2311yescharacteristic
56C23×Dic11C2312yes—
57C23×Dic11C2312yes—
58C23×Dic11C2311yescharacteristic
59C23×Dic11C2311yescharacteristic
60C23×Dic11C2311yescharacteristic
61C22×C4×D11—24no—
62C22×C4×D11—24no—
63C22×C4×D11—24no—
64C22×C4×D11—24no—
65C22×C4×D11—24no—
66C22×C4×D11—24no—
67C22×C4×D11C2×C418yes—
68C22×C4×D11D418yes—
69C22×C4×D11Q818yes—
70C22×C4×D11C2314yes—
71C22×C4×D11C2314yes—
72C22×C4×D11C2314yes—
73C2×C11×C4⋊C4—24no—
74C2×C11×C4⋊C4—28no—
75C2×C11×C4⋊C4C2×C418yescomplemented
76C2×C11×C4⋊C4C2314yes—
77C2×C11×C4⋊C4C2318yes—
78C2×C11×C4⋊C4C2314yes—
79C2×C42×C11—24no—
80C2×C42×C11C2314yes—
81C2×(C2×D11)⋊C4—28no—
82C2×(C2×D11)⋊C4C2×C4116yes—
83C2×(C2×D11)⋊C4C2318yes—
84C2×(C2×D11)⋊C4C2318yes—
85C2×C4⋊Dic11—24no—
86C2×C4⋊Dic11—28no—
87C2×C4⋊Dic11C2×C418yescomplemented
88C2×C4⋊Dic11C2314yes—
89C2×C4⋊Dic11C2318yes—
90C2×C4⋊Dic11C2314yes—
91C2×Dic11⋊C4—28no—
92C2×Dic11⋊C4—28no—
93C2×Dic11⋊C4C2318yes—
94C2×Dic11⋊C4C2318yes—
95C2×C4×Dic11—24no—
96C2×C4×Dic11—24no—
97C2×C4×Dic11—24no—
98C2×C4×Dic11—28no—
99C2×C4×Dic11C2×C4116yescomplemented
100C2×C4×Dic11C2314yes—
101C2×C4×Dic11C2314yes—
102C2×C4×Dic11C2314yes—
103C2×C4×Dic11C2318yes—
104C2×C4×Dic11C2318yes—
105#66945—232no—
106#66945C2×C4164yescomplemented
107C42×D11—232no—
108C11×#95C2318yes—
109C11⋊#95C2318yes—
110C11⋊#95C2318yes—
111C11⋊#95C2318yes—
112C2×#2296—111nomaximal, Sylow
113C24×C11C2411yescharacteristic
114C23×D11—22no—
115C23×D11—22no—
116C23×D11—22no—
117C23×D11—22no—
118C23×D11C22×C414yes—
119C23×D11C2×D414yes—
120C23×D11C2×Q814yes—
121C23×D11C2412yes—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—24no—
125C22×C4×C11—24no—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11—24no—
129C22×C4×C11—24no—
130C22×C4×C11—24no—
131C22×C4×C11C22×C418yes—
132C22×C4×C11C22×C414yes—
133C22×C4×C11C2×D414yes—
134C22×C4×C11C2×Q814yes—
135C22×C4×C11#4114yes—
136C22×C4×C11#4114yes—
137C22×C4×C11C2414yes—
138C22×C4×C11C2414yes—
139C22×C4×C11C2412yes—
140C22×C4×C11C2412yes—
141C22×C4×C11C2412yes—
142C22×Dic11—22no—
143C22×Dic11—22no—
144C22×Dic11—24no—
145C22×Dic11—24no—
146C22×Dic11—24no—
147C22×Dic11—22no—
148C22×Dic11—22no—
149C22×Dic11—24no—
150C22×Dic11—24no—
151C22×Dic11C22×C418yes—
152C22×Dic11C22×C414yes—
153C22×Dic11C2×D414yes—
154C22×Dic11C2×Q814yes—
155C22×Dic11#4114yes—
156C22×Dic11#4114yes—
157C22×Dic11C2414yes—
158C22×Dic11C2414yes—
159C22×Dic11C2412yes—
160C22×Dic11C2412yes—
161C22×Dic11C2412yes—
162C2×C4×D11—232no—
163C2×C4×D11—232no—
164C2×C4×D11—28no—
165C2×C4×D11—28no—
166C2×C4×D11—28no—
167C2×C4×D11—28no—
168C2×C4×D11—28no—
169C2×C4×D11—28no—
170C2×C4×D11C4⋊C4164yescomplemented
171C2×C4×D11C22×C4116yes—
172C2×C4×D11C2×D4116yes—
173C2×C4×D11C2×Q8116yes—
174C11×C4⋊C4—28no—
175C11×C4⋊C4—216no—
176C11×C4⋊C4C22×C4116yescomplemented
177C42×C11—28no—
178(C2×D11)⋊C4—216no—
179(C2×D11)⋊C4C22×C4132yes—
180C4⋊Dic11—216no—
181C4⋊Dic11—28no—
182C4⋊Dic11C22×C4116yescomplemented
183Dic11⋊C4—216no—
184Dic11⋊C4—216no—
185C4×Dic11—28no—
186C4×Dic11—28no—
187C4×Dic11—216no—
188C4×Dic11—28no—
189C4×Dic11C22×C4132yescomplemented
190C22×#117—111no—
191C22×#117—111no—
192C23×C42—111no—
193#2296—1116no—
194C2×#389—111no—
195C2×#389—111no—
196C2×#389—111no—
197C2×#389D1111yescharacteristic, complemented
198C2×#385—112no—
199C2×#385—112no—
200C2×C4×C4⋊C4—112no—
201C2×C4×C4⋊C4—112no—
202C23×C11C23×C412yes—
203C23×C11C22×D412yes—
204C23×C11C22×Q812yes—
205C23×C11C2×#4112yes—
206C23×C11C2×#4112yes—
207C23×C11C2×#4112yes—
208C23×C11C2×#4112yes—
209C23×C11C2511yescharacteristic
210C22×D11—28no—
211C22×D11—28no—
212C22×D11—28no—
213C22×D11—28no—
214C22×D11—28no—
215C22×D11—28no—
216C22×D11—22no—
217C22×D11—22no—
218C22×D11—22no—
219C22×D11—22no—
220C22×D11C2×C4⋊C4116yes—
221C22×D11C23×C414yes—
222C22×D11C22×D414yes—
223C22×D11C22×Q814yes—
224C2×C4×C11—216no—
225C2×C4×C11—28no—
226C2×C4×C11—28no—
227C2×C4×C11—22no—
228C2×C4×C11—22no—
229C2×C4×C11—24no—
230C2×C4×C11—24no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—24no—
234C2×C4×C11—24no—
235C2×C4×C11—24no—
236C2×C4×C11—48no—
237C2×C4×C11C2×C4⋊C4116yes—
238C2×C4×C11C23×C418yes—
239C2×C4×C11C23×C414yes—
240C2×C4×C11C22×D414yes—
241C2×C4×C11C22×Q814yes—
242C2×C4×C11C2×#4114yes—
243C2×C4×C11C2×#4114yes—
244C2×Dic11—216no—
245C2×Dic11—28no—
246C2×Dic11—28no—
247C2×Dic11—22no—
248C2×Dic11—22no—
249C2×Dic11—24no—
250C2×Dic11—24no—
251C2×Dic11—22no—
252C2×Dic11—22no—
253C2×Dic11—24no—
254C2×Dic11—24no—
255C2×Dic11—24no—
256C2×Dic11—48no—
257C2×Dic11C2×C4⋊C4116yes—
258C2×Dic11C23×C418yes—
259C2×Dic11C23×C414yes—
260C2×Dic11C22×D414yes—
261C2×Dic11C22×Q814yes—
262C2×Dic11C2×#4114yes—
263C2×Dic11C2×#4114yes—
264C4×D11—232no—
265C4×D11—232no—
266C4×D11C2×C4⋊C4164yescomplemented
267C24×C4—111no—
268C24×C4—111no—
269C24×C4—111no—
270C2×#117—118no—
271C2×#117—118no—
272C2×#117—1116no—
273C2×#117—228no—
274C22×C4⋊C4—111no—
275C22×C4⋊C4—112no—
276C22×C4⋊C4—112no—
277C22×C4⋊C4—111no—
278C22×C4⋊C4—112no—
279C22×C4⋊C4C2×D1111yescharacteristic
280C22×C4⋊C4C2×D1112yes—
281C22×C4⋊C4C2×D1111yescharacteristic
282C22×C22⋊C4—112no—
283C22×C22⋊C4—112no—
284C22×C42—112no—
285C22×C42—111no—
286C22×C42—111no—
287C22×C42—111no—
288C22×C42—112no—
289C22×C42—118no—
290C22×C42—228no—
291C22×C42C2×D1111yescharacteristic
292#389—118no—
293#389—118no—
294#389—118no—
295#389C2×D1118yescomplemented
296#385—1116no—
297#385—1116no—
298C4×C4⋊C4—1116no—
299C4×C4⋊C4—1116no—
300C2×#95—112no—
301C2×#95—112no—
302C2×#95—112no—
303C2×#95C2×D1112yes—
304C22×C11C22×C4⋊C414yes—
305C22×C11C4×#4114yes—
306C22×C11C4×#4114yes—
307C22×C11#52514yes—
308C22×C11#52514yes—
309C22×C11#53314yes—
310C22×C11#53314yes—
311C22×C11C24×C411yescharacteristic
312C22×C11C23×D411yescharacteristic
313C22×C11C23×Q811yescharacteristic
314C22×C11C22×#4111yescharacteristic
315C22×C11C22×#4111yescharacteristic
316C22×C11C22×#4111yescharacteristic
317C22×C11C22×#4111yescharacteristic
318C2×D11—24no—
319C2×D11—24no—
320C2×D11—24no—
321C2×D11—24no—
322C2×D11—24no—
323C2×D11—24no—
324C2×D11—232no—
325C2×D11C22×C4⋊C418yes—
326C4×C11—28no—
327C4×C11—24no—
328C4×C11—24no—
329C4×C11—44no—
330C4×C11C22×C4⋊C418yes—
331Dic11—28no—
332Dic11—24no—
333Dic11—24no—
334Dic11—44no—
335Dic11C22×C4⋊C418yes—
336C25—111no—
337C23×C4—111no—
338C23×C4—118no—
339C23×C4—118no—
340C23×C4—118no—
341C23×C4—114no—
342C23×C4—112no—
343C23×C4—111no—
344C23×C4—111no—
345C23×C4—112no—
346C23×C4—114no—
347C23×C4—114no—
348C23×C4—224no—
349C23×C4—224no—
350C23×C4—224no—
351C23×C4—224no—
352C23×C4—224no—
353C23×C4—224no—
354C23×C4C22×D1112yes—
355C23×C4C22×D1112yes—
356C23×C4C22×D1111yescharacteristic
357C23×C4C22×D1111yescharacteristic
358C23×C4C22×D1111yescharacteristic
359#117—1164no—
360#117—2232no—
361C2×C4⋊C4—24no—
362C2×C4⋊C4—28no—
363C2×C4⋊C4—118no—
364C2×C4⋊C4—114no—
365C2×C4⋊C4—114no—
366C2×C4⋊C4—118no—
367C2×C4⋊C4—118no—
368C2×C4⋊C4—118no—
369C2×C4⋊C4—228no—
370C2×C4⋊C4—228no—
371C2×C4⋊C4—224no—
372C2×C4⋊C4—228no—
373C2×C4⋊C4C4×D1118yescomplemented
374C2×C4⋊C4C22×D1114yes—
375C2×C4⋊C4C22×D1118yes—
376C2×C4⋊C4C22×D1114yes—
377C2×C22⋊C4—1116no—
378C2×C22⋊C4—118no—
379C2×C22⋊C4—118no—
380C2×C22⋊C4—228no—
381C2×C42—24no—
382C2×C42—1116no—
383C2×C42—118no—
384C2×C42—118no—
385C2×C42—114no—
386C2×C42—114no—
387C2×C42—114no—
388C2×C42—2232no—
389C2×C42—228no—
390C2×C42—224no—
391C2×C42—224no—
392C2×C42—224no—
393C2×C42C22×D1114yes—
394#95—118no—
395#95—118no—
396#95—118no—
397#95C22×D1118yes—
398C2×C11#229618yescomplemented
399C2×C11C23×C4⋊C411yescharacteristic
400C2×C11C2×C4×#4111yescharacteristic
401C2×C11C2×C4×#4111yescharacteristic
402C2×C11C2×#52511yescharacteristic
403C2×C11C2×#52511yescharacteristic
404C2×C11C2×#53311yescharacteristic
405C2×C11C2×#53311yescharacteristic
406D11—28no—
407C24—114no—
408C24—114no—
409C24—114no—
410C24—112no—
411C24—222no—
412C24—222no—
413C24—222no—
414C24—222no—
415C24C23×D1111yescharacteristic
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—24no—
419C22×C4—24no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—24no—
423C22×C4—24no—
424C22×C4—24no—
425C22×C4—114no—
426C22×C4—114no—
427C22×C4—114no—
428C22×C4—112no—
429C22×C4—1164no—
430C22×C4—1116no—
431C22×C4—1116no—
432C22×C4—1116no—
433C22×C4—118no—
434C22×C4—114no—
435C22×C4—114no—
436C22×C4—112no—
437C22×C4—112no—
438C22×C4—114no—
439C22×C4—114no—
440C22×C4—228no—
441C22×C4—228no—
442C22×C4—228no—
443C22×C4—228no—
444C22×C4—2232no—
445C22×C4—2232no—
446C22×C4—222no—
447C22×C4—222no—
448C22×C4—222no—
449C22×C4—224no—
450C22×C4—222no—
451C22×C4—224no—
452C22×C4—228no—
453C22×C4—228no—
454C22×C4—224no—
455C22×C4—224no—
456C22×C4—224no—
457C22×C4C2×C4×D1118yes—
458C22×C4C2×C4×D1114yes—
459C22×C4D4×D1114yes—
460C22×C4#434114yes—
461C22×C4Q8×D1114yes—
462C22×C4#434314yes—
463C22×C4C23×D1114yes—
464C22×C4C23×D1114yes—
465C22×C4C23×D1112yes—
466C22×C4C23×D1112yes—
467C22×C4C23×D1112yes—
468C4⋊C4—28no—
469C4⋊C4—216no—
470C4⋊C4—1116no—
471C4⋊C4—2216no—
472C4⋊C4—2216no—
473C4⋊C4—228no—
474C4⋊C4—2216no—
475C4⋊C4C2×C4×D11116yescomplemented
476C22⋊C4—1132no—
477C22⋊C4—2216no—
478C42—28no—
479C42—1132no—
480C42—228no—
481C42—228no—
482C42—2216no—
483C42—228no—
484C11C2×#229611yescharacteristic, complemented, Sylow
485C23—1116no—
486C23—114no—
487C23—114no—
488C23—114no—
489C23—228no—
490C23—228no—
491C23—228no—
492C23—228no—
493C23—228no—
494C23—222no—
495C23—222no—
496C23—222no—
497C23—222no—
498C23—228no—
499C23C22×C4×D1112yes—
500C23C2×D4×D1112yes—
501C23C2×#434112yes—
502C23C2×Q8×D1112yes—
503C23C2×#434312yes—
504C23#41×D1112yes—
505C23#41×D1112yes—
506C23C24×D1111yescharacteristic
507C2×C4—216no—
508C2×C4—28no—
509C2×C4—28no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—24no—
513C2×C4—24no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—24no—
517C2×C4—24no—
518C2×C4—24no—
519C2×C4—48no—
520C2×C4—1116no—
521C2×C4—114no—
522C2×C4—114no—
523C2×C4—114no—
524C2×C4—1164no—
525C2×C4—118no—
526C2×C4—114no—
527C2×C4—114no—
528C2×C4—2232no—
529C2×C4—2232no—
530C2×C4—2216no—
531C2×C4—228no—
532C2×C4—228no—
533C2×C4—222no—
534C2×C4—222no—
535C2×C4—222no—
536C2×C4—224no—
537C2×C4—222no—
538C2×C4—224no—
539C2×C4—224no—
540C2×C4—224no—
541C2×C4—224no—
542C2×C4—448no—
543C2×C4C4⋊C4×D11116yes—
544C2×C4C22×C4×D1118yes—
545C2×C4C22×C4×D1114yes—
546C2×C4C2×D4×D1114yes—
547C2×C4C2×#434114yes—
548C2×C4C2×Q8×D1114yes—
549C2×C4C2×#434314yes—
550C22—118no—
551C22—224no—
552C22—224no—
553C22—224no—
554C22—224no—
555C22—224no—
556C22—224no—
557C22—2232no—
558C22C2×C4⋊C4×D1114yes—
559C22C4×#434114yes—
560C22C4×#434314yes—
561C22#1062313714yes—
562C22#1062315814yes—
563C22#1062321914yes—
564C22#1062325914yes—
565C22C23×C4×D1111yescharacteristic
566C22C22×D4×D1111yescharacteristic
567C22C22×#434111yescharacteristic
568C22C22×Q8×D1111yescharacteristic
569C22C22×#434311yescharacteristic
570C22C2×#41×D1111yescharacteristic
571C22C2×#41×D1111yescharacteristic
572C4—24no—
573C4—24no—
574C4—28no—
575C4—44no—
576C4—118no—
577C4—224no—
578C4—224no—
579C4—228no—
580C4—444no—
581C4C2×C4⋊C4×D1118yes—
582C2—228no—
583C2#1307109718yesdirect product factor
584C2C22×C4⋊C4×D1111yescharacteristic
585C2C2×C4×#434111yescharacteristic
586C2C2×C4×#434311yescharacteristic
587C2C2×#1062313711yescharacteristic
588C2C2×#1062315811yescharacteristic
589C2C2×#1062325911yescharacteristic
590C2C2×#1062321911yescharacteristic
subgroupG/H
centerC24C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC2×C11×#389C2
socleC24×C11C24
prime radicalC24×D11C23
cosocleC23×C11C25
hypercenterC2×#389D11
hypocenterC11C2×#2296
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
4. #13071097C2direct (N × H)
5. C2×#10622598C2semidirect
6. C2×#10622541C2semidirect
7. C2×#10622586C2semidirect
10. C2×C4⋊C4×Dic11C2semidirect
11. C2×#10622262C2semidirect
12. C2×C11×#389C2semidirect
33. C2×#66945C4semidirect
38. C11×#389C22semidirect
44. #10622598C22semidirect
45. C4⋊C4×Dic11C22semidirect
46. #10622586C22semidirect
47. #10622541C22semidirect
49. #10622262C22semidirect
75. C2×C11×C4⋊C4C2×C4semidirect
87. C2×C4⋊Dic11C2×C4semidirect
99. C2×C4×Dic11C2×C4semidirect
106. #66945C2×C4semidirect
170. C2×C4×D11C4⋊C4semidirect
176. C11×C4⋊C4C22×C4semidirect
182. C4⋊Dic11C22×C4semidirect
189. C4×Dic11C22×C4semidirect
197. C2×#389D11semidirect
266. C4×D11C2×C4⋊C4semidirect
295. #389C2×D11semidirect
373. C2×C4⋊C4C4×D11semidirect
398. C2×C11#2296semidirect
475. C4⋊C4C2×C4×D11semidirect
484. C11C2×#2296semidirect
583. C2#13071097direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669452
C22×C42×D112
#130710972
C2×#106225982
C2×#106225412
C2×#106225862
C2×#106222812
C2×#106226022
C2×C4⋊C4×Dic112
C2×#106222622
C2×C11×#3892
C2×#229611