Finite Group Databasebeta

← C2×#13078778 #15621911

Subgroups — C2×#13078778 #15621911

Order 2816.

2150 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623001C211yesmaximal, characteristic, complemented
2#13078778C2116yesmaximal, direct product factor
3C2×#10622609C212yesmaximal, complemented
4C2×#10622634C211yesmaximal, characteristic, complemented
5C2×#10622621C211yesmaximal, characteristic, complemented
6C2×#10622644C211yesmaximal, characteristic, complemented
7C2×#10622632C211yesmaximal, characteristic, complemented
8C2×#10622852C212yesmaximal
9C2×#10622643C212yesmaximal, complemented
10C2×#10622631C212yesmaximal, complemented
11C2×#10622539C211yesmaximal, characteristic, complemented
12C2×C4×C11×#41C211yesmaximal, characteristic
13C22×C11×#41C2211yescharacteristic
14C4×C11×#41—24no—
15C4×C11×#41C2218yes—
16C2×C4×Q8×C11C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×C4×D4×C11—21no—
19C2×C4×D4×C11—21no—
20C2×C4×D4×C11C2211yescharacteristic
21C2×C4×D4×C11C2211yescharacteristic
22C2×C11×#117—21no—
23C2×C11×#117C2211yescharacteristic
24C22×C42×C11—21no—
25C22×C42×C11C2211yescharacteristic
26C22×#4326C2212yes—
27C22×#4324C2212yes—
28C2×#66979—21no—
29C2×#66977—21no—
30C2×#66977C2212yes—
31#10623001—24no—
32#10623001C2218yescomplemented
33C2×#66923—21no—
34C2×#66922C2211yescharacteristic
35C2×#66922C2211yescharacteristic
36C2×C4×Dic22—21no—
37C2×C4×Dic22C2212yes—
38#10622852C22116yes—
39C2×#66899C2212yes—
40C2×#66896C2212yes—
41C2×C22⋊(C11⋊C8)C2212yes—
42#10622644C2218yescomplemented
43#10622643C22116yescomplemented
44#10622634C2218yescomplemented
45#10622632C2218yescomplemented
46#10622631C22116yescomplemented
47#10622621C2218yescomplemented
48#10622609C22116yescomplemented
49C2×#66874C2212yes—
50C2×#66874C2212yes—
51C2×#66872C2212yes—
52C2×#66871C2212yes—
53#10622539C2218yescomplemented
54C2×C4⋊(C11⋊C8)C2211yescharacteristic
55C2×C4⋊(C11⋊C8)C2211yescharacteristic
56C2×#66867C2212yes—
57C2×C11×#41—24no—
58C2×C11×#41—24no—
59C2×C11×#41—22no—
60C2×C11×#41C2314yes—
61C22×Q8×C11C2311yescharacteristic
62C22×D4×C11—21no—
63C22×D4×C11C2311yescharacteristic
64C23×C4×C11—21no—
65C23×C4×C11—21no—
66C23×C4×C11—21no—
67C23×C4×C11D411yescharacteristic
68C23×C4×C11D411yescharacteristic
69C23×C4×C11C2311yescharacteristic
70C22×Dic22—21no—
71C22×Dic22C2312yes—
72C4×Q8×C11—22no—
73C4×Q8×C11—22no—
74C4×Q8×C11C2314yes—
75C4×Q8×C11C2314yes—
76C4×D4×C11—28no—
77C4×D4×C11—28no—
78C4×D4×C11—22no—
79C4×D4×C11—22no—
80C4×D4×C11C2314yes—
81C4×D4×C11C2314yes—
82C11×#117—22no—
83C11×#117—28no—
84C11×#117C2314yes—
85C2×C11×C4⋊C4—21no—
86C2×C11×C4⋊C4—21no—
87C2×C11×C4⋊C4C2311yescharacteristic
88C2×C11×C4⋊C4C2311yescharacteristic
89C2×C11×C22⋊C4—21no—
90C2×C11×C22⋊C4—21no—
91C2×C11×C22⋊C4—21no—
92C2×C42×C11—21no—
93C2×C42×C11—21no—
94C2×C42×C11—21no—
95C2×C42×C11—28no—
96C2×C42×C11D411yescharacteristic
97C2×C42×C11D411yescharacteristic
98C2×C42×C11D414yes—
99C2×C42×C11C2311yescharacteristic
100C2×C42×C11C2311yescharacteristic
101C2×C42×C11C2314yes—
102C2×C22⋊Dic11—22no—
103C2×#4326—28no—
104C2×#4326C2318yes—
105C2×#4324—28no—
106C2×#4324C2318yes—
107#66979—28no—
108C2×C4⋊Dic11—21no—
109C2×C4⋊Dic11—21no—
110C2×C4⋊Dic11—21no—
111C2×C4⋊Dic11C2312yes—
112#66977—24no—
113#66977—28no—
114#66977C2318yes—
115C2×Dic11⋊C4—22no—
116C2×Dic11⋊C4—22no—
117C2×C4×Dic11—22no—
118C22×C11⋊C8C2312yes—
119C22×C11⋊C8C2312yes—
120#66923—28no—
121#66922—22no—
122#66922—22no—
123#66922C2314yes—
124#66922C2314yes—
125C4×Dic22—28no—
126C4×Dic22—24no—
127C4×Dic22C2318yes—
128#66899C2318yes—
129#66896C2318yes—
130C22⋊(C11⋊C8)C2318yes—
131#66874C2318yes—
132#66874C2318yes—
133#66872C2318yes—
134#66871C2318yes—
135C4⋊(C11⋊C8)C2314yes—
136C4⋊(C11⋊C8)C2314yes—
137#66867C2318yes—
138C2×#3116—111nomaximal, Sylow
139C24×C11—21no—
140C24×C11C2×D411yescharacteristic
141C11×#41—216no—
142C11×#41—28no—
143C11×#41—28no—
144C2×Q8×C11—21no—
145C2×Q8×C11—22no—
146C2×Q8×C11#4114yes—
147C2×Q8×C11C2412yes—
148C2×D4×C11—28no—
149C2×D4×C11—24no—
150C2×D4×C11—21no—
151C2×D4×C11—22no—
152C2×D4×C11#4114yes—
153C2×D4×C11C2412yes—
154C22×C4×C11—28no—
155C22×C4×C11—21no—
156C22×C4×C11—24no—
157C22×C4×C11—24no—
158C22×C4×C11—22no—
159C22×C4×C11—22no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—24no—
163C22×C4×C11—24no—
164C22×C4×C11—42no—
165C22×C4×C11—44no—
166C22×C4×C11—44no—
167C22×C4×C11C2×D411yescharacteristic
168C22×C4×C11C2×D411yescharacteristic
169C22×C4×C11C2×D411yescharacteristic
170C22×C4×C11C2×D412yes—
171C22×C4×C11C2×D411yescharacteristic
172C22×C4×C11C2×D414yes—
173C22×C4×C11C2×D414yes—
174C22×C4×C11C2×D411yescharacteristic
175C22×C4×C11C2412yes—
176C22×C4×C11C2411yescharacteristic
177C22×Dic11—22no—
178C22×Dic11—22no—
179C2×Dic22—22no—
180C2×Dic22—24no—
181C2×Dic22—24no—
182C2×Dic22—24no—
183C2×Dic22—44no—
184C2×Dic22C2414yes—
185C11×C4⋊C4—24no—
186C11×C4⋊C4—24no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—21no—
189C11×C4⋊C4C2412yes—
190C11×C4⋊C4C2412yes—
191C11×C22⋊C4—24no—
192C11×C22⋊C4—24no—
193C11×C22⋊C4—24no—
194C42×C11—24no—
195C42×C11—24no—
196C42×C11—24no—
197C42×C11C2×D414yes—
198C42×C11C2×D412yes—
199C42×C11C2×D412yes—
200C42×C11C2×D414yes—
201C42×C11C2412yes—
202C42×C11C2412yes—
203C22⋊Dic11—28no—
204#4326—216no—
205#4324—216no—
206C4⋊Dic11—22no—
207C4⋊Dic11—24no—
208C4⋊Dic11—24no—
209C4⋊Dic11—24no—
210C4⋊Dic11C2414yes—
211Dic11⋊C4—28no—
212Dic11⋊C4—28no—
213C4×Dic11—28no—
214C2×C11⋊C8—24no—
215C2×C11⋊C8—24no—
216C2×C11⋊C8C2414yes—
217C2×C11⋊C8C2414yes—
218C2×#533—111no—
219C2×C4×#41D1111yescharacteristic
220#3116—1116no—
221C2×#485—112no—
222C2×#477—111no—
223C2×#476—111no—
224C2×#462—111no—
225C2×#461—111no—
226C2×#452—112no—
227C2×#441—112no—
228C2×#440—112no—
229C2×#432—111no—
230C23×C11—22no—
231C23×C11—24no—
232C23×C11—22no—
233C23×C11—22no—
234C23×C11—22no—
235C23×C11—42no—
236C23×C11—42no—
237C23×C11C22×D412yes—
238C23×C11C22×D411yescharacteristic
239Q8×C11—24no—
240Q8×C11—22no—
241Q8×C11C2×#4114yes—
242D4×C11—216no—
243D4×C11—24no—
244D4×C11—22no—
245D4×C11C2×#4114yes—
246C2×C4×C11—216no—
247C2×C4×C11—22no—
248C2×C4×C11—24no—
249C2×C4×C11—22no—
250C2×C4×C11—22no—
251C2×C4×C11—22no—
252C2×C4×C11—22no—
253C2×C4×C11—24no—
254C2×C4×C11—28no—
255C2×C4×C11—22no—
256C2×C4×C11—22no—
257C2×C4×C11—22no—
258C2×C4×C11—22no—
259C2×C4×C11—44no—
260C2×C4×C11—48no—
261C2×C4×C11—42no—
262C2×C4×C11—42no—
263C2×C4×C11—48no—
264C2×C4×C11#13714yes—
265C2×C4×C11C22×D412yes—
266C2×C4×C11C22×D412yes—
267C2×C4×C11C22×D412yes—
268C2×C4×C11C22×D412yes—
269C2×C4×C11C22×D411yescharacteristic
270C2×C4×C11C22×D412yes—
271C2×C4×C11C2×#4112yes—
272C2×C4×C11C2×#4112yes—
273C2×C4×C11C2511yescharacteristic
274C2×Dic11—24no—
275C2×Dic11—24no—
276C2×Dic11—44no—
277C2×Dic11—44no—
278Dic22—24no—
279Dic22—24no—
280Dic22—48no—
281Dic22—44no—
282C11⋊C8—24no—
283C11⋊C8—24no—
284C22×#41C2×D1111yescharacteristic
285C22×Q16—112no—
286C22×SD16—112no—
287#533—118no—
288#533—224no—
289C2×C4⋊Q8—111no—
290C2×C4⋊Q8—111no—
291C2×#125—221no—
292C2×C22⋊Q8—112no—
293C2×C22⋊Q8—221no—
294C4×#41—24no—
295C4×#41C2×D1118yes—
296C2×C4×Q8—112no—
297C2×C4×Q8—221no—
298C2×C4×Q8C2×D1111yescharacteristic
299C2×C4×Q8C2×D1111yescharacteristic
300C2×C4×D4—21no—
301C2×C4×D4—21no—
302C2×C4×D4C2×D1111yescharacteristic
303C2×C4×D4C2×D1111yescharacteristic
304C2×#117—21no—
305C2×#117—221no—
306C2×#117C2×D1111yescharacteristic
307C22×C42—21no—
308C22×C42C2×D1111yescharacteristic
309#485—1116no—
310#477—118no—
311#476—118no—
312#462—118no—
313#461—118no—
314#452—1116no—
315#441—1116no—
316#440—1116no—
317#432—118no—
318C2×#107—112no—
319C2×#106—112no—
320C2×C4⋊C8—111no—
321C2×C4⋊C8—111no—
322C2×#103—112no—
323C2×#103—112no—
324C2×#103—112no—
325C2×#102—112no—
326C2×C22⋊C8—112no—
327C2×#97—112no—
328C22×C11—22no—
329C22×C11—24no—
330C22×C11—22no—
331C22×C11—22no—
332C22×C11—44no—
333C22×C11—48no—
334C22×C11—42no—
335C22×C11—42no—
336C22×C11#52512yes—
337C22×C11C2×#13712yes—
338C22×C11#57512yes—
339C22×C11C23×D411yescharacteristic
340C4×C11—22no—
341C4×C11—24no—
342C4×C11—22no—
343C4×C11—22no—
344C4×C11—22no—
345C4×C11—42no—
346C4×C11—42no—
347C4×C11#52512yes—
348C4×C11C2×#13714yes—
349C4×C11C22×#4111yescharacteristic
350C4×C11C22×#4111yescharacteristic
351Dic11—44no—
352Dic11—44no—
353C2×#41—24no—
354C2×#41—24no—
355C2×#41—22no—
356C2×#41C22×D1114yes—
357C22×Q8—112no—
358C22×Q8—221no—
359C22×Q8C22×D1111yescharacteristic
360C22×D4—21no—
361C22×D4C22×D1111yescharacteristic
362C23×C4—21no—
363C23×C4—21no—
364C23×C4—21no—
365C23×C4C22⋊D1111yescharacteristic
366C23×C4C22⋊D1111yescharacteristic
367C23×C4C22×D1111yescharacteristic
368C2×Q16—118no—
369C2×Q16—228no—
370C2×SD16—118no—
371C2×SD16—228no—
372C22×C8—112no—
373C22×C8—112no—
374C4⋊Q8—114no—
375C4⋊Q8—114no—
376C4⋊Q8—222no—
377C4⋊Q8—222no—
378#125—228no—
379C22⋊Q8—118no—
380C22⋊Q8—224no—
381C22⋊Q8—228no—
382C4×Q8—22no—
383C4×Q8—22no—
384C4×Q8—118no—
385C4×Q8—224no—
386C4×Q8—228no—
387C4×Q8C22×D1114yes—
388C4×Q8C22×D1114yes—
389C4×D4—28no—
390C4×D4—28no—
391C4×D4—22no—
392C4×D4—22no—
393C4×D4C22×D1114yes—
394C4×D4C22×D1114yes—
395#117—22no—
396#117—28no—
397#117—228no—
398#117C22×D1114yes—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—112no—
402C2×C4⋊C4—221no—
403C2×C4⋊C4—221no—
404C2×C4⋊C4—222no—
405C2×C4⋊C4—222no—
406C2×C4⋊C4—221no—
407C2×C4⋊C4C22×D1111yescharacteristic
408C2×C4⋊C4C22×D1111yescharacteristic
409C2×C22⋊C4—21no—
410C2×C22⋊C4—21no—
411C2×C22⋊C4—21no—
412C2×C22⋊C4—222no—
413C2×C42—21no—
414C2×C42—21no—
415C2×C42—21no—
416C2×C42—28no—
417C2×C42—222no—
418C2×C42C22⋊D1111yescharacteristic
419C2×C42C22⋊D1114yes—
420C2×C42C22⋊D1111yescharacteristic
421C2×C42C22×D1111yescharacteristic
422C2×C42C22×D1111yescharacteristic
423C2×C42C22×D1114yes—
424#107—118no—
425#106—118no—
426C4⋊C8—114no—
427C4⋊C8—114no—
428#103—118no—
429#103—118no—
430#103—118no—
431#102—118no—
432C22⋊C8—118no—
433#97—118no—
434C2×C11—42no—
435C2×C11—44no—
436C2×C11#311614yescomplemented
437C2×C11C2×#52511yescharacteristic
438C2×C11C22×#13711yescharacteristic
439C2×C11C2×#57511yescharacteristic
440C24—21no—
441C24C2×C22⋊D1111yescharacteristic
442#41—216no—
443#41—28no—
444#41—28no—
445C2×Q8—22no—
446C2×Q8—21no—
447C2×Q8—114no—
448C2×Q8—224no—
449C2×Q8—222no—
450C2×Q8—224no—
451C2×Q8—224no—
452C2×Q8—444no—
453C2×Q8#433914yes—
454C2×Q8C23×D1112yes—
455C2×D4—28no—
456C2×D4—24no—
457C2×D4—22no—
458C2×D4—21no—
459C2×D4#433914yes—
460C2×D4C23×D1112yes—
461C22×C4—28no—
462C22×C4—21no—
463C22×C4—24no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—24no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—24no—
470C22×C4—24no—
471C22×C4—42no—
472C22×C4—44no—
473C22×C4—44no—
474C22×C4—222no—
475C22×C4—222no—
476C22×C4C2×C22⋊D1114yes—
477C22×C4C2×C22⋊D1112yes—
478C22×C4C2×C22⋊D1111yescharacteristic
479C22×C4C2×C22⋊D1111yescharacteristic
480C22×C4C2×C22⋊D1111yescharacteristic
481C22×C4C2×C22⋊D1111yescharacteristic
482C22×C4C2×C22⋊D1114yes—
483C22×C4C2×C22⋊D1111yescharacteristic
484C22×C4C23×D1112yes—
485C22×C4C23×D1111yescharacteristic
486Q16—2216no—
487SD16—2216no—
488C2×C8—114no—
489C2×C8—114no—
490C2×C8—224no—
491C2×C8—224no—
492C4⋊C4—24no—
493C4⋊C4—24no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—114no—
497C4⋊C4—222no—
498C4⋊C4—224no—
499C4⋊C4—224no—
500C4⋊C4—228no—
501C4⋊C4—228no—
502C4⋊C4—224no—
503C4⋊C4C23×D1112yes—
504C4⋊C4C23×D1112yes—
505C22⋊C4—24no—
506C22⋊C4—24no—
507C22⋊C4—24no—
508C22⋊C4—228no—
509C42—24no—
510C42—24no—
511C42—24no—
512C42—228no—
513C42C2×C22⋊D1114yes—
514C42C2×C22⋊D1114yes—
515C42C2×C22⋊D1112yes—
516C42C2×C22⋊D1112yes—
517C42C23×D1112yes—
518C42C23×D1112yes—
519C11C2×#311611yescharacteristic, complemented, Sylow
520C23—22no—
521C23—24no—
522C23—22no—
523C23—22no—
524C23—22no—
525C23—42no—
526C23—42no—
527C23C22×C22⋊D1112yes—
528C23C22×C22⋊D1111yescharacteristic
529Q8—24no—
530Q8—22no—
531Q8—224no—
532Q8—224no—
533Q8—448no—
534Q8—444no—
535Q8C2×#433914yes—
536D4—216no—
537D4—24no—
538D4—22no—
539D4C2×#433914yes—
540C2×C4—216no—
541C2×C4—22no—
542C2×C4—24no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—24no—
548C2×C4—28no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—44no—
554C2×C4—48no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—48no—
558C2×C4—224no—
559C2×C4—224no—
560C2×C4—444no—
561C2×C4—444no—
562C2×C4#6700414yes—
563C2×C4C2×#433912yes—
564C2×C4C2×#433912yes—
565C2×C4C22×C22⋊D1112yes—
566C2×C4C22×C22⋊D1112yes—
567C2×C4C22×C22⋊D1112yes—
568C2×C4C22×C22⋊D1112yes—
569C2×C4C22×C22⋊D1111yescharacteristic
570C2×C4C22×C22⋊D1112yes—
571C2×C4C24×D1111yescharacteristic
572C8—224no—
573C8—224no—
574C22—22no—
575C22—24no—
576C22—22no—
577C22—22no—
578C22—42no—
579C22—42no—
580C22—44no—
581C22—48no—
582C22#1062332212yes—
583C22#1062335312yes—
584C22C2×#6700412yes—
585C22C23×C22⋊D1111yescharacteristic
586C4—22no—
587C4—24no—
588C4—22no—
589C4—22no—
590C4—22no—
591C4—42no—
592C4—42no—
593C4—444no—
594C4—444no—
595C4#1062332212yes—
596C4C2×#6700414yes—
597C4C22×#433911yescharacteristic
598C4C22×#433911yescharacteristic
599C2—42no—
600C2—44no—
601C2#1307877814yesdirect product factor
602C2C2×#1062332211yescharacteristic
603C2C22×#6700411yescharacteristic
604C2C2×#1062335311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C4×C11×#41C2
socleC23×C11C22×D4
prime radicalC22×C11×#41C22
hypercenterC2×C4×#41D11
hypocenterC11C2×#3116
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×C4×#41

Complements

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

NH ≅ G/Ntype
1. C2×#10623001C2semidirect
2. #13078778C2direct (N × H)
3. C2×#10622609C2semidirect
4. C2×#10622634C2semidirect
5. C2×#10622621C2semidirect
6. C2×#10622644C2semidirect
7. C2×#10622632C2semidirect
9. C2×#10622643C2semidirect
10. C2×#10622631C2semidirect
11. C2×#10622539C2semidirect
32. #10623001C22semidirect
42. #10622644C22semidirect
43. #10622643C22semidirect
44. #10622634C22semidirect
45. #10622632C22semidirect
46. #10622631C22semidirect
47. #10622621C22semidirect
48. #10622609C22semidirect
53. #10622539C22semidirect
436. C2×C11#3116semidirect
519. C11C2×#3116semidirect
601. C2#13078778direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230012
#130787782
C2×#106226092
C2×#106226342
C2×#106226212
C2×#106226442
C2×#106226322
C2×#106228522
C2×#106226432
C2×#106226312
C2×#106225392
C2×C4×C11×#412
C2×#311611