Finite Group Databasebeta

← C2×#13078772 #15621905

Subgroups — C2×#13078772 #15621905

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×C4×#4339C211yesmaximal, characteristic
2#13078772C2116yesmaximal, direct product factor
3C2×#10622658C212yesmaximal, complemented
4C2×#10622704C211yesmaximal, characteristic, complemented
5C2×#10622697C211yesmaximal, characteristic, complemented
6C2×#10622703C211yesmaximal, characteristic, complemented
7C2×#10622696C211yesmaximal, characteristic, complemented
8C2×#10622660C212yesmaximal
9C2×#10622643C212yesmaximal, complemented
10C2×#10622639C212yesmaximal, complemented
11C2×#10622539C211yesmaximal, characteristic, complemented
12C2×C11×#533C211yesmaximal, characteristic, complemented
13C22×#4339C2211yescharacteristic
14C11×#533—24no—
15C11×#533C2218yescomplemented
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×C11×C4⋊Q8C2211yescharacteristic
18C2×C11×#125—21no—
19C2×C11×C22⋊Q8—21no—
20C2×C11×C22⋊Q8C2212yes—
21C2×C4×Q8×C11—21no—
22C2×C4×Q8×C11C2212yes—
23C2×C11×#117—21no—
24C22×C42×C11C2211yescharacteristic
25C22×#4326C2212yes—
26C22×#4325C2212yes—
27C2×C4×C22⋊D11—21no—
28C2×C4×C22⋊D11—21no—
29C2×#66979C2211yescharacteristic
30C4×#4339—24no—
31C4×#4339C2218yes—
32C2×C4×D44C2211yescharacteristic
33C2×C4×D44C2211yescharacteristic
34C2×#66925—21no—
35C2×C42×D11—21no—
36C2×C4×Dic22C2211yescharacteristic
37C2×C4×Dic22C2211yescharacteristic
38C2×#66899C2212yes—
39C2×#66899C2212yes—
40C2×C22⋊(C11⋊C8)C2212yes—
41#10622704C2218yescomplemented
42#10622703C2218yescomplemented
43#10622697C2218yescomplemented
44#10622696C2218yescomplemented
45#10622660C22116yes—
46#10622658C22116yescomplemented
47#10622643C22116yescomplemented
48#10622639C22116yescomplemented
49C2×#66874C2212yes—
50C2×#66873C2212yes—
51C2×#66872C2212yes—
52C2×#66871C2212yes—
53#10622539C2218yescomplemented
54C2×C4⋊(C11⋊C8)C2211yescharacteristic
55C2×C4⋊(C11⋊C8)C2211yescharacteristic
56C2×#66867C2212yes—
57C22×Q8×C11—21no—
58C22×Q8×C11C2312yes—
59C23×C4×C11D411yescharacteristic
60C23×C4×C11D411yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C22×C22⋊D11—21no—
63C2×#4339—22no—
64C2×#4339—24no—
65C2×#4339—24no—
66C2×#4339C2314yes—
67C22×D44C2311yescharacteristic
68C22×C4×D11—21no—
69C22×C4×D11—21no—
70C22×C4×D11—21no—
71C22×Dic22C2311yescharacteristic
72C11×C4⋊Q8—22no—
73C11×C4⋊Q8—22no—
74C11×C4⋊Q8C2314yes—
75C11×C4⋊Q8C2314yes—
76C11×#125—28no—
77C11×C22⋊Q8—28no—
78C11×C22⋊Q8—24no—
79C11×C22⋊Q8C2318yes—
80C4×Q8×C11—28no—
81C4×Q8×C11—24no—
82C4×Q8×C11C2318yes—
83C11×#117—28no—
84C2×C11×C4⋊C4—21no—
85C2×C11×C4⋊C4—21no—
86C2×C11×C4⋊C4—21no—
87C2×C11×C4⋊C4—22no—
88C2×C11×C4⋊C4—22no—
89C2×C11×C4⋊C4C2312yes—
90C2×C11×C22⋊C4—22no—
91C2×C42×C11—22no—
92C2×C42×C11D411yescharacteristic
93C2×C42×C11D411yescharacteristic
94C2×C42×C11D414yes—
95C2×C42×C11C2311yescharacteristic
96C2×C42×C11C2311yescharacteristic
97C2×C42×C11C2314yes—
98C2×C22⋊Dic11—21no—
99C2×#4326—28no—
100C2×#4326C2318yes—
101C2×#4325—28no—
102C2×#4325C2318yes—
103C4×C22⋊D11—28no—
104C4×C22⋊D11—28no—
105C2×(C2×D11)⋊C4—21no—
106C2×(C2×D11)⋊C4—21no—
107#66979—22no—
108#66979C2314yes—
109C2×C4⋊Dic11C2311yescharacteristic
110C2×C4⋊Dic11C2311yescharacteristic
111C2×Dic11⋊C4—21no—
112C2×Dic11⋊C4—21no—
113C2×C4×Dic11—21no—
114C2×C4×Dic11—21no—
115C2×C4×Dic11—21no—
116C22×C11⋊C8C2312yes—
117C22×C11⋊C8C2312yes—
118C4×D44—22no—
119C4×D44—22no—
120C4×D44C2314yes—
121C4×D44C2314yes—
122#66925—28no—
123C42×D11—28no—
124C4×Dic22—22no—
125C4×Dic22—22no—
126C4×Dic22C2314yes—
127C4×Dic22C2314yes—
128#66899C2318yes—
129#66899C2318yes—
130C22⋊(C11⋊C8)C2318yes—
131#66874C2318yes—
132#66873C2318yes—
133#66872C2318yes—
134#66871C2318yes—
135C4⋊(C11⋊C8)C2314yes—
136C4⋊(C11⋊C8)C2314yes—
137#66867C2318yes—
138C2×#3116—111nomaximal, Sylow
139C24×C11C2×D411yescharacteristic
140C23×D11—21no—
141C2×Q8×C11—22no—
142C2×Q8×C11—24no—
143C2×Q8×C11—24no—
144C2×Q8×C11—24no—
145C2×Q8×C11—44no—
146C2×Q8×C11C2414yes—
147C22×C4×C11—24no—
148C22×C4×C11—22no—
149C22×C4×C11—22no—
150C22×C4×C11—22no—
151C22×C4×C11—22no—
152C22×C4×C11—42no—
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×D412yes—
158C22×C4×C11C2×D414yes—
159C22×C4×C11C2×D414yes—
160C22×C4×C11C2×D411yescharacteristic
161C22×C4×C11C2412yes—
162C22×C4×C11C2411yescharacteristic
163C2×C22⋊D11—28no—
164C2×C22⋊D11—24no—
165C22×Dic11—21no—
166C22×Dic11—21no—
167C22×Dic11—21no—
168#4339—216no—
169#4339—28no—
170#4339—28no—
171C2×D44—21no—
172C2×D44—22no—
173C2×D44#4114yes—
174C2×D44C2412yes—
175C2×C4×D11—28no—
176C2×C4×D11—24no—
177C2×C4×D11—24no—
178C2×C4×D11—24no—
179C2×C4×D11—44no—
180C2×C4×D11—44no—
181C2×Dic22—21no—
182C2×Dic22—22no—
183C2×Dic22#4114yes—
184C2×Dic22C2412yes—
185C11×C4⋊C4—24no—
186C11×C4⋊C4—24no—
187C11×C4⋊C4—24no—
188C11×C4⋊C4—28no—
189C11×C4⋊C4—28no—
190C11×C4⋊C4—22no—
191C11×C4⋊C4C2414yes—
192C11×C22⋊C4—28no—
193C42×C11—28no—
194C42×C11C2×D412yes—
195C42×C11C2×D412yes—
196C42×C11C2×D414yes—
197C42×C11C2×D414yes—
198C42×C11C2412yes—
199C42×C11C2412yes—
200C22⋊Dic11—24no—
201#4326—216no—
202#4325—216no—
203(C2×D11)⋊C4—24no—
204(C2×D11)⋊C4—24no—
205C4⋊Dic11—21no—
206C4⋊Dic11—21no—
207C4⋊Dic11C2412yes—
208C4⋊Dic11C2412yes—
209Dic11⋊C4—24no—
210Dic11⋊C4—24no—
211C4×Dic11—24no—
212C4×Dic11—24no—
213C4×Dic11—24no—
214C2×C11⋊C8—24no—
215C2×C11⋊C8—24no—
216C2×C11⋊C8C2414yes—
217C2×C11⋊C8C2414yes—
218C2×#533D1111yescharacteristic, complemented
219C2×C4×#41—111no—
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—22no—
232C23×C11—22no—
233C23×C11C22×D412yes—
234C23×C11C22×D411yescharacteristic
235C22×D11—24no—
236C22×D11—22no—
237C22×D11—42no—
238C22×D11—42no—
239Q8×C11—24no—
240Q8×C11—24no—
241Q8×C11—48no—
242Q8×C11—44no—
243C2×C4×C11—22no—
244C2×C4×C11—22no—
245C2×C4×C11—22no—
246C2×C4×C11—22no—
247C2×C4×C11—24no—
248C2×C4×C11—28no—
249C2×C4×C11—22no—
250C2×C4×C11—22no—
251C2×C4×C11—24no—
252C2×C4×C11—24no—
253C2×C4×C11—44no—
254C2×C4×C11—44no—
255C2×C4×C11—44no—
256C2×C4×C11#13714yes—
257C2×C4×C11C22×D412yes—
258C2×C4×C11C22×D412yes—
259C2×C4×C11C22×D412yes—
260C2×C4×C11C22×D412yes—
261C2×C4×C11C22×D411yescharacteristic
262C2×C4×C11C22×D412yes—
263C2×C4×C11C2×#4112yes—
264C2×C4×C11C2×#4112yes—
265C2×C4×C11C2511yescharacteristic
266C22⋊D11—216no—
267C2×Dic11—24no—
268C2×Dic11—22no—
269C2×Dic11—22no—
270C2×Dic11—22no—
271C2×Dic11—42no—
272C2×Dic11—42no—
273D44—24no—
274D44—22no—
275D44C2×#4114yes—
276C4×D11—216no—
277C4×D11—48no—
278C4×D11—48no—
279Dic22—24no—
280Dic22—22no—
281Dic22C2×#4114yes—
282C11⋊C8—24no—
283C11⋊C8—24no—
284C22×#41—111no—
285C22×Q16—112no—
286C22×SD16—112no—
287#533—24no—
288#533C2×D1118yescomplemented
289C2×C4⋊Q8C2×D1111yescharacteristic
290C2×C4⋊Q8C2×D1111yescharacteristic
291C2×#125—21no—
292C2×C22⋊Q8—21no—
293C2×C22⋊Q8C2×D1112yes—
294C4×#41—118no—
295C4×#41—224no—
296C2×C4×Q8—21no—
297C2×C4×Q8—111no—
298C2×C4×Q8—111no—
299C2×C4×Q8C2×D1112yes—
300C2×C4×D4—111no—
301C2×C4×D4—111no—
302C2×C4×D4—221no—
303C2×C4×D4—221no—
304C2×#117—21no—
305C2×#117—111no—
306C2×#117—221no—
307C22×C42—221no—
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—22no—
330C22×C11—22no—
331C22×C11—44no—
332C22×C11#52512yes—
333C22×C11C2×#13712yes—
334C22×C11#57512yes—
335C22×C11C23×D411yescharacteristic
336C2×D11—24no—
337C2×D11—48no—
338C2×D11—42no—
339C2×D11—42no—
340C4×C11—22no—
341C4×C11—22no—
342C4×C11—22no—
343C4×C11—22no—
344C4×C11—44no—
345C4×C11—44no—
346C4×C11#52512yes—
347C4×C11C2×#13714yes—
348C4×C11C22×#4111yescharacteristic
349C4×C11C22×#4111yescharacteristic
350Dic11—24no—
351Dic11—42no—
352Dic11—42no—
353C2×#41—114no—
354C2×#41—224no—
355C2×#41—224no—
356C2×#41—222no—
357C22×Q8—21no—
358C22×Q8—111no—
359C22×Q8C22×D1112yes—
360C22×D4—111no—
361C22×D4—221no—
362C23×C4—221no—
363C23×C4—221no—
364C23×C4—221no—
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—22no—
375C4⋊Q8—22no—
376C4⋊Q8C22×D1114yes—
377C4⋊Q8C22×D1114yes—
378#125—28no—
379C22⋊Q8—28no—
380C22⋊Q8—24no—
381C22⋊Q8C22×D1118yes—
382C4×Q8—28no—
383C4×Q8—24no—
384C4×Q8—114no—
385C4×Q8—114no—
386C4×Q8—222no—
387C4×Q8—222no—
388C4×Q8C22×D1118yes—
389C4×D4—114no—
390C4×D4—114no—
391C4×D4—228no—
392C4×D4—228no—
393C4×D4—222no—
394C4×D4—222no—
395#117—28no—
396#117—114no—
397#117—222no—
398#117—228no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—111no—
405C2×C4⋊C4—111no—
406C2×C4⋊C4—221no—
407C2×C4⋊C4—221no—
408C2×C4⋊C4C22×D1112yes—
409C2×C22⋊C4—22no—
410C2×C22⋊C4—221no—
411C2×C22⋊C4—221no—
412C2×C22⋊C4—221no—
413C2×C42—22no—
414C2×C42—221no—
415C2×C42—221no—
416C2×C42—221no—
417C2×C42—228no—
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#311614yescomplemented
436C2×C11C2×#52511yescharacteristic
437C2×C11C22×#13711yescharacteristic
438C2×C11C2×#57511yescharacteristic
439D11—44no—
440C24—221no—
441C24C2×C22⋊D1111yescharacteristic
442#41—228no—
443#41—228no—
444#41—2216no—
445C2×Q8—22no—
446C2×Q8—24no—
447C2×Q8—24no—
448C2×Q8—24no—
449C2×Q8—44no—
450C2×Q8—114no—
451C2×Q8—112no—
452C2×Q8—222no—
453C2×Q8—221no—
454C2×Q8C23×D1114yes—
455C2×D4—114no—
456C2×D4—112no—
457C2×D4—228no—
458C2×D4—224no—
459C2×D4—222no—
460C2×D4—221no—
461C22×C4—24no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—42no—
467C22×C4—228no—
468C22×C4—221no—
469C22×C4—224no—
470C22×C4—221no—
471C22×C4—221no—
472C22×C4—224no—
473C22×C4—224no—
474C22×C4—444no—
475C22×C4—444no—
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—24no—
495C4⋊C4—28no—
496C4⋊C4—28no—
497C4⋊C4—22no—
498C4⋊C4—112no—
499C4⋊C4—112no—
500C4⋊C4—221no—
501C4⋊C4—221no—
502C4⋊C4—224no—
503C4⋊C4—224no—
504C4⋊C4C23×D1114yes—
505C22⋊C4—28no—
506C22⋊C4—224no—
507C22⋊C4—224no—
508C22⋊C4—224no—
509C42—28no—
510C42—224no—
511C42—224no—
512C42—224no—
513C42C2×C22⋊D1114yes—
514C42C2×C22⋊D1114yes—
515C42C2×C22⋊D1112yes—
516C42C2×C22⋊D1112yes—
517C42C23×D1112yes—
518C42C23×D1112yes—
519C11C2×#311611yescharacteristic, complemented, Sylow
520C23—22no—
521C23—22no—
522C23—22no—
523C23—224no—
524C23—222no—
525C23—442no—
526C23—442no—
527C23C22×C22⋊D1112yes—
528C23C22×C22⋊D1111yescharacteristic
529Q8—24no—
530Q8—24no—
531Q8—48no—
532Q8—44no—
533Q8—114no—
534Q8—224no—
535Q8—222no—
536D4—114no—
537D4—2216no—
538D4—224no—
539D4—222no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—28no—
545C2×C4—24no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—24no—
549C2×C4—24no—
550C2×C4—44no—
551C2×C4—44no—
552C2×C4—44no—
553C2×C4—2216no—
554C2×C4—224no—
555C2×C4—222no—
556C2×C4—222no—
557C2×C4—222no—
558C2×C4—448no—
559C2×C4—442no—
560C2×C4—442no—
561C2×C4—448no—
562C2×C4#6699514yes—
563C2×C4#41×D1112yes—
564C2×C4#41×D1112yes—
565C2×C4C22×C22⋊D1112yes—
566C2×C4C22×C22⋊D1112yes—
567C2×C4C22×C22⋊D1112yes—
568C2×C4C22×C22⋊D1112yes—
569C2×C4C22×C22⋊D1112yes—
570C2×C4C22×C22⋊D1111yescharacteristic
571C2×C4C24×D1111yescharacteristic
572C8—224no—
573C8—224no—
574C22—22no—
575C22—22no—
576C22—22no—
577C22—44no—
578C22—224no—
579C22—442no—
580C22—442no—
581C22—448no—
582C22C2×#6699512yes—
583C22#1062335312yes—
584C22#1062335912yes—
585C22C23×C22⋊D1111yescharacteristic
586C4—22no—
587C4—22no—
588C4—22no—
589C4—22no—
590C4—44no—
591C4—44no—
592C4—224no—
593C4—442no—
594C4—442no—
595C4C2×#6699514yes—
596C4#1062335912yes—
597C4C2×#41×D1111yescharacteristic
598C4C2×#41×D1111yescharacteristic
599C2—42no—
600C2—444no—
601C2#1307877214yesdirect product factor
602C2C2×#1062335911yescharacteristic
603C2C22×#6699511yescharacteristic
604C2C2×#1062335311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#533C2
socleC23×C11C22×D4
prime radicalC22×#4339C22
hypercenterC2×#533D11
hypocenterC11C2×#3116
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
2. #13078772C2direct (N × H)
3. C2×#10622658C2semidirect
4. C2×#10622704C2semidirect
5. C2×#10622697C2semidirect
6. C2×#10622703C2semidirect
7. C2×#10622696C2semidirect
9. C2×#10622643C2semidirect
10. C2×#10622639C2semidirect
11. C2×#10622539C2semidirect
12. C2×C11×#533C2semidirect
15. C11×#533C22semidirect
41. #10622704C22semidirect
42. #10622703C22semidirect
43. #10622697C22semidirect
44. #10622696C22semidirect
46. #10622658C22semidirect
47. #10622643C22semidirect
48. #10622639C22semidirect
53. #10622539C22semidirect
218. C2×#533D11semidirect
288. #533C2×D11semidirect
435. C2×C11#3116semidirect
519. C11C2×#3116semidirect
601. C2#13078772direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×#43392
#130787722
C2×#106226582
C2×#106227042
C2×#106226972
C2×#106227032
C2×#106226962
C2×#106226602
C2×#106226432
C2×#106226392
C2×#106225392
C2×C11×#5332
C2×#311611