Finite Group Databasebeta

← C2×#13077434 #15617846

Subgroups — C2×#13077434 #15617846

Order 2816.

2810 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66962C211yesmaximal, characteristic
2C2×#10623053C211yesmaximal, characteristic
3C22×#66940C211yesmaximal, characteristic, complemented
4#13077434C2116yesmaximal, direct product factor
5C2×#10622466C212yesmaximal, complemented
6C2×#10622502C212yesmaximal, complemented
7C2×#10622486C212yesmaximal, complemented
8C2×#10622465C212yesmaximal, complemented
9C2×#10622579C211yesmaximal, characteristic
10C2×#10622617C211yesmaximal, characteristic, complemented
11C2×M16×Dic11C211yesmaximal, characteristic, complemented
12C2×C11×#428C211yesmaximal, characteristic, complemented
13C22×#4339C2211yescharacteristic
14C23×Dic22C2211yescharacteristic
15C22×C11×M16C2211yescharacteristic
16C2×C11×#117C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×Dic11⋊C4—21no—
19C22×C4×Dic11—21no—
20C22×C4×Dic11C2211yescharacteristic
21C22×#4318C2211yescharacteristic
22C2×#66962C4116yescomplemented
23C2×#66962C2218yes—
24C22×Dic44C2212yes—
25C22×#4314C2212yes—
26#10623053—24no—
27#10623053C2218yes—
28C2×#66946C2211yescharacteristic
29C2×#66946C2211yescharacteristic
30C2×#66940—24no—
31C2×#66940—21no—
32C2×#66940—21no—
33C2×#66940C2212yes—
34C2×#66940C2211yescharacteristic
35C2×#66940C2212yes—
36C2×#66940C2211yescharacteristic
37C2×#66940C2218yescomplemented
38C2×(C22⋊D11)⋊C4—21no—
39C2×(C22⋊D11)⋊C4—21no—
40C2×#66925—21no—
41C2×C42×D11—21no—
42C11×#428C2218yescomplemented
43C2×C11×#107C2212yes—
44C2×C11×#106C2212yes—
45M16×Dic11C2218yescomplemented
46C2×#66879C2212yes—
47C2×C8×Dic11C2212yes—
48#10622617C2218yescomplemented
49C2×#66874C2212yes—
50C2×#66874C2212yes—
51C2×#66874C2212yes—
52#10622579C2218yes—
53C2×#66873C2212yes—
54#10622502C22116yescomplemented
55#10622486C22116yescomplemented
56#10622466C22116yescomplemented
57#10622465C22116yescomplemented
58C23×C4×C11—21no—
59C23×C4×C11C2311yescharacteristic
60C22×C22⋊D11—21no—
61C23×Dic11—21no—
62C23×Dic11D411yescharacteristic
63C23×Dic11D411yescharacteristic
64C2×#4339—22no—
65C2×#4339—24no—
66C2×#4339C2×C418yes—
67C2×#4339C2314yes—
68C22×D44C2311yescharacteristic
69C22×C4×D11—21no—
70C22×C4×D11—21no—
71C22×C4×D11—21no—
72C22×Dic22—21no—
73C22×Dic22—22no—
74C22×Dic22—24no—
75C22×Dic22C2×C418yescomplemented
76C22×Dic22C2312yes—
77C22×Dic22C2311yescharacteristic
78C22×Dic22C2314yes—
79C2×C11×M16C2×C418yescomplemented
80C2×C11×M16C2314yes—
81C22×C8×C11C2312yes—
82C11×#117—22no—
83C11×#117C2314yes—
84C2×C11×C4⋊C4—21no—
85C2×C11×C4⋊C4—22no—
86C2×C11×C4⋊C4C2312yes—
87C2×C11×C4⋊C4C2311yescharacteristic
88C2×C11×C4⋊C4C2311yescharacteristic
89C2×C11×C4⋊C4C2314yes—
90C2×C11×C22⋊C4—21no—
91C2×C42×C11—21no—
92C2×(C2×D11)⋊C4—21no—
93C2×(C2×D11)⋊C4—21no—
94C2×Dic11⋊C4—21no—
95C2×Dic11⋊C4—21no—
96C2×Dic11⋊C4—22no—
97C2×Dic11⋊C4—22no—
98C2×Dic11⋊C4—28no—
99C2×C4×Dic11—21no—
100C2×C4×Dic11—21no—
101C2×C4×Dic11—22no—
102C2×C4×Dic11—22no—
103C2×C4×Dic11—28no—
104C2×C4×Dic11D411yescharacteristic
105C2×C4×Dic11D411yescharacteristic
106C2×C4×Dic11D414yes—
107C2×C4×Dic11C2314yes—
108C2×C4×Dic11C2311yescharacteristic
109C2×C4×Dic11C2311yescharacteristic
110C2×#4318—24no—
111C2×#4318C2314yes—
112C22×C11⋊C8C2312yes—
113#66962C2×C4164yescomplemented
114C2×Dic44C2×C4116yescomplemented
115C2×Dic44C2318yes—
116C2×#4314C2×C4116yescomplemented
117C2×#4314C2318yes—
118#66946—22no—
119#66946—22no—
120#66946C2314yes—
121#66946C2314yes—
122#66940—24no—
123#66940—24no—
124#66940—28no—
125#66940—28no—
126#66940—22no—
127#66940—22no—
128#66940C2318yes—
129#66940C2314yes—
130#66940C2318yes—
131#66940C2314yes—
132(C22⋊D11)⋊C4—28no—
133(C22⋊D11)⋊C4—28no—
134#66925—28no—
135C42×D11—28no—
136C11×#107C2318yes—
137C11×#106C2318yes—
138#66879C2318yes—
139C8×Dic11C2318yes—
140#66874C2318yes—
141#66874C2318yes—
142#66874C2318yes—
143#66873C2318yes—
144C2×C4×#137—111nomaximal, Sylow
145C24×C11C2×D411yescharacteristic
146C23×D11—21no—
147C22×C4×C11—24no—
148C22×C4×C11—22no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—44no—
152C22×C4×C11C22×C414yes—
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D412yes—
155C22×C4×C11#4114yes—
156C22×C4×C11C2411yescharacteristic
157C22×C4×C11C2412yes—
158C2×C22⋊D11—28no—
159C2×C22⋊D11—24no—
160C22×Dic11—24no—
161C22×Dic11—28no—
162C22×Dic11—24no—
163C22×Dic11—22no—
164C22×Dic11—21no—
165C22×Dic11—42no—
166C22×Dic11C2×D414yes—
167C22×Dic11C2×D411yescharacteristic
168C22×Dic11C2×D411yescharacteristic
169C22×Dic11C2×D411yescharacteristic
170C22×Dic11C2×D414yes—
171C22×Dic11C2×D411yescharacteristic
172#4339—216no—
173#4339—28no—
174#4339C22×C4116yes—
175C2×D44—21no—
176C2×D44—22no—
177C2×D44C22×C414yes—
178C2×D44C2412yes—
179C2×C4×D11—24no—
180C2×C4×D11—24no—
181C2×C4×D11—28no—
182C2×C4×D11—24no—
183C2×C4×D11—44no—
184C2×C4×D11—44no—
185C2×Dic22—28no—
186C2×Dic22—216no—
187C2×Dic22—24no—
188C2×Dic22—22no—
189C2×Dic22—21no—
190C2×Dic22—24no—
191C2×Dic22—28no—
192C2×Dic22—22no—
193C2×Dic22C22×C418yes—
194C2×Dic22C22×C414yes—
195C2×Dic22C22×C4116yescomplemented
196C2×Dic22C2414yes—
197C2×Dic22C2412yes—
198C11×M16C22×C4116yescomplemented
199C2×C8×C11C22×C418yes—
200C2×C8×C11C2414yes—
201C11×C4⋊C4—24no—
202C11×C4⋊C4—22no—
203C11×C4⋊C4—21no—
204C11×C4⋊C4—21no—
205C11×C4⋊C4C2414yes—
206C11×C4⋊C4C2412yes—
207C11×C4⋊C4C2412yes—
208C11×C22⋊C4—24no—
209C42×C11—24no—
210(C2×D11)⋊C4—24no—
211(C2×D11)⋊C4—24no—
212Dic11⋊C4—24no—
213Dic11⋊C4—24no—
214Dic11⋊C4—28no—
215Dic11⋊C4—28no—
216C4×Dic11—24no—
217C4×Dic11—24no—
218C4×Dic11—28no—
219C4×Dic11—28no—
220C4×Dic11C2×D414yes—
221C4×Dic11C2×D414yes—
222C4×Dic11C2×D412yes—
223C4×Dic11C2×D412yes—
224C4×Dic11C2412yes—
225C4×Dic11C2412yes—
226#4318—28no—
227C2×C11⋊C8—24no—
228C2×C11⋊C8C2414yes—
229Dic44C22×C4132yescomplemented
230#4314C22×C4132yescomplemented
231C22×#137—111no—
232C2×C4×#41—111no—
233C22×C4×Q8—111no—
234C4×#137—1116no—
235C2×#441—112no—
236C2×#440—112no—
237C2×C4×Q16—112no—
238C2×C4×SD16—112no—
239C2×#428D1111yescharacteristic, complemented
240C2×#417—111no—
241C2×#419—111no—
242C2×C4×M16—111no—
243C23×C11—22no—
244C23×C11—22no—
245C23×C11C4×D414yes—
246C23×C11C22×D412yes—
247C23×C11C22×D411yescharacteristic
248C22×D11—24no—
249C22×D11—22no—
250C22×D11—42no—
251C22×D11—42no—
252C2×C4×C11—24no—
253C2×C4×C11—22no—
254C2×C4×C11—22no—
255C2×C4×C11—48no—
256C2×C4×C11—42no—
257C2×C4×C11—42no—
258C2×C4×C11—44no—
259C2×C4×C11C4×D414yes—
260C2×C4×C11C4×D418yes—
261C2×C4×C11C23×C412yes—
262C2×C4×C11C23×C414yes—
263C2×C4×C11C22×D412yes—
264C2×C4×C11C22×D411yescharacteristic
265C2×C4×C11C2×#4112yes—
266C2×C4×C11C2×#4114yes—
267C2×C4×C11C2511yescharacteristic
268C22⋊D11—216no—
269C2×Dic11—28no—
270C2×Dic11—216no—
271C2×Dic11—24no—
272C2×Dic11—22no—
273C2×Dic11—22no—
274C2×Dic11—22no—
275C2×Dic11—24no—
276C2×Dic11—22no—
277C2×Dic11—28no—
278C2×Dic11—44no—
279C2×Dic11#13714yescomplemented
280C2×Dic11C22×D412yes—
281C2×Dic11C22×D412yes—
282C2×Dic11C22×D412yes—
283C2×Dic11C22×D412yes—
284D44—24no—
285D44—22no—
286D44C23×C414yes—
287C4×D11—216no—
288C4×D11—48no—
289C4×D11—48no—
290Dic22—28no—
291Dic22—216no—
292Dic22—24no—
293Dic22—24no—
294Dic22—22no—
295Dic22C23×C418yes—
296Dic22C23×C414yes—
297C8×C11C23×C418yes—
298C11⋊C8—24no—
299C22×#41—111no—
300C23×Q8—111no—
301C2×#137—118no—
302C2×#137—1116no—
303C22×Q16—112no—
304C22×SD16—112no—
305C22×M16—111no—
306C22×M16C2×D1111yescharacteristic
307C4×#41—118no—
308C4×#41—224no—
309C2×C4×Q8—112no—
310C2×C4×Q8—112no—
311C2×C4×Q8—111no—
312C2×C4×Q8—111no—
313C2×C4×Q8—118no—
314C2×C4×Q8—221no—
315C2×C4×Q8—224no—
316C2×C4×Q8—221no—
317C2×C4×D4—111no—
318C2×C4×D4—111no—
319C2×C4×D4—221no—
320C2×C4×D4—221no—
321C2×#117—221no—
322C2×#117C2×D1111yescharacteristic
323C22×C4⋊C4—221no—
324C22×C4⋊C4C2×D1111yescharacteristic
325C22×C42—111no—
326C22×C42—221no—
327C22×C42—221no—
328#441—1116no—
329#440—1116no—
330C4×Q16—1116no—
331C4×SD16—1116no—
332#428C2×D1118yescomplemented
333C2×#107C2×D1112yes—
334C2×#106C2×D1112yes—
335#419—118no—
336#417—118no—
337C2×#103—112no—
338C2×#103—112no—
339C2×#103—112no—
340C2×#102—112no—
341C4×M16—118no—
342C2×#97—112no—
343C2×C4×C8—112no—
344C22×C11—28no—
345C22×C11—22no—
346C22×C11—22no—
347C22×C11C2×C4×D414yes—
348C22×C11C2×C4×D412yes—
349C22×C11C2×#13712yes—
350C22×C11#57512yes—
351C22×C11C23×D411yescharacteristic
352C2×D11—24no—
353C2×D11—48no—
354C2×D11—42no—
355C2×D11—42no—
356C4×C11—42no—
357C4×C11—44no—
358C4×C11—42no—
359C4×C11C2×C4×D412yes—
360C4×C11C2×C4×D414yes—
361C4×C11C24×C411yescharacteristic
362C4×C11C22×#4111yescharacteristic
363Dic11—28no—
364Dic11—24no—
365Dic11—22no—
366Dic11—22no—
367Dic11—22no—
368Dic11C2×#13714yescomplemented
369C2×#41—118no—
370C2×#41—114no—
371C2×#41—222no—
372C2×#41—224no—
373C22×Q8—118no—
374C22×Q8—112no—
375C22×Q8—111no—
376C22×Q8—114no—
377C22×Q8—222no—
378C22×Q8—221no—
379C22×Q8—224no—
380C22×D4—111no—
381C22×D4—221no—
382C23×C4—21no—
383C23×C4—111no—
384C23×C4—111no—
385C23×C4—221no—
386C23×C4—221no—
387C23×C4—221no—
388C23×C4—221no—
389C23×C4C22×D1111yescharacteristic
390#137—1164no—
391C2×Q16—1116no—
392C2×Q16—118no—
393C2×SD16—1116no—
394C2×SD16—118no—
395C2×M16—114no—
396C2×M16—224no—
397C2×M16C4×D1118yescomplemented
398C2×M16C22×D1114yes—
399C22×C8—112no—
400C22×C8C22×D1112yes—
401C4×Q8—118no—
402C4×Q8—118no—
403C4×Q8—114no—
404C4×Q8—114no—
405C4×Q8—228no—
406C4×Q8—228no—
407C4×Q8—224no—
408C4×Q8—224no—
409C4×Q8—222no—
410C4×Q8—222no—
411C4×D4—114no—
412C4×D4—114no—
413C4×D4—222no—
414C4×D4—222no—
415C4×D4—228no—
416C4×D4—228no—
417#117—22no—
418#117—228no—
419#117C22×D1114yes—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—228no—
423C2×C4⋊C4—222no—
424C2×C4⋊C4—222no—
425C2×C4⋊C4—221no—
426C2×C4⋊C4—221no—
427C2×C4⋊C4C22×D1112yes—
428C2×C4⋊C4C22×D1114yes—
429C2×C4⋊C4C22×D1111yescharacteristic
430C2×C4⋊C4C22×D1111yescharacteristic
431C2×C22⋊C4—21no—
432C2×C22⋊C4—221no—
433C2×C22⋊C4—221no—
434C2×C42—21no—
435C2×C42—111no—
436C2×C42—114no—
437C2×C42—111no—
438C2×C42—111no—
439C2×C42—111no—
440C2×C42—114no—
441C2×C42—228no—
442C2×C42—221no—
443C2×C42—221no—
444C2×C42—228no—
445C2×C42—222no—
446C2×C42—222no—
447#107C22×D1118yes—
448#106C22×D1118yes—
449#103—118no—
450#103—118no—
451#103—118no—
452#102—118no—
453#97—118no—
454C4×C8—118no—
455C2×C11—24no—
456C2×C11C4×#13714yescomplemented
457C2×C11C22×C4×D411yescharacteristic
458C2×C11C22×#13711yescharacteristic
459C2×C11C2×#57511yescharacteristic
460D11—44no—
461C24—221no—
462C24D4×D1111yescharacteristic
463#41—1116no—
464#41—2216no—
465#41—228no—
466C2×Q8—118no—
467C2×Q8—114no—
468C2×Q8—1116no—
469C2×Q8—114no—
470C2×Q8—112no—
471C2×Q8—228no—
472C2×Q8—2216no—
473C2×Q8—224no—
474C2×Q8—222no—
475C2×Q8—221no—
476C2×Q8—224no—
477C2×Q8—228no—
478C2×Q8—222no—
479C2×D4—114no—
480C2×D4—112no—
481C2×D4—228no—
482C2×D4—224no—
483C2×D4—221no—
484C2×D4—222no—
485C22×C4—24no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—22no—
489C22×C4—44no—
490C22×C4—111no—
491C22×C4—114no—
492C22×C4—111no—
493C22×C4—111no—
494C22×C4—111no—
495C22×C4—114no—
496C22×C4—224no—
497C22×C4—224no—
498C22×C4—224no—
499C22×C4—228no—
500C22×C4—224no—
501C22×C4—221no—
502C22×C4—222no—
503C22×C4—228no—
504C22×C4—224no—
505C22×C4—444no—
506C22×C4—444no—
507C22×C4—442no—
508C22×C4C2×C4×D1114yes—
509C22×C4D4×D1112yes—
510C22×C4D4×D1111yescharacteristic
511C22×C4#434314yes—
512C22×C4C23×D1112yes—
513C22×C4C23×D1111yescharacteristic
514Q16—1132no—
515SD16—1132no—
516M16—228no—
517M16C2×C4×D11116yescomplemented
518C2×C8—114no—
519C2×C8—224no—
520C2×C8C2×C4×D1118yes—
521C2×C8C23×D1114yes—
522C4⋊C4—24no—
523C4⋊C4—22no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—228no—
527C4⋊C4—228no—
528C4⋊C4—224no—
529C4⋊C4—224no—
530C4⋊C4C23×D1114yes—
531C4⋊C4C23×D1112yes—
532C4⋊C4C23×D1112yes—
533C22⋊C4—24no—
534C22⋊C4—224no—
535C22⋊C4—224no—
536C42—24no—
537C42—114no—
538C42—114no—
539C42—112no—
540C42—112no—
541C42—112no—
542C42—112no—
543C42—224no—
544C42—224no—
545C42—228no—
546C42—228no—
547C11C2×C4×#13711yescharacteristic, complemented, Sylow
548C23—22no—
549C23—22no—
550C23—224no—
551C23—222no—
552C23—442no—
553C23—442no—
554C23#6694614yes—
555C23C2×D4×D1112yes—
556C23C2×D4×D1111yescharacteristic
557Q8—118no—
558Q8—114no—
559Q8—2216no—
560Q8—228no—
561Q8—224no—
562Q8—224no—
563Q8—222no—
564D4—114no—
565D4—2216no—
566D4—224no—
567D4—222no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—24no—
571C2×C4—48no—
572C2×C4—44no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—114no—
576C2×C4—112no—
577C2×C4—112no—
578C2×C4—112no—
579C2×C4—112no—
580C2×C4—228no—
581C2×C4—224no—
582C2×C4—2216no—
583C2×C4—228no—
584C2×C4—222no—
585C2×C4—222no—
586C2×C4—222no—
587C2×C4—222no—
588C2×C4—224no—
589C2×C4—2216no—
590C2×C4—448no—
591C2×C4—448no—
592C2×C4—444no—
593C2×C4#6694614yes—
594C2×C4#6694618yes—
595C2×C4C22×C4×D1112yes—
596C2×C4C22×C4×D1114yes—
597C2×C4C2×D4×D1112yes—
598C2×C4C2×D4×D1111yescharacteristic
599C2×C4C2×#434312yes—
600C2×C4C2×#434314yes—
601C2×C4C24×D1111yescharacteristic
602C8—224no—
603C8C22×C4×D1118yes—
604C22—28no—
605C22—22no—
606C22—22no—
607C22—224no—
608C22—448no—
609C22—442no—
610C22—442no—
611C22C2×#6694614yes—
612C22C2×#6694612yes—
613C22#1062330412yes—
614C22D11×#13712yes—
615C22C22×D4×D1111yescharacteristic
616C4—42no—
617C4—44no—
618C4—42no—
619C4—114no—
620C4—224no—
621C4—228no—
622C4—222no—
623C4—222no—
624C4—222no—
625C4C2×#6694614yes—
626C4C2×#6694612yes—
627C4C23×C4×D1111yescharacteristic
628C4C22×#434311yescharacteristic
629C2—24no—
630C2—444no—
631C2#1307743414yesdirect product factor
632C2C22×#6694611yescharacteristic
633C2C2×D11×#13711yescharacteristic
634C2C2×#1062330411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC4×C11C24×C4
FrattiniC2×C4C24×D11
FittingC2×C11×#428C2
socleC23×C11C22×D4
prime radicalC22×#4339C22
cosocleC2×C4×C11C25
hypercenterC2×#428D11
hypocenterC11C2×C4×#137
LCSG ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#428

Complements

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

NH ≅ G/Ntype
3. C22×#66940C2semidirect
4. #13077434C2direct (N × H)
5. C2×#10622466C2semidirect
6. C2×#10622502C2semidirect
7. C2×#10622486C2semidirect
8. C2×#10622465C2semidirect
10. C2×#10622617C2semidirect
11. C2×M16×Dic11C2semidirect
12. C2×C11×#428C2semidirect
22. C2×#66962C4semidirect
37. C2×#66940C22semidirect
42. C11×#428C22semidirect
45. M16×Dic11C22semidirect
48. #10622617C22semidirect
54. #10622502C22semidirect
55. #10622486C22semidirect
56. #10622466C22semidirect
57. #10622465C22semidirect
75. C22×Dic22C2×C4semidirect
79. C2×C11×M16C2×C4semidirect
113. #66962C2×C4semidirect
114. C2×Dic44C2×C4semidirect
116. C2×#4314C2×C4semidirect
195. C2×Dic22C22×C4semidirect
198. C11×M16C22×C4semidirect
229. Dic44C22×C4semidirect
230. #4314C22×C4semidirect
239. C2×#428D11semidirect
279. C2×Dic11#137semidirect
332. #428C2×D11semidirect
368. Dic11C2×#137semidirect
397. C2×M16C4×D11semidirect
456. C2×C11C4×#137semidirect
517. M16C2×C4×D11semidirect
547. C11C2×C4×#137semidirect
631. C2#13077434direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669622
C2×#106230532
C22×#669402
#130774342
C2×#106224662
C2×#106225022
C2×#106224862
C2×#106224652
C2×#106225792
C2×#106226172
C2×M16×Dic112
C2×C11×#4282
C2×C4×#13711