Finite Group Databasebeta

← C2×#13078100 #15620626

Subgroups — C2×#13078100 #15620626

Order 2816.

2790 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66971C212yesmaximal
2C2×D11×C4⋊Q8C211yesmaximal, characteristic, complemented
3C2×C4×#4343C211yesmaximal, characteristic
4#13078100C2116yesmaximal, direct product factor
5C2×#10622644C211yesmaximal, characteristic, complemented
6C2×#10622795C212yesmaximal, complemented
7C2×#10622454C211yesmaximal, characteristic, complemented
8C2×#10622431C212yesmaximal, complemented
9C2×#10622696C211yesmaximal, characteristic, complemented
10C2×#10622450C211yesmaximal, characteristic, complemented
11C2×#10622415C212yesmaximal, complemented
12C2×C11×#462C211yesmaximal, characteristic, complemented
13C22×#4343C2211yescharacteristic
14C22×Q8×D11C2212yes—
15C22×C11×Q16C2212yes—
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×Q8×Dic11C2211yescharacteristic
19C2×#66997C2212yes—
20C22×#4326C2212yes—
21C22×#4325C2212yes—
22C2×#66971—216no—
23C2×#66971C22116yes—
24C22×#4314C2212yes—
25C22×#4313C2212yes—
26D11×C4⋊Q8—24no—
27D11×C4⋊Q8C2218yescomplemented
28C4×#4343—24no—
29C4×#4343C2218yes—
30C2×#66946—21no—
31C2×#66946C2211yescharacteristic
32C2×#66945—21no—
33C2×#66945C2211yescharacteristic
34C2×C4⋊C4×D11—21no—
35C2×C4⋊C4×D11—21no—
36C2×#66941—21no—
37C2×#66941—21no—
38C2×C4×D44—21no—
39C2×C4×D44C2211yescharacteristic
40C2×C42×D11—21no—
41C2×C42×D11C2211yescharacteristic
42C2×#66922C2211yescharacteristic
43C11×#462C2218yescomplemented
44C2×C11×C4⋊C8C2211yescharacteristic
45C2×C11×#103C2212yes—
46C2×#66899C2212yes—
47#10622795C22116yescomplemented
48C2×#66880C2212yes—
49C2×Dic11⋊C8C2212yes—
50#10622696C2218yescomplemented
51#10622644C2218yescomplemented
52C2×#66874C2212yes—
53C2×C4⋊(C11⋊C8)C2211yescharacteristic
54#10622454C2218yescomplemented
55#10622450C2218yescomplemented
56#10622431C22116yescomplemented
57#10622415C22116yescomplemented
58C22×Q8×C11C2312yes—
59C22×Q8×C11C2311yescharacteristic
60C2×#4343—22no—
61C2×#4343—24no—
62C2×#4343D418yes—
63C2×#4343C2314yes—
64C2×Q8×D11—24no—
65C2×Q8×D11—28no—
66C2×Q8×D11—28no—
67C2×Q8×D11C2318yes—
68C22×D44—21no—
69C22×D44C2311yescharacteristic
70C22×C4×D11—21no—
71C22×C4×D11—22no—
72C22×C4×D11—21no—
73C22×C4×D11—21no—
74C22×C4×D11D411yescharacteristic
75C22×C4×D11D411yescharacteristic
76C22×C4×D11C2311yescharacteristic
77C22×Dic22—22no—
78C22×Dic22C2312yes—
79C2×C11×Q16—28no—
80C2×C11×Q16C2318yes—
81C22×C8×C11C2312yes—
82C11×C4⋊Q8—22no—
83C11×C4⋊Q8C2314yes—
84C4×Q8×C11—22no—
85C4×Q8×C11C2314yes—
86C2×C11×C4⋊C4—21no—
87C2×C11×C4⋊C4—21no—
88C2×C11×C4⋊C4—21no—
89C2×C11×C4⋊C4C2311yescharacteristic
90C2×C42×C11—21no—
91C2×C42×C11C2311yescharacteristic
92Q8×Dic11—22no—
93Q8×Dic11C2314yes—
94#66997—24no—
95#66997C2318yes—
96C2×#4326—28no—
97C2×#4326C2318yes—
98C2×#4325—28no—
99C2×#4325C2318yes—
100C2×(C2×D11)⋊C4—21no—
101C2×(C2×D11)⋊C4—21no—
102C2×(C2×D11)⋊C4—21no—
103C2×C4⋊Dic11—21no—
104C2×C4⋊Dic11—21no—
105C2×C4⋊Dic11—21no—
106C2×C4⋊Dic11C2311yescharacteristic
107C2×Dic11⋊C4—22no—
108C2×Dic11⋊C4—22no—
109C2×C4×Dic11—21no—
110C2×C4×Dic11—21no—
111C2×C4×Dic11D411yescharacteristic
112C2×C4×Dic11D411yescharacteristic
113C2×C4×Dic11C2311yescharacteristic
114C22×C11⋊C8C2312yes—
115#66971—264no—
116C2×#4314—28no—
117C2×#4314C2318yes—
118C2×#4313—28no—
119C2×#4313C2318yes—
120#66946—28no—
121#66946—22no—
122#66946C2314yes—
123#66945—22no—
124#66945—28no—
125#66945C2314yes—
126C4⋊C4×D11—28no—
127C4⋊C4×D11—28no—
128#66941—28no—
129#66941—28no—
130C4×D44—28no—
131C4×D44—22no—
132C4×D44C2314yes—
133C42×D11—28no—
134C42×D11D414yes—
135C42×D11C2314yes—
136#66922—22no—
137#66922C2314yes—
138C11×C4⋊C8C2314yes—
139C11×#103C2318yes—
140#66899C2318yes—
141#66880C2318yes—
142Dic11⋊C8C2318yes—
143#66874C2318yes—
144C4⋊(C11⋊C8)C2314yes—
145C2×#3039—111nomaximal, Sylow
146C23×D11—21no—
147C23×D11C2×D411yescharacteristic
148C2×Q8×C11—21no—
149C2×Q8×C11—22no—
150C2×Q8×C11—22no—
151C2×Q8×C11—24no—
152C2×Q8×C11—24no—
153C2×Q8×C11C2×D414yes—
154C2×Q8×C11C2414yes—
155C2×Q8×C11C2412yes—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—22no—
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11C2×D411yescharacteristic
161C22×C4×C11C2411yescharacteristic
162C22×Dic11—21no—
163C22×Dic11—22no—
164C22×Dic11C2×D411yescharacteristic
165C22×Dic11C2×D411yescharacteristic
166C22×Dic11C2×D411yescharacteristic
167#4343—216no—
168#4343—28no—
169#4343C2×D4116yes—
170Q8×D11—216no—
171Q8×D11—216no—
172Q8×D11—416no—
173C2×D44—28no—
174C2×D44—24no—
175C2×D44—21no—
176C2×D44—22no—
177C2×D44C2×D414yes—
178C2×D44C2412yes—
179C2×C4×D11—28no—
180C2×C4×D11—24no—
181C2×C4×D11—24no—
182C2×C4×D11—24no—
183C2×C4×D11—28no—
184C2×C4×D11—24no—
185C2×C4×D11—24no—
186C2×C4×D11—44no—
187C2×C4×D11—48no—
188C2×C4×D11—44no—
189C2×C4×D11C2×D414yes—
190C2×C4×D11C2×D414yes—
191C2×C4×D11C2×D414yes—
192C2×C4×D11C2×D412yes—
193C2×C4×D11#4114yes—
194C2×C4×D11C2412yes—
195C2×Dic22—28no—
196C2×Dic22—24no—
197C2×Dic22—22no—
198C2×Dic22—24no—
199C2×Dic22—48no—
200C2×Dic22C2414yes—
201C11×Q16—216no—
202C2×C8×C11—24no—
203C2×C8×C11C2414yes—
204C11×C4⋊C4—24no—
205C11×C4⋊C4—24no—
206C11×C4⋊C4—24no—
207C11×C4⋊C4—21no—
208C11×C4⋊C4C2412yes—
209C42×C11—24no—
210C42×C11C2×D412yes—
211C42×C11C2412yes—
212#4326—216no—
213#4325—216no—
214(C2×D11)⋊C4—24no—
215(C2×D11)⋊C4—24no—
216(C2×D11)⋊C4—24no—
217C4⋊Dic11—24no—
218C4⋊Dic11—24no—
219C4⋊Dic11—24no—
220C4⋊Dic11—21no—
221C4⋊Dic11C2412yes—
222Dic11⋊C4—28no—
223Dic11⋊C4—28no—
224C4×Dic11—24no—
225C4×Dic11—24no—
226C4×Dic11C2×D414yes—
227C4×Dic11C2×D412yes—
228C4×Dic11C2×D414yes—
229C4×Dic11C2412yes—
230C2×C11⋊C8—24no—
231C2×C11⋊C8C2414yes—
232#4314—216no—
233#4313—216no—
234C22×#137—112no—
235C22×C4⋊Q8—111no—
236C2×C4×#41—111no—
237#3039—1116no—
238C2×#462—112no—
239C2×#462—111no—
240C2×#462D1111yescharacteristic, complemented
241C2×#461—111no—
242C2×#461—112no—
243C2×#461—111no—
244C2×#423—111no—
245C2×#419—112no—
246C23×C11C22×D411yescharacteristic
247C22×D11—22no—
248C22×D11—22no—
249C22×D11—24no—
250C22×D11—22no—
251C22×D11—42no—
252C22×D11—42no—
253C22×D11#12114yes—
254C22×D11C22×D412yes—
255Q8×C11—24no—
256Q8×C11—22no—
257Q8×C11—24no—
258Q8×C11—24no—
259Q8×C11—44no—
260Q8×C11C22×D414yes—
261C2×C4×C11—24no—
262C2×C4×C11—22no—
263C2×C4×C11—22no—
264C2×C4×C11—22no—
265C2×C4×C11—24no—
266C2×C4×C11—44no—
267C2×C4×C11—42no—
268C2×C4×C11#13714yescomplemented
269C2×C4×C11C22×D412yes—
270C2×C4×C11C22×D411yescharacteristic
271C2×C4×C11C22×D412yes—
272C2×C4×C11C22×D412yes—
273C2×C4×C11C2×#4112yes—
274C2×C4×C11C2511yescharacteristic
275C2×Dic11—22no—
276C2×Dic11—22no—
277C2×Dic11—24no—
278C2×Dic11—44no—
279C2×Dic11—42no—
280C2×Dic11#12114yes—
281C2×Dic11#13714yescomplemented
282C2×Dic11C22×D412yes—
283C2×Dic11C22×D412yes—
284C2×Dic11C22×D412yes—
285D44—216no—
286D44—24no—
287D44—22no—
288D44C22×D414yes—
289C4×D11—28no—
290C4×D11—216no—
291C4×D11—28no—
292C4×D11—416no—
293C4×D11—48no—
294C4×D11—48no—
295C4×D11#12118yes—
296C4×D11C22×D414yes—
297C4×D11C2×#4114yes—
298Dic22—24no—
299Dic22—24no—
300Dic22—44no—
301Dic22—416no—
302C8×C11—24no—
303C11⋊C8—24no—
304C22×#41—111no—
305C23×Q8—112no—
306C2×#137—1116no—
307C2×#137—2216no—
308C22×Q16—112no—
309C22×Q16C2×D1112yes—
310C22×SD16—112no—
311C22×SD16—112no—
312C22×M16—112no—
313C2×C4⋊Q8—112no—
314C2×C4⋊Q8—118no—
315C2×C4⋊Q8—111no—
316C2×C4⋊Q8—221no—
317C2×C4⋊Q8—221no—
318C2×C4⋊Q8—224no—
319C2×C4⋊Q8C2×D1111yescharacteristic
320C4×#41—118no—
321C4×#41—224no—
322C2×C4×Q8—111no—
323C2×C4×Q8C2×D1111yescharacteristic
324C2×C4×D4—111no—
325C2×C4×D4—111no—
326C2×C4×D4—221no—
327C2×C4×D4—221no—
328C2×#117—111no—
329C2×#117—221no—
330C22×C4⋊C4—221no—
331C22×C4⋊C4—221no—
332C22×C42—111no—
333C22×C42—221no—
334#462—1116no—
335#462—118no—
336#462C2×D1118yescomplemented
337#461—118no—
338#461—118no—
339#461—1116no—
340#423—118no—
341C2×C4⋊C8—112no—
342C2×C4⋊C8—111no—
343C2×C4⋊C8C2×D1111yescharacteristic
344#419—1116no—
345C2×#103—112no—
346C2×#103—112no—
347C2×#103—112no—
348C2×#103C2×D1112yes—
349C22×C11C2×#12112yes—
350C22×C11C2×#13712yes—
351C22×C11C2×#13712yes—
352C22×C11C23×D411yescharacteristic
353C2×D11—28no—
354C2×D11—22no—
355C2×D11—22no—
356C2×D11—24no—
357C2×D11—48no—
358C2×D11—42no—
359C2×D11—42no—
360C2×D11C2×#12114yes—
361C4×C11—24no—
362C4×C11—22no—
363C4×C11—44no—
364C4×C11—42no—
365C4×C11C2×#12112yes—
366C4×C11C2×#13714yescomplemented
367C4×C11C23×D411yescharacteristic
368C4×C11C22×#4111yescharacteristic
369Dic11—22no—
370Dic11—44no—
371Dic11—42no—
372Dic11C2×#12114yes—
373Dic11C2×#13714yescomplemented
374C2×#41—118no—
375C2×#41—114no—
376C2×#41—222no—
377C2×#41—224no—
378C22×Q8—118no—
379C22×Q8—112no—
380C22×Q8—222no—
381C22×Q8—224no—
382C22×Q8—228no—
383C22×Q8—228no—
384C22×Q8C22×D1112yes—
385C22×Q8C22×D1111yescharacteristic
386C22×D4—111no—
387C22×D4—221no—
388C23×C4—111no—
389C23×C4—111no—
390C23×C4—111no—
391C23×C4—221no—
392C23×C4—221no—
393C23×C4—222no—
394C23×C4—221no—
395#137—2264no—
396C2×Q16—28no—
397C2×Q16—118no—
398C2×Q16—228no—
399C2×Q16C22×D1118yes—
400C2×SD16—118no—
401C2×SD16—118no—
402C2×SD16—228no—
403C2×SD16—228no—
404C2×M16—118no—
405C2×M16—228no—
406C22×C8—112no—
407C22×C8C22×D1112yes—
408C4⋊Q8—22no—
409C4⋊Q8—118no—
410C4⋊Q8—114no—
411C4⋊Q8—228no—
412C4⋊Q8—228no—
413C4⋊Q8—224no—
414C4⋊Q8—222no—
415C4⋊Q8C22×D1114yes—
416C4×Q8—22no—
417C4×Q8—114no—
418C4×Q8—222no—
419C4×Q8C22×D1114yes—
420C4×D4—114no—
421C4×D4—114no—
422C4×D4—228no—
423C4×D4—222no—
424C4×D4—228no—
425C4×D4—222no—
426#117—114no—
427#117—228no—
428#117—222no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—111no—
433C2×C4⋊C4—228no—
434C2×C4⋊C4—228no—
435C2×C4⋊C4—222no—
436C2×C4⋊C4—222no—
437C2×C4⋊C4—221no—
438C2×C4⋊C4—221no—
439C2×C4⋊C4—221no—
440C2×C4⋊C4C22×D1111yescharacteristic
441C2×C22⋊C4—221no—
442C2×C22⋊C4—221no—
443C2×C22⋊C4—221no—
444C2×C42—21no—
445C2×C42—111no—
446C2×C42—111no—
447C2×C42—111no—
448C2×C42—114no—
449C2×C42—114no—
450C2×C42—228no—
451C2×C42—221no—
452C2×C42—221no—
453C2×C42C22×D1111yescharacteristic
454C4⋊C8—118no—
455C4⋊C8—114no—
456C4⋊C8C22×D1114yes—
457#103—118no—
458#103—118no—
459#103—118no—
460#103C22×D1118yes—
461C2×C11#303914yescomplemented
462C2×C11C22×#12111yescharacteristic
463C2×C11C22×#13711yescharacteristic
464C2×C11C22×#13711yescharacteristic
465D11—24no—
466D11—44no—
467C24—111no—
468C24—221no—
469#41—1116no—
470#41—2216no—
471#41—228no—
472C2×Q8—21no—
473C2×Q8—22no—
474C2×Q8—22no—
475C2×Q8—24no—
476C2×Q8—24no—
477C2×Q8—114no—
478C2×Q8—228no—
479C2×Q8—2216no—
480C2×Q8—2216no—
481C2×Q8—222no—
482C2×Q8—224no—
483C2×Q8—224no—
484C2×Q8—448no—
485C2×Q8—4416no—
486C2×Q8D4×D1114yes—
487C2×Q8C23×D1114yes—
488C2×Q8C23×D1112yes—
489C2×D4—114no—
490C2×D4—112no—
491C2×D4—224no—
492C2×D4—228no—
493C2×D4—221no—
494C2×D4—222no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—22no—
498C22×C4—111no—
499C22×C4—111no—
500C22×C4—112no—
501C22×C4—114no—
502C22×C4—114no—
503C22×C4—112no—
504C22×C4—111no—
505C22×C4—114no—
506C22×C4—114no—
507C22×C4—224no—
508C22×C4—224no—
509C22×C4—228no—
510C22×C4—224no—
511C22×C4—228no—
512C22×C4—224no—
513C22×C4—221no—
514C22×C4—222no—
515C22×C4—224no—
516C22×C4—444no—
517C22×C4—448no—
518C22×C4—444no—
519C22×C4D4×D1111yescharacteristic
520C22×C4D4×D1111yescharacteristic
521C22×C4C23×D1111yescharacteristic
522Q16—216no—
523Q16—2216no—
524SD16—2216no—
525SD16—2216no—
526M16—2216no—
527C2×C8—24no—
528C2×C8—114no—
529C2×C8—224no—
530C2×C8C23×D1114yes—
531C4⋊C4—24no—
532C4⋊C4—24no—
533C4⋊C4—24no—
534C4⋊C4—21no—
535C4⋊C4—112no—
536C4⋊C4—228no—
537C4⋊C4—228no—
538C4⋊C4—224no—
539C4⋊C4—221no—
540C4⋊C4—224no—
541C4⋊C4—224no—
542C4⋊C4C23×D1112yes—
543C22⋊C4—224no—
544C22⋊C4—224no—
545C22⋊C4—224no—
546C42—24no—
547C42—114no—
548C42—114no—
549C42—112no—
550C42—112no—
551C42—224no—
552C42—224no—
553C42D4×D1112yes—
554C42C23×D1112yes—
555C11C2×#303911yescharacteristic, complemented, Sylow
556C23—114no—
557C23—112no—
558C23—222no—
559C23—222no—
560C23—224no—
561C23—222no—
562C23—442no—
563C23—442no—
564C23C2×D4×D1111yescharacteristic
565Q8—24no—
566Q8—22no—
567Q8—24no—
568Q8—24no—
569Q8—44no—
570Q8—224no—
571Q8—224no—
572Q8—4416no—
573Q8—444no—
574Q8C2×D4×D1114yes—
575D4—114no—
576D4—2216no—
577D4—224no—
578D4—222no—
579C2×C4—22no—
580C2×C4—24no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—24no—
584C2×C4—42no—
585C2×C4—44no—
586C2×C4—114no—
587C2×C4—114no—
588C2×C4—112no—
589C2×C4—112no—
590C2×C4—118no—
591C2×C4—114no—
592C2×C4—114no—
593C2×C4—112no—
594C2×C4—228no—
595C2×C4—2216no—
596C2×C4—222no—
597C2×C4—228no—
598C2×C4—222no—
599C2×C4—224no—
600C2×C4—448no—
601C2×C4—4416no—
602C2×C4—442no—
603C2×C4—444no—
604C2×C4—448no—
605C2×C4#6697114yescomplemented
606C2×C4C2×D4×D1112yes—
607C2×C4C2×D4×D1112yes—
608C2×C4C2×D4×D1111yescharacteristic
609C2×C4C2×D4×D1112yes—
610C2×C4#41×D1112yes—
611C2×C4C24×D1111yescharacteristic
612C8—24no—
613C8—224no—
614C22—114no—
615C22—228no—
616C22—222no—
617C22—222no—
618C22—224no—
619C22—448no—
620C22—442no—
621C22—442no—
622C22D11×#12112yes—
623C22C2×#6697112yes—
624C22D11×#13712yes—
625C22C22×D4×D1111yescharacteristic
626C4—22no—
627C4—24no—
628C4—42no—
629C4—44no—
630C4—114no—
631C4—114no—
632C4—222no—
633C4—442no—
634C4—444no—
635C4D11×#12112yes—
636C4C2×#6697114yescomplemented
637C4C22×D4×D1111yescharacteristic
638C4C2×#41×D1111yescharacteristic
639C2—224no—
640C2—444no—
641C2#1307810014yesdirect product factor
642C2C2×D11×#12111yescharacteristic
643C2C2×D11×#13711yescharacteristic
644C2C22×#6697111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#462C2
socleC23×C11C22×D4
prime radicalC22×#4343C22
hypercenterC2×#462D11
hypocenterC11C2×#3039
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#462

Complements

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

NH ≅ G/Ntype
2. C2×D11×C4⋊Q8C2semidirect
4. #13078100C2direct (N × H)
5. C2×#10622644C2semidirect
6. C2×#10622795C2semidirect
7. C2×#10622454C2semidirect
8. C2×#10622431C2semidirect
9. C2×#10622696C2semidirect
10. C2×#10622450C2semidirect
11. C2×#10622415C2semidirect
12. C2×C11×#462C2semidirect
27. D11×C4⋊Q8C22semidirect
43. C11×#462C22semidirect
47. #10622795C22semidirect
50. #10622696C22semidirect
51. #10622644C22semidirect
54. #10622454C22semidirect
55. #10622450C22semidirect
56. #10622431C22semidirect
57. #10622415C22semidirect
240. C2×#462D11semidirect
268. C2×C4×C11#137semidirect
281. C2×Dic11#137semidirect
336. #462C2×D11semidirect
366. C4×C11C2×#137semidirect
373. Dic11C2×#137semidirect
461. C2×C11#3039semidirect
555. C11C2×#3039semidirect
605. C2×C4#66971semidirect
636. C4C2×#66971semidirect
641. C2#13078100direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669712
C2×D11×C4⋊Q82
C2×C4×#43432
#130781002
C2×#106226442
C2×#106227952
C2×#106224542
C2×#106224312
C2×#106226962
C2×#106224502
C2×#106224152
C2×C11×#4622
C2×#303911