Finite Group Databasebeta

← C2×#13079540 #15624955

Subgroups — C2×#13079540 #15624955

Order 2816.

2414 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623079C211yesmaximal, characteristic
2C2×D11×C4⋊Q8C211yesmaximal, characteristic, complemented
3#13079540C2116yesmaximal, direct product factor
4C2×#10622788C212yesmaximal, complemented
5C2×#10622405C212yesmaximal, complemented
6C2×#10622454C211yesmaximal, characteristic, complemented
7C2×#10622632C211yesmaximal, characteristic, complemented
8C2×#10622696C211yesmaximal, characteristic, complemented
9C2×#10622419C212yesmaximal, complemented
10C2×#10622783C212yesmaximal, complemented
11C2×#10622446C211yesmaximal, characteristic, complemented
12C2×C11×#461C211yesmaximal, characteristic, complemented
13C22×Q8×D11C2212yes—
14C22×#4339—21no—
15C22×C11×SD16C2212yes—
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C2×#66997C2212yes—
19C22×#4325C2212yes—
20C2×#66993C2211yescharacteristic
21C2×#66991C2211yescharacteristic
22C22×#4324C2212yes—
23C2×C4×C22⋊D11—21no—
24C22×#4314C2212yes—
25D11×C4⋊Q8—24no—
26D11×C4⋊Q8C2218yescomplemented
27#10623079—24no—
28#10623079C2218yes—
29C2×#66948C2211yescharacteristic
30C2×C4⋊C4×D11—21no—
31C2×C4⋊C4×D11—21no—
32C2×#66941—21no—
33C2×#66941—21no—
34C2×#66941C2211yescharacteristic
35C2×#66938—21no—
36C2×#66937—21no—
37C2×C4×D44C2211yescharacteristic
38C2×C42×D11C2211yescharacteristic
39C2×#66922C2211yescharacteristic
40C11×#461C2218yescomplemented
41C2×C11×C4⋊C8C2211yescharacteristic
42C2×C11×#103C2212yes—
43C2×#66899C2212yes—
44#10622788C22116yescomplemented
45#10622783C22116yescomplemented
46C2×(C2×D11)⋊C8C2212yes—
47C2×#66880C2212yes—
48C2×C8×Dic11C2212yes—
49#10622696C2218yescomplemented
50#10622632C2218yescomplemented
51C2×#66874C2212yes—
52C2×C4⋊(C11⋊C8)C2211yescharacteristic
53#10622454C2218yescomplemented
54#10622446C2218yescomplemented
55#10622419C22116yescomplemented
56#10622405C22116yescomplemented
57C22×Q8×C11C2312yes—
58C22×D4×C11C2311yescharacteristic
59C23×C4×C11—21no—
60C22×C22⋊D11—21no—
61C22×C22⋊D11—21no—
62C22×C22⋊D11—21no—
63C2×Q8×D11—24no—
64C2×Q8×D11—44no—
65C2×Q8×D11—44no—
66C2×Q8×D11C2318yes—
67C2×#4339—28no—
68C2×#4339—48no—
69C22×D44—21no—
70C22×D44C2311yescharacteristic
71C22×C4×D11—22no—
72C22×C4×D11—21no—
73C22×C4×D11D411yescharacteristic
74C22×C4×D11D411yescharacteristic
75C22×C4×D11C2311yescharacteristic
76C22×Dic22—21no—
77C22×Dic22—22no—
78C22×Dic22C2312yes—
79C2×C11×SD16—44no—
80C2×C11×SD16C2318yes—
81C22×C8×C11C2312yes—
82C11×C4⋊Q8—22no—
83C11×C4⋊Q8C2314yes—
84C4×D4×C11—22no—
85C4×D4×C11C2314yes—
86C2×C11×C4⋊C4—21no—
87C2×C11×C4⋊C4—21no—
88C2×C11×C4⋊C4C2311yescharacteristic
89C2×C11×C22⋊C4—21no—
90C2×C42×C11C2311yescharacteristic
91C2×C22⋊Dic11—21no—
92#66997—24no—
93#66997C2318yes—
94C2×#4325—44no—
95C2×#4325C2318yes—
96#66993—22no—
97#66993C2314yes—
98#66991—22no—
99#66991C2314yes—
100C2×#4324—44no—
101C2×#4324C2318yes—
102C4×C22⋊D11—28no—
103C2×(C2×D11)⋊C4—21no—
104C2×(C2×D11)⋊C4—21no—
105C2×C4⋊Dic11—21no—
106C2×C4⋊Dic11—21no—
107C2×C4⋊Dic11C2311yescharacteristic
108C2×Dic11⋊C4—21no—
109C2×Dic11⋊C4—22no—
110C2×Dic11⋊C4—22no—
111C2×C4×Dic11D411yescharacteristic
112C2×C4×Dic11D411yescharacteristic
113C2×C4×Dic11C2311yescharacteristic
114C22×C11⋊C8C2312yes—
115C2×#4314—44no—
116C2×#4314C2318yes—
117#66948—22no—
118#66948C2314yes—
119C4⋊C4×D11—28no—
120C4⋊C4×D11—28no—
121#66941—28no—
122#66941—28no—
123#66941—22no—
124#66941C2314yes—
125#66938—28no—
126#66937—28no—
127C4×D44—22no—
128C4×D44C2314yes—
129C42×D11D414yes—
130C42×D11C2314yes—
131#66922—22no—
132#66922C2314yes—
133C11×C4⋊C8C2314yes—
134C11×#103C2318yes—
135#66899C2318yes—
136(C2×D11)⋊C8C2318yes—
137#66880C2318yes—
138C8×Dic11C2318yes—
139#66874C2318yes—
140C4⋊(C11⋊C8)C2314yes—
141C2×#3206—111nomaximal, Sylow
142C24×C11—21no—
143C23×D11—21no—
144C23×D11C2×D411yescharacteristic
145C2×Q8×C11—22no—
146C2×Q8×C11—24no—
147C2×Q8×C11—24no—
148C2×Q8×C11C2414yes—
149C2×D4×C11—21no—
150C2×D4×C11—22no—
151C2×D4×C11—22no—
152C2×D4×C11C2412yes—
153C22×C4×C11—22no—
154C22×C4×C11—21no—
155C22×C4×C11—24no—
156C22×C4×C11—44no—
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11C2411yescharacteristic
160C2×C22⋊D11—24no—
161C2×C22⋊D11—24no—
162C2×C22⋊D11—24no—
163C2×C22⋊D11—44no—
164C2×C22⋊D11—44no—
165C2×C22⋊D11—44no—
166C22×Dic11—22no—
167C22×Dic11—21no—
168C22×Dic11C2×D411yescharacteristic
169C22×Dic11C2×D411yescharacteristic
170C22×Dic11C2×D411yescharacteristic
171Q8×D11—48no—
172Q8×D11—48no—
173Q8×D11—416no—
174#4339—432no—
175C2×D44—24no—
176C2×D44—21no—
177C2×D44—22no—
178C2×D44—22no—
179C2×D44—44no—
180C2×D44C2412yes—
181C2×C4×D11—24no—
182C2×C4×D11—28no—
183C2×C4×D11—24no—
184C2×C4×D11—22no—
185C2×C4×D11—22no—
186C2×C4×D11—48no—
187C2×C4×D11—44no—
188C2×C4×D11SD1618yescomplemented
189C2×C4×D11C2×D412yes—
190C2×C4×D11C2×D414yes—
191C2×C4×D11C2×D414yes—
192C2×C4×D11C2412yes—
193C2×Dic22—24no—
194C2×Dic22—28no—
195C2×Dic22—22no—
196C2×Dic22—24no—
197C2×Dic22—24no—
198C2×Dic22—48no—
199C2×Dic22—44no—
200C2×Dic22C2414yes—
201C11×SD16—48no—
202C2×C8×C11—24no—
203C2×C8×C11C2414yes—
204C11×C4⋊C4—24no—
205C11×C4⋊C4—24no—
206C11×C4⋊C4—21no—
207C11×C4⋊C4C2412yes—
208C11×C22⋊C4—24no—
209C42×C11C2×D412yes—
210C42×C11C2412yes—
211C22⋊Dic11—24no—
212#4325—48no—
213#4324—48no—
214(C2×D11)⋊C4—24no—
215(C2×D11)⋊C4—24no—
216C4⋊Dic11—24no—
217C4⋊Dic11—24no—
218C4⋊Dic11—21no—
219C4⋊Dic11C2412yes—
220Dic11⋊C4—24no—
221Dic11⋊C4—28no—
222Dic11⋊C4—28no—
223C4×Dic11C2×D412yes—
224C4×Dic11C2×D414yes—
225C4×Dic11C2×D414yes—
226C4×Dic11C2412yes—
227C2×C11⋊C8—24no—
228C2×C11⋊C8C2414yes—
229#4314—48no—
230C2×#532—111no—
231C22×C4⋊Q8—111no—
232#3206—1116no—
233C2×#492—112no—
234C2×#487—112no—
235C2×#461—111no—
236C2×#461—111no—
237C2×#461—111no—
238C2×#461D1111yescharacteristic, complemented
239C2×#448—112no—
240C2×#448—112no—
241C2×#431—111no—
242C23×C11—22no—
243C23×C11—42no—
244C23×C11—42no—
245C23×C11—42no—
246C23×C11C22×D411yescharacteristic
247C22×D11—22no—
248C22×D11—22no—
249C22×D11—22no—
250C22×D11—42no—
251C22×D11—42no—
252C22×D11—42no—
253C22×D11C2×SD1614yes—
254C22×D11C22×D412yes—
255Q8×C11—24no—
256Q8×C11—24no—
257Q8×C11—44no—
258D4×C11—22no—
259D4×C11—22no—
260D4×C11—42no—
261C2×C4×C11—22no—
262C2×C4×C11—24no—
263C2×C4×C11—22no—
264C2×C4×C11—44no—
265C2×C4×C11—42no—
266C2×C4×C11—48no—
267C2×C4×C11C2×SD1614yes—
268C2×C4×C11C22×D412yes—
269C2×C4×C11C22×D411yescharacteristic
270C2×C4×C11C22×D412yes—
271C2×C4×C11H(5,𝔽2)12yes—
272C2×C4×C11H(5,𝔽2)12yes—
273C2×C4×C11C2511yescharacteristic
274C22⋊D11—48no—
275C22⋊D11—48no—
276C22⋊D11—48no—
277C2×Dic11—22no—
278C2×Dic11—24no—
279C2×Dic11—22no—
280C2×Dic11—44no—
281C2×Dic11—42no—
282C2×Dic11C2×SD1614yes—
283C2×Dic11#13714yes—
284C2×Dic11C22×D412yes—
285C2×Dic11C22×D412yes—
286C2×Dic11C22×D412yes—
287D44—22no—
288D44—22no—
289D44—48no—
290D44—42no—
291C4×D11—24no—
292C4×D11—22no—
293C4×D11—22no—
294C4×D11—28no—
295C4×D11—416no—
296C4×D11—48no—
297C4×D11C2×SD16116yescomplemented
298Dic22—24no—
299Dic22—24no—
300Dic22—416no—
301Dic22—44no—
302Dic22—48no—
303C8×C11—24no—
304C11⋊C8—24no—
305C22×#41—221no—
306C23×Q8—112no—
307C22×SD16—112no—
308C22×SD16—112no—
309C22×SD16—112no—
310C22×SD16C2×D1112yes—
311#532—118no—
312#532—224no—
313C2×C4⋊Q8—111no—
314C2×C4⋊Q8—112no—
315C2×C4⋊Q8—118no—
316C2×C4⋊Q8—111no—
317C2×C4⋊Q8—221no—
318C2×C4⋊Q8—221no—
319C2×C4⋊Q8—224no—
320C2×C4⋊Q8C2×D1111yescharacteristic
321C2×#127—111no—
322C2×#124—221no—
323C2×#121—111no—
324C2×#121—111no—
325C2×#121—221no—
326C2×C4×D4—111no—
327C2×C4×D4—221no—
328C2×C4×D4C2×D1111yescharacteristic
329C22×C4⋊C4—221no—
330C22×C4⋊C4—221no—
331C22×C42—111no—
332#492—1116no—
333#487—1116no—
334#461—118no—
335#461—118no—
336#461—118no—
337#461C2×D1118yescomplemented
338#448—1116no—
339#448—1116no—
340#431—118no—
341C2×C4⋊C8—111no—
342C2×C4⋊C8C2×D1111yescharacteristic
343C2×#103—112no—
344C2×#103—112no—
345C2×#103—112no—
346C2×#103C2×D1112yes—
347C2×C22⋊C8—112no—
348C2×C4×C8—112no—
349C22×C11—42no—
350C22×C11—42no—
351C22×C11—42no—
352C22×C11—84no—
353C22×C11#53512yes—
354C22×C11C22×SD1612yes—
355C22×C11C2×#13712yes—
356C22×C11C23×D411yescharacteristic
357C2×D11—22no—
358C2×D11—28no—
359C2×D11—22no—
360C2×D11—42no—
361C2×D11—42no—
362C2×D11—42no—
363C2×D11—84no—
364C2×D11C22×SD1614yes—
365C4×C11—22no—
366C4×C11—44no—
367C4×C11—42no—
368C4×C11#53512yes—
369C4×C11C22×SD1614yes—
370C4×C11C2×H(5,𝔽2)11yescharacteristic
371C4×C11C2×H(5,𝔽2)11yescharacteristic
372Dic11—22no—
373Dic11—44no—
374Dic11—42no—
375Dic11C22×SD1614yes—
376Dic11C2×#13714yes—
377C2×#41—228no—
378C2×#41—448no—
379C22×Q8—118no—
380C22×Q8—112no—
381C22×Q8—221no—
382C22×Q8—222no—
383C22×Q8—224no—
384C22×Q8—444no—
385C22×Q8—444no—
386C22×Q8C22×D1112yes—
387C22×D4—111no—
388C22×D4—221no—
389C22×D4—221no—
390C22×D4—221no—
391C22×D4—221no—
392C22×D4C22×D1111yescharacteristic
393C23×C4—21no—
394C23×C4—111no—
395C23×C4—111no—
396C23×C4—111no—
397C23×C4—222no—
398C23×C4—221no—
399C2×SD16—44no—
400C2×SD16—118no—
401C2×SD16—118no—
402C2×SD16—118no—
403C2×SD16—444no—
404C2×SD16—444no—
405C2×SD16—444no—
406C2×SD16C22×D1118yes—
407C22×C8—112no—
408C22×C8C22×D1112yes—
409C4⋊Q8—22no—
410C4⋊Q8—114no—
411C4⋊Q8—118no—
412C4⋊Q8—114no—
413C4⋊Q8—228no—
414C4⋊Q8—228no—
415C4⋊Q8—222no—
416C4⋊Q8—224no—
417C4⋊Q8—222no—
418C4⋊Q8C22×D1114yes—
419#127—114no—
420#127—222no—
421#124—228no—
422#121—114no—
423#121—114no—
424#121—228no—
425#121—222no—
426#121—222no—
427C4×D4—22no—
428C4×D4—114no—
429C4×D4—228no—
430C4×D4—222no—
431C4×D4C22×D1114yes—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—111no—
435C2×C4⋊C4—228no—
436C2×C4⋊C4—228no—
437C2×C4⋊C4—222no—
438C2×C4⋊C4—222no—
439C2×C4⋊C4—221no—
440C2×C4⋊C4—221no—
441C2×C4⋊C4—221no—
442C2×C4⋊C4C22×D1111yescharacteristic
443C2×C22⋊C4—21no—
444C2×C22⋊C4—221no—
445C2×C22⋊C4—221no—
446C2×C22⋊C4—221no—
447C2×C42—111no—
448C2×C42—111no—
449C2×C42—111no—
450C2×C42—114no—
451C2×C42—114no—
452C2×C42C22×D1111yescharacteristic
453C4⋊C8—114no—
454C4⋊C8C22×D1114yes—
455#103—118no—
456#103—118no—
457#103—118no—
458#103C22×D1118yes—
459C22⋊C8—118no—
460C4×C8—118no—
461C2×C11—82no—
462C2×C11#320614yescomplemented
463C2×C11C2×#53511yescharacteristic
464C2×C11C23×SD1611yescharacteristic
465C2×C11C22×#13711yescharacteristic
466D11—24no—
467D11—82no—
468C24—21no—
469C24—111no—
470C24—221no—
471#41—4432no—
472C2×Q8—22no—
473C2×Q8—24no—
474C2×Q8—24no—
475C2×Q8—114no—
476C2×Q8—224no—
477C2×Q8—228no—
478C2×Q8—222no—
479C2×Q8—224no—
480C2×Q8—224no—
481C2×Q8—444no—
482C2×Q8—448no—
483C2×Q8—448no—
484C2×Q8—448no—
485C2×Q8—4416no—
486C2×Q8C23×D1114yes—
487C2×D4—21no—
488C2×D4—22no—
489C2×D4—22no—
490C2×D4—112no—
491C2×D4—224no—
492C2×D4—224no—
493C2×D4—224no—
494C2×D4—224no—
495C2×D4—221no—
496C2×D4—222no—
497C2×D4—222no—
498C2×D4—444no—
499C2×D4—444no—
500C2×D4—444no—
501C2×D4—444no—
502C2×D4C23×D1112yes—
503C22×C4—21no—
504C22×C4—22no—
505C22×C4—24no—
506C22×C4—44no—
507C22×C4—111no—
508C22×C4—111no—
509C22×C4—118no—
510C22×C4—114no—
511C22×C4—111no—
512C22×C4—114no—
513C22×C4—112no—
514C22×C4—112no—
515C22×C4—224no—
516C22×C4—228no—
517C22×C4—222no—
518C22×C4—222no—
519C22×C4—221no—
520C22×C4—222no—
521C22×C4—224no—
522C22×C4—448no—
523C22×C4—444no—
524C22×C4D4×D1111yescharacteristic
525C22×C4D4×D1111yescharacteristic
526C22×C4C23×D1111yescharacteristic
527SD16—48no—
528SD16—448no—
529SD16—448no—
530SD16—448no—
531C2×C8—24no—
532C2×C8—114no—
533C2×C8—224no—
534C2×C8C23×D1114yes—
535C4⋊C4—24no—
536C4⋊C4—24no—
537C4⋊C4—21no—
538C4⋊C4—112no—
539C4⋊C4—228no—
540C4⋊C4—228no—
541C4⋊C4—224no—
542C4⋊C4—221no—
543C4⋊C4—224no—
544C4⋊C4—224no—
545C4⋊C4C23×D1112yes—
546C22⋊C4—24no—
547C22⋊C4—224no—
548C22⋊C4—224no—
549C22⋊C4—224no—
550C42—114no—
551C42—114no—
552C42—112no—
553C42—112no—
554C42D4×D1112yes—
555C42C23×D1112yes—
556C11C2×#320611yescharacteristic, complemented, Sylow
557C23—22no—
558C23—42no—
559C23—42no—
560C23—42no—
561C23—114no—
562C23—112no—
563C23—222no—
564C23—222no—
565C23—222no—
566C23—442no—
567C23—442no—
568C23—442no—
569C23C2×D4×D1111yescharacteristic
570Q8—24no—
571Q8—24no—
572Q8—44no—
573Q8—224no—
574Q8—224no—
575Q8—448no—
576Q8—4416no—
577Q8—444no—
578D4—22no—
579D4—22no—
580D4—42no—
581D4—222no—
582D4—222no—
583D4—448no—
584D4—448no—
585D4—448no—
586D4—448no—
587D4—442no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—24no—
591C2×C4—42no—
592C2×C4—44no—
593C2×C4—48no—
594C2×C4—114no—
595C2×C4—114no—
596C2×C4—112no—
597C2×C4—112no—
598C2×C4—1116no—
599C2×C4—112no—
600C2×C4—228no—
601C2×C4—222no—
602C2×C4—224no—
603C2×C4—222no—
604C2×C4—222no—
605C2×C4—222no—
606C2×C4—224no—
607C2×C4—4416no—
608C2×C4—442no—
609C2×C4—444no—
610C2×C4—448no—
611C2×C4SD16×D1114yes—
612C2×C4C2×D4×D1112yes—
613C2×C4C2×D4×D1112yes—
614C2×C4C2×D4×D1111yescharacteristic
615C2×C4#6703712yes—
616C2×C4#6704212yes—
617C2×C4C24×D1111yescharacteristic
618C8—24no—
619C8—224no—
620C22—42no—
621C22—42no—
622C22—42no—
623C22—84no—
624C22—114no—
625C22—222no—
626C22—222no—
627C22—228no—
628C22—442no—
629C22—442no—
630C22—442no—
631C22—884no—
632C22#1062313812yes—
633C22C2×SD16×D1112yes—
634C22D11×#13712yes—
635C22C22×D4×D1111yescharacteristic
636C4—22no—
637C4—44no—
638C4—42no—
639C4—114no—
640C4—114no—
641C4—222no—
642C4—444no—
643C4—442no—
644C4#1062313812yes—
645C4C2×SD16×D1114yes—
646C4C2×#6703711yescharacteristic
647C4C2×#6704211yescharacteristic
648C2—82no—
649C2—224no—
650C2—882no—
651C2#1307954014yesdirect product factor
652C2C2×#1062313811yescharacteristic
653C2C22×SD16×D1111yescharacteristic
654C2C2×D11×#13711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#461C2
socleC23×C11C22×D4
prime radicalC2×#10623079C2
hypercenterC2×#461D11
hypocenterC11C2×#3206
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#461

Complements

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

NH ≅ G/Ntype
2. C2×D11×C4⋊Q8C2semidirect
3. #13079540C2direct (N × H)
4. C2×#10622788C2semidirect
5. C2×#10622405C2semidirect
6. C2×#10622454C2semidirect
7. C2×#10622632C2semidirect
8. C2×#10622696C2semidirect
9. C2×#10622419C2semidirect
10. C2×#10622783C2semidirect
11. C2×#10622446C2semidirect
12. C2×C11×#461C2semidirect
26. D11×C4⋊Q8C22semidirect
40. C11×#461C22semidirect
44. #10622788C22semidirect
45. #10622783C22semidirect
49. #10622696C22semidirect
50. #10622632C22semidirect
53. #10622454C22semidirect
54. #10622446C22semidirect
55. #10622419C22semidirect
56. #10622405C22semidirect
188. C2×C4×D11SD16semidirect
238. C2×#461D11semidirect
297. C4×D11C2×SD16semidirect
337. #461C2×D11semidirect
462. C2×C11#3206semidirect
556. C11C2×#3206semidirect
651. C2#13079540direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230792
C2×D11×C4⋊Q82
#130795402
C2×#106227882
C2×#106224052
C2×#106224542
C2×#106226322
C2×#106226962
C2×#106224192
C2×#106227832
C2×#106224462
C2×C11×#4612
C2×#320611