Finite Group Databasebeta

← C2×#13080005 #15626647

Subgroups — C2×#13080005 #15626647

Order 2816.

2146 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623259C211yesmaximal, characteristic, complemented
2C2×#10623079C211yesmaximal, characteristic
3#13080005C2116yesmaximal, direct product factor
4C2×#10622488C212yesmaximal, complemented
5C2×#10622700C211yesmaximal, characteristic, complemented
6C2×#10622499C212yesmaximal, complemented
7C2×#10622393C212yesmaximal, complemented
8C2×#10622375C212yesmaximal, complemented
9C2×#10622454C211yesmaximal, characteristic, complemented
10C2×#10622632C211yesmaximal, characteristic, complemented
11C2×#10622450C211yesmaximal, characteristic, complemented
12C2×C11×#474C211yesmaximal, characteristic, complemented
13C22×#4339—21no—
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C4×D4×C11C2211yescharacteristic
16C2×#66999—21no—
17C2×Q8×Dic11—21no—
18C2×#66993C2211yescharacteristic
19C2×#66991C2211yescharacteristic
20C22×#4324C2212yes—
21C2×C4×C22⋊D11—21no—
22C22×#4314C2212yes—
23C22×#4313C2212yes—
24#10623259—24no—
25#10623259C2218yescomplemented
26#10623079—24no—
27#10623079C2218yes—
28C2×#66950C2212yes—
29C2×#66948C2211yescharacteristic
30C2×#66945—21no—
31C2×#66943—21no—
32C2×#66941C2211yescharacteristic
33C2×#66940C2212yes—
34C2×#66938—21no—
35C2×#66937—21no—
36C2×C4×D44C2211yescharacteristic
37C2×C42×D11C2211yescharacteristic
38C2×#66922C2211yescharacteristic
39C11×#474C2218yescomplemented
40C2×C11×#107C2212yes—
41C2×C11×C4⋊C8C2211yescharacteristic
42C2×C11×#102C2212yes—
43C2×#66880C2212yes—
44C2×Dic11⋊C8C2212yes—
45#10622700C2218yescomplemented
46#10622632C2218yescomplemented
47C2×#66874C2212yes—
48C2×#66873C2212yes—
49C2×#66871C2212yes—
50C2×C4⋊(C11⋊C8)C2211yescharacteristic
51#10622499C22116yescomplemented
52#10622488C22116yescomplemented
53#10622454C2218yescomplemented
54#10622450C2218yescomplemented
55#10622393C22116yescomplemented
56#10622375C22116yescomplemented
57C22×Q8×C11—21no—
58C22×D4×C11C2311yescharacteristic
59C23×C4×C11—21no—
60C22×C22⋊D11—21no—
61C22×C22⋊D11—21no—
62C22×C22⋊D11—21no—
63C2×#4339—28no—
64C2×#4339—48no—
65C22×D44—21no—
66C22×D44C2311yescharacteristic
67C22×C4×D11—21no—
68C22×C4×D11D411yescharacteristic
69C22×C4×D11D411yescharacteristic
70C22×C4×D11C2311yescharacteristic
71C22×Dic22—21no—
72C22×Dic22C2312yes—
73C22×C8×C11C2312yes—
74C11×C4⋊Q8—22no—
75C11×C4⋊Q8C2314yes—
76C4×D4×C11—22no—
77C4×D4×C11C2314yes—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4C2312yes—
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C22⋊C4—21no—
82C2×C42×C11C2311yescharacteristic
83C2×C22⋊Dic11—21no—
84#66999—28no—
85Q8×Dic11—28no—
86#66993—22no—
87#66993C2314yes—
88#66991—22no—
89#66991C2314yes—
90C2×#4324—44no—
91C2×#4324C2318yes—
92C4×C22⋊D11—28no—
93C2×(C2×D11)⋊C4—22no—
94C2×(C2×D11)⋊C4—21no—
95C2×(C2×D11)⋊C4—21no—
96C2×C4⋊Dic11—21no—
97C2×C4⋊Dic11—21no—
98C2×C4⋊Dic11—22no—
99C2×C4⋊Dic11C2311yescharacteristic
100C2×Dic11⋊C4—21no—
101C2×Dic11⋊C4—22no—
102C2×C4×Dic11—22no—
103C2×C4×Dic11D411yescharacteristic
104C2×C4×Dic11D411yescharacteristic
105C2×C4×Dic11C2311yescharacteristic
106C22×C11⋊C8C2312yes—
107C2×#4314—44no—
108C2×#4314C2318yes—
109C2×#4313—44no—
110C2×#4313C2318yes—
111#66950—24no—
112#66950C2318yes—
113#66948—22no—
114#66948C2314yes—
115#66945—28no—
116#66943—28no—
117#66941—22no—
118#66941C2314yes—
119#66940—24no—
120#66940C2318yes—
121#66938—28no—
122#66937—28no—
123C4×D44—22no—
124C4×D44C2314yes—
125C42×D11D414yes—
126C42×D11C2314yes—
127#66922—22no—
128#66922C2314yes—
129C11×#107C2318yes—
130C11×C4⋊C8C2314yes—
131C11×#102C2318yes—
132#66880C2318yes—
133Dic11⋊C8C2318yes—
134#66874C2318yes—
135#66873C2318yes—
136#66871C2318yes—
137C4⋊(C11⋊C8)C2314yes—
138C2×#3254—111nomaximal, Sylow
139C24×C11—21no—
140C23×D11—21no—
141C23×D11C2×D411yescharacteristic
142C2×Q8×C11—24no—
143C2×Q8×C11—44no—
144C2×D4×C11—21no—
145C2×D4×C11—22no—
146C2×D4×C11—22no—
147C2×D4×C11C2412yes—
148C22×C4×C11—22no—
149C22×C4×C11—21no—
150C22×C4×C11—24no—
151C22×C4×C11—44no—
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2411yescharacteristic
155C2×C22⋊D11—24no—
156C2×C22⋊D11—24no—
157C2×C22⋊D11—24no—
158C2×C22⋊D11—44no—
159C2×C22⋊D11—44no—
160C2×C22⋊D11—44no—
161C22×Dic11—22no—
162C22×Dic11—21no—
163C22×Dic11C2×D411yescharacteristic
164C22×Dic11C2×D411yescharacteristic
165C22×Dic11C2×D411yescharacteristic
166#4339—432no—
167C2×D44—24no—
168C2×D44—21no—
169C2×D44—22no—
170C2×D44—22no—
171C2×D44—44no—
172C2×D44C2412yes—
173C2×C4×D11—24no—
174C2×C4×D11—24no—
175C2×C4×D11—24no—
176C2×C4×D11—22no—
177C2×C4×D11—22no—
178C2×C4×D11—44no—
179C2×C4×D11C2×D412yes—
180C2×C4×D11C2×D414yes—
181C2×C4×D11C2×D414yes—
182C2×C4×D11C2412yes—
183C2×Dic22—24no—
184C2×Dic22—22no—
185C2×Dic22—24no—
186C2×Dic22—24no—
187C2×Dic22—44no—
188C2×Dic22C2414yes—
189C2×C8×C11—24no—
190C2×C8×C11C2414yes—
191C11×C4⋊C4—22no—
192C11×C4⋊C4—21no—
193C11×C4⋊C4—24no—
194C11×C4⋊C4C2414yes—
195C11×C4⋊C4C2412yes—
196C11×C22⋊C4—24no—
197C42×C11C2×D412yes—
198C42×C11C2412yes—
199C22⋊Dic11—24no—
200#4324—48no—
201(C2×D11)⋊C4—24no—
202(C2×D11)⋊C4—28no—
203(C2×D11)⋊C4—24no—
204C4⋊Dic11—28no—
205C4⋊Dic11—24no—
206C4⋊Dic11—24no—
207C4⋊Dic11—21no—
208C4⋊Dic11C2412yes—
209Dic11⋊C4—24no—
210Dic11⋊C4—28no—
211C4×Dic11—28no—
212C4×Dic11C2×D412yes—
213C4×Dic11C2×D414yes—
214C4×Dic11C2×D414yes—
215C4×Dic11C2412yes—
216C2×C11⋊C8—24no—
217C2×C11⋊C8C2414yes—
218#4314—48no—
219#4313—48no—
220C2×#533—111no—
221C2×#532—111no—
222#3254—1116no—
223C2×#477—112no—
224C2×#474—111no—
225C2×#474D1111yescharacteristic, complemented
226C2×#468—112no—
227C2×#468—112no—
228C2×#460—112no—
229C2×#461—111no—
230C2×#461—111no—
231C2×#423—111no—
232C23×C11—22no—
233C23×C11—42no—
234C23×C11—42no—
235C23×C11—42no—
236C23×C11C22×D411yescharacteristic
237C22×D11—22no—
238C22×D11—22no—
239C22×D11—22no—
240C22×D11—22no—
241C22×D11—42no—
242C22×D11—42no—
243C22×D11—42no—
244C22×D11C22×D412yes—
245Q8×C11—48no—
246D4×C11—22no—
247D4×C11—22no—
248D4×C11—42no—
249C2×C4×C11—22no—
250C2×C4×C11—24no—
251C2×C4×C11—22no—
252C2×C4×C11—42no—
253C2×C4×C11—44no—
254C2×C4×C11—48no—
255C2×C4×C11AGL(1,ℤ/8)14yes—
256C2×C4×C11C22×D412yes—
257C2×C4×C11C22×D411yescharacteristic
258C2×C4×C11C22×D412yes—
259C2×C4×C11H(5,𝔽2)12yes—
260C2×C4×C112−1+412yes—
261C2×C4×C11C2511yescharacteristic
262C22⋊D11—48no—
263C22⋊D11—48no—
264C22⋊D11—48no—
265C2×Dic11—22no—
266C2×Dic11—22no—
267C2×Dic11—24no—
268C2×Dic11—22no—
269C2×Dic11—44no—
270C2×Dic11—42no—
271C2×Dic11#13714yes—
272C2×Dic11C22×D412yes—
273C2×Dic11C22×D412yes—
274C2×Dic11C22×D412yes—
275D44—22no—
276D44—22no—
277D44—48no—
278D44—42no—
279C4×D11—24no—
280C4×D11—28no—
281C4×D11—22no—
282C4×D11—22no—
283C4×D11—28no—
284C4×D11—48no—
285Dic22—24no—
286Dic22—24no—
287Dic22—48no—
288Dic22—44no—
289C8×C11—24no—
290C11⋊C8—24no—
291C22×#41—221no—
292C22×SD16—112no—
293C22×SD16—112no—
294C22×M16—112no—
295#533—118no—
296#533—224no—
297#532—118no—
298#532—224no—
299C2×C4⋊Q8—111no—
300C2×C4⋊Q8—111no—
301C2×C4⋊Q8C2×D1111yescharacteristic
302C2×#127—111no—
303C2×#125—221no—
304C2×#124—221no—
305C2×C22⋊Q8—112no—
306C2×C22⋊Q8—221no—
307C2×#121—111no—
308C2×#121—111no—
309C2×#121—221no—
310C2×C4×Q8—112no—
311C2×C4×Q8—221no—
312C2×C4×D4—111no—
313C2×C4×D4—221no—
314C2×C4×D4C2×D1111yescharacteristic
315C2×#117—221no—
316C22×C42—111no—
317#477—1116no—
318#474—118no—
319#474C2×D1118yescomplemented
320#468—1116no—
321#468—1116no—
322#461—118no—
323#461—118no—
324#460—1116no—
325C2×#107—112no—
326C2×#107C2×D1112yes—
327#423—118no—
328C2×C4⋊C8—112no—
329C2×C4⋊C8—111no—
330C2×C4⋊C8C2×D1111yescharacteristic
331C2×#103—112no—
332C2×#103—112no—
333C2×#102—112no—
334C2×#102C2×D1112yes—
335C22×C11—42no—
336C22×C11—42no—
337C22×C11—42no—
338C22×C11—84no—
339C22×C11#53712yes—
340C22×C11C2×AGL(1,ℤ/8)12yes—
341C22×C11C2×#13712yes—
342C22×C11C23×D411yescharacteristic
343C2×D11—22no—
344C2×D11—22no—
345C2×D11—22no—
346C2×D11—44no—
347C2×D11—42no—
348C2×D11—42no—
349C2×D11—42no—
350C2×D11—84no—
351C4×C11—22no—
352C4×C11—42no—
353C4×C11—44no—
354C4×C11#53712yes—
355C4×C11C2×AGL(1,ℤ/8)14yes—
356C4×C11C2×H(5,𝔽2)11yescharacteristic
357C4×C11C2×2−1+411yescharacteristic
358Dic11—22no—
359Dic11—22no—
360Dic11—44no—
361Dic11—42no—
362Dic11C2×#13714yes—
363C2×#41—228no—
364C2×#41—448no—
365C22×Q8—21no—
366C22×Q8—112no—
367C22×Q8—221no—
368C22×D4—111no—
369C22×D4—221no—
370C22×D4—221no—
371C22×D4—221no—
372C22×D4—221no—
373C22×D4C22×D1111yescharacteristic
374C23×C4—21no—
375C23×C4—111no—
376C23×C4—111no—
377C23×C4—111no—
378C23×C4—221no—
379C2×SD16—118no—
380C2×SD16—118no—
381C2×SD16—444no—
382C2×SD16—444no—
383C2×M16—118no—
384C2×M16—444no—
385C22×C8—112no—
386C22×C8C22×D1112yes—
387C4⋊Q8—22no—
388C4⋊Q8—114no—
389C4⋊Q8—114no—
390C4⋊Q8—222no—
391C4⋊Q8—222no—
392C4⋊Q8C22×D1114yes—
393#127—114no—
394#127—222no—
395#125—228no—
396#124—228no—
397C22⋊Q8—118no—
398C22⋊Q8—224no—
399C22⋊Q8—228no—
400#121—114no—
401#121—114no—
402#121—228no—
403#121—222no—
404#121—222no—
405C4×Q8—118no—
406C4×Q8—224no—
407C4×Q8—228no—
408C4×D4—22no—
409C4×D4—114no—
410C4×D4—228no—
411C4×D4—222no—
412C4×D4C22×D1114yes—
413#117—228no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—111no—
416C2×C4⋊C4—221no—
417C2×C4⋊C4—222no—
418C2×C4⋊C4—222no—
419C2×C4⋊C4—221no—
420C2×C4⋊C4—221no—
421C2×C4⋊C4C22×D1111yescharacteristic
422C2×C4⋊C4C22×D1112yes—
423C2×C22⋊C4—21no—
424C2×C22⋊C4—221no—
425C2×C22⋊C4—222no—
426C2×C22⋊C4—221no—
427C2×C22⋊C4—221no—
428C2×C42—111no—
429C2×C42—111no—
430C2×C42—111no—
431C2×C42—114no—
432C2×C42—114no—
433C2×C42—222no—
434C2×C42C22×D1111yescharacteristic
435#107—118no—
436#107C22×D1118yes—
437C4⋊C8—118no—
438C4⋊C8—114no—
439C4⋊C8C22×D1114yes—
440#103—118no—
441#103—118no—
442#102—118no—
443#102C22×D1118yes—
444C2×C11—82no—
445C2×C11#325414yescomplemented
446C2×C11C2×#53711yescharacteristic
447C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
448C2×C11C22×#13711yescharacteristic
449D11—42no—
450D11—82no—
451C24—21no—
452C24—111no—
453C24—221no—
454#41—4432no—
455C2×Q8—24no—
456C2×Q8—44no—
457C2×Q8—114no—
458C2×Q8—224no—
459C2×Q8—222no—
460C2×Q8—224no—
461C2×Q8—224no—
462C2×Q8—444no—
463C2×D4—21no—
464C2×D4—22no—
465C2×D4—22no—
466C2×D4—112no—
467C2×D4—224no—
468C2×D4—224no—
469C2×D4—224no—
470C2×D4—224no—
471C2×D4—221no—
472C2×D4—222no—
473C2×D4—222no—
474C2×D4—444no—
475C2×D4—444no—
476C2×D4—444no—
477C2×D4—444no—
478C2×D4C23×D1112yes—
479C22×C4—22no—
480C22×C4—21no—
481C22×C4—24no—
482C22×C4—44no—
483C22×C4—111no—
484C22×C4—111no—
485C22×C4—111no—
486C22×C4—114no—
487C22×C4—112no—
488C22×C4—114no—
489C22×C4—112no—
490C22×C4—224no—
491C22×C4—224no—
492C22×C4—222no—
493C22×C4—222no—
494C22×C4—222no—
495C22×C4—221no—
496C22×C4—224no—
497C22×C4—444no—
498C22×C4D4×D1111yescharacteristic
499C22×C4D4×D1111yescharacteristic
500C22×C4C23×D1111yescharacteristic
501SD16—448no—
502SD16—448no—
503M16—448no—
504C2×C8—24no—
505C2×C8—114no—
506C2×C8—224no—
507C2×C8C23×D1114yes—
508C4⋊C4—24no—
509C4⋊C4—21no—
510C4⋊C4—22no—
511C4⋊C4—112no—
512C4⋊C4—224no—
513C4⋊C4—228no—
514C4⋊C4—228no—
515C4⋊C4—221no—
516C4⋊C4—224no—
517C4⋊C4—224no—
518C4⋊C4C23×D1114yes—
519C4⋊C4C23×D1112yes—
520C22⋊C4—24no—
521C22⋊C4—224no—
522C22⋊C4—228no—
523C22⋊C4—224no—
524C22⋊C4—224no—
525C42—114no—
526C42—112no—
527C42—114no—
528C42—112no—
529C42—228no—
530C42D4×D1112yes—
531C42C23×D1112yes—
532C11C2×#325411yescharacteristic, complemented, Sylow
533C23—22no—
534C23—42no—
535C23—42no—
536C23—42no—
537C23—112no—
538C23—222no—
539C23—222no—
540C23—222no—
541C23—222no—
542C23—442no—
543C23—442no—
544C23—442no—
545C23C2×D4×D1111yescharacteristic
546Q8—48no—
547Q8—224no—
548Q8—224no—
549Q8—448no—
550Q8—444no—
551D4—22no—
552D4—22no—
553D4—42no—
554D4—222no—
555D4—222no—
556D4—448no—
557D4—448no—
558D4—448no—
559D4—448no—
560D4—442no—
561C2×C4—22no—
562C2×C4—24no—
563C2×C4—22no—
564C2×C4—42no—
565C2×C4—44no—
566C2×C4—48no—
567C2×C4—114no—
568C2×C4—112no—
569C2×C4—112no—
570C2×C4—112no—
571C2×C4—228no—
572C2×C4—222no—
573C2×C4—222no—
574C2×C4—228no—
575C2×C4—224no—
576C2×C4—222no—
577C2×C4—222no—
578C2×C4—224no—
579C2×C4—222no—
580C2×C4—442no—
581C2×C4—444no—
582C2×C4—448no—
583C2×C4#6696414yes—
584C2×C4C2×D4×D1112yes—
585C2×C4C2×D4×D1112yes—
586C2×C4C2×D4×D1111yescharacteristic
587C2×C4#6704012yes—
588C2×C4#6704212yes—
589C2×C4C24×D1111yescharacteristic
590C8—24no—
591C8—224no—
592C22—42no—
593C22—42no—
594C22—42no—
595C22—84no—
596C22—222no—
597C22—222no—
598C22—222no—
599C22—444no—
600C22—442no—
601C22—442no—
602C22—442no—
603C22—884no—
604C22#1062316012yes—
605C22C2×#6696412yes—
606C22D11×#13712yes—
607C22C22×D4×D1111yescharacteristic
608C4—22no—
609C4—42no—
610C4—44no—
611C4—114no—
612C4—222no—
613C4—222no—
614C4—444no—
615C4—442no—
616C4#1062316012yes—
617C4C2×#6696414yes—
618C4C2×#6704011yescharacteristic
619C4C2×#6704211yescharacteristic
620C2—82no—
621C2—442no—
622C2—882no—
623C2#1308000514yesdirect product factor
624C2C2×#1062316011yescharacteristic
625C2C22×#6696411yescharacteristic
626C2C2×D11×#13711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#474C2
socleC23×C11C22×D4
prime radicalC2×#10623079C2
hypercenterC2×#474D11
hypocenterC11C2×#3254
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#474

Complements

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

NH ≅ G/Ntype
1. C2×#10623259C2semidirect
3. #13080005C2direct (N × H)
4. C2×#10622488C2semidirect
5. C2×#10622700C2semidirect
6. C2×#10622499C2semidirect
7. C2×#10622393C2semidirect
8. C2×#10622375C2semidirect
9. C2×#10622454C2semidirect
10. C2×#10622632C2semidirect
11. C2×#10622450C2semidirect
12. C2×C11×#474C2semidirect
25. #10623259C22semidirect
39. C11×#474C22semidirect
45. #10622700C22semidirect
46. #10622632C22semidirect
51. #10622499C22semidirect
52. #10622488C22semidirect
53. #10622454C22semidirect
54. #10622450C22semidirect
55. #10622393C22semidirect
56. #10622375C22semidirect
225. C2×#474D11semidirect
319. #474C2×D11semidirect
445. C2×C11#3254semidirect
532. C11C2×#3254semidirect
623. C2#13080005direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232592
C2×#106230792
#130800052
C2×#106224882
C2×#106227002
C2×#106224992
C2×#106223932
C2×#106223752
C2×#106224542
C2×#106226322
C2×#106224502
C2×C11×#4742
C2×#325411