Finite Group Databasebeta

← C2×#13079931 #15626554

Subgroups — C2×#13079931 #15626554

Order 2816.

2178 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623109C211yesmaximal, characteristic, complemented
2C2×#10623256C211yesmaximal, characteristic
3#13079931C2116yesmaximal, direct product factor
4C2×#10622707C211yesmaximal, characteristic, complemented
5C2×#10622483C212yesmaximal, complemented
6C2×#10622420C212yesmaximal, complemented
7C2×#10622477C212yesmaximal, complemented
8C2×#10622461C211yesmaximal, characteristic, complemented
9C2×#10622640C211yesmaximal, characteristic, complemented
10C2×#10622431C212yesmaximal, complemented
11C2×D11×C4⋊C8C211yesmaximal, characteristic, complemented
12C2×C11×#475C211yesmaximal, characteristic, complemented
13C22×#4343—21no—
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C4×Q8×C11C2211yescharacteristic
16C2×#67000—21no—
17C2×#66999C2211yescharacteristic
18C2×#66997C2211yescharacteristic
19C22×#4325C2212yes—
20C22×#4314C2212yes—
21C22×C8×D11C2212yes—
22#10623256—24no—
23#10623256C2218yes—
24#10623109—24no—
25#10623109C2218yescomplemented
26C2×#66950C2211yescharacteristic
27C2×#66949—21no—
28C2×#66948—21no—
29C2×#66948C2212yes—
30C2×#66946—21no—
31C2×#66946C2212yes—
32C2×#66942—21no—
33C2×#66941C2211yescharacteristic
34C2×#66927C2211yescharacteristic
35C2×#66925—21no—
36C2×C42×D11C2211yescharacteristic
37C2×C4×Dic22—21no—
38C2×C4×Dic22C2211yescharacteristic
39C11×#475C2218yescomplemented
40C2×C11×#106C2212yes—
41C2×C11×C4⋊C8C2211yescharacteristic
42C2×C11×#103C2212yes—
43C2×#66885C2212yes—
44C2×Dic11⋊C8C2212yes—
45#10622707C2218yescomplemented
46#10622640C2218yescomplemented
47C2×#66874C2212yes—
48C2×#66873C2212yes—
49C2×#66872C2212yes—
50C2×C4⋊(C11⋊C8)C2211yescharacteristic
51#10622483C22116yescomplemented
52#10622477C22116yescomplemented
53#10622461C2218yescomplemented
54D11×C4⋊C8C2218yescomplemented
55#10622431C22116yescomplemented
56#10622420C22116yescomplemented
57C22×Q8×C11—21no—
58C22×Q8×C11C2311yescharacteristic
59C2×#4343—28no—
60C2×#4343—48no—
61C22×D44—22no—
62C22×D44—21no—
63C22×D44—21no—
64C22×D44C2312yes—
65C22×C4×D11—22no—
66C22×C4×D11D411yescharacteristic
67C22×C4×D11D411yescharacteristic
68C22×C4×D11C2311yescharacteristic
69C22×Dic22—21no—
70C22×Dic22C2311yescharacteristic
71C22×C8×C11C2312yes—
72C11×C4⋊Q8—22no—
73C11×C4⋊Q8C2314yes—
74C4×Q8×C11—22no—
75C4×Q8×C11C2314yes—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C4⋊C4C2312yes—
80C2×C42×C11—21no—
81C2×C42×C11C2311yescharacteristic
82#67000—28no—
83#66999—22no—
84#66999C2314yes—
85#66997—22no—
86#66997C2314yes—
87C2×#4325—44no—
88C2×#4325C2318yes—
89C2×(C2×D11)⋊C4—21no—
90C2×(C2×D11)⋊C4—21no—
91C2×(C2×D11)⋊C4—22no—
92C2×(C2×D11)⋊C4—22no—
93C2×C4⋊Dic11—21no—
94C2×C4⋊Dic11C2311yescharacteristic
95C2×Dic11⋊C4—21no—
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4—21no—
98C2×Dic11⋊C4—21no—
99C2×Dic11⋊C4—21no—
100C2×C4×Dic11—21no—
101C2×C4×Dic11D411yescharacteristic
102C2×C4×Dic11D411yescharacteristic
103C2×C4×Dic11C2311yescharacteristic
104C22×C11⋊C8C2312yes—
105C2×#4314—44no—
106C2×#4314C2318yes—
107C2×C8×D11—44no—
108C2×C8×D11C2318yes—
109#66950—22no—
110#66950C2314yes—
111#66949—28no—
112#66948—24no—
113#66948—28no—
114#66948C2318yes—
115#66946—24no—
116#66946—28no—
117#66946C2318yes—
118#66942—28no—
119#66941—22no—
120#66941C2314yes—
121#66927—22no—
122#66927C2314yes—
123#66925—28no—
124C42×D11D414yes—
125C42×D11C2314yes—
126C4×Dic22—22no—
127C4×Dic22—28no—
128C4×Dic22C2314yes—
129C11×#106C2318yes—
130C11×C4⋊C8C2314yes—
131C11×#103C2318yes—
132#66885C2318yes—
133Dic11⋊C8C2318yes—
134#66874C2318yes—
135#66873C2318yes—
136#66872C2318yes—
137C4⋊(C11⋊C8)C2314yes—
138C2×#3246—111nomaximal, Sylow
139C23×D11—22no—
140C23×D11C2×D411yescharacteristic
141C2×Q8×C11—21no—
142C2×Q8×C11—24no—
143C2×Q8×C11—22no—
144C2×Q8×C11—22no—
145C2×Q8×C11—44no—
146C2×Q8×C11C2412yes—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—22no—
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2411yescharacteristic
153C22×Dic11—21no—
154C22×Dic11—21no—
155C22×Dic11C2×D411yescharacteristic
156C22×Dic11C2×D411yescharacteristic
157C22×Dic11C2×D411yescharacteristic
158#4343—432no—
159C2×D44—28no—
160C2×D44—22no—
161C2×D44—24no—
162C2×D44—24no—
163C2×D44—24no—
164C2×D44—24no—
165C2×D44—44no—
166C2×D44—48no—
167C2×D44—44no—
168C2×D44C2414yes—
169C2×C4×D11—28no—
170C2×C4×D11—22no—
171C2×C4×D11—22no—
172C2×C4×D11—42no—
173C2×C4×D11—48no—
174C2×C4×D11SD1618yescomplemented
175C2×C4×D11C2×D412yes—
176C2×C4×D11C2×D414yes—
177C2×C4×D11C2×D414yes—
178C2×C4×D11C2412yes—
179C2×Dic22—24no—
180C2×Dic22—21no—
181C2×Dic22—22no—
182C2×Dic22—22no—
183C2×Dic22—44no—
184C2×Dic22C2412yes—
185C2×C8×C11—24no—
186C2×C8×C11C2414yes—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—24no—
189C11×C4⋊C4—24no—
190C11×C4⋊C4—22no—
191C11×C4⋊C4C2414yes—
192C11×C4⋊C4C2412yes—
193C42×C11—24no—
194C42×C11C2×D412yes—
195C42×C11C2412yes—
196#4325—48no—
197(C2×D11)⋊C4—28no—
198(C2×D11)⋊C4—28no—
199(C2×D11)⋊C4—24no—
200(C2×D11)⋊C4—24no—
201C4⋊Dic11—24no—
202C4⋊Dic11—21no—
203C4⋊Dic11C2412yes—
204Dic11⋊C4—24no—
205Dic11⋊C4—24no—
206Dic11⋊C4—24no—
207Dic11⋊C4—24no—
208Dic11⋊C4—24no—
209C4×Dic11—24no—
210C4×Dic11C2×D414yes—
211C4×Dic11C2×D412yes—
212C4×Dic11C2×D414yes—
213C4×Dic11C2412yes—
214C2×C11⋊C8—24no—
215C2×C11⋊C8C2414yes—
216#4314—48no—
217C8×D11—48no—
218C2×#533—111no—
219C2×#532—111no—
220#3246—1116no—
221C2×#475—111no—
222C2×#475D1111yescharacteristic, complemented
223C2×#476—112no—
224C2×#465—112no—
225C2×#465—112no—
226C2×#460—111no—
227C2×#460—111no—
228C2×#461—112no—
229C22×C4⋊C8—111no—
230C23×C11C22×D411yescharacteristic
231C22×D11—22no—
232C22×D11—22no—
233C22×D11—24no—
234C22×D11—44no—
235C22×D11—44no—
236C22×D11—44no—
237C22×D11C2×SD1614yes—
238C22×D11C22×D412yes—
239Q8×C11—22no—
240Q8×C11—22no—
241Q8×C11—42no—
242Q8×C11—48no—
243C2×C4×C11—22no—
244C2×C4×C11—22no—
245C2×C4×C11—22no—
246C2×C4×C11—24no—
247C2×C4×C11—42no—
248C2×C4×C11—44no—
249C2×C4×C11—42no—
250C2×C4×C11C2×SD1614yes—
251C2×C4×C11C22×D412yes—
252C2×C4×C11C22×D411yescharacteristic
253C2×C4×C11C22×D412yes—
254C2×C4×C11H(5,𝔽2)12yes—
255C2×C4×C112−1+412yes—
256C2×C4×C11C2511yescharacteristic
257C2×Dic11—22no—
258C2×Dic11—22no—
259C2×Dic11—22no—
260C2×Dic11—22no—
261C2×Dic11—42no—
262C2×Dic11—42no—
263C2×Dic11C2×SD1614yes—
264C2×Dic11C22×D412yes—
265C2×Dic11C22×D412yes—
266C2×Dic11C22×D412yes—
267D44—24no—
268D44—24no—
269D44—48no—
270D44—416no—
271D44—44no—
272D44—48no—
273C4×D11—24no—
274C4×D11—22no—
275C4×D11—22no—
276C4×D11—44no—
277C4×D11—416no—
278C4×D11C2×SD16116yescomplemented
279Dic22—22no—
280Dic22—22no—
281Dic22—48no—
282Dic22—42no—
283C8×C11—24no—
284C11⋊C8—24no—
285C22×#41—221no—
286C22×SD16—112no—
287C22×SD16—112no—
288C23×C8—112no—
289#533—118no—
290#533—224no—
291#532—118no—
292#532—224no—
293C2×C4⋊Q8—111no—
294C2×C4⋊Q8—111no—
295C2×C4⋊Q8C2×D1111yescharacteristic
296C2×#127—111no—
297C2×#125—221no—
298C2×#124—221no—
299C2×C22⋊Q8—111no—
300C2×C22⋊Q8—111no—
301C2×C22⋊Q8—221no—
302C2×#121—112no—
303C2×#121—221no—
304C2×C4×Q8—111no—
305C2×C4×Q8—221no—
306C2×C4×Q8C2×D1111yescharacteristic
307C2×C4×D4—112no—
308C2×C4×D4—221no—
309C2×#117—221no—
310C22×C42—111no—
311#476—1116no—
312#475—118no—
313#475C2×D1118yescomplemented
314#465—1116no—
315#465—1116no—
316#461—1116no—
317#460—118no—
318#460—118no—
319C2×#106—112no—
320C2×#106C2×D1112yes—
321C2×C4⋊C8—112no—
322C2×C4⋊C8—111no—
323C2×C4⋊C8—118no—
324C2×C4⋊C8C2×D1111yescharacteristic
325C2×#103—112no—
326C2×#103C2×D1112yes—
327C2×#102—112no—
328C2×#102—112no—
329C22×C11#53712yes—
330C22×C11C22×SD1612yes—
331C22×C11#57512yes—
332C22×C11C23×D411yescharacteristic
333C2×D11—22no—
334C2×D11—28no—
335C2×D11—22no—
336C2×D11—44no—
337C2×D11—44no—
338C2×D11—44no—
339C2×D11—88no—
340C2×D11C22×SD1614yes—
341C4×C11—22no—
342C4×C11—42no—
343C4×C11—44no—
344C4×C11—42no—
345C4×C11#53712yes—
346C4×C11C22×SD1614yes—
347C4×C11C2×H(5,𝔽2)11yescharacteristic
348C4×C11C2×2−1+411yescharacteristic
349Dic11—22no—
350Dic11—22no—
351Dic11—42no—
352Dic11—42no—
353Dic11C22×SD1614yes—
354C2×#41—228no—
355C2×#41—448no—
356C22×Q8—21no—
357C22×Q8—111no—
358C22×Q8—221no—
359C22×Q8C22×D1111yescharacteristic
360C22×D4—112no—
361C22×D4—222no—
362C22×D4—221no—
363C22×D4—221no—
364C23×C4—111no—
365C23×C4—111no—
366C23×C4—111no—
367C23×C4—222no—
368C2×SD16—118no—
369C2×SD16—118no—
370C2×SD16—444no—
371C2×SD16—444no—
372C22×C8—112no—
373C22×C8—118no—
374C22×C8—444no—
375C22×C8C22×D1112yes—
376C4⋊Q8—22no—
377C4⋊Q8—114no—
378C4⋊Q8—114no—
379C4⋊Q8—222no—
380C4⋊Q8—222no—
381C4⋊Q8C22×D1114yes—
382#127—114no—
383#127—222no—
384#125—228no—
385#124—228no—
386C22⋊Q8—114no—
387C22⋊Q8—114no—
388C22⋊Q8—222no—
389C22⋊Q8—228no—
390C22⋊Q8—222no—
391#121—118no—
392#121—224no—
393#121—228no—
394C4×Q8—22no—
395C4×Q8—114no—
396C4×Q8—228no—
397C4×Q8—222no—
398C4×Q8C22×D1114yes—
399C4×D4—118no—
400C4×D4—224no—
401C4×D4—228no—
402#117—228no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—111no—
406C2×C4⋊C4—221no—
407C2×C4⋊C4—221no—
408C2×C4⋊C4—221no—
409C2×C4⋊C4—221no—
410C2×C4⋊C4—221no—
411C2×C4⋊C4—221no—
412C2×C4⋊C4C22×D1112yes—
413C2×C4⋊C4C22×D1111yescharacteristic
414C2×C22⋊C4—222no—
415C2×C22⋊C4—222no—
416C2×C22⋊C4—221no—
417C2×C22⋊C4—221no—
418C2×C42—21no—
419C2×C42—111no—
420C2×C42—111no—
421C2×C42—111no—
422C2×C42—114no—
423C2×C42—114no—
424C2×C42—221no—
425C2×C42C22×D1111yescharacteristic
426#106—118no—
427#106C22×D1118yes—
428C4⋊C8—118no—
429C4⋊C8—114no—
430C4⋊C8C22×D1114yes—
431#103—118no—
432#103C22×D1118yes—
433#102—118no—
434#102—118no—
435C2×C11#324614yescomplemented
436C2×C11C2×#53711yescharacteristic
437C2×C11C23×SD1611yescharacteristic
438C2×C11C2×#57511yescharacteristic
439D11—24no—
440D11—84no—
441C24—111no—
442C24—222no—
443#41—4432no—
444C2×Q8—21no—
445C2×Q8—24no—
446C2×Q8—22no—
447C2×Q8—22no—
448C2×Q8—44no—
449C2×Q8—112no—
450C2×Q8—224no—
451C2×Q8—221no—
452C2×Q8—222no—
453C2×Q8—222no—
454C2×Q8—444no—
455C2×Q8C23×D1112yes—
456C2×D4—114no—
457C2×D4—228no—
458C2×D4—224no—
459C2×D4—222no—
460C2×D4—224no—
461C2×D4—224no—
462C2×D4—224no—
463C2×D4—444no—
464C2×D4—448no—
465C2×D4—444no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—22no—
469C22×C4—111no—
470C22×C4—118no—
471C22×C4—114no—
472C22×C4—111no—
473C22×C4—111no—
474C22×C4—112no—
475C22×C4—112no—
476C22×C4—114no—
477C22×C4—228no—
478C22×C4—222no—
479C22×C4—222no—
480C22×C4—221no—
481C22×C4—221no—
482C22×C4—442no—
483C22×C4—448no—
484C22×C4D4×D1111yescharacteristic
485C22×C4D4×D1111yescharacteristic
486C22×C4C23×D1111yescharacteristic
487SD16—448no—
488SD16—448no—
489C2×C8—24no—
490C2×C8—114no—
491C2×C8—224no—
492C2×C8—448no—
493C2×C8C23×D1114yes—
494C4⋊C4—24no—
495C4⋊C4—24no—
496C4⋊C4—22no—
497C4⋊C4—21no—
498C4⋊C4—112no—
499C4⋊C4—224no—
500C4⋊C4—224no—
501C4⋊C4—224no—
502C4⋊C4—224no—
503C4⋊C4—224no—
504C4⋊C4—221no—
505C4⋊C4—224no—
506C4⋊C4C23×D1112yes—
507C4⋊C4C23×D1114yes—
508C22⋊C4—228no—
509C22⋊C4—228no—
510C22⋊C4—224no—
511C22⋊C4—224no—
512C42—24no—
513C42—114no—
514C42—112no—
515C42—114no—
516C42—112no—
517C42—224no—
518C42D4×D1112yes—
519C42C23×D1112yes—
520C11C2×#324611yescharacteristic, complemented, Sylow
521C23—114no—
522C23—112no—
523C23—222no—
524C23—222no—
525C23—224no—
526C23—444no—
527C23—444no—
528C23—444no—
529C23C2×D4×D1111yescharacteristic
530Q8—22no—
531Q8—22no—
532Q8—48no—
533Q8—42no—
534Q8—222no—
535Q8—222no—
536Q8—448no—
537Q8—442no—
538D4—224no—
539D4—224no—
540D4—448no—
541D4—4416no—
542D4—448no—
543D4—444no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—24no—
548C2×C4—44no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—114no—
552C2×C4—112no—
553C2×C4—1116no—
554C2×C4—112no—
555C2×C4—112no—
556C2×C4—222no—
557C2×C4—222no—
558C2×C4—224no—
559C2×C4—222no—
560C2×C4—222no—
561C2×C4—222no—
562C2×C4—222no—
563C2×C4—444no—
564C2×C4—4416no—
565C2×C4—442no—
566C2×C4—442no—
567C2×C4SD16×D1114yes—
568C2×C4C2×D4×D1112yes—
569C2×C4C2×D4×D1112yes—
570C2×C4C2×D4×D1111yescharacteristic
571C2×C4#6704012yes—
572C2×C4#6704212yes—
573C2×C4C24×D1111yescharacteristic
574C8—24no—
575C8—224no—
576C22—114no—
577C22—222no—
578C22—228no—
579C22—222no—
580C22—444no—
581C22—444no—
582C22—444no—
583C22—888no—
584C22#1062316012yes—
585C22C2×SD16×D1112yes—
586C22#1062330812yes—
587C22C22×D4×D1111yescharacteristic
588C4—22no—
589C4—42no—
590C4—44no—
591C4—42no—
592C4—114no—
593C4—222no—
594C4—222no—
595C4—442no—
596C4—442no—
597C4#1062316012yes—
598C4C2×SD16×D1114yes—
599C4C2×#6704011yescharacteristic
600C4C2×#6704211yescharacteristic
601C2—224no—
602C2—884no—
603C2#1307993114yesdirect product factor
604C2C2×#1062316011yescharacteristic
605C2C22×SD16×D1111yescharacteristic
606C2C2×#1062330811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#475C2
socleC23×C11C22×D4
prime radicalC2×#10623256C2
hypercenterC2×#475D11
hypocenterC11C2×#3246
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#475

Complements

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

NH ≅ G/Ntype
1. C2×#10623109C2semidirect
3. #13079931C2direct (N × H)
4. C2×#10622707C2semidirect
5. C2×#10622483C2semidirect
6. C2×#10622420C2semidirect
7. C2×#10622477C2semidirect
8. C2×#10622461C2semidirect
9. C2×#10622640C2semidirect
10. C2×#10622431C2semidirect
11. C2×D11×C4⋊C8C2semidirect
12. C2×C11×#475C2semidirect
25. #10623109C22semidirect
39. C11×#475C22semidirect
45. #10622707C22semidirect
46. #10622640C22semidirect
51. #10622483C22semidirect
52. #10622477C22semidirect
53. #10622461C22semidirect
54. D11×C4⋊C8C22semidirect
55. #10622431C22semidirect
56. #10622420C22semidirect
174. C2×C4×D11SD16semidirect
222. C2×#475D11semidirect
278. C4×D11C2×SD16semidirect
313. #475C2×D11semidirect
435. C2×C11#3246semidirect
520. C11C2×#3246semidirect
603. C2#13079931direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231092
C2×#106232562
#130799312
C2×#106227072
C2×#106224832
C2×#106224202
C2×#106224772
C2×#106224612
C2×#106226402
C2×#106224312
C2×D11×C4⋊C82
C2×C11×#4752
C2×#324611