Finite Group Databasebeta

← C2×#13080346 #15629026

Subgroups — C2×#13080346 #15629026

Order 2816.

2858 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#67003C212yesmaximal, complemented
2C2×#10623082C211yesmaximal, characteristic, complemented
3#13080346C2116yesmaximal, direct product factor
4C2×#10622689C211yesmaximal, characteristic, complemented
5C2×#10622654C212yesmaximal, complemented
6C2×#10622644C211yesmaximal, characteristic, complemented
7C2×#10622685C211yesmaximal, characteristic, complemented
8C2×#10622852C212yesmaximal, complemented
9C2×#10622650C212yesmaximal, complemented
10C2×C4×#4325C211yesmaximal, characteristic, complemented
11C2×D4×C11⋊C8C211yesmaximal, characteristic, complemented
12C2×C11×#550C211yesmaximal, characteristic, complemented
13C22×C11×#41C2212yes—
14C22×#4339C2212yes—
15C11×#550—24no—
16C11×#550C2218yescomplemented
17C2×C11×#127—21no—
18C2×C11×#127C2211yescharacteristic
19C2×C11×#121—22no—
20C2×C11×#121C2212yes—
21C2×C4×Q8×C11C2211yescharacteristic
22C2×C4×D4×C11—21no—
23C2×C4×D4×C11C2211yescharacteristic
24C2×#67003—216no—
25C2×#67003C22116yescomplemented
26C22×#4326C2212yes—
27C22×#4325C2211yescharacteristic
28C2×#66991—21no—
29C22×#4324C2212yes—
30C22×#4324C2212yes—
31C22×#4323C2212yes—
32C2×#66977C2212yes—
33C23×C11⋊C8C2212yes—
34#10623082—24no—
35#10623082C2218yescomplemented
36C2×C4⋊C4×D11—21no—
37C2×#66936—22no—
38C2×C4×D44C2211yescharacteristic
39C2×#66922C2211yescharacteristic
40#10622852C22116yescomplemented
41C2×#66899C2211yescharacteristic
42C2×#66896C2212yes—
43C2×C22⋊(C11⋊C8)C2212yes—
44#10622689C2218yescomplemented
45#10622685C2218yescomplemented
46#10622654C22116yescomplemented
47#10622650C22116yescomplemented
48#10622644C2218yescomplemented
49C4×#4325C2218yescomplemented
50D4×C11⋊C8C2218yescomplemented
51C2×#66874C2212yes—
52C2×#66873C2211yescharacteristic
53C2×#66872C2211yescharacteristic
54C2×C4⋊(C11⋊C8)C2211yescharacteristic
55C2×C4×C11⋊C8C2211yescharacteristic
56C2×C11×#41—24no—
57C2×C11×#41—28no—
58C2×C11×#41—44no—
59C2×C11×#41C2318yes—
60C22×Q8×C11C2311yescharacteristic
61C22×D4×C11—22no—
62C22×D4×C11—22no—
63C22×D4×C11—21no—
64C22×D4×C11—21no—
65C22×D4×C11D411yescharacteristic
66C22×D4×C11C2312yes—
67C23×C4×C11—22no—
68C23×C4×C11C2312yes—
69C22×C22⋊D11—22no—
70C2×#4339—24no—
71C2×#4339—28no—
72C2×#4339—44no—
73C2×#4339C2318yes—
74C22×D44C2311yescharacteristic
75C22×C4×D11—21no—
76C22×C4×D11—22no—
77C22×Dic22C2312yes—
78C11×#127—28no—
79C11×#127—22no—
80C11×#127C2314yes—
81C11×#121—24no—
82C11×#121—216no—
83C11×#121C2318yes—
84C4×Q8×C11—22no—
85C4×Q8×C11C2314yes—
86C4×D4×C11—28no—
87C4×D4×C11D414yes—
88C4×D4×C11C2314yes—
89C2×C11×C4⋊C4—21no—
90C2×C11×C4⋊C4D411yescharacteristic
91C2×C11×C4⋊C4C2311yescharacteristic
92C2×C11×C22⋊C4—22no—
93C2×C11×C22⋊C4D412yes—
94C2×C42×C11—21no—
95C2×C42×C11C2311yescharacteristic
96C2×C22⋊Dic11—22no—
97#67003—264no—
98C2×#4326—28no—
99C2×#4326C2318yes—
100C2×#4325D418yescomplemented
101C2×#4325C2314yes—
102#66991—28no—
103C2×#4324—28no—
104C2×#4324—44no—
105C2×#4324C2318yes—
106C2×#4324C2318yes—
107C2×#4323—28no—
108C2×#4323C2318yes—
109C2×(C2×D11)⋊C4—21no—
110C2×C4⋊Dic11—21no—
111C2×C4⋊Dic11—21no—
112C2×C4⋊Dic11C2311yescharacteristic
113#66977—24no—
114#66977C2318yes—
115C2×Dic11⋊C4—22no—
116C22×C11⋊C8—28no—
117C22×C11⋊C8C2311yescharacteristic
118C22×C11⋊C8C2312yes—
119C22×C11⋊C8C2318yes—
120C22×C11⋊C8C2311yescharacteristic
121C4⋊C4×D11—28no—
122#66936—216no—
123C4×D44—22no—
124C4×D44C2314yes—
125#66922—22no—
126#66922C2314yes—
127#66899C2314yes—
128#66896C2318yes—
129C22⋊(C11⋊C8)C2318yes—
130#66874C2318yes—
131#66873C2314yes—
132#66872C2314yes—
133C4⋊(C11⋊C8)C2314yes—
134C4×C11⋊C8C2314yes—
135C2×#3284—111nomaximal, Sylow
136C24×C11—22no—
137C24×C11C2×D412yes—
138C23×D11—21no—
139C11×#41—216no—
140C11×#41—48no—
141C11×#41—416no—
142C2×Q8×C11—21no—
143C2×Q8×C11—22no—
144C2×Q8×C11C2×D414yes—
145C2×Q8×C11C2412yes—
146C2×D4×C11—28no—
147C2×D4×C11—28no—
148C2×D4×C11—24no—
149C2×D4×C11—24no—
150C2×D4×C11—24no—
151C2×D4×C11—22no—
152C2×D4×C11—24no—
153C2×D4×C11—24no—
154C2×D4×C11—48no—
155C2×D4×C11—44no—
156C2×D4×C11—82no—
157C2×D4×C11—84no—
158C2×D4×C11C2×D414yes—
159C2×D4×C11C2414yes—
160C22×C4×C11—21no—
161C22×C4×C11—24no—
162C22×C4×C11—24no—
163C22×C4×C11—21no—
164C22×C4×C11—28no—
165C22×C4×C11—48no—
166C22×C4×C11C2×D412yes—
167C22×C4×C11C2×D414yes—
168C22×C4×C11C2×D411yescharacteristic
169C22×C4×C11C2×D411yescharacteristic
170C22×C4×C11C2414yes—
171C22×C4×C11C2411yescharacteristic
172C2×C22⋊D11—28no—
173C2×C22⋊D11—48no—
174C22×Dic11—21no—
175C22×Dic11—22no—
176#4339—216no—
177#4339—48no—
178#4339—416no—
179C2×D44—21no—
180C2×D44—22no—
181C2×D44C2×D414yes—
182C2×D44C2412yes—
183C2×C4×D11—24no—
184C2×C4×D11—28no—
185C2×C4×D11—48no—
186C2×C4×D11—44no—
187C2×Dic22—24no—
188C2×Dic22—22no—
189C2×Dic22—24no—
190C2×Dic22C2414yes—
191C11×C4⋊C4—24no—
192C11×C4⋊C4—21no—
193C11×C4⋊C4C2×D414yes—
194C11×C4⋊C4C2412yes—
195C11×C22⋊C4—28no—
196C11×C22⋊C4C2×D418yes—
197C42×C11—24no—
198C42×C11C2×D412yes—
199C42×C11C2412yes—
200C22⋊Dic11—28no—
201#4326—216no—
202#4325C2×D4116yescomplemented
203#4324—216no—
204#4324—48no—
205#4323—216no—
206(C2×D11)⋊C4—24no—
207C4⋊Dic11—24no—
208C4⋊Dic11—24no—
209C4⋊Dic11—21no—
210C4⋊Dic11C2412yes—
211Dic11⋊C4—28no—
212C2×C11⋊C8—216no—
213C2×C11⋊C8—24no—
214C2×C11⋊C8—22no—
215C2×C11⋊C8C2×D414yes—
216C2×C11⋊C8C2412yes—
217C2×C11⋊C8C2414yes—
218C2×C11⋊C8C2412yes—
219C22×#135—112no—
220C2×#550D1111yescharacteristic, complemented
221C2×#547—111no—
222#3284—1116no—
223C2×#492—111no—
224C2×#465—112no—
225C2×#462—111no—
226C2×#459—111no—
227C2×#452—112no—
228C2×#449—112no—
229C2×C4×SD16—111no—
230C2×C8×D4—111no—
231C23×C11—24no—
232C23×C11—24no—
233C23×C11—24no—
234C23×C11—24no—
235C23×C11—44no—
236C23×C11—44no—
237C23×C11—44no—
238C23×C11C22×D414yes—
239C23×C11C22×D411yescharacteristic
240C22×D11—24no—
241C22×D11—22no—
242C22×D11—42no—
243C22×D11—42no—
244Q8×C11—24no—
245Q8×C11—22no—
246Q8×C11C22×D414yes—
247D4×C11—28no—
248D4×C11—24no—
249D4×C11—24no—
250D4×C11—416no—
251D4×C11—44no—
252D4×C11—48no—
253D4×C11—84no—
254D4×C11—88no—
255C2×C4×C11—24no—
256C2×C4×C11—24no—
257C2×C4×C11—22no—
258C2×C4×C11—22no—
259C2×C4×C11—28no—
260C2×C4×C11—24no—
261C2×C4×C11—24no—
262C2×C4×C11—22no—
263C2×C4×C11—416no—
264C2×C4×C11—42no—
265C2×C4×C11#13514yescomplemented
266C2×C4×C11C22×D412yes—
267C2×C4×C11C22×D414yes—
268C2×C4×C11C22×D412yes—
269C2×C4×C11C22×D411yescharacteristic
270C2×C4×C11C22×D412yes—
271C2×C4×C11H(5,𝔽2)12yes—
272C2×C4×C11C2511yescharacteristic
273C22⋊D11—416no—
274C2×Dic11—22no—
275C2×Dic11—24no—
276C2×Dic11—44no—
277C2×Dic11—42no—
278D44—24no—
279D44—22no—
280D44C22×D414yes—
281C4×D11—416no—
282C4×D11—48no—
283Dic22—24no—
284Dic22—24no—
285Dic22—44no—
286C11⋊C8—24no—
287C11⋊C8—22no—
288C11⋊C8C22×D414yes—
289C22×#41—112no—
290C22×#41C2×D1112yes—
291C2×#135—1116no—
292C2×#135—2216no—
293C22×Q16—112no—
294C22×SD16—111no—
295C22×SD16—112no—
296C22×SD16—112no—
297C22×D8—112no—
298C23×C8—112no—
299#550—24no—
300#550C2×D1118yescomplemented
301#547—118no—
302#547—224no—
303C2×C4⋊Q8—111no—
304C2×#127—21no—
305C2×#127C2×D1111yescharacteristic
306C2×#123—222no—
307C2×C22⋊Q8—112no—
308C2×#121—22no—
309C2×#121—221no—
310C2×#121C2×D1112yes—
311C2×C4×Q8C2×D1111yescharacteristic
312C2×C4×D4—21no—
313C2×C4×D4—111no—
314C2×C4×D4C2×D1111yescharacteristic
315C22×C4⋊C4—221no—
316#492—118no—
317#465—1116no—
318#462—118no—
319#459—118no—
320#452—1116no—
321#449—1116no—
322C4×SD16—118no—
323C8×D4—118no—
324C2×#106—111no—
325C2×C4⋊C8—111no—
326C2×#103—111no—
327C2×#103—112no—
328C2×#102—112no—
329C2×#102—111no—
330C2×C22⋊C8—112no—
331C2×C4×C8—111no—
332C22×C11—24no—
333C22×C11—24no—
334C22×C11—24no—
335C22×C11—48no—
336C22×C11—44no—
337C22×C11—44no—
338C22×C11—44no—
339C22×C11—88no—
340C22×C11D4212yes—
341C22×C11C2×#13512yes—
342C22×C11#57712yes—
343C22×C11C23×D411yescharacteristic
344C2×D11—24no—
345C2×D11—48no—
346C2×D11—42no—
347C2×D11—42no—
348C4×C11—24no—
349C4×C11—24no—
350C4×C11—22no—
351C4×C11—42no—
352C4×C11D4212yes—
353C4×C11C2×#13514yescomplemented
354C4×C11C23×D411yescharacteristic
355C4×C11C2×H(5,𝔽2)11yescharacteristic
356Dic11—44no—
357Dic11—42no—
358C2×#41—24no—
359C2×#41—28no—
360C2×#41—44no—
361C2×#41—118no—
362C2×#41—228no—
363C2×#41—224no—
364C2×#41—444no—
365C2×#41C22×D1118yes—
366C22×Q8—112no—
367C22×Q8C22×D1111yescharacteristic
368C22×D4—22no—
369C22×D4—22no—
370C22×D4—21no—
371C22×D4—21no—
372C22×D4—111no—
373C22×D4—222no—
374C22×D4C22⋊D1111yescharacteristic
375C22×D4C22×D1112yes—
376C23×C4—22no—
377C23×C4—221no—
378C23×C4—222no—
379C23×C4C22×D1112yes—
380#135—2264no—
381C2×Q16—118no—
382C2×Q16—228no—
383C2×SD16—118no—
384C2×SD16—114no—
385C2×SD16—118no—
386C2×SD16—118no—
387C2×SD16—228no—
388C2×SD16—444no—
389C2×D8—118no—
390C2×D8—228no—
391C22×C8—111no—
392C22×C8—112no—
393C22×C8—118no—
394C22×C8—111no—
395C22×C8—228no—
396C4⋊Q8—114no—
397C4⋊Q8—222no—
398#127—28no—
399#127—22no—
400#127C22×D1114yes—
401#123—2216no—
402C22⋊Q8—118no—
403C22⋊Q8—224no—
404#121—24no—
405#121—216no—
406#121—228no—
407#121C22×D1118yes—
408C4×Q8—22no—
409C4×Q8C22×D1114yes—
410C4×D4—28no—
411C4×D4—114no—
412C4×D4—222no—
413C4×D4C22⋊D1114yes—
414C4×D4C22×D1114yes—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—111no—
417C2×C4⋊C4—221no—
418C2×C4⋊C4—222no—
419C2×C4⋊C4—221no—
420C2×C4⋊C4—228no—
421C2×C4⋊C4C22⋊D1111yescharacteristic
422C2×C4⋊C4C22×D1111yescharacteristic
423C2×C22⋊C4—22no—
424C2×C22⋊C4—222no—
425C2×C22⋊C4—221no—
426C2×C22⋊C4C22⋊D1112yes—
427C2×C42—21no—
428C2×C42C22×D1111yescharacteristic
429#106—114no—
430C4⋊C8—114no—
431#103—114no—
432#103—118no—
433#102—118no—
434#102—114no—
435C22⋊C8—118no—
436C4×C8—114no—
437C2×C11—44no—
438C2×C11—84no—
439C2×C11#328414yescomplemented
440C2×C11C2×D4211yescharacteristic
441C2×C11C22×#13511yescharacteristic
442C2×C11C2×#57711yescharacteristic
443D11—44no—
444C24—22no—
445C24—221no—
446C24C2×C22⋊D1112yes—
447#41—216no—
448#41—48no—
449#41—416no—
450#41—2216no—
451#41—448no—
452#41—4416no—
453C2×Q8—22no—
454C2×Q8—21no—
455C2×Q8—114no—
456C2×Q8—222no—
457C2×Q8—224no—
458C2×Q8—224no—
459C2×Q8D4×D1114yes—
460C2×Q8C23×D1112yes—
461C2×D4—28no—
462C2×D4—28no—
463C2×D4—24no—
464C2×D4—24no—
465C2×D4—24no—
466C2×D4—24no—
467C2×D4—22no—
468C2×D4—24no—
469C2×D4—48no—
470C2×D4—44no—
471C2×D4—82no—
472C2×D4—84no—
473C2×D4—114no—
474C2×D4—112no—
475C2×D4—228no—
476C2×D4—222no—
477C2×D4—221no—
478C2×D4—448no—
479C2×D4C2×C22⋊D1114yes—
480C2×D4C23×D1114yes—
481C22×C4—21no—
482C22×C4—24no—
483C22×C4—24no—
484C22×C4—21no—
485C22×C4—28no—
486C22×C4—48no—
487C22×C4—221no—
488C22×C4—222no—
489C22×C4—224no—
490C22×C4—228no—
491C22×C4—448no—
492C22×C4—444no—
493C22×C4C2×C22⋊D1114yes—
494C22×C4C2×C22⋊D1111yescharacteristic
495C22×C4C2×C22⋊D1112yes—
496C22×C4C2×C22⋊D1111yescharacteristic
497C22×C4C23×D1114yes—
498C22×C4C23×D1111yescharacteristic
499Q16—2216no—
500SD16—1116no—
501SD16—2216no—
502SD16—448no—
503D8—2216no—
504C2×C8—114no—
505C2×C8—112no—
506C2×C8—112no—
507C2×C8—114no—
508C2×C8—2216no—
509C2×C8—224no—
510C2×C8—222no—
511C4⋊C4—24no—
512C4⋊C4—21no—
513C4⋊C4—112no—
514C4⋊C4—221no—
515C4⋊C4—224no—
516C4⋊C4—228no—
517C4⋊C4—224no—
518C4⋊C4C2×C22⋊D1114yes—
519C4⋊C4C23×D1112yes—
520C22⋊C4—28no—
521C22⋊C4—228no—
522C22⋊C4—224no—
523C22⋊C4C2×C22⋊D1118yes—
524C42—24no—
525C42C2×C22⋊D1112yes—
526C42C23×D1112yes—
527C11C2×#328411yescharacteristic, complemented, Sylow
528C23—24no—
529C23—24no—
530C23—24no—
531C23—24no—
532C23—44no—
533C23—44no—
534C23—44no—
535C23—224no—
536C23—222no—
537C23—442no—
538C23—442no—
539C23C22×C22⋊D1114yes—
540C23C22×C22⋊D1111yescharacteristic
541Q8—24no—
542Q8—22no—
543Q8—224no—
544Q8—224no—
545Q8—444no—
546Q8C2×D4×D1114yes—
547D4—28no—
548D4—24no—
549D4—24no—
550D4—416no—
551D4—44no—
552D4—48no—
553D4—84no—
554D4—88no—
555D4—114no—
556D4—224no—
557D4—222no—
558D4—4416no—
559C2×C4—24no—
560C2×C4—24no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—28no—
564C2×C4—24no—
565C2×C4—24no—
566C2×C4—22no—
567C2×C4—416no—
568C2×C4—42no—
569C2×C4—222no—
570C2×C4—224no—
571C2×C4—4416no—
572C2×C4—444no—
573C2×C4—442no—
574C2×C4—448no—
575C2×C4#6700314yescomplemented
576C2×C4C2×D4×D1112yes—
577C2×C4#6703712yes—
578C2×C4C22×C22⋊D1112yes—
579C2×C4C22×C22⋊D1114yes—
580C2×C4C22×C22⋊D1111yescharacteristic
581C2×C4C22×C22⋊D1112yes—
582C2×C4C24×D1111yescharacteristic
583C8—114no—
584C8—224no—
585C8—222no—
586C22—24no—
587C22—24no—
588C22—24no—
589C22—48no—
590C22—44no—
591C22—44no—
592C22—44no—
593C22—88no—
594C22—224no—
595C22—448no—
596C22—442no—
597C22—442no—
598C22D4×C22⋊D1112yes—
599C22C2×#6700312yes—
600C22#1062336712yes—
601C22C23×C22⋊D1111yescharacteristic
602C4—24no—
603C4—24no—
604C4—22no—
605C4—42no—
606C4—444no—
607C4—442no—
608C4D4×C22⋊D1112yes—
609C4C2×#6700314yescomplemented
610C4C22×D4×D1111yescharacteristic
611C4C2×#6703711yescharacteristic
612C2—44no—
613C2—84no—
614C2—444no—
615C2#1308034614yesdirect product factor
616C2C2×D4×C22⋊D1111yescharacteristic
617C2C22×#6700311yescharacteristic
618C2C2×#1062336711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#550C2
socleC23×C11C22×D4
hypercenterC2×#550D11
hypocenterC11C2×#3284
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#550

Complements

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

NH ≅ G/Ntype
1. C22×#67003C2semidirect
2. C2×#10623082C2semidirect
3. #13080346C2direct (N × H)
4. C2×#10622689C2semidirect
5. C2×#10622654C2semidirect
6. C2×#10622644C2semidirect
7. C2×#10622685C2semidirect
8. C2×#10622852C2semidirect
9. C2×#10622650C2semidirect
10. C2×C4×#4325C2semidirect
11. C2×D4×C11⋊C8C2semidirect
12. C2×C11×#550C2semidirect
16. C11×#550C22semidirect
25. C2×#67003C22semidirect
35. #10623082C22semidirect
40. #10622852C22semidirect
44. #10622689C22semidirect
45. #10622685C22semidirect
46. #10622654C22semidirect
47. #10622650C22semidirect
48. #10622644C22semidirect
49. C4×#4325C22semidirect
50. D4×C11⋊C8C22semidirect
100. C2×#4325D4semidirect
202. #4325C2×D4semidirect
220. C2×#550D11semidirect
265. C2×C4×C11#135semidirect
300. #550C2×D11semidirect
353. C4×C11C2×#135semidirect
439. C2×C11#3284semidirect
527. C11C2×#3284semidirect
575. C2×C4#67003semidirect
609. C4C2×#67003semidirect
615. C2#13080346direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#670032
C2×#106230822
#130803462
C2×#106226892
C2×#106226542
C2×#106226442
C2×#106226852
C2×#106228522
C2×#106226502
C2×C4×#43252
C2×D4×C11⋊C82
C2×C11×#5502
C2×#328411