Finite Group Databasebeta

← C2×#13080258 #15628915

Subgroups — C2×#13080258 #15628915

Order 2816.

2742 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#67004C212yesmaximal, complemented
2C2×D4×Dic22C211yesmaximal, characteristic, complemented
3#13080258C2116yesmaximal, direct product factor
4C2×#10622705C211yesmaximal, characteristic, complemented
5C2×#10622665C212yesmaximal, complemented
6C2×#10622703C211yesmaximal, characteristic, complemented
7C2×#10622632C211yesmaximal, characteristic, complemented
8C2×#10622852C212yesmaximal, complemented
9C2×#10622663C212yesmaximal, complemented
10C2×C4×#4324C211yesmaximal, characteristic, complemented
11C2×#10622625C211yesmaximal, characteristic, complemented
12C2×C11×#547C211yesmaximal, characteristic
13C22×C11×#41C2212yes—
14C23×Dic22C2212yes—
15C11×#547—24no—
16C11×#547C2218yes—
17C2×C11×C4⋊Q8C2211yescharacteristic
18C2×C11×#123—22no—
19C2×C11×C22⋊Q8C2212yes—
20C2×C11×#121—21no—
21C2×C4×D4×C11C2211yescharacteristic
22C2×C4×D4×C11C2211yescharacteristic
23C22×C11×C4⋊C4—21no—
24C2×#67004—216no—
25C2×#67004C22116yescomplemented
26C22×#4326C2212yes—
27C22×#4326C2212yes—
28C22×#4326C2212yes—
29C2×D4×Dic11—21no—
30C22×#4324C2212yes—
31C22×#4324C2211yescharacteristic
32C2×#66977C2212yes—
33C22×#4318C2212yes—
34D4×Dic22—24no—
35D4×Dic22C2218yescomplemented
36C2×#66941—21no—
37C2×#66931—22no—
38C2×#66922C2211yescharacteristic
39C2×C4×Dic22C2211yescharacteristic
40#10622852C22116yescomplemented
41C2×#66899C2212yes—
42C2×#66896C2211yescharacteristic
43C2×C22⋊(C11⋊C8)C2212yes—
44#10622705C2218yescomplemented
45#10622703C2218yescomplemented
46#10622665C22116yescomplemented
47#10622663C22116yescomplemented
48#10622632C2218yescomplemented
49C4×#4324C2218yescomplemented
50#10622625C2218yescomplemented
51C2×#66874C2212yes—
52C2×#66874C2211yescharacteristic
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×C11C2312yes—
61C22×D4×C11—22no—
62C22×D4×C11D411yescharacteristic
63C22×D4×C11C2311yescharacteristic
64C23×C4×C11—21no—
65C23×C4×C11—22no—
66C23×C4×C11C2312yes—
67C23×Dic11—22no—
68C22×Dic22—28no—
69C22×Dic22—22no—
70C22×Dic22—24no—
71C22×Dic22—44no—
72C22×Dic22C2312yes—
73C22×Dic22C2318yes—
74C22×Dic22C2311yescharacteristic
75C11×C4⋊Q8—22no—
76C11×C4⋊Q8C2314yes—
77C11×#123—216no—
78C11×C22⋊Q8—24no—
79C11×C22⋊Q8C2318yes—
80C11×#121—28no—
81C4×D4×C11—22no—
82C4×D4×C11D414yes—
83C4×D4×C11C2314yes—
84C4×D4×C11C2314yes—
85C2×C11×C4⋊C4—21no—
86C2×C11×C4⋊C4—22no—
87C2×C11×C4⋊C4—21no—
88C2×C11×C4⋊C4—28no—
89C2×C11×C4⋊C4D411yescharacteristic
90C2×C11×C4⋊C4C2311yescharacteristic
91C2×C11×C22⋊C4—22no—
92C2×C11×C22⋊C4—21no—
93C2×C11×C22⋊C4D412yes—
94C2×C42×C11C2311yescharacteristic
95C2×C22⋊Dic11—22no—
96#67004—264no—
97C2×#4326—28no—
98C2×#4326—28no—
99C2×#4326—44no—
100C2×#4326C2318yes—
101C2×#4326C2318yes—
102C2×#4326C2318yes—
103D4×Dic11—28no—
104C2×#4324—28no—
105C2×#4324D418yescomplemented
106C2×#4324C2318yes—
107C2×#4324C2314yes—
108C2×C4⋊Dic11—21no—
109C2×C4⋊Dic11—21no—
110C2×C4⋊Dic11C2311yescharacteristic
111#66977—24no—
112#66977C2318yes—
113C2×Dic11⋊C4—21no—
114C2×Dic11⋊C4—22no—
115C2×C4×Dic11—21no—
116C2×#4318—28no—
117C2×#4318C2318yes—
118C22×C11⋊C8C2311yescharacteristic
119C22×C11⋊C8C2312yes—
120C22×C11⋊C8C2311yescharacteristic
121#66941—28no—
122#66931—216no—
123#66922—22no—
124#66922C2314yes—
125C4×Dic22—22no—
126C4×Dic22C2314yes—
127#66899C2318yes—
128#66896C2314yes—
129C22⋊(C11⋊C8)C2318yes—
130#66874C2314yes—
131#66874C2318yes—
132#66872C2314yes—
133C4⋊(C11⋊C8)C2314yes—
134C4×C11⋊C8C2314yes—
135C2×#3276—111nomaximal, Sylow
136C24×C11—21no—
137C24×C11C2×D412yes—
138C11×#41—216no—
139C11×#41—48no—
140C11×#41—416no—
141C2×Q8×C11—22no—
142C2×Q8×C11—24no—
143C2×Q8×C11—24no—
144C2×Q8×C11C2414yes—
145C2×D4×C11—28no—
146C2×D4×C11—24no—
147C2×D4×C11—21no—
148C2×D4×C11—22no—
149C2×D4×C11—48no—
150C2×D4×C11C2×D414yes—
151C2×D4×C11C2×D414yes—
152C2×D4×C11C2412yes—
153C22×C4×C11—24no—
154C22×C4×C11—24no—
155C22×C4×C11—21no—
156C22×C4×C11—22no—
157C22×C4×C11—24no—
158C22×C4×C11—28no—
159C22×C4×C11—48no—
160C22×C4×C11—44no—
161C22×C4×C11C2×D411yescharacteristic
162C22×C4×C11C2×D412yes—
163C22×C4×C11C2×D414yes—
164C22×C4×C11C2×D411yescharacteristic
165C22×C4×C11C2414yes—
166C22×C4×C11C2411yescharacteristic
167C22×Dic11—21no—
168C22×Dic11—28no—
169C22×Dic11—21no—
170C22×Dic11—22no—
171C22×Dic11—48no—
172C2×Dic22—216no—
173C2×Dic22—21no—
174C2×Dic22—24no—
175C2×Dic22—22no—
176C2×Dic22—28no—
177C2×Dic22—22no—
178C2×Dic22—24no—
179C2×Dic22—48no—
180C2×Dic22—416no—
181C2×Dic22—48no—
182C2×Dic22C2×D414yes—
183C2×Dic22C2414yes—
184C2×Dic22C2412yes—
185C11×C4⋊C4—24no—
186C11×C4⋊C4—28no—
187C11×C4⋊C4—24no—
188C11×C4⋊C4—21no—
189C11×C4⋊C4C2×D414yes—
190C11×C4⋊C4C2412yes—
191C11×C22⋊C4—28no—
192C11×C22⋊C4—24no—
193C11×C22⋊C4C2×D418yes—
194C42×C11C2×D412yes—
195C42×C11C2412yes—
196C22⋊Dic11—28no—
197#4326—216no—
198#4326—216no—
199#4326—48no—
200#4324—216no—
201#4324C2×D4116yescomplemented
202C4⋊Dic11—21no—
203C4⋊Dic11—24no—
204C4⋊Dic11—24no—
205C4⋊Dic11C2412yes—
206Dic11⋊C4—24no—
207Dic11⋊C4—28no—
208C4×Dic11—24no—
209#4318—216no—
210C2×C11⋊C8—24no—
211C2×C11⋊C8—22no—
212C2×C11⋊C8C2×D414yes—
213C2×C11⋊C8C2412yes—
214C2×C11⋊C8C2414yes—
215C2×C11⋊C8C2412yes—
216C22×#137—112no—
217C2×D4×Q8—111no—
218C2×#547D1111yescharacteristic
219#3276—1116no—
220C2×#494—111no—
221C2×#470—112no—
222C2×#462—111no—
223C2×#461—111no—
224C2×#452—112no—
225C2×#451—112no—
226C2×C4×SD16—111no—
227C2×#436—111no—
228C23×C11—24no—
229C23×C11—24no—
230C23×C11—24no—
231C23×C11—24no—
232C23×C11—22no—
233C23×C11—42no—
234C23×C11—42no—
235C23×C11C22×D414yes—
236C23×C11C22×D411yescharacteristic
237Q8×C11—24no—
238Q8×C11—24no—
239Q8×C11—44no—
240D4×C11—24no—
241D4×C11—28no—
242D4×C11—22no—
243D4×C11—416no—
244D4×C11C22×D414yes—
245C2×C4×C11—24no—
246C2×C4×C11—22no—
247C2×C4×C11—28no—
248C2×C4×C11—24no—
249C2×C4×C11—24no—
250C2×C4×C11—22no—
251C2×C4×C11—24no—
252C2×C4×C11—416no—
253C2×C4×C11—44no—
254C2×C4×C11—42no—
255C2×C4×C11—48no—
256C2×C4×C11#13714yescomplemented
257C2×C4×C11C22×D412yes—
258C2×C4×C11C22×D412yes—
259C2×C4×C11C22×D414yes—
260C2×C4×C11C22×D411yescharacteristic
261C2×C4×C11C22×D412yes—
262C2×C4×C11H(5,𝔽2)12yes—
263C2×C4×C11C2511yescharacteristic
264C2×Dic11—24no—
265C2×Dic11—22no—
266C2×Dic11—22no—
267C2×Dic11—24no—
268C2×Dic11—416no—
269C2×Dic11—44no—
270C2×Dic11—42no—
271Dic22—24no—
272Dic22—22no—
273Dic22—24no—
274Dic22—24no—
275Dic22—416no—
276Dic22—44no—
277Dic22C22×D414yes—
278C11⋊C8—24no—
279C11⋊C8—22no—
280C11⋊C8C22×D414yes—
281C22×#41C2×D1112yes—
282C23×Q8—112no—
283C2×#137—1116no—
284C2×#137—2216no—
285C22×Q16—112no—
286C22×Q16—112no—
287C22×Q16—112no—
288C22×SD16—111no—
289C22×SD16—112no—
290C22×M16—112no—
291D4×Q8—118no—
292D4×Q8—224no—
293#547—24no—
294#547C2×D1118yes—
295C2×C4⋊Q8—111no—
296C2×C4⋊Q8—221no—
297C2×C4⋊Q8C2×D1111yescharacteristic
298C2×#123—22no—
299C2×C22⋊Q8—112no—
300C2×C22⋊Q8—222no—
301C2×C22⋊Q8C2×D1112yes—
302C2×#121—21no—
303C2×C4×Q8—111no—
304C2×C4×D4—221no—
305C2×C4×D4C2×D1111yescharacteristic
306C2×C4×D4C2×D1111yescharacteristic
307C22×C4⋊C4—21no—
308#494—118no—
309#470—1116no—
310#462—118no—
311#461—118no—
312#452—1116no—
313#451—1116no—
314C4×SD16—118no—
315#436—118no—
316C2×#106—111no—
317C2×C4⋊C8—111no—
318C2×#103—112no—
319C2×#103—111no—
320C2×#103—112no—
321C2×#102—111no—
322C2×C22⋊C8—112no—
323C2×C4×C8—111no—
324C22×C11—24no—
325C22×C11—24no—
326C22×C11—24no—
327C22×C11—24no—
328C22×C11—48no—
329C22×C11—48no—
330C22×C11—42no—
331C22×C11—42no—
332C22×C11D4212yes—
333C22×C11C2×#13712yes—
334C22×C11#57812yes—
335C22×C11C23×D411yescharacteristic
336C4×C11—24no—
337C4×C11—22no—
338C4×C11—44no—
339C4×C11—42no—
340C4×C11D4212yes—
341C4×C11C2×#13714yescomplemented
342C4×C11C23×D411yescharacteristic
343C4×C11C2×H(5,𝔽2)11yescharacteristic
344Dic11—24no—
345Dic11—44no—
346Dic11—42no—
347C2×#41—24no—
348C2×#41—28no—
349C2×#41—44no—
350C2×#41C22×D1118yes—
351C22×Q8—111no—
352C22×Q8—112no—
353C22×Q8—118no—
354C22×Q8—228no—
355C22×Q8—222no—
356C22×Q8—224no—
357C22×Q8—444no—
358C22×Q8C22×D1112yes—
359C22×D4—22no—
360C22×D4C22⋊D1111yescharacteristic
361C22×D4C22×D1111yescharacteristic
362C23×C4—21no—
363C23×C4—22no—
364C23×C4—222no—
365C23×C4C22×D1112yes—
366#137—2264no—
367C2×Q16—118no—
368C2×Q16—118no—
369C2×Q16—118no—
370C2×Q16—228no—
371C2×Q16—228no—
372C2×Q16—444no—
373C2×SD16—118no—
374C2×SD16—114no—
375C2×SD16—118no—
376C2×SD16—228no—
377C2×M16—118no—
378C2×M16—228no—
379C22×C8—111no—
380C22×C8—112no—
381C22×C8—111no—
382C4⋊Q8—22no—
383C4⋊Q8—114no—
384C4⋊Q8—228no—
385C4⋊Q8—222no—
386C4⋊Q8C22×D1114yes—
387#123—216no—
388C22⋊Q8—24no—
389C22⋊Q8—118no—
390C22⋊Q8—224no—
391C22⋊Q8—2216no—
392C22⋊Q8C22×D1118yes—
393#121—28no—
394C4×Q8—114no—
395C4×Q8—222no—
396C4×D4—22no—
397C4×D4—228no—
398C4×D4C22⋊D1114yes—
399C4×D4C22×D1114yes—
400C4×D4C22×D1114yes—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—28no—
405C2×C4⋊C4—111no—
406C2×C4⋊C4—221no—
407C2×C4⋊C4—221no—
408C2×C4⋊C4—222no—
409C2×C4⋊C4—221no—
410C2×C4⋊C4C22⋊D1111yescharacteristic
411C2×C4⋊C4C22×D1111yescharacteristic
412C2×C22⋊C4—22no—
413C2×C22⋊C4—21no—
414C2×C22⋊C4—222no—
415C2×C22⋊C4C22⋊D1112yes—
416C2×C42—221no—
417C2×C42C22×D1111yescharacteristic
418#106—114no—
419C4⋊C8—114no—
420#103—118no—
421#103—114no—
422#103—118no—
423#102—114no—
424C22⋊C8—118no—
425C4×C8—114no—
426C2×C11—44no—
427C2×C11—44no—
428C2×C11#327614yescomplemented
429C2×C11C2×D4211yescharacteristic
430C2×C11C22×#13711yescharacteristic
431C2×C11C2×#57811yescharacteristic
432C24—21no—
433C24C2×C22⋊D1112yes—
434#41—216no—
435#41—48no—
436#41—416no—
437C2×Q8—22no—
438C2×Q8—24no—
439C2×Q8—24no—
440C2×Q8—114no—
441C2×Q8—112no—
442C2×Q8—114no—
443C2×Q8—2216no—
444C2×Q8—222no—
445C2×Q8—221no—
446C2×Q8—228no—
447C2×Q8—222no—
448C2×Q8—224no—
449C2×Q8—224no—
450C2×Q8—448no—
451C2×Q8—448no—
452C2×Q8—4416no—
453C2×Q8C23×D1114yes—
454C2×D4—28no—
455C2×D4—24no—
456C2×D4—22no—
457C2×D4—21no—
458C2×D4—48no—
459C2×D4D4×D1114yes—
460C2×D4C2×C22⋊D1114yes—
461C2×D4C23×D1112yes—
462C22×C4—24no—
463C22×C4—24no—
464C22×C4—21no—
465C22×C4—22no—
466C22×C4—24no—
467C22×C4—28no—
468C22×C4—48no—
469C22×C4—44no—
470C22×C4—221no—
471C22×C4—228no—
472C22×C4—221no—
473C22×C4—222no—
474C22×C4—448no—
475C22×C4C2×C22⋊D1114yes—
476C22×C4C2×C22⋊D1111yescharacteristic
477C22×C4C2×C22⋊D1112yes—
478C22×C4C2×C22⋊D1111yescharacteristic
479C22×C4C23×D1114yes—
480C22×C4C23×D1111yescharacteristic
481Q16—2216no—
482Q16—2216no—
483Q16—448no—
484SD16—1116no—
485SD16—2216no—
486M16—2216no—
487C2×C8—114no—
488C2×C8—112no—
489C2×C8—112no—
490C2×C8—114no—
491C2×C8—224no—
492C2×C8—222no—
493C4⋊C4—24no—
494C4⋊C4—28no—
495C4⋊C4—24no—
496C4⋊C4—21no—
497C4⋊C4—112no—
498C4⋊C4—221no—
499C4⋊C4—224no—
500C4⋊C4—224no—
501C4⋊C4—228no—
502C4⋊C4—224no—
503C4⋊C4C2×C22⋊D1114yes—
504C4⋊C4C23×D1112yes—
505C22⋊C4—28no—
506C22⋊C4—24no—
507C22⋊C4—228no—
508C22⋊C4C2×C22⋊D1118yes—
509C42—224no—
510C42C2×C22⋊D1112yes—
511C42C23×D1112yes—
512C11C2×#327611yescharacteristic, complemented, Sylow
513C23—24no—
514C23—24no—
515C23—24no—
516C23—24no—
517C23—22no—
518C23—42no—
519C23—42no—
520C23C22×C22⋊D1114yes—
521C23C22×C22⋊D1111yescharacteristic
522Q8—24no—
523Q8—24no—
524Q8—44no—
525Q8—114no—
526Q8—224no—
527Q8—222no—
528Q8—224no—
529Q8—224no—
530Q8—4416no—
531Q8—444no—
532D4—24no—
533D4—28no—
534D4—22no—
535D4—416no—
536D4C2×D4×D1114yes—
537C2×C4—24no—
538C2×C4—22no—
539C2×C4—28no—
540C2×C4—24no—
541C2×C4—24no—
542C2×C4—22no—
543C2×C4—24no—
544C2×C4—416no—
545C2×C4—44no—
546C2×C4—42no—
547C2×C4—48no—
548C2×C4—224no—
549C2×C4—222no—
550C2×C4—222no—
551C2×C4—224no—
552C2×C4—4416no—
553C2×C4—444no—
554C2×C4—442no—
555C2×C4#6700414yescomplemented
556C2×C4C2×D4×D1112yes—
557C2×C4#6703712yes—
558C2×C4C22×C22⋊D1112yes—
559C2×C4C22×C22⋊D1114yes—
560C2×C4C22×C22⋊D1111yescharacteristic
561C2×C4C22×C22⋊D1112yes—
562C2×C4C24×D1111yescharacteristic
563C8—114no—
564C8—224no—
565C8—222no—
566C22—24no—
567C22—24no—
568C22—24no—
569C22—24no—
570C22—48no—
571C22—48no—
572C22—42no—
573C22—42no—
574C22D4×C22⋊D1112yes—
575C22C2×#6700412yes—
576C22#1062336912yes—
577C22C23×C22⋊D1111yescharacteristic
578C4—24no—
579C4—22no—
580C4—44no—
581C4—42no—
582C4—224no—
583C4—444no—
584C4—442no—
585C4D4×C22⋊D1112yes—
586C4C2×#6700414yescomplemented
587C4C22×D4×D1111yescharacteristic
588C4C2×#6703711yescharacteristic
589C2—44no—
590C2—44no—
591C2#1308025814yesdirect product factor
592C2C2×D4×C22⋊D1111yescharacteristic
593C2C22×#6700411yescharacteristic
594C2C2×#1062336911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
Fitting, prime radicalC2×C11×#547C2
socleC23×C11C22×D4
hypercenterC2×#547D11
hypocenterC11C2×#3276
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. C22×#67004C2semidirect
2. C2×D4×Dic22C2semidirect
3. #13080258C2direct (N × H)
4. C2×#10622705C2semidirect
5. C2×#10622665C2semidirect
6. C2×#10622703C2semidirect
7. C2×#10622632C2semidirect
8. C2×#10622852C2semidirect
9. C2×#10622663C2semidirect
10. C2×C4×#4324C2semidirect
11. C2×#10622625C2semidirect
25. C2×#67004C22semidirect
35. D4×Dic22C22semidirect
40. #10622852C22semidirect
44. #10622705C22semidirect
45. #10622703C22semidirect
46. #10622665C22semidirect
47. #10622663C22semidirect
48. #10622632C22semidirect
49. C4×#4324C22semidirect
50. #10622625C22semidirect
105. C2×#4324D4semidirect
201. #4324C2×D4semidirect
256. C2×C4×C11#137semidirect
341. C4×C11C2×#137semidirect
428. C2×C11#3276semidirect
512. C11C2×#3276semidirect
555. C2×C4#67004semidirect
586. C4C2×#67004semidirect
591. C2#13080258direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#670042
C2×D4×Dic222
#130802582
C2×#106227052
C2×#106226652
C2×#106227032
C2×#106226322
C2×#106228522
C2×#106226632
C2×C4×#43242
C2×#106226252
C2×C11×#5472
C2×#327611