Finite Group Databasebeta

← C2×#13071321 #14912553

Subgroups — C2×#13071321 #14912553

Order 2816.

4150 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×Dic11C212yesmaximal, complemented
2#13071321C2116yesmaximal, direct product factor
3C2×#10622564C212yesmaximal, complemented
4C2×#10622594C212yesmaximal, complemented
5C2×#10622833C212yesmaximal, complemented
6C2×#10622833C212yesmaximal, complemented
7C2×#10622563C212yesmaximal, complemented
8C2×#10622825C211yesmaximal, characteristic, complemented
9C22×C11⋊#95C211yesmaximal, characteristic, complemented
10C22×C11×#121C211yesmaximal, characteristic
11C23×D4×C11C2212yes—
12C23×D4×C11C2211yescharacteristic
13C24×C4×C11C2211yescharacteristic
14C24×Dic11C2211yescharacteristic
15C24×Dic11C2212yes—
16C24×Dic11C2211yescharacteristic
17C2×C11×#121C4116yescomplemented
18C2×C11×#121C2218yes—
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2212yes—
21C22×C22⋊Dic11C2212yes—
22C22×C22⋊Dic11C2212yes—
23C22×C22⋊Dic11C2212yes—
24C22×C22⋊Dic11C2212yes—
25C2×D4×Dic11—216no—
26C2×D4×Dic11C22116yescomplemented
27C22×C4⋊Dic11C2212yes—
28C22×C4⋊Dic11C2211yescharacteristic
29C22×C4⋊Dic11C2211yescharacteristic
30C22×C4×Dic11C2212yes—
31#10622833C22116yescomplemented
32#10622833C22116yescomplemented
33#10622825C2218yescomplemented
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38C2×C11⋊#95C2212yes—
39C2×C11⋊#95C2218yescomplemented
40#10622594C22116yescomplemented
41#10622564C22116yescomplemented
42#10622563C22116yescomplemented
43C25×C11C2312yes—
44C25×C11C2311yescharacteristic
45C22×D4×C11—28no—
46C22×D4×C11—28no—
47C22×D4×C11—42no—
48C22×D4×C11—42no—
49C22×D4×C11C2×C4116yescomplemented
50C22×D4×C11C2×C418yescomplemented
51C22×D4×C11C2318yes—
52C22×D4×C11C2314yes—
53C23×C4×C11—42no—
54C23×C4×C11—42no—
55C23×C4×C11C2×C418yescomplemented
56C23×C4×C11C2312yes—
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2314yes—
60C23×Dic11—24no—
61C23×Dic11—28no—
62C23×Dic11—42no—
63C23×Dic11—42no—
64C23×Dic11—44no—
65C23×Dic11—44no—
66C23×Dic11—42no—
67C23×Dic11—42no—
68C23×Dic11D418yescomplemented
69C23×Dic11C2312yes—
70C23×Dic11C2312yes—
71C23×Dic11C2312yes—
72C23×Dic11C2312yes—
73C23×Dic11C2318yes—
74C23×Dic11C2314yes—
75C23×Dic11C2314yes—
76C11×#121C2×C4164yescomplemented
77C2×C11×C4⋊C4C2×C418yescomplemented
78C2×C11×C4⋊C4C2314yes—
79C2×C11×C22⋊C4C2×C4116yescomplemented
80C2×C11×C22⋊C4C2318yes—
81C2×C22⋊Dic11—28no—
82C2×C22⋊Dic11—28no—
83C2×C22⋊Dic11—44no—
84C2×C22⋊Dic11—44no—
85C2×C22⋊Dic11C2318yes—
86C2×C22⋊Dic11C2318yes—
87C2×C22⋊Dic11C2318yes—
88C2×C22⋊Dic11C2318yes—
89D4×Dic11—264no—
90C2×C4⋊Dic11—28no—
91C2×C4⋊Dic11—42no—
92C2×C4⋊Dic11—42no—
93C2×C4⋊Dic11C2318yes—
94C2×C4⋊Dic11C2314yes—
95C2×C4⋊Dic11C2314yes—
96C2×C4×Dic11—28no—
97C2×C4×Dic11C2318yes—
98C11⋊#95C2318yes—
99C11⋊#95C2318yes—
100C11⋊#95C2318yes—
101C11⋊#95C2318yes—
102C11⋊#95C2318yes—
103C2×#2325—111nomaximal, Sylow
104C24×C11—22no—
105C24×C11—22no—
106C24×C11—22no—
107C24×C11—22no—
108C24×C11—24no—
109C24×C11—24no—
110C24×C11—24no—
111C24×C11—24no—
112C24×C11—24no—
113C24×C11—24no—
114C24×C11C22×C418yes—
115C24×C11C22×C414yes—
116C24×C11C2×D414yes—
117C24×C11#4114yes—
118C24×C11C2414yes—
119C24×C11C2412yes—
120C24×C11C2411yescharacteristic
121C2×D4×C11—264no—
122C2×D4×C11—216no—
123C2×D4×C11—216no—
124C2×D4×C11—416no—
125C2×D4×C11—44no—
126C2×D4×C11—44no—
127C2×D4×C11C22×C4132yescomplemented
128C2×D4×C11C22×C4116yescomplemented
129C22×C4×C11—24no—
130C22×C4×C11—24no—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—416no—
136C22×C4×C11—44no—
137C22×C4×C11—44no—
138C22×C4×C11C22×C414yes—
139C22×C4×C11C22×C418yes—
140C22×C4×C11C22×C414yes—
141C22×C4×C11C22×C4116yescomplemented
142C22×C4×C11C2412yes—
143C22×C4×C11C2414yes—
144C22×C4×C11C2412yes—
145C22×Dic11—216no—
146C22×Dic11—24no—
147C22×Dic11—24no—
148C22×Dic11—28no—
149C22×Dic11—24no—
150C22×Dic11—24no—
151C22×Dic11—24no—
152C22×Dic11—24no—
153C22×Dic11—24no—
154C22×Dic11—24no—
155C22×Dic11—24no—
156C22×Dic11—24no—
157C22×Dic11—24no—
158C22×Dic11—416no—
159C22×Dic11—44no—
160C22×Dic11—44no—
161C22×Dic11—44no—
162C22×Dic11—44no—
163C22×Dic11—48no—
164C22×Dic11—48no—
165C22×Dic11—416no—
166C22×Dic11—432no—
167C22×Dic11C2×D418yes—
168C22×Dic11C2×D4116yescomplemented
169C22×Dic11C2414yes—
170C22×Dic11C2414yes—
171C22×Dic11C2414yes—
172C22×Dic11C2414yes—
173C11×C4⋊C4C22×C4116yescomplemented
174C11×C22⋊C4C22×C4132yescomplemented
175C22⋊Dic11—216no—
176C22⋊Dic11—216no—
177C22⋊Dic11—48no—
178C22⋊Dic11—48no—
179C4⋊Dic11—216no—
180C4⋊Dic11—44no—
181C4⋊Dic11—44no—
182C4×Dic11—216no—
183C22×#121D1111yescharacteristic
184C22×C4×D4—112no—
185#2325—1116no—
186C2×#388—112no—
187C2×#387—112no—
188C2×#386—112no—
189C2×#386—112no—
190C2×#385—112no—
191C2×#380—111no—
192C22×#95—111no—
193C23×C11—28no—
194C23×C11—28no—
195C23×C11—28no—
196C23×C11—28no—
197C23×C11—28no—
198C23×C11—28no—
199C23×C11—22no—
200C23×C11—22no—
201C23×C11—22no—
202C23×C11—22no—
203C23×C11—216no—
204C23×C11—216no—
205C23×C11—216no—
206C23×C11—24no—
207C23×C11—24no—
208C23×C11—24no—
209C23×C11—24no—
210C23×C11—24no—
211C23×C11—24no—
212C23×C11—48no—
213C23×C11—48no—
214C23×C11—48no—
215C23×C11—48no—
216C23×C11C4×D4116yes—
217C23×C11C23×C418yes—
218C23×C11C23×C414yes—
219C23×C11C23×C412yes—
220C23×C11C22×D414yes—
221C23×C11C22×D412yes—
222C23×C11C2×#4114yes—
223C23×C11C2×#4112yes—
224C23×C11H(5,𝔽2)12yes—
225C23×C11H(5,𝔽2)12yes—
226C23×C11H(5,𝔽2)12yes—
227C23×C112−1+412yes—
228C23×C11C2511yescharacteristic
229D4×C11—264no—
230D4×C11—416no—
231C2×C4×C11—216no—
232C2×C4×C11—28no—
233C2×C4×C11—28no—
234C2×C4×C11—24no—
235C2×C4×C11—24no—
236C2×C4×C11—22no—
237C2×C4×C11—22no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—416no—
241C2×C4×C11C23×C414yes—
242C2×C4×C11C23×C418yes—
243C2×C4×C11C23×C414yes—
244C2×Dic11—216no—
245C2×Dic11—24no—
246C2×Dic11—24no—
247C2×Dic11—24no—
248C2×Dic11—24no—
249C2×Dic11—24no—
250C2×Dic11—24no—
251C2×Dic11—24no—
252C2×Dic11—24no—
253C2×Dic11—24no—
254C2×Dic11—24no—
255C2×Dic11—24no—
256C2×Dic11—416no—
257C2×Dic11—432no—
258C2×Dic11—416no—
259C2×Dic11—48no—
260C2×Dic11—48no—
261C2×Dic11—48no—
262C2×Dic11C22×D418yes—
263C23×D4C2×D1112yes—
264C23×D4C2×D1111yescharacteristic
265C24×C4—111no—
266C24×C4—112no—
267C24×C4—111no—
268C24×C4C2×D1111yescharacteristic
269C2×#121Dic11116yescomplemented
270C2×#121C2×D1118yes—
271C2×C4×D4—1116no—
272C2×C4×D4—2216no—
273C22×C4⋊C4—112no—
274C22×C4⋊C4—111no—
275C22×C4⋊C4—111no—
276C22×C4⋊C4C2×D1111yescharacteristic
277C22×C22⋊C4—112no—
278C22×C22⋊C4—112no—
279C22×C22⋊C4—112no—
280C22×C22⋊C4—112no—
281C22×C22⋊C4C2×D1112yes—
282C22×C42—112no—
283#388—1116no—
284#387—1116no—
285#386—1116no—
286#386—1116no—
287#385—1116no—
288#380—118no—
289C2×#95—118no—
290C2×#95—112no—
291C2×#95—112no—
292C2×#95—112no—
293C2×#95—112no—
294C2×#95—112no—
295C22×C11—232no—
296C22×C11—24no—
297C22×C11—24no—
298C22×C11—24no—
299C22×C11—24no—
300C22×C11—24no—
301C22×C11—24no—
302C22×C11—28no—
303C22×C11—28no—
304C22×C11—28no—
305C22×C11—432no—
306C22×C11—44no—
307C22×C11—44no—
308C22×C11—44no—
309C22×C11—44no—
310C22×C11C2×C4×D418yes—
311C22×C11C2×C4×D414yes—
312C22×C11#51814yes—
313C22×C11#52014yes—
314C22×C11#53414yes—
315C22×C11#53714yes—
316C22×C11#53814yes—
317C22×C11#53914yes—
318C22×C11C24×C411yescharacteristic
319C22×C11C23×D411yescharacteristic
320C22×C11C22×#4111yescharacteristic
321C22×C11C2×H(5,𝔽2)11yescharacteristic
322C22×C11C2×H(5,𝔽2)11yescharacteristic
323C22×C11C2×H(5,𝔽2)11yescharacteristic
324C22×C11C2×2−1+411yescharacteristic
325C4×C11—28no—
326C4×C11—24no—
327C4×C11—24no—
328Dic11—28no—
329Dic11—44no—
330Dic11—44no—
331Dic11—44no—
332C25C22×D1112yes—
333C25C22×D1111yescharacteristic
334C22×D4—28no—
335C22×D4—28no—
336C22×D4—42no—
337C22×D4—42no—
338C22×D4C2×Dic11116yescomplemented
339C22×D4C2×Dic1118yescomplemented
340C22×D4C22×D1118yes—
341C22×D4C22×D1114yes—
342C23×C4—42no—
343C23×C4—42no—
344C23×C4—112no—
345C23×C4—118no—
346C23×C4—114no—
347C23×C4—112no—
348C23×C4—112no—
349C23×C4—112no—
350C23×C4—118no—
351C23×C4—114no—
352C23×C4—228no—
353C23×C4—224no—
354C23×C4—442no—
355C23×C4—444no—
356C23×C4—442no—
357C23×C4—444no—
358C23×C4—442no—
359C23×C4—442no—
360C23×C4C2×Dic1118yescomplemented
361C23×C4C22×D1111yescharacteristic
362C23×C4C22×D1112yes—
363C23×C4C22×D1111yescharacteristic
364C23×C4C22×D1114yes—
365#121C2×Dic11164yescomplemented
366C4×D4—2264no—
367C2×C4⋊C4—118no—
368C2×C4⋊C4—114no—
369C2×C4⋊C4—114no—
370C2×C4⋊C4—228no—
371C2×C4⋊C4—442no—
372C2×C4⋊C4—442no—
373C2×C4⋊C4C2×Dic1118yescomplemented
374C2×C4⋊C4C22×D1114yes—
375C2×C22⋊C4—118no—
376C2×C22⋊C4—118no—
377C2×C22⋊C4—118no—
378C2×C22⋊C4—118no—
379C2×C22⋊C4—228no—
380C2×C22⋊C4—228no—
381C2×C22⋊C4—444no—
382C2×C22⋊C4—444no—
383C2×C22⋊C4C2×Dic11116yescomplemented
384C2×C22⋊C4C22×D1118yes—
385C2×C42—118no—
386C2×C42—228no—
387#95—118no—
388#95—118no—
389#95—118no—
390#95—118no—
391#95—118no—
392C2×C11—28no—
393C2×C11—48no—
394C2×C11#232518yescomplemented
395C2×C11C22×C4×D411yescharacteristic
396C2×C11C2×#51811yescharacteristic
397C2×C11C2×#52011yescharacteristic
398C2×C11C2×#53411yescharacteristic
399C2×C11C2×#53711yescharacteristic
400C2×C11C2×#53811yescharacteristic
401C2×C11C2×#53911yescharacteristic
402C24—22no—
403C24—22no—
404C24—22no—
405C24—22no—
406C24—24no—
407C24—24no—
408C24—24no—
409C24—24no—
410C24—24no—
411C24—24no—
412C24D4×D1114yes—
413C24#434114yes—
414C24C22×Dic1118yes—
415C24C22×Dic1114yes—
416C24C23×D1114yes—
417C24C23×D1112yes—
418C24C23×D1111yescharacteristic
419C2×D4—264no—
420C2×D4—216no—
421C2×D4—216no—
422C2×D4—44no—
423C2×D4—44no—
424C2×D4—416no—
425C2×D4C22×Dic11132yescomplemented
426C2×D4C22×Dic11116yescomplemented
427C22×C4—24no—
428C22×C4—24no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—44no—
434C22×C4—44no—
435C22×C4—416no—
436C22×C4—118no—
437C22×C4—114no—
438C22×C4—1116no—
439C22×C4—114no—
440C22×C4—114no—
441C22×C4—114no—
442C22×C4—2216no—
443C22×C4—224no—
444C22×C4—224no—
445C22×C4—224no—
446C22×C4—224no—
447C22×C4—228no—
448C22×C4—224no—
449C22×C4—224no—
450C22×C4—224no—
451C22×C4—224no—
452C22×C4—224no—
453C22×C4—224no—
454C22×C4—224no—
455C22×C4—4416no—
456C22×C4—444no—
457C22×C4—448no—
458C22×C4—444no—
459C22×C4—448no—
460C22×C4—444no—
461C22×C4—444no—
462C22×C4—4432no—
463C22×C4—4416no—
464C22×C4C22×Dic1114yes—
465C22×C4C22×Dic1118yes—
466C22×C4C22×Dic1114yes—
467C22×C4C22×Dic11116yescomplemented
468C22×C4C23×D1112yes—
469C22×C4C23×D1114yes—
470C22×C4C23×D1112yes—
471C4⋊C4—2216no—
472C4⋊C4—444no—
473C4⋊C4—444no—
474C4⋊C4C22×Dic11116yescomplemented
475C22⋊C4—2216no—
476C22⋊C4—2216no—
477C22⋊C4—448no—
478C22⋊C4—448no—
479C22⋊C4C22×Dic11132yescomplemented
480C42—2216no—
481C11C2×#232511yescharacteristic, complemented, Sylow
482C23—28no—
483C23—28no—
484C23—28no—
485C23—28no—
486C23—28no—
487C23—28no—
488C23—22no—
489C23—22no—
490C23—22no—
491C23—22no—
492C23—216no—
493C23—216no—
494C23—216no—
495C23—24no—
496C23—24no—
497C23—24no—
498C23—24no—
499C23—24no—
500C23—24no—
501C23—48no—
502C23—48no—
503C23—48no—
504C23—48no—
505C23D4×Dic11116yes—
506C23C2×D4×D1114yes—
507C23C2×D4×D1112yes—
508C23C2×#434114yes—
509C23C2×#434112yes—
510C23#6703712yes—
511C23#6703712yes—
512C23#6704212yes—
513C23#6704312yes—
514C23C23×Dic1118yes—
515C23C23×Dic1114yes—
516C23C23×Dic1112yes—
517C23C24×D1111yescharacteristic
518D4—264no—
519D4—416no—
520C2×C4—216no—
521C2×C4—28no—
522C2×C4—28no—
523C2×C4—24no—
524C2×C4—24no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—416no—
530C2×C4—118no—
531C2×C4—2216no—
532C2×C4—224no—
533C2×C4—224no—
534C2×C4—224no—
535C2×C4—224no—
536C2×C4—224no—
537C2×C4—224no—
538C2×C4—224no—
539C2×C4—224no—
540C2×C4—224no—
541C2×C4—224no—
542C2×C4—224no—
543C2×C4—4416no—
544C2×C4—4432no—
545C2×C4—4416no—
546C2×C4—448no—
547C2×C4—448no—
548C2×C4—448no—
549C2×C4C23×Dic1114yes—
550C2×C4C23×Dic1118yes—
551C2×C4C23×Dic1114yes—
552C22—24no—
553C22—24no—
554C22—24no—
555C22—24no—
556C22—24no—
557C22—24no—
558C22—232no—
559C22—28no—
560C22—28no—
561C22—28no—
562C22—44no—
563C22—44no—
564C22—44no—
565C22—44no—
566C22—432no—
567C22#1062312814yes—
568C22#1062313314yes—
569C22#1062313614yes—
570C22#1062314814yes—
571C22C2×D4×Dic1118yes—
572C22C2×D4×Dic1114yes—
573C22#1062332914yes—
574C22#1062335814yes—
575C22C22×D4×D1111yescharacteristic
576C22C22×#434111yescharacteristic
577C22C2×#6703711yescharacteristic
578C22C2×#6703711yescharacteristic
579C22C2×#6704211yescharacteristic
580C22C2×#6704311yescharacteristic
581C22C24×Dic1111yescharacteristic
582C4—28no—
583C4—24no—
584C4—24no—
585C4—228no—
586C4—444no—
587C4—444no—
588C4—444no—
589C2—28no—
590C2—48no—
591C2#1307132118yesdirect product factor
592C2C22×D4×Dic1111yescharacteristic
593C2C2×#1062332911yescharacteristic
594C2C2×#1062335811yescharacteristic
595C2C2×#1062313611yescharacteristic
596C2C2×#1062312811yescharacteristic
597C2C2×#1062314811yescharacteristic
598C2C2×#1062313311yescharacteristic
subgroupG/H
centerC24C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
Fitting, prime radicalC22×C11×#121C2
socleC24×C11C24
cosocleC23×C11C25
hypercenterC22×#121D11
hypocenterC11C2×#2325
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×#121

Complements

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

NH ≅ G/Ntype
1. C22×D4×Dic11C2semidirect
2. #13071321C2direct (N × H)
3. C2×#10622564C2semidirect
4. C2×#10622594C2semidirect
5. C2×#10622833C2semidirect
6. C2×#10622833C2semidirect
7. C2×#10622563C2semidirect
8. C2×#10622825C2semidirect
9. C22×C11⋊#95C2semidirect
17. C2×C11×#121C4semidirect
26. C2×D4×Dic11C22semidirect
31. #10622833C22semidirect
32. #10622833C22semidirect
33. #10622825C22semidirect
39. C2×C11⋊#95C22semidirect
40. #10622594C22semidirect
41. #10622564C22semidirect
42. #10622563C22semidirect
49. C22×D4×C11C2×C4semidirect
50. C22×D4×C11C2×C4semidirect
55. C23×C4×C11C2×C4semidirect
68. C23×Dic11D4semidirect
76. C11×#121C2×C4semidirect
77. C2×C11×C4⋊C4C2×C4semidirect
79. C2×C11×C22⋊C4C2×C4semidirect
127. C2×D4×C11C22×C4semidirect
128. C2×D4×C11C22×C4semidirect
141. C22×C4×C11C22×C4semidirect
168. C22×Dic11C2×D4semidirect
173. C11×C4⋊C4C22×C4semidirect
174. C11×C22⋊C4C22×C4semidirect
269. C2×#121Dic11semidirect
338. C22×D4C2×Dic11semidirect
339. C22×D4C2×Dic11semidirect
360. C23×C4C2×Dic11semidirect
365. #121C2×Dic11semidirect
373. C2×C4⋊C4C2×Dic11semidirect
383. C2×C22⋊C4C2×Dic11semidirect
394. C2×C11#2325semidirect
425. C2×D4C22×Dic11semidirect
426. C2×D4C22×Dic11semidirect
467. C22×C4C22×Dic11semidirect
474. C4⋊C4C22×Dic11semidirect
479. C22⋊C4C22×Dic11semidirect
481. C11C2×#2325semidirect
591. C2#13071321direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D4×Dic112
#130713212
C2×#106225642
C2×#106225942
C2×#106228332
C2×#106225632
C2×#106228252
C22×C11⋊#952
C22×C11×#1212
C2×#232511