Finite Group Databasebeta

← C2×#13071489 #14913014

Subgroups — C2×#13071489 #14913014

Order 2816.

3094 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊C4×D11C211yesmaximal, characteristic
2#13071489C2116yesmaximal, direct product factor
3C2×#10622541C211yesmaximal, characteristic, complemented
4C2×#10622586C211yesmaximal, characteristic, complemented
5C2×#10622546C212yesmaximal, complemented
6C2×#10622265C212yesmaximal, complemented
7C2×#10622280C212yesmaximal
8C2×#10622600C211yesmaximal, characteristic
9C2×C4⋊C4×Dic11C211yesmaximal, characteristic, complemented
10C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic
11C2×C4×(C2×D11)⋊C4C212yesmaximal
12C2×C4×C11×C4⋊C4C211yesmaximal, characteristic, complemented
13C23×C4×D11C2211yescharacteristic
14C23×C4×D11C2212yes—
15C22×C11×C4⋊C4C2211yescharacteristic
16C22×C11×C4⋊C4C2211yescharacteristic
17C22×C42×C11C2211yescharacteristic
18C22×C42×C11C2212yes—
19C22×(C2×D11)⋊C4C2212yes—
20C22×(C2×D11)⋊C4C2211yescharacteristic
21C22×(C2×D11)⋊C4C2211yescharacteristic
22C22×C4⋊Dic11C2211yescharacteristic
23C22×C4⋊Dic11C2211yescharacteristic
24C22×Dic11⋊C4C2212yes—
25C22×Dic11⋊C4C2212yes—
26C22×Dic11⋊C4C2212yes—
27C22×C4×Dic11C2211yescharacteristic
28C22×C4×Dic11C2212yes—
29C2×C4⋊C4×D11C4116yescomplemented
30C2×C4⋊C4×D11C2218yes—
31C4×C11×C4⋊C4C2218yescomplemented
32C2×C11×#95C2212yes—
33C2×C11⋊#95C2211yescharacteristic
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2211yescharacteristic
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38C2×C11⋊#95C2212yes—
39#10622600C2218yes—
40C4⋊C4×Dic11C2218yescomplemented
41#10622586C2218yescomplemented
42C4×(C2×D11)⋊C4C2218yes—
43C4×(C2×D11)⋊C4C22116yes—
44#10622546C22116yescomplemented
45#10622541C2218yescomplemented
46#10622280C22116yes—
47#10622265C22116yescomplemented
48C24×D11C2311yescharacteristic
49C23×C4×C11C2311yescharacteristic
50C23×C4×C11C2312yes—
51C23×C4×C11C2312yes—
52C23×C4×C11C2311yescharacteristic
53C23×C4×C11C2311yescharacteristic
54C23×Dic11C2311yescharacteristic
55C23×Dic11C2312yes—
56C23×Dic11C2312yes—
57C23×Dic11C2311yescharacteristic
58C23×Dic11C2311yescharacteristic
59C22×C4×D11—24no—
60C22×C4×D11—24no—
61C22×C4×D11—44no—
62C22×C4×D11—44no—
63C22×C4×D11C2×C418yes—
64C22×C4×D11C2×C4116yes—
65C22×C4×D11C2314yes—
66C22×C4×D11C2318yes—
67C2×C11×C4⋊C4—24no—
68C2×C11×C4⋊C4C2×C418yes—
69C2×C11×C4⋊C4C2314yes—
70C2×C11×C4⋊C4C2314yes—
71C2×C42×C11—24no—
72C2×C42×C11—44no—
73C2×C42×C11C2314yes—
74C2×C42×C11C2318yes—
75C2×(C2×D11)⋊C4—28no—
76C2×(C2×D11)⋊C4—24no—
77C2×(C2×D11)⋊C4Q818yes—
78C2×(C2×D11)⋊C4C2314yes—
79C2×(C2×D11)⋊C4C2318yes—
80C2×(C2×D11)⋊C4C2314yes—
81C2×C4⋊Dic11—24no—
82C2×C4⋊Dic11C2×C418yes—
83C2×C4⋊Dic11C2314yes—
84C2×C4⋊Dic11C2314yes—
85C2×Dic11⋊C4—44no—
86C2×Dic11⋊C4—44no—
87C2×Dic11⋊C4C2×C4116yes—
88C2×Dic11⋊C4C2318yes—
89C2×Dic11⋊C4C2318yes—
90C2×Dic11⋊C4C2318yes—
91C2×C4×Dic11—24no—
92C2×C4×Dic11—44no—
93C2×C4×Dic11C2314yes—
94C2×C4×Dic11C2318yes—
95C4⋊C4×D11C2×C4164yescomplemented
96C11×#95C2318yes—
97C11⋊#95C2314yes—
98C11⋊#95C2318yes—
99C11⋊#95C2318yes—
100C11⋊#95C2318yes—
101C11⋊#95C2318yes—
102C11⋊#95C2314yes—
103C2×#2345—111nomaximal, Sylow
104C24×C11C2411yescharacteristic
105C23×D11—22no—
106C23×D11—22no—
107C23×D11—22no—
108C23×D11—22no—
109C23×D11C22×C414yes—
110C23×D11C2×Q814yes—
111C23×D11#4114yes—
112C23×D11C2412yes—
113C22×C4×C11—22no—
114C22×C4×C11—24no—
115C22×C4×C11—22no—
116C22×C4×C11—24no—
117C22×C4×C11—22no—
118C22×C4×C11—24no—
119C22×C4×C11—22no—
120C22×C4×C11—24no—
121C22×C4×C11—22no—
122C22×C4×C11—24no—
123C22×C4×C11C22×C418yes—
124C22×C4×C11C22×C414yes—
125C22×C4×C11C2×Q814yes—
126C22×C4×C11#4114yes—
127C22×C4×C11#4114yes—
128C22×C4×C11C2414yes—
129C22×C4×C11C2412yes—
130C22×C4×C11C2414yes—
131C22×C4×C11C2412yes—
132C22×C4×C11C2412yes—
133C22×Dic11—22no—
134C22×Dic11—22no—
135C22×Dic11—22no—
136C22×Dic11—22no—
137C22×Dic11—24no—
138C22×Dic11—22no—
139C22×Dic11—24no—
140C22×Dic11—22no—
141C22×Dic11—24no—
142C22×Dic11—24no—
143C22×Dic11—24no—
144C22×Dic11—22no—
145C22×Dic11C22×C414yes—
146C22×Dic11C22×C418yes—
147C22×Dic11C2×Q814yes—
148C22×Dic11C2412yes—
149C22×Dic11C2414yes—
150C22×Dic11C2412yes—
151C22×Dic11C2414yes—
152C22×Dic11C2412yes—
153C2×C4×D11—232no—
154C2×C4×D11—28no—
155C2×C4×D11—28no—
156C2×C4×D11—432no—
157C2×C4×D11—48no—
158C2×C4×D11—48no—
159C2×C4×D11C22×C4116yes—
160C2×C4×D11C22×C4132yes—
161C11×C4⋊C4—28no—
162C11×C4⋊C4C22×C4116yes—
163C42×C11—28no—
164C42×C11—48no—
165(C2×D11)⋊C4—28no—
166(C2×D11)⋊C4—216no—
167(C2×D11)⋊C4C2×Q8116yes—
168C4⋊Dic11—28no—
169C4⋊Dic11C22×C4116yes—
170Dic11⋊C4—48no—
171Dic11⋊C4—48no—
172Dic11⋊C4C22×C4132yes—
173C4×Dic11—28no—
174C4×Dic11—48no—
175C23×C4⋊C4—111no—
176#2345—1116no—
177C2×#389—111no—
178C2×#389—111no—
179C2×#387—112no—
180C2×#387—112no—
181C2×#380—112no—
182C2×#380—111no—
183C2×C4×C4⋊C4—111no—
184C2×C4×C4⋊C4D1111yescharacteristic, complemented
185C2×C4×C22⋊C4—111no—
186C2×C4×C22⋊C4—112no—
187C23×C11C23×C412yes—
188C23×C11C22×Q812yes—
189C23×C11C2×#4112yes—
190C23×C11C2×#4112yes—
191C23×C11C2×#4112yes—
192C23×C11H(5,𝔽2)12yes—
193C23×C11H(5,𝔽2)12yes—
194C23×C11C2511yescharacteristic
195C22×D11—28no—
196C22×D11—28no—
197C22×D11—28no—
198C22×D11—28no—
199C22×D11—28no—
200C22×D11—28no—
201C22×D11—22no—
202C22×D11—22no—
203C22×D11—22no—
204C22×D11—22no—
205C22×D11C4×Q8116yes—
206C22×D11C23×C414yes—
207C22×D11C22×Q814yes—
208C22×D11C2×#4114yes—
209C2×C4×C11—216no—
210C2×C4×C11—28no—
211C2×C4×C11—22no—
212C2×C4×C11—24no—
213C2×C4×C11—22no—
214C2×C4×C11—24no—
215C2×C4×C11—24no—
216C2×C4×C11—22no—
217C2×C4×C11—22no—
218C2×C4×C11—24no—
219C2×C4×C11—22no—
220C2×C4×C11—24no—
221C2×C4×C11—44no—
222C2×C4×C11—48no—
223C2×C4×C11#117116yes—
224C2×C4×C11C23×C418yes—
225C2×C4×C11C23×C414yes—
226C2×C4×C11C22×Q814yes—
227C2×C4×C11C2×#4114yes—
228C2×C4×C11C2×#4114yes—
229C2×Dic11—28no—
230C2×Dic11—216no—
231C2×Dic11—28no—
232C2×Dic11—22no—
233C2×Dic11—22no—
234C2×Dic11—22no—
235C2×Dic11—22no—
236C2×Dic11—24no—
237C2×Dic11—24no—
238C2×Dic11—22no—
239C2×Dic11—24no—
240C2×Dic11—22no—
241C2×Dic11—24no—
242C2×Dic11—24no—
243C2×Dic11—22no—
244C2×Dic11—48no—
245C2×Dic11—44no—
246C2×Dic11C23×C414yes—
247C2×Dic11C23×C418yes—
248C2×Dic11C22×Q814yes—
249C4×D11—232no—
250C4×D11—432no—
251C24×C4—111no—
252C24×C4—112no—
253C22×C4⋊C4—112no—
254C22×C4⋊C4—111no—
255C22×C4⋊C4—118no—
256C22×C4⋊C4—1116no—
257C22×C4⋊C4—111no—
258C22×C4⋊C4—112no—
259C22×C4⋊C4—112no—
260C22×C4⋊C4C2×D1111yescharacteristic
261C22×C4⋊C4C2×D1111yescharacteristic
262C22×C22⋊C4—111no—
263C22×C22⋊C4—111no—
264C22×C22⋊C4—112no—
265C22×C42—111no—
266C22×C42—112no—
267C22×C42C2×D1111yescharacteristic
268C22×C42C2×D1112yes—
269#389—118no—
270#389—118no—
271#387—1116no—
272#387—1116no—
273#380—118no—
274#380—1116no—
275C4×C4⋊C4—118no—
276C4×C4⋊C4C2×D1118yescomplemented
277C4×C22⋊C4—118no—
278C4×C22⋊C4—1116no—
279C2×#95—111no—
280C2×#95—111no—
281C2×#95—112no—
282C2×#95—112no—
283C2×#95—112no—
284C2×#95—112no—
285C2×#95C2×D1112yes—
286C22×C11C2×#11714yes—
287C22×C11C2×C4×Q814yes—
288C22×C11#51814yes—
289C22×C11#55314yes—
290C22×C11#55314yes—
291C22×C11#55414yes—
292C22×C11#55414yes—
293C22×C11C24×C411yescharacteristic
294C22×C11C23×Q811yescharacteristic
295C22×C11C22×#4111yescharacteristic
296C22×C11C22×#4111yescharacteristic
297C22×C11C22×#4111yescharacteristic
298C22×C11C2×H(5,𝔽2)11yescharacteristic
299C22×C11C2×H(5,𝔽2)11yescharacteristic
300C2×D11—232no—
301C2×D11—24no—
302C2×D11—24no—
303C2×D11—24no—
304C2×D11—24no—
305C2×D11—24no—
306C2×D11—24no—
307C2×D11C2×C4×Q818yes—
308C4×C11—28no—
309C4×C11—24no—
310C4×C11—42no—
311C4×C11—44no—
312C4×C11C2×#11718yes—
313Dic11—24no—
314Dic11—28no—
315Dic11—24no—
316Dic11—44no—
317Dic11—42no—
318C25—111no—
319C23×C4—111no—
320C23×C4—112no—
321C23×C4—111no—
322C23×C4—118no—
323C23×C4—114no—
324C23×C4—1116no—
325C23×C4—118no—
326C23×C4—111no—
327C23×C4—112no—
328C23×C4—224no—
329C23×C4—224no—
330C23×C4—444no—
331C23×C4—444no—
332C23×C4C22×D1111yescharacteristic
333C23×C4C22×D1112yes—
334C23×C4C22×D1112yes—
335C23×C4C22×D1111yescharacteristic
336C23×C4C22×D1111yescharacteristic
337C2×C4⋊C4—24no—
338C2×C4⋊C4—1116no—
339C2×C4⋊C4—118no—
340C2×C4⋊C4—118no—
341C2×C4⋊C4—114no—
342C2×C4⋊C4—1164no—
343C2×C4⋊C4—114no—
344C2×C4⋊C4—118no—
345C2×C4⋊C4—118no—
346C2×C4⋊C4—224no—
347C2×C4⋊C4—444no—
348C2×C4⋊C4—444no—
349C2×C4⋊C4C4×D1118yes—
350C2×C4⋊C4C22×D1114yes—
351C2×C4⋊C4C22×D1114yes—
352C2×C22⋊C4—118no—
353C2×C22⋊C4—114no—
354C2×C22⋊C4—118no—
355C2×C22⋊C4—114no—
356C2×C22⋊C4—224no—
357C2×C22⋊C4—228no—
358C2×C42—24no—
359C2×C42—44no—
360C2×C42—114no—
361C2×C42—118no—
362C2×C42—224no—
363C2×C42—444no—
364C2×C42C22×D1114yes—
365C2×C42C22×D1118yes—
366#95—114no—
367#95—114no—
368#95—118no—
369#95—118no—
370#95—118no—
371#95—118no—
372#95C22×D1118yes—
373C2×C11#234518yescomplemented
374C2×C11C22×#11711yescharacteristic
375C2×C11C22×C4×Q811yescharacteristic
376C2×C11C2×#51811yescharacteristic
377C2×C11C2×#55311yescharacteristic
378C2×C11C2×#55311yescharacteristic
379C2×C11C2×#55411yescharacteristic
380C2×C11C2×#55411yescharacteristic
381D11—28no—
382C24—114no—
383C24—114no—
384C24—114no—
385C24—112no—
386C24—222no—
387C24—222no—
388C24—222no—
389C24—222no—
390C24C23×D1111yescharacteristic
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—24no—
394C22×C4—24no—
395C22×C4—22no—
396C22×C4—24no—
397C22×C4—24no—
398C22×C4—22no—
399C22×C4—24no—
400C22×C4—22no—
401C22×C4—114no—
402C22×C4—118no—
403C22×C4—114no—
404C22×C4—112no—
405C22×C4—112no—
406C22×C4—114no—
407C22×C4—1116no—
408C22×C4—1132no—
409C22×C4—112no—
410C22×C4—114no—
411C22×C4—222no—
412C22×C4—222no—
413C22×C4—222no—
414C22×C4—224no—
415C22×C4—222no—
416C22×C4—224no—
417C22×C4—2232no—
418C22×C4—228no—
419C22×C4—228no—
420C22×C4—222no—
421C22×C4—224no—
422C22×C4—222no—
423C22×C4—224no—
424C22×C4—222no—
425C22×C4—224no—
426C22×C4—4432no—
427C22×C4—448no—
428C22×C4—448no—
429C22×C4C2×C4×D1118yes—
430C22×C4C2×C4×D1114yes—
431C22×C4#433914yes—
432C22×C4#433914yes—
433C22×C4Q8×D1114yes—
434C22×C4C23×D1114yes—
435C22×C4C23×D1112yes—
436C22×C4C23×D1114yes—
437C22×C4C23×D1112yes—
438C22×C4C23×D1112yes—
439C4⋊C4—28no—
440C4⋊C4—1132no—
441C4⋊C4—1116no—
442C4⋊C4—228no—
443C4⋊C4—448no—
444C4⋊C4—448no—
445C4⋊C4C2×C4×D11116yes—
446C22⋊C4—1116no—
447C22⋊C4—228no—
448C22⋊C4—2216no—
449C42—28no—
450C42—48no—
451C42—228no—
452C42—448no—
453C11C2×#234511yescharacteristic, complemented, Sylow
454C23—1116no—
455C23—114no—
456C23—114no—
457C23—114no—
458C23—228no—
459C23—228no—
460C23—228no—
461C23—228no—
462C23—228no—
463C23—228no—
464C23—222no—
465C23—222no—
466C23—222no—
467C23—222no—
468C23C22×C4×D1112yes—
469C23C2×#433912yes—
470C23C2×#433912yes—
471C23#6703712yes—
472C23C2×Q8×D1112yes—
473C23#41×D1112yes—
474C23#6704212yes—
475C23C24×D1111yescharacteristic
476C2×C4—28no—
477C2×C4—216no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—24no—
481C2×C4—24no—
482C2×C4—22no—
483C2×C4—24no—
484C2×C4—24no—
485C2×C4—22no—
486C2×C4—24no—
487C2×C4—22no—
488C2×C4—44no—
489C2×C4—48no—
490C2×C4—114no—
491C2×C4—118no—
492C2×C4—114no—
493C2×C4—228no—
494C2×C4—2216no—
495C2×C4—228no—
496C2×C4—222no—
497C2×C4—222no—
498C2×C4—222no—
499C2×C4—224no—
500C2×C4—222no—
501C2×C4—224no—
502C2×C4—2232no—
503C2×C4—222no—
504C2×C4—224no—
505C2×C4—222no—
506C2×C4—224no—
507C2×C4—222no—
508C2×C4—224no—
509C2×C4—4432no—
510C2×C4—448no—
511C2×C4—444no—
512C2×C4#66925116yes—
513C2×C4C22×C4×D1118yes—
514C2×C4C22×C4×D1114yes—
515C2×C4C2×#433914yes—
516C2×C4C2×#433914yes—
517C2×C4C2×Q8×D1114yes—
518C22—118no—
519C22—224no—
520C22—224no—
521C22—224no—
522C22—224no—
523C22—2232no—
524C22—224no—
525C22—224no—
526C22C2×#6692514yes—
527C22#1062304214yes—
528C22#1062306114yes—
529C22#1062307614yes—
530C22#1062308914yes—
531C22C4×Q8×D1114yes—
532C22#1062311014yes—
533C22C23×C4×D1111yescharacteristic
534C22C22×#433911yescharacteristic
535C22C22×#433911yescharacteristic
536C22C2×#6703711yescharacteristic
537C22C22×Q8×D1111yescharacteristic
538C22C2×#41×D1111yescharacteristic
539C22C2×#6704211yescharacteristic
540C4—24no—
541C4—28no—
542C4—42no—
543C4—44no—
544C4—224no—
545C4—224no—
546C4—228no—
547C4—444no—
548C4—442no—
549C4C2×#6692518yes—
550C2—228no—
551C2#1307148918yesdirect product factor
552C2C22×#6692511yescharacteristic
553C2C2×C4×Q8×D1111yescharacteristic
554C2C2×#1062307611yescharacteristic
555C2C2×#1062306111yescharacteristic
556C2C2×#1062308911yescharacteristic
557C2C2×#1062304211yescharacteristic
558C2C2×#1062311011yescharacteristic
subgroupG/H
centerC24C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC2×C4×C11×C4⋊C4C2
socleC24×C11C24
prime radicalC24×D11C23
cosocleC23×C11C25
hypercenterC2×C4×C4⋊C4D11
hypocenterC11C2×#2345
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #13071489C2direct (N × H)
3. C2×#10622541C2semidirect
4. C2×#10622586C2semidirect
5. C2×#10622546C2semidirect
6. C2×#10622265C2semidirect
9. C2×C4⋊C4×Dic11C2semidirect
12. C2×C4×C11×C4⋊C4C2semidirect
29. C2×C4⋊C4×D11C4semidirect
31. C4×C11×C4⋊C4C22semidirect
40. C4⋊C4×Dic11C22semidirect
41. #10622586C22semidirect
44. #10622546C22semidirect
45. #10622541C22semidirect
47. #10622265C22semidirect
95. C4⋊C4×D11C2×C4semidirect
184. C2×C4×C4⋊C4D11semidirect
276. C4×C4⋊C4C2×D11semidirect
373. C2×C11#2345semidirect
453. C11C2×#2345semidirect
551. C2#13071489direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4⋊C4×D112
#130714892
C2×#106225412
C2×#106225862
C2×#106225462
C2×#106222652
C2×#106222802
C2×#106226002
C2×C4⋊C4×Dic112
C2×C4×(C2×D11)⋊C42
C2×C4×C11×C4⋊C42
C2×#234511