Finite Group Databasebeta

← C2×#13079388 #15624315

Subgroups — C2×#13079388 #15624315

Order 2816.

2354 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66977C211yesmaximal, characteristic
2#13079388C2116yesmaximal, direct product factor
3C2×#10622583C212yesmaximal, complemented
4C2×#10622657C212yesmaximal, complemented
5C2×#10622664C214yesmaximal, complemented
6C2×#10622841C212yesmaximal, complemented
7C2×#10622663C212yesmaximal, complemented
8C22×C22⋊(C11⋊C8)C211yesmaximal, characteristic
9C22×C11×C22⋊Q8C211yesmaximal, characteristic
10C23×Q8×C11C2211yescharacteristic
11C24×C4×C11C2211yescharacteristic
12C23×Dic22C2211yescharacteristic
13C2×C11×C22⋊Q8—21no—
14C2×C11×C22⋊Q8—21no—
15C2×C11×C22⋊Q8—24no—
16C2×C11×C22⋊Q8C2212yes—
17C2×C11×C22⋊Q8C2218yes—
18C2×C11×C22⋊Q8C2212yes—
19C22×C11×C4⋊C4—21no—
20C22×C11×C4⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4—21no—
22C22×C22⋊Dic11—21no—
23C22×#4326C2214yescomplemented
24C22×C4⋊Dic11C2211yescharacteristic
25C2×#66977—21no—
26C2×#66977—21no—
27C2×#66977—24no—
28C2×#66977C2212yes—
29C2×#66977C2218yes—
30C2×#66977C2212yes—
31C22×Dic11⋊C4—21no—
32C23×C11⋊C8C2212yes—
33#10622841C22116yescomplemented
34C2×#66899C2214yescomplemented
35C2×C22⋊(C11⋊C8)C2212yes—
36C2×C22⋊(C11⋊C8)C2212yes—
37C2×C22⋊(C11⋊C8)C2218yes—
38#10622664C22132yescomplemented
39#10622663C22116yescomplemented
40#10622657C22116yescomplemented
41#10622583C22116yescomplemented
42C2×#66874C2214yescomplemented
43C2×#66871C2214yescomplemented
44C25×C11D411yescharacteristic
45C22×Q8×C11—21no—
46C22×Q8×C11—22no—
47C22×Q8×C11—44no—
48C22×Q8×C11C2312yes—
49C22×Q8×C11C2314yes—
50C23×C4×C11—21no—
51C23×C4×C11—21no—
52C23×C4×C11—44no—
53C23×C4×C11D411yescharacteristic
54C23×C4×C11D411yescharacteristic
55C23×C4×C11D414yes—
56C23×C4×C11D411yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2314yes—
61C23×Dic11—21no—
62C23×Dic11—21no—
63C22×Dic22—21no—
64C22×Dic22—22no—
65C22×Dic22—44no—
66C22×Dic22C2312yes—
67C22×Dic22C2314yes—
68C11×C22⋊Q8—24no—
69C11×C22⋊Q8—24no—
70C11×C22⋊Q8—28no—
71C11×C22⋊Q8—28no—
72C11×C22⋊Q8C2318yes—
73C11×C22⋊Q8C2318yes—
74C2×C11×C4⋊C4—22no—
75C2×C11×C4⋊C4—22no—
76C2×C11×C4⋊C4—28no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4—22no—
79C2×C11×C4⋊C4C2312yes—
80C2×C11×C4⋊C4C2314yes—
81C2×C11×C22⋊C4—22no—
82C2×C11×C22⋊C4—22no—
83C2×C11×C22⋊C4—28no—
84C2×C22⋊Dic11—22no—
85C2×C22⋊Dic11—22no—
86C2×C22⋊Dic11—28no—
87C2×#4326—48no—
88C2×#4326C23116yescomplemented
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11—22no—
91C2×C4⋊Dic11C2312yes—
92C2×C4⋊Dic11C2314yes—
93#66977—24no—
94#66977—24no—
95#66977—28no—
96#66977—28no—
97#66977C2318yes—
98#66977C2318yes—
99C2×Dic11⋊C4—22no—
100C2×Dic11⋊C4—22no—
101C2×Dic11⋊C4—28no—
102C22×C11⋊C8—44no—
103C22×C11⋊C8C2314yes—
104C22×C11⋊C8C2318yes—
105#66899C23116yescomplemented
106C22⋊(C11⋊C8)C2318yes—
107C22⋊(C11⋊C8)C2318yes—
108#66874C23116yescomplemented
109#66871C23116yescomplemented
110C2×#3189—111nomaximal, Sylow
111C24×C11—42no—
112C24×C11—42no—
113C24×C11Q1618yescomplemented
114C24×C11C2×D411yescharacteristic
115C24×C11C2×D411yescharacteristic
116C24×C11C2×D411yescharacteristic
117C24×C11C2×D414yes—
118C2×Q8×C11—24no—
119C2×Q8×C11—22no—
120C2×Q8×C11—28no—
121C2×Q8×C11—48no—
122C2×Q8×C11—44no—
123C2×Q8×C11—48no—
124C2×Q8×C11C2414yes—
125C22×C4×C11—24no—
126C22×C4×C11—24no—
127C22×C4×C11—24no—
128C22×C4×C11—24no—
129C22×C4×C11—22no—
130C22×C4×C11—24no—
131C22×C4×C11—22no—
132C22×C4×C11—48no—
133C22×C4×C11—48no—
134C22×C4×C11—42no—
135C22×C4×C11—42no—
136C22×C4×C11—42no—
137C22×C4×C11—44no—
138C22×C4×C11—44no—
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D412yes—
142C22×C4×C11C2×D412yes—
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D412yes—
145C22×C4×C11C2×D414yes—
146C22×C4×C11C2×D414yes—
147C22×C4×C11C2×D414yes—
148C22×C4×C11C2412yes—
149C22×C4×C11C2412yes—
150C22×C4×C11C2412yes—
151C22×C4×C11C2411yescharacteristic
152C22×Dic11—24no—
153C22×Dic11—22no—
154C22×Dic11—24no—
155C22×Dic11—22no—
156C22×Dic11—44no—
157C22×Dic11—44no—
158C2×Dic22—24no—
159C2×Dic22—22no—
160C2×Dic22—28no—
161C2×Dic22—48no—
162C2×Dic22—44no—
163C2×Dic22—48no—
164C2×Dic22C2414yes—
165C11×C4⋊C4—28no—
166C11×C4⋊C4—28no—
167C11×C4⋊C4—24no—
168C11×C4⋊C4—22no—
169C11×C4⋊C4C2414yes—
170C11×C22⋊C4—28no—
171C11×C22⋊C4—28no—
172C22⋊Dic11—28no—
173C22⋊Dic11—28no—
174#4326—416no—
175C4⋊Dic11—24no—
176C4⋊Dic11—22no—
177C4⋊Dic11C2414yes—
178Dic11⋊C4—28no—
179Dic11⋊C4—28no—
180C2×C11⋊C8—28no—
181C2×C11⋊C8—48no—
182C2×C11⋊C8C2418yes—
183C22×C22⋊Q8—111no—
184C22×C22⋊Q8D1111yescharacteristic
185#3189—1116no—
186C2×#484—112no—
187C2×#484—112no—
188C2×#467—114no—
189C2×#451—112no—
190C2×#451—112no—
191C22×C22⋊C8—111no—
192C23×C11—22no—
193C23×C11—22no—
194C23×C11—22no—
195C23×C11—22no—
196C23×C11—22no—
197C23×C11—22no—
198C23×C11—44no—
199C23×C11—416no—
200C23×C11—44no—
201C23×C11C2×Q1614yes—
202C23×C11C2×Q1614yes—
203C23×C11C2×Q1614yes—
204C23×C11C2×Q16116yescomplemented
205C23×C11C22×D412yes—
206C23×C11C22×D412yes—
207C23×C11C22×D412yes—
208C23×C11C22×D411yescharacteristic
209Q8×C11—28no—
210Q8×C11—48no—
211Q8×C11—44no—
212C2×C4×C11—22no—
213C2×C4×C11—22no—
214C2×C4×C11—22no—
215C2×C4×C11—24no—
216C2×C4×C11—24no—
217C2×C4×C11—24no—
218C2×C4×C11—24no—
219C2×C4×C11—24no—
220C2×C4×C11—24no—
221C2×C4×C11—24no—
222C2×C4×C11—24no—
223C2×C4×C11—44no—
224C2×C4×C11—44no—
225C2×C4×C11—44no—
226C2×C4×C11—48no—
227C2×C4×C11—48no—
228C2×C4×C11—44no—
229C2×C4×C11—44no—
230C2×C4×C11C22×D412yes—
231C2×C4×C11C22×D412yes—
232C2×C4×C11C22×D412yes—
233C2×C4×C11C22×D411yescharacteristic
234C2×C4×C11H(5,𝔽2)14yes—
235C2×C4×C11C2511yescharacteristic
236C2×Dic11—24no—
237C2×Dic11—24no—
238C2×Dic11—48no—
239C2×Dic11—48no—
240C2×Dic11—44no—
241C2×Dic11—44no—
242Dic22—28no—
243Dic22—48no—
244Dic22—44no—
245C11⋊C8—28no—
246C23×Q8—111no—
247C23×Q8C2×D1111yescharacteristic
248C24×C4C2×D1111yescharacteristic
249C22×Q16—114no—
250C23×C8—112no—
251C2×C22⋊Q8—21no—
252C2×C22⋊Q8—24no—
253C2×C22⋊Q8—21no—
254C2×C22⋊Q8—112no—
255C2×C22⋊Q8—118no—
256C2×C22⋊Q8—112no—
257C2×C22⋊Q8—221no—
258C2×C22⋊Q8—224no—
259C2×C22⋊Q8—221no—
260C2×C22⋊Q8C2×D1112yes—
261C2×C22⋊Q8C2×D1118yes—
262C2×C22⋊Q8C2×D1112yes—
263C22×C4⋊C4—21no—
264C22×C4⋊C4—111no—
265C22×C4⋊C4—221no—
266C22×C4⋊C4C2×D1111yescharacteristic
267C22×C22⋊C4—21no—
268C22×C22⋊C4—221no—
269#484—1116no—
270#484—1116no—
271#467—1132no—
272#451—1116no—
273#451—1116no—
274C2×#107—114no—
275C2×#103—114no—
276C2×#103—114no—
277C2×C22⋊C8—112no—
278C2×C22⋊C8—112no—
279C2×C22⋊C8—118no—
280C22×C11—28no—
281C22×C11—28no—
282C22×C11—28no—
283C22×C11—22no—
284C22×C11—22no—
285C22×C11—22no—
286C22×C11—22no—
287C22×C11—22no—
288C22×C11—22no—
289C22×C11—416no—
290C22×C11#53412yes—
291C22×C11C22×Q1614yes—
292C22×C11C22×Q1614yes—
293C22×C11C22×Q1614yes—
294C22×C11C22×Q1612yes—
295C22×C11#57512yes—
296C22×C11C23×D411yescharacteristic
297C4×C11—22no—
298C4×C11—22no—
299C4×C11—22no—
300C4×C11—44no—
301C4×C11—44no—
302C4×C11#53412yes—
303C4×C11C2×H(5,𝔽2)12yes—
304Dic11—44no—
305Dic11—44no—
306C25C22⋊D1111yescharacteristic
307C22×Q8—22no—
308C22×Q8—21no—
309C22×Q8—44no—
310C22×Q8—112no—
311C22×Q8—114no—
312C22×Q8—222no—
313C22×Q8—221no—
314C22×Q8—444no—
315C22×Q8C22×D1112yes—
316C22×Q8C22×D1114yes—
317C23×C4—21no—
318C23×C4—21no—
319C23×C4—44no—
320C23×C4—221no—
321C23×C4—221no—
322C23×C4C22⋊D1111yescharacteristic
323C23×C4C22⋊D1111yescharacteristic
324C23×C4C22⋊D1114yes—
325C23×C4C22⋊D1111yescharacteristic
326C23×C4C22×D1111yescharacteristic
327C23×C4C22×D1111yescharacteristic
328C23×C4C22×D1111yescharacteristic
329C23×C4C22×D1114yes—
330C2×Q16—1116no—
331C2×Q16—448no—
332C22×C8—114no—
333C22×C8—118no—
334C22×C8—444no—
335C22⋊Q8—24no—
336C22⋊Q8—24no—
337C22⋊Q8—28no—
338C22⋊Q8—28no—
339C22⋊Q8—118no—
340C22⋊Q8—118no—
341C22⋊Q8—224no—
342C22⋊Q8—224no—
343C22⋊Q8—228no—
344C22⋊Q8—228no—
345C22⋊Q8C22×D1118yes—
346C22⋊Q8C22×D1118yes—
347C2×C4⋊C4—28no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—112no—
353C2×C4⋊C4—114no—
354C2×C4⋊C4—222no—
355C2×C4⋊C4—221no—
356C2×C4⋊C4—228no—
357C2×C4⋊C4—222no—
358C2×C4⋊C4—222no—
359C2×C4⋊C4C22×D1112yes—
360C2×C4⋊C4C22×D1114yes—
361C2×C22⋊C4—28no—
362C2×C22⋊C4—22no—
363C2×C22⋊C4—22no—
364C2×C22⋊C4—228no—
365C2×C22⋊C4—222no—
366C2×C22⋊C4—222no—
367#107—1116no—
368#103—1116no—
369#103—1116no—
370C22⋊C8—118no—
371C22⋊C8—118no—
372C2×C11—24no—
373C2×C11—24no—
374C2×C11—24no—
375C2×C11#318914yescomplemented
376C2×C11C2×#53411yescharacteristic
377C2×C11C23×Q1611yescharacteristic
378C2×C11C2×#57511yescharacteristic
379C24—42no—
380C24—42no—
381C24#432618yescomplemented
382C24C2×C22⋊D1111yescharacteristic
383C24C2×C22⋊D1111yescharacteristic
384C24C2×C22⋊D1111yescharacteristic
385C24C2×C22⋊D1114yes—
386C2×Q8—24no—
387C2×Q8—22no—
388C2×Q8—28no—
389C2×Q8—48no—
390C2×Q8—44no—
391C2×Q8—48no—
392C2×Q8—114no—
393C2×Q8—224no—
394C2×Q8—222no—
395C2×Q8—228no—
396C2×Q8—448no—
397C2×Q8—444no—
398C2×Q8—448no—
399C2×Q8C23×D1114yes—
400C22×C4—24no—
401C22×C4—24no—
402C22×C4—24no—
403C22×C4—24no—
404C22×C4—24no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—48no—
408C22×C4—48no—
409C22×C4—42no—
410C22×C4—42no—
411C22×C4—42no—
412C22×C4—44no—
413C22×C4—44no—
414C22×C4—224no—
415C22×C4—224no—
416C22×C4—222no—
417C22×C4—222no—
418C22×C4—444no—
419C22×C4—444no—
420C22×C4C2×C22⋊D1112yes—
421C22×C4C2×C22⋊D1112yes—
422C22×C4C2×C22⋊D1112yes—
423C22×C4C2×C22⋊D1111yescharacteristic
424C22×C4C2×C22⋊D1111yescharacteristic
425C22×C4C2×C22⋊D1111yescharacteristic
426C22×C4C2×C22⋊D1114yes—
427C22×C4C2×C22⋊D1114yes—
428C22×C4C2×C22⋊D1114yes—
429C22×C4C23×D1112yes—
430C22×C4C23×D1112yes—
431C22×C4C23×D1112yes—
432C22×C4C23×D1111yescharacteristic
433Q16—4416no—
434C2×C8—118no—
435C2×C8—228no—
436C2×C8—448no—
437C4⋊C4—28no—
438C4⋊C4—28no—
439C4⋊C4—24no—
440C4⋊C4—22no—
441C4⋊C4—114no—
442C4⋊C4—224no—
443C4⋊C4—222no—
444C4⋊C4—228no—
445C4⋊C4—228no—
446C4⋊C4C23×D1114yes—
447C22⋊C4—28no—
448C22⋊C4—28no—
449C22⋊C4—228no—
450C22⋊C4—228no—
451C11C2×#318911yescharacteristic, complemented, Sylow
452C23—22no—
453C23—22no—
454C23—22no—
455C23—22no—
456C23—22no—
457C23—22no—
458C23—44no—
459C23—416no—
460C23—44no—
461C23C2×#432614yes—
462C23C2×#432614yes—
463C23C2×#432614yes—
464C23C2×#4326116yescomplemented
465C23C22×C22⋊D1112yes—
466C23C22×C22⋊D1112yes—
467C23C22×C22⋊D1112yes—
468C23C22×C22⋊D1111yescharacteristic
469Q8—28no—
470Q8—48no—
471Q8—44no—
472Q8—228no—
473Q8—448no—
474Q8—444no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—24no—
479C2×C4—24no—
480C2×C4—24no—
481C2×C4—24no—
482C2×C4—24no—
483C2×C4—24no—
484C2×C4—24no—
485C2×C4—24no—
486C2×C4—44no—
487C2×C4—44no—
488C2×C4—44no—
489C2×C4—48no—
490C2×C4—48no—
491C2×C4—44no—
492C2×C4—44no—
493C2×C4—224no—
494C2×C4—224no—
495C2×C4—448no—
496C2×C4—448no—
497C2×C4—444no—
498C2×C4—444no—
499C2×C4#6703714yes—
500C2×C4C22×C22⋊D1112yes—
501C2×C4C22×C22⋊D1112yes—
502C2×C4C22×C22⋊D1112yes—
503C2×C4C22×C22⋊D1111yescharacteristic
504C2×C4C24×D1111yescharacteristic
505C8—228no—
506C22—22no—
507C22—22no—
508C22—22no—
509C22—28no—
510C22—28no—
511C22—28no—
512C22—22no—
513C22—22no—
514C22—22no—
515C22—416no—
516C22#1062333512yes—
517C22C22×#432614yes—
518C22C22×#432614yes—
519C22C22×#432614yes—
520C22C22×#432612yes—
521C22#1062335312yes—
522C22C23×C22⋊D1111yescharacteristic
523C4—22no—
524C4—22no—
525C4—22no—
526C4—44no—
527C4—44no—
528C4—444no—
529C4—444no—
530C4#1062333512yes—
531C4C2×#6703712yes—
532C2—24no—
533C2—24no—
534C2—24no—
535C2#1307938814yesdirect product factor
536C2C2×#1062333511yescharacteristic
537C2C23×#432611yescharacteristic
538C2C2×#1062335311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC22×C11×C22⋊Q8C2
socleC23×C11C22×D4
prime radicalC25×C11D4
hypercenterC22×C22⋊Q8D11
hypocenterC11C2×#3189
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C24×C4 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. #13079388C2direct (N × H)
3. C2×#10622583C2semidirect
4. C2×#10622657C2semidirect
5. C2×#10622664C2semidirect
6. C2×#10622841C2semidirect
7. C2×#10622663C2semidirect
23. C22×#4326C22semidirect
33. #10622841C22semidirect
34. C2×#66899C22semidirect
38. #10622664C22semidirect
39. #10622663C22semidirect
40. #10622657C22semidirect
41. #10622583C22semidirect
42. C2×#66874C22semidirect
43. C2×#66871C22semidirect
88. C2×#4326C23semidirect
105. #66899C23semidirect
108. #66874C23semidirect
109. #66871C23semidirect
113. C24×C11Q16semidirect
204. C23×C11C2×Q16semidirect
375. C2×C11#3189semidirect
381. C24#4326semidirect
451. C11C2×#3189semidirect
464. C23C2×#4326semidirect
535. C2#13079388direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669772
#130793882
C2×#106225832
C2×#106226572
C2×#106226642
C2×#106228412
C2×#106226632
C22×C22⋊(C11⋊C8)2
C22×C11×C22⋊Q82
C2×#318911