Finite Group Databasebeta

← C2×#13081491 #15634212

Subgroups — C2×#13081491 #15634212

Order 2816.

1842 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623098C211yesmaximal, characteristic, complemented
2#13081491C2116yesmaximal, direct product factor
3C2×#10622677C212yesmaximal, complemented
4C2×#10622692C211yesmaximal, characteristic, complemented
5C2×#10622676C212yesmaximal, complemented
6C2×#10622704C211yesmaximal, characteristic, complemented
7C2×#10622622C212yesmaximal
8C2×#10622620C211yesmaximal, characteristic
9C2×Q8×C11⋊C8C211yesmaximal, characteristic, complemented
10C2×C4×#4324C211yesmaximal, characteristic
11C2×C4×#4324C212yesmaximal
12C2×C11×#554C211yesmaximal, characteristic
13C11×#554—24no—
14C11×#554C2218yes—
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×C11×#125C2212yes—
17C2×C11×C22⋊Q8—21no—
18C2×C11×C22⋊Q8—22no—
19C2×C4×Q8×C11C2211yescharacteristic
20C2×C4×D4×C11C2211yescharacteristic
21C2×C4×D4×C11C2212yes—
22C22×C11×C4⋊C4—21no—
23C2×#66997—21no—
24C22×#4324C2211yescharacteristic
25#10623098—24no—
26#10623098C2218yescomplemented
27C2×#66942—22no—
28C2×#66940—21no—
29C2×#66923C2212yes—
30C2×#66922C2211yescharacteristic
31C2×C4×Dic22C2211yescharacteristic
32C2×C4×Dic22C2212yes—
33C2×#66896C2212yes—
34C2×#66896C2211yescharacteristic
35#10622704C2218yescomplemented
36#10622692C2218yescomplemented
37#10622677C22116yescomplemented
38#10622676C22116yescomplemented
39Q8×C11⋊C8C2218yescomplemented
40C4×#4324C22116yes—
41C4×#4324C2218yes—
42#10622622C22116yes—
43#10622620C2218yes—
44C2×#66874C2212yes—
45C2×#66874C2211yescharacteristic
46C2×#66872C2212yes—
47C2×#66872C2212yes—
48C2×#66872C2211yescharacteristic
49C2×#66871C2212yes—
50C2×#66871C2212yes—
51C2×C4⋊(C11⋊C8)C2211yescharacteristic
52C2×C4⋊(C11⋊C8)C2212yes—
53C2×C4×C11⋊C8C2211yescharacteristic
54C2×C4×C11⋊C8C2212yes—
55C22×Q8×C11—21no—
56C22×Q8×C11D411yescharacteristic
57C22×D4×C11C2311yescharacteristic
58C23×C4×C11—21no—
59C23×C4×C11—22no—
60C22×Dic22—21no—
61C22×Dic22C2311yescharacteristic
62C11×C4⋊Q8—22no—
63C11×C4⋊Q8C2314yes—
64C11×#125—24no—
65C11×#125C2318yes—
66C11×C22⋊Q8—28no—
67C11×C22⋊Q8—216no—
68C4×Q8×C11D414yes—
69C4×Q8×C11C2314yes—
70C4×D4×C11—22no—
71C4×D4×C11—24no—
72C4×D4×C11C2314yes—
73C4×D4×C11C2318yes—
74C2×C11×C4⋊C4—22no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—22no—
77C2×C11×C4⋊C4—28no—
78C2×C11×C4⋊C4D411yescharacteristic
79C2×C11×C4⋊C4D412yes—
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C4⋊C4C2312yes—
82C2×C11×C22⋊C4—21no—
83C2×C11×C22⋊C4—22no—
84C2×C42×C11C2311yescharacteristic
85C2×C42×C11C2312yes—
86#66997—28no—
87C2×#4324Q818yescomplemented
88C2×#4324C2314yes—
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11C2312yes—
91C2×C4⋊Dic11C2311yescharacteristic
92C2×Dic11⋊C4—21no—
93C2×Dic11⋊C4—22no—
94C2×Dic11⋊C4—22no—
95C2×Dic11⋊C4—22no—
96C2×C4×Dic11—22no—
97C2×C4×Dic11—21no—
98C22×C11⋊C8C2312yes—
99C22×C11⋊C8C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101#66942—216no—
102#66940—28no—
103#66923—24no—
104#66923C2318yes—
105#66922—22no—
106#66922C2314yes—
107C4×Dic22—24no—
108C4×Dic22—22no—
109C4×Dic22C2318yes—
110C4×Dic22C2314yes—
111#66896C2318yes—
112#66896C2314yes—
113#66874C2314yes—
114#66874C2318yes—
115#66872C2318yes—
116#66872C2314yes—
117#66872C2318yes—
118#66871C2318yes—
119#66871C2318yes—
120C4⋊(C11⋊C8)C2314yes—
121C4⋊(C11⋊C8)C2318yes—
122C4×C11⋊C8C2318yes—
123C4×C11⋊C8C2314yes—
124C2×#3381—111nomaximal, Sylow
125C24×C11—21no—
126C2×Q8×C11—24no—
127C2×Q8×C11—24no—
128C2×Q8×C11—82no—
129C2×Q8×C11C2×D414yes—
130C2×D4×C11—21no—
131C2×D4×C11—22no—
132C2×D4×C11C2×Q814yes—
133C2×D4×C11C2412yes—
134C22×C4×C11—21no—
135C22×C4×C11—22no—
136C22×C4×C11—24no—
137C22×C4×C11—28no—
138C22×C4×C11—44no—
139C22×C4×C11—84no—
140C22×C4×C11C2×D412yes—
141C22×C4×C11C2×D412yes—
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2411yescharacteristic
145C22×Dic11—21no—
146C22×Dic11—21no—
147C22×Dic11—22no—
148C2×Dic22—21no—
149C2×Dic22—24no—
150C2×Dic22—22no—
151C2×Dic22—44no—
152C2×Dic22C2×Q814yes—
153C2×Dic22C2412yes—
154C11×C4⋊C4—28no—
155C11×C4⋊C4—24no—
156C11×C4⋊C4—28no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—22no—
159C11×C4⋊C4C2×D414yes—
160C11×C4⋊C4C2×D418yes—
161C11×C4⋊C4C2412yes—
162C11×C4⋊C4C2414yes—
163C11×C22⋊C4—24no—
164C11×C22⋊C4—28no—
165C42×C11C2×D412yes—
166C42×C11C2×D414yes—
167C42×C11C2412yes—
168C42×C11C2414yes—
169#4324C2×Q8116yescomplemented
170C4⋊Dic11—22no—
171C4⋊Dic11—21no—
172C4⋊Dic11—24no—
173C4⋊Dic11C2412yes—
174C4⋊Dic11C2414yes—
175Dic11⋊C4—24no—
176Dic11⋊C4—28no—
177Dic11⋊C4—28no—
178Dic11⋊C4—28no—
179C4×Dic11—28no—
180C4×Dic11—24no—
181C2×C11⋊C8—24no—
182C2×C11⋊C8—22no—
183C2×C11⋊C8C2×Q814yes—
184C2×C11⋊C8C2414yes—
185C2×C11⋊C8C2412yes—
186C2×C11⋊C8C2412yes—
187C2×#557—111no—
188C2×#554D1111yescharacteristic
189#3381—1116no—
190C2×#499—112no—
191C2×#498—111no—
192C2×#479—112no—
193C2×#477—111no—
194C2×#478—112no—
195C2×#474—111no—
196C2×C8×Q8—111no—
197C2×C4×SD16—112no—
198C2×C4×SD16—111no—
199C23×C11—24no—
200C23×C11—22no—
201C23×C11—42no—
202C23×C11—42no—
203C23×C11C22×D411yescharacteristic
204Q8×C11—28no—
205Q8×C11—84no—
206D4×C11—24no—
207D4×C11—22no—
208D4×C11C22×Q814yes—
209C2×C4×C11—24no—
210C2×C4×C11—24no—
211C2×C4×C11—22no—
212C2×C4×C11—22no—
213C2×C4×C11—24no—
214C2×C4×C11—42no—
215C2×C4×C11—44no—
216C2×C4×C11—48no—
217C2×C4×C11—88no—
218C2×C4×C11#13514yes—
219C2×C4×C11C22×D414yes—
220C2×C4×C11C22×D414yes—
221C2×C4×C11C22×D412yes—
222C2×C4×C11C22×D411yescharacteristic
223C2×C4×C11C22×D412yes—
224C2×C4×C11C22×Q812yes—
225C2×C4×C112−1+412yes—
226C2×C4×C11C2511yescharacteristic
227C2×Dic11—24no—
228C2×Dic11—22no—
229C2×Dic11—22no—
230C2×Dic11—24no—
231C2×Dic11—44no—
232C2×Dic11—42no—
233Dic22—24no—
234Dic22—22no—
235Dic22—48no—
236Dic22C22×Q814yes—
237C11⋊C8—24no—
238C11⋊C8—22no—
239C11⋊C8C22×Q814yes—
240C22×SD16—111no—
241#557—118no—
242#557—224no—
243#554—24no—
244#554C2×D1118yes—
245C2×C4⋊Q8—111no—
246C2×C4⋊Q8—221no—
247C2×C4⋊Q8C2×D1111yescharacteristic
248C2×#125—112no—
249C2×#125—222no—
250C2×#125C2×D1112yes—
251C2×C22⋊Q8—21no—
252C2×C22⋊Q8—22no—
253C2×C4×Q8—111no—
254C2×C4×Q8—112no—
255C2×C4×Q8—221no—
256C2×C4×Q8C2×D1111yescharacteristic
257C2×C4×D4C2×D1112yes—
258C2×C4×D4C2×D1111yescharacteristic
259C22×C4⋊C4—21no—
260#499—1116no—
261#498—118no—
262#479—1116no—
263#478—1116no—
264#477—118no—
265#474—118no—
266C8×Q8—118no—
267C4×SD16—118no—
268C4×SD16—1116no—
269C2×#107—112no—
270C2×#107—112no—
271C2×#106—112no—
272C2×#106—112no—
273C2×#106—111no—
274C2×C4⋊C8—112no—
275C2×C4⋊C8—111no—
276C2×#103—112no—
277C2×#103—111no—
278C2×#102—111no—
279C2×#102—112no—
280C2×C4×C8—111no—
281C2×C4×C8—112no—
282C22×C11—24no—
283C22×C11—48no—
284C22×C11—42no—
285C22×C11—42no—
286C22×C11D4×Q812yes—
287C22×C11C2×#13512yes—
288C22×C11#57712yes—
289C22×C11C23×D411yescharacteristic
290C4×C11—24no—
291C4×C11—24no—
292C4×C11—22no—
293C4×C11—42no—
294C4×C11—44no—
295C4×C11D4×Q812yes—
296C4×C11C2×#13514yes—
297C4×C11C23×Q811yescharacteristic
298C4×C11C2×2−1+411yescharacteristic
299Dic11—24no—
300Dic11—44no—
301Dic11—42no—
302C22×Q8—21no—
303C22×Q8—111no—
304C22×Q8—221no—
305C22×Q8C22⋊D1111yescharacteristic
306C22×D4C22×D1111yescharacteristic
307C23×C4—21no—
308C23×C4—22no—
309C2×SD16—118no—
310C2×SD16—114no—
311C22×C8—111no—
312C22×C8—111no—
313C22×C8—112no—
314C4⋊Q8—22no—
315C4⋊Q8—114no—
316C4⋊Q8—228no—
317C4⋊Q8—222no—
318C4⋊Q8C22×D1114yes—
319#125—24no—
320#125—118no—
321#125—2216no—
322#125—224no—
323#125C22×D1118yes—
324C22⋊Q8—28no—
325C22⋊Q8—216no—
326C4×Q8—114no—
327C4×Q8—118no—
328C4×Q8—228no—
329C4×Q8—224no—
330C4×Q8—222no—
331C4×Q8C22⋊D1114yes—
332C4×Q8C22×D1114yes—
333C4×D4—24no—
334C4×D4—22no—
335C4×D4C22×D1114yes—
336C4×D4C22×D1118yes—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—28no—
341C2×C4⋊C4—111no—
342C2×C4⋊C4—112no—
343C2×C4⋊C4—221no—
344C2×C4⋊C4—222no—
345C2×C4⋊C4—222no—
346C2×C4⋊C4—222no—
347C2×C4⋊C4—221no—
348C2×C4⋊C4C22⋊D1111yescharacteristic
349C2×C4⋊C4C22⋊D1112yes—
350C2×C4⋊C4C22×D1111yescharacteristic
351C2×C4⋊C4C22×D1112yes—
352C2×C22⋊C4—21no—
353C2×C22⋊C4—22no—
354C2×C42—222no—
355C2×C42—221no—
356C2×C42C22×D1112yes—
357C2×C42C22×D1111yescharacteristic
358#107—118no—
359#107—118no—
360#106—118no—
361#106—114no—
362#106—118no—
363C4⋊C8—114no—
364C4⋊C8—118no—
365#103—118no—
366#103—114no—
367#102—118no—
368#102—114no—
369C4×C8—114no—
370C4×C8—118no—
371C2×C11—44no—
372C2×C11#338114yescomplemented
373C2×C11C2×D4×Q811yescharacteristic
374C2×C11C22×#13511yescharacteristic
375C2×C11C2×#57711yescharacteristic
376C24—21no—
377C2×Q8—24no—
378C2×Q8—24no—
379C2×Q8—82no—
380C2×Q8—114no—
381C2×Q8—112no—
382C2×Q8—222no—
383C2×Q8—221no—
384C2×Q8—224no—
385C2×Q8—444no—
386C2×Q8C2×C22⋊D1114yes—
387C2×D4—22no—
388C2×D4—21no—
389C2×D4Q8×D1114yes—
390C2×D4C23×D1112yes—
391C22×C4—21no—
392C22×C4—22no—
393C22×C4—24no—
394C22×C4—28no—
395C22×C4—44no—
396C22×C4—84no—
397C22×C4—221no—
398C22×C4—221no—
399C22×C4—222no—
400C22×C4C2×C22⋊D1112yes—
401C22×C4C2×C22⋊D1112yes—
402C22×C4C2×C22⋊D1111yescharacteristic
403C22×C4C2×C22⋊D1111yescharacteristic
404C22×C4C23×D1111yescharacteristic
405SD16—1116no—
406C2×C8—114no—
407C2×C8—112no—
408C2×C8—112no—
409C2×C8—114no—
410C2×C8—222no—
411C2×C8—224no—
412C4⋊C4—28no—
413C4⋊C4—24no—
414C4⋊C4—28no—
415C4⋊C4—21no—
416C4⋊C4—22no—
417C4⋊C4—114no—
418C4⋊C4—112no—
419C4⋊C4—221no—
420C4⋊C4—222no—
421C4⋊C4—224no—
422C4⋊C4—228no—
423C4⋊C4—228no—
424C4⋊C4—228no—
425C4⋊C4—224no—
426C4⋊C4C2×C22⋊D1114yes—
427C4⋊C4C2×C22⋊D1118yes—
428C4⋊C4C23×D1114yes—
429C4⋊C4C23×D1112yes—
430C22⋊C4—24no—
431C22⋊C4—28no—
432C42—228no—
433C42—224no—
434C42C2×C22⋊D1114yes—
435C42C2×C22⋊D1112yes—
436C42C23×D1114yes—
437C42C23×D1112yes—
438C11C2×#338111yescharacteristic, complemented, Sylow
439C23—24no—
440C23—22no—
441C23—42no—
442C23—42no—
443C23C22×C22⋊D1111yescharacteristic
444Q8—28no—
445Q8—84no—
446Q8—114no—
447Q8—224no—
448Q8—222no—
449Q8—448no—
450D4—24no—
451D4—22no—
452D4C2×Q8×D1114yes—
453C2×C4—24no—
454C2×C4—24no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—24no—
458C2×C4—42no—
459C2×C4—44no—
460C2×C4—48no—
461C2×C4—88no—
462C2×C4—224no—
463C2×C4—222no—
464C2×C4—222no—
465C2×C4—224no—
466C2×C4—444no—
467C2×C4—442no—
468C2×C4#6700314yes—
469C2×C4C2×Q8×D1112yes—
470C2×C4#6704012yes—
471C2×C4C22×C22⋊D1114yes—
472C2×C4C22×C22⋊D1114yes—
473C2×C4C22×C22⋊D1112yes—
474C2×C4C22×C22⋊D1111yescharacteristic
475C2×C4C22×C22⋊D1112yes—
476C2×C4C24×D1111yescharacteristic
477C8—114no—
478C8—222no—
479C8—224no—
480C22—24no—
481C22—48no—
482C22—42no—
483C22—42no—
484C22Q8×C22⋊D1112yes—
485C22C2×#6700312yes—
486C22#1062336712yes—
487C22C23×C22⋊D1111yescharacteristic
488C4—24no—
489C4—24no—
490C4—22no—
491C4—42no—
492C4—44no—
493C4—224no—
494C4—444no—
495C4—442no—
496C4Q8×C22⋊D1112yes—
497C4C2×#6700314yes—
498C4C22×Q8×D1111yescharacteristic
499C4C2×#6704011yescharacteristic
500C2—44no—
501C2#1308149114yesdirect product factor
502C2C2×Q8×C22⋊D1111yescharacteristic
503C2C22×#6700311yescharacteristic
504C2C2×#1062336711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#554C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenterC2×#554D11
hypocenterC11C2×#3381
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. C2×#10623098C2semidirect
2. #13081491C2direct (N × H)
3. C2×#10622677C2semidirect
4. C2×#10622692C2semidirect
5. C2×#10622676C2semidirect
6. C2×#10622704C2semidirect
9. C2×Q8×C11⋊C8C2semidirect
26. #10623098C22semidirect
35. #10622704C22semidirect
36. #10622692C22semidirect
37. #10622677C22semidirect
38. #10622676C22semidirect
39. Q8×C11⋊C8C22semidirect
87. C2×#4324Q8semidirect
169. #4324C2×Q8semidirect
372. C2×C11#3381semidirect
438. C11C2×#3381semidirect
501. C2#13081491direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230982
#130814912
C2×#106226772
C2×#106226922
C2×#106226762
C2×#106227042
C2×#106226222
C2×#106226202
C2×Q8×C11⋊C82
C2×C4×#43242
C2×C11×#5542
C2×#338111