Finite Group Databasebeta

← C2×#13070594 #14907720

Subgroups — C2×#13070594 #14907720

Order 2816.

1078 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622808C211yesmaximal, characteristic, complemented
2C22×#66893C211yesmaximal, characteristic, complemented
3C2×#10622756C211yesmaximal, characteristic, complemented
4#13070594C218yesmaximal, direct product factor
5C2×#10622203C211yesmaximal, characteristic, complemented
6C2×#10622205C211yesmaximal, characteristic, complemented
7C2×#10622199C211yesmaximal, characteristic, complemented
8C2×C11×#578C211yesmaximal, characteristic
9C2×C11×2−1+4—21no—
10C11×#578—22no—
11C11×#578—22no—
12C11×#578—22no—
13C11×#578C2214yes—
14C2×C11×#137—22no—
15C2×C11×#137—21no—
16C2×C11×#135—21no—
17C2×C11×#135C2211yescharacteristic
18C22×C11×Q16—21no—
19C22×C11×Q16C2211yescharacteristic
20C2×C11×#131C2211yescharacteristic
21C2×#67004—21no—
22C22×Dic44C2211yescharacteristic
23#10622808—22no—
24#10622808C2214yescomplemented
25C2×#66893—22no—
26C2×#66893—22no—
27C2×#66893—21no—
28C2×#66893C2214yescomplemented
29C2×#66891—21no—
30#10622756—22no—
31#10622756C2214yescomplemented
32C2×#66888—21no—
33C2×#66883C2211yescharacteristic
34C2×#66876C2211yescharacteristic
35C22×C11⋊C16C2211yescharacteristic
36#10622205C2214yescomplemented
37#10622203C2214yescomplemented
38#10622199C2214yescomplemented
39C11×2−1+4—24no—
40C11×2−1+4—24no—
41C11×2−1+4—42no—
42C11×2−1+4—42no—
43C2×C11×#41—22no—
44C2×C11×#41—21no—
45C2×C11×#41—42no—
46C2×C11×#41—41no—
47C2×C11×#41D411yescharacteristic
48C22×Q8×C11—22no—
49C22×Q8×C11—21no—
50C22×Q8×C11—41no—
51C22×Dic22—21no—
52C11×#137—28no—
53C11×#137—24no—
54C11×#137—28no—
55C11×#137—24no—
56C11×#135—24no—
57C11×#135—24no—
58C11×#135—21no—
59C11×#135—21no—
60C11×#135D412yes—
61C11×#135C2312yes—
62C2×C11×Q16—22no—
63C2×C11×Q16—24no—
64C2×C11×Q16—24no—
65C2×C11×Q16—21no—
66C2×C11×Q16—21no—
67C2×C11×Q16—21no—
68C2×C11×Q16D411yescharacteristic
69C2×C11×Q16D412yes—
70C2×C11×Q16D412yes—
71C2×C11×Q16C2312yes—
72C2×C11×SD16—22no—
73C2×C11×SD16—21no—
74C2×C11×D8D411yescharacteristic
75C11×#131—21no—
76C11×#131—21no—
77C11×#131D412yes—
78C11×#131C2312yes—
79C2×C11×M16—21no—
80C2×C11×M16D411yescharacteristic
81C22×C8×C11—21no—
82C22×C8×C11C2311yescharacteristic
83#67004—24no—
84#67004—42no—
85C2×#4326—41no—
86C2×#4324—41no—
87C2×#4318—21no—
88C2×Dic44—21no—
89C2×Dic44—21no—
90C2×Dic44—21no—
91C2×Dic44—21no—
92C2×Dic44—21no—
93C2×Dic44C2312yes—
94#66893—28no—
95#66893—24no—
96#66891—24no—
97#66888—24no—
98#66883—21no—
99#66883C2312yes—
100#66876—21no—
101#66876C2312yes—
102C2×C11⋊C16—21no—
103C2×C11⋊C16—21no—
104C2×C11⋊C16—21no—
105C2×C11⋊C16C2312yes—
106C2×#2195—111nomaximal, Sylow
107C11×#41—21no—
108C11×#41—21no—
109C11×#41—28no—
110C11×#41—22no—
111C11×#41—22no—
112C11×#41—44no—
113C11×#41—48no—
114C11×#41—48no—
115C11×#41—44no—
116C11×#41—44no—
117C11×#41—41no—
118C11×#41—41no—
119C11×#41D812yes—
120C11×#41C2×D412yes—
121C2×Q8×C11—28no—
122C2×Q8×C11—22no—
123C2×Q8×C11—21no—
124C2×Q8×C11—22no—
125C2×Q8×C11—22no—
126C2×Q8×C11—42no—
127C2×Q8×C11—44no—
128C2×Q8×C11—44no—
129C2×Q8×C11—44no—
130C2×Q8×C11—41no—
131C2×Q8×C11—41no—
132C2×Q8×C11—41no—
133C2×Q8×C11D811yescharacteristic
134C2×D4×C11—21no—
135C2×D4×C11—21no—
136C2×D4×C11—42no—
137C2×D4×C11—41no—
138C2×D4×C11D811yescharacteristic
139C22×C4×C11—21no—
140C22×C4×C11—42no—
141C22×C4×C11—42no—
142C22×C4×C11—41no—
143C22×C4×C11—41no—
144C22×C4×C11C2×D411yescharacteristic
145C22×Dic11—41no—
146C2×Dic22—22no—
147C2×Dic22—41no—
148C2×Dic22—41no—
149C2×Dic22—41no—
150C2×Dic22—41no—
151C2×Dic22—41no—
152C11×Q16—28no—
153C11×Q16—21no—
154C11×Q16—22no—
155C11×Q16—22no—
156C11×Q16—22no—
157C11×Q16C2×D412yes—
158C11×Q16C2×D414yes—
159C11×SD16—28no—
160C11×SD16—22no—
161C11×SD16—22no—
162C11×D8—21no—
163C11×D8C2×D412yes—
164C11×M16—22no—
165C11×M16—22no—
166C11×M16—21no—
167C11×M16C2×D412yes—
168C2×C8×C11—22no—
169C2×C8×C11—22no—
170C2×C8×C11—21no—
171C2×C8×C11C2×D411yescharacteristic
172C2×C8×C11C2×D411yescharacteristic
173C2×C8×C11C2×D411yescharacteristic
174C2×C8×C11C2×D411yescharacteristic
175C2×C8×C11C2×D411yescharacteristic
176C2×C8×C11C2411yescharacteristic
177#4326—44no—
178#4324—44no—
179#4318—22no—
180#4318—41no—
181C2×C11⋊C8—41no—
182Dic44—22no—
183Dic44—22no—
184Dic44—41no—
185Dic44—41no—
186C11⋊C16—22no—
187C11⋊C16—22no—
188C2×#578D1111yescharacteristic
189C2×#510—111no—
190C22×Q32—111no—
191C2×#473—111no—
192#2195—118no—
193C2×#362—111no—
194C2×#359—111no—
195C2×#350—111no—
196C23×C11—21no—
197C23×C11—41no—
198C23×C11AGL(1,ℤ/8)11yescharacteristic
199Q8×C11—21no—
200Q8×C11—24no—
201Q8×C11—22no—
202Q8×C11—48no—
203Q8×C11—42no—
204Q8×C11—41no—
205Q8×C11—42no—
206Q8×C11—42no—
207Q8×C11C2×D812yes—
208D4×C11—22no—
209D4×C11—22no—
210D4×C11—22no—
211D4×C11—21no—
212D4×C11—48no—
213D4×C11—42no—
214D4×C11—42no—
215D4×C11—41no—
216D4×C11C2×D812yes—
217C2×C4×C11—21no—
218C2×C4×C11—22no—
219C2×C4×C11—22no—
220C2×C4×C11—48no—
221C2×C4×C11—48no—
222C2×C4×C11—42no—
223C2×C4×C11—42no—
224C2×C4×C11—41no—
225C2×C4×C11—42no—
226C2×C4×C11—42no—
227C2×C4×C11—42no—
228C2×C4×C11#12011yescharacteristic
229C2×C4×C11#12011yescharacteristic
230C2×C4×C11C2×D811yescharacteristic
231C2×C4×C11C2×D811yescharacteristic
232C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
233C2×C4×C11C22×D411yescharacteristic
234C2×Dic11—42no—
235C2×Dic11—81no—
236C2×Dic11—81no—
237Dic22—42no—
238Dic22—42no—
239Dic22—81no—
240Dic22—81no—
241C8×C11—22no—
242C8×C11#12011yescharacteristic
243C8×C11#12011yescharacteristic
244C8×C11C22×D411yescharacteristic
245C8×C11C22×D411yescharacteristic
246C11⋊C8—42no—
247C2×2−1+4—21no—
248#578—22no—
249#578—22no—
250#578—22no—
251#578C2×D1114yes—
252C2×#137—22no—
253C2×#137—21no—
254C2×#137—221no—
255C2×#135—21no—
256C2×#135C2×D1111yescharacteristic
257C22×Q16—21no—
258C22×Q16—111no—
259C22×Q16C2×D1111yescharacteristic
260C2×#131C2×D1111yescharacteristic
261#510—114no—
262#510—222no—
263C2×Q32—114no—
264C2×Q32—222no—
265C2×Q32—222no—
266C2×Q32—221no—
267C2×SD32—221no—
268C2×M32—111no—
269C22×C16—111no—
270#473—114no—
271#473—222no—
272C2×#108—111no—
273C2×#101—221no—
274#362—114no—
275#359—114no—
276#350—114no—
277C22×C11—22no—
278C22×C11—22no—
279C22×C11—42no—
280C22×C11—42no—
281C22×C11—82no—
282C22×C11#44711yescharacteristic
283C22×C11#44711yescharacteristic
284C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
285C4×C11—22no—
286C4×C11—44no—
287C4×C11—42no—
288C4×C11#44711yescharacteristic
289C4×C11#44711yescharacteristic
290C4×C11C2×#12011yescharacteristic
291C4×C11C22×D811yescharacteristic
292Dic11—82no—
2932−1+4—24no—
2942−1+4—24no—
2952−1+4—42no—
2962−1+4—42no—
297C2×#41—22no—
298C2×#41—21no—
299C2×#41—42no—
300C2×#41—41no—
301C2×#41C22⋊D1111yescharacteristic
302C22×Q8—22no—
303C22×Q8—21no—
304C22×Q8—41no—
305C22×Q8—221no—
306#137—24no—
307#137—28no—
308#137—28no—
309#137—24no—
310#137—224no—
311#137—442no—
312#135—24no—
313#135—24no—
314#135—21no—
315#135—21no—
316#135C22⋊D1112yes—
317#135C22×D1112yes—
318C2×Q16—22no—
319C2×Q16—24no—
320C2×Q16—24no—
321C2×Q16—21no—
322C2×Q16—21no—
323C2×Q16—21no—
324C2×Q16—112no—
325C2×Q16—221no—
326C2×Q16—221no—
327C2×Q16—221no—
328C2×Q16—221no—
329C2×Q16—221no—
330C2×Q16—441no—
331C2×Q16C22⋊D1111yescharacteristic
332C2×Q16C22⋊D1112yes—
333C2×Q16C22⋊D1112yes—
334C2×Q16C22×D1112yes—
335C2×SD16—22no—
336C2×SD16—21no—
337C2×SD16—441no—
338C2×D8C22⋊D1111yescharacteristic
339#131—21no—
340#131—21no—
341#131C22⋊D1112yes—
342#131C22×D1112yes—
343C2×M16—21no—
344C2×M16—221no—
345C2×M16C22⋊D1111yescharacteristic
346C22×C8—21no—
347C22×C8C22×D1111yescharacteristic
348Q32—228no—
349Q32—224no—
350SD32—224no—
351M32—112no—
352M32—221no—
353C2×C16—112no—
354C2×C16—221no—
355C2×C16—221no—
356C2×C16—221no—
357#108—112no—
358#108—221no—
359#101—224no—
360C2×C11—21no—
361C2×C11—21no—
362C2×C11—42no—
363C2×C11—82no—
364C2×C11#219512yescomplemented
365C2×C11C2×#44711yescharacteristic
366#41—21no—
367#41—21no—
368#41—28no—
369#41—22no—
370#41—22no—
371#41—44no—
372#41—48no—
373#41—48no—
374#41—44no—
375#41—44no—
376#41—41no—
377#41—41no—
378#41#432312yes—
379#41C2×C22⋊D1112yes—
380C2×Q8—28no—
381C2×Q8—22no—
382C2×Q8—21no—
383C2×Q8—22no—
384C2×Q8—22no—
385C2×Q8—42no—
386C2×Q8—44no—
387C2×Q8—44no—
388C2×Q8—44no—
389C2×Q8—41no—
390C2×Q8—41no—
391C2×Q8—41no—
392C2×Q8—222no—
393C2×Q8—441no—
394C2×Q8—441no—
395C2×Q8—441no—
396C2×Q8—441no—
397C2×Q8—441no—
398C2×Q8#432311yescharacteristic
399C2×D4—21no—
400C2×D4—21no—
401C2×D4—42no—
402C2×D4—41no—
403C2×D4#432311yescharacteristic
404C22×C4—21no—
405C22×C4—42no—
406C22×C4—42no—
407C22×C4—41no—
408C22×C4—41no—
409C22×C4—441no—
410C22×C4C2×C22⋊D1111yescharacteristic
411Q16—28no—
412Q16—21no—
413Q16—22no—
414Q16—22no—
415Q16—22no—
416Q16—222no—
417Q16—222no—
418Q16—444no—
419Q16—441no—
420Q16—441no—
421Q16C2×C22⋊D1112yes—
422Q16C2×C22⋊D1114yes—
423SD16—28no—
424SD16—22no—
425SD16—22no—
426SD16—444no—
427D8—21no—
428D8C2×C22⋊D1112yes—
429M16—21no—
430M16—22no—
431M16—22no—
432M16—222no—
433M16—441no—
434M16C2×C22⋊D1112yes—
435C2×C8—21no—
436C2×C8—22no—
437C2×C8—22no—
438C2×C8—441no—
439C2×C8C2×C22⋊D1111yescharacteristic
440C2×C8C2×C22⋊D1111yescharacteristic
441C2×C8C2×C22⋊D1111yescharacteristic
442C2×C8C2×C22⋊D1111yescharacteristic
443C2×C8C2×C22⋊D1111yescharacteristic
444C2×C8C23×D1111yescharacteristic
445C16—222no—
446C16—222no—
447C11C2×#219511yescharacteristic, complemented, Sylow
448C23—21no—
449C23—41no—
450C23#6698511yescharacteristic
451Q8—21no—
452Q8—24no—
453Q8—22no—
454Q8—48no—
455Q8—42no—
456Q8—41no—
457Q8—42no—
458Q8—42no—
459Q8—442no—
460Q8—442no—
461Q8—881no—
462Q8—881no—
463Q8C2×#432312yes—
464D4—22no—
465D4—22no—
466D4—21no—
467D4—22no—
468D4—48no—
469D4—42no—
470D4—42no—
471D4—41no—
472D4C2×#432312yes—
473C2×C4—21no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—48no—
477C2×C4—48no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—42no—
481C2×C4—41no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—442no—
485C2×C4—881no—
486C2×C4—881no—
487C2×C4C2×#432311yescharacteristic
488C2×C4C2×#432311yescharacteristic
489C2×C4#6698511yescharacteristic
490C2×C4#6700611yescharacteristic
491C2×C4#6700611yescharacteristic
492C2×C4C22×C22⋊D1111yescharacteristic
493C8—22no—
494C8—442no—
495C8#6700611yescharacteristic
496C8#6700611yescharacteristic
497C8C22×C22⋊D1111yescharacteristic
498C8C22×C22⋊D1111yescharacteristic
499C22—22no—
500C22—22no—
501C22—42no—
502C22—42no—
503C22—82no—
504C22#1062283011yescharacteristic
505C22#1062283011yescharacteristic
506C22C2×#6698511yescharacteristic
507C4—22no—
508C4—44no—
509C4—42no—
510C4—882no—
511C4#1062283011yescharacteristic
512C4#1062283011yescharacteristic
513C4C22×#432311yescharacteristic
514C4C2×#6700611yescharacteristic
515C2—21no—
516C2—21no—
517C2—42no—
518C2—82no—
519C2#1307059412yesdirect product factor
520C2C2×#1062283011yescharacteristic
subgroupG/H
centerC22#10622830
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
Fitting, prime radicalC2×C11×#578C2
socleC22×C11#447
hypercenterC2×#578D11
hypocenterC11C2×#2195
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#131 ◁ C2×#578

Complements

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

NH ≅ G/Ntype
1. C2×#10622808C2semidirect
2. C22×#66893C2semidirect
3. C2×#10622756C2semidirect
4. #13070594C2direct (N × H)
5. C2×#10622203C2semidirect
6. C2×#10622205C2semidirect
7. C2×#10622199C2semidirect
24. #10622808C22semidirect
28. C2×#66893C22semidirect
31. #10622756C22semidirect
36. #10622205C22semidirect
37. #10622203C22semidirect
38. #10622199C22semidirect
364. C2×C11#2195semidirect
447. C11C2×#2195semidirect
519. C2#13070594direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106228082
C22×#668932
C2×#106227562
#130705942
C2×#106222032
C2×#106222052
C2×#106221992
C2×C11×#5782
C2×#219511